1,1,19,21,0.019206,"\int \frac{x^2}{(-1+x)^2 (1+x)^2} \, dx","IntegrateAlgebraic[x^2/((-1 + x)^2*(1 + x)^2),x]","-\frac{x}{2 \left(x^2-1\right)}-\frac{1}{2} \tanh ^{-1}(x)","\frac{x}{2 \left(1-x^2\right)}-\frac{1}{2} \tanh ^{-1}(x)",1,"-1/2*x/(-1 + x^2) - ArcTanh[x]/2","A",1
2,1,40,55,0.0144321,"\int x^2 (a+b x) (a c-b c x)^3 \, dx","IntegrateAlgebraic[x^2*(a + b*x)*(a*c - b*c*x)^3,x]","-\frac{1}{42} c^3 x^3 \left(-14 a^4+21 a^3 b x-14 a b^3 x^3+6 b^4 x^4\right)","\frac{1}{3} a^4 c^3 x^3-\frac{1}{2} a^3 b c^3 x^4+\frac{1}{3} a b^3 c^3 x^6-\frac{1}{7} b^4 c^3 x^7",1,"-1/42*(c^3*x^3*(-14*a^4 + 21*a^3*b*x - 14*a*b^3*x^3 + 6*b^4*x^4))","A",1
3,1,40,55,0.0124643,"\int x (a+b x) (a c-b c x)^3 \, dx","IntegrateAlgebraic[x*(a + b*x)*(a*c - b*c*x)^3,x]","-\frac{1}{30} c^3 x^2 \left(-15 a^4+20 a^3 b x-12 a b^3 x^3+5 b^4 x^4\right)","\frac{1}{2} a^4 c^3 x^2-\frac{2}{3} a^3 b c^3 x^3+\frac{2}{5} a b^3 c^3 x^5-\frac{1}{6} b^4 c^3 x^6",1,"-1/30*(c^3*x^2*(-15*a^4 + 20*a^3*b*x - 12*a*b^3*x^3 + 5*b^4*x^4))","A",1
4,1,38,38,0.0005723,"\int (a+b x) (a c-b c x)^3 \, dx","IntegrateAlgebraic[(a + b*x)*(a*c - b*c*x)^3,x]","-\frac{1}{10} c^3 x \left(-10 a^4+10 a^3 b x-5 a b^3 x^3+2 b^4 x^4\right)","\frac{c^3 (a-b x)^5}{5 b}-\frac{a c^3 (a-b x)^4}{2 b}",1,"-1/10*(c^3*x*(-10*a^4 + 10*a^3*b*x - 5*a*b^3*x^3 + 2*b^4*x^4))","A",1
5,1,49,47,0.0247617,"\int \frac{(a+b x) (a c-b c x)^3}{x} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^3)/x,x]","a^4 c^3 \log (b x)+\frac{1}{12} c^3 \left(19 a^4-24 a^3 b x+8 a b^3 x^3-3 b^4 x^4\right)","a^4 c^3 \log (x)-2 a^3 b c^3 x+\frac{2}{3} a b^3 c^3 x^3-\frac{1}{4} b^4 c^3 x^4",1,"(c^3*(19*a^4 - 24*a^3*b*x + 8*a*b^3*x^3 - 3*b^4*x^4))/12 + a^4*c^3*Log[b*x]","A",1
6,1,44,47,0.0167384,"\int \frac{(a+b x) (a c-b c x)^3}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^3)/x^2,x]","-\frac{c^3 \left(3 a^4-3 a b^3 x^3+b^4 x^4\right)}{3 x}-2 a^3 b c^3 \log (x)","-\frac{a^4 c^3}{x}-2 a^3 b c^3 \log (x)+a b^3 c^3 x^2-\frac{1}{3} b^4 c^3 x^3",1,"-1/3*(c^3*(3*a^4 - 3*a*b^3*x^3 + b^4*x^4))/x - 2*a^3*b*c^3*Log[x]","A",1
7,1,49,18,0.0120959,"\int \frac{(a+b x) (a c-b c x)^3}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^3)/x^3,x]","\frac{a^4 \left(-c^3\right)+4 a^3 b c^3 x+4 a b^3 c^3 x^3-b^4 c^3 x^4}{2 x^2}","-\frac{c^3 (a-b x)^4}{2 x^2}",1,"(-(a^4*c^3) + 4*a^3*b*c^3*x + 4*a*b^3*c^3*x^3 - b^4*c^3*x^4)/(2*x^2)","B",1
8,1,41,45,0.016001,"\int \frac{(a+b x) (a c-b c x)^3}{x^4} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^3)/x^4,x]","2 a b^3 c^3 \log (x)-\frac{c^3 \left(a^4-3 a^3 b x+3 b^4 x^4\right)}{3 x^3}","-\frac{a^4 c^3}{3 x^3}+\frac{a^3 b c^3}{x^2}+2 a b^3 c^3 \log (x)-b^4 c^3 x",1,"-1/3*(c^3*(a^4 - 3*a^3*b*x + 3*b^4*x^4))/x^3 + 2*a*b^3*c^3*Log[x]","A",1
9,1,43,50,0.0170342,"\int \frac{(a+b x) (a c-b c x)^3}{x^5} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^3)/x^5,x]","b^4 \left(-c^3\right) \log (x)-\frac{a c^3 \left(3 a^3-8 a^2 b x+24 b^3 x^3\right)}{12 x^4}","-\frac{a^4 c^3}{4 x^4}+\frac{2 a^3 b c^3}{3 x^3}-\frac{2 a b^3 c^3}{x}-b^4 c^3 \log (x)",1,"-1/12*(a*c^3*(3*a^3 - 8*a^2*b*x + 24*b^3*x^3))/x^4 - b^4*c^3*Log[x]","A",1
10,1,49,50,0.0119936,"\int \frac{(a+b x) (a c-b c x)^3}{x^6} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^3)/x^6,x]","\frac{-2 a^4 c^3+5 a^3 b c^3 x-10 a b^3 c^3 x^3+10 b^4 c^3 x^4}{10 x^5}","-\frac{a^4 c^3}{5 x^5}+\frac{a^3 b c^3}{2 x^4}-\frac{a b^3 c^3}{x^2}+\frac{b^4 c^3}{x}",1,"(-2*a^4*c^3 + 5*a^3*b*c^3*x - 10*a*b^3*c^3*x^3 + 10*b^4*c^3*x^4)/(10*x^5)","A",1
11,1,49,55,0.0116773,"\int \frac{(a+b x) (a c-b c x)^3}{x^7} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^3)/x^7,x]","\frac{-5 a^4 c^3+12 a^3 b c^3 x-20 a b^3 c^3 x^3+15 b^4 c^3 x^4}{30 x^6}","-\frac{a^4 c^3}{6 x^6}+\frac{2 a^3 b c^3}{5 x^5}-\frac{2 a b^3 c^3}{3 x^3}+\frac{b^4 c^3}{2 x^2}",1,"(-5*a^4*c^3 + 12*a^3*b*c^3*x - 20*a*b^3*c^3*x^3 + 15*b^4*c^3*x^4)/(30*x^6)","A",1
12,1,49,55,0.0116535,"\int \frac{(a+b x) (a c-b c x)^3}{x^8} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^3)/x^8,x]","\frac{-6 a^4 c^3+14 a^3 b c^3 x-21 a b^3 c^3 x^3+14 b^4 c^3 x^4}{42 x^7}","-\frac{a^4 c^3}{7 x^7}+\frac{a^3 b c^3}{3 x^6}-\frac{a b^3 c^3}{2 x^4}+\frac{b^4 c^3}{3 x^3}",1,"(-6*a^4*c^3 + 14*a^3*b*c^3*x - 21*a*b^3*c^3*x^3 + 14*b^4*c^3*x^4)/(42*x^7)","A",1
13,1,62,87,0.0149562,"\int x^4 (a+b x) (a c-b c x)^4 \, dx","IntegrateAlgebraic[x^4*(a + b*x)*(a*c - b*c*x)^4,x]","\frac{1}{420} c^4 x^5 \left(84 a^5-210 a^4 b x+120 a^3 b^2 x^2+105 a^2 b^3 x^3-140 a b^4 x^4+42 b^5 x^5\right)","\frac{1}{5} a^5 c^4 x^5-\frac{1}{2} a^4 b c^4 x^6+\frac{2}{7} a^3 b^2 c^4 x^7+\frac{1}{4} a^2 b^3 c^4 x^8-\frac{1}{3} a b^4 c^4 x^9+\frac{1}{10} b^5 c^4 x^{10}",1,"(c^4*x^5*(84*a^5 - 210*a^4*b*x + 120*a^3*b^2*x^2 + 105*a^2*b^3*x^3 - 140*a*b^4*x^4 + 42*b^5*x^5))/420","A",1
14,1,62,87,0.0140628,"\int x^3 (a+b x) (a c-b c x)^4 \, dx","IntegrateAlgebraic[x^3*(a + b*x)*(a*c - b*c*x)^4,x]","\frac{c^4 x^4 \left(630 a^5-1512 a^4 b x+840 a^3 b^2 x^2+720 a^2 b^3 x^3-945 a b^4 x^4+280 b^5 x^5\right)}{2520}","\frac{1}{4} a^5 c^4 x^4-\frac{3}{5} a^4 b c^4 x^5+\frac{1}{3} a^3 b^2 c^4 x^6+\frac{2}{7} a^2 b^3 c^4 x^7-\frac{3}{8} a b^4 c^4 x^8+\frac{1}{9} b^5 c^4 x^9",1,"(c^4*x^4*(630*a^5 - 1512*a^4*b*x + 840*a^3*b^2*x^2 + 720*a^2*b^3*x^3 - 945*a*b^4*x^4 + 280*b^5*x^5))/2520","A",1
15,1,62,80,0.0137227,"\int x^2 (a+b x) (a c-b c x)^4 \, dx","IntegrateAlgebraic[x^2*(a + b*x)*(a*c - b*c*x)^4,x]","\frac{1}{840} c^4 x^3 \left(280 a^5-630 a^4 b x+336 a^3 b^2 x^2+280 a^2 b^3 x^3-360 a b^4 x^4+105 b^5 x^5\right)","-\frac{2 a^3 c^4 (a-b x)^5}{5 b^3}+\frac{5 a^2 c^4 (a-b x)^6}{6 b^3}+\frac{c^4 (a-b x)^8}{8 b^3}-\frac{4 a c^4 (a-b x)^7}{7 b^3}",1,"(c^4*x^3*(280*a^5 - 630*a^4*b*x + 336*a^3*b^2*x^2 + 280*a^2*b^3*x^3 - 360*a*b^4*x^4 + 105*b^5*x^5))/840","A",1
16,1,62,59,0.0141412,"\int x (a+b x) (a c-b c x)^4 \, dx","IntegrateAlgebraic[x*(a + b*x)*(a*c - b*c*x)^4,x]","\frac{1}{70} c^4 x^2 \left(35 a^5-70 a^4 b x+35 a^3 b^2 x^2+28 a^2 b^3 x^3-35 a b^4 x^4+10 b^5 x^5\right)","-\frac{2 a^2 c^4 (a-b x)^5}{5 b^2}-\frac{c^4 (a-b x)^7}{7 b^2}+\frac{a c^4 (a-b x)^6}{2 b^2}",1,"(c^4*x^2*(35*a^5 - 70*a^4*b*x + 35*a^3*b^2*x^2 + 28*a^2*b^3*x^3 - 35*a*b^4*x^4 + 10*b^5*x^5))/70","A",1
17,1,60,38,0.0139183,"\int (a+b x) (a c-b c x)^4 \, dx","IntegrateAlgebraic[(a + b*x)*(a*c - b*c*x)^4,x]","\frac{1}{30} c^4 x \left(30 a^5-45 a^4 b x+20 a^3 b^2 x^2+15 a^2 b^3 x^3-18 a b^4 x^4+5 b^5 x^5\right)","\frac{c^4 (a-b x)^6}{6 b}-\frac{2 a c^4 (a-b x)^5}{5 b}",1,"(c^4*x*(30*a^5 - 45*a^4*b*x + 20*a^3*b^2*x^2 + 15*a^2*b^3*x^3 - 18*a*b^4*x^4 + 5*b^5*x^5))/30","A",1
18,1,63,76,0.0314236,"\int \frac{(a+b x) (a c-b c x)^4}{x} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^4)/x,x]","a^5 c^4 \log (b c x)+\frac{1}{60} b c^4 x \left(-180 a^4+60 a^3 b x+40 a^2 b^2 x^2-45 a b^3 x^3+12 b^4 x^4\right)","a^5 c^4 \log (x)-3 a^4 b c^4 x+a^3 b^2 c^4 x^2+\frac{2}{3} a^2 b^3 c^4 x^3-\frac{3}{4} a b^4 c^4 x^4+\frac{1}{5} b^5 c^4 x^5",1,"(b*c^4*x*(-180*a^4 + 60*a^3*b*x + 40*a^2*b^2*x^2 - 45*a*b^3*x^3 + 12*b^4*x^4))/60 + a^5*c^4*Log[b*c*x]","A",1
19,1,66,73,0.0218995,"\int \frac{(a+b x) (a c-b c x)^4}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^4)/x^2,x]","\frac{c^4 \left(-4 a^5+8 a^3 b^2 x^2+4 a^2 b^3 x^3-4 a b^4 x^4+b^5 x^5\right)}{4 x}-3 a^4 b c^4 \log (x)","-\frac{a^5 c^4}{x}-3 a^4 b c^4 \log (x)+2 a^3 b^2 c^4 x+a^2 b^3 c^4 x^2-a b^4 c^4 x^3+\frac{1}{4} b^5 c^4 x^4",1,"(c^4*(-4*a^5 + 8*a^3*b^2*x^2 + 4*a^2*b^3*x^3 - 4*a*b^4*x^4 + b^5*x^5))/(4*x) - 3*a^4*b*c^4*Log[x]","A",1
20,1,65,78,0.0216367,"\int \frac{(a+b x) (a c-b c x)^4}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^4)/x^3,x]","2 a^3 b^2 c^4 \log (x)+\frac{c^4 \left(-3 a^5+18 a^4 b x+12 a^2 b^3 x^3-9 a b^4 x^4+2 b^5 x^5\right)}{6 x^2}","-\frac{a^5 c^4}{2 x^2}+\frac{3 a^4 b c^4}{x}+2 a^3 b^2 c^4 \log (x)+2 a^2 b^3 c^4 x-\frac{3}{2} a b^4 c^4 x^2+\frac{1}{3} b^5 c^4 x^3",1,"(c^4*(-3*a^5 + 18*a^4*b*x + 12*a^2*b^3*x^3 - 9*a*b^4*x^4 + 2*b^5*x^5))/(6*x^2) + 2*a^3*b^2*c^4*Log[x]","A",1
21,1,65,78,0.0217657,"\int \frac{(a+b x) (a c-b c x)^4}{x^4} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^4)/x^4,x]","2 a^2 b^3 c^4 \log (x)+\frac{c^4 \left(-2 a^5+9 a^4 b x-12 a^3 b^2 x^2-18 a b^4 x^4+3 b^5 x^5\right)}{6 x^3}","-\frac{a^5 c^4}{3 x^3}+\frac{3 a^4 b c^4}{2 x^2}-\frac{2 a^3 b^2 c^4}{x}+2 a^2 b^3 c^4 \log (x)-3 a b^4 c^4 x+\frac{1}{2} b^5 c^4 x^2",1,"(c^4*(-2*a^5 + 9*a^4*b*x - 12*a^3*b^2*x^2 - 18*a*b^4*x^4 + 3*b^5*x^5))/(6*x^3) + 2*a^2*b^3*c^4*Log[x]","A",1
22,1,65,72,0.0210573,"\int \frac{(a+b x) (a c-b c x)^4}{x^5} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^4)/x^5,x]","\frac{c^4 \left(-a^5+4 a^4 b x-4 a^3 b^2 x^2-8 a^2 b^3 x^3+4 b^5 x^5\right)}{4 x^4}-3 a b^4 c^4 \log (x)","-\frac{a^5 c^4}{4 x^4}+\frac{a^4 b c^4}{x^3}-\frac{a^3 b^2 c^4}{x^2}-\frac{2 a^2 b^3 c^4}{x}-3 a b^4 c^4 \log (x)+b^5 c^4 x",1,"(c^4*(-a^5 + 4*a^4*b*x - 4*a^3*b^2*x^2 - 8*a^2*b^3*x^3 + 4*b^5*x^5))/(4*x^4) - 3*a*b^4*c^4*Log[x]","A",1
23,1,62,79,0.0227477,"\int \frac{(a+b x) (a c-b c x)^4}{x^6} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^4)/x^6,x]","b^5 c^4 \log (x)-\frac{a c^4 \left(12 a^4-45 a^3 b x+40 a^2 b^2 x^2+60 a b^3 x^3-180 b^4 x^4\right)}{60 x^5}","-\frac{a^5 c^4}{5 x^5}+\frac{3 a^4 b c^4}{4 x^4}-\frac{2 a^3 b^2 c^4}{3 x^3}-\frac{a^2 b^3 c^4}{x^2}+\frac{3 a b^4 c^4}{x}+b^5 c^4 \log (x)",1,"-1/60*(a*c^4*(12*a^4 - 45*a^3*b*x + 40*a^2*b^2*x^2 + 60*a*b^3*x^3 - 180*b^4*x^4))/x^5 + b^5*c^4*Log[x]","A",1
24,1,77,41,0.0156536,"\int \frac{(a+b x) (a c-b c x)^4}{x^7} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^4)/x^7,x]","\frac{-5 a^5 c^4+18 a^4 b c^4 x-15 a^3 b^2 c^4 x^2-20 a^2 b^3 c^4 x^3+45 a b^4 c^4 x^4-30 b^5 c^4 x^5}{30 x^6}","-\frac{c^4 (a-b x)^5}{6 x^6}-\frac{7 b c^4 (a-b x)^5}{30 a x^5}",1,"(-5*a^5*c^4 + 18*a^4*b*c^4*x - 15*a^3*b^2*c^4*x^2 - 20*a^2*b^3*c^4*x^3 + 45*a*b^4*c^4*x^4 - 30*b^5*c^4*x^5)/(30*x^6)","A",1
25,1,77,84,0.0151501,"\int \frac{(a+b x) (a c-b c x)^4}{x^8} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^4)/x^8,x]","\frac{-10 a^5 c^4+35 a^4 b c^4 x-28 a^3 b^2 c^4 x^2-35 a^2 b^3 c^4 x^3+70 a b^4 c^4 x^4-35 b^5 c^4 x^5}{70 x^7}","-\frac{a^5 c^4}{7 x^7}+\frac{a^4 b c^4}{2 x^6}-\frac{2 a^3 b^2 c^4}{5 x^5}-\frac{a^2 b^3 c^4}{2 x^4}+\frac{a b^4 c^4}{x^3}-\frac{b^5 c^4}{2 x^2}",1,"(-10*a^5*c^4 + 35*a^4*b*c^4*x - 28*a^3*b^2*c^4*x^2 - 35*a^2*b^3*c^4*x^3 + 70*a*b^4*c^4*x^4 - 35*b^5*c^4*x^5)/(70*x^7)","A",1
26,1,77,87,0.0154542,"\int \frac{(a+b x) (a c-b c x)^4}{x^9} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^4)/x^9,x]","\frac{-105 a^5 c^4+360 a^4 b c^4 x-280 a^3 b^2 c^4 x^2-336 a^2 b^3 c^4 x^3+630 a b^4 c^4 x^4-280 b^5 c^4 x^5}{840 x^8}","-\frac{a^5 c^4}{8 x^8}+\frac{3 a^4 b c^4}{7 x^7}-\frac{a^3 b^2 c^4}{3 x^6}-\frac{2 a^2 b^3 c^4}{5 x^5}+\frac{3 a b^4 c^4}{4 x^4}-\frac{b^5 c^4}{3 x^3}",1,"(-105*a^5*c^4 + 360*a^4*b*c^4*x - 280*a^3*b^2*c^4*x^2 - 336*a^2*b^3*c^4*x^3 + 630*a*b^4*c^4*x^4 - 280*b^5*c^4*x^5)/(840*x^8)","A",1
27,1,62,87,0.0198643,"\int x^4 (a+b x) (a c-b c x)^5 \, dx","IntegrateAlgebraic[x^4*(a + b*x)*(a*c - b*c*x)^5,x]","-\frac{c^5 x^5 \left(-693 a^6+2310 a^5 b x-2475 a^4 b^2 x^2+1925 a^2 b^4 x^4-1386 a b^5 x^5+315 b^6 x^6\right)}{3465}","\frac{1}{5} a^6 c^5 x^5-\frac{2}{3} a^5 b c^5 x^6+\frac{5}{7} a^4 b^2 c^5 x^7-\frac{5}{9} a^2 b^4 c^5 x^9+\frac{2}{5} a b^5 c^5 x^{10}-\frac{1}{11} b^6 c^5 x^{11}",1,"-1/3465*(c^5*x^5*(-693*a^6 + 2310*a^5*b*x - 2475*a^4*b^2*x^2 + 1925*a^2*b^4*x^4 - 1386*a*b^5*x^5 + 315*b^6*x^6))","A",1
28,1,62,87,0.0178043,"\int x^3 (a+b x) (a c-b c x)^5 \, dx","IntegrateAlgebraic[x^3*(a + b*x)*(a*c - b*c*x)^5,x]","-\frac{1}{360} c^5 x^4 \left(-90 a^6+288 a^5 b x-300 a^4 b^2 x^2+225 a^2 b^4 x^4-160 a b^5 x^5+36 b^6 x^6\right)","\frac{1}{4} a^6 c^5 x^4-\frac{4}{5} a^5 b c^5 x^5+\frac{5}{6} a^4 b^2 c^5 x^6-\frac{5}{8} a^2 b^4 c^5 x^8+\frac{4}{9} a b^5 c^5 x^9-\frac{1}{10} b^6 c^5 x^{10}",1,"-1/360*(c^5*x^4*(-90*a^6 + 288*a^5*b*x - 300*a^4*b^2*x^2 + 225*a^2*b^4*x^4 - 160*a*b^5*x^5 + 36*b^6*x^6))","A",1
29,1,62,80,0.0172189,"\int x^2 (a+b x) (a c-b c x)^5 \, dx","IntegrateAlgebraic[x^2*(a + b*x)*(a*c - b*c*x)^5,x]","-\frac{1}{126} c^5 x^3 \left(-42 a^6+126 a^5 b x-126 a^4 b^2 x^2+90 a^2 b^4 x^4-63 a b^5 x^5+14 b^6 x^6\right)","-\frac{a^3 c^5 (a-b x)^6}{3 b^3}+\frac{5 a^2 c^5 (a-b x)^7}{7 b^3}+\frac{c^5 (a-b x)^9}{9 b^3}-\frac{a c^5 (a-b x)^8}{2 b^3}",1,"-1/126*(c^5*x^3*(-42*a^6 + 126*a^5*b*x - 126*a^4*b^2*x^2 + 90*a^2*b^4*x^4 - 63*a*b^5*x^5 + 14*b^6*x^6))","A",1
30,1,62,59,0.0169614,"\int x (a+b x) (a c-b c x)^5 \, dx","IntegrateAlgebraic[x*(a + b*x)*(a*c - b*c*x)^5,x]","-\frac{1}{168} c^5 x^2 \left(-84 a^6+224 a^5 b x-210 a^4 b^2 x^2+140 a^2 b^4 x^4-96 a b^5 x^5+21 b^6 x^6\right)","-\frac{a^2 c^5 (a-b x)^6}{3 b^2}-\frac{c^5 (a-b x)^8}{8 b^2}+\frac{3 a c^5 (a-b x)^7}{7 b^2}",1,"-1/168*(c^5*x^2*(-84*a^6 + 224*a^5*b*x - 210*a^4*b^2*x^2 + 140*a^2*b^4*x^4 - 96*a*b^5*x^5 + 21*b^6*x^6))","A",1
31,1,60,38,0.0164254,"\int (a+b x) (a c-b c x)^5 \, dx","IntegrateAlgebraic[(a + b*x)*(a*c - b*c*x)^5,x]","-\frac{1}{21} c^5 x \left(-21 a^6+42 a^5 b x-35 a^4 b^2 x^2+21 a^2 b^4 x^4-14 a b^5 x^5+3 b^6 x^6\right)","\frac{c^5 (a-b x)^7}{7 b}-\frac{a c^5 (a-b x)^6}{3 b}",1,"-1/21*(c^5*x*(-21*a^6 + 42*a^5*b*x - 35*a^4*b^2*x^2 + 21*a^2*b^4*x^4 - 14*a*b^5*x^5 + 3*b^6*x^6))","A",1
32,1,62,79,0.0287352,"\int \frac{(a+b x) (a c-b c x)^5}{x} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^5)/x,x]","a^6 c^5 \log (b x)-\frac{1}{60} b c^5 x \left(240 a^5-150 a^4 b x+75 a^2 b^3 x^3-48 a b^4 x^4+10 b^5 x^5\right)","a^6 c^5 \log (x)-4 a^5 b c^5 x+\frac{5}{2} a^4 b^2 c^5 x^2-\frac{5}{4} a^2 b^4 c^5 x^4+\frac{4}{5} a b^5 c^5 x^5-\frac{1}{6} b^6 c^5 x^6",1,"-1/60*(b*c^5*x*(240*a^5 - 150*a^4*b*x + 75*a^2*b^3*x^3 - 48*a*b^4*x^4 + 10*b^5*x^5)) + a^6*c^5*Log[b*x]","A",1
33,1,67,75,0.0219998,"\int \frac{(a+b x) (a c-b c x)^5}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^5)/x^2,x]","-4 a^5 b c^5 \log (x)-\frac{c^5 \left(15 a^6-75 a^4 b^2 x^2+25 a^2 b^4 x^4-15 a b^5 x^5+3 b^6 x^6\right)}{15 x}","-\frac{a^6 c^5}{x}-4 a^5 b c^5 \log (x)+5 a^4 b^2 c^5 x-\frac{5}{3} a^2 b^4 c^5 x^3+a b^5 c^5 x^4-\frac{1}{5} b^6 c^5 x^5",1,"-1/15*(c^5*(15*a^6 - 75*a^4*b^2*x^2 + 25*a^2*b^4*x^4 - 15*a*b^5*x^5 + 3*b^6*x^6))/x - 4*a^5*b*c^5*Log[x]","A",1
34,1,65,82,0.023212,"\int \frac{(a+b x) (a c-b c x)^5}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^5)/x^3,x]","5 a^4 b^2 c^5 \log (x)-\frac{c^5 \left(6 a^6-48 a^5 b x+30 a^2 b^4 x^4-16 a b^5 x^5+3 b^6 x^6\right)}{12 x^2}","-\frac{a^6 c^5}{2 x^2}+\frac{4 a^5 b c^5}{x}+5 a^4 b^2 c^5 \log (x)-\frac{5}{2} a^2 b^4 c^5 x^2+\frac{4}{3} a b^5 c^5 x^3-\frac{1}{4} b^6 c^5 x^4",1,"-1/12*(c^5*(6*a^6 - 48*a^5*b*x + 30*a^2*b^4*x^4 - 16*a*b^5*x^5 + 3*b^6*x^6))/x^2 + 5*a^4*b^2*c^5*Log[x]","A",1
35,1,77,18,0.014431,"\int \frac{(a+b x) (a c-b c x)^5}{x^4} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^5)/x^4,x]","\frac{a^6 \left(-c^5\right)+6 a^5 b c^5 x-15 a^4 b^2 c^5 x^2-15 a^2 b^4 c^5 x^4+6 a b^5 c^5 x^5-b^6 c^5 x^6}{3 x^3}","-\frac{c^5 (a-b x)^6}{3 x^3}",1,"(-(a^6*c^5) + 6*a^5*b*c^5*x - 15*a^4*b^2*c^5*x^2 - 15*a^2*b^4*c^5*x^4 + 6*a*b^5*c^5*x^5 - b^6*c^5*x^6)/(3*x^3)","B",1
36,1,65,80,0.0225462,"\int \frac{(a+b x) (a c-b c x)^5}{x^5} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^5)/x^5,x]","-5 a^2 b^4 c^5 \log (x)-\frac{c^5 \left(3 a^6-16 a^5 b x+30 a^4 b^2 x^2-48 a b^5 x^5+6 b^6 x^6\right)}{12 x^4}","-\frac{a^6 c^5}{4 x^4}+\frac{4 a^5 b c^5}{3 x^3}-\frac{5 a^4 b^2 c^5}{2 x^2}-5 a^2 b^4 c^5 \log (x)+4 a b^5 c^5 x-\frac{1}{2} b^6 c^5 x^2",1,"-1/12*(c^5*(3*a^6 - 16*a^5*b*x + 30*a^4*b^2*x^2 - 48*a*b^5*x^5 + 6*b^6*x^6))/x^4 - 5*a^2*b^4*c^5*Log[x]","A",1
37,1,65,75,0.0217839,"\int \frac{(a+b x) (a c-b c x)^5}{x^6} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^5)/x^6,x]","4 a b^5 c^5 \log (x)-\frac{c^5 \left(3 a^6-15 a^5 b x+25 a^4 b^2 x^2-75 a^2 b^4 x^4+15 b^6 x^6\right)}{15 x^5}","-\frac{a^6 c^5}{5 x^5}+\frac{a^5 b c^5}{x^4}-\frac{5 a^4 b^2 c^5}{3 x^3}+\frac{5 a^2 b^4 c^5}{x}+4 a b^5 c^5 \log (x)-b^6 c^5 x",1,"-1/15*(c^5*(3*a^6 - 15*a^5*b*x + 25*a^4*b^2*x^2 - 75*a^2*b^4*x^4 + 15*b^6*x^6))/x^5 + 4*a*b^5*c^5*Log[x]","A",1
38,1,63,82,0.0220799,"\int \frac{(a+b x) (a c-b c x)^5}{x^7} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^5)/x^7,x]","b^6 \left(-c^5\right) \log (x)-\frac{a c^5 \left(10 a^5-48 a^4 b x+75 a^3 b^2 x^2-150 a b^4 x^4+240 b^5 x^5\right)}{60 x^6}","-\frac{a^6 c^5}{6 x^6}+\frac{4 a^5 b c^5}{5 x^5}-\frac{5 a^4 b^2 c^5}{4 x^4}+\frac{5 a^2 b^4 c^5}{2 x^2}-\frac{4 a b^5 c^5}{x}-b^6 c^5 \log (x)",1,"-1/60*(a*c^5*(10*a^5 - 48*a^4*b*x + 75*a^3*b^2*x^2 - 150*a*b^4*x^4 + 240*b^5*x^5))/x^6 - b^6*c^5*Log[x]","A",1
39,1,77,41,0.0152532,"\int \frac{(a+b x) (a c-b c x)^5}{x^8} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^5)/x^8,x]","\frac{-3 a^6 c^5+14 a^5 b c^5 x-21 a^4 b^2 c^5 x^2+35 a^2 b^4 c^5 x^4-42 a b^5 c^5 x^5+21 b^6 c^5 x^6}{21 x^7}","-\frac{c^5 (a-b x)^6}{7 x^7}-\frac{4 b c^5 (a-b x)^6}{21 a x^6}",1,"(-3*a^6*c^5 + 14*a^5*b*c^5*x - 21*a^4*b^2*c^5*x^2 + 35*a^2*b^4*c^5*x^4 - 42*a*b^5*c^5*x^5 + 21*b^6*c^5*x^6)/(21*x^7)","A",1
40,1,77,65,0.0153462,"\int \frac{(a+b x) (a c-b c x)^5}{x^9} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^5)/x^9,x]","\frac{-21 a^6 c^5+96 a^5 b c^5 x-140 a^4 b^2 c^5 x^2+210 a^2 b^4 c^5 x^4-224 a b^5 c^5 x^5+84 b^6 c^5 x^6}{168 x^8}","-\frac{5 b^2 c^5 (a-b x)^6}{168 a^2 x^6}-\frac{c^5 (a-b x)^6}{8 x^8}-\frac{5 b c^5 (a-b x)^6}{28 a x^7}",1,"(-21*a^6*c^5 + 96*a^5*b*c^5*x - 140*a^4*b^2*c^5*x^2 + 210*a^2*b^4*c^5*x^4 - 224*a*b^5*c^5*x^5 + 84*b^6*c^5*x^6)/(168*x^8)","A",1
41,1,77,82,0.014808,"\int \frac{(a+b x) (a c-b c x)^5}{x^{10}} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^5)/x^10,x]","\frac{-14 a^6 c^5+63 a^5 b c^5 x-90 a^4 b^2 c^5 x^2+126 a^2 b^4 c^5 x^4-126 a b^5 c^5 x^5+42 b^6 c^5 x^6}{126 x^9}","-\frac{a^6 c^5}{9 x^9}+\frac{a^5 b c^5}{2 x^8}-\frac{5 a^4 b^2 c^5}{7 x^7}+\frac{a^2 b^4 c^5}{x^5}-\frac{a b^5 c^5}{x^4}+\frac{b^6 c^5}{3 x^3}",1,"(-14*a^6*c^5 + 63*a^5*b*c^5*x - 90*a^4*b^2*c^5*x^2 + 126*a^2*b^4*c^5*x^4 - 126*a*b^5*c^5*x^5 + 42*b^6*c^5*x^6)/(126*x^9)","A",1
42,1,77,87,0.015074,"\int \frac{(a+b x) (a c-b c x)^5}{x^{11}} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^5)/x^11,x]","\frac{-36 a^6 c^5+160 a^5 b c^5 x-225 a^4 b^2 c^5 x^2+300 a^2 b^4 c^5 x^4-288 a b^5 c^5 x^5+90 b^6 c^5 x^6}{360 x^{10}}","-\frac{a^6 c^5}{10 x^{10}}+\frac{4 a^5 b c^5}{9 x^9}-\frac{5 a^4 b^2 c^5}{8 x^8}+\frac{5 a^2 b^4 c^5}{6 x^6}-\frac{4 a b^5 c^5}{5 x^5}+\frac{b^6 c^5}{4 x^4}",1,"(-36*a^6*c^5 + 160*a^5*b*c^5*x - 225*a^4*b^2*c^5*x^2 + 300*a^2*b^4*c^5*x^4 - 288*a*b^5*c^5*x^5 + 90*b^6*c^5*x^6)/(360*x^10)","A",1
43,1,77,87,0.013996,"\int \frac{(a+b x) (a c-b c x)^5}{x^{12}} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^5)/x^12,x]","\frac{-315 a^6 c^5+1386 a^5 b c^5 x-1925 a^4 b^2 c^5 x^2+2475 a^2 b^4 c^5 x^4-2310 a b^5 c^5 x^5+693 b^6 c^5 x^6}{3465 x^{11}}","-\frac{a^6 c^5}{11 x^{11}}+\frac{2 a^5 b c^5}{5 x^{10}}-\frac{5 a^4 b^2 c^5}{9 x^9}+\frac{5 a^2 b^4 c^5}{7 x^7}-\frac{2 a b^5 c^5}{3 x^6}+\frac{b^6 c^5}{5 x^5}",1,"(-315*a^6*c^5 + 1386*a^5*b*c^5*x - 1925*a^4*b^2*c^5*x^2 + 2475*a^2*b^4*c^5*x^4 - 2310*a*b^5*c^5*x^5 + 693*b^6*c^5*x^6)/(3465*x^11)","A",1
44,1,84,113,0.0308066,"\int \frac{(a+b x) (a c-b c x)^6}{x^8} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^6)/x^8,x]","b^7 c^6 \log (x)-\frac{a c^6 \left(60 a^6-350 a^5 b x+756 a^4 b^2 x^2-525 a^3 b^3 x^3-700 a^2 b^4 x^4+1890 a b^5 x^5-2100 b^6 x^6\right)}{420 x^7}","-\frac{a^7 c^6}{7 x^7}+\frac{5 a^6 b c^6}{6 x^6}-\frac{9 a^5 b^2 c^6}{5 x^5}+\frac{5 a^4 b^3 c^6}{4 x^4}+\frac{5 a^3 b^4 c^6}{3 x^3}-\frac{9 a^2 b^5 c^6}{2 x^2}+\frac{5 a b^6 c^6}{x}+b^7 c^6 \log (x)",1,"-1/420*(a*c^6*(60*a^6 - 350*a^5*b*x + 756*a^4*b^2*x^2 - 525*a^3*b^3*x^3 - 700*a^2*b^4*x^4 + 1890*a*b^5*x^5 - 2100*b^6*x^6))/x^7 + b^7*c^6*Log[x]","A",1
45,1,105,41,0.0179477,"\int \frac{(a+b x) (a c-b c x)^6}{x^9} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^6)/x^9,x]","\frac{-7 a^7 c^6+40 a^6 b c^6 x-84 a^5 b^2 c^6 x^2+56 a^4 b^3 c^6 x^3+70 a^3 b^4 c^6 x^4-168 a^2 b^5 c^6 x^5+140 a b^6 c^6 x^6-56 b^7 c^6 x^7}{56 x^8}","-\frac{c^6 (a-b x)^7}{8 x^8}-\frac{9 b c^6 (a-b x)^7}{56 a x^7}",1,"(-7*a^7*c^6 + 40*a^6*b*c^6*x - 84*a^5*b^2*c^6*x^2 + 56*a^4*b^3*c^6*x^3 + 70*a^3*b^4*c^6*x^4 - 168*a^2*b^5*c^6*x^5 + 140*a*b^6*c^6*x^6 - 56*b^7*c^6*x^7)/(56*x^8)","B",1
46,1,105,65,0.0178424,"\int \frac{(a+b x) (a c-b c x)^6}{x^{10}} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^6)/x^10,x]","\frac{-56 a^7 c^6+315 a^6 b c^6 x-648 a^5 b^2 c^6 x^2+420 a^4 b^3 c^6 x^3+504 a^3 b^4 c^6 x^4-1134 a^2 b^5 c^6 x^5+840 a b^6 c^6 x^6-252 b^7 c^6 x^7}{504 x^9}","-\frac{11 b^2 c^6 (a-b x)^7}{504 a^2 x^7}-\frac{c^6 (a-b x)^7}{9 x^9}-\frac{11 b c^6 (a-b x)^7}{72 a x^8}",1,"(-56*a^7*c^6 + 315*a^6*b*c^6*x - 648*a^5*b^2*c^6*x^2 + 420*a^4*b^3*c^6*x^3 + 504*a^3*b^4*c^6*x^4 - 1134*a^2*b^5*c^6*x^5 + 840*a*b^6*c^6*x^6 - 252*b^7*c^6*x^7)/(504*x^9)","A",1
47,1,105,89,0.0170921,"\int \frac{(a+b x) (a c-b c x)^6}{x^{11}} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^6)/x^11,x]","\frac{-252 a^7 c^6+1400 a^6 b c^6 x-2835 a^5 b^2 c^6 x^2+1800 a^4 b^3 c^6 x^3+2100 a^3 b^4 c^6 x^4-4536 a^2 b^5 c^6 x^5+3150 a b^6 c^6 x^6-840 b^7 c^6 x^7}{2520 x^{10}}","-\frac{13 b^3 c^6 (a-b x)^7}{2520 a^3 x^7}-\frac{13 b^2 c^6 (a-b x)^7}{360 a^2 x^8}-\frac{c^6 (a-b x)^7}{10 x^{10}}-\frac{13 b c^6 (a-b x)^7}{90 a x^9}",1,"(-252*a^7*c^6 + 1400*a^6*b*c^6*x - 2835*a^5*b^2*c^6*x^2 + 1800*a^4*b^3*c^6*x^3 + 2100*a^3*b^4*c^6*x^4 - 4536*a^2*b^5*c^6*x^5 + 3150*a*b^6*c^6*x^6 - 840*b^7*c^6*x^7)/(2520*x^10)","A",1
48,1,105,114,0.0172495,"\int \frac{(a+b x) (a c-b c x)^6}{x^{12}} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^6)/x^12,x]","\frac{-56 a^7 c^6+308 a^6 b c^6 x-616 a^5 b^2 c^6 x^2+385 a^4 b^3 c^6 x^3+440 a^3 b^4 c^6 x^4-924 a^2 b^5 c^6 x^5+616 a b^6 c^6 x^6-154 b^7 c^6 x^7}{616 x^{11}}","-\frac{a^7 c^6}{11 x^{11}}+\frac{a^6 b c^6}{2 x^{10}}-\frac{a^5 b^2 c^6}{x^9}+\frac{5 a^4 b^3 c^6}{8 x^8}+\frac{5 a^3 b^4 c^6}{7 x^7}-\frac{3 a^2 b^5 c^6}{2 x^6}+\frac{a b^6 c^6}{x^5}-\frac{b^7 c^6}{4 x^4}",1,"(-56*a^7*c^6 + 308*a^6*b*c^6*x - 616*a^5*b^2*c^6*x^2 + 385*a^4*b^3*c^6*x^3 + 440*a^3*b^4*c^6*x^4 - 924*a^2*b^5*c^6*x^5 + 616*a*b^6*c^6*x^6 - 154*b^7*c^6*x^7)/(616*x^11)","A",1
49,1,105,119,0.0168964,"\int \frac{(a+b x) (a c-b c x)^6}{x^{13}} \, dx","IntegrateAlgebraic[((a + b*x)*(a*c - b*c*x)^6)/x^13,x]","\frac{-2310 a^7 c^6+12600 a^6 b c^6 x-24948 a^5 b^2 c^6 x^2+15400 a^4 b^3 c^6 x^3+17325 a^3 b^4 c^6 x^4-35640 a^2 b^5 c^6 x^5+23100 a b^6 c^6 x^6-5544 b^7 c^6 x^7}{27720 x^{12}}","-\frac{a^7 c^6}{12 x^{12}}+\frac{5 a^6 b c^6}{11 x^{11}}-\frac{9 a^5 b^2 c^6}{10 x^{10}}+\frac{5 a^4 b^3 c^6}{9 x^9}+\frac{5 a^3 b^4 c^6}{8 x^8}-\frac{9 a^2 b^5 c^6}{7 x^7}+\frac{5 a b^6 c^6}{6 x^6}-\frac{b^7 c^6}{5 x^5}",1,"(-2310*a^7*c^6 + 12600*a^6*b*c^6*x - 24948*a^5*b^2*c^6*x^2 + 15400*a^4*b^3*c^6*x^3 + 17325*a^3*b^4*c^6*x^4 - 35640*a^2*b^5*c^6*x^5 + 23100*a*b^6*c^6*x^6 - 5544*b^7*c^6*x^7)/(27720*x^12)","A",1
50,1,109,106,0.0874534,"\int \frac{(e x)^{5/2}}{(a+b x) (a c-b c x)} \, dx","IntegrateAlgebraic[(e*x)^(5/2)/((a + b*x)*(a*c - b*c*x)),x]","-\frac{a^{3/2} e^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{b^{7/2} c}+\frac{a^{3/2} e^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{b^{7/2} c}-\frac{2 e^2 x \sqrt{e x}}{3 b^2 c}","-\frac{a^{3/2} e^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{b^{7/2} c}+\frac{a^{3/2} e^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{b^{7/2} c}-\frac{2 e (e x)^{3/2}}{3 b^2 c}",1,"(-2*e^2*x*Sqrt[e*x])/(3*b^2*c) - (a^(3/2)*e^(5/2)*ArcTan[(Sqrt[b]*Sqrt[e*x])/(Sqrt[a]*Sqrt[e])])/(b^(7/2)*c) + (a^(3/2)*e^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[e*x])/(Sqrt[a]*Sqrt[e])])/(b^(7/2)*c)","A",1
51,1,103,103,0.0666238,"\int \frac{(e x)^{3/2}}{(a+b x) (a c-b c x)} \, dx","IntegrateAlgebraic[(e*x)^(3/2)/((a + b*x)*(a*c - b*c*x)),x]","\frac{\sqrt{a} e^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{b^{5/2} c}+\frac{\sqrt{a} e^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{b^{5/2} c}-\frac{2 e \sqrt{e x}}{b^2 c}","\frac{\sqrt{a} e^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{b^{5/2} c}+\frac{\sqrt{a} e^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{b^{5/2} c}-\frac{2 e \sqrt{e x}}{b^2 c}",1,"(-2*e*Sqrt[e*x])/(b^2*c) + (Sqrt[a]*e^(3/2)*ArcTan[(Sqrt[b]*Sqrt[e*x])/(Sqrt[a]*Sqrt[e])])/(b^(5/2)*c) + (Sqrt[a]*e^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[e*x])/(Sqrt[a]*Sqrt[e])])/(b^(5/2)*c)","A",1
52,1,88,88,0.0568315,"\int \frac{\sqrt{e x}}{(a+b x) (a c-b c x)} \, dx","IntegrateAlgebraic[Sqrt[e*x]/((a + b*x)*(a*c - b*c*x)),x]","\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{\sqrt{a} b^{3/2} c}-\frac{\sqrt{e} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{\sqrt{a} b^{3/2} c}","\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{\sqrt{a} b^{3/2} c}-\frac{\sqrt{e} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{\sqrt{a} b^{3/2} c}",1,"-((Sqrt[e]*ArcTan[(Sqrt[b]*Sqrt[e*x])/(Sqrt[a]*Sqrt[e])])/(Sqrt[a]*b^(3/2)*c)) + (Sqrt[e]*ArcTanh[(Sqrt[b]*Sqrt[e*x])/(Sqrt[a]*Sqrt[e])])/(Sqrt[a]*b^(3/2)*c)","A",1
53,1,87,87,0.0529934,"\int \frac{1}{\sqrt{e x} (a+b x) (a c-b c x)} \, dx","IntegrateAlgebraic[1/(Sqrt[e*x]*(a + b*x)*(a*c - b*c*x)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{a^{3/2} \sqrt{b} c \sqrt{e}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{a^{3/2} \sqrt{b} c \sqrt{e}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{a^{3/2} \sqrt{b} c \sqrt{e}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{a^{3/2} \sqrt{b} c \sqrt{e}}",1,"ArcTan[(Sqrt[b]*Sqrt[e*x])/(Sqrt[a]*Sqrt[e])]/(a^(3/2)*Sqrt[b]*c*Sqrt[e]) + ArcTanh[(Sqrt[b]*Sqrt[e*x])/(Sqrt[a]*Sqrt[e])]/(a^(3/2)*Sqrt[b]*c*Sqrt[e])","A",1
54,1,109,106,0.0858843,"\int \frac{1}{(e x)^{3/2} (a+b x) (a c-b c x)} \, dx","IntegrateAlgebraic[1/((e*x)^(3/2)*(a + b*x)*(a*c - b*c*x)),x]","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{a^{5/2} c e^{3/2}}+\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{a^{5/2} c e^{3/2}}-\frac{2 \sqrt{e x}}{a^2 c e^2 x}","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{a^{5/2} c e^{3/2}}+\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{a^{5/2} c e^{3/2}}-\frac{2}{a^2 c e \sqrt{e x}}",1,"(-2*Sqrt[e*x])/(a^2*c*e^2*x) - (Sqrt[b]*ArcTan[(Sqrt[b]*Sqrt[e*x])/(Sqrt[a]*Sqrt[e])])/(a^(5/2)*c*e^(3/2)) + (Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[e*x])/(Sqrt[a]*Sqrt[e])])/(a^(5/2)*c*e^(3/2))","A",1
55,1,110,107,0.0763452,"\int \frac{1}{(e x)^{5/2} (a+b x) (a c-b c x)} \, dx","IntegrateAlgebraic[1/((e*x)^(5/2)*(a + b*x)*(a*c - b*c*x)),x]","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{a^{7/2} c e^{5/2}}+\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{a^{7/2} c e^{5/2}}-\frac{2 \sqrt{e x}}{3 a^2 c e^3 x^2}","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{a^{7/2} c e^{5/2}}+\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)}{a^{7/2} c e^{5/2}}-\frac{2}{3 a^2 c e (e x)^{3/2}}",1,"(-2*Sqrt[e*x])/(3*a^2*c*e^3*x^2) + (b^(3/2)*ArcTan[(Sqrt[b]*Sqrt[e*x])/(Sqrt[a]*Sqrt[e])])/(a^(7/2)*c*e^(5/2)) + (b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[e*x])/(Sqrt[a]*Sqrt[e])])/(a^(7/2)*c*e^(5/2))","A",1
56,0,0,156,0.043572,"\int (e x)^m (2-2 a x)^3 (1+a x)^4 \, dx","IntegrateAlgebraic[(e*x)^m*(2 - 2*a*x)^3*(1 + a*x)^4,x]","\int (e x)^m (2-2 a x)^3 (1+a x)^4 \, dx","-\frac{8 a^7 (e x)^{m+8}}{e^8 (m+8)}-\frac{8 a^6 (e x)^{m+7}}{e^7 (m+7)}+\frac{24 a^5 (e x)^{m+6}}{e^6 (m+6)}+\frac{24 a^4 (e x)^{m+5}}{e^5 (m+5)}-\frac{24 a^3 (e x)^{m+4}}{e^4 (m+4)}-\frac{24 a^2 (e x)^{m+3}}{e^3 (m+3)}+\frac{8 a (e x)^{m+2}}{e^2 (m+2)}+\frac{8 (e x)^{m+1}}{e (m+1)}",1,"Could not integrate","F",-1
57,0,0,116,0.0337072,"\int (e x)^m (2-2 a x)^2 (1+a x)^3 \, dx","IntegrateAlgebraic[(e*x)^m*(2 - 2*a*x)^2*(1 + a*x)^3,x]","\int (e x)^m (2-2 a x)^2 (1+a x)^3 \, dx","\frac{4 a^5 (e x)^{m+6}}{e^6 (m+6)}+\frac{4 a^4 (e x)^{m+5}}{e^5 (m+5)}-\frac{8 a^3 (e x)^{m+4}}{e^4 (m+4)}-\frac{8 a^2 (e x)^{m+3}}{e^3 (m+3)}+\frac{4 a (e x)^{m+2}}{e^2 (m+2)}+\frac{4 (e x)^{m+1}}{e (m+1)}",1,"Could not integrate","F",-1
58,0,0,76,0.0258763,"\int (e x)^m (2-2 a x) (1+a x)^2 \, dx","IntegrateAlgebraic[(e*x)^m*(2 - 2*a*x)*(1 + a*x)^2,x]","\int (e x)^m (2-2 a x) (1+a x)^2 \, dx","-\frac{2 a^3 (e x)^{m+4}}{e^4 (m+4)}-\frac{2 a^2 (e x)^{m+3}}{e^3 (m+3)}+\frac{2 a (e x)^{m+2}}{e^2 (m+2)}+\frac{2 (e x)^{m+1}}{e (m+1)}",1,"Could not integrate","F",-1
59,0,0,86,0.0438204,"\int \frac{(e x)^m}{(2-2 a x)^2 (1+a x)} \, dx","IntegrateAlgebraic[(e*x)^m/((2 - 2*a*x)^2*(1 + a*x)),x]","\int \frac{(e x)^m}{(2-2 a x)^2 (1+a x)} \, dx","\frac{a (e x)^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{4 e^2 (m+2)}+\frac{(e x)^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{4 e (m+1)}",1,"Could not integrate","F",-1
60,0,0,86,0.0414251,"\int \frac{(e x)^m}{(2-2 a x)^3 (1+a x)^2} \, dx","IntegrateAlgebraic[(e*x)^m/((2 - 2*a*x)^3*(1 + a*x)^2),x]","\int \frac{(e x)^m}{(2-2 a x)^3 (1+a x)^2} \, dx","\frac{a (e x)^{m+2} \, _2F_1\left(3,\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{8 e^2 (m+2)}+\frac{(e x)^{m+1} \, _2F_1\left(3,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{8 e (m+1)}",1,"Could not integrate","F",-1
61,0,0,86,0.0540038,"\int \frac{(e x)^m}{(2-2 a x)^4 (1+a x)^3} \, dx","IntegrateAlgebraic[(e*x)^m/((2 - 2*a*x)^4*(1 + a*x)^3),x]","\int \frac{(e x)^m}{(2-2 a x)^4 (1+a x)^3} \, dx","\frac{a (e x)^{m+2} \, _2F_1\left(4,\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{16 e^2 (m+2)}+\frac{(e x)^{m+1} \, _2F_1\left(4,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{16 e (m+1)}",1,"Could not integrate","F",-1
62,0,0,197,0.0719703,"\int (e x)^m (a+b x)^4 (a d-b d x)^3 \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x)^4*(a*d - b*d*x)^3,x]","\int (e x)^m (a+b x)^4 (a d-b d x)^3 \, dx","\frac{a^7 d^3 (e x)^{m+1}}{e (m+1)}+\frac{a^6 b d^3 (e x)^{m+2}}{e^2 (m+2)}-\frac{3 a^5 b^2 d^3 (e x)^{m+3}}{e^3 (m+3)}-\frac{3 a^4 b^3 d^3 (e x)^{m+4}}{e^4 (m+4)}+\frac{3 a^3 b^4 d^3 (e x)^{m+5}}{e^5 (m+5)}+\frac{3 a^2 b^5 d^3 (e x)^{m+6}}{e^6 (m+6)}-\frac{a b^6 d^3 (e x)^{m+7}}{e^7 (m+7)}-\frac{b^7 d^3 (e x)^{m+8}}{e^8 (m+8)}",1,"Could not integrate","F",-1
63,0,0,143,0.0454659,"\int (e x)^m (a+b x)^3 (a d-b d x)^2 \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x)^3*(a*d - b*d*x)^2,x]","\int (e x)^m (a+b x)^3 (a d-b d x)^2 \, dx","\frac{a^5 d^2 (e x)^{m+1}}{e (m+1)}+\frac{a^4 b d^2 (e x)^{m+2}}{e^2 (m+2)}-\frac{2 a^3 b^2 d^2 (e x)^{m+3}}{e^3 (m+3)}-\frac{2 a^2 b^3 d^2 (e x)^{m+4}}{e^4 (m+4)}+\frac{a b^4 d^2 (e x)^{m+5}}{e^5 (m+5)}+\frac{b^5 d^2 (e x)^{m+6}}{e^6 (m+6)}",1,"Could not integrate","F",-1
64,0,0,85,0.0319762,"\int (e x)^m (a+b x)^2 (a d-b d x) \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x)^2*(a*d - b*d*x),x]","\int (e x)^m (a+b x)^2 (a d-b d x) \, dx","\frac{a^3 d (e x)^{m+1}}{e (m+1)}+\frac{a^2 b d (e x)^{m+2}}{e^2 (m+2)}-\frac{a b^2 d (e x)^{m+3}}{e^3 (m+3)}-\frac{b^3 d (e x)^{m+4}}{e^4 (m+4)}",1,"Could not integrate","F",-1
65,0,0,98,0.0570885,"\int \frac{(e x)^m}{(a+b x) (a d-b d x)^2} \, dx","IntegrateAlgebraic[(e*x)^m/((a + b*x)*(a*d - b*d*x)^2),x]","\int \frac{(e x)^m}{(a+b x) (a d-b d x)^2} \, dx","\frac{b (e x)^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};\frac{b^2 x^2}{a^2}\right)}{a^4 d^2 e^2 (m+2)}+\frac{(e x)^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};\frac{b^2 x^2}{a^2}\right)}{a^3 d^2 e (m+1)}",1,"Could not integrate","F",-1
66,0,0,98,0.0589703,"\int \frac{(e x)^m}{(a+b x)^2 (a d-b d x)^3} \, dx","IntegrateAlgebraic[(e*x)^m/((a + b*x)^2*(a*d - b*d*x)^3),x]","\int \frac{(e x)^m}{(a+b x)^2 (a d-b d x)^3} \, dx","\frac{b (e x)^{m+2} \, _2F_1\left(3,\frac{m+2}{2};\frac{m+4}{2};\frac{b^2 x^2}{a^2}\right)}{a^6 d^3 e^2 (m+2)}+\frac{(e x)^{m+1} \, _2F_1\left(3,\frac{m+1}{2};\frac{m+3}{2};\frac{b^2 x^2}{a^2}\right)}{a^5 d^3 e (m+1)}",1,"Could not integrate","F",-1
67,0,0,98,0.2102675,"\int \frac{(e x)^m}{(a+b x)^3 (a d-b d x)^4} \, dx","IntegrateAlgebraic[(e*x)^m/((a + b*x)^3*(a*d - b*d*x)^4),x]","\int \frac{(e x)^m}{(a+b x)^3 (a d-b d x)^4} \, dx","\frac{b (e x)^{m+2} \, _2F_1\left(4,\frac{m+2}{2};\frac{m+4}{2};\frac{b^2 x^2}{a^2}\right)}{a^8 d^4 e^2 (m+2)}+\frac{(e x)^{m+1} \, _2F_1\left(4,\frac{m+1}{2};\frac{m+3}{2};\frac{b^2 x^2}{a^2}\right)}{a^7 d^4 e (m+1)}",1,"Could not integrate","F",-1
68,0,0,145,0.0403132,"\int (e x)^m (a+b x) (a c-b c x)^4 \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x)*(a*c - b*c*x)^4,x]","\int (e x)^m (a+b x) (a c-b c x)^4 \, dx","\frac{a^5 c^4 (e x)^{m+1}}{e (m+1)}-\frac{3 a^4 b c^4 (e x)^{m+2}}{e^2 (m+2)}+\frac{2 a^3 b^2 c^4 (e x)^{m+3}}{e^3 (m+3)}+\frac{2 a^2 b^3 c^4 (e x)^{m+4}}{e^4 (m+4)}-\frac{3 a b^4 c^4 (e x)^{m+5}}{e^5 (m+5)}+\frac{b^5 c^4 (e x)^{m+6}}{e^6 (m+6)}",1,"Could not integrate","F",-1
69,0,0,94,0.0344115,"\int (e x)^m (a+b x) (a c-b c x)^3 \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x)*(a*c - b*c*x)^3,x]","\int (e x)^m (a+b x) (a c-b c x)^3 \, dx","\frac{a^4 c^3 (e x)^{m+1}}{e (m+1)}-\frac{2 a^3 b c^3 (e x)^{m+2}}{e^2 (m+2)}+\frac{2 a b^3 c^3 (e x)^{m+4}}{e^4 (m+4)}-\frac{b^4 c^3 (e x)^{m+5}}{e^5 (m+5)}",1,"Could not integrate","F",-1
70,0,0,93,0.0314111,"\int (e x)^m (a+b x) (a c-b c x)^2 \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x)*(a*c - b*c*x)^2,x]","\int (e x)^m (a+b x) (a c-b c x)^2 \, dx","\frac{a^3 c^2 (e x)^{m+1}}{e (m+1)}-\frac{a^2 b c^2 (e x)^{m+2}}{e^2 (m+2)}-\frac{a b^2 c^2 (e x)^{m+3}}{e^3 (m+3)}+\frac{b^3 c^2 (e x)^{m+4}}{e^4 (m+4)}",1,"Could not integrate","F",-1
71,0,0,42,0.0245686,"\int (e x)^m (a+b x) (a c-b c x) \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x)*(a*c - b*c*x),x]","\int (e x)^m (a+b x) (a c-b c x) \, dx","\frac{a^2 c (e x)^{m+1}}{e (m+1)}-\frac{b^2 c (e x)^{m+3}}{e^3 (m+3)}",1,"Could not integrate","F",-1
72,0,0,55,0.0445116,"\int \frac{(e x)^m (a+b x)}{a c-b c x} \, dx","IntegrateAlgebraic[((e*x)^m*(a + b*x))/(a*c - b*c*x),x]","\int \frac{(e x)^m (a+b x)}{a c-b c x} \, dx","\frac{2 (e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{b x}{a}\right)}{c e (m+1)}-\frac{(e x)^{m+1}}{c e (m+1)}",1,"Could not integrate","F",-1
73,0,0,66,0.0352928,"\int \frac{(e x)^m (a+b x)}{(a c-b c x)^2} \, dx","IntegrateAlgebraic[((e*x)^m*(a + b*x))/(a*c - b*c*x)^2,x]","\int \frac{(e x)^m (a+b x)}{(a c-b c x)^2} \, dx","\frac{2 (e x)^{m+1}}{c^2 e (a-b x)}-\frac{(2 m+1) (e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{b x}{a}\right)}{a c^2 e (m+1)}",1,"Could not integrate","F",-1
74,0,0,107,0.0558371,"\int \frac{(e x)^m (a c-b c x)^3}{a+b x} \, dx","IntegrateAlgebraic[((e*x)^m*(a*c - b*c*x)^3)/(a + b*x),x]","\int \frac{(e x)^m (a c-b c x)^3}{a+b x} \, dx","\frac{8 a^2 c^3 (e x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{e (m+1)}-\frac{7 a^2 c^3 (e x)^{m+1}}{e (m+1)}+\frac{4 a b c^3 (e x)^{m+2}}{e^2 (m+2)}-\frac{b^2 c^3 (e x)^{m+3}}{e^3 (m+3)}",1,"Could not integrate","F",-1
75,0,0,78,0.0517198,"\int \frac{(e x)^m (a c-b c x)^2}{a+b x} \, dx","IntegrateAlgebraic[((e*x)^m*(a*c - b*c*x)^2)/(a + b*x),x]","\int \frac{(e x)^m (a c-b c x)^2}{a+b x} \, dx","\frac{4 a c^2 (e x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{e (m+1)}-\frac{3 a c^2 (e x)^{m+1}}{e (m+1)}+\frac{b c^2 (e x)^{m+2}}{e^2 (m+2)}",1,"Could not integrate","F",-1
76,0,0,52,0.0415781,"\int \frac{(e x)^m (a c-b c x)}{a+b x} \, dx","IntegrateAlgebraic[((e*x)^m*(a*c - b*c*x))/(a + b*x),x]","\int \frac{(e x)^m (a c-b c x)}{a+b x} \, dx","\frac{2 c (e x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{e (m+1)}-\frac{c (e x)^{m+1}}{e (m+1)}",1,"Could not integrate","F",-1
77,0,0,48,0.0663472,"\int \frac{(e x)^m}{(a+b x) (a c-b c x)} \, dx","IntegrateAlgebraic[(e*x)^m/((a + b*x)*(a*c - b*c*x)),x]","\int \frac{(e x)^m}{(a+b x) (a c-b c x)} \, dx","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};\frac{b^2 x^2}{a^2}\right)}{a^2 c e (m+1)}",1,"Could not integrate","F",-1
78,0,0,98,0.0556169,"\int \frac{(e x)^m}{(a+b x) (a c-b c x)^2} \, dx","IntegrateAlgebraic[(e*x)^m/((a + b*x)*(a*c - b*c*x)^2),x]","\int \frac{(e x)^m}{(a+b x) (a c-b c x)^2} \, dx","\frac{b (e x)^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};\frac{b^2 x^2}{a^2}\right)}{a^4 c^2 e^2 (m+2)}+\frac{(e x)^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};\frac{b^2 x^2}{a^2}\right)}{a^3 c^2 e (m+1)}",1,"Could not integrate","F",-1
79,0,0,151,0.0594942,"\int \frac{(e x)^m}{(a+b x) (a c-b c x)^3} \, dx","IntegrateAlgebraic[(e*x)^m/((a + b*x)*(a*c - b*c*x)^3),x]","\int \frac{(e x)^m}{(a+b x) (a c-b c x)^3} \, dx","\frac{\left(2 m^2-4 m+1\right) (e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{b x}{a}\right)}{8 a^4 c^3 e (m+1)}+\frac{(e x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{8 a^4 c^3 e (m+1)}+\frac{(2-m) (e x)^{m+1}}{4 a^3 c^3 e (a-b x)}+\frac{(e x)^{m+1}}{4 a^2 c^3 e (a-b x)^2}",1,"Could not integrate","F",-1
80,1,29,33,0.0156743,"\int x^4 (a+b x) (A+B x) \, dx","IntegrateAlgebraic[x^4*(a + b*x)*(A + B*x),x]","\frac{1}{210} x^5 \left(42 a A+35 a B x+35 A b x+30 b B x^2\right)","\frac{1}{6} x^6 (a B+A b)+\frac{1}{5} a A x^5+\frac{1}{7} b B x^7",1,"(x^5*(42*a*A + 35*A*b*x + 35*a*B*x + 30*b*B*x^2))/210","A",1
81,1,29,33,0.0148262,"\int x^3 (a+b x) (A+B x) \, dx","IntegrateAlgebraic[x^3*(a + b*x)*(A + B*x),x]","\frac{1}{60} x^4 \left(15 a A+12 a B x+12 A b x+10 b B x^2\right)","\frac{1}{5} x^5 (a B+A b)+\frac{1}{4} a A x^4+\frac{1}{6} b B x^6",1,"(x^4*(15*a*A + 12*A*b*x + 12*a*B*x + 10*b*B*x^2))/60","A",1
82,1,29,33,0.0145497,"\int x^2 (a+b x) (A+B x) \, dx","IntegrateAlgebraic[x^2*(a + b*x)*(A + B*x),x]","\frac{1}{60} x^3 \left(20 a A+15 a B x+15 A b x+12 b B x^2\right)","\frac{1}{4} x^4 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{5} b B x^5",1,"(x^3*(20*a*A + 15*A*b*x + 15*a*B*x + 12*b*B*x^2))/60","A",1
83,1,29,33,0.0136414,"\int x (a+b x) (A+B x) \, dx","IntegrateAlgebraic[x*(a + b*x)*(A + B*x),x]","\frac{1}{12} x^2 \left(6 a A+4 a B x+4 A b x+3 b B x^2\right)","\frac{1}{3} x^3 (a B+A b)+\frac{1}{2} a A x^2+\frac{1}{4} b B x^4",1,"(x^2*(6*a*A + 4*A*b*x + 4*a*B*x + 3*b*B*x^2))/12","A",1
84,1,27,28,0.0128752,"\int (a+b x) (A+B x) \, dx","IntegrateAlgebraic[(a + b*x)*(A + B*x),x]","\frac{1}{6} x \left(6 a A+3 a B x+3 A b x+2 b B x^2\right)","\frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} b B x^3",1,"(x*(6*a*A + 3*A*b*x + 3*a*B*x + 2*b*B*x^2))/6","A",1
85,1,24,24,0.0136272,"\int \frac{(a+b x) (A+B x)}{x} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/x,x]","\frac{1}{2} x (2 a B+2 A b+b B x)+a A \log (x)","x (a B+A b)+a A \log (x)+\frac{1}{2} b B x^2",1,"(x*(2*A*b + 2*a*B + b*B*x))/2 + a*A*Log[x]","A",1
86,1,26,22,0.017165,"\int \frac{(a+b x) (A+B x)}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/x^2,x]","\frac{b B x^2-a A}{x}+\log (x) (a B+A b)","\log (x) (a B+A b)-\frac{a A}{x}+b B x",1,"(-(a*A) + b*B*x^2)/x + (A*b + a*B)*Log[x]","A",1
87,1,28,27,0.0216179,"\int \frac{(a+b x) (A+B x)}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/x^3,x]","\frac{-a A-2 a B x-2 A b x}{2 x^2}+b B \log (x)","-\frac{a B+A b}{x}-\frac{a A}{2 x^2}+b B \log (x)",1,"(-(a*A) - 2*A*b*x - 2*a*B*x)/(2*x^2) + b*B*Log[x]","A",1
88,1,29,31,0.0158379,"\int \frac{(a+b x) (A+B x)}{x^4} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/x^4,x]","\frac{-2 a A-3 a B x-3 A b x-6 b B x^2}{6 x^3}","-\frac{a B+A b}{2 x^2}-\frac{a A}{3 x^3}-\frac{b B}{x}",1,"(-2*a*A - 3*A*b*x - 3*a*B*x - 6*b*B*x^2)/(6*x^3)","A",1
89,1,29,33,0.0141565,"\int \frac{(a+b x) (A+B x)}{x^5} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/x^5,x]","\frac{-3 a A-4 a B x-4 A b x-6 b B x^2}{12 x^4}","-\frac{a B+A b}{3 x^3}-\frac{a A}{4 x^4}-\frac{b B}{2 x^2}",1,"(-3*a*A - 4*A*b*x - 4*a*B*x - 6*b*B*x^2)/(12*x^4)","A",1
90,1,29,33,0.0164287,"\int \frac{(a+b x) (A+B x)}{x^6} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/x^6,x]","\frac{-12 a A-15 a B x-15 A b x-20 b B x^2}{60 x^5}","-\frac{a B+A b}{4 x^4}-\frac{a A}{5 x^5}-\frac{b B}{3 x^3}",1,"(-12*a*A - 15*A*b*x - 15*a*B*x - 20*b*B*x^2)/(60*x^5)","A",1
91,1,57,55,0.0208711,"\int x^4 (a+b x)^2 (A+B x) \, dx","IntegrateAlgebraic[x^4*(a + b*x)^2*(A + B*x),x]","\frac{1}{840} \left(168 a^2 A x^5+140 a^2 B x^6+280 a A b x^6+240 a b B x^7+120 A b^2 x^7+105 b^2 B x^8\right)","\frac{1}{5} a^2 A x^5+\frac{1}{7} b x^7 (2 a B+A b)+\frac{1}{6} a x^6 (a B+2 A b)+\frac{1}{8} b^2 B x^8",1,"(168*a^2*A*x^5 + 280*a*A*b*x^6 + 140*a^2*B*x^6 + 120*A*b^2*x^7 + 240*a*b*B*x^7 + 105*b^2*B*x^8)/840","A",1
92,1,57,55,0.0191184,"\int x^3 (a+b x)^2 (A+B x) \, dx","IntegrateAlgebraic[x^3*(a + b*x)^2*(A + B*x),x]","\frac{1}{420} \left(105 a^2 A x^4+84 a^2 B x^5+168 a A b x^5+140 a b B x^6+70 A b^2 x^6+60 b^2 B x^7\right)","\frac{1}{4} a^2 A x^4+\frac{1}{6} b x^6 (2 a B+A b)+\frac{1}{5} a x^5 (a B+2 A b)+\frac{1}{7} b^2 B x^7",1,"(105*a^2*A*x^4 + 168*a*A*b*x^5 + 84*a^2*B*x^5 + 70*A*b^2*x^6 + 140*a*b*B*x^6 + 60*b^2*B*x^7)/420","A",1
93,1,53,55,0.024591,"\int x^2 (a+b x)^2 (A+B x) \, dx","IntegrateAlgebraic[x^2*(a + b*x)^2*(A + B*x),x]","\frac{1}{60} x^3 \left(20 a^2 A+15 a^2 B x+30 a A b x+24 a b B x^2+12 A b^2 x^2+10 b^2 B x^3\right)","\frac{1}{3} a^2 A x^3+\frac{1}{5} b x^5 (2 a B+A b)+\frac{1}{4} a x^4 (a B+2 A b)+\frac{1}{6} b^2 B x^6",1,"(x^3*(20*a^2*A + 30*a*A*b*x + 15*a^2*B*x + 12*A*b^2*x^2 + 24*a*b*B*x^2 + 10*b^2*B*x^3))/60","A",1
94,1,53,55,0.0222251,"\int x (a+b x)^2 (A+B x) \, dx","IntegrateAlgebraic[x*(a + b*x)^2*(A + B*x),x]","\frac{1}{60} x^2 \left(30 a^2 A+20 a^2 B x+40 a A b x+30 a b B x^2+15 A b^2 x^2+12 b^2 B x^3\right)","\frac{1}{2} a^2 A x^2+\frac{1}{4} b x^4 (2 a B+A b)+\frac{1}{3} a x^3 (a B+2 A b)+\frac{1}{5} b^2 B x^5",1,"(x^2*(30*a^2*A + 40*a*A*b*x + 20*a^2*B*x + 15*A*b^2*x^2 + 30*a*b*B*x^2 + 12*b^2*B*x^3))/60","A",1
95,1,51,38,0.0214144,"\int (a+b x)^2 (A+B x) \, dx","IntegrateAlgebraic[(a + b*x)^2*(A + B*x),x]","\frac{1}{12} x \left(12 a^2 A+6 a^2 B x+12 a A b x+8 a b B x^2+4 A b^2 x^2+3 b^2 B x^3\right)","\frac{(a+b x)^3 (A b-a B)}{3 b^2}+\frac{B (a+b x)^4}{4 b^2}",1,"(x*(12*a^2*A + 12*a*A*b*x + 6*a^2*B*x + 4*A*b^2*x^2 + 8*a*b*B*x^2 + 3*b^2*B*x^3))/12","A",1
96,1,47,40,0.0271337,"\int \frac{(a+b x)^2 (A+B x)}{x} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/x,x]","\frac{1}{6} x \left(6 a^2 B+12 a A b+6 a b B x+3 A b^2 x+2 b^2 B x^2\right)+a^2 A \log (x)","a^2 A \log (x)+2 a A b x+\frac{B (a+b x)^3}{3 b}+\frac{1}{2} A b^2 x^2",1,"(x*(12*a*A*b + 6*a^2*B + 3*A*b^2*x + 6*a*b*B*x + 2*b^2*B*x^2))/6 + a^2*A*Log[x]","A",1
97,1,54,44,0.036966,"\int \frac{(a+b x)^2 (A+B x)}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/x^2,x]","\frac{-2 a^2 A+4 a b B x^2+2 A b^2 x^2+b^2 B x^3}{2 x}+\log (x) \left(a^2 B+2 a A b\right)","-\frac{a^2 A}{x}+b x (2 a B+A b)+a \log (x) (a B+2 A b)+\frac{1}{2} b^2 B x^2",1,"(-2*a^2*A + 2*A*b^2*x^2 + 4*a*b*B*x^2 + b^2*B*x^3)/(2*x) + (2*a*A*b + a^2*B)*Log[x]","A",1
98,1,51,44,0.0384852,"\int \frac{(a+b x)^2 (A+B x)}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/x^3,x]","\frac{-a^2 A-2 a^2 B x-4 a A b x+2 b^2 B x^3}{2 x^2}+\log (x) \left(2 a b B+A b^2\right)","-\frac{a^2 A}{2 x^2}-\frac{a (a B+2 A b)}{x}+b \log (x) (2 a B+A b)+b^2 B x",1,"(-(a^2*A) - 4*a*A*b*x - 2*a^2*B*x + 2*b^2*B*x^3)/(2*x^2) + (A*b^2 + 2*a*b*B)*Log[x]","A",1
99,1,52,49,0.0423599,"\int \frac{(a+b x)^2 (A+B x)}{x^4} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/x^4,x]","\frac{-2 a^2 A-3 a^2 B x-6 a A b x-12 a b B x^2-6 A b^2 x^2}{6 x^3}+b^2 B \log (x)","-\frac{a^2 A}{3 x^3}-\frac{a (a B+2 A b)}{2 x^2}-\frac{b (2 a B+A b)}{x}+b^2 B \log (x)",1,"(-2*a^2*A - 6*a*A*b*x - 3*a^2*B*x - 6*A*b^2*x^2 - 12*a*b*B*x^2)/(6*x^3) + b^2*B*Log[x]","A",1
100,1,53,44,0.0230092,"\int \frac{(a+b x)^2 (A+B x)}{x^5} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/x^5,x]","\frac{-3 a^2 A-4 a^2 B x-8 a A b x-12 a b B x^2-6 A b^2 x^2-12 b^2 B x^3}{12 x^4}","\frac{(a+b x)^3 (A b-4 a B)}{12 a^2 x^3}-\frac{A (a+b x)^3}{4 a x^4}",1,"(-3*a^2*A - 8*a*A*b*x - 4*a^2*B*x - 6*A*b^2*x^2 - 12*a*b*B*x^2 - 12*b^2*B*x^3)/(12*x^4)","A",1
101,1,53,55,0.023084,"\int \frac{(a+b x)^2 (A+B x)}{x^6} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/x^6,x]","\frac{-12 a^2 A-15 a^2 B x-30 a A b x-40 a b B x^2-20 A b^2 x^2-30 b^2 B x^3}{60 x^5}","-\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{4 x^4}-\frac{b (2 a B+A b)}{3 x^3}-\frac{b^2 B}{2 x^2}",1,"(-12*a^2*A - 30*a*A*b*x - 15*a^2*B*x - 20*A*b^2*x^2 - 40*a*b*B*x^2 - 30*b^2*B*x^3)/(60*x^5)","A",1
102,1,53,55,0.0238596,"\int \frac{(a+b x)^2 (A+B x)}{x^7} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/x^7,x]","\frac{-10 a^2 A-12 a^2 B x-24 a A b x-30 a b B x^2-15 A b^2 x^2-20 b^2 B x^3}{60 x^6}","-\frac{a^2 A}{6 x^6}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{4 x^4}-\frac{b^2 B}{3 x^3}",1,"(-10*a^2*A - 24*a*A*b*x - 12*a^2*B*x - 15*A*b^2*x^2 - 30*a*b*B*x^2 - 20*b^2*B*x^3)/(60*x^6)","A",1
103,1,53,55,0.0240673,"\int \frac{(a+b x)^2 (A+B x)}{x^8} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/x^8,x]","\frac{-60 a^2 A-70 a^2 B x-140 a A b x-168 a b B x^2-84 A b^2 x^2-105 b^2 B x^3}{420 x^7}","-\frac{a^2 A}{7 x^7}-\frac{a (a B+2 A b)}{6 x^6}-\frac{b (2 a B+A b)}{5 x^5}-\frac{b^2 B}{4 x^4}",1,"(-60*a^2*A - 140*a*A*b*x - 70*a^2*B*x - 84*A*b^2*x^2 - 168*a*b*B*x^2 - 105*b^2*B*x^3)/(420*x^7)","A",1
104,1,81,75,0.0289692,"\int x^4 (a+b x)^3 (A+B x) \, dx","IntegrateAlgebraic[x^4*(a + b*x)^3*(A + B*x),x]","\frac{504 a^3 A x^5+420 a^3 B x^6+1260 a^2 A b x^6+1080 a^2 b B x^7+1080 a A b^2 x^7+945 a b^2 B x^8+315 A b^3 x^8+280 b^3 B x^9}{2520}","\frac{1}{5} a^3 A x^5+\frac{1}{6} a^2 x^6 (a B+3 A b)+\frac{1}{8} b^2 x^8 (3 a B+A b)+\frac{3}{7} a b x^7 (a B+A b)+\frac{1}{9} b^3 B x^9",1,"(504*a^3*A*x^5 + 1260*a^2*A*b*x^6 + 420*a^3*B*x^6 + 1080*a*A*b^2*x^7 + 1080*a^2*b*B*x^7 + 315*A*b^3*x^8 + 945*a*b^2*B*x^8 + 280*b^3*B*x^9)/2520","A",1
105,1,81,75,0.0271316,"\int x^3 (a+b x)^3 (A+B x) \, dx","IntegrateAlgebraic[x^3*(a + b*x)^3*(A + B*x),x]","\frac{1}{280} \left(70 a^3 A x^4+56 a^3 B x^5+168 a^2 A b x^5+140 a^2 b B x^6+140 a A b^2 x^6+120 a b^2 B x^7+40 A b^3 x^7+35 b^3 B x^8\right)","\frac{1}{4} a^3 A x^4+\frac{1}{5} a^2 x^5 (a B+3 A b)+\frac{1}{7} b^2 x^7 (3 a B+A b)+\frac{1}{2} a b x^6 (a B+A b)+\frac{1}{8} b^3 B x^8",1,"(70*a^3*A*x^4 + 168*a^2*A*b*x^5 + 56*a^3*B*x^5 + 140*a*A*b^2*x^6 + 140*a^2*b*B*x^6 + 40*A*b^3*x^7 + 120*a*b^2*B*x^7 + 35*b^3*B*x^8)/280","A",1
106,1,81,75,0.0260625,"\int x^2 (a+b x)^3 (A+B x) \, dx","IntegrateAlgebraic[x^2*(a + b*x)^3*(A + B*x),x]","\frac{1}{420} \left(140 a^3 A x^3+105 a^3 B x^4+315 a^2 A b x^4+252 a^2 b B x^5+252 a A b^2 x^5+210 a b^2 B x^6+70 A b^3 x^6+60 b^3 B x^7\right)","\frac{1}{3} a^3 A x^3+\frac{1}{4} a^2 x^4 (a B+3 A b)+\frac{1}{6} b^2 x^6 (3 a B+A b)+\frac{3}{5} a b x^5 (a B+A b)+\frac{1}{7} b^3 B x^7",1,"(140*a^3*A*x^3 + 315*a^2*A*b*x^4 + 105*a^3*B*x^4 + 252*a*A*b^2*x^5 + 252*a^2*b*B*x^5 + 70*A*b^3*x^6 + 210*a*b^2*B*x^6 + 60*b^3*B*x^7)/420","A",1
107,1,77,61,0.0318453,"\int x (a+b x)^3 (A+B x) \, dx","IntegrateAlgebraic[x*(a + b*x)^3*(A + B*x),x]","\frac{1}{60} x^2 \left(30 a^3 A+20 a^3 B x+60 a^2 A b x+45 a^2 b B x^2+45 a A b^2 x^2+36 a b^2 B x^3+12 A b^3 x^3+10 b^3 B x^4\right)","\frac{(a+b x)^5 (A b-2 a B)}{5 b^3}-\frac{a (a+b x)^4 (A b-a B)}{4 b^3}+\frac{B (a+b x)^6}{6 b^3}",1,"(x^2*(30*a^3*A + 60*a^2*A*b*x + 20*a^3*B*x + 45*a*A*b^2*x^2 + 45*a^2*b*B*x^2 + 12*A*b^3*x^3 + 36*a*b^2*B*x^3 + 10*b^3*B*x^4))/60","A",1
108,1,79,38,0.0267238,"\int (a+b x)^3 (A+B x) \, dx","IntegrateAlgebraic[(a + b*x)^3*(A + B*x),x]","\frac{1}{20} \left(20 a^3 A x+10 a^3 B x^2+30 a^2 A b x^2+20 a^2 b B x^3+20 a A b^2 x^3+15 a b^2 B x^4+5 A b^3 x^4+4 b^3 B x^5\right)","\frac{(a+b x)^4 (A b-a B)}{4 b^2}+\frac{B (a+b x)^5}{5 b^2}",1,"(20*a^3*A*x + 30*a^2*A*b*x^2 + 10*a^3*B*x^2 + 20*a*A*b^2*x^3 + 20*a^2*b*B*x^3 + 5*A*b^3*x^4 + 15*a*b^2*B*x^4 + 4*b^3*B*x^5)/20","B",1
109,1,71,54,0.0432519,"\int \frac{(a+b x)^3 (A+B x)}{x} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/x,x]","a^3 A \log (x)+\frac{1}{12} x \left(12 a^3 B+36 a^2 A b+18 a^2 b B x+18 a A b^2 x+12 a b^2 B x^2+4 A b^3 x^2+3 b^3 B x^3\right)","a^3 A \log (x)+3 a^2 A b x+\frac{3}{2} a A b^2 x^2+\frac{B (a+b x)^4}{4 b}+\frac{1}{3} A b^3 x^3",1,"(x*(36*a^2*A*b + 12*a^3*B + 18*a*A*b^2*x + 18*a^2*b*B*x + 4*A*b^3*x^2 + 12*a*b^2*B*x^2 + 3*b^3*B*x^3))/12 + a^3*A*Log[x]","A",1
110,1,79,65,0.0448982,"\int \frac{(a+b x)^3 (A+B x)}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/x^2,x]","\frac{-6 a^3 A+18 a^2 b B x^2+18 a A b^2 x^2+9 a b^2 B x^3+3 A b^3 x^3+2 b^3 B x^4}{6 x}+\log (x) \left(a^3 B+3 a^2 A b\right)","-\frac{a^3 A}{x}+a^2 \log (x) (a B+3 A b)+\frac{1}{2} b^2 x^2 (3 a B+A b)+3 a b x (a B+A b)+\frac{1}{3} b^3 B x^3",1,"(-6*a^3*A + 18*a*A*b^2*x^2 + 18*a^2*b*B*x^2 + 3*A*b^3*x^3 + 9*a*b^2*B*x^3 + 2*b^3*B*x^4)/(6*x) + (3*a^2*A*b + a^3*B)*Log[x]","A",1
111,1,74,65,0.0410299,"\int \frac{(a+b x)^3 (A+B x)}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/x^3,x]","3 \log (x) \left(a^2 b B+a A b^2\right)+\frac{-a^3 A-2 a^3 B x-6 a^2 A b x+6 a b^2 B x^3+2 A b^3 x^3+b^3 B x^4}{2 x^2}","-\frac{a^3 A}{2 x^2}-\frac{a^2 (a B+3 A b)}{x}+b^2 x (3 a B+A b)+3 a b \log (x) (a B+A b)+\frac{1}{2} b^3 B x^2",1,"(-(a^3*A) - 6*a^2*A*b*x - 2*a^3*B*x + 2*A*b^3*x^3 + 6*a*b^2*B*x^3 + b^3*B*x^4)/(2*x^2) + 3*(a*A*b^2 + a^2*b*B)*Log[x]","A",1
112,1,75,64,0.0531313,"\int \frac{(a+b x)^3 (A+B x)}{x^4} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/x^4,x]","\frac{-2 a^3 A-3 a^3 B x-9 a^2 A b x-18 a^2 b B x^2-18 a A b^2 x^2+6 b^3 B x^4}{6 x^3}+\log (x) \left(3 a b^2 B+A b^3\right)","-\frac{a^3 A}{3 x^3}-\frac{a^2 (a B+3 A b)}{2 x^2}+b^2 \log (x) (3 a B+A b)-\frac{3 a b (a B+A b)}{x}+b^3 B x",1,"(-2*a^3*A - 9*a^2*A*b*x - 3*a^3*B*x - 18*a*A*b^2*x^2 - 18*a^2*b*B*x^2 + 6*b^3*B*x^4)/(6*x^3) + (A*b^3 + 3*a*b^2*B)*Log[x]","A",1
113,1,76,59,0.0474099,"\int \frac{(a+b x)^3 (A+B x)}{x^5} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/x^5,x]","\frac{-3 a^3 A-4 a^3 B x-12 a^2 A b x-18 a^2 b B x^2-18 a A b^2 x^2-36 a b^2 B x^3-12 A b^3 x^3}{12 x^4}+b^3 B \log (x)","-\frac{a^3 B}{3 x^3}-\frac{3 a^2 b B}{2 x^2}-\frac{A (a+b x)^4}{4 a x^4}-\frac{3 a b^2 B}{x}+b^3 B \log (x)",1,"(-3*a^3*A - 12*a^2*A*b*x - 4*a^3*B*x - 18*a*A*b^2*x^2 - 18*a^2*b*B*x^2 - 12*A*b^3*x^3 - 36*a*b^2*B*x^3)/(12*x^4) + b^3*B*Log[x]","A",1
114,1,77,44,0.0295781,"\int \frac{(a+b x)^3 (A+B x)}{x^6} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/x^6,x]","\frac{-4 a^3 A-5 a^3 B x-15 a^2 A b x-20 a^2 b B x^2-20 a A b^2 x^2-30 a b^2 B x^3-10 A b^3 x^3-20 b^3 B x^4}{20 x^5}","\frac{(a+b x)^4 (A b-5 a B)}{20 a^2 x^4}-\frac{A (a+b x)^4}{5 a x^5}",1,"(-4*a^3*A - 15*a^2*A*b*x - 5*a^3*B*x - 20*a*A*b^2*x^2 - 20*a^2*b*B*x^2 - 10*A*b^3*x^3 - 30*a*b^2*B*x^3 - 20*b^3*B*x^4)/(20*x^5)","A",1
115,1,77,75,0.0303218,"\int \frac{(a+b x)^3 (A+B x)}{x^7} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/x^7,x]","\frac{-10 a^3 A-12 a^3 B x-36 a^2 A b x-45 a^2 b B x^2-45 a A b^2 x^2-60 a b^2 B x^3-20 A b^3 x^3-30 b^3 B x^4}{60 x^6}","-\frac{a^3 A}{6 x^6}-\frac{a^2 (a B+3 A b)}{5 x^5}-\frac{b^2 (3 a B+A b)}{3 x^3}-\frac{3 a b (a B+A b)}{4 x^4}-\frac{b^3 B}{2 x^2}",1,"(-10*a^3*A - 36*a^2*A*b*x - 12*a^3*B*x - 45*a*A*b^2*x^2 - 45*a^2*b*B*x^2 - 20*A*b^3*x^3 - 60*a*b^2*B*x^3 - 30*b^3*B*x^4)/(60*x^6)","A",1
116,1,77,75,0.029976,"\int \frac{(a+b x)^3 (A+B x)}{x^8} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/x^8,x]","\frac{-60 a^3 A-70 a^3 B x-210 a^2 A b x-252 a^2 b B x^2-252 a A b^2 x^2-315 a b^2 B x^3-105 A b^3 x^3-140 b^3 B x^4}{420 x^7}","-\frac{a^3 A}{7 x^7}-\frac{a^2 (a B+3 A b)}{6 x^6}-\frac{b^2 (3 a B+A b)}{4 x^4}-\frac{3 a b (a B+A b)}{5 x^5}-\frac{b^3 B}{3 x^3}",1,"(-60*a^3*A - 210*a^2*A*b*x - 70*a^3*B*x - 252*a*A*b^2*x^2 - 252*a^2*b*B*x^2 - 105*A*b^3*x^3 - 315*a*b^2*B*x^3 - 140*b^3*B*x^4)/(420*x^7)","A",1
117,1,77,75,0.030542,"\int \frac{(a+b x)^3 (A+B x)}{x^9} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/x^9,x]","\frac{-35 a^3 A-40 a^3 B x-120 a^2 A b x-140 a^2 b B x^2-140 a A b^2 x^2-168 a b^2 B x^3-56 A b^3 x^3-70 b^3 B x^4}{280 x^8}","-\frac{a^3 A}{8 x^8}-\frac{a^2 (a B+3 A b)}{7 x^7}-\frac{b^2 (3 a B+A b)}{5 x^5}-\frac{a b (a B+A b)}{2 x^6}-\frac{b^3 B}{4 x^4}",1,"(-35*a^3*A - 120*a^2*A*b*x - 40*a^3*B*x - 140*a*A*b^2*x^2 - 140*a^2*b*B*x^2 - 56*A*b^3*x^3 - 168*a*b^2*B*x^3 - 70*b^3*B*x^4)/(280*x^8)","A",1
118,1,77,75,0.0308223,"\int \frac{(a+b x)^3 (A+B x)}{x^{10}} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/x^10,x]","\frac{-280 a^3 A-315 a^3 B x-945 a^2 A b x-1080 a^2 b B x^2-1080 a A b^2 x^2-1260 a b^2 B x^3-420 A b^3 x^3-504 b^3 B x^4}{2520 x^9}","-\frac{a^3 A}{9 x^9}-\frac{a^2 (a B+3 A b)}{8 x^8}-\frac{b^2 (3 a B+A b)}{6 x^6}-\frac{3 a b (a B+A b)}{7 x^7}-\frac{b^3 B}{5 x^5}",1,"(-280*a^3*A - 945*a^2*A*b*x - 315*a^3*B*x - 1080*a*A*b^2*x^2 - 1080*a^2*b*B*x^2 - 420*A*b^3*x^3 - 1260*a*b^2*B*x^3 - 504*b^3*B*x^4)/(2520*x^9)","A",1
119,1,129,117,0.0471683,"\int x^5 (a+b x)^5 (A+B x) \, dx","IntegrateAlgebraic[x^5*(a + b*x)^5*(A + B*x),x]","\frac{924 a^5 A x^6+792 a^5 B x^7+3960 a^4 A b x^7+3465 a^4 b B x^8+6930 a^3 A b^2 x^8+6160 a^3 b^2 B x^9+6160 a^2 A b^3 x^9+5544 a^2 b^3 B x^{10}+2772 a A b^4 x^{10}+2520 a b^4 B x^{11}+504 A b^5 x^{11}+462 b^5 B x^{12}}{5544}","\frac{1}{6} a^5 A x^6+\frac{1}{7} a^4 x^7 (a B+5 A b)+\frac{5}{8} a^3 b x^8 (a B+2 A b)+\frac{10}{9} a^2 b^2 x^9 (a B+A b)+\frac{1}{11} b^4 x^{11} (5 a B+A b)+\frac{1}{2} a b^3 x^{10} (2 a B+A b)+\frac{1}{12} b^5 B x^{12}",1,"(924*a^5*A*x^6 + 3960*a^4*A*b*x^7 + 792*a^5*B*x^7 + 6930*a^3*A*b^2*x^8 + 3465*a^4*b*B*x^8 + 6160*a^2*A*b^3*x^9 + 6160*a^3*b^2*B*x^9 + 2772*a*A*b^4*x^10 + 5544*a^2*b^3*B*x^10 + 504*A*b^5*x^11 + 2520*a*b^4*B*x^11 + 462*b^5*B*x^12)/5544","A",1
120,1,129,117,0.0409603,"\int x^4 (a+b x)^5 (A+B x) \, dx","IntegrateAlgebraic[x^4*(a + b*x)^5*(A + B*x),x]","\frac{2772 a^5 A x^5+2310 a^5 B x^6+11550 a^4 A b x^6+9900 a^4 b B x^7+19800 a^3 A b^2 x^7+17325 a^3 b^2 B x^8+17325 a^2 A b^3 x^8+15400 a^2 b^3 B x^9+7700 a A b^4 x^9+6930 a b^4 B x^{10}+1386 A b^5 x^{10}+1260 b^5 B x^{11}}{13860}","\frac{1}{5} a^5 A x^5+\frac{1}{6} a^4 x^6 (a B+5 A b)+\frac{5}{7} a^3 b x^7 (a B+2 A b)+\frac{5}{4} a^2 b^2 x^8 (a B+A b)+\frac{1}{10} b^4 x^{10} (5 a B+A b)+\frac{5}{9} a b^3 x^9 (2 a B+A b)+\frac{1}{11} b^5 B x^{11}",1,"(2772*a^5*A*x^5 + 11550*a^4*A*b*x^6 + 2310*a^5*B*x^6 + 19800*a^3*A*b^2*x^7 + 9900*a^4*b*B*x^7 + 17325*a^2*A*b^3*x^8 + 17325*a^3*b^2*B*x^8 + 7700*a*A*b^4*x^9 + 15400*a^2*b^3*B*x^9 + 1386*A*b^5*x^10 + 6930*a*b^4*B*x^10 + 1260*b^5*B*x^11)/13860","A",1
121,1,129,112,0.0409378,"\int x^3 (a+b x)^5 (A+B x) \, dx","IntegrateAlgebraic[x^3*(a + b*x)^5*(A + B*x),x]","\frac{630 a^5 A x^4+504 a^5 B x^5+2520 a^4 A b x^5+2100 a^4 b B x^6+4200 a^3 A b^2 x^6+3600 a^3 b^2 B x^7+3600 a^2 A b^3 x^7+3150 a^2 b^3 B x^8+1575 a A b^4 x^8+1400 a b^4 B x^9+280 A b^5 x^9+252 b^5 B x^{10}}{2520}","-\frac{a^3 (a+b x)^6 (A b-a B)}{6 b^5}+\frac{a^2 (a+b x)^7 (3 A b-4 a B)}{7 b^5}+\frac{(a+b x)^9 (A b-4 a B)}{9 b^5}-\frac{3 a (a+b x)^8 (A b-2 a B)}{8 b^5}+\frac{B (a+b x)^{10}}{10 b^5}",1,"(630*a^5*A*x^4 + 2520*a^4*A*b*x^5 + 504*a^5*B*x^5 + 4200*a^3*A*b^2*x^6 + 2100*a^4*b*B*x^6 + 3600*a^2*A*b^3*x^7 + 3600*a^3*b^2*B*x^7 + 1575*a*A*b^4*x^8 + 3150*a^2*b^3*B*x^8 + 280*A*b^5*x^9 + 1400*a*b^4*B*x^9 + 252*b^5*B*x^10)/2520","A",1
122,1,129,87,0.03997,"\int x^2 (a+b x)^5 (A+B x) \, dx","IntegrateAlgebraic[x^2*(a + b*x)^5*(A + B*x),x]","\frac{1}{504} \left(168 a^5 A x^3+126 a^5 B x^4+630 a^4 A b x^4+504 a^4 b B x^5+1008 a^3 A b^2 x^5+840 a^3 b^2 B x^6+840 a^2 A b^3 x^6+720 a^2 b^3 B x^7+360 a A b^4 x^7+315 a b^4 B x^8+63 A b^5 x^8+56 b^5 B x^9\right)","\frac{a^2 (a+b x)^6 (A b-a B)}{6 b^4}+\frac{(a+b x)^8 (A b-3 a B)}{8 b^4}-\frac{a (a+b x)^7 (2 A b-3 a B)}{7 b^4}+\frac{B (a+b x)^9}{9 b^4}",1,"(168*a^5*A*x^3 + 630*a^4*A*b*x^4 + 126*a^5*B*x^4 + 1008*a^3*A*b^2*x^5 + 504*a^4*b*B*x^5 + 840*a^2*A*b^3*x^6 + 840*a^3*b^2*B*x^6 + 360*a*A*b^4*x^7 + 720*a^2*b^3*B*x^7 + 63*A*b^5*x^8 + 315*a*b^4*B*x^8 + 56*b^5*B*x^9)/504","A",1
123,1,129,61,0.0396212,"\int x (a+b x)^5 (A+B x) \, dx","IntegrateAlgebraic[x*(a + b*x)^5*(A + B*x),x]","\frac{1}{168} \left(84 a^5 A x^2+56 a^5 B x^3+280 a^4 A b x^3+210 a^4 b B x^4+420 a^3 A b^2 x^4+336 a^3 b^2 B x^5+336 a^2 A b^3 x^5+280 a^2 b^3 B x^6+140 a A b^4 x^6+120 a b^4 B x^7+24 A b^5 x^7+21 b^5 B x^8\right)","\frac{(a+b x)^7 (A b-2 a B)}{7 b^3}-\frac{a (a+b x)^6 (A b-a B)}{6 b^3}+\frac{B (a+b x)^8}{8 b^3}",1,"(84*a^5*A*x^2 + 280*a^4*A*b*x^3 + 56*a^5*B*x^3 + 420*a^3*A*b^2*x^4 + 210*a^4*b*B*x^4 + 336*a^2*A*b^3*x^5 + 336*a^3*b^2*B*x^5 + 140*a*A*b^4*x^6 + 280*a^2*b^3*B*x^6 + 24*A*b^5*x^7 + 120*a*b^4*B*x^7 + 21*b^5*B*x^8)/168","B",1
124,1,127,38,0.0387282,"\int (a+b x)^5 (A+B x) \, dx","IntegrateAlgebraic[(a + b*x)^5*(A + B*x),x]","\frac{1}{42} \left(42 a^5 A x+21 a^5 B x^2+105 a^4 A b x^2+70 a^4 b B x^3+140 a^3 A b^2 x^3+105 a^3 b^2 B x^4+105 a^2 A b^3 x^4+84 a^2 b^3 B x^5+42 a A b^4 x^5+35 a b^4 B x^6+7 A b^5 x^6+6 b^5 B x^7\right)","\frac{(a+b x)^6 (A b-a B)}{6 b^2}+\frac{B (a+b x)^7}{7 b^2}",1,"(42*a^5*A*x + 105*a^4*A*b*x^2 + 21*a^5*B*x^2 + 140*a^3*A*b^2*x^3 + 70*a^4*b*B*x^3 + 105*a^2*A*b^3*x^4 + 105*a^3*b^2*B*x^4 + 42*a*A*b^4*x^5 + 84*a^2*b^3*B*x^5 + 7*A*b^5*x^6 + 35*a*b^4*B*x^6 + 6*b^5*B*x^7)/42","B",1
125,1,124,80,0.0641738,"\int \frac{(a+b x)^5 (A+B x)}{x} \, dx","IntegrateAlgebraic[((a + b*x)^5*(A + B*x))/x,x]","a^5 A \log (x)+\frac{1}{60} \left(60 a^5 B x+300 a^4 A b x+150 a^4 b B x^2+300 a^3 A b^2 x^2+200 a^3 b^2 B x^3+200 a^2 A b^3 x^3+150 a^2 b^3 B x^4+75 a A b^4 x^4+60 a b^4 B x^5+12 A b^5 x^5+10 b^5 B x^6\right)","a^5 A \log (x)+5 a^4 A b x+5 a^3 A b^2 x^2+\frac{10}{3} a^2 A b^3 x^3+\frac{5}{4} a A b^4 x^4+\frac{B (a+b x)^6}{6 b}+\frac{1}{5} A b^5 x^5",1,"(300*a^4*A*b*x + 60*a^5*B*x + 300*a^3*A*b^2*x^2 + 150*a^4*b*B*x^2 + 200*a^2*A*b^3*x^3 + 200*a^3*b^2*B*x^3 + 75*a*A*b^4*x^4 + 150*a^2*b^3*B*x^4 + 12*A*b^5*x^5 + 60*a*b^4*B*x^5 + 10*b^5*B*x^6)/60 + a^5*A*Log[x]","A",1
126,1,127,105,0.0709844,"\int \frac{(a+b x)^5 (A+B x)}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)^5*(A + B*x))/x^2,x]","\log (x) \left(a^5 B+5 a^4 A b\right)+\frac{-60 a^5 A+300 a^4 b B x^2+600 a^3 A b^2 x^2+300 a^3 b^2 B x^3+300 a^2 A b^3 x^3+200 a^2 b^3 B x^4+100 a A b^4 x^4+75 a b^4 B x^5+15 A b^5 x^5+12 b^5 B x^6}{60 x}","-\frac{a^5 A}{x}+a^4 \log (x) (a B+5 A b)+5 a^3 b x (a B+2 A b)+5 a^2 b^2 x^2 (a B+A b)+\frac{1}{4} b^4 x^4 (5 a B+A b)+\frac{5}{3} a b^3 x^3 (2 a B+A b)+\frac{1}{5} b^5 B x^5",1,"(-60*a^5*A + 600*a^3*A*b^2*x^2 + 300*a^4*b*B*x^2 + 300*a^2*A*b^3*x^3 + 300*a^3*b^2*B*x^3 + 100*a*A*b^4*x^4 + 200*a^2*b^3*B*x^4 + 15*A*b^5*x^5 + 75*a*b^4*B*x^5 + 12*b^5*B*x^6)/(60*x) + (5*a^4*A*b + a^5*B)*Log[x]","A",1
127,1,124,108,0.0706952,"\int \frac{(a+b x)^5 (A+B x)}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)^5*(A + B*x))/x^3,x]","5 \log (x) \left(a^4 b B+2 a^3 A b^2\right)+\frac{-6 a^5 A-12 a^5 B x-60 a^4 A b x+120 a^3 b^2 B x^3+120 a^2 A b^3 x^3+60 a^2 b^3 B x^4+30 a A b^4 x^4+20 a b^4 B x^5+4 A b^5 x^5+3 b^5 B x^6}{12 x^2}","-\frac{a^5 A}{2 x^2}-\frac{a^4 (a B+5 A b)}{x}+5 a^3 b \log (x) (a B+2 A b)+10 a^2 b^2 x (a B+A b)+\frac{1}{3} b^4 x^3 (5 a B+A b)+\frac{5}{2} a b^3 x^2 (2 a B+A b)+\frac{1}{4} b^5 B x^4",1,"(-6*a^5*A - 60*a^4*A*b*x - 12*a^5*B*x + 120*a^2*A*b^3*x^3 + 120*a^3*b^2*B*x^3 + 30*a*A*b^4*x^4 + 60*a^2*b^3*B*x^4 + 4*A*b^5*x^5 + 20*a*b^4*B*x^5 + 3*b^5*B*x^6)/(12*x^2) + 5*(2*a^3*A*b^2 + a^4*b*B)*Log[x]","A",1
128,1,123,108,0.0544785,"\int \frac{(a+b x)^5 (A+B x)}{x^4} \, dx","IntegrateAlgebraic[((a + b*x)^5*(A + B*x))/x^4,x]","10 \log (x) \left(a^3 b^2 B+a^2 A b^3\right)+\frac{-2 a^5 A-3 a^5 B x-15 a^4 A b x-30 a^4 b B x^2-60 a^3 A b^2 x^2+60 a^2 b^3 B x^4+30 a A b^4 x^4+15 a b^4 B x^5+3 A b^5 x^5+2 b^5 B x^6}{6 x^3}","-\frac{a^5 A}{3 x^3}-\frac{a^4 (a B+5 A b)}{2 x^2}-\frac{5 a^3 b (a B+2 A b)}{x}+10 a^2 b^2 \log (x) (a B+A b)+\frac{1}{2} b^4 x^2 (5 a B+A b)+5 a b^3 x (2 a B+A b)+\frac{1}{3} b^5 B x^3",1,"(-2*a^5*A - 15*a^4*A*b*x - 3*a^5*B*x - 60*a^3*A*b^2*x^2 - 30*a^4*b*B*x^2 + 30*a*A*b^4*x^4 + 60*a^2*b^3*B*x^4 + 3*A*b^5*x^5 + 15*a*b^4*B*x^5 + 2*b^5*B*x^6)/(6*x^3) + 10*(a^2*A*b^3 + a^3*b^2*B)*Log[x]","A",1
129,1,124,107,0.0805791,"\int \frac{(a+b x)^5 (A+B x)}{x^5} \, dx","IntegrateAlgebraic[((a + b*x)^5*(A + B*x))/x^5,x]","5 \log (x) \left(2 a^2 b^3 B+a A b^4\right)+\frac{-3 a^5 A-4 a^5 B x-20 a^4 A b x-30 a^4 b B x^2-60 a^3 A b^2 x^2-120 a^3 b^2 B x^3-120 a^2 A b^3 x^3+60 a b^4 B x^5+12 A b^5 x^5+6 b^5 B x^6}{12 x^4}","-\frac{a^5 A}{4 x^4}-\frac{a^4 (a B+5 A b)}{3 x^3}-\frac{5 a^3 b (a B+2 A b)}{2 x^2}-\frac{10 a^2 b^2 (a B+A b)}{x}+b^4 x (5 a B+A b)+5 a b^3 \log (x) (2 a B+A b)+\frac{1}{2} b^5 B x^2",1,"(-3*a^5*A - 20*a^4*A*b*x - 4*a^5*B*x - 60*a^3*A*b^2*x^2 - 30*a^4*b*B*x^2 - 120*a^2*A*b^3*x^3 - 120*a^3*b^2*B*x^3 + 12*A*b^5*x^5 + 60*a*b^4*B*x^5 + 6*b^5*B*x^6)/(12*x^4) + 5*(a*A*b^4 + 2*a^2*b^3*B)*Log[x]","A",1
130,1,123,104,0.0866364,"\int \frac{(a+b x)^5 (A+B x)}{x^6} \, dx","IntegrateAlgebraic[((a + b*x)^5*(A + B*x))/x^6,x]","\frac{-12 a^5 A-15 a^5 B x-75 a^4 A b x-100 a^4 b B x^2-200 a^3 A b^2 x^2-300 a^3 b^2 B x^3-300 a^2 A b^3 x^3-600 a^2 b^3 B x^4-300 a A b^4 x^4+60 b^5 B x^6}{60 x^5}+\log (x) \left(5 a b^4 B+A b^5\right)","-\frac{a^5 A}{5 x^5}-\frac{a^4 (a B+5 A b)}{4 x^4}-\frac{5 a^3 b (a B+2 A b)}{3 x^3}-\frac{5 a^2 b^2 (a B+A b)}{x^2}+b^4 \log (x) (5 a B+A b)-\frac{5 a b^3 (2 a B+A b)}{x}+b^5 B x",1,"(-12*a^5*A - 75*a^4*A*b*x - 15*a^5*B*x - 200*a^3*A*b^2*x^2 - 100*a^4*b*B*x^2 - 300*a^2*A*b^3*x^3 - 300*a^3*b^2*B*x^3 - 300*a*A*b^4*x^4 - 600*a^2*b^3*B*x^4 + 60*b^5*B*x^6)/(60*x^5) + (A*b^5 + 5*a*b^4*B)*Log[x]","A",1
131,1,124,85,0.0740889,"\int \frac{(a+b x)^5 (A+B x)}{x^7} \, dx","IntegrateAlgebraic[((a + b*x)^5*(A + B*x))/x^7,x]","\frac{-10 a^5 A-12 a^5 B x-60 a^4 A b x-75 a^4 b B x^2-150 a^3 A b^2 x^2-200 a^3 b^2 B x^3-200 a^2 A b^3 x^3-300 a^2 b^3 B x^4-150 a A b^4 x^4-300 a b^4 B x^5-60 A b^5 x^5}{60 x^6}+b^5 B \log (x)","-\frac{a^5 B}{5 x^5}-\frac{5 a^4 b B}{4 x^4}-\frac{10 a^3 b^2 B}{3 x^3}-\frac{5 a^2 b^3 B}{x^2}-\frac{A (a+b x)^6}{6 a x^6}-\frac{5 a b^4 B}{x}+b^5 B \log (x)",1,"(-10*a^5*A - 60*a^4*A*b*x - 12*a^5*B*x - 150*a^3*A*b^2*x^2 - 75*a^4*b*B*x^2 - 200*a^2*A*b^3*x^3 - 200*a^3*b^2*B*x^3 - 150*a*A*b^4*x^4 - 300*a^2*b^3*B*x^4 - 60*A*b^5*x^5 - 300*a*b^4*B*x^5)/(60*x^6) + b^5*B*Log[x]","A",1
132,1,125,44,0.0430722,"\int \frac{(a+b x)^5 (A+B x)}{x^8} \, dx","IntegrateAlgebraic[((a + b*x)^5*(A + B*x))/x^8,x]","\frac{-6 a^5 A-7 a^5 B x-35 a^4 A b x-42 a^4 b B x^2-84 a^3 A b^2 x^2-105 a^3 b^2 B x^3-105 a^2 A b^3 x^3-140 a^2 b^3 B x^4-70 a A b^4 x^4-105 a b^4 B x^5-21 A b^5 x^5-42 b^5 B x^6}{42 x^7}","\frac{(a+b x)^6 (A b-7 a B)}{42 a^2 x^6}-\frac{A (a+b x)^6}{7 a x^7}",1,"(-6*a^5*A - 35*a^4*A*b*x - 7*a^5*B*x - 84*a^3*A*b^2*x^2 - 42*a^4*b*B*x^2 - 105*a^2*A*b^3*x^3 - 105*a^3*b^2*B*x^3 - 70*a*A*b^4*x^4 - 140*a^2*b^3*B*x^4 - 21*A*b^5*x^5 - 105*a*b^4*B*x^5 - 42*b^5*B*x^6)/(42*x^7)","B",1
133,1,125,70,0.0424915,"\int \frac{(a+b x)^5 (A+B x)}{x^9} \, dx","IntegrateAlgebraic[((a + b*x)^5*(A + B*x))/x^9,x]","\frac{-21 a^5 A-24 a^5 B x-120 a^4 A b x-140 a^4 b B x^2-280 a^3 A b^2 x^2-336 a^3 b^2 B x^3-336 a^2 A b^3 x^3-420 a^2 b^3 B x^4-210 a A b^4 x^4-280 a b^4 B x^5-56 A b^5 x^5-84 b^5 B x^6}{168 x^8}","-\frac{b (a+b x)^6 (A b-4 a B)}{168 a^3 x^6}+\frac{(a+b x)^6 (A b-4 a B)}{28 a^2 x^7}-\frac{A (a+b x)^6}{8 a x^8}",1,"(-21*a^5*A - 120*a^4*A*b*x - 24*a^5*B*x - 280*a^3*A*b^2*x^2 - 140*a^4*b*B*x^2 - 336*a^2*A*b^3*x^3 - 336*a^3*b^2*B*x^3 - 210*a*A*b^4*x^4 - 420*a^2*b^3*B*x^4 - 56*A*b^5*x^5 - 280*a*b^4*B*x^5 - 84*b^5*B*x^6)/(168*x^8)","A",1
134,1,125,115,0.0431853,"\int \frac{(a+b x)^5 (A+B x)}{x^{10}} \, dx","IntegrateAlgebraic[((a + b*x)^5*(A + B*x))/x^10,x]","\frac{-56 a^5 A-63 a^5 B x-315 a^4 A b x-360 a^4 b B x^2-720 a^3 A b^2 x^2-840 a^3 b^2 B x^3-840 a^2 A b^3 x^3-1008 a^2 b^3 B x^4-504 a A b^4 x^4-630 a b^4 B x^5-126 A b^5 x^5-168 b^5 B x^6}{504 x^9}","-\frac{a^5 A}{9 x^9}-\frac{a^4 (a B+5 A b)}{8 x^8}-\frac{5 a^3 b (a B+2 A b)}{7 x^7}-\frac{5 a^2 b^2 (a B+A b)}{3 x^6}-\frac{b^4 (5 a B+A b)}{4 x^4}-\frac{a b^3 (2 a B+A b)}{x^5}-\frac{b^5 B}{3 x^3}",1,"(-56*a^5*A - 315*a^4*A*b*x - 63*a^5*B*x - 720*a^3*A*b^2*x^2 - 360*a^4*b*B*x^2 - 840*a^2*A*b^3*x^3 - 840*a^3*b^2*B*x^3 - 504*a*A*b^4*x^4 - 1008*a^2*b^3*B*x^4 - 126*A*b^5*x^5 - 630*a*b^4*B*x^5 - 168*b^5*B*x^6)/(504*x^9)","A",1
135,1,125,117,0.0446836,"\int \frac{(a+b x)^5 (A+B x)}{x^{11}} \, dx","IntegrateAlgebraic[((a + b*x)^5*(A + B*x))/x^11,x]","\frac{-252 a^5 A-280 a^5 B x-1400 a^4 A b x-1575 a^4 b B x^2-3150 a^3 A b^2 x^2-3600 a^3 b^2 B x^3-3600 a^2 A b^3 x^3-4200 a^2 b^3 B x^4-2100 a A b^4 x^4-2520 a b^4 B x^5-504 A b^5 x^5-630 b^5 B x^6}{2520 x^{10}}","-\frac{a^5 A}{10 x^{10}}-\frac{a^4 (a B+5 A b)}{9 x^9}-\frac{5 a^3 b (a B+2 A b)}{8 x^8}-\frac{10 a^2 b^2 (a B+A b)}{7 x^7}-\frac{b^4 (5 a B+A b)}{5 x^5}-\frac{5 a b^3 (2 a B+A b)}{6 x^6}-\frac{b^5 B}{4 x^4}",1,"(-252*a^5*A - 1400*a^4*A*b*x - 280*a^5*B*x - 3150*a^3*A*b^2*x^2 - 1575*a^4*b*B*x^2 - 3600*a^2*A*b^3*x^3 - 3600*a^3*b^2*B*x^3 - 2100*a*A*b^4*x^4 - 4200*a^2*b^3*B*x^4 - 504*A*b^5*x^5 - 2520*a*b^4*B*x^5 - 630*b^5*B*x^6)/(2520*x^10)","A",1
136,1,125,117,0.0440164,"\int \frac{(a+b x)^5 (A+B x)}{x^{12}} \, dx","IntegrateAlgebraic[((a + b*x)^5*(A + B*x))/x^12,x]","\frac{-1260 a^5 A-1386 a^5 B x-6930 a^4 A b x-7700 a^4 b B x^2-15400 a^3 A b^2 x^2-17325 a^3 b^2 B x^3-17325 a^2 A b^3 x^3-19800 a^2 b^3 B x^4-9900 a A b^4 x^4-11550 a b^4 B x^5-2310 A b^5 x^5-2772 b^5 B x^6}{13860 x^{11}}","-\frac{a^5 A}{11 x^{11}}-\frac{a^4 (a B+5 A b)}{10 x^{10}}-\frac{5 a^3 b (a B+2 A b)}{9 x^9}-\frac{5 a^2 b^2 (a B+A b)}{4 x^8}-\frac{b^4 (5 a B+A b)}{6 x^6}-\frac{5 a b^3 (2 a B+A b)}{7 x^7}-\frac{b^5 B}{5 x^5}",1,"(-1260*a^5*A - 6930*a^4*A*b*x - 1386*a^5*B*x - 15400*a^3*A*b^2*x^2 - 7700*a^4*b*B*x^2 - 17325*a^2*A*b^3*x^3 - 17325*a^3*b^2*B*x^3 - 9900*a*A*b^4*x^4 - 19800*a^2*b^3*B*x^4 - 2310*A*b^5*x^5 - 11550*a*b^4*B*x^5 - 2772*b^5*B*x^6)/(13860*x^11)","A",1
137,1,249,229,0.1027068,"\int x^{10} (a+b x)^{10} (A+B x) \, dx","IntegrateAlgebraic[x^10*(a + b*x)^10*(A + B*x),x]","\frac{705432 a^{10} A x^{11}+646646 a^{10} B x^{12}+6466460 a^9 A b x^{12}+5969040 a^9 b B x^{13}+26860680 a^8 A b^2 x^{13}+24942060 a^8 b^2 B x^{14}+66512160 a^7 A b^3 x^{14}+62078016 a^7 b^3 B x^{15}+108636528 a^6 A b^4 x^{15}+101846745 a^6 b^4 B x^{16}+122216094 a^5 A b^5 x^{16}+115026912 a^5 b^5 B x^{17}+95855760 a^4 A b^6 x^{17}+90530440 a^4 b^6 B x^{18}+51731680 a^3 A b^7 x^{18}+49008960 a^3 b^7 B x^{19}+18378360 a^2 A b^8 x^{19}+17459442 a^2 b^8 B x^{20}+3879876 a A b^9 x^{20}+3695120 a b^9 B x^{21}+369512 A b^{10} x^{21}+352716 b^{10} B x^{22}}{7759752}","\frac{1}{11} a^{10} A x^{11}+\frac{1}{12} a^9 x^{12} (a B+10 A b)+\frac{5}{13} a^8 b x^{13} (2 a B+9 A b)+\frac{15}{14} a^7 b^2 x^{14} (3 a B+8 A b)+2 a^6 b^3 x^{15} (4 a B+7 A b)+\frac{21}{8} a^5 b^4 x^{16} (5 a B+6 A b)+\frac{42}{17} a^4 b^5 x^{17} (6 a B+5 A b)+\frac{5}{3} a^3 b^6 x^{18} (7 a B+4 A b)+\frac{15}{19} a^2 b^7 x^{19} (8 a B+3 A b)+\frac{1}{21} b^9 x^{21} (10 a B+A b)+\frac{1}{4} a b^8 x^{20} (9 a B+2 A b)+\frac{1}{22} b^{10} B x^{22}",1,"(705432*a^10*A*x^11 + 6466460*a^9*A*b*x^12 + 646646*a^10*B*x^12 + 26860680*a^8*A*b^2*x^13 + 5969040*a^9*b*B*x^13 + 66512160*a^7*A*b^3*x^14 + 24942060*a^8*b^2*B*x^14 + 108636528*a^6*A*b^4*x^15 + 62078016*a^7*b^3*B*x^15 + 122216094*a^5*A*b^5*x^16 + 101846745*a^6*b^4*B*x^16 + 95855760*a^4*A*b^6*x^17 + 115026912*a^5*b^5*B*x^17 + 51731680*a^3*A*b^7*x^18 + 90530440*a^4*b^6*B*x^18 + 18378360*a^2*A*b^8*x^19 + 49008960*a^3*b^7*B*x^19 + 3879876*a*A*b^9*x^20 + 17459442*a^2*b^8*B*x^20 + 369512*A*b^10*x^21 + 3695120*a*b^9*B*x^21 + 352716*b^10*B*x^22)/7759752","A",1
138,1,249,231,0.0813113,"\int x^9 (a+b x)^{10} (A+B x) \, dx","IntegrateAlgebraic[x^9*(a + b*x)^10*(A + B*x),x]","\frac{3879876 a^{10} A x^{10}+3527160 a^{10} B x^{11}+35271600 a^9 A b x^{11}+32332300 a^9 b B x^{12}+145495350 a^8 A b^2 x^{12}+134303400 a^8 b^2 B x^{13}+358142400 a^7 A b^3 x^{13}+332560800 a^7 b^3 B x^{14}+581981400 a^6 A b^4 x^{14}+543182640 a^6 b^4 B x^{15}+651819168 a^5 A b^5 x^{15}+611080470 a^5 b^5 B x^{16}+509233725 a^4 A b^6 x^{16}+479278800 a^4 b^6 B x^{17}+273873600 a^3 A b^7 x^{17}+258658400 a^3 b^7 B x^{18}+96996900 a^2 A b^8 x^{18}+91891800 a^2 b^8 B x^{19}+20420400 a A b^9 x^{19}+19399380 a b^9 B x^{20}+1939938 A b^{10} x^{20}+1847560 b^{10} B x^{21}}{38798760}","\frac{1}{10} a^{10} A x^{10}+\frac{1}{11} a^9 x^{11} (a B+10 A b)+\frac{5}{12} a^8 b x^{12} (2 a B+9 A b)+\frac{15}{13} a^7 b^2 x^{13} (3 a B+8 A b)+\frac{15}{7} a^6 b^3 x^{14} (4 a B+7 A b)+\frac{14}{5} a^5 b^4 x^{15} (5 a B+6 A b)+\frac{21}{8} a^4 b^5 x^{16} (6 a B+5 A b)+\frac{30}{17} a^3 b^6 x^{17} (7 a B+4 A b)+\frac{5}{6} a^2 b^7 x^{18} (8 a B+3 A b)+\frac{1}{20} b^9 x^{20} (10 a B+A b)+\frac{5}{19} a b^8 x^{19} (9 a B+2 A b)+\frac{1}{21} b^{10} B x^{21}",1,"(3879876*a^10*A*x^10 + 35271600*a^9*A*b*x^11 + 3527160*a^10*B*x^11 + 145495350*a^8*A*b^2*x^12 + 32332300*a^9*b*B*x^12 + 358142400*a^7*A*b^3*x^13 + 134303400*a^8*b^2*B*x^13 + 581981400*a^6*A*b^4*x^14 + 332560800*a^7*b^3*B*x^14 + 651819168*a^5*A*b^5*x^15 + 543182640*a^6*b^4*B*x^15 + 509233725*a^4*A*b^6*x^16 + 611080470*a^5*b^5*B*x^16 + 273873600*a^3*A*b^7*x^17 + 479278800*a^4*b^6*B*x^17 + 96996900*a^2*A*b^8*x^18 + 258658400*a^3*b^7*B*x^18 + 20420400*a*A*b^9*x^19 + 91891800*a^2*b^8*B*x^19 + 1939938*A*b^10*x^20 + 19399380*a*b^9*B*x^20 + 1847560*b^10*B*x^21)/38798760","A",1
139,1,249,240,0.0842365,"\int x^8 (a+b x)^{10} (A+B x) \, dx","IntegrateAlgebraic[x^8*(a + b*x)^10*(A + B*x),x]","\frac{1847560 a^{10} A x^9+1662804 a^{10} B x^{10}+16628040 a^9 A b x^{10}+15116400 a^9 b B x^{11}+68023800 a^8 A b^2 x^{11}+62355150 a^8 b^2 B x^{12}+166280400 a^7 A b^3 x^{12}+153489600 a^7 b^3 B x^{13}+268606800 a^6 A b^4 x^{13}+249420600 a^6 b^4 B x^{14}+299304720 a^5 A b^5 x^{14}+279351072 a^5 b^5 B x^{15}+232792560 a^4 A b^6 x^{15}+218243025 a^4 b^6 B x^{16}+124710300 a^3 A b^7 x^{16}+117374400 a^3 b^7 B x^{17}+44015400 a^2 A b^8 x^{17}+41570100 a^2 b^8 B x^{18}+9237800 a A b^9 x^{18}+8751600 a b^9 B x^{19}+875160 A b^{10} x^{19}+831402 b^{10} B x^{20}}{16628040}","\frac{a^8 (a+b x)^{11} (A b-a B)}{11 b^{10}}-\frac{a^7 (a+b x)^{12} (8 A b-9 a B)}{12 b^{10}}+\frac{4 a^6 (a+b x)^{13} (7 A b-9 a B)}{13 b^{10}}-\frac{2 a^5 (a+b x)^{14} (2 A b-3 a B)}{b^{10}}+\frac{14 a^4 (a+b x)^{15} (5 A b-9 a B)}{15 b^{10}}-\frac{7 a^3 (a+b x)^{16} (4 A b-9 a B)}{8 b^{10}}+\frac{28 a^2 (a+b x)^{17} (A b-3 a B)}{17 b^{10}}+\frac{(a+b x)^{19} (A b-9 a B)}{19 b^{10}}-\frac{2 a (a+b x)^{18} (2 A b-9 a B)}{9 b^{10}}+\frac{B (a+b x)^{20}}{20 b^{10}}",1,"(1847560*a^10*A*x^9 + 16628040*a^9*A*b*x^10 + 1662804*a^10*B*x^10 + 68023800*a^8*A*b^2*x^11 + 15116400*a^9*b*B*x^11 + 166280400*a^7*A*b^3*x^12 + 62355150*a^8*b^2*B*x^12 + 268606800*a^6*A*b^4*x^13 + 153489600*a^7*b^3*B*x^13 + 299304720*a^5*A*b^5*x^14 + 249420600*a^6*b^4*B*x^14 + 232792560*a^4*A*b^6*x^15 + 279351072*a^5*b^5*B*x^15 + 124710300*a^3*A*b^7*x^16 + 218243025*a^4*b^6*B*x^16 + 44015400*a^2*A*b^8*x^17 + 117374400*a^3*b^7*B*x^17 + 9237800*a*A*b^9*x^18 + 41570100*a^2*b^8*B*x^18 + 875160*A*b^10*x^19 + 8751600*a*b^9*B*x^19 + 831402*b^10*B*x^20)/16628040","A",1
140,1,249,215,0.0815814,"\int x^7 (a+b x)^{10} (A+B x) \, dx","IntegrateAlgebraic[x^7*(a + b*x)^10*(A + B*x),x]","\frac{831402 a^{10} A x^8+739024 a^{10} B x^9+7390240 a^9 A b x^9+6651216 a^9 b B x^{10}+29930472 a^8 A b^2 x^{10}+27209520 a^8 b^2 B x^{11}+72558720 a^7 A b^3 x^{11}+66512160 a^7 b^3 B x^{12}+116396280 a^6 A b^4 x^{12}+107442720 a^6 b^4 B x^{13}+128931264 a^5 A b^5 x^{13}+119721888 a^5 b^5 B x^{14}+99768240 a^4 A b^6 x^{14}+93117024 a^4 b^6 B x^{15}+53209728 a^3 A b^7 x^{15}+49884120 a^3 b^7 B x^{16}+18706545 a^2 A b^8 x^{16}+17606160 a^2 b^8 B x^{17}+3912480 a A b^9 x^{17}+3695120 a b^9 B x^{18}+369512 A b^{10} x^{18}+350064 b^{10} B x^{19}}{6651216}","-\frac{a^7 (a+b x)^{11} (A b-a B)}{11 b^9}+\frac{a^6 (a+b x)^{12} (7 A b-8 a B)}{12 b^9}-\frac{7 a^5 (a+b x)^{13} (3 A b-4 a B)}{13 b^9}+\frac{a^4 (a+b x)^{14} (5 A b-8 a B)}{2 b^9}-\frac{7 a^3 (a+b x)^{15} (A b-2 a B)}{3 b^9}+\frac{7 a^2 (a+b x)^{16} (3 A b-8 a B)}{16 b^9}+\frac{(a+b x)^{18} (A b-8 a B)}{18 b^9}-\frac{7 a (a+b x)^{17} (A b-4 a B)}{17 b^9}+\frac{B (a+b x)^{19}}{19 b^9}",1,"(831402*a^10*A*x^8 + 7390240*a^9*A*b*x^9 + 739024*a^10*B*x^9 + 29930472*a^8*A*b^2*x^10 + 6651216*a^9*b*B*x^10 + 72558720*a^7*A*b^3*x^11 + 27209520*a^8*b^2*B*x^11 + 116396280*a^6*A*b^4*x^12 + 66512160*a^7*b^3*B*x^12 + 128931264*a^5*A*b^5*x^13 + 107442720*a^6*b^4*B*x^13 + 99768240*a^4*A*b^6*x^14 + 119721888*a^5*b^5*B*x^14 + 53209728*a^3*A*b^7*x^15 + 93117024*a^4*b^6*B*x^15 + 18706545*a^2*A*b^8*x^16 + 49884120*a^3*b^7*B*x^16 + 3912480*a*A*b^9*x^17 + 17606160*a^2*b^8*B*x^17 + 369512*A*b^10*x^18 + 3695120*a*b^9*B*x^18 + 350064*b^10*B*x^19)/6651216","A",1
141,1,249,191,0.0817397,"\int x^6 (a+b x)^{10} (A+B x) \, dx","IntegrateAlgebraic[x^6*(a + b*x)^10*(A + B*x),x]","\frac{350064 a^{10} A x^7+306306 a^{10} B x^8+3063060 a^9 A b x^8+2722720 a^9 b B x^9+12252240 a^8 A b^2 x^9+11027016 a^8 b^2 B x^{10}+29405376 a^7 A b^3 x^{10}+26732160 a^7 b^3 B x^{11}+46781280 a^6 A b^4 x^{11}+42882840 a^6 b^4 B x^{12}+51459408 a^5 A b^5 x^{12}+47500992 a^5 b^5 B x^{13}+39584160 a^4 A b^6 x^{13}+36756720 a^4 b^6 B x^{14}+21003840 a^3 A b^7 x^{14}+19603584 a^3 b^7 B x^{15}+7351344 a^2 A b^8 x^{15}+6891885 a^2 b^8 B x^{16}+1531530 a A b^9 x^{16}+1441440 a b^9 B x^{17}+144144 A b^{10} x^{17}+136136 b^{10} B x^{18}}{2450448}","\frac{a^6 (a+b x)^{11} (A b-a B)}{11 b^8}-\frac{a^5 (a+b x)^{12} (6 A b-7 a B)}{12 b^8}+\frac{3 a^4 (a+b x)^{13} (5 A b-7 a B)}{13 b^8}-\frac{5 a^3 (a+b x)^{14} (4 A b-7 a B)}{14 b^8}+\frac{a^2 (a+b x)^{15} (3 A b-7 a B)}{3 b^8}+\frac{(a+b x)^{17} (A b-7 a B)}{17 b^8}-\frac{3 a (a+b x)^{16} (2 A b-7 a B)}{16 b^8}+\frac{B (a+b x)^{18}}{18 b^8}",1,"(350064*a^10*A*x^7 + 3063060*a^9*A*b*x^8 + 306306*a^10*B*x^8 + 12252240*a^8*A*b^2*x^9 + 2722720*a^9*b*B*x^9 + 29405376*a^7*A*b^3*x^10 + 11027016*a^8*b^2*B*x^10 + 46781280*a^6*A*b^4*x^11 + 26732160*a^7*b^3*B*x^11 + 51459408*a^5*A*b^5*x^12 + 42882840*a^6*b^4*B*x^12 + 39584160*a^4*A*b^6*x^13 + 47500992*a^5*b^5*B*x^13 + 21003840*a^3*A*b^7*x^14 + 36756720*a^4*b^6*B*x^14 + 7351344*a^2*A*b^8*x^15 + 19603584*a^3*b^7*B*x^15 + 1531530*a*A*b^9*x^16 + 6891885*a^2*b^8*B*x^16 + 144144*A*b^10*x^17 + 1441440*a*b^9*B*x^17 + 136136*b^10*B*x^18)/2450448","A",1
142,1,249,163,0.079272,"\int x^5 (a+b x)^{10} (A+B x) \, dx","IntegrateAlgebraic[x^5*(a + b*x)^10*(A + B*x),x]","\frac{136136 a^{10} A x^6+116688 a^{10} B x^7+1166880 a^9 A b x^7+1021020 a^9 b B x^8+4594590 a^8 A b^2 x^8+4084080 a^8 b^2 B x^9+10890880 a^7 A b^3 x^9+9801792 a^7 b^3 B x^{10}+17153136 a^6 A b^4 x^{10}+15593760 a^6 b^4 B x^{11}+18712512 a^5 A b^5 x^{11}+17153136 a^5 b^5 B x^{12}+14294280 a^4 A b^6 x^{12}+13194720 a^4 b^6 B x^{13}+7539840 a^3 A b^7 x^{13}+7001280 a^3 b^7 B x^{14}+2625480 a^2 A b^8 x^{14}+2450448 a^2 b^8 B x^{15}+544544 a A b^9 x^{15}+510510 a b^9 B x^{16}+51051 A b^{10} x^{16}+48048 b^{10} B x^{17}}{816816}","-\frac{a^5 (a+b x)^{11} (A b-a B)}{11 b^7}+\frac{a^4 (a+b x)^{12} (5 A b-6 a B)}{12 b^7}-\frac{5 a^3 (a+b x)^{13} (2 A b-3 a B)}{13 b^7}+\frac{5 a^2 (a+b x)^{14} (A b-2 a B)}{7 b^7}+\frac{(a+b x)^{16} (A b-6 a B)}{16 b^7}-\frac{a (a+b x)^{15} (A b-3 a B)}{3 b^7}+\frac{B (a+b x)^{17}}{17 b^7}",1,"(136136*a^10*A*x^6 + 1166880*a^9*A*b*x^7 + 116688*a^10*B*x^7 + 4594590*a^8*A*b^2*x^8 + 1021020*a^9*b*B*x^8 + 10890880*a^7*A*b^3*x^9 + 4084080*a^8*b^2*B*x^9 + 17153136*a^6*A*b^4*x^10 + 9801792*a^7*b^3*B*x^10 + 18712512*a^5*A*b^5*x^11 + 15593760*a^6*b^4*B*x^11 + 14294280*a^4*A*b^6*x^12 + 17153136*a^5*b^5*B*x^12 + 7539840*a^3*A*b^7*x^13 + 13194720*a^4*b^6*B*x^13 + 2625480*a^2*A*b^8*x^14 + 7001280*a^3*b^7*B*x^14 + 544544*a*A*b^9*x^15 + 2450448*a^2*b^8*B*x^15 + 51051*A*b^10*x^16 + 510510*a*b^9*B*x^16 + 48048*b^10*B*x^17)/816816","A",1
143,1,249,139,0.0789729,"\int x^4 (a+b x)^{10} (A+B x) \, dx","IntegrateAlgebraic[x^4*(a + b*x)^10*(A + B*x),x]","\frac{48048 a^{10} A x^5+40040 a^{10} B x^6+400400 a^9 A b x^6+343200 a^9 b B x^7+1544400 a^8 A b^2 x^7+1351350 a^8 b^2 B x^8+3603600 a^7 A b^3 x^8+3203200 a^7 b^3 B x^9+5605600 a^6 A b^4 x^9+5045040 a^6 b^4 B x^{10}+6054048 a^5 A b^5 x^{10}+5503680 a^5 b^5 B x^{11}+4586400 a^4 A b^6 x^{11}+4204200 a^4 b^6 B x^{12}+2402400 a^3 A b^7 x^{12}+2217600 a^3 b^7 B x^{13}+831600 a^2 A b^8 x^{13}+772200 a^2 b^8 B x^{14}+171600 a A b^9 x^{14}+160160 a b^9 B x^{15}+16016 A b^{10} x^{15}+15015 b^{10} B x^{16}}{240240}","\frac{a^4 (a+b x)^{11} (A b-a B)}{11 b^6}-\frac{a^3 (a+b x)^{12} (4 A b-5 a B)}{12 b^6}+\frac{2 a^2 (a+b x)^{13} (3 A b-5 a B)}{13 b^6}+\frac{(a+b x)^{15} (A b-5 a B)}{15 b^6}-\frac{a (a+b x)^{14} (2 A b-5 a B)}{7 b^6}+\frac{B (a+b x)^{16}}{16 b^6}",1,"(48048*a^10*A*x^5 + 400400*a^9*A*b*x^6 + 40040*a^10*B*x^6 + 1544400*a^8*A*b^2*x^7 + 343200*a^9*b*B*x^7 + 3603600*a^7*A*b^3*x^8 + 1351350*a^8*b^2*B*x^8 + 5605600*a^6*A*b^4*x^9 + 3203200*a^7*b^3*B*x^9 + 6054048*a^5*A*b^5*x^10 + 5045040*a^6*b^4*B*x^10 + 4586400*a^4*A*b^6*x^11 + 5503680*a^5*b^5*B*x^11 + 2402400*a^3*A*b^7*x^12 + 4204200*a^4*b^6*B*x^12 + 831600*a^2*A*b^8*x^13 + 2217600*a^3*b^7*B*x^13 + 171600*a*A*b^9*x^14 + 772200*a^2*b^8*B*x^14 + 16016*A*b^10*x^15 + 160160*a*b^9*B*x^15 + 15015*b^10*B*x^16)/240240","A",1
144,1,249,112,0.0841786,"\int x^3 (a+b x)^{10} (A+B x) \, dx","IntegrateAlgebraic[x^3*(a + b*x)^10*(A + B*x),x]","\frac{15015 a^{10} A x^4+12012 a^{10} B x^5+120120 a^9 A b x^5+100100 a^9 b B x^6+450450 a^8 A b^2 x^6+386100 a^8 b^2 B x^7+1029600 a^7 A b^3 x^7+900900 a^7 b^3 B x^8+1576575 a^6 A b^4 x^8+1401400 a^6 b^4 B x^9+1681680 a^5 A b^5 x^9+1513512 a^5 b^5 B x^{10}+1261260 a^4 A b^6 x^{10}+1146600 a^4 b^6 B x^{11}+655200 a^3 A b^7 x^{11}+600600 a^3 b^7 B x^{12}+225225 a^2 A b^8 x^{12}+207900 a^2 b^8 B x^{13}+46200 a A b^9 x^{13}+42900 a b^9 B x^{14}+4290 A b^{10} x^{14}+4004 b^{10} B x^{15}}{60060}","-\frac{a^3 (a+b x)^{11} (A b-a B)}{11 b^5}+\frac{a^2 (a+b x)^{12} (3 A b-4 a B)}{12 b^5}+\frac{(a+b x)^{14} (A b-4 a B)}{14 b^5}-\frac{3 a (a+b x)^{13} (A b-2 a B)}{13 b^5}+\frac{B (a+b x)^{15}}{15 b^5}",1,"(15015*a^10*A*x^4 + 120120*a^9*A*b*x^5 + 12012*a^10*B*x^5 + 450450*a^8*A*b^2*x^6 + 100100*a^9*b*B*x^6 + 1029600*a^7*A*b^3*x^7 + 386100*a^8*b^2*B*x^7 + 1576575*a^6*A*b^4*x^8 + 900900*a^7*b^3*B*x^8 + 1681680*a^5*A*b^5*x^9 + 1401400*a^6*b^4*B*x^9 + 1261260*a^4*A*b^6*x^10 + 1513512*a^5*b^5*B*x^10 + 655200*a^3*A*b^7*x^11 + 1146600*a^4*b^6*B*x^11 + 225225*a^2*A*b^8*x^12 + 600600*a^3*b^7*B*x^12 + 46200*a*A*b^9*x^13 + 207900*a^2*b^8*B*x^13 + 4290*A*b^10*x^14 + 42900*a*b^9*B*x^14 + 4004*b^10*B*x^15)/60060","B",1
145,1,249,87,0.0788443,"\int x^2 (a+b x)^{10} (A+B x) \, dx","IntegrateAlgebraic[x^2*(a + b*x)^10*(A + B*x),x]","\frac{4004 a^{10} A x^3+3003 a^{10} B x^4+30030 a^9 A b x^4+24024 a^9 b B x^5+108108 a^8 A b^2 x^5+90090 a^8 b^2 B x^6+240240 a^7 A b^3 x^6+205920 a^7 b^3 B x^7+360360 a^6 A b^4 x^7+315315 a^6 b^4 B x^8+378378 a^5 A b^5 x^8+336336 a^5 b^5 B x^9+280280 a^4 A b^6 x^9+252252 a^4 b^6 B x^{10}+144144 a^3 A b^7 x^{10}+131040 a^3 b^7 B x^{11}+49140 a^2 A b^8 x^{11}+45045 a^2 b^8 B x^{12}+10010 a A b^9 x^{12}+9240 a b^9 B x^{13}+924 A b^{10} x^{13}+858 b^{10} B x^{14}}{12012}","\frac{a^2 (a+b x)^{11} (A b-a B)}{11 b^4}+\frac{(a+b x)^{13} (A b-3 a B)}{13 b^4}-\frac{a (a+b x)^{12} (2 A b-3 a B)}{12 b^4}+\frac{B (a+b x)^{14}}{14 b^4}",1,"(4004*a^10*A*x^3 + 30030*a^9*A*b*x^4 + 3003*a^10*B*x^4 + 108108*a^8*A*b^2*x^5 + 24024*a^9*b*B*x^5 + 240240*a^7*A*b^3*x^6 + 90090*a^8*b^2*B*x^6 + 360360*a^6*A*b^4*x^7 + 205920*a^7*b^3*B*x^7 + 378378*a^5*A*b^5*x^8 + 315315*a^6*b^4*B*x^8 + 280280*a^4*A*b^6*x^9 + 336336*a^5*b^5*B*x^9 + 144144*a^3*A*b^7*x^10 + 252252*a^4*b^6*B*x^10 + 49140*a^2*A*b^8*x^11 + 131040*a^3*b^7*B*x^11 + 10010*a*A*b^9*x^12 + 45045*a^2*b^8*B*x^12 + 924*A*b^10*x^13 + 9240*a*b^9*B*x^13 + 858*b^10*B*x^14)/12012","B",1
146,1,249,61,0.0956358,"\int x (a+b x)^{10} (A+B x) \, dx","IntegrateAlgebraic[x*(a + b*x)^10*(A + B*x),x]","\frac{858 a^{10} A x^2+572 a^{10} B x^3+5720 a^9 A b x^3+4290 a^9 b B x^4+19305 a^8 A b^2 x^4+15444 a^8 b^2 B x^5+41184 a^7 A b^3 x^5+34320 a^7 b^3 B x^6+60060 a^6 A b^4 x^6+51480 a^6 b^4 B x^7+61776 a^5 A b^5 x^7+54054 a^5 b^5 B x^8+45045 a^4 A b^6 x^8+40040 a^4 b^6 B x^9+22880 a^3 A b^7 x^9+20592 a^3 b^7 B x^{10}+7722 a^2 A b^8 x^{10}+7020 a^2 b^8 B x^{11}+1560 a A b^9 x^{11}+1430 a b^9 B x^{12}+143 A b^{10} x^{12}+132 b^{10} B x^{13}}{1716}","\frac{(a+b x)^{12} (A b-2 a B)}{12 b^3}-\frac{a (a+b x)^{11} (A b-a B)}{11 b^3}+\frac{B (a+b x)^{13}}{13 b^3}",1,"(858*a^10*A*x^2 + 5720*a^9*A*b*x^3 + 572*a^10*B*x^3 + 19305*a^8*A*b^2*x^4 + 4290*a^9*b*B*x^4 + 41184*a^7*A*b^3*x^5 + 15444*a^8*b^2*B*x^5 + 60060*a^6*A*b^4*x^6 + 34320*a^7*b^3*B*x^6 + 61776*a^5*A*b^5*x^7 + 51480*a^6*b^4*B*x^7 + 45045*a^4*A*b^6*x^8 + 54054*a^5*b^5*B*x^8 + 22880*a^3*A*b^7*x^9 + 40040*a^4*b^6*B*x^9 + 7722*a^2*A*b^8*x^10 + 20592*a^3*b^7*B*x^10 + 1560*a*A*b^9*x^11 + 7020*a^2*b^8*B*x^11 + 143*A*b^10*x^12 + 1430*a*b^9*B*x^12 + 132*b^10*B*x^13)/1716","B",1
147,1,243,38,0.1320532,"\int (a+b x)^{10} (A+B x) \, dx","IntegrateAlgebraic[(a + b*x)^10*(A + B*x),x]","\frac{1}{132} x \left(132 a^{10} A+66 a^{10} B x+660 a^9 A b x+440 a^9 b B x^2+1980 a^8 A b^2 x^2+1485 a^8 b^2 B x^3+3960 a^7 A b^3 x^3+3168 a^7 b^3 B x^4+5544 a^6 A b^4 x^4+4620 a^6 b^4 B x^5+5544 a^5 A b^5 x^5+4752 a^5 b^5 B x^6+3960 a^4 A b^6 x^6+3465 a^4 b^6 B x^7+1980 a^3 A b^7 x^7+1760 a^3 b^7 B x^8+660 a^2 A b^8 x^8+594 a^2 b^8 B x^9+132 a A b^9 x^9+120 a b^9 B x^{10}+12 A b^{10} x^{10}+11 b^{10} B x^{11}\right)","\frac{(a+b x)^{11} (A b-a B)}{11 b^2}+\frac{B (a+b x)^{12}}{12 b^2}",1,"(x*(132*a^10*A + 660*a^9*A*b*x + 66*a^10*B*x + 1980*a^8*A*b^2*x^2 + 440*a^9*b*B*x^2 + 3960*a^7*A*b^3*x^3 + 1485*a^8*b^2*B*x^3 + 5544*a^6*A*b^4*x^4 + 3168*a^7*b^3*B*x^4 + 5544*a^5*A*b^5*x^5 + 4620*a^6*b^4*B*x^5 + 3960*a^4*A*b^6*x^6 + 4752*a^5*b^5*B*x^6 + 1980*a^3*A*b^7*x^7 + 3465*a^4*b^6*B*x^7 + 660*a^2*A*b^8*x^8 + 1760*a^3*b^7*B*x^8 + 132*a*A*b^9*x^9 + 594*a^2*b^8*B*x^9 + 12*A*b^10*x^10 + 120*a*b^9*B*x^10 + 11*b^10*B*x^11))/132","B",1
148,1,244,148,0.1091842,"\int \frac{(a+b x)^{10} (A+B x)}{x} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x,x]","a^{10} A \log (x)+\frac{27720 a^{10} B x+277200 a^9 A b x+138600 a^9 b B x^2+623700 a^8 A b^2 x^2+415800 a^8 b^2 B x^3+1108800 a^7 A b^3 x^3+831600 a^7 b^3 B x^4+1455300 a^6 A b^4 x^4+1164240 a^6 b^4 B x^5+1397088 a^5 A b^5 x^5+1164240 a^5 b^5 B x^6+970200 a^4 A b^6 x^6+831600 a^4 b^6 B x^7+475200 a^3 A b^7 x^7+415800 a^3 b^7 B x^8+155925 a^2 A b^8 x^8+138600 a^2 b^8 B x^9+30800 a A b^9 x^9+27720 a b^9 B x^{10}+2772 A b^{10} x^{10}+2520 b^{10} B x^{11}}{27720}","a^{10} A \log (x)+10 a^9 A b x+\frac{45}{2} a^8 A b^2 x^2+40 a^7 A b^3 x^3+\frac{105}{2} a^6 A b^4 x^4+\frac{252}{5} a^5 A b^5 x^5+35 a^4 A b^6 x^6+\frac{120}{7} a^3 A b^7 x^7+\frac{45}{8} a^2 A b^8 x^8+\frac{10}{9} a A b^9 x^9+\frac{B (a+b x)^{11}}{11 b}+\frac{1}{10} A b^{10} x^{10}",1,"(277200*a^9*A*b*x + 27720*a^10*B*x + 623700*a^8*A*b^2*x^2 + 138600*a^9*b*B*x^2 + 1108800*a^7*A*b^3*x^3 + 415800*a^8*b^2*B*x^3 + 1455300*a^6*A*b^4*x^4 + 831600*a^7*b^3*B*x^4 + 1397088*a^5*A*b^5*x^5 + 1164240*a^6*b^4*B*x^5 + 970200*a^4*A*b^6*x^6 + 1164240*a^5*b^5*B*x^6 + 475200*a^3*A*b^7*x^7 + 831600*a^4*b^6*B*x^7 + 155925*a^2*A*b^8*x^8 + 415800*a^3*b^7*B*x^8 + 30800*a*A*b^9*x^9 + 138600*a^2*b^8*B*x^9 + 2772*A*b^10*x^10 + 27720*a*b^9*B*x^10 + 2520*b^10*B*x^11)/27720 + a^10*A*Log[x]","A",1
149,1,247,217,0.1451845,"\int \frac{(a+b x)^{10} (A+B x)}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^2,x]","\log (x) \left(a^{10} B+10 a^9 A b\right)+\frac{-2520 a^{10} A+25200 a^9 b B x^2+113400 a^8 A b^2 x^2+56700 a^8 b^2 B x^3+151200 a^7 A b^3 x^3+100800 a^7 b^3 B x^4+176400 a^6 A b^4 x^4+132300 a^6 b^4 B x^5+158760 a^5 A b^5 x^5+127008 a^5 b^5 B x^6+105840 a^4 A b^6 x^6+88200 a^4 b^6 B x^7+50400 a^3 A b^7 x^7+43200 a^3 b^7 B x^8+16200 a^2 A b^8 x^8+14175 a^2 b^8 B x^9+3150 a A b^9 x^9+2800 a b^9 B x^{10}+280 A b^{10} x^{10}+252 b^{10} B x^{11}}{2520 x}","-\frac{a^{10} A}{x}+a^9 \log (x) (a B+10 A b)+5 a^8 b x (2 a B+9 A b)+\frac{15}{2} a^7 b^2 x^2 (3 a B+8 A b)+10 a^6 b^3 x^3 (4 a B+7 A b)+\frac{21}{2} a^5 b^4 x^4 (5 a B+6 A b)+\frac{42}{5} a^4 b^5 x^5 (6 a B+5 A b)+5 a^3 b^6 x^6 (7 a B+4 A b)+\frac{15}{7} a^2 b^7 x^7 (8 a B+3 A b)+\frac{1}{9} b^9 x^9 (10 a B+A b)+\frac{5}{8} a b^8 x^8 (9 a B+2 A b)+\frac{1}{10} b^{10} B x^{10}",1,"(-2520*a^10*A + 113400*a^8*A*b^2*x^2 + 25200*a^9*b*B*x^2 + 151200*a^7*A*b^3*x^3 + 56700*a^8*b^2*B*x^3 + 176400*a^6*A*b^4*x^4 + 100800*a^7*b^3*B*x^4 + 158760*a^5*A*b^5*x^5 + 132300*a^6*b^4*B*x^5 + 105840*a^4*A*b^6*x^6 + 127008*a^5*b^5*B*x^6 + 50400*a^3*A*b^7*x^7 + 88200*a^4*b^6*B*x^7 + 16200*a^2*A*b^8*x^8 + 43200*a^3*b^7*B*x^8 + 3150*a*A*b^9*x^9 + 14175*a^2*b^8*B*x^9 + 280*A*b^10*x^10 + 2800*a*b^9*B*x^10 + 252*b^10*B*x^11)/(2520*x) + (10*a^9*A*b + a^10*B)*Log[x]","A",1
150,1,245,216,0.151644,"\int \frac{(a+b x)^{10} (A+B x)}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^3,x]","5 \log (x) \left(2 a^9 b B+9 a^8 A b^2\right)+\frac{-252 a^{10} A-504 a^{10} B x-5040 a^9 A b x+22680 a^8 b^2 B x^3+60480 a^7 A b^3 x^3+30240 a^7 b^3 B x^4+52920 a^6 A b^4 x^4+35280 a^6 b^4 B x^5+42336 a^5 A b^5 x^5+31752 a^5 b^5 B x^6+26460 a^4 A b^6 x^6+21168 a^4 b^6 B x^7+12096 a^3 A b^7 x^7+10080 a^3 b^7 B x^8+3780 a^2 A b^8 x^8+3240 a^2 b^8 B x^9+720 a A b^9 x^9+630 a b^9 B x^{10}+63 A b^{10} x^{10}+56 b^{10} B x^{11}}{504 x^2}","-\frac{a^{10} A}{2 x^2}-\frac{a^9 (a B+10 A b)}{x}+5 a^8 b \log (x) (2 a B+9 A b)+15 a^7 b^2 x (3 a B+8 A b)+15 a^6 b^3 x^2 (4 a B+7 A b)+14 a^5 b^4 x^3 (5 a B+6 A b)+\frac{21}{2} a^4 b^5 x^4 (6 a B+5 A b)+6 a^3 b^6 x^5 (7 a B+4 A b)+\frac{5}{2} a^2 b^7 x^6 (8 a B+3 A b)+\frac{1}{8} b^9 x^8 (10 a B+A b)+\frac{5}{7} a b^8 x^7 (9 a B+2 A b)+\frac{1}{9} b^{10} B x^9",1,"(-252*a^10*A - 5040*a^9*A*b*x - 504*a^10*B*x + 60480*a^7*A*b^3*x^3 + 22680*a^8*b^2*B*x^3 + 52920*a^6*A*b^4*x^4 + 30240*a^7*b^3*B*x^4 + 42336*a^5*A*b^5*x^5 + 35280*a^6*b^4*B*x^5 + 26460*a^4*A*b^6*x^6 + 31752*a^5*b^5*B*x^6 + 12096*a^3*A*b^7*x^7 + 21168*a^4*b^6*B*x^7 + 3780*a^2*A*b^8*x^8 + 10080*a^3*b^7*B*x^8 + 720*a*A*b^9*x^9 + 3240*a^2*b^8*B*x^9 + 63*A*b^10*x^10 + 630*a*b^9*B*x^10 + 56*b^10*B*x^11)/(504*x^2) + 5*(9*a^8*A*b^2 + 2*a^9*b*B)*Log[x]","A",1
151,1,245,216,0.1575127,"\int \frac{(a+b x)^{10} (A+B x)}{x^4} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^4,x]","15 \log (x) \left(3 a^8 b^2 B+8 a^7 A b^3\right)+\frac{-56 a^{10} A-84 a^{10} B x-840 a^9 A b x-1680 a^9 b B x^2-7560 a^8 A b^2 x^2+20160 a^7 b^3 B x^4+35280 a^6 A b^4 x^4+17640 a^6 b^4 B x^5+21168 a^5 A b^5 x^5+14112 a^5 b^5 B x^6+11760 a^4 A b^6 x^6+8820 a^4 b^6 B x^7+5040 a^3 A b^7 x^7+4032 a^3 b^7 B x^8+1512 a^2 A b^8 x^8+1260 a^2 b^8 B x^9+280 a A b^9 x^9+240 a b^9 B x^{10}+24 A b^{10} x^{10}+21 b^{10} B x^{11}}{168 x^3}","-\frac{a^{10} A}{3 x^3}-\frac{a^9 (a B+10 A b)}{2 x^2}-\frac{5 a^8 b (2 a B+9 A b)}{x}+15 a^7 b^2 \log (x) (3 a B+8 A b)+30 a^6 b^3 x (4 a B+7 A b)+21 a^5 b^4 x^2 (5 a B+6 A b)+14 a^4 b^5 x^3 (6 a B+5 A b)+\frac{15}{2} a^3 b^6 x^4 (7 a B+4 A b)+3 a^2 b^7 x^5 (8 a B+3 A b)+\frac{1}{7} b^9 x^7 (10 a B+A b)+\frac{5}{6} a b^8 x^6 (9 a B+2 A b)+\frac{1}{8} b^{10} B x^8",1,"(-56*a^10*A - 840*a^9*A*b*x - 84*a^10*B*x - 7560*a^8*A*b^2*x^2 - 1680*a^9*b*B*x^2 + 35280*a^6*A*b^4*x^4 + 20160*a^7*b^3*B*x^4 + 21168*a^5*A*b^5*x^5 + 17640*a^6*b^4*B*x^5 + 11760*a^4*A*b^6*x^6 + 14112*a^5*b^5*B*x^6 + 5040*a^3*A*b^7*x^7 + 8820*a^4*b^6*B*x^7 + 1512*a^2*A*b^8*x^8 + 4032*a^3*b^7*B*x^8 + 280*a*A*b^9*x^9 + 1260*a^2*b^8*B*x^9 + 24*A*b^10*x^10 + 240*a*b^9*B*x^10 + 21*b^10*B*x^11)/(168*x^3) + 15*(8*a^7*A*b^3 + 3*a^8*b^2*B)*Log[x]","A",1
152,1,245,215,0.1416023,"\int \frac{(a+b x)^{10} (A+B x)}{x^5} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^5,x]","30 \log (x) \left(4 a^7 b^3 B+7 a^6 A b^4\right)+\frac{-21 a^{10} A-28 a^{10} B x-280 a^9 A b x-420 a^9 b B x^2-1890 a^8 A b^2 x^2-3780 a^8 b^2 B x^3-10080 a^7 A b^3 x^3+17640 a^6 b^4 B x^5+21168 a^5 A b^5 x^5+10584 a^5 b^5 B x^6+8820 a^4 A b^6 x^6+5880 a^4 b^6 B x^7+3360 a^3 A b^7 x^7+2520 a^3 b^7 B x^8+945 a^2 A b^8 x^8+756 a^2 b^8 B x^9+168 a A b^9 x^9+140 a b^9 B x^{10}+14 A b^{10} x^{10}+12 b^{10} B x^{11}}{84 x^4}","-\frac{a^{10} A}{4 x^4}-\frac{a^9 (a B+10 A b)}{3 x^3}-\frac{5 a^8 b (2 a B+9 A b)}{2 x^2}-\frac{15 a^7 b^2 (3 a B+8 A b)}{x}+30 a^6 b^3 \log (x) (4 a B+7 A b)+42 a^5 b^4 x (5 a B+6 A b)+21 a^4 b^5 x^2 (6 a B+5 A b)+10 a^3 b^6 x^3 (7 a B+4 A b)+\frac{15}{4} a^2 b^7 x^4 (8 a B+3 A b)+\frac{1}{6} b^9 x^6 (10 a B+A b)+a b^8 x^5 (9 a B+2 A b)+\frac{1}{7} b^{10} B x^7",1,"(-21*a^10*A - 280*a^9*A*b*x - 28*a^10*B*x - 1890*a^8*A*b^2*x^2 - 420*a^9*b*B*x^2 - 10080*a^7*A*b^3*x^3 - 3780*a^8*b^2*B*x^3 + 21168*a^5*A*b^5*x^5 + 17640*a^6*b^4*B*x^5 + 8820*a^4*A*b^6*x^6 + 10584*a^5*b^5*B*x^6 + 3360*a^3*A*b^7*x^7 + 5880*a^4*b^6*B*x^7 + 945*a^2*A*b^8*x^8 + 2520*a^3*b^7*B*x^8 + 168*a*A*b^9*x^9 + 756*a^2*b^8*B*x^9 + 14*A*b^10*x^10 + 140*a*b^9*B*x^10 + 12*b^10*B*x^11)/(84*x^4) + 30*(7*a^6*A*b^4 + 4*a^7*b^3*B)*Log[x]","A",1
153,1,245,218,0.1487832,"\int \frac{(a+b x)^{10} (A+B x)}{x^6} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^6,x]","42 \log (x) \left(5 a^6 b^4 B+6 a^5 A b^5\right)+\frac{-12 a^{10} A-15 a^{10} B x-150 a^9 A b x-200 a^9 b B x^2-900 a^8 A b^2 x^2-1350 a^8 b^2 B x^3-3600 a^7 A b^3 x^3-7200 a^7 b^3 B x^4-12600 a^6 A b^4 x^4+15120 a^5 b^5 B x^6+12600 a^4 A b^6 x^6+6300 a^4 b^6 B x^7+3600 a^3 A b^7 x^7+2400 a^3 b^7 B x^8+900 a^2 A b^8 x^8+675 a^2 b^8 B x^9+150 a A b^9 x^9+120 a b^9 B x^{10}+12 A b^{10} x^{10}+10 b^{10} B x^{11}}{60 x^5}","-\frac{a^{10} A}{5 x^5}-\frac{a^9 (a B+10 A b)}{4 x^4}-\frac{5 a^8 b (2 a B+9 A b)}{3 x^3}-\frac{15 a^7 b^2 (3 a B+8 A b)}{2 x^2}-\frac{30 a^6 b^3 (4 a B+7 A b)}{x}+42 a^5 b^4 \log (x) (5 a B+6 A b)+42 a^4 b^5 x (6 a B+5 A b)+15 a^3 b^6 x^2 (7 a B+4 A b)+5 a^2 b^7 x^3 (8 a B+3 A b)+\frac{1}{5} b^9 x^5 (10 a B+A b)+\frac{5}{4} a b^8 x^4 (9 a B+2 A b)+\frac{1}{6} b^{10} B x^6",1,"(-12*a^10*A - 150*a^9*A*b*x - 15*a^10*B*x - 900*a^8*A*b^2*x^2 - 200*a^9*b*B*x^2 - 3600*a^7*A*b^3*x^3 - 1350*a^8*b^2*B*x^3 - 12600*a^6*A*b^4*x^4 - 7200*a^7*b^3*B*x^4 + 12600*a^4*A*b^6*x^6 + 15120*a^5*b^5*B*x^6 + 3600*a^3*A*b^7*x^7 + 6300*a^4*b^6*B*x^7 + 900*a^2*A*b^8*x^8 + 2400*a^3*b^7*B*x^8 + 150*a*A*b^9*x^9 + 675*a^2*b^8*B*x^9 + 12*A*b^10*x^10 + 120*a*b^9*B*x^10 + 10*b^10*B*x^11)/(60*x^5) + 42*(6*a^5*A*b^5 + 5*a^6*b^4*B)*Log[x]","A",1
154,1,245,218,0.1442405,"\int \frac{(a+b x)^{10} (A+B x)}{x^7} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^7,x]","42 \log (x) \left(6 a^5 b^5 B+5 a^4 A b^6\right)+\frac{-10 a^{10} A-12 a^{10} B x-120 a^9 A b x-150 a^9 b B x^2-675 a^8 A b^2 x^2-900 a^8 b^2 B x^3-2400 a^7 A b^3 x^3-3600 a^7 b^3 B x^4-6300 a^6 A b^4 x^4-12600 a^6 b^4 B x^5-15120 a^5 A b^5 x^5+12600 a^4 b^6 B x^7+7200 a^3 A b^7 x^7+3600 a^3 b^7 B x^8+1350 a^2 A b^8 x^8+900 a^2 b^8 B x^9+200 a A b^9 x^9+150 a b^9 B x^{10}+15 A b^{10} x^{10}+12 b^{10} B x^{11}}{60 x^6}","-\frac{a^{10} A}{6 x^6}-\frac{a^9 (a B+10 A b)}{5 x^5}-\frac{5 a^8 b (2 a B+9 A b)}{4 x^4}-\frac{5 a^7 b^2 (3 a B+8 A b)}{x^3}-\frac{15 a^6 b^3 (4 a B+7 A b)}{x^2}-\frac{42 a^5 b^4 (5 a B+6 A b)}{x}+42 a^4 b^5 \log (x) (6 a B+5 A b)+30 a^3 b^6 x (7 a B+4 A b)+\frac{15}{2} a^2 b^7 x^2 (8 a B+3 A b)+\frac{1}{4} b^9 x^4 (10 a B+A b)+\frac{5}{3} a b^8 x^3 (9 a B+2 A b)+\frac{1}{5} b^{10} B x^5",1,"(-10*a^10*A - 120*a^9*A*b*x - 12*a^10*B*x - 675*a^8*A*b^2*x^2 - 150*a^9*b*B*x^2 - 2400*a^7*A*b^3*x^3 - 900*a^8*b^2*B*x^3 - 6300*a^6*A*b^4*x^4 - 3600*a^7*b^3*B*x^4 - 15120*a^5*A*b^5*x^5 - 12600*a^6*b^4*B*x^5 + 7200*a^3*A*b^7*x^7 + 12600*a^4*b^6*B*x^7 + 1350*a^2*A*b^8*x^8 + 3600*a^3*b^7*B*x^8 + 200*a*A*b^9*x^9 + 900*a^2*b^8*B*x^9 + 15*A*b^10*x^10 + 150*a*b^9*B*x^10 + 12*b^10*B*x^11)/(60*x^6) + 42*(5*a^4*A*b^6 + 6*a^5*b^5*B)*Log[x]","A",1
155,1,245,216,0.1536096,"\int \frac{(a+b x)^{10} (A+B x)}{x^8} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^8,x]","30 \log (x) \left(7 a^4 b^6 B+4 a^3 A b^7\right)+\frac{-12 a^{10} A-14 a^{10} B x-140 a^9 A b x-168 a^9 b B x^2-756 a^8 A b^2 x^2-945 a^8 b^2 B x^3-2520 a^7 A b^3 x^3-3360 a^7 b^3 B x^4-5880 a^6 A b^4 x^4-8820 a^6 b^4 B x^5-10584 a^5 A b^5 x^5-21168 a^5 b^5 B x^6-17640 a^4 A b^6 x^6+10080 a^3 b^7 B x^8+3780 a^2 A b^8 x^8+1890 a^2 b^8 B x^9+420 a A b^9 x^9+280 a b^9 B x^{10}+28 A b^{10} x^{10}+21 b^{10} B x^{11}}{84 x^7}","-\frac{a^{10} A}{7 x^7}-\frac{a^9 (a B+10 A b)}{6 x^6}-\frac{a^8 b (2 a B+9 A b)}{x^5}-\frac{15 a^7 b^2 (3 a B+8 A b)}{4 x^4}-\frac{10 a^6 b^3 (4 a B+7 A b)}{x^3}-\frac{21 a^5 b^4 (5 a B+6 A b)}{x^2}-\frac{42 a^4 b^5 (6 a B+5 A b)}{x}+30 a^3 b^6 \log (x) (7 a B+4 A b)+15 a^2 b^7 x (8 a B+3 A b)+\frac{1}{3} b^9 x^3 (10 a B+A b)+\frac{5}{2} a b^8 x^2 (9 a B+2 A b)+\frac{1}{4} b^{10} B x^4",1,"(-12*a^10*A - 140*a^9*A*b*x - 14*a^10*B*x - 756*a^8*A*b^2*x^2 - 168*a^9*b*B*x^2 - 2520*a^7*A*b^3*x^3 - 945*a^8*b^2*B*x^3 - 5880*a^6*A*b^4*x^4 - 3360*a^7*b^3*B*x^4 - 10584*a^5*A*b^5*x^5 - 8820*a^6*b^4*B*x^5 - 17640*a^4*A*b^6*x^6 - 21168*a^5*b^5*B*x^6 + 3780*a^2*A*b^8*x^8 + 10080*a^3*b^7*B*x^8 + 420*a*A*b^9*x^9 + 1890*a^2*b^8*B*x^9 + 28*A*b^10*x^10 + 280*a*b^9*B*x^10 + 21*b^10*B*x^11)/(84*x^7) + 30*(4*a^3*A*b^7 + 7*a^4*b^6*B)*Log[x]","A",1
156,1,245,216,0.1524731,"\int \frac{(a+b x)^{10} (A+B x)}{x^9} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^9,x]","15 \log (x) \left(8 a^3 b^7 B+3 a^2 A b^8\right)+\frac{-21 a^{10} A-24 a^{10} B x-240 a^9 A b x-280 a^9 b B x^2-1260 a^8 A b^2 x^2-1512 a^8 b^2 B x^3-4032 a^7 A b^3 x^3-5040 a^7 b^3 B x^4-8820 a^6 A b^4 x^4-11760 a^6 b^4 B x^5-14112 a^5 A b^5 x^5-21168 a^5 b^5 B x^6-17640 a^4 A b^6 x^6-35280 a^4 b^6 B x^7-20160 a^3 A b^7 x^7+7560 a^2 b^8 B x^9+1680 a A b^9 x^9+840 a b^9 B x^{10}+84 A b^{10} x^{10}+56 b^{10} B x^{11}}{168 x^8}","-\frac{a^{10} A}{8 x^8}-\frac{a^9 (a B+10 A b)}{7 x^7}-\frac{5 a^8 b (2 a B+9 A b)}{6 x^6}-\frac{3 a^7 b^2 (3 a B+8 A b)}{x^5}-\frac{15 a^6 b^3 (4 a B+7 A b)}{2 x^4}-\frac{14 a^5 b^4 (5 a B+6 A b)}{x^3}-\frac{21 a^4 b^5 (6 a B+5 A b)}{x^2}-\frac{30 a^3 b^6 (7 a B+4 A b)}{x}+15 a^2 b^7 \log (x) (8 a B+3 A b)+\frac{1}{2} b^9 x^2 (10 a B+A b)+5 a b^8 x (9 a B+2 A b)+\frac{1}{3} b^{10} B x^3",1,"(-21*a^10*A - 240*a^9*A*b*x - 24*a^10*B*x - 1260*a^8*A*b^2*x^2 - 280*a^9*b*B*x^2 - 4032*a^7*A*b^3*x^3 - 1512*a^8*b^2*B*x^3 - 8820*a^6*A*b^4*x^4 - 5040*a^7*b^3*B*x^4 - 14112*a^5*A*b^5*x^5 - 11760*a^6*b^4*B*x^5 - 17640*a^4*A*b^6*x^6 - 21168*a^5*b^5*B*x^6 - 20160*a^3*A*b^7*x^7 - 35280*a^4*b^6*B*x^7 + 1680*a*A*b^9*x^9 + 7560*a^2*b^8*B*x^9 + 84*A*b^10*x^10 + 840*a*b^9*B*x^10 + 56*b^10*B*x^11)/(168*x^8) + 15*(3*a^2*A*b^8 + 8*a^3*b^7*B)*Log[x]","A",1
157,1,245,215,0.1636526,"\int \frac{(a+b x)^{10} (A+B x)}{x^{10}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^10,x]","5 \log (x) \left(9 a^2 b^8 B+2 a A b^9\right)+\frac{-56 a^{10} A-63 a^{10} B x-630 a^9 A b x-720 a^9 b B x^2-3240 a^8 A b^2 x^2-3780 a^8 b^2 B x^3-10080 a^7 A b^3 x^3-12096 a^7 b^3 B x^4-21168 a^6 A b^4 x^4-26460 a^6 b^4 B x^5-31752 a^5 A b^5 x^5-42336 a^5 b^5 B x^6-35280 a^4 A b^6 x^6-52920 a^4 b^6 B x^7-30240 a^3 A b^7 x^7-60480 a^3 b^7 B x^8-22680 a^2 A b^8 x^8+5040 a b^9 B x^{10}+504 A b^{10} x^{10}+252 b^{10} B x^{11}}{504 x^9}","-\frac{a^{10} A}{9 x^9}-\frac{a^9 (a B+10 A b)}{8 x^8}-\frac{5 a^8 b (2 a B+9 A b)}{7 x^7}-\frac{5 a^7 b^2 (3 a B+8 A b)}{2 x^6}-\frac{6 a^6 b^3 (4 a B+7 A b)}{x^5}-\frac{21 a^5 b^4 (5 a B+6 A b)}{2 x^4}-\frac{14 a^4 b^5 (6 a B+5 A b)}{x^3}-\frac{15 a^3 b^6 (7 a B+4 A b)}{x^2}-\frac{15 a^2 b^7 (8 a B+3 A b)}{x}+b^9 x (10 a B+A b)+5 a b^8 \log (x) (9 a B+2 A b)+\frac{1}{2} b^{10} B x^2",1,"(-56*a^10*A - 630*a^9*A*b*x - 63*a^10*B*x - 3240*a^8*A*b^2*x^2 - 720*a^9*b*B*x^2 - 10080*a^7*A*b^3*x^3 - 3780*a^8*b^2*B*x^3 - 21168*a^6*A*b^4*x^4 - 12096*a^7*b^3*B*x^4 - 31752*a^5*A*b^5*x^5 - 26460*a^6*b^4*B*x^5 - 35280*a^4*A*b^6*x^6 - 42336*a^5*b^5*B*x^6 - 30240*a^3*A*b^7*x^7 - 52920*a^4*b^6*B*x^7 - 22680*a^2*A*b^8*x^8 - 60480*a^3*b^7*B*x^8 + 504*A*b^10*x^10 + 5040*a*b^9*B*x^10 + 252*b^10*B*x^11)/(504*x^9) + 5*(2*a*A*b^9 + 9*a^2*b^8*B)*Log[x]","A",1
158,1,243,216,0.1671925,"\int \frac{(a+b x)^{10} (A+B x)}{x^{11}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^11,x]","\frac{-252 a^{10} A-280 a^{10} B x-2800 a^9 A b x-3150 a^9 b B x^2-14175 a^8 A b^2 x^2-16200 a^8 b^2 B x^3-43200 a^7 A b^3 x^3-50400 a^7 b^3 B x^4-88200 a^6 A b^4 x^4-105840 a^6 b^4 B x^5-127008 a^5 A b^5 x^5-158760 a^5 b^5 B x^6-132300 a^4 A b^6 x^6-176400 a^4 b^6 B x^7-100800 a^3 A b^7 x^7-151200 a^3 b^7 B x^8-56700 a^2 A b^8 x^8-113400 a^2 b^8 B x^9-25200 a A b^9 x^9+2520 b^{10} B x^{11}}{2520 x^{10}}+\log (x) \left(10 a b^9 B+A b^{10}\right)","-\frac{a^{10} A}{10 x^{10}}-\frac{a^9 (a B+10 A b)}{9 x^9}-\frac{5 a^8 b (2 a B+9 A b)}{8 x^8}-\frac{15 a^7 b^2 (3 a B+8 A b)}{7 x^7}-\frac{5 a^6 b^3 (4 a B+7 A b)}{x^6}-\frac{42 a^5 b^4 (5 a B+6 A b)}{5 x^5}-\frac{21 a^4 b^5 (6 a B+5 A b)}{2 x^4}-\frac{10 a^3 b^6 (7 a B+4 A b)}{x^3}-\frac{15 a^2 b^7 (8 a B+3 A b)}{2 x^2}+b^9 \log (x) (10 a B+A b)-\frac{5 a b^8 (9 a B+2 A b)}{x}+b^{10} B x",1,"(-252*a^10*A - 2800*a^9*A*b*x - 280*a^10*B*x - 14175*a^8*A*b^2*x^2 - 3150*a^9*b*B*x^2 - 43200*a^7*A*b^3*x^3 - 16200*a^8*b^2*B*x^3 - 88200*a^6*A*b^4*x^4 - 50400*a^7*b^3*B*x^4 - 127008*a^5*A*b^5*x^5 - 105840*a^6*b^4*B*x^5 - 132300*a^4*A*b^6*x^6 - 158760*a^5*b^5*B*x^6 - 100800*a^3*A*b^7*x^7 - 176400*a^4*b^6*B*x^7 - 56700*a^2*A*b^8*x^8 - 151200*a^3*b^7*B*x^8 - 25200*a*A*b^9*x^9 - 113400*a^2*b^8*B*x^9 + 2520*b^10*B*x^11)/(2520*x^10) + (A*b^10 + 10*a*b^9*B)*Log[x]","A",1
159,1,244,153,0.1797422,"\int \frac{(a+b x)^{10} (A+B x)}{x^{12}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^12,x]","\frac{-2520 a^{10} A-2772 a^{10} B x-27720 a^9 A b x-30800 a^9 b B x^2-138600 a^8 A b^2 x^2-155925 a^8 b^2 B x^3-415800 a^7 A b^3 x^3-475200 a^7 b^3 B x^4-831600 a^6 A b^4 x^4-970200 a^6 b^4 B x^5-1164240 a^5 A b^5 x^5-1397088 a^5 b^5 B x^6-1164240 a^4 A b^6 x^6-1455300 a^4 b^6 B x^7-831600 a^3 A b^7 x^7-1108800 a^3 b^7 B x^8-415800 a^2 A b^8 x^8-623700 a^2 b^8 B x^9-138600 a A b^9 x^9-277200 a b^9 B x^{10}-27720 A b^{10} x^{10}}{27720 x^{11}}+b^{10} B \log (x)","-\frac{a^{10} B}{10 x^{10}}-\frac{10 a^9 b B}{9 x^9}-\frac{45 a^8 b^2 B}{8 x^8}-\frac{120 a^7 b^3 B}{7 x^7}-\frac{35 a^6 b^4 B}{x^6}-\frac{252 a^5 b^5 B}{5 x^5}-\frac{105 a^4 b^6 B}{2 x^4}-\frac{40 a^3 b^7 B}{x^3}-\frac{45 a^2 b^8 B}{2 x^2}-\frac{A (a+b x)^{11}}{11 a x^{11}}-\frac{10 a b^9 B}{x}+b^{10} B \log (x)",1,"(-2520*a^10*A - 27720*a^9*A*b*x - 2772*a^10*B*x - 138600*a^8*A*b^2*x^2 - 30800*a^9*b*B*x^2 - 415800*a^7*A*b^3*x^3 - 155925*a^8*b^2*B*x^3 - 831600*a^6*A*b^4*x^4 - 475200*a^7*b^3*B*x^4 - 1164240*a^5*A*b^5*x^5 - 970200*a^6*b^4*B*x^5 - 1164240*a^4*A*b^6*x^6 - 1397088*a^5*b^5*B*x^6 - 831600*a^3*A*b^7*x^7 - 1455300*a^4*b^6*B*x^7 - 415800*a^2*A*b^8*x^8 - 1108800*a^3*b^7*B*x^8 - 138600*a*A*b^9*x^9 - 623700*a^2*b^8*B*x^9 - 27720*A*b^10*x^10 - 277200*a*b^9*B*x^10)/(27720*x^11) + b^10*B*Log[x]","A",1
160,1,245,44,0.0772357,"\int \frac{(a+b x)^{10} (A+B x)}{x^{13}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^13,x]","\frac{-11 a^{10} A-12 a^{10} B x-120 a^9 A b x-132 a^9 b B x^2-594 a^8 A b^2 x^2-660 a^8 b^2 B x^3-1760 a^7 A b^3 x^3-1980 a^7 b^3 B x^4-3465 a^6 A b^4 x^4-3960 a^6 b^4 B x^5-4752 a^5 A b^5 x^5-5544 a^5 b^5 B x^6-4620 a^4 A b^6 x^6-5544 a^4 b^6 B x^7-3168 a^3 A b^7 x^7-3960 a^3 b^7 B x^8-1485 a^2 A b^8 x^8-1980 a^2 b^8 B x^9-440 a A b^9 x^9-660 a b^9 B x^{10}-66 A b^{10} x^{10}-132 b^{10} B x^{11}}{132 x^{12}}","\frac{(a+b x)^{11} (A b-12 a B)}{132 a^2 x^{11}}-\frac{A (a+b x)^{11}}{12 a x^{12}}",1,"(-11*a^10*A - 120*a^9*A*b*x - 12*a^10*B*x - 594*a^8*A*b^2*x^2 - 132*a^9*b*B*x^2 - 1760*a^7*A*b^3*x^3 - 660*a^8*b^2*B*x^3 - 3465*a^6*A*b^4*x^4 - 1980*a^7*b^3*B*x^4 - 4752*a^5*A*b^5*x^5 - 3960*a^6*b^4*B*x^5 - 4620*a^4*A*b^6*x^6 - 5544*a^5*b^5*B*x^6 - 3168*a^3*A*b^7*x^7 - 5544*a^4*b^6*B*x^7 - 1485*a^2*A*b^8*x^8 - 3960*a^3*b^7*B*x^8 - 440*a*A*b^9*x^9 - 1980*a^2*b^8*B*x^9 - 66*A*b^10*x^10 - 660*a*b^9*B*x^10 - 132*b^10*B*x^11)/(132*x^12)","B",1
161,1,245,72,0.0768104,"\int \frac{(a+b x)^{10} (A+B x)}{x^{14}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^14,x]","\frac{-132 a^{10} A-143 a^{10} B x-1430 a^9 A b x-1560 a^9 b B x^2-7020 a^8 A b^2 x^2-7722 a^8 b^2 B x^3-20592 a^7 A b^3 x^3-22880 a^7 b^3 B x^4-40040 a^6 A b^4 x^4-45045 a^6 b^4 B x^5-54054 a^5 A b^5 x^5-61776 a^5 b^5 B x^6-51480 a^4 A b^6 x^6-60060 a^4 b^6 B x^7-34320 a^3 A b^7 x^7-41184 a^3 b^7 B x^8-15444 a^2 A b^8 x^8-19305 a^2 b^8 B x^9-4290 a A b^9 x^9-5720 a b^9 B x^{10}-572 A b^{10} x^{10}-858 b^{10} B x^{11}}{1716 x^{13}}","-\frac{b (a+b x)^{11} (2 A b-13 a B)}{1716 a^3 x^{11}}+\frac{(a+b x)^{11} (2 A b-13 a B)}{156 a^2 x^{12}}-\frac{A (a+b x)^{11}}{13 a x^{13}}",1,"(-132*a^10*A - 1430*a^9*A*b*x - 143*a^10*B*x - 7020*a^8*A*b^2*x^2 - 1560*a^9*b*B*x^2 - 20592*a^7*A*b^3*x^3 - 7722*a^8*b^2*B*x^3 - 40040*a^6*A*b^4*x^4 - 22880*a^7*b^3*B*x^4 - 54054*a^5*A*b^5*x^5 - 45045*a^6*b^4*B*x^5 - 51480*a^4*A*b^6*x^6 - 61776*a^5*b^5*B*x^6 - 34320*a^3*A*b^7*x^7 - 60060*a^4*b^6*B*x^7 - 15444*a^2*A*b^8*x^8 - 41184*a^3*b^7*B*x^8 - 4290*a*A*b^9*x^9 - 19305*a^2*b^8*B*x^9 - 572*A*b^10*x^10 - 5720*a*b^9*B*x^10 - 858*b^10*B*x^11)/(1716*x^13)","B",1
162,1,245,101,0.0767482,"\int \frac{(a+b x)^{10} (A+B x)}{x^{15}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^15,x]","\frac{-858 a^{10} A-924 a^{10} B x-9240 a^9 A b x-10010 a^9 b B x^2-45045 a^8 A b^2 x^2-49140 a^8 b^2 B x^3-131040 a^7 A b^3 x^3-144144 a^7 b^3 B x^4-252252 a^6 A b^4 x^4-280280 a^6 b^4 B x^5-336336 a^5 A b^5 x^5-378378 a^5 b^5 B x^6-315315 a^4 A b^6 x^6-360360 a^4 b^6 B x^7-205920 a^3 A b^7 x^7-240240 a^3 b^7 B x^8-90090 a^2 A b^8 x^8-108108 a^2 b^8 B x^9-24024 a A b^9 x^9-30030 a b^9 B x^{10}-3003 A b^{10} x^{10}-4004 b^{10} B x^{11}}{12012 x^{14}}","\frac{b^2 (a+b x)^{11} (3 A b-14 a B)}{12012 a^4 x^{11}}-\frac{b (a+b x)^{11} (3 A b-14 a B)}{1092 a^3 x^{12}}+\frac{(a+b x)^{11} (3 A b-14 a B)}{182 a^2 x^{13}}-\frac{A (a+b x)^{11}}{14 a x^{14}}",1,"(-858*a^10*A - 9240*a^9*A*b*x - 924*a^10*B*x - 45045*a^8*A*b^2*x^2 - 10010*a^9*b*B*x^2 - 131040*a^7*A*b^3*x^3 - 49140*a^8*b^2*B*x^3 - 252252*a^6*A*b^4*x^4 - 144144*a^7*b^3*B*x^4 - 336336*a^5*A*b^5*x^5 - 280280*a^6*b^4*B*x^5 - 315315*a^4*A*b^6*x^6 - 378378*a^5*b^5*B*x^6 - 205920*a^3*A*b^7*x^7 - 360360*a^4*b^6*B*x^7 - 90090*a^2*A*b^8*x^8 - 240240*a^3*b^7*B*x^8 - 24024*a*A*b^9*x^9 - 108108*a^2*b^8*B*x^9 - 3003*A*b^10*x^10 - 30030*a*b^9*B*x^10 - 4004*b^10*B*x^11)/(12012*x^14)","B",1
163,1,245,130,0.0766419,"\int \frac{(a+b x)^{10} (A+B x)}{x^{16}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^16,x]","\frac{-4004 a^{10} A-4290 a^{10} B x-42900 a^9 A b x-46200 a^9 b B x^2-207900 a^8 A b^2 x^2-225225 a^8 b^2 B x^3-600600 a^7 A b^3 x^3-655200 a^7 b^3 B x^4-1146600 a^6 A b^4 x^4-1261260 a^6 b^4 B x^5-1513512 a^5 A b^5 x^5-1681680 a^5 b^5 B x^6-1401400 a^4 A b^6 x^6-1576575 a^4 b^6 B x^7-900900 a^3 A b^7 x^7-1029600 a^3 b^7 B x^8-386100 a^2 A b^8 x^8-450450 a^2 b^8 B x^9-100100 a A b^9 x^9-120120 a b^9 B x^{10}-12012 A b^{10} x^{10}-15015 b^{10} B x^{11}}{60060 x^{15}}","-\frac{b^3 (a+b x)^{11} (4 A b-15 a B)}{60060 a^5 x^{11}}+\frac{b^2 (a+b x)^{11} (4 A b-15 a B)}{5460 a^4 x^{12}}-\frac{b (a+b x)^{11} (4 A b-15 a B)}{910 a^3 x^{13}}+\frac{(a+b x)^{11} (4 A b-15 a B)}{210 a^2 x^{14}}-\frac{A (a+b x)^{11}}{15 a x^{15}}",1,"(-4004*a^10*A - 42900*a^9*A*b*x - 4290*a^10*B*x - 207900*a^8*A*b^2*x^2 - 46200*a^9*b*B*x^2 - 600600*a^7*A*b^3*x^3 - 225225*a^8*b^2*B*x^3 - 1146600*a^6*A*b^4*x^4 - 655200*a^7*b^3*B*x^4 - 1513512*a^5*A*b^5*x^5 - 1261260*a^6*b^4*B*x^5 - 1401400*a^4*A*b^6*x^6 - 1681680*a^5*b^5*B*x^6 - 900900*a^3*A*b^7*x^7 - 1576575*a^4*b^6*B*x^7 - 386100*a^2*A*b^8*x^8 - 1029600*a^3*b^7*B*x^8 - 100100*a*A*b^9*x^9 - 450450*a^2*b^8*B*x^9 - 12012*A*b^10*x^10 - 120120*a*b^9*B*x^10 - 15015*b^10*B*x^11)/(60060*x^15)","A",1
164,1,245,159,0.0970636,"\int \frac{(a+b x)^{10} (A+B x)}{x^{17}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^17,x]","\frac{-15015 a^{10} A-16016 a^{10} B x-160160 a^9 A b x-171600 a^9 b B x^2-772200 a^8 A b^2 x^2-831600 a^8 b^2 B x^3-2217600 a^7 A b^3 x^3-2402400 a^7 b^3 B x^4-4204200 a^6 A b^4 x^4-4586400 a^6 b^4 B x^5-5503680 a^5 A b^5 x^5-6054048 a^5 b^5 B x^6-5045040 a^4 A b^6 x^6-5605600 a^4 b^6 B x^7-3203200 a^3 A b^7 x^7-3603600 a^3 b^7 B x^8-1351350 a^2 A b^8 x^8-1544400 a^2 b^8 B x^9-343200 a A b^9 x^9-400400 a b^9 B x^{10}-40040 A b^{10} x^{10}-48048 b^{10} B x^{11}}{240240 x^{16}}","\frac{b^4 (a+b x)^{11} (5 A b-16 a B)}{240240 a^6 x^{11}}-\frac{b^3 (a+b x)^{11} (5 A b-16 a B)}{21840 a^5 x^{12}}+\frac{b^2 (a+b x)^{11} (5 A b-16 a B)}{3640 a^4 x^{13}}-\frac{b (a+b x)^{11} (5 A b-16 a B)}{840 a^3 x^{14}}+\frac{(a+b x)^{11} (5 A b-16 a B)}{240 a^2 x^{15}}-\frac{A (a+b x)^{11}}{16 a x^{16}}",1,"(-15015*a^10*A - 160160*a^9*A*b*x - 16016*a^10*B*x - 772200*a^8*A*b^2*x^2 - 171600*a^9*b*B*x^2 - 2217600*a^7*A*b^3*x^3 - 831600*a^8*b^2*B*x^3 - 4204200*a^6*A*b^4*x^4 - 2402400*a^7*b^3*B*x^4 - 5503680*a^5*A*b^5*x^5 - 4586400*a^6*b^4*B*x^5 - 5045040*a^4*A*b^6*x^6 - 6054048*a^5*b^5*B*x^6 - 3203200*a^3*A*b^7*x^7 - 5605600*a^4*b^6*B*x^7 - 1351350*a^2*A*b^8*x^8 - 3603600*a^3*b^7*B*x^8 - 343200*a*A*b^9*x^9 - 1544400*a^2*b^8*B*x^9 - 40040*A*b^10*x^10 - 400400*a*b^9*B*x^10 - 48048*b^10*B*x^11)/(240240*x^16)","A",1
165,1,245,188,0.0926854,"\int \frac{(a+b x)^{10} (A+B x)}{x^{18}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^18,x]","\frac{-48048 a^{10} A-51051 a^{10} B x-510510 a^9 A b x-544544 a^9 b B x^2-2450448 a^8 A b^2 x^2-2625480 a^8 b^2 B x^3-7001280 a^7 A b^3 x^3-7539840 a^7 b^3 B x^4-13194720 a^6 A b^4 x^4-14294280 a^6 b^4 B x^5-17153136 a^5 A b^5 x^5-18712512 a^5 b^5 B x^6-15593760 a^4 A b^6 x^6-17153136 a^4 b^6 B x^7-9801792 a^3 A b^7 x^7-10890880 a^3 b^7 B x^8-4084080 a^2 A b^8 x^8-4594590 a^2 b^8 B x^9-1021020 a A b^9 x^9-1166880 a b^9 B x^{10}-116688 A b^{10} x^{10}-136136 b^{10} B x^{11}}{816816 x^{17}}","-\frac{b^5 (a+b x)^{11} (6 A b-17 a B)}{816816 a^7 x^{11}}+\frac{b^4 (a+b x)^{11} (6 A b-17 a B)}{74256 a^6 x^{12}}-\frac{b^3 (a+b x)^{11} (6 A b-17 a B)}{12376 a^5 x^{13}}+\frac{b^2 (a+b x)^{11} (6 A b-17 a B)}{2856 a^4 x^{14}}-\frac{b (a+b x)^{11} (6 A b-17 a B)}{816 a^3 x^{15}}+\frac{(a+b x)^{11} (6 A b-17 a B)}{272 a^2 x^{16}}-\frac{A (a+b x)^{11}}{17 a x^{17}}",1,"(-48048*a^10*A - 510510*a^9*A*b*x - 51051*a^10*B*x - 2450448*a^8*A*b^2*x^2 - 544544*a^9*b*B*x^2 - 7001280*a^7*A*b^3*x^3 - 2625480*a^8*b^2*B*x^3 - 13194720*a^6*A*b^4*x^4 - 7539840*a^7*b^3*B*x^4 - 17153136*a^5*A*b^5*x^5 - 14294280*a^6*b^4*B*x^5 - 15593760*a^4*A*b^6*x^6 - 18712512*a^5*b^5*B*x^6 - 9801792*a^3*A*b^7*x^7 - 17153136*a^4*b^6*B*x^7 - 4084080*a^2*A*b^8*x^8 - 10890880*a^3*b^7*B*x^8 - 1021020*a*A*b^9*x^9 - 4594590*a^2*b^8*B*x^9 - 116688*A*b^10*x^10 - 1166880*a*b^9*B*x^10 - 136136*b^10*B*x^11)/(816816*x^17)","A",1
166,1,245,229,0.0960251,"\int \frac{(a+b x)^{10} (A+B x)}{x^{19}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^19,x]","\frac{-136136 a^{10} A-144144 a^{10} B x-1441440 a^9 A b x-1531530 a^9 b B x^2-6891885 a^8 A b^2 x^2-7351344 a^8 b^2 B x^3-19603584 a^7 A b^3 x^3-21003840 a^7 b^3 B x^4-36756720 a^6 A b^4 x^4-39584160 a^6 b^4 B x^5-47500992 a^5 A b^5 x^5-51459408 a^5 b^5 B x^6-42882840 a^4 A b^6 x^6-46781280 a^4 b^6 B x^7-26732160 a^3 A b^7 x^7-29405376 a^3 b^7 B x^8-11027016 a^2 A b^8 x^8-12252240 a^2 b^8 B x^9-2722720 a A b^9 x^9-3063060 a b^9 B x^{10}-306306 A b^{10} x^{10}-350064 b^{10} B x^{11}}{2450448 x^{18}}","-\frac{a^{10} A}{18 x^{18}}-\frac{a^9 (a B+10 A b)}{17 x^{17}}-\frac{5 a^8 b (2 a B+9 A b)}{16 x^{16}}-\frac{a^7 b^2 (3 a B+8 A b)}{x^{15}}-\frac{15 a^6 b^3 (4 a B+7 A b)}{7 x^{14}}-\frac{42 a^5 b^4 (5 a B+6 A b)}{13 x^{13}}-\frac{7 a^4 b^5 (6 a B+5 A b)}{2 x^{12}}-\frac{30 a^3 b^6 (7 a B+4 A b)}{11 x^{11}}-\frac{3 a^2 b^7 (8 a B+3 A b)}{2 x^{10}}-\frac{b^9 (10 a B+A b)}{8 x^8}-\frac{5 a b^8 (9 a B+2 A b)}{9 x^9}-\frac{b^{10} B}{7 x^7}",1,"(-136136*a^10*A - 1441440*a^9*A*b*x - 144144*a^10*B*x - 6891885*a^8*A*b^2*x^2 - 1531530*a^9*b*B*x^2 - 19603584*a^7*A*b^3*x^3 - 7351344*a^8*b^2*B*x^3 - 36756720*a^6*A*b^4*x^4 - 21003840*a^7*b^3*B*x^4 - 47500992*a^5*A*b^5*x^5 - 39584160*a^6*b^4*B*x^5 - 42882840*a^4*A*b^6*x^6 - 51459408*a^5*b^5*B*x^6 - 26732160*a^3*A*b^7*x^7 - 46781280*a^4*b^6*B*x^7 - 11027016*a^2*A*b^8*x^8 - 29405376*a^3*b^7*B*x^8 - 2722720*a*A*b^9*x^9 - 12252240*a^2*b^8*B*x^9 - 306306*A*b^10*x^10 - 3063060*a*b^9*B*x^10 - 350064*b^10*B*x^11)/(2450448*x^18)","A",1
167,1,245,227,0.0951779,"\int \frac{(a+b x)^{10} (A+B x)}{x^{20}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^20,x]","\frac{-350064 a^{10} A-369512 a^{10} B x-3695120 a^9 A b x-3912480 a^9 b B x^2-17606160 a^8 A b^2 x^2-18706545 a^8 b^2 B x^3-49884120 a^7 A b^3 x^3-53209728 a^7 b^3 B x^4-93117024 a^6 A b^4 x^4-99768240 a^6 b^4 B x^5-119721888 a^5 A b^5 x^5-128931264 a^5 b^5 B x^6-107442720 a^4 A b^6 x^6-116396280 a^4 b^6 B x^7-66512160 a^3 A b^7 x^7-72558720 a^3 b^7 B x^8-27209520 a^2 A b^8 x^8-29930472 a^2 b^8 B x^9-6651216 a A b^9 x^9-7390240 a b^9 B x^{10}-739024 A b^{10} x^{10}-831402 b^{10} B x^{11}}{6651216 x^{19}}","-\frac{a^{10} A}{19 x^{19}}-\frac{a^9 (a B+10 A b)}{18 x^{18}}-\frac{5 a^8 b (2 a B+9 A b)}{17 x^{17}}-\frac{15 a^7 b^2 (3 a B+8 A b)}{16 x^{16}}-\frac{2 a^6 b^3 (4 a B+7 A b)}{x^{15}}-\frac{3 a^5 b^4 (5 a B+6 A b)}{x^{14}}-\frac{42 a^4 b^5 (6 a B+5 A b)}{13 x^{13}}-\frac{5 a^3 b^6 (7 a B+4 A b)}{2 x^{12}}-\frac{15 a^2 b^7 (8 a B+3 A b)}{11 x^{11}}-\frac{b^9 (10 a B+A b)}{9 x^9}-\frac{a b^8 (9 a B+2 A b)}{2 x^{10}}-\frac{b^{10} B}{8 x^8}",1,"(-350064*a^10*A - 3695120*a^9*A*b*x - 369512*a^10*B*x - 17606160*a^8*A*b^2*x^2 - 3912480*a^9*b*B*x^2 - 49884120*a^7*A*b^3*x^3 - 18706545*a^8*b^2*B*x^3 - 93117024*a^6*A*b^4*x^4 - 53209728*a^7*b^3*B*x^4 - 119721888*a^5*A*b^5*x^5 - 99768240*a^6*b^4*B*x^5 - 107442720*a^4*A*b^6*x^6 - 128931264*a^5*b^5*B*x^6 - 66512160*a^3*A*b^7*x^7 - 116396280*a^4*b^6*B*x^7 - 27209520*a^2*A*b^8*x^8 - 72558720*a^3*b^7*B*x^8 - 6651216*a*A*b^9*x^9 - 29930472*a^2*b^8*B*x^9 - 739024*A*b^10*x^10 - 7390240*a*b^9*B*x^10 - 831402*b^10*B*x^11)/(6651216*x^19)","A",1
168,1,245,229,0.0966834,"\int \frac{(a+b x)^{10} (A+B x)}{x^{21}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/x^21,x]","\frac{-831402 a^{10} A-875160 a^{10} B x-8751600 a^9 A b x-9237800 a^9 b B x^2-41570100 a^8 A b^2 x^2-44015400 a^8 b^2 B x^3-117374400 a^7 A b^3 x^3-124710300 a^7 b^3 B x^4-218243025 a^6 A b^4 x^4-232792560 a^6 b^4 B x^5-279351072 a^5 A b^5 x^5-299304720 a^5 b^5 B x^6-249420600 a^4 A b^6 x^6-268606800 a^4 b^6 B x^7-153489600 a^3 A b^7 x^7-166280400 a^3 b^7 B x^8-62355150 a^2 A b^8 x^8-68023800 a^2 b^8 B x^9-15116400 a A b^9 x^9-16628040 a b^9 B x^{10}-1662804 A b^{10} x^{10}-1847560 b^{10} B x^{11}}{16628040 x^{20}}","-\frac{a^{10} A}{20 x^{20}}-\frac{a^9 (a B+10 A b)}{19 x^{19}}-\frac{5 a^8 b (2 a B+9 A b)}{18 x^{18}}-\frac{15 a^7 b^2 (3 a B+8 A b)}{17 x^{17}}-\frac{15 a^6 b^3 (4 a B+7 A b)}{8 x^{16}}-\frac{14 a^5 b^4 (5 a B+6 A b)}{5 x^{15}}-\frac{3 a^4 b^5 (6 a B+5 A b)}{x^{14}}-\frac{30 a^3 b^6 (7 a B+4 A b)}{13 x^{13}}-\frac{5 a^2 b^7 (8 a B+3 A b)}{4 x^{12}}-\frac{b^9 (10 a B+A b)}{10 x^{10}}-\frac{5 a b^8 (9 a B+2 A b)}{11 x^{11}}-\frac{b^{10} B}{9 x^9}",1,"(-831402*a^10*A - 8751600*a^9*A*b*x - 875160*a^10*B*x - 41570100*a^8*A*b^2*x^2 - 9237800*a^9*b*B*x^2 - 117374400*a^7*A*b^3*x^3 - 44015400*a^8*b^2*B*x^3 - 218243025*a^6*A*b^4*x^4 - 124710300*a^7*b^3*B*x^4 - 279351072*a^5*A*b^5*x^5 - 232792560*a^6*b^4*B*x^5 - 249420600*a^4*A*b^6*x^6 - 299304720*a^5*b^5*B*x^6 - 153489600*a^3*A*b^7*x^7 - 268606800*a^4*b^6*B*x^7 - 62355150*a^2*A*b^8*x^8 - 166280400*a^3*b^7*B*x^8 - 15116400*a*A*b^9*x^9 - 68023800*a^2*b^8*B*x^9 - 1662804*A*b^10*x^10 - 16628040*a*b^9*B*x^10 - 1847560*b^10*B*x^11)/(16628040*x^20)","A",1
169,1,393,114,0.1898717,"\int x^3 (a+b x) (c+d x)^{16} \, dx","IntegrateAlgebraic[x^3*(a + b*x)*(c + d*x)^16,x]","\frac{101745 a c^{16} x^4+1302336 a c^{15} d x^5+8139600 a c^{14} d^2 x^6+32558400 a c^{13} d^3 x^7+92587950 a c^{12} d^4 x^8+197520960 a c^{11} d^5 x^9+325909584 a c^{10} d^6 x^{10}+423259200 a c^9 d^7 x^{11}+436486050 a c^8 d^8 x^{12}+358142400 a c^7 d^9 x^{13}+232792560 a c^6 d^{10} x^{14}+118512576 a c^5 d^{11} x^{15}+46293975 a c^4 d^{12} x^{16}+13406400 a c^3 d^{13} x^{17}+2713200 a c^2 d^{14} x^{18}+342720 a c d^{15} x^{19}+20349 a d^{16} x^{20}+81396 b c^{16} x^5+1085280 b c^{15} d x^6+6976800 b c^{14} d^2 x^7+28488600 b c^{13} d^3 x^8+82300400 b c^{12} d^4 x^9+177768864 b c^{11} d^5 x^{10}+296281440 b c^{10} d^6 x^{11}+387987600 b c^9 d^7 x^{12}+402910200 b c^8 d^8 x^{13}+332560800 b c^7 d^9 x^{14}+217273056 b c^6 d^{10} x^{15}+111105540 b c^5 d^{11} x^{16}+43570800 b c^4 d^{12} x^{17}+12661600 b c^3 d^{13} x^{18}+2570400 b c^2 d^{14} x^{19}+325584 b c d^{15} x^{20}+19380 b d^{16} x^{21}}{406980}","\frac{c^3 (c+d x)^{17} (b c-a d)}{17 d^5}-\frac{c^2 (c+d x)^{18} (4 b c-3 a d)}{18 d^5}-\frac{(c+d x)^{20} (4 b c-a d)}{20 d^5}+\frac{3 c (c+d x)^{19} (2 b c-a d)}{19 d^5}+\frac{b (c+d x)^{21}}{21 d^5}",1,"(101745*a*c^16*x^4 + 81396*b*c^16*x^5 + 1302336*a*c^15*d*x^5 + 1085280*b*c^15*d*x^6 + 8139600*a*c^14*d^2*x^6 + 6976800*b*c^14*d^2*x^7 + 32558400*a*c^13*d^3*x^7 + 28488600*b*c^13*d^3*x^8 + 92587950*a*c^12*d^4*x^8 + 82300400*b*c^12*d^4*x^9 + 197520960*a*c^11*d^5*x^9 + 177768864*b*c^11*d^5*x^10 + 325909584*a*c^10*d^6*x^10 + 296281440*b*c^10*d^6*x^11 + 423259200*a*c^9*d^7*x^11 + 387987600*b*c^9*d^7*x^12 + 436486050*a*c^8*d^8*x^12 + 402910200*b*c^8*d^8*x^13 + 358142400*a*c^7*d^9*x^13 + 332560800*b*c^7*d^9*x^14 + 232792560*a*c^6*d^10*x^14 + 217273056*b*c^6*d^10*x^15 + 118512576*a*c^5*d^11*x^15 + 111105540*b*c^5*d^11*x^16 + 46293975*a*c^4*d^12*x^16 + 43570800*b*c^4*d^12*x^17 + 13406400*a*c^3*d^13*x^17 + 12661600*b*c^3*d^13*x^18 + 2713200*a*c^2*d^14*x^18 + 2570400*b*c^2*d^14*x^19 + 342720*a*c*d^15*x^19 + 325584*b*c*d^15*x^20 + 20349*a*d^16*x^20 + 19380*b*d^16*x^21)/406980","B",1
170,1,393,88,0.1565217,"\int x^2 (a+b x) (c+d x)^{16} \, dx","IntegrateAlgebraic[x^2*(a + b*x)*(c + d*x)^16,x]","\frac{19380 a c^{16} x^3+232560 a c^{15} d x^4+1395360 a c^{14} d^2 x^5+5426400 a c^{13} d^3 x^6+15116400 a c^{12} d^4 x^7+31744440 a c^{11} d^5 x^8+51731680 a c^{10} d^6 x^9+66512160 a c^9 d^7 x^{10}+68023800 a c^8 d^8 x^{11}+55426800 a c^7 d^9 x^{12}+35814240 a c^6 d^{10} x^{13}+18139680 a c^5 d^{11} x^{14}+7054320 a c^4 d^{12} x^{15}+2034900 a c^3 d^{13} x^{16}+410400 a c^2 d^{14} x^{17}+51680 a c d^{15} x^{18}+3060 a d^{16} x^{19}+14535 b c^{16} x^4+186048 b c^{15} d x^5+1162800 b c^{14} d^2 x^6+4651200 b c^{13} d^3 x^7+13226850 b c^{12} d^4 x^8+28217280 b c^{11} d^5 x^9+46558512 b c^{10} d^6 x^{10}+60465600 b c^9 d^7 x^{11}+62355150 b c^8 d^8 x^{12}+51163200 b c^7 d^9 x^{13}+33256080 b c^6 d^{10} x^{14}+16930368 b c^5 d^{11} x^{15}+6613425 b c^4 d^{12} x^{16}+1915200 b c^3 d^{13} x^{17}+387600 b c^2 d^{14} x^{18}+48960 b c d^{15} x^{19}+2907 b d^{16} x^{20}}{58140}","-\frac{c^2 (c+d x)^{17} (b c-a d)}{17 d^4}-\frac{(c+d x)^{19} (3 b c-a d)}{19 d^4}+\frac{c (c+d x)^{18} (3 b c-2 a d)}{18 d^4}+\frac{b (c+d x)^{20}}{20 d^4}",1,"(19380*a*c^16*x^3 + 14535*b*c^16*x^4 + 232560*a*c^15*d*x^4 + 186048*b*c^15*d*x^5 + 1395360*a*c^14*d^2*x^5 + 1162800*b*c^14*d^2*x^6 + 5426400*a*c^13*d^3*x^6 + 4651200*b*c^13*d^3*x^7 + 15116400*a*c^12*d^4*x^7 + 13226850*b*c^12*d^4*x^8 + 31744440*a*c^11*d^5*x^8 + 28217280*b*c^11*d^5*x^9 + 51731680*a*c^10*d^6*x^9 + 46558512*b*c^10*d^6*x^10 + 66512160*a*c^9*d^7*x^10 + 60465600*b*c^9*d^7*x^11 + 68023800*a*c^8*d^8*x^11 + 62355150*b*c^8*d^8*x^12 + 55426800*a*c^7*d^9*x^12 + 51163200*b*c^7*d^9*x^13 + 35814240*a*c^6*d^10*x^13 + 33256080*b*c^6*d^10*x^14 + 18139680*a*c^5*d^11*x^14 + 16930368*b*c^5*d^11*x^15 + 7054320*a*c^4*d^12*x^15 + 6613425*b*c^4*d^12*x^16 + 2034900*a*c^3*d^13*x^16 + 1915200*b*c^3*d^13*x^17 + 410400*a*c^2*d^14*x^17 + 387600*b*c^2*d^14*x^18 + 51680*a*c*d^15*x^18 + 48960*b*c*d^15*x^19 + 3060*a*d^16*x^19 + 2907*b*d^16*x^20)/58140","B",1
171,1,393,62,0.1523022,"\int x (a+b x) (c+d x)^{16} \, dx","IntegrateAlgebraic[x*(a + b*x)*(c + d*x)^16,x]","\frac{2907 a c^{16} x^2+31008 a c^{15} d x^3+174420 a c^{14} d^2 x^4+651168 a c^{13} d^3 x^5+1763580 a c^{12} d^4 x^6+3627936 a c^{11} d^5 x^7+5819814 a c^{10} d^6 x^8+7390240 a c^9 d^7 x^9+7482618 a c^8 d^8 x^{10}+6046560 a c^7 d^9 x^{11}+3879876 a c^6 d^{10} x^{12}+1953504 a c^5 d^{11} x^{13}+755820 a c^4 d^{12} x^{14}+217056 a c^3 d^{13} x^{15}+43605 a c^2 d^{14} x^{16}+5472 a c d^{15} x^{17}+323 a d^{16} x^{18}+1938 b c^{16} x^3+23256 b c^{15} d x^4+139536 b c^{14} d^2 x^5+542640 b c^{13} d^3 x^6+1511640 b c^{12} d^4 x^7+3174444 b c^{11} d^5 x^8+5173168 b c^{10} d^6 x^9+6651216 b c^9 d^7 x^{10}+6802380 b c^8 d^8 x^{11}+5542680 b c^7 d^9 x^{12}+3581424 b c^6 d^{10} x^{13}+1813968 b c^5 d^{11} x^{14}+705432 b c^4 d^{12} x^{15}+203490 b c^3 d^{13} x^{16}+41040 b c^2 d^{14} x^{17}+5168 b c d^{15} x^{18}+306 b d^{16} x^{19}}{5814}","-\frac{(c+d x)^{18} (2 b c-a d)}{18 d^3}+\frac{c (c+d x)^{17} (b c-a d)}{17 d^3}+\frac{b (c+d x)^{19}}{19 d^3}",1,"(2907*a*c^16*x^2 + 1938*b*c^16*x^3 + 31008*a*c^15*d*x^3 + 23256*b*c^15*d*x^4 + 174420*a*c^14*d^2*x^4 + 139536*b*c^14*d^2*x^5 + 651168*a*c^13*d^3*x^5 + 542640*b*c^13*d^3*x^6 + 1763580*a*c^12*d^4*x^6 + 1511640*b*c^12*d^4*x^7 + 3627936*a*c^11*d^5*x^7 + 3174444*b*c^11*d^5*x^8 + 5819814*a*c^10*d^6*x^8 + 5173168*b*c^10*d^6*x^9 + 7390240*a*c^9*d^7*x^9 + 6651216*b*c^9*d^7*x^10 + 7482618*a*c^8*d^8*x^10 + 6802380*b*c^8*d^8*x^11 + 6046560*a*c^7*d^9*x^11 + 5542680*b*c^7*d^9*x^12 + 3879876*a*c^6*d^10*x^12 + 3581424*b*c^6*d^10*x^13 + 1953504*a*c^5*d^11*x^13 + 1813968*b*c^5*d^11*x^14 + 755820*a*c^4*d^12*x^14 + 705432*b*c^4*d^12*x^15 + 217056*a*c^3*d^13*x^15 + 203490*b*c^3*d^13*x^16 + 43605*a*c^2*d^14*x^16 + 41040*b*c^2*d^14*x^17 + 5472*a*c*d^15*x^17 + 5168*b*c*d^15*x^18 + 323*a*d^16*x^18 + 306*b*d^16*x^19)/5814","B",1
172,1,391,38,0.1400732,"\int (a+b x) (c+d x)^{16} \, dx","IntegrateAlgebraic[(a + b*x)*(c + d*x)^16,x]","\frac{1}{306} \left(306 a c^{16} x+2448 a c^{15} d x^2+12240 a c^{14} d^2 x^3+42840 a c^{13} d^3 x^4+111384 a c^{12} d^4 x^5+222768 a c^{11} d^5 x^6+350064 a c^{10} d^6 x^7+437580 a c^9 d^7 x^8+437580 a c^8 d^8 x^9+350064 a c^7 d^9 x^{10}+222768 a c^6 d^{10} x^{11}+111384 a c^5 d^{11} x^{12}+42840 a c^4 d^{12} x^{13}+12240 a c^3 d^{13} x^{14}+2448 a c^2 d^{14} x^{15}+306 a c d^{15} x^{16}+18 a d^{16} x^{17}+153 b c^{16} x^2+1632 b c^{15} d x^3+9180 b c^{14} d^2 x^4+34272 b c^{13} d^3 x^5+92820 b c^{12} d^4 x^6+190944 b c^{11} d^5 x^7+306306 b c^{10} d^6 x^8+388960 b c^9 d^7 x^9+393822 b c^8 d^8 x^{10}+318240 b c^7 d^9 x^{11}+204204 b c^6 d^{10} x^{12}+102816 b c^5 d^{11} x^{13}+39780 b c^4 d^{12} x^{14}+11424 b c^3 d^{13} x^{15}+2295 b c^2 d^{14} x^{16}+288 b c d^{15} x^{17}+17 b d^{16} x^{18}\right)","\frac{b (c+d x)^{18}}{18 d^2}-\frac{(c+d x)^{17} (b c-a d)}{17 d^2}",1,"(306*a*c^16*x + 153*b*c^16*x^2 + 2448*a*c^15*d*x^2 + 1632*b*c^15*d*x^3 + 12240*a*c^14*d^2*x^3 + 9180*b*c^14*d^2*x^4 + 42840*a*c^13*d^3*x^4 + 34272*b*c^13*d^3*x^5 + 111384*a*c^12*d^4*x^5 + 92820*b*c^12*d^4*x^6 + 222768*a*c^11*d^5*x^6 + 190944*b*c^11*d^5*x^7 + 350064*a*c^10*d^6*x^7 + 306306*b*c^10*d^6*x^8 + 437580*a*c^9*d^7*x^8 + 388960*b*c^9*d^7*x^9 + 437580*a*c^8*d^8*x^9 + 393822*b*c^8*d^8*x^10 + 350064*a*c^7*d^9*x^10 + 318240*b*c^7*d^9*x^11 + 222768*a*c^6*d^10*x^11 + 204204*b*c^6*d^10*x^12 + 111384*a*c^5*d^11*x^12 + 102816*b*c^5*d^11*x^13 + 42840*a*c^4*d^12*x^13 + 39780*b*c^4*d^12*x^14 + 12240*a*c^3*d^13*x^14 + 11424*b*c^3*d^13*x^15 + 2448*a*c^2*d^14*x^15 + 2295*b*c^2*d^14*x^16 + 306*a*c*d^15*x^16 + 288*b*c*d^15*x^17 + 18*a*d^16*x^17 + 17*b*d^16*x^18)/306","B",1
173,1,12,12,0.008231,"\int x^2 (2+x)^5 (2+3 x) \, dx","IntegrateAlgebraic[x^2*(2 + x)^5*(2 + 3*x),x]","\frac{1}{3} x^3 (x+2)^6","\frac{1}{3} x^3 (x+2)^6",1,"(x^3*(2 + x)^6)/3","A",1
174,1,114,108,0.0696116,"\int \frac{x^4 (A+B x)}{a+b x} \, dx","IntegrateAlgebraic[(x^4*(A + B*x))/(a + b*x),x]","\frac{\left(a^4 A b-a^5 B\right) \log (a+b x)}{b^6}+\frac{x \left(60 a^4 B-60 a^3 A b-30 a^3 b B x+30 a^2 A b^2 x+20 a^2 b^2 B x^2-20 a A b^3 x^2-15 a b^3 B x^3+15 A b^4 x^3+12 b^4 B x^4\right)}{60 b^5}","\frac{a^4 (A b-a B) \log (a+b x)}{b^6}-\frac{a^3 x (A b-a B)}{b^5}+\frac{a^2 x^2 (A b-a B)}{2 b^4}-\frac{a x^3 (A b-a B)}{3 b^3}+\frac{x^4 (A b-a B)}{4 b^2}+\frac{B x^5}{5 b}",1,"(x*(-60*a^3*A*b + 60*a^4*B + 30*a^2*A*b^2*x - 30*a^3*b*B*x - 20*a*A*b^3*x^2 + 20*a^2*b^2*B*x^2 + 15*A*b^4*x^3 - 15*a*b^3*B*x^3 + 12*b^4*B*x^4))/(60*b^5) + ((a^4*A*b - a^5*B)*Log[a + b*x])/b^6","A",1
175,1,90,87,0.0500162,"\int \frac{x^3 (A+B x)}{a+b x} \, dx","IntegrateAlgebraic[(x^3*(A + B*x))/(a + b*x),x]","\frac{\left(a^4 B-a^3 A b\right) \log (a+b x)}{b^5}+\frac{x \left(-12 a^3 B+12 a^2 A b+6 a^2 b B x-6 a A b^2 x-4 a b^2 B x^2+4 A b^3 x^2+3 b^3 B x^3\right)}{12 b^4}","-\frac{a^3 (A b-a B) \log (a+b x)}{b^5}+\frac{a^2 x (A b-a B)}{b^4}-\frac{a x^2 (A b-a B)}{2 b^3}+\frac{x^3 (A b-a B)}{3 b^2}+\frac{B x^4}{4 b}",1,"(x*(12*a^2*A*b - 12*a^3*B - 6*a*A*b^2*x + 6*a^2*b*B*x + 4*A*b^3*x^2 - 4*a*b^2*B*x^2 + 3*b^3*B*x^3))/(12*b^4) + ((-(a^3*A*b) + a^4*B)*Log[a + b*x])/b^5","A",1
176,1,66,66,0.0385433,"\int \frac{x^2 (A+B x)}{a+b x} \, dx","IntegrateAlgebraic[(x^2*(A + B*x))/(a + b*x),x]","\frac{x \left(6 a^2 B-6 a A b-3 a b B x+3 A b^2 x+2 b^2 B x^2\right)}{6 b^3}+\frac{\left(a^2 A b-a^3 B\right) \log (a+b x)}{b^4}","\frac{a^2 (A b-a B) \log (a+b x)}{b^4}-\frac{a x (A b-a B)}{b^3}+\frac{x^2 (A b-a B)}{2 b^2}+\frac{B x^3}{3 b}",1,"(x*(-6*a*A*b + 6*a^2*B + 3*A*b^2*x - 3*a*b*B*x + 2*b^2*B*x^2))/(6*b^3) + ((a^2*A*b - a^3*B)*Log[a + b*x])/b^4","A",1
177,1,43,45,0.0250278,"\int \frac{x (A+B x)}{a+b x} \, dx","IntegrateAlgebraic[(x*(A + B*x))/(a + b*x),x]","\frac{\left(a^2 B-a A b\right) \log (a+b x)}{b^3}+\frac{x (-2 a B+2 A b+b B x)}{2 b^2}","-\frac{a (A b-a B) \log (a+b x)}{b^3}+\frac{x (A b-a B)}{b^2}+\frac{B x^2}{2 b}",1,"(x*(2*A*b - 2*a*B + b*B*x))/(2*b^2) + ((-(a*A*b) + a^2*B)*Log[a + b*x])/b^3","A",1
178,1,25,25,0.0143334,"\int \frac{A+B x}{a+b x} \, dx","IntegrateAlgebraic[(A + B*x)/(a + b*x),x]","\frac{(A b-a B) \log (a+b x)}{b^2}+\frac{B x}{b}","\frac{(A b-a B) \log (a+b x)}{b^2}+\frac{B x}{b}",1,"(B*x)/b + ((A*b - a*B)*Log[a + b*x])/b^2","A",1
179,1,29,30,0.0176856,"\int \frac{A+B x}{x (a+b x)} \, dx","IntegrateAlgebraic[(A + B*x)/(x*(a + b*x)),x]","\frac{(a B-A b) \log (a+b x)}{a b}+\frac{A \log (x)}{a}","\frac{A \log (x)}{a}-\frac{(A b-a B) \log (a+b x)}{a b}",1,"(A*Log[x])/a + ((-(A*b) + a*B)*Log[a + b*x])/(a*b)","A",1
180,1,42,43,0.027832,"\int \frac{A+B x}{x^2 (a+b x)} \, dx","IntegrateAlgebraic[(A + B*x)/(x^2*(a + b*x)),x]","\frac{\log (x) (a B-A b)}{a^2}+\frac{(A b-a B) \log (a+b x)}{a^2}-\frac{A}{a x}","-\frac{\log (x) (A b-a B)}{a^2}+\frac{(A b-a B) \log (a+b x)}{a^2}-\frac{A}{a x}",1,"-(A/(a*x)) + ((-(A*b) + a*B)*Log[x])/a^2 + ((A*b - a*B)*Log[a + b*x])/a^2","A",1
181,1,64,62,0.0508927,"\int \frac{A+B x}{x^3 (a+b x)} \, dx","IntegrateAlgebraic[(A + B*x)/(x^3*(a + b*x)),x]","\frac{\log (x) \left(A b^2-a b B\right)}{a^3}+\frac{\left(a b B-A b^2\right) \log (a+b x)}{a^3}+\frac{-a A-2 a B x+2 A b x}{2 a^2 x^2}","\frac{b \log (x) (A b-a B)}{a^3}-\frac{b (A b-a B) \log (a+b x)}{a^3}+\frac{A b-a B}{a^2 x}-\frac{A}{2 a x^2}",1,"(-(a*A) + 2*A*b*x - 2*a*B*x)/(2*a^2*x^2) + ((A*b^2 - a*b*B)*Log[x])/a^3 + ((-(A*b^2) + a*b*B)*Log[a + b*x])/a^3","A",1
182,1,90,86,0.0750656,"\int \frac{A+B x}{x^4 (a+b x)} \, dx","IntegrateAlgebraic[(A + B*x)/(x^4*(a + b*x)),x]","\frac{\log (x) \left(a b^2 B-A b^3\right)}{a^4}+\frac{\left(A b^3-a b^2 B\right) \log (a+b x)}{a^4}+\frac{-2 a^2 A-3 a^2 B x+3 a A b x+6 a b B x^2-6 A b^2 x^2}{6 a^3 x^3}","-\frac{b^2 \log (x) (A b-a B)}{a^4}+\frac{b^2 (A b-a B) \log (a+b x)}{a^4}-\frac{b (A b-a B)}{a^3 x}+\frac{A b-a B}{2 a^2 x^2}-\frac{A}{3 a x^3}",1,"(-2*a^2*A + 3*a*A*b*x - 3*a^2*B*x - 6*A*b^2*x^2 + 6*a*b*B*x^2)/(6*a^3*x^3) + ((-(A*b^3) + a*b^2*B)*Log[x])/a^4 + ((A*b^3 - a*b^2*B)*Log[a + b*x])/a^4","A",1
183,1,114,106,0.0925658,"\int \frac{A+B x}{x^5 (a+b x)} \, dx","IntegrateAlgebraic[(A + B*x)/(x^5*(a + b*x)),x]","\frac{\log (x) \left(A b^4-a b^3 B\right)}{a^5}+\frac{\left(a b^3 B-A b^4\right) \log (a+b x)}{a^5}+\frac{-3 a^3 A-4 a^3 B x+4 a^2 A b x+6 a^2 b B x^2-6 a A b^2 x^2-12 a b^2 B x^3+12 A b^3 x^3}{12 a^4 x^4}","\frac{b^3 \log (x) (A b-a B)}{a^5}-\frac{b^3 (A b-a B) \log (a+b x)}{a^5}+\frac{b^2 (A b-a B)}{a^4 x}-\frac{b (A b-a B)}{2 a^3 x^2}+\frac{A b-a B}{3 a^2 x^3}-\frac{A}{4 a x^4}",1,"(-3*a^3*A + 4*a^2*A*b*x - 4*a^3*B*x - 6*a*A*b^2*x^2 + 6*a^2*b*B*x^2 + 12*A*b^3*x^3 - 12*a*b^2*B*x^3)/(12*a^4*x^4) + ((A*b^4 - a*b^3*B)*Log[x])/a^5 + ((-(A*b^4) + a*b^3*B)*Log[a + b*x])/a^5","A",1
184,1,145,113,0.0886227,"\int \frac{x^4 (A+B x)}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x^4*(A + B*x))/(a + b*x)^2,x]","\frac{\left(5 a^4 B-4 a^3 A b\right) \log (a+b x)}{b^6}+\frac{12 a^5 B-12 a^4 A b-48 a^4 b B x+36 a^3 A b^2 x-30 a^3 b^2 B x^2+24 a^2 A b^3 x^2+10 a^2 b^3 B x^3-8 a A b^4 x^3-5 a b^4 B x^4+4 A b^5 x^4+3 b^5 B x^5}{12 b^6 (a+b x)}","-\frac{a^4 (A b-a B)}{b^6 (a+b x)}-\frac{a^3 (4 A b-5 a B) \log (a+b x)}{b^6}+\frac{a^2 x (3 A b-4 a B)}{b^5}-\frac{a x^2 (2 A b-3 a B)}{2 b^4}+\frac{x^3 (A b-2 a B)}{3 b^3}+\frac{B x^4}{4 b^2}",1,"(-12*a^4*A*b + 12*a^5*B + 36*a^3*A*b^2*x - 48*a^4*b*B*x + 24*a^2*A*b^3*x^2 - 30*a^3*b^2*B*x^2 - 8*a*A*b^4*x^3 + 10*a^2*b^3*B*x^3 + 4*A*b^5*x^4 - 5*a*b^4*B*x^4 + 3*b^5*B*x^5)/(12*b^6*(a + b*x)) + ((-4*a^3*A*b + 5*a^4*B)*Log[a + b*x])/b^6","A",1
185,1,121,90,0.0819529,"\int \frac{x^3 (A+B x)}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x^3*(A + B*x))/(a + b*x)^2,x]","\frac{\left(3 a^2 A b-4 a^3 B\right) \log (a+b x)}{b^5}+\frac{-6 a^4 B+6 a^3 A b+18 a^3 b B x-12 a^2 A b^2 x+12 a^2 b^2 B x^2-9 a A b^3 x^2-4 a b^3 B x^3+3 A b^4 x^3+2 b^4 B x^4}{6 b^5 (a+b x)}","\frac{a^3 (A b-a B)}{b^5 (a+b x)}+\frac{a^2 (3 A b-4 a B) \log (a+b x)}{b^5}-\frac{a x (2 A b-3 a B)}{b^4}+\frac{x^2 (A b-2 a B)}{2 b^3}+\frac{B x^3}{3 b^2}",1,"(6*a^3*A*b - 6*a^4*B - 12*a^2*A*b^2*x + 18*a^3*b*B*x - 9*a*A*b^3*x^2 + 12*a^2*b^2*B*x^2 + 3*A*b^4*x^3 - 4*a*b^3*B*x^3 + 2*b^4*B*x^4)/(6*b^5*(a + b*x)) + ((3*a^2*A*b - 4*a^3*B)*Log[a + b*x])/b^5","A",1
186,1,94,69,0.0811931,"\int \frac{x^2 (A+B x)}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x^2*(A + B*x))/(a + b*x)^2,x]","\frac{\left(3 a^2 B-2 a A b\right) \log (a+b x)}{b^4}+\frac{2 a^3 B-2 a^2 A b-4 a^2 b B x+2 a A b^2 x-3 a b^2 B x^2+2 A b^3 x^2+b^3 B x^3}{2 b^4 (a+b x)}","-\frac{a^2 (A b-a B)}{b^4 (a+b x)}-\frac{a (2 A b-3 a B) \log (a+b x)}{b^4}+\frac{x (A b-2 a B)}{b^3}+\frac{B x^2}{2 b^2}",1,"(-2*a^2*A*b + 2*a^3*B + 2*a*A*b^2*x - 4*a^2*b*B*x + 2*A*b^3*x^2 - 3*a*b^2*B*x^2 + b^3*B*x^3)/(2*b^4*(a + b*x)) + ((-2*a*A*b + 3*a^2*B)*Log[a + b*x])/b^4","A",1
187,1,54,45,0.0425336,"\int \frac{x (A+B x)}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x*(A + B*x))/(a + b*x)^2,x]","\frac{a^2 (-B)+a A b+a b B x+b^2 B x^2}{b^3 (a+b x)}+\frac{(A b-2 a B) \log (a+b x)}{b^3}","\frac{a (A b-a B)}{b^3 (a+b x)}+\frac{(A b-2 a B) \log (a+b x)}{b^3}+\frac{B x}{b^2}",1,"(a*A*b - a^2*B + a*b*B*x + b^2*B*x^2)/(b^3*(a + b*x)) + ((A*b - 2*a*B)*Log[a + b*x])/b^3","A",1
188,1,31,32,0.0194727,"\int \frac{A+B x}{(a+b x)^2} \, dx","IntegrateAlgebraic[(A + B*x)/(a + b*x)^2,x]","\frac{a B-A b}{b^2 (a+b x)}+\frac{B \log (a+b x)}{b^2}","\frac{B \log (a+b x)}{b^2}-\frac{A b-a B}{b^2 (a+b x)}",1,"(-(A*b) + a*B)/(b^2*(a + b*x)) + (B*Log[a + b*x])/b^2","A",1
189,1,42,42,0.0389698,"\int \frac{A+B x}{x (a+b x)^2} \, dx","IntegrateAlgebraic[(A + B*x)/(x*(a + b*x)^2),x]","-\frac{A \log (a+b x)}{a^2}+\frac{A \log (x)}{a^2}+\frac{A b-a B}{a b (a+b x)}","-\frac{A \log (a+b x)}{a^2}+\frac{A \log (x)}{a^2}+\frac{A b-a B}{a b (a+b x)}",1,"(A*b - a*B)/(a*b*(a + b*x)) + (A*Log[x])/a^2 - (A*Log[a + b*x])/a^2","A",1
190,1,62,65,0.0561727,"\int \frac{A+B x}{x^2 (a+b x)^2} \, dx","IntegrateAlgebraic[(A + B*x)/(x^2*(a + b*x)^2),x]","\frac{\log (x) (a B-2 A b)}{a^3}+\frac{(2 A b-a B) \log (a+b x)}{a^3}+\frac{-a A+a B x-2 A b x}{a^2 x (a+b x)}","-\frac{\log (x) (2 A b-a B)}{a^3}+\frac{(2 A b-a B) \log (a+b x)}{a^3}-\frac{A b-a B}{a^2 (a+b x)}-\frac{A}{a^2 x}",1,"(-(a*A) - 2*A*b*x + a*B*x)/(a^2*x*(a + b*x)) + ((-2*A*b + a*B)*Log[x])/a^3 + ((2*A*b - a*B)*Log[a + b*x])/a^3","A",1
191,1,95,85,0.0930162,"\int \frac{A+B x}{x^3 (a+b x)^2} \, dx","IntegrateAlgebraic[(A + B*x)/(x^3*(a + b*x)^2),x]","\frac{\log (x) \left(3 A b^2-2 a b B\right)}{a^4}+\frac{\left(2 a b B-3 A b^2\right) \log (a+b x)}{a^4}+\frac{a^2 (-A)-2 a^2 B x+3 a A b x-4 a b B x^2+6 A b^2 x^2}{2 a^3 x^2 (a+b x)}","\frac{b \log (x) (3 A b-2 a B)}{a^4}-\frac{b (3 A b-2 a B) \log (a+b x)}{a^4}+\frac{2 A b-a B}{a^3 x}+\frac{b (A b-a B)}{a^3 (a+b x)}-\frac{A}{2 a^2 x^2}",1,"(-(a^2*A) + 3*a*A*b*x - 2*a^2*B*x + 6*A*b^2*x^2 - 4*a*b*B*x^2)/(2*a^3*x^2*(a + b*x)) + ((3*A*b^2 - 2*a*b*B)*Log[x])/a^4 + ((-3*A*b^2 + 2*a*b*B)*Log[a + b*x])/a^4","A",1
192,1,123,113,0.1172364,"\int \frac{A+B x}{x^4 (a+b x)^2} \, dx","IntegrateAlgebraic[(A + B*x)/(x^4*(a + b*x)^2),x]","\frac{\log (x) \left(3 a b^2 B-4 A b^3\right)}{a^5}+\frac{\left(4 A b^3-3 a b^2 B\right) \log (a+b x)}{a^5}+\frac{-2 a^3 A-3 a^3 B x+4 a^2 A b x+9 a^2 b B x^2-12 a A b^2 x^2+18 a b^2 B x^3-24 A b^3 x^3}{6 a^4 x^3 (a+b x)}","-\frac{b^2 \log (x) (4 A b-3 a B)}{a^5}+\frac{b^2 (4 A b-3 a B) \log (a+b x)}{a^5}-\frac{b^2 (A b-a B)}{a^4 (a+b x)}-\frac{b (3 A b-2 a B)}{a^4 x}+\frac{2 A b-a B}{2 a^3 x^2}-\frac{A}{3 a^2 x^3}",1,"(-2*a^3*A + 4*a^2*A*b*x - 3*a^3*B*x - 12*a*A*b^2*x^2 + 9*a^2*b*B*x^2 - 24*A*b^3*x^3 + 18*a*b^2*B*x^3)/(6*a^4*x^3*(a + b*x)) + ((-4*A*b^3 + 3*a*b^2*B)*Log[x])/a^5 + ((4*A*b^3 - 3*a*b^2*B)*Log[a + b*x])/a^5","A",1
193,1,146,116,0.1026379,"\int \frac{x^4 (A+B x)}{(a+b x)^3} \, dx","IntegrateAlgebraic[(x^4*(A + B*x))/(a + b*x)^3,x]","\frac{-27 a^5 B+21 a^4 A b+6 a^4 b B x+6 a^3 A b^2 x+63 a^3 b^2 B x^2-33 a^2 A b^3 x^2+20 a^2 b^3 B x^3-12 a A b^4 x^3-5 a b^4 B x^4+3 A b^5 x^4+2 b^5 B x^5}{6 b^6 (a+b x)^2}-\frac{2 \left(5 a^3 B-3 a^2 A b\right) \log (a+b x)}{b^6}","-\frac{a^4 (A b-a B)}{2 b^6 (a+b x)^2}+\frac{a^3 (4 A b-5 a B)}{b^6 (a+b x)}+\frac{2 a^2 (3 A b-5 a B) \log (a+b x)}{b^6}-\frac{3 a x (A b-2 a B)}{b^5}+\frac{x^2 (A b-3 a B)}{2 b^4}+\frac{B x^3}{3 b^3}",1,"(21*a^4*A*b - 27*a^5*B + 6*a^3*A*b^2*x + 6*a^4*b*B*x - 33*a^2*A*b^3*x^2 + 63*a^3*b^2*B*x^2 - 12*a*A*b^4*x^3 + 20*a^2*b^3*B*x^3 + 3*A*b^5*x^4 - 5*a*b^4*B*x^4 + 2*b^5*B*x^5)/(6*b^6*(a + b*x)^2) - (2*(-3*a^2*A*b + 5*a^3*B)*Log[a + b*x])/b^6","A",1
194,1,119,94,0.082292,"\int \frac{x^3 (A+B x)}{(a+b x)^3} \, dx","IntegrateAlgebraic[(x^3*(A + B*x))/(a + b*x)^3,x]","\frac{3 \left(2 a^2 B-a A b\right) \log (a+b x)}{b^5}+\frac{7 a^4 B-5 a^3 A b+2 a^3 b B x-4 a^2 A b^2 x-11 a^2 b^2 B x^2+4 a A b^3 x^2-4 a b^3 B x^3+2 A b^4 x^3+b^4 B x^4}{2 b^5 (a+b x)^2}","\frac{a^3 (A b-a B)}{2 b^5 (a+b x)^2}-\frac{a^2 (3 A b-4 a B)}{b^5 (a+b x)}-\frac{3 a (A b-2 a B) \log (a+b x)}{b^5}+\frac{x (A b-3 a B)}{b^4}+\frac{B x^2}{2 b^3}",1,"(-5*a^3*A*b + 7*a^4*B - 4*a^2*A*b^2*x + 2*a^3*b*B*x + 4*a*A*b^3*x^2 - 11*a^2*b^2*B*x^2 + 2*A*b^4*x^3 - 4*a*b^3*B*x^3 + b^4*B*x^4)/(2*b^5*(a + b*x)^2) + (3*(-(a*A*b) + 2*a^2*B)*Log[a + b*x])/b^5","A",1
195,1,82,71,0.051247,"\int \frac{x^2 (A+B x)}{(a+b x)^3} \, dx","IntegrateAlgebraic[(x^2*(A + B*x))/(a + b*x)^3,x]","\frac{-5 a^3 B+3 a^2 A b-4 a^2 b B x+4 a A b^2 x+4 a b^2 B x^2+2 b^3 B x^3}{2 b^4 (a+b x)^2}+\frac{(A b-3 a B) \log (a+b x)}{b^4}","-\frac{a^2 (A b-a B)}{2 b^4 (a+b x)^2}+\frac{a (2 A b-3 a B)}{b^4 (a+b x)}+\frac{(A b-3 a B) \log (a+b x)}{b^4}+\frac{B x}{b^3}",1,"(3*a^2*A*b - 5*a^3*B + 4*a*A*b^2*x - 4*a^2*b*B*x + 4*a*b^2*B*x^2 + 2*b^3*B*x^3)/(2*b^4*(a + b*x)^2) + ((A*b - 3*a*B)*Log[a + b*x])/b^4","A",1
196,1,51,55,0.0330728,"\int \frac{x (A+B x)}{(a+b x)^3} \, dx","IntegrateAlgebraic[(x*(A + B*x))/(a + b*x)^3,x]","\frac{3 a^2 B-a A b+4 a b B x-2 A b^2 x}{2 b^3 (a+b x)^2}+\frac{B \log (a+b x)}{b^3}","-\frac{A b-2 a B}{b^3 (a+b x)}+\frac{a (A b-a B)}{2 b^3 (a+b x)^2}+\frac{B \log (a+b x)}{b^3}",1,"(-(a*A*b) + 3*a^2*B - 2*A*b^2*x + 4*a*b*B*x)/(2*b^3*(a + b*x)^2) + (B*Log[a + b*x])/b^3","A",1
197,1,28,28,0.0155452,"\int \frac{A+B x}{(a+b x)^3} \, dx","IntegrateAlgebraic[(A + B*x)/(a + b*x)^3,x]","\frac{-a B-A b-2 b B x}{2 b^2 (a+b x)^2}","-\frac{(A+B x)^2}{2 (a+b x)^2 (A b-a B)}",1,"(-(A*b) - a*B - 2*b*B*x)/(2*b^2*(a + b*x)^2)","A",1
