1,1,142,147,0.2227641,"\int \left(b x+c x^2\right)^{7/2} \, dx","Integrate[(b*x + c*x^2)^(7/2),x]","\frac{\sqrt{x (b+c x)} \left(\frac{105 b^{15/2} \sinh ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{x} \sqrt{\frac{c x}{b}+1}}+\sqrt{c} \left(-105 b^7+70 b^6 c x-56 b^5 c^2 x^2+48 b^4 c^3 x^3+10880 b^3 c^4 x^4+25856 b^2 c^5 x^5+21504 b c^6 x^6+6144 c^7 x^7\right)\right)}{49152 c^{9/2}}","\frac{35 b^8 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{16384 c^{9/2}}-\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{(b+2 c x) \left(b x+c x^2\right)^{7/2}}{16 c}",1,"(Sqrt[x*(b + c*x)]*(Sqrt[c]*(-105*b^7 + 70*b^6*c*x - 56*b^5*c^2*x^2 + 48*b^4*c^3*x^3 + 10880*b^3*c^4*x^4 + 25856*b^2*c^5*x^5 + 21504*b*c^6*x^6 + 6144*c^7*x^7) + (105*b^(15/2)*ArcSinh[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[x]*Sqrt[1 + (c*x)/b])))/(49152*c^(9/2))","A",1
2,1,119,121,0.0948913,"\int \left(3 i x+4 x^2\right)^{7/2} \, dx","Integrate[((3*I)*x + 4*x^2)^(7/2),x]","\frac{\sqrt{x (4 x+3 i)} \left(2 \sqrt{3-4 i x} \sqrt{x} \left(33554432 x^7+88080384 i x^6-79429632 x^5-25067520 i x^4+82944 x^3-72576 i x^2-68040 x+76545 i\right)-229635 \sqrt[4]{-1} \sin ^{-1}\left((1+i) \sqrt{\frac{2}{3}} \sqrt{x}\right)\right)}{8388608 \sqrt{3-4 i x} \sqrt{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}",1,"(Sqrt[x*(3*I + 4*x)]*(2*Sqrt[3 - (4*I)*x]*Sqrt[x]*(76545*I - 68040*x - (72576*I)*x^2 + 82944*x^3 - (25067520*I)*x^4 - 79429632*x^5 + (88080384*I)*x^6 + 33554432*x^7) - 229635*(-1)^(1/4)*ArcSin[(1 + I)*Sqrt[2/3]*Sqrt[x]]))/(8388608*Sqrt[3 - (4*I)*x]*Sqrt[x])","A",1
3,1,88,95,0.0794641,"\int \left(3 i x+4 x^2\right)^{5/2} \, dx","Integrate[((3*I)*x + 4*x^2)^(5/2),x]","\frac{\sqrt{x (4 x+3 i)} \left(524288 x^5+983040 i x^4-497664 x^3-6912 i x^2-6480 x-\frac{10935 \sqrt[4]{-1} \sin ^{-1}\left((1+i) \sqrt{\frac{2}{3}} \sqrt{x}\right)}{\sqrt{3-4 i x} \sqrt{x}}+7290 i\right)}{196608}","\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,"(Sqrt[x*(3*I + 4*x)]*(7290*I - 6480*x - (6912*I)*x^2 - 497664*x^3 + (983040*I)*x^4 + 524288*x^5 - (10935*(-1)^(1/4)*ArcSin[(1 + I)*Sqrt[2/3]*Sqrt[x]])/(Sqrt[3 - (4*I)*x]*Sqrt[x])))/196608","A",1
4,1,76,69,0.0637403,"\int \left(3 i x+4 x^2\right)^{3/2} \, dx","Integrate[((3*I)*x + 4*x^2)^(3/2),x]","\frac{\sqrt{x (4 x+3 i)} \left(2048 x^3+2304 i x^2-144 x-\frac{243 \sqrt[4]{-1} \sin ^{-1}\left((1+i) \sqrt{\frac{2}{3}} \sqrt{x}\right)}{\sqrt{3-4 i x} \sqrt{x}}+162 i\right)}{2048}","\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,"(Sqrt[x*(3*I + 4*x)]*(162*I - 144*x + (2304*I)*x^2 + 2048*x^3 - (243*(-1)^(1/4)*ArcSin[(1 + I)*Sqrt[2/3]*Sqrt[x]])/(Sqrt[3 - (4*I)*x]*Sqrt[x])))/2048","A",1
5,1,64,43,0.0486263,"\int \sqrt{3 i x+4 x^2} \, dx","Integrate[Sqrt[(3*I)*x + 4*x^2],x]","\frac{1}{32} \sqrt{x (4 x+3 i)} \left(16 x-\frac{9 \sqrt[4]{-1} \sin ^{-1}\left((1+i) \sqrt{\frac{2}{3}} \sqrt{x}\right)}{\sqrt{3-4 i x} \sqrt{x}}+6 i\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,"(Sqrt[x*(3*I + 4*x)]*(6*I + 16*x - (9*(-1)^(1/4)*ArcSin[(1 + I)*Sqrt[2/3]*Sqrt[x]])/(Sqrt[3 - (4*I)*x]*Sqrt[x])))/32","A",1
6,1,88,101,0.0665113,"\int \left(3 x-4 x^2\right)^{7/2} \, dx","Integrate[(3*x - 4*x^2)^(7/2),x]","\frac{2 x \left(134217728 x^8-452984832 x^7+581959680 x^6-338558976 x^5+75534336 x^4+41472 x^3+54432 x^2+102060 x-229635\right)-229635 \sqrt{3-4 x} \sqrt{x} \sin ^{-1}\left(\sqrt{1-\frac{4 x}{3}}\right)}{8388608 \sqrt{-x (4 x-3)}}","-\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,"(2*x*(-229635 + 102060*x + 54432*x^2 + 41472*x^3 + 75534336*x^4 - 338558976*x^5 + 581959680*x^6 - 452984832*x^7 + 134217728*x^8) - 229635*Sqrt[3 - 4*x]*Sqrt[x]*ArcSin[Sqrt[1 - (4*x)/3]])/(8388608*Sqrt[-(x*(-3 + 4*x))])","A",1
7,1,78,79,0.0470432,"\int \left(3 x-4 x^2\right)^{5/2} \, dx","Integrate[(3*x - 4*x^2)^(5/2),x]","\frac{2 x \left(-1048576 x^6+2752512 x^5-2469888 x^4+760320 x^3+2592 x^2+4860 x-10935\right)-10935 \sqrt{3-4 x} \sqrt{x} \sin ^{-1}\left(\sqrt{1-\frac{4 x}{3}}\right)}{196608 \sqrt{-x (4 x-3)}}","-\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,"(2*x*(-10935 + 4860*x + 2592*x^2 + 760320*x^3 - 2469888*x^4 + 2752512*x^5 - 1048576*x^6) - 10935*Sqrt[3 - 4*x]*Sqrt[x]*ArcSin[Sqrt[1 - (4*x)/3]])/(196608*Sqrt[-(x*(-3 + 4*x))])","A",1
8,1,68,57,0.0460827,"\int \left(3 x-4 x^2\right)^{3/2} \, dx","Integrate[(3*x - 4*x^2)^(3/2),x]","\frac{2 x \left(4096 x^4-7680 x^3+3744 x^2+108 x-243\right)-243 \sqrt{3-4 x} \sqrt{x} \sin ^{-1}\left(\sqrt{1-\frac{4 x}{3}}\right)}{2048 \sqrt{-x (4 x-3)}}","-\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,"(2*x*(-243 + 108*x + 3744*x^2 - 7680*x^3 + 4096*x^4) - 243*Sqrt[3 - 4*x]*Sqrt[x]*ArcSin[Sqrt[1 - (4*x)/3]])/(2048*Sqrt[-(x*(-3 + 4*x))])","A",1
9,1,58,35,0.0321759,"\int \sqrt{3 x-4 x^2} \, dx","Integrate[Sqrt[3*x - 4*x^2],x]","\frac{-2 x \left(32 x^2-36 x+9\right)-9 \sqrt{3-4 x} \sqrt{x} \sin ^{-1}\left(\sqrt{1-\frac{4 x}{3}}\right)}{32 \sqrt{-x (4 x-3)}}","-\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,"(-2*x*(9 - 36*x + 32*x^2) - 9*Sqrt[3 - 4*x]*Sqrt[x]*ArcSin[Sqrt[1 - (4*x)/3]])/(32*Sqrt[-(x*(-3 + 4*x))])","A",1
10,1,32,35,0.0392335,"\int \sqrt{6 x-x^2} \, dx","Integrate[Sqrt[6*x - x^2],x]","\frac{1}{2} (x-3) \sqrt{-((x-6) x)}-9 \sin ^{-1}\left(\sqrt{1-\frac{x}{6}}\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 - 9*ArcSin[Sqrt[1 - x/6]]","A",1
11,1,58,35,0.0339509,"\int \sqrt{5 x-9 x^2} \, dx","Integrate[Sqrt[5*x - 9*x^2],x]","\frac{-3 x \left(162 x^2-135 x+25\right)-25 \sqrt{5-9 x} \sqrt{x} \sin ^{-1}\left(\sqrt{1-\frac{9 x}{5}}\right)}{108 \sqrt{-x (9 x-5)}}","-\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,"(-3*x*(25 - 135*x + 162*x^2) - 25*Sqrt[5 - 9*x]*Sqrt[x]*ArcSin[Sqrt[1 - (9*x)/5]])/(108*Sqrt[-(x*(-5 + 9*x))])","A",1
