1,1,147,0,0.0543799,"\int \left(b x+c x^2\right)^{7/2} \, dx","Int[(b*x + c*x^2)^(7/2),x]","-\frac{35 b^6 (b+2 c x) \sqrt{b x+c x^2}}{16384 c^4}+\frac{35 b^4 (b+2 c x) \left(b x+c x^2\right)^{3/2}}{6144 c^3}-\frac{7 b^2 (b+2 c x) \left(b x+c x^2\right)^{5/2}}{384 c^2}+\frac{35 b^8 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{16384 c^{9/2}}+\frac{(b+2 c x) \left(b x+c x^2\right)^{7/2}}{16 c}","-\frac{35 b^6 (b+2 c x) \sqrt{b x+c x^2}}{16384 c^4}+\frac{35 b^4 (b+2 c x) \left(b x+c x^2\right)^{3/2}}{6144 c^3}-\frac{7 b^2 (b+2 c x) \left(b x+c x^2\right)^{5/2}}{384 c^2}+\frac{35 b^8 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{16384 c^{9/2}}+\frac{(b+2 c x) \left(b x+c x^2\right)^{7/2}}{16 c}",1,"(-35*b^6*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(16384*c^4) + (35*b^4*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(6144*c^3) - (7*b^2*(b + 2*c*x)*(b*x + c*x^2)^(5/2))/(384*c^2) + ((b + 2*c*x)*(b*x + c*x^2)^(7/2))/(16*c) + (35*b^8*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(16384*c^(9/2))","A",6,3,13,0.2308,1,"{612, 620, 206}"
2,1,121,0,0.0308269,"\int \left(3 i x+4 x^2\right)^{7/2} \, dx","Int[((3*I)*x + 4*x^2)^(7/2),x]","\frac{1}{64} (8 x+3 i) \left(4 x^2+3 i x\right)^{7/2}+\frac{21 (8 x+3 i) \left(4 x^2+3 i x\right)^{5/2}}{2048}+\frac{945 (8 x+3 i) \left(4 x^2+3 i x\right)^{3/2}}{131072}+\frac{25515 (8 x+3 i) \sqrt{4 x^2+3 i x}}{4194304}+\frac{229635 i \sin ^{-1}\left(1-\frac{8 i x}{3}\right)}{16777216}","\frac{1}{64} (8 x+3 i) \left(4 x^2+3 i x\right)^{7/2}+\frac{21 (8 x+3 i) \left(4 x^2+3 i x\right)^{5/2}}{2048}+\frac{945 (8 x+3 i) \left(4 x^2+3 i x\right)^{3/2}}{131072}+\frac{25515 (8 x+3 i) \sqrt{4 x^2+3 i x}}{4194304}+\frac{229635 i \sin ^{-1}\left(1-\frac{8 i x}{3}\right)}{16777216}",1,"(25515*(3*I + 8*x)*Sqrt[(3*I)*x + 4*x^2])/4194304 + (945*(3*I + 8*x)*((3*I)*x + 4*x^2)^(3/2))/131072 + (21*(3*I + 8*x)*((3*I)*x + 4*x^2)^(5/2))/2048 + ((3*I + 8*x)*((3*I)*x + 4*x^2)^(7/2))/64 + ((229635*I)/16777216)*ArcSin[1 - ((8*I)/3)*x]","A",6,3,15,0.2000,1,"{612, 619, 215}"
3,1,95,0,0.02172,"\int \left(3 i x+4 x^2\right)^{5/2} \, dx","Int[((3*I)*x + 4*x^2)^(5/2),x]","\frac{1}{48} (8 x+3 i) \left(4 x^2+3 i x\right)^{5/2}+\frac{15 (8 x+3 i) \left(4 x^2+3 i x\right)^{3/2}}{1024}+\frac{405 (8 x+3 i) \sqrt{4 x^2+3 i x}}{32768}+\frac{3645 i \sin ^{-1}\left(1-\frac{8 i x}{3}\right)}{131072}","\frac{1}{48} (8 x+3 i) \left(4 x^2+3 i x\right)^{5/2}+\frac{15 (8 x+3 i) \left(4 x^2+3 i x\right)^{3/2}}{1024}+\frac{405 (8 x+3 i) \sqrt{4 x^2+3 i x}}{32768}+\frac{3645 i \sin ^{-1}\left(1-\frac{8 i x}{3}\right)}{131072}",1,"(405*(3*I + 8*x)*Sqrt[(3*I)*x + 4*x^2])/32768 + (15*(3*I + 8*x)*((3*I)*x + 4*x^2)^(3/2))/1024 + ((3*I + 8*x)*((3*I)*x + 4*x^2)^(5/2))/48 + ((3645*I)/131072)*ArcSin[1 - ((8*I)/3)*x]","A",5,3,15,0.2000,1,"{612, 619, 215}"
4,1,69,0,0.0148143,"\int \left(3 i x+4 x^2\right)^{3/2} \, dx","Int[((3*I)*x + 4*x^2)^(3/2),x]","\frac{1}{32} (8 x+3 i) \left(4 x^2+3 i x\right)^{3/2}+\frac{27 (8 x+3 i) \sqrt{4 x^2+3 i x}}{1024}+\frac{243 i \sin ^{-1}\left(1-\frac{8 i x}{3}\right)}{4096}","\frac{1}{32} (8 x+3 i) \left(4 x^2+3 i x\right)^{3/2}+\frac{27 (8 x+3 i) \sqrt{4 x^2+3 i x}}{1024}+\frac{243 i \sin ^{-1}\left(1-\frac{8 i x}{3}\right)}{4096}",1,"(27*(3*I + 8*x)*Sqrt[(3*I)*x + 4*x^2])/1024 + ((3*I + 8*x)*((3*I)*x + 4*x^2)^(3/2))/32 + ((243*I)/4096)*ArcSin[1 - ((8*I)/3)*x]","A",4,3,15,0.2000,1,"{612, 619, 215}"
5,1,43,0,0.0101643,"\int \sqrt{3 i x+4 x^2} \, dx","Int[Sqrt[(3*I)*x + 4*x^2],x]","\frac{1}{16} \sqrt{4 x^2+3 i x} (8 x+3 i)+\frac{9}{64} i \sin ^{-1}\left(1-\frac{8 i x}{3}\right)","\frac{1}{16} \sqrt{4 x^2+3 i x} (8 x+3 i)+\frac{9}{64} i \sin ^{-1}\left(1-\frac{8 i x}{3}\right)",1,"((3*I + 8*x)*Sqrt[(3*I)*x + 4*x^2])/16 + ((9*I)/64)*ArcSin[1 - ((8*I)/3)*x]","A",3,3,15,0.2000,1,"{612, 619, 215}"
6,1,101,0,0.0275681,"\int \left(3 x-4 x^2\right)^{7/2} \, dx","Int[(3*x - 4*x^2)^(7/2),x]","-\frac{1}{64} (3-8 x) \left(3 x-4 x^2\right)^{7/2}-\frac{21 (3-8 x) \left(3 x-4 x^2\right)^{5/2}}{2048}-\frac{945 (3-8 x) \left(3 x-4 x^2\right)^{3/2}}{131072}-\frac{25515 (3-8 x) \sqrt{3 x-4 x^2}}{4194304}-\frac{229635 \sin ^{-1}\left(1-\frac{8 x}{3}\right)}{16777216}","-\frac{1}{64} (3-8 x) \left(3 x-4 x^2\right)^{7/2}-\frac{21 (3-8 x) \left(3 x-4 x^2\right)^{5/2}}{2048}-\frac{945 (3-8 x) \left(3 x-4 x^2\right)^{3/2}}{131072}-\frac{25515 (3-8 x) \sqrt{3 x-4 x^2}}{4194304}-\frac{229635 \sin ^{-1}\left(1-\frac{8 x}{3}\right)}{16777216}",1,"(-25515*(3 - 8*x)*Sqrt[3*x - 4*x^2])/4194304 - (945*(3 - 8*x)*(3*x - 4*x^2)^(3/2))/131072 - (21*(3 - 8*x)*(3*x - 4*x^2)^(5/2))/2048 - ((3 - 8*x)*(3*x - 4*x^2)^(7/2))/64 - (229635*ArcSin[1 - (8*x)/3])/16777216","A",6,3,13,0.2308,1,"{612, 619, 216}"
7,1,79,0,0.0192173,"\int \left(3 x-4 x^2\right)^{5/2} \, dx","Int[(3*x - 4*x^2)^(5/2),x]","-\frac{1}{48} (3-8 x) \left(3 x-4 x^2\right)^{5/2}-\frac{15 (3-8 x) \left(3 x-4 x^2\right)^{3/2}}{1024}-\frac{405 (3-8 x) \sqrt{3 x-4 x^2}}{32768}-\frac{3645 \sin ^{-1}\left(1-\frac{8 x}{3}\right)}{131072}","-\frac{1}{48} (3-8 x) \left(3 x-4 x^2\right)^{5/2}-\frac{15 (3-8 x) \left(3 x-4 x^2\right)^{3/2}}{1024}-\frac{405 (3-8 x) \sqrt{3 x-4 x^2}}{32768}-\frac{3645 \sin ^{-1}\left(1-\frac{8 x}{3}\right)}{131072}",1,"(-405*(3 - 8*x)*Sqrt[3*x - 4*x^2])/32768 - (15*(3 - 8*x)*(3*x - 4*x^2)^(3/2))/1024 - ((3 - 8*x)*(3*x - 4*x^2)^(5/2))/48 - (3645*ArcSin[1 - (8*x)/3])/131072","A",5,3,13,0.2308,1,"{612, 619, 216}"
8,1,57,0,0.0128725,"\int \left(3 x-4 x^2\right)^{3/2} \, dx","Int[(3*x - 4*x^2)^(3/2),x]","-\frac{1}{32} (3-8 x) \left(3 x-4 x^2\right)^{3/2}-\frac{27 (3-8 x) \sqrt{3 x-4 x^2}}{1024}-\frac{243 \sin ^{-1}\left(1-\frac{8 x}{3}\right)}{4096}","-\frac{1}{32} (3-8 x) \left(3 x-4 x^2\right)^{3/2}-\frac{27 (3-8 x) \sqrt{3 x-4 x^2}}{1024}-\frac{243 \sin ^{-1}\left(1-\frac{8 x}{3}\right)}{4096}",1,"(-27*(3 - 8*x)*Sqrt[3*x - 4*x^2])/1024 - ((3 - 8*x)*(3*x - 4*x^2)^(3/2))/32 - (243*ArcSin[1 - (8*x)/3])/4096","A",4,3,13,0.2308,1,"{612, 619, 216}"
9,1,35,0,0.0091721,"\int \sqrt{3 x-4 x^2} \, dx","Int[Sqrt[3*x - 4*x^2],x]","-\frac{1}{16} \sqrt{3 x-4 x^2} (3-8 x)-\frac{9}{64} \sin ^{-1}\left(1-\frac{8 x}{3}\right)","-\frac{1}{16} \sqrt{3 x-4 x^2} (3-8 x)-\frac{9}{64} \sin ^{-1}\left(1-\frac{8 x}{3}\right)",1,"-((3 - 8*x)*Sqrt[3*x - 4*x^2])/16 - (9*ArcSin[1 - (8*x)/3])/64","A",3,3,13,0.2308,1,"{612, 619, 216}"
10,1,35,0,0.0098087,"\int \sqrt{6 x-x^2} \, dx","Int[Sqrt[6*x - x^2],x]","-\frac{1}{2} \sqrt{6 x-x^2} (3-x)-\frac{9}{2} \sin ^{-1}\left(1-\frac{x}{3}\right)","-\frac{1}{2} \sqrt{6 x-x^2} (3-x)-\frac{9}{2} \sin ^{-1}\left(1-\frac{x}{3}\right)",1,"-((3 - x)*Sqrt[6*x - x^2])/2 - (9*ArcSin[1 - x/3])/2","A",3,3,13,0.2308,1,"{612, 619, 216}"
11,1,35,0,0.0097332,"\int \sqrt{5 x-9 x^2} \, dx","Int[Sqrt[5*x - 9*x^2],x]","-\frac{1}{36} \sqrt{5 x-9 x^2} (5-18 x)-\frac{25}{216} \sin ^{-1}\left(1-\frac{18 x}{5}\right)","-\frac{1}{36} \sqrt{5 x-9 x^2} (5-18 x)-\frac{25}{216} \sin ^{-1}\left(1-\frac{18 x}{5}\right)",1,"-((5 - 18*x)*Sqrt[5*x - 9*x^2])/36 - (25*ArcSin[1 - (18*x)/5])/216","A",3,3,13,0.2308,1,"{612, 619, 216}"
12,1,51,0,0.0101865,"\int \left(x-x^2\right)^{3/2} \, dx","Int[(x - x^2)^(3/2),x]","-\frac{1}{8} (1-2 x) \left(x-x^2\right)^{3/2}-\frac{3}{64} (1-2 x) \sqrt{x-x^2}-\frac{3}{128} \sin ^{-1}(1-2 x)","-\frac{1}{8} (1-2 x) \left(x-x^2\right)^{3/2}-\frac{3}{64} (1-2 x) \sqrt{x-x^2}-\frac{3}{128} \sin ^{-1}(1-2 x)",1,"(-3*(1 - 2*x)*Sqrt[x - x^2])/64 - ((1 - 2*x)*(x - x^2)^(3/2))/8 - (3*ArcSin[1 - 2*x])/128","A",4,3,11,0.2727,1,"{612, 619, 216}"
13,1,35,0,0.0071598,"\int \sqrt{4 x+x^2} \, dx","Int[Sqrt[4*x + x^2],x]","\frac{1}{2} (x+2) \sqrt{x^2+4 x}-4 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2+4 x}}\right)","\frac{1}{2} (x+2) \sqrt{x^2+4 x}-4 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2+4 x}}\right)",1,"((2 + x)*Sqrt[4*x + x^2])/2 - 4*ArcTanh[x/Sqrt[4*x + x^2]]","A",3,3,11,0.2727,1,"{612, 620, 206}"
14,1,37,0,0.0066753,"\int \sqrt{-8 x+x^2} \, dx","Int[Sqrt[-8*x + x^2],x]","-\frac{1}{2} \sqrt{x^2-8 x} (4-x)-16 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-8 x}}\right)","-\frac{1}{2} \sqrt{x^2-8 x} (4-x)-16 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-8 x}}\right)",1,"-((4 - x)*Sqrt[-8*x + x^2])/2 - 16*ArcTanh[x/Sqrt[-8*x + x^2]]","A",3,3,11,0.2727,1,"{612, 620, 206}"
15,1,39,0,0.006844,"\int \sqrt{-x+x^2} \, dx","Int[Sqrt[-x + x^2],x]","-\frac{1}{4} \sqrt{x^2-x} (1-2 x)-\frac{1}{4} \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-x}}\right)","-\frac{1}{4} \sqrt{x^2-x} (1-2 x)-\frac{1}{4} \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-x}}\right)",1,"-((1 - 2*x)*Sqrt[-x + x^2])/4 - ArcTanh[x/Sqrt[-x + x^2]]/4","A",3,3,11,0.2727,1,"{612, 620, 206}"
16,1,83,0,0.0184755,"\int \frac{1}{\left(b x+c x^2\right)^{7/2}} \, dx","Int[(b*x + c*x^2)^(-7/2),x]","-\frac{256 c^2 (b+2 c x)}{15 b^6 \sqrt{b x+c x^2}}+\frac{32 c (b+2 c x)}{15 b^4 \left(b x+c x^2\right)^{3/2}}-\frac{2 (b+2 c x)}{5 b^2 \left(b x+c x^2\right)^{5/2}}","-\frac{256 c^2 (b+2 c x)}{15 b^6 \sqrt{b x+c x^2}}+\frac{32 c (b+2 c x)}{15 b^4 \left(b x+c x^2\right)^{3/2}}-\frac{2 (b+2 c x)}{5 b^2 \left(b x+c x^2\right)^{5/2}}",1,"(-2*(b + 2*c*x))/(5*b^2*(b*x + c*x^2)^(5/2)) + (32*c*(b + 2*c*x))/(15*b^4*(b*x + c*x^2)^(3/2)) - (256*c^2*(b + 2*c*x))/(15*b^6*Sqrt[b*x + c*x^2])","A",3,2,13,0.1538,1,"{614, 613}"
17,1,16,0,0.0064543,"\int \frac{1}{\sqrt{3 i x+4 x^2}} \, dx","Int[1/Sqrt[(3*I)*x + 4*x^2],x]","\frac{1}{2} i \sin ^{-1}\left(1-\frac{8 i x}{3}\right)","\frac{1}{2} i \sin ^{-1}\left(1-\frac{8 i x}{3}\right)",1,"(I/2)*ArcSin[1 - ((8*I)/3)*x]","A",2,2,15,0.1333,1,"{619, 215}"
18,1,26,0,0.0025989,"\int \frac{1}{\left(3 i x+4 x^2\right)^{3/2}} \, dx","Int[((3*I)*x + 4*x^2)^(-3/2),x]","\frac{2 (8 x+3 i)}{9 \sqrt{4 x^2+3 i x}}","\frac{2 (8 x+3 i)}{9 \sqrt{4 x^2+3 i x}}",1,"(2*(3*I + 8*x))/(9*Sqrt[(3*I)*x + 4*x^2])","A",1,1,15,0.06667,1,"{613}"
