1,1,23,0,0.673312," ","integrate(sin(x)^6/(a-a*cos(x)^2),x, algorithm=""fricas"")","\frac{{\left(2 \, \cos\left(x\right)^{3} - 5 \, \cos\left(x\right)\right)} \sin\left(x\right) + 3 \, x}{8 \, a}"," ",0,"1/8*((2*cos(x)^3 - 5*cos(x))*sin(x) + 3*x)/a","A",0
2,1,14,0,1.084979," ","integrate(sin(x)^5/(a-a*cos(x)^2),x, algorithm=""fricas"")","\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
3,1,14,0,1.136845," ","integrate(sin(x)^4/(a-a*cos(x)^2),x, algorithm=""fricas"")","-\frac{\cos\left(x\right) \sin\left(x\right) - x}{2 \, a}"," ",0,"-1/2*(cos(x)*sin(x) - x)/a","A",0
4,1,7,0,0.632564," ","integrate(sin(x)^3/(a-a*cos(x)^2),x, algorithm=""fricas"")","-\frac{\cos\left(x\right)}{a}"," ",0,"-cos(x)/a","A",0
5,1,5,0,0.626441," ","integrate(sin(x)^2/(a-a*cos(x)^2),x, algorithm=""fricas"")","\frac{x}{a}"," ",0,"x/a","A",0
6,1,22,0,0.629177," ","integrate(sin(x)/(a-a*cos(x)^2),x, algorithm=""fricas"")","-\frac{\log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{2 \, a}"," ",0,"-1/2*(log(1/2*cos(x) + 1/2) - log(-1/2*cos(x) + 1/2))/a","B",0
7,1,48,0,1.451819," ","integrate(csc(x)/(a-a*cos(x)^2),x, algorithm=""fricas"")","-\frac{{\left(\cos\left(x\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - {\left(\cos\left(x\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - 2 \, \cos\left(x\right)}{4 \, {\left(a \cos\left(x\right)^{2} - a\right)}}"," ",0,"-1/4*((cos(x)^2 - 1)*log(1/2*cos(x) + 1/2) - (cos(x)^2 - 1)*log(-1/2*cos(x) + 1/2) - 2*cos(x))/(a*cos(x)^2 - a)","B",0
8,1,29,0,0.465422," ","integrate(csc(x)^2/(a-a*cos(x)^2),x, algorithm=""fricas"")","-\frac{2 \, \cos\left(x\right)^{3} - 3 \, \cos\left(x\right)}{3 \, {\left(a \cos\left(x\right)^{2} - a\right)} \sin\left(x\right)}"," ",0,"-1/3*(2*cos(x)^3 - 3*cos(x))/((a*cos(x)^2 - a)*sin(x))","A",0
9,1,72,0,0.583110," ","integrate(csc(x)^3/(a-a*cos(x)^2),x, algorithm=""fricas"")","\frac{6 \, \cos\left(x\right)^{3} - 3 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + 3 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - 10 \, \cos\left(x\right)}{16 \, {\left(a \cos\left(x\right)^{4} - 2 \, a \cos\left(x\right)^{2} + a\right)}}"," ",0,"1/16*(6*cos(x)^3 - 3*(cos(x)^4 - 2*cos(x)^2 + 1)*log(1/2*cos(x) + 1/2) + 3*(cos(x)^4 - 2*cos(x)^2 + 1)*log(-1/2*cos(x) + 1/2) - 10*cos(x))/(a*cos(x)^4 - 2*a*cos(x)^2 + a)","B",0
10,1,225,0,0.711768," ","integrate(sin(x)^7/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{6 \, a b^{3} \cos\left(x\right)^{5} - 10 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cos\left(x\right)^{3} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{-a b} \log\left(-\frac{b \cos\left(x\right)^{2} + 2 \, \sqrt{-a b} \cos\left(x\right) - a}{b \cos\left(x\right)^{2} + a}\right) + 30 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cos\left(x\right)}{30 \, a b^{4}}, \frac{3 \, a b^{3} \cos\left(x\right)^{5} - 5 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cos\left(x\right)^{3} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} \cos\left(x\right)}{a}\right) + 15 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cos\left(x\right)}{15 \, a b^{4}}\right]"," ",0,"[1/30*(6*a*b^3*cos(x)^5 - 10*(a^2*b^2 + 3*a*b^3)*cos(x)^3 - 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt(-a*b)*log(-(b*cos(x)^2 + 2*sqrt(-a*b)*cos(x) - a)/(b*cos(x)^2 + a)) + 30*(a^3*b + 3*a^2*b^2 + 3*a*b^3)*cos(x))/(a*b^4), 1/15*(3*a*b^3*cos(x)^5 - 5*(a^2*b^2 + 3*a*b^3)*cos(x)^3 - 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt(a*b)*arctan(sqrt(a*b)*cos(x)/a) + 15*(a^3*b + 3*a^2*b^2 + 3*a*b^3)*cos(x))/(a*b^4)]","A",0
11,1,152,0,1.297512," ","integrate(sin(x)^5/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[-\frac{2 \, a b^{2} \cos\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{-a b} \log\left(-\frac{b \cos\left(x\right)^{2} + 2 \, \sqrt{-a b} \cos\left(x\right) - a}{b \cos\left(x\right)^{2} + a}\right) - 6 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cos\left(x\right)}{6 \, a b^{3}}, -\frac{a b^{2} \cos\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} \cos\left(x\right)}{a}\right) - 3 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cos\left(x\right)}{3 \, a b^{3}}\right]"," ",0,"[-1/6*(2*a*b^2*cos(x)^3 + 3*(a^2 + 2*a*b + b^2)*sqrt(-a*b)*log(-(b*cos(x)^2 + 2*sqrt(-a*b)*cos(x) - a)/(b*cos(x)^2 + a)) - 6*(a^2*b + 2*a*b^2)*cos(x))/(a*b^3), -1/3*(a*b^2*cos(x)^3 + 3*(a^2 + 2*a*b + b^2)*sqrt(a*b)*arctan(sqrt(a*b)*cos(x)/a) - 3*(a^2*b + 2*a*b^2)*cos(x))/(a*b^3)]","A",0
12,1,95,0,0.547925," ","integrate(sin(x)^3/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{2 \, a b \cos\left(x\right) - \sqrt{-a b} {\left(a + b\right)} \log\left(-\frac{b \cos\left(x\right)^{2} + 2 \, \sqrt{-a b} \cos\left(x\right) - a}{b \cos\left(x\right)^{2} + a}\right)}{2 \, a b^{2}}, \frac{a b \cos\left(x\right) - \sqrt{a b} {\left(a + b\right)} \arctan\left(\frac{\sqrt{a b} \cos\left(x\right)}{a}\right)}{a b^{2}}\right]"," ",0,"[1/2*(2*a*b*cos(x) - sqrt(-a*b)*(a + b)*log(-(b*cos(x)^2 + 2*sqrt(-a*b)*cos(x) - a)/(b*cos(x)^2 + a)))/(a*b^2), (a*b*cos(x) - sqrt(a*b)*(a + b)*arctan(sqrt(a*b)*cos(x)/a))/(a*b^2)]","A",0
13,1,73,0,0.739055," ","integrate(sin(x)/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b} \log\left(-\frac{b \cos\left(x\right)^{2} + 2 \, \sqrt{-a b} \cos\left(x\right) - a}{b \cos\left(x\right)^{2} + a}\right)}{2 \, a b}, -\frac{\sqrt{a b} \arctan\left(\frac{\sqrt{a b} \cos\left(x\right)}{a}\right)}{a b}\right]"," ",0,"[-1/2*sqrt(-a*b)*log(-(b*cos(x)^2 + 2*sqrt(-a*b)*cos(x) - a)/(b*cos(x)^2 + a))/(a*b), -sqrt(a*b)*arctan(sqrt(a*b)*cos(x)/a)/(a*b)]","A",0
14,1,113,0,0.745473," ","integrate(csc(x)/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{b}{a}} \log\left(\frac{b \cos\left(x\right)^{2} - 2 \, a \sqrt{-\frac{b}{a}} \cos\left(x\right) - a}{b \cos\left(x\right)^{2} + a}\right) - \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{2 \, {\left(a + b\right)}}, -\frac{2 \, \sqrt{\frac{b}{a}} \arctan\left(\sqrt{\frac{b}{a}} \cos\left(x\right)\right) + \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{2 \, {\left(a + b\right)}}\right]"," ",0,"[1/2*(sqrt(-b/a)*log((b*cos(x)^2 - 2*a*sqrt(-b/a)*cos(x) - a)/(b*cos(x)^2 + a)) - log(1/2*cos(x) + 1/2) + log(-1/2*cos(x) + 1/2))/(a + b), -1/2*(2*sqrt(b/a)*arctan(sqrt(b/a)*cos(x)) + log(1/2*cos(x) + 1/2) - log(-1/2*cos(x) + 1/2))/(a + b)]","A",0
15,1,274,0,0.666408," ","integrate(csc(x)^3/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b \cos\left(x\right)^{2} - b\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b \cos\left(x\right)^{2} - 2 \, a \sqrt{-\frac{b}{a}} \cos\left(x\right) - a}{b \cos\left(x\right)^{2} + a}\right) + 2 \, {\left(a + b\right)} \cos\left(x\right) - {\left({\left(a + 3 \, b\right)} \cos\left(x\right)^{2} - a - 3 \, b\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + {\left({\left(a + 3 \, b\right)} \cos\left(x\right)^{2} - a - 3 \, b\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cos\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)}}, -\frac{4 \, {\left(b \cos\left(x\right)^{2} - b\right)} \sqrt{\frac{b}{a}} \arctan\left(\sqrt{\frac{b}{a}} \cos\left(x\right)\right) - 2 \, {\left(a + b\right)} \cos\left(x\right) + {\left({\left(a + 3 \, b\right)} \cos\left(x\right)^{2} - a - 3 \, b\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - {\left({\left(a + 3 \, b\right)} \cos\left(x\right)^{2} - a - 3 \, b\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cos\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)}}\right]"," ",0,"[1/4*(2*(b*cos(x)^2 - b)*sqrt(-b/a)*log((b*cos(x)^2 - 2*a*sqrt(-b/a)*cos(x) - a)/(b*cos(x)^2 + a)) + 2*(a + b)*cos(x) - ((a + 3*b)*cos(x)^2 - a - 3*b)*log(1/2*cos(x) + 1/2) + ((a + 3*b)*cos(x)^2 - a - 3*b)*log(-1/2*cos(x) + 1/2))/((a^2 + 2*a*b + b^2)*cos(x)^2 - a^2 - 2*a*b - b^2), -1/4*(4*(b*cos(x)^2 - b)*sqrt(b/a)*arctan(sqrt(b/a)*cos(x)) - 2*(a + b)*cos(x) + ((a + 3*b)*cos(x)^2 - a - 3*b)*log(1/2*cos(x) + 1/2) - ((a + 3*b)*cos(x)^2 - a - 3*b)*log(-1/2*cos(x) + 1/2))/((a^2 + 2*a*b + b^2)*cos(x)^2 - a^2 - 2*a*b - b^2)]","B",0
16,1,592,0,0.871026," ","integrate(csc(x)^5/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cos\left(x\right)^{3} + 8 \, {\left(b^{2} \cos\left(x\right)^{4} - 2 \, b^{2} \cos\left(x\right)^{2} + b^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b \cos\left(x\right)^{2} - 2 \, a \sqrt{-\frac{b}{a}} \cos\left(x\right) - a}{b \cos\left(x\right)^{2} + a}\right) - 2 \, {\left(5 \, a^{2} + 14 \, a b + 9 \, b^{2}\right)} \cos\left(x\right) - {\left({\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cos\left(x\right)^{2} + 3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + {\left({\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cos\left(x\right)^{2} + 3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{16 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cos\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cos\left(x\right)^{2}\right)}}, \frac{2 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cos\left(x\right)^{3} - 16 \, {\left(b^{2} \cos\left(x\right)^{4} - 2 \, b^{2} \cos\left(x\right)^{2} + b^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(\sqrt{\frac{b}{a}} \cos\left(x\right)\right) - 2 \, {\left(5 \, a^{2} + 14 \, a b + 9 \, b^{2}\right)} \cos\left(x\right) - {\left({\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cos\left(x\right)^{2} + 3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + {\left({\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cos\left(x\right)^{2} + 3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{16 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cos\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cos\left(x\right)^{2}\right)}}\right]"," ",0,"[1/16*(2*(3*a^2 + 10*a*b + 7*b^2)*cos(x)^3 + 8*(b^2*cos(x)^4 - 2*b^2*cos(x)^2 + b^2)*sqrt(-b/a)*log((b*cos(x)^2 - 2*a*sqrt(-b/a)*cos(x) - a)/(b*cos(x)^2 + a)) - 2*(5*a^2 + 14*a*b + 9*b^2)*cos(x) - ((3*a^2 + 10*a*b + 15*b^2)*cos(x)^4 - 2*(3*a^2 + 10*a*b + 15*b^2)*cos(x)^2 + 3*a^2 + 10*a*b + 15*b^2)*log(1/2*cos(x) + 1/2) + ((3*a^2 + 10*a*b + 15*b^2)*cos(x)^4 - 2*(3*a^2 + 10*a*b + 15*b^2)*cos(x)^2 + 3*a^2 + 10*a*b + 15*b^2)*log(-1/2*cos(x) + 1/2))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cos(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cos(x)^2), 1/16*(2*(3*a^2 + 10*a*b + 7*b^2)*cos(x)^3 - 16*(b^2*cos(x)^4 - 2*b^2*cos(x)^2 + b^2)*sqrt(b/a)*arctan(sqrt(b/a)*cos(x)) - 2*(5*a^2 + 14*a*b + 9*b^2)*cos(x) - ((3*a^2 + 10*a*b + 15*b^2)*cos(x)^4 - 2*(3*a^2 + 10*a*b + 15*b^2)*cos(x)^2 + 3*a^2 + 10*a*b + 15*b^2)*log(1/2*cos(x) + 1/2) + ((3*a^2 + 10*a*b + 15*b^2)*cos(x)^4 - 2*(3*a^2 + 10*a*b + 15*b^2)*cos(x)^2 + 3*a^2 + 10*a*b + 15*b^2)*log(-1/2*cos(x) + 1/2))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cos(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cos(x)^2)]","B",0
17,1,285,0,2.474043," ","integrate(sin(x)^6/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{-\frac{a + b}{a}} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, a^{2} + 3 \, a b\right)} \cos\left(x\right)^{2} - 4 \, {\left({\left(2 \, a^{2} + a b\right)} \cos\left(x\right)^{3} - a^{2} \cos\left(x\right)\right)} \sqrt{-\frac{a + b}{a}} \sin\left(x\right) + a^{2}}{b^{2} \cos\left(x\right)^{4} + 2 \, a b \cos\left(x\right)^{2} + a^{2}}\right) - {\left(8 \, a^{2} + 20 \, a b + 15 \, b^{2}\right)} x - {\left(2 \, b^{2} \cos\left(x\right)^{3} - {\left(4 \, a b + 9 \, b^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{8 \, b^{3}}, -\frac{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{\frac{a + b}{a}} \arctan\left(\frac{{\left({\left(2 \, a + b\right)} \cos\left(x\right)^{2} - a\right)} \sqrt{\frac{a + b}{a}}}{2 \, {\left(a + b\right)} \cos\left(x\right) \sin\left(x\right)}\right) + {\left(8 \, a^{2} + 20 \, a b + 15 \, b^{2}\right)} x + {\left(2 \, b^{2} \cos\left(x\right)^{3} - {\left(4 \, a b + 9 \, b^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{8 \, b^{3}}\right]"," ",0,"[1/8*(2*(a^2 + 2*a*b + b^2)*sqrt(-(a + b)/a)*log(((8*a^2 + 8*a*b + b^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b)*cos(x)^2 - 4*((2*a^2 + a*b)*cos(x)^3 - a^2*cos(x))*sqrt(-(a + b)/a)*sin(x) + a^2)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2)) - (8*a^2 + 20*a*b + 15*b^2)*x - (2*b^2*cos(x)^3 - (4*a*b + 9*b^2)*cos(x))*sin(x))/b^3, -1/8*(4*(a^2 + 2*a*b + b^2)*sqrt((a + b)/a)*arctan(1/2*((2*a + b)*cos(x)^2 - a)*sqrt((a + b)/a)/((a + b)*cos(x)*sin(x))) + (8*a^2 + 20*a*b + 15*b^2)*x + (2*b^2*cos(x)^3 - (4*a*b + 9*b^2)*cos(x))*sin(x))/b^3]","A",0
18,1,211,0,0.616003," ","integrate(sin(x)^4/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{2 \, b \cos\left(x\right) \sin\left(x\right) + {\left(a + b\right)} \sqrt{-\frac{a + b}{a}} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, a^{2} + 3 \, a b\right)} \cos\left(x\right)^{2} - 4 \, {\left({\left(2 \, a^{2} + a b\right)} \cos\left(x\right)^{3} - a^{2} \cos\left(x\right)\right)} \sqrt{-\frac{a + b}{a}} \sin\left(x\right) + a^{2}}{b^{2} \cos\left(x\right)^{4} + 2 \, a b \cos\left(x\right)^{2} + a^{2}}\right) - 2 \, {\left(2 \, a + 3 \, b\right)} x}{4 \, b^{2}}, \frac{b \cos\left(x\right) \sin\left(x\right) - {\left(a + b\right)} \sqrt{\frac{a + b}{a}} \arctan\left(\frac{{\left({\left(2 \, a + b\right)} \cos\left(x\right)^{2} - a\right)} \sqrt{\frac{a + b}{a}}}{2 \, {\left(a + b\right)} \cos\left(x\right) \sin\left(x\right)}\right) - {\left(2 \, a + 3 \, b\right)} x}{2 \, b^{2}}\right]"," ",0,"[1/4*(2*b*cos(x)*sin(x) + (a + b)*sqrt(-(a + b)/a)*log(((8*a^2 + 8*a*b + b^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b)*cos(x)^2 - 4*((2*a^2 + a*b)*cos(x)^3 - a^2*cos(x))*sqrt(-(a + b)/a)*sin(x) + a^2)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2)) - 2*(2*a + 3*b)*x)/b^2, 1/2*(b*cos(x)*sin(x) - (a + b)*sqrt((a + b)/a)*arctan(1/2*((2*a + b)*cos(x)^2 - a)*sqrt((a + b)/a)/((a + b)*cos(x)*sin(x))) - (2*a + 3*b)*x)/b^2]","A",0
19,1,177,0,0.746008," ","integrate(sin(x)^2/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{a + b}{a}} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, a^{2} + 3 \, a b\right)} \cos\left(x\right)^{2} - 4 \, {\left({\left(2 \, a^{2} + a b\right)} \cos\left(x\right)^{3} - a^{2} \cos\left(x\right)\right)} \sqrt{-\frac{a + b}{a}} \sin\left(x\right) + a^{2}}{b^{2} \cos\left(x\right)^{4} + 2 \, a b \cos\left(x\right)^{2} + a^{2}}\right) - 4 \, x}{4 \, b}, -\frac{\sqrt{\frac{a + b}{a}} \arctan\left(\frac{{\left({\left(2 \, a + b\right)} \cos\left(x\right)^{2} - a\right)} \sqrt{\frac{a + b}{a}}}{2 \, {\left(a + b\right)} \cos\left(x\right) \sin\left(x\right)}\right) + 2 \, x}{2 \, b}\right]"," ",0,"[1/4*(sqrt(-(a + b)/a)*log(((8*a^2 + 8*a*b + b^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b)*cos(x)^2 - 4*((2*a^2 + a*b)*cos(x)^3 - a^2*cos(x))*sqrt(-(a + b)/a)*sin(x) + a^2)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2)) - 4*x)/b, -1/2*(sqrt((a + b)/a)*arctan(1/2*((2*a + b)*cos(x)^2 - a)*sqrt((a + b)/a)/((a + b)*cos(x)*sin(x))) + 2*x)/b]","A",0
20,1,163,0,0.576559," ","integrate(1/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} - a b} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, a^{2} + 3 \, a b\right)} \cos\left(x\right)^{2} + 4 \, {\left({\left(2 \, a + b\right)} \cos\left(x\right)^{3} - a \cos\left(x\right)\right)} \sqrt{-a^{2} - a b} \sin\left(x\right) + a^{2}}{b^{2} \cos\left(x\right)^{4} + 2 \, a b \cos\left(x\right)^{2} + a^{2}}\right)}{4 \, {\left(a^{2} + a b\right)}}, -\frac{\arctan\left(\frac{{\left(2 \, a + b\right)} \cos\left(x\right)^{2} - a}{2 \, \sqrt{a^{2} + a b} \cos\left(x\right) \sin\left(x\right)}\right)}{2 \, \sqrt{a^{2} + a b}}\right]"," ",0,"[-1/4*sqrt(-a^2 - a*b)*log(((8*a^2 + 8*a*b + b^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b)*cos(x)^2 + 4*((2*a + b)*cos(x)^3 - a*cos(x))*sqrt(-a^2 - a*b)*sin(x) + a^2)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2))/(a^2 + a*b), -1/2*arctan(1/2*((2*a + b)*cos(x)^2 - a)/(sqrt(a^2 + a*b)*cos(x)*sin(x)))/sqrt(a^2 + a*b)]","B",0
21,1,228,0,0.670305," ","integrate(csc(x)^2/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} - a b} b \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, a^{2} + 3 \, a b\right)} \cos\left(x\right)^{2} + 4 \, {\left({\left(2 \, a + b\right)} \cos\left(x\right)^{3} - a \cos\left(x\right)\right)} \sqrt{-a^{2} - a b} \sin\left(x\right) + a^{2}}{b^{2} \cos\left(x\right)^{4} + 2 \, a b \cos\left(x\right)^{2} + a^{2}}\right) \sin\left(x\right) + 4 \, {\left(a^{2} + a b\right)} \cos\left(x\right)}{4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sin\left(x\right)}, -\frac{\sqrt{a^{2} + a b} b \arctan\left(\frac{{\left(2 \, a + b\right)} \cos\left(x\right)^{2} - a}{2 \, \sqrt{a^{2} + a b} \cos\left(x\right) \sin\left(x\right)}\right) \sin\left(x\right) + 2 \, {\left(a^{2} + a b\right)} \cos\left(x\right)}{2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sin\left(x\right)}\right]"," ",0,"[-1/4*(sqrt(-a^2 - a*b)*b*log(((8*a^2 + 8*a*b + b^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b)*cos(x)^2 + 4*((2*a + b)*cos(x)^3 - a*cos(x))*sqrt(-a^2 - a*b)*sin(x) + a^2)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2))*sin(x) + 4*(a^2 + a*b)*cos(x))/((a^3 + 2*a^2*b + a*b^2)*sin(x)), -1/2*(sqrt(a^2 + a*b)*b*arctan(1/2*((2*a + b)*cos(x)^2 - a)/(sqrt(a^2 + a*b)*cos(x)*sin(x)))*sin(x) + 2*(a^2 + a*b)*cos(x))/((a^3 + 2*a^2*b + a*b^2)*sin(x))]","B",0
