1,1,9581948,484,1.069000," ","int(cot(e*x+d)^5/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2,1,9581713,339,0.952000," ","int(cot(e*x+d)^3/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
3,1,9339148,261,0.916000," ","int(cot(e*x+d)/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
4,1,49657,308,5.491000," ","int(tan(e*x+d)/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
5,1,1829775,442,26.219000," ","int(tan(e*x+d)^3/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
6,1,17768513,875,1.076000," ","int(cot(e*x+d)^5*(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
7,1,17768080,668,0.967000," ","int(cot(e*x+d)^3*(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
8,1,21948746,541,0.920000," ","int(cot(e*x+d)*(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
9,1,248562,513,21.837000," ","int((a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2)*tan(e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","C"
10,1,4238722,620,108.733000," ","int((a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2)*tan(e*x+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
11,1,13068424,1096,1.085000," ","int(cot(e*x+d)^7/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
12,1,13067692,794,0.934000," ","int(cot(e*x+d)^5/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
13,1,13067316,629,0.873000," ","int(cot(e*x+d)^3/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
14,1,13067191,580,0.862000," ","int(cot(e*x+d)/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
15,1,21263243,684,86.888000," ","int(tan(e*x+d)/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
16,-1,0,923,180.000000," ","int(tan(e*x+d)^3/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(3/2),x)","\int \frac{\tan^{3}\left(e x +d \right)}{\left(a +b \cot \left(e x +d \right)+c \left(\cot^{2}\left(e x +d \right)\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(tan(e*x+d)^3/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(3/2),x)","F"
17,1,240,158,0.745000," ","int(cot(e*x+d)^5/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x)","-\frac{\sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}}{2 c e}+\frac{b \ln \left(\frac{c \left(\cot^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\right)}{4 e \,c^{\frac{3}{2}}}+\frac{\ln \left(\frac{c \left(\cot^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\right)}{2 e \sqrt{c}}+\frac{\ln \left(\frac{2 a -2 b +2 c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+2 \sqrt{a -b +c}\, \sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}}{\cot^{2}\left(e x +d \right)+1}\right)}{2 e \sqrt{a -b +c}}"," ",0,"-1/2*(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)/c/e+1/4/e*b/c^(3/2)*ln((c*cot(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2))+1/2/e*ln((c*cot(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2))/c^(1/2)+1/2/e/(a-b+c)^(1/2)*ln((2*a-2*b+2*c+(b-2*c)*(cot(e*x+d)^2+1)+2*(a-b+c)^(1/2)*((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2))/(cot(e*x+d)^2+1))","A"
18,1,155,121,0.594000," ","int(cot(e*x+d)^3/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x)","-\frac{\ln \left(\frac{c \left(\cot^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\right)}{2 e \sqrt{c}}-\frac{\ln \left(\frac{2 a -2 b +2 c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+2 \sqrt{a -b +c}\, \sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}}{\cot^{2}\left(e x +d \right)+1}\right)}{2 e \sqrt{a -b +c}}"," ",0,"-1/2/e*ln((c*cot(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2))/c^(1/2)-1/2/e/(a-b+c)^(1/2)*ln((2*a-2*b+2*c+(b-2*c)*(cot(e*x+d)^2+1)+2*(a-b+c)^(1/2)*((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2))/(cot(e*x+d)^2+1))","A"
