1,1,18,16,0.265690,"\text{Not used}","int(-3/(4*cos(x) - 5),x)","x+2\,\mathrm{atan}\left(3\,\mathrm{tan}\left(\frac{x}{2}\right)\right)-2\,\mathrm{atan}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)","Not used",1,"x + 2*atan(3*tan(x/2)) - 2*atan(tan(x/2))","B"
2,1,12,19,0.306654,"\text{Not used}","int((cos(x) + 2*sin(x) + 1)/(2*sin(x) - 2*cos(x)*sin(x) + cos(x)^2 + 3),x)","\mathrm{atan}\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+\mathrm{tan}\left(\frac{x}{2}\right)\right)","Not used",1,"atan(tan(x/2) + tan(x/2)^2)","B"
3,1,32,19,0.848266,"\text{Not used}","int((cos(x) + 5*sin(x) + 2)/(4*cos(x) - 2*sin(x) + cos(x)*sin(x) - 2*sin(x)^2),x)","-2\,\mathrm{atanh}\left(\frac{\frac{252\,\mathrm{tan}\left(\frac{x}{2}\right)}{19}+\frac{1260}{19}}{19\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+5\,\mathrm{tan}\left(\frac{x}{2}\right)-32}+\frac{37}{19}\right)","Not used",1,"-2*atanh(((252*tan(x/2))/19 + 1260/19)/(5*tan(x/2) + 19*tan(x/2)^2 - 32) + 37/19)","B"
4,1,23,19,0.548791,"\text{Not used}","int((7*cos(x) + 2*sin(x) + 3)/(4*cos(x) - 5*sin(x) - cos(x)*sin(x) + 3*cos(x)^2 + 1),x)","\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+\mathrm{tan}\left(\frac{x}{2}\right)+2\right)-\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\frac{1}{2}\right)","Not used",1,"log(tan(x/2) + tan(x/2)^2 + 2) - log(tan(x/2) - 1/2)","B"
5,1,27,43,0.304153,"\text{Not used}","int(-(4*cos(x) + 5*cos(x)^2 - 1)/(4*cos(x) + 3*cos(x)^2 - 4*cos(x)^3 + 1),x)","x-2\,\mathrm{atan}\left(2\,\mathrm{tan}\left(\frac{x}{2}\right)-{\mathrm{tan}\left(\frac{x}{2}\right)}^3\right)-2\,\mathrm{atan}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)","Not used",1,"x - 2*atan(2*tan(x/2) - tan(x/2)^3) - 2*atan(tan(x/2))","B"
6,1,25,25,0.303075,"\text{Not used}","int((2*cos(x) + 7*cos(x)^2 - 5)/(2*cos(x) - 9*cos(x)^2 + 4*cos(x)^3 - 1),x)","x-2\,\mathrm{atan}\left(\mathrm{tan}\left(\frac{x}{2}\right)-2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\right)-2\,\mathrm{atan}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)","Not used",1,"x - 2*atan(tan(x/2) - 2*tan(x/2)^3) - 2*atan(tan(x/2))","B"
7,1,20,14,0.221340,"\text{Not used}","int(3/(4*sin(x) + 5),x)","x+2\,\mathrm{atan}\left(\frac{5\,\mathrm{tan}\left(\frac{x}{2}\right)}{3}+\frac{4}{3}\right)-2\,\mathrm{atan}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)","Not used",1,"x + 2*atan((5*tan(x/2))/3 + 4/3) - 2*atan(tan(x/2))","B"
8,1,24,34,0.209127,"\text{Not used}","int(2/(cos(x)^2 + 1),x)","\sqrt{2}\,\left(x-\mathrm{atan}\left(\mathrm{tan}\left(x\right)\right)\right)+\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)}{2}\right)","Not used",1,"2^(1/2)*(x - atan(tan(x))) + 2^(1/2)*atan((2^(1/2)*tan(x))/2)","B"
9,1,68,54,0.319431,"\text{Not used}","int(1/(p + q*cos(x) + r*sin(x)),x)","\left\{\begin{array}{cl} \frac{\ln\left(q+r\,\mathrm{tan}\left(\frac{x}{2}\right)\right)}{r} & \text{\ if\ \ }p=q\\ \frac{2\,\mathrm{atan}\left(\frac{r+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(p-q\right)}{\sqrt{p^2-q^2-r^2}}\right)}{\sqrt{p^2-q^2-r^2}} & \text{\ if\ \ }p\neq q \end{array}\right.","Not used",1,"piecewise(p == q, log(q + r*tan(x/2))/r, p ~= q, (2*atan((r + tan(x/2)*(p - q))/(p^2 - q^2 - r^2)^(1/2)))/(p^2 - q^2 - r^2)^(1/2))","B"