198,1,56,57,0.0588133,"\int \frac{A+B x}{x (a+b x)^3} \, dx","IntegrateAlgebraic[(A + B*x)/(x*(a + b*x)^3),x]","-\frac{A \log (a+b x)}{a^3}+\frac{A \log (x)}{a^3}+\frac{a^2 (-B)+3 a A b+2 A b^2 x}{2 a^2 b (a+b x)^2}","-\frac{A \log (a+b x)}{a^3}+\frac{A \log (x)}{a^3}+\frac{A}{a^2 (a+b x)}+\frac{A b-a B}{2 a b (a+b x)^2}",1,"(3*a*A*b - a^2*B + 2*A*b^2*x)/(2*a^2*b*(a + b*x)^2) + (A*Log[x])/a^3 - (A*Log[a + b*x])/a^3","A",1
199,1,88,88,0.0742227,"\int \frac{A+B x}{x^2 (a+b x)^3} \, dx","IntegrateAlgebraic[(A + B*x)/(x^2*(a + b*x)^3),x]","\frac{\log (x) (a B-3 A b)}{a^4}+\frac{(3 A b-a B) \log (a+b x)}{a^4}+\frac{-2 a^2 A+3 a^2 B x-9 a A b x+2 a b B x^2-6 A b^2 x^2}{2 a^3 x (a+b x)^2}","-\frac{\log (x) (3 A b-a B)}{a^4}+\frac{(3 A b-a B) \log (a+b x)}{a^4}-\frac{2 A b-a B}{a^3 (a+b x)}-\frac{A}{a^3 x}-\frac{A b-a B}{2 a^2 (a+b x)^2}",1,"(-2*a^2*A - 9*a*A*b*x + 3*a^2*B*x - 6*A*b^2*x^2 + 2*a*b*B*x^2)/(2*a^3*x*(a + b*x)^2) + ((-3*A*b + a*B)*Log[x])/a^4 + ((3*A*b - a*B)*Log[a + b*x])/a^4","A",1
200,1,119,110,0.1157074,"\int \frac{A+B x}{x^3 (a+b x)^3} \, dx","IntegrateAlgebraic[(A + B*x)/(x^3*(a + b*x)^3),x]","-\frac{3 \log (x) \left(a b B-2 A b^2\right)}{a^5}+\frac{3 \left(a b B-2 A b^2\right) \log (a+b x)}{a^5}+\frac{a^3 (-A)-2 a^3 B x+4 a^2 A b x-9 a^2 b B x^2+18 a A b^2 x^2-6 a b^2 B x^3+12 A b^3 x^3}{2 a^4 x^2 (a+b x)^2}","\frac{3 b \log (x) (2 A b-a B)}{a^5}-\frac{3 b (2 A b-a B) \log (a+b x)}{a^5}+\frac{3 A b-a B}{a^4 x}+\frac{b (3 A b-2 a B)}{a^4 (a+b x)}+\frac{b (A b-a B)}{2 a^3 (a+b x)^2}-\frac{A}{2 a^3 x^2}",1,"(-(a^3*A) + 4*a^2*A*b*x - 2*a^3*B*x + 18*a*A*b^2*x^2 - 9*a^2*b*B*x^2 + 12*A*b^3*x^3 - 6*a*b^2*B*x^3)/(2*a^4*x^2*(a + b*x)^2) - (3*(-2*A*b^2 + a*b*B)*Log[x])/a^5 + (3*(-2*A*b^2 + a*b*B)*Log[a + b*x])/a^5","A",1
201,1,149,140,0.1669063,"\int \frac{A+B x}{x^4 (a+b x)^3} \, dx","IntegrateAlgebraic[(A + B*x)/(x^4*(a + b*x)^3),x]","\frac{2 \log (x) \left(3 a b^2 B-5 A b^3\right)}{a^6}-\frac{2 \left(3 a b^2 B-5 A b^3\right) \log (a+b x)}{a^6}+\frac{-2 a^4 A-3 a^4 B x+5 a^3 A b x+12 a^3 b B x^2-20 a^2 A b^2 x^2+54 a^2 b^2 B x^3-90 a A b^3 x^3+36 a b^3 B x^4-60 A b^4 x^4}{6 a^5 x^3 (a+b x)^2}","-\frac{2 b^2 \log (x) (5 A b-3 a B)}{a^6}+\frac{2 b^2 (5 A b-3 a B) \log (a+b x)}{a^6}-\frac{b^2 (4 A b-3 a B)}{a^5 (a+b x)}-\frac{3 b (2 A b-a B)}{a^5 x}-\frac{b^2 (A b-a B)}{2 a^4 (a+b x)^2}+\frac{3 A b-a B}{2 a^4 x^2}-\frac{A}{3 a^3 x^3}",1,"(-2*a^4*A + 5*a^3*A*b*x - 3*a^4*B*x - 20*a^2*A*b^2*x^2 + 12*a^3*b*B*x^2 - 90*a*A*b^3*x^3 + 54*a^2*b^2*B*x^3 - 60*A*b^4*x^4 + 36*a*b^3*B*x^4)/(6*a^5*x^3*(a + b*x)^2) + (2*(-5*A*b^3 + 3*a*b^2*B)*Log[x])/a^6 - (2*(-5*A*b^3 + 3*a*b^2*B)*Log[a + b*x])/a^6","A",1
202,1,672,177,0.3277005,"\int x^3 (a+b x)^2 (c+d x)^{16} \, dx","IntegrateAlgebraic[x^3*(a + b*x)^2*(c + d*x)^16,x]","\frac{1119195 a^2 c^{16} x^4+14325696 a^2 c^{15} d x^5+89535600 a^2 c^{14} d^2 x^6+358142400 a^2 c^{13} d^3 x^7+1018467450 a^2 c^{12} d^4 x^8+2172730560 a^2 c^{11} d^5 x^9+3585005424 a^2 c^{10} d^6 x^{10}+4655851200 a^2 c^9 d^7 x^{11}+4801346550 a^2 c^8 d^8 x^{12}+3939566400 a^2 c^7 d^9 x^{13}+2560718160 a^2 c^6 d^{10} x^{14}+1303638336 a^2 c^5 d^{11} x^{15}+509233725 a^2 c^4 d^{12} x^{16}+147470400 a^2 c^3 d^{13} x^{17}+29845200 a^2 c^2 d^{14} x^{18}+3769920 a^2 c d^{15} x^{19}+223839 a^2 d^{16} x^{20}+1790712 a b c^{16} x^5+23876160 a b c^{15} d x^6+153489600 a b c^{14} d^2 x^7+626749200 a b c^{13} d^3 x^8+1810608800 a b c^{12} d^4 x^9+3910915008 a b c^{11} d^5 x^{10}+6518191680 a b c^{10} d^6 x^{11}+8535727200 a b c^9 d^7 x^{12}+8864024400 a b c^8 d^8 x^{13}+7316337600 a b c^7 d^9 x^{14}+4780007232 a b c^6 d^{10} x^{15}+2444321880 a b c^5 d^{11} x^{16}+958557600 a b c^4 d^{12} x^{17}+278555200 a b c^3 d^{13} x^{18}+56548800 a b c^2 d^{14} x^{19}+7162848 a b c d^{15} x^{20}+426360 a b d^{16} x^{21}+746130 b^2 c^{16} x^6+10232640 b^2 c^{15} d x^7+67151700 b^2 c^{14} d^2 x^8+278555200 b^2 c^{13} d^3 x^9+814773960 b^2 c^{12} d^4 x^{10}+1777688640 b^2 c^{11} d^5 x^{11}+2987504520 b^2 c^{10} d^6 x^{12}+3939566400 b^2 c^9 d^7 x^{13}+4115439900 b^2 c^8 d^8 x^{14}+3414290880 b^2 c^7 d^9 x^{15}+2240628390 b^2 c^6 d^{10} x^{16}+1150269120 b^2 c^5 d^{11} x^{17}+452652200 b^2 c^4 d^{12} x^{18}+131947200 b^2 c^3 d^{13} x^{19}+26860680 b^2 c^2 d^{14} x^{20}+3410880 b^2 c d^{15} x^{21}+203490 b^2 d^{16} x^{22}}{4476780}","\frac{(c+d x)^{20} \left(a^2 d^2-8 a b c d+10 b^2 c^2\right)}{20 d^6}-\frac{c (c+d x)^{19} \left(3 a^2 d^2-12 a b c d+10 b^2 c^2\right)}{19 d^6}-\frac{c^3 (c+d x)^{17} (b c-a d)^2}{17 d^6}+\frac{c^2 (c+d x)^{18} (5 b c-3 a d) (b c-a d)}{18 d^6}-\frac{b (c+d x)^{21} (5 b c-2 a d)}{21 d^6}+\frac{b^2 (c+d x)^{22}}{22 d^6}",1,"(1119195*a^2*c^16*x^4 + 1790712*a*b*c^16*x^5 + 14325696*a^2*c^15*d*x^5 + 746130*b^2*c^16*x^6 + 23876160*a*b*c^15*d*x^6 + 89535600*a^2*c^14*d^2*x^6 + 10232640*b^2*c^15*d*x^7 + 153489600*a*b*c^14*d^2*x^7 + 358142400*a^2*c^13*d^3*x^7 + 67151700*b^2*c^14*d^2*x^8 + 626749200*a*b*c^13*d^3*x^8 + 1018467450*a^2*c^12*d^4*x^8 + 278555200*b^2*c^13*d^3*x^9 + 1810608800*a*b*c^12*d^4*x^9 + 2172730560*a^2*c^11*d^5*x^9 + 814773960*b^2*c^12*d^4*x^10 + 3910915008*a*b*c^11*d^5*x^10 + 3585005424*a^2*c^10*d^6*x^10 + 1777688640*b^2*c^11*d^5*x^11 + 6518191680*a*b*c^10*d^6*x^11 + 4655851200*a^2*c^9*d^7*x^11 + 2987504520*b^2*c^10*d^6*x^12 + 8535727200*a*b*c^9*d^7*x^12 + 4801346550*a^2*c^8*d^8*x^12 + 3939566400*b^2*c^9*d^7*x^13 + 8864024400*a*b*c^8*d^8*x^13 + 3939566400*a^2*c^7*d^9*x^13 + 4115439900*b^2*c^8*d^8*x^14 + 7316337600*a*b*c^7*d^9*x^14 + 2560718160*a^2*c^6*d^10*x^14 + 3414290880*b^2*c^7*d^9*x^15 + 4780007232*a*b*c^6*d^10*x^15 + 1303638336*a^2*c^5*d^11*x^15 + 2240628390*b^2*c^6*d^10*x^16 + 2444321880*a*b*c^5*d^11*x^16 + 509233725*a^2*c^4*d^12*x^16 + 1150269120*b^2*c^5*d^11*x^17 + 958557600*a*b*c^4*d^12*x^17 + 147470400*a^2*c^3*d^13*x^17 + 452652200*b^2*c^4*d^12*x^18 + 278555200*a*b*c^3*d^13*x^18 + 29845200*a^2*c^2*d^14*x^18 + 131947200*b^2*c^3*d^13*x^19 + 56548800*a*b*c^2*d^14*x^19 + 3769920*a^2*c*d^15*x^19 + 26860680*b^2*c^2*d^14*x^20 + 7162848*a*b*c*d^15*x^20 + 223839*a^2*d^16*x^20 + 3410880*b^2*c*d^15*x^21 + 426360*a*b*d^16*x^21 + 203490*b^2*d^16*x^22)/4476780","B",1
203,1,672,137,0.2525123,"\int x^2 (a+b x)^2 (c+d x)^{16} \, dx","IntegrateAlgebraic[x^2*(a + b*x)^2*(c + d*x)^16,x]","\frac{67830 a^2 c^{16} x^3+813960 a^2 c^{15} d x^4+4883760 a^2 c^{14} d^2 x^5+18992400 a^2 c^{13} d^3 x^6+52907400 a^2 c^{12} d^4 x^7+111105540 a^2 c^{11} d^5 x^8+181060880 a^2 c^{10} d^6 x^9+232792560 a^2 c^9 d^7 x^{10}+238083300 a^2 c^8 d^8 x^{11}+193993800 a^2 c^7 d^9 x^{12}+125349840 a^2 c^6 d^{10} x^{13}+63488880 a^2 c^5 d^{11} x^{14}+24690120 a^2 c^4 d^{12} x^{15}+7122150 a^2 c^3 d^{13} x^{16}+1436400 a^2 c^2 d^{14} x^{17}+180880 a^2 c d^{15} x^{18}+10710 a^2 d^{16} x^{19}+101745 a b c^{16} x^4+1302336 a b c^{15} d x^5+8139600 a b c^{14} d^2 x^6+32558400 a b c^{13} d^3 x^7+92587950 a b c^{12} d^4 x^8+197520960 a b c^{11} d^5 x^9+325909584 a b c^{10} d^6 x^{10}+423259200 a b c^9 d^7 x^{11}+436486050 a b c^8 d^8 x^{12}+358142400 a b c^7 d^9 x^{13}+232792560 a b c^6 d^{10} x^{14}+118512576 a b c^5 d^{11} x^{15}+46293975 a b c^4 d^{12} x^{16}+13406400 a b c^3 d^{13} x^{17}+2713200 a b c^2 d^{14} x^{18}+342720 a b c d^{15} x^{19}+20349 a b d^{16} x^{20}+40698 b^2 c^{16} x^5+542640 b^2 c^{15} d x^6+3488400 b^2 c^{14} d^2 x^7+14244300 b^2 c^{13} d^3 x^8+41150200 b^2 c^{12} d^4 x^9+88884432 b^2 c^{11} d^5 x^{10}+148140720 b^2 c^{10} d^6 x^{11}+193993800 b^2 c^9 d^7 x^{12}+201455100 b^2 c^8 d^8 x^{13}+166280400 b^2 c^7 d^9 x^{14}+108636528 b^2 c^6 d^{10} x^{15}+55552770 b^2 c^5 d^{11} x^{16}+21785400 b^2 c^4 d^{12} x^{17}+6330800 b^2 c^3 d^{13} x^{18}+1285200 b^2 c^2 d^{14} x^{19}+162792 b^2 c d^{15} x^{20}+9690 b^2 d^{16} x^{21}}{203490}","\frac{(c+d x)^{19} \left(a^2 d^2-6 a b c d+6 b^2 c^2\right)}{19 d^5}+\frac{c^2 (c+d x)^{17} (b c-a d)^2}{17 d^5}-\frac{b (c+d x)^{20} (2 b c-a d)}{10 d^5}-\frac{c (c+d x)^{18} (b c-a d) (2 b c-a d)}{9 d^5}+\frac{b^2 (c+d x)^{21}}{21 d^5}",1,"(67830*a^2*c^16*x^3 + 101745*a*b*c^16*x^4 + 813960*a^2*c^15*d*x^4 + 40698*b^2*c^16*x^5 + 1302336*a*b*c^15*d*x^5 + 4883760*a^2*c^14*d^2*x^5 + 542640*b^2*c^15*d*x^6 + 8139600*a*b*c^14*d^2*x^6 + 18992400*a^2*c^13*d^3*x^6 + 3488400*b^2*c^14*d^2*x^7 + 32558400*a*b*c^13*d^3*x^7 + 52907400*a^2*c^12*d^4*x^7 + 14244300*b^2*c^13*d^3*x^8 + 92587950*a*b*c^12*d^4*x^8 + 111105540*a^2*c^11*d^5*x^8 + 41150200*b^2*c^12*d^4*x^9 + 197520960*a*b*c^11*d^5*x^9 + 181060880*a^2*c^10*d^6*x^9 + 88884432*b^2*c^11*d^5*x^10 + 325909584*a*b*c^10*d^6*x^10 + 232792560*a^2*c^9*d^7*x^10 + 148140720*b^2*c^10*d^6*x^11 + 423259200*a*b*c^9*d^7*x^11 + 238083300*a^2*c^8*d^8*x^11 + 193993800*b^2*c^9*d^7*x^12 + 436486050*a*b*c^8*d^8*x^12 + 193993800*a^2*c^7*d^9*x^12 + 201455100*b^2*c^8*d^8*x^13 + 358142400*a*b*c^7*d^9*x^13 + 125349840*a^2*c^6*d^10*x^13 + 166280400*b^2*c^7*d^9*x^14 + 232792560*a*b*c^6*d^10*x^14 + 63488880*a^2*c^5*d^11*x^14 + 108636528*b^2*c^6*d^10*x^15 + 118512576*a*b*c^5*d^11*x^15 + 24690120*a^2*c^4*d^12*x^15 + 55552770*b^2*c^5*d^11*x^16 + 46293975*a*b*c^4*d^12*x^16 + 7122150*a^2*c^3*d^13*x^16 + 21785400*b^2*c^4*d^12*x^17 + 13406400*a*b*c^3*d^13*x^17 + 1436400*a^2*c^2*d^14*x^17 + 6330800*b^2*c^3*d^13*x^18 + 2713200*a*b*c^2*d^14*x^18 + 180880*a^2*c*d^15*x^18 + 1285200*b^2*c^2*d^14*x^19 + 342720*a*b*c*d^15*x^19 + 10710*a^2*d^16*x^19 + 162792*b^2*c*d^15*x^20 + 20349*a*b*d^16*x^20 + 9690*b^2*d^16*x^21)/203490","B",1
204,1,672,98,0.2493526,"\int x (a+b x)^2 (c+d x)^{16} \, dx","IntegrateAlgebraic[x*(a + b*x)^2*(c + d*x)^16,x]","\frac{29070 a^2 c^{16} x^2+310080 a^2 c^{15} d x^3+1744200 a^2 c^{14} d^2 x^4+6511680 a^2 c^{13} d^3 x^5+17635800 a^2 c^{12} d^4 x^6+36279360 a^2 c^{11} d^5 x^7+58198140 a^2 c^{10} d^6 x^8+73902400 a^2 c^9 d^7 x^9+74826180 a^2 c^8 d^8 x^{10}+60465600 a^2 c^7 d^9 x^{11}+38798760 a^2 c^6 d^{10} x^{12}+19535040 a^2 c^5 d^{11} x^{13}+7558200 a^2 c^4 d^{12} x^{14}+2170560 a^2 c^3 d^{13} x^{15}+436050 a^2 c^2 d^{14} x^{16}+54720 a^2 c d^{15} x^{17}+3230 a^2 d^{16} x^{18}+38760 a b c^{16} x^3+465120 a b c^{15} d x^4+2790720 a b c^{14} d^2 x^5+10852800 a b c^{13} d^3 x^6+30232800 a b c^{12} d^4 x^7+63488880 a b c^{11} d^5 x^8+103463360 a b c^{10} d^6 x^9+133024320 a b c^9 d^7 x^{10}+136047600 a b c^8 d^8 x^{11}+110853600 a b c^7 d^9 x^{12}+71628480 a b c^6 d^{10} x^{13}+36279360 a b c^5 d^{11} x^{14}+14108640 a b c^4 d^{12} x^{15}+4069800 a b c^3 d^{13} x^{16}+820800 a b c^2 d^{14} x^{17}+103360 a b c d^{15} x^{18}+6120 a b d^{16} x^{19}+14535 b^2 c^{16} x^4+186048 b^2 c^{15} d x^5+1162800 b^2 c^{14} d^2 x^6+4651200 b^2 c^{13} d^3 x^7+13226850 b^2 c^{12} d^4 x^8+28217280 b^2 c^{11} d^5 x^9+46558512 b^2 c^{10} d^6 x^{10}+60465600 b^2 c^9 d^7 x^{11}+62355150 b^2 c^8 d^8 x^{12}+51163200 b^2 c^7 d^9 x^{13}+33256080 b^2 c^6 d^{10} x^{14}+16930368 b^2 c^5 d^{11} x^{15}+6613425 b^2 c^4 d^{12} x^{16}+1915200 b^2 c^3 d^{13} x^{17}+387600 b^2 c^2 d^{14} x^{18}+48960 b^2 c d^{15} x^{19}+2907 b^2 d^{16} x^{20}}{58140}","-\frac{b (c+d x)^{19} (3 b c-2 a d)}{19 d^4}+\frac{(c+d x)^{18} (b c-a d) (3 b c-a d)}{18 d^4}-\frac{c (c+d x)^{17} (b c-a d)^2}{17 d^4}+\frac{b^2 (c+d x)^{20}}{20 d^4}",1,"(29070*a^2*c^16*x^2 + 38760*a*b*c^16*x^3 + 310080*a^2*c^15*d*x^3 + 14535*b^2*c^16*x^4 + 465120*a*b*c^15*d*x^4 + 1744200*a^2*c^14*d^2*x^4 + 186048*b^2*c^15*d*x^5 + 2790720*a*b*c^14*d^2*x^5 + 6511680*a^2*c^13*d^3*x^5 + 1162800*b^2*c^14*d^2*x^6 + 10852800*a*b*c^13*d^3*x^6 + 17635800*a^2*c^12*d^4*x^6 + 4651200*b^2*c^13*d^3*x^7 + 30232800*a*b*c^12*d^4*x^7 + 36279360*a^2*c^11*d^5*x^7 + 13226850*b^2*c^12*d^4*x^8 + 63488880*a*b*c^11*d^5*x^8 + 58198140*a^2*c^10*d^6*x^8 + 28217280*b^2*c^11*d^5*x^9 + 103463360*a*b*c^10*d^6*x^9 + 73902400*a^2*c^9*d^7*x^9 + 46558512*b^2*c^10*d^6*x^10 + 133024320*a*b*c^9*d^7*x^10 + 74826180*a^2*c^8*d^8*x^10 + 60465600*b^2*c^9*d^7*x^11 + 136047600*a*b*c^8*d^8*x^11 + 60465600*a^2*c^7*d^9*x^11 + 62355150*b^2*c^8*d^8*x^12 + 110853600*a*b*c^7*d^9*x^12 + 38798760*a^2*c^6*d^10*x^12 + 51163200*b^2*c^7*d^9*x^13 + 71628480*a*b*c^6*d^10*x^13 + 19535040*a^2*c^5*d^11*x^13 + 33256080*b^2*c^6*d^10*x^14 + 36279360*a*b*c^5*d^11*x^14 + 7558200*a^2*c^4*d^12*x^14 + 16930368*b^2*c^5*d^11*x^15 + 14108640*a*b*c^4*d^12*x^15 + 2170560*a^2*c^3*d^13*x^15 + 6613425*b^2*c^4*d^12*x^16 + 4069800*a*b*c^3*d^13*x^16 + 436050*a^2*c^2*d^14*x^16 + 1915200*b^2*c^3*d^13*x^17 + 820800*a*b*c^2*d^14*x^17 + 54720*a^2*c*d^15*x^17 + 387600*b^2*c^2*d^14*x^18 + 103360*a*b*c*d^15*x^18 + 3230*a^2*d^16*x^18 + 48960*b^2*c*d^15*x^19 + 6120*a*b*d^16*x^19 + 2907*b^2*d^16*x^20)/58140","B",1
205,1,90,87,0.0536795,"\int \frac{x^3 (c+d x)}{a+b x} \, dx","IntegrateAlgebraic[(x^3*(c + d*x))/(a + b*x),x]","\frac{\left(a^4 d-a^3 b c\right) \log (a+b x)}{b^5}+\frac{x \left(-12 a^3 d+12 a^2 b c+6 a^2 b d x-6 a b^2 c x-4 a b^2 d x^2+4 b^3 c x^2+3 b^3 d x^3\right)}{12 b^4}","-\frac{a^3 (b c-a d) \log (a+b x)}{b^5}+\frac{a^2 x (b c-a d)}{b^4}-\frac{a x^2 (b c-a d)}{2 b^3}+\frac{x^3 (b c-a d)}{3 b^2}+\frac{d x^4}{4 b}",1,"(x*(12*a^2*b*c - 12*a^3*d - 6*a*b^2*c*x + 6*a^2*b*d*x + 4*b^3*c*x^2 - 4*a*b^2*d*x^2 + 3*b^3*d*x^3))/(12*b^4) + ((-(a^3*b*c) + a^4*d)*Log[a + b*x])/b^5","A",1
206,1,66,66,0.0379401,"\int \frac{x^2 (c+d x)}{a+b x} \, dx","IntegrateAlgebraic[(x^2*(c + d*x))/(a + b*x),x]","\frac{x \left(6 a^2 d-6 a b c-3 a b d x+3 b^2 c x+2 b^2 d x^2\right)}{6 b^3}+\frac{\left(a^2 b c-a^3 d\right) \log (a+b x)}{b^4}","\frac{a^2 (b c-a d) \log (a+b x)}{b^4}-\frac{a x (b c-a d)}{b^3}+\frac{x^2 (b c-a d)}{2 b^2}+\frac{d x^3}{3 b}",1,"(x*(-6*a*b*c + 6*a^2*d + 3*b^2*c*x - 3*a*b*d*x + 2*b^2*d*x^2))/(6*b^3) + ((a^2*b*c - a^3*d)*Log[a + b*x])/b^4","A",1
207,1,43,45,0.0231087,"\int \frac{x (c+d x)}{a+b x} \, dx","IntegrateAlgebraic[(x*(c + d*x))/(a + b*x),x]","\frac{\left(a^2 d-a b c\right) \log (a+b x)}{b^3}+\frac{x (-2 a d+2 b c+b d x)}{2 b^2}","-\frac{a (b c-a d) \log (a+b x)}{b^3}+\frac{x (b c-a d)}{b^2}+\frac{d x^2}{2 b}",1,"(x*(2*b*c - 2*a*d + b*d*x))/(2*b^2) + ((-(a*b*c) + a^2*d)*Log[a + b*x])/b^3","A",1
208,1,25,25,0.0005806,"\int \frac{c+d x}{a+b x} \, dx","IntegrateAlgebraic[(c + d*x)/(a + b*x),x]","\frac{(b c-a d) \log (a+b x)}{b^2}+\frac{d x}{b}","\frac{(b c-a d) \log (a+b x)}{b^2}+\frac{d x}{b}",1,"(d*x)/b + ((b*c - a*d)*Log[a + b*x])/b^2","A",1
209,1,29,30,0.0170963,"\int \frac{c+d x}{x (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)/(x*(a + b*x)),x]","\frac{(a d-b c) \log (a+b x)}{a b}+\frac{c \log (x)}{a}","\frac{c \log (x)}{a}-\frac{(b c-a d) \log (a+b x)}{a b}",1,"(c*Log[x])/a + ((-(b*c) + a*d)*Log[a + b*x])/(a*b)","A",1
210,1,42,43,0.0276625,"\int \frac{c+d x}{x^2 (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)/(x^2*(a + b*x)),x]","\frac{\log (x) (a d-b c)}{a^2}+\frac{(b c-a d) \log (a+b x)}{a^2}-\frac{c}{a x}","-\frac{\log (x) (b c-a d)}{a^2}+\frac{(b c-a d) \log (a+b x)}{a^2}-\frac{c}{a x}",1,"-(c/(a*x)) + ((-(b*c) + a*d)*Log[x])/a^2 + ((b*c - a*d)*Log[a + b*x])/a^2","A",1
211,1,64,62,0.0507538,"\int \frac{c+d x}{x^3 (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)/(x^3*(a + b*x)),x]","\frac{\log (x) \left(b^2 c-a b d\right)}{a^3}+\frac{\left(a b d-b^2 c\right) \log (a+b x)}{a^3}+\frac{-a c-2 a d x+2 b c x}{2 a^2 x^2}","\frac{b \log (x) (b c-a d)}{a^3}-\frac{b (b c-a d) \log (a+b x)}{a^3}+\frac{b c-a d}{a^2 x}-\frac{c}{2 a x^2}",1,"(-(a*c) + 2*b*c*x - 2*a*d*x)/(2*a^2*x^2) + ((b^2*c - a*b*d)*Log[x])/a^3 + ((-(b^2*c) + a*b*d)*Log[a + b*x])/a^3","A",1
212,1,90,86,0.0750988,"\int \frac{c+d x}{x^4 (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)/(x^4*(a + b*x)),x]","\frac{\log (x) \left(a b^2 d-b^3 c\right)}{a^4}+\frac{\left(b^3 c-a b^2 d\right) \log (a+b x)}{a^4}+\frac{-2 a^2 c-3 a^2 d x+3 a b c x+6 a b d x^2-6 b^2 c x^2}{6 a^3 x^3}","-\frac{b^2 \log (x) (b c-a d)}{a^4}+\frac{b^2 (b c-a d) \log (a+b x)}{a^4}-\frac{b (b c-a d)}{a^3 x}+\frac{b c-a d}{2 a^2 x^2}-\frac{c}{3 a x^3}",1,"(-2*a^2*c + 3*a*b*c*x - 3*a^2*d*x - 6*b^2*c*x^2 + 6*a*b*d*x^2)/(6*a^3*x^3) + ((-(b^3*c) + a*b^2*d)*Log[x])/a^4 + ((b^3*c - a*b^2*d)*Log[a + b*x])/a^4","A",1
213,1,161,117,0.1032499,"\int \frac{x^3 (c+d x)^2}{a+b x} \, dx","IntegrateAlgebraic[(x^3*(c + d*x)^2)/(a + b*x),x]","\frac{x \left(60 a^4 d^2-120 a^3 b c d-30 a^3 b d^2 x+60 a^2 b^2 c^2+60 a^2 b^2 c d x+20 a^2 b^2 d^2 x^2-30 a b^3 c^2 x-40 a b^3 c d x^2-15 a b^3 d^2 x^3+20 b^4 c^2 x^2+30 b^4 c d x^3+12 b^4 d^2 x^4\right)}{60 b^5}-\frac{a^3 (a d-b c)^2 \log (a+b x)}{b^6}","-\frac{a^3 (b c-a d)^2 \log (a+b x)}{b^6}+\frac{a^2 x (b c-a d)^2}{b^5}-\frac{a x^2 (b c-a d)^2}{2 b^4}+\frac{x^3 (b c-a d)^2}{3 b^3}+\frac{d x^4 (2 b c-a d)}{4 b^2}+\frac{d^2 x^5}{5 b}",1,"(x*(60*a^2*b^2*c^2 - 120*a^3*b*c*d + 60*a^4*d^2 - 30*a*b^3*c^2*x + 60*a^2*b^2*c*d*x - 30*a^3*b*d^2*x + 20*b^4*c^2*x^2 - 40*a*b^3*c*d*x^2 + 20*a^2*b^2*d^2*x^2 + 30*b^4*c*d*x^3 - 15*a*b^3*d^2*x^3 + 12*b^4*d^2*x^4))/(60*b^5) - (a^3*(-(b*c) + a*d)^2*Log[a + b*x])/b^6","A",1
214,1,119,94,0.0659987,"\int \frac{x^2 (c+d x)^2}{a+b x} \, dx","IntegrateAlgebraic[(x^2*(c + d*x)^2)/(a + b*x),x]","\frac{a^2 (a d-b c)^2 \log (a+b x)}{b^5}+\frac{x \left(-12 a^3 d^2+24 a^2 b c d+6 a^2 b d^2 x-12 a b^2 c^2-12 a b^2 c d x-4 a b^2 d^2 x^2+6 b^3 c^2 x+8 b^3 c d x^2+3 b^3 d^2 x^3\right)}{12 b^4}","\frac{a^2 (b c-a d)^2 \log (a+b x)}{b^5}-\frac{a x (b c-a d)^2}{b^4}+\frac{x^2 (b c-a d)^2}{2 b^3}+\frac{d x^3 (2 b c-a d)}{3 b^2}+\frac{d^2 x^4}{4 b}",1,"(x*(-12*a*b^2*c^2 + 24*a^2*b*c*d - 12*a^3*d^2 + 6*b^3*c^2*x - 12*a*b^2*c*d*x + 6*a^2*b*d^2*x + 8*b^3*c*d*x^2 - 4*a*b^2*d^2*x^2 + 3*b^3*d^2*x^3))/(12*b^4) + (a^2*(-(b*c) + a*d)^2*Log[a + b*x])/b^5","A",1
215,1,81,71,0.0477747,"\int \frac{x (c+d x)^2}{a+b x} \, dx","IntegrateAlgebraic[(x*(c + d*x)^2)/(a + b*x),x]","\frac{x \left(6 a^2 d^2-12 a b c d-3 a b d^2 x+6 b^2 c^2+6 b^2 c d x+2 b^2 d^2 x^2\right)}{6 b^3}-\frac{a (a d-b c)^2 \log (a+b x)}{b^4}","-\frac{a (b c-a d)^2 \log (a+b x)}{b^4}+\frac{x (b c-a d)^2}{b^3}+\frac{d x^2 (2 b c-a d)}{2 b^2}+\frac{d^2 x^3}{3 b}",1,"(x*(6*b^2*c^2 - 12*a*b*c*d + 6*a^2*d^2 + 6*b^2*c*d*x - 3*a*b*d^2*x + 2*b^2*d^2*x^2))/(6*b^3) - (a*(-(b*c) + a*d)^2*Log[a + b*x])/b^4","A",1
216,1,43,49,0.0005743,"\int \frac{(c+d x)^2}{a+b x} \, dx","IntegrateAlgebraic[(c + d*x)^2/(a + b*x),x]","\frac{(b c-a d)^2 \log (a+b x)}{b^3}+\frac{d x (-2 a d+4 b c+b d x)}{2 b^2}","\frac{(b c-a d)^2 \log (a+b x)}{b^3}+\frac{d x (b c-a d)}{b^2}+\frac{(c+d x)^2}{2 b}",1,"(d*x*(4*b*c - 2*a*d + b*d*x))/(2*b^2) + ((b*c - a*d)^2*Log[a + b*x])/b^3","A",1
217,1,42,42,0.0290298,"\int \frac{(c+d x)^2}{x (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^2/(x*(a + b*x)),x]","-\frac{(a d-b c)^2 \log (a+b x)}{a b^2}+\frac{c^2 \log (x)}{a}+\frac{d^2 x}{b}","-\frac{(b c-a d)^2 \log (a+b x)}{a b^2}+\frac{c^2 \log (x)}{a}+\frac{d^2 x}{b}",1,"(d^2*x)/b + (c^2*Log[x])/a - ((-(b*c) + a*d)^2*Log[a + b*x])/(a*b^2)","A",1
218,1,53,51,0.0368391,"\int \frac{(c+d x)^2}{x^2 (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^2/(x^2*(a + b*x)),x]","\frac{\log (x) \left(2 a c d-b c^2\right)}{a^2}+\frac{(a d-b c)^2 \log (a+b x)}{a^2 b}-\frac{c^2}{a x}","-\frac{c \log (x) (b c-2 a d)}{a^2}+\frac{(b c-a d)^2 \log (a+b x)}{a^2 b}-\frac{c^2}{a x}",1,"-(c^2/(a*x)) + ((-(b*c^2) + 2*a*c*d)*Log[x])/a^2 + ((-(b*c) + a*d)^2*Log[a + b*x])/(a^2*b)","A",1
219,1,63,67,0.0744936,"\int \frac{(c+d x)^2}{x^3 (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^2/(x^3*(a + b*x)),x]","\frac{\log (x) (a d-b c)^2}{a^3}-\frac{(a d-b c)^2 \log (a+b x)}{a^3}-\frac{c (a c+4 a d x-2 b c x)}{2 a^2 x^2}","\frac{\log (x) (b c-a d)^2}{a^3}-\frac{(b c-a d)^2 \log (a+b x)}{a^3}+\frac{c (b c-2 a d)}{a^2 x}-\frac{c^2}{2 a x^2}",1,"-1/2*(c*(a*c - 2*b*c*x + 4*a*d*x))/(a^2*x^2) + ((-(b*c) + a*d)^2*Log[x])/a^3 - ((-(b*c) + a*d)^2*Log[a + b*x])/a^3","A",1
220,1,106,90,0.0752026,"\int \frac{(c+d x)^2}{x^4 (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^2/(x^4*(a + b*x)),x]","-\frac{b \log (x) (a d-b c)^2}{a^4}+\frac{b (a d-b c)^2 \log (a+b x)}{a^4}+\frac{-2 a^2 c^2-6 a^2 c d x-6 a^2 d^2 x^2+3 a b c^2 x+12 a b c d x^2-6 b^2 c^2 x^2}{6 a^3 x^3}","-\frac{b \log (x) (b c-a d)^2}{a^4}+\frac{b (b c-a d)^2 \log (a+b x)}{a^4}-\frac{(b c-a d)^2}{a^3 x}+\frac{c (b c-2 a d)}{2 a^2 x^2}-\frac{c^2}{3 a x^3}",1,"(-2*a^2*c^2 + 3*a*b*c^2*x - 6*a^2*c*d*x - 6*b^2*c^2*x^2 + 12*a*b*c*d*x^2 - 6*a^2*d^2*x^2)/(6*a^3*x^3) - (b*(-(b*c) + a*d)^2*Log[x])/a^4 + (b*(-(b*c) + a*d)^2*Log[a + b*x])/a^4","A",1
221,1,149,114,0.122612,"\int \frac{(c+d x)^2}{x^5 (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^2/(x^5*(a + b*x)),x]","\frac{b^2 \log (x) (a d-b c)^2}{a^5}-\frac{b^2 (a d-b c)^2 \log (a+b x)}{a^5}+\frac{-3 a^3 c^2-8 a^3 c d x-6 a^3 d^2 x^2+4 a^2 b c^2 x+12 a^2 b c d x^2+12 a^2 b d^2 x^3-6 a b^2 c^2 x^2-24 a b^2 c d x^3+12 b^3 c^2 x^3}{12 a^4 x^4}","\frac{b^2 \log (x) (b c-a d)^2}{a^5}-\frac{b^2 (b c-a d)^2 \log (a+b x)}{a^5}+\frac{b (b c-a d)^2}{a^4 x}-\frac{(b c-a d)^2}{2 a^3 x^2}+\frac{c (b c-2 a d)}{3 a^2 x^3}-\frac{c^2}{4 a x^4}",1,"(-3*a^3*c^2 + 4*a^2*b*c^2*x - 8*a^3*c*d*x - 6*a*b^2*c^2*x^2 + 12*a^2*b*c*d*x^2 - 6*a^3*d^2*x^2 + 12*b^3*c^2*x^3 - 24*a*b^2*c*d*x^3 + 12*a^2*b*d^2*x^3)/(12*a^4*x^4) + (b^2*(-(b*c) + a*d)^2*Log[x])/a^5 - (b^2*(-(b*c) + a*d)^2*Log[a + b*x])/a^5","A",1
222,1,247,152,0.1455038,"\int \frac{x^3 (c+d x)^3}{a+b x} \, dx","IntegrateAlgebraic[(x^3*(c + d*x)^3)/(a + b*x),x]","\frac{a^3 (a d-b c)^3 \log (a+b x)}{b^7}+\frac{x \left(-60 a^5 d^3+180 a^4 b c d^2+30 a^4 b d^3 x-180 a^3 b^2 c^2 d-90 a^3 b^2 c d^2 x-20 a^3 b^2 d^3 x^2+60 a^2 b^3 c^3+90 a^2 b^3 c^2 d x+60 a^2 b^3 c d^2 x^2+15 a^2 b^3 d^3 x^3-30 a b^4 c^3 x-60 a b^4 c^2 d x^2-45 a b^4 c d^2 x^3-12 a b^4 d^3 x^4+20 b^5 c^3 x^2+45 b^5 c^2 d x^3+36 b^5 c d^2 x^4+10 b^5 d^3 x^5\right)}{60 b^6}","-\frac{a^3 (b c-a d)^3 \log (a+b x)}{b^7}+\frac{a^2 x (b c-a d)^3}{b^6}+\frac{d x^4 \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{4 b^3}-\frac{a x^2 (b c-a d)^3}{2 b^5}+\frac{x^3 (b c-a d)^3}{3 b^4}+\frac{d^2 x^5 (3 b c-a d)}{5 b^2}+\frac{d^3 x^6}{6 b}",1,"(x*(60*a^2*b^3*c^3 - 180*a^3*b^2*c^2*d + 180*a^4*b*c*d^2 - 60*a^5*d^3 - 30*a*b^4*c^3*x + 90*a^2*b^3*c^2*d*x - 90*a^3*b^2*c*d^2*x + 30*a^4*b*d^3*x + 20*b^5*c^3*x^2 - 60*a*b^4*c^2*d*x^2 + 60*a^2*b^3*c*d^2*x^2 - 20*a^3*b^2*d^3*x^2 + 45*b^5*c^2*d*x^3 - 45*a*b^4*c*d^2*x^3 + 15*a^2*b^3*d^3*x^3 + 36*b^5*c*d^2*x^4 - 12*a*b^4*d^3*x^4 + 10*b^5*d^3*x^5))/(60*b^6) + (a^3*(-(b*c) + a*d)^3*Log[a + b*x])/b^7","A",1
223,1,190,129,0.101298,"\int \frac{x^2 (c+d x)^3}{a+b x} \, dx","IntegrateAlgebraic[(x^2*(c + d*x)^3)/(a + b*x),x]","\frac{x \left(60 a^4 d^3-180 a^3 b c d^2-30 a^3 b d^3 x+180 a^2 b^2 c^2 d+90 a^2 b^2 c d^2 x+20 a^2 b^2 d^3 x^2-60 a b^3 c^3-90 a b^3 c^2 d x-60 a b^3 c d^2 x^2-15 a b^3 d^3 x^3+30 b^4 c^3 x+60 b^4 c^2 d x^2+45 b^4 c d^2 x^3+12 b^4 d^3 x^4\right)}{60 b^5}-\frac{a^2 (a d-b c)^3 \log (a+b x)}{b^6}","\frac{a^2 (b c-a d)^3 \log (a+b x)}{b^6}+\frac{d x^3 \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{3 b^3}-\frac{a x (b c-a d)^3}{b^5}+\frac{x^2 (b c-a d)^3}{2 b^4}+\frac{d^2 x^4 (3 b c-a d)}{4 b^2}+\frac{d^3 x^5}{5 b}",1,"(x*(-60*a*b^3*c^3 + 180*a^2*b^2*c^2*d - 180*a^3*b*c*d^2 + 60*a^4*d^3 + 30*b^4*c^3*x - 90*a*b^3*c^2*d*x + 90*a^2*b^2*c*d^2*x - 30*a^3*b*d^3*x + 60*b^4*c^2*d*x^2 - 60*a*b^3*c*d^2*x^2 + 20*a^2*b^2*d^3*x^2 + 45*b^4*c*d^2*x^3 - 15*a*b^3*d^3*x^3 + 12*b^4*d^3*x^4))/(60*b^5) - (a^2*(-(b*c) + a*d)^3*Log[a + b*x])/b^6","A",1
224,1,133,106,0.0736999,"\int \frac{x (c+d x)^3}{a+b x} \, dx","IntegrateAlgebraic[(x*(c + d*x)^3)/(a + b*x),x]","\frac{x \left(-12 a^3 d^3+36 a^2 b c d^2+6 a^2 b d^3 x-36 a b^2 c^2 d-18 a b^2 c d^2 x-4 a b^2 d^3 x^2+12 b^3 c^3+18 b^3 c^2 d x+12 b^3 c d^2 x^2+3 b^3 d^3 x^3\right)}{12 b^4}+\frac{a (a d-b c)^3 \log (a+b x)}{b^5}","\frac{d x^2 \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{2 b^3}-\frac{a (b c-a d)^3 \log (a+b x)}{b^5}+\frac{x (b c-a d)^3}{b^4}+\frac{d^2 x^3 (3 b c-a d)}{3 b^2}+\frac{d^3 x^4}{4 b}",1,"(x*(12*b^3*c^3 - 36*a*b^2*c^2*d + 36*a^2*b*c*d^2 - 12*a^3*d^3 + 18*b^3*c^2*d*x - 18*a*b^2*c*d^2*x + 6*a^2*b*d^3*x + 12*b^3*c*d^2*x^2 - 4*a*b^2*d^3*x^2 + 3*b^3*d^3*x^3))/(12*b^4) + (a*(-(b*c) + a*d)^3*Log[a + b*x])/b^5","A",1
225,1,80,73,0.0005826,"\int \frac{(c+d x)^3}{a+b x} \, dx","IntegrateAlgebraic[(c + d*x)^3/(a + b*x),x]","\frac{d x \left(6 a^2 d^2-18 a b c d-3 a b d^2 x+18 b^2 c^2+9 b^2 c d x+2 b^2 d^2 x^2\right)}{6 b^3}+\frac{(b c-a d)^3 \log (a+b x)}{b^4}","\frac{(b c-a d)^3 \log (a+b x)}{b^4}+\frac{d x (b c-a d)^2}{b^3}+\frac{(c+d x)^2 (b c-a d)}{2 b^2}+\frac{(c+d x)^3}{3 b}",1,"(d*x*(18*b^2*c^2 - 18*a*b*c*d + 6*a^2*d^2 + 9*b^2*c*d*x - 3*a*b*d^2*x + 2*b^2*d^2*x^2))/(6*b^3) + ((b*c - a*d)^3*Log[a + b*x])/b^4","A",1
226,1,57,64,0.0419377,"\int \frac{(c+d x)^3}{x (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^3/(x*(a + b*x)),x]","\frac{(a d-b c)^3 \log (a+b x)}{a b^3}+\frac{d^2 x (-2 a d+6 b c+b d x)}{2 b^2}+\frac{c^3 \log (x)}{a}","-\frac{(b c-a d)^3 \log (a+b x)}{a b^3}+\frac{d^2 x (3 b c-a d)}{b^2}+\frac{c^3 \log (x)}{a}+\frac{d^3 x^2}{2 b}",1,"(d^2*x*(6*b*c - 2*a*d + b*d*x))/(2*b^2) + (c^3*Log[x])/a + ((-(b*c) + a*d)^3*Log[a + b*x])/(a*b^3)","A",1
227,1,70,61,0.0525349,"\int \frac{(c+d x)^3}{x^2 (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^3/(x^2*(a + b*x)),x]","-\frac{(a d-b c)^3 \log (a+b x)}{a^2 b^2}+\frac{\log (x) \left(3 a c^2 d-b c^3\right)}{a^2}+\frac{a d^3 x^2-b c^3}{a b x}","\frac{(b c-a d)^3 \log (a+b x)}{a^2 b^2}-\frac{c^2 \log (x) (b c-3 a d)}{a^2}-\frac{c^3}{a x}+\frac{d^3 x}{b}",1,"(-(b*c^3) + a*d^3*x^2)/(a*b*x) + ((-(b*c^3) + 3*a*c^2*d)*Log[x])/a^2 - ((-(b*c) + a*d)^3*Log[a + b*x])/(a^2*b^2)","A",1
228,1,82,85,0.1065449,"\int \frac{(c+d x)^3}{x^3 (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^3/(x^3*(a + b*x)),x]","\frac{(a d-b c)^3 \log (a+b x)}{a^3 b}-\frac{c^2 (a c+6 a d x-2 b c x)}{2 a^2 x^2}+\frac{\log (x) \left(3 a^2 c d^2-3 a b c^2 d+b^2 c^3\right)}{a^3}","-\frac{(b c-a d)^3 \log (a+b x)}{a^3 b}+\frac{c^2 (b c-3 a d)}{a^2 x}+\frac{c \log (x) \left(3 a^2 d^2-3 a b c d+b^2 c^2\right)}{a^3}-\frac{c^3}{2 a x^2}",1,"-1/2*(c^2*(a*c - 2*b*c*x + 6*a*d*x))/(a^2*x^2) + ((b^2*c^3 - 3*a*b*c^2*d + 3*a^2*c*d^2)*Log[x])/a^3 + ((-(b*c) + a*d)^3*Log[a + b*x])/(a^3*b)","A",1
229,1,105,103,0.0911337,"\int \frac{(c+d x)^3}{x^4 (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^3/(x^4*(a + b*x)),x]","\frac{\log (x) (a d-b c)^3}{a^4}-\frac{(a d-b c)^3 \log (a+b x)}{a^4}-\frac{c \left(2 a^2 c^2+9 a^2 c d x+18 a^2 d^2 x^2-3 a b c^2 x-18 a b c d x^2+6 b^2 c^2 x^2\right)}{6 a^3 x^3}","-\frac{\log (x) (b c-a d)^3}{a^4}+\frac{(b c-a d)^3 \log (a+b x)}{a^4}+\frac{c^2 (b c-3 a d)}{2 a^2 x^2}-\frac{c \left(3 a^2 d^2-3 a b c d+b^2 c^2\right)}{a^3 x}-\frac{c^3}{3 a x^3}",1,"-1/6*(c*(2*a^2*c^2 - 3*a*b*c^2*x + 9*a^2*c*d*x + 6*b^2*c^2*x^2 - 18*a*b*c*d*x^2 + 18*a^2*d^2*x^2))/(a^3*x^3) + ((-(b*c) + a*d)^3*Log[x])/a^4 - ((-(b*c) + a*d)^3*Log[a + b*x])/a^4","A",1
230,1,164,124,0.1410874,"\int \frac{(c+d x)^3}{x^5 (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^3/(x^5*(a + b*x)),x]","-\frac{b \log (x) (a d-b c)^3}{a^5}+\frac{b (a d-b c)^3 \log (a+b x)}{a^5}+\frac{-3 a^3 c^3-12 a^3 c^2 d x-18 a^3 c d^2 x^2-12 a^3 d^3 x^3+4 a^2 b c^3 x+18 a^2 b c^2 d x^2+36 a^2 b c d^2 x^3-6 a b^2 c^3 x^2-36 a b^2 c^2 d x^3+12 b^3 c^3 x^3}{12 a^4 x^4}","\frac{b \log (x) (b c-a d)^3}{a^5}-\frac{b (b c-a d)^3 \log (a+b x)}{a^5}+\frac{(b c-a d)^3}{a^4 x}+\frac{c^2 (b c-3 a d)}{3 a^2 x^3}-\frac{c \left(3 a^2 d^2-3 a b c d+b^2 c^2\right)}{2 a^3 x^2}-\frac{c^3}{4 a x^4}",1,"(-3*a^3*c^3 + 4*a^2*b*c^3*x - 12*a^3*c^2*d*x - 6*a*b^2*c^3*x^2 + 18*a^2*b*c^2*d*x^2 - 18*a^3*c*d^2*x^2 + 12*b^3*c^3*x^3 - 36*a*b^2*c^2*d*x^3 + 36*a^2*b*c*d^2*x^3 - 12*a^3*d^3*x^3)/(12*a^4*x^4) - (b*(-(b*c) + a*d)^3*Log[x])/a^5 + (b*(-(b*c) + a*d)^3*Log[a + b*x])/a^5","A",1
231,1,224,150,0.1243999,"\int \frac{(c+d x)^3}{x^6 (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^3/(x^6*(a + b*x)),x]","\frac{b^2 \log (x) (a d-b c)^3}{a^6}-\frac{b^2 (a d-b c)^3 \log (a+b x)}{a^6}+\frac{-12 a^4 c^3-45 a^4 c^2 d x-60 a^4 c d^2 x^2-30 a^4 d^3 x^3+15 a^3 b c^3 x+60 a^3 b c^2 d x^2+90 a^3 b c d^2 x^3+60 a^3 b d^3 x^4-20 a^2 b^2 c^3 x^2-90 a^2 b^2 c^2 d x^3-180 a^2 b^2 c d^2 x^4+30 a b^3 c^3 x^3+180 a b^3 c^2 d x^4-60 b^4 c^3 x^4}{60 a^5 x^5}","-\frac{b^2 \log (x) (b c-a d)^3}{a^6}+\frac{b^2 (b c-a d)^3 \log (a+b x)}{a^6}-\frac{b (b c-a d)^3}{a^5 x}+\frac{(b c-a d)^3}{2 a^4 x^2}+\frac{c^2 (b c-3 a d)}{4 a^2 x^4}-\frac{c \left(3 a^2 d^2-3 a b c d+b^2 c^2\right)}{3 a^3 x^3}-\frac{c^3}{5 a x^5}",1,"(-12*a^4*c^3 + 15*a^3*b*c^3*x - 45*a^4*c^2*d*x - 20*a^2*b^2*c^3*x^2 + 60*a^3*b*c^2*d*x^2 - 60*a^4*c*d^2*x^2 + 30*a*b^3*c^3*x^3 - 90*a^2*b^2*c^2*d*x^3 + 90*a^3*b*c*d^2*x^3 - 30*a^4*d^3*x^3 - 60*b^4*c^3*x^4 + 180*a*b^3*c^2*d*x^4 - 180*a^2*b^2*c*d^2*x^4 + 60*a^3*b*d^3*x^4)/(60*a^5*x^5) + (b^2*(-(b*c) + a*d)^3*Log[x])/a^6 - (b^2*(-(b*c) + a*d)^3*Log[a + b*x])/a^6","A",1
232,1,163,145,0.1051105,"\int \frac{x^5}{(a+b x) (c+d x)} \, dx","IntegrateAlgebraic[x^5/((a + b*x)*(c + d*x)),x]","-\frac{a^5 \log (a+b x)}{b^5 (b c-a d)}+\frac{x \left(-12 a^3 d^3-12 a^2 b c d^2+6 a^2 b d^3 x-12 a b^2 c^2 d+6 a b^2 c d^2 x-4 a b^2 d^3 x^2-12 b^3 c^3+6 b^3 c^2 d x-4 b^3 c d^2 x^2+3 b^3 d^3 x^3\right)}{12 b^4 d^4}-\frac{c^5 \log (c+d x)}{d^5 (a d-b c)}","-\frac{a^5 \log (a+b x)}{b^5 (b c-a d)}-\frac{x (a d+b c) \left(a^2 d^2+b^2 c^2\right)}{b^4 d^4}+\frac{x^2 \left(a^2 d^2+a b c d+b^2 c^2\right)}{2 b^3 d^3}-\frac{x^3 (a d+b c)}{3 b^2 d^2}+\frac{c^5 \log (c+d x)}{d^5 (b c-a d)}+\frac{x^4}{4 b d}",1,"(x*(-12*b^3*c^3 - 12*a*b^2*c^2*d - 12*a^2*b*c*d^2 - 12*a^3*d^3 + 6*b^3*c^2*d*x + 6*a*b^2*c*d^2*x + 6*a^2*b*d^3*x - 4*b^3*c*d^2*x^2 - 4*a*b^2*d^3*x^2 + 3*b^3*d^3*x^3))/(12*b^4*d^4) - (a^5*Log[a + b*x])/(b^5*(b*c - a*d)) - (c^5*Log[c + d*x])/(d^5*(-(b*c) + a*d))","A",1
233,1,108,109,0.0816224,"\int \frac{x^4}{(a+b x) (c+d x)} \, dx","IntegrateAlgebraic[x^4/((a + b*x)*(c + d*x)),x]","\frac{a^4 \log (a+b x)}{b^4 (b c-a d)}+\frac{x \left(6 a^2 d^2+6 a b c d-3 a b d^2 x+6 b^2 c^2-3 b^2 c d x+2 b^2 d^2 x^2\right)}{6 b^3 d^3}+\frac{c^4 \log (c+d x)}{d^4 (a d-b c)}","\frac{a^4 \log (a+b x)}{b^4 (b c-a d)}+\frac{x \left(a^2 d^2+a b c d+b^2 c^2\right)}{b^3 d^3}-\frac{x^2 (a d+b c)}{2 b^2 d^2}-\frac{c^4 \log (c+d x)}{d^4 (b c-a d)}+\frac{x^3}{3 b d}",1,"(x*(6*b^2*c^2 + 6*a*b*c*d + 6*a^2*d^2 - 3*b^2*c*d*x - 3*a*b*d^2*x + 2*b^2*d^2*x^2))/(6*b^3*d^3) + (a^4*Log[a + b*x])/(b^4*(b*c - a*d)) + (c^4*Log[c + d*x])/(d^4*(-(b*c) + a*d))","A",1
234,1,73,77,0.0550335,"\int \frac{x^3}{(a+b x) (c+d x)} \, dx","IntegrateAlgebraic[x^3/((a + b*x)*(c + d*x)),x]","-\frac{a^3 \log (a+b x)}{b^3 (b c-a d)}+\frac{x (-2 a d-2 b c+b d x)}{2 b^2 d^2}-\frac{c^3 \log (c+d x)}{d^3 (a d-b c)}","-\frac{a^3 \log (a+b x)}{b^3 (b c-a d)}-\frac{x (a d+b c)}{b^2 d^2}+\frac{c^3 \log (c+d x)}{d^3 (b c-a d)}+\frac{x^2}{2 b d}",1,"(x*(-2*b*c - 2*a*d + b*d*x))/(2*b^2*d^2) - (a^3*Log[a + b*x])/(b^3*(b*c - a*d)) - (c^3*Log[c + d*x])/(d^3*(-(b*c) + a*d))","A",1
235,1,55,56,0.0401677,"\int \frac{x^2}{(a+b x) (c+d x)} \, dx","IntegrateAlgebraic[x^2/((a + b*x)*(c + d*x)),x]","\frac{a^2 \log (a+b x)}{b^2 (b c-a d)}+\frac{c^2 \log (c+d x)}{d^2 (a d-b c)}+\frac{x}{b d}","\frac{a^2 \log (a+b x)}{b^2 (b c-a d)}-\frac{c^2 \log (c+d x)}{d^2 (b c-a d)}+\frac{x}{b d}",1,"x/(b*d) + (a^2*Log[a + b*x])/(b^2*(b*c - a*d)) + (c^2*Log[c + d*x])/(d^2*(-(b*c) + a*d))","A",1
236,1,45,44,0.0286114,"\int \frac{x}{(a+b x) (c+d x)} \, dx","IntegrateAlgebraic[x/((a + b*x)*(c + d*x)),x]","-\frac{a \log (a+b x)}{b (b c-a d)}-\frac{c \log (c+d x)}{d (a d-b c)}","\frac{c \log (c+d x)}{d (b c-a d)}-\frac{a \log (a+b x)}{b (b c-a d)}",1,"-((a*Log[a + b*x])/(b*(b*c - a*d))) - (c*Log[c + d*x])/(d*(-(b*c) + a*d))","A",1
237,1,35,36,0.0005825,"\int \frac{1}{(a+b x) (c+d x)} \, dx","IntegrateAlgebraic[1/((a + b*x)*(c + d*x)),x]","\frac{\log (a+b x)}{b c-a d}+\frac{\log (c+d x)}{a d-b c}","\frac{\log (a+b x)}{b c-a d}-\frac{\log (c+d x)}{b c-a d}",1,"Log[a + b*x]/(b*c - a*d) + Log[c + d*x]/(-(b*c) + a*d)","A",1
238,1,52,53,0.0417622,"\int \frac{1}{x (a+b x) (c+d x)} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)*(c + d*x)),x]","\frac{b \log (a+b x)}{a (a d-b c)}+\frac{d \log (c+d x)}{c (b c-a d)}+\frac{\log (x)}{a c}","-\frac{b \log (a+b x)}{a (b c-a d)}+\frac{d \log (c+d x)}{c (b c-a d)}+\frac{\log (x)}{a c}",1,"Log[x]/(a*c) + (b*Log[a + b*x])/(a*(-(b*c) + a*d)) + (d*Log[c + d*x])/(c*(b*c - a*d))","A",1
239,1,78,76,0.0591096,"\int \frac{1}{x^2 (a+b x) (c+d x)} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)*(c + d*x)),x]","-\frac{b^2 \log (a+b x)}{a^2 (a d-b c)}+\frac{\log (x) (-a d-b c)}{a^2 c^2}-\frac{d^2 \log (c+d x)}{c^2 (b c-a d)}-\frac{1}{a c x}","\frac{b^2 \log (a+b x)}{a^2 (b c-a d)}-\frac{\log (x) (a d+b c)}{a^2 c^2}-\frac{d^2 \log (c+d x)}{c^2 (b c-a d)}-\frac{1}{a c x}",1,"-(1/(a*c*x)) + ((-(b*c) - a*d)*Log[x])/(a^2*c^2) - (b^2*Log[a + b*x])/(a^2*(-(b*c) + a*d)) - (d^2*Log[c + d*x])/(c^2*(b*c - a*d))","A",1
240,1,104,107,0.0777036,"\int \frac{1}{x^3 (a+b x) (c+d x)} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)*(c + d*x)),x]","\frac{b^3 \log (a+b x)}{a^3 (a d-b c)}+\frac{-a c+2 a d x+2 b c x}{2 a^2 c^2 x^2}+\frac{\log (x) \left(a^2 d^2+a b c d+b^2 c^2\right)}{a^3 c^3}+\frac{d^3 \log (c+d x)}{c^3 (b c-a d)}","-\frac{b^3 \log (a+b x)}{a^3 (b c-a d)}+\frac{a d+b c}{a^2 c^2 x}+\frac{\log (x) \left(a^2 d^2+a b c d+b^2 c^2\right)}{a^3 c^3}+\frac{d^3 \log (c+d x)}{c^3 (b c-a d)}-\frac{1}{2 a c x^2}",1,"(-(a*c) + 2*b*c*x + 2*a*d*x)/(2*a^2*c^2*x^2) + ((b^2*c^2 + a*b*c*d + a^2*d^2)*Log[x])/(a^3*c^3) + (b^3*Log[a + b*x])/(a^3*(-(b*c) + a*d)) + (d^3*Log[c + d*x])/(c^3*(b*c - a*d))","A",1
241,1,164,144,0.1106221,"\int \frac{1}{x^4 (a+b x) (c+d x)} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x)*(c + d*x)),x]","-\frac{b^4 \log (a+b x)}{a^4 (a d-b c)}+\frac{-2 a^2 c^2+3 a^2 c d x-6 a^2 d^2 x^2+3 a b c^2 x-6 a b c d x^2-6 b^2 c^2 x^2}{6 a^3 c^3 x^3}+\frac{\log (x) \left(-a^3 d^3-a^2 b c d^2-a b^2 c^2 d-b^3 c^3\right)}{a^4 c^4}-\frac{d^4 \log (c+d x)}{c^4 (b c-a d)}","\frac{b^4 \log (a+b x)}{a^4 (b c-a d)}+\frac{a d+b c}{2 a^2 c^2 x^2}-\frac{\log (x) (a d+b c) \left(a^2 d^2+b^2 c^2\right)}{a^4 c^4}-\frac{a^2 d^2+a b c d+b^2 c^2}{a^3 c^3 x}-\frac{d^4 \log (c+d x)}{c^4 (b c-a d)}-\frac{1}{3 a c x^3}",1,"(-2*a^2*c^2 + 3*a*b*c^2*x + 3*a^2*c*d*x - 6*b^2*c^2*x^2 - 6*a*b*c*d*x^2 - 6*a^2*d^2*x^2)/(6*a^3*c^3*x^3) + ((-(b^3*c^3) - a*b^2*c^2*d - a^2*b*c*d^2 - a^3*d^3)*Log[x])/(a^4*c^4) - (b^4*Log[a + b*x])/(a^4*(-(b*c) + a*d)) - (d^4*Log[c + d*x])/(c^4*(b*c - a*d))","A",1
242,1,256,147,0.2100898,"\int \frac{x^5}{(a+b x) (c+d x)^2} \, dx","IntegrateAlgebraic[x^5/((a + b*x)*(c + d*x)^2),x]","-\frac{a^5 \log (a+b x)}{b^4 (b c-a d)^2}+\frac{-6 a^3 c d^4 x-6 a^3 d^5 x^2-6 a^2 b c^2 d^3 x-3 a^2 b c d^4 x^2+3 a^2 b d^5 x^3-6 a b^2 c^3 d^2 x-3 a b^2 c^2 d^3 x^2+a b^2 c d^4 x^3-2 a b^2 d^5 x^4-6 b^3 c^5+18 b^3 c^4 d x+12 b^3 c^3 d^2 x^2-4 b^3 c^2 d^3 x^3+2 b^3 c d^4 x^4}{6 b^3 d^5 (c+d x) (b c-a d)}+\frac{\left(5 a c^4 d-4 b c^5\right) \log (c+d x)}{d^5 (a d-b c)^2}","-\frac{a^5 \log (a+b x)}{b^4 (b c-a d)^2}+\frac{x \left(a^2 d^2+2 a b c d+3 b^2 c^2\right)}{b^3 d^4}-\frac{x^2 (a d+2 b c)}{2 b^2 d^3}-\frac{c^5}{d^5 (c+d x) (b c-a d)}-\frac{c^4 (4 b c-5 a d) \log (c+d x)}{d^5 (b c-a d)^2}+\frac{x^3}{3 b d^2}",1,"(-6*b^3*c^5 + 18*b^3*c^4*d*x - 6*a*b^2*c^3*d^2*x - 6*a^2*b*c^2*d^3*x - 6*a^3*c*d^4*x + 12*b^3*c^3*d^2*x^2 - 3*a*b^2*c^2*d^3*x^2 - 3*a^2*b*c*d^4*x^2 - 6*a^3*d^5*x^2 - 4*b^3*c^2*d^3*x^3 + a*b^2*c*d^4*x^3 + 3*a^2*b*d^5*x^3 + 2*b^3*c*d^4*x^4 - 2*a*b^2*d^5*x^4)/(6*b^3*d^5*(b*c - a*d)*(c + d*x)) - (a^5*Log[a + b*x])/(b^4*(b*c - a*d)^2) + ((-4*b*c^5 + 5*a*c^4*d)*Log[c + d*x])/(d^5*(-(b*c) + a*d)^2)","A",1
243,1,181,110,0.2414871,"\int \frac{x^4}{(a+b x) (c+d x)^2} \, dx","IntegrateAlgebraic[x^4/((a + b*x)*(c + d*x)^2),x]","\frac{a^4 \log (a+b x)}{b^3 (b c-a d)^2}+\frac{2 a^2 c d^3 x+2 a^2 d^4 x^2+2 a b c^2 d^2 x+a b c d^3 x^2-a b d^4 x^3+2 b^2 c^4-4 b^2 c^3 d x-3 b^2 c^2 d^2 x^2+b^2 c d^3 x^3}{2 b^2 d^4 (c+d x) (b c-a d)}+\frac{\left(3 b c^4-4 a c^3 d\right) \log (c+d x)}{d^4 (a d-b c)^2}","\frac{a^4 \log (a+b x)}{b^3 (b c-a d)^2}-\frac{x (a d+2 b c)}{b^2 d^3}+\frac{c^4}{d^4 (c+d x) (b c-a d)}+\frac{c^3 (3 b c-4 a d) \log (c+d x)}{d^4 (b c-a d)^2}+\frac{x^2}{2 b d^2}",1,"(2*b^2*c^4 - 4*b^2*c^3*d*x + 2*a*b*c^2*d^2*x + 2*a^2*c*d^3*x - 3*b^2*c^2*d^2*x^2 + a*b*c*d^3*x^2 + 2*a^2*d^4*x^2 + b^2*c*d^3*x^3 - a*b*d^4*x^3)/(2*b^2*d^4*(b*c - a*d)*(c + d*x)) + (a^4*Log[a + b*x])/(b^3*(b*c - a*d)^2) + ((3*b*c^4 - 4*a*c^3*d)*Log[c + d*x])/(d^4*(-(b*c) + a*d)^2)","A",1
244,1,123,91,0.1447539,"\int \frac{x^3}{(a+b x) (c+d x)^2} \, dx","IntegrateAlgebraic[x^3/((a + b*x)*(c + d*x)^2),x]","-\frac{a^3 \log (a+b x)}{b^2 (b c-a d)^2}+\frac{\left(3 a c^2 d-2 b c^3\right) \log (c+d x)}{d^3 (a d-b c)^2}+\frac{-a c d^2 x-a d^3 x^2-b c^3+b c^2 d x+b c d^2 x^2}{b d^3 (c+d x) (b c-a d)}","-\frac{a^3 \log (a+b x)}{b^2 (b c-a d)^2}-\frac{c^3}{d^3 (c+d x) (b c-a d)}-\frac{c^2 (2 b c-3 a d) \log (c+d x)}{d^3 (b c-a d)^2}+\frac{x}{b d^2}",1,"(-(b*c^3) + b*c^2*d*x - a*c*d^2*x + b*c*d^2*x^2 - a*d^3*x^2)/(b*d^3*(b*c - a*d)*(c + d*x)) - (a^3*Log[a + b*x])/(b^2*(b*c - a*d)^2) + ((-2*b*c^3 + 3*a*c^2*d)*Log[c + d*x])/(d^3*(-(b*c) + a*d)^2)","A",1
245,1,80,77,0.0724918,"\int \frac{x^2}{(a+b x) (c+d x)^2} \, dx","IntegrateAlgebraic[x^2/((a + b*x)*(c + d*x)^2),x]","\frac{a^2 \log (a+b x)}{b (b c-a d)^2}-\frac{c^2}{d^2 (c+d x) (a d-b c)}+\frac{\left(b c^2-2 a c d\right) \log (c+d x)}{d^2 (a d-b c)^2}","\frac{a^2 \log (a+b x)}{b (b c-a d)^2}+\frac{c^2}{d^2 (c+d x) (b c-a d)}+\frac{c (b c-2 a d) \log (c+d x)}{d^2 (b c-a d)^2}",1,"-(c^2/(d^2*(-(b*c) + a*d)*(c + d*x))) + (a^2*Log[a + b*x])/(b*(b*c - a*d)^2) + ((b*c^2 - 2*a*c*d)*Log[c + d*x])/(d^2*(-(b*c) + a*d)^2)","A",1
246,1,60,61,0.0512431,"\int \frac{x}{(a+b x) (c+d x)^2} \, dx","IntegrateAlgebraic[x/((a + b*x)*(c + d*x)^2),x]","\frac{c}{d (c+d x) (a d-b c)}-\frac{a \log (a+b x)}{(b c-a d)^2}+\frac{a \log (c+d x)}{(b c-a d)^2}","-\frac{c}{d (c+d x) (b c-a d)}-\frac{a \log (a+b x)}{(b c-a d)^2}+\frac{a \log (c+d x)}{(b c-a d)^2}",1,"c/(d*(-(b*c) + a*d)*(c + d*x)) - (a*Log[a + b*x])/(b*c - a*d)^2 + (a*Log[c + d*x])/(b*c - a*d)^2","A",1
247,1,56,56,0.0005813,"\int \frac{1}{(a+b x) (c+d x)^2} \, dx","IntegrateAlgebraic[1/((a + b*x)*(c + d*x)^2),x]","\frac{1}{(c+d x) (b c-a d)}+\frac{b \log (a+b x)}{(b c-a d)^2}-\frac{b \log (c+d x)}{(b c-a d)^2}","\frac{1}{(c+d x) (b c-a d)}+\frac{b \log (a+b x)}{(b c-a d)^2}-\frac{b \log (c+d x)}{(b c-a d)^2}",1,"1/((b*c - a*d)*(c + d*x)) + (b*Log[a + b*x])/(b*c - a*d)^2 - (b*Log[c + d*x])/(b*c - a*d)^2","A",1
248,1,89,87,0.1422984,"\int \frac{1}{x (a+b x) (c+d x)^2} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)*(c + d*x)^2),x]","-\frac{b^2 \log (a+b x)}{a (a d-b c)^2}+\frac{\left(2 b c d-a d^2\right) \log (c+d x)}{c^2 (b c-a d)^2}-\frac{d}{c (c+d x) (b c-a d)}+\frac{\log (x)}{a c^2}","-\frac{b^2 \log (a+b x)}{a (b c-a d)^2}+\frac{d (2 b c-a d) \log (c+d x)}{c^2 (b c-a d)^2}-\frac{d}{c (c+d x) (b c-a d)}+\frac{\log (x)}{a c^2}",1,"-(d/(c*(b*c - a*d)*(c + d*x))) + Log[x]/(a*c^2) - (b^2*Log[a + b*x])/(a*(-(b*c) + a*d)^2) + ((2*b*c*d - a*d^2)*Log[c + d*x])/(c^2*(b*c - a*d)^2)","A",1
249,1,126,110,0.1383014,"\int \frac{1}{x^2 (a+b x) (c+d x)^2} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)*(c + d*x)^2),x]","\frac{b^3 \log (a+b x)}{a^2 (a d-b c)^2}+\frac{\log (x) (-2 a d-b c)}{a^2 c^3}+\frac{\left(2 a d^3-3 b c d^2\right) \log (c+d x)}{c^3 (b c-a d)^2}+\frac{-a c d-2 a d^2 x+b c^2+b c d x}{a c^2 x (c+d x) (a d-b c)}","\frac{b^3 \log (a+b x)}{a^2 (b c-a d)^2}-\frac{\log (x) (2 a d+b c)}{a^2 c^3}-\frac{d^2 (3 b c-2 a d) \log (c+d x)}{c^3 (b c-a d)^2}+\frac{d^2}{c^2 (c+d x) (b c-a d)}-\frac{1}{a c^2 x}",1,"(b*c^2 - a*c*d + b*c*d*x - 2*a*d^2*x)/(a*c^2*(-(b*c) + a*d)*x*(c + d*x)) + ((-(b*c) - 2*a*d)*Log[x])/(a^2*c^3) + (b^3*Log[a + b*x])/(a^2*(-(b*c) + a*d)^2) + ((-3*b*c*d^2 + 2*a*d^3)*Log[c + d*x])/(c^3*(b*c - a*d)^2)","A",1
250,1,198,144,0.5053825,"\int \frac{1}{x^3 (a+b x) (c+d x)^2} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)*(c + d*x)^2),x]","-\frac{b^4 \log (a+b x)}{a^3 (a d-b c)^2}+\frac{-a^2 c^2 d+3 a^2 c d^2 x+6 a^2 d^3 x^2+a b c^3-a b c^2 d x-2 a b c d^2 x^2-2 b^2 c^3 x-2 b^2 c^2 d x^2}{2 a^2 c^3 x^2 (c+d x) (a d-b c)}+\frac{\log (x) \left(3 a^2 d^2+2 a b c d+b^2 c^2\right)}{a^3 c^4}+\frac{\left(4 b c d^3-3 a d^4\right) \log (c+d x)}{c^4 (b c-a d)^2}","-\frac{b^4 \log (a+b x)}{a^3 (b c-a d)^2}+\frac{2 a d+b c}{a^2 c^3 x}+\frac{\log (x) \left(3 a^2 d^2+2 a b c d+b^2 c^2\right)}{a^3 c^4}+\frac{d^3 (4 b c-3 a d) \log (c+d x)}{c^4 (b c-a d)^2}-\frac{d^3}{c^3 (c+d x) (b c-a d)}-\frac{1}{2 a c^2 x^2}",1,"(a*b*c^3 - a^2*c^2*d - 2*b^2*c^3*x - a*b*c^2*d*x + 3*a^2*c*d^2*x - 2*b^2*c^2*d*x^2 - 2*a*b*c*d^2*x^2 + 6*a^2*d^3*x^2)/(2*a^2*c^3*(-(b*c) + a*d)*x^2*(c + d*x)) + ((b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*Log[x])/(a^3*c^4) - (b^4*Log[a + b*x])/(a^3*(-(b*c) + a*d)^2) + ((4*b*c*d^3 - 3*a*d^4)*Log[c + d*x])/(c^4*(b*c - a*d)^2)","A",1
251,1,288,161,0.2687303,"\int \frac{x^5}{(a+b x) (c+d x)^3} \, dx","IntegrateAlgebraic[x^5/((a + b*x)*(c + d*x)^3),x]","-\frac{a^5 \log (a+b x)}{b^3 (b c-a d)^3}-\frac{\left(10 a^2 c^3 d^2-15 a b c^4 d+6 b^2 c^5\right) \log (c+d x)}{d^5 (a d-b c)^3}+\frac{-2 a^3 c^2 d^4 x-4 a^3 c d^5 x^2-2 a^3 d^6 x^3-2 a^2 b c^3 d^3 x-3 a^2 b c^2 d^4 x^2+a^2 b d^6 x^4-9 a b^2 c^5 d+18 a b^2 c^3 d^3 x^2+6 a b^2 c^2 d^4 x^3-2 a b^2 c d^5 x^4+7 b^3 c^6+2 b^3 c^5 d x-11 b^3 c^4 d^2 x^2-4 b^3 c^3 d^3 x^3+b^3 c^2 d^4 x^4}{2 b^2 d^5 (c+d x)^2 (b c-a d)^2}","-\frac{a^5 \log (a+b x)}{b^3 (b c-a d)^3}+\frac{c^3 \left(10 a^2 d^2-15 a b c d+6 b^2 c^2\right) \log (c+d x)}{d^5 (b c-a d)^3}-\frac{x (a d+3 b c)}{b^2 d^4}-\frac{c^5}{2 d^5 (c+d x)^2 (b c-a d)}+\frac{c^4 (4 b c-5 a d)}{d^5 (c+d x) (b c-a d)^2}+\frac{x^2}{2 b d^3}",1,"(7*b^3*c^6 - 9*a*b^2*c^5*d + 2*b^3*c^5*d*x - 2*a^2*b*c^3*d^3*x - 2*a^3*c^2*d^4*x - 11*b^3*c^4*d^2*x^2 + 18*a*b^2*c^3*d^3*x^2 - 3*a^2*b*c^2*d^4*x^2 - 4*a^3*c*d^5*x^2 - 4*b^3*c^3*d^3*x^3 + 6*a*b^2*c^2*d^4*x^3 - 2*a^3*d^6*x^3 + b^3*c^2*d^4*x^4 - 2*a*b^2*c*d^5*x^4 + a^2*b*d^6*x^4)/(2*b^2*d^5*(b*c - a*d)^2*(c + d*x)^2) - (a^5*Log[a + b*x])/(b^3*(b*c - a*d)^3) - ((6*b^2*c^5 - 15*a*b*c^4*d + 10*a^2*c^3*d^2)*Log[c + d*x])/(d^5*(-(b*c) + a*d)^3)","A",1
252,1,225,140,0.2054147,"\int \frac{x^4}{(a+b x) (c+d x)^3} \, dx","IntegrateAlgebraic[x^4/((a + b*x)*(c + d*x)^3),x]","\frac{a^4 \log (a+b x)}{b^2 (b c-a d)^3}-\frac{\left(-6 a^2 c^2 d^2+8 a b c^3 d-3 b^2 c^4\right) \log (c+d x)}{d^4 (a d-b c)^3}+\frac{2 a^2 c^2 d^3 x+4 a^2 c d^4 x^2+2 a^2 d^5 x^3+7 a b c^4 d+4 a b c^3 d^2 x-8 a b c^2 d^3 x^2-4 a b c d^4 x^3-5 b^2 c^5-4 b^2 c^4 d x+4 b^2 c^3 d^2 x^2+2 b^2 c^2 d^3 x^3}{2 b d^4 (c+d x)^2 (b c-a d)^2}","\frac{a^4 \log (a+b x)}{b^2 (b c-a d)^3}-\frac{c^2 \left(6 a^2 d^2-8 a b c d+3 b^2 c^2\right) \log (c+d x)}{d^4 (b c-a d)^3}+\frac{c^4}{2 d^4 (c+d x)^2 (b c-a d)}-\frac{c^3 (3 b c-4 a d)}{d^4 (c+d x) (b c-a d)^2}+\frac{x}{b d^3}",1,"(-5*b^2*c^5 + 7*a*b*c^4*d - 4*b^2*c^4*d*x + 4*a*b*c^3*d^2*x + 2*a^2*c^2*d^3*x + 4*b^2*c^3*d^2*x^2 - 8*a*b*c^2*d^3*x^2 + 4*a^2*c*d^4*x^2 + 2*b^2*c^2*d^3*x^3 - 4*a*b*c*d^4*x^3 + 2*a^2*d^5*x^3)/(2*b*d^4*(b*c - a*d)^2*(c + d*x)^2) + (a^4*Log[a + b*x])/(b^2*(b*c - a*d)^3) - ((-3*b^2*c^4 + 8*a*b*c^3*d - 6*a^2*c^2*d^2)*Log[c + d*x])/(d^4*(-(b*c) + a*d)^3)","A",1
253,1,123,128,0.1043661,"\int \frac{x^3}{(a+b x) (c+d x)^3} \, dx","IntegrateAlgebraic[x^3/((a + b*x)*(c + d*x)^3),x]","-\frac{a^3 \log (a+b x)}{b (b c-a d)^3}-\frac{\left(3 a^2 c d^2-3 a b c^2 d+b^2 c^3\right) \log (c+d x)}{d^3 (a d-b c)^3}+\frac{c^2 \left(-5 a c d-6 a d^2 x+3 b c^2+4 b c d x\right)}{2 d^3 (c+d x)^2 (a d-b c)^2}","-\frac{a^3 \log (a+b x)}{b (b c-a d)^3}+\frac{c \left(3 a^2 d^2-3 a b c d+b^2 c^2\right) \log (c+d x)}{d^3 (b c-a d)^3}-\frac{c^3}{2 d^3 (c+d x)^2 (b c-a d)}+\frac{c^2 (2 b c-3 a d)}{d^3 (c+d x) (b c-a d)^2}",1,"(c^2*(3*b*c^2 - 5*a*c*d + 4*b*c*d*x - 6*a*d^2*x))/(2*d^3*(-(b*c) + a*d)^2*(c + d*x)^2) - (a^3*Log[a + b*x])/(b*(b*c - a*d)^3) - ((b^2*c^3 - 3*a*b*c^2*d + 3*a^2*c*d^2)*Log[c + d*x])/(d^3*(-(b*c) + a*d)^3)","A",1
254,1,91,100,0.102381,"\int \frac{x^2}{(a+b x) (c+d x)^3} \, dx","IntegrateAlgebraic[x^2/((a + b*x)*(c + d*x)^3),x]","\frac{a^2 \log (a+b x)}{(b c-a d)^3}-\frac{a^2 \log (c+d x)}{(b c-a d)^3}-\frac{c \left(-3 a c d-4 a d^2 x+b c^2+2 b c d x\right)}{2 d^2 (c+d x)^2 (a d-b c)^2}","\frac{a^2 \log (a+b x)}{(b c-a d)^3}-\frac{a^2 \log (c+d x)}{(b c-a d)^3}+\frac{c^2}{2 d^2 (c+d x)^2 (b c-a d)}-\frac{c (b c-2 a d)}{d^2 (c+d x) (b c-a d)^2}",1,"-1/2*(c*(b*c^2 - 3*a*c*d + 2*b*c*d*x - 4*a*d^2*x))/(d^2*(-(b*c) + a*d)^2*(c + d*x)^2) + (a^2*Log[a + b*x])/(b*c - a*d)^3 - (a^2*Log[c + d*x])/(b*c - a*d)^3","A",1
255,1,83,85,0.0763925,"\int \frac{x}{(a+b x) (c+d x)^3} \, dx","IntegrateAlgebraic[x/((a + b*x)*(c + d*x)^3),x]","\frac{-a c d-2 a d^2 x-b c^2}{2 d (c+d x)^2 (a d-b c)^2}-\frac{a b \log (a+b x)}{(b c-a d)^3}+\frac{a b \log (c+d x)}{(b c-a d)^3}","-\frac{a}{(c+d x) (b c-a d)^2}-\frac{c}{2 d (c+d x)^2 (b c-a d)}-\frac{a b \log (a+b x)}{(b c-a d)^3}+\frac{a b \log (c+d x)}{(b c-a d)^3}",1,"(-(b*c^2) - a*c*d - 2*a*d^2*x)/(2*d*(-(b*c) + a*d)^2*(c + d*x)^2) - (a*b*Log[a + b*x])/(b*c - a*d)^3 + (a*b*Log[c + d*x])/(b*c - a*d)^3","A",1
256,1,77,82,0.0006188,"\int \frac{1}{(a+b x) (c+d x)^3} \, dx","IntegrateAlgebraic[1/((a + b*x)*(c + d*x)^3),x]","\frac{b^2 \log (a+b x)}{(b c-a d)^3}-\frac{b^2 \log (c+d x)}{(b c-a d)^3}+\frac{-a d+3 b c+2 b d x}{2 (c+d x)^2 (b c-a d)^2}","\frac{b^2 \log (a+b x)}{(b c-a d)^3}-\frac{b^2 \log (c+d x)}{(b c-a d)^3}+\frac{b}{(c+d x) (b c-a d)^2}+\frac{1}{2 (c+d x)^2 (b c-a d)}",1,"(3*b*c - a*d + 2*b*d*x)/(2*(b*c - a*d)^2*(c + d*x)^2) + (b^2*Log[a + b*x])/(b*c - a*d)^3 - (b^2*Log[c + d*x])/(b*c - a*d)^3","A",1
257,1,128,134,0.305521,"\int \frac{1}{x (a+b x) (c+d x)^3} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)*(c + d*x)^3),x]","\frac{\left(a^2 d^3-3 a b c d^2+3 b^2 c^2 d\right) \log (c+d x)}{c^3 (b c-a d)^3}+\frac{b^3 \log (a+b x)}{a (a d-b c)^3}-\frac{d \left(-3 a c d-2 a d^2 x+5 b c^2+4 b c d x\right)}{2 c^2 (c+d x)^2 (b c-a d)^2}+\frac{\log (x)}{a c^3}","\frac{d \left(a^2 d^2-3 a b c d+3 b^2 c^2\right) \log (c+d x)}{c^3 (b c-a d)^3}-\frac{b^3 \log (a+b x)}{a (b c-a d)^3}-\frac{d (2 b c-a d)}{c^2 (c+d x) (b c-a d)^2}-\frac{d}{2 c (c+d x)^2 (b c-a d)}+\frac{\log (x)}{a c^3}",1,"-1/2*(d*(5*b*c^2 - 3*a*c*d + 4*b*c*d*x - 2*a*d^2*x))/(c^2*(b*c - a*d)^2*(c + d*x)^2) + Log[x]/(a*c^3) + (b^3*Log[a + b*x])/(a*(-(b*c) + a*d)^3) + ((3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*Log[c + d*x])/(c^3*(b*c - a*d)^3)","A",1
258,1,216,160,0.2256475,"\int \frac{1}{x^2 (a+b x) (c+d x)^3} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)*(c + d*x)^3),x]","-\frac{b^4 \log (a+b x)}{a^2 (a d-b c)^3}+\frac{\left(-3 a^2 d^4+8 a b c d^3-6 b^2 c^2 d^2\right) \log (c+d x)}{c^4 (b c-a d)^3}+\frac{-2 a^2 c^2 d^2-9 a^2 c d^3 x-6 a^2 d^4 x^2+4 a b c^3 d+15 a b c^2 d^2 x+10 a b c d^3 x^2-2 b^2 c^4-4 b^2 c^3 d x-2 b^2 c^2 d^2 x^2}{2 a c^3 x (c+d x)^2 (a d-b c)^2}+\frac{\log (x) (-3 a d-b c)}{a^2 c^4}","\frac{b^4 \log (a+b x)}{a^2 (b c-a d)^3}-\frac{d^2 \left(3 a^2 d^2-8 a b c d+6 b^2 c^2\right) \log (c+d x)}{c^4 (b c-a d)^3}-\frac{\log (x) (3 a d+b c)}{a^2 c^4}+\frac{d^2 (3 b c-2 a d)}{c^3 (c+d x) (b c-a d)^2}+\frac{d^2}{2 c^2 (c+d x)^2 (b c-a d)}-\frac{1}{a c^3 x}",1,"(-2*b^2*c^4 + 4*a*b*c^3*d - 2*a^2*c^2*d^2 - 4*b^2*c^3*d*x + 15*a*b*c^2*d^2*x - 9*a^2*c*d^3*x - 2*b^2*c^2*d^2*x^2 + 10*a*b*c*d^3*x^2 - 6*a^2*d^4*x^2)/(2*a*c^3*(-(b*c) + a*d)^2*x*(c + d*x)^2) + ((-(b*c) - 3*a*d)*Log[x])/(a^2*c^4) - (b^4*Log[a + b*x])/(a^2*(-(b*c) + a*d)^3) + ((-6*b^2*c^2*d^2 + 8*a*b*c*d^3 - 3*a^2*d^4)*Log[c + d*x])/(c^4*(b*c - a*d)^3)","A",1
259,1,264,165,0.1607068,"\int \frac{x^4 (c+d x)^2}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x^4*(c + d*x)^2)/(a + b*x)^2,x]","\frac{-30 a^6 d^2+60 a^5 b c d+150 a^5 b d^2 x-30 a^4 b^2 c^2-240 a^4 b^2 c d x+90 a^4 b^2 d^2 x^2+90 a^3 b^3 c^2 x-150 a^3 b^3 c d x^2-30 a^3 b^3 d^2 x^3+60 a^2 b^4 c^2 x^2+50 a^2 b^4 c d x^3+15 a^2 b^4 d^2 x^4-20 a b^5 c^2 x^3-25 a b^5 c d x^4-9 a b^5 d^2 x^5+10 b^6 c^2 x^4+15 b^6 c d x^5+6 b^6 d^2 x^6}{30 b^7 (a+b x)}-\frac{2 \left(3 a^5 d^2-5 a^4 b c d+2 a^3 b^2 c^2\right) \log (a+b x)}{b^7}","-\frac{a^4 (b c-a d)^2}{b^7 (a+b x)}-\frac{2 a^3 (2 b c-3 a d) (b c-a d) \log (a+b x)}{b^7}+\frac{a^2 x (3 b c-5 a d) (b c-a d)}{b^6}-\frac{a x^2 (b c-2 a d) (b c-a d)}{b^5}+\frac{x^3 (b c-3 a d) (b c-a d)}{3 b^4}+\frac{d x^4 (b c-a d)}{2 b^3}+\frac{d^2 x^5}{5 b^2}",1,"(-30*a^4*b^2*c^2 + 60*a^5*b*c*d - 30*a^6*d^2 + 90*a^3*b^3*c^2*x - 240*a^4*b^2*c*d*x + 150*a^5*b*d^2*x + 60*a^2*b^4*c^2*x^2 - 150*a^3*b^3*c*d*x^2 + 90*a^4*b^2*d^2*x^2 - 20*a*b^5*c^2*x^3 + 50*a^2*b^4*c*d*x^3 - 30*a^3*b^3*d^2*x^3 + 10*b^6*c^2*x^4 - 25*a*b^5*c*d*x^4 + 15*a^2*b^4*d^2*x^4 + 15*b^6*c*d*x^5 - 9*a*b^5*d^2*x^5 + 6*b^6*d^2*x^6)/(30*b^7*(a + b*x)) - (2*(2*a^3*b^2*c^2 - 5*a^4*b*c*d + 3*a^5*d^2)*Log[a + b*x])/b^7","A",1
260,1,222,136,0.1266069,"\int \frac{x^3 (c+d x)^2}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x^3*(c + d*x)^2)/(a + b*x)^2,x]","\frac{\left(5 a^4 d^2-8 a^3 b c d+3 a^2 b^2 c^2\right) \log (a+b x)}{b^6}+\frac{12 a^5 d^2-24 a^4 b c d-48 a^4 b d^2 x+12 a^3 b^2 c^2+72 a^3 b^2 c d x-30 a^3 b^2 d^2 x^2-24 a^2 b^3 c^2 x+48 a^2 b^3 c d x^2+10 a^2 b^3 d^2 x^3-18 a b^4 c^2 x^2-16 a b^4 c d x^3-5 a b^4 d^2 x^4+6 b^5 c^2 x^3+8 b^5 c d x^4+3 b^5 d^2 x^5}{12 b^6 (a+b x)}","\frac{a^3 (b c-a d)^2}{b^6 (a+b x)}+\frac{a^2 (3 b c-5 a d) (b c-a d) \log (a+b x)}{b^6}-\frac{2 a x (b c-2 a d) (b c-a d)}{b^5}+\frac{x^2 (b c-3 a d) (b c-a d)}{2 b^4}+\frac{2 d x^3 (b c-a d)}{3 b^3}+\frac{d^2 x^4}{4 b^2}",1,"(12*a^3*b^2*c^2 - 24*a^4*b*c*d + 12*a^5*d^2 - 24*a^2*b^3*c^2*x + 72*a^3*b^2*c*d*x - 48*a^4*b*d^2*x - 18*a*b^4*c^2*x^2 + 48*a^2*b^3*c*d*x^2 - 30*a^3*b^2*d^2*x^2 + 6*b^5*c^2*x^3 - 16*a*b^4*c*d*x^3 + 10*a^2*b^3*d^2*x^3 + 8*b^5*c*d*x^4 - 5*a*b^4*d^2*x^4 + 3*b^5*d^2*x^5)/(12*b^6*(a + b*x)) + ((3*a^2*b^2*c^2 - 8*a^3*b*c*d + 5*a^4*d^2)*Log[a + b*x])/b^6","A",1
261,1,178,104,0.1134362,"\int \frac{x^2 (c+d x)^2}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x^2*(c + d*x)^2)/(a + b*x)^2,x]","\frac{-3 a^4 d^2+6 a^3 b c d+9 a^3 b d^2 x-3 a^2 b^2 c^2-12 a^2 b^2 c d x+6 a^2 b^2 d^2 x^2+3 a b^3 c^2 x-9 a b^3 c d x^2-2 a b^3 d^2 x^3+3 b^4 c^2 x^2+3 b^4 c d x^3+b^4 d^2 x^4}{3 b^5 (a+b x)}-\frac{2 \left(2 a^3 d^2-3 a^2 b c d+a b^2 c^2\right) \log (a+b x)}{b^5}","-\frac{a^2 (b c-a d)^2}{b^5 (a+b x)}-\frac{2 a (b c-2 a d) (b c-a d) \log (a+b x)}{b^5}+\frac{x (b c-3 a d) (b c-a d)}{b^4}+\frac{d x^2 (b c-a d)}{b^3}+\frac{d^2 x^3}{3 b^2}",1,"(-3*a^2*b^2*c^2 + 6*a^3*b*c*d - 3*a^4*d^2 + 3*a*b^3*c^2*x - 12*a^2*b^2*c*d*x + 9*a^3*b*d^2*x + 3*b^4*c^2*x^2 - 9*a*b^3*c*d*x^2 + 6*a^2*b^2*d^2*x^2 + 3*b^4*c*d*x^3 - 2*a*b^3*d^2*x^3 + b^4*d^2*x^4)/(3*b^5*(a + b*x)) - (2*(a*b^2*c^2 - 3*a^2*b*c*d + 2*a^3*d^2)*Log[a + b*x])/b^5","A",1
262,1,124,77,0.0760356,"\int \frac{x (c+d x)^2}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x*(c + d*x)^2)/(a + b*x)^2,x]","\frac{\left(3 a^2 d^2-4 a b c d+b^2 c^2\right) \log (a+b x)}{b^4}+\frac{2 a^3 d^2-4 a^2 b c d-4 a^2 b d^2 x+2 a b^2 c^2+4 a b^2 c d x-3 a b^2 d^2 x^2+4 b^3 c d x^2+b^3 d^2 x^3}{2 b^4 (a+b x)}","\frac{a (b c-a d)^2}{b^4 (a+b x)}+\frac{(b c-3 a d) (b c-a d) \log (a+b x)}{b^4}+\frac{2 d x (b c-a d)}{b^3}+\frac{d^2 x^2}{2 b^2}",1,"(2*a*b^2*c^2 - 4*a^2*b*c*d + 2*a^3*d^2 + 4*a*b^2*c*d*x - 4*a^2*b*d^2*x + 4*b^3*c*d*x^2 - 3*a*b^2*d^2*x^2 + b^3*d^2*x^3)/(2*b^4*(a + b*x)) + ((b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*Log[a + b*x])/b^4","A",1
263,1,74,51,0.000575,"\int \frac{(c+d x)^2}{(a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^2/(a + b*x)^2,x]","\frac{-a^2 d^2+2 a b c d+a b d^2 x-b^2 c^2+b^2 d^2 x^2}{b^3 (a+b x)}+\frac{2 \left(b c d-a d^2\right) \log (a+b x)}{b^3}","-\frac{(b c-a d)^2}{b^3 (a+b x)}+\frac{2 d (b c-a d) \log (a+b x)}{b^3}+\frac{d^2 x}{b^2}",1,"(-(b^2*c^2) + 2*a*b*c*d - a^2*d^2 + a*b*d^2*x + b^2*d^2*x^2)/(b^3*(a + b*x)) + (2*(b*c*d - a*d^2)*Log[a + b*x])/b^3","A",1
264,1,63,58,0.069012,"\int \frac{(c+d x)^2}{x (a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^2/(x*(a + b*x)^2),x]","\frac{\left(a^2 d^2-b^2 c^2\right) \log (a+b x)}{a^2 b^2}+\frac{c^2 \log (x)}{a^2}+\frac{(a d-b c)^2}{a b^2 (a+b x)}","-\left(\frac{c^2}{a^2}-\frac{d^2}{b^2}\right) \log (a+b x)+\frac{c^2 \log (x)}{a^2}+\frac{(b c-a d)^2}{a b^2 (a+b x)}",1,"(-(b*c) + a*d)^2/(a*b^2*(a + b*x)) + (c^2*Log[x])/a^2 + ((-(b^2*c^2) + a^2*d^2)*Log[a + b*x])/(a^2*b^2)","A",1
265,1,91,73,0.0999564,"\int \frac{(c+d x)^2}{x^2 (a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^2/(x^2*(a + b*x)^2),x]","\frac{2 \log (x) \left(a c d-b c^2\right)}{a^3}-\frac{2 \left(a c d-b c^2\right) \log (a+b x)}{a^3}+\frac{-a^2 d^2 x-a b c^2+2 a b c d x-2 b^2 c^2 x}{a^2 b x (a+b x)}","-\frac{2 c \log (x) (b c-a d)}{a^3}+\frac{2 c (b c-a d) \log (a+b x)}{a^3}-\frac{(b c-a d)^2}{a^2 b (a+b x)}-\frac{c^2}{a^2 x}",1,"(-(a*b*c^2) - 2*b^2*c^2*x + 2*a*b*c*d*x - a^2*d^2*x)/(a^2*b*x*(a + b*x)) + (2*(-(b*c^2) + a*c*d)*Log[x])/a^3 - (2*(-(b*c^2) + a*c*d)*Log[a + b*x])/a^3","A",1
266,1,135,103,0.1355853,"\int \frac{(c+d x)^2}{x^3 (a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^2/(x^3*(a + b*x)^2),x]","\frac{\log (x) \left(a^2 d^2-4 a b c d+3 b^2 c^2\right)}{a^4}+\frac{\left(-a^2 d^2+4 a b c d-3 b^2 c^2\right) \log (a+b x)}{a^4}+\frac{a^2 \left(-c^2\right)-4 a^2 c d x+2 a^2 d^2 x^2+3 a b c^2 x-8 a b c d x^2+6 b^2 c^2 x^2}{2 a^3 x^2 (a+b x)}","\frac{\log (x) (b c-a d) (3 b c-a d)}{a^4}-\frac{(b c-a d) (3 b c-a d) \log (a+b x)}{a^4}+\frac{2 c (b c-a d)}{a^3 x}+\frac{(b c-a d)^2}{a^3 (a+b x)}-\frac{c^2}{2 a^2 x^2}",1,"(-(a^2*c^2) + 3*a*b*c^2*x - 4*a^2*c*d*x + 6*b^2*c^2*x^2 - 8*a*b*c*d*x^2 + 2*a^2*d^2*x^2)/(2*a^3*x^2*(a + b*x)) + ((3*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*Log[x])/a^4 + ((-3*b^2*c^2 + 4*a*b*c*d - a^2*d^2)*Log[a + b*x])/a^4","A",1
267,1,181,132,0.1890995,"\int \frac{(c+d x)^2}{x^4 (a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^2/(x^4*(a + b*x)^2),x]","-\frac{2 \log (x) \left(a^2 b d^2-3 a b^2 c d+2 b^3 c^2\right)}{a^5}+\frac{2 \left(a^2 b d^2-3 a b^2 c d+2 b^3 c^2\right) \log (a+b x)}{a^5}+\frac{a^3 \left(-c^2\right)-3 a^3 c d x-3 a^3 d^2 x^2+2 a^2 b c^2 x+9 a^2 b c d x^2-6 a^2 b d^2 x^3-6 a b^2 c^2 x^2+18 a b^2 c d x^3-12 b^3 c^2 x^3}{3 a^4 x^3 (a+b x)}","-\frac{2 b \log (x) (b c-a d) (2 b c-a d)}{a^5}+\frac{2 b (b c-a d) (2 b c-a d) \log (a+b x)}{a^5}-\frac{(b c-a d) (3 b c-a d)}{a^4 x}-\frac{b (b c-a d)^2}{a^4 (a+b x)}+\frac{c (b c-a d)}{a^3 x^2}-\frac{c^2}{3 a^2 x^3}",1,"(-(a^3*c^2) + 2*a^2*b*c^2*x - 3*a^3*c*d*x - 6*a*b^2*c^2*x^2 + 9*a^2*b*c*d*x^2 - 3*a^3*d^2*x^2 - 12*b^3*c^2*x^3 + 18*a*b^2*c*d*x^3 - 6*a^2*b*d^2*x^3)/(3*a^4*x^3*(a + b*x)) - (2*(2*b^3*c^2 - 3*a*b^2*c*d + a^2*b*d^2)*Log[x])/a^5 + (2*(2*b^3*c^2 - 3*a*b^2*c*d + a^2*b*d^2)*Log[a + b*x])/a^5","A",1
268,1,226,167,0.1894249,"\int \frac{(c+d x)^2}{x^5 (a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^2/(x^5*(a + b*x)^2),x]","\frac{\log (x) \left(3 a^2 b^2 d^2-8 a b^3 c d+5 b^4 c^2\right)}{a^6}+\frac{\left(-3 a^2 b^2 d^2+8 a b^3 c d-5 b^4 c^2\right) \log (a+b x)}{a^6}+\frac{-3 a^4 c^2-8 a^4 c d x-6 a^4 d^2 x^2+5 a^3 b c^2 x+16 a^3 b c d x^2+18 a^3 b d^2 x^3-10 a^2 b^2 c^2 x^2-48 a^2 b^2 c d x^3+36 a^2 b^2 d^2 x^4+30 a b^3 c^2 x^3-96 a b^3 c d x^4+60 b^4 c^2 x^4}{12 a^5 x^4 (a+b x)}","\frac{b^2 \log (x) (5 b c-3 a d) (b c-a d)}{a^6}-\frac{b^2 (5 b c-3 a d) (b c-a d) \log (a+b x)}{a^6}+\frac{b^2 (b c-a d)^2}{a^5 (a+b x)}+\frac{2 b (b c-a d) (2 b c-a d)}{a^5 x}-\frac{(b c-a d) (3 b c-a d)}{2 a^4 x^2}+\frac{2 c (b c-a d)}{3 a^3 x^3}-\frac{c^2}{4 a^2 x^4}",1,"(-3*a^4*c^2 + 5*a^3*b*c^2*x - 8*a^4*c*d*x - 10*a^2*b^2*c^2*x^2 + 16*a^3*b*c*d*x^2 - 6*a^4*d^2*x^2 + 30*a*b^3*c^2*x^3 - 48*a^2*b^2*c*d*x^3 + 18*a^3*b*d^2*x^3 + 60*b^4*c^2*x^4 - 96*a*b^3*c*d*x^4 + 36*a^2*b^2*d^2*x^4)/(12*a^5*x^4*(a + b*x)) + ((5*b^4*c^2 - 8*a*b^3*c*d + 3*a^2*b^2*d^2)*Log[x])/a^6 + ((-5*b^4*c^2 + 8*a*b^3*c*d - 3*a^2*b^2*d^2)*Log[a + b*x])/a^6","A",1
269,1,380,200,0.1452956,"\int \frac{x^4 (c+d x)^3}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x^4*(c + d*x)^3)/(a + b*x)^2,x]","\frac{\left(7 a^4 d-4 a^3 b c\right) (a d-b c)^2 \log (a+b x)}{b^8}+\frac{60 a^7 d^3-180 a^6 b c d^2-360 a^6 b d^3 x+180 a^5 b^2 c^2 d+900 a^5 b^2 c d^2 x-210 a^5 b^2 d^3 x^2-60 a^4 b^3 c^3-720 a^4 b^3 c^2 d x+540 a^4 b^3 c d^2 x^2+70 a^4 b^3 d^3 x^3+180 a^3 b^4 c^3 x-450 a^3 b^4 c^2 d x^2-180 a^3 b^4 c d^2 x^3-35 a^3 b^4 d^3 x^4+120 a^2 b^5 c^3 x^2+150 a^2 b^5 c^2 d x^3+90 a^2 b^5 c d^2 x^4+21 a^2 b^5 d^3 x^5-40 a b^6 c^3 x^3-75 a b^6 c^2 d x^4-54 a b^6 c d^2 x^5-14 a b^6 d^3 x^6+20 b^7 c^3 x^4+45 b^7 c^2 d x^5+36 b^7 c d^2 x^6+10 b^7 d^3 x^7}{60 b^8 (a+b x)}","-\frac{a^4 (b c-a d)^3}{b^8 (a+b x)}-\frac{a^3 (4 b c-7 a d) (b c-a d)^2 \log (a+b x)}{b^8}+\frac{3 a^2 x (b c-2 a d) (b c-a d)^2}{b^7}-\frac{a x^2 (2 b c-5 a d) (b c-a d)^2}{2 b^6}+\frac{x^3 (b c-4 a d) (b c-a d)^2}{3 b^5}+\frac{3 d x^4 (b c-a d)^2}{4 b^4}+\frac{d^2 x^5 (3 b c-2 a d)}{5 b^3}+\frac{d^3 x^6}{6 b^2}",1,"(-60*a^4*b^3*c^3 + 180*a^5*b^2*c^2*d - 180*a^6*b*c*d^2 + 60*a^7*d^3 + 180*a^3*b^4*c^3*x - 720*a^4*b^3*c^2*d*x + 900*a^5*b^2*c*d^2*x - 360*a^6*b*d^3*x + 120*a^2*b^5*c^3*x^2 - 450*a^3*b^4*c^2*d*x^2 + 540*a^4*b^3*c*d^2*x^2 - 210*a^5*b^2*d^3*x^2 - 40*a*b^6*c^3*x^3 + 150*a^2*b^5*c^2*d*x^3 - 180*a^3*b^4*c*d^2*x^3 + 70*a^4*b^3*d^3*x^3 + 20*b^7*c^3*x^4 - 75*a*b^6*c^2*d*x^4 + 90*a^2*b^5*c*d^2*x^4 - 35*a^3*b^4*d^3*x^4 + 45*b^7*c^2*d*x^5 - 54*a*b^6*c*d^2*x^5 + 21*a^2*b^5*d^3*x^5 + 36*b^7*c*d^2*x^6 - 14*a*b^6*d^3*x^6 + 10*b^7*d^3*x^7)/(60*b^8*(a + b*x)) + ((-(b*c) + a*d)^2*(-4*a^3*b*c + 7*a^4*d)*Log[a + b*x])/b^8","A",1
270,1,323,164,0.1243165,"\int \frac{x^3 (c+d x)^3}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x^3*(c + d*x)^3)/(a + b*x)^2,x]","\frac{-20 a^6 d^3+60 a^5 b c d^2+100 a^5 b d^3 x-60 a^4 b^2 c^2 d-240 a^4 b^2 c d^2 x+60 a^4 b^2 d^3 x^2+20 a^3 b^3 c^3+180 a^3 b^3 c^2 d x-150 a^3 b^3 c d^2 x^2-20 a^3 b^3 d^3 x^3-40 a^2 b^4 c^3 x+120 a^2 b^4 c^2 d x^2+50 a^2 b^4 c d^2 x^3+10 a^2 b^4 d^3 x^4-30 a b^5 c^3 x^2-40 a b^5 c^2 d x^3-25 a b^5 c d^2 x^4-6 a b^5 d^3 x^5+10 b^6 c^3 x^3+20 b^6 c^2 d x^4+15 b^6 c d^2 x^5+4 b^6 d^3 x^6}{20 b^7 (a+b x)}-\frac{3 (a d-b c)^2 \left(2 a^3 d-a^2 b c\right) \log (a+b x)}{b^7}","\frac{a^3 (b c-a d)^3}{b^7 (a+b x)}+\frac{3 a^2 (b c-2 a d) (b c-a d)^2 \log (a+b x)}{b^7}-\frac{a x (2 b c-5 a d) (b c-a d)^2}{b^6}+\frac{x^2 (b c-4 a d) (b c-a d)^2}{2 b^5}+\frac{d x^3 (b c-a d)^2}{b^4}+\frac{d^2 x^4 (3 b c-2 a d)}{4 b^3}+\frac{d^3 x^5}{5 b^2}",1,"(20*a^3*b^3*c^3 - 60*a^4*b^2*c^2*d + 60*a^5*b*c*d^2 - 20*a^6*d^3 - 40*a^2*b^4*c^3*x + 180*a^3*b^3*c^2*d*x - 240*a^4*b^2*c*d^2*x + 100*a^5*b*d^3*x - 30*a*b^5*c^3*x^2 + 120*a^2*b^4*c^2*d*x^2 - 150*a^3*b^3*c*d^2*x^2 + 60*a^4*b^2*d^3*x^2 + 10*b^6*c^3*x^3 - 40*a*b^5*c^2*d*x^3 + 50*a^2*b^4*c*d^2*x^3 - 20*a^3*b^3*d^3*x^3 + 20*b^6*c^2*d*x^4 - 25*a*b^5*c*d^2*x^4 + 10*a^2*b^4*d^3*x^4 + 15*b^6*c*d^2*x^5 - 6*a*b^5*d^3*x^5 + 4*b^6*d^3*x^6)/(20*b^7*(a + b*x)) - (3*(-(b*c) + a*d)^2*(-(a^2*b*c) + 2*a^3*d)*Log[a + b*x])/b^7","A",1
271,1,262,136,0.1103716,"\int \frac{x^2 (c+d x)^3}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x^2*(c + d*x)^3)/(a + b*x)^2,x]","\frac{\left(5 a^2 d-2 a b c\right) (a d-b c)^2 \log (a+b x)}{b^6}+\frac{12 a^5 d^3-36 a^4 b c d^2-48 a^4 b d^3 x+36 a^3 b^2 c^2 d+108 a^3 b^2 c d^2 x-30 a^3 b^2 d^3 x^2-12 a^2 b^3 c^3-72 a^2 b^3 c^2 d x+72 a^2 b^3 c d^2 x^2+10 a^2 b^3 d^3 x^3+12 a b^4 c^3 x-54 a b^4 c^2 d x^2-24 a b^4 c d^2 x^3-5 a b^4 d^3 x^4+12 b^5 c^3 x^2+18 b^5 c^2 d x^3+12 b^5 c d^2 x^4+3 b^5 d^3 x^5}{12 b^6 (a+b x)}","-\frac{a^2 (b c-a d)^3}{b^6 (a+b x)}-\frac{a (2 b c-5 a d) (b c-a d)^2 \log (a+b x)}{b^6}+\frac{x (b c-4 a d) (b c-a d)^2}{b^5}+\frac{3 d x^2 (b c-a d)^2}{2 b^4}+\frac{d^2 x^3 (3 b c-2 a d)}{3 b^3}+\frac{d^3 x^4}{4 b^2}",1,"(-12*a^2*b^3*c^3 + 36*a^3*b^2*c^2*d - 36*a^4*b*c*d^2 + 12*a^5*d^3 + 12*a*b^4*c^3*x - 72*a^2*b^3*c^2*d*x + 108*a^3*b^2*c*d^2*x - 48*a^4*b*d^3*x + 12*b^5*c^3*x^2 - 54*a*b^4*c^2*d*x^2 + 72*a^2*b^3*c*d^2*x^2 - 30*a^3*b^2*d^3*x^2 + 18*b^5*c^2*d*x^3 - 24*a*b^4*c*d^2*x^3 + 10*a^2*b^3*d^3*x^3 + 12*b^5*c*d^2*x^4 - 5*a*b^4*d^3*x^4 + 3*b^5*d^3*x^5)/(12*b^6*(a + b*x)) + ((-(b*c) + a*d)^2*(-2*a*b*c + 5*a^2*d)*Log[a + b*x])/b^6","A",1
272,1,191,103,0.1120408,"\int \frac{x (c+d x)^3}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x*(c + d*x)^3)/(a + b*x)^2,x]","\frac{-6 a^4 d^3+18 a^3 b c d^2+18 a^3 b d^3 x-18 a^2 b^2 c^2 d-36 a^2 b^2 c d^2 x+12 a^2 b^2 d^3 x^2+6 a b^3 c^3+18 a b^3 c^2 d x-27 a b^3 c d^2 x^2-4 a b^3 d^3 x^3+18 b^4 c^2 d x^2+9 b^4 c d^2 x^3+2 b^4 d^3 x^4}{6 b^5 (a+b x)}+\frac{(b c-4 a d) (b c-a d)^2 \log (a+b x)}{b^5}","\frac{a (b c-a d)^3}{b^5 (a+b x)}+\frac{(b c-4 a d) (b c-a d)^2 \log (a+b x)}{b^5}+\frac{3 d x (b c-a d)^2}{b^4}+\frac{d^2 x^2 (3 b c-2 a d)}{2 b^3}+\frac{d^3 x^3}{3 b^2}",1,"(6*a*b^3*c^3 - 18*a^2*b^2*c^2*d + 18*a^3*b*c*d^2 - 6*a^4*d^3 + 18*a*b^3*c^2*d*x - 36*a^2*b^2*c*d^2*x + 18*a^3*b*d^3*x + 18*b^4*c^2*d*x^2 - 27*a*b^3*c*d^2*x^2 + 12*a^2*b^2*d^3*x^2 + 9*b^4*c*d^2*x^3 - 4*a*b^3*d^3*x^3 + 2*b^4*d^3*x^4)/(6*b^5*(a + b*x)) + ((b*c - 4*a*d)*(b*c - a*d)^2*Log[a + b*x])/b^5","A",1
273,1,129,75,0.0005857,"\int \frac{(c+d x)^3}{(a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^3/(a + b*x)^2,x]","\frac{2 a^3 d^3-6 a^2 b c d^2-4 a^2 b d^3 x+6 a b^2 c^2 d+6 a b^2 c d^2 x-3 a b^2 d^3 x^2-2 b^3 c^3+6 b^3 c d^2 x^2+b^3 d^3 x^3}{2 b^4 (a+b x)}+\frac{3 d (b c-a d)^2 \log (a+b x)}{b^4}","-\frac{(b c-a d)^3}{b^4 (a+b x)}+\frac{3 d (b c-a d)^2 \log (a+b x)}{b^4}+\frac{d^2 x (3 b c-2 a d)}{b^3}+\frac{d^3 x^2}{2 b^2}",1,"(-2*b^3*c^3 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + 2*a^3*d^3 + 6*a*b^2*c*d^2*x - 4*a^2*b*d^3*x + 6*b^3*c*d^2*x^2 - 3*a*b^2*d^3*x^2 + b^3*d^3*x^3)/(2*b^4*(a + b*x)) + (3*d*(b*c - a*d)^2*Log[a + b*x])/b^4","A",1
274,1,112,74,0.0898878,"\int \frac{(c+d x)^3}{x (a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^3/(x*(a + b*x)^2),x]","-\frac{(a d-b c)^2 (2 a d+b c) \log (a+b x)}{a^2 b^3}+\frac{c^3 \log (x)}{a^2}+\frac{-a^3 d^3+3 a^2 b c d^2+a^2 b d^3 x-3 a b^2 c^2 d+a b^2 d^3 x^2+b^3 c^3}{a b^3 (a+b x)}","-\frac{(b c-a d)^2 (2 a d+b c) \log (a+b x)}{a^2 b^3}+\frac{c^3 \log (x)}{a^2}+\frac{(b c-a d)^3}{a b^3 (a+b x)}+\frac{d^3 x}{b^2}",1,"(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3 + a^2*b*d^3*x + a*b^2*d^3*x^2)/(a*b^3*(a + b*x)) + (c^3*Log[x])/a^2 - ((-(b*c) + a*d)^2*(b*c + 2*a*d)*Log[a + b*x])/(a^2*b^3)","A",1
275,1,118,87,0.1016283,"\int \frac{(c+d x)^3}{x^2 (a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^3/(x^2*(a + b*x)^2),x]","\frac{(a d+2 b c) (a d-b c)^2 \log (a+b x)}{a^3 b^2}+\frac{\log (x) \left(3 a c^2 d-2 b c^3\right)}{a^3}+\frac{a^3 d^3 x-3 a^2 b c d^2 x-a b^2 c^3+3 a b^2 c^2 d x-2 b^3 c^3 x}{a^2 b^2 x (a+b x)}","\frac{(b c-a d)^2 (a d+2 b c) \log (a+b x)}{a^3 b^2}-\frac{c^2 \log (x) (2 b c-3 a d)}{a^3}-\frac{(b c-a d)^3}{a^2 b^2 (a+b x)}-\frac{c^3}{a^2 x}",1,"(-(a*b^2*c^3) - 2*b^3*c^3*x + 3*a*b^2*c^2*d*x - 3*a^2*b*c*d^2*x + a^3*d^3*x)/(a^2*b^2*x*(a + b*x)) + ((-2*b*c^3 + 3*a*c^2*d)*Log[x])/a^3 + ((-(b*c) + a*d)^2*(2*b*c + a*d)*Log[a + b*x])/(a^3*b^2)","A",1
276,1,140,97,0.141592,"\int \frac{(c+d x)^3}{x^3 (a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^3/(x^3*(a + b*x)^2),x]","\frac{3 c \log (x) (a d-b c)^2}{a^4}-\frac{3 c (a d-b c)^2 \log (a+b x)}{a^4}+\frac{-2 a^3 d^3 x^2-a^2 b c^3-6 a^2 b c^2 d x+6 a^2 b c d^2 x^2+3 a b^2 c^3 x-12 a b^2 c^2 d x^2+6 b^3 c^3 x^2}{2 a^3 b x^2 (a+b x)}","\frac{3 c \log (x) (b c-a d)^2}{a^4}-\frac{3 c (b c-a d)^2 \log (a+b x)}{a^4}+\frac{c^2 (2 b c-3 a d)}{a^3 x}+\frac{(b c-a d)^3}{a^3 b (a+b x)}-\frac{c^3}{2 a^2 x^2}",1,"(-(a^2*b*c^3) + 3*a*b^2*c^3*x - 6*a^2*b*c^2*d*x + 6*b^3*c^3*x^2 - 12*a*b^2*c^2*d*x^2 + 6*a^2*b*c*d^2*x^2 - 2*a^3*d^3*x^2)/(2*a^3*b*x^2*(a + b*x)) + (3*c*(-(b*c) + a*d)^2*Log[x])/a^4 - (3*c*(-(b*c) + a*d)^2*Log[a + b*x])/a^4","A",1
277,1,185,132,0.1186113,"\int \frac{(c+d x)^3}{x^4 (a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^3/(x^4*(a + b*x)^2),x]","\frac{\log (x) (a d-4 b c) (a d-b c)^2}{a^5}-\frac{(a d-4 b c) (a d-b c)^2 \log (a+b x)}{a^5}+\frac{-2 a^3 c^3-9 a^3 c^2 d x-18 a^3 c d^2 x^2+6 a^3 d^3 x^3+4 a^2 b c^3 x+27 a^2 b c^2 d x^2-36 a^2 b c d^2 x^3-12 a b^2 c^3 x^2+54 a b^2 c^2 d x^3-24 b^3 c^3 x^3}{6 a^4 x^3 (a+b x)}","-\frac{\log (x) (b c-a d)^2 (4 b c-a d)}{a^5}+\frac{(b c-a d)^2 (4 b c-a d) \log (a+b x)}{a^5}-\frac{3 c (b c-a d)^2}{a^4 x}-\frac{(b c-a d)^3}{a^4 (a+b x)}+\frac{c^2 (2 b c-3 a d)}{2 a^3 x^2}-\frac{c^3}{3 a^2 x^3}",1,"(-2*a^3*c^3 + 4*a^2*b*c^3*x - 9*a^3*c^2*d*x - 12*a*b^2*c^3*x^2 + 27*a^2*b*c^2*d*x^2 - 18*a^3*c*d^2*x^2 - 24*b^3*c^3*x^3 + 54*a*b^2*c^2*d*x^3 - 36*a^2*b*c*d^2*x^3 + 6*a^3*d^3*x^3)/(6*a^4*x^3*(a + b*x)) + ((-4*b*c + a*d)*(-(b*c) + a*d)^2*Log[x])/a^5 - ((-4*b*c + a*d)*(-(b*c) + a*d)^2*Log[a + b*x])/a^5","A",1
278,1,249,162,0.1390481,"\int \frac{(c+d x)^3}{x^5 (a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^3/(x^5*(a + b*x)^2),x]","-\frac{\log (x) \left(2 a b d-5 b^2 c\right) (a d-b c)^2}{a^6}+\frac{\left(2 a b d-5 b^2 c\right) (a d-b c)^2 \log (a+b x)}{a^6}+\frac{-3 a^4 c^3-12 a^4 c^2 d x-18 a^4 c d^2 x^2-12 a^4 d^3 x^3+5 a^3 b c^3 x+24 a^3 b c^2 d x^2+54 a^3 b c d^2 x^3-24 a^3 b d^3 x^4-10 a^2 b^2 c^3 x^2-72 a^2 b^2 c^2 d x^3+108 a^2 b^2 c d^2 x^4+30 a b^3 c^3 x^3-144 a b^3 c^2 d x^4+60 b^4 c^3 x^4}{12 a^5 x^4 (a+b x)}","\frac{b \log (x) (5 b c-2 a d) (b c-a d)^2}{a^6}-\frac{b (5 b c-2 a d) (b c-a d)^2 \log (a+b x)}{a^6}+\frac{(b c-a d)^2 (4 b c-a d)}{a^5 x}+\frac{b (b c-a d)^3}{a^5 (a+b x)}-\frac{3 c (b c-a d)^2}{2 a^4 x^2}+\frac{c^2 (2 b c-3 a d)}{3 a^3 x^3}-\frac{c^3}{4 a^2 x^4}",1,"(-3*a^4*c^3 + 5*a^3*b*c^3*x - 12*a^4*c^2*d*x - 10*a^2*b^2*c^3*x^2 + 24*a^3*b*c^2*d*x^2 - 18*a^4*c*d^2*x^2 + 30*a*b^3*c^3*x^3 - 72*a^2*b^2*c^2*d*x^3 + 54*a^3*b*c*d^2*x^3 - 12*a^4*d^3*x^3 + 60*b^4*c^3*x^4 - 144*a*b^3*c^2*d*x^4 + 108*a^2*b^2*c*d^2*x^4 - 24*a^3*b*d^3*x^4)/(12*a^5*x^4*(a + b*x)) - ((-(b*c) + a*d)^2*(-5*b^2*c + 2*a*b*d)*Log[x])/a^6 + ((-(b*c) + a*d)^2*(-5*b^2*c + 2*a*b*d)*Log[a + b*x])/a^6","A",1
279,1,310,199,0.1720358,"\int \frac{(c+d x)^3}{x^6 (a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^3/(x^6*(a + b*x)^2),x]","\frac{3 \log (x) \left(a b^2 d-2 b^3 c\right) (a d-b c)^2}{a^7}-\frac{3 \left(a b^2 d-2 b^3 c\right) (a d-b c)^2 \log (a+b x)}{a^7}+\frac{-4 a^5 c^3-15 a^5 c^2 d x-20 a^5 c d^2 x^2-10 a^5 d^3 x^3+6 a^4 b c^3 x+25 a^4 b c^2 d x^2+40 a^4 b c d^2 x^3+30 a^4 b d^3 x^4-10 a^3 b^2 c^3 x^2-50 a^3 b^2 c^2 d x^3-120 a^3 b^2 c d^2 x^4+60 a^3 b^2 d^3 x^5+20 a^2 b^3 c^3 x^3+150 a^2 b^3 c^2 d x^4-240 a^2 b^3 c d^2 x^5-60 a b^4 c^3 x^4+300 a b^4 c^2 d x^5-120 b^5 c^3 x^5}{20 a^6 x^5 (a+b x)}","-\frac{3 b^2 \log (x) (b c-a d)^2 (2 b c-a d)}{a^7}+\frac{3 b^2 (b c-a d)^2 (2 b c-a d) \log (a+b x)}{a^7}-\frac{b^2 (b c-a d)^3}{a^6 (a+b x)}-\frac{b (5 b c-2 a d) (b c-a d)^2}{a^6 x}+\frac{(b c-a d)^2 (4 b c-a d)}{2 a^5 x^2}-\frac{c (b c-a d)^2}{a^4 x^3}+\frac{c^2 (2 b c-3 a d)}{4 a^3 x^4}-\frac{c^3}{5 a^2 x^5}",1,"(-4*a^5*c^3 + 6*a^4*b*c^3*x - 15*a^5*c^2*d*x - 10*a^3*b^2*c^3*x^2 + 25*a^4*b*c^2*d*x^2 - 20*a^5*c*d^2*x^2 + 20*a^2*b^3*c^3*x^3 - 50*a^3*b^2*c^2*d*x^3 + 40*a^4*b*c*d^2*x^3 - 10*a^5*d^3*x^3 - 60*a*b^4*c^3*x^4 + 150*a^2*b^3*c^2*d*x^4 - 120*a^3*b^2*c*d^2*x^4 + 30*a^4*b*d^3*x^4 - 120*b^5*c^3*x^5 + 300*a*b^4*c^2*d*x^5 - 240*a^2*b^3*c*d^2*x^5 + 60*a^3*b^2*d^3*x^5)/(20*a^6*x^5*(a + b*x)) + (3*(-(b*c) + a*d)^2*(-2*b^3*c + a*b^2*d)*Log[x])/a^7 - (3*(-(b*c) + a*d)^2*(-2*b^3*c + a*b^2*d)*Log[a + b*x])/a^7","A",1
280,1,439,179,0.3106479,"\int \frac{x^6}{(a+b x)^2 (c+d x)^2} \, dx","IntegrateAlgebraic[x^6/((a + b*x)^2*(c + d*x)^2),x]","\frac{2 \left(2 a^6 d-3 a^5 b c\right) \log (a+b x)}{b^5 (b c-a d)^3}+\frac{-3 a^6 c d^5-3 a^6 d^6 x+9 a^5 b c d^5 x+9 a^5 b d^6 x^2-6 a^4 b^2 c^2 d^4 x+6 a^4 b^2 d^6 x^3-6 a^3 b^3 c^3 d^3 x-9 a^3 b^3 c^2 d^4 x^2-5 a^3 b^3 c d^5 x^3-2 a^3 b^3 d^6 x^4-6 a^2 b^4 c^4 d^2 x-9 a^2 b^4 c^3 d^3 x^2-2 a^2 b^4 c^2 d^4 x^3+2 a^2 b^4 c d^5 x^4+a^2 b^4 d^6 x^5-3 a b^5 c^6+9 a b^5 c^5 d x-5 a b^5 c^3 d^3 x^3+2 a b^5 c^2 d^4 x^4-2 a b^5 c d^5 x^5-3 b^6 c^6 x+9 b^6 c^5 d x^2+6 b^6 c^4 d^2 x^3-2 b^6 c^3 d^3 x^4+b^6 c^2 d^4 x^5}{3 b^5 d^5 (a+b x) (c+d x) (b c-a d)^2}+\frac{2 \left(2 b c^6-3 a c^5 d\right) \log (c+d x)}{d^5 (a d-b c)^3}","-\frac{a^6}{b^5 (a+b x) (b c-a d)^2}-\frac{2 a^5 (3 b c-2 a d) \log (a+b x)}{b^5 (b c-a d)^3}+\frac{x \left(3 a^2 d^2+4 a b c d+3 b^2 c^2\right)}{b^4 d^4}-\frac{x^2 (a d+b c)}{b^3 d^3}-\frac{c^6}{d^5 (c+d x) (b c-a d)^2}-\frac{2 c^5 (2 b c-3 a d) \log (c+d x)}{d^5 (b c-a d)^3}+\frac{x^3}{3 b^2 d^2}",1,"(-3*a*b^5*c^6 - 3*a^6*c*d^5 - 3*b^6*c^6*x + 9*a*b^5*c^5*d*x - 6*a^2*b^4*c^4*d^2*x - 6*a^3*b^3*c^3*d^3*x - 6*a^4*b^2*c^2*d^4*x + 9*a^5*b*c*d^5*x - 3*a^6*d^6*x + 9*b^6*c^5*d*x^2 - 9*a^2*b^4*c^3*d^3*x^2 - 9*a^3*b^3*c^2*d^4*x^2 + 9*a^5*b*d^6*x^2 + 6*b^6*c^4*d^2*x^3 - 5*a*b^5*c^3*d^3*x^3 - 2*a^2*b^4*c^2*d^4*x^3 - 5*a^3*b^3*c*d^5*x^3 + 6*a^4*b^2*d^6*x^3 - 2*b^6*c^3*d^3*x^4 + 2*a*b^5*c^2*d^4*x^4 + 2*a^2*b^4*c*d^5*x^4 - 2*a^3*b^3*d^6*x^4 + b^6*c^2*d^4*x^5 - 2*a*b^5*c*d^5*x^5 + a^2*b^4*d^6*x^5)/(3*b^5*d^5*(b*c - a*d)^2*(a + b*x)*(c + d*x)) + (2*(-3*a^5*b*c + 2*a^6*d)*Log[a + b*x])/(b^5*(b*c - a*d)^3) + (2*(2*b*c^6 - 3*a*c^5*d)*Log[c + d*x])/(d^5*(-(b*c) + a*d)^3)","B",1
281,1,360,142,0.2425823,"\int \frac{x^5}{(a+b x)^2 (c+d x)^2} \, dx","IntegrateAlgebraic[x^5/((a + b*x)^2*(c + d*x)^2),x]","-\frac{\left(3 a^5 d-5 a^4 b c\right) \log (a+b x)}{b^4 (b c-a d)^3}+\frac{2 a^5 c d^4+2 a^5 d^5 x-4 a^4 b c d^4 x-4 a^4 b d^5 x^2+4 a^3 b^2 c^2 d^3 x+a^3 b^2 c d^4 x^2-3 a^3 b^2 d^5 x^3+4 a^2 b^3 c^3 d^2 x+6 a^2 b^3 c^2 d^3 x^2+3 a^2 b^3 c d^4 x^3+a^2 b^3 d^5 x^4+2 a b^4 c^5-4 a b^4 c^4 d x+a b^4 c^3 d^2 x^2+3 a b^4 c^2 d^3 x^3-2 a b^4 c d^4 x^4+2 b^5 c^5 x-4 b^5 c^4 d x^2-3 b^5 c^3 d^2 x^3+b^5 c^2 d^3 x^4}{2 b^4 d^4 (a+b x) (c+d x) (b c-a d)^2}-\frac{\left(3 b c^5-5 a c^4 d\right) \log (c+d x)}{d^4 (a d-b c)^3}","\frac{a^5}{b^4 (a+b x) (b c-a d)^2}+\frac{a^4 (5 b c-3 a d) \log (a+b x)}{b^4 (b c-a d)^3}-\frac{2 x (a d+b c)}{b^3 d^3}+\frac{c^5}{d^4 (c+d x) (b c-a d)^2}+\frac{c^4 (3 b c-5 a d) \log (c+d x)}{d^4 (b c-a d)^3}+\frac{x^2}{2 b^2 d^2}",1,"(2*a*b^4*c^5 + 2*a^5*c*d^4 + 2*b^5*c^5*x - 4*a*b^4*c^4*d*x + 4*a^2*b^3*c^3*d^2*x + 4*a^3*b^2*c^2*d^3*x - 4*a^4*b*c*d^4*x + 2*a^5*d^5*x - 4*b^5*c^4*d*x^2 + a*b^4*c^3*d^2*x^2 + 6*a^2*b^3*c^2*d^3*x^2 + a^3*b^2*c*d^4*x^2 - 4*a^4*b*d^5*x^2 - 3*b^5*c^3*d^2*x^3 + 3*a*b^4*c^2*d^3*x^3 + 3*a^2*b^3*c*d^4*x^3 - 3*a^3*b^2*d^5*x^3 + b^5*c^2*d^3*x^4 - 2*a*b^4*c*d^4*x^4 + a^2*b^3*d^5*x^4)/(2*b^4*d^4*(b*c - a*d)^2*(a + b*x)*(c + d*x)) - ((-5*a^4*b*c + 3*a^5*d)*Log[a + b*x])/(b^4*(b*c - a*d)^3) - ((3*b*c^5 - 5*a*c^4*d)*Log[c + d*x])/(d^4*(-(b*c) + a*d)^3)","B",1
282,1,263,124,0.2067816,"\int \frac{x^4}{(a+b x)^2 (c+d x)^2} \, dx","IntegrateAlgebraic[x^4/((a + b*x)^2*(c + d*x)^2),x]","\frac{2 \left(a^4 d-2 a^3 b c\right) \log (a+b x)}{b^3 (b c-a d)^3}+\frac{a^4 (-c) d^3-a^4 d^4 x+a^3 b c d^3 x+a^3 b d^4 x^2-2 a^2 b^2 c^2 d^2 x-a^2 b^2 c d^3 x^2+a^2 b^2 d^4 x^3-a b^3 c^4+a b^3 c^3 d x-a b^3 c^2 d^2 x^2-2 a b^3 c d^3 x^3-b^4 c^4 x+b^4 c^3 d x^2+b^4 c^2 d^2 x^3}{b^3 d^3 (a+b x) (c+d x) (b c-a d)^2}+\frac{2 \left(b c^4-2 a c^3 d\right) \log (c+d x)}{d^3 (a d-b c)^3}","-\frac{a^4}{b^3 (a+b x) (b c-a d)^2}-\frac{2 a^3 (2 b c-a d) \log (a+b x)}{b^3 (b c-a d)^3}-\frac{c^4}{d^3 (c+d x) (b c-a d)^2}-\frac{2 c^3 (b c-2 a d) \log (c+d x)}{d^3 (b c-a d)^3}+\frac{x}{b^2 d^2}",1,"(-(a*b^3*c^4) - a^4*c*d^3 - b^4*c^4*x + a*b^3*c^3*d*x - 2*a^2*b^2*c^2*d^2*x + a^3*b*c*d^3*x - a^4*d^4*x + b^4*c^3*d*x^2 - a*b^3*c^2*d^2*x^2 - a^2*b^2*c*d^3*x^2 + a^3*b*d^4*x^2 + b^4*c^2*d^2*x^3 - 2*a*b^3*c*d^3*x^3 + a^2*b^2*d^4*x^3)/(b^3*d^3*(b*c - a*d)^2*(a + b*x)*(c + d*x)) + (2*(-2*a^3*b*c + a^4*d)*Log[a + b*x])/(b^3*(b*c - a*d)^3) + (2*(b*c^4 - 2*a*c^3*d)*Log[c + d*x])/(d^3*(-(b*c) + a*d)^3)","B",1
283,1,133,112,0.213639,"\int \frac{x^3}{(a+b x)^2 (c+d x)^2} \, dx","IntegrateAlgebraic[x^3/((a + b*x)^2*(c + d*x)^2),x]","\frac{a^3 c d^2+a^3 d^3 x+a b^2 c^3+b^3 c^3 x}{b^2 d^2 (a+b x) (c+d x) (b c-a d)^2}-\frac{\left(a^3 d-3 a^2 b c\right) \log (a+b x)}{b^2 (b c-a d)^3}-\frac{\left(b c^3-3 a c^2 d\right) \log (c+d x)}{d^2 (a d-b c)^3}","\frac{a^3}{b^2 (a+b x) (b c-a d)^2}+\frac{a^2 (3 b c-a d) \log (a+b x)}{b^2 (b c-a d)^3}+\frac{c^3}{d^2 (c+d x) (b c-a d)^2}+\frac{c^2 (b c-3 a d) \log (c+d x)}{d^2 (b c-a d)^3}",1,"(a*b^2*c^3 + a^3*c*d^2 + b^3*c^3*x + a^3*d^3*x)/(b^2*d^2*(b*c - a*d)^2*(a + b*x)*(c + d*x)) - ((-3*a^2*b*c + a^3*d)*Log[a + b*x])/(b^2*(b*c - a*d)^3) - ((b*c^3 - 3*a*c^2*d)*Log[c + d*x])/(d^2*(-(b*c) + a*d)^3)","A",1
284,1,105,91,0.1840137,"\int \frac{x^2}{(a+b x)^2 (c+d x)^2} \, dx","IntegrateAlgebraic[x^2/((a + b*x)^2*(c + d*x)^2),x]","\frac{a^2 (-c) d-a^2 d^2 x-a b c^2-b^2 c^2 x}{b d (a+b x) (c+d x) (b c-a d)^2}-\frac{2 a c \log (a+b x)}{(b c-a d)^3}+\frac{2 a c \log (c+d x)}{(b c-a d)^3}","-\frac{a^2}{b (a+b x) (b c-a d)^2}-\frac{c^2}{d (c+d x) (b c-a d)^2}-\frac{2 a c \log (a+b x)}{(b c-a d)^3}+\frac{2 a c \log (c+d x)}{(b c-a d)^3}",1,"(-(a*b*c^2) - a^2*c*d - b^2*c^2*x - a^2*d^2*x)/(b*d*(b*c - a*d)^2*(a + b*x)*(c + d*x)) - (2*a*c*Log[a + b*x])/(b*c - a*d)^3 + (2*a*c*Log[c + d*x])/(b*c - a*d)^3","A",1
285,1,89,88,0.108945,"\int \frac{x}{(a+b x)^2 (c+d x)^2} \, dx","IntegrateAlgebraic[x/((a + b*x)^2*(c + d*x)^2),x]","\frac{2 a c+a d x+b c x}{(a+b x) (c+d x) (b c-a d)^2}+\frac{(a d+b c) \log (a+b x)}{(b c-a d)^3}+\frac{(-a d-b c) \log (c+d x)}{(b c-a d)^3}","\frac{a}{(a+b x) (b c-a d)^2}+\frac{c}{(c+d x) (b c-a d)^2}+\frac{(a d+b c) \log (a+b x)}{(b c-a d)^3}-\frac{(a d+b c) \log (c+d x)}{(b c-a d)^3}",1,"(2*a*c + b*c*x + a*d*x)/((b*c - a*d)^2*(a + b*x)*(c + d*x)) + ((b*c + a*d)*Log[a + b*x])/(b*c - a*d)^3 + ((-(b*c) - a*d)*Log[c + d*x])/(b*c - a*d)^3","A",1
286,1,80,81,0.0006087,"\int \frac{1}{(a+b x)^2 (c+d x)^2} \, dx","IntegrateAlgebraic[1/((a + b*x)^2*(c + d*x)^2),x]","\frac{-a d-b c-2 b d x}{(a+b x) (c+d x) (b c-a d)^2}-\frac{2 b d \log (a+b x)}{(b c-a d)^3}+\frac{2 b d \log (c+d x)}{(b c-a d)^3}","-\frac{b}{(a+b x) (b c-a d)^2}-\frac{d}{(c+d x) (b c-a d)^2}-\frac{2 b d \log (a+b x)}{(b c-a d)^3}+\frac{2 b d \log (c+d x)}{(b c-a d)^3}",1,"(-(b*c) - a*d - 2*b*d*x)/((b*c - a*d)^2*(a + b*x)*(c + d*x)) - (2*b*d*Log[a + b*x])/(b*c - a*d)^3 + (2*b*d*Log[c + d*x])/(b*c - a*d)^3","A",1
287,1,136,123,0.2433789,"\int \frac{1}{x (a+b x)^2 (c+d x)^2} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)^2*(c + d*x)^2),x]","\frac{a^2 d^2+a b d^2 x+b^2 c^2+b^2 c d x}{a c (a+b x) (c+d x) (a d-b c)^2}+\frac{\left(b^3 c-3 a b^2 d\right) \log (a+b x)}{a^2 (a d-b c)^3}+\frac{\log (x)}{a^2 c^2}+\frac{\left(a d^3-3 b c d^2\right) \log (c+d x)}{c^2 (b c-a d)^3}","-\frac{b^2 (b c-3 a d) \log (a+b x)}{a^2 (b c-a d)^3}+\frac{\log (x)}{a^2 c^2}+\frac{b^2}{a (a+b x) (b c-a d)^2}-\frac{d^2 (3 b c-a d) \log (c+d x)}{c^2 (b c-a d)^3}+\frac{d^2}{c (c+d x) (b c-a d)^2}",1,"(b^2*c^2 + a^2*d^2 + b^2*c*d*x + a*b*d^2*x)/(a*c*(-(b*c) + a*d)^2*(a + b*x)*(c + d*x)) + Log[x]/(a^2*c^2) + ((b^3*c - 3*a*b^2*d)*Log[a + b*x])/(a^2*(-(b*c) + a*d)^3) + ((-3*b*c*d^2 + a*d^3)*Log[c + d*x])/(c^2*(b*c - a*d)^3)","A",1
288,1,226,144,0.2371184,"\int \frac{1}{x^2 (a+b x)^2 (c+d x)^2} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^2*(c + d*x)^2),x]","\frac{2 \left(2 a b^3 d-b^4 c\right) \log (a+b x)}{a^3 (a d-b c)^3}-\frac{2 \log (x) (a d+b c)}{a^3 c^3}+\frac{a^3 (-c) d^2-2 a^3 d^3 x+2 a^2 b c^2 d+a^2 b c d^2 x-2 a^2 b d^3 x^2-a b^2 c^3+a b^2 c^2 d x+2 a b^2 c d^2 x^2-2 b^3 c^3 x-2 b^3 c^2 d x^2}{a^2 c^2 x (a+b x) (c+d x) (a d-b c)^2}+\frac{2 \left(2 b c d^3-a d^4\right) \log (c+d x)}{c^3 (b c-a d)^3}","\frac{2 b^3 (b c-2 a d) \log (a+b x)}{a^3 (b c-a d)^3}-\frac{2 \log (x) (a d+b c)}{a^3 c^3}-\frac{b^3}{a^2 (a+b x) (b c-a d)^2}-\frac{1}{a^2 c^2 x}+\frac{2 d^3 (2 b c-a d) \log (c+d x)}{c^3 (b c-a d)^3}-\frac{d^3}{c^2 (c+d x) (b c-a d)^2}",1,"(-(a*b^2*c^3) + 2*a^2*b*c^2*d - a^3*c*d^2 - 2*b^3*c^3*x + a*b^2*c^2*d*x + a^2*b*c*d^2*x - 2*a^3*d^3*x - 2*b^3*c^2*d*x^2 + 2*a*b^2*c*d^2*x^2 - 2*a^2*b*d^3*x^2)/(a^2*c^2*(-(b*c) + a*d)^2*x*(a + b*x)*(c + d*x)) - (2*(b*c + a*d)*Log[x])/(a^3*c^3) + (2*(-(b^4*c) + 2*a*b^3*d)*Log[a + b*x])/(a^3*(-(b*c) + a*d)^3) + (2*(2*b*c*d^3 - a*d^4)*Log[c + d*x])/(c^3*(b*c - a*d)^3)","A",1
289,1,336,178,0.2624868,"\int \frac{1}{x^3 (a+b x)^2 (c+d x)^2} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)^2*(c + d*x)^2),x]","\frac{\left(3 b^5 c-5 a b^4 d\right) \log (a+b x)}{a^4 (a d-b c)^3}+\frac{\log (x) \left(3 a^2 d^2+4 a b c d+3 b^2 c^2\right)}{a^4 c^4}+\frac{a^4 \left(-c^2\right) d^2+3 a^4 c d^3 x+6 a^4 d^4 x^2+2 a^3 b c^3 d-3 a^3 b c^2 d^2 x-a^3 b c d^3 x^2+6 a^3 b d^4 x^3-a^2 b^2 c^4-3 a^2 b^2 c^3 d x-6 a^2 b^2 c^2 d^2 x^2-4 a^2 b^2 c d^3 x^3+3 a b^3 c^4 x-a b^3 c^3 d x^2-4 a b^3 c^2 d^2 x^3+6 b^4 c^4 x^2+6 b^4 c^3 d x^3}{2 a^3 c^3 x^2 (a+b x) (c+d x) (a d-b c)^2}+\frac{\left(3 a d^5-5 b c d^4\right) \log (c+d x)}{c^4 (b c-a d)^3}","-\frac{b^4 (3 b c-5 a d) \log (a+b x)}{a^4 (b c-a d)^3}+\frac{b^4}{a^3 (a+b x) (b c-a d)^2}+\frac{2 (a d+b c)}{a^3 c^3 x}-\frac{1}{2 a^2 c^2 x^2}+\frac{\log (x) \left(3 a^2 d^2+4 a b c d+3 b^2 c^2\right)}{a^4 c^4}-\frac{d^4 (5 b c-3 a d) \log (c+d x)}{c^4 (b c-a d)^3}+\frac{d^4}{c^3 (c+d x) (b c-a d)^2}",1,"(-(a^2*b^2*c^4) + 2*a^3*b*c^3*d - a^4*c^2*d^2 + 3*a*b^3*c^4*x - 3*a^2*b^2*c^3*d*x - 3*a^3*b*c^2*d^2*x + 3*a^4*c*d^3*x + 6*b^4*c^4*x^2 - a*b^3*c^3*d*x^2 - 6*a^2*b^2*c^2*d^2*x^2 - a^3*b*c*d^3*x^2 + 6*a^4*d^4*x^2 + 6*b^4*c^3*d*x^3 - 4*a*b^3*c^2*d^2*x^3 - 4*a^2*b^2*c*d^3*x^3 + 6*a^3*b*d^4*x^3)/(2*a^3*c^3*(-(b*c) + a*d)^2*x^2*(a + b*x)*(c + d*x)) + ((3*b^2*c^2 + 4*a*b*c*d + 3*a^2*d^2)*Log[x])/(a^4*c^4) + ((3*b^5*c - 5*a*b^4*d)*Log[a + b*x])/(a^4*(-(b*c) + a*d)^3) + ((-5*b*c*d^4 + 3*a*d^5)*Log[c + d*x])/(c^4*(b*c - a*d)^3)","A",1
290,1,703,231,0.4669176,"\int \frac{x^7}{(a+b x)^2 (c+d x)^3} \, dx","IntegrateAlgebraic[x^7/((a + b*x)^2*(c + d*x)^3),x]","\frac{\left(-21 a^2 c^5 d^2+28 a b c^6 d-10 b^2 c^7\right) \log (c+d x)}{d^6 (a d-b c)^4}+\frac{\left(7 a^6 b c-4 a^7 d\right) \log (a+b x)}{b^5 (b c-a d)^4}+\frac{6 a^7 c^2 d^6+12 a^7 c d^7 x+6 a^7 d^8 x^2-18 a^6 b c^2 d^6 x-36 a^6 b c d^7 x^2-18 a^6 b d^8 x^3+18 a^5 b^2 c^3 d^5 x+24 a^5 b^2 c^2 d^6 x^2-6 a^5 b^2 c d^7 x^3-12 a^5 b^2 d^8 x^4+18 a^4 b^3 c^4 d^4 x+45 a^4 b^3 c^3 d^5 x^2+40 a^4 b^3 c^2 d^6 x^3+17 a^4 b^3 c d^7 x^4+4 a^4 b^3 d^8 x^5+18 a^3 b^4 c^5 d^3 x+45 a^3 b^4 c^4 d^4 x^2+33 a^3 b^4 c^3 d^5 x^3+a^3 b^4 c^2 d^6 x^4-7 a^3 b^4 c d^7 x^5-2 a^3 b^4 d^8 x^6+39 a^2 b^5 c^7 d-30 a^2 b^5 c^6 d^2 x-105 a^2 b^5 c^5 d^3 x^2-9 a^2 b^5 c^4 d^4 x^3+15 a^2 b^5 c^3 d^5 x^4-3 a^2 b^5 c^2 d^6 x^5+6 a^2 b^5 c d^7 x^6-27 a b^6 c^8+45 a b^6 c^7 d x+33 a b^6 c^6 d^2 x^2-103 a b^6 c^5 d^3 x^3-41 a b^6 c^4 d^4 x^4+11 a b^6 c^3 d^5 x^5-6 a b^6 c^2 d^6 x^6-27 b^7 c^8 x+6 b^7 c^7 d x^2+63 b^7 c^6 d^2 x^3+20 b^7 c^5 d^3 x^4-5 b^7 c^4 d^4 x^5+2 b^7 c^3 d^5 x^6}{6 b^5 d^6 (a+b x) (c+d x)^2 (b c-a d)^3}","\frac{a^7}{b^5 (a+b x) (b c-a d)^3}+\frac{a^6 (7 b c-4 a d) \log (a+b x)}{b^5 (b c-a d)^4}-\frac{c^5 \left(21 a^2 d^2-28 a b c d+10 b^2 c^2\right) \log (c+d x)}{d^6 (b c-a d)^4}+\frac{3 x \left(a^2 d^2+2 a b c d+2 b^2 c^2\right)}{b^4 d^5}-\frac{x^2 (2 a d+3 b c)}{2 b^3 d^4}+\frac{c^7}{2 d^6 (c+d x)^2 (b c-a d)^2}-\frac{c^6 (5 b c-7 a d)}{d^6 (c+d x) (b c-a d)^3}+\frac{x^3}{3 b^2 d^3}",1,"(-27*a*b^6*c^8 + 39*a^2*b^5*c^7*d + 6*a^7*c^2*d^6 - 27*b^7*c^8*x + 45*a*b^6*c^7*d*x - 30*a^2*b^5*c^6*d^2*x + 18*a^3*b^4*c^5*d^3*x + 18*a^4*b^3*c^4*d^4*x + 18*a^5*b^2*c^3*d^5*x - 18*a^6*b*c^2*d^6*x + 12*a^7*c*d^7*x + 6*b^7*c^7*d*x^2 + 33*a*b^6*c^6*d^2*x^2 - 105*a^2*b^5*c^5*d^3*x^2 + 45*a^3*b^4*c^4*d^4*x^2 + 45*a^4*b^3*c^3*d^5*x^2 + 24*a^5*b^2*c^2*d^6*x^2 - 36*a^6*b*c*d^7*x^2 + 6*a^7*d^8*x^2 + 63*b^7*c^6*d^2*x^3 - 103*a*b^6*c^5*d^3*x^3 - 9*a^2*b^5*c^4*d^4*x^3 + 33*a^3*b^4*c^3*d^5*x^3 + 40*a^4*b^3*c^2*d^6*x^3 - 6*a^5*b^2*c*d^7*x^3 - 18*a^6*b*d^8*x^3 + 20*b^7*c^5*d^3*x^4 - 41*a*b^6*c^4*d^4*x^4 + 15*a^2*b^5*c^3*d^5*x^4 + a^3*b^4*c^2*d^6*x^4 + 17*a^4*b^3*c*d^7*x^4 - 12*a^5*b^2*d^8*x^4 - 5*b^7*c^4*d^4*x^5 + 11*a*b^6*c^3*d^5*x^5 - 3*a^2*b^5*c^2*d^6*x^5 - 7*a^3*b^4*c*d^7*x^5 + 4*a^4*b^3*d^8*x^5 + 2*b^7*c^3*d^5*x^6 - 6*a*b^6*c^2*d^6*x^6 + 6*a^2*b^5*c*d^7*x^6 - 2*a^3*b^4*d^8*x^6)/(6*b^5*d^6*(b*c - a*d)^3*(a + b*x)*(c + d*x)^2) + ((7*a^6*b*c - 4*a^7*d)*Log[a + b*x])/(b^5*(b*c - a*d)^4) + ((-10*b^2*c^7 + 28*a*b*c^6*d - 21*a^2*c^5*d^2)*Log[c + d*x])/(d^6*(-(b*c) + a*d)^4)","B",1
291,1,548,198,0.3809404,"\int \frac{x^6}{(a+b x)^2 (c+d x)^3} \, dx","IntegrateAlgebraic[x^6/((a + b*x)^2*(c + d*x)^3),x]","\frac{3 \left(5 a^2 c^4 d^2-6 a b c^5 d+2 b^2 c^6\right) \log (c+d x)}{d^5 (a d-b c)^4}+\frac{3 \left(a^6 d-2 a^5 b c\right) \log (a+b x)}{b^4 (b c-a d)^4}+\frac{-2 a^6 c^2 d^5-4 a^6 c d^6 x-2 a^6 d^7 x^2+4 a^5 b c^2 d^5 x+8 a^5 b c d^6 x^2+4 a^5 b d^7 x^3-6 a^4 b^2 c^3 d^4 x-9 a^4 b^2 c^2 d^5 x^2+3 a^4 b^2 d^7 x^4-6 a^3 b^3 c^4 d^3 x-15 a^3 b^3 c^3 d^4 x^2-13 a^3 b^3 c^2 d^5 x^3-5 a^3 b^3 c d^6 x^4-a^3 b^3 d^7 x^5-11 a^2 b^4 c^6 d+2 a^2 b^4 c^5 d^2 x+19 a^2 b^4 c^4 d^3 x^2-a^2 b^4 c^3 d^4 x^3-3 a^2 b^4 c^2 d^5 x^4+3 a^2 b^4 c d^6 x^5+7 a b^5 c^7-9 a b^5 c^6 d x-9 a b^5 c^5 d^2 x^2+21 a b^5 c^4 d^3 x^3+9 a b^5 c^3 d^4 x^4-3 a b^5 c^2 d^5 x^5+7 b^6 c^7 x+2 b^6 c^6 d x^2-11 b^6 c^5 d^2 x^3-4 b^6 c^4 d^3 x^4+b^6 c^3 d^4 x^5}{2 b^4 d^5 (a+b x) (c+d x)^2 (b c-a d)^3}","-\frac{a^6}{b^4 (a+b x) (b c-a d)^3}-\frac{3 a^5 (2 b c-a d) \log (a+b x)}{b^4 (b c-a d)^4}+\frac{3 c^4 \left(5 a^2 d^2-6 a b c d+2 b^2 c^2\right) \log (c+d x)}{d^5 (b c-a d)^4}-\frac{x (2 a d+3 b c)}{b^3 d^4}-\frac{c^6}{2 d^5 (c+d x)^2 (b c-a d)^2}+\frac{2 c^5 (2 b c-3 a d)}{d^5 (c+d x) (b c-a d)^3}+\frac{x^2}{2 b^2 d^3}",1,"(7*a*b^5*c^7 - 11*a^2*b^4*c^6*d - 2*a^6*c^2*d^5 + 7*b^6*c^7*x - 9*a*b^5*c^6*d*x + 2*a^2*b^4*c^5*d^2*x - 6*a^3*b^3*c^4*d^3*x - 6*a^4*b^2*c^3*d^4*x + 4*a^5*b*c^2*d^5*x - 4*a^6*c*d^6*x + 2*b^6*c^6*d*x^2 - 9*a*b^5*c^5*d^2*x^2 + 19*a^2*b^4*c^4*d^3*x^2 - 15*a^3*b^3*c^3*d^4*x^2 - 9*a^4*b^2*c^2*d^5*x^2 + 8*a^5*b*c*d^6*x^2 - 2*a^6*d^7*x^2 - 11*b^6*c^5*d^2*x^3 + 21*a*b^5*c^4*d^3*x^3 - a^2*b^4*c^3*d^4*x^3 - 13*a^3*b^3*c^2*d^5*x^3 + 4*a^5*b*d^7*x^3 - 4*b^6*c^4*d^3*x^4 + 9*a*b^5*c^3*d^4*x^4 - 3*a^2*b^4*c^2*d^5*x^4 - 5*a^3*b^3*c*d^6*x^4 + 3*a^4*b^2*d^7*x^4 + b^6*c^3*d^4*x^5 - 3*a*b^5*c^2*d^5*x^5 + 3*a^2*b^4*c*d^6*x^5 - a^3*b^3*d^7*x^5)/(2*b^4*d^5*(b*c - a*d)^3*(a + b*x)*(c + d*x)^2) + (3*(-2*a^5*b*c + a^6*d)*Log[a + b*x])/(b^4*(b*c - a*d)^4) + (3*(2*b^2*c^6 - 6*a*b*c^5*d + 5*a^2*c^4*d^2)*Log[c + d*x])/(d^5*(-(b*c) + a*d)^4)","B",1
292,1,439,173,0.3197455,"\int \frac{x^5}{(a+b x)^2 (c+d x)^3} \, dx","IntegrateAlgebraic[x^5/((a + b*x)^2*(c + d*x)^3),x]","\frac{\left(-10 a^2 c^3 d^2+10 a b c^4 d-3 b^2 c^5\right) \log (c+d x)}{d^4 (a d-b c)^4}+\frac{\left(5 a^4 b c-2 a^5 d\right) \log (a+b x)}{b^3 (b c-a d)^4}+\frac{2 a^5 c^2 d^4+4 a^5 c d^5 x+2 a^5 d^6 x^2-2 a^4 b c^2 d^4 x-4 a^4 b c d^5 x^2-2 a^4 b d^6 x^3+6 a^3 b^2 c^3 d^3 x+10 a^3 b^2 c^2 d^4 x^2+2 a^3 b^2 c d^5 x^3-2 a^3 b^2 d^6 x^4+9 a^2 b^3 c^5 d+4 a^2 b^3 c^4 d^2 x-6 a^2 b^3 c^3 d^3 x^2+6 a^2 b^3 c^2 d^4 x^3+6 a^2 b^3 c d^5 x^4-5 a b^4 c^6+5 a b^4 c^5 d x+8 a b^4 c^4 d^2 x^2-10 a b^4 c^3 d^3 x^3-6 a b^4 c^2 d^4 x^4-5 b^5 c^6 x-4 b^5 c^5 d x^2+4 b^5 c^4 d^2 x^3+2 b^5 c^3 d^3 x^4}{2 b^3 d^4 (a+b x) (c+d x)^2 (b c-a d)^3}","\frac{a^5}{b^3 (a+b x) (b c-a d)^3}+\frac{a^4 (5 b c-2 a d) \log (a+b x)}{b^3 (b c-a d)^4}-\frac{c^3 \left(10 a^2 d^2-10 a b c d+3 b^2 c^2\right) \log (c+d x)}{d^4 (b c-a d)^4}+\frac{c^5}{2 d^4 (c+d x)^2 (b c-a d)^2}-\frac{c^4 (3 b c-5 a d)}{d^4 (c+d x) (b c-a d)^3}+\frac{x}{b^2 d^3}",1,"(-5*a*b^4*c^6 + 9*a^2*b^3*c^5*d + 2*a^5*c^2*d^4 - 5*b^5*c^6*x + 5*a*b^4*c^5*d*x + 4*a^2*b^3*c^4*d^2*x + 6*a^3*b^2*c^3*d^3*x - 2*a^4*b*c^2*d^4*x + 4*a^5*c*d^5*x - 4*b^5*c^5*d*x^2 + 8*a*b^4*c^4*d^2*x^2 - 6*a^2*b^3*c^3*d^3*x^2 + 10*a^3*b^2*c^2*d^4*x^2 - 4*a^4*b*c*d^5*x^2 + 2*a^5*d^6*x^2 + 4*b^5*c^4*d^2*x^3 - 10*a*b^4*c^3*d^3*x^3 + 6*a^2*b^3*c^2*d^4*x^3 + 2*a^3*b^2*c*d^5*x^3 - 2*a^4*b*d^6*x^3 + 2*b^5*c^3*d^3*x^4 - 6*a*b^4*c^2*d^4*x^4 + 6*a^2*b^3*c*d^5*x^4 - 2*a^3*b^2*d^6*x^4)/(2*b^3*d^4*(b*c - a*d)^3*(a + b*x)*(c + d*x)^2) + ((5*a^4*b*c - 2*a^5*d)*Log[a + b*x])/(b^3*(b*c - a*d)^4) + ((-3*b^2*c^5 + 10*a*b*c^4*d - 10*a^2*c^3*d^2)*Log[c + d*x])/(d^4*(-(b*c) + a*d)^4)","B",1
293,1,231,164,0.3088163,"\int \frac{x^4}{(a+b x)^2 (c+d x)^3} \, dx","IntegrateAlgebraic[x^4/((a + b*x)^2*(c + d*x)^3),x]","\frac{\left(6 a^2 c^2 d^2-4 a b c^3 d+b^2 c^4\right) \log (c+d x)}{d^3 (a d-b c)^4}+\frac{\left(a^4 d-4 a^3 b c\right) \log (a+b x)}{b^2 (b c-a d)^4}+\frac{-2 a^4 c^2 d^3-4 a^4 c d^4 x-2 a^4 d^5 x^2-7 a^2 b^2 c^4 d-8 a^2 b^2 c^3 d^2 x+3 a b^3 c^5-3 a b^3 c^4 d x-8 a b^3 c^3 d^2 x^2+3 b^4 c^5 x+4 b^4 c^4 d x^2}{2 b^2 d^3 (a+b x) (c+d x)^2 (b c-a d)^3}","-\frac{a^4}{b^2 (a+b x) (b c-a d)^3}-\frac{a^3 (4 b c-a d) \log (a+b x)}{b^2 (b c-a d)^4}+\frac{c^2 \left(6 a^2 d^2-4 a b c d+b^2 c^2\right) \log (c+d x)}{d^3 (b c-a d)^4}-\frac{c^4}{2 d^3 (c+d x)^2 (b c-a d)^2}+\frac{2 c^3 (b c-2 a d)}{d^3 (c+d x) (b c-a d)^3}",1,"(3*a*b^3*c^5 - 7*a^2*b^2*c^4*d - 2*a^4*c^2*d^3 + 3*b^4*c^5*x - 3*a*b^3*c^4*d*x - 8*a^2*b^2*c^3*d^2*x - 4*a^4*c*d^4*x + 4*b^4*c^4*d*x^2 - 8*a*b^3*c^3*d^2*x^2 - 2*a^4*d^5*x^2)/(2*b^2*d^3*(b*c - a*d)^3*(a + b*x)*(c + d*x)^2) + ((-4*a^3*b*c + a^4*d)*Log[a + b*x])/(b^2*(b*c - a*d)^4) + ((b^2*c^4 - 4*a*b*c^3*d + 6*a^2*c^2*d^2)*Log[c + d*x])/(d^3*(-(b*c) + a*d)^4)","A",1
294,1,191,129,0.2277248,"\int \frac{x^3}{(a+b x)^2 (c+d x)^3} \, dx","IntegrateAlgebraic[x^3/((a + b*x)^2*(c + d*x)^3),x]","\frac{3 a^2 c \log (a+b x)}{(b c-a d)^4}-\frac{3 a^2 c \log (c+d x)}{(b c-a d)^4}+\frac{2 a^3 c^2 d^2+4 a^3 c d^3 x+2 a^3 d^4 x^2+5 a^2 b c^3 d+6 a^2 b c^2 d^2 x-a b^2 c^4+3 a b^2 c^3 d x+6 a b^2 c^2 d^2 x^2-b^3 c^4 x-2 b^3 c^3 d x^2}{2 b d^2 (a+b x) (c+d x)^2 (b c-a d)^3}","\frac{a^3}{b (a+b x) (b c-a d)^3}+\frac{3 a^2 c \log (a+b x)}{(b c-a d)^4}-\frac{3 a^2 c \log (c+d x)}{(b c-a d)^4}+\frac{c^3}{2 d^2 (c+d x)^2 (b c-a d)^2}-\frac{c^2 (b c-3 a d)}{d^2 (c+d x) (b c-a d)^3}",1,"(-(a*b^2*c^4) + 5*a^2*b*c^3*d + 2*a^3*c^2*d^2 - b^3*c^4*x + 3*a*b^2*c^3*d*x + 6*a^2*b*c^2*d^2*x + 4*a^3*c*d^3*x - 2*b^3*c^3*d*x^2 + 6*a*b^2*c^2*d^2*x^2 + 2*a^3*d^4*x^2)/(2*b*d^2*(b*c - a*d)^3*(a + b*x)*(c + d*x)^2) + (3*a^2*c*Log[a + b*x])/(b*c - a*d)^4 - (3*a^2*c*Log[c + d*x])/(b*c - a*d)^4","A",1
295,1,154,124,0.1902196,"\int \frac{x^2}{(a+b x)^2 (c+d x)^3} \, dx","IntegrateAlgebraic[x^2/((a + b*x)^2*(c + d*x)^3),x]","\frac{5 a^2 c^2 d+8 a^2 c d^2 x+2 a^2 d^3 x^2+a b c^3+3 a b c^2 d x+4 a b c d^2 x^2+b^2 c^3 x}{2 d (a+b x) (c+d x)^2 (a d-b c)^3}+\frac{\left(a^2 (-d)-2 a b c\right) \log (a+b x)}{(b c-a d)^4}+\frac{\left(a^2 d+2 a b c\right) \log (c+d x)}{(b c-a d)^4}","-\frac{a^2}{(a+b x) (b c-a d)^3}-\frac{c^2}{2 d (c+d x)^2 (b c-a d)^2}-\frac{2 a c}{(c+d x) (b c-a d)^3}-\frac{a (a d+2 b c) \log (a+b x)}{(b c-a d)^4}+\frac{a (a d+2 b c) \log (c+d x)}{(b c-a d)^4}",1,"(a*b*c^3 + 5*a^2*c^2*d + b^2*c^3*x + 3*a*b*c^2*d*x + 8*a^2*c*d^2*x + 4*a*b*c*d^2*x^2 + 2*a^2*d^3*x^2)/(2*d*(-(b*c) + a*d)^3*(a + b*x)*(c + d*x)^2) + ((-2*a*b*c - a^2*d)*Log[a + b*x])/(b*c - a*d)^4 + ((2*a*b*c + a^2*d)*Log[c + d*x])/(b*c - a*d)^4","A",1
296,1,145,121,0.156823,"\int \frac{x}{(a+b x)^2 (c+d x)^3} \, dx","IntegrateAlgebraic[x/((a + b*x)^2*(c + d*x)^3),x]","\frac{a^2 c d+2 a^2 d^2 x+5 a b c^2+7 a b c d x+4 a b d^2 x^2+3 b^2 c^2 x+2 b^2 c d x^2}{2 (a+b x) (c+d x)^2 (b c-a d)^3}+\frac{\left(2 a b d+b^2 c\right) \log (a+b x)}{(b c-a d)^4}+\frac{\left(b^2 (-c)-2 a b d\right) \log (c+d x)}{(b c-a d)^4}","\frac{a b}{(a+b x) (b c-a d)^3}+\frac{a d+b c}{(c+d x) (b c-a d)^3}+\frac{c}{2 (c+d x)^2 (b c-a d)^2}+\frac{b (2 a d+b c) \log (a+b x)}{(b c-a d)^4}-\frac{b (2 a d+b c) \log (c+d x)}{(b c-a d)^4}",1,"(5*a*b*c^2 + a^2*c*d + 3*b^2*c^2*x + 7*a*b*c*d*x + 2*a^2*d^2*x + 2*b^2*c*d*x^2 + 4*a*b*d^2*x^2)/(2*(b*c - a*d)^3*(a + b*x)*(c + d*x)^2) + ((b^2*c + 2*a*b*d)*Log[a + b*x])/(b*c - a*d)^4 + ((-(b^2*c) - 2*a*b*d)*Log[c + d*x])/(b*c - a*d)^4","A",1
297,1,122,110,0.0006205,"\int \frac{1}{(a+b x)^2 (c+d x)^3} \, dx","IntegrateAlgebraic[1/((a + b*x)^2*(c + d*x)^3),x]","\frac{a^2 d^2-5 a b c d-3 a b d^2 x-2 b^2 c^2-9 b^2 c d x-6 b^2 d^2 x^2}{2 (a+b x) (c+d x)^2 (b c-a d)^3}-\frac{3 b^2 d \log (a+b x)}{(b c-a d)^4}+\frac{3 b^2 d \log (c+d x)}{(b c-a d)^4}","-\frac{b^2}{(a+b x) (b c-a d)^3}-\frac{3 b^2 d \log (a+b x)}{(b c-a d)^4}+\frac{3 b^2 d \log (c+d x)}{(b c-a d)^4}-\frac{2 b d}{(c+d x) (b c-a d)^3}-\frac{d}{2 (c+d x)^2 (b c-a d)^2}",1,"(-2*b^2*c^2 - 5*a*b*c*d + a^2*d^2 - 9*b^2*c*d*x - 3*a*b*d^2*x - 6*b^2*d^2*x^2)/(2*(b*c - a*d)^3*(a + b*x)*(c + d*x)^2) - (3*b^2*d*Log[a + b*x])/(b*c - a*d)^4 + (3*b^2*d*Log[c + d*x])/(b*c - a*d)^4","A",1
298,1,238,172,0.3062734,"\int \frac{1}{x (a+b x)^2 (c+d x)^3} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)^2*(c + d*x)^3),x]","\frac{\left(-a^2 d^4+4 a b c d^3-6 b^2 c^2 d^2\right) \log (c+d x)}{c^3 (b c-a d)^4}+\frac{\left(4 a b^3 d-b^4 c\right) \log (a+b x)}{a^2 (a d-b c)^4}+\frac{\log (x)}{a^2 c^3}+\frac{3 a^3 c d^3+2 a^3 d^4 x-7 a^2 b c^2 d^2-3 a^2 b c d^3 x+2 a^2 b d^4 x^2-7 a b^2 c^2 d^2 x-6 a b^2 c d^3 x^2-2 b^3 c^4-4 b^3 c^3 d x-2 b^3 c^2 d^2 x^2}{2 a c^2 (a+b x) (c+d x)^2 (a d-b c)^3}","-\frac{b^3 (b c-4 a d) \log (a+b x)}{a^2 (b c-a d)^4}-\frac{d^2 \left(a^2 d^2-4 a b c d+6 b^2 c^2\right) \log (c+d x)}{c^3 (b c-a d)^4}+\frac{\log (x)}{a^2 c^3}+\frac{b^3}{a (a+b x) (b c-a d)^3}+\frac{d^2 (3 b c-a d)}{c^2 (c+d x) (b c-a d)^3}+\frac{d^2}{2 c (c+d x)^2 (b c-a d)^2}",1,"(-2*b^3*c^4 - 7*a^2*b*c^2*d^2 + 3*a^3*c*d^3 - 4*b^3*c^3*d*x - 7*a*b^2*c^2*d^2*x - 3*a^2*b*c*d^3*x + 2*a^3*d^4*x - 2*b^3*c^2*d^2*x^2 - 6*a*b^2*c*d^3*x^2 + 2*a^2*b*d^4*x^2)/(2*a*c^2*(-(b*c) + a*d)^3*(a + b*x)*(c + d*x)^2) + Log[x]/(a^2*c^3) + ((-(b^4*c) + 4*a*b^3*d)*Log[a + b*x])/(a^2*(-(b*c) + a*d)^4) + ((-6*b^2*c^2*d^2 + 4*a*b*c*d^3 - a^2*d^4)*Log[c + d*x])/(c^3*(b*c - a*d)^4)","A",1
299,1,365,195,0.3477847,"\int \frac{1}{x^2 (a+b x)^2 (c+d x)^3} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^2*(c + d*x)^3),x]","\frac{\left(2 b^5 c-5 a b^4 d\right) \log (a+b x)}{a^3 (a d-b c)^4}+\frac{\log (x) (-3 a d-2 b c)}{a^3 c^4}+\frac{\left(3 a^2 d^5-10 a b c d^4+10 b^2 c^2 d^3\right) \log (c+d x)}{c^4 (b c-a d)^4}+\frac{-2 a^4 c^2 d^3-9 a^4 c d^4 x-6 a^4 d^5 x^2+6 a^3 b c^3 d^2+19 a^3 b c^2 d^3 x+5 a^3 b c d^4 x^2-6 a^3 b d^5 x^3-6 a^2 b^2 c^4 d-6 a^2 b^2 c^3 d^2 x+15 a^2 b^2 c^2 d^3 x^2+14 a^2 b^2 c d^4 x^3+2 a b^3 c^5-2 a b^3 c^4 d x-10 a b^3 c^3 d^2 x^2-6 a b^3 c^2 d^3 x^3+4 b^4 c^5 x+8 b^4 c^4 d x^2+4 b^4 c^3 d^2 x^3}{2 a^2 c^3 x (a+b x) (c+d x)^2 (a d-b c)^3}","\frac{b^4 (2 b c-5 a d) \log (a+b x)}{a^3 (b c-a d)^4}-\frac{\log (x) (3 a d+2 b c)}{a^3 c^4}-\frac{b^4}{a^2 (a+b x) (b c-a d)^3}+\frac{d^3 \left(3 a^2 d^2-10 a b c d+10 b^2 c^2\right) \log (c+d x)}{c^4 (b c-a d)^4}-\frac{1}{a^2 c^3 x}-\frac{2 d^3 (2 b c-a d)}{c^3 (c+d x) (b c-a d)^3}-\frac{d^3}{2 c^2 (c+d x)^2 (b c-a d)^2}",1,"(2*a*b^3*c^5 - 6*a^2*b^2*c^4*d + 6*a^3*b*c^3*d^2 - 2*a^4*c^2*d^3 + 4*b^4*c^5*x - 2*a*b^3*c^4*d*x - 6*a^2*b^2*c^3*d^2*x + 19*a^3*b*c^2*d^3*x - 9*a^4*c*d^4*x + 8*b^4*c^4*d*x^2 - 10*a*b^3*c^3*d^2*x^2 + 15*a^2*b^2*c^2*d^3*x^2 + 5*a^3*b*c*d^4*x^2 - 6*a^4*d^5*x^2 + 4*b^4*c^3*d^2*x^3 - 6*a*b^3*c^2*d^3*x^3 + 14*a^2*b^2*c*d^4*x^3 - 6*a^3*b*d^5*x^3)/(2*a^2*c^3*(-(b*c) + a*d)^3*x*(a + b*x)*(c + d*x)^2) + ((-2*b*c - 3*a*d)*Log[x])/(a^3*c^4) + ((2*b^5*c - 5*a*b^4*d)*Log[a + b*x])/(a^3*(-(b*c) + a*d)^4) + ((10*b^2*c^2*d^3 - 10*a*b*c*d^4 + 3*a^2*d^5)*Log[c + d*x])/(c^4*(b*c - a*d)^4)","A",1
300,1,492,228,0.394758,"\int \frac{1}{x^3 (a+b x)^2 (c+d x)^3} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)^2*(c + d*x)^3),x]","\frac{3 \left(2 a b^5 d-b^6 c\right) \log (a+b x)}{a^4 (a d-b c)^4}-\frac{3 \left(2 a^2 d^6-6 a b c d^5+5 b^2 c^2 d^4\right) \log (c+d x)}{c^5 (b c-a d)^4}+\frac{3 \log (x) \left(2 a^2 d^2+2 a b c d+b^2 c^2\right)}{a^4 c^5}+\frac{-a^5 c^3 d^3+4 a^5 c^2 d^4 x+18 a^5 c d^5 x^2+12 a^5 d^6 x^3+3 a^4 b c^4 d^2-9 a^4 b c^3 d^3 x-32 a^4 b c^2 d^4 x^2-6 a^4 b c d^5 x^3+12 a^4 b d^6 x^4-3 a^3 b^2 c^5 d+3 a^3 b^2 c^4 d^2 x+a^3 b^2 c^3 d^3 x^2-30 a^3 b^2 c^2 d^4 x^3-24 a^3 b^2 c d^5 x^4+a^2 b^3 c^6+5 a^2 b^3 c^5 d x+13 a^2 b^3 c^4 d^2 x^2+15 a^2 b^3 c^3 d^3 x^3+6 a^2 b^3 c^2 d^4 x^4-3 a b^4 c^6 x+9 a b^4 c^4 d^2 x^3+6 a b^4 c^3 d^3 x^4-6 b^5 c^6 x^2-12 b^5 c^5 d x^3-6 b^5 c^4 d^2 x^4}{2 a^3 c^4 x^2 (a+b x) (c+d x)^2 (a d-b c)^3}","-\frac{3 b^5 (b c-2 a d) \log (a+b x)}{a^4 (b c-a d)^4}+\frac{b^5}{a^3 (a+b x) (b c-a d)^3}+\frac{3 a d+2 b c}{a^3 c^4 x}-\frac{3 d^4 \left(2 a^2 d^2-6 a b c d+5 b^2 c^2\right) \log (c+d x)}{c^5 (b c-a d)^4}-\frac{1}{2 a^2 c^3 x^2}+\frac{3 \log (x) \left(2 a^2 d^2+2 a b c d+b^2 c^2\right)}{a^4 c^5}+\frac{d^4 (5 b c-3 a d)}{c^4 (c+d x) (b c-a d)^3}+\frac{d^4}{2 c^3 (c+d x)^2 (b c-a d)^2}",1,"(a^2*b^3*c^6 - 3*a^3*b^2*c^5*d + 3*a^4*b*c^4*d^2 - a^5*c^3*d^3 - 3*a*b^4*c^6*x + 5*a^2*b^3*c^5*d*x + 3*a^3*b^2*c^4*d^2*x - 9*a^4*b*c^3*d^3*x + 4*a^5*c^2*d^4*x - 6*b^5*c^6*x^2 + 13*a^2*b^3*c^4*d^2*x^2 + a^3*b^2*c^3*d^3*x^2 - 32*a^4*b*c^2*d^4*x^2 + 18*a^5*c*d^5*x^2 - 12*b^5*c^5*d*x^3 + 9*a*b^4*c^4*d^2*x^3 + 15*a^2*b^3*c^3*d^3*x^3 - 30*a^3*b^2*c^2*d^4*x^3 - 6*a^4*b*c*d^5*x^3 + 12*a^5*d^6*x^3 - 6*b^5*c^4*d^2*x^4 + 6*a*b^4*c^3*d^3*x^4 + 6*a^2*b^3*c^2*d^4*x^4 - 24*a^3*b^2*c*d^5*x^4 + 12*a^4*b*d^6*x^4)/(2*a^3*c^4*(-(b*c) + a*d)^3*x^2*(a + b*x)*(c + d*x)^2) + (3*(b^2*c^2 + 2*a*b*c*d + 2*a^2*d^2)*Log[x])/(a^4*c^5) + (3*(-(b^6*c) + 2*a*b^5*d)*Log[a + b*x])/(a^4*(-(b*c) + a*d)^4) - (3*(5*b^2*c^2*d^4 - 6*a*b*c*d^5 + 2*a^2*d^6)*Log[c + d*x])/(c^5*(b*c - a*d)^4)","B",1
301,1,338,196,0.2142119,"\int \frac{x^3 (c+d x)^3}{(a+b x)^3} \, dx","IntegrateAlgebraic[(x^3*(c + d*x)^3)/(a + b*x)^3,x]","\frac{3 \left(5 a^4 d^3-10 a^3 b c d^2+6 a^2 b^2 c^2 d-a b^3 c^3\right) \log (a+b x)}{b^7}+\frac{22 a^6 d^3-54 a^5 b c d^2-16 a^5 b d^3 x+42 a^4 b^2 c^2 d+12 a^4 b^2 c d^2 x-68 a^4 b^2 d^3 x^2-10 a^3 b^3 c^3+12 a^3 b^3 c^2 d x+126 a^3 b^3 c d^2 x^2-20 a^3 b^3 d^3 x^3-8 a^2 b^4 c^3 x-66 a^2 b^4 c^2 d x^2+40 a^2 b^4 c d^2 x^3+5 a^2 b^4 d^3 x^4+8 a b^5 c^3 x^2-24 a b^5 c^2 d x^3-10 a b^5 c d^2 x^4-2 a b^5 d^3 x^5+4 b^6 c^3 x^3+6 b^6 c^2 d x^4+4 b^6 c d^2 x^5+b^6 d^3 x^6}{4 b^7 (a+b x)^2}","\frac{a^3 (b c-a d)^3}{2 b^7 (a+b x)^2}-\frac{3 a^2 (b c-2 a d) (b c-a d)^2}{b^7 (a+b x)}-\frac{3 a (b c-a d) \left(5 a^2 d^2-5 a b c d+b^2 c^2\right) \log (a+b x)}{b^7}+\frac{x (b c-a d) \left(10 a^2 d^2-8 a b c d+b^2 c^2\right)}{b^6}+\frac{3 d x^2 (b c-2 a d) (b c-a d)}{2 b^5}+\frac{d^2 x^3 (b c-a d)}{b^4}+\frac{d^3 x^4}{4 b^3}",1,"(-10*a^3*b^3*c^3 + 42*a^4*b^2*c^2*d - 54*a^5*b*c*d^2 + 22*a^6*d^3 - 8*a^2*b^4*c^3*x + 12*a^3*b^3*c^2*d*x + 12*a^4*b^2*c*d^2*x - 16*a^5*b*d^3*x + 8*a*b^5*c^3*x^2 - 66*a^2*b^4*c^2*d*x^2 + 126*a^3*b^3*c*d^2*x^2 - 68*a^4*b^2*d^3*x^2 + 4*b^6*c^3*x^3 - 24*a*b^5*c^2*d*x^3 + 40*a^2*b^4*c*d^2*x^3 - 20*a^3*b^3*d^3*x^3 + 6*b^6*c^2*d*x^4 - 10*a*b^5*c*d^2*x^4 + 5*a^2*b^4*d^3*x^4 + 4*b^6*c*d^2*x^5 - 2*a*b^5*d^3*x^5 + b^6*d^3*x^6)/(4*b^7*(a + b*x)^2) + (3*(-(a*b^3*c^3) + 6*a^2*b^2*c^2*d - 10*a^3*b*c*d^2 + 5*a^4*d^3)*Log[a + b*x])/b^7","A",1
302,1,265,156,0.1404156,"\int \frac{x^2 (c+d x)^3}{(a+b x)^3} \, dx","IntegrateAlgebraic[(x^2*(c + d*x)^3)/(a + b*x)^3,x]","\frac{\left(-10 a^3 d^3+18 a^2 b c d^2-9 a b^2 c^2 d+b^3 c^3\right) \log (a+b x)}{b^6}+\frac{-27 a^5 d^3+63 a^4 b c d^2+6 a^4 b d^3 x-45 a^3 b^2 c^2 d+18 a^3 b^2 c d^2 x+63 a^3 b^2 d^3 x^2+9 a^2 b^3 c^3-36 a^2 b^3 c^2 d x-99 a^2 b^3 c d^2 x^2+20 a^2 b^3 d^3 x^3+12 a b^4 c^3 x+36 a b^4 c^2 d x^2-36 a b^4 c d^2 x^3-5 a b^4 d^3 x^4+18 b^5 c^2 d x^3+9 b^5 c d^2 x^4+2 b^5 d^3 x^5}{6 b^6 (a+b x)^2}","-\frac{a^2 (b c-a d)^3}{2 b^6 (a+b x)^2}+\frac{\left(10 a^2 d^2-8 a b c d+b^2 c^2\right) (b c-a d) \log (a+b x)}{b^6}+\frac{a (2 b c-5 a d) (b c-a d)^2}{b^6 (a+b x)}+\frac{3 d x (b c-2 a d) (b c-a d)}{b^5}+\frac{3 d^2 x^2 (b c-a d)}{2 b^4}+\frac{d^3 x^3}{3 b^3}",1,"(9*a^2*b^3*c^3 - 45*a^3*b^2*c^2*d + 63*a^4*b*c*d^2 - 27*a^5*d^3 + 12*a*b^4*c^3*x - 36*a^2*b^3*c^2*d*x + 18*a^3*b^2*c*d^2*x + 6*a^4*b*d^3*x + 36*a*b^4*c^2*d*x^2 - 99*a^2*b^3*c*d^2*x^2 + 63*a^3*b^2*d^3*x^2 + 18*b^5*c^2*d*x^3 - 36*a*b^4*c*d^2*x^3 + 20*a^2*b^3*d^3*x^3 + 9*b^5*c*d^2*x^4 - 5*a*b^4*d^3*x^4 + 2*b^5*d^3*x^5)/(6*b^6*(a + b*x)^2) + ((b^3*c^3 - 9*a*b^2*c^2*d + 18*a^2*b*c*d^2 - 10*a^3*d^3)*Log[a + b*x])/b^6","A",1
303,1,195,114,0.1080231,"\int \frac{x (c+d x)^3}{(a+b x)^3} \, dx","IntegrateAlgebraic[(x*(c + d*x)^3)/(a + b*x)^3,x]","\frac{3 \left(2 a^2 d^3-3 a b c d^2+b^2 c^2 d\right) \log (a+b x)}{b^5}+\frac{7 a^4 d^3-15 a^3 b c d^2+2 a^3 b d^3 x+9 a^2 b^2 c^2 d-12 a^2 b^2 c d^2 x-11 a^2 b^2 d^3 x^2-a b^3 c^3+12 a b^3 c^2 d x+12 a b^3 c d^2 x^2-4 a b^3 d^3 x^3-2 b^4 c^3 x+6 b^4 c d^2 x^3+b^4 d^3 x^4}{2 b^5 (a+b x)^2}","-\frac{(b c-4 a d) (b c-a d)^2}{b^5 (a+b x)}+\frac{a (b c-a d)^3}{2 b^5 (a+b x)^2}+\frac{3 d (b c-2 a d) (b c-a d) \log (a+b x)}{b^5}+\frac{3 d^2 x (b c-a d)}{b^4}+\frac{d^3 x^2}{2 b^3}",1,"(-(a*b^3*c^3) + 9*a^2*b^2*c^2*d - 15*a^3*b*c*d^2 + 7*a^4*d^3 - 2*b^4*c^3*x + 12*a*b^3*c^2*d*x - 12*a^2*b^2*c*d^2*x + 2*a^3*b*d^3*x + 12*a*b^3*c*d^2*x^2 - 11*a^2*b^2*d^3*x^2 + 6*b^4*c*d^2*x^3 - 4*a*b^3*d^3*x^3 + b^4*d^3*x^4)/(2*b^5*(a + b*x)^2) + (3*(b^2*c^2*d - 3*a*b*c*d^2 + 2*a^2*d^3)*Log[a + b*x])/b^5","A",1
304,1,130,78,0.0006754,"\int \frac{(c+d x)^3}{(a+b x)^3} \, dx","IntegrateAlgebraic[(c + d*x)^3/(a + b*x)^3,x]","\frac{-5 a^3 d^3+9 a^2 b c d^2-4 a^2 b d^3 x-3 a b^2 c^2 d+12 a b^2 c d^2 x+4 a b^2 d^3 x^2+b^3 \left(-c^3\right)-6 b^3 c^2 d x+2 b^3 d^3 x^3}{2 b^4 (a+b x)^2}+\frac{3 \left(b c d^2-a d^3\right) \log (a+b x)}{b^4}","\frac{3 d^2 (b c-a d) \log (a+b x)}{b^4}-\frac{3 d (b c-a d)^2}{b^4 (a+b x)}-\frac{(b c-a d)^3}{2 b^4 (a+b x)^2}+\frac{d^3 x}{b^3}",1,"(-(b^3*c^3) - 3*a*b^2*c^2*d + 9*a^2*b*c*d^2 - 5*a^3*d^3 - 6*b^3*c^2*d*x + 12*a*b^2*c*d^2*x - 4*a^2*b*d^3*x + 4*a*b^2*d^3*x^2 + 2*b^3*d^3*x^3)/(2*b^4*(a + b*x)^2) + (3*(b*c*d^2 - a*d^3)*Log[a + b*x])/b^4","A",1
305,1,91,93,0.1221353,"\int \frac{(c+d x)^3}{x (a+b x)^3} \, dx","IntegrateAlgebraic[(c + d*x)^3/(x*(a + b*x)^3),x]","\frac{\left(a^3 d^3-b^3 c^3\right) \log (a+b x)}{a^3 b^3}+\frac{c^3 \log (x)}{a^3}+\frac{(a d-b c)^2 \left(3 a^2 d+3 a b c+4 a b d x+2 b^2 c x\right)}{2 a^2 b^3 (a+b x)^2}","-\left(\frac{c^3}{a^3}-\frac{d^3}{b^3}\right) \log (a+b x)+\frac{c^3 \log (x)}{a^3}+\frac{(b c-a d)^2 (2 a d+b c)}{a^2 b^3 (a+b x)}+\frac{(b c-a d)^3}{2 a b^3 (a+b x)^2}",1,"((-(b*c) + a*d)^2*(3*a*b*c + 3*a^2*d + 2*b^2*c*x + 4*a*b*d*x))/(2*a^2*b^3*(a + b*x)^2) + (c^3*Log[x])/a^3 + ((-(b^3*c^3) + a^3*d^3)*Log[a + b*x])/(a^3*b^3)","A",1
306,1,156,112,0.1440052,"\int \frac{(c+d x)^3}{x^2 (a+b x)^3} \, dx","IntegrateAlgebraic[(c + d*x)^3/(x^2*(a + b*x)^3),x]","\frac{3 \log (x) \left(a c^2 d-b c^3\right)}{a^4}-\frac{3 \left(a c^2 d-b c^3\right) \log (a+b x)}{a^4}+\frac{a^4 \left(-d^3\right) x-3 a^3 b c d^2 x-2 a^3 b d^3 x^2-2 a^2 b^2 c^3+9 a^2 b^2 c^2 d x-9 a b^3 c^3 x+6 a b^3 c^2 d x^2-6 b^4 c^3 x^2}{2 a^3 b^2 x (a+b x)^2}","-\frac{3 c^2 \log (x) (b c-a d)}{a^4}+\frac{3 c^2 (b c-a d) \log (a+b x)}{a^4}-\frac{(b c-a d)^2 (a d+2 b c)}{a^3 b^2 (a+b x)}-\frac{c^3}{a^3 x}-\frac{(b c-a d)^3}{2 a^2 b^2 (a+b x)^2}",1,"(-2*a^2*b^2*c^3 - 9*a*b^3*c^3*x + 9*a^2*b^2*c^2*d*x - 3*a^3*b*c*d^2*x - a^4*d^3*x - 6*b^4*c^3*x^2 + 6*a*b^3*c^2*d*x^2 - 2*a^3*b*d^3*x^2)/(2*a^3*b^2*x*(a + b*x)^2) + (3*(-(b*c^3) + a*c^2*d)*Log[x])/a^4 - (3*(-(b*c^3) + a*c^2*d)*Log[a + b*x])/a^4","A",1
307,1,212,137,0.204638,"\int \frac{(c+d x)^3}{x^3 (a+b x)^3} \, dx","IntegrateAlgebraic[(c + d*x)^3/(x^3*(a + b*x)^3),x]","\frac{3 \log (x) \left(a^2 c d^2-3 a b c^2 d+2 b^2 c^3\right)}{a^5}-\frac{3 \left(a^2 c d^2-3 a b c^2 d+2 b^2 c^3\right) \log (a+b x)}{a^5}+\frac{a^4 \left(-d^3\right) x^2-a^3 b c^3-6 a^3 b c^2 d x+9 a^3 b c d^2 x^2+4 a^2 b^2 c^3 x-27 a^2 b^2 c^2 d x^2+6 a^2 b^2 c d^2 x^3+18 a b^3 c^3 x^2-18 a b^3 c^2 d x^3+12 b^4 c^3 x^3}{2 a^4 b x^2 (a+b x)^2}","\frac{3 c \log (x) (b c-a d) (2 b c-a d)}{a^5}-\frac{3 c (b c-a d) (2 b c-a d) \log (a+b x)}{a^5}+\frac{3 c^2 (b c-a d)}{a^4 x}+\frac{3 c (b c-a d)^2}{a^4 (a+b x)}+\frac{(b c-a d)^3}{2 a^3 b (a+b x)^2}-\frac{c^3}{2 a^3 x^2}",1,"(-(a^3*b*c^3) + 4*a^2*b^2*c^3*x - 6*a^3*b*c^2*d*x + 18*a*b^3*c^3*x^2 - 27*a^2*b^2*c^2*d*x^2 + 9*a^3*b*c*d^2*x^2 - a^4*d^3*x^2 + 12*b^4*c^3*x^3 - 18*a*b^3*c^2*d*x^3 + 6*a^2*b^2*c*d^2*x^3)/(2*a^4*b*x^2*(a + b*x)^2) + (3*(2*b^2*c^3 - 3*a*b*c^2*d + a^2*c*d^2)*Log[x])/a^5 - (3*(2*b^2*c^3 - 3*a*b*c^2*d + a^2*c*d^2)*Log[a + b*x])/a^5","A",1
308,1,277,193,0.2054261,"\int \frac{(c+d x)^3}{x^4 (a+b x)^3} \, dx","IntegrateAlgebraic[(c + d*x)^3/(x^4*(a + b*x)^3),x]","\frac{\log (x) \left(a^3 d^3-9 a^2 b c d^2+18 a b^2 c^2 d-10 b^3 c^3\right)}{a^6}+\frac{\left(-a^3 d^3+9 a^2 b c d^2-18 a b^2 c^2 d+10 b^3 c^3\right) \log (a+b x)}{a^6}+\frac{-2 a^4 c^3-9 a^4 c^2 d x-18 a^4 c d^2 x^2+9 a^4 d^3 x^3+5 a^3 b c^3 x+36 a^3 b c^2 d x^2-81 a^3 b c d^2 x^3+6 a^3 b d^3 x^4-20 a^2 b^2 c^3 x^2+162 a^2 b^2 c^2 d x^3-54 a^2 b^2 c d^2 x^4-90 a b^3 c^3 x^3+108 a b^3 c^2 d x^4-60 b^4 c^3 x^4}{6 a^5 x^3 (a+b x)^2}","-\frac{3 c (b c-a d) (2 b c-a d)}{a^5 x}-\frac{(b c-a d)^2 (4 b c-a d)}{a^5 (a+b x)}+\frac{3 c^2 (b c-a d)}{2 a^4 x^2}-\frac{(b c-a d)^3}{2 a^4 (a+b x)^2}-\frac{c^3}{3 a^3 x^3}-\frac{\log (x) (b c-a d) \left(a^2 d^2-8 a b c d+10 b^2 c^2\right)}{a^6}+\frac{(b c-a d) \left(a^2 d^2-8 a b c d+10 b^2 c^2\right) \log (a+b x)}{a^6}",1,"(-2*a^4*c^3 + 5*a^3*b*c^3*x - 9*a^4*c^2*d*x - 20*a^2*b^2*c^3*x^2 + 36*a^3*b*c^2*d*x^2 - 18*a^4*c*d^2*x^2 - 90*a*b^3*c^3*x^3 + 162*a^2*b^2*c^2*d*x^3 - 81*a^3*b*c*d^2*x^3 + 9*a^4*d^3*x^3 - 60*b^4*c^3*x^4 + 108*a*b^3*c^2*d*x^4 - 54*a^2*b^2*c*d^2*x^4 + 6*a^3*b*d^3*x^4)/(6*a^5*x^3*(a + b*x)^2) + ((-10*b^3*c^3 + 18*a*b^2*c^2*d - 9*a^2*b*c*d^2 + a^3*d^3)*Log[x])/a^6 + ((10*b^3*c^3 - 18*a*b^2*c^2*d + 9*a^2*b*c*d^2 - a^3*d^3)*Log[a + b*x])/a^6","A",1
309,1,815,245,0.6008364,"\int \frac{x^7}{(a+b x)^3 (c+d x)^3} \, dx","IntegrateAlgebraic[x^7/((a + b*x)^3*(c + d*x)^3),x]","\frac{7 c^2 d^6 a^8+7 d^8 x^2 a^8+14 c d^7 x a^8-13 b c^3 d^5 a^7+2 b d^8 x^3 a^7-9 b c d^7 x^2 a^7-24 b c^2 d^6 x a^7-11 b^2 d^8 x^4 a^6-18 b^2 c d^7 x^3 a^6-3 b^2 c^2 d^6 x^2 a^6+4 b^2 c^3 d^5 x a^6-4 b^3 d^8 x^5 a^5+24 b^3 c d^7 x^4 a^5+48 b^3 c^2 d^6 x^3 a^5+8 b^3 c^3 d^5 x^2 a^5-12 b^3 c^4 d^4 x a^5+b^4 d^8 x^6 a^4+12 b^4 c d^7 x^5 a^4+3 b^4 c^2 d^6 x^4 a^4-38 b^4 c^3 d^5 x^3 a^4-42 b^4 c^4 d^4 x^2 a^4-12 b^4 c^5 d^3 x a^4-4 b^5 c d^7 x^6 a^3-8 b^5 c^2 d^6 x^5 a^3-32 b^5 c^3 d^5 x^4 a^3-38 b^5 c^4 d^4 x^3 a^3+8 b^5 c^5 d^3 x^2 a^3-13 b^5 c^7 d a^3+4 b^5 c^6 d^2 x a^3+7 b^6 c^8 a^2+6 b^6 c^2 d^6 x^6 a^2-8 b^6 c^3 d^5 x^5 a^2+3 b^6 c^4 d^4 x^4 a^2+48 b^6 c^5 d^3 x^3 a^2-3 b^6 c^6 d^2 x^2 a^2-24 b^6 c^7 d x a^2-4 b^7 c^3 d^5 x^6 a+12 b^7 c^4 d^4 x^5 a+24 b^7 c^5 d^3 x^4 a-18 b^7 c^6 d^2 x^3 a-9 b^7 c^7 d x^2 a+14 b^7 c^8 x a+b^8 c^4 d^4 x^6-4 b^8 c^5 d^3 x^5-11 b^8 c^6 d^2 x^4+2 b^8 c^7 d x^3+7 b^8 c^8 x^2}{2 b^5 d^5 (b c-a d)^4 (a+b x)^2 (c+d x)^2}-\frac{3 \left(2 d^2 a^7-7 b c d a^6+7 b^2 c^2 a^5\right) \log (a+b x)}{b^5 (b c-a d)^5}-\frac{3 \left(2 b^2 c^7-7 a b d c^6+7 a^2 d^2 c^5\right) \log (c+d x)}{d^5 (a d-b c)^5}","\frac{a^7}{2 b^5 (a+b x)^2 (b c-a d)^3}-\frac{a^6 (7 b c-4 a d)}{b^5 (a+b x) (b c-a d)^4}+\frac{3 c^5 \left(7 a^2 d^2-7 a b c d+2 b^2 c^2\right) \log (c+d x)}{d^5 (b c-a d)^5}-\frac{3 a^5 \left(2 a^2 d^2-7 a b c d+7 b^2 c^2\right) \log (a+b x)}{b^5 (b c-a d)^5}-\frac{3 x (a d+b c)}{b^4 d^4}-\frac{c^7}{2 d^5 (c+d x)^2 (b c-a d)^3}+\frac{c^6 (4 b c-7 a d)}{d^5 (c+d x) (b c-a d)^4}+\frac{x^2}{2 b^3 d^3}",1,"(7*a^2*b^6*c^8 - 13*a^3*b^5*c^7*d - 13*a^7*b*c^3*d^5 + 7*a^8*c^2*d^6 + 14*a*b^7*c^8*x - 24*a^2*b^6*c^7*d*x + 4*a^3*b^5*c^6*d^2*x - 12*a^4*b^4*c^5*d^3*x - 12*a^5*b^3*c^4*d^4*x + 4*a^6*b^2*c^3*d^5*x - 24*a^7*b*c^2*d^6*x + 14*a^8*c*d^7*x + 7*b^8*c^8*x^2 - 9*a*b^7*c^7*d*x^2 - 3*a^2*b^6*c^6*d^2*x^2 + 8*a^3*b^5*c^5*d^3*x^2 - 42*a^4*b^4*c^4*d^4*x^2 + 8*a^5*b^3*c^3*d^5*x^2 - 3*a^6*b^2*c^2*d^6*x^2 - 9*a^7*b*c*d^7*x^2 + 7*a^8*d^8*x^2 + 2*b^8*c^7*d*x^3 - 18*a*b^7*c^6*d^2*x^3 + 48*a^2*b^6*c^5*d^3*x^3 - 38*a^3*b^5*c^4*d^4*x^3 - 38*a^4*b^4*c^3*d^5*x^3 + 48*a^5*b^3*c^2*d^6*x^3 - 18*a^6*b^2*c*d^7*x^3 + 2*a^7*b*d^8*x^3 - 11*b^8*c^6*d^2*x^4 + 24*a*b^7*c^5*d^3*x^4 + 3*a^2*b^6*c^4*d^4*x^4 - 32*a^3*b^5*c^3*d^5*x^4 + 3*a^4*b^4*c^2*d^6*x^4 + 24*a^5*b^3*c*d^7*x^4 - 11*a^6*b^2*d^8*x^4 - 4*b^8*c^5*d^3*x^5 + 12*a*b^7*c^4*d^4*x^5 - 8*a^2*b^6*c^3*d^5*x^5 - 8*a^3*b^5*c^2*d^6*x^5 + 12*a^4*b^4*c*d^7*x^5 - 4*a^5*b^3*d^8*x^5 + b^8*c^4*d^4*x^6 - 4*a*b^7*c^3*d^5*x^6 + 6*a^2*b^6*c^2*d^6*x^6 - 4*a^3*b^5*c*d^7*x^6 + a^4*b^4*d^8*x^6)/(2*b^5*d^5*(b*c - a*d)^4*(a + b*x)^2*(c + d*x)^2) - (3*(7*a^5*b^2*c^2 - 7*a^6*b*c*d + 2*a^7*d^2)*Log[a + b*x])/(b^5*(b*c - a*d)^5) - (3*(2*b^2*c^7 - 7*a*b*c^6*d + 7*a^2*c^5*d^2)*Log[c + d*x])/(d^5*(-(b*c) + a*d)^5)","B",1
310,1,657,222,0.4994141,"\int \frac{x^6}{(a+b x)^3 (c+d x)^3} \, dx","IntegrateAlgebraic[x^6/((a + b*x)^3*(c + d*x)^3),x]","\frac{3 \left(5 a^2 c^4 d^2-4 a b c^5 d+b^2 c^6\right) \log (c+d x)}{d^4 (a d-b c)^5}+\frac{3 \left(a^6 d^2-4 a^5 b c d+5 a^4 b^2 c^2\right) \log (a+b x)}{b^4 (b c-a d)^5}+\frac{-5 a^7 c^2 d^5-10 a^7 c d^6 x-5 a^7 d^7 x^2+11 a^6 b c^3 d^4+18 a^6 b c^2 d^5 x+3 a^6 b c d^6 x^2-4 a^6 b d^7 x^3+4 a^5 b^2 c^3 d^4 x+12 a^5 b^2 c^2 d^5 x^2+12 a^5 b^2 c d^6 x^3+4 a^5 b^2 d^7 x^4+12 a^4 b^3 c^4 d^3 x+8 a^4 b^3 c^3 d^4 x^2-18 a^4 b^3 c^2 d^5 x^3-12 a^4 b^3 c d^6 x^4+2 a^4 b^3 d^7 x^5+11 a^3 b^4 c^6 d+4 a^3 b^4 c^5 d^2 x+8 a^3 b^4 c^4 d^3 x^2+32 a^3 b^4 c^3 d^4 x^3+8 a^3 b^4 c^2 d^5 x^4-8 a^3 b^4 c d^6 x^5-5 a^2 b^5 c^7+18 a^2 b^5 c^6 d x+12 a^2 b^5 c^5 d^2 x^2-18 a^2 b^5 c^4 d^3 x^3+8 a^2 b^5 c^3 d^4 x^4+12 a^2 b^5 c^2 d^5 x^5-10 a b^6 c^7 x+3 a b^6 c^6 d x^2+12 a b^6 c^5 d^2 x^3-12 a b^6 c^4 d^3 x^4-8 a b^6 c^3 d^4 x^5-5 b^7 c^7 x^2-4 b^7 c^6 d x^3+4 b^7 c^5 d^2 x^4+2 b^7 c^4 d^3 x^5}{2 b^4 d^4 (a+b x)^2 (c+d x)^2 (b c-a d)^4}","-\frac{a^6}{2 b^4 (a+b x)^2 (b c-a d)^3}+\frac{3 a^5 (2 b c-a d)}{b^4 (a+b x) (b c-a d)^4}-\frac{3 c^4 \left(5 a^2 d^2-4 a b c d+b^2 c^2\right) \log (c+d x)}{d^4 (b c-a d)^5}+\frac{3 a^4 \left(a^2 d^2-4 a b c d+5 b^2 c^2\right) \log (a+b x)}{b^4 (b c-a d)^5}+\frac{c^6}{2 d^4 (c+d x)^2 (b c-a d)^3}-\frac{3 c^5 (b c-2 a d)}{d^4 (c+d x) (b c-a d)^4}+\frac{x}{b^3 d^3}",1,"(-5*a^2*b^5*c^7 + 11*a^3*b^4*c^6*d + 11*a^6*b*c^3*d^4 - 5*a^7*c^2*d^5 - 10*a*b^6*c^7*x + 18*a^2*b^5*c^6*d*x + 4*a^3*b^4*c^5*d^2*x + 12*a^4*b^3*c^4*d^3*x + 4*a^5*b^2*c^3*d^4*x + 18*a^6*b*c^2*d^5*x - 10*a^7*c*d^6*x - 5*b^7*c^7*x^2 + 3*a*b^6*c^6*d*x^2 + 12*a^2*b^5*c^5*d^2*x^2 + 8*a^3*b^4*c^4*d^3*x^2 + 8*a^4*b^3*c^3*d^4*x^2 + 12*a^5*b^2*c^2*d^5*x^2 + 3*a^6*b*c*d^6*x^2 - 5*a^7*d^7*x^2 - 4*b^7*c^6*d*x^3 + 12*a*b^6*c^5*d^2*x^3 - 18*a^2*b^5*c^4*d^3*x^3 + 32*a^3*b^4*c^3*d^4*x^3 - 18*a^4*b^3*c^2*d^5*x^3 + 12*a^5*b^2*c*d^6*x^3 - 4*a^6*b*d^7*x^3 + 4*b^7*c^5*d^2*x^4 - 12*a*b^6*c^4*d^3*x^4 + 8*a^2*b^5*c^3*d^4*x^4 + 8*a^3*b^4*c^2*d^5*x^4 - 12*a^4*b^3*c*d^6*x^4 + 4*a^5*b^2*d^7*x^4 + 2*b^7*c^4*d^3*x^5 - 8*a*b^6*c^3*d^4*x^5 + 12*a^2*b^5*c^2*d^5*x^5 - 8*a^3*b^4*c*d^6*x^5 + 2*a^4*b^3*d^7*x^5)/(2*b^4*d^4*(b*c - a*d)^4*(a + b*x)^2*(c + d*x)^2) + (3*(5*a^4*b^2*c^2 - 4*a^5*b*c*d + a^6*d^2)*Log[a + b*x])/(b^4*(b*c - a*d)^5) + (3*(b^2*c^6 - 4*a*b*c^5*d + 5*a^2*c^4*d^2)*Log[c + d*x])/(d^4*(-(b*c) + a*d)^5)","B",1
311,1,390,213,0.4981261,"\int \frac{x^5}{(a+b x)^3 (c+d x)^3} \, dx","IntegrateAlgebraic[x^5/((a + b*x)^3*(c + d*x)^3),x]","-\frac{\left(10 a^2 c^3 d^2-5 a b c^4 d+b^2 c^5\right) \log (c+d x)}{d^3 (a d-b c)^5}-\frac{\left(a^5 d^2-5 a^4 b c d+10 a^3 b^2 c^2\right) \log (a+b x)}{b^3 (b c-a d)^5}+\frac{3 a^6 c^2 d^4+6 a^6 c d^5 x+3 a^6 d^6 x^2-9 a^5 b c^3 d^3-14 a^5 b c^2 d^4 x-a^5 b c d^5 x^2+4 a^5 b d^6 x^3-10 a^4 b^2 c^3 d^3 x-20 a^4 b^2 c^2 d^4 x^2-10 a^4 b^2 c d^5 x^3-9 a^3 b^3 c^5 d-10 a^3 b^3 c^4 d^2 x+3 a^2 b^4 c^6-14 a^2 b^4 c^5 d x-20 a^2 b^4 c^4 d^2 x^2+6 a b^5 c^6 x-a b^5 c^5 d x^2-10 a b^5 c^4 d^2 x^3+3 b^6 c^6 x^2+4 b^6 c^5 d x^3}{2 b^3 d^3 (a+b x)^2 (c+d x)^2 (b c-a d)^4}","\frac{a^5}{2 b^3 (a+b x)^2 (b c-a d)^3}-\frac{a^4 (5 b c-2 a d)}{b^3 (a+b x) (b c-a d)^4}+\frac{c^3 \left(10 a^2 d^2-5 a b c d+b^2 c^2\right) \log (c+d x)}{d^3 (b c-a d)^5}-\frac{a^3 \left(a^2 d^2-5 a b c d+10 b^2 c^2\right) \log (a+b x)}{b^3 (b c-a d)^5}-\frac{c^5}{2 d^3 (c+d x)^2 (b c-a d)^3}+\frac{c^4 (2 b c-5 a d)}{d^3 (c+d x) (b c-a d)^4}",1,"(3*a^2*b^4*c^6 - 9*a^3*b^3*c^5*d - 9*a^5*b*c^3*d^3 + 3*a^6*c^2*d^4 + 6*a*b^5*c^6*x - 14*a^2*b^4*c^5*d*x - 10*a^3*b^3*c^4*d^2*x - 10*a^4*b^2*c^3*d^3*x - 14*a^5*b*c^2*d^4*x + 6*a^6*c*d^5*x + 3*b^6*c^6*x^2 - a*b^5*c^5*d*x^2 - 20*a^2*b^4*c^4*d^2*x^2 - 20*a^4*b^2*c^2*d^4*x^2 - a^5*b*c*d^5*x^2 + 3*a^6*d^6*x^2 + 4*b^6*c^5*d*x^3 - 10*a*b^5*c^4*d^2*x^3 - 10*a^4*b^2*c*d^5*x^3 + 4*a^5*b*d^6*x^3)/(2*b^3*d^3*(b*c - a*d)^4*(a + b*x)^2*(c + d*x)^2) - ((10*a^3*b^2*c^2 - 5*a^4*b*c*d + a^5*d^2)*Log[a + b*x])/(b^3*(b*c - a*d)^5) - ((b^2*c^5 - 5*a*b*c^4*d + 10*a^2*c^3*d^2)*Log[c + d*x])/(d^3*(-(b*c) + a*d)^5)","A",1
312,1,327,169,0.3409376,"\int \frac{x^4}{(a+b x)^3 (c+d x)^3} \, dx","IntegrateAlgebraic[x^4/((a + b*x)^3*(c + d*x)^3),x]","\frac{6 a^2 c^2 \log (a+b x)}{(b c-a d)^5}-\frac{6 a^2 c^2 \log (c+d x)}{(b c-a d)^5}+\frac{a^5 \left(-c^2\right) d^3-2 a^5 c d^4 x-a^5 d^5 x^2+7 a^4 b c^3 d^2+12 a^4 b c^2 d^3 x+3 a^4 b c d^4 x^2-2 a^4 b d^5 x^3+7 a^3 b^2 c^4 d+16 a^3 b^2 c^3 d^2 x+16 a^3 b^2 c^2 d^3 x^2+8 a^3 b^2 c d^4 x^3-a^2 b^3 c^5+12 a^2 b^3 c^4 d x+16 a^2 b^3 c^3 d^2 x^2-2 a b^4 c^5 x+3 a b^4 c^4 d x^2+8 a b^4 c^3 d^2 x^3-b^5 c^5 x^2-2 b^5 c^4 d x^3}{2 b^2 d^2 (a+b x)^2 (c+d x)^2 (b c-a d)^4}","-\frac{a^4}{2 b^2 (a+b x)^2 (b c-a d)^3}+\frac{a^3 (4 b c-a d)}{b^2 (a+b x) (b c-a d)^4}+\frac{6 a^2 c^2 \log (a+b x)}{(b c-a d)^5}-\frac{6 a^2 c^2 \log (c+d x)}{(b c-a d)^5}+\frac{c^4}{2 d^2 (c+d x)^2 (b c-a d)^3}-\frac{c^3 (b c-4 a d)}{d^2 (c+d x) (b c-a d)^4}",1,"(-(a^2*b^3*c^5) + 7*a^3*b^2*c^4*d + 7*a^4*b*c^3*d^2 - a^5*c^2*d^3 - 2*a*b^4*c^5*x + 12*a^2*b^3*c^4*d*x + 16*a^3*b^2*c^3*d^2*x + 12*a^4*b*c^2*d^3*x - 2*a^5*c*d^4*x - b^5*c^5*x^2 + 3*a*b^4*c^4*d*x^2 + 16*a^2*b^3*c^3*d^2*x^2 + 16*a^3*b^2*c^2*d^3*x^2 + 3*a^4*b*c*d^4*x^2 - a^5*d^5*x^2 - 2*b^5*c^4*d*x^3 + 8*a*b^4*c^3*d^2*x^3 + 8*a^3*b^2*c*d^4*x^3 - 2*a^4*b*d^5*x^3)/(2*b^2*d^2*(b*c - a*d)^4*(a + b*x)^2*(c + d*x)^2) + (6*a^2*c^2*Log[a + b*x])/(b*c - a*d)^5 - (6*a^2*c^2*Log[c + d*x])/(b*c - a*d)^5","A",1
313,1,271,155,0.3249203,"\int \frac{x^3}{(a+b x)^3 (c+d x)^3} \, dx","IntegrateAlgebraic[x^3/((a + b*x)^3*(c + d*x)^3),x]","-\frac{3 \left(a^2 c d+a b c^2\right) \log (a+b x)}{(b c-a d)^5}+\frac{3 \left(a^2 c d+a b c^2\right) \log (c+d x)}{(b c-a d)^5}+\frac{a^4 \left(-c^2\right) d^2-2 a^4 c d^3 x-a^4 d^4 x^2-10 a^3 b c^3 d-16 a^3 b c^2 d^2 x-5 a^3 b c d^3 x^2-a^2 b^2 c^4-16 a^2 b^2 c^3 d x-24 a^2 b^2 c^2 d^2 x^2-6 a^2 b^2 c d^3 x^3-2 a b^3 c^4 x-5 a b^3 c^3 d x^2-6 a b^3 c^2 d^2 x^3-b^4 c^4 x^2}{2 b d (a+b x)^2 (c+d x)^2 (b c-a d)^4}","\frac{a^3}{2 b (a+b x)^2 (b c-a d)^3}-\frac{3 a^2 c}{(a+b x) (b c-a d)^4}-\frac{c^3}{2 d (c+d x)^2 (b c-a d)^3}-\frac{3 a c^2}{(c+d x) (b c-a d)^4}-\frac{3 a c (a d+b c) \log (a+b x)}{(b c-a d)^5}+\frac{3 a c (a d+b c) \log (c+d x)}{(b c-a d)^5}",1,"(-(a^2*b^2*c^4) - 10*a^3*b*c^3*d - a^4*c^2*d^2 - 2*a*b^3*c^4*x - 16*a^2*b^2*c^3*d*x - 16*a^3*b*c^2*d^2*x - 2*a^4*c*d^3*x - b^4*c^4*x^2 - 5*a*b^3*c^3*d*x^2 - 24*a^2*b^2*c^2*d^2*x^2 - 5*a^3*b*c*d^3*x^2 - a^4*d^4*x^2 - 6*a*b^3*c^2*d^2*x^3 - 6*a^2*b^2*c*d^3*x^3)/(2*b*d*(b*c - a*d)^4*(a + b*x)^2*(c + d*x)^2) - (3*(a*b*c^2 + a^2*c*d)*Log[a + b*x])/(b*c - a*d)^5 + (3*(a*b*c^2 + a^2*c*d)*Log[c + d*x])/(b*c - a*d)^5","A",1
314,1,242,180,0.2551476,"\int \frac{x^2}{(a+b x)^3 (c+d x)^3} \, dx","IntegrateAlgebraic[x^2/((a + b*x)^3*(c + d*x)^3),x]","\frac{\left(a^2 d^2+4 a b c d+b^2 c^2\right) \log (a+b x)}{(b c-a d)^5}+\frac{\left(-a^2 d^2-4 a b c d-b^2 c^2\right) \log (c+d x)}{(b c-a d)^5}+\frac{6 a^3 c^2 d+10 a^3 c d^2 x+3 a^3 d^3 x^2+6 a^2 b c^3+16 a^2 b c^2 d x+15 a^2 b c d^2 x^2+2 a^2 b d^3 x^3+10 a b^2 c^3 x+15 a b^2 c^2 d x^2+8 a b^2 c d^2 x^3+3 b^3 c^3 x^2+2 b^3 c^2 d x^3}{2 (a+b x)^2 (c+d x)^2 (b c-a d)^4}","\frac{\left(a^2 d^2+4 a b c d+b^2 c^2\right) \log (a+b x)}{(b c-a d)^5}-\frac{\left(a^2 d^2+4 a b c d+b^2 c^2\right) \log (c+d x)}{(b c-a d)^5}-\frac{a^2}{2 (a+b x)^2 (b c-a d)^3}+\frac{c^2}{2 (c+d x)^2 (b c-a d)^3}+\frac{a (a d+2 b c)}{(a+b x) (b c-a d)^4}+\frac{c (2 a d+b c)}{(c+d x) (b c-a d)^4}",1,"(6*a^2*b*c^3 + 6*a^3*c^2*d + 10*a*b^2*c^3*x + 16*a^2*b*c^2*d*x + 10*a^3*c*d^2*x + 3*b^3*c^3*x^2 + 15*a*b^2*c^2*d*x^2 + 15*a^2*b*c*d^2*x^2 + 3*a^3*d^3*x^2 + 2*b^3*c^2*d*x^3 + 8*a*b^2*c*d^2*x^3 + 2*a^2*b*d^3*x^3)/(2*(b*c - a*d)^4*(a + b*x)^2*(c + d*x)^2) + ((b^2*c^2 + 4*a*b*c*d + a^2*d^2)*Log[a + b*x])/(b*c - a*d)^5 + ((-(b^2*c^2) - 4*a*b*c*d - a^2*d^2)*Log[c + d*x])/(b*c - a*d)^5","A",1
315,1,221,157,0.2227589,"\int \frac{x}{(a+b x)^3 (c+d x)^3} \, dx","IntegrateAlgebraic[x/((a + b*x)^3*(c + d*x)^3),x]","\frac{a^3 (-c) d^2-2 a^3 d^3 x-10 a^2 b c^2 d-16 a^2 b c d^2 x-9 a^2 b d^3 x^2-a b^2 c^3-16 a b^2 c^2 d x-18 a b^2 c d^2 x^2-6 a b^2 d^3 x^3-2 b^3 c^3 x-9 b^3 c^2 d x^2-6 b^3 c d^2 x^3}{2 (a+b x)^2 (c+d x)^2 (b c-a d)^4}-\frac{3 \left(a b d^2+b^2 c d\right) \log (a+b x)}{(b c-a d)^5}+\frac{3 \left(a b d^2+b^2 c d\right) \log (c+d x)}{(b c-a d)^5}","-\frac{b (2 a d+b c)}{(a+b x) (b c-a d)^4}+\frac{a b}{2 (a+b x)^2 (b c-a d)^3}-\frac{d (a d+2 b c)}{(c+d x) (b c-a d)^4}-\frac{c d}{2 (c+d x)^2 (b c-a d)^3}-\frac{3 b d (a d+b c) \log (a+b x)}{(b c-a d)^5}+\frac{3 b d (a d+b c) \log (c+d x)}{(b c-a d)^5}",1,"(-(a*b^2*c^3) - 10*a^2*b*c^2*d - a^3*c*d^2 - 2*b^3*c^3*x - 16*a*b^2*c^2*d*x - 16*a^2*b*c*d^2*x - 2*a^3*d^3*x - 9*b^3*c^2*d*x^2 - 18*a*b^2*c*d^2*x^2 - 9*a^2*b*d^3*x^2 - 6*b^3*c*d^2*x^3 - 6*a*b^2*d^3*x^3)/(2*(b*c - a*d)^4*(a + b*x)^2*(c + d*x)^2) - (3*(b^2*c*d + a*b*d^2)*Log[a + b*x])/(b*c - a*d)^5 + (3*(b^2*c*d + a*b*d^2)*Log[c + d*x])/(b*c - a*d)^5","A",1
316,1,180,143,0.0005943,"\int \frac{1}{(a+b x)^3 (c+d x)^3} \, dx","IntegrateAlgebraic[1/((a + b*x)^3*(c + d*x)^3),x]","\frac{-a^3 d^3+7 a^2 b c d^2+4 a^2 b d^3 x+7 a b^2 c^2 d+28 a b^2 c d^2 x+18 a b^2 d^3 x^2+b^3 \left(-c^3\right)+4 b^3 c^2 d x+18 b^3 c d^2 x^2+12 b^3 d^3 x^3}{2 (a+b x)^2 (c+d x)^2 (b c-a d)^4}+\frac{6 b^2 d^2 \log (a+b x)}{(b c-a d)^5}-\frac{6 b^2 d^2 \log (c+d x)}{(b c-a d)^5}","\frac{6 b^2 d^2 \log (a+b x)}{(b c-a d)^5}-\frac{6 b^2 d^2 \log (c+d x)}{(b c-a d)^5}+\frac{3 b^2 d}{(a+b x) (b c-a d)^4}-\frac{b^2}{2 (a+b x)^2 (b c-a d)^3}+\frac{3 b d^2}{(c+d x) (b c-a d)^4}+\frac{d^2}{2 (c+d x)^2 (b c-a d)^3}",1,"(-(b^3*c^3) + 7*a*b^2*c^2*d + 7*a^2*b*c*d^2 - a^3*d^3 + 4*b^3*c^2*d*x + 28*a*b^2*c*d^2*x + 4*a^2*b*d^3*x + 18*b^3*c*d^2*x^2 + 18*a*b^2*d^3*x^2 + 12*b^3*d^3*x^3)/(2*(b*c - a*d)^4*(a + b*x)^2*(c + d*x)^2) + (6*b^2*d^2*Log[a + b*x])/(b*c - a*d)^5 - (6*b^2*d^2*Log[c + d*x])/(b*c - a*d)^5","A",1
317,1,380,221,0.4865974,"\int \frac{1}{x (a+b x)^3 (c+d x)^3} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)^3*(c + d*x)^3),x]","\frac{\log (x)}{a^3 c^3}+\frac{\left(a^2 d^5-5 a b c d^4+10 b^2 c^2 d^3\right) \log (c+d x)}{c^3 (b c-a d)^5}+\frac{\left(10 a^2 b^3 d^2-5 a b^4 c d+b^5 c^2\right) \log (a+b x)}{a^3 (a d-b c)^5}+\frac{3 a^5 c d^4+2 a^5 d^5 x-9 a^4 b c^2 d^3-2 a^4 b c d^4 x+4 a^4 b d^5 x^2-18 a^3 b^2 c^2 d^3 x-13 a^3 b^2 c d^4 x^2+2 a^3 b^2 d^5 x^3-9 a^2 b^3 c^4 d-18 a^2 b^3 c^3 d^2 x-18 a^2 b^3 c^2 d^3 x^2-8 a^2 b^3 c d^4 x^3+3 a b^4 c^5-2 a b^4 c^4 d x-13 a b^4 c^3 d^2 x^2-8 a b^4 c^2 d^3 x^3+2 b^5 c^5 x+4 b^5 c^4 d x^2+2 b^5 c^3 d^2 x^3}{2 a^2 c^2 (a+b x)^2 (c+d x)^2 (a d-b c)^4}","\frac{\log (x)}{a^3 c^3}+\frac{b^3 (b c-4 a d)}{a^2 (a+b x) (b c-a d)^4}+\frac{d^3 \left(a^2 d^2-5 a b c d+10 b^2 c^2\right) \log (c+d x)}{c^3 (b c-a d)^5}-\frac{b^3 \left(10 a^2 d^2-5 a b c d+b^2 c^2\right) \log (a+b x)}{a^3 (b c-a d)^5}+\frac{b^3}{2 a (a+b x)^2 (b c-a d)^3}-\frac{d^3 (4 b c-a d)}{c^2 (c+d x) (b c-a d)^4}-\frac{d^3}{2 c (c+d x)^2 (b c-a d)^3}",1,"(3*a*b^4*c^5 - 9*a^2*b^3*c^4*d - 9*a^4*b*c^2*d^3 + 3*a^5*c*d^4 + 2*b^5*c^5*x - 2*a*b^4*c^4*d*x - 18*a^2*b^3*c^3*d^2*x - 18*a^3*b^2*c^2*d^3*x - 2*a^4*b*c*d^4*x + 2*a^5*d^5*x + 4*b^5*c^4*d*x^2 - 13*a*b^4*c^3*d^2*x^2 - 18*a^2*b^3*c^2*d^3*x^2 - 13*a^3*b^2*c*d^4*x^2 + 4*a^4*b*d^5*x^2 + 2*b^5*c^3*d^2*x^3 - 8*a*b^4*c^2*d^3*x^3 - 8*a^2*b^3*c*d^4*x^3 + 2*a^3*b^2*d^5*x^3)/(2*a^2*c^2*(-(b*c) + a*d)^4*(a + b*x)^2*(c + d*x)^2) + Log[x]/(a^3*c^3) + ((b^5*c^2 - 5*a*b^4*c*d + 10*a^2*b^3*d^2)*Log[a + b*x])/(a^3*(-(b*c) + a*d)^5) + ((10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*Log[c + d*x])/(c^3*(b*c - a*d)^5)","A",1
318,1,524,242,0.4900211,"\int \frac{1}{x^2 (a+b x)^3 (c+d x)^3} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^3*(c + d*x)^3),x]","-\frac{3 \log (x) (a d+b c)}{a^4 c^4}-\frac{3 \left(a^2 d^6-4 a b c d^5+5 b^2 c^2 d^4\right) \log (c+d x)}{c^4 (b c-a d)^5}-\frac{3 \left(5 a^2 b^4 d^2-4 a b^5 c d+b^6 c^2\right) \log (a+b x)}{a^4 (a d-b c)^5}+\frac{-2 a^6 c^2 d^4-9 a^6 c d^5 x-6 a^6 d^6 x^2+8 a^5 b c^3 d^3+23 a^5 b c^2 d^4 x-12 a^5 b d^6 x^3-12 a^4 b^2 c^4 d^2-8 a^4 b^2 c^3 d^3 x+40 a^4 b^2 c^2 d^4 x^2+27 a^4 b^2 c d^5 x^3-6 a^4 b^2 d^6 x^4+8 a^3 b^3 c^5 d-8 a^3 b^3 c^4 d^2 x-32 a^3 b^3 c^3 d^3 x^2+3 a^3 b^3 c^2 d^4 x^3+18 a^3 b^3 c d^5 x^4-2 a^2 b^4 c^6+23 a^2 b^4 c^5 d x+40 a^2 b^4 c^4 d^2 x^2+3 a^2 b^4 c^3 d^3 x^3-12 a^2 b^4 c^2 d^4 x^4-9 a b^5 c^6 x+27 a b^5 c^4 d^2 x^3+18 a b^5 c^3 d^3 x^4-6 b^6 c^6 x^2-12 b^6 c^5 d x^3-6 b^6 c^4 d^2 x^4}{2 a^3 c^3 x (a+b x)^2 (c+d x)^2 (a d-b c)^4}","-\frac{3 \log (x) (a d+b c)}{a^4 c^4}-\frac{b^4 (2 b c-5 a d)}{a^3 (a+b x) (b c-a d)^4}-\frac{1}{a^3 c^3 x}-\frac{b^4}{2 a^2 (a+b x)^2 (b c-a d)^3}-\frac{3 d^4 \left(a^2 d^2-4 a b c d+5 b^2 c^2\right) \log (c+d x)}{c^4 (b c-a d)^5}+\frac{3 b^4 \left(5 a^2 d^2-4 a b c d+b^2 c^2\right) \log (a+b x)}{a^4 (b c-a d)^5}+\frac{d^4 (5 b c-2 a d)}{c^3 (c+d x) (b c-a d)^4}+\frac{d^4}{2 c^2 (c+d x)^2 (b c-a d)^3}",1,"(-2*a^2*b^4*c^6 + 8*a^3*b^3*c^5*d - 12*a^4*b^2*c^4*d^2 + 8*a^5*b*c^3*d^3 - 2*a^6*c^2*d^4 - 9*a*b^5*c^6*x + 23*a^2*b^4*c^5*d*x - 8*a^3*b^3*c^4*d^2*x - 8*a^4*b^2*c^3*d^3*x + 23*a^5*b*c^2*d^4*x - 9*a^6*c*d^5*x - 6*b^6*c^6*x^2 + 40*a^2*b^4*c^4*d^2*x^2 - 32*a^3*b^3*c^3*d^3*x^2 + 40*a^4*b^2*c^2*d^4*x^2 - 6*a^6*d^6*x^2 - 12*b^6*c^5*d*x^3 + 27*a*b^5*c^4*d^2*x^3 + 3*a^2*b^4*c^3*d^3*x^3 + 3*a^3*b^3*c^2*d^4*x^3 + 27*a^4*b^2*c*d^5*x^3 - 12*a^5*b*d^6*x^3 - 6*b^6*c^4*d^2*x^4 + 18*a*b^5*c^3*d^3*x^4 - 12*a^2*b^4*c^2*d^4*x^4 + 18*a^3*b^3*c*d^5*x^4 - 6*a^4*b^2*d^6*x^4)/(2*a^3*c^3*(-(b*c) + a*d)^4*x*(a + b*x)^2*(c + d*x)^2) - (3*(b*c + a*d)*Log[x])/(a^4*c^4) - (3*(b^6*c^2 - 4*a*b^5*c*d + 5*a^2*b^4*d^2)*Log[a + b*x])/(a^4*(-(b*c) + a*d)^5) - (3*(5*b^2*c^2*d^4 - 4*a*b*c*d^5 + a^2*d^6)*Log[c + d*x])/(c^4*(b*c - a*d)^5)","B",1
319,1,39,39,0.0250904,"\int x^{7/2} (a+b x) (A+B x) \, dx","IntegrateAlgebraic[x^(7/2)*(a + b*x)*(A + B*x),x]","\frac{2}{11} x^{11/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{13} b B x^{13/2}","\frac{2}{11} x^{11/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{13} b B x^{13/2}",1,"(2*a*A*x^(9/2))/9 + (2*(A*b + a*B)*x^(11/2))/11 + (2*b*B*x^(13/2))/13","A",1
320,1,39,39,0.020092,"\int x^{5/2} (a+b x) (A+B x) \, dx","IntegrateAlgebraic[x^(5/2)*(a + b*x)*(A + B*x),x]","\frac{2}{9} x^{9/2} (a B+A b)+\frac{2}{7} a A x^{7/2}+\frac{2}{11} b B x^{11/2}","\frac{2}{9} x^{9/2} (a B+A b)+\frac{2}{7} a A x^{7/2}+\frac{2}{11} b B x^{11/2}",1,"(2*a*A*x^(7/2))/7 + (2*(A*b + a*B)*x^(9/2))/9 + (2*b*B*x^(11/2))/11","A",1
321,1,39,39,0.0225703,"\int x^{3/2} (a+b x) (A+B x) \, dx","IntegrateAlgebraic[x^(3/2)*(a + b*x)*(A + B*x),x]","\frac{2}{7} x^{7/2} (a B+A b)+\frac{2}{5} a A x^{5/2}+\frac{2}{9} b B x^{9/2}","\frac{2}{7} x^{7/2} (a B+A b)+\frac{2}{5} a A x^{5/2}+\frac{2}{9} b B x^{9/2}",1,"(2*a*A*x^(5/2))/5 + (2*(A*b + a*B)*x^(7/2))/7 + (2*b*B*x^(9/2))/9","A",1
322,1,39,39,0.0362645,"\int \sqrt{x} (a+b x) (A+B x) \, dx","IntegrateAlgebraic[Sqrt[x]*(a + b*x)*(A + B*x),x]","\frac{2}{5} x^{5/2} (a B+A b)+\frac{2}{3} a A x^{3/2}+\frac{2}{7} b B x^{7/2}","\frac{2}{5} x^{5/2} (a B+A b)+\frac{2}{3} a A x^{3/2}+\frac{2}{7} b B x^{7/2}",1,"(2*a*A*x^(3/2))/3 + (2*(A*b + a*B)*x^(5/2))/5 + (2*b*B*x^(7/2))/7","A",1
323,1,37,37,0.0223107,"\int \frac{(a+b x) (A+B x)}{\sqrt{x}} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/Sqrt[x],x]","\frac{2}{3} x^{3/2} (a B+A b)+2 a A \sqrt{x}+\frac{2}{5} b B x^{5/2}","\frac{2}{3} x^{3/2} (a B+A b)+2 a A \sqrt{x}+\frac{2}{5} b B x^{5/2}",1,"2*a*A*Sqrt[x] + (2*(A*b + a*B)*x^(3/2))/3 + (2*b*B*x^(5/2))/5","A",1
324,1,35,35,0.0289642,"\int \frac{(a+b x) (A+B x)}{x^{3/2}} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/x^(3/2),x]","2 \sqrt{x} (a B+A b)-\frac{2 a A}{\sqrt{x}}+\frac{2}{3} b B x^{3/2}","2 \sqrt{x} (a B+A b)-\frac{2 a A}{\sqrt{x}}+\frac{2}{3} b B x^{3/2}",1,"(-2*a*A)/Sqrt[x] + 2*(A*b + a*B)*Sqrt[x] + (2*b*B*x^(3/2))/3","A",1
325,1,35,35,0.028968,"\int \frac{(a+b x) (A+B x)}{x^{5/2}} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/x^(5/2),x]","-\frac{2 (a B+A b)}{\sqrt{x}}-\frac{2 a A}{3 x^{3/2}}+2 b B \sqrt{x}","-\frac{2 (a B+A b)}{\sqrt{x}}-\frac{2 a A}{3 x^{3/2}}+2 b B \sqrt{x}",1,"(-2*a*A)/(3*x^(3/2)) - (2*(A*b + a*B))/Sqrt[x] + 2*b*B*Sqrt[x]","A",1
326,1,37,37,0.029436,"\int \frac{(a+b x) (A+B x)}{x^{7/2}} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/x^(7/2),x]","-\frac{2 (a B+A b)}{3 x^{3/2}}-\frac{2 a A}{5 x^{5/2}}-\frac{2 b B}{\sqrt{x}}","-\frac{2 (a B+A b)}{3 x^{3/2}}-\frac{2 a A}{5 x^{5/2}}-\frac{2 b B}{\sqrt{x}}",1,"(-2*a*A)/(5*x^(5/2)) - (2*(A*b + a*B))/(3*x^(3/2)) - (2*b*B)/Sqrt[x]","A",1
327,1,67,63,0.0356439,"\int x^{7/2} (a+b x)^2 (A+B x) \, dx","IntegrateAlgebraic[x^(7/2)*(a + b*x)^2*(A + B*x),x]","\frac{2}{11} x^{11/2} \left(a^2 B+2 a A b\right)+\frac{2}{9} a^2 A x^{9/2}+\frac{2}{13} x^{13/2} \left(2 a b B+A b^2\right)+\frac{2}{15} b^2 B x^{15/2}","\frac{2}{9} a^2 A x^{9/2}+\frac{2}{13} b x^{13/2} (2 a B+A b)+\frac{2}{11} a x^{11/2} (a B+2 A b)+\frac{2}{15} b^2 B x^{15/2}",1,"(2*a^2*A*x^(9/2))/9 + (2*(2*a*A*b + a^2*B)*x^(11/2))/11 + (2*(A*b^2 + 2*a*b*B)*x^(13/2))/13 + (2*b^2*B*x^(15/2))/15","A",1
328,1,67,63,0.0321153,"\int x^{5/2} (a+b x)^2 (A+B x) \, dx","IntegrateAlgebraic[x^(5/2)*(a + b*x)^2*(A + B*x),x]","\frac{2}{9} x^{9/2} \left(a^2 B+2 a A b\right)+\frac{2}{7} a^2 A x^{7/2}+\frac{2}{11} x^{11/2} \left(2 a b B+A b^2\right)+\frac{2}{13} b^2 B x^{13/2}","\frac{2}{7} a^2 A x^{7/2}+\frac{2}{11} b x^{11/2} (2 a B+A b)+\frac{2}{9} a x^{9/2} (a B+2 A b)+\frac{2}{13} b^2 B x^{13/2}",1,"(2*a^2*A*x^(7/2))/7 + (2*(2*a*A*b + a^2*B)*x^(9/2))/9 + (2*(A*b^2 + 2*a*b*B)*x^(11/2))/11 + (2*b^2*B*x^(13/2))/13","A",1
329,1,67,63,0.0307642,"\int x^{3/2} (a+b x)^2 (A+B x) \, dx","IntegrateAlgebraic[x^(3/2)*(a + b*x)^2*(A + B*x),x]","\frac{2}{7} x^{7/2} \left(a^2 B+2 a A b\right)+\frac{2}{5} a^2 A x^{5/2}+\frac{2}{9} x^{9/2} \left(2 a b B+A b^2\right)+\frac{2}{11} b^2 B x^{11/2}","\frac{2}{5} a^2 A x^{5/2}+\frac{2}{9} b x^{9/2} (2 a B+A b)+\frac{2}{7} a x^{7/2} (a B+2 A b)+\frac{2}{11} b^2 B x^{11/2}",1,"(2*a^2*A*x^(5/2))/5 + (2*(2*a*A*b + a^2*B)*x^(7/2))/7 + (2*(A*b^2 + 2*a*b*B)*x^(9/2))/9 + (2*b^2*B*x^(11/2))/11","A",1
330,1,67,63,0.0303772,"\int \sqrt{x} (a+b x)^2 (A+B x) \, dx","IntegrateAlgebraic[Sqrt[x]*(a + b*x)^2*(A + B*x),x]","\frac{2}{5} x^{5/2} \left(a^2 B+2 a A b\right)+\frac{2}{3} a^2 A x^{3/2}+\frac{2}{7} x^{7/2} \left(2 a b B+A b^2\right)+\frac{2}{9} b^2 B x^{9/2}","\frac{2}{3} a^2 A x^{3/2}+\frac{2}{7} b x^{7/2} (2 a B+A b)+\frac{2}{5} a x^{5/2} (a B+2 A b)+\frac{2}{9} b^2 B x^{9/2}",1,"(2*a^2*A*x^(3/2))/3 + (2*(2*a*A*b + a^2*B)*x^(5/2))/5 + (2*(A*b^2 + 2*a*b*B)*x^(7/2))/7 + (2*b^2*B*x^(9/2))/9","A",1
331,1,65,61,0.0311179,"\int \frac{(a+b x)^2 (A+B x)}{\sqrt{x}} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/Sqrt[x],x]","\frac{2}{3} x^{3/2} \left(a^2 B+2 a A b\right)+2 a^2 A \sqrt{x}+\frac{2}{5} x^{5/2} \left(2 a b B+A b^2\right)+\frac{2}{7} b^2 B x^{7/2}","2 a^2 A \sqrt{x}+\frac{2}{5} b x^{5/2} (2 a B+A b)+\frac{2}{3} a x^{3/2} (a B+2 A b)+\frac{2}{7} b^2 B x^{7/2}",1,"2*a^2*A*Sqrt[x] + (2*(2*a*A*b + a^2*B)*x^(3/2))/3 + (2*(A*b^2 + 2*a*b*B)*x^(5/2))/5 + (2*b^2*B*x^(7/2))/7","A",1
332,1,63,59,0.0382782,"\int \frac{(a+b x)^2 (A+B x)}{x^{3/2}} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/x^(3/2),x]","2 \sqrt{x} \left(a^2 B+2 a A b\right)-\frac{2 a^2 A}{\sqrt{x}}+\frac{2}{3} x^{3/2} \left(2 a b B+A b^2\right)+\frac{2}{5} b^2 B x^{5/2}","-\frac{2 a^2 A}{\sqrt{x}}+\frac{2}{3} b x^{3/2} (2 a B+A b)+2 a \sqrt{x} (a B+2 A b)+\frac{2}{5} b^2 B x^{5/2}",1,"(-2*a^2*A)/Sqrt[x] + 2*(2*a*A*b + a^2*B)*Sqrt[x] + (2*(A*b^2 + 2*a*b*B)*x^(3/2))/3 + (2*b^2*B*x^(5/2))/5","A",1
333,1,63,59,0.0454486,"\int \frac{(a+b x)^2 (A+B x)}{x^{5/2}} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/x^(5/2),x]","-\frac{2 \left(a^2 B+2 a A b\right)}{\sqrt{x}}-\frac{2 a^2 A}{3 x^{3/2}}+2 \sqrt{x} \left(2 a b B+A b^2\right)+\frac{2}{3} b^2 B x^{3/2}","-\frac{2 a^2 A}{3 x^{3/2}}-\frac{2 a (a B+2 A b)}{\sqrt{x}}+2 b \sqrt{x} (2 a B+A b)+\frac{2}{3} b^2 B x^{3/2}",1,"(-2*a^2*A)/(3*x^(3/2)) - (2*(2*a*A*b + a^2*B))/Sqrt[x] + 2*(A*b^2 + 2*a*b*B)*Sqrt[x] + (2*b^2*B*x^(3/2))/3","A",1
334,1,63,59,0.0457688,"\int \frac{(a+b x)^2 (A+B x)}{x^{7/2}} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/x^(7/2),x]","-\frac{2 \left(a^2 B+2 a A b\right)}{3 x^{3/2}}-\frac{2 a^2 A}{5 x^{5/2}}-\frac{2 \left(2 a b B+A b^2\right)}{\sqrt{x}}+2 b^2 B \sqrt{x}","-\frac{2 a^2 A}{5 x^{5/2}}-\frac{2 a (a B+2 A b)}{3 x^{3/2}}-\frac{2 b (2 a B+A b)}{\sqrt{x}}+2 b^2 B \sqrt{x}",1,"(-2*a^2*A)/(5*x^(5/2)) - (2*(2*a*A*b + a^2*B))/(3*x^(3/2)) - (2*(A*b^2 + 2*a*b*B))/Sqrt[x] + 2*b^2*B*Sqrt[x]","A",1
335,1,93,85,0.0460141,"\int x^{7/2} (a+b x)^3 (A+B x) \, dx","IntegrateAlgebraic[x^(7/2)*(a + b*x)^3*(A + B*x),x]","\frac{2}{9} a^3 A x^{9/2}+\frac{6}{13} x^{13/2} \left(a^2 b B+a A b^2\right)+\frac{2}{11} x^{11/2} \left(a^3 B+3 a^2 A b\right)+\frac{2}{15} x^{15/2} \left(3 a b^2 B+A b^3\right)+\frac{2}{17} b^3 B x^{17/2}","\frac{2}{9} a^3 A x^{9/2}+\frac{2}{11} a^2 x^{11/2} (a B+3 A b)+\frac{2}{15} b^2 x^{15/2} (3 a B+A b)+\frac{6}{13} a b x^{13/2} (a B+A b)+\frac{2}{17} b^3 B x^{17/2}",1,"(2*a^3*A*x^(9/2))/9 + (2*(3*a^2*A*b + a^3*B)*x^(11/2))/11 + (6*(a*A*b^2 + a^2*b*B)*x^(13/2))/13 + (2*(A*b^3 + 3*a*b^2*B)*x^(15/2))/15 + (2*b^3*B*x^(17/2))/17","A",1
336,1,93,85,0.0413692,"\int x^{5/2} (a+b x)^3 (A+B x) \, dx","IntegrateAlgebraic[x^(5/2)*(a + b*x)^3*(A + B*x),x]","\frac{2}{7} a^3 A x^{7/2}+\frac{6}{11} x^{11/2} \left(a^2 b B+a A b^2\right)+\frac{2}{9} x^{9/2} \left(a^3 B+3 a^2 A b\right)+\frac{2}{13} x^{13/2} \left(3 a b^2 B+A b^3\right)+\frac{2}{15} b^3 B x^{15/2}","\frac{2}{7} a^3 A x^{7/2}+\frac{2}{9} a^2 x^{9/2} (a B+3 A b)+\frac{2}{13} b^2 x^{13/2} (3 a B+A b)+\frac{6}{11} a b x^{11/2} (a B+A b)+\frac{2}{15} b^3 B x^{15/2}",1,"(2*a^3*A*x^(7/2))/7 + (2*(3*a^2*A*b + a^3*B)*x^(9/2))/9 + (6*(a*A*b^2 + a^2*b*B)*x^(11/2))/11 + (2*(A*b^3 + 3*a*b^2*B)*x^(13/2))/13 + (2*b^3*B*x^(15/2))/15","A",1
337,1,93,85,0.0430149,"\int x^{3/2} (a+b x)^3 (A+B x) \, dx","IntegrateAlgebraic[x^(3/2)*(a + b*x)^3*(A + B*x),x]","\frac{2}{5} a^3 A x^{5/2}+\frac{2}{3} x^{9/2} \left(a^2 b B+a A b^2\right)+\frac{2}{7} x^{7/2} \left(a^3 B+3 a^2 A b\right)+\frac{2}{11} x^{11/2} \left(3 a b^2 B+A b^3\right)+\frac{2}{13} b^3 B x^{13/2}","\frac{2}{5} a^3 A x^{5/2}+\frac{2}{7} a^2 x^{7/2} (a B+3 A b)+\frac{2}{11} b^2 x^{11/2} (3 a B+A b)+\frac{2}{3} a b x^{9/2} (a B+A b)+\frac{2}{13} b^3 B x^{13/2}",1,"(2*a^3*A*x^(5/2))/5 + (2*(3*a^2*A*b + a^3*B)*x^(7/2))/7 + (2*(a*A*b^2 + a^2*b*B)*x^(9/2))/3 + (2*(A*b^3 + 3*a*b^2*B)*x^(11/2))/11 + (2*b^3*B*x^(13/2))/13","A",1
338,1,93,85,0.0424394,"\int \sqrt{x} (a+b x)^3 (A+B x) \, dx","IntegrateAlgebraic[Sqrt[x]*(a + b*x)^3*(A + B*x),x]","\frac{2}{3} a^3 A x^{3/2}+\frac{6}{7} x^{7/2} \left(a^2 b B+a A b^2\right)+\frac{2}{5} x^{5/2} \left(a^3 B+3 a^2 A b\right)+\frac{2}{9} x^{9/2} \left(3 a b^2 B+A b^3\right)+\frac{2}{11} b^3 B x^{11/2}","\frac{2}{3} a^3 A x^{3/2}+\frac{2}{5} a^2 x^{5/2} (a B+3 A b)+\frac{2}{9} b^2 x^{9/2} (3 a B+A b)+\frac{6}{7} a b x^{7/2} (a B+A b)+\frac{2}{11} b^3 B x^{11/2}",1,"(2*a^3*A*x^(3/2))/3 + (2*(3*a^2*A*b + a^3*B)*x^(5/2))/5 + (6*(a*A*b^2 + a^2*b*B)*x^(7/2))/7 + (2*(A*b^3 + 3*a*b^2*B)*x^(9/2))/9 + (2*b^3*B*x^(11/2))/11","A",1
339,1,91,83,0.04182,"\int \frac{(a+b x)^3 (A+B x)}{\sqrt{x}} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/Sqrt[x],x]","2 a^3 A \sqrt{x}+\frac{6}{5} x^{5/2} \left(a^2 b B+a A b^2\right)+\frac{2}{3} x^{3/2} \left(a^3 B+3 a^2 A b\right)+\frac{2}{7} x^{7/2} \left(3 a b^2 B+A b^3\right)+\frac{2}{9} b^3 B x^{9/2}","2 a^3 A \sqrt{x}+\frac{2}{3} a^2 x^{3/2} (a B+3 A b)+\frac{2}{7} b^2 x^{7/2} (3 a B+A b)+\frac{6}{5} a b x^{5/2} (a B+A b)+\frac{2}{9} b^3 B x^{9/2}",1,"2*a^3*A*Sqrt[x] + (2*(3*a^2*A*b + a^3*B)*x^(3/2))/3 + (6*(a*A*b^2 + a^2*b*B)*x^(5/2))/5 + (2*(A*b^3 + 3*a*b^2*B)*x^(7/2))/7 + (2*b^3*B*x^(9/2))/9","A",1
340,1,87,79,0.0578876,"\int \frac{(a+b x)^3 (A+B x)}{x^{3/2}} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/x^(3/2),x]","-\frac{2 a^3 A}{\sqrt{x}}+2 x^{3/2} \left(a^2 b B+a A b^2\right)+2 \sqrt{x} \left(a^3 B+3 a^2 A b\right)+\frac{2}{5} x^{5/2} \left(3 a b^2 B+A b^3\right)+\frac{2}{7} b^3 B x^{7/2}","-\frac{2 a^3 A}{\sqrt{x}}+2 a^2 \sqrt{x} (a B+3 A b)+\frac{2}{5} b^2 x^{5/2} (3 a B+A b)+2 a b x^{3/2} (a B+A b)+\frac{2}{7} b^3 B x^{7/2}",1,"(-2*a^3*A)/Sqrt[x] + 2*(3*a^2*A*b + a^3*B)*Sqrt[x] + 2*(a*A*b^2 + a^2*b*B)*x^(3/2) + (2*(A*b^3 + 3*a*b^2*B)*x^(5/2))/5 + (2*b^3*B*x^(7/2))/7","A",1
341,1,89,81,0.0571005,"\int \frac{(a+b x)^3 (A+B x)}{x^{5/2}} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/x^(5/2),x]","-\frac{2 a^3 A}{3 x^{3/2}}+6 \sqrt{x} \left(a^2 b B+a A b^2\right)-\frac{2 \left(a^3 B+3 a^2 A b\right)}{\sqrt{x}}+\frac{2}{3} x^{3/2} \left(3 a b^2 B+A b^3\right)+\frac{2}{5} b^3 B x^{5/2}","-\frac{2 a^3 A}{3 x^{3/2}}-\frac{2 a^2 (a B+3 A b)}{\sqrt{x}}+\frac{2}{3} b^2 x^{3/2} (3 a B+A b)+6 a b \sqrt{x} (a B+A b)+\frac{2}{5} b^3 B x^{5/2}",1,"(-2*a^3*A)/(3*x^(3/2)) - (2*(3*a^2*A*b + a^3*B))/Sqrt[x] + 6*(a*A*b^2 + a^2*b*B)*Sqrt[x] + (2*(A*b^3 + 3*a*b^2*B)*x^(3/2))/3 + (2*b^3*B*x^(5/2))/5","A",1
342,1,89,81,0.0577027,"\int \frac{(a+b x)^3 (A+B x)}{x^{7/2}} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/x^(7/2),x]","-\frac{2 a^3 A}{5 x^{5/2}}-\frac{6 \left(a^2 b B+a A b^2\right)}{\sqrt{x}}-\frac{2 \left(a^3 B+3 a^2 A b\right)}{3 x^{3/2}}+2 \sqrt{x} \left(3 a b^2 B+A b^3\right)+\frac{2}{3} b^3 B x^{3/2}","-\frac{2 a^3 A}{5 x^{5/2}}-\frac{2 a^2 (a B+3 A b)}{3 x^{3/2}}+2 b^2 \sqrt{x} (3 a B+A b)-\frac{6 a b (a B+A b)}{\sqrt{x}}+\frac{2}{3} b^3 B x^{3/2}",1,"(-2*a^3*A)/(5*x^(5/2)) - (2*(3*a^2*A*b + a^3*B))/(3*x^(3/2)) - (6*(a*A*b^2 + a^2*b*B))/Sqrt[x] + 2*(A*b^3 + 3*a*b^2*B)*Sqrt[x] + (2*b^3*B*x^(3/2))/3","A",1
343,1,44,44,0.0348771,"\int \frac{(2-3 x)^3 \sqrt{x}}{(1+x)^2} \, dx","IntegrateAlgebraic[((2 - 3*x)^3*Sqrt[x])/(1 + x)^2,x]","-\frac{54 x^{5/2}}{5}+72 x^{3/2}-\frac{125 \sqrt{x}}{x+1}-450 \sqrt{x}+575 \tan ^{-1}\left(\sqrt{x}\right)","-\frac{54 x^{5/2}}{5}+72 x^{3/2}-\frac{125 \sqrt{x}}{x+1}-450 \sqrt{x}+575 \tan ^{-1}\left(\sqrt{x}\right)",1,"-450*Sqrt[x] + 72*x^(3/2) - (54*x^(5/2))/5 - (125*Sqrt[x])/(1 + x) + 575*ArcTan[Sqrt[x]]","A",1
344,1,146,136,0.1404008,"\int \frac{x^{7/2} (A+B x)}{a+b x} \, dx","IntegrateAlgebraic[(x^(7/2)*(A + B*x))/(a + b*x),x]","-\frac{2 \left(a^{9/2} B-a^{7/2} A b\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{11/2}}-\frac{2 x^{5/2} \left(a A b-a^2 B\right)}{5 b^3}-\frac{2 \sqrt{x} \left(a^3 A b-a^4 B\right)}{b^5}+\frac{2 x^{3/2} \left(a^2 A b-a^3 B\right)}{3 b^4}+\frac{2 x^{7/2} (A b-a B)}{7 b^2}+\frac{2 B x^{9/2}}{9 b}","\frac{2 a^{7/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{11/2}}-\frac{2 a^3 \sqrt{x} (A b-a B)}{b^5}+\frac{2 a^2 x^{3/2} (A b-a B)}{3 b^4}-\frac{2 a x^{5/2} (A b-a B)}{5 b^3}+\frac{2 x^{7/2} (A b-a B)}{7 b^2}+\frac{2 B x^{9/2}}{9 b}",1,"(-2*(a^3*A*b - a^4*B)*Sqrt[x])/b^5 + (2*(a^2*A*b - a^3*B)*x^(3/2))/(3*b^4) - (2*(a*A*b - a^2*B)*x^(5/2))/(5*b^3) + (2*(A*b - a*B)*x^(7/2))/(7*b^2) + (2*B*x^(9/2))/(9*b) - (2*(-(a^(7/2)*A*b) + a^(9/2)*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(11/2)","A",1
345,1,121,113,0.1085968,"\int \frac{x^{5/2} (A+B x)}{a+b x} \, dx","IntegrateAlgebraic[(x^(5/2)*(A + B*x))/(a + b*x),x]","\frac{2 \left(a^{7/2} B-a^{5/2} A b\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{9/2}}-\frac{2 x^{3/2} \left(a A b-a^2 B\right)}{3 b^3}+\frac{2 \sqrt{x} \left(a^2 A b-a^3 B\right)}{b^4}+\frac{2 x^{5/2} (A b-a B)}{5 b^2}+\frac{2 B x^{7/2}}{7 b}","-\frac{2 a^{5/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{9/2}}+\frac{2 a^2 \sqrt{x} (A b-a B)}{b^4}-\frac{2 a x^{3/2} (A b-a B)}{3 b^3}+\frac{2 x^{5/2} (A b-a B)}{5 b^2}+\frac{2 B x^{7/2}}{7 b}",1,"(2*(a^2*A*b - a^3*B)*Sqrt[x])/b^4 - (2*(a*A*b - a^2*B)*x^(3/2))/(3*b^3) + (2*(A*b - a*B)*x^(5/2))/(5*b^2) + (2*B*x^(7/2))/(7*b) + (2*(-(a^(5/2)*A*b) + a^(7/2)*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(9/2)","A",1