22,1,396,0,0.626232," ","integrate(csc(x)^4/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(2 \, a^{3} + 7 \, a^{2} b + 5 \, a b^{2}\right)} \cos\left(x\right)^{3} + 3 \, {\left(b^{2} \cos\left(x\right)^{2} - b^{2}\right)} \sqrt{-a^{2} - a b} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, a^{2} + 3 \, a b\right)} \cos\left(x\right)^{2} + 4 \, {\left({\left(2 \, a + b\right)} \cos\left(x\right)^{3} - a \cos\left(x\right)\right)} \sqrt{-a^{2} - a b} \sin\left(x\right) + a^{2}}{b^{2} \cos\left(x\right)^{4} + 2 \, a b \cos\left(x\right)^{2} + a^{2}}\right) \sin\left(x\right) - 12 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cos\left(x\right)}{12 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} - {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}, \frac{2 \, {\left(2 \, a^{3} + 7 \, a^{2} b + 5 \, a b^{2}\right)} \cos\left(x\right)^{3} + 3 \, {\left(b^{2} \cos\left(x\right)^{2} - b^{2}\right)} \sqrt{a^{2} + a b} \arctan\left(\frac{{\left(2 \, a + b\right)} \cos\left(x\right)^{2} - a}{2 \, \sqrt{a^{2} + a b} \cos\left(x\right) \sin\left(x\right)}\right) \sin\left(x\right) - 6 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cos\left(x\right)}{6 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} - {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}\right]"," ",0,"[1/12*(4*(2*a^3 + 7*a^2*b + 5*a*b^2)*cos(x)^3 + 3*(b^2*cos(x)^2 - b^2)*sqrt(-a^2 - a*b)*log(((8*a^2 + 8*a*b + b^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b)*cos(x)^2 + 4*((2*a + b)*cos(x)^3 - a*cos(x))*sqrt(-a^2 - a*b)*sin(x) + a^2)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2))*sin(x) - 12*(a^3 + 3*a^2*b + 2*a*b^2)*cos(x))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3 - (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cos(x)^2)*sin(x)), 1/6*(2*(2*a^3 + 7*a^2*b + 5*a*b^2)*cos(x)^3 + 3*(b^2*cos(x)^2 - b^2)*sqrt(a^2 + a*b)*arctan(1/2*((2*a + b)*cos(x)^2 - a)/(sqrt(a^2 + a*b)*cos(x)*sin(x)))*sin(x) - 6*(a^3 + 3*a^2*b + 2*a*b^2)*cos(x))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3 - (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cos(x)^2)*sin(x))]","B",0
23,1,610,0,0.864092," ","integrate(csc(x)^6/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(8 \, a^{4} + 34 \, a^{3} b + 59 \, a^{2} b^{2} + 33 \, a b^{3}\right)} \cos\left(x\right)^{5} - 20 \, {\left(4 \, a^{4} + 17 \, a^{3} b + 28 \, a^{2} b^{2} + 15 \, a b^{3}\right)} \cos\left(x\right)^{3} + 15 \, {\left(b^{3} \cos\left(x\right)^{4} - 2 \, b^{3} \cos\left(x\right)^{2} + b^{3}\right)} \sqrt{-a^{2} - a b} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, a^{2} + 3 \, a b\right)} \cos\left(x\right)^{2} + 4 \, {\left({\left(2 \, a + b\right)} \cos\left(x\right)^{3} - a \cos\left(x\right)\right)} \sqrt{-a^{2} - a b} \sin\left(x\right) + a^{2}}{b^{2} \cos\left(x\right)^{4} + 2 \, a b \cos\left(x\right)^{2} + a^{2}}\right) \sin\left(x\right) + 60 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cos\left(x\right)}{60 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} + {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cos\left(x\right)^{4} - 2 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}, -\frac{2 \, {\left(8 \, a^{4} + 34 \, a^{3} b + 59 \, a^{2} b^{2} + 33 \, a b^{3}\right)} \cos\left(x\right)^{5} - 10 \, {\left(4 \, a^{4} + 17 \, a^{3} b + 28 \, a^{2} b^{2} + 15 \, a b^{3}\right)} \cos\left(x\right)^{3} + 15 \, {\left(b^{3} \cos\left(x\right)^{4} - 2 \, b^{3} \cos\left(x\right)^{2} + b^{3}\right)} \sqrt{a^{2} + a b} \arctan\left(\frac{{\left(2 \, a + b\right)} \cos\left(x\right)^{2} - a}{2 \, \sqrt{a^{2} + a b} \cos\left(x\right) \sin\left(x\right)}\right) \sin\left(x\right) + 30 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cos\left(x\right)}{30 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} + {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cos\left(x\right)^{4} - 2 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}\right]"," ",0,"[-1/60*(4*(8*a^4 + 34*a^3*b + 59*a^2*b^2 + 33*a*b^3)*cos(x)^5 - 20*(4*a^4 + 17*a^3*b + 28*a^2*b^2 + 15*a*b^3)*cos(x)^3 + 15*(b^3*cos(x)^4 - 2*b^3*cos(x)^2 + b^3)*sqrt(-a^2 - a*b)*log(((8*a^2 + 8*a*b + b^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b)*cos(x)^2 + 4*((2*a + b)*cos(x)^3 - a*cos(x))*sqrt(-a^2 - a*b)*sin(x) + a^2)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2))*sin(x) + 60*(a^4 + 4*a^3*b + 6*a^2*b^2 + 3*a*b^3)*cos(x))/((a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4 + (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cos(x)^4 - 2*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cos(x)^2)*sin(x)), -1/30*(2*(8*a^4 + 34*a^3*b + 59*a^2*b^2 + 33*a*b^3)*cos(x)^5 - 10*(4*a^4 + 17*a^3*b + 28*a^2*b^2 + 15*a*b^3)*cos(x)^3 + 15*(b^3*cos(x)^4 - 2*b^3*cos(x)^2 + b^3)*sqrt(a^2 + a*b)*arctan(1/2*((2*a + b)*cos(x)^2 - a)/(sqrt(a^2 + a*b)*cos(x)*sin(x)))*sin(x) + 30*(a^4 + 4*a^3*b + 6*a^2*b^2 + 3*a*b^3)*cos(x))/((a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4 + (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cos(x)^4 - 2*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cos(x)^2)*sin(x))]","B",0
24,1,71,0,0.572174," ","integrate(sin(x)/(4-3*cos(x)^3),x, algorithm=""fricas"")","-\frac{1}{12} \cdot 6^{\frac{1}{6}} \sqrt{2} \arctan\left(\frac{1}{6} \cdot 6^{\frac{1}{6}} {\left(6^{\frac{2}{3}} \sqrt{2} \cos\left(x\right) + 6^{\frac{1}{3}} \sqrt{2}\right)}\right) - \frac{1}{72} \cdot 6^{\frac{2}{3}} \log\left(-3 \, \cos\left(x\right)^{2} - 6^{\frac{2}{3}} \cos\left(x\right) - 2 \cdot 6^{\frac{1}{3}}\right) + \frac{1}{36} \cdot 6^{\frac{2}{3}} \log\left(6^{\frac{2}{3}} - 3 \, \cos\left(x\right)\right)"," ",0,"-1/12*6^(1/6)*sqrt(2)*arctan(1/6*6^(1/6)*(6^(2/3)*sqrt(2)*cos(x) + 6^(1/3)*sqrt(2))) - 1/72*6^(2/3)*log(-3*cos(x)^2 - 6^(2/3)*cos(x) - 2*6^(1/3)) + 1/36*6^(2/3)*log(6^(2/3) - 3*cos(x))","A",0
25,1,8,0,0.441184," ","integrate(1/(1-cos(x)^2),x, algorithm=""fricas"")","-\frac{\cos\left(x\right)}{\sin\left(x\right)}"," ",0,"-cos(x)/sin(x)","A",0
26,1,25,0,1.004210," ","integrate(1/(1-cos(x)^2)^2,x, algorithm=""fricas"")","-\frac{2 \, \cos\left(x\right)^{3} - 3 \, \cos\left(x\right)}{3 \, {\left(\cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}"," ",0,"-1/3*(2*cos(x)^3 - 3*cos(x))/((cos(x)^2 - 1)*sin(x))","B",0
27,1,37,0,0.581562," ","integrate(1/(1-cos(x)^2)^3,x, algorithm=""fricas"")","-\frac{8 \, \cos\left(x\right)^{5} - 20 \, \cos\left(x\right)^{3} + 15 \, \cos\left(x\right)}{15 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)} \sin\left(x\right)}"," ",0,"-1/15*(8*cos(x)^5 - 20*cos(x)^3 + 15*cos(x))/((cos(x)^4 - 2*cos(x)^2 + 1)*sin(x))","B",0
28,1,259,0,2.131170," ","integrate(cos(x)^7/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{a b + b^{2}} a^{3} \log\left(-\frac{b \cos\left(x\right)^{2} + 2 \, \sqrt{a b + b^{2}} \sin\left(x\right) - a - 2 \, b}{b \cos\left(x\right)^{2} + a}\right) + 2 \, {\left(3 \, {\left(a b^{3} + b^{4}\right)} \cos\left(x\right)^{4} + 15 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} + 8 \, b^{4} - {\left(5 \, a^{2} b^{2} + a b^{3} - 4 \, b^{4}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{30 \, {\left(a b^{4} + b^{5}\right)}}, \frac{15 \, \sqrt{-a b - b^{2}} a^{3} \arctan\left(\frac{\sqrt{-a b - b^{2}} \sin\left(x\right)}{a + b}\right) + {\left(3 \, {\left(a b^{3} + b^{4}\right)} \cos\left(x\right)^{4} + 15 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} + 8 \, b^{4} - {\left(5 \, a^{2} b^{2} + a b^{3} - 4 \, b^{4}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{15 \, {\left(a b^{4} + b^{5}\right)}}\right]"," ",0,"[1/30*(15*sqrt(a*b + b^2)*a^3*log(-(b*cos(x)^2 + 2*sqrt(a*b + b^2)*sin(x) - a - 2*b)/(b*cos(x)^2 + a)) + 2*(3*(a*b^3 + b^4)*cos(x)^4 + 15*a^3*b + 5*a^2*b^2 - 2*a*b^3 + 8*b^4 - (5*a^2*b^2 + a*b^3 - 4*b^4)*cos(x)^2)*sin(x))/(a*b^4 + b^5), 1/15*(15*sqrt(-a*b - b^2)*a^3*arctan(sqrt(-a*b - b^2)*sin(x)/(a + b)) + (3*(a*b^3 + b^4)*cos(x)^4 + 15*a^3*b + 5*a^2*b^2 - 2*a*b^3 + 8*b^4 - (5*a^2*b^2 + a*b^3 - 4*b^4)*cos(x)^2)*sin(x))/(a*b^4 + b^5)]","A",0
29,1,191,0,0.651680," ","integrate(cos(x)^5/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a b + b^{2}} a^{2} \log\left(-\frac{b \cos\left(x\right)^{2} - 2 \, \sqrt{a b + b^{2}} \sin\left(x\right) - a - 2 \, b}{b \cos\left(x\right)^{2} + a}\right) - 2 \, {\left(3 \, a^{2} b + a b^{2} - 2 \, b^{3} - {\left(a b^{2} + b^{3}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{6 \, {\left(a b^{3} + b^{4}\right)}}, -\frac{3 \, \sqrt{-a b - b^{2}} a^{2} \arctan\left(\frac{\sqrt{-a b - b^{2}} \sin\left(x\right)}{a + b}\right) + {\left(3 \, a^{2} b + a b^{2} - 2 \, b^{3} - {\left(a b^{2} + b^{3}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{3 \, {\left(a b^{3} + b^{4}\right)}}\right]"," ",0,"[1/6*(3*sqrt(a*b + b^2)*a^2*log(-(b*cos(x)^2 - 2*sqrt(a*b + b^2)*sin(x) - a - 2*b)/(b*cos(x)^2 + a)) - 2*(3*a^2*b + a*b^2 - 2*b^3 - (a*b^2 + b^3)*cos(x)^2)*sin(x))/(a*b^3 + b^4), -1/3*(3*sqrt(-a*b - b^2)*a^2*arctan(sqrt(-a*b - b^2)*sin(x)/(a + b)) + (3*a^2*b + a*b^2 - 2*b^3 - (a*b^2 + b^3)*cos(x)^2)*sin(x))/(a*b^3 + b^4)]","A",0
30,1,134,0,0.629399," ","integrate(cos(x)^3/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a b + b^{2}} a \log\left(-\frac{b \cos\left(x\right)^{2} + 2 \, \sqrt{a b + b^{2}} \sin\left(x\right) - a - 2 \, b}{b \cos\left(x\right)^{2} + a}\right) + 2 \, {\left(a b + b^{2}\right)} \sin\left(x\right)}{2 \, {\left(a b^{2} + b^{3}\right)}}, \frac{\sqrt{-a b - b^{2}} a \arctan\left(\frac{\sqrt{-a b - b^{2}} \sin\left(x\right)}{a + b}\right) + {\left(a b + b^{2}\right)} \sin\left(x\right)}{a b^{2} + b^{3}}\right]"," ",0,"[1/2*(sqrt(a*b + b^2)*a*log(-(b*cos(x)^2 + 2*sqrt(a*b + b^2)*sin(x) - a - 2*b)/(b*cos(x)^2 + a)) + 2*(a*b + b^2)*sin(x))/(a*b^2 + b^3), (sqrt(-a*b - b^2)*a*arctan(sqrt(-a*b - b^2)*sin(x)/(a + b)) + (a*b + b^2)*sin(x))/(a*b^2 + b^3)]","A",0
31,1,95,0,0.561760," ","integrate(cos(x)/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{b \cos\left(x\right)^{2} - 2 \, \sqrt{a b + b^{2}} \sin\left(x\right) - a - 2 \, b}{b \cos\left(x\right)^{2} + a}\right)}{2 \, \sqrt{a b + b^{2}}}, -\frac{\sqrt{-a b - b^{2}} \arctan\left(\frac{\sqrt{-a b - b^{2}} \sin\left(x\right)}{a + b}\right)}{a b + b^{2}}\right]"," ",0,"[1/2*log(-(b*cos(x)^2 - 2*sqrt(a*b + b^2)*sin(x) - a - 2*b)/(b*cos(x)^2 + a))/sqrt(a*b + b^2), -sqrt(-a*b - b^2)*arctan(sqrt(-a*b - b^2)*sin(x)/(a + b))/(a*b + b^2)]","B",0
32,1,119,0,0.595894," ","integrate(sec(x)/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{b}{a + b}} \log\left(-\frac{b \cos\left(x\right)^{2} + 2 \, {\left(a + b\right)} \sqrt{\frac{b}{a + b}} \sin\left(x\right) - a - 2 \, b}{b \cos\left(x\right)^{2} + a}\right) + \log\left(\sin\left(x\right) + 1\right) - \log\left(-\sin\left(x\right) + 1\right)}{2 \, a}, \frac{2 \, \sqrt{-\frac{b}{a + b}} \arctan\left(\sqrt{-\frac{b}{a + b}} \sin\left(x\right)\right) + \log\left(\sin\left(x\right) + 1\right) - \log\left(-\sin\left(x\right) + 1\right)}{2 \, a}\right]"," ",0,"[1/2*(sqrt(b/(a + b))*log(-(b*cos(x)^2 + 2*(a + b)*sqrt(b/(a + b))*sin(x) - a - 2*b)/(b*cos(x)^2 + a)) + log(sin(x) + 1) - log(-sin(x) + 1))/a, 1/2*(2*sqrt(-b/(a + b))*arctan(sqrt(-b/(a + b))*sin(x)) + log(sin(x) + 1) - log(-sin(x) + 1))/a]","A",0
33,1,186,0,0.674276," ","integrate(sec(x)^3/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{2 \, b \sqrt{\frac{b}{a + b}} \cos\left(x\right)^{2} \log\left(-\frac{b \cos\left(x\right)^{2} - 2 \, {\left(a + b\right)} \sqrt{\frac{b}{a + b}} \sin\left(x\right) - a - 2 \, b}{b \cos\left(x\right)^{2} + a}\right) + {\left(a - 2 \, b\right)} \cos\left(x\right)^{2} \log\left(\sin\left(x\right) + 1\right) - {\left(a - 2 \, b\right)} \cos\left(x\right)^{2} \log\left(-\sin\left(x\right) + 1\right) + 2 \, a \sin\left(x\right)}{4 \, a^{2} \cos\left(x\right)^{2}}, -\frac{4 \, b \sqrt{-\frac{b}{a + b}} \arctan\left(\sqrt{-\frac{b}{a + b}} \sin\left(x\right)\right) \cos\left(x\right)^{2} - {\left(a - 2 \, b\right)} \cos\left(x\right)^{2} \log\left(\sin\left(x\right) + 1\right) + {\left(a - 2 \, b\right)} \cos\left(x\right)^{2} \log\left(-\sin\left(x\right) + 1\right) - 2 \, a \sin\left(x\right)}{4 \, a^{2} \cos\left(x\right)^{2}}\right]"," ",0,"[1/4*(2*b*sqrt(b/(a + b))*cos(x)^2*log(-(b*cos(x)^2 - 2*(a + b)*sqrt(b/(a + b))*sin(x) - a - 2*b)/(b*cos(x)^2 + a)) + (a - 2*b)*cos(x)^2*log(sin(x) + 1) - (a - 2*b)*cos(x)^2*log(-sin(x) + 1) + 2*a*sin(x))/(a^2*cos(x)^2), -1/4*(4*b*sqrt(-b/(a + b))*arctan(sqrt(-b/(a + b))*sin(x))*cos(x)^2 - (a - 2*b)*cos(x)^2*log(sin(x) + 1) + (a - 2*b)*cos(x)^2*log(-sin(x) + 1) - 2*a*sin(x))/(a^2*cos(x)^2)]","A",0
34,1,270,0,0.937496," ","integrate(sec(x)^5/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{8 \, b^{2} \sqrt{\frac{b}{a + b}} \cos\left(x\right)^{4} \log\left(-\frac{b \cos\left(x\right)^{2} + 2 \, {\left(a + b\right)} \sqrt{\frac{b}{a + b}} \sin\left(x\right) - a - 2 \, b}{b \cos\left(x\right)^{2} + a}\right) + {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cos\left(x\right)^{4} \log\left(\sin\left(x\right) + 1\right) - {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cos\left(x\right)^{4} \log\left(-\sin\left(x\right) + 1\right) + 2 \, {\left({\left(3 \, a^{2} - 4 \, a b\right)} \cos\left(x\right)^{2} + 2 \, a^{2}\right)} \sin\left(x\right)}{16 \, a^{3} \cos\left(x\right)^{4}}, \frac{16 \, b^{2} \sqrt{-\frac{b}{a + b}} \arctan\left(\sqrt{-\frac{b}{a + b}} \sin\left(x\right)\right) \cos\left(x\right)^{4} + {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cos\left(x\right)^{4} \log\left(\sin\left(x\right) + 1\right) - {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cos\left(x\right)^{4} \log\left(-\sin\left(x\right) + 1\right) + 2 \, {\left({\left(3 \, a^{2} - 4 \, a b\right)} \cos\left(x\right)^{2} + 2 \, a^{2}\right)} \sin\left(x\right)}{16 \, a^{3} \cos\left(x\right)^{4}}\right]"," ",0,"[1/16*(8*b^2*sqrt(b/(a + b))*cos(x)^4*log(-(b*cos(x)^2 + 2*(a + b)*sqrt(b/(a + b))*sin(x) - a - 2*b)/(b*cos(x)^2 + a)) + (3*a^2 - 4*a*b + 8*b^2)*cos(x)^4*log(sin(x) + 1) - (3*a^2 - 4*a*b + 8*b^2)*cos(x)^4*log(-sin(x) + 1) + 2*((3*a^2 - 4*a*b)*cos(x)^2 + 2*a^2)*sin(x))/(a^3*cos(x)^4), 1/16*(16*b^2*sqrt(-b/(a + b))*arctan(sqrt(-b/(a + b))*sin(x))*cos(x)^4 + (3*a^2 - 4*a*b + 8*b^2)*cos(x)^4*log(sin(x) + 1) - (3*a^2 - 4*a*b + 8*b^2)*cos(x)^4*log(-sin(x) + 1) + 2*((3*a^2 - 4*a*b)*cos(x)^2 + 2*a^2)*sin(x))/(a^3*cos(x)^4)]","A",0
35,1,273,0,1.014919," ","integrate(cos(x)^6/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{2 \, a^{2} \sqrt{-\frac{a}{a + b}} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, a^{2} + 3 \, a b\right)} \cos\left(x\right)^{2} + 4 \, {\left({\left(2 \, a^{2} + 3 \, a b + b^{2}\right)} \cos\left(x\right)^{3} - {\left(a^{2} + a b\right)} \cos\left(x\right)\right)} \sqrt{-\frac{a}{a + b}} \sin\left(x\right) + a^{2}}{b^{2} \cos\left(x\right)^{4} + 2 \, a b \cos\left(x\right)^{2} + a^{2}}\right) + {\left(8 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} x + {\left(2 \, b^{2} \cos\left(x\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{8 \, b^{3}}, \frac{4 \, a^{2} \sqrt{\frac{a}{a + b}} \arctan\left(\frac{{\left({\left(2 \, a + b\right)} \cos\left(x\right)^{2} - a\right)} \sqrt{\frac{a}{a + b}}}{2 \, a \cos\left(x\right) \sin\left(x\right)}\right) + {\left(8 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} x + {\left(2 \, b^{2} \cos\left(x\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{8 \, b^{3}}\right]"," ",0,"[1/8*(2*a^2*sqrt(-a/(a + b))*log(((8*a^2 + 8*a*b + b^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b)*cos(x)^2 + 4*((2*a^2 + 3*a*b + b^2)*cos(x)^3 - (a^2 + a*b)*cos(x))*sqrt(-a/(a + b))*sin(x) + a^2)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2)) + (8*a^2 - 4*a*b + 3*b^2)*x + (2*b^2*cos(x)^3 - (4*a*b - 3*b^2)*cos(x))*sin(x))/b^3, 1/8*(4*a^2*sqrt(a/(a + b))*arctan(1/2*((2*a + b)*cos(x)^2 - a)*sqrt(a/(a + b))/(a*cos(x)*sin(x))) + (8*a^2 - 4*a*b + 3*b^2)*x + (2*b^2*cos(x)^3 - (4*a*b - 3*b^2)*cos(x))*sin(x))/b^3]","A",0