19,1,102,69,0.661000," ","int(cot(e*x+d)/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x)","\frac{\ln \left(\frac{2 a -2 b +2 c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+2 \sqrt{a -b +c}\, \sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}}{\cot^{2}\left(e x +d \right)+1}\right)}{2 e \sqrt{a -b +c}}"," ",0,"1/2/e/(a-b+c)^(1/2)*ln((2*a-2*b+2*c+(b-2*c)*(cot(e*x+d)^2+1)+2*(a-b+c)^(1/2)*((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2))/(cot(e*x+d)^2+1))","A"
20,0,0,122,2.354000," ","int(tan(e*x+d)/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x)","\int \frac{\tan \left(e x +d \right)}{\sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}}\, dx"," ",0,"int(tan(e*x+d)/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x)","F"
21,0,0,215,2.378000," ","int(tan(e*x+d)^3/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x)","\int \frac{\tan^{3}\left(e x +d \right)}{\sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}}\, dx"," ",0,"int(tan(e*x+d)^3/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x)","F"
22,1,684,242,0.500000," ","int(cot(e*x+d)^5*(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x)","-\frac{\left(a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)\right)^{\frac{3}{2}}}{6 c e}+\frac{b \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\, \left(\cot^{2}\left(e x +d \right)\right)}{8 e c}+\frac{b^{2} \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}}{16 e \,c^{2}}+\frac{b \ln \left(\frac{c \left(\cot^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\right) a}{8 e \,c^{\frac{3}{2}}}-\frac{b^{3} \ln \left(\frac{c \left(\cot^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\right)}{32 e \,c^{\frac{5}{2}}}+\frac{\sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\, \left(\cot^{2}\left(e x +d \right)\right)}{4 e}+\frac{\sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\, b}{8 e c}+\frac{\ln \left(\frac{c \left(\cot^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\right) a}{4 e \sqrt{c}}-\frac{\ln \left(\frac{c \left(\cot^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\right) b^{2}}{16 e \,c^{\frac{3}{2}}}-\frac{\sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}}{2 e}-\frac{\ln \left(\frac{\frac{b}{2}-c +\left(\cot^{2}\left(e x +d \right)+1\right) c}{\sqrt{c}}+\sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}\right) b}{4 e \sqrt{c}}+\frac{\ln \left(\frac{\frac{b}{2}-c +\left(\cot^{2}\left(e x +d \right)+1\right) c}{\sqrt{c}}+\sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}\right) \sqrt{c}}{2 e}+\frac{\sqrt{a -b +c}\, \ln \left(\frac{2 a -2 b +2 c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+2 \sqrt{a -b +c}\, \sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}}{\cot^{2}\left(e x +d \right)+1}\right)}{2 e}"," ",0,"-1/6*(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(3/2)/c/e+1/8/e*b/c*(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)*cot(e*x+d)^2+1/16/e*b^2/c^2*(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)+1/8/e*b/c^(3/2)*ln((c*cot(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2))*a-1/32/e*b^3/c^(5/2)*ln((c*cot(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2))+1/4/e*(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)*cot(e*x+d)^2+1/8/e/c*(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)*b+1/4/e/c^(1/2)*ln((c*cot(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2))*a-1/16/e/c^(3/2)*ln((c*cot(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2))*b^2-1/2/e*((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2)-1/4/e*ln((1/2*b-c+(cot(e*x+d)^2+1)*c)/c^(1/2)+((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2))/c^(1/2)*b+1/2/e*ln((1/2*b-c+(cot(e*x+d)^2+1)*c)/c^(1/2)+((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2))*c^(1/2)+1/2/e*(a-b+c)^(1/2)*ln((2*a-2*b+2*c+(b-2*c)*(cot(e*x+d)^2+1)+2*(a-b+c)^(1/2)*((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2))/(cot(e*x+d)^2+1))","B"