12,1,44,51,0.0632128,"\int \left(x-x^2\right)^{3/2} \, dx","Integrate[(x - x^2)^(3/2),x]","\frac{1}{64} \left(-\sqrt{-((x-1) x)} \left(16 x^3-24 x^2+2 x+3\right)-3 \sin ^{-1}\left(\sqrt{1-x}\right)\right)","-\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,"(-(Sqrt[-((-1 + x)*x)]*(3 + 2*x - 24*x^2 + 16*x^3)) - 3*ArcSin[Sqrt[1 - x]])/64","A",1
13,1,40,35,0.0271548,"\int \sqrt{4 x+x^2} \, dx","Integrate[Sqrt[4*x + x^2],x]","\frac{1}{2} \sqrt{x (x+4)} \left(x-\frac{8 \sinh ^{-1}\left(\frac{\sqrt{x}}{2}\right)}{\sqrt{x+4} \sqrt{x}}+2\right)","\frac{1}{2} (x+2) \sqrt{x^2+4 x}-4 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2+4 x}}\right)",1,"(Sqrt[x*(4 + x)]*(2 + x - (8*ArcSinh[Sqrt[x]/2])/(Sqrt[x]*Sqrt[4 + x])))/2","A",1
14,1,48,37,0.0358716,"\int \sqrt{-8 x+x^2} \, dx","Integrate[Sqrt[-8*x + x^2],x]","\frac{x \left(x^2-12 x+32\right)+32 \sqrt{-((x-8) x)} \sin ^{-1}\left(\sqrt{1-\frac{x}{8}}\right)}{2 \sqrt{(x-8) x}}","-\frac{1}{2} \sqrt{x^2-8 x} (4-x)-16 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-8 x}}\right)",1,"(x*(32 - 12*x + x^2) + 32*Sqrt[-((-8 + x)*x)]*ArcSin[Sqrt[1 - x/8]])/(2*Sqrt[(-8 + x)*x])","A",0
15,1,46,39,0.0257238,"\int \sqrt{-x+x^2} \, dx","Integrate[Sqrt[-x + x^2],x]","\frac{2 x^3-3 x^2+x+\sqrt{-((x-1) x)} \sin ^{-1}\left(\sqrt{1-x}\right)}{4 \sqrt{(x-1) x}}","-\frac{1}{4} \sqrt{x^2-x} (1-2 x)-\frac{1}{4} \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-x}}\right)",1,"(x - 3*x^2 + 2*x^3 + Sqrt[-((-1 + x)*x)]*ArcSin[Sqrt[1 - x]])/(4*Sqrt[(-1 + x)*x])","A",0
16,1,70,83,0.0212304,"\int \frac{1}{\left(b x+c x^2\right)^{7/2}} \, dx","Integrate[(b*x + c*x^2)^(-7/2),x]","-\frac{2 \left(3 b^5-10 b^4 c x+80 b^3 c^2 x^2+480 b^2 c^3 x^3+640 b c^4 x^4+256 c^5 x^5\right)}{15 b^6 (x (b+c x))^{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*(3*b^5 - 10*b^4*c*x + 80*b^3*c^2*x^2 + 480*b^2*c^3*x^3 + 640*b*c^4*x^4 + 256*c^5*x^5))/(15*b^6*(x*(b + c*x))^(5/2))","A",1
17,1,53,16,0.0119269,"\int \frac{1}{\sqrt{3 i x+4 x^2}} \, dx","Integrate[1/Sqrt[(3*I)*x + 4*x^2],x]","-\frac{(-1)^{3/4} \sqrt{3-4 i x} \sqrt{x} \sin ^{-1}\left((1+i) \sqrt{\frac{2}{3}} \sqrt{x}\right)}{\sqrt{x (4 x+3 i)}}","\frac{1}{2} i \sin ^{-1}\left(1-\frac{8 i x}{3}\right)",1,"-(((-1)^(3/4)*Sqrt[3 - (4*I)*x]*Sqrt[x]*ArcSin[(1 + I)*Sqrt[2/3]*Sqrt[x]])/Sqrt[x*(3*I + 4*x)])","B",1
18,1,24,26,0.0050306,"\int \frac{1}{\left(3 i x+4 x^2\right)^{3/2}} \, dx","Integrate[((3*I)*x + 4*x^2)^(-3/2),x]","\frac{2 (8 x+3 i)}{9 \sqrt{x (4 x+3 i)}}","\frac{2 (8 x+3 i)}{9 \sqrt{4 x^2+3 i x}}",1,"(2*(3*I + 8*x))/(9*Sqrt[x*(3*I + 4*x)])","A",1
19,1,36,53,0.0096572,"\int \frac{1}{\left(3 i x+4 x^2\right)^{5/2}} \, dx","Integrate[((3*I)*x + 4*x^2)^(-5/2),x]","\frac{2048 x^3+2304 i x^2-432 x+54 i}{243 (x (4 x+3 i))^{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,"(54*I - 432*x + (2304*I)*x^2 + 2048*x^3)/(243*(x*(3*I + 4*x))^(3/2))","A",1
20,1,48,79,0.0121296,"\int \frac{1}{\left(3 i x+4 x^2\right)^{7/2}} \, dx","Integrate[((3*I)*x + 4*x^2)^(-7/2),x]","\frac{524288 x^5+983040 i x^4-552960 x^3-69120 i x^2-6480 x+1458 i}{10935 (x (4 x+3 i))^{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,"(1458*I - 6480*x - (69120*I)*x^2 - 552960*x^3 + (983040*I)*x^4 + 524288*x^5)/(10935*(x*(3*I + 4*x))^(5/2))","A",1
21,1,40,12,0.0119114,"\int \frac{1}{\sqrt{3 x-4 x^2}} \, dx","Integrate[1/Sqrt[3*x - 4*x^2],x]","-\frac{\sqrt{-x (4 x-3)} \sin ^{-1}\left(\sqrt{1-\frac{4 x}{3}}\right)}{\sqrt{3-4 x} \sqrt{x}}","-\frac{1}{2} \sin ^{-1}\left(1-\frac{8 x}{3}\right)",1,"-((Sqrt[-(x*(-3 + 4*x))]*ArcSin[Sqrt[1 - (4*x)/3]])/(Sqrt[3 - 4*x]*Sqrt[x]))","B",1
22,1,21,22,0.0047741,"\int \frac{1}{\left(3 x-4 x^2\right)^{3/2}} \, dx","Integrate[(3*x - 4*x^2)^(-3/2),x]","\frac{2 (8 x-3)}{9 \sqrt{-x (4 x-3)}}","-\frac{2 (3-8 x)}{9 \sqrt{3 x-4 x^2}}",1,"(2*(-3 + 8*x))/(9*Sqrt[-(x*(-3 + 4*x))])","A",1
23,1,31,45,0.0089402,"\int \frac{1}{\left(3 x-4 x^2\right)^{5/2}} \, dx","Integrate[(3*x - 4*x^2)^(-5/2),x]","-\frac{2048 x^3-2304 x^2+432 x+54}{243 (-x (4 x-3))^{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,"-1/243*(54 + 432*x - 2304*x^2 + 2048*x^3)/(-(x*(-3 + 4*x)))^(3/2)","A",1
24,1,51,67,0.0127316,"\int \frac{1}{\left(3 x-4 x^2\right)^{7/2}} \, dx","Integrate[(3*x - 4*x^2)^(-7/2),x]","\frac{2 \left(262144 x^5-491520 x^4+276480 x^3-34560 x^2-3240 x-729\right)}{10935 (3-4 x)^2 x^2 \sqrt{-x (4 x-3)}}","-\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*(-729 - 3240*x - 34560*x^2 + 276480*x^3 - 491520*x^4 + 262144*x^5))/(10935*(3 - 4*x)^2*x^2*Sqrt[-(x*(-3 + 4*x))])","A",1
25,1,47,12,0.0127159,"\int \frac{1}{\sqrt{b x-b^2 x^2}} \, dx","Integrate[1/Sqrt[b*x - b^2*x^2],x]","\frac{2 \sqrt{x} \sqrt{1-b x} \sin ^{-1}\left(\sqrt{b} \sqrt{x}\right)}{\sqrt{b} \sqrt{-b x (b x-1)}}","-\frac{\sin ^{-1}(1-2 b x)}{b}",1,"(2*Sqrt[x]*Sqrt[1 - b*x]*ArcSin[Sqrt[b]*Sqrt[x]])/(Sqrt[b]*Sqrt[-(b*x*(-1 + b*x))])","B",1
26,1,45,24,0.0174602,"\int \frac{1}{\sqrt{b x+b^2 x^2}} \, dx","Integrate[1/Sqrt[b*x + b^2*x^2],x]","\frac{2 \sqrt{x} \sqrt{b x+1} \sinh ^{-1}\left(\sqrt{b} \sqrt{x}\right)}{\sqrt{b} \sqrt{b x (b x+1)}}","\frac{2 \tanh ^{-1}\left(\frac{b x}{\sqrt{b^2 x^2+b x}}\right)}{b}",1,"(2*Sqrt[x]*Sqrt[1 + b*x]*ArcSinh[Sqrt[b]*Sqrt[x]])/(Sqrt[b]*Sqrt[b*x*(1 + b*x)])","A",1
27,1,14,10,0.0081228,"\int \frac{1}{\sqrt{6 x-x^2}} \, dx","Integrate[1/Sqrt[6*x - x^2],x]","-2 \sin ^{-1}\left(\sqrt{1-\frac{x}{6}}\right)","-\sin ^{-1}\left(1-\frac{x}{3}\right)",1,"-2*ArcSin[Sqrt[1 - x/6]]","A",1
28,1,33,16,0.005972,"\int \frac{1}{\sqrt{4 x+x^2}} \, dx","Integrate[1/Sqrt[4*x + x^2],x]","\frac{2 \sqrt{x} \sqrt{x+4} \sinh ^{-1}\left(\frac{\sqrt{x}}{2}\right)}{\sqrt{x (x+4)}}","2 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2+4 x}}\right)",1,"(2*Sqrt[x]*Sqrt[4 + x]*ArcSinh[Sqrt[x]/2])/Sqrt[x*(4 + x)]","B",1