346,1,96,90,0.0855626,"\int \frac{x^{3/2} (A+B x)}{a+b x} \, dx","IntegrateAlgebraic[(x^(3/2)*(A + B*x))/(a + b*x),x]","-\frac{2 \left(a^{5/2} B-a^{3/2} A b\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}-\frac{2 \sqrt{x} \left(a A b-a^2 B\right)}{b^3}+\frac{2 x^{3/2} (A b-a B)}{3 b^2}+\frac{2 B x^{5/2}}{5 b}","\frac{2 a^{3/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}-\frac{2 a \sqrt{x} (A b-a B)}{b^3}+\frac{2 x^{3/2} (A b-a B)}{3 b^2}+\frac{2 B x^{5/2}}{5 b}",1,"(-2*(a*A*b - a^2*B)*Sqrt[x])/b^3 + (2*(A*b - a*B)*x^(3/2))/(3*b^2) + (2*B*x^(5/2))/(5*b) - (2*(-(a^(3/2)*A*b) + a^(5/2)*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(7/2)","A",1
347,1,73,69,0.0620292,"\int \frac{\sqrt{x} (A+B x)}{a+b x} \, dx","IntegrateAlgebraic[(Sqrt[x]*(A + B*x))/(a + b*x),x]","\frac{2 \left(a^{3/2} B-\sqrt{a} A b\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{5/2}}+\frac{2 \sqrt{x} (A b-a B)}{b^2}+\frac{2 B x^{3/2}}{3 b}","-\frac{2 \sqrt{a} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{5/2}}+\frac{2 \sqrt{x} (A b-a B)}{b^2}+\frac{2 B x^{3/2}}{3 b}",1,"(2*(A*b - a*B)*Sqrt[x])/b^2 + (2*B*x^(3/2))/(3*b) + (2*(-(Sqrt[a]*A*b) + a^(3/2)*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(5/2)","A",1
348,1,49,49,0.044528,"\int \frac{A+B x}{\sqrt{x} (a+b x)} \, dx","IntegrateAlgebraic[(A + B*x)/(Sqrt[x]*(a + b*x)),x]","\frac{2 B \sqrt{x}}{b}-\frac{2 (a B-A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}","\frac{2 (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}+\frac{2 B \sqrt{x}}{b}",1,"(2*B*Sqrt[x])/b - (2*(-(A*b) + a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[a]*b^(3/2))","A",1
349,1,49,49,0.0436535,"\int \frac{A+B x}{x^{3/2} (a+b x)} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(3/2)*(a + b*x)),x]","\frac{2 (a B-A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b}}-\frac{2 A}{a \sqrt{x}}","-\frac{2 (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b}}-\frac{2 A}{a \sqrt{x}}",1,"(-2*A)/(a*Sqrt[x]) + (2*(-(A*b) + a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(a^(3/2)*Sqrt[b])","A",1
350,1,73,69,0.0797641,"\int \frac{A+B x}{x^{5/2} (a+b x)} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(5/2)*(a + b*x)),x]","-\frac{2 \left(a \sqrt{b} B-A b^{3/2}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{2 (a B-A b)}{a^2 \sqrt{x}}-\frac{2 A}{3 a x^{3/2}}","\frac{2 \sqrt{b} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{2 (A b-a B)}{a^2 \sqrt{x}}-\frac{2 A}{3 a x^{3/2}}",1,"(-2*A)/(3*a*x^(3/2)) - (2*(-(A*b) + a*B))/(a^2*Sqrt[x]) - (2*(-(A*b^(3/2)) + a*Sqrt[b]*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(5/2)","A",1
351,1,96,90,0.0882431,"\int \frac{A+B x}{x^{7/2} (a+b x)} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(7/2)*(a + b*x)),x]","\frac{2 \left(a b^{3/2} B-A b^{5/2}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{2 \left(a b B-A b^2\right)}{a^3 \sqrt{x}}-\frac{2 (a B-A b)}{3 a^2 x^{3/2}}-\frac{2 A}{5 a x^{5/2}}","-\frac{2 b^{3/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2}}-\frac{2 b (A b-a B)}{a^3 \sqrt{x}}+\frac{2 (A b-a B)}{3 a^2 x^{3/2}}-\frac{2 A}{5 a x^{5/2}}",1,"(-2*A)/(5*a*x^(5/2)) - (2*(-(A*b) + a*B))/(3*a^2*x^(3/2)) + (2*(-(A*b^2) + a*b*B))/(a^3*Sqrt[x]) + (2*(-(A*b^(5/2)) + a*b^(3/2)*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(7/2)","A",1
352,1,121,113,0.1102826,"\int \frac{A+B x}{x^{9/2} (a+b x)} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(9/2)*(a + b*x)),x]","-\frac{2 \left(a b^{5/2} B-A b^{7/2}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{9/2}}-\frac{2 \left(a b^2 B-A b^3\right)}{a^4 \sqrt{x}}+\frac{2 \left(a b B-A b^2\right)}{3 a^3 x^{3/2}}-\frac{2 (a B-A b)}{5 a^2 x^{5/2}}-\frac{2 A}{7 a x^{7/2}}","\frac{2 b^{5/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{9/2}}+\frac{2 b^2 (A b-a B)}{a^4 \sqrt{x}}-\frac{2 b (A b-a B)}{3 a^3 x^{3/2}}+\frac{2 (A b-a B)}{5 a^2 x^{5/2}}-\frac{2 A}{7 a x^{7/2}}",1,"(-2*A)/(7*a*x^(7/2)) - (2*(-(A*b) + a*B))/(5*a^2*x^(5/2)) + (2*(-(A*b^2) + a*b*B))/(3*a^3*x^(3/2)) - (2*(-(A*b^3) + a*b^2*B))/(a^4*Sqrt[x]) - (2*(-(A*b^(7/2)) + a*b^(5/2)*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(9/2)","A",1
353,1,146,136,0.1265375,"\int \frac{A+B x}{x^{11/2} (a+b x)} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(11/2)*(a + b*x)),x]","\frac{2 \left(a b^{7/2} B-A b^{9/2}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{11/2}}+\frac{2 \left(a b^3 B-A b^4\right)}{a^5 \sqrt{x}}-\frac{2 \left(a b^2 B-A b^3\right)}{3 a^4 x^{3/2}}+\frac{2 \left(a b B-A b^2\right)}{5 a^3 x^{5/2}}-\frac{2 (a B-A b)}{7 a^2 x^{7/2}}-\frac{2 A}{9 a x^{9/2}}","-\frac{2 b^{7/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{11/2}}-\frac{2 b^3 (A b-a B)}{a^5 \sqrt{x}}+\frac{2 b^2 (A b-a B)}{3 a^4 x^{3/2}}-\frac{2 b (A b-a B)}{5 a^3 x^{5/2}}+\frac{2 (A b-a B)}{7 a^2 x^{7/2}}-\frac{2 A}{9 a x^{9/2}}",1,"(-2*A)/(9*a*x^(9/2)) - (2*(-(A*b) + a*B))/(7*a^2*x^(7/2)) + (2*(-(A*b^2) + a*b*B))/(5*a^3*x^(5/2)) - (2*(-(A*b^3) + a*b^2*B))/(3*a^4*x^(3/2)) + (2*(-(A*b^4) + a*b^3*B))/(a^5*Sqrt[x]) + (2*(-(A*b^(9/2)) + a*b^(7/2)*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(11/2)","A",1
354,1,158,154,0.1562009,"\int \frac{x^{7/2} (A+B x)}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x^(7/2)*(A + B*x))/(a + b*x)^2,x]","\left(\frac{9 a^{7/2} B}{b^{11/2}}-\frac{7 a^{5/2} A}{b^{9/2}}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\frac{x^{5/2} \left(126 a^2 b^2 B-98 a A b^3\right)+\sqrt{x} \left(735 a^3 A b-945 a^4 B\right)+x^{3/2} \left(490 a^2 A b^2-630 a^3 b B\right)+x^{7/2} \left(42 A b^4-54 a b^3 B\right)+30 b^4 B x^{9/2}}{105 b^5 (a+b x)}","-\frac{a^{5/2} (7 A b-9 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{11/2}}+\frac{a^2 \sqrt{x} (7 A b-9 a B)}{b^5}-\frac{a x^{3/2} (7 A b-9 a B)}{3 b^4}+\frac{x^{5/2} (7 A b-9 a B)}{5 b^3}-\frac{x^{7/2} (7 A b-9 a B)}{7 a b^2}+\frac{x^{9/2} (A b-a B)}{a b (a+b x)}",1,"((735*a^3*A*b - 945*a^4*B)*Sqrt[x] + (490*a^2*A*b^2 - 630*a^3*b*B)*x^(3/2) + (-98*a*A*b^3 + 126*a^2*b^2*B)*x^(5/2) + (42*A*b^4 - 54*a*b^3*B)*x^(7/2) + 30*b^4*B*x^(9/2))/(105*b^5*(a + b*x)) + ((-7*a^(5/2)*A)/b^(9/2) + (9*a^(7/2)*B)/b^(11/2))*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]","A",1
355,1,133,130,0.1223134,"\int \frac{x^{5/2} (A+B x)}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x^(5/2)*(A + B*x))/(a + b*x)^2,x]","\left(\frac{5 a^{3/2} A}{b^{7/2}}-\frac{7 a^{5/2} B}{b^{9/2}}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\frac{x^{3/2} \left(70 a^2 b B-50 a A b^2\right)+\sqrt{x} \left(105 a^3 B-75 a^2 A b\right)+x^{5/2} \left(10 A b^3-14 a b^2 B\right)+6 b^3 B x^{7/2}}{15 b^4 (a+b x)}","\frac{a^{3/2} (5 A b-7 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{9/2}}-\frac{a \sqrt{x} (5 A b-7 a B)}{b^4}+\frac{x^{3/2} (5 A b-7 a B)}{3 b^3}-\frac{x^{5/2} (5 A b-7 a B)}{5 a b^2}+\frac{x^{7/2} (A b-a B)}{a b (a+b x)}",1,"((-75*a^2*A*b + 105*a^3*B)*Sqrt[x] + (-50*a*A*b^2 + 70*a^2*b*B)*x^(3/2) + (10*A*b^3 - 14*a*b^2*B)*x^(5/2) + 6*b^3*B*x^(7/2))/(15*b^4*(a + b*x)) + ((5*a^(3/2)*A)/b^(7/2) - (7*a^(5/2)*B)/b^(9/2))*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]","A",1
356,1,108,108,0.1046059,"\int \frac{x^{3/2} (A+B x)}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x^(3/2)*(A + B*x))/(a + b*x)^2,x]","\left(\frac{5 a^{3/2} B}{b^{7/2}}-\frac{3 \sqrt{a} A}{b^{5/2}}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\frac{\sqrt{x} \left(9 a A b-15 a^2 B\right)+x^{3/2} \left(6 A b^2-10 a b B\right)+2 b^2 B x^{5/2}}{3 b^3 (a+b x)}","-\frac{\sqrt{a} (3 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}+\frac{\sqrt{x} (3 A b-5 a B)}{b^3}-\frac{x^{3/2} (3 A b-5 a B)}{3 a b^2}+\frac{x^{5/2} (A b-a B)}{a b (a+b x)}",1,"((9*a*A*b - 15*a^2*B)*Sqrt[x] + (6*A*b^2 - 10*a*b*B)*x^(3/2) + 2*b^2*B*x^(5/2))/(3*b^3*(a + b*x)) + ((-3*Sqrt[a]*A)/b^(5/2) + (5*a^(3/2)*B)/b^(7/2))*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]","A",1
357,1,81,85,0.0930127,"\int \frac{\sqrt{x} (A+B x)}{(a+b x)^2} \, dx","IntegrateAlgebraic[(Sqrt[x]*(A + B*x))/(a + b*x)^2,x]","\left(\frac{A}{\sqrt{a} b^{3/2}}-\frac{3 \sqrt{a} B}{b^{5/2}}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\frac{\sqrt{x} (3 a B-A b)+2 b B x^{3/2}}{b^2 (a+b x)}","\frac{(A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} b^{5/2}}-\frac{\sqrt{x} (A b-3 a B)}{a b^2}+\frac{x^{3/2} (A b-a B)}{a b (a+b x)}",1,"((-(A*b) + 3*a*B)*Sqrt[x] + 2*b*B*x^(3/2))/(b^2*(a + b*x)) + (A/(Sqrt[a]*b^(3/2)) - (3*Sqrt[a]*B)/b^(5/2))*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]","A",1
358,1,69,63,0.0650824,"\int \frac{A+B x}{\sqrt{x} (a+b x)^2} \, dx","IntegrateAlgebraic[(A + B*x)/(Sqrt[x]*(a + b*x)^2),x]","\left(\frac{A}{a^{3/2} \sqrt{b}}+\frac{B}{\sqrt{a} b^{3/2}}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\frac{\sqrt{x} \left(\frac{A}{a}-\frac{B}{b}\right)}{a+b x}","\frac{(a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{3/2} b^{3/2}}+\frac{\sqrt{x} (A b-a B)}{a b (a+b x)}",1,"((A/a - B/b)*Sqrt[x])/(a + b*x) + (A/(a^(3/2)*Sqrt[b]) + B/(Sqrt[a]*b^(3/2)))*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]","A",1
359,1,82,88,0.0546937,"\int \frac{A+B x}{x^{3/2} (a+b x)^2} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(3/2)*(a + b*x)^2),x]","\left(\frac{B}{a^{3/2} \sqrt{b}}-\frac{3 A \sqrt{b}}{a^{5/2}}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\frac{-2 a A+a B x-3 A b x}{a^3 \sqrt{x}+a^2 b x^{3/2}}","-\frac{(3 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{5/2} \sqrt{b}}-\frac{3 A b-a B}{a^2 b \sqrt{x}}+\frac{A b-a B}{a b \sqrt{x} (a+b x)}",1,"(-2*a*A - 3*A*b*x + a*B*x)/(a^3*Sqrt[x] + a^2*b*x^(3/2)) + ((-3*A*Sqrt[b])/a^(5/2) + B/(a^(3/2)*Sqrt[b]))*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]","A",1
360,1,108,107,0.1033858,"\int \frac{A+B x}{x^{5/2} (a+b x)^2} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(5/2)*(a + b*x)^2),x]","\left(\frac{5 A b^{3/2}}{a^{7/2}}-\frac{3 \sqrt{b} B}{a^{5/2}}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\frac{-2 a^2 A-6 a^2 B x+10 a A b x-9 a b B x^2+15 A b^2 x^2}{3 a^4 x^{3/2}+3 a^3 b x^{5/2}}","\frac{\sqrt{b} (5 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{5 A b-3 a B}{a^3 \sqrt{x}}-\frac{5 A b-3 a B}{3 a^2 b x^{3/2}}+\frac{A b-a B}{a b x^{3/2} (a+b x)}",1,"(-2*a^2*A + 10*a*A*b*x - 6*a^2*B*x + 15*A*b^2*x^2 - 9*a*b*B*x^2)/(3*a^4*x^(3/2) + 3*a^3*b*x^(5/2)) + ((5*A*b^(3/2))/a^(7/2) - (3*Sqrt[b]*B)/a^(5/2))*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]","A",1
361,1,132,131,0.1119582,"\int \frac{A+B x}{x^{7/2} (a+b x)^2} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(7/2)*(a + b*x)^2),x]","\left(\frac{5 b^{3/2} B}{a^{7/2}}-\frac{7 A b^{5/2}}{a^{9/2}}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\frac{-6 a^3 A-10 a^3 B x+14 a^2 A b x+50 a^2 b B x^2-70 a A b^2 x^2+75 a b^2 B x^3-105 A b^3 x^3}{15 a^5 x^{5/2}+15 a^4 b x^{7/2}}","-\frac{b^{3/2} (7 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{9/2}}-\frac{b (7 A b-5 a B)}{a^4 \sqrt{x}}+\frac{7 A b-5 a B}{3 a^3 x^{3/2}}-\frac{7 A b-5 a B}{5 a^2 b x^{5/2}}+\frac{A b-a B}{a b x^{5/2} (a+b x)}",1,"(-6*a^3*A + 14*a^2*A*b*x - 10*a^3*B*x - 70*a*A*b^2*x^2 + 50*a^2*b*B*x^2 - 105*A*b^3*x^3 + 75*a*b^2*B*x^3)/(15*a^5*x^(5/2) + 15*a^4*b*x^(7/2)) + ((-7*A*b^(5/2))/a^(9/2) + (5*b^(3/2)*B)/a^(7/2))*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]","A",1
362,1,156,153,0.1476785,"\int \frac{A+B x}{x^{9/2} (a+b x)^2} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(9/2)*(a + b*x)^2),x]","\left(\frac{9 A b^{7/2}}{a^{11/2}}-\frac{7 b^{5/2} B}{a^{9/2}}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\frac{-30 a^4 A-42 a^4 B x+54 a^3 A b x+98 a^3 b B x^2-126 a^2 A b^2 x^2-490 a^2 b^2 B x^3+630 a A b^3 x^3-735 a b^3 B x^4+945 A b^4 x^4}{105 a^6 x^{7/2}+105 a^5 b x^{9/2}}","\frac{b^{5/2} (9 A b-7 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{11/2}}+\frac{b^2 (9 A b-7 a B)}{a^5 \sqrt{x}}-\frac{b (9 A b-7 a B)}{3 a^4 x^{3/2}}+\frac{9 A b-7 a B}{5 a^3 x^{5/2}}-\frac{9 A b-7 a B}{7 a^2 b x^{7/2}}+\frac{A b-a B}{a b x^{7/2} (a+b x)}",1,"(-30*a^4*A + 54*a^3*A*b*x - 42*a^4*B*x - 126*a^2*A*b^2*x^2 + 98*a^3*b*B*x^2 + 630*a*A*b^3*x^3 - 490*a^2*b^2*B*x^3 + 945*A*b^4*x^4 - 735*a*b^3*B*x^4)/(105*a^6*x^(7/2) + 105*a^5*b*x^(9/2)) + ((9*A*b^(7/2))/a^(11/2) - (7*b^(5/2)*B)/a^(9/2))*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]","A",1
363,1,162,169,0.1553884,"\int \frac{x^{7/2} (A+B x)}{(a+b x)^3} \, dx","IntegrateAlgebraic[(x^(7/2)*(A + B*x))/(a + b*x)^3,x]","\left(\frac{35 a^{3/2} A}{4 b^{9/2}}-\frac{63 a^{5/2} B}{4 b^{11/2}}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\frac{x^{5/2} \left(504 a^2 b^2 B-280 a A b^3\right)+\sqrt{x} \left(945 a^4 B-525 a^3 A b\right)+x^{3/2} \left(1575 a^3 b B-875 a^2 A b^2\right)+x^{7/2} \left(40 A b^4-72 a b^3 B\right)+24 b^4 B x^{9/2}}{60 b^5 (a+b x)^2}","\frac{7 a^{3/2} (5 A b-9 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{11/2}}-\frac{7 a \sqrt{x} (5 A b-9 a B)}{4 b^5}+\frac{7 x^{3/2} (5 A b-9 a B)}{12 b^4}-\frac{7 x^{5/2} (5 A b-9 a B)}{20 a b^3}+\frac{x^{7/2} (5 A b-9 a B)}{4 a b^2 (a+b x)}+\frac{x^{9/2} (A b-a B)}{2 a b (a+b x)^2}",1,"((-525*a^3*A*b + 945*a^4*B)*Sqrt[x] + (-875*a^2*A*b^2 + 1575*a^3*b*B)*x^(3/2) + (-280*a*A*b^3 + 504*a^2*b^2*B)*x^(5/2) + (40*A*b^4 - 72*a*b^3*B)*x^(7/2) + 24*b^4*B*x^(9/2))/(60*b^5*(a + b*x)^2) + ((35*a^(3/2)*A)/(4*b^(9/2)) - (63*a^(5/2)*B)/(4*b^(11/2)))*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]","A",1
364,1,137,147,0.129781,"\int \frac{x^{5/2} (A+B x)}{(a+b x)^3} \, dx","IntegrateAlgebraic[(x^(5/2)*(A + B*x))/(a + b*x)^3,x]","\left(\frac{35 a^{3/2} B}{4 b^{9/2}}-\frac{15 \sqrt{a} A}{4 b^{7/2}}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\frac{x^{3/2} \left(75 a A b^2-175 a^2 b B\right)+\sqrt{x} \left(45 a^2 A b-105 a^3 B\right)+x^{5/2} \left(24 A b^3-56 a b^2 B\right)+8 b^3 B x^{7/2}}{12 b^4 (a+b x)^2}","-\frac{5 \sqrt{a} (3 A b-7 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{9/2}}+\frac{5 \sqrt{x} (3 A b-7 a B)}{4 b^4}-\frac{5 x^{3/2} (3 A b-7 a B)}{12 a b^3}+\frac{x^{5/2} (3 A b-7 a B)}{4 a b^2 (a+b x)}+\frac{x^{7/2} (A b-a B)}{2 a b (a+b x)^2}",1,"((45*a^2*A*b - 105*a^3*B)*Sqrt[x] + (75*a*A*b^2 - 175*a^2*b*B)*x^(3/2) + (24*A*b^3 - 56*a*b^2*B)*x^(5/2) + 8*b^3*B*x^(7/2))/(12*b^4*(a + b*x)^2) + ((-15*Sqrt[a]*A)/(4*b^(7/2)) + (35*a^(3/2)*B)/(4*b^(9/2)))*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]","A",1
365,1,112,123,0.1039029,"\int \frac{x^{3/2} (A+B x)}{(a+b x)^3} \, dx","IntegrateAlgebraic[(x^(3/2)*(A + B*x))/(a + b*x)^3,x]","\frac{\sqrt{x} \left(15 a^2 B-3 a A b\right)+x^{3/2} \left(25 a b B-5 A b^2\right)+8 b^2 B x^{5/2}}{4 b^3 (a+b x)^2}+\left(\frac{3 A}{4 \sqrt{a} b^{5/2}}-\frac{15 \sqrt{a} B}{4 b^{7/2}}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)","\frac{3 (A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 \sqrt{a} b^{7/2}}-\frac{3 \sqrt{x} (A b-5 a B)}{4 a b^3}+\frac{x^{3/2} (A b-5 a B)}{4 a b^2 (a+b x)}+\frac{x^{5/2} (A b-a B)}{2 a b (a+b x)^2}",1,"((-3*a*A*b + 15*a^2*B)*Sqrt[x] + (-5*A*b^2 + 25*a*b*B)*x^(3/2) + 8*b^2*B*x^(5/2))/(4*b^3*(a + b*x)^2) + ((3*A)/(4*Sqrt[a]*b^(5/2)) - (15*Sqrt[a]*B)/(4*b^(7/2)))*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]","A",1
366,1,103,100,0.1124022,"\int \frac{\sqrt{x} (A+B x)}{(a+b x)^3} \, dx","IntegrateAlgebraic[(Sqrt[x]*(A + B*x))/(a + b*x)^3,x]","\left(\frac{A}{4 a^{3/2} b^{3/2}}+\frac{3 B}{4 \sqrt{a} b^{5/2}}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\frac{\sqrt{x} \left(\frac{x \left(A b^2-5 a b B\right)}{4 a b^2}-\frac{3 a B}{4 b^2}-\frac{A}{4 b}\right)}{(a+b x)^2}","\frac{(3 a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{3/2} b^{5/2}}-\frac{\sqrt{x} (3 a B+A b)}{4 a b^2 (a+b x)}+\frac{x^{3/2} (A b-a B)}{2 a b (a+b x)^2}",1,"(Sqrt[x]*(-1/4*A/b - (3*a*B)/(4*b^2) + ((A*b^2 - 5*a*b*B)*x)/(4*a*b^2)))/(a + b*x)^2 + (A/(4*a^(3/2)*b^(3/2)) + (3*B)/(4*Sqrt[a]*b^(5/2)))*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]","A",1
367,1,102,100,0.0933924,"\int \frac{A+B x}{\sqrt{x} (a+b x)^3} \, dx","IntegrateAlgebraic[(A + B*x)/(Sqrt[x]*(a + b*x)^3),x]","\left(\frac{3 A}{4 a^{5/2} \sqrt{b}}+\frac{B}{4 a^{3/2} b^{3/2}}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\frac{\sqrt{x} \left(\frac{x \left(a b B+3 A b^2\right)}{4 a^2 b}+\frac{5 A}{4 a}-\frac{B}{4 b}\right)}{(a+b x)^2}","\frac{(a B+3 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{5/2} b^{3/2}}+\frac{\sqrt{x} (a B+3 A b)}{4 a^2 b (a+b x)}+\frac{\sqrt{x} (A b-a B)}{2 a b (a+b x)^2}",1,"(Sqrt[x]*((5*A)/(4*a) - B/(4*b) + ((3*A*b^2 + a*b*B)*x)/(4*a^2*b)))/(a + b*x)^2 + ((3*A)/(4*a^(5/2)*Sqrt[b]) + B/(4*a^(3/2)*b^(3/2)))*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]","A",1
368,1,123,126,0.0895655,"\int \frac{A+B x}{x^{3/2} (a+b x)^3} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(3/2)*(a + b*x)^3),x]","\left(\frac{3 B}{4 a^{5/2} \sqrt{b}}-\frac{15 A \sqrt{b}}{4 a^{7/2}}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)-\frac{2 A}{a^3 \sqrt{x}}+\frac{\sqrt{x} \left(\frac{B}{2 a}-\frac{A b}{2 a^2}\right)}{(a+b x)^2}+\frac{\sqrt{x} \left(\frac{3 B}{4 a^2}-\frac{7 A b}{4 a^3}\right)}{a+b x}","-\frac{3 (5 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{7/2} \sqrt{b}}-\frac{3 (5 A b-a B)}{4 a^3 b \sqrt{x}}+\frac{5 A b-a B}{4 a^2 b \sqrt{x} (a+b x)}+\frac{A b-a B}{2 a b \sqrt{x} (a+b x)^2}",1,"(-2*A)/(a^3*Sqrt[x]) + ((-1/2*(A*b)/a^2 + B/(2*a))*Sqrt[x])/(a + b*x)^2 + (((-7*A*b)/(4*a^3) + (3*B)/(4*a^2))*Sqrt[x])/(a + b*x) + ((-15*A*Sqrt[b])/(4*a^(7/2)) + (3*B)/(4*a^(5/2)*Sqrt[b]))*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]","A",1
369,1,143,147,0.1264546,"\int \frac{A+B x}{x^{5/2} (a+b x)^3} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(5/2)*(a + b*x)^3),x]","\left(\frac{35 A b^{3/2}}{4 a^{9/2}}-\frac{15 \sqrt{b} B}{4 a^{7/2}}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\frac{\frac{x^3 \left(105 A b^3-45 a b^2 B\right)}{12 a^4}+\frac{x^2 \left(175 a A b^2-75 a^2 b B\right)}{12 a^4}+\frac{x \left(56 a^2 A b-24 a^3 B\right)}{12 a^4}-\frac{2 A}{3 a}}{x^{3/2} (a+b x)^2}","\frac{5 \sqrt{b} (7 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{9/2}}+\frac{5 (7 A b-3 a B)}{4 a^4 \sqrt{x}}-\frac{5 (7 A b-3 a B)}{12 a^3 b x^{3/2}}+\frac{7 A b-3 a B}{4 a^2 b x^{3/2} (a+b x)}+\frac{A b-a B}{2 a b x^{3/2} (a+b x)^2}",1,"((-2*A)/(3*a) + ((56*a^2*A*b - 24*a^3*B)*x)/(12*a^4) + ((175*a*A*b^2 - 75*a^2*b*B)*x^2)/(12*a^4) + ((105*A*b^3 - 45*a*b^2*B)*x^3)/(12*a^4))/(x^(3/2)*(a + b*x)^2) + ((35*A*b^(3/2))/(4*a^(9/2)) - (15*Sqrt[b]*B)/(4*a^(7/2)))*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]","A",1
370,1,172,169,0.1492855,"\int \frac{A+B x}{x^{7/2} (a+b x)^3} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(7/2)*(a + b*x)^3),x]","\left(\frac{35 b^{3/2} B}{4 a^{9/2}}-\frac{63 A b^{5/2}}{4 a^{11/2}}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\frac{\frac{x^4 \left(525 a b^3 B-945 A b^4\right)}{60 a^5}+\frac{x^3 \left(875 a^2 b^2 B-1575 a A b^3\right)}{60 a^5}+\frac{x \left(72 a^3 A b-40 a^4 B\right)}{60 a^5}+\frac{x^2 \left(280 a^3 b B-504 a^2 A b^2\right)}{60 a^5}-\frac{2 A}{5 a}}{x^{5/2} (a+b x)^2}","-\frac{7 b^{3/2} (9 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{11/2}}-\frac{7 b (9 A b-5 a B)}{4 a^5 \sqrt{x}}+\frac{7 (9 A b-5 a B)}{12 a^4 x^{3/2}}-\frac{7 (9 A b-5 a B)}{20 a^3 b x^{5/2}}+\frac{9 A b-5 a B}{4 a^2 b x^{5/2} (a+b x)}+\frac{A b-a B}{2 a b x^{5/2} (a+b x)^2}",1,"((-2*A)/(5*a) + ((72*a^3*A*b - 40*a^4*B)*x)/(60*a^5) + ((-504*a^2*A*b^2 + 280*a^3*b*B)*x^2)/(60*a^5) + ((-1575*a*A*b^3 + 875*a^2*b^2*B)*x^3)/(60*a^5) + ((-945*A*b^4 + 525*a*b^3*B)*x^4)/(60*a^5))/(x^(5/2)*(a + b*x)^2) + ((-63*A*b^(5/2))/(4*a^(11/2)) + (35*b^(3/2)*B)/(4*a^(9/2)))*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]]","A",1
371,0,0,125,0.0545981,"\int x^m (a+b x)^4 (A+B x) \, dx","IntegrateAlgebraic[x^m*(a + b*x)^4*(A + B*x),x]","\int x^m (a+b x)^4 (A+B x) \, dx","\frac{a^4 A x^{m+1}}{m+1}+\frac{a^3 x^{m+2} (a B+4 A b)}{m+2}+\frac{2 a^2 b x^{m+3} (2 a B+3 A b)}{m+3}+\frac{b^3 x^{m+5} (4 a B+A b)}{m+5}+\frac{2 a b^2 x^{m+4} (3 a B+2 A b)}{m+4}+\frac{b^4 B x^{m+6}}{m+6}",1,"Could not integrate","F",-1
372,0,0,96,0.0352297,"\int x^m (a+b x)^3 (A+B x) \, dx","IntegrateAlgebraic[x^m*(a + b*x)^3*(A + B*x),x]","\int x^m (a+b x)^3 (A+B x) \, dx","\frac{a^3 A x^{m+1}}{m+1}+\frac{a^2 x^{m+2} (a B+3 A b)}{m+2}+\frac{b^2 x^{m+4} (3 a B+A b)}{m+4}+\frac{3 a b x^{m+3} (a B+A b)}{m+3}+\frac{b^3 B x^{m+5}}{m+5}",1,"Could not integrate","F",-1
373,0,0,71,0.029566,"\int x^m (a+b x)^2 (A+B x) \, dx","IntegrateAlgebraic[x^m*(a + b*x)^2*(A + B*x),x]","\int x^m (a+b x)^2 (A+B x) \, dx","\frac{a^2 A x^{m+1}}{m+1}+\frac{a x^{m+2} (a B+2 A b)}{m+2}+\frac{b x^{m+3} (2 a B+A b)}{m+3}+\frac{b^2 B x^{m+4}}{m+4}",1,"Could not integrate","F",-1
374,0,0,45,0.0220703,"\int x^m (a+b x) (A+B x) \, dx","IntegrateAlgebraic[x^m*(a + b*x)*(A + B*x),x]","\int x^m (a+b x) (A+B x) \, dx","\frac{x^{m+2} (a B+A b)}{m+2}+\frac{a A x^{m+1}}{m+1}+\frac{b B x^{m+3}}{m+3}",1,"Could not integrate","F",-1
375,0,0,56,0.0418194,"\int \frac{x^m (A+B x)}{a+b x} \, dx","IntegrateAlgebraic[(x^m*(A + B*x))/(a + b*x),x]","\int \frac{x^m (A+B x)}{a+b x} \, dx","\frac{x^{m+1} (A b-a B) \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{a b (m+1)}+\frac{B x^{m+1}}{b (m+1)}",1,"Could not integrate","F",-1
376,0,0,73,0.0340374,"\int \frac{x^m (A+B x)}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x^m*(A + B*x))/(a + b*x)^2,x]","\int \frac{x^m (A+B x)}{(a+b x)^2} \, dx","\frac{x^{m+1} (A b-a B)}{a b (a+b x)}-\frac{x^{m+1} (A b m-a B (m+1)) \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{a^2 b (m+1)}",1,"Could not integrate","F",-1
377,0,0,81,0.0362309,"\int \frac{x^m (A+B x)}{(a+b x)^3} \, dx","IntegrateAlgebraic[(x^m*(A + B*x))/(a + b*x)^3,x]","\int \frac{x^m (A+B x)}{(a+b x)^3} \, dx","\frac{x^{m+1} (a B (m+1)+A b (1-m)) \, _2F_1\left(2,m+1;m+2;-\frac{b x}{a}\right)}{2 a^3 b (m+1)}+\frac{x^{m+1} (A b-a B)}{2 a b (a+b x)^2}",1,"Could not integrate","F",-1
378,0,0,231,0.3233291,"\int x^m (a+b x)^2 (c+d x)^5 \, dx","IntegrateAlgebraic[x^m*(a + b*x)^2*(c + d*x)^5,x]","\int x^m (a+b x)^2 (c+d x)^5 \, dx","\frac{5 c^2 d x^{m+4} \left(2 a^2 d^2+4 a b c d+b^2 c^2\right)}{m+4}+\frac{5 c d^2 x^{m+5} \left(a^2 d^2+4 a b c d+2 b^2 c^2\right)}{m+5}+\frac{d^3 x^{m+6} \left(a^2 d^2+10 a b c d+10 b^2 c^2\right)}{m+6}+\frac{c^3 x^{m+3} \left(10 a^2 d^2+10 a b c d+b^2 c^2\right)}{m+3}+\frac{a^2 c^5 x^{m+1}}{m+1}+\frac{a c^4 x^{m+2} (5 a d+2 b c)}{m+2}+\frac{b d^4 x^{m+7} (2 a d+5 b c)}{m+7}+\frac{b^2 d^5 x^{m+8}}{m+8}",1,"Could not integrate","F",-1
379,0,0,127,0.0622056,"\int \frac{x^m (c+d x)^3}{a+b x} \, dx","IntegrateAlgebraic[(x^m*(c + d*x)^3)/(a + b*x),x]","\int \frac{x^m (c+d x)^3}{a+b x} \, dx","\frac{d x^{m+1} \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{b^3 (m+1)}+\frac{x^{m+1} (b c-a d)^3 \, _2F_1\left(1,1;1-m;\frac{a}{a+b x}\right)}{b^3 m (a+b x)}+\frac{d^2 x^{m+2} (3 b c-a d)}{b^2 (m+2)}+\frac{d^3 x^{m+3}}{b (m+3)}",1,"Could not integrate","F",-1
380,0,0,99,0.0504335,"\int \frac{x^m (c+d x)^2}{a+b x} \, dx","IntegrateAlgebraic[(x^m*(c + d*x)^2)/(a + b*x),x]","\int \frac{x^m (c+d x)^2}{a+b x} \, dx","\frac{x^{m+1} (b c-a d)^2 \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{a b^2 (m+1)}+\frac{d x^{m+1} (b c-a d)}{b^2 (m+1)}+\frac{c d x^{m+1}}{b (m+1)}+\frac{d^2 x^{m+2}}{b (m+2)}",1,"Could not integrate","F",-1
381,0,0,56,0.1408219,"\int \frac{x^m (c+d x)}{a+b x} \, dx","IntegrateAlgebraic[(x^m*(c + d*x))/(a + b*x),x]","\int \frac{x^m (c+d x)}{a+b x} \, dx","\frac{x^{m+1} (b c-a d) \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{a b (m+1)}+\frac{d x^{m+1}}{b (m+1)}",1,"Could not integrate","F",-1
382,0,0,82,0.0618977,"\int \frac{x^m}{(a+b x) (c+d x)} \, dx","IntegrateAlgebraic[x^m/((a + b*x)*(c + d*x)),x]","\int \frac{x^m}{(a+b x) (c+d x)} \, dx","\frac{b x^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{a (m+1) (b c-a d)}-\frac{d x^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{d x}{c}\right)}{c (m+1) (b c-a d)}",1,"Could not integrate","F",-1
383,0,0,125,0.0567055,"\int \frac{x^m}{(a+b x) (c+d x)^2} \, dx","IntegrateAlgebraic[x^m/((a + b*x)*(c + d*x)^2),x]","\int \frac{x^m}{(a+b x) (c+d x)^2} \, dx","\frac{b^2 x^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{a (m+1) (b c-a d)^2}-\frac{d x^{m+1} (a d m+b c (1-m)) \, _2F_1\left(1,m+1;m+2;-\frac{d x}{c}\right)}{c^2 (m+1) (b c-a d)^2}-\frac{d x^{m+1}}{c (c+d x) (b c-a d)}",1,"Could not integrate","F",-1
384,0,0,206,0.0688477,"\int \frac{x^m}{(a+b x) (c+d x)^3} \, dx","IntegrateAlgebraic[x^m/((a + b*x)*(c + d*x)^3),x]","\int \frac{x^m}{(a+b x) (c+d x)^3} \, dx","\frac{d x^{m+1} \left(a^2 d^2 (1-m) m-2 a b c d (2-m) m-b^2 c^2 \left(m^2-3 m+2\right)\right) \, _2F_1\left(1,m+1;m+2;-\frac{d x}{c}\right)}{2 c^3 (m+1) (b c-a d)^3}+\frac{b^3 x^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{a (m+1) (b c-a d)^3}+\frac{d x^{m+1} (a d (1-m)-b c (3-m))}{2 c^2 (c+d x) (b c-a d)^2}-\frac{d x^{m+1}}{2 c (c+d x)^2 (b c-a d)}",1,"Could not integrate","F",-1
385,0,0,36,0.0159827,"\int \frac{b^2 x^m}{\left(b+a x^2\right)^2} \, dx","IntegrateAlgebraic[(b^2*x^m)/(b + a*x^2)^2,x]","\int \frac{b^2 x^m}{\left(b+a x^2\right)^2} \, dx","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};-\frac{a x^2}{b}\right)}{m+1}",1,"Could not integrate","F",-1
386,0,0,36,0.2113115,"\int \frac{x^m}{\left(1-\frac{\sqrt{a} x}{\sqrt{-b}}\right)^2 \left(1+\frac{\sqrt{a} x}{\sqrt{-b}}\right)^2} \, dx","IntegrateAlgebraic[x^m/((1 - (Sqrt[a]*x)/Sqrt[-b])^2*(1 + (Sqrt[a]*x)/Sqrt[-b])^2),x]","\int \frac{x^m}{\left(1-\frac{\sqrt{a} x}{\sqrt{-b}}\right)^2 \left(1+\frac{\sqrt{a} x}{\sqrt{-b}}\right)^2} \, dx","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};-\frac{a x^2}{b}\right)}{m+1}",1,"Could not integrate","F",-1
387,1,146,151,0.0539306,"\int x^4 \sqrt{a+b x} (A+B x) \, dx","IntegrateAlgebraic[x^4*Sqrt[a + b*x]*(A + B*x),x]","-\frac{2 \sqrt{a+b x} \left(1280 a^6 B-1664 a^5 A b-640 a^5 b B x+832 a^4 A b^2 x+480 a^4 b^2 B x^2-624 a^3 A b^3 x^2-400 a^3 b^3 B x^3+520 a^2 A b^4 x^3+350 a^2 b^4 B x^4-455 a A b^5 x^4-315 a b^5 B x^5-4095 A b^6 x^5-3465 b^6 B x^6\right)}{45045 b^6}","\frac{2 a^4 (a+b x)^{3/2} (A b-a B)}{3 b^6}-\frac{2 a^3 (a+b x)^{5/2} (4 A b-5 a B)}{5 b^6}+\frac{4 a^2 (a+b x)^{7/2} (3 A b-5 a B)}{7 b^6}+\frac{2 (a+b x)^{11/2} (A b-5 a B)}{11 b^6}-\frac{4 a (a+b x)^{9/2} (2 A b-5 a B)}{9 b^6}+\frac{2 B (a+b x)^{13/2}}{13 b^6}",1,"(-2*Sqrt[a + b*x]*(-1664*a^5*A*b + 1280*a^6*B + 832*a^4*A*b^2*x - 640*a^5*b*B*x - 624*a^3*A*b^3*x^2 + 480*a^4*b^2*B*x^2 + 520*a^2*A*b^4*x^3 - 400*a^3*b^3*B*x^3 - 455*a*A*b^5*x^4 + 350*a^2*b^4*B*x^4 - 4095*A*b^6*x^5 - 315*a*b^5*B*x^5 - 3465*b^6*B*x^6))/(45045*b^6)","A",1
388,1,122,122,0.0430207,"\int x^3 \sqrt{a+b x} (A+B x) \, dx","IntegrateAlgebraic[x^3*Sqrt[a + b*x]*(A + B*x),x]","\frac{2 \sqrt{a+b x} \left(128 a^5 B-176 a^4 A b-64 a^4 b B x+88 a^3 A b^2 x+48 a^3 b^2 B x^2-66 a^2 A b^3 x^2-40 a^2 b^3 B x^3+55 a A b^4 x^3+35 a b^4 B x^4+385 A b^5 x^4+315 b^5 B x^5\right)}{3465 b^5}","-\frac{2 a^3 (a+b x)^{3/2} (A b-a B)}{3 b^5}+\frac{2 a^2 (a+b x)^{5/2} (3 A b-4 a B)}{5 b^5}+\frac{2 (a+b x)^{9/2} (A b-4 a B)}{9 b^5}-\frac{6 a (a+b x)^{7/2} (A b-2 a B)}{7 b^5}+\frac{2 B (a+b x)^{11/2}}{11 b^5}",1,"(2*Sqrt[a + b*x]*(-176*a^4*A*b + 128*a^5*B + 88*a^3*A*b^2*x - 64*a^4*b*B*x - 66*a^2*A*b^3*x^2 + 48*a^3*b^2*B*x^2 + 55*a*A*b^4*x^3 - 40*a^2*b^3*B*x^3 + 385*A*b^5*x^4 + 35*a*b^4*B*x^4 + 315*b^5*B*x^5))/(3465*b^5)","A",1
389,1,98,95,0.0365256,"\int x^2 \sqrt{a+b x} (A+B x) \, dx","IntegrateAlgebraic[x^2*Sqrt[a + b*x]*(A + B*x),x]","-\frac{2 \sqrt{a+b x} \left(16 a^4 B-24 a^3 A b-8 a^3 b B x+12 a^2 A b^2 x+6 a^2 b^2 B x^2-9 a A b^3 x^2-5 a b^3 B x^3-45 A b^4 x^3-35 b^4 B x^4\right)}{315 b^4}","\frac{2 a^2 (a+b x)^{3/2} (A b-a B)}{3 b^4}+\frac{2 (a+b x)^{7/2} (A b-3 a B)}{7 b^4}-\frac{2 a (a+b x)^{5/2} (2 A b-3 a B)}{5 b^4}+\frac{2 B (a+b x)^{9/2}}{9 b^4}",1,"(-2*Sqrt[a + b*x]*(-24*a^3*A*b + 16*a^4*B + 12*a^2*A*b^2*x - 8*a^3*b*B*x - 9*a*A*b^3*x^2 + 6*a^2*b^2*B*x^2 - 45*A*b^4*x^3 - 5*a*b^3*B*x^3 - 35*b^4*B*x^4))/(315*b^4)","A",1
390,1,74,67,0.0266387,"\int x \sqrt{a+b x} (A+B x) \, dx","IntegrateAlgebraic[x*Sqrt[a + b*x]*(A + B*x),x]","\frac{2 \sqrt{a+b x} \left(8 a^3 B-14 a^2 A b-4 a^2 b B x+7 a A b^2 x+3 a b^2 B x^2+21 A b^3 x^2+15 b^3 B x^3\right)}{105 b^3}","\frac{2 (a+b x)^{5/2} (A b-2 a B)}{5 b^3}-\frac{2 a (a+b x)^{3/2} (A b-a B)}{3 b^3}+\frac{2 B (a+b x)^{7/2}}{7 b^3}",1,"(2*Sqrt[a + b*x]*(-14*a^2*A*b + 8*a^3*B + 7*a*A*b^2*x - 4*a^2*b*B*x + 21*A*b^3*x^2 + 3*a*b^2*B*x^2 + 15*b^3*B*x^3))/(105*b^3)","A",1
391,1,50,42,0.0177909,"\int \sqrt{a+b x} (A+B x) \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*(A + B*x),x]","-\frac{2 \sqrt{a+b x} \left(2 a^2 B-5 a A b-a b B x-5 A b^2 x-3 b^2 B x^2\right)}{15 b^2}","\frac{2 (a+b x)^{3/2} (A b-a B)}{3 b^2}+\frac{2 B (a+b x)^{5/2}}{5 b^2}",1,"(-2*Sqrt[a + b*x]*(-5*a*A*b + 2*a^2*B - 5*A*b^2*x - a*b*B*x - 3*b^2*B*x^2))/(15*b^2)","A",1
392,1,53,54,0.0460777,"\int \frac{\sqrt{a+b x} (A+B x)}{x} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/x,x]","\frac{2 \sqrt{a+b x} (a B+3 A b+b B x)}{3 b}-2 \sqrt{a} A \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","2 A \sqrt{a+b x}-2 \sqrt{a} A \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{2 B (a+b x)^{3/2}}{3 b}",1,"(2*Sqrt[a + b*x]*(3*A*b + a*B + b*B*x))/(3*b) - 2*Sqrt[a]*A*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
393,1,53,71,0.0653351,"\int \frac{\sqrt{a+b x} (A+B x)}{x^2} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/x^2,x]","\frac{\sqrt{a+b x} (2 B x-A)}{x}+\frac{(-2 a B-A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{\sqrt{a+b x} (2 a B+A b)}{a}-\frac{(2 a B+A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{A (a+b x)^{3/2}}{a x}",1,"(Sqrt[a + b*x]*(-A + 2*B*x))/x + ((-(A*b) - 2*a*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/Sqrt[a]","A",1
394,1,71,82,0.2798062,"\int \frac{\sqrt{a+b x} (A+B x)}{x^3} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/x^3,x]","\frac{\left(A b^2-4 a b B\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{3/2}}+\frac{\sqrt{a+b x} (-2 a A-4 a B x-A b x)}{4 a x^2}","\frac{b (A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{3/2}}+\frac{\sqrt{a+b x} (A b-4 a B)}{4 a x}-\frac{A (a+b x)^{3/2}}{2 a x^2}",1,"(Sqrt[a + b*x]*(-2*a*A - A*b*x - 4*a*B*x))/(4*a*x^2) + ((A*b^2 - 4*a*b*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(4*a^(3/2))","A",1
395,1,96,112,0.1022406,"\int \frac{\sqrt{a+b x} (A+B x)}{x^4} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/x^4,x]","\frac{\left(2 a b^2 B-A b^3\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{5/2}}+\frac{\sqrt{a+b x} \left(-8 a^2 A-12 a^2 B x-2 a A b x-6 a b B x^2+3 A b^2 x^2\right)}{24 a^2 x^3}","-\frac{b^2 (A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{5/2}}+\frac{b \sqrt{a+b x} (A b-2 a B)}{8 a^2 x}+\frac{\sqrt{a+b x} (A b-2 a B)}{4 a x^2}-\frac{A (a+b x)^{3/2}}{3 a x^3}",1,"(Sqrt[a + b*x]*(-8*a^2*A - 2*a*A*b*x - 12*a^2*B*x + 3*A*b^2*x^2 - 6*a*b*B*x^2))/(24*a^2*x^3) + ((-(A*b^3) + 2*a*b^2*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(8*a^(5/2))","A",1
396,1,120,146,0.1700118,"\int \frac{\sqrt{a+b x} (A+B x)}{x^5} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/x^5,x]","\frac{\left(5 A b^4-8 a b^3 B\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{64 a^{7/2}}+\frac{\sqrt{a+b x} \left(-48 a^3 A-64 a^3 B x-8 a^2 A b x-16 a^2 b B x^2+10 a A b^2 x^2+24 a b^2 B x^3-15 A b^3 x^3\right)}{192 a^3 x^4}","\frac{b^3 (5 A b-8 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{64 a^{7/2}}-\frac{b^2 \sqrt{a+b x} (5 A b-8 a B)}{64 a^3 x}+\frac{b \sqrt{a+b x} (5 A b-8 a B)}{96 a^2 x^2}+\frac{\sqrt{a+b x} (5 A b-8 a B)}{24 a x^3}-\frac{A (a+b x)^{3/2}}{4 a x^4}",1,"(Sqrt[a + b*x]*(-48*a^3*A - 8*a^2*A*b*x - 64*a^3*B*x + 10*a*A*b^2*x^2 - 16*a^2*b*B*x^2 - 15*A*b^3*x^3 + 24*a*b^2*B*x^3))/(192*a^3*x^4) + ((5*A*b^4 - 8*a*b^3*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(64*a^(7/2))","A",1
397,1,144,177,0.2157948,"\int \frac{\sqrt{a+b x} (A+B x)}{x^6} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/x^6,x]","\frac{\left(10 a b^4 B-7 A b^5\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{128 a^{9/2}}+\frac{\sqrt{a+b x} \left(-384 a^4 A-480 a^4 B x-48 a^3 A b x-80 a^3 b B x^2+56 a^2 A b^2 x^2+100 a^2 b^2 B x^3-70 a A b^3 x^3-150 a b^3 B x^4+105 A b^4 x^4\right)}{1920 a^4 x^5}","-\frac{b^4 (7 A b-10 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{128 a^{9/2}}+\frac{b^3 \sqrt{a+b x} (7 A b-10 a B)}{128 a^4 x}-\frac{b^2 \sqrt{a+b x} (7 A b-10 a B)}{192 a^3 x^2}+\frac{b \sqrt{a+b x} (7 A b-10 a B)}{240 a^2 x^3}+\frac{\sqrt{a+b x} (7 A b-10 a B)}{40 a x^4}-\frac{A (a+b x)^{3/2}}{5 a x^5}",1,"(Sqrt[a + b*x]*(-384*a^4*A - 48*a^3*A*b*x - 480*a^4*B*x + 56*a^2*A*b^2*x^2 - 80*a^3*b*B*x^2 - 70*a*A*b^3*x^3 + 100*a^2*b^2*B*x^3 + 105*A*b^4*x^4 - 150*a*b^3*B*x^4))/(1920*a^4*x^5) + ((-7*A*b^5 + 10*a*b^4*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(128*a^(9/2))","A",1
398,1,170,151,0.0544643,"\int x^4 (a+b x)^{3/2} (A+B x) \, dx","IntegrateAlgebraic[x^4*(a + b*x)^(3/2)*(A + B*x),x]","-\frac{2 \sqrt{a+b x} \left(256 a^7 B-384 a^6 A b-128 a^6 b B x+192 a^5 A b^2 x+96 a^5 b^2 B x^2-144 a^4 A b^3 x^2-80 a^4 b^3 B x^3+120 a^3 A b^4 x^3+70 a^3 b^4 B x^4-105 a^2 A b^5 x^4-63 a^2 b^5 B x^5-4410 a A b^6 x^5-3696 a b^6 B x^6-3465 A b^7 x^6-3003 b^7 B x^7\right)}{45045 b^6}","\frac{2 a^4 (a+b x)^{5/2} (A b-a B)}{5 b^6}-\frac{2 a^3 (a+b x)^{7/2} (4 A b-5 a B)}{7 b^6}+\frac{4 a^2 (a+b x)^{9/2} (3 A b-5 a B)}{9 b^6}+\frac{2 (a+b x)^{13/2} (A b-5 a B)}{13 b^6}-\frac{4 a (a+b x)^{11/2} (2 A b-5 a B)}{11 b^6}+\frac{2 B (a+b x)^{15/2}}{15 b^6}",1,"(-2*Sqrt[a + b*x]*(-384*a^6*A*b + 256*a^7*B + 192*a^5*A*b^2*x - 128*a^6*b*B*x - 144*a^4*A*b^3*x^2 + 96*a^5*b^2*B*x^2 + 120*a^3*A*b^4*x^3 - 80*a^4*b^3*B*x^3 - 105*a^2*A*b^5*x^4 + 70*a^3*b^4*B*x^4 - 4410*a*A*b^6*x^5 - 63*a^2*b^5*B*x^5 - 3465*A*b^7*x^6 - 3696*a*b^6*B*x^6 - 3003*b^7*B*x^7))/(45045*b^6)","A",1
399,1,146,122,0.0439449,"\int x^3 (a+b x)^{3/2} (A+B x) \, dx","IntegrateAlgebraic[x^3*(a + b*x)^(3/2)*(A + B*x),x]","\frac{2 \sqrt{a+b x} \left(128 a^6 B-208 a^5 A b-64 a^5 b B x+104 a^4 A b^2 x+48 a^4 b^2 B x^2-78 a^3 A b^3 x^2-40 a^3 b^3 B x^3+65 a^2 A b^4 x^3+35 a^2 b^4 B x^4+1820 a A b^5 x^4+1470 a b^5 B x^5+1365 A b^6 x^5+1155 b^6 B x^6\right)}{15015 b^5}","-\frac{2 a^3 (a+b x)^{5/2} (A b-a B)}{5 b^5}+\frac{2 a^2 (a+b x)^{7/2} (3 A b-4 a B)}{7 b^5}+\frac{2 (a+b x)^{11/2} (A b-4 a B)}{11 b^5}-\frac{2 a (a+b x)^{9/2} (A b-2 a B)}{3 b^5}+\frac{2 B (a+b x)^{13/2}}{13 b^5}",1,"(2*Sqrt[a + b*x]*(-208*a^5*A*b + 128*a^6*B + 104*a^4*A*b^2*x - 64*a^5*b*B*x - 78*a^3*A*b^3*x^2 + 48*a^4*b^2*B*x^2 + 65*a^2*A*b^4*x^3 - 40*a^3*b^3*B*x^3 + 1820*a*A*b^5*x^4 + 35*a^2*b^4*B*x^4 + 1365*A*b^6*x^5 + 1470*a*b^5*B*x^5 + 1155*b^6*B*x^6))/(15015*b^5)","A",1
400,1,122,95,0.0368371,"\int x^2 (a+b x)^{3/2} (A+B x) \, dx","IntegrateAlgebraic[x^2*(a + b*x)^(3/2)*(A + B*x),x]","-\frac{2 \sqrt{a+b x} \left(48 a^5 B-88 a^4 A b-24 a^4 b B x+44 a^3 A b^2 x+18 a^3 b^2 B x^2-33 a^2 A b^3 x^2-15 a^2 b^3 B x^3-550 a A b^4 x^3-420 a b^4 B x^4-385 A b^5 x^4-315 b^5 B x^5\right)}{3465 b^4}","\frac{2 a^2 (a+b x)^{5/2} (A b-a B)}{5 b^4}+\frac{2 (a+b x)^{9/2} (A b-3 a B)}{9 b^4}-\frac{2 a (a+b x)^{7/2} (2 A b-3 a B)}{7 b^4}+\frac{2 B (a+b x)^{11/2}}{11 b^4}",1,"(-2*Sqrt[a + b*x]*(-88*a^4*A*b + 48*a^5*B + 44*a^3*A*b^2*x - 24*a^4*b*B*x - 33*a^2*A*b^3*x^2 + 18*a^3*b^2*B*x^2 - 550*a*A*b^4*x^3 - 15*a^2*b^3*B*x^3 - 385*A*b^5*x^4 - 420*a*b^4*B*x^4 - 315*b^5*B*x^5))/(3465*b^4)","A",1
401,1,98,67,0.0275628,"\int x (a+b x)^{3/2} (A+B x) \, dx","IntegrateAlgebraic[x*(a + b*x)^(3/2)*(A + B*x),x]","\frac{2 \sqrt{a+b x} \left(8 a^4 B-18 a^3 A b-4 a^3 b B x+9 a^2 A b^2 x+3 a^2 b^2 B x^2+72 a A b^3 x^2+50 a b^3 B x^3+45 A b^4 x^3+35 b^4 B x^4\right)}{315 b^3}","\frac{2 (a+b x)^{7/2} (A b-2 a B)}{7 b^3}-\frac{2 a (a+b x)^{5/2} (A b-a B)}{5 b^3}+\frac{2 B (a+b x)^{9/2}}{9 b^3}",1,"(2*Sqrt[a + b*x]*(-18*a^3*A*b + 8*a^4*B + 9*a^2*A*b^2*x - 4*a^3*b*B*x + 72*a*A*b^3*x^2 + 3*a^2*b^2*B*x^2 + 45*A*b^4*x^3 + 50*a*b^3*B*x^3 + 35*b^4*B*x^4))/(315*b^3)","A",1
402,1,74,42,0.0209436,"\int (a+b x)^{3/2} (A+B x) \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)*(A + B*x),x]","-\frac{2 \sqrt{a+b x} \left(2 a^3 B-7 a^2 A b-a^2 b B x-14 a A b^2 x-8 a b^2 B x^2-7 A b^3 x^2-5 b^3 B x^3\right)}{35 b^2}","\frac{2 (a+b x)^{5/2} (A b-a B)}{5 b^2}+\frac{2 B (a+b x)^{7/2}}{7 b^2}",1,"(-2*Sqrt[a + b*x]*(-7*a^2*A*b + 2*a^3*B - 14*a*A*b^2*x - a^2*b*B*x - 7*A*b^3*x^2 - 8*a*b^2*B*x^2 - 5*b^3*B*x^3))/(35*b^2)","A",1
403,1,75,69,0.0607321,"\int \frac{(a+b x)^{3/2} (A+B x)}{x} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/x,x]","\frac{2 \sqrt{a+b x} \left(3 a^2 B+20 a A b+6 a b B x+5 A b^2 x+3 b^2 B x^2\right)}{15 b}-2 a^{3/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","-2 a^{3/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{2}{3} A (a+b x)^{3/2}+2 a A \sqrt{a+b x}+\frac{2 B (a+b x)^{5/2}}{5 b}",1,"(2*Sqrt[a + b*x]*(20*a*A*b + 3*a^2*B + 5*A*b^2*x + 6*a*b*B*x + 3*b^2*B*x^2))/(15*b) - 2*a^(3/2)*A*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
404,1,74,95,0.1104924,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/x^2,x]","\left(-2 a^{3/2} B-3 \sqrt{a} A b\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{\sqrt{a+b x} \left(-3 a A+8 a B x+6 A b x+2 b B x^2\right)}{3 x}","\frac{(a+b x)^{3/2} (2 a B+3 A b)}{3 a}+\sqrt{a+b x} (2 a B+3 A b)-\sqrt{a} (2 a B+3 A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)-\frac{A (a+b x)^{5/2}}{a x}",1,"(Sqrt[a + b*x]*(-3*a*A + 6*A*b*x + 8*a*B*x + 2*b*B*x^2))/(3*x) + (-3*Sqrt[a]*A*b - 2*a^(3/2)*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
405,1,75,107,0.0925342,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/x^3,x]","\frac{\sqrt{a+b x} \left(-2 a A-4 a B x-5 A b x+8 b B x^2\right)}{4 x^2}-\frac{3 \left(4 a b B+A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 \sqrt{a}}","-\frac{(a+b x)^{3/2} (4 a B+A b)}{4 a x}+\frac{3 b \sqrt{a+b x} (4 a B+A b)}{4 a}-\frac{3 b (4 a B+A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{A (a+b x)^{5/2}}{2 a x^2}",1,"(Sqrt[a + b*x]*(-2*a*A - 5*A*b*x - 4*a*B*x + 8*b*B*x^2))/(4*x^2) - (3*(A*b^2 + 4*a*b*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(4*Sqrt[a])","A",1
406,1,95,112,0.1330433,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^4} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/x^4,x]","\frac{\left(A b^3-6 a b^2 B\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{3/2}}+\frac{\sqrt{a+b x} \left(-8 a^2 A-12 a^2 B x-14 a A b x-30 a b B x^2-3 A b^2 x^2\right)}{24 a x^3}","\frac{b^2 (A b-6 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{3/2}}+\frac{(a+b x)^{3/2} (A b-6 a B)}{12 a x^2}+\frac{b \sqrt{a+b x} (A b-6 a B)}{8 a x}-\frac{A (a+b x)^{5/2}}{3 a x^3}",1,"(Sqrt[a + b*x]*(-8*a^2*A - 14*a*A*b*x - 12*a^2*B*x - 3*A*b^2*x^2 - 30*a*b*B*x^2))/(24*a*x^3) + ((A*b^3 - 6*a*b^2*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(8*a^(3/2))","A",1
407,1,120,146,0.1647079,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^5} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/x^5,x]","\frac{\left(8 a b^3 B-3 A b^4\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{64 a^{5/2}}+\frac{\sqrt{a+b x} \left(-48 a^3 A-64 a^3 B x-72 a^2 A b x-112 a^2 b B x^2-6 a A b^2 x^2-24 a b^2 B x^3+9 A b^3 x^3\right)}{192 a^2 x^4}","-\frac{b^3 (3 A b-8 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{64 a^{5/2}}+\frac{b^2 \sqrt{a+b x} (3 A b-8 a B)}{64 a^2 x}+\frac{(a+b x)^{3/2} (3 A b-8 a B)}{24 a x^3}+\frac{b \sqrt{a+b x} (3 A b-8 a B)}{32 a x^2}-\frac{A (a+b x)^{5/2}}{4 a x^4}",1,"(Sqrt[a + b*x]*(-48*a^3*A - 72*a^2*A*b*x - 64*a^3*B*x - 6*a*A*b^2*x^2 - 112*a^2*b*B*x^2 + 9*A*b^3*x^3 - 24*a*b^2*B*x^3))/(192*a^2*x^4) + ((-3*A*b^4 + 8*a*b^3*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(64*a^(5/2))","A",1
408,1,144,172,0.1933954,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^6} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/x^6,x]","\frac{\sqrt{a+b x} \left(-128 a^4 A-160 a^4 B x-176 a^3 A b x-240 a^3 b B x^2-8 a^2 A b^2 x^2-20 a^2 b^2 B x^3+10 a A b^3 x^3+30 a b^3 B x^4-15 A b^4 x^4\right)}{640 a^3 x^5}-\frac{3 \left(2 a b^4 B-A b^5\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{128 a^{7/2}}","\frac{3 b^4 (A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{128 a^{7/2}}-\frac{3 b^3 \sqrt{a+b x} (A b-2 a B)}{128 a^3 x}+\frac{b^2 \sqrt{a+b x} (A b-2 a B)}{64 a^2 x^2}+\frac{(a+b x)^{3/2} (A b-2 a B)}{8 a x^4}+\frac{b \sqrt{a+b x} (A b-2 a B)}{16 a x^3}-\frac{A (a+b x)^{5/2}}{5 a x^5}",1,"(Sqrt[a + b*x]*(-128*a^4*A - 176*a^3*A*b*x - 160*a^4*B*x - 8*a^2*A*b^2*x^2 - 240*a^3*b*B*x^2 + 10*a*A*b^3*x^3 - 20*a^2*b^2*B*x^3 - 15*A*b^4*x^4 + 30*a*b^3*B*x^4))/(640*a^3*x^5) - (3*(-(A*b^5) + 2*a*b^4*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(128*a^(7/2))","A",1
409,1,168,208,0.2483616,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^7} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/x^7,x]","\frac{\left(12 a b^5 B-7 A b^6\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{512 a^{9/2}}+\frac{\sqrt{a+b x} \left(-1280 a^5 A-1536 a^5 B x-1664 a^4 A b x-2112 a^4 b B x^2-48 a^3 A b^2 x^2-96 a^3 b^2 B x^3+56 a^2 A b^3 x^3+120 a^2 b^3 B x^4-70 a A b^4 x^4-180 a b^4 B x^5+105 A b^5 x^5\right)}{7680 a^4 x^6}","-\frac{b^5 (7 A b-12 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{512 a^{9/2}}+\frac{b^4 \sqrt{a+b x} (7 A b-12 a B)}{512 a^4 x}-\frac{b^3 \sqrt{a+b x} (7 A b-12 a B)}{768 a^3 x^2}+\frac{b^2 \sqrt{a+b x} (7 A b-12 a B)}{960 a^2 x^3}+\frac{(a+b x)^{3/2} (7 A b-12 a B)}{60 a x^5}+\frac{b \sqrt{a+b x} (7 A b-12 a B)}{160 a x^4}-\frac{A (a+b x)^{5/2}}{6 a x^6}",1,"(Sqrt[a + b*x]*(-1280*a^5*A - 1664*a^4*A*b*x - 1536*a^5*B*x - 48*a^3*A*b^2*x^2 - 2112*a^4*b*B*x^2 + 56*a^2*A*b^3*x^3 - 96*a^3*b^2*B*x^3 - 70*a*A*b^4*x^4 + 120*a^2*b^3*B*x^4 + 105*A*b^5*x^5 - 180*a*b^4*B*x^5))/(7680*a^4*x^6) + ((-7*A*b^6 + 12*a*b^5*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(512*a^(9/2))","A",1
410,1,194,151,0.0576795,"\int x^4 (a+b x)^{5/2} (A+B x) \, dx","IntegrateAlgebraic[x^4*(a + b*x)^(5/2)*(A + B*x),x]","-\frac{2 \sqrt{a+b x} \left(1280 a^8 B-2176 a^7 A b-640 a^7 b B x+1088 a^6 A b^2 x+480 a^6 b^2 B x^2-816 a^5 A b^3 x^2-400 a^5 b^3 B x^3+680 a^4 A b^4 x^3+350 a^4 b^4 B x^4-595 a^3 A b^5 x^4-315 a^3 b^5 B x^5-76041 a^2 A b^6 x^5-63525 a^2 b^6 B x^6-121737 a A b^7 x^6-105105 a b^7 B x^7-51051 A b^8 x^7-45045 b^8 B x^8\right)}{765765 b^6}","\frac{2 a^4 (a+b x)^{7/2} (A b-a B)}{7 b^6}-\frac{2 a^3 (a+b x)^{9/2} (4 A b-5 a B)}{9 b^6}+\frac{4 a^2 (a+b x)^{11/2} (3 A b-5 a B)}{11 b^6}+\frac{2 (a+b x)^{15/2} (A b-5 a B)}{15 b^6}-\frac{4 a (a+b x)^{13/2} (2 A b-5 a B)}{13 b^6}+\frac{2 B (a+b x)^{17/2}}{17 b^6}",1,"(-2*Sqrt[a + b*x]*(-2176*a^7*A*b + 1280*a^8*B + 1088*a^6*A*b^2*x - 640*a^7*b*B*x - 816*a^5*A*b^3*x^2 + 480*a^6*b^2*B*x^2 + 680*a^4*A*b^4*x^3 - 400*a^5*b^3*B*x^3 - 595*a^3*A*b^5*x^4 + 350*a^4*b^4*B*x^4 - 76041*a^2*A*b^6*x^5 - 315*a^3*b^5*B*x^5 - 121737*a*A*b^7*x^6 - 63525*a^2*b^6*B*x^6 - 51051*A*b^8*x^7 - 105105*a*b^7*B*x^7 - 45045*b^8*B*x^8))/(765765*b^6)","A",1
411,1,170,122,0.0462467,"\int x^3 (a+b x)^{5/2} (A+B x) \, dx","IntegrateAlgebraic[x^3*(a + b*x)^(5/2)*(A + B*x),x]","\frac{2 \sqrt{a+b x} \left(128 a^7 B-240 a^6 A b-64 a^6 b B x+120 a^5 A b^2 x+48 a^5 b^2 B x^2-90 a^4 A b^3 x^2-40 a^4 b^3 B x^3+75 a^3 A b^4 x^3+35 a^3 b^4 B x^4+5565 a^2 A b^5 x^4+4473 a^2 b^5 B x^5+8505 a A b^6 x^5+7161 a b^6 B x^6+3465 A b^7 x^6+3003 b^7 B x^7\right)}{45045 b^5}","-\frac{2 a^3 (a+b x)^{7/2} (A b-a B)}{7 b^5}+\frac{2 a^2 (a+b x)^{9/2} (3 A b-4 a B)}{9 b^5}+\frac{2 (a+b x)^{13/2} (A b-4 a B)}{13 b^5}-\frac{6 a (a+b x)^{11/2} (A b-2 a B)}{11 b^5}+\frac{2 B (a+b x)^{15/2}}{15 b^5}",1,"(2*Sqrt[a + b*x]*(-240*a^6*A*b + 128*a^7*B + 120*a^5*A*b^2*x - 64*a^6*b*B*x - 90*a^4*A*b^3*x^2 + 48*a^5*b^2*B*x^2 + 75*a^3*A*b^4*x^3 - 40*a^4*b^3*B*x^3 + 5565*a^2*A*b^5*x^4 + 35*a^3*b^4*B*x^4 + 8505*a*A*b^6*x^5 + 4473*a^2*b^5*B*x^5 + 3465*A*b^7*x^6 + 7161*a*b^6*B*x^6 + 3003*b^7*B*x^7))/(45045*b^5)","A",1
412,1,146,95,0.0387666,"\int x^2 (a+b x)^{5/2} (A+B x) \, dx","IntegrateAlgebraic[x^2*(a + b*x)^(5/2)*(A + B*x),x]","-\frac{2 \sqrt{a+b x} \left(48 a^6 B-104 a^5 A b-24 a^5 b B x+52 a^4 A b^2 x+18 a^4 b^2 B x^2-39 a^3 A b^3 x^2-15 a^3 b^3 B x^3-1469 a^2 A b^4 x^3-1113 a^2 b^4 B x^4-2093 a A b^5 x^4-1701 a b^5 B x^5-819 A b^6 x^5-693 b^6 B x^6\right)}{9009 b^4}","\frac{2 a^2 (a+b x)^{7/2} (A b-a B)}{7 b^4}+\frac{2 (a+b x)^{11/2} (A b-3 a B)}{11 b^4}-\frac{2 a (a+b x)^{9/2} (2 A b-3 a B)}{9 b^4}+\frac{2 B (a+b x)^{13/2}}{13 b^4}",1,"(-2*Sqrt[a + b*x]*(-104*a^5*A*b + 48*a^6*B + 52*a^4*A*b^2*x - 24*a^5*b*B*x - 39*a^3*A*b^3*x^2 + 18*a^4*b^2*B*x^2 - 1469*a^2*A*b^4*x^3 - 15*a^3*b^3*B*x^3 - 2093*a*A*b^5*x^4 - 1113*a^2*b^4*B*x^4 - 819*A*b^6*x^5 - 1701*a*b^5*B*x^5 - 693*b^6*B*x^6))/(9009*b^4)","A",1
413,1,122,67,0.0304929,"\int x (a+b x)^{5/2} (A+B x) \, dx","IntegrateAlgebraic[x*(a + b*x)^(5/2)*(A + B*x),x]","\frac{2 \sqrt{a+b x} \left(8 a^5 B-22 a^4 A b-4 a^4 b B x+11 a^3 A b^2 x+3 a^3 b^2 B x^2+165 a^2 A b^3 x^2+113 a^2 b^3 B x^3+209 a A b^4 x^3+161 a b^4 B x^4+77 A b^5 x^4+63 b^5 B x^5\right)}{693 b^3}","\frac{2 (a+b x)^{9/2} (A b-2 a B)}{9 b^3}-\frac{2 a (a+b x)^{7/2} (A b-a B)}{7 b^3}+\frac{2 B (a+b x)^{11/2}}{11 b^3}",1,"(2*Sqrt[a + b*x]*(-22*a^4*A*b + 8*a^5*B + 11*a^3*A*b^2*x - 4*a^4*b*B*x + 165*a^2*A*b^3*x^2 + 3*a^3*b^2*B*x^2 + 209*a*A*b^4*x^3 + 113*a^2*b^3*B*x^3 + 77*A*b^5*x^4 + 161*a*b^4*B*x^4 + 63*b^5*B*x^5))/(693*b^3)","A",1
414,1,98,42,0.0224255,"\int (a+b x)^{5/2} (A+B x) \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)*(A + B*x),x]","-\frac{2 \sqrt{a+b x} \left(2 a^4 B-9 a^3 A b-a^3 b B x-27 a^2 A b^2 x-15 a^2 b^2 B x^2-27 a A b^3 x^2-19 a b^3 B x^3-9 A b^4 x^3-7 b^4 B x^4\right)}{63 b^2}","\frac{2 (a+b x)^{7/2} (A b-a B)}{7 b^2}+\frac{2 B (a+b x)^{9/2}}{9 b^2}",1,"(-2*Sqrt[a + b*x]*(-9*a^3*A*b + 2*a^4*B - 27*a^2*A*b^2*x - a^3*b*B*x - 27*a*A*b^3*x^2 - 15*a^2*b^2*B*x^2 - 9*A*b^4*x^3 - 19*a*b^3*B*x^3 - 7*b^4*B*x^4))/(63*b^2)","B",1
415,1,99,86,0.0687179,"\int \frac{(a+b x)^{5/2} (A+B x)}{x} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/x,x]","\frac{2 \sqrt{a+b x} \left(15 a^3 B+161 a^2 A b+45 a^2 b B x+77 a A b^2 x+45 a b^2 B x^2+21 A b^3 x^2+15 b^3 B x^3\right)}{105 b}-2 a^{5/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","-2 a^{5/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+2 a^2 A \sqrt{a+b x}+\frac{2}{5} A (a+b x)^{5/2}+\frac{2}{3} a A (a+b x)^{3/2}+\frac{2 B (a+b x)^{7/2}}{7 b}",1,"(2*Sqrt[a + b*x]*(161*a^2*A*b + 15*a^3*B + 77*a*A*b^2*x + 45*a^2*b*B*x + 21*A*b^3*x^2 + 45*a*b^2*B*x^2 + 15*b^3*B*x^3))/(105*b) - 2*a^(5/2)*A*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
416,1,98,118,0.123869,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/x^2,x]","\left(-5 a^{3/2} A b-2 a^{5/2} B\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{\sqrt{a+b x} \left(-15 a^2 A+46 a^2 B x+70 a A b x+22 a b B x^2+10 A b^2 x^2+6 b^2 B x^3\right)}{15 x}","-a^{3/2} (2 a B+5 A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{(a+b x)^{5/2} (2 a B+5 A b)}{5 a}+\frac{1}{3} (a+b x)^{3/2} (2 a B+5 A b)+a \sqrt{a+b x} (2 a B+5 A b)-\frac{A (a+b x)^{7/2}}{a x}",1,"(Sqrt[a + b*x]*(-15*a^2*A + 70*a*A*b*x + 46*a^2*B*x + 10*A*b^2*x^2 + 22*a*b*B*x^2 + 6*b^2*B*x^3))/(15*x) + (-5*a^(3/2)*A*b - 2*a^(5/2)*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
417,1,104,133,0.0923245,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/x^3,x]","\frac{\sqrt{a+b x} \left(-6 a^2 A-12 a^2 B x-27 a A b x+56 a b B x^2+24 A b^2 x^2+8 b^2 B x^3\right)}{12 x^2}-\frac{5}{4} \left(4 a^{3/2} b B+3 \sqrt{a} A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","-\frac{(a+b x)^{5/2} (4 a B+3 A b)}{4 a x}+\frac{5 b (a+b x)^{3/2} (4 a B+3 A b)}{12 a}+\frac{5}{4} b \sqrt{a+b x} (4 a B+3 A b)-\frac{5}{4} \sqrt{a} b (4 a B+3 A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)-\frac{A (a+b x)^{7/2}}{2 a x^2}",1,"(Sqrt[a + b*x]*(-6*a^2*A - 27*a*A*b*x - 12*a^2*B*x + 24*A*b^2*x^2 + 56*a*b*B*x^2 + 8*b^2*B*x^3))/(12*x^2) - (5*(3*Sqrt[a]*A*b^2 + 4*a^(3/2)*b*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/4","A",1
418,1,101,139,0.1330421,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^4} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/x^4,x]","\frac{\sqrt{a+b x} \left(-8 a^2 A-12 a^2 B x-26 a A b x-54 a b B x^2-33 A b^2 x^2+48 b^2 B x^3\right)}{24 x^3}-\frac{5 \left(6 a b^2 B+A b^3\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 \sqrt{a}}","\frac{5 b^2 \sqrt{a+b x} (6 a B+A b)}{8 a}-\frac{5 b^2 (6 a B+A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 \sqrt{a}}-\frac{(a+b x)^{5/2} (6 a B+A b)}{12 a x^2}-\frac{5 b (a+b x)^{3/2} (6 a B+A b)}{24 a x}-\frac{A (a+b x)^{7/2}}{3 a x^3}",1,"(Sqrt[a + b*x]*(-8*a^2*A - 26*a*A*b*x - 12*a^2*B*x - 33*A*b^2*x^2 - 54*a*b*B*x^2 + 48*b^2*B*x^3))/(24*x^3) - (5*(A*b^3 + 6*a*b^2*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(8*Sqrt[a])","A",1
419,1,120,142,0.1808672,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^5} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/x^5,x]","\frac{\sqrt{a+b x} \left(-48 a^3 A-64 a^3 B x-136 a^2 A b x-208 a^2 b B x^2-118 a A b^2 x^2-264 a b^2 B x^3-15 A b^3 x^3\right)}{192 a x^4}-\frac{5 \left(8 a b^3 B-A b^4\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{64 a^{3/2}}","\frac{5 b^3 (A b-8 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{64 a^{3/2}}+\frac{5 b^2 \sqrt{a+b x} (A b-8 a B)}{64 a x}+\frac{(a+b x)^{5/2} (A b-8 a B)}{24 a x^3}+\frac{5 b (a+b x)^{3/2} (A b-8 a B)}{96 a x^2}-\frac{A (a+b x)^{7/2}}{4 a x^4}",1,"(Sqrt[a + b*x]*(-48*a^3*A - 136*a^2*A*b*x - 64*a^3*B*x - 118*a*A*b^2*x^2 - 208*a^2*b*B*x^2 - 15*A*b^3*x^3 - 264*a*b^2*B*x^3))/(192*a*x^4) - (5*(-(A*b^4) + 8*a*b^3*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(64*a^(3/2))","A",1
420,1,144,177,0.2173732,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^6} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/x^6,x]","\frac{\left(10 a b^4 B-3 A b^5\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{128 a^{5/2}}+\frac{\sqrt{a+b x} \left(-384 a^4 A-480 a^4 B x-1008 a^3 A b x-1360 a^3 b B x^2-744 a^2 A b^2 x^2-1180 a^2 b^2 B x^3-30 a A b^3 x^3-150 a b^3 B x^4+45 A b^4 x^4\right)}{1920 a^2 x^5}","-\frac{b^4 (3 A b-10 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{128 a^{5/2}}+\frac{b^3 \sqrt{a+b x} (3 A b-10 a B)}{128 a^2 x}+\frac{b^2 \sqrt{a+b x} (3 A b-10 a B)}{64 a x^2}+\frac{(a+b x)^{5/2} (3 A b-10 a B)}{40 a x^4}+\frac{b (a+b x)^{3/2} (3 A b-10 a B)}{48 a x^3}-\frac{A (a+b x)^{7/2}}{5 a x^5}",1,"(Sqrt[a + b*x]*(-384*a^4*A - 1008*a^3*A*b*x - 480*a^4*B*x - 744*a^2*A*b^2*x^2 - 1360*a^3*b*B*x^2 - 30*a*A*b^3*x^3 - 1180*a^2*b^2*B*x^3 + 45*A*b^4*x^4 - 150*a*b^3*B*x^4))/(1920*a^2*x^5) + ((-3*A*b^5 + 10*a*b^4*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(128*a^(5/2))","A",1
421,1,168,208,0.2343665,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^7} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/x^7,x]","\frac{\left(5 A b^6-12 a b^5 B\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{512 a^{7/2}}+\frac{\sqrt{a+b x} \left(-1280 a^5 A-1536 a^5 B x-3200 a^4 A b x-4032 a^4 b B x^2-2160 a^3 A b^2 x^2-2976 a^3 b^2 B x^3-40 a^2 A b^3 x^3-120 a^2 b^3 B x^4+50 a A b^4 x^4+180 a b^4 B x^5-75 A b^5 x^5\right)}{7680 a^3 x^6}","\frac{b^5 (5 A b-12 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{512 a^{7/2}}-\frac{b^4 \sqrt{a+b x} (5 A b-12 a B)}{512 a^3 x}+\frac{b^3 \sqrt{a+b x} (5 A b-12 a B)}{768 a^2 x^2}+\frac{b^2 \sqrt{a+b x} (5 A b-12 a B)}{192 a x^3}+\frac{(a+b x)^{5/2} (5 A b-12 a B)}{60 a x^5}+\frac{b (a+b x)^{3/2} (5 A b-12 a B)}{96 a x^4}-\frac{A (a+b x)^{7/2}}{6 a x^6}",1,"(Sqrt[a + b*x]*(-1280*a^5*A - 3200*a^4*A*b*x - 1536*a^5*B*x - 2160*a^3*A*b^2*x^2 - 4032*a^4*b*B*x^2 - 40*a^2*A*b^3*x^3 - 2976*a^3*b^2*B*x^3 + 50*a*A*b^4*x^4 - 120*a^2*b^3*B*x^4 - 75*A*b^5*x^5 + 180*a*b^4*B*x^5))/(7680*a^3*x^6) + ((5*A*b^6 - 12*a*b^5*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(512*a^(7/2))","A",1
422,1,192,232,0.2844586,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^8} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/x^8,x]","\frac{5 \left(2 a b^6 B-A b^7\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{1024 a^{9/2}}+\frac{\sqrt{a+b x} \left(-3072 a^6 A-3584 a^6 B x-7424 a^5 A b x-8960 a^5 b B x^2-4736 a^4 A b^2 x^2-6048 a^4 b^2 B x^3-48 a^3 A b^3 x^3-112 a^3 b^3 B x^4+56 a^2 A b^4 x^4+140 a^2 b^4 B x^5-70 a A b^5 x^5-210 a b^5 B x^6+105 A b^6 x^6\right)}{21504 a^4 x^7}","-\frac{5 b^6 (A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{1024 a^{9/2}}+\frac{5 b^5 \sqrt{a+b x} (A b-2 a B)}{1024 a^4 x}-\frac{5 b^4 \sqrt{a+b x} (A b-2 a B)}{1536 a^3 x^2}+\frac{b^3 \sqrt{a+b x} (A b-2 a B)}{384 a^2 x^3}+\frac{b^2 \sqrt{a+b x} (A b-2 a B)}{64 a x^4}+\frac{(a+b x)^{5/2} (A b-2 a B)}{12 a x^6}+\frac{b (a+b x)^{3/2} (A b-2 a B)}{24 a x^5}-\frac{A (a+b x)^{7/2}}{7 a x^7}",1,"(Sqrt[a + b*x]*(-3072*a^6*A - 7424*a^5*A*b*x - 3584*a^6*B*x - 4736*a^4*A*b^2*x^2 - 8960*a^5*b*B*x^2 - 48*a^3*A*b^3*x^3 - 6048*a^4*b^2*B*x^3 + 56*a^2*A*b^4*x^4 - 112*a^3*b^3*B*x^4 - 70*a*A*b^5*x^5 + 140*a^2*b^4*B*x^5 + 105*A*b^6*x^6 - 210*a*b^5*B*x^6))/(21504*a^4*x^7) + (5*(-(A*b^7) + 2*a*b^6*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(1024*a^(9/2))","A",1
423,1,122,149,0.0505422,"\int \frac{x^4 (A+B x)}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(x^4*(A + B*x))/Sqrt[a + b*x],x]","-\frac{2 \sqrt{a+b x} \left(1280 a^5 B-1408 a^4 A b-640 a^4 b B x+704 a^3 A b^2 x+480 a^3 b^2 B x^2-528 a^2 A b^3 x^2-400 a^2 b^3 B x^3+440 a A b^4 x^3+350 a b^4 B x^4-385 A b^5 x^4-315 b^5 B x^5\right)}{3465 b^6}","\frac{2 a^4 \sqrt{a+b x} (A b-a B)}{b^6}-\frac{2 a^3 (a+b x)^{3/2} (4 A b-5 a B)}{3 b^6}+\frac{4 a^2 (a+b x)^{5/2} (3 A b-5 a B)}{5 b^6}+\frac{2 (a+b x)^{9/2} (A b-5 a B)}{9 b^6}-\frac{4 a (a+b x)^{7/2} (2 A b-5 a B)}{7 b^6}+\frac{2 B (a+b x)^{11/2}}{11 b^6}",1,"(-2*Sqrt[a + b*x]*(-1408*a^4*A*b + 1280*a^5*B + 704*a^3*A*b^2*x - 640*a^4*b*B*x - 528*a^2*A*b^3*x^2 + 480*a^3*b^2*B*x^2 + 440*a*A*b^4*x^3 - 400*a^2*b^3*B*x^3 - 385*A*b^5*x^4 + 350*a*b^4*B*x^4 - 315*b^5*B*x^5))/(3465*b^6)","A",1
424,1,98,120,0.0455096,"\int \frac{x^3 (A+B x)}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(x^3*(A + B*x))/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \left(128 a^4 B-144 a^3 A b-64 a^3 b B x+72 a^2 A b^2 x+48 a^2 b^2 B x^2-54 a A b^3 x^2-40 a b^3 B x^3+45 A b^4 x^3+35 b^4 B x^4\right)}{315 b^5}","-\frac{2 a^3 \sqrt{a+b x} (A b-a B)}{b^5}+\frac{2 a^2 (a+b x)^{3/2} (3 A b-4 a B)}{3 b^5}+\frac{2 (a+b x)^{7/2} (A b-4 a B)}{7 b^5}-\frac{6 a (a+b x)^{5/2} (A b-2 a B)}{5 b^5}+\frac{2 B (a+b x)^{9/2}}{9 b^5}",1,"(2*Sqrt[a + b*x]*(-144*a^3*A*b + 128*a^4*B + 72*a^2*A*b^2*x - 64*a^3*b*B*x - 54*a*A*b^3*x^2 + 48*a^2*b^2*B*x^2 + 45*A*b^4*x^3 - 40*a*b^3*B*x^3 + 35*b^4*B*x^4))/(315*b^5)","A",1
425,1,74,93,0.0329478,"\int \frac{x^2 (A+B x)}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(x^2*(A + B*x))/Sqrt[a + b*x],x]","-\frac{2 \sqrt{a+b x} \left(48 a^3 B-56 a^2 A b-24 a^2 b B x+28 a A b^2 x+18 a b^2 B x^2-21 A b^3 x^2-15 b^3 B x^3\right)}{105 b^4}","\frac{2 a^2 \sqrt{a+b x} (A b-a B)}{b^4}+\frac{2 (a+b x)^{5/2} (A b-3 a B)}{5 b^4}-\frac{2 a (a+b x)^{3/2} (2 A b-3 a B)}{3 b^4}+\frac{2 B (a+b x)^{7/2}}{7 b^4}",1,"(-2*Sqrt[a + b*x]*(-56*a^2*A*b + 48*a^3*B + 28*a*A*b^2*x - 24*a^2*b*B*x - 21*A*b^3*x^2 + 18*a*b^2*B*x^2 - 15*b^3*B*x^3))/(105*b^4)","A",1
426,1,50,65,0.0253441,"\int \frac{x (A+B x)}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(x*(A + B*x))/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \left(8 a^2 B-10 a A b-4 a b B x+5 A b^2 x+3 b^2 B x^2\right)}{15 b^3}","\frac{2 (a+b x)^{3/2} (A b-2 a B)}{3 b^3}-\frac{2 a \sqrt{a+b x} (A b-a B)}{b^3}+\frac{2 B (a+b x)^{5/2}}{5 b^3}",1,"(2*Sqrt[a + b*x]*(-10*a*A*b + 8*a^2*B + 5*A*b^2*x - 4*a*b*B*x + 3*b^2*B*x^2))/(15*b^3)","A",1
427,1,29,40,0.0153243,"\int \frac{A+B x}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(A + B*x)/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} (-2 a B+3 A b+b B x)}{3 b^2}","\frac{2 \sqrt{a+b x} (A b-a B)}{b^2}+\frac{2 B (a+b x)^{3/2}}{3 b^2}",1,"(2*Sqrt[a + b*x]*(3*A*b - 2*a*B + b*B*x))/(3*b^2)","A",1
428,1,40,40,0.0317189,"\int \frac{A+B x}{x \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(A + B*x)/(x*Sqrt[a + b*x]),x]","\frac{2 B \sqrt{a+b x}}{b}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{2 B \sqrt{a+b x}}{b}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(2*B*Sqrt[a + b*x])/b - (2*A*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/Sqrt[a]","A",1
429,1,49,49,0.0612536,"\int \frac{A+B x}{x^2 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^2*Sqrt[a + b*x]),x]","\frac{(A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{A \sqrt{a+b x}}{a x}","\frac{(A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{A \sqrt{a+b x}}{a x}",1,"-((A*Sqrt[a + b*x])/(a*x)) + ((A*b - 2*a*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/a^(3/2)","A",1
430,1,72,84,0.0961165,"\int \frac{A+B x}{x^3 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^3*Sqrt[a + b*x]),x]","\frac{\left(4 a b B-3 A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{5/2}}+\frac{\sqrt{a+b x} (-2 a A-4 a B x+3 A b x)}{4 a^2 x^2}","-\frac{b (3 A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{5/2}}+\frac{\sqrt{a+b x} (3 A b-4 a B)}{4 a^2 x}-\frac{A \sqrt{a+b x}}{2 a x^2}",1,"(Sqrt[a + b*x]*(-2*a*A + 3*A*b*x - 4*a*B*x))/(4*a^2*x^2) + ((-3*A*b^2 + 4*a*b*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(4*a^(5/2))","A",1
431,1,96,115,0.1329665,"\int \frac{A+B x}{x^4 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^4*Sqrt[a + b*x]),x]","\frac{\left(5 A b^3-6 a b^2 B\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{7/2}}+\frac{\sqrt{a+b x} \left(-8 a^2 A-12 a^2 B x+10 a A b x+18 a b B x^2-15 A b^2 x^2\right)}{24 a^3 x^3}","\frac{b^2 (5 A b-6 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{7/2}}-\frac{b \sqrt{a+b x} (5 A b-6 a B)}{8 a^3 x}+\frac{\sqrt{a+b x} (5 A b-6 a B)}{12 a^2 x^2}-\frac{A \sqrt{a+b x}}{3 a x^3}",1,"(Sqrt[a + b*x]*(-8*a^2*A + 10*a*A*b*x - 12*a^2*B*x - 15*A*b^2*x^2 + 18*a*b*B*x^2))/(24*a^3*x^3) + ((5*A*b^3 - 6*a*b^2*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(8*a^(7/2))","A",1
432,1,120,146,0.1738526,"\int \frac{A+B x}{x^5 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^5*Sqrt[a + b*x]),x]","\frac{5 \left(8 a b^3 B-7 A b^4\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{64 a^{9/2}}+\frac{\sqrt{a+b x} \left(-48 a^3 A-64 a^3 B x+56 a^2 A b x+80 a^2 b B x^2-70 a A b^2 x^2-120 a b^2 B x^3+105 A b^3 x^3\right)}{192 a^4 x^4}","-\frac{5 b^3 (7 A b-8 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{64 a^{9/2}}+\frac{5 b^2 \sqrt{a+b x} (7 A b-8 a B)}{64 a^4 x}-\frac{5 b \sqrt{a+b x} (7 A b-8 a B)}{96 a^3 x^2}+\frac{\sqrt{a+b x} (7 A b-8 a B)}{24 a^2 x^3}-\frac{A \sqrt{a+b x}}{4 a x^4}",1,"(Sqrt[a + b*x]*(-48*a^3*A + 56*a^2*A*b*x - 64*a^3*B*x - 70*a*A*b^2*x^2 + 80*a^2*b*B*x^2 + 105*A*b^3*x^3 - 120*a*b^2*B*x^3))/(192*a^4*x^4) + (5*(-7*A*b^4 + 8*a*b^3*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(64*a^(9/2))","A",1
433,1,144,177,0.2092237,"\int \frac{A+B x}{x^6 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^6*Sqrt[a + b*x]),x]","\frac{\sqrt{a+b x} \left(-384 a^4 A-480 a^4 B x+432 a^3 A b x+560 a^3 b B x^2-504 a^2 A b^2 x^2-700 a^2 b^2 B x^3+630 a A b^3 x^3+1050 a b^3 B x^4-945 A b^4 x^4\right)}{1920 a^5 x^5}-\frac{7 \left(10 a b^4 B-9 A b^5\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{128 a^{11/2}}","\frac{7 b^4 (9 A b-10 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{128 a^{11/2}}-\frac{7 b^3 \sqrt{a+b x} (9 A b-10 a B)}{128 a^5 x}+\frac{7 b^2 \sqrt{a+b x} (9 A b-10 a B)}{192 a^4 x^2}-\frac{7 b \sqrt{a+b x} (9 A b-10 a B)}{240 a^3 x^3}+\frac{\sqrt{a+b x} (9 A b-10 a B)}{40 a^2 x^4}-\frac{A \sqrt{a+b x}}{5 a x^5}",1,"(Sqrt[a + b*x]*(-384*a^4*A + 432*a^3*A*b*x - 480*a^4*B*x - 504*a^2*A*b^2*x^2 + 560*a^3*b*B*x^2 + 630*a*A*b^3*x^3 - 700*a^2*b^2*B*x^3 - 945*A*b^4*x^4 + 1050*a*b^3*B*x^4))/(1920*a^5*x^5) - (7*(-9*A*b^5 + 10*a*b^4*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(128*a^(11/2))","A",1
434,1,122,147,0.0677454,"\int \frac{x^4 (A+B x)}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(x^4*(A + B*x))/(a + b*x)^(3/2),x]","\frac{2 \left(1280 a^5 B-1152 a^4 A b+640 a^4 b B x-576 a^3 A b^2 x-160 a^3 b^2 B x^2+144 a^2 A b^3 x^2+80 a^2 b^3 B x^3-72 a A b^4 x^3-50 a b^4 B x^4+45 A b^5 x^4+35 b^5 B x^5\right)}{315 b^6 \sqrt{a+b x}}","-\frac{2 a^4 (A b-a B)}{b^6 \sqrt{a+b x}}-\frac{2 a^3 \sqrt{a+b x} (4 A b-5 a B)}{b^6}+\frac{4 a^2 (a+b x)^{3/2} (3 A b-5 a B)}{3 b^6}+\frac{2 (a+b x)^{7/2} (A b-5 a B)}{7 b^6}-\frac{4 a (a+b x)^{5/2} (2 A b-5 a B)}{5 b^6}+\frac{2 B (a+b x)^{9/2}}{9 b^6}",1,"(2*(-1152*a^4*A*b + 1280*a^5*B - 576*a^3*A*b^2*x + 640*a^4*b*B*x + 144*a^2*A*b^3*x^2 - 160*a^3*b^2*B*x^2 - 72*a*A*b^4*x^3 + 80*a^2*b^3*B*x^3 + 45*A*b^5*x^4 - 50*a*b^4*B*x^4 + 35*b^5*B*x^5))/(315*b^6*Sqrt[a + b*x])","A",1
435,1,98,116,0.0565011,"\int \frac{x^3 (A+B x)}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(x^3*(A + B*x))/(a + b*x)^(3/2),x]","-\frac{2 \left(128 a^4 B-112 a^3 A b+64 a^3 b B x-56 a^2 A b^2 x-16 a^2 b^2 B x^2+14 a A b^3 x^2+8 a b^3 B x^3-7 A b^4 x^3-5 b^4 B x^4\right)}{35 b^5 \sqrt{a+b x}}","\frac{2 a^3 (A b-a B)}{b^5 \sqrt{a+b x}}+\frac{2 a^2 \sqrt{a+b x} (3 A b-4 a B)}{b^5}+\frac{2 (a+b x)^{5/2} (A b-4 a B)}{5 b^5}-\frac{2 a (a+b x)^{3/2} (A b-2 a B)}{b^5}+\frac{2 B (a+b x)^{7/2}}{7 b^5}",1,"(-2*(-112*a^3*A*b + 128*a^4*B - 56*a^2*A*b^2*x + 64*a^3*b*B*x + 14*a*A*b^3*x^2 - 16*a^2*b^2*B*x^2 - 7*A*b^4*x^3 + 8*a*b^3*B*x^3 - 5*b^4*B*x^4))/(35*b^5*Sqrt[a + b*x])","A",1
436,1,74,91,0.0480679,"\int \frac{x^2 (A+B x)}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(x^2*(A + B*x))/(a + b*x)^(3/2),x]","\frac{2 \left(48 a^3 B-40 a^2 A b+24 a^2 b B x-20 a A b^2 x-6 a b^2 B x^2+5 A b^3 x^2+3 b^3 B x^3\right)}{15 b^4 \sqrt{a+b x}}","-\frac{2 a^2 (A b-a B)}{b^4 \sqrt{a+b x}}+\frac{2 (a+b x)^{3/2} (A b-3 a B)}{3 b^4}-\frac{2 a \sqrt{a+b x} (2 A b-3 a B)}{b^4}+\frac{2 B (a+b x)^{5/2}}{5 b^4}",1,"(2*(-40*a^2*A*b + 48*a^3*B - 20*a*A*b^2*x + 24*a^2*b*B*x + 5*A*b^3*x^2 - 6*a*b^2*B*x^2 + 3*b^3*B*x^3))/(15*b^4*Sqrt[a + b*x])","A",1
437,1,50,63,0.0316501,"\int \frac{x (A+B x)}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(x*(A + B*x))/(a + b*x)^(3/2),x]","-\frac{2 \left(8 a^2 B-6 a A b+4 a b B x-3 A b^2 x-b^2 B x^2\right)}{3 b^3 \sqrt{a+b x}}","\frac{2 \sqrt{a+b x} (A b-2 a B)}{b^3}+\frac{2 a (A b-a B)}{b^3 \sqrt{a+b x}}+\frac{2 B (a+b x)^{3/2}}{3 b^3}",1,"(-2*(-6*a*A*b + 8*a^2*B - 3*A*b^2*x + 4*a*b*B*x - b^2*B*x^2))/(3*b^3*Sqrt[a + b*x])","A",1
438,1,27,38,0.0203376,"\int \frac{A+B x}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(a + b*x)^(3/2),x]","\frac{2 (2 a B-A b+b B x)}{b^2 \sqrt{a+b x}}","\frac{2 B \sqrt{a+b x}}{b^2}-\frac{2 (A b-a B)}{b^2 \sqrt{a+b x}}",1,"(2*(-(A*b) + 2*a*B + b*B*x))/(b^2*Sqrt[a + b*x])","A",1
439,1,50,50,0.0654364,"\int \frac{A+B x}{x (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x*(a + b*x)^(3/2)),x]","-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{2 (a B-A b)}{a b \sqrt{a+b x}}","\frac{2 (A b-a B)}{a b \sqrt{a+b x}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{3/2}}",1,"(-2*(-(A*b) + a*B))/(a*b*Sqrt[a + b*x]) - (2*A*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/a^(3/2)","A",1
440,1,63,73,0.105052,"\int \frac{A+B x}{x^2 (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^2*(a + b*x)^(3/2)),x]","\frac{(3 A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{-a A+2 a B x-3 A b x}{a^2 x \sqrt{a+b x}}","\frac{(3 A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{3 A b-2 a B}{a^2 \sqrt{a+b x}}-\frac{A}{a x \sqrt{a+b x}}",1,"(-(a*A) - 3*A*b*x + 2*a*B*x)/(a^2*x*Sqrt[a + b*x]) + ((3*A*b - 2*a*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/a^(5/2)","A",1
441,1,94,110,0.1078002,"\int \frac{A+B x}{x^3 (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^3*(a + b*x)^(3/2)),x]","\frac{3 \left(4 a b B-5 A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{7/2}}+\frac{-2 a^2 A-4 a^2 B x+5 a A b x-12 a b B x^2+15 A b^2 x^2}{4 a^3 x^2 \sqrt{a+b x}}","-\frac{3 b (5 A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{7/2}}+\frac{3 b (5 A b-4 a B)}{4 a^3 \sqrt{a+b x}}+\frac{5 A b-4 a B}{4 a^2 x \sqrt{a+b x}}-\frac{A}{2 a x^2 \sqrt{a+b x}}",1,"(-2*a^2*A + 5*a*A*b*x - 4*a^2*B*x + 15*A*b^2*x^2 - 12*a*b*B*x^2)/(4*a^3*x^2*Sqrt[a + b*x]) + (3*(-5*A*b^2 + 4*a*b*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(4*a^(7/2))","A",1
442,1,120,143,0.1571822,"\int \frac{A+B x}{x^4 (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^4*(a + b*x)^(3/2)),x]","\frac{-8 a^3 A-12 a^3 B x+14 a^2 A b x+30 a^2 b B x^2-35 a A b^2 x^2+90 a b^2 B x^3-105 A b^3 x^3}{24 a^4 x^3 \sqrt{a+b x}}-\frac{5 \left(6 a b^2 B-7 A b^3\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{9/2}}","\frac{5 b^2 (7 A b-6 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{9/2}}-\frac{5 b^2 (7 A b-6 a B)}{8 a^4 \sqrt{a+b x}}-\frac{5 b (7 A b-6 a B)}{24 a^3 x \sqrt{a+b x}}+\frac{7 A b-6 a B}{12 a^2 x^2 \sqrt{a+b x}}-\frac{A}{3 a x^3 \sqrt{a+b x}}",1,"(-8*a^3*A + 14*a^2*A*b*x - 12*a^3*B*x - 35*a*A*b^2*x^2 + 30*a^2*b*B*x^2 - 105*A*b^3*x^3 + 90*a*b^2*B*x^3)/(24*a^4*x^3*Sqrt[a + b*x]) - (5*(-7*A*b^3 + 6*a*b^2*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(8*a^(9/2))","A",1
443,1,144,174,0.2200098,"\int \frac{A+B x}{x^5 (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^5*(a + b*x)^(3/2)),x]","\frac{35 \left(8 a b^3 B-9 A b^4\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{64 a^{11/2}}+\frac{-48 a^4 A-64 a^4 B x+72 a^3 A b x+112 a^3 b B x^2-126 a^2 A b^2 x^2-280 a^2 b^2 B x^3+315 a A b^3 x^3-840 a b^3 B x^4+945 A b^4 x^4}{192 a^5 x^4 \sqrt{a+b x}}","-\frac{35 b^3 (9 A b-8 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{64 a^{11/2}}+\frac{35 b^3 (9 A b-8 a B)}{64 a^5 \sqrt{a+b x}}+\frac{35 b^2 (9 A b-8 a B)}{192 a^4 x \sqrt{a+b x}}-\frac{7 b (9 A b-8 a B)}{96 a^3 x^2 \sqrt{a+b x}}+\frac{9 A b-8 a B}{24 a^2 x^3 \sqrt{a+b x}}-\frac{A}{4 a x^4 \sqrt{a+b x}}",1,"(-48*a^4*A + 72*a^3*A*b*x - 64*a^4*B*x - 126*a^2*A*b^2*x^2 + 112*a^3*b*B*x^2 + 315*a*A*b^3*x^3 - 280*a^2*b^2*B*x^3 + 945*A*b^4*x^4 - 840*a*b^3*B*x^4)/(192*a^5*x^4*Sqrt[a + b*x]) + (35*(-9*A*b^4 + 8*a*b^3*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(64*a^(11/2))","A",1
444,1,122,147,0.0718131,"\int \frac{x^4 (A+B x)}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(x^4*(A + B*x))/(a + b*x)^(5/2),x]","-\frac{2 \left(1280 a^5 B-896 a^4 A b+1920 a^4 b B x-1344 a^3 A b^2 x+480 a^3 b^2 B x^2-336 a^2 A b^3 x^2-80 a^2 b^3 B x^3+56 a A b^4 x^3+30 a b^4 B x^4-21 A b^5 x^4-15 b^5 B x^5\right)}{105 b^6 (a+b x)^{3/2}}","-\frac{2 a^4 (A b-a B)}{3 b^6 (a+b x)^{3/2}}+\frac{2 a^3 (4 A b-5 a B)}{b^6 \sqrt{a+b x}}+\frac{4 a^2 \sqrt{a+b x} (3 A b-5 a B)}{b^6}-\frac{4 a (a+b x)^{3/2} (2 A b-5 a B)}{3 b^6}+\frac{2 (a+b x)^{5/2} (A b-5 a B)}{5 b^6}+\frac{2 B (a+b x)^{7/2}}{7 b^6}",1,"(-2*(-896*a^4*A*b + 1280*a^5*B - 1344*a^3*A*b^2*x + 1920*a^4*b*B*x - 336*a^2*A*b^3*x^2 + 480*a^3*b^2*B*x^2 + 56*a*A*b^4*x^3 - 80*a^2*b^3*B*x^3 - 21*A*b^5*x^4 + 30*a*b^4*B*x^4 - 15*b^5*B*x^5))/(105*b^6*(a + b*x)^(3/2))","A",1
445,1,98,118,0.0595901,"\int \frac{x^3 (A+B x)}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(x^3*(A + B*x))/(a + b*x)^(5/2),x]","\frac{2 \left(128 a^4 B-80 a^3 A b+192 a^3 b B x-120 a^2 A b^2 x+48 a^2 b^2 B x^2-30 a A b^3 x^2-8 a b^3 B x^3+5 A b^4 x^3+3 b^4 B x^4\right)}{15 b^5 (a+b x)^{3/2}}","\frac{2 a^3 (A b-a B)}{3 b^5 (a+b x)^{3/2}}-\frac{2 a^2 (3 A b-4 a B)}{b^5 \sqrt{a+b x}}-\frac{6 a \sqrt{a+b x} (A b-2 a B)}{b^5}+\frac{2 (a+b x)^{3/2} (A b-4 a B)}{3 b^5}+\frac{2 B (a+b x)^{5/2}}{5 b^5}",1,"(2*(-80*a^3*A*b + 128*a^4*B - 120*a^2*A*b^2*x + 192*a^3*b*B*x - 30*a*A*b^3*x^2 + 48*a^2*b^2*B*x^2 + 5*A*b^4*x^3 - 8*a*b^3*B*x^3 + 3*b^4*B*x^4))/(15*b^5*(a + b*x)^(3/2))","A",1
446,1,74,91,0.0423955,"\int \frac{x^2 (A+B x)}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(x^2*(A + B*x))/(a + b*x)^(5/2),x]","-\frac{2 \left(16 a^3 B-8 a^2 A b+24 a^2 b B x-12 a A b^2 x+6 a b^2 B x^2-3 A b^3 x^2-b^3 B x^3\right)}{3 b^4 (a+b x)^{3/2}}","-\frac{2 a^2 (A b-a B)}{3 b^4 (a+b x)^{3/2}}+\frac{2 a (2 A b-3 a B)}{b^4 \sqrt{a+b x}}+\frac{2 \sqrt{a+b x} (A b-3 a B)}{b^4}+\frac{2 B (a+b x)^{3/2}}{3 b^4}",1,"(-2*(-8*a^2*A*b + 16*a^3*B - 12*a*A*b^2*x + 24*a^2*b*B*x - 3*A*b^3*x^2 + 6*a*b^2*B*x^2 - b^3*B*x^3))/(3*b^4*(a + b*x)^(3/2))","A",1
447,1,50,63,0.0534747,"\int \frac{x (A+B x)}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(x*(A + B*x))/(a + b*x)^(5/2),x]","\frac{2 \left(8 a^2 B-2 a A b+12 a b B x-3 A b^2 x+3 b^2 B x^2\right)}{3 b^3 (a+b x)^{3/2}}","-\frac{2 (A b-2 a B)}{b^3 \sqrt{a+b x}}+\frac{2 a (A b-a B)}{3 b^3 (a+b x)^{3/2}}+\frac{2 B \sqrt{a+b x}}{b^3}",1,"(2*(-2*a*A*b + 8*a^2*B - 3*A*b^2*x + 12*a*b*B*x + 3*b^2*B*x^2))/(3*b^3*(a + b*x)^(3/2))","A",1
448,1,29,40,0.0218876,"\int \frac{A+B x}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(a + b*x)^(5/2),x]","-\frac{2 (2 a B+A b+3 b B x)}{3 b^2 (a+b x)^{3/2}}","-\frac{2 (A b-a B)}{3 b^2 (a+b x)^{3/2}}-\frac{2 B}{b^2 \sqrt{a+b x}}",1,"(-2*(A*b + 2*a*B + 3*b*B*x))/(3*b^2*(a + b*x)^(3/2))","A",1
449,1,62,67,0.070698,"\int \frac{A+B x}{x (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x*(a + b*x)^(5/2)),x]","-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{2 \left(a^2 B-4 a A b-3 A b^2 x\right)}{3 a^2 b (a+b x)^{3/2}}","-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{2 A}{a^2 \sqrt{a+b x}}+\frac{2 (A b-a B)}{3 a b (a+b x)^{3/2}}",1,"(-2*(-4*a*A*b + a^2*B - 3*A*b^2*x))/(3*a^2*b*(a + b*x)^(3/2)) - (2*A*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/a^(5/2)","A",1
450,1,88,98,0.1257515,"\int \frac{A+B x}{x^2 (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^2*(a + b*x)^(5/2)),x]","\frac{(5 A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{-3 a^2 A+8 a^2 B x-20 a A b x+6 a b B x^2-15 A b^2 x^2}{3 a^3 x (a+b x)^{3/2}}","\frac{(5 A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a^{7/2}}-\frac{5 A b-2 a B}{a^3 \sqrt{a+b x}}+\frac{2 a B-5 A b}{3 a^2 (a+b x)^{3/2}}-\frac{A}{a x (a+b x)^{3/2}}",1,"(-3*a^2*A - 20*a*A*b*x + 8*a^2*B*x - 15*A*b^2*x^2 + 6*a*b*B*x^2)/(3*a^3*x*(a + b*x)^(3/2)) + ((5*A*b - 2*a*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/a^(7/2)","A",1
451,1,118,136,0.1569858,"\int \frac{A+B x}{x^3 (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^3*(a + b*x)^(5/2)),x]","\frac{5 \left(4 a b B-7 A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{9/2}}+\frac{-6 a^3 A-12 a^3 B x+21 a^2 A b x-80 a^2 b B x^2+140 a A b^2 x^2-60 a b^2 B x^3+105 A b^3 x^3}{12 a^4 x^2 (a+b x)^{3/2}}","-\frac{5 b (7 A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{9/2}}+\frac{5 b (7 A b-4 a B)}{4 a^4 \sqrt{a+b x}}+\frac{5 b (7 A b-4 a B)}{12 a^3 (a+b x)^{3/2}}+\frac{7 A b-4 a B}{4 a^2 x (a+b x)^{3/2}}-\frac{A}{2 a x^2 (a+b x)^{3/2}}",1,"(-6*a^3*A + 21*a^2*A*b*x - 12*a^3*B*x + 140*a*A*b^2*x^2 - 80*a^2*b*B*x^2 + 105*A*b^3*x^3 - 60*a*b^2*B*x^3)/(12*a^4*x^2*(a + b*x)^(3/2)) + (5*(-7*A*b^2 + 4*a*b*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(4*a^(9/2))","A",1
452,1,144,171,0.2102861,"\int \frac{A+B x}{x^4 (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^4*(a + b*x)^(5/2)),x]","\frac{-8 a^4 A-12 a^4 B x+18 a^3 A b x+42 a^3 b B x^2-63 a^2 A b^2 x^2+280 a^2 b^2 B x^3-420 a A b^3 x^3+210 a b^3 B x^4-315 A b^4 x^4}{24 a^5 x^3 (a+b x)^{3/2}}-\frac{35 \left(2 a b^2 B-3 A b^3\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{11/2}}","\frac{35 b^2 (3 A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{8 a^{11/2}}-\frac{35 b^2 (3 A b-2 a B)}{8 a^5 \sqrt{a+b x}}-\frac{35 b^2 (3 A b-2 a B)}{24 a^4 (a+b x)^{3/2}}-\frac{7 b (3 A b-2 a B)}{8 a^3 x (a+b x)^{3/2}}+\frac{3 A b-2 a B}{4 a^2 x^2 (a+b x)^{3/2}}-\frac{A}{3 a x^3 (a+b x)^{3/2}}",1,"(-8*a^4*A + 18*a^3*A*b*x - 12*a^4*B*x - 63*a^2*A*b^2*x^2 + 42*a^3*b*B*x^2 - 420*a*A*b^3*x^3 + 280*a^2*b^2*B*x^3 - 315*A*b^4*x^4 + 210*a*b^3*B*x^4)/(24*a^5*x^3*(a + b*x)^(3/2)) - (35*(-3*A*b^3 + 2*a*b^2*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(8*a^(11/2))","A",1
453,1,168,202,0.2502867,"\int \frac{A+B x}{x^5 (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^5*(a + b*x)^(5/2)),x]","\frac{105 \left(8 a b^3 B-11 A b^4\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{64 a^{13/2}}+\frac{-48 a^5 A-64 a^5 B x+88 a^4 A b x+144 a^4 b B x^2-198 a^3 A b^2 x^2-504 a^3 b^2 B x^3+693 a^2 A b^3 x^3-3360 a^2 b^3 B x^4+4620 a A b^4 x^4-2520 a b^4 B x^5+3465 A b^5 x^5}{192 a^6 x^4 (a+b x)^{3/2}}","-\frac{105 b^3 (11 A b-8 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{64 a^{13/2}}+\frac{105 b^3 (11 A b-8 a B)}{64 a^6 \sqrt{a+b x}}+\frac{35 b^3 (11 A b-8 a B)}{64 a^5 (a+b x)^{3/2}}+\frac{21 b^2 (11 A b-8 a B)}{64 a^4 x (a+b x)^{3/2}}-\frac{3 b (11 A b-8 a B)}{32 a^3 x^2 (a+b x)^{3/2}}+\frac{11 A b-8 a B}{24 a^2 x^3 (a+b x)^{3/2}}-\frac{A}{4 a x^4 (a+b x)^{3/2}}",1,"(-48*a^5*A + 88*a^4*A*b*x - 64*a^5*B*x - 198*a^3*A*b^2*x^2 + 144*a^4*b*B*x^2 + 693*a^2*A*b^3*x^3 - 504*a^3*b^2*B*x^3 + 4620*a*A*b^4*x^4 - 3360*a^2*b^3*B*x^4 + 3465*A*b^5*x^5 - 2520*a*b^4*B*x^5)/(192*a^6*x^4*(a + b*x)^(3/2)) + (105*(-11*A*b^4 + 8*a*b^3*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(64*a^(13/2))","A",1
454,1,67,71,0.105679,"\int \frac{(a+b x)^2}{x^2 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^2/(x^2*Sqrt[c + d*x]),x]","\frac{\sqrt{c+d x} \left(2 b^2 c x-a^2 d\right)}{c d x}+\frac{\left(a^2 d-4 a b c\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{c^{3/2}}","-\frac{a^2 \sqrt{c+d x}}{c x}-\frac{a (4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{c^{3/2}}+\frac{2 b^2 \sqrt{c+d x}}{d}",1,"((-(a^2*d) + 2*b^2*c*x)*Sqrt[c + d*x])/(c*d*x) + ((-4*a*b*c + a^2*d)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/c^(3/2)","A",1
455,1,340,209,0.2561311,"\int \frac{x^3 (c+d x)^{5/2}}{a+b x} \, dx","IntegrateAlgebraic[(x^3*(c + d*x)^(5/2))/(a + b*x),x]","-\frac{2 a^3 (a d-b c)^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{b^{13/2}}-\frac{2 \sqrt{c+d x} \left(3465 a^5 d^5-8085 a^4 b c d^4-1155 a^4 b d^5 x+5313 a^3 b^2 c^2 d^3+2541 a^3 b^2 c d^4 x+693 a^3 b^2 d^5 x^2-495 a^2 b^3 c^3 d^2-1485 a^2 b^3 c^2 d^3 x-1485 a^2 b^3 c d^4 x^2-495 a^2 b^3 d^5 x^3-110 a b^4 c^4 d+55 a b^4 c^3 d^2 x+825 a b^4 c^2 d^3 x^2+1045 a b^4 c d^4 x^3+385 a b^4 d^5 x^4-40 b^5 c^5+20 b^5 c^4 d x-15 b^5 c^3 d^2 x^2-565 b^5 c^2 d^3 x^3-805 b^5 c d^4 x^4-315 b^5 d^5 x^5\right)}{3465 b^6 d^3}","\frac{2 a^3 (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{13/2}}-\frac{2 a^3 \sqrt{c+d x} (b c-a d)^2}{b^6}-\frac{2 a^3 (c+d x)^{3/2} (b c-a d)}{3 b^5}-\frac{2 a^3 (c+d x)^{5/2}}{5 b^4}+\frac{2 (c+d x)^{7/2} \left(a^2 d^2+a b c d+b^2 c^2\right)}{7 b^3 d^3}-\frac{2 (c+d x)^{9/2} (a d+2 b c)}{9 b^2 d^3}+\frac{2 (c+d x)^{11/2}}{11 b d^3}",1,"(-2*Sqrt[c + d*x]*(-40*b^5*c^5 - 110*a*b^4*c^4*d - 495*a^2*b^3*c^3*d^2 + 5313*a^3*b^2*c^2*d^3 - 8085*a^4*b*c*d^4 + 3465*a^5*d^5 + 20*b^5*c^4*d*x + 55*a*b^4*c^3*d^2*x - 1485*a^2*b^3*c^2*d^3*x + 2541*a^3*b^2*c*d^4*x - 1155*a^4*b*d^5*x - 15*b^5*c^3*d^2*x^2 + 825*a*b^4*c^2*d^3*x^2 - 1485*a^2*b^3*c*d^4*x^2 + 693*a^3*b^2*d^5*x^2 - 565*b^5*c^2*d^3*x^3 + 1045*a*b^4*c*d^4*x^3 - 495*a^2*b^3*d^5*x^3 - 805*b^5*c*d^4*x^4 + 385*a*b^4*d^5*x^4 - 315*b^5*d^5*x^5))/(3465*b^6*d^3) - (2*a^3*(-(b*c) + a*d)^(5/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/b^(13/2)","A",1
456,1,253,169,0.209471,"\int \frac{x^2 (c+d x)^{5/2}}{a+b x} \, dx","IntegrateAlgebraic[(x^2*(c + d*x)^(5/2))/(a + b*x),x]","\frac{2 a^2 (a d-b c)^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{b^{11/2}}+\frac{2 \sqrt{c+d x} \left(315 a^4 d^4-735 a^3 b c d^3-105 a^3 b d^4 x+483 a^2 b^2 c^2 d^2+231 a^2 b^2 c d^3 x+63 a^2 b^2 d^4 x^2-45 a b^3 c^3 d-135 a b^3 c^2 d^2 x-135 a b^3 c d^3 x^2-45 a b^3 d^4 x^3-10 b^4 c^4+5 b^4 c^3 d x+75 b^4 c^2 d^2 x^2+95 b^4 c d^3 x^3+35 b^4 d^4 x^4\right)}{315 b^5 d^2}","-\frac{2 a^2 (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{11/2}}+\frac{2 a^2 \sqrt{c+d x} (b c-a d)^2}{b^5}+\frac{2 a^2 (c+d x)^{3/2} (b c-a d)}{3 b^4}+\frac{2 a^2 (c+d x)^{5/2}}{5 b^3}-\frac{2 (c+d x)^{7/2} (a d+b c)}{7 b^2 d^2}+\frac{2 (c+d x)^{9/2}}{9 b d^2}",1,"(2*Sqrt[c + d*x]*(-10*b^4*c^4 - 45*a*b^3*c^3*d + 483*a^2*b^2*c^2*d^2 - 735*a^3*b*c*d^3 + 315*a^4*d^4 + 5*b^4*c^3*d*x - 135*a*b^3*c^2*d^2*x + 231*a^2*b^2*c*d^3*x - 105*a^3*b*d^4*x + 75*b^4*c^2*d^2*x^2 - 135*a*b^3*c*d^3*x^2 + 63*a^2*b^2*d^4*x^2 + 95*b^4*c*d^3*x^3 - 45*a*b^3*d^4*x^3 + 35*b^4*d^4*x^4))/(315*b^5*d^2) + (2*a^2*(-(b*c) + a*d)^(5/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/b^(11/2)","A",1
457,1,181,135,0.1421185,"\int \frac{x (c+d x)^{5/2}}{a+b x} \, dx","IntegrateAlgebraic[(x*(c + d*x)^(5/2))/(a + b*x),x]","-\frac{2 \sqrt{c+d x} \left(105 a^3 d^3-245 a^2 b c d^2-35 a^2 b d^3 x+161 a b^2 c^2 d+77 a b^2 c d^2 x+21 a b^2 d^3 x^2-15 b^3 c^3-45 b^3 c^2 d x-45 b^3 c d^2 x^2-15 b^3 d^3 x^3\right)}{105 b^4 d}-\frac{2 a (a d-b c)^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{b^{9/2}}","\frac{2 a (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{9/2}}-\frac{2 a \sqrt{c+d x} (b c-a d)^2}{b^4}-\frac{2 a (c+d x)^{3/2} (b c-a d)}{3 b^3}-\frac{2 a (c+d x)^{5/2}}{5 b^2}+\frac{2 (c+d x)^{7/2}}{7 b d}",1,"(-2*Sqrt[c + d*x]*(-15*b^3*c^3 + 161*a*b^2*c^2*d - 245*a^2*b*c*d^2 + 105*a^3*d^3 - 45*b^3*c^2*d*x + 77*a*b^2*c*d^2*x - 35*a^2*b*d^3*x - 45*b^3*c*d^2*x^2 + 21*a*b^2*d^3*x^2 - 15*b^3*d^3*x^3))/(105*b^4*d) - (2*a*(-(b*c) + a*d)^(5/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/b^(9/2)","A",1
458,1,124,112,0.0006092,"\int \frac{(c+d x)^{5/2}}{a+b x} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(a + b*x),x]","\frac{2 \sqrt{c+d x} \left(15 a^2 d^2-35 a b c d-5 a b d^2 x+23 b^2 c^2+11 b^2 c d x+3 b^2 d^2 x^2\right)}{15 b^3}+\frac{2 (a d-b c)^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{b^{7/2}}","-\frac{2 (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{7/2}}+\frac{2 \sqrt{c+d x} (b c-a d)^2}{b^3}+\frac{2 (c+d x)^{3/2} (b c-a d)}{3 b^2}+\frac{2 (c+d x)^{5/2}}{5 b}",1,"(2*Sqrt[c + d*x]*(23*b^2*c^2 - 35*a*b*c*d + 15*a^2*d^2 + 11*b^2*c*d*x - 5*a*b*d^2*x + 3*b^2*d^2*x^2))/(15*b^3) + (2*(-(b*c) + a*d)^(5/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/b^(7/2)","A",1
459,1,121,118,0.2103892,"\int \frac{(c+d x)^{5/2}}{x (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x*(a + b*x)),x]","-\frac{2 (a d-b c)^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{a b^{5/2}}+\frac{2 \sqrt{c+d x} \left(-3 a d^2+7 b c d+b d^2 x\right)}{3 b^2}-\frac{2 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a}","\frac{2 (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{a b^{5/2}}+\frac{2 d \sqrt{c+d x} (2 b c-a d)}{b^2}-\frac{2 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a}+\frac{2 d (c+d x)^{3/2}}{3 b}",1,"(2*Sqrt[c + d*x]*(7*b*c*d - 3*a*d^2 + b*d^2*x))/(3*b^2) - (2*(-(b*c) + a*d)^(5/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(a*b^(5/2)) - (2*c^(5/2)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/a","A",1
460,1,132,128,0.2369928,"\int \frac{(c+d x)^{5/2}}{x^2 (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^2*(a + b*x)),x]","\frac{2 (a d-b c)^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{a^2 b^{3/2}}+\frac{\left(2 b c^{5/2}-5 a c^{3/2} d\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^2}+\frac{\sqrt{c+d x} \left(2 a d^2 x-b c^2\right)}{a b x}","-\frac{2 (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{a^2 b^{3/2}}+\frac{c^{3/2} (2 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^2}+\frac{d \sqrt{c+d x} (2 a d+b c)}{a b}-\frac{c (c+d x)^{3/2}}{a x}",1,"(Sqrt[c + d*x]*(-(b*c^2) + 2*a*d^2*x))/(a*b*x) + (2*(-(b*c) + a*d)^(5/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(a^2*b^(3/2)) + ((2*b*c^(5/2) - 5*a*c^(3/2)*d)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/a^2","A",1
461,1,157,151,0.3484469,"\int \frac{(c+d x)^{5/2}}{x^3 (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^3*(a + b*x)),x]","-\frac{2 (a d-b c)^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{a^3 \sqrt{b}}+\frac{\sqrt{c+d x} \left(-2 a c^2-9 a c d x+4 b c^2 x\right)}{4 a^2 x^2}+\frac{\left(-15 a^2 \sqrt{c} d^2+20 a b c^{3/2} d-8 b^2 c^{5/2}\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{4 a^3}","\frac{2 (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{a^3 \sqrt{b}}+\frac{c \sqrt{c+d x} (4 b c-7 a d)}{4 a^2 x}-\frac{\sqrt{c} \left(15 a^2 d^2-20 a b c d+8 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{4 a^3}-\frac{c (c+d x)^{3/2}}{2 a x^2}",1,"(Sqrt[c + d*x]*(-2*a*c^2 + 4*b*c^2*x - 9*a*c*d*x))/(4*a^2*x^2) - (2*(-(b*c) + a*d)^(5/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(a^3*Sqrt[b]) + ((-8*b^2*c^(5/2) + 20*a*b*c^(3/2)*d - 15*a^2*Sqrt[c]*d^2)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/(4*a^3)","A",1
462,1,201,207,0.4544113,"\int \frac{(c+d x)^{5/2}}{x^4 (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^4*(a + b*x)),x]","\frac{2 \sqrt{b} (a d-b c)^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{a^4}+\frac{\sqrt{c+d x} \left(-8 a^2 c^2-26 a^2 c d x-33 a^2 d^2 x^2+12 a b c^2 x+54 a b c d x^2-24 b^2 c^2 x^2\right)}{24 a^3 x^3}+\frac{\left(-5 a^3 d^3+30 a^2 b c d^2-40 a b^2 c^2 d+16 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{8 a^4 \sqrt{c}}","-\frac{2 \sqrt{b} (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{a^4}+\frac{c \sqrt{c+d x} (2 b c-3 a d)}{4 a^2 x^2}-\frac{\sqrt{c+d x} \left(11 a^2 d^2-18 a b c d+8 b^2 c^2\right)}{8 a^3 x}+\frac{\left(-5 a^3 d^3+30 a^2 b c d^2-40 a b^2 c^2 d+16 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{8 a^4 \sqrt{c}}-\frac{c (c+d x)^{3/2}}{3 a x^3}",1,"(Sqrt[c + d*x]*(-8*a^2*c^2 + 12*a*b*c^2*x - 26*a^2*c*d*x - 24*b^2*c^2*x^2 + 54*a*b*c*d*x^2 - 33*a^2*d^2*x^2))/(24*a^3*x^3) + (2*Sqrt[b]*(-(b*c) + a*d)^(5/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/a^4 + ((16*b^3*c^3 - 40*a*b^2*c^2*d + 30*a^2*b*c*d^2 - 5*a^3*d^3)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/(8*a^4*Sqrt[c])","A",1
463,0,0,199,15.4749621,"\int \frac{1}{\sqrt[3]{x} \sqrt{c+d x} (4 c+d x)} \, dx","IntegrateAlgebraic[1/(x^(1/3)*Sqrt[c + d*x]*(4*c + d*x)),x]","\int \frac{1}{\sqrt[3]{x} \sqrt{c+d x} (4 c+d x)} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{2} \sqrt[3]{d} \sqrt[3]{x}\right)}{\sqrt{c+d x}}\right)}{2^{2/3} \sqrt{3} c^{5/6} d^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{3} \sqrt{c}}\right)}{2^{2/3} \sqrt{3} c^{5/6} d^{2/3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{c} \left(\sqrt[3]{c}-\sqrt[3]{2} \sqrt[3]{d} \sqrt[3]{x}\right)}{\sqrt{c+d x}}\right)}{2^{2/3} c^{5/6} d^{2/3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{3\ 2^{2/3} c^{5/6} d^{2/3}}",1,"Could not integrate","F",-1
464,0,0,143,15.7174289,"\int \frac{1}{\sqrt[3]{x} (8 c-d x) \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/(x^(1/3)*(8*c - d*x)*Sqrt[c + d*x]),x]","\int \frac{1}{\sqrt[3]{x} (8 c-d x) \sqrt{c+d x}} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} \sqrt[3]{x}\right)}{\sqrt{c+d x}}\right)}{2 \sqrt{3} c^{5/6} d^{2/3}}+\frac{\tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} \sqrt[3]{x}\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x}}\right)}{6 c^{5/6} d^{2/3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x}}{3 \sqrt{c}}\right)}{6 c^{5/6} d^{2/3}}",1,"Could not integrate","F",-1
465,1,138,140,0.3216172,"\int \frac{\sqrt{c+d x}}{x^2 (a+b x)^2} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(x^2*(a + b*x)^2),x]","\frac{\left(3 a \sqrt{b} d-4 b^{3/2} c\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{a^3 \sqrt{a d-b c}}+\frac{(4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3 \sqrt{c}}+\frac{(-a-2 b x) \sqrt{c+d x}}{a^2 x (a+b x)}","-\frac{\sqrt{b} (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{a^3 \sqrt{b c-a d}}+\frac{(4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3 \sqrt{c}}-\frac{2 b \sqrt{c+d x}}{a^2 (a+b x)}-\frac{\sqrt{c+d x}}{a x (a+b x)}",1,"((-a - 2*b*x)*Sqrt[c + d*x])/(a^2*x*(a + b*x)) + ((-4*b^(3/2)*c + 3*a*Sqrt[b]*d)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(a^3*Sqrt[-(b*c) + a*d]) + ((4*b*c - a*d)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/(a^3*Sqrt[c])","A",1
466,1,126,115,0.3800746,"\int \frac{(c+d x)^{3/2}}{x (a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(x*(a + b*x)^2),x]","-\frac{\sqrt{a d-b c} (a d+2 b c) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{a^2 b^{3/2}}-\frac{2 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^2}+\frac{\sqrt{c+d x} (b c-a d)}{a b (a+b x)}","\frac{\sqrt{b c-a d} (a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{a^2 b^{3/2}}-\frac{2 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^2}+\frac{\sqrt{c+d x} (b c-a d)}{a b (a+b x)}",1,"((b*c - a*d)*Sqrt[c + d*x])/(a*b*(a + b*x)) - (Sqrt[-(b*c) + a*d]*(2*b*c + a*d)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(a^2*b^(3/2)) - (2*c^(3/2)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/a^2","A",1
467,1,158,149,0.3449844,"\int \frac{(c+d x)^{3/2}}{x^2 (a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(x^2*(a + b*x)^2),x]","\frac{\left(4 b c^{3/2}-3 a \sqrt{c} d\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3}+\frac{\sqrt{c+d x} (-a c+a d x-2 b c x)}{a^2 x (a+b x)}+\frac{\left(-a^2 d^2+5 a b c d-4 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{a^3 \sqrt{b} \sqrt{a d-b c}}","\frac{\sqrt{c} (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3}-\frac{\sqrt{b c-a d} (4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{a^3 \sqrt{b}}-\frac{\sqrt{c+d x} (2 b c-a d)}{a^2 (a+b x)}-\frac{c \sqrt{c+d x}}{a x (a+b x)}",1,"(Sqrt[c + d*x]*(-(a*c) - 2*b*c*x + a*d*x))/(a^2*x*(a + b*x)) + ((-4*b^2*c^2 + 5*a*b*c*d - a^2*d^2)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(a^3*Sqrt[b]*Sqrt[-(b*c) + a*d]) + ((4*b*c^(3/2) - 3*a*Sqrt[c]*d)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/a^3","A",1
468,1,342,220,0.3372801,"\int \frac{x^3 (c+d x)^{5/2}}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x^3*(c + d*x)^(5/2))/(a + b*x)^2,x]","\frac{\sqrt{c+d x} \left(3465 a^5 d^4-6510 a^4 b c d^3+2310 a^4 b d^4 x+3213 a^3 b^2 c^2 d^2-4494 a^3 b^2 c d^3 x-462 a^3 b^2 d^4 x^2-180 a^2 b^3 c^3 d+2358 a^2 b^3 c^2 d^2 x+846 a^2 b^3 c d^3 x^2+198 a^2 b^3 d^4 x^3-20 a b^4 c^4-170 a b^4 c^3 d x-390 a b^4 c^2 d^2 x^2-350 a b^4 c d^3 x^3-110 a b^4 d^4 x^4-20 b^5 c^4 x+10 b^5 c^3 d x^2+150 b^5 c^2 d^2 x^3+190 b^5 c d^3 x^4+70 b^5 d^4 x^5\right)}{315 b^6 d^2 (a+b x)}-\frac{(a d-b c)^{3/2} \left(6 a^2 b c-11 a^3 d\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{b^{13/2}}","-\frac{a^2 (6 b c-11 a d) (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{13/2}}+\frac{a^2 \sqrt{c+d x} (6 b c-11 a d) (b c-a d)}{b^6}+\frac{a^2 (c+d x)^{3/2} (6 b c-11 a d)}{3 b^5}-\frac{(c+d x)^{5/2} \left(-693 a^2 d^2-5 b d x (10 b c-99 a d)+180 a b c d+20 b^2 c^2\right)}{315 b^4 d^2}-\frac{x^3 (c+d x)^{5/2}}{b (a+b x)}+\frac{11 x^2 (c+d x)^{5/2}}{9 b^2}",1,"(Sqrt[c + d*x]*(-20*a*b^4*c^4 - 180*a^2*b^3*c^3*d + 3213*a^3*b^2*c^2*d^2 - 6510*a^4*b*c*d^3 + 3465*a^5*d^4 - 20*b^5*c^4*x - 170*a*b^4*c^3*d*x + 2358*a^2*b^3*c^2*d^2*x - 4494*a^3*b^2*c*d^3*x + 2310*a^4*b*d^4*x + 10*b^5*c^3*d*x^2 - 390*a*b^4*c^2*d^2*x^2 + 846*a^2*b^3*c*d^3*x^2 - 462*a^3*b^2*d^4*x^2 + 150*b^5*c^2*d^2*x^3 - 350*a*b^4*c*d^3*x^3 + 198*a^2*b^3*d^4*x^3 + 190*b^5*c*d^3*x^4 - 110*a*b^4*d^4*x^4 + 70*b^5*d^4*x^5))/(315*b^6*d^2*(a + b*x)) - ((-(b*c) + a*d)^(3/2)*(6*a^2*b*c - 11*a^3*d)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/b^(13/2)","A",1
469,1,252,204,0.3008922,"\int \frac{x^2 (c+d x)^{5/2}}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x^2*(c + d*x)^(5/2))/(a + b*x)^2,x]","\frac{\left(4 a b c-9 a^2 d\right) (a d-b c)^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{b^{11/2}}+\frac{\sqrt{c+d x} \left(-945 a^4 d^3+1680 a^3 b c d^2-630 a^3 b d^3 x-749 a^2 b^2 c^2 d+1162 a^2 b^2 c d^2 x+126 a^2 b^2 d^3 x^2+30 a b^3 c^3-554 a b^3 c^2 d x-218 a b^3 c d^2 x^2-54 a b^3 d^3 x^3+30 b^4 c^3 x+90 b^4 c^2 d x^2+90 b^4 c d^2 x^3+30 b^4 d^3 x^4\right)}{105 b^5 d (a+b x)}","-\frac{a^2 (c+d x)^{7/2}}{b^2 (a+b x) (b c-a d)}+\frac{a (4 b c-9 a d) (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{11/2}}-\frac{a \sqrt{c+d x} (4 b c-9 a d) (b c-a d)}{b^5}-\frac{a (c+d x)^{3/2} (4 b c-9 a d)}{3 b^4}-\frac{a (c+d x)^{5/2} (4 b c-9 a d)}{5 b^3 (b c-a d)}+\frac{2 (c+d x)^{7/2}}{7 b^2 d}",1,"(Sqrt[c + d*x]*(30*a*b^3*c^3 - 749*a^2*b^2*c^2*d + 1680*a^3*b*c*d^2 - 945*a^4*d^3 + 30*b^4*c^3*x - 554*a*b^3*c^2*d*x + 1162*a^2*b^2*c*d^2*x - 630*a^3*b*d^3*x + 90*b^4*c^2*d*x^2 - 218*a*b^3*c*d^2*x^2 + 126*a^2*b^2*d^3*x^2 + 90*b^4*c*d^2*x^3 - 54*a*b^3*d^3*x^3 + 30*b^4*d^3*x^4))/(105*b^5*d*(a + b*x)) + ((-(b*c) + a*d)^(3/2)*(4*a*b*c - 9*a^2*d)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/b^(11/2)","A",1
470,1,177,178,0.1880637,"\int \frac{x (c+d x)^{5/2}}{(a+b x)^2} \, dx","IntegrateAlgebraic[(x*(c + d*x)^(5/2))/(a + b*x)^2,x]","\frac{\sqrt{c+d x} \left(105 a^3 d^2-170 a^2 b c d+70 a^2 b d^2 x+61 a b^2 c^2-118 a b^2 c d x-14 a b^2 d^2 x^2+46 b^3 c^2 x+22 b^3 c d x^2+6 b^3 d^2 x^3\right)}{15 b^4 (a+b x)}-\frac{(2 b c-7 a d) (a d-b c)^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{b^{9/2}}","-\frac{(2 b c-7 a d) (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{9/2}}+\frac{\sqrt{c+d x} (2 b c-7 a d) (b c-a d)}{b^4}+\frac{(c+d x)^{3/2} (2 b c-7 a d)}{3 b^3}+\frac{(c+d x)^{5/2} (2 b c-7 a d)}{5 b^2 (b c-a d)}+\frac{a (c+d x)^{7/2}}{b (a+b x) (b c-a d)}",1,"(Sqrt[c + d*x]*(61*a*b^2*c^2 - 170*a^2*b*c*d + 105*a^3*d^2 + 46*b^3*c^2*x - 118*a*b^2*c*d*x + 70*a^2*b*d^2*x + 22*b^3*c*d*x^2 - 14*a*b^2*d^2*x^2 + 6*b^3*d^2*x^3))/(15*b^4*(a + b*x)) - ((2*b*c - 7*a*d)*(-(b*c) + a*d)^(3/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/b^(9/2)","A",1
471,1,132,110,0.0005886,"\int \frac{(c+d x)^{5/2}}{(a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(a + b*x)^2,x]","\frac{\sqrt{c+d x} \left(-15 a^2 d^2+20 a b c d-10 a b d^2 x-3 b^2 c^2+14 b^2 c d x+2 b^2 d^2 x^2\right)}{3 b^3 (a+b x)}-\frac{5 d (a d-b c)^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{b^{7/2}}","-\frac{5 d (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{7/2}}+\frac{5 d \sqrt{c+d x} (b c-a d)}{b^3}-\frac{(c+d x)^{5/2}}{b (a+b x)}+\frac{5 d (c+d x)^{3/2}}{3 b^2}",1,"(Sqrt[c + d*x]*(-3*b^2*c^2 + 20*a*b*c*d - 15*a^2*d^2 + 14*b^2*c*d*x - 10*a*b*d^2*x + 2*b^2*d^2*x^2))/(3*b^3*(a + b*x)) - (5*d*(-(b*c) + a*d)^(3/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/b^(7/2)","A",1
472,1,148,142,0.2856308,"\int \frac{(c+d x)^{5/2}}{x (a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x*(a + b*x)^2),x]","\frac{(a d-b c)^{3/2} (3 a d+2 b c) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{a^2 b^{5/2}}+\frac{\sqrt{c+d x} \left(3 a^2 d^2-2 a b c d+2 a b d^2 x+b^2 c^2\right)}{a b^2 (a+b x)}-\frac{2 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^2}","\frac{(b c-a d)^{3/2} (3 a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{a^2 b^{5/2}}-\frac{2 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^2}-\frac{d \sqrt{c+d x} (b c-3 a d)}{a b^2}+\frac{(c+d x)^{3/2} (b c-a d)}{a b (a+b x)}",1,"(Sqrt[c + d*x]*(b^2*c^2 - 2*a*b*c*d + 3*a^2*d^2 + 2*a*b*d^2*x))/(a*b^2*(a + b*x)) + ((-(b*c) + a*d)^(3/2)*(2*b*c + 3*a*d)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(a^2*b^(5/2)) - (2*c^(5/2)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/a^2","A",1
473,1,166,147,0.3057589,"\int \frac{(c+d x)^{5/2}}{x^2 (a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^2*(a + b*x)^2),x]","-\frac{(a d+4 b c) (a d-b c)^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{a^3 b^{3/2}}+\frac{\left(4 b c^{5/2}-5 a c^{3/2} d\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3}+\frac{\sqrt{c+d x} \left(-a^2 d^2 x-a b c^2+2 a b c d x-2 b^2 c^2 x\right)}{a^2 b x (a+b x)}","-\frac{(b c-a d)^{3/2} (a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{a^3 b^{3/2}}+\frac{c^{3/2} (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3}-\frac{\sqrt{c+d x} (b c-a d)^2}{a^2 b (a+b x)}-\frac{c^2 \sqrt{c+d x}}{a^2 x}",1,"(Sqrt[c + d*x]*(-(a*b*c^2) - 2*b^2*c^2*x + 2*a*b*c*d*x - a^2*d^2*x))/(a^2*b*x*(a + b*x)) - ((-(b*c) + a*d)^(3/2)*(4*b*c + a*d)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(a^3*b^(3/2)) + ((4*b*c^(5/2) - 5*a*c^(3/2)*d)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/a^3","A",1
474,1,208,219,0.5414247,"\int \frac{(c+d x)^{5/2}}{x^3 (a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^3*(a + b*x)^2),x]","\frac{(6 b c-a d) (a d-b c)^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{a^4 \sqrt{b}}+\frac{\left(-15 a^2 \sqrt{c} d^2+40 a b c^{3/2} d-24 b^2 c^{5/2}\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{4 a^4}+\frac{\sqrt{c+d x} \left(-2 a^2 c^2-9 a^2 c d x+4 a^2 d^2 x^2+6 a b c^2 x-17 a b c d x^2+12 b^2 c^2 x^2\right)}{4 a^3 x^2 (a+b x)}","\frac{(6 b c-a d) (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{a^4 \sqrt{b}}+\frac{c \sqrt{c+d x} (6 b c-7 a d)}{4 a^2 x (a+b x)}-\frac{\sqrt{c} \left(15 a^2 d^2-40 a b c d+24 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{4 a^4}+\frac{\sqrt{c+d x} \left(4 a^2 d^2-17 a b c d+12 b^2 c^2\right)}{4 a^3 (a+b x)}-\frac{c (c+d x)^{3/2}}{2 a x^2 (a+b x)}",1,"(Sqrt[c + d*x]*(-2*a^2*c^2 + 6*a*b*c^2*x - 9*a^2*c*d*x + 12*b^2*c^2*x^2 - 17*a*b*c*d*x^2 + 4*a^2*d^2*x^2))/(4*a^3*x^2*(a + b*x)) + ((6*b*c - a*d)*(-(b*c) + a*d)^(3/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(a^4*Sqrt[b]) + ((-24*b^2*c^(5/2) + 40*a*b*c^(3/2)*d - 15*a^2*Sqrt[c]*d^2)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/(4*a^4)","A",1
475,1,260,284,0.7250499,"\int \frac{(c+d x)^{5/2}}{x^4 (a+b x)^2} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^4*(a + b*x)^2),x]","-\frac{\left(8 b^{3/2} c-3 a \sqrt{b} d\right) (a d-b c)^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{a^5}+\frac{\left(-5 a^3 d^3+60 a^2 b c d^2-120 a b^2 c^2 d+64 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{8 a^5 \sqrt{c}}+\frac{\sqrt{c+d x} \left(-8 a^3 c^2-26 a^3 c d x-33 a^3 d^2 x^2+16 a^2 b c^2 x+82 a^2 b c d x^2-57 a^2 b d^2 x^3-48 a b^2 c^2 x^2+156 a b^2 c d x^3-96 b^3 c^2 x^3\right)}{24 a^4 x^3 (a+b x)}","-\frac{\sqrt{b} (8 b c-3 a d) (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{a^5}+\frac{c \sqrt{c+d x} (8 b c-9 a d)}{12 a^2 x^2 (a+b x)}-\frac{b \sqrt{c+d x} \left(19 a^2 d^2-52 a b c d+32 b^2 c^2\right)}{8 a^4 (a+b x)}-\frac{\sqrt{c+d x} \left(33 a^2 d^2-82 a b c d+48 b^2 c^2\right)}{24 a^3 x (a+b x)}+\frac{\left(-5 a^3 d^3+60 a^2 b c d^2-120 a b^2 c^2 d+64 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{8 a^5 \sqrt{c}}-\frac{c (c+d x)^{3/2}}{3 a x^3 (a+b x)}",1,"(Sqrt[c + d*x]*(-8*a^3*c^2 + 16*a^2*b*c^2*x - 26*a^3*c*d*x - 48*a*b^2*c^2*x^2 + 82*a^2*b*c*d*x^2 - 33*a^3*d^2*x^2 - 96*b^3*c^2*x^3 + 156*a*b^2*c*d*x^3 - 57*a^2*b*d^2*x^3))/(24*a^4*x^3*(a + b*x)) - ((-(b*c) + a*d)^(3/2)*(8*b^(3/2)*c - 3*a*Sqrt[b]*d)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/a^5 + ((64*b^3*c^3 - 120*a*b^2*c^2*d + 60*a^2*b*c*d^2 - 5*a^3*d^3)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/(8*a^5*Sqrt[c])","A",1
476,1,166,164,0.5891732,"\int \frac{1}{x^2 (a+b x)^2 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^2*Sqrt[c + d*x]),x]","\frac{\left(4 b^{5/2} c-5 a b^{3/2} d\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{a^3 (a d-b c)^{3/2}}+\frac{(a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3 c^{3/2}}+\frac{\sqrt{c+d x} \left(a^2 (-d)+a b c-a b d x+2 b^2 c x\right)}{a^2 c x (a+b x) (a d-b c)}","-\frac{b^{3/2} (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{a^3 (b c-a d)^{3/2}}+\frac{(a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3 c^{3/2}}-\frac{b \sqrt{c+d x} (2 b c-a d)}{a^2 c (a+b x) (b c-a d)}-\frac{\sqrt{c+d x}}{a c x (a+b x)}",1,"(Sqrt[c + d*x]*(a*b*c - a^2*d + 2*b^2*c*x - a*b*d*x))/(a^2*c*(-(b*c) + a*d)*x*(a + b*x)) + ((4*b^(5/2)*c - 5*a*b^(3/2)*d)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(a^3*(-(b*c) + a*d)^(3/2)) + ((4*b*c + a*d)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/(a^3*c^(3/2))","A",1
477,1,247,216,0.7679187,"\int \frac{1}{x^2 (a+b x)^2 (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^2*(c + d*x)^(3/2)),x]","\frac{\left(7 a b^{5/2} d-4 b^{7/2} c\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{a^3 (a d-b c)^{5/2}}+\frac{(3 a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3 c^{5/2}}+\frac{a^3 (-c) d^2-3 a^3 d^3 x+2 a^2 b c^2 d+a^2 b c d^2 x-3 a^2 b d^3 x^2-a b^2 c^3+a b^2 c^2 d x+2 a b^2 c d^2 x^2-2 b^3 c^3 x-2 b^3 c^2 d x^2}{a^2 c^2 x (a+b x) \sqrt{c+d x} (a d-b c)^2}","-\frac{b^{5/2} (4 b c-7 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{a^3 (b c-a d)^{5/2}}+\frac{(3 a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3 c^{5/2}}-\frac{d \left(3 a^2 d^2-2 a b c d+2 b^2 c^2\right)}{a^2 c^2 \sqrt{c+d x} (b c-a d)^2}-\frac{b (2 b c-a d)}{a^2 c (a+b x) \sqrt{c+d x} (b c-a d)}-\frac{1}{a c x (a+b x) \sqrt{c+d x}}",1,"(-(a*b^2*c^3) + 2*a^2*b*c^2*d - a^3*c*d^2 - 2*b^3*c^3*x + a*b^2*c^2*d*x + a^2*b*c*d^2*x - 3*a^3*d^3*x - 2*b^3*c^2*d*x^2 + 2*a*b^2*c*d^2*x^2 - 3*a^2*b*d^3*x^2)/(a^2*c^2*(-(b*c) + a*d)^2*x*(a + b*x)*Sqrt[c + d*x]) + ((-4*b^(7/2)*c + 7*a*b^(5/2)*d)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(a^3*(-(b*c) + a*d)^(5/2)) + ((4*b*c + 3*a*d)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/(a^3*c^(5/2))","A",1
478,1,373,277,0.9393636,"\int \frac{1}{x^2 (a+b x)^2 (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^2*(c + d*x)^(5/2)),x]","\frac{\left(4 b^{9/2} c-9 a b^{7/2} d\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{a^3 (a d-b c)^{7/2}}+\frac{(5 a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3 c^{7/2}}+\frac{-3 a^4 c^2 d^3-20 a^4 c d^4 x-15 a^4 d^5 x^2+9 a^3 b c^3 d^2+41 a^3 b c^2 d^3 x+13 a^3 b c d^4 x^2-15 a^3 b d^5 x^3-9 a^2 b^2 c^4 d-9 a^2 b^2 c^3 d^2 x+35 a^2 b^2 c^2 d^3 x^2+33 a^2 b^2 c d^4 x^3+3 a b^3 c^5-3 a b^3 c^4 d x-15 a b^3 c^3 d^2 x^2-9 a b^3 c^2 d^3 x^3+6 b^4 c^5 x+12 b^4 c^4 d x^2+6 b^4 c^3 d^2 x^3}{3 a^2 c^3 x (a+b x) (c+d x)^{3/2} (a d-b c)^3}","-\frac{b^{7/2} (4 b c-9 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{a^3 (b c-a d)^{7/2}}+\frac{(5 a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3 c^{7/2}}-\frac{d \left(5 a^2 d^2-6 a b c d+6 b^2 c^2\right)}{3 a^2 c^2 (c+d x)^{3/2} (b c-a d)^2}-\frac{d (2 b c-a d) \left(5 a^2 d^2-a b c d+b^2 c^2\right)}{a^2 c^3 \sqrt{c+d x} (b c-a d)^3}-\frac{b (2 b c-a d)}{a^2 c (a+b x) (c+d x)^{3/2} (b c-a d)}-\frac{1}{a c x (a+b x) (c+d x)^{3/2}}",1,"(3*a*b^3*c^5 - 9*a^2*b^2*c^4*d + 9*a^3*b*c^3*d^2 - 3*a^4*c^2*d^3 + 6*b^4*c^5*x - 3*a*b^3*c^4*d*x - 9*a^2*b^2*c^3*d^2*x + 41*a^3*b*c^2*d^3*x - 20*a^4*c*d^4*x + 12*b^4*c^4*d*x^2 - 15*a*b^3*c^3*d^2*x^2 + 35*a^2*b^2*c^2*d^3*x^2 + 13*a^3*b*c*d^4*x^2 - 15*a^4*d^5*x^2 + 6*b^4*c^3*d^2*x^3 - 9*a*b^3*c^2*d^3*x^3 + 33*a^2*b^2*c*d^4*x^3 - 15*a^3*b*d^5*x^3)/(3*a^2*c^3*(-(b*c) + a*d)^3*x*(a + b*x)*(c + d*x)^(3/2)) + ((4*b^(9/2)*c - 9*a*b^(7/2)*d)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(a^3*(-(b*c) + a*d)^(7/2)) + ((4*b*c + 5*a*d)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/(a^3*c^(7/2))","A",1
479,1,6957,192,95.3333677,"\int x^{5/2} \sqrt{a+b x} (A+B x) \, dx","IntegrateAlgebraic[x^(5/2)*Sqrt[a + b*x]*(A + B*x),x]","\text{Result too large to show}","-\frac{a^4 (10 A b-7 a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{128 b^{9/2}}+\frac{a^3 \sqrt{x} \sqrt{a+b x} (10 A b-7 a B)}{128 b^4}-\frac{a^2 x^{3/2} \sqrt{a+b x} (10 A b-7 a B)}{192 b^3}+\frac{a x^{5/2} \sqrt{a+b x} (10 A b-7 a B)}{240 b^2}+\frac{x^{7/2} \sqrt{a+b x} (10 A b-7 a B)}{40 b}+\frac{B x^{7/2} (a+b x)^{3/2}}{5 b}",1,"Result too large to show","B",0
480,1,4557,159,48.8284552,"\int x^{3/2} \sqrt{a+b x} (A+B x) \, dx","IntegrateAlgebraic[x^(3/2)*Sqrt[a + b*x]*(A + B*x),x]","\text{Result too large to show}","\frac{a^3 (8 A b-5 a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{64 b^{7/2}}-\frac{a^2 \sqrt{x} \sqrt{a+b x} (8 A b-5 a B)}{64 b^3}+\frac{a x^{3/2} \sqrt{a+b x} (8 A b-5 a B)}{96 b^2}+\frac{x^{5/2} \sqrt{a+b x} (8 A b-5 a B)}{24 b}+\frac{B x^{5/2} (a+b x)^{3/2}}{4 b}",1,"((3072*a^10*A*b + 5632*a^9*A*b^2 - 6784*a^8*A*b^3 - 22720*a^7*A*b^4 - 18624*a^6*A*b^5 - 5760*a^5*A*b^6 - 512*a^4*A*b^7 - 1920*a^11*B - 3520*a^10*b*B - 1904*a^9*b^2*B - 7304*a^8*b^3*B - 16776*a^7*b^4*B - 13680*a^6*b^5*B - 4288*a^5*b^6*B - 384*a^4*b^7*B)*Sqrt[a + b*x] + (-3072*a^10*A*b + 6144*a^9*A*b^2 + 15616*a^8*A*b^3 - 32000*a^7*A*b^4 - 82264*a^6*A*b^5 - 56256*a^5*A*b^6 - 12928*a^4*A*b^7 - 512*a^3*A*b^8 + 1920*a^11*B - 3840*a^10*b*B - 9760*a^9*b^2*B - 4576*a^8*b^3*B - 28457*a^7*b^4*B - 60072*a^6*b^5*B - 41456*a^5*b^6*B - 9664*a^4*b^7*B - 384*a^3*b^8*B)*Sqrt[x]*Sqrt[a + b*x] + (-7680*a^9*A*b^2 + 9984*a^8*A*b^3 + 9792*a^7*A*b^4 - 100224*a^6*A*b^5 - 164736*a^5*A*b^6 - 84480*a^4*A*b^7 - 12288*a^3*A*b^8 + 4800*a^10*b*B - 6240*a^9*b^2*B - 15336*a^8*b^3*B - 15696*a^7*b^4*B - 77904*a^6*b^5*B - 120000*a^5*b^6*B - 62592*a^4*b^7*B - 9216*a^3*b^8*B)*x*Sqrt[a + b*x] + (-4096*a^9*A*b^2 - 15872*a^8*A*b^3 + 11520*a^7*A*b^4 - 23904*a^6*A*b^5 - 184752*a^5*A*b^6 - 208640*a^4*A*b^7 - 75520*a^3*A*b^8 - 5120*a^2*A*b^9 + 2560*a^10*b*B + 9920*a^9*b^2*B - 7200*a^8*b^3*B - 15780*a^7*b^4*B - 38130*a^6*b^5*B - 136480*a^5*b^6*B - 152480*a^4*b^7*B - 56320*a^3*b^8*B - 3840*a^2*b^9*B)*x^(3/2)*Sqrt[a + b*x] + (-11392*a^8*A*b^3 - 23616*a^7*A*b^4 + 3072*a^6*A*b^5 - 70656*a^5*A*b^6 - 217600*a^4*A*b^7 - 174080*a^3*A*b^8 - 40960*a^2*A*b^9 + 7120*a^9*b^2*B + 14760*a^8*b^3*B - 5760*a^7*b^4*B - 15360*a^6*b^5*B - 63680*a^5*b^6*B - 158080*a^4*b^7*B - 128000*a^3*b^8*B - 30720*a^2*b^9*B)*x^2*Sqrt[a + b*x] + (8448*a^8*A*b^3 + 2304*a^7*A*b^4 - 12624*a^6*A*b^5 - 7296*a^5*A*b^6 - 87360*a^4*A*b^7 - 167424*a^3*A*b^8 - 95232*a^2*A*b^9 - 12288*a*A*b^10 + 864*a^9*b^2*B + 10848*a^8*b^3*B + 15570*a^7*b^4*B - 3120*a^6*b^5*B - 15624*a^5*b^6*B - 68160*a^4*b^7*B - 121344*a^3*b^8*B - 70656*a^2*b^9*B - 9216*a*b^10*B)*x^(5/2)*Sqrt[a + b*x] + (36544*a^7*A*b^4 + 52608*a^6*A*b^5 + 15360*a^5*A*b^6 - 9216*a^4*A*b^7 - 59392*a^3*A*b^8 - 81920*a^2*A*b^9 - 32768*a*A*b^10 + 1736*a^8*b^3*B + 10128*a^7*b^4*B + 11520*a^6*b^5*B - 1536*a^5*b^6*B - 12416*a^4*b^7*B - 44032*a^3*b^8*B - 59392*a^2*b^9*B - 24576*a*b^10*B)*x^3*Sqrt[a + b*x] + (18176*a^7*A*b^4 + 108064*a^6*A*b^5 + 124704*a^5*A*b^6 + 36096*a^4*A*b^7 - 3840*a^3*A*b^8 - 19456*a^2*A*b^9 - 22528*a*A*b^10 - 8192*A*b^11 + 7072*a^8*b^3*B + 15404*a^7*b^4*B + 14220*a^6*b^5*B + 7584*a^5*b^6*B - 624*a^4*b^7*B - 5120*a^3*b^8*B - 14336*a^2*b^9*B - 16384*a*b^10*B - 6144*b^11*B)*x^(7/2)*Sqrt[a + b*x] + (63168*a^6*A*b^5 + 196224*a^5*A*b^6 + 161280*a^4*A*b^7 + 30720*a^3*A*b^8 + 28104*a^7*b^4*B + 49392*a^6*b^5*B + 25536*a^5*b^6*B + 4992*a^4*b^7*B)*x^4*Sqrt[a + b*x] + (10728*a^6*A*b^5 + 121536*a^5*A*b^6 + 233600*a^4*A*b^7 + 130048*a^3*A*b^8 + 11264*a^2*A*b^9 + 13263*a^7*b^4*B + 79176*a^6*b^5*B + 95440*a^5*b^6*B + 32192*a^4*b^7*B + 2176*a^3*b^8*B)*x^(9/2)*Sqrt[a + b*x] + (29568*a^5*A*b^6 + 146944*a^4*A*b^7 + 186368*a^3*A*b^8 + 65536*a^2*A*b^9 + 46032*a^6*b^5*B + 142016*a^5*b^6*B + 117376*a^4*b^7*B + 23552*a^3*b^8*B)*x^5*Sqrt[a + b*x] + (2064*a^5*A*b^6 + 39168*a^4*A*b^7 + 115200*a^3*A*b^8 + 98304*a^2*A*b^9 + 18432*a*A*b^10 + 7926*a^6*b^5*B + 88992*a^5*b^6*B + 169440*a^4*b^7*B + 93696*a^3*b^8*B + 8448*a^2*b^9*B)*x^(11/2)*Sqrt[a + b*x] + (3584*a^4*A*b^7 + 28672*a^3*A*b^8 + 57344*a^2*A*b^9 + 32768*a*A*b^10 + 21952*a^5*b^6*B + 108416*a^4*b^7*B + 136192*a^3*b^8*B + 47104*a^2*b^9*B)*x^6*Sqrt[a + b*x] + (64*a^4*A*b^7 + 2048*a^3*A*b^8 + 10240*a^2*A*b^9 + 16384*a*A*b^10 + 8192*A*b^11 + 1544*a^5*b^6*B + 29248*a^4*b^7*B + 85760*a^3*b^8*B + 72704*a^2*b^9*B + 13312*a*b^10*B)*x^(13/2)*Sqrt[a + b*x] + (2688*a^4*b^7*B + 21504*a^3*b^8*B + 43008*a^2*b^9*B + 24576*a*b^10*B)*x^7*Sqrt[a + b*x] + (48*a^4*b^7*B + 1536*a^3*b^8*B + 7680*a^2*b^9*B + 12288*a*b^10*B + 6144*b^11*B)*x^(15/2)*Sqrt[a + b*x] + Sqrt[a + b]*(-3072*a^10*A*b - 4096*a^9*A*b^2 + 8448*a^8*A*b^3 + 18176*a^7*A*b^4 + 10728*a^6*A*b^5 + 2064*a^5*A*b^6 + 64*a^4*A*b^7 + 1920*a^11*B + 2560*a^10*b*B + 864*a^9*b^2*B + 7072*a^8*b^3*B + 13263*a^7*b^4*B + 7926*a^6*b^5*B + 1544*a^5*b^6*B + 48*a^4*b^7*B + (3072*a^10*A*b - 7680*a^9*A*b^2 - 11392*a^8*A*b^3 + 36544*a^7*A*b^4 + 63168*a^6*A*b^5 + 29568*a^5*A*b^6 + 3584*a^4*A*b^7 - 1920*a^11*B + 4800*a^10*b*B + 7120*a^9*b^2*B + 1736*a^8*b^3*B + 28104*a^7*b^4*B + 46032*a^6*b^5*B + 21952*a^5*b^6*B + 2688*a^4*b^7*B)*Sqrt[x] + (6144*a^9*A*b^2 - 15872*a^8*A*b^3 + 2304*a^7*A*b^4 + 108064*a^6*A*b^5 + 121536*a^5*A*b^6 + 39168*a^4*A*b^7 + 2048*a^3*A*b^8 - 3840*a^10*b*B + 9920*a^9*b^2*B + 10848*a^8*b^3*B + 15404*a^7*b^4*B + 79176*a^6*b^5*B + 88992*a^5*b^6*B + 29248*a^4*b^7*B + 1536*a^3*b^8*B)*x + (5632*a^9*A*b^2 + 9984*a^8*A*b^3 - 23616*a^7*A*b^4 + 52608*a^6*A*b^5 + 196224*a^5*A*b^6 + 146944*a^4*A*b^7 + 28672*a^3*A*b^8 - 3520*a^10*b*B - 6240*a^9*b^2*B + 14760*a^8*b^3*B + 10128*a^7*b^4*B + 49392*a^6*b^5*B + 142016*a^5*b^6*B + 108416*a^4*b^7*B + 21504*a^3*b^8*B)*x^(3/2) + (15616*a^8*A*b^3 + 11520*a^7*A*b^4 - 12624*a^6*A*b^5 + 124704*a^5*A*b^6 + 233600*a^4*A*b^7 + 115200*a^3*A*b^8 + 10240*a^2*A*b^9 - 9760*a^9*b^2*B - 7200*a^8*b^3*B + 15570*a^7*b^4*B + 14220*a^6*b^5*B + 95440*a^5*b^6*B + 169440*a^4*b^7*B + 85760*a^3*b^8*B + 7680*a^2*b^9*B)*x^2 + (-6784*a^8*A*b^3 + 9792*a^7*A*b^4 + 3072*a^6*A*b^5 + 15360*a^5*A*b^6 + 161280*a^4*A*b^7 + 186368*a^3*A*b^8 + 57344*a^2*A*b^9 - 1904*a^9*b^2*B - 15336*a^8*b^3*B - 5760*a^7*b^4*B + 11520*a^6*b^5*B + 25536*a^5*b^6*B + 117376*a^4*b^7*B + 136192*a^3*b^8*B + 43008*a^2*b^9*B)*x^(5/2) + (-32000*a^7*A*b^4 - 23904*a^6*A*b^5 - 7296*a^5*A*b^6 + 36096*a^4*A*b^7 + 130048*a^3*A*b^8 + 98304*a^2*A*b^9 + 16384*a*A*b^10 - 4576*a^8*b^3*B - 15780*a^7*b^4*B - 3120*a^6*b^5*B + 7584*a^5*b^6*B + 32192*a^4*b^7*B + 93696*a^3*b^8*B + 72704*a^2*b^9*B + 12288*a*b^10*B)*x^3 + (-22720*a^7*A*b^4 - 100224*a^6*A*b^5 - 70656*a^5*A*b^6 - 9216*a^4*A*b^7 + 30720*a^3*A*b^8 + 65536*a^2*A*b^9 + 32768*a*A*b^10 - 7304*a^8*b^3*B - 15696*a^7*b^4*B - 15360*a^6*b^5*B - 1536*a^5*b^6*B + 4992*a^4*b^7*B + 23552*a^3*b^8*B + 47104*a^2*b^9*B + 24576*a*b^10*B)*x^(7/2) + (-82264*a^6*A*b^5 - 184752*a^5*A*b^6 - 87360*a^4*A*b^7 - 3840*a^3*A*b^8 + 11264*a^2*A*b^9 + 18432*a*A*b^10 + 8192*A*b^11 - 28457*a^7*b^4*B - 38130*a^6*b^5*B - 15624*a^5*b^6*B - 624*a^4*b^7*B + 2176*a^3*b^8*B + 8448*a^2*b^9*B + 13312*a*b^10*B + 6144*b^11*B)*x^4 + (-18624*a^6*A*b^5 - 164736*a^5*A*b^6 - 217600*a^4*A*b^7 - 59392*a^3*A*b^8 - 16776*a^7*b^4*B - 77904*a^6*b^5*B - 63680*a^5*b^6*B - 12416*a^4*b^7*B)*x^(9/2) + (-56256*a^5*A*b^6 - 208640*a^4*A*b^7 - 167424*a^3*A*b^8 - 19456*a^2*A*b^9 - 60072*a^6*b^5*B - 136480*a^5*b^6*B - 68160*a^4*b^7*B - 5120*a^3*b^8*B)*x^5 + (-5760*a^5*A*b^6 - 84480*a^4*A*b^7 - 174080*a^3*A*b^8 - 81920*a^2*A*b^9 - 13680*a^6*b^5*B - 120000*a^5*b^6*B - 158080*a^4*b^7*B - 44032*a^3*b^8*B)*x^(11/2) + (-12928*a^4*A*b^7 - 75520*a^3*A*b^8 - 95232*a^2*A*b^9 - 22528*a*A*b^10 - 41456*a^5*b^6*B - 152480*a^4*b^7*B - 121344*a^3*b^8*B - 14336*a^2*b^9*B)*x^6 + (-512*a^4*A*b^7 - 12288*a^3*A*b^8 - 40960*a^2*A*b^9 - 32768*a*A*b^10 - 4288*a^5*b^6*B - 62592*a^4*b^7*B - 128000*a^3*b^8*B - 59392*a^2*b^9*B)*x^(13/2) + (-512*a^3*A*b^8 - 5120*a^2*A*b^9 - 12288*a*A*b^10 - 8192*A*b^11 - 9664*a^4*b^7*B - 56320*a^3*b^8*B - 70656*a^2*b^9*B - 16384*a*b^10*B)*x^7 + (-384*a^4*b^7*B - 9216*a^3*b^8*B - 30720*a^2*b^9*B - 24576*a*b^10*B)*x^(15/2) + (-384*a^3*b^8*B - 3840*a^2*b^9*B - 9216*a*b^10*B - 6144*b^11*B)*x^8))/(192*b^3*(128*a^8 + 256*a^7*b + 160*a^6*b^2 + 32*a^5*b^3 + a^4*b^4) + 192*b^3*(a^4*b^4 + 32*a^3*b^5 + 160*a^2*b^6 + 256*a*b^7 + 128*b^8)*x^4 + 192*b^3*Sqrt[a + b]*(-128*a^7 - 192*a^6*b - 80*a^5*b^2 - 8*a^4*b^3)*Sqrt[a + b*x] + x*(192*b^3*(256*a^7*b + 1472*a^6*b^2 + 1760*a^5*b^3 + 604*a^4*b^4 + 32*a^3*b^5) + 192*b^3*Sqrt[a + b]*(-192*a^6*b - 1248*a^5*b^2 - 1080*a^4*b^3 - 192*a^3*b^4)*Sqrt[a + b*x]) + Sqrt[x]*(192*b^3*(512*a^7*b + 896*a^6*b^2 + 448*a^5*b^3 + 56*a^4*b^4) + 192*b^3*Sqrt[a + b]*(-512*a^6*b - 640*a^5*b^2 - 192*a^4*b^3 - 8*a^3*b^4)*Sqrt[a + b*x]) + x^2*(192*b^3*(160*a^6*b^2 + 1760*a^5*b^3 + 3270*a^4*b^4 + 1760*a^3*b^5 + 160*a^2*b^6) + 192*b^3*Sqrt[a + b]*(-80*a^5*b^2 - 1080*a^4*b^3 - 1920*a^3*b^4 - 640*a^2*b^5)*Sqrt[a + b*x]) + x^(3/2)*(192*b^3*(896*a^6*b^2 + 2688*a^5*b^3 + 2184*a^4*b^4 + 448*a^3*b^5) + 192*b^3*Sqrt[a + b]*(-640*a^5*b^2 - 1920*a^4*b^3 - 1080*a^3*b^4 - 80*a^2*b^5)*Sqrt[a + b*x]) + x^3*(192*b^3*(32*a^5*b^3 + 604*a^4*b^4 + 1760*a^3*b^5 + 1472*a^2*b^6 + 256*a*b^7) + 192*b^3*Sqrt[a + b]*(-8*a^4*b^3 - 192*a^3*b^4 - 640*a^2*b^5 - 512*a*b^6)*Sqrt[a + b*x]) + x^(5/2)*(192*b^3*(448*a^5*b^3 + 2184*a^4*b^4 + 2688*a^3*b^5 + 896*a^2*b^6) + 192*b^3*Sqrt[a + b]*(-192*a^4*b^3 - 1080*a^3*b^4 - 1248*a^2*b^5 - 192*a*b^6)*Sqrt[a + b*x]) + x^(7/2)*(192*b^3*(56*a^4*b^4 + 448*a^3*b^5 + 896*a^2*b^6 + 512*a*b^7) + 192*b^3*Sqrt[a + b]*(-8*a^3*b^4 - 80*a^2*b^5 - 192*a*b^6 - 128*b^7)*Sqrt[a + b*x])) + (-1/4*(a^3*A)/b^(5/2) + (5*a^4*B)/(32*b^(7/2)))*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",1
481,1,2635,126,18.5128863,"\int \sqrt{x} \sqrt{a+b x} (A+B x) \, dx","IntegrateAlgebraic[Sqrt[x]*Sqrt[a + b*x]*(A + B*x),x]","\text{Result too large to show}","-\frac{a^2 (2 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 b^{5/2}}+\frac{a \sqrt{x} \sqrt{a+b x} (2 A b-a B)}{8 b^2}+\frac{x^{3/2} \sqrt{a+b x} (2 A b-a B)}{4 b}+\frac{B x^{3/2} (a+b x)^{3/2}}{3 b}",1,"((-192*a^7*A*b - 768*a^6*A*b^2 - 996*a^5*A*b^3 - 492*a^4*A*b^4 - 72*a^3*A*b^5 + 96*a^8*B + 128*a^7*b*B - 270*a^6*b^2*B - 570*a^5*b^3*B - 316*a^4*b^4*B - 48*a^3*b^5*B)*Sqrt[a + b*x] + (192*a^7*A*b - 288*a^6*A*b^2 - 2052*a^5*A*b^3 - 2478*a^4*A*b^4 - 972*a^3*A*b^5 - 72*a^2*A*b^6 - 96*a^8*B + 144*a^7*b*B + 258*a^6*b^2*B - 873*a^5*b^3*B - 1482*a^4*b^4*B - 636*a^3*b^5*B - 48*a^2*b^6*B)*Sqrt[x]*Sqrt[a + b*x] + (384*a^6*A*b^2 - 840*a^5*A*b^3 - 3588*a^4*A*b^4 - 3264*a^3*A*b^5 - 864*a^2*A*b^6 - 192*a^7*b*B + 164*a^6*b^2*B - 30*a^5*b^3*B - 1824*a^4*b^4*B - 2032*a^3*b^5*B - 576*a^2*b^6*B)*x*Sqrt[a + b*x] + (672*a^6*A*b^2 + 1368*a^5*A*b^3 - 1110*a^4*A*b^4 - 3888*a^3*A*b^5 - 2544*a^2*A*b^6 - 384*a*A*b^7 - 80*a^7*b*B - 300*a^6*b^2*B + 123*a^5*b^3*B - 512*a^4*b^4*B - 2184*a^3*b^5*B - 1632*a^2*b^6*B - 256*a*b^7*B)*x^(3/2)*Sqrt[a + b*x] + (1836*a^5*A*b^3 + 2460*a^4*A*b^4 - 864*a^3*A*b^5 - 2592*a^2*A*b^6 - 1152*a*A*b^7 - 150*a^6*b^2*B - 318*a^5*b^3*B - 672*a^3*b^5*B - 1536*a^2*b^6*B - 768*a*b^7*B)*x^2*Sqrt[a + b*x] + (684*a^5*A*b^3 + 3366*a^4*A*b^4 + 2832*a^3*A*b^5 - 336*a^2*A*b^6 - 960*a*A*b^7 - 384*A*b^8 + 298*a^6*b^2*B + 333*a^5*b^3*B - 48*a^4*b^4*B - 32*a^3*b^5*B - 336*a^2*b^6*B - 576*a*b^7*B - 256*b^8*B)*x^(5/2)*Sqrt[a + b*x] + (1620*a^4*A*b^4 + 3840*a^3*A*b^5 + 2016*a^2*A*b^6 + 918*a^5*b^3*B + 1120*a^4*b^4*B + 192*a^3*b^5*B)*x^3*Sqrt[a + b*x] + (222*a^4*A*b^4 + 2016*a^3*A*b^5 + 2736*a^2*A*b^6 + 768*a*A*b^7 + 417*a^5*b^3*B + 1896*a^4*b^4*B + 1536*a^3*b^5*B + 144*a^2*b^6*B)*x^(7/2)*Sqrt[a + b*x] + (360*a^3*A*b^5 + 1440*a^2*A*b^6 + 1152*a*A*b^7 + 1020*a^4*b^4*B + 2320*a^3*b^5*B + 1152*a^2*b^6*B)*x^4*Sqrt[a + b*x] + (12*a^3*A*b^5 + 216*a^2*A*b^6 + 576*a*A*b^7 + 384*A*b^8 + 146*a^4*b^4*B + 1308*a^3*b^5*B + 1728*a^2*b^6*B + 448*a*b^7*B)*x^(9/2)*Sqrt[a + b*x] + (240*a^3*b^5*B + 960*a^2*b^6*B + 768*a*b^7*B)*x^5*Sqrt[a + b*x] + (8*a^3*b^5*B + 144*a^2*b^6*B + 384*a*b^7*B + 256*b^8*B)*x^(11/2)*Sqrt[a + b*x] + Sqrt[a + b]*(192*a^7*A*b + 672*a^6*A*b^2 + 684*a^5*A*b^3 + 222*a^4*A*b^4 + 12*a^3*A*b^5 - 96*a^8*B - 80*a^7*b*B + 298*a^6*b^2*B + 417*a^5*b^3*B + 146*a^4*b^4*B + 8*a^3*b^5*B + (-192*a^7*A*b + 384*a^6*A*b^2 + 1836*a^5*A*b^3 + 1620*a^4*A*b^4 + 360*a^3*A*b^5 + 96*a^8*B - 192*a^7*b*B - 150*a^6*b^2*B + 918*a^5*b^3*B + 1020*a^4*b^4*B + 240*a^3*b^5*B)*Sqrt[x] + (-288*a^6*A*b^2 + 1368*a^5*A*b^3 + 3366*a^4*A*b^4 + 2016*a^3*A*b^5 + 216*a^2*A*b^6 + 144*a^7*b*B - 300*a^6*b^2*B + 333*a^5*b^3*B + 1896*a^4*b^4*B + 1308*a^3*b^5*B + 144*a^2*b^6*B)*x + (-768*a^6*A*b^2 - 840*a^5*A*b^3 + 2460*a^4*A*b^4 + 3840*a^3*A*b^5 + 1440*a^2*A*b^6 + 128*a^7*b*B + 164*a^6*b^2*B - 318*a^5*b^3*B + 1120*a^4*b^4*B + 2320*a^3*b^5*B + 960*a^2*b^6*B)*x^(3/2) + (-2052*a^5*A*b^3 - 1110*a^4*A*b^4 + 2832*a^3*A*b^5 + 2736*a^2*A*b^6 + 576*a*A*b^7 + 258*a^6*b^2*B + 123*a^5*b^3*B - 48*a^4*b^4*B + 1536*a^3*b^5*B + 1728*a^2*b^6*B + 384*a*b^7*B)*x^2 + (-996*a^5*A*b^3 - 3588*a^4*A*b^4 - 864*a^3*A*b^5 + 2016*a^2*A*b^6 + 1152*a*A*b^7 - 270*a^6*b^2*B - 30*a^5*b^3*B + 192*a^3*b^5*B + 1152*a^2*b^6*B + 768*a*b^7*B)*x^(5/2) + (-2478*a^4*A*b^4 - 3888*a^3*A*b^5 - 336*a^2*A*b^6 + 768*a*A*b^7 + 384*A*b^8 - 873*a^5*b^3*B - 512*a^4*b^4*B - 32*a^3*b^5*B + 144*a^2*b^6*B + 448*a*b^7*B + 256*b^8*B)*x^3 + (-492*a^4*A*b^4 - 3264*a^3*A*b^5 - 2592*a^2*A*b^6 - 570*a^5*b^3*B - 1824*a^4*b^4*B - 672*a^3*b^5*B)*x^(7/2) + (-972*a^3*A*b^5 - 2544*a^2*A*b^6 - 960*a*A*b^7 - 1482*a^4*b^4*B - 2184*a^3*b^5*B - 336*a^2*b^6*B)*x^4 + (-72*a^3*A*b^5 - 864*a^2*A*b^6 - 1152*a*A*b^7 - 316*a^4*b^4*B - 2032*a^3*b^5*B - 1536*a^2*b^6*B)*x^(9/2) + (-72*a^2*A*b^6 - 384*a*A*b^7 - 384*A*b^8 - 636*a^3*b^5*B - 1632*a^2*b^6*B - 576*a*b^7*B)*x^5 + (-48*a^3*b^5*B - 576*a^2*b^6*B - 768*a*b^7*B)*x^(11/2) + (-48*a^2*b^6*B - 256*a*b^7*B - 256*b^8*B)*x^6))/(24*b^2*(32*a^6 + 48*a^5*b + 18*a^4*b^2 + a^3*b^3) + 24*b^2*(a^3*b^3 + 18*a^2*b^4 + 48*a*b^5 + 32*b^6)*x^3 + 24*b^2*Sqrt[a + b]*(-32*a^5 - 32*a^4*b - 6*a^3*b^2)*Sqrt[a + b*x] + x*(24*b^2*(48*a^5*b + 204*a^4*b^2 + 159*a^3*b^3 + 18*a^2*b^4) + 24*b^2*Sqrt[a + b]*(-32*a^4*b - 164*a^3*b^2 - 72*a^2*b^3)*Sqrt[a + b*x]) + Sqrt[x]*(24*b^2*(96*a^5*b + 120*a^4*b^2 + 30*a^3*b^3) + 24*b^2*Sqrt[a + b]*(-96*a^4*b - 72*a^3*b^2 - 6*a^2*b^3)*Sqrt[a + b*x]) + x^2*(24*b^2*(18*a^4*b^2 + 159*a^3*b^3 + 204*a^2*b^4 + 48*a*b^5) + 24*b^2*Sqrt[a + b]*(-6*a^3*b^2 - 72*a^2*b^3 - 96*a*b^4)*Sqrt[a + b*x]) + x^(3/2)*(24*b^2*(120*a^4*b^2 + 260*a^3*b^3 + 120*a^2*b^4) + 24*b^2*Sqrt[a + b]*(-72*a^3*b^2 - 164*a^2*b^3 - 32*a*b^4)*Sqrt[a + b*x]) + x^(5/2)*(24*b^2*(30*a^3*b^3 + 120*a^2*b^4 + 96*a*b^5) + 24*b^2*Sqrt[a + b]*(-6*a^2*b^3 - 32*a*b^4 - 32*b^5)*Sqrt[a + b*x])) + ((a^2*A)/(2*b^(3/2)) - (a^3*B)/(4*b^(5/2)))*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",1
482,1,1152,93,2.109517,"\int \frac{\sqrt{a+b x} (A+B x)}{\sqrt{x}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/Sqrt[x],x]","\frac{\left(\frac{\sqrt{x}}{4 b}-\frac{1}{4 b}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(-4 B a^5-16 A b a^4-13 b B a^4-13 b B x a^4-18 b B \sqrt{x} a^4+4 \sqrt{a+b} B \sqrt{a+b x} a^4-20 A b^2 a^3-11 b^2 B x^2 a^3-35 b^2 B x^{3/2} a^3-11 b^2 B a^3-20 A b^2 x a^3-48 b^2 B x a^3-40 A b^2 \sqrt{x} a^3-35 b^2 B \sqrt{x} a^3+11 b \sqrt{a+b} B \sqrt{a+b x} a^3+11 b \sqrt{a+b} B x \sqrt{a+b x} a^3+16 A b \sqrt{a+b} \sqrt{a+b x} a^3+18 b \sqrt{a+b} B \sqrt{x} \sqrt{a+b x} a^3-4 A b^3 a^2-2 b^3 B x^3 a^2-18 b^3 B x^{5/2} a^2-4 A b^3 x^2 a^2-48 b^3 B x^2 a^2-36 A b^3 x^{3/2} a^2-60 b^3 B x^{3/2} a^2-2 b^3 B a^2-64 A b^3 x a^2-48 b^3 B x a^2-36 A b^3 \sqrt{x} a^2-18 b^3 B \sqrt{x} a^2+6 b^2 \sqrt{a+b} B x^2 \sqrt{a+b x} a^2+26 b^2 \sqrt{a+b} B x^{3/2} \sqrt{a+b x} a^2+6 b^2 \sqrt{a+b} B \sqrt{a+b x} a^2+36 b^2 \sqrt{a+b} B x \sqrt{a+b x} a^2+12 A b^2 \sqrt{a+b} x \sqrt{a+b x} a^2+12 A b^2 \sqrt{a+b} \sqrt{a+b x} a^2+26 b^2 \sqrt{a+b} B \sqrt{x} \sqrt{a+b x} a^2+40 A b^2 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a^2-16 b^4 B x^3 a-24 b^4 B x^{5/2} a-32 A b^4 x^2 a-48 b^4 B x^2 a-48 A b^4 x^{3/2} a-24 b^4 B x^{3/2} a-32 A b^4 x a-16 b^4 B x a+8 b^3 \sqrt{a+b} B x^{5/2} \sqrt{a+b x} a+24 b^3 \sqrt{a+b} B x^2 \sqrt{a+b x} a+32 b^3 \sqrt{a+b} B x^{3/2} \sqrt{a+b x} a+16 A b^3 \sqrt{a+b} x^{3/2} \sqrt{a+b x} a+24 b^3 \sqrt{a+b} B x \sqrt{a+b x} a+48 A b^3 \sqrt{a+b} x \sqrt{a+b x} a+8 b^3 \sqrt{a+b} B \sqrt{x} \sqrt{a+b x} a+16 A b^3 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a-16 b^5 B x^3-32 A b^5 x^2-16 b^5 B x^2+16 b^4 \sqrt{a+b} B x^{5/2} \sqrt{a+b x}+16 b^4 \sqrt{a+b} B x^{3/2} \sqrt{a+b x}+32 A b^4 \sqrt{a+b} x^{3/2} \sqrt{a+b x}\right)}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^4}+\left(\frac{a^2 B}{2 b^{3/2}}-\frac{2 a A}{\sqrt{b}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \left(\sqrt{x}-1\right)}{\sqrt{a+b}-\sqrt{a+b x}}\right)","\frac{a (4 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{4 b^{3/2}}+\frac{\sqrt{x} \sqrt{a+b x} (4 A b-a B)}{4 b}+\frac{B \sqrt{x} (a+b x)^{3/2}}{2 b}",1,"((-1/4*1/b + Sqrt[x]/(4*b))*(Sqrt[a + b] - Sqrt[a + b*x])*(-16*a^4*A*b - 20*a^3*A*b^2 - 4*a^2*A*b^3 - 4*a^5*B - 13*a^4*b*B - 11*a^3*b^2*B - 2*a^2*b^3*B - 40*a^3*A*b^2*Sqrt[x] - 36*a^2*A*b^3*Sqrt[x] - 18*a^4*b*B*Sqrt[x] - 35*a^3*b^2*B*Sqrt[x] - 18*a^2*b^3*B*Sqrt[x] - 20*a^3*A*b^2*x - 64*a^2*A*b^3*x - 32*a*A*b^4*x - 13*a^4*b*B*x - 48*a^3*b^2*B*x - 48*a^2*b^3*B*x - 16*a*b^4*B*x - 36*a^2*A*b^3*x^(3/2) - 48*a*A*b^4*x^(3/2) - 35*a^3*b^2*B*x^(3/2) - 60*a^2*b^3*B*x^(3/2) - 24*a*b^4*B*x^(3/2) - 4*a^2*A*b^3*x^2 - 32*a*A*b^4*x^2 - 32*A*b^5*x^2 - 11*a^3*b^2*B*x^2 - 48*a^2*b^3*B*x^2 - 48*a*b^4*B*x^2 - 16*b^5*B*x^2 - 18*a^2*b^3*B*x^(5/2) - 24*a*b^4*B*x^(5/2) - 2*a^2*b^3*B*x^3 - 16*a*b^4*B*x^3 - 16*b^5*B*x^3 + 16*a^3*A*b*Sqrt[a + b]*Sqrt[a + b*x] + 12*a^2*A*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a^4*Sqrt[a + b]*B*Sqrt[a + b*x] + 11*a^3*b*Sqrt[a + b]*B*Sqrt[a + b*x] + 6*a^2*b^2*Sqrt[a + b]*B*Sqrt[a + b*x] + 40*a^2*A*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 16*a*A*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 18*a^3*b*Sqrt[a + b]*B*Sqrt[x]*Sqrt[a + b*x] + 26*a^2*b^2*Sqrt[a + b]*B*Sqrt[x]*Sqrt[a + b*x] + 8*a*b^3*Sqrt[a + b]*B*Sqrt[x]*Sqrt[a + b*x] + 12*a^2*A*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] + 48*a*A*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] + 11*a^3*b*Sqrt[a + b]*B*x*Sqrt[a + b*x] + 36*a^2*b^2*Sqrt[a + b]*B*x*Sqrt[a + b*x] + 24*a*b^3*Sqrt[a + b]*B*x*Sqrt[a + b*x] + 16*a*A*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 32*A*b^4*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 26*a^2*b^2*Sqrt[a + b]*B*x^(3/2)*Sqrt[a + b*x] + 32*a*b^3*Sqrt[a + b]*B*x^(3/2)*Sqrt[a + b*x] + 16*b^4*Sqrt[a + b]*B*x^(3/2)*Sqrt[a + b*x] + 6*a^2*b^2*Sqrt[a + b]*B*x^2*Sqrt[a + b*x] + 24*a*b^3*Sqrt[a + b]*B*x^2*Sqrt[a + b*x] + 8*a*b^3*Sqrt[a + b]*B*x^(5/2)*Sqrt[a + b*x] + 16*b^4*Sqrt[a + b]*B*x^(5/2)*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4 + ((-2*a*A)/Sqrt[b] + (a^2*B)/(2*b^(3/2)))*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",1
483,1,466,82,1.5963792,"\int \frac{\sqrt{a+b x} (A+B x)}{x^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/x^(3/2),x]","\frac{\left(2 a A-2 a A \sqrt{x}\right) \left(-2 \sqrt{a+b} \sqrt{a+b x}+\sqrt{x} \sqrt{a+b} \sqrt{a+b x}+a \left(-\sqrt{x}\right)+2 a+b x-2 b \sqrt{x}+2 b\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)}{\sqrt{x} \left(-2 a^2 \sqrt{x}+4 a^2-a b x^{3/2}+2 a b x-a b \sqrt{x}-4 a \sqrt{a+b} \sqrt{a+b x}+2 a \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-2 b \sqrt{a+b} \sqrt{a+b x}+4 a b+2 b^2 \sqrt{x}\right)}+\left(-\frac{2 a B}{\sqrt{b}}-4 A \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \left(\sqrt{x}-1\right)}{\sqrt{a+b}-\sqrt{a+b x}}\right)+\frac{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^3 \left(2 B \sqrt{a+b} \sqrt{a+b x}-a B \sqrt{x}-a B-2 b B \sqrt{x}\right)}{\left(\sqrt{a+b} \sqrt{a+b x}-a-b \sqrt{x}\right)^2}+\frac{\left(-4 \sqrt{a+b} \sqrt{a+b x}+a \sqrt{x}+3 a+2 b \sqrt{x}+2 b\right) \left(B \sqrt{a+b x}-B \sqrt{a+b}\right)}{\sqrt{a+b} \sqrt{a+b x}-a-b \sqrt{x}}","\frac{\sqrt{x} \sqrt{a+b x} (a B+2 A b)}{a}+\frac{(a B+2 A b) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{\sqrt{b}}-\frac{2 A (a+b x)^{3/2}}{a \sqrt{x}}",1,"((3*a + 2*b + a*Sqrt[x] + 2*b*Sqrt[x] - 4*Sqrt[a + b]*Sqrt[a + b*x])*(-(Sqrt[a + b]*B) + B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x]) + ((Sqrt[a + b] - Sqrt[a + b*x])^3*(-(a*B) - a*B*Sqrt[x] - 2*b*B*Sqrt[x] + 2*Sqrt[a + b]*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 + ((2*a*A - 2*a*A*Sqrt[x])*(Sqrt[a + b] - Sqrt[a + b*x])*(2*a + 2*b - a*Sqrt[x] - 2*b*Sqrt[x] + b*x - 2*Sqrt[a + b]*Sqrt[a + b*x] + Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(Sqrt[x]*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])) + (-4*A*Sqrt[b] - (2*a*B)/Sqrt[b])*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",1
484,1,2638,69,10.7320836,"\int \frac{\sqrt{a+b x} (A+B x)}{x^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/x^(5/2),x]","\text{Result too large to show}","-\frac{2 A (a+b x)^{3/2}}{3 a x^{3/2}}-\frac{2 B \sqrt{a+b x}}{\sqrt{x}}+2 \sqrt{b} B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)",1,"(-2*(-256*a^6*A - 768*a^5*A*b - 816*a^4*A*b^2 - 352*a^3*A*b^3 - 48*a^2*A*b^4)*Sqrt[a + b*x] - 2*(384*a^6*A + 960*a^5*A*b + 600*a^4*A*b^2 - 156*a^3*A*b^3 - 204*a^2*A*b^4 - 24*a*A*b^5)*Sqrt[x]*Sqrt[a + b*x] - 2*(-192*a^6*A - 1024*a^5*A*b - 1764*a^4*A*b^2 - 1404*a^3*A*b^3 - 616*a^2*A*b^4 - 144*a*A*b^5 - 768*a^6*B - 2304*a^5*b*B - 2448*a^4*b^2*B - 1056*a^3*b^3*B - 144*a^2*b^4*B)*x*Sqrt[a + b*x] - 2*(288*a^6*A + 2160*a^5*A*b + 4194*a^4*A*b^2 + 3013*a^3*A*b^3 + 606*a^2*A*b^4 - 132*a*A*b^5 - 48*A*b^6 + 1920*a^6*B + 5568*a^5*b*B + 5304*a^4*b^2*B + 1572*a^3*b^3*B - 132*a^2*b^4*B - 48*a*b^5*B)*x^(3/2)*Sqrt[a + b*x] - 2*(-384*a^6*A - 2016*a^5*A*b - 3576*a^4*A*b^2 - 2346*a^3*A*b^3 - 252*a^2*A*b^4 + 144*a*A*b^5 - 1728*a^6*B - 5760*a^5*b*B - 6084*a^4*b^2*B - 1908*a^3*b^3*B + 144*a^2*b^4*B)*x^2*Sqrt[a + b*x] - 2*(192*a^6*A + 1008*a^5*A*b + 2544*a^4*A*b^2 + 2763*a^3*A*b^3 + 1165*a^2*A*b^4 + 192*a*A*b^5 + 48*A*b^6 + 672*a^6*B + 4080*a^5*b*B + 6234*a^4*b^2*B + 2949*a^3*b^3*B + 168*a^2*b^4*B + 48*a*b^5*B)*x^(5/2)*Sqrt[a + b*x] - 2*(-32*a^6*A - 480*a^5*A*b - 1746*a^4*A*b^2 - 2212*a^3*A*b^3 - 900*a^2*A*b^4 - 96*a^6*B - 2208*a^5*b*B - 4578*a^4*b^2*B - 2484*a^3*b^3*B)*x^3*Sqrt[a + b*x] - 2*(192*a^5*A*b + 690*a^4*A*b^2 + 939*a^3*A*b^3 + 405*a^2*A*b^4 - 36*a*A*b^5 + 720*a^5*b*B + 2124*a^4*b^2*B + 1413*a^3*b^3*B - 36*a^2*b^4*B)*x^(7/2)*Sqrt[a + b*x] - 2*(-32*a^5*A*b - 156*a^4*A*b^2 - 330*a^3*A*b^3 - 220*a^2*A*b^4 - 96*a^5*b*B - 696*a^4*b^2*B - 660*a^3*b^3*B)*x^4*Sqrt[a + b*x] - 2*(36*a^4*A*b^2 + 97*a^3*A*b^3 + 75*a^2*A*b^4 + 162*a^4*b^2*B + 207*a^3*b^3*B)*x^(9/2)*Sqrt[a + b*x] - 2*(-6*a^4*A*b^2 - 12*a^3*A*b^3 - 12*a^2*A*b^4 - 18*a^4*b^2*B - 36*a^3*b^3*B)*x^5*Sqrt[a + b*x] - 2*(a^2*A*b^4 + 3*a^3*b^3*B)*x^(11/2)*Sqrt[a + b*x] + Sqrt[a + b]*(-2*(256*a^6*A + 640*a^5*A*b + 528*a^4*A*b^2 + 152*a^3*A*b^3 + 8*a^2*A*b^4) - 2*(-384*a^6*A - 768*a^5*A*b - 264*a^4*A*b^2 + 216*a^3*A*b^3 + 96*a^2*A*b^4)*Sqrt[x] - 2*(192*a^6*A + 1056*a^5*A*b + 1644*a^4*A*b^2 + 1110*a^3*A*b^3 + 384*a^2*A*b^4 + 48*a*A*b^5 + 768*a^6*B + 1920*a^5*b*B + 1584*a^4*b^2*B + 456*a^3*b^3*B + 24*a^2*b^4*B)*x - 2*(-288*a^6*A - 2208*a^5*A*b - 3606*a^4*A*b^2 - 1768*a^3*A*b^3 + 32*a^2*A*b^4 + 144*a*A*b^5 - 1920*a^6*B - 4608*a^5*b*B - 3240*a^4*b^2*B - 408*a^3*b^3*B + 144*a^2*b^4*B)*x^(3/2) - 2*(384*a^6*A + 1920*a^5*A*b + 3144*a^4*A*b^2 + 1776*a^3*A*b^3 + 252*a^2*A*b^4 + 84*a*A*b^5 + 48*A*b^6 + 1728*a^6*B + 5280*a^5*b*B + 4812*a^4*b^2*B + 1278*a^3*b^3*B + 84*a^2*b^4*B + 48*a*b^5*B)*x^2 - 2*(-192*a^6*A - 1056*a^5*A*b - 3072*a^4*A*b^2 - 3324*a^3*A*b^3 - 1260*a^2*A*b^4 - 144*a*A*b^5 - 672*a^6*B - 4704*a^5*b*B - 6750*a^4*b^2*B - 2772*a^3*b^3*B - 144*a^2*b^4*B)*x^(5/2) - 2*(32*a^6*A + 656*a^5*A*b + 2406*a^4*A*b^2 + 2765*a^3*A*b^3 + 779*a^2*A*b^4 - 168*a*A*b^5 - 48*A*b^6 + 96*a^6*B + 3024*a^5*b*B + 5862*a^4*b^2*B + 2679*a^3*b^3*B - 144*a^2*b^4*B - 48*a*b^5*B)*x^3 - 2*(-288*a^5*A*b - 1014*a^4*A*b^2 - 1494*a^3*A*b^3 - 684*a^2*A*b^4 - 1056*a^5*b*B - 3396*a^4*b^2*B - 2268*a^3*b^3*B)*x^(7/2) - 2*(48*a^5*A*b + 324*a^4*A*b^2 + 807*a^3*A*b^3 + 567*a^2*A*b^4 + 36*a*A*b^5 + 144*a^5*b*B + 1512*a^4*b^2*B + 1539*a^3*b^3*B + 36*a^2*b^4*B)*x^4 - 2*(-108*a^4*A*b^2 - 280*a^3*A*b^3 - 220*a^2*A*b^4 - 438*a^4*b^2*B - 660*a^3*b^3*B)*x^(9/2) - 2*(18*a^4*A*b^2 + 45*a^3*A*b^3 + 57*a^2*A*b^4 + 54*a^4*b^2*B + 189*a^3*b^3*B)*x^5 - 2*(-6*a^3*A*b^3 - 12*a^2*A*b^4 - 36*a^3*b^3*B)*x^(11/2) - 2*(a^3*A*b^3 + a^2*A*b^4 + 3*a^3*b^3*B)*x^6))/(-18*a^3*b^3*x^(11/2) + 3*a^3*b^3*x^6 + x^5*(3*(18*a^4*b^2 + 27*a^3*b^3 - 6*a^2*b^4) - 18*a^3*b^2*Sqrt[a + b]*Sqrt[a + b*x]) + x^4*(3*(48*a^5*b + 276*a^4*b^2 + 267*a^3*b^3 + 48*a^2*b^4 + 24*a*b^5) + 3*Sqrt[a + b]*(-32*a^4*b - 92*a^3*b^2)*Sqrt[a + b*x]) + x^3*(3*(32*a^6 + 624*a^5*b + 1170*a^4*b^2 + 565*a^3*b^3 - 78*a^2*b^4 - 96*a*b^5 - 32*b^6) + 3*Sqrt[a + b]*(-32*a^5 - 416*a^4*b - 486*a^3*b^2 - 72*a^2*b^3)*Sqrt[a + b*x]) + x^(9/2)*(3*(-108*a^4*b^2 - 128*a^3*b^3) + 3*Sqrt[a + b]*(36*a^3*b^2 + 6*a^2*b^3)*Sqrt[a + b*x]) + x^(7/2)*(3*(-288*a^5*b - 624*a^4*b^2 - 270*a^3*b^3 + 72*a^2*b^4) + 3*Sqrt[a + b]*(192*a^4*b + 240*a^3*b^2 - 36*a^2*b^3 - 24*a*b^4)*Sqrt[a + b*x]) + x^(3/2)*(3*(-256*a^6 - 768*a^5*b - 816*a^4*b^2 - 352*a^3*b^3 - 48*a^2*b^4) + 3*Sqrt[a + b]*(256*a^5 + 640*a^4*b + 528*a^3*b^2 + 152*a^2*b^3 + 8*a*b^4)*Sqrt[a + b*x]) + x^2*(3*(384*a^6 + 960*a^5*b + 600*a^4*b^2 - 156*a^3*b^3 - 204*a^2*b^4 - 24*a*b^5) + 3*Sqrt[a + b]*(-384*a^5 - 768*a^4*b - 264*a^3*b^2 + 216*a^2*b^3 + 96*a*b^4)*Sqrt[a + b*x]) + x^(5/2)*(3*(-192*a^6 - 768*a^5*b - 996*a^4*b^2 - 588*a^3*b^3 - 264*a^2*b^4 - 96*a*b^5) + 3*Sqrt[a + b]*(192*a^5 + 544*a^4*b + 364*a^3*b^2 + 54*a^2*b^3 + 80*a*b^4 + 32*b^5)*Sqrt[a + b*x])) - 4*Sqrt[b]*B*ArcTanh[(-Sqrt[b] + Sqrt[b]*Sqrt[x])/(Sqrt[a + b] - Sqrt[a + b*x])]","B",1
485,-1,0,53,180.064549,"\int \frac{\sqrt{a+b x} (A+B x)}{x^{7/2}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/x^(7/2),x]","\text{\$Aborted}","\frac{2 (a+b x)^{3/2} (2 A b-5 a B)}{15 a^2 x^{3/2}}-\frac{2 A (a+b x)^{3/2}}{5 a x^{5/2}}",1,"$Aborted","F",-1
486,-1,0,84,180.2505467,"\int \frac{\sqrt{a+b x} (A+B x)}{x^{9/2}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/x^(9/2),x]","\text{\$Aborted}","-\frac{4 b (a+b x)^{3/2} (4 A b-7 a B)}{105 a^3 x^{3/2}}+\frac{2 (a+b x)^{3/2} (4 A b-7 a B)}{35 a^2 x^{5/2}}-\frac{2 A (a+b x)^{3/2}}{7 a x^{7/2}}",1,"$Aborted","F",-1
487,-1,0,117,180.7405575,"\int \frac{\sqrt{a+b x} (A+B x)}{x^{11/2}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/x^(11/2),x]","\text{\$Aborted}","\frac{16 b^2 (a+b x)^{3/2} (2 A b-3 a B)}{315 a^4 x^{3/2}}-\frac{8 b (a+b x)^{3/2} (2 A b-3 a B)}{105 a^3 x^{5/2}}+\frac{2 (a+b x)^{3/2} (2 A b-3 a B)}{21 a^2 x^{7/2}}-\frac{2 A (a+b x)^{3/2}}{9 a x^{9/2}}",1,"$Aborted","F",-1
488,-1,0,150,181.9417334,"\int \frac{\sqrt{a+b x} (A+B x)}{x^{13/2}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/x^(13/2),x]","\text{\$Aborted}","-\frac{32 b^3 (a+b x)^{3/2} (8 A b-11 a B)}{3465 a^5 x^{3/2}}+\frac{16 b^2 (a+b x)^{3/2} (8 A b-11 a B)}{1155 a^4 x^{5/2}}-\frac{4 b (a+b x)^{3/2} (8 A b-11 a B)}{231 a^3 x^{7/2}}+\frac{2 (a+b x)^{3/2} (8 A b-11 a B)}{99 a^2 x^{9/2}}-\frac{2 A (a+b x)^{3/2}}{11 a x^{11/2}}",1,"$Aborted","F",-1
489,-1,0,183,180.0856739,"\int \frac{\sqrt{a+b x} (A+B x)}{x^{15/2}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/x^(15/2),x]","\text{\$Aborted}","\frac{256 b^4 (a+b x)^{3/2} (10 A b-13 a B)}{45045 a^6 x^{3/2}}-\frac{128 b^3 (a+b x)^{3/2} (10 A b-13 a B)}{15015 a^5 x^{5/2}}+\frac{32 b^2 (a+b x)^{3/2} (10 A b-13 a B)}{3003 a^4 x^{7/2}}-\frac{16 b (a+b x)^{3/2} (10 A b-13 a B)}{1287 a^3 x^{9/2}}+\frac{2 (a+b x)^{3/2} (10 A b-13 a B)}{143 a^2 x^{11/2}}-\frac{2 A (a+b x)^{3/2}}{13 a x^{13/2}}",1,"$Aborted","F",-1
490,1,9853,225,157.3512313,"\int x^{5/2} (a+b x)^{3/2} (A+B x) \, dx","IntegrateAlgebraic[x^(5/2)*(a + b*x)^(3/2)*(A + B*x),x]","\text{Result too large to show}","-\frac{a^5 (12 A b-7 a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{512 b^{9/2}}+\frac{a^4 \sqrt{x} \sqrt{a+b x} (12 A b-7 a B)}{512 b^4}-\frac{a^3 x^{3/2} \sqrt{a+b x} (12 A b-7 a B)}{768 b^3}+\frac{a^2 x^{5/2} \sqrt{a+b x} (12 A b-7 a B)}{960 b^2}+\frac{a x^{7/2} \sqrt{a+b x} (12 A b-7 a B)}{160 b}+\frac{x^{7/2} (a+b x)^{3/2} (12 A b-7 a B)}{60 b}+\frac{B x^{7/2} (a+b x)^{5/2}}{6 b}",1,"Result too large to show","B",0
491,1,6957,192,97.0036287,"\int x^{3/2} (a+b x)^{3/2} (A+B x) \, dx","IntegrateAlgebraic[x^(3/2)*(a + b*x)^(3/2)*(A + B*x),x]","\text{Result too large to show}","\frac{3 a^4 (2 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{128 b^{7/2}}-\frac{3 a^3 \sqrt{x} \sqrt{a+b x} (2 A b-a B)}{128 b^3}+\frac{a^2 x^{3/2} \sqrt{a+b x} (2 A b-a B)}{64 b^2}+\frac{a x^{5/2} \sqrt{a+b x} (2 A b-a B)}{16 b}+\frac{x^{5/2} (a+b x)^{3/2} (2 A b-a B)}{8 b}+\frac{B x^{5/2} (a+b x)^{5/2}}{5 b}",1,"Result too large to show","B",0