36,1,213,0,0.698153," ","integrate(cos(x)^4/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{2 \, b \cos\left(x\right) \sin\left(x\right) + a \sqrt{-\frac{a}{a + b}} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, a^{2} + 3 \, a b\right)} \cos\left(x\right)^{2} - 4 \, {\left({\left(2 \, a^{2} + 3 \, a b + b^{2}\right)} \cos\left(x\right)^{3} - {\left(a^{2} + a b\right)} \cos\left(x\right)\right)} \sqrt{-\frac{a}{a + b}} \sin\left(x\right) + a^{2}}{b^{2} \cos\left(x\right)^{4} + 2 \, a b \cos\left(x\right)^{2} + a^{2}}\right) - 2 \, {\left(2 \, a - b\right)} x}{4 \, b^{2}}, \frac{b \cos\left(x\right) \sin\left(x\right) - a \sqrt{\frac{a}{a + b}} \arctan\left(\frac{{\left({\left(2 \, a + b\right)} \cos\left(x\right)^{2} - a\right)} \sqrt{\frac{a}{a + b}}}{2 \, a \cos\left(x\right) \sin\left(x\right)}\right) - {\left(2 \, a - b\right)} x}{2 \, b^{2}}\right]"," ",0,"[1/4*(2*b*cos(x)*sin(x) + a*sqrt(-a/(a + b))*log(((8*a^2 + 8*a*b + b^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b)*cos(x)^2 - 4*((2*a^2 + 3*a*b + b^2)*cos(x)^3 - (a^2 + a*b)*cos(x))*sqrt(-a/(a + b))*sin(x) + a^2)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2)) - 2*(2*a - b)*x)/b^2, 1/2*(b*cos(x)*sin(x) - a*sqrt(a/(a + b))*arctan(1/2*((2*a + b)*cos(x)^2 - a)*sqrt(a/(a + b))/(a*cos(x)*sin(x))) - (2*a - b)*x)/b^2]","A",0
37,1,183,0,0.623273," ","integrate(cos(x)^2/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{a}{a + b}} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, a^{2} + 3 \, a b\right)} \cos\left(x\right)^{2} + 4 \, {\left({\left(2 \, a^{2} + 3 \, a b + b^{2}\right)} \cos\left(x\right)^{3} - {\left(a^{2} + a b\right)} \cos\left(x\right)\right)} \sqrt{-\frac{a}{a + b}} \sin\left(x\right) + a^{2}}{b^{2} \cos\left(x\right)^{4} + 2 \, a b \cos\left(x\right)^{2} + a^{2}}\right) + 4 \, x}{4 \, b}, \frac{\sqrt{\frac{a}{a + b}} \arctan\left(\frac{{\left({\left(2 \, a + b\right)} \cos\left(x\right)^{2} - a\right)} \sqrt{\frac{a}{a + b}}}{2 \, a \cos\left(x\right) \sin\left(x\right)}\right) + 2 \, x}{2 \, b}\right]"," ",0,"[1/4*(sqrt(-a/(a + b))*log(((8*a^2 + 8*a*b + b^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b)*cos(x)^2 + 4*((2*a^2 + 3*a*b + b^2)*cos(x)^3 - (a^2 + a*b)*cos(x))*sqrt(-a/(a + b))*sin(x) + a^2)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2)) + 4*x)/b, 1/2*(sqrt(a/(a + b))*arctan(1/2*((2*a + b)*cos(x)^2 - a)*sqrt(a/(a + b))/(a*cos(x)*sin(x))) + 2*x)/b]","A",0
38,1,163,0,0.500749," ","integrate(1/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} - a b} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, a^{2} + 3 \, a b\right)} \cos\left(x\right)^{2} + 4 \, {\left({\left(2 \, a + b\right)} \cos\left(x\right)^{3} - a \cos\left(x\right)\right)} \sqrt{-a^{2} - a b} \sin\left(x\right) + a^{2}}{b^{2} \cos\left(x\right)^{4} + 2 \, a b \cos\left(x\right)^{2} + a^{2}}\right)}{4 \, {\left(a^{2} + a b\right)}}, -\frac{\arctan\left(\frac{{\left(2 \, a + b\right)} \cos\left(x\right)^{2} - a}{2 \, \sqrt{a^{2} + a b} \cos\left(x\right) \sin\left(x\right)}\right)}{2 \, \sqrt{a^{2} + a b}}\right]"," ",0,"[-1/4*sqrt(-a^2 - a*b)*log(((8*a^2 + 8*a*b + b^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b)*cos(x)^2 + 4*((2*a + b)*cos(x)^3 - a*cos(x))*sqrt(-a^2 - a*b)*sin(x) + a^2)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2))/(a^2 + a*b), -1/2*arctan(1/2*((2*a + b)*cos(x)^2 - a)/(sqrt(a^2 + a*b)*cos(x)*sin(x)))/sqrt(a^2 + a*b)]","B",0
39,1,216,0,0.733880," ","integrate(sec(x)^2/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} - a b} b \cos\left(x\right) \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, a^{2} + 3 \, a b\right)} \cos\left(x\right)^{2} - 4 \, {\left({\left(2 \, a + b\right)} \cos\left(x\right)^{3} - a \cos\left(x\right)\right)} \sqrt{-a^{2} - a b} \sin\left(x\right) + a^{2}}{b^{2} \cos\left(x\right)^{4} + 2 \, a b \cos\left(x\right)^{2} + a^{2}}\right) - 4 \, {\left(a^{2} + a b\right)} \sin\left(x\right)}{4 \, {\left(a^{3} + a^{2} b\right)} \cos\left(x\right)}, \frac{\sqrt{a^{2} + a b} b \arctan\left(\frac{{\left(2 \, a + b\right)} \cos\left(x\right)^{2} - a}{2 \, \sqrt{a^{2} + a b} \cos\left(x\right) \sin\left(x\right)}\right) \cos\left(x\right) + 2 \, {\left(a^{2} + a b\right)} \sin\left(x\right)}{2 \, {\left(a^{3} + a^{2} b\right)} \cos\left(x\right)}\right]"," ",0,"[-1/4*(sqrt(-a^2 - a*b)*b*cos(x)*log(((8*a^2 + 8*a*b + b^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b)*cos(x)^2 - 4*((2*a + b)*cos(x)^3 - a*cos(x))*sqrt(-a^2 - a*b)*sin(x) + a^2)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2)) - 4*(a^2 + a*b)*sin(x))/((a^3 + a^2*b)*cos(x)), 1/2*(sqrt(a^2 + a*b)*b*arctan(1/2*((2*a + b)*cos(x)^2 - a)/(sqrt(a^2 + a*b)*cos(x)*sin(x)))*cos(x) + 2*(a^2 + a*b)*sin(x))/((a^3 + a^2*b)*cos(x))]","B",0
40,1,276,0,0.950281," ","integrate(sec(x)^4/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{-a^{2} - a b} b^{2} \cos\left(x\right)^{3} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, a^{2} + 3 \, a b\right)} \cos\left(x\right)^{2} + 4 \, {\left({\left(2 \, a + b\right)} \cos\left(x\right)^{3} - a \cos\left(x\right)\right)} \sqrt{-a^{2} - a b} \sin\left(x\right) + a^{2}}{b^{2} \cos\left(x\right)^{4} + 2 \, a b \cos\left(x\right)^{2} + a^{2}}\right) - 4 \, {\left(a^{3} + a^{2} b + {\left(2 \, a^{3} - a^{2} b - 3 \, a b^{2}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{12 \, {\left(a^{4} + a^{3} b\right)} \cos\left(x\right)^{3}}, -\frac{3 \, \sqrt{a^{2} + a b} b^{2} \arctan\left(\frac{{\left(2 \, a + b\right)} \cos\left(x\right)^{2} - a}{2 \, \sqrt{a^{2} + a b} \cos\left(x\right) \sin\left(x\right)}\right) \cos\left(x\right)^{3} - 2 \, {\left(a^{3} + a^{2} b + {\left(2 \, a^{3} - a^{2} b - 3 \, a b^{2}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{6 \, {\left(a^{4} + a^{3} b\right)} \cos\left(x\right)^{3}}\right]"," ",0,"[-1/12*(3*sqrt(-a^2 - a*b)*b^2*cos(x)^3*log(((8*a^2 + 8*a*b + b^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b)*cos(x)^2 + 4*((2*a + b)*cos(x)^3 - a*cos(x))*sqrt(-a^2 - a*b)*sin(x) + a^2)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2)) - 4*(a^3 + a^2*b + (2*a^3 - a^2*b - 3*a*b^2)*cos(x)^2)*sin(x))/((a^4 + a^3*b)*cos(x)^3), -1/6*(3*sqrt(a^2 + a*b)*b^2*arctan(1/2*((2*a + b)*cos(x)^2 - a)/(sqrt(a^2 + a*b)*cos(x)*sin(x)))*cos(x)^3 - 2*(a^3 + a^2*b + (2*a^3 - a^2*b - 3*a*b^2)*cos(x)^2)*sin(x))/((a^4 + a^3*b)*cos(x)^3)]","B",0
41,1,348,0,1.200789," ","integrate(sec(x)^6/(a+b*cos(x)^2),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{-a^{2} - a b} b^{3} \cos\left(x\right)^{5} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, a^{2} + 3 \, a b\right)} \cos\left(x\right)^{2} - 4 \, {\left({\left(2 \, a + b\right)} \cos\left(x\right)^{3} - a \cos\left(x\right)\right)} \sqrt{-a^{2} - a b} \sin\left(x\right) + a^{2}}{b^{2} \cos\left(x\right)^{4} + 2 \, a b \cos\left(x\right)^{2} + a^{2}}\right) - 4 \, {\left({\left(8 \, a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} + 15 \, a b^{3}\right)} \cos\left(x\right)^{4} + 3 \, a^{4} + 3 \, a^{3} b + {\left(4 \, a^{4} - a^{3} b - 5 \, a^{2} b^{2}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{60 \, {\left(a^{5} + a^{4} b\right)} \cos\left(x\right)^{5}}, \frac{15 \, \sqrt{a^{2} + a b} b^{3} \arctan\left(\frac{{\left(2 \, a + b\right)} \cos\left(x\right)^{2} - a}{2 \, \sqrt{a^{2} + a b} \cos\left(x\right) \sin\left(x\right)}\right) \cos\left(x\right)^{5} + 2 \, {\left({\left(8 \, a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} + 15 \, a b^{3}\right)} \cos\left(x\right)^{4} + 3 \, a^{4} + 3 \, a^{3} b + {\left(4 \, a^{4} - a^{3} b - 5 \, a^{2} b^{2}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{30 \, {\left(a^{5} + a^{4} b\right)} \cos\left(x\right)^{5}}\right]"," ",0,"[-1/60*(15*sqrt(-a^2 - a*b)*b^3*cos(x)^5*log(((8*a^2 + 8*a*b + b^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b)*cos(x)^2 - 4*((2*a + b)*cos(x)^3 - a*cos(x))*sqrt(-a^2 - a*b)*sin(x) + a^2)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2)) - 4*((8*a^4 - 2*a^3*b + 5*a^2*b^2 + 15*a*b^3)*cos(x)^4 + 3*a^4 + 3*a^3*b + (4*a^4 - a^3*b - 5*a^2*b^2)*cos(x)^2)*sin(x))/((a^5 + a^4*b)*cos(x)^5), 1/30*(15*sqrt(a^2 + a*b)*b^3*arctan(1/2*((2*a + b)*cos(x)^2 - a)/(sqrt(a^2 + a*b)*cos(x)*sin(x)))*cos(x)^5 + 2*((8*a^4 - 2*a^3*b + 5*a^2*b^2 + 15*a*b^3)*cos(x)^4 + 3*a^4 + 3*a^3*b + (4*a^4 - a^3*b - 5*a^2*b^2)*cos(x)^2)*sin(x))/((a^5 + a^4*b)*cos(x)^5)]","B",0
42,1,326,0,0.743942," ","integrate(1/(a+b*cos(x)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a^{2} b + a b^{2}\right)} \cos\left(x\right) \sin\left(x\right) + {\left({\left(2 \, a b + b^{2}\right)} \cos\left(x\right)^{2} + 2 \, a^{2} + a b\right)} \sqrt{-a^{2} - a b} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, a^{2} + 3 \, a b\right)} \cos\left(x\right)^{2} + 4 \, {\left({\left(2 \, a + b\right)} \cos\left(x\right)^{3} - a \cos\left(x\right)\right)} \sqrt{-a^{2} - a b} \sin\left(x\right) + a^{2}}{b^{2} \cos\left(x\right)^{4} + 2 \, a b \cos\left(x\right)^{2} + a^{2}}\right)}{8 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2} + {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cos\left(x\right)^{2}\right)}}, -\frac{2 \, {\left(a^{2} b + a b^{2}\right)} \cos\left(x\right) \sin\left(x\right) + {\left({\left(2 \, a b + b^{2}\right)} \cos\left(x\right)^{2} + 2 \, a^{2} + a b\right)} \sqrt{a^{2} + a b} \arctan\left(\frac{{\left(2 \, a + b\right)} \cos\left(x\right)^{2} - a}{2 \, \sqrt{a^{2} + a b} \cos\left(x\right) \sin\left(x\right)}\right)}{4 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2} + {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cos\left(x\right)^{2}\right)}}\right]"," ",0,"[-1/8*(4*(a^2*b + a*b^2)*cos(x)*sin(x) + ((2*a*b + b^2)*cos(x)^2 + 2*a^2 + a*b)*sqrt(-a^2 - a*b)*log(((8*a^2 + 8*a*b + b^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b)*cos(x)^2 + 4*((2*a + b)*cos(x)^3 - a*cos(x))*sqrt(-a^2 - a*b)*sin(x) + a^2)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2)))/(a^5 + 2*a^4*b + a^3*b^2 + (a^4*b + 2*a^3*b^2 + a^2*b^3)*cos(x)^2), -1/4*(2*(a^2*b + a*b^2)*cos(x)*sin(x) + ((2*a*b + b^2)*cos(x)^2 + 2*a^2 + a*b)*sqrt(a^2 + a*b)*arctan(1/2*((2*a + b)*cos(x)^2 - a)/(sqrt(a^2 + a*b)*cos(x)*sin(x))))/(a^5 + 2*a^4*b + a^3*b^2 + (a^4*b + 2*a^3*b^2 + a^2*b^3)*cos(x)^2)]","B",0
43,1,616,0,0.765010," ","integrate(1/(a+b*cos(x)^2)^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cos\left(x\right)^{4} + 8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, {\left(8 \, a^{3} b + 8 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cos\left(x\right)^{2}\right)} \sqrt{-a^{2} - a b} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cos\left(x\right)^{4} - 2 \, {\left(4 \, a^{2} + 3 \, a b\right)} \cos\left(x\right)^{2} + 4 \, {\left({\left(2 \, a + b\right)} \cos\left(x\right)^{3} - a \cos\left(x\right)\right)} \sqrt{-a^{2} - a b} \sin\left(x\right) + a^{2}}{b^{2} \cos\left(x\right)^{4} + 2 \, a b \cos\left(x\right)^{2} + a^{2}}\right) + 4 \, {\left(3 \, {\left(2 \, a^{3} b^{2} + 3 \, a^{2} b^{3} + a b^{4}\right)} \cos\left(x\right)^{3} + {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{32 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3} + {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cos\left(x\right)^{4} + 2 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} \cos\left(x\right)^{2}\right)}}, -\frac{{\left({\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cos\left(x\right)^{4} + 8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, {\left(8 \, a^{3} b + 8 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cos\left(x\right)^{2}\right)} \sqrt{a^{2} + a b} \arctan\left(\frac{{\left(2 \, a + b\right)} \cos\left(x\right)^{2} - a}{2 \, \sqrt{a^{2} + a b} \cos\left(x\right) \sin\left(x\right)}\right) + 2 \, {\left(3 \, {\left(2 \, a^{3} b^{2} + 3 \, a^{2} b^{3} + a b^{4}\right)} \cos\left(x\right)^{3} + {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{16 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3} + {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cos\left(x\right)^{4} + 2 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} \cos\left(x\right)^{2}\right)}}\right]"," ",0,"[-1/32*(((8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cos(x)^4 + 8*a^4 + 8*a^3*b + 3*a^2*b^2 + 2*(8*a^3*b + 8*a^2*b^2 + 3*a*b^3)*cos(x)^2)*sqrt(-a^2 - a*b)*log(((8*a^2 + 8*a*b + b^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b)*cos(x)^2 + 4*((2*a + b)*cos(x)^3 - a*cos(x))*sqrt(-a^2 - a*b)*sin(x) + a^2)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2)) + 4*(3*(2*a^3*b^2 + 3*a^2*b^3 + a*b^4)*cos(x)^3 + (8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*cos(x))*sin(x))/(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3 + (a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cos(x)^4 + 2*(a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*cos(x)^2), -1/16*(((8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cos(x)^4 + 8*a^4 + 8*a^3*b + 3*a^2*b^2 + 2*(8*a^3*b + 8*a^2*b^2 + 3*a*b^3)*cos(x)^2)*sqrt(a^2 + a*b)*arctan(1/2*((2*a + b)*cos(x)^2 - a)/(sqrt(a^2 + a*b)*cos(x)*sin(x))) + 2*(3*(2*a^3*b^2 + 3*a^2*b^3 + a*b^4)*cos(x)^3 + (8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*cos(x))*sin(x))/(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3 + (a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cos(x)^4 + 2*(a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*cos(x)^2)]","B",0
44,1,31,0,2.581501," ","integrate(1/(1+cos(x)^2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(x\right)^{2} - \sqrt{2}}{4 \, \cos\left(x\right) \sin\left(x\right)}\right)"," ",0,"-1/4*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(x)^2 - sqrt(2))/(cos(x)*sin(x)))","A",0
45,1,57,0,0.618863," ","integrate(1/(1+cos(x)^2)^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(\sqrt{2} \cos\left(x\right)^{2} + \sqrt{2}\right)} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(x\right)^{2} - \sqrt{2}}{4 \, \cos\left(x\right) \sin\left(x\right)}\right) + 4 \, \cos\left(x\right) \sin\left(x\right)}{16 \, {\left(\cos\left(x\right)^{2} + 1\right)}}"," ",0,"-1/16*(3*(sqrt(2)*cos(x)^2 + sqrt(2))*arctan(1/4*(3*sqrt(2)*cos(x)^2 - sqrt(2))/(cos(x)*sin(x))) + 4*cos(x)*sin(x))/(cos(x)^2 + 1)","A",0
46,1,81,0,1.753893," ","integrate(1/(1+cos(x)^2)^3,x, algorithm=""fricas"")","-\frac{19 \, {\left(\sqrt{2} \cos\left(x\right)^{4} + 2 \, \sqrt{2} \cos\left(x\right)^{2} + \sqrt{2}\right)} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(x\right)^{2} - \sqrt{2}}{4 \, \cos\left(x\right) \sin\left(x\right)}\right) + 4 \, {\left(9 \, \cos\left(x\right)^{3} + 13 \, \cos\left(x\right)\right)} \sin\left(x\right)}{128 \, {\left(\cos\left(x\right)^{4} + 2 \, \cos\left(x\right)^{2} + 1\right)}}"," ",0,"-1/128*(19*(sqrt(2)*cos(x)^4 + 2*sqrt(2)*cos(x)^2 + sqrt(2))*arctan(1/4*(3*sqrt(2)*cos(x)^2 - sqrt(2))/(cos(x)*sin(x))) + 4*(9*cos(x)^3 + 13*cos(x))*sin(x))/(cos(x)^4 + 2*cos(x)^2 + 1)","A",0
47,1,4,0,0.688826," ","integrate((1-cos(x)^2)^(1/2),x, algorithm=""fricas"")","-\cos\left(x\right)"," ",0,"-cos(x)","A",0
48,1,1,0,1.465816," ","integrate((-1+cos(x)^2)^(1/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
49,1,11,0,0.679565," ","integrate((1-cos(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{3} \, \cos\left(x\right)^{3} - \cos\left(x\right)"," ",0,"1/3*cos(x)^3 - cos(x)","A",0
50,1,1,0,0.446953," ","integrate((-1+cos(x)^2)^(3/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
51,1,19,0,1.348939," ","integrate(1/(1-cos(x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{2} \, \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"-1/2*log(1/2*cos(x) + 1/2) + 1/2*log(-1/2*cos(x) + 1/2)","A",0
52,-2,0,0,0.000000," ","integrate(1/(-1+cos(x)^2)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
53,1,44,0,0.602895," ","integrate(1/(1-cos(x)^2)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(\cos\left(x\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - {\left(\cos\left(x\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - 2 \, \cos\left(x\right)}{4 \, {\left(\cos\left(x\right)^{2} - 1\right)}}"," ",0,"-1/4*((cos(x)^2 - 1)*log(1/2*cos(x) + 1/2) - (cos(x)^2 - 1)*log(-1/2*cos(x) + 1/2) - 2*cos(x))/(cos(x)^2 - 1)","A",0
54,-2,0,0,0.000000," ","integrate(1/(-1+cos(x)^2)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
55,0,0,0,0.626319," ","integrate((1+cos(x)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\cos\left(x\right)^{2} + 1}, x\right)"," ",0,"integral(sqrt(cos(x)^2 + 1), x)","F",0