29,1,33,16,0.0118627,"\int \frac{1}{\sqrt{-2 x+x^2}} \, dx","Integrate[1/Sqrt[-2*x + x^2],x]","\frac{2 \sqrt{(x-2) x} \sin ^{-1}\left(\sqrt{1-\frac{x}{2}}\right)}{\sqrt{-((x-2) x)}}","2 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-2 x}}\right)",1,"(2*Sqrt[(-2 + x)*x]*ArcSin[Sqrt[1 - x/2]])/Sqrt[-((-2 + x)*x)]","B",1
30,1,48,448,0.0135953,"\int \left(b x+c x^2\right)^{4/3} \, dx","Integrate[(b*x + c*x^2)^(4/3),x]","\frac{3 b x^2 \sqrt[3]{x (b+c x)} \, _2F_1\left(-\frac{4}{3},\frac{7}{3};\frac{10}{3};-\frac{c x}{b}\right)}{7 \sqrt[3]{\frac{c x}{b}+1}}","\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*b*x^2*(x*(b + c*x))^(1/3)*Hypergeometric2F1[-4/3, 7/3, 10/3, -((c*x)/b)])/(7*(1 + (c*x)/b)^(1/3))","C",1
31,1,45,387,0.0090419,"\int \sqrt[3]{b x+c x^2} \, dx","Integrate[(b*x + c*x^2)^(1/3),x]","\frac{3 x \sqrt[3]{x (b+c x)} \, _2F_1\left(-\frac{1}{3},\frac{4}{3};\frac{7}{3};-\frac{c x}{b}\right)}{4 \sqrt[3]{\frac{c x}{b}+1}}","\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*x*(x*(b + c*x))^(1/3)*Hypergeometric2F1[-1/3, 4/3, 7/3, -((c*x)/b)])/(4*(1 + (c*x)/b)^(1/3))","C",1
32,1,43,322,0.0105828,"\int \frac{1}{\left(b x+c x^2\right)^{2/3}} \, dx","Integrate[(b*x + c*x^2)^(-2/3),x]","\frac{3 x \left(\frac{c x}{b}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{c x}{b}\right)}{(x (b+c x))^{2/3}}","\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)^{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,"(3*x*(1 + (c*x)/b)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((c*x)/b)])/(x*(b + c*x))^(2/3)","C",1
33,1,47,384,0.0114295,"\int \frac{1}{\left(b x+c x^2\right)^{5/3}} \, dx","Integrate[(b*x + c*x^2)^(-5/3),x]","-\frac{3 \left(\frac{c x}{b}+1\right)^{2/3} \, _2F_1\left(-\frac{2}{3},\frac{5}{3};\frac{1}{3};-\frac{c x}{b}\right)}{2 b (x (b+c x))^{2/3}}","\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*(1 + (c*x)/b)^(2/3)*Hypergeometric2F1[-2/3, 5/3, 1/3, -((c*x)/b)])/(2*b*(x*(b + c*x))^(2/3))","C",1
34,1,50,448,0.0120546,"\int \frac{1}{\left(b x+c x^2\right)^{8/3}} \, dx","Integrate[(b*x + c*x^2)^(-8/3),x]","-\frac{3 \left(\frac{c x}{b}+1\right)^{2/3} \, _2F_1\left(-\frac{5}{3},\frac{8}{3};-\frac{2}{3};-\frac{c x}{b}\right)}{5 b^2 x (x (b+c x))^{2/3}}","\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*(1 + (c*x)/b)^(2/3)*Hypergeometric2F1[-5/3, 8/3, -2/3, -((c*x)/b)])/(5*b^2*x*(x*(b + c*x))^(2/3))","C",1
35,1,48,842,0.0133929,"\int \left(b x+c x^2\right)^{5/3} \, dx","Integrate[(b*x + c*x^2)^(5/3),x]","\frac{3 b x^2 (x (b+c x))^{2/3} \, _2F_1\left(-\frac{5}{3},\frac{8}{3};\frac{11}{3};-\frac{c x}{b}\right)}{8 \left(\frac{c x}{b}+1\right)^{2/3}}","-\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,"(3*b*x^2*(x*(b + c*x))^(2/3)*Hypergeometric2F1[-5/3, 8/3, 11/3, -((c*x)/b)])/(8*(1 + (c*x)/b)^(2/3))","C",1
36,1,45,781,0.0087839,"\int \left(b x+c x^2\right)^{2/3} \, dx","Integrate[(b*x + c*x^2)^(2/3),x]","\frac{3 x (x (b+c x))^{2/3} \, _2F_1\left(-\frac{2}{3},\frac{5}{3};\frac{8}{3};-\frac{c x}{b}\right)}{5 \left(\frac{c x}{b}+1\right)^{2/3}}","\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*x*(x*(b + c*x))^(2/3)*Hypergeometric2F1[-2/3, 5/3, 8/3, -((c*x)/b)])/(5*(1 + (c*x)/b)^(2/3))","C",1
37,1,45,715,0.0096704,"\int \frac{1}{\sqrt[3]{b x+c x^2}} \, dx","Integrate[(b*x + c*x^2)^(-1/3),x]","\frac{3 x \sqrt[3]{\frac{c x}{b}+1} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{c x}{b}\right)}{2 \sqrt[3]{x (b+c 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}}}",1,"(3*x*(1 + (c*x)/b)^(1/3)*Hypergeometric2F1[1/3, 2/3, 5/3, -((c*x)/b)])/(2*(x*(b + c*x))^(1/3))","C",1
38,1,45,773,0.011112,"\int \frac{1}{\left(b x+c x^2\right)^{4/3}} \, dx","Integrate[(b*x + c*x^2)^(-4/3),x]","-\frac{3 \sqrt[3]{\frac{c x}{b}+1} \, _2F_1\left(-\frac{1}{3},\frac{4}{3};\frac{2}{3};-\frac{c x}{b}\right)}{b \sqrt[3]{x (b+c 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}}}",1,"(-3*(1 + (c*x)/b)^(1/3)*Hypergeometric2F1[-1/3, 4/3, 2/3, -((c*x)/b)])/(b*(x*(b + c*x))^(1/3))","C",1
39,1,50,838,0.0120226,"\int \frac{1}{\left(b x+c x^2\right)^{7/3}} \, dx","Integrate[(b*x + c*x^2)^(-7/3),x]","-\frac{3 \sqrt[3]{\frac{c x}{b}+1} \, _2F_1\left(-\frac{4}{3},\frac{7}{3};-\frac{1}{3};-\frac{c x}{b}\right)}{4 b^2 x \sqrt[3]{x (b+c 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}}",1,"(-3*(1 + (c*x)/b)^(1/3)*Hypergeometric2F1[-4/3, 7/3, -1/3, -((c*x)/b)])/(4*b^2*x*(x*(b + c*x))^(1/3))","C",1
40,1,48,119,0.0143205,"\int \left(b x+c x^2\right)^{5/4} \, dx","Integrate[(b*x + c*x^2)^(5/4),x]","\frac{4 b x^2 \sqrt[4]{x (b+c x)} \, _2F_1\left(-\frac{5}{4},\frac{9}{4};\frac{13}{4};-\frac{c x}{b}\right)}{9 \sqrt[4]{\frac{c x}{b}+1}}","-\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,"(4*b*x^2*(x*(b + c*x))^(1/4)*Hypergeometric2F1[-5/4, 9/4, 13/4, -((c*x)/b)])/(9*(1 + (c*x)/b)^(1/4))","C",1
41,1,45,90,0.0117614,"\int \left(b x+c x^2\right)^{3/4} \, dx","Integrate[(b*x + c*x^2)^(3/4),x]","\frac{4 x (x (b+c x))^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{7}{4};\frac{11}{4};-\frac{c x}{b}\right)}{7 \left(\frac{c x}{b}+1\right)^{3/4}}","\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,"(4*x*(x*(b + c*x))^(3/4)*Hypergeometric2F1[-3/4, 7/4, 11/4, -((c*x)/b)])/(7*(1 + (c*x)/b)^(3/4))","C",1
42,1,45,90,0.0090243,"\int \sqrt[4]{b x+c x^2} \, dx","Integrate[(b*x + c*x^2)^(1/4),x]","\frac{4 x \sqrt[4]{x (b+c x)} \, _2F_1\left(-\frac{1}{4},\frac{5}{4};\frac{9}{4};-\frac{c x}{b}\right)}{5 \sqrt[4]{\frac{c x}{b}+1}}","\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,"(4*x*(x*(b + c*x))^(1/4)*Hypergeometric2F1[-1/4, 5/4, 9/4, -((c*x)/b)])/(5*(1 + (c*x)/b)^(1/4))","C",1
43,1,45,58,0.0097427,"\int \frac{1}{\sqrt[4]{b x+c x^2}} \, dx","Integrate[(b*x + c*x^2)^(-1/4),x]","\frac{4 x \sqrt[4]{\frac{c x}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{7}{4};-\frac{c x}{b}\right)}{3 \sqrt[4]{x (b+c 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}}",1,"(4*x*(1 + (c*x)/b)^(1/4)*Hypergeometric2F1[1/4, 3/4, 7/4, -((c*x)/b)])/(3*(x*(b + c*x))^(1/4))","C",1
