1,1,13,0,1.074001," ","integrate(3/(5-4*cos(x)),x, algorithm=""maxima"")","2 \, \arctan\left(\frac{3 \, \sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"2*arctan(3*sin(x)/(cos(x) + 1))","A",0
2,0,0,0,0.000000," ","integrate((1+cos(x)+2*sin(x))/(3+cos(x)^2+2*sin(x)-2*cos(x)*sin(x)),x, algorithm=""maxima"")","\int \frac{\cos\left(x\right) + 2 \, \sin\left(x\right) + 1}{\cos\left(x\right)^{2} - 2 \, \cos\left(x\right) \sin\left(x\right) + 2 \, \sin\left(x\right) + 3}\,{d x}"," ",0,"integrate((cos(x) + 2*sin(x) + 1)/(cos(x)^2 - 2*cos(x)*sin(x) + 2*sin(x) + 3), x)","F",0
3,1,53,0,1.479959," ","integrate((2+cos(x)+5*sin(x))/(4*cos(x)-2*sin(x)+cos(x)*sin(x)-2*sin(x)^2),x, algorithm=""maxima"")","-\log\left(\frac{2 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right) + \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 2\right) - \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)"," ",0,"-log(2*sin(x)/(cos(x) + 1) - 1) + log(sin(x)/(cos(x) + 1) + sin(x)^2/(cos(x) + 1)^2 + 2) - log(sin(x)/(cos(x) + 1) + 1)","B",0
4,1,39,0,1.513919," ","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=""maxima"")","-\log\left(\frac{2 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right) + \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 2\right)"," ",0,"-log(2*sin(x)/(cos(x) + 1) - 1) + log(sin(x)/(cos(x) + 1) + sin(x)^2/(cos(x) + 1)^2 + 2)","B",0
5,1,63,0,11.092254," ","integrate((-1+4*cos(x)+5*cos(x)^2)/(-1-4*cos(x)-3*cos(x)^2+4*cos(x)^3),x, algorithm=""maxima"")","-\arctan\left(\sin\left(3 \, x\right) + \frac{1}{2} \, \sin\left(2 \, x\right) + \sin\left(x\right), \cos\left(3 \, x\right) + \frac{1}{2} \, \cos\left(2 \, x\right) + \cos\left(x\right) - \frac{1}{2}\right) + \arctan\left(\sin\left(3 \, x\right) - 2 \, \sin\left(2 \, x\right) - \sin\left(x\right), \cos\left(3 \, x\right) - 2 \, \cos\left(2 \, x\right) - \cos\left(x\right) - 2\right)"," ",0,"-arctan2(sin(3*x) + 1/2*sin(2*x) + sin(x), cos(3*x) + 1/2*cos(2*x) + cos(x) - 1/2) + arctan2(sin(3*x) - 2*sin(2*x) - sin(x), cos(3*x) - 2*cos(2*x) - cos(x) - 2)","A",0
6,1,63,0,11.018554," ","integrate((-5+2*cos(x)+7*cos(x)^2)/(-1+2*cos(x)-9*cos(x)^2+4*cos(x)^3),x, algorithm=""maxima"")","-\arctan\left(\sin\left(3 \, x\right) - \frac{1}{2} \, \sin\left(2 \, x\right) + 2 \, \sin\left(x\right), \cos\left(3 \, x\right) - \frac{1}{2} \, \cos\left(2 \, x\right) + 2 \, \cos\left(x\right) - \frac{1}{2}\right) + \arctan\left(\sin\left(3 \, x\right) - 4 \, \sin\left(2 \, x\right) + \sin\left(x\right), \cos\left(3 \, x\right) - 4 \, \cos\left(2 \, x\right) + \cos\left(x\right) - 2\right)"," ",0,"-arctan2(sin(3*x) - 1/2*sin(2*x) + 2*sin(x), cos(3*x) - 1/2*cos(2*x) + 2*cos(x) - 1/2) + arctan2(sin(3*x) - 4*sin(2*x) + sin(x), cos(3*x) - 4*cos(2*x) + cos(x) - 2)","B",0
7,1,15,0,1.135394," ","integrate(3/(5+4*sin(x)),x, algorithm=""maxima"")","2 \, \arctan\left(\frac{5 \, \sin\left(x\right)}{3 \, {\left(\cos\left(x\right) + 1\right)}} + \frac{4}{3}\right)"," ",0,"2*arctan(5/3*sin(x)/(cos(x) + 1) + 4/3)","A",0
8,1,12,0,1.434440," ","integrate(2/(1+cos(x)^2),x, algorithm=""maxima"")","\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \tan\left(x\right)\right)"," ",0,"sqrt(2)*arctan(1/2*sqrt(2)*tan(x))","A",0
9,-2,0,0,0.000000," ","integrate(1/(p+q*cos(x)+r*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(r^2+q^2-p^2>0)', see `assume?` for more details)Is r^2+q^2-p^2 positive or negative?","F(-2)",0
