1,1,17767396,874,2.127000," ","int((a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(1/2)*tan(e*x+d)^5,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2,1,17247437,795,0.971000," ","int((a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(1/2)*tan(e*x+d)^4,x)","\text{output too large to display}"," ",0,"result too large to display","B"
3,1,17766851,669,0.997000," ","int((a+b*tan(e*x+d)+c*tan(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"
4,1,17246975,610,0.946000," ","int((a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(1/2)*tan(e*x+d)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
5,1,17766655,540,0.778000," ","int((a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(1/2)*tan(e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
6,1,17246812,516,0.831000," ","int((a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
7,1,53065,514,9.102000," ","int(cot(e*x+d)*(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
8,1,1165398,552,27.166000," ","int(cot(e*x+d)^2*(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
9,1,2844525,619,152.533000," ","int(cot(e*x+d)^3*(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
10,1,9581348,485,0.844000," ","int(tan(e*x+d)^5/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
11,1,7491876,436,0.823000," ","int(tan(e*x+d)^4/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
12,1,9581103,338,0.813000," ","int(tan(e*x+d)^3/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
13,1,7491751,311,0.790000," ","int(tan(e*x+d)^2/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
14,1,9338543,261,0.834000," ","int(tan(e*x+d)/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
15,1,7300213,265,0.786000," ","int(1/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
16,1,28519,309,4.291000," ","int(cot(e*x+d)/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
17,1,636822,350,21.380000," ","int(cot(e*x+d)^2/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
18,1,2045168,441,52.267000," ","int(cot(e*x+d)^3/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
19,1,13067521,1097,0.924000," ","int(tan(e*x+d)^7/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
20,1,13066795,793,0.890000," ","int(tan(e*x+d)^5/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
21,1,13066487,629,0.858000," ","int(tan(e*x+d)^3/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
22,1,11847956,583,0.827000," ","int(tan(e*x+d)^2/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
23,1,13066297,580,0.805000," ","int(tan(e*x+d)/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
24,1,15830985,685,168.926000," ","int(cot(e*x+d)/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
25,-1,0,760,180.000000," ","int(cot(e*x+d)^2/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x)","\int \frac{\cot^{2}\left(e x +d \right)}{\left(a +b \tan \left(e x +d \right)+c \left(\tan^{2}\left(e x +d \right)\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(cot(e*x+d)^2/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x)","F"
26,-1,0,922,180.000000," ","int(cot(e*x+d)^3/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x)","\int \frac{\cot^{3}\left(e x +d \right)}{\left(a +b \tan \left(e x +d \right)+c \left(\tan^{2}\left(e x +d \right)\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(cot(e*x+d)^3/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x)","F"
27,1,684,242,0.674000," ","int((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*tan(e*x+d)^5,x)","\frac{\left(a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)\right)^{\frac{3}{2}}}{6 c e}-\frac{b \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(\tan^{2}\left(e x +d \right)\right)}{8 e c}-\frac{b^{2} \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}{16 e \,c^{2}}-\frac{b \ln \left(\frac{c \left(\tan^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\right) a}{8 e \,c^{\frac{3}{2}}}+\frac{b^{3} \ln \left(\frac{c \left(\tan^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\right)}{32 e \,c^{\frac{5}{2}}}-\frac{\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(\tan^{2}\left(e x +d \right)\right)}{4 e}-\frac{\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, b}{8 e c}-\frac{\ln \left(\frac{c \left(\tan^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\right) a}{4 e \sqrt{c}}+\frac{\ln \left(\frac{c \left(\tan^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\right) b^{2}}{16 e \,c^{\frac{3}{2}}}+\frac{\sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\right)+a -b +c}}{2 e}+\frac{\ln \left(\frac{\frac{b}{2}-c +\left(1+\tan^{2}\left(e x +d \right)\right) c}{\sqrt{c}}+\sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\right)+a -b +c}\right) b}{4 e \sqrt{c}}-\frac{\ln \left(\frac{\frac{b}{2}-c +\left(1+\tan^{2}\left(e x +d \right)\right) c}{\sqrt{c}}+\sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\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(1+\tan^{2}\left(e x +d \right)\right)+2 \sqrt{a -b +c}\, \sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\right)+a -b +c}}{1+\tan^{2}\left(e x +d \right)}\right)}{2 