56,0,0,0,0.829182," ","integrate((-1-cos(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(e^{\left(2 i \, x\right)} - e^{\left(i \, x\right)}\right)} {\rm integral}\left(\frac{4 \, \sqrt{e^{\left(4 i \, x\right)} + 6 \, e^{\left(2 i \, x\right)} + 1} {\left(e^{\left(2 i \, x\right)} + 1\right)}}{e^{\left(6 i \, x\right)} - 2 \, e^{\left(5 i \, x\right)} + 7 \, e^{\left(4 i \, x\right)} - 12 \, e^{\left(3 i \, x\right)} + 7 \, e^{\left(2 i \, x\right)} - 2 \, e^{\left(i \, x\right)} + 1}, x\right) + \sqrt{e^{\left(4 i \, x\right)} + 6 \, e^{\left(2 i \, x\right)} + 1} {\left(e^{\left(i \, x\right)} + 1\right)}}{2 \, {\left(e^{\left(2 i \, x\right)} - e^{\left(i \, x\right)}\right)}}"," ",0,"1/2*(2*(e^(2*I*x) - e^(I*x))*integral(4*sqrt(e^(4*I*x) + 6*e^(2*I*x) + 1)*(e^(2*I*x) + 1)/(e^(6*I*x) - 2*e^(5*I*x) + 7*e^(4*I*x) - 12*e^(3*I*x) + 7*e^(2*I*x) - 2*e^(I*x) + 1), x) + sqrt(e^(4*I*x) + 6*e^(2*I*x) + 1)*(e^(I*x) + 1))/(e^(2*I*x) - e^(I*x))","F",0
57,0,0,0,0.592525," ","integrate((a+b*cos(x)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \cos\left(x\right)^{2} + a}, x\right)"," ",0,"integral(sqrt(b*cos(x)^2 + a), x)","F",0
58,0,0,0,0.573731," ","integrate((1+cos(x)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(\cos\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((cos(x)^2 + 1)^(3/2), x)","F",0
59,0,0,0,0.630131," ","integrate((-1-cos(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{24 \, {\left(e^{\left(4 i \, x\right)} - e^{\left(3 i \, x\right)}\right)} {\rm integral}\left(-\frac{4 \, \sqrt{e^{\left(4 i \, x\right)} + 6 \, e^{\left(2 i \, x\right)} + 1} {\left(5 \, e^{\left(2 i \, x\right)} + 2 \, e^{\left(i \, x\right)} + 5\right)}}{3 \, {\left(e^{\left(6 i \, x\right)} - 2 \, e^{\left(5 i \, x\right)} + 7 \, e^{\left(4 i \, x\right)} - 12 \, e^{\left(3 i \, x\right)} + 7 \, e^{\left(2 i \, x\right)} - 2 \, e^{\left(i \, x\right)} + 1\right)}}, x\right) - {\left(e^{\left(5 i \, x\right)} - e^{\left(4 i \, x\right)} + 24 \, e^{\left(3 i \, x\right)} + 24 \, e^{\left(2 i \, x\right)} - e^{\left(i \, x\right)} + 1\right)} \sqrt{e^{\left(4 i \, x\right)} + 6 \, e^{\left(2 i \, x\right)} + 1}}{24 \, {\left(e^{\left(4 i \, x\right)} - e^{\left(3 i \, x\right)}\right)}}"," ",0,"1/24*(24*(e^(4*I*x) - e^(3*I*x))*integral(-4/3*sqrt(e^(4*I*x) + 6*e^(2*I*x) + 1)*(5*e^(2*I*x) + 2*e^(I*x) + 5)/(e^(6*I*x) - 2*e^(5*I*x) + 7*e^(4*I*x) - 12*e^(3*I*x) + 7*e^(2*I*x) - 2*e^(I*x) + 1), x) - (e^(5*I*x) - e^(4*I*x) + 24*e^(3*I*x) + 24*e^(2*I*x) - e^(I*x) + 1)*sqrt(e^(4*I*x) + 6*e^(2*I*x) + 1))/(e^(4*I*x) - e^(3*I*x))","F",0
60,0,0,0,0.512242," ","integrate((a+b*cos(x)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(x\right)^{2} + a\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((b*cos(x)^2 + a)^(3/2), x)","F",0
61,0,0,0,0.470247," ","integrate(1/(1+cos(x)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{\cos\left(x\right)^{2} + 1}}, x\right)"," ",0,"integral(1/sqrt(cos(x)^2 + 1), x)","F",0
62,0,0,0,0.508979," ","integrate(1/(-1-cos(x)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{2}{\sqrt{e^{\left(4 i \, x\right)} + 6 \, e^{\left(2 i \, x\right)} + 1}}, x\right)"," ",0,"integral(-2/sqrt(e^(4*I*x) + 6*e^(2*I*x) + 1), x)","F",0
63,0,0,0,0.531426," ","integrate(1/(a+b*cos(x)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b \cos\left(x\right)^{2} + a}}, x\right)"," ",0,"integral(1/sqrt(b*cos(x)^2 + a), x)","F",0
64,0,0,0,0.681085," ","integrate(1/(1+cos(x)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(x\right)^{2} + 1}}{\cos\left(x\right)^{4} + 2 \, \cos\left(x\right)^{2} + 1}, x\right)"," ",0,"integral(sqrt(cos(x)^2 + 1)/(cos(x)^4 + 2*cos(x)^2 + 1), x)","F",0
65,0,0,0,0.580481," ","integrate(1/(-1-cos(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(e^{\left(4 i \, x\right)} + 6 \, e^{\left(2 i \, x\right)} + 1\right)} {\rm integral}\left(\frac{e^{\left(2 i \, x\right)} + 3}{2 \, \sqrt{e^{\left(4 i \, x\right)} + 6 \, e^{\left(2 i \, x\right)} + 1}}, x\right) - \sqrt{e^{\left(4 i \, x\right)} + 6 \, e^{\left(2 i \, x\right)} + 1} {\left(e^{\left(3 i \, x\right)} + 3 \, e^{\left(i \, x\right)}\right)}}{2 \, {\left(e^{\left(4 i \, x\right)} + 6 \, e^{\left(2 i \, x\right)} + 1\right)}}"," ",0,"1/2*(2*(e^(4*I*x) + 6*e^(2*I*x) + 1)*integral(1/2*(e^(2*I*x) + 3)/sqrt(e^(4*I*x) + 6*e^(2*I*x) + 1), x) - sqrt(e^(4*I*x) + 6*e^(2*I*x) + 1)*(e^(3*I*x) + 3*e^(I*x)))/(e^(4*I*x) + 6*e^(2*I*x) + 1)","F",0
66,0,0,0,0.568662," ","integrate(1/(a+b*cos(x)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(x\right)^{2} + a}}{b^{2} \cos\left(x\right)^{4} + 2 \, a b \cos\left(x\right)^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(x)^2 + a)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2), x)","F",0
67,1,49,0,0.628341," ","integrate(cos(x)/(1+cos(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \arctan\left(\frac{\sqrt{\cos\left(x\right)^{2} + 1} \cos\left(x\right)^{2} \sin\left(x\right) - \cos\left(x\right) \sin\left(x\right)}{\cos\left(x\right)^{4} + \cos\left(x\right)^{2} - 1}\right) + \frac{1}{2} \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)"," ",0,"1/2*arctan((sqrt(cos(x)^2 + 1)*cos(x)^2*sin(x) - cos(x)*sin(x))/(cos(x)^4 + cos(x)^2 - 1)) + 1/2*arctan(sin(x)/cos(x))","B",0
68,1,89,0,1.389867," ","integrate(cos(5+3*x)/(3+cos(5+3*x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \arctan\left(\frac{\sqrt{\cos\left(3 \, x + 5\right)^{2} + 3} {\left(\cos\left(3 \, x + 5\right)^{2} + 1\right)} \sin\left(3 \, x + 5\right) - 4 \, \cos\left(3 \, x + 5\right) \sin\left(3 \, x + 5\right)}{\cos\left(3 \, x + 5\right)^{4} + 6 \, \cos\left(3 \, x + 5\right)^{2} - 3}\right) + \frac{1}{6} \, \arctan\left(\frac{\sin\left(3 \, x + 5\right)}{\cos\left(3 \, x + 5\right)}\right)"," ",0,"1/6*arctan((sqrt(cos(3*x + 5)^2 + 3)*(cos(3*x + 5)^2 + 1)*sin(3*x + 5) - 4*cos(3*x + 5)*sin(3*x + 5))/(cos(3*x + 5)^4 + 6*cos(3*x + 5)^2 - 3)) + 1/6*arctan(sin(3*x + 5)/cos(3*x + 5))","B",0
69,1,39,0,1.211261," ","integrate(cos(x)/(4-cos(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \log\left(8 \, \cos\left(x\right)^{4} - 4 \, {\left(2 \, \cos\left(x\right)^{2} - 5\right)} \sqrt{-\cos\left(x\right)^{2} + 4} \sin\left(x\right) - 40 \, \cos\left(x\right)^{2} + 41\right)"," ",0,"1/4*log(8*cos(x)^4 - 4*(2*cos(x)^2 - 5)*sqrt(-cos(x)^2 + 4)*sin(x) - 40*cos(x)^2 + 41)","B",0
70,1,809,0,0.860929," ","integrate(1/(a+b*cos(x)^4),x, algorithm=""fricas"")","-\frac{1}{8} \, \sqrt{-\frac{{\left(a^{2} + a b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} + 1}{a^{2} + a b}} \log\left(b \cos\left(x\right)^{2} + 2 \, {\left(a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{4} + a^{3} b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} \cos\left(x\right) \sin\left(x\right)\right)} \sqrt{-\frac{{\left(a^{2} + a b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} + 1}{a^{2} + a b}} - {\left(a^{3} + a^{2} b - 2 \, {\left(a^{3} + a^{2} b\right)} \cos\left(x\right)^{2}\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}}\right) + \frac{1}{8} \, \sqrt{-\frac{{\left(a^{2} + a b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} + 1}{a^{2} + a b}} \log\left(b \cos\left(x\right)^{2} - 2 \, {\left(a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{4} + a^{3} b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} \cos\left(x\right) \sin\left(x\right)\right)} \sqrt{-\frac{{\left(a^{2} + a b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} + 1}{a^{2} + a b}} - {\left(a^{3} + a^{2} b - 2 \, {\left(a^{3} + a^{2} b\right)} \cos\left(x\right)^{2}\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}}\right) + \frac{1}{8} \, \sqrt{\frac{{\left(a^{2} + a b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} - 1}{a^{2} + a b}} \log\left(-b \cos\left(x\right)^{2} + 2 \, {\left(a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{4} + a^{3} b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} \cos\left(x\right) \sin\left(x\right)\right)} \sqrt{\frac{{\left(a^{2} + a b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} - 1}{a^{2} + a b}} - {\left(a^{3} + a^{2} b - 2 \, {\left(a^{3} + a^{2} b\right)} \cos\left(x\right)^{2}\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}}\right) - \frac{1}{8} \, \sqrt{\frac{{\left(a^{2} + a b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} - 1}{a^{2} + a b}} \log\left(-b \cos\left(x\right)^{2} - 2 \, {\left(a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{4} + a^{3} b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} \cos\left(x\right) \sin\left(x\right)\right)} \sqrt{\frac{{\left(a^{2} + a b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} - 1}{a^{2} + a b}} - {\left(a^{3} + a^{2} b - 2 \, {\left(a^{3} + a^{2} b\right)} \cos\left(x\right)^{2}\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}}\right)"," ",0,"-1/8*sqrt(-((a^2 + a*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) + 1)/(a^2 + a*b))*log(b*cos(x)^2 + 2*(a*b*cos(x)*sin(x) + (a^4 + a^3*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2))*cos(x)*sin(x))*sqrt(-((a^2 + a*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) + 1)/(a^2 + a*b)) - (a^3 + a^2*b - 2*(a^3 + a^2*b)*cos(x)^2)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2))) + 1/8*sqrt(-((a^2 + a*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) + 1)/(a^2 + a*b))*log(b*cos(x)^2 - 2*(a*b*cos(x)*sin(x) + (a^4 + a^3*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2))*cos(x)*sin(x))*sqrt(-((a^2 + a*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) + 1)/(a^2 + a*b)) - (a^3 + a^2*b - 2*(a^3 + a^2*b)*cos(x)^2)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2))) + 1/8*sqrt(((a^2 + a*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) - 1)/(a^2 + a*b))*log(-b*cos(x)^2 + 2*(a*b*cos(x)*sin(x) - (a^4 + a^3*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2))*cos(x)*sin(x))*sqrt(((a^2 + a*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) - 1)/(a^2 + a*b)) - (a^3 + a^2*b - 2*(a^3 + a^2*b)*cos(x)^2)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2))) - 1/8*sqrt(((a^2 + a*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) - 1)/(a^2 + a*b))*log(-b*cos(x)^2 - 2*(a*b*cos(x)*sin(x) - (a^4 + a^3*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2))*cos(x)*sin(x))*sqrt(((a^2 + a*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) - 1)/(a^2 + a*b)) - (a^3 + a^2*b - 2*(a^3 + a^2*b)*cos(x)^2)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)))","B",0
71,1,817,0,0.712674," ","integrate(1/(a-b*cos(x)^4),x, algorithm=""fricas"")","-\frac{1}{8} \, \sqrt{-\frac{{\left(a^{2} - a b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} + 1}{a^{2} - a b}} \log\left(b \cos\left(x\right)^{2} + 2 \, {\left(a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{4} - a^{3} b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} \cos\left(x\right) \sin\left(x\right)\right)} \sqrt{-\frac{{\left(a^{2} - a b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} + 1}{a^{2} - a b}} + {\left(a^{3} - a^{2} b - 2 \, {\left(a^{3} - a^{2} b\right)} \cos\left(x\right)^{2}\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}}\right) + \frac{1}{8} \, \sqrt{-\frac{{\left(a^{2} - a b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} + 1}{a^{2} - a b}} \log\left(b \cos\left(x\right)^{2} - 2 \, {\left(a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{4} - a^{3} b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} \cos\left(x\right) \sin\left(x\right)\right)} \sqrt{-\frac{{\left(a^{2} - a b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} + 1}{a^{2} - a b}} + {\left(a^{3} - a^{2} b - 2 \, {\left(a^{3} - a^{2} b\right)} \cos\left(x\right)^{2}\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}}\right) + \frac{1}{8} \, \sqrt{\frac{{\left(a^{2} - a b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} - 1}{a^{2} - a b}} \log\left(-b \cos\left(x\right)^{2} + 2 \, {\left(a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{4} - a^{3} b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} \cos\left(x\right) \sin\left(x\right)\right)} \sqrt{\frac{{\left(a^{2} - a b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} - 1}{a^{2} - a b}} + {\left(a^{3} - a^{2} b - 2 \, {\left(a^{3} - a^{2} b\right)} \cos\left(x\right)^{2}\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}}\right) - \frac{1}{8} \, \sqrt{\frac{{\left(a^{2} - a b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} - 1}{a^{2} - a b}} \log\left(-b \cos\left(x\right)^{2} - 2 \, {\left(a b \cos\left(x\right) \sin\left(x\right) + {\left(a^{4} - a^{3} b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} \cos\left(x\right) \sin\left(x\right)\right)} \sqrt{\frac{{\left(a^{2} - a b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} - 1}{a^{2} - a b}} + {\left(a^{3} - a^{2} b - 2 \, {\left(a^{3} - a^{2} b\right)} \cos\left(x\right)^{2}\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}}\right)"," ",0,"-1/8*sqrt(-((a^2 - a*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) + 1)/(a^2 - a*b))*log(b*cos(x)^2 + 2*(a*b*cos(x)*sin(x) - (a^4 - a^3*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2))*cos(x)*sin(x))*sqrt(-((a^2 - a*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) + 1)/(a^2 - a*b)) + (a^3 - a^2*b - 2*(a^3 - a^2*b)*cos(x)^2)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2))) + 1/8*sqrt(-((a^2 - a*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) + 1)/(a^2 - a*b))*log(b*cos(x)^2 - 2*(a*b*cos(x)*sin(x) - (a^4 - a^3*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2))*cos(x)*sin(x))*sqrt(-((a^2 - a*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) + 1)/(a^2 - a*b)) + (a^3 - a^2*b - 2*(a^3 - a^2*b)*cos(x)^2)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2))) + 1/8*sqrt(((a^2 - a*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) - 1)/(a^2 - a*b))*log(-b*cos(x)^2 + 2*(a*b*cos(x)*sin(x) + (a^4 - a^3*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2))*cos(x)*sin(x))*sqrt(((a^2 - a*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) - 1)/(a^2 - a*b)) + (a^3 - a^2*b - 2*(a^3 - a^2*b)*cos(x)^2)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2))) - 1/8*sqrt(((a^2 - a*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) - 1)/(a^2 - a*b))*log(-b*cos(x)^2 - 2*(a*b*cos(x)*sin(x) + (a^4 - a^3*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2))*cos(x)*sin(x))*sqrt(((a^2 - a*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) - 1)/(a^2 - a*b)) + (a^3 - a^2*b - 2*(a^3 - a^2*b)*cos(x)^2)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)))","B",0
72,1,3830,0,42.422957," ","integrate(1/(1+cos(x)^4),x, algorithm=""fricas"")","-\frac{1}{32} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 1\right)} \log\left(-{\left(4 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} + 4 \, {\left(\sqrt{2} - 1\right)} \cos\left(x\right)^{2} + {\left(2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 4\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 1\right) + \frac{1}{32} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 1\right)} \log\left(-{\left(4 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} + 4 \, {\left(\sqrt{2} - 1\right)} \cos\left(x\right)^{2} - {\left(2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 4\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 1\right) - \frac{1}{16} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{32 \, {\left(\sqrt{2} {\left(3 \, \sqrt{2} + 2\right)} - 2 \, \sqrt{2} - 6\right)} \cos\left(x\right)^{16} - 16 \, {\left(\sqrt{2} {\left(19 \, \sqrt{2} + 22\right)} - 8 \, \sqrt{2} - 52\right)} \cos\left(x\right)^{14} + 32 \, {\left(\sqrt{2} {\left(8 \, \sqrt{2} + 19\right)} + 2 \, \sqrt{2} - 37\right)} \cos\left(x\right)^{12} + 16 \, {\left(2 \, \sqrt{2} {\left(4 \, \sqrt{2} - 13\right)} - 22 \, \sqrt{2} + 39\right)} \cos\left(x\right)^{10} - 8 \, {\left(\sqrt{2} {\left(41 \, \sqrt{2} - 10\right)} - 42 \, \sqrt{2} - 2\right)} \cos\left(x\right)^{8} + 4 \, {\left(\sqrt{2} {\left(49 \, \sqrt{2} + 6\right)} - 32 \, \sqrt{2} - 32\right)} \cos\left(x\right)^{6} - 8 \, {\left(\sqrt{2} {\left(6 \, \sqrt{2} + 1\right)} - 2 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} + 2 \, {\left(8 \, {\left(2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 1\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{15} - 8 \, {\left(2^{\frac{3}{4}} {\left(3 \, \sqrt{2} + 2\right)} - 4 \cdot 2^{\frac{1}{4}} {\left(4 \, \sqrt{2} + 5\right)}\right)} \cos\left(x\right)^{13} - 4 \, {\left(2 \cdot 2^{\frac{3}{4}} {\left(3 \, \sqrt{2} - 10\right)} + 2^{\frac{1}{4}} {\left(19 \, \sqrt{2} + 58\right)}\right)} \cos\left(x\right)^{11} + 4 \, {\left(6 \cdot 2^{\frac{3}{4}} {\left(3 \, \sqrt{2} - 4\right)} - 2^{\frac{1}{4}} {\left(19 \, \sqrt{2} - 32\right)}\right)} \cos\left(x\right)^{9} - 2 \, {\left(2^{\frac{3}{4}} {\left(28 \, \sqrt{2} - 27\right)} - 4 \cdot 2^{\frac{1}{4}} {\left(15 \, \sqrt{2} - 2\right)}\right)} \cos\left(x\right)^{7} + 2 \, {\left(2^{\frac{3}{4}} {\left(9 \, \sqrt{2} - 8\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(15 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{5} - {\left(2 \cdot 2^{\frac{3}{4}} {\left(\sqrt{2} - 1\right)} - 2^{\frac{1}{4}} {\left(13 