1,1,15,0,1.308622," ","integrate(3/(5-4*cos(x)),x, algorithm=""fricas"")","-\arctan\left(\frac{5 \, \cos\left(x\right) - 4}{3 \, \sin\left(x\right)}\right)"," ",0,"-arctan(1/3*(5*cos(x) - 4)/sin(x))","A",0
2,1,48,0,0.827755," ","integrate((1+cos(x)+2*sin(x))/(3+cos(x)^2+2*sin(x)-2*cos(x)*sin(x)),x, algorithm=""fricas"")","\frac{1}{2} \, \arctan\left(-\frac{3 \, \cos\left(x\right)^{2} - 2 \, {\left(3 \, \cos\left(x\right) + 1\right)} \sin\left(x\right) - 4 \, \cos\left(x\right) - 3}{2 \, {\left(2 \, \cos\left(x\right)^{2} + {\left(\cos\left(x\right) - 3\right)} \sin\left(x\right) + 4 \, \cos\left(x\right) - 2\right)}}\right)"," ",0,"1/2*arctan(-1/2*(3*cos(x)^2 - 2*(3*cos(x) + 1)*sin(x) - 4*cos(x) - 3)/(2*cos(x)^2 + (cos(x) - 3)*sin(x) + 4*cos(x) - 2))","B",0
3,1,43,0,0.907541," ","integrate((2+cos(x)+5*sin(x))/(4*cos(x)-2*sin(x)+cos(x)*sin(x)-2*sin(x)^2),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(2 \, \cos\left(x\right)^{2} - \frac{1}{2} \, {\left(3 \, \cos\left(x\right) - 1\right)} \sin\left(x\right) - \frac{3}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{2} \, \log\left(\frac{1}{2} \, {\left(\cos\left(x\right) + 3\right)} \sin\left(x\right) + \frac{3}{2} \, \cos\left(x\right) + \frac{5}{2}\right)"," ",0,"-1/2*log(2*cos(x)^2 - 1/2*(3*cos(x) - 1)*sin(x) - 3/2*cos(x) + 1/2) + 1/2*log(1/2*(cos(x) + 3)*sin(x) + 3/2*cos(x) + 5/2)","B",0
4,1,41,0,0.974052," ","integrate((3+7*cos(x)+2*sin(x))/(1+4*cos(x)+3*cos(x)^2-5*sin(x)-cos(x)*sin(x)),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(-\frac{3}{4} \, \cos\left(x\right)^{2} - {\left(\cos\left(x\right) + 1\right)} \sin\left(x\right) + \frac{1}{2} \, \cos\left(x\right) + \frac{5}{4}\right) + \frac{1}{2} \, \log\left(\frac{1}{2} \, {\left(\cos\left(x\right) + 3\right)} \sin\left(x\right) + \frac{3}{2} \, \cos\left(x\right) + \frac{5}{2}\right)"," ",0,"-1/2*log(-3/4*cos(x)^2 - (cos(x) + 1)*sin(x) + 1/2*cos(x) + 5/4) + 1/2*log(1/2*(cos(x) + 3)*sin(x) + 3/2*cos(x) + 5/2)","B",0
5,1,31,0,0.934187," ","integrate((-1+4*cos(x)+5*cos(x)^2)/(-1-4*cos(x)-3*cos(x)^2+4*cos(x)^3),x, algorithm=""fricas"")","\arctan\left(\frac{5 \, \cos\left(x\right)^{3} - \cos\left(x\right)}{{\left(3 \, \cos\left(x\right)^{2} + 4 \, \cos\left(x\right) + 1\right)} \sin\left(x\right)}\right)"," ",0,"arctan((5*cos(x)^3 - cos(x))/((3*cos(x)^2 + 4*cos(x) + 1)*sin(x)))","A",0
6,1,37,0,0.956676," ","integrate((-5+2*cos(x)+7*cos(x)^2)/(-1+2*cos(x)-9*cos(x)^2+4*cos(x)^3),x, algorithm=""fricas"")","\arctan\left(\frac{5 \, \cos\left(x\right)^{3} - 6 \, \cos\left(x\right)^{2} + 5 \, \cos\left(x\right)}{{\left(3 \, \cos\left(x\right)^{2} + 2 \, \cos\left(x\right) - 1\right)} \sin\left(x\right)}\right)"," ",0,"arctan((5*cos(x)^3 - 6*cos(x)^2 + 5*cos(x))/((3*cos(x)^2 + 2*cos(x) - 1)*sin(x)))","A",0