e}"," ",0,"1/6*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2)/c/e-1/8/e*b/c*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*tan(e*x+d)^2-1/16/e*b^2/c^2*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)-1/8/e*b/c^(3/2)*ln((c*tan(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2))*a+1/32/e*b^3/c^(5/2)*ln((c*tan(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2))-1/4/e*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*tan(e*x+d)^2-1/8/e/c*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*b-1/4/e/c^(1/2)*ln((c*tan(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2))*a+1/16/e/c^(3/2)*ln((c*tan(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2))*b^2+1/2/e*((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+a-b+c)^(1/2)+1/4/e*ln((1/2*b-c+(1+tan(e*x+d)^2)*c)/c^(1/2)+((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+a-b+c)^(1/2))/c^(1/2)*b-1/2/e*ln((1/2*b-c+(1+tan(e*x+d)^2)*c)/c^(1/2)+((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+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)*(1+tan(e*x+d)^2)+2*(a-b+c)^(1/2)*((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+a-b+c)^(1/2))/(1+tan(e*x+d)^2))","B"
28,1,467,185,0.435000," ","int((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*tan(e*x+d)^3,x)","\frac{\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(\tan^{2}\left(e x +d \right)\right)}{4 e}+\frac{\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, b}{8 e c}+\frac{\ln \left(\frac{c \left(\tan^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\right) a}{4 e \sqrt{c}}-\frac{\ln \left(\frac{c \left(\tan^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\right) b^{2}}{16 e \,c^{\frac{3}{2}}}-\frac{\sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\right)+a -b +c}}{2 e}-\frac{\ln \left(\frac{\frac{b}{2}-c +\left(1+\tan^{2}\left(e x +d \right)\right) c}{\sqrt{c}}+\sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\right)+a -b +c}\right) b}{4 e \sqrt{c}}+\frac{\ln \left(\frac{\frac{b}{2}-c +\left(1+\tan^{2}\left(e x +d \right)\right) c}{\sqrt{c}}+\sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\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(1+\tan^{2}\left(e x +d \right)\right)+2 \sqrt{a -b +c}\, \sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\right)+a -b +c}}{1+\tan^{2}\left(e x +d \right)}\right)}{2 e}"," ",0,"1/4/e*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*tan(e*x+d)^2+1/8/e/c*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*b+1/4/e/c^(1/2)*ln((c*tan(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2))*a-1/16/e/c^(3/2)*ln((c*tan(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2))*b^2-1/2/e*((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+a-b+c)^(1/2)-1/4/e*ln((1/2*b-c+(1+tan(e*x+d)^2)*c)/c^(1/2)+((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+a-b+c)^(1/2))/c^(1/2)*b+1/2/e*ln((1/2*b-c+(1+tan(e*x+d)^2)*c)/c^(1/2)+((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+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)*(1+tan(e*x+d)^2)+2*(a-b+c)^(1/2)*((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+a-b+c)^(1/2))/(1+tan(e*x+d)^2))","B"
29,1,289,155,0.396000," ","int((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*tan(e*x+d),x)","\frac{\sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\right)+a -b +c}}{2 e}+\frac{\ln \left(\frac{\frac{b}{2}-c +\left(1+\tan^{2}\left(e x +d \right)\right) c}{\sqrt{c}}+\sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\right)+a -b +c}\right) b}{4 e \sqrt{c}}-\frac{\ln \left(\frac{\frac{b}{2}-c +\left(1+\tan^{2}\left(e x +d \right)\right) c}{\sqrt{c}}+\sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\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(1+\tan^{2}\left(e x +d \right)\right)+2 \sqrt{a -b +c}\, \sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\right)+a -b +c}}{1+\tan^{2}\left(e x +d \right)}\right)}{2 e}"," ",0,"1/2/e*((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+a-b+c)^(1/2)+1/4/e*ln((1/2*b-c+(1+tan(e*x+d)^2)*c)/c^(1/2)+((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+a-b+c)^(1/2))/c^(1/2)*b-1/2/e*ln((1/2*b-c+(1+tan(e*x+d)^2)*c)/c^(1/2)+((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+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)*(1+tan(e*x+d)^2)+2*(a-b+c)^(1/2)*((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+a-b+c)^(1/2))/(1+tan(e*x+d)^2))","A"
30,0,0,173,1.494000," ","int(cot(e*x+d)*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","\int \cot \left(e x +d \right) \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, dx"," ",0,"int(cot(e*x+d)*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","F"
31,0,0,371,1.371000," ","int(cot(e*x+d)^3*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","\int \left(\cot^{3}\left(e x +d \right)\right) \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, dx"," ",0,"int(cot(e*x+d)^3*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","F"