492,1,4557,159,57.1164691,"\int \sqrt{x} (a+b x)^{3/2} (A+B x) \, dx","IntegrateAlgebraic[Sqrt[x]*(a + b*x)^(3/2)*(A + B*x),x]","\text{Result too large to show}","-\frac{a^3 (8 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{64 b^{5/2}}+\frac{a^2 \sqrt{x} \sqrt{a+b x} (8 A b-3 a B)}{64 b^2}+\frac{a x^{3/2} \sqrt{a+b x} (8 A b-3 a B)}{32 b}+\frac{x^{3/2} (a+b x)^{3/2} (8 A b-3 a B)}{24 b}+\frac{B x^{3/2} (a+b x)^{5/2}}{4 b}",1,"((-3072*a^10*A*b - 22016*a^9*A*b^2 - 50560*a^8*A*b^3 - 53056*a^7*A*b^4 - 27456*a^6*A*b^5 - 6528*a^5*A*b^6 - 512*a^4*A*b^7 + 1152*a^11*B + 2112*a^10*b*B - 8688*a^9*b^2*B - 30024*a^8*b^3*B - 35400*a^7*b^4*B - 19440*a^6*b^5*B - 4800*a^5*b^6*B - 384*a^4*b^7*B)*Sqrt[a + b*x] + (3072*a^10*A*b - 6144*a^9*A*b^2 - 81152*a^8*A*b^3 - 180992*a^7*A*b^4 - 171688*a^6*A*b^5 - 75840*a^5*A*b^6 - 13696*a^4*A*b^7 - 512*a^3*A*b^8 - 1152*a^11*B + 2304*a^10*b*B + 5856*a^9*b^2*B - 36576*a^8*b^3*B - 110721*a^7*b^4*B - 116328*a^6*b^5*B - 54384*a^5*b^6*B - 10176*a^4*b^7*B - 384*a^3*b^8*B)*Sqrt[x]*Sqrt[a + b*x] + (7680*a^9*A*b^2 - 34560*a^8*A*b^3 - 218688*a^7*A*b^4 - 382080*a^6*A*b^5 - 296064*a^5*A*b^6 - 102912*a^4*A*b^7 - 12288*a^3*A*b^8 - 2880*a^10*b*B + 3744*a^9*b^2*B - 5544*a^8*b^3*B - 115920*a^7*b^4*B - 242640*a^6*b^5*B - 204480*a^5*b^6*B - 74880*a^4*b^7*B - 9216*a^3*b^8*B)*x*Sqrt[a + b*x] + (20480*a^9*A*b^2 + 48640*a^8*A*b^3 - 72960*a^7*A*b^4 - 381600*a^6*A*b^5 - 526800*a^5*A*b^6 - 323840*a^4*A*b^7 - 83200*a^3*A*b^8 - 5120*a^2*A*b^9 - 1536*a^10*b*B - 5952*a^9*b^2*B + 4320*a^8*b^3*B - 39684*a^7*b^4*B - 222882*a^6*b^5*B - 345120*a^5*b^6*B - 228000*a^4*b^7*B - 61440*a^3*b^8*B - 3840*a^2*b^9*B)*x^(3/2)*Sqrt[a + b*x] + (76928*a^8*A*b^3 + 128064*a^7*A*b^4 - 104448*a^6*A*b^5 - 454656*a^5*A*b^6 - 494080*a^4*A*b^7 - 235520*a^3*A*b^8 - 40960*a^2*A*b^9 - 4272*a^9*b^2*B - 8856*a^8*b^3*B - 2688*a^7*b^4*B - 86016*a^6*b^5*B - 281280*a^5*b^6*B - 332160*a^4*b^7*B - 168960*a^3*b^8*B - 30720*a^2*b^9*B)*x^2*Sqrt[a + b*x] + (40704*a^8*A*b^3 + 218880*a^7*A*b^4 + 233808*a^6*A*b^5 - 98688*a^5*A*b^6 - 369216*a^4*A*b^7 - 314880*a^3*A*b^8 - 113664*a^2*A*b^9 - 12288*a*A*b^10 + 9312*a^9*b^2*B + 13152*a^8*b^3*B + 2946*a^7*b^4*B - 10416*a^6*b^5*B - 102984*a^5*b^6*B - 235584*a^4*b^7*B - 216576*a^3*b^8*B - 82944*a^2*b^9*B - 9216*a*b^10*B)*x^(5/2)*Sqrt[a + b*x] + (143680*a^7*A*b^4 + 405120*a^6*A*b^5 + 294912*a^5*A*b^6 - 58368*a^4*A*b^7 - 194560*a^3*A*b^8 - 131072*a^2*A*b^9 - 32768*a*A*b^10 + 38280*a^8*b^3*B + 62736*a^7*b^4*B + 26880*a^6*b^5*B - 10752*a^5*b^6*B - 71808*a^4*b^7*B - 125952*a^3*b^8*B - 92160*a^2*b^9*B - 24576*a*b^10*B)*x^3*Sqrt[a + b*x] + (35072*a^7*A*b^4 + 305632*a^6*A*b^5 + 518112*a^5*A*b^6 + 254208*a^4*A*b^7 - 17664*a^3*A*b^8 - 56320*a^2*A*b^9 - 34816*a*A*b^10 - 8192*A*b^11 + 25248*a^8*b^3*B + 123468*a^7*b^4*B + 138924*a^6*b^5*B + 43680*a^5*b^6*B - 4464*a^4*b^7*B - 24576*a^3*b^8*B - 36864*a^2*b^9*B - 24576*a*b^10*B - 6144*b^11*B)*x^(7/2)*Sqrt[a + b*x] + (108864*a^6*A*b^5 + 427392*a^5*A*b^6 + 462336*a^4*A*b^7 + 141312*a^3*A*b^8 + 91272*a^7*b^4*B + 245616*a^6*b^5*B + 186816*a^5*b^6*B + 35712*a^4*b^7*B)*x^4*Sqrt[a + b*x] + (13848*a^6*A*b^5 + 181056*a^5*A*b^6 + 410240*a^4*A*b^7 + 283648*a^3*A*b^8 + 41984*a^2*A*b^9 + 23991*a^7*b^4*B + 200712*a^6*b^5*B + 329040*a^5*b^6*B + 162240*a^4*b^7*B + 13440*a^3*b^8*B)*x^(9/2)*Sqrt[a + b*x] + (34944*a^5*A*b^6 + 189952*a^4*A*b^7 + 272384*a^3*A*b^8 + 114688*a^2*A*b^9 + 75600*a^6*b^5*B + 288960*a^5*b^6*B + 303744*a^4*b^7*B + 89088*a^3*b^8*B)*x^5*Sqrt[a + b*x] + (2160*a^5*A*b^6 + 42240*a^4*A*b^7 + 130560*a^3*A*b^8 + 122880*a^2*A*b^9 + 30720*a*A*b^10 + 9990*a^6*b^5*B + 128160*a^5*b^6*B + 284640*a^4*b^7*B + 192000*a^3*b^8*B + 26880*a^2*b^9*B)*x^(11/2)*Sqrt[a + b*x] + (3584*a^4*A*b^7 + 28672*a^3*A*b^8 + 57344*a^2*A*b^9 + 32768*a*A*b^10 + 25536*a^5*b^6*B + 137088*a^4*b^7*B + 193536*a^3*b^8*B + 79872*a^2*b^9*B)*x^6*Sqrt[a + b*x] + (64*a^4*A*b^7 + 2048*a^3*A*b^8 + 10240*a^2*A*b^9 + 16384*a*A*b^10 + 8192*A*b^11 + 1608*a^5*b^6*B + 31296*a^4*b^7*B + 96000*a^3*b^8*B + 89088*a^2*b^9*B + 21504*a*b^10*B)*x^(13/2)*Sqrt[a + b*x] + (2688*a^4*b^7*B + 21504*a^3*b^8*B + 43008*a^2*b^9*B + 24576*a*b^10*B)*x^7*Sqrt[a + b*x] + (48*a^4*b^7*B + 1536*a^3*b^8*B + 7680*a^2*b^9*B + 12288*a*b^10*B + 6144*b^11*B)*x^(15/2)*Sqrt[a + b*x] + Sqrt[a + b]*(3072*a^10*A*b + 20480*a^9*A*b^2 + 40704*a^8*A*b^3 + 35072*a^7*A*b^4 + 13848*a^6*A*b^5 + 2160*a^5*A*b^6 + 64*a^4*A*b^7 - 1152*a^11*B - 1536*a^10*b*B + 9312*a^9*b^2*B + 25248*a^8*b^3*B + 23991*a^7*b^4*B + 9990*a^6*b^5*B + 1608*a^5*b^6*B + 48*a^4*b^7*B + (-3072*a^10*A*b + 7680*a^9*A*b^2 + 76928*a^8*A*b^3 + 143680*a^7*A*b^4 + 108864*a^6*A*b^5 + 34944*a^5*A*b^6 + 3584*a^4*A*b^7 + 1152*a^11*B - 2880*a^10*b*B - 4272*a^9*b^2*B + 38280*a^8*b^3*B + 91272*a^7*b^4*B + 75600*a^6*b^5*B + 25536*a^5*b^6*B + 2688*a^4*b^7*B)*Sqrt[x] + (-6144*a^9*A*b^2 + 48640*a^8*A*b^3 + 218880*a^7*A*b^4 + 305632*a^6*A*b^5 + 181056*a^5*A*b^6 + 42240*a^4*A*b^7 + 2048*a^3*A*b^8 + 2304*a^10*b*B - 5952*a^9*b^2*B + 13152*a^8*b^3*B + 123468*a^7*b^4*B + 200712*a^6*b^5*B + 128160*a^5*b^6*B + 31296*a^4*b^7*B + 1536*a^3*b^8*B)*x + (-22016*a^9*A*b^2 - 34560*a^8*A*b^3 + 128064*a^7*A*b^4 + 405120*a^6*A*b^5 + 427392*a^5*A*b^6 + 189952*a^4*A*b^7 + 28672*a^3*A*b^8 + 2112*a^10*b*B + 3744*a^9*b^2*B - 8856*a^8*b^3*B + 62736*a^7*b^4*B + 245616*a^6*b^5*B + 288960*a^5*b^6*B + 137088*a^4*b^7*B + 21504*a^3*b^8*B)*x^(3/2) + (-81152*a^8*A*b^3 - 72960*a^7*A*b^4 + 233808*a^6*A*b^5 + 518112*a^5*A*b^6 + 410240*a^4*A*b^7 + 130560*a^3*A*b^8 + 10240*a^2*A*b^9 + 5856*a^9*b^2*B + 4320*a^8*b^3*B + 2946*a^7*b^4*B + 138924*a^6*b^5*B + 329040*a^5*b^6*B + 284640*a^4*b^7*B + 96000*a^3*b^8*B + 7680*a^2*b^9*B)*x^2 + (-50560*a^8*A*b^3 - 218688*a^7*A*b^4 - 104448*a^6*A*b^5 + 294912*a^5*A*b^6 + 462336*a^4*A*b^7 + 272384*a^3*A*b^8 + 57344*a^2*A*b^9 - 8688*a^9*b^2*B - 5544*a^8*b^3*B - 2688*a^7*b^4*B + 26880*a^6*b^5*B + 186816*a^5*b^6*B + 303744*a^4*b^7*B + 193536*a^3*b^8*B + 43008*a^2*b^9*B)*x^(5/2) + (-180992*a^7*A*b^4 - 381600*a^6*A*b^5 - 98688*a^5*A*b^6 + 254208*a^4*A*b^7 + 283648*a^3*A*b^8 + 122880*a^2*A*b^9 + 16384*a*A*b^10 - 36576*a^8*b^3*B - 39684*a^7*b^4*B - 10416*a^6*b^5*B + 43680*a^5*b^6*B + 162240*a^4*b^7*B + 192000*a^3*b^8*B + 89088*a^2*b^9*B + 12288*a*b^10*B)*x^3 + (-53056*a^7*A*b^4 - 382080*a^6*A*b^5 - 454656*a^5*A*b^6 - 58368*a^4*A*b^7 + 141312*a^3*A*b^8 + 114688*a^2*A*b^9 + 32768*a*A*b^10 - 30024*a^8*b^3*B - 115920*a^7*b^4*B - 86016*a^6*b^5*B - 10752*a^5*b^6*B + 35712*a^4*b^7*B + 89088*a^3*b^8*B + 79872*a^2*b^9*B + 24576*a*b^10*B)*x^(7/2) + (-171688*a^6*A*b^5 - 526800*a^5*A*b^6 - 369216*a^4*A*b^7 - 17664*a^3*A*b^8 + 41984*a^2*A*b^9 + 30720*a*A*b^10 + 8192*A*b^11 - 110721*a^7*b^4*B - 222882*a^6*b^5*B - 102984*a^5*b^6*B - 4464*a^4*b^7*B + 13440*a^3*b^8*B + 26880*a^2*b^9*B + 21504*a*b^10*B + 6144*b^11*B)*x^4 + (-27456*a^6*A*b^5 - 296064*a^5*A*b^6 - 494080*a^4*A*b^7 - 194560*a^3*A*b^8 - 35400*a^7*b^4*B - 242640*a^6*b^5*B - 281280*a^5*b^6*B - 71808*a^4*b^7*B)*x^(9/2) + (-75840*a^5*A*b^6 - 323840*a^4*A*b^7 - 314880*a^3*A*b^8 - 56320*a^2*A*b^9 - 116328*a^6*b^5*B - 345120*a^5*b^6*B - 235584*a^4*b^7*B - 24576*a^3*b^8*B)*x^5 + (-6528*a^5*A*b^6 - 102912*a^4*A*b^7 - 235520*a^3*A*b^8 - 131072*a^2*A*b^9 - 19440*a^6*b^5*B - 204480*a^5*b^6*B - 332160*a^4*b^7*B - 125952*a^3*b^8*B)*x^(11/2) + (-13696*a^4*A*b^7 - 83200*a^3*A*b^8 - 113664*a^2*A*b^9 - 34816*a*A*b^10 - 54384*a^5*b^6*B - 228000*a^4*b^7*B - 216576*a^3*b^8*B - 36864*a^2*b^9*B)*x^6 + (-512*a^4*A*b^7 - 12288*a^3*A*b^8 - 40960*a^2*A*b^9 - 32768*a*A*b^10 - 4800*a^5*b^6*B - 74880*a^4*b^7*B - 168960*a^3*b^8*B - 92160*a^2*b^9*B)*x^(13/2) + (-512*a^3*A*b^8 - 5120*a^2*A*b^9 - 12288*a*A*b^10 - 8192*A*b^11 - 10176*a^4*b^7*B - 61440*a^3*b^8*B - 82944*a^2*b^9*B - 24576*a*b^10*B)*x^7 + (-384*a^4*b^7*B - 9216*a^3*b^8*B - 30720*a^2*b^9*B - 24576*a*b^10*B)*x^(15/2) + (-384*a^3*b^8*B - 3840*a^2*b^9*B - 9216*a*b^10*B - 6144*b^11*B)*x^8))/(192*b^2*(128*a^8 + 256*a^7*b + 160*a^6*b^2 + 32*a^5*b^3 + a^4*b^4) + 192*b^2*(a^4*b^4 + 32*a^3*b^5 + 160*a^2*b^6 + 256*a*b^7 + 128*b^8)*x^4 + 192*b^2*Sqrt[a + b]*(-128*a^7 - 192*a^6*b - 80*a^5*b^2 - 8*a^4*b^3)*Sqrt[a + b*x] + x*(192*b^2*(256*a^7*b + 1472*a^6*b^2 + 1760*a^5*b^3 + 604*a^4*b^4 + 32*a^3*b^5) + 192*b^2*Sqrt[a + b]*(-192*a^6*b - 1248*a^5*b^2 - 1080*a^4*b^3 - 192*a^3*b^4)*Sqrt[a + b*x]) + Sqrt[x]*(192*b^2*(512*a^7*b + 896*a^6*b^2 + 448*a^5*b^3 + 56*a^4*b^4) + 192*b^2*Sqrt[a + b]*(-512*a^6*b - 640*a^5*b^2 - 192*a^4*b^3 - 8*a^3*b^4)*Sqrt[a + b*x]) + x^2*(192*b^2*(160*a^6*b^2 + 1760*a^5*b^3 + 3270*a^4*b^4 + 1760*a^3*b^5 + 160*a^2*b^6) + 192*b^2*Sqrt[a + b]*(-80*a^5*b^2 - 1080*a^4*b^3 - 1920*a^3*b^4 - 640*a^2*b^5)*Sqrt[a + b*x]) + x^(3/2)*(192*b^2*(896*a^6*b^2 + 2688*a^5*b^3 + 2184*a^4*b^4 + 448*a^3*b^5) + 192*b^2*Sqrt[a + b]*(-640*a^5*b^2 - 1920*a^4*b^3 - 1080*a^3*b^4 - 80*a^2*b^5)*Sqrt[a + b*x]) + x^3*(192*b^2*(32*a^5*b^3 + 604*a^4*b^4 + 1760*a^3*b^5 + 1472*a^2*b^6 + 256*a*b^7) + 192*b^2*Sqrt[a + b]*(-8*a^4*b^3 - 192*a^3*b^4 - 640*a^2*b^5 - 512*a*b^6)*Sqrt[a + b*x]) + x^(5/2)*(192*b^2*(448*a^5*b^3 + 2184*a^4*b^4 + 2688*a^3*b^5 + 896*a^2*b^6) + 192*b^2*Sqrt[a + b]*(-192*a^4*b^3 - 1080*a^3*b^4 - 1248*a^2*b^5 - 192*a*b^6)*Sqrt[a + b*x]) + x^(7/2)*(192*b^2*(56*a^4*b^4 + 448*a^3*b^5 + 896*a^2*b^6 + 512*a*b^7) + 192*b^2*Sqrt[a + b]*(-8*a^3*b^4 - 80*a^2*b^5 - 192*a*b^6 - 128*b^7)*Sqrt[a + b*x])) + ((a^3*A)/(4*b^(3/2)) - (3*a^4*B)/(32*b^(5/2)))*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",1
493,1,2627,126,15.9726345,"\int \frac{(a+b x)^{3/2} (A+B x)}{\sqrt{x}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/Sqrt[x],x]","\text{Result too large to show}","\frac{a^2 (6 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 b^{3/2}}+\frac{\sqrt{x} (a+b x)^{3/2} (6 A b-a B)}{12 b}+\frac{a \sqrt{x} \sqrt{a+b x} (6 A b-a B)}{8 b}+\frac{B \sqrt{x} (a+b x)^{5/2}}{3 b}",1,"((-960*a^7*A*b - 2304*a^6*A*b^2 - 1908*a^5*A*b^3 - 636*a^4*A*b^4 - 72*a^3*A*b^5 - 96*a^8*B - 640*a^7*b*B - 1266*a^6*b^2*B - 1062*a^5*b^3*B - 388*a^4*b^4*B - 48*a^3*b^5*B)*Sqrt[a + b*x] + (960*a^7*A*b - 1440*a^6*A*b^2 - 5652*a^5*A*b^3 - 4326*a^4*A*b^4 - 1116*a^3*A*b^5 - 72*a^2*A*b^6 + 96*a^8*B - 144*a^7*b*B - 1794*a^6*b^2*B - 3351*a^5*b^3*B - 2454*a^4*b^4*B - 708*a^3*b^5*B - 48*a^2*b^6*B)*Sqrt[x]*Sqrt[a + b*x] + (1920*a^6*A*b^2 - 2664*a^5*A*b^3 - 8532*a^4*A*b^4 - 4992*a^3*A*b^5 - 864*a^2*A*b^6 + 192*a^7*b*B - 676*a^6*b^2*B - 3618*a^5*b^3*B - 5088*a^4*b^4*B - 2896*a^3*b^5*B - 576*a^2*b^6*B)*x*Sqrt[a + b*x] + (1824*a^6*A*b^2 + 4536*a^5*A*b^3 - 2958*a^4*A*b^4 - 8160*a^3*A*b^5 - 3312*a^2*A*b^6 - 384*a*A*b^7 + 592*a^7*b*B + 1068*a^6*b^2*B - 987*a^5*b^3*B - 4400*a^4*b^4*B - 4728*a^3*b^5*B - 2016*a^2*b^6*B - 256*a*b^7*B)*x^(3/2)*Sqrt[a + b*x] + (4572*a^5*A*b^3 + 6828*a^4*A*b^4 - 2016*a^3*A*b^5 - 4896*a^2*A*b^6 - 1152*a*A*b^7 + 1686*a^6*b^2*B + 2142*a^5*b^3*B - 864*a^4*b^4*B - 3264*a^3*b^5*B - 2688*a^2*b^6*B - 768*a*b^7*B)*x^2*Sqrt[a + b*x] + (1116*a^5*A*b^3 + 7038*a^4*A*b^4 + 6816*a^3*A*b^5 - 720*a^2*A*b^6 - 1728*a*A*b^7 - 384*A*b^8 + 982*a^6*b^2*B + 3699*a^5*b^3*B + 2784*a^4*b^4*B - 368*a^3*b^5*B - 1296*a^2*b^6*B - 960*a*b^7*B - 256*b^8*B)*x^(5/2)*Sqrt[a + b*x] + (2340*a^4*A*b^4 + 6720*a^3*A*b^5 + 4320*a^2*A*b^6 + 2538*a^5*b^3*B + 4960*a^4*b^4*B + 2208*a^3*b^5*B)*x^3*Sqrt[a + b*x] + (246*a^4*A*b^4 + 2448*a^3*A*b^5 + 3888*a^2*A*b^6 + 1536*a*A*b^7 + 639*a^5*b^3*B + 3912*a^4*b^4*B + 4272*a^3*b^5*B + 912*a^2*b^6*B)*x^(7/2)*Sqrt[a + b*x] + (360*a^3*A*b^5 + 1440*a^2*A*b^6 + 1152*a*A*b^7 + 1380*a^4*b^4*B + 3760*a^3*b^5*B + 2304*a^2*b^6*B)*x^4*Sqrt[a + b*x] + (12*a^3*A*b^5 + 216*a^2*A*b^6 + 576*a*A*b^7 + 384*A*b^8 + 158*a^4*b^4*B + 1524*a^3*b^5*B + 2304*a^2*b^6*B + 832*a*b^7*B)*x^(9/2)*Sqrt[a + b*x] + (240*a^3*b^5*B + 960*a^2*b^6*B + 768*a*b^7*B)*x^5*Sqrt[a + b*x] + (8*a^3*b^5*B + 144*a^2*b^6*B + 384*a*b^7*B + 256*b^8*B)*x^(11/2)*Sqrt[a + b*x] + Sqrt[a + b]*(960*a^7*A*b + 1824*a^6*A*b^2 + 1116*a^5*A*b^3 + 246*a^4*A*b^4 + 12*a^3*A*b^5 + 96*a^8*B + 592*a^7*b*B + 982*a^6*b^2*B + 639*a^5*b^3*B + 158*a^4*b^4*B + 8*a^3*b^5*B + (-960*a^7*A*b + 1920*a^6*A*b^2 + 4572*a^5*A*b^3 + 2340*a^4*A*b^4 + 360*a^3*A*b^5 - 96*a^8*B + 192*a^7*b*B + 1686*a^6*b^2*B + 2538*a^5*b^3*B + 1380*a^4*b^4*B + 240*a^3*b^5*B)*Sqrt[x] + (-1440*a^6*A*b^2 + 4536*a^5*A*b^3 + 7038*a^4*A*b^4 + 2448*a^3*A*b^5 + 216*a^2*A*b^6 - 144*a^7*b*B + 1068*a^6*b^2*B + 3699*a^5*b^3*B + 3912*a^4*b^4*B + 1524*a^3*b^5*B + 144*a^2*b^6*B)*x + (-2304*a^6*A*b^2 - 2664*a^5*A*b^3 + 6828*a^4*A*b^4 + 6720*a^3*A*b^5 + 1440*a^2*A*b^6 - 640*a^7*b*B - 676*a^6*b^2*B + 2142*a^5*b^3*B + 4960*a^4*b^4*B + 3760*a^3*b^5*B + 960*a^2*b^6*B)*x^(3/2) + (-5652*a^5*A*b^3 - 2958*a^4*A*b^4 + 6816*a^3*A*b^5 + 3888*a^2*A*b^6 + 576*a*A*b^7 - 1794*a^6*b^2*B - 987*a^5*b^3*B + 2784*a^4*b^4*B + 4272*a^3*b^5*B + 2304*a^2*b^6*B + 384*a*b^7*B)*x^2 + (-1908*a^5*A*b^3 - 8532*a^4*A*b^4 - 2016*a^3*A*b^5 + 4320*a^2*A*b^6 + 1152*a*A*b^7 - 1266*a^6*b^2*B - 3618*a^5*b^3*B - 864*a^4*b^4*B + 2208*a^3*b^5*B + 2304*a^2*b^6*B + 768*a*b^7*B)*x^(5/2) + (-4326*a^4*A*b^4 - 8160*a^3*A*b^5 - 720*a^2*A*b^6 + 1536*a*A*b^7 + 384*A*b^8 - 3351*a^5*b^3*B - 4400*a^4*b^4*B - 368*a^3*b^5*B + 912*a^2*b^6*B + 832*a*b^7*B + 256*b^8*B)*x^3 + (-636*a^4*A*b^4 - 4992*a^3*A*b^5 - 4896*a^2*A*b^6 - 1062*a^5*b^3*B - 5088*a^4*b^4*B - 3264*a^3*b^5*B)*x^(7/2) + (-1116*a^3*A*b^5 - 3312*a^2*A*b^6 - 1728*a*A*b^7 - 2454*a^4*b^4*B - 4728*a^3*b^5*B - 1296*a^2*b^6*B)*x^4 + (-72*a^3*A*b^5 - 864*a^2*A*b^6 - 1152*a*A*b^7 - 388*a^4*b^4*B - 2896*a^3*b^5*B - 2688*a^2*b^6*B)*x^(9/2) + (-72*a^2*A*b^6 - 384*a*A*b^7 - 384*A*b^8 - 708*a^3*b^5*B - 2016*a^2*b^6*B - 960*a*b^7*B)*x^5 + (-48*a^3*b^5*B - 576*a^2*b^6*B - 768*a*b^7*B)*x^(11/2) + (-48*a^2*b^6*B - 256*a*b^7*B - 256*b^8*B)*x^6))/(24*b*(32*a^6 + 48*a^5*b + 18*a^4*b^2 + a^3*b^3) + 24*b*(a^3*b^3 + 18*a^2*b^4 + 48*a*b^5 + 32*b^6)*x^3 + 24*b*Sqrt[a + b]*(-32*a^5 - 32*a^4*b - 6*a^3*b^2)*Sqrt[a + b*x] + x*(24*b*(48*a^5*b + 204*a^4*b^2 + 159*a^3*b^3 + 18*a^2*b^4) + 24*b*Sqrt[a + b]*(-32*a^4*b - 164*a^3*b^2 - 72*a^2*b^3)*Sqrt[a + b*x]) + Sqrt[x]*(24*b*(96*a^5*b + 120*a^4*b^2 + 30*a^3*b^3) + 24*b*Sqrt[a + b]*(-96*a^4*b - 72*a^3*b^2 - 6*a^2*b^3)*Sqrt[a + b*x]) + x^2*(24*b*(18*a^4*b^2 + 159*a^3*b^3 + 204*a^2*b^4 + 48*a*b^5) + 24*b*Sqrt[a + b]*(-6*a^3*b^2 - 72*a^2*b^3 - 96*a*b^4)*Sqrt[a + b*x]) + x^(3/2)*(24*b*(120*a^4*b^2 + 260*a^3*b^3 + 120*a^2*b^4) + 24*b*Sqrt[a + b]*(-72*a^3*b^2 - 164*a^2*b^3 - 32*a*b^4)*Sqrt[a + b*x]) + x^(5/2)*(24*b*(30*a^3*b^3 + 120*a^2*b^4 + 96*a*b^5) + 24*b*Sqrt[a + b]*(-6*a^2*b^3 - 32*a*b^4 - 32*b^5)*Sqrt[a + b*x])) + ((-3*a^2*A)/(2*Sqrt[b]) + (a^3*B)/(4*b^(3/2)))*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",1
494,1,966,115,7.2984282,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^{3/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/x^(3/2),x]","\frac{\left(-\frac{3 B a^2}{2}-\frac{1}{2} B \sqrt{x} a^2-2 b B a-4 b B \sqrt{x} a+2 \sqrt{a+b} B \sqrt{a+b x} a-4 b^2 B \sqrt{x}+4 b \sqrt{a+b} B \sqrt{a+b x}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^7}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^4}+\frac{\left(-\frac{13 B a^2}{2}-\frac{3}{2} B \sqrt{x} a^2-12 b B a-12 b B \sqrt{x} a+8 \sqrt{a+b} B \sqrt{a+b x} a-4 b^2 B-12 b^2 B \sqrt{x}+16 b \sqrt{a+b} B \sqrt{a+b x}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^5}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^3}+\frac{\left(-\frac{39 B a^2}{4}-\frac{9}{4} B \sqrt{x} a^2-A b a-20 b B a-A b \sqrt{x} a-12 b B \sqrt{x} a+12 \sqrt{a+b} B \sqrt{a+b x} a-10 b^2 B-2 A b^2 \sqrt{x}-10 b^2 B \sqrt{x}+20 b \sqrt{a+b} B \sqrt{a+b x}+2 A b \sqrt{a+b} \sqrt{a+b x}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^3}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^2}+\frac{\left(2 a^2 A-2 a^2 A \sqrt{x}\right) \left(-\sqrt{x} a+2 a+2 b+b x-2 b \sqrt{x}-2 \sqrt{a+b} \sqrt{a+b x}+\sqrt{a+b} \sqrt{x} \sqrt{a+b x}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)}{\sqrt{x} \left(-2 \sqrt{x} a^2+4 a^2-b x^{3/2} a+4 b a+2 b x a-b \sqrt{x} a-4 \sqrt{a+b} \sqrt{a+b x} a+2 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a+2 b^2 \sqrt{x}-2 b \sqrt{a+b} \sqrt{a+b x}\right)}+\frac{\left(\frac{1}{4} \sqrt{a+b x}-\frac{\sqrt{a+b}}{4}\right) \left(27 B a^2+5 B \sqrt{x} a^2+12 A b a+48 b B a+4 A b \sqrt{x} a+16 b B \sqrt{x} a-32 \sqrt{a+b} B \sqrt{a+b x} a+8 A b^2+24 b^2 B+8 A b^2 \sqrt{x}+8 b^2 B \sqrt{x}-32 b \sqrt{a+b} B \sqrt{a+b x}-16 A b \sqrt{a+b} \sqrt{a+b x}\right)}{-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}}+\left(-\frac{3 B a^2}{2 \sqrt{b}}-6 A \sqrt{b} a\right) \tanh ^{-1}\left(\frac{\sqrt{b} \left(\sqrt{x}-1\right)}{\sqrt{a+b}-\sqrt{a+b x}}\right)","\frac{\sqrt{x} (a+b x)^{3/2} (a B+4 A b)}{2 a}+\frac{3}{4} \sqrt{x} \sqrt{a+b x} (a B+4 A b)+\frac{3 a (a B+4 A b) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{4 \sqrt{b}}-\frac{2 A (a+b x)^{5/2}}{a \sqrt{x}}",1,"((-1/4*Sqrt[a + b] + Sqrt[a + b*x]/4)*(12*a*A*b + 8*A*b^2 + 27*a^2*B + 48*a*b*B + 24*b^2*B + 4*a*A*b*Sqrt[x] + 8*A*b^2*Sqrt[x] + 5*a^2*B*Sqrt[x] + 16*a*b*B*Sqrt[x] + 8*b^2*B*Sqrt[x] - 16*A*b*Sqrt[a + b]*Sqrt[a + b*x] - 32*a*Sqrt[a + b]*B*Sqrt[a + b*x] - 32*b*Sqrt[a + b]*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x]) + ((Sqrt[a + b] - Sqrt[a + b*x])^7*((-3*a^2*B)/2 - 2*a*b*B - (a^2*B*Sqrt[x])/2 - 4*a*b*B*Sqrt[x] - 4*b^2*B*Sqrt[x] + 2*a*Sqrt[a + b]*B*Sqrt[a + b*x] + 4*b*Sqrt[a + b]*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4 + ((Sqrt[a + b] - Sqrt[a + b*x])^5*((-13*a^2*B)/2 - 12*a*b*B - 4*b^2*B - (3*a^2*B*Sqrt[x])/2 - 12*a*b*B*Sqrt[x] - 12*b^2*B*Sqrt[x] + 8*a*Sqrt[a + b]*B*Sqrt[a + b*x] + 16*b*Sqrt[a + b]*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^3 + ((Sqrt[a + b] - Sqrt[a + b*x])^3*(-(a*A*b) - (39*a^2*B)/4 - 20*a*b*B - 10*b^2*B - a*A*b*Sqrt[x] - 2*A*b^2*Sqrt[x] - (9*a^2*B*Sqrt[x])/4 - 12*a*b*B*Sqrt[x] - 10*b^2*B*Sqrt[x] + 2*A*b*Sqrt[a + b]*Sqrt[a + b*x] + 12*a*Sqrt[a + b]*B*Sqrt[a + b*x] + 20*b*Sqrt[a + b]*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 + ((2*a^2*A - 2*a^2*A*Sqrt[x])*(Sqrt[a + b] - Sqrt[a + b*x])*(2*a + 2*b - a*Sqrt[x] - 2*b*Sqrt[x] + b*x - 2*Sqrt[a + b]*Sqrt[a + b*x] + Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(Sqrt[x]*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])) + (-6*a*A*Sqrt[b] - (3*a^2*B)/(2*Sqrt[b]))*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",1
495,1,2359,117,36.0050794,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^{5/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/x^(5/2),x]","\text{Result too large to show}","-\frac{2 (a+b x)^{3/2} (3 a B+2 A b)}{3 a \sqrt{x}}+\frac{b \sqrt{x} \sqrt{a+b x} (3 a B+2 A b)}{a}+\sqrt{b} (3 a B+2 A b) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)-\frac{2 A (a+b x)^{5/2}}{3 a x^{3/2}}",1,"((-3*a - 2*b - a*Sqrt[x] - 2*b*Sqrt[x] + 4*Sqrt[a + b]*Sqrt[a + b*x])*(b*Sqrt[a + b]*B - b*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x]) + ((Sqrt[a + b] - Sqrt[a + b*x])^3*(-(a*b*B) - a*b*B*Sqrt[x] - 2*b^2*B*Sqrt[x] + 2*b*Sqrt[a + b]*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 + ((Sqrt[a + b] - Sqrt[a + b*x])^5*(72*a^3*A + (512*a^7*A)/(3*b^4) + (512*a^6*A)/b^3 + (1664*a^5*A)/(3*b^2) + (832*a^4*A)/(3*b) + 8*a^2*A*b - 164*a^3*A*Sqrt[x] - (128*a^6*A*Sqrt[x])/(3*b^3) - (496*a^5*A*Sqrt[x])/(3*b^2) - (766*a^4*A*Sqrt[x])/(3*b) - 32*a^2*A*b*Sqrt[x] + (466*a^3*A*x)/3 + (128*a^6*A*x)/b^3 + (376*a^5*A*x)/b^2 + (1178*a^4*A*x)/(3*b) + 12*a^2*A*b*x - 34*a^3*A*x^(3/2) - (64*a^5*A*x^(3/2))/(3*b^2) - (52*a^4*A*x^(3/2))/b - 4*a^2*A*b*x^(3/2) + 8*a^2*A*Sqrt[a + b]*Sqrt[a + b*x] - (512*a^6*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^4) - (1280*a^5*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^3) - (1088*a^4*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^2) - (96*a^3*A*Sqrt[a + b]*Sqrt[a + b*x])/b + 12*a^2*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + (128*a^5*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/(3*b^3) + (144*a^4*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/b^2 + (314*a^3*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/(3*b) - 4*a^2*A*Sqrt[a + b]*x*Sqrt[a + b*x] - (128*a^5*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^3) - (296*a^4*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^2) - (54*a^3*A*Sqrt[a + b]*x*Sqrt[a + b*x])/b))/(x*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])^2) + ((Sqrt[a + b] - Sqrt[a + b*x])^9*((16*a^3*A)/3 + (64*a^6*A)/(3*b^3) + (48*a^5*A)/b^2 + (32*a^4*A)/b - 32*a^3*A*Sqrt[x] - (256*a^7*A*Sqrt[x])/(3*b^4) - (928*a^6*A*Sqrt[x])/(3*b^3) - (392*a^5*A*Sqrt[x])/b^2 - (200*a^4*A*Sqrt[x])/b + 8*a^3*A*x + (128*a^7*A*x)/(3*b^4) + (160*a^6*A*x)/b^3 + (584*a^5*A*x)/(3*b^2) + (256*a^4*A*x)/(3*b) - (8*a^3*A*x^(3/2))/3 - (64*a^6*A*x^(3/2))/(3*b^3) - (128*a^5*A*x^(3/2))/(3*b^2) - (24*a^4*A*x^(3/2))/b + (64*a^5*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^3) + (112*a^4*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^2) + (16*a^3*A*Sqrt[a + b]*Sqrt[a + b*x])/b + (256*a^6*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/(3*b^4) + (160*a^5*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/b^3 + (248*a^4*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/(3*b^2) + (8*a^3*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/b - (128*a^6*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^4) - (224*a^5*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^3) - (104*a^4*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^2) - (8*a^3*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b)))/(x^(3/2)*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])^3) + (((-2*a*Sqrt[a + b])/(3*b^2) + (2*a*Sqrt[a + b*x])/(3*b^2))*(-144*a^4*A - 304*a^3*A*b - 203*a^2*A*b^2 - 57*a*A*b^3 - 12*A*b^4 - 6*a^2*b^2*B - 6*a*b^3*B + 28*a^3*A*b*Sqrt[x] + 53*a^2*A*b^2*Sqrt[x] + 48*a*A*b^3*Sqrt[x] + 24*A*b^4*Sqrt[x] + 9*a^2*b^2*B*Sqrt[x] + 12*a*b^3*B*Sqrt[x] - 108*a^3*A*b*x - 200*a^2*A*b^2*x - 102*a*A*b^3*x - 18*A*b^4*x - 3*a^2*b^2*B*x - 9*a*b^3*B*x + 14*a^2*A*b^2*x^(3/2) + 15*a*A*b^3*x^(3/2) + 6*A*b^4*x^(3/2) + 3*a*b^3*B*x^(3/2) + 144*a^3*A*Sqrt[a + b]*Sqrt[a + b*x] + 232*a^2*A*b*Sqrt[a + b]*Sqrt[a + b*x] + 105*a*A*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 12*A*b^3*Sqrt[a + b]*Sqrt[a + b*x] + 6*a*b^2*Sqrt[a + b]*B*Sqrt[a + b*x] - 28*a^2*A*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 39*a*A*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 18*A*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 9*a*b^2*Sqrt[a + b]*B*Sqrt[x]*Sqrt[a + b*x] + 36*a^2*A*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 30*a*A*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] + 6*A*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] + 3*a*b^2*Sqrt[a + b]*B*x*Sqrt[a + b*x]))/(Sqrt[x]*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])) + (-4*A*b^(3/2) - 6*a*Sqrt[b]*B)*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",0
496,1,7481,89,78.8875131,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^{7/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/x^(7/2),x]","\text{Result too large to show}","-\frac{2 A (a+b x)^{5/2}}{5 a x^{5/2}}+2 b^{3/2} B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)-\frac{2 B (a+b x)^{3/2}}{3 x^{3/2}}-\frac{2 b B \sqrt{a+b x}}{\sqrt{x}}",1,"Result too large to show","B",1
497,-1,0,53,180.2683113,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^{9/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/x^(9/2),x]","\text{\$Aborted}","\frac{2 (a+b x)^{5/2} (2 A b-7 a B)}{35 a^2 x^{5/2}}-\frac{2 A (a+b x)^{5/2}}{7 a x^{7/2}}",1,"$Aborted","F",-1
498,-1,0,84,180.7500742,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^{11/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/x^(11/2),x]","\text{\$Aborted}","-\frac{4 b (a+b x)^{5/2} (4 A b-9 a B)}{315 a^3 x^{5/2}}+\frac{2 (a+b x)^{5/2} (4 A b-9 a B)}{63 a^2 x^{7/2}}-\frac{2 A (a+b x)^{5/2}}{9 a x^{9/2}}",1,"$Aborted","F",-1
499,-1,0,117,181.8319244,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^{13/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/x^(13/2),x]","\text{\$Aborted}","\frac{16 b^2 (a+b x)^{5/2} (6 A b-11 a B)}{3465 a^4 x^{5/2}}-\frac{8 b (a+b x)^{5/2} (6 A b-11 a B)}{693 a^3 x^{7/2}}+\frac{2 (a+b x)^{5/2} (6 A b-11 a B)}{99 a^2 x^{9/2}}-\frac{2 A (a+b x)^{5/2}}{11 a x^{11/2}}",1,"$Aborted","F",-1
500,-1,0,150,180.0886617,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^{15/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/x^(15/2),x]","\text{\$Aborted}","-\frac{32 b^3 (a+b x)^{5/2} (8 A b-13 a B)}{15015 a^5 x^{5/2}}+\frac{16 b^2 (a+b x)^{5/2} (8 A b-13 a B)}{3003 a^4 x^{7/2}}-\frac{4 b (a+b x)^{5/2} (8 A b-13 a B)}{429 a^3 x^{9/2}}+\frac{2 (a+b x)^{5/2} (8 A b-13 a B)}{143 a^2 x^{11/2}}-\frac{2 A (a+b x)^{5/2}}{13 a x^{13/2}}",1,"$Aborted","F",-1
501,-1,0,183,180.1369265,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^{17/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/x^(17/2),x]","\text{\$Aborted}","\frac{256 b^4 (a+b x)^{5/2} (2 A b-3 a B)}{45045 a^6 x^{5/2}}-\frac{128 b^3 (a+b x)^{5/2} (2 A b-3 a B)}{9009 a^5 x^{7/2}}+\frac{32 b^2 (a+b x)^{5/2} (2 A b-3 a B)}{1287 a^4 x^{9/2}}-\frac{16 b (a+b x)^{5/2} (2 A b-3 a B)}{429 a^3 x^{11/2}}+\frac{2 (a+b x)^{5/2} (2 A b-3 a B)}{39 a^2 x^{13/2}}-\frac{2 A (a+b x)^{5/2}}{15 a x^{15/2}}",1,"$Aborted","F",-1
502,1,9853,225,161.4159578,"\int x^{3/2} (a+b x)^{5/2} (A+B x) \, dx","IntegrateAlgebraic[x^(3/2)*(a + b*x)^(5/2)*(A + B*x),x]","\text{Result too large to show}","\frac{a^5 (12 A b-5 a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{512 b^{7/2}}-\frac{a^4 \sqrt{x} \sqrt{a+b x} (12 A b-5 a B)}{512 b^3}+\frac{a^3 x^{3/2} \sqrt{a+b x} (12 A b-5 a B)}{768 b^2}+\frac{a^2 x^{5/2} \sqrt{a+b x} (12 A b-5 a B)}{192 b}+\frac{a x^{5/2} (a+b x)^{3/2} (12 A b-5 a B)}{96 b}+\frac{x^{5/2} (a+b x)^{5/2} (12 A b-5 a B)}{60 b}+\frac{B x^{5/2} (a+b x)^{7/2}}{6 b}",1,"Result too large to show","B",0
503,1,6957,192,102.2497941,"\int \sqrt{x} (a+b x)^{5/2} (A+B x) \, dx","IntegrateAlgebraic[Sqrt[x]*(a + b*x)^(5/2)*(A + B*x),x]","\text{Result too large to show}","-\frac{a^4 (10 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{128 b^{5/2}}+\frac{a^3 \sqrt{x} \sqrt{a+b x} (10 A b-3 a B)}{128 b^2}+\frac{a^2 x^{3/2} \sqrt{a+b x} (10 A b-3 a B)}{64 b}+\frac{a x^{3/2} (a+b x)^{3/2} (10 A b-3 a B)}{48 b}+\frac{x^{3/2} (a+b x)^{5/2} (10 A b-3 a B)}{40 b}+\frac{B x^{3/2} (a+b x)^{7/2}}{5 b}",1,"Result too large to show","B",0
504,1,4523,159,55.6564123,"\int \frac{(a+b x)^{5/2} (A+B x)}{\sqrt{x}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/Sqrt[x],x]","\text{Result too large to show}","\frac{5 a^3 (8 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{64 b^{3/2}}+\frac{5 a^2 \sqrt{x} \sqrt{a+b x} (8 A b-a B)}{64 b}+\frac{\sqrt{x} (a+b x)^{5/2} (8 A b-a B)}{24 b}+\frac{5 a \sqrt{x} (a+b x)^{3/2} (8 A b-a B)}{96 b}+\frac{B \sqrt{x} (a+b x)^{7/2}}{4 b}",1,"((-33792*a^10*A*b - 111104*a^9*A*b^2 - 146560*a^8*A*b^3 - 100288*a^7*A*b^4 - 37824*a^6*A*b^5 - 7296*a^5*A*b^6 - 512*a^4*A*b^7 - 1920*a^11*B - 19904*a^10*b*B - 59248*a^9*b^2*B - 83080*a^8*b^3*B - 62856*a^7*b^4*B - 25968*a^6*b^5*B - 5312*a^5*b^6*B - 384*a^4*b^7*B)*Sqrt[a + b*x] + (33792*a^10*A*b - 67584*a^9*A*b^2 - 368384*a^8*A*b^3 - 483584*a^7*A*b^4 - 299320*a^6*A*b^5 - 96960*a^5*A*b^6 - 14464*a^4*A*b^7 - 512*a^3*A*b^8 + 1920*a^11*B - 3840*a^10*b*B - 75296*a^9*b^2*B - 217568*a^8*b^3*B - 282409*a^7*b^4*B - 192168*a^6*b^5*B - 68080*a^5*b^6*B - 10688*a^4*b^7*B - 384*a^3*b^8*B)*Sqrt[x]*Sqrt[a + b*x] + (84480*a^9*A*b^2 - 183552*a^8*A*b^3 - 808128*a^7*A*b^4 - 897408*a^6*A*b^5 - 464256*a^5*A*b^6 - 121344*a^4*A*b^7 - 12288*a^3*A*b^8 + 4800*a^10*b*B - 30816*a^9*b^2*B - 224232*a^8*b^3*B - 498000*a^7*b^4*B - 538704*a^6*b^5*B - 307392*a^5*b^6*B - 87168*a^4*b^7*B - 9216*a^3*b^8*B)*x*Sqrt[a + b*x] + (94208*a^9*A*b^2 + 272896*a^8*A*b^3 - 311040*a^7*A*b^4 - 1199328*a^6*A*b^5 - 1085424*a^5*A*b^6 - 454400*a^4*A*b^7 - 90880*a^3*A*b^8 - 5120*a^2*A*b^9 + 18944*a^10*b*B + 42688*a^9*b^2*B - 68640*a^8*b^3*B - 421284*a^7*b^4*B - 749682*a^6*b^5*B - 668960*a^5*b^6*B - 311200*a^4*b^7*B - 66560*a^3*b^8*B - 3840*a^2*b^9*B)*x^(3/2)*Sqrt[a + b*x] + (321920*a^8*A*b^3 + 573120*a^7*A*b^4 - 368640*a^6*A*b^5 - 1244160*a^5*A*b^6 - 893440*a^4*A*b^7 - 296960*a^3*A*b^8 - 40960*a^2*A*b^9 + 72656*a^9*b^2*B + 119208*a^8*b^3*B - 107136*a^7*b^4*B - 540672*a^6*b^5*B - 775360*a^5*b^6*B - 567680*a^4*b^7*B - 209920*a^3*b^8*B - 30720*a^2*b^9*B)*x^2*Sqrt[a + b*x] + (103680*a^8*A*b^3 + 736512*a^7*A*b^4 + 863856*a^6*A*b^5 - 299136*a^5*A*b^6 - 896832*a^4*A*b^7 - 499200*a^3*A*b^8 - 132096*a^2*A*b^9 - 12288*a*A*b^10 + 50016*a^9*b^2*B + 232032*a^8*b^3*B + 236754*a^7*b^4*B - 109104*a^6*b^5*B - 472200*a^5*b^6*B - 550464*a^4*b^7*B - 330240*a^3*b^8*B - 95232*a^2*b^9*B - 9216*a*b^10*B)*x^(5/2)*Sqrt[a + b*x] + (335296*a^7*A*b^4 + 1138560*a^6*A*b^5 + 930816*a^5*A*b^6 - 156672*a^4*A*b^7 - 428032*a^3*A*b^8 - 180224*a^2*A*b^9 - 32768*a*A*b^10 + 181960*a^8*b^3*B + 467856*a^7*b^4*B + 321792*a^6*b^5*B - 69120*a^5*b^6*B - 266368*a^4*b^7*B - 257024*a^3*b^8*B - 124928*a^2*b^9*B - 24576*a*b^10*B)*x^3*Sqrt[a + b*x] + (58112*a^7*A*b^4 + 617632*a^6*A*b^5 + 1232544*a^5*A*b^6 + 702720*a^4*A*b^7 - 43776*a^3*A*b^8 - 117760*a^2*A*b^9 - 47104*a*A*b^10 - 8192*A*b^11 + 60320*a^8*b^3*B + 429100*a^7*b^4*B + 657036*a^6*b^5*B + 297888*a^5*b^6*B - 22128*a^4*b^7*B - 80896*a^3*b^8*B - 71680*a^2*b^9*B - 32768*a*b^10*B - 6144*b^11*B)*x^(7/2)*Sqrt[a + b*x] + (165312*a^6*A*b^5 + 744576*a^5*A*b^6 + 935424*a^4*A*b^7 + 350208*a^3*A*b^8 + 200136*a^7*b^4*B + 673008*a^6*b^5*B + 649152*a^5*b^6*B + 177024*a^4*b^7*B)*x^4*Sqrt[a + b*x] + (17160*a^6*A*b^5 + 246720*a^5*A*b^6 + 617600*a^4*A*b^7 + 486400*a^3*A*b^8 + 97280*a^2*A*b^9 + 37839*a^7*b^4*B + 381768*a^6*b^5*B + 739280*a^5*b^6*B + 445888*a^4*b^7*B + 55424*a^3*b^8*B)*x^(9/2)*Sqrt[a + b*x] + (40320*a^5*A*b^6 + 232960*a^4*A*b^7 + 358400*a^3*A*b^8 + 163840*a^2*A*b^9 + 110544*a^6*b^5*B + 478912*a^5*b^6*B + 576128*a^4*b^7*B + 203776*a^3*b^8*B)*x^5*Sqrt[a + b*x] + (2256*a^5*A*b^6 + 45312*a^4*A*b^7 + 145920*a^3*A*b^8 + 147456*a^2*A*b^9 + 43008*a*A*b^10 + 12150*a^6*b^5*B + 170400*a^5*b^6*B + 415200*a^4*b^7*B + 314880*a^3*b^8*B + 57600*a^2*b^9*B)*x^(11/2)*Sqrt[a + b*x] + (3584*a^4*A*b^7 + 28672*a^3*A*b^8 + 57344*a^2*A*b^9 + 32768*a*A*b^10 + 29120*a^5*b^6*B + 165760*a^4*b^7*B + 250880*a^3*b^8*B + 112640*a^2*b^9*B)*x^6*Sqrt[a + b*x] + (64*a^4*A*b^7 + 2048*a^3*A*b^8 + 10240*a^2*A*b^9 + 16384*a*A*b^10 + 8192*A*b^11 + 1672*a^5*b^6*B + 33344*a^4*b^7*B + 106240*a^3*b^8*B + 105472*a^2*b^9*B + 29696*a*b^10*B)*x^(13/2)*Sqrt[a + b*x] + (2688*a^4*b^7*B + 21504*a^3*b^8*B + 43008*a^2*b^9*B + 24576*a*b^10*B)*x^7*Sqrt[a + b*x] + (48*a^4*b^7*B + 1536*a^3*b^8*B + 7680*a^2*b^9*B + 12288*a*b^10*B + 6144*b^11*B)*x^(15/2)*Sqrt[a + b*x] + Sqrt[a + b]*(33792*a^10*A*b + 94208*a^9*A*b^2 + 103680*a^8*A*b^3 + 58112*a^7*A*b^4 + 17160*a^6*A*b^5 + 2256*a^5*A*b^6 + 64*a^4*A*b^7 + 1920*a^11*B + 18944*a^10*b*B + 50016*a^9*b^2*B + 60320*a^8*b^3*B + 37839*a^7*b^4*B + 12150*a^6*b^5*B + 1672*a^5*b^6*B + 48*a^4*b^7*B + (-33792*a^10*A*b + 84480*a^9*A*b^2 + 321920*a^8*A*b^3 + 335296*a^7*A*b^4 + 165312*a^6*A*b^5 + 40320*a^5*A*b^6 + 3584*a^4*A*b^7 - 1920*a^11*B + 4800*a^10*b*B + 72656*a^9*b^2*B + 181960*a^8*b^3*B + 200136*a^7*b^4*B + 110544*a^6*b^5*B + 29120*a^5*b^6*B + 2688*a^4*b^7*B)*Sqrt[x] + (-67584*a^9*A*b^2 + 272896*a^8*A*b^3 + 736512*a^7*A*b^4 + 617632*a^6*A*b^5 + 246720*a^5*A*b^6 + 45312*a^4*A*b^7 + 2048*a^3*A*b^8 - 3840*a^10*b*B + 42688*a^9*b^2*B + 232032*a^8*b^3*B + 429100*a^7*b^4*B + 381768*a^6*b^5*B + 170400*a^5*b^6*B + 33344*a^4*b^7*B + 1536*a^3*b^8*B)*x + (-111104*a^9*A*b^2 - 183552*a^8*A*b^3 + 573120*a^7*A*b^4 + 1138560*a^6*A*b^5 + 744576*a^5*A*b^6 + 232960*a^4*A*b^7 + 28672*a^3*A*b^8 - 19904*a^10*b*B - 30816*a^9*b^2*B + 119208*a^8*b^3*B + 467856*a^7*b^4*B + 673008*a^6*b^5*B + 478912*a^5*b^6*B + 165760*a^4*b^7*B + 21504*a^3*b^8*B)*x^(3/2) + (-368384*a^8*A*b^3 - 311040*a^7*A*b^4 + 863856*a^6*A*b^5 + 1232544*a^5*A*b^6 + 617600*a^4*A*b^7 + 145920*a^3*A*b^8 + 10240*a^2*A*b^9 - 75296*a^9*b^2*B - 68640*a^8*b^3*B + 236754*a^7*b^4*B + 657036*a^6*b^5*B + 739280*a^5*b^6*B + 415200*a^4*b^7*B + 106240*a^3*b^8*B + 7680*a^2*b^9*B)*x^2 + (-146560*a^8*A*b^3 - 808128*a^7*A*b^4 - 368640*a^6*A*b^5 + 930816*a^5*A*b^6 + 935424*a^4*A*b^7 + 358400*a^3*A*b^8 + 57344*a^2*A*b^9 - 59248*a^9*b^2*B - 224232*a^8*b^3*B - 107136*a^7*b^4*B + 321792*a^6*b^5*B + 649152*a^5*b^6*B + 576128*a^4*b^7*B + 250880*a^3*b^8*B + 43008*a^2*b^9*B)*x^(5/2) + (-483584*a^7*A*b^4 - 1199328*a^6*A*b^5 - 299136*a^5*A*b^6 + 702720*a^4*A*b^7 + 486400*a^3*A*b^8 + 147456*a^2*A*b^9 + 16384*a*A*b^10 - 217568*a^8*b^3*B - 421284*a^7*b^4*B - 109104*a^6*b^5*B + 297888*a^5*b^6*B + 445888*a^4*b^7*B + 314880*a^3*b^8*B + 105472*a^2*b^9*B + 12288*a*b^10*B)*x^3 + (-100288*a^7*A*b^4 - 897408*a^6*A*b^5 - 1244160*a^5*A*b^6 - 156672*a^4*A*b^7 + 350208*a^3*A*b^8 + 163840*a^2*A*b^9 + 32768*a*A*b^10 - 83080*a^8*b^3*B - 498000*a^7*b^4*B - 540672*a^6*b^5*B - 69120*a^5*b^6*B + 177024*a^4*b^7*B + 203776*a^3*b^8*B + 112640*a^2*b^9*B + 24576*a*b^10*B)*x^(7/2) + (-299320*a^6*A*b^5 - 1085424*a^5*A*b^6 - 896832*a^4*A*b^7 - 43776*a^3*A*b^8 + 97280*a^2*A*b^9 + 43008*a*A*b^10 + 8192*A*b^11 - 282409*a^7*b^4*B - 749682*a^6*b^5*B - 472200*a^5*b^6*B - 22128*a^4*b^7*B + 55424*a^3*b^8*B + 57600*a^2*b^9*B + 29696*a*b^10*B + 6144*b^11*B)*x^4 + (-37824*a^6*A*b^5 - 464256*a^5*A*b^6 - 893440*a^4*A*b^7 - 428032*a^3*A*b^8 - 62856*a^7*b^4*B - 538704*a^6*b^5*B - 775360*a^5*b^6*B - 266368*a^4*b^7*B)*x^(9/2) + (-96960*a^5*A*b^6 - 454400*a^4*A*b^7 - 499200*a^3*A*b^8 - 117760*a^2*A*b^9 - 192168*a^6*b^5*B - 668960*a^5*b^6*B - 550464*a^4*b^7*B - 80896*a^3*b^8*B)*x^5 + (-7296*a^5*A*b^6 - 121344*a^4*A*b^7 - 296960*a^3*A*b^8 - 180224*a^2*A*b^9 - 25968*a^6*b^5*B - 307392*a^5*b^6*B - 567680*a^4*b^7*B - 257024*a^3*b^8*B)*x^(11/2) + (-14464*a^4*A*b^7 - 90880*a^3*A*b^8 - 132096*a^2*A*b^9 - 47104*a*A*b^10 - 68080*a^5*b^6*B - 311200*a^4*b^7*B - 330240*a^3*b^8*B - 71680*a^2*b^9*B)*x^6 + (-512*a^4*A*b^7 - 12288*a^3*A*b^8 - 40960*a^2*A*b^9 - 32768*a*A*b^10 - 5312*a^5*b^6*B - 87168*a^4*b^7*B - 209920*a^3*b^8*B - 124928*a^2*b^9*B)*x^(13/2) + (-512*a^3*A*b^8 - 5120*a^2*A*b^9 - 12288*a*A*b^10 - 8192*A*b^11 - 10688*a^4*b^7*B - 66560*a^3*b^8*B - 95232*a^2*b^9*B - 32768*a*b^10*B)*x^7 + (-384*a^4*b^7*B - 9216*a^3*b^8*B - 30720*a^2*b^9*B - 24576*a*b^10*B)*x^(15/2) + (-384*a^3*b^8*B - 3840*a^2*b^9*B - 9216*a*b^10*B - 6144*b^11*B)*x^8))/(192*b*(128*a^8 + 256*a^7*b + 160*a^6*b^2 + 32*a^5*b^3 + a^4*b^4) + 192*b*(a^4*b^4 + 32*a^3*b^5 + 160*a^2*b^6 + 256*a*b^7 + 128*b^8)*x^4 + 192*b*Sqrt[a + b]*(-128*a^7 - 192*a^6*b - 80*a^5*b^2 - 8*a^4*b^3)*Sqrt[a + b*x] + x*(192*b*(256*a^7*b + 1472*a^6*b^2 + 1760*a^5*b^3 + 604*a^4*b^4 + 32*a^3*b^5) + 192*b*Sqrt[a + b]*(-192*a^6*b - 1248*a^5*b^2 - 1080*a^4*b^3 - 192*a^3*b^4)*Sqrt[a + b*x]) + Sqrt[x]*(192*b*(512*a^7*b + 896*a^6*b^2 + 448*a^5*b^3 + 56*a^4*b^4) + 192*b*Sqrt[a + b]*(-512*a^6*b - 640*a^5*b^2 - 192*a^4*b^3 - 8*a^3*b^4)*Sqrt[a + b*x]) + x^2*(192*b*(160*a^6*b^2 + 1760*a^5*b^3 + 3270*a^4*b^4 + 1760*a^3*b^5 + 160*a^2*b^6) + 192*b*Sqrt[a + b]*(-80*a^5*b^2 - 1080*a^4*b^3 - 1920*a^3*b^4 - 640*a^2*b^5)*Sqrt[a + b*x]) + x^(3/2)*(192*b*(896*a^6*b^2 + 2688*a^5*b^3 + 2184*a^4*b^4 + 448*a^3*b^5) + 192*b*Sqrt[a + b]*(-640*a^5*b^2 - 1920*a^4*b^3 - 1080*a^3*b^4 - 80*a^2*b^5)*Sqrt[a + b*x]) + x^3*(192*b*(32*a^5*b^3 + 604*a^4*b^4 + 1760*a^3*b^5 + 1472*a^2*b^6 + 256*a*b^7) + 192*b*Sqrt[a + b]*(-8*a^4*b^3 - 192*a^3*b^4 - 640*a^2*b^5 - 512*a*b^6)*Sqrt[a + b*x]) + x^(5/2)*(192*b*(448*a^5*b^3 + 2184*a^4*b^4 + 2688*a^3*b^5 + 896*a^2*b^6) + 192*b*Sqrt[a + b]*(-192*a^4*b^3 - 1080*a^3*b^4 - 1248*a^2*b^5 - 192*a*b^6)*Sqrt[a + b*x]) + x^(7/2)*(192*b*(56*a^4*b^4 + 448*a^3*b^5 + 896*a^2*b^6 + 512*a*b^7) + 192*b*Sqrt[a + b]*(-8*a^3*b^4 - 80*a^2*b^5 - 192*a*b^6 - 128*b^7)*Sqrt[a + b*x])) + ((-5*a^3*A)/(4*Sqrt[b]) + (5*a^4*B)/(32*b^(3/2)))*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",1
505,1,1882,144,25.2425216,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{3/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/x^(3/2),x]","\frac{\left(-\frac{5 B a^3}{3}-\frac{1}{3} B \sqrt{x} a^3-\frac{20}{3} b B a^2-6 b B \sqrt{x} a^2+2 \sqrt{a+b} B \sqrt{a+b x} a^2-\frac{16}{3} b^2 B a-16 b^2 B \sqrt{x} a+\frac{32}{3} b \sqrt{a+b} B \sqrt{a+b x} a-\frac{32}{3} b^3 B \sqrt{x}+\frac{32}{3} b^2 \sqrt{a+b} B \sqrt{a+b x}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^{11}}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^6}+\frac{\left(-\frac{31 B a^3}{3}-\frac{5}{3} B \sqrt{x} a^3-46 b B a^2-30 b B \sqrt{x} a^2+12 \sqrt{a+b} B \sqrt{a+b x} a^2-48 b^2 B a-80 b^2 B \sqrt{x} a+64 b \sqrt{a+b} B \sqrt{a+b x} a-\frac{32 b^3 B}{3}-\frac{160}{3} b^3 B \sqrt{x}+64 b^2 \sqrt{a+b} B \sqrt{a+b x}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^9}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^5}+\frac{\left(-\frac{105 B a^3}{4}-\frac{15}{4} B \sqrt{x} a^3-\frac{3}{2} A b a^2-120 b B a^2-\frac{1}{2} A b \sqrt{x} a^2-60 b B \sqrt{x} a^2+30 \sqrt{a+b} B \sqrt{a+b x} a^2-2 A b^2 a-144 b^2 B a-4 A b^2 \sqrt{x} a-150 b^2 B \sqrt{x} a+150 b \sqrt{a+b} B \sqrt{a+b x} a+2 A b \sqrt{a+b} \sqrt{a+b x} a-48 b^3 B-4 A b^3 \sqrt{x}-96 b^3 B \sqrt{x}+144 b^2 \sqrt{a+b} B \sqrt{a+b x}+4 A b^2 \sqrt{a+b} \sqrt{a+b x}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^7}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^4}+\frac{\left(-\frac{425 B a^3}{12}-\frac{55}{12} B \sqrt{x} a^3-\frac{13}{2} A b a^2-\frac{460}{3} b B a^2-\frac{3}{2} A b \sqrt{x} a^2-60 b B \sqrt{x} a^2+40 \sqrt{a+b} B \sqrt{a+b x} a^2-12 A b^2 a-\frac{578}{3} b^2 B a-12 A b^2 \sqrt{x} a-130 b^2 B \sqrt{x} a+\frac{520}{3} b \sqrt{a+b} B \sqrt{a+b x} a+8 A b \sqrt{a+b} \sqrt{a+b x} a-4 A b^3-\frac{224 b^3 B}{3}-12 A b^3 \sqrt{x}-\frac{224}{3} b^3 B \sqrt{x}+\frac{448}{3} b^2 \sqrt{a+b} B \sqrt{a+b x}+16 A b^2 \sqrt{a+b} \sqrt{a+b x}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^5}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^3}+\frac{\left(-\frac{635 B a^3}{24}-\frac{85}{24} B \sqrt{x} a^3-\frac{43}{4} A b a^2-100 b B a^2-\frac{13}{4} A b \sqrt{x} a^2-30 b B \sqrt{x} a^2+30 \sqrt{a+b} B \sqrt{a+b x} a^2-20 A b^2 a-120 b^2 B a-14 A b^2 \sqrt{x} a-50 b^2 B \sqrt{x} a+100 b \sqrt{a+b} B \sqrt{a+b x} a+14 A b \sqrt{a+b} \sqrt{a+b x} a-10 A b^3-\frac{140 b^3 B}{3}-10 A b^3 \sqrt{x}-\frac{70}{3} b^3 B \sqrt{x}+70 b^2 \sqrt{a+b} B \sqrt{a+b x}+20 A b^2 \sqrt{a+b} \sqrt{a+b x}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^3}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^2}+\frac{\left(2 a^3 A-2 a^3 A \sqrt{x}\right) \left(-\sqrt{x} a+2 a+2 b+b x-2 b \sqrt{x}-2 \sqrt{a+b} \sqrt{a+b x}+\sqrt{a+b} \sqrt{x} \sqrt{a+b x}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)}{\sqrt{x} \left(-2 \sqrt{x} a^2+4 a^2-b x^{3/2} a+4 b a+2 b x a-b \sqrt{x} a-4 \sqrt{a+b} \sqrt{a+b x} a+2 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a+2 b^2 \sqrt{x}-2 b \sqrt{a+b} \sqrt{a+b x}\right)}+\frac{\left(\frac{\sqrt{a+b}}{8}-\frac{1}{8} \sqrt{a+b x}\right) \left(-85 B a^3-11 B \sqrt{x} a^3-78 A b a^2-240 b B a^2-18 A b \sqrt{x} a^2-48 b B \sqrt{x} a^2+96 \sqrt{a+b} B \sqrt{a+b x} a^2-112 A b^2 a-240 b^2 B a-48 A b^2 \sqrt{x} a-48 b^2 B \sqrt{x} a+192 b \sqrt{a+b} B \sqrt{a+b x} a+96 A b \sqrt{a+b} \sqrt{a+b x} a-48 A b^3-80 b^3 B-16 A b^3 \sqrt{x}-16 b^3 B \sqrt{x}+96 b^2 \sqrt{a+b} B \sqrt{a+b x}+64 A b^2 \sqrt{a+b} \sqrt{a+b x}\right)}{-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}}+\left(-\frac{5 B a^3}{4 \sqrt{b}}-\frac{15}{2} A \sqrt{b} a^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \left(\sqrt{x}-1\right)}{\sqrt{a+b}-\sqrt{a+b x}}\right)","\frac{5 a^2 (a B+6 A b) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 \sqrt{b}}+\frac{\sqrt{x} (a+b x)^{5/2} (a B+6 A b)}{3 a}+\frac{5}{12} \sqrt{x} (a+b x)^{3/2} (a B+6 A b)+\frac{5}{8} a \sqrt{x} \sqrt{a+b x} (a B+6 A b)-\frac{2 A (a+b x)^{7/2}}{a \sqrt{x}}",1,"((Sqrt[a + b] - Sqrt[a + b*x])^11*((-5*a^3*B)/3 - (20*a^2*b*B)/3 - (16*a*b^2*B)/3 - (a^3*B*Sqrt[x])/3 - 6*a^2*b*B*Sqrt[x] - 16*a*b^2*B*Sqrt[x] - (32*b^3*B*Sqrt[x])/3 + 2*a^2*Sqrt[a + b]*B*Sqrt[a + b*x] + (32*a*b*Sqrt[a + b]*B*Sqrt[a + b*x])/3 + (32*b^2*Sqrt[a + b]*B*Sqrt[a + b*x])/3))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^6 + ((Sqrt[a + b] - Sqrt[a + b*x])^9*((-31*a^3*B)/3 - 46*a^2*b*B - 48*a*b^2*B - (32*b^3*B)/3 - (5*a^3*B*Sqrt[x])/3 - 30*a^2*b*B*Sqrt[x] - 80*a*b^2*B*Sqrt[x] - (160*b^3*B*Sqrt[x])/3 + 12*a^2*Sqrt[a + b]*B*Sqrt[a + b*x] + 64*a*b*Sqrt[a + b]*B*Sqrt[a + b*x] + 64*b^2*Sqrt[a + b]*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^5 + ((Sqrt[a + b] - Sqrt[a + b*x])^3*((-43*a^2*A*b)/4 - 20*a*A*b^2 - 10*A*b^3 - (635*a^3*B)/24 - 100*a^2*b*B - 120*a*b^2*B - (140*b^3*B)/3 - (13*a^2*A*b*Sqrt[x])/4 - 14*a*A*b^2*Sqrt[x] - 10*A*b^3*Sqrt[x] - (85*a^3*B*Sqrt[x])/24 - 30*a^2*b*B*Sqrt[x] - 50*a*b^2*B*Sqrt[x] - (70*b^3*B*Sqrt[x])/3 + 14*a*A*b*Sqrt[a + b]*Sqrt[a + b*x] + 20*A*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 30*a^2*Sqrt[a + b]*B*Sqrt[a + b*x] + 100*a*b*Sqrt[a + b]*B*Sqrt[a + b*x] + 70*b^2*Sqrt[a + b]*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 + ((Sqrt[a + b]/8 - Sqrt[a + b*x]/8)*(-78*a^2*A*b - 112*a*A*b^2 - 48*A*b^3 - 85*a^3*B - 240*a^2*b*B - 240*a*b^2*B - 80*b^3*B - 18*a^2*A*b*Sqrt[x] - 48*a*A*b^2*Sqrt[x] - 16*A*b^3*Sqrt[x] - 11*a^3*B*Sqrt[x] - 48*a^2*b*B*Sqrt[x] - 48*a*b^2*B*Sqrt[x] - 16*b^3*B*Sqrt[x] + 96*a*A*b*Sqrt[a + b]*Sqrt[a + b*x] + 64*A*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 96*a^2*Sqrt[a + b]*B*Sqrt[a + b*x] + 192*a*b*Sqrt[a + b]*B*Sqrt[a + b*x] + 96*b^2*Sqrt[a + b]*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x]) + ((Sqrt[a + b] - Sqrt[a + b*x])^7*((-3*a^2*A*b)/2 - 2*a*A*b^2 - (105*a^3*B)/4 - 120*a^2*b*B - 144*a*b^2*B - 48*b^3*B - (a^2*A*b*Sqrt[x])/2 - 4*a*A*b^2*Sqrt[x] - 4*A*b^3*Sqrt[x] - (15*a^3*B*Sqrt[x])/4 - 60*a^2*b*B*Sqrt[x] - 150*a*b^2*B*Sqrt[x] - 96*b^3*B*Sqrt[x] + 2*a*A*b*Sqrt[a + b]*Sqrt[a + b*x] + 4*A*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 30*a^2*Sqrt[a + b]*B*Sqrt[a + b*x] + 150*a*b*Sqrt[a + b]*B*Sqrt[a + b*x] + 144*b^2*Sqrt[a + b]*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4 + ((Sqrt[a + b] - Sqrt[a + b*x])^5*((-13*a^2*A*b)/2 - 12*a*A*b^2 - 4*A*b^3 - (425*a^3*B)/12 - (460*a^2*b*B)/3 - (578*a*b^2*B)/3 - (224*b^3*B)/3 - (3*a^2*A*b*Sqrt[x])/2 - 12*a*A*b^2*Sqrt[x] - 12*A*b^3*Sqrt[x] - (55*a^3*B*Sqrt[x])/12 - 60*a^2*b*B*Sqrt[x] - 130*a*b^2*B*Sqrt[x] - (224*b^3*B*Sqrt[x])/3 + 8*a*A*b*Sqrt[a + b]*Sqrt[a + b*x] + 16*A*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 40*a^2*Sqrt[a + b]*B*Sqrt[a + b*x] + (520*a*b*Sqrt[a + b]*B*Sqrt[a + b*x])/3 + (448*b^2*Sqrt[a + b]*B*Sqrt[a + b*x])/3))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^3 + ((2*a^3*A - 2*a^3*A*Sqrt[x])*(Sqrt[a + b] - Sqrt[a + b*x])*(2*a + 2*b - a*Sqrt[x] - 2*b*Sqrt[x] + b*x - 2*Sqrt[a + b]*Sqrt[a + b*x] + Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(Sqrt[x]*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])) + ((-15*a^2*A*Sqrt[b])/2 - (5*a^3*B)/(4*Sqrt[b]))*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",0
506,1,2886,152,97.3261226,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{5/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/x^(5/2),x]","\text{Result too large to show}","-\frac{2 (a+b x)^{5/2} (3 a B+4 A b)}{3 a \sqrt{x}}+\frac{5 b \sqrt{x} (a+b x)^{3/2} (3 a B+4 A b)}{6 a}+\frac{5}{4} b \sqrt{x} \sqrt{a+b x} (3 a B+4 A b)+\frac{5}{4} a \sqrt{b} (3 a B+4 A b) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)-\frac{2 A (a+b x)^{7/2}}{3 a x^{3/2}}",1,"(((b*Sqrt[a + b])/4 - (b*Sqrt[a + b*x])/4)*(-12*a*A*b - 8*A*b^2 - 39*a^2*B - 56*a*b*B - 24*b^2*B - 4*a*A*b*Sqrt[x] - 8*A*b^2*Sqrt[x] - 9*a^2*B*Sqrt[x] - 24*a*b*B*Sqrt[x] - 8*b^2*B*Sqrt[x] + 16*A*b*Sqrt[a + b]*Sqrt[a + b*x] + 48*a*Sqrt[a + b]*B*Sqrt[a + b*x] + 32*b*Sqrt[a + b]*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x]) + ((Sqrt[a + b] - Sqrt[a + b*x])^7*((-3*a^2*b*B)/2 - 2*a*b^2*B - (a^2*b*B*Sqrt[x])/2 - 4*a*b^2*B*Sqrt[x] - 4*b^3*B*Sqrt[x] + 2*a*b*Sqrt[a + b]*B*Sqrt[a + b*x] + 4*b^2*Sqrt[a + b]*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4 + ((Sqrt[a + b] - Sqrt[a + b*x])^5*((-13*a^2*b*B)/2 - 12*a*b^2*B - 4*b^3*B - (3*a^2*b*B*Sqrt[x])/2 - 12*a*b^2*B*Sqrt[x] - 12*b^3*B*Sqrt[x] + 8*a*b*Sqrt[a + b]*B*Sqrt[a + b*x] + 16*b^2*Sqrt[a + b]*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^3 + ((Sqrt[a + b] - Sqrt[a + b*x])^3*(-(a*A*b^2) - (43*a^2*b*B)/4 - 20*a*b^2*B - 10*b^3*B - a*A*b^2*Sqrt[x] - 2*A*b^3*Sqrt[x] - (13*a^2*b*B*Sqrt[x])/4 - 14*a*b^2*B*Sqrt[x] - 10*b^3*B*Sqrt[x] + 2*A*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 14*a*b*Sqrt[a + b]*B*Sqrt[a + b*x] + 20*b^2*Sqrt[a + b]*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 + ((Sqrt[a + b] - Sqrt[a + b*x])^5*(72*a^4*A + (512*a^8*A)/(3*b^4) + (512*a^7*A)/b^3 + (1664*a^6*A)/(3*b^2) + (832*a^5*A)/(3*b) + 8*a^3*A*b - 164*a^4*A*Sqrt[x] - (128*a^7*A*Sqrt[x])/(3*b^3) - (496*a^6*A*Sqrt[x])/(3*b^2) - (766*a^5*A*Sqrt[x])/(3*b) - 32*a^3*A*b*Sqrt[x] + (466*a^4*A*x)/3 + (128*a^7*A*x)/b^3 + (376*a^6*A*x)/b^2 + (1178*a^5*A*x)/(3*b) + 12*a^3*A*b*x - 34*a^4*A*x^(3/2) - (64*a^6*A*x^(3/2))/(3*b^2) - (52*a^5*A*x^(3/2))/b - 4*a^3*A*b*x^(3/2) + 8*a^3*A*Sqrt[a + b]*Sqrt[a + b*x] - (512*a^7*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^4) - (1280*a^6*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^3) - (1088*a^5*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^2) - (96*a^4*A*Sqrt[a + b]*Sqrt[a + b*x])/b + 12*a^3*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + (128*a^6*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/(3*b^3) + (144*a^5*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/b^2 + (314*a^4*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/(3*b) - 4*a^3*A*Sqrt[a + b]*x*Sqrt[a + b*x] - (128*a^6*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^3) - (296*a^5*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^2) - (54*a^4*A*Sqrt[a + b]*x*Sqrt[a + b*x])/b))/(x*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])^2) + ((Sqrt[a + b] - Sqrt[a + b*x])^9*((16*a^4*A)/3 + (64*a^7*A)/(3*b^3) + (48*a^6*A)/b^2 + (32*a^5*A)/b - 32*a^4*A*Sqrt[x] - (256*a^8*A*Sqrt[x])/(3*b^4) - (928*a^7*A*Sqrt[x])/(3*b^3) - (392*a^6*A*Sqrt[x])/b^2 - (200*a^5*A*Sqrt[x])/b + 8*a^4*A*x + (128*a^8*A*x)/(3*b^4) + (160*a^7*A*x)/b^3 + (584*a^6*A*x)/(3*b^2) + (256*a^5*A*x)/(3*b) - (8*a^4*A*x^(3/2))/3 - (64*a^7*A*x^(3/2))/(3*b^3) - (128*a^6*A*x^(3/2))/(3*b^2) - (24*a^5*A*x^(3/2))/b + (64*a^6*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^3) + (112*a^5*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^2) + (16*a^4*A*Sqrt[a + b]*Sqrt[a + b*x])/b + (256*a^7*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/(3*b^4) + (160*a^6*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/b^3 + (248*a^5*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/(3*b^2) + (8*a^4*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/b - (128*a^7*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^4) - (224*a^6*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^3) - (104*a^5*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^2) - (8*a^4*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b)))/(x^(3/2)*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])^3) + (((-2*a^2*Sqrt[a + b])/(3*b^2) + (2*a^2*Sqrt[a + b*x])/(3*b^2))*(-144*a^4*A - 304*a^3*A*b - 203*a^2*A*b^2 - 63*a*A*b^3 - 18*A*b^4 - 6*a^2*b^2*B - 6*a*b^3*B + 28*a^3*A*b*Sqrt[x] + 53*a^2*A*b^2*Sqrt[x] + 57*a*A*b^3*Sqrt[x] + 36*A*b^4*Sqrt[x] + 9*a^2*b^2*B*Sqrt[x] + 12*a*b^3*B*Sqrt[x] - 108*a^3*A*b*x - 200*a^2*A*b^2*x - 105*a*A*b^3*x - 27*A*b^4*x - 3*a^2*b^2*B*x - 9*a*b^3*B*x + 14*a^2*A*b^2*x^(3/2) + 15*a*A*b^3*x^(3/2) + 9*A*b^4*x^(3/2) + 3*a*b^3*B*x^(3/2) + 144*a^3*A*Sqrt[a + b]*Sqrt[a + b*x] + 232*a^2*A*b*Sqrt[a + b]*Sqrt[a + b*x] + 105*a*A*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 18*A*b^3*Sqrt[a + b]*Sqrt[a + b*x] + 6*a*b^2*Sqrt[a + b]*B*Sqrt[a + b*x] - 28*a^2*A*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 39*a*A*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 27*A*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 9*a*b^2*Sqrt[a + b]*B*Sqrt[x]*Sqrt[a + b*x] + 36*a^2*A*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 30*a*A*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] + 9*A*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] + 3*a*b^2*Sqrt[a + b]*B*x*Sqrt[a + b*x]))/(Sqrt[x]*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])) + (-10*a*A*b^(3/2) - (15*a^2*Sqrt[b]*B)/2)*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",0
507,-1,0,150,180.0224943,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{7/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/x^(7/2),x]","\text{\$Aborted}","b^{3/2} (5 a B+2 A b) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)+\frac{b^2 \sqrt{x} \sqrt{a+b x} (5 a B+2 A b)}{a}-\frac{2 (a+b x)^{5/2} (5 a B+2 A b)}{15 a x^{3/2}}-\frac{2 b (a+b x)^{3/2} (5 a B+2 A b)}{3 a \sqrt{x}}-\frac{2 A (a+b x)^{7/2}}{5 a x^{5/2}}",1,"$Aborted","F",-1
508,-1,0,111,180.0669894,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{9/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/x^(9/2),x]","\text{\$Aborted}","-\frac{2 A (a+b x)^{7/2}}{7 a x^{7/2}}+2 b^{5/2} B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)-\frac{2 b^2 B \sqrt{a+b x}}{\sqrt{x}}-\frac{2 B (a+b x)^{5/2}}{5 x^{5/2}}-\frac{2 b B (a+b x)^{3/2}}{3 x^{3/2}}",1,"$Aborted","F",-1
509,-1,0,53,180.7597889,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{11/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/x^(11/2),x]","\text{\$Aborted}","\frac{2 (a+b x)^{7/2} (2 A b-9 a B)}{63 a^2 x^{7/2}}-\frac{2 A (a+b x)^{7/2}}{9 a x^{9/2}}",1,"$Aborted","F",-1
510,-1,0,84,181.8407661,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{13/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/x^(13/2),x]","\text{\$Aborted}","-\frac{4 b (a+b x)^{7/2} (4 A b-11 a B)}{693 a^3 x^{7/2}}+\frac{2 (a+b x)^{7/2} (4 A b-11 a B)}{99 a^2 x^{9/2}}-\frac{2 A (a+b x)^{7/2}}{11 a x^{11/2}}",1,"$Aborted","F",-1
511,-1,0,117,180.0908974,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{15/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/x^(15/2),x]","\text{\$Aborted}","\frac{16 b^2 (a+b x)^{7/2} (6 A b-13 a B)}{9009 a^4 x^{7/2}}-\frac{8 b (a+b x)^{7/2} (6 A b-13 a B)}{1287 a^3 x^{9/2}}+\frac{2 (a+b x)^{7/2} (6 A b-13 a B)}{143 a^2 x^{11/2}}-\frac{2 A (a+b x)^{7/2}}{13 a x^{13/2}}",1,"$Aborted","F",-1
512,-1,0,150,180.1421351,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{17/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/x^(17/2),x]","\text{\$Aborted}","-\frac{32 b^3 (a+b x)^{7/2} (8 A b-15 a B)}{45045 a^5 x^{7/2}}+\frac{16 b^2 (a+b x)^{7/2} (8 A b-15 a B)}{6435 a^4 x^{9/2}}-\frac{4 b (a+b x)^{7/2} (8 A b-15 a B)}{715 a^3 x^{11/2}}+\frac{2 (a+b x)^{7/2} (8 A b-15 a B)}{195 a^2 x^{13/2}}-\frac{2 A (a+b x)^{7/2}}{15 a x^{15/2}}",1,"$Aborted","F",-1
513,-1,0,183,180.1983475,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{19/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/x^(19/2),x]","\text{\$Aborted}","\frac{256 b^4 (a+b x)^{7/2} (10 A b-17 a B)}{765765 a^6 x^{7/2}}-\frac{128 b^3 (a+b x)^{7/2} (10 A b-17 a B)}{109395 a^5 x^{9/2}}+\frac{32 b^2 (a+b x)^{7/2} (10 A b-17 a B)}{12155 a^4 x^{11/2}}-\frac{16 b (a+b x)^{7/2} (10 A b-17 a B)}{3315 a^3 x^{13/2}}+\frac{2 (a+b x)^{7/2} (10 A b-17 a B)}{255 a^2 x^{15/2}}-\frac{2 A (a+b x)^{7/2}}{17 a x^{17/2}}",1,"$Aborted","F",-1
514,1,6957,192,100.0354119,"\int \frac{x^{7/2} (A+B x)}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(x^(7/2)*(A + B*x))/Sqrt[a + b*x],x]","\text{Result too large to show}","\frac{7 a^4 (10 A b-9 a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{128 b^{11/2}}-\frac{7 a^3 \sqrt{x} \sqrt{a+b x} (10 A b-9 a B)}{128 b^5}+\frac{7 a^2 x^{3/2} \sqrt{a+b x} (10 A b-9 a B)}{192 b^4}-\frac{7 a x^{5/2} \sqrt{a+b x} (10 A b-9 a B)}{240 b^3}+\frac{x^{7/2} \sqrt{a+b x} (10 A b-9 a B)}{40 b^2}+\frac{B x^{9/2} \sqrt{a+b x}}{5 b}",1,"Result too large to show","B",0
515,1,4557,159,56.0942644,"\int \frac{x^{5/2} (A+B x)}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(x^(5/2)*(A + B*x))/Sqrt[a + b*x],x]","\text{Result too large to show}","-\frac{5 a^3 (8 A b-7 a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{64 b^{9/2}}+\frac{5 a^2 \sqrt{x} \sqrt{a+b x} (8 A b-7 a B)}{64 b^4}-\frac{5 a x^{3/2} \sqrt{a+b x} (8 A b-7 a B)}{96 b^3}+\frac{x^{5/2} \sqrt{a+b x} (8 A b-7 a B)}{24 b^2}+\frac{B x^{7/2} \sqrt{a+b x}}{4 b}",1,"((-15360*a^10*A*b - 28160*a^9*A*b^2 - 15232*a^8*A*b^3 - 9280*a^7*A*b^4 - 11328*a^6*A*b^5 - 4992*a^5*A*b^6 - 512*a^4*A*b^7 + 13440*a^11*B + 24640*a^10*b*B + 13328*a^9*b^2*B + 1976*a^8*b^3*B - 5448*a^7*b^4*B - 8688*a^6*b^5*B - 3776*a^5*b^6*B - 384*a^4*b^7*B)*Sqrt[a + b*x] + (15360*a^10*A*b - 30720*a^9*A*b^2 - 78080*a^8*A*b^3 - 36608*a^7*A*b^4 - 31048*a^6*A*b^5 - 38208*a^5*A*b^6 - 12160*a^4*A*b^7 - 512*a^3*A*b^8 - 13440*a^11*B + 26880*a^10*b*B + 68320*a^9*b^2*B + 32032*a^8*b^3*B + 2591*a^7*b^4*B - 21864*a^6*b^5*B - 29296*a^5*b^6*B - 9152*a^4*b^7*B - 384*a^3*b^8*B)*Sqrt[x]*Sqrt[a + b*x] + (38400*a^9*A*b^2 - 49920*a^8*A*b^3 - 122688*a^7*A*b^4 - 51840*a^6*A*b^5 - 70272*a^5*A*b^6 - 66048*a^4*A*b^7 - 12288*a^3*A*b^8 - 33600*a^10*b*B + 43680*a^9*b^2*B + 107352*a^8*b^3*B + 36144*a^7*b^4*B - 7632*a^6*b^5*B - 53952*a^5*b^6*B - 50304*a^4*b^7*B - 9216*a^3*b^8*B)*x*Sqrt[a + b*x] + (20480*a^9*A*b^2 + 79360*a^8*A*b^3 - 57600*a^7*A*b^4 - 126240*a^6*A*b^5 - 59280*a^5*A*b^6 - 108800*a^4*A*b^7 - 67840*a^3*A*b^8 - 5120*a^2*A*b^9 - 17920*a^10*b*B - 69440*a^9*b^2*B + 50400*a^8*b^3*B + 110460*a^7*b^4*B + 21150*a^6*b^5*B - 27680*a^5*b^6*B - 84640*a^4*b^7*B - 51200*a^3*b^8*B - 3840*a^2*b^9*B)*x^(3/2)*Sqrt[a + b*x] + (56960*a^8*A*b^3 + 118080*a^7*A*b^4 - 46080*a^6*A*b^5 - 92160*a^5*A*b^6 - 64000*a^4*A*b^7 - 112640*a^3*A*b^8 - 40960*a^2*A*b^9 - 49840*a^9*b^2*B - 103320*a^8*b^3*B + 40320*a^7*b^4*B + 76800*a^6*b^5*B + 320*a^5*b^6*B - 45440*a^4*b^7*B - 87040*a^3*b^8*B - 30720*a^2*b^9*B)*x^2*Sqrt[a + b*x] + (6912*a^8*A*b^3 + 86784*a^7*A*b^4 + 124560*a^6*A*b^5 - 24960*a^5*A*b^6 - 51264*a^4*A*b^7 - 56832*a^3*A*b^8 - 76800*a^2*A*b^9 - 12288*a*A*b^10 - 6048*a^9*b^2*B - 75936*a^8*b^3*B - 108990*a^7*b^4*B + 21840*a^6*b^5*B + 35640*a^5*b^6*B - 11328*a^4*b^7*B - 44544*a^3*b^8*B - 58368*a^2*b^9*B - 9216*a*b^10*B)*x^(5/2)*Sqrt[a + b*x] + (13888*a^7*A*b^4 + 81024*a^6*A*b^5 + 92160*a^5*A*b^6 - 9216*a^4*A*b^7 - 22528*a^3*A*b^8 - 32768*a^2*A*b^9 - 32768*a*A*b^10 - 12152*a^8*b^3*B - 70896*a^7*b^4*B - 80640*a^6*b^5*B + 7680*a^5*b^6*B + 10112*a^4*b^7*B - 11264*a^3*b^8*B - 26624*a^2*b^9*B - 24576*a*b^10*B)*x^3*Sqrt[a + b*x] + (7424*a^7*A*b^4 + 24928*a^6*A*b^5 + 52320*a^5*A*b^6 + 48384*a^4*A*b^7 - 2304*a^3*A*b^8 - 7168*a^2*A*b^9 - 10240*a*A*b^10 - 8192*A*b^11 - 352*a^8*b^3*B - 9524*a^7*b^4*B - 38100*a^6*b^5*B - 40800*a^5*b^6*B + 1680*a^4*b^7*B + 2048*a^3*b^8*B - 4096*a^2*b^9*B - 8192*a*b^10*B - 6144*b^11*B)*x^(7/2)*Sqrt[a + b*x] + (28224*a^6*A*b^5 + 51072*a^5*A*b^6 + 32256*a^4*A*b^7 + 18432*a^3*A*b^8 - 120*a^7*b^4*B - 1680*a^6*b^5*B - 6720*a^5*b^6*B - 13440*a^4*b^7*B)*x^4*Sqrt[a + b*x] + (7800*a^6*A*b^5 + 68160*a^5*A*b^6 + 87680*a^4*A*b^7 + 25600*a^3*A*b^8 + 5120*a^2*A*b^9 + 5463*a^7*b^4*B + 11016*a^6*b^5*B + 7760*a^5*b^6*B + 6592*a^4*b^7*B - 2944*a^3*b^8*B)*x^(9/2)*Sqrt[a + b*x] + (24192*a^5*A*b^6 + 103936*a^4*A*b^7 + 100352*a^3*A*b^8 + 16384*a^2*A*b^9 + 21840*a^6*b^5*B + 38080*a^5*b^6*B + 17024*a^4*b^7*B + 7168*a^3*b^8*B)*x^5*Sqrt[a + b*x] + (1968*a^5*A*b^6 + 36096*a^4*A*b^7 + 99840*a^3*A*b^8 + 73728*a^2*A*b^9 + 6144*a*A*b^10 + 5958*a^6*b^5*B + 52896*a^5*b^6*B + 69600*a^4*b^7*B + 19968*a^3*b^8*B + 2304*a^2*b^9*B)*x^(11/2)*Sqrt[a + b*x] + (3584*a^4*A*b^7 + 28672*a^3*A*b^8 + 57344*a^2*A*b^9 + 32768*a*A*b^10 + 18368*a^5*b^6*B + 79744*a^4*b^7*B + 78848*a^3*b^8*B + 14336*a^2*b^9*B)*x^6*Sqrt[a + b*x] + (64*a^4*A*b^7 + 2048*a^3*A*b^8 + 10240*a^2*A*b^9 + 16384*a*A*b^10 + 8192*A*b^11 + 1480*a^5*b^6*B + 27200*a^4*b^7*B + 75520*a^3*b^8*B + 56320*a^2*b^9*B + 5120*a*b^10*B)*x^(13/2)*Sqrt[a + b*x] + (2688*a^4*b^7*B + 21504*a^3*b^8*B + 43008*a^2*b^9*B + 24576*a*b^10*B)*x^7*Sqrt[a + b*x] + (48*a^4*b^7*B + 1536*a^3*b^8*B + 7680*a^2*b^9*B + 12288*a*b^10*B + 6144*b^11*B)*x^(15/2)*Sqrt[a + b*x] + Sqrt[a + b]*(15360*a^10*A*b + 20480*a^9*A*b^2 + 6912*a^8*A*b^3 + 7424*a^7*A*b^4 + 7800*a^6*A*b^5 + 1968*a^5*A*b^6 + 64*a^4*A*b^7 - 13440*a^11*B - 17920*a^10*b*B - 6048*a^9*b^2*B - 352*a^8*b^3*B + 5463*a^7*b^4*B + 5958*a^6*b^5*B + 1480*a^5*b^6*B + 48*a^4*b^7*B + (-15360*a^10*A*b + 38400*a^9*A*b^2 + 56960*a^8*A*b^3 + 13888*a^7*A*b^4 + 28224*a^6*A*b^5 + 24192*a^5*A*b^6 + 3584*a^4*A*b^7 + 13440*a^11*B - 33600*a^10*b*B - 49840*a^9*b^2*B - 12152*a^8*b^3*B - 120*a^7*b^4*B + 21840*a^6*b^5*B + 18368*a^5*b^6*B + 2688*a^4*b^7*B)*Sqrt[x] + (-30720*a^9*A*b^2 + 79360*a^8*A*b^3 + 86784*a^7*A*b^4 + 24928*a^6*A*b^5 + 68160*a^5*A*b^6 + 36096*a^4*A*b^7 + 2048*a^3*A*b^8 + 26880*a^10*b*B - 69440*a^9*b^2*B - 75936*a^8*b^3*B - 9524*a^7*b^4*B + 11016*a^6*b^5*B + 52896*a^5*b^6*B + 27200*a^4*b^7*B + 1536*a^3*b^8*B)*x + (-28160*a^9*A*b^2 - 49920*a^8*A*b^3 + 118080*a^7*A*b^4 + 81024*a^6*A*b^5 + 51072*a^5*A*b^6 + 103936*a^4*A*b^7 + 28672*a^3*A*b^8 + 24640*a^10*b*B + 43680*a^9*b^2*B - 103320*a^8*b^3*B - 70896*a^7*b^4*B - 1680*a^6*b^5*B + 38080*a^5*b^6*B + 79744*a^4*b^7*B + 21504*a^3*b^8*B)*x^(3/2) + (-78080*a^8*A*b^3 - 57600*a^7*A*b^4 + 124560*a^6*A*b^5 + 52320*a^5*A*b^6 + 87680*a^4*A*b^7 + 99840*a^3*A*b^8 + 10240*a^2*A*b^9 + 68320*a^9*b^2*B + 50400*a^8*b^3*B - 108990*a^7*b^4*B - 38100*a^6*b^5*B + 7760*a^5*b^6*B + 69600*a^4*b^7*B + 75520*a^3*b^8*B + 7680*a^2*b^9*B)*x^2 + (-15232*a^8*A*b^3 - 122688*a^7*A*b^4 - 46080*a^6*A*b^5 + 92160*a^5*A*b^6 + 32256*a^4*A*b^7 + 100352*a^3*A*b^8 + 57344*a^2*A*b^9 + 13328*a^9*b^2*B + 107352*a^8*b^3*B + 40320*a^7*b^4*B - 80640*a^6*b^5*B - 6720*a^5*b^6*B + 17024*a^4*b^7*B + 78848*a^3*b^8*B + 43008*a^2*b^9*B)*x^(5/2) + (-36608*a^7*A*b^4 - 126240*a^6*A*b^5 - 24960*a^5*A*b^6 + 48384*a^4*A*b^7 + 25600*a^3*A*b^8 + 73728*a^2*A*b^9 + 16384*a*A*b^10 + 32032*a^8*b^3*B + 110460*a^7*b^4*B + 21840*a^6*b^5*B - 40800*a^5*b^6*B + 6592*a^4*b^7*B + 19968*a^3*b^8*B + 56320*a^2*b^9*B + 12288*a*b^10*B)*x^3 + (-9280*a^7*A*b^4 - 51840*a^6*A*b^5 - 92160*a^5*A*b^6 - 9216*a^4*A*b^7 + 18432*a^3*A*b^8 + 16384*a^2*A*b^9 + 32768*a*A*b^10 + 1976*a^8*b^3*B + 36144*a^7*b^4*B + 76800*a^6*b^5*B + 7680*a^5*b^6*B - 13440*a^4*b^7*B + 7168*a^3*b^8*B + 14336*a^2*b^9*B + 24576*a*b^10*B)*x^(7/2) + (-31048*a^6*A*b^5 - 59280*a^5*A*b^6 - 51264*a^4*A*b^7 - 2304*a^3*A*b^8 + 5120*a^2*A*b^9 + 6144*a*A*b^10 + 8192*A*b^11 + 2591*a^7*b^4*B + 21150*a^6*b^5*B + 35640*a^5*b^6*B + 1680*a^4*b^7*B - 2944*a^3*b^8*B + 2304*a^2*b^9*B + 5120*a*b^10*B + 6144*b^11*B)*x^4 + (-11328*a^6*A*b^5 - 70272*a^5*A*b^6 - 64000*a^4*A*b^7 - 22528*a^3*A*b^8 - 5448*a^7*b^4*B - 7632*a^6*b^5*B + 320*a^5*b^6*B + 10112*a^4*b^7*B)*x^(9/2) + (-38208*a^5*A*b^6 - 108800*a^4*A*b^7 - 56832*a^3*A*b^8 - 7168*a^2*A*b^9 - 21864*a^6*b^5*B - 27680*a^5*b^6*B - 11328*a^4*b^7*B + 2048*a^3*b^8*B)*x^5 + (-4992*a^5*A*b^6 - 66048*a^4*A*b^7 - 112640*a^3*A*b^8 - 32768*a^2*A*b^9 - 8688*a^6*b^5*B - 53952*a^5*b^6*B - 45440*a^4*b^7*B - 11264*a^3*b^8*B)*x^(11/2) + (-12160*a^4*A*b^7 - 67840*a^3*A*b^8 - 76800*a^2*A*b^9 - 10240*a*A*b^10 - 29296*a^5*b^6*B - 84640*a^4*b^7*B - 44544*a^3*b^8*B - 4096*a^2*b^9*B)*x^6 + (-512*a^4*A*b^7 - 12288*a^3*A*b^8 - 40960*a^2*A*b^9 - 32768*a*A*b^10 - 3776*a^5*b^6*B - 50304*a^4*b^7*B - 87040*a^3*b^8*B - 26624*a^2*b^9*B)*x^(13/2) + (-512*a^3*A*b^8 - 5120*a^2*A*b^9 - 12288*a*A*b^10 - 8192*A*b^11 - 9152*a^4*b^7*B - 51200*a^3*b^8*B - 58368*a^2*b^9*B - 8192*a*b^10*B)*x^7 + (-384*a^4*b^7*B - 9216*a^3*b^8*B - 30720*a^2*b^9*B - 24576*a*b^10*B)*x^(15/2) + (-384*a^3*b^8*B - 3840*a^2*b^9*B - 9216*a*b^10*B - 6144*b^11*B)*x^8))/(192*b^4*(128*a^8 + 256*a^7*b + 160*a^6*b^2 + 32*a^5*b^3 + a^4*b^4) + 192*b^4*(a^4*b^4 + 32*a^3*b^5 + 160*a^2*b^6 + 256*a*b^7 + 128*b^8)*x^4 + 192*b^4*Sqrt[a + b]*(-128*a^7 - 192*a^6*b - 80*a^5*b^2 - 8*a^4*b^3)*Sqrt[a + b*x] + x*(192*b^4*(256*a^7*b + 1472*a^6*b^2 + 1760*a^5*b^3 + 604*a^4*b^4 + 32*a^3*b^5) + 192*b^4*Sqrt[a + b]*(-192*a^6*b - 1248*a^5*b^2 - 1080*a^4*b^3 - 192*a^3*b^4)*Sqrt[a + b*x]) + Sqrt[x]*(192*b^4*(512*a^7*b + 896*a^6*b^2 + 448*a^5*b^3 + 56*a^4*b^4) + 192*b^4*Sqrt[a + b]*(-512*a^6*b - 640*a^5*b^2 - 192*a^4*b^3 - 8*a^3*b^4)*Sqrt[a + b*x]) + x^2*(192*b^4*(160*a^6*b^2 + 1760*a^5*b^3 + 3270*a^4*b^4 + 1760*a^3*b^5 + 160*a^2*b^6) + 192*b^4*Sqrt[a + b]*(-80*a^5*b^2 - 1080*a^4*b^3 - 1920*a^3*b^4 - 640*a^2*b^5)*Sqrt[a + b*x]) + x^(3/2)*(192*b^4*(896*a^6*b^2 + 2688*a^5*b^3 + 2184*a^4*b^4 + 448*a^3*b^5) + 192*b^4*Sqrt[a + b]*(-640*a^5*b^2 - 1920*a^4*b^3 - 1080*a^3*b^4 - 80*a^2*b^5)*Sqrt[a + b*x]) + x^3*(192*b^4*(32*a^5*b^3 + 604*a^4*b^4 + 1760*a^3*b^5 + 1472*a^2*b^6 + 256*a*b^7) + 192*b^4*Sqrt[a + b]*(-8*a^4*b^3 - 192*a^3*b^4 - 640*a^2*b^5 - 512*a*b^6)*Sqrt[a + b*x]) + x^(5/2)*(192*b^4*(448*a^5*b^3 + 2184*a^4*b^4 + 2688*a^3*b^5 + 896*a^2*b^6) + 192*b^4*Sqrt[a + b]*(-192*a^4*b^3 - 1080*a^3*b^4 - 1248*a^2*b^5 - 192*a*b^6)*Sqrt[a + b*x]) + x^(7/2)*(192*b^4*(56*a^4*b^4 + 448*a^3*b^5 + 896*a^2*b^6 + 512*a*b^7) + 192*b^4*Sqrt[a + b]*(-8*a^3*b^4 - 80*a^2*b^5 - 192*a*b^6 - 128*b^7)*Sqrt[a + b*x])) + ((5*a^3*A)/(4*b^(7/2)) - (35*a^4*B)/(32*b^(9/2)))*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",1
516,1,2621,126,14.8026289,"\int \frac{x^{3/2} (A+B x)}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(x^(3/2)*(A + B*x))/Sqrt[a + b*x],x]","\text{Result too large to show}","\frac{a^2 (6 A b-5 a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 b^{7/2}}-\frac{a \sqrt{x} \sqrt{a+b x} (6 A b-5 a B)}{8 b^3}+\frac{x^{3/2} \sqrt{a+b x} (6 A b-5 a B)}{12 b^2}+\frac{B x^{5/2} \sqrt{a+b x}}{3 b}",1,"((576*a^7*A*b + 768*a^6*A*b^2 - 84*a^5*A*b^3 - 348*a^4*A*b^4 - 72*a^3*A*b^5 - 480*a^8*B - 640*a^7*b*B - 186*a^6*b^2*B - 222*a^5*b^3*B - 244*a^4*b^4*B - 48*a^3*b^5*B)*Sqrt[a + b*x] + (-576*a^7*A*b + 864*a^6*A*b^2 + 1548*a^5*A*b^3 - 630*a^4*A*b^4 - 828*a^3*A*b^5 - 72*a^2*A*b^6 + 480*a^8*B - 720*a^7*b*B - 1290*a^6*b^2*B - 243*a^5*b^3*B - 654*a^4*b^4*B - 564*a^3*b^5*B - 48*a^2*b^6*B)*Sqrt[x]*Sqrt[a + b*x] + (-1152*a^6*A*b^2 + 984*a^5*A*b^3 + 1356*a^4*A*b^4 - 1536*a^3*A*b^5 - 864*a^2*A*b^6 + 960*a^7*b*B - 820*a^6*b^2*B - 1386*a^5*b^3*B - 288*a^4*b^4*B - 1168*a^3*b^5*B - 576*a^2*b^6*B)*x*Sqrt[a + b*x] + (-480*a^6*A*b^2 - 1800*a^5*A*b^3 + 738*a^4*A*b^4 + 384*a^3*A*b^5 - 1776*a^2*A*b^6 - 384*a*A*b^7 + 400*a^7*b*B + 1500*a^6*b^2*B - 615*a^5*b^3*B - 896*a^4*b^4*B - 408*a^3*b^5*B - 1248*a^2*b^6*B - 256*a*b^7*B)*x^(3/2)*Sqrt[a + b*x] + (-900*a^5*A*b^3 - 1908*a^4*A*b^4 + 288*a^3*A*b^5 - 288*a^2*A*b^6 - 1152*a*A*b^7 + 750*a^6*b^2*B + 1590*a^5*b^3*B - 288*a^4*b^4*B - 384*a^3*b^5*B - 384*a^2*b^6*B - 768*a*b^7*B)*x^2*Sqrt[a + b*x] + (252*a^5*A*b^3 - 306*a^4*A*b^4 - 1152*a^3*A*b^5 + 48*a^2*A*b^6 - 192*a*A*b^7 - 384*A*b^8 + 46*a^6*b^2*B + 639*a^5*b^3*B + 1104*a^4*b^4*B - 80*a^3*b^5*B - 144*a^2*b^6*B - 192*a*b^7*B - 256*b^8*B)*x^(5/2)*Sqrt[a + b*x] + (900*a^4*A*b^4 + 960*a^3*A*b^5 - 288*a^2*A*b^6 + 18*a^5*b^3*B + 160*a^4*b^4*B + 480*a^3*b^5*B)*x^3*Sqrt[a + b*x] + (198*a^4*A*b^4 + 1584*a^3*A*b^5 + 1584*a^2*A*b^6 + 219*a^5*b^3*B + 312*a^4*b^4*B - 48*a^3*b^5*B + 144*a^2*b^6*B)*x^(7/2)*Sqrt[a + b*x] + (360*a^3*A*b^5 + 1440*a^2*A*b^6 + 1152*a*A*b^7 + 660*a^4*b^4*B + 880*a^3*b^5*B)*x^4*Sqrt[a + b*x] + (12*a^3*A*b^5 + 216*a^2*A*b^6 + 576*a*A*b^7 + 384*A*b^8 + 134*a^4*b^4*B + 1092*a^3*b^5*B + 1152*a^2*b^6*B + 64*a*b^7*B)*x^(9/2)*Sqrt[a + b*x] + (240*a^3*b^5*B + 960*a^2*b^6*B + 768*a*b^7*B)*x^5*Sqrt[a + b*x] + (8*a^3*b^5*B + 144*a^2*b^6*B + 384*a*b^7*B + 256*b^8*B)*x^(11/2)*Sqrt[a + b*x] + Sqrt[a + b]*(-576*a^7*A*b - 480*a^6*A*b^2 + 252*a^5*A*b^3 + 198*a^4*A*b^4 + 12*a^3*A*b^5 + 480*a^8*B + 400*a^7*b*B + 46*a^6*b^2*B + 219*a^5*b^3*B + 134*a^4*b^4*B + 8*a^3*b^5*B + (576*a^7*A*b - 1152*a^6*A*b^2 - 900*a^5*A*b^3 + 900*a^4*A*b^4 + 360*a^3*A*b^5 - 480*a^8*B + 960*a^7*b*B + 750*a^6*b^2*B + 18*a^5*b^3*B + 660*a^4*b^4*B + 240*a^3*b^5*B)*Sqrt[x] + (864*a^6*A*b^2 - 1800*a^5*A*b^3 - 306*a^4*A*b^4 + 1584*a^3*A*b^5 + 216*a^2*A*b^6 - 720*a^7*b*B + 1500*a^6*b^2*B + 639*a^5*b^3*B + 312*a^4*b^4*B + 1092*a^3*b^5*B + 144*a^2*b^6*B)*x + (768*a^6*A*b^2 + 984*a^5*A*b^3 - 1908*a^4*A*b^4 + 960*a^3*A*b^5 + 1440*a^2*A*b^6 - 640*a^7*b*B - 820*a^6*b^2*B + 1590*a^5*b^3*B + 160*a^4*b^4*B + 880*a^3*b^5*B + 960*a^2*b^6*B)*x^(3/2) + (1548*a^5*A*b^3 + 738*a^4*A*b^4 - 1152*a^3*A*b^5 + 1584*a^2*A*b^6 + 576*a*A*b^7 - 1290*a^6*b^2*B - 615*a^5*b^3*B + 1104*a^4*b^4*B - 48*a^3*b^5*B + 1152*a^2*b^6*B + 384*a*b^7*B)*x^2 + (-84*a^5*A*b^3 + 1356*a^4*A*b^4 + 288*a^3*A*b^5 - 288*a^2*A*b^6 + 1152*a*A*b^7 - 186*a^6*b^2*B - 1386*a^5*b^3*B - 288*a^4*b^4*B + 480*a^3*b^5*B + 768*a*b^7*B)*x^(5/2) + (-630*a^4*A*b^4 + 384*a^3*A*b^5 + 48*a^2*A*b^6 + 384*A*b^8 - 243*a^5*b^3*B - 896*a^4*b^4*B - 80*a^3*b^5*B + 144*a^2*b^6*B + 64*a*b^7*B + 256*b^8*B)*x^3 + (-348*a^4*A*b^4 - 1536*a^3*A*b^5 - 288*a^2*A*b^6 - 222*a^5*b^3*B - 288*a^4*b^4*B - 384*a^3*b^5*B)*x^(7/2) + (-828*a^3*A*b^5 - 1776*a^2*A*b^6 - 192*a*A*b^7 - 654*a^4*b^4*B - 408*a^3*b^5*B - 144*a^2*b^6*B)*x^4 + (-72*a^3*A*b^5 - 864*a^2*A*b^6 - 1152*a*A*b^7 - 244*a^4*b^4*B - 1168*a^3*b^5*B - 384*a^2*b^6*B)*x^(9/2) + (-72*a^2*A*b^6 - 384*a*A*b^7 - 384*A*b^8 - 564*a^3*b^5*B - 1248*a^2*b^6*B - 192*a*b^7*B)*x^5 + (-48*a^3*b^5*B - 576*a^2*b^6*B - 768*a*b^7*B)*x^(11/2) + (-48*a^2*b^6*B - 256*a*b^7*B - 256*b^8*B)*x^6))/(24*b^3*(32*a^6 + 48*a^5*b + 18*a^4*b^2 + a^3*b^3) + 24*b^3*(a^3*b^3 + 18*a^2*b^4 + 48*a*b^5 + 32*b^6)*x^3 + 24*b^3*Sqrt[a + b]*(-32*a^5 - 32*a^4*b - 6*a^3*b^2)*Sqrt[a + b*x] + x*(24*b^3*(48*a^5*b + 204*a^4*b^2 + 159*a^3*b^3 + 18*a^2*b^4) + 24*b^3*Sqrt[a + b]*(-32*a^4*b - 164*a^3*b^2 - 72*a^2*b^3)*Sqrt[a + b*x]) + Sqrt[x]*(24*b^3*(96*a^5*b + 120*a^4*b^2 + 30*a^3*b^3) + 24*b^3*Sqrt[a + b]*(-96*a^4*b - 72*a^3*b^2 - 6*a^2*b^3)*Sqrt[a + b*x]) + x^2*(24*b^3*(18*a^4*b^2 + 159*a^3*b^3 + 204*a^2*b^4 + 48*a*b^5) + 24*b^3*Sqrt[a + b]*(-6*a^3*b^2 - 72*a^2*b^3 - 96*a*b^4)*Sqrt[a + b*x]) + x^(3/2)*(24*b^3*(120*a^4*b^2 + 260*a^3*b^3 + 120*a^2*b^4) + 24*b^3*Sqrt[a + b]*(-72*a^3*b^2 - 164*a^2*b^3 - 32*a*b^4)*Sqrt[a + b*x]) + x^(5/2)*(24*b^3*(30*a^3*b^3 + 120*a^2*b^4 + 96*a*b^5) + 24*b^3*Sqrt[a + b]*(-6*a^2*b^3 - 32*a*b^4 - 32*b^5)*Sqrt[a + b*x])) + ((-3*a^2*A)/(2*b^(5/2)) + (5*a^3*B)/(4*b^(7/2)))*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",1
517,1,1122,93,2.0103517,"\int \frac{\sqrt{x} (A+B x)}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(Sqrt[x]*(A + B*x))/Sqrt[a + b*x],x]","\frac{\left(\frac{1}{4 b^2}-\frac{\sqrt{x}}{4 b^2}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(-12 B a^5+16 A b a^4-7 b B a^4-7 b B x a^4-22 b B \sqrt{x} a^4+12 \sqrt{a+b} B \sqrt{a+b x} a^4+20 A b^2 a^3+7 b^2 B x^2 a^3-b^2 B x^{3/2} a^3+7 b^2 B a^3+20 A b^2 x a^3-16 b^2 B x a^3+40 A b^2 \sqrt{x} a^3-b^2 B \sqrt{x} a^3+b \sqrt{a+b} B \sqrt{a+b x} a^3+b \sqrt{a+b} B x \sqrt{a+b x} a^3-16 A b \sqrt{a+b} \sqrt{a+b x} a^3+22 b \sqrt{a+b} B \sqrt{x} \sqrt{a+b x} a^3+4 A b^3 a^2+2 b^3 B x^3 a^2+18 b^3 B x^{5/2} a^2+4 A b^3 x^2 a^2+16 b^3 B x^2 a^2+36 A b^3 x^{3/2} a^2+12 b^3 B x^{3/2} a^2+2 b^3 B a^2+64 A b^3 x a^2+16 b^3 B x a^2+36 A b^3 \sqrt{x} a^2+18 b^3 B \sqrt{x} a^2-6 b^2 \sqrt{a+b} B x^2 \sqrt{a+b x} a^2-10 b^2 \sqrt{a+b} B x^{3/2} \sqrt{a+b x} a^2-6 b^2 \sqrt{a+b} B \sqrt{a+b x} a^2+12 b^2 \sqrt{a+b} B x \sqrt{a+b x} a^2-12 A b^2 \sqrt{a+b} x \sqrt{a+b x} a^2-12 A b^2 \sqrt{a+b} \sqrt{a+b x} a^2-10 b^2 \sqrt{a+b} B \sqrt{x} \sqrt{a+b x} a^2-40 A b^2 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a^2+16 b^4 B x^3 a+24 b^4 B x^{5/2} a+32 A b^4 x^2 a+16 b^4 B x^2 a+48 A b^4 x^{3/2} a+24 b^4 B x^{3/2} a+32 A b^4 x a+16 b^4 B x a-8 b^3 \sqrt{a+b} B x^{5/2} \sqrt{a+b x} a-24 b^3 \sqrt{a+b} B x^2 \sqrt{a+b x} a-16 A b^3 \sqrt{a+b} x^{3/2} \sqrt{a+b x} a-24 b^3 \sqrt{a+b} B x \sqrt{a+b x} a-48 A b^3 \sqrt{a+b} x \sqrt{a+b x} a-8 b^3 \sqrt{a+b} B \sqrt{x} \sqrt{a+b x} a-16 A b^3 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a+16 b^5 B x^3+32 A b^5 x^2+16 b^5 B x^2-16 b^4 \sqrt{a+b} B x^{5/2} \sqrt{a+b x}-16 b^4 \sqrt{a+b} B x^{3/2} \sqrt{a+b x}-32 A b^4 \sqrt{a+b} x^{3/2} \sqrt{a+b x}\right)}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^4}+\left(\frac{2 a A}{b^{3/2}}-\frac{3 a^2 B}{2 b^{5/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \left(\sqrt{x}-1\right)}{\sqrt{a+b}-\sqrt{a+b x}}\right)","-\frac{a (4 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{4 b^{5/2}}+\frac{\sqrt{x} \sqrt{a+b x} (4 A b-3 a B)}{4 b^2}+\frac{B x^{3/2} \sqrt{a+b x}}{2 b}",1,"((1/(4*b^2) - Sqrt[x]/(4*b^2))*(Sqrt[a + b] - Sqrt[a + b*x])*(16*a^4*A*b + 20*a^3*A*b^2 + 4*a^2*A*b^3 - 12*a^5*B - 7*a^4*b*B + 7*a^3*b^2*B + 2*a^2*b^3*B + 40*a^3*A*b^2*Sqrt[x] + 36*a^2*A*b^3*Sqrt[x] - 22*a^4*b*B*Sqrt[x] - a^3*b^2*B*Sqrt[x] + 18*a^2*b^3*B*Sqrt[x] + 20*a^3*A*b^2*x + 64*a^2*A*b^3*x + 32*a*A*b^4*x - 7*a^4*b*B*x - 16*a^3*b^2*B*x + 16*a^2*b^3*B*x + 16*a*b^4*B*x + 36*a^2*A*b^3*x^(3/2) + 48*a*A*b^4*x^(3/2) - a^3*b^2*B*x^(3/2) + 12*a^2*b^3*B*x^(3/2) + 24*a*b^4*B*x^(3/2) + 4*a^2*A*b^3*x^2 + 32*a*A*b^4*x^2 + 32*A*b^5*x^2 + 7*a^3*b^2*B*x^2 + 16*a^2*b^3*B*x^2 + 16*a*b^4*B*x^2 + 16*b^5*B*x^2 + 18*a^2*b^3*B*x^(5/2) + 24*a*b^4*B*x^(5/2) + 2*a^2*b^3*B*x^3 + 16*a*b^4*B*x^3 + 16*b^5*B*x^3 - 16*a^3*A*b*Sqrt[a + b]*Sqrt[a + b*x] - 12*a^2*A*b^2*Sqrt[a + b]*Sqrt[a + b*x] + 12*a^4*Sqrt[a + b]*B*Sqrt[a + b*x] + a^3*b*Sqrt[a + b]*B*Sqrt[a + b*x] - 6*a^2*b^2*Sqrt[a + b]*B*Sqrt[a + b*x] - 40*a^2*A*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 16*a*A*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 22*a^3*b*Sqrt[a + b]*B*Sqrt[x]*Sqrt[a + b*x] - 10*a^2*b^2*Sqrt[a + b]*B*Sqrt[x]*Sqrt[a + b*x] - 8*a*b^3*Sqrt[a + b]*B*Sqrt[x]*Sqrt[a + b*x] - 12*a^2*A*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] - 48*a*A*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] + a^3*b*Sqrt[a + b]*B*x*Sqrt[a + b*x] + 12*a^2*b^2*Sqrt[a + b]*B*x*Sqrt[a + b*x] - 24*a*b^3*Sqrt[a + b]*B*x*Sqrt[a + b*x] - 16*a*A*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 32*A*b^4*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 10*a^2*b^2*Sqrt[a + b]*B*x^(3/2)*Sqrt[a + b*x] - 16*b^4*Sqrt[a + b]*B*x^(3/2)*Sqrt[a + b*x] - 6*a^2*b^2*Sqrt[a + b]*B*x^2*Sqrt[a + b*x] - 24*a*b^3*Sqrt[a + b]*B*x^2*Sqrt[a + b*x] - 8*a*b^3*Sqrt[a + b]*B*x^(5/2)*Sqrt[a + b*x] - 16*b^4*Sqrt[a + b]*B*x^(5/2)*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4 + ((2*a*A)/b^(3/2) - (3*a^2*B)/(2*b^(5/2)))*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",1
518,1,191,56,0.4938749,"\int \frac{A+B x}{\sqrt{x} \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(A + B*x)/(Sqrt[x]*Sqrt[a + b*x]),x]","\frac{\left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(a^2+a b x+a b \sqrt{x}-a \sqrt{a+b} \sqrt{a+b x}-2 b \sqrt{x} \sqrt{a+b} \sqrt{a+b x}+a b+2 b^2 x\right) \left(\frac{B}{b}-\frac{B \sqrt{x}}{b}\right)}{\left(\sqrt{a+b} \sqrt{a+b x}-a-b \sqrt{x}\right)^2}+\left(\frac{2 a B}{b^{3/2}}-\frac{4 A}{\sqrt{b}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \left(\sqrt{x}-1\right)}{\sqrt{a+b}-\sqrt{a+b x}}\right)","\frac{(2 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{3/2}}+\frac{B \sqrt{x} \sqrt{a+b x}}{b}",1,"((B/b - (B*Sqrt[x])/b)*(Sqrt[a + b] - Sqrt[a + b*x])*(a^2 + a*b + a*b*Sqrt[x] + a*b*x + 2*b^2*x - a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 + ((-4*A)/Sqrt[b] + (2*a*B)/b^(3/2))*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",1
519,1,271,50,0.6154761,"\int \frac{A+B x}{x^{3/2} \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(3/2)*Sqrt[a + b*x]),x]","\frac{\left(2 A-2 A \sqrt{x}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(-2 \sqrt{a+b} \sqrt{a+b x}+\sqrt{x} \sqrt{a+b} \sqrt{a+b x}+a \left(-\sqrt{x}\right)+2 a+b x-2 b \sqrt{x}+2 b\right)}{\sqrt{x} \left(-2 a^2 \sqrt{x}+4 a^2-a b x^{3/2}+2 a b x-a b \sqrt{x}-4 a \sqrt{a+b} \sqrt{a+b x}+2 a \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-2 b \sqrt{a+b} \sqrt{a+b x}+4 a b+2 b^2 \sqrt{x}\right)}-\frac{4 B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}-\sqrt{b}}{\sqrt{a+b}-\sqrt{a+b x}}\right)}{\sqrt{b}}","\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{\sqrt{b}}-\frac{2 A \sqrt{a+b x}}{a \sqrt{x}}",1,"((2*A - 2*A*Sqrt[x])*(Sqrt[a + b] - Sqrt[a + b*x])*(2*a + 2*b - a*Sqrt[x] - 2*b*Sqrt[x] + b*x - 2*Sqrt[a + b]*Sqrt[a + b*x] + Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(Sqrt[x]*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])) - (4*B*ArcTanh[(-Sqrt[b] + Sqrt[b]*Sqrt[x])/(Sqrt[a + b] - Sqrt[a + b*x])])/Sqrt[b]","B",1
520,1,1908,53,16.2890025,"\int \frac{A+B x}{x^{5/2} \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(5/2)*Sqrt[a + b*x]),x]","\frac{\left(\frac{\sqrt{x}}{48}-\frac{1}{48}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^{12} \left(\frac{\left(192 a B+192 b B+96 b x B-96 a \sqrt{x} B-192 b \sqrt{x} B-192 \sqrt{a+b} \sqrt{a+b x} B+96 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} B\right) \left(-2 x a^2+4 \sqrt{x} a^2-b x^2 a+2 b x^{3/2} a-b x a+4 b \sqrt{x} a+2 \sqrt{a+b} x \sqrt{a+b x} a-4 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a+2 b^2 x-2 b \sqrt{a+b} \sqrt{x} \sqrt{a+b x}\right)^2}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^{10}}+\frac{-512 A x^{5/2} a^5+2560 A x^2 a^5-3584 A x^{3/2} a^5+4096 A a^5+1024 A x a^5-2048 A \sqrt{x} a^5-640 A b x^{7/2} a^4+3200 A b x^3 a^4-4352 A b x^{5/2} a^4+1408 A b x^2 a^4-2432 A b x^{3/2} a^4+11264 A b a^4+1792 A b x a^4-2560 A b \sqrt{x} a^4+512 A \sqrt{a+b} x^{5/2} \sqrt{a+b x} a^4-2560 A \sqrt{a+b} x^2 \sqrt{a+b x} a^4+3584 A \sqrt{a+b} x^{3/2} \sqrt{a+b x} a^4-1024 A \sqrt{a+b} x \sqrt{a+b x} a^4-4096 A \sqrt{a+b} \sqrt{a+b x} a^4+2048 A \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a^4-160 A b^2 x^{9/2} a^3+800 A b^2 x^4 a^3-800 A b^2 x^{7/2} a^3-1280 A b^2 x^3 a^3+6816 A b^2 x^{5/2} a^3+10496 A b^2 a^3-18528 A b^2 x^2 a^3+16288 A b^2 x^{3/2} a^3-2240 A b^2 x a^3+3968 A b^2 \sqrt{x} a^3+384 A b \sqrt{a+b} x^{7/2} \sqrt{a+b x} a^3-1920 A b \sqrt{a+b} x^3 \sqrt{a+b x} a^3+2304 A b \sqrt{a+b} x^{5/2} \sqrt{a+b x} a^3+384 A b \sqrt{a+b} x^2 \sqrt{a+b x} a^3-384 A b \sqrt{a+b} x^{3/2} \sqrt{a+b x} a^3+768 A b \sqrt{a+b} x \sqrt{a+b x} a^3-9216 A b \sqrt{a+b} \sqrt{a+b x} a^3+1536 A b \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a^3+160 A b^3 x^{9/2} a^2-1408 A b^3 x^4 a^2+6720 A b^3 x^{7/2} a^2+3584 A b^3 a^2-17856 A b^3 x^3 a^2+26400 A b^3 x^{5/2} a^2-29952 A b^3 x^2 a^2+24704 A b^3 x^{3/2} a^2-4032 A b^3 x a^2+7040 A b^3 \sqrt{x} a^2+32 A b^2 \sqrt{a+b} x^{9/2} \sqrt{a+b x} a^2-160 A b^2 \sqrt{a+b} x^4 \sqrt{a+b x} a^2-224 A b^2 \sqrt{a+b} x^{7/2} \sqrt{a+b x} a^2+2560 A b^2 \sqrt{a+b} x^3 \sqrt{a+b x} a^2-8352 A b^2 \sqrt{a+b} x^{5/2} \sqrt{a+b x} a^2+17376 A b^2 \sqrt{a+b} x^2 \sqrt{a+b x} a^2-16928 A b^2 \sqrt{a+b} x^{3/2} \sqrt{a+b x} a^2+7360 A b^2 \sqrt{a+b} x \sqrt{a+b x} a^2-6400 A b^2 \sqrt{a+b} \sqrt{a+b x} a^2-4480 A b^2 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a^2-64 A b^4 x^5 a+640 A b^4 x^{9/2} a+256 A b^4 a-2880 A b^4 x^4 a+7680 A b^4 x^{7/2} a-14016 A b^4 x^3 a+16128 A b^4 x^{5/2} a-11968 A b^4 x^2 a+9600 A b^4 x^{3/2} a-256 A b^4 x a+2560 A b^4 \sqrt{x} a-64 A b^3 \sqrt{a+b} x^{9/2} \sqrt{a+b x} a+640 A b^3 \sqrt{a+b} x^4 \sqrt{a+b x} a-2880 A b^3 \sqrt{a+b} x^{7/2} \sqrt{a+b x} a+7680 A b^3 \sqrt{a+b} x^3 \sqrt{a+b x} a-12864 A b^3 \sqrt{a+b} x^{5/2} \sqrt{a+b x} a+16128 A b^3 \sqrt{a+b} x^2 \sqrt{a+b x} a-14528 A b^3 \sqrt{a+b} x^{3/2} \sqrt{a+b x} a+5760 A b^3 \sqrt{a+b} x \sqrt{a+b x} a-1280 A b^3 \sqrt{a+b} \sqrt{a+b x} a-4736 A b^3 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a+768 A b^5 x^2+768 A b^5 x-768 A b^4 \sqrt{a+b} x^{3/2} \sqrt{a+b x}-768 A b^4 \sqrt{a+b} \sqrt{x} \sqrt{a+b x}}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^{10}}\right)}{\left(\sqrt{a+b x}-\sqrt{a+b}\right) \left(-2 x a^2+4 \sqrt{x} a^2-b x^2 a+2 b x^{3/2} a-b x a+4 b \sqrt{x} a+2 \sqrt{a+b} x \sqrt{a+b x} a-4 \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a+2 b^2 x-2 b \sqrt{a+b} \sqrt{x} \sqrt{a+b x}\right)^3}","\frac{2 \sqrt{a+b x} (2 A b-3 a B)}{3 a^2 \sqrt{x}}-\frac{2 A \sqrt{a+b x}}{3 a x^{3/2}}",1,"((-1/48 + Sqrt[x]/48)*(Sqrt[a + b] - Sqrt[a + b*x])^12*(((192*a*B + 192*b*B - 96*a*B*Sqrt[x] - 192*b*B*Sqrt[x] + 96*b*B*x - 192*Sqrt[a + b]*B*Sqrt[a + b*x] + 96*Sqrt[a + b]*B*Sqrt[x]*Sqrt[a + b*x])*(4*a^2*Sqrt[x] + 4*a*b*Sqrt[x] - 2*a^2*x - a*b*x + 2*b^2*x + 2*a*b*x^(3/2) - a*b*x^2 - 4*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*x*Sqrt[a + b*x])^2)/(Sqrt[a + b] - Sqrt[a + b*x])^10 + (4096*a^5*A + 11264*a^4*A*b + 10496*a^3*A*b^2 + 3584*a^2*A*b^3 + 256*a*A*b^4 - 2048*a^5*A*Sqrt[x] - 2560*a^4*A*b*Sqrt[x] + 3968*a^3*A*b^2*Sqrt[x] + 7040*a^2*A*b^3*Sqrt[x] + 2560*a*A*b^4*Sqrt[x] + 1024*a^5*A*x + 1792*a^4*A*b*x - 2240*a^3*A*b^2*x - 4032*a^2*A*b^3*x - 256*a*A*b^4*x + 768*A*b^5*x - 3584*a^5*A*x^(3/2) - 2432*a^4*A*b*x^(3/2) + 16288*a^3*A*b^2*x^(3/2) + 24704*a^2*A*b^3*x^(3/2) + 9600*a*A*b^4*x^(3/2) + 2560*a^5*A*x^2 + 1408*a^4*A*b*x^2 - 18528*a^3*A*b^2*x^2 - 29952*a^2*A*b^3*x^2 - 11968*a*A*b^4*x^2 + 768*A*b^5*x^2 - 512*a^5*A*x^(5/2) - 4352*a^4*A*b*x^(5/2) + 6816*a^3*A*b^2*x^(5/2) + 26400*a^2*A*b^3*x^(5/2) + 16128*a*A*b^4*x^(5/2) + 3200*a^4*A*b*x^3 - 1280*a^3*A*b^2*x^3 - 17856*a^2*A*b^3*x^3 - 14016*a*A*b^4*x^3 - 640*a^4*A*b*x^(7/2) - 800*a^3*A*b^2*x^(7/2) + 6720*a^2*A*b^3*x^(7/2) + 7680*a*A*b^4*x^(7/2) + 800*a^3*A*b^2*x^4 - 1408*a^2*A*b^3*x^4 - 2880*a*A*b^4*x^4 - 160*a^3*A*b^2*x^(9/2) + 160*a^2*A*b^3*x^(9/2) + 640*a*A*b^4*x^(9/2) - 64*a*A*b^4*x^5 - 4096*a^4*A*Sqrt[a + b]*Sqrt[a + b*x] - 9216*a^3*A*b*Sqrt[a + b]*Sqrt[a + b*x] - 6400*a^2*A*b^2*Sqrt[a + b]*Sqrt[a + b*x] - 1280*a*A*b^3*Sqrt[a + b]*Sqrt[a + b*x] + 2048*a^4*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 1536*a^3*A*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 4480*a^2*A*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 4736*a*A*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 768*A*b^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 1024*a^4*A*Sqrt[a + b]*x*Sqrt[a + b*x] + 768*a^3*A*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 7360*a^2*A*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] + 5760*a*A*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] + 3584*a^4*A*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 384*a^3*A*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 16928*a^2*A*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 14528*a*A*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 768*A*b^4*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 2560*a^4*A*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 384*a^3*A*b*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 17376*a^2*A*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 16128*a*A*b^3*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 512*a^4*A*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 2304*a^3*A*b*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 8352*a^2*A*b^2*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 12864*a*A*b^3*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] - 1920*a^3*A*b*Sqrt[a + b]*x^3*Sqrt[a + b*x] + 2560*a^2*A*b^2*Sqrt[a + b]*x^3*Sqrt[a + b*x] + 7680*a*A*b^3*Sqrt[a + b]*x^3*Sqrt[a + b*x] + 384*a^3*A*b*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 224*a^2*A*b^2*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 2880*a*A*b^3*Sqrt[a + b]*x^(7/2)*Sqrt[a + b*x] - 160*a^2*A*b^2*Sqrt[a + b]*x^4*Sqrt[a + b*x] + 640*a*A*b^3*Sqrt[a + b]*x^4*Sqrt[a + b*x] + 32*a^2*A*b^2*Sqrt[a + b]*x^(9/2)*Sqrt[a + b*x] - 64*a*A*b^3*Sqrt[a + b]*x^(9/2)*Sqrt[a + b*x])/(Sqrt[a + b] - Sqrt[a + b*x])^10))/((-Sqrt[a + b] + Sqrt[a + b*x])*(4*a^2*Sqrt[x] + 4*a*b*Sqrt[x] - 2*a^2*x - a*b*x + 2*b^2*x + 2*a*b*x^(3/2) - a*b*x^2 - 4*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*x*Sqrt[a + b*x])^3)","B",1
521,1,6757,84,163.5446405,"\int \frac{A+B x}{x^{7/2} \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(7/2)*Sqrt[a + b*x]),x]","\text{Result too large to show}","-\frac{4 b \sqrt{a+b x} (4 A b-5 a B)}{15 a^3 \sqrt{x}}+\frac{2 \sqrt{a+b x} (4 A b-5 a B)}{15 a^2 x^{3/2}}-\frac{2 A \sqrt{a+b x}}{5 a x^{5/2}}",1,"Result too large to show","B",1
522,-1,0,117,180.0682357,"\int \frac{A+B x}{x^{9/2} \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(9/2)*Sqrt[a + b*x]),x]","\text{\$Aborted}","\frac{16 b^2 \sqrt{a+b x} (6 A b-7 a B)}{105 a^4 \sqrt{x}}-\frac{8 b \sqrt{a+b x} (6 A b-7 a B)}{105 a^3 x^{3/2}}+\frac{2 \sqrt{a+b x} (6 A b-7 a B)}{35 a^2 x^{5/2}}-\frac{2 A \sqrt{a+b x}}{7 a x^{7/2}}",1,"$Aborted","F",-1
523,-1,0,150,180.1552649,"\int \frac{A+B x}{x^{11/2} \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(11/2)*Sqrt[a + b*x]),x]","\text{\$Aborted}","-\frac{32 b^3 \sqrt{a+b x} (8 A b-9 a B)}{315 a^5 \sqrt{x}}+\frac{16 b^2 \sqrt{a+b x} (8 A b-9 a B)}{315 a^4 x^{3/2}}-\frac{4 b \sqrt{a+b x} (8 A b-9 a B)}{105 a^3 x^{5/2}}+\frac{2 \sqrt{a+b x} (8 A b-9 a B)}{63 a^2 x^{7/2}}-\frac{2 A \sqrt{a+b x}}{9 a x^{9/2}}",1,"$Aborted","F",-1
524,-1,0,183,180.2669823,"\int \frac{A+B x}{x^{13/2} \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(13/2)*Sqrt[a + b*x]),x]","\text{\$Aborted}","\frac{256 b^4 \sqrt{a+b x} (10 A b-11 a B)}{3465 a^6 \sqrt{x}}-\frac{128 b^3 \sqrt{a+b x} (10 A b-11 a B)}{3465 a^5 x^{3/2}}+\frac{32 b^2 \sqrt{a+b x} (10 A b-11 a B)}{1155 a^4 x^{5/2}}-\frac{16 b \sqrt{a+b x} (10 A b-11 a B)}{693 a^3 x^{7/2}}+\frac{2 \sqrt{a+b x} (10 A b-11 a B)}{99 a^2 x^{9/2}}-\frac{2 A \sqrt{a+b x}}{11 a x^{11/2}}",1,"$Aborted","F",-1
525,-1,0,216,180.4229283,"\int \frac{A+B x}{x^{15/2} \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(15/2)*Sqrt[a + b*x]),x]","\text{\$Aborted}","-\frac{512 b^5 \sqrt{a+b x} (12 A b-13 a B)}{9009 a^7 \sqrt{x}}+\frac{256 b^4 \sqrt{a+b x} (12 A b-13 a B)}{9009 a^6 x^{3/2}}-\frac{64 b^3 \sqrt{a+b x} (12 A b-13 a B)}{3003 a^5 x^{5/2}}+\frac{160 b^2 \sqrt{a+b x} (12 A b-13 a B)}{9009 a^4 x^{7/2}}-\frac{20 b \sqrt{a+b x} (12 A b-13 a B)}{1287 a^3 x^{9/2}}+\frac{2 \sqrt{a+b x} (12 A b-13 a B)}{143 a^2 x^{11/2}}-\frac{2 A \sqrt{a+b x}}{13 a x^{13/2}}",1,"$Aborted","F",-1
526,1,3436,200,126.2051183,"\int \frac{x^{7/2} (A+B x)}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(x^(7/2)*(A + B*x))/(a + b*x)^(3/2),x]","\text{Result too large to show}","-\frac{35 a^3 (8 A b-9 a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{64 b^{11/2}}+\frac{35 a^2 \sqrt{x} \sqrt{a+b x} (8 A b-9 a B)}{64 b^5}-\frac{35 a x^{3/2} \sqrt{a+b x} (8 A b-9 a B)}{96 b^4}+\frac{7 x^{5/2} \sqrt{a+b x} (8 A b-9 a B)}{24 b^3}-\frac{x^{7/2} \sqrt{a+b x} (8 A b-9 a B)}{4 a b^2}+\frac{2 x^{9/2} (A b-a B)}{a b \sqrt{a+b x}}",1,"((Sqrt[a + b] - Sqrt[a + b*x])^15*((-7*a^4*B)/(4*b^5) - (14*a^3*B)/b^4 - (28*a^2*B)/b^3 - (16*a*B)/b^2 - (a^4*B*Sqrt[x])/(4*b^5) - (8*a^3*B*Sqrt[x])/b^4 - (40*a^2*B*Sqrt[x])/b^3 - (64*a*B*Sqrt[x])/b^2 - (32*B*Sqrt[x])/b + (2*a^3*Sqrt[a + b]*B*Sqrt[a + b*x])/b^5 + (20*a^2*Sqrt[a + b]*B*Sqrt[a + b*x])/b^4 + (48*a*Sqrt[a + b]*B*Sqrt[a + b*x])/b^3 + (32*Sqrt[a + b]*B*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^8 + ((Sqrt[a + b] - Sqrt[a + b*x])^3*((157*a^3*A)/(24*b^4) - (20*a^2*A)/b^3 - (80*a*A)/b^2 - (140*A)/(3*b) - (407*a^4*B)/(64*b^5) + (20*a^3*B)/b^4 - (32*a^2*B)/b^3 - (196*a*B)/b^2 - (126*B)/b - (13*a^3*A*Sqrt[x])/(24*b^4) + (6*a^2*A*Sqrt[x])/b^3 - (10*a*A*Sqrt[x])/b^2 - (70*A*Sqrt[x])/(3*b) + (23*a^4*B*Sqrt[x])/(64*b^5) - (6*a^3*B*Sqrt[x])/b^4 + (10*a^2*B*Sqrt[x])/b^3 - (14*a*B*Sqrt[x])/b^2 - (42*B*Sqrt[x])/b - (6*a^2*A*Sqrt[a + b]*Sqrt[a + b*x])/b^4 + (20*a*A*Sqrt[a + b]*Sqrt[a + b*x])/b^3 + (70*A*Sqrt[a + b]*Sqrt[a + b*x])/b^2 + (6*a^3*Sqrt[a + b]*B*Sqrt[a + b*x])/b^5 - (20*a^2*Sqrt[a + b]*B*Sqrt[a + b*x])/b^4 + (42*a*Sqrt[a + b]*B*Sqrt[a + b*x])/b^3 + (168*Sqrt[a + b]*B*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 + ((Sqrt[a + b] - Sqrt[a + b*x])^13*((-57*a^4*B)/(4*b^5) - (120*a^3*B)/b^4 - (264*a^2*B)/b^3 - (192*a*B)/b^2 - (32*B)/b - (7*a^4*B*Sqrt[x])/(4*b^5) - (56*a^3*B*Sqrt[x])/b^4 - (280*a^2*B*Sqrt[x])/b^3 - (448*a*B*Sqrt[x])/b^2 - (224*B*Sqrt[x])/b + (16*a^3*Sqrt[a + b]*B*Sqrt[a + b*x])/b^5 + (160*a^2*Sqrt[a + b]*B*Sqrt[a + b*x])/b^4 + (384*a*Sqrt[a + b]*B*Sqrt[a + b*x])/b^3 + (256*Sqrt[a + b]*B*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^7 + ((Sqrt[a + b] - Sqrt[a + b*x])^5*((-113*a^3*A)/(12*b^4) - (316*a^2*A)/(3*b^3) - (530*a*A)/(3*b^2) - (224*A)/(3*b) + (299*a^4*B)/(32*b^5) - (44*a^3*B)/b^4 - (570*a^2*B)/b^3 - (952*a*B)/b^2 - (420*B)/b + (17*a^3*A*Sqrt[x])/(12*b^4) - (12*a^2*A*Sqrt[x])/b^3 - (82*a*A*Sqrt[x])/b^2 - (224*A*Sqrt[x])/(3*b) - (43*a^4*B*Sqrt[x])/(32*b^5) + (12*a^3*B*Sqrt[x])/b^4 - (30*a^2*B*Sqrt[x])/b^3 - (280*a*B*Sqrt[x])/b^2 - (252*B*Sqrt[x])/b + (8*a^2*A*Sqrt[a + b]*Sqrt[a + b*x])/b^4 + (328*a*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^3) + (448*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^2) - (8*a^3*Sqrt[a + b]*B*Sqrt[a + b*x])/b^5 + (40*a^2*Sqrt[a + b]*B*Sqrt[a + b*x])/b^4 + (560*a*Sqrt[a + b]*B*Sqrt[a + b*x])/b^3 + (672*Sqrt[a + b]*B*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^3 + ((Sqrt[a + b] - Sqrt[a + b*x])^11*((-5*a^3*A)/(3*b^4) - (20*a^2*A)/(3*b^3) - (16*a*A)/(3*b^2) - (337*a^4*B)/(8*b^5) - (396*a^3*B)/b^4 - (972*a^2*B)/b^3 - (832*a*B)/b^2 - (208*B)/b - (a^3*A*Sqrt[x])/(3*b^4) - (6*a^2*A*Sqrt[x])/b^3 - (16*a*A*Sqrt[x])/b^2 - (32*A*Sqrt[x])/(3*b) - (31*a^4*B*Sqrt[x])/(8*b^5) - (138*a^3*B*Sqrt[x])/b^4 - (732*a^2*B*Sqrt[x])/b^3 - (1216*a*B*Sqrt[x])/b^2 - (624*B*Sqrt[x])/b + (2*a^2*A*Sqrt[a + b]*Sqrt[a + b*x])/b^4 + (32*a*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^3) + (32*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^2) + (46*a^3*Sqrt[a + b]*B*Sqrt[a + b*x])/b^5 + (488*a^2*Sqrt[a + b]*B*Sqrt[a + b*x])/b^4 + (1216*a*Sqrt[a + b]*B*Sqrt[a + b*x])/b^3 + (832*Sqrt[a + b]*B*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^6 + ((Sqrt[a + b] - Sqrt[a + b*x])^7*((-81*a^3*A)/(4*b^4) - (112*a^2*A)/b^3 - (144*a*A)/b^2 - (48*A)/b - (375*a^4*B)/(32*b^5) - (400*a^3*B)/b^4 - (1548*a^2*B)/b^3 - (1836*a*B)/b^2 - (660*B)/b - (7*a^3*A*Sqrt[x])/(4*b^4) - (44*a^2*A*Sqrt[x])/b^3 - (134*a*A*Sqrt[x])/b^2 - (96*A*Sqrt[x])/b + (55*a^4*B*Sqrt[x])/(32*b^5) - (20*a^3*B*Sqrt[x])/b^4 - (410*a^2*B*Sqrt[x])/b^3 - (1032*a*B*Sqrt[x])/b^2 - (660*B*Sqrt[x])/b + (22*a^2*A*Sqrt[a + b]*Sqrt[a + b*x])/b^4 + (134*a*A*Sqrt[a + b]*Sqrt[a + b*x])/b^3 + (144*A*Sqrt[a + b]*Sqrt[a + b*x])/b^2 + (10*a^3*Sqrt[a + b]*B*Sqrt[a + b*x])/b^5 + (410*a^2*Sqrt[a + b]*B*Sqrt[a + b*x])/b^4 + (1548*a*Sqrt[a + b]*B*Sqrt[a + b*x])/b^3 + (1320*Sqrt[a + b]*B*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4 + ((Sqrt[a + b] - Sqrt[a + b*x])^9*((-31*a^3*A)/(3*b^4) - (46*a^2*A)/b^3 - (48*a*A)/b^2 - (32*A)/(3*b) - (401*a^4*B)/(8*b^5) - (610*a^3*B)/b^4 - (1748*a^2*B)/b^3 - (1728*a*B)/b^2 - (528*B)/b - (5*a^3*A*Sqrt[x])/(3*b^4) - (30*a^2*A*Sqrt[x])/b^3 - (80*a*A*Sqrt[x])/b^2 - (160*A*Sqrt[x])/(3*b) - (15*a^4*B*Sqrt[x])/(8*b^5) - (130*a^3*B*Sqrt[x])/b^4 - (860*a^2*B*Sqrt[x])/b^3 - (1600*a*B*Sqrt[x])/b^2 - (880*B*Sqrt[x])/b + (12*a^2*A*Sqrt[a + b]*Sqrt[a + b*x])/b^4 + (64*a*A*Sqrt[a + b]*Sqrt[a + b*x])/b^3 + (64*A*Sqrt[a + b]*Sqrt[a + b*x])/b^2 + (52*a^3*Sqrt[a + b]*B*Sqrt[a + b*x])/b^5 + (688*a^2*Sqrt[a + b]*B*Sqrt[a + b*x])/b^4 + (1920*a*Sqrt[a + b]*B*Sqrt[a + b*x])/b^3 + (1408*Sqrt[a + b]*B*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^5 + ((-1/64*Sqrt[a + b]/b^5 + Sqrt[a + b*x]/(64*b^5))*(104*a^3*A*b - 384*a^2*A*b^2 + 384*a*A*b^3 + 640*A*b^4 - 69*a^4*B + 384*a^3*b*B - 384*a^2*b^2*B + 384*a*b^3*B + 896*b^4*B + 152*a^3*A*b*Sqrt[x] + 128*a^2*A*b^2*Sqrt[x] - 128*a*A*b^3*Sqrt[x] + 128*A*b^4*Sqrt[x] - 187*a^4*B*Sqrt[x] - 128*a^3*b*B*Sqrt[x] + 128*a^2*b^2*B*Sqrt[x] - 128*a*b^3*B*Sqrt[x] + 128*b^4*B*Sqrt[x] - 256*a^2*A*b*Sqrt[a + b]*Sqrt[a + b*x] + 512*a*A*b^2*Sqrt[a + b]*Sqrt[a + b*x] - 768*A*b^3*Sqrt[a + b]*Sqrt[a + b*x] + 256*a^3*Sqrt[a + b]*B*Sqrt[a + b*x] - 512*a^2*b*Sqrt[a + b]*B*Sqrt[a + b*x] + 768*a*b^2*Sqrt[a + b]*B*Sqrt[a + b*x] - 1024*b^3*Sqrt[a + b]*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x]) + (((-2*a^4*A)/(b^4*(a + b)) + (2*a^5*B)/(b^5*(a + b)) + (2*a^4*A*Sqrt[x])/(b^4*(a + b)) - (2*a^5*B*Sqrt[x])/(b^5*(a + b)))*(Sqrt[a + b] - Sqrt[a + b*x])*(a^2 + 3*a*b + 2*b^2 - 2*a*b*Sqrt[x] - 2*b^2*Sqrt[x] + a*b*x + b^2*x - a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x]) + ((35*a^3*A)/(4*b^(9/2)) - (315*a^4*B)/(32*b^(11/2)))*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",0
527,1,2128,167,37.3176111,"\int \frac{x^{5/2} (A+B x)}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(x^(5/2)*(A + B*x))/(a + b*x)^(3/2),x]","\text{Result too large to show}","\frac{5 a^2 (6 A b-7 a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 b^{9/2}}-\frac{5 a \sqrt{x} \sqrt{a+b x} (6 A b-7 a B)}{8 b^4}+\frac{5 x^{3/2} \sqrt{a+b x} (6 A b-7 a B)}{12 b^3}-\frac{x^{5/2} \sqrt{a+b x} (6 A b-7 a B)}{3 a b^2}+\frac{2 x^{7/2} (A b-a B)}{a b \sqrt{a+b x}}",1,"((Sqrt[a + b] - Sqrt[a + b*x])^11*((-5*a^3*B)/(3*b^4) - (20*a^2*B)/(3*b^3) - (16*a*B)/(3*b^2) - (a^3*B*Sqrt[x])/(3*b^4) - (6*a^2*B*Sqrt[x])/b^3 - (16*a*B*Sqrt[x])/b^2 - (32*B*Sqrt[x])/(3*b) + (2*a^2*Sqrt[a + b]*B*Sqrt[a + b*x])/b^4 + (32*a*Sqrt[a + b]*B*Sqrt[a + b*x])/(3*b^3) + (32*Sqrt[a + b]*B*Sqrt[a + b*x])/(3*b^2)))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^6 + ((Sqrt[a + b] - Sqrt[a + b*x])^9*((-31*a^3*B)/(3*b^4) - (46*a^2*B)/b^3 - (48*a*B)/b^2 - (32*B)/(3*b) - (5*a^3*B*Sqrt[x])/(3*b^4) - (30*a^2*B*Sqrt[x])/b^3 - (80*a*B*Sqrt[x])/b^2 - (160*B*Sqrt[x])/(3*b) + (12*a^2*Sqrt[a + b]*B*Sqrt[a + b*x])/b^4 + (64*a*Sqrt[a + b]*B*Sqrt[a + b*x])/b^3 + (64*Sqrt[a + b]*B*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^5 + ((Sqrt[a + b] - Sqrt[a + b*x])^3*((-27*a^2*A)/(4*b^3) - (20*a*A)/b^2 - (10*A)/b + (157*a^3*B)/(24*b^4) - (20*a^2*B)/b^3 - (80*a*B)/b^2 - (140*B)/(3*b) + (3*a^2*A*Sqrt[x])/(4*b^3) - (6*a*A*Sqrt[x])/b^2 - (10*A*Sqrt[x])/b - (13*a^3*B*Sqrt[x])/(24*b^4) + (6*a^2*B*Sqrt[x])/b^3 - (10*a*B*Sqrt[x])/b^2 - (70*B*Sqrt[x])/(3*b) + (6*a*A*Sqrt[a + b]*Sqrt[a + b*x])/b^3 + (20*A*Sqrt[a + b]*Sqrt[a + b*x])/b^2 - (6*a^2*Sqrt[a + b]*B*Sqrt[a + b*x])/b^4 + (20*a*Sqrt[a + b]*B*Sqrt[a + b*x])/b^3 + (70*Sqrt[a + b]*B*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 + ((Sqrt[a + b] - Sqrt[a + b*x])^7*((-3*a^2*A)/(2*b^3) - (2*a*A)/b^2 - (81*a^3*B)/(4*b^4) - (112*a^2*B)/b^3 - (144*a*B)/b^2 - (48*B)/b - (a^2*A*Sqrt[x])/(2*b^3) - (4*a*A*Sqrt[x])/b^2 - (4*A*Sqrt[x])/b - (7*a^3*B*Sqrt[x])/(4*b^4) - (44*a^2*B*Sqrt[x])/b^3 - (134*a*B*Sqrt[x])/b^2 - (96*B*Sqrt[x])/b + (2*a*A*Sqrt[a + b]*Sqrt[a + b*x])/b^3 + (4*A*Sqrt[a + b]*Sqrt[a + b*x])/b^2 + (22*a^2*Sqrt[a + b]*B*Sqrt[a + b*x])/b^4 + (134*a*Sqrt[a + b]*B*Sqrt[a + b*x])/b^3 + (144*Sqrt[a + b]*B*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4 + ((Sqrt[a + b] - Sqrt[a + b*x])^5*((-13*a^2*A)/(2*b^3) - (12*a*A)/b^2 - (4*A)/b - (113*a^3*B)/(12*b^4) - (316*a^2*B)/(3*b^3) - (530*a*B)/(3*b^2) - (224*B)/(3*b) - (3*a^2*A*Sqrt[x])/(2*b^3) - (12*a*A*Sqrt[x])/b^2 - (12*A*Sqrt[x])/b + (17*a^3*B*Sqrt[x])/(12*b^4) - (12*a^2*B*Sqrt[x])/b^3 - (82*a*B*Sqrt[x])/b^2 - (224*B*Sqrt[x])/(3*b) + (8*a*A*Sqrt[a + b]*Sqrt[a + b*x])/b^3 + (16*A*Sqrt[a + b]*Sqrt[a + b*x])/b^2 + (8*a^2*Sqrt[a + b]*B*Sqrt[a + b*x])/b^4 + (328*a*Sqrt[a + b]*B*Sqrt[a + b*x])/(3*b^3) + (448*Sqrt[a + b]*B*Sqrt[a + b*x])/(3*b^2)))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^3 + ((-1/8*Sqrt[a + b]/b^4 + Sqrt[a + b*x]/(8*b^4))*(-18*a^2*A*b + 48*a*A*b^2 + 48*A*b^3 + 13*a^3*B - 48*a^2*b*B + 48*a*b^2*B + 80*b^3*B - 14*a^2*A*b*Sqrt[x] - 16*a*A*b^2*Sqrt[x] + 16*A*b^3*Sqrt[x] + 19*a^3*B*Sqrt[x] + 16*a^2*b*B*Sqrt[x] - 16*a*b^2*B*Sqrt[x] + 16*b^3*B*Sqrt[x] + 32*a*A*b*Sqrt[a + b]*Sqrt[a + b*x] - 64*A*b^2*Sqrt[a + b]*Sqrt[a + b*x] - 32*a^2*Sqrt[a + b]*B*Sqrt[a + b*x] + 64*a*b*Sqrt[a + b]*B*Sqrt[a + b*x] - 96*b^2*Sqrt[a + b]*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x]) + (((2*a^3*A)/(b^3*(a + b)) - (2*a^4*B)/(b^4*(a + b)) - (2*a^3*A*Sqrt[x])/(b^3*(a + b)) + (2*a^4*B*Sqrt[x])/(b^4*(a + b)))*(Sqrt[a + b] - Sqrt[a + b*x])*(a^2 + 3*a*b + 2*b^2 - 2*a*b*Sqrt[x] - 2*b^2*Sqrt[x] + a*b*x + b^2*x - a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x]) + ((-15*a^2*A)/(2*b^(7/2)) + (35*a^3*B)/(4*b^(9/2)))*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",0
528,1,1170,134,9.8689017,"\int \frac{x^{3/2} (A+B x)}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(x^(3/2)*(A + B*x))/(a + b*x)^(3/2),x]","\frac{\left(-\frac{3 B a^2}{2 b^3}-\frac{B \sqrt{x} a^2}{2 b^3}-\frac{2 B a}{b^2}-\frac{4 B \sqrt{x} a}{b^2}+\frac{2 \sqrt{a+b} B \sqrt{a+b x} a}{b^3}-\frac{4 B \sqrt{x}}{b}+\frac{4 \sqrt{a+b} B \sqrt{a+b x}}{b^2}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^7}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^4}+\frac{\left(-\frac{13 B a^2}{2 b^3}-\frac{3 B \sqrt{x} a^2}{2 b^3}-\frac{12 B a}{b^2}-\frac{12 B \sqrt{x} a}{b^2}+\frac{8 \sqrt{a+b} B \sqrt{a+b x} a}{b^3}-\frac{4 B}{b}-\frac{12 B \sqrt{x}}{b}+\frac{16 \sqrt{a+b} B \sqrt{a+b x}}{b^2}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^5}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^3}+\frac{\left(-\frac{27 B a^2}{4 b^3}+\frac{3 B \sqrt{x} a^2}{4 b^3}-\frac{20 B a}{b^2}-\frac{6 B \sqrt{x} a}{b^2}-\frac{A \sqrt{x} a}{b^2}+\frac{6 \sqrt{a+b} B \sqrt{a+b x} a}{b^3}-\frac{A a}{b^2}-\frac{10 B}{b}-\frac{10 B \sqrt{x}}{b}-\frac{2 A \sqrt{x}}{b}+\frac{20 \sqrt{a+b} B \sqrt{a+b x}}{b^2}+\frac{2 A \sqrt{a+b} \sqrt{a+b x}}{b^2}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^3}{\left(-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}\right)^2}+\frac{\left(\frac{2 B a^3}{b^3 (a+b)}-\frac{2 B \sqrt{x} a^3}{b^3 (a+b)}+\frac{2 A \sqrt{x} a^2}{b^2 (a+b)}-\frac{2 A a^2}{b^2 (a+b)}\right) \left(a^2+3 b a+b x a-2 b \sqrt{x} a-\sqrt{a+b} \sqrt{a+b x} a+2 b^2+b^2 x-2 b^2 \sqrt{x}-2 b \sqrt{a+b} \sqrt{a+b x}+b \sqrt{a+b} \sqrt{x} \sqrt{a+b x}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)}{-2 a^3-5 b a^2-3 b x a^2+2 b \sqrt{x} a^2+2 \sqrt{a+b} \sqrt{a+b x} a^2-2 b^2 a-b^2 x^2 a+2 b^2 x^{3/2} a-5 b^2 x a+2 b \sqrt{a+b} x \sqrt{a+b x} a+4 b \sqrt{a+b} \sqrt{a+b x} a-2 b \sqrt{a+b} \sqrt{x} \sqrt{a+b x} a-2 b^3 x+2 b^2 \sqrt{a+b} \sqrt{x} \sqrt{a+b x}}+\frac{\left(\frac{\sqrt{a+b x}}{4 b^3}-\frac{\sqrt{a+b}}{4 b^3}\right) \left(-9 B a^2-7 B \sqrt{x} a^2+12 A b a+24 b B a+4 A b \sqrt{x} a-8 b B \sqrt{x} a+16 \sqrt{a+b} B \sqrt{a+b x} a+8 A b^2+24 b^2 B+8 A b^2 \sqrt{x}+8 b^2 B \sqrt{x}-32 b \sqrt{a+b} B \sqrt{a+b x}-16 A b \sqrt{a+b} \sqrt{a+b x}\right)}{-a-b \sqrt{x}+\sqrt{a+b} \sqrt{a+b x}}+\left(\frac{6 a A}{b^{5/2}}-\frac{15 a^2 B}{2 b^{7/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \left(\sqrt{x}-1\right)}{\sqrt{a+b}-\sqrt{a+b x}}\right)","-\frac{3 a (4 A b-5 a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{4 b^{7/2}}+\frac{3 \sqrt{x} \sqrt{a+b x} (4 A b-5 a B)}{4 b^3}-\frac{x^{3/2} \sqrt{a+b x} (4 A b-5 a B)}{2 a b^2}+\frac{2 x^{5/2} (A b-a B)}{a b \sqrt{a+b x}}",1,"((Sqrt[a + b] - Sqrt[a + b*x])^7*((-3*a^2*B)/(2*b^3) - (2*a*B)/b^2 - (a^2*B*Sqrt[x])/(2*b^3) - (4*a*B*Sqrt[x])/b^2 - (4*B*Sqrt[x])/b + (2*a*Sqrt[a + b]*B*Sqrt[a + b*x])/b^3 + (4*Sqrt[a + b]*B*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^4 + ((Sqrt[a + b] - Sqrt[a + b*x])^5*((-13*a^2*B)/(2*b^3) - (12*a*B)/b^2 - (4*B)/b - (3*a^2*B*Sqrt[x])/(2*b^3) - (12*a*B*Sqrt[x])/b^2 - (12*B*Sqrt[x])/b + (8*a*Sqrt[a + b]*B*Sqrt[a + b*x])/b^3 + (16*Sqrt[a + b]*B*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^3 + ((Sqrt[a + b] - Sqrt[a + b*x])^3*(-((a*A)/b^2) - (27*a^2*B)/(4*b^3) - (20*a*B)/b^2 - (10*B)/b - (a*A*Sqrt[x])/b^2 - (2*A*Sqrt[x])/b + (3*a^2*B*Sqrt[x])/(4*b^3) - (6*a*B*Sqrt[x])/b^2 - (10*B*Sqrt[x])/b + (2*A*Sqrt[a + b]*Sqrt[a + b*x])/b^2 + (6*a*Sqrt[a + b]*B*Sqrt[a + b*x])/b^3 + (20*Sqrt[a + b]*B*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 + ((-1/4*Sqrt[a + b]/b^3 + Sqrt[a + b*x]/(4*b^3))*(12*a*A*b + 8*A*b^2 - 9*a^2*B + 24*a*b*B + 24*b^2*B + 4*a*A*b*Sqrt[x] + 8*A*b^2*Sqrt[x] - 7*a^2*B*Sqrt[x] - 8*a*b*B*Sqrt[x] + 8*b^2*B*Sqrt[x] - 16*A*b*Sqrt[a + b]*Sqrt[a + b*x] + 16*a*Sqrt[a + b]*B*Sqrt[a + b*x] - 32*b*Sqrt[a + b]*B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x]) + (((-2*a^2*A)/(b^2*(a + b)) + (2*a^3*B)/(b^3*(a + b)) + (2*a^2*A*Sqrt[x])/(b^2*(a + b)) - (2*a^3*B*Sqrt[x])/(b^3*(a + b)))*(Sqrt[a + b] - Sqrt[a + b*x])*(a^2 + 3*a*b + 2*b^2 - 2*a*b*Sqrt[x] - 2*b^2*Sqrt[x] + a*b*x + b^2*x - a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x]) + ((6*a*A)/b^(5/2) - (15*a^2*B)/(2*b^(7/2)))*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",1
529,1,638,98,2.9921993,"\int \frac{\sqrt{x} (A+B x)}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[x]*(A + B*x))/(a + b*x)^(3/2),x]","\frac{\left(a^2+a b x-2 a b \sqrt{x}-a \sqrt{a+b} \sqrt{a+b x}-2 b \sqrt{a+b} \sqrt{a+b x}+b \sqrt{x} \sqrt{a+b} \sqrt{a+b x}+3 a b+b^2 x-2 b^2 \sqrt{x}+2 b^2\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(\frac{2 a^2 B \sqrt{x}}{b^2 (a+b)}-\frac{2 a^2 B}{b^2 (a+b)}-\frac{2 a A \sqrt{x}}{b (a+b)}+\frac{2 a A}{b (a+b)}\right)}{-2 a^3-3 a^2 b x+2 a^2 b \sqrt{x}+2 a^2 \sqrt{a+b} \sqrt{a+b x}-5 a^2 b+2 a b^2 x^{3/2}-a b^2 x^2-5 a b^2 x+2 b^2 \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-2 a b^2+2 a b x \sqrt{a+b} \sqrt{a+b x}+4 a b \sqrt{a+b} \sqrt{a+b x}-2 a b \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-2 b^3 x}+\left(\frac{6 a B}{b^{5/2}}-\frac{4 A}{b^{3/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{b} \left(\sqrt{x}-1\right)}{\sqrt{a+b}-\sqrt{a+b x}}\right)+\frac{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^3 \left(-\frac{a B \sqrt{x}}{b^2}+\frac{2 B \sqrt{a+b} \sqrt{a+b x}}{b^2}-\frac{a B}{b^2}-\frac{2 B \sqrt{x}}{b}\right)}{\left(\sqrt{a+b} \sqrt{a+b x}-a-b \sqrt{x}\right)^2}+\frac{\left(-\frac{a \sqrt{x}}{b^2}+\frac{4 \sqrt{a+b} \sqrt{a+b x}}{b^2}-\frac{3 a}{b^2}-\frac{2 \sqrt{x}}{b}-\frac{2}{b}\right) \left(B \sqrt{a+b}-B \sqrt{a+b x}\right)}{\sqrt{a+b} \sqrt{a+b x}-a-b \sqrt{x}}","\frac{(2 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{5/2}}-\frac{\sqrt{x} \sqrt{a+b x} (2 A b-3 a B)}{a b^2}+\frac{2 x^{3/2} (A b-a B)}{a b \sqrt{a+b x}}",1,"(((-3*a)/b^2 - 2/b - (a*Sqrt[x])/b^2 - (2*Sqrt[x])/b + (4*Sqrt[a + b]*Sqrt[a + b*x])/b^2)*(Sqrt[a + b]*B - B*Sqrt[a + b*x]))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x]) + ((Sqrt[a + b] - Sqrt[a + b*x])^3*(-((a*B)/b^2) - (a*B*Sqrt[x])/b^2 - (2*B*Sqrt[x])/b + (2*Sqrt[a + b]*B*Sqrt[a + b*x])/b^2))/(-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2 + (((2*a*A)/(b*(a + b)) - (2*a^2*B)/(b^2*(a + b)) - (2*a*A*Sqrt[x])/(b*(a + b)) + (2*a^2*B*Sqrt[x])/(b^2*(a + b)))*(Sqrt[a + b] - Sqrt[a + b*x])*(a^2 + 3*a*b + 2*b^2 - 2*a*b*Sqrt[x] - 2*b^2*Sqrt[x] + a*b*x + b^2*x - a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x]) + ((-4*A)/b^(3/2) + (6*a*B)/b^(5/2))*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])]","B",1
530,1,681,60,1.567418,"\int \frac{A+B x}{\sqrt{x} (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(Sqrt[x]*(a + b*x)^(3/2)),x]","\frac{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^4 \left(\frac{\left(a^2+a b x-2 a b \sqrt{x}-a \sqrt{a+b} \sqrt{a+b x}-2 b \sqrt{a+b} \sqrt{a+b x}+b \sqrt{x} \sqrt{a+b} \sqrt{a+b x}+3 a b+b^2 x-2 b^2 \sqrt{x}+2 b^2\right) \left(\frac{2 A \sqrt{x}}{a+b}-\frac{2 A}{a+b}-\frac{2 a B \sqrt{x}}{b (a+b)}+\frac{2 a B}{b (a+b)}\right)}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^3}+\frac{\left(\frac{8 a^3 B}{b^{3/2}}-\frac{8 a^2 B \sqrt{a+b} \sqrt{a+b x}}{b^{3/2}}+\frac{12 a^2 B x}{\sqrt{b}}-\frac{8 a^2 B \sqrt{x}}{\sqrt{b}}+\frac{20 a^2 B}{\sqrt{b}}-8 a \sqrt{b} B x^{3/2}+4 a \sqrt{b} B x^2+20 a \sqrt{b} B x-\frac{16 a B \sqrt{a+b} \sqrt{a+b x}}{\sqrt{b}}-\frac{8 a B x \sqrt{a+b} \sqrt{a+b x}}{\sqrt{b}}+\frac{8 a B \sqrt{x} \sqrt{a+b} \sqrt{a+b x}}{\sqrt{b}}-8 \sqrt{b} B \sqrt{x} \sqrt{a+b} \sqrt{a+b x}+8 a \sqrt{b} B+8 b^{3/2} B x\right) \tanh ^{-1}\left(\frac{\sqrt{b} \left(\sqrt{x}-1\right)}{\sqrt{a+b}-\sqrt{a+b x}}\right)}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^4}\right)}{-2 a^3-3 a^2 b x+2 a^2 b \sqrt{x}+2 a^2 \sqrt{a+b} \sqrt{a+b x}-5 a^2 b+2 a b^2 x^{3/2}-a b^2 x^2-5 a b^2 x+2 b^2 \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-2 a b^2+2 a b x \sqrt{a+b} \sqrt{a+b x}+4 a b \sqrt{a+b} \sqrt{a+b x}-2 a b \sqrt{x} \sqrt{a+b} \sqrt{a+b x}-2 b^3 x}","\frac{2 \sqrt{x} (A b-a B)}{a b \sqrt{a+b x}}+\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{3/2}}",1,"((Sqrt[a + b] - Sqrt[a + b*x])^4*((((-2*A)/(a + b) + (2*a*B)/(b*(a + b)) + (2*A*Sqrt[x])/(a + b) - (2*a*B*Sqrt[x])/(b*(a + b)))*(a^2 + 3*a*b + 2*b^2 - 2*a*b*Sqrt[x] - 2*b^2*Sqrt[x] + a*b*x + b^2*x - a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^3 + (((8*a^3*B)/b^(3/2) + (20*a^2*B)/Sqrt[b] + 8*a*Sqrt[b]*B - (8*a^2*B*Sqrt[x])/Sqrt[b] + (12*a^2*B*x)/Sqrt[b] + 20*a*Sqrt[b]*B*x + 8*b^(3/2)*B*x - 8*a*Sqrt[b]*B*x^(3/2) + 4*a*Sqrt[b]*B*x^2 - (8*a^2*Sqrt[a + b]*B*Sqrt[a + b*x])/b^(3/2) - (16*a*Sqrt[a + b]*B*Sqrt[a + b*x])/Sqrt[b] + (8*a*Sqrt[a + b]*B*Sqrt[x]*Sqrt[a + b*x])/Sqrt[b] - 8*Sqrt[b]*Sqrt[a + b]*B*Sqrt[x]*Sqrt[a + b*x] - (8*a*Sqrt[a + b]*B*x*Sqrt[a + b*x])/Sqrt[b])*ArcTanh[(Sqrt[b]*(-1 + Sqrt[x]))/(Sqrt[a + b] - Sqrt[a + b*x])])/(Sqrt[a + b] - Sqrt[a + b*x])^4))/(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x])","B",1
531,1,2027,49,15.1111157,"\int \frac{A+B x}{x^{3/2} (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(3/2)*(a + b*x)^(3/2)),x]","\text{Result too large to show}","-\frac{2 \sqrt{x} (2 A b-a B)}{a^2 \sqrt{a+b x}}-\frac{2 A}{a \sqrt{x} \sqrt{a+b x}}",1,"((-1/4*1/(a + b) + Sqrt[x]/(4*(a + b)))*(Sqrt[a + b] - Sqrt[a + b*x])^8*(((-1 + Sqrt[x])^2*(-8*a^3*B - 8*a^2*b*B + 8*a^2*b*B*Sqrt[x] - 8*a^2*b*B*x + 8*a^2*Sqrt[a + b]*B*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^4 + ((-a - b*Sqrt[x] + Sqrt[a + b]*Sqrt[a + b*x])^2*(16*a*b*B + 16*b^2*B - 8*a*b*B*Sqrt[x] - 16*b^2*B*Sqrt[x] + 8*b^2*B*x - 16*b*Sqrt[a + b]*B*Sqrt[a + b*x] + 8*b*Sqrt[a + b]*B*Sqrt[x]*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^6 + ((8*a^2*A + 8*a*A*b - 8*a*A*b*Sqrt[x] + 8*a*A*b*x - 8*a*A*Sqrt[a + b]*Sqrt[a + b*x])*(4*a^2 + 8*a*b + 3*b^2 - 2*a^2*Sqrt[x] - 10*a*b*Sqrt[x] - 6*b^2*Sqrt[x] + 8*a*b*x + 9*b^2*x - 2*a*b*x^(3/2) - 6*b^2*x^(3/2) + 2*b^2*x^2 - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 6*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 9*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 6*b*Sqrt[a + b]*x*Sqrt[a + b*x] + b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^6 + ((8*a*A*b + 8*A*b^2 - 8*A*b^2*Sqrt[x] + 8*A*b^2*x - 8*A*b*Sqrt[a + b]*Sqrt[a + b*x])*(6*a^2 + 11*a*b + 4*b^2 - 4*a^2*Sqrt[x] - 14*a*b*Sqrt[x] - 8*b^2*Sqrt[x] + 11*a*b*x + 12*b^2*x - 4*a*b*x^(3/2) - 8*b^2*x^(3/2) + 2*b^2*x^2 - 6*a*Sqrt[a + b]*Sqrt[a + b*x] - 8*b*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 12*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 8*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 2*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^6 + (32*a^4*B - 24*a^3*b*B - 72*a^2*b^2*B - 16*a*b^3*B + 176*a^3*b*B*Sqrt[x] + 240*a^2*b^2*B*Sqrt[x] + 48*a*b^3*B*Sqrt[x] - 88*a^3*b*B*x - 224*a^2*b^2*B*x - 88*a*b^3*B*x + 32*a^3*b*B*x^(3/2) + 232*a^2*b^2*B*x^(3/2) + 160*a*b^3*B*x^(3/2) - 104*a^2*b^2*B*x^2 - 112*a*b^3*B*x^2 + 24*a^2*b^2*B*x^(5/2) + 48*a*b^3*B*x^(5/2) - 8*a*b^3*B*x^3 - 32*a^3*Sqrt[a + b]*B*Sqrt[a + b*x] + 40*a^2*b*Sqrt[a + b]*B*Sqrt[a + b*x] + 48*a*b^2*Sqrt[a + b]*B*Sqrt[a + b*x] - 176*a^2*b*Sqrt[a + b]*B*Sqrt[x]*Sqrt[a + b*x] - 152*a*b^2*Sqrt[a + b]*B*Sqrt[x]*Sqrt[a + b*x] + 104*a^2*b*Sqrt[a + b]*B*x*Sqrt[a + b*x] + 160*a*b^2*Sqrt[a + b]*B*x*Sqrt[a + b*x] - 32*a^2*b*Sqrt[a + b]*B*x^(3/2)*Sqrt[a + b*x] - 128*a*b^2*Sqrt[a + b]*B*x^(3/2)*Sqrt[a + b*x] + 48*a*b^2*Sqrt[a + b]*B*x^2*Sqrt[a + b*x] - 8*a*b^2*Sqrt[a + b]*B*x^(5/2)*Sqrt[a + b*x])/(Sqrt[a + b] - Sqrt[a + b*x])^6))/((-Sqrt[a + b] + Sqrt[a + b*x])*(16*a^5*Sqrt[x] + 56*a^4*b*Sqrt[x] + 56*a^3*b^2*Sqrt[x] + 16*a^2*b^3*Sqrt[x] - 8*a^5*x - 40*a^4*b*x - 25*a^3*b^2*x + 16*a^2*b^3*x + 8*a*b^4*x + 40*a^4*b*x^(3/2) + 84*a^3*b^2*x^(3/2) + 56*a^2*b^3*x^(3/2) + 16*a*b^4*x^(3/2) - 16*a^4*b*x^2 - 54*a^3*b^2*x^2 - 25*a^2*b^3*x^2 + 16*a*b^4*x^2 + 8*b^5*x^2 + 28*a^3*b^2*x^(5/2) + 28*a^2*b^3*x^(5/2) - 9*a^3*b^2*x^3 - 14*a^2*b^3*x^3 + 4*a^2*b^3*x^(7/2) - a^2*b^3*x^4 - 16*a^4*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 48*a^3*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 34*a^2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 4*a*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 8*a^4*Sqrt[a + b]*x*Sqrt[a + b*x] + 36*a^3*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 8*a^2*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] - 16*a*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] - 32*a^3*b*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 40*a^2*b^2*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 12*a*b^3*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] - 8*b^4*Sqrt[a + b]*x^(3/2)*Sqrt[a + b*x] + 12*a^3*b*Sqrt[a + b]*x^2*Sqrt[a + b*x] + 28*a^2*b^2*Sqrt[a + b]*x^2*Sqrt[a + b*x] - 14*a^2*b^2*Sqrt[a + b]*x^(5/2)*Sqrt[a + b*x] + 4*a^2*b^2*Sqrt[a + b]*x^3*Sqrt[a + b*x]))","B",1
532,1,2411,83,36.884859,"\int \frac{A+B x}{x^{5/2} (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(5/2)*(a + b*x)^(3/2)),x]","\text{Result too large to show}","\frac{4 \sqrt{a+b x} (4 A b-3 a B)}{3 a^3 \sqrt{x}}-\frac{2 (4 A b-3 a B)}{3 a^2 \sqrt{x} \sqrt{a+b x}}-\frac{2 A}{3 a x^{3/2} \sqrt{a+b x}}",1,"((Sqrt[a + b] - Sqrt[a + b*x])^5*(72*A + (512*a^4*A)/(3*b^4) + (512*a^3*A)/b^3 + (1664*a^2*A)/(3*b^2) + (832*a*A)/(3*b) + (8*A*b)/a - 164*A*Sqrt[x] - (128*a^3*A*Sqrt[x])/(3*b^3) - (496*a^2*A*Sqrt[x])/(3*b^2) - (766*a*A*Sqrt[x])/(3*b) - (32*A*b*Sqrt[x])/a + (466*A*x)/3 + (128*a^3*A*x)/b^3 + (376*a^2*A*x)/b^2 + (1178*a*A*x)/(3*b) + (12*A*b*x)/a - 34*A*x^(3/2) - (64*a^2*A*x^(3/2))/(3*b^2) - (52*a*A*x^(3/2))/b - (4*A*b*x^(3/2))/a + (8*A*Sqrt[a + b]*Sqrt[a + b*x])/a - (512*a^3*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^4) - (1280*a^2*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^3) - (1088*a*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^2) - (96*A*Sqrt[a + b]*Sqrt[a + b*x])/b + (12*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/a + (128*a^2*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/(3*b^3) + (144*a*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/b^2 + (314*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/(3*b) - (4*A*Sqrt[a + b]*x*Sqrt[a + b*x])/a - (128*a^2*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^3) - (296*a*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^2) - (54*A*Sqrt[a + b]*x*Sqrt[a + b*x])/b))/(x*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])^2) + ((Sqrt[a + b] - Sqrt[a + b*x])^9*((16*A)/3 + (64*a^3*A)/(3*b^3) + (48*a^2*A)/b^2 + (32*a*A)/b - 32*A*Sqrt[x] - (256*a^4*A*Sqrt[x])/(3*b^4) - (928*a^3*A*Sqrt[x])/(3*b^3) - (392*a^2*A*Sqrt[x])/b^2 - (200*a*A*Sqrt[x])/b + 8*A*x + (128*a^4*A*x)/(3*b^4) + (160*a^3*A*x)/b^3 + (584*a^2*A*x)/(3*b^2) + (256*a*A*x)/(3*b) - (8*A*x^(3/2))/3 - (64*a^3*A*x^(3/2))/(3*b^3) - (128*a^2*A*x^(3/2))/(3*b^2) - (24*a*A*x^(3/2))/b + (64*a^2*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^3) + (112*a*A*Sqrt[a + b]*Sqrt[a + b*x])/(3*b^2) + (16*A*Sqrt[a + b]*Sqrt[a + b*x])/b + (256*a^3*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/(3*b^4) + (160*a^2*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/b^3 + (248*a*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/(3*b^2) + (8*A*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])/b - (128*a^3*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^4) - (224*a^2*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^3) - (104*a*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b^2) - (8*A*Sqrt[a + b]*x*Sqrt[a + b*x])/(3*b)))/(x^(3/2)*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x])^3) + (((-2*A*b^2)/(a^2*(a + b)) + (2*b*B)/(a*(a + b)) + (2*A*b^2*Sqrt[x])/(a^2*(a + b)) - (2*b*B*Sqrt[x])/(a*(a + b)))*(Sqrt[a + b] - Sqrt[a + b*x])*(a^2 + 3*a*b + 2*b^2 - 2*a*b*Sqrt[x] - 2*b^2*Sqrt[x] + a*b*x + b^2*x - a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))/(-2*a^3 - 5*a^2*b - 2*a*b^2 + 2*a^2*b*Sqrt[x] - 3*a^2*b*x - 5*a*b^2*x - 2*b^3*x + 2*a*b^2*x^(3/2) - a*b^2*x^2 + 2*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*Sqrt[a + b*x] - 2*a*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x]) + (((-2*Sqrt[a + b])/(3*a^2*b^2) + (2*Sqrt[a + b*x])/(3*a^2*b^2))*(-144*a^4*A - 304*a^3*A*b - 203*a^2*A*b^2 - 39*a*A*b^3 + 6*A*b^4 - 6*a^2*b^2*B - 6*a*b^3*B + 28*a^3*A*b*Sqrt[x] + 53*a^2*A*b^2*Sqrt[x] + 21*a*A*b^3*Sqrt[x] - 12*A*b^4*Sqrt[x] + 9*a^2*b^2*B*Sqrt[x] + 12*a*b^3*B*Sqrt[x] - 108*a^3*A*b*x - 200*a^2*A*b^2*x - 93*a*A*b^3*x + 9*A*b^4*x - 3*a^2*b^2*B*x - 9*a*b^3*B*x + 14*a^2*A*b^2*x^(3/2) + 15*a*A*b^3*x^(3/2) - 3*A*b^4*x^(3/2) + 3*a*b^3*B*x^(3/2) + 144*a^3*A*Sqrt[a + b]*Sqrt[a + b*x] + 232*a^2*A*b*Sqrt[a + b]*Sqrt[a + b*x] + 105*a*A*b^2*Sqrt[a + b]*Sqrt[a + b*x] - 6*A*b^3*Sqrt[a + b]*Sqrt[a + b*x] + 6*a*b^2*Sqrt[a + b]*B*Sqrt[a + b*x] - 28*a^2*A*b*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 39*a*A*b^2*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] + 9*A*b^3*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x] - 9*a*b^2*Sqrt[a + b]*B*Sqrt[x]*Sqrt[a + b*x] + 36*a^2*A*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 30*a*A*b^2*Sqrt[a + b]*x*Sqrt[a + b*x] - 3*A*b^3*Sqrt[a + b]*x*Sqrt[a + b*x] + 3*a*b^2*Sqrt[a + b]*B*x*Sqrt[a + b*x]))/(Sqrt[x]*(4*a^2 + 4*a*b - 2*a^2*Sqrt[x] - a*b*Sqrt[x] + 2*b^2*Sqrt[x] + 2*a*b*x - a*b*x^(3/2) - 4*a*Sqrt[a + b]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*Sqrt[x]*Sqrt[a + b*x]))","B",1
533,-1,0,114,180.2125997,"\int \frac{A+B x}{x^{7/2} (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(7/2)*(a + b*x)^(3/2)),x]","\text{\$Aborted}","-\frac{16 b \sqrt{a+b x} (6 A b-5 a B)}{15 a^4 \sqrt{x}}+\frac{8 \sqrt{a+b x} (6 A b-5 a B)}{15 a^3 x^{3/2}}-\frac{2 (6 A b-5 a B)}{5 a^2 x^{3/2} \sqrt{a+b x}}-\frac{2 A}{5 a x^{5/2} \sqrt{a+b x}}",1,"$Aborted","F",-1
534,-1,0,147,180.0940825,"\int \frac{A+B x}{x^{9/2} (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(9/2)*(a + b*x)^(3/2)),x]","\text{\$Aborted}","\frac{32 b^2 \sqrt{a+b x} (8 A b-7 a B)}{35 a^5 \sqrt{x}}-\frac{16 b \sqrt{a+b x} (8 A b-7 a B)}{35 a^4 x^{3/2}}+\frac{12 \sqrt{a+b x} (8 A b-7 a B)}{35 a^3 x^{5/2}}-\frac{2 (8 A b-7 a B)}{7 a^2 x^{5/2} \sqrt{a+b x}}-\frac{2 A}{7 a x^{7/2} \sqrt{a+b x}}",1,"$Aborted","F",-1
535,-1,0,180,180.1229092,"\int \frac{A+B x}{x^{11/2} (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(11/2)*(a + b*x)^(3/2)),x]","\text{\$Aborted}","-\frac{256 b^3 \sqrt{a+b x} (10 A b-9 a B)}{315 a^6 \sqrt{x}}+\frac{128 b^2 \sqrt{a+b x} (10 A b-9 a B)}{315 a^5 x^{3/2}}-\frac{32 b \sqrt{a+b x} (10 A b-9 a B)}{105 a^4 x^{5/2}}+\frac{16 \sqrt{a+b x} (10 A b-9 a B)}{63 a^3 x^{7/2}}-\frac{2 (10 A b-9 a B)}{9 a^2 x^{7/2} \sqrt{a+b x}}-\frac{2 A}{9 a x^{9/2} \sqrt{a+b x}}",1,"$Aborted","F",-1
536,-1,0,213,180.0560735,"\int \frac{A+B x}{x^{13/2} (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(13/2)*(a + b*x)^(3/2)),x]","\text{\$Aborted}","\frac{512 b^4 \sqrt{a+b x} (12 A b-11 a B)}{693 a^7 \sqrt{x}}-\frac{256 b^3 \sqrt{a+b x} (12 A b-11 a B)}{693 a^6 x^{3/2}}+\frac{64 b^2 \sqrt{a+b x} (12 A b-11 a B)}{231 a^5 x^{5/2}}-\frac{160 b \sqrt{a+b x} (12 A b-11 a B)}{693 a^4 x^{7/2}}+\frac{20 \sqrt{a+b x} (12 A b-11 a B)}{99 a^3 x^{9/2}}-\frac{2 (12 A b-11 a B)}{11 a^2 x^{9/2} \sqrt{a+b x}}-\frac{2 A}{11 a x^{11/2} \sqrt{a+b x}}",1,"$Aborted","F",-1
537,-1,0,200,180.0566723,"\int \frac{x^{7/2} (A+B x)}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(x^(7/2)*(A + B*x))/(a + b*x)^(5/2),x]","\text{\$Aborted}","\frac{35 a^2 (2 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{8 b^{11/2}}-\frac{35 a \sqrt{x} \sqrt{a+b x} (2 A b-3 a B)}{8 b^5}+\frac{35 x^{3/2} \sqrt{a+b x} (2 A b-3 a B)}{12 b^4}-\frac{7 x^{5/2} \sqrt{a+b x} (2 A b-3 a B)}{3 a b^3}+\frac{2 x^{7/2} (2 A b-3 a B)}{a b^2 \sqrt{a+b x}}+\frac{2 x^{9/2} (A b-a B)}{3 a b (a+b x)^{3/2}}",1,"$Aborted","F",-1
538,-1,0,169,180.1161117,"\int \frac{x^{5/2} (A+B x)}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(x^(5/2)*(A + B*x))/(a + b*x)^(5/2),x]","\text{\$Aborted}","-\frac{5 a (4 A b-7 a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{4 b^{9/2}}+\frac{5 \sqrt{x} \sqrt{a+b x} (4 A b-7 a B)}{4 b^4}-\frac{5 x^{3/2} \sqrt{a+b x} (4 A b-7 a B)}{6 a b^3}+\frac{2 x^{5/2} (4 A b-7 a B)}{3 a b^2 \sqrt{a+b x}}+\frac{2 x^{7/2} (A b-a B)}{3 a b (a+b x)^{3/2}}",1,"$Aborted","F",-1
539,-1,0,133,180.0311439,"\int \frac{x^{3/2} (A+B x)}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(x^(3/2)*(A + B*x))/(a + b*x)^(5/2),x]","\text{\$Aborted}","\frac{(2 A b-5 a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{7/2}}-\frac{\sqrt{x} \sqrt{a+b x} (2 A b-5 a B)}{a b^3}+\frac{2 x^{3/2} (2 A b-5 a B)}{3 a b^2 \sqrt{a+b x}}+\frac{2 x^{5/2} (A b-a B)}{3 a b (a+b x)^{3/2}}",1,"$Aborted","F",-1
540,1,4165,82,47.4029278,"\int \frac{\sqrt{x} (A+B x)}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[x]*(A + B*x))/(a + b*x)^(5/2),x]","\text{Result too large to show}","\frac{2 x^{3/2} (A b-a B)}{3 a b (a+b x)^{3/2}}+\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+b x}}\right)}{b^{5/2}}-\frac{2 B \sqrt{x}}{b^2 \sqrt{a+b x}}",1,"(-2*(32*a^8*A*b^2 + 256*a^7*A*b^3 + 806*a^6*A*b^4 + 1258*a^5*A*b^5 + 1004*a^4*A*b^6 + 376*a^3*A*b^7 + 48*a^2*A*b^8 - 96*a^10*B - 896*a^9*b*B - 3442*a^8*b^2*B - 6998*a^7*b^3*B - 8044*a^6*b^4*B - 5144*a^5*b^5*B - 1648*a^4*b^6*B - 192*a^3*b^7*B)*Sqrt[a + b*x] - 2*(-96*a^7*A*b^3 - 504*a^6*A*b^4 - 846*a^5*A*b^5 - 360*a^4*A*b^6 + 270*a^3*A*b^7 + 216*a^2*A*b^8 + 24*a*A*b^9 + 96*a^10*B + 1200*a^9*b*B + 5502*a^8*b^2*B + 12237*a^7*b^3*B + 13998*a^6*b^4*B + 7557*a^5*b^5*B + 1050*a^4*b^6*B - 420*a^3*b^7*B - 72*a^2*b^8*B)*Sqrt[x]*Sqrt[a + b*x] - 2*(128*a^7*A*b^3 + 964*a^6*A*b^4 + 2534*a^5*A*b^5 + 3010*a^4*A*b^6 + 1856*a^3*A*b^7 + 688*a^2*A*b^8 + 144*a*A*b^9 - 672*a^9*b*B - 5348*a^8*b^2*B - 16372*a^7*b^3*B - 24602*a^6*b^4*B - 19282*a^5*b^5*B - 7904*a^4*b^6*B - 1816*a^3*b^7*B - 288*a^2*b^8*B)*x*Sqrt[a + b*x] - 2*(-32*a^8*A*b^2 - 304*a^7*A*b^3 - 1514*a^6*A*b^4 - 3925*a^5*A*b^5 - 4958*a^4*A*b^6 - 2857*a^3*A*b^7 - 474*a^2*A*b^8 + 156*a*A*b^9 + 48*A*b^10 + 368*a^9*b*B + 4252*a^8*b^2*B + 16823*a^7*b^3*B + 31009*a^6*b^4*B + 28967*a^5*b^5*B + 13075*a^4*b^6*B + 1962*a^3*b^7*B - 312*a^2*b^8*B - 96*a*b^9*B)*x^(3/2)*Sqrt[a + b*x] - 2*(96*a^7*A*b^3 + 846*a^6*A*b^4 + 2964*a^5*A*b^5 + 4542*a^4*A*b^6 + 2868*a^3*A*b^7 + 396*a^2*A*b^8 - 144*a*A*b^9 - 1482*a^8*b^2*B - 9942*a^7*b^3*B - 24504*a^6*b^4*B - 28074*a^5*b^5*B - 14622*a^4*b^6*B - 2304*a^3*b^7*B + 288*a^2*b^8*B)*x^2*Sqrt[a + b*x] - 2*(-80*a^7*A*b^3 - 700*a^6*A*b^4 - 2591*a^5*A*b^5 - 4555*a^4*A*b^6 - 3617*a^3*A*b^7 - 1129*a^2*A*b^8 - 144*a*A*b^9 - 48*A*b^10 + 518*a^8*b^2*B + 5275*a^7*b^3*B + 17075*a^6*b^4*B + 24415*a^5*b^5*B + 16067*a^4*b^6*B + 4186*a^3*b^7*B + 312*a^2*b^8*B + 96*a*b^9*B)*x^(5/2)*Sqrt[a + b*x] - 2*(168*a^6*A*b^4 + 1006*a^5*A*b^5 + 2276*a^4*A*b^6 + 2122*a^3*A*b^7 + 684*a^2*A*b^8 - 1344*a^7*b^3*B - 7138*a^6*b^4*B - 13280*a^5*b^5*B - 10438*a^4*b^6*B - 2952*a^3*b^7*B)*x^3*Sqrt[a + b*x] - 2*(-66*a^6*A*b^4 - 459*a^5*A*b^5 - 1185*a^4*A*b^6 - 1341*a^3*A*b^7 - 585*a^2*A*b^8 - 36*a*A*b^9 + 321*a^7*b^3*B + 2607*a^6*b^4*B + 6237*a^5*b^5*B + 6057*a^4*b^6*B + 2178*a^3*b^7*B + 72*a^2*b^8*B)*x^(7/2)*Sqrt[a + b*x] - 2*(78*a^5*A*b^5 + 298*a^4*A*b^6 + 440*a^3*A*b^7 + 220*a^2*A*b^8 - 480*a^6*b^4*B - 1762*a^5*b^5*B - 2162*a^4*b^6*B - 880*a^3*b^7*B)*x^4*Sqrt[a + b*x] - 2*(-19*a^5*A*b^5 - 77*a^4*A*b^6 - 133*a^3*A*b^7 - 75*a^2*A*b^8 + 79*a^6*b^4*B + 404*a^5*b^5*B + 607*a^4*b^6*B + 282*a^3*b^7*B)*x^(9/2)*Sqrt[a + b*x] - 2*(6*a^4*A*b^6 + 18*a^3*A*b^7 + 12*a^2*A*b^8 - 42*a^5*b^5*B - 90*a^4*b^6*B - 48*a^3*b^7*B)*x^5*Sqrt[a + b*x] - 2*(-(a^4*A*b^6) - 2*a^3*A*b^7 - a^2*A*b^8 + 4*a^5*b^5*B + 8*a^4*b^6*B + 4*a^3*b^7*B)*x^(11/2)*Sqrt[a + b*x] + Sqrt[a + b]*(-2*(-32*a^8*A*b^2 - 240*a^7*A*b^3 - 690*a^6*A*b^4 - 941*a^5*A*b^5 - 606*a^4*A*b^6 - 156*a^3*A*b^7 - 8*a^2*A*b^8 + 96*a^10*B + 848*a^9*b*B + 3030*a^8*b^2*B + 5583*a^7*b^3*B + 5582*a^6*b^4*B + 2892*a^5*b^5*B + 648*a^4*b^6*B + 32*a^3*b^7*B) - 2*(96*a^7*A*b^3 + 456*a^6*A*b^4 + 630*a^5*A*b^5 + 96*a^4*A*b^6 - 264*a^3*A*b^7 - 96*a^2*A*b^8 - 96*a^10*B - 1152*a^9*b*B - 4938*a^8*b^2*B - 9906*a^7*b^3*B - 9594*a^6*b^4*B - 3732*a^5*b^5*B + 72*a^4*b^6*B + 240*a^3*b^7*B)*Sqrt[x] - 2*(-144*a^7*A*b^3 - 1020*a^6*A*b^4 - 2445*a^5*A*b^5 - 2535*a^4*A*b^6 - 1338*a^3*A*b^7 - 408*a^2*A*b^8 - 48*a*A*b^9 + 720*a^9*b*B + 5436*a^8*b^2*B + 15465*a^7*b^3*B + 21003*a^6*b^4*B + 14424*a^5*b^5*B + 5118*a^4*b^6*B + 1056*a^3*b^7*B + 120*a^2*b^8*B)*x - 2*(32*a^8*A*b^2 + 288*a^7*A*b^3 + 1422*a^6*A*b^4 + 3500*a^5*A*b^5 + 3792*a^4*A*b^6 + 1500*a^3*A*b^7 - 104*a^2*A*b^8 - 144*a*A*b^9 - 416*a^9*b*B - 4644*a^8*b^2*B - 17304*a^7*b^3*B - 29030*a^6*b^4*B - 23340*a^5*b^5*B - 7908*a^4*b^6*B - 232*a^3*b^7*B + 288*a^2*b^8*B)*x^(3/2) - 2*(-96*a^7*A*b^3 - 858*a^6*A*b^4 - 2997*a^5*A*b^5 - 4311*a^4*A*b^6 - 2385*a^3*A*b^7 - 396*a^2*A*b^8 - 108*a*A*b^9 - 48*A*b^10 + 1806*a^8*b^2*B + 11601*a^7*b^3*B + 26685*a^6*b^4*B + 27495*a^5*b^5*B + 12204*a^4*b^6*B + 1746*a^3*b^7*B + 216*a^2*b^8*B + 96*a*b^9*B)*x^2 - 2*(96*a^7*A*b^3 + 804*a^6*A*b^4 + 2946*a^5*A*b^5 + 5076*a^4*A*b^6 + 3774*a^3*A*b^7 + 1116*a^2*A*b^8 + 144*a*A*b^9 - 690*a^8*b^2*B - 6906*a^7*b^3*B - 21432*a^6*b^4*B - 28494*a^5*b^5*B - 16842*a^4*b^6*B - 3888*a^3*b^7*B - 288*a^2*b^8*B)*x^(5/2) - 2*(-216*a^6*A*b^4 - 1307*a^5*A*b^5 - 3027*a^4*A*b^6 - 2763*a^3*A*b^7 - 755*a^2*A*b^8 + 120*a*A*b^9 + 48*A*b^10 + 2007*a^7*b^3*B + 10493*a^6*b^4*B + 18705*a^5*b^5*B + 13677*a^4*b^6*B + 3290*a^3*b^7*B - 264*a^2*b^8*B - 96*a*b^9*B)*x^3 - 2*(102*a^6*A*b^4 + 720*a^5*A*b^5 + 1950*a^4*A*b^6 + 2268*a^3*A*b^7 + 900*a^2*A*b^8 - 540*a^7*b^3*B - 4518*a^6*b^4*B - 10824*a^5*b^5*B - 10266*a^4*b^6*B - 3384*a^3*b^7*B)*x^(7/2) - 2*(-150*a^5*A*b^5 - 627*a^4*A*b^6 - 963*a^3*A*b^7 - 423*a^2*A*b^8 + 36*a*A*b^9 + 1005*a^6*b^4*B + 3885*a^5*b^5*B + 4797*a^4*b^6*B + 1818*a^3*b^7*B - 72*a^2*b^8*B)*x^4 - 2*(44*a^5*A*b^5 + 216*a^4*A*b^6 + 390*a^3*A*b^7 + 220*a^2*A*b^8 - 194*a^6*b^4*B - 1170*a^5*b^5*B - 1854*a^4*b^6*B - 880*a^3*b^7*B)*x^(9/2) - 2*(-30*a^4*A*b^6 - 75*a^3*A*b^7 - 57*a^2*A*b^8 + 183*a^5*b^5*B + 417*a^4*b^6*B + 246*a^3*b^7*B)*x^5 - 2*(6*a^4*A*b^6 + 12*a^3*A*b^7 + 12*a^2*A*b^8 - 24*a^5*b^5*B - 66*a^4*b^6*B - 48*a^3*b^7*B)*x^(11/2) - 2*(-(a^2*A*b^8) + 3*a^4*b^6*B + 4*a^3*b^7*B)*x^6))/(3*b^2*(a + b)^2*(32*a^9 + 240*a^8*b + 690*a^7*b^2 + 941*a^6*b^3 + 606*a^5*b^4 + 156*a^4*b^5 + 8*a^3*b^6) - 18*a^3*b^8*(a + b)^2*x^(11/2) + 3*a^3*b^8*(a + b)^2*x^6 + 3*b^2*(a + b)^(5/2)*(-32*a^8 - 224*a^7*b - 582*a^6*b^2 - 676*a^5*b^3 - 328*a^4*b^4 - 48*a^3*b^5)*Sqrt[a + b*x] + x^5*(3*b^2*(a + b)^2*(21*a^4*b^5 + 39*a^3*b^6 + 6*a^2*b^7) - 18*a^3*b^7*(a + b)^(5/2)*Sqrt[a + b*x]) + x^4*(3*b^2*(a + b)^2*(105*a^5*b^4 + 405*a^4*b^5 + 297*a^3*b^6 + 48*a^2*b^7 + 24*a*b^8) + 3*b^2*(a + b)^(5/2)*(-50*a^4*b^4 - 128*a^3*b^5)*Sqrt[a + b*x]) + x*(3*b^2*(a + b)^2*(144*a^8*b + 1020*a^7*b^2 + 2445*a^6*b^3 + 2535*a^5*b^4 + 1338*a^4*b^5 + 408*a^3*b^6 + 48*a^2*b^7) + 3*b^2*(a + b)^(5/2)*(-128*a^7*b - 836*a^6*b^2 - 1698*a^5*b^3 - 1312*a^4*b^4 - 544*a^3*b^5 - 144*a^2*b^6)*Sqrt[a + b*x]) + x^3*(3*b^2*(a + b)^2*(231*a^6*b^3 + 1233*a^5*b^4 + 1641*a^4*b^5 + 749*a^3*b^6 + 174*a^2*b^7 + 96*a*b^8 + 32*b^9) + 3*b^2*(a + b)^(5/2)*(-146*a^5*b^3 - 644*a^4*b^4 - 486*a^3*b^5 - 72*a^2*b^6)*Sqrt[a + b*x]) + Sqrt[x]*(3*b^2*(a + b)^2*(-96*a^8*b - 456*a^7*b^2 - 630*a^6*b^3 - 96*a^5*b^4 + 264*a^4*b^5 + 96*a^3*b^6) + 3*b^2*(a + b)^(5/2)*(96*a^7*b + 408*a^6*b^2 + 438*a^5*b^3 - 78*a^4*b^4 - 192*a^3*b^5 - 24*a^2*b^6)*Sqrt[a + b*x]) + x^(9/2)*(3*b^2*(a + b)^2*(-90*a^4*b^5 - 92*a^3*b^6) + 3*b^2*(a + b)^(5/2)*(30*a^3*b^5 - 6*a^2*b^6)*Sqrt[a + b*x]) + x^2*(3*b^2*(a + b)^2*(258*a^7*b^2 + 1647*a^6*b^3 + 3105*a^5*b^4 + 2295*a^4*b^5 + 882*a^3*b^6 + 348*a^2*b^7 + 72*a*b^8) + 3*b^2*(a + b)^(5/2)*(-198*a^6*b^2 - 1128*a^5*b^3 - 1602*a^4*b^4 - 708*a^3*b^5 - 216*a^2*b^6 - 96*a*b^7)*Sqrt[a + b*x]) + x^(3/2)*(3*b^2*(a + b)^2*(-360*a^7*b^2 - 1436*a^6*b^3 - 1530*a^5*b^4 - 120*a^4*b^5 + 528*a^3*b^6 + 192*a^2*b^7) + 3*b^2*(a + b)^(5/2)*(312*a^6*b^2 + 1052*a^5*b^3 + 728*a^4*b^4 - 180*a^3*b^5 - 272*a^2*b^6 - 56*a*b^7)*Sqrt[a + b*x]) + x^(7/2)*(3*b^2*(a + b)^2*(-330*a^5*b^4 - 708*a^4*b^5 - 270*a^3*b^6 + 72*a^2*b^7) + 3*b^2*(a + b)^(5/2)*(180*a^4*b^4 + 216*a^3*b^5 - 36*a^2*b^6 - 24*a*b^7)*Sqrt[a + b*x]) + x^(5/2)*(3*b^2*(a + b)^2*(-510*a^6*b^3 - 1596*a^5*b^4 - 1170*a^4*b^5 + 48*a^3*b^6 + 264*a^2*b^7 + 96*a*b^8) + 3*b^2*(a + b)^(5/2)*(366*a^5*b^3 + 866*a^4*b^4 + 254*a^3*b^5 - 126*a^2*b^6 - 80*a*b^7 - 32*b^8)*Sqrt[a + b*x])) - (4*B*ArcTanh[(-Sqrt[b] + Sqrt[b]*Sqrt[x])/(Sqrt[a + b] - Sqrt[a + b*x])])/b^(5/2)","B",1
541,1,7480,65,31.6377932,"\int \frac{A+B x}{\sqrt{x} (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(Sqrt[x]*(a + b*x)^(5/2)),x]","\text{Result too large to show}","\frac{2 \sqrt{x} (a B+2 A b)}{3 a^2 b \sqrt{a+b x}}+\frac{2 \sqrt{x} (A b-a B)}{3 a b (a+b x)^{3/2}}",1,"Result too large to show","B",1
542,1,15712,81,149.0301817,"\int \frac{A+B x}{x^{3/2} (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(3/2)*(a + b*x)^(5/2)),x]","\text{Result too large to show}","-\frac{4 \sqrt{x} (4 A b-a B)}{3 a^3 \sqrt{a+b x}}-\frac{2 \sqrt{x} (4 A b-a B)}{3 a^2 (a+b x)^{3/2}}-\frac{2 A}{a \sqrt{x} (a+b x)^{3/2}}",1,"Result too large to show","B",1
543,-1,0,113,180.470598,"\int \frac{A+B x}{x^{5/2} (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(5/2)*(a + b*x)^(5/2)),x]","\text{\$Aborted}","\frac{16 \sqrt{a+b x} (2 A b-a B)}{3 a^4 \sqrt{x}}-\frac{8 (2 A b-a B)}{3 a^3 \sqrt{x} \sqrt{a+b x}}-\frac{2 (2 A b-a B)}{3 a^2 \sqrt{x} (a+b x)^{3/2}}-\frac{2 A}{3 a x^{3/2} (a+b x)^{3/2}}",1,"$Aborted","F",-1
544,-1,0,144,180.0985999,"\int \frac{A+B x}{x^{7/2} (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(7/2)*(a + b*x)^(5/2)),x]","\text{\$Aborted}","-\frac{32 b \sqrt{a+b x} (8 A b-5 a B)}{15 a^5 \sqrt{x}}+\frac{16 \sqrt{a+b x} (8 A b-5 a B)}{15 a^4 x^{3/2}}-\frac{4 (8 A b-5 a B)}{5 a^3 x^{3/2} \sqrt{a+b x}}-\frac{2 (8 A b-5 a B)}{15 a^2 x^{3/2} (a+b x)^{3/2}}-\frac{2 A}{5 a x^{5/2} (a+b x)^{3/2}}",1,"$Aborted","F",-1
545,-1,0,177,180.295019,"\int \frac{A+B x}{x^{9/2} (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(9/2)*(a + b*x)^(5/2)),x]","\text{\$Aborted}","\frac{256 b^2 \sqrt{a+b x} (10 A b-7 a B)}{105 a^6 \sqrt{x}}-\frac{128 b \sqrt{a+b x} (10 A b-7 a B)}{105 a^5 x^{3/2}}+\frac{32 \sqrt{a+b x} (10 A b-7 a B)}{35 a^4 x^{5/2}}-\frac{16 (10 A b-7 a B)}{21 a^3 x^{5/2} \sqrt{a+b x}}-\frac{2 (10 A b-7 a B)}{21 a^2 x^{5/2} (a+b x)^{3/2}}-\frac{2 A}{7 a x^{7/2} (a+b x)^{3/2}}",1,"$Aborted","F",-1
546,-1,0,210,180.4633834,"\int \frac{A+B x}{x^{11/2} (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(x^(11/2)*(a + b*x)^(5/2)),x]","\text{\$Aborted}","-\frac{512 b^3 \sqrt{a+b x} (4 A b-3 a B)}{63 a^7 \sqrt{x}}+\frac{256 b^2 \sqrt{a+b x} (4 A b-3 a B)}{63 a^6 x^{3/2}}-\frac{64 b \sqrt{a+b x} (4 A b-3 a B)}{21 a^5 x^{5/2}}+\frac{160 \sqrt{a+b x} (4 A b-3 a B)}{63 a^4 x^{7/2}}-\frac{20 (4 A b-3 a B)}{9 a^3 x^{7/2} \sqrt{a+b x}}-\frac{2 (4 A b-3 a B)}{9 a^2 x^{7/2} (a+b x)^{3/2}}-\frac{2 A}{9 a x^{9/2} (a+b x)^{3/2}}",1,"$Aborted","F",-1
547,-1,0,302,180.0213896,"\int x^3 \sqrt{a+b x} \sqrt{c+d x} \, dx","IntegrateAlgebraic[x^3*Sqrt[a + b*x]*Sqrt[c + d*x],x]","\text{\$Aborted}","\frac{(a d+b c) \left(7 a^2 d^2+2 a b c d+7 b^2 c^2\right) (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{9/2} d^{9/2}}-\frac{(a+b x)^{3/2} \sqrt{c+d x} (a d+b c) \left(7 a^2 d^2+2 a b c d+7 b^2 c^2\right)}{64 b^4 d^3}+\frac{(a+b x)^{3/2} (c+d x)^{3/2} \left(35 a^2 d^2-42 b d x (a d+b c)+38 a b c d+35 b^2 c^2\right)}{240 b^3 d^3}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-7 a^4 d^4-2 a^3 b c d^3+2 a b^3 c^3 d+7 b^4 c^4\right)}{128 b^4 d^4}+\frac{x^2 (a+b x)^{3/2} (c+d x)^{3/2}}{5 b d}",1,"$Aborted","F",-1
548,-1,0,237,180.0112955,"\int x^2 \sqrt{a+b x} \sqrt{c+d x} \, dx","IntegrateAlgebraic[x^2*Sqrt[a + b*x]*Sqrt[c + d*x],x]","\text{\$Aborted}","\frac{\left(4 a b c d-5 (a d+b c)^2\right) (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{7/2} d^{7/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(4 a b c d-5 (a d+b c)^2\right) (b c-a d)}{64 b^3 d^3}-\frac{(a+b x)^{3/2} \sqrt{c+d x} \left(4 a b c d-5 (a d+b c)^2\right)}{32 b^3 d^2}-\frac{5 (a+b x)^{3/2} (c+d x)^{3/2} (a d+b c)}{24 b^2 d^2}+\frac{x (a+b x)^{3/2} (c+d x)^{3/2}}{4 b d}",1,"$Aborted","F",-1
549,-1,0,163,180.086938,"\int x \sqrt{a+b x} \sqrt{c+d x} \, dx","IntegrateAlgebraic[x*Sqrt[a + b*x]*Sqrt[c + d*x],x]","\text{\$Aborted}","\frac{1}{8} \sqrt{a+b x} \sqrt{c+d x} \left(\frac{a^2}{b^2}-\frac{c^2}{d^2}\right)+\frac{(a d+b c) (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{5/2} d^{5/2}}-\frac{(a+b x)^{3/2} \sqrt{c+d x} (a d+b c)}{4 b^2 d}+\frac{(a+b x)^{3/2} (c+d x)^{3/2}}{3 b d}",1,"$Aborted","F",-1
550,1,1505,116,0.0009631,"\int \sqrt{a+b x} \sqrt{c+d x} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*Sqrt[c + d*x],x]","\frac{\left(\frac{\sqrt{a+b}}{4 b d}-\frac{\sqrt{a+b x}}{4 b d}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(c b+d b+d x b-\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}\right) \left(2 c^4 b^4+2 c^2 d^2 b^4+16 d^4 x^2 b^4+16 c d^3 x^2 b^4+2 c^2 d^2 x^2 b^4+5 c^3 d b^4+16 c d^3 x b^4+22 c^2 d^2 x b^4+5 c^3 d x b^4-16 c d^2 \sqrt{c+d} x \sqrt{c+d x} b^4-4 c^2 d \sqrt{c+d} x \sqrt{c+d x} b^4-2 c^3 \sqrt{c+d} \sqrt{c+d x} b^4-4 c^2 d \sqrt{c+d} \sqrt{c+d x} b^4+12 a c d^3 b^3+11 a c^2 d^2 b^3+16 a d^4 x^2 b^3+12 a c d^3 x^2 b^3+2 a c^3 d b^3+16 a d^4 x b^3+20 a c d^3 x b^3+11 a c^2 d^2 x b^3+12 \sqrt{a+b} c^2 d^2 \sqrt{a+b x} b^3+10 \sqrt{a+b} c^3 d \sqrt{a+b x} b^3+16 \sqrt{a+b} c d^3 x \sqrt{a+b x} b^3+12 \sqrt{a+b} c^2 d^2 x \sqrt{a+b x} b^3+16 a d^3 \sqrt{c+d} x \sqrt{c+d x} b^3-8 a c d^2 \sqrt{c+d} x \sqrt{c+d x} b^3-8 a c d^2 \sqrt{c+d} \sqrt{c+d x} b^3-2 a c^2 d \sqrt{c+d} \sqrt{c+d x} b^3-16 \sqrt{a+b} d^3 \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x} b^3-8 \sqrt{a+b} c d^2 \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x} b^3-8 \sqrt{a+b} c d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b^3-10 \sqrt{a+b} c^2 d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b^3+2 a^2 d^4 b^2+11 a^2 c d^3 b^2+8 a^2 c^2 d^2 b^2+2 a^2 d^4 x^2 b^2+22 a^2 d^4 x b^2+11 a^2 c d^3 x b^2-8 a \sqrt{a+b} c d^3 \sqrt{a+b x} b^2-6 a \sqrt{a+b} c^2 d^2 \sqrt{a+b x} b^2-16 a \sqrt{a+b} d^4 x \sqrt{a+b x} b^2-8 a \sqrt{a+b} c d^3 x \sqrt{a+b x} b^2+12 a^2 d^3 \sqrt{c+d} x \sqrt{c+d x} b^2+12 a^2 d^3 \sqrt{c+d} \sqrt{c+d x} b^2-6 a^2 c d^2 \sqrt{c+d} \sqrt{c+d x} b^2-8 a \sqrt{a+b} d^3 \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x} b^2-8 a \sqrt{a+b} d^3 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b^2+4 a \sqrt{a+b} c d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b^2+5 a^3 d^4 b+2 a^3 c d^3 b+5 a^3 d^4 x b-4 a^2 \sqrt{a+b} d^4 \sqrt{a+b x} b-2 a^2 \sqrt{a+b} c d^3 \sqrt{a+b x} b-4 a^2 \sqrt{a+b} d^4 x \sqrt{a+b x} b+10 a^3 d^3 \sqrt{c+d} \sqrt{c+d x} b-10 a^2 \sqrt{a+b} d^3 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b+2 a^4 d^4-2 a^3 \sqrt{a+b} d^4 \sqrt{a+b x}\right)}{\left(-c b+\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}\right)^4}-\frac{(b c-a d)^2 \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b} \sqrt{d}}{\sqrt{b}}-\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b}}}{\sqrt{c+d}-\sqrt{c+d x}}\right)}{2 b^{3/2} d^{3/2}}","-\frac{(b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{3/2} d^{3/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 b d}+\frac{(a+b x)^{3/2} \sqrt{c+d x}}{2 b}",1,"((Sqrt[a + b]/(4*b*d) - Sqrt[a + b*x]/(4*b*d))*(Sqrt[c + d] - Sqrt[c + d*x])*(b*c + a*d + b*d + b*d*x - Sqrt[a + b]*d*Sqrt[a + b*x] - b*Sqrt[c + d]*Sqrt[c + d*x])*(2*b^4*c^4 + 2*a*b^3*c^3*d + 5*b^4*c^3*d + 8*a^2*b^2*c^2*d^2 + 11*a*b^3*c^2*d^2 + 2*b^4*c^2*d^2 + 2*a^3*b*c*d^3 + 11*a^2*b^2*c*d^3 + 12*a*b^3*c*d^3 + 2*a^4*d^4 + 5*a^3*b*d^4 + 2*a^2*b^2*d^4 + 5*b^4*c^3*d*x + 11*a*b^3*c^2*d^2*x + 22*b^4*c^2*d^2*x + 11*a^2*b^2*c*d^3*x + 20*a*b^3*c*d^3*x + 16*b^4*c*d^3*x + 5*a^3*b*d^4*x + 22*a^2*b^2*d^4*x + 16*a*b^3*d^4*x + 2*b^4*c^2*d^2*x^2 + 12*a*b^3*c*d^3*x^2 + 16*b^4*c*d^3*x^2 + 2*a^2*b^2*d^4*x^2 + 16*a*b^3*d^4*x^2 + 16*b^4*d^4*x^2 + 10*b^3*Sqrt[a + b]*c^3*d*Sqrt[a + b*x] - 6*a*b^2*Sqrt[a + b]*c^2*d^2*Sqrt[a + b*x] + 12*b^3*Sqrt[a + b]*c^2*d^2*Sqrt[a + b*x] - 2*a^2*b*Sqrt[a + b]*c*d^3*Sqrt[a + b*x] - 8*a*b^2*Sqrt[a + b]*c*d^3*Sqrt[a + b*x] - 2*a^3*Sqrt[a + b]*d^4*Sqrt[a + b*x] - 4*a^2*b*Sqrt[a + b]*d^4*Sqrt[a + b*x] + 12*b^3*Sqrt[a + b]*c^2*d^2*x*Sqrt[a + b*x] - 8*a*b^2*Sqrt[a + b]*c*d^3*x*Sqrt[a + b*x] + 16*b^3*Sqrt[a + b]*c*d^3*x*Sqrt[a + b*x] - 4*a^2*b*Sqrt[a + b]*d^4*x*Sqrt[a + b*x] - 16*a*b^2*Sqrt[a + b]*d^4*x*Sqrt[a + b*x] - 2*b^4*c^3*Sqrt[c + d]*Sqrt[c + d*x] - 2*a*b^3*c^2*d*Sqrt[c + d]*Sqrt[c + d*x] - 4*b^4*c^2*d*Sqrt[c + d]*Sqrt[c + d*x] - 6*a^2*b^2*c*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 8*a*b^3*c*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 10*a^3*b*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 12*a^2*b^2*d^3*Sqrt[c + d]*Sqrt[c + d*x] - 4*b^4*c^2*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 8*a*b^3*c*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 16*b^4*c*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 12*a^2*b^2*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] + 16*a*b^3*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] - 10*b^3*Sqrt[a + b]*c^2*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 4*a*b^2*Sqrt[a + b]*c*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*b^3*Sqrt[a + b]*c*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 10*a^2*b*Sqrt[a + b]*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*a*b^2*Sqrt[a + b]*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*b^3*Sqrt[a + b]*c*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*a*b^2*Sqrt[a + b]*d^3*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 16*b^3*Sqrt[a + b]*d^3*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^4 - ((b*c - a*d)^2*ArcTanh[((Sqrt[a + b]*Sqrt[d])/Sqrt[b] - (Sqrt[d]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[c + d] - Sqrt[c + d*x])])/(2*b^(3/2)*d^(3/2))","B",1
551,1,1513,110,78.1785277,"\int \frac{\sqrt{a+b x} \sqrt{c+d x}}{x} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*Sqrt[c + d*x])/x,x]","\frac{\left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(c^2 b^2+c d b^2+2 d^2 x b^2+c d x b^2-c \sqrt{c+d} \sqrt{c+d x} b^2+a d^2 b+a d^2 x b+\sqrt{a+b} c d \sqrt{a+b x} b+a d \sqrt{c+d} \sqrt{c+d x} b-2 \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b+a^2 d^2-a \sqrt{a+b} d^2 \sqrt{a+b x}\right)}{\left(-c b+\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}\right)^2}+\left(\frac{2 \sqrt{d} a}{\sqrt{b}}+\frac{2 \sqrt{b} c}{\sqrt{d}}\right) \tanh ^{-1}\left(\frac{\sqrt{a+b} \sqrt{d}-\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \left(\sqrt{c+d}-\sqrt{c+d x}\right)}\right)-\frac{1}{2} a c \text{RootSum}\left[d^4 \text{$\#$1}^8-8 a d^3 \text{$\#$1}^6-4 b d^3 \text{$\#$1}^6-16 a c d^2 \text{$\#$1}^6-8 b c d^2 \text{$\#$1}^6+16 b^2 c^2 \text{$\#$1}^4+16 a^2 d^2 \text{$\#$1}^4+6 b^2 d^2 \text{$\#$1}^4+16 a b d^2 \text{$\#$1}^4+16 b^2 c d \text{$\#$1}^4-8 b^3 c \text{$\#$1}^2-16 a b^2 c \text{$\#$1}^2-4 b^3 d \text{$\#$1}^2-8 a b^2 d \text{$\#$1}^2+b^4\&,\frac{-d^3 \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^6+d^3 \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^6-4 \sqrt{a+b} d^2 \sqrt{c+d} \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^5+4 \sqrt{a+b} d^2 \sqrt{c+d} \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^5-4 a d^2 \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^4-5 b d^2 \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^4-4 b c d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^4+4 a d^2 \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^4+5 b d^2 \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^4+4 b c d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^4+4 b^2 c \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2+5 b^2 d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2+4 a b d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2-4 b^2 c \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2-5 b^2 d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2-4 a b d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2+4 b^2 \sqrt{a+b} \sqrt{c+d} \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}-4 b^2 \sqrt{a+b} \sqrt{c+d} \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}+b^3 \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)-b^3 \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right)}{d^4 \text{$\#$1}^7-6 a d^3 \text{$\#$1}^5-3 b d^3 \text{$\#$1}^5-12 a c d^2 \text{$\#$1}^5-6 b c d^2 \text{$\#$1}^5+8 b^2 c^2 \text{$\#$1}^3+8 a^2 d^2 \text{$\#$1}^3+3 b^2 d^2 \text{$\#$1}^3+8 a b d^2 \text{$\#$1}^3+8 b^2 c d \text{$\#$1}^3-2 b^3 c \text{$\#$1}-4 a b^2 c \text{$\#$1}-b^3 d \text{$\#$1}-2 a b^2 d \text{$\#$1}}\&\right]","\sqrt{a+b x} \sqrt{c+d x}-2 \sqrt{a} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\frac{(a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b} \sqrt{d}}",1,"((Sqrt[a + b] - Sqrt[a + b*x])*(Sqrt[c + d] - Sqrt[c + d*x])*(b^2*c^2 + b^2*c*d + a^2*d^2 + a*b*d^2 + b^2*c*d*x + a*b*d^2*x + 2*b^2*d^2*x + b*Sqrt[a + b]*c*d*Sqrt[a + b*x] - a*Sqrt[a + b]*d^2*Sqrt[a + b*x] - b^2*c*Sqrt[c + d]*Sqrt[c + d*x] + a*b*d*Sqrt[c + d]*Sqrt[c + d*x] - 2*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^2 + ((2*Sqrt[b]*c)/Sqrt[d] + (2*a*Sqrt[d])/Sqrt[b])*ArcTanh[(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*(Sqrt[c + d] - Sqrt[c + d*x]))] - (a*c*RootSum[b^4 - 16*a*b^2*c*#1^2 - 8*b^3*c*#1^2 - 8*a*b^2*d*#1^2 - 4*b^3*d*#1^2 + 16*b^2*c^2*#1^4 + 16*b^2*c*d*#1^4 + 16*a^2*d^2*#1^4 + 16*a*b*d^2*#1^4 + 6*b^2*d^2*#1^4 - 16*a*c*d^2*#1^6 - 8*b*c*d^2*#1^6 - 8*a*d^3*#1^6 - 4*b*d^3*#1^6 + d^4*#1^8 & , (b^3*Log[Sqrt[c + d] - Sqrt[c + d*x]] - b^3*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + 4*b^2*Sqrt[a + b]*Sqrt[c + d]*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1 - 4*b^2*Sqrt[a + b]*Sqrt[c + d]*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1 + 4*b^2*c*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 + 4*a*b*d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 + 5*b^2*d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - 4*b^2*c*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2 - 4*a*b*d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2 - 5*b^2*d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2 - 4*b*c*d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^4 - 4*a*d^2*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^4 - 5*b*d^2*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^4 + 4*b*c*d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^4 + 4*a*d^2*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^4 + 5*b*d^2*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^4 - 4*Sqrt[a + b]*d^2*Sqrt[c + d]*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^5 + 4*Sqrt[a + b]*d^2*Sqrt[c + d]*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^5 - d^3*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^6 + d^3*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^6)/(-4*a*b^2*c*#1 - 2*b^3*c*#1 - 2*a*b^2*d*#1 - b^3*d*#1 + 8*b^2*c^2*#1^3 + 8*b^2*c*d*#1^3 + 8*a^2*d^2*#1^3 + 8*a*b*d^2*#1^3 + 3*b^2*d^2*#1^3 - 12*a*c*d^2*#1^5 - 6*b*c*d^2*#1^5 - 6*a*d^3*#1^5 - 3*b*d^3*#1^5 + d^4*#1^7) & ])/2","C",1