44,1,43,59,0.0089099,"\int \frac{1}{\left(b x+c x^2\right)^{3/4}} \, dx","Integrate[(b*x + c*x^2)^(-3/4),x]","\frac{4 x \left(\frac{c x}{b}+1\right)^{3/4} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{5}{4};-\frac{c x}{b}\right)}{(x (b+c x))^{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,"(4*x*(1 + (c*x)/b)^(3/4)*Hypergeometric2F1[1/4, 3/4, 5/4, -((c*x)/b)])/(x*(b + c*x))^(3/4)","C",1
45,1,45,83,0.0107881,"\int \frac{1}{\left(b x+c x^2\right)^{5/4}} \, dx","Integrate[(b*x + c*x^2)^(-5/4),x]","-\frac{4 \sqrt[4]{\frac{c x}{b}+1} \, _2F_1\left(-\frac{1}{4},\frac{5}{4};\frac{3}{4};-\frac{c x}{b}\right)}{b \sqrt[4]{x (b+c 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}}",1,"(-4*(1 + (c*x)/b)^(1/4)*Hypergeometric2F1[-1/4, 5/4, 3/4, -((c*x)/b)])/(b*(x*(b + c*x))^(1/4))","C",1
46,1,50,115,0.011337,"\int \frac{1}{\left(b x+c x^2\right)^{9/4}} \, dx","Integrate[(b*x + c*x^2)^(-9/4),x]","-\frac{4 \sqrt[4]{\frac{c x}{b}+1} \, _2F_1\left(-\frac{5}{4},\frac{9}{4};-\frac{1}{4};-\frac{c x}{b}\right)}{5 b^2 x \sqrt[4]{x (b+c 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}}",1,"(-4*(1 + (c*x)/b)^(1/4)*Hypergeometric2F1[-5/4, 9/4, -1/4, -((c*x)/b)])/(5*b^2*x*(x*(b + c*x))^(1/4))","C",1
47,1,50,146,0.0116806,"\int \frac{1}{\left(b x+c x^2\right)^{13/4}} \, dx","Integrate[(b*x + c*x^2)^(-13/4),x]","-\frac{4 \sqrt[4]{\frac{c x}{b}+1} \, _2F_1\left(-\frac{9}{4},\frac{13}{4};-\frac{5}{4};-\frac{c x}{b}\right)}{9 b^3 x^2 \sqrt[4]{x (b+c x)}}","-\frac{448 c^2 (b+2 c x)}{15 b^6 \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 \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}}",1,"(-4*(1 + (c*x)/b)^(1/4)*Hypergeometric2F1[-9/4, 13/4, -5/4, -((c*x)/b)])/(9*b^3*x^2*(x*(b + c*x))^(1/4))","C",1
48,1,45,55,0.0090602,"\int \left(b x+c x^2\right)^p \, dx","Integrate[(b*x + c*x^2)^p,x]","\frac{x (x (b+c x))^p \left(\frac{c x}{b}+1\right)^{-p} \, _2F_1\left(-p,p+1;p+2;-\frac{c x}{b}\right)}{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,"(x*(x*(b + c*x))^p*Hypergeometric2F1[-p, 1 + p, 2 + p, -((c*x)/b)])/((1 + p)*(1 + (c*x)/b)^p)","A",1
49,1,51,51,0.0023253,"\int \left(a+c x^2\right)^4 \, dx","Integrate[(a + c*x^2)^4,x]","a^4 x+\frac{4}{3} a^3 c x^3+\frac{6}{5} a^2 c^2 x^5+\frac{4}{7} a c^3 x^7+\frac{c^4 x^9}{9}","a^4 x+\frac{4}{3} a^3 c x^3+\frac{6}{5} a^2 c^2 x^5+\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",1
50,1,35,35,0.0015149,"\int \left(a+c x^2\right)^3 \, dx","Integrate[(a + c*x^2)^3,x]","a^3 x+a^2 c x^3+\frac{3}{5} a c^2 x^5+\frac{c^3 x^7}{7}","a^3 x+a^2 c x^3+\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",1
51,1,25,25,0.0012152,"\int \left(a+c x^2\right)^2 \, dx","Integrate[(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",1
52,1,12,12,0.0001221,"\int \left(a+c x^2\right) \, dx","Integrate[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
53,1,24,24,0.0085433,"\int \frac{1}{a+c x^2} \, dx","Integrate[(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
54,1,45,45,0.0243089,"\int \frac{1}{\left(a+c x^2\right)^2} \, dx","Integrate[(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",1
55,1,55,62,0.0330921,"\int \frac{1}{\left(a+c x^2\right)^3} \, dx","Integrate[(a + c*x^2)^(-3),x]","\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{c}}+\frac{5 a x+3 c x^3}{8 a^2 \left(a+c x^2\right)^2}","\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{c}}+\frac{3 x}{8 a^2 \left(a+c x^2\right)}+\frac{x}{4 a \left(a+c x^2\right)^2}",1,"(5*a*x + 3*c*x^3)/(8*a^2*(a + c*x^2)^2) + (3*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*Sqrt[c])","A",1
56,1,76,84,0.1082503,"\int \left(a+c x^2\right)^{5/2} \, dx","Integrate[(a + c*x^2)^(5/2),x]","\frac{1}{48} \sqrt{a+c x^2} \left(\frac{15 a^{5/2} \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{c} \sqrt{\frac{c x^2}{a}+1}}+33 a^2 x+26 a c x^3+8 c^2 x^5\right)","\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 \sqrt{c}}+\frac{5}{16} a^2 x \sqrt{a+c x^2}+\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,"(Sqrt[a + c*x^2]*(33*a^2*x + 26*a*c*x^3 + 8*c^2*x^5 + (15*a^(5/2)*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[c]*Sqrt[1 + (c*x^2)/a])))/48","A",1
57,1,65,65,0.080028,"\int \left(a+c x^2\right)^{3/2} \, dx","Integrate[(a + c*x^2)^(3/2),x]","\frac{1}{8} \sqrt{a+c x^2} \left(\frac{3 a^{3/2} \sinh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{c} \sqrt{\frac{c x^2}{a}+1}}+5 a x+2 c x^3\right)","\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,"(Sqrt[a + c*x^2]*(5*a*x + 2*c*x^3 + (3*a^(3/2)*ArcSinh[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[c]*Sqrt[1 + (c*x^2)/a])))/8","A",1
58,1,49,46,0.0194682,"\int \sqrt{a+c x^2} \, dx","Integrate[Sqrt[a + c*x^2],x]","\frac{1}{2} x \sqrt{a+c x^2}+\frac{a \log \left(\sqrt{c} \sqrt{a+c x^2}+c x\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*Log[c*x + Sqrt[c]*Sqrt[a + c*x^2]])/(2*Sqrt[c])","A",1
59,1,25,25,0.0058163,"\int \frac{1}{\sqrt{a+c x^2}} \, dx","Integrate[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",1
60,1,16,16,0.0044229,"\int \frac{1}{\left(a+c x^2\right)^{3/2}} \, dx","Integrate[(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
61,1,29,39,0.0077285,"\int \frac{1}{\left(a+c x^2\right)^{5/2}} \, dx","Integrate[(a + c*x^2)^(-5/2),x]","\frac{x \left(3 a+2 c x^2\right)}{3 a^2 \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 + 2*c*x^2))/(3*a^2*(a + c*x^2)^(3/2))","A",1
62,1,40,58,0.0103441,"\int \frac{1}{\left(a+c x^2\right)^{7/2}} \, dx","Integrate[(a + c*x^2)^(-7/2),x]","\frac{x \left(15 a^2+20 a c x^2+8 c^2 x^4\right)}{15 a^3 \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*(15*a^2 + 20*a*c*x^2 + 8*c^2*x^4))/(15*a^3*(a + c*x^2)^(5/2))","A",1