32,1,1945,1286,0.417000," ","int((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*tan(e*x+d)^2,x)","\frac{\frac{\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \tan \left(e x +d \right)}{3}+\frac{a \sqrt{2}\, \sqrt{4-\frac{2 \left(-b +\sqrt{-4 c a +b^{2}}\right) \left(\tan^{2}\left(e x +d \right)\right)}{a}}\, \sqrt{4+\frac{2 \left(b +\sqrt{-4 c a +b^{2}}\right) \left(\tan^{2}\left(e x +d \right)\right)}{a}}\, \EllipticF \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, \frac{\sqrt{-4+\frac{2 b \left(b +\sqrt{-4 c a +b^{2}}\right)}{a c}}}{2}\right)}{6 \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}-\frac{b a \sqrt{2}\, \sqrt{4-\frac{2 \left(-b +\sqrt{-4 c a +b^{2}}\right) \left(\tan^{2}\left(e x +d \right)\right)}{a}}\, \sqrt{4+\frac{2 \left(b +\sqrt{-4 c a +b^{2}}\right) \left(\tan^{2}\left(e x +d \right)\right)}{a}}\, \left(\EllipticF \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, \frac{\sqrt{-4+\frac{2 b \left(b +\sqrt{-4 c a +b^{2}}\right)}{a c}}}{2}\right)-\EllipticE \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, \frac{\sqrt{-4+\frac{2 b \left(b +\sqrt{-4 c a +b^{2}}\right)}{a c}}}{2}\right)\right)}{6 \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(b +\sqrt{-4 c a +b^{2}}\right)}-\frac{\sqrt{2}\, \sqrt{4+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) b}{a}-\frac{2 \left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{4+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) b}{a}+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{a}}\, \EllipticF \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, \frac{\sqrt{-4+\frac{2 b \left(b +\sqrt{-4 c a +b^{2}}\right)}{a c}}}{2}\right) b}{4 \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}+\frac{\sqrt{2}\, \sqrt{4+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) b}{a}-\frac{2 \left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{4+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) b}{a}+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{a}}\, \EllipticF \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, \frac{\sqrt{-4+\frac{2 b \left(b +\sqrt{-4 c a +b^{2}}\right)}{a c}}}{2}\right) c}{4 \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}+\frac{c a \sqrt{2}\, \sqrt{4+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) b}{a}-\frac{2 \left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{4+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) b}{a}+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{a}}\, \EllipticF \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, \frac{\sqrt{-4+\frac{2 b \left(b +\sqrt{-4 c a +b^{2}}\right)}{a c}}}{2}\right)}{2 \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(b +\sqrt{-4 c a +b^{2}}\right)}-\frac{c a \sqrt{2}\, \sqrt{4+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) b}{a}-\frac{2 \left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{4+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) b}{a}+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{a}}\, \EllipticE \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, \frac{\sqrt{-4+\frac{2 b \left(b +\sqrt{-4 c a +b^{2}}\right)}{a c}}}{2}\right)}{2 \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(b +\sqrt{-4 c a +b^{2}}\right)}-\frac{a \sqrt{2}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}-\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}+\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \EllipticPi \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, -\frac{2 a}{-b +\sqrt{-4 c a +b^{2}}}, \frac{\sqrt{-\frac{b +\sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}\right)}{\sqrt{-\frac{b}{a}+\frac{\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}+\frac{b \sqrt{2}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}-\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}+\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \EllipticPi \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, -\frac{2 a}{-b +\sqrt{-4 c a +b^{2}}}, \frac{\sqrt{-\frac{b +\sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}\right)}{\sqrt{-\frac{b}{a}+\frac{\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}-\frac{c \sqrt{2}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}-\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}+\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \EllipticPi \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, -\frac{2 a}{-b +\sqrt{-4 c a +b^{2}}}, \frac{\sqrt{-\frac{b +\sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}\right)}{\sqrt{-\frac{b}{a}+\frac{\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}}{e}"," ",0,"1/e*(1/3*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*tan(e*x+d)+1/6*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(4-2*(-b+(-4*a*c+b^2)^(1/2))/a*tan(e*x+d)^2)^(1/2)*(4+2*(b+(-4*a*c+b^2)^(1/2))/a*tan(e*x+d)^2)^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))-1/6*b*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(4-2*(-b+(-4*a*c+b^2)^(1/2))/a*tan(e*x+d)^2)^(1/2)*(4+2*(b+(-4*a*c+b^2)^(1/2))/a*tan(e*x+d)^2)^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))-EllipticE(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2)))-1/4*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))*b+1/4*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))*c+1/2*c*a*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))-1/2*c*a*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*EllipticE(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))-a*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b-1