7,1,13,0,0.874751," ","integrate(3/(5+4*sin(x)),x, algorithm=""fricas"")","\arctan\left(\frac{5 \, \sin\left(x\right) + 4}{3 \, \cos\left(x\right)}\right)"," ",0,"arctan(1/3*(5*sin(x) + 4)/cos(x))","A",0
8,1,31,0,0.976493," ","integrate(2/(1+cos(x)^2),x, algorithm=""fricas"")","-\frac{1}{2} \, \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,"-1/2*sqrt(2)*arctan(1/4*(3*sqrt(2)*cos(x)^2 - sqrt(2))/(cos(x)*sin(x)))","A",0
9,1,364,0,1.020801," ","integrate(1/(p+q*cos(x)+r*sin(x)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-p^{2} + q^{2} + r^{2}} \log\left(-\frac{p^{2} q^{2} - 2 \, q^{4} - r^{4} - {\left(p^{2} + 3 \, q^{2}\right)} r^{2} - {\left(2 \, p^{2} q^{2} - q^{4} - 2 \, p^{2} r^{2} + r^{4}\right)} \cos\left(x\right)^{2} - 2 \, {\left(p q^{3} + p q r^{2}\right)} \cos\left(x\right) - 2 \, {\left(p q^{2} r + p r^{3} - {\left(q r^{3} - {\left(2 \, p^{2} q - q^{3}\right)} r\right)} \cos\left(x\right)\right)} \sin\left(x\right) + 2 \, {\left(2 \, p q r \cos\left(x\right)^{2} - p q r + {\left(q^{2} r + r^{3}\right)} \cos\left(x\right) - {\left(q^{3} + q r^{2} + {\left(p q^{2} - p r^{2}\right)} \cos\left(x\right)\right)} \sin\left(x\right)\right)} \sqrt{-p^{2} + q^{2} + r^{2}}}{2 \, p q \cos\left(x\right) + {\left(q^{2} - r^{2}\right)} \cos\left(x\right)^{2} + p^{2} + r^{2} + 2 \, {\left(q r \cos\left(x\right) + p r\right)} \sin\left(x\right)}\right)}{2 \, {\left(p^{2} - q^{2} - r^{2}\right)}}, \frac{\arctan\left(-\frac{{\left(p q \cos\left(x\right) + p r \sin\left(x\right) + q^{2} + r^{2}\right)} \sqrt{p^{2} - q^{2} - r^{2}}}{{\left(r^{3} - {\left(p^{2} - q^{2}\right)} r\right)} \cos\left(x\right) + {\left(p^{2} q - q^{3} - q r^{2}\right)} \sin\left(x\right)}\right)}{\sqrt{p^{2} - q^{2} - r^{2}}}\right]"," ",0,"[-1/2*sqrt(-p^2 + q^2 + r^2)*log(-(p^2*q^2 - 2*q^4 - r^4 - (p^2 + 3*q^2)*r^2 - (2*p^2*q^2 - q^4 - 2*p^2*r^2 + r^4)*cos(x)^2 - 2*(p*q^3 + p*q*r^2)*cos(x) - 2*(p*q^2*r + p*r^3 - (q*r^3 - (2*p^2*q - q^3)*r)*cos(x))*sin(x) + 2*(2*p*q*r*cos(x)^2 - p*q*r + (q^2*r + r^3)*cos(x) - (q^3 + q*r^2 + (p*q^2 - p*r^2)*cos(x))*sin(x))*sqrt(-p^2 + q^2 + r^2))/(2*p*q*cos(x) + (q^2 - r^2)*cos(x)^2 + p^2 + r^2 + 2*(q*r*cos(x) + p*r)*sin(x)))/(p^2 - q^2 - r^2), arctan(-(p*q*cos(x) + p*r*sin(x) + q^2 + r^2)*sqrt(p^2 - q^2 - r^2)/((r^3 - (p^2 - q^2)*r)*cos(x) + (p^2*q - q^3 - q*r^2)*sin(x)))/sqrt(p^2 - q^2 - r^2)]","A",0