63,1,51,77,0.0131414,"\int \frac{1}{\left(a+c x^2\right)^{9/2}} \, dx","Integrate[(a + c*x^2)^(-9/2),x]","\frac{x \left(35 a^3+70 a^2 c x^2+56 a c^2 x^4+16 c^3 x^6\right)}{35 a^4 \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*(35*a^3 + 70*a^2*c*x^2 + 56*a*c^2*x^4 + 16*c^3*x^6))/(35*a^4*(a + c*x^2)^(7/2))","A",1
64,1,20,23,0.0369083,"\int \left(4+12 x+9 x^2\right)^{3/2} \, dx","Integrate[(4 + 12*x + 9*x^2)^(3/2),x]","\frac{1}{12} (3 x+2) \left((3 x+2)^2\right)^{3/2}","\frac{1}{12} (3 x+2) \left(9 x^2+12 x+4\right)^{3/2}",1,"((2 + 3*x)*((2 + 3*x)^2)^(3/2))/12","A",1
65,1,25,23,0.0050883,"\int \sqrt{4+12 x+9 x^2} \, dx","Integrate[Sqrt[4 + 12*x + 9*x^2],x]","\frac{x \sqrt{(3 x+2)^2} (3 x+4)}{6 x+4}","\frac{1}{6} (3 x+2) \sqrt{9 x^2+12 x+4}",1,"(x*Sqrt[(2 + 3*x)^2]*(4 + 3*x))/(4 + 6*x)","A",1
66,1,26,29,0.005094,"\int \frac{1}{\sqrt{4+12 x+9 x^2}} \, dx","Integrate[1/Sqrt[4 + 12*x + 9*x^2],x]","\frac{(3 x+2) \log (3 x+2)}{3 \sqrt{(3 x+2)^2}}","\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[(2 + 3*x)^2])","A",1
67,1,20,25,0.0046671,"\int \frac{1}{\left(4+12 x+9 x^2\right)^{3/2}} \, dx","Integrate[(4 + 12*x + 9*x^2)^(-3/2),x]","-\frac{3 x+2}{6 \left((3 x+2)^2\right)^{3/2}}","-\frac{1}{6 (3 x+2) \sqrt{9 x^2+12 x+4}}",1,"-1/6*(2 + 3*x)/((2 + 3*x)^2)^(3/2)","A",1
68,1,25,23,0.0092779,"\int \sqrt{4-12 x+9 x^2} \, dx","Integrate[Sqrt[4 - 12*x + 9*x^2],x]","\frac{\sqrt{(2-3 x)^2} x (3 x-4)}{6 x-4}","-\frac{1}{6} (2-3 x) \sqrt{9 x^2-12 x+4}",1,"(Sqrt[(2 - 3*x)^2]*x*(-4 + 3*x))/(-4 + 6*x)","A",1
69,1,26,29,0.0084571,"\int \frac{1}{\sqrt{4-12 x+9 x^2}} \, dx","Integrate[1/Sqrt[4 - 12*x + 9*x^2],x]","-\frac{(2-3 x) \log (2-3 x)}{3 \sqrt{(2-3 x)^2}}","-\frac{(2-3 x) \log (2-3 x)}{3 \sqrt{9 x^2-12 x+4}}",1,"-1/3*((2 - 3*x)*Log[2 - 3*x])/Sqrt[(2 - 3*x)^2]","A",1
70,1,27,23,0.0071262,"\int \sqrt{-4+12 x-9 x^2} \, dx","Integrate[Sqrt[-4 + 12*x - 9*x^2],x]","\frac{\sqrt{-(2-3 x)^2} x (3 x-4)}{6 x-4}","-\frac{1}{6} (2-3 x) \sqrt{-9 x^2+12 x-4}",1,"(Sqrt[-(2 - 3*x)^2]*x*(-4 + 3*x))/(-4 + 6*x)","A",1
71,1,28,29,0.0064825,"\int \frac{1}{\sqrt{-4+12 x-9 x^2}} \, dx","Integrate[1/Sqrt[-4 + 12*x - 9*x^2],x]","-\frac{(2-3 x) \log (2-3 x)}{3 \sqrt{-(2-3 x)^2}}","-\frac{(2-3 x) \log (2-3 x)}{3 \sqrt{-9 x^2+12 x-4}}",1,"-1/3*((2 - 3*x)*Log[2 - 3*x])/Sqrt[-(2 - 3*x)^2]","A",1
72,1,27,23,0.0056217,"\int \sqrt{-4-12 x-9 x^2} \, dx","Integrate[Sqrt[-4 - 12*x - 9*x^2],x]","\frac{x \sqrt{-(3 x+2)^2} (3 x+4)}{6 x+4}","\frac{1}{6} (3 x+2) \sqrt{-9 x^2-12 x-4}",1,"(x*Sqrt[-(2 + 3*x)^2]*(4 + 3*x))/(4 + 6*x)","A",1
73,1,28,29,0.0035934,"\int \frac{1}{\sqrt{-4-12 x-9 x^2}} \, dx","Integrate[1/Sqrt[-4 - 12*x - 9*x^2],x]","\frac{(3 x+2) \log (3 x+2)}{3 \sqrt{-(3 x+2)^2}}","\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[-(2 + 3*x)^2])","A",1
74,1,207,109,0.0300564,"\int \left(\frac{-1+b^2}{4 c}+b x+c x^2\right)^5 \, dx","Integrate[((-1 + b^2)/(4*c) + b*x + c*x^2)^5,x]","\frac{5}{8} \left(3 b^3-b\right) c^2 x^8+\frac{\left(b^2-1\right)^5 x}{1024 c^5}+\frac{5 b \left(b^2-1\right)^4 x^2}{512 c^4}+\frac{5}{36} \left(9 b^2-1\right) c^3 x^9+\frac{5 \left(b^2-1\right)^3 \left(9 b^2-1\right) x^3}{768 c^3}+\frac{5 b \left(b^2-1\right)^2 \left(3 b^2-1\right) x^4}{64 c^2}+\frac{5}{56} \left(21 b^4-14 b^2+1\right) c x^7+\frac{\left(b^2-1\right) \left(21 b^4-14 b^2+1\right) x^5}{32 c}+\frac{1}{48} b \left(63 b^4-70 b^2+15\right) x^6+\frac{1}{2} b c^4 x^{10}+\frac{c^5 x^{11}}{11}","-\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)^5*x)/(1024*c^5) + (5*b*(-1 + b^2)^4*x^2)/(512*c^4) + (5*(-1 + b^2)^3*(-1 + 9*b^2)*x^3)/(768*c^3) + (5*b*(-1 + b^2)^2*(-1 + 3*b^2)*x^4)/(64*c^2) + ((-1 + b^2)*(1 - 14*b^2 + 21*b^4)*x^5)/(32*c) + (b*(15 - 70*b^2 + 63*b^4)*x^6)/48 + (5*(1 - 14*b^2 + 21*b^4)*c*x^7)/56 + (5*(-b + 3*b^3)*c^2*x^8)/8 + (5*(-1 + 9*b^2)*c^3*x^9)/36 + (b*c^4*x^10)/2 + (c^5*x^11)/11","A",1
75,1,207,109,0.0410317,"\int \left(\frac{-4+b^2}{4 c}+b x+c x^2\right)^5 \, dx","Integrate[((-4 + b^2)/(4*c) + b*x + c*x^2)^5,x]","\frac{5}{8} \left(3 b^3-4 b\right) c^2 x^8+\frac{\left(b^2-4\right)^5 x}{1024 c^5}+\frac{5 b \left(b^2-4\right)^4 x^2}{512 c^4}+\frac{5}{36} \left(9 b^2-4\right) c^3 x^9+\frac{5 \left(b^2-4\right)^3 \left(9 b^2-4\right) x^3}{768 c^3}+\frac{5 b \left(b^2-4\right)^2 \left(3 b^2-4\right) x^4}{64 c^2}+\frac{5}{56} \left(21 b^4-56 b^2+16\right) c x^7+\frac{\left(b^2-4\right) \left(21 b^4-56 b^2+16\right) x^5}{32 c}+\frac{1}{48} b \left(63 b^4-280 b^2+240\right) x^6+\frac{1}{2} b c^4 x^{10}+\frac{c^5 x^{11}}{11}","-\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,"((-4 + b^2)^5*x)/(1024*c^5) + (5*b*(-4 + b^2)^4*x^2)/(512*c^4) + (5*(-4 + b^2)^3*(-4 + 9*b^2)*x^3)/(768*c^3) + (5*b*(-4 + b^2)^2*(-4 + 3*b^2)*x^4)/(64*c^2) + ((-4 + b^2)*(16 - 56*b^2 + 21*b^4)*x^5)/(32*c) + (b*(240 - 280*b^2 + 63*b^4)*x^6)/48 + (5*(16 - 56*b^2 + 21*b^4)*c*x^7)/56 + (5*(-4*b + 3*b^3)*c^2*x^8)/8 + (5*(-4 + 9*b^2)*c^3*x^9)/36 + (b*c^4*x^10)/2 + (c^5*x^11)/11","A",1
76,1,199,109,0.0279273,"\int \left(\frac{-9+b^2}{4 c}+b x+c x^2\right)^5 \, dx","Integrate[((-9 + b^2)/(4*c) + b*x + c*x^2)^5,x]","\frac{15}{8} \left(b^3-3 b\right) c^2 x^8+\frac{\left(b^2-9\right)^5 x}{1024 c^5}+\frac{5 b \left(b^2-9\right)^4 x^2}{512 c^4}+\frac{5}{4} \left(b^2-1\right) c^3 x^9+\frac{15 \left(b^2-9\right)^3 \left(b^2-1\right) x^3}{256 c^3}+\frac{15 b \left(b^2-9\right)^2 \left(b^2-3\right) x^4}{64 c^2}+\frac{15}{56} \left(7 b^4-42 b^2+27\right) c x^7+\frac{3 \left(b^2-9\right) \left(7 b^4-42 b^2+27\right) x^5}{32 c}+\frac{3}{16} b \left(7 b^4-70 b^2+135\right) x^6+\frac{1}{2} b c^4 x^{10}+\frac{c^5 x^{11}}{11}","-\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,"((-9 + b^2)^5*x)/(1024*c^5) + (5*b*(-9 + b^2)^4*x^2)/(512*c^4) + (15*(-9 + b^2)^3*(-1 + b^2)*x^3)/(256*c^3) + (15*b*(-9 + b^2)^2*(-3 + b^2)*x^4)/(64*c^2) + (3*(-9 + b^2)*(27 - 42*b^2 + 7*b^4)*x^5)/(32*c) + (3*b*(135 - 70*b^2 + 7*b^4)*x^6)/16 + (15*(27 - 42*b^2 + 7*b^4)*c*x^7)/56 + (15*(-3*b + b^3)*c^2*x^8)/8 + (5*(-1 + b^2)*c^3*x^9)/4 + (b*c^4*x^10)/2 + (c^5*x^11)/11","A",1