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{3} - 2^{\frac{3}{4}} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 4 \, \cos\left(x\right)^{2} + {\left(16 \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} - 6\right)} - 8 \, \sqrt{2} + 4\right)} \cos\left(x\right)^{14} - 56 \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} - 6\right)} - 8 \, \sqrt{2} + 4\right)} \cos\left(x\right)^{12} + 8 \, {\left(\sqrt{2} {\left(49 \, \sqrt{2} - 62\right)} - 76 \, \sqrt{2} + 54\right)} \cos\left(x\right)^{10} - 40 \, {\left(\sqrt{2} {\left(7 \, \sqrt{2} - 10\right)} - 10 \, \sqrt{2} + 13\right)} \cos\left(x\right)^{8} + 4 \, {\left(\sqrt{2} {\left(27 \, \sqrt{2} - 46\right)} - 32 \, \sqrt{2} + 92\right)} \cos\left(x\right)^{6} - 2 \, {\left(11 \, \sqrt{2} {\left(\sqrt{2} - 2\right)} - 8 \, \sqrt{2} + 72\right)} \cos\left(x\right)^{4} + 2 \, {\left(\sqrt{2} {\left(\sqrt{2} - 2\right)} + 14\right)} \cos\left(x\right)^{2} + {\left(8 \, {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} - 11\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} - 6\right)}\right)} \cos\left(x\right)^{13} - 24 \, {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} - 11\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} - 6\right)}\right)} \cos\left(x\right)^{11} + 4 \, {\left(2 \cdot 2^{\frac{3}{4}} {\left(28 \, \sqrt{2} - 39\right)} - 2^{\frac{1}{4}} {\left(73 \, \sqrt{2} - 94\right)}\right)} \cos\left(x\right)^{9} - 8 \, {\left(2^{\frac{3}{4}} {\left(16 \, \sqrt{2} - 23\right)} - 2^{\frac{1}{4}} {\left(23 \, \sqrt{2} - 34\right)}\right)} \cos\left(x\right)^{7} + 2 \, {\left(9 \cdot 2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 3\right)} - 8 \cdot 2^{\frac{1}{4}} {\left(4 \, \sqrt{2} - 7\right)}\right)} \cos\left(x\right)^{5} - 2 \, {\left(2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 3\right)} - 6 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)}\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) - 2\right)} \sqrt{-4 \, {\left(4 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} + 16 \, {\left(\sqrt{2} - 1\right)} \cos\left(x\right)^{2} + 4 \, {\left(2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 4\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 4}}{4 \, {\left(112 \, \cos\left(x\right)^{16} - 448 \, \cos\left(x\right)^{14} + 608 \, \cos\left(x\right)^{12} - 256 \, \cos\left(x\right)^{10} - 152 \, \cos\left(x\right)^{8} + 208 \, \cos\left(x\right)^{6} - 88 \, \cos\left(x\right)^{4} + 16 \, \cos\left(x\right)^{2} - 1\right)}}\right) + \frac{1}{16} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(-\frac{32 \, {\left(\sqrt{2} {\left(3 \, \sqrt{2} + 2\right)} - 2 \, \sqrt{2} - 6\right)} \cos\left(x\right)^{16} - 16 \, {\left(\sqrt{2} {\left(19 \, \sqrt{2} + 22\right)} - 8 \, \sqrt{2} - 52\right)} \cos\left(x\right)^{14} + 32 \, {\left(\sqrt{2} {\left(8 \, \sqrt{2} + 19\right)} + 2 \, \sqrt{2} - 37\right)} \cos\left(x\right)^{12} + 16 \, {\left(2 \, \sqrt{2} {\left(4 \, \sqrt{2} - 13\right)} - 22 \, \sqrt{2} + 39\right)} \cos\left(x\right)^{10} - 8 \, {\left(\sqrt{2} {\left(41 \, \sqrt{2} - 10\right)} - 42 \, \sqrt{2} - 2\right)} \cos\left(x\right)^{8} + 4 \, {\left(\sqrt{2} {\left(49 \, \sqrt{2} + 6\right)} - 32 \, \sqrt{2} - 32\right)} \cos\left(x\right)^{6} - 8 \, {\left(\sqrt{2} {\left(6 \, \sqrt{2} + 1\right)} - 2 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} + 2 \, {\left(8 \, {\left(2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 1\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{15} - 8 \, {\left(2^{\frac{3}{4}} {\left(3 \, \sqrt{2} + 2\right)} - 4 \cdot 2^{\frac{1}{4}} {\left(4 \, \sqrt{2} + 5\right)}\right)} \cos\left(x\right)^{13} - 4 \, {\left(2 \cdot 2^{\frac{3}{4}} {\left(3 \, \sqrt{2} - 10\right)} + 2^{\frac{1}{4}} {\left(19 \, \sqrt{2} + 58\right)}\right)} \cos\left(x\right)^{11} + 4 \, {\left(6 \cdot 2^{\frac{3}{4}} {\left(3 \, \sqrt{2} - 4\right)} - 2^{\frac{1}{4}} {\left(19 \, \sqrt{2} - 32\right)}\right)} \cos\left(x\right)^{9} - 2 \, {\left(2^{\frac{3}{4}} {\left(28 \, \sqrt{2} - 27\right)} - 4 \cdot 2^{\frac{1}{4}} {\left(15 \, \sqrt{2} - 2\right)}\right)} \cos\left(x\right)^{7} + 2 \, {\left(2^{\frac{3}{4}} {\left(9 \, \sqrt{2} - 8\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(15 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{5} - {\left(2 \cdot 2^{\frac{3}{4}} {\left(\sqrt{2} - 1\right)} - 2^{\frac{1}{4}} {\left(13 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{3} - 2^{\frac{3}{4}} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 4 \, \cos\left(x\right)^{2} - {\left(16 \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} - 6\right)} - 8 \, \sqrt{2} + 4\right)} \cos\left(x\right)^{14} - 56 \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} - 6\right)} - 8 \, \sqrt{2} + 4\right)} \cos\left(x\right)^{12} + 8 \, {\left(\sqrt{2} {\left(49 \, \sqrt{2} - 62\right)} - 76 \, \sqrt{2} + 54\right)} \cos\left(x\right)^{10} - 40 \, {\left(\sqrt{2} {\left(7 \, \sqrt{2} - 10\right)} - 10 \, \sqrt{2} + 13\right)} \cos\left(x\right)^{8} + 4 \, {\left(\sqrt{2} {\left(27 \, \sqrt{2} - 46\right)} - 32 \, \sqrt{2} + 92\right)} \cos\left(x\right)^{6} - 2 \, {\left(11 \, \sqrt{2} {\left(\sqrt{2} - 2\right)} - 8 \, \sqrt{2} + 72\right)} \cos\left(x\right)^{4} + 2 \, {\left(\sqrt{2} {\left(\sqrt{2} - 2\right)} + 14\right)} \cos\left(x\right)^{2} + {\left(8 \, {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} - 11\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} - 6\right)}\right)} \cos\left(x\right)^{13} - 24 \, {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} - 11\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} - 6\right)}\right)} \cos\left(x\right)^{11} + 4 \, {\left(2 \cdot 2^{\frac{3}{4}} {\left(28 \, \sqrt{2} - 39\right)} - 2^{\frac{1}{4}} {\left(73 \, \sqrt{2} - 94\right)}\right)} \cos\left(x\right)^{9} - 8 \, {\left(2^{\frac{3}{4}} {\left(16 \, \sqrt{2} - 23\right)} - 2^{\frac{1}{4}} {\left(23 \, \sqrt{2} - 34\right)}\right)} \cos\left(x\right)^{7} + 2 \, {\left(9 \cdot 2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 3\right)} - 8 \cdot 2^{\frac{1}{4}} {\left(4 \, \sqrt{2} - 7\right)}\right)} \cos\left(x\right)^{5} - 2 \, {\left(2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 3\right)} - 6 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)}\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) - 2\right)} \sqrt{-4 \, {\left(4 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} + 16 \, {\left(\sqrt{2} - 1\right)} \cos\left(x\right)^{2} + 4 \, {\left(2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 4\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 4}}{4 \, {\left(112 \, \cos\left(x\right)^{16} - 448 \, \cos\left(x\right)^{14} + 608 \, \cos\left(x\right)^{12} - 256 \, \cos\left(x\right)^{10} - 152 \, \cos\left(x\right)^{8} + 208 \, \cos\left(x\right)^{6} - 88 \, \cos\left(x\right)^{4} + 16 \, \cos\left(x\right)^{2} - 1\right)}}\right) - \frac{1}{16} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(-\frac{32 \, {\left(\sqrt{2} {\left(3 \, \sqrt{2} + 2\right)} - 2 \, \sqrt{2} - 6\right)} \cos\left(x\right)^{16} - 16 \, {\left(\sqrt{2} {\left(19 \, \sqrt{2} + 22\right)} - 8 \, \sqrt{2} - 52\right)} \cos\left(x\right)^{14} + 32 \, {\left(\sqrt{2} {\left(8 \, \sqrt{2} + 19\right)} + 2 \, \sqrt{2} - 37\right)} \cos\left(x\right)^{12} + 16 \, {\left(2 \, \sqrt{2} {\left(4 \, \sqrt{2} - 13\right)} - 22 \, \sqrt{2} + 39\right)} \cos\left(x\right)^{10} - 8 \, {\left(\sqrt{2} {\left(41 \, \sqrt{2} - 10\right)} - 42 \, \sqrt{2} - 2\right)} \cos\left(x\right)^{8} + 4 \, {\left(\sqrt{2} {\left(49 \, \sqrt{2} + 6\right)} - 32 \, \sqrt{2} - 32\right)} \cos\left(x\right)^{6} - 8 \, {\left(\sqrt{2} {\left(6 \, \sqrt{2} + 1\right)} - 2 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} - 2 \, {\left(8 \, {\left(2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 1\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{15} - 8 \, {\left(2^{\frac{3}{4}} {\left(3 \, \sqrt{2} + 2\right)} - 4 \cdot 2^{\frac{1}{4}} {\left(4 \, \sqrt{2} + 5\right)}\right)} \cos\left(x\right)^{13} - 4 \, {\left(2 \cdot 2^{\frac{3}{4}} {\left(3 \, \sqrt{2} - 10\right)} + 2^{\frac{1}{4}} {\left(19 \, \sqrt{2} + 58\right)}\right)} \cos\left(x\right)^{11} + 4 \, {\left(6 \cdot 2^{\frac{3}{4}} {\left(3 \, \sqrt{2} - 4\right)} - 2^{\frac{1}{4}} {\left(19 \, \sqrt{2} - 32\right)}\right)} \cos\left(x\right)^{9} - 2 \, {\left(2^{\frac{3}{4}} {\left(28 \, \sqrt{2} - 27\right)} - 4 \cdot 2^{\frac{1}{4}} {\left(15 \, \sqrt{2} - 2\right)}\right)} \cos\left(x\right)^{7} + 2 \, {\left(2^{\frac{3}{4}} {\left(9 \, \sqrt{2} - 8\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(15 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{5} - {\left(2 \cdot 2^{\frac{3}{4}} {\left(\sqrt{2} - 1\right)} - 2^{\frac{1}{4}} {\left(13 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{3} - 2^{\frac{3}{4}} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 4 \, \cos\left(x\right)^{2} + {\left(16 \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} - 6\right)} - 8 \, \sqrt{2} + 4\right)} \cos\left(x\right)^{14} - 56 \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} - 6\right)} - 8 \, \sqrt{2} + 4\right)} \cos\left(x\right)^{12} + 8 \, {\left(\sqrt{2} {\left(49 \, \sqrt{2} - 62\right)} - 76 \, \sqrt{2} + 54\right)} \cos\left(x\right)^{10} - 40 \, {\left(\sqrt{2} {\left(7 \, \sqrt{2} - 10\right)} - 10 \, \sqrt{2} + 13\right)} \cos\left(x\right)^{8} + 4 \, {\left(\sqrt{2} {\left(27 \, \sqrt{2} - 46\right)} - 32 \, \sqrt{2} + 92\right)} \cos\left(x\right)^{6} - 2 \, {\left(11 \, \sqrt{2} {\left(\sqrt{2} - 2\right)} - 8 \, \sqrt{2} + 72\right)} \cos\left(x\right)^{4} + 2 \, {\left(\sqrt{2} {\left(\sqrt{2} - 2\right)} + 14\right)} \cos\left(x\right)^{2} - {\left(8 \, {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} - 11\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} - 6\right)}\right)} \cos\left(x\right)^{13} - 24 \, {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} - 11\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} - 6\right)}\right)} \cos\left(x\right)^{11} + 4 \, {\left(2 \cdot 2^{\frac{3}{4}} {\left(28 \, \sqrt{2} - 39\right)} - 2^{\frac{1}{4}} {\left(73 \, \sqrt{2} - 94\right)}\right)} \cos\left(x\right)^{9} - 8 \, {\left(2^{\frac{3}{4}} {\left(16 \, \sqrt{2} - 23\right)} - 2^{\frac{1}{4}} {\left(23 \, \sqrt{2} - 34\right)}\right)} \cos\left(x\right)^{7} + 2 \, {\left(9 \cdot 2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 3\right)} - 8 \cdot 2^{\frac{1}{4}} {\left(4 \, \sqrt{2} - 7\right)}\right)} \cos\left(x\right)^{5} - 2 \, {\left(2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 3\right)} - 6 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)}\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) - 2\right)} \sqrt{-4 \, {\left(4 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} + 16 \, {\left(\sqrt{2} - 1\right)} \cos\left(x\right)^{2} - 4 \, {\left(2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 4\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 4}}{4 \, {\left(112 \, \cos\left(x\right)^{16} - 448 \, \cos\left(x\right)^{14} + 608 \, \cos\left(x\right)^{12} - 256 \, \cos\left(x\right)^{10} - 152 \, \cos\left(x\right)^{8} + 208 \, \cos\left(x\right)^{6} - 88 \, \cos\left(x\right)^{4} + 16 \, \cos\left(x\right)^{2} - 1\right)}}\right) + \frac{1}{16} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{32 \, {\left(\sqrt{2} {\left(3 \, \sqrt{2} + 2\right)} - 2 \, \sqrt{2} - 6\right)} \cos\left(x\right)^{16} - 16 \, {\left(\sqrt{2} {\left(19 \, \sqrt{2} + 22\right)} - 8 \, \sqrt{2} - 52\right)} \cos\left(x\right)^{14} + 32 \, {\left(\sqrt{2} {\left(8 \, \sqrt{2} + 19\right)} + 2 \, \sqrt{2} - 37\right)} \cos\left(x\right)^{12} + 16 \, {\left(2 \, \sqrt{2} {\left(4 \, \sqrt{2} - 13\right)} - 22 \, \sqrt{2} + 39\right)} \cos\left(x\right)^{10} - 8 \, {\left(\sqrt{2} {\left(41 \, \sqrt{2} - 10\right)} - 42 \, \sqrt{2} - 2\right)} \cos\left(x\right)^{8} + 4 \, {\left(\sqrt{2} {\left(49 \, \sqrt{2} + 6\right)} - 32 \, \sqrt{2} - 32\right)} \cos\left(x\right)^{6} - 8 \, {\left(\sqrt{2} {\left(6 \, \sqrt{2} + 1\right)} - 2 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} - 2 \, {\left(8 \, {\left(2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 1\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{15} - 8 \, {\left(2^{\frac{3}{4}} {\left(3 \, \sqrt{2} + 2\right)} - 4 \cdot 2^{\frac{1}{4}} {\left(4 \, \sqrt{2} + 5\right)}\right)} \cos\left(x\right)^{13} - 4 \, {\left(2 \cdot 2^{\frac{3}{4}} {\left(3 \, \sqrt{2} - 10\right)} + 2^{\frac{1}{4}} {\left(19 \, \sqrt{2} + 58\right)}\right)} \cos\left(x\right)^{11} + 4 \, {\left(6 \cdot 2^{\frac{3}{4}} {\left(3 \, \sqrt{2} - 4\right)} - 2^{\frac{1}{4}} {\left(19 \, \sqrt{2} - 32\right)}\right)} \cos\left(x\right)^{9} - 2 \, {\left(2^{\frac{3}{4}} {\left(28 \, \sqrt{2} - 27\right)} - 4 \cdot 2^{\frac{1}{4}} {\left(15 \, \sqrt{2} - 2\right)}\right)} \cos\left(x\right)^{7} + 2 \, {\left(2^{\frac{3}{4}} {\left(9 \, \sqrt{2} - 8\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(15 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{5} - {\left(2 \cdot 2^{\frac{3}{4}} {\left(\sqrt{2} - 1\right)} - 2^{\frac{1}{4}} {\left(13 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{3} - 2^{\frac{3}{4}} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 4 \, \cos\left(x\right)^{2} - {\left(16 \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} - 6\right)} - 8 \, \sqrt{2} + 4\right)} \cos\left(x\right)^{14} - 56 \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} - 6\right)} - 8 \, \sqrt{2} + 4\right)} \cos\left(x\right)^{12} + 8 \, {\left(\sqrt{2} {\left(49 \, \sqrt{2} - 62\right)} - 76 \, \sqrt{2} + 54\right)} \cos\left(x\right)^{10} - 40 \, {\left(\sqrt{2} {\left(7 \, \sqrt{2} - 10\right)} - 10 \, \sqrt{2} + 13\right)} \cos\left(x\right)^{8} + 4 \, {\left(\sqrt{2} {\left(27 \, \sqrt{2} - 46\right)} - 32 \, \sqrt{2} + 92\right)} \cos\left(x\right)^{6} - 2 \, {\left(11 \, \sqrt{2} {\left(\sqrt{2} - 2\right)} - 8 \, \sqrt{2} + 72\right)} \cos\left(x\right)^{4} + 2 \, {\left(\sqrt{2} {\left(\sqrt{2} - 2\right)} + 14\right)} \cos\left(x\right)^{2} - {\left(8 \, {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} - 11\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} - 6\right)}\right)} \cos\left(x\right)^{13} - 24 \, {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} - 11\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} - 6\right)}\right)} \cos\left(x\right)^{11} + 4 \, {\left(2 \cdot 2^{\frac{3}{4}} {\left(28 \, \sqrt{2} - 39\right)} - 2^{\frac{1}{4}} {\left(73 \, \sqrt{2} - 94\right)}\right)} \cos\left(x\right)^{9} - 8 \, {\left(2^{\frac{3}{4}} {\left(16 \, \sqrt{2} - 23\right)} - 2^{\frac{1}{4}} {\left(23 \, \sqrt{2} - 34\right)}\right)} \cos\left(x\right)^{7} + 2 \, {\left(9 \cdot 2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 3\right)} - 8 \cdot 2^{\frac{1}{4}} {\left(4 \, \sqrt{2} - 7\right)}\right)} \cos\left(x\right)^{5} - 2 \, {\left(2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 3\right)} - 6 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)}\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) - 2\right)} \sqrt{-4 \, {\left(4 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} + 16 \, {\left(\sqrt{2} - 1\right)} \cos\left(x\right)^{2} - 4 \, {\left(2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 4\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 4}}{4 \, {\left(112 \, \cos\left(x\right)^{16} - 448 \, \cos\left(x\right)^{14} + 608 \, \cos\left(x\right)^{12} - 256 \, \cos\left(x\right)^{10} - 152 \, \cos\left(x\right)^{8} + 208 \, \cos\left(x\right)^{6} - 88 \, \cos\left(x\right)^{4} + 16 \, \cos\left(x\right)^{2} - 1\right)}}\right)"," ",0,"-1/32*2^(1/4)*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 1)*log(-(4*sqrt(2) - 5)*cos(x)^4 + 4*(sqrt(2) - 1)*cos(x)^2 + (2^(1/4)*(3*sqrt(2) - 4)*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 1) + 1/32*2^(1/4)*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 1)*log(-(4*sqrt(2) - 5)*cos(x)^4 + 4*(sqrt(2) - 1)*cos(x)^2 - (2^(1/4)*(3*sqrt(2) - 4)*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 1) - 1/16*2^(1/4)*sqrt(2*sqrt(2) + 4)*arctan(1/4*(32*(sqrt(2)*(3*sqrt(2) + 2) - 2*sqrt(2) - 6)*cos(x)^16 - 16*(sqrt(2)*(19*sqrt(2) + 22) - 8*sqrt(2) - 52)*cos(x)^14 + 32*(sqrt(2)*(8*sqrt(2) + 19) + 2*sqrt(2) - 37)*cos(x)^12 + 16*(2*sqrt(2)*(4*sqrt(2) - 13) - 22*sqrt(2) + 39)*cos(x)^10 - 8*(sqrt(2)*(41*sqrt(2) - 10) - 42*sqrt(2) - 2)*cos(x)^8 + 4*(sqrt(2)*(49*sqrt(2) + 6) - 32*sqrt(2) - 32)*cos(x)^6 - 8*(sqrt(2)*(6*sqrt(2) + 1) - 2*sqrt(2) - 5)*cos(x)^4 + 2*(8*(2^(3/4)*(2*sqrt(2) - 1) - 2*2^(1/4)*(3*sqrt(2) + 