19,1,53,0,0.0074662,"\int \frac{1}{\left(3 i x+4 x^2\right)^{5/2}} \, dx","Int[((3*I)*x + 4*x^2)^(-5/2),x]","\frac{64 (8 x+3 i)}{243 \sqrt{4 x^2+3 i x}}+\frac{2 (8 x+3 i)}{27 \left(4 x^2+3 i x\right)^{3/2}}","\frac{64 (8 x+3 i)}{243 \sqrt{4 x^2+3 i x}}+\frac{2 (8 x+3 i)}{27 \left(4 x^2+3 i x\right)^{3/2}}",1,"(2*(3*I + 8*x))/(27*((3*I)*x + 4*x^2)^(3/2)) + (64*(3*I + 8*x))/(243*Sqrt[(3*I)*x + 4*x^2])","A",2,2,15,0.1333,1,"{614, 613}"
20,1,79,0,0.0124143,"\int \frac{1}{\left(3 i x+4 x^2\right)^{7/2}} \, dx","Int[((3*I)*x + 4*x^2)^(-7/2),x]","\frac{4096 (8 x+3 i)}{10935 \sqrt{4 x^2+3 i x}}+\frac{128 (8 x+3 i)}{1215 \left(4 x^2+3 i x\right)^{3/2}}+\frac{2 (8 x+3 i)}{45 \left(4 x^2+3 i x\right)^{5/2}}","\frac{4096 (8 x+3 i)}{10935 \sqrt{4 x^2+3 i x}}+\frac{128 (8 x+3 i)}{1215 \left(4 x^2+3 i x\right)^{3/2}}+\frac{2 (8 x+3 i)}{45 \left(4 x^2+3 i x\right)^{5/2}}",1,"(2*(3*I + 8*x))/(45*((3*I)*x + 4*x^2)^(5/2)) + (128*(3*I + 8*x))/(1215*((3*I)*x + 4*x^2)^(3/2)) + (4096*(3*I + 8*x))/(10935*Sqrt[(3*I)*x + 4*x^2])","A",3,2,15,0.1333,1,"{614, 613}"
21,1,12,0,0.0056575,"\int \frac{1}{\sqrt{3 x-4 x^2}} \, dx","Int[1/Sqrt[3*x - 4*x^2],x]","-\frac{1}{2} \sin ^{-1}\left(1-\frac{8 x}{3}\right)","-\frac{1}{2} \sin ^{-1}\left(1-\frac{8 x}{3}\right)",1,"-ArcSin[1 - (8*x)/3]/2","A",2,2,13,0.1538,1,"{619, 216}"
22,1,22,0,0.0023807,"\int \frac{1}{\left(3 x-4 x^2\right)^{3/2}} \, dx","Int[(3*x - 4*x^2)^(-3/2),x]","-\frac{2 (3-8 x)}{9 \sqrt{3 x-4 x^2}}","-\frac{2 (3-8 x)}{9 \sqrt{3 x-4 x^2}}",1,"(-2*(3 - 8*x))/(9*Sqrt[3*x - 4*x^2])","A",1,1,13,0.07692,1,"{613}"
23,1,45,0,0.0062287,"\int \frac{1}{\left(3 x-4 x^2\right)^{5/2}} \, dx","Int[(3*x - 4*x^2)^(-5/2),x]","-\frac{64 (3-8 x)}{243 \sqrt{3 x-4 x^2}}-\frac{2 (3-8 x)}{27 \left(3 x-4 x^2\right)^{3/2}}","-\frac{64 (3-8 x)}{243 \sqrt{3 x-4 x^2}}-\frac{2 (3-8 x)}{27 \left(3 x-4 x^2\right)^{3/2}}",1,"(-2*(3 - 8*x))/(27*(3*x - 4*x^2)^(3/2)) - (64*(3 - 8*x))/(243*Sqrt[3*x - 4*x^2])","A",2,2,13,0.1538,1,"{614, 613}"
24,1,67,0,0.0115283,"\int \frac{1}{\left(3 x-4 x^2\right)^{7/2}} \, dx","Int[(3*x - 4*x^2)^(-7/2),x]","-\frac{4096 (3-8 x)}{10935 \sqrt{3 x-4 x^2}}-\frac{128 (3-8 x)}{1215 \left(3 x-4 x^2\right)^{3/2}}-\frac{2 (3-8 x)}{45 \left(3 x-4 x^2\right)^{5/2}}","-\frac{4096 (3-8 x)}{10935 \sqrt{3 x-4 x^2}}-\frac{128 (3-8 x)}{1215 \left(3 x-4 x^2\right)^{3/2}}-\frac{2 (3-8 x)}{45 \left(3 x-4 x^2\right)^{5/2}}",1,"(-2*(3 - 8*x))/(45*(3*x - 4*x^2)^(5/2)) - (128*(3 - 8*x))/(1215*(3*x - 4*x^2)^(3/2)) - (4096*(3 - 8*x))/(10935*Sqrt[3*x - 4*x^2])","A",3,2,13,0.1538,1,"{614, 613}"
25,1,12,0,0.0076931,"\int \frac{1}{\sqrt{b x-b^2 x^2}} \, dx","Int[1/Sqrt[b*x - b^2*x^2],x]","-\frac{\sin ^{-1}(1-2 b x)}{b}","-\frac{\sin ^{-1}(1-2 b x)}{b}",1,"-(ArcSin[1 - 2*b*x]/b)","A",2,2,16,0.1250,1,"{619, 216}"
26,1,24,0,0.0077753,"\int \frac{1}{\sqrt{b x+b^2 x^2}} \, dx","Int[1/Sqrt[b*x + b^2*x^2],x]","\frac{2 \tanh ^{-1}\left(\frac{b x}{\sqrt{b^2 x^2+b x}}\right)}{b}","\frac{2 \tanh ^{-1}\left(\frac{b x}{\sqrt{b^2 x^2+b x}}\right)}{b}",1,"(2*ArcTanh[(b*x)/Sqrt[b*x + b^2*x^2]])/b","A",2,2,15,0.1333,1,"{620, 206}"
27,1,10,0,0.0062504,"\int \frac{1}{\sqrt{6 x-x^2}} \, dx","Int[1/Sqrt[6*x - x^2],x]","-\sin ^{-1}\left(1-\frac{x}{3}\right)","-\sin ^{-1}\left(1-\frac{x}{3}\right)",1,"-ArcSin[1 - x/3]","A",2,2,13,0.1538,1,"{619, 216}"
28,1,16,0,0.0038626,"\int \frac{1}{\sqrt{4 x+x^2}} \, dx","Int[1/Sqrt[4*x + x^2],x]","2 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2+4 x}}\right)","2 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2+4 x}}\right)",1,"2*ArcTanh[x/Sqrt[4*x + x^2]]","A",2,2,11,0.1818,1,"{620, 206}"
29,1,16,0,0.0040644,"\int \frac{1}{\sqrt{-2 x+x^2}} \, dx","Int[1/Sqrt[-2*x + x^2],x]","2 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-2 x}}\right)","2 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-2 x}}\right)",1,"2*ArcTanh[x/Sqrt[-2*x + x^2]]","A",2,2,11,0.1818,1,"{620, 206}"
30,1,448,0,0.7169362,"\int \left(b x+c x^2\right)^{4/3} \, dx","Int[(b*x + c*x^2)^(4/3),x]","\frac{3 \left(-\frac{c x (b+c x)}{b^2}\right)^{4/3} (b+2 c x) \left(b x+c x^2\right)^{4/3}}{22 c \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{4/3}}+\frac{3 \sqrt[3]{-\frac{c x (b+c x)}{b^2}} (b+2 c x) \left(b x+c x^2\right)^{4/3}}{55 c \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{4/3}}+\frac{\sqrt[3]{2} 3^{3/4} \sqrt{2-\sqrt{3}} b^2 \left(b x+c x^2\right)^{4/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{55 c (b+2 c x) \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{4/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}","\frac{3 \left(-\frac{c x (b+c x)}{b^2}\right)^{4/3} (b+2 c x) \left(b x+c x^2\right)^{4/3}}{22 c \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{4/3}}+\frac{3 \sqrt[3]{-\frac{c x (b+c x)}{b^2}} (b+2 c x) \left(b x+c x^2\right)^{4/3}}{55 c \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{4/3}}+\frac{\sqrt[3]{2} 3^{3/4} \sqrt{2-\sqrt{3}} b^2 \left(b x+c x^2\right)^{4/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{55 c (b+2 c x) \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{4/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}",1,"(3*(-((c*x*(b + c*x))/b^2))^(1/3)*(b + 2*c*x)*(b*x + c*x^2)^(4/3))/(55*c*(-((c*(b*x + c*x^2))/b^2))^(4/3)) + (3*(-((c*x*(b + c*x))/b^2))^(4/3)*(b + 2*c*x)*(b*x + c*x^2)^(4/3))/(22*c*(-((c*(b*x + c*x^2))/b^2))^(4/3)) + (2^(1/3)*3^(3/4)*Sqrt[2 - Sqrt[3]]*b^2*(b*x + c*x^2)^(4/3)*(1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3) + 2*2^(1/3)*(-((c*x*(b + c*x))/b^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))], -7 + 4*Sqrt[3]])/(55*c*(b + 2*c*x)*(-((c*(b*x + c*x^2))/b^2))^(4/3)*Sqrt[-((1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2)])","A",6,5,13,0.3846,1,"{622, 619, 195, 236, 219}"
31,1,387,0,0.4491613,"\int \sqrt[3]{b x+c x^2} \, dx","Int[(b*x + c*x^2)^(1/3),x]","\frac{3 \sqrt[3]{-\frac{c x (b+c x)}{b^2}} (b+2 c x) \sqrt[3]{b x+c x^2}}{10 c \sqrt[3]{-\frac{c \left(b x+c x^2\right)}{b^2}}}+\frac{3^{3/4} \sqrt{2-\sqrt{3}} b^2 \sqrt[3]{b x+c x^2} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{5\ 2^{2/3} c (b+2 c x) \sqrt[3]{-\frac{c \left(b x+c x^2\right)}{b^2}} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}","\frac{3 \sqrt[3]{-\frac{c x (b+c x)}{b^2}} (b+2 c x) \sqrt[3]{b x+c x^2}}{10 c \sqrt[3]{-\frac{c \left(b x+c x^2\right)}{b^2}}}+\frac{3^{3/4} \sqrt{2-\sqrt{3}} b^2 \sqrt[3]{b x+c x^2} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{5\ 2^{2/3} c (b+2 c x) \sqrt[3]{-\frac{c \left(b x+c x^2\right)}{b^2}} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}",1,"(3*(-((c*x*(b + c*x))/b^2))^(1/3)*(b + 2*c*x)*(b*x + c*x^2)^(1/3))/(10*c*(-((c*(b*x + c*x^2))/b^2))^(1/3)) + (3^(3/4)*Sqrt[2 - Sqrt[3]]*b^2*(b*x + c*x^2)^(1/3)*(1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3) + 2*2^(1/3)*(-((c*x*(b + c*x))/b^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))], -7 + 4*Sqrt[3]])/(5*2^(2/3)*c*(b + 2*c*x)*(-((c*(b*x + c*x^2))/b^2))^(1/3)*Sqrt[-((1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2)])","A",5,5,13,0.3846,1,"{622, 619, 195, 236, 219}"
32,1,322,0,0.3942855,"\int \frac{1}{\left(b x+c x^2\right)^{2/3}} \, dx","Int[(b*x + c*x^2)^(-2/3),x]","\frac{\sqrt[3]{2} 3^{3/4} \sqrt{2-\sqrt{3}} b^2 \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{2/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{c (b+2 c x) \left(b x+c x^2\right)^{2/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}","\frac{\sqrt[3]{2} 3^{3/4} \sqrt{2-\sqrt{3}} b^2 \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{2/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{c (b+2 c x) \left(b x+c x^2\right)^{2/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}",1,"(2^(1/3)*3^(3/4)*Sqrt[2 - Sqrt[3]]*b^2*(-((c*(b*x + c*x^2))/b^2))^(2/3)*(1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3) + 2*2^(1/3)*(-((c*x*(b + c*x))/b^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))], -7 + 4*Sqrt[3]])/(c*(b + 2*c*x)*(b*x + c*x^2)^(2/3)*Sqrt[-((1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2)])","A",4,4,13,0.3077,1,"{622, 619, 236, 219}"
33,1,384,0,0.4571389,"\int \frac{1}{\left(b x+c x^2\right)^{5/3}} \, dx","Int[(b*x + c*x^2)^(-5/3),x]","\frac{3 (b+2 c x) \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{5/3}}{2 c \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3} \left(b x+c x^2\right)^{5/3}}+\frac{\sqrt[3]{2} 3^{3/4} \sqrt{2-\sqrt{3}} b^2 \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{5/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{c (b+2 c x) \left(b x+c x^2\right)^{5/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}","\frac{3 (b+2 c x) \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{5/3}}{2 c \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3} \left(b x+c x^2\right)^{5/3}}+\frac{\sqrt[3]{2} 3^{3/4} \sqrt{2-\sqrt{3}} b^2 \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{5/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{c (b+2 c x) \left(b x+c x^2\right)^{5/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}",1,"(3*(b + 2*c*x)*(-((c*(b*x + c*x^2))/b^2))^(5/3))/(2*c*(-((c*x*(b + c*x))/b^2))^(2/3)*(b*x + c*x^2)^(5/3)) + (2^(1/3)*3^(3/4)*Sqrt[2 - Sqrt[3]]*b^2*(-((c*(b*x + c*x^2))/b^2))^(5/3)*(1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3) + 2*2^(1/3)*(-((c*x*(b + c*x))/b^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))], -7 + 4*Sqrt[3]])/(c*(b + 2*c*x)*(b*x + c*x^2)^(5/3)*Sqrt[-((1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2)])","A",5,5,13,0.3846,1,"{622, 619, 199, 236, 219}"