552,-1,0,115,180.7460148,"\int \frac{\sqrt{a+b x} \sqrt{c+d x}}{x^2} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*Sqrt[c + d*x])/x^2,x]","\text{\$Aborted}","-\frac{\sqrt{a+b x} \sqrt{c+d x}}{x}-\frac{(a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{a} \sqrt{c}}+2 \sqrt{b} \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)",1,"$Aborted","F",-1
553,1,3808,122,107.1636229,"\int \frac{\sqrt{a+b x} \sqrt{c+d x}}{x^3} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*Sqrt[c + d*x])/x^3,x]","\text{Result too large to show}","\frac{(b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{3/2} c^{3/2}}-\frac{\sqrt{a+b x} (c+d x)^{3/2}}{2 c x^2}-\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 a c x}",1,"(Sqrt[c + d]*Sqrt[a + b*x]*(16*a*b^4*c^5 - 32*a^2*b^3*c^4*d + 8*a*b^4*c^4*d + 48*a^3*b^2*c^3*d^2 + 16*a^2*b^3*c^3*d^2 - 32*a^4*b*c^2*d^3 - 24*a^3*b^2*c^2*d^3 + 8*b^5*c^5*x + 16*a*b^4*c^4*d*x + 4*b^5*c^4*d*x - 8*a^2*b^3*c^3*d^2*x + 52*a*b^4*c^3*d^2*x + 32*a^3*b^2*c^2*d^3*x - 20*a^2*b^3*c^2*d^3*x - 48*a^4*b*c*d^4*x - 36*a^3*b^2*c*d^4*x - 32*a^2*b^3*c^4*d*x^2 - 48*a*b^4*c^4*d*x^2 - 4*b^5*c^4*d*x^2 + 48*a^3*b^2*c^3*d^2*x^2 + 32*a^2*b^3*c^3*d^2*x^2 - 16*a*b^4*c^3*d^2*x^2 + 8*b^5*c^3*d^2*x^2 - 32*a^4*b*c^2*d^3*x^2 - 8*a^3*b^2*c^2*d^3*x^2 + 40*a^2*b^3*c^2*d^3*x^2 + 40*a*b^4*c^2*d^3*x^2 + 16*a^5*c*d^4*x^2 + 16*a^4*b*c*d^4*x^2 - 16*a^3*b^2*c*d^4*x^2 - 40*a^2*b^3*c*d^4*x^2 + 8*a^5*d^5*x^2 - 4*a^4*b*d^5*x^2 - 8*a^3*b^2*d^5*x^2 - 24*a^2*b^3*c^3*d^2*x^3 - 36*a*b^4*c^3*d^2*x^3 - 8*b^5*c^3*d^2*x^3 + 16*a^3*b^2*c^2*d^3*x^3 - 20*a^2*b^3*c^2*d^3*x^3 - 40*a*b^4*c^2*d^3*x^3 + 8*a^4*b*c*d^4*x^3 + 52*a^3*b^2*c*d^4*x^3 + 40*a^2*b^3*c*d^4*x^3 + 4*a^4*b*d^5*x^3 + 8*a^3*b^2*d^5*x^3) + Sqrt[a + b*x]*Sqrt[c + d*x]*(-16*a*b^4*c^5 + 32*a^2*b^3*c^4*d - 16*a*b^4*c^4*d - 48*a^3*b^2*c^3*d^2 - 2*a*b^4*c^3*d^2 + 32*a^4*b*c^2*d^3 - 12*a^2*b^3*c^2*d^3 - 16*a^5*c*d^4 - 16*a^4*b*c*d^4 - 2*a^3*b^2*c*d^4 - 8*b^5*c^5*x - 8*a*b^4*c^4*d*x - 8*b^5*c^4*d*x - 8*a^2*b^3*c^3*d^2*x - 52*a*b^4*c^3*d^2*x - b^5*c^3*d^2*x - 8*a^3*b^2*c^2*d^3*x + 24*a^2*b^3*c^2*d^3*x - 23*a*b^4*c^2*d^3*x - 8*a^4*b*c*d^4*x - 52*a^3*b^2*c*d^4*x - 23*a^2*b^3*c*d^4*x - 8*a^5*d^5*x - 8*a^4*b*d^5*x - a^3*b^2*d^5*x + 32*a^2*b^3*c^4*d*x^2 + 48*a*b^4*c^4*d*x^2 + 8*b^5*c^4*d*x^2 - 48*a^3*b^2*c^3*d^2*x^2 - 16*a^2*b^3*c^3*d^2*x^2 + 42*a*b^4*c^3*d^2*x^2 - 2*b^5*c^3*d^2*x^2 + 32*a^4*b*c^2*d^3*x^2 - 16*a^3*b^2*c^2*d^3*x^2 - 52*a^2*b^3*c^2*d^3*x^2 - 14*a*b^4*c^2*d^3*x^2 - 4*b^5*c^2*d^3*x^2 + 48*a^4*b*c*d^4*x^2 + 42*a^3*b^2*c*d^4*x^2 - 14*a^2*b^3*c*d^4*x^2 - 24*a*b^4*c*d^4*x^2 + 8*a^4*b*d^5*x^2 - 2*a^3*b^2*d^5*x^2 - 4*a^2*b^3*d^5*x^2 + 8*a^2*b^3*c^3*d^2*x^3 + 12*a*b^4*c^3*d^2*x^3 + 3*b^5*c^3*d^2*x^3 + 8*a^3*b^2*c^2*d^3*x^3 + 40*a^2*b^3*c^2*d^3*x^3 + 37*a*b^4*c^2*d^3*x^3 + 4*b^5*c^2*d^3*x^3 + 12*a^3*b^2*c*d^4*x^3 + 37*a^2*b^3*c*d^4*x^3 + 24*a*b^4*c*d^4*x^3 + 3*a^3*b^2*d^5*x^3 + 4*a^2*b^3*d^5*x^3) + Sqrt[a + b]*(Sqrt[c + d*x]*(-32*a^2*b^3*c^4*d + 48*a^3*b^2*c^3*d^2 - 24*a^2*b^3*c^3*d^2 - 32*a^4*b*c^2*d^3 + 16*a^3*b^2*c^2*d^3 + 16*a^5*c*d^4 + 8*a^4*b*c*d^4 - 48*a*b^4*c^4*d*x + 32*a^2*b^3*c^3*d^2*x - 36*a*b^4*c^3*d^2*x - 8*a^3*b^2*c^2*d^3*x - 20*a^2*b^3*c^2*d^3*x + 16*a^4*b*c*d^4*x + 52*a^3*b^2*c*d^4*x + 8*a^5*d^5*x + 4*a^4*b*d^5*x + 16*a*b^4*c^5*x^2 + 8*b^5*c^5*x^2 - 32*a^2*b^3*c^4*d*x^2 + 16*a*b^4*c^4*d*x^2 - 4*b^5*c^4*d*x^2 + 48*a^3*b^2*c^3*d^2*x^2 - 8*a^2*b^3*c^3*d^2*x^2 - 16*a*b^4*c^3*d^2*x^2 - 8*b^5*c^3*d^2*x^2 - 32*a^4*b*c^2*d^3*x^2 + 32*a^3*b^2*c^2*d^3*x^2 + 40*a^2*b^3*c^2*d^3*x^2 - 40*a*b^4*c^2*d^3*x^2 - 48*a^4*b*c*d^4*x^2 - 16*a^3*b^2*c*d^4*x^2 + 40*a^2*b^3*c*d^4*x^2 - 4*a^4*b*d^5*x^2 + 8*a^3*b^2*d^5*x^2 + 8*a*b^4*c^4*d*x^3 + 4*b^5*c^4*d*x^3 + 16*a^2*b^3*c^3*d^2*x^3 + 52*a*b^4*c^3*d^2*x^3 + 8*b^5*c^3*d^2*x^3 - 24*a^3*b^2*c^2*d^3*x^3 - 20*a^2*b^3*c^2*d^3*x^3 + 40*a*b^4*c^2*d^3*x^3 - 36*a^3*b^2*c*d^4*x^3 - 40*a^2*b^3*c*d^4*x^3 - 8*a^3*b^2*d^5*x^3) + Sqrt[c + d]*(32*a^2*b^3*c^4*d - 48*a^3*b^2*c^3*d^2 + 8*a^2*b^3*c^3*d^2 + 32*a^4*b*c^2*d^3 + 8*a^3*b^2*c^2*d^3 + 48*a*b^4*c^4*d*x - 16*a^2*b^3*c^3*d^2*x + 12*a*b^4*c^3*d^2*x - 16*a^3*b^2*c^2*d^3*x + 40*a^2*b^3*c^2*d^3*x + 48*a^4*b*c*d^4*x + 12*a^3*b^2*c*d^4*x - 16*a*b^4*c^5*x^2 - 8*b^5*c^5*x^2 + 32*a^2*b^3*c^4*d*x^2 - 8*a*b^4*c^4*d*x^2 + 8*b^5*c^4*d*x^2 - 48*a^3*b^2*c^3*d^2*x^2 - 8*a^2*b^3*c^3*d^2*x^2 + 42*a*b^4*c^3*d^2*x^2 + 3*b^5*c^3*d^2*x^2 + 32*a^4*b*c^2*d^3*x^2 - 8*a^3*b^2*c^2*d^3*x^2 - 52*a^2*b^3*c^2*d^3*x^2 + 37*a*b^4*c^2*d^3*x^2 - 16*a^5*c*d^4*x^2 - 8*a^4*b*c*d^4*x^2 + 42*a^3*b^2*c*d^4*x^2 + 37*a^2*b^3*c*d^4*x^2 - 8*a^5*d^5*x^2 + 8*a^4*b*d^5*x^2 + 3*a^3*b^2*d^5*x^2 - 16*a*b^4*c^4*d*x^3 - 8*b^5*c^4*d*x^3 - 52*a*b^4*c^3*d^2*x^3 - 2*b^5*c^3*d^2*x^3 + 24*a^2*b^3*c^2*d^3*x^3 - 14*a*b^4*c^2*d^3*x^3 + 4*b^5*c^2*d^3*x^3 - 16*a^4*b*c*d^4*x^3 - 52*a^3*b^2*c*d^4*x^3 - 14*a^2*b^3*c*d^4*x^3 + 24*a*b^4*c*d^4*x^3 - 8*a^4*b*d^5*x^3 - 2*a^3*b^2*d^5*x^3 + 4*a^2*b^3*d^5*x^3 - 2*a*b^4*c^3*d^2*x^4 - b^5*c^3*d^2*x^4 - 12*a^2*b^3*c^2*d^3*x^4 - 23*a*b^4*c^2*d^3*x^4 - 4*b^5*c^2*d^3*x^4 - 2*a^3*b^2*c*d^4*x^4 - 23*a^2*b^3*c*d^4*x^4 - 24*a*b^4*c*d^4*x^4 - a^3*b^2*d^5*x^4 - 4*a^2*b^3*d^5*x^4)))/(4*a*c*Sqrt[c + d]*x^2*Sqrt[c + d*x]*(-8*b^4*c^3 + 16*a*b^3*c^2*d - 4*b^4*c^2*d - 24*a^2*b^2*c*d^2 - 8*a*b^3*c*d^2 + 16*a^3*b*d^3 + 12*a^2*b^2*d^3 - 4*b^4*c^2*d*x - 8*a*b^3*c*d^2*x - 16*b^4*c*d^2*x + 12*a^2*b^2*d^3*x + 16*a*b^3*d^3*x) + 4*a*c*x^2*(8*b^4*c^4 - 16*a*b^3*c^3*d + 8*b^4*c^3*d + 24*a^2*b^2*c^2*d^2 + b^4*c^2*d^2 - 16*a^3*b*c*d^3 + 6*a*b^3*c*d^3 + 8*a^4*d^4 + 8*a^3*b*d^4 + a^2*b^2*d^4 + 8*b^4*c^3*d*x + 22*b^4*c^2*d^2*x - 12*a*b^3*c*d^3*x + 8*b^4*c*d^3*x + 8*a^3*b*d^4*x + 22*a^2*b^2*d^4*x + 8*a*b^3*d^4*x + b^4*c^2*d^2*x^2 + 6*a*b^3*c*d^3*x^2 + 8*b^4*c*d^3*x^2 + a^2*b^2*d^4*x^2 + 8*a*b^3*d^4*x^2 + 8*b^4*d^4*x^2) + Sqrt[a + b]*Sqrt[a + b*x]*(4*a*c*Sqrt[c + d]*x^2*Sqrt[c + d*x]*(-16*b^3*c^2*d + 24*a*b^2*c*d^2 - 4*b^3*c*d^2 - 16*a^2*b*d^3 - 4*a*b^2*d^3 - 4*b^3*c*d^2*x - 4*a*b^2*d^3*x - 8*b^3*d^3*x) + 4*a*c*x^2*(16*b^3*c^3*d - 24*a*b^2*c^2*d^2 + 12*b^3*c^2*d^2 + 16*a^2*b*c*d^3 - 8*a*b^2*c*d^3 - 8*a^3*d^4 - 4*a^2*b*d^4 + 12*b^3*c^2*d^2*x - 8*a*b^2*c*d^3*x + 16*b^3*c*d^3*x - 4*a^2*b*d^4*x - 16*a*b^2*d^4*x))) - ((b*c - a*d)^2*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ])/(8*a*c)","C",1
554,-1,0,172,180.1214525,"\int \frac{\sqrt{a+b x} \sqrt{c+d x}}{x^4} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*Sqrt[c + d*x])/x^4,x]","\text{\$Aborted}","-\frac{(a d+b c) (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 a^{5/2} c^{5/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(\frac{b^2}{a^2}-\frac{d^2}{c^2}\right)}{8 x}+\frac{\sqrt{a+b x} (c+d x)^{3/2} (a d+b c)}{4 a c^2 x^2}-\frac{(a+b x)^{3/2} (c+d x)^{3/2}}{3 a c x^3}",1,"$Aborted","F",-1
555,-1,0,256,180.0164327,"\int \frac{\sqrt{a+b x} \sqrt{c+d x}}{x^5} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*Sqrt[c + d*x])/x^5,x]","\text{\$Aborted}","\frac{\sqrt{a+b x} \sqrt{c+d x} \left(5 a^2 d^2-2 a b c d+5 b^2 c^2\right)}{96 a^2 c^2 x^2}+\frac{\left(5 a^2 d^2+6 a b c d+5 b^2 c^2\right) (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{7/2} c^{7/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (a d+b c) \left(15 a^2 d^2-22 a b c d+15 b^2 c^2\right)}{192 a^3 c^3 x}-\frac{\sqrt{a+b x} \sqrt{c+d x}}{4 x^4}-\frac{\sqrt{a+b x} \sqrt{c+d x} (a d+b c)}{24 a c x^3}",1,"$Aborted","F",-1
556,-1,0,345,180.0696823,"\int \frac{\sqrt{a+b x} \sqrt{c+d x}}{x^6} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*Sqrt[c + d*x])/x^6,x]","\text{\$Aborted}","\frac{\sqrt{a+b x} \sqrt{c+d x} \left(7 a^2 d^2-2 a b c d+7 b^2 c^2\right)}{240 a^2 c^2 x^3}-\frac{(a d+b c) \left(7 a^2 d^2+2 a b c d+7 b^2 c^2\right) (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{128 a^{9/2} c^{9/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (a d+b c) \left(35 a^2 d^2-46 a b c d+35 b^2 c^2\right)}{960 a^3 c^3 x^2}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(105 a^4 d^4-40 a^3 b c d^3-34 a^2 b^2 c^2 d^2-40 a b^3 c^3 d+105 b^4 c^4\right)}{1920 a^4 c^4 x}-\frac{\sqrt{a+b x} \sqrt{c+d x}}{5 x^5}-\frac{\sqrt{a+b x} \sqrt{c+d x} (a d+b c)}{40 a c x^4}",1,"$Aborted","F",-1
557,-1,0,315,180.0261373,"\int x^2 \sqrt{a+b x} (c+d x)^{3/2} \, dx","IntegrateAlgebraic[x^2*Sqrt[a + b*x]*(c + d*x)^(3/2),x]","\text{\$Aborted}","-\frac{\left(7 a^2 d^2+6 a b c d+3 b^2 c^2\right) (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{9/2} d^{7/2}}+\frac{(a+b x)^{3/2} \sqrt{c+d x} \left(7 a^2 d^2+6 a b c d+3 b^2 c^2\right) (b c-a d)}{64 b^4 d^2}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(7 a^2 d^2+6 a b c d+3 b^2 c^2\right) (b c-a d)^2}{128 b^4 d^3}+\frac{(a+b x)^{3/2} (c+d x)^{3/2} \left(7 a^2 d^2+6 a b c d+3 b^2 c^2\right)}{48 b^3 d^2}-\frac{(a+b x)^{3/2} (c+d x)^{5/2} (7 a d+5 b c)}{40 b^2 d^2}+\frac{x (a+b x)^{3/2} (c+d x)^{5/2}}{5 b d}",1,"$Aborted","F",-1
558,-1,0,221,180.0177467,"\int x \sqrt{a+b x} (c+d x)^{3/2} \, dx","IntegrateAlgebraic[x*Sqrt[a + b*x]*(c + d*x)^(3/2),x]","\text{\$Aborted}","\frac{(5 a d+3 b c) (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{7/2} d^{5/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (5 a d+3 b c) (b c-a d)^2}{64 b^3 d^2}-\frac{(a+b x)^{3/2} \sqrt{c+d x} (5 a d+3 b c) (b c-a d)}{32 b^3 d}-\frac{(a+b x)^{3/2} (c+d x)^{3/2} (5 a d+3 b c)}{24 b^2 d}+\frac{(a+b x)^{3/2} (c+d x)^{5/2}}{4 b d}",1,"$Aborted","F",-1
559,-1,0,151,180.0099974,"\int \sqrt{a+b x} (c+d x)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*(c + d*x)^(3/2),x]","\text{\$Aborted}","-\frac{(b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{5/2} d^{3/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 b^2 d}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{4 b^2}+\frac{(a+b x)^{3/2} (c+d x)^{3/2}}{3 b}",1,"$Aborted","F",-1
560,-1,0,165,180.1072609,"\int \frac{\sqrt{a+b x} (c+d x)^{3/2}}{x} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(c + d*x)^(3/2))/x,x]","\text{\$Aborted}","\frac{\left(-a^2 d^2+6 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{3/2} \sqrt{d}}-2 \sqrt{a} c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\frac{1}{2} \sqrt{a+b x} (c+d x)^{3/2}+\frac{\sqrt{a+b x} \sqrt{c+d x} (a d+3 b c)}{4 b}",1,"$Aborted","F",-1
561,1,1709,144,114.227422,"\int \frac{\sqrt{a+b x} (c+d x)^{3/2}}{x^2} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(c + d*x)^(3/2))/x^2,x]","\frac{\left(-\frac{c d b^3}{\sqrt{a+b}}+\frac{2 d^2 \sqrt{c+d x} b^3}{\sqrt{a+b} \sqrt{c+d}}+\frac{2 c d \sqrt{c+d x} b^3}{\sqrt{a+b} \sqrt{c+d}}+\frac{a d^2 b^2}{\sqrt{a+b}}-\frac{a c d b^2}{\sqrt{a+b}}-2 d^2 \sqrt{a+b x} b^2-c d \sqrt{a+b x} b^2+\frac{2 a d^2 \sqrt{c+d x} b^2}{\sqrt{a+b} \sqrt{c+d}}+\frac{2 a c d \sqrt{c+d x} b^2}{\sqrt{a+b} \sqrt{c+d}}+\frac{a^2 d^2 b}{\sqrt{a+b}}-a d^2 \sqrt{a+b x} b\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)^3}{\left(-c b+\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}\right)^2}+\frac{\left(\frac{c \sqrt{a+b x}}{\sqrt{a+b} \sqrt{c+d}}-\frac{c}{\sqrt{c+d}}\right) \left(\sqrt{a+b} c d \sqrt{c+d} a^2-c d \sqrt{c+d} \sqrt{a+b x} a^2+\sqrt{a+b} d^2 \sqrt{c+d x} a^2+\sqrt{a+b} c d \sqrt{c+d x} a^2-d^2 \sqrt{a+b x} \sqrt{c+d x} a^2-c d \sqrt{a+b x} \sqrt{c+d x} a^2+b \sqrt{a+b} d^2 \sqrt{c+d} x a+2 b \sqrt{a+b} c d \sqrt{c+d} x a+b \sqrt{a+b} c^2 \sqrt{c+d} a+2 b \sqrt{a+b} c d \sqrt{c+d} a+b c^2 \sqrt{c+d} \sqrt{a+b x} a-b c d \sqrt{c+d} \sqrt{a+b x} a-b \sqrt{a+b} c^2 \sqrt{c+d x} a-b \sqrt{a+b} c d \sqrt{c+d x} a-b c^2 \sqrt{a+b x} \sqrt{c+d x} a-b d^2 \sqrt{a+b x} \sqrt{c+d x} a-2 b c d \sqrt{a+b x} \sqrt{c+d x} a+b^2 \sqrt{a+b} c d \sqrt{c+d} x+b^2 c^2 \sqrt{c+d} \sqrt{a+b x}-b^2 c^2 \sqrt{a+b x} \sqrt{c+d x}-b^2 c d \sqrt{a+b x} \sqrt{c+d x}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{x \left(-2 c^2 b^2-c d b^2-2 d^2 x b^2-c d x b^2+2 c \sqrt{c+d} \sqrt{c+d x} b^2-a d^2 b+2 a c d b-a d^2 x b-2 \sqrt{a+b} c d \sqrt{a+b x} b-2 a d \sqrt{c+d} \sqrt{c+d x} b+2 \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b-2 a^2 d^2+2 a \sqrt{a+b} d^2 \sqrt{a+b x}\right)}+\left(\frac{2 a d^{3/2}}{\sqrt{b}}+6 \sqrt{b} c \sqrt{d}\right) \tanh ^{-1}\left(\frac{\sqrt{a+b} \sqrt{d}-\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \left(\sqrt{c+d}-\sqrt{c+d x}\right)}\right)+\left(\frac{b c^2}{2}+\frac{3 a d c}{2}\right) \text{RootSum}\left[d^2 \text{$\#$1}^4-4 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^3+4 b c \text{$\#$1}^2+4 a d \text{$\#$1}^2+6 b d \text{$\#$1}^2-4 b \sqrt{a+b} \sqrt{c+d} \text{$\#$1}+b^2\&,\frac{d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2-d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2-b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)+b \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right)}{d^2 \text{$\#$1}^3-3 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^2+2 b c \text{$\#$1}+2 a d \text{$\#$1}+3 b d \text{$\#$1}-b \sqrt{a+b} \sqrt{c+d}}\&\right]+\frac{\left(d \sqrt{c+d} a^2-3 b c \sqrt{c+d} a-b d \sqrt{c+d} a-\sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} a+4 b c \sqrt{c+d x} a+4 b d \sqrt{c+d x} a-3 b^2 c \sqrt{c+d}-2 b^2 d \sqrt{c+d}-b \sqrt{a+b} c \sqrt{c+d} \sqrt{a+b x}-2 b \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x}+4 b^2 c \sqrt{c+d x}+4 b^2 d \sqrt{c+d x}\right) \left(\frac{d}{\sqrt{a+b}}-\frac{d \sqrt{c+d x}}{\sqrt{a+b} \sqrt{c+d}}\right)}{-c b+\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}}","-\frac{\sqrt{a+b x} (c+d x)^{3/2}}{x}+2 d \sqrt{a+b x} \sqrt{c+d x}-\frac{\sqrt{c} (3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{a}}+\frac{\sqrt{d} (a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b}}",1,"((Sqrt[c + d] - Sqrt[c + d*x])^3*(-((a*b^2*c*d)/Sqrt[a + b]) - (b^3*c*d)/Sqrt[a + b] + (a^2*b*d^2)/Sqrt[a + b] + (a*b^2*d^2)/Sqrt[a + b] - b^2*c*d*Sqrt[a + b*x] - a*b*d^2*Sqrt[a + b*x] - 2*b^2*d^2*Sqrt[a + b*x] + (2*a*b^2*c*d*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[c + d]) + (2*b^3*c*d*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[c + d]) + (2*a*b^2*d^2*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[c + d]) + (2*b^3*d^2*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[c + d])))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^2 + ((-3*a*b*c*Sqrt[c + d] - 3*b^2*c*Sqrt[c + d] + a^2*d*Sqrt[c + d] - a*b*d*Sqrt[c + d] - 2*b^2*d*Sqrt[c + d] - b*Sqrt[a + b]*c*Sqrt[c + d]*Sqrt[a + b*x] - a*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x] + 4*a*b*c*Sqrt[c + d*x] + 4*b^2*c*Sqrt[c + d*x] + 4*a*b*d*Sqrt[c + d*x] + 4*b^2*d*Sqrt[c + d*x])*(d/Sqrt[a + b] - (d*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[c + d])))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x]) + ((-(c/Sqrt[c + d]) + (c*Sqrt[a + b*x])/(Sqrt[a + b]*Sqrt[c + d]))*(Sqrt[c + d] - Sqrt[c + d*x])*(a*b*Sqrt[a + b]*c^2*Sqrt[c + d] + a^2*Sqrt[a + b]*c*d*Sqrt[c + d] + 2*a*b*Sqrt[a + b]*c*d*Sqrt[c + d] + 2*a*b*Sqrt[a + b]*c*d*Sqrt[c + d]*x + b^2*Sqrt[a + b]*c*d*Sqrt[c + d]*x + a*b*Sqrt[a + b]*d^2*Sqrt[c + d]*x + a*b*c^2*Sqrt[c + d]*Sqrt[a + b*x] + b^2*c^2*Sqrt[c + d]*Sqrt[a + b*x] - a^2*c*d*Sqrt[c + d]*Sqrt[a + b*x] - a*b*c*d*Sqrt[c + d]*Sqrt[a + b*x] - a*b*Sqrt[a + b]*c^2*Sqrt[c + d*x] + a^2*Sqrt[a + b]*c*d*Sqrt[c + d*x] - a*b*Sqrt[a + b]*c*d*Sqrt[c + d*x] + a^2*Sqrt[a + b]*d^2*Sqrt[c + d*x] - a*b*c^2*Sqrt[a + b*x]*Sqrt[c + d*x] - b^2*c^2*Sqrt[a + b*x]*Sqrt[c + d*x] - a^2*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - 2*a*b*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - b^2*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - a^2*d^2*Sqrt[a + b*x]*Sqrt[c + d*x] - a*b*d^2*Sqrt[a + b*x]*Sqrt[c + d*x]))/(x*(-2*b^2*c^2 + 2*a*b*c*d - b^2*c*d - 2*a^2*d^2 - a*b*d^2 - b^2*c*d*x - a*b*d^2*x - 2*b^2*d^2*x - 2*b*Sqrt[a + b]*c*d*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*d^2*Sqrt[a + b*x] + 2*b^2*c*Sqrt[c + d]*Sqrt[c + d*x] - 2*a*b*d*Sqrt[c + d]*Sqrt[c + d*x] + 2*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x])) + (6*Sqrt[b]*c*Sqrt[d] + (2*a*d^(3/2))/Sqrt[b])*ArcTanh[(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*(Sqrt[c + d] - Sqrt[c + d*x]))] + ((b*c^2)/2 + (3*a*c*d)/2)*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ]","C",1
562,-1,0,170,180.1262814,"\int \frac{\sqrt{a+b x} (c+d x)^{3/2}}{x^3} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(c + d*x)^(3/2))/x^3,x]","\text{\$Aborted}","\frac{\left(-3 a^2 d^2-6 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{3/2} \sqrt{c}}+2 \sqrt{b} d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)-\frac{\sqrt{a+b x} (c+d x)^{3/2}}{2 x^2}-\frac{\sqrt{a+b x} \sqrt{c+d x} (3 a d+b c)}{4 a x}",1,"$Aborted","F",-1
563,-1,0,163,180.1278427,"\int \frac{\sqrt{a+b x} (c+d x)^{3/2}}{x^4} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(c + d*x)^(3/2))/x^4,x]","\text{\$Aborted}","-\frac{(b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 a^{5/2} c^{3/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 a^2 c x}-\frac{\sqrt{a+b x} (c+d x)^{5/2}}{3 c x^3}-\frac{\sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}{12 a c x^2}",1,"$Aborted","F",-1
564,-1,0,233,180.0218862,"\int \frac{\sqrt{a+b x} (c+d x)^{3/2}}{x^5} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(c + d*x)^(3/2))/x^5,x]","\text{\$Aborted}","\frac{(3 a d+5 b c) (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{7/2} c^{5/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (3 a d+5 b c) (b c-a d)^2}{64 a^3 c^2 x}+\frac{\sqrt{a+b x} (c+d x)^{3/2} (3 a d+5 b c) (b c-a d)}{96 a^2 c^2 x^2}+\frac{\sqrt{a+b x} (c+d x)^{5/2} (3 a d+5 b c)}{24 a c^2 x^3}-\frac{(a+b x)^{3/2} (c+d x)^{5/2}}{4 a c x^4}",1,"$Aborted","F",-1
565,-1,0,340,180.0708523,"\int \frac{\sqrt{a+b x} (c+d x)^{3/2}}{x^6} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(c + d*x)^(3/2))/x^6,x]","\text{\$Aborted}","-\frac{\left(3 a^2 d^2+6 a b c d+7 b^2 c^2\right) (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{128 a^{9/2} c^{7/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-15 a^3 d^3+9 a^2 b c d^2-61 a b^2 c^2 d+35 b^3 c^3\right)}{960 a^3 c^2 x^2}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-45 a^4 d^4+30 a^3 b c d^3+36 a^2 b^2 c^2 d^2-190 a b^3 c^3 d+105 b^4 c^4\right)}{1920 a^4 c^3 x}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(\frac{7 b^2 c}{a}-\frac{3 a d^2}{c}-12 b d\right)}{240 a x^3}-\frac{\sqrt{a+b x} (c+d x)^{3/2}}{5 x^5}-\frac{\sqrt{a+b x} \sqrt{c+d x} (3 a d+b c)}{40 a x^4}",1,"$Aborted","F",-1
566,-1,0,376,180.0356386,"\int x^2 \sqrt{a+b x} (c+d x)^{5/2} \, dx","IntegrateAlgebraic[x^2*Sqrt[a + b*x]*(c + d*x)^(5/2),x]","\text{\$Aborted}","-\frac{\left(21 a^2 d^2+14 a b c d+5 b^2 c^2\right) (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{512 b^{11/2} d^{7/2}}+\frac{(a+b x)^{3/2} \sqrt{c+d x} \left(21 a^2 d^2+14 a b c d+5 b^2 c^2\right) (b c-a d)^2}{256 b^5 d^2}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(21 a^2 d^2+14 a b c d+5 b^2 c^2\right) (b c-a d)^3}{512 b^5 d^3}+\frac{(a+b x)^{3/2} (c+d x)^{3/2} \left(21 a^2 d^2+14 a b c d+5 b^2 c^2\right) (b c-a d)}{192 b^4 d^2}+\frac{(a+b x)^{3/2} (c+d x)^{5/2} \left(21 a^2 d^2+14 a b c d+5 b^2 c^2\right)}{160 b^3 d^2}-\frac{(a+b x)^{3/2} (c+d x)^{7/2} (9 a d+5 b c)}{60 b^2 d^2}+\frac{x (a+b x)^{3/2} (c+d x)^{7/2}}{6 b d}",1,"$Aborted","F",-1
567,-1,0,268,180.022293,"\int x \sqrt{a+b x} (c+d x)^{5/2} \, dx","IntegrateAlgebraic[x*Sqrt[a + b*x]*(c + d*x)^(5/2),x]","\text{\$Aborted}","\frac{(7 a d+3 b c) (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{9/2} d^{5/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (7 a d+3 b c) (b c-a d)^3}{128 b^4 d^2}-\frac{(a+b x)^{3/2} \sqrt{c+d x} (7 a d+3 b c) (b c-a d)^2}{64 b^4 d}-\frac{(a+b x)^{3/2} (c+d x)^{3/2} (7 a d+3 b c) (b c-a d)}{48 b^3 d}-\frac{(a+b x)^{3/2} (c+d x)^{5/2} (7 a d+3 b c)}{40 b^2 d}+\frac{(a+b x)^{3/2} (c+d x)^{7/2}}{5 b d}",1,"$Aborted","F",-1
568,-1,0,186,180.0230506,"\int \sqrt{a+b x} (c+d x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*(c + d*x)^(5/2),x]","\text{\$Aborted}","-\frac{5 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{7/2} d^{3/2}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 b^3 d}+\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}{32 b^3}+\frac{5 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}{24 b^2}+\frac{(a+b x)^{3/2} (c+d x)^{5/2}}{4 b}",1,"$Aborted","F",-1
569,-1,0,219,180.0067422,"\int \frac{\sqrt{a+b x} (c+d x)^{5/2}}{x} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(c + d*x)^(5/2))/x,x]","\text{\$Aborted}","\frac{\left(a^3 d^3-5 a^2 b c d^2+15 a b^2 c^2 d+5 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{5/2} \sqrt{d}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (5 b c-a d) (a d+b c)}{8 b^2}-2 \sqrt{a} c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\frac{1}{3} \sqrt{a+b x} (c+d x)^{5/2}+\frac{\sqrt{a+b x} (c+d x)^{3/2} (a d+5 b c)}{12 b}",1,"$Aborted","F",-1
570,-1,0,198,180.044201,"\int \frac{\sqrt{a+b x} (c+d x)^{5/2}}{x^2} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(c + d*x)^(5/2))/x^2,x]","\text{\$Aborted}","\frac{\sqrt{d} \left(-a^2 d^2+10 a b c d+15 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{3/2}}-\frac{c^{3/2} (5 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{a}}-\frac{\sqrt{a+b x} (c+d x)^{5/2}}{x}+\frac{3}{2} d \sqrt{a+b x} (c+d x)^{3/2}+\frac{d \sqrt{a+b x} \sqrt{c+d x} (a d+11 b c)}{4 b}",1,"$Aborted","F",-1
571,-1,0,211,180.0580585,"\int \frac{\sqrt{a+b x} (c+d x)^{5/2}}{x^3} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(c + d*x)^(5/2))/x^3,x]","\text{\$Aborted}","\frac{\sqrt{c} \left(-15 a^2 d^2-10 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{3/2}}+\frac{d^{3/2} (a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b}}-\frac{\sqrt{a+b x} (c+d x)^{5/2}}{2 x^2}-\frac{\sqrt{a+b x} (c+d x)^{3/2} (5 a d+b c)}{4 a x}+\frac{d \sqrt{a+b x} \sqrt{c+d x} (11 a d+b c)}{4 a}",1,"$Aborted","F",-1
572,-1,0,227,180.0364267,"\int \frac{\sqrt{a+b x} (c+d x)^{5/2}}{x^4} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(c + d*x)^(5/2))/x^4,x]","\text{\$Aborted}","\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-5 a d) (a d+b c)}{8 a^2 x}-\frac{\left(5 a^3 d^3+15 a^2 b c d^2-5 a b^2 c^2 d+b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 a^{5/2} \sqrt{c}}+2 \sqrt{b} d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)-\frac{\sqrt{a+b x} (c+d x)^{5/2}}{3 x^3}-\frac{\sqrt{a+b x} (c+d x)^{3/2} (5 a d+b c)}{12 a x^2}",1,"$Aborted","F",-1
573,-1,0,204,180.0184986,"\int \frac{\sqrt{a+b x} (c+d x)^{5/2}}{x^5} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(c + d*x)^(5/2))/x^5,x]","\text{\$Aborted}","\frac{5 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{7/2} c^{3/2}}-\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 a^3 c x}+\frac{5 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^2}{96 a^2 c x^2}-\frac{\sqrt{a+b x} (c+d x)^{7/2}}{4 c x^4}-\frac{\sqrt{a+b x} (c+d x)^{5/2} (b c-a d)}{24 a c x^3}",1,"$Aborted","F",-1
574,-1,0,283,180.0656872,"\int \frac{\sqrt{a+b x} (c+d x)^{5/2}}{x^6} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(c + d*x)^(5/2))/x^6,x]","\text{\$Aborted}","-\frac{(3 a d+7 b c) (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{128 a^{9/2} c^{5/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (3 a d+7 b c) (b c-a d)^3}{128 a^4 c^2 x}-\frac{\sqrt{a+b x} (c+d x)^{3/2} (3 a d+7 b c) (b c-a d)^2}{192 a^3 c^2 x^2}+\frac{\sqrt{a+b x} (c+d x)^{5/2} (3 a d+7 b c) (b c-a d)}{240 a^2 c^2 x^3}+\frac{\sqrt{a+b x} (c+d x)^{7/2} (3 a d+7 b c)}{40 a c^2 x^4}-\frac{(a+b x)^{3/2} (c+d x)^{7/2}}{5 a c x^5}",1,"$Aborted","F",-1
575,-1,0,436,180.0995231,"\int \frac{\sqrt{a+b x} (c+d x)^{5/2}}{x^7} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(c + d*x)^(5/2))/x^7,x]","\text{\$Aborted}","\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-5 a^2 d^2-6 a b c d+3 b^2 c^2\right)}{160 a^2 x^4}+\frac{\left(5 a^2 d^2+14 a b c d+21 b^2 c^2\right) (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{512 a^{11/2} c^{7/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(5 a^3 d^3+51 a^2 b c d^2-61 a b^2 c^2 d+21 b^3 c^3\right)}{960 a^3 c x^3}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(25 a^4 d^4-20 a^3 b c d^3+262 a^2 b^2 c^2 d^2-308 a b^3 c^3 d+105 b^4 c^4\right)}{3840 a^4 c^2 x^2}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(75 a^5 d^5-65 a^4 b c d^4-90 a^3 b^2 c^2 d^3+838 a^2 b^3 c^3 d^2-945 a b^4 c^4 d+315 b^5 c^5\right)}{7680 a^5 c^3 x}-\frac{\sqrt{a+b x} (c+d x)^{5/2}}{6 x^6}-\frac{\sqrt{a+b x} (c+d x)^{3/2} (5 a d+b c)}{60 a x^5}",1,"$Aborted","F",-1
576,-1,0,251,180.016847,"\int \frac{x^3 \sqrt{a+b x}}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(x^3*Sqrt[a + b*x])/Sqrt[c + d*x],x]","\text{\$Aborted}","\frac{(a+b x)^{3/2} \sqrt{c+d x} \left(15 a^2 d^2-4 b d x (5 a d+7 b c)+22 a b c d+35 b^2 c^2\right)}{96 b^3 d^3}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(5 a^3 d^3+9 a^2 b c d^2+15 a b^2 c^2 d+35 b^3 c^3\right)}{64 b^3 d^4}+\frac{(b c-a d) \left(5 a^3 d^3+9 a^2 b c d^2+15 a b^2 c^2 d+35 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{7/2} d^{9/2}}+\frac{x^2 (a+b x)^{3/2} \sqrt{c+d x}}{4 b d}",1,"$Aborted","F",-1
577,-1,0,191,180.0098188,"\int \frac{x^2 \sqrt{a+b x}}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(x^2*Sqrt[a + b*x])/Sqrt[c + d*x],x]","\text{\$Aborted}","\frac{\sqrt{a+b x} \sqrt{c+d x} \left(a^2 d^2+2 a b c d+5 b^2 c^2\right)}{8 b^2 d^3}-\frac{(b c-a d) \left(a^2 d^2+2 a b c d+5 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{5/2} d^{7/2}}-\frac{(a+b x)^{3/2} \sqrt{c+d x} (3 a d+5 b c)}{12 b^2 d^2}+\frac{x (a+b x)^{3/2} \sqrt{c+d x}}{3 b d}",1,"$Aborted","F",-1
578,1,2937,125,7.8382028,"\int \frac{x \sqrt{a+b x}}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(x*Sqrt[a + b*x])/Sqrt[c + d*x],x]","\text{Result too large to show}","\frac{(b c-a d) (a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{3/2} d^{5/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (a d+3 b c)}{4 b d^2}+\frac{(a+b x)^{3/2} \sqrt{c+d x}}{2 b d}",1,"((-1/4*Sqrt[a + b]/(b*d^2) + Sqrt[a + b*x]/(4*b*d^2))*(Sqrt[c + d] - Sqrt[c + d*x])*(12*b^5*c^5 - 30*a*b^4*c^4*d + 7*b^5*c^4*d + 42*a^2*b^3*c^3*d^2 - 6*a*b^4*c^3*d^2 - 7*b^5*c^3*d^2 - 30*a^3*b^2*c^2*d^3 - 6*a^2*b^3*c^2*d^3 + 3*a*b^4*c^2*d^3 - 2*b^5*c^2*d^3 + 10*a^4*b*c*d^4 + 2*a^3*b^2*c*d^4 - 17*a^2*b^3*c*d^4 - 12*a*b^4*c*d^4 - 4*a^5*d^5 - 13*a^4*b*d^5 - 11*a^3*b^2*d^5 - 2*a^2*b^3*d^5 + 7*b^5*c^4*d*x - 6*a*b^4*c^3*d^2*x + 16*b^5*c^3*d^2*x - 6*a^2*b^3*c^2*d^3*x - 48*a*b^4*c^2*d^3*x - 16*b^5*c^2*d^3*x + 2*a^3*b^2*c*d^4*x + 16*a^2*b^3*c*d^4*x - 16*a*b^4*c*d^4*x - 16*b^5*c*d^4*x - 13*a^4*b*d^5*x - 48*a^3*b^2*d^5*x - 48*a^2*b^3*d^5*x - 16*a*b^4*d^5*x - 7*b^5*c^3*d^2*x^2 + 3*a*b^4*c^2*d^3*x^2 - 16*b^5*c^2*d^3*x^2 - 17*a^2*b^3*c*d^4*x^2 - 16*a*b^4*c*d^4*x^2 - 16*b^5*c*d^4*x^2 - 11*a^3*b^2*d^5*x^2 - 48*a^2*b^3*d^5*x^2 - 48*a*b^4*d^5*x^2 - 16*b^5*d^5*x^2 - 2*b^5*c^2*d^3*x^3 - 12*a*b^4*c*d^4*x^3 - 16*b^5*c*d^4*x^3 - 2*a^2*b^3*d^5*x^3 - 16*a*b^4*d^5*x^3 - 16*b^5*d^5*x^3 + 22*b^4*Sqrt[a + b]*c^4*d*Sqrt[a + b*x] - 46*a*b^3*Sqrt[a + b]*c^3*d^2*Sqrt[a + b*x] + b^4*Sqrt[a + b]*c^3*d^2*Sqrt[a + b*x] + 30*a^2*b^2*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] - 15*a*b^3*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] - 18*b^4*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] - 10*a^3*b*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] + 3*a^2*b^2*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] + 12*a*b^3*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] + 4*a^4*Sqrt[a + b]*d^5*Sqrt[a + b*x] + 11*a^3*b*Sqrt[a + b]*d^5*Sqrt[a + b*x] + 6*a^2*b^2*Sqrt[a + b]*d^5*Sqrt[a + b*x] + b^4*Sqrt[a + b]*c^3*d^2*x*Sqrt[a + b*x] - 15*a*b^3*Sqrt[a + b]*c^2*d^3*x*Sqrt[a + b*x] - 12*b^4*Sqrt[a + b]*c^2*d^3*x*Sqrt[a + b*x] + 3*a^2*b^2*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] - 24*a*b^3*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] - 24*b^4*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] + 11*a^3*b*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] + 36*a^2*b^2*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] + 24*a*b^3*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] - 18*b^4*Sqrt[a + b]*c^2*d^3*x^2*Sqrt[a + b*x] + 12*a*b^3*Sqrt[a + b]*c*d^4*x^2*Sqrt[a + b*x] - 24*b^4*Sqrt[a + b]*c*d^4*x^2*Sqrt[a + b*x] + 6*a^2*b^2*Sqrt[a + b]*d^5*x^2*Sqrt[a + b*x] + 24*a*b^3*Sqrt[a + b]*d^5*x^2*Sqrt[a + b*x] - 12*b^5*c^4*Sqrt[c + d]*Sqrt[c + d*x] + 30*a*b^4*c^3*d*Sqrt[c + d]*Sqrt[c + d*x] - b^5*c^3*d*Sqrt[c + d]*Sqrt[c + d*x] - 42*a^2*b^3*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 9*a*b^4*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 6*b^5*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 42*a^3*b^2*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 45*a^2*b^3*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 12*a*b^4*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] - 18*a^4*b*d^4*Sqrt[c + d]*Sqrt[c + d*x] - 35*a^3*b^2*d^4*Sqrt[c + d]*Sqrt[c + d*x] - 18*a^2*b^3*d^4*Sqrt[c + d]*Sqrt[c + d*x] - b^5*c^3*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 9*a*b^4*c^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 12*b^5*c^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 45*a^2*b^3*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] + 72*a*b^4*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] + 24*b^5*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] - 35*a^3*b^2*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] - 60*a^2*b^3*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] - 24*a*b^4*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] + 6*b^5*c^2*d^2*Sqrt[c + d]*x^2*Sqrt[c + d*x] + 12*a*b^4*c*d^3*Sqrt[c + d]*x^2*Sqrt[c + d*x] + 24*b^5*c*d^3*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 18*a^2*b^3*d^4*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 24*a*b^4*d^4*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 22*b^4*Sqrt[a + b]*c^3*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 46*a*b^3*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 10*b^4*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 42*a^2*b^2*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 20*a*b^3*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 8*b^4*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 18*a^3*b*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 26*a^2*b^2*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 8*a*b^3*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 10*b^4*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 20*a*b^3*Sqrt[a + b]*c*d^3*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 26*a^2*b^2*Sqrt[a + b]*d^4*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 32*a*b^3*Sqrt[a + b]*d^4*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 16*b^4*Sqrt[a + b]*d^4*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 8*b^4*Sqrt[a + b]*c*d^3*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x] + 8*a*b^3*Sqrt[a + b]*d^4*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x] + 16*b^4*Sqrt[a + b]*d^4*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^4 + ((3*Sqrt[b]*c^2)/(2*d^(5/2)) - (a*c)/(Sqrt[b]*d^(3/2)) - a^2/(2*b^(3/2)*Sqrt[d]))*ArcTanh[(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*(Sqrt[c + d] - Sqrt[c + d*x]))]","B",1
579,1,350,73,0.0006257,"\int \frac{\sqrt{a+b x}}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/Sqrt[c + d*x],x]","\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(\frac{\sqrt{a+b}}{d}-\frac{\sqrt{a+b x}}{d}\right) \left(a^2 d^2+b c d \sqrt{a+b} \sqrt{a+b x}+a b d \sqrt{c+d} \sqrt{c+d x}-2 b d \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+a b d^2 x-a d^2 \sqrt{a+b} \sqrt{a+b x}+a b d^2+b^2 c^2+b^2 c d x-b^2 c \sqrt{c+d} \sqrt{c+d x}+b^2 c d+2 b^2 d^2 x\right)}{\left(-d \sqrt{a+b} \sqrt{a+b x}+a d+b \sqrt{c+d} \sqrt{c+d x}+b (-c)\right)^2}+\left(\frac{2 a}{\sqrt{b} \sqrt{d}}-\frac{2 \sqrt{b} c}{d^{3/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b}-\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \left(\sqrt{c+d}-\sqrt{c+d x}\right)}\right)","\frac{\sqrt{a+b x} \sqrt{c+d x}}{d}-\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b} d^{3/2}}",1,"((Sqrt[a + b]/d - Sqrt[a + b*x]/d)*(Sqrt[c + d] - Sqrt[c + d*x])*(b^2*c^2 + b^2*c*d + a^2*d^2 + a*b*d^2 + b^2*c*d*x + a*b*d^2*x + 2*b^2*d^2*x + b*Sqrt[a + b]*c*d*Sqrt[a + b*x] - a*Sqrt[a + b]*d^2*Sqrt[a + b*x] - b^2*c*Sqrt[c + d]*Sqrt[c + d*x] + a*b*d*Sqrt[c + d]*Sqrt[c + d*x] - 2*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^2 + ((-2*Sqrt[b]*c)/d^(3/2) + (2*a)/(Sqrt[b]*Sqrt[d]))*ArcTanh[(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*(Sqrt[c + d] - Sqrt[c + d*x]))]","B",1
580,1,370,85,1.2723239,"\int \frac{\sqrt{a+b x}}{x \sqrt{c+d x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(x*Sqrt[c + d*x]),x]","a \text{RootSum}\left[\text{$\#$1}^4 d^2-4 \text{$\#$1}^3 d \sqrt{a+b} \sqrt{c+d}+4 \text{$\#$1}^2 a d+4 \text{$\#$1}^2 b c+6 \text{$\#$1}^2 b d-4 \text{$\#$1} b \sqrt{a+b} \sqrt{c+d}+b^2\&,\frac{-\text{$\#$1}^2 d \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)+\text{$\#$1}^2 d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)+b \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)-b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{\text{$\#$1}^3 d^2-3 \text{$\#$1}^2 d \sqrt{a+b} \sqrt{c+d}+2 \text{$\#$1} a d+2 \text{$\#$1} b c+3 \text{$\#$1} b d-b \sqrt{a+b} \sqrt{c+d}}\&\right]+\frac{4 \sqrt{b} \tanh ^{-1}\left(\frac{\frac{\sqrt{d} \sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b}}}{\sqrt{c+d}-\sqrt{c+d x}}\right)}{\sqrt{d}}","\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{d}}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{c}}",1,"(4*Sqrt[b]*ArcTanh[((Sqrt[a + b]*Sqrt[d])/Sqrt[b] - (Sqrt[d]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[c + d] - Sqrt[c + d*x])])/Sqrt[d] + a*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ]","C",1
581,1,842,77,7.5650044,"\int \frac{\sqrt{a+b x}}{x^2 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(x^2*Sqrt[c + d*x]),x]","\frac{\sqrt{a+b} \left(-2 b^2 x c^3-b^2 d x^2 c^2+2 a b d c^2-b^2 d x c^2+2 a b d x c^2+2 a b d^2 c-b^2 d^2 x^2 c-a b d^2 x^2 c-2 a^2 d^2 x c+b^2 d^2 x c+3 a b d^2 x c-a b d^3 x^2-2 a^2 d^3 x+a b d^3 x+\sqrt{c+d} \sqrt{c+d x} \left(2 b^2 x c^2-2 a b d c-2 a b d x c+2 a^2 d^2\right)\right)+\sqrt{a+b x} \left(2 b^2 c^3+2 b^2 d c^2-2 a b d c^2-2 a b d x c^2-2 a b d^2 c+2 a^2 d^2 x c-2 a b d^2 x c+2 a^2 d^3 x+\sqrt{c+d} \sqrt{c+d x} \left(-2 c^2 b^2-c d b^2+c d x b^2-a d^2 b+2 a c d b+a d^2 x b+2 a c d x b-2 a^2 d^2\right)\right)}{c \left(-2 c^2 b^2-2 c d b^2+2 a d^2 b+2 a c d b\right) \sqrt{c+d x} x+\sqrt{a+b} c \left(-2 b d^2-2 b c d\right) \sqrt{a+b x} \sqrt{c+d x} x+\sqrt{c+d} \left(c \left(2 c^2 b^2+c d b^2+2 d^2 x b^2+c d x b^2+a d^2 b-2 a c d b+a d^2 x b+2 a^2 d^2\right) x+\sqrt{a+b} c \left(2 b c d-2 a d^2\right) \sqrt{a+b x} x\right)}+\left(\frac{b}{2}-\frac{a d}{2 c}\right) \text{RootSum}\left[d^2 \text{$\#$1}^4-4 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^3+4 b c \text{$\#$1}^2+4 a d \text{$\#$1}^2+6 b d \text{$\#$1}^2-4 b \sqrt{a+b} \sqrt{c+d} \text{$\#$1}+b^2\&,\frac{d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2-d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2-b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)+b \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right)}{d^2 \text{$\#$1}^3-3 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^2+2 b c \text{$\#$1}+2 a d \text{$\#$1}+3 b d \text{$\#$1}-b \sqrt{a+b} \sqrt{c+d}}\&\right]","-\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{a} c^{3/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x}}{c x}",1,"(Sqrt[a + b]*(2*a*b*c^2*d + 2*a*b*c*d^2 - 2*b^2*c^3*x + 2*a*b*c^2*d*x - b^2*c^2*d*x - 2*a^2*c*d^2*x + 3*a*b*c*d^2*x + b^2*c*d^2*x - 2*a^2*d^3*x + a*b*d^3*x - b^2*c^2*d*x^2 - a*b*c*d^2*x^2 - b^2*c*d^2*x^2 - a*b*d^3*x^2 + Sqrt[c + d]*Sqrt[c + d*x]*(-2*a*b*c*d + 2*a^2*d^2 + 2*b^2*c^2*x - 2*a*b*c*d*x)) + Sqrt[a + b*x]*(2*b^2*c^3 - 2*a*b*c^2*d + 2*b^2*c^2*d - 2*a*b*c*d^2 - 2*a*b*c^2*d*x + 2*a^2*c*d^2*x - 2*a*b*c*d^2*x + 2*a^2*d^3*x + Sqrt[c + d]*Sqrt[c + d*x]*(-2*b^2*c^2 + 2*a*b*c*d - b^2*c*d - 2*a^2*d^2 - a*b*d^2 + 2*a*b*c*d*x + b^2*c*d*x + a*b*d^2*x)))/(c*(-2*b^2*c^2 + 2*a*b*c*d - 2*b^2*c*d + 2*a*b*d^2)*x*Sqrt[c + d*x] + Sqrt[a + b]*c*(-2*b*c*d - 2*b*d^2)*x*Sqrt[a + b*x]*Sqrt[c + d*x] + Sqrt[c + d]*(Sqrt[a + b]*c*(2*b*c*d - 2*a*d^2)*x*Sqrt[a + b*x] + c*x*(2*b^2*c^2 - 2*a*b*c*d + b^2*c*d + 2*a^2*d^2 + a*b*d^2 + b^2*c*d*x + a*b*d^2*x + 2*b^2*d^2*x))) + (b/2 - (a*d)/(2*c))*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ]","C",1
582,1,4557,131,102.6529386,"\int \frac{\sqrt{a+b x}}{x^3 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(x^3*Sqrt[c + d*x]),x]","\text{Result too large to show}","\frac{(b c-a d) (3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{3/2} c^{5/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (3 a d+b c)}{4 a c^2 x}-\frac{(a+b x)^{3/2} \sqrt{c+d x}}{2 a c x^2}",1,"(Sqrt[a + b]*(32*a^2*b^3*c^5*d - 48*a^3*b^2*c^4*d^2 + 40*a^2*b^3*c^4*d^2 + 32*a^4*b*c^3*d^3 - 40*a^3*b^2*c^3*d^3 + 8*a^2*b^3*c^3*d^3 + 32*a^4*b*c^2*d^4 + 8*a^3*b^2*c^2*d^4 + 48*a*b^4*c^5*d*x - 80*a^2*b^3*c^4*d^2*x + 60*a*b^4*c^4*d^2*x + 80*a^3*b^2*c^3*d^3*x - 56*a^2*b^3*c^3*d^3*x + 12*a*b^4*c^3*d^3*x - 16*a^4*b*c^2*d^4*x + 76*a^3*b^2*c^2*d^4*x + 24*a^2*b^3*c^2*d^4*x - 16*a^4*b*c*d^5*x - 4*a^3*b^2*c*d^5*x - 16*a*b^4*c^6*x^2 - 8*b^5*c^6*x^2 + 32*a^2*b^3*c^5*d*x^2 + 8*a*b^4*c^5*d*x^2 - 48*a^3*b^2*c^4*d^2*x^2 - 40*a^2*b^3*c^4*d^2*x^2 + 34*a*b^4*c^4*d^2*x^2 + 11*b^5*c^4*d^2*x^2 + 32*a^4*b*c^3*d^3*x^2 + 40*a^3*b^2*c^3*d^3*x^2 - 108*a^2*b^3*c^3*d^3*x^2 + 35*a*b^4*c^3*d^3*x^2 + 3*b^5*c^3*d^3*x^2 - 16*a^5*c^2*d^4*x^2 - 40*a^4*b*c^2*d^4*x^2 + 146*a^3*b^2*c^2*d^4*x^2 - 39*a^2*b^3*c^2*d^4*x^2 + 25*a*b^4*c^2*d^4*x^2 + 8*a^5*c*d^5*x^2 - 96*a^4*b*c*d^5*x^2 + 49*a^3*b^2*c*d^5*x^2 - 3*a^2*b^3*c*d^5*x^2 + 24*a^5*d^6*x^2 - 24*a^4*b*d^6*x^2 - 9*a^3*b^2*d^6*x^2 - 16*a*b^4*c^5*d*x^3 - 8*b^5*c^5*d*x^3 - 36*a*b^4*c^4*d^2*x^3 - 10*b^5*c^4*d^2*x^3 + 24*a^2*b^3*c^3*d^3*x^3 - 26*a*b^4*c^3*d^3*x^3 + 2*b^5*c^3*d^3*x^3 - 16*a^4*b*c^2*d^4*x^3 - 52*a^3*b^2*c^2*d^4*x^3 + 26*a^2*b^3*c^2*d^4*x^3 + 2*a*b^4*c^2*d^4*x^3 + 4*b^5*c^2*d^4*x^3 + 8*a^4*b*c*d^5*x^3 - 46*a^3*b^2*c*d^5*x^3 - 10*a^2*b^3*c*d^5*x^3 + 8*a*b^4*c*d^5*x^3 + 24*a^4*b*d^6*x^3 + 6*a^3*b^2*d^6*x^3 - 12*a^2*b^3*d^6*x^3 - 2*a*b^4*c^4*d^2*x^4 - b^5*c^4*d^2*x^4 - 12*a^2*b^3*c^3*d^3*x^4 - 21*a*b^4*c^3*d^3*x^4 - 5*b^5*c^3*d^3*x^4 - 2*a^3*b^2*c^2*d^4*x^4 - 11*a^2*b^3*c^2*d^4*x^4 - 27*a*b^4*c^2*d^4*x^4 - 4*b^5*c^2*d^4*x^4 + a^3*b^2*c*d^5*x^4 + 13*a^2*b^3*c*d^5*x^4 - 8*a*b^4*c*d^5*x^4 + 3*a^3*b^2*d^6*x^4 + 12*a^2*b^3*d^6*x^4 + Sqrt[c + d]*Sqrt[c + d*x]*(-32*a^2*b^3*c^4*d + 48*a^3*b^2*c^3*d^2 - 24*a^2*b^3*c^3*d^2 - 32*a^4*b*c^2*d^3 + 16*a^3*b^2*c^2*d^3 + 16*a^5*c*d^4 + 8*a^4*b*c*d^4 - 48*a*b^4*c^4*d*x + 96*a^2*b^3*c^3*d^2*x - 36*a*b^4*c^3*d^2*x - 104*a^3*b^2*c^2*d^3*x + 28*a^2*b^3*c^2*d^3*x + 80*a^4*b*c*d^4*x + 20*a^3*b^2*c*d^4*x - 24*a^5*d^5*x - 12*a^4*b*d^5*x + 16*a*b^4*c^5*x^2 + 8*b^5*c^5*x^2 - 32*a^2*b^3*c^4*d*x^2 - 16*a*b^4*c^4*d*x^2 - 4*b^5*c^4*d*x^2 + 48*a^3*b^2*c^3*d^2*x^2 + 56*a^2*b^3*c^3*d^2*x^2 - 8*b^5*c^3*d^2*x^2 - 32*a^4*b*c^2*d^3*x^2 - 64*a^3*b^2*c^2*d^3*x^2 + 24*a^2*b^3*c^2*d^3*x^2 - 8*a*b^4*c^2*d^3*x^2 + 16*a^4*b*c*d^4*x^2 - 32*a^3*b^2*c*d^4*x^2 + 40*a^2*b^3*c*d^4*x^2 + 12*a^4*b*d^5*x^2 - 24*a^3*b^2*d^5*x^2 + 8*a*b^4*c^4*d*x^3 + 4*b^5*c^4*d*x^3 + 16*a^2*b^3*c^3*d^2*x^3 + 36*a*b^4*c^3*d^2*x^3 + 8*b^5*c^3*d^2*x^3 - 24*a^3*b^2*c^2*d^3*x^3 - 52*a^2*b^3*c^2*d^3*x^3 + 8*a*b^4*c^2*d^3*x^3 + 12*a^3*b^2*c*d^4*x^3 - 40*a^2*b^3*c*d^4*x^3 + 24*a^3*b^2*d^5*x^3)) + Sqrt[a + b*x]*(16*a*b^4*c^6 - 32*a^2*b^3*c^5*d + 24*a*b^4*c^5*d + 48*a^3*b^2*c^4*d^2 - 16*a^2*b^3*c^4*d^2 + 8*a*b^4*c^4*d^2 - 32*a^4*b*c^3*d^3 + 24*a^3*b^2*c^3*d^3 + 16*a^2*b^3*c^3*d^3 - 32*a^4*b*c^2*d^4 - 24*a^3*b^2*c^2*d^4 + 8*b^5*c^6*x - 16*a*b^4*c^5*d*x + 12*b^5*c^5*d*x + 56*a^2*b^3*c^4*d^2*x + 20*a*b^4*c^4*d^2*x + 4*b^5*c^4*d^2*x - 64*a^3*b^2*c^3*d^3*x + 4*a^2*b^3*c^3*d^3*x + 36*a*b^4*c^3*d^3*x + 16*a^4*b*c^2*d^4*x - 52*a^3*b^2*c^2*d^4*x - 52*a^2*b^3*c^2*d^4*x + 16*a^4*b*c*d^5*x + 12*a^3*b^2*c*d^5*x - 32*a^2*b^3*c^5*d*x^2 - 48*a*b^4*c^5*d*x^2 - 4*b^5*c^5*d*x^2 + 48*a^3*b^2*c^4*d^2*x^2 + 64*a^2*b^3*c^4*d^2*x^2 - 48*a*b^4*c^4*d^2*x^2 + 4*b^5*c^4*d^2*x^2 - 32*a^4*b*c^3*d^3*x^2 - 56*a^3*b^2*c^3*d^3*x^2 + 120*a^2*b^3*c^3*d^3*x^2 + 8*a*b^4*c^3*d^3*x^2 + 8*b^5*c^3*d^3*x^2 + 16*a^5*c^2*d^4*x^2 + 48*a^4*b*c^2*d^4*x^2 - 136*a^3*b^2*c^2*d^4*x^2 - 16*a^2*b^3*c^2*d^4*x^2 + 8*a*b^4*c^2*d^4*x^2 - 8*a^5*c*d^5*x^2 + 92*a^4*b*c*d^5*x^2 - 8*a^3*b^2*c*d^5*x^2 - 40*a^2*b^3*c*d^5*x^2 - 24*a^5*d^6*x^2 + 12*a^4*b*d^6*x^2 + 24*a^3*b^2*d^6*x^2 - 24*a^2*b^3*c^4*d^2*x^3 - 36*a*b^4*c^4*d^2*x^3 - 8*b^5*c^4*d^2*x^3 + 16*a^3*b^2*c^3*d^3*x^3 + 4*a^2*b^3*c^3*d^3*x^3 - 44*a*b^4*c^3*d^3*x^3 - 8*b^5*c^3*d^3*x^3 + 8*a^4*b*c^2*d^4*x^3 + 36*a^3*b^2*c^2*d^4*x^3 + 68*a^2*b^3*c^2*d^4*x^3 - 8*a*b^4*c^2*d^4*x^3 - 4*a^4*b*c*d^5*x^3 - 4*a^3*b^2*c*d^5*x^3 + 40*a^2*b^3*c*d^5*x^3 - 12*a^4*b*d^6*x^3 - 24*a^3*b^2*d^6*x^3 + Sqrt[c + d]*Sqrt[c + d*x]*(-16*a*b^4*c^5 + 32*a^2*b^3*c^4*d - 16*a*b^4*c^4*d - 48*a^3*b^2*c^3*d^2 - 2*a*b^4*c^3*d^2 + 32*a^4*b*c^2*d^3 - 12*a^2*b^3*c^2*d^3 - 16*a^5*c*d^4 - 16*a^4*b*c*d^4 - 2*a^3*b^2*c*d^4 - 8*b^5*c^5*x + 24*a*b^4*c^4*d*x - 8*b^5*c^4*d*x - 72*a^2*b^3*c^3*d^2*x - 20*a*b^4*c^3*d^2*x - b^5*c^3*d^2*x + 88*a^3*b^2*c^2*d^3*x + 24*a^2*b^3*c^2*d^3*x - 19*a*b^4*c^2*d^3*x - 72*a^4*b*c*d^4*x - 52*a^3*b^2*c*d^4*x + a^2*b^3*c*d^4*x + 24*a^5*d^5*x + 24*a^4*b*d^5*x + 3*a^3*b^2*d^5*x + 32*a^2*b^3*c^4*d*x^2 + 48*a*b^4*c^4*d*x^2 + 8*b^5*c^4*d*x^2 - 48*a^3*b^2*c^3*d^2*x^2 - 80*a^2*b^3*c^3*d^2*x^2 + 10*a*b^4*c^3*d^2*x^2 - 2*b^5*c^3*d^2*x^2 + 32*a^4*b*c^2*d^3*x^2 + 80*a^3*b^2*c^2*d^3*x^2 - 36*a^2*b^3*c^2*d^3*x^2 - 6*a*b^4*c^2*d^3*x^2 - 4*b^5*c^2*d^3*x^2 - 16*a^4*b*c*d^4*x^2 + 58*a^3*b^2*c*d^4*x^2 + 2*a^2*b^3*c*d^4*x^2 - 8*a*b^4*c*d^4*x^2 - 24*a^4*b*d^5*x^2 + 6*a^3*b^2*d^5*x^2 + 12*a^2*b^3*d^5*x^2 + 8*a^2*b^3*c^3*d^2*x^3 + 12*a*b^4*c^3*d^2*x^3 + 3*b^5*c^3*d^2*x^3 + 8*a^3*b^2*c^2*d^3*x^3 + 24*a^2*b^3*c^2*d^3*x^3 + 25*a*b^4*c^2*d^3*x^3 + 4*b^5*c^2*d^3*x^3 - 4*a^3*b^2*c*d^4*x^3 - 3*a^2*b^3*c*d^4*x^3 + 8*a*b^4*c*d^4*x^3 - 9*a^3*b^2*d^5*x^3 - 12*a^2*b^3*d^5*x^3)))/(4*a*Sqrt[a + b]*c^2*x^2*Sqrt[a + b*x]*Sqrt[c + d*x]*(-16*b^3*c^3*d + 24*a*b^2*c^2*d^2 - 20*b^3*c^2*d^2 - 16*a^2*b*c*d^3 + 20*a*b^2*c*d^3 - 4*b^3*c*d^3 - 16*a^2*b*d^4 - 4*a*b^2*d^4 - 4*b^3*c^2*d^2*x - 4*a*b^2*c*d^3*x - 12*b^3*c*d^3*x - 4*a*b^2*d^4*x - 8*b^3*d^4*x) + 4*a*c^2*x^2*Sqrt[c + d*x]*(-8*b^4*c^4 + 16*a*b^3*c^3*d - 12*b^4*c^3*d - 24*a^2*b^2*c^2*d^2 + 8*a*b^3*c^2*d^2 - 4*b^4*c^2*d^2 + 16*a^3*b*c*d^3 - 12*a^2*b^2*c*d^3 - 8*a*b^3*c*d^3 + 16*a^3*b*d^4 + 12*a^2*b^2*d^4 - 4*b^4*c^3*d*x - 8*a*b^3*c^2*d^2*x - 20*b^4*c^2*d^2*x + 12*a^2*b^2*c*d^3*x + 8*a*b^3*c*d^3*x - 16*b^4*c*d^3*x + 12*a^2*b^2*d^4*x + 16*a*b^3*d^4*x) + Sqrt[c + d]*(4*a*Sqrt[a + b]*c^2*x^2*Sqrt[a + b*x]*(16*b^3*c^3*d - 24*a*b^2*c^2*d^2 + 12*b^3*c^2*d^2 + 16*a^2*b*c*d^3 - 8*a*b^2*c*d^3 - 8*a^3*d^4 - 4*a^2*b*d^4 + 12*b^3*c^2*d^2*x - 8*a*b^2*c*d^3*x + 16*b^3*c*d^3*x - 4*a^2*b*d^4*x - 16*a*b^2*d^4*x) + 4*a*c^2*x^2*(8*b^4*c^4 - 16*a*b^3*c^3*d + 8*b^4*c^3*d + 24*a^2*b^2*c^2*d^2 + b^4*c^2*d^2 - 16*a^3*b*c*d^3 + 6*a*b^3*c*d^3 + 8*a^4*d^4 + 8*a^3*b*d^4 + a^2*b^2*d^4 + 8*b^4*c^3*d*x + 22*b^4*c^2*d^2*x - 12*a*b^3*c*d^3*x + 8*b^4*c*d^3*x + 8*a^3*b*d^4*x + 22*a^2*b^2*d^4*x + 8*a*b^3*d^4*x + b^4*c^2*d^2*x^2 + 6*a*b^3*c*d^3*x^2 + 8*b^4*c*d^3*x^2 + a^2*b^2*d^4*x^2 + 8*a*b^3*d^4*x^2 + 8*b^4*d^4*x^2))) + (-1/8*b^2/a - (b*d)/(4*c) + (3*a*d^2)/(8*c^2))*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ]","C",1
583,-1,0,190,180.0689249,"\int \frac{\sqrt{a+b x}}{x^4 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(x^4*Sqrt[c + d*x]),x]","\text{\$Aborted}","\frac{\sqrt{a+b x} \sqrt{c+d x} (3 b c-5 a d) (3 a d+b c)}{24 a^2 c^3 x}-\frac{(b c-a d) \left(5 a^2 d^2+2 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 a^{5/2} c^{7/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-5 a d)}{12 a c^2 x^2}-\frac{\sqrt{a+b x} \sqrt{c+d x}}{3 c x^3}",1,"$Aborted","F",-1
584,-1,0,279,180.0645958,"\int \frac{\sqrt{a+b x}}{x^5 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(x^5*Sqrt[c + d*x]),x]","\text{\$Aborted}","\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-35 a^2 d^2+6 a b c d+5 b^2 c^2\right)}{96 a^2 c^3 x^2}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-105 a^3 d^3+25 a^2 b c d^2+17 a b^2 c^2 d+15 b^3 c^3\right)}{192 a^3 c^4 x}+\frac{(b c-a d) \left(35 a^3 d^3+15 a^2 b c d^2+9 a b^2 c^2 d+5 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{7/2} c^{9/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-7 a d)}{24 a c^2 x^3}-\frac{\sqrt{a+b x} \sqrt{c+d x}}{4 c x^4}",1,"$Aborted","F",-1
585,-1,0,189,180.0294425,"\int \frac{x^2 \sqrt{a+b x}}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(x^2*Sqrt[a + b*x])/(c + d*x)^(3/2),x]","\text{\$Aborted}","\frac{\left(-a^2 d^2-6 a b c d+15 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{3/2} d^{7/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(\frac{a^2 d}{b}+6 a c-\frac{15 b c^2}{d}\right)}{4 d^2 (b c-a d)}+\frac{2 c^2 (a+b x)^{3/2}}{d^2 \sqrt{c+d x} (b c-a d)}+\frac{(a+b x)^{3/2} \sqrt{c+d x}}{2 b d^2}",1,"$Aborted","F",-1
586,1,1217,127,84.552263,"\int \frac{x \sqrt{a+b x}}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(x*Sqrt[a + b*x])/(c + d*x)^(3/2),x]","\frac{\left(-\frac{2 \sqrt{a+b x} b^2}{d}-\frac{c \sqrt{a+b x} b^2}{d^2}+\frac{2 \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x} b^2}{d^2}-\frac{\sqrt{a+b} c b^2}{d^2}-\frac{a \sqrt{a+b x} b}{d}+\frac{a \sqrt{a+b} b}{d}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)^3}{\left(-c b+\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}\right)^2}+\frac{\left(\frac{2 b \sqrt{a+b x} c^2}{d^2 (c+d)}-\frac{2 b \sqrt{a+b} c^2}{d^2 (c+d)}-\frac{2 a \sqrt{a+b x} c}{d (c+d)}+\frac{2 a \sqrt{a+b} c}{d (c+d)}\right) \left(b c^2+2 a d c+3 b d c+b d x c-2 \sqrt{a+b} d \sqrt{a+b x} c-b \sqrt{c+d} \sqrt{c+d x} c+2 a d^2+2 b d^2+b d^2 x-2 \sqrt{a+b} d^2 \sqrt{a+b x}-a d \sqrt{c+d} \sqrt{c+d x}-2 b d \sqrt{c+d} \sqrt{c+d x}+\sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{-2 b^2 c^3-5 b^2 d c^2-2 a b d c^2-3 b^2 d x c^2+2 b \sqrt{a+b} d \sqrt{a+b x} c^2+2 b^2 \sqrt{c+d} \sqrt{c+d x} c^2+2 a^2 d^2 c-2 b^2 d^2 c+a b d^2 c-b^2 d^2 x^2 c-5 b^2 d^2 x c-a b d^2 x c-2 a \sqrt{a+b} d^2 \sqrt{a+b x} c+2 b \sqrt{a+b} d^2 x \sqrt{a+b x} c+2 b^2 d \sqrt{c+d} x \sqrt{c+d x} c+4 b^2 d \sqrt{c+d} \sqrt{c+d x} c+2 a b d \sqrt{c+d} \sqrt{c+d x} c-2 b \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} c+a b d^3 x^2+2 a^2 d^3 x-2 b^2 d^3 x+a b d^3 x-2 a \sqrt{a+b} d^3 x \sqrt{a+b x}-2 a b d^2 \sqrt{c+d} x \sqrt{c+d x}-4 a^2 d^2 \sqrt{c+d} \sqrt{c+d x}-4 a b d^2 \sqrt{c+d} \sqrt{c+d x}+4 a \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+2 b \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}}+\frac{\left(\frac{\sqrt{c+d}}{d^2}-\frac{\sqrt{c+d x}}{d^2}\right) \left(-3 \sqrt{a+b} c b-2 \sqrt{a+b} d b-c \sqrt{a+b x} b-2 d \sqrt{a+b x} b+4 \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x} b+a \sqrt{a+b} d-a d \sqrt{a+b x}\right)}{-c b+\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}}+\left(\frac{2 a}{\sqrt{b} d^{3/2}}-\frac{6 \sqrt{b} c}{d^{5/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{a+b} \sqrt{d}-\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \left(\sqrt{c+d}-\sqrt{c+d x}\right)}\right)","-\frac{(3 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b} d^{5/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (3 b c-a d)}{d^2 (b c-a d)}-\frac{2 c (a+b x)^{3/2}}{d \sqrt{c+d x} (b c-a d)}",1,"((Sqrt[c + d]/d^2 - Sqrt[c + d*x]/d^2)*(-3*b*Sqrt[a + b]*c + a*Sqrt[a + b]*d - 2*b*Sqrt[a + b]*d - b*c*Sqrt[a + b*x] - a*d*Sqrt[a + b*x] - 2*b*d*Sqrt[a + b*x] + 4*b*Sqrt[a + b]*Sqrt[c + d]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x]) + ((Sqrt[c + d] - Sqrt[c + d*x])^3*(-((b^2*Sqrt[a + b]*c)/d^2) + (a*b*Sqrt[a + b])/d - (b^2*c*Sqrt[a + b*x])/d^2 - (a*b*Sqrt[a + b*x])/d - (2*b^2*Sqrt[a + b*x])/d + (2*b^2*Sqrt[a + b]*Sqrt[c + d]*Sqrt[c + d*x])/d^2))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^2 + (((-2*b*Sqrt[a + b]*c^2)/(d^2*(c + d)) + (2*a*Sqrt[a + b]*c)/(d*(c + d)) + (2*b*c^2*Sqrt[a + b*x])/(d^2*(c + d)) - (2*a*c*Sqrt[a + b*x])/(d*(c + d)))*(Sqrt[c + d] - Sqrt[c + d*x])*(b*c^2 + 2*a*c*d + 3*b*c*d + 2*a*d^2 + 2*b*d^2 + b*c*d*x + b*d^2*x - 2*Sqrt[a + b]*c*d*Sqrt[a + b*x] - 2*Sqrt[a + b]*d^2*Sqrt[a + b*x] - b*c*Sqrt[c + d]*Sqrt[c + d*x] - a*d*Sqrt[c + d]*Sqrt[c + d*x] - 2*b*d*Sqrt[c + d]*Sqrt[c + d*x] + Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-2*b^2*c^3 - 2*a*b*c^2*d - 5*b^2*c^2*d + 2*a^2*c*d^2 + a*b*c*d^2 - 2*b^2*c*d^2 - 3*b^2*c^2*d*x - a*b*c*d^2*x - 5*b^2*c*d^2*x + 2*a^2*d^3*x + a*b*d^3*x - 2*b^2*d^3*x - b^2*c*d^2*x^2 + a*b*d^3*x^2 + 2*b*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] - 2*a*Sqrt[a + b]*c*d^2*Sqrt[a + b*x] + 2*b*Sqrt[a + b]*c*d^2*x*Sqrt[a + b*x] - 2*a*Sqrt[a + b]*d^3*x*Sqrt[a + b*x] + 2*b^2*c^2*Sqrt[c + d]*Sqrt[c + d*x] + 2*a*b*c*d*Sqrt[c + d]*Sqrt[c + d*x] + 4*b^2*c*d*Sqrt[c + d]*Sqrt[c + d*x] - 4*a^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 4*a*b*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 2*b^2*c*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 2*a*b*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 2*b*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 4*a*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 2*b*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]) + ((-6*Sqrt[b]*c)/d^(5/2) + (2*a)/(Sqrt[b]*d^(3/2)))*ArcTanh[(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*(Sqrt[c + d] - Sqrt[c + d*x]))]","B",1
587,1,660,66,0.0007034,"\int \frac{\sqrt{a+b x}}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(c + d*x)^(3/2),x]","\frac{\sqrt{a+b} \left(2 \sqrt{c+d} (a d-b c) \left(6 a c d+2 a d^2 x+4 a d^2+2 b c^2+5 b c d x+5 b c d+b d^2 x^2+5 b d^2 x+2 b d^2\right)+2 \sqrt{c+d x} (a d-b c) \left(-6 a c d-6 a d^2-2 b c^2-4 b c d x-6 b c d-4 b d^2 x-4 b d^2\right)\right)+2 \sqrt{c+d} \sqrt{a+b x} (a d-b c) \left(-6 a c d-2 a d^2 x-4 a d^2-2 b c^2-2 b c d x-8 b c d-4 b d^2 x-4 b d^2\right)+2 \sqrt{a+b x} \sqrt{c+d x} (a d-b c) \left(6 a c d+6 a d^2+2 b c^2+b c d x+9 b c d+b d^2 x+7 b d^2\right)}{d (c+d)^{3/2} \sqrt{c+d x} \left(4 a^2 d^2-2 a b c d+2 a b d^2 x+4 a b d^2-2 b^2 c^2-2 b^2 c d x-4 b^2 c d\right)+d (c+d) \left(-2 a^2 c d^2-2 a^2 d^3 x+2 a b c^2 d+a b c d^2 x-a b c d^2-a b d^3 x^2-a b d^3 x+2 b^2 c^3+3 b^2 c^2 d x+5 b^2 c^2 d+b^2 c d^2 x^2+5 b^2 c d^2 x+2 b^2 c d^2+2 b^2 d^3 x\right)+\sqrt{a+b} \sqrt{a+b x} \left(d (c+d) \left(2 a c d^2+2 a d^3 x-2 b c^2 d-2 b c d^2 x\right)+d (c+d)^{3/2} \sqrt{c+d x} \left(-4 a d^2+2 b c d-2 b d^2\right)\right)}+\frac{4 \sqrt{b} \tanh ^{-1}\left(\frac{\frac{\sqrt{d} \sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b}}}{\sqrt{c+d}-\sqrt{c+d x}}\right)}{d^{3/2}}","\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{3/2}}-\frac{2 \sqrt{a+b x}}{d \sqrt{c+d x}}",1,"(2*Sqrt[c + d]*(-(b*c) + a*d)*Sqrt[a + b*x]*(-2*b*c^2 - 6*a*c*d - 8*b*c*d - 4*a*d^2 - 4*b*d^2 - 2*b*c*d*x - 2*a*d^2*x - 4*b*d^2*x) + 2*(-(b*c) + a*d)*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*b*c^2 + 6*a*c*d + 9*b*c*d + 6*a*d^2 + 7*b*d^2 + b*c*d*x + b*d^2*x) + Sqrt[a + b]*(2*(-(b*c) + a*d)*Sqrt[c + d*x]*(-2*b*c^2 - 6*a*c*d - 6*b*c*d - 6*a*d^2 - 4*b*d^2 - 4*b*c*d*x - 4*b*d^2*x) + 2*Sqrt[c + d]*(-(b*c) + a*d)*(2*b*c^2 + 6*a*c*d + 5*b*c*d + 4*a*d^2 + 2*b*d^2 + 5*b*c*d*x + 2*a*d^2*x + 5*b*d^2*x + b*d^2*x^2)))/(d*(c + d)^(3/2)*Sqrt[c + d*x]*(-2*b^2*c^2 - 2*a*b*c*d - 4*b^2*c*d + 4*a^2*d^2 + 4*a*b*d^2 - 2*b^2*c*d*x + 2*a*b*d^2*x) + d*(c + d)*(2*b^2*c^3 + 2*a*b*c^2*d + 5*b^2*c^2*d - 2*a^2*c*d^2 - a*b*c*d^2 + 2*b^2*c*d^2 + 3*b^2*c^2*d*x + a*b*c*d^2*x + 5*b^2*c*d^2*x - 2*a^2*d^3*x - a*b*d^3*x + 2*b^2*d^3*x + b^2*c*d^2*x^2 - a*b*d^3*x^2) + Sqrt[a + b]*Sqrt[a + b*x]*(d*(c + d)^(3/2)*(2*b*c*d - 4*a*d^2 - 2*b*d^2)*Sqrt[c + d*x] + d*(c + d)*(-2*b*c^2*d + 2*a*c*d^2 - 2*b*c*d^2*x + 2*a*d^3*x))) + (4*Sqrt[b]*ArcTanh[((Sqrt[a + b]*Sqrt[d])/Sqrt[b] - (Sqrt[d]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[c + d] - Sqrt[c + d*x])])/d^(3/2)","B",1
588,1,471,66,2.045347,"\int \frac{\sqrt{a+b x}}{x (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(x*(c + d*x)^(3/2)),x]","\frac{a \text{RootSum}\left[\text{$\#$1}^4 d^2-4 \text{$\#$1}^3 d \sqrt{a+b} \sqrt{c+d}+4 \text{$\#$1}^2 a d+4 \text{$\#$1}^2 b c+6 \text{$\#$1}^2 b d-4 \text{$\#$1} b \sqrt{a+b} \sqrt{c+d}+b^2\&,\frac{-\text{$\#$1}^2 d \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)+\text{$\#$1}^2 d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)+b \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)-b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{\text{$\#$1}^3 d^2-3 \text{$\#$1}^2 d \sqrt{a+b} \sqrt{c+d}+2 \text{$\#$1} a d+2 \text{$\#$1} b c+3 \text{$\#$1} b d-b \sqrt{a+b} \sqrt{c+d}}\&\right]}{c}+\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(-\frac{2 a d \sqrt{a+b x}}{c}+\frac{2 a d \sqrt{a+b}}{c}+2 b \sqrt{a+b x}-2 b \sqrt{a+b}\right)}{d \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}-a d \sqrt{c+d} \sqrt{c+d x}-b c^2-b c d x+b c \sqrt{c+d} \sqrt{c+d x}-b c d-b d^2 x}","\frac{2 \sqrt{a+b x}}{c \sqrt{c+d x}}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{c^{3/2}}",1,"((-2*b*Sqrt[a + b] + (2*a*Sqrt[a + b]*d)/c + 2*b*Sqrt[a + b*x] - (2*a*d*Sqrt[a + b*x])/c)*(Sqrt[c + d] - Sqrt[c + d*x]))/(-(b*c^2) - b*c*d - b*c*d*x - b*d^2*x + b*c*Sqrt[c + d]*Sqrt[c + d*x] - a*d*Sqrt[c + d]*Sqrt[c + d*x] + Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]) + (a*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ])/c","C",1
589,1,1226,113,35.6172035,"\int \frac{\sqrt{a+b x}}{x^2 (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(x^2*(c + d*x)^(3/2)),x]","\frac{\left(\frac{2 a \sqrt{a+b x} d^2}{c^2}-\frac{2 a \sqrt{a+b} d^2}{c^2}-\frac{2 b \sqrt{a+b x} d}{c}+\frac{2 b \sqrt{a+b} d}{c}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{-b c^2-b d c-b d x c+b \sqrt{c+d} \sqrt{c+d x} c-b d^2 x-a d \sqrt{c+d} \sqrt{c+d x}+\sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}}+\frac{\left(\frac{\sqrt{a+b x}}{\sqrt{a+b} c^2 \sqrt{c+d}}-\frac{1}{c^2 \sqrt{c+d}}\right) \left(\sqrt{a+b} c d \sqrt{c+d} a^2-c d \sqrt{c+d} \sqrt{a+b x} a^2+\sqrt{a+b} d^2 \sqrt{c+d x} a^2+\sqrt{a+b} c d \sqrt{c+d x} a^2-d^2 \sqrt{a+b x} \sqrt{c+d x} a^2-c d \sqrt{a+b x} \sqrt{c+d x} a^2+b \sqrt{a+b} d^2 \sqrt{c+d} x a+2 b \sqrt{a+b} c d \sqrt{c+d} x a+b \sqrt{a+b} c^2 \sqrt{c+d} a+2 b \sqrt{a+b} c d \sqrt{c+d} a+b c^2 \sqrt{c+d} \sqrt{a+b x} a-b c d \sqrt{c+d} \sqrt{a+b x} a-b \sqrt{a+b} c^2 \sqrt{c+d x} a-b \sqrt{a+b} c d \sqrt{c+d x} a-b c^2 \sqrt{a+b x} \sqrt{c+d x} a-b d^2 \sqrt{a+b x} \sqrt{c+d x} a-2 b c d \sqrt{a+b x} \sqrt{c+d x} a+b^2 \sqrt{a+b} c d \sqrt{c+d} x+b^2 c^2 \sqrt{c+d} \sqrt{a+b x}-b^2 c^2 \sqrt{a+b x} \sqrt{c+d x}-b^2 c d \sqrt{a+b x} \sqrt{c+d x}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{x \left(-2 c^2 b^2-c d b^2-2 d^2 x b^2-c d x b^2+2 c \sqrt{c+d} \sqrt{c+d x} b^2-a d^2 b+2 a c d b-a d^2 x b-2 \sqrt{a+b} c d \sqrt{a+b x} b-2 a d \sqrt{c+d} \sqrt{c+d x} b+2 \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b-2 a^2 d^2+2 a \sqrt{a+b} d^2 \sqrt{a+b x}\right)}+\left(\frac{b}{2 c}-\frac{3 a d}{2 c^2}\right) \text{RootSum}\left[d^2 \text{$\#$1}^4-4 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^3+4 b c \text{$\#$1}^2+4 a d \text{$\#$1}^2+6 b d \text{$\#$1}^2-4 b \sqrt{a+b} \sqrt{c+d} \text{$\#$1}+b^2\&,\frac{d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2-d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2-b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)+b \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right)}{d^2 \text{$\#$1}^3-3 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^2+2 b c \text{$\#$1}+2 a d \text{$\#$1}+3 b d \text{$\#$1}-b \sqrt{a+b} \sqrt{c+d}}\&\right]","-\frac{(b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{a} c^{5/2}}+\frac{\sqrt{a+b x} (b c-3 a d)}{a c^2 \sqrt{c+d x}}-\frac{(a+b x)^{3/2}}{a c x \sqrt{c+d x}}",1,"(((2*b*Sqrt[a + b]*d)/c - (2*a*Sqrt[a + b]*d^2)/c^2 - (2*b*d*Sqrt[a + b*x])/c + (2*a*d^2*Sqrt[a + b*x])/c^2)*(Sqrt[c + d] - Sqrt[c + d*x]))/(-(b*c^2) - b*c*d - b*c*d*x - b*d^2*x + b*c*Sqrt[c + d]*Sqrt[c + d*x] - a*d*Sqrt[c + d]*Sqrt[c + d*x] + Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]) + ((-(1/(c^2*Sqrt[c + d])) + Sqrt[a + b*x]/(Sqrt[a + b]*c^2*Sqrt[c + d]))*(Sqrt[c + d] - Sqrt[c + d*x])*(a*b*Sqrt[a + b]*c^2*Sqrt[c + d] + a^2*Sqrt[a + b]*c*d*Sqrt[c + d] + 2*a*b*Sqrt[a + b]*c*d*Sqrt[c + d] + 2*a*b*Sqrt[a + b]*c*d*Sqrt[c + d]*x + b^2*Sqrt[a + b]*c*d*Sqrt[c + d]*x + a*b*Sqrt[a + b]*d^2*Sqrt[c + d]*x + a*b*c^2*Sqrt[c + d]*Sqrt[a + b*x] + b^2*c^2*Sqrt[c + d]*Sqrt[a + b*x] - a^2*c*d*Sqrt[c + d]*Sqrt[a + b*x] - a*b*c*d*Sqrt[c + d]*Sqrt[a + b*x] - a*b*Sqrt[a + b]*c^2*Sqrt[c + d*x] + a^2*Sqrt[a + b]*c*d*Sqrt[c + d*x] - a*b*Sqrt[a + b]*c*d*Sqrt[c + d*x] + a^2*Sqrt[a + b]*d^2*Sqrt[c + d*x] - a*b*c^2*Sqrt[a + b*x]*Sqrt[c + d*x] - b^2*c^2*Sqrt[a + b*x]*Sqrt[c + d*x] - a^2*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - 2*a*b*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - b^2*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - a^2*d^2*Sqrt[a + b*x]*Sqrt[c + d*x] - a*b*d^2*Sqrt[a + b*x]*Sqrt[c + d*x]))/(x*(-2*b^2*c^2 + 2*a*b*c*d - b^2*c*d - 2*a^2*d^2 - a*b*d^2 - b^2*c*d*x - a*b*d^2*x - 2*b^2*d^2*x - 2*b*Sqrt[a + b]*c*d*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*d^2*Sqrt[a + b*x] + 2*b^2*c*Sqrt[c + d]*Sqrt[c + d*x] - 2*a*b*d*Sqrt[c + d]*Sqrt[c + d*x] + 2*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x])) + (b/(2*c) - (3*a*d)/(2*c^2))*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ]","C",1
590,-1,0,171,180.0425256,"\int \frac{\sqrt{a+b x}}{x^3 (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(x^3*(c + d*x)^(3/2)),x]","\text{\$Aborted}","\frac{\left(-15 a^2 d^2+6 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{3/2} c^{7/2}}-\frac{d \sqrt{a+b x} (b c-15 a d)}{4 a c^3 \sqrt{c+d x}}-\frac{\sqrt{a+b x} (b c-5 a d)}{4 a c^2 x \sqrt{c+d x}}-\frac{\sqrt{a+b x}}{2 c x^2 \sqrt{c+d x}}",1,"$Aborted","F",-1
591,-1,0,218,180.0432336,"\int \frac{x^3 \sqrt{a+b x}}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(x^3*Sqrt[a + b*x])/(c + d*x)^(5/2),x]","\text{\$Aborted}","-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(3 a^2 d^2-2 b d x (35 b c-31 a d)-100 a b c d+105 b^2 c^2\right)}{12 b d^4 (b c-a d)}+\frac{\left(-a^2 d^2-10 a b c d+35 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{3/2} d^{9/2}}-\frac{2 x^2 \sqrt{a+b x} (7 b c-6 a d)}{3 d^2 \sqrt{c+d x} (b c-a d)}-\frac{2 x^3 \sqrt{a+b x}}{3 d (c+d x)^{3/2}}",1,"$Aborted","F",-1
592,-1,0,165,180.0046447,"\int \frac{x^2 \sqrt{a+b x}}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(x^2*Sqrt[a + b*x])/(c + d*x)^(5/2),x]","\text{\$Aborted}","\frac{2 c^2 (a+b x)^{3/2}}{3 d^2 (c+d x)^{3/2} (b c-a d)}-\frac{(5 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b} d^{7/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (5 b c-a d)}{d^3 (b c-a d)}-\frac{4 c (a+b x)^{3/2}}{d^2 \sqrt{c+d x} (b c-a d)}",1,"$Aborted","F",-1
593,-1,0,102,180.1589906,"\int \frac{x \sqrt{a+b x}}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(x*Sqrt[a + b*x])/(c + d*x)^(5/2),x]","\text{\$Aborted}","\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{5/2}}-\frac{2 \sqrt{a+b x}}{d^2 \sqrt{c+d x}}-\frac{2 c (a+b x)^{3/2}}{3 d (c+d x)^{3/2} (b c-a d)}",1,"$Aborted","F",-1
594,1,1738,32,0.0010291,"\int \frac{\sqrt{a+b x}}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(c + d*x)^(5/2),x]","\frac{\left(\frac{\sqrt{a+b x}}{6 (c+d)^{3/2}}-\frac{\sqrt{a+b}}{6 (c+d)^{3/2}}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)^6 \left(\frac{4 a^2 d^2 \left(\sqrt{a+b}-\sqrt{a+b x}\right)^2}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^2}+\frac{24 d^2 \sqrt{c+d} \sqrt{c+d x} a^3+24 b d^3 a^2+56 b c d^2 a^2+16 b c^2 d a^2+24 b d^3 x a^2+8 b c d^2 x a^2+24 b d^2 \sqrt{c+d} x \sqrt{c+d x} a^2-24 b d^2 \sqrt{c+d} \sqrt{c+d x} a^2-16 b c d \sqrt{c+d} \sqrt{c+d x} a^2-24 \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} a^2+24 b^2 c^3 a+12 b^2 d^3 a+40 b^2 c d^2 a+24 b^2 d^3 x^2 a+16 b^2 c d^2 x^2 a+44 b^2 c^2 d a+36 b^2 d^3 x a+80 b^2 c d^2 x a+44 b^2 c^2 d x a-24 b \sqrt{a+b} d^3 \sqrt{a+b x} a-56 b \sqrt{a+b} c d^2 \sqrt{a+b x} a-16 b \sqrt{a+b} c^2 d \sqrt{a+b x} a-24 b \sqrt{a+b} d^3 x \sqrt{a+b x} a-8 b \sqrt{a+b} c d^2 x \sqrt{a+b x} a-24 b^2 d^2 \sqrt{c+d} x \sqrt{c+d x} a-32 b^2 c d \sqrt{c+d} x \sqrt{c+d x} a-24 b^2 c^2 \sqrt{c+d} \sqrt{c+d x} a-24 b^2 d^2 \sqrt{c+d} \sqrt{c+d x} a-32 b^2 c d \sqrt{c+d} \sqrt{c+d x} a-12 b \sqrt{a+b} d^2 \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x} a+36 b \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} a+16 b \sqrt{a+b} c d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} a}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4}+\frac{8 c^3 b^3+24 d^3 x^2 b^3+24 c d^2 x^2 b^3+4 c^2 d x^2 b^3+4 c^2 d b^3+8 c^3 x b^3+24 c d^2 x b^3+32 c^2 d x b^3-8 c^2 \sqrt{c+d} x \sqrt{c+d x} b^3-24 c d \sqrt{c+d} x \sqrt{c+d x} b^3-8 c^2 \sqrt{c+d} \sqrt{c+d x} b^3-8 a c^3 b^2-12 a d^3 b^2-24 a c d^2 b^2-28 a c^2 d b^2-12 a d^3 x b^2-48 a c d^2 x b^2-28 a c^2 d x b^2+8 \sqrt{a+b} c^3 \sqrt{a+b x} b^2+16 \sqrt{a+b} c^2 d \sqrt{a+b x} b^2+24 \sqrt{a+b} c d^2 x \sqrt{a+b x} b^2+16 \sqrt{a+b} c^2 d x \sqrt{a+b x} b^2+48 a d^2 \sqrt{c+d} x \sqrt{c+d x} b^2+24 a c d \sqrt{c+d} x \sqrt{c+d x} b^2+8 a c^2 \sqrt{c+d} \sqrt{c+d x} b^2+24 a d^2 \sqrt{c+d} \sqrt{c+d x} b^2+24 a c d \sqrt{c+d} \sqrt{c+d x} b^2-24 \sqrt{a+b} d^2 \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x} b^2-12 \sqrt{a+b} c d \sqrt{c+d} x \sqrt{a+b x} \sqrt{c+d x} b^2-8 \sqrt{a+b} c^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b^2-12 \sqrt{a+b} c d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b^2-24 a^2 d^3 b-48 a^2 c d^2 b-24 a^2 c^2 d b+24 a \sqrt{a+b} d^3 \sqrt{a+b x} b+48 a \sqrt{a+b} c d^2 \sqrt{a+b x} b+24 a \sqrt{a+b} c^2 d \sqrt{a+b x} b+48 a^2 d^2 \sqrt{c+d} \sqrt{c+d x} b+24 a^2 c d \sqrt{c+d} \sqrt{c+d x} b-48 a \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b-24 a \sqrt{a+b} c d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4}\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(b \sqrt{c+d} c-b \sqrt{c+d x} c+b d \sqrt{c+d} x+a d \sqrt{c+d x}-\sqrt{a+b} d \sqrt{a+b x} \sqrt{c+d x}\right)^3}","\frac{2 (a+b x)^{3/2}}{3 (c+d x)^{3/2} (b c-a d)}",1,"((-1/6*Sqrt[a + b]/(c + d)^(3/2) + Sqrt[a + b*x]/(6*(c + d)^(3/2)))*(Sqrt[c + d] - Sqrt[c + d*x])^6*((4*a^2*d^2*(Sqrt[a + b] - Sqrt[a + b*x])^2)/(Sqrt[c + d] - Sqrt[c + d*x])^2 + (24*a*b^2*c^3 + 16*a^2*b*c^2*d + 44*a*b^2*c^2*d + 56*a^2*b*c*d^2 + 40*a*b^2*c*d^2 + 24*a^2*b*d^3 + 12*a*b^2*d^3 + 44*a*b^2*c^2*d*x + 8*a^2*b*c*d^2*x + 80*a*b^2*c*d^2*x + 24*a^2*b*d^3*x + 36*a*b^2*d^3*x + 16*a*b^2*c*d^2*x^2 + 24*a*b^2*d^3*x^2 - 16*a*b*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] - 56*a*b*Sqrt[a + b]*c*d^2*Sqrt[a + b*x] - 24*a*b*Sqrt[a + b]*d^3*Sqrt[a + b*x] - 8*a*b*Sqrt[a + b]*c*d^2*x*Sqrt[a + b*x] - 24*a*b*Sqrt[a + b]*d^3*x*Sqrt[a + b*x] - 24*a*b^2*c^2*Sqrt[c + d]*Sqrt[c + d*x] - 16*a^2*b*c*d*Sqrt[c + d]*Sqrt[c + d*x] - 32*a*b^2*c*d*Sqrt[c + d]*Sqrt[c + d*x] + 24*a^3*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 24*a^2*b*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 24*a*b^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 32*a*b^2*c*d*Sqrt[c + d]*x*Sqrt[c + d*x] + 24*a^2*b*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 24*a*b^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 16*a*b*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 24*a^2*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 36*a*b*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 12*a*b*Sqrt[a + b]*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x])/(Sqrt[c + d] - Sqrt[c + d*x])^4 + (-8*a*b^2*c^3 + 8*b^3*c^3 - 24*a^2*b*c^2*d - 28*a*b^2*c^2*d + 4*b^3*c^2*d - 48*a^2*b*c*d^2 - 24*a*b^2*c*d^2 - 24*a^2*b*d^3 - 12*a*b^2*d^3 + 8*b^3*c^3*x - 28*a*b^2*c^2*d*x + 32*b^3*c^2*d*x - 48*a*b^2*c*d^2*x + 24*b^3*c*d^2*x - 12*a*b^2*d^3*x + 4*b^3*c^2*d*x^2 + 24*b^3*c*d^2*x^2 + 24*b^3*d^3*x^2 + 8*b^2*Sqrt[a + b]*c^3*Sqrt[a + b*x] + 24*a*b*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] + 16*b^2*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] + 48*a*b*Sqrt[a + b]*c*d^2*Sqrt[a + b*x] + 24*a*b*Sqrt[a + b]*d^3*Sqrt[a + b*x] + 16*b^2*Sqrt[a + b]*c^2*d*x*Sqrt[a + b*x] + 24*b^2*Sqrt[a + b]*c*d^2*x*Sqrt[a + b*x] + 8*a*b^2*c^2*Sqrt[c + d]*Sqrt[c + d*x] - 8*b^3*c^2*Sqrt[c + d]*Sqrt[c + d*x] + 24*a^2*b*c*d*Sqrt[c + d]*Sqrt[c + d*x] + 24*a*b^2*c*d*Sqrt[c + d]*Sqrt[c + d*x] + 48*a^2*b*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 24*a*b^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 8*b^3*c^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 24*a*b^2*c*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 24*b^3*c*d*Sqrt[c + d]*x*Sqrt[c + d*x] + 48*a*b^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 8*b^2*Sqrt[a + b]*c^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 24*a*b*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 12*b^2*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 48*a*b*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 12*b^2*Sqrt[a + b]*c*d*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 24*b^2*Sqrt[a + b]*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x])/(Sqrt[c + d] - Sqrt[c + d*x])^4))/((-Sqrt[c + d] + Sqrt[c + d*x])*(b*c*Sqrt[c + d] + b*d*Sqrt[c + d]*x - b*c*Sqrt[c + d*x] + a*d*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x])^3)","B",1
595,-1,0,102,180.2038944,"\int \frac{\sqrt{a+b x}}{x (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(x*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{c^{5/2}}+\frac{2 \sqrt{a+b x}}{c^2 \sqrt{c+d x}}-\frac{2 d (a+b x)^{3/2}}{3 c (c+d x)^{3/2} (b c-a d)}",1,"$Aborted","F",-1
596,-1,0,148,180.0569393,"\int \frac{\sqrt{a+b x}}{x^2 (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(x^2*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{(b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{a} c^{7/2}}-\frac{d \sqrt{a+b x} (13 b c-15 a d)}{3 c^3 \sqrt{c+d x} (b c-a d)}-\frac{5 d \sqrt{a+b x}}{3 c^2 (c+d x)^{3/2}}-\frac{\sqrt{a+b x}}{c x (c+d x)^{3/2}}",1,"$Aborted","F",-1
597,-1,0,234,180.1798459,"\int \frac{\sqrt{a+b x}}{x^3 (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(x^3*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{d \sqrt{a+b x} \left(105 a^2 d^2-100 a b c d+3 b^2 c^2\right)}{12 a c^4 \sqrt{c+d x} (b c-a d)}+\frac{\left(-35 a^2 d^2+10 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{3/2} c^{9/2}}-\frac{d \sqrt{a+b x} (3 b c-35 a d)}{12 a c^3 (c+d x)^{3/2}}-\frac{\sqrt{a+b x} (b c-7 a d)}{4 a c^2 x (c+d x)^{3/2}}-\frac{\sqrt{a+b x}}{2 c x^2 (c+d x)^{3/2}}",1,"$Aborted","F",-1
598,-1,0,315,180.0240025,"\int x^2 (a+b x)^{3/2} \sqrt{c+d x} \, dx","IntegrateAlgebraic[x^2*(a + b*x)^(3/2)*Sqrt[c + d*x],x]","\text{\$Aborted}","\frac{\left(3 a^2 d^2+6 a b c d+7 b^2 c^2\right) (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{7/2} d^{9/2}}+\frac{(a+b x)^{5/2} \sqrt{c+d x} \left(3 a^2 d^2+6 a b c d+7 b^2 c^2\right)}{48 b^3 d^2}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(3 a^2 d^2+6 a b c d+7 b^2 c^2\right) (b c-a d)^2}{128 b^3 d^4}+\frac{(a+b x)^{3/2} \sqrt{c+d x} \left(3 a^2 d^2+6 a b c d+7 b^2 c^2\right) (b c-a d)}{192 b^3 d^3}-\frac{(a+b x)^{5/2} (c+d x)^{3/2} (5 a d+7 b c)}{40 b^2 d^2}+\frac{x (a+b x)^{5/2} (c+d x)^{3/2}}{5 b d}",1,"$Aborted","F",-1
599,-1,0,221,180.0212838,"\int x (a+b x)^{3/2} \sqrt{c+d x} \, dx","IntegrateAlgebraic[x*(a + b*x)^(3/2)*Sqrt[c + d*x],x]","\text{\$Aborted}","-\frac{(3 a d+5 b c) (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{5/2} d^{7/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (3 a d+5 b c) (b c-a d)^2}{64 b^2 d^3}-\frac{(a+b x)^{3/2} \sqrt{c+d x} (3 a d+5 b c) (b c-a d)}{96 b^2 d^2}-\frac{(a+b x)^{5/2} \sqrt{c+d x} (3 a d+5 b c)}{24 b^2 d}+\frac{(a+b x)^{5/2} (c+d x)^{3/2}}{4 b d}",1,"$Aborted","F",-1
600,-1,0,154,180.0975735,"\int (a+b x)^{3/2} \sqrt{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)*Sqrt[c + d*x],x]","\text{\$Aborted}","\frac{(b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{3/2} d^{5/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 b d^2}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{12 b d}+\frac{(a+b x)^{5/2} \sqrt{c+d x}}{3 b}",1,"$Aborted","F",-1
601,-1,0,164,180.1082372,"\int \frac{(a+b x)^{3/2} \sqrt{c+d x}}{x} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*Sqrt[c + d*x])/x,x]","\text{\$Aborted}","-2 a^{3/2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)-\frac{\left(-3 a^2 d^2-6 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 \sqrt{b} d^{3/2}}+\frac{1}{2} (a+b x)^{3/2} \sqrt{c+d x}+\frac{\sqrt{a+b x} \sqrt{c+d x} (3 a d+b c)}{4 d}",1,"$Aborted","F",-1
602,1,1696,144,120.2801643,"\int \frac{(a+b x)^{3/2} \sqrt{c+d x}}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*Sqrt[c + d*x])/x^2,x]","\frac{\left(-\frac{c b^4}{\sqrt{a+b}}+\frac{2 c \sqrt{c+d x} b^4}{\sqrt{a+b} \sqrt{c+d}}+\frac{2 d \sqrt{c+d x} b^4}{\sqrt{a+b} \sqrt{c+d}}-\frac{a c b^3}{\sqrt{a+b}}+\frac{a d b^3}{\sqrt{a+b}}-c \sqrt{a+b x} b^3-2 d \sqrt{a+b x} b^3+\frac{2 a c \sqrt{c+d x} b^3}{\sqrt{a+b} \sqrt{c+d}}+\frac{2 a d \sqrt{c+d x} b^3}{\sqrt{a+b} \sqrt{c+d}}+\frac{a^2 d b^2}{\sqrt{a+b}}-a d \sqrt{a+b x} b^2\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)^3}{\left(-c b+\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}\right)^2}+\frac{\left(\frac{a \sqrt{a+b x}}{\sqrt{a+b} \sqrt{c+d}}-\frac{a}{\sqrt{c+d}}\right) \left(\sqrt{a+b} c d \sqrt{c+d} a^2-c d \sqrt{c+d} \sqrt{a+b x} a^2+\sqrt{a+b} d^2 \sqrt{c+d x} a^2+\sqrt{a+b} c d \sqrt{c+d x} a^2-d^2 \sqrt{a+b x} \sqrt{c+d x} a^2-c d \sqrt{a+b x} \sqrt{c+d x} a^2+b \sqrt{a+b} d^2 \sqrt{c+d} x a+2 b \sqrt{a+b} c d \sqrt{c+d} x a+b \sqrt{a+b} c^2 \sqrt{c+d} a+2 b \sqrt{a+b} c d \sqrt{c+d} a+b c^2 \sqrt{c+d} \sqrt{a+b x} a-b c d \sqrt{c+d} \sqrt{a+b x} a-b \sqrt{a+b} c^2 \sqrt{c+d x} a-b \sqrt{a+b} c d \sqrt{c+d x} a-b c^2 \sqrt{a+b x} \sqrt{c+d x} a-b d^2 \sqrt{a+b x} \sqrt{c+d x} a-2 b c d \sqrt{a+b x} \sqrt{c+d x} a+b^2 \sqrt{a+b} c d \sqrt{c+d} x+b^2 c^2 \sqrt{c+d} \sqrt{a+b x}-b^2 c^2 \sqrt{a+b x} \sqrt{c+d x}-b^2 c d \sqrt{a+b x} \sqrt{c+d x}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{x \left(-2 c^2 b^2-c d b^2-2 d^2 x b^2-c d x b^2+2 c \sqrt{c+d} \sqrt{c+d x} b^2-a d^2 b+2 a c d b-a d^2 x b-2 \sqrt{a+b} c d \sqrt{a+b x} b-2 a d \sqrt{c+d} \sqrt{c+d x} b+2 \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b-2 a^2 d^2+2 a \sqrt{a+b} d^2 \sqrt{a+b x}\right)}+\left(\frac{2 c b^{3/2}}{\sqrt{d}}+6 a \sqrt{d} \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{a+b} \sqrt{d}-\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \left(\sqrt{c+d}-\sqrt{c+d x}\right)}\right)+\left(\frac{d a^2}{2}+\frac{3 b c a}{2}\right) \text{RootSum}\left[d^2 \text{$\#$1}^4-4 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^3+4 b c \text{$\#$1}^2+4 a d \text{$\#$1}^2+6 b d \text{$\#$1}^2-4 b \sqrt{a+b} \sqrt{c+d} \text{$\#$1}+b^2\&,\frac{d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2-d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2-b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)+b \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right)}{d^2 \text{$\#$1}^3-3 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^2+2 b c \text{$\#$1}+2 a d \text{$\#$1}+3 b d \text{$\#$1}-b \sqrt{a+b} \sqrt{c+d}}\&\right]+\frac{\left(d \sqrt{c+d} a^2-3 b c \sqrt{c+d} a-b d \sqrt{c+d} a-\sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} a+4 b c \sqrt{c+d x} a+4 b d \sqrt{c+d x} a-3 b^2 c \sqrt{c+d}-2 b^2 d \sqrt{c+d}-b \sqrt{a+b} c \sqrt{c+d} \sqrt{a+b x}-2 b \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x}+4 b^2 c \sqrt{c+d x}+4 b^2 d \sqrt{c+d x}\right) \left(\frac{b}{\sqrt{a+b}}-\frac{b \sqrt{c+d x}}{\sqrt{a+b} \sqrt{c+d}}\right)}{-c b+\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}}","-\frac{(a+b x)^{3/2} \sqrt{c+d x}}{x}+2 b \sqrt{a+b x} \sqrt{c+d x}-\frac{\sqrt{a} (a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{c}}+\frac{\sqrt{b} (3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{d}}",1,"((Sqrt[c + d] - Sqrt[c + d*x])^3*(-((a*b^3*c)/Sqrt[a + b]) - (b^4*c)/Sqrt[a + b] + (a^2*b^2*d)/Sqrt[a + b] + (a*b^3*d)/Sqrt[a + b] - b^3*c*Sqrt[a + b*x] - a*b^2*d*Sqrt[a + b*x] - 2*b^3*d*Sqrt[a + b*x] + (2*a*b^3*c*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[c + d]) + (2*b^4*c*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[c + d]) + (2*a*b^3*d*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[c + d]) + (2*b^4*d*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[c + d])))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^2 + ((-3*a*b*c*Sqrt[c + d] - 3*b^2*c*Sqrt[c + d] + a^2*d*Sqrt[c + d] - a*b*d*Sqrt[c + d] - 2*b^2*d*Sqrt[c + d] - b*Sqrt[a + b]*c*Sqrt[c + d]*Sqrt[a + b*x] - a*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x] + 4*a*b*c*Sqrt[c + d*x] + 4*b^2*c*Sqrt[c + d*x] + 4*a*b*d*Sqrt[c + d*x] + 4*b^2*d*Sqrt[c + d*x])*(b/Sqrt[a + b] - (b*Sqrt[c + d*x])/(Sqrt[a + b]*Sqrt[c + d])))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x]) + ((-(a/Sqrt[c + d]) + (a*Sqrt[a + b*x])/(Sqrt[a + b]*Sqrt[c + d]))*(Sqrt[c + d] - Sqrt[c + d*x])*(a*b*Sqrt[a + b]*c^2*Sqrt[c + d] + a^2*Sqrt[a + b]*c*d*Sqrt[c + d] + 2*a*b*Sqrt[a + b]*c*d*Sqrt[c + d] + 2*a*b*Sqrt[a + b]*c*d*Sqrt[c + d]*x + b^2*Sqrt[a + b]*c*d*Sqrt[c + d]*x + a*b*Sqrt[a + b]*d^2*Sqrt[c + d]*x + a*b*c^2*Sqrt[c + d]*Sqrt[a + b*x] + b^2*c^2*Sqrt[c + d]*Sqrt[a + b*x] - a^2*c*d*Sqrt[c + d]*Sqrt[a + b*x] - a*b*c*d*Sqrt[c + d]*Sqrt[a + b*x] - a*b*Sqrt[a + b]*c^2*Sqrt[c + d*x] + a^2*Sqrt[a + b]*c*d*Sqrt[c + d*x] - a*b*Sqrt[a + b]*c*d*Sqrt[c + d*x] + a^2*Sqrt[a + b]*d^2*Sqrt[c + d*x] - a*b*c^2*Sqrt[a + b*x]*Sqrt[c + d*x] - b^2*c^2*Sqrt[a + b*x]*Sqrt[c + d*x] - a^2*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - 2*a*b*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - b^2*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - a^2*d^2*Sqrt[a + b*x]*Sqrt[c + d*x] - a*b*d^2*Sqrt[a + b*x]*Sqrt[c + d*x]))/(x*(-2*b^2*c^2 + 2*a*b*c*d - b^2*c*d - 2*a^2*d^2 - a*b*d^2 - b^2*c*d*x - a*b*d^2*x - 2*b^2*d^2*x - 2*b*Sqrt[a + b]*c*d*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*d^2*Sqrt[a + b*x] + 2*b^2*c*Sqrt[c + d]*Sqrt[c + d*x] - 2*a*b*d*Sqrt[c + d]*Sqrt[c + d*x] + 2*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x])) + ((2*b^(3/2)*c)/Sqrt[d] + 6*a*Sqrt[b]*Sqrt[d])*ArcTanh[(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*(Sqrt[c + d] - Sqrt[c + d*x]))] + ((3*a*b*c)/2 + (a^2*d)/2)*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ]","C",1
603,-1,0,171,180.1266298,"\int \frac{(a+b x)^{3/2} \sqrt{c+d x}}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*Sqrt[c + d*x])/x^3,x]","\text{\$Aborted}","-\frac{\left(-a^2 d^2+6 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 \sqrt{a} c^{3/2}}+2 b^{3/2} \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)-\frac{(a+b x)^{3/2} \sqrt{c+d x}}{2 x^2}-\frac{\sqrt{a+b x} \sqrt{c+d x} (a d+3 b c)}{4 c x}",1,"$Aborted","F",-1
604,-1,0,160,180.1344832,"\int \frac{(a+b x)^{3/2} \sqrt{c+d x}}{x^4} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*Sqrt[c + d*x])/x^4,x]","\text{\$Aborted}","\frac{(b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 a^{3/2} c^{5/2}}-\frac{\sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}{4 c^2 x^2}-\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 a c^2 x}-\frac{(a+b x)^{3/2} (c+d x)^{3/2}}{3 c x^3}",1,"$Aborted","F",-1
605,-1,0,233,180.0228009,"\int \frac{(a+b x)^{3/2} \sqrt{c+d x}}{x^5} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*Sqrt[c + d*x])/x^5,x]","\text{\$Aborted}","-\frac{(5 a d+3 b c) (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{5/2} c^{7/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (5 a d+3 b c) (b c-a d)^2}{64 a^2 c^3 x}+\frac{\sqrt{a+b x} (c+d x)^{3/2} (5 a d+3 b c) (b c-a d)}{32 a c^3 x^2}+\frac{(a+b x)^{3/2} (c+d x)^{3/2} (5 a d+3 b c)}{24 a c^2 x^3}-\frac{(a+b x)^{5/2} (c+d x)^{3/2}}{4 a c x^4}",1,"$Aborted","F",-1
606,-1,0,340,180.0735664,"\int \frac{(a+b x)^{3/2} \sqrt{c+d x}}{x^6} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*Sqrt[c + d*x])/x^6,x]","\text{\$Aborted}","\frac{\left(7 a^2 d^2+6 a b c d+3 b^2 c^2\right) (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{128 a^{7/2} c^{9/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-35 a^3 d^3+61 a^2 b c d^2-9 a b^2 c^2 d+15 b^3 c^3\right)}{960 a^2 c^3 x^2}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-105 a^4 d^4+190 a^3 b c d^3-36 a^2 b^2 c^2 d^2-30 a b^3 c^3 d+45 b^4 c^4\right)}{1920 a^3 c^4 x}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(\frac{3 b^2 c}{a}-\frac{7 a d^2}{c}+12 b d\right)}{240 c x^3}-\frac{(a+b x)^{3/2} \sqrt{c+d x}}{5 x^5}-\frac{\sqrt{a+b x} \sqrt{c+d x} (a d+3 b c)}{40 c x^4}",1,"$Aborted","F",-1
607,-1,0,349,180.0368238,"\int x^2 (a+b x)^{3/2} (c+d x)^{3/2} \, dx","IntegrateAlgebraic[x^2*(a + b*x)^(3/2)*(c + d*x)^(3/2),x]","\text{\$Aborted}","-\frac{\left(4 a b c d-7 (a d+b c)^2\right) (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{512 b^{9/2} d^{9/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(4 a b c d-7 (a d+b c)^2\right) (b c-a d)^3}{512 b^4 d^4}-\frac{(a+b x)^{3/2} \sqrt{c+d x} \left(4 a b c d-7 (a d+b c)^2\right) (b c-a d)^2}{768 b^4 d^3}-\frac{(a+b x)^{5/2} \sqrt{c+d x} \left(4 a b c d-7 (a d+b c)^2\right) (b c-a d)}{192 b^4 d^2}-\frac{(a+b x)^{5/2} (c+d x)^{3/2} \left(4 a b c d-7 (a d+b c)^2\right)}{96 b^3 d^2}-\frac{7 (a+b x)^{5/2} (c+d x)^{5/2} (a d+b c)}{60 b^2 d^2}+\frac{x (a+b x)^{5/2} (c+d x)^{5/2}}{6 b d}",1,"$Aborted","F",-1
608,-1,0,258,180.0269029,"\int x (a+b x)^{3/2} (c+d x)^{3/2} \, dx","IntegrateAlgebraic[x*(a + b*x)^(3/2)*(c + d*x)^(3/2),x]","\text{\$Aborted}","-\frac{3 (a d+b c) (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{7/2} d^{7/2}}+\frac{3 \sqrt{a+b x} \sqrt{c+d x} (a d+b c) (b c-a d)^3}{128 b^3 d^3}-\frac{(a+b x)^{3/2} \sqrt{c+d x} (a d+b c) (b c-a d)^2}{64 b^3 d^2}-\frac{(a+b x)^{5/2} \sqrt{c+d x} (a d+b c) (b c-a d)}{16 b^3 d}-\frac{(a+b x)^{5/2} (c+d x)^{3/2} (a d+b c)}{8 b^2 d}+\frac{(a+b x)^{5/2} (c+d x)^{5/2}}{5 b d}",1,"$Aborted","F",-1
609,-1,0,189,180.0190019,"\int (a+b x)^{3/2} (c+d x)^{3/2} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)*(c + d*x)^(3/2),x]","\text{\$Aborted}","\frac{3 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{5/2} d^{5/2}}-\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 b^2 d^2}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}{32 b^2 d}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)}{8 b^2}+\frac{(a+b x)^{5/2} (c+d x)^{3/2}}{4 b}",1,"$Aborted","F",-1
610,-1,0,213,180.2939704,"\int \frac{(a+b x)^{3/2} (c+d x)^{3/2}}{x} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(c + d*x)^(3/2))/x,x]","\text{\$Aborted}","-2 a^{3/2} c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)-\frac{(a d+b c) \left(a^2 d^2-10 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{3/2} d^{3/2}}+\frac{1}{8} \sqrt{a+b x} \sqrt{c+d x} \left(\frac{a^2 d}{b}+8 a c-\frac{b c^2}{d}\right)+\frac{1}{3} (a+b x)^{3/2} (c+d x)^{3/2}+\frac{\sqrt{a+b x} (c+d x)^{3/2} (a d+b c)}{4 d}",1,"$Aborted","F",-1
611,-1,0,191,180.0431612,"\int \frac{(a+b x)^{3/2} (c+d x)^{3/2}}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(c + d*x)^(3/2))/x^2,x]","\text{\$Aborted}","\frac{3 \left(a^2 d^2+6 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 \sqrt{b} \sqrt{d}}-\frac{(a+b x)^{3/2} (c+d x)^{3/2}}{x}+\frac{3}{2} b \sqrt{a+b x} (c+d x)^{3/2}+\frac{3}{4} \sqrt{a+b x} \sqrt{c+d x} (3 a d+b c)-3 \sqrt{a} \sqrt{c} (a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)",1,"$Aborted","F",-1
612,-1,0,209,180.0365199,"\int \frac{(a+b x)^{3/2} (c+d x)^{3/2}}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(c + d*x)^(3/2))/x^3,x]","\text{\$Aborted}","-\frac{3 \left(a^2 d^2+6 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 \sqrt{a} \sqrt{c}}-\frac{(a+b x)^{3/2} (c+d x)^{3/2}}{2 x^2}-\frac{3 \sqrt{a+b x} (c+d x)^{3/2} (a d+b c)}{4 c x}+\frac{3 d \sqrt{a+b x} \sqrt{c+d x} (a d+3 b c)}{4 c}+3 \sqrt{b} \sqrt{d} (a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)",1,"$Aborted","F",-1
613,-1,0,222,180.0480693,"\int \frac{(a+b x)^{3/2} (c+d x)^{3/2}}{x^4} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(c + d*x)^(3/2))/x^4,x]","\text{\$Aborted}","\frac{(a d+b c) \left(a^2 d^2-10 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 a^{3/2} c^{3/2}}+2 b^{3/2} d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(\frac{b^2 c}{a}-\frac{a d^2}{c}+8 b d\right)}{8 x}-\frac{(a+b x)^{3/2} (c+d x)^{3/2}}{3 x^3}-\frac{\sqrt{a+b x} (c+d x)^{3/2} (a d+b c)}{4 c x^2}",1,"$Aborted","F",-1
614,-1,0,201,180.0167759,"\int \frac{(a+b x)^{3/2} (c+d x)^{3/2}}{x^5} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(c + d*x)^(3/2))/x^5,x]","\text{\$Aborted}","-\frac{3 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{5/2} c^{5/2}}+\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 a^2 c^2 x}-\frac{\sqrt{a+b x} (c+d x)^{5/2} (b c-a d)}{8 c^2 x^3}-\frac{\sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^2}{32 a c^2 x^2}-\frac{(a+b x)^{3/2} (c+d x)^{5/2}}{4 c x^4}",1,"$Aborted","F",-1
615,-1,0,273,180.0746205,"\int \frac{(a+b x)^{3/2} (c+d x)^{3/2}}{x^6} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(c + d*x)^(3/2))/x^6,x]","\text{\$Aborted}","\frac{3 (a d+b c) (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{128 a^{7/2} c^{7/2}}-\frac{3 \sqrt{a+b x} \sqrt{c+d x} (a d+b c) (b c-a d)^3}{128 a^3 c^3 x}+\frac{\sqrt{a+b x} (c+d x)^{3/2} (a d+b c) (b c-a d)^2}{64 a^2 c^3 x^2}+\frac{\sqrt{a+b x} (c+d x)^{5/2} (a d+b c) (b c-a d)}{16 a c^3 x^3}+\frac{(a+b x)^{3/2} (c+d x)^{5/2} (a d+b c)}{8 a c^2 x^4}-\frac{(a+b x)^{5/2} (c+d x)^{5/2}}{5 a c x^5}",1,"$Aborted","F",-1
616,-1,0,437,180.0627836,"\int x^2 (a+b x)^{3/2} (c+d x)^{5/2} \, dx","IntegrateAlgebraic[x^2*(a + b*x)^(3/2)*(c + d*x)^(5/2),x]","\text{\$Aborted}","\frac{\left(9 a^2 d^2+10 a b c d+5 b^2 c^2\right) (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{1024 b^{11/2} d^{9/2}}+\frac{(a+b x)^{5/2} \sqrt{c+d x} \left(9 a^2 d^2+10 a b c d+5 b^2 c^2\right) (b c-a d)^2}{384 b^5 d^2}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(9 a^2 d^2+10 a b c d+5 b^2 c^2\right) (b c-a d)^4}{1024 b^5 d^4}+\frac{(a+b x)^{3/2} \sqrt{c+d x} \left(9 a^2 d^2+10 a b c d+5 b^2 c^2\right) (b c-a d)^3}{1536 b^5 d^3}+\frac{(a+b x)^{5/2} (c+d x)^{3/2} \left(9 a^2 d^2+10 a b c d+5 b^2 c^2\right) (b c-a d)}{192 b^4 d^2}+\frac{(a+b x)^{5/2} (c+d x)^{5/2} \left(9 a^2 d^2+10 a b c d+5 b^2 c^2\right)}{120 b^3 d^2}-\frac{(a+b x)^{5/2} (c+d x)^{7/2} (9 a d+7 b c)}{84 b^2 d^2}+\frac{x (a+b x)^{5/2} (c+d x)^{7/2}}{7 b d}",1,"$Aborted","F",-1
617,-1,0,315,180.0371021,"\int x (a+b x)^{3/2} (c+d x)^{5/2} \, dx","IntegrateAlgebraic[x*(a + b*x)^(3/2)*(c + d*x)^(5/2),x]","\text{\$Aborted}","-\frac{(7 a d+5 b c) (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{512 b^{9/2} d^{7/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (7 a d+5 b c) (b c-a d)^4}{512 b^4 d^3}-\frac{(a+b x)^{3/2} \sqrt{c+d x} (7 a d+5 b c) (b c-a d)^3}{768 b^4 d^2}-\frac{(a+b x)^{5/2} \sqrt{c+d x} (7 a d+5 b c) (b c-a d)^2}{192 b^4 d}-\frac{(a+b x)^{5/2} (c+d x)^{3/2} (7 a d+5 b c) (b c-a d)}{96 b^3 d}-\frac{(a+b x)^{5/2} (c+d x)^{5/2} (7 a d+5 b c)}{60 b^2 d}+\frac{(a+b x)^{5/2} (c+d x)^{7/2}}{6 b d}",1,"$Aborted","F",-1
618,-1,0,224,180.0229408,"\int (a+b x)^{3/2} (c+d x)^{5/2} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)*(c + d*x)^(5/2),x]","\text{\$Aborted}","\frac{3 (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{7/2} d^{5/2}}-\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^4}{128 b^3 d^2}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^3}{64 b^3 d}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^2}{16 b^3}+\frac{(a+b x)^{5/2} (c+d x)^{3/2} (b c-a d)}{8 b^2}+\frac{(a+b x)^{5/2} (c+d x)^{5/2}}{5 b}",1,"$Aborted","F",-1
619,-1,0,304,180.0157495,"\int \frac{(a+b x)^{3/2} (c+d x)^{5/2}}{x} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(c + d*x)^(5/2))/x,x]","\text{\$Aborted}","-2 a^{3/2} c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\frac{1}{96} \sqrt{a+b x} (c+d x)^{3/2} \left(\frac{3 a^2 d}{b}+50 a c-\frac{5 b c^2}{d}\right)-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(3 a^3 d^3-17 a^2 b c d^2-55 a b^2 c^2 d+5 b^3 c^3\right)}{64 b^2 d}-\frac{\left(-3 a^4 d^4+20 a^3 b c d^3-90 a^2 b^2 c^2 d^2-60 a b^3 c^3 d+5 b^4 c^4\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{5/2} d^{3/2}}+\frac{1}{4} (a+b x)^{3/2} (c+d x)^{5/2}+\frac{\sqrt{a+b x} (c+d x)^{5/2} (3 a d+5 b c)}{24 d}",1,"$Aborted","F",-1
620,-1,0,257,180.0523832,"\int \frac{(a+b x)^{3/2} (c+d x)^{5/2}}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^2,x]","\text{\$Aborted}","\frac{\sqrt{a+b x} \sqrt{c+d x} \left(a^2 d^2+26 a b c d+5 b^2 c^2\right)}{8 b}+\frac{\left(-a^3 d^3+15 a^2 b c d^2+45 a b^2 c^2 d+5 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{3/2} \sqrt{d}}-\sqrt{a} c^{3/2} (5 a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)-\frac{(a+b x)^{3/2} (c+d x)^{5/2}}{x}+\frac{4}{3} b \sqrt{a+b x} (c+d x)^{5/2}+\frac{1}{12} \sqrt{a+b x} (c+d x)^{3/2} (19 a d+5 b c)",1,"$Aborted","F",-1
621,-1,0,258,180.0659671,"\int \frac{(a+b x)^{3/2} (c+d x)^{5/2}}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^3,x]","\text{\$Aborted}","-\frac{3 \sqrt{c} \left(5 a^2 d^2+10 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 \sqrt{a}}+\frac{3 \sqrt{d} \left(a^2 d^2+10 a b c d+5 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 \sqrt{b}}-\frac{(a+b x)^{3/2} (c+d x)^{5/2}}{2 x^2}-\frac{\sqrt{a+b x} (c+d x)^{5/2} (5 a d+3 b c)}{4 c x}+\frac{d \sqrt{a+b x} (c+d x)^{3/2} (5 a d+7 b c)}{4 c}+3 d \sqrt{a+b x} \sqrt{c+d x} (a d+b c)",1,"$Aborted","F",-1
622,-1,0,292,180.0893149,"\int \frac{(a+b x)^{3/2} (c+d x)^{5/2}}{x^4} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^4,x]","\text{\$Aborted}","\frac{d \sqrt{a+b x} \sqrt{c+d x} \left(5 a^2 d^2+26 a b c d+b^2 c^2\right)}{8 a c}+\frac{\left(-5 a^3 d^3-45 a^2 b c d^2-15 a b^2 c^2 d+b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 a^{3/2} \sqrt{c}}-\frac{\sqrt{a+b x} (c+d x)^{3/2} \left(\frac{3 b^2 c}{a}+\frac{5 a d^2}{c}+40 b d\right)}{24 x}+\sqrt{b} d^{3/2} (3 a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)-\frac{(a+b x)^{3/2} (c+d x)^{5/2}}{3 x^3}-\frac{\sqrt{a+b x} (c+d x)^{5/2} (5 a d+3 b c)}{12 c x^2}",1,"$Aborted","F",-1
623,-1,0,316,180.1120897,"\int \frac{(a+b x)^{3/2} (c+d x)^{5/2}}{x^5} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^5,x]","\text{\$Aborted}","\frac{\sqrt{a+b x} \sqrt{c+d x} \left(5 a^3 d^3-55 a^2 b c d^2-17 a b^2 c^2 d+3 b^3 c^3\right)}{64 a^2 c x}-\frac{\left(-5 a^4 d^4+60 a^3 b c d^3+90 a^2 b^2 c^2 d^2-20 a b^3 c^3 d+3 b^4 c^4\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{5/2} c^{3/2}}+2 b^{3/2} d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)-\frac{\sqrt{a+b x} (c+d x)^{3/2} \left(\frac{3 b^2 c}{a}-\frac{5 a d^2}{c}+50 b d\right)}{96 x^2}-\frac{(a+b x)^{3/2} (c+d x)^{5/2}}{4 x^4}-\frac{\sqrt{a+b x} (c+d x)^{5/2} (5 a d+3 b c)}{24 c x^3}",1,"$Aborted","F",-1
624,-1,0,242,180.0687762,"\int \frac{(a+b x)^{3/2} (c+d x)^{5/2}}{x^6} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^6,x]","\text{\$Aborted}","\frac{3 (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{128 a^{7/2} c^{5/2}}-\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^4}{128 a^3 c^2 x}+\frac{\sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^3}{64 a^2 c^2 x^2}-\frac{3 \sqrt{a+b x} (c+d x)^{7/2} (b c-a d)}{40 c^2 x^4}-\frac{\sqrt{a+b x} (c+d x)^{5/2} (b c-a d)^2}{80 a c^2 x^3}-\frac{(a+b x)^{3/2} (c+d x)^{7/2}}{5 c x^5}",1,"$Aborted","F",-1
625,-1,0,333,180.11243,"\int \frac{(a+b x)^{3/2} (c+d x)^{5/2}}{x^7} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^7,x]","\text{\$Aborted}","-\frac{(5 a d+7 b c) (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{512 a^{9/2} c^{7/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (5 a d+7 b c) (b c-a d)^4}{512 a^4 c^3 x}-\frac{\sqrt{a+b x} (c+d x)^{3/2} (5 a d+7 b c) (b c-a d)^3}{768 a^3 c^3 x^2}+\frac{\sqrt{a+b x} (c+d x)^{5/2} (5 a d+7 b c) (b c-a d)^2}{960 a^2 c^3 x^3}+\frac{\sqrt{a+b x} (c+d x)^{7/2} (5 a d+7 b c) (b c-a d)}{160 a c^3 x^4}+\frac{(a+b x)^{3/2} (c+d x)^{7/2} (5 a d+7 b c)}{60 a c^2 x^5}-\frac{(a+b x)^{5/2} (c+d x)^{7/2}}{6 a c x^6}",1,"$Aborted","F",-1
626,-1,0,254,180.0113941,"\int \frac{x^2 (a+b x)^{3/2}}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(x^2*(a + b*x)^(3/2))/Sqrt[c + d*x],x]","\text{\$Aborted}","-\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d) \left(3 a^2 d^2+10 a b c d+35 b^2 c^2\right)}{64 b^2 d^4}+\frac{(a+b x)^{3/2} \sqrt{c+d x} \left(3 a^2 d^2+10 a b c d+35 b^2 c^2\right)}{96 b^2 d^3}+\frac{(b c-a d)^2 \left(3 a^2 d^2+10 a b c d+35 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{5/2} d^{9/2}}-\frac{(a+b x)^{5/2} \sqrt{c+d x} (3 a d+7 b c)}{24 b^2 d^2}+\frac{x (a+b x)^{5/2} \sqrt{c+d x}}{4 b d}",1,"$Aborted","F",-1
627,-1,0,171,180.0924888,"\int \frac{x (a+b x)^{3/2}}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(x*(a + b*x)^(3/2))/Sqrt[c + d*x],x]","\text{\$Aborted}","-\frac{(b c-a d)^2 (a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{3/2} d^{7/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d) (a d+5 b c)}{8 b d^3}-\frac{(a+b x)^{3/2} \sqrt{c+d x} (a d+5 b c)}{12 b d^2}+\frac{(a+b x)^{5/2} \sqrt{c+d x}}{3 b d}",1,"$Aborted","F",-1
628,1,2910,113,0.0010019,"\int \frac{(a+b x)^{3/2}}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/Sqrt[c + d*x],x]","\text{Result too large to show}","\frac{3 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 \sqrt{b} d^{5/2}}-\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 d^2}+\frac{(a+b x)^{3/2} \sqrt{c+d x}}{2 d}",1,"((-1/4*Sqrt[a + b]/d^2 + Sqrt[a + b*x]/(4*d^2))*(Sqrt[c + d] - Sqrt[c + d*x])*(12*b^5*c^5 - 46*a*b^4*c^4*d + 7*b^5*c^4*d + 66*a^2*b^3*c^3*d^2 - 26*a*b^4*c^3*d^2 - 7*b^5*c^3*d^2 - 78*a^3*b^2*c^2*d^3 - 18*a^2*b^3*c^2*d^3 - a*b^4*c^2*d^3 - 2*b^5*c^2*d^3 + 34*a^4*b*c*d^4 - 10*a^3*b^2*c*d^4 - 41*a^2*b^3*c*d^4 - 12*a*b^4*c*d^4 - 20*a^5*d^5 - 33*a^4*b*d^5 - 15*a^3*b^2*d^5 - 2*a^2*b^3*d^5 + 7*b^5*c^4*d*x - 26*a*b^4*c^3*d^2*x + 16*b^5*c^3*d^2*x - 18*a^2*b^3*c^2*d^3*x - 112*a*b^4*c^2*d^3*x - 16*b^5*c^2*d^3*x - 10*a^3*b^2*c*d^4*x + 16*a^2*b^3*c*d^4*x - 48*a*b^4*c*d^4*x - 16*b^5*c*d^4*x - 33*a^4*b*d^5*x - 112*a^3*b^2*d^5*x - 80*a^2*b^3*d^5*x - 16*a*b^4*d^5*x - 7*b^5*c^3*d^2*x^2 - a*b^4*c^2*d^3*x^2 - 16*b^5*c^2*d^3*x^2 - 41*a^2*b^3*c*d^4*x^2 - 48*a*b^4*c*d^4*x^2 - 16*b^5*c*d^4*x^2 - 15*a^3*b^2*d^5*x^2 - 80*a^2*b^3*d^5*x^2 - 80*a*b^4*d^5*x^2 - 16*b^5*d^5*x^2 - 2*b^5*c^2*d^3*x^3 - 12*a*b^4*c*d^4*x^3 - 16*b^5*c*d^4*x^3 - 2*a^2*b^3*d^5*x^3 - 16*a*b^4*d^5*x^3 - 16*b^5*d^5*x^3 + 22*b^4*Sqrt[a + b]*c^4*d*Sqrt[a + b*x] - 86*a*b^3*Sqrt[a + b]*c^3*d^2*Sqrt[a + b*x] + b^4*Sqrt[a + b]*c^3*d^2*Sqrt[a + b*x] + 78*a^2*b^2*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] - 51*a*b^3*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] - 18*b^4*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] - 34*a^3*b*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] + 27*a^2*b^2*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] + 12*a*b^3*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] + 20*a^4*Sqrt[a + b]*d^5*Sqrt[a + b*x] + 23*a^3*b*Sqrt[a + b]*d^5*Sqrt[a + b*x] + 6*a^2*b^2*Sqrt[a + b]*d^5*Sqrt[a + b*x] + b^4*Sqrt[a + b]*c^3*d^2*x*Sqrt[a + b*x] - 51*a*b^3*Sqrt[a + b]*c^2*d^3*x*Sqrt[a + b*x] - 12*b^4*Sqrt[a + b]*c^2*d^3*x*Sqrt[a + b*x] + 27*a^2*b^2*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] - 72*a*b^3*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] - 24*b^4*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] + 23*a^3*b*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] + 84*a^2*b^2*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] + 24*a*b^3*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] - 18*b^4*Sqrt[a + b]*c^2*d^3*x^2*Sqrt[a + b*x] + 12*a*b^3*Sqrt[a + b]*c*d^4*x^2*Sqrt[a + b*x] - 24*b^4*Sqrt[a + b]*c*d^4*x^2*Sqrt[a + b*x] + 6*a^2*b^2*Sqrt[a + b]*d^5*x^2*Sqrt[a + b*x] + 24*a*b^3*Sqrt[a + b]*d^5*x^2*Sqrt[a + b*x] - 12*b^5*c^4*Sqrt[c + d]*Sqrt[c + d*x] + 46*a*b^4*c^3*d*Sqrt[c + d]*Sqrt[c + d*x] - b^5*c^3*d*Sqrt[c + d]*Sqrt[c + d*x] - 66*a^2*b^3*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 3*a*b^4*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 6*b^5*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 90*a^3*b^2*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 69*a^2*b^3*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 12*a*b^4*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] - 58*a^4*b*d^4*Sqrt[c + d]*Sqrt[c + d*x] - 71*a^3*b^2*d^4*Sqrt[c + d]*Sqrt[c + d*x] - 18*a^2*b^3*d^4*Sqrt[c + d]*Sqrt[c + d*x] - b^5*c^3*d*Sqrt[c + d]*x*Sqrt[c + d*x] + 3*a*b^4*c^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 12*b^5*c^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 69*a^2*b^3*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] + 120*a*b^4*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] + 24*b^5*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] - 71*a^3*b^2*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] - 108*a^2*b^3*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] - 24*a*b^4*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] + 6*b^5*c^2*d^2*Sqrt[c + d]*x^2*Sqrt[c + d*x] + 12*a*b^4*c*d^3*Sqrt[c + d]*x^2*Sqrt[c + d*x] + 24*b^5*c*d^3*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 18*a^2*b^3*d^4*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 24*a*b^4*d^4*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 22*b^4*Sqrt[a + b]*c^3*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 86*a*b^3*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 10*b^4*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 90*a^2*b^2*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 4*a*b^3*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 8*b^4*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 58*a^3*b*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 42*a^2*b^2*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 8*a*b^3*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 10*b^4*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 4*a*b^3*Sqrt[a + b]*c*d^3*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 42*a^2*b^2*Sqrt[a + b]*d^4*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 64*a*b^3*Sqrt[a + b]*d^4*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 16*b^4*Sqrt[a + b]*d^4*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 8*b^4*Sqrt[a + b]*c*d^3*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x] + 8*a*b^3*Sqrt[a + b]*d^4*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x] + 16*b^4*Sqrt[a + b]*d^4*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^4 + (3*(b*c - a*d)^2*ArcTanh[((Sqrt[a + b]*Sqrt[d])/Sqrt[b] - (Sqrt[d]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[c + d] - Sqrt[c + d*x])])/(2*Sqrt[b]*d^(5/2))","B",1
629,1,1523,116,83.2681875,"\int \frac{(a+b x)^{3/2}}{x \sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(x*Sqrt[c + d*x]),x]","-\frac{1}{2} \text{RootSum}\left[d^4 \text{$\#$1}^8-8 a d^3 \text{$\#$1}^6-4 b d^3 \text{$\#$1}^6-16 a c d^2 \text{$\#$1}^6-8 b c d^2 \text{$\#$1}^6+16 b^2 c^2 \text{$\#$1}^4+16 a^2 d^2 \text{$\#$1}^4+6 b^2 d^2 \text{$\#$1}^4+16 a b d^2 \text{$\#$1}^4+16 b^2 c d \text{$\#$1}^4-8 b^3 c \text{$\#$1}^2-16 a b^2 c \text{$\#$1}^2-4 b^3 d \text{$\#$1}^2-8 a b^2 d \text{$\#$1}^2+b^4\&,\frac{-d^3 \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^6+d^3 \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^6-4 \sqrt{a+b} d^2 \sqrt{c+d} \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^5+4 \sqrt{a+b} d^2 \sqrt{c+d} \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^5-4 a d^2 \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^4-5 b d^2 \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^4-4 b c d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^4+4 a d^2 \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^4+5 b d^2 \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^4+4 b c d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^4+4 b^2 c \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2+5 b^2 d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2+4 a b d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2-4 b^2 c \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2-5 b^2 d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2-4 a b d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2+4 b^2 \sqrt{a+b} \sqrt{c+d} \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}-4 b^2 \sqrt{a+b} \sqrt{c+d} \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}+b^3 \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)-b^3 \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right)}{d^4 \text{$\#$1}^7-6 a d^3 \text{$\#$1}^5-3 b d^3 \text{$\#$1}^5-12 a c d^2 \text{$\#$1}^5-6 b c d^2 \text{$\#$1}^5+8 b^2 c^2 \text{$\#$1}^3+8 a^2 d^2 \text{$\#$1}^3+3 b^2 d^2 \text{$\#$1}^3+8 a b d^2 \text{$\#$1}^3+8 b^2 c d \text{$\#$1}^3-2 b^3 c \text{$\#$1}-4 a b^2 c \text{$\#$1}-b^3 d \text{$\#$1}-2 a b^2 d \text{$\#$1}}\&\right] a^2+\frac{\left(\frac{b \sqrt{a+b}}{d}-\frac{b \sqrt{a+b x}}{d}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(c^2 b^2+c d b^2+2 d^2 x b^2+c d x b^2-c \sqrt{c+d} \sqrt{c+d x} b^2+a d^2 b+a d^2 x b+\sqrt{a+b} c d \sqrt{a+b x} b+a d \sqrt{c+d} \sqrt{c+d x} b-2 \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b+a^2 d^2-a \sqrt{a+b} d^2 \sqrt{a+b x}\right)}{\left(-c b+\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}\right)^2}+\left(\frac{6 a \sqrt{b}}{\sqrt{d}}-\frac{2 b^{3/2} c}{d^{3/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{a+b} \sqrt{d}-\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \left(\sqrt{c+d}-\sqrt{c+d x}\right)}\right)","-\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{c}}-\frac{\sqrt{b} (b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{3/2}}+\frac{b \sqrt{a+b x} \sqrt{c+d x}}{d}",1,"(((b*Sqrt[a + b])/d - (b*Sqrt[a + b*x])/d)*(Sqrt[c + d] - Sqrt[c + d*x])*(b^2*c^2 + b^2*c*d + a^2*d^2 + a*b*d^2 + b^2*c*d*x + a*b*d^2*x + 2*b^2*d^2*x + b*Sqrt[a + b]*c*d*Sqrt[a + b*x] - a*Sqrt[a + b]*d^2*Sqrt[a + b*x] - b^2*c*Sqrt[c + d]*Sqrt[c + d*x] + a*b*d*Sqrt[c + d]*Sqrt[c + d*x] - 2*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^2 + ((-2*b^(3/2)*c)/d^(3/2) + (6*a*Sqrt[b])/Sqrt[d])*ArcTanh[(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*(Sqrt[c + d] - Sqrt[c + d*x]))] - (a^2*RootSum[b^4 - 16*a*b^2*c*#1^2 - 8*b^3*c*#1^2 - 8*a*b^2*d*#1^2 - 4*b^3*d*#1^2 + 16*b^2*c^2*#1^4 + 16*b^2*c*d*#1^4 + 16*a^2*d^2*#1^4 + 16*a*b*d^2*#1^4 + 6*b^2*d^2*#1^4 - 16*a*c*d^2*#1^6 - 8*b*c*d^2*#1^6 - 8*a*d^3*#1^6 - 4*b*d^3*#1^6 + d^4*#1^8 & , (b^3*Log[Sqrt[c + d] - Sqrt[c + d*x]] - b^3*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + 4*b^2*Sqrt[a + b]*Sqrt[c + d]*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1 - 4*b^2*Sqrt[a + b]*Sqrt[c + d]*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1 + 4*b^2*c*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 + 4*a*b*d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 + 5*b^2*d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - 4*b^2*c*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2 - 4*a*b*d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2 - 5*b^2*d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2 - 4*b*c*d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^4 - 4*a*d^2*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^4 - 5*b*d^2*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^4 + 4*b*c*d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^4 + 4*a*d^2*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^4 + 5*b*d^2*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^4 - 4*Sqrt[a + b]*d^2*Sqrt[c + d]*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^5 + 4*Sqrt[a + b]*d^2*Sqrt[c + d]*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^5 - d^3*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^6 + d^3*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^6)/(-4*a*b^2*c*#1 - 2*b^3*c*#1 - 2*a*b^2*d*#1 - b^3*d*#1 + 8*b^2*c^2*#1^3 + 8*b^2*c*d*#1^3 + 8*a^2*d^2*#1^3 + 8*a*b*d^2*#1^3 + 3*b^2*d^2*#1^3 - 12*a*c*d^2*#1^5 - 6*b*c*d^2*#1^5 - 6*a*d^3*#1^5 - 3*b*d^3*#1^5 + d^4*#1^7) & ])/2","C",1
630,1,929,121,35.9147379,"\int \frac{(a+b x)^{3/2}}{x^2 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(x^2*Sqrt[c + d*x]),x]","\frac{4 \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b} \sqrt{d}}{\sqrt{b}}-\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b}}}{\sqrt{c+d}-\sqrt{c+d x}}\right) b^{3/2}}{\sqrt{d}}+\frac{\sqrt{a+b x} \left(-a \sqrt{c+d} \sqrt{c+d x} \left(2 c^2 b^2+c d b^2-c d x b^2+a d^2 b-2 a c d b-a d^2 x b-2 a c d x b+2 a^2 d^2\right)-a \left(-2 b^2 c^3-2 b^2 d c^2+2 a b d c^2+2 a b d x c^2+2 a b d^2 c-2 a^2 d^2 x c+2 a b d^2 x c-2 a^2 d^3 x\right)\right)+\sqrt{a+b} \left(-a \sqrt{c+d} \sqrt{c+d x} \left(-2 b^2 x c^2+2 a b d c+2 a b d x c-2 a^2 d^2\right)-a \left(2 b^2 x c^3+b^2 d x^2 c^2-2 a b d c^2+b^2 d x c^2-2 a b d x c^2-2 a b d^2 c+b^2 d^2 x^2 c+a b d^2 x^2 c+2 a^2 d^2 x c-b^2 d^2 x c-3 a b d^2 x c+a b d^3 x^2+2 a^2 d^3 x-a b d^3 x\right)\right)}{c \left(-2 c^2 b^2-2 c d b^2+2 a d^2 b+2 a c d b\right) \sqrt{c+d x} x+\sqrt{a+b} c \left(-2 b d^2-2 b c d\right) \sqrt{a+b x} \sqrt{c+d x} x+\sqrt{c+d} \left(c \left(2 c^2 b^2+c d b^2+2 d^2 x b^2+c d x b^2+a d^2 b-2 a c d b+a d^2 x b+2 a^2 d^2\right) x+\sqrt{a+b} c \left(2 b c d-2 a d^2\right) \sqrt{a+b x} x\right)}+\left(\frac{3 a b}{2}-\frac{a^2 d}{2 c}\right) \text{RootSum}\left[d^2 \text{$\#$1}^4-4 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^3+4 b c \text{$\#$1}^2+4 a d \text{$\#$1}^2+6 b d \text{$\#$1}^2-4 b \sqrt{a+b} \sqrt{c+d} \text{$\#$1}+b^2\&,\frac{d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2-d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2-b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)+b \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right)}{d^2 \text{$\#$1}^3-3 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^2+2 b c \text{$\#$1}+2 a d \text{$\#$1}+3 b d \text{$\#$1}-b \sqrt{a+b} \sqrt{c+d}}\&\right]","\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{d}}-\frac{\sqrt{a} (3 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{c^{3/2}}-\frac{a \sqrt{a+b x} \sqrt{c+d x}}{c x}",1,"(Sqrt[a + b*x]*(-(a*Sqrt[c + d]*Sqrt[c + d*x]*(2*b^2*c^2 - 2*a*b*c*d + b^2*c*d + 2*a^2*d^2 + a*b*d^2 - 2*a*b*c*d*x - b^2*c*d*x - a*b*d^2*x)) - a*(-2*b^2*c^3 + 2*a*b*c^2*d - 2*b^2*c^2*d + 2*a*b*c*d^2 + 2*a*b*c^2*d*x - 2*a^2*c*d^2*x + 2*a*b*c*d^2*x - 2*a^2*d^3*x)) + Sqrt[a + b]*(-(a*Sqrt[c + d]*Sqrt[c + d*x]*(2*a*b*c*d - 2*a^2*d^2 - 2*b^2*c^2*x + 2*a*b*c*d*x)) - a*(-2*a*b*c^2*d - 2*a*b*c*d^2 + 2*b^2*c^3*x - 2*a*b*c^2*d*x + b^2*c^2*d*x + 2*a^2*c*d^2*x - 3*a*b*c*d^2*x - b^2*c*d^2*x + 2*a^2*d^3*x - a*b*d^3*x + b^2*c^2*d*x^2 + a*b*c*d^2*x^2 + b^2*c*d^2*x^2 + a*b*d^3*x^2)))/(c*(-2*b^2*c^2 + 2*a*b*c*d - 2*b^2*c*d + 2*a*b*d^2)*x*Sqrt[c + d*x] + Sqrt[a + b]*c*(-2*b*c*d - 2*b*d^2)*x*Sqrt[a + b*x]*Sqrt[c + d*x] + Sqrt[c + d]*(Sqrt[a + b]*c*(2*b*c*d - 2*a*d^2)*x*Sqrt[a + b*x] + c*x*(2*b^2*c^2 - 2*a*b*c*d + b^2*c*d + 2*a^2*d^2 + a*b*d^2 + b^2*c*d*x + a*b*d^2*x + 2*b^2*d^2*x))) + (4*b^(3/2)*ArcTanh[((Sqrt[a + b]*Sqrt[d])/Sqrt[b] - (Sqrt[d]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[c + d] - Sqrt[c + d*x])])/Sqrt[d] + ((3*a*b)/2 - (a^2*d)/(2*c))*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ]","C",1
631,1,4554,119,119.6869784,"\int \frac{(a+b x)^{3/2}}{x^3 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(x^3*Sqrt[c + d*x]),x]","\text{Result too large to show}","-\frac{3 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 \sqrt{a} c^{5/2}}-\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 c^2 x}-\frac{(a+b x)^{3/2} \sqrt{c+d x}}{2 c x^2}",1,"(Sqrt[a + b]*(32*a^2*b^3*c^5*d - 48*a^3*b^2*c^4*d^2 + 40*a^2*b^3*c^4*d^2 + 32*a^4*b*c^3*d^3 - 40*a^3*b^2*c^3*d^3 + 8*a^2*b^3*c^3*d^3 + 32*a^4*b*c^2*d^4 + 8*a^3*b^2*c^2*d^4 + 112*a*b^4*c^5*d*x - 176*a^2*b^3*c^4*d^2*x + 140*a*b^4*c^4*d^2*x + 144*a^3*b^2*c^3*d^3*x - 136*a^2*b^3*c^3*d^3*x + 28*a*b^4*c^3*d^3*x - 16*a^4*b*c^2*d^4*x + 140*a^3*b^2*c^2*d^4*x + 40*a^2*b^3*c^2*d^4*x - 16*a^4*b*c*d^5*x - 4*a^3*b^2*c*d^5*x - 16*a*b^4*c^6*x^2 - 40*b^5*c^6*x^2 + 32*a^2*b^3*c^5*d*x^2 + 72*a*b^4*c^5*d*x^2 - 48*a^3*b^2*c^4*d^2*x^2 - 136*a^2*b^3*c^4*d^2*x^2 + 82*a*b^4*c^4*d^2*x^2 + 55*b^5*c^4*d^2*x^2 + 32*a^4*b*c^3*d^3*x^2 + 104*a^3*b^2*c^3*d^3*x^2 - 220*a^2*b^3*c^3*d^3*x^2 + 59*a*b^4*c^3*d^3*x^2 + 15*b^5*c^3*d^3*x^2 - 16*a^5*c^2*d^4*x^2 - 72*a^4*b*c^2*d^4*x^2 + 242*a^3*b^2*c^2*d^4*x^2 - 43*a^2*b^3*c^2*d^4*x^2 + 65*a*b^4*c^2*d^4*x^2 + 8*a^5*c*d^5*x^2 - 128*a^4*b*c*d^5*x^2 + 81*a^3*b^2*c*d^5*x^2 + 9*a^2*b^3*c*d^5*x^2 + 24*a^5*d^6*x^2 - 24*a^4*b*d^6*x^2 - 9*a^3*b^2*d^6*x^2 - 16*a*b^4*c^5*d*x^3 - 40*b^5*c^5*d*x^3 - 36*a*b^4*c^4*d^2*x^3 - 50*b^5*c^4*d^2*x^3 + 24*a^2*b^3*c^3*d^3*x^3 - 42*a*b^4*c^3*d^3*x^3 + 10*b^5*c^3*d^3*x^3 - 16*a^4*b*c^2*d^4*x^3 - 84*a^3*b^2*c^2*d^4*x^3 + 18*a^2*b^3*c^2*d^4*x^3 + 2*a*b^4*c^2*d^4*x^3 + 20*b^5*c^2*d^4*x^3 + 8*a^4*b*c*d^5*x^3 - 78*a^3*b^2*c*d^5*x^3 - 18*a^2*b^3*c*d^5*x^3 + 24*a*b^4*c*d^5*x^3 + 24*a^4*b*d^6*x^3 + 6*a^3*b^2*d^6*x^3 - 12*a^2*b^3*d^6*x^3 - 2*a*b^4*c^4*d^2*x^4 - 5*b^5*c^4*d^2*x^4 - 12*a^2*b^3*c^3*d^3*x^4 - 45*a*b^4*c^3*d^3*x^4 - 25*b^5*c^3*d^3*x^4 - 2*a^3*b^2*c^2*d^4*x^4 - 15*a^2*b^3*c^2*d^4*x^4 - 67*a*b^4*c^2*d^4*x^4 - 20*b^5*c^2*d^4*x^4 + a^3*b^2*c*d^5*x^4 + 9*a^2*b^3*c*d^5*x^4 - 24*a*b^4*c*d^5*x^4 + 3*a^3*b^2*d^6*x^4 + 12*a^2*b^3*d^6*x^4 + Sqrt[c + d]*Sqrt[c + d*x]*(-32*a^2*b^3*c^4*d + 48*a^3*b^2*c^3*d^2 - 24*a^2*b^3*c^3*d^2 - 32*a^4*b*c^2*d^3 + 16*a^3*b^2*c^2*d^3 + 16*a^5*c*d^4 + 8*a^4*b*c*d^4 - 112*a*b^4*c^4*d*x + 192*a^2*b^3*c^3*d^2*x - 84*a*b^4*c^3*d^2*x - 168*a^3*b^2*c^2*d^3*x + 60*a^2*b^3*c^2*d^3*x + 112*a^4*b*c*d^4*x + 36*a^3*b^2*c*d^4*x - 24*a^5*d^5*x - 12*a^4*b*d^5*x + 16*a*b^4*c^5*x^2 + 40*b^5*c^5*x^2 - 32*a^2*b^3*c^4*d*x^2 - 80*a*b^4*c^4*d*x^2 - 20*b^5*c^4*d*x^2 + 48*a^3*b^2*c^3*d^2*x^2 + 152*a^2*b^3*c^3*d^2*x^2 + 16*a*b^4*c^3*d^2*x^2 - 40*b^5*c^3*d^2*x^2 - 32*a^4*b*c^2*d^3*x^2 - 128*a^3*b^2*c^2*d^3*x^2 + 40*a^2*b^3*c^2*d^3*x^2 - 8*a*b^4*c^2*d^3*x^2 + 16*a^4*b*c*d^4*x^2 - 48*a^3*b^2*c*d^4*x^2 + 72*a^2*b^3*c*d^4*x^2 + 12*a^4*b*d^5*x^2 - 24*a^3*b^2*d^5*x^2 + 8*a*b^4*c^4*d*x^3 + 20*b^5*c^4*d*x^3 + 16*a^2*b^3*c^3*d^2*x^3 + 68*a*b^4*c^3*d^2*x^3 + 40*b^5*c^3*d^2*x^3 - 24*a^3*b^2*c^2*d^3*x^3 - 100*a^2*b^3*c^2*d^3*x^3 + 8*a*b^4*c^2*d^3*x^3 + 12*a^3*b^2*c*d^4*x^3 - 72*a^2*b^3*c*d^4*x^3 + 24*a^3*b^2*d^5*x^3)) + Sqrt[a + b*x]*(16*a*b^4*c^6 - 32*a^2*b^3*c^5*d + 24*a*b^4*c^5*d + 48*a^3*b^2*c^4*d^2 - 16*a^2*b^3*c^4*d^2 + 8*a*b^4*c^4*d^2 - 32*a^4*b*c^3*d^3 + 24*a^3*b^2*c^3*d^3 + 16*a^2*b^3*c^3*d^3 - 32*a^4*b*c^2*d^4 - 24*a^3*b^2*c^2*d^4 + 40*b^5*c^6*x - 80*a*b^4*c^5*d*x + 60*b^5*c^5*d*x + 152*a^2*b^3*c^4*d^2*x - 12*a*b^4*c^4*d^2*x + 20*b^5*c^4*d^2*x - 128*a^3*b^2*c^3*d^3*x + 52*a^2*b^3*c^3*d^3*x + 68*a*b^4*c^3*d^3*x + 16*a^4*b*c^2*d^4*x - 116*a^3*b^2*c^2*d^4*x - 100*a^2*b^3*c^2*d^4*x + 16*a^4*b*c*d^5*x + 12*a^3*b^2*c*d^5*x - 32*a^2*b^3*c^5*d*x^2 - 112*a*b^4*c^5*d*x^2 - 20*b^5*c^5*d*x^2 + 48*a^3*b^2*c^4*d^2*x^2 + 160*a^2*b^3*c^4*d^2*x^2 - 96*a*b^4*c^4*d^2*x^2 + 20*b^5*c^4*d^2*x^2 - 32*a^4*b*c^3*d^3*x^2 - 120*a^3*b^2*c^3*d^3*x^2 + 232*a^2*b^3*c^3*d^3*x^2 + 24*a*b^4*c^3*d^3*x^2 + 40*b^5*c^3*d^3*x^2 + 16*a^5*c^2*d^4*x^2 + 80*a^4*b*c^2*d^4*x^2 - 216*a^3*b^2*c^2*d^4*x^2 - 32*a^2*b^3*c^2*d^4*x^2 + 8*a*b^4*c^2*d^4*x^2 - 8*a^5*c*d^5*x^2 + 124*a^4*b*c*d^5*x^2 - 24*a^3*b^2*c*d^5*x^2 - 72*a^2*b^3*c*d^5*x^2 - 24*a^5*d^6*x^2 + 12*a^4*b*d^6*x^2 + 24*a^3*b^2*d^6*x^2 - 24*a^2*b^3*c^4*d^2*x^3 - 84*a*b^4*c^4*d^2*x^3 - 40*b^5*c^4*d^2*x^3 + 16*a^3*b^2*c^3*d^3*x^3 + 36*a^2*b^3*c^3*d^3*x^3 - 92*a*b^4*c^3*d^3*x^3 - 40*b^5*c^3*d^3*x^3 + 8*a^4*b*c^2*d^4*x^3 + 52*a^3*b^2*c^2*d^4*x^3 + 132*a^2*b^3*c^2*d^4*x^3 - 8*a*b^4*c^2*d^4*x^3 - 4*a^4*b*c*d^5*x^3 + 12*a^3*b^2*c*d^5*x^3 + 72*a^2*b^3*c*d^5*x^3 - 12*a^4*b*d^6*x^3 - 24*a^3*b^2*d^6*x^3 + Sqrt[c + d]*Sqrt[c + d*x]*(-16*a*b^4*c^5 + 32*a^2*b^3*c^4*d - 16*a*b^4*c^4*d - 48*a^3*b^2*c^3*d^2 - 2*a*b^4*c^3*d^2 + 32*a^4*b*c^2*d^3 - 12*a^2*b^3*c^2*d^3 - 16*a^5*c*d^4 - 16*a^4*b*c*d^4 - 2*a^3*b^2*c*d^4 - 40*b^5*c^5*x + 88*a*b^4*c^4*d*x - 40*b^5*c^4*d*x - 168*a^2*b^3*c^3*d^2*x - 20*a*b^4*c^3*d^2*x - 5*b^5*c^3*d^2*x + 152*a^3*b^2*c^2*d^3*x + 24*a^2*b^3*c^2*d^3*x - 43*a*b^4*c^2*d^3*x - 104*a^4*b*c*d^4*x - 84*a^3*b^2*c*d^4*x - 3*a^2*b^3*c*d^4*x + 24*a^5*d^5*x + 24*a^4*b*d^5*x + 3*a^3*b^2*d^5*x + 32*a^2*b^3*c^4*d*x^2 + 112*a*b^4*c^4*d*x^2 + 40*b^5*c^4*d*x^2 - 48*a^3*b^2*c^3*d^2*x^2 - 176*a^2*b^3*c^3*d^2*x^2 - 6*a*b^4*c^3*d^2*x^2 - 10*b^5*c^3*d^2*x^2 + 32*a^4*b*c^2*d^3*x^2 + 144*a^3*b^2*c^2*d^3*x^2 - 52*a^2*b^3*c^2*d^3*x^2 - 22*a*b^4*c^2*d^3*x^2 - 20*b^5*c^2*d^3*x^2 - 16*a^4*b*c*d^4*x^2 + 90*a^3*b^2*c*d^4*x^2 - 6*a^2*b^3*c*d^4*x^2 - 24*a*b^4*c*d^4*x^2 - 24*a^4*b*d^5*x^2 + 6*a^3*b^2*d^5*x^2 + 12*a^2*b^3*d^5*x^2 + 8*a^2*b^3*c^3*d^2*x^3 + 28*a*b^4*c^3*d^2*x^3 + 15*b^5*c^3*d^2*x^3 + 8*a^3*b^2*c^2*d^3*x^3 + 40*a^2*b^3*c^2*d^3*x^3 + 65*a*b^4*c^2*d^3*x^3 + 20*b^5*c^2*d^3*x^3 - 4*a^3*b^2*c*d^4*x^3 + 9*a^2*b^3*c*d^4*x^3 + 24*a*b^4*c*d^4*x^3 - 9*a^3*b^2*d^5*x^3 - 12*a^2*b^3*d^5*x^3)))/(4*Sqrt[a + b]*c^2*x^2*Sqrt[a + b*x]*Sqrt[c + d*x]*(-16*b^3*c^3*d + 24*a*b^2*c^2*d^2 - 20*b^3*c^2*d^2 - 16*a^2*b*c*d^3 + 20*a*b^2*c*d^3 - 4*b^3*c*d^3 - 16*a^2*b*d^4 - 4*a*b^2*d^4 - 4*b^3*c^2*d^2*x - 4*a*b^2*c*d^3*x - 12*b^3*c*d^3*x - 4*a*b^2*d^4*x - 8*b^3*d^4*x) + 4*c^2*x^2*Sqrt[c + d*x]*(-8*b^4*c^4 + 16*a*b^3*c^3*d - 12*b^4*c^3*d - 24*a^2*b^2*c^2*d^2 + 8*a*b^3*c^2*d^2 - 4*b^4*c^2*d^2 + 16*a^3*b*c*d^3 - 12*a^2*b^2*c*d^3 - 8*a*b^3*c*d^3 + 16*a^3*b*d^4 + 12*a^2*b^2*d^4 - 4*b^4*c^3*d*x - 8*a*b^3*c^2*d^2*x - 20*b^4*c^2*d^2*x + 12*a^2*b^2*c*d^3*x + 8*a*b^3*c*d^3*x - 16*b^4*c*d^3*x + 12*a^2*b^2*d^4*x + 16*a*b^3*d^4*x) + Sqrt[c + d]*(4*Sqrt[a + b]*c^2*x^2*Sqrt[a + b*x]*(16*b^3*c^3*d - 24*a*b^2*c^2*d^2 + 12*b^3*c^2*d^2 + 16*a^2*b*c*d^3 - 8*a*b^2*c*d^3 - 8*a^3*d^4 - 4*a^2*b*d^4 + 12*b^3*c^2*d^2*x - 8*a*b^2*c*d^3*x + 16*b^3*c*d^3*x - 4*a^2*b*d^4*x - 16*a*b^2*d^4*x) + 4*c^2*x^2*(8*b^4*c^4 - 16*a*b^3*c^3*d + 8*b^4*c^3*d + 24*a^2*b^2*c^2*d^2 + b^4*c^2*d^2 - 16*a^3*b*c*d^3 + 6*a*b^3*c*d^3 + 8*a^4*d^4 + 8*a^3*b*d^4 + a^2*b^2*d^4 + 8*b^4*c^3*d*x + 22*b^4*c^2*d^2*x - 12*a*b^3*c*d^3*x + 8*b^4*c*d^3*x + 8*a^3*b*d^4*x + 22*a^2*b^2*d^4*x + 8*a*b^3*d^4*x + b^4*c^2*d^2*x^2 + 6*a*b^3*c*d^3*x^2 + 8*b^4*c*d^3*x^2 + a^2*b^2*d^4*x^2 + 8*a*b^3*d^4*x^2 + 8*b^4*d^4*x^2))) + (3*(b*c - a*d)^2*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ])/(8*c^2)","C",1
632,-1,0,180,180.0351992,"\int \frac{(a+b x)^{3/2}}{x^4 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(x^4*Sqrt[c + d*x]),x]","\text{\$Aborted}","\frac{(b c-a d)^2 (5 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 a^{3/2} c^{7/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d) (5 a d+b c)}{8 a c^3 x}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (5 a d+b c)}{12 a c^2 x^2}-\frac{(a+b x)^{5/2} \sqrt{c+d x}}{3 a c x^3}",1,"$Aborted","F",-1
633,-1,0,266,180.0884498,"\int \frac{(a+b x)^{3/2}}{x^5 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(x^5*Sqrt[c + d*x]),x]","\text{\$Aborted}","-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(35 a^2 d^2-46 a b c d+3 b^2 c^2\right)}{96 a c^3 x^2}-\frac{\left(35 a^2 d^2+10 a b c d+3 b^2 c^2\right) (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{5/2} c^{9/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(105 a^3 d^3-145 a^2 b c d^2+15 a b^2 c^2 d+9 b^3 c^3\right)}{192 a^2 c^4 x}-\frac{\sqrt{a+b x} \sqrt{c+d x} (9 b c-7 a d)}{24 c^2 x^3}-\frac{a \sqrt{a+b x} \sqrt{c+d x}}{4 c x^4}",1,"$Aborted","F",-1
634,-1,0,248,180.005137,"\int \frac{x^2 (a+b x)^{3/2}}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(x^2*(a + b*x)^(3/2))/(c + d*x)^(3/2),x]","\text{\$Aborted}","\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-a^2 d^2-10 a b c d+35 b^2 c^2\right)}{8 b d^4}-\frac{(b c-a d) \left(-a^2 d^2-10 a b c d+35 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{3/2} d^{9/2}}+\frac{(a+b x)^{3/2} \sqrt{c+d x} \left(\frac{a^2 d}{b}+10 a c-\frac{35 b c^2}{d}\right)}{12 d^2 (b c-a d)}+\frac{2 c^2 (a+b x)^{5/2}}{d^2 \sqrt{c+d x} (b c-a d)}+\frac{(a+b x)^{5/2} \sqrt{c+d x}}{3 b d^2}",1,"$Aborted","F",-1
635,-1,0,174,180.0289443,"\int \frac{x (a+b x)^{3/2}}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(x*(a + b*x)^(3/2))/(c + d*x)^(3/2),x]","\text{\$Aborted}","\frac{3 (b c-a d) (5 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 \sqrt{b} d^{7/2}}-\frac{3 \sqrt{a+b x} \sqrt{c+d x} (5 b c-a d)}{4 d^3}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (5 b c-a d)}{2 d^2 (b c-a d)}-\frac{2 c (a+b x)^{5/2}}{d \sqrt{c+d x} (b c-a d)}",1,"$Aborted","F",-1
636,1,1195,98,0.0007702,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(c + d*x)^(3/2),x]","\frac{\left(-\frac{2 \sqrt{a+b x} b^3}{d}-\frac{c \sqrt{a+b x} b^3}{d^2}+\frac{2 \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x} b^3}{d^2}-\frac{\sqrt{a+b} c b^3}{d^2}-\frac{a \sqrt{a+b x} b^2}{d}+\frac{a \sqrt{a+b} b^2}{d}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)^3}{\left(-c b+\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}\right)^2}+\frac{\left(\frac{2 (b c-a d)^2 \sqrt{a+b x}}{d^2 (c+d)}-\frac{2 \sqrt{a+b} (b c-a d)^2}{d^2 (c+d)}\right) \left(b c^2+2 a d c+3 b d c+b d x c-2 \sqrt{a+b} d \sqrt{a+b x} c-b \sqrt{c+d} \sqrt{c+d x} c+2 a d^2+2 b d^2+b d^2 x-2 \sqrt{a+b} d^2 \sqrt{a+b x}-a d \sqrt{c+d} \sqrt{c+d x}-2 b d \sqrt{c+d} \sqrt{c+d x}+\sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{-2 b^2 c^3-5 b^2 d c^2-2 a b d c^2-3 b^2 d x c^2+2 b \sqrt{a+b} d \sqrt{a+b x} c^2+2 b^2 \sqrt{c+d} \sqrt{c+d x} c^2+2 a^2 d^2 c-2 b^2 d^2 c+a b d^2 c-b^2 d^2 x^2 c-5 b^2 d^2 x c-a b d^2 x c-2 a \sqrt{a+b} d^2 \sqrt{a+b x} c+2 b \sqrt{a+b} d^2 x \sqrt{a+b x} c+2 b^2 d \sqrt{c+d} x \sqrt{c+d x} c+4 b^2 d \sqrt{c+d} \sqrt{c+d x} c+2 a b d \sqrt{c+d} \sqrt{c+d x} c-2 b \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} c+a b d^3 x^2+2 a^2 d^3 x-2 b^2 d^3 x+a b d^3 x-2 a \sqrt{a+b} d^3 x \sqrt{a+b x}-2 a b d^2 \sqrt{c+d} x \sqrt{c+d x}-4 a^2 d^2 \sqrt{c+d} \sqrt{c+d x}-4 a b d^2 \sqrt{c+d} \sqrt{c+d x}+4 a \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+2 b \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}}+\frac{\left(\frac{b \sqrt{c+d}}{d^2}-\frac{b \sqrt{c+d x}}{d^2}\right) \left(-3 \sqrt{a+b} c b-2 \sqrt{a+b} d b-c \sqrt{a+b x} b-2 d \sqrt{a+b x} b+4 \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x} b+a \sqrt{a+b} d-a d \sqrt{a+b x}\right)}{-c b+\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}}+\left(\frac{6 a \sqrt{b}}{d^{3/2}}-\frac{6 b^{3/2} c}{d^{5/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{a+b} \sqrt{d}-\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \left(\sqrt{c+d}-\sqrt{c+d x}\right)}\right)","-\frac{3 \sqrt{b} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{5/2}}+\frac{3 b \sqrt{a+b x} \sqrt{c+d x}}{d^2}-\frac{2 (a+b x)^{3/2}}{d \sqrt{c+d x}}",1,"(((b*Sqrt[c + d])/d^2 - (b*Sqrt[c + d*x])/d^2)*(-3*b*Sqrt[a + b]*c + a*Sqrt[a + b]*d - 2*b*Sqrt[a + b]*d - b*c*Sqrt[a + b*x] - a*d*Sqrt[a + b*x] - 2*b*d*Sqrt[a + b*x] + 4*b*Sqrt[a + b]*Sqrt[c + d]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x]) + ((Sqrt[c + d] - Sqrt[c + d*x])^3*(-((b^3*Sqrt[a + b]*c)/d^2) + (a*b^2*Sqrt[a + b])/d - (b^3*c*Sqrt[a + b*x])/d^2 - (a*b^2*Sqrt[a + b*x])/d - (2*b^3*Sqrt[a + b*x])/d + (2*b^3*Sqrt[a + b]*Sqrt[c + d]*Sqrt[c + d*x])/d^2))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^2 + (((-2*Sqrt[a + b]*(b*c - a*d)^2)/(d^2*(c + d)) + (2*(b*c - a*d)^2*Sqrt[a + b*x])/(d^2*(c + d)))*(Sqrt[c + d] - Sqrt[c + d*x])*(b*c^2 + 2*a*c*d + 3*b*c*d + 2*a*d^2 + 2*b*d^2 + b*c*d*x + b*d^2*x - 2*Sqrt[a + b]*c*d*Sqrt[a + b*x] - 2*Sqrt[a + b]*d^2*Sqrt[a + b*x] - b*c*Sqrt[c + d]*Sqrt[c + d*x] - a*d*Sqrt[c + d]*Sqrt[c + d*x] - 2*b*d*Sqrt[c + d]*Sqrt[c + d*x] + Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-2*b^2*c^3 - 2*a*b*c^2*d - 5*b^2*c^2*d + 2*a^2*c*d^2 + a*b*c*d^2 - 2*b^2*c*d^2 - 3*b^2*c^2*d*x - a*b*c*d^2*x - 5*b^2*c*d^2*x + 2*a^2*d^3*x + a*b*d^3*x - 2*b^2*d^3*x - b^2*c*d^2*x^2 + a*b*d^3*x^2 + 2*b*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] - 2*a*Sqrt[a + b]*c*d^2*Sqrt[a + b*x] + 2*b*Sqrt[a + b]*c*d^2*x*Sqrt[a + b*x] - 2*a*Sqrt[a + b]*d^3*x*Sqrt[a + b*x] + 2*b^2*c^2*Sqrt[c + d]*Sqrt[c + d*x] + 2*a*b*c*d*Sqrt[c + d]*Sqrt[c + d*x] + 4*b^2*c*d*Sqrt[c + d]*Sqrt[c + d*x] - 4*a^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 4*a*b*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 2*b^2*c*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 2*a*b*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 2*b*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 4*a*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 2*b*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]) + ((-6*b^(3/2)*c)/d^(5/2) + (6*a*Sqrt[b])/d^(3/2))*ArcTanh[(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*(Sqrt[c + d] - Sqrt[c + d*x]))]","B",1
637,1,548,119,11.1223629,"\int \frac{(a+b x)^{3/2}}{x (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(x*(c + d*x)^(3/2)),x]","\frac{a^2 \text{RootSum}\left[\text{$\#$1}^4 d^2-4 \text{$\#$1}^3 d \sqrt{a+b} \sqrt{c+d}+4 \text{$\#$1}^2 a d+4 \text{$\#$1}^2 b c+6 \text{$\#$1}^2 b d-4 \text{$\#$1} b \sqrt{a+b} \sqrt{c+d}+b^2\&,\frac{-\text{$\#$1}^2 d \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)+\text{$\#$1}^2 d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)+b \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)-b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{\text{$\#$1}^3 d^2-3 \text{$\#$1}^2 d \sqrt{a+b} \sqrt{c+d}+2 \text{$\#$1} a d+2 \text{$\#$1} b c+3 \text{$\#$1} b d-b \sqrt{a+b} \sqrt{c+d}}\&\right]}{c}+\frac{4 b^{3/2} \tanh ^{-1}\left(\frac{\frac{\sqrt{d} \sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b}}}{\sqrt{c+d}-\sqrt{c+d x}}\right)}{d^{3/2}}+\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(\frac{2 \sqrt{a+b} (b c-a d)^2}{c d}-\frac{2 \sqrt{a+b x} (b c-a d)^2}{c d}\right)}{d \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}-a d \sqrt{c+d} \sqrt{c+d x}-b c^2-b c d x+b c \sqrt{c+d} \sqrt{c+d x}-b c d-b d^2 x}","-\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{c^{3/2}}+\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{3/2}}-\frac{2 \sqrt{a+b x} (b c-a d)}{c d \sqrt{c+d x}}",1,"(((2*Sqrt[a + b]*(b*c - a*d)^2)/(c*d) - (2*(b*c - a*d)^2*Sqrt[a + b*x])/(c*d))*(Sqrt[c + d] - Sqrt[c + d*x]))/(-(b*c^2) - b*c*d - b*c*d*x - b*d^2*x + b*c*Sqrt[c + d]*Sqrt[c + d*x] - a*d*Sqrt[c + d]*Sqrt[c + d*x] + Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]) + (4*b^(3/2)*ArcTanh[((Sqrt[a + b]*Sqrt[d])/Sqrt[b] - (Sqrt[d]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[c + d] - Sqrt[c + d*x])])/d^(3/2) + (a^2*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ])/c","C",1
638,1,1213,108,39.3067482,"\int \frac{(a+b x)^{3/2}}{x^2 (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(x^2*(c + d*x)^(3/2)),x]","\frac{\left(\frac{2 (b c-a d)^2 \sqrt{a+b x}}{c^2}-\frac{2 \sqrt{a+b} (b c-a d)^2}{c^2}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{-b c^2-b d c-b d x c+b \sqrt{c+d} \sqrt{c+d x} c-b d^2 x-a d \sqrt{c+d} \sqrt{c+d x}+\sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}}+\frac{\left(\frac{a \sqrt{a+b x}}{\sqrt{a+b} c^2 \sqrt{c+d}}-\frac{a}{c^2 \sqrt{c+d}}\right) \left(\sqrt{a+b} c d \sqrt{c+d} a^2-c d \sqrt{c+d} \sqrt{a+b x} a^2+\sqrt{a+b} d^2 \sqrt{c+d x} a^2+\sqrt{a+b} c d \sqrt{c+d x} a^2-d^2 \sqrt{a+b x} \sqrt{c+d x} a^2-c d \sqrt{a+b x} \sqrt{c+d x} a^2+b \sqrt{a+b} d^2 \sqrt{c+d} x a+2 b \sqrt{a+b} c d \sqrt{c+d} x a+b \sqrt{a+b} c^2 \sqrt{c+d} a+2 b \sqrt{a+b} c d \sqrt{c+d} a+b c^2 \sqrt{c+d} \sqrt{a+b x} a-b c d \sqrt{c+d} \sqrt{a+b x} a-b \sqrt{a+b} c^2 \sqrt{c+d x} a-b \sqrt{a+b} c d \sqrt{c+d x} a-b c^2 \sqrt{a+b x} \sqrt{c+d x} a-b d^2 \sqrt{a+b x} \sqrt{c+d x} a-2 b c d \sqrt{a+b x} \sqrt{c+d x} a+b^2 \sqrt{a+b} c d \sqrt{c+d} x+b^2 c^2 \sqrt{c+d} \sqrt{a+b x}-b^2 c^2 \sqrt{a+b x} \sqrt{c+d x}-b^2 c d \sqrt{a+b x} \sqrt{c+d x}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{x \left(-2 c^2 b^2-c d b^2-2 d^2 x b^2-c d x b^2+2 c \sqrt{c+d} \sqrt{c+d x} b^2-a d^2 b+2 a c d b-a d^2 x b-2 \sqrt{a+b} c d \sqrt{a+b x} b-2 a d \sqrt{c+d} \sqrt{c+d x} b+2 \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b-2 a^2 d^2+2 a \sqrt{a+b} d^2 \sqrt{a+b x}\right)}+\left(\frac{3 a b}{2 c}-\frac{3 a^2 d}{2 c^2}\right) \text{RootSum}\left[d^2 \text{$\#$1}^4-4 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^3+4 b c \text{$\#$1}^2+4 a d \text{$\#$1}^2+6 b d \text{$\#$1}^2-4 b \sqrt{a+b} \sqrt{c+d} \text{$\#$1}+b^2\&,\frac{d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2-d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2-b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)+b \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right)}{d^2 \text{$\#$1}^3-3 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^2+2 b c \text{$\#$1}+2 a d \text{$\#$1}+3 b d \text{$\#$1}-b \sqrt{a+b} \sqrt{c+d}}\&\right]","-\frac{3 \sqrt{a} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{c^{5/2}}+\frac{3 \sqrt{a+b x} (b c-a d)}{c^2 \sqrt{c+d x}}-\frac{(a+b x)^{3/2}}{c x \sqrt{c+d x}}",1,"(((-2*Sqrt[a + b]*(b*c - a*d)^2)/c^2 + (2*(b*c - a*d)^2*Sqrt[a + b*x])/c^2)*(Sqrt[c + d] - Sqrt[c + d*x]))/(-(b*c^2) - b*c*d - b*c*d*x - b*d^2*x + b*c*Sqrt[c + d]*Sqrt[c + d*x] - a*d*Sqrt[c + d]*Sqrt[c + d*x] + Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]) + ((-(a/(c^2*Sqrt[c + d])) + (a*Sqrt[a + b*x])/(Sqrt[a + b]*c^2*Sqrt[c + d]))*(Sqrt[c + d] - Sqrt[c + d*x])*(a*b*Sqrt[a + b]*c^2*Sqrt[c + d] + a^2*Sqrt[a + b]*c*d*Sqrt[c + d] + 2*a*b*Sqrt[a + b]*c*d*Sqrt[c + d] + 2*a*b*Sqrt[a + b]*c*d*Sqrt[c + d]*x + b^2*Sqrt[a + b]*c*d*Sqrt[c + d]*x + a*b*Sqrt[a + b]*d^2*Sqrt[c + d]*x + a*b*c^2*Sqrt[c + d]*Sqrt[a + b*x] + b^2*c^2*Sqrt[c + d]*Sqrt[a + b*x] - a^2*c*d*Sqrt[c + d]*Sqrt[a + b*x] - a*b*c*d*Sqrt[c + d]*Sqrt[a + b*x] - a*b*Sqrt[a + b]*c^2*Sqrt[c + d*x] + a^2*Sqrt[a + b]*c*d*Sqrt[c + d*x] - a*b*Sqrt[a + b]*c*d*Sqrt[c + d*x] + a^2*Sqrt[a + b]*d^2*Sqrt[c + d*x] - a*b*c^2*Sqrt[a + b*x]*Sqrt[c + d*x] - b^2*c^2*Sqrt[a + b*x]*Sqrt[c + d*x] - a^2*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - 2*a*b*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - b^2*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - a^2*d^2*Sqrt[a + b*x]*Sqrt[c + d*x] - a*b*d^2*Sqrt[a + b*x]*Sqrt[c + d*x]))/(x*(-2*b^2*c^2 + 2*a*b*c*d - b^2*c*d - 2*a^2*d^2 - a*b*d^2 - b^2*c*d*x - a*b*d^2*x - 2*b^2*d^2*x - 2*b*Sqrt[a + b]*c*d*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*d^2*Sqrt[a + b*x] + 2*b^2*c*Sqrt[c + d]*Sqrt[c + d*x] - 2*a*b*d*Sqrt[c + d]*Sqrt[c + d*x] + 2*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x])) + ((3*a*b)/(2*c) - (3*a^2*d)/(2*c^2))*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ]","C",1
639,-1,0,175,180.0537745,"\int \frac{(a+b x)^{3/2}}{x^3 (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(x^3*(c + d*x)^(3/2)),x]","\text{\$Aborted}","-\frac{3 (b c-5 a d) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 \sqrt{a} c^{7/2}}+\frac{3 \sqrt{a+b x} (b c-5 a d) (b c-a d)}{4 a c^3 \sqrt{c+d x}}-\frac{(a+b x)^{3/2} (b c-5 a d)}{4 a c^2 x \sqrt{c+d x}}-\frac{(a+b x)^{5/2}}{2 a c x^2 \sqrt{c+d x}}",1,"$Aborted","F",-1
640,-1,0,240,180.1318497,"\int \frac{(a+b x)^{3/2}}{x^4 (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(x^4*(c + d*x)^(3/2)),x]","\text{\$Aborted}","-\frac{d \sqrt{a+b x} \left(105 a^2 d^2-100 a b c d+3 b^2 c^2\right)}{24 a c^4 \sqrt{c+d x}}+\frac{(b c-a d) \left(-35 a^2 d^2+10 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 a^{3/2} c^{9/2}}-\frac{\sqrt{a+b x} (3 b c-35 a d) (b c-a d)}{24 a c^3 x \sqrt{c+d x}}-\frac{7 \sqrt{a+b x} (b c-a d)}{12 c^2 x^2 \sqrt{c+d x}}-\frac{a \sqrt{a+b x}}{3 c x^3 \sqrt{c+d x}}",1,"$Aborted","F",-1
641,-1,0,267,180.0416915,"\int \frac{x^2 (a+b x)^{3/2}}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(x^2*(a + b*x)^(3/2))/(c + d*x)^(5/2),x]","\text{\$Aborted}","\frac{\left(3 a^2 d^2-30 a b c d+35 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 \sqrt{b} d^{9/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(3 a^2 d^2-30 a b c d+35 b^2 c^2\right)}{4 d^4 (b c-a d)}+\frac{(a+b x)^{3/2} \sqrt{c+d x} \left(3 a^2 d^2-30 a b c d+35 b^2 c^2\right)}{6 d^3 (b c-a d)^2}+\frac{2 c^2 (a+b x)^{5/2}}{3 d^2 (c+d x)^{3/2} (b c-a d)}-\frac{4 c (a+b x)^{5/2} (4 b c-3 a d)}{3 d^2 \sqrt{c+d x} (b c-a d)^2}",1,"$Aborted","F",-1
642,-1,0,174,180.006099,"\int \frac{x (a+b x)^{3/2}}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(x*(a + b*x)^(3/2))/(c + d*x)^(5/2),x]","\text{\$Aborted}","-\frac{\sqrt{b} (5 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{7/2}}+\frac{b \sqrt{a+b x} \sqrt{c+d x} (5 b c-3 a d)}{d^3 (b c-a d)}-\frac{2 (a+b x)^{3/2} (5 b c-3 a d)}{3 d^2 \sqrt{c+d x} (b c-a d)}-\frac{2 c (a+b x)^{5/2}}{3 d (c+d x)^{3/2} (b c-a d)}",1,"$Aborted","F",-1
643,-1,0,92,180.1899086,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(c + d*x)^(5/2),x]","\text{\$Aborted}","\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{5/2}}-\frac{2 b \sqrt{a+b x}}{d^2 \sqrt{c+d x}}-\frac{2 (a+b x)^{3/2}}{3 d (c+d x)^{3/2}}",1,"$Aborted","F",-1
644,-1,0,92,180.2331329,"\int \frac{(a+b x)^{3/2}}{x (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(x*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{c^{5/2}}+\frac{2 a \sqrt{a+b x}}{c^2 \sqrt{c+d x}}+\frac{2 (a+b x)^{3/2}}{3 c (c+d x)^{3/2}}",1,"$Aborted","F",-1
645,-1,0,149,180.058364,"\int \frac{(a+b x)^{3/2}}{x^2 (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(x^2*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{\sqrt{a} (3 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{c^{7/2}}+\frac{\sqrt{a+b x} (3 b c-5 a d)}{c^3 \sqrt{c+d x}}+\frac{(a+b x)^{3/2} (3 b c-5 a d)}{3 a c^2 (c+d x)^{3/2}}-\frac{(a+b x)^{5/2}}{a c x (c+d x)^{3/2}}",1,"$Aborted","F",-1
646,-1,0,204,180.1935597,"\int \frac{(a+b x)^{3/2}}{x^3 (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(x^3*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{\left(35 a^2 d^2-30 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 \sqrt{a} c^{9/2}}-\frac{5 d \sqrt{a+b x} (11 b c-21 a d)}{12 c^4 \sqrt{c+d x}}-\frac{d \sqrt{a+b x} (23 b c-35 a d)}{12 c^3 (c+d x)^{3/2}}-\frac{\sqrt{a+b x} (5 b c-7 a d)}{4 c^2 x (c+d x)^{3/2}}-\frac{a \sqrt{a+b x}}{2 c x^2 (c+d x)^{3/2}}",1,"$Aborted","F",-1
647,-1,0,376,180.037837,"\int x^2 (a+b x)^{5/2} \sqrt{c+d x} \, dx","IntegrateAlgebraic[x^2*(a + b*x)^(5/2)*Sqrt[c + d*x],x]","\text{\$Aborted}","-\frac{\left(5 a^2 d^2+14 a b c d+21 b^2 c^2\right) (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{512 b^{7/2} d^{11/2}}+\frac{(a+b x)^{7/2} \sqrt{c+d x} \left(5 a^2 d^2+14 a b c d+21 b^2 c^2\right)}{160 b^3 d^2}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(5 a^2 d^2+14 a b c d+21 b^2 c^2\right) (b c-a d)^3}{512 b^3 d^5}-\frac{(a+b x)^{3/2} \sqrt{c+d x} \left(5 a^2 d^2+14 a b c d+21 b^2 c^2\right) (b c-a d)^2}{768 b^3 d^4}+\frac{(a+b x)^{5/2} \sqrt{c+d x} \left(5 a^2 d^2+14 a b c d+21 b^2 c^2\right) (b c-a d)}{960 b^3 d^3}-\frac{(a+b x)^{7/2} (c+d x)^{3/2} (5 a d+9 b c)}{60 b^2 d^2}+\frac{x (a+b x)^{7/2} (c+d x)^{3/2}}{6 b d}",1,"$Aborted","F",-1
648,-1,0,268,180.0221329,"\int x (a+b x)^{5/2} \sqrt{c+d x} \, dx","IntegrateAlgebraic[x*(a + b*x)^(5/2)*Sqrt[c + d*x],x]","\text{\$Aborted}","\frac{(3 a d+7 b c) (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{5/2} d^{9/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (3 a d+7 b c) (b c-a d)^3}{128 b^2 d^4}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (3 a d+7 b c) (b c-a d)^2}{192 b^2 d^3}-\frac{(a+b x)^{5/2} \sqrt{c+d x} (3 a d+7 b c) (b c-a d)}{240 b^2 d^2}-\frac{(a+b x)^{7/2} \sqrt{c+d x} (3 a d+7 b c)}{40 b^2 d}+\frac{(a+b x)^{7/2} (c+d x)^{3/2}}{5 b d}",1,"$Aborted","F",-1
649,-1,0,192,180.0197633,"\int (a+b x)^{5/2} \sqrt{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)*Sqrt[c + d*x],x]","\text{\$Aborted}","-\frac{5 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{3/2} d^{7/2}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 b d^3}-\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}{96 b d^2}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)}{24 b d}+\frac{(a+b x)^{7/2} \sqrt{c+d x}}{4 b}",1,"$Aborted","F",-1
650,-1,0,218,180.2846946,"\int \frac{(a+b x)^{5/2} \sqrt{c+d x}}{x} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*Sqrt[c + d*x])/x,x]","\text{\$Aborted}","-2 a^{5/2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\frac{\left(5 a^3 d^3+15 a^2 b c d^2-5 a b^2 c^2 d+b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 \sqrt{b} d^{5/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-5 a d) (a d+b c)}{8 d^2}+\frac{1}{3} (a+b x)^{5/2} \sqrt{c+d x}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (5 a d+b c)}{12 d}",1,"$Aborted","F",-1
651,-1,0,197,180.0500909,"\int \frac{(a+b x)^{5/2} \sqrt{c+d x}}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*Sqrt[c + d*x])/x^2,x]","\text{\$Aborted}","-\frac{a^{3/2} (a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{c}}-\frac{\sqrt{b} \left(-15 a^2 d^2-10 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 d^{3/2}}-\frac{(a+b x)^{5/2} \sqrt{c+d x}}{x}+\frac{3}{2} b (a+b x)^{3/2} \sqrt{c+d x}+\frac{b \sqrt{a+b x} \sqrt{c+d x} (11 a d+b c)}{4 d}",1,"$Aborted","F",-1
652,-1,0,212,180.0613101,"\int \frac{(a+b x)^{5/2} \sqrt{c+d x}}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*Sqrt[c + d*x])/x^3,x]","\text{\$Aborted}","-\frac{\sqrt{a} \left(-a^2 d^2+10 a b c d+15 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 c^{3/2}}+\frac{b^{3/2} (5 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{d}}-\frac{(a+b x)^{5/2} \sqrt{c+d x}}{2 x^2}-\frac{(a+b x)^{3/2} \sqrt{c+d x} (a d+5 b c)}{4 c x}+\frac{b \sqrt{a+b x} \sqrt{c+d x} (a d+11 b c)}{4 c}",1,"$Aborted","F",-1
653,-1,0,228,180.0355451,"\int \frac{(a+b x)^{5/2} \sqrt{c+d x}}{x^4} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*Sqrt[c + d*x])/x^4,x]","\text{\$Aborted}","-\frac{\left(a^3 d^3-5 a^2 b c d^2+15 a b^2 c^2 d+5 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 \sqrt{a} c^{5/2}}+2 b^{5/2} \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)-\frac{\sqrt{a+b x} \sqrt{c+d x} (5 b c-a d) (a d+b c)}{8 c^2 x}-\frac{(a+b x)^{5/2} \sqrt{c+d x}}{3 x^3}-\frac{(a+b x)^{3/2} \sqrt{c+d x} (a d+5 b c)}{12 c x^2}",1,"$Aborted","F",-1
654,-1,0,198,180.0158018,"\int \frac{(a+b x)^{5/2} \sqrt{c+d x}}{x^5} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*Sqrt[c + d*x])/x^5,x]","\text{\$Aborted}","\frac{5 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{3/2} c^{7/2}}-\frac{5 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^2}{32 c^3 x^2}-\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}{64 a c^3 x}-\frac{5 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}{24 c^2 x^3}-\frac{(a+b x)^{5/2} (c+d x)^{3/2}}{4 c x^4}",1,"$Aborted","F",-1
655,-1,0,283,180.0695128,"\int \frac{(a+b x)^{5/2} \sqrt{c+d x}}{x^6} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*Sqrt[c + d*x])/x^6,x]","\text{\$Aborted}","-\frac{(7 a d+3 b c) (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{128 a^{5/2} c^{9/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (7 a d+3 b c) (b c-a d)^3}{128 a^2 c^4 x}+\frac{\sqrt{a+b x} (c+d x)^{3/2} (7 a d+3 b c) (b c-a d)^2}{64 a c^4 x^2}+\frac{(a+b x)^{3/2} (c+d x)^{3/2} (7 a d+3 b c) (b c-a d)}{48 a c^3 x^3}+\frac{(a+b x)^{5/2} (c+d x)^{3/2} (7 a d+3 b c)}{40 a c^2 x^4}-\frac{(a+b x)^{7/2} (c+d x)^{3/2}}{5 a c x^5}",1,"$Aborted","F",-1