2))*cos(x)^15 - 8*(2^(3/4)*(3*sqrt(2) + 2) - 4*2^(1/4)*(4*sqrt(2) + 5))*cos(x)^13 - 4*(2*2^(3/4)*(3*sqrt(2) - 10) + 2^(1/4)*(19*sqrt(2) + 58))*cos(x)^11 + 4*(6*2^(3/4)*(3*sqrt(2) - 4) - 2^(1/4)*(19*sqrt(2) - 32))*cos(x)^9 - 2*(2^(3/4)*(28*sqrt(2) - 27) - 4*2^(1/4)*(15*sqrt(2) - 2))*cos(x)^7 + 2*(2^(3/4)*(9*sqrt(2) - 8) - 2*2^(1/4)*(15*sqrt(2) + 2))*cos(x)^5 - (2*2^(3/4)*(sqrt(2) - 1) - 2^(1/4)*(13*sqrt(2) + 2))*cos(x)^3 - 2^(3/4)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 4*cos(x)^2 + (16*(sqrt(2)*(5*sqrt(2) - 6) - 8*sqrt(2) + 4)*cos(x)^14 - 56*(sqrt(2)*(5*sqrt(2) - 6) - 8*sqrt(2) + 4)*cos(x)^12 + 8*(sqrt(2)*(49*sqrt(2) - 62) - 76*sqrt(2) + 54)*cos(x)^10 - 40*(sqrt(2)*(7*sqrt(2) - 10) - 10*sqrt(2) + 13)*cos(x)^8 + 4*(sqrt(2)*(27*sqrt(2) - 46) - 32*sqrt(2) + 92)*cos(x)^6 - 2*(11*sqrt(2)*(sqrt(2) - 2) - 8*sqrt(2) + 72)*cos(x)^4 + 2*(sqrt(2)*(sqrt(2) - 2) + 14)*cos(x)^2 + (8*(2^(3/4)*(8*sqrt(2) - 11) - 2*2^(1/4)*(5*sqrt(2) - 6))*cos(x)^13 - 24*(2^(3/4)*(8*sqrt(2) - 11) - 2*2^(1/4)*(5*sqrt(2) - 6))*cos(x)^11 + 4*(2*2^(3/4)*(28*sqrt(2) - 39) - 2^(1/4)*(73*sqrt(2) - 94))*cos(x)^9 - 8*(2^(3/4)*(16*sqrt(2) - 23) - 2^(1/4)*(23*sqrt(2) - 34))*cos(x)^7 + 2*(9*2^(3/4)*(2*sqrt(2) - 3) - 8*2^(1/4)*(4*sqrt(2) - 7))*cos(x)^5 - 2*(2^(3/4)*(2*sqrt(2) - 3) - 6*2^(1/4)*(sqrt(2) - 2))*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) - 2)*sqrt(-4*(4*sqrt(2) - 5)*cos(x)^4 + 16*(sqrt(2) - 1)*cos(x)^2 + 4*(2^(1/4)*(3*sqrt(2) - 4)*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 4))/(112*cos(x)^16 - 448*cos(x)^14 + 608*cos(x)^12 - 256*cos(x)^10 - 152*cos(x)^8 + 208*cos(x)^6 - 88*cos(x)^4 + 16*cos(x)^2 - 1)) + 1/16*2^(1/4)*sqrt(2*sqrt(2) + 4)*arctan(-1/4*(32*(sqrt(2)*(3*sqrt(2) + 2) - 2*sqrt(2) - 6)*cos(x)^16 - 16*(sqrt(2)*(19*sqrt(2) + 22) - 8*sqrt(2) - 52)*cos(x)^14 + 32*(sqrt(2)*(8*sqrt(2) + 19) + 2*sqrt(2) - 37)*cos(x)^12 + 16*(2*sqrt(2)*(4*sqrt(2) - 13) - 22*sqrt(2) + 39)*cos(x)^10 - 8*(sqrt(2)*(41*sqrt(2) - 10) - 42*sqrt(2) - 2)*cos(x)^8 + 4*(sqrt(2)*(49*sqrt(2) + 6) - 32*sqrt(2) - 32)*cos(x)^6 - 8*(sqrt(2)*(6*sqrt(2) + 1) - 2*sqrt(2) - 5)*cos(x)^4 + 2*(8*(2^(3/4)*(2*sqrt(2) - 1) - 2*2^(1/4)*(3*sqrt(2) + 2))*cos(x)^15 - 8*(2^(3/4)*(3*sqrt(2) + 2) - 4*2^(1/4)*(4*sqrt(2) + 5))*cos(x)^13 - 4*(2*2^(3/4)*(3*sqrt(2) - 10) + 2^(1/4)*(19*sqrt(2) + 58))*cos(x)^11 + 4*(6*2^(3/4)*(3*sqrt(2) - 4) - 2^(1/4)*(19*sqrt(2) - 32))*cos(x)^9 - 2*(2^(3/4)*(28*sqrt(2) - 27) - 4*2^(1/4)*(15*sqrt(2) - 2))*cos(x)^7 + 2*(2^(3/4)*(9*sqrt(2) - 8) - 2*2^(1/4)*(15*sqrt(2) + 2))*cos(x)^5 - (2*2^(3/4)*(sqrt(2) - 1) - 2^(1/4)*(13*sqrt(2) + 2))*cos(x)^3 - 2^(3/4)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 4*cos(x)^2 - (16*(sqrt(2)*(5*sqrt(2) - 6) - 8*sqrt(2) + 4)*cos(x)^14 - 56*(sqrt(2)*(5*sqrt(2) - 6) - 8*sqrt(2) + 4)*cos(x)^12 + 8*(sqrt(2)*(49*sqrt(2) - 62) - 76*sqrt(2) + 54)*cos(x)^10 - 40*(sqrt(2)*(7*sqrt(2) - 10) - 10*sqrt(2) + 13)*cos(x)^8 + 4*(sqrt(2)*(27*sqrt(2) - 46) - 32*sqrt(2) + 92)*cos(x)^6 - 2*(11*sqrt(2)*(sqrt(2) - 2) - 8*sqrt(2) + 72)*cos(x)^4 + 2*(sqrt(2)*(sqrt(2) - 2) + 14)*cos(x)^2 + (8*(2^(3/4)*(8*sqrt(2) - 11) - 2*2^(1/4)*(5*sqrt(2) - 6))*cos(x)^13 - 24*(2^(3/4)*(8*sqrt(2) - 11) - 2*2^(1/4)*(5*sqrt(2) - 6))*cos(x)^11 + 4*(2*2^(3/4)*(28*sqrt(2) - 39) - 2^(1/4)*(73*sqrt(2) - 94))*cos(x)^9 - 8*(2^(3/4)*(16*sqrt(2) - 23) - 2^(1/4)*(23*sqrt(2) - 34))*cos(x)^7 + 2*(9*2^(3/4)*(2*sqrt(2) - 3) - 8*2^(1/4)*(4*sqrt(2) - 7))*cos(x)^5 - 2*(2^(3/4)*(2*sqrt(2) - 3) - 6*2^(1/4)*(sqrt(2) - 2))*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) - 2)*sqrt(-4*(4*sqrt(2) - 5)*cos(x)^4 + 16*(sqrt(2) - 1)*cos(x)^2 + 4*(2^(1/4)*(3*sqrt(2) - 4)*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 4))/(112*cos(x)^16 - 448*cos(x)^14 + 608*cos(x)^12 - 256*cos(x)^10 - 152*cos(x)^8 + 208*cos(x)^6 - 88*cos(x)^4 + 16*cos(x)^2 - 1)) - 1/16*2^(1/4)*sqrt(2*sqrt(2) + 4)*arctan(-1/4*(32*(sqrt(2)*(3*sqrt(2) + 2) - 2*sqrt(2) - 6)*cos(x)^16 - 16*(sqrt(2)*(19*sqrt(2) + 22) - 8*sqrt(2) - 52)*cos(x)^14 + 32*(sqrt(2)*(8*sqrt(2) + 19) + 2*sqrt(2) - 37)*cos(x)^12 + 16*(2*sqrt(2)*(4*sqrt(2) - 13) - 22*sqrt(2) + 39)*cos(x)^10 - 8*(sqrt(2)*(41*sqrt(2) - 10) - 42*sqrt(2) - 2)*cos(x)^8 + 4*(sqrt(2)*(49*sqrt(2) + 6) - 32*sqrt(2) - 32)*cos(x)^6 - 8*(sqrt(2)*(6*sqrt(2) + 1) - 2*sqrt(2) - 5)*cos(x)^4 - 2*(8*(2^(3/4)*(2*sqrt(2) - 1) - 2*2^(1/4)*(3*sqrt(2) + 2))*cos(x)^15 - 8*(2^(3/4)*(3*sqrt(2) + 2) - 4*2^(1/4)*(4*sqrt(2) + 5))*cos(x)^13 - 4*(2*2^(3/4)*(3*sqrt(2) - 10) + 2^(1/4)*(19*sqrt(2) + 58))*cos(x)^11 + 4*(6*2^(3/4)*(3*sqrt(2) - 4) - 2^(1/4)*(19*sqrt(2) - 32))*cos(x)^9 - 2*(2^(3/4)*(28*sqrt(2) - 27) - 4*2^(1/4)*(15*sqrt(2) - 2))*cos(x)^7 + 2*(2^(3/4)*(9*sqrt(2) - 8) - 2*2^(1/4)*(15*sqrt(2) + 2))*cos(x)^5 - (2*2^(3/4)*(sqrt(2) - 1) - 2^(1/4)*(13*sqrt(2) + 2))*cos(x)^3 - 2^(3/4)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 4*cos(x)^2 + (16*(sqrt(2)*(5*sqrt(2) - 6) - 8*sqrt(2) + 4)*cos(x)^14 - 56*(sqrt(2)*(5*sqrt(2) - 6) - 8*sqrt(2) + 4)*cos(x)^12 + 8*(sqrt(2)*(49*sqrt(2) - 62) - 76*sqrt(2) + 54)*cos(x)^10 - 40*(sqrt(2)*(7*sqrt(2) - 10) - 10*sqrt(2) + 13)*cos(x)^8 + 4*(sqrt(2)*(27*sqrt(2) - 46) - 32*sqrt(2) + 92)*cos(x)^6 - 2*(11*sqrt(2)*(sqrt(2) - 2) - 8*sqrt(2) + 72)*cos(x)^4 + 2*(sqrt(2)*(sqrt(2) - 2) + 14)*cos(x)^2 - (8*(2^(3/4)*(8*sqrt(2) - 11) - 2*2^(1/4)*(5*sqrt(2) - 6))*cos(x)^13 - 24*(2^(3/4)*(8*sqrt(2) - 11) - 2*2^(1/4)*(5*sqrt(2) - 6))*cos(x)^11 + 4*(2*2^(3/4)*(28*sqrt(2) - 39) - 2^(1/4)*(73*sqrt(2) - 94))*cos(x)^9 - 8*(2^(3/4)*(16*sqrt(2) - 23) - 2^(1/4)*(23*sqrt(2) - 34))*cos(x)^7 + 2*(9*2^(3/4)*(2*sqrt(2) - 3) - 8*2^(1/4)*(4*sqrt(2) - 7))*cos(x)^5 - 2*(2^(3/4)*(2*sqrt(2) - 3) - 6*2^(1/4)*(sqrt(2) - 2))*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) - 2)*sqrt(-4*(4*sqrt(2) - 5)*cos(x)^4 + 16*(sqrt(2) - 1)*cos(x)^2 - 4*(2^(1/4)*(3*sqrt(2) - 4)*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 4))/(112*cos(x)^16 - 448*cos(x)^14 + 608*cos(x)^12 - 256*cos(x)^10 - 152*cos(x)^8 + 208*cos(x)^6 - 88*cos(x)^4 + 16*cos(x)^2 - 1)) + 1/16*2^(1/4)*sqrt(2*sqrt(2) + 4)*arctan(1/4*(32*(sqrt(2)*(3*sqrt(2) + 2) - 2*sqrt(2) - 6)*cos(x)^16 - 16*(sqrt(2)*(19*sqrt(2) + 22) - 8*sqrt(2) - 52)*cos(x)^14 + 32*(sqrt(2)*(8*sqrt(2) + 19) + 2*sqrt(2) - 37)*cos(x)^12 + 16*(2*sqrt(2)*(4*sqrt(2) - 13) - 22*sqrt(2) + 39)*cos(x)^10 - 8*(sqrt(2)*(41*sqrt(2) - 10) - 42*sqrt(2) - 2)*cos(x)^8 + 4*(sqrt(2)*(49*sqrt(2) + 6) - 32*sqrt(2) - 32)*cos(x)^6 - 8*(sqrt(2)*(6*sqrt(2) + 1) - 2*sqrt(2) - 5)*cos(x)^4 - 2*(8*(2^(3/4)*(2*sqrt(2) - 1) - 2*2^(1/4)*(3*sqrt(2) + 2))*cos(x)^15 - 8*(2^(3/4)*(3*sqrt(2) + 2) - 4*2^(1/4)*(4*sqrt(2) + 5))*cos(x)^13 - 4*(2*2^(3/4)*(3*sqrt(2) - 10) + 2^(1/4)*(19*sqrt(2) + 58))*cos(x)^11 + 4*(6*2^(3/4)*(3*sqrt(2) - 4) - 2^(1/4)*(19*sqrt(2) - 32))*cos(x)^9 - 2*(2^(3/4)*(28*sqrt(2) - 27) - 4*2^(1/4)*(15*sqrt(2) - 2))*cos(x)^7 + 2*(2^(3/4)*(9*sqrt(2) - 8) - 2*2^(1/4)*(15*sqrt(2) + 2))*cos(x)^5 - (2*2^(3/4)*(sqrt(2) - 1) - 2^(1/4)*(13*sqrt(2) + 2))*cos(x)^3 - 2^(3/4)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 4*cos(x)^2 - (16*(sqrt(2)*(5*sqrt(2) - 6) - 8*sqrt(2) + 4)*cos(x)^14 - 56*(sqrt(2)*(5*sqrt(2) - 6) - 8*sqrt(2) + 4)*cos(x)^12 + 8*(sqrt(2)*(49*sqrt(2) - 62) - 76*sqrt(2) + 54)*cos(x)^10 - 40*(sqrt(2)*(7*sqrt(2) - 10) - 10*sqrt(2) + 13)*cos(x)^8 + 4*(sqrt(2)*(27*sqrt(2) - 46) - 32*sqrt(2) + 92)*cos(x)^6 - 2*(11*sqrt(2)*(sqrt(2) - 2) - 8*sqrt(2) + 72)*cos(x)^4 + 2*(sqrt(2)*(sqrt(2) - 2) + 14)*cos(x)^2 - (8*(2^(3/4)*(8*sqrt(2) - 11) - 2*2^(1/4)*(5*sqrt(2) - 6))*cos(x)^13 - 24*(2^(3/4)*(8*sqrt(2) - 11) - 2*2^(1/4)*(5*sqrt(2) - 6))*cos(x)^11 + 4*(2*2^(3/4)*(28*sqrt(2) - 39) - 2^(1/4)*(73*sqrt(2) - 94))*cos(x)^9 - 8*(2^(3/4)*(16*sqrt(2) - 23) - 2^(1/4)*(23*sqrt(2) - 34))*cos(x)^7 + 2*(9*2^(3/4)*(2*sqrt(2) - 3) - 8*2^(1/4)*(4*sqrt(2) - 7))*cos(x)^5 - 2*(2^(3/4)*(2*sqrt(2) - 3) - 6*2^(1/4)*(sqrt(2) - 2))*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) - 2)*sqrt(-4*(4*sqrt(2) - 5)*cos(x)^4 + 16*(sqrt(2) - 1)*cos(x)^2 - 4*(2^(1/4)*(3*sqrt(2) - 4)*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 4))/(112*cos(x)^16 - 448*cos(x)^14 + 608*cos(x)^12 - 256*cos(x)^10 - 152*cos(x)^8 + 208*cos(x)^6 - 88*cos(x)^4 + 16*cos(x)^2 - 1))","B",0
73,1,43,0,0.680911," ","integrate(1/(1-cos(x)^4),x, algorithm=""fricas"")","-\frac{\sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(x\right)^{2} - \sqrt{2}}{4 \, \cos\left(x\right) \sin\left(x\right)}\right) \sin\left(x\right) + 4 \, \cos\left(x\right)}{8 \, \sin\left(x\right)}"," ",0,"-1/8*(sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(x)^2 - sqrt(2))/(cos(x)*sin(x)))*sin(x) + 4*cos(x))/sin(x)","A",0
74,-2,0,0,0.000000," ","integrate(1/(a+b*cos(x)^5),x, algorithm=""fricas"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> no explicit roots found","F(-2)",0
75,-1,0,0,0.000000," ","integrate(1/(a+b*cos(x)^6),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,-1,0,0,0.000000," ","integrate(1/(a+b*cos(x)^8),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,-2,0,0,0.000000," ","integrate(1/(a-b*cos(x)^5),x, algorithm=""fricas"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> no explicit roots found","F(-2)",0
78,-1,0,0,0.000000," ","integrate(1/(a-b*cos(x)^6),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate(1/(a-b*cos(x)^8),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate(1/(1+cos(x)^5),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,1,138,0,3.085871," ","integrate(1/(1+cos(x)^6),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \arctan\left(\frac{4 \, \sqrt{3} \cos\left(x\right) \sin\left(x\right) + \sqrt{3}}{3 \, {\left(2 \, \cos\left(x\right)^{2} - 1\right)}}\right) + \frac{1}{12} \, \sqrt{3} \arctan\left(\frac{4 \, \sqrt{3} \cos\left(x\right) \sin\left(x\right) - \sqrt{3}}{3 \, {\left(2 \, \cos\left(x\right)^{2} - 1\right)}}\right) - \frac{1}{12} \, \sqrt{2} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(x\right)^{2} - \sqrt{2}}{4 \, \cos\left(x\right) \sin\left(x\right)}\right) - \frac{1}{24} \, \log\left(-\cos\left(x\right)^{4} + \cos\left(x\right)^{2} + 2 \, \cos\left(x\right) \sin\left(x\right) + 1\right) + \frac{1}{24} \, \log\left(-\cos\left(x\right)^{4} + \cos\left(x\right)^{2} - 2 \, \cos\left(x\right) \sin\left(x\right) + 1\right)"," ",0,"1/12*sqrt(3)*arctan(1/3*(4*sqrt(3)*cos(x)*sin(x) + sqrt(3))/(2*cos(x)^2 - 1)) + 1/12*sqrt(3)*arctan(1/3*(4*sqrt(3)*cos(x)*sin(x) - sqrt(3))/(2*cos(x)^2 - 1)) - 1/12*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(x)^2 - sqrt(2))/(cos(x)*sin(x))) - 1/24*log(-cos(x)^4 + cos(x)^2 + 2*cos(x)*sin(x) + 1) + 1/24*log(-cos(x)^4 + cos(x)^2 - 2*cos(x)*sin(x) + 1)","B",0
82,-1,0,0,0.000000," ","integrate(1/(1+cos(x)^8),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,-1,0,0,0.000000," ","integrate(1/(1-cos(x)^5),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,-1,0,0,0.000000," ","integrate(1/(1-cos(x)^6),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,1,3963,0,63.662464," ","integrate(1/(1-cos(x)^8),x, algorithm=""fricas"")","-\frac{2 \, {\left(2^{\frac{1}{4}} \cos\left(x\right)^{2} - 2^{\frac{1}{4}}\right)} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{32 \, {\left(\sqrt{2} {\left(3 \, \sqrt{2} + 2\right)} - 2 \, \sqrt{2} - 6\right)} \cos\left(x\right)^{16} - 16 \, {\left(\sqrt{2} {\left(19 \, \sqrt{2} + 22\right)} - 8 \, \sqrt{2} - 52\right)} \cos\left(x\right)^{14} + 32 \, {\left(\sqrt{2} {\left(8 \, \sqrt{2} + 19\right)} + 2 \, \sqrt{2} - 37\right)} \cos\left(x\right)^{12} + 16 \, {\left(2 \, \sqrt{2} {\left(4 \, \sqrt{2} - 13\right)} - 22 \, \sqrt{2} + 39\right)} \cos\left(x\right)^{10} - 8 \, {\left(\sqrt{2} {\left(41 \, \sqrt{2} - 10\right)} - 42 \, \sqrt{2} - 2\right)} \cos\left(x\right)^{8} + 4 \, {\left(\sqrt{2} {\left(49 \, \sqrt{2} + 6\right)} - 32 \, \sqrt{2} - 32\right)} \cos\left(x\right)^{6} - 8 \, {\left(\sqrt{2} {\left(6 \, \sqrt{2} + 1\right)} - 2 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} + 2 \, {\left(8 \, {\left(2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 1\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{15} - 8 \, {\left(2^{\frac{3}{4}} {\left(3 \, \sqrt{2} + 2\right)} - 4 \cdot 2^{\frac{1}{4}} {\left(4 \, \sqrt{2} + 5\right)}\right)} \cos\left(x\right)^{13} - 4 \, {\left(2 \cdot 2^{\frac{3}{4}} {\left(3 \, \sqrt{2} - 10\right)} + 2^{\frac{1}{4}} {\left(19 \, \sqrt{2} + 58\right)}\right)} \cos\left(x\right)^{11} + 4 \, {\left(6 \cdot 2^{\frac{3}{4}} {\left(3 \, \sqrt{2} - 4\right)} - 2^{\frac{1}{4}} {\left(19 \, \sqrt{2} - 32\right)}\right)} \cos\left(x\right)^{9} - 2 \, {\left(2^{\frac{3}{4}} {\left(28 \, \sqrt{2} - 27\right)} - 4 \cdot 2^{\frac{1}{4}} {\left(15 \, \sqrt{2} - 2\right)}\right)} \cos\left(x\right)^{7} + 2 \, {\left(2^{\frac{3}{4}} {\left(9 \, \sqrt{2} - 8\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(15 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{5} - {\left(2 \cdot 2^{\frac{3}{4}} {\left(\sqrt{2} - 1\right)} - 2^{\frac{1}{4}} {\left(13 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{3} - 2^{\frac{3}{4}} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 4 \, \cos\left(x\right)^{2} + {\left(16 \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} - 6\right)} - 8 \, \sqrt{2} + 4\right)} \cos\left(x\right)^{14} - 56 \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} - 6\right)} - 8 \, \sqrt{2} + 4\right)} \cos\left(x\right)^{12} + 8 \, {\left(\sqrt{2} {\left(49 \, \sqrt{2} - 62\right)} - 76 \, \sqrt{2} + 54\right)} \cos\left(x\right)^{10} - 40 \, {\left(\sqrt{2} {\left(7 \, \sqrt{2} - 10\right)} - 10 \, \sqrt{2} + 13\right)} \cos\left(x\right)^{8} + 4 \, {\left(\sqrt{2} {\left(27 \, \sqrt{2} - 46\right)} - 32 \, \sqrt{2} + 92\right)} \cos\left(x\right)^{6} - 2 \, {\left(11 \, \sqrt{2} {\left(\sqrt{2} - 2\right)} - 8 \, \sqrt{2} + 72\right)} \cos\left(x\right)^{4} + 2 \, {\left(\sqrt{2} {\left(\sqrt{2} - 2\right)} + 14\right)} \cos\left(x\right)^{2} + {\left(8 \, {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} - 11\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} - 6\right)}\right)} \cos\left(x\right)^{13} - 24 \, {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} - 11\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} - 6\right)}\right)} \cos\left(x\right)^{11} + 4 \, {\left(2 \cdot 2^{\frac{3}{4}} {\left(28 \, \sqrt{2} - 39\right)} - 2^{\frac{1}{4}} {\left(73 \, \sqrt{2} - 94\right)}\right)} \cos\left(x\right)^{9} - 8 \, {\left(2^{\frac{3}{4}} {\left(16 \, \sqrt{2} - 23\right)} - 2^{\frac{1}{4}} {\left(23 \, \sqrt{2} - 34\right)}\right)} \cos\left(x\right)^{7} + 2 \, {\left(9 \cdot 2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 3\right)} - 8 \cdot 2^{\frac{1}{4}} {\left(4 \, \sqrt{2} - 7\right)}\right)} \cos\left(x\right)^{5} - 2 \, {\left(2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 3\right)} - 6 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)}\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) - 2\right)} \sqrt{-4 \, {\left(4 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} + 16 \, {\left(\sqrt{2} - 1\right)} \cos\left(x\right)^{2} + 4 \, {\left(2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 4\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 4}}{4 \, {\left(112 \, \cos\left(x\right)^{16} - 448 \, \cos\left(x\right)^{14} + 608 \, \cos\left(x\right)^{12} - 256 \, \cos\left(x\right)^{10} - 152 \, \cos\left(x\right)^{8} + 208 \, \cos\left(x\right)^{6} - 88 \, \cos\left(x\right)^{4} + 16 \, \cos\left(x\right)^{2} - 1\right)}}\right) - 2 \, {\left(2^{\frac{1}{4}} \cos\left(x\right)^{2} - 2^{\frac{1}{4}}\right)} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(-\frac{32 \, {\left(\sqrt{2} {\left(3 \, \sqrt{2} + 2\right)} - 2 \, \sqrt{2} - 6\right)} \cos\left(x\right)^{16} - 16 \, {\left(\sqrt{2} {\left(19 \, \sqrt{2} + 22\right)} - 8 \, \sqrt{2} - 52\right)} \cos\left(x\right)^{14} + 32 \, {\left(\sqrt{2} {\left(8 \, \sqrt{2} + 19\right)} + 2 \, \sqrt{2} - 37\right)} \cos\left(x\right)^{12} + 16 \, {\left(2 \, \sqrt{2} {\left(4 \, \sqrt{2} - 13\right)} - 22 \, \sqrt{2} + 39\right)} \cos\left(x\right)^{10} - 8 \, {\left(\sqrt{2} {\left(41 \, \sqrt{2} - 10\right)} - 42 \, \sqrt{2} - 2\right)} \cos\left(x\right)^{8} + 4 \, {\left(\sqrt{2} {\left(49 \, \sqrt{2} + 6\right)} - 32 \, \sqrt{2} - 32\right)} \cos\left(x\right)^{6} - 8 \, {\left(\sqrt{2} {\left(6 \, \sqrt{2} + 1\right)} - 2 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} + 2 \, {\left(8 \, {\left(2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 1\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{15} - 8 \, {\left(2^{\frac{3}{4}} {\left(3 \, \sqrt{2} + 2\right)} - 4 \cdot 2^{\frac{1}{4}} {\left(4 \, \sqrt{2} + 5\right)}\right)} \cos\left(x\right)^{13} - 4 \, {\left(2 \cdot 2^{\frac{3}{4}} {\left(3 \, \sqrt{2} - 10\right)} + 2^{\frac{1}{4}} {\left(19 \, \sqrt{2} + 