34,1,448,0,0.5097233,"\int \frac{1}{\left(b x+c x^2\right)^{8/3}} \, dx","Int[(b*x + c*x^2)^(-8/3),x]","\frac{21 (b+2 c x) \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{8/3}}{5 c \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3} \left(b x+c x^2\right)^{8/3}}+\frac{3 (b+2 c x) \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{8/3}}{5 c \left(-\frac{c x (b+c x)}{b^2}\right)^{5/3} \left(b x+c x^2\right)^{8/3}}+\frac{14 \sqrt[3]{2} 3^{3/4} \sqrt{2-\sqrt{3}} b^2 \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{8/3} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{5 c (b+2 c x) \left(b x+c x^2\right)^{8/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}","\frac{21 (b+2 c x) \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{8/3}}{5 c \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3} \left(b x+c x^2\right)^{8/3}}+\frac{3 (b+2 c x) \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{8/3}}{5 c \left(-\frac{c x (b+c x)}{b^2}\right)^{5/3} \left(b x+c x^2\right)^{8/3}}+\frac{14 \sqrt[3]{2} 3^{3/4} \sqrt{2-\sqrt{3}} b^2 \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{8/3} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{5 c (b+2 c x) \left(b x+c x^2\right)^{8/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}",1,"(3*(b + 2*c*x)*(-((c*(b*x + c*x^2))/b^2))^(8/3))/(5*c*(-((c*x*(b + c*x))/b^2))^(5/3)*(b*x + c*x^2)^(8/3)) + (21*(b + 2*c*x)*(-((c*(b*x + c*x^2))/b^2))^(8/3))/(5*c*(-((c*x*(b + c*x))/b^2))^(2/3)*(b*x + c*x^2)^(8/3)) + (14*2^(1/3)*3^(3/4)*Sqrt[2 - Sqrt[3]]*b^2*(-((c*(b*x + c*x^2))/b^2))^(8/3)*(1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3) + 2*2^(1/3)*(-((c*x*(b + c*x))/b^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))], -7 + 4*Sqrt[3]])/(5*c*(b + 2*c*x)*(b*x + c*x^2)^(8/3)*Sqrt[-((1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2)])","A",6,5,13,0.3846,1,"{622, 619, 199, 236, 219}"
35,1,842,0,1.0579538,"\int \left(b x+c x^2\right)^{5/3} \, dx","Int[(b*x + c*x^2)^(5/3),x]","-\frac{15 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(c x^2+b x\right)^{5/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right) b^2}{364 \sqrt[3]{2} c (b+2 c x) \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{5/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}+\frac{5\ 3^{3/4} \left(c x^2+b x\right)^{5/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right) b^2}{91\ 2^{5/6} c (b+2 c x) \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{5/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}-\frac{15 (b+2 c x) \left(c x^2+b x\right)^{5/3}}{182 \sqrt[3]{2} c \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{5/3} \left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)}+\frac{3 \left(-\frac{c x (b+c x)}{b^2}\right)^{5/3} (b+2 c x) \left(c x^2+b x\right)^{5/3}}{26 c \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{5/3}}+\frac{15 \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3} (b+2 c x) \left(c x^2+b x\right)^{5/3}}{364 c \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{5/3}}","-\frac{15 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(c x^2+b x\right)^{5/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right) b^2}{364 \sqrt[3]{2} c (b+2 c x) \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{5/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}+\frac{5\ 3^{3/4} \left(c x^2+b x\right)^{5/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right) b^2}{91\ 2^{5/6} c (b+2 c x) \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{5/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}-\frac{15 (b+2 c x) \left(c x^2+b x\right)^{5/3}}{182 \sqrt[3]{2} c \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{5/3} \left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)}+\frac{3 \left(-\frac{c x (b+c x)}{b^2}\right)^{5/3} (b+2 c x) \left(c x^2+b x\right)^{5/3}}{26 c \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{5/3}}+\frac{15 \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3} (b+2 c x) \left(c x^2+b x\right)^{5/3}}{364 c \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{5/3}}",1,"(15*(-((c*x*(b + c*x))/b^2))^(2/3)*(b + 2*c*x)*(b*x + c*x^2)^(5/3))/(364*c*(-((c*(b*x + c*x^2))/b^2))^(5/3)) + (3*(-((c*x*(b + c*x))/b^2))^(5/3)*(b + 2*c*x)*(b*x + c*x^2)^(5/3))/(26*c*(-((c*(b*x + c*x^2))/b^2))^(5/3)) - (15*(b + 2*c*x)*(b*x + c*x^2)^(5/3))/(182*2^(1/3)*c*(-((c*(b*x + c*x^2))/b^2))^(5/3)*(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))) - (15*3^(1/4)*Sqrt[2 + Sqrt[3]]*b^2*(b*x + c*x^2)^(5/3)*(1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3) + 2*2^(1/3)*(-((c*x*(b + c*x))/b^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))], -7 + 4*Sqrt[3]])/(364*2^(1/3)*c*(b + 2*c*x)*(-((c*(b*x + c*x^2))/b^2))^(5/3)*Sqrt[-((1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2)]) + (5*3^(3/4)*b^2*(b*x + c*x^2)^(5/3)*(1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3) + 2*2^(1/3)*(-((c*x*(b + c*x))/b^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))], -7 + 4*Sqrt[3]])/(91*2^(5/6)*c*(b + 2*c*x)*(-((c*(b*x + c*x^2))/b^2))^(5/3)*Sqrt[-((1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2)])","A",8,7,13,0.5385,1,"{622, 619, 195, 235, 304, 219, 1879}"
36,1,781,0,0.9470935,"\int \left(b x+c x^2\right)^{2/3} \, dx","Int[(b*x + c*x^2)^(2/3),x]","\frac{3 \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3} (b+2 c x) \left(b x+c x^2\right)^{2/3}}{14 c \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{2/3}}-\frac{3 (b+2 c x) \left(b x+c x^2\right)^{2/3}}{7 \sqrt[3]{2} c \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{2/3} \left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)}+\frac{\sqrt[6]{2} 3^{3/4} b^2 \left(b x+c x^2\right)^{2/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{7 c (b+2 c x) \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{2/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}-\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} b^2 \left(b x+c x^2\right)^{2/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{14 \sqrt[3]{2} c (b+2 c x) \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{2/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}","\frac{3 \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3} (b+2 c x) \left(b x+c x^2\right)^{2/3}}{14 c \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{2/3}}-\frac{3 (b+2 c x) \left(b x+c x^2\right)^{2/3}}{7 \sqrt[3]{2} c \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{2/3} \left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)}+\frac{\sqrt[6]{2} 3^{3/4} b^2 \left(b x+c x^2\right)^{2/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{7 c (b+2 c x) \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{2/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}-\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} b^2 \left(b x+c x^2\right)^{2/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{14 \sqrt[3]{2} c (b+2 c x) \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{2/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}",1,"(3*(-((c*x*(b + c*x))/b^2))^(2/3)*(b + 2*c*x)*(b*x + c*x^2)^(2/3))/(14*c*(-((c*(b*x + c*x^2))/b^2))^(2/3)) - (3*(b + 2*c*x)*(b*x + c*x^2)^(2/3))/(7*2^(1/3)*c*(-((c*(b*x + c*x^2))/b^2))^(2/3)*(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))) - (3*3^(1/4)*Sqrt[2 + Sqrt[3]]*b^2*(b*x + c*x^2)^(2/3)*(1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3) + 2*2^(1/3)*(-((c*x*(b + c*x))/b^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))], -7 + 4*Sqrt[3]])/(14*2^(1/3)*c*(b + 2*c*x)*(-((c*(b*x + c*x^2))/b^2))^(2/3)*Sqrt[-((1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2)]) + (2^(1/6)*3^(3/4)*b^2*(b*x + c*x^2)^(2/3)*(1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3) + 2*2^(1/3)*(-((c*x*(b + c*x))/b^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))], -7 + 4*Sqrt[3]])/(7*c*(b + 2*c*x)*(-((c*(b*x + c*x^2))/b^2))^(2/3)*Sqrt[-((1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2)])","A",7,7,13,0.5385,1,"{622, 619, 195, 235, 304, 219, 1879}"
37,1,715,0,0.86049,"\int \frac{1}{\sqrt[3]{b x+c x^2}} \, dx","Int[(b*x + c*x^2)^(-1/3),x]","-\frac{3 (b+2 c x) \sqrt[3]{-\frac{c \left(b x+c x^2\right)}{b^2}}}{\sqrt[3]{2} c \sqrt[3]{b x+c x^2} \left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)}+\frac{\sqrt[6]{2} 3^{3/4} b^2 \sqrt[3]{-\frac{c \left(b x+c x^2\right)}{b^2}} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{c (b+2 c x) \sqrt[3]{b x+c x^2} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}-\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} b^2 \sqrt[3]{-\frac{c \left(b x+c x^2\right)}{b^2}} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2 \sqrt[3]{2} c (b+2 c x) \sqrt[3]{b x+c x^2} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}","-\frac{3 (b+2 c x) \sqrt[3]{-\frac{c \left(b x+c x^2\right)}{b^2}}}{\sqrt[3]{2} c \sqrt[3]{b x+c x^2} \left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)}+\frac{\sqrt[6]{2} 3^{3/4} b^2 \sqrt[3]{-\frac{c \left(b x+c x^2\right)}{b^2}} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{c (b+2 c x) \sqrt[3]{b x+c x^2} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}-\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} b^2 \sqrt[3]{-\frac{c \left(b x+c x^2\right)}{b^2}} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2 \sqrt[3]{2} c (b+2 c x) \sqrt[3]{b x+c x^2} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}",1,"(-3*(b + 2*c*x)*(-((c*(b*x + c*x^2))/b^2))^(1/3))/(2^(1/3)*c*(b*x + c*x^2)^(1/3)*(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))) - (3*3^(1/4)*Sqrt[2 + Sqrt[3]]*b^2*(-((c*(b*x + c*x^2))/b^2))^(1/3)*(1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3) + 2*2^(1/3)*(-((c*x*(b + c*x))/b^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))], -7 + 4*Sqrt[3]])/(2*2^(1/3)*c*(b + 2*c*x)*(b*x + c*x^2)^(1/3)*Sqrt[-((1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2)]) + (2^(1/6)*3^(3/4)*b^2*(-((c*(b*x + c*x^2))/b^2))^(1/3)*(1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3) + 2*2^(1/3)*(-((c*x*(b + c*x))/b^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))], -7 + 4*Sqrt[3]])/(c*(b + 2*c*x)*(b*x + c*x^2)^(1/3)*Sqrt[-((1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2)])","A",6,6,13,0.4615,1,"{622, 619, 235, 304, 219, 1879}"