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b+1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticPi(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),-2/(-b+(-4*a*c+b^2)^(1/2))*a,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))+b*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b-1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b+1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticPi(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),-2/(-b+(-4*a*c+b^2)^(1/2))*a,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))-c*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b-1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b+1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticPi(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),-2/(-b+(-4*a*c+b^2)^(1/2))*a,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)))","A"
33,1,1497,849,0.480000," ","int((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","\frac{\frac{\sqrt{2}\, \sqrt{4+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) b}{a}-\frac{2 \left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{4+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) b}{a}+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{a}}\, \EllipticF \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, \frac{\sqrt{-4+\frac{2 b \left(b +\sqrt{-4 c a +b^{2}}\right)}{a c}}}{2}\right) b}{4 \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}-\frac{\sqrt{2}\, \sqrt{4+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) b}{a}-\frac{2 \left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{4+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) b}{a}+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{a}}\, \EllipticF \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, \frac{\sqrt{-4+\frac{2 b \left(b +\sqrt{-4 c a +b^{2}}\right)}{a c}}}{2}\right) c}{4 \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}-\frac{c a \sqrt{2}\, \sqrt{4+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) b}{a}-\frac{2 \left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{4+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) b}{a}+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{a}}\, \EllipticF \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, \frac{\sqrt{-4+\frac{2 b \left(b +\sqrt{-4 c a +b^{2}}\right)}{a c}}}{2}\right)}{2 \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(b +\sqrt{-4 c a +b^{2}}\right)}+\frac{c a \sqrt{2}\, \sqrt{4+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) b}{a}-\frac{2 \left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{4+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) b}{a}+\frac{2 \left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{a}}\, \EllipticE \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, \frac{\sqrt{-4+\frac{2 b \left(b +\sqrt{-4 c a +b^{2}}\right)}{a c}}}{2}\right)}{2 \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(b +\sqrt{-4 c a +b^{2}}\right)}+\frac{a \sqrt{2}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}-\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}+\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \EllipticPi \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, -\frac{2 a}{-b +\sqrt{-4 c a +b^{2}}}, \frac{\sqrt{-\frac{b +\sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}\right)}{\sqrt{-\frac{b}{a}+\frac{\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}-\frac{b \sqrt{2}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}-\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}+\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \EllipticPi \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, -\frac{2 a}{-b +\sqrt{-4 c a +b^{2}}}, \frac{\sqrt{-\frac{b +\sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}\right)}{\sqrt{-\frac{b}{a}+\frac{\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}+\frac{c \sqrt{2}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}-\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}+\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \EllipticPi \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, -\frac{2 a}{-b +\sqrt{-4 c a +b^{2}}}, \frac{\sqrt{-\frac{b +\sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}\right)}{\sqrt{-\frac{b}{a}+\frac{\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}}{e}"," ",0,"1/e*(1/4*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))*b-1/4*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))*c-1/2*c*a*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))+1/2*c*a*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*EllipticE(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))+a*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b-1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b+1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticPi(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),-2/(-b+(-4*a*c+b^2)^(1/2))*a,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))-b*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b-1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b+1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticPi(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),-2/(-b+(-4*a*c+b^2)^(1/2))*a,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))+c*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b-1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b+1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticPi(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),-2/(-b+(-4*a*c+b^2)^(1/2))*a,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)))","A"