58\right)}\right)} \cos\left(x\right)^{11} + 4 \, {\left(6 \cdot 2^{\frac{3}{4}} {\left(3 \, \sqrt{2} - 4\right)} - 2^{\frac{1}{4}} {\left(19 \, \sqrt{2} - 32\right)}\right)} \cos\left(x\right)^{9} - 2 \, {\left(2^{\frac{3}{4}} {\left(28 \, \sqrt{2} - 27\right)} - 4 \cdot 2^{\frac{1}{4}} {\left(15 \, \sqrt{2} - 2\right)}\right)} \cos\left(x\right)^{7} + 2 \, {\left(2^{\frac{3}{4}} {\left(9 \, \sqrt{2} - 8\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(15 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{5} - {\left(2 \cdot 2^{\frac{3}{4}} {\left(\sqrt{2} - 1\right)} - 2^{\frac{1}{4}} {\left(13 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{3} - 2^{\frac{3}{4}} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 4 \, \cos\left(x\right)^{2} - {\left(16 \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} - 6\right)} - 8 \, \sqrt{2} + 4\right)} \cos\left(x\right)^{14} - 56 \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} - 6\right)} - 8 \, \sqrt{2} + 4\right)} \cos\left(x\right)^{12} + 8 \, {\left(\sqrt{2} {\left(49 \, \sqrt{2} - 62\right)} - 76 \, \sqrt{2} + 54\right)} \cos\left(x\right)^{10} - 40 \, {\left(\sqrt{2} {\left(7 \, \sqrt{2} - 10\right)} - 10 \, \sqrt{2} + 13\right)} \cos\left(x\right)^{8} + 4 \, {\left(\sqrt{2} {\left(27 \, \sqrt{2} - 46\right)} - 32 \, \sqrt{2} + 92\right)} \cos\left(x\right)^{6} - 2 \, {\left(11 \, \sqrt{2} {\left(\sqrt{2} - 2\right)} - 8 \, \sqrt{2} + 72\right)} \cos\left(x\right)^{4} + 2 \, {\left(\sqrt{2} {\left(\sqrt{2} - 2\right)} + 14\right)} \cos\left(x\right)^{2} + {\left(8 \, {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} - 11\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} - 6\right)}\right)} \cos\left(x\right)^{13} - 24 \, {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} - 11\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} - 6\right)}\right)} \cos\left(x\right)^{11} + 4 \, {\left(2 \cdot 2^{\frac{3}{4}} {\left(28 \, \sqrt{2} - 39\right)} - 2^{\frac{1}{4}} {\left(73 \, \sqrt{2} - 94\right)}\right)} \cos\left(x\right)^{9} - 8 \, {\left(2^{\frac{3}{4}} {\left(16 \, \sqrt{2} - 23\right)} - 2^{\frac{1}{4}} {\left(23 \, \sqrt{2} - 34\right)}\right)} \cos\left(x\right)^{7} + 2 \, {\left(9 \cdot 2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 3\right)} - 8 \cdot 2^{\frac{1}{4}} {\left(4 \, \sqrt{2} - 7\right)}\right)} \cos\left(x\right)^{5} - 2 \, {\left(2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 3\right)} - 6 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)}\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) - 2\right)} \sqrt{-4 \, {\left(4 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} + 16 \, {\left(\sqrt{2} - 1\right)} \cos\left(x\right)^{2} + 4 \, {\left(2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 4\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 4}}{4 \, {\left(112 \, \cos\left(x\right)^{16} - 448 \, \cos\left(x\right)^{14} + 608 \, \cos\left(x\right)^{12} - 256 \, \cos\left(x\right)^{10} - 152 \, \cos\left(x\right)^{8} + 208 \, \cos\left(x\right)^{6} - 88 \, \cos\left(x\right)^{4} + 16 \, \cos\left(x\right)^{2} - 1\right)}}\right) + 2 \, {\left(2^{\frac{1}{4}} \cos\left(x\right)^{2} - 2^{\frac{1}{4}}\right)} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(-\frac{32 \, {\left(\sqrt{2} {\left(3 \, \sqrt{2} + 2\right)} - 2 \, \sqrt{2} - 6\right)} \cos\left(x\right)^{16} - 16 \, {\left(\sqrt{2} {\left(19 \, \sqrt{2} + 22\right)} - 8 \, \sqrt{2} - 52\right)} \cos\left(x\right)^{14} + 32 \, {\left(\sqrt{2} {\left(8 \, \sqrt{2} + 19\right)} + 2 \, \sqrt{2} - 37\right)} \cos\left(x\right)^{12} + 16 \, {\left(2 \, \sqrt{2} {\left(4 \, \sqrt{2} - 13\right)} - 22 \, \sqrt{2} + 39\right)} \cos\left(x\right)^{10} - 8 \, {\left(\sqrt{2} {\left(41 \, \sqrt{2} - 10\right)} - 42 \, \sqrt{2} - 2\right)} \cos\left(x\right)^{8} + 4 \, {\left(\sqrt{2} {\left(49 \, \sqrt{2} + 6\right)} - 32 \, \sqrt{2} - 32\right)} \cos\left(x\right)^{6} - 8 \, {\left(\sqrt{2} {\left(6 \, \sqrt{2} + 1\right)} - 2 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} - 2 \, {\left(8 \, {\left(2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 1\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{15} - 8 \, {\left(2^{\frac{3}{4}} {\left(3 \, \sqrt{2} + 2\right)} - 4 \cdot 2^{\frac{1}{4}} {\left(4 \, \sqrt{2} + 5\right)}\right)} \cos\left(x\right)^{13} - 4 \, {\left(2 \cdot 2^{\frac{3}{4}} {\left(3 \, \sqrt{2} - 10\right)} + 2^{\frac{1}{4}} {\left(19 \, \sqrt{2} + 58\right)}\right)} \cos\left(x\right)^{11} + 4 \, {\left(6 \cdot 2^{\frac{3}{4}} {\left(3 \, \sqrt{2} - 4\right)} - 2^{\frac{1}{4}} {\left(19 \, \sqrt{2} - 32\right)}\right)} \cos\left(x\right)^{9} - 2 \, {\left(2^{\frac{3}{4}} {\left(28 \, \sqrt{2} - 27\right)} - 4 \cdot 2^{\frac{1}{4}} {\left(15 \, \sqrt{2} - 2\right)}\right)} \cos\left(x\right)^{7} + 2 \, {\left(2^{\frac{3}{4}} {\left(9 \, \sqrt{2} - 8\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(15 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{5} - {\left(2 \cdot 2^{\frac{3}{4}} {\left(\sqrt{2} - 1\right)} - 2^{\frac{1}{4}} {\left(13 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{3} - 2^{\frac{3}{4}} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 4 \, \cos\left(x\right)^{2} + {\left(16 \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} - 6\right)} - 8 \, \sqrt{2} + 4\right)} \cos\left(x\right)^{14} - 56 \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} - 6\right)} - 8 \, \sqrt{2} + 4\right)} \cos\left(x\right)^{12} + 8 \, {\left(\sqrt{2} {\left(49 \, \sqrt{2} - 62\right)} - 76 \, \sqrt{2} + 54\right)} \cos\left(x\right)^{10} - 40 \, {\left(\sqrt{2} {\left(7 \, \sqrt{2} - 10\right)} - 10 \, \sqrt{2} + 13\right)} \cos\left(x\right)^{8} + 4 \, {\left(\sqrt{2} {\left(27 \, \sqrt{2} - 46\right)} - 32 \, \sqrt{2} + 92\right)} \cos\left(x\right)^{6} - 2 \, {\left(11 \, \sqrt{2} {\left(\sqrt{2} - 2\right)} - 8 \, \sqrt{2} + 72\right)} \cos\left(x\right)^{4} + 2 \, {\left(\sqrt{2} {\left(\sqrt{2} - 2\right)} + 14\right)} \cos\left(x\right)^{2} - {\left(8 \, {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} - 11\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} - 6\right)}\right)} \cos\left(x\right)^{13} - 24 \, {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} - 11\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} - 6\right)}\right)} \cos\left(x\right)^{11} + 4 \, {\left(2 \cdot 2^{\frac{3}{4}} {\left(28 \, \sqrt{2} - 39\right)} - 2^{\frac{1}{4}} {\left(73 \, \sqrt{2} - 94\right)}\right)} \cos\left(x\right)^{9} - 8 \, {\left(2^{\frac{3}{4}} {\left(16 \, \sqrt{2} - 23\right)} - 2^{\frac{1}{4}} {\left(23 \, \sqrt{2} - 34\right)}\right)} \cos\left(x\right)^{7} + 2 \, {\left(9 \cdot 2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 3\right)} - 8 \cdot 2^{\frac{1}{4}} {\left(4 \, \sqrt{2} - 7\right)}\right)} \cos\left(x\right)^{5} - 2 \, {\left(2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 3\right)} - 6 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)}\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) - 2\right)} \sqrt{-4 \, {\left(4 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} + 16 \, {\left(\sqrt{2} - 1\right)} \cos\left(x\right)^{2} - 4 \, {\left(2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 4\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 4}}{4 \, {\left(112 \, \cos\left(x\right)^{16} - 448 \, \cos\left(x\right)^{14} + 608 \, \cos\left(x\right)^{12} - 256 \, \cos\left(x\right)^{10} - 152 \, \cos\left(x\right)^{8} + 208 \, \cos\left(x\right)^{6} - 88 \, \cos\left(x\right)^{4} + 16 \, \cos\left(x\right)^{2} - 1\right)}}\right) - 2 \, {\left(2^{\frac{1}{4}} \cos\left(x\right)^{2} - 2^{\frac{1}{4}}\right)} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{32 \, {\left(\sqrt{2} {\left(3 \, \sqrt{2} + 2\right)} - 2 \, \sqrt{2} - 6\right)} \cos\left(x\right)^{16} - 16 \, {\left(\sqrt{2} {\left(19 \, \sqrt{2} + 22\right)} - 8 \, \sqrt{2} - 52\right)} \cos\left(x\right)^{14} + 32 \, {\left(\sqrt{2} {\left(8 \, \sqrt{2} + 19\right)} + 2 \, \sqrt{2} - 37\right)} \cos\left(x\right)^{12} + 16 \, {\left(2 \, \sqrt{2} {\left(4 \, \sqrt{2} - 13\right)} - 22 \, \sqrt{2} + 39\right)} \cos\left(x\right)^{10} - 8 \, {\left(\sqrt{2} {\left(41 \, \sqrt{2} - 10\right)} - 42 \, \sqrt{2} - 2\right)} \cos\left(x\right)^{8} + 4 \, {\left(\sqrt{2} {\left(49 \, \sqrt{2} + 6\right)} - 32 \, \sqrt{2} - 32\right)} \cos\left(x\right)^{6} - 8 \, {\left(\sqrt{2} {\left(6 \, \sqrt{2} + 1\right)} - 2 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} - 2 \, {\left(8 \, {\left(2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 1\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{15} - 8 \, {\left(2^{\frac{3}{4}} {\left(3 \, \sqrt{2} + 2\right)} - 4 \cdot 2^{\frac{1}{4}} {\left(4 \, \sqrt{2} + 5\right)}\right)} \cos\left(x\right)^{13} - 4 \, {\left(2 \cdot 2^{\frac{3}{4}} {\left(3 \, \sqrt{2} - 10\right)} + 2^{\frac{1}{4}} {\left(19 \, \sqrt{2} + 58\right)}\right)} \cos\left(x\right)^{11} + 4 \, {\left(6 \cdot 2^{\frac{3}{4}} {\left(3 \, \sqrt{2} - 4\right)} - 2^{\frac{1}{4}} {\left(19 \, \sqrt{2} - 32\right)}\right)} \cos\left(x\right)^{9} - 2 \, {\left(2^{\frac{3}{4}} {\left(28 \, \sqrt{2} - 27\right)} - 4 \cdot 2^{\frac{1}{4}} {\left(15 \, \sqrt{2} - 2\right)}\right)} \cos\left(x\right)^{7} + 2 \, {\left(2^{\frac{3}{4}} {\left(9 \, \sqrt{2} - 8\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(15 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{5} - {\left(2 \cdot 2^{\frac{3}{4}} {\left(\sqrt{2} - 1\right)} - 2^{\frac{1}{4}} {\left(13 \, \sqrt{2} + 2\right)}\right)} \cos\left(x\right)^{3} - 2^{\frac{3}{4}} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 4 \, \cos\left(x\right)^{2} - {\left(16 \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} - 6\right)} - 8 \, \sqrt{2} + 4\right)} \cos\left(x\right)^{14} - 56 \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} - 6\right)} - 8 \, \sqrt{2} + 4\right)} \cos\left(x\right)^{12} + 8 \, {\left(\sqrt{2} {\left(49 \, \sqrt{2} - 62\right)} - 76 \, \sqrt{2} + 54\right)} \cos\left(x\right)^{10} - 40 \, {\left(\sqrt{2} {\left(7 \, \sqrt{2} - 10\right)} - 10 \, \sqrt{2} + 13\right)} \cos\left(x\right)^{8} + 4 \, {\left(\sqrt{2} {\left(27 \, \sqrt{2} - 46\right)} - 32 \, \sqrt{2} + 92\right)} \cos\left(x\right)^{6} - 2 \, {\left(11 \, \sqrt{2} {\left(\sqrt{2} - 2\right)} - 8 \, \sqrt{2} + 72\right)} \cos\left(x\right)^{4} + 2 \, {\left(\sqrt{2} {\left(\sqrt{2} - 2\right)} + 14\right)} \cos\left(x\right)^{2} - {\left(8 \, {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} - 11\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} - 6\right)}\right)} \cos\left(x\right)^{13} - 24 \, {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} - 11\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} - 6\right)}\right)} \cos\left(x\right)^{11} + 4 \, {\left(2 \cdot 2^{\frac{3}{4}} {\left(28 \, \sqrt{2} - 39\right)} - 2^{\frac{1}{4}} {\left(73 \, \sqrt{2} - 94\right)}\right)} \cos\left(x\right)^{9} - 8 \, {\left(2^{\frac{3}{4}} {\left(16 \, \sqrt{2} - 23\right)} - 2^{\frac{1}{4}} {\left(23 \, \sqrt{2} - 34\right)}\right)} \cos\left(x\right)^{7} + 2 \, {\left(9 \cdot 2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 3\right)} - 8 \cdot 2^{\frac{1}{4}} {\left(4 \, \sqrt{2} - 7\right)}\right)} \cos\left(x\right)^{5} - 2 \, {\left(2^{\frac{3}{4}} {\left(2 \, \sqrt{2} - 3\right)} - 6 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)}\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) - 2\right)} \sqrt{-4 \, {\left(4 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} + 16 \, {\left(\sqrt{2} - 1\right)} \cos\left(x\right)^{2} - 4 \, {\left(2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 4\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 4}}{4 \, {\left(112 \, \cos\left(x\right)^{16} - 448 \, \cos\left(x\right)^{14} + 608 \, \cos\left(x\right)^{12} - 256 \, \cos\left(x\right)^{10} - 152 \, \cos\left(x\right)^{8} + 208 \, \cos\left(x\right)^{6} - 88 \, \cos\left(x\right)^{4} + 16 \, \cos\left(x\right)^{2} - 1\right)}}\right) + {\left(2^{\frac{1}{4}} {\left(\sqrt{2} - 1\right)} \cos\left(x\right)^{2} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 1\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} \log\left(-{\left(4 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} + 4 \, {\left(\sqrt{2} - 1\right)} \cos\left(x\right)^{2} + {\left(2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 4\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 1\right) - {\left(2^{\frac{1}{4}} {\left(\sqrt{2} - 1\right)} \cos\left(x\right)^{2} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 1\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} \log\left(-{\left(4 \, \sqrt{2} - 5\right)} \cos\left(x\right)^{4} + 4 \, {\left(\sqrt{2} - 1\right)} \cos\left(x\right)^{2} - {\left(2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 4\right)} \cos\left(x\right)^{3} - 2^{\frac{1}{4}} {\left(\sqrt{2} - 2\right)} \cos\left(x\right)\right)} \sqrt{2 \, \sqrt{2} + 4} \sin\left(x\right) + 1\right) + 4 \, {\left(\sqrt{2} \cos\left(x\right)^{2} - \sqrt{2}\right)} \arctan\left(\frac{3 \, \sqrt{2} \cos\left(x\right)^{2} - \sqrt{2}}{4 \, \cos\left(x\right) \sin\left(x\right)}\right) - 16 \, \cos\left(x\right) \sin\left(x\right)}{64 \, {\left(\cos\left(x\right)^{2} - 1\right)}}"," ",0,"-1/64*(2*(2^(1/4)*cos(x)^2 - 2^(1/4))*sqrt(2*sqrt(2) + 4)*arctan(1/4*(32*(sqrt(2)*(3*sqrt(2) + 2) - 2*sqrt(2) - 6)*cos(x)^16 - 16*(sqrt(2)*(19*sqrt(2) + 22) - 8*sqrt(2) - 52)*cos(x)^14 + 32*(sqrt(2)*(8*sqrt(2) + 19) + 2*sqrt(2) - 37)*cos(x)^12 + 16*(2*sqrt(2)*(4*sqrt(2) - 13) - 22*sqrt(2) + 39)*cos(x)^10 - 8*(sqrt(2)*(41*sqrt(2) - 10) - 42*sqrt(2) - 2)*cos(x)^8 + 4*(sqrt(2)*(49*sqrt(2) + 6) - 32*sqrt(2) - 32)*cos(x)^6 - 8*(sqrt(2)*(6*sqrt(2) + 1) - 2*sqrt(2) - 5)*cos(x)^4 + 2*(8*(2^(3/4)*(2*sqrt(2) - 1) - 2*2^(1/4)*(3*sqrt(2) + 2))*cos(x)^15 - 8*(2^(3/4)*(3*sqrt(2) + 2) - 4*2^(1/4)*(4*sqrt(2) + 5))*cos(x)^13 - 4*(2*2^(3/4)*(3*sqrt(2) - 10) + 2^(1/4)*(19*sqrt(2) + 58))*cos(x)^11 + 4*(6*2^(3/4)*(3*sqrt(2) - 4) - 2^(1/4)*(19*sqrt(2) - 32))*cos(x)^9 - 2*(2^(3/4)*(28*sqrt(2) - 27) - 4*2^(1/4)*(15*sqrt(2) - 2))*cos(x)^7 + 2*(2^(3/4)*(9*sqrt(2) - 8) - 2*2^(1/4)*(15*sqrt(2) + 2))*cos(x)^5 - (2*2^(3/4)*(sqrt(2) - 1) - 2^(1/4)*(13*sqrt(2) + 2))*cos(x)^3 - 2^(3/4)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 4*cos(x)^2 + (16*(sqrt(2)*(5*sqrt(2) - 6) - 8*sqrt(2) + 4)*cos(x)^14 - 56*(sqrt(2)*(5*sqrt(2) - 6) - 8*sqrt(2) + 4)*cos(x)^12 + 8*(sqrt(2)*(49*sqrt(2) - 62) - 76*sqrt(2) + 54)*cos(x)^10 - 40*(sqrt(2)*(7*sqrt(2) - 10) - 10*sqrt(2) + 13)*cos(x)^8 + 4*(sqrt(2)*(27*sqrt(2) - 46) - 32*sqrt(2) + 92)*cos(x)^6 - 2*(11*sqrt(2)*(sqrt(2) - 2) - 8*sqrt(2) + 72)*cos(x)^4 + 2*(sqrt(2)*(sqrt(2) - 2) + 14)*cos(x)^2 + (8*(2^(3/4)*(8*sqrt(2) - 11) - 2*2^(1/4)*(5*sqrt(2) - 6))*cos(x)^13 - 24*(2^(3/4)*(8*sqrt(2) - 11) - 2*2^(1/4)*(5*sqrt(2) - 6))*cos(x)^11 + 4*(2*2^(3/4)*(28*sqrt(2) - 39) - 2^(1/4)*(73*sqrt(2) - 94))*cos(x)^9 - 8*(2^(3/4)*(16*sqrt(2) - 23) - 2^(1/4)*(23*sqrt(2) - 34))*cos(x)^7 + 2*(9*2^(3/4)*(2*sqrt(2) - 3) - 8*2^(1/4)*(4*sqrt(2) - 7))*cos(x)^5 - 2*(2^(3/4)*(2*sqrt(2) - 3) - 6*2^(1/4)*(sqrt(2) - 2))*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) - 2)*sqrt(-4*(4*sqrt(2) - 5)*cos(x)^4 + 16*(sqrt(2) - 1)*cos(x)^2 + 4*(2^(1/4)*(3*sqrt(2) - 4)*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 4))/(112*cos(x)^16 - 448*cos(x)^14 + 608*cos(x)^12 - 256*cos(x)^10 - 152*cos(x)^8 + 208*cos(x)^6 - 88*cos(x)^4 + 16*cos(x)^2 - 1)) - 2*(2^(1/4)*cos(x)^2 - 2^(1/4))*sqrt(2*sqrt(2) + 4)*arctan(-1/4*(32*(sqrt(2)*(3*sqrt(2) + 2) - 2*sqrt(2) - 6)*cos(x)^16 - 16*(sqrt(2)*(19*sqrt(2) + 22) - 8*sqrt(2) - 52)*cos(x)^14 + 32*(sqrt(2)*(8*sqrt(2) + 19) + 2*sqrt(2) - 37)*cos(x)^12 + 16*(2*sqrt(2)*(4*sqrt(2) - 13) - 22*sqrt(2) + 39)*cos(x)^10 - 8*(sqrt(2)*(41*sqrt(2) - 10) - 42*sqrt(2) - 2)*cos(x)^8 + 4*(sqrt(2)*(49*sqrt(2) + 6) - 32*sqrt(2) - 32)*cos(x)^6 - 8*(sqrt(2)*(6*sqrt(2) + 1) - 2*sqrt(2) - 5)*cos(x)^4 + 2*(8*(2^(3/4)*(2*sqrt(2) - 1) - 2*2^(1/4)*(3*sqrt(2) + 2))*cos(x)^15 - 8*(2^(3/4)*(3*sqrt(2) + 2) - 4*2^(1/4)*(4*sqrt(2) + 5))*cos(x)^13 - 4*(2*2^(3/4)*(3*sqrt(2) - 10) + 2^(1/4)*(19*sqrt(2) + 58))*cos(x)^11 + 4*(6*2^(3/4)*(3*sqrt(2) - 4) - 2^(1/4)*(19*sqrt(2) - 32))*cos(x)^9 - 2*(2^(3/4)*(28*sqrt(2) - 27) - 4*2^(1/4)*(15*sqrt(2) - 2))*cos(x)^7 + 2*(2^(3/4)*(9*sqrt(2) - 8) - 2*2^(1/4)*(15*sqrt(2) + 2))*cos(x)^5 - (2*2^(3/4)*(sqrt(2) - 1) - 2^(1/4)*(13*sqrt(2) + 2))*cos(x)^3 - 2^(3/4)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 4*cos(x)^2 - (16*(sqrt(2)*(5*sqrt(2) - 6) - 8*sqrt(2) + 4)*cos(x)^14 - 56*(sqrt(2)*(5*sqrt(2) - 6) - 8*sqrt(2) + 4)*cos(x)^12 + 8*(sqrt(2)*(49*sqrt(2) - 62) - 76*sqrt(2) + 