38,1,773,0,0.9466519,"\int \frac{1}{\left(b x+c x^2\right)^{4/3}} \, dx","Int[(b*x + c*x^2)^(-4/3),x]","\frac{3 (b+2 c x) \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{4/3}}{c \sqrt[3]{-\frac{c x (b+c x)}{b^2}} \left(b x+c x^2\right)^{4/3}}+\frac{3\ 2^{2/3} (b+2 c x) \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{4/3}}{c \left(b x+c x^2\right)^{4/3} \left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)}-\frac{2 \sqrt[6]{2} 3^{3/4} b^2 \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{4/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{c (b+2 c x) \left(b x+c x^2\right)^{4/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}+\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} b^2 \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{4/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{2} c (b+2 c x) \left(b x+c x^2\right)^{4/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}","\frac{3 (b+2 c x) \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{4/3}}{c \sqrt[3]{-\frac{c x (b+c x)}{b^2}} \left(b x+c x^2\right)^{4/3}}+\frac{3\ 2^{2/3} (b+2 c x) \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{4/3}}{c \left(b x+c x^2\right)^{4/3} \left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)}-\frac{2 \sqrt[6]{2} 3^{3/4} b^2 \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{4/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{c (b+2 c x) \left(b x+c x^2\right)^{4/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}+\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} b^2 \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{4/3} \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{2} c (b+2 c x) \left(b x+c x^2\right)^{4/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}",1,"(3*(b + 2*c*x)*(-((c*(b*x + c*x^2))/b^2))^(4/3))/(c*(-((c*x*(b + c*x))/b^2))^(1/3)*(b*x + c*x^2)^(4/3)) + (3*2^(2/3)*(b + 2*c*x)*(-((c*(b*x + c*x^2))/b^2))^(4/3))/(c*(b*x + c*x^2)^(4/3)*(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))) + (3*3^(1/4)*Sqrt[2 + Sqrt[3]]*b^2*(-((c*(b*x + c*x^2))/b^2))^(4/3)*(1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3) + 2*2^(1/3)*(-((c*x*(b + c*x))/b^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))], -7 + 4*Sqrt[3]])/(2^(1/3)*c*(b + 2*c*x)*(b*x + c*x^2)^(4/3)*Sqrt[-((1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2)]) - (2*2^(1/6)*3^(3/4)*b^2*(-((c*(b*x + c*x^2))/b^2))^(4/3)*(1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3) + 2*2^(1/3)*(-((c*x*(b + c*x))/b^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))], -7 + 4*Sqrt[3]])/(c*(b + 2*c*x)*(b*x + c*x^2)^(4/3)*Sqrt[-((1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2)])","A",7,7,13,0.5385,1,"{622, 619, 199, 235, 304, 219, 1879}"
39,1,838,0,1.0357263,"\int \frac{1}{\left(b x+c x^2\right)^{7/3}} \, dx","Int[(b*x + c*x^2)^(-7/3),x]","\frac{15 \sqrt[4]{3} \sqrt{2+\sqrt{3}} b^2 \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right) \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{7/3}}{2 \sqrt[3]{2} c (b+2 c x) \left(c x^2+b x\right)^{7/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}-\frac{5 \sqrt[6]{2} 3^{3/4} b^2 \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right) \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{7/3}}{c (b+2 c x) \left(c x^2+b x\right)^{7/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}+\frac{15 (b+2 c x) \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{7/3}}{\sqrt[3]{2} c \left(c x^2+b x\right)^{7/3} \left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)}+\frac{15 (b+2 c x) \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{7/3}}{2 c \sqrt[3]{-\frac{c x (b+c x)}{b^2}} \left(c x^2+b x\right)^{7/3}}+\frac{3 (b+2 c x) \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{7/3}}{4 c \left(-\frac{c x (b+c x)}{b^2}\right)^{4/3} \left(c x^2+b x\right)^{7/3}}","\frac{15 \sqrt[4]{3} \sqrt{2+\sqrt{3}} b^2 \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right) \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{7/3}}{2 \sqrt[3]{2} c (b+2 c x) \left(c x^2+b x\right)^{7/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}-\frac{5 \sqrt[6]{2} 3^{3/4} b^2 \left(1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{c x (b+c x)}{b^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right) \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{7/3}}{c (b+2 c x) \left(c x^2+b x\right)^{7/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)^2}}}+\frac{15 (b+2 c x) \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{7/3}}{\sqrt[3]{2} c \left(c x^2+b x\right)^{7/3} \left(-2^{2/3} \sqrt[3]{-\frac{c x (b+c x)}{b^2}}-\sqrt{3}+1\right)}+\frac{15 (b+2 c x) \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{7/3}}{2 c \sqrt[3]{-\frac{c x (b+c x)}{b^2}} \left(c x^2+b x\right)^{7/3}}+\frac{3 (b+2 c x) \left(-\frac{c \left(c x^2+b x\right)}{b^2}\right)^{7/3}}{4 c \left(-\frac{c x (b+c x)}{b^2}\right)^{4/3} \left(c x^2+b x\right)^{7/3}}",1,"(3*(b + 2*c*x)*(-((c*(b*x + c*x^2))/b^2))^(7/3))/(4*c*(-((c*x*(b + c*x))/b^2))^(4/3)*(b*x + c*x^2)^(7/3)) + (15*(b + 2*c*x)*(-((c*(b*x + c*x^2))/b^2))^(7/3))/(2*c*(-((c*x*(b + c*x))/b^2))^(1/3)*(b*x + c*x^2)^(7/3)) + (15*(b + 2*c*x)*(-((c*(b*x + c*x^2))/b^2))^(7/3))/(2^(1/3)*c*(b*x + c*x^2)^(7/3)*(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))) + (15*3^(1/4)*Sqrt[2 + Sqrt[3]]*b^2*(-((c*(b*x + c*x^2))/b^2))^(7/3)*(1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3) + 2*2^(1/3)*(-((c*x*(b + c*x))/b^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))], -7 + 4*Sqrt[3]])/(2*2^(1/3)*c*(b + 2*c*x)*(b*x + c*x^2)^(7/3)*Sqrt[-((1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2)]) - (5*2^(1/6)*3^(3/4)*b^2*(-((c*(b*x + c*x^2))/b^2))^(7/3)*(1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3) + 2*2^(1/3)*(-((c*x*(b + c*x))/b^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))], -7 + 4*Sqrt[3]])/(c*(b + 2*c*x)*(b*x + c*x^2)^(7/3)*Sqrt[-((1 - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((c*x*(b + c*x))/b^2))^(1/3))^2)])","A",8,7,13,0.5385,1,"{622, 619, 199, 235, 304, 219, 1879}"
40,1,119,0,0.0462408,"\int \left(b x+c x^2\right)^{5/4} \, dx","Int[(b*x + c*x^2)^(5/4),x]","-\frac{5 b^2 (b+2 c x) \sqrt[4]{b x+c x^2}}{84 c^2}+\frac{5 b^5 \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{2 c x}{b}+1\right)\right|2\right)}{84 \sqrt{2} c^3 \left(b x+c x^2\right)^{3/4}}+\frac{(b+2 c x) \left(b x+c x^2\right)^{5/4}}{7 c}","-\frac{5 b^2 (b+2 c x) \sqrt[4]{b x+c x^2}}{84 c^2}+\frac{5 b^5 \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{2 c x}{b}+1\right)\right|2\right)}{84 \sqrt{2} c^3 \left(b x+c x^2\right)^{3/4}}+\frac{(b+2 c x) \left(b x+c x^2\right)^{5/4}}{7 c}",1,"(-5*b^2*(b + 2*c*x)*(b*x + c*x^2)^(1/4))/(84*c^2) + ((b + 2*c*x)*(b*x + c*x^2)^(5/4))/(7*c) + (5*b^5*(-((c*(b*x + c*x^2))/b^2))^(3/4)*EllipticF[ArcSin[1 + (2*c*x)/b]/2, 2])/(84*Sqrt[2]*c^3*(b*x + c*x^2)^(3/4))","A",5,4,13,0.3077,1,"{612, 622, 619, 232}"
41,1,90,0,0.0339669,"\int \left(b x+c x^2\right)^{3/4} \, dx","Int[(b*x + c*x^2)^(3/4),x]","\frac{(b+2 c x) \left(b x+c x^2\right)^{3/4}}{5 c}-\frac{3 b^3 \sqrt[4]{-\frac{c \left(b x+c x^2\right)}{b^2}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{2 c x}{b}+1\right)\right|2\right)}{10 \sqrt{2} c^2 \sqrt[4]{b x+c x^2}}","\frac{(b+2 c x) \left(b x+c x^2\right)^{3/4}}{5 c}-\frac{3 b^3 \sqrt[4]{-\frac{c \left(b x+c x^2\right)}{b^2}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{2 c x}{b}+1\right)\right|2\right)}{10 \sqrt{2} c^2 \sqrt[4]{b x+c x^2}}",1,"((b + 2*c*x)*(b*x + c*x^2)^(3/4))/(5*c) - (3*b^3*(-((c*(b*x + c*x^2))/b^2))^(1/4)*EllipticE[ArcSin[1 + (2*c*x)/b]/2, 2])/(10*Sqrt[2]*c^2*(b*x + c*x^2)^(1/4))","A",4,4,13,0.3077,1,"{612, 622, 619, 228}"
42,1,90,0,0.0327646,"\int \sqrt[4]{b x+c x^2} \, dx","Int[(b*x + c*x^2)^(1/4),x]","\frac{(b+2 c x) \sqrt[4]{b x+c x^2}}{3 c}-\frac{b^3 \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{2 c x}{b}+1\right)\right|2\right)}{3 \sqrt{2} c^2 \left(b x+c x^2\right)^{3/4}}","\frac{(b+2 c x) \sqrt[4]{b x+c x^2}}{3 c}-\frac{b^3 \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{2 c x}{b}+1\right)\right|2\right)}{3 \sqrt{2} c^2 \left(b x+c x^2\right)^{3/4}}",1,"((b + 2*c*x)*(b*x + c*x^2)^(1/4))/(3*c) - (b^3*(-((c*(b*x + c*x^2))/b^2))^(3/4)*EllipticF[ArcSin[1 + (2*c*x)/b]/2, 2])/(3*Sqrt[2]*c^2*(b*x + c*x^2)^(3/4))","A",4,4,13,0.3077,1,"{612, 622, 619, 232}"
43,1,58,0,0.0226108,"\int \frac{1}{\sqrt[4]{b x+c x^2}} \, dx","Int[(b*x + c*x^2)^(-1/4),x]","\frac{\sqrt{2} b \sqrt[4]{-\frac{c \left(b x+c x^2\right)}{b^2}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{2 c x}{b}+1\right)\right|2\right)}{c \sqrt[4]{b x+c x^2}}","\frac{\sqrt{2} b \sqrt[4]{-\frac{c \left(b x+c x^2\right)}{b^2}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{2 c x}{b}+1\right)\right|2\right)}{c \sqrt[4]{b x+c x^2}}",1,"(Sqrt[2]*b*(-((c*(b*x + c*x^2))/b^2))^(1/4)*EllipticE[ArcSin[1 + (2*c*x)/b]/2, 2])/(c*(b*x + c*x^2)^(1/4))","A",3,3,13,0.2308,1,"{622, 619, 228}"
44,1,59,0,0.0234089,"\int \frac{1}{\left(b x+c x^2\right)^{3/4}} \, dx","Int[(b*x + c*x^2)^(-3/4),x]","\frac{2 \sqrt{2} b \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{2 c x}{b}+1\right)\right|2\right)}{c \left(b x+c x^2\right)^{3/4}}","\frac{2 \sqrt{2} b \left(-\frac{c \left(b x+c x^2\right)}{b^2}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{2 c x}{b}+1\right)\right|2\right)}{c \left(b x+c x^2\right)^{3/4}}",1,"(2*Sqrt[2]*b*(-((c*(b*x + c*x^2))/b^2))^(3/4)*EllipticF[ArcSin[1 + (2*c*x)/b]/2, 2])/(c*(b*x + c*x^2)^(3/4))","A",3,3,13,0.2308,1,"{622, 619, 232}"
45,1,83,0,0.0316459,"\int \frac{1}{\left(b x+c x^2\right)^{5/4}} \, dx","Int[(b*x + c*x^2)^(-5/4),x]","\frac{4 \sqrt{2} \sqrt[4]{-\frac{c \left(b x+c x^2\right)}{b^2}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{2 c x}{b}+1\right)\right|2\right)}{b \sqrt[4]{b x+c x^2}}-\frac{4 (b+2 c x)}{b^2 \sqrt[4]{b x+c x^2}}","\frac{4 \sqrt{2} \sqrt[4]{-\frac{c \left(b x+c x^2\right)}{b^2}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{2 c x}{b}+1\right)\right|2\right)}{b \sqrt[4]{b x+c x^2}}-\frac{4 (b+2 c x)}{b^2 \sqrt[4]{b x+c x^2}}",1,"(-4*(b + 2*c*x))/(b^2*(b*x + c*x^2)^(1/4)) + (4*Sqrt[2]*(-((c*(b*x + c*x^2))/b^2))^(1/4)*EllipticE[ArcSin[1 + (2*c*x)/b]/2, 2])/(b*(b*x + c*x^2)^(1/4))","A",4,4,13,0.3077,1,"{614, 622, 619, 228}"