77,1,207,109,0.0424239,"\int \left(\frac{-16+b^2}{4 c}+b x+c x^2\right)^5 \, dx","Integrate[((-16 + b^2)/(4*c) + b*x + c*x^2)^5,x]","\frac{5}{8} \left(3 b^3-16 b\right) c^2 x^8+\frac{\left(b^2-16\right)^5 x}{1024 c^5}+\frac{5 b \left(b^2-16\right)^4 x^2}{512 c^4}+\frac{5}{36} \left(9 b^2-16\right) c^3 x^9+\frac{5 \left(b^2-16\right)^3 \left(9 b^2-16\right) x^3}{768 c^3}+\frac{5 b \left(b^2-16\right)^2 \left(3 b^2-16\right) x^4}{64 c^2}+\frac{5}{56} \left(21 b^4-224 b^2+256\right) c x^7+\frac{\left(b^2-16\right) \left(21 b^4-224 b^2+256\right) x^5}{32 c}+\frac{1}{48} b \left(63 b^4-1120 b^2+3840\right) x^6+\frac{1}{2} b c^4 x^{10}+\frac{c^5 x^{11}}{11}","-\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,"((-16 + b^2)^5*x)/(1024*c^5) + (5*b*(-16 + b^2)^4*x^2)/(512*c^4) + (5*(-16 + b^2)^3*(-16 + 9*b^2)*x^3)/(768*c^3) + (5*b*(-16 + b^2)^2*(-16 + 3*b^2)*x^4)/(64*c^2) + ((-16 + b^2)*(256 - 224*b^2 + 21*b^4)*x^5)/(32*c) + (b*(3840 - 1120*b^2 + 63*b^4)*x^6)/48 + (5*(256 - 224*b^2 + 21*b^4)*c*x^7)/56 + (5*(-16*b + 3*b^3)*c^2*x^8)/8 + (5*(-16 + 9*b^2)*c^3*x^9)/36 + (b*c^4*x^10)/2 + (c^5*x^11)/11","A",1
78,1,18,18,0.0092069,"\int \frac{1}{2+4 x+3 x^2} \, dx","Integrate[(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",1
79,1,12,12,0.0130848,"\int \frac{1}{4-2 \sqrt{3} x+x^2} \, dx","Integrate[(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",1
80,1,34,19,0.0191284,"\int \frac{1}{2+4 x-3 x^2} \, dx","Integrate[(2 + 4*x - 3*x^2)^(-1),x]","\frac{\log \left(3 x+\sqrt{10}-2\right)-\log \left(-3 x+\sqrt{10}+2\right)}{2 \sqrt{10}}","-\frac{\tanh ^{-1}\left(\frac{2-3 x}{\sqrt{10}}\right)}{\sqrt{10}}",1,"(-Log[2 + Sqrt[10] - 3*x] + Log[-2 + Sqrt[10] + 3*x])/(2*Sqrt[10])","A",1
81,1,13,13,0.002654,"\int \frac{1}{2+5 x+3 x^2} \, dx","Integrate[(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",1
82,1,21,21,0.002726,"\int \frac{1}{2+5 x-3 x^2} \, dx","Integrate[(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,"-1/7*Log[2 - x] + Log[1 + 3*x]/7","A",1
83,1,17,6,0.0025232,"\int \frac{1}{3+4 x+x^2} \, dx","Integrate[(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",1
84,1,27,27,0.0076885,"\int \frac{1}{1+\pi  x+2 x^2} \, dx","Integrate[(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",1
85,1,29,27,0.0077586,"\int \frac{1}{1+\pi  x-2 x^2} \, dx","Integrate[(1 + Pi*x - 2*x^2)^(-1),x]","\frac{2 \tanh ^{-1}\left(\frac{4 x-\pi }{\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",1
86,1,31,31,0.007779,"\int \frac{1}{1+\pi  x+3 x^2} \, dx","Integrate[(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",1
87,1,29,27,0.0074759,"\int \frac{1}{1+\pi  x-3 x^2} \, dx","Integrate[(1 + Pi*x - 3*x^2)^(-1),x]","\frac{2 \tanh ^{-1}\left(\frac{6 x-\pi }{\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",1
88,1,38,38,0.0104783,"\int \frac{1}{a+c x+b x^2} \, dx","Integrate[(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",1
89,1,34,35,0.0087557,"\int \frac{1}{b+2 a x+b x^2} \, dx","Integrate[(b + 2*a*x + b*x^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{a+b x}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}","-\frac{\tanh ^{-1}\left(\frac{a+b x}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}",1,"ArcTan[(a + b*x)/Sqrt[-a^2 + b^2]]/Sqrt[-a^2 + b^2]","A",1
90,1,41,32,0.010331,"\int \frac{1}{b+2 a x-b x^2} \, dx","Integrate[(b + 2*a*x - b*x^2)^(-1),x]","-\frac{\tan ^{-1}\left(\frac{b x-a}{\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,"-(ArcTan[(-a + b*x)/Sqrt[-a^2 - b^2]]/Sqrt[-a^2 - b^2])","A",1
91,1,43,43,0.0218647,"\int \frac{1}{\left(2+4 x+3 x^2\right)^2} \, dx","Integrate[(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",1
92,1,62,43,0.0244892,"\int \frac{1}{\left(2+4 x-3 x^2\right)^2} \, dx","Integrate[(2 + 4*x - 3*x^2)^(-2),x]","\frac{2-3 x}{20 \left(3 x^2-4 x-2\right)}-\frac{3 \log \left(-3 x+\sqrt{10}+2\right)}{40 \sqrt{10}}+\frac{3 \log \left(3 x+\sqrt{10}-2\right)}{40 \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*Log[2 + Sqrt[10] - 3*x])/(40*Sqrt[10]) + (3*Log[-2 + Sqrt[10] + 3*x])/(40*Sqrt[10])","A",1
93,1,33,34,0.0103271,"\int \frac{1}{\left(2+5 x+3 x^2\right)^2} \, dx","Integrate[(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",1
94,1,42,42,0.0130799,"\int \frac{1}{\left(2+5 x-3 x^2\right)^2} \, dx","Integrate[(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",1
95,1,70,71,0.0583621,"\int \frac{1}{\left(a+c x+b x^2\right)^2} \, dx","Integrate[(a + c*x + b*x^2)^(-2),x]","\frac{2 b x+c}{\left(4 a b-c^2\right) (a+x (b x+c))}+\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 + x*(c + b*x))) + (4*b*ArcTan[(c + 2*b*x)/Sqrt[4*a*b - c^2]])/(4*a*b - c^2)^(3/2)","A",1
96,1,72,72,0.0435581,"\int \frac{1}{\left(b+2 a x+b x^2\right)^2} \, dx","Integrate[(b + 2*a*x + b*x^2)^(-2),x]","\frac{a+b x}{2 \left(b^2-a^2\right) \left(2 a x+b x^2+b\right)}+\frac{b \tan ^{-1}\left(\frac{a+b x}{\sqrt{b^2-a^2}}\right)}{2 \left(b^2-a^2\right)^{3/2}}","\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*ArcTan[(a + b*x)/Sqrt[-a^2 + b^2]])/(2*(-a^2 + b^2)^(3/2))","A",1
97,1,78,69,0.0596633,"\int \frac{1}{\left(b+2 a x-b x^2\right)^2} \, dx","Integrate[(b + 2*a*x - b*x^2)^(-2),x]","\frac{\frac{b x-a}{2 a x-b x^2+b}-\frac{b \tan ^{-1}\left(\frac{b x-a}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}}{2 \left(a^2+b^2\right)}","-\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)/(b + 2*a*x - b*x^2) - (b*ArcTan[(-a + b*x)/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2])/(2*(a^2 + b^2))","A",1