656,-1,0,437,180.0587028,"\int x^2 (a+b x)^{5/2} (c+d x)^{3/2} \, dx","IntegrateAlgebraic[x^2*(a + b*x)^(5/2)*(c + d*x)^(3/2),x]","\text{\$Aborted}","-\frac{\left(5 a^2 d^2+10 a b c d+9 b^2 c^2\right) (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{1024 b^{9/2} d^{11/2}}+\frac{(a+b x)^{7/2} \sqrt{c+d x} \left(5 a^2 d^2+10 a b c d+9 b^2 c^2\right) (b c-a d)}{320 b^4 d^2}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(5 a^2 d^2+10 a b c d+9 b^2 c^2\right) (b c-a d)^4}{1024 b^4 d^5}-\frac{(a+b x)^{3/2} \sqrt{c+d x} \left(5 a^2 d^2+10 a b c d+9 b^2 c^2\right) (b c-a d)^3}{1536 b^4 d^4}+\frac{(a+b x)^{5/2} \sqrt{c+d x} \left(5 a^2 d^2+10 a b c d+9 b^2 c^2\right) (b c-a d)^2}{1920 b^4 d^3}+\frac{(a+b x)^{7/2} (c+d x)^{3/2} \left(5 a^2 d^2+10 a b c d+9 b^2 c^2\right)}{120 b^3 d^2}-\frac{(a+b x)^{7/2} (c+d x)^{5/2} (7 a d+9 b c)}{84 b^2 d^2}+\frac{x (a+b x)^{7/2} (c+d x)^{5/2}}{7 b d}",1,"$Aborted","F",-1
657,-1,0,315,180.0363105,"\int x (a+b x)^{5/2} (c+d x)^{3/2} \, dx","IntegrateAlgebraic[x*(a + b*x)^(5/2)*(c + d*x)^(3/2),x]","\text{\$Aborted}","\frac{(5 a d+7 b c) (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{512 b^{7/2} d^{9/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (5 a d+7 b c) (b c-a d)^4}{512 b^3 d^4}+\frac{(a+b x)^{3/2} \sqrt{c+d x} (5 a d+7 b c) (b c-a d)^3}{768 b^3 d^3}-\frac{(a+b x)^{5/2} \sqrt{c+d x} (5 a d+7 b c) (b c-a d)^2}{960 b^3 d^2}-\frac{(a+b x)^{7/2} \sqrt{c+d x} (5 a d+7 b c) (b c-a d)}{160 b^3 d}-\frac{(a+b x)^{7/2} (c+d x)^{3/2} (5 a d+7 b c)}{60 b^2 d}+\frac{(a+b x)^{7/2} (c+d x)^{5/2}}{6 b d}",1,"$Aborted","F",-1
658,-1,0,227,180.0231261,"\int (a+b x)^{5/2} (c+d x)^{3/2} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)*(c + d*x)^(3/2),x]","\text{\$Aborted}","-\frac{3 (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{5/2} d^{7/2}}+\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^4}{128 b^2 d^3}-\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^3}{64 b^2 d^2}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^2}{80 b^2 d}+\frac{3 (a+b x)^{7/2} \sqrt{c+d x} (b c-a d)}{40 b^2}+\frac{(a+b x)^{7/2} (c+d x)^{3/2}}{5 b}",1,"$Aborted","F",-1
659,-1,0,299,180.0165718,"\int \frac{(a+b x)^{5/2} (c+d x)^{3/2}}{x} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(c + d*x)^(3/2))/x,x]","\text{\$Aborted}","-2 a^{5/2} c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(64 a^2 b c d^2+(b c-5 a d) (b c-a d) (a d+3 b c)\right)}{64 b d^2}+\frac{\left(-5 a^4 d^4+60 a^3 b c d^3+90 a^2 b^2 c^2 d^2-20 a b^3 c^3 d+3 b^4 c^4\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{3/2} d^{5/2}}-\frac{\sqrt{a+b x} (c+d x)^{3/2} (b c-5 a d) (a d+3 b c)}{32 d^2}+\frac{1}{4} (a+b x)^{5/2} (c+d x)^{3/2}+\frac{(a+b x)^{3/2} (c+d x)^{3/2} (5 a d+3 b c)}{24 d}",1,"$Aborted","F",-1
660,-1,0,259,180.0481,"\int \frac{(a+b x)^{5/2} (c+d x)^{3/2}}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(c + d*x)^(3/2))/x^2,x]","\text{\$Aborted}","-a^{3/2} \sqrt{c} (3 a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-19 a^2 d^2-14 a b c d+b^2 c^2\right)}{8 d}-\frac{\left(-5 a^3 d^3-45 a^2 b c d^2-15 a b^2 c^2 d+b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 \sqrt{b} d^{3/2}}-\frac{(a+b x)^{5/2} (c+d x)^{3/2}}{x}+\frac{4}{3} b (a+b x)^{3/2} (c+d x)^{3/2}+\frac{b \sqrt{a+b x} (c+d x)^{3/2} (7 a d+b c)}{4 d}",1,"$Aborted","F",-1
661,-1,0,275,180.0716544,"\int \frac{(a+b x)^{5/2} (c+d x)^{3/2}}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(c + d*x)^(3/2))/x^3,x]","\text{\$Aborted}","\frac{3 \sqrt{a+b x} \sqrt{c+d x} \left(a^2 d^2+6 a b c d+b^2 c^2\right)}{4 c}-\frac{3 \sqrt{a} \left(a^2 d^2+10 a b c d+5 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 \sqrt{c}}+\frac{3 \sqrt{b} \left(5 a^2 d^2+10 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 \sqrt{d}}-\frac{(a+b x)^{5/2} (c+d x)^{3/2}}{2 x^2}-\frac{(a+b x)^{3/2} (c+d x)^{3/2} (3 a d+5 b c)}{4 c x}+\frac{3 b \sqrt{a+b x} (c+d x)^{3/2} (a d+3 b c)}{4 c}",1,"$Aborted","F",-1
662,-1,0,294,180.0958416,"\int \frac{(a+b x)^{5/2} (c+d x)^{3/2}}{x^4} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(c + d*x)^(3/2))/x^4,x]","\text{\$Aborted}","-\frac{\sqrt{a+b x} (c+d x)^{3/2} \left(-a^2 d^2+12 a b c d+5 b^2 c^2\right)}{8 c^2 x}+\frac{d \sqrt{a+b x} \sqrt{c+d x} \left(-a^2 d^2+14 a b c d+19 b^2 c^2\right)}{8 c^2}-\frac{\left(-a^3 d^3+15 a^2 b c d^2+45 a b^2 c^2 d+5 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 \sqrt{a} c^{3/2}}+b^{3/2} \sqrt{d} (5 a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)-\frac{(a+b x)^{5/2} (c+d x)^{3/2}}{3 x^3}-\frac{(a+b x)^{3/2} (c+d x)^{3/2} (3 a d+5 b c)}{12 c x^2}",1,"$Aborted","F",-1
663,-1,0,313,180.1234286,"\int \frac{(a+b x)^{5/2} (c+d x)^{3/2}}{x^5} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(c + d*x)^(3/2))/x^5,x]","\text{\$Aborted}","-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(3 a^3 d^3-17 a^2 b c d^2+73 a b^2 c^2 d+5 b^3 c^3\right)}{64 a c^2 x}+\frac{\left(-3 a^4 d^4+20 a^3 b c d^3-90 a^2 b^2 c^2 d^2-60 a b^3 c^3 d+5 b^4 c^4\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{3/2} c^{5/2}}+2 b^{5/2} d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)-\frac{\sqrt{a+b x} (c+d x)^{3/2} (5 b c-a d) (3 a d+b c)}{32 c^2 x^2}-\frac{(a+b x)^{5/2} (c+d x)^{3/2}}{4 x^4}-\frac{(a+b x)^{3/2} (c+d x)^{3/2} (3 a d+5 b c)}{24 c x^3}",1,"$Aborted","F",-1
664,-1,0,239,180.0710215,"\int \frac{(a+b x)^{5/2} (c+d x)^{3/2}}{x^6} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(c + d*x)^(3/2))/x^6,x]","\text{\$Aborted}","-\frac{3 (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{128 a^{5/2} c^{7/2}}+\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^4}{128 a^2 c^3 x}-\frac{\sqrt{a+b x} (c+d x)^{5/2} (b c-a d)^2}{16 c^3 x^3}-\frac{\sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^3}{64 a c^3 x^2}-\frac{(a+b x)^{3/2} (c+d x)^{5/2} (b c-a d)}{8 c^2 x^4}-\frac{(a+b x)^{5/2} (c+d x)^{5/2}}{5 c x^5}",1,"$Aborted","F",-1
665,-1,0,348,180.0595326,"\int x (a+b x)^{5/2} (c+d x)^{5/2} \, dx","IntegrateAlgebraic[x*(a + b*x)^(5/2)*(c + d*x)^(5/2),x]","\text{\$Aborted}","\frac{5 (a d+b c) (b c-a d)^6 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{1024 b^{9/2} d^{9/2}}-\frac{5 \sqrt{a+b x} \sqrt{c+d x} (a d+b c) (b c-a d)^5}{1024 b^4 d^4}+\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (a d+b c) (b c-a d)^4}{1536 b^4 d^3}-\frac{(a+b x)^{5/2} \sqrt{c+d x} (a d+b c) (b c-a d)^3}{384 b^4 d^2}-\frac{(a+b x)^{7/2} \sqrt{c+d x} (a d+b c) (b c-a d)^2}{64 b^4 d}-\frac{(a+b x)^{7/2} (c+d x)^{3/2} (a d+b c) (b c-a d)}{24 b^3 d}-\frac{(a+b x)^{7/2} (c+d x)^{5/2} (a d+b c)}{12 b^2 d}+\frac{(a+b x)^{7/2} (c+d x)^{7/2}}{7 b d}",1,"$Aborted","F",-1
666,-1,0,262,180.0377263,"\int (a+b x)^{5/2} (c+d x)^{5/2} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)*(c + d*x)^(5/2),x]","\text{\$Aborted}","-\frac{5 (b c-a d)^6 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{512 b^{7/2} d^{7/2}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^5}{512 b^3 d^3}-\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^4}{768 b^3 d^2}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (b c-a d)^3}{192 b^3 d}+\frac{(a+b x)^{7/2} \sqrt{c+d x} (b c-a d)^2}{32 b^3}+\frac{(a+b x)^{7/2} (c+d x)^{3/2} (b c-a d)}{12 b^2}+\frac{(a+b x)^{7/2} (c+d x)^{5/2}}{6 b}",1,"$Aborted","F",-1
667,-1,0,391,180.0248386,"\int \frac{(a+b x)^{5/2} (c+d x)^{5/2}}{x} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(c + d*x)^(5/2))/x,x]","\text{\$Aborted}","-2 a^{5/2} c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)-\frac{\sqrt{a+b x} (c+d x)^{5/2} \left(-3 a^2 d^2-16 a b c d+3 b^2 c^2\right)}{48 d^2}+\frac{\sqrt{a+b x} (c+d x)^{3/2} \left(3 a^3 d^3+109 a^2 b c d^2-19 a b^2 c^2 d+3 b^3 c^3\right)}{192 b d^2}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-3 a^4 d^4+22 a^3 b c d^3+128 a^2 b^2 c^2 d^2-22 a b^3 c^3 d+3 b^4 c^4\right)}{128 b^2 d^2}+\frac{(a d+b c) \left(3 a^4 d^4-28 a^3 b c d^3+178 a^2 b^2 c^2 d^2-28 a b^3 c^3 d+3 b^4 c^4\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{5/2} d^{5/2}}+\frac{1}{5} (a+b x)^{5/2} (c+d x)^{5/2}+\frac{(a+b x)^{3/2} (c+d x)^{5/2} (a d+b c)}{8 d}",1,"$Aborted","F",-1
668,-1,0,334,180.0703881,"\int \frac{(a+b x)^{5/2} (c+d x)^{5/2}}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^2,x]","\text{\$Aborted}","-5 a^{3/2} c^{3/2} (a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)-\frac{5 \sqrt{a+b x} (c+d x)^{3/2} \left(-31 a^2 d^2-18 a b c d+b^2 c^2\right)}{96 d}-\frac{5 \sqrt{a+b x} \sqrt{c+d x} \left(-a^3 d^3-45 a^2 b c d^2-19 a b^2 c^2 d+b^3 c^3\right)}{64 b d}-\frac{5 \left(a^4 d^4-20 a^3 b c d^3-90 a^2 b^2 c^2 d^2-20 a b^3 c^3 d+b^4 c^4\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{3/2} d^{3/2}}-\frac{(a+b x)^{5/2} (c+d x)^{5/2}}{x}+\frac{5}{4} b (a+b x)^{3/2} (c+d x)^{5/2}+\frac{5 b \sqrt{a+b x} (c+d x)^{5/2} (7 a d+b c)}{24 d}",1,"$Aborted","F",-1
669,-1,0,319,180.1542542,"\int \frac{(a+b x)^{5/2} (c+d x)^{5/2}}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^3,x]","\text{\$Aborted}","\frac{5 \sqrt{a+b x} (c+d x)^{3/2} \left(3 a^2 d^2+8 a b c d+b^2 c^2\right)}{12 c}+\frac{5}{8} \sqrt{a+b x} \sqrt{c+d x} \left(5 a^2 d^2+10 a b c d+b^2 c^2\right)+\frac{5 (a d+b c) \left(a^2 d^2+14 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 \sqrt{b} \sqrt{d}}-\frac{(a+b x)^{5/2} (c+d x)^{5/2}}{2 x^2}-\frac{5 (a+b x)^{3/2} (c+d x)^{5/2} (a d+b c)}{4 c x}+\frac{5 b \sqrt{a+b x} (c+d x)^{5/2} (3 a d+5 b c)}{12 c}-\frac{5}{4} \sqrt{a} \sqrt{c} (a d+3 b c) (3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)",1,"$Aborted","F",-1
670,-1,0,339,180.0944333,"\int \frac{(a+b x)^{5/2} (c+d x)^{5/2}}{x^4} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^4,x]","\text{\$Aborted}","-\frac{5 \sqrt{a+b x} (c+d x)^{5/2} \left(a^2 d^2+12 a b c d+3 b^2 c^2\right)}{24 c^2 x}+\frac{5 d \sqrt{a+b x} (c+d x)^{3/2} \left(a^2 d^2+14 a b c d+9 b^2 c^2\right)}{24 c^2}+\frac{5 d \sqrt{a+b x} \sqrt{c+d x} \left(a^2 d^2+10 a b c d+5 b^2 c^2\right)}{8 c}-\frac{5 (a d+b c) \left(a^2 d^2+14 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 \sqrt{a} \sqrt{c}}-\frac{(a+b x)^{5/2} (c+d x)^{5/2}}{3 x^3}-\frac{5 (a+b x)^{3/2} (c+d x)^{5/2} (a d+b c)}{12 c x^2}+\frac{5}{4} \sqrt{b} \sqrt{d} (a d+3 b c) (3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)",1,"$Aborted","F",-1
671,-1,0,380,180.0455203,"\int \frac{(a+b x)^{5/2} (c+d x)^{5/2}}{x^5} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^5,x]","\text{\$Aborted}","-\frac{5 \sqrt{a+b x} (c+d x)^{5/2} \left(-a^2 d^2+14 a b c d+3 b^2 c^2\right)}{96 c^2 x^2}-\frac{5 \sqrt{a+b x} (c+d x)^{3/2} (a d+3 b c) \left(-a^2 d^2+24 a b c d+b^2 c^2\right)}{192 a c^2 x}+\frac{5 d \sqrt{a+b x} \sqrt{c+d x} \left(-a^3 d^3+19 a^2 b c d^2+45 a b^2 c^2 d+b^3 c^3\right)}{64 a c^2}+\frac{5 \left(a^4 d^4-20 a^3 b c d^3-90 a^2 b^2 c^2 d^2-20 a b^3 c^3 d+b^4 c^4\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{3/2} c^{3/2}}+5 b^{3/2} d^{3/2} (a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)-\frac{(a+b x)^{5/2} (c+d x)^{5/2}}{4 x^4}-\frac{5 (a+b x)^{3/2} (c+d x)^{5/2} (a d+b c)}{24 c x^3}",1,"$Aborted","F",-1
672,-1,0,406,180.1093013,"\int \frac{(a+b x)^{5/2} (c+d x)^{5/2}}{x^6} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^6,x]","\text{\$Aborted}","-\frac{\sqrt{a+b x} (c+d x)^{5/2} \left(-3 a^2 d^2+16 a b c d+3 b^2 c^2\right)}{48 c^2 x^3}-\frac{\sqrt{a+b x} (c+d x)^{3/2} \left(3 a^3 d^3-19 a^2 b c d^2+109 a b^2 c^2 d+3 b^3 c^3\right)}{192 a c^2 x^2}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-3 a^4 d^4+22 a^3 b c d^3-128 a^2 b^2 c^2 d^2-22 a b^3 c^3 d+3 b^4 c^4\right)}{128 a^2 c^2 x}-\frac{(a d+b c) \left(3 a^4 d^4-28 a^3 b c d^3+178 a^2 b^2 c^2 d^2-28 a b^3 c^3 d+3 b^4 c^4\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{128 a^{5/2} c^{5/2}}+2 b^{5/2} d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)-\frac{(a+b x)^{5/2} (c+d x)^{5/2}}{5 x^5}-\frac{(a+b x)^{3/2} (c+d x)^{5/2} (a d+b c)}{8 c x^4}",1,"$Aborted","F",-1
673,-1,0,280,180.1113187,"\int \frac{(a+b x)^{5/2} (c+d x)^{5/2}}{x^7} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^7,x]","\text{\$Aborted}","\frac{5 (b c-a d)^6 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{512 a^{7/2} c^{7/2}}-\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^5}{512 a^3 c^3 x}+\frac{5 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^4}{768 a^2 c^3 x^2}-\frac{\sqrt{a+b x} (c+d x)^{7/2} (b c-a d)^2}{32 c^3 x^4}-\frac{\sqrt{a+b x} (c+d x)^{5/2} (b c-a d)^3}{192 a c^3 x^3}-\frac{(a+b x)^{3/2} (c+d x)^{7/2} (b c-a d)}{12 c^2 x^5}-\frac{(a+b x)^{5/2} (c+d x)^{7/2}}{6 c x^6}",1,"$Aborted","F",-1
674,-1,0,314,180.0236233,"\int \frac{x^2 (a+b x)^{5/2}}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(x^2*(a + b*x)^(5/2))/Sqrt[c + d*x],x]","\text{\$Aborted}","\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2 \left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right)}{128 b^2 d^5}-\frac{(a+b x)^{3/2} \sqrt{c+d x} (b c-a d) \left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right)}{192 b^2 d^4}+\frac{(a+b x)^{5/2} \sqrt{c+d x} \left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right)}{240 b^2 d^3}-\frac{(b c-a d)^3 \left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{5/2} d^{11/2}}-\frac{3 (a+b x)^{7/2} \sqrt{c+d x} (a d+3 b c)}{40 b^2 d^2}+\frac{x (a+b x)^{7/2} \sqrt{c+d x}}{5 b d}",1,"$Aborted","F",-1
675,-1,0,217,180.0160157,"\int \frac{x (a+b x)^{5/2}}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(x*(a + b*x)^(5/2))/Sqrt[c + d*x],x]","\text{\$Aborted}","\frac{5 (b c-a d)^3 (a d+7 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{3/2} d^{9/2}}-\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2 (a d+7 b c)}{64 b d^4}+\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d) (a d+7 b c)}{96 b d^3}-\frac{(a+b x)^{5/2} \sqrt{c+d x} (a d+7 b c)}{24 b d^2}+\frac{(a+b x)^{7/2} \sqrt{c+d x}}{4 b d}",1,"$Aborted","F",-1
676,-1,0,148,180.1023788,"\int \frac{(a+b x)^{5/2}}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/Sqrt[c + d*x],x]","\text{\$Aborted}","-\frac{5 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 \sqrt{b} d^{7/2}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 d^3}-\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{12 d^2}+\frac{(a+b x)^{5/2} \sqrt{c+d x}}{3 d}",1,"$Aborted","F",-1
677,-1,0,171,180.0005219,"\int \frac{(a+b x)^{5/2}}{x \sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(x*Sqrt[c + d*x]),x]","\text{\$Aborted}","-\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{c}}+\frac{\sqrt{b} \left(15 a^2 d^2-10 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 d^{5/2}}-\frac{b \sqrt{a+b x} \sqrt{c+d x} (3 b c-7 a d)}{4 d^2}+\frac{b (a+b x)^{3/2} \sqrt{c+d x}}{2 d}",1,"$Aborted","F",-1
678,-1,0,162,180.0587734,"\int \frac{(a+b x)^{5/2}}{x^2 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(x^2*Sqrt[c + d*x]),x]","\text{\$Aborted}","-\frac{a^{3/2} (5 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{c^{3/2}}-\frac{b^{3/2} (b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{3/2}}-\frac{a (a+b x)^{3/2} \sqrt{c+d x}}{c x}+\frac{b \sqrt{a+b x} \sqrt{c+d x} (a d+b c)}{c d}",1,"$Aborted","F",-1
679,-1,0,177,180.0074123,"\int \frac{(a+b x)^{5/2}}{x^3 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(x^3*Sqrt[c + d*x]),x]","\text{\$Aborted}","-\frac{\sqrt{a} \left(3 a^2 d^2-10 a b c d+15 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 c^{5/2}}+\frac{2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{d}}-\frac{a \sqrt{a+b x} \sqrt{c+d x} (7 b c-3 a d)}{4 c^2 x}-\frac{a (a+b x)^{3/2} \sqrt{c+d x}}{2 c x^2}",1,"$Aborted","F",-1
680,-1,0,157,180.0420108,"\int \frac{(a+b x)^{5/2}}{x^4 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(x^4*Sqrt[c + d*x]),x]","\text{\$Aborted}","-\frac{5 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 \sqrt{a} c^{7/2}}-\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 c^3 x}-\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)}{12 c^2 x^2}-\frac{(a+b x)^{5/2} \sqrt{c+d x}}{3 c x^3}",1,"$Aborted","F",-1
681,-1,0,229,180.1019807,"\int \frac{(a+b x)^{5/2}}{x^5 \sqrt{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(x^5*Sqrt[c + d*x]),x]","\text{\$Aborted}","\frac{5 (b c-a d)^3 (7 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{3/2} c^{9/2}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2 (7 a d+b c)}{64 a c^4 x}+\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (b c-a d) (7 a d+b c)}{96 a c^3 x^2}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (7 a d+b c)}{24 a c^2 x^3}-\frac{(a+b x)^{7/2} \sqrt{c+d x}}{4 a c x^4}",1,"$Aborted","F",-1
682,-1,0,309,180.0433239,"\int \frac{x^2 (a+b x)^{5/2}}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(x^2*(a + b*x)^(5/2))/(c + d*x)^(3/2),x]","\text{\$Aborted}","-\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d) \left(-a^2 d^2-14 a b c d+63 b^2 c^2\right)}{64 b d^5}+\frac{5 (a+b x)^{3/2} \sqrt{c+d x} \left(-a^2 d^2-14 a b c d+63 b^2 c^2\right)}{96 b d^4}+\frac{5 (b c-a d)^2 \left(-a^2 d^2-14 a b c d+63 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{3/2} d^{11/2}}+\frac{(a+b x)^{5/2} \sqrt{c+d x} \left(\frac{a^2 d}{b}+14 a c-\frac{63 b c^2}{d}\right)}{24 d^2 (b c-a d)}+\frac{2 c^2 (a+b x)^{7/2}}{d^2 \sqrt{c+d x} (b c-a d)}+\frac{(a+b x)^{7/2} \sqrt{c+d x}}{4 b d^2}",1,"$Aborted","F",-1
683,-1,0,218,180.0073882,"\int \frac{x (a+b x)^{5/2}}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(x*(a + b*x)^(5/2))/(c + d*x)^(3/2),x]","\text{\$Aborted}","-\frac{5 (b c-a d)^2 (7 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 \sqrt{b} d^{9/2}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d) (7 b c-a d)}{8 d^4}-\frac{5 (a+b x)^{3/2} \sqrt{c+d x} (7 b c-a d)}{12 d^3}+\frac{(a+b x)^{5/2} \sqrt{c+d x} (7 b c-a d)}{3 d^2 (b c-a d)}-\frac{2 c (a+b x)^{7/2}}{d \sqrt{c+d x} (b c-a d)}",1,"$Aborted","F",-1
684,1,2048,138,0.0010129,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(c + d*x)^(3/2),x]","\text{Result too large to show}","\frac{15 \sqrt{b} (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 d^{7/2}}-\frac{15 b \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 d^3}+\frac{5 b (a+b x)^{3/2} \sqrt{c+d x}}{2 d^2}-\frac{2 (a+b x)^{5/2}}{d \sqrt{c+d x}}",1,"((Sqrt[c + d] - Sqrt[c + d*x])^7*((-3*b^6*Sqrt[a + b]*c^2)/(2*d^3) + (a*b^5*Sqrt[a + b]*c)/d^2 - (2*b^6*Sqrt[a + b]*c)/d^2 + (a^2*b^4*Sqrt[a + b])/(2*d) + (2*a*b^5*Sqrt[a + b])/d - (b^6*c^2*Sqrt[a + b*x])/(2*d^3) - (3*a*b^5*c*Sqrt[a + b*x])/d^2 - (4*b^6*c*Sqrt[a + b*x])/d^2 - (a^2*b^4*Sqrt[a + b*x])/(2*d) - (4*a*b^5*Sqrt[a + b*x])/d - (4*b^6*Sqrt[a + b*x])/d + (2*b^6*Sqrt[a + b]*c^2*Sqrt[c + d*x])/(d^3*Sqrt[c + d]) + (2*a*b^5*Sqrt[a + b]*c*Sqrt[c + d*x])/(d^2*Sqrt[c + d]) + (6*b^6*Sqrt[a + b]*c*Sqrt[c + d*x])/(d^2*Sqrt[c + d]) + (2*a*b^5*Sqrt[a + b]*Sqrt[c + d*x])/(d*Sqrt[c + d]) + (4*b^6*Sqrt[a + b]*Sqrt[c + d*x])/(d*Sqrt[c + d])))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^4 + ((Sqrt[c + d] - Sqrt[c + d*x])^5*((-13*b^5*Sqrt[a + b]*c^2)/(2*d^3) + (a*b^4*Sqrt[a + b]*c)/d^2 - (12*b^5*Sqrt[a + b]*c)/d^2 + (3*a^2*b^3*Sqrt[a + b])/(2*d) + (4*a*b^4*Sqrt[a + b])/d - (4*b^5*Sqrt[a + b])/d - (3*b^5*c^2*Sqrt[a + b*x])/(2*d^3) - (9*a*b^4*c*Sqrt[a + b*x])/d^2 - (12*b^5*c*Sqrt[a + b*x])/d^2 - (3*a^2*b^3*Sqrt[a + b*x])/(2*d) - (12*a*b^4*Sqrt[a + b*x])/d - (12*b^5*Sqrt[a + b*x])/d + (8*b^5*Sqrt[a + b]*c^2*Sqrt[c + d*x])/(d^3*Sqrt[c + d]) + (8*a*b^4*Sqrt[a + b]*c*Sqrt[c + d*x])/(d^2*Sqrt[c + d]) + (24*b^5*Sqrt[a + b]*c*Sqrt[c + d*x])/(d^2*Sqrt[c + d]) + (8*a*b^4*Sqrt[a + b]*Sqrt[c + d*x])/(d*Sqrt[c + d]) + (16*b^5*Sqrt[a + b]*Sqrt[c + d*x])/(d*Sqrt[c + d])))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^3 + ((Sqrt[c + d] - Sqrt[c + d*x])^3*((-27*b^4*Sqrt[a + b]*c^2)/(4*d^3) - (13*a*b^3*Sqrt[a + b]*c)/(2*d^2) - (20*b^4*Sqrt[a + b]*c)/d^2 + (13*a^2*b^2*Sqrt[a + b])/(4*d) - (10*b^4*Sqrt[a + b])/d + (3*b^4*c^2*Sqrt[a + b*x])/(4*d^3) - (15*a*b^3*c*Sqrt[a + b*x])/(2*d^2) - (6*b^4*c*Sqrt[a + b*x])/d^2 - (13*a^2*b^2*Sqrt[a + b*x])/(4*d) - (14*a*b^3*Sqrt[a + b*x])/d - (10*b^4*Sqrt[a + b*x])/d + (6*b^4*Sqrt[a + b]*c^2*Sqrt[c + d*x])/(d^3*Sqrt[c + d]) + (14*a*b^3*Sqrt[a + b]*c*Sqrt[c + d*x])/(d^2*Sqrt[c + d]) + (26*b^4*Sqrt[a + b]*c*Sqrt[c + d*x])/(d^2*Sqrt[c + d]) + (14*a*b^3*Sqrt[a + b]*Sqrt[c + d*x])/(d*Sqrt[c + d]) + (20*b^4*Sqrt[a + b]*Sqrt[c + d*x])/(d*Sqrt[c + d])))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^2 + ((9*b^2*Sqrt[a + b]*c^2*Sqrt[c + d] - 42*a*b*Sqrt[a + b]*c*d*Sqrt[c + d] - 24*b^2*Sqrt[a + b]*c*d*Sqrt[c + d] + 9*a^2*Sqrt[a + b]*d^2*Sqrt[c + d] - 24*a*b*Sqrt[a + b]*d^2*Sqrt[c + d] - 24*b^2*Sqrt[a + b]*d^2*Sqrt[c + d] + 7*b^2*c^2*Sqrt[c + d]*Sqrt[a + b*x] - 6*a*b*c*d*Sqrt[c + d]*Sqrt[a + b*x] + 8*b^2*c*d*Sqrt[c + d]*Sqrt[a + b*x] - 9*a^2*d^2*Sqrt[c + d]*Sqrt[a + b*x] - 24*a*b*d^2*Sqrt[c + d]*Sqrt[a + b*x] - 8*b^2*d^2*Sqrt[c + d]*Sqrt[a + b*x] - 16*b^2*Sqrt[a + b]*c^2*Sqrt[c + d*x] + 48*a*b*Sqrt[a + b]*c*d*Sqrt[c + d*x] + 16*b^2*Sqrt[a + b]*c*d*Sqrt[c + d*x] + 48*a*b*Sqrt[a + b]*d^2*Sqrt[c + d*x] + 32*b^2*Sqrt[a + b]*d^2*Sqrt[c + d*x])*(b/(4*d^3) - (b*Sqrt[c + d*x])/(4*d^3*Sqrt[c + d])))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x]) + (((2*Sqrt[a + b]*(b*c - a*d)^3)/d^3 - (2*(b*c - a*d)^3*Sqrt[a + b*x])/d^3)*(Sqrt[c + d] - Sqrt[c + d*x]))/(-(b*c^2) - b*c*d - b*c*d*x - b*d^2*x + b*c*Sqrt[c + d]*Sqrt[c + d*x] - a*d*Sqrt[c + d]*Sqrt[c + d*x] + Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]) + (15*Sqrt[b]*(b*c - a*d)^2*ArcTanh[((Sqrt[a + b]*Sqrt[d])/Sqrt[b] - (Sqrt[d]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[c + d] - Sqrt[c + d*x])])/(2*d^(7/2))","B",0
685,-1,0,163,180.2249335,"\int \frac{(a+b x)^{5/2}}{x (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(x*(c + d*x)^(3/2)),x]","\text{\$Aborted}","-\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{c^{3/2}}-\frac{b^{3/2} (3 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{5/2}}+\frac{b \sqrt{a+b x} \sqrt{c+d x} (3 b c-2 a d)}{c d^2}-\frac{2 (a+b x)^{3/2} (b c-a d)}{c d \sqrt{c+d x}}",1,"$Aborted","F",-1
686,-1,0,164,180.0362374,"\int \frac{(a+b x)^{5/2}}{x^2 (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(x^2*(c + d*x)^(3/2)),x]","\text{\$Aborted}","-\frac{a^{3/2} (5 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{c^{5/2}}+\frac{2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{3/2}}-\frac{\sqrt{a+b x} (2 b c-3 a d) (b c-a d)}{c^2 d \sqrt{c+d x}}-\frac{a (a+b x)^{3/2}}{c x \sqrt{c+d x}}",1,"$Aborted","F",-1
687,-1,0,154,180.0590019,"\int \frac{(a+b x)^{5/2}}{x^3 (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(x^3*(c + d*x)^(3/2)),x]","\text{\$Aborted}","-\frac{15 \sqrt{a} (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 c^{7/2}}+\frac{15 \sqrt{a+b x} (b c-a d)^2}{4 c^3 \sqrt{c+d x}}-\frac{5 (a+b x)^{3/2} (b c-a d)}{4 c^2 x \sqrt{c+d x}}-\frac{(a+b x)^{5/2}}{2 c x^2 \sqrt{c+d x}}",1,"$Aborted","F",-1
688,-1,0,226,180.1559391,"\int \frac{(a+b x)^{5/2}}{x^4 (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(x^4*(c + d*x)^(3/2)),x]","\text{\$Aborted}","-\frac{5 (b c-7 a d) (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 \sqrt{a} c^{9/2}}+\frac{5 \sqrt{a+b x} (b c-7 a d) (b c-a d)^2}{8 a c^4 \sqrt{c+d x}}-\frac{5 (a+b x)^{3/2} (b c-7 a d) (b c-a d)}{24 a c^3 x \sqrt{c+d x}}-\frac{(a+b x)^{5/2} (b c-7 a d)}{12 a c^2 x^2 \sqrt{c+d x}}-\frac{(a+b x)^{7/2}}{3 a c x^3 \sqrt{c+d x}}",1,"$Aborted","F",-1
689,-1,0,317,180.1524757,"\int \frac{(a+b x)^{5/2}}{x^5 (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(x^5*(c + d*x)^(3/2)),x]","\text{\$Aborted}","-\frac{\sqrt{a+b x} \left(315 a^2 d^2-322 a b c d+15 b^2 c^2\right) (b c-a d)}{192 a c^4 x \sqrt{c+d x}}+\frac{5 \left(-63 a^2 d^2+14 a b c d+b^2 c^2\right) (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{3/2} c^{11/2}}-\frac{d \sqrt{a+b x} \left(-945 a^3 d^3+1785 a^2 b c d^2-839 a b^2 c^2 d+15 b^3 c^3\right)}{192 a c^5 \sqrt{c+d x}}-\frac{\sqrt{a+b x} (59 b c-63 a d) (b c-a d)}{96 c^3 x^2 \sqrt{c+d x}}-\frac{a \sqrt{a+b x} (11 b c-9 a d)}{24 c^2 x^3 \sqrt{c+d x}}-\frac{a (a+b x)^{3/2}}{4 c x^4 \sqrt{c+d x}}",1,"$Aborted","F",-1
690,-1,0,377,180.0490901,"\int \frac{x^3 (a+b x)^{5/2}}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(x^3*(a + b*x)^(5/2))/(c + d*x)^(5/2),x]","\text{\$Aborted}","-\frac{(a+b x)^{5/2} \sqrt{c+d x} \left(5 a^2 d^2-2 b d x (99 b c-59 a d)-156 a b c d+231 b^2 c^2\right)}{24 b d^4 (b c-a d)}-\frac{5 \sqrt{a+b x} \sqrt{c+d x} \left(a^3 d^3+21 a^2 b c d^2-189 a b^2 c^2 d+231 b^3 c^3\right)}{64 b d^6}+\frac{5 (a+b x)^{3/2} \sqrt{c+d x} \left(a^3 d^3+21 a^2 b c d^2-189 a b^2 c^2 d+231 b^3 c^3\right)}{96 b d^5 (b c-a d)}+\frac{5 (b c-a d) \left(a^3 d^3+21 a^2 b c d^2-189 a b^2 c^2 d+231 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{3/2} d^{13/2}}-\frac{2 x^2 (a+b x)^{5/2} (11 b c-6 a d)}{3 d^2 \sqrt{c+d x} (b c-a d)}-\frac{2 x^3 (a+b x)^{5/2}}{3 d (c+d x)^{3/2}}",1,"$Aborted","F",-1
691,-1,0,319,180.0525195,"\int \frac{x^2 (a+b x)^{5/2}}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(x^2*(a + b*x)^(5/2))/(c + d*x)^(5/2),x]","\text{\$Aborted}","-\frac{5 (b c-a d) \left(a^2 d^2-14 a b c d+21 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 \sqrt{b} d^{11/2}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} \left(a^2 d^2-14 a b c d+21 b^2 c^2\right)}{8 d^5}-\frac{5 (a+b x)^{3/2} \sqrt{c+d x} \left(a^2 d^2-14 a b c d+21 b^2 c^2\right)}{12 d^4 (b c-a d)}+\frac{(a+b x)^{5/2} \sqrt{c+d x} \left(a^2 d^2-14 a b c d+21 b^2 c^2\right)}{3 d^3 (b c-a d)^2}+\frac{2 c^2 (a+b x)^{7/2}}{3 d^2 (c+d x)^{3/2} (b c-a d)}-\frac{4 c (a+b x)^{7/2} (5 b c-3 a d)}{3 d^2 \sqrt{c+d x} (b c-a d)^2}",1,"$Aborted","F",-1
692,-1,0,222,180.0513437,"\int \frac{x (a+b x)^{5/2}}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(x*(a + b*x)^(5/2))/(c + d*x)^(5/2),x]","\text{\$Aborted}","\frac{5 \sqrt{b} (7 b c-3 a d) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 d^{9/2}}-\frac{5 b \sqrt{a+b x} \sqrt{c+d x} (7 b c-3 a d)}{4 d^4}+\frac{5 b (a+b x)^{3/2} \sqrt{c+d x} (7 b c-3 a d)}{6 d^3 (b c-a d)}-\frac{2 (a+b x)^{5/2} (7 b c-3 a d)}{3 d^2 \sqrt{c+d x} (b c-a d)}-\frac{2 c (a+b x)^{7/2}}{3 d (c+d x)^{3/2} (b c-a d)}",1,"$Aborted","F",-1
693,-1,0,128,180.0200254,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(c + d*x)^(5/2),x]","\text{\$Aborted}","-\frac{5 b^{3/2} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{7/2}}+\frac{5 b^2 \sqrt{a+b x} \sqrt{c+d x}}{d^3}-\frac{10 b (a+b x)^{3/2}}{3 d^2 \sqrt{c+d x}}-\frac{2 (a+b x)^{5/2}}{3 d (c+d x)^{3/2}}",1,"$Aborted","F",-1
694,-1,0,157,180.0477207,"\int \frac{(a+b x)^{5/2}}{x (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(x*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{c^{5/2}}+\frac{2 \sqrt{a+b x} \left(\frac{a^2}{c^2}-\frac{b^2}{d^2}\right)}{\sqrt{c+d x}}+\frac{2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{d^{5/2}}-\frac{2 (a+b x)^{3/2} (b c-a d)}{3 c d (c+d x)^{3/2}}",1,"$Aborted","F",-1
695,-1,0,142,180.060542,"\int \frac{(a+b x)^{5/2}}{x^2 (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(x^2*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{5 a^{3/2} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{c^{7/2}}+\frac{5 a \sqrt{a+b x} (b c-a d)}{c^3 \sqrt{c+d x}}+\frac{5 (a+b x)^{3/2} (b c-a d)}{3 c^2 (c+d x)^{3/2}}-\frac{(a+b x)^{5/2}}{c x (c+d x)^{3/2}}",1,"$Aborted","F",-1
696,-1,0,220,180.2339079,"\int \frac{(a+b x)^{5/2}}{x^3 (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(x^3*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{5 \sqrt{a} (3 b c-7 a d) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 c^{9/2}}+\frac{5 \sqrt{a+b x} (3 b c-7 a d) (b c-a d)}{4 c^4 \sqrt{c+d x}}+\frac{5 (a+b x)^{3/2} (3 b c-7 a d) (b c-a d)}{12 a c^3 (c+d x)^{3/2}}-\frac{(a+b x)^{5/2} (3 b c-7 a d)}{4 a c^2 x (c+d x)^{3/2}}-\frac{(a+b x)^{7/2}}{2 a c x^2 (c+d x)^{3/2}}",1,"$Aborted","F",-1
697,-1,0,278,180.0606264,"\int \frac{(a+b x)^{5/2}}{x^4 (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(x^4*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{5 (b c-a d) \left(21 a^2 d^2-14 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 \sqrt{a} c^{11/2}}-\frac{d \sqrt{a+b x} \left(315 a^2 d^2-420 a b c d+113 b^2 c^2\right)}{24 c^5 \sqrt{c+d x}}-\frac{7 d \sqrt{a+b x} (7 b c-15 a d) (b c-a d)}{24 c^4 (c+d x)^{3/2}}-\frac{\sqrt{a+b x} (11 b c-21 a d) (b c-a d)}{8 c^3 x (c+d x)^{3/2}}-\frac{3 a \sqrt{a+b x} (b c-a d)}{4 c^2 x^2 (c+d x)^{3/2}}-\frac{a (a+b x)^{3/2}}{3 c x^3 (c+d x)^{3/2}}",1,"$Aborted","F",-1
698,-1,0,388,180.1631961,"\int \frac{(a+b x)^{5/2}}{x^5 (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)/(x^5*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{d \sqrt{a+b x} (b c-a d) \left(385 a^2 d^2-238 a b c d+5 b^2 c^2\right)}{64 a c^5 (c+d x)^{3/2}}-\frac{\sqrt{a+b x} (b c-a d) \left(231 a^2 d^2-156 a b c d+5 b^2 c^2\right)}{64 a c^4 x (c+d x)^{3/2}}-\frac{d \sqrt{a+b x} \left(-1155 a^3 d^3+1715 a^2 b c d^2-581 a b^2 c^2 d+5 b^3 c^3\right)}{64 a c^6 \sqrt{c+d x}}+\frac{5 (b c-a d) \left(231 a^3 d^3-189 a^2 b c d^2+21 a b^2 c^2 d+b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{3/2} c^{13/2}}-\frac{\sqrt{a+b x} (59 b c-99 a d) (b c-a d)}{96 c^3 x^2 (c+d x)^{3/2}}-\frac{11 a \sqrt{a+b x} (b c-a d)}{24 c^2 x^3 (c+d x)^{3/2}}-\frac{a (a+b x)^{3/2}}{4 c x^4 (c+d x)^{3/2}}",1,"$Aborted","F",-1
699,-1,0,191,180.0850002,"\int \frac{x^2 \sqrt{c+d x}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(x^2*Sqrt[c + d*x])/Sqrt[a + b*x],x]","\text{\$Aborted}","\frac{(b c-a d) \left(5 a^2 d^2+2 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{7/2} d^{5/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(5 a^2 d^2+2 a b c d+b^2 c^2\right)}{8 b^3 d^2}-\frac{\sqrt{a+b x} (c+d x)^{3/2} (5 a d+3 b c)}{12 b^2 d^2}+\frac{x \sqrt{a+b x} (c+d x)^{3/2}}{3 b d}",1,"$Aborted","F",-1
700,1,2937,125,7.6354918,"\int \frac{x \sqrt{c+d x}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(x*Sqrt[c + d*x])/Sqrt[a + b*x],x]","\text{Result too large to show}","-\frac{(b c-a d) (3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{5/2} d^{3/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (3 a d+b c)}{4 b^2 d}+\frac{\sqrt{a+b x} (c+d x)^{3/2}}{2 b d}",1,"((Sqrt[a + b]/(4*b^2*d) - Sqrt[a + b*x]/(4*b^2*d))*(Sqrt[c + d] - Sqrt[c + d*x])*(4*b^5*c^5 - 10*a*b^4*c^4*d + 13*b^5*c^4*d + 30*a^2*b^3*c^3*d^2 - 2*a*b^4*c^3*d^2 + 11*b^5*c^3*d^2 - 42*a^3*b^2*c^2*d^3 + 6*a^2*b^3*c^2*d^3 + 17*a*b^4*c^2*d^3 + 2*b^5*c^2*d^3 + 30*a^4*b*c*d^4 + 6*a^3*b^2*c*d^4 - 3*a^2*b^3*c*d^4 + 12*a*b^4*c*d^4 - 12*a^5*d^5 - 7*a^4*b*d^5 + 7*a^3*b^2*d^5 + 2*a^2*b^3*d^5 + 13*b^5*c^4*d*x - 2*a*b^4*c^3*d^2*x + 48*b^5*c^3*d^2*x + 6*a^2*b^3*c^2*d^3*x - 16*a*b^4*c^2*d^3*x + 48*b^5*c^2*d^3*x + 6*a^3*b^2*c*d^4*x + 48*a^2*b^3*c*d^4*x + 16*a*b^4*c*d^4*x + 16*b^5*c*d^4*x - 7*a^4*b*d^5*x - 16*a^3*b^2*d^5*x + 16*a^2*b^3*d^5*x + 16*a*b^4*d^5*x + 11*b^5*c^3*d^2*x^2 + 17*a*b^4*c^2*d^3*x^2 + 48*b^5*c^2*d^3*x^2 - 3*a^2*b^3*c*d^4*x^2 + 16*a*b^4*c*d^4*x^2 + 48*b^5*c*d^4*x^2 + 7*a^3*b^2*d^5*x^2 + 16*a^2*b^3*d^5*x^2 + 16*a*b^4*d^5*x^2 + 16*b^5*d^5*x^2 + 2*b^5*c^2*d^3*x^3 + 12*a*b^4*c*d^4*x^3 + 16*b^5*c*d^4*x^3 + 2*a^2*b^3*d^5*x^3 + 16*a*b^4*d^5*x^3 + 16*b^5*d^5*x^3 + 18*b^4*Sqrt[a + b]*c^4*d*Sqrt[a + b*x] - 42*a*b^3*Sqrt[a + b]*c^3*d^2*Sqrt[a + b*x] + 35*b^4*Sqrt[a + b]*c^3*d^2*Sqrt[a + b*x] + 42*a^2*b^2*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] - 45*a*b^3*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] + 18*b^4*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] - 30*a^3*b*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] + 9*a^2*b^2*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] - 12*a*b^3*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] + 12*a^4*Sqrt[a + b]*d^5*Sqrt[a + b*x] + a^3*b*Sqrt[a + b]*d^5*Sqrt[a + b*x] - 6*a^2*b^2*Sqrt[a + b]*d^5*Sqrt[a + b*x] + 35*b^4*Sqrt[a + b]*c^3*d^2*x*Sqrt[a + b*x] - 45*a*b^3*Sqrt[a + b]*c^2*d^3*x*Sqrt[a + b*x] + 60*b^4*Sqrt[a + b]*c^2*d^3*x*Sqrt[a + b*x] + 9*a^2*b^2*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] - 72*a*b^3*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] + 24*b^4*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] + a^3*b*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] + 12*a^2*b^2*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] - 24*a*b^3*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] + 18*b^4*Sqrt[a + b]*c^2*d^3*x^2*Sqrt[a + b*x] - 12*a*b^3*Sqrt[a + b]*c*d^4*x^2*Sqrt[a + b*x] + 24*b^4*Sqrt[a + b]*c*d^4*x^2*Sqrt[a + b*x] - 6*a^2*b^2*Sqrt[a + b]*d^5*x^2*Sqrt[a + b*x] - 24*a*b^3*Sqrt[a + b]*d^5*x^2*Sqrt[a + b*x] - 4*b^5*c^4*Sqrt[c + d]*Sqrt[c + d*x] + 10*a*b^4*c^3*d*Sqrt[c + d]*Sqrt[c + d*x] - 11*b^5*c^3*d*Sqrt[c + d]*Sqrt[c + d*x] - 30*a^2*b^3*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 3*a*b^4*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 6*b^5*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 46*a^3*b^2*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 15*a^2*b^3*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] - 12*a*b^4*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] - 22*a^4*b*d^4*Sqrt[c + d]*Sqrt[c + d*x] - a^3*b^2*d^4*Sqrt[c + d]*Sqrt[c + d*x] + 18*a^2*b^3*d^4*Sqrt[c + d]*Sqrt[c + d*x] - 11*b^5*c^3*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 3*a*b^4*c^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 36*b^5*c^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 15*a^2*b^3*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] + 24*a*b^4*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] - 24*b^5*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] - a^3*b^2*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] + 12*a^2*b^3*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] + 24*a*b^4*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] - 6*b^5*c^2*d^2*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 12*a*b^4*c*d^3*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 24*b^5*c*d^3*Sqrt[c + d]*x^2*Sqrt[c + d*x] + 18*a^2*b^3*d^4*Sqrt[c + d]*x^2*Sqrt[c + d*x] + 24*a*b^4*d^4*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 18*b^4*Sqrt[a + b]*c^3*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 42*a*b^3*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 26*b^4*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 46*a^2*b^2*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 20*a*b^3*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*b^4*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 22*a^3*b*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 10*a^2*b^2*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*a*b^3*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 26*b^4*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 20*a*b^3*Sqrt[a + b]*c*d^3*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 32*b^4*Sqrt[a + b]*c*d^3*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 10*a^2*b^2*Sqrt[a + b]*d^4*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 16*b^4*Sqrt[a + b]*d^4*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*b^4*Sqrt[a + b]*c*d^3*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*a*b^3*Sqrt[a + b]*d^4*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x] - 16*b^4*Sqrt[a + b]*d^4*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^4 + (-1/2*c^2/(Sqrt[b]*d^(3/2)) - (a*c)/(b^(3/2)*Sqrt[d]) + (3*a^2*Sqrt[d])/(2*b^(5/2)))*ArcTanh[(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*(Sqrt[c + d] - Sqrt[c + d*x]))]","B",1
701,1,350,72,0.0006183,"\int \frac{\sqrt{c+d x}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/Sqrt[a + b*x],x]","\frac{\left(\frac{\sqrt{a+b}}{b}-\frac{\sqrt{a+b x}}{b}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(a^2 d^2+b c d \sqrt{a+b} \sqrt{a+b x}+a b d \sqrt{c+d} \sqrt{c+d x}-2 b d \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+a b d^2 x-a d^2 \sqrt{a+b} \sqrt{a+b x}+a b d^2+b^2 c^2+b^2 c d x-b^2 c \sqrt{c+d} \sqrt{c+d x}+b^2 c d+2 b^2 d^2 x\right)}{\left(-d \sqrt{a+b} \sqrt{a+b x}+a d+b \sqrt{c+d} \sqrt{c+d x}+b (-c)\right)^2}+\left(\frac{2 c}{\sqrt{b} \sqrt{d}}-\frac{2 a \sqrt{d}}{b^{3/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b}-\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \left(\sqrt{c+d}-\sqrt{c+d x}\right)}\right)","\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{3/2} \sqrt{d}}+\frac{\sqrt{a+b x} \sqrt{c+d x}}{b}",1,"((Sqrt[a + b]/b - Sqrt[a + b*x]/b)*(Sqrt[c + d] - Sqrt[c + d*x])*(b^2*c^2 + b^2*c*d + a^2*d^2 + a*b*d^2 + b^2*c*d*x + a*b*d^2*x + 2*b^2*d^2*x + b*Sqrt[a + b]*c*d*Sqrt[a + b*x] - a*Sqrt[a + b]*d^2*Sqrt[a + b*x] - b^2*c*Sqrt[c + d]*Sqrt[c + d*x] + a*b*d*Sqrt[c + d]*Sqrt[c + d*x] - 2*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^2 + ((2*c)/(Sqrt[b]*Sqrt[d]) - (2*a*Sqrt[d])/b^(3/2))*ArcTanh[(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*(Sqrt[c + d] - Sqrt[c + d*x]))]","B",1
702,1,370,85,3.0997766,"\int \frac{\sqrt{c+d x}}{x \sqrt{a+b x}} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(x*Sqrt[a + b*x]),x]","c \text{RootSum}\left[\text{$\#$1}^4 d^2-4 \text{$\#$1}^3 d \sqrt{a+b} \sqrt{c+d}+4 \text{$\#$1}^2 a d+4 \text{$\#$1}^2 b c+6 \text{$\#$1}^2 b d-4 \text{$\#$1} b \sqrt{a+b} \sqrt{c+d}+b^2\&,\frac{-\text{$\#$1}^2 d \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)+\text{$\#$1}^2 d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)+b \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)-b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{\text{$\#$1}^3 d^2-3 \text{$\#$1}^2 d \sqrt{a+b} \sqrt{c+d}+2 \text{$\#$1} a d+2 \text{$\#$1} b c+3 \text{$\#$1} b d-b \sqrt{a+b} \sqrt{c+d}}\&\right]+\frac{4 \sqrt{d} \tanh ^{-1}\left(\frac{\frac{\sqrt{d} \sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b}}}{\sqrt{c+d}-\sqrt{c+d x}}\right)}{\sqrt{b}}","\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b}}-\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{a}}",1,"(4*Sqrt[d]*ArcTanh[((Sqrt[a + b]*Sqrt[d])/Sqrt[b] - (Sqrt[d]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[c + d] - Sqrt[c + d*x])])/Sqrt[b] + c*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ]","C",1
703,1,844,76,6.7175608,"\int \frac{\sqrt{c+d x}}{x^2 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(x^2*Sqrt[a + b*x]),x]","\frac{\sqrt{c+d x} \left(2 d^2 a^3+2 b d^2 a^2-2 b c d a^2-2 b c d x a^2-2 b^2 c d a+2 b^2 c^2 x a-2 b^2 c d x a+2 b^3 c^2 x\right)+\sqrt{a+b} \sqrt{a+b x} \sqrt{c+d x} \left(-2 c^2 b^2-c d b^2+c d x b^2-a d^2 b+2 a c d b+a d^2 x b+2 a c d x b-2 a^2 d^2\right)+\sqrt{c+d} \left(-2 d^2 x a^3-b d^2 x^2 a^2+2 b c d a^2-b d^2 x a^2+2 b c d x a^2-b^2 d^2 x^2 a-b^2 c d x^2 a+2 b^2 c d a-2 b^2 c^2 x a+b^2 d^2 x a+3 b^2 c d x a-b^3 c d x^2-2 b^3 c^2 x+b^3 c d x+\sqrt{a+b} \sqrt{a+b x} \left(2 b^2 c^2-2 a b d c-2 a b d x c+2 a^2 d^2 x\right)\right)}{\sqrt{a+b x} \left(a \left(2 c d b^2-2 a d^2 b+2 a c d b-2 a^2 d^2\right) x+a \sqrt{c+d} \left(-2 d b^2-2 a d b\right) \sqrt{c+d x} x\right)+\sqrt{a+b} \left(a \left(2 c^2 b^2+c d b^2+2 d^2 x b^2+c d x b^2+a d^2 b-2 a c d b+a d^2 x b+2 a^2 d^2\right) x+a \sqrt{c+d} \left(2 a b d-2 b^2 c\right) \sqrt{c+d x} x\right)}+\left(\frac{d}{2}-\frac{b c}{2 a}\right) \text{RootSum}\left[d^2 \text{$\#$1}^4-4 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^3+4 b c \text{$\#$1}^2+4 a d \text{$\#$1}^2+6 b d \text{$\#$1}^2-4 b \sqrt{a+b} \sqrt{c+d} \text{$\#$1}+b^2\&,\frac{d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2-d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2-b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)+b \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right)}{d^2 \text{$\#$1}^3-3 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^2+2 b c \text{$\#$1}+2 a d \text{$\#$1}+3 b d \text{$\#$1}-b \sqrt{a+b} \sqrt{c+d}}\&\right]","\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{3/2} \sqrt{c}}-\frac{\sqrt{a+b x} \sqrt{c+d x}}{a x}",1,"(Sqrt[c + d*x]*(-2*a^2*b*c*d - 2*a*b^2*c*d + 2*a^3*d^2 + 2*a^2*b*d^2 + 2*a*b^2*c^2*x + 2*b^3*c^2*x - 2*a^2*b*c*d*x - 2*a*b^2*c*d*x) + Sqrt[a + b]*Sqrt[a + b*x]*Sqrt[c + d*x]*(-2*b^2*c^2 + 2*a*b*c*d - b^2*c*d - 2*a^2*d^2 - a*b*d^2 + 2*a*b*c*d*x + b^2*c*d*x + a*b*d^2*x) + Sqrt[c + d]*(2*a^2*b*c*d + 2*a*b^2*c*d - 2*a*b^2*c^2*x - 2*b^3*c^2*x + 2*a^2*b*c*d*x + 3*a*b^2*c*d*x + b^3*c*d*x - 2*a^3*d^2*x - a^2*b*d^2*x + a*b^2*d^2*x - a*b^2*c*d*x^2 - b^3*c*d*x^2 - a^2*b*d^2*x^2 - a*b^2*d^2*x^2 + Sqrt[a + b]*Sqrt[a + b*x]*(2*b^2*c^2 - 2*a*b*c*d - 2*a*b*c*d*x + 2*a^2*d^2*x)))/(Sqrt[a + b*x]*(a*(2*a*b*c*d + 2*b^2*c*d - 2*a^2*d^2 - 2*a*b*d^2)*x + a*Sqrt[c + d]*(-2*a*b*d - 2*b^2*d)*x*Sqrt[c + d*x]) + Sqrt[a + b]*(a*Sqrt[c + d]*(-2*b^2*c + 2*a*b*d)*x*Sqrt[c + d*x] + a*x*(2*b^2*c^2 - 2*a*b*c*d + b^2*c*d + 2*a^2*d^2 + a*b*d^2 + b^2*c*d*x + a*b*d^2*x + 2*b^2*d^2*x))) + (-1/2*(b*c)/a + d/2)*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ]","C",1
704,1,4559,131,154.0580887,"\int \frac{\sqrt{c+d x}}{x^3 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(x^3*Sqrt[a + b*x]),x]","\text{Result too large to show}","-\frac{(b c-a d) (a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{5/2} c^{3/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (a d+3 b c)}{4 a^2 c x}-\frac{\sqrt{a+b x} (c+d x)^{3/2}}{2 a c x^2}",1,"(Sqrt[a + b]*Sqrt[a + b*x]*Sqrt[c + d*x]*(-16*a*b^4*c^5 + 32*a^2*b^3*c^4*d - 16*a*b^4*c^4*d - 48*a^3*b^2*c^3*d^2 - 2*a*b^4*c^3*d^2 + 32*a^4*b*c^2*d^3 - 12*a^2*b^3*c^2*d^3 - 16*a^5*c*d^4 - 16*a^4*b*c*d^4 - 2*a^3*b^2*c*d^4 + 24*b^5*c^5*x - 72*a*b^4*c^4*d*x + 24*b^5*c^4*d*x + 88*a^2*b^3*c^3*d^2*x - 52*a*b^4*c^3*d^2*x + 3*b^5*c^3*d^2*x - 72*a^3*b^2*c^2*d^3*x + 24*a^2*b^3*c^2*d^3*x + a*b^4*c^2*d^3*x + 24*a^4*b*c*d^4*x - 20*a^3*b^2*c*d^4*x - 19*a^2*b^3*c*d^4*x - 8*a^5*d^5*x - 8*a^4*b*d^5*x - a^3*b^2*d^5*x + 32*a^2*b^3*c^4*d*x^2 - 16*a*b^4*c^4*d*x^2 - 24*b^5*c^4*d*x^2 - 48*a^3*b^2*c^3*d^2*x^2 + 80*a^2*b^3*c^3*d^2*x^2 + 58*a*b^4*c^3*d^2*x^2 + 6*b^5*c^3*d^2*x^2 + 32*a^4*b*c^2*d^3*x^2 - 80*a^3*b^2*c^2*d^3*x^2 - 36*a^2*b^3*c^2*d^3*x^2 + 2*a*b^4*c^2*d^3*x^2 + 12*b^5*c^2*d^3*x^2 + 48*a^4*b*c*d^4*x^2 + 10*a^3*b^2*c*d^4*x^2 - 6*a^2*b^3*c*d^4*x^2 - 8*a*b^4*c*d^4*x^2 + 8*a^4*b*d^5*x^2 - 2*a^3*b^2*d^5*x^2 - 4*a^2*b^3*d^5*x^2 + 8*a^2*b^3*c^3*d^2*x^3 - 4*a*b^4*c^3*d^2*x^3 - 9*b^5*c^3*d^2*x^3 + 8*a^3*b^2*c^2*d^3*x^3 + 24*a^2*b^3*c^2*d^3*x^3 - 3*a*b^4*c^2*d^3*x^3 - 12*b^5*c^2*d^3*x^3 + 12*a^3*b^2*c*d^4*x^3 + 25*a^2*b^3*c*d^4*x^3 + 8*a*b^4*c*d^4*x^3 + 3*a^3*b^2*d^5*x^3 + 4*a^2*b^3*d^5*x^3) + Sqrt[c + d*x]*(-32*a^3*b^3*c^4*d - 32*a^2*b^4*c^4*d + 48*a^4*b^2*c^3*d^2 + 24*a^3*b^3*c^3*d^2 - 24*a^2*b^4*c^3*d^2 - 32*a^5*b*c^2*d^3 - 16*a^4*b^2*c^2*d^3 + 16*a^3*b^3*c^2*d^3 + 16*a^6*c*d^4 + 24*a^5*b*c*d^4 + 8*a^4*b^2*c*d^4 + 16*a^2*b^4*c^4*d*x + 16*a*b^5*c^4*d*x - 64*a^3*b^3*c^3*d^2*x - 52*a^2*b^4*c^3*d^2*x + 12*a*b^5*c^3*d^2*x + 56*a^4*b^2*c^2*d^3*x + 4*a^3*b^3*c^2*d^3*x - 52*a^2*b^4*c^2*d^3*x - 16*a^5*b*c*d^4*x + 20*a^4*b^2*c*d^4*x + 36*a^3*b^3*c*d^4*x + 8*a^6*d^5*x + 12*a^5*b*d^5*x + 4*a^4*b^2*d^5*x + 16*a^2*b^4*c^5*x^2 - 8*a*b^5*c^5*x^2 - 24*b^6*c^5*x^2 - 32*a^3*b^3*c^4*d*x^2 + 48*a^2*b^4*c^4*d*x^2 + 92*a*b^5*c^4*d*x^2 + 12*b^6*c^4*d*x^2 + 48*a^4*b^2*c^3*d^2*x^2 - 56*a^3*b^3*c^3*d^2*x^2 - 136*a^2*b^4*c^3*d^2*x^2 - 8*a*b^5*c^3*d^2*x^2 + 24*b^6*c^3*d^2*x^2 - 32*a^5*b*c^2*d^3*x^2 + 64*a^4*b^2*c^2*d^3*x^2 + 120*a^3*b^3*c^2*d^3*x^2 - 16*a^2*b^4*c^2*d^3*x^2 - 40*a*b^5*c^2*d^3*x^2 - 48*a^5*b*c*d^4*x^2 - 48*a^4*b^2*c*d^4*x^2 + 8*a^3*b^3*c*d^4*x^2 + 8*a^2*b^4*c*d^4*x^2 - 4*a^5*b*d^5*x^2 + 4*a^4*b^2*d^5*x^2 + 8*a^3*b^3*d^5*x^2 + 8*a^2*b^4*c^4*d*x^3 - 4*a*b^5*c^4*d*x^3 - 12*b^6*c^4*d*x^3 + 16*a^3*b^3*c^3*d^2*x^3 + 36*a^2*b^4*c^3*d^2*x^3 - 4*a*b^5*c^3*d^2*x^3 - 24*b^6*c^3*d^2*x^3 - 24*a^4*b^2*c^2*d^3*x^3 + 4*a^3*b^3*c^2*d^3*x^3 + 68*a^2*b^4*c^2*d^3*x^3 + 40*a*b^5*c^2*d^3*x^3 - 36*a^4*b^2*c*d^4*x^3 - 44*a^3*b^3*c*d^4*x^3 - 8*a^2*b^4*c*d^4*x^3 - 8*a^4*b^2*d^5*x^3 - 8*a^3*b^3*d^5*x^3) + Sqrt[c + d]*(32*a^3*b^3*c^4*d + 32*a^2*b^4*c^4*d - 48*a^4*b^2*c^3*d^2 - 40*a^3*b^3*c^3*d^2 + 8*a^2*b^4*c^3*d^2 + 32*a^5*b*c^2*d^3 + 40*a^4*b^2*c^2*d^3 + 8*a^3*b^3*c^2*d^3 - 16*a^2*b^4*c^4*d*x - 16*a*b^5*c^4*d*x + 80*a^3*b^3*c^3*d^2*x + 76*a^2*b^4*c^3*d^2*x - 4*a*b^5*c^3*d^2*x - 80*a^4*b^2*c^2*d^3*x - 56*a^3*b^3*c^2*d^3*x + 24*a^2*b^4*c^2*d^3*x + 48*a^5*b*c*d^4*x + 60*a^4*b^2*c*d^4*x + 12*a^3*b^3*c*d^4*x - 16*a^2*b^4*c^5*x^2 + 8*a*b^5*c^5*x^2 + 24*b^6*c^5*x^2 + 32*a^3*b^3*c^4*d*x^2 - 40*a^2*b^4*c^4*d*x^2 - 96*a*b^5*c^4*d*x^2 - 24*b^6*c^4*d*x^2 - 48*a^4*b^2*c^3*d^2*x^2 + 40*a^3*b^3*c^3*d^2*x^2 + 146*a^2*b^4*c^3*d^2*x^2 + 49*a*b^5*c^3*d^2*x^2 - 9*b^6*c^3*d^2*x^2 + 32*a^5*b*c^2*d^3*x^2 - 40*a^4*b^2*c^2*d^3*x^2 - 108*a^3*b^3*c^2*d^3*x^2 - 39*a^2*b^4*c^2*d^3*x^2 - 3*a*b^5*c^2*d^3*x^2 - 16*a^6*c*d^4*x^2 + 8*a^5*b*c*d^4*x^2 + 34*a^4*b^2*c*d^4*x^2 + 35*a^3*b^3*c*d^4*x^2 + 25*a^2*b^4*c*d^4*x^2 - 8*a^6*d^5*x^2 + 11*a^4*b^2*d^5*x^2 + 3*a^3*b^3*d^5*x^2 - 16*a^2*b^4*c^4*d*x^3 + 8*a*b^5*c^4*d*x^3 + 24*b^6*c^4*d*x^3 - 52*a^2*b^4*c^3*d^2*x^3 - 46*a*b^5*c^3*d^2*x^3 + 6*b^6*c^3*d^2*x^3 + 24*a^3*b^3*c^2*d^3*x^3 + 26*a^2*b^4*c^2*d^3*x^3 - 10*a*b^5*c^2*d^3*x^3 - 12*b^6*c^2*d^3*x^3 - 16*a^5*b*c*d^4*x^3 - 36*a^4*b^2*c*d^4*x^3 - 26*a^3*b^3*c*d^4*x^3 + 2*a^2*b^4*c*d^4*x^3 + 8*a*b^5*c*d^4*x^3 - 8*a^5*b*d^5*x^3 - 10*a^4*b^2*d^5*x^3 + 2*a^3*b^3*d^5*x^3 + 4*a^2*b^4*d^5*x^3 - 2*a^2*b^4*c^3*d^2*x^4 + a*b^5*c^3*d^2*x^4 + 3*b^6*c^3*d^2*x^4 - 12*a^3*b^3*c^2*d^3*x^4 - 11*a^2*b^4*c^2*d^3*x^4 + 13*a*b^5*c^2*d^3*x^4 + 12*b^6*c^2*d^3*x^4 - 2*a^4*b^2*c*d^4*x^4 - 21*a^3*b^3*c*d^4*x^4 - 27*a^2*b^4*c*d^4*x^4 - 8*a*b^5*c*d^4*x^4 - a^4*b^2*d^5*x^4 - 5*a^3*b^3*d^5*x^4 - 4*a^2*b^4*d^5*x^4 + Sqrt[a + b]*Sqrt[a + b*x]*(16*a*b^4*c^5 - 32*a^2*b^3*c^4*d + 8*a*b^4*c^4*d + 48*a^3*b^2*c^3*d^2 + 16*a^2*b^3*c^3*d^2 - 32*a^4*b*c^2*d^3 - 24*a^3*b^2*c^2*d^3 - 24*b^5*c^5*x + 80*a*b^4*c^4*d*x - 12*b^5*c^4*d*x - 104*a^2*b^3*c^3*d^2*x + 20*a*b^4*c^3*d^2*x + 96*a^3*b^2*c^2*d^3*x + 28*a^2*b^3*c^2*d^3*x - 48*a^4*b*c*d^4*x - 36*a^3*b^2*c*d^4*x - 32*a^2*b^3*c^4*d*x^2 + 16*a*b^4*c^4*d*x^2 + 12*b^5*c^4*d*x^2 + 48*a^3*b^2*c^3*d^2*x^2 - 64*a^2*b^3*c^3*d^2*x^2 - 32*a*b^4*c^3*d^2*x^2 - 24*b^5*c^3*d^2*x^2 - 32*a^4*b*c^2*d^3*x^2 + 56*a^3*b^2*c^2*d^3*x^2 + 24*a^2*b^3*c^2*d^3*x^2 + 40*a*b^4*c^2*d^3*x^2 + 16*a^5*c*d^4*x^2 - 16*a^4*b*c*d^4*x^2 - 8*a^2*b^3*c*d^4*x^2 + 8*a^5*d^5*x^2 - 4*a^4*b*d^5*x^2 - 8*a^3*b^2*d^5*x^2 - 24*a^2*b^3*c^3*d^2*x^3 + 12*a*b^4*c^3*d^2*x^3 + 24*b^5*c^3*d^2*x^3 + 16*a^3*b^2*c^2*d^3*x^3 - 52*a^2*b^3*c^2*d^3*x^3 - 40*a*b^4*c^2*d^3*x^3 + 8*a^4*b*c*d^4*x^3 + 36*a^3*b^2*c*d^4*x^3 + 8*a^2*b^3*c*d^4*x^3 + 4*a^4*b*d^5*x^3 + 8*a^3*b^2*d^5*x^3)))/(Sqrt[a + b*x]*(4*a^2*c*Sqrt[c + d]*x^2*Sqrt[c + d*x]*(-16*a*b^3*c^2*d - 16*b^4*c^2*d + 24*a^2*b^2*c*d^2 + 20*a*b^3*c*d^2 - 4*b^4*c*d^2 - 16*a^3*b*d^3 - 20*a^2*b^2*d^3 - 4*a*b^3*d^3 - 4*a*b^3*c*d^2*x - 4*b^4*c*d^2*x - 4*a^2*b^2*d^3*x - 12*a*b^3*d^3*x - 8*b^4*d^3*x) + 4*a^2*c*x^2*(16*a*b^3*c^3*d + 16*b^4*c^3*d - 24*a^2*b^2*c^2*d^2 - 12*a*b^3*c^2*d^2 + 12*b^4*c^2*d^2 + 16*a^3*b*c*d^3 + 8*a^2*b^2*c*d^3 - 8*a*b^3*c*d^3 - 8*a^4*d^4 - 12*a^3*b*d^4 - 4*a^2*b^2*d^4 + 12*a*b^3*c^2*d^2*x + 12*b^4*c^2*d^2*x - 8*a^2*b^2*c*d^3*x + 8*a*b^3*c*d^3*x + 16*b^4*c*d^3*x - 4*a^3*b*d^4*x - 20*a^2*b^2*d^4*x - 16*a*b^3*d^4*x)) + Sqrt[a + b]*(4*a^2*c*Sqrt[c + d]*x^2*Sqrt[c + d*x]*(-8*b^4*c^3 + 16*a*b^3*c^2*d - 4*b^4*c^2*d - 24*a^2*b^2*c*d^2 - 8*a*b^3*c*d^2 + 16*a^3*b*d^3 + 12*a^2*b^2*d^3 - 4*b^4*c^2*d*x - 8*a*b^3*c*d^2*x - 16*b^4*c*d^2*x + 12*a^2*b^2*d^3*x + 16*a*b^3*d^3*x) + 4*a^2*c*x^2*(8*b^4*c^4 - 16*a*b^3*c^3*d + 8*b^4*c^3*d + 24*a^2*b^2*c^2*d^2 + b^4*c^2*d^2 - 16*a^3*b*c*d^3 + 6*a*b^3*c*d^3 + 8*a^4*d^4 + 8*a^3*b*d^4 + a^2*b^2*d^4 + 8*b^4*c^3*d*x + 22*b^4*c^2*d^2*x - 12*a*b^3*c*d^3*x + 8*b^4*c*d^3*x + 8*a^3*b*d^4*x + 22*a^2*b^2*d^4*x + 8*a*b^3*d^4*x + b^4*c^2*d^2*x^2 + 6*a*b^3*c*d^3*x^2 + 8*b^4*c*d^3*x^2 + a^2*b^2*d^4*x^2 + 8*a*b^3*d^4*x^2 + 8*b^4*d^4*x^2))) + ((3*b^2*c)/(8*a^2) - (b*d)/(4*a) - d^2/(8*c))*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ]","C",1
705,-1,0,191,180.0700136,"\int \frac{\sqrt{c+d x}}{x^4 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(x^4*Sqrt[a + b*x]),x]","\text{\$Aborted}","-\frac{\sqrt{a+b x} \sqrt{c+d x} (5 b c-3 a d) (a d+3 b c)}{24 a^3 c^2 x}+\frac{\sqrt{a+b x} \sqrt{c+d x} (5 b c-a d)}{12 a^2 c x^2}+\frac{(b c-a d) \left(a^2 d^2+2 a b c d+5 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 a^{7/2} c^{5/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x}}{3 a x^3}",1,"$Aborted","F",-1
706,-1,0,254,180.0169138,"\int \frac{x^2 (c+d x)^{3/2}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(x^2*(c + d*x)^(3/2))/Sqrt[a + b*x],x]","\text{\$Aborted}","\frac{(b c-a d)^2 \left(35 a^2 d^2+10 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{9/2} d^{5/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d) \left(35 a^2 d^2+10 a b c d+3 b^2 c^2\right)}{64 b^4 d^2}+\frac{\sqrt{a+b x} (c+d x)^{3/2} \left(35 a^2 d^2+10 a b c d+3 b^2 c^2\right)}{96 b^3 d^2}-\frac{\sqrt{a+b x} (c+d x)^{5/2} (7 a d+3 b c)}{24 b^2 d^2}+\frac{x \sqrt{a+b x} (c+d x)^{5/2}}{4 b d}",1,"$Aborted","F",-1
707,-1,0,171,180.0938861,"\int \frac{x (c+d x)^{3/2}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(x*(c + d*x)^(3/2))/Sqrt[a + b*x],x]","\text{\$Aborted}","-\frac{(b c-a d)^2 (5 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{7/2} d^{3/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d) (5 a d+b c)}{8 b^3 d}-\frac{\sqrt{a+b x} (c+d x)^{3/2} (5 a d+b c)}{12 b^2 d}+\frac{\sqrt{a+b x} (c+d x)^{5/2}}{3 b d}",1,"$Aborted","F",-1
708,1,2908,113,0.0010943,"\int \frac{(c+d x)^{3/2}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/Sqrt[a + b*x],x]","\text{Result too large to show}","\frac{3 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{5/2} \sqrt{d}}+\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 b^2}+\frac{\sqrt{a+b x} (c+d x)^{3/2}}{2 b}",1,"((Sqrt[a + b]/(4*b^2) - Sqrt[a + b*x]/(4*b^2))*(Sqrt[c + d] - Sqrt[c + d*x])*(20*b^5*c^5 - 34*a*b^4*c^4*d + 33*b^5*c^4*d + 78*a^2*b^3*c^3*d^2 + 10*a*b^4*c^3*d^2 + 15*b^5*c^3*d^2 - 66*a^3*b^2*c^2*d^3 + 18*a^2*b^3*c^2*d^3 + 41*a*b^4*c^2*d^3 + 2*b^5*c^2*d^3 + 46*a^4*b*c*d^4 + 26*a^3*b^2*c*d^4 + a^2*b^3*c*d^4 + 12*a*b^4*c*d^4 - 12*a^5*d^5 - 7*a^4*b*d^5 + 7*a^3*b^2*d^5 + 2*a^2*b^3*d^5 + 33*b^5*c^4*d*x + 10*a*b^4*c^3*d^2*x + 112*b^5*c^3*d^2*x + 18*a^2*b^3*c^2*d^3*x - 16*a*b^4*c^2*d^3*x + 80*b^5*c^2*d^3*x + 26*a^3*b^2*c*d^4*x + 112*a^2*b^3*c*d^4*x + 48*a*b^4*c*d^4*x + 16*b^5*c*d^4*x - 7*a^4*b*d^5*x - 16*a^3*b^2*d^5*x + 16*a^2*b^3*d^5*x + 16*a*b^4*d^5*x + 15*b^5*c^3*d^2*x^2 + 41*a*b^4*c^2*d^3*x^2 + 80*b^5*c^2*d^3*x^2 + a^2*b^3*c*d^4*x^2 + 48*a*b^4*c*d^4*x^2 + 80*b^5*c*d^4*x^2 + 7*a^3*b^2*d^5*x^2 + 16*a^2*b^3*d^5*x^2 + 16*a*b^4*d^5*x^2 + 16*b^5*d^5*x^2 + 2*b^5*c^2*d^3*x^3 + 12*a*b^4*c*d^4*x^3 + 16*b^5*c*d^4*x^3 + 2*a^2*b^3*d^5*x^3 + 16*a*b^4*d^5*x^3 + 16*b^5*d^5*x^3 + 58*b^4*Sqrt[a + b]*c^4*d*Sqrt[a + b*x] - 90*a*b^3*Sqrt[a + b]*c^3*d^2*Sqrt[a + b*x] + 71*b^4*Sqrt[a + b]*c^3*d^2*Sqrt[a + b*x] + 66*a^2*b^2*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] - 69*a*b^3*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] + 18*b^4*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] - 46*a^3*b*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] - 3*a^2*b^2*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] - 12*a*b^3*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] + 12*a^4*Sqrt[a + b]*d^5*Sqrt[a + b*x] + a^3*b*Sqrt[a + b]*d^5*Sqrt[a + b*x] - 6*a^2*b^2*Sqrt[a + b]*d^5*Sqrt[a + b*x] + 71*b^4*Sqrt[a + b]*c^3*d^2*x*Sqrt[a + b*x] - 69*a*b^3*Sqrt[a + b]*c^2*d^3*x*Sqrt[a + b*x] + 108*b^4*Sqrt[a + b]*c^2*d^3*x*Sqrt[a + b*x] - 3*a^2*b^2*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] - 120*a*b^3*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] + 24*b^4*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] + a^3*b*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] + 12*a^2*b^2*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] - 24*a*b^3*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] + 18*b^4*Sqrt[a + b]*c^2*d^3*x^2*Sqrt[a + b*x] - 12*a*b^3*Sqrt[a + b]*c*d^4*x^2*Sqrt[a + b*x] + 24*b^4*Sqrt[a + b]*c*d^4*x^2*Sqrt[a + b*x] - 6*a^2*b^2*Sqrt[a + b]*d^5*x^2*Sqrt[a + b*x] - 24*a*b^3*Sqrt[a + b]*d^5*x^2*Sqrt[a + b*x] - 20*b^5*c^4*Sqrt[c + d]*Sqrt[c + d*x] + 34*a*b^4*c^3*d*Sqrt[c + d]*Sqrt[c + d*x] - 23*b^5*c^3*d*Sqrt[c + d]*Sqrt[c + d*x] - 78*a^2*b^3*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 27*a*b^4*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 6*b^5*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 86*a^3*b^2*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 51*a^2*b^3*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] - 12*a*b^4*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] - 22*a^4*b*d^4*Sqrt[c + d]*Sqrt[c + d*x] - a^3*b^2*d^4*Sqrt[c + d]*Sqrt[c + d*x] + 18*a^2*b^3*d^4*Sqrt[c + d]*Sqrt[c + d*x] - 23*b^5*c^3*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 27*a*b^4*c^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 84*b^5*c^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 51*a^2*b^3*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] + 72*a*b^4*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] - 24*b^5*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] - a^3*b^2*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] + 12*a^2*b^3*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] + 24*a*b^4*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] - 6*b^5*c^2*d^2*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 12*a*b^4*c*d^3*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 24*b^5*c*d^3*Sqrt[c + d]*x^2*Sqrt[c + d*x] + 18*a^2*b^3*d^4*Sqrt[c + d]*x^2*Sqrt[c + d*x] + 24*a*b^4*d^4*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 58*b^4*Sqrt[a + b]*c^3*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 90*a*b^3*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 42*b^4*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 86*a^2*b^2*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 4*a*b^3*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*b^4*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 22*a^3*b*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 10*a^2*b^2*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*a*b^3*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 42*b^4*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 4*a*b^3*Sqrt[a + b]*c*d^3*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 64*b^4*Sqrt[a + b]*c*d^3*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 10*a^2*b^2*Sqrt[a + b]*d^4*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 16*b^4*Sqrt[a + b]*d^4*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*b^4*Sqrt[a + b]*c*d^3*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x] - 8*a*b^3*Sqrt[a + b]*d^4*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x] - 16*b^4*Sqrt[a + b]*d^4*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^4 + (3*(b*c - a*d)^2*ArcTanh[((Sqrt[a + b]*Sqrt[d])/Sqrt[b] - (Sqrt[d]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[c + d] - Sqrt[c + d*x])])/(2*b^(5/2)*Sqrt[d])","B",1
709,1,1523,116,68.7026593,"\int \frac{(c+d x)^{3/2}}{x \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(x*Sqrt[a + b*x]),x]","-\frac{1}{2} \text{RootSum}\left[d^4 \text{$\#$1}^8-8 a d^3 \text{$\#$1}^6-4 b d^3 \text{$\#$1}^6-16 a c d^2 \text{$\#$1}^6-8 b c d^2 \text{$\#$1}^6+16 b^2 c^2 \text{$\#$1}^4+16 a^2 d^2 \text{$\#$1}^4+6 b^2 d^2 \text{$\#$1}^4+16 a b d^2 \text{$\#$1}^4+16 b^2 c d \text{$\#$1}^4-8 b^3 c \text{$\#$1}^2-16 a b^2 c \text{$\#$1}^2-4 b^3 d \text{$\#$1}^2-8 a b^2 d \text{$\#$1}^2+b^4\&,\frac{-d^3 \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^6+d^3 \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^6-4 \sqrt{a+b} d^2 \sqrt{c+d} \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^5+4 \sqrt{a+b} d^2 \sqrt{c+d} \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^5-4 a d^2 \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^4-5 b d^2 \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^4-4 b c d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^4+4 a d^2 \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^4+5 b d^2 \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^4+4 b c d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^4+4 b^2 c \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2+5 b^2 d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2+4 a b d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2-4 b^2 c \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2-5 b^2 d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2-4 a b d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2+4 b^2 \sqrt{a+b} \sqrt{c+d} \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}-4 b^2 \sqrt{a+b} \sqrt{c+d} \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}+b^3 \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)-b^3 \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right)}{d^4 \text{$\#$1}^7-6 a d^3 \text{$\#$1}^5-3 b d^3 \text{$\#$1}^5-12 a c d^2 \text{$\#$1}^5-6 b c d^2 \text{$\#$1}^5+8 b^2 c^2 \text{$\#$1}^3+8 a^2 d^2 \text{$\#$1}^3+3 b^2 d^2 \text{$\#$1}^3+8 a b d^2 \text{$\#$1}^3+8 b^2 c d \text{$\#$1}^3-2 b^3 c \text{$\#$1}-4 a b^2 c \text{$\#$1}-b^3 d \text{$\#$1}-2 a b^2 d \text{$\#$1}}\&\right] c^2+\frac{\left(\frac{\sqrt{a+b} d}{b}-\frac{d \sqrt{a+b x}}{b}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(c^2 b^2+c d b^2+2 d^2 x b^2+c d x b^2-c \sqrt{c+d} \sqrt{c+d x} b^2+a d^2 b+a d^2 x b+\sqrt{a+b} c d \sqrt{a+b x} b+a d \sqrt{c+d} \sqrt{c+d x} b-2 \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b+a^2 d^2-a \sqrt{a+b} d^2 \sqrt{a+b x}\right)}{\left(-c b+\sqrt{c+d} \sqrt{c+d x} b+a d-\sqrt{a+b} d \sqrt{a+b x}\right)^2}+\left(\frac{6 c \sqrt{d}}{\sqrt{b}}-\frac{2 a d^{3/2}}{b^{3/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{a+b} \sqrt{d}-\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \left(\sqrt{c+d}-\sqrt{c+d x}\right)}\right)","\frac{\sqrt{d} (3 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{3/2}}-\frac{2 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{a}}+\frac{d \sqrt{a+b x} \sqrt{c+d x}}{b}",1,"(((Sqrt[a + b]*d)/b - (d*Sqrt[a + b*x])/b)*(Sqrt[c + d] - Sqrt[c + d*x])*(b^2*c^2 + b^2*c*d + a^2*d^2 + a*b*d^2 + b^2*c*d*x + a*b*d^2*x + 2*b^2*d^2*x + b*Sqrt[a + b]*c*d*Sqrt[a + b*x] - a*Sqrt[a + b]*d^2*Sqrt[a + b*x] - b^2*c*Sqrt[c + d]*Sqrt[c + d*x] + a*b*d*Sqrt[c + d]*Sqrt[c + d*x] - 2*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^2 + ((6*c*Sqrt[d])/Sqrt[b] - (2*a*d^(3/2))/b^(3/2))*ArcTanh[(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*(Sqrt[c + d] - Sqrt[c + d*x]))] - (c^2*RootSum[b^4 - 16*a*b^2*c*#1^2 - 8*b^3*c*#1^2 - 8*a*b^2*d*#1^2 - 4*b^3*d*#1^2 + 16*b^2*c^2*#1^4 + 16*b^2*c*d*#1^4 + 16*a^2*d^2*#1^4 + 16*a*b*d^2*#1^4 + 6*b^2*d^2*#1^4 - 16*a*c*d^2*#1^6 - 8*b*c*d^2*#1^6 - 8*a*d^3*#1^6 - 4*b*d^3*#1^6 + d^4*#1^8 & , (b^3*Log[Sqrt[c + d] - Sqrt[c + d*x]] - b^3*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + 4*b^2*Sqrt[a + b]*Sqrt[c + d]*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1 - 4*b^2*Sqrt[a + b]*Sqrt[c + d]*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1 + 4*b^2*c*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 + 4*a*b*d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 + 5*b^2*d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - 4*b^2*c*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2 - 4*a*b*d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2 - 5*b^2*d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2 - 4*b*c*d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^4 - 4*a*d^2*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^4 - 5*b*d^2*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^4 + 4*b*c*d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^4 + 4*a*d^2*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^4 + 5*b*d^2*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^4 - 4*Sqrt[a + b]*d^2*Sqrt[c + d]*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^5 + 4*Sqrt[a + b]*d^2*Sqrt[c + d]*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^5 - d^3*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^6 + d^3*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^6)/(-4*a*b^2*c*#1 - 2*b^3*c*#1 - 2*a*b^2*d*#1 - b^3*d*#1 + 8*b^2*c^2*#1^3 + 8*b^2*c*d*#1^3 + 8*a^2*d^2*#1^3 + 8*a*b*d^2*#1^3 + 3*b^2*d^2*#1^3 - 12*a*c*d^2*#1^5 - 6*b*c*d^2*#1^5 - 6*a*d^3*#1^5 - 3*b*d^3*#1^5 + d^4*#1^7) & ])/2","C",1
710,1,929,119,29.0160202,"\int \frac{(c+d x)^{3/2}}{x^2 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(x^2*Sqrt[a + b*x]),x]","\frac{4 \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b} \sqrt{d}}{\sqrt{b}}-\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b}}}{\sqrt{c+d}-\sqrt{c+d x}}\right) d^{3/2}}{\sqrt{b}}+\frac{-c \sqrt{c+d x} \left(-2 d^2 a^3-2 b d^2 a^2+2 b c d a^2+2 b c d x a^2+2 b^2 c d a-2 b^2 c^2 x a+2 b^2 c d x a-2 b^3 c^2 x\right)-\sqrt{a+b} c \sqrt{a+b x} \sqrt{c+d x} \left(2 c^2 b^2+c d b^2-c d x b^2+a d^2 b-2 a c d b-a d^2 x b-2 a c d x b+2 a^2 d^2\right)+\sqrt{c+d} \left(-\sqrt{a+b} c \sqrt{a+b x} \left(-2 b^2 c^2+2 a b d c+2 a b d x c-2 a^2 d^2 x\right)-c \left(2 d^2 x a^3+b d^2 x^2 a^2-2 b c d a^2+b d^2 x a^2-2 b c d x a^2+b^2 d^2 x^2 a+b^2 c d x^2 a-2 b^2 c d a+2 b^2 c^2 x a-b^2 d^2 x a-3 b^2 c d x a+b^3 c d x^2+2 b^3 c^2 x-b^3 c d x\right)\right)}{\sqrt{a+b x} \left(a \left(2 c d b^2-2 a d^2 b+2 a c d b-2 a^2 d^2\right) x+a \sqrt{c+d} \left(-2 d b^2-2 a d b\right) \sqrt{c+d x} x\right)+\sqrt{a+b} \left(a \left(2 c^2 b^2+c d b^2+2 d^2 x b^2+c d x b^2+a d^2 b-2 a c d b+a d^2 x b+2 a^2 d^2\right) x+a \sqrt{c+d} \left(2 a b d-2 b^2 c\right) \sqrt{c+d x} x\right)}+\left(\frac{3 c d}{2}-\frac{b c^2}{2 a}\right) \text{RootSum}\left[d^2 \text{$\#$1}^4-4 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^3+4 b c \text{$\#$1}^2+4 a d \text{$\#$1}^2+6 b d \text{$\#$1}^2-4 b \sqrt{a+b} \sqrt{c+d} \text{$\#$1}+b^2\&,\frac{d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2-d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2-b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)+b \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right)}{d^2 \text{$\#$1}^3-3 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^2+2 b c \text{$\#$1}+2 a d \text{$\#$1}+3 b d \text{$\#$1}-b \sqrt{a+b} \sqrt{c+d}}\&\right]","\frac{\sqrt{c} (b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{3/2}}+\frac{2 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b}}-\frac{c \sqrt{a+b x} \sqrt{c+d x}}{a x}",1,"(-(c*Sqrt[c + d*x]*(2*a^2*b*c*d + 2*a*b^2*c*d - 2*a^3*d^2 - 2*a^2*b*d^2 - 2*a*b^2*c^2*x - 2*b^3*c^2*x + 2*a^2*b*c*d*x + 2*a*b^2*c*d*x)) - Sqrt[a + b]*c*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*b^2*c^2 - 2*a*b*c*d + b^2*c*d + 2*a^2*d^2 + a*b*d^2 - 2*a*b*c*d*x - b^2*c*d*x - a*b*d^2*x) + Sqrt[c + d]*(-(Sqrt[a + b]*c*Sqrt[a + b*x]*(-2*b^2*c^2 + 2*a*b*c*d + 2*a*b*c*d*x - 2*a^2*d^2*x)) - c*(-2*a^2*b*c*d - 2*a*b^2*c*d + 2*a*b^2*c^2*x + 2*b^3*c^2*x - 2*a^2*b*c*d*x - 3*a*b^2*c*d*x - b^3*c*d*x + 2*a^3*d^2*x + a^2*b*d^2*x - a*b^2*d^2*x + a*b^2*c*d*x^2 + b^3*c*d*x^2 + a^2*b*d^2*x^2 + a*b^2*d^2*x^2)))/(Sqrt[a + b*x]*(a*(2*a*b*c*d + 2*b^2*c*d - 2*a^2*d^2 - 2*a*b*d^2)*x + a*Sqrt[c + d]*(-2*a*b*d - 2*b^2*d)*x*Sqrt[c + d*x]) + Sqrt[a + b]*(a*Sqrt[c + d]*(-2*b^2*c + 2*a*b*d)*x*Sqrt[c + d*x] + a*x*(2*b^2*c^2 - 2*a*b*c*d + b^2*c*d + 2*a^2*d^2 + a*b*d^2 + b^2*c*d*x + a*b*d^2*x + 2*b^2*d^2*x))) + (4*d^(3/2)*ArcTanh[((Sqrt[a + b]*Sqrt[d])/Sqrt[b] - (Sqrt[d]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[c + d] - Sqrt[c + d*x])])/Sqrt[b] + (-1/2*(b*c^2)/a + (3*c*d)/2)*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ]","C",1
711,1,4556,119,126.8886869,"\int \frac{(c+d x)^{3/2}}{x^3 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(x^3*Sqrt[a + b*x]),x]","\text{Result too large to show}","-\frac{3 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{5/2} \sqrt{c}}+\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 a^2 x}-\frac{\sqrt{a+b x} (c+d x)^{3/2}}{2 a x^2}",1,"(Sqrt[a + b]*Sqrt[a + b*x]*Sqrt[c + d*x]*(-16*a*b^4*c^5 + 32*a^2*b^3*c^4*d - 16*a*b^4*c^4*d - 48*a^3*b^2*c^3*d^2 - 2*a*b^4*c^3*d^2 + 32*a^4*b*c^2*d^3 - 12*a^2*b^3*c^2*d^3 - 16*a^5*c*d^4 - 16*a^4*b*c*d^4 - 2*a^3*b^2*c*d^4 + 24*b^5*c^5*x - 104*a*b^4*c^4*d*x + 24*b^5*c^4*d*x + 152*a^2*b^3*c^3*d^2*x - 84*a*b^4*c^3*d^2*x + 3*b^5*c^3*d^2*x - 168*a^3*b^2*c^2*d^3*x + 24*a^2*b^3*c^2*d^3*x - 3*a*b^4*c^2*d^3*x + 88*a^4*b*c*d^4*x - 20*a^3*b^2*c*d^4*x - 43*a^2*b^3*c*d^4*x - 40*a^5*d^5*x - 40*a^4*b*d^5*x - 5*a^3*b^2*d^5*x + 32*a^2*b^3*c^4*d*x^2 - 16*a*b^4*c^4*d*x^2 - 24*b^5*c^4*d*x^2 - 48*a^3*b^2*c^3*d^2*x^2 + 144*a^2*b^3*c^3*d^2*x^2 + 90*a*b^4*c^3*d^2*x^2 + 6*b^5*c^3*d^2*x^2 + 32*a^4*b*c^2*d^3*x^2 - 176*a^3*b^2*c^2*d^3*x^2 - 52*a^2*b^3*c^2*d^3*x^2 - 6*a*b^4*c^2*d^3*x^2 + 12*b^5*c^2*d^3*x^2 + 112*a^4*b*c*d^4*x^2 - 6*a^3*b^2*c*d^4*x^2 - 22*a^2*b^3*c*d^4*x^2 - 24*a*b^4*c*d^4*x^2 + 40*a^4*b*d^5*x^2 - 10*a^3*b^2*d^5*x^2 - 20*a^2*b^3*d^5*x^2 + 8*a^2*b^3*c^3*d^2*x^3 - 4*a*b^4*c^3*d^2*x^3 - 9*b^5*c^3*d^2*x^3 + 8*a^3*b^2*c^2*d^3*x^3 + 40*a^2*b^3*c^2*d^3*x^3 + 9*a*b^4*c^2*d^3*x^3 - 12*b^5*c^2*d^3*x^3 + 28*a^3*b^2*c*d^4*x^3 + 65*a^2*b^3*c*d^4*x^3 + 24*a*b^4*c*d^4*x^3 + 15*a^3*b^2*d^5*x^3 + 20*a^2*b^3*d^5*x^3) + Sqrt[c + d*x]*(-32*a^3*b^3*c^4*d - 32*a^2*b^4*c^4*d + 48*a^4*b^2*c^3*d^2 + 24*a^3*b^3*c^3*d^2 - 24*a^2*b^4*c^3*d^2 - 32*a^5*b*c^2*d^3 - 16*a^4*b^2*c^2*d^3 + 16*a^3*b^3*c^2*d^3 + 16*a^6*c*d^4 + 24*a^5*b*c*d^4 + 8*a^4*b^2*c*d^4 + 16*a^2*b^4*c^4*d*x + 16*a*b^5*c^4*d*x - 128*a^3*b^3*c^3*d^2*x - 116*a^2*b^4*c^3*d^2*x + 12*a*b^5*c^3*d^2*x + 152*a^4*b^2*c^2*d^3*x + 52*a^3*b^3*c^2*d^3*x - 100*a^2*b^4*c^2*d^3*x - 80*a^5*b*c*d^4*x - 12*a^4*b^2*c*d^4*x + 68*a^3*b^3*c*d^4*x + 40*a^6*d^5*x + 60*a^5*b*d^5*x + 20*a^4*b^2*d^5*x + 16*a^2*b^4*c^5*x^2 - 8*a*b^5*c^5*x^2 - 24*b^6*c^5*x^2 - 32*a^3*b^3*c^4*d*x^2 + 80*a^2*b^4*c^4*d*x^2 + 124*a*b^5*c^4*d*x^2 + 12*b^6*c^4*d*x^2 + 48*a^4*b^2*c^3*d^2*x^2 - 120*a^3*b^3*c^3*d^2*x^2 - 216*a^2*b^4*c^3*d^2*x^2 - 24*a*b^5*c^3*d^2*x^2 + 24*b^6*c^3*d^2*x^2 - 32*a^5*b*c^2*d^3*x^2 + 160*a^4*b^2*c^2*d^3*x^2 + 232*a^3*b^3*c^2*d^3*x^2 - 32*a^2*b^4*c^2*d^3*x^2 - 72*a*b^5*c^2*d^3*x^2 - 112*a^5*b*c*d^4*x^2 - 96*a^4*b^2*c*d^4*x^2 + 24*a^3*b^3*c*d^4*x^2 + 8*a^2*b^4*c*d^4*x^2 - 20*a^5*b*d^5*x^2 + 20*a^4*b^2*d^5*x^2 + 40*a^3*b^3*d^5*x^2 + 8*a^2*b^4*c^4*d*x^3 - 4*a*b^5*c^4*d*x^3 - 12*b^6*c^4*d*x^3 + 16*a^3*b^3*c^3*d^2*x^3 + 52*a^2*b^4*c^3*d^2*x^3 + 12*a*b^5*c^3*d^2*x^3 - 24*b^6*c^3*d^2*x^3 - 24*a^4*b^2*c^2*d^3*x^3 + 36*a^3*b^3*c^2*d^3*x^3 + 132*a^2*b^4*c^2*d^3*x^3 + 72*a*b^5*c^2*d^3*x^3 - 84*a^4*b^2*c*d^4*x^3 - 92*a^3*b^3*c*d^4*x^3 - 8*a^2*b^4*c*d^4*x^3 - 40*a^4*b^2*d^5*x^3 - 40*a^3*b^3*d^5*x^3) + Sqrt[c + d]*(32*a^3*b^3*c^4*d + 32*a^2*b^4*c^4*d - 48*a^4*b^2*c^3*d^2 - 40*a^3*b^3*c^3*d^2 + 8*a^2*b^4*c^3*d^2 + 32*a^5*b*c^2*d^3 + 40*a^4*b^2*c^2*d^3 + 8*a^3*b^3*c^2*d^3 - 16*a^2*b^4*c^4*d*x - 16*a*b^5*c^4*d*x + 144*a^3*b^3*c^3*d^2*x + 140*a^2*b^4*c^3*d^2*x - 4*a*b^5*c^3*d^2*x - 176*a^4*b^2*c^2*d^3*x - 136*a^3*b^3*c^2*d^3*x + 40*a^2*b^4*c^2*d^3*x + 112*a^5*b*c*d^4*x + 140*a^4*b^2*c*d^4*x + 28*a^3*b^3*c*d^4*x - 16*a^2*b^4*c^5*x^2 + 8*a*b^5*c^5*x^2 + 24*b^6*c^5*x^2 + 32*a^3*b^3*c^4*d*x^2 - 72*a^2*b^4*c^4*d*x^2 - 128*a*b^5*c^4*d*x^2 - 24*b^6*c^4*d*x^2 - 48*a^4*b^2*c^3*d^2*x^2 + 104*a^3*b^3*c^3*d^2*x^2 + 242*a^2*b^4*c^3*d^2*x^2 + 81*a*b^5*c^3*d^2*x^2 - 9*b^6*c^3*d^2*x^2 + 32*a^5*b*c^2*d^3*x^2 - 136*a^4*b^2*c^2*d^3*x^2 - 220*a^3*b^3*c^2*d^3*x^2 - 43*a^2*b^4*c^2*d^3*x^2 + 9*a*b^5*c^2*d^3*x^2 - 16*a^6*c*d^4*x^2 + 72*a^5*b*c*d^4*x^2 + 82*a^4*b^2*c*d^4*x^2 + 59*a^3*b^3*c*d^4*x^2 + 65*a^2*b^4*c*d^4*x^2 - 40*a^6*d^5*x^2 + 55*a^4*b^2*d^5*x^2 + 15*a^3*b^3*d^5*x^2 - 16*a^2*b^4*c^4*d*x^3 + 8*a*b^5*c^4*d*x^3 + 24*b^6*c^4*d*x^3 - 84*a^2*b^4*c^3*d^2*x^3 - 78*a*b^5*c^3*d^2*x^3 + 6*b^6*c^3*d^2*x^3 + 24*a^3*b^3*c^2*d^3*x^3 + 18*a^2*b^4*c^2*d^3*x^3 - 18*a*b^5*c^2*d^3*x^3 - 12*b^6*c^2*d^3*x^3 - 16*a^5*b*c*d^4*x^3 - 36*a^4*b^2*c*d^4*x^3 - 42*a^3*b^3*c*d^4*x^3 + 2*a^2*b^4*c*d^4*x^3 + 24*a*b^5*c*d^4*x^3 - 40*a^5*b*d^5*x^3 - 50*a^4*b^2*d^5*x^3 + 10*a^3*b^3*d^5*x^3 + 20*a^2*b^4*d^5*x^3 - 2*a^2*b^4*c^3*d^2*x^4 + a*b^5*c^3*d^2*x^4 + 3*b^6*c^3*d^2*x^4 - 12*a^3*b^3*c^2*d^3*x^4 - 15*a^2*b^4*c^2*d^3*x^4 + 9*a*b^5*c^2*d^3*x^4 + 12*b^6*c^2*d^3*x^4 - 2*a^4*b^2*c*d^4*x^4 - 45*a^3*b^3*c*d^4*x^4 - 67*a^2*b^4*c*d^4*x^4 - 24*a*b^5*c*d^4*x^4 - 5*a^4*b^2*d^5*x^4 - 25*a^3*b^3*d^5*x^4 - 20*a^2*b^4*d^5*x^4 + Sqrt[a + b]*Sqrt[a + b*x]*(16*a*b^4*c^5 - 32*a^2*b^3*c^4*d + 8*a*b^4*c^4*d + 48*a^3*b^2*c^3*d^2 + 16*a^2*b^3*c^3*d^2 - 32*a^4*b*c^2*d^3 - 24*a^3*b^2*c^2*d^3 - 24*b^5*c^5*x + 112*a*b^4*c^4*d*x - 12*b^5*c^4*d*x - 168*a^2*b^3*c^3*d^2*x + 36*a*b^4*c^3*d^2*x + 192*a^3*b^2*c^2*d^3*x + 60*a^2*b^3*c^2*d^3*x - 112*a^4*b*c*d^4*x - 84*a^3*b^2*c*d^4*x - 32*a^2*b^3*c^4*d*x^2 + 16*a*b^4*c^4*d*x^2 + 12*b^5*c^4*d*x^2 + 48*a^3*b^2*c^3*d^2*x^2 - 128*a^2*b^3*c^3*d^2*x^2 - 48*a*b^4*c^3*d^2*x^2 - 24*b^5*c^3*d^2*x^2 - 32*a^4*b*c^2*d^3*x^2 + 152*a^3*b^2*c^2*d^3*x^2 + 40*a^2*b^3*c^2*d^3*x^2 + 72*a*b^4*c^2*d^3*x^2 + 16*a^5*c*d^4*x^2 - 80*a^4*b*c*d^4*x^2 + 16*a^3*b^2*c*d^4*x^2 - 8*a^2*b^3*c*d^4*x^2 + 40*a^5*d^5*x^2 - 20*a^4*b*d^5*x^2 - 40*a^3*b^2*d^5*x^2 - 24*a^2*b^3*c^3*d^2*x^3 + 12*a*b^4*c^3*d^2*x^3 + 24*b^5*c^3*d^2*x^3 + 16*a^3*b^2*c^2*d^3*x^3 - 100*a^2*b^3*c^2*d^3*x^3 - 72*a*b^4*c^2*d^3*x^3 + 8*a^4*b*c*d^4*x^3 + 68*a^3*b^2*c*d^4*x^3 + 8*a^2*b^3*c*d^4*x^3 + 20*a^4*b*d^5*x^3 + 40*a^3*b^2*d^5*x^3)))/(Sqrt[a + b*x]*(4*a^2*Sqrt[c + d]*x^2*Sqrt[c + d*x]*(-16*a*b^3*c^2*d - 16*b^4*c^2*d + 24*a^2*b^2*c*d^2 + 20*a*b^3*c*d^2 - 4*b^4*c*d^2 - 16*a^3*b*d^3 - 20*a^2*b^2*d^3 - 4*a*b^3*d^3 - 4*a*b^3*c*d^2*x - 4*b^4*c*d^2*x - 4*a^2*b^2*d^3*x - 12*a*b^3*d^3*x - 8*b^4*d^3*x) + 4*a^2*x^2*(16*a*b^3*c^3*d + 16*b^4*c^3*d - 24*a^2*b^2*c^2*d^2 - 12*a*b^3*c^2*d^2 + 12*b^4*c^2*d^2 + 16*a^3*b*c*d^3 + 8*a^2*b^2*c*d^3 - 8*a*b^3*c*d^3 - 8*a^4*d^4 - 12*a^3*b*d^4 - 4*a^2*b^2*d^4 + 12*a*b^3*c^2*d^2*x + 12*b^4*c^2*d^2*x - 8*a^2*b^2*c*d^3*x + 8*a*b^3*c*d^3*x + 16*b^4*c*d^3*x - 4*a^3*b*d^4*x - 20*a^2*b^2*d^4*x - 16*a*b^3*d^4*x)) + Sqrt[a + b]*(4*a^2*Sqrt[c + d]*x^2*Sqrt[c + d*x]*(-8*b^4*c^3 + 16*a*b^3*c^2*d - 4*b^4*c^2*d - 24*a^2*b^2*c*d^2 - 8*a*b^3*c*d^2 + 16*a^3*b*d^3 + 12*a^2*b^2*d^3 - 4*b^4*c^2*d*x - 8*a*b^3*c*d^2*x - 16*b^4*c*d^2*x + 12*a^2*b^2*d^3*x + 16*a*b^3*d^3*x) + 4*a^2*x^2*(8*b^4*c^4 - 16*a*b^3*c^3*d + 8*b^4*c^3*d + 24*a^2*b^2*c^2*d^2 + b^4*c^2*d^2 - 16*a^3*b*c*d^3 + 6*a*b^3*c*d^3 + 8*a^4*d^4 + 8*a^3*b*d^4 + a^2*b^2*d^4 + 8*b^4*c^3*d*x + 22*b^4*c^2*d^2*x - 12*a*b^3*c*d^3*x + 8*b^4*c*d^3*x + 8*a^3*b*d^4*x + 22*a^2*b^2*d^4*x + 8*a*b^3*d^4*x + b^4*c^2*d^2*x^2 + 6*a*b^3*c*d^3*x^2 + 8*b^4*c*d^3*x^2 + a^2*b^2*d^4*x^2 + 8*a*b^3*d^4*x^2 + 8*b^4*d^4*x^2))) + (3*(b*c - a*d)^2*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ])/(8*a^2)","C",1
712,-1,0,180,180.0776183,"\int \frac{(c+d x)^{3/2}}{x^4 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(x^4*Sqrt[a + b*x]),x]","\text{\$Aborted}","\frac{(b c-a d)^2 (a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 a^{7/2} c^{3/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d) (a d+5 b c)}{8 a^3 c x}+\frac{\sqrt{a+b x} (c+d x)^{3/2} (a d+5 b c)}{12 a^2 c x^2}-\frac{\sqrt{a+b x} (c+d x)^{5/2}}{3 a c x^3}",1,"$Aborted","F",-1
713,-1,0,266,180.1020703,"\int \frac{(c+d x)^{3/2}}{x^5 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(x^5*Sqrt[a + b*x]),x]","\text{\$Aborted}","\frac{\sqrt{a+b x} \sqrt{c+d x} (7 b c-9 a d)}{24 a^2 x^3}-\frac{\left(3 a^2 d^2+10 a b c d+35 b^2 c^2\right) (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{9/2} c^{5/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(3 a^2 d^2-46 a b c d+35 b^2 c^2\right)}{96 a^3 c x^2}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(9 a^3 d^3+15 a^2 b c d^2-145 a b^2 c^2 d+105 b^3 c^3\right)}{192 a^4 c^2 x}-\frac{c \sqrt{a+b x} \sqrt{c+d x}}{4 a x^4}",1,"$Aborted","F",-1
714,-1,0,314,180.0232422,"\int \frac{x^2 (c+d x)^{5/2}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(x^2*(c + d*x)^(5/2))/Sqrt[a + b*x],x]","\text{\$Aborted}","\frac{(b c-a d)^3 \left(63 a^2 d^2+14 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{11/2} d^{5/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2 \left(63 a^2 d^2+14 a b c d+3 b^2 c^2\right)}{128 b^5 d^2}+\frac{\sqrt{a+b x} (c+d x)^{3/2} (b c-a d) \left(63 a^2 d^2+14 a b c d+3 b^2 c^2\right)}{192 b^4 d^2}+\frac{\sqrt{a+b x} (c+d x)^{5/2} \left(63 a^2 d^2+14 a b c d+3 b^2 c^2\right)}{240 b^3 d^2}-\frac{3 \sqrt{a+b x} (c+d x)^{7/2} (3 a d+b c)}{40 b^2 d^2}+\frac{x \sqrt{a+b x} (c+d x)^{7/2}}{5 b d}",1,"$Aborted","F",-1
715,-1,0,217,180.0253908,"\int \frac{x (c+d x)^{5/2}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(x*(c + d*x)^(5/2))/Sqrt[a + b*x],x]","\text{\$Aborted}","-\frac{5 (b c-a d)^3 (7 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{9/2} d^{3/2}}-\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2 (7 a d+b c)}{64 b^4 d}-\frac{5 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d) (7 a d+b c)}{96 b^3 d}-\frac{\sqrt{a+b x} (c+d x)^{5/2} (7 a d+b c)}{24 b^2 d}+\frac{\sqrt{a+b x} (c+d x)^{7/2}}{4 b d}",1,"$Aborted","F",-1
716,-1,0,148,180.1009036,"\int \frac{(c+d x)^{5/2}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/Sqrt[a + b*x],x]","\text{\$Aborted}","\frac{5 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{7/2} \sqrt{d}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 b^3}+\frac{5 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}{12 b^2}+\frac{\sqrt{a+b x} (c+d x)^{5/2}}{3 b}",1,"$Aborted","F",-1
717,-1,0,171,180.0185805,"\int \frac{(c+d x)^{5/2}}{x \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x*Sqrt[a + b*x]),x]","\text{\$Aborted}","\frac{\sqrt{d} \left(3 a^2 d^2-10 a b c d+15 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{5/2}}+\frac{d \sqrt{a+b x} \sqrt{c+d x} (7 b c-3 a d)}{4 b^2}-\frac{2 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{a}}+\frac{d \sqrt{a+b x} (c+d x)^{3/2}}{2 b}",1,"$Aborted","F",-1
718,-1,0,160,180.0638512,"\int \frac{(c+d x)^{5/2}}{x^2 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^2*Sqrt[a + b*x]),x]","\text{\$Aborted}","\frac{c^{3/2} (b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{3/2}}+\frac{d^{3/2} (5 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{3/2}}-\frac{c \sqrt{a+b x} (c+d x)^{3/2}}{a x}+\frac{d \sqrt{a+b x} \sqrt{c+d x} (a d+b c)}{a b}",1,"$Aborted","F",-1
719,-1,0,177,180.0086245,"\int \frac{(c+d x)^{5/2}}{x^3 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^3*Sqrt[a + b*x]),x]","\text{\$Aborted}","\frac{c \sqrt{a+b x} \sqrt{c+d x} (3 b c-7 a d)}{4 a^2 x}-\frac{\sqrt{c} \left(15 a^2 d^2-10 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{5/2}}+\frac{2 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b}}-\frac{c \sqrt{a+b x} (c+d x)^{3/2}}{2 a x^2}",1,"$Aborted","F",-1
720,-1,0,157,180.0003627,"\int \frac{(c+d x)^{5/2}}{x^4 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^4*Sqrt[a + b*x]),x]","\text{\$Aborted}","\frac{5 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 a^{7/2} \sqrt{c}}-\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}{8 a^3 x}+\frac{5 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}{12 a^2 x^2}-\frac{\sqrt{a+b x} (c+d x)^{5/2}}{3 a x^3}",1,"$Aborted","F",-1
721,-1,0,229,180.101866,"\int \frac{(c+d x)^{5/2}}{x^5 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^5*Sqrt[a + b*x]),x]","\text{\$Aborted}","-\frac{5 (b c-a d)^3 (a d+7 b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{9/2} c^{3/2}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2 (a d+7 b c)}{64 a^4 c x}-\frac{5 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d) (a d+7 b c)}{96 a^3 c x^2}+\frac{\sqrt{a+b x} (c+d x)^{5/2} (a d+7 b c)}{24 a^2 c x^3}-\frac{\sqrt{a+b x} (c+d x)^{7/2}}{4 a c x^4}",1,"$Aborted","F",-1
722,-1,0,346,180.038433,"\int \frac{(c+d x)^{5/2}}{x^6 \sqrt{a+b x}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^6*Sqrt[a + b*x]),x]","\text{\$Aborted}","\frac{c \sqrt{a+b x} \sqrt{c+d x} (9 b c-13 a d)}{40 a^2 x^4}+\frac{\left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right) (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{128 a^{11/2} c^{5/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(93 a^2 d^2-148 a b c d+63 b^2 c^2\right)}{240 a^3 x^3}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-15 a^3 d^3+481 a^2 b c d^2-749 a b^2 c^2 d+315 b^3 c^3\right)}{960 a^4 c x^2}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-45 a^4 d^4-90 a^3 b c d^3+1564 a^2 b^2 c^2 d^2-2310 a b^3 c^3 d+945 b^4 c^4\right)}{1920 a^5 c^2 x}-\frac{c \sqrt{a+b x} (c+d x)^{3/2}}{5 a x^5}",1,"$Aborted","F",-1
723,1,612,118,0.5746869,"\int \frac{x^4 (1+x)^{3/2}}{\sqrt{1-x}} \, dx","IntegrateAlgebraic[(x^4*(1 + x)^(3/2))/Sqrt[1 - x],x]","\frac{\left(\frac{4 \sqrt{1-x}}{15}-\frac{4}{15}\right) \left(\sqrt{x+1}-1\right) \left(40 x^{11}+440 \sqrt{1-x} x^{10}-440 \sqrt{x+1} x^{10}+96 x^{10}+16456 \sqrt{1-x} x^9-4600 \sqrt{1-x} \sqrt{x+1} x^9+14344 \sqrt{x+1} x^9-70810 x^9-78870 \sqrt{1-x} x^8-11040 \sqrt{1-x} \sqrt{x+1} x^8+152790 \sqrt{x+1} x^8-170080 x^8-678898 \sqrt{1-x} x^7+329590 \sqrt{1-x} \sqrt{x+1} x^7-119922 \sqrt{x+1} x^7+524335 x^7-986029 \sqrt{1-x} x^6+806656 \sqrt{1-x} \sqrt{x+1} x^6-1035859 \sqrt{x+1} x^6+1499392 x^6-39123 \sqrt{1-x} x^5+259785 \sqrt{1-x} \sqrt{x+1} x^5-951507 \sqrt{x+1} x^5+1036935 x^5+729274 \sqrt{1-x} x^4-524288 \sqrt{1-x} \sqrt{x+1} x^4-204986 \sqrt{x+1} x^4+262144 x^4+243884 \sqrt{1-x} x^3-409860 \sqrt{1-x} \sqrt{x+1} x^3-280404 \sqrt{x+1} x^3+1183820 x^3-146384 \sqrt{1-x} x^2+524288 \sqrt{1-x} \sqrt{x+1} x^2-2999344 \sqrt{x+1} x^2+4718592 x^2+6900304 \sqrt{1-x} x-2732400 \sqrt{1-x} \sqrt{x+1} x-1488304 \sqrt{x+1} x-2674320 x+8393888 \sqrt{1-x}-8388608 \sqrt{1-x} \sqrt{x+1}+8383328 \sqrt{x+1}-8388608\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^{12}}-\frac{11}{4} \tan ^{-1}\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)","-\frac{1}{6} \sqrt{1-x} (x+1)^{5/2} x^3-\frac{1}{15} \sqrt{1-x} (x+1)^{5/2} x^2-\frac{11}{48} \sqrt{1-x} (x+1)^{3/2}-\frac{1}{120} \sqrt{1-x} (x+1)^{5/2} (19 x+18)-\frac{11}{16} \sqrt{1-x} \sqrt{x+1}+\frac{11}{16} \sin ^{-1}(x)",1,"((-4/15 + (4*Sqrt[1 - x])/15)*(-1 + Sqrt[1 + x])*(-8388608 + 8393888*Sqrt[1 - x] - 2674320*x + 6900304*Sqrt[1 - x]*x + 4718592*x^2 - 146384*Sqrt[1 - x]*x^2 + 1183820*x^3 + 243884*Sqrt[1 - x]*x^3 + 262144*x^4 + 729274*Sqrt[1 - x]*x^4 + 1036935*x^5 - 39123*Sqrt[1 - x]*x^5 + 1499392*x^6 - 986029*Sqrt[1 - x]*x^6 + 524335*x^7 - 678898*Sqrt[1 - x]*x^7 - 170080*x^8 - 78870*Sqrt[1 - x]*x^8 - 70810*x^9 + 16456*Sqrt[1 - x]*x^9 + 96*x^10 + 440*Sqrt[1 - x]*x^10 + 40*x^11 + 8383328*Sqrt[1 + x] - 8388608*Sqrt[1 - x]*Sqrt[1 + x] - 1488304*x*Sqrt[1 + x] - 2732400*Sqrt[1 - x]*x*Sqrt[1 + x] - 2999344*x^2*Sqrt[1 + x] + 524288*Sqrt[1 - x]*x^2*Sqrt[1 + x] - 280404*x^3*Sqrt[1 + x] - 409860*Sqrt[1 - x]*x^3*Sqrt[1 + x] - 204986*x^4*Sqrt[1 + x] - 524288*Sqrt[1 - x]*x^4*Sqrt[1 + x] - 951507*x^5*Sqrt[1 + x] + 259785*Sqrt[1 - x]*x^5*Sqrt[1 + x] - 1035859*x^6*Sqrt[1 + x] + 806656*Sqrt[1 - x]*x^6*Sqrt[1 + x] - 119922*x^7*Sqrt[1 + x] + 329590*Sqrt[1 - x]*x^7*Sqrt[1 + x] + 152790*x^8*Sqrt[1 + x] - 11040*Sqrt[1 - x]*x^8*Sqrt[1 + x] + 14344*x^9*Sqrt[1 + x] - 4600*Sqrt[1 - x]*x^9*Sqrt[1 + x] - 440*x^10*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^12 - (11*ArcTan[(-1 + Sqrt[1 - x])/(-1 + Sqrt[1 + x])])/4","B",1
724,1,522,110,0.5289024,"\int \frac{x^3 (1+x)^{3/2}}{\sqrt{1-x}} \, dx","IntegrateAlgebraic[(x^3*(1 + x)^(3/2))/Sqrt[1 - x],x]","\frac{\left(\frac{8}{5}-\frac{8 \sqrt{1-x}}{5}\right) \left(\sqrt{x+1}-1\right) \left(-36 \sqrt{1-x} x^8+4 \sqrt{1-x} \sqrt{x+1} x^8-36 \sqrt{x+1} x^8+304 x^8+690 \sqrt{1-x} x^7+10 \sqrt{1-x} \sqrt{x+1} x^7-870 \sqrt{x+1} x^7+760 x^7+6162 \sqrt{1-x} x^6-2900 \sqrt{1-x} \sqrt{x+1} x^6+2262 \sqrt{x+1} x^6-7296 x^6+8349 \sqrt{1-x} x^5-7265 \sqrt{1-x} \sqrt{x+1} x^5+12981 \sqrt{x+1} x^5-19380 x^5-4195 \sqrt{1-x} x^4-232 \sqrt{1-x} \sqrt{x+1} x^4+13235 \sqrt{x+1} x^4-14872 x^4-13496 \sqrt{1-x} x^3+10280 \sqrt{1-x} \sqrt{x+1} x^3+4776 \sqrt{x+1} x^3-11020 x^3-11476 \sqrt{1-x} x^2+6144 \sqrt{1-x} \sqrt{x+1} x^2+23764 \sqrt{x+1} x^2-43008 x^2-79992 \sqrt{1-x} x+31800 \sqrt{1-x} \sqrt{x+1} x+18312 \sqrt{x+1} x+29640 x-98544 \sqrt{1-x}+98304 \sqrt{1-x} \sqrt{x+1}-98064 \sqrt{x+1}+98304\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^{10}}-3 \tan ^{-1}\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)","-\frac{1}{5} \sqrt{1-x} x^2 (x+1)^{5/2}-\frac{1}{10} \sqrt{1-x} (x+1)^{7/2}-\frac{1}{10} \sqrt{1-x} (x+1)^{5/2}-\frac{1}{4} \sqrt{1-x} (x+1)^{3/2}-\frac{3}{4} \sqrt{1-x} \sqrt{x+1}+\frac{3}{4} \sin ^{-1}(x)",1,"((8/5 - (8*Sqrt[1 - x])/5)*(-1 + Sqrt[1 + x])*(98304 - 98544*Sqrt[1 - x] + 29640*x - 79992*Sqrt[1 - x]*x - 43008*x^2 - 11476*Sqrt[1 - x]*x^2 - 11020*x^3 - 13496*Sqrt[1 - x]*x^3 - 14872*x^4 - 4195*Sqrt[1 - x]*x^4 - 19380*x^5 + 8349*Sqrt[1 - x]*x^5 - 7296*x^6 + 6162*Sqrt[1 - x]*x^6 + 760*x^7 + 690*Sqrt[1 - x]*x^7 + 304*x^8 - 36*Sqrt[1 - x]*x^8 - 98064*Sqrt[1 + x] + 98304*Sqrt[1 - x]*Sqrt[1 + x] + 18312*x*Sqrt[1 + x] + 31800*Sqrt[1 - x]*x*Sqrt[1 + x] + 23764*x^2*Sqrt[1 + x] + 6144*Sqrt[1 - x]*x^2*Sqrt[1 + x] + 4776*x^3*Sqrt[1 + x] + 10280*Sqrt[1 - x]*x^3*Sqrt[1 + x] + 13235*x^4*Sqrt[1 + x] - 232*Sqrt[1 - x]*x^4*Sqrt[1 + x] + 12981*x^5*Sqrt[1 + x] - 7265*Sqrt[1 - x]*x^5*Sqrt[1 + x] + 2262*x^6*Sqrt[1 + x] - 2900*Sqrt[1 - x]*x^6*Sqrt[1 + x] - 870*x^7*Sqrt[1 + x] + 10*Sqrt[1 - x]*x^7*Sqrt[1 + x] - 36*x^8*Sqrt[1 + x] + 4*Sqrt[1 - x]*x^8*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^10 - 3*ArcTan[(-1 + Sqrt[1 - x])/(-1 + Sqrt[1 + x])]","B",1
725,1,404,88,0.3705289,"\int \frac{x^2 (1+x)^{3/2}}{\sqrt{1-x}} \, dx","IntegrateAlgebraic[(x^2*(1 + x)^(3/2))/Sqrt[1 - x],x]","\frac{\left(\frac{2}{3}-\frac{2 \sqrt{1-x}}{3}\right) \left(\sqrt{x+1}-1\right) \left(6 x^7+42 \sqrt{1-x} x^6-42 \sqrt{x+1} x^6+16 x^6+658 \sqrt{1-x} x^5-270 \sqrt{1-x} \sqrt{x+1} x^5+434 \sqrt{x+1} x^5-1353 x^5+595 \sqrt{1-x} x^4-720 \sqrt{1-x} \sqrt{x+1} x^4+2317 \sqrt{x+1} x^4-3632 x^4-2113 \sqrt{1-x} x^3+759 \sqrt{1-x} \sqrt{x+1} x^3+2815 \sqrt{x+1} x^3-3441 x^3-4600 \sqrt{1-x} x^2+3072 \sqrt{1-x} \sqrt{x+1} x^2+2552 \sqrt{x+1} x^2-5120 x^2-13652 \sqrt{1-x} x+5964 \sqrt{1-x} \sqrt{x+1} x+2732 \sqrt{x+1} x+4788 x-16552 \sqrt{1-x}+16384 \sqrt{1-x} \sqrt{x+1}-16216 \sqrt{x+1}+16384\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^8}-\frac{7}{2} \tan ^{-1}\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)","-\frac{1}{4} \sqrt{1-x} x (x+1)^{5/2}-\frac{1}{6} \sqrt{1-x} (x+1)^{5/2}-\frac{7}{24} \sqrt{1-x} (x+1)^{3/2}-\frac{7}{8} \sqrt{1-x} \sqrt{x+1}+\frac{7}{8} \sin ^{-1}(x)",1,"((2/3 - (2*Sqrt[1 - x])/3)*(-1 + Sqrt[1 + x])*(16384 - 16552*Sqrt[1 - x] + 4788*x - 13652*Sqrt[1 - x]*x - 5120*x^2 - 4600*Sqrt[1 - x]*x^2 - 3441*x^3 - 2113*Sqrt[1 - x]*x^3 - 3632*x^4 + 595*Sqrt[1 - x]*x^4 - 1353*x^5 + 658*Sqrt[1 - x]*x^5 + 16*x^6 + 42*Sqrt[1 - x]*x^6 + 6*x^7 - 16216*Sqrt[1 + x] + 16384*Sqrt[1 - x]*Sqrt[1 + x] + 2732*x*Sqrt[1 + x] + 5964*Sqrt[1 - x]*x*Sqrt[1 + x] + 2552*x^2*Sqrt[1 + x] + 3072*Sqrt[1 - x]*x^2*Sqrt[1 + x] + 2815*x^3*Sqrt[1 + x] + 759*Sqrt[1 - x]*x^3*Sqrt[1 + x] + 2317*x^4*Sqrt[1 + x] - 720*Sqrt[1 - x]*x^4*Sqrt[1 + x] + 434*x^5*Sqrt[1 + x] - 270*Sqrt[1 - x]*x^5*Sqrt[1 + x] - 42*x^6*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^8 - (7*ArcTan[(-1 + Sqrt[1 - x])/(-1 + Sqrt[1 + x])])/2","B",1
726,1,313,61,0.3081578,"\int \frac{x (1+x)^{3/2}}{\sqrt{1-x}} \, dx","IntegrateAlgebraic[(x*(1 + x)^(3/2))/Sqrt[1 - x],x]","\frac{\left(\frac{8 \sqrt{1-x}}{3}-\frac{8}{3}\right) \left(\sqrt{x+1}-1\right) \left(-5 \sqrt{1-x} x^4+\sqrt{1-x} \sqrt{x+1} x^4-5 \sqrt{x+1} x^4+22 x^4+10 \sqrt{1-x} x^3+3 \sqrt{1-x} \sqrt{x+1} x^3-40 \sqrt{x+1} x^3+66 x^3+84 \sqrt{1-x} x^2-37 \sqrt{1-x} \sqrt{x+1} x^2-66 \sqrt{x+1} x^2+93 x^2+256 \sqrt{1-x} x-126 \sqrt{1-x} \sqrt{x+1} x-52 \sqrt{x+1} x-66 x+332 \sqrt{1-x}-320 \sqrt{1-x} \sqrt{x+1}+308 \sqrt{x+1}-320\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^6}-4 \tan ^{-1}\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)","-\frac{1}{3} \sqrt{1-x} (x+1)^{5/2}-\frac{1}{3} \sqrt{1-x} (x+1)^{3/2}-\sqrt{1-x} \sqrt{x+1}+\sin ^{-1}(x)",1,"((-8/3 + (8*Sqrt[1 - x])/3)*(-1 + Sqrt[1 + x])*(-320 + 332*Sqrt[1 - x] - 66*x + 256*Sqrt[1 - x]*x + 93*x^2 + 84*Sqrt[1 - x]*x^2 + 66*x^3 + 10*Sqrt[1 - x]*x^3 + 22*x^4 - 5*Sqrt[1 - x]*x^4 + 308*Sqrt[1 + x] - 320*Sqrt[1 - x]*Sqrt[1 + x] - 52*x*Sqrt[1 + x] - 126*Sqrt[1 - x]*x*Sqrt[1 + x] - 66*x^2*Sqrt[1 + x] - 37*Sqrt[1 - x]*x^2*Sqrt[1 + x] - 40*x^3*Sqrt[1 + x] + 3*Sqrt[1 - x]*x^3*Sqrt[1 + x] - 5*x^4*Sqrt[1 + x] + Sqrt[1 - x]*x^4*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^6 - 4*ArcTan[(-1 + Sqrt[1 - x])/(-1 + Sqrt[1 + x])]","B",1
727,1,188,47,0.000588,"\int \frac{(1+x)^{3/2}}{\sqrt{1-x}} \, dx","IntegrateAlgebraic[(1 + x)^(3/2)/Sqrt[1 - x],x]","\frac{\left(2 \sqrt{1-x}-2\right) \left(\sqrt{x+1}-1\right) \left(x^3+3 \sqrt{1-x} x^2-3 \sqrt{x+1} x^2+4 x^2+17 \sqrt{1-x} x-7 \sqrt{1-x} \sqrt{x+1} x-7 \sqrt{x+1} x-x+34 \sqrt{1-x}-32 \sqrt{1-x} \sqrt{x+1}+30 \sqrt{x+1}-32\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^4}-6 \tan ^{-1}\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)","-\frac{1}{2} \sqrt{1-x} (x+1)^{3/2}-\frac{3}{2} \sqrt{1-x} \sqrt{x+1}+\frac{3}{2} \sin ^{-1}(x)",1,"((-2 + 2*Sqrt[1 - x])*(-1 + Sqrt[1 + x])*(-32 + 34*Sqrt[1 - x] - x + 17*Sqrt[1 - x]*x + 4*x^2 + 3*Sqrt[1 - x]*x^2 + x^3 + 30*Sqrt[1 + x] - 32*Sqrt[1 - x]*Sqrt[1 + x] - 7*x*Sqrt[1 + x] - 7*Sqrt[1 - x]*x*Sqrt[1 + x] - 3*x^2*Sqrt[1 + x]))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^4 - 6*ArcTan[(-1 + Sqrt[1 - x])/(-1 + Sqrt[1 + x])]","B",1
728,1,140,43,0.1434105,"\int \frac{(1+x)^{3/2}}{\sqrt{1-x} x} \, dx","IntegrateAlgebraic[(1 + x)^(3/2)/(Sqrt[1 - x]*x),x]","\frac{2 \left(\sqrt{x+1}-1\right)^4}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^2}+\frac{4 \left(\sqrt{x+1}-1\right)^2}{\sqrt{1-x}+\sqrt{x+1}-2}-\log \left(\sqrt{1-x}-1\right)+\log \left(x+\sqrt{1-x}-\sqrt{x+1}\right)-\log \left(\sqrt{x+1}-1\right)-8 \tan ^{-1}\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)","-\sqrt{1-x} \sqrt{x+1}+2 \sin ^{-1}(x)-\tanh ^{-1}\left(\sqrt{1-x} \sqrt{x+1}\right)",1,"(2*(-1 + Sqrt[1 + x])^4)/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^2 + (4*(-1 + Sqrt[1 + x])^2)/(-2 + Sqrt[1 - x] + Sqrt[1 + x]) - 8*ArcTan[(-1 + Sqrt[1 - x])/(-1 + Sqrt[1 + x])] - Log[-1 + Sqrt[1 - x]] + Log[Sqrt[1 - x] + x - Sqrt[1 + x]] - Log[-1 + Sqrt[1 + x]]","B",1
729,0,0,44,0.8263995,"\int \frac{(1+x)^{3/2}}{\sqrt{1-x} x^2} \, dx","IntegrateAlgebraic[(1 + x)^(3/2)/(Sqrt[1 - x]*x^2),x]","\int \frac{(1+x)^{3/2}}{\sqrt{1-x} x^2} \, dx","-\frac{\sqrt{1-x} \sqrt{x+1}}{x}+\sin ^{-1}(x)-2 \tanh ^{-1}\left(\sqrt{1-x} \sqrt{x+1}\right)",1,"Could not integrate","F",-1
730,0,0,69,1.7728964,"\int \frac{(1+x)^{3/2}}{\sqrt{1-x} x^3} \, dx","IntegrateAlgebraic[(1 + x)^(3/2)/(Sqrt[1 - x]*x^3),x]","\int \frac{(1+x)^{3/2}}{\sqrt{1-x} x^3} \, dx","-\frac{\sqrt{1-x} (x+1)^{3/2}}{2 x^2}-\frac{3 \sqrt{1-x} \sqrt{x+1}}{2 x}-\frac{3}{2} \tanh ^{-1}\left(\sqrt{1-x} \sqrt{x+1}\right)",1,"Could not integrate","F",-1
731,0,0,88,2.1232492,"\int \frac{(1+x)^{3/2}}{\sqrt{1-x} x^4} \, dx","IntegrateAlgebraic[(1 + x)^(3/2)/(Sqrt[1 - x]*x^4),x]","\int \frac{(1+x)^{3/2}}{\sqrt{1-x} x^4} \, dx","-\frac{\sqrt{1-x} (x+1)^{5/2}}{3 x^3}-\frac{\sqrt{1-x} (x+1)^{3/2}}{3 x^2}-\frac{\sqrt{1-x} \sqrt{x+1}}{x}-\tanh ^{-1}\left(\sqrt{1-x} \sqrt{x+1}\right)",1,"Could not integrate","F",-1
732,0,0,115,2.2822905,"\int \frac{(1+x)^{3/2}}{\sqrt{1-x} x^5} \, dx","IntegrateAlgebraic[(1 + x)^(3/2)/(Sqrt[1 - x]*x^5),x]","\int \frac{(1+x)^{3/2}}{\sqrt{1-x} x^5} \, dx","-\frac{\sqrt{1-x} \sqrt{x+1}}{4 x^4}-\frac{2 \sqrt{1-x} \sqrt{x+1}}{3 x^3}-\frac{7 \sqrt{1-x} \sqrt{x+1}}{8 x^2}-\frac{4 \sqrt{1-x} \sqrt{x+1}}{3 x}-\frac{7}{8} \tanh ^{-1}\left(\sqrt{1-x} \sqrt{x+1}\right)",1,"Could not integrate","F",-1
733,-1,0,169,180.0847726,"\int \frac{x^3}{\sqrt{a+b x} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[x^3/(Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\text{\$Aborted}","-\frac{(a d+b c) \left(5 a^2 d^2-2 a b c d+5 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{7/2} d^{7/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(15 a^2 d^2-10 b d x (a d+b c)+14 a b c d+15 b^2 c^2\right)}{24 b^3 d^3}+\frac{x^2 \sqrt{a+b x} \sqrt{c+d x}}{3 b d}",1,"$Aborted","F",-1
734,1,2892,127,7.5560226,"\int \frac{x^2}{\sqrt{a+b x} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[x^2/(Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\text{Result too large to show}","-\frac{\left(4 a b c d-3 (a d+b c)^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{5/2} d^{5/2}}-\frac{3 \sqrt{a+b x} \sqrt{c+d x} (a d+b c)}{4 b^2 d^2}+\frac{x \sqrt{a+b x} \sqrt{c+d x}}{2 b d}",1,"((-1/4*Sqrt[a + b]/(b^2*d^2) + Sqrt[a + b*x]/(4*b^2*d^2))*(Sqrt[c + d] - Sqrt[c + d*x])*(12*b^5*c^5 - 14*a*b^4*c^4*d + 7*b^5*c^4*d + 18*a^2*b^3*c^3*d^2 + 14*a*b^4*c^3*d^2 - 7*b^5*c^3*d^2 + 18*a^3*b^2*c^2*d^3 + 6*a^2*b^3*c^2*d^3 + 7*a*b^4*c^2*d^3 - 2*b^5*c^2*d^3 - 14*a^4*b*c*d^4 + 14*a^3*b^2*c*d^4 + 7*a^2*b^3*c*d^4 - 12*a*b^4*c*d^4 + 12*a^5*d^5 + 7*a^4*b*d^5 - 7*a^3*b^2*d^5 - 2*a^2*b^3*d^5 + 7*b^5*c^4*d*x + 14*a*b^4*c^3*d^2*x + 16*b^5*c^3*d^2*x + 6*a^2*b^3*c^2*d^3*x + 16*a*b^4*c^2*d^3*x - 16*b^5*c^2*d^3*x + 14*a^3*b^2*c*d^4*x + 16*a^2*b^3*c*d^4*x + 16*a*b^4*c*d^4*x - 16*b^5*c*d^4*x + 7*a^4*b*d^5*x + 16*a^3*b^2*d^5*x - 16*a^2*b^3*d^5*x - 16*a*b^4*d^5*x - 7*b^5*c^3*d^2*x^2 + 7*a*b^4*c^2*d^3*x^2 - 16*b^5*c^2*d^3*x^2 + 7*a^2*b^3*c*d^4*x^2 + 16*a*b^4*c*d^4*x^2 - 16*b^5*c*d^4*x^2 - 7*a^3*b^2*d^5*x^2 - 16*a^2*b^3*d^5*x^2 - 16*a*b^4*d^5*x^2 - 16*b^5*d^5*x^2 - 2*b^5*c^2*d^3*x^3 - 12*a*b^4*c*d^4*x^3 - 16*b^5*c*d^4*x^3 - 2*a^2*b^3*d^5*x^3 - 16*a*b^4*d^5*x^3 - 16*b^5*d^5*x^3 + 22*b^4*Sqrt[a + b]*c^4*d*Sqrt[a + b*x] - 6*a*b^3*Sqrt[a + b]*c^3*d^2*Sqrt[a + b*x] + b^4*Sqrt[a + b]*c^3*d^2*Sqrt[a + b*x] - 18*a^2*b^2*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] + 21*a*b^3*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] - 18*b^4*Sqrt[a + b]*c^2*d^3*Sqrt[a + b*x] + 14*a^3*b*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] - 21*a^2*b^2*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] + 12*a*b^3*Sqrt[a + b]*c*d^4*Sqrt[a + b*x] - 12*a^4*Sqrt[a + b]*d^5*Sqrt[a + b*x] - a^3*b*Sqrt[a + b]*d^5*Sqrt[a + b*x] + 6*a^2*b^2*Sqrt[a + b]*d^5*Sqrt[a + b*x] + b^4*Sqrt[a + b]*c^3*d^2*x*Sqrt[a + b*x] + 21*a*b^3*Sqrt[a + b]*c^2*d^3*x*Sqrt[a + b*x] - 12*b^4*Sqrt[a + b]*c^2*d^3*x*Sqrt[a + b*x] - 21*a^2*b^2*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] + 24*a*b^3*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] - 24*b^4*Sqrt[a + b]*c*d^4*x*Sqrt[a + b*x] - a^3*b*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] - 12*a^2*b^2*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] + 24*a*b^3*Sqrt[a + b]*d^5*x*Sqrt[a + b*x] - 18*b^4*Sqrt[a + b]*c^2*d^3*x^2*Sqrt[a + b*x] + 12*a*b^3*Sqrt[a + b]*c*d^4*x^2*Sqrt[a + b*x] - 24*b^4*Sqrt[a + b]*c*d^4*x^2*Sqrt[a + b*x] + 6*a^2*b^2*Sqrt[a + b]*d^5*x^2*Sqrt[a + b*x] + 24*a*b^3*Sqrt[a + b]*d^5*x^2*Sqrt[a + b*x] - 12*b^5*c^4*Sqrt[c + d]*Sqrt[c + d*x] + 14*a*b^4*c^3*d*Sqrt[c + d]*Sqrt[c + d*x] - b^5*c^3*d*Sqrt[c + d]*Sqrt[c + d*x] - 18*a^2*b^3*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 21*a*b^4*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 6*b^5*c^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 6*a^3*b^2*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 21*a^2*b^3*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 12*a*b^4*c*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 22*a^4*b*d^4*Sqrt[c + d]*Sqrt[c + d*x] + a^3*b^2*d^4*Sqrt[c + d]*Sqrt[c + d*x] - 18*a^2*b^3*d^4*Sqrt[c + d]*Sqrt[c + d*x] - b^5*c^3*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 21*a*b^4*c^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 12*b^5*c^2*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 21*a^2*b^3*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] + 24*a*b^4*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] + 24*b^5*c*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] + a^3*b^2*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] - 12*a^2*b^3*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] - 24*a*b^4*d^4*Sqrt[c + d]*x*Sqrt[c + d*x] + 6*b^5*c^2*d^2*Sqrt[c + d]*x^2*Sqrt[c + d*x] + 12*a*b^4*c*d^3*Sqrt[c + d]*x^2*Sqrt[c + d*x] + 24*b^5*c*d^3*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 18*a^2*b^3*d^4*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 24*a*b^4*d^4*Sqrt[c + d]*x^2*Sqrt[c + d*x] - 22*b^4*Sqrt[a + b]*c^3*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 6*a*b^3*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 10*b^4*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 6*a^2*b^2*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 36*a*b^3*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 8*b^4*Sqrt[a + b]*c*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 22*a^3*b*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 10*a^2*b^2*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 8*a*b^3*Sqrt[a + b]*d^4*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 10*b^4*Sqrt[a + b]*c^2*d^2*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] - 36*a*b^3*Sqrt[a + b]*c*d^3*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 10*a^2*b^2*Sqrt[a + b]*d^4*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 16*b^4*Sqrt[a + b]*d^4*Sqrt[c + d]*x*Sqrt[a + b*x]*Sqrt[c + d*x] + 8*b^4*Sqrt[a + b]*c*d^3*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x] + 8*a*b^3*Sqrt[a + b]*d^4*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x] + 16*b^4*Sqrt[a + b]*d^4*Sqrt[c + d]*x^2*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^4 + ((3*c^2)/(2*Sqrt[b]*d^(5/2)) + (a*c)/(b^(3/2)*d^(3/2)) + (3*a^2)/(2*b^(5/2)*Sqrt[d]))*ArcTanh[(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*(Sqrt[c + d] - Sqrt[c + d*x]))]","B",1
735,1,356,75,1.1070507,"\int \frac{x}{\sqrt{a+b x} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[x/(Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(\frac{\sqrt{a+b}}{b d}-\frac{\sqrt{a+b x}}{b d}\right) \left(a^2 d^2+b c d \sqrt{a+b} \sqrt{a+b x}+a b d \sqrt{c+d} \sqrt{c+d x}-2 b d \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+a b d^2 x-a d^2 \sqrt{a+b} \sqrt{a+b x}+a b d^2+b^2 c^2+b^2 c d x-b^2 c \sqrt{c+d} \sqrt{c+d x}+b^2 c d+2 b^2 d^2 x\right)}{\left(-d \sqrt{a+b} \sqrt{a+b x}+a d+b \sqrt{c+d} \sqrt{c+d x}+b (-c)\right)^2}+\left(-\frac{2 a}{b^{3/2} \sqrt{d}}-\frac{2 c}{\sqrt{b} d^{3/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b}-\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \left(\sqrt{c+d}-\sqrt{c+d x}\right)}\right)","\frac{\sqrt{a+b x} \sqrt{c+d x}}{b d}-\frac{(a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{3/2} d^{3/2}}",1,"((Sqrt[a + b]/(b*d) - Sqrt[a + b*x]/(b*d))*(Sqrt[c + d] - Sqrt[c + d*x])*(b^2*c^2 + b^2*c*d + a^2*d^2 + a*b*d^2 + b^2*c*d*x + a*b*d^2*x + 2*b^2*d^2*x + b*Sqrt[a + b]*c*d*Sqrt[a + b*x] - a*Sqrt[a + b]*d^2*Sqrt[a + b*x] - b^2*c*Sqrt[c + d]*Sqrt[c + d*x] + a*b*d*Sqrt[c + d]*Sqrt[c + d*x] - 2*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^2 + ((-2*c)/(Sqrt[b]*d^(3/2)) - (2*a)/(b^(3/2)*Sqrt[d]))*ArcTanh[(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*(Sqrt[c + d] - Sqrt[c + d*x]))]","B",1
736,1,75,42,0.0005608,"\int \frac{1}{\sqrt{a+b x} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\frac{4 \tanh ^{-1}\left(\frac{\frac{\sqrt{d} \sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b}}}{\sqrt{c+d}-\sqrt{c+d x}}\right)}{\sqrt{b} \sqrt{d}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b} \sqrt{d}}",1,"(4*ArcTanh[((Sqrt[a + b]*Sqrt[d])/Sqrt[b] - (Sqrt[d]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[c + d] - Sqrt[c + d*x])])/(Sqrt[b]*Sqrt[d])","A",1
737,1,294,42,2.7443839,"\int \frac{1}{x \sqrt{a+b x} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[a + b*x]*Sqrt[c + d*x]),x]","-\text{RootSum}\left[\text{$\#$1}^4 d^2-4 \text{$\#$1}^3 d \sqrt{a+b} \sqrt{c+d}+4 \text{$\#$1}^2 a d+4 \text{$\#$1}^2 b c+6 \text{$\#$1}^2 b d-4 \text{$\#$1} b \sqrt{a+b} \sqrt{c+d}+b^2\&,\frac{\text{$\#$1}^2 d \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)+\text{$\#$1}^2 (-d) \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)-b \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)+b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{\text{$\#$1}^3 d^2-3 \text{$\#$1}^2 d \sqrt{a+b} \sqrt{c+d}+2 \text{$\#$1} a d+2 \text{$\#$1} b c+3 \text{$\#$1} b d-b \sqrt{a+b} \sqrt{c+d}}\&\right]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{a} \sqrt{c}}",1,"-RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (b*Log[Sqrt[c + d] - Sqrt[c + d*x]] - b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] - d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 + d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ]","C",1
738,-1,0,78,181.7264874,"\int \frac{1}{x^2 \sqrt{a+b x} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/(x^2*Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\text{\$Aborted}","\frac{(a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{3/2} c^{3/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x}}{a c x}",1,"$Aborted","F",-1
739,-1,0,137,180.0658806,"\int \frac{1}{x^3 \sqrt{a+b x} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/(x^3*Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\text{\$Aborted}","\frac{3 \sqrt{a+b x} \sqrt{c+d x} (a d+b c)}{4 a^2 c^2 x}-\frac{\left(3 a^2 d^2+2 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{5/2} c^{5/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x}}{2 a c x^2}",1,"$Aborted","F",-1
740,-1,0,198,180.1029293,"\int \frac{1}{x^4 \sqrt{a+b x} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[1/(x^4*Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\text{\$Aborted}","\frac{5 \sqrt{a+b x} \sqrt{c+d x} (a d+b c)}{12 a^2 c^2 x^2}+\frac{\left(5 a^2 d^2-2 a b c d+5 b^2 c^2\right) (a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 a^{7/2} c^{7/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(15 a^2 d^2+14 a b c d+15 b^2 c^2\right)}{24 a^3 c^3 x}-\frac{\sqrt{a+b x} \sqrt{c+d x}}{3 a c x^3}",1,"$Aborted","F",-1
741,-1,0,175,180.0316468,"\int \frac{x^3}{\sqrt{a+b x} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[x^3/(Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\text{\$Aborted}","\frac{3 \left(a^2 d^2+2 a b c d+5 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{5/2} d^{7/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} ((5 b c-3 a d) (a d+3 b c)-2 b d x (5 b c-a d))}{4 b^2 d^3 (b c-a d)}-\frac{2 c x^2 \sqrt{a+b x}}{d \sqrt{c+d x} (b c-a d)}",1,"$Aborted","F",-1
742,1,674,112,17.7857221,"\int \frac{x^2}{\sqrt{a+b x} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[x^2/(Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\left(-\frac{2 a}{b^{3/2} d^{3/2}}-\frac{6 c}{\sqrt{b} d^{5/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b}-\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \left(\sqrt{c+d}-\sqrt{c+d x}\right)}\right)+\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(\frac{2 c^2 \sqrt{a+b x}}{d^2}-\frac{2 c^2 \sqrt{a+b}}{d^2}\right)}{d \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}-a d \sqrt{c+d} \sqrt{c+d x}-b c^2-b c d x+b c \sqrt{c+d} \sqrt{c+d x}-b c d-b d^2 x}+\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^3 \left(-\frac{b c \sqrt{a+b x}}{d^2}+\frac{2 b c \sqrt{a+b} \sqrt{c+d x}}{d^2 \sqrt{c+d}}-\frac{b c \sqrt{a+b}}{d^2}+\frac{2 b \sqrt{a+b} \sqrt{c+d x}}{d \sqrt{c+d}}-\frac{a \sqrt{a+b x}}{d}-\frac{2 b \sqrt{a+b x}}{d}+\frac{a \sqrt{a+b}}{d}\right)}{\left(-d \sqrt{a+b} \sqrt{a+b x}+a d+b \sqrt{c+d} \sqrt{c+d x}+b (-c)\right)^2}+\frac{\left(\frac{\sqrt{c+d x}}{b d^2 \sqrt{c+d}}-\frac{1}{b d^2}\right) \left(b c \sqrt{c+d} \sqrt{a+b x}-4 b c \sqrt{a+b} \sqrt{c+d x}+a d \sqrt{c+d} \sqrt{a+b x}+2 b d \sqrt{c+d} \sqrt{a+b x}-4 b d \sqrt{a+b} \sqrt{c+d x}+3 b c \sqrt{a+b} \sqrt{c+d}-a d \sqrt{a+b} \sqrt{c+d}+2 b d \sqrt{a+b} \sqrt{c+d}\right)}{-d \sqrt{a+b} \sqrt{a+b x}+a d+b \sqrt{c+d} \sqrt{c+d x}+b (-c)}","-\frac{(a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{3/2} d^{5/2}}+\frac{2 c^2 \sqrt{a+b x}}{d^2 \sqrt{c+d x} (b c-a d)}+\frac{\sqrt{a+b x} \sqrt{c+d x}}{b d^2}",1,"((Sqrt[c + d] - Sqrt[c + d*x])^3*(-((b*Sqrt[a + b]*c)/d^2) + (a*Sqrt[a + b])/d - (b*c*Sqrt[a + b*x])/d^2 - (a*Sqrt[a + b*x])/d - (2*b*Sqrt[a + b*x])/d + (2*b*Sqrt[a + b]*c*Sqrt[c + d*x])/(d^2*Sqrt[c + d]) + (2*b*Sqrt[a + b]*Sqrt[c + d*x])/(d*Sqrt[c + d])))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x])^2 + ((3*b*Sqrt[a + b]*c*Sqrt[c + d] - a*Sqrt[a + b]*d*Sqrt[c + d] + 2*b*Sqrt[a + b]*d*Sqrt[c + d] + b*c*Sqrt[c + d]*Sqrt[a + b*x] + a*d*Sqrt[c + d]*Sqrt[a + b*x] + 2*b*d*Sqrt[c + d]*Sqrt[a + b*x] - 4*b*Sqrt[a + b]*c*Sqrt[c + d*x] - 4*b*Sqrt[a + b]*d*Sqrt[c + d*x])*(-(1/(b*d^2)) + Sqrt[c + d*x]/(b*d^2*Sqrt[c + d])))/(-(b*c) + a*d - Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[c + d*x]) + (((-2*Sqrt[a + b]*c^2)/d^2 + (2*c^2*Sqrt[a + b*x])/d^2)*(Sqrt[c + d] - Sqrt[c + d*x]))/(-(b*c^2) - b*c*d - b*c*d*x - b*d^2*x + b*c*Sqrt[c + d]*Sqrt[c + d*x] - a*d*Sqrt[c + d]*Sqrt[c + d*x] + Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]) + ((-6*c)/(Sqrt[b]*d^(5/2)) - (2*a)/(b^(3/2)*d^(3/2)))*ArcTanh[(Sqrt[a + b]*Sqrt[d] - Sqrt[d]*Sqrt[a + b*x])/(Sqrt[b]*(Sqrt[c + d] - Sqrt[c + d*x]))]","B",1
743,1,632,77,4.7071943,"\int \frac{x}{\sqrt{a+b x} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[x/(Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\frac{\sqrt{a+b} \left(-2 c \sqrt{c+d} \left(6 a c d+2 a d^2 x+4 a d^2+2 b c^2+5 b c d x+5 b c d+b d^2 x^2+5 b d^2 x+2 b d^2\right)-2 c \sqrt{c+d x} \left(-6 a c d-6 a d^2-2 b c^2-4 b c d x-6 b c d-4 b d^2 x-4 b d^2\right)\right)-2 c \sqrt{c+d} \sqrt{a+b x} \left(-6 a c d-2 a d^2 x-4 a d^2-2 b c^2-2 b c d x-8 b c d-4 b d^2 x-4 b d^2\right)-2 c \sqrt{a+b x} \sqrt{c+d x} \left(6 a c d+6 a d^2+2 b c^2+b c d x+9 b c d+b d^2 x+7 b d^2\right)}{d (c+d)^{3/2} \sqrt{c+d x} \left(4 a^2 d^2-2 a b c d+2 a b d^2 x+4 a b d^2-2 b^2 c^2-2 b^2 c d x-4 b^2 c d\right)+d (c+d) \left(-2 a^2 c d^2-2 a^2 d^3 x+2 a b c^2 d+a b c d^2 x-a b c d^2-a b d^3 x^2-a b d^3 x+2 b^2 c^3+3 b^2 c^2 d x+5 b^2 c^2 d+b^2 c d^2 x^2+5 b^2 c d^2 x+2 b^2 c d^2+2 b^2 d^3 x\right)+\sqrt{a+b} \sqrt{a+b x} \left(d (c+d) \left(2 a c d^2+2 a d^3 x-2 b c^2 d-2 b c d^2 x\right)+d (c+d)^{3/2} \sqrt{c+d x} \left(-4 a d^2+2 b c d-2 b d^2\right)\right)}+\frac{4 \tanh ^{-1}\left(\frac{\frac{\sqrt{d} \sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b}}}{\sqrt{c+d}-\sqrt{c+d x}}\right)}{\sqrt{b} d^{3/2}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b} d^{3/2}}-\frac{2 c \sqrt{a+b x}}{d \sqrt{c+d x} (b c-a d)}",1,"(-2*c*Sqrt[c + d]*Sqrt[a + b*x]*(-2*b*c^2 - 6*a*c*d - 8*b*c*d - 4*a*d^2 - 4*b*d^2 - 2*b*c*d*x - 2*a*d^2*x - 4*b*d^2*x) - 2*c*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*b*c^2 + 6*a*c*d + 9*b*c*d + 6*a*d^2 + 7*b*d^2 + b*c*d*x + b*d^2*x) + Sqrt[a + b]*(-2*c*Sqrt[c + d*x]*(-2*b*c^2 - 6*a*c*d - 6*b*c*d - 6*a*d^2 - 4*b*d^2 - 4*b*c*d*x - 4*b*d^2*x) - 2*c*Sqrt[c + d]*(2*b*c^2 + 6*a*c*d + 5*b*c*d + 4*a*d^2 + 2*b*d^2 + 5*b*c*d*x + 2*a*d^2*x + 5*b*d^2*x + b*d^2*x^2)))/(d*(c + d)^(3/2)*Sqrt[c + d*x]*(-2*b^2*c^2 - 2*a*b*c*d - 4*b^2*c*d + 4*a^2*d^2 + 4*a*b*d^2 - 2*b^2*c*d*x + 2*a*b*d^2*x) + d*(c + d)*(2*b^2*c^3 + 2*a*b*c^2*d + 5*b^2*c^2*d - 2*a^2*c*d^2 - a*b*c*d^2 + 2*b^2*c*d^2 + 3*b^2*c^2*d*x + a*b*c*d^2*x + 5*b^2*c*d^2*x - 2*a^2*d^3*x - a*b*d^3*x + 2*b^2*d^3*x + b^2*c*d^2*x^2 - a*b*d^3*x^2) + Sqrt[a + b]*Sqrt[a + b*x]*(d*(c + d)^(3/2)*(2*b*c*d - 4*a*d^2 - 2*b*d^2)*Sqrt[c + d*x] + d*(c + d)*(-2*b*c^2*d + 2*a*c*d^2 - 2*b*c*d^2*x + 2*a*d^3*x))) + (4*ArcTanh[((Sqrt[a + b]*Sqrt[d])/Sqrt[b] - (Sqrt[d]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[c + d] - Sqrt[c + d*x])])/(Sqrt[b]*d^(3/2))","B",1
744,1,690,30,0.0007172,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4 \left(\frac{\sqrt{a+b}}{c+d}-\frac{\sqrt{a+b x}}{c+d}\right) \left(\frac{\left(d \sqrt{a+b x}-d \sqrt{a+b}\right) \left(2 \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x}+c \sqrt{a+b x}-3 c \sqrt{a+b}+d \sqrt{a+b x}-3 d \sqrt{a+b}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^2}+b c+b d\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(-4 a^2 d^2 \sqrt{c+d} \sqrt{c+d x}+2 a^2 c d^2+2 a^2 d^3 x+2 b c^2 d \sqrt{a+b} \sqrt{a+b x}-2 a b c^2 d-a b c d^2 x-2 a c d^2 \sqrt{a+b} \sqrt{a+b x}+2 b c d^2 x \sqrt{a+b} \sqrt{a+b x}-2 a b d^2 x \sqrt{c+d} \sqrt{c+d x}-4 a b d^2 \sqrt{c+d} \sqrt{c+d x}+4 a d^2 \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+2 b d^2 \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+a b c d^2+2 a b c d \sqrt{c+d} \sqrt{c+d x}-2 b c d \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+a b d^3 x^2+a b d^3 x-2 a d^3 x \sqrt{a+b} \sqrt{a+b x}-2 b^2 c^3-3 b^2 c^2 d x+2 b^2 c^2 \sqrt{c+d} \sqrt{c+d x}-5 b^2 c^2 d-b^2 c d^2 x^2-5 b^2 c d^2 x-2 b^2 c d^2+2 b^2 c d x \sqrt{c+d} \sqrt{c+d x}+4 b^2 c d \sqrt{c+d} \sqrt{c+d x}-2 b^2 d^3 x\right)}","\frac{2 \sqrt{a+b x}}{\sqrt{c+d x} (b c-a d)}",1,"((Sqrt[a + b]/(c + d) - Sqrt[a + b*x]/(c + d))*(Sqrt[c + d] - Sqrt[c + d*x])^4*(b*c + b*d + ((-(Sqrt[a + b]*d) + d*Sqrt[a + b*x])*(-3*Sqrt[a + b]*c - 3*Sqrt[a + b]*d + c*Sqrt[a + b*x] + d*Sqrt[a + b*x] + 2*Sqrt[a + b]*Sqrt[c + d]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^2))/((-Sqrt[c + d] + Sqrt[c + d*x])*(-2*b^2*c^3 - 2*a*b*c^2*d - 5*b^2*c^2*d + 2*a^2*c*d^2 + a*b*c*d^2 - 2*b^2*c*d^2 - 3*b^2*c^2*d*x - a*b*c*d^2*x - 5*b^2*c*d^2*x + 2*a^2*d^3*x + a*b*d^3*x - 2*b^2*d^3*x - b^2*c*d^2*x^2 + a*b*d^3*x^2 + 2*b*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] - 2*a*Sqrt[a + b]*c*d^2*Sqrt[a + b*x] + 2*b*Sqrt[a + b]*c*d^2*x*Sqrt[a + b*x] - 2*a*Sqrt[a + b]*d^3*x*Sqrt[a + b*x] + 2*b^2*c^2*Sqrt[c + d]*Sqrt[c + d*x] + 2*a*b*c*d*Sqrt[c + d]*Sqrt[c + d*x] + 4*b^2*c*d*Sqrt[c + d]*Sqrt[c + d*x] - 4*a^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 4*a*b*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 2*b^2*c*d*Sqrt[c + d]*x*Sqrt[c + d*x] - 2*a*b*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] - 2*b*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 4*a*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 2*b*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))","B",1
745,1,444,77,5.4037763,"\int \frac{1}{x \sqrt{a+b x} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\frac{\text{RootSum}\left[\text{$\#$1}^4 d^2-4 \text{$\#$1}^3 d \sqrt{a+b} \sqrt{c+d}+4 \text{$\#$1}^2 a d+4 \text{$\#$1}^2 b c+6 \text{$\#$1}^2 b d-4 \text{$\#$1} b \sqrt{a+b} \sqrt{c+d}+b^2\&,\frac{-\text{$\#$1}^2 d \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)+\text{$\#$1}^2 d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)+b \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)-b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{\text{$\#$1}^3 d^2-3 \text{$\#$1}^2 d \sqrt{a+b} \sqrt{c+d}+2 \text{$\#$1} a d+2 \text{$\#$1} b c+3 \text{$\#$1} b d-b \sqrt{a+b} \sqrt{c+d}}\&\right]}{c}+\frac{2 d \sqrt{c+d} \sqrt{a+b x}-2 d \sqrt{a+b x} \sqrt{c+d x}+\sqrt{a+b} \left(2 d \sqrt{c+d x}-2 d \sqrt{c+d}\right)}{\sqrt{c+d} \sqrt{c+d x} \left(c (a d-b c)-c d \sqrt{a+b} \sqrt{a+b x}\right)+c \left(b c^2+b c d x+b c d+b d^2 x\right)}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{a} c^{3/2}}-\frac{2 d \sqrt{a+b x}}{c \sqrt{c+d x} (b c-a d)}",1,"(2*d*Sqrt[c + d]*Sqrt[a + b*x] - 2*d*Sqrt[a + b*x]*Sqrt[c + d*x] + Sqrt[a + b]*(-2*d*Sqrt[c + d] + 2*d*Sqrt[c + d*x]))/(c*(b*c^2 + b*c*d + b*c*d*x + b*d^2*x) + Sqrt[c + d]*Sqrt[c + d*x]*(c*(-(b*c) + a*d) - Sqrt[a + b]*c*d*Sqrt[a + b*x])) + RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ]/c","C",1
746,-1,0,124,180.0527267,"\int \frac{1}{x^2 \sqrt{a+b x} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^2*Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\text{\$Aborted}","\frac{(3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{3/2} c^{5/2}}-\frac{d \sqrt{a+b x} (b c-3 a d)}{a c^2 \sqrt{c+d x} (b c-a d)}-\frac{\sqrt{a+b x}}{a c x \sqrt{c+d x}}",1,"$Aborted","F",-1
747,-1,0,194,180.1097813,"\int \frac{1}{x^3 \sqrt{a+b x} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^3*Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\text{\$Aborted}","\frac{d \sqrt{a+b x} (3 b c-5 a d) (3 a d+b c)}{4 a^2 c^3 \sqrt{c+d x} (b c-a d)}+\frac{\sqrt{a+b x} (5 a d+3 b c)}{4 a^2 c^2 x \sqrt{c+d x}}-\frac{3 \left(5 a^2 d^2+2 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{5/2} c^{7/2}}-\frac{\sqrt{a+b x}}{2 a c x^2 \sqrt{c+d x}}",1,"$Aborted","F",-1
748,-1,0,258,180.0556541,"\int \frac{x^4}{\sqrt{a+b x} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[x^4/(Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\text{\$Aborted}","\frac{\left(3 a^2 d^2+10 a b c d+35 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{5/2} d^{9/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(9 a^3 d^3-2 b d x \left(3 a^2 d^2-46 a b c d+35 b^2 c^2\right)+15 a^2 b c d^2-145 a b^2 c^2 d+105 b^3 c^3\right)}{12 b^2 d^4 (b c-a d)^2}-\frac{2 c x^2 \sqrt{a+b x} (7 b c-9 a d)}{3 d^2 \sqrt{c+d x} (b c-a d)^2}-\frac{2 c x^3 \sqrt{a+b x}}{3 d (c+d x)^{3/2} (b c-a d)}",1,"$Aborted","F",-1
749,-1,0,174,180.0449833,"\int \frac{x^3}{\sqrt{a+b x} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[x^3/(Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\text{\$Aborted}","\frac{\sqrt{a+b x} \left(c \left(3 a^2 d^2-22 a b c d+15 b^2 c^2\right)+d x (5 b c-3 a d) (b c-a d)\right)}{3 b d^3 \sqrt{c+d x} (b c-a d)^2}-\frac{(a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{3/2} d^{7/2}}-\frac{2 c x^2 \sqrt{a+b x}}{3 d (c+d x)^{3/2} (b c-a d)}",1,"$Aborted","F",-1
750,1,2001,126,35.3329582,"\int \frac{x^2}{\sqrt{a+b x} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[x^2/(Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\text{Result too large to show}","\frac{2 c^2 \sqrt{a+b x}}{3 d^2 (c+d x)^{3/2} (b c-a d)}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b} d^{5/2}}-\frac{4 c \sqrt{a+b x} (2 b c-3 a d)}{3 d^2 \sqrt{c+d x} (b c-a d)^2}",1,"((Sqrt[c + d] - Sqrt[c + d*x])^5*((8*a^3*c^4)/(3*Sqrt[a + b]*(c + d)^(9/2)) - (6*a^2*b*c^4)/(Sqrt[a + b]*(c + d)^(9/2)) - (8*a*b^2*c^4)/(Sqrt[a + b]*(c + d)^(9/2)) + (2*b^3*c^4)/(3*Sqrt[a + b]*(c + d)^(9/2)) + (2*a*b^2*c^6)/(Sqrt[a + b]*d^2*(c + d)^(9/2)) + (2*b^3*c^6)/(Sqrt[a + b]*d^2*(c + d)^(9/2)) - (14*a^2*b*c^5)/(3*Sqrt[a + b]*d*(c + d)^(9/2)) - (4*a*b^2*c^5)/(3*Sqrt[a + b]*d*(c + d)^(9/2)) + (10*b^3*c^5)/(3*Sqrt[a + b]*d*(c + d)^(9/2)) + (16*a^3*c^3*d)/(3*Sqrt[a + b]*(c + d)^(9/2)) + (2*a^2*b*c^3*d)/(Sqrt[a + b]*(c + d)^(9/2)) - (4*a*b^2*c^3*d)/(Sqrt[a + b]*(c + d)^(9/2)) - (2*b^3*c^3*d)/(3*Sqrt[a + b]*(c + d)^(9/2)) + (8*a^3*c^2*d^2)/(3*Sqrt[a + b]*(c + d)^(9/2)) + (10*a^2*b*c^2*d^2)/(3*Sqrt[a + b]*(c + d)^(9/2)) + (2*a*b^2*c^2*d^2)/(3*Sqrt[a + b]*(c + d)^(9/2)) - (8*a^2*c^4*Sqrt[a + b*x])/(3*(c + d)^(9/2)) + (14*a*b*c^4*Sqrt[a + b*x])/(3*(c + d)^(9/2)) + (10*b^2*c^4*Sqrt[a + b*x])/(3*(c + d)^(9/2)) - (2*b^2*c^6*Sqrt[a + b*x])/(3*d^2*(c + d)^(9/2)) + (10*a*b*c^5*Sqrt[a + b*x])/(3*d*(c + d)^(9/2)) + (2*b^2*c^5*Sqrt[a + b*x])/(3*d*(c + d)^(9/2)) - (16*a^2*c^3*d*Sqrt[a + b*x])/(3*(c + d)^(9/2)) - (2*a*b*c^3*d*Sqrt[a + b*x])/(3*(c + d)^(9/2)) + (2*b^2*c^3*d*Sqrt[a + b*x])/(c + d)^(9/2) - (8*a^2*c^2*d^2*Sqrt[a + b*x])/(3*(c + d)^(9/2)) - (2*a*b*c^2*d^2*Sqrt[a + b*x])/(c + d)^(9/2) - (4*a*b^2*c^3*Sqrt[c + d*x])/(3*Sqrt[a + b]*d^2*(c + d)^2) - (4*b^3*c^3*Sqrt[c + d*x])/(3*Sqrt[a + b]*d^2*(c + d)^2) + (4*a^2*b*c^2*Sqrt[c + d*x])/(3*Sqrt[a + b]*d*(c + d)^2) + (4*a*b^2*c^2*Sqrt[c + d*x])/(3*Sqrt[a + b]*d*(c + d)^2)))/(b*c*Sqrt[c + d] + b*d*Sqrt[c + d]*x - b*c*Sqrt[c + d*x] + a*d*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x])^3 + ((Sqrt[c + d] - Sqrt[c + d*x])^3*((-6*a*b*c^3)/(Sqrt[a + b]*d^2*(c + d)^2) - (6*b^2*c^3)/(Sqrt[a + b]*d^2*(c + d)^2) + (8*a^2*c^2)/(Sqrt[a + b]*d*(c + d)^2) + (10*a*b*c^2)/(Sqrt[a + b]*d*(c + d)^2) + (2*b^2*c^2)/(Sqrt[a + b]*d*(c + d)^2) + (4*b*c^3*Sqrt[a + b*x])/(3*d^2*(c + d)^2) - (16*a*c^2*Sqrt[a + b*x])/(3*d*(c + d)^2) - (4*b*c^2*Sqrt[a + b*x])/(d*(c + d)^2) - (16*a^2*c^3*Sqrt[c + d*x])/(3*Sqrt[a + b]*(c + d)^(9/2)) + (10*a*b*c^3*Sqrt[c + d*x])/(3*Sqrt[a + b]*(c + d)^(9/2)) + (26*b^2*c^3*Sqrt[c + d*x])/(3*Sqrt[a + b]*(c + d)^(9/2)) + (14*a*b*c^5*Sqrt[c + d*x])/(3*Sqrt[a + b]*d^2*(c + d)^(9/2)) + (14*b^2*c^5*Sqrt[c + d*x])/(3*Sqrt[a + b]*d^2*(c + d)^(9/2)) - (8*a^2*c^4*Sqrt[c + d*x])/(3*Sqrt[a + b]*d*(c + d)^(9/2)) + (26*a*b*c^4*Sqrt[c + d*x])/(3*Sqrt[a + b]*d*(c + d)^(9/2)) + (34*b^2*c^4*Sqrt[c + d*x])/(3*Sqrt[a + b]*d*(c + d)^(9/2)) - (8*a^2*c^2*d*Sqrt[c + d*x])/(3*Sqrt[a + b]*(c + d)^(9/2)) - (2*a*b*c^2*d*Sqrt[c + d*x])/(3*Sqrt[a + b]*(c + d)^(9/2)) + (2*b^2*c^2*d*Sqrt[c + d*x])/(Sqrt[a + b]*(c + d)^(9/2))))/(b*c*Sqrt[c + d] + b*d*Sqrt[c + d]*x - b*c*Sqrt[c + d*x] + a*d*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x])^2 + (((-2*c)/(Sqrt[a + b]*d^2*(c + d)^2) + (2*c*Sqrt[c + d*x])/(Sqrt[a + b]*(c + d)^(9/2)) + (2*c^3*Sqrt[c + d*x])/(Sqrt[a + b]*d^2*(c + d)^(9/2)) + (4*c^2*Sqrt[c + d*x])/(Sqrt[a + b]*d*(c + d)^(9/2)))*(-(a*c^2) - b*c^2 + a*c*d + b*c*d + 2*a*d^2 + 2*b*d^2 - Sqrt[a + b]*c^2*Sqrt[a + b*x] - 3*Sqrt[a + b]*c*d*Sqrt[a + b*x] - 2*Sqrt[a + b]*d^2*Sqrt[a + b*x] + 2*a*c*Sqrt[c + d]*Sqrt[c + d*x] + 2*b*c*Sqrt[c + d]*Sqrt[c + d*x]))/(b*c*Sqrt[c + d] + b*d*Sqrt[c + d]*x - b*c*Sqrt[c + d*x] + a*d*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x]) + (4*ArcTanh[((Sqrt[a + b]*Sqrt[d])/Sqrt[b] - (Sqrt[d]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[c + d] - Sqrt[c + d*x])])/(Sqrt[b]*d^(5/2))","B",1
751,1,1113,80,5.6912913,"\int \frac{x}{\sqrt{a+b x} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[x/(Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\frac{\left(\frac{\sqrt{a+b x}}{6 \sqrt{a+b} (c+d)^{3/2}}-\frac{1}{6 (c+d)^{3/2}}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)^6 \left(\frac{\left(12 a \sqrt{a+b} x d^3+3 b \sqrt{a+b} x d^3+6 a \sqrt{a+b} d^3+3 b \sqrt{a+b} d^3+6 a \sqrt{a+b x} d^3-6 b \sqrt{a+b x} d^3+20 a \sqrt{a+b} c d^2+3 b \sqrt{a+b} c d^2+8 a \sqrt{a+b} c x d^2+3 b \sqrt{a+b} c x d^2+12 a c \sqrt{a+b x} d^2-6 b c \sqrt{a+b x} d^2-12 a \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x} d^2-12 a \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} d^2+10 a \sqrt{a+b} c^2 d+6 a c^2 \sqrt{a+b x} d-10 a \sqrt{a+b} c \sqrt{c+d} \sqrt{c+d x} d-6 a c \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} d\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^2}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4}+\frac{-3 \sqrt{a+b} c \sqrt{c+d} b^2-9 \sqrt{a+b} d \sqrt{c+d} b^2+6 c \sqrt{c+d} \sqrt{a+b x} b^2+12 d \sqrt{c+d} \sqrt{a+b x} b^2-3 \sqrt{a+b} c \sqrt{c+d x} b^2-3 \sqrt{a+b} d \sqrt{c+d x} b^2}{\sqrt{c+d}-\sqrt{c+d x}}+\frac{\left(2 b \sqrt{a+b x}-2 b \sqrt{a+b}\right) \left(4 a \sqrt{c+d} c^2-2 b \sqrt{c+d} c^2+2 \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} c^2-4 a \sqrt{c+d x} c^2+2 b \sqrt{c+d x} c^2-2 \sqrt{a+b} \sqrt{a+b x} \sqrt{c+d x} c^2+3 a d \sqrt{c+d} x c+3 b d \sqrt{c+d} x c+12 a d \sqrt{c+d} c-6 b d \sqrt{c+d} c+3 \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} c-9 a d \sqrt{c+d x} c+9 b d \sqrt{c+d x} c-9 \sqrt{a+b} d \sqrt{a+b x} \sqrt{c+d x} c+6 a d^2 \sqrt{c+d} x+6 b d^2 \sqrt{c+d} x+9 a d^2 \sqrt{c+d}-3 b d^2 \sqrt{c+d}-3 \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x}-3 a d^2 \sqrt{c+d x}+9 b d^2 \sqrt{c+d x}-9 \sqrt{a+b} d^2 \sqrt{a+b x} \sqrt{c+d x}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^3}\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(b \sqrt{c+d} c-b \sqrt{c+d x} c+b d \sqrt{c+d} x+a d \sqrt{c+d x}-\sqrt{a+b} d \sqrt{a+b x} \sqrt{c+d x}\right)^3}","\frac{2 \sqrt{a+b x} (b c-3 a d)}{3 d \sqrt{c+d x} (b c-a d)^2}-\frac{2 c \sqrt{a+b x}}{3 d (c+d x)^{3/2} (b c-a d)}",1,"((-1/6*1/(c + d)^(3/2) + Sqrt[a + b*x]/(6*Sqrt[a + b]*(c + d)^(3/2)))*(Sqrt[c + d] - Sqrt[c + d*x])^6*((-3*b^2*Sqrt[a + b]*c*Sqrt[c + d] - 9*b^2*Sqrt[a + b]*d*Sqrt[c + d] + 6*b^2*c*Sqrt[c + d]*Sqrt[a + b*x] + 12*b^2*d*Sqrt[c + d]*Sqrt[a + b*x] - 3*b^2*Sqrt[a + b]*c*Sqrt[c + d*x] - 3*b^2*Sqrt[a + b]*d*Sqrt[c + d*x])/(Sqrt[c + d] - Sqrt[c + d*x]) + ((-2*b*Sqrt[a + b] + 2*b*Sqrt[a + b*x])*(4*a*c^2*Sqrt[c + d] - 2*b*c^2*Sqrt[c + d] + 12*a*c*d*Sqrt[c + d] - 6*b*c*d*Sqrt[c + d] + 9*a*d^2*Sqrt[c + d] - 3*b*d^2*Sqrt[c + d] + 3*a*c*d*Sqrt[c + d]*x + 3*b*c*d*Sqrt[c + d]*x + 6*a*d^2*Sqrt[c + d]*x + 6*b*d^2*Sqrt[c + d]*x + 2*Sqrt[a + b]*c^2*Sqrt[c + d]*Sqrt[a + b*x] + 3*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x] - 3*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x] - 4*a*c^2*Sqrt[c + d*x] + 2*b*c^2*Sqrt[c + d*x] - 9*a*c*d*Sqrt[c + d*x] + 9*b*c*d*Sqrt[c + d*x] - 3*a*d^2*Sqrt[c + d*x] + 9*b*d^2*Sqrt[c + d*x] - 2*Sqrt[a + b]*c^2*Sqrt[a + b*x]*Sqrt[c + d*x] - 9*Sqrt[a + b]*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - 9*Sqrt[a + b]*d^2*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^3 + ((Sqrt[a + b] - Sqrt[a + b*x])^2*(10*a*Sqrt[a + b]*c^2*d + 20*a*Sqrt[a + b]*c*d^2 + 3*b*Sqrt[a + b]*c*d^2 + 6*a*Sqrt[a + b]*d^3 + 3*b*Sqrt[a + b]*d^3 + 8*a*Sqrt[a + b]*c*d^2*x + 3*b*Sqrt[a + b]*c*d^2*x + 12*a*Sqrt[a + b]*d^3*x + 3*b*Sqrt[a + b]*d^3*x + 6*a*c^2*d*Sqrt[a + b*x] + 12*a*c*d^2*Sqrt[a + b*x] - 6*b*c*d^2*Sqrt[a + b*x] + 6*a*d^3*Sqrt[a + b*x] - 6*b*d^3*Sqrt[a + b*x] - 10*a*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[c + d*x] - 12*a*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 6*a*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 12*a*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^4))/((-Sqrt[c + d] + Sqrt[c + d*x])*(b*c*Sqrt[c + d] + b*d*Sqrt[c + d]*x - b*c*Sqrt[c + d*x] + a*d*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x])^3)","B",1
752,1,784,66,0.0007214,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^6 \left(\frac{\sqrt{a+b x}}{6 \sqrt{a+b} (c+d)^{3/2}}-\frac{1}{6 (c+d)^{3/2}}\right) \left(\frac{6 b^2 d \sqrt{c+d} \sqrt{a+b x}-3 b^2 c \sqrt{a+b} \sqrt{c+d x}-3 b^2 d \sqrt{a+b} \sqrt{c+d x}+3 b^2 c \sqrt{a+b} \sqrt{c+d}-3 b^2 d \sqrt{a+b} \sqrt{c+d}}{\sqrt{c+d}-\sqrt{c+d x}}+\frac{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^2 \left(3 b c d^2 x \sqrt{a+b}-6 b c d^2 \sqrt{a+b x}-2 a d^2 \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x}-6 a d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+8 a c d^2 \sqrt{a+b}+3 b c d^2 \sqrt{a+b}+4 a d^3 x \sqrt{a+b}+3 b d^3 x \sqrt{a+b}-6 b d^3 \sqrt{a+b x}+4 a d^3 \sqrt{a+b}+3 b d^3 \sqrt{a+b}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4}+\frac{\left(2 b d \sqrt{a+b x}-2 b d \sqrt{a+b}\right) \left(c \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x}-c \sqrt{a+b} \sqrt{a+b x} \sqrt{c+d x}-3 d \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x}-3 d \sqrt{a+b} \sqrt{a+b x} \sqrt{c+d x}-5 a c \sqrt{c+d x}+3 a d x \sqrt{c+d}-3 a d \sqrt{c+d x}+5 a c \sqrt{c+d}+6 a d \sqrt{c+d}+b c \sqrt{c+d x}+3 b d x \sqrt{c+d}+3 b d \sqrt{c+d x}-b c \sqrt{c+d}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^3}\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(-d \sqrt{a+b} \sqrt{a+b x} \sqrt{c+d x}+a d \sqrt{c+d x}-b c \sqrt{c+d x}+b d x \sqrt{c+d}+b c \sqrt{c+d}\right)^3}","\frac{4 b \sqrt{a+b x}}{3 \sqrt{c+d x} (b c-a d)^2}+\frac{2 \sqrt{a+b x}}{3 (c+d x)^{3/2} (b c-a d)}",1,"((-1/6*1/(c + d)^(3/2) + Sqrt[a + b*x]/(6*Sqrt[a + b]*(c + d)^(3/2)))*(Sqrt[c + d] - Sqrt[c + d*x])^6*((3*b^2*Sqrt[a + b]*c*Sqrt[c + d] - 3*b^2*Sqrt[a + b]*d*Sqrt[c + d] + 6*b^2*d*Sqrt[c + d]*Sqrt[a + b*x] - 3*b^2*Sqrt[a + b]*c*Sqrt[c + d*x] - 3*b^2*Sqrt[a + b]*d*Sqrt[c + d*x])/(Sqrt[c + d] - Sqrt[c + d*x]) + ((-2*b*Sqrt[a + b]*d + 2*b*d*Sqrt[a + b*x])*(5*a*c*Sqrt[c + d] - b*c*Sqrt[c + d] + 6*a*d*Sqrt[c + d] + 3*a*d*Sqrt[c + d]*x + 3*b*d*Sqrt[c + d]*x + Sqrt[a + b]*c*Sqrt[c + d]*Sqrt[a + b*x] - 3*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x] - 5*a*c*Sqrt[c + d*x] + b*c*Sqrt[c + d*x] - 3*a*d*Sqrt[c + d*x] + 3*b*d*Sqrt[c + d*x] - Sqrt[a + b]*c*Sqrt[a + b*x]*Sqrt[c + d*x] - 3*Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^3 + ((Sqrt[a + b] - Sqrt[a + b*x])^2*(8*a*Sqrt[a + b]*c*d^2 + 3*b*Sqrt[a + b]*c*d^2 + 4*a*Sqrt[a + b]*d^3 + 3*b*Sqrt[a + b]*d^3 + 3*b*Sqrt[a + b]*c*d^2*x + 4*a*Sqrt[a + b]*d^3*x + 3*b*Sqrt[a + b]*d^3*x - 6*b*c*d^2*Sqrt[a + b*x] - 6*b*d^3*Sqrt[a + b*x] - 2*a*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 6*a*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^4))/((-Sqrt[c + d] + Sqrt[c + d*x])*(b*c*Sqrt[c + d] + b*d*Sqrt[c + d]*x - b*c*Sqrt[c + d*x] + a*d*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x])^3)","B",1
753,-1,0,124,180.054856,"\int \frac{1}{x \sqrt{a+b x} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{a} c^{5/2}}-\frac{2 d \sqrt{a+b x} (5 b c-3 a d)}{3 c^2 \sqrt{c+d x} (b c-a d)^2}-\frac{2 d \sqrt{a+b x}}{3 c (c+d x)^{3/2} (b c-a d)}",1,"$Aborted","F",-1
754,-1,0,189,180.1108288,"\int \frac{1}{x^2 \sqrt{a+b x} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^2*Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\text{\$Aborted}","\frac{(5 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{3/2} c^{7/2}}-\frac{d \sqrt{a+b x} \left(15 a^2 d^2-22 a b c d+3 b^2 c^2\right)}{3 a c^3 \sqrt{c+d x} (b c-a d)^2}-\frac{d \sqrt{a+b x} (3 b c-5 a d)}{3 a c^2 (c+d x)^{3/2} (b c-a d)}-\frac{\sqrt{a+b x}}{a c x (c+d x)^{3/2}}",1,"$Aborted","F",-1
755,-1,0,277,180.0861777,"\int \frac{1}{x^3 \sqrt{a+b x} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^3*Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\text{\$Aborted}","\frac{d \sqrt{a+b x} \left(-35 a^2 d^2+18 a b c d+9 b^2 c^2\right)}{12 a^2 c^3 (c+d x)^{3/2} (b c-a d)}+\frac{\sqrt{a+b x} (7 a d+3 b c)}{4 a^2 c^2 x (c+d x)^{3/2}}-\frac{\left(35 a^2 d^2+10 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{5/2} c^{9/2}}+\frac{d \sqrt{a+b x} \left(105 a^3 d^3-145 a^2 b c d^2+15 a b^2 c^2 d+9 b^3 c^3\right)}{12 a^2 c^4 \sqrt{c+d x} (b c-a d)^2}-\frac{\sqrt{a+b x}}{2 a c x^2 (c+d x)^{3/2}}",1,"$Aborted","F",-1
756,1,328,21,0.5602533,"\int \frac{1}{x \sqrt{c x} \sqrt{a+b x}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[c*x]*Sqrt[a + b*x]),x]","\frac{\left(\sqrt{c x}-\sqrt{c}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^4 \left(\frac{b \left(\sqrt{c x}-\sqrt{c}\right)^2}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^2}+\frac{2 c \sqrt{a+b}-2 \sqrt{c} \sqrt{a+b} \sqrt{c x}}{\sqrt{a+b}-\sqrt{a+b x}}+c\right)}{\left(\sqrt{a+b x}-\sqrt{a+b}\right) \left(4 a^2 c^{3/2} \sqrt{c x}-2 a^2 c^2 x+4 a b c^{3/2} \sqrt{c x}+2 a b c^{3/2} x \sqrt{c x}-4 a c^{3/2} \sqrt{a+b} \sqrt{c x} \sqrt{a+b x}-2 b c^{3/2} \sqrt{a+b} \sqrt{c x} \sqrt{a+b x}-a b c^2 x^2-a b c^2 x+2 a c^2 x \sqrt{a+b} \sqrt{a+b x}+2 b^2 c^2 x\right)}","-\frac{2 \sqrt{a+b x}}{a \sqrt{c x}}",1,"((-Sqrt[c] + Sqrt[c*x])*(Sqrt[a + b] - Sqrt[a + b*x])^4*(c + (b*(-Sqrt[c] + Sqrt[c*x])^2)/(Sqrt[a + b] - Sqrt[a + b*x])^2 + (2*Sqrt[a + b]*c - 2*Sqrt[a + b]*Sqrt[c]*Sqrt[c*x])/(Sqrt[a + b] - Sqrt[a + b*x])))/((-Sqrt[a + b] + Sqrt[a + b*x])*(-2*a^2*c^2*x - a*b*c^2*x + 2*b^2*c^2*x - a*b*c^2*x^2 + 4*a^2*c^(3/2)*Sqrt[c*x] + 4*a*b*c^(3/2)*Sqrt[c*x] + 2*a*b*c^(3/2)*x*Sqrt[c*x] + 2*a*Sqrt[a + b]*c^2*x*Sqrt[a + b*x] - 4*a*Sqrt[a + b]*c^(3/2)*Sqrt[c*x]*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*c^(3/2)*Sqrt[c*x]*Sqrt[a + b*x]))","B",1
757,1,313,42,1.3802401,"\int \frac{1}{x \sqrt{a+b x} \sqrt{a c-b c x}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]),x]","\text{RootSum}\left[\text{$\#$1}^4 b c^2+4 \text{$\#$1}^3 c \sqrt{a+b} \sqrt{-(c (b-a))}-6 \text{$\#$1}^2 b c-4 \text{$\#$1} \sqrt{a+b} \sqrt{-(c (b-a))}+b\&,\frac{\text{$\#$1}^2 (-c) \log \left(\sqrt{a c-b c}-\sqrt{a c-b c x}\right)+\text{$\#$1}^2 c \log \left(\text{$\#$1} \sqrt{a c-b c x}+\text{$\#$1} \left(-\sqrt{a c-b c}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)+\log \left(\text{$\#$1} \sqrt{a c-b c x}+\text{$\#$1} \left(-\sqrt{a c-b c}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)-\log \left(\sqrt{a c-b c}-\sqrt{a c-b c x}\right)}{\text{$\#$1}^3 b c^2+3 \text{$\#$1}^2 c \sqrt{a+b} \sqrt{c (a-b)}-3 \text{$\#$1} b c-\sqrt{a+b} \sqrt{c (a-b)}}\&\right]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x} \sqrt{a c-b c x}}{a \sqrt{c}}\right)}{a \sqrt{c}}",1,"RootSum[b - 4*Sqrt[a + b]*Sqrt[-((-a + b)*c)]*#1 - 6*b*c*#1^2 + 4*Sqrt[a + b]*c*Sqrt[-((-a + b)*c)]*#1^3 + b*c^2*#1^4 & , (-Log[Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x]] + Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[a*c - b*c]*#1 + Sqrt[a*c - b*c*x]*#1] - c*Log[Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x]]*#1^2 + c*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[a*c - b*c]*#1 + Sqrt[a*c - b*c*x]*#1]*#1^2)/(-(Sqrt[a + b]*Sqrt[(a - b)*c]) - 3*b*c*#1 + 3*Sqrt[a + b]*c*Sqrt[(a - b)*c]*#1^2 + b*c^2*#1^3) & ]","C",1
758,-1,0,54,180.0026542,"\int \frac{1}{x \sqrt{1-a-b x} \sqrt{1+a+b x}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x]),x]","\text{\$Aborted}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{\sqrt{1-a^2}}",1,"$Aborted","F",-1
759,-1,0,271,180.039854,"\int \frac{x^3 (c+d x)^{3/2}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(x^3*(c + d*x)^(3/2))/(a + b*x)^(3/2),x]","\text{\$Aborted}","-\frac{\sqrt{a+b x} (c+d x)^{3/2} \left(-105 a^2 d^2-4 b d x (b c-21 a d)+14 a b c d+3 b^2 c^2\right)}{32 b^4 d^2}+\frac{3 (b c-a d) \left(-105 a^3 d^3+35 a^2 b c d^2+5 a b^2 c^2 d+b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{11/2} d^{5/2}}+\frac{3 \sqrt{a+b x} \sqrt{c+d x} \left(-105 a^3 d^3+35 a^2 b c d^2+5 a b^2 c^2 d+b^3 c^3\right)}{64 b^5 d^2}+\frac{9 x^2 \sqrt{a+b x} (c+d x)^{3/2}}{4 b^2}-\frac{2 x^3 (c+d x)^{3/2}}{b \sqrt{a+b x}}",1,"$Aborted","F",-1
760,-1,0,246,180.0201439,"\int \frac{x^2 (c+d x)^{3/2}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(x^2*(c + d*x)^(3/2))/(a + b*x)^(3/2),x]","\text{\$Aborted}","-\frac{\sqrt{a+b x} (c+d x)^{3/2} \left(-\frac{35 a^2 d}{b}+10 a c+\frac{b c^2}{d}\right)}{12 b^2 (b c-a d)}-\frac{2 a^2 (c+d x)^{5/2}}{b^2 \sqrt{a+b x} (b c-a d)}-\frac{(b c-a d) \left(-35 a^2 d^2+10 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{9/2} d^{3/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-35 a^2 d^2+10 a b c d+b^2 c^2\right)}{8 b^4 d}+\frac{\sqrt{a+b x} (c+d x)^{5/2}}{3 b^2 d}",1,"$Aborted","F",-1
761,-1,0,171,180.0309103,"\int \frac{x (c+d x)^{3/2}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(x*(c + d*x)^(3/2))/(a + b*x)^(3/2),x]","\text{\$Aborted}","\frac{3 (b c-5 a d) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{7/2} \sqrt{d}}+\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-5 a d)}{4 b^3}+\frac{\sqrt{a+b x} (c+d x)^{3/2} (b c-5 a d)}{2 b^2 (b c-a d)}+\frac{2 a (c+d x)^{5/2}}{b \sqrt{a+b x} (b c-a d)}",1,"$Aborted","F",-1
762,-1,0,98,180.0430406,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(a + b*x)^(3/2),x]","\text{\$Aborted}","\frac{3 \sqrt{d} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{5/2}}+\frac{3 d \sqrt{a+b x} \sqrt{c+d x}}{b^2}-\frac{2 (c+d x)^{3/2}}{b \sqrt{a+b x}}",1,"$Aborted","F",-1
763,1,548,119,14.0462736,"\int \frac{(c+d x)^{3/2}}{x (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(x*(a + b*x)^(3/2)),x]","\frac{c^2 \text{RootSum}\left[\text{$\#$1}^4 d^2-4 \text{$\#$1}^3 d \sqrt{a+b} \sqrt{c+d}+4 \text{$\#$1}^2 a d+4 \text{$\#$1}^2 b c+6 \text{$\#$1}^2 b d-4 \text{$\#$1} b \sqrt{a+b} \sqrt{c+d}+b^2\&,\frac{-\text{$\#$1}^2 d \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)+\text{$\#$1}^2 d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)+b \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)-b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{\text{$\#$1}^3 d^2-3 \text{$\#$1}^2 d \sqrt{a+b} \sqrt{c+d}+2 \text{$\#$1} a d+2 \text{$\#$1} b c+3 \text{$\#$1} b d-b \sqrt{a+b} \sqrt{c+d}}\&\right]}{a}+\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(\frac{2 \sqrt{a+b} (b c-a d)^2}{a b}-\frac{2 \sqrt{a+b x} (b c-a d)^2}{a b}\right)}{a^2 (-d)+b \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}-b c \sqrt{a+b} \sqrt{a+b x}-a b d x+a d \sqrt{a+b} \sqrt{a+b x}-a b d-b^2 d x}+\frac{4 d^{3/2} \tanh ^{-1}\left(\frac{\frac{\sqrt{d} \sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b}}}{\sqrt{c+d}-\sqrt{c+d x}}\right)}{b^{3/2}}","-\frac{2 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{3/2}}+\frac{2 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{3/2}}+\frac{2 \sqrt{c+d x} (b c-a d)}{a b \sqrt{a+b x}}",1,"(((2*Sqrt[a + b]*(b*c - a*d)^2)/(a*b) - (2*(b*c - a*d)^2*Sqrt[a + b*x])/(a*b))*(Sqrt[c + d] - Sqrt[c + d*x]))/(-(a^2*d) - a*b*d - a*b*d*x - b^2*d*x - b*Sqrt[a + b]*c*Sqrt[a + b*x] + a*Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[a + b]*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]) + (4*d^(3/2)*ArcTanh[((Sqrt[a + b]*Sqrt[d])/Sqrt[b] - (Sqrt[d]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[c + d] - Sqrt[c + d*x])])/b^(3/2) + (c^2*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ])/a","C",1
764,1,1213,108,86.5545087,"\int \frac{(c+d x)^{3/2}}{x^2 (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(x^2*(a + b*x)^(3/2)),x]","\frac{\left(\frac{2 (b c-a d)^2 \sqrt{a+b x}}{a^2}-\frac{2 \sqrt{a+b} (b c-a d)^2}{a^2}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{-d a^2-b d a-b d x a+\sqrt{a+b} d \sqrt{a+b x} a-b^2 d x-b \sqrt{a+b} c \sqrt{a+b x}+b \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}}+\frac{\left(\frac{c \sqrt{a+b x}}{a^2 \sqrt{a+b} \sqrt{c+d}}-\frac{c}{a^2 \sqrt{c+d}}\right) \left(\sqrt{a+b} c d \sqrt{c+d} a^2-c d \sqrt{c+d} \sqrt{a+b x} a^2+\sqrt{a+b} d^2 \sqrt{c+d x} a^2+\sqrt{a+b} c d \sqrt{c+d x} a^2-d^2 \sqrt{a+b x} \sqrt{c+d x} a^2-c d \sqrt{a+b x} \sqrt{c+d x} a^2+b \sqrt{a+b} d^2 \sqrt{c+d} x a+2 b \sqrt{a+b} c d \sqrt{c+d} x a+b \sqrt{a+b} c^2 \sqrt{c+d} a+2 b \sqrt{a+b} c d \sqrt{c+d} a+b c^2 \sqrt{c+d} \sqrt{a+b x} a-b c d \sqrt{c+d} \sqrt{a+b x} a-b \sqrt{a+b} c^2 \sqrt{c+d x} a-b \sqrt{a+b} c d \sqrt{c+d x} a-b c^2 \sqrt{a+b x} \sqrt{c+d x} a-b d^2 \sqrt{a+b x} \sqrt{c+d x} a-2 b c d \sqrt{a+b x} \sqrt{c+d x} a+b^2 \sqrt{a+b} c d \sqrt{c+d} x+b^2 c^2 \sqrt{c+d} \sqrt{a+b x}-b^2 c^2 \sqrt{a+b x} \sqrt{c+d x}-b^2 c d \sqrt{a+b x} \sqrt{c+d x}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{x \left(-2 c^2 b^2-c d b^2-2 d^2 x b^2-c d x b^2+2 c \sqrt{c+d} \sqrt{c+d x} b^2-a d^2 b+2 a c d b-a d^2 x b-2 \sqrt{a+b} c d \sqrt{a+b x} b-2 a d \sqrt{c+d} \sqrt{c+d x} b+2 \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b-2 a^2 d^2+2 a \sqrt{a+b} d^2 \sqrt{a+b x}\right)}+\left(\frac{3 c d}{2 a}-\frac{3 b c^2}{2 a^2}\right) \text{RootSum}\left[d^2 \text{$\#$1}^4-4 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^3+4 b c \text{$\#$1}^2+4 a d \text{$\#$1}^2+6 b d \text{$\#$1}^2-4 b \sqrt{a+b} \sqrt{c+d} \text{$\#$1}+b^2\&,\frac{d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right) \text{$\#$1}^2-d \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2-b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)+b \log \left(-\sqrt{c+d} \text{$\#$1}+\sqrt{c+d x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right)}{d^2 \text{$\#$1}^3-3 \sqrt{a+b} d \sqrt{c+d} \text{$\#$1}^2+2 b c \text{$\#$1}+2 a d \text{$\#$1}+3 b d \text{$\#$1}-b \sqrt{a+b} \sqrt{c+d}}\&\right]","\frac{3 \sqrt{c} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{5/2}}-\frac{3 \sqrt{c+d x} (b c-a d)}{a^2 \sqrt{a+b x}}-\frac{(c+d x)^{3/2}}{a x \sqrt{a+b x}}",1,"(((-2*Sqrt[a + b]*(b*c - a*d)^2)/a^2 + (2*(b*c - a*d)^2*Sqrt[a + b*x])/a^2)*(Sqrt[c + d] - Sqrt[c + d*x]))/(-(a^2*d) - a*b*d - a*b*d*x - b^2*d*x - b*Sqrt[a + b]*c*Sqrt[a + b*x] + a*Sqrt[a + b]*d*Sqrt[a + b*x] + b*Sqrt[a + b]*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]) + ((-(c/(a^2*Sqrt[c + d])) + (c*Sqrt[a + b*x])/(a^2*Sqrt[a + b]*Sqrt[c + d]))*(Sqrt[c + d] - Sqrt[c + d*x])*(a*b*Sqrt[a + b]*c^2*Sqrt[c + d] + a^2*Sqrt[a + b]*c*d*Sqrt[c + d] + 2*a*b*Sqrt[a + b]*c*d*Sqrt[c + d] + 2*a*b*Sqrt[a + b]*c*d*Sqrt[c + d]*x + b^2*Sqrt[a + b]*c*d*Sqrt[c + d]*x + a*b*Sqrt[a + b]*d^2*Sqrt[c + d]*x + a*b*c^2*Sqrt[c + d]*Sqrt[a + b*x] + b^2*c^2*Sqrt[c + d]*Sqrt[a + b*x] - a^2*c*d*Sqrt[c + d]*Sqrt[a + b*x] - a*b*c*d*Sqrt[c + d]*Sqrt[a + b*x] - a*b*Sqrt[a + b]*c^2*Sqrt[c + d*x] + a^2*Sqrt[a + b]*c*d*Sqrt[c + d*x] - a*b*Sqrt[a + b]*c*d*Sqrt[c + d*x] + a^2*Sqrt[a + b]*d^2*Sqrt[c + d*x] - a*b*c^2*Sqrt[a + b*x]*Sqrt[c + d*x] - b^2*c^2*Sqrt[a + b*x]*Sqrt[c + d*x] - a^2*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - 2*a*b*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - b^2*c*d*Sqrt[a + b*x]*Sqrt[c + d*x] - a^2*d^2*Sqrt[a + b*x]*Sqrt[c + d*x] - a*b*d^2*Sqrt[a + b*x]*Sqrt[c + d*x]))/(x*(-2*b^2*c^2 + 2*a*b*c*d - b^2*c*d - 2*a^2*d^2 - a*b*d^2 - b^2*c*d*x - a*b*d^2*x - 2*b^2*d^2*x - 2*b*Sqrt[a + b]*c*d*Sqrt[a + b*x] + 2*a*Sqrt[a + b]*d^2*Sqrt[a + b*x] + 2*b^2*c*Sqrt[c + d]*Sqrt[c + d*x] - 2*a*b*d*Sqrt[c + d]*Sqrt[c + d*x] + 2*b*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x])) + ((-3*b*c^2)/(2*a^2) + (3*c*d)/(2*a))*RootSum[b^2 - 4*b*Sqrt[a + b]*Sqrt[c + d]*#1 + 4*b*c*#1^2 + 4*a*d*#1^2 + 6*b*d*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*#1^3 + d^2*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]) + 2*b*c*#1 + 2*a*d*#1 + 3*b*d*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*#1^2 + d^2*#1^3) & ]","C",1