46,1,115,0,0.0435125,"\int \frac{1}{\left(b x+c x^2\right)^{9/4}} \, dx","Int[(b*x + c*x^2)^(-9/4),x]","\frac{48 c (b+2 c x)}{5 b^4 \sqrt[4]{b x+c x^2}}-\frac{4 (b+2 c x)}{5 b^2 \left(b x+c x^2\right)^{5/4}}-\frac{48 \sqrt{2} c \sqrt[4]{-\frac{c \left(b x+c x^2\right)}{b^2}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{2 c x}{b}+1\right)\right|2\right)}{5 b^3 \sqrt[4]{b x+c x^2}}","\frac{48 c (b+2 c x)}{5 b^4 \sqrt[4]{b x+c x^2}}-\frac{4 (b+2 c x)}{5 b^2 \left(b x+c x^2\right)^{5/4}}-\frac{48 \sqrt{2} c \sqrt[4]{-\frac{c \left(b x+c x^2\right)}{b^2}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{2 c x}{b}+1\right)\right|2\right)}{5 b^3 \sqrt[4]{b x+c x^2}}",1,"(-4*(b + 2*c*x))/(5*b^2*(b*x + c*x^2)^(5/4)) + (48*c*(b + 2*c*x))/(5*b^4*(b*x + c*x^2)^(1/4)) - (48*Sqrt[2]*c*(-((c*(b*x + c*x^2))/b^2))^(1/4)*EllipticE[ArcSin[1 + (2*c*x)/b]/2, 2])/(5*b^3*(b*x + c*x^2)^(1/4))","A",5,4,13,0.3077,1,"{614, 622, 619, 228}"
47,1,146,0,0.0601218,"\int \frac{1}{\left(b x+c x^2\right)^{13/4}} \, dx","Int[(b*x + c*x^2)^(-13/4),x]","-\frac{448 c^2 (b+2 c x)}{15 b^6 \sqrt[4]{b x+c x^2}}+\frac{448 \sqrt{2} c^2 \sqrt[4]{-\frac{c \left(b x+c x^2\right)}{b^2}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{2 c x}{b}+1\right)\right|2\right)}{15 b^5 \sqrt[4]{b x+c x^2}}+\frac{112 c (b+2 c x)}{45 b^4 \left(b x+c x^2\right)^{5/4}}-\frac{4 (b+2 c x)}{9 b^2 \left(b x+c x^2\right)^{9/4}}","-\frac{448 c^2 (b+2 c x)}{15 b^6 \sqrt[4]{b x+c x^2}}+\frac{448 \sqrt{2} c^2 \sqrt[4]{-\frac{c \left(b x+c x^2\right)}{b^2}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{2 c x}{b}+1\right)\right|2\right)}{15 b^5 \sqrt[4]{b x+c x^2}}+\frac{112 c (b+2 c x)}{45 b^4 \left(b x+c x^2\right)^{5/4}}-\frac{4 (b+2 c x)}{9 b^2 \left(b x+c x^2\right)^{9/4}}",1,"(-4*(b + 2*c*x))/(9*b^2*(b*x + c*x^2)^(9/4)) + (112*c*(b + 2*c*x))/(45*b^4*(b*x + c*x^2)^(5/4)) - (448*c^2*(b + 2*c*x))/(15*b^6*(b*x + c*x^2)^(1/4)) + (448*Sqrt[2]*c^2*(-((c*(b*x + c*x^2))/b^2))^(1/4)*EllipticE[ArcSin[1 + (2*c*x)/b]/2, 2])/(15*b^5*(b*x + c*x^2)^(1/4))","A",6,4,13,0.3077,1,"{614, 622, 619, 228}"
48,1,55,0,0.0104559,"\int \left(b x+c x^2\right)^p \, dx","Int[(b*x + c*x^2)^p,x]","-\frac{\left(-\frac{c x}{b}\right)^{-p-1} \left(b x+c x^2\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{b+c x}{b}\right)}{b (p+1)}","-\frac{\left(-\frac{c x}{b}\right)^{-p-1} \left(b x+c x^2\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{b+c x}{b}\right)}{b (p+1)}",1,"-(((-((c*x)/b))^(-1 - p)*(b*x + c*x^2)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + c*x)/b])/(b*(1 + p)))","A",1,1,11,0.09091,1,"{624}"
49,1,51,0,0.0173736,"\int \left(a+c x^2\right)^4 \, dx","Int[(a + c*x^2)^4,x]","\frac{6}{5} a^2 c^2 x^5+\frac{4}{3} a^3 c x^3+a^4 x+\frac{4}{7} a c^3 x^7+\frac{c^4 x^9}{9}","\frac{6}{5} a^2 c^2 x^5+\frac{4}{3} a^3 c x^3+a^4 x+\frac{4}{7} a c^3 x^7+\frac{c^4 x^9}{9}",1,"a^4*x + (4*a^3*c*x^3)/3 + (6*a^2*c^2*x^5)/5 + (4*a*c^3*x^7)/7 + (c^4*x^9)/9","A",2,1,9,0.1111,1,"{194}"
50,1,35,0,0.0114554,"\int \left(a+c x^2\right)^3 \, dx","Int[(a + c*x^2)^3,x]","a^2 c x^3+a^3 x+\frac{3}{5} a c^2 x^5+\frac{c^3 x^7}{7}","a^2 c x^3+a^3 x+\frac{3}{5} a c^2 x^5+\frac{c^3 x^7}{7}",1,"a^3*x + a^2*c*x^3 + (3*a*c^2*x^5)/5 + (c^3*x^7)/7","A",2,1,9,0.1111,1,"{194}"
51,1,25,0,0.0071073,"\int \left(a+c x^2\right)^2 \, dx","Int[(a + c*x^2)^2,x]","a^2 x+\frac{2}{3} a c x^3+\frac{c^2 x^5}{5}","a^2 x+\frac{2}{3} a c x^3+\frac{c^2 x^5}{5}",1,"a^2*x + (2*a*c*x^3)/3 + (c^2*x^5)/5","A",2,1,9,0.1111,1,"{194}"
52,1,12,0,0.0019781,"\int \left(a+c x^2\right) \, dx","Int[a + c*x^2,x]","a x+\frac{c x^3}{3}","a x+\frac{c x^3}{3}",1,"a*x + (c*x^3)/3","A",1,0,7,0,1,"{}"
53,1,24,0,0.0050706,"\int \frac{1}{a+c x^2} \, dx","Int[(a + c*x^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{c}}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{c}}",1,"ArcTan[(Sqrt[c]*x)/Sqrt[a]]/(Sqrt[a]*Sqrt[c])","A",1,1,9,0.1111,1,"{205}"
54,1,45,0,0.009972,"\int \frac{1}{\left(a+c x^2\right)^2} \, dx","Int[(a + c*x^2)^(-2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{c}}+\frac{x}{2 a \left(a+c x^2\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{c}}+\frac{x}{2 a \left(a+c x^2\right)}",1,"x/(2*a*(a + c*x^2)) + ArcTan[(Sqrt[c]*x)/Sqrt[a]]/(2*a^(3/2)*Sqrt[c])","A",2,2,9,0.2222,1,"{199, 205}"
55,1,62,0,0.0159544,"\int \frac{1}{\left(a+c x^2\right)^3} \, dx","Int[(a + c*x^2)^(-3),x]","\frac{3 x}{8 a^2 \left(a+c x^2\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{c}}+\frac{x}{4 a \left(a+c x^2\right)^2}","\frac{3 x}{8 a^2 \left(a+c x^2\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{c}}+\frac{x}{4 a \left(a+c x^2\right)^2}",1,"x/(4*a*(a + c*x^2)^2) + (3*x)/(8*a^2*(a + c*x^2)) + (3*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*Sqrt[c])","A",3,2,9,0.2222,1,"{199, 205}"
56,1,84,0,0.0224621,"\int \left(a+c x^2\right)^{5/2} \, dx","Int[(a + c*x^2)^(5/2),x]","\frac{5}{16} a^2 x \sqrt{a+c x^2}+\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 \sqrt{c}}+\frac{5}{24} a x \left(a+c x^2\right)^{3/2}+\frac{1}{6} x \left(a+c x^2\right)^{5/2}","\frac{5}{16} a^2 x \sqrt{a+c x^2}+\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 \sqrt{c}}+\frac{5}{24} a x \left(a+c x^2\right)^{3/2}+\frac{1}{6} x \left(a+c x^2\right)^{5/2}",1,"(5*a^2*x*Sqrt[a + c*x^2])/16 + (5*a*x*(a + c*x^2)^(3/2))/24 + (x*(a + c*x^2)^(5/2))/6 + (5*a^3*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(16*Sqrt[c])","A",5,3,11,0.2727,1,"{195, 217, 206}"
57,1,65,0,0.0143466,"\int \left(a+c x^2\right)^{3/2} \, dx","Int[(a + c*x^2)^(3/2),x]","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 \sqrt{c}}+\frac{3}{8} a x \sqrt{a+c x^2}+\frac{1}{4} x \left(a+c x^2\right)^{3/2}","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 \sqrt{c}}+\frac{3}{8} a x \sqrt{a+c x^2}+\frac{1}{4} x \left(a+c x^2\right)^{3/2}",1,"(3*a*x*Sqrt[a + c*x^2])/8 + (x*(a + c*x^2)^(3/2))/4 + (3*a^2*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*Sqrt[c])","A",4,3,11,0.2727,1,"{195, 217, 206}"
58,1,46,0,0.0089727,"\int \sqrt{a+c x^2} \, dx","Int[Sqrt[a + c*x^2],x]","\frac{1}{2} x \sqrt{a+c x^2}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 \sqrt{c}}","\frac{1}{2} x \sqrt{a+c x^2}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 \sqrt{c}}",1,"(x*Sqrt[a + c*x^2])/2 + (a*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*Sqrt[c])","A",3,3,11,0.2727,1,"{195, 217, 206}"
59,1,25,0,0.0052679,"\int \frac{1}{\sqrt{a+c x^2}} \, dx","Int[1/Sqrt[a + c*x^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c}}",1,"ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]]/Sqrt[c]","A",2,2,11,0.1818,1,"{217, 206}"
60,1,16,0,0.0019738,"\int \frac{1}{\left(a+c x^2\right)^{3/2}} \, dx","Int[(a + c*x^2)^(-3/2),x]","\frac{x}{a \sqrt{a+c x^2}}","\frac{x}{a \sqrt{a+c x^2}}",1,"x/(a*Sqrt[a + c*x^2])","A",1,1,11,0.09091,1,"{191}"
61,1,39,0,0.0056857,"\int \frac{1}{\left(a+c x^2\right)^{5/2}} \, dx","Int[(a + c*x^2)^(-5/2),x]","\frac{2 x}{3 a^2 \sqrt{a+c x^2}}+\frac{x}{3 a \left(a+c x^2\right)^{3/2}}","\frac{2 x}{3 a^2 \sqrt{a+c x^2}}+\frac{x}{3 a \left(a+c x^2\right)^{3/2}}",1,"x/(3*a*(a + c*x^2)^(3/2)) + (2*x)/(3*a^2*Sqrt[a + c*x^2])","A",2,2,11,0.1818,1,"{192, 191}"
62,1,58,0,0.0104298,"\int \frac{1}{\left(a+c x^2\right)^{7/2}} \, dx","Int[(a + c*x^2)^(-7/2),x]","\frac{8 x}{15 a^3 \sqrt{a+c x^2}}+\frac{4 x}{15 a^2 \left(a+c x^2\right)^{3/2}}+\frac{x}{5 a \left(a+c x^2\right)^{5/2}}","\frac{8 x}{15 a^3 \sqrt{a+c x^2}}+\frac{4 x}{15 a^2 \left(a+c x^2\right)^{3/2}}+\frac{x}{5 a \left(a+c x^2\right)^{5/2}}",1,"x/(5*a*(a + c*x^2)^(5/2)) + (4*x)/(15*a^2*(a + c*x^2)^(3/2)) + (8*x)/(15*a^3*Sqrt[a + c*x^2])","A",3,2,11,0.1818,1,"{192, 191}"
63,1,77,0,0.0159789,"\int \frac{1}{\left(a+c x^2\right)^{9/2}} \, dx","Int[(a + c*x^2)^(-9/2),x]","\frac{16 x}{35 a^4 \sqrt{a+c x^2}}+\frac{8 x}{35 a^3 \left(a+c x^2\right)^{3/2}}+\frac{6 x}{35 a^2 \left(a+c x^2\right)^{5/2}}+\frac{x}{7 a \left(a+c x^2\right)^{7/2}}","\frac{16 x}{35 a^4 \sqrt{a+c x^2}}+\frac{8 x}{35 a^3 \left(a+c x^2\right)^{3/2}}+\frac{6 x}{35 a^2 \left(a+c x^2\right)^{5/2}}+\frac{x}{7 a \left(a+c x^2\right)^{7/2}}",1,"x/(7*a*(a + c*x^2)^(7/2)) + (6*x)/(35*a^2*(a + c*x^2)^(5/2)) + (8*x)/(35*a^3*(a + c*x^2)^(3/2)) + (16*x)/(35*a^4*Sqrt[a + c*x^2])","A",4,2,11,0.1818,1,"{192, 191}"
64,1,23,0,0.0028427,"\int \left(4+12 x+9 x^2\right)^{3/2} \, dx","Int[(4 + 12*x + 9*x^2)^(3/2),x]","\frac{1}{12} (3 x+2) \left(9 x^2+12 x+4\right)^{3/2}","\frac{1}{12} (3 x+2) \left(9 x^2+12 x+4\right)^{3/2}",1,"((2 + 3*x)*(4 + 12*x + 9*x^2)^(3/2))/12","A",1,1,14,0.07143,1,"{609}"
65,1,23,0,0.0031282,"\int \sqrt{4+12 x+9 x^2} \, dx","Int[Sqrt[4 + 12*x + 9*x^2],x]","\frac{1}{6} (3 x+2) \sqrt{9 x^2+12 x+4}","\frac{1}{6} (3 x+2) \sqrt{9 x^2+12 x+4}",1,"((2 + 3*x)*Sqrt[4 + 12*x + 9*x^2])/6","A",1,1,14,0.07143,1,"{609}"
66,1,29,0,0.0048338,"\int \frac{1}{\sqrt{4+12 x+9 x^2}} \, dx","Int[1/Sqrt[4 + 12*x + 9*x^2],x]","\frac{(3 x+2) \log (3 x+2)}{3 \sqrt{9 x^2+12 x+4}}","\frac{(3 x+2) \log (3 x+2)}{3 \sqrt{9 x^2+12 x+4}}",1,"((2 + 3*x)*Log[2 + 3*x])/(3*Sqrt[4 + 12*x + 9*x^2])","A",2,2,14,0.1429,1,"{608, 31}"
67,1,25,0,0.0026011,"\int \frac{1}{\left(4+12 x+9 x^2\right)^{3/2}} \, dx","Int[(4 + 12*x + 9*x^2)^(-3/2),x]","-\frac{1}{6 (3 x+2) \sqrt{9 x^2+12 x+4}}","-\frac{1}{6 (3 x+2) \sqrt{9 x^2+12 x+4}}",1,"-1/(6*(2 + 3*x)*Sqrt[4 + 12*x + 9*x^2])","A",1,1,14,0.07143,1,"{607}"
68,1,23,0,0.0029693,"\int \sqrt{4-12 x+9 x^2} \, dx","Int[Sqrt[4 - 12*x + 9*x^2],x]","-\frac{1}{6} (2-3 x) \sqrt{9 x^2-12 x+4}","-\frac{1}{6} (2-3 x) \sqrt{9 x^2-12 x+4}",1,"-((2 - 3*x)*Sqrt[4 - 12*x + 9*x^2])/6","A",1,1,14,0.07143,1,"{609}"