23,1,467,185,0.498000," ","int(cot(e*x+d)^3*(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x)","-\frac{\sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\, \left(\cot^{2}\left(e x +d \right)\right)}{4 e}-\frac{\sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\, b}{8 e c}-\frac{\ln \left(\frac{c \left(\cot^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\right) a}{4 e \sqrt{c}}+\frac{\ln \left(\frac{c \left(\cot^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\right) b^{2}}{16 e \,c^{\frac{3}{2}}}+\frac{\sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}}{2 e}+\frac{\ln \left(\frac{\frac{b}{2}-c +\left(\cot^{2}\left(e x +d \right)+1\right) c}{\sqrt{c}}+\sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}\right) b}{4 e \sqrt{c}}-\frac{\ln \left(\frac{\frac{b}{2}-c +\left(\cot^{2}\left(e x +d \right)+1\right) c}{\sqrt{c}}+\sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}\right) \sqrt{c}}{2 e}-\frac{\sqrt{a -b +c}\, \ln \left(\frac{2 a -2 b +2 c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+2 \sqrt{a -b +c}\, \sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}}{\cot^{2}\left(e x +d \right)+1}\right)}{2 e}"," ",0,"-1/4/e*(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)*cot(e*x+d)^2-1/8/e/c*(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)*b-1/4/e/c^(1/2)*ln((c*cot(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2))*a+1/16/e/c^(3/2)*ln((c*cot(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2))*b^2+1/2/e*((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2)+1/4/e*ln((1/2*b-c+(cot(e*x+d)^2+1)*c)/c^(1/2)+((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2))/c^(1/2)*b-1/2/e*ln((1/2*b-c+(cot(e*x+d)^2+1)*c)/c^(1/2)+((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2))*c^(1/2)-1/2/e*(a-b+c)^(1/2)*ln((2*a-2*b+2*c+(b-2*c)*(cot(e*x+d)^2+1)+2*(a-b+c)^(1/2)*((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2))/(cot(e*x+d)^2+1))","B"
24,1,289,155,0.534000," ","int(cot(e*x+d)*(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x)","-\frac{\sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}}{2 e}-\frac{\ln \left(\frac{\frac{b}{2}-c +\left(\cot^{2}\left(e x +d \right)+1\right) c}{\sqrt{c}}+\sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}\right) b}{4 e \sqrt{c}}+\frac{\ln \left(\frac{\frac{b}{2}-c +\left(\cot^{2}\left(e x +d \right)+1\right) c}{\sqrt{c}}+\sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}\right) \sqrt{c}}{2 e}+\frac{\sqrt{a -b +c}\, \ln \left(\frac{2 a -2 b +2 c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+2 \sqrt{a -b +c}\, \sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}}{\cot^{2}\left(e x +d \right)+1}\right)}{2 e}"," ",0,"-1/2/e*((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2)-1/4/e*ln((1/2*b-c+(cot(e*x+d)^2+1)*c)/c^(1/2)+((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2))/c^(1/2)*b+1/2/e*ln((1/2*b-c+(cot(e*x+d)^2+1)*c)/c^(1/2)+((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2))*c^(1/2)+1/2/e*(a-b+c)^(1/2)*ln((2*a-2*b+2*c+(b-2*c)*(cot(e*x+d)^2+1)+2*(a-b+c)^(1/2)*((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2))/(cot(e*x+d)^2+1))","A"
25,0,0,173,1.988000," ","int((a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)*tan(e*x+d),x)","\int \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\, \tan \left(e x +d \right)\, dx"," ",0,"int((a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)*tan(e*x+d),x)","F"