765,-1,0,178,180.0541909,"\int \frac{(c+d x)^{3/2}}{x^3 (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(x^3*(a + b*x)^(3/2)),x]","\text{\$Aborted}","-\frac{3 (b c-a d) (5 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{7/2} \sqrt{c}}+\frac{3 \sqrt{c+d x} (b c-a d) (5 b c-a d)}{4 a^3 c \sqrt{a+b x}}+\frac{(c+d x)^{3/2} (5 b c-a d)}{4 a^2 c x \sqrt{a+b x}}-\frac{(c+d x)^{5/2}}{2 a c x^2 \sqrt{a+b x}}",1,"$Aborted","F",-1
766,-1,0,241,180.1261344,"\int \frac{(c+d x)^{3/2}}{x^4 (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/(x^4*(a + b*x)^(3/2)),x]","\text{\$Aborted}","-\frac{\sqrt{c+d x} (35 b c-3 a d) (b c-a d)}{24 a^3 c x \sqrt{a+b x}}+\frac{7 \sqrt{c+d x} (b c-a d)}{12 a^2 x^2 \sqrt{a+b x}}+\frac{(b c-a d) \left(-a^2 d^2-10 a b c d+35 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 a^{9/2} c^{3/2}}-\frac{b \sqrt{c+d x} \left(3 a^2 d^2-100 a b c d+105 b^2 c^2\right)}{24 a^4 c \sqrt{a+b x}}-\frac{c \sqrt{c+d x}}{3 a x^3 \sqrt{a+b x}}",1,"$Aborted","F",-1
767,-1,0,346,180.0576221,"\int \frac{x^3 (c+d x)^{5/2}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(x^3*(c + d*x)^(5/2))/(a + b*x)^(3/2),x]","\text{\$Aborted}","-\frac{\sqrt{a+b x} (c+d x)^{5/2} \left(-231 a^2 d^2-2 b d x (5 b c-99 a d)+30 a b c d+5 b^2 c^2\right)}{80 b^4 d^2}+\frac{3 (b c-a d)^2 \left(-231 a^3 d^3+63 a^2 b c d^2+7 a b^2 c^2 d+b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{13/2} d^{5/2}}+\frac{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d) \left(-231 a^3 d^3+63 a^2 b c d^2+7 a b^2 c^2 d+b^3 c^3\right)}{128 b^6 d^2}+\frac{\sqrt{a+b x} (c+d x)^{3/2} \left(-231 a^3 d^3+63 a^2 b c d^2+7 a b^2 c^2 d+b^3 c^3\right)}{64 b^5 d^2}+\frac{11 x^2 \sqrt{a+b x} (c+d x)^{5/2}}{5 b^2}-\frac{2 x^3 (c+d x)^{5/2}}{b \sqrt{a+b x}}",1,"$Aborted","F",-1
768,-1,0,306,180.0379058,"\int \frac{x^2 (c+d x)^{5/2}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(x^2*(c + d*x)^(5/2))/(a + b*x)^(3/2),x]","\text{\$Aborted}","-\frac{\sqrt{a+b x} (c+d x)^{5/2} \left(-\frac{63 a^2 d}{b}+14 a c+\frac{b c^2}{d}\right)}{24 b^2 (b c-a d)}-\frac{2 a^2 (c+d x)^{7/2}}{b^2 \sqrt{a+b x} (b c-a d)}-\frac{5 (b c-a d)^2 \left(-63 a^2 d^2+14 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{11/2} d^{3/2}}-\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-a d) \left(-63 a^2 d^2+14 a b c d+b^2 c^2\right)}{64 b^5 d}-\frac{5 \sqrt{a+b x} (c+d x)^{3/2} \left(-63 a^2 d^2+14 a b c d+b^2 c^2\right)}{96 b^4 d}+\frac{\sqrt{a+b x} (c+d x)^{7/2}}{4 b^2 d}",1,"$Aborted","F",-1
769,-1,0,214,180.021116,"\int \frac{x (c+d x)^{5/2}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(x*(c + d*x)^(5/2))/(a + b*x)^(3/2),x]","\text{\$Aborted}","\frac{5 (b c-7 a d) (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{9/2} \sqrt{d}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} (b c-7 a d) (b c-a d)}{8 b^4}+\frac{5 \sqrt{a+b x} (c+d x)^{3/2} (b c-7 a d)}{12 b^3}+\frac{\sqrt{a+b x} (c+d x)^{5/2} (b c-7 a d)}{3 b^2 (b c-a d)}+\frac{2 a (c+d x)^{7/2}}{b \sqrt{a+b x} (b c-a d)}",1,"$Aborted","F",-1
770,-1,0,138,180.0329887,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(a + b*x)^(3/2),x]","\text{\$Aborted}","\frac{15 \sqrt{d} (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{7/2}}+\frac{15 d \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}{4 b^3}+\frac{5 d \sqrt{a+b x} (c+d x)^{3/2}}{2 b^2}-\frac{2 (c+d x)^{5/2}}{b \sqrt{a+b x}}",1,"$Aborted","F",-1
771,-1,0,163,180.2191263,"\int \frac{(c+d x)^{5/2}}{x (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x*(a + b*x)^(3/2)),x]","\text{\$Aborted}","-\frac{2 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{3/2}}+\frac{d^{3/2} (5 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{5/2}}-\frac{d \sqrt{a+b x} \sqrt{c+d x} (2 b c-3 a d)}{a b^2}+\frac{2 (c+d x)^{3/2} (b c-a d)}{a b \sqrt{a+b x}}",1,"$Aborted","F",-1
772,-1,0,163,180.0377411,"\int \frac{(c+d x)^{5/2}}{x^2 (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^2*(a + b*x)^(3/2)),x]","\text{\$Aborted}","\frac{c^{3/2} (3 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{5/2}}-\frac{\sqrt{c+d x} (3 b c-2 a d) (b c-a d)}{a^2 b \sqrt{a+b x}}+\frac{2 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{3/2}}-\frac{c (c+d x)^{3/2}}{a x \sqrt{a+b x}}",1,"$Aborted","F",-1
773,-1,0,154,180.0588665,"\int \frac{(c+d x)^{5/2}}{x^3 (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^3*(a + b*x)^(3/2)),x]","\text{\$Aborted}","-\frac{15 \sqrt{c} (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{7/2}}+\frac{15 \sqrt{c+d x} (b c-a d)^2}{4 a^3 \sqrt{a+b x}}+\frac{5 (c+d x)^{3/2} (b c-a d)}{4 a^2 x \sqrt{a+b x}}-\frac{(c+d x)^{5/2}}{2 a x^2 \sqrt{a+b x}}",1,"$Aborted","F",-1
774,-1,0,230,180.1518515,"\int \frac{(c+d x)^{5/2}}{x^4 (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^4*(a + b*x)^(3/2)),x]","\text{\$Aborted}","\frac{5 (b c-a d)^2 (7 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 a^{9/2} \sqrt{c}}-\frac{5 \sqrt{c+d x} (b c-a d)^2 (7 b c-a d)}{8 a^4 c \sqrt{a+b x}}-\frac{5 (c+d x)^{3/2} (b c-a d) (7 b c-a d)}{24 a^3 c x \sqrt{a+b x}}+\frac{(c+d x)^{5/2} (7 b c-a d)}{12 a^2 c x^2 \sqrt{a+b x}}-\frac{(c+d x)^{7/2}}{3 a c x^3 \sqrt{a+b x}}",1,"$Aborted","F",-1
775,-1,0,318,180.0583411,"\int \frac{(c+d x)^{5/2}}{x^5 (a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^5*(a + b*x)^(3/2)),x]","\text{\$Aborted}","-\frac{\sqrt{c+d x} (63 b c-59 a d) (b c-a d)}{96 a^3 x^2 \sqrt{a+b x}}+\frac{c \sqrt{c+d x} (9 b c-11 a d)}{24 a^2 x^3 \sqrt{a+b x}}-\frac{5 \left(-a^2 d^2-14 a b c d+63 b^2 c^2\right) (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{11/2} c^{3/2}}+\frac{\sqrt{c+d x} \left(15 a^2 d^2-322 a b c d+315 b^2 c^2\right) (b c-a d)}{192 a^4 c x \sqrt{a+b x}}+\frac{b \sqrt{c+d x} \left(-15 a^3 d^3+839 a^2 b c d^2-1785 a b^2 c^2 d+945 b^3 c^3\right)}{192 a^5 c \sqrt{a+b x}}-\frac{c (c+d x)^{3/2}}{4 a x^4 \sqrt{a+b x}}",1,"$Aborted","F",-1
776,-1,0,250,180.0503799,"\int \frac{x^4}{(a+b x)^{3/2} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[x^4/((a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","\text{\$Aborted}","\frac{3 \left(5 a^2 d^2+6 a b c d+5 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{7/2} d^{7/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left((a d+b c) \left(15 a^2 d^2-22 a b c d+15 b^2 c^2\right)-2 b d x \left(5 a^2 d^2-2 a b c d+5 b^2 c^2\right)\right)}{4 b^3 d^3 (b c-a d)^2}+\frac{2 a x^3}{b \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}-\frac{2 c x^2 \sqrt{a+b x} (a d+b c)}{b d \sqrt{c+d x} (b c-a d)^2}",1,"$Aborted","F",-1
777,-1,0,167,180.2610552,"\int \frac{x^3}{(a+b x)^{3/2} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[x^3/((a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","\text{\$Aborted}","\frac{\sqrt{a+b x} \left(c \left(3 a^2 d^2-2 a b c d+3 b^2 c^2\right)+d x (b c-3 a d) (b c-a d)\right)}{b^2 d^2 \sqrt{c+d x} (b c-a d)^2}-\frac{3 (a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{5/2} d^{5/2}}+\frac{2 a x^2}{b \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}",1,"$Aborted","F",-1
778,1,391,130,9.02897,"\int \frac{x^2}{(a+b x)^{3/2} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[x^2/((a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(\frac{2 a^2}{b (a d-b c)}-\frac{2 a^2 \sqrt{a+b x}}{b \sqrt{a+b} (a d-b c)}\right)}{b \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}-b c \sqrt{a+b x}+b d x \left(-\sqrt{a+b}\right)+a d \sqrt{a+b x}-a d \sqrt{a+b}}+\frac{4 \tanh ^{-1}\left(\frac{\frac{\sqrt{d} \sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b}}}{\sqrt{c+d}-\sqrt{c+d x}}\right)}{b^{3/2} d^{3/2}}+\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right) \left(\frac{2 c^2 \sqrt{a+b x}}{d \sqrt{c+d} (b c-a d)}-\frac{2 c^2 \sqrt{a+b}}{d \sqrt{c+d} (b c-a d)}\right)}{-d \sqrt{a+b} \sqrt{a+b x} \sqrt{c+d x}+a d \sqrt{c+d x}-b c \sqrt{c+d x}+b d x \sqrt{c+d}+b c \sqrt{c+d}}","-\frac{2 \sqrt{a+b x} \left(a^2 d^2+b^2 c^2\right)}{b^2 d \sqrt{c+d x} (b c-a d)^2}-\frac{2 a^2}{b^2 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{3/2} d^{3/2}}",1,"(((-2*Sqrt[a + b]*c^2)/(d*Sqrt[c + d]*(b*c - a*d)) + (2*c^2*Sqrt[a + b*x])/(d*Sqrt[c + d]*(b*c - a*d)))*(Sqrt[c + d] - Sqrt[c + d*x]))/(b*c*Sqrt[c + d] + b*d*Sqrt[c + d]*x - b*c*Sqrt[c + d*x] + a*d*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x]) + (((2*a^2)/(b*(-(b*c) + a*d)) - (2*a^2*Sqrt[a + b*x])/(b*Sqrt[a + b]*(-(b*c) + a*d)))*(Sqrt[c + d] - Sqrt[c + d*x]))/(-(a*Sqrt[a + b]*d) - b*Sqrt[a + b]*d*x - b*c*Sqrt[a + b*x] + a*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]) + (4*ArcTanh[((Sqrt[a + b]*Sqrt[d])/Sqrt[b] - (Sqrt[d]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[c + d] - Sqrt[c + d*x])])/(b^(3/2)*d^(3/2))","B",1
779,1,332,75,2.1221083,"\int \frac{x}{(a+b x)^{3/2} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[x/((a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4 \left(\frac{1}{\sqrt{c+d}}-\frac{\sqrt{a+b x}}{\sqrt{a+b} \sqrt{c+d}}\right) \left(\frac{\left(\sqrt{a+b}-\sqrt{a+b x}\right) \left(2 \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x}-2 c \sqrt{a+b}-d \sqrt{a+b x}-d \sqrt{a+b}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^2}+b\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(-d \sqrt{a+b} \sqrt{a+b x} \sqrt{c+d x}+a d \sqrt{c+d x}-b c \sqrt{c+d x}+b d x \sqrt{c+d}+b c \sqrt{c+d}\right) \left(b \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}-b c \sqrt{a+b x}+b d x \left(-\sqrt{a+b}\right)+a d \sqrt{a+b x}-a d \sqrt{a+b}\right)}","\frac{2 \sqrt{c+d x} (a d+b c)}{d \sqrt{a+b x} (b c-a d)^2}-\frac{2 c}{d \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}",1,"((1/Sqrt[c + d] - Sqrt[a + b*x]/(Sqrt[a + b]*Sqrt[c + d]))*(Sqrt[c + d] - Sqrt[c + d*x])^4*(b + ((Sqrt[a + b] - Sqrt[a + b*x])*(-2*Sqrt[a + b]*c - Sqrt[a + b]*d - d*Sqrt[a + b*x] + 2*Sqrt[a + b]*Sqrt[c + d]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^2))/((-Sqrt[c + d] + Sqrt[c + d*x])*(b*c*Sqrt[c + d] + b*d*Sqrt[c + d]*x - b*c*Sqrt[c + d*x] + a*d*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x])*(-(a*Sqrt[a + b]*d) - b*Sqrt[a + b]*d*x - b*c*Sqrt[a + b*x] + a*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))","B",1
780,1,277,62,0.0009835,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4 \left(\frac{1}{\sqrt{c+d}}-\frac{\sqrt{a+b x}}{\sqrt{a+b} \sqrt{c+d}}\right) \left(\frac{d \left(\sqrt{a+b}-\sqrt{a+b x}\right)^2}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^2}+b\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(-d \sqrt{a+b} \sqrt{a+b x} \sqrt{c+d x}+a d \sqrt{c+d x}-b c \sqrt{c+d x}+b d x \sqrt{c+d}+b c \sqrt{c+d}\right) \left(b \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}-b c \sqrt{a+b x}+b d x \left(-\sqrt{a+b}\right)+a d \sqrt{a+b x}-a d \sqrt{a+b}\right)}","-\frac{4 d \sqrt{a+b x}}{\sqrt{c+d x} (b c-a d)^2}-\frac{2}{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)}",1,"((1/Sqrt[c + d] - Sqrt[a + b*x]/(Sqrt[a + b]*Sqrt[c + d]))*(Sqrt[c + d] - Sqrt[c + d*x])^4*(b + (d*(Sqrt[a + b] - Sqrt[a + b*x])^2)/(Sqrt[c + d] - Sqrt[c + d*x])^2))/((-Sqrt[c + d] + Sqrt[c + d*x])*(b*c*Sqrt[c + d] + b*d*Sqrt[c + d]*x - b*c*Sqrt[c + d*x] + a*d*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x])*(-(a*Sqrt[a + b]*d) - b*Sqrt[a + b]*d*x - b*c*Sqrt[a + b*x] + a*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))","B",1
781,-1,0,121,180.6618446,"\int \frac{1}{x (a+b x)^{3/2} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","\text{\$Aborted}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{3/2} c^{3/2}}+\frac{2 b}{a \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}+\frac{2 d \sqrt{a+b x} (a d+b c)}{a c \sqrt{c+d x} (b c-a d)^2}",1,"$Aborted","F",-1
782,-1,0,185,180.0991938,"\int \frac{1}{x^2 (a+b x)^{3/2} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","\text{\$Aborted}","\frac{3 (a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{5/2} c^{5/2}}-\frac{d \sqrt{a+b x} \left(3 a^2 d^2-2 a b c d+3 b^2 c^2\right)}{a^2 c^2 \sqrt{c+d x} (b c-a d)^2}-\frac{b (3 b c-a d)}{a^2 c \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}-\frac{1}{a c x \sqrt{a+b x} \sqrt{c+d x}}",1,"$Aborted","F",-1
783,-1,0,268,180.2639728,"\int \frac{1}{x^3 (a+b x)^{3/2} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","\text{\$Aborted}","\frac{5 (a d+b c)}{4 a^2 c^2 x \sqrt{a+b x} \sqrt{c+d x}}-\frac{3 \left(5 a^2 d^2+6 a b c d+5 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{7/2} c^{7/2}}+\frac{b \left(-5 a^2 d^2-2 a b c d+15 b^2 c^2\right)}{4 a^3 c^2 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)}+\frac{d \sqrt{a+b x} \left(15 a^2 d^2-22 a b c d+15 b^2 c^2\right) (a d+b c)}{4 a^3 c^3 \sqrt{c+d x} (b c-a d)^2}-\frac{1}{2 a c x^2 \sqrt{a+b x} \sqrt{c+d x}}",1,"$Aborted","F",-1
784,-1,0,351,180.151689,"\int \frac{x^5}{(a+b x)^{3/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[x^5/((a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{2 c x^2 \sqrt{a+b x} \left(-3 a^2 d^2-12 a b c d+7 b^2 c^2\right)}{3 b d^2 \sqrt{c+d x} (b c-a d)^3}+\frac{5 \left(3 a^2 d^2+6 a b c d+7 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{7/2} d^{9/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-45 a^4 d^4+30 a^3 b c d^3+36 a^2 b^2 c^2 d^2-2 b d x \left(-15 a^3 d^3+9 a^2 b c d^2-61 a b^2 c^2 d+35 b^3 c^3\right)-190 a b^3 c^3 d+105 b^4 c^4\right)}{12 b^3 d^4 (b c-a d)^3}+\frac{2 a x^4}{b \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}-\frac{2 c x^3 \sqrt{a+b x} (3 a d+b c)}{3 b d (c+d x)^{3/2} (b c-a d)^2}",1,"$Aborted","F",-1
785,-1,0,251,180.0953008,"\int \frac{x^4}{(a+b x)^{3/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[x^4/((a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","\frac{\sqrt{a+b x} \left(d x (b c-a d) \left(9 a^2 d^2-6 a b c d+5 b^2 c^2\right)+c \left(-9 a^3 d^3+9 a^2 b c d^2-31 a b^2 c^2 d+15 b^3 c^3\right)\right)}{3 b^2 d^3 \sqrt{c+d x} (b c-a d)^3}-\frac{(3 a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{5/2} d^{7/2}}+\frac{2 a x^3}{b \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}-\frac{2 c x^2 \sqrt{a+b x} (3 a d+b c)}{3 b d (c+d x)^{3/2} (b c-a d)^2}",1,"$Aborted","F",-1
786,-1,0,165,180.0435594,"\int \frac{x^3}{(a+b x)^{3/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[x^3/((a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{2 c \sqrt{a+b x} \left(2 d x \left(-3 a^2 d^2-3 a b c d+2 b^2 c^2\right)+c (b c-3 a d) (a d+3 b c)\right)}{3 b d^2 (c+d x)^{3/2} (b c-a d)^3}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{3/2} d^{5/2}}+\frac{2 a x^2}{b \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}",1,"$Aborted","F",-1
787,1,1795,151,33.4737364,"\int \frac{x^2}{(a+b x)^{3/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[x^2/((a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\frac{\left(\frac{1}{12 (c+d)^{3/2}}-\frac{\sqrt{a+b x}}{12 \sqrt{a+b} (c+d)^{3/2}}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)^8 \left(3 c b^3+3 d b^3+\frac{\left(b^2 \sqrt{a+b}-b^2 \sqrt{a+b x}\right) \left(4 \sqrt{a+b} c^2-16 \sqrt{a+b x} c^2+27 \sqrt{a+b} d c-57 d \sqrt{a+b x} c+12 \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x} c+27 \sqrt{a+b} d^2-45 d^2 \sqrt{a+b x}+18 \sqrt{a+b} d \sqrt{c+d} \sqrt{c+d x}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^2}+\frac{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^2 \left(-8 b^2 c^3+24 a b c^3+8 b \sqrt{a+b} \sqrt{a+b x} c^3-40 b^2 d c^2+88 a b d c^2+16 b^2 d x c^2+16 a b d x c^2+24 b \sqrt{a+b} d \sqrt{a+b x} c^2+8 b^2 \sqrt{c+d} \sqrt{c+d x} c^2-24 a b \sqrt{c+d} \sqrt{c+d x} c^2-8 b \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} c^2-51 b^2 d^2 c+126 a b d^2 c+57 b^2 d^2 x c+48 a b d^2 x c-6 b \sqrt{a+b} d^2 \sqrt{a+b x} c+48 b^2 d \sqrt{c+d} \sqrt{c+d x} c-48 a b d \sqrt{c+d} \sqrt{c+d x} c-48 b \sqrt{a+b} d \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} c-15 b^2 d^3+66 a b d^3+45 b^2 d^3 x+36 a b d^3 x-30 b \sqrt{a+b} d^3 \sqrt{a+b x}+60 b^2 d^2 \sqrt{c+d} \sqrt{c+d x}-12 a b d^2 \sqrt{c+d} \sqrt{c+d x}-60 b \sqrt{a+b} d^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4}+\frac{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^3 \left(-36 a \sqrt{a+b} x d^4-9 b \sqrt{a+b} x d^4-12 a \sqrt{a+b} d^4-15 b \sqrt{a+b} d^4-12 a \sqrt{a+b x} d^4+27 b \sqrt{a+b x} d^4-36 a x \sqrt{a+b x} d^4-3 b x \sqrt{a+b x} d^4-72 a \sqrt{a+b} c d^3-27 b \sqrt{a+b} c d^3-96 a \sqrt{a+b} c x d^3-21 b \sqrt{a+b} c x d^3-72 a c \sqrt{a+b x} d^3+51 b c \sqrt{a+b x} d^3-48 a c x \sqrt{a+b x} d^3-3 b c x \sqrt{a+b x} d^3+24 a \sqrt{a+b} \sqrt{c+d} x \sqrt{c+d x} d^3+18 b \sqrt{a+b} \sqrt{c+d} x \sqrt{c+d x} d^3+36 a \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x} d^3+18 b \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x} d^3+36 a \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} d^3-36 b \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} d^3-128 a \sqrt{a+b} c^2 d^2-12 b \sqrt{a+b} c^2 d^2-56 a \sqrt{a+b} c^2 x d^2-12 b \sqrt{a+b} c^2 x d^2-88 a c^2 \sqrt{a+b x} d^2+24 b c^2 \sqrt{a+b x} d^2-16 a c^2 x \sqrt{a+b x} d^2+24 a \sqrt{a+b} c \sqrt{c+d} x \sqrt{c+d x} d^2+12 b \sqrt{a+b} c \sqrt{c+d} x \sqrt{c+d x} d^2+96 a \sqrt{a+b} c \sqrt{c+d} \sqrt{c+d x} d^2+12 b \sqrt{a+b} c \sqrt{c+d} \sqrt{c+d x} d^2+72 a c \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} d^2-24 b c \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} d^2-64 a \sqrt{a+b} c^3 d-32 a c^3 \sqrt{a+b x} d+64 a \sqrt{a+b} c^2 \sqrt{c+d} \sqrt{c+d x} d+32 a c^2 \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} d\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^6}\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(b \sqrt{c+d} c-b \sqrt{c+d x} c+b d \sqrt{c+d} x+a d \sqrt{c+d x}-\sqrt{a+b} d \sqrt{a+b x} \sqrt{c+d x}\right)^3 \left(-\sqrt{a+b} d x b-c \sqrt{a+b x} b+\sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b-a \sqrt{a+b} d+a d \sqrt{a+b x}\right)}","\frac{2 \sqrt{a+b x} \left(-3 a^2 d^2-6 a b c d+b^2 c^2\right)}{3 b d \sqrt{c+d x} (b c-a d)^3}-\frac{2 \sqrt{a+b x} \left(3 a^2 d^2+b^2 c^2\right)}{3 b^2 d (c+d x)^{3/2} (b c-a d)^2}-\frac{2 a^2}{b^2 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}",1,"((1/(12*(c + d)^(3/2)) - Sqrt[a + b*x]/(12*Sqrt[a + b]*(c + d)^(3/2)))*(Sqrt[c + d] - Sqrt[c + d*x])^8*(3*b^3*c + 3*b^3*d + ((b^2*Sqrt[a + b] - b^2*Sqrt[a + b*x])*(4*Sqrt[a + b]*c^2 + 27*Sqrt[a + b]*c*d + 27*Sqrt[a + b]*d^2 - 16*c^2*Sqrt[a + b*x] - 57*c*d*Sqrt[a + b*x] - 45*d^2*Sqrt[a + b*x] + 12*Sqrt[a + b]*c*Sqrt[c + d]*Sqrt[c + d*x] + 18*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^2 + ((Sqrt[a + b] - Sqrt[a + b*x])^2*(24*a*b*c^3 - 8*b^2*c^3 + 88*a*b*c^2*d - 40*b^2*c^2*d + 126*a*b*c*d^2 - 51*b^2*c*d^2 + 66*a*b*d^3 - 15*b^2*d^3 + 16*a*b*c^2*d*x + 16*b^2*c^2*d*x + 48*a*b*c*d^2*x + 57*b^2*c*d^2*x + 36*a*b*d^3*x + 45*b^2*d^3*x + 8*b*Sqrt[a + b]*c^3*Sqrt[a + b*x] + 24*b*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] - 6*b*Sqrt[a + b]*c*d^2*Sqrt[a + b*x] - 30*b*Sqrt[a + b]*d^3*Sqrt[a + b*x] - 24*a*b*c^2*Sqrt[c + d]*Sqrt[c + d*x] + 8*b^2*c^2*Sqrt[c + d]*Sqrt[c + d*x] - 48*a*b*c*d*Sqrt[c + d]*Sqrt[c + d*x] + 48*b^2*c*d*Sqrt[c + d]*Sqrt[c + d*x] - 12*a*b*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 60*b^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 8*b*Sqrt[a + b]*c^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 48*b*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 60*b*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^4 + ((Sqrt[a + b] - Sqrt[a + b*x])^3*(-64*a*Sqrt[a + b]*c^3*d - 128*a*Sqrt[a + b]*c^2*d^2 - 12*b*Sqrt[a + b]*c^2*d^2 - 72*a*Sqrt[a + b]*c*d^3 - 27*b*Sqrt[a + b]*c*d^3 - 12*a*Sqrt[a + b]*d^4 - 15*b*Sqrt[a + b]*d^4 - 56*a*Sqrt[a + b]*c^2*d^2*x - 12*b*Sqrt[a + b]*c^2*d^2*x - 96*a*Sqrt[a + b]*c*d^3*x - 21*b*Sqrt[a + b]*c*d^3*x - 36*a*Sqrt[a + b]*d^4*x - 9*b*Sqrt[a + b]*d^4*x - 32*a*c^3*d*Sqrt[a + b*x] - 88*a*c^2*d^2*Sqrt[a + b*x] + 24*b*c^2*d^2*Sqrt[a + b*x] - 72*a*c*d^3*Sqrt[a + b*x] + 51*b*c*d^3*Sqrt[a + b*x] - 12*a*d^4*Sqrt[a + b*x] + 27*b*d^4*Sqrt[a + b*x] - 16*a*c^2*d^2*x*Sqrt[a + b*x] - 48*a*c*d^3*x*Sqrt[a + b*x] - 3*b*c*d^3*x*Sqrt[a + b*x] - 36*a*d^4*x*Sqrt[a + b*x] - 3*b*d^4*x*Sqrt[a + b*x] + 64*a*Sqrt[a + b]*c^2*d*Sqrt[c + d]*Sqrt[c + d*x] + 96*a*Sqrt[a + b]*c*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 12*b*Sqrt[a + b]*c*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 36*a*Sqrt[a + b]*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 18*b*Sqrt[a + b]*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 24*a*Sqrt[a + b]*c*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 12*b*Sqrt[a + b]*c*d^2*Sqrt[c + d]*x*Sqrt[c + d*x] + 24*a*Sqrt[a + b]*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] + 18*b*Sqrt[a + b]*d^3*Sqrt[c + d]*x*Sqrt[c + d*x] + 32*a*c^2*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 72*a*c*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 24*b*c*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] + 36*a*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 36*b*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^6))/((-Sqrt[c + d] + Sqrt[c + d*x])*(b*c*Sqrt[c + d] + b*d*Sqrt[c + d]*x - b*c*Sqrt[c + d*x] + a*d*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x])^3*(-(a*Sqrt[a + b]*d) - b*Sqrt[a + b]*d*x - b*c*Sqrt[a + b*x] + a*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))","B",1
788,1,1104,118,25.6596375,"\int \frac{x}{(a+b x)^{3/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[x/((a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\frac{\left(\frac{1}{12 (c+d)^{3/2}}-\frac{\sqrt{a+b x}}{12 \sqrt{a+b} (c+d)^{3/2}}\right) \left(\sqrt{c+d}-\sqrt{c+d x}\right)^8 \left(\frac{\left(6 a d^4-9 b d^4+12 a x d^4+3 b x d^4+6 \sqrt{a+b} \sqrt{a+b x} d^4+20 a c d^3-15 b c d^3+8 a c x d^3+3 b c x d^3+12 \sqrt{a+b} c \sqrt{a+b x} d^3-12 a \sqrt{c+d} \sqrt{c+d x} d^3+12 b \sqrt{c+d} \sqrt{c+d x} d^3-12 \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} d^3+10 a c^2 d^2-6 b c^2 d^2+6 \sqrt{a+b} c^2 \sqrt{a+b x} d^2-10 a c \sqrt{c+d} \sqrt{c+d x} d^2+6 b c \sqrt{c+d} \sqrt{c+d x} d^2-6 \sqrt{a+b} c \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} d^2\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^4}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^6}+\frac{\left(-3 b^2 d^3+30 a b d^3+21 b^2 x d^3+12 a b x d^3-18 b \sqrt{a+b} \sqrt{a+b x} d^3-11 b^2 c d^2+38 a b c d^2+17 b^2 c x d^2+8 a b c x d^2-6 b \sqrt{a+b} c \sqrt{a+b x} d^2+24 b^2 \sqrt{c+d} \sqrt{c+d x} d^2-24 b \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} d^2-4 b^2 c^2 d+12 a b c^2 d+4 b \sqrt{a+b} c^2 \sqrt{a+b x} d+4 b^2 c \sqrt{c+d} \sqrt{c+d x} d-12 a b c \sqrt{c+d} \sqrt{c+d x} d-4 b \sqrt{a+b} c \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} d\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^2}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4}+3 b^3 c+3 b^3 d+\frac{\left(b^2 \sqrt{a+b}-b^2 \sqrt{a+b x}\right) \left(-6 \sqrt{a+b} c^2-\sqrt{a+b} d c-17 d \sqrt{a+b x} c+6 \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x} c+9 \sqrt{a+b} d^2-21 d^2 \sqrt{a+b x}+12 \sqrt{a+b} d \sqrt{c+d} \sqrt{c+d x}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^2}\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(b \sqrt{c+d} c-b \sqrt{c+d x} c+b d \sqrt{c+d} x+a d \sqrt{c+d x}-\sqrt{a+b} d \sqrt{a+b x} \sqrt{c+d x}\right)^3 \left(-\sqrt{a+b} d x b-c \sqrt{a+b x} b+\sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x} b-a \sqrt{a+b} d+a d \sqrt{a+b x}\right)}","\frac{2 a}{b \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}+\frac{4 \sqrt{a+b x} (3 a d+b c)}{3 \sqrt{c+d x} (b c-a d)^3}+\frac{2 \sqrt{a+b x} (3 a d+b c)}{3 b (c+d x)^{3/2} (b c-a d)^2}",1,"((1/(12*(c + d)^(3/2)) - Sqrt[a + b*x]/(12*Sqrt[a + b]*(c + d)^(3/2)))*(Sqrt[c + d] - Sqrt[c + d*x])^8*(3*b^3*c + 3*b^3*d + ((b^2*Sqrt[a + b] - b^2*Sqrt[a + b*x])*(-6*Sqrt[a + b]*c^2 - Sqrt[a + b]*c*d + 9*Sqrt[a + b]*d^2 - 17*c*d*Sqrt[a + b*x] - 21*d^2*Sqrt[a + b*x] + 6*Sqrt[a + b]*c*Sqrt[c + d]*Sqrt[c + d*x] + 12*Sqrt[a + b]*d*Sqrt[c + d]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^2 + ((Sqrt[a + b] - Sqrt[a + b*x])^2*(12*a*b*c^2*d - 4*b^2*c^2*d + 38*a*b*c*d^2 - 11*b^2*c*d^2 + 30*a*b*d^3 - 3*b^2*d^3 + 8*a*b*c*d^2*x + 17*b^2*c*d^2*x + 12*a*b*d^3*x + 21*b^2*d^3*x + 4*b*Sqrt[a + b]*c^2*d*Sqrt[a + b*x] - 6*b*Sqrt[a + b]*c*d^2*Sqrt[a + b*x] - 18*b*Sqrt[a + b]*d^3*Sqrt[a + b*x] - 12*a*b*c*d*Sqrt[c + d]*Sqrt[c + d*x] + 4*b^2*c*d*Sqrt[c + d]*Sqrt[c + d*x] + 24*b^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 4*b*Sqrt[a + b]*c*d*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 24*b*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^4 + ((Sqrt[a + b] - Sqrt[a + b*x])^4*(10*a*c^2*d^2 - 6*b*c^2*d^2 + 20*a*c*d^3 - 15*b*c*d^3 + 6*a*d^4 - 9*b*d^4 + 8*a*c*d^3*x + 3*b*c*d^3*x + 12*a*d^4*x + 3*b*d^4*x + 6*Sqrt[a + b]*c^2*d^2*Sqrt[a + b*x] + 12*Sqrt[a + b]*c*d^3*Sqrt[a + b*x] + 6*Sqrt[a + b]*d^4*Sqrt[a + b*x] - 10*a*c*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 6*b*c*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 12*a*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 12*b*d^3*Sqrt[c + d]*Sqrt[c + d*x] - 6*Sqrt[a + b]*c*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x] - 12*Sqrt[a + b]*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^6))/((-Sqrt[c + d] + Sqrt[c + d*x])*(b*c*Sqrt[c + d] + b*d*Sqrt[c + d]*x - b*c*Sqrt[c + d*x] + a*d*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x])^3*(-(a*Sqrt[a + b]*d) - b*Sqrt[a + b]*d*x - b*c*Sqrt[a + b*x] + a*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))","B",1
789,1,776,98,0.0009967,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\frac{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^8 \left(\frac{1}{12 (c+d)^{3/2}}-\frac{\sqrt{a+b x}}{12 \sqrt{a+b} (c+d)^{3/2}}\right) \left(\frac{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^2 \left(2 b c d^2 \sqrt{a+b} \sqrt{a+b x}+12 a b d^2 \sqrt{c+d} \sqrt{c+d x}-20 b d^2 \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}+6 a b c d^2+4 a b d^3 x-6 b d^3 \sqrt{a+b} \sqrt{a+b x}+10 a b d^3+9 b^2 c d^2 x+20 b^2 d^2 \sqrt{c+d} \sqrt{c+d x}-11 b^2 c d^2+13 b^2 d^3 x-7 b^2 d^3\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^4}+\frac{\left(b^2 d \sqrt{a+b}-b^2 d \sqrt{a+b x}\right) \left(6 \sqrt{a+b} \sqrt{c+d} \sqrt{c+d x}-9 c \sqrt{a+b x}+3 c \sqrt{a+b}-13 d \sqrt{a+b x}+7 d \sqrt{a+b}\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^2}+\frac{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^4 \left(-6 d^3 \sqrt{a+b} \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}-2 a d^3 \sqrt{c+d} \sqrt{c+d x}+8 a c d^3+4 a d^4 x+4 a d^4+3 b c d^3 x+6 b d^3 \sqrt{c+d} \sqrt{c+d x}-3 b c d^3+3 b d^4 x-3 b d^4\right)}{\left(\sqrt{c+d}-\sqrt{c+d x}\right)^6}+3 b^3 c+3 b^3 d\right)}{\left(\sqrt{c+d x}-\sqrt{c+d}\right) \left(-d \sqrt{a+b} \sqrt{a+b x} \sqrt{c+d x}+a d \sqrt{c+d x}-b c \sqrt{c+d x}+b d x \sqrt{c+d}+b c \sqrt{c+d}\right)^3 \left(b \sqrt{c+d} \sqrt{a+b x} \sqrt{c+d x}-b c \sqrt{a+b x}+b d x \left(-\sqrt{a+b}\right)+a d \sqrt{a+b x}-a d \sqrt{a+b}\right)}","-\frac{16 b d \sqrt{a+b x}}{3 \sqrt{c+d x} (b c-a d)^3}-\frac{8 d \sqrt{a+b x}}{3 (c+d x)^{3/2} (b c-a d)^2}-\frac{2}{\sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}",1,"((1/(12*(c + d)^(3/2)) - Sqrt[a + b*x]/(12*Sqrt[a + b]*(c + d)^(3/2)))*(Sqrt[c + d] - Sqrt[c + d*x])^8*(3*b^3*c + 3*b^3*d + ((b^2*Sqrt[a + b]*d - b^2*d*Sqrt[a + b*x])*(3*Sqrt[a + b]*c + 7*Sqrt[a + b]*d - 9*c*Sqrt[a + b*x] - 13*d*Sqrt[a + b*x] + 6*Sqrt[a + b]*Sqrt[c + d]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^2 + ((Sqrt[a + b] - Sqrt[a + b*x])^2*(6*a*b*c*d^2 - 11*b^2*c*d^2 + 10*a*b*d^3 - 7*b^2*d^3 + 9*b^2*c*d^2*x + 4*a*b*d^3*x + 13*b^2*d^3*x + 2*b*Sqrt[a + b]*c*d^2*Sqrt[a + b*x] - 6*b*Sqrt[a + b]*d^3*Sqrt[a + b*x] + 12*a*b*d^2*Sqrt[c + d]*Sqrt[c + d*x] + 20*b^2*d^2*Sqrt[c + d]*Sqrt[c + d*x] - 20*b*Sqrt[a + b]*d^2*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^4 + ((Sqrt[a + b] - Sqrt[a + b*x])^4*(8*a*c*d^3 - 3*b*c*d^3 + 4*a*d^4 - 3*b*d^4 + 3*b*c*d^3*x + 4*a*d^4*x + 3*b*d^4*x - 2*a*d^3*Sqrt[c + d]*Sqrt[c + d*x] + 6*b*d^3*Sqrt[c + d]*Sqrt[c + d*x] - 6*Sqrt[a + b]*d^3*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))/(Sqrt[c + d] - Sqrt[c + d*x])^6))/((-Sqrt[c + d] + Sqrt[c + d*x])*(b*c*Sqrt[c + d] + b*d*Sqrt[c + d]*x - b*c*Sqrt[c + d*x] + a*d*Sqrt[c + d*x] - Sqrt[a + b]*d*Sqrt[a + b*x]*Sqrt[c + d*x])^3*(-(a*Sqrt[a + b]*d) - b*Sqrt[a + b]*d*x - b*c*Sqrt[a + b*x] + a*d*Sqrt[a + b*x] + b*Sqrt[c + d]*Sqrt[a + b*x]*Sqrt[c + d*x]))","B",1
790,-1,0,180,180.1317538,"\int \frac{1}{x (a+b x)^{3/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{3/2} c^{5/2}}+\frac{2 d \sqrt{a+b x} (3 b c-a d) (3 a d+b c)}{3 a c^2 \sqrt{c+d x} (b c-a d)^3}+\frac{2 b}{a \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}+\frac{2 d \sqrt{a+b x} (a d+3 b c)}{3 a c (c+d x)^{3/2} (b c-a d)^2}",1,"$Aborted","F",-1
791,-1,0,264,180.2725819,"\int \frac{1}{x^2 (a+b x)^{3/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","\frac{(5 a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{5/2} c^{7/2}}-\frac{d \sqrt{a+b x} \left(5 a^2 d^2-6 a b c d+9 b^2 c^2\right)}{3 a^2 c^2 (c+d x)^{3/2} (b c-a d)^2}-\frac{b (3 b c-a d)}{a^2 c \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}-\frac{d \sqrt{a+b x} \left(-15 a^3 d^3+31 a^2 b c d^2-9 a b^2 c^2 d+9 b^3 c^3\right)}{3 a^2 c^3 \sqrt{c+d x} (b c-a d)^3}-\frac{1}{a c x \sqrt{a+b x} (c+d x)^{3/2}}",1,"$Aborted","F",-1
792,-1,0,361,180.1538067,"\int \frac{1}{x^3 (a+b x)^{3/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","\frac{7 a d+5 b c}{4 a^2 c^2 x \sqrt{a+b x} (c+d x)^{3/2}}-\frac{5 \left(7 a^2 d^2+6 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{7/2} c^{9/2}}+\frac{b \left(15 b^2 c^2-7 a^2 d^2\right)}{4 a^3 c^2 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}+\frac{d \sqrt{a+b x} \left(35 a^3 d^3-33 a^2 b c d^2-15 a b^2 c^2 d+45 b^3 c^3\right)}{12 a^3 c^3 (c+d x)^{3/2} (b c-a d)^2}+\frac{d \sqrt{a+b x} \left(-105 a^4 d^4+190 a^3 b c d^3-36 a^2 b^2 c^2 d^2-30 a b^3 c^3 d+45 b^4 c^4\right)}{12 a^3 c^4 \sqrt{c+d x} (b c-a d)^3}-\frac{1}{2 a c x^2 \sqrt{a+b x} (c+d x)^{3/2}}",1,"$Aborted","F",-1
793,-1,0,497,180.0437929,"\int \frac{x^4 (c+d x)^{5/2}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(x^4*(c + d*x)^(5/2))/(a + b*x)^(5/2),x]","\text{\$Aborted}","-\frac{\sqrt{a+b x} (c+d x)^{5/2} \left(3003 a^3 d^3-2 b d x \left(1287 a^2 d^2-902 a b c d+15 b^2 c^2\right)-2343 a^2 b c d^2+125 a b^2 c^2 d+15 b^3 c^3\right)}{240 b^5 d^2 (b c-a d)}+\frac{(b c-a d) \left(3003 a^4 d^4-2772 a^3 b c d^3+378 a^2 b^2 c^2 d^2+28 a b^3 c^3 d+3 b^4 c^4\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{128 b^{15/2} d^{5/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(3003 a^4 d^4-2772 a^3 b c d^3+378 a^2 b^2 c^2 d^2+28 a b^3 c^3 d+3 b^4 c^4\right)}{128 b^7 d^2}+\frac{\sqrt{a+b x} (c+d x)^{3/2} \left(3003 a^4 d^4-2772 a^3 b c d^3+378 a^2 b^2 c^2 d^2+28 a b^3 c^3 d+3 b^4 c^4\right)}{192 b^6 d^2 (b c-a d)}+\frac{x^2 \sqrt{a+b x} (c+d x)^{5/2} (93 b c-143 a d)}{15 b^3 (b c-a d)}-\frac{2 x^3 (c+d x)^{5/2} (8 b c-13 a d)}{3 b^2 \sqrt{a+b x} (b c-a d)}-\frac{2 x^4 (c+d x)^{5/2}}{3 b (a+b x)^{3/2}}",1,"$Aborted","F",-1
794,-1,0,377,180.1816892,"\int \frac{x^3 (c+d x)^{5/2}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(x^3*(c + d*x)^(5/2))/(a + b*x)^(5/2),x]","\text{\$Aborted}","\frac{\sqrt{a+b x} (c+d x)^{5/2} \left(231 a^2 d^2+2 b d x (59 b c-99 a d)-156 a b c d+5 b^2 c^2\right)}{24 b^4 d (b c-a d)}-\frac{5 (b c-a d) \left(231 a^3 d^3-189 a^2 b c d^2+21 a b^2 c^2 d+b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{64 b^{13/2} d^{3/2}}-\frac{5 \sqrt{a+b x} \sqrt{c+d x} \left(231 a^3 d^3-189 a^2 b c d^2+21 a b^2 c^2 d+b^3 c^3\right)}{64 b^6 d}-\frac{5 \sqrt{a+b x} (c+d x)^{3/2} \left(231 a^3 d^3-189 a^2 b c d^2+21 a b^2 c^2 d+b^3 c^3\right)}{96 b^5 d (b c-a d)}-\frac{2 x^2 (c+d x)^{5/2} (6 b c-11 a d)}{3 b^2 \sqrt{a+b x} (b c-a d)}-\frac{2 x^3 (c+d x)^{5/2}}{3 b (a+b x)^{3/2}}",1,"$Aborted","F",-1
795,-1,0,319,180.0484419,"\int \frac{x^2 (c+d x)^{5/2}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(x^2*(c + d*x)^(5/2))/(a + b*x)^(5/2),x]","\text{\$Aborted}","-\frac{2 a^2 (c+d x)^{7/2}}{3 b^2 (a+b x)^{3/2} (b c-a d)}+\frac{5 (b c-a d) \left(21 a^2 d^2-14 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{8 b^{11/2} \sqrt{d}}+\frac{5 \sqrt{a+b x} \sqrt{c+d x} \left(21 a^2 d^2-14 a b c d+b^2 c^2\right)}{8 b^5}+\frac{5 \sqrt{a+b x} (c+d x)^{3/2} \left(21 a^2 d^2-14 a b c d+b^2 c^2\right)}{12 b^4 (b c-a d)}+\frac{\sqrt{a+b x} (c+d x)^{5/2} \left(21 a^2 d^2-14 a b c d+b^2 c^2\right)}{3 b^3 (b c-a d)^2}+\frac{4 a (c+d x)^{7/2} (3 b c-5 a d)}{3 b^2 \sqrt{a+b x} (b c-a d)^2}",1,"$Aborted","F",-1
796,-1,0,222,180.0489869,"\int \frac{x (c+d x)^{5/2}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(x*(c + d*x)^(5/2))/(a + b*x)^(5/2),x]","\text{\$Aborted}","\frac{5 \sqrt{d} (3 b c-7 a d) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{9/2}}+\frac{5 d \sqrt{a+b x} \sqrt{c+d x} (3 b c-7 a d)}{4 b^4}+\frac{5 d \sqrt{a+b x} (c+d x)^{3/2} (3 b c-7 a d)}{6 b^3 (b c-a d)}-\frac{2 (c+d x)^{5/2} (3 b c-7 a d)}{3 b^2 \sqrt{a+b x} (b c-a d)}+\frac{2 a (c+d x)^{7/2}}{3 b (a+b x)^{3/2} (b c-a d)}",1,"$Aborted","F",-1
797,-1,0,128,180.2439955,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(a + b*x)^(5/2),x]","\text{\$Aborted}","\frac{5 d^{3/2} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{7/2}}+\frac{5 d^2 \sqrt{a+b x} \sqrt{c+d x}}{b^3}-\frac{10 d (c+d x)^{3/2}}{3 b^2 \sqrt{a+b x}}-\frac{2 (c+d x)^{5/2}}{3 b (a+b x)^{3/2}}",1,"$Aborted","F",-1
798,-1,0,157,180.0410064,"\int \frac{(c+d x)^{5/2}}{x (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x*(a + b*x)^(5/2)),x]","\text{\$Aborted}","-\frac{2 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{5/2}}+\frac{2 \sqrt{c+d x} \left(\frac{c^2}{a^2}-\frac{d^2}{b^2}\right)}{\sqrt{a+b x}}+\frac{2 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{5/2}}+\frac{2 (c+d x)^{3/2} (b c-a d)}{3 a b (a+b x)^{3/2}}",1,"$Aborted","F",-1
799,-1,0,142,180.0434239,"\int \frac{(c+d x)^{5/2}}{x^2 (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^2*(a + b*x)^(5/2)),x]","\text{\$Aborted}","\frac{5 c^{3/2} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{7/2}}-\frac{5 c \sqrt{c+d x} (b c-a d)}{a^3 \sqrt{a+b x}}-\frac{5 (c+d x)^{3/2} (b c-a d)}{3 a^2 (a+b x)^{3/2}}-\frac{(c+d x)^{5/2}}{a x (a+b x)^{3/2}}",1,"$Aborted","F",-1
800,-1,0,220,180.1982028,"\int \frac{(c+d x)^{5/2}}{x^3 (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^3*(a + b*x)^(5/2)),x]","\text{\$Aborted}","-\frac{5 \sqrt{c} (7 b c-3 a d) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{9/2}}+\frac{5 \sqrt{c+d x} (7 b c-3 a d) (b c-a d)}{4 a^4 \sqrt{a+b x}}+\frac{5 (c+d x)^{3/2} (7 b c-3 a d) (b c-a d)}{12 a^3 c (a+b x)^{3/2}}+\frac{(c+d x)^{5/2} (7 b c-3 a d)}{4 a^2 c x (a+b x)^{3/2}}-\frac{(c+d x)^{7/2}}{2 a c x^2 (a+b x)^{3/2}}",1,"$Aborted","F",-1
801,-1,0,278,180.0851185,"\int \frac{(c+d x)^{5/2}}{x^4 (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^4*(a + b*x)^(5/2)),x]","\text{\$Aborted}","-\frac{7 b \sqrt{c+d x} (15 b c-7 a d) (b c-a d)}{24 a^4 (a+b x)^{3/2}}-\frac{\sqrt{c+d x} (21 b c-11 a d) (b c-a d)}{8 a^3 x (a+b x)^{3/2}}+\frac{3 c \sqrt{c+d x} (b c-a d)}{4 a^2 x^2 (a+b x)^{3/2}}+\frac{5 (b c-a d) \left(a^2 d^2-14 a b c d+21 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{8 a^{11/2} \sqrt{c}}-\frac{b \sqrt{c+d x} \left(113 a^2 d^2-420 a b c d+315 b^2 c^2\right)}{24 a^5 \sqrt{a+b x}}-\frac{c (c+d x)^{3/2}}{3 a x^3 (a+b x)^{3/2}}",1,"$Aborted","F",-1
802,-1,0,388,180.1633166,"\int \frac{(c+d x)^{5/2}}{x^5 (a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(c + d*x)^(5/2)/(x^5*(a + b*x)^(5/2)),x]","\text{\$Aborted}","-\frac{\sqrt{c+d x} (99 b c-59 a d) (b c-a d)}{96 a^3 x^2 (a+b x)^{3/2}}+\frac{11 c \sqrt{c+d x} (b c-a d)}{24 a^2 x^3 (a+b x)^{3/2}}+\frac{b \sqrt{c+d x} (b c-a d) \left(5 a^2 d^2-238 a b c d+385 b^2 c^2\right)}{64 a^5 c (a+b x)^{3/2}}+\frac{\sqrt{c+d x} (b c-a d) \left(5 a^2 d^2-156 a b c d+231 b^2 c^2\right)}{64 a^4 c x (a+b x)^{3/2}}-\frac{5 (b c-a d) \left(a^3 d^3+21 a^2 b c d^2-189 a b^2 c^2 d+231 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{64 a^{13/2} c^{3/2}}+\frac{b \sqrt{c+d x} \left(-5 a^3 d^3+581 a^2 b c d^2-1715 a b^2 c^2 d+1155 b^3 c^3\right)}{64 a^6 c \sqrt{a+b x}}-\frac{c (c+d x)^{3/2}}{4 a x^4 (a+b x)^{3/2}}",1,"$Aborted","F",-1
803,-1,0,126,180.1623219,"\int \frac{x^2}{(a+b x)^{5/2} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[x^2/((a + b*x)^(5/2)*Sqrt[c + d*x]),x]","\text{\$Aborted}","-\frac{2 a^2 \sqrt{c+d x}}{3 b^2 (a+b x)^{3/2} (b c-a d)}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{5/2} \sqrt{d}}+\frac{4 a \sqrt{c+d x} (3 b c-2 a d)}{3 b^2 \sqrt{a+b x} (b c-a d)^2}",1,"$Aborted","F",-1
804,-1,0,445,180.4759568,"\int \frac{x^6}{(a+b x)^{5/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[x^6/((a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{2 c x^3 \sqrt{a+b x} \left(-7 a^2 d^2+14 a b c d+b^2 c^2\right)}{3 b^2 d (c+d x)^{3/2} (b c-a d)^3}-\frac{2 c x^2 \sqrt{a+b x} (a d+b c) \left(7 a^2 d^2-22 a b c d+7 b^2 c^2\right)}{3 b^2 d^2 \sqrt{c+d x} (b c-a d)^4}+\frac{5 \left(7 a^2 d^2+10 a b c d+7 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{4 b^{9/2} d^{9/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left((a d+b c) \left(105 a^4 d^4-340 a^3 b c d^3+406 a^2 b^2 c^2 d^2-340 a b^3 c^3 d+105 b^4 c^4\right)-2 b d x \left(35 a^4 d^4-76 a^3 b c d^3+18 a^2 b^2 c^2 d^2-76 a b^3 c^3 d+35 b^4 c^4\right)\right)}{12 b^4 d^4 (b c-a d)^4}+\frac{2 a x^4 (13 b c-7 a d)}{3 b^2 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^2}+\frac{2 a x^5}{3 b (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}",1,"$Aborted","F",-1
805,-1,0,341,180.1862285,"\int \frac{x^5}{(a+b x)^{5/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[x^5/((a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{2 c x^2 \sqrt{a+b x} \left(-5 a^2 d^2+12 a b c d+b^2 c^2\right)}{3 b^2 d (c+d x)^{3/2} (b c-a d)^3}+\frac{\sqrt{a+b x} \left(d x (b c-a d) \left(-15 a^3 d^3+35 a^2 b c d^2-9 a b^2 c^2 d+5 b^3 c^3\right)+c \left(15 a^4 d^4-40 a^3 b c d^3+18 a^2 b^2 c^2 d^2-40 a b^3 c^3 d+15 b^4 c^4\right)\right)}{3 b^3 d^3 \sqrt{c+d x} (b c-a d)^4}-\frac{5 (a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{7/2} d^{7/2}}+\frac{2 a x^3 (11 b c-5 a d)}{3 b^2 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^2}+\frac{2 a x^4}{3 b (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}",1,"$Aborted","F",-1
806,-1,0,241,180.1497566,"\int \frac{x^4}{(a+b x)^{5/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[x^4/((a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{2 c \sqrt{a+b x} \left(c (a d+b c) \left(3 a^2 d^2-14 a b c d+3 b^2 c^2\right)+2 d x \left(3 a^3 d^3-12 a^2 b c d^2-a b^2 c^2 d+2 b^3 c^3\right)\right)}{3 b^2 d^2 (c+d x)^{3/2} (b c-a d)^4}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{b^{5/2} d^{5/2}}+\frac{2 a x^2 (3 b c-a d)}{b^2 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^2}+\frac{2 a x^3}{3 b (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}",1,"$Aborted","F",-1
807,-1,0,189,180.1011536,"\int \frac{x^3}{(a+b x)^{5/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[x^3/((a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","\frac{4 c \sqrt{a+b x} \left(-3 a^2 d^2-6 a b c d+b^2 c^2\right)}{3 b d \sqrt{c+d x} (b c-a d)^4}-\frac{4 c \sqrt{a+b x} \left(3 a^2 d^2+b^2 c^2\right)}{3 b^2 d (c+d x)^{3/2} (b c-a d)^3}-\frac{4 a^2 c}{b^2 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^2}-\frac{2 x^3}{3 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}",1,"$Aborted","F",-1
808,-1,0,186,180.0159222,"\int \frac{x^2}{(a+b x)^{5/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[x^2/((a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","\frac{4 \sqrt{a+b x} \left(a^2 d^2+6 a b c d+b^2 c^2\right)}{3 b \sqrt{c+d x} (b c-a d)^4}+\frac{2 \sqrt{a+b x} \left(a^2 d^2+6 a b c d+b^2 c^2\right)}{3 b^2 (c+d x)^{3/2} (b c-a d)^3}-\frac{2 a^2}{3 b^2 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}+\frac{4 a c}{b \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^2}",1,"$Aborted","F",-1
809,-1,0,158,180.0444263,"\int \frac{x}{(a+b x)^{5/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[x/((a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{2 c}{3 d (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}-\frac{16 d \sqrt{a+b x} (a d+b c)}{3 \sqrt{c+d x} (b c-a d)^4}-\frac{8 (a d+b c)}{3 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^3}+\frac{2 (a d+b c)}{3 d (a+b x)^{3/2} \sqrt{c+d x} (b c-a d)^2}",1,"$Aborted","F",-1
810,-1,0,135,180.027183,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","\frac{32 b d^2 \sqrt{a+b x}}{3 \sqrt{c+d x} (b c-a d)^4}+\frac{16 d^2 \sqrt{a+b x}}{3 (c+d x)^{3/2} (b c-a d)^3}+\frac{4 d}{\sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^2}-\frac{2}{3 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}",1,"$Aborted","F",-1
811,-1,0,252,180.2189054,"\int \frac{1}{x (a+b x)^{5/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{5/2} c^{5/2}}+\frac{2 d \sqrt{a+b x} (a d+b c) \left(3 a^2 d^2-14 a b c d+3 b^2 c^2\right)}{3 a^2 c^2 \sqrt{c+d x} (b c-a d)^4}+\frac{2 d \sqrt{a+b x} \left(-a^2 d^2-10 a b c d+3 b^2 c^2\right)}{3 a^2 c (c+d x)^{3/2} (b c-a d)^3}+\frac{2 b (b c-3 a d)}{a^2 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^2}+\frac{2 b}{3 a (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}",1,"$Aborted","F",-1
812,-1,0,352,180.6072225,"\int \frac{1}{x^2 (a+b x)^{5/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","\frac{5 (a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{7/2} c^{7/2}}-\frac{b (5 b c-3 a d)}{3 a^2 c (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}-\frac{b \left(a^2 d^2-10 a b c d+5 b^2 c^2\right)}{a^3 c \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^2}-\frac{d \sqrt{a+b x} \left(-5 a^3 d^3+9 a^2 b c d^2-35 a b^2 c^2 d+15 b^3 c^3\right)}{3 a^3 c^2 (c+d x)^{3/2} (b c-a d)^3}-\frac{d \sqrt{a+b x} \left(15 a^4 d^4-40 a^3 b c d^3+18 a^2 b^2 c^2 d^2-40 a b^3 c^3 d+15 b^4 c^4\right)}{3 a^3 c^3 \sqrt{c+d x} (b c-a d)^4}-\frac{1}{a c x (a+b x)^{3/2} (c+d x)^{3/2}}",1,"$Aborted","F",-1
813,-1,0,462,180.1577445,"\int \frac{1}{x^3 (a+b x)^{5/2} (c+d x)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\text{\$Aborted}","\frac{7 (a d+b c)}{4 a^2 c^2 x (a+b x)^{3/2} (c+d x)^{3/2}}-\frac{5 \left(7 a^2 d^2+10 a b c d+7 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{4 a^{9/2} c^{9/2}}+\frac{b \left(-21 a^2 d^2-6 a b c d+35 b^2 c^2\right)}{12 a^3 c^2 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)}+\frac{b \left(7 a^3 d^3-3 a^2 b c d^2-55 a b^2 c^2 d+35 b^3 c^3\right)}{4 a^4 c^2 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^2}+\frac{d \sqrt{a+b x} \left(105 a^4 d^4-340 a^3 b c d^3+406 a^2 b^2 c^2 d^2-340 a b^3 c^3 d+105 b^4 c^4\right) (a d+b c)}{12 a^4 c^4 \sqrt{c+d x} (b c-a d)^4}+\frac{d \sqrt{a+b x} \left(-35 a^4 d^4+48 a^3 b c d^3+18 a^2 b^2 c^2 d^2-200 a b^3 c^3 d+105 b^4 c^4\right)}{12 a^4 c^3 (c+d x)^{3/2} (b c-a d)^3}-\frac{1}{2 a c x^2 (a+b x)^{3/2} (c+d x)^{3/2}}",1,"$Aborted","F",-1
814,0,0,28,52.1166961,"\int \frac{x^2 \sqrt{a+b x}}{\sqrt{-a-b x}} \, dx","IntegrateAlgebraic[(x^2*Sqrt[a + b*x])/Sqrt[-a - b*x],x]","\int \frac{x^2 \sqrt{a+b x}}{\sqrt{-a-b x}} \, dx","\frac{x^3 \sqrt{a+b x}}{3 \sqrt{-a-b x}}",1,"Could not integrate","F",-1
815,1,2727,28,6.6767744,"\int \frac{x \sqrt{a+b x}}{\sqrt{-a-b x}} \, dx","IntegrateAlgebraic[(x*Sqrt[a + b*x])/Sqrt[-a - b*x],x]","\text{Result too large to show}","\frac{x^2 \sqrt{a+b x}}{2 \sqrt{-a-b x}}",1,"(((Sqrt[-a - b]*Sqrt[-a^2 - 2*a*b - b^2])/(4*b^2*(a + b)) - (Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[-a - b*x])/(4*b^2*(a + b)))*(Sqrt[a + b] - Sqrt[a + b*x])^8*(((16*Sqrt[-a - b]*b^2 - 16*b^2*Sqrt[-a - b*x])*(-2*a - b - b*x - Sqrt[-a - b]*Sqrt[-a - b*x] + Sqrt[a + b]*Sqrt[a + b*x])^2)/(Sqrt[a + b] - Sqrt[a + b*x])^5 + ((-16*a*Sqrt[-a - b] + 16*a*Sqrt[-a - b*x])*(-5*a^3 - 5*a^2*b - a*b^2 - 4*a*Sqrt[-a - b]*Sqrt[a + b]*Sqrt[-a^2 - 2*a*b - b^2] - Sqrt[-a - b]*b*Sqrt[a + b]*Sqrt[-a^2 - 2*a*b - b^2] - 5*a^2*b*x - 3*a*b^2*x - 3*Sqrt[-a - b]*b*Sqrt[a + b]*Sqrt[-a^2 - 2*a*b - b^2]*x - a*b^2*x^2 - 4*a^2*Sqrt[-a - b]*Sqrt[-a - b*x] - 2*a*Sqrt[-a - b]*b*Sqrt[-a - b*x] + 4*a*Sqrt[a + b]*Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[-a - b*x] + 2*b*Sqrt[a + b]*Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[-a - b*x] - 2*a*Sqrt[-a - b]*b*x*Sqrt[-a - b*x] + 2*b*Sqrt[a + b]*Sqrt[-a^2 - 2*a*b - b^2]*x*Sqrt[-a - b*x] + 4*a^2*Sqrt[a + b]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*Sqrt[a + b*x] + 4*a*Sqrt[-a - b]*Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[a + b*x] + 2*Sqrt[-a - b]*b*Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*x*Sqrt[a + b*x] + 2*Sqrt[-a - b]*b*Sqrt[-a^2 - 2*a*b - b^2]*x*Sqrt[a + b*x] + 3*a*Sqrt[-a - b]*Sqrt[a + b]*Sqrt[-a - b*x]*Sqrt[a + b*x] - 4*a*Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[-a - b*x]*Sqrt[a + b*x] - 3*b*Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[-a - b*x]*Sqrt[a + b*x] - b*Sqrt[-a^2 - 2*a*b - b^2]*x*Sqrt[-a - b*x]*Sqrt[a + b*x]))/(Sqrt[a + b] - Sqrt[a + b*x])^5 + (512*a^3*Sqrt[-a - b]*b*Sqrt[a + b] + 304*a^2*Sqrt[-a - b]*b^2*Sqrt[a + b] + 32*a*Sqrt[-a - b]*b^3*Sqrt[a + b] - 288*a^3*b*Sqrt[-a^2 - 2*a*b - b^2] - 432*a^2*b^2*Sqrt[-a^2 - 2*a*b - b^2] - 176*a*b^3*Sqrt[-a^2 - 2*a*b - b^2] - 16*b^4*Sqrt[-a^2 - 2*a*b - b^2] + 720*a^2*Sqrt[-a - b]*b^2*Sqrt[a + b]*x + 240*a*Sqrt[-a - b]*b^3*Sqrt[a + b]*x - 432*a^2*b^2*Sqrt[-a^2 - 2*a*b - b^2]*x - 512*a*b^3*Sqrt[-a^2 - 2*a*b - b^2]*x - 128*b^4*Sqrt[-a^2 - 2*a*b - b^2]*x + 240*a*Sqrt[-a - b]*b^3*Sqrt[a + b]*x^2 - 176*a*b^3*Sqrt[-a^2 - 2*a*b - b^2]*x^2 - 128*b^4*Sqrt[-a^2 - 2*a*b - b^2]*x^2 - 16*b^4*Sqrt[-a^2 - 2*a*b - b^2]*x^3 - 512*a^3*b*Sqrt[a + b]*Sqrt[-a - b*x] - 512*a^2*b^2*Sqrt[a + b]*Sqrt[-a - b*x] - 96*a*b^3*Sqrt[a + b]*Sqrt[-a - b*x] - 256*a^2*Sqrt[-a - b]*b*Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[-a - b*x] - 256*a*Sqrt[-a - b]*b^2*Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[-a - b*x] - 48*Sqrt[-a - b]*b^3*Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[-a - b*x] - 512*a^2*b^2*Sqrt[a + b]*x*Sqrt[-a - b*x] - 320*a*b^3*Sqrt[a + b]*x*Sqrt[-a - b*x] - 256*a*Sqrt[-a - b]*b^2*Sqrt[-a^2 - 2*a*b - b^2]*x*Sqrt[-a - b*x] - 160*Sqrt[-a - b]*b^3*Sqrt[-a^2 - 2*a*b - b^2]*x*Sqrt[-a - b*x] - 96*a*b^3*Sqrt[a + b]*x^2*Sqrt[-a - b*x] - 48*Sqrt[-a - b]*b^3*Sqrt[-a^2 - 2*a*b - b^2]*x^2*Sqrt[-a - b*x] - 512*a^3*Sqrt[-a - b]*b*Sqrt[a + b*x] - 512*a^2*Sqrt[-a - b]*b^2*Sqrt[a + b*x] - 96*a*Sqrt[-a - b]*b^3*Sqrt[a + b*x] + 256*a^2*b*Sqrt[a + b]*Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[a + b*x] + 256*a*b^2*Sqrt[a + b]*Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[a + b*x] + 48*b^3*Sqrt[a + b]*Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[a + b*x] - 512*a^2*Sqrt[-a - b]*b^2*x*Sqrt[a + b*x] - 320*a*Sqrt[-a - b]*b^3*x*Sqrt[a + b*x] + 256*a*b^2*Sqrt[a + b]*Sqrt[-a^2 - 2*a*b - b^2]*x*Sqrt[a + b*x] + 160*b^3*Sqrt[a + b]*Sqrt[-a^2 - 2*a*b - b^2]*x*Sqrt[a + b*x] - 96*a*Sqrt[-a - b]*b^3*x^2*Sqrt[a + b*x] + 48*b^3*Sqrt[a + b]*Sqrt[-a^2 - 2*a*b - b^2]*x^2*Sqrt[a + b*x] + 512*a^3*b*Sqrt[-a - b*x]*Sqrt[a + b*x] + 720*a^2*b^2*Sqrt[-a - b*x]*Sqrt[a + b*x] + 240*a*b^3*Sqrt[-a - b*x]*Sqrt[a + b*x] + 224*a*Sqrt[-a - b]*b*Sqrt[a + b]*Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[-a - b*x]*Sqrt[a + b*x] + 112*Sqrt[-a - b]*b^2*Sqrt[a + b]*Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[-a - b*x]*Sqrt[a + b*x] + 304*a^2*b^2*x*Sqrt[-a - b*x]*Sqrt[a + b*x] + 240*a*b^3*x*Sqrt[-a - b*x]*Sqrt[a + b*x] + 112*Sqrt[-a - b]*b^2*Sqrt[a + b]*Sqrt[-a^2 - 2*a*b - b^2]*x*Sqrt[-a - b*x]*Sqrt[a + b*x] + 32*a*b^3*x^2*Sqrt[-a - b*x]*Sqrt[a + b*x])/(Sqrt[a + b] - Sqrt[a + b*x])^6))/((-Sqrt[a + b] + Sqrt[a + b*x])*(Sqrt[-a - b]*Sqrt[-a - b*x] + Sqrt[a + b]*Sqrt[a + b*x])^4)","B",0
816,1,444,23,0.8757484,"\int \frac{\sqrt{a+b x}}{\sqrt{-a-b x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/Sqrt[-a - b*x],x]","\frac{\left(\frac{\sqrt{-a-b} \sqrt{-a^2-2 a b-b^2}}{b (a+b)}-\frac{\sqrt{-a^2-2 a b-b^2} \sqrt{-a-b x}}{b (a+b)}\right) \left(\sqrt{a+b}-\sqrt{a+b x}\right)^4 \left(\frac{-2 b x \sqrt{-a^2-2 a b-b^2}-2 \sqrt{-a-b} \sqrt{-a^2-2 a b-b^2} \sqrt{-a-b x}+2 \sqrt{a+b} \sqrt{-a^2-2 a b-b^2} \sqrt{a+b x}-4 a \sqrt{-a^2-2 a b-b^2}-2 b \sqrt{-a^2-2 a b-b^2}}{\left(\sqrt{a+b}-\sqrt{a+b x}\right)^2}+\frac{2 a \sqrt{-a-b}-2 a \sqrt{-a-b x}}{\sqrt{a+b}-\sqrt{a+b x}}+\frac{2 b \sqrt{-a-b}-2 b \sqrt{-a-b x}}{\sqrt{a+b}-\sqrt{a+b x}}\right)}{\left(\sqrt{a+b x}-\sqrt{a+b}\right) \left(\sqrt{-a-b} \sqrt{-a-b x}+\sqrt{a+b} \sqrt{a+b x}\right)^2}","\frac{x \sqrt{a+b x}}{\sqrt{-a-b x}}",1,"(((Sqrt[-a - b]*Sqrt[-a^2 - 2*a*b - b^2])/(b*(a + b)) - (Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[-a - b*x])/(b*(a + b)))*(Sqrt[a + b] - Sqrt[a + b*x])^4*((2*a*Sqrt[-a - b] - 2*a*Sqrt[-a - b*x])/(Sqrt[a + b] - Sqrt[a + b*x]) + (2*Sqrt[-a - b]*b - 2*b*Sqrt[-a - b*x])/(Sqrt[a + b] - Sqrt[a + b*x]) + (-4*a*Sqrt[-a^2 - 2*a*b - b^2] - 2*b*Sqrt[-a^2 - 2*a*b - b^2] - 2*b*Sqrt[-a^2 - 2*a*b - b^2]*x - 2*Sqrt[-a - b]*Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[-a - b*x] + 2*Sqrt[a + b]*Sqrt[-a^2 - 2*a*b - b^2]*Sqrt[a + b*x])/(Sqrt[a + b] - Sqrt[a + b*x])^2))/((-Sqrt[a + b] + Sqrt[a + b*x])*(Sqrt[-a - b]*Sqrt[-a - b*x] + Sqrt[a + b]*Sqrt[a + b*x])^2)","B",0
817,-1,0,24,180.2859204,"\int \frac{\sqrt{a+b x}}{x \sqrt{-a-b x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(x*Sqrt[-a - b*x]),x]","\text{\$Aborted}","\frac{\log (x) \sqrt{a+b x}}{\sqrt{-a-b x}}",1,"$Aborted","F",-1
818,0,0,26,58.2583949,"\int \frac{\sqrt{a+b x}}{x^2 \sqrt{-a-b x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(x^2*Sqrt[-a - b*x]),x]","\int \frac{\sqrt{a+b x}}{x^2 \sqrt{-a-b x}} \, dx","-\frac{\sqrt{a+b x}}{x \sqrt{-a-b x}}",1,"Could not integrate","F",-1
819,0,0,28,64.4059098,"\int \frac{\sqrt{a+b x}}{x^3 \sqrt{-a-b x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(x^3*Sqrt[-a - b*x]),x]","\int \frac{\sqrt{a+b x}}{x^3 \sqrt{-a-b x}} \, dx","-\frac{\sqrt{a+b x}}{2 x^2 \sqrt{-a-b x}}",1,"Could not integrate","F",-1
820,0,0,36,0.1170001,"\int \frac{x^{-m} \sqrt{a+b x}}{\sqrt{-a-b x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(x^m*Sqrt[-a - b*x]),x]","\int \frac{x^{-m} \sqrt{a+b x}}{\sqrt{-a-b x}} \, dx","\frac{x^{1-m} \sqrt{a+b x}}{(1-m) \sqrt{-a-b x}}",1,"Could not integrate","F",-1
821,0,0,26,0.0462305,"\int x^2 (-a-b x)^{-n} (a+b x)^n \, dx","IntegrateAlgebraic[(x^2*(a + b*x)^n)/(-a - b*x)^n,x]","\int x^2 (-a-b x)^{-n} (a+b x)^n \, dx","\frac{1}{3} x^3 (-a-b x)^{-n} (a+b x)^n",1,"Could not integrate","F",-1
822,0,0,26,0.0378208,"\int x (-a-b x)^{-n} (a+b x)^n \, dx","IntegrateAlgebraic[(x*(a + b*x)^n)/(-a - b*x)^n,x]","\int x (-a-b x)^{-n} (a+b x)^n \, dx","\frac{1}{2} x^2 (-a-b x)^{-n} (a+b x)^n",1,"Could not integrate","F",-1
823,0,0,21,0.0115402,"\int (-a-b x)^{-n} (a+b x)^n \, dx","IntegrateAlgebraic[(a + b*x)^n/(-a - b*x)^n,x]","\int (-a-b x)^{-n} (a+b x)^n \, dx","x (-a-b x)^{-n} (a+b x)^n",1,"Could not integrate","F",-1
824,0,0,22,0.0465438,"\int \frac{(-a-b x)^{-n} (a+b x)^n}{x} \, dx","IntegrateAlgebraic[(a + b*x)^n/(x*(-a - b*x)^n),x]","\int \frac{(-a-b x)^{-n} (a+b x)^n}{x} \, dx","\log (x) (-a-b x)^{-n} (a+b x)^n",1,"Could not integrate","F",-1
825,0,0,24,0.0382288,"\int \frac{(-a-b x)^{-n} (a+b x)^n}{x^2} \, dx","IntegrateAlgebraic[(a + b*x)^n/(x^2*(-a - b*x)^n),x]","\int \frac{(-a-b x)^{-n} (a+b x)^n}{x^2} \, dx","-\frac{(-a-b x)^{-n} (a+b x)^n}{x}",1,"Could not integrate","F",-1
826,0,0,26,0.0459035,"\int \frac{(-a-b x)^{-n} (a+b x)^n}{x^3} \, dx","IntegrateAlgebraic[(a + b*x)^n/(x^3*(-a - b*x)^n),x]","\int \frac{(-a-b x)^{-n} (a+b x)^n}{x^3} \, dx","-\frac{(-a-b x)^{-n} (a+b x)^n}{2 x^2}",1,"Could not integrate","F",-1
827,0,0,34,0.0316463,"\int x^{-m} (-a-b x)^{-n} (a+b x)^n \, dx","IntegrateAlgebraic[(a + b*x)^n/(x^m*(-a - b*x)^n),x]","\int x^{-m} (-a-b x)^{-n} (a+b x)^n \, dx","\frac{x^{1-m} (-a-b x)^{-n} (a+b x)^n}{1-m}",1,"Could not integrate","F",-1
828,1,392,78,2.059319,"\int \frac{x^3 \sqrt{1+x}}{(1-x)^{5/2}} \, dx","IntegrateAlgebraic[(x^3*Sqrt[1 + x])/(1 - x)^(5/2),x]","\frac{\left(\frac{4 \sqrt{1-x}}{3}-\frac{4}{3}\right) \left(\sqrt{x+1}-1\right) \left(3 x^6+3 \sqrt{1-x} \sqrt{x+1} x^5-36 \sqrt{x+1} x^5+111 x^5+312 \sqrt{1-x} x^4-84 \sqrt{1-x} \sqrt{x+1} x^4-144 \sqrt{x+1} x^4+101 x^4+2184 \sqrt{1-x} x^3-879 \sqrt{1-x} \sqrt{x+1} x^3+1308 \sqrt{x+1} x^3-5559 x^3-6760 \sqrt{1-x} x^2-752 \sqrt{1-x} \sqrt{x+1} x^2+6608 \sqrt{x+1} x^2+3572 x^2-9880 \sqrt{1-x} x+15348 \sqrt{1-x} \sqrt{x+1} x-21608 \sqrt{x+1} x+16140 x+13312 \sqrt{1-x}-13048 \sqrt{1-x} \sqrt{x+1}+13312 \sqrt{x+1}-13576\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^4 \left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^3}-22 \tan ^{-1}\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)","\frac{2 \sqrt{x+1} x^3}{3 (1-x)^{3/2}}-\frac{13 \sqrt{x+1} x^2}{3 \sqrt{1-x}}-\frac{1}{6} \sqrt{1-x} \sqrt{x+1} (33 x+52)+\frac{11}{2} \sin ^{-1}(x)",1,"((-4/3 + (4*Sqrt[1 - x])/3)*(-1 + Sqrt[1 + x])*(-13576 + 13312*Sqrt[1 - x] + 16140*x - 9880*Sqrt[1 - x]*x + 3572*x^2 - 6760*Sqrt[1 - x]*x^2 - 5559*x^3 + 2184*Sqrt[1 - x]*x^3 + 101*x^4 + 312*Sqrt[1 - x]*x^4 + 111*x^5 + 3*x^6 + 13312*Sqrt[1 + x] - 13048*Sqrt[1 - x]*Sqrt[1 + x] - 21608*x*Sqrt[1 + x] + 15348*Sqrt[1 - x]*x*Sqrt[1 + x] + 6608*x^2*Sqrt[1 + x] - 752*Sqrt[1 - x]*x^2*Sqrt[1 + x] + 1308*x^3*Sqrt[1 + x] - 879*Sqrt[1 - x]*x^3*Sqrt[1 + x] - 144*x^4*Sqrt[1 + x] - 84*Sqrt[1 - x]*x^4*Sqrt[1 + x] - 36*x^5*Sqrt[1 + x] + 3*Sqrt[1 - x]*x^5*Sqrt[1 + x]))/((-2 + Sqrt[1 - x] + Sqrt[1 + x])^4*(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^3) - 22*ArcTan[(-1 + Sqrt[1 - x])/(-1 + Sqrt[1 + x])]","B",1
829,1,290,61,0.3724021,"\int \frac{x^2 \sqrt{1+x}}{(1-x)^{5/2}} \, dx","IntegrateAlgebraic[(x^2*Sqrt[1 + x])/(1 - x)^(5/2),x]","\frac{\left(\frac{4}{3}-\frac{4 \sqrt{1-x}}{3}\right) \left(\sqrt{x+1}-1\right) \left(-3 x^4-24 \sqrt{1-x} x^3+3 \sqrt{1-x} \sqrt{x+1} x^3+72 x^3+128 \sqrt{1-x} x^2+37 \sqrt{1-x} \sqrt{x+1} x^2-184 \sqrt{x+1} x^2-39 x^2+376 \sqrt{1-x} x-474 \sqrt{1-x} \sqrt{x+1} x+680 \sqrt{x+1} x-582 x-448 \sqrt{1-x}+412 \sqrt{1-x} \sqrt{x+1}-448 \sqrt{x+1}+484\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^2 \left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^3}-12 \tan ^{-1}\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)","\frac{(x+1)^{3/2}}{3 (1-x)^{3/2}}-\sqrt{1-x} \sqrt{x+1}-\frac{4 \sqrt{x+1}}{\sqrt{1-x}}+3 \sin ^{-1}(x)",1,"((4/3 - (4*Sqrt[1 - x])/3)*(-1 + Sqrt[1 + x])*(484 - 448*Sqrt[1 - x] - 582*x + 376*Sqrt[1 - x]*x - 39*x^2 + 128*Sqrt[1 - x]*x^2 + 72*x^3 - 24*Sqrt[1 - x]*x^3 - 3*x^4 - 448*Sqrt[1 + x] + 412*Sqrt[1 - x]*Sqrt[1 + x] + 680*x*Sqrt[1 + x] - 474*Sqrt[1 - x]*x*Sqrt[1 + x] - 184*x^2*Sqrt[1 + x] + 37*Sqrt[1 - x]*x^2*Sqrt[1 + x] + 3*Sqrt[1 - x]*x^3*Sqrt[1 + x]))/((-2 + Sqrt[1 - x] + Sqrt[1 + x])^2*(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^3) - 12*ArcTan[(-1 + Sqrt[1 - x])/(-1 + Sqrt[1 + x])]","B",1
830,1,176,41,0.2052441,"\int \frac{x \sqrt{1+x}}{(1-x)^{5/2}} \, dx","IntegrateAlgebraic[(x*Sqrt[1 + x])/(1 - x)^(5/2),x]","\frac{\left(\frac{4 \sqrt{1-x}}{3}-\frac{4}{3}\right) \left(\sqrt{x+1}-1\right) \left(x^2-10 \sqrt{1-x} x+6 \sqrt{1-x} \sqrt{x+1} x-14 \sqrt{x+1} x+18 x+10 \sqrt{1-x}-7 \sqrt{1-x} \sqrt{x+1}+10 \sqrt{x+1}-13\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^3}-4 \tan ^{-1}\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)","\frac{(x+1)^{3/2}}{3 (1-x)^{3/2}}-\frac{2 \sqrt{x+1}}{\sqrt{1-x}}+\sin ^{-1}(x)",1,"((-4/3 + (4*Sqrt[1 - x])/3)*(-1 + Sqrt[1 + x])*(-13 + 10*Sqrt[1 - x] + 18*x - 10*Sqrt[1 - x]*x + x^2 + 10*Sqrt[1 + x] - 7*Sqrt[1 - x]*Sqrt[1 + x] - 14*x*Sqrt[1 + x] + 6*Sqrt[1 - x]*x*Sqrt[1 + x]))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^3 - 4*ArcTan[(-1 + Sqrt[1 - x])/(-1 + Sqrt[1 + x])]","B",1
831,1,133,20,0.0007593,"\int \frac{\sqrt{1+x}}{(1-x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[1 + x]/(1 - x)^(5/2),x]","\frac{\left(\sqrt{x+1}-1\right)^6 \left(\frac{\left(\sqrt{1-x}-1\right)^5}{2 \left(\sqrt{x+1}-1\right)^5}-\frac{\left(\sqrt{1-x}-1\right)^3}{3 \left(\sqrt{x+1}-1\right)^3}+\frac{\frac{\sqrt{1-x}}{2}-\frac{1}{2}}{\sqrt{x+1}-1}\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^3}","\frac{(x+1)^{3/2}}{3 (1-x)^{3/2}}",1,"((-1 + Sqrt[1 + x])^6*((-1 + Sqrt[1 - x])^5/(2*(-1 + Sqrt[1 + x])^5) - (-1 + Sqrt[1 - x])^3/(3*(-1 + Sqrt[1 + x])^3) + (-1/2 + Sqrt[1 - x]/2)/(-1 + Sqrt[1 + x])))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^3","B",1
832,1,223,18,2.4683783,"\int \frac{\sqrt{1+x}}{(-1+x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[1 + x]/(-1 + x)^(5/2),x]","\frac{\left(\frac{1}{6}-\frac{\sqrt{x-1}}{6}\right) \left(\sqrt{3}-\sqrt{x+1}\right)^6 \left(\frac{9 \left(\sqrt{x-1}-1\right)^4}{\left(\sqrt{3}-\sqrt{x+1}\right)^4}+\frac{24 \sqrt{3} \left(\sqrt{x-1}-1\right)^3}{\left(\sqrt{3}-\sqrt{x+1}\right)^3}+\frac{70 \left(\sqrt{x-1}-1\right)^2}{\left(\sqrt{3}-\sqrt{x+1}\right)^2}+\frac{24 \sqrt{3} \sqrt{x-1}-24 \sqrt{3}}{\sqrt{3}-\sqrt{x+1}}+9\right)}{\left(\sqrt{x+1}-\sqrt{3}\right) \left(-x-2 \sqrt{x-1}+\sqrt{3} \sqrt{x-1} \sqrt{x+1}+1\right)^3}","-\frac{(x+1)^{3/2}}{3 (x-1)^{3/2}}",1,"((1/6 - Sqrt[-1 + x]/6)*(Sqrt[3] - Sqrt[1 + x])^6*(9 + (9*(-1 + Sqrt[-1 + x])^4)/(Sqrt[3] - Sqrt[1 + x])^4 + (24*Sqrt[3]*(-1 + Sqrt[-1 + x])^3)/(Sqrt[3] - Sqrt[1 + x])^3 + (70*(-1 + Sqrt[-1 + x])^2)/(Sqrt[3] - Sqrt[1 + x])^2 + (-24*Sqrt[3] + 24*Sqrt[3]*Sqrt[-1 + x])/(Sqrt[3] - Sqrt[1 + x])))/((-Sqrt[3] + Sqrt[1 + x])*(1 - 2*Sqrt[-1 + x] - x + Sqrt[3]*Sqrt[-1 + x]*Sqrt[1 + x])^3)","B",1
833,1,199,59,0.2321608,"\int \frac{\sqrt{1+x}}{(1-x)^{5/2} x} \, dx","IntegrateAlgebraic[Sqrt[1 + x]/((1 - x)^(5/2)*x),x]","\frac{\left(\frac{4}{3}-\frac{4 \sqrt{1-x}}{3}\right) \left(\sqrt{x+1}-1\right) \left(-x^2-14 \sqrt{1-x} x+6 \sqrt{1-x} \sqrt{x+1} x-10 \sqrt{x+1} x+18 x+14 \sqrt{1-x}-5 \sqrt{1-x} \sqrt{x+1}+14 \sqrt{x+1}-23\right)}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^3}-\log \left(\sqrt{1-x}-1\right)+\log \left(x+\sqrt{1-x}-\sqrt{x+1}\right)-\log \left(\sqrt{x+1}-1\right)","\frac{(x+1)^{3/2}}{3 (1-x)^{3/2}}+\frac{2 \sqrt{x+1}}{\sqrt{1-x}}-\tanh ^{-1}\left(\sqrt{1-x} \sqrt{x+1}\right)",1,"((4/3 - (4*Sqrt[1 - x])/3)*(-1 + Sqrt[1 + x])*(-23 + 14*Sqrt[1 - x] + 18*x - 14*Sqrt[1 - x]*x - x^2 + 14*Sqrt[1 + x] - 5*Sqrt[1 - x]*Sqrt[1 + x] - 10*x*Sqrt[1 + x] + 6*Sqrt[1 - x]*x*Sqrt[1 + x]))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^3 - Log[-1 + Sqrt[1 - x]] + Log[Sqrt[1 - x] + x - Sqrt[1 + x]] - Log[-1 + Sqrt[1 + x]]","B",1
834,1,372,87,0.4036343,"\int \frac{\sqrt{1+x}}{(1-x)^{5/2} x^2} \, dx","IntegrateAlgebraic[Sqrt[1 + x]/((1 - x)^(5/2)*x^2),x]","\frac{\left(\frac{40 \sqrt{1-x}}{3}-\frac{16 \sqrt{x+1}}{3}-8\right) \left(\sqrt{x+1}-1\right)^5}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^3}+\frac{\left(\frac{40 \sqrt{1-x}}{3}-\frac{44 \sqrt{x+1}}{3}+\frac{4}{3}\right) \left(\sqrt{x+1}-1\right)^3}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^2}+\frac{\left(\frac{1}{2}-\frac{\sqrt{1-x}}{2}\right) \left(\sqrt{x+1}-1\right)}{x+\sqrt{1-x}-\sqrt{x+1}}+\frac{\left(10 \sqrt{1-x}-8 \sqrt{x+1}-2\right) \left(\sqrt{x+1}-1\right)}{-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1}+\frac{\frac{\sqrt{x+1}}{4}-\frac{1}{4}}{\sqrt{1-x}-1}+\frac{\frac{1}{4}-\frac{\sqrt{1-x}}{4}}{\sqrt{x+1}-1}-3 \log \left(\sqrt{1-x}-1\right)+3 \log \left(x+\sqrt{1-x}-\sqrt{x+1}\right)-3 \log \left(\sqrt{x+1}-1\right)","\frac{14 \sqrt{x+1}}{3 \sqrt{1-x}}-\frac{5 \sqrt{x+1}}{3 \sqrt{1-x} x}+\frac{2 \sqrt{x+1}}{3 (1-x)^{3/2} x}-3 \tanh ^{-1}\left(\sqrt{1-x} \sqrt{x+1}\right)",1,"(-1/4 + Sqrt[1 + x]/4)/(-1 + Sqrt[1 - x]) + (1/4 - Sqrt[1 - x]/4)/(-1 + Sqrt[1 + x]) + ((1/2 - Sqrt[1 - x]/2)*(-1 + Sqrt[1 + x]))/(Sqrt[1 - x] + x - Sqrt[1 + x]) + ((-8 + (40*Sqrt[1 - x])/3 - (16*Sqrt[1 + x])/3)*(-1 + Sqrt[1 + x])^5)/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^3 + ((4/3 + (40*Sqrt[1 - x])/3 - (44*Sqrt[1 + x])/3)*(-1 + Sqrt[1 + x])^3)/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^2 + ((-2 + 10*Sqrt[1 - x] - 8*Sqrt[1 + x])*(-1 + Sqrt[1 + x]))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x]) - 3*Log[-1 + Sqrt[1 - x]] + 3*Log[Sqrt[1 - x] + x - Sqrt[1 + x]] - 3*Log[-1 + Sqrt[1 + x]]","B",1
835,1,480,112,1.2193635,"\int \frac{\sqrt{1+x}}{(1-x)^{5/2} x^3} \, dx","IntegrateAlgebraic[Sqrt[1 + x]/((1 - x)^(5/2)*x^3),x]","\frac{\left(\frac{40 \sqrt{1-x}}{3}-\frac{16 \sqrt{x+1}}{3}-8\right) \left(\sqrt{x+1}-1\right)^5}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^3}-\frac{\left(\sqrt{x+1}-1\right)^4}{8 \left(x+\sqrt{1-x}-\sqrt{x+1}\right)^2}+\frac{\left(\frac{40 \sqrt{1-x}}{3}-\frac{44 \sqrt{x+1}}{3}+\frac{4}{3}\right) \left(\sqrt{x+1}-1\right)^3}{\left(-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1\right)^2}+\frac{\left(\sqrt{x+1}-1\right)^2}{32 \left(\sqrt{1-x}-1\right)^2}+\frac{\left(14 \sqrt{1-x}-8 \sqrt{x+1}-6\right) \left(\sqrt{x+1}-1\right)}{-x-2 \sqrt{1-x}+\sqrt{1-x} \sqrt{x+1}+1}+\frac{\frac{3 \sqrt{x+1}}{4}-\frac{3}{4}}{\sqrt{1-x}-1}+\frac{\left(\frac{\sqrt{x+1}}{4}-\frac{1}{4}\right) \left(-6 \sqrt{1-x}+\sqrt{x+1}+5\right)}{x+\sqrt{1-x}-\sqrt{x+1}}+\frac{\frac{3}{4}-\frac{3 \sqrt{1-x}}{4}}{\sqrt{x+1}-1}+\frac{\left(\sqrt{1-x}-1\right)^2}{32 \left(\sqrt{x+1}-1\right)^2}-\frac{11}{2} \log \left(\sqrt{1-x}-1\right)+\frac{11}{2} \log \left(x+\sqrt{1-x}-\sqrt{x+1}\right)-\frac{11}{2} \log \left(\sqrt{x+1}-1\right)","-\frac{7 \sqrt{x+1}}{6 \sqrt{1-x} x^2}+\frac{2 \sqrt{x+1}}{3 (1-x)^{3/2} x^2}+\frac{26 \sqrt{x+1}}{3 \sqrt{1-x}}-\frac{19 \sqrt{x+1}}{6 \sqrt{1-x} x}-\frac{11}{2} \tanh ^{-1}\left(\sqrt{1-x} \sqrt{x+1}\right)",1,"(-3/4 + (3*Sqrt[1 + x])/4)/(-1 + Sqrt[1 - x]) + (-1 + Sqrt[1 - x])^2/(32*(-1 + Sqrt[1 + x])^2) + (3/4 - (3*Sqrt[1 - x])/4)/(-1 + Sqrt[1 + x]) + (-1 + Sqrt[1 + x])^2/(32*(-1 + Sqrt[1 - x])^2) - (-1 + Sqrt[1 + x])^4/(8*(Sqrt[1 - x] + x - Sqrt[1 + x])^2) + ((-1/4 + Sqrt[1 + x]/4)*(5 - 6*Sqrt[1 - x] + Sqrt[1 + x]))/(Sqrt[1 - x] + x - Sqrt[1 + x]) + ((-8 + (40*Sqrt[1 - x])/3 - (16*Sqrt[1 + x])/3)*(-1 + Sqrt[1 + x])^5)/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^3 + ((4/3 + (40*Sqrt[1 - x])/3 - (44*Sqrt[1 + x])/3)*(-1 + Sqrt[1 + x])^3)/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x])^2 + ((-6 + 14*Sqrt[1 - x] - 8*Sqrt[1 + x])*(-1 + Sqrt[1 + x]))/(1 - 2*Sqrt[1 - x] - x + Sqrt[1 - x]*Sqrt[1 + x]) - (11*Log[-1 + Sqrt[1 - x]])/2 + (11*Log[Sqrt[1 - x] + x - Sqrt[1 + x]])/2 - (11*Log[-1 + Sqrt[1 + x]])/2","B",1
836,1,204,26,1.3420769,"\int \frac{x^2}{\sqrt{-1+x} \sqrt{1+x}} \, dx","IntegrateAlgebraic[x^2/(Sqrt[-1 + x]*Sqrt[1 + x]),x]","\frac{\sqrt{x+1} \left(-20 x^3-4 x^2+96 x+48\right)+\sqrt{x-1} \sqrt{x+1} \left(-7 x^3-28 x^2+10 x+84\right)+\sqrt{3} \left(4 x^4+14 x^3-18 x^2+\sqrt{x-1} \left(12 x^3+20 x^2-32 x-48\right)-70 x-28\right)}{2 \left(-7 x^2-28 x-14\right)+2 \sqrt{3} \sqrt{x+1} (12 x+8)+\sqrt{x-1} \left(2 (-20 x-24)+2 \sqrt{3} \sqrt{x+1} (4 x+14)\right)}-2 \tanh ^{-1}\left(\frac{\sqrt{3}-\sqrt{x+1}}{\sqrt{x-1}-1}\right)","\frac{1}{2} \sqrt{x-1} \sqrt{x+1} x+\frac{1}{2} \cosh ^{-1}(x)",1,"(Sqrt[1 + x]*(48 + 96*x - 4*x^2 - 20*x^3) + Sqrt[-1 + x]*Sqrt[1 + x]*(84 + 10*x - 28*x^2 - 7*x^3) + Sqrt[3]*(-28 - 70*x - 18*x^2 + 14*x^3 + 4*x^4 + Sqrt[-1 + x]*(-48 - 32*x + 20*x^2 + 12*x^3)))/(2*Sqrt[3]*Sqrt[1 + x]*(8 + 12*x) + 2*(-14 - 28*x - 7*x^2) + Sqrt[-1 + x]*(2*(-24 - 20*x) + 2*Sqrt[3]*Sqrt[1 + x]*(14 + 4*x))) - 2*ArcTanh[(Sqrt[3] - Sqrt[1 + x])/(-1 + Sqrt[-1 + x])]","B",1
837,1,141,15,1.0522377,"\int \frac{x}{\sqrt{-1+x} \sqrt{1+x}} \, dx","IntegrateAlgebraic[x/(Sqrt[-1 + x]*Sqrt[1 + x]),x]","\frac{\left(2 \sqrt{x-1}-2\right) \left(\sqrt{3}-\sqrt{x+1}\right)^4 \left(\frac{\left(\sqrt{x-1}-1\right)^2}{\left(\sqrt{3}-\sqrt{x+1}\right)^2}+\frac{\sqrt{3} \sqrt{x-1}-\sqrt{3}}{\sqrt{3}-\sqrt{x+1}}+1\right)}{\left(\sqrt{x+1}-\sqrt{3}\right) \left(\sqrt{x-1}-\sqrt{3} \sqrt{x+1}+2\right)^2}","\sqrt{x-1} \sqrt{x+1}",1,"((-2 + 2*Sqrt[-1 + x])*(Sqrt[3] - Sqrt[1 + x])^4*(1 + (-1 + Sqrt[-1 + x])^2/(Sqrt[3] - Sqrt[1 + x])^2 + (-Sqrt[3] + Sqrt[3]*Sqrt[-1 + x])/(Sqrt[3] - Sqrt[1 + x])))/((-Sqrt[3] + Sqrt[1 + x])*(2 + Sqrt[-1 + x] - Sqrt[3]*Sqrt[1 + x])^2)","B",1
838,1,30,2,1.0020436,"\int \frac{1}{\sqrt{-1+x} \sqrt{1+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-1 + x]*Sqrt[1 + x]),x]","-4 \tanh ^{-1}\left(\frac{\sqrt{3}-\sqrt{x+1}}{\sqrt{x-1}-1}\right)","\cosh ^{-1}(x)",1,"-4*ArcTanh[(Sqrt[3] - Sqrt[1 + x])/(-1 + Sqrt[-1 + x])]","B",1
839,1,91,16,1.1819384,"\int \frac{1}{\sqrt{-1+x} x \sqrt{1+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-1 + x]*x*Sqrt[1 + x]),x]","-2 \tan ^{-1}\left(\frac{-2 x+\sqrt{x-1} \left(\sqrt{3} \sqrt{x+1}-1\right)+\sqrt{3} \sqrt{x+1}-1}{-\sqrt{x+1} \sqrt{x-1}+\sqrt{3} \sqrt{x-1}+\sqrt{x+1}-\sqrt{3}}\right)","\tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)",1,"-2*ArcTan[(-1 - 2*x + Sqrt[3]*Sqrt[1 + x] + Sqrt[-1 + x]*(-1 + Sqrt[3]*Sqrt[1 + x]))/(-Sqrt[3] + Sqrt[3]*Sqrt[-1 + x] + Sqrt[1 + x] - Sqrt[-1 + x]*Sqrt[1 + x])]","B",1
840,1,141,18,1.0666526,"\int \frac{1}{\sqrt{-1+x} x^2 \sqrt{1+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-1 + x]*x^2*Sqrt[1 + x]),x]","\frac{\left(\sqrt{3}-\sqrt{x+1}\right)^4 \left(\frac{\left(\sqrt{x-1}-1\right)^3}{4 \left(\sqrt{3}-\sqrt{x+1}\right)^3}+\frac{\frac{\sqrt{x-1}}{4}-\frac{1}{4}}{\sqrt{3}-\sqrt{x+1}}\right)}{-2 x^2-2 \sqrt{x-1} x+\sqrt{3} \sqrt{x-1} \sqrt{x+1} x+2 \sqrt{3} \sqrt{x+1} x-3 x}","\frac{\sqrt{x-1} \sqrt{x+1}}{x}",1,"((Sqrt[3] - Sqrt[1 + x])^4*((-1 + Sqrt[-1 + x])^3/(4*(Sqrt[3] - Sqrt[1 + x])^3) + (-1/4 + Sqrt[-1 + x]/4)/(Sqrt[3] - Sqrt[1 + x])))/(-3*x - 2*Sqrt[-1 + x]*x - 2*x^2 + 2*Sqrt[3]*x*Sqrt[1 + x] + Sqrt[3]*Sqrt[-1 + x]*x*Sqrt[1 + x])","B",1
841,1,326,45,1.6873754,"\int \sqrt{-1+x} x^2 \sqrt{1+x} \, dx","IntegrateAlgebraic[Sqrt[-1 + x]*x^2*Sqrt[1 + x],x]","\frac{\sqrt{x+1} \left(-1136 x^7-4752 x^6-1096 x^5+7240 x^4+17296 x^3+55360 x^2+28224 x-18816\right)+\sqrt{x-1} \sqrt{x+1} \left(-194 x^7-3120 x^6-6079 x^5-104 x^4+6992 x^3+38632 x^2+74488 x+32592\right)+\sqrt{3} \left(112 x^8+1800 x^7+3416 x^6-1148 x^5-6678 x^4-23268 x^3-41440 x^2+\sqrt{x-1} \left(656 x^7+3408 x^6+3832 x^5-1192 x^4-10928 x^3-41472 x^2-52416 x-18816\right)-10872 x+10864\right)}{8 \sqrt{3} \sqrt{x+1} \left(328 x^3+1376 x^2+704 x-448\right)+\sqrt{x-1} \left(8 \left(-568 x^3-2944 x^2-3776 x-1344\right)+8 \sqrt{3} \sqrt{x+1} \left(56 x^3+900 x^2+1792 x+776\right)\right)+8 \left(-97 x^4-1560 x^3-3088 x^2-832 x+776\right)}+\frac{1}{2} \tanh ^{-1}\left(\frac{\sqrt{3}-\sqrt{x+1}}{\sqrt{x-1}-1}\right)","\frac{1}{4} (x-1)^{3/2} x (x+1)^{3/2}+\frac{1}{8} \sqrt{x-1} x \sqrt{x+1}-\frac{1}{8} \cosh ^{-1}(x)",1,"(Sqrt[1 + x]*(-18816 + 28224*x + 55360*x^2 + 17296*x^3 + 7240*x^4 - 1096*x^5 - 4752*x^6 - 1136*x^7) + Sqrt[-1 + x]*Sqrt[1 + x]*(32592 + 74488*x + 38632*x^2 + 6992*x^3 - 104*x^4 - 6079*x^5 - 3120*x^6 - 194*x^7) + Sqrt[3]*(10864 - 10872*x - 41440*x^2 - 23268*x^3 - 6678*x^4 - 1148*x^5 + 3416*x^6 + 1800*x^7 + 112*x^8 + Sqrt[-1 + x]*(-18816 - 52416*x - 41472*x^2 - 10928*x^3 - 1192*x^4 + 3832*x^5 + 3408*x^6 + 656*x^7)))/(8*Sqrt[3]*Sqrt[1 + x]*(-448 + 704*x + 1376*x^2 + 328*x^3) + 8*(776 - 832*x - 3088*x^2 - 1560*x^3 - 97*x^4) + Sqrt[-1 + x]*(8*(-1344 - 3776*x - 2944*x^2 - 568*x^3) + 8*Sqrt[3]*Sqrt[1 + x]*(776 + 1792*x + 900*x^2 + 56*x^3))) + ArcTanh[(Sqrt[3] - Sqrt[1 + x])/(-1 + Sqrt[-1 + x])]/2","B",1
842,1,407,18,2.1831403,"\int \sqrt{-1+x} x \sqrt{1+x} \, dx","IntegrateAlgebraic[Sqrt[-1 + x]*x*Sqrt[1 + x],x]","\frac{\left(\frac{\sqrt{x-1}}{24}-\frac{1}{24}\right) \left(\sqrt{3}-\sqrt{x+1}\right)^{12} \left(\frac{9 \left(\sqrt{x-1}-1\right)^{10}}{\left(\sqrt{3}-\sqrt{x+1}\right)^{10}}+\frac{33 \sqrt{3} \left(\sqrt{x-1}-1\right)^9}{\left(\sqrt{3}-\sqrt{x+1}\right)^9}+\frac{181 \left(\sqrt{x-1}-1\right)^8}{\left(\sqrt{3}-\sqrt{x+1}\right)^8}+\frac{228 \sqrt{3} \left(\sqrt{x-1}-1\right)^7}{\left(\sqrt{3}-\sqrt{x+1}\right)^7}+\frac{642 \left(\sqrt{x-1}-1\right)^6}{\left(\sqrt{3}-\sqrt{x+1}\right)^6}+\frac{438 \sqrt{3} \left(\sqrt{x-1}-1\right)^5}{\left(\sqrt{3}-\sqrt{x+1}\right)^5}+\frac{642 \left(\sqrt{x-1}-1\right)^4}{\left(\sqrt{3}-\sqrt{x+1}\right)^4}+\frac{228 \sqrt{3} \left(\sqrt{x-1}-1\right)^3}{\left(\sqrt{3}-\sqrt{x+1}\right)^3}+\frac{181 \left(\sqrt{x-1}-1\right)^2}{\left(\sqrt{3}-\sqrt{x+1}\right)^2}+\frac{33 \sqrt{3} \sqrt{x-1}-33 \sqrt{3}}{\sqrt{3}-\sqrt{x+1}}+9\right)}{\left(\sqrt{x+1}-\sqrt{3}\right) \left(\sqrt{x-1}-\sqrt{3} \sqrt{x+1}+2\right)^6}","\frac{1}{3} (x-1)^{3/2} (x+1)^{3/2}",1,"((-1/24 + Sqrt[-1 + x]/24)*(Sqrt[3] - Sqrt[1 + x])^12*(9 + (9*(-1 + Sqrt[-1 + x])^10)/(Sqrt[3] - Sqrt[1 + x])^10 + (33*Sqrt[3]*(-1 + Sqrt[-1 + x])^9)/(Sqrt[3] - Sqrt[1 + x])^9 + (181*(-1 + Sqrt[-1 + x])^8)/(Sqrt[3] - Sqrt[1 + x])^8 + (228*Sqrt[3]*(-1 + Sqrt[-1 + x])^7)/(Sqrt[3] - Sqrt[1 + x])^7 + (642*(-1 + Sqrt[-1 + x])^6)/(Sqrt[3] - Sqrt[1 + x])^6 + (438*Sqrt[3]*(-1 + Sqrt[-1 + x])^5)/(Sqrt[3] - Sqrt[1 + x])^5 + (642*(-1 + Sqrt[-1 + x])^4)/(Sqrt[3] - Sqrt[1 + x])^4 + (228*Sqrt[3]*(-1 + Sqrt[-1 + x])^3)/(Sqrt[3] - Sqrt[1 + x])^3 + (181*(-1 + Sqrt[-1 + x])^2)/(Sqrt[3] - Sqrt[1 + x])^2 + (-33*Sqrt[3] + 33*Sqrt[3]*Sqrt[-1 + x])/(Sqrt[3] - Sqrt[1 + x])))/((-Sqrt[3] + Sqrt[1 + x])*(2 + Sqrt[-1 + x] - Sqrt[3]*Sqrt[1 + x])^6)","B",1
843,1,204,26,1.2637223,"\int \sqrt{-1+x} \sqrt{1+x} \, dx","IntegrateAlgebraic[Sqrt[-1 + x]*Sqrt[1 + x],x]","\frac{\sqrt{x+1} \left(-20 x^3-4 x^2+96 x+48\right)+\sqrt{x-1} \sqrt{x+1} \left(-7 x^3-28 x^2+10 x+84\right)+\sqrt{3} \left(4 x^4+14 x^3-18 x^2+\sqrt{x-1} \left(12 x^3+20 x^2-32 x-48\right)-70 x-28\right)}{2 \left(-7 x^2-28 x-14\right)+2 \sqrt{3} \sqrt{x+1} (12 x+8)+\sqrt{x-1} \left(2 (-20 x-24)+2 \sqrt{3} \sqrt{x+1} (4 x+14)\right)}+2 \tanh ^{-1}\left(\frac{\sqrt{3}-\sqrt{x+1}}{\sqrt{x-1}-1}\right)","\frac{1}{2} \sqrt{x-1} x \sqrt{x+1}-\frac{1}{2} \cosh ^{-1}(x)",1,"(Sqrt[1 + x]*(48 + 96*x - 4*x^2 - 20*x^3) + Sqrt[-1 + x]*Sqrt[1 + x]*(84 + 10*x - 28*x^2 - 7*x^3) + Sqrt[3]*(-28 - 70*x - 18*x^2 + 14*x^3 + 4*x^4 + Sqrt[-1 + x]*(-48 - 32*x + 20*x^2 + 12*x^3)))/(2*Sqrt[3]*Sqrt[1 + x]*(8 + 12*x) + 2*(-14 - 28*x - 7*x^2) + Sqrt[-1 + x]*(2*(-24 - 20*x) + 2*Sqrt[3]*Sqrt[1 + x]*(14 + 4*x))) + 2*ArcTanh[(Sqrt[3] - Sqrt[1 + x])/(-1 + Sqrt[-1 + x])]","B",1
844,1,191,34,1.2337276,"\int \frac{\sqrt{-1+x} \sqrt{1+x}}{x} \, dx","IntegrateAlgebraic[(Sqrt[-1 + x]*Sqrt[1 + x])/x,x]","\frac{\left(2-2 \sqrt{x-1}\right) \left(\sqrt{3}-\sqrt{x+1}\right) \left(2 x+\sqrt{x-1}-\sqrt{3} \sqrt{x-1} \sqrt{x+1}-\sqrt{3} \sqrt{x+1}+1\right)}{\left(\sqrt{x-1}-\sqrt{3} \sqrt{x+1}+2\right)^2}+2 \tan ^{-1}\left(\frac{-2 x+\sqrt{x-1} \left(\sqrt{3} \sqrt{x+1}-1\right)+\sqrt{3} \sqrt{x+1}-1}{-\sqrt{x+1} \sqrt{x-1}+\sqrt{3} \sqrt{x-1}+\sqrt{x+1}-\sqrt{3}}\right)","\sqrt{x-1} \sqrt{x+1}-\tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)",1,"((2 - 2*Sqrt[-1 + x])*(Sqrt[3] - Sqrt[1 + x])*(1 + Sqrt[-1 + x] + 2*x - Sqrt[3]*Sqrt[1 + x] - Sqrt[3]*Sqrt[-1 + x]*Sqrt[1 + x]))/(2 + Sqrt[-1 + x] - Sqrt[3]*Sqrt[1 + x])^2 + 2*ArcTan[(-1 - 2*x + Sqrt[3]*Sqrt[1 + x] + Sqrt[-1 + x]*(-1 + Sqrt[3]*Sqrt[1 + x]))/(-Sqrt[3] + Sqrt[3]*Sqrt[-1 + x] + Sqrt[1 + x] - Sqrt[-1 + x]*Sqrt[1 + x])]","B",1
845,1,140,22,1.1125804,"\int \frac{\sqrt{-1+x} \sqrt{1+x}}{x^2} \, dx","IntegrateAlgebraic[(Sqrt[-1 + x]*Sqrt[1 + x])/x^2,x]","\frac{\left(\frac{\sqrt{x-1}}{2}-\frac{1}{2}\right) \left(\sqrt{3}-\sqrt{x+1}\right) \left(-x+\sqrt{x-1}+\sqrt{3} \sqrt{x+1}-2\right)}{x \left(-2 x-2 \sqrt{x-1}+\sqrt{3} \sqrt{x-1} \sqrt{x+1}+2 \sqrt{3} \sqrt{x+1}-3\right)}-4 \tanh ^{-1}\left(\frac{\sqrt{3}-\sqrt{x+1}}{\sqrt{x-1}-1}\right)","\cosh ^{-1}(x)-\frac{\sqrt{x-1} \sqrt{x+1}}{x}",1,"((-1/2 + Sqrt[-1 + x]/2)*(Sqrt[3] - Sqrt[1 + x])*(-2 + Sqrt[-1 + x] - x + Sqrt[3]*Sqrt[1 + x]))/(x*(-3 - 2*Sqrt[-1 + x] - 2*x + 2*Sqrt[3]*Sqrt[1 + x] + Sqrt[3]*Sqrt[-1 + x]*Sqrt[1 + x])) - 4*ArcTanh[(Sqrt[3] - Sqrt[1 + x])/(-1 + Sqrt[-1 + x])]","B",1
846,1,34,16,1.045527,"\int \frac{1}{\sqrt{1+2 x} \sqrt{3+2 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 + 2*x]*Sqrt[3 + 2*x]),x]","-2 \tanh ^{-1}\left(\frac{\sqrt{3}-\sqrt{2 x+3}}{\sqrt{2 x+1}-1}\right)","\sinh ^{-1}\left(\frac{\sqrt{2 x+1}}{\sqrt{2}}\right)",1,"-2*ArcTanh[(Sqrt[3] - Sqrt[3 + 2*x])/(-1 + Sqrt[1 + 2*x])]","B",1
847,1,194,35,1.5420023,"\int \frac{1}{x \sqrt{-2+3 x} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[-2 + 3*x]*Sqrt[3 + 5*x]),x]","\text{RootSum}\left[-25 \text{$\#$1}^4+40 \sqrt{2} \text{$\#$1}^3-86 \text{$\#$1}^2+24 \sqrt{2} \text{$\#$1}-9\&,\frac{5 \text{$\#$1}^2 \log \left(2 \sqrt{2}-\sqrt{5 x+3}\right)-5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+2 \sqrt{2} \text{$\#$1}+\sqrt{3 x-2}-1\right)+3 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+2 \sqrt{2} \text{$\#$1}+\sqrt{3 x-2}-1\right)-3 \log \left(2 \sqrt{2}-\sqrt{5 x+3}\right)}{25 \text{$\#$1}^3-30 \sqrt{2} \text{$\#$1}^2+43 \text{$\#$1}-6 \sqrt{2}}\&\right]","\sqrt{\frac{2}{3}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} \sqrt{3 x-2}}{\sqrt{5 x+3}}\right)",1,"RootSum[-9 + 24*Sqrt[2]*#1 - 86*#1^2 + 40*Sqrt[2]*#1^3 - 25*#1^4 & , (-3*Log[2*Sqrt[2] - Sqrt[3 + 5*x]] + 3*Log[-1 + Sqrt[-2 + 3*x] + 2*Sqrt[2]*#1 - Sqrt[3 + 5*x]*#1] + 5*Log[2*Sqrt[2] - Sqrt[3 + 5*x]]*#1^2 - 5*Log[-1 + Sqrt[-2 + 3*x] + 2*Sqrt[2]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[2] + 43*#1 - 30*Sqrt[2]*#1^2 + 25*#1^3) & ]","C",1
848,1,206,35,1.3649681,"\int \frac{1}{(-1+x)^{3/2} x (1+x)^{3/2}} \, dx","IntegrateAlgebraic[1/((-1 + x)^(3/2)*x*(1 + x)^(3/2)),x]","\frac{\sqrt{3} \left(x^2+2 \sqrt{x-1} x-2 x-4\right)+\sqrt{x+1} (8-2 x)-2 \sqrt{x-1} x \sqrt{x+1}}{-3 x^2+\sqrt{3} \sqrt{x+1} (2 x-2)+\sqrt{x-1} \left(-6 x+\sqrt{3} \sqrt{x+1} (2 x+3)-6\right)+3}+2 \tan ^{-1}\left(\frac{-2 x+\sqrt{x-1} \left(\sqrt{3} \sqrt{x+1}-1\right)+\sqrt{3} \sqrt{x+1}-1}{-\sqrt{x+1} \sqrt{x-1}+\sqrt{3} \sqrt{x-1}+\sqrt{x+1}-\sqrt{3}}\right)","-\frac{1}{\sqrt{x-1} \sqrt{x+1}}-\tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)",1,"((8 - 2*x)*Sqrt[1 + x] - 2*Sqrt[-1 + x]*x*Sqrt[1 + x] + Sqrt[3]*(-4 - 2*x + 2*Sqrt[-1 + x]*x + x^2))/(3 - 3*x^2 + Sqrt[3]*Sqrt[1 + x]*(-2 + 2*x) + Sqrt[-1 + x]*(-6 - 6*x + Sqrt[3]*Sqrt[1 + x]*(3 + 2*x))) + 2*ArcTan[(-1 - 2*x + Sqrt[3]*Sqrt[1 + x] + Sqrt[-1 + x]*(-1 + Sqrt[3]*Sqrt[1 + x]))/(-Sqrt[3] + Sqrt[3]*Sqrt[-1 + x] + Sqrt[1 + x] - Sqrt[-1 + x]*Sqrt[1 + x])]","B",1
849,1,161,20,0.434176,"\int \sqrt{1-x} x \sqrt{1+x} \, dx","IntegrateAlgebraic[Sqrt[1 - x]*x*Sqrt[1 + x],x]","\frac{\left(\sqrt{1-x}-1\right)^2 \left(\sqrt{x+1}-1\right)^{10} \left(-\frac{\left(\sqrt{1-x}-1\right)^8}{8 \left(\sqrt{x+1}-1\right)^8}+\frac{\left(\sqrt{1-x}-1\right)^6}{2 \left(\sqrt{x+1}-1\right)^6}-\frac{17 \left(\sqrt{1-x}-1\right)^4}{12 \left(\sqrt{x+1}-1\right)^4}+\frac{\left(\sqrt{1-x}-1\right)^2}{2 \left(\sqrt{x+1}-1\right)^2}-\frac{1}{8}\right)}{\left(\sqrt{1-x}+\sqrt{x+1}-2\right)^6}","-\frac{1}{3} (1-x)^{3/2} (x+1)^{3/2}",1,"((-1 + Sqrt[1 - x])^2*(-1 + Sqrt[1 + x])^10*(-1/8 - (-1 + Sqrt[1 - x])^8/(8*(-1 + Sqrt[1 + x])^8) + (-1 + Sqrt[1 - x])^6/(2*(-1 + Sqrt[1 + x])^6) - (17*(-1 + Sqrt[1 - x])^4)/(12*(-1 + Sqrt[1 + x])^4) + (-1 + Sqrt[1 - x])^2/(2*(-1 + Sqrt[1 + x])^2)))/(-2 + Sqrt[1 - x] + Sqrt[1 + x])^6","B",1
850,1,267,146,2.1695804,"\int x^3 (2+3 x)^{3/2} \sqrt{1+4 x} \, dx","IntegrateAlgebraic[x^3*(2 + 3*x)^(3/2)*Sqrt[1 + 4*x],x]","\frac{\sqrt{3 x+2} \sqrt{4 x+1} \left(106168320 x^5+94666752 x^4+4119552 x^3-1849728 x^2+1089592 x-881613\right) \left(-2985984 x^6-94058496 x^5-550229760 x^4-1266520320 x^3-1380155760 x^2-715575096 x-142365209\right)+\sqrt{5} \sqrt{4 x+1} \left(106168320 x^5+94666752 x^4+4119552 x^3-1849728 x^2+1089592 x-881613\right) \left(17915904 x^6+208521216 x^5+780917760 x^4+1347390720 x^3+1186990560 x^2+520099176 x+90039664\right)}{212336640 \sqrt{5} \sqrt{3 x+2} \left(5971968 x^5+65525760 x^4+216622080 x^3+304715520 x^2+192519840 x+45019832\right)+212336640 \left(-2985984 x^6-94058496 x^5-550229760 x^4-1266520320 x^3-1380155760 x^2-715575096 x-142365209\right)}-\frac{1067875 \tanh ^{-1}\left(\frac{\sqrt{\frac{5}{3}}-\frac{2 \sqrt{3 x+2}}{\sqrt{3}}}{\sqrt{4 x+1}}\right)}{42467328 \sqrt{3}}","\frac{1}{72} x^2 (4 x+1)^{3/2} (3 x+2)^{5/2}+\frac{(4103-7968 x) (4 x+1)^{3/2} (3 x+2)^{5/2}}{829440}-\frac{8543 \sqrt{4 x+1} (3 x+2)^{5/2}}{995328}+\frac{42715 \sqrt{4 x+1} (3 x+2)^{3/2}}{15925248}+\frac{213575 \sqrt{4 x+1} \sqrt{3 x+2}}{42467328}+\frac{1067875 \sinh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{4 x+1}\right)}{84934656 \sqrt{3}}",1,"(Sqrt[2 + 3*x]*Sqrt[1 + 4*x]*(-881613 + 1089592*x - 1849728*x^2 + 4119552*x^3 + 94666752*x^4 + 106168320*x^5)*(-142365209 - 715575096*x - 1380155760*x^2 - 1266520320*x^3 - 550229760*x^4 - 94058496*x^5 - 2985984*x^6) + Sqrt[5]*Sqrt[1 + 4*x]*(-881613 + 1089592*x - 1849728*x^2 + 4119552*x^3 + 94666752*x^4 + 106168320*x^5)*(90039664 + 520099176*x + 1186990560*x^2 + 1347390720*x^3 + 780917760*x^4 + 208521216*x^5 + 17915904*x^6))/(212336640*Sqrt[5]*Sqrt[2 + 3*x]*(45019832 + 192519840*x + 304715520*x^2 + 216622080*x^3 + 65525760*x^4 + 5971968*x^5) + 212336640*(-142365209 - 715575096*x - 1380155760*x^2 - 1266520320*x^3 - 550229760*x^4 - 94058496*x^5 - 2985984*x^6)) - (1067875*ArcTanh[(Sqrt[5/3] - (2*Sqrt[2 + 3*x])/Sqrt[3])/Sqrt[1 + 4*x]])/(42467328*Sqrt[3])","A",1
851,1,51,22,0.3128987,"\int \frac{1}{\sqrt{-1+a+b x} \sqrt{1+a+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]),x]","-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{a+b x-1}-\sqrt{a+b-1}}{\sqrt{a+b+1}-\sqrt{a+b x+1}}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{a+b x-1}}{\sqrt{2}}\right)}{b}",1,"(-4*ArcTanh[(-Sqrt[-1 + a + b] + Sqrt[-1 + a + b*x])/(Sqrt[1 + a + b] - Sqrt[1 + a + b*x])])/b","B",1
852,0,0,75,0.4577075,"\int \frac{1}{\sqrt{x} \sqrt{a-b x} \sqrt{a+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*Sqrt[a - b*x]*Sqrt[a + b*x]),x]","\int \frac{1}{\sqrt{x} \sqrt{a-b x} \sqrt{a+b x}} \, dx","\frac{2 \sqrt{a} \sqrt{1-\frac{b x}{a}} \sqrt{\frac{b x}{a}+1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)\right|-1\right)}{\sqrt{b} \sqrt{a-b x} \sqrt{a+b x}}",1,"Could not integrate","F",-1
853,0,0,77,0.4597587,"\int \frac{1}{\sqrt{-x} \sqrt{a-b x} \sqrt{a+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-x]*Sqrt[a - b*x]*Sqrt[a + b*x]),x]","\int \frac{1}{\sqrt{-x} \sqrt{a-b x} \sqrt{a+b x}} \, dx","-\frac{2 \sqrt{a} \sqrt{1-\frac{b x}{a}} \sqrt{\frac{b x}{a}+1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{-x}}{\sqrt{a}}\right)\right|-1\right)}{\sqrt{b} \sqrt{a-b x} \sqrt{a+b x}}",1,"Could not integrate","F",-1
854,0,0,87,0.6812858,"\int \frac{1}{\sqrt{e x} \sqrt{a-b x} \sqrt{a+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[e*x]*Sqrt[a - b*x]*Sqrt[a + b*x]),x]","\int \frac{1}{\sqrt{e x} \sqrt{a-b x} \sqrt{a+b x}} \, dx","\frac{2 \sqrt{a} \sqrt{1-\frac{b x}{a}} \sqrt{\frac{b x}{a}+1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right)\right|-1\right)}{\sqrt{b} \sqrt{e} \sqrt{a-b x} \sqrt{a+b x}}",1,"Could not integrate","F",-1
855,0,0,30,0.5356883,"\int \frac{1}{\sqrt{x} \sqrt{2-b x} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*Sqrt[2 - b*x]*Sqrt[2 + b*x]),x]","\int \frac{1}{\sqrt{x} \sqrt{2-b x} \sqrt{2+b x}} \, dx","\frac{\sqrt{2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)\right|-1\right)}{\sqrt{b}}",1,"Could not integrate","F",-1
856,0,0,33,0.5008097,"\int \frac{1}{\sqrt{-x} \sqrt{2-b x} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-x]*Sqrt[2 - b*x]*Sqrt[2 + b*x]),x]","\int \frac{1}{\sqrt{-x} \sqrt{2-b x} \sqrt{2+b x}} \, dx","-\frac{\sqrt{2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{-x}}{\sqrt{2}}\right)\right|-1\right)}{\sqrt{b}}",1,"Could not integrate","F",-1
857,0,0,42,0.5982596,"\int \frac{1}{\sqrt{e x} \sqrt{2-b x} \sqrt{2+b x}} \, dx","IntegrateAlgebraic[1/(Sqrt[e*x]*Sqrt[2 - b*x]*Sqrt[2 + b*x]),x]","\int \frac{1}{\sqrt{e x} \sqrt{2-b x} \sqrt{2+b x}} \, dx","\frac{\sqrt{2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{2} \sqrt{e}}\right)\right|-1\right)}{\sqrt{b} \sqrt{e}}",1,"Could not integrate","F",-1
858,0,0,24,0.3922831,"\int \frac{1}{\sqrt{2-3 x} \sqrt{x} \sqrt{2+3 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[2 - 3*x]*Sqrt[x]*Sqrt[2 + 3*x]),x]","\int \frac{1}{\sqrt{2-3 x} \sqrt{x} \sqrt{2+3 x}} \, dx","\sqrt{\frac{2}{3}} F\left(\left.\sin ^{-1}\left(\sqrt{\frac{3}{2}} \sqrt{x}\right)\right|-1\right)",1,"Could not integrate","F",-1
859,0,0,27,0.3032272,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-x} \sqrt{2+3 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[2 - 3*x]*Sqrt[-x]*Sqrt[2 + 3*x]),x]","\int \frac{1}{\sqrt{2-3 x} \sqrt{-x} \sqrt{2+3 x}} \, dx","-\sqrt{\frac{2}{3}} F\left(\left.\sin ^{-1}\left(\sqrt{\frac{3}{2}} \sqrt{-x}\right)\right|-1\right)",1,"Could not integrate","F",-1
860,0,0,36,0.5846259,"\int \frac{1}{\sqrt{2-3 x} \sqrt{e x} \sqrt{2+3 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[2 - 3*x]*Sqrt[e*x]*Sqrt[2 + 3*x]),x]","\int \frac{1}{\sqrt{2-3 x} \sqrt{e x} \sqrt{2+3 x}} \, dx","\frac{\sqrt{\frac{2}{3}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{\frac{3}{2}} \sqrt{e x}}{\sqrt{e}}\right)\right|-1\right)}{\sqrt{e}}",1,"Could not integrate","F",-1
861,0,0,10,0.3744946,"\int \frac{1}{\sqrt{1-x} \sqrt{x} \sqrt{1+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - x]*Sqrt[x]*Sqrt[1 + x]),x]","\int \frac{1}{\sqrt{1-x} \sqrt{x} \sqrt{1+x}} \, dx","2 F\left(\left.\sin ^{-1}\left(\sqrt{x}\right)\right|-1\right)",1,"Could not integrate","F",-1
862,0,0,10,12.4042659,"\int \frac{1}{\sqrt{1+x} \sqrt{x-x^2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 + x]*Sqrt[x - x^2]),x]","\int \frac{1}{\sqrt{1+x} \sqrt{x-x^2}} \, dx","2 F\left(\left.\sin ^{-1}\left(\sqrt{x}\right)\right|-1\right)",1,"Could not integrate","F",-1
863,0,0,33,0.4950032,"\int \frac{1}{\sqrt{b x} \sqrt{1-c x} \sqrt{1+c x}} \, dx","IntegrateAlgebraic[1/(Sqrt[b*x]*Sqrt[1 - c*x]*Sqrt[1 + c*x]),x]","\int \frac{1}{\sqrt{b x} \sqrt{1-c x} \sqrt{1+c x}} \, dx","\frac{2 F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{b x}}{\sqrt{b}}\right)\right|-1\right)}{\sqrt{b} \sqrt{c}}",1,"Could not integrate","F",-1
864,0,0,38,0.8783254,"\int \frac{1}{\sqrt{b x} \sqrt{1-c x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[1/(Sqrt[b*x]*Sqrt[1 - c*x]*Sqrt[1 + d*x]),x]","\int \frac{1}{\sqrt{b x} \sqrt{1-c x} \sqrt{1+d x}} \, dx","\frac{2 F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{b x}}{\sqrt{b}}\right)|-\frac{d}{c}\right)}{\sqrt{b} \sqrt{c}}",1,"Could not integrate","F",-1
865,0,0,10,0.2472388,"\int \frac{\sqrt{1+x}}{\sqrt{1-x} \sqrt{x}} \, dx","IntegrateAlgebraic[Sqrt[1 + x]/(Sqrt[1 - x]*Sqrt[x]),x]","\int \frac{\sqrt{1+x}}{\sqrt{1-x} \sqrt{x}} \, dx","2 E\left(\left.\sin ^{-1}\left(\sqrt{x}\right)\right|-1\right)",1,"Could not integrate","F",-1
866,0,0,10,13.136643,"\int \frac{\sqrt{1+x}}{\sqrt{x-x^2}} \, dx","IntegrateAlgebraic[Sqrt[1 + x]/Sqrt[x - x^2],x]","\int \frac{\sqrt{1+x}}{\sqrt{x-x^2}} \, dx","2 E\left(\left.\sin ^{-1}\left(\sqrt{x}\right)\right|-1\right)",1,"Could not integrate","F",-1
867,0,0,33,0.4171844,"\int \frac{\sqrt{1+c x}}{\sqrt{b x} \sqrt{1-c x}} \, dx","IntegrateAlgebraic[Sqrt[1 + c*x]/(Sqrt[b*x]*Sqrt[1 - c*x]),x]","\int \frac{\sqrt{1+c x}}{\sqrt{b x} \sqrt{1-c x}} \, dx","\frac{2 E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{b x}}{\sqrt{b}}\right)\right|-1\right)}{\sqrt{b} \sqrt{c}}",1,"Could not integrate","F",-1
868,0,0,38,1.0304153,"\int \frac{\sqrt{1+c x}}{\sqrt{b x} \sqrt{1-d x}} \, dx","IntegrateAlgebraic[Sqrt[1 + c*x]/(Sqrt[b*x]*Sqrt[1 - d*x]),x]","\int \frac{\sqrt{1+c x}}{\sqrt{b x} \sqrt{1-d x}} \, dx","\frac{2 E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{b x}}{\sqrt{b}}\right)|-\frac{c}{d}\right)}{\sqrt{b} \sqrt{d}}",1,"Could not integrate","F",-1
869,0,0,24,0.2206134,"\int \frac{\sqrt{1-x}}{\sqrt{x} \sqrt{1+x}} \, dx","IntegrateAlgebraic[Sqrt[1 - x]/(Sqrt[x]*Sqrt[1 + x]),x]","\int \frac{\sqrt{1-x}}{\sqrt{x} \sqrt{1+x}} \, dx","-\frac{2 \sqrt{-x} E\left(\left.\sin ^{-1}\left(\sqrt{-x}\right)\right|-1\right)}{\sqrt{x}}",1,"Could not integrate","F",-1
870,0,0,24,0.7455799,"\int \frac{\sqrt{-1+\frac{1}{x}} \sqrt{\frac{1}{x}} \sqrt{x}}{\sqrt{1+x}} \, dx","IntegrateAlgebraic[(Sqrt[-1 + x^(-1)]*Sqrt[x^(-1)]*Sqrt[x])/Sqrt[1 + x],x]","\int \frac{\sqrt{-1+\frac{1}{x}} \sqrt{\frac{1}{x}} \sqrt{x}}{\sqrt{1+x}} \, dx","-\frac{2 \sqrt{-x} E\left(\left.\sin ^{-1}\left(\sqrt{-x}\right)\right|-1\right)}{\sqrt{x}}",1,"Could not integrate","F",-1
871,0,0,37,0.6998338,"\int \frac{\sqrt{1-c x}}{\sqrt{b x} \sqrt{1+c x}} \, dx","IntegrateAlgebraic[Sqrt[1 - c*x]/(Sqrt[b*x]*Sqrt[1 + c*x]),x]","\int \frac{\sqrt{1-c x}}{\sqrt{b x} \sqrt{1+c x}} \, dx","-\frac{2 E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{b x}}{\sqrt{-b}}\right)\right|-1\right)}{\sqrt{-b} \sqrt{c}}",1,"Could not integrate","F",-1
872,0,0,42,1.0436387,"\int \frac{\sqrt{1-c x}}{\sqrt{b x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[Sqrt[1 - c*x]/(Sqrt[b*x]*Sqrt[1 + d*x]),x]","\int \frac{\sqrt{1-c x}}{\sqrt{b x} \sqrt{1+d x}} \, dx","-\frac{2 E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{b x}}{\sqrt{-b}}\right)|-\frac{c}{d}\right)}{\sqrt{-b} \sqrt{d}}",1,"Could not integrate","F",-1
873,0,0,51,0.4614253,"\int \frac{1}{\sqrt{2-3 x} \sqrt{x} \sqrt{d+e x}} \, dx","IntegrateAlgebraic[1/(Sqrt[2 - 3*x]*Sqrt[x]*Sqrt[d + e*x]),x]","\int \frac{1}{\sqrt{2-3 x} \sqrt{x} \sqrt{d+e x}} \, dx","\frac{2 \sqrt{\frac{e x}{d}+1} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} \sqrt{x}\right)|-\frac{2 e}{3 d}\right)}{\sqrt{3} \sqrt{d+e x}}",1,"Could not integrate","F",-1
874,0,0,51,0.4994327,"\int \frac{\sqrt{d+e x}}{\sqrt{2-3 x} \sqrt{x}} \, dx","IntegrateAlgebraic[Sqrt[d + e*x]/(Sqrt[2 - 3*x]*Sqrt[x]),x]","\int \frac{\sqrt{d+e x}}{\sqrt{2-3 x} \sqrt{x}} \, dx","\frac{2 \sqrt{d+e x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} \sqrt{x}\right)|-\frac{2 e}{3 d}\right)}{\sqrt{3} \sqrt{\frac{e x}{d}+1}}",1,"Could not integrate","F",-1
875,0,0,752,4.0328649,"\int \frac{x^4}{\sqrt[3]{1-x} \sqrt[3]{2-x}} \, dx","IntegrateAlgebraic[x^4/((1 - x)^(1/3)*(2 - x)^(1/3)),x]","\int \frac{x^4}{\sqrt[3]{1-x} \sqrt[3]{2-x}} \, dx","\frac{3}{13} (1-x)^{2/3} (2-x)^{2/3} x^3+\frac{99}{130} (1-x)^{2/3} (2-x)^{2/3} x^2-\frac{891\ 2^{2/3} \sqrt{(3-2 x)^2} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2}}{91 (3-2 x) \sqrt[3]{1-x} \sqrt[3]{2-x} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)}-\frac{594 \sqrt[6]{2} 3^{3/4} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+1\right) \sqrt{\frac{2 \sqrt[3]{2} \left(x^2-3 x+2\right)^{2/3}-2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}-\sqrt{3}+1}{2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{91 (3-2 x) \sqrt{(3-2 x)^2} \sqrt[3]{1-x} \sqrt[3]{2-x} \sqrt{\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}}}+\frac{891 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+1\right) \sqrt{\frac{2 \sqrt[3]{2} \left(x^2-3 x+2\right)^{2/3}-2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}-\sqrt{3}+1}{2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt[3]{2} (3-2 x) \sqrt{(3-2 x)^2} \sqrt[3]{1-x} \sqrt[3]{2-x} \sqrt{\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}}}+\frac{27}{455} (1-x)^{2/3} (2-x)^{2/3} (34 x+89)",1,"Could not integrate","F",-1
876,0,0,727,3.877995,"\int \frac{x^3}{\sqrt[3]{1-x} \sqrt[3]{2-x}} \, dx","IntegrateAlgebraic[x^3/((1 - x)^(1/3)*(2 - x)^(1/3)),x]","\int \frac{x^3}{\sqrt[3]{1-x} \sqrt[3]{2-x}} \, dx","\frac{3}{10} (1-x)^{2/3} (2-x)^{2/3} x^2-\frac{81 \sqrt{(3-2 x)^2} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2}}{7 \sqrt[3]{2} (3-2 x) \sqrt[3]{1-x} \sqrt[3]{2-x} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)}-\frac{27 \sqrt[6]{2} 3^{3/4} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+1\right) \sqrt{\frac{2 \sqrt[3]{2} \left(x^2-3 x+2\right)^{2/3}-2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}-\sqrt{3}+1}{2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7 (3-2 x) \sqrt{(3-2 x)^2} \sqrt[3]{1-x} \sqrt[3]{2-x} \sqrt{\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}}}+\frac{81 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+1\right) \sqrt{\frac{2 \sqrt[3]{2} \left(x^2-3 x+2\right)^{2/3}-2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}-\sqrt{3}+1}{2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{14 \sqrt[3]{2} (3-2 x) \sqrt{(3-2 x)^2} \sqrt[3]{1-x} \sqrt[3]{2-x} \sqrt{\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}}}+\frac{9}{70} (1-x)^{2/3} (2-x)^{2/3} (8 x+23)",1,"Could not integrate","F",-1
877,0,0,720,3.8692453,"\int \frac{x^2}{\sqrt[3]{1-x} \sqrt[3]{2-x}} \, dx","IntegrateAlgebraic[x^2/((1 - x)^(1/3)*(2 - x)^(1/3)),x]","\int \frac{x^2}{\sqrt[3]{1-x} \sqrt[3]{2-x}} \, dx","-\frac{99 \sqrt{(3-2 x)^2} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2}}{14 \sqrt[3]{2} (3-2 x) \sqrt[3]{1-x} \sqrt[3]{2-x} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)}-\frac{33\ 3^{3/4} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+1\right) \sqrt{\frac{2 \sqrt[3]{2} \left(x^2-3 x+2\right)^{2/3}-2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}-\sqrt{3}+1}{2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7\ 2^{5/6} (3-2 x) \sqrt{(3-2 x)^2} \sqrt[3]{1-x} \sqrt[3]{2-x} \sqrt{\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}}}+\frac{99 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+1\right) \sqrt{\frac{2 \sqrt[3]{2} \left(x^2-3 x+2\right)^{2/3}-2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}-\sqrt{3}+1}{2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{28 \sqrt[3]{2} (3-2 x) \sqrt{(3-2 x)^2} \sqrt[3]{1-x} \sqrt[3]{2-x} \sqrt{\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}}}+\frac{3}{7} (1-x)^{2/3} (2-x)^{2/3} x+\frac{45}{28} (1-x)^{2/3} (2-x)^{2/3}",1,"Could not integrate","F",-1
878,0,0,695,3.524736,"\int \frac{x}{\sqrt[3]{1-x} \sqrt[3]{2-x}} \, dx","IntegrateAlgebraic[x/((1 - x)^(1/3)*(2 - x)^(1/3)),x]","\int \frac{x}{\sqrt[3]{1-x} \sqrt[3]{2-x}} \, dx","-\frac{9 \sqrt{(3-2 x)^2} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2}}{2 \sqrt[3]{2} (3-2 x) \sqrt[3]{1-x} \sqrt[3]{2-x} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)}-\frac{3\ 3^{3/4} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+1\right) \sqrt{\frac{2 \sqrt[3]{2} \left(x^2-3 x+2\right)^{2/3}-2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}-\sqrt{3}+1}{2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2^{5/6} (3-2 x) \sqrt{(3-2 x)^2} \sqrt[3]{1-x} \sqrt[3]{2-x} \sqrt{\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}}}+\frac{9 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+1\right) \sqrt{\frac{2 \sqrt[3]{2} \left(x^2-3 x+2\right)^{2/3}-2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}-\sqrt{3}+1}{2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt[3]{2} (3-2 x) \sqrt{(3-2 x)^2} \sqrt[3]{1-x} \sqrt[3]{2-x} \sqrt{\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}}}+\frac{3}{4} (1-x)^{2/3} (2-x)^{2/3}",1,"Could not integrate","F",-1
879,0,0,671,3.4938841,"\int \frac{1}{\sqrt[3]{1-x} \sqrt[3]{2-x}} \, dx","IntegrateAlgebraic[1/((1 - x)^(1/3)*(2 - x)^(1/3)),x]","\int \frac{1}{\sqrt[3]{1-x} \sqrt[3]{2-x}} \, dx","-\frac{3 \sqrt{(3-2 x)^2} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2}}{\sqrt[3]{2} (3-2 x) \sqrt[3]{1-x} \sqrt[3]{2-x} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)}-\frac{\sqrt[6]{2} 3^{3/4} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+1\right) \sqrt{\frac{2 \sqrt[3]{2} \left(x^2-3 x+2\right)^{2/3}-2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}-\sqrt{3}+1}{2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{(3-2 x) \sqrt{(3-2 x)^2} \sqrt[3]{1-x} \sqrt[3]{2-x} \sqrt{\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}}}+\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+1\right) \sqrt{\frac{2 \sqrt[3]{2} \left(x^2-3 x+2\right)^{2/3}-2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}-\sqrt{3}+1}{2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[3]{2} (3-2 x) \sqrt{(3-2 x)^2} \sqrt[3]{1-x} \sqrt[3]{2-x} \sqrt{\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}}}",1,"Could not integrate","F",-1
880,1,158,99,0.3082752,"\int \frac{1}{\sqrt[3]{1-x} \sqrt[3]{2-x} x} \, dx","IntegrateAlgebraic[1/((1 - x)^(1/3)*(2 - x)^(1/3)*x),x]","\frac{\log \left(2 \sqrt[3]{1-x}-\sqrt[3]{2} (2-x)^{2/3}\right)}{2 \sqrt[3]{2}}-\frac{\log \left(2^{2/3} (2-x)^{4/3}+2 \sqrt[3]{2} \sqrt[3]{1-x} (2-x)^{2/3}+4 (1-x)^{2/3}\right)}{4 \sqrt[3]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{1-x}}{\sqrt[3]{2} (2-x)^{2/3}+\sqrt[3]{1-x}}\right)}{2 \sqrt[3]{2}}","\frac{3 \log \left(\frac{(2-x)^{2/3}}{2^{2/3}}-\sqrt[3]{1-x}\right)}{4 \sqrt[3]{2}}-\frac{\log (x)}{2 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{2} (2-x)^{2/3}}{\sqrt{3} \sqrt[3]{1-x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{2}}",1,"(Sqrt[3]*ArcTan[(Sqrt[3]*(1 - x)^(1/3))/((1 - x)^(1/3) + 2^(1/3)*(2 - x)^(2/3))])/(2*2^(1/3)) + Log[2*(1 - x)^(1/3) - 2^(1/3)*(2 - x)^(2/3)]/(2*2^(1/3)) - Log[4*(1 - x)^(2/3) + 2*2^(1/3)*(1 - x)^(1/3)*(2 - x)^(2/3) + 2^(2/3)*(2 - x)^(4/3)]/(4*2^(1/3))","A",1
881,0,0,796,13.3740291,"\int \frac{1}{\sqrt[3]{1-x} \sqrt[3]{2-x} x^2} \, dx","IntegrateAlgebraic[1/((1 - x)^(1/3)*(2 - x)^(1/3)*x^2),x]","\int \frac{1}{\sqrt[3]{1-x} \sqrt[3]{2-x} x^2} \, dx","-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{2} (2-x)^{2/3}}{\sqrt{3} \sqrt[3]{1-x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{2}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+1\right) \sqrt{\frac{2 \sqrt[3]{2} \left(x^2-3 x+2\right)^{2/3}-2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}-\sqrt{3}+1}{2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt[3]{2} (3-2 x) \sqrt{(3-2 x)^2} \sqrt[3]{1-x} \sqrt[3]{2-x} \sqrt{\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}}}-\frac{\sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+1\right) \sqrt{\frac{2 \sqrt[3]{2} \left(x^2-3 x+2\right)^{2/3}-2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}-\sqrt{3}+1}{2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2^{5/6} \sqrt[4]{3} (3-2 x) \sqrt{(3-2 x)^2} \sqrt[3]{1-x} \sqrt[3]{2-x} \sqrt{\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}}}+\frac{3 \log \left(\frac{(2-x)^{2/3}}{2^{2/3}}-\sqrt[3]{1-x}\right)}{8 \sqrt[3]{2}}-\frac{\log (x)}{4 \sqrt[3]{2}}-\frac{(1-x)^{2/3} (2-x)^{2/3}}{2 x}-\frac{\sqrt{(3-2 x)^2} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2}}{2 \sqrt[3]{2} (3-2 x) \sqrt[3]{1-x} \sqrt[3]{2-x} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)}",1,"Could not integrate","F",-1
882,0,0,821,18.4111058,"\int \frac{1}{\sqrt[3]{1-x} \sqrt[3]{2-x} x^3} \, dx","IntegrateAlgebraic[1/((1 - x)^(1/3)*(2 - x)^(1/3)*x^3),x]","\int \frac{1}{\sqrt[3]{1-x} \sqrt[3]{2-x} x^3} \, dx","-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2} (2-x)^{2/3}}{\sqrt{3} \sqrt[3]{1-x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+1\right) \sqrt{\frac{2 \sqrt[3]{2} \left(x^2-3 x+2\right)^{2/3}-2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}-\sqrt{3}+1}{2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt[3]{2} (3-2 x) \sqrt{(3-2 x)^2} \sqrt[3]{1-x} \sqrt[3]{2-x} \sqrt{\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}}}-\frac{\sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+1\right) \sqrt{\frac{2 \sqrt[3]{2} \left(x^2-3 x+2\right)^{2/3}-2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}-\sqrt{3}+1}{2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2^{5/6} \sqrt[4]{3} (3-2 x) \sqrt{(3-2 x)^2} \sqrt[3]{1-x} \sqrt[3]{2-x} \sqrt{\frac{2^{2/3} \sqrt[3]{x^2-3 x+2}+1}{\left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)^2}}}+\frac{\log \left(\frac{(2-x)^{2/3}}{2^{2/3}}-\sqrt[3]{1-x}\right)}{4 \sqrt[3]{2}}-\frac{\log (x)}{6 \sqrt[3]{2}}-\frac{(1-x)^{2/3} (2-x)^{2/3}}{2 x}-\frac{\sqrt{(3-2 x)^2} \sqrt{(2 x-3)^2} \sqrt[3]{x^2-3 x+2}}{2 \sqrt[3]{2} (3-2 x) \sqrt[3]{1-x} \sqrt[3]{2-x} \left(2^{2/3} \sqrt[3]{x^2-3 x+2}+\sqrt{3}+1\right)}-\frac{(1-x)^{2/3} (2-x)^{2/3}}{4 x^2}",1,"Could not integrate","F",-1
883,0,0,340,11.2671776,"\int \frac{x^3 \sqrt[4]{a+b x}}{\sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[(x^3*(a + b*x)^(1/4))/(c + d*x)^(1/4),x]","\int \frac{x^3 \sqrt[4]{a+b x}}{\sqrt[4]{c+d x}} \, dx","\frac{(a+b x)^{5/4} (c+d x)^{3/4} \left(77 a^2 d^2-8 b d x (11 a d+13 b c)+94 a b c d+117 b^2 c^2\right)}{384 b^3 d^3}-\frac{\sqrt[4]{a+b x} (c+d x)^{3/4} \left(77 a^3 d^3+105 a^2 b c d^2+135 a b^2 c^2 d+195 b^3 c^3\right)}{512 b^3 d^4}+\frac{(b c-a d) \left(77 a^3 d^3+105 a^2 b c d^2+135 a b^2 c^2 d+195 b^3 c^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{1024 b^{15/4} d^{17/4}}+\frac{(b c-a d) \left(77 a^3 d^3+105 a^2 b c d^2+135 a b^2 c^2 d+195 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{1024 b^{15/4} d^{17/4}}+\frac{x^2 (a+b x)^{5/4} (c+d x)^{3/4}}{4 b d}",1,"Could not integrate","F",-1
884,0,0,268,10.2103838,"\int \frac{x^2 \sqrt[4]{a+b x}}{\sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[(x^2*(a + b*x)^(1/4))/(c + d*x)^(1/4),x]","\int \frac{x^2 \sqrt[4]{a+b x}}{\sqrt[4]{c+d x}} \, dx","\frac{\sqrt[4]{a+b x} (c+d x)^{3/4} \left(7 a^2 d^2+10 a b c d+15 b^2 c^2\right)}{32 b^2 d^3}-\frac{(b c-a d) \left(7 a^2 d^2+10 a b c d+15 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{64 b^{11/4} d^{13/4}}-\frac{(b c-a d) \left(7 a^2 d^2+10 a b c d+15 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{64 b^{11/4} d^{13/4}}-\frac{(a+b x)^{5/4} (c+d x)^{3/4} (7 a d+9 b c)}{24 b^2 d^2}+\frac{x (a+b x)^{5/4} (c+d x)^{3/4}}{3 b d}",1,"Could not integrate","F",-1
885,0,0,188,9.296111,"\int \frac{x \sqrt[4]{a+b x}}{\sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[(x*(a + b*x)^(1/4))/(c + d*x)^(1/4),x]","\int \frac{x \sqrt[4]{a+b x}}{\sqrt[4]{c+d x}} \, dx","\frac{(b c-a d) (3 a d+5 b c) \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 b^{7/4} d^{9/4}}+\frac{(b c-a d) (3 a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 b^{7/4} d^{9/4}}-\frac{\sqrt[4]{a+b x} (c+d x)^{3/4} (3 a d+5 b c)}{8 b d^2}+\frac{(a+b x)^{5/4} (c+d x)^{3/4}}{2 b d}",1,"Could not integrate","F",-1
886,0,0,127,0.0005937,"\int \frac{\sqrt[4]{a+b x}}{\sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/4)/(c + d*x)^(1/4),x]","\int \frac{\sqrt[4]{a+b x}}{\sqrt[4]{c+d x}} \, dx","-\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 b^{3/4} d^{5/4}}-\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 b^{3/4} d^{5/4}}+\frac{\sqrt[4]{a+b x} (c+d x)^{3/4}}{d}",1,"Could not integrate","F",-1
887,0,0,169,14.9331044,"\int \frac{\sqrt[4]{a+b x}}{x \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/4)/(x*(c + d*x)^(1/4)),x]","\int \frac{\sqrt[4]{a+b x}}{x \sqrt[4]{c+d x}} \, dx","-\frac{2 \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{\sqrt[4]{c}}+\frac{2 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{\sqrt[4]{d}}-\frac{2 \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{\sqrt[4]{c}}+\frac{2 \sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{\sqrt[4]{d}}",1,"Could not integrate","F",-1
888,1,173,131,5.3792112,"\int \frac{\sqrt[4]{a+b x}}{x^2 \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/4)/(x^2*(c + d*x)^(1/4)),x]","\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{c+d x}}{\sqrt[4]{c} \sqrt[4]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}}\right)}{2 a^{3/4} c^{5/4}}+\frac{(a d-b c) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{2 a^{3/4} c^{5/4}}-\frac{(c+d x)^{3/4} \sqrt[4]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}}{c x}","-\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{2 a^{3/4} c^{5/4}}-\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{2 a^{3/4} c^{5/4}}-\frac{\sqrt[4]{a+b x} (c+d x)^{3/4}}{c x}",1,"-(((c + d*x)^(3/4)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/4))/(c*x)) + ((b*c - a*d)*ArcTan[(a^(1/4)*(c + d*x)^(1/4))/(c^(1/4)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/4))])/(2*a^(3/4)*c^(5/4)) + ((-(b*c) + a*d)*ArcTanh[(c^(1/4)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))])/(2*a^(3/4)*c^(5/4))","A",1
889,0,0,194,24.6907359,"\int \frac{\sqrt[4]{a+b x}}{x^3 \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/4)/(x^3*(c + d*x)^(1/4)),x]","\int \frac{\sqrt[4]{a+b x}}{x^3 \sqrt[4]{c+d x}} \, dx","\frac{(b c-a d) (5 a d+3 b c) \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{16 a^{7/4} c^{9/4}}+\frac{(b c-a d) (5 a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{16 a^{7/4} c^{9/4}}+\frac{\sqrt[4]{a+b x} (c+d x)^{3/4} (5 a d+3 b c)}{8 a c^2 x}-\frac{(a+b x)^{5/4} (c+d x)^{3/4}}{2 a c x^2}",1,"Could not integrate","F",-1
890,0,0,266,25.4827802,"\int \frac{\sqrt[4]{a+b x}}{x^4 \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/4)/(x^4*(c + d*x)^(1/4)),x]","\int \frac{\sqrt[4]{a+b x}}{x^4 \sqrt[4]{c+d x}} \, dx","\frac{\sqrt[4]{a+b x} (c+d x)^{3/4} (7 b c-15 a d) (3 a d+b c)}{96 a^2 c^3 x}-\frac{(b c-a d) \left(15 a^2 d^2+10 a b c d+7 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{64 a^{11/4} c^{13/4}}-\frac{(b c-a d) \left(15 a^2 d^2+10 a b c d+7 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{64 a^{11/4} c^{13/4}}-\frac{\sqrt[4]{a+b x} (c+d x)^{3/4} (b c-9 a d)}{24 a c^2 x^2}-\frac{\sqrt[4]{a+b x} (c+d x)^{3/4}}{3 c x^3}",1,"Could not integrate","F",-1
891,0,0,368,26.8096213,"\int \frac{\sqrt[4]{a+b x}}{x^5 \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/4)/(x^5*(c + d*x)^(1/4)),x]","\int \frac{\sqrt[4]{a+b x}}{x^5 \sqrt[4]{c+d x}} \, dx","\frac{\sqrt[4]{a+b x} (c+d x)^{3/4} \left(-117 a^2 d^2+10 a b c d+11 b^2 c^2\right)}{384 a^2 c^3 x^2}-\frac{\sqrt[4]{a+b x} (c+d x)^{3/4} \left(-585 a^3 d^3+63 a^2 b c d^2+61 a b^2 c^2 d+77 b^3 c^3\right)}{1536 a^3 c^4 x}+\frac{(b c-a d) \left(195 a^3 d^3+135 a^2 b c d^2+105 a b^2 c^2 d+77 b^3 c^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{1024 a^{15/4} c^{17/4}}+\frac{(b c-a d) \left(195 a^3 d^3+135 a^2 b c d^2+105 a b^2 c^2 d+77 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{1024 a^{15/4} c^{17/4}}-\frac{\sqrt[4]{a+b x} (c+d x)^{3/4} (b c-13 a d)}{48 a c^2 x^3}-\frac{\sqrt[4]{a+b x} (c+d x)^{3/4}}{4 c x^4}",1,"Could not integrate","F",-1
892,1,146,234,0.383345,"\int \frac{x^2 \sqrt[4]{1+x}}{\sqrt[4]{1-x}} \, dx","IntegrateAlgebraic[(x^2*(1 + x)^(1/4))/(1 - x)^(1/4),x]","\frac{1}{24} (1-x)^{3/4} \left(-8 (x+1)^{9/4}+6 (x+1)^{5/4}-9 \sqrt[4]{x+1}\right)+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-x} \sqrt[4]{x+1}}{\sqrt{1-x}-\sqrt{x+1}}\right)}{8 \sqrt{2}}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-x} \sqrt[4]{x+1}}{\sqrt{1-x}+\sqrt{x+1}}\right)}{8 \sqrt{2}}","-\frac{1}{3} (1-x)^{3/4} x (x+1)^{5/4}-\frac{1}{12} (1-x)^{3/4} (x+1)^{5/4}-\frac{3}{8} (1-x)^{3/4} \sqrt[4]{x+1}-\frac{3 \log \left(\frac{\sqrt{1-x}}{\sqrt{x+1}}-\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)}{16 \sqrt{2}}+\frac{3 \log \left(\frac{\sqrt{1-x}}{\sqrt{x+1}}+\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)}{16 \sqrt{2}}+\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}\right)}{8 \sqrt{2}}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)}{8 \sqrt{2}}",1,"((1 - x)^(3/4)*(-9*(1 + x)^(1/4) + 6*(1 + x)^(5/4) - 8*(1 + x)^(9/4)))/24 + (3*ArcTan[(Sqrt[2]*(1 - x)^(1/4)*(1 + x)^(1/4))/(Sqrt[1 - x] - Sqrt[1 + x])])/(8*Sqrt[2]) + (3*ArcTanh[(Sqrt[2]*(1 - x)^(1/4)*(1 + x)^(1/4))/(Sqrt[1 - x] + Sqrt[1 + x])])/(8*Sqrt[2])","A",1
893,1,137,213,0.3141053,"\int \frac{x \sqrt[4]{1+x}}{\sqrt[4]{1-x}} \, dx","IntegrateAlgebraic[(x*(1 + x)^(1/4))/(1 - x)^(1/4),x]","\frac{1}{4} (1-x)^{3/4} \left(-2 (x+1)^{5/4}-\sqrt[4]{x+1}\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-x} \sqrt[4]{x+1}}{\sqrt{1-x}-\sqrt{x+1}}\right)}{4 \sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-x} \sqrt[4]{x+1}}{\sqrt{1-x}+\sqrt{x+1}}\right)}{4 \sqrt{2}}","-\frac{1}{2} (1-x)^{3/4} (x+1)^{5/4}-\frac{1}{4} (1-x)^{3/4} \sqrt[4]{x+1}-\frac{\log \left(\frac{\sqrt{1-x}}{\sqrt{x+1}}-\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)}{8 \sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-x}}{\sqrt{x+1}}+\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)}{8 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)}{4 \sqrt{2}}",1,"((1 - x)^(3/4)*(-(1 + x)^(1/4) - 2*(1 + x)^(5/4)))/4 + ArcTan[(Sqrt[2]*(1 - x)^(1/4)*(1 + x)^(1/4))/(Sqrt[1 - x] - Sqrt[1 + x])]/(4*Sqrt[2]) + ArcTanh[(Sqrt[2]*(1 - x)^(1/4)*(1 + x)^(1/4))/(Sqrt[1 - x] + Sqrt[1 + x])]/(4*Sqrt[2])","A",1
894,1,117,186,0.4795151,"\int \frac{\sqrt[4]{1+x}}{\sqrt[4]{1-x}} \, dx","IntegrateAlgebraic[(1 + x)^(1/4)/(1 - x)^(1/4),x]","-(1-x)^{3/4} \sqrt[4]{x+1}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-x} \sqrt[4]{x+1}}{\sqrt{1-x}-\sqrt{x+1}}\right)}{\sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-x} \sqrt[4]{x+1}}{\sqrt{1-x}+\sqrt{x+1}}\right)}{\sqrt{2}}","-(1-x)^{3/4} \sqrt[4]{x+1}-\frac{\log \left(\frac{\sqrt{1-x}}{\sqrt{x+1}}-\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)}{2 \sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-x}}{\sqrt{x+1}}+\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)}{\sqrt{2}}",1,"-((1 - x)^(3/4)*(1 + x)^(1/4)) + ArcTan[(Sqrt[2]*(1 - x)^(1/4)*(1 + x)^(1/4))/(Sqrt[1 - x] - Sqrt[1 + x])]/Sqrt[2] + ArcTanh[(Sqrt[2]*(1 - x)^(1/4)*(1 + x)^(1/4))/(Sqrt[1 - x] + Sqrt[1 + x])]/Sqrt[2]","A",1
895,1,149,203,0.3088109,"\int \frac{\sqrt[4]{1+x}}{\sqrt[4]{1-x} x} \, dx","IntegrateAlgebraic[(1 + x)^(1/4)/((1 - x)^(1/4)*x),x]","2 \tan ^{-1}\left(\frac{(1-x)^{3/4} \sqrt[4]{x+1}}{x-1}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-x} \sqrt[4]{x+1}}{\sqrt{1-x}-\sqrt{x+1}}\right)+2 \tanh ^{-1}\left(\frac{(1-x)^{3/4} \sqrt[4]{x+1}}{x-1}\right)+\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-x} \sqrt[4]{x+1}}{\sqrt{1-x}+\sqrt{x+1}}\right)","-\frac{\log \left(\frac{\sqrt{1-x}}{\sqrt{x+1}}-\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-x}}{\sqrt{x+1}}+\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)}{\sqrt{2}}-2 \tan ^{-1}\left(\frac{\sqrt[4]{x+1}}{\sqrt[4]{1-x}}\right)+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-x}}{\sqrt[4]{x+1}}+1\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{x+1}}{\sqrt[4]{1-x}}\right)",1,"2*ArcTan[((1 - x)^(3/4)*(1 + x)^(1/4))/(-1 + x)] + Sqrt[2]*ArcTan[(Sqrt[2]*(1 - x)^(1/4)*(1 + x)^(1/4))/(Sqrt[1 - x] - Sqrt[1 + x])] + 2*ArcTanh[((1 - x)^(3/4)*(1 + x)^(1/4))/(-1 + x)] + Sqrt[2]*ArcTanh[(Sqrt[2]*(1 - x)^(1/4)*(1 + x)^(1/4))/(Sqrt[1 - x] + Sqrt[1 + x])]","A",1
896,1,68,62,0.2340959,"\int \frac{\sqrt[4]{1+x}}{\sqrt[4]{1-x} x^2} \, dx","IntegrateAlgebraic[(1 + x)^(1/4)/((1 - x)^(1/4)*x^2),x]","-\frac{(1-x)^{3/4} \sqrt[4]{x+1}}{x}+\tan ^{-1}\left(\frac{(1-x)^{3/4} \sqrt[4]{x+1}}{x-1}\right)+\tanh ^{-1}\left(\frac{(1-x)^{3/4} \sqrt[4]{x+1}}{x-1}\right)","-\frac{(1-x)^{3/4} \sqrt[4]{x+1}}{x}-\tan ^{-1}\left(\frac{\sqrt[4]{x+1}}{\sqrt[4]{1-x}}\right)-\tanh ^{-1}\left(\frac{\sqrt[4]{x+1}}{\sqrt[4]{1-x}}\right)",1,"-(((1 - x)^(3/4)*(1 + x)^(1/4))/x) + ArcTan[((1 - x)^(3/4)*(1 + x)^(1/4))/(-1 + x)] + ArcTanh[((1 - x)^(3/4)*(1 + x)^(1/4))/(-1 + x)]","A",1
897,1,88,91,0.2792519,"\int \frac{\sqrt[4]{1+x}}{\sqrt[4]{1-x} x^3} \, dx","IntegrateAlgebraic[(1 + x)^(1/4)/((1 - x)^(1/4)*x^3),x]","\frac{(1-x)^{3/4} \left(\sqrt[4]{x+1}-3 (x+1)^{5/4}\right)}{4 x^2}+\frac{1}{4} \tan ^{-1}\left(\frac{(1-x)^{3/4} \sqrt[4]{x+1}}{x-1}\right)+\frac{1}{4} \tanh ^{-1}\left(\frac{(1-x)^{3/4} \sqrt[4]{x+1}}{x-1}\right)","-\frac{(1-x)^{3/4} (x+1)^{5/4}}{2 x^2}-\frac{(1-x)^{3/4} \sqrt[4]{x+1}}{4 x}-\frac{1}{4} \tan ^{-1}\left(\frac{\sqrt[4]{x+1}}{\sqrt[4]{1-x}}\right)-\frac{1}{4} \tanh ^{-1}\left(\frac{\sqrt[4]{x+1}}{\sqrt[4]{1-x}}\right)",1,"((1 - x)^(3/4)*((1 + x)^(1/4) - 3*(1 + x)^(5/4)))/(4*x^2) + ArcTan[((1 - x)^(3/4)*(1 + x)^(1/4))/(-1 + x)]/4 + ArcTanh[((1 - x)^(3/4)*(1 + x)^(1/4))/(-1 + x)]/4","A",1
898,1,99,114,0.3274714,"\int \frac{\sqrt[4]{1+x}}{\sqrt[4]{1-x} x^4} \, dx","IntegrateAlgebraic[(1 + x)^(1/4)/((1 - x)^(1/4)*x^4),x]","\frac{(1-x)^{3/4} \left(-11 (x+1)^{9/4}+12 (x+1)^{5/4}-9 \sqrt[4]{x+1}\right)}{24 x^3}+\frac{3}{8} \tan ^{-1}\left(\frac{(1-x)^{3/4} \sqrt[4]{x+1}}{x-1}\right)+\frac{3}{8} \tanh ^{-1}\left(\frac{(1-x)^{3/4} \sqrt[4]{x+1}}{x-1}\right)","-\frac{(1-x)^{3/4} \sqrt[4]{x+1}}{3 x^3}-\frac{5 (1-x)^{3/4} \sqrt[4]{x+1}}{12 x^2}-\frac{11 (1-x)^{3/4} \sqrt[4]{x+1}}{24 x}-\frac{3}{8} \tan ^{-1}\left(\frac{\sqrt[4]{x+1}}{\sqrt[4]{1-x}}\right)-\frac{3}{8} \tanh ^{-1}\left(\frac{\sqrt[4]{x+1}}{\sqrt[4]{1-x}}\right)",1,"((1 - x)^(3/4)*(-9*(1 + x)^(1/4) + 12*(1 + x)^(5/4) - 11*(1 + x)^(9/4)))/(24*x^3) + (3*ArcTan[((1 - x)^(3/4)*(1 + x)^(1/4))/(-1 + x)])/8 + (3*ArcTanh[((1 - x)^(3/4)*(1 + x)^(1/4))/(-1 + x)])/8","A",1
899,1,108,137,0.3500981,"\int \frac{\sqrt[4]{1+x}}{\sqrt[4]{1-x} x^5} \, dx","IntegrateAlgebraic[(1 + x)^(1/4)/((1 - x)^(1/4)*x^5),x]","\frac{(1-x)^{3/4} \left(-83 (x+1)^{13/4}+191 (x+1)^{9/4}-189 (x+1)^{5/4}+33 \sqrt[4]{x+1}\right)}{192 x^4}+\frac{11}{64} \tan ^{-1}\left(\frac{(1-x)^{3/4} \sqrt[4]{x+1}}{x-1}\right)+\frac{11}{64} \tanh ^{-1}\left(\frac{(1-x)^{3/4} \sqrt[4]{x+1}}{x-1}\right)","-\frac{(1-x)^{3/4} \sqrt[4]{x+1}}{4 x^4}-\frac{7 (1-x)^{3/4} \sqrt[4]{x+1}}{24 x^3}-\frac{29 (1-x)^{3/4} \sqrt[4]{x+1}}{96 x^2}-\frac{83 (1-x)^{3/4} \sqrt[4]{x+1}}{192 x}-\frac{11}{64} \tan ^{-1}\left(\frac{\sqrt[4]{x+1}}{\sqrt[4]{1-x}}\right)-\frac{11}{64} \tanh ^{-1}\left(\frac{\sqrt[4]{x+1}}{\sqrt[4]{1-x}}\right)",1,"((1 - x)^(3/4)*(33*(1 + x)^(1/4) - 189*(1 + x)^(5/4) + 191*(1 + x)^(9/4) - 83*(1 + x)^(13/4)))/(192*x^4) + (11*ArcTan[((1 - x)^(3/4)*(1 + x)^(1/4))/(-1 + x)])/64 + (11*ArcTanh[((1 - x)^(3/4)*(1 + x)^(1/4))/(-1 + x)])/64","A",1
900,0,0,259,15.4172157,"\int \frac{x^3}{(a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[x^3/((a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","\int \frac{x^3}{(a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","\frac{\sqrt[4]{a+b x} (c+d x)^{3/4} \left(77 a^2 d^2-4 b d x (11 a d+9 b c)+54 a b c d+45 b^2 c^2\right)}{96 b^3 d^3}-\frac{\left(77 a^3 d^3+21 a^2 b c d^2+15 a b^2 c^2 d+15 b^3 c^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{64 b^{15/4} d^{13/4}}-\frac{\left(77 a^3 d^3+21 a^2 b c d^2+15 a b^2 c^2 d+15 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{64 b^{15/4} d^{13/4}}+\frac{x^2 \sqrt[4]{a+b x} (c+d x)^{3/4}}{3 b d}",1,"Could not integrate","F",-1
901,0,0,201,10.8326413,"\int \frac{x^2}{(a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[x^2/((a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","\int \frac{x^2}{(a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 b^{11/4} d^{9/4}}+\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{16 b^{11/4} d^{9/4}}-\frac{\sqrt[4]{a+b x} (c+d x)^{3/4} (7 a d+5 b c)}{8 b^2 d^2}+\frac{x \sqrt[4]{a+b x} (c+d x)^{3/4}}{2 b d}",1,"Could not integrate","F",-1
902,0,0,130,8.7156578,"\int \frac{x}{(a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[x/((a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","\int \frac{x}{(a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","-\frac{(3 a d+b c) \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 b^{7/4} d^{5/4}}-\frac{(3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{2 b^{7/4} d^{5/4}}+\frac{\sqrt[4]{a+b x} (c+d x)^{3/4}}{b d}",1,"Could not integrate","F",-1
903,1,113,85,0.0006075,"\int \frac{1}{(a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{\frac{d (a+b x)}{b}-\frac{a d}{b}+c}}{\sqrt[4]{d} \sqrt[4]{a+b x}}\right)}{b^{3/4} \sqrt[4]{d}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{\frac{d (a+b x)}{b}-\frac{a d}{b}+c}}{\sqrt[4]{d} \sqrt[4]{a+b x}}\right)}{b^{3/4} \sqrt[4]{d}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{b^{3/4} \sqrt[4]{d}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{a+b x}}{\sqrt[4]{b} \sqrt[4]{c+d x}}\right)}{b^{3/4} \sqrt[4]{d}}",1,"(-2*ArcTan[(b^(1/4)*(c - (a*d)/b + (d*(a + b*x))/b)^(1/4))/(d^(1/4)*(a + b*x)^(1/4))])/(b^(3/4)*d^(1/4)) + (2*ArcTanh[(b^(1/4)*(c - (a*d)/b + (d*(a + b*x))/b)^(1/4))/(d^(1/4)*(a + b*x)^(1/4))])/(b^(3/4)*d^(1/4))","A",1
904,1,113,85,2.6934292,"\int \frac{1}{x (a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[1/(x*(a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{\frac{d (a+b x)}{b}-\frac{a d}{b}+c}}{\sqrt[4]{c} \sqrt[4]{a+b x}}\right)}{a^{3/4} \sqrt[4]{c}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{\frac{d (a+b x)}{b}-\frac{a d}{b}+c}}{\sqrt[4]{c} \sqrt[4]{a+b x}}\right)}{a^{3/4} \sqrt[4]{c}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{a^{3/4} \sqrt[4]{c}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{a^{3/4} \sqrt[4]{c}}",1,"(2*ArcTan[(a^(1/4)*(c - (a*d)/b + (d*(a + b*x))/b)^(1/4))/(c^(1/4)*(a + b*x)^(1/4))])/(a^(3/4)*c^(1/4)) - (2*ArcTanh[(a^(1/4)*(c - (a*d)/b + (d*(a + b*x))/b)^(1/4))/(c^(1/4)*(a + b*x)^(1/4))])/(a^(3/4)*c^(1/4))","A",1
905,1,177,134,6.3869963,"\int \frac{1}{x^2 (a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","\frac{(-a d-3 b c) \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{\frac{d (a+b x)}{b}-\frac{a d}{b}+c}}{\sqrt[4]{c} \sqrt[4]{a+b x}}\right)}{2 a^{7/4} c^{5/4}}+\frac{(a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{\frac{d (a+b x)}{b}-\frac{a d}{b}+c}}{\sqrt[4]{c} \sqrt[4]{a+b x}}\right)}{2 a^{7/4} c^{5/4}}-\frac{\sqrt[4]{a+b x} \left(\frac{d (a+b x)}{b}-\frac{a d}{b}+c\right)^{3/4}}{a c x}","\frac{(a d+3 b c) \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{2 a^{7/4} c^{5/4}}+\frac{(a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{2 a^{7/4} c^{5/4}}-\frac{\sqrt[4]{a+b x} (c+d x)^{3/4}}{a c x}",1,"-(((a + b*x)^(1/4)*(c - (a*d)/b + (d*(a + b*x))/b)^(3/4))/(a*c*x)) + ((-3*b*c - a*d)*ArcTan[(a^(1/4)*(c - (a*d)/b + (d*(a + b*x))/b)^(1/4))/(c^(1/4)*(a + b*x)^(1/4))])/(2*a^(7/4)*c^(5/4)) + ((3*b*c + a*d)*ArcTanh[(a^(1/4)*(c - (a*d)/b + (d*(a + b*x))/b)^(1/4))/(c^(1/4)*(a + b*x)^(1/4))])/(2*a^(7/4)*c^(5/4))","A",1
906,0,0,206,29.2388711,"\int \frac{1}{x^3 (a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","\int \frac{1}{x^3 (a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","\frac{\sqrt[4]{a+b x} (c+d x)^{3/4} (5 a d+7 b c)}{8 a^2 c^2 x}-\frac{\left(5 a^2 d^2+6 a b c d+21 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{16 a^{11/4} c^{9/4}}-\frac{\left(5 a^2 d^2+6 a b c d+21 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{16 a^{11/4} c^{9/4}}-\frac{\sqrt[4]{a+b x} (c+d x)^{3/4}}{2 a c x^2}",1,"Could not integrate","F",-1
907,0,0,288,29.0014083,"\int \frac{1}{x^4 (a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","\int \frac{1}{x^4 (a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","\frac{\sqrt[4]{a+b x} (c+d x)^{3/4} (9 a d+11 b c)}{24 a^2 c^2 x^2}-\frac{\sqrt[4]{a+b x} (c+d x)^{3/4} \left(45 a^2 d^2+54 a b c d+77 b^2 c^2\right)}{96 a^3 c^3 x}+\frac{\left(15 a^3 d^3+15 a^2 b c d^2+21 a b^2 c^2 d+77 b^3 c^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{64 a^{15/4} c^{13/4}}+\frac{\left(15 a^3 d^3+15 a^2 b c d^2+21 a b^2 c^2 d+77 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{a+b x}}{\sqrt[4]{a} \sqrt[4]{c+d x}}\right)}{64 a^{15/4} c^{13/4}}-\frac{\sqrt[4]{a+b x} (c+d x)^{3/4}}{3 a c x^3}",1,"Could not integrate","F",-1
908,0,0,244,1.6586047,"\int \frac{(e x)^{3/2}}{\sqrt[4]{1-x} \sqrt[4]{1+x}} \, dx","IntegrateAlgebraic[(e*x)^(3/2)/((1 - x)^(1/4)*(1 + x)^(1/4)),x]","\int \frac{(e x)^{3/2}}{\sqrt[4]{1-x} \sqrt[4]{1+x}} \, dx","-\frac{e^{3/2} \log \left(\frac{\sqrt{e} x}{\sqrt{1-x^2}}-\frac{\sqrt{2} \sqrt{e x}}{\sqrt[4]{1-x^2}}+\sqrt{e}\right)}{8 \sqrt{2}}+\frac{e^{3/2} \log \left(\frac{\sqrt{e} x}{\sqrt{1-x^2}}+\frac{\sqrt{2} \sqrt{e x}}{\sqrt[4]{1-x^2}}+\sqrt{e}\right)}{8 \sqrt{2}}-\frac{e^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e x}}{\sqrt{e} \sqrt[4]{1-x^2}}\right)}{4 \sqrt{2}}+\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{e x}}{\sqrt{e} \sqrt[4]{1-x^2}}+1\right)}{4 \sqrt{2}}-\frac{1}{2} e \left(1-x^2\right)^{3/4} \sqrt{e x}",1,"Could not integrate","F",-1
909,0,0,216,1.1217827,"\int \frac{1}{\sqrt[4]{1-x} \sqrt{e x} \sqrt[4]{1+x}} \, dx","IntegrateAlgebraic[1/((1 - x)^(1/4)*Sqrt[e*x]*(1 + x)^(1/4)),x]","\int \frac{1}{\sqrt[4]{1-x} \sqrt{e x} \sqrt[4]{1+x}} \, dx","-\frac{\log \left(\frac{\sqrt{e} x}{\sqrt{1-x^2}}-\frac{\sqrt{2} \sqrt{e x}}{\sqrt[4]{1-x^2}}+\sqrt{e}\right)}{2 \sqrt{2} \sqrt{e}}+\frac{\log \left(\frac{\sqrt{e} x}{\sqrt{1-x^2}}+\frac{\sqrt{2} \sqrt{e x}}{\sqrt[4]{1-x^2}}+\sqrt{e}\right)}{2 \sqrt{2} \sqrt{e}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e x}}{\sqrt{e} \sqrt[4]{1-x^2}}\right)}{\sqrt{2} \sqrt{e}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{e x}}{\sqrt{e} \sqrt[4]{1-x^2}}+1\right)}{\sqrt{2} \sqrt{e}}",1,"Could not integrate","F",-1
910,0,0,30,1.4628536,"\int \frac{1}{\sqrt[4]{1-x} (e x)^{5/2} \sqrt[4]{1+x}} \, dx","IntegrateAlgebraic[1/((1 - x)^(1/4)*(e*x)^(5/2)*(1 + x)^(1/4)),x]","\int \frac{1}{\sqrt[4]{1-x} (e x)^{5/2} \sqrt[4]{1+x}} \, dx","-\frac{2 (1-x)^{3/4} (x+1)^{3/4}}{3 e (e x)^{3/2}}",1,"Could not integrate","F",-1
911,0,0,51,1.9228486,"\int \frac{1}{\sqrt[4]{1-x} (e x)^{9/2} \sqrt[4]{1+x}} \, dx","IntegrateAlgebraic[1/((1 - x)^(1/4)*(e*x)^(9/2)*(1 + x)^(1/4)),x]","\int \frac{1}{\sqrt[4]{1-x} (e x)^{9/2} \sqrt[4]{1+x}} \, dx","\frac{8 \left(1-x^2\right)^{7/4}}{21 e (e x)^{7/2}}-\frac{2 \left(1-x^2\right)^{3/4}}{3 e (e x)^{7/2}}",1,"Could not integrate","F",-1
912,0,0,76,1.9328782,"\int \frac{1}{\sqrt[4]{1-x} (e x)^{13/2} \sqrt[4]{1+x}} \, dx","IntegrateAlgebraic[1/((1 - x)^(1/4)*(e*x)^(13/2)*(1 + x)^(1/4)),x]","\int \frac{1}{\sqrt[4]{1-x} (e x)^{13/2} \sqrt[4]{1+x}} \, dx","-\frac{64 \left(1-x^2\right)^{11/4}}{231 e (e x)^{11/2}}+\frac{16 \left(1-x^2\right)^{7/4}}{21 e (e x)^{11/2}}-\frac{2 \left(1-x^2\right)^{3/4}}{3 e (e x)^{11/2}}",1,"Could not integrate","F",-1
913,0,0,93,1.9621586,"\int \frac{(e x)^{5/2}}{\sqrt[4]{1-x} \sqrt[4]{1+x}} \, dx","IntegrateAlgebraic[(e*x)^(5/2)/((1 - x)^(1/4)*(1 + x)^(1/4)),x]","\int \frac{(e x)^{5/2}}{\sqrt[4]{1-x} \sqrt[4]{1+x}} \, dx","-\frac{e^3 \left(1-x^2\right)^{3/4}}{2 \sqrt{e x}}+\frac{e^2 \sqrt[4]{1-\frac{1}{x^2}} \sqrt{e x} E\left(\left.\frac{1}{2} \csc ^{-1}(x)\right|2\right)}{2 \sqrt[4]{1-x^2}}-\frac{1}{3} e \left(1-x^2\right)^{3/4} (e x)^{3/2}",1,"Could not integrate","F",-1
914,0,0,60,1.082621,"\int \frac{\sqrt{e x}}{\sqrt[4]{1-x} \sqrt[4]{1+x}} \, dx","IntegrateAlgebraic[Sqrt[e*x]/((1 - x)^(1/4)*(1 + x)^(1/4)),x]","\int \frac{\sqrt{e x}}{\sqrt[4]{1-x} \sqrt[4]{1+x}} \, dx","\frac{\sqrt[4]{1-\frac{1}{x^2}} \sqrt{e x} E\left(\left.\frac{1}{2} \csc ^{-1}(x)\right|2\right)}{\sqrt[4]{1-x^2}}-\frac{e \left(1-x^2\right)^{3/4}}{\sqrt{e x}}",1,"Could not integrate","F",-1
915,0,0,42,1.4737634,"\int \frac{1}{\sqrt[4]{1-x} (e x)^{3/2} \sqrt[4]{1+x}} \, dx","IntegrateAlgebraic[1/((1 - x)^(1/4)*(e*x)^(3/2)*(1 + x)^(1/4)),x]","\int \frac{1}{\sqrt[4]{1-x} (e x)^{3/2} \sqrt[4]{1+x}} \, dx","-\frac{2 \sqrt[4]{1-\frac{1}{x^2}} \sqrt{e x} E\left(\left.\frac{1}{2} \csc ^{-1}(x)\right|2\right)}{e^2 \sqrt[4]{1-x^2}}",1,"Could not integrate","F",-1
916,0,0,70,1.6109555,"\int \frac{1}{\sqrt[4]{1-x} (e x)^{7/2} \sqrt[4]{1+x}} \, dx","IntegrateAlgebraic[1/((1 - x)^(1/4)*(e*x)^(7/2)*(1 + x)^(1/4)),x]","\int \frac{1}{\sqrt[4]{1-x} (e x)^{7/2} \sqrt[4]{1+x}} \, dx","-\frac{4 \sqrt[4]{1-\frac{1}{x^2}} \sqrt{e x} E\left(\left.\frac{1}{2} \csc ^{-1}(x)\right|2\right)}{5 e^4 \sqrt[4]{1-x^2}}-\frac{2 \left(1-x^2\right)^{3/4}}{5 e (e x)^{5/2}}",1,"Could not integrate","F",-1
917,0,0,95,1.8691331,"\int \frac{1}{\sqrt[4]{1-x} (e x)^{11/2} \sqrt[4]{1+x}} \, dx","IntegrateAlgebraic[1/((1 - x)^(1/4)*(e*x)^(11/2)*(1 + x)^(1/4)),x]","\int \frac{1}{\sqrt[4]{1-x} (e x)^{11/2} \sqrt[4]{1+x}} \, dx","-\frac{8 \sqrt[4]{1-\frac{1}{x^2}} \sqrt{e x} E\left(\left.\frac{1}{2} \csc ^{-1}(x)\right|2\right)}{15 e^6 \sqrt[4]{1-x^2}}-\frac{4 \left(1-x^2\right)^{3/4}}{15 e^3 (e x)^{5/2}}-\frac{2 \left(1-x^2\right)^{3/4}}{9 e (e x)^{9/2}}",1,"Could not integrate","F",-1
918,0,0,104,0.0386631,"\int x^2 (a+b x)^n (c+d x) \, dx","IntegrateAlgebraic[x^2*(a + b*x)^n*(c + d*x),x]","\int x^2 (a+b x)^n (c+d x) \, dx","\frac{a^2 (b c-a d) (a+b x)^{n+1}}{b^4 (n+1)}-\frac{a (2 b c-3 a d) (a+b x)^{n+2}}{b^4 (n+2)}+\frac{(b c-3 a d) (a+b x)^{n+3}}{b^4 (n+3)}+\frac{d (a+b x)^{n+4}}{b^4 (n+4)}",1,"Could not integrate","F",-1
919,0,0,74,0.0328851,"\int x (a+b x)^n (c+d x) \, dx","IntegrateAlgebraic[x*(a + b*x)^n*(c + d*x),x]","\int x (a+b x)^n (c+d x) \, dx","-\frac{a (b c-a d) (a+b x)^{n+1}}{b^3 (n+1)}+\frac{(b c-2 a d) (a+b x)^{n+2}}{b^3 (n+2)}+\frac{d (a+b x)^{n+3}}{b^3 (n+3)}",1,"Could not integrate","F",-1
920,0,0,46,0.0281198,"\int (a+b x)^n (c+d x) \, dx","IntegrateAlgebraic[(a + b*x)^n*(c + d*x),x]","\int (a+b x)^n (c+d x) \, dx","\frac{(b c-a d) (a+b x)^{n+1}}{b^2 (n+1)}+\frac{d (a+b x)^{n+2}}{b^2 (n+2)}",1,"Could not integrate","F",-1
921,0,0,56,0.0337521,"\int \frac{(a+b x)^n (c+d x)}{x} \, dx","IntegrateAlgebraic[((a + b*x)^n*(c + d*x))/x,x]","\int \frac{(a+b x)^n (c+d x)}{x} \, dx","\frac{d (a+b x)^{n+1}}{b (n+1)}-\frac{c (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}",1,"Could not integrate","F",-1
922,0,0,62,0.0344531,"\int \frac{(a+b x)^n (c+d x)}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)^n*(c + d*x))/x^2,x]","\int \frac{(a+b x)^n (c+d x)}{x^2} \, dx","-\frac{(a+b x)^{n+1} (a d+b c n) \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1)}-\frac{c (a+b x)^{n+1}}{a x}",1,"Could not integrate","F",-1
923,0,0,157,0.0482259,"\int x^2 (a+b x)^n (c+d x)^2 \, dx","IntegrateAlgebraic[x^2*(a + b*x)^n*(c + d*x)^2,x]","\int x^2 (a+b x)^n (c+d x)^2 \, dx","\frac{a^2 (b c-a d)^2 (a+b x)^{n+1}}{b^5 (n+1)}+\frac{\left(6 a^2 d^2-6 a b c d+b^2 c^2\right) (a+b x)^{n+3}}{b^5 (n+3)}-\frac{2 a (b c-2 a d) (b c-a d) (a+b x)^{n+2}}{b^5 (n+2)}+\frac{2 d (b c-2 a d) (a+b x)^{n+4}}{b^5 (n+4)}+\frac{d^2 (a+b x)^{n+5}}{b^5 (n+5)}",1,"Could not integrate","F",-1
924,0,0,114,0.2059004,"\int x (a+b x)^n (c+d x)^2 \, dx","IntegrateAlgebraic[x*(a + b*x)^n*(c + d*x)^2,x]","\int x (a+b x)^n (c+d x)^2 \, dx","-\frac{a (b c-a d)^2 (a+b x)^{n+1}}{b^4 (n+1)}+\frac{(b c-3 a d) (b c-a d) (a+b x)^{n+2}}{b^4 (n+2)}+\frac{d (2 b c-3 a d) (a+b x)^{n+3}}{b^4 (n+3)}+\frac{d^2 (a+b x)^{n+4}}{b^4 (n+4)}",1,"Could not integrate","F",-1
925,0,0,78,0.034972,"\int (a+b x)^n (c+d x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^n*(c + d*x)^2,x]","\int (a+b x)^n (c+d x)^2 \, dx","\frac{(b c-a d)^2 (a+b x)^{n+1}}{b^3 (n+1)}+\frac{2 d (b c-a d) (a+b x)^{n+2}}{b^3 (n+2)}+\frac{d^2 (a+b x)^{n+3}}{b^3 (n+3)}",1,"Could not integrate","F",-1
926,0,0,88,0.0434345,"\int \frac{(a+b x)^n (c+d x)^2}{x} \, dx","IntegrateAlgebraic[((a + b*x)^n*(c + d*x)^2)/x,x]","\int \frac{(a+b x)^n (c+d x)^2}{x} \, dx","\frac{d (2 b c-a d) (a+b x)^{n+1}}{b^2 (n+1)}+\frac{d^2 (a+b x)^{n+2}}{b^2 (n+2)}-\frac{c^2 (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}",1,"Could not integrate","F",-1
927,0,0,87,0.0458887,"\int \frac{(a+b x)^n (c+d x)^2}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)^n*(c + d*x)^2)/x^2,x]","\int \frac{(a+b x)^n (c+d x)^2}{x^2} \, dx","-\frac{c (a+b x)^{n+1} (2 a d+b c n) \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1)}-\frac{c^2 (a+b x)^{n+1}}{a x}+\frac{d^2 (a+b x)^{n+1}}{b (n+1)}",1,"Could not integrate","F",-1
928,0,0,124,0.0466845,"\int \frac{(a+b x)^n (c+d x)^2}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)^n*(c + d*x)^2)/x^3,x]","\int \frac{(a+b x)^n (c+d x)^2}{x^3} \, dx","-\frac{c (a+b x)^{n+1} (4 a d-b c (1-n))}{2 a^2 x}-\frac{(a+b x)^{n+1} \left(2 a^2 d^2+4 a b c d n-b^2 c^2 (1-n) n\right) \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{2 a^3 (n+1)}-\frac{c^2 (a+b x)^{n+1}}{2 a x^2}",1,"Could not integrate","F",-1
929,0,0,130,0.0501609,"\int \frac{(a+b x)^n (c+d x)^2}{x^4} \, dx","IntegrateAlgebraic[((a + b*x)^n*(c + d*x)^2)/x^4,x]","\int \frac{(a+b x)^n (c+d x)^2}{x^4} \, dx","-\frac{c (a+b x)^{n+1} (6 a d-b c (2-n))}{6 a^2 x^2}+\frac{b (a+b x)^{n+1} \left(6 a^2 d^2-6 a b c d (1-n)+b^2 c^2 \left(n^2-3 n+2\right)\right) \, _2F_1\left(2,n+1;n+2;\frac{b x}{a}+1\right)}{6 a^4 (n+1)}-\frac{c^2 (a+b x)^{n+1}}{3 a x^3}",1,"Could not integrate","F",-1
930,0,0,212,0.0610018,"\int x^2 (a+b x)^n (c+d x)^3 \, dx","IntegrateAlgebraic[x^2*(a + b*x)^n*(c + d*x)^3,x]","\int x^2 (a+b x)^n (c+d x)^3 \, dx","\frac{a^2 (b c-a d)^3 (a+b x)^{n+1}}{b^6 (n+1)}+\frac{(b c-a d) \left(10 a^2 d^2-8 a b c d+b^2 c^2\right) (a+b x)^{n+3}}{b^6 (n+3)}+\frac{d \left(10 a^2 d^2-12 a b c d+3 b^2 c^2\right) (a+b x)^{n+4}}{b^6 (n+4)}+\frac{d^2 (3 b c-5 a d) (a+b x)^{n+5}}{b^6 (n+5)}-\frac{a (2 b c-5 a d) (b c-a d)^2 (a+b x)^{n+2}}{b^6 (n+2)}+\frac{d^3 (a+b x)^{n+6}}{b^6 (n+6)}",1,"Could not integrate","F",-1
931,0,0,154,0.3461396,"\int x (a+b x)^n (c+d x)^3 \, dx","IntegrateAlgebraic[x*(a + b*x)^n*(c + d*x)^3,x]","\int x (a+b x)^n (c+d x)^3 \, dx","\frac{d^2 (3 b c-4 a d) (a+b x)^{n+4}}{b^5 (n+4)}-\frac{a (b c-a d)^3 (a+b x)^{n+1}}{b^5 (n+1)}+\frac{(b c-4 a d) (b c-a d)^2 (a+b x)^{n+2}}{b^5 (n+2)}+\frac{3 d (b c-2 a d) (b c-a d) (a+b x)^{n+3}}{b^5 (n+3)}+\frac{d^3 (a+b x)^{n+5}}{b^5 (n+5)}",1,"Could not integrate","F",-1
932,0,0,110,0.0374459,"\int (a+b x)^n (c+d x)^3 \, dx","IntegrateAlgebraic[(a + b*x)^n*(c + d*x)^3,x]","\int (a+b x)^n (c+d x)^3 \, dx","\frac{3 d^2 (b c-a d) (a+b x)^{n+3}}{b^4 (n+3)}+\frac{(b c-a d)^3 (a+b x)^{n+1}}{b^4 (n+1)}+\frac{3 d (b c-a d)^2 (a+b x)^{n+2}}{b^4 (n+2)}+\frac{d^3 (a+b x)^{n+4}}{b^4 (n+4)}",1,"Could not integrate","F",-1
933,0,0,131,0.360708,"\int \frac{(a+b x)^n (c+d x)^3}{x} \, dx","IntegrateAlgebraic[((a + b*x)^n*(c + d*x)^3)/x,x]","\int \frac{(a+b x)^n (c+d x)^3}{x} \, dx","\frac{d \left(a^2 d^2-3 a b c d+3 b^2 c^2\right) (a+b x)^{n+1}}{b^3 (n+1)}+\frac{d^2 (3 b c-2 a d) (a+b x)^{n+2}}{b^3 (n+2)}+\frac{d^3 (a+b x)^{n+3}}{b^3 (n+3)}-\frac{c^3 (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}",1,"Could not integrate","F",-1
934,0,0,143,0.0499782,"\int \frac{(a+b x)^n (c+d x)^3}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)^n*(c + d*x)^3)/x^2,x]","\int \frac{(a+b x)^n (c+d x)^3}{x^2} \, dx","-\frac{c^2 (a+b x)^{n+1} (3 a d+b c n) \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 (n+1)}-\frac{(a+b x)^{n+1} \left(b c^2 (n+1) (a d+b c (n+2))+a d^2 x (a d-b c (n+4))\right)}{a b^2 (n+1) (n+2) x}+\frac{d (c+d x)^2 (a+b x)^{n+1}}{b (n+2) x}",1,"Could not integrate","F",-1
935,0,0,176,0.0532553,"\int \frac{(a+b x)^n (c+d x)^3}{x^3} \, dx","IntegrateAlgebraic[((a + b*x)^n*(c + d*x)^3)/x^3,x]","\int \frac{(a+b x)^n (c+d x)^3}{x^3} \, dx","-\frac{c (a+b x)^{n+1} \left(x \left(4 a^2 d^2+6 a b c d (n+1)-b^2 c^2 \left(1-n^2\right)\right)+a c (2 a d+b c (n+1))\right)}{2 a^2 b (n+1) x^2}-\frac{c (a+b x)^{n+1} \left(6 a^2 d^2+6 a b c d n-b^2 c^2 (1-n) n\right) \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{2 a^3 (n+1)}+\frac{d (c+d x)^2 (a+b x)^{n+1}}{b (n+1) x^2}",1,"Could not integrate","F",-1
936,0,0,22,0.033696,"\int x^{1+2 n} (a+b x)^n (2 a+3 b x) \, dx","IntegrateAlgebraic[x^(1 + 2*n)*(a + b*x)^n*(2*a + 3*b*x),x]","\int x^{1+2 n} (a+b x)^n (2 a+3 b x) \, dx","\frac{x^{2 (n+1)} (a+b x)^{n+1}}{n+1}",1,"Could not integrate","F",-1
937,0,0,108,0.4283515,"\int \frac{x^2 (a+b x)^n}{c+d x} \, dx","IntegrateAlgebraic[(x^2*(a + b*x)^n)/(c + d*x),x]","\int \frac{x^2 (a+b x)^n}{c+d x} \, dx","-\frac{(a d+b c) (a+b x)^{n+1}}{b^2 d^2 (n+1)}+\frac{(a+b x)^{n+2}}{b^2 d (n+2)}+\frac{c^2 (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{d^2 (n+1) (b c-a d)}",1,"Could not integrate","F",-1
938,0,0,78,0.4672049,"\int \frac{x (a+b x)^n}{c+d x} \, dx","IntegrateAlgebraic[(x*(a + b*x)^n)/(c + d*x),x]","\int \frac{x (a+b x)^n}{c+d x} \, dx","\frac{(a+b x)^{n+1}}{b d (n+1)}-\frac{c (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{d (n+1) (b c-a d)}",1,"Could not integrate","F",-1
939,0,0,51,0.0406725,"\int \frac{(a+b x)^n}{c+d x} \, dx","IntegrateAlgebraic[(a + b*x)^n/(c + d*x),x]","\int \frac{(a+b x)^n}{c+d x} \, dx","\frac{(a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{(n+1) (b c-a d)}",1,"Could not integrate","F",-1
940,0,0,95,0.2272613,"\int \frac{(a+b x)^n}{x (c+d x)} \, dx","IntegrateAlgebraic[(a + b*x)^n/(x*(c + d*x)),x]","\int \frac{(a+b x)^n}{x (c+d x)} \, dx","-\frac{d (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{c (n+1) (b c-a d)}-\frac{(a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a c (n+1)}",1,"Could not integrate","F",-1
941,0,0,124,0.0565506,"\int \frac{(a+b x)^n}{x^2 (c+d x)} \, dx","IntegrateAlgebraic[(a + b*x)^n/(x^2*(c + d*x)),x]","\int \frac{(a+b x)^n}{x^2 (c+d x)} \, dx","\frac{(a+b x)^{n+1} (a d-b c n) \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 c^2 (n+1)}+\frac{d^2 (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{c^2 (n+1) (b c-a d)}-\frac{(a+b x)^{n+1}}{a c x}",1,"Could not integrate","F",-1
942,0,0,203,0.0571895,"\int \frac{x^3 (a+b x)^n}{(c+d x)^2} \, dx","IntegrateAlgebraic[(x^3*(a + b*x)^n)/(c + d*x)^2,x]","\int \frac{x^3 (a+b x)^n}{(c+d x)^2} \, dx","-\frac{(a+b x)^{n+1} (d x (b c-a d) (a d+b c (n+3))+c (b c (n+2) (a d+b c (n+3))-a d (a d+b c (3 n+5))))}{b^2 d^3 (n+1) (n+2) (c+d x) (b c-a d)}-\frac{c^2 (a+b x)^{n+1} (3 a d-b c (n+3)) \, _2F_1\left(1,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{d^3 (n+1) (b c-a d)^2}+\frac{x^2 (a+b x)^{n+1}}{b d (n+2) (c+d x)}",1,"Could not integrate","F",-1
943,0,0,122,0.2218249,"\int \frac{x^2 (a+b x)^n}{(c+d x)^2} \, dx","IntegrateAlgebraic[(x^2*(a + b*x)^n)/(c + d*x)^2,x]","\int \frac{x^2 (a+b x)^n}{(c+d x)^2} \, dx","\frac{c^2 (a+b x)^{n+1}}{d^2 (c+d x) (b c-a d)}+\frac{c (a+b x)^{n+1} (2 a d-b c (n+2)) \, _2F_1\left(1,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{d^2 (n+1) (b c-a d)^2}+\frac{(a+b x)^{n+1}}{b d^2 (n+1)}",1,"Could not integrate","F",-1
944,0,0,99,0.0406456,"\int \frac{x (a+b x)^n}{(c+d x)^2} \, dx","IntegrateAlgebraic[(x*(a + b*x)^n)/(c + d*x)^2,x]","\int \frac{x (a+b x)^n}{(c+d x)^2} \, dx","-\frac{(a+b x)^{n+1} (a d-b c (n+1)) \, _2F_1\left(1,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{d (n+1) (b c-a d)^2}-\frac{c (a+b x)^{n+1}}{d (c+d x) (b c-a d)}",1,"Could not integrate","F",-1
945,0,0,52,0.0359032,"\int \frac{(a+b x)^n}{(c+d x)^2} \, dx","IntegrateAlgebraic[(a + b*x)^n/(c + d*x)^2,x]","\int \frac{(a+b x)^n}{(c+d x)^2} \, dx","\frac{b (a+b x)^{n+1} \, _2F_1\left(2,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{(n+1) (b c-a d)^2}",1,"Could not integrate","F",-1