69,1,29,0,0.004519,"\int \frac{1}{\sqrt{4-12 x+9 x^2}} \, dx","Int[1/Sqrt[4 - 12*x + 9*x^2],x]","-\frac{(2-3 x) \log (2-3 x)}{3 \sqrt{9 x^2-12 x+4}}","-\frac{(2-3 x) \log (2-3 x)}{3 \sqrt{9 x^2-12 x+4}}",1,"-((2 - 3*x)*Log[2 - 3*x])/(3*Sqrt[4 - 12*x + 9*x^2])","A",2,2,14,0.1429,1,"{608, 31}"
70,1,23,0,0.0026217,"\int \sqrt{-4+12 x-9 x^2} \, dx","Int[Sqrt[-4 + 12*x - 9*x^2],x]","-\frac{1}{6} (2-3 x) \sqrt{-9 x^2+12 x-4}","-\frac{1}{6} (2-3 x) \sqrt{-9 x^2+12 x-4}",1,"-((2 - 3*x)*Sqrt[-4 + 12*x - 9*x^2])/6","A",1,1,14,0.07143,1,"{609}"
71,1,29,0,0.0047919,"\int \frac{1}{\sqrt{-4+12 x-9 x^2}} \, dx","Int[1/Sqrt[-4 + 12*x - 9*x^2],x]","-\frac{(2-3 x) \log (2-3 x)}{3 \sqrt{-9 x^2+12 x-4}}","-\frac{(2-3 x) \log (2-3 x)}{3 \sqrt{-9 x^2+12 x-4}}",1,"-((2 - 3*x)*Log[2 - 3*x])/(3*Sqrt[-4 + 12*x - 9*x^2])","A",2,2,14,0.1429,1,"{608, 31}"
72,1,23,0,0.0025759,"\int \sqrt{-4-12 x-9 x^2} \, dx","Int[Sqrt[-4 - 12*x - 9*x^2],x]","\frac{1}{6} (3 x+2) \sqrt{-9 x^2-12 x-4}","\frac{1}{6} (3 x+2) \sqrt{-9 x^2-12 x-4}",1,"((2 + 3*x)*Sqrt[-4 - 12*x - 9*x^2])/6","A",1,1,14,0.07143,1,"{609}"
73,1,29,0,0.0056675,"\int \frac{1}{\sqrt{-4-12 x-9 x^2}} \, dx","Int[1/Sqrt[-4 - 12*x - 9*x^2],x]","\frac{(3 x+2) \log (3 x+2)}{3 \sqrt{-9 x^2-12 x-4}}","\frac{(3 x+2) \log (3 x+2)}{3 \sqrt{-9 x^2-12 x-4}}",1,"((2 + 3*x)*Log[2 + 3*x])/(3*Sqrt[-4 - 12*x - 9*x^2])","A",2,2,14,0.1429,1,"{608, 31}"
74,1,109,0,0.1398847,"\int \left(\frac{-1+b^2}{4 c}+b x+c x^2\right)^5 \, dx","Int[((-1 + b^2)/(4*c) + b*x + c*x^2)^5,x]","-\frac{(-b-2 c x+1)^{11}}{22528 c^6}+\frac{(-b-2 c x+1)^{10}}{2048 c^6}-\frac{5 (-b-2 c x+1)^9}{2304 c^6}+\frac{5 (-b-2 c x+1)^8}{1024 c^6}-\frac{5 (-b-2 c x+1)^7}{896 c^6}+\frac{(-b-2 c x+1)^6}{384 c^6}","-\frac{(-b-2 c x+1)^{11}}{22528 c^6}+\frac{(-b-2 c x+1)^{10}}{2048 c^6}-\frac{5 (-b-2 c x+1)^9}{2304 c^6}+\frac{5 (-b-2 c x+1)^8}{1024 c^6}-\frac{5 (-b-2 c x+1)^7}{896 c^6}+\frac{(-b-2 c x+1)^6}{384 c^6}",1,"(1 - b - 2*c*x)^6/(384*c^6) - (5*(1 - b - 2*c*x)^7)/(896*c^6) + (5*(1 - b - 2*c*x)^8)/(1024*c^6) - (5*(1 - b - 2*c*x)^9)/(2304*c^6) + (1 - b - 2*c*x)^10/(2048*c^6) - (1 - b - 2*c*x)^11/(22528*c^6)","A",3,2,23,0.08696,1,"{610, 43}"
75,1,109,0,0.1365606,"\int \left(\frac{-4+b^2}{4 c}+b x+c x^2\right)^5 \, dx","Int[((-4 + b^2)/(4*c) + b*x + c*x^2)^5,x]","-\frac{(-b-2 c x+2)^{11}}{22528 c^6}+\frac{(-b-2 c x+2)^{10}}{1024 c^6}-\frac{5 (-b-2 c x+2)^9}{576 c^6}+\frac{5 (-b-2 c x+2)^8}{128 c^6}-\frac{5 (-b-2 c x+2)^7}{56 c^6}+\frac{(-b-2 c x+2)^6}{12 c^6}","-\frac{(-b-2 c x+2)^{11}}{22528 c^6}+\frac{(-b-2 c x+2)^{10}}{1024 c^6}-\frac{5 (-b-2 c x+2)^9}{576 c^6}+\frac{5 (-b-2 c x+2)^8}{128 c^6}-\frac{5 (-b-2 c x+2)^7}{56 c^6}+\frac{(-b-2 c x+2)^6}{12 c^6}",1,"(2 - b - 2*c*x)^6/(12*c^6) - (5*(2 - b - 2*c*x)^7)/(56*c^6) + (5*(2 - b - 2*c*x)^8)/(128*c^6) - (5*(2 - b - 2*c*x)^9)/(576*c^6) + (2 - b - 2*c*x)^10/(1024*c^6) - (2 - b - 2*c*x)^11/(22528*c^6)","A",3,2,23,0.08696,1,"{610, 43}"
76,1,109,0,0.142473,"\int \left(\frac{-9+b^2}{4 c}+b x+c x^2\right)^5 \, dx","Int[((-9 + b^2)/(4*c) + b*x + c*x^2)^5,x]","-\frac{(-b-2 c x+3)^{11}}{22528 c^6}+\frac{3 (-b-2 c x+3)^{10}}{2048 c^6}-\frac{5 (-b-2 c x+3)^9}{256 c^6}+\frac{135 (-b-2 c x+3)^8}{1024 c^6}-\frac{405 (-b-2 c x+3)^7}{896 c^6}+\frac{81 (-b-2 c x+3)^6}{128 c^6}","-\frac{(-b-2 c x+3)^{11}}{22528 c^6}+\frac{3 (-b-2 c x+3)^{10}}{2048 c^6}-\frac{5 (-b-2 c x+3)^9}{256 c^6}+\frac{135 (-b-2 c x+3)^8}{1024 c^6}-\frac{405 (-b-2 c x+3)^7}{896 c^6}+\frac{81 (-b-2 c x+3)^6}{128 c^6}",1,"(81*(3 - b - 2*c*x)^6)/(128*c^6) - (405*(3 - b - 2*c*x)^7)/(896*c^6) + (135*(3 - b - 2*c*x)^8)/(1024*c^6) - (5*(3 - b - 2*c*x)^9)/(256*c^6) + (3*(3 - b - 2*c*x)^10)/(2048*c^6) - (3 - b - 2*c*x)^11/(22528*c^6)","A",3,2,23,0.08696,1,"{610, 43}"
77,1,109,0,0.1398487,"\int \left(\frac{-16+b^2}{4 c}+b x+c x^2\right)^5 \, dx","Int[((-16 + b^2)/(4*c) + b*x + c*x^2)^5,x]","-\frac{(-b-2 c x+4)^{11}}{22528 c^6}+\frac{(-b-2 c x+4)^{10}}{512 c^6}-\frac{5 (-b-2 c x+4)^9}{144 c^6}+\frac{5 (-b-2 c x+4)^8}{16 c^6}-\frac{10 (-b-2 c x+4)^7}{7 c^6}+\frac{8 (-b-2 c x+4)^6}{3 c^6}","-\frac{(-b-2 c x+4)^{11}}{22528 c^6}+\frac{(-b-2 c x+4)^{10}}{512 c^6}-\frac{5 (-b-2 c x+4)^9}{144 c^6}+\frac{5 (-b-2 c x+4)^8}{16 c^6}-\frac{10 (-b-2 c x+4)^7}{7 c^6}+\frac{8 (-b-2 c x+4)^6}{3 c^6}",1,"(8*(4 - b - 2*c*x)^6)/(3*c^6) - (10*(4 - b - 2*c*x)^7)/(7*c^6) + (5*(4 - b - 2*c*x)^8)/(16*c^6) - (5*(4 - b - 2*c*x)^9)/(144*c^6) + (4 - b - 2*c*x)^10/(512*c^6) - (4 - b - 2*c*x)^11/(22528*c^6)","A",3,2,23,0.08696,1,"{610, 43}"
78,1,18,0,0.0112172,"\int \frac{1}{2+4 x+3 x^2} \, dx","Int[(2 + 4*x + 3*x^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{3 x+2}{\sqrt{2}}\right)}{\sqrt{2}}","\frac{\tan ^{-1}\left(\frac{3 x+2}{\sqrt{2}}\right)}{\sqrt{2}}",1,"ArcTan[(2 + 3*x)/Sqrt[2]]/Sqrt[2]","A",2,2,12,0.1667,1,"{618, 204}"
79,1,12,0,0.0086108,"\int \frac{1}{4-2 \sqrt{3} x+x^2} \, dx","Int[(4 - 2*Sqrt[3]*x + x^2)^(-1),x]","-\tan ^{-1}\left(\sqrt{3}-x\right)","-\tan ^{-1}\left(\sqrt{3}-x\right)",1,"-ArcTan[Sqrt[3] - x]","A",2,2,15,0.1333,1,"{618, 204}"
80,1,19,0,0.0192329,"\int \frac{1}{2+4 x-3 x^2} \, dx","Int[(2 + 4*x - 3*x^2)^(-1),x]","-\frac{\tanh ^{-1}\left(\frac{2-3 x}{\sqrt{10}}\right)}{\sqrt{10}}","-\frac{\tanh ^{-1}\left(\frac{2-3 x}{\sqrt{10}}\right)}{\sqrt{10}}",1,"-(ArcTanh[(2 - 3*x)/Sqrt[10]]/Sqrt[10])","A",2,2,12,0.1667,1,"{618, 206}"
81,1,13,0,0.0052461,"\int \frac{1}{2+5 x+3 x^2} \, dx","Int[(2 + 5*x + 3*x^2)^(-1),x]","\log (3 x+2)-\log (x+1)","\log (3 x+2)-\log (x+1)",1,"-Log[1 + x] + Log[2 + 3*x]","A",3,2,12,0.1667,1,"{616, 31}"
82,1,21,0,0.0055975,"\int \frac{1}{2+5 x-3 x^2} \, dx","Int[(2 + 5*x - 3*x^2)^(-1),x]","\frac{1}{7} \log (3 x+1)-\frac{1}{7} \log (2-x)","\frac{1}{7} \log (3 x+1)-\frac{1}{7} \log (2-x)",1,"-Log[2 - x]/7 + Log[1 + 3*x]/7","A",3,2,12,0.1667,1,"{616, 31}"
83,1,17,0,0.0036109,"\int \frac{1}{3+4 x+x^2} \, dx","Int[(3 + 4*x + x^2)^(-1),x]","\frac{1}{2} \log (x+1)-\frac{1}{2} \log (x+3)","-\tanh ^{-1}(x+2)",1,"Log[1 + x]/2 - Log[3 + x]/2","B",3,2,10,0.2000,1,"{616, 31}"
84,1,27,0,0.0186286,"\int \frac{1}{1+\pi  x+2 x^2} \, dx","Int[(1 + Pi*x + 2*x^2)^(-1),x]","-\frac{2 \tanh ^{-1}\left(\frac{4 x+\pi }{\sqrt{\pi ^2-8}}\right)}{\sqrt{\pi ^2-8}}","-\frac{2 \tanh ^{-1}\left(\frac{4 x+\pi }{\sqrt{\pi ^2-8}}\right)}{\sqrt{\pi ^2-8}}",1,"(-2*ArcTanh[(Pi + 4*x)/Sqrt[-8 + Pi^2]])/Sqrt[-8 + Pi^2]","A",2,2,12,0.1667,1,"{618, 206}"
85,1,27,0,0.01862,"\int \frac{1}{1+\pi  x-2 x^2} \, dx","Int[(1 + Pi*x - 2*x^2)^(-1),x]","-\frac{2 \tanh ^{-1}\left(\frac{\pi -4 x}{\sqrt{8+\pi ^2}}\right)}{\sqrt{8+\pi ^2}}","-\frac{2 \tanh ^{-1}\left(\frac{\pi -4 x}{\sqrt{8+\pi ^2}}\right)}{\sqrt{8+\pi ^2}}",1,"(-2*ArcTanh[(Pi - 4*x)/Sqrt[8 + Pi^2]])/Sqrt[8 + Pi^2]","A",2,2,12,0.1667,1,"{618, 206}"
86,1,31,0,0.0202124,"\int \frac{1}{1+\pi  x+3 x^2} \, dx","Int[(1 + Pi*x + 3*x^2)^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{6 x+\pi }{\sqrt{12-\pi ^2}}\right)}{\sqrt{12-\pi ^2}}","\frac{2 \tan ^{-1}\left(\frac{6 x+\pi }{\sqrt{12-\pi ^2}}\right)}{\sqrt{12-\pi ^2}}",1,"(2*ArcTan[(Pi + 6*x)/Sqrt[12 - Pi^2]])/Sqrt[12 - Pi^2]","A",2,2,12,0.1667,1,"{618, 204}"
87,1,27,0,0.0182718,"\int \frac{1}{1+\pi  x-3 x^2} \, dx","Int[(1 + Pi*x - 3*x^2)^(-1),x]","-\frac{2 \tanh ^{-1}\left(\frac{\pi -6 x}{\sqrt{12+\pi ^2}}\right)}{\sqrt{12+\pi ^2}}","-\frac{2 \tanh ^{-1}\left(\frac{\pi -6 x}{\sqrt{12+\pi ^2}}\right)}{\sqrt{12+\pi ^2}}",1,"(-2*ArcTanh[(Pi - 6*x)/Sqrt[12 + Pi^2]])/Sqrt[12 + Pi^2]","A",2,2,12,0.1667,1,"{618, 206}"
88,1,38,0,0.0340968,"\int \frac{1}{a+c x+b x^2} \, dx","Int[(a + c*x + b*x^2)^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{2 b x+c}{\sqrt{4 a b-c^2}}\right)}{\sqrt{4 a b-c^2}}","\frac{2 \tan ^{-1}\left(\frac{2 b x+c}{\sqrt{4 a b-c^2}}\right)}{\sqrt{4 a b-c^2}}",1,"(2*ArcTan[(c + 2*b*x)/Sqrt[4*a*b - c^2]])/Sqrt[4*a*b - c^2]","A",2,2,12,0.1667,1,"{618, 204}"
89,1,35,0,0.0273843,"\int \frac{1}{b+2 a x+b x^2} \, dx","Int[(b + 2*a*x + b*x^2)^(-1),x]","-\frac{\tanh ^{-1}\left(\frac{a+b x}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}","-\frac{\tanh ^{-1}\left(\frac{a+b x}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}",1,"-(ArcTanh[(a + b*x)/Sqrt[a^2 - b^2]]/Sqrt[a^2 - b^2])","A",2,2,13,0.1538,1,"{618, 206}"
90,1,32,0,0.0254946,"\int \frac{1}{b+2 a x-b x^2} \, dx","Int[(b + 2*a*x - b*x^2)^(-1),x]","-\frac{\tanh ^{-1}\left(\frac{a-b x}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2}}","-\frac{\tanh ^{-1}\left(\frac{a-b x}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2}}",1,"-(ArcTanh[(a - b*x)/Sqrt[a^2 + b^2]]/Sqrt[a^2 + b^2])","A",2,2,14,0.1429,1,"{618, 206}"
91,1,43,0,0.0146884,"\int \frac{1}{\left(2+4 x+3 x^2\right)^2} \, dx","Int[(2 + 4*x + 3*x^2)^(-2),x]","\frac{3 x+2}{4 \left(3 x^2+4 x+2\right)}+\frac{3 \tan ^{-1}\left(\frac{3 x+2}{\sqrt{2}}\right)}{4 \sqrt{2}}","\frac{3 x+2}{4 \left(3 x^2+4 x+2\right)}+\frac{3 \tan ^{-1}\left(\frac{3 x+2}{\sqrt{2}}\right)}{4 \sqrt{2}}",1,"(2 + 3*x)/(4*(2 + 4*x + 3*x^2)) + (3*ArcTan[(2 + 3*x)/Sqrt[2]])/(4*Sqrt[2])","A",3,3,12,0.2500,1,"{614, 618, 204}"
92,1,43,0,0.0158066,"\int \frac{1}{\left(2+4 x-3 x^2\right)^2} \, dx","Int[(2 + 4*x - 3*x^2)^(-2),x]","-\frac{2-3 x}{20 \left(-3 x^2+4 x+2\right)}-\frac{3 \tanh ^{-1}\left(\frac{2-3 x}{\sqrt{10}}\right)}{20 \sqrt{10}}","-\frac{2-3 x}{20 \left(-3 x^2+4 x+2\right)}-\frac{3 \tanh ^{-1}\left(\frac{2-3 x}{\sqrt{10}}\right)}{20 \sqrt{10}}",1,"-(2 - 3*x)/(20*(2 + 4*x - 3*x^2)) - (3*ArcTanh[(2 - 3*x)/Sqrt[10]])/(20*Sqrt[10])","A",3,3,12,0.2500,1,"{614, 618, 206}"
93,1,34,0,0.0080393,"\int \frac{1}{\left(2+5 x+3 x^2\right)^2} \, dx","Int[(2 + 5*x + 3*x^2)^(-2),x]","-\frac{6 x+5}{3 x^2+5 x+2}+6 \log (x+1)-6 \log (3 x+2)","-\frac{6 x+5}{3 x^2+5 x+2}+6 \log (x+1)-6 \log (3 x+2)",1,"-((5 + 6*x)/(2 + 5*x + 3*x^2)) + 6*Log[1 + x] - 6*Log[2 + 3*x]","A",4,3,12,0.2500,1,"{614, 616, 31}"
94,1,42,0,0.0090168,"\int \frac{1}{\left(2+5 x-3 x^2\right)^2} \, dx","Int[(2 + 5*x - 3*x^2)^(-2),x]","-\frac{5-6 x}{49 \left(-3 x^2+5 x+2\right)}-\frac{6}{343} \log (2-x)+\frac{6}{343} \log (3 x+1)","-\frac{5-6 x}{49 \left(-3 x^2+5 x+2\right)}-\frac{6}{343} \log (2-x)+\frac{6}{343} \log (3 x+1)",1,"-(5 - 6*x)/(49*(2 + 5*x - 3*x^2)) - (6*Log[2 - x])/343 + (6*Log[1 + 3*x])/343","A",4,3,12,0.2500,1,"{614, 616, 31}"