26,0,0,371,2.167000," ","int((a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)*tan(e*x+d)^3,x)","\int \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\, \left(\tan^{3}\left(e x +d \right)\right)\, dx"," ",0,"int((a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)*tan(e*x+d)^3,x)","F"
27,1,828,215,0.707000," ","int(cot(e*x+d)^7/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(3/2),x)","\frac{\cot^{2}\left(e x +d \right)}{2 e c \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}}-\frac{b}{4 e \,c^{2} \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}}-\frac{b^{2} \left(\cot^{2}\left(e x +d \right)\right)}{2 e c \left(4 c a -b^{2}\right) \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}}-\frac{b^{3}}{4 e \,c^{2} \left(4 c a -b^{2}\right) \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}}-\frac{\ln \left(\frac{c \left(\cot^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\right)}{2 e \,c^{\frac{3}{2}}}-\frac{b \left(\cot^{2}\left(e x +d \right)\right)}{e \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}-\frac{2 a}{e \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}-\frac{2 c \left(\cot^{2}\left(e x +d \right)\right)}{e \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}-\frac{b}{e \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}+\frac{2 c \sqrt{\left(\cot^{2}\left(e x +d \right)+\frac{b +\sqrt{-4 c a +b^{2}}}{2 c}\right)^{2} c -\sqrt{-4 c a +b^{2}}\, \left(\cot^{2}\left(e x +d \right)+\frac{b +\sqrt{-4 c a +b^{2}}}{2 c}\right)}}{e \left(b -2 c +\sqrt{-4 c a +b^{2}}\right) \left(-4 c a +b^{2}\right) \left(\cot^{2}\left(e x +d \right)+\frac{\sqrt{-4 c a +b^{2}}}{2 c}+\frac{b}{2 c}\right)}-\frac{2 c \sqrt{\left(\cot^{2}\left(e x +d \right)-\frac{-b +\sqrt{-4 c a +b^{2}}}{2 c}\right)^{2} c +\sqrt{-4 c a +b^{2}}\, \left(\cot^{2}\left(e x +d \right)-\frac{-b +\sqrt{-4 c a +b^{2}}}{2 c}\right)}}{e \left(\sqrt{-4 c a +b^{2}}-b +2 c \right) \left(-4 c a +b^{2}\right) \left(\cot^{2}\left(e x +d \right)-\frac{\sqrt{-4 c a +b^{2}}}{2 c}+\frac{b}{2 c}\right)}+\frac{2 c \ln \left(\frac{2 a -2 b +2 c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+2 \sqrt{a -b +c}\, \sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}}{\cot^{2}\left(e x +d \right)+1}\right)}{e \left(\sqrt{-4 c a +b^{2}}-b +2 c \right) \left(b -2 c +\sqrt{-4 c a +b^{2}}\right) \sqrt{a -b +c}}"," ",0,"1/2/e*cot(e*x+d)^2/c/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)-1/4/e*b/c^2/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)-1/2/e*b^2/c/(4*a*c-b^2)/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)*cot(e*x+d)^2-1/4/e*b^3/c^2/(4*a*c-b^2)/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)-1/2/e/c^(3/2)*ln((c*cot(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2))-1/e/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)/(4*a*c-b^2)*b*cot(e*x+d)^2-2/e/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)/(4*a*c-b^2)*a-2/e/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)/(4*a*c-b^2)*c*cot(e*x+d)^2-1/e/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)/(4*a*c-b^2)*b+2/e*c/(b-2*c+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)/(cot(e*x+d)^2+1/2/c*(-4*a*c+b^2)^(1/2)+1/2*b/c)*((cot(e*x+d)^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*c-(-4*a*c+b^2)^(1/2)*(cot(e*x+d)^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c))^(1/2)-2/e*c/((-4*a*c+b^2)^(1/2)-b+2*c)/(-4*a*c+b^2)/(cot(e*x+d)^2-1/2/c*(-4*a*c+b^2)^(1/2)+1/2*b/c)*((cot(e*x+d)^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*c+(-4*a*c+b^2)^(1/2)*(cot(e*x+d)^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c))^(1/2)+2/e*c/((-4*a*c+b^2)^(1/2)-b+2*c)/(b-2*c+(-4*a*c+b^2)^(1/2))/(a-b+c)^(1/2)*ln((2*a-2*b+2*c+(b-2*c)*(cot(e*x+d)^2+1)+2*(a-b+c)^(1/2)*((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2))/(cot(e*x+d)^2+1))","B"