54)*cos(x)^10 - 40*(sqrt(2)*(7*sqrt(2) - 10) - 10*sqrt(2) + 13)*cos(x)^8 + 4*(sqrt(2)*(27*sqrt(2) - 46) - 32*sqrt(2) + 92)*cos(x)^6 - 2*(11*sqrt(2)*(sqrt(2) - 2) - 8*sqrt(2) + 72)*cos(x)^4 + 2*(sqrt(2)*(sqrt(2) - 2) + 14)*cos(x)^2 + (8*(2^(3/4)*(8*sqrt(2) - 11) - 2*2^(1/4)*(5*sqrt(2) - 6))*cos(x)^13 - 24*(2^(3/4)*(8*sqrt(2) - 11) - 2*2^(1/4)*(5*sqrt(2) - 6))*cos(x)^11 + 4*(2*2^(3/4)*(28*sqrt(2) - 39) - 2^(1/4)*(73*sqrt(2) - 94))*cos(x)^9 - 8*(2^(3/4)*(16*sqrt(2) - 23) - 2^(1/4)*(23*sqrt(2) - 34))*cos(x)^7 + 2*(9*2^(3/4)*(2*sqrt(2) - 3) - 8*2^(1/4)*(4*sqrt(2) - 7))*cos(x)^5 - 2*(2^(3/4)*(2*sqrt(2) - 3) - 6*2^(1/4)*(sqrt(2) - 2))*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) - 2)*sqrt(-4*(4*sqrt(2) - 5)*cos(x)^4 + 16*(sqrt(2) - 1)*cos(x)^2 + 4*(2^(1/4)*(3*sqrt(2) - 4)*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 4))/(112*cos(x)^16 - 448*cos(x)^14 + 608*cos(x)^12 - 256*cos(x)^10 - 152*cos(x)^8 + 208*cos(x)^6 - 88*cos(x)^4 + 16*cos(x)^2 - 1)) + 2*(2^(1/4)*cos(x)^2 - 2^(1/4))*sqrt(2*sqrt(2) + 4)*arctan(-1/4*(32*(sqrt(2)*(3*sqrt(2) + 2) - 2*sqrt(2) - 6)*cos(x)^16 - 16*(sqrt(2)*(19*sqrt(2) + 22) - 8*sqrt(2) - 52)*cos(x)^14 + 32*(sqrt(2)*(8*sqrt(2) + 19) + 2*sqrt(2) - 37)*cos(x)^12 + 16*(2*sqrt(2)*(4*sqrt(2) - 13) - 22*sqrt(2) + 39)*cos(x)^10 - 8*(sqrt(2)*(41*sqrt(2) - 10) - 42*sqrt(2) - 2)*cos(x)^8 + 4*(sqrt(2)*(49*sqrt(2) + 6) - 32*sqrt(2) - 32)*cos(x)^6 - 8*(sqrt(2)*(6*sqrt(2) + 1) - 2*sqrt(2) - 5)*cos(x)^4 - 2*(8*(2^(3/4)*(2*sqrt(2) - 1) - 2*2^(1/4)*(3*sqrt(2) + 2))*cos(x)^15 - 8*(2^(3/4)*(3*sqrt(2) + 2) - 4*2^(1/4)*(4*sqrt(2) + 5))*cos(x)^13 - 4*(2*2^(3/4)*(3*sqrt(2) - 10) + 2^(1/4)*(19*sqrt(2) + 58))*cos(x)^11 + 4*(6*2^(3/4)*(3*sqrt(2) - 4) - 2^(1/4)*(19*sqrt(2) - 32))*cos(x)^9 - 2*(2^(3/4)*(28*sqrt(2) - 27) - 4*2^(1/4)*(15*sqrt(2) - 2))*cos(x)^7 + 2*(2^(3/4)*(9*sqrt(2) - 8) - 2*2^(1/4)*(15*sqrt(2) + 2))*cos(x)^5 - (2*2^(3/4)*(sqrt(2) - 1) - 2^(1/4)*(13*sqrt(2) + 2))*cos(x)^3 - 2^(3/4)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 4*cos(x)^2 + (16*(sqrt(2)*(5*sqrt(2) - 6) - 8*sqrt(2) + 4)*cos(x)^14 - 56*(sqrt(2)*(5*sqrt(2) - 6) - 8*sqrt(2) + 4)*cos(x)^12 + 8*(sqrt(2)*(49*sqrt(2) - 62) - 76*sqrt(2) + 54)*cos(x)^10 - 40*(sqrt(2)*(7*sqrt(2) - 10) - 10*sqrt(2) + 13)*cos(x)^8 + 4*(sqrt(2)*(27*sqrt(2) - 46) - 32*sqrt(2) + 92)*cos(x)^6 - 2*(11*sqrt(2)*(sqrt(2) - 2) - 8*sqrt(2) + 72)*cos(x)^4 + 2*(sqrt(2)*(sqrt(2) - 2) + 14)*cos(x)^2 - (8*(2^(3/4)*(8*sqrt(2) - 11) - 2*2^(1/4)*(5*sqrt(2) - 6))*cos(x)^13 - 24*(2^(3/4)*(8*sqrt(2) - 11) - 2*2^(1/4)*(5*sqrt(2) - 6))*cos(x)^11 + 4*(2*2^(3/4)*(28*sqrt(2) - 39) - 2^(1/4)*(73*sqrt(2) - 94))*cos(x)^9 - 8*(2^(3/4)*(16*sqrt(2) - 23) - 2^(1/4)*(23*sqrt(2) - 34))*cos(x)^7 + 2*(9*2^(3/4)*(2*sqrt(2) - 3) - 8*2^(1/4)*(4*sqrt(2) - 7))*cos(x)^5 - 2*(2^(3/4)*(2*sqrt(2) - 3) - 6*2^(1/4)*(sqrt(2) - 2))*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) - 2)*sqrt(-4*(4*sqrt(2) - 5)*cos(x)^4 + 16*(sqrt(2) - 1)*cos(x)^2 - 4*(2^(1/4)*(3*sqrt(2) - 4)*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 4))/(112*cos(x)^16 - 448*cos(x)^14 + 608*cos(x)^12 - 256*cos(x)^10 - 152*cos(x)^8 + 208*cos(x)^6 - 88*cos(x)^4 + 16*cos(x)^2 - 1)) - 2*(2^(1/4)*cos(x)^2 - 2^(1/4))*sqrt(2*sqrt(2) + 4)*arctan(1/4*(32*(sqrt(2)*(3*sqrt(2) + 2) - 2*sqrt(2) - 6)*cos(x)^16 - 16*(sqrt(2)*(19*sqrt(2) + 22) - 8*sqrt(2) - 52)*cos(x)^14 + 32*(sqrt(2)*(8*sqrt(2) + 19) + 2*sqrt(2) - 37)*cos(x)^12 + 16*(2*sqrt(2)*(4*sqrt(2) - 13) - 22*sqrt(2) + 39)*cos(x)^10 - 8*(sqrt(2)*(41*sqrt(2) - 10) - 42*sqrt(2) - 2)*cos(x)^8 + 4*(sqrt(2)*(49*sqrt(2) + 6) - 32*sqrt(2) - 32)*cos(x)^6 - 8*(sqrt(2)*(6*sqrt(2) + 1) - 2*sqrt(2) - 5)*cos(x)^4 - 2*(8*(2^(3/4)*(2*sqrt(2) - 1) - 2*2^(1/4)*(3*sqrt(2) + 2))*cos(x)^15 - 8*(2^(3/4)*(3*sqrt(2) + 2) - 4*2^(1/4)*(4*sqrt(2) + 5))*cos(x)^13 - 4*(2*2^(3/4)*(3*sqrt(2) - 10) + 2^(1/4)*(19*sqrt(2) + 58))*cos(x)^11 + 4*(6*2^(3/4)*(3*sqrt(2) - 4) - 2^(1/4)*(19*sqrt(2) - 32))*cos(x)^9 - 2*(2^(3/4)*(28*sqrt(2) - 27) - 4*2^(1/4)*(15*sqrt(2) - 2))*cos(x)^7 + 2*(2^(3/4)*(9*sqrt(2) - 8) - 2*2^(1/4)*(15*sqrt(2) + 2))*cos(x)^5 - (2*2^(3/4)*(sqrt(2) - 1) - 2^(1/4)*(13*sqrt(2) + 2))*cos(x)^3 - 2^(3/4)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 4*cos(x)^2 - (16*(sqrt(2)*(5*sqrt(2) - 6) - 8*sqrt(2) + 4)*cos(x)^14 - 56*(sqrt(2)*(5*sqrt(2) - 6) - 8*sqrt(2) + 4)*cos(x)^12 + 8*(sqrt(2)*(49*sqrt(2) - 62) - 76*sqrt(2) + 54)*cos(x)^10 - 40*(sqrt(2)*(7*sqrt(2) - 10) - 10*sqrt(2) + 13)*cos(x)^8 + 4*(sqrt(2)*(27*sqrt(2) - 46) - 32*sqrt(2) + 92)*cos(x)^6 - 2*(11*sqrt(2)*(sqrt(2) - 2) - 8*sqrt(2) + 72)*cos(x)^4 + 2*(sqrt(2)*(sqrt(2) - 2) + 14)*cos(x)^2 - (8*(2^(3/4)*(8*sqrt(2) - 11) - 2*2^(1/4)*(5*sqrt(2) - 6))*cos(x)^13 - 24*(2^(3/4)*(8*sqrt(2) - 11) - 2*2^(1/4)*(5*sqrt(2) - 6))*cos(x)^11 + 4*(2*2^(3/4)*(28*sqrt(2) - 39) - 2^(1/4)*(73*sqrt(2) - 94))*cos(x)^9 - 8*(2^(3/4)*(16*sqrt(2) - 23) - 2^(1/4)*(23*sqrt(2) - 34))*cos(x)^7 + 2*(9*2^(3/4)*(2*sqrt(2) - 3) - 8*2^(1/4)*(4*sqrt(2) - 7))*cos(x)^5 - 2*(2^(3/4)*(2*sqrt(2) - 3) - 6*2^(1/4)*(sqrt(2) - 2))*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) - 2)*sqrt(-4*(4*sqrt(2) - 5)*cos(x)^4 + 16*(sqrt(2) - 1)*cos(x)^2 - 4*(2^(1/4)*(3*sqrt(2) - 4)*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 4))/(112*cos(x)^16 - 448*cos(x)^14 + 608*cos(x)^12 - 256*cos(x)^10 - 152*cos(x)^8 + 208*cos(x)^6 - 88*cos(x)^4 + 16*cos(x)^2 - 1)) + (2^(1/4)*(sqrt(2) - 1)*cos(x)^2 - 2^(1/4)*(sqrt(2) - 1))*sqrt(2*sqrt(2) + 4)*log(-(4*sqrt(2) - 5)*cos(x)^4 + 4*(sqrt(2) - 1)*cos(x)^2 + (2^(1/4)*(3*sqrt(2) - 4)*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 1) - (2^(1/4)*(sqrt(2) - 1)*cos(x)^2 - 2^(1/4)*(sqrt(2) - 1))*sqrt(2*sqrt(2) + 4)*log(-(4*sqrt(2) - 5)*cos(x)^4 + 4*(sqrt(2) - 1)*cos(x)^2 - (2^(1/4)*(3*sqrt(2) - 4)*cos(x)^3 - 2^(1/4)*(sqrt(2) - 2)*cos(x))*sqrt(2*sqrt(2) + 4)*sin(x) + 1) + 4*(sqrt(2)*cos(x)^2 - sqrt(2))*arctan(1/4*(3*sqrt(2)*cos(x)^2 - sqrt(2))/(cos(x)*sin(x))) - 16*cos(x)*sin(x))/(cos(x)^2 - 1)","B",0
86,1,19,0,0.527516," ","integrate(tan(x)/(1+cos(x)^2),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(\frac{1}{2} \, \cos\left(x\right)^{2} + \frac{1}{2}\right) - \log\left(-\cos\left(x\right)\right)"," ",0,"1/2*log(1/2*cos(x)^2 + 1/2) - log(-cos(x))","A",0
87,1,90,0,2.083600," ","integrate((a+b*cos(x)^2)^(1/2)*tan(x),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{a} \log\left(\frac{b \cos\left(x\right)^{2} + 2 \, \sqrt{b \cos\left(x\right)^{2} + a} \sqrt{a} + 2 \, a}{\cos\left(x\right)^{2}}\right) - \sqrt{b \cos\left(x\right)^{2} + a}, -\sqrt{-a} \arctan\left(\frac{\sqrt{b \cos\left(x\right)^{2} + a} \sqrt{-a}}{a}\right) - \sqrt{b \cos\left(x\right)^{2} + a}\right]"," ",0,"[1/2*sqrt(a)*log((b*cos(x)^2 + 2*sqrt(b*cos(x)^2 + a)*sqrt(a) + 2*a)/cos(x)^2) - sqrt(b*cos(x)^2 + a), -sqrt(-a)*arctan(sqrt(b*cos(x)^2 + a)*sqrt(-a)/a) - sqrt(b*cos(x)^2 + a)]","A",0
88,1,21,0,0.497184," ","integrate((1-cos(x)^2)^(1/2)*tan(x),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(\sin\left(x\right) + 1\right) - \frac{1}{2} \, \log\left(-\sin\left(x\right) + 1\right) - \sin\left(x\right)"," ",0,"1/2*log(sin(x) + 1) - 1/2*log(-sin(x) + 1) - sin(x)","A",0
89,1,67,0,0.801245," ","integrate(tan(x)/(a+b*cos(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b \cos\left(x\right)^{2} + 2 \, \sqrt{b \cos\left(x\right)^{2} + a} \sqrt{a} + 2 \, a}{\cos\left(x\right)^{2}}\right)}{2 \, \sqrt{a}}, -\frac{\sqrt{-a} \arctan\left(\frac{\sqrt{b \cos\left(x\right)^{2} + a} \sqrt{-a}}{a}\right)}{a}\right]"," ",0,"[1/2*log((b*cos(x)^2 + 2*sqrt(b*cos(x)^2 + a)*sqrt(a) + 2*a)/cos(x)^2)/sqrt(a), -sqrt(-a)*arctan(sqrt(b*cos(x)^2 + a)*sqrt(-a)/a)/a]","A",0
90,1,16,0,0.674759," ","integrate(tan(x)/(1+cos(x)^2)^(1/2),x, algorithm=""fricas"")","\log\left(\frac{\sqrt{\cos\left(x\right)^{2} + 1} + 1}{\cos\left(x\right)}\right)"," ",0,"log((sqrt(cos(x)^2 + 1) + 1)/cos(x))","A",0
91,1,17,0,0.641008," ","integrate(tan(x)/(1-cos(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(\sin\left(x\right) + 1\right) - \frac{1}{2} \, \log\left(-\sin\left(x\right) + 1\right)"," ",0,"1/2*log(sin(x) + 1) - 1/2*log(-sin(x) + 1)","B",0
92,1,1690,0,46.275621," ","integrate(tan(x)^3/(a+b*cos(x)^3),x, algorithm=""fricas"")","\frac{6 \, \sqrt{\frac{1}{3}} a \sqrt{\frac{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a + 4}{a^{2}}} \arctan\left(-\frac{2 \, \sqrt{\frac{1}{3}} \sqrt{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{4} + 4 \, b^{2} \cos\left(x\right)^{2} - 4 \, a b \cos\left(x\right) + 2 \, {\left(a^{2} b \cos\left(x\right) - 2 \, a^{3}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} + 4 \, a^{2}} {\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a^{3} - 2 \, a^{2}\right)} \sqrt{\frac{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a + 4}{a^{2}}} + \sqrt{\frac{1}{3}} {\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{5} - 8 \, a^{2} b \cos\left(x\right) + 4 \, a^{3} + 4 \, {\left(a^{3} b \cos\left(x\right) - a^{4}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}\right)} \sqrt{\frac{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a + 4}{a^{2}}}}{8 \, b^{2}}\right) \cos\left(x\right)^{2} - 6 \, \sqrt{\frac{1}{3}} a \sqrt{\frac{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a + 4}{a^{2}}} \arctan\left(-\frac{2 \, \sqrt{\frac{1}{3}} \sqrt{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{4} + 4 \, b^{2} \cos\left(x\right)^{2} - 4 \, a b \cos\left(x\right) + 2 \, {\left(a^{2} b \cos\left(x\right) - 2 \, a^{3}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} + 4 \, a^{2}} {\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a^{3} - 2 \, a^{2}\right)} \sqrt{\frac{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a + 4}{a^{2}}} - \sqrt{\frac{1}{3}} {\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{5} - 8 \, a^{2} b \cos\left(x\right) + 4 \, a^{3} + 4 \, {\left(a^{3} b \cos\left(x\right) - a^{4}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}\right)} \sqrt{\frac{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a + 4}{a^{2}}}}{8 \, b^{2}}\right) \cos\left(x\right)^{2} - {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a \cos\left(x\right)^{2} \log\left(\frac{1}{4} \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{4} + b^{2} \cos\left(x\right)^{2} + 2 \, a b \cos\left(x\right) - {\left(a^{2} b \cos\left(x\right) + a^{3}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} + a^{2}\right) + 12 \, \cos\left(x\right)^{2} \log\left(-\cos\left(x\right)\right) + {\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a \cos\left(x\right)^{2} - 6 \, \cos\left(x\right)^{2}\right)} \log\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{4} + 4 \, b^{2} \cos\left(x\right)^{2} - 4 \, a b \cos\left(x\right) + 2 \, {\left(a^{2} b \cos\left(x\right) - 2 \, a^{3}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} + 4 \, a^{2}\right) + 6}{12 \, a \cos\left(x\right)^{2}}"," ",0,"1/12*(6*sqrt(1/3)*a*sqrt((((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^2 - 4*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)*a + 4)/a^2)*arctan(-1/8*(2*sqrt(1/3)*sqrt(((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^4 + 4*b^2*cos(x)^2 - 4*a*b*cos(x) + 2*(a^2*b*cos(x) - 2*a^3)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a) + 4*a^2)*(((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)*a^3 - 2*a^2)*sqrt((((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^2 - 4*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)*a + 4)/a^2) + sqrt(1/3)*(((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^5 - 8*a^2*b*cos(x) + 4*a^3 + 4*(a^3*b*cos(x) - a^4)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a))*sqrt((((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^2 - 4*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)*a + 4)/a^2))/b^2)*cos(x)^2 - 6*sqrt(1/3)*a*sqrt((((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^2 - 4*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)*a + 4)/a^2)*arctan(-1/8*(2*sqrt(1/3)*sqrt(((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^4 + 4*b^2*cos(x)^2 - 4*a*b*cos(x) + 2*(a^2*b*cos(x) - 2*a^3)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a) + 4*a^2)*(((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)*a^3 - 2*a^2)*sqrt((((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^2 - 4*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)*a + 4)/a^2) - sqrt(1/3)*(((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^5 - 8*a^2*b*cos(x) + 4*a^3 + 4*(a^3*b*cos(x) - a^4)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a))*sqrt((((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^2 - 4*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)*a + 4)/a^2))/b^2)*cos(x)^2 - ((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)*a*cos(x)^2*log(1/4*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^4 + b^2*cos(x)^2 + 2*a*b*cos(x) - (a^2*b*cos(x) + a^3)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a) + a^2) + 12*cos(x)^2*log(-cos(x)) + (((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)*a*cos(x)^2 - 6*cos(x)^2)*log(((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^4 + 4*b^2*cos(x)^2 - 4*a*b*cos(x) + 2*(a^2*b*cos(x) - 2*a^3)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a) + 4*a^2) + 6)/(a*cos(x)^2)","C",0
93,1,123,0,5.093387," ","integrate((a+b*cos(x)^3)^(1/2)*tan(x),x, algorithm=""fricas"")","\left[\frac{1}{6} \, \sqrt{a} \log\left(-\frac{b^{2} \cos\left(x\right)^{6} + 8 \, a b \cos\left(x\right)^{3} + 4 \, {\left(b \cos\left(x\right)^{3} + 2 \, a\right)} \sqrt{b \cos\left(x\right)^{3} + a} \sqrt{a} + 8 \, a^{2}}{\cos\left(x\right)^{6}}\right) - \frac{2}{3} \, \sqrt{b \cos\left(x\right)^{3} + a}, -\frac{1}{3} \, \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{b \cos\left(x\right)^{3} + a} \sqrt{-a}}{b \cos\left(x\right)^{3} + 2 \, a}\right) - \frac{2}{3} \, \sqrt{b \cos\left(x\right)^{3} + a}\right]"," ",0,"[1/6*sqrt(a)*log(-(b^2*cos(x)^6 + 8*a*b*cos(x)^3 + 4*(b*cos(x)^3 + 2*a)*sqrt(b*cos(x)^3 + a)*sqrt(a) + 8*a^2)/cos(x)^6) - 2/3*sqrt(b*cos(x)^3 + a), -1/3*sqrt(-a)*arctan(2*sqrt(b*cos(x)^3 + a)*sqrt(-a)/(b*cos(x)^3 + 2*a)) - 2/3*sqrt(b*cos(x)^3 + a)]","A",0
94,-2,0,0,0.000000," ","integrate(tan(x)/(a+b*cos(x)^3)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   failed of mode Union(SparseUnivariatePolynomial(Expression(Complex(Integer))),failed) cannot be coerced to mode SparseUnivariatePolynomial(Expression(Complex(Integer)))","F(-2)",0
95,1,90,0,0.910210," ","integrate((a+b*cos(x)^4)^(1/2)*tan(x),x, algorithm=""fricas"")","\left[\frac{1}{4} \, \sqrt{a} \log\left(\frac{b \cos\left(x\right)^{4} + 2 \, \sqrt{b \cos\left(x\right)^{4} + a} \sqrt{a} + 2 \, a}{\cos\left(x\right)^{4}}\right) - \frac{1}{2} \, \sqrt{b \cos\left(x\right)^{4} + a}, -\frac{1}{2} \, \sqrt{-a} \arctan\left(\frac{\sqrt{b \cos\left(x\right)^{4} + a} \sqrt{-a}}{a}\right) - \frac{1}{2} \, \sqrt{b \cos\left(x\right)^{4} + a}\right]"," ",0,"[1/4*sqrt(a)*log((b*cos(x)^4 + 2*sqrt(b*cos(x)^4 + a)*sqrt(a) + 2*a)/cos(x)^4) - 1/2*sqrt(b*cos(x)^4 + a), -1/2*sqrt(-a)*arctan(sqrt(b*cos(x)^4 + a)*sqrt(-a)/a) - 1/2*sqrt(b*cos(x)^4 + a)]","A",0
96,1,67,0,0.910002," ","integrate(tan(x)/(a+b*cos(x)^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b \cos\left(x\right)^{4} + 2 \, \sqrt{b \cos\left(x\right)^{4} + a} \sqrt{a} + 2 \, a}{\cos\left(x\right)^{4}}\right)}{4 \, \sqrt{a}}, -\frac{\sqrt{-a} \arctan\left(\frac{\sqrt{b \cos\left(x\right)^{4} + a} \sqrt{-a}}{a}\right)}{2 \, a}\right]"," ",0,"[1/4*log((b*cos(x)^4 + 2*sqrt(b*cos(x)^4 + a)*sqrt(a) + 2*a)/cos(x)^4)/sqrt(a), -1/2*sqrt(-a)*arctan(sqrt(b*cos(x)^4 + a)*sqrt(-a)/a)/a]","A",0
97,1,97,0,0.527578," ","integrate((a+b*cos(x)^n)^(1/2)*tan(x),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} \log\left(\frac{b \cos\left(x\right)^{n} + 2 \, \sqrt{b \cos\left(x\right)^{n} + a} \sqrt{a} + 2 \, a}{\cos\left(x\right)^{n}}\right) - 2 \, \sqrt{b \cos\left(x\right)^{n} + a}}{n}, -\frac{2 \, {\left(\sqrt{-a} \arctan\left(\frac{\sqrt{b \cos\left(x\right)^{n} + a} \sqrt{-a}}{a}\right) + \sqrt{b \cos\left(x\right)^{n} + a}\right)}}{n}\right]"," ",0,"[(sqrt(a)*log((b*cos(x)^n + 2*sqrt(b*cos(x)^n + a)*sqrt(a) + 2*a)/cos(x)^n) - 2*sqrt(b*cos(x)^n + a))/n, -2*(sqrt(-a)*arctan(sqrt(b*cos(x)^n + a)*sqrt(-a)/a) + sqrt(b*cos(x)^n + a))/n]","A",0
98,1,74,0,0.535151," ","integrate(tan(x)/(a+b*cos(x)^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b \cos\left(x\right)^{n} + 2 \, \sqrt{b \cos\left(x\right)^{n} + a} \sqrt{a} + 2 \, a}{\cos\left(x\right)^{n}}\right)}{\sqrt{a} n}, -\frac{2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{b \cos\left(x\right)^{n} + a} \sqrt{-a}}{a}\right)}{a n}\right]"," ",0,"[log((b*cos(x)^n + 2*sqrt(b*cos(x)^n + a)*sqrt(a) + 2*a)/cos(x)^n)/(sqrt(a)*n), -2*sqrt(-a)*arctan(sqrt(b*cos(x)^n + a)*sqrt(-a)/a)/(a*n)]","A",0