95,1,71,0,0.0397878,"\int \frac{1}{\left(a+c x+b x^2\right)^2} \, dx","Int[(a + c*x + b*x^2)^(-2),x]","\frac{2 b x+c}{\left(4 a b-c^2\right) \left(a+b x^2+c x\right)}+\frac{4 b \tan ^{-1}\left(\frac{2 b x+c}{\sqrt{4 a b-c^2}}\right)}{\left(4 a b-c^2\right)^{3/2}}","\frac{2 b x+c}{\left(4 a b-c^2\right) \left(a+b x^2+c x\right)}+\frac{4 b \tan ^{-1}\left(\frac{2 b x+c}{\sqrt{4 a b-c^2}}\right)}{\left(4 a b-c^2\right)^{3/2}}",1,"(c + 2*b*x)/((4*a*b - c^2)*(a + c*x + b*x^2)) + (4*b*ArcTan[(c + 2*b*x)/Sqrt[4*a*b - c^2]])/(4*a*b - c^2)^(3/2)","A",3,3,12,0.2500,1,"{614, 618, 204}"
96,1,72,0,0.0355411,"\int \frac{1}{\left(b+2 a x+b x^2\right)^2} \, dx","Int[(b + 2*a*x + b*x^2)^(-2),x]","\frac{b \tanh ^{-1}\left(\frac{a+b x}{\sqrt{a^2-b^2}}\right)}{2 \left(a^2-b^2\right)^{3/2}}-\frac{a+b x}{2 \left(a^2-b^2\right) \left(2 a x+b x^2+b\right)}","\frac{b \tanh ^{-1}\left(\frac{a+b x}{\sqrt{a^2-b^2}}\right)}{2 \left(a^2-b^2\right)^{3/2}}-\frac{a+b x}{2 \left(a^2-b^2\right) \left(2 a x+b x^2+b\right)}",1,"-(a + b*x)/(2*(a^2 - b^2)*(b + 2*a*x + b*x^2)) + (b*ArcTanh[(a + b*x)/Sqrt[a^2 - b^2]])/(2*(a^2 - b^2)^(3/2))","A",3,3,13,0.2308,1,"{614, 618, 206}"
97,1,69,0,0.0336722,"\int \frac{1}{\left(b+2 a x-b x^2\right)^2} \, dx","Int[(b + 2*a*x - b*x^2)^(-2),x]","-\frac{a-b x}{2 \left(a^2+b^2\right) \left(2 a x-b x^2+b\right)}-\frac{b \tanh ^{-1}\left(\frac{a-b x}{\sqrt{a^2+b^2}}\right)}{2 \left(a^2+b^2\right)^{3/2}}","-\frac{a-b x}{2 \left(a^2+b^2\right) \left(2 a x-b x^2+b\right)}-\frac{b \tanh ^{-1}\left(\frac{a-b x}{\sqrt{a^2+b^2}}\right)}{2 \left(a^2+b^2\right)^{3/2}}",1,"-(a - b*x)/(2*(a^2 + b^2)*(b + 2*a*x - b*x^2)) - (b*ArcTanh[(a - b*x)/Sqrt[a^2 + b^2]])/(2*(a^2 + b^2)^(3/2))","A",3,3,14,0.2143,1,"{614, 618, 206}"
98,1,62,0,0.157198,"\int \frac{1}{\left(\frac{a}{b}\right)^{2/n}+x^2-2 \left(\frac{a}{b}\right)^{\frac{1}{n}} x \cos \left(\frac{\pi -2 k \pi }{n}\right)} \, dx","Int[((a/b)^(2/n) + x^2 - 2*(a/b)^n^(-1)*x*Cos[(Pi - 2*k*Pi)/n])^(-1),x]","-\left(\frac{a}{b}\right)^{-1/n} \csc \left(\frac{\pi -2 \pi  k}{n}\right) \tan ^{-1}\left(\cot \left(\frac{\pi -2 \pi  k}{n}\right)-x \left(\frac{a}{b}\right)^{-1/n} \csc \left(\frac{\pi -2 \pi  k}{n}\right)\right)","-\left(\frac{a}{b}\right)^{-1/n} \csc \left(\frac{\pi -2 \pi  k}{n}\right) \tan ^{-1}\left(\cot \left(\frac{\pi -2 \pi  k}{n}\right)-x \left(\frac{a}{b}\right)^{-1/n} \csc \left(\frac{\pi -2 \pi  k}{n}\right)\right)",1,"-((ArcTan[Cot[(Pi - 2*k*Pi)/n] - (x*Csc[(Pi - 2*k*Pi)/n])/(a/b)^n^(-1)]*Csc[(Pi - 2*k*Pi)/n])/(a/b)^n^(-1))","A",2,2,40,0.05000,1,"{618, 204}"
99,1,58,0,0.0357354,"\int \frac{1}{a b+\sqrt{b^2-4 a b^3} x-b^2 x^2} \, dx","Int[(a*b + Sqrt[b^2 - 4*a*b^3]*x - b^2*x^2)^(-1),x]","\frac{\log \left(-\sqrt{b^2-4 a b^3}+2 b^2 x+b\right)}{b}-\frac{\log \left(\sqrt{b^2-4 a b^3}-2 b^2 x+b\right)}{b}","\frac{2 \tanh ^{-1}\left(\frac{2 b^2 x-\sqrt{b^2-4 a b^3}}{b}\right)}{b}",1,"-(Log[b + Sqrt[b^2 - 4*a*b^3] - 2*b^2*x]/b) + Log[b - Sqrt[b^2 - 4*a*b^3] + 2*b^2*x]/b","A",3,2,30,0.06667,1,"{616, 31}"
100,1,58,0,0.0291565,"\int \frac{1}{a b-\sqrt{b^2-4 a b^3} x-b^2 x^2} \, dx","Int[(a*b - Sqrt[b^2 - 4*a*b^3]*x - b^2*x^2)^(-1),x]","\frac{\log \left(\sqrt{b^2-4 a b^3}+2 b^2 x+b\right)}{b}-\frac{\log \left(-\sqrt{b^2-4 a b^3}-2 b^2 x+b\right)}{b}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b^2-4 a b^3}+2 b^2 x}{b}\right)}{b}",1,"-(Log[b - Sqrt[b^2 - 4*a*b^3] - 2*b^2*x]/b) + Log[b + Sqrt[b^2 - 4*a*b^3] + 2*b^2*x]/b","A",3,2,31,0.06452,1,"{616, 31}"
101,1,17,0,0.0175999,"\int \frac{1}{1+x^2+2 x \cos \left(\frac{1}{7}\right)} \, dx","Int[(1 + x^2 + 2*x*Cos[1/7])^(-1),x]","\csc \left(\frac{1}{7}\right) \tan ^{-1}\left(\csc \left(\frac{1}{7}\right) \left(x+\cos \left(\frac{1}{7}\right)\right)\right)","\csc \left(\frac{1}{7}\right) \tan ^{-1}\left(\csc \left(\frac{1}{7}\right) \left(x+\cos \left(\frac{1}{7}\right)\right)\right)",1,"ArcTan[(x + Cos[1/7])*Csc[1/7]]*Csc[1/7]","A",2,2,14,0.1429,1,"{618, 204}"
102,1,23,0,0.0277957,"\int \frac{1}{1+x^2+2 x \cos \left(\frac{\pi }{7}\right)} \, dx","Int[(1 + x^2 + 2*x*Cos[Pi/7])^(-1),x]","\csc \left(\frac{\pi }{7}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{7}\right) \left(x+\cos \left(\frac{\pi }{7}\right)\right)\right)","\csc \left(\frac{\pi }{7}\right) \tan ^{-1}\left(x \csc \left(\frac{\pi }{7}\right)+\cot \left(\frac{\pi }{7}\right)\right)",1,"ArcTan[(x + Cos[Pi/7])*Csc[Pi/7]]*Csc[Pi/7]","A",2,2,16,0.1250,1,"{618, 204}"
103,1,38,0,0.0113981,"\int \sqrt{5-6 x+9 x^2} \, dx","Int[Sqrt[5 - 6*x + 9*x^2],x]","\frac{2}{3} \sinh ^{-1}\left(\frac{1}{2} (3 x-1)\right)-\frac{1}{6} (1-3 x) \sqrt{9 x^2-6 x+5}","\frac{2}{3} \sinh ^{-1}\left(\frac{1}{2} (3 x-1)\right)-\frac{1}{6} (1-3 x) \sqrt{9 x^2-6 x+5}",1,"-((1 - 3*x)*Sqrt[5 - 6*x + 9*x^2])/6 + (2*ArcSinh[(-1 + 3*x)/2])/3","A",3,3,14,0.2143,1,"{612, 619, 215}"
104,1,30,0,0.0101856,"\int \sqrt{3-4 x-4 x^2} \, dx","Int[Sqrt[3 - 4*x - 4*x^2],x]","\frac{1}{4} \sqrt{-4 x^2-4 x+3} (2 x+1)+\sin ^{-1}\left(x+\frac{1}{2}\right)","\frac{1}{4} \sqrt{-4 x^2-4 x+3} (2 x+1)+\sin ^{-1}\left(x+\frac{1}{2}\right)",1,"((1 + 2*x)*Sqrt[3 - 4*x - 4*x^2])/4 + ArcSin[1/2 + x]","A",3,3,14,0.2143,1,"{612, 619, 216}"
105,1,49,0,0.0103741,"\int \sqrt{-8+6 x+9 x^2} \, dx","Int[Sqrt[-8 + 6*x + 9*x^2],x]","\frac{1}{6} (3 x+1) \sqrt{9 x^2+6 x-8}-\frac{3}{2} \tanh ^{-1}\left(\frac{3 x+1}{\sqrt{9 x^2+6 x-8}}\right)","\frac{1}{6} (3 x+1) \sqrt{9 x^2+6 x-8}-\frac{3}{2} \tanh ^{-1}\left(\frac{3 x+1}{\sqrt{9 x^2+6 x-8}}\right)",1,"((1 + 3*x)*Sqrt[-8 + 6*x + 9*x^2])/6 - (3*ArcTanh[(1 + 3*x)/Sqrt[-8 + 6*x + 9*x^2]])/2","A",3,3,14,0.2143,1,"{612, 621, 206}"
106,1,45,0,0.0153222,"\int \sqrt{2+4 x+3 x^2} \, dx","Int[Sqrt[2 + 4*x + 3*x^2],x]","\frac{1}{6} \sqrt{3 x^2+4 x+2} (3 x+2)+\frac{\sinh ^{-1}\left(\frac{3 x+2}{\sqrt{2}}\right)}{3 \sqrt{3}}","\frac{1}{6} \sqrt{3 x^2+4 x+2} (3 x+2)+\frac{\sinh ^{-1}\left(\frac{3 x+2}{\sqrt{2}}\right)}{3 \sqrt{3}}",1,"((2 + 3*x)*Sqrt[2 + 4*x + 3*x^2])/6 + ArcSinh[(2 + 3*x)/Sqrt[2]]/(3*Sqrt[3])","A",3,3,14,0.2143,1,"{612, 619, 215}"
107,1,45,0,0.0159289,"\int \sqrt{2+4 x-3 x^2} \, dx","Int[Sqrt[2 + 4*x - 3*x^2],x]","-\frac{1}{6} \sqrt{-3 x^2+4 x+2} (2-3 x)-\frac{5 \sin ^{-1}\left(\frac{2-3 x}{\sqrt{10}}\right)}{3 \sqrt{3}}","-\frac{1}{6} \sqrt{-3 x^2+4 x+2} (2-3 x)-\frac{5 \sin ^{-1}\left(\frac{2-3 x}{\sqrt{10}}\right)}{3 \sqrt{3}}",1,"-((2 - 3*x)*Sqrt[2 + 4*x - 3*x^2])/6 - (5*ArcSin[(2 - 3*x)/Sqrt[10]])/(3*Sqrt[3])","A",3,3,14,0.2143,1,"{612, 619, 216}"
108,1,62,0,0.014675,"\int \sqrt{2+5 x+3 x^2} \, dx","Int[Sqrt[2 + 5*x + 3*x^2],x]","\frac{1}{12} (6 x+5) \sqrt{3 x^2+5 x+2}-\frac{\tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{24 \sqrt{3}}","\frac{1}{12} (6 x+5) \sqrt{3 x^2+5 x+2}-\frac{\tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{24 \sqrt{3}}",1,"((5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/12 - ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])]/(24*Sqrt[3])","A",3,3,14,0.2143,1,"{612, 621, 206}"
109,1,43,0,0.0122895,"\int \sqrt{2+5 x-3 x^2} \, dx","Int[Sqrt[2 + 5*x - 3*x^2],x]","-\frac{1}{12} \sqrt{-3 x^2+5 x+2} (5-6 x)-\frac{49 \sin ^{-1}\left(\frac{1}{7} (5-6 x)\right)}{24 \sqrt{3}}","-\frac{1}{12} \sqrt{-3 x^2+5 x+2} (5-6 x)-\frac{49 \sin ^{-1}\left(\frac{1}{7} (5-6 x)\right)}{24 \sqrt{3}}",1,"-((5 - 6*x)*Sqrt[2 + 5*x - 3*x^2])/12 - (49*ArcSin[(5 - 6*x)/7])/(24*Sqrt[3])","A",3,3,14,0.2143,1,"{612, 619, 216}"
110,1,59,0,0.0129886,"\int \sqrt{-2+4 x+3 x^2} \, dx","Int[Sqrt[-2 + 4*x + 3*x^2],x]","\frac{1}{6} (3 x+2) \sqrt{3 x^2+4 x-2}-\frac{5 \tanh ^{-1}\left(\frac{3 x+2}{\sqrt{3} \sqrt{3 x^2+4 x-2}}\right)}{3 \sqrt{3}}","\frac{1}{6} (3 x+2) \sqrt{3 x^2+4 x-2}-\frac{5 \tanh ^{-1}\left(\frac{3 x+2}{\sqrt{3} \sqrt{3 x^2+4 x-2}}\right)}{3 \sqrt{3}}",1,"((2 + 3*x)*Sqrt[-2 + 4*x + 3*x^2])/6 - (5*ArcTanh[(2 + 3*x)/(Sqrt[3]*Sqrt[-2 + 4*x + 3*x^2])])/(3*Sqrt[3])","A",3,3,14,0.2143,1,"{612, 621, 206}"
111,1,59,0,0.0157649,"\int \sqrt{-2+4 x-3 x^2} \, dx","Int[Sqrt[-2 + 4*x - 3*x^2],x]","\frac{\tan ^{-1}\left(\frac{2-3 x}{\sqrt{3} \sqrt{-3 x^2+4 x-2}}\right)}{3 \sqrt{3}}-\frac{1}{6} (2-3 x) \sqrt{-3 x^2+4 x-2}","\frac{\tan ^{-1}\left(\frac{2-3 x}{\sqrt{3} \sqrt{-3 x^2+4 x-2}}\right)}{3 \sqrt{3}}-\frac{1}{6} (2-3 x) \sqrt{-3 x^2+4 x-2}",1,"-((2 - 3*x)*Sqrt[-2 + 4*x - 3*x^2])/6 + ArcTan[(2 - 3*x)/(Sqrt[3]*Sqrt[-2 + 4*x - 3*x^2])]/(3*Sqrt[3])","A",3,3,14,0.2143,1,"{612, 621, 204}"
112,1,62,0,0.0132514,"\int \sqrt{-2+5 x+3 x^2} \, dx","Int[Sqrt[-2 + 5*x + 3*x^2],x]","\frac{1}{12} (6 x+5) \sqrt{3 x^2+5 x-2}-\frac{49 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x-2}}\right)}{24 \sqrt{3}}","\frac{1}{12} (6 x+5) \sqrt{3 x^2+5 x-2}-\frac{49 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x-2}}\right)}{24 \sqrt{3}}",1,"((5 + 6*x)*Sqrt[-2 + 5*x + 3*x^2])/12 - (49*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[-2 + 5*x + 3*x^2])])/(24*Sqrt[3])","A",3,3,14,0.2143,1,"{612, 621, 206}"
113,1,39,0,0.0076886,"\int \sqrt{-2+5 x-3 x^2} \, dx","Int[Sqrt[-2 + 5*x - 3*x^2],x]","-\frac{1}{12} \sqrt{-3 x^2+5 x-2} (5-6 x)-\frac{\sin ^{-1}(5-6 x)}{24 \sqrt{3}}","-\frac{1}{12} \sqrt{-3 x^2+5 x-2} (5-6 x)-\frac{\sin ^{-1}(5-6 x)}{24 \sqrt{3}}",1,"-((5 - 6*x)*Sqrt[-2 + 5*x - 3*x^2])/12 - ArcSin[5 - 6*x]/(24*Sqrt[3])","A",3,3,14,0.2143,1,"{612, 619, 216}"
114,1,14,0,0.0070962,"\int \frac{1}{\sqrt{5-6 x+9 x^2}} \, dx","Int[1/Sqrt[5 - 6*x + 9*x^2],x]","\frac{1}{3} \sinh ^{-1}\left(\frac{1}{2} (3 x-1)\right)","\frac{1}{3} \sinh ^{-1}\left(\frac{1}{2} (3 x-1)\right)",1,"ArcSinh[(-1 + 3*x)/2]/3","A",2,2,14,0.1429,1,"{619, 215}"
115,1,10,0,0.0067516,"\int \frac{1}{\sqrt{3-4 x-4 x^2}} \, dx","Int[1/Sqrt[3 - 4*x - 4*x^2],x]","\frac{1}{2} \sin ^{-1}\left(x+\frac{1}{2}\right)","\frac{1}{2} \sin ^{-1}\left(x+\frac{1}{2}\right)",1,"ArcSin[1/2 + x]/2","A",2,2,14,0.1429,1,"{619, 216}"