28,1,599,149,0.560000," ","int(cot(e*x+d)^5/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(3/2),x)","\frac{b \left(\cot^{2}\left(e x +d \right)\right)}{e \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}+\frac{2 a}{e \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}+\frac{2 c \left(\cot^{2}\left(e x +d \right)\right)}{e \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}+\frac{b}{e \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}-\frac{2 c \sqrt{\left(\cot^{2}\left(e x +d \right)+\frac{b +\sqrt{-4 c a +b^{2}}}{2 c}\right)^{2} c -\sqrt{-4 c a +b^{2}}\, \left(\cot^{2}\left(e x +d \right)+\frac{b +\sqrt{-4 c a +b^{2}}}{2 c}\right)}}{e \left(b -2 c +\sqrt{-4 c a +b^{2}}\right) \left(-4 c a +b^{2}\right) \left(\cot^{2}\left(e x +d \right)+\frac{\sqrt{-4 c a +b^{2}}}{2 c}+\frac{b}{2 c}\right)}+\frac{2 c \sqrt{\left(\cot^{2}\left(e x +d \right)-\frac{-b +\sqrt{-4 c a +b^{2}}}{2 c}\right)^{2} c +\sqrt{-4 c a +b^{2}}\, \left(\cot^{2}\left(e x +d \right)-\frac{-b +\sqrt{-4 c a +b^{2}}}{2 c}\right)}}{e \left(\sqrt{-4 c a +b^{2}}-b +2 c \right) \left(-4 c a +b^{2}\right) \left(\cot^{2}\left(e x +d \right)-\frac{\sqrt{-4 c a +b^{2}}}{2 c}+\frac{b}{2 c}\right)}-\frac{2 c \ln \left(\frac{2 a -2 b +2 c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+2 \sqrt{a -b +c}\, \sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}}{\cot^{2}\left(e x +d \right)+1}\right)}{e \left(\sqrt{-4 c a +b^{2}}-b +2 c \right) \left(b -2 c +\sqrt{-4 c a +b^{2}}\right) \sqrt{a -b +c}}"," ",0,"1/e/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)/(4*a*c-b^2)*b*cot(e*x+d)^2+2/e/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)/(4*a*c-b^2)*a+2/e/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)/(4*a*c-b^2)*c*cot(e*x+d)^2+1/e/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)/(4*a*c-b^2)*b-2/e*c/(b-2*c+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)/(cot(e*x+d)^2+1/2/c*(-4*a*c+b^2)^(1/2)+1/2*b/c)*((cot(e*x+d)^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*c-(-4*a*c+b^2)^(1/2)*(cot(e*x+d)^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c))^(1/2)+2/e*c/((-4*a*c+b^2)^(1/2)-b+2*c)/(-4*a*c+b^2)/(cot(e*x+d)^2-1/2/c*(-4*a*c+b^2)^(1/2)+1/2*b/c)*((cot(e*x+d)^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*c+(-4*a*c+b^2)^(1/2)*(cot(e*x+d)^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c))^(1/2)-2/e*c/((-4*a*c+b^2)^(1/2)-b+2*c)/(b-2*c+(-4*a*c+b^2)^(1/2))/(a-b+c)^(1/2)*ln((2*a-2*b+2*c+(b-2*c)*(cot(e*x+d)^2+1)+2*(a-b+c)^(1/2)*((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2))/(cot(e*x+d)^2+1))","B"
29,1,509,141,0.564000," ","int(cot(e*x+d)^3/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(3/2),x)","-\frac{2 c \left(\cot^{2}\left(e x +d \right)\right)}{e \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}-\frac{b}{e \sqrt{a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}+\frac{2 c \sqrt{\left(\cot^{2}\left(e x +d \right)+\frac{b +\sqrt{-4 c a +b^{2}}}{2 c}\right)^{2} c -\sqrt{-4 c a +b^{2}}\, \left(\cot^{2}\left(e x +d \right)+\frac{b +\sqrt{-4 c a +b^{2}}}{2 c}\right)}}{e \left(b -2 c +\sqrt{-4 c a +b^{2}}\right) \left(-4 c a +b^{2}\right) \left(\cot^{2}\left(e x +d \right)+\frac{\sqrt{-4 c a +b^{2}}}{2 c}+\frac{b}{2 c}\right)}-\frac{2 c \sqrt{\left(\cot^{2}\left(e x +d \right)-\frac{-b +\sqrt{-4 c a +b^{2}}}{2 c}\right)^{2} c +\sqrt{-4 c a +b^{2}}\, \left(\cot^{2}\left(e x +d \right)-\frac{-b +\sqrt{-4 c a +b^{2}}}{2 c}\right)}}{e \left(\sqrt{-4 c a +b^{2}}-b +2 c \right) \left(-4 c a +b^{2}\right) \left(\cot^{2}\left(e x +d \right)-\frac{\sqrt{-4 c a +b^{2}}}{2 c}+\frac{b}{2 c}\right)}+\frac{2 c \ln \left(\frac{2 a -2 b +2 c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+2 \sqrt{a -b +c}\, \sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}}{\cot^{2}\left(e x +d \right)+1}\right)}{e \left(\sqrt{-4 c a +b^{2}}-b +2 c \right) \left(b -2 c +\sqrt{-4 c a +b^{2}}\right) \sqrt{a -b +c}}"," ",0,"-2/e/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)/(4*a*c-b^2)*c*cot(e*x+d)^2-1/e/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)/(4*a*c-b^2)*b+2/e*c/(b-2*c+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)/(cot(e*x+d)^2+1/2/c*(-4*a*c+b^2)^(1/2)+1/2*b/c)*((cot(e*x+d)^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*c-(-4*a*c+b^2)^(1/2)*(cot(e*x+d)^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c))^(1/2)-2/e*c/((-4*a*c+b^2)^(1/2)-b+2*c)/(-4*a*c+b^2)/(cot(e*x+d)^2-1/2/c*(-4*a*c+b^2)^(1/2)+1/2*b/c)*((cot(e*x+d)^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*c+(-4*a*c+b^2)^(1/2)*(cot(e*x+d)^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c))^(1/2)+2/e*c/((-4*a*c+b^2)^(1/2)-b+2*c)/(b-2*c+(-4*a*c+b^2)^(1/2))/(a-b+c)^(1/2)*ln((2*a-2*b+2*c+(b-2*c)*(cot(e*x+d)^2+1)+2*(a-b+c)^(1/2)*((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2))/(cot(e*x+d)^2+1))","B"
30,1,417,145,0.638000," ","int(cot(e*x+d)/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(3/2),x)","-\frac{2 c \sqrt{\left(\cot^{2}\left(e x +d \right)+\frac{b +\sqrt{-4 c a +b^{2}}}{2 c}\right)^{2} c -\sqrt{-4 c a +b^{2}}\, \left(\cot^{2}\left(e x +d \right)+\frac{b +\sqrt{-4 c a +b^{2}}}{2 c}\right)}}{e \left(b -2 c +\sqrt{-4 c a +b^{2}}\right) \left(-4 c a +b^{2}\right) \left(\cot^{2}\left(e x +d \right)+\frac{\sqrt{-4 c a +b^{2}}}{2 c}+\frac{b}{2 c}\right)}+\frac{2 c \sqrt{\left(\cot^{2}\left(e x +d \right)-\frac{-b +\sqrt{-4 c a +b^{2}}}{2 c}\right)^{2} c +\sqrt{-4 c a +b^{2}}\, \left(\cot^{2}\left(e x +d \right)-\frac{-b +\sqrt{-4 c a +b^{2}}}{2 c}\right)}}{e \left(\sqrt{-4 c a +b^{2}}-b +2 c \right) \left(-4 c a +b^{2}\right) \left(\cot^{2}\left(e x +d \right)-\frac{\sqrt{-4 c a +b^{2}}}{2 c}+\frac{b}{2 c}\right)}-\frac{2 c \ln \left(\frac{2 a -2 b +2 c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+2 \sqrt{a -b +c}\, \sqrt{\left(\cot^{2}\left(e x +d \right)+1\right)^{2} c +\left(b -2 c \right) \left(\cot^{2}\left(e x +d \right)+1\right)+a -b +c}}{\cot^{2}\left(e x +d \right)+1}\right)}{e \left(\sqrt{-4 c a +b^{2}}-b +2 c \right) \left(b -2 c +\sqrt{-4 c a +b^{2}}\right) \sqrt{a -b +c}}"," ",0,"-2/e*c/(b-2*c+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)/(cot(e*x+d)^2+1/2/c*(-4*a*c+b^2)^(1/2)+1/2*b/c)*((cot(e*x+d)^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*c-(-4*a*c+b^2)^(1/2)*(cot(e*x+d)^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c))^(1/2)+2/e*c/((-4*a*c+b^2)^(1/2)-b+2*c)/(-4*a*c+b^2)/(cot(e*x+d)^2-1/2/c*(-4*a*c+b^2)^(1/2)+1/2*b/c)*((cot(e*x+d)^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*c+(-4*a*c+b^2)^(1/2)*(cot(e*x+d)^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c))^(1/2)-2/e*c/((-4*a*c+b^2)^(1/2)-b+2*c)/(b-2*c+(-4*a*c+b^2)^(1/2))/(a-b+c)^(1/2)*ln((2*a-2*b+2*c+(b-2*c)*(cot(e*x+d)^2+1)+2*(a-b+c)^(1/2)*((cot(e*x+d)^2+1)^2*c+(b-2*c)*(cot(e*x+d)^2+1)+a-b+c)^(1/2))/(cot(e*x+d)^2+1))","B"
31,0,0,258,2.175000," ","int(tan(e*x+d)/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(3/2),x)","\int \frac{\tan \left(e x +d \right)}{\left(a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(tan(e*x+d)/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(3/2),x)","F"
32,0,0,439,2.169000," ","int(tan(e*x+d)^3/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(3/2),x)","\int \frac{\tan^{3}\left(e x +d \right)}{\left(a +b \left(\cot^{2}\left(e x +d \right)\right)+c \left(\cot^{4}\left(e x +d \right)\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(tan(e*x+d)^3/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(3/2),x)","F"