98,1,65,62,0.0958497,"\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","Integrate[((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(\frac{\tan \left(\frac{\pi -2 \pi  k}{2 n}\right) \left(\left(\frac{a}{b}\right)^{\frac{1}{n}}+x\right)}{\left(\frac{a}{b}\right)^{\frac{1}{n}}-x}\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[(((a/b)^n^(-1) + x)*Tan[(Pi - 2*k*Pi)/(2*n)])/((a/b)^n^(-1) - x)]*Csc[(Pi - 2*k*Pi)/n])/(a/b)^n^(-1)","A",1
99,1,34,33,0.0316118,"\int \frac{1}{a b+\sqrt{b^2-4 a b^3} x-b^2 x^2} \, dx","Integrate[(a*b + Sqrt[b^2 - 4*a*b^3]*x - b^2*x^2)^(-1),x]","\frac{2 \tanh ^{-1}\left(\frac{2 b^2 x-\sqrt{-b^2 (4 a b-1)}}{b}\right)}{b}","\frac{2 \tanh ^{-1}\left(\frac{2 b^2 x-\sqrt{b^2-4 a b^3}}{b}\right)}{b}",1,"(2*ArcTanh[(-Sqrt[-(b^2*(-1 + 4*a*b))] + 2*b^2*x)/b])/b","A",1
100,1,32,31,0.0294476,"\int \frac{1}{a b-\sqrt{b^2-4 a b^3} x-b^2 x^2} \, dx","Integrate[(a*b - Sqrt[b^2 - 4*a*b^3]*x - b^2*x^2)^(-1),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{-b^2 (4 a b-1)}+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,"(2*ArcTanh[(Sqrt[-(b^2*(-1 + 4*a*b))] + 2*b^2*x)/b])/b","A",1
101,1,19,17,0.0199937,"\int \frac{1}{1+x^2+2 x \cos \left(\frac{1}{7}\right)} \, dx","Integrate[(1 + x^2 + 2*x*Cos[1/7])^(-1),x]","\csc \left(\frac{1}{7}\right) \tan ^{-1}\left(\frac{(x-1) \tan \left(\frac{1}{14}\right)}{x+1}\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[((-1 + x)*Tan[1/14])/(1 + x)]*Csc[1/7]","A",1
102,1,56,23,0.038903,"\int \frac{1}{1+x^2+2 x \cos \left(\frac{\pi }{7}\right)} \, dx","Integrate[(1 + x^2 + 2*x*Cos[Pi/7])^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{2 x-(-1)^{6/7}+\sqrt[7]{-1}}{\sqrt{2-(-1)^{2/7}+(-1)^{5/7}}}\right)}{\sqrt{2-(-1)^{2/7}+(-1)^{5/7}}}","\csc \left(\frac{\pi }{7}\right) \tan ^{-1}\left(x \csc \left(\frac{\pi }{7}\right)+\cot \left(\frac{\pi }{7}\right)\right)",1,"(2*ArcTan[((-1)^(1/7) - (-1)^(6/7) + 2*x)/Sqrt[2 - (-1)^(2/7) + (-1)^(5/7)]])/Sqrt[2 - (-1)^(2/7) + (-1)^(5/7)]","B",0
103,1,39,38,0.0162122,"\int \sqrt{5-6 x+9 x^2} \, dx","Integrate[Sqrt[5 - 6*x + 9*x^2],x]","\sqrt{9 x^2-6 x+5} \left(\frac{x}{2}-\frac{1}{6}\right)+\frac{2}{3} \sinh ^{-1}\left(\frac{1}{2} (3 x-1)\right)","\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,"(-1/6 + x/2)*Sqrt[5 - 6*x + 9*x^2] + (2*ArcSinh[(-1 + 3*x)/2])/3","A",1
104,1,30,30,0.0131578,"\int \sqrt{3-4 x-4 x^2} \, dx","Integrate[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",1
105,1,49,49,0.0153193,"\int \sqrt{-8+6 x+9 x^2} \, dx","Integrate[Sqrt[-8 + 6*x + 9*x^2],x]","\left(\frac{x}{2}+\frac{1}{6}\right) \sqrt{9 x^2+6 x-8}-\frac{3}{2} \log \left(\sqrt{9 x^2+6 x-8}+3 x+1\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,"(1/6 + x/2)*Sqrt[-8 + 6*x + 9*x^2] - (3*Log[1 + 3*x + Sqrt[-8 + 6*x + 9*x^2]])/2","A",1
106,1,46,45,0.0172234,"\int \sqrt{2+4 x+3 x^2} \, dx","Integrate[Sqrt[2 + 4*x + 3*x^2],x]","\sqrt{3 x^2+4 x+2} \left(\frac{x}{2}+\frac{1}{3}\right)+\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,"(1/3 + x/2)*Sqrt[2 + 4*x + 3*x^2] + ArcSinh[(2 + 3*x)/Sqrt[2]]/(3*Sqrt[3])","A",1
107,1,46,45,0.0174619,"\int \sqrt{2+4 x-3 x^2} \, dx","Integrate[Sqrt[2 + 4*x - 3*x^2],x]","\left(\frac{x}{2}-\frac{1}{3}\right) \sqrt{-3 x^2+4 x+2}-\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,"(-1/3 + x/2)*Sqrt[2 + 4*x - 3*x^2] - (5*ArcSin[(2 - 3*x)/Sqrt[10]])/(3*Sqrt[3])","A",1
108,1,55,62,0.0264197,"\int \sqrt{2+5 x+3 x^2} \, dx","Integrate[Sqrt[2 + 5*x + 3*x^2],x]","\frac{1}{72} \left(6 (6 x+5) \sqrt{3 x^2+5 x+2}-\sqrt{3} \log \left(2 \sqrt{9 x^2+15 x+6}+6 x+5\right)\right)","\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,"(6*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2] - Sqrt[3]*Log[5 + 6*x + 2*Sqrt[6 + 15*x + 9*x^2]])/72","A",1
109,1,44,43,0.0185702,"\int \sqrt{2+5 x-3 x^2} \, dx","Integrate[Sqrt[2 + 5*x - 3*x^2],x]","\left(\frac{x}{2}-\frac{5}{12}\right) \sqrt{-3 x^2+5 x+2}-\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,"(-5/12 + x/2)*Sqrt[2 + 5*x - 3*x^2] - (49*ArcSin[(5 - 6*x)/7])/(24*Sqrt[3])","A",1
110,1,53,59,0.0194485,"\int \sqrt{-2+4 x+3 x^2} \, dx","Integrate[Sqrt[-2 + 4*x + 3*x^2],x]","\frac{1}{6} (3 x+2) \sqrt{3 x^2+4 x-2}-\frac{5 \log \left(\sqrt{9 x^2+12 x-6}+3 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*Log[2 + 3*x + Sqrt[-6 + 12*x + 9*x^2]])/(3*Sqrt[3])","A",1
111,1,54,59,0.0249046,"\int \sqrt{-2+4 x-3 x^2} \, dx","Integrate[Sqrt[-2 + 4*x - 3*x^2],x]","\frac{1}{6} \sqrt{-3 x^2+4 x-2} (3 x-2)+\frac{\tan ^{-1}\left(\frac{2-3 x}{\sqrt{-9 x^2+12 x-6}}\right)}{3 \sqrt{3}}","\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[-6 + 12*x - 9*x^2]]/(3*Sqrt[3])","A",1
112,1,55,62,0.0249643,"\int \sqrt{-2+5 x+3 x^2} \, dx","Integrate[Sqrt[-2 + 5*x + 3*x^2],x]","\frac{1}{72} \left(6 (6 x+5) \sqrt{3 x^2+5 x-2}-49 \sqrt{3} \log \left(2 \sqrt{9 x^2+15 x-6}+6 x+5\right)\right)","\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,"(6*(5 + 6*x)*Sqrt[-2 + 5*x + 3*x^2] - 49*Sqrt[3]*Log[5 + 6*x + 2*Sqrt[-6 + 15*x + 9*x^2]])/72","A",1
113,1,40,39,0.0181573,"\int \sqrt{-2+5 x-3 x^2} \, dx","Integrate[Sqrt[-2 + 5*x - 3*x^2],x]","\left(\frac{x}{2}-\frac{5}{12}\right) \sqrt{-3 x^2+5 x-2}-\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,"(-5/12 + x/2)*Sqrt[-2 + 5*x - 3*x^2] - ArcSin[5 - 6*x]/(24*Sqrt[3])","A",1
114,1,14,14,0.0052795,"\int \frac{1}{\sqrt{5-6 x+9 x^2}} \, dx","Integrate[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",1
115,1,14,10,0.0055534,"\int \frac{1}{\sqrt{3-4 x-4 x^2}} \, dx","Integrate[1/Sqrt[3 - 4*x - 4*x^2],x]","-\frac{1}{2} \sin ^{-1}\left(\frac{1}{2} (-2 x-1)\right)","\frac{1}{2} \sin ^{-1}\left(x+\frac{1}{2}\right)",1,"-1/2*ArcSin[(-1 - 2*x)/2]","A",1
116,1,24,25,0.0049079,"\int \frac{1}{\sqrt{-8+6 x+9 x^2}} \, dx","Integrate[1/Sqrt[-8 + 6*x + 9*x^2],x]","\frac{1}{3} \log \left(\sqrt{9 x^2+6 x-8}+3 x+1\right)","\frac{1}{3} \tanh ^{-1}\left(\frac{3 x+1}{\sqrt{9 x^2+6 x-8}}\right)",1,"Log[1 + 3*x + Sqrt[-8 + 6*x + 9*x^2]]/3","A",1