116,1,25,0,0.0058374,"\int \frac{1}{\sqrt{-8+6 x+9 x^2}} \, dx","Int[1/Sqrt[-8 + 6*x + 9*x^2],x]","\frac{1}{3} \tanh ^{-1}\left(\frac{3 x+1}{\sqrt{9 x^2+6 x-8}}\right)","\frac{1}{3} \tanh ^{-1}\left(\frac{3 x+1}{\sqrt{9 x^2+6 x-8}}\right)",1,"ArcTanh[(1 + 3*x)/Sqrt[-8 + 6*x + 9*x^2]]/3","A",2,2,14,0.1429,1,"{621, 206}"
117,1,18,0,0.0095382,"\int \frac{1}{\sqrt{2+4 x+3 x^2}} \, dx","Int[1/Sqrt[2 + 4*x + 3*x^2],x]","\frac{\sinh ^{-1}\left(\frac{3 x+2}{\sqrt{2}}\right)}{\sqrt{3}}","\frac{\sinh ^{-1}\left(\frac{3 x+2}{\sqrt{2}}\right)}{\sqrt{3}}",1,"ArcSinh[(2 + 3*x)/Sqrt[2]]/Sqrt[3]","A",2,2,14,0.1429,1,"{619, 215}"
118,1,19,0,0.0102533,"\int \frac{1}{\sqrt{2+4 x-3 x^2}} \, dx","Int[1/Sqrt[2 + 4*x - 3*x^2],x]","-\frac{\sin ^{-1}\left(\frac{2-3 x}{\sqrt{10}}\right)}{\sqrt{3}}","-\frac{\sin ^{-1}\left(\frac{2-3 x}{\sqrt{10}}\right)}{\sqrt{3}}",1,"-(ArcSin[(2 - 3*x)/Sqrt[10]]/Sqrt[3])","A",2,2,14,0.1429,1,"{619, 216}"
119,1,35,0,0.0081287,"\int \frac{1}{\sqrt{2+5 x+3 x^2}} \, dx","Int[1/Sqrt[2 + 5*x + 3*x^2],x]","\frac{\tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{\sqrt{3}}","\frac{\tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{\sqrt{3}}",1,"ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])]/Sqrt[3]","A",2,2,14,0.1429,1,"{621, 206}"
120,1,17,0,0.006666,"\int \frac{1}{\sqrt{2+5 x-3 x^2}} \, dx","Int[1/Sqrt[2 + 5*x - 3*x^2],x]","-\frac{\sin ^{-1}\left(\frac{1}{7} (5-6 x)\right)}{\sqrt{3}}","-\frac{\sin ^{-1}\left(\frac{1}{7} (5-6 x)\right)}{\sqrt{3}}",1,"-(ArcSin[(5 - 6*x)/7]/Sqrt[3])","A",2,2,14,0.1429,1,"{619, 216}"
121,1,32,0,0.0077246,"\int \frac{1}{\sqrt{-2+4 x+3 x^2}} \, dx","Int[1/Sqrt[-2 + 4*x + 3*x^2],x]","\frac{\tanh ^{-1}\left(\frac{3 x+2}{\sqrt{3} \sqrt{3 x^2+4 x-2}}\right)}{\sqrt{3}}","\frac{\tanh ^{-1}\left(\frac{3 x+2}{\sqrt{3} \sqrt{3 x^2+4 x-2}}\right)}{\sqrt{3}}",1,"ArcTanh[(2 + 3*x)/(Sqrt[3]*Sqrt[-2 + 4*x + 3*x^2])]/Sqrt[3]","A",2,2,14,0.1429,1,"{621, 206}"
122,1,33,0,0.0077835,"\int \frac{1}{\sqrt{-2+4 x-3 x^2}} \, dx","Int[1/Sqrt[-2 + 4*x - 3*x^2],x]","-\frac{\tan ^{-1}\left(\frac{2-3 x}{\sqrt{3} \sqrt{-3 x^2+4 x-2}}\right)}{\sqrt{3}}","-\frac{\tan ^{-1}\left(\frac{2-3 x}{\sqrt{3} \sqrt{-3 x^2+4 x-2}}\right)}{\sqrt{3}}",1,"-(ArcTan[(2 - 3*x)/(Sqrt[3]*Sqrt[-2 + 4*x - 3*x^2])]/Sqrt[3])","A",2,2,14,0.1429,1,"{621, 204}"
123,1,35,0,0.0081826,"\int \frac{1}{\sqrt{-2+5 x+3 x^2}} \, dx","Int[1/Sqrt[-2 + 5*x + 3*x^2],x]","\frac{\tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x-2}}\right)}{\sqrt{3}}","\frac{\tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x-2}}\right)}{\sqrt{3}}",1,"ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[-2 + 5*x + 3*x^2])]/Sqrt[3]","A",2,2,14,0.1429,1,"{621, 206}"
124,1,13,0,0.0040812,"\int \frac{1}{\sqrt{-2+5 x-3 x^2}} \, dx","Int[1/Sqrt[-2 + 5*x - 3*x^2],x]","-\frac{\sin ^{-1}(5-6 x)}{\sqrt{3}}","-\frac{\sin ^{-1}(5-6 x)}{\sqrt{3}}",1,"-(ArcSin[5 - 6*x]/Sqrt[3])","A",2,2,14,0.1429,1,"{619, 216}"
125,1,22,0,0.0131654,"\int \frac{1}{\sqrt{\frac{b^2+4 c}{4 c}+b x+c x^2}} \, dx","Int[1/Sqrt[(b^2 + 4*c)/(4*c) + b*x + c*x^2],x]","\frac{\sinh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)}{\sqrt{c}}","\frac{\sinh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)}{\sqrt{c}}",1,"ArcSinh[(b + 2*c*x)/(2*Sqrt[c])]/Sqrt[c]","A",2,2,27,0.07407,1,"{619, 215}"
126,1,23,0,0.0133389,"\int \frac{1}{\sqrt{\frac{-b^2+4 c}{4 c}+b x-c x^2}} \, dx","Int[1/Sqrt[(-b^2 + 4*c)/(4*c) + b*x - c*x^2],x]","-\frac{\sin ^{-1}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)}{\sqrt{c}}","-\frac{\sin ^{-1}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)}{\sqrt{c}}",1,"-(ArcSin[(b - 2*c*x)/(2*Sqrt[c])]/Sqrt[c])","A",2,2,30,0.06667,1,"{619, 216}"
127,1,20,0,0.0106786,"\int \frac{1}{\sqrt{\frac{-b^2+c}{4 c}+b x-c x^2}} \, dx","Int[1/Sqrt[(-b^2 + c)/(4*c) + b*x - c*x^2],x]","-\frac{\sin ^{-1}\left(\frac{b-2 c x}{\sqrt{c}}\right)}{\sqrt{c}}","-\frac{\sin ^{-1}\left(\frac{b-2 c x}{\sqrt{c}}\right)}{\sqrt{c}}",1,"-(ArcSin[(b - 2*c*x)/Sqrt[c]]/Sqrt[c])","A",2,2,28,0.07143,1,"{619, 216}"
128,1,19,0,0.0023999,"\int \frac{1}{\left(2+3 x+x^2\right)^{3/2}} \, dx","Int[(2 + 3*x + x^2)^(-3/2),x]","-\frac{2 (2 x+3)}{\sqrt{x^2+3 x+2}}","-\frac{2 (2 x+3)}{\sqrt{x^2+3 x+2}}",1,"(-2*(3 + 2*x))/Sqrt[2 + 3*x + x^2]","A",1,1,12,0.08333,1,"{613}"
129,1,23,0,0.0026535,"\int \frac{1}{\left(27-24 x+4 x^2\right)^{3/2}} \, dx","Int[(27 - 24*x + 4*x^2)^(-3/2),x]","\frac{3-x}{9 \sqrt{4 x^2-24 x+27}}","\frac{3-x}{9 \sqrt{4 x^2-24 x+27}}",1,"(3 - x)/(9*Sqrt[27 - 24*x + 4*x^2])","A",1,1,14,0.07143,1,"{613}"
130,1,23,0,0.0045149,"\int \frac{x}{\left(5-4 x-x^2\right)^{3/2}} \, dx","Int[x/(5 - 4*x - x^2)^(3/2),x]","\frac{5-2 x}{9 \sqrt{-x^2-4 x+5}}","\frac{5-2 x}{9 \sqrt{-x^2-4 x+5}}",1,"(5 - 2*x)/(9*Sqrt[5 - 4*x - x^2])","A",1,1,16,0.06250,1,"{636}"
131,1,43,0,0.0066557,"\int \frac{1}{\left(5-4 x-x^2\right)^{5/2}} \, dx","Int[(5 - 4*x - x^2)^(-5/2),x]","\frac{2 (x+2)}{243 \sqrt{-x^2-4 x+5}}+\frac{x+2}{27 \left(-x^2-4 x+5\right)^{3/2}}","\frac{2 (x+2)}{243 \sqrt{-x^2-4 x+5}}+\frac{x+2}{27 \left(-x^2-4 x+5\right)^{3/2}}",1,"(2 + x)/(27*(5 - 4*x - x^2)^(3/2)) + (2*(2 + x))/(243*Sqrt[5 - 4*x - x^2])","A",2,2,14,0.1429,1,"{614, 613}"
132,1,122,0,0.0359996,"\int \left(a+b x+c x^2\right)^p \, dx","Int[(a + b*x + c*x^2)^p,x]","-\frac{2^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(a+b x+c x^2\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{(p+1) \sqrt{b^2-4 a c}}","-\frac{2^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(a+b x+c x^2\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{(p+1) \sqrt{b^2-4 a c}}",1,"-((2^(1 + p)*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x + c*x^2)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(1 + p)))","A",1,1,12,0.08333,1,"{624}"
133,1,37,0,0.0155656,"\int \left(3+4 x+5 x^2\right)^p \, dx","Int[(3 + 4*x + 5*x^2)^p,x]","5^{-p-1} 11^p (5 x+2) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{1}{11} (5 x+2)^2\right)","5^{-p-1} 11^p (5 x+2) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{1}{11} (5 x+2)^2\right)",1,"5^(-1 - p)*11^p*(2 + 5*x)*Hypergeometric2F1[1/2, -p, 3/2, -(2 + 5*x)^2/11]","A",2,2,12,0.1667,1,"{619, 245}"
134,1,32,0,0.0137135,"\int \left(3+4 x+4 x^2\right)^p \, dx","Int[(3 + 4*x + 4*x^2)^p,x]","2^{p-1} (2 x+1) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{1}{2} (2 x+1)^2\right)","2^{p-1} (2 x+1) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{1}{2} (2 x+1)^2\right)",1,"2^(-1 + p)*(1 + 2*x)*Hypergeometric2F1[1/2, -p, 3/2, -(1 + 2*x)^2/2]","A",2,2,12,0.1667,1,"{619, 245}"
135,1,37,0,0.0155058,"\int \left(3+4 x+3 x^2\right)^p \, dx","Int[(3 + 4*x + 3*x^2)^p,x]","3^{-p-1} 5^p (3 x+2) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{1}{5} (3 x+2)^2\right)","3^{-p-1} 5^p (3 x+2) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{1}{5} (3 x+2)^2\right)",1,"3^(-1 - p)*5^p*(2 + 3*x)*Hypergeometric2F1[1/2, -p, 3/2, -(2 + 3*x)^2/5]","A",2,2,12,0.1667,1,"{619, 245}"
136,1,21,0,0.0104273,"\int \left(3+4 x+2 x^2\right)^p \, dx","Int[(3 + 4*x + 2*x^2)^p,x]","(x+1) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-2 (x+1)^2\right)","(x+1) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-2 (x+1)^2\right)",1,"(1 + x)*Hypergeometric2F1[1/2, -p, 3/2, -2*(1 + x)^2]","A",2,2,12,0.1667,1,"{619, 245}"
137,1,54,0,0.0102118,"\int \left(3+4 x+x^2\right)^p \, dx","Int[(3 + 4*x + x^2)^p,x]","-\frac{2^{2 p+1} (-2 x-2)^{-p-1} \left(x^2+4 x+3\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{x+3}{2}\right)}{p+1}","-\frac{2^{2 p+1} (-2 x-2)^{-p-1} \left(x^2+4 x+3\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{x+3}{2}\right)}{p+1}",1,"-((2^(1 + 2*p)*(-2 - 2*x)^(-1 - p)*(3 + 4*x + x^2)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (3 + x)/2])/(1 + p))","A",1,1,10,0.1000,1,"{624}"
138,1,18,0,0.0018257,"\int (3+4 x)^p \, dx","Int[(3 + 4*x)^p,x]","\frac{(4 x+3)^{p+1}}{4 (p+1)}","\frac{(4 x+3)^{p+1}}{4 (p+1)}",1,"(3 + 4*x)^(1 + p)/(4*(1 + p))","A",1,1,7,0.1429,1,"{32}"
139,1,31,0,0.011873,"\int \left(3+4 x-x^2\right)^p \, dx","Int[(3 + 4*x - x^2)^p,x]","-7^p (2-x) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{1}{7} (2-x)^2\right)","-7^p (2-x) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{1}{7} (2-x)^2\right)",1,"-(7^p*(2 - x)*Hypergeometric2F1[1/2, -p, 3/2, (2 - x)^2/7])","A",2,2,12,0.1667,1,"{619, 245}"
140,1,31,0,0.0107076,"\int \left(3+4 x-2 x^2\right)^p \, dx","Int[(3 + 4*x - 2*x^2)^p,x]","-5^p (1-x) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{2}{5} (1-x)^2\right)","-5^p (1-x) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{2}{5} (1-x)^2\right)",1,"-(5^p*(1 - x)*Hypergeometric2F1[1/2, -p, 3/2, (2*(1 - x)^2)/5])","A",2,2,12,0.1667,1,"{619, 245}"
141,1,38,0,0.0131742,"\int \left(3+4 x-3 x^2\right)^p \, dx","Int[(3 + 4*x - 3*x^2)^p,x]","-3^{-p-1} 13^p (2-3 x) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{1}{13} (2-3 x)^2\right)","-3^{-p-1} 13^p (2-3 x) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{1}{13} (2-3 x)^2\right)",1,"-(3^(-1 - p)*13^p*(2 - 3*x)*Hypergeometric2F1[1/2, -p, 3/2, (2 - 3*x)^2/13])","A",2,2,12,0.1667,1,"{619, 245}"
142,1,35,0,0.0133281,"\int \left(3+4 x-4 x^2\right)^p \, dx","Int[(3 + 4*x - 4*x^2)^p,x]","-2^{2 p-1} (1-2 x) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{1}{4} (1-2 x)^2\right)","-2^{2 p-1} (1-2 x) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{1}{4} (1-2 x)^2\right)",1,"-(2^(-1 + 2*p)*(1 - 2*x)*Hypergeometric2F1[1/2, -p, 3/2, (1 - 2*x)^2/4])","A",2,2,12,0.1667,1,"{619, 245}"
143,1,38,0,0.0127279,"\int \left(3+4 x-5 x^2\right)^p \, dx","Int[(3 + 4*x - 5*x^2)^p,x]","-5^{-p-1} 19^p (2-5 x) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{1}{19} (2-5 x)^2\right)","-5^{-p-1} 19^p (2-5 x) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{1}{19} (2-5 x)^2\right)",1,"-(5^(-1 - p)*19^p*(2 - 5*x)*Hypergeometric2F1[1/2, -p, 3/2, (2 - 5*x)^2/19])","A",2,2,12,0.1667,1,"{619, 245}"