34,0,0,879,1.374000," ","int(cot(e*x+d)^2*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","\int \left(\cot^{2}\left(e x +d \right)\right) \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, dx"," ",0,"int(cot(e*x+d)^2*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","F"
35,0,0,951,1.316000," ","int(cot(e*x+d)^4*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","\int \left(\cot^{4}\left(e x +d \right)\right) \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, dx"," ",0,"int(cot(e*x+d)^4*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","F"
36,1,240,158,0.476000," ","int(tan(e*x+d)^5/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","\frac{\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}{2 c e}-\frac{b \ln \left(\frac{c \left(\tan^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\right)}{4 e \,c^{\frac{3}{2}}}-\frac{\ln \left(\frac{c \left(\tan^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{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(1+\tan^{2}\left(e x +d \right)\right)+2 \sqrt{a -b +c}\, \sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\right)+a -b +c}}{1+\tan^{2}\left(e x +d \right)}\right)}{2 e \sqrt{a -b +c}}"," ",0,"1/2*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/c/e-1/4/e*b/c^(3/2)*ln((c*tan(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2))-1/2/e*ln((c*tan(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*tan(e*x+d)^2+c*tan(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)*(1+tan(e*x+d)^2)+2*(a-b+c)^(1/2)*((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+a-b+c)^(1/2))/(1+tan(e*x+d)^2))","A"
37,1,155,121,0.437000," ","int(tan(e*x+d)^3/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","\frac{\ln \left(\frac{c \left(\tan^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{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(1+\tan^{2}\left(e x +d \right)\right)+2 \sqrt{a -b +c}\, \sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\right)+a -b +c}}{1+\tan^{2}\left(e x +d \right)}\right)}{2 e \sqrt{a -b +c}}"," ",0,"1/2/e*ln((c*tan(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*tan(e*x+d)^2+c*tan(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)*(1+tan(e*x+d)^2)+2*(a-b+c)^(1/2)*((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+a-b+c)^(1/2))/(1+tan(e*x+d)^2))","A"
38,1,102,69,0.394000," ","int(tan(e*x+d)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","-\frac{\ln \left(\frac{2 a -2 b +2 c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\right)+2 \sqrt{a -b +c}\, \sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\right)+a -b +c}}{1+\tan^{2}\left(e x +d \right)}\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)*(1+tan(e*x+d)^2)+2*(a-b+c)^(1/2)*((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+a-b+c)^(1/2))/(1+tan(e*x+d)^2))","A"
39,0,0,122,1.733000," ","int(cot(e*x+d)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","\int \frac{\cot \left(e x +d \right)}{\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}\, dx"," ",0,"int(cot(e*x+d)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","F"
40,0,0,215,1.721000," ","int(cot(e*x+d)^3/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","\int \frac{\cot^{3}\left(e x +d \right)}{\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}\, dx"," ",0,"int(cot(e*x+d)^3/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","F"
41,1,646,667,0.456000," ","int(tan(e*x+d)^4/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","\frac{-\frac{a \sqrt{2}\, \sqrt{4-\frac{2 \left(-b +\sqrt{-4 c a +b^{2}}\right) \left(\tan^{2}\left(e x +d \right)\right)}{a}}\, \sqrt{4+\frac{2 \left(b +\sqrt{-4 c a +b^{2}}\right) \left(\tan^{2}\left(e x +d \right)\right)}{a}}\, \left(\EllipticF \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, \frac{\sqrt{-4+\frac{2 b \left(b +\sqrt{-4 c a +b^{2}}\right)}{a c}}}{2}\right)-\EllipticE \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, \frac{\sqrt{-4+\frac{2 b \left(b +\sqrt{-4 c a +b^{2}}\right)}{a c}}}{2}\right)\right)}{2 \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(b +\sqrt{-4 c a +b^{2}}\right)}-\frac{\sqrt{2}\, \sqrt{4-\frac{2 \left(-b +\sqrt{-4 c a +b^{2}}\right) \left(\tan^{2}\left(e x +d \right)\right)}{a}}\, \sqrt{4+\frac{2 \left(b +\sqrt{-4 c a +b^{2}}\right) \left(\tan^{2}\left(e x +d \right)\right)}{a}}\, \EllipticF \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, \frac{\sqrt{-4+\frac{2 b \left(b +\sqrt{-4 c a +b^{2}}\right)}{a c}}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}+\frac{\sqrt{2}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}-\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}+\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \EllipticPi \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, -\frac{2 a}{-b +\sqrt{-4 c a +b^{2}}}, \frac{\sqrt{-\frac{b +\sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}\right)}{\sqrt{-\frac{b}{a}+\frac{\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}}{e}"," ",0,"1/e*(-1/2*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(4-2*(-b+(-4*a*c+b^2)^(1/2))/a*tan(e*x+d)^2)^(1/2)*(4+2*(b+(-4*a*c+b^2)^(1/2))/a*tan(e*x+d)^2)^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))-EllipticE(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2)))-1/4*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(4-2*(-b+(-4*a*c+b^2)^(1/2))/a*tan(e*x+d)^2)^(1/2)*(4+2*(b+(-4*a*c+b^2)^(1/2))/a*tan(e*x+d)^2)^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))+2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b-1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b+1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticPi(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),-2/(-b+(-4*a*c+b^2)^(1/2))*a,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)))","A"
42,1,402,436,0.424000," ","int(tan(e*x+d)^2/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","\frac{\frac{\sqrt{2}\, \sqrt{4-\frac{2 \left(-b +\sqrt{-4 c a +b^{2}}\right) \left(\tan^{2}\left(e x +d \right)\right)}{a}}\, \sqrt{4+\frac{2 \left(b +\sqrt{-4 c a +b^{2}}\right) \left(\tan^{2}\left(e x +d \right)\right)}{a}}\, \EllipticF \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, \frac{\sqrt{-4+\frac{2 b \left(b +\sqrt{-4 c a +b^{2}}\right)}{a c}}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}-\frac{\sqrt{2}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}-\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}+\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \EllipticPi \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, -\frac{2 a}{-b +\sqrt{-4 c a +b^{2}}}, \frac{\sqrt{-\frac{b +\sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}\right)}{\sqrt{-\frac{b}{a}+\frac{\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}}{e}"," ",0,"1/e*(1/4*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(4-2*(-b+(-4*a*c+b^2)^(1/2))/a*tan(e*x+d)^2)^(1/2)*(4+2*(b+(-4*a*c+b^2)^(1/2))/a*tan(e*x+d)^2)^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))-2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b-1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b+1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticPi(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),-2/(-b+(-4*a*c+b^2)^(1/2))*a,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)))","A"
43,1,231,436,0.573000," ","int(1/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}-\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{1+\frac{\left(\tan^{2}\left(e x +d \right)\right) b}{2 a}+\frac{\left(\tan^{2}\left(e x +d \right)\right) \sqrt{-4 c a +b^{2}}}{2 a}}\, \EllipticPi \left(\frac{\tan \left(e x +d \right) \sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}{2}, -\frac{2 a}{-b +\sqrt{-4 c a +b^{2}}}, \frac{\sqrt{-\frac{b +\sqrt{-4 c a +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 c a +b^{2}}}{a}}}\right)}{e \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 c a +b^{2}}}{a}}\, \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}"," ",0,"1/e*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b-1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b+1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticPi(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),-2/(-b+(-4*a*c+b^2)^(1/2))*a,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))","A"
44,0,0,710,1.475000," ","int(cot(e*x+d)^2/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","\int \frac{\cot^{2}\left(e x +d \right)}{\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}\, dx"," ",0,"int(cot(e*x+d)^2/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2),x)","F"
45,1,826,213,0.552000," ","int(tan(e*x+d)^7/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2),x)","-\frac{\tan^{2}\left(e x +d \right)}{2 e c \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}+\frac{b}{4 e \,c^{2} \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}+\frac{b^{2} \left(\tan^{2}\left(e x +d \right)\right)}{2 e c \left(4 c a -b^{2}\right) \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{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(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}}+\frac{\ln \left(\frac{c \left(\tan^{2}\left(e x +d \right)\right)+\frac{b}{2}}{\sqrt{c}}+\sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\right)}{2 e \,c^{\frac{3}{2}}}+\frac{b \left(\tan^{2}\left(e x +d \right)\right)}{e \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}+\frac{2 a}{e \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}+\frac{2 c \left(\tan^{2}\left(e x +d \right)\right)}{e \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}+\frac{b}{e \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}+\frac{2 c \sqrt{\left(\tan^{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(\tan^{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(\tan^{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(1+\tan^{2}\left(e x +d \right)\right)+2 \sqrt{a -b +c}\, \sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\right)+a -b +c}}{1+\tan^{2}\left(e x +d \right)}\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}}-\frac{2 c \sqrt{\left(\tan^{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(\tan^{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(\tan^{2}\left(e x +d \right)+\frac{\sqrt{-4 c a +b^{2}}}{2 c}+\frac{b}{2 c}\right)}"," ",0,"-1/2/e*tan(e*x+d)^2/c/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)+1/4/e*b/c^2/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)+1/2/e*b^2/c/(4*a*c-b^2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*tan(e*x+d)^2+1/4/e*b^3/c^2/(4*a*c-b^2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)+1/2/e/c^(3/2)*ln((c*tan(e*x+d)^2+1/2*b)/c^(1/2)+(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2))+1/e/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(4*a*c-b^2)*b*tan(e*x+d)^2+2/e/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(4*a*c-b^2)*a+2/e/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(4*a*c-b^2)*c*tan(e*x+d)^2+1/e/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(4*a*c-b^2)*b+2/e*c/((-4*a*c+b^2)^(1/2)-b+2*c)/(-4*a*c+b^2)/(tan(e*x+d)^2-1/2/c*(-4*a*c+b^2)^(1/2)+1/2*b/c)*((tan(e*x+d)^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*c+(-4*a*c+b^2)^(1/2)*(tan(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)*(1+tan(e*x+d)^2)+2*(a-b+c)^(1/2)*((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+a-b+c)^(1/2))/(1+tan(e*x+d)^2))-2/e*c/(b-2*c+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)/(tan(e*x+d)^2+1/2/c*(-4*a*c+b^2)^(1/2)+1/2*b/c)*((tan(e*x+d)^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*c-(-4*a*c+b^2)^(1/2)*(tan(e*x+d)^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c))^(1/2)","B"
46,1,601,147,0.446000," ","int(tan(e*x+d)^5/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2),x)","-\frac{b \left(\tan^{2}\left(e x +d \right)\right)}{e \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}-\frac{2 a}{e \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}-\frac{2 c \left(\tan^{2}\left(e x +d \right)\right)}{e \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}-\frac{b}{e \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}-\frac{2 c \sqrt{\left(\tan^{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(\tan^{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(\tan^{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(1+\tan^{2}\left(e x +d \right)\right)+2 \sqrt{a -b +c}\, \sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\right)+a -b +c}}{1+\tan^{2}\left(e x +d \right)}\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}}+\frac{2 c \sqrt{\left(\tan^{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(\tan^{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(\tan^{2}\left(e x +d \right)+\frac{\sqrt{-4 c a +b^{2}}}{2 c}+\frac{b}{2 c}\right)}"," ",0,"-1/e/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(4*a*c-b^2)*b*tan(e*x+d)^2-2/e/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(4*a*c-b^2)*a-2/e/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(4*a*c-b^2)*c*tan(e*x+d)^2-1/e/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(4*a*c-b^2)*b-2/e*c/((-4*a*c+b^2)^(1/2)-b+2*c)/(-4*a*c+b^2)/(tan(e*x+d)^2-1/2/c*(-4*a*c+b^2)^(1/2)+1/2*b/c)*((tan(e*x+d)^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*c+(-4*a*c+b^2)^(1/2)*(tan(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)*(1+tan(e*x+d)^2)+2*(a-b+c)^(1/2)*((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+a-b+c)^(1/2))/(1+tan(e*x+d)^2))+2/e*c/(b-2*c+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)/(tan(e*x+d)^2+1/2/c*(-4*a*c+b^2)^(1/2)+1/2*b/c)*((tan(e*x+d)^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*c-(-4*a*c+b^2)^(1/2)*(tan(e*x+d)^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c))^(1/2)","B"
47,1,508,143,0.451000," ","int(tan(e*x+d)^3/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2),x)","\frac{2 c \left(\tan^{2}\left(e x +d \right)\right)}{e \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}+\frac{b}{e \sqrt{a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)}\, \left(4 c a -b^{2}\right)}+\frac{2 c \sqrt{\left(\tan^{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(\tan^{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(\tan^{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(1+\tan^{2}\left(e x +d \right)\right)+2 \sqrt{a -b +c}\, \sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\right)+a -b +c}}{1+\tan^{2}\left(e x +d \right)}\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}}-\frac{2 c \sqrt{\left(\tan^{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(\tan^{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(\tan^{2}\left(e x +d \right)+\frac{\sqrt{-4 c a +b^{2}}}{2 c}+\frac{b}{2 c}\right)}"," ",0,"2/e/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(4*a*c-b^2)*c*tan(e*x+d)^2+1/e/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(4*a*c-b^2)*b+2/e*c/((-4*a*c+b^2)^(1/2)-b+2*c)/(-4*a*c+b^2)/(tan(e*x+d)^2-1/2/c*(-4*a*c+b^2)^(1/2)+1/2*b/c)*((tan(e*x+d)^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*c+(-4*a*c+b^2)^(1/2)*(tan(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)*(1+tan(e*x+d)^2)+2*(a-b+c)^(1/2)*((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+a-b+c)^(1/2))/(1+tan(e*x+d)^2))-2/e*c/(b-2*c+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)/(tan(e*x+d)^2+1/2/c*(-4*a*c+b^2)^(1/2)+1/2*b/c)*((tan(e*x+d)^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*c-(-4*a*c+b^2)^(1/2)*(tan(e*x+d)^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c))^(1/2)","B"