117,1,18,18,0.0060373,"\int \frac{1}{\sqrt{2+4 x+3 x^2}} \, dx","Integrate[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",1
118,1,19,19,0.0064215,"\int \frac{1}{\sqrt{2+4 x-3 x^2}} \, dx","Integrate[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",1
119,1,28,35,0.0052942,"\int \frac{1}{\sqrt{2+5 x+3 x^2}} \, dx","Integrate[1/Sqrt[2 + 5*x + 3*x^2],x]","\frac{\log \left(2 \sqrt{9 x^2+15 x+6}+6 x+5\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,"Log[5 + 6*x + 2*Sqrt[6 + 15*x + 9*x^2]]/Sqrt[3]","A",1
120,1,17,17,0.0058057,"\int \frac{1}{\sqrt{2+5 x-3 x^2}} \, dx","Integrate[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",1
121,1,26,32,0.0055223,"\int \frac{1}{\sqrt{-2+4 x+3 x^2}} \, dx","Integrate[1/Sqrt[-2 + 4*x + 3*x^2],x]","\frac{\log \left(\sqrt{9 x^2+12 x-6}+3 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,"Log[2 + 3*x + Sqrt[-6 + 12*x + 9*x^2]]/Sqrt[3]","A",1
122,1,28,33,0.0077764,"\int \frac{1}{\sqrt{-2+4 x-3 x^2}} \, dx","Integrate[1/Sqrt[-2 + 4*x - 3*x^2],x]","-\frac{\tan ^{-1}\left(\frac{2-3 x}{\sqrt{-9 x^2+12 x-6}}\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[-6 + 12*x - 9*x^2]]/Sqrt[3])","A",1
123,1,28,35,0.0055545,"\int \frac{1}{\sqrt{-2+5 x+3 x^2}} \, dx","Integrate[1/Sqrt[-2 + 5*x + 3*x^2],x]","\frac{\log \left(2 \sqrt{9 x^2+15 x-6}+6 x+5\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,"Log[5 + 6*x + 2*Sqrt[-6 + 15*x + 9*x^2]]/Sqrt[3]","A",1
124,1,13,13,0.0059897,"\int \frac{1}{\sqrt{-2+5 x-3 x^2}} \, dx","Integrate[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",1
125,1,22,22,0.025888,"\int \frac{1}{\sqrt{\frac{b^2+4 c}{4 c}+b x+c x^2}} \, dx","Integrate[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",1
126,1,23,23,0.0262043,"\int \frac{1}{\sqrt{\frac{-b^2+4 c}{4 c}+b x-c x^2}} \, dx","Integrate[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",1
127,1,20,20,0.02514,"\int \frac{1}{\sqrt{\frac{-b^2+c}{4 c}+b x-c x^2}} \, dx","Integrate[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",1
128,1,19,19,0.0051869,"\int \frac{1}{\left(2+3 x+x^2\right)^{3/2}} \, dx","Integrate[(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
129,1,23,23,0.0064386,"\int \frac{1}{\left(27-24 x+4 x^2\right)^{3/2}} \, dx","Integrate[(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
130,1,23,23,0.0518406,"\int \frac{x}{\left(5-4 x-x^2\right)^{3/2}} \, dx","Integrate[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
131,1,31,43,0.0085603,"\int \frac{1}{\left(5-4 x-x^2\right)^{5/2}} \, dx","Integrate[(5 - 4*x - x^2)^(-5/2),x]","-\frac{(x+2) \left(2 x^2+8 x-19\right)}{243 \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,"-1/243*((2 + x)*(-19 + 8*x + 2*x^2))/(5 - 4*x - x^2)^(3/2)","A",1
132,1,126,122,0.1445232,"\int \left(a+b x+c x^2\right)^p \, dx","Integrate[(a + b*x + c*x^2)^p,x]","\frac{2^{p-1} \left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p} (a+x (b+c x))^p \, _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)}{c (p+1)}","-\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)*(a + x*(b + c*x))^p*Hypergeometric2F1[-p, 1 + p, 2 + p, (-b + Sqrt[b^2 - 4*a*c] - 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/(c*(1 + p)*((b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c])^p)","A",1
133,1,37,37,0.0103992,"\int \left(3+4 x+5 x^2\right)^p \, dx","Integrate[(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, -1/11*(2 + 5*x)^2]","A",1
134,1,32,32,0.0069145,"\int \left(3+4 x+4 x^2\right)^p \, dx","Integrate[(3 + 4*x + 4*x^2)^p,x]","2^{p-3} (8 x+4) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{1}{32} (8 x+4)^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^(-3 + p)*(4 + 8*x)*Hypergeometric2F1[1/2, -p, 3/2, -1/32*(4 + 8*x)^2]","A",1
135,1,37,37,0.0091662,"\int \left(3+4 x+3 x^2\right)^p \, dx","Integrate[(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, -1/5*(2 + 3*x)^2]","A",1
136,1,21,21,0.0051356,"\int \left(3+4 x+2 x^2\right)^p \, dx","Integrate[(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",1
137,1,48,54,0.0199141,"\int \left(3+4 x+x^2\right)^p \, dx","Integrate[(3 + 4*x + x^2)^p,x]","\frac{2^p (x+1) (x+3)^{-p} \left(x^2+4 x+3\right)^p \, _2F_1\left(-p,p+1;p+2;\frac{1}{2} (-x-1)\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^p*(1 + x)*(3 + 4*x + x^2)^p*Hypergeometric2F1[-p, 1 + p, 2 + p, (-1 - x)/2])/((1 + p)*(3 + x)^p)","A",1
138,1,17,18,0.0069696,"\int (3+4 x)^p \, dx","Integrate[(3 + 4*x)^p,x]","\frac{(4 x+3)^{p+1}}{4 p+4}","\frac{(4 x+3)^{p+1}}{4 (p+1)}",1,"(3 + 4*x)^(1 + p)/(4 + 4*p)","A",1
139,1,26,31,0.0062823,"\int \left(3+4 x-x^2\right)^p \, dx","Integrate[(3 + 4*x - x^2)^p,x]","7^p (x-2) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{1}{7} (x-2)^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",1
140,1,26,31,0.0069419,"\int \left(3+4 x-2 x^2\right)^p \, dx","Integrate[(3 + 4*x - 2*x^2)^p,x]","5^p (x-1) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{2}{5} (x-1)^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",1
141,1,37,38,0.0093087,"\int \left(3+4 x-3 x^2\right)^p \, dx","Integrate[(3 + 4*x - 3*x^2)^p,x]","3^{-p-1} 13^p (3 x-2) \, _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",1
142,1,35,35,0.007884,"\int \left(3+4 x-4 x^2\right)^p \, dx","Integrate[(3 + 4*x - 4*x^2)^p,x]","-2^{2 p-3} (4-8 x) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{1}{64} (4-8 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^(-3 + 2*p)*(4 - 8*x)*Hypergeometric2F1[1/2, -p, 3/2, (4 - 8*x)^2/64])","A",1
143,1,37,38,0.0095549,"\int \left(3+4 x-5 x^2\right)^p \, dx","Integrate[(3 + 4*x - 5*x^2)^p,x]","5^{-p-1} 19^p (5 x-2) \, _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",1