48,1,417,143,0.380000," ","int(tan(e*x+d)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2),x)","-\frac{2 c \sqrt{\left(\tan^{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(\tan^{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(\tan^{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(1+\tan^{2}\left(e x +d \right)\right)+2 \sqrt{a -b +c}\, \sqrt{\left(1+\tan^{2}\left(e x +d \right)\right)^{2} c +\left(b -2 c \right) \left(1+\tan^{2}\left(e x +d \right)\right)+a -b +c}}{1+\tan^{2}\left(e x +d \right)}\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}}+\frac{2 c \sqrt{\left(\tan^{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(\tan^{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(\tan^{2}\left(e x +d \right)+\frac{\sqrt{-4 c a +b^{2}}}{2 c}+\frac{b}{2 c}\right)}"," ",0,"-2/e*c/((-4*a*c+b^2)^(1/2)-b+2*c)/(-4*a*c+b^2)/(tan(e*x+d)^2-1/2/c*(-4*a*c+b^2)^(1/2)+1/2*b/c)*((tan(e*x+d)^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*c+(-4*a*c+b^2)^(1/2)*(tan(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)*(1+tan(e*x+d)^2)+2*(a-b+c)^(1/2)*((1+tan(e*x+d)^2)^2*c+(b-2*c)*(1+tan(e*x+d)^2)+a-b+c)^(1/2))/(1+tan(e*x+d)^2))+2/e*c/(b-2*c+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)/(tan(e*x+d)^2+1/2/c*(-4*a*c+b^2)^(1/2)+1/2*b/c)*((tan(e*x+d)^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*c-(-4*a*c+b^2)^(1/2)*(tan(e*x+d)^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c))^(1/2)","B"
49,0,0,257,1.549000," ","int(cot(e*x+d)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2),x)","\int \frac{\cot \left(e x +d \right)}{\left(a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(cot(e*x+d)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2),x)","F"
50,0,0,439,1.580000," ","int(cot(e*x+d)^3/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2),x)","\int \frac{\cot^{3}\left(e x +d \right)}{\left(a +b \left(\tan^{2}\left(e x +d \right)\right)+c \left(\tan^{4}\left(e x +d \right)\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(cot(e*x+d)^3/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2),x)","F"
51,1,3598,995,0.560000," ","int(tan(e*x+d)^2/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2),x)","\text{output too large to display}"," ",0,"1/e*(-2*c*(1/2/a*b/(4*a*c-b^2)*tan(e*x+d)^3-1/2*(2*a*c-b^2)/a/(4*a*c-b^2)/c*tan(e*x+d))/((tan(e*x+d)^4+b/c*tan(e*x+d)^2+a/c)*c)^(1/2)+1/4*(1/a-(2*a*c-b^2)/a/(4*a*c-b^2))*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(4-2*(-b+(-4*a*c+b^2)^(1/2))/a*tan(e*x+d)^2)^(1/2)*(4+2*(b+(-4*a*c+b^2)^(1/2))/a*tan(e*x+d)^2)^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))-1/2*b/(4*a*c-b^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(4-2*(-b+(-4*a*c+b^2)^(1/2))/a*tan(e*x+d)^2)^(1/2)*(4+2*(b+(-4*a*c+b^2)^(1/2))/a*tan(e*x+d)^2)^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))-EllipticE(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2)))+2*c*(1/2*(2*a*c-b^2+b*c)/a/(4*a*c-b^2)/(a-b+c)*tan(e*x+d)^3+1/2*(3*a*b*c-2*a*c^2-b^3+b^2*c)/a/(4*a*c-b^2)/(a-b+c)/c*tan(e*x+d))/((tan(e*x+d)^4+b/c*tan(e*x+d)^2+a/c)*c)^(1/2)+1/4*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))/a/(a-b+c)*b-1/4*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))/a/(a-b+c)*c-3/4*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))/(4*a*c-b^2)/(a-b+c)*b*c+1/2*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))/(4*a*c-b^2)/(a-b+c)*c^2+1/4*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))/a/(4*a*c-b^2)/(a-b+c)*b^3-1/4*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))/a*b^2/(4*a*c-b^2)*c/(a-b+c)+c^2/(a-b+c)/(4*a*c-b^2)*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))*a-1/2*c/(a-b+c)/(4*a*c-b^2)*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))*b^2+1/2*c^2/(a-b+c)/(4*a*c-b^2)*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*EllipticF(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))*b-c^2/(a-b+c)/(4*a*c-b^2)*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*EllipticE(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))*a+1/2*c/(a-b+c)/(4*a*c-b^2)*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*EllipticE(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))*b^2-1/2*c^2/(a-b+c)/(4*a*c-b^2)*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b-2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(4+2/a*tan(e*x+d)^2*b+2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*EllipticE(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))*b-1/(a-b+c)*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b-1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*tan(e*x+d)^2*b+1/2/a*tan(e*x+d)^2*(-4*a*c+b^2)^(1/2))^(1/2)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(1/2)*EllipticPi(1/2*tan(e*x+d)*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),-2/(-b+(-4*a*c+b^2)^(1/2))*a,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)))","B"