946,0,0,139,0.0473706,"\int \frac{(a+b x)^n}{x (c+d x)^2} \, dx","IntegrateAlgebraic[(a + b*x)^n/(x*(c + d*x)^2),x]","\int \frac{(a+b x)^n}{x (c+d x)^2} \, dx","\frac{d (a+b x)^{n+1} (a d-b c (1-n)) \, _2F_1\left(1,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{c^2 (n+1) (b c-a d)^2}-\frac{(a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a c^2 (n+1)}-\frac{d (a+b x)^{n+1}}{c (c+d x) (b c-a d)}",1,"Could not integrate","F",-1
947,0,0,190,0.225871,"\int \frac{(a+b x)^n}{x^2 (c+d x)^2} \, dx","IntegrateAlgebraic[(a + b*x)^n/(x^2*(c + d*x)^2),x]","\int \frac{(a+b x)^n}{x^2 (c+d x)^2} \, dx","\frac{(a+b x)^{n+1} (2 a d-b c n) \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a^2 c^3 (n+1)}-\frac{d^2 (a+b x)^{n+1} (2 a d-b c (2-n)) \, _2F_1\left(1,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{c^3 (n+1) (b c-a d)^2}-\frac{d (b c-2 a d) (a+b x)^{n+1}}{a c^2 (c+d x) (b c-a d)}-\frac{(a+b x)^{n+1}}{a c x (c+d x)}",1,"Could not integrate","F",-1
948,0,0,195,0.1634051,"\int (b x)^{5/2} (c+d x)^n (e+f x)^2 \, dx","IntegrateAlgebraic[(b*x)^(5/2)*(c + d*x)^n*(e + f*x)^2,x]","\int (b x)^{5/2} (c+d x)^n (e+f x)^2 \, dx","\frac{2 (b x)^{7/2} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} \left(63 c^2 f^2-14 c d e f (2 n+11)+d^2 e^2 \left(4 n^2+40 n+99\right)\right) \, _2F_1\left(\frac{7}{2},-n;\frac{9}{2};-\frac{d x}{c}\right)}{7 b d^2 (2 n+9) (2 n+11)}-\frac{2 f (b x)^{7/2} (c+d x)^{n+1} (9 c f-d e (2 n+13))}{b d^2 (2 n+9) (2 n+11)}+\frac{2 f (b x)^{7/2} (e+f x) (c+d x)^{n+1}}{b d (2 n+11)}",1,"Could not integrate","F",-1
949,0,0,107,0.2762023,"\int (b x)^{5/2} (c+d x)^n (e+f x) \, dx","IntegrateAlgebraic[(b*x)^(5/2)*(c + d*x)^n*(e + f*x),x]","\int (b x)^{5/2} (c+d x)^n (e+f x) \, dx","\frac{2 f (b x)^{7/2} (c+d x)^{n+1}}{b d (2 n+9)}-\frac{2 (b x)^{7/2} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} (7 c f-d e (2 n+9)) \, _2F_1\left(\frac{7}{2},-n;\frac{9}{2};-\frac{d x}{c}\right)}{7 b d (2 n+9)}",1,"Could not integrate","F",-1
950,0,0,61,0.2944717,"\int \frac{(b x)^{5/2} (c+d x)^n}{e+f x} \, dx","IntegrateAlgebraic[((b*x)^(5/2)*(c + d*x)^n)/(e + f*x),x]","\int \frac{(b x)^{5/2} (c+d x)^n}{e+f x} \, dx","\frac{2 (b x)^{7/2} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} F_1\left(\frac{7}{2};-n,1;\frac{9}{2};-\frac{d x}{c},-\frac{f x}{e}\right)}{7 b e}",1,"Could not integrate","F",-1
951,0,0,61,0.2113209,"\int \frac{(b x)^{5/2} (c+d x)^n}{(e+f x)^2} \, dx","IntegrateAlgebraic[((b*x)^(5/2)*(c + d*x)^n)/(e + f*x)^2,x]","\int \frac{(b x)^{5/2} (c+d x)^n}{(e+f x)^2} \, dx","\frac{2 (b x)^{7/2} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} F_1\left(\frac{7}{2};-n,2;\frac{9}{2};-\frac{d x}{c},-\frac{f x}{e}\right)}{7 b e^2}",1,"Could not integrate","F",-1
952,0,0,209,0.204871,"\int (b x)^m (c+d x)^n (e+f x)^2 \, dx","IntegrateAlgebraic[(b*x)^m*(c + d*x)^n*(e + f*x)^2,x]","\int (b x)^m (c+d x)^n (e+f x)^2 \, dx","\frac{(b x)^{m+1} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} \left(c^2 f^2 \left(m^2+3 m+2\right)-2 c d e f (m+1) (m+n+3)+d^2 e^2 \left(m^2+m (2 n+5)+n^2+5 n+6\right)\right) \, _2F_1\left(m+1,-n;m+2;-\frac{d x}{c}\right)}{b d^2 (m+1) (m+n+2) (m+n+3)}-\frac{f (b x)^{m+1} (c+d x)^{n+1} (c f (m+2)-d e (m+n+4))}{b d^2 (m+n+2) (m+n+3)}+\frac{f (b x)^{m+1} (e+f x) (c+d x)^{n+1}}{b d (m+n+3)}",1,"Could not integrate","F",-1
953,0,0,108,0.0298382,"\int (b x)^m (c+d x)^n (e+f x) \, dx","IntegrateAlgebraic[(b*x)^m*(c + d*x)^n*(e + f*x),x]","\int (b x)^m (c+d x)^n (e+f x) \, dx","\frac{f (b x)^{m+1} (c+d x)^{n+1}}{b d (m+n+2)}-\frac{(b x)^{m+1} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} (c f (m+1)-d e (m+n+2)) \, _2F_1\left(m+1,-n;m+2;-\frac{d x}{c}\right)}{b d (m+1) (m+n+2)}",1,"Could not integrate","F",-1
954,0,0,63,0.0466874,"\int \frac{(b x)^m (c+d x)^n}{e+f x} \, dx","IntegrateAlgebraic[((b*x)^m*(c + d*x)^n)/(e + f*x),x]","\int \frac{(b x)^m (c+d x)^n}{e+f x} \, dx","\frac{(b x)^{m+1} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{d x}{c},-\frac{f x}{e}\right)}{b e (m+1)}",1,"Could not integrate","F",-1
955,0,0,63,0.0384291,"\int \frac{(b x)^m (c+d x)^n}{(e+f x)^2} \, dx","IntegrateAlgebraic[((b*x)^m*(c + d*x)^n)/(e + f*x)^2,x]","\int \frac{(b x)^m (c+d x)^n}{(e+f x)^2} \, dx","\frac{(b x)^{m+1} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} F_1\left(m+1;-n,2;m+2;-\frac{d x}{c},-\frac{f x}{e}\right)}{b e^2 (m+1)}",1,"Could not integrate","F",-1
956,0,0,81,0.0326103,"\int (b x)^m (c+d x)^n (e+f x)^p \, dx","IntegrateAlgebraic[(b*x)^m*(c + d*x)^n*(e + f*x)^p,x]","\int (b x)^m (c+d x)^n (e+f x)^p \, dx","\frac{(b x)^{m+1} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} (e+f x)^p \left(\frac{f x}{e}+1\right)^{-p} F_1\left(m+1;-n,-p;m+2;-\frac{d x}{c},-\frac{f x}{e}\right)}{b (m+1)}",1,"Could not integrate","F",-1
957,0,0,211,0.2179264,"\int (e x)^m (a-b x)^{2+n} (a+b x)^n \, dx","IntegrateAlgebraic[(e*x)^m*(a - b*x)^(2 + n)*(a + b*x)^n,x]","\int (e x)^m (a-b x)^{2+n} (a+b x)^n \, dx","-\frac{2 a b (e x)^{m+2} (a-b x)^n (a+b x)^n \left(1-\frac{b^2 x^2}{a^2}\right)^{-n} \, _2F_1\left(\frac{m+2}{2},-n;\frac{m+4}{2};\frac{b^2 x^2}{a^2}\right)}{e^2 (m+2)}+\frac{2 a^2 (m+n+2) (e x)^{m+1} (a-b x)^n (a+b x)^n \left(1-\frac{b^2 x^2}{a^2}\right)^{-n} \, _2F_1\left(\frac{m+1}{2},-n;\frac{m+3}{2};\frac{b^2 x^2}{a^2}\right)}{e (m+1) (m+2 n+3)}-\frac{(e x)^{m+1} (a-b x)^{n+1} (a+b x)^{n+1}}{e (m+2 n+3)}",1,"Could not integrate","F",-1
958,0,0,206,0.0332137,"\int x^2 (a+b x)^n (c+d x)^p \, dx","IntegrateAlgebraic[x^2*(a + b*x)^n*(c + d*x)^p,x]","\int x^2 (a+b x)^n (c+d x)^p \, dx","-\frac{(a+b x)^{n+1} (c+d x)^{p+1} \left(a^2 d^2 \left(p^2+3 p+2\right)+2 a b c d (n+1) (p+1)+b^2 c^2 \left(n^2+3 n+2\right)\right) \, _2F_1\left(1,n+p+2;p+2;\frac{b (c+d x)}{b c-a d}\right)}{b^2 d^2 (p+1) (n+p+2) (n+p+3) (b c-a d)}-\frac{(a+b x)^{n+1} (c+d x)^{p+1} (a d (p+2)+b c (n+2))}{b^2 d^2 (n+p+2) (n+p+3)}+\frac{x (a+b x)^{n+1} (c+d x)^{p+1}}{b d (n+p+3)}",1,"Could not integrate","F",-1
959,0,0,117,0.0281882,"\int x (a+b x)^n (c+d x)^p \, dx","IntegrateAlgebraic[x*(a + b*x)^n*(c + d*x)^p,x]","\int x (a+b x)^n (c+d x)^p \, dx","\frac{(a+b x)^{n+1} (c+d x)^{p+1} (a d (p+1)+b c (n+1)) \, _2F_1\left(1,n+p+2;p+2;\frac{b (c+d x)}{b c-a d}\right)}{b d (p+1) (n+p+2) (b c-a d)}+\frac{(a+b x)^{n+1} (c+d x)^{p+1}}{b d (n+p+2)}",1,"Could not integrate","F",-1
960,0,0,61,0.0242532,"\int (a+b x)^n (c+d x)^p \, dx","IntegrateAlgebraic[(a + b*x)^n*(c + d*x)^p,x]","\int (a+b x)^n (c+d x)^p \, dx","-\frac{(a+b x)^{n+1} (c+d x)^{p+1} \, _2F_1\left(1,n+p+2;p+2;\frac{b (c+d x)}{b c-a d}\right)}{(p+1) (b c-a d)}",1,"Could not integrate","F",-1
961,0,0,85,0.0278625,"\int \frac{(a+b x)^n (c+d x)^p}{x} \, dx","IntegrateAlgebraic[((a + b*x)^n*(c + d*x)^p)/x,x]","\int \frac{(a+b x)^n (c+d x)^p}{x} \, dx","-\frac{(a+b x)^{n+1} (c+d x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-p} F_1\left(n+1;-p,1;n+2;-\frac{d (a+b x)}{b c-a d},\frac{a+b x}{a}\right)}{a (n+1)}",1,"Could not integrate","F",-1
962,0,0,85,0.0301366,"\int \frac{(a+b x)^n (c+d x)^p}{x^2} \, dx","IntegrateAlgebraic[((a + b*x)^n*(c + d*x)^p)/x^2,x]","\int \frac{(a+b x)^n (c+d x)^p}{x^2} \, dx","\frac{b (a+b x)^{n+1} (c+d x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-p} F_1\left(n+1;-p,2;n+2;-\frac{d (a+b x)}{b c-a d},\frac{a+b x}{a}\right)}{a^2 (n+1)}",1,"Could not integrate","F",-1
963,0,0,79,0.0639025,"\int (b x)^{3/2} (c+d x)^n (e+f x)^p \, dx","IntegrateAlgebraic[(b*x)^(3/2)*(c + d*x)^n*(e + f*x)^p,x]","\int (b x)^{3/2} (c+d x)^n (e+f x)^p \, dx","\frac{2 (b x)^{5/2} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} (e+f x)^p \left(\frac{f x}{e}+1\right)^{-p} F_1\left(\frac{5}{2};-n,-p;\frac{7}{2};-\frac{d x}{c},-\frac{f x}{e}\right)}{5 b}",1,"Could not integrate","F",-1
964,0,0,79,0.0589423,"\int \sqrt{b x} (c+d x)^n (e+f x)^p \, dx","IntegrateAlgebraic[Sqrt[b*x]*(c + d*x)^n*(e + f*x)^p,x]","\int \sqrt{b x} (c+d x)^n (e+f x)^p \, dx","\frac{2 (b x)^{3/2} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} (e+f x)^p \left(\frac{f x}{e}+1\right)^{-p} F_1\left(\frac{3}{2};-n,-p;\frac{5}{2};-\frac{d x}{c},-\frac{f x}{e}\right)}{3 b}",1,"Could not integrate","F",-1
965,0,0,77,0.3481803,"\int \frac{(c+d x)^n (e+f x)^p}{\sqrt{b x}} \, dx","IntegrateAlgebraic[((c + d*x)^n*(e + f*x)^p)/Sqrt[b*x],x]","\int \frac{(c+d x)^n (e+f x)^p}{\sqrt{b x}} \, dx","\frac{2 \sqrt{b x} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} (e+f x)^p \left(\frac{f x}{e}+1\right)^{-p} F_1\left(\frac{1}{2};-n,-p;\frac{3}{2};-\frac{d x}{c},-\frac{f x}{e}\right)}{b}",1,"Could not integrate","F",-1
966,0,0,49,0.1834361,"\int (b x)^m (\pi +d x)^n (e+f x)^p \, dx","IntegrateAlgebraic[(b*x)^m*(Pi + d*x)^n*(E + f*x)^p,x]","\int (b x)^m (\pi +d x)^n (e+f x)^p \, dx","\frac{\pi ^n e^p (b x)^{m+1} F_1\left(m+1;-n,-p;m+2;-\frac{d x}{\pi },-\frac{f x}{e}\right)}{b (m+1)}",1,"Could not integrate","F",-1
967,0,0,65,0.032105,"\int (b x)^m (\pi +d x)^n (e+f x)^p \, dx","IntegrateAlgebraic[(b*x)^m*(Pi + d*x)^n*(e + f*x)^p,x]","\int (b x)^m (\pi +d x)^n (e+f x)^p \, dx","\frac{\pi ^n (b x)^{m+1} (e+f x)^p \left(\frac{f x}{e}+1\right)^{-p} F_1\left(m+1;-n,-p;m+2;-\frac{d x}{\pi },-\frac{f x}{e}\right)}{b (m+1)}",1,"Could not integrate","F",-1
968,0,0,47,0.0669871,"\int (b x)^{5/2} (\pi +d x)^n (e+f x)^p \, dx","IntegrateAlgebraic[(b*x)^(5/2)*(Pi + d*x)^n*(E + f*x)^p,x]","\int (b x)^{5/2} (\pi +d x)^n (e+f x)^p \, dx","\frac{2 \pi ^n e^p (b x)^{7/2} F_1\left(\frac{7}{2};-n,-p;\frac{9}{2};-\frac{d x}{\pi },-\frac{f x}{e}\right)}{7 b}",1,"Could not integrate","F",-1
969,0,0,63,0.0664462,"\int (b x)^{5/2} (\pi +d x)^n (e+f x)^p \, dx","IntegrateAlgebraic[(b*x)^(5/2)*(Pi + d*x)^n*(e + f*x)^p,x]","\int (b x)^{5/2} (\pi +d x)^n (e+f x)^p \, dx","\frac{2 \pi ^n (b x)^{7/2} (e+f x)^p \left(\frac{f x}{e}+1\right)^{-p} F_1\left(\frac{7}{2};-n,-p;\frac{9}{2};-\frac{d x}{\pi },-\frac{f x}{e}\right)}{7 b}",1,"Could not integrate","F",-1
970,0,0,295,0.0340716,"\int x^3 (a+b x)^n (c+d x)^{-n} \, dx","IntegrateAlgebraic[(x^3*(a + b*x)^n)/(c + d*x)^n,x]","\int x^3 (a+b x)^n (c+d x)^{-n} \, dx","\frac{(a+b x)^{n+1} (c+d x)^{1-n} \left(a^2 d^2 \left(n^2-5 n+6\right)+2 a b c d \left(3-n^2\right)-2 b d x (a d (3-n)+b c (n+3))+b^2 c^2 \left(n^2+5 n+6\right)\right)}{24 b^3 d^3}-\frac{(a+b x)^{n+1} (c+d x)^{-n} \left(a^3 d^3 \left(-n^3+6 n^2-11 n+6\right)+3 a^2 b c d^2 \left(n^3-2 n^2-n+2\right)+3 a b^2 c^2 d \left(-n^3-2 n^2+n+2\right)+b^3 c^3 \left(n^3+6 n^2+11 n+6\right)\right) \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{24 b^4 d^3 (n+1)}+\frac{x^2 (a+b x)^{n+1} (c+d x)^{1-n}}{4 b d}",1,"Could not integrate","F",-1
971,0,0,199,0.0330501,"\int x^2 (a+b x)^n (c+d x)^{-n} \, dx","IntegrateAlgebraic[(x^2*(a + b*x)^n)/(c + d*x)^n,x]","\int x^2 (a+b x)^n (c+d x)^{-n} \, dx","\frac{(a+b x)^{n+1} (c+d x)^{-n} \left(a^2 d^2 \left(n^2-3 n+2\right)+2 a b c d \left(1-n^2\right)+b^2 c^2 \left(n^2+3 n+2\right)\right) \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{6 b^3 d^2 (n+1)}-\frac{(a+b x)^{n+1} (c+d x)^{1-n} (a d (2-n)+b c (n+2))}{6 b^2 d^2}+\frac{x (a+b x)^{n+1} (c+d x)^{1-n}}{3 b d}",1,"Could not integrate","F",-1
972,0,0,124,0.0296772,"\int x (a+b x)^n (c+d x)^{-n} \, dx","IntegrateAlgebraic[(x*(a + b*x)^n)/(c + d*x)^n,x]","\int x (a+b x)^n (c+d x)^{-n} \, dx","\frac{(a+b x)^{n+1} (c+d x)^{1-n}}{2 b d}-\frac{(a+b x)^{n+1} (c+d x)^{-n} (a d (1-n)+b c (n+1)) \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{2 b^2 d (n+1)}",1,"Could not integrate","F",-1
973,0,0,72,0.0005559,"\int (a+b x)^n (c+d x)^{-n} \, dx","IntegrateAlgebraic[(a + b*x)^n/(c + d*x)^n,x]","\int (a+b x)^n (c+d x)^{-n} \, dx","\frac{(a+b x)^{n+1} (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n+1;n+2;-\frac{d (a+b x)}{b c-a d}\right)}{b (n+1)}",1,"Could not integrate","F",-1
974,0,0,108,0.0288687,"\int \frac{(a+b x)^n (c+d x)^{-n}}{x} \, dx","IntegrateAlgebraic[(a + b*x)^n/(x*(c + d*x)^n),x]","\int \frac{(a+b x)^n (c+d x)^{-n}}{x} \, dx","\frac{(a+b x)^n (c+d x)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n;n+1;-\frac{d (a+b x)}{b c-a d}\right)}{n}-\frac{(a+b x)^n (c+d x)^{-n} \, _2F_1\left(1,n;n+1;\frac{c (a+b x)}{a (c+d x)}\right)}{n}",1,"Could not integrate","F",-1
975,0,0,62,0.2001524,"\int \frac{(a+b x)^n (c+d x)^{-n}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x)^n/(x^2*(c + d*x)^n),x]","\int \frac{(a+b x)^n (c+d x)^{-n}}{x^2} \, dx","\frac{(b c-a d) (a+b x)^{n+1} (c+d x)^{-n-1} \, _2F_1\left(2,n+1;n+2;\frac{c (a+b x)}{a (c+d x)}\right)}{a^2 (n+1)}",1,"Could not integrate","F",-1
976,0,0,117,0.0340562,"\int \frac{(a+b x)^n (c+d x)^{-n}}{x^3} \, dx","IntegrateAlgebraic[(a + b*x)^n/(x^3*(c + d*x)^n),x]","\int \frac{(a+b x)^n (c+d x)^{-n}}{x^3} \, dx","-\frac{(b c-a d) (a+b x)^{n+1} (c+d x)^{-n-1} (a d (n+1)+b (c-c n)) \, _2F_1\left(2,n+1;n+2;\frac{c (a+b x)}{a (c+d x)}\right)}{2 a^3 c (n+1)}-\frac{(a+b x)^{n+1} (c+d x)^{1-n}}{2 a c x^2}",1,"Could not integrate","F",-1
977,0,0,194,0.036443,"\int \frac{(a+b x)^n (c+d x)^{-n}}{x^4} \, dx","IntegrateAlgebraic[(a + b*x)^n/(x^4*(c + d*x)^n),x]","\int \frac{(a+b x)^n (c+d x)^{-n}}{x^4} \, dx","\frac{(a+b x)^{n+1} (c+d x)^{1-n} (a d (n+2)+b c (2-n))}{6 a^2 c^2 x^2}+\frac{(b c-a d) (a+b x)^{n+1} (c+d x)^{-n-1} \left(a^2 d^2 \left(n^2+3 n+2\right)+2 a b c d \left(1-n^2\right)+b^2 c^2 \left(n^2-3 n+2\right)\right) \, _2F_1\left(2,n+1;n+2;\frac{c (a+b x)}{a (c+d x)}\right)}{6 a^4 c^2 (n+1)}-\frac{(a+b x)^{n+1} (c+d x)^{1-n}}{3 a c x^3}",1,"Could not integrate","F",-1
978,0,0,105,0.0225876,"\int (1-x)^n x^3 (1+x)^{-n} \, dx","IntegrateAlgebraic[((1 - x)^n*x^3)/(1 + x)^n,x]","\int (1-x)^n x^3 (1+x)^{-n} \, dx","\frac{2^{-n} n \left(n^2+2\right) (1-x)^{n+1} \, _2F_1\left(n,n+1;n+2;\frac{1-x}{2}\right)}{3 (n+1)}-\frac{1}{12} (1-x)^{n+1} \left(2 n^2-2 n x+3\right) (x+1)^{1-n}-\frac{1}{4} x^2 (1-x)^{n+1} (x+1)^{1-n}",1,"Could not integrate","F",-1
979,0,0,94,0.1890341,"\int (1-x)^n x^2 (1+x)^{-n} \, dx","IntegrateAlgebraic[((1 - x)^n*x^2)/(1 + x)^n,x]","\int (1-x)^n x^2 (1+x)^{-n} \, dx","-\frac{2^{-n} \left(2 n^2+1\right) (1-x)^{n+1} \, _2F_1\left(n,n+1;n+2;\frac{1-x}{2}\right)}{3 (n+1)}+\frac{1}{3} n (1-x)^{n+1} (x+1)^{1-n}-\frac{1}{3} x (1-x)^{n+1} (x+1)^{1-n}",1,"Could not integrate","F",-1
980,0,0,61,0.0191381,"\int (1-x)^n x (1+x)^{-n} \, dx","IntegrateAlgebraic[((1 - x)^n*x)/(1 + x)^n,x]","\int (1-x)^n x (1+x)^{-n} \, dx","\frac{2^{-n} n (1-x)^{n+1} \, _2F_1\left(n,n+1;n+2;\frac{1-x}{2}\right)}{n+1}-\frac{1}{2} (1-x)^{n+1} (x+1)^{1-n}",1,"Could not integrate","F",-1
981,0,0,38,0.0219344,"\int (1-x)^n (1+x)^{-n} \, dx","IntegrateAlgebraic[(1 - x)^n/(1 + x)^n,x]","\int (1-x)^n (1+x)^{-n} \, dx","-\frac{2^{-n} (1-x)^{n+1} \, _2F_1\left(n,n+1;n+2;\frac{1-x}{2}\right)}{n+1}",1,"Could not integrate","F",-1
982,0,0,68,0.0214016,"\int \frac{(1-x)^n (1+x)^{-n}}{x} \, dx","IntegrateAlgebraic[(1 - x)^n/(x*(1 + x)^n),x]","\int \frac{(1-x)^n (1+x)^{-n}}{x} \, dx","\frac{2^{-n} (1-x)^n \, _2F_1\left(n,n;n+1;\frac{1-x}{2}\right)}{n}-\frac{(1-x)^n (x+1)^{-n} \, _2F_1\left(1,n;n+1;\frac{1-x}{x+1}\right)}{n}",1,"Could not integrate","F",-1
983,0,0,44,0.0217569,"\int \frac{(1-x)^n (1+x)^{-n}}{x^2} \, dx","IntegrateAlgebraic[(1 - x)^n/(x^2*(1 + x)^n),x]","\int \frac{(1-x)^n (1+x)^{-n}}{x^2} \, dx","-\frac{2 (1-x)^{n+1} (x+1)^{-n-1} \, _2F_1\left(2,n+1;n+2;\frac{1-x}{x+1}\right)}{n+1}",1,"Could not integrate","F",-1
984,0,0,71,0.0219281,"\int \frac{(1-x)^n (1+x)^{-n}}{x^3} \, dx","IntegrateAlgebraic[(1 - x)^n/(x^3*(1 + x)^n),x]","\int \frac{(1-x)^n (1+x)^{-n}}{x^3} \, dx","\frac{2 n (1-x)^{n+1} (x+1)^{-n-1} \, _2F_1\left(2,n+1;n+2;\frac{1-x}{x+1}\right)}{n+1}-\frac{(1-x)^{n+1} (x+1)^{1-n}}{2 x^2}",1,"Could not integrate","F",-1
985,0,0,105,0.0226218,"\int \frac{(1-x)^n (1+x)^{-n}}{x^4} \, dx","IntegrateAlgebraic[(1 - x)^n/(x^4*(1 + x)^n),x]","\int \frac{(1-x)^n (1+x)^{-n}}{x^4} \, dx","-\frac{2 \left(2 n^2+1\right) (1-x)^{n+1} (x+1)^{-n-1} \, _2F_1\left(2,n+1;n+2;\frac{1-x}{x+1}\right)}{3 (n+1)}-\frac{(1-x)^{n+1} (x+1)^{1-n}}{3 x^3}+\frac{n (1-x)^{n+1} (x+1)^{1-n}}{3 x^2}",1,"Could not integrate","F",-1
986,0,0,36,0.0259588,"\int x^m (1-a x)^n (1+a x)^n \, dx","IntegrateAlgebraic[x^m*(1 - a*x)^n*(1 + a*x)^n,x]","\int x^m (1-a x)^n (1+a x)^n \, dx","\frac{x^{m+1} \, _2F_1\left(\frac{m+1}{2},-n;\frac{m+3}{2};a^2 x^2\right)}{m+1}",1,"Could not integrate","F",-1
987,0,0,39,0.027865,"\int x^m (1-a x)^n (2+2 a x)^n \, dx","IntegrateAlgebraic[x^m*(1 - a*x)^n*(2 + 2*a*x)^n,x]","\int x^m (1-a x)^n (2+2 a x)^n \, dx","\frac{2^n x^{m+1} \, _2F_1\left(\frac{m+1}{2},-n;\frac{m+3}{2};a^2 x^2\right)}{m+1}",1,"Could not integrate","F",-1
988,0,0,42,0.0261461,"\int x^m (2-a x)^n (2+a x)^n \, dx","IntegrateAlgebraic[x^m*(2 - a*x)^n*(2 + a*x)^n,x]","\int x^m (2-a x)^n (2+a x)^n \, dx","\frac{4^n x^{m+1} \, _2F_1\left(\frac{m+1}{2},-n;\frac{m+3}{2};\frac{a^2 x^2}{4}\right)}{m+1}",1,"Could not integrate","F",-1
989,0,0,42,0.0287217,"\int x^m \left(1-\frac{a x}{2}\right)^n (2+a x)^n \, dx","IntegrateAlgebraic[x^m*(1 - (a*x)/2)^n*(2 + a*x)^n,x]","\int x^m \left(1-\frac{a x}{2}\right)^n (2+a x)^n \, dx","\frac{2^n x^{m+1} \, _2F_1\left(\frac{m+1}{2},-n;\frac{m+3}{2};\frac{a^2 x^2}{4}\right)}{m+1}",1,"Could not integrate","F",-1
990,0,0,151,0.0362574,"\int x^m (3-2 a x)^{2+n} (6+4 a x)^n \, dx","IntegrateAlgebraic[x^m*(3 - 2*a*x)^(2 + n)*(6 + 4*a*x)^n,x]","\int x^m (3-2 a x)^{2+n} (6+4 a x)^n \, dx","\frac{2^n 9^{n+1} x^{m+1} \, _2F_1\left(\frac{m+1}{2},-n;\frac{m+3}{2};\frac{4 a^2 x^2}{9}\right)}{m+1}-\frac{a 2^{n+2} 3^{2 n+1} x^{m+2} \, _2F_1\left(\frac{m+2}{2},-n;\frac{m+4}{2};\frac{4 a^2 x^2}{9}\right)}{m+2}+\frac{a^2 2^{n+2} 9^n x^{m+3} \, _2F_1\left(\frac{m+3}{2},-n;\frac{m+5}{2};\frac{4 a^2 x^2}{9}\right)}{m+3}",1,"Could not integrate","F",-1
991,0,0,99,0.0339524,"\int x^m (3-2 a x)^{1+n} (6+4 a x)^n \, dx","IntegrateAlgebraic[x^m*(3 - 2*a*x)^(1 + n)*(6 + 4*a*x)^n,x]","\int x^m (3-2 a x)^{1+n} (6+4 a x)^n \, dx","\frac{2^n 3^{2 n+1} x^{m+1} \, _2F_1\left(\frac{m+1}{2},-n;\frac{m+3}{2};\frac{4 a^2 x^2}{9}\right)}{m+1}-\frac{a 2^{n+1} 9^n x^{m+2} \, _2F_1\left(\frac{m+2}{2},-n;\frac{m+4}{2};\frac{4 a^2 x^2}{9}\right)}{m+2}",1,"Could not integrate","F",-1
992,0,0,42,0.0289788,"\int x^m (3-2 a x)^n (6+4 a x)^n \, dx","IntegrateAlgebraic[x^m*(3 - 2*a*x)^n*(6 + 4*a*x)^n,x]","\int x^m (3-2 a x)^n (6+4 a x)^n \, dx","\frac{18^n x^{m+1} \, _2F_1\left(\frac{m+1}{2},-n;\frac{m+3}{2};\frac{4 a^2 x^2}{9}\right)}{m+1}",1,"Could not integrate","F",-1
993,0,0,104,0.0373143,"\int x^m (3-2 a x)^{-1+n} (6+4 a x)^n \, dx","IntegrateAlgebraic[x^m*(3 - 2*a*x)^(-1 + n)*(6 + 4*a*x)^n,x]","\int x^m (3-2 a x)^{-1+n} (6+4 a x)^n \, dx","\frac{2^n 3^{2 n-1} x^{m+1} \, _2F_1\left(\frac{m+1}{2},1-n;\frac{m+3}{2};\frac{4 a^2 x^2}{9}\right)}{m+1}+\frac{a 2^{n+1} 9^{n-1} x^{m+2} \, _2F_1\left(\frac{m+2}{2},1-n;\frac{m+4}{2};\frac{4 a^2 x^2}{9}\right)}{m+2}",1,"Could not integrate","F",-1
994,0,0,158,0.0370569,"\int x^m (3-2 a x)^{-2+n} (6+4 a x)^n \, dx","IntegrateAlgebraic[x^m*(3 - 2*a*x)^(-2 + n)*(6 + 4*a*x)^n,x]","\int x^m (3-2 a x)^{-2+n} (6+4 a x)^n \, dx","\frac{2^n 9^{n-1} x^{m+1} \, _2F_1\left(\frac{m+1}{2},2-n;\frac{m+3}{2};\frac{4 a^2 x^2}{9}\right)}{m+1}+\frac{a 2^{n+2} 3^{2 n-3} x^{m+2} \, _2F_1\left(\frac{m+2}{2},2-n;\frac{m+4}{2};\frac{4 a^2 x^2}{9}\right)}{m+2}+\frac{a^2 2^{n+2} 9^{n-2} x^{m+3} \, _2F_1\left(\frac{m+3}{2},2-n;\frac{m+5}{2};\frac{4 a^2 x^2}{9}\right)}{m+3}",1,"Could not integrate","F",-1
995,0,0,79,0.0362064,"\int x^m (a+b x)^{1+n} (c+d x)^n \, dx","IntegrateAlgebraic[x^m*(a + b*x)^(1 + n)*(c + d*x)^n,x]","\int x^m (a+b x)^{1+n} (c+d x)^n \, dx","\frac{a x^{m+1} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} F_1\left(m+1;-n-1,-n;m+2;-\frac{b x}{a},-\frac{d x}{c}\right)}{m+1}",1,"Could not integrate","F",-1
996,0,0,79,0.0318562,"\int (a-x)^m (f x)^p (c+d x)^n \, dx","IntegrateAlgebraic[(a - x)^m*(f*x)^p*(c + d*x)^n,x]","\int (a-x)^m (f x)^p (c+d x)^n \, dx","\frac{(a-x)^m \left(1-\frac{x}{a}\right)^{-m} (f x)^{p+1} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} F_1\left(p+1;-m,-n;p+2;\frac{x}{a},-\frac{d x}{c}\right)}{f (p+1)}",1,"Could not integrate","F",-1
997,0,0,83,0.0493932,"\int (1-x)^{-\frac{1}{2}+p} (c x)^{-2 (1+p)} (1+x)^{\frac{1}{2}+p} \, dx","IntegrateAlgebraic[((1 - x)^(-1/2 + p)*(1 + x)^(1/2 + p))/(c*x)^(2*(1 + p)),x]","\int (1-x)^{-\frac{1}{2}+p} (c x)^{-2 (1+p)} (1+x)^{\frac{1}{2}+p} \, dx","-\frac{4^{p+1} (1-x)^{p+\frac{1}{2}} \left(\frac{x}{x+1}\right)^{2 (p+1)} (x+1)^{p+\frac{3}{2}} (c x)^{-2 (p+1)} \, _2F_1\left(p+\frac{1}{2},2 (p+1);p+\frac{3}{2};\frac{1-x}{x+1}\right)}{2 p+1}",1,"Could not integrate","F",-1
998,0,0,70,0.0521039,"\int \frac{\left(1-\frac{x}{a}\right)^{-n/2} \left(1+\frac{x}{a}\right)^{n/2}}{x^2} \, dx","IntegrateAlgebraic[(1 + x/a)^(n/2)/(x^2*(1 - x/a)^(n/2)),x]","\int \frac{\left(1-\frac{x}{a}\right)^{-n/2} \left(1+\frac{x}{a}\right)^{n/2}}{x^2} \, dx","-\frac{4 \left(1-\frac{x}{a}\right)^{1-\frac{n}{2}} \left(\frac{x}{a}+1\right)^{\frac{n-2}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{a-x}{a+x}\right)}{a (2-n)}",1,"Could not integrate","F",-1
999,0,0,50,0.0426306,"\int (b x)^{-2-2 m} (1-a x)^m (1+a x)^m \, dx","IntegrateAlgebraic[(b*x)^(-2 - 2*m)*(1 - a*x)^m*(1 + a*x)^m,x]","\int (b x)^{-2-2 m} (1-a x)^m (1+a x)^m \, dx","-\frac{(b x)^{-2 m-1} \, _2F_1\left(\frac{1}{2} (-2 m-1),-m;\frac{1}{2} (1-2 m);a^2 x^2\right)}{b (2 m+1)}",1,"Could not integrate","F",-1
1000,0,0,86,0.0453989,"\int \frac{(1-a x)^{-n} (1+a x)^n}{x} \, dx","IntegrateAlgebraic[(1 + a*x)^n/(x*(1 - a*x)^n),x]","\int \frac{(1-a x)^{-n} (1+a x)^n}{x} \, dx","\frac{(1-a x)^{-n} (a x+1)^n \, _2F_1\left(1,-n;1-n;\frac{1-a x}{a x+1}\right)}{n}-\frac{2^n (1-a x)^{-n} \, _2F_1\left(-n,-n;1-n;\frac{1}{2} (1-a x)\right)}{n}",1,"Could not integrate","F",-1
1001,0,0,106,0.030567,"\int \frac{(1-a x)^{1-n} (1+a x)^{1+n}}{x^2} \, dx","IntegrateAlgebraic[((1 - a*x)^(1 - n)*(1 + a*x)^(1 + n))/x^2,x]","\int \frac{(1-a x)^{1-n} (1+a x)^{1+n}}{x^2} \, dx","\frac{a 2^n (1-a x)^{1-n} \, _2F_1\left(1-n,-n;2-n;\frac{1}{2} (1-a x)\right)}{1-n}-\frac{2 a (1-a x)^{1-n} (a x+1)^{n-1} \, _2F_1\left(2,1-n;2-n;\frac{1-a x}{a x+1}\right)}{1-n}",1,"Could not integrate","F",-1
1002,1,27,28,0.0232688,"\int \frac{x^2}{(1-a x)^7 (1+a x)^4} \, dx","IntegrateAlgebraic[x^2/((1 - a*x)^7*(1 + a*x)^4),x]","\frac{3 a x-1}{24 a^3 (a x-1)^6 (a x+1)^3}","-\frac{1-3 a x}{24 a^3 (1-a x)^6 (a x+1)^3}",1,"(-1 + 3*a*x)/(24*a^3*(-1 + a*x)^6*(1 + a*x)^3)","A",1
1003,1,27,28,0.0297719,"\int \frac{x^2}{(1-a x)^{11} (1+a x)^7} \, dx","IntegrateAlgebraic[x^2/((1 - a*x)^11*(1 + a*x)^7),x]","\frac{4 a x-1}{60 a^3 (a x-1)^{10} (a x+1)^6}","-\frac{1-4 a x}{60 a^3 (1-a x)^{10} (a x+1)^6}",1,"(-1 + 4*a*x)/(60*a^3*(-1 + a*x)^10*(1 + a*x)^6)","A",1
1004,1,27,28,0.3471759,"\int \frac{x^2}{(1-a x)^{16} (1+a x)^{11}} \, dx","IntegrateAlgebraic[x^2/((1 - a*x)^16*(1 + a*x)^11),x]","\frac{1-5 a x}{120 a^3 (a x-1)^{15} (a x+1)^{10}}","-\frac{1-5 a x}{120 a^3 (1-a x)^{15} (a x+1)^{10}}",1,"(1 - 5*a*x)/(120*a^3*(-1 + a*x)^15*(1 + a*x)^10)","A",1
1005,0,0,54,0.2852282,"\int x^2 (1-a x)^{-1-\frac{1}{2} n (1+n)} (1+a x)^{-1-\frac{1}{2} (-1+n) n} \, dx","IntegrateAlgebraic[x^2*(1 - a*x)^(-1 - (n*(1 + n))/2)*(1 + a*x)^(-1 - ((-1 + n)*n)/2),x]","\int x^2 (1-a x)^{-1-\frac{1}{2} n (1+n)} (1+a x)^{-1-\frac{1}{2} (-1+n) n} \, dx","\frac{(1-a x)^{-\frac{1}{2} n (n+1)} (a x+1)^{\frac{1}{2} (1-n) n} (1-a n x)}{a^3 n \left(1-n^2\right)}",1,"Could not integrate","F",-1
1006,0,0,142,0.0299474,"\int \frac{(a-b x)^{-n} (a+b x)^{1+n}}{x} \, dx","IntegrateAlgebraic[(a + b*x)^(1 + n)/(x*(a - b*x)^n),x]","\int \frac{(a-b x)^{-n} (a+b x)^{1+n}}{x} \, dx","-\frac{a (a+b x)^n (a-b x)^{-n} \, _2F_1\left(1,n;n+1;\frac{a+b x}{a-b x}\right)}{n}+\frac{2^{-n-1} (2 n+1) \left(\frac{a-b x}{a}\right)^n (a+b x)^{n+1} (a-b x)^{-n} \, _2F_1\left(n,n+1;n+2;\frac{a+b x}{2 a}\right)}{n (n+1)}+\frac{(a+b x)^n (a-b x)^{1-n}}{2 n}",1,"Could not integrate","F",-1
1007,0,0,140,0.032365,"\int \frac{(a-b x)^{-n} (a+b x)^{1+n}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x)^(1 + n)/(x^2*(a - b*x)^n),x]","\int \frac{(a-b x)^{-n} (a+b x)^{1+n}}{x^2} \, dx","\frac{b (2 n+1) (a+b x)^n (a-b x)^{-n} \, _2F_1\left(1,-n;1-n;\frac{a-b x}{a+b x}\right)}{n}-\frac{b 2^n (a+b x)^n \left(\frac{a+b x}{a}\right)^{-n} (a-b x)^{-n} \, _2F_1\left(-n,-n;1-n;\frac{a-b x}{2 a}\right)}{n}-\frac{(a+b x)^{n+1} (a-b x)^{-n}}{x}",1,"Could not integrate","F",-1
1008,0,0,62,0.0348908,"\int \frac{(a-b x)^{-n} (a+b x)^{1+n}}{x^3} \, dx","IntegrateAlgebraic[(a + b*x)^(1 + n)/(x^3*(a - b*x)^n),x]","\int \frac{(a-b x)^{-n} (a+b x)^{1+n}}{x^3} \, dx","-\frac{4 b^2 (a-b x)^{1-n} (a+b x)^{n-1} \, _2F_1\left(3,1-n;2-n;\frac{a-b x}{a+b x}\right)}{a (1-n)}",1,"Could not integrate","F",-1
1009,0,0,101,0.0361967,"\int \frac{(a-b x)^{-n} (a+b x)^{1+n}}{x^4} \, dx","IntegrateAlgebraic[(a + b*x)^(1 + n)/(x^4*(a - b*x)^n),x]","\int \frac{(a-b x)^{-n} (a+b x)^{1+n}}{x^4} \, dx","-\frac{4 b^3 (2 n+1) (a+b x)^{n-1} (a-b x)^{1-n} \, _2F_1\left(3,1-n;2-n;\frac{a-b x}{a+b x}\right)}{3 a^2 (1-n)}-\frac{(a+b x)^{n+2} (a-b x)^{1-n}}{3 a^2 x^3}",1,"Could not integrate","F",-1
1010,0,0,139,0.2077018,"\int \frac{(a-b x)^{-n} (a+b x)^{1+n}}{x^5} \, dx","IntegrateAlgebraic[(a + b*x)^(1 + n)/(x^5*(a - b*x)^n),x]","\int \frac{(a-b x)^{-n} (a+b x)^{1+n}}{x^5} \, dx","-\frac{4 b^4 \left(n^2+n+1\right) (a+b x)^{n-1} (a-b x)^{1-n} \, _2F_1\left(3,1-n;2-n;\frac{a-b x}{a+b x}\right)}{3 a^3 (1-n)}-\frac{b (2 n+1) (a+b x)^{n+2} (a-b x)^{1-n}}{12 a^3 x^3}-\frac{(a+b x)^{n+2} (a-b x)^{1-n}}{4 a^2 x^4}",1,"Could not integrate","F",-1
1011,1,223,77,0.4014856,"\int (a+b x) (A+B x) (d+e x)^4 \, dx","IntegrateAlgebraic[(a + b*x)*(A + B*x)*(d + e*x)^4,x]","\frac{1}{210} \left(210 a A d^4 x+420 a A d^3 e x^2+420 a A d^2 e^2 x^3+210 a A d e^3 x^4+42 a A e^4 x^5+105 a B d^4 x^2+280 a B d^3 e x^3+315 a B d^2 e^2 x^4+168 a B d e^3 x^5+35 a B e^4 x^6+105 A b d^4 x^2+280 A b d^3 e x^3+315 A b d^2 e^2 x^4+168 A b d e^3 x^5+35 A b e^4 x^6+70 b B d^4 x^3+210 b B d^3 e x^4+252 b B d^2 e^2 x^5+140 b B d e^3 x^6+30 b B e^4 x^7\right)","-\frac{(d+e x)^6 (-a B e-A b e+2 b B d)}{6 e^3}+\frac{(d+e x)^5 (b d-a e) (B d-A e)}{5 e^3}+\frac{b B (d+e x)^7}{7 e^3}",1,"(210*a*A*d^4*x + 105*A*b*d^4*x^2 + 105*a*B*d^4*x^2 + 420*a*A*d^3*e*x^2 + 70*b*B*d^4*x^3 + 280*A*b*d^3*e*x^3 + 280*a*B*d^3*e*x^3 + 420*a*A*d^2*e^2*x^3 + 210*b*B*d^3*e*x^4 + 315*A*b*d^2*e^2*x^4 + 315*a*B*d^2*e^2*x^4 + 210*a*A*d*e^3*x^4 + 252*b*B*d^2*e^2*x^5 + 168*A*b*d*e^3*x^5 + 168*a*B*d*e^3*x^5 + 42*a*A*e^4*x^5 + 140*b*B*d*e^3*x^6 + 35*A*b*e^4*x^6 + 35*a*B*e^4*x^6 + 30*b*B*e^4*x^7)/210","B",1
1012,1,171,77,0.2176799,"\int (a+b x) (A+B x) (d+e x)^3 \, dx","IntegrateAlgebraic[(a + b*x)*(A + B*x)*(d + e*x)^3,x]","\frac{1}{60} \left(60 a A d^3 x+90 a A d^2 e x^2+60 a A d e^2 x^3+15 a A e^3 x^4+30 a B d^3 x^2+60 a B d^2 e x^3+45 a B d e^2 x^4+12 a B e^3 x^5+30 A b d^3 x^2+60 A b d^2 e x^3+45 A b d e^2 x^4+12 A b e^3 x^5+20 b B d^3 x^3+45 b B d^2 e x^4+36 b B d e^2 x^5+10 b B e^3 x^6\right)","-\frac{(d+e x)^5 (-a B e-A b e+2 b B d)}{5 e^3}+\frac{(d+e x)^4 (b d-a e) (B d-A e)}{4 e^3}+\frac{b B (d+e x)^6}{6 e^3}",1,"(60*a*A*d^3*x + 30*A*b*d^3*x^2 + 30*a*B*d^3*x^2 + 90*a*A*d^2*e*x^2 + 20*b*B*d^3*x^3 + 60*A*b*d^2*e*x^3 + 60*a*B*d^2*e*x^3 + 60*a*A*d*e^2*x^3 + 45*b*B*d^2*e*x^4 + 45*A*b*d*e^2*x^4 + 45*a*B*d*e^2*x^4 + 15*a*A*e^3*x^4 + 36*b*B*d*e^2*x^5 + 12*A*b*e^3*x^5 + 12*a*B*e^3*x^5 + 10*b*B*e^3*x^6)/60","B",1
1013,1,119,77,0.0702439,"\int (a+b x) (A+B x) (d+e x)^2 \, dx","IntegrateAlgebraic[(a + b*x)*(A + B*x)*(d + e*x)^2,x]","\frac{1}{60} \left(60 a A d^2 x+60 a A d e x^2+20 a A e^2 x^3+30 a B d^2 x^2+40 a B d e x^3+15 a B e^2 x^4+30 A b d^2 x^2+40 A b d e x^3+15 A b e^2 x^4+20 b B d^2 x^3+30 b B d e x^4+12 b B e^2 x^5\right)","-\frac{(d+e x)^4 (-a B e-A b e+2 b B d)}{4 e^3}+\frac{(d+e x)^3 (b d-a e) (B d-A e)}{3 e^3}+\frac{b B (d+e x)^5}{5 e^3}",1,"(60*a*A*d^2*x + 30*A*b*d^2*x^2 + 30*a*B*d^2*x^2 + 60*a*A*d*e*x^2 + 20*b*B*d^2*x^3 + 40*A*b*d*e*x^3 + 40*a*B*d*e*x^3 + 20*a*A*e^2*x^3 + 30*b*B*d*e*x^4 + 15*A*b*e^2*x^4 + 15*a*B*e^2*x^4 + 12*b*B*e^2*x^5)/60","A",1
1014,1,61,56,0.0466809,"\int (a+b x) (A+B x) (d+e x) \, dx","IntegrateAlgebraic[(a + b*x)*(A + B*x)*(d + e*x),x]","\frac{1}{12} x \left(12 a A d+6 a A e x+6 a B d x+4 a B e x^2+6 A b d x+4 A b e x^2+4 b B d x^2+3 b B e x^3\right)","\frac{1}{3} x^3 (a B e+A b e+b B d)+\frac{1}{2} x^2 (a A e+a B d+A b d)+a A d x+\frac{1}{4} b B e x^4",1,"(x*(12*a*A*d + 6*A*b*d*x + 6*a*B*d*x + 6*a*A*e*x + 4*b*B*d*x^2 + 4*A*b*e*x^2 + 4*a*B*e*x^2 + 3*b*B*e*x^3))/12","A",1
1015,1,27,28,0.0005802,"\int (a+b x) (A+B x) \, dx","IntegrateAlgebraic[(a + b*x)*(A + B*x),x]","\frac{1}{6} x \left(6 a A+3 a B x+3 A b x+2 b B x^2\right)","\frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} b B x^3",1,"(x*(6*a*A + 3*A*b*x + 3*a*B*x + 2*b*B*x^2))/6","A",1
1016,1,65,60,0.0405904,"\int \frac{(a+b x) (A+B x)}{d+e x} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/(d + e*x),x]","\frac{\log (d+e x) \left(a A e^2-a B d e-A b d e+b B d^2\right)}{e^3}+\frac{x (2 a B e+2 A b e-2 b B d+b B e x)}{2 e^2}","\frac{(b d-a e) (B d-A e) \log (d+e x)}{e^3}+\frac{B (a+b x)^2}{2 b e}-\frac{b x (B d-A e)}{e^2}",1,"(x*(-2*b*B*d + 2*A*b*e + 2*a*B*e + b*B*e*x))/(2*e^2) + ((b*B*d^2 - A*b*d*e - a*B*d*e + a*A*e^2)*Log[d + e*x])/e^3","A",1
1017,1,76,63,0.0703563,"\int \frac{(a+b x) (A+B x)}{(d+e x)^2} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/(d + e*x)^2,x]","\frac{-a A e^2+a B d e+A b d e-b B d^2+b B d e x+b B e^2 x^2}{e^3 (d+e x)}+\frac{\log (d+e x) (a B e+A b e-2 b B d)}{e^3}","-\frac{(b d-a e) (B d-A e)}{e^3 (d+e x)}-\frac{\log (d+e x) (-a B e-A b e+2 b B d)}{e^3}+\frac{b B x}{e^2}",1,"(-(b*B*d^2) + A*b*d*e + a*B*d*e - a*A*e^2 + b*B*d*e*x + b*B*e^2*x^2)/(e^3*(d + e*x)) + ((-2*b*B*d + A*b*e + a*B*e)*Log[d + e*x])/e^3","A",1
1018,1,77,70,0.0637911,"\int \frac{(a+b x) (A+B x)}{(d+e x)^3} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/(d + e*x)^3,x]","\frac{-a A e^2-a B d e-2 a B e^2 x-A b d e-2 A b e^2 x+3 b B d^2+4 b B d e x}{2 e^3 (d+e x)^2}+\frac{b B \log (d+e x)}{e^3}","-\frac{(b d-a e) (B d-A e)}{2 e^3 (d+e x)^2}+\frac{-a B e-A b e+2 b B d}{e^3 (d+e x)}+\frac{b B \log (d+e x)}{e^3}",1,"(3*b*B*d^2 - A*b*d*e - a*B*d*e - a*A*e^2 + 4*b*B*d*e*x - 2*A*b*e^2*x - 2*a*B*e^2*x)/(2*e^3*(d + e*x)^2) + (b*B*Log[d + e*x])/e^3","A",1
1019,1,74,75,0.0435556,"\int \frac{(a+b x) (A+B x)}{(d+e x)^4} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/(d + e*x)^4,x]","\frac{-2 a A e^2-a B d e-3 a B e^2 x-A b d e-3 A b e^2 x-2 b B d^2-6 b B d e x-6 b B e^2 x^2}{6 e^3 (d+e x)^3}","\frac{-a B e-A b e+2 b B d}{2 e^3 (d+e x)^2}-\frac{(b d-a e) (B d-A e)}{3 e^3 (d+e x)^3}-\frac{b B}{e^3 (d+e x)}",1,"(-2*b*B*d^2 - A*b*d*e - a*B*d*e - 2*a*A*e^2 - 6*b*B*d*e*x - 3*A*b*e^2*x - 3*a*B*e^2*x - 6*b*B*e^2*x^2)/(6*e^3*(d + e*x)^3)","A",1
1020,1,74,77,0.0412094,"\int \frac{(a+b x) (A+B x)}{(d+e x)^5} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/(d + e*x)^5,x]","\frac{-3 a A e^2-a B d e-4 a B e^2 x-A b d e-4 A b e^2 x-b B d^2-4 b B d e x-6 b B e^2 x^2}{12 e^3 (d+e x)^4}","\frac{-a B e-A b e+2 b B d}{3 e^3 (d+e x)^3}-\frac{(b d-a e) (B d-A e)}{4 e^3 (d+e x)^4}-\frac{b B}{2 e^3 (d+e x)^2}",1,"(-(b*B*d^2) - A*b*d*e - a*B*d*e - 3*a*A*e^2 - 4*b*B*d*e*x - 4*A*b*e^2*x - 4*a*B*e^2*x - 6*b*B*e^2*x^2)/(12*e^3*(d + e*x)^4)","A",1
1021,1,74,77,0.043491,"\int \frac{(a+b x) (A+B x)}{(d+e x)^6} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/(d + e*x)^6,x]","\frac{-12 a A e^2-3 a B d e-15 a B e^2 x-3 A b d e-15 A b e^2 x-2 b B d^2-10 b B d e x-20 b B e^2 x^2}{60 e^3 (d+e x)^5}","\frac{-a B e-A b e+2 b B d}{4 e^3 (d+e x)^4}-\frac{(b d-a e) (B d-A e)}{5 e^3 (d+e x)^5}-\frac{b B}{3 e^3 (d+e x)^3}",1,"(-2*b*B*d^2 - 3*A*b*d*e - 3*a*B*d*e - 12*a*A*e^2 - 10*b*B*d*e*x - 15*A*b*e^2*x - 15*a*B*e^2*x - 20*b*B*e^2*x^2)/(60*e^3*(d + e*x)^5)","A",1
1022,1,383,120,0.2237968,"\int (a+b x)^2 (A+B x) (d+e x)^4 \, dx","IntegrateAlgebraic[(a + b*x)^2*(A + B*x)*(d + e*x)^4,x]","\frac{1}{840} \left(840 a^2 A d^4 x+1680 a^2 A d^3 e x^2+1680 a^2 A d^2 e^2 x^3+840 a^2 A d e^3 x^4+168 a^2 A e^4 x^5+420 a^2 B d^4 x^2+1120 a^2 B d^3 e x^3+1260 a^2 B d^2 e^2 x^4+672 a^2 B d e^3 x^5+140 a^2 B e^4 x^6+840 a A b d^4 x^2+2240 a A b d^3 e x^3+2520 a A b d^2 e^2 x^4+1344 a A b d e^3 x^5+280 a A b e^4 x^6+560 a b B d^4 x^3+1680 a b B d^3 e x^4+2016 a b B d^2 e^2 x^5+1120 a b B d e^3 x^6+240 a b B e^4 x^7+280 A b^2 d^4 x^3+840 A b^2 d^3 e x^4+1008 A b^2 d^2 e^2 x^5+560 A b^2 d e^3 x^6+120 A b^2 e^4 x^7+210 b^2 B d^4 x^4+672 b^2 B d^3 e x^5+840 b^2 B d^2 e^2 x^6+480 b^2 B d e^3 x^7+105 b^2 B e^4 x^8\right)","-\frac{b (d+e x)^7 (-2 a B e-A b e+3 b B d)}{7 e^4}+\frac{(d+e x)^6 (b d-a e) (-a B e-2 A b e+3 b B d)}{6 e^4}-\frac{(d+e x)^5 (b d-a e)^2 (B d-A e)}{5 e^4}+\frac{b^2 B (d+e x)^8}{8 e^4}",1,"(840*a^2*A*d^4*x + 840*a*A*b*d^4*x^2 + 420*a^2*B*d^4*x^2 + 1680*a^2*A*d^3*e*x^2 + 280*A*b^2*d^4*x^3 + 560*a*b*B*d^4*x^3 + 2240*a*A*b*d^3*e*x^3 + 1120*a^2*B*d^3*e*x^3 + 1680*a^2*A*d^2*e^2*x^3 + 210*b^2*B*d^4*x^4 + 840*A*b^2*d^3*e*x^4 + 1680*a*b*B*d^3*e*x^4 + 2520*a*A*b*d^2*e^2*x^4 + 1260*a^2*B*d^2*e^2*x^4 + 840*a^2*A*d*e^3*x^4 + 672*b^2*B*d^3*e*x^5 + 1008*A*b^2*d^2*e^2*x^5 + 2016*a*b*B*d^2*e^2*x^5 + 1344*a*A*b*d*e^3*x^5 + 672*a^2*B*d*e^3*x^5 + 168*a^2*A*e^4*x^5 + 840*b^2*B*d^2*e^2*x^6 + 560*A*b^2*d*e^3*x^6 + 1120*a*b*B*d*e^3*x^6 + 280*a*A*b*e^4*x^6 + 140*a^2*B*e^4*x^6 + 480*b^2*B*d*e^3*x^7 + 120*A*b^2*e^4*x^7 + 240*a*b*B*e^4*x^7 + 105*b^2*B*e^4*x^8)/840","B",1
1023,1,295,120,0.1630629,"\int (a+b x)^2 (A+B x) (d+e x)^3 \, dx","IntegrateAlgebraic[(a + b*x)^2*(A + B*x)*(d + e*x)^3,x]","\frac{1}{420} \left(420 a^2 A d^3 x+630 a^2 A d^2 e x^2+420 a^2 A d e^2 x^3+105 a^2 A e^3 x^4+210 a^2 B d^3 x^2+420 a^2 B d^2 e x^3+315 a^2 B d e^2 x^4+84 a^2 B e^3 x^5+420 a A b d^3 x^2+840 a A b d^2 e x^3+630 a A b d e^2 x^4+168 a A b e^3 x^5+280 a b B d^3 x^3+630 a b B d^2 e x^4+504 a b B d e^2 x^5+140 a b B e^3 x^6+140 A b^2 d^3 x^3+315 A b^2 d^2 e x^4+252 A b^2 d e^2 x^5+70 A b^2 e^3 x^6+105 b^2 B d^3 x^4+252 b^2 B d^2 e x^5+210 b^2 B d e^2 x^6+60 b^2 B e^3 x^7\right)","-\frac{b (d+e x)^6 (-2 a B e-A b e+3 b B d)}{6 e^4}+\frac{(d+e x)^5 (b d-a e) (-a B e-2 A b e+3 b B d)}{5 e^4}-\frac{(d+e x)^4 (b d-a e)^2 (B d-A e)}{4 e^4}+\frac{b^2 B (d+e x)^7}{7 e^4}",1,"(420*a^2*A*d^3*x + 420*a*A*b*d^3*x^2 + 210*a^2*B*d^3*x^2 + 630*a^2*A*d^2*e*x^2 + 140*A*b^2*d^3*x^3 + 280*a*b*B*d^3*x^3 + 840*a*A*b*d^2*e*x^3 + 420*a^2*B*d^2*e*x^3 + 420*a^2*A*d*e^2*x^3 + 105*b^2*B*d^3*x^4 + 315*A*b^2*d^2*e*x^4 + 630*a*b*B*d^2*e*x^4 + 630*a*A*b*d*e^2*x^4 + 315*a^2*B*d*e^2*x^4 + 105*a^2*A*e^3*x^4 + 252*b^2*B*d^2*e*x^5 + 252*A*b^2*d*e^2*x^5 + 504*a*b*B*d*e^2*x^5 + 168*a*A*b*e^3*x^5 + 84*a^2*B*e^3*x^5 + 210*b^2*B*d*e^2*x^6 + 70*A*b^2*e^3*x^6 + 140*a*b*B*e^3*x^6 + 60*b^2*B*e^3*x^7)/420","B",1
1024,1,207,118,0.1164254,"\int (a+b x)^2 (A+B x) (d+e x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^2*(A + B*x)*(d + e*x)^2,x]","\frac{1}{60} \left(60 a^2 A d^2 x+60 a^2 A d e x^2+20 a^2 A e^2 x^3+30 a^2 B d^2 x^2+40 a^2 B d e x^3+15 a^2 B e^2 x^4+60 a A b d^2 x^2+80 a A b d e x^3+30 a A b e^2 x^4+40 a b B d^2 x^3+60 a b B d e x^4+24 a b B e^2 x^5+20 A b^2 d^2 x^3+30 A b^2 d e x^4+12 A b^2 e^2 x^5+15 b^2 B d^2 x^4+24 b^2 B d e x^5+10 b^2 B e^2 x^6\right)","\frac{e (a+b x)^5 (-3 a B e+A b e+2 b B d)}{5 b^4}+\frac{(a+b x)^4 (b d-a e) (-3 a B e+2 A b e+b B d)}{4 b^4}+\frac{(a+b x)^3 (A b-a B) (b d-a e)^2}{3 b^4}+\frac{B e^2 (a+b x)^6}{6 b^4}",1,"(60*a^2*A*d^2*x + 60*a*A*b*d^2*x^2 + 30*a^2*B*d^2*x^2 + 60*a^2*A*d*e*x^2 + 20*A*b^2*d^2*x^3 + 40*a*b*B*d^2*x^3 + 80*a*A*b*d*e*x^3 + 40*a^2*B*d*e*x^3 + 20*a^2*A*e^2*x^3 + 15*b^2*B*d^2*x^4 + 30*A*b^2*d*e*x^4 + 60*a*b*B*d*e*x^4 + 30*a*A*b*e^2*x^4 + 15*a^2*B*e^2*x^4 + 24*b^2*B*d*e*x^5 + 12*A*b^2*e^2*x^5 + 24*a*b*B*e^2*x^5 + 10*b^2*B*e^2*x^6)/60","A",1
1025,1,119,75,0.0638496,"\int (a+b x)^2 (A+B x) (d+e x) \, dx","IntegrateAlgebraic[(a + b*x)^2*(A + B*x)*(d + e*x),x]","\frac{1}{60} \left(60 a^2 A d x+30 a^2 A e x^2+30 a^2 B d x^2+20 a^2 B e x^3+60 a A b d x^2+40 a A b e x^3+40 a b B d x^3+30 a b B e x^4+20 A b^2 d x^3+15 A b^2 e x^4+15 b^2 B d x^4+12 b^2 B e x^5\right)","\frac{(a+b x)^4 (-2 a B e+A b e+b B d)}{4 b^3}+\frac{(a+b x)^3 (A b-a B) (b d-a e)}{3 b^3}+\frac{B e (a+b x)^5}{5 b^3}",1,"(60*a^2*A*d*x + 60*a*A*b*d*x^2 + 30*a^2*B*d*x^2 + 30*a^2*A*e*x^2 + 20*A*b^2*d*x^3 + 40*a*b*B*d*x^3 + 40*a*A*b*e*x^3 + 20*a^2*B*e*x^3 + 15*b^2*B*d*x^4 + 15*A*b^2*e*x^4 + 30*a*b*B*e*x^4 + 12*b^2*B*e*x^5)/60","A",1
1026,1,51,38,0.0005915,"\int (a+b x)^2 (A+B x) \, dx","IntegrateAlgebraic[(a + b*x)^2*(A + B*x),x]","\frac{1}{12} x \left(12 a^2 A+6 a^2 B x+12 a A b x+8 a b B x^2+4 A b^2 x^2+3 b^2 B x^3\right)","\frac{(a+b x)^3 (A b-a B)}{3 b^2}+\frac{B (a+b x)^4}{4 b^2}",1,"(x*(12*a^2*A + 12*a*A*b*x + 6*a^2*B*x + 4*A*b^2*x^2 + 8*a*b*B*x^2 + 3*b^2*B*x^3))/12","A",1
1027,1,120,92,0.0966442,"\int \frac{(a+b x)^2 (A+B x)}{d+e x} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/(d + e*x),x]","\frac{x \left(6 a^2 B e^2+12 a A b e^2-12 a b B d e+6 a b B e^2 x-6 A b^2 d e+3 A b^2 e^2 x+6 b^2 B d^2-3 b^2 B d e x+2 b^2 B e^2 x^2\right)}{6 e^3}-\frac{(b d-a e)^2 (B d-A e) \log (d+e x)}{e^4}","-\frac{(b d-a e)^2 (B d-A e) \log (d+e x)}{e^4}+\frac{b x (b d-a e) (B d-A e)}{e^3}-\frac{(a+b x)^2 (B d-A e)}{2 e^2}+\frac{B (a+b x)^3}{3 b e}",1,"(x*(6*b^2*B*d^2 - 6*A*b^2*d*e - 12*a*b*B*d*e + 12*a*A*b*e^2 + 6*a^2*B*e^2 - 3*b^2*B*d*e*x + 3*A*b^2*e^2*x + 6*a*b*B*e^2*x + 2*b^2*B*e^2*x^2))/(6*e^3) - ((b*d - a*e)^2*(B*d - A*e)*Log[d + e*x])/e^4","A",1
1028,1,202,101,0.1298213,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^2} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/(d + e*x)^2,x]","\frac{\log (d+e x) \left(a^2 B e^2+2 a A b e^2-4 a b B d e-2 A b^2 d e+3 b^2 B d^2\right)}{e^4}+\frac{-2 a^2 A e^3+2 a^2 B d e^2+4 a A b d e^2-4 a b B d^2 e+4 a b B d e^2 x+4 a b B e^3 x^2-2 A b^2 d^2 e+2 A b^2 d e^2 x+2 A b^2 e^3 x^2+2 b^2 B d^3-4 b^2 B d^2 e x-3 b^2 B d e^2 x^2+b^2 B e^3 x^3}{2 e^4 (d+e x)}","\frac{(b d-a e)^2 (B d-A e)}{e^4 (d+e x)}+\frac{(b d-a e) \log (d+e x) (-a B e-2 A b e+3 b B d)}{e^4}-\frac{b x (-2 a B e-A b e+2 b B d)}{e^3}+\frac{b^2 B x^2}{2 e^2}",1,"(2*b^2*B*d^3 - 2*A*b^2*d^2*e - 4*a*b*B*d^2*e + 4*a*A*b*d*e^2 + 2*a^2*B*d*e^2 - 2*a^2*A*e^3 - 4*b^2*B*d^2*e*x + 2*A*b^2*d*e^2*x + 4*a*b*B*d*e^2*x - 3*b^2*B*d*e^2*x^2 + 2*A*b^2*e^3*x^2 + 4*a*b*B*e^3*x^2 + b^2*B*e^3*x^3)/(2*e^4*(d + e*x)) + ((3*b^2*B*d^2 - 2*A*b^2*d*e - 4*a*b*B*d*e + 2*a*A*b*e^2 + a^2*B*e^2)*Log[d + e*x])/e^4","A",1
1029,1,178,106,0.1325662,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^3} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/(d + e*x)^3,x]","\frac{-a^2 A e^3-a^2 B d e^2-2 a^2 B e^3 x-2 a A b d e^2-4 a A b e^3 x+6 a b B d^2 e+8 a b B d e^2 x+3 A b^2 d^2 e+4 A b^2 d e^2 x-5 b^2 B d^3-4 b^2 B d^2 e x+4 b^2 B d e^2 x^2+2 b^2 B e^3 x^3}{2 e^4 (d+e x)^2}+\frac{\log (d+e x) \left(2 a b B e+A b^2 e-3 b^2 B d\right)}{e^4}","-\frac{(b d-a e) (-a B e-2 A b e+3 b B d)}{e^4 (d+e x)}+\frac{(b d-a e)^2 (B d-A e)}{2 e^4 (d+e x)^2}-\frac{b \log (d+e x) (-2 a B e-A b e+3 b B d)}{e^4}+\frac{b^2 B x}{e^3}",1,"(-5*b^2*B*d^3 + 3*A*b^2*d^2*e + 6*a*b*B*d^2*e - 2*a*A*b*d*e^2 - a^2*B*d*e^2 - a^2*A*e^3 - 4*b^2*B*d^2*e*x + 4*A*b^2*d*e^2*x + 8*a*b*B*d*e^2*x - 4*a*A*b*e^3*x - 2*a^2*B*e^3*x + 4*b^2*B*d*e^2*x^2 + 2*b^2*B*e^3*x^3)/(2*e^4*(d + e*x)^2) + ((-3*b^2*B*d + A*b^2*e + 2*a*b*B*e)*Log[d + e*x])/e^4","A",1
1030,1,173,101,0.1207134,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^4} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/(d + e*x)^4,x]","\frac{-2 a^2 A e^3-a^2 B d e^2-3 a^2 B e^3 x-2 a A b d e^2-6 a A b e^3 x-4 a b B d^2 e-12 a b B d e^2 x-12 a b B e^3 x^2-2 A b^2 d^2 e-6 A b^2 d e^2 x-6 A b^2 e^3 x^2+11 b^2 B d^3+27 b^2 B d^2 e x+18 b^2 B d e^2 x^2}{6 e^4 (d+e x)^3}+\frac{b^2 B \log (d+e x)}{e^4}","-\frac{(a+b x)^3 (B d-A e)}{3 e (d+e x)^3 (b d-a e)}+\frac{2 b B (b d-a e)}{e^4 (d+e x)}-\frac{B (b d-a e)^2}{2 e^4 (d+e x)^2}+\frac{b^2 B \log (d+e x)}{e^4}",1,"(11*b^2*B*d^3 - 2*A*b^2*d^2*e - 4*a*b*B*d^2*e - 2*a*A*b*d*e^2 - a^2*B*d*e^2 - 2*a^2*A*e^3 + 27*b^2*B*d^2*e*x - 6*A*b^2*d*e^2*x - 12*a*b*B*d*e^2*x - 6*a*A*b*e^3*x - 3*a^2*B*e^3*x + 18*b^2*B*d*e^2*x^2 - 6*A*b^2*e^3*x^2 - 12*a*b*B*e^3*x^2)/(6*e^4*(d + e*x)^3) + (b^2*B*Log[d + e*x])/e^4","A",1
1031,1,170,86,0.0793058,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^5} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/(d + e*x)^5,x]","\frac{-3 a^2 A e^3-a^2 B d e^2-4 a^2 B e^3 x-2 a A b d e^2-8 a A b e^3 x-2 a b B d^2 e-8 a b B d e^2 x-12 a b B e^3 x^2-A b^2 d^2 e-4 A b^2 d e^2 x-6 A b^2 e^3 x^2-3 b^2 B d^3-12 b^2 B d^2 e x-18 b^2 B d e^2 x^2-12 b^2 B e^3 x^3}{12 e^4 (d+e x)^4}","\frac{(a+b x)^3 (-4 a B e+A b e+3 b B d)}{12 e (d+e x)^3 (b d-a e)^2}-\frac{(a+b x)^3 (B d-A e)}{4 e (d+e x)^4 (b d-a e)}",1,"(-3*b^2*B*d^3 - A*b^2*d^2*e - 2*a*b*B*d^2*e - 2*a*A*b*d*e^2 - a^2*B*d*e^2 - 3*a^2*A*e^3 - 12*b^2*B*d^2*e*x - 4*A*b^2*d*e^2*x - 8*a*b*B*d*e^2*x - 8*a*A*b*e^3*x - 4*a^2*B*e^3*x - 18*b^2*B*d*e^2*x^2 - 6*A*b^2*e^3*x^2 - 12*a*b*B*e^3*x^2 - 12*b^2*B*e^3*x^3)/(12*e^4*(d + e*x)^4)","A",1
1032,1,170,120,0.0806258,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^6} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/(d + e*x)^6,x]","\frac{-12 a^2 A e^3-3 a^2 B d e^2-15 a^2 B e^3 x-6 a A b d e^2-30 a A b e^3 x-4 a b B d^2 e-20 a b B d e^2 x-40 a b B e^3 x^2-2 A b^2 d^2 e-10 A b^2 d e^2 x-20 A b^2 e^3 x^2-3 b^2 B d^3-15 b^2 B d^2 e x-30 b^2 B d e^2 x^2-30 b^2 B e^3 x^3}{60 e^4 (d+e x)^5}","\frac{b (-2 a B e-A b e+3 b B d)}{3 e^4 (d+e x)^3}-\frac{(b d-a e) (-a B e-2 A b e+3 b B d)}{4 e^4 (d+e x)^4}+\frac{(b d-a e)^2 (B d-A e)}{5 e^4 (d+e x)^5}-\frac{b^2 B}{2 e^4 (d+e x)^2}",1,"(-3*b^2*B*d^3 - 2*A*b^2*d^2*e - 4*a*b*B*d^2*e - 6*a*A*b*d*e^2 - 3*a^2*B*d*e^2 - 12*a^2*A*e^3 - 15*b^2*B*d^2*e*x - 10*A*b^2*d*e^2*x - 20*a*b*B*d*e^2*x - 30*a*A*b*e^3*x - 15*a^2*B*e^3*x - 30*b^2*B*d*e^2*x^2 - 20*A*b^2*e^3*x^2 - 40*a*b*B*e^3*x^2 - 30*b^2*B*e^3*x^3)/(60*e^4*(d + e*x)^5)","A",1
1033,1,170,120,0.0791402,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^7} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/(d + e*x)^7,x]","\frac{-10 a^2 A e^3-2 a^2 B d e^2-12 a^2 B e^3 x-4 a A b d e^2-24 a A b e^3 x-2 a b B d^2 e-12 a b B d e^2 x-30 a b B e^3 x^2-A b^2 d^2 e-6 A b^2 d e^2 x-15 A b^2 e^3 x^2-b^2 B d^3-6 b^2 B d^2 e x-15 b^2 B d e^2 x^2-20 b^2 B e^3 x^3}{60 e^4 (d+e x)^6}","\frac{b (-2 a B e-A b e+3 b B d)}{4 e^4 (d+e x)^4}-\frac{(b d-a e) (-a B e-2 A b e+3 b B d)}{5 e^4 (d+e x)^5}+\frac{(b d-a e)^2 (B d-A e)}{6 e^4 (d+e x)^6}-\frac{b^2 B}{3 e^4 (d+e x)^3}",1,"(-(b^2*B*d^3) - A*b^2*d^2*e - 2*a*b*B*d^2*e - 4*a*A*b*d*e^2 - 2*a^2*B*d*e^2 - 10*a^2*A*e^3 - 6*b^2*B*d^2*e*x - 6*A*b^2*d*e^2*x - 12*a*b*B*d*e^2*x - 24*a*A*b*e^3*x - 12*a^2*B*e^3*x - 15*b^2*B*d*e^2*x^2 - 15*A*b^2*e^3*x^2 - 30*a*b*B*e^3*x^2 - 20*b^2*B*e^3*x^3)/(60*e^4*(d + e*x)^6)","A",1
1034,1,170,120,0.0801576,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^8} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/(d + e*x)^8,x]","\frac{-60 a^2 A e^3-10 a^2 B d e^2-70 a^2 B e^3 x-20 a A b d e^2-140 a A b e^3 x-8 a b B d^2 e-56 a b B d e^2 x-168 a b B e^3 x^2-4 A b^2 d^2 e-28 A b^2 d e^2 x-84 A b^2 e^3 x^2-3 b^2 B d^3-21 b^2 B d^2 e x-63 b^2 B d e^2 x^2-105 b^2 B e^3 x^3}{420 e^4 (d+e x)^7}","\frac{b (-2 a B e-A b e+3 b B d)}{5 e^4 (d+e x)^5}-\frac{(b d-a e) (-a B e-2 A b e+3 b B d)}{6 e^4 (d+e x)^6}+\frac{(b d-a e)^2 (B d-A e)}{7 e^4 (d+e x)^7}-\frac{b^2 B}{4 e^4 (d+e x)^4}",1,"(-3*b^2*B*d^3 - 4*A*b^2*d^2*e - 8*a*b*B*d^2*e - 20*a*A*b*d*e^2 - 10*a^2*B*d*e^2 - 60*a^2*A*e^3 - 21*b^2*B*d^2*e*x - 28*A*b^2*d*e^2*x - 56*a*b*B*d*e^2*x - 140*a*A*b*e^3*x - 70*a^2*B*e^3*x - 63*b^2*B*d*e^2*x^2 - 84*A*b^2*e^3*x^2 - 168*a*b*B*e^3*x^2 - 105*b^2*B*e^3*x^3)/(420*e^4*(d + e*x)^7)","A",1
1035,1,667,163,0.392583,"\int (a+b x)^3 (A+B x) (d+e x)^5 \, dx","IntegrateAlgebraic[(a + b*x)^3*(A + B*x)*(d + e*x)^5,x]","\frac{2520 a^3 A d^5 x+6300 a^3 A d^4 e x^2+8400 a^3 A d^3 e^2 x^3+6300 a^3 A d^2 e^3 x^4+2520 a^3 A d e^4 x^5+420 a^3 A e^5 x^6+1260 a^3 B d^5 x^2+4200 a^3 B d^4 e x^3+6300 a^3 B d^3 e^2 x^4+5040 a^3 B d^2 e^3 x^5+2100 a^3 B d e^4 x^6+360 a^3 B e^5 x^7+3780 a^2 A b d^5 x^2+12600 a^2 A b d^4 e x^3+18900 a^2 A b d^3 e^2 x^4+15120 a^2 A b d^2 e^3 x^5+6300 a^2 A b d e^4 x^6+1080 a^2 A b e^5 x^7+2520 a^2 b B d^5 x^3+9450 a^2 b B d^4 e x^4+15120 a^2 b B d^3 e^2 x^5+12600 a^2 b B d^2 e^3 x^6+5400 a^2 b B d e^4 x^7+945 a^2 b B e^5 x^8+2520 a A b^2 d^5 x^3+9450 a A b^2 d^4 e x^4+15120 a A b^2 d^3 e^2 x^5+12600 a A b^2 d^2 e^3 x^6+5400 a A b^2 d e^4 x^7+945 a A b^2 e^5 x^8+1890 a b^2 B d^5 x^4+7560 a b^2 B d^4 e x^5+12600 a b^2 B d^3 e^2 x^6+10800 a b^2 B d^2 e^3 x^7+4725 a b^2 B d e^4 x^8+840 a b^2 B e^5 x^9+630 A b^3 d^5 x^4+2520 A b^3 d^4 e x^5+4200 A b^3 d^3 e^2 x^6+3600 A b^3 d^2 e^3 x^7+1575 A b^3 d e^4 x^8+280 A b^3 e^5 x^9+504 b^3 B d^5 x^5+2100 b^3 B d^4 e x^6+3600 b^3 B d^3 e^2 x^7+3150 b^3 B d^2 e^3 x^8+1400 b^3 B d e^4 x^9+252 b^3 B e^5 x^{10}}{2520}","-\frac{b^2 (d+e x)^9 (-3 a B e-A b e+4 b B d)}{9 e^5}+\frac{3 b (d+e x)^8 (b d-a e) (-a B e-A b e+2 b B d)}{8 e^5}-\frac{(d+e x)^7 (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{7 e^5}+\frac{(d+e x)^6 (b d-a e)^3 (B d-A e)}{6 e^5}+\frac{b^3 B (d+e x)^{10}}{10 e^5}",1,"(2520*a^3*A*d^5*x + 3780*a^2*A*b*d^5*x^2 + 1260*a^3*B*d^5*x^2 + 6300*a^3*A*d^4*e*x^2 + 2520*a*A*b^2*d^5*x^3 + 2520*a^2*b*B*d^5*x^3 + 12600*a^2*A*b*d^4*e*x^3 + 4200*a^3*B*d^4*e*x^3 + 8400*a^3*A*d^3*e^2*x^3 + 630*A*b^3*d^5*x^4 + 1890*a*b^2*B*d^5*x^4 + 9450*a*A*b^2*d^4*e*x^4 + 9450*a^2*b*B*d^4*e*x^4 + 18900*a^2*A*b*d^3*e^2*x^4 + 6300*a^3*B*d^3*e^2*x^4 + 6300*a^3*A*d^2*e^3*x^4 + 504*b^3*B*d^5*x^5 + 2520*A*b^3*d^4*e*x^5 + 7560*a*b^2*B*d^4*e*x^5 + 15120*a*A*b^2*d^3*e^2*x^5 + 15120*a^2*b*B*d^3*e^2*x^5 + 15120*a^2*A*b*d^2*e^3*x^5 + 5040*a^3*B*d^2*e^3*x^5 + 2520*a^3*A*d*e^4*x^5 + 2100*b^3*B*d^4*e*x^6 + 4200*A*b^3*d^3*e^2*x^6 + 12600*a*b^2*B*d^3*e^2*x^6 + 12600*a*A*b^2*d^2*e^3*x^6 + 12600*a^2*b*B*d^2*e^3*x^6 + 6300*a^2*A*b*d*e^4*x^6 + 2100*a^3*B*d*e^4*x^6 + 420*a^3*A*e^5*x^6 + 3600*b^3*B*d^3*e^2*x^7 + 3600*A*b^3*d^2*e^3*x^7 + 10800*a*b^2*B*d^2*e^3*x^7 + 5400*a*A*b^2*d*e^4*x^7 + 5400*a^2*b*B*d*e^4*x^7 + 1080*a^2*A*b*e^5*x^7 + 360*a^3*B*e^5*x^7 + 3150*b^3*B*d^2*e^3*x^8 + 1575*A*b^3*d*e^4*x^8 + 4725*a*b^2*B*d*e^4*x^8 + 945*a*A*b^2*e^5*x^8 + 945*a^2*b*B*e^5*x^8 + 1400*b^3*B*d*e^4*x^9 + 280*A*b^3*e^5*x^9 + 840*a*b^2*B*e^5*x^9 + 252*b^3*B*e^5*x^10)/2520","B",1
1036,1,543,163,0.3041614,"\int (a+b x)^3 (A+B x) (d+e x)^4 \, dx","IntegrateAlgebraic[(a + b*x)^3*(A + B*x)*(d + e*x)^4,x]","\frac{2520 a^3 A d^4 x+5040 a^3 A d^3 e x^2+5040 a^3 A d^2 e^2 x^3+2520 a^3 A d e^3 x^4+504 a^3 A e^4 x^5+1260 a^3 B d^4 x^2+3360 a^3 B d^3 e x^3+3780 a^3 B d^2 e^2 x^4+2016 a^3 B d e^3 x^5+420 a^3 B e^4 x^6+3780 a^2 A b d^4 x^2+10080 a^2 A b d^3 e x^3+11340 a^2 A b d^2 e^2 x^4+6048 a^2 A b d e^3 x^5+1260 a^2 A b e^4 x^6+2520 a^2 b B d^4 x^3+7560 a^2 b B d^3 e x^4+9072 a^2 b B d^2 e^2 x^5+5040 a^2 b B d e^3 x^6+1080 a^2 b B e^4 x^7+2520 a A b^2 d^4 x^3+7560 a A b^2 d^3 e x^4+9072 a A b^2 d^2 e^2 x^5+5040 a A b^2 d e^3 x^6+1080 a A b^2 e^4 x^7+1890 a b^2 B d^4 x^4+6048 a b^2 B d^3 e x^5+7560 a b^2 B d^2 e^2 x^6+4320 a b^2 B d e^3 x^7+945 a b^2 B e^4 x^8+630 A b^3 d^4 x^4+2016 A b^3 d^3 e x^5+2520 A b^3 d^2 e^2 x^6+1440 A b^3 d e^3 x^7+315 A b^3 e^4 x^8+504 b^3 B d^4 x^5+1680 b^3 B d^3 e x^6+2160 b^3 B d^2 e^2 x^7+1260 b^3 B d e^3 x^8+280 b^3 B e^4 x^9}{2520}","-\frac{b^2 (d+e x)^8 (-3 a B e-A b e+4 b B d)}{8 e^5}+\frac{3 b (d+e x)^7 (b d-a e) (-a B e-A b e+2 b B d)}{7 e^5}-\frac{(d+e x)^6 (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{6 e^5}+\frac{(d+e x)^5 (b d-a e)^3 (B d-A e)}{5 e^5}+\frac{b^3 B (d+e x)^9}{9 e^5}",1,"(2520*a^3*A*d^4*x + 3780*a^2*A*b*d^4*x^2 + 1260*a^3*B*d^4*x^2 + 5040*a^3*A*d^3*e*x^2 + 2520*a*A*b^2*d^4*x^3 + 2520*a^2*b*B*d^4*x^3 + 10080*a^2*A*b*d^3*e*x^3 + 3360*a^3*B*d^3*e*x^3 + 5040*a^3*A*d^2*e^2*x^3 + 630*A*b^3*d^4*x^4 + 1890*a*b^2*B*d^4*x^4 + 7560*a*A*b^2*d^3*e*x^4 + 7560*a^2*b*B*d^3*e*x^4 + 11340*a^2*A*b*d^2*e^2*x^4 + 3780*a^3*B*d^2*e^2*x^4 + 2520*a^3*A*d*e^3*x^4 + 504*b^3*B*d^4*x^5 + 2016*A*b^3*d^3*e*x^5 + 6048*a*b^2*B*d^3*e*x^5 + 9072*a*A*b^2*d^2*e^2*x^5 + 9072*a^2*b*B*d^2*e^2*x^5 + 6048*a^2*A*b*d*e^3*x^5 + 2016*a^3*B*d*e^3*x^5 + 504*a^3*A*e^4*x^5 + 1680*b^3*B*d^3*e*x^6 + 2520*A*b^3*d^2*e^2*x^6 + 7560*a*b^2*B*d^2*e^2*x^6 + 5040*a*A*b^2*d*e^3*x^6 + 5040*a^2*b*B*d*e^3*x^6 + 1260*a^2*A*b*e^4*x^6 + 420*a^3*B*e^4*x^6 + 2160*b^3*B*d^2*e^2*x^7 + 1440*A*b^3*d*e^3*x^7 + 4320*a*b^2*B*d*e^3*x^7 + 1080*a*A*b^2*e^4*x^7 + 1080*a^2*b*B*e^4*x^7 + 1260*b^3*B*d*e^3*x^8 + 315*A*b^3*e^4*x^8 + 945*a*b^2*B*e^4*x^8 + 280*b^3*B*e^4*x^9)/2520","B",1
1037,1,419,159,0.2313338,"\int (a+b x)^3 (A+B x) (d+e x)^3 \, dx","IntegrateAlgebraic[(a + b*x)^3*(A + B*x)*(d + e*x)^3,x]","\frac{1}{280} \left(280 a^3 A d^3 x+420 a^3 A d^2 e x^2+280 a^3 A d e^2 x^3+70 a^3 A e^3 x^4+140 a^3 B d^3 x^2+280 a^3 B d^2 e x^3+210 a^3 B d e^2 x^4+56 a^3 B e^3 x^5+420 a^2 A b d^3 x^2+840 a^2 A b d^2 e x^3+630 a^2 A b d e^2 x^4+168 a^2 A b e^3 x^5+280 a^2 b B d^3 x^3+630 a^2 b B d^2 e x^4+504 a^2 b B d e^2 x^5+140 a^2 b B e^3 x^6+280 a A b^2 d^3 x^3+630 a A b^2 d^2 e x^4+504 a A b^2 d e^2 x^5+140 a A b^2 e^3 x^6+210 a b^2 B d^3 x^4+504 a b^2 B d^2 e x^5+420 a b^2 B d e^2 x^6+120 a b^2 B e^3 x^7+70 A b^3 d^3 x^4+168 A b^3 d^2 e x^5+140 A b^3 d e^2 x^6+40 A b^3 e^3 x^7+56 b^3 B d^3 x^5+140 b^3 B d^2 e x^6+120 b^3 B d e^2 x^7+35 b^3 B e^3 x^8\right)","\frac{e^2 (a+b x)^7 (-4 a B e+A b e+3 b B d)}{7 b^5}+\frac{e (a+b x)^6 (b d-a e) (-2 a B e+A b e+b B d)}{2 b^5}+\frac{(a+b x)^5 (b d-a e)^2 (-4 a B e+3 A b e+b B d)}{5 b^5}+\frac{(a+b x)^4 (A b-a B) (b d-a e)^3}{4 b^5}+\frac{B e^3 (a+b x)^8}{8 b^5}",1,"(280*a^3*A*d^3*x + 420*a^2*A*b*d^3*x^2 + 140*a^3*B*d^3*x^2 + 420*a^3*A*d^2*e*x^2 + 280*a*A*b^2*d^3*x^3 + 280*a^2*b*B*d^3*x^3 + 840*a^2*A*b*d^2*e*x^3 + 280*a^3*B*d^2*e*x^3 + 280*a^3*A*d*e^2*x^3 + 70*A*b^3*d^3*x^4 + 210*a*b^2*B*d^3*x^4 + 630*a*A*b^2*d^2*e*x^4 + 630*a^2*b*B*d^2*e*x^4 + 630*a^2*A*b*d*e^2*x^4 + 210*a^3*B*d*e^2*x^4 + 70*a^3*A*e^3*x^4 + 56*b^3*B*d^3*x^5 + 168*A*b^3*d^2*e*x^5 + 504*a*b^2*B*d^2*e*x^5 + 504*a*A*b^2*d*e^2*x^5 + 504*a^2*b*B*d*e^2*x^5 + 168*a^2*A*b*e^3*x^5 + 56*a^3*B*e^3*x^5 + 140*b^3*B*d^2*e*x^6 + 140*A*b^3*d*e^2*x^6 + 420*a*b^2*B*d*e^2*x^6 + 140*a*A*b^2*e^3*x^6 + 140*a^2*b*B*e^3*x^6 + 120*b^3*B*d*e^2*x^7 + 40*A*b^3*e^3*x^7 + 120*a*b^2*B*e^3*x^7 + 35*b^3*B*e^3*x^8)/280","B",1
1038,1,295,118,0.1701936,"\int (a+b x)^3 (A+B x) (d+e x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^3*(A + B*x)*(d + e*x)^2,x]","\frac{1}{420} \left(420 a^3 A d^2 x+420 a^3 A d e x^2+140 a^3 A e^2 x^3+210 a^3 B d^2 x^2+280 a^3 B d e x^3+105 a^3 B e^2 x^4+630 a^2 A b d^2 x^2+840 a^2 A b d e x^3+315 a^2 A b e^2 x^4+420 a^2 b B d^2 x^3+630 a^2 b B d e x^4+252 a^2 b B e^2 x^5+420 a A b^2 d^2 x^3+630 a A b^2 d e x^4+252 a A b^2 e^2 x^5+315 a b^2 B d^2 x^4+504 a b^2 B d e x^5+210 a b^2 B e^2 x^6+105 A b^3 d^2 x^4+168 A b^3 d e x^5+70 A b^3 e^2 x^6+84 b^3 B d^2 x^5+140 b^3 B d e x^6+60 b^3 B e^2 x^7\right)","\frac{e (a+b x)^6 (-3 a B e+A b e+2 b B d)}{6 b^4}+\frac{(a+b x)^5 (b d-a e) (-3 a B e+2 A b e+b B d)}{5 b^4}+\frac{(a+b x)^4 (A b-a B) (b d-a e)^2}{4 b^4}+\frac{B e^2 (a+b x)^7}{7 b^4}",1,"(420*a^3*A*d^2*x + 630*a^2*A*b*d^2*x^2 + 210*a^3*B*d^2*x^2 + 420*a^3*A*d*e*x^2 + 420*a*A*b^2*d^2*x^3 + 420*a^2*b*B*d^2*x^3 + 840*a^2*A*b*d*e*x^3 + 280*a^3*B*d*e*x^3 + 140*a^3*A*e^2*x^3 + 105*A*b^3*d^2*x^4 + 315*a*b^2*B*d^2*x^4 + 630*a*A*b^2*d*e*x^4 + 630*a^2*b*B*d*e*x^4 + 315*a^2*A*b*e^2*x^4 + 105*a^3*B*e^2*x^4 + 84*b^3*B*d^2*x^5 + 168*A*b^3*d*e*x^5 + 504*a*b^2*B*d*e*x^5 + 252*a*A*b^2*e^2*x^5 + 252*a^2*b*B*e^2*x^5 + 140*b^3*B*d*e*x^6 + 70*A*b^3*e^2*x^6 + 210*a*b^2*B*e^2*x^6 + 60*b^3*B*e^2*x^7)/420","B",1
1039,1,171,75,0.0964351,"\int (a+b x)^3 (A+B x) (d+e x) \, dx","IntegrateAlgebraic[(a + b*x)^3*(A + B*x)*(d + e*x),x]","\frac{1}{60} \left(60 a^3 A d x+30 a^3 A e x^2+30 a^3 B d x^2+20 a^3 B e x^3+90 a^2 A b d x^2+60 a^2 A b e x^3+60 a^2 b B d x^3+45 a^2 b B e x^4+60 a A b^2 d x^3+45 a A b^2 e x^4+45 a b^2 B d x^4+36 a b^2 B e x^5+15 A b^3 d x^4+12 A b^3 e x^5+12 b^3 B d x^5+10 b^3 B e x^6\right)","\frac{(a+b x)^5 (-2 a B e+A b e+b B d)}{5 b^3}+\frac{(a+b x)^4 (A b-a B) (b d-a e)}{4 b^3}+\frac{B e (a+b x)^6}{6 b^3}",1,"(60*a^3*A*d*x + 90*a^2*A*b*d*x^2 + 30*a^3*B*d*x^2 + 30*a^3*A*e*x^2 + 60*a*A*b^2*d*x^3 + 60*a^2*b*B*d*x^3 + 60*a^2*A*b*e*x^3 + 20*a^3*B*e*x^3 + 15*A*b^3*d*x^4 + 45*a*b^2*B*d*x^4 + 45*a*A*b^2*e*x^4 + 45*a^2*b*B*e*x^4 + 12*b^3*B*d*x^5 + 12*A*b^3*e*x^5 + 36*a*b^2*B*e*x^5 + 10*b^3*B*e*x^6)/60","B",1
1040,1,79,38,0.0005661,"\int (a+b x)^3 (A+B x) \, dx","IntegrateAlgebraic[(a + b*x)^3*(A + B*x),x]","\frac{1}{20} \left(20 a^3 A x+10 a^3 B x^2+30 a^2 A b x^2+20 a^2 b B x^3+20 a A b^2 x^3+15 a b^2 B x^4+5 A b^3 x^4+4 b^3 B x^5\right)","\frac{(a+b x)^4 (A b-a B)}{4 b^2}+\frac{B (a+b x)^5}{5 b^2}",1,"(20*a^3*A*x + 30*a^2*A*b*x^2 + 10*a^3*B*x^2 + 20*a*A*b^2*x^3 + 20*a^2*b*B*x^3 + 5*A*b^3*x^4 + 15*a*b^2*B*x^4 + 4*b^3*B*x^5)/20","B",1
1041,1,215,124,0.1595186,"\int \frac{(a+b x)^3 (A+B x)}{d+e x} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/(d + e*x),x]","\frac{x \left(12 a^3 B e^3+36 a^2 A b e^3-36 a^2 b B d e^2+18 a^2 b B e^3 x-36 a A b^2 d e^2+18 a A b^2 e^3 x+36 a b^2 B d^2 e-18 a b^2 B d e^2 x+12 a b^2 B e^3 x^2+12 A b^3 d^2 e-6 A b^3 d e^2 x+4 A b^3 e^3 x^2-12 b^3 B d^3+6 b^3 B d^2 e x-4 b^3 B d e^2 x^2+3 b^3 B e^3 x^3\right)}{12 e^4}+\frac{(b d-a e)^3 (B d-A e) \log (d+e x)}{e^5}","\frac{(b d-a e)^3 (B d-A e) \log (d+e x)}{e^5}-\frac{b x (b d-a e)^2 (B d-A e)}{e^4}+\frac{(a+b x)^2 (b d-a e) (B d-A e)}{2 e^3}-\frac{(a+b x)^3 (B d-A e)}{3 e^2}+\frac{B (a+b x)^4}{4 b e}",1,"(x*(-12*b^3*B*d^3 + 12*A*b^3*d^2*e + 36*a*b^2*B*d^2*e - 36*a*A*b^2*d*e^2 - 36*a^2*b*B*d*e^2 + 36*a^2*A*b*e^3 + 12*a^3*B*e^3 + 6*b^3*B*d^2*e*x - 6*A*b^3*d*e^2*x - 18*a*b^2*B*d*e^2*x + 18*a*A*b^2*e^3*x + 18*a^2*b*B*e^3*x - 4*b^3*B*d*e^2*x^2 + 4*A*b^3*e^3*x^2 + 12*a*b^2*B*e^3*x^2 + 3*b^3*B*e^3*x^3))/(12*e^4) + ((b*d - a*e)^3*(B*d - A*e)*Log[d + e*x])/e^5","A",1
1042,1,363,150,0.1965176,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^2} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/(d + e*x)^2,x]","\frac{\log (d+e x) \left(a^3 B e^3+3 a^2 A b e^3-6 a^2 b B d e^2-6 a A b^2 d e^2+9 a b^2 B d^2 e+3 A b^3 d^2 e-4 b^3 B d^3\right)}{e^5}+\frac{-6 a^3 A e^4+6 a^3 B d e^3+18 a^2 A b d e^3-18 a^2 b B d^2 e^2+18 a^2 b B d e^3 x+18 a^2 b B e^4 x^2-18 a A b^2 d^2 e^2+18 a A b^2 d e^3 x+18 a A b^2 e^4 x^2+18 a b^2 B d^3 e-36 a b^2 B d^2 e^2 x-27 a b^2 B d e^3 x^2+9 a b^2 B e^4 x^3+6 A b^3 d^3 e-12 A b^3 d^2 e^2 x-9 A b^3 d e^3 x^2+3 A b^3 e^4 x^3-6 b^3 B d^4+18 b^3 B d^3 e x+12 b^3 B d^2 e^2 x^2-4 b^3 B d e^3 x^3+2 b^3 B e^4 x^4}{6 e^5 (d+e x)}","-\frac{b^2 (d+e x)^2 (-3 a B e-A b e+4 b B d)}{2 e^5}-\frac{(b d-a e)^3 (B d-A e)}{e^5 (d+e x)}-\frac{(b d-a e)^2 \log (d+e x) (-a B e-3 A b e+4 b B d)}{e^5}+\frac{3 b x (b d-a e) (-a B e-A b e+2 b B d)}{e^4}+\frac{b^3 B (d+e x)^3}{3 e^5}",1,"(-6*b^3*B*d^4 + 6*A*b^3*d^3*e + 18*a*b^2*B*d^3*e - 18*a*A*b^2*d^2*e^2 - 18*a^2*b*B*d^2*e^2 + 18*a^2*A*b*d*e^3 + 6*a^3*B*d*e^3 - 6*a^3*A*e^4 + 18*b^3*B*d^3*e*x - 12*A*b^3*d^2*e^2*x - 36*a*b^2*B*d^2*e^2*x + 18*a*A*b^2*d*e^3*x + 18*a^2*b*B*d*e^3*x + 12*b^3*B*d^2*e^2*x^2 - 9*A*b^3*d*e^3*x^2 - 27*a*b^2*B*d*e^3*x^2 + 18*a*A*b^2*e^4*x^2 + 18*a^2*b*B*e^4*x^2 - 4*b^3*B*d*e^3*x^3 + 3*A*b^3*e^4*x^3 + 9*a*b^2*B*e^4*x^3 + 2*b^3*B*e^4*x^4)/(6*e^5*(d + e*x)) + ((-4*b^3*B*d^3 + 3*A*b^3*d^2*e + 9*a*b^2*B*d^2*e - 6*a*A*b^2*d*e^2 - 6*a^2*b*B*d*e^2 + 3*a^2*A*b*e^3 + a^3*B*e^3)*Log[d + e*x])/e^5","B",1
1043,1,332,145,0.2016056,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^3} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/(d + e*x)^3,x]","\frac{3 \log (d+e x) \left(a^2 b B e^2+a A b^2 e^2-3 a b^2 B d e-A b^3 d e+2 b^3 B d^2\right)}{e^5}+\frac{-a^3 A e^4-a^3 B d e^3-2 a^3 B e^4 x-3 a^2 A b d e^3-6 a^2 A b e^4 x+9 a^2 b B d^2 e^2+12 a^2 b B d e^3 x+9 a A b^2 d^2 e^2+12 a A b^2 d e^3 x-15 a b^2 B d^3 e-12 a b^2 B d^2 e^2 x+12 a b^2 B d e^3 x^2+6 a b^2 B e^4 x^3-5 A b^3 d^3 e-4 A b^3 d^2 e^2 x+4 A b^3 d e^3 x^2+2 A b^3 e^4 x^3+7 b^3 B d^4+2 b^3 B d^3 e x-11 b^3 B d^2 e^2 x^2-4 b^3 B d e^3 x^3+b^3 B e^4 x^4}{2 e^5 (d+e x)^2}","-\frac{b^2 x (-3 a B e-A b e+3 b B d)}{e^4}+\frac{(b d-a e)^2 (-a B e-3 A b e+4 b B d)}{e^5 (d+e x)}-\frac{(b d-a e)^3 (B d-A e)}{2 e^5 (d+e x)^2}+\frac{3 b (b d-a e) \log (d+e x) (-a B e-A b e+2 b B d)}{e^5}+\frac{b^3 B x^2}{2 e^3}",1,"(7*b^3*B*d^4 - 5*A*b^3*d^3*e - 15*a*b^2*B*d^3*e + 9*a*A*b^2*d^2*e^2 + 9*a^2*b*B*d^2*e^2 - 3*a^2*A*b*d*e^3 - a^3*B*d*e^3 - a^3*A*e^4 + 2*b^3*B*d^3*e*x - 4*A*b^3*d^2*e^2*x - 12*a*b^2*B*d^2*e^2*x + 12*a*A*b^2*d*e^3*x + 12*a^2*b*B*d*e^3*x - 6*a^2*A*b*e^4*x - 2*a^3*B*e^4*x - 11*b^3*B*d^2*e^2*x^2 + 4*A*b^3*d*e^3*x^2 + 12*a*b^2*B*d*e^3*x^2 - 4*b^3*B*d*e^3*x^3 + 2*A*b^3*e^4*x^3 + 6*a*b^2*B*e^4*x^3 + b^3*B*e^4*x^4)/(2*e^5*(d + e*x)^2) + (3*(2*b^3*B*d^2 - A*b^3*d*e - 3*a*b^2*B*d*e + a*A*b^2*e^2 + a^2*b*B*e^2)*Log[d + e*x])/e^5","B",1
1044,1,310,149,0.2028737,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^4} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/(d + e*x)^4,x]","\frac{-2 a^3 A e^4-a^3 B d e^3-3 a^3 B e^4 x-3 a^2 A b d e^3-9 a^2 A b e^4 x-6 a^2 b B d^2 e^2-18 a^2 b B d e^3 x-18 a^2 b B e^4 x^2-6 a A b^2 d^2 e^2-18 a A b^2 d e^3 x-18 a A b^2 e^4 x^2+33 a b^2 B d^3 e+81 a b^2 B d^2 e^2 x+54 a b^2 B d e^3 x^2+11 A b^3 d^3 e+27 A b^3 d^2 e^2 x+18 A b^3 d e^3 x^2-26 b^3 B d^4-54 b^3 B d^3 e x-18 b^3 B d^2 e^2 x^2+18 b^3 B d e^3 x^3+6 b^3 B e^4 x^4}{6 e^5 (d+e x)^3}+\frac{\log (d+e x) \left(3 a b^2 B e+A b^3 e-4 b^3 B d\right)}{e^5}","-\frac{b^2 \log (d+e x) (-3 a B e-A b e+4 b B d)}{e^5}-\frac{3 b (b d-a e) (-a B e-A b e+2 b B d)}{e^5 (d+e x)}+\frac{(b d-a e)^2 (-a B e-3 A b e+4 b B d)}{2 e^5 (d+e x)^2}-\frac{(b d-a e)^3 (B d-A e)}{3 e^5 (d+e x)^3}+\frac{b^3 B x}{e^4}",1,"(-26*b^3*B*d^4 + 11*A*b^3*d^3*e + 33*a*b^2*B*d^3*e - 6*a*A*b^2*d^2*e^2 - 6*a^2*b*B*d^2*e^2 - 3*a^2*A*b*d*e^3 - a^3*B*d*e^3 - 2*a^3*A*e^4 - 54*b^3*B*d^3*e*x + 27*A*b^3*d^2*e^2*x + 81*a*b^2*B*d^2*e^2*x - 18*a*A*b^2*d*e^3*x - 18*a^2*b*B*d*e^3*x - 9*a^2*A*b*e^4*x - 3*a^3*B*e^4*x - 18*b^3*B*d^2*e^2*x^2 + 18*A*b^3*d*e^3*x^2 + 54*a*b^2*B*d*e^3*x^2 - 18*a*A*b^2*e^4*x^2 - 18*a^2*b*B*e^4*x^2 + 18*b^3*B*d*e^3*x^3 + 6*b^3*B*e^4*x^4)/(6*e^5*(d + e*x)^3) + ((-4*b^3*B*d + A*b^3*e + 3*a*b^2*B*e)*Log[d + e*x])/e^5","B",1
1045,1,305,129,0.2241432,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^5} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/(d + e*x)^5,x]","\frac{-3 a^3 A e^4-a^3 B d e^3-4 a^3 B e^4 x-3 a^2 A b d e^3-12 a^2 A b e^4 x-3 a^2 b B d^2 e^2-12 a^2 b B d e^3 x-18 a^2 b B e^4 x^2-3 a A b^2 d^2 e^2-12 a A b^2 d e^3 x-18 a A b^2 e^4 x^2-9 a b^2 B d^3 e-36 a b^2 B d^2 e^2 x-54 a b^2 B d e^3 x^2-36 a b^2 B e^4 x^3-3 A b^3 d^3 e-12 A b^3 d^2 e^2 x-18 A b^3 d e^3 x^2-12 A b^3 e^4 x^3+25 b^3 B d^4+88 b^3 B d^3 e x+108 b^3 B d^2 e^2 x^2+48 b^3 B d e^3 x^3}{12 e^5 (d+e x)^4}+\frac{b^3 B \log (d+e x)}{e^5}","-\frac{(a+b x)^4 (B d-A e)}{4 e (d+e x)^4 (b d-a e)}+\frac{3 b^2 B (b d-a e)}{e^5 (d+e x)}-\frac{3 b B (b d-a e)^2}{2 e^5 (d+e x)^2}+\frac{B (b d-a e)^3}{3 e^5 (d+e x)^3}+\frac{b^3 B \log (d+e x)}{e^5}",1,"(25*b^3*B*d^4 - 3*A*b^3*d^3*e - 9*a*b^2*B*d^3*e - 3*a*A*b^2*d^2*e^2 - 3*a^2*b*B*d^2*e^2 - 3*a^2*A*b*d*e^3 - a^3*B*d*e^3 - 3*a^3*A*e^4 + 88*b^3*B*d^3*e*x - 12*A*b^3*d^2*e^2*x - 36*a*b^2*B*d^2*e^2*x - 12*a*A*b^2*d*e^3*x - 12*a^2*b*B*d*e^3*x - 12*a^2*A*b*e^4*x - 4*a^3*B*e^4*x + 108*b^3*B*d^2*e^2*x^2 - 18*A*b^3*d*e^3*x^2 - 54*a*b^2*B*d*e^3*x^2 - 18*a*A*b^2*e^4*x^2 - 18*a^2*b*B*e^4*x^2 + 48*b^3*B*d*e^3*x^3 - 12*A*b^3*e^4*x^3 - 36*a*b^2*B*e^4*x^3)/(12*e^5*(d + e*x)^4) + (b^3*B*Log[d + e*x])/e^5","B",1
1046,1,302,86,0.1274338,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^6} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/(d + e*x)^6,x]","\frac{-4 a^3 A e^4-a^3 B d e^3-5 a^3 B e^4 x-3 a^2 A b d e^3-15 a^2 A b e^4 x-2 a^2 b B d^2 e^2-10 a^2 b B d e^3 x-20 a^2 b B e^4 x^2-2 a A b^2 d^2 e^2-10 a A b^2 d e^3 x-20 a A b^2 e^4 x^2-3 a b^2 B d^3 e-15 a b^2 B d^2 e^2 x-30 a b^2 B d e^3 x^2-30 a b^2 B e^4 x^3-A b^3 d^3 e-5 A b^3 d^2 e^2 x-10 A b^3 d e^3 x^2-10 A b^3 e^4 x^3-4 b^3 B d^4-20 b^3 B d^3 e x-40 b^3 B d^2 e^2 x^2-40 b^3 B d e^3 x^3-20 b^3 B e^4 x^4}{20 e^5 (d+e x)^5}","\frac{(a+b x)^4 (-5 a B e+A b e+4 b B d)}{20 e (d+e x)^4 (b d-a e)^2}-\frac{(a+b x)^4 (B d-A e)}{5 e (d+e x)^5 (b d-a e)}",1,"(-4*b^3*B*d^4 - A*b^3*d^3*e - 3*a*b^2*B*d^3*e - 2*a*A*b^2*d^2*e^2 - 2*a^2*b*B*d^2*e^2 - 3*a^2*A*b*d*e^3 - a^3*B*d*e^3 - 4*a^3*A*e^4 - 20*b^3*B*d^3*e*x - 5*A*b^3*d^2*e^2*x - 15*a*b^2*B*d^2*e^2*x - 10*a*A*b^2*d*e^3*x - 10*a^2*b*B*d*e^3*x - 15*a^2*A*b*e^4*x - 5*a^3*B*e^4*x - 40*b^3*B*d^2*e^2*x^2 - 10*A*b^3*d*e^3*x^2 - 30*a*b^2*B*d*e^3*x^2 - 20*a*A*b^2*e^4*x^2 - 20*a^2*b*B*e^4*x^2 - 40*b^3*B*d*e^3*x^3 - 10*A*b^3*e^4*x^3 - 30*a*b^2*B*e^4*x^3 - 20*b^3*B*e^4*x^4)/(20*e^5*(d + e*x)^5)","B",1
1047,1,302,133,0.1282358,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^7} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/(d + e*x)^7,x]","\frac{-10 a^3 A e^4-2 a^3 B d e^3-12 a^3 B e^4 x-6 a^2 A b d e^3-36 a^2 A b e^4 x-3 a^2 b B d^2 e^2-18 a^2 b B d e^3 x-45 a^2 b B e^4 x^2-3 a A b^2 d^2 e^2-18 a A b^2 d e^3 x-45 a A b^2 e^4 x^2-3 a b^2 B d^3 e-18 a b^2 B d^2 e^2 x-45 a b^2 B d e^3 x^2-60 a b^2 B e^4 x^3-A b^3 d^3 e-6 A b^3 d^2 e^2 x-15 A b^3 d e^3 x^2-20 A b^3 e^4 x^3-2 b^3 B d^4-12 b^3 B d^3 e x-30 b^3 B d^2 e^2 x^2-40 b^3 B d e^3 x^3-30 b^3 B e^4 x^4}{60 e^5 (d+e x)^6}","\frac{b (a+b x)^4 (-3 a B e+A b e+2 b B d)}{60 e (d+e x)^4 (b d-a e)^3}+\frac{(a+b x)^4 (-3 a B e+A b e+2 b B d)}{15 e (d+e x)^5 (b d-a e)^2}-\frac{(a+b x)^4 (B d-A e)}{6 e (d+e x)^6 (b d-a e)}",1,"(-2*b^3*B*d^4 - A*b^3*d^3*e - 3*a*b^2*B*d^3*e - 3*a*A*b^2*d^2*e^2 - 3*a^2*b*B*d^2*e^2 - 6*a^2*A*b*d*e^3 - 2*a^3*B*d*e^3 - 10*a^3*A*e^4 - 12*b^3*B*d^3*e*x - 6*A*b^3*d^2*e^2*x - 18*a*b^2*B*d^2*e^2*x - 18*a*A*b^2*d*e^3*x - 18*a^2*b*B*d*e^3*x - 36*a^2*A*b*e^4*x - 12*a^3*B*e^4*x - 30*b^3*B*d^2*e^2*x^2 - 15*A*b^3*d*e^3*x^2 - 45*a*b^2*B*d*e^3*x^2 - 45*a*A*b^2*e^4*x^2 - 45*a^2*b*B*e^4*x^2 - 40*b^3*B*d*e^3*x^3 - 20*A*b^3*e^4*x^3 - 60*a*b^2*B*e^4*x^3 - 30*b^3*B*e^4*x^4)/(60*e^5*(d + e*x)^6)","B",1
1048,1,302,163,0.1240355,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^8} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/(d + e*x)^8,x]","\frac{-60 a^3 A e^4-10 a^3 B d e^3-70 a^3 B e^4 x-30 a^2 A b d e^3-210 a^2 A b e^4 x-12 a^2 b B d^2 e^2-84 a^2 b B d e^3 x-252 a^2 b B e^4 x^2-12 a A b^2 d^2 e^2-84 a A b^2 d e^3 x-252 a A b^2 e^4 x^2-9 a b^2 B d^3 e-63 a b^2 B d^2 e^2 x-189 a b^2 B d e^3 x^2-315 a b^2 B e^4 x^3-3 A b^3 d^3 e-21 A b^3 d^2 e^2 x-63 A b^3 d e^3 x^2-105 A b^3 e^4 x^3-4 b^3 B d^4-28 b^3 B d^3 e x-84 b^3 B d^2 e^2 x^2-140 b^3 B d e^3 x^3-140 b^3 B e^4 x^4}{420 e^5 (d+e x)^7}","\frac{b^2 (-3 a B e-A b e+4 b B d)}{4 e^5 (d+e x)^4}-\frac{3 b (b d-a e) (-a B e-A b e+2 b B d)}{5 e^5 (d+e x)^5}+\frac{(b d-a e)^2 (-a B e-3 A b e+4 b B d)}{6 e^5 (d+e x)^6}-\frac{(b d-a e)^3 (B d-A e)}{7 e^5 (d+e x)^7}-\frac{b^3 B}{3 e^5 (d+e x)^3}",1,"(-4*b^3*B*d^4 - 3*A*b^3*d^3*e - 9*a*b^2*B*d^3*e - 12*a*A*b^2*d^2*e^2 - 12*a^2*b*B*d^2*e^2 - 30*a^2*A*b*d*e^3 - 10*a^3*B*d*e^3 - 60*a^3*A*e^4 - 28*b^3*B*d^3*e*x - 21*A*b^3*d^2*e^2*x - 63*a*b^2*B*d^2*e^2*x - 84*a*A*b^2*d*e^3*x - 84*a^2*b*B*d*e^3*x - 210*a^2*A*b*e^4*x - 70*a^3*B*e^4*x - 84*b^3*B*d^2*e^2*x^2 - 63*A*b^3*d*e^3*x^2 - 189*a*b^2*B*d*e^3*x^2 - 252*a*A*b^2*e^4*x^2 - 252*a^2*b*B*e^4*x^2 - 140*b^3*B*d*e^3*x^3 - 105*A*b^3*e^4*x^3 - 315*a*b^2*B*e^4*x^3 - 140*b^3*B*e^4*x^4)/(420*e^5*(d + e*x)^7)","A",1
1049,1,302,163,0.1213049,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^9} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/(d + e*x)^9,x]","\frac{-35 a^3 A e^4-5 a^3 B d e^3-40 a^3 B e^4 x-15 a^2 A b d e^3-120 a^2 A b e^4 x-5 a^2 b B d^2 e^2-40 a^2 b B d e^3 x-140 a^2 b B e^4 x^2-5 a A b^2 d^2 e^2-40 a A b^2 d e^3 x-140 a A b^2 e^4 x^2-3 a b^2 B d^3 e-24 a b^2 B d^2 e^2 x-84 a b^2 B d e^3 x^2-168 a b^2 B e^4 x^3-A b^3 d^3 e-8 A b^3 d^2 e^2 x-28 A b^3 d e^3 x^2-56 A b^3 e^4 x^3-b^3 B d^4-8 b^3 B d^3 e x-28 b^3 B d^2 e^2 x^2-56 b^3 B d e^3 x^3-70 b^3 B e^4 x^4}{280 e^5 (d+e x)^8}","\frac{b^2 (-3 a B e-A b e+4 b B d)}{5 e^5 (d+e x)^5}-\frac{b (b d-a e) (-a B e-A b e+2 b B d)}{2 e^5 (d+e x)^6}+\frac{(b d-a e)^2 (-a B e-3 A b e+4 b B d)}{7 e^5 (d+e x)^7}-\frac{(b d-a e)^3 (B d-A e)}{8 e^5 (d+e x)^8}-\frac{b^3 B}{4 e^5 (d+e x)^4}",1,"(-(b^3*B*d^4) - A*b^3*d^3*e - 3*a*b^2*B*d^3*e - 5*a*A*b^2*d^2*e^2 - 5*a^2*b*B*d^2*e^2 - 15*a^2*A*b*d*e^3 - 5*a^3*B*d*e^3 - 35*a^3*A*e^4 - 8*b^3*B*d^3*e*x - 8*A*b^3*d^2*e^2*x - 24*a*b^2*B*d^2*e^2*x - 40*a*A*b^2*d*e^3*x - 40*a^2*b*B*d*e^3*x - 120*a^2*A*b*e^4*x - 40*a^3*B*e^4*x - 28*b^3*B*d^2*e^2*x^2 - 28*A*b^3*d*e^3*x^2 - 84*a*b^2*B*d*e^3*x^2 - 140*a*A*b^2*e^4*x^2 - 140*a^2*b*B*e^4*x^2 - 56*b^3*B*d*e^3*x^3 - 56*A*b^3*e^4*x^3 - 168*a*b^2*B*e^4*x^3 - 70*b^3*B*e^4*x^4)/(280*e^5*(d + e*x)^8)","A",1
1050,1,302,163,0.1324386,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^{10}} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/(d + e*x)^10,x]","\frac{-280 a^3 A e^4-35 a^3 B d e^3-315 a^3 B e^4 x-105 a^2 A b d e^3-945 a^2 A b e^4 x-30 a^2 b B d^2 e^2-270 a^2 b B d e^3 x-1080 a^2 b B e^4 x^2-30 a A b^2 d^2 e^2-270 a A b^2 d e^3 x-1080 a A b^2 e^4 x^2-15 a b^2 B d^3 e-135 a b^2 B d^2 e^2 x-540 a b^2 B d e^3 x^2-1260 a b^2 B e^4 x^3-5 A b^3 d^3 e-45 A b^3 d^2 e^2 x-180 A b^3 d e^3 x^2-420 A b^3 e^4 x^3-4 b^3 B d^4-36 b^3 B d^3 e x-144 b^3 B d^2 e^2 x^2-336 b^3 B d e^3 x^3-504 b^3 B e^4 x^4}{2520 e^5 (d+e x)^9}","\frac{b^2 (-3 a B e-A b e+4 b B d)}{6 e^5 (d+e x)^6}-\frac{3 b (b d-a e) (-a B e-A b e+2 b B d)}{7 e^5 (d+e x)^7}+\frac{(b d-a e)^2 (-a B e-3 A b e+4 b B d)}{8 e^5 (d+e x)^8}-\frac{(b d-a e)^3 (B d-A e)}{9 e^5 (d+e x)^9}-\frac{b^3 B}{5 e^5 (d+e x)^5}",1,"(-4*b^3*B*d^4 - 5*A*b^3*d^3*e - 15*a*b^2*B*d^3*e - 30*a*A*b^2*d^2*e^2 - 30*a^2*b*B*d^2*e^2 - 105*a^2*A*b*d*e^3 - 35*a^3*B*d*e^3 - 280*a^3*A*e^4 - 36*b^3*B*d^3*e*x - 45*A*b^3*d^2*e^2*x - 135*a*b^2*B*d^2*e^2*x - 270*a*A*b^2*d*e^3*x - 270*a^2*b*B*d*e^3*x - 945*a^2*A*b*e^4*x - 315*a^3*B*e^4*x - 144*b^3*B*d^2*e^2*x^2 - 180*A*b^3*d*e^3*x^2 - 540*a*b^2*B*d*e^3*x^2 - 1080*a*A*b^2*e^4*x^2 - 1080*a^2*b*B*e^4*x^2 - 336*b^3*B*d*e^3*x^3 - 420*A*b^3*e^4*x^3 - 1260*a*b^2*B*e^4*x^3 - 504*b^3*B*e^4*x^4)/(2520*e^5*(d + e*x)^9)","A",1
1051,1,1951,292,1.2201197,"\int (a+b x)^6 (A+B x) (d+e x)^8 \, dx","IntegrateAlgebraic[(a + b*x)^6*(A + B*x)*(d + e*x)^8,x]","\frac{45045 b^6 B e^8 x^{16}+48048 A b^6 e^8 x^{15}+288288 a b^5 B e^8 x^{15}+384384 b^6 B d e^7 x^{15}+308880 a A b^5 e^8 x^{14}+772200 a^2 b^4 B e^8 x^{14}+411840 A b^6 d e^7 x^{14}+2471040 a b^5 B d e^7 x^{14}+1441440 b^6 B d^2 e^6 x^{14}+831600 a^2 A b^4 e^8 x^{13}+1108800 a^3 b^3 B e^8 x^{13}+2661120 a A b^5 d e^7 x^{13}+6652800 a^2 b^4 B d e^7 x^{13}+1552320 A b^6 d^2 e^6 x^{13}+9313920 a b^5 B d^2 e^6 x^{13}+3104640 b^6 B d^3 e^5 x^{13}+1201200 a^3 A b^3 e^8 x^{12}+900900 a^4 b^2 B e^8 x^{12}+7207200 a^2 A b^4 d e^7 x^{12}+9609600 a^3 b^3 B d e^7 x^{12}+10090080 a A b^5 d^2 e^6 x^{12}+25225200 a^2 b^4 B d^2 e^6 x^{12}+3363360 A b^6 d^3 e^5 x^{12}+20180160 a b^5 B d^3 e^5 x^{12}+4204200 b^6 B d^4 e^4 x^{12}+982800 a^4 A b^2 e^8 x^{11}+393120 a^5 b B e^8 x^{11}+10483200 a^3 A b^3 d e^7 x^{11}+7862400 a^4 b^2 B d e^7 x^{11}+27518400 a^2 A b^4 d^2 e^6 x^{11}+36691200 a^3 b^3 B d^2 e^6 x^{11}+22014720 a A b^5 d^3 e^5 x^{11}+55036800 a^2 b^4 B d^3 e^5 x^{11}+4586400 A b^6 d^4 e^4 x^{11}+27518400 a b^5 B d^4 e^4 x^{11}+3669120 b^6 B d^5 e^3 x^{11}+432432 a^5 A b e^8 x^{10}+72072 a^6 B e^8 x^{10}+8648640 a^4 A b^2 d e^7 x^{10}+3459456 a^5 b B d e^7 x^{10}+40360320 a^3 A b^3 d^2 e^6 x^{10}+30270240 a^4 b^2 B d^2 e^6 x^{10}+60540480 a^2 A b^4 d^3 e^5 x^{10}+80720640 a^3 b^3 B d^3 e^5 x^{10}+30270240 a A b^5 d^4 e^4 x^{10}+75675600 a^2 b^4 B d^4 e^4 x^{10}+4036032 A b^6 d^5 e^3 x^{10}+24216192 a b^5 B d^5 e^3 x^{10}+2018016 b^6 B d^6 e^2 x^{10}+80080 a^6 A e^8 x^9+3843840 a^5 A b d e^7 x^9+640640 a^6 B d e^7 x^9+33633600 a^4 A b^2 d^2 e^6 x^9+13453440 a^5 b B d^2 e^6 x^9+89689600 a^3 A b^3 d^3 e^5 x^9+67267200 a^4 b^2 B d^3 e^5 x^9+84084000 a^2 A b^4 d^4 e^4 x^9+112112000 a^3 b^3 B d^4 e^4 x^9+26906880 a A b^5 d^5 e^3 x^9+67267200 a^2 b^4 B d^5 e^3 x^9+2242240 A b^6 d^6 e^2 x^9+13453440 a b^5 B d^6 e^2 x^9+640640 b^6 B d^7 e x^9+90090 b^6 B d^8 x^8+720720 a^6 A d e^7 x^8+15135120 a^5 A b d^2 e^6 x^8+2522520 a^6 B d^2 e^6 x^8+75675600 a^4 A b^2 d^3 e^5 x^8+30270240 a^5 b B d^3 e^5 x^8+126126000 a^3 A b^3 d^4 e^4 x^8+94594500 a^4 b^2 B d^4 e^4 x^8+75675600 a^2 A b^4 d^5 e^3 x^8+100900800 a^3 b^3 B d^5 e^3 x^8+15135120 a A b^5 d^6 e^2 x^8+37837800 a^2 b^4 B d^6 e^2 x^8+720720 A b^6 d^7 e x^8+4324320 a b^5 B d^7 e x^8+102960 A b^6 d^8 x^7+617760 a b^5 B d^8 x^7+2882880 a^6 A d^2 e^6 x^7+34594560 a^5 A b d^3 e^5 x^7+5765760 a^6 B d^3 e^5 x^7+108108000 a^4 A b^2 d^4 e^4 x^7+43243200 a^5 b B d^4 e^4 x^7+115315200 a^3 A b^3 d^5 e^3 x^7+86486400 a^4 b^2 B d^5 e^3 x^7+43243200 a^2 A b^4 d^6 e^2 x^7+57657600 a^3 b^3 B d^6 e^2 x^7+4942080 a A b^5 d^7 e x^7+12355200 a^2 b^4 B d^7 e x^7+720720 a A b^5 d^8 x^6+1801800 a^2 b^4 B d^8 x^6+6726720 a^6 A d^3 e^5 x^6+50450400 a^5 A b d^4 e^4 x^6+8408400 a^6 B d^4 e^4 x^6+100900800 a^4 A b^2 d^5 e^3 x^6+40360320 a^5 b B d^5 e^3 x^6+67267200 a^3 A b^3 d^6 e^2 x^6+50450400 a^4 b^2 B d^6 e^2 x^6+14414400 a^2 A b^4 d^7 e x^6+19219200 a^3 b^3 B d^7 e x^6+2162160 a^2 A b^4 d^8 x^5+2882880 a^3 b^3 B d^8 x^5+10090080 a^6 A d^4 e^4 x^5+48432384 a^5 A b d^5 e^3 x^5+8072064 a^6 B d^5 e^3 x^5+60540480 a^4 A b^2 d^6 e^2 x^5+24216192 a^5 b B d^6 e^2 x^5+23063040 a^3 A b^3 d^7 e x^5+17297280 a^4 b^2 B d^7 e x^5+3603600 a^3 A b^3 d^8 x^4+2702700 a^4 b^2 B d^8 x^4+10090080 a^6 A d^5 e^3 x^4+30270240 a^5 A b d^6 e^2 x^4+5045040 a^6 B d^6 e^2 x^4+21621600 a^4 A b^2 d^7 e x^4+8648640 a^5 b B d^7 e x^4+3603600 a^4 A b^2 d^8 x^3+1441440 a^5 b B d^8 x^3+6726720 a^6 A d^6 e^2 x^3+11531520 a^5 A b d^7 e x^3+1921920 a^6 B d^7 e x^3+2162160 a^5 A b d^8 x^2+360360 a^6 B d^8 x^2+2882880 a^6 A d^7 e x^2+720720 a^6 A d^8 x}{720720}","-\frac{b^5 (d+e x)^{15} (-6 a B e-A b e+7 b B d)}{15 e^8}+\frac{3 b^4 (d+e x)^{14} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{14 e^8}-\frac{5 b^3 (d+e x)^{13} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{13 e^8}+\frac{5 b^2 (d+e x)^{12} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{12 e^8}-\frac{3 b (d+e x)^{11} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{11 e^8}+\frac{(d+e x)^{10} (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{10 e^8}-\frac{(d+e x)^9 (b d-a e)^6 (B d-A e)}{9 e^8}+\frac{b^6 B (d+e x)^{16}}{16 e^8}",1,"(720720*a^6*A*d^8*x + 2162160*a^5*A*b*d^8*x^2 + 360360*a^6*B*d^8*x^2 + 2882880*a^6*A*d^7*e*x^2 + 3603600*a^4*A*b^2*d^8*x^3 + 1441440*a^5*b*B*d^8*x^3 + 11531520*a^5*A*b*d^7*e*x^3 + 1921920*a^6*B*d^7*e*x^3 + 6726720*a^6*A*d^6*e^2*x^3 + 3603600*a^3*A*b^3*d^8*x^4 + 2702700*a^4*b^2*B*d^8*x^4 + 21621600*a^4*A*b^2*d^7*e*x^4 + 8648640*a^5*b*B*d^7*e*x^4 + 30270240*a^5*A*b*d^6*e^2*x^4 + 5045040*a^6*B*d^6*e^2*x^4 + 10090080*a^6*A*d^5*e^3*x^4 + 2162160*a^2*A*b^4*d^8*x^5 + 2882880*a^3*b^3*B*d^8*x^5 + 23063040*a^3*A*b^3*d^7*e*x^5 + 17297280*a^4*b^2*B*d^7*e*x^5 + 60540480*a^4*A*b^2*d^6*e^2*x^5 + 24216192*a^5*b*B*d^6*e^2*x^5 + 48432384*a^5*A*b*d^5*e^3*x^5 + 8072064*a^6*B*d^5*e^3*x^5 + 10090080*a^6*A*d^4*e^4*x^5 + 720720*a*A*b^5*d^8*x^6 + 1801800*a^2*b^4*B*d^8*x^6 + 14414400*a^2*A*b^4*d^7*e*x^6 + 19219200*a^3*b^3*B*d^7*e*x^6 + 67267200*a^3*A*b^3*d^6*e^2*x^6 + 50450400*a^4*b^2*B*d^6*e^2*x^6 + 100900800*a^4*A*b^2*d^5*e^3*x^6 + 40360320*a^5*b*B*d^5*e^3*x^6 + 50450400*a^5*A*b*d^4*e^4*x^6 + 8408400*a^6*B*d^4*e^4*x^6 + 6726720*a^6*A*d^3*e^5*x^6 + 102960*A*b^6*d^8*x^7 + 617760*a*b^5*B*d^8*x^7 + 4942080*a*A*b^5*d^7*e*x^7 + 12355200*a^2*b^4*B*d^7*e*x^7 + 43243200*a^2*A*b^4*d^6*e^2*x^7 + 57657600*a^3*b^3*B*d^6*e^2*x^7 + 115315200*a^3*A*b^3*d^5*e^3*x^7 + 86486400*a^4*b^2*B*d^5*e^3*x^7 + 108108000*a^4*A*b^2*d^4*e^4*x^7 + 43243200*a^5*b*B*d^4*e^4*x^7 + 34594560*a^5*A*b*d^3*e^5*x^7 + 5765760*a^6*B*d^3*e^5*x^7 + 2882880*a^6*A*d^2*e^6*x^7 + 90090*b^6*B*d^8*x^8 + 720720*A*b^6*d^7*e*x^8 + 4324320*a*b^5*B*d^7*e*x^8 + 15135120*a*A*b^5*d^6*e^2*x^8 + 37837800*a^2*b^4*B*d^6*e^2*x^8 + 75675600*a^2*A*b^4*d^5*e^3*x^8 + 100900800*a^3*b^3*B*d^5*e^3*x^8 + 126126000*a^3*A*b^3*d^4*e^4*x^8 + 94594500*a^4*b^2*B*d^4*e^4*x^8 + 75675600*a^4*A*b^2*d^3*e^5*x^8 + 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1261260*A*b^6*d^4*e^3*x^10 + 7567560*a*b^5*B*d^4*e^3*x^10 + 7567560*a*A*b^5*d^3*e^4*x^10 + 18918900*a^2*b^4*B*d^3*e^4*x^10 + 11351340*a^2*A*b^4*d^2*e^5*x^10 + 15135120*a^3*b^3*B*d^2*e^5*x^10 + 5045040*a^3*A*b^3*d*e^6*x^10 + 3783780*a^4*b^2*B*d*e^6*x^10 + 540540*a^4*A*b^2*e^7*x^10 + 216216*a^5*b*B*e^7*x^10 + 1146600*b^6*B*d^4*e^3*x^11 + 1146600*A*b^6*d^3*e^4*x^11 + 6879600*a*b^5*B*d^3*e^4*x^11 + 4127760*a*A*b^5*d^2*e^5*x^11 + 10319400*a^2*b^4*B*d^2*e^5*x^11 + 3439800*a^2*A*b^4*d*e^6*x^11 + 4586400*a^3*b^3*B*d*e^6*x^11 + 655200*a^3*A*b^3*e^7*x^11 + 491400*a^4*b^2*B*e^7*x^11 + 1051050*b^6*B*d^3*e^4*x^12 + 630630*A*b^6*d^2*e^5*x^12 + 3783780*a*b^5*B*d^2*e^5*x^12 + 1261260*a*A*b^5*d*e^6*x^12 + 3153150*a^2*b^4*B*d*e^6*x^12 + 450450*a^2*A*b^4*e^7*x^12 + 600600*a^3*b^3*B*e^7*x^12 + 582120*b^6*B*d^2*e^5*x^13 + 194040*A*b^6*d*e^6*x^13 + 1164240*a*b^5*B*d*e^6*x^13 + 166320*a*A*b^5*e^7*x^13 + 415800*a^2*b^4*B*e^7*x^13 + 180180*b^6*B*d*e^6*x^14 + 25740*A*b^6*e^7*x^14 + 154440*a*b^5*B*e^7*x^14 + 24024*b^6*B*e^7*x^15)/360360","B",1
1053,1,1487,290,0.8451188,"\int (a+b x)^6 (A+B x) (d+e x)^6 \, dx","IntegrateAlgebraic[(a + b*x)^6*(A + B*x)*(d + e*x)^6,x]","\frac{1716 b^6 B e^6 x^{14}+1848 A b^6 e^6 x^{13}+11088 a b^5 B e^6 x^{13}+11088 b^6 B d e^5 x^{13}+12012 a A b^5 e^6 x^{12}+30030 a^2 b^4 B e^6 x^{12}+12012 A b^6 d e^5 x^{12}+72072 a b^5 B d e^5 x^{12}+30030 b^6 B d^2 e^4 x^{12}+32760 a^2 A b^4 e^6 x^{11}+43680 a^3 b^3 B e^6 x^{11}+78624 a A b^5 d e^5 x^{11}+196560 a^2 b^4 B d e^5 x^{11}+32760 A b^6 d^2 e^4 x^{11}+196560 a b^5 B d^2 e^4 x^{11}+43680 b^6 B d^3 e^3 x^{11}+48048 a^3 A b^3 e^6 x^{10}+36036 a^4 b^2 B e^6 x^{10}+216216 a^2 A b^4 d e^5 x^{10}+288288 a^3 b^3 B d e^5 x^{10}+216216 a A b^5 d^2 e^4 x^{10}+540540 a^2 b^4 B d^2 e^4 x^{10}+48048 A b^6 d^3 e^3 x^{10}+288288 a b^5 B d^3 e^3 x^{10}+36036 b^6 B d^4 e^2 x^{10}+40040 a^4 A b^2 e^6 x^9+16016 a^5 b B e^6 x^9+320320 a^3 A b^3 d e^5 x^9+240240 a^4 b^2 B d e^5 x^9+600600 a^2 A b^4 d^2 e^4 x^9+800800 a^3 b^3 B d^2 e^4 x^9+320320 a A b^5 d^3 e^3 x^9+800800 a^2 b^4 B d^3 e^3 x^9+40040 A b^6 d^4 e^2 x^9+240240 a b^5 B d^4 e^2 x^9+16016 b^6 B d^5 e x^9+3003 b^6 B d^6 x^8+18018 a^5 A b e^6 x^8+3003 a^6 B e^6 x^8+270270 a^4 A b^2 d e^5 x^8+108108 a^5 b B d e^5 x^8+900900 a^3 A b^3 d^2 e^4 x^8+675675 a^4 b^2 B d^2 e^4 x^8+900900 a^2 A b^4 d^3 e^3 x^8+1201200 a^3 b^3 B d^3 e^3 x^8+270270 a A b^5 d^4 e^2 x^8+675675 a^2 b^4 B d^4 e^2 x^8+18018 A b^6 d^5 e x^8+108108 a b^5 B d^5 e x^8+3432 A b^6 d^6 x^7+20592 a b^5 B d^6 x^7+3432 a^6 A e^6 x^7+123552 a^5 A b d e^5 x^7+20592 a^6 B d e^5 x^7+772200 a^4 A b^2 d^2 e^4 x^7+308880 a^5 b B d^2 e^4 x^7+1372800 a^3 A b^3 d^3 e^3 x^7+1029600 a^4 b^2 B d^3 e^3 x^7+772200 a^2 A b^4 d^4 e^2 x^7+1029600 a^3 b^3 B d^4 e^2 x^7+123552 a A b^5 d^5 e x^7+308880 a^2 b^4 B d^5 e x^7+24024 a A b^5 d^6 x^6+60060 a^2 b^4 B d^6 x^6+24024 a^6 A d e^5 x^6+360360 a^5 A b d^2 e^4 x^6+60060 a^6 B d^2 e^4 x^6+1201200 a^4 A b^2 d^3 e^3 x^6+480480 a^5 b B d^3 e^3 x^6+1201200 a^3 A b^3 d^4 e^2 x^6+900900 a^4 b^2 B d^4 e^2 x^6+360360 a^2 A b^4 d^5 e x^6+480480 a^3 b^3 B d^5 e x^6+72072 a^2 A b^4 d^6 x^5+96096 a^3 b^3 B d^6 x^5+72072 a^6 A d^2 e^4 x^5+576576 a^5 A b d^3 e^3 x^5+96096 a^6 B d^3 e^3 x^5+1081080 a^4 A b^2 d^4 e^2 x^5+432432 a^5 b B d^4 e^2 x^5+576576 a^3 A b^3 d^5 e x^5+432432 a^4 b^2 B d^5 e x^5+120120 a^3 A b^3 d^6 x^4+90090 a^4 b^2 B d^6 x^4+120120 a^6 A d^3 e^3 x^4+540540 a^5 A b d^4 e^2 x^4+90090 a^6 B d^4 e^2 x^4+540540 a^4 A b^2 d^5 e x^4+216216 a^5 b B d^5 e x^4+120120 a^4 A b^2 d^6 x^3+48048 a^5 b B d^6 x^3+120120 a^6 A d^4 e^2 x^3+288288 a^5 A b d^5 e x^3+48048 a^6 B d^5 e x^3+72072 a^5 A b d^6 x^2+12012 a^6 B d^6 x^2+72072 a^6 A d^5 e x^2+24024 a^6 A d^6 x}{24024}","\frac{e^5 (a+b x)^{13} (-7 a B e+A b e+6 b B d)}{13 b^8}+\frac{e^4 (a+b x)^{12} (b d-a e) (-7 a B e+2 A b e+5 b B d)}{4 b^8}+\frac{5 e^3 (a+b x)^{11} (b d-a e)^2 (-7 a B e+3 A b e+4 b B d)}{11 b^8}+\frac{e^2 (a+b x)^{10} (b d-a e)^3 (-7 a B e+4 A b e+3 b B d)}{2 b^8}+\frac{e (a+b x)^9 (b d-a e)^4 (-7 a B e+5 A b e+2 b B d)}{3 b^8}+\frac{(a+b x)^8 (b d-a e)^5 (-7 a B e+6 A b e+b B d)}{8 b^8}+\frac{(a+b x)^7 (A b-a B) (b d-a e)^6}{7 b^8}+\frac{B e^6 (a+b x)^{14}}{14 b^8}",1,"(24024*a^6*A*d^6*x + 72072*a^5*A*b*d^6*x^2 + 12012*a^6*B*d^6*x^2 + 72072*a^6*A*d^5*e*x^2 + 120120*a^4*A*b^2*d^6*x^3 + 48048*a^5*b*B*d^6*x^3 + 288288*a^5*A*b*d^5*e*x^3 + 48048*a^6*B*d^5*e*x^3 + 120120*a^6*A*d^4*e^2*x^3 + 120120*a^3*A*b^3*d^6*x^4 + 90090*a^4*b^2*B*d^6*x^4 + 540540*a^4*A*b^2*d^5*e*x^4 + 216216*a^5*b*B*d^5*e*x^4 + 540540*a^5*A*b*d^4*e^2*x^4 + 90090*a^6*B*d^4*e^2*x^4 + 120120*a^6*A*d^3*e^3*x^4 + 72072*a^2*A*b^4*d^6*x^5 + 96096*a^3*b^3*B*d^6*x^5 + 576576*a^3*A*b^3*d^5*e*x^5 + 432432*a^4*b^2*B*d^5*e*x^5 + 1081080*a^4*A*b^2*d^4*e^2*x^5 + 432432*a^5*b*B*d^4*e^2*x^5 + 576576*a^5*A*b*d^3*e^3*x^5 + 96096*a^6*B*d^3*e^3*x^5 + 72072*a^6*A*d^2*e^4*x^5 + 24024*a*A*b^5*d^6*x^6 + 60060*a^2*b^4*B*d^6*x^6 + 360360*a^2*A*b^4*d^5*e*x^6 + 480480*a^3*b^3*B*d^5*e*x^6 + 1201200*a^3*A*b^3*d^4*e^2*x^6 + 900900*a^4*b^2*B*d^4*e^2*x^6 + 1201200*a^4*A*b^2*d^3*e^3*x^6 + 480480*a^5*b*B*d^3*e^3*x^6 + 360360*a^5*A*b*d^2*e^4*x^6 + 60060*a^6*B*d^2*e^4*x^6 + 24024*a^6*A*d*e^5*x^6 + 3432*A*b^6*d^6*x^7 + 20592*a*b^5*B*d^6*x^7 + 123552*a*A*b^5*d^5*e*x^7 + 308880*a^2*b^4*B*d^5*e*x^7 + 772200*a^2*A*b^4*d^4*e^2*x^7 + 1029600*a^3*b^3*B*d^4*e^2*x^7 + 1372800*a^3*A*b^3*d^3*e^3*x^7 + 1029600*a^4*b^2*B*d^3*e^3*x^7 + 772200*a^4*A*b^2*d^2*e^4*x^7 + 308880*a^5*b*B*d^2*e^4*x^7 + 123552*a^5*A*b*d*e^5*x^7 + 20592*a^6*B*d*e^5*x^7 + 3432*a^6*A*e^6*x^7 + 3003*b^6*B*d^6*x^8 + 18018*A*b^6*d^5*e*x^8 + 108108*a*b^5*B*d^5*e*x^8 + 270270*a*A*b^5*d^4*e^2*x^8 + 675675*a^2*b^4*B*d^4*e^2*x^8 + 900900*a^2*A*b^4*d^3*e^3*x^8 + 1201200*a^3*b^3*B*d^3*e^3*x^8 + 900900*a^3*A*b^3*d^2*e^4*x^8 + 675675*a^4*b^2*B*d^2*e^4*x^8 + 270270*a^4*A*b^2*d*e^5*x^8 + 108108*a^5*b*B*d*e^5*x^8 + 18018*a^5*A*b*e^6*x^8 + 3003*a^6*B*e^6*x^8 + 16016*b^6*B*d^5*e*x^9 + 40040*A*b^6*d^4*e^2*x^9 + 240240*a*b^5*B*d^4*e^2*x^9 + 320320*a*A*b^5*d^3*e^3*x^9 + 800800*a^2*b^4*B*d^3*e^3*x^9 + 600600*a^2*A*b^4*d^2*e^4*x^9 + 800800*a^3*b^3*B*d^2*e^4*x^9 + 320320*a^3*A*b^3*d*e^5*x^9 + 240240*a^4*b^2*B*d*e^5*x^9 + 40040*a^4*A*b^2*e^6*x^9 + 16016*a^5*b*B*e^6*x^9 + 36036*b^6*B*d^4*e^2*x^10 + 48048*A*b^6*d^3*e^3*x^10 + 288288*a*b^5*B*d^3*e^3*x^10 + 216216*a*A*b^5*d^2*e^4*x^10 + 540540*a^2*b^4*B*d^2*e^4*x^10 + 216216*a^2*A*b^4*d*e^5*x^10 + 288288*a^3*b^3*B*d*e^5*x^10 + 48048*a^3*A*b^3*e^6*x^10 + 36036*a^4*b^2*B*e^6*x^10 + 43680*b^6*B*d^3*e^3*x^11 + 32760*A*b^6*d^2*e^4*x^11 + 196560*a*b^5*B*d^2*e^4*x^11 + 78624*a*A*b^5*d*e^5*x^11 + 196560*a^2*b^4*B*d*e^5*x^11 + 32760*a^2*A*b^4*e^6*x^11 + 43680*a^3*b^3*B*e^6*x^11 + 30030*b^6*B*d^2*e^4*x^12 + 12012*A*b^6*d*e^5*x^12 + 72072*a*b^5*B*d*e^5*x^12 + 12012*a*A*b^5*e^6*x^12 + 30030*a^2*b^4*B*e^6*x^12 + 11088*b^6*B*d*e^5*x^13 + 1848*A*b^6*e^6*x^13 + 11088*a*b^5*B*e^6*x^13 + 1716*b^6*B*e^6*x^14)/24024","B",1
1054,1,1255,240,0.719701,"\int (a+b x)^6 (A+B x) (d+e x)^5 \, dx","IntegrateAlgebraic[(a + b*x)^6*(A + B*x)*(d + e*x)^5,x]","\frac{5544 b^6 B e^5 x^{13}+6006 A b^6 e^5 x^{12}+36036 a b^5 B e^5 x^{12}+30030 b^6 B d e^4 x^{12}+39312 a A b^5 e^5 x^{11}+98280 a^2 b^4 B e^5 x^{11}+32760 A b^6 d e^4 x^{11}+196560 a b^5 B d e^4 x^{11}+65520 b^6 B d^2 e^3 x^{11}+108108 a^2 A b^4 e^5 x^{10}+144144 a^3 b^3 B e^5 x^{10}+216216 a A b^5 d e^4 x^{10}+540540 a^2 b^4 B d e^4 x^{10}+72072 A b^6 d^2 e^3 x^{10}+432432 a b^5 B d^2 e^3 x^{10}+72072 b^6 B d^3 e^2 x^{10}+160160 a^3 A b^3 e^5 x^9+120120 a^4 b^2 B e^5 x^9+600600 a^2 A b^4 d e^4 x^9+800800 a^3 b^3 B d e^4 x^9+480480 a A b^5 d^2 e^3 x^9+1201200 a^2 b^4 B d^2 e^3 x^9+80080 A b^6 d^3 e^2 x^9+480480 a b^5 B d^3 e^2 x^9+40040 b^6 B d^4 e x^9+9009 b^6 B d^5 x^8+135135 a^4 A b^2 e^5 x^8+54054 a^5 b B e^5 x^8+900900 a^3 A b^3 d e^4 x^8+675675 a^4 b^2 B d e^4 x^8+1351350 a^2 A b^4 d^2 e^3 x^8+1801800 a^3 b^3 B d^2 e^3 x^8+540540 a A b^5 d^3 e^2 x^8+1351350 a^2 b^4 B d^3 e^2 x^8+45045 A b^6 d^4 e x^8+270270 a b^5 B d^4 e x^8+10296 A b^6 d^5 x^7+61776 a b^5 B d^5 x^7+61776 a^5 A b e^5 x^7+10296 a^6 B e^5 x^7+772200 a^4 A b^2 d e^4 x^7+308880 a^5 b B d e^4 x^7+2059200 a^3 A b^3 d^2 e^3 x^7+1544400 a^4 b^2 B d^2 e^3 x^7+1544400 a^2 A b^4 d^3 e^2 x^7+2059200 a^3 b^3 B d^3 e^2 x^7+308880 a A b^5 d^4 e x^7+772200 a^2 b^4 B d^4 e x^7+72072 a A b^5 d^5 x^6+180180 a^2 b^4 B d^5 x^6+12012 a^6 A e^5 x^6+360360 a^5 A b d e^4 x^6+60060 a^6 B d e^4 x^6+1801800 a^4 A b^2 d^2 e^3 x^6+720720 a^5 b B d^2 e^3 x^6+2402400 a^3 A b^3 d^3 e^2 x^6+1801800 a^4 b^2 B d^3 e^2 x^6+900900 a^2 A b^4 d^4 e x^6+1201200 a^3 b^3 B d^4 e x^6+216216 a^2 A b^4 d^5 x^5+288288 a^3 b^3 B d^5 x^5+72072 a^6 A d e^4 x^5+864864 a^5 A b d^2 e^3 x^5+144144 a^6 B d^2 e^3 x^5+2162160 a^4 A b^2 d^3 e^2 x^5+864864 a^5 b B d^3 e^2 x^5+1441440 a^3 A b^3 d^4 e x^5+1081080 a^4 b^2 B d^4 e x^5+360360 a^3 A b^3 d^5 x^4+270270 a^4 b^2 B d^5 x^4+180180 a^6 A d^2 e^3 x^4+1081080 a^5 A b d^3 e^2 x^4+180180 a^6 B d^3 e^2 x^4+1351350 a^4 A b^2 d^4 e x^4+540540 a^5 b B d^4 e x^4+360360 a^4 A b^2 d^5 x^3+144144 a^5 b B d^5 x^3+240240 a^6 A d^3 e^2 x^3+720720 a^5 A b d^4 e x^3+120120 a^6 B d^4 e x^3+216216 a^5 A b d^5 x^2+36036 a^6 B d^5 x^2+180180 a^6 A d^4 e x^2+72072 a^6 A d^5 x}{72072}","\frac{e^4 (a+b x)^{12} (-6 a B e+A b e+5 b B d)}{12 b^7}+\frac{5 e^3 (a+b x)^{11} (b d-a e) (-3 a B e+A b e+2 b B d)}{11 b^7}+\frac{e^2 (a+b x)^{10} (b d-a e)^2 (-2 a B e+A b e+b B d)}{b^7}+\frac{5 e (a+b x)^9 (b d-a e)^3 (-3 a B e+2 A b e+b B d)}{9 b^7}+\frac{(a+b x)^8 (b d-a e)^4 (-6 a B e+5 A b e+b B d)}{8 b^7}+\frac{(a+b x)^7 (A b-a B) (b d-a e)^5}{7 b^7}+\frac{B e^5 (a+b x)^{13}}{13 b^7}",1,"(72072*a^6*A*d^5*x + 216216*a^5*A*b*d^5*x^2 + 36036*a^6*B*d^5*x^2 + 180180*a^6*A*d^4*e*x^2 + 360360*a^4*A*b^2*d^5*x^3 + 144144*a^5*b*B*d^5*x^3 + 720720*a^5*A*b*d^4*e*x^3 + 120120*a^6*B*d^4*e*x^3 + 240240*a^6*A*d^3*e^2*x^3 + 360360*a^3*A*b^3*d^5*x^4 + 270270*a^4*b^2*B*d^5*x^4 + 1351350*a^4*A*b^2*d^4*e*x^4 + 540540*a^5*b*B*d^4*e*x^4 + 1081080*a^5*A*b*d^3*e^2*x^4 + 180180*a^6*B*d^3*e^2*x^4 + 180180*a^6*A*d^2*e^3*x^4 + 216216*a^2*A*b^4*d^5*x^5 + 288288*a^3*b^3*B*d^5*x^5 + 1441440*a^3*A*b^3*d^4*e*x^5 + 1081080*a^4*b^2*B*d^4*e*x^5 + 2162160*a^4*A*b^2*d^3*e^2*x^5 + 864864*a^5*b*B*d^3*e^2*x^5 + 864864*a^5*A*b*d^2*e^3*x^5 + 144144*a^6*B*d^2*e^3*x^5 + 72072*a^6*A*d*e^4*x^5 + 72072*a*A*b^5*d^5*x^6 + 180180*a^2*b^4*B*d^5*x^6 + 900900*a^2*A*b^4*d^4*e*x^6 + 1201200*a^3*b^3*B*d^4*e*x^6 + 2402400*a^3*A*b^3*d^3*e^2*x^6 + 1801800*a^4*b^2*B*d^3*e^2*x^6 + 1801800*a^4*A*b^2*d^2*e^3*x^6 + 720720*a^5*b*B*d^2*e^3*x^6 + 360360*a^5*A*b*d*e^4*x^6 + 60060*a^6*B*d*e^4*x^6 + 12012*a^6*A*e^5*x^6 + 10296*A*b^6*d^5*x^7 + 61776*a*b^5*B*d^5*x^7 + 308880*a*A*b^5*d^4*e*x^7 + 772200*a^2*b^4*B*d^4*e*x^7 + 1544400*a^2*A*b^4*d^3*e^2*x^7 + 2059200*a^3*b^3*B*d^3*e^2*x^7 + 2059200*a^3*A*b^3*d^2*e^3*x^7 + 1544400*a^4*b^2*B*d^2*e^3*x^7 + 772200*a^4*A*b^2*d*e^4*x^7 + 308880*a^5*b*B*d*e^4*x^7 + 61776*a^5*A*b*e^5*x^7 + 10296*a^6*B*e^5*x^7 + 9009*b^6*B*d^5*x^8 + 45045*A*b^6*d^4*e*x^8 + 270270*a*b^5*B*d^4*e*x^8 + 540540*a*A*b^5*d^3*e^2*x^8 + 1351350*a^2*b^4*B*d^3*e^2*x^8 + 1351350*a^2*A*b^4*d^2*e^3*x^8 + 1801800*a^3*b^3*B*d^2*e^3*x^8 + 900900*a^3*A*b^3*d*e^4*x^8 + 675675*a^4*b^2*B*d*e^4*x^8 + 135135*a^4*A*b^2*e^5*x^8 + 54054*a^5*b*B*e^5*x^8 + 40040*b^6*B*d^4*e*x^9 + 80080*A*b^6*d^3*e^2*x^9 + 480480*a*b^5*B*d^3*e^2*x^9 + 480480*a*A*b^5*d^2*e^3*x^9 + 1201200*a^2*b^4*B*d^2*e^3*x^9 + 600600*a^2*A*b^4*d*e^4*x^9 + 800800*a^3*b^3*B*d*e^4*x^9 + 160160*a^3*A*b^3*e^5*x^9 + 120120*a^4*b^2*B*e^5*x^9 + 72072*b^6*B*d^3*e^2*x^10 + 72072*A*b^6*d^2*e^3*x^10 + 432432*a*b^5*B*d^2*e^3*x^10 + 216216*a*A*b^5*d*e^4*x^10 + 540540*a^2*b^4*B*d*e^4*x^10 + 108108*a^2*A*b^4*e^5*x^10 + 144144*a^3*b^3*B*e^5*x^10 + 65520*b^6*B*d^2*e^3*x^11 + 32760*A*b^6*d*e^4*x^11 + 196560*a*b^5*B*d*e^4*x^11 + 39312*a*A*b^5*e^5*x^11 + 98280*a^2*b^4*B*e^5*x^11 + 30030*b^6*B*d*e^4*x^12 + 6006*A*b^6*e^5*x^12 + 36036*a*b^5*B*e^5*x^12 + 5544*b^6*B*e^5*x^13)/72072","B",1
1055,1,1023,204,0.5941949,"\int (a+b x)^6 (A+B x) (d+e x)^4 \, dx","IntegrateAlgebraic[(a + b*x)^6*(A + B*x)*(d + e*x)^4,x]","\frac{2310 b^6 B e^4 x^{12}+2520 A b^6 e^4 x^{11}+15120 a b^5 B e^4 x^{11}+10080 b^6 B d e^3 x^{11}+16632 a A b^5 e^4 x^{10}+41580 a^2 b^4 B e^4 x^{10}+11088 A b^6 d e^3 x^{10}+66528 a b^5 B d e^3 x^{10}+16632 b^6 B d^2 e^2 x^{10}+46200 a^2 A b^4 e^4 x^9+61600 a^3 b^3 B e^4 x^9+73920 a A b^5 d e^3 x^9+184800 a^2 b^4 B d e^3 x^9+18480 A b^6 d^2 e^2 x^9+110880 a b^5 B d^2 e^2 x^9+12320 b^6 B d^3 e x^9+3465 b^6 B d^4 x^8+69300 a^3 A b^3 e^4 x^8+51975 a^4 b^2 B e^4 x^8+207900 a^2 A b^4 d e^3 x^8+277200 a^3 b^3 B d e^3 x^8+124740 a A b^5 d^2 e^2 x^8+311850 a^2 b^4 B d^2 e^2 x^8+13860 A b^6 d^3 e x^8+83160 a b^5 B d^3 e x^8+3960 A b^6 d^4 x^7+23760 a b^5 B d^4 x^7+59400 a^4 A b^2 e^4 x^7+23760 a^5 b B e^4 x^7+316800 a^3 A b^3 d e^3 x^7+237600 a^4 b^2 B d e^3 x^7+356400 a^2 A b^4 d^2 e^2 x^7+475200 a^3 b^3 B d^2 e^2 x^7+95040 a A b^5 d^3 e x^7+237600 a^2 b^4 B d^3 e x^7+27720 a A b^5 d^4 x^6+69300 a^2 b^4 B d^4 x^6+27720 a^5 A b e^4 x^6+4620 a^6 B e^4 x^6+277200 a^4 A b^2 d e^3 x^6+110880 a^5 b B d e^3 x^6+554400 a^3 A b^3 d^2 e^2 x^6+415800 a^4 b^2 B d^2 e^2 x^6+277200 a^2 A b^4 d^3 e x^6+369600 a^3 b^3 B d^3 e x^6+83160 a^2 A b^4 d^4 x^5+110880 a^3 b^3 B d^4 x^5+5544 a^6 A e^4 x^5+133056 a^5 A b d e^3 x^5+22176 a^6 B d e^3 x^5+498960 a^4 A b^2 d^2 e^2 x^5+199584 a^5 b B d^2 e^2 x^5+443520 a^3 A b^3 d^3 e x^5+332640 a^4 b^2 B d^3 e x^5+138600 a^3 A b^3 d^4 x^4+103950 a^4 b^2 B d^4 x^4+27720 a^6 A d e^3 x^4+249480 a^5 A b d^2 e^2 x^4+41580 a^6 B d^2 e^2 x^4+415800 a^4 A b^2 d^3 e x^4+166320 a^5 b B d^3 e x^4+138600 a^4 A b^2 d^4 x^3+55440 a^5 b B d^4 x^3+55440 a^6 A d^2 e^2 x^3+221760 a^5 A b d^3 e x^3+36960 a^6 B d^3 e x^3+83160 a^5 A b d^4 x^2+13860 a^6 B d^4 x^2+55440 a^6 A d^3 e x^2+27720 a^6 A d^4 x}{27720}","\frac{e^3 (a+b x)^{11} (-5 a B e+A b e+4 b B d)}{11 b^6}+\frac{e^2 (a+b x)^{10} (b d-a e) (-5 a B e+2 A b e+3 b B d)}{5 b^6}+\frac{2 e (a+b x)^9 (b d-a e)^2 (-5 a B e+3 A b e+2 b B d)}{9 b^6}+\frac{(a+b x)^8 (b d-a e)^3 (-5 a B e+4 A b e+b B d)}{8 b^6}+\frac{(a+b x)^7 (A b-a B) (b d-a e)^4}{7 b^6}+\frac{B e^4 (a+b x)^{12}}{12 b^6}",1,"(27720*a^6*A*d^4*x + 83160*a^5*A*b*d^4*x^2 + 13860*a^6*B*d^4*x^2 + 55440*a^6*A*d^3*e*x^2 + 138600*a^4*A*b^2*d^4*x^3 + 55440*a^5*b*B*d^4*x^3 + 221760*a^5*A*b*d^3*e*x^3 + 36960*a^6*B*d^3*e*x^3 + 55440*a^6*A*d^2*e^2*x^3 + 138600*a^3*A*b^3*d^4*x^4 + 103950*a^4*b^2*B*d^4*x^4 + 415800*a^4*A*b^2*d^3*e*x^4 + 166320*a^5*b*B*d^3*e*x^4 + 249480*a^5*A*b*d^2*e^2*x^4 + 41580*a^6*B*d^2*e^2*x^4 + 27720*a^6*A*d*e^3*x^4 + 83160*a^2*A*b^4*d^4*x^5 + 110880*a^3*b^3*B*d^4*x^5 + 443520*a^3*A*b^3*d^3*e*x^5 + 332640*a^4*b^2*B*d^3*e*x^5 + 498960*a^4*A*b^2*d^2*e^2*x^5 + 199584*a^5*b*B*d^2*e^2*x^5 + 133056*a^5*A*b*d*e^3*x^5 + 22176*a^6*B*d*e^3*x^5 + 5544*a^6*A*e^4*x^5 + 27720*a*A*b^5*d^4*x^6 + 69300*a^2*b^4*B*d^4*x^6 + 277200*a^2*A*b^4*d^3*e*x^6 + 369600*a^3*b^3*B*d^3*e*x^6 + 554400*a^3*A*b^3*d^2*e^2*x^6 + 415800*a^4*b^2*B*d^2*e^2*x^6 + 277200*a^4*A*b^2*d*e^3*x^6 + 110880*a^5*b*B*d*e^3*x^6 + 27720*a^5*A*b*e^4*x^6 + 4620*a^6*B*e^4*x^6 + 3960*A*b^6*d^4*x^7 + 23760*a*b^5*B*d^4*x^7 + 95040*a*A*b^5*d^3*e*x^7 + 237600*a^2*b^4*B*d^3*e*x^7 + 356400*a^2*A*b^4*d^2*e^2*x^7 + 475200*a^3*b^3*B*d^2*e^2*x^7 + 316800*a^3*A*b^3*d*e^3*x^7 + 237600*a^4*b^2*B*d*e^3*x^7 + 59400*a^4*A*b^2*e^4*x^7 + 23760*a^5*b*B*e^4*x^7 + 3465*b^6*B*d^4*x^8 + 13860*A*b^6*d^3*e*x^8 + 83160*a*b^5*B*d^3*e*x^8 + 124740*a*A*b^5*d^2*e^2*x^8 + 311850*a^2*b^4*B*d^2*e^2*x^8 + 207900*a^2*A*b^4*d*e^3*x^8 + 277200*a^3*b^3*B*d*e^3*x^8 + 69300*a^3*A*b^3*e^4*x^8 + 51975*a^4*b^2*B*e^4*x^8 + 12320*b^6*B*d^3*e*x^9 + 18480*A*b^6*d^2*e^2*x^9 + 110880*a*b^5*B*d^2*e^2*x^9 + 73920*a*A*b^5*d*e^3*x^9 + 184800*a^2*b^4*B*d*e^3*x^9 + 46200*a^2*A*b^4*e^4*x^9 + 61600*a^3*b^3*B*e^4*x^9 + 16632*b^6*B*d^2*e^2*x^10 + 11088*A*b^6*d*e^3*x^10 + 66528*a*b^5*B*d*e^3*x^10 + 16632*a*A*b^5*e^4*x^10 + 41580*a^2*b^4*B*e^4*x^10 + 10080*b^6*B*d*e^3*x^11 + 2520*A*b^6*e^4*x^11 + 15120*a*b^5*B*e^4*x^11 + 2310*b^6*B*e^4*x^12)/27720","B",1
1056,1,791,159,0.452482,"\int (a+b x)^6 (A+B x) (d+e x)^3 \, dx","IntegrateAlgebraic[(a + b*x)^6*(A + B*x)*(d + e*x)^3,x]","\frac{9240 a^6 A d^3 x+13860 a^6 A d^2 e x^2+9240 a^6 A d e^2 x^3+2310 a^6 A e^3 x^4+4620 a^6 B d^3 x^2+9240 a^6 B d^2 e x^3+6930 a^6 B d e^2 x^4+1848 a^6 B e^3 x^5+27720 a^5 A b d^3 x^2+55440 a^5 A b d^2 e x^3+41580 a^5 A b d e^2 x^4+11088 a^5 A b e^3 x^5+18480 a^5 b B d^3 x^3+41580 a^5 b B d^2 e x^4+33264 a^5 b B d e^2 x^5+9240 a^5 b B e^3 x^6+46200 a^4 A b^2 d^3 x^3+103950 a^4 A b^2 d^2 e x^4+83160 a^4 A b^2 d e^2 x^5+23100 a^4 A b^2 e^3 x^6+34650 a^4 b^2 B d^3 x^4+83160 a^4 b^2 B d^2 e x^5+69300 a^4 b^2 B d e^2 x^6+19800 a^4 b^2 B e^3 x^7+46200 a^3 A b^3 d^3 x^4+110880 a^3 A b^3 d^2 e x^5+92400 a^3 A b^3 d e^2 x^6+26400 a^3 A b^3 e^3 x^7+36960 a^3 b^3 B d^3 x^5+92400 a^3 b^3 B d^2 e x^6+79200 a^3 b^3 B d e^2 x^7+23100 a^3 b^3 B e^3 x^8+27720 a^2 A b^4 d^3 x^5+69300 a^2 A b^4 d^2 e x^6+59400 a^2 A b^4 d e^2 x^7+17325 a^2 A b^4 e^3 x^8+23100 a^2 b^4 B d^3 x^6+59400 a^2 b^4 B d^2 e x^7+51975 a^2 b^4 B d e^2 x^8+15400 a^2 b^4 B e^3 x^9+9240 a A b^5 d^3 x^6+23760 a A b^5 d^2 e x^7+20790 a A b^5 d e^2 x^8+6160 a A b^5 e^3 x^9+7920 a b^5 B d^3 x^7+20790 a b^5 B d^2 e x^8+18480 a b^5 B d e^2 x^9+5544 a b^5 B e^3 x^{10}+1320 A b^6 d^3 x^7+3465 A b^6 d^2 e x^8+3080 A b^6 d e^2 x^9+924 A b^6 e^3 x^{10}+1155 b^6 B d^3 x^8+3080 b^6 B d^2 e x^9+2772 b^6 B d e^2 x^{10}+840 b^6 B e^3 x^{11}}{9240}","\frac{e^2 (a+b x)^{10} (-4 a B e+A b e+3 b B d)}{10 b^5}+\frac{e (a+b x)^9 (b d-a e) (-2 a B e+A b e+b B d)}{3 b^5}+\frac{(a+b x)^8 (b d-a e)^2 (-4 a B e+3 A b e+b B d)}{8 b^5}+\frac{(a+b x)^7 (A b-a B) (b d-a e)^3}{7 b^5}+\frac{B e^3 (a+b x)^{11}}{11 b^5}",1,"(9240*a^6*A*d^3*x + 27720*a^5*A*b*d^3*x^2 + 4620*a^6*B*d^3*x^2 + 13860*a^6*A*d^2*e*x^2 + 46200*a^4*A*b^2*d^3*x^3 + 18480*a^5*b*B*d^3*x^3 + 55440*a^5*A*b*d^2*e*x^3 + 9240*a^6*B*d^2*e*x^3 + 9240*a^6*A*d*e^2*x^3 + 46200*a^3*A*b^3*d^3*x^4 + 34650*a^4*b^2*B*d^3*x^4 + 103950*a^4*A*b^2*d^2*e*x^4 + 41580*a^5*b*B*d^2*e*x^4 + 41580*a^5*A*b*d*e^2*x^4 + 6930*a^6*B*d*e^2*x^4 + 2310*a^6*A*e^3*x^4 + 27720*a^2*A*b^4*d^3*x^5 + 36960*a^3*b^3*B*d^3*x^5 + 110880*a^3*A*b^3*d^2*e*x^5 + 83160*a^4*b^2*B*d^2*e*x^5 + 83160*a^4*A*b^2*d*e^2*x^5 + 33264*a^5*b*B*d*e^2*x^5 + 11088*a^5*A*b*e^3*x^5 + 1848*a^6*B*e^3*x^5 + 9240*a*A*b^5*d^3*x^6 + 23100*a^2*b^4*B*d^3*x^6 + 69300*a^2*A*b^4*d^2*e*x^6 + 92400*a^3*b^3*B*d^2*e*x^6 + 92400*a^3*A*b^3*d*e^2*x^6 + 69300*a^4*b^2*B*d*e^2*x^6 + 23100*a^4*A*b^2*e^3*x^6 + 9240*a^5*b*B*e^3*x^6 + 1320*A*b^6*d^3*x^7 + 7920*a*b^5*B*d^3*x^7 + 23760*a*A*b^5*d^2*e*x^7 + 59400*a^2*b^4*B*d^2*e*x^7 + 59400*a^2*A*b^4*d*e^2*x^7 + 79200*a^3*b^3*B*d*e^2*x^7 + 26400*a^3*A*b^3*e^3*x^7 + 19800*a^4*b^2*B*e^3*x^7 + 1155*b^6*B*d^3*x^8 + 3465*A*b^6*d^2*e*x^8 + 20790*a*b^5*B*d^2*e*x^8 + 20790*a*A*b^5*d*e^2*x^8 + 51975*a^2*b^4*B*d*e^2*x^8 + 17325*a^2*A*b^4*e^3*x^8 + 23100*a^3*b^3*B*e^3*x^8 + 3080*b^6*B*d^2*e*x^9 + 3080*A*b^6*d*e^2*x^9 + 18480*a*b^5*B*d*e^2*x^9 + 6160*a*A*b^5*e^3*x^9 + 15400*a^2*b^4*B*e^3*x^9 + 2772*b^6*B*d*e^2*x^10 + 924*A*b^6*e^3*x^10 + 5544*a*b^5*B*e^3*x^10 + 840*b^6*B*e^3*x^11)/9240","B",1
1057,1,559,118,0.492906,"\int (a+b x)^6 (A+B x) (d+e x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^6*(A + B*x)*(d + e*x)^2,x]","\frac{2520 a^6 A d^2 x+2520 a^6 A d e x^2+840 a^6 A e^2 x^3+1260 a^6 B d^2 x^2+1680 a^6 B d e x^3+630 a^6 B e^2 x^4+7560 a^5 A b d^2 x^2+10080 a^5 A b d e x^3+3780 a^5 A b e^2 x^4+5040 a^5 b B d^2 x^3+7560 a^5 b B d e x^4+3024 a^5 b B e^2 x^5+12600 a^4 A b^2 d^2 x^3+18900 a^4 A b^2 d e x^4+7560 a^4 A b^2 e^2 x^5+9450 a^4 b^2 B d^2 x^4+15120 a^4 b^2 B d e x^5+6300 a^4 b^2 B e^2 x^6+12600 a^3 A b^3 d^2 x^4+20160 a^3 A b^3 d e x^5+8400 a^3 A b^3 e^2 x^6+10080 a^3 b^3 B d^2 x^5+16800 a^3 b^3 B d e x^6+7200 a^3 b^3 B e^2 x^7+7560 a^2 A b^4 d^2 x^5+12600 a^2 A b^4 d e x^6+5400 a^2 A b^4 e^2 x^7+6300 a^2 b^4 B d^2 x^6+10800 a^2 b^4 B d e x^7+4725 a^2 b^4 B e^2 x^8+2520 a A b^5 d^2 x^6+4320 a A b^5 d e x^7+1890 a A b^5 e^2 x^8+2160 a b^5 B d^2 x^7+3780 a b^5 B d e x^8+1680 a b^5 B e^2 x^9+360 A b^6 d^2 x^7+630 A b^6 d e x^8+280 A b^6 e^2 x^9+315 b^6 B d^2 x^8+560 b^6 B d e x^9+252 b^6 B e^2 x^{10}}{2520}","\frac{e (a+b x)^9 (-3 a B e+A b e+2 b B d)}{9 b^4}+\frac{(a+b x)^8 (b d-a e) (-3 a B e+2 A b e+b B d)}{8 b^4}+\frac{(a+b x)^7 (A b-a B) (b d-a e)^2}{7 b^4}+\frac{B e^2 (a+b x)^{10}}{10 b^4}",1,"(2520*a^6*A*d^2*x + 7560*a^5*A*b*d^2*x^2 + 1260*a^6*B*d^2*x^2 + 2520*a^6*A*d*e*x^2 + 12600*a^4*A*b^2*d^2*x^3 + 5040*a^5*b*B*d^2*x^3 + 10080*a^5*A*b*d*e*x^3 + 1680*a^6*B*d*e*x^3 + 840*a^6*A*e^2*x^3 + 12600*a^3*A*b^3*d^2*x^4 + 9450*a^4*b^2*B*d^2*x^4 + 18900*a^4*A*b^2*d*e*x^4 + 7560*a^5*b*B*d*e*x^4 + 3780*a^5*A*b*e^2*x^4 + 630*a^6*B*e^2*x^4 + 7560*a^2*A*b^4*d^2*x^5 + 10080*a^3*b^3*B*d^2*x^5 + 20160*a^3*A*b^3*d*e*x^5 + 15120*a^4*b^2*B*d*e*x^5 + 7560*a^4*A*b^2*e^2*x^5 + 3024*a^5*b*B*e^2*x^5 + 2520*a*A*b^5*d^2*x^6 + 6300*a^2*b^4*B*d^2*x^6 + 12600*a^2*A*b^4*d*e*x^6 + 16800*a^3*b^3*B*d*e*x^6 + 8400*a^3*A*b^3*e^2*x^6 + 6300*a^4*b^2*B*e^2*x^6 + 360*A*b^6*d^2*x^7 + 2160*a*b^5*B*d^2*x^7 + 4320*a*A*b^5*d*e*x^7 + 10800*a^2*b^4*B*d*e*x^7 + 5400*a^2*A*b^4*e^2*x^7 + 7200*a^3*b^3*B*e^2*x^7 + 315*b^6*B*d^2*x^8 + 630*A*b^6*d*e*x^8 + 3780*a*b^5*B*d*e*x^8 + 1890*a*A*b^5*e^2*x^8 + 4725*a^2*b^4*B*e^2*x^8 + 560*b^6*B*d*e*x^9 + 280*A*b^6*e^2*x^9 + 1680*a*b^5*B*e^2*x^9 + 252*b^6*B*e^2*x^10)/2520","B",1
1058,1,327,75,0.2895526,"\int (a+b x)^6 (A+B x) (d+e x) \, dx","IntegrateAlgebraic[(a + b*x)^6*(A + B*x)*(d + e*x),x]","\frac{1}{504} \left(504 a^6 A d x+252 a^6 A e x^2+252 a^6 B d x^2+168 a^6 B e x^3+1512 a^5 A b d x^2+1008 a^5 A b e x^3+1008 a^5 b B d x^3+756 a^5 b B e x^4+2520 a^4 A b^2 d x^3+1890 a^4 A b^2 e x^4+1890 a^4 b^2 B d x^4+1512 a^4 b^2 B e x^5+2520 a^3 A b^3 d x^4+2016 a^3 A b^3 e x^5+2016 a^3 b^3 B d x^5+1680 a^3 b^3 B e x^6+1512 a^2 A b^4 d x^5+1260 a^2 A b^4 e x^6+1260 a^2 b^4 B d x^6+1080 a^2 b^4 B e x^7+504 a A b^5 d x^6+432 a A b^5 e x^7+432 a b^5 B d x^7+378 a b^5 B e x^8+72 A b^6 d x^7+63 A b^6 e x^8+63 b^6 B d x^8+56 b^6 B e x^9\right)","\frac{(a+b x)^8 (-2 a B e+A b e+b B d)}{8 b^3}+\frac{(a+b x)^7 (A b-a B) (b d-a e)}{7 b^3}+\frac{B e (a+b x)^9}{9 b^3}",1,"(504*a^6*A*d*x + 1512*a^5*A*b*d*x^2 + 252*a^6*B*d*x^2 + 252*a^6*A*e*x^2 + 2520*a^4*A*b^2*d*x^3 + 1008*a^5*b*B*d*x^3 + 1008*a^5*A*b*e*x^3 + 168*a^6*B*e*x^3 + 2520*a^3*A*b^3*d*x^4 + 1890*a^4*b^2*B*d*x^4 + 1890*a^4*A*b^2*e*x^4 + 756*a^5*b*B*e*x^4 + 1512*a^2*A*b^4*d*x^5 + 2016*a^3*b^3*B*d*x^5 + 2016*a^3*A*b^3*e*x^5 + 1512*a^4*b^2*B*e*x^5 + 504*a*A*b^5*d*x^6 + 1260*a^2*b^4*B*d*x^6 + 1260*a^2*A*b^4*e*x^6 + 1680*a^3*b^3*B*e*x^6 + 72*A*b^6*d*x^7 + 432*a*b^5*B*d*x^7 + 432*a*A*b^5*e*x^7 + 1080*a^2*b^4*B*e*x^7 + 63*b^6*B*d*x^8 + 63*A*b^6*e*x^8 + 378*a*b^5*B*e*x^8 + 56*b^6*B*e*x^9)/504","B",1
1059,1,147,38,0.091233,"\int (a+b x)^6 (A+B x) \, dx","IntegrateAlgebraic[(a + b*x)^6*(A + B*x),x]","\frac{1}{56} x \left(56 a^6 A+28 a^6 B x+168 a^5 A b x+112 a^5 b B x^2+280 a^4 A b^2 x^2+210 a^4 b^2 B x^3+280 a^3 A b^3 x^3+224 a^3 b^3 B x^4+168 a^2 A b^4 x^4+140 a^2 b^4 B x^5+56 a A b^5 x^5+48 a b^5 B x^6+8 A b^6 x^6+7 b^6 B x^7\right)","\frac{(a+b x)^7 (A b-a B)}{7 b^2}+\frac{B (a+b x)^8}{8 b^2}",1,"(x*(56*a^6*A + 168*a^5*A*b*x + 28*a^6*B*x + 280*a^4*A*b^2*x^2 + 112*a^5*b*B*x^2 + 280*a^3*A*b^3*x^3 + 210*a^4*b^2*B*x^3 + 168*a^2*A*b^4*x^4 + 224*a^3*b^3*B*x^4 + 56*a*A*b^5*x^5 + 140*a^2*b^4*B*x^5 + 8*A*b^6*x^6 + 48*a*b^5*B*x^6 + 7*b^6*B*x^7))/56","B",1
1060,1,754,220,0.4837501,"\int \frac{(a+b x)^6 (A+B x)}{d+e x} \, dx","IntegrateAlgebraic[((a + b*x)^6*(A + B*x))/(d + e*x),x]","\frac{420 a^6 B e^6 x+2520 a^5 A b e^6 x-2520 a^5 b B d e^5 x+1260 a^5 b B e^6 x^2-6300 a^4 A b^2 d e^5 x+3150 a^4 A b^2 e^6 x^2+6300 a^4 b^2 B d^2 e^4 x-3150 a^4 b^2 B d e^5 x^2+2100 a^4 b^2 B e^6 x^3+8400 a^3 A b^3 d^2 e^4 x-4200 a^3 A b^3 d e^5 x^2+2800 a^3 A b^3 e^6 x^3-8400 a^3 b^3 B d^3 e^3 x+4200 a^3 b^3 B d^2 e^4 x^2-2800 a^3 b^3 B d e^5 x^3+2100 a^3 b^3 B e^6 x^4-6300 a^2 A b^4 d^3 e^3 x+3150 a^2 A b^4 d^2 e^4 x^2-2100 a^2 A b^4 d e^5 x^3+1575 a^2 A b^4 e^6 x^4+6300 a^2 b^4 B d^4 e^2 x-3150 a^2 b^4 B d^3 e^3 x^2+2100 a^2 b^4 B d^2 e^4 x^3-1575 a^2 b^4 B d e^5 x^4+1260 a^2 b^4 B e^6 x^5+2520 a A b^5 d^4 e^2 x-1260 a A b^5 d^3 e^3 x^2+840 a A b^5 d^2 e^4 x^3-630 a A b^5 d e^5 x^4+504 a A b^5 e^6 x^5-2520 a b^5 B d^5 e x+1260 a b^5 B d^4 e^2 x^2-840 a b^5 B d^3 e^3 x^3+630 a b^5 B d^2 e^4 x^4-504 a b^5 B d e^5 x^5+420 a b^5 B e^6 x^6-420 A b^6 d^5 e x+210 A b^6 d^4 e^2 x^2-140 A b^6 d^3 e^3 x^3+105 A b^6 d^2 e^4 x^4-84 A b^6 d e^5 x^5+70 A b^6 e^6 x^6+420 b^6 B d^6 x-210 b^6 B d^5 e x^2+140 b^6 B d^4 e^2 x^3-105 b^6 B d^3 e^3 x^4+84 b^6 B d^2 e^4 x^5-70 b^6 B d e^5 x^6+60 b^6 B e^6 x^7}{420 e^7}-\frac{(b d-a e)^6 (B d-A e) \log (d+e x)}{e^8}","-\frac{(b d-a e)^6 (B d-A e) \log (d+e x)}{e^8}+\frac{b x (b d-a e)^5 (B d-A e)}{e^7}-\frac{(a+b x)^2 (b d-a e)^4 (B d-A e)}{2 e^6}+\frac{(a+b x)^3 (b d-a e)^3 (B d-A e)}{3 e^5}-\frac{(a+b x)^4 (b d-a e)^2 (B d-A e)}{4 e^4}+\frac{(a+b x)^5 (b d-a e) (B d-A e)}{5 e^3}-\frac{(a+b x)^6 (B d-A e)}{6 e^2}+\frac{B (a+b x)^7}{7 b e}",1,"(420*b^6*B*d^6*x - 420*A*b^6*d^5*e*x - 2520*a*b^5*B*d^5*e*x + 2520*a*A*b^5*d^4*e^2*x + 6300*a^2*b^4*B*d^4*e^2*x - 6300*a^2*A*b^4*d^3*e^3*x - 8400*a^3*b^3*B*d^3*e^3*x + 8400*a^3*A*b^3*d^2*e^4*x + 6300*a^4*b^2*B*d^2*e^4*x - 6300*a^4*A*b^2*d*e^5*x - 2520*a^5*b*B*d*e^5*x + 2520*a^5*A*b*e^6*x + 420*a^6*B*e^6*x - 210*b^6*B*d^5*e*x^2 + 210*A*b^6*d^4*e^2*x^2 + 1260*a*b^5*B*d^4*e^2*x^2 - 1260*a*A*b^5*d^3*e^3*x^2 - 3150*a^2*b^4*B*d^3*e^3*x^2 + 3150*a^2*A*b^4*d^2*e^4*x^2 + 4200*a^3*b^3*B*d^2*e^4*x^2 - 4200*a^3*A*b^3*d*e^5*x^2 - 3150*a^4*b^2*B*d*e^5*x^2 + 3150*a^4*A*b^2*e^6*x^2 + 1260*a^5*b*B*e^6*x^2 + 140*b^6*B*d^4*e^2*x^3 - 140*A*b^6*d^3*e^3*x^3 - 840*a*b^5*B*d^3*e^3*x^3 + 840*a*A*b^5*d^2*e^4*x^3 + 2100*a^2*b^4*B*d^2*e^4*x^3 - 2100*a^2*A*b^4*d*e^5*x^3 - 2800*a^3*b^3*B*d*e^5*x^3 + 2800*a^3*A*b^3*e^6*x^3 + 2100*a^4*b^2*B*e^6*x^3 - 105*b^6*B*d^3*e^3*x^4 + 105*A*b^6*d^2*e^4*x^4 + 630*a*b^5*B*d^2*e^4*x^4 - 630*a*A*b^5*d*e^5*x^4 - 1575*a^2*b^4*B*d*e^5*x^4 + 1575*a^2*A*b^4*e^6*x^4 + 2100*a^3*b^3*B*e^6*x^4 + 84*b^6*B*d^2*e^4*x^5 - 84*A*b^6*d*e^5*x^5 - 504*a*b^5*B*d*e^5*x^5 + 504*a*A*b^5*e^6*x^5 + 1260*a^2*b^4*B*e^6*x^5 - 70*b^6*B*d*e^5*x^6 + 70*A*b^6*e^6*x^6 + 420*a*b^5*B*e^6*x^6 + 60*b^6*B*e^6*x^7)/(420*e^7) - ((b*d - a*e)^6*(B*d - A*e)*Log[d + e*x])/e^8","B",1
1061,1,1065,277,0.5079697,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^2} \, dx","IntegrateAlgebraic[((a + b*x)^6*(A + B*x))/(d + e*x)^2,x]","\frac{60 b^6 B d^7-60 A b^6 e d^6-360 a b^5 B e d^6-360 b^6 B e x d^6+360 a A b^5 e^2 d^5+900 a^2 b^4 B e^2 d^5-210 b^6 B e^2 x^2 d^5+300 A b^6 e^2 x d^5+1800 a b^5 B e^2 x d^5-900 a^2 A b^4 e^3 d^4-1200 a^3 b^3 B e^3 d^4+70 b^6 B e^3 x^3 d^4+180 A b^6 e^3 x^2 d^4+1080 a b^5 B e^3 x^2 d^4-1440 a A b^5 e^3 x d^4-3600 a^2 b^4 B e^3 x d^4+1200 a^3 A b^3 e^4 d^3+900 a^4 b^2 B e^4 d^3-35 b^6 B e^4 x^4 d^3-60 A b^6 e^4 x^3 d^3-360 a b^5 B e^4 x^3 d^3-900 a A b^5 e^4 x^2 d^3-2250 a^2 b^4 B e^4 x^2 d^3+2700 a^2 A b^4 e^4 x d^3+3600 a^3 b^3 B e^4 x d^3-900 a^4 A b^2 e^5 d^2-360 a^5 b B e^5 d^2+21 b^6 B e^5 x^5 d^2+30 A b^6 e^5 x^4 d^2+180 a b^5 B e^5 x^4 d^2+300 a A b^5 e^5 x^3 d^2+750 a^2 b^4 B e^5 x^3 d^2+1800 a^2 A b^4 e^5 x^2 d^2+2400 a^3 b^3 B e^5 x^2 d^2-2400 a^3 A b^3 e^5 x d^2-1800 a^4 b^2 B e^5 x d^2+360 a^5 A b e^6 d+60 a^6 B e^6 d-14 b^6 B e^6 x^6 d-18 A b^6 e^6 x^5 d-108 a b^5 B e^6 x^5 d-150 a A b^5 e^6 x^4 d-375 a^2 b^4 B e^6 x^4 d-600 a^2 A b^4 e^6 x^3 d-800 a^3 b^3 B e^6 x^3 d-1800 a^3 A b^3 e^6 x^2 d-1350 a^4 b^2 B e^6 x^2 d+900 a^4 A b^2 e^6 x d+360 a^5 b B e^6 x d-60 a^6 A e^7+10 b^6 B e^7 x^7+12 A b^6 e^7 x^6+72 a b^5 B e^7 x^6+90 a A b^5 e^7 x^5+225 a^2 b^4 B e^7 x^5+300 a^2 A b^4 e^7 x^4+400 a^3 b^3 B e^7 x^4+600 a^3 A b^3 e^7 x^3+450 a^4 b^2 B e^7 x^3+900 a^4 A b^2 e^7 x^2+360 a^5 b B e^7 x^2}{60 e^8 (d+e x)}+\frac{\left(7 B d^6 b^6-6 A d^5 e b^6+30 a A d^4 e^2 b^5-36 a B d^5 e b^5-60 a^2 A d^3 e^3 b^4+75 a^2 B d^4 e^2 b^4+60 a^3 A d^2 e^4 b^3-80 a^3 B d^3 e^3 b^3-30 a^4 A d e^5 b^2+45 a^4 B d^2 e^4 b^2+6 a^5 A e^6 b-12 a^5 B d e^5 b+a^6 B e^6\right) \log (d+e x)}{e^8}","-\frac{b^5 (d+e x)^5 (-6 a B e-A b e+7 b B d)}{5 e^8}+\frac{3 b^4 (d+e x)^4 (b d-a e) (-5 a B e-2 A b e+7 b B d)}{4 e^8}-\frac{5 b^3 (d+e x)^3 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{3 e^8}+\frac{5 b^2 (d+e x)^2 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{2 e^8}+\frac{(b d-a e)^6 (B d-A e)}{e^8 (d+e x)}+\frac{(b d-a e)^5 \log (d+e x) (-a B e-6 A b e+7 b B d)}{e^8}-\frac{3 b x (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{e^7}+\frac{b^6 B (d+e x)^6}{6 e^8}",1,"(60*b^6*B*d^7 - 60*A*b^6*d^6*e - 360*a*b^5*B*d^6*e + 360*a*A*b^5*d^5*e^2 + 900*a^2*b^4*B*d^5*e^2 - 900*a^2*A*b^4*d^4*e^3 - 1200*a^3*b^3*B*d^4*e^3 + 1200*a^3*A*b^3*d^3*e^4 + 900*a^4*b^2*B*d^3*e^4 - 900*a^4*A*b^2*d^2*e^5 - 360*a^5*b*B*d^2*e^5 + 360*a^5*A*b*d*e^6 + 60*a^6*B*d*e^6 - 60*a^6*A*e^7 - 360*b^6*B*d^6*e*x + 300*A*b^6*d^5*e^2*x + 1800*a*b^5*B*d^5*e^2*x - 1440*a*A*b^5*d^4*e^3*x - 3600*a^2*b^4*B*d^4*e^3*x + 2700*a^2*A*b^4*d^3*e^4*x + 3600*a^3*b^3*B*d^3*e^4*x - 2400*a^3*A*b^3*d^2*e^5*x - 1800*a^4*b^2*B*d^2*e^5*x + 900*a^4*A*b^2*d*e^6*x + 360*a^5*b*B*d*e^6*x - 210*b^6*B*d^5*e^2*x^2 + 180*A*b^6*d^4*e^3*x^2 + 1080*a*b^5*B*d^4*e^3*x^2 - 900*a*A*b^5*d^3*e^4*x^2 - 2250*a^2*b^4*B*d^3*e^4*x^2 + 1800*a^2*A*b^4*d^2*e^5*x^2 + 2400*a^3*b^3*B*d^2*e^5*x^2 - 1800*a^3*A*b^3*d*e^6*x^2 - 1350*a^4*b^2*B*d*e^6*x^2 + 900*a^4*A*b^2*e^7*x^2 + 360*a^5*b*B*e^7*x^2 + 70*b^6*B*d^4*e^3*x^3 - 60*A*b^6*d^3*e^4*x^3 - 360*a*b^5*B*d^3*e^4*x^3 + 300*a*A*b^5*d^2*e^5*x^3 + 750*a^2*b^4*B*d^2*e^5*x^3 - 600*a^2*A*b^4*d*e^6*x^3 - 800*a^3*b^3*B*d*e^6*x^3 + 600*a^3*A*b^3*e^7*x^3 + 450*a^4*b^2*B*e^7*x^3 - 35*b^6*B*d^3*e^4*x^4 + 30*A*b^6*d^2*e^5*x^4 + 180*a*b^5*B*d^2*e^5*x^4 - 150*a*A*b^5*d*e^6*x^4 - 375*a^2*b^4*B*d*e^6*x^4 + 300*a^2*A*b^4*e^7*x^4 + 400*a^3*b^3*B*e^7*x^4 + 21*b^6*B*d^2*e^5*x^5 - 18*A*b^6*d*e^6*x^5 - 108*a*b^5*B*d*e^6*x^5 + 90*a*A*b^5*e^7*x^5 + 225*a^2*b^4*B*e^7*x^5 - 14*b^6*B*d*e^6*x^6 + 12*A*b^6*e^7*x^6 + 72*a*b^5*B*e^7*x^6 + 10*b^6*B*e^7*x^7)/(60*e^8*(d + e*x)) + ((7*b^6*B*d^6 - 6*A*b^6*d^5*e - 36*a*b^5*B*d^5*e + 30*a*A*b^5*d^4*e^2 + 75*a^2*b^4*B*d^4*e^2 - 60*a^2*A*b^4*d^3*e^3 - 80*a^3*b^3*B*d^3*e^3 + 60*a^3*A*b^3*d^2*e^4 + 45*a^4*b^2*B*d^2*e^4 - 30*a^4*A*b^2*d*e^5 - 12*a^5*b*B*d*e^5 + 6*a^5*A*b*e^6 + a^6*B*e^6)*Log[d + e*x])/e^8","B",1
1062,1,1035,276,0.3947748,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^3} \, dx","IntegrateAlgebraic[((a + b*x)^6*(A + B*x))/(d + e*x)^3,x]","\frac{-130 b^6 B d^7+110 A b^6 e d^6+660 a b^5 B e d^6+160 b^6 B e x d^6-540 a A b^5 e^2 d^5-1350 a^2 b^4 B e^2 d^5+500 b^6 B e^2 x^2 d^5-80 A b^6 e^2 x d^5-480 a b^5 B e^2 x d^5+1050 a^2 A b^4 e^3 d^4+1400 a^3 b^3 B e^3 d^4+140 b^6 B e^3 x^3 d^4-340 A b^6 e^3 x^2 d^4-2040 a b^5 B e^3 x^2 d^4+120 a A b^5 e^3 x d^4+300 a^2 b^4 B e^3 x d^4-1000 a^3 A b^3 e^4 d^3-750 a^4 b^2 B e^4 d^3-35 b^6 B e^4 x^4 d^3-100 A b^6 e^4 x^3 d^3-600 a b^5 B e^4 x^3 d^3+1260 a A b^5 e^4 x^2 d^3+3150 a^2 b^4 B e^4 x^2 d^3+300 a^2 A b^4 e^4 x d^3+400 a^3 b^3 B e^4 x d^3+450 a^4 A b^2 e^5 d^2+180 a^5 b B e^5 d^2+14 b^6 B e^5 x^5 d^2+25 A b^6 e^5 x^4 d^2+150 a b^5 B e^5 x^4 d^2+400 a A b^5 e^5 x^3 d^2+1000 a^2 b^4 B e^5 x^3 d^2-1650 a^2 A b^4 e^5 x^2 d^2-2200 a^3 b^3 B e^5 x^2 d^2-800 a^3 A b^3 e^5 x d^2-600 a^4 b^2 B e^5 x d^2-60 a^5 A b e^6 d-10 a^6 B e^6 d-7 b^6 B e^6 x^6 d-10 A b^6 e^6 x^5 d-60 a b^5 B e^6 x^5 d-100 a A b^5 e^6 x^4 d-250 a^2 b^4 B e^6 x^4 d-600 a^2 A b^4 e^6 x^3 d-800 a^3 b^3 B e^6 x^3 d+800 a^3 A b^3 e^6 x^2 d+600 a^4 b^2 B e^6 x^2 d+600 a^4 A b^2 e^6 x d+240 a^5 b B e^6 x d-10 a^6 A e^7+4 b^6 B e^7 x^7+5 A b^6 e^7 x^6+30 a b^5 B e^7 x^6+40 a A b^5 e^7 x^5+100 a^2 b^4 B e^7 x^5+150 a^2 A b^4 e^7 x^4+200 a^3 b^3 B e^7 x^4+400 a^3 A b^3 e^7 x^3+300 a^4 b^2 B e^7 x^3-120 a^5 A b e^7 x-20 a^6 B e^7 x}{20 e^8 (d+e x)^2}-\frac{3 \left(7 B d^5 b^6-5 A d^4 e b^6+20 a A d^3 e^2 b^5-30 a B d^4 e b^5-30 a^2 A d^2 e^3 b^4+50 a^2 B d^3 e^2 b^4+20 a^3 A d e^4 b^3-40 a^3 B d^2 e^3 b^3-5 a^4 A e^5 b^2+15 a^4 B d e^4 b^2-2 a^5 B e^5 b\right) \log (d+e x)}{e^8}","-\frac{b^5 (d+e x)^4 (-6 a B e-A b e+7 b B d)}{4 e^8}+\frac{b^4 (d+e x)^3 (b d-a e) (-5 a B e-2 A b e+7 b B d)}{e^8}-\frac{5 b^3 (d+e x)^2 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{2 e^8}+\frac{5 b^2 x (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{e^7}-\frac{(b d-a e)^5 (-a B e-6 A b e+7 b B d)}{e^8 (d+e x)}+\frac{(b d-a e)^6 (B d-A e)}{2 e^8 (d+e x)^2}-\frac{3 b (b d-a e)^4 \log (d+e x) (-2 a B e-5 A b e+7 b B d)}{e^8}+\frac{b^6 B (d+e x)^5}{5 e^8}",1,"(-130*b^6*B*d^7 + 110*A*b^6*d^6*e + 660*a*b^5*B*d^6*e - 540*a*A*b^5*d^5*e^2 - 1350*a^2*b^4*B*d^5*e^2 + 1050*a^2*A*b^4*d^4*e^3 + 1400*a^3*b^3*B*d^4*e^3 - 1000*a^3*A*b^3*d^3*e^4 - 750*a^4*b^2*B*d^3*e^4 + 450*a^4*A*b^2*d^2*e^5 + 180*a^5*b*B*d^2*e^5 - 60*a^5*A*b*d*e^6 - 10*a^6*B*d*e^6 - 10*a^6*A*e^7 + 160*b^6*B*d^6*e*x - 80*A*b^6*d^5*e^2*x - 480*a*b^5*B*d^5*e^2*x + 120*a*A*b^5*d^4*e^3*x + 300*a^2*b^4*B*d^4*e^3*x + 300*a^2*A*b^4*d^3*e^4*x + 400*a^3*b^3*B*d^3*e^4*x - 800*a^3*A*b^3*d^2*e^5*x - 600*a^4*b^2*B*d^2*e^5*x + 600*a^4*A*b^2*d*e^6*x + 240*a^5*b*B*d*e^6*x - 120*a^5*A*b*e^7*x - 20*a^6*B*e^7*x + 500*b^6*B*d^5*e^2*x^2 - 340*A*b^6*d^4*e^3*x^2 - 2040*a*b^5*B*d^4*e^3*x^2 + 1260*a*A*b^5*d^3*e^4*x^2 + 3150*a^2*b^4*B*d^3*e^4*x^2 - 1650*a^2*A*b^4*d^2*e^5*x^2 - 2200*a^3*b^3*B*d^2*e^5*x^2 + 800*a^3*A*b^3*d*e^6*x^2 + 600*a^4*b^2*B*d*e^6*x^2 + 140*b^6*B*d^4*e^3*x^3 - 100*A*b^6*d^3*e^4*x^3 - 600*a*b^5*B*d^3*e^4*x^3 + 400*a*A*b^5*d^2*e^5*x^3 + 1000*a^2*b^4*B*d^2*e^5*x^3 - 600*a^2*A*b^4*d*e^6*x^3 - 800*a^3*b^3*B*d*e^6*x^3 + 400*a^3*A*b^3*e^7*x^3 + 300*a^4*b^2*B*e^7*x^3 - 35*b^6*B*d^3*e^4*x^4 + 25*A*b^6*d^2*e^5*x^4 + 150*a*b^5*B*d^2*e^5*x^4 - 100*a*A*b^5*d*e^6*x^4 - 250*a^2*b^4*B*d*e^6*x^4 + 150*a^2*A*b^4*e^7*x^4 + 200*a^3*b^3*B*e^7*x^4 + 14*b^6*B*d^2*e^5*x^5 - 10*A*b^6*d*e^6*x^5 - 60*a*b^5*B*d*e^6*x^5 + 40*a*A*b^5*e^7*x^5 + 100*a^2*b^4*B*e^7*x^5 - 7*b^6*B*d*e^6*x^6 + 5*A*b^6*e^7*x^6 + 30*a*b^5*B*e^7*x^6 + 4*b^6*B*e^7*x^7)/(20*e^8*(d + e*x)^2) - (3*(7*b^6*B*d^5 - 5*A*b^6*d^4*e - 30*a*b^5*B*d^4*e + 20*a*A*b^5*d^3*e^2 + 50*a^2*b^4*B*d^3*e^2 - 30*a^2*A*b^4*d^2*e^3 - 40*a^3*b^3*B*d^2*e^3 + 20*a^3*A*b^3*d*e^4 + 15*a^4*b^2*B*d*e^4 - 5*a^4*A*b^2*e^5 - 2*a^5*b*B*e^5)*Log[d + e*x])/e^8","B",1
1063,1,1005,279,0.4073921,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^4} \, dx","IntegrateAlgebraic[((a + b*x)^6*(A + B*x))/(d + e*x)^4,x]","\frac{214 b^6 B d^7-148 A b^6 e d^6-888 a b^5 B e d^6+222 b^6 B e x d^6+564 a A b^5 e^2 d^5+1410 a^2 b^4 B e^2 d^5-408 b^6 B e^2 x^2 d^5-204 A b^6 e^2 x d^5-1224 a b^5 B e^2 x d^5-780 a^2 A b^4 e^3 d^4-1040 a^3 b^3 B e^3 d^4-556 b^6 B e^3 x^3 d^4+156 A b^6 e^3 x^2 d^4+936 a b^5 B e^3 x^2 d^4+972 a A b^5 e^3 x d^4+2430 a^2 b^4 B e^3 x d^4+440 a^3 A b^3 e^4 d^3+330 a^4 b^2 B e^4 d^3-105 b^6 B e^4 x^4 d^3+292 A b^6 e^4 x^3 d^3+1752 a b^5 B e^4 x^3 d^3-108 a A b^5 e^4 x^2 d^3-270 a^2 b^4 B e^4 x^2 d^3-1620 a^2 A b^4 e^4 x d^3-2160 a^3 b^3 B e^4 x d^3-60 a^4 A b^2 e^5 d^2-24 a^5 b B e^5 d^2+21 b^6 B e^5 x^5 d^2+60 A b^6 e^5 x^4 d^2+360 a b^5 B e^5 x^4 d^2-756 a A b^5 e^5 x^3 d^2-1890 a^2 b^4 B e^5 x^3 d^2-540 a^2 A b^4 e^5 x^2 d^2-720 a^3 b^3 B e^5 x^2 d^2+1080 a^3 A b^3 e^5 x d^2+810 a^4 b^2 B e^5 x d^2-12 a^5 A b e^6 d-2 a^6 B e^6 d-7 b^6 B e^6 x^6 d-12 A b^6 e^6 x^5 d-72 a b^5 B e^6 x^5 d-180 a A b^5 e^6 x^4 d-450 a^2 b^4 B e^6 x^4 d+540 a^2 A b^4 e^6 x^3 d+720 a^3 b^3 B e^6 x^3 d+720 a^3 A b^3 e^6 x^2 d+540 a^4 b^2 B e^6 x^2 d-180 a^4 A b^2 e^6 x d-72 a^5 b B e^6 x d-4 a^6 A e^7+3 b^6 B e^7 x^7+4 A b^6 e^7 x^6+24 a b^5 B e^7 x^6+36 a A b^5 e^7 x^5+90 a^2 b^4 B e^7 x^5+180 a^2 A b^4 e^7 x^4+240 a^3 b^3 B e^7 x^4-180 a^4 A b^2 e^7 x^2-72 a^5 b B e^7 x^2-36 a^5 A b e^7 x-6 a^6 B e^7 x}{12 e^8 (d+e x)^3}+\frac{5 \left(7 B d^4 b^6-4 A d^3 e b^6+12 a A d^2 e^2 b^5-24 a B d^3 e b^5-12 a^2 A d e^3 b^4+30 a^2 B d^2 e^2 b^4+4 a^3 A e^4 b^3-16 a^3 B d e^3 b^3+3 a^4 B e^4 b^2\right) \log (d+e x)}{e^8}","-\frac{b^5 (d+e x)^3 (-6 a B e-A b e+7 b B d)}{3 e^8}+\frac{3 b^4 (d+e x)^2 (b d-a e) (-5 a B e-2 A b e+7 b B d)}{2 e^8}-\frac{5 b^3 x (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{e^7}+\frac{5 b^2 (b d-a e)^3 \log (d+e x) (-3 a B e-4 A b e+7 b B d)}{e^8}+\frac{3 b (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{e^8 (d+e x)}-\frac{(b d-a e)^5 (-a B e-6 A b e+7 b B d)}{2 e^8 (d+e x)^2}+\frac{(b d-a e)^6 (B d-A e)}{3 e^8 (d+e x)^3}+\frac{b^6 B (d+e x)^4}{4 e^8}",1,"(214*b^6*B*d^7 - 148*A*b^6*d^6*e - 888*a*b^5*B*d^6*e + 564*a*A*b^5*d^5*e^2 + 1410*a^2*b^4*B*d^5*e^2 - 780*a^2*A*b^4*d^4*e^3 - 1040*a^3*b^3*B*d^4*e^3 + 440*a^3*A*b^3*d^3*e^4 + 330*a^4*b^2*B*d^3*e^4 - 60*a^4*A*b^2*d^2*e^5 - 24*a^5*b*B*d^2*e^5 - 12*a^5*A*b*d*e^6 - 2*a^6*B*d*e^6 - 4*a^6*A*e^7 + 222*b^6*B*d^6*e*x - 204*A*b^6*d^5*e^2*x - 1224*a*b^5*B*d^5*e^2*x + 972*a*A*b^5*d^4*e^3*x + 2430*a^2*b^4*B*d^4*e^3*x - 1620*a^2*A*b^4*d^3*e^4*x - 2160*a^3*b^3*B*d^3*e^4*x + 1080*a^3*A*b^3*d^2*e^5*x + 810*a^4*b^2*B*d^2*e^5*x - 180*a^4*A*b^2*d*e^6*x - 72*a^5*b*B*d*e^6*x - 36*a^5*A*b*e^7*x - 6*a^6*B*e^7*x - 408*b^6*B*d^5*e^2*x^2 + 156*A*b^6*d^4*e^3*x^2 + 936*a*b^5*B*d^4*e^3*x^2 - 108*a*A*b^5*d^3*e^4*x^2 - 270*a^2*b^4*B*d^3*e^4*x^2 - 540*a^2*A*b^4*d^2*e^5*x^2 - 720*a^3*b^3*B*d^2*e^5*x^2 + 720*a^3*A*b^3*d*e^6*x^2 + 540*a^4*b^2*B*d*e^6*x^2 - 180*a^4*A*b^2*e^7*x^2 - 72*a^5*b*B*e^7*x^2 - 556*b^6*B*d^4*e^3*x^3 + 292*A*b^6*d^3*e^4*x^3 + 1752*a*b^5*B*d^3*e^4*x^3 - 756*a*A*b^5*d^2*e^5*x^3 - 1890*a^2*b^4*B*d^2*e^5*x^3 + 540*a^2*A*b^4*d*e^6*x^3 + 720*a^3*b^3*B*d*e^6*x^3 - 105*b^6*B*d^3*e^4*x^4 + 60*A*b^6*d^2*e^5*x^4 + 360*a*b^5*B*d^2*e^5*x^4 - 180*a*A*b^5*d*e^6*x^4 - 450*a^2*b^4*B*d*e^6*x^4 + 180*a^2*A*b^4*e^7*x^4 + 240*a^3*b^3*B*e^7*x^4 + 21*b^6*B*d^2*e^5*x^5 - 12*A*b^6*d*e^6*x^5 - 72*a*b^5*B*d*e^6*x^5 + 36*a*A*b^5*e^7*x^5 + 90*a^2*b^4*B*e^7*x^5 - 7*b^6*B*d*e^6*x^6 + 4*A*b^6*e^7*x^6 + 24*a*b^5*B*e^7*x^6 + 3*b^6*B*e^7*x^7)/(12*e^8*(d + e*x)^3) + (5*(7*b^6*B*d^4 - 4*A*b^6*d^3*e - 24*a*b^5*B*d^3*e + 12*a*A*b^5*d^2*e^2 + 30*a^2*b^4*B*d^2*e^2 - 12*a^2*A*b^4*d*e^3 - 16*a^3*b^3*B*d*e^3 + 4*a^3*A*b^3*e^4 + 3*a^4*b^2*B*e^4)*Log[d + e*x])/e^8","B",1
1064,1,975,279,0.4127551,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^5} \, dx","IntegrateAlgebraic[((a + b*x)^6*(A + B*x))/(d + e*x)^5,x]","\frac{-319 b^6 B d^7+171 A b^6 e d^6+1026 a b^5 B e d^6-856 b^6 B e x d^6-462 a A b^5 e^2 d^5-1155 a^2 b^4 B e^2 d^5-444 b^6 B e^2 x^2 d^5+504 A b^6 e^2 x d^5+3024 a b^5 B e^2 x d^5+375 a^2 A b^4 e^3 d^4+500 a^3 b^3 B e^3 d^4+544 b^6 B e^3 x^3 d^4+396 A b^6 e^3 x^2 d^4+2376 a b^5 B e^3 x^2 d^4-1488 a A b^5 e^3 x d^4-3720 a^2 b^4 B e^3 x d^4-60 a^3 A b^3 e^4 d^3-45 a^4 b^2 B e^4 d^3+556 b^6 B e^4 x^4 d^3-96 A b^6 e^4 x^3 d^3-576 a b^5 B e^4 x^3 d^3-1512 a A b^5 e^4 x^2 d^3-3780 a^2 b^4 B e^4 x^2 d^3+1320 a^2 A b^4 e^4 x d^3+1760 a^3 b^3 B e^4 x d^3-15 a^4 A b^2 e^5 d^2-6 a^5 b B e^5 d^2+84 b^6 B e^5 x^5 d^2-204 A b^6 e^5 x^4 d^2-1224 a b^5 B e^5 x^4 d^2-288 a A b^5 e^5 x^3 d^2-720 a^2 b^4 B e^5 x^3 d^2+1620 a^2 A b^4 e^5 x^2 d^2+2160 a^3 b^3 B e^5 x^2 d^2-240 a^3 A b^3 e^5 x d^2-180 a^4 b^2 B e^5 x d^2-6 a^5 A b e^6 d-a^6 B e^6 d-14 b^6 B e^6 x^6 d-36 A b^6 e^6 x^5 d-216 a b^5 B e^6 x^5 d+288 a A b^5 e^6 x^4 d+720 a^2 b^4 B e^6 x^4 d+720 a^2 A b^4 e^6 x^3 d+960 a^3 b^3 B e^6 x^3 d-360 a^3 A b^3 e^6 x^2 d-270 a^4 b^2 B e^6 x^2 d-60 a^4 A b^2 e^6 x d-24 a^5 b B e^6 x d-3 a^6 A e^7+4 b^6 B e^7 x^7+6 A b^6 e^7 x^6+36 a b^5 B e^7 x^6+72 a A b^5 e^7 x^5+180 a^2 b^4 B e^7 x^5-240 a^3 A b^3 e^7 x^3-180 a^4 b^2 B e^7 x^3-90 a^4 A b^2 e^7 x^2-36 a^5 b B e^7 x^2-24 a^5 A b e^7 x-4 a^6 B e^7 x}{12 e^8 (d+e x)^4}-\frac{5 \left(7 B d^3 b^6-3 A d^2 e b^6+6 a A d e^2 b^5-18 a B d^2 e b^5-3 a^2 A e^3 b^4+15 a^2 B d e^2 b^4-4 a^3 B e^3 b^3\right) \log (d+e x)}{e^8}","-\frac{b^5 (d+e x)^2 (-6 a B e-A b e+7 b B d)}{2 e^8}+\frac{3 b^4 x (b d-a e) (-5 a B e-2 A b e+7 b B d)}{e^7}-\frac{5 b^3 (b d-a e)^2 \log (d+e x) (-4 a B e-3 A b e+7 b B d)}{e^8}-\frac{5 b^2 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{e^8 (d+e x)}+\frac{3 b (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{2 e^8 (d+e x)^2}-\frac{(b d-a e)^5 (-a B e-6 A b e+7 b B d)}{3 e^8 (d+e x)^3}+\frac{(b d-a e)^6 (B d-A e)}{4 e^8 (d+e x)^4}+\frac{b^6 B (d+e x)^3}{3 e^8}",1,"(-319*b^6*B*d^7 + 171*A*b^6*d^6*e + 1026*a*b^5*B*d^6*e - 462*a*A*b^5*d^5*e^2 - 1155*a^2*b^4*B*d^5*e^2 + 375*a^2*A*b^4*d^4*e^3 + 500*a^3*b^3*B*d^4*e^3 - 60*a^3*A*b^3*d^3*e^4 - 45*a^4*b^2*B*d^3*e^4 - 15*a^4*A*b^2*d^2*e^5 - 6*a^5*b*B*d^2*e^5 - 6*a^5*A*b*d*e^6 - a^6*B*d*e^6 - 3*a^6*A*e^7 - 856*b^6*B*d^6*e*x + 504*A*b^6*d^5*e^2*x + 3024*a*b^5*B*d^5*e^2*x - 1488*a*A*b^5*d^4*e^3*x - 3720*a^2*b^4*B*d^4*e^3*x + 1320*a^2*A*b^4*d^3*e^4*x + 1760*a^3*b^3*B*d^3*e^4*x - 240*a^3*A*b^3*d^2*e^5*x - 180*a^4*b^2*B*d^2*e^5*x - 60*a^4*A*b^2*d*e^6*x - 24*a^5*b*B*d*e^6*x - 24*a^5*A*b*e^7*x - 4*a^6*B*e^7*x - 444*b^6*B*d^5*e^2*x^2 + 396*A*b^6*d^4*e^3*x^2 + 2376*a*b^5*B*d^4*e^3*x^2 - 1512*a*A*b^5*d^3*e^4*x^2 - 3780*a^2*b^4*B*d^3*e^4*x^2 + 1620*a^2*A*b^4*d^2*e^5*x^2 + 2160*a^3*b^3*B*d^2*e^5*x^2 - 360*a^3*A*b^3*d*e^6*x^2 - 270*a^4*b^2*B*d*e^6*x^2 - 90*a^4*A*b^2*e^7*x^2 - 36*a^5*b*B*e^7*x^2 + 544*b^6*B*d^4*e^3*x^3 - 96*A*b^6*d^3*e^4*x^3 - 576*a*b^5*B*d^3*e^4*x^3 - 288*a*A*b^5*d^2*e^5*x^3 - 720*a^2*b^4*B*d^2*e^5*x^3 + 720*a^2*A*b^4*d*e^6*x^3 + 960*a^3*b^3*B*d*e^6*x^3 - 240*a^3*A*b^3*e^7*x^3 - 180*a^4*b^2*B*e^7*x^3 + 556*b^6*B*d^3*e^4*x^4 - 204*A*b^6*d^2*e^5*x^4 - 1224*a*b^5*B*d^2*e^5*x^4 + 288*a*A*b^5*d*e^6*x^4 + 720*a^2*b^4*B*d*e^6*x^4 + 84*b^6*B*d^2*e^5*x^5 - 36*A*b^6*d*e^6*x^5 - 216*a*b^5*B*d*e^6*x^5 + 72*a*A*b^5*e^7*x^5 + 180*a^2*b^4*B*e^7*x^5 - 14*b^6*B*d*e^6*x^6 + 6*A*b^6*e^7*x^6 + 36*a*b^5*B*e^7*x^6 + 4*b^6*B*e^7*x^7)/(12*e^8*(d + e*x)^4) - (5*(7*b^6*B*d^3 - 3*A*b^6*d^2*e - 18*a*b^5*B*d^2*e + 6*a*A*b^5*d*e^2 + 15*a^2*b^4*B*d*e^2 - 3*a^2*A*b^4*e^3 - 4*a^3*b^3*B*e^3)*Log[d + e*x])/e^8","B",1
1065,1,947,272,0.5581816,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^6} \, dx","IntegrateAlgebraic[((a + b*x)^6*(A + B*x))/(d + e*x)^6,x]","\frac{459 b^6 B d^7-174 A b^6 e d^6-1044 a b^5 B e d^6+1875 b^6 B e x d^6+274 a A b^5 e^2 d^5+685 a^2 b^4 B e^2 d^5+2700 b^6 B e^2 x^2 d^5-750 A b^6 e^2 x d^5-4500 a b^5 B e^2 x d^5-60 a^2 A b^4 e^3 d^4-80 a^3 b^3 B e^3 d^4+1300 b^6 B e^3 x^3 d^4-1200 A b^6 e^3 x^2 d^4-7200 a b^5 B e^3 x^2 d^4+1250 a A b^5 e^3 x d^4+3125 a^2 b^4 B e^3 x d^4-20 a^3 A b^3 e^4 d^3-15 a^4 b^2 B e^4 d^3-400 b^6 B e^4 x^4 d^3-800 A b^6 e^4 x^3 d^3-4800 a b^5 B e^4 x^3 d^3+2200 a A b^5 e^4 x^2 d^3+5500 a^2 b^4 B e^4 x^2 d^3-300 a^2 A b^4 e^4 x d^3-400 a^3 b^3 B e^4 x d^3-10 a^4 A b^2 e^5 d^2-4 a^5 b B e^5 d^2-500 b^6 B e^5 x^5 d^2-100 A b^6 e^5 x^4 d^2-600 a b^5 B e^5 x^4 d^2+1800 a A b^5 e^5 x^3 d^2+4500 a^2 b^4 B e^5 x^3 d^2-600 a^2 A b^4 e^5 x^2 d^2-800 a^3 b^3 B e^5 x^2 d^2-100 a^3 A b^3 e^5 x d^2-75 a^4 b^2 B e^5 x d^2-6 a^5 A b e^6 d-a^6 B e^6 d-70 b^6 B e^6 x^6 d+100 A b^6 e^6 x^5 d+600 a b^5 B e^6 x^5 d+600 a A b^5 e^6 x^4 d+1500 a^2 b^4 B e^6 x^4 d-600 a^2 A b^4 e^6 x^3 d-800 a^3 b^3 B e^6 x^3 d-200 a^3 A b^3 e^6 x^2 d-150 a^4 b^2 B e^6 x^2 d-50 a^4 A b^2 e^6 x d-20 a^5 b B e^6 x d-4 a^6 A e^7+10 b^6 B e^7 x^7+20 A b^6 e^7 x^6+120 a b^5 B e^7 x^6-300 a^2 A b^4 e^7 x^4-400 a^3 b^3 B e^7 x^4-200 a^3 A b^3 e^7 x^3-150 a^4 b^2 B e^7 x^3-100 a^4 A b^2 e^7 x^2-40 a^5 b B e^7 x^2-30 a^5 A b e^7 x-5 a^6 B e^7 x}{20 e^8 (d+e x)^5}+\frac{3 \left(7 B d^2 b^6-2 A d e b^6+2 a A e^2 b^5-12 a B d e b^5+5 a^2 B e^2 b^4\right) \log (d+e x)}{e^8}","-\frac{b^5 x (-6 a B e-A b e+6 b B d)}{e^7}+\frac{3 b^4 (b d-a e) \log (d+e x) (-5 a B e-2 A b e+7 b B d)}{e^8}+\frac{5 b^3 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{e^8 (d+e x)}-\frac{5 b^2 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{2 e^8 (d+e x)^2}+\frac{b (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{e^8 (d+e x)^3}-\frac{(b d-a e)^5 (-a B e-6 A b e+7 b B d)}{4 e^8 (d+e x)^4}+\frac{(b d-a e)^6 (B d-A e)}{5 e^8 (d+e x)^5}+\frac{b^6 B x^2}{2 e^6}",1,"(459*b^6*B*d^7 - 174*A*b^6*d^6*e - 1044*a*b^5*B*d^6*e + 274*a*A*b^5*d^5*e^2 + 685*a^2*b^4*B*d^5*e^2 - 60*a^2*A*b^4*d^4*e^3 - 80*a^3*b^3*B*d^4*e^3 - 20*a^3*A*b^3*d^3*e^4 - 15*a^4*b^2*B*d^3*e^4 - 10*a^4*A*b^2*d^2*e^5 - 4*a^5*b*B*d^2*e^5 - 6*a^5*A*b*d*e^6 - a^6*B*d*e^6 - 4*a^6*A*e^7 + 1875*b^6*B*d^6*e*x - 750*A*b^6*d^5*e^2*x - 4500*a*b^5*B*d^5*e^2*x + 1250*a*A*b^5*d^4*e^3*x + 3125*a^2*b^4*B*d^4*e^3*x - 300*a^2*A*b^4*d^3*e^4*x - 400*a^3*b^3*B*d^3*e^4*x - 100*a^3*A*b^3*d^2*e^5*x - 75*a^4*b^2*B*d^2*e^5*x - 50*a^4*A*b^2*d*e^6*x - 20*a^5*b*B*d*e^6*x - 30*a^5*A*b*e^7*x - 5*a^6*B*e^7*x + 2700*b^6*B*d^5*e^2*x^2 - 1200*A*b^6*d^4*e^3*x^2 - 7200*a*b^5*B*d^4*e^3*x^2 + 2200*a*A*b^5*d^3*e^4*x^2 + 5500*a^2*b^4*B*d^3*e^4*x^2 - 600*a^2*A*b^4*d^2*e^5*x^2 - 800*a^3*b^3*B*d^2*e^5*x^2 - 200*a^3*A*b^3*d*e^6*x^2 - 150*a^4*b^2*B*d*e^6*x^2 - 100*a^4*A*b^2*e^7*x^2 - 40*a^5*b*B*e^7*x^2 + 1300*b^6*B*d^4*e^3*x^3 - 800*A*b^6*d^3*e^4*x^3 - 4800*a*b^5*B*d^3*e^4*x^3 + 1800*a*A*b^5*d^2*e^5*x^3 + 4500*a^2*b^4*B*d^2*e^5*x^3 - 600*a^2*A*b^4*d*e^6*x^3 - 800*a^3*b^3*B*d*e^6*x^3 - 200*a^3*A*b^3*e^7*x^3 - 150*a^4*b^2*B*e^7*x^3 - 400*b^6*B*d^3*e^4*x^4 - 100*A*b^6*d^2*e^5*x^4 - 600*a*b^5*B*d^2*e^5*x^4 + 600*a*A*b^5*d*e^6*x^4 + 1500*a^2*b^4*B*d*e^6*x^4 - 300*a^2*A*b^4*e^7*x^4 - 400*a^3*b^3*B*e^7*x^4 - 500*b^6*B*d^2*e^5*x^5 + 100*A*b^6*d*e^6*x^5 + 600*a*b^5*B*d*e^6*x^5 - 70*b^6*B*d*e^6*x^6 + 20*A*b^6*e^7*x^6 + 120*a*b^5*B*e^7*x^6 + 10*b^6*B*e^7*x^7)/(20*e^8*(d + e*x)^5) + (3*(7*b^6*B*d^2 - 2*A*b^6*d*e - 12*a*b^5*B*d*e + 2*a*A*b^5*e^2 + 5*a^2*b^4*B*e^2)*Log[d + e*x])/e^8","B",1
1066,1,922,278,0.6374295,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^7} \, dx","IntegrateAlgebraic[((a + b*x)^6*(A + B*x))/(d + e*x)^7,x]","\frac{-669 b^6 B d^7+147 A b^6 e d^6+882 a b^5 B e d^6-3594 b^6 B e x d^6-60 a A b^5 e^2 d^5-150 a^2 b^4 B e^2 d^5-7725 b^6 B e^2 x^2 d^5+822 A b^6 e^2 x d^5+4932 a b^5 B e^2 x d^5-30 a^2 A b^4 e^3 d^4-40 a^3 b^3 B e^3 d^4-8200 b^6 B e^3 x^3 d^4+1875 A b^6 e^3 x^2 d^4+11250 a b^5 B e^3 x^2 d^4-360 a A b^5 e^3 x d^4-900 a^2 b^4 B e^3 x d^4-20 a^3 A b^3 e^4 d^3-15 a^4 b^2 B e^4 d^3-4050 b^6 B e^4 x^4 d^3+2200 A b^6 e^4 x^3 d^3+13200 a b^5 B e^4 x^3 d^3-900 a A b^5 e^4 x^2 d^3-2250 a^2 b^4 B e^4 x^2 d^3-180 a^2 A b^4 e^4 x d^3-240 a^3 b^3 B e^4 x d^3-15 a^4 A b^2 e^5 d^2-6 a^5 b B e^5 d^2-360 b^6 B e^5 x^5 d^2+1350 A b^6 e^5 x^4 d^2+8100 a b^5 B e^5 x^4 d^2-1200 a A b^5 e^5 x^3 d^2-3000 a^2 b^4 B e^5 x^3 d^2-450 a^2 A b^4 e^5 x^2 d^2-600 a^3 b^3 B e^5 x^2 d^2-120 a^3 A b^3 e^5 x d^2-90 a^4 b^2 B e^5 x d^2-12 a^5 A b e^6 d-2 a^6 B e^6 d+360 b^6 B e^6 x^6 d+360 A b^6 e^6 x^5 d+2160 a b^5 B e^6 x^5 d-900 a A b^5 e^6 x^4 d-2250 a^2 b^4 B e^6 x^4 d-600 a^2 A b^4 e^6 x^3 d-800 a^3 b^3 B e^6 x^3 d-300 a^3 A b^3 e^6 x^2 d-225 a^4 b^2 B e^6 x^2 d-90 a^4 A b^2 e^6 x d-36 a^5 b B e^6 x d-10 a^6 A e^7+60 b^6 B e^7 x^7-360 a A b^5 e^7 x^5-900 a^2 b^4 B e^7 x^5-450 a^2 A b^4 e^7 x^4-600 a^3 b^3 B e^7 x^4-400 a^3 A b^3 e^7 x^3-300 a^4 b^2 B e^7 x^3-225 a^4 A b^2 e^7 x^2-90 a^5 b B e^7 x^2-72 a^5 A b e^7 x-12 a^6 B e^7 x}{60 e^8 (d+e x)^6}+\frac{\left(-7 B d b^6+A e b^6+6 a B e b^5\right) \log (d+e x)}{e^8}","-\frac{b^5 \log (d+e x) (-6 a B e-A b e+7 b B d)}{e^8}-\frac{3 b^4 (b d-a e) (-5 a B e-2 A b e+7 b B d)}{e^8 (d+e x)}+\frac{5 b^3 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{2 e^8 (d+e x)^2}-\frac{5 b^2 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{3 e^8 (d+e x)^3}+\frac{3 b (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{4 e^8 (d+e x)^4}-\frac{(b d-a e)^5 (-a B e-6 A b e+7 b B d)}{5 e^8 (d+e x)^5}+\frac{(b d-a e)^6 (B d-A e)}{6 e^8 (d+e x)^6}+\frac{b^6 B x}{e^7}",1,"(-669*b^6*B*d^7 + 147*A*b^6*d^6*e + 882*a*b^5*B*d^6*e - 60*a*A*b^5*d^5*e^2 - 150*a^2*b^4*B*d^5*e^2 - 30*a^2*A*b^4*d^4*e^3 - 40*a^3*b^3*B*d^4*e^3 - 20*a^3*A*b^3*d^3*e^4 - 15*a^4*b^2*B*d^3*e^4 - 15*a^4*A*b^2*d^2*e^5 - 6*a^5*b*B*d^2*e^5 - 12*a^5*A*b*d*e^6 - 2*a^6*B*d*e^6 - 10*a^6*A*e^7 - 3594*b^6*B*d^6*e*x + 822*A*b^6*d^5*e^2*x + 4932*a*b^5*B*d^5*e^2*x - 360*a*A*b^5*d^4*e^3*x - 900*a^2*b^4*B*d^4*e^3*x - 180*a^2*A*b^4*d^3*e^4*x - 240*a^3*b^3*B*d^3*e^4*x - 120*a^3*A*b^3*d^2*e^5*x - 90*a^4*b^2*B*d^2*e^5*x - 90*a^4*A*b^2*d*e^6*x - 36*a^5*b*B*d*e^6*x - 72*a^5*A*b*e^7*x - 12*a^6*B*e^7*x - 7725*b^6*B*d^5*e^2*x^2 + 1875*A*b^6*d^4*e^3*x^2 + 11250*a*b^5*B*d^4*e^3*x^2 - 900*a*A*b^5*d^3*e^4*x^2 - 2250*a^2*b^4*B*d^3*e^4*x^2 - 450*a^2*A*b^4*d^2*e^5*x^2 - 600*a^3*b^3*B*d^2*e^5*x^2 - 300*a^3*A*b^3*d*e^6*x^2 - 225*a^4*b^2*B*d*e^6*x^2 - 225*a^4*A*b^2*e^7*x^2 - 90*a^5*b*B*e^7*x^2 - 8200*b^6*B*d^4*e^3*x^3 + 2200*A*b^6*d^3*e^4*x^3 + 13200*a*b^5*B*d^3*e^4*x^3 - 1200*a*A*b^5*d^2*e^5*x^3 - 3000*a^2*b^4*B*d^2*e^5*x^3 - 600*a^2*A*b^4*d*e^6*x^3 - 800*a^3*b^3*B*d*e^6*x^3 - 400*a^3*A*b^3*e^7*x^3 - 300*a^4*b^2*B*e^7*x^3 - 4050*b^6*B*d^3*e^4*x^4 + 1350*A*b^6*d^2*e^5*x^4 + 8100*a*b^5*B*d^2*e^5*x^4 - 900*a*A*b^5*d*e^6*x^4 - 2250*a^2*b^4*B*d*e^6*x^4 - 450*a^2*A*b^4*e^7*x^4 - 600*a^3*b^3*B*e^7*x^4 - 360*b^6*B*d^2*e^5*x^5 + 360*A*b^6*d*e^6*x^5 + 2160*a*b^5*B*d*e^6*x^5 - 360*a*A*b^5*e^7*x^5 - 900*a^2*b^4*B*e^7*x^5 + 360*b^6*B*d*e^6*x^6 + 60*b^6*B*e^7*x^7)/(60*e^8*(d + e*x)^6) + ((-7*b^6*B*d + A*b^6*e + 6*a*b^5*B*e)*Log[d + e*x])/e^8","B",1
1067,1,917,213,0.7971469,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^8} \, dx","IntegrateAlgebraic[((a + b*x)^6*(A + B*x))/(d + e*x)^8,x]","\frac{B \log (d+e x) b^6}{e^8}+\frac{1089 b^6 B d^7-60 A b^6 e d^6-360 a b^5 B e d^6+7203 b^6 B e x d^6-60 a A b^5 e^2 d^5-150 a^2 b^4 B e^2 d^5+20139 b^6 B e^2 x^2 d^5-420 A b^6 e^2 x d^5-2520 a b^5 B e^2 x d^5-60 a^2 A b^4 e^3 d^4-80 a^3 b^3 B e^3 d^4+30625 b^6 B e^3 x^3 d^4-1260 A b^6 e^3 x^2 d^4-7560 a b^5 B e^3 x^2 d^4-420 a A b^5 e^3 x d^4-1050 a^2 b^4 B e^3 x d^4-60 a^3 A b^3 e^4 d^3-45 a^4 b^2 B e^4 d^3+26950 b^6 B e^4 x^4 d^3-2100 A b^6 e^4 x^3 d^3-12600 a b^5 B e^4 x^3 d^3-1260 a A b^5 e^4 x^2 d^3-3150 a^2 b^4 B e^4 x^2 d^3-420 a^2 A b^4 e^4 x d^3-560 a^3 b^3 B e^4 x d^3-60 a^4 A b^2 e^5 d^2-24 a^5 b B e^5 d^2+13230 b^6 B e^5 x^5 d^2-2100 A b^6 e^5 x^4 d^2-12600 a b^5 B e^5 x^4 d^2-2100 a A b^5 e^5 x^3 d^2-5250 a^2 b^4 B e^5 x^3 d^2-1260 a^2 A b^4 e^5 x^2 d^2-1680 a^3 b^3 B e^5 x^2 d^2-420 a^3 A b^3 e^5 x d^2-315 a^4 b^2 B e^5 x d^2-60 a^5 A b e^6 d-10 a^6 B e^6 d+2940 b^6 B e^6 x^6 d-1260 A b^6 e^6 x^5 d-7560 a b^5 B e^6 x^5 d-2100 a A b^5 e^6 x^4 d-5250 a^2 b^4 B e^6 x^4 d-2100 a^2 A b^4 e^6 x^3 d-2800 a^3 b^3 B e^6 x^3 d-1260 a^3 A b^3 e^6 x^2 d-945 a^4 b^2 B e^6 x^2 d-420 a^4 A b^2 e^6 x d-168 a^5 b B e^6 x d-60 a^6 A e^7-420 A b^6 e^7 x^6-2520 a b^5 B e^7 x^6-1260 a A b^5 e^7 x^5-3150 a^2 b^4 B e^7 x^5-2100 a^2 A b^4 e^7 x^4-2800 a^3 b^3 B e^7 x^4-2100 a^3 A b^3 e^7 x^3-1575 a^4 b^2 B e^7 x^3-1260 a^4 A b^2 e^7 x^2-504 a^5 b B e^7 x^2-420 a^5 A b e^7 x-70 a^6 B e^7 x}{420 e^8 (d+e x)^7}","-\frac{(a+b x)^7 (B d-A e)}{7 e (d+e x)^7 (b d-a e)}+\frac{6 b^5 B (b d-a e)}{e^8 (d+e x)}-\frac{15 b^4 B (b d-a e)^2}{2 e^8 (d+e x)^2}+\frac{20 b^3 B (b d-a e)^3}{3 e^8 (d+e x)^3}-\frac{15 b^2 B (b d-a e)^4}{4 e^8 (d+e x)^4}+\frac{6 b B (b d-a e)^5}{5 e^8 (d+e x)^5}-\frac{B (b d-a e)^6}{6 e^8 (d+e x)^6}+\frac{b^6 B \log (d+e x)}{e^8}",1,"(1089*b^6*B*d^7 - 60*A*b^6*d^6*e - 360*a*b^5*B*d^6*e - 60*a*A*b^5*d^5*e^2 - 150*a^2*b^4*B*d^5*e^2 - 60*a^2*A*b^4*d^4*e^3 - 80*a^3*b^3*B*d^4*e^3 - 60*a^3*A*b^3*d^3*e^4 - 45*a^4*b^2*B*d^3*e^4 - 60*a^4*A*b^2*d^2*e^5 - 24*a^5*b*B*d^2*e^5 - 60*a^5*A*b*d*e^6 - 10*a^6*B*d*e^6 - 60*a^6*A*e^7 + 7203*b^6*B*d^6*e*x - 420*A*b^6*d^5*e^2*x - 2520*a*b^5*B*d^5*e^2*x - 420*a*A*b^5*d^4*e^3*x - 1050*a^2*b^4*B*d^4*e^3*x - 420*a^2*A*b^4*d^3*e^4*x - 560*a^3*b^3*B*d^3*e^4*x - 420*a^3*A*b^3*d^2*e^5*x - 315*a^4*b^2*B*d^2*e^5*x - 420*a^4*A*b^2*d*e^6*x - 168*a^5*b*B*d*e^6*x - 420*a^5*A*b*e^7*x - 70*a^6*B*e^7*x + 20139*b^6*B*d^5*e^2*x^2 - 1260*A*b^6*d^4*e^3*x^2 - 7560*a*b^5*B*d^4*e^3*x^2 - 1260*a*A*b^5*d^3*e^4*x^2 - 3150*a^2*b^4*B*d^3*e^4*x^2 - 1260*a^2*A*b^4*d^2*e^5*x^2 - 1680*a^3*b^3*B*d^2*e^5*x^2 - 1260*a^3*A*b^3*d*e^6*x^2 - 945*a^4*b^2*B*d*e^6*x^2 - 1260*a^4*A*b^2*e^7*x^2 - 504*a^5*b*B*e^7*x^2 + 30625*b^6*B*d^4*e^3*x^3 - 2100*A*b^6*d^3*e^4*x^3 - 12600*a*b^5*B*d^3*e^4*x^3 - 2100*a*A*b^5*d^2*e^5*x^3 - 5250*a^2*b^4*B*d^2*e^5*x^3 - 2100*a^2*A*b^4*d*e^6*x^3 - 2800*a^3*b^3*B*d*e^6*x^3 - 2100*a^3*A*b^3*e^7*x^3 - 1575*a^4*b^2*B*e^7*x^3 + 26950*b^6*B*d^3*e^4*x^4 - 2100*A*b^6*d^2*e^5*x^4 - 12600*a*b^5*B*d^2*e^5*x^4 - 2100*a*A*b^5*d*e^6*x^4 - 5250*a^2*b^4*B*d*e^6*x^4 - 2100*a^2*A*b^4*e^7*x^4 - 2800*a^3*b^3*B*e^7*x^4 + 13230*b^6*B*d^2*e^5*x^5 - 1260*A*b^6*d*e^6*x^5 - 7560*a*b^5*B*d*e^6*x^5 - 1260*a*A*b^5*e^7*x^5 - 3150*a^2*b^4*B*e^7*x^5 + 2940*b^6*B*d*e^6*x^6 - 420*A*b^6*e^7*x^6 - 2520*a*b^5*B*e^7*x^6)/(420*e^8*(d + e*x)^7) + (b^6*B*Log[d + e*x])/e^8","B",1
1068,1,914,86,0.3989902,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^9} \, dx","IntegrateAlgebraic[((a + b*x)^6*(A + B*x))/(d + e*x)^9,x]","\frac{-7 b^6 B d^7-A b^6 e d^6-6 a b^5 B e d^6-56 b^6 B e x d^6-2 a A b^5 e^2 d^5-5 a^2 b^4 B e^2 d^5-196 b^6 B e^2 x^2 d^5-8 A b^6 e^2 x d^5-48 a b^5 B e^2 x d^5-3 a^2 A b^4 e^3 d^4-4 a^3 b^3 B e^3 d^4-392 b^6 B e^3 x^3 d^4-28 A b^6 e^3 x^2 d^4-168 a b^5 B e^3 x^2 d^4-16 a A b^5 e^3 x d^4-40 a^2 b^4 B e^3 x d^4-4 a^3 A b^3 e^4 d^3-3 a^4 b^2 B e^4 d^3-490 b^6 B e^4 x^4 d^3-56 A b^6 e^4 x^3 d^3-336 a b^5 B e^4 x^3 d^3-56 a A b^5 e^4 x^2 d^3-140 a^2 b^4 B e^4 x^2 d^3-24 a^2 A b^4 e^4 x d^3-32 a^3 b^3 B e^4 x d^3-5 a^4 A b^2 e^5 d^2-2 a^5 b B e^5 d^2-392 b^6 B e^5 x^5 d^2-70 A b^6 e^5 x^4 d^2-420 a b^5 B e^5 x^4 d^2-112 a A b^5 e^5 x^3 d^2-280 a^2 b^4 B e^5 x^3 d^2-84 a^2 A b^4 e^5 x^2 d^2-112 a^3 b^3 B e^5 x^2 d^2-32 a^3 A b^3 e^5 x d^2-24 a^4 b^2 B e^5 x d^2-6 a^5 A b e^6 d-a^6 B e^6 d-196 b^6 B e^6 x^6 d-56 A b^6 e^6 x^5 d-336 a b^5 B e^6 x^5 d-140 a A b^5 e^6 x^4 d-350 a^2 b^4 B e^6 x^4 d-168 a^2 A b^4 e^6 x^3 d-224 a^3 b^3 B e^6 x^3 d-112 a^3 A b^3 e^6 x^2 d-84 a^4 b^2 B e^6 x^2 d-40 a^4 A b^2 e^6 x d-16 a^5 b B e^6 x d-7 a^6 A e^7-56 b^6 B e^7 x^7-28 A b^6 e^7 x^6-168 a b^5 B e^7 x^6-112 a A b^5 e^7 x^5-280 a^2 b^4 B e^7 x^5-210 a^2 A b^4 e^7 x^4-280 a^3 b^3 B e^7 x^4-224 a^3 A b^3 e^7 x^3-168 a^4 b^2 B e^7 x^3-140 a^4 A b^2 e^7 x^2-56 a^5 b B e^7 x^2-48 a^5 A b e^7 x-8 a^6 B e^7 x}{56 e^8 (d+e x)^8}","\frac{(a+b x)^7 (-8 a B e+A b e+7 b B d)}{56 e (d+e x)^7 (b d-a e)^2}-\frac{(a+b x)^7 (B d-A e)}{8 e (d+e x)^8 (b d-a e)}",1,"(-7*b^6*B*d^7 - A*b^6*d^6*e - 6*a*b^5*B*d^6*e - 2*a*A*b^5*d^5*e^2 - 5*a^2*b^4*B*d^5*e^2 - 3*a^2*A*b^4*d^4*e^3 - 4*a^3*b^3*B*d^4*e^3 - 4*a^3*A*b^3*d^3*e^4 - 3*a^4*b^2*B*d^3*e^4 - 5*a^4*A*b^2*d^2*e^5 - 2*a^5*b*B*d^2*e^5 - 6*a^5*A*b*d*e^6 - a^6*B*d*e^6 - 7*a^6*A*e^7 - 56*b^6*B*d^6*e*x - 8*A*b^6*d^5*e^2*x - 48*a*b^5*B*d^5*e^2*x - 16*a*A*b^5*d^4*e^3*x - 40*a^2*b^4*B*d^4*e^3*x - 24*a^2*A*b^4*d^3*e^4*x - 32*a^3*b^3*B*d^3*e^4*x - 32*a^3*A*b^3*d^2*e^5*x - 24*a^4*b^2*B*d^2*e^5*x - 40*a^4*A*b^2*d*e^6*x - 16*a^5*b*B*d*e^6*x - 48*a^5*A*b*e^7*x - 8*a^6*B*e^7*x - 196*b^6*B*d^5*e^2*x^2 - 28*A*b^6*d^4*e^3*x^2 - 168*a*b^5*B*d^4*e^3*x^2 - 56*a*A*b^5*d^3*e^4*x^2 - 140*a^2*b^4*B*d^3*e^4*x^2 - 84*a^2*A*b^4*d^2*e^5*x^2 - 112*a^3*b^3*B*d^2*e^5*x^2 - 112*a^3*A*b^3*d*e^6*x^2 - 84*a^4*b^2*B*d*e^6*x^2 - 140*a^4*A*b^2*e^7*x^2 - 56*a^5*b*B*e^7*x^2 - 392*b^6*B*d^4*e^3*x^3 - 56*A*b^6*d^3*e^4*x^3 - 336*a*b^5*B*d^3*e^4*x^3 - 112*a*A*b^5*d^2*e^5*x^3 - 280*a^2*b^4*B*d^2*e^5*x^3 - 168*a^2*A*b^4*d*e^6*x^3 - 224*a^3*b^3*B*d*e^6*x^3 - 224*a^3*A*b^3*e^7*x^3 - 168*a^4*b^2*B*e^7*x^3 - 490*b^6*B*d^3*e^4*x^4 - 70*A*b^6*d^2*e^5*x^4 - 420*a*b^5*B*d^2*e^5*x^4 - 140*a*A*b^5*d*e^6*x^4 - 350*a^2*b^4*B*d*e^6*x^4 - 210*a^2*A*b^4*e^7*x^4 - 280*a^3*b^3*B*e^7*x^4 - 392*b^6*B*d^2*e^5*x^5 - 56*A*b^6*d*e^6*x^5 - 336*a*b^5*B*d*e^6*x^5 - 112*a*A*b^5*e^7*x^5 - 280*a^2*b^4*B*e^7*x^5 - 196*b^6*B*d*e^6*x^6 - 28*A*b^6*e^7*x^6 - 168*a*b^5*B*e^7*x^6 - 56*b^6*B*e^7*x^7)/(56*e^8*(d + e*x)^8)","B",1
1069,1,914,135,0.3565297,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^{10}} \, dx","IntegrateAlgebraic[((a + b*x)^6*(A + B*x))/(d + e*x)^10,x]","\frac{-7 b^6 B d^7-2 A b^6 e d^6-12 a b^5 B e d^6-63 b^6 B e x d^6-6 a A b^5 e^2 d^5-15 a^2 b^4 B e^2 d^5-252 b^6 B e^2 x^2 d^5-18 A b^6 e^2 x d^5-108 a b^5 B e^2 x d^5-12 a^2 A b^4 e^3 d^4-16 a^3 b^3 B e^3 d^4-588 b^6 B e^3 x^3 d^4-72 A b^6 e^3 x^2 d^4-432 a b^5 B e^3 x^2 d^4-54 a A b^5 e^3 x d^4-135 a^2 b^4 B e^3 x d^4-20 a^3 A b^3 e^4 d^3-15 a^4 b^2 B e^4 d^3-882 b^6 B e^4 x^4 d^3-168 A b^6 e^4 x^3 d^3-1008 a b^5 B e^4 x^3 d^3-216 a A b^5 e^4 x^2 d^3-540 a^2 b^4 B e^4 x^2 d^3-108 a^2 A b^4 e^4 x d^3-144 a^3 b^3 B e^4 x d^3-30 a^4 A b^2 e^5 d^2-12 a^5 b B e^5 d^2-882 b^6 B e^5 x^5 d^2-252 A b^6 e^5 x^4 d^2-1512 a b^5 B e^5 x^4 d^2-504 a A b^5 e^5 x^3 d^2-1260 a^2 b^4 B e^5 x^3 d^2-432 a^2 A b^4 e^5 x^2 d^2-576 a^3 b^3 B e^5 x^2 d^2-180 a^3 A b^3 e^5 x d^2-135 a^4 b^2 B e^5 x d^2-42 a^5 A b e^6 d-7 a^6 B e^6 d-588 b^6 B e^6 x^6 d-252 A b^6 e^6 x^5 d-1512 a b^5 B e^6 x^5 d-756 a A b^5 e^6 x^4 d-1890 a^2 b^4 B e^6 x^4 d-1008 a^2 A b^4 e^6 x^3 d-1344 a^3 b^3 B e^6 x^3 d-720 a^3 A b^3 e^6 x^2 d-540 a^4 b^2 B e^6 x^2 d-270 a^4 A b^2 e^6 x d-108 a^5 b B e^6 x d-56 a^6 A e^7-252 b^6 B e^7 x^7-168 A b^6 e^7 x^6-1008 a b^5 B e^7 x^6-756 a A b^5 e^7 x^5-1890 a^2 b^4 B e^7 x^5-1512 a^2 A b^4 e^7 x^4-2016 a^3 b^3 B e^7 x^4-1680 a^3 A b^3 e^7 x^3-1260 a^4 b^2 B e^7 x^3-1080 a^4 A b^2 e^7 x^2-432 a^5 b B e^7 x^2-378 a^5 A b e^7 x-63 a^6 B e^7 x}{504 e^8 (d+e x)^9}","\frac{b (a+b x)^7 (-9 a B e+2 A b e+7 b B d)}{504 e (d+e x)^7 (b d-a e)^3}+\frac{(a+b x)^7 (-9 a B e+2 A b e+7 b B d)}{72 e (d+e x)^8 (b d-a e)^2}-\frac{(a+b x)^7 (B d-A e)}{9 e (d+e x)^9 (b d-a e)}",1,"(-7*b^6*B*d^7 - 2*A*b^6*d^6*e - 12*a*b^5*B*d^6*e - 6*a*A*b^5*d^5*e^2 - 15*a^2*b^4*B*d^5*e^2 - 12*a^2*A*b^4*d^4*e^3 - 16*a^3*b^3*B*d^4*e^3 - 20*a^3*A*b^3*d^3*e^4 - 15*a^4*b^2*B*d^3*e^4 - 30*a^4*A*b^2*d^2*e^5 - 12*a^5*b*B*d^2*e^5 - 42*a^5*A*b*d*e^6 - 7*a^6*B*d*e^6 - 56*a^6*A*e^7 - 63*b^6*B*d^6*e*x - 18*A*b^6*d^5*e^2*x - 108*a*b^5*B*d^5*e^2*x - 54*a*A*b^5*d^4*e^3*x - 135*a^2*b^4*B*d^4*e^3*x - 108*a^2*A*b^4*d^3*e^4*x - 144*a^3*b^3*B*d^3*e^4*x - 180*a^3*A*b^3*d^2*e^5*x - 135*a^4*b^2*B*d^2*e^5*x - 270*a^4*A*b^2*d*e^6*x - 108*a^5*b*B*d*e^6*x - 378*a^5*A*b*e^7*x - 63*a^6*B*e^7*x - 252*b^6*B*d^5*e^2*x^2 - 72*A*b^6*d^4*e^3*x^2 - 432*a*b^5*B*d^4*e^3*x^2 - 216*a*A*b^5*d^3*e^4*x^2 - 540*a^2*b^4*B*d^3*e^4*x^2 - 432*a^2*A*b^4*d^2*e^5*x^2 - 576*a^3*b^3*B*d^2*e^5*x^2 - 720*a^3*A*b^3*d*e^6*x^2 - 540*a^4*b^2*B*d*e^6*x^2 - 1080*a^4*A*b^2*e^7*x^2 - 432*a^5*b*B*e^7*x^2 - 588*b^6*B*d^4*e^3*x^3 - 168*A*b^6*d^3*e^4*x^3 - 1008*a*b^5*B*d^3*e^4*x^3 - 504*a*A*b^5*d^2*e^5*x^3 - 1260*a^2*b^4*B*d^2*e^5*x^3 - 1008*a^2*A*b^4*d*e^6*x^3 - 1344*a^3*b^3*B*d*e^6*x^3 - 1680*a^3*A*b^3*e^7*x^3 - 1260*a^4*b^2*B*e^7*x^3 - 882*b^6*B*d^3*e^4*x^4 - 252*A*b^6*d^2*e^5*x^4 - 1512*a*b^5*B*d^2*e^5*x^4 - 756*a*A*b^5*d*e^6*x^4 - 1890*a^2*b^4*B*d*e^6*x^4 - 1512*a^2*A*b^4*e^7*x^4 - 2016*a^3*b^3*B*e^7*x^4 - 882*b^6*B*d^2*e^5*x^5 - 252*A*b^6*d*e^6*x^5 - 1512*a*b^5*B*d*e^6*x^5 - 756*a*A*b^5*e^7*x^5 - 1890*a^2*b^4*B*e^7*x^5 - 588*b^6*B*d*e^6*x^6 - 168*A*b^6*e^7*x^6 - 1008*a*b^5*B*e^7*x^6 - 252*b^6*B*e^7*x^7)/(504*e^8*(d + e*x)^9)","B",1
1070,1,914,185,0.3505103,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^{11}} \, dx","IntegrateAlgebraic[((a + b*x)^6*(A + B*x))/(d + e*x)^11,x]","\frac{-7 b^6 B d^7-3 A b^6 e d^6-18 a b^5 B e d^6-70 b^6 B e x d^6-12 a A b^5 e^2 d^5-30 a^2 b^4 B e^2 d^5-315 b^6 B e^2 x^2 d^5-30 A b^6 e^2 x d^5-180 a b^5 B e^2 x d^5-30 a^2 A b^4 e^3 d^4-40 a^3 b^3 B e^3 d^4-840 b^6 B e^3 x^3 d^4-135 A b^6 e^3 x^2 d^4-810 a b^5 B e^3 x^2 d^4-120 a A b^5 e^3 x d^4-300 a^2 b^4 B e^3 x d^4-60 a^3 A b^3 e^4 d^3-45 a^4 b^2 B e^4 d^3-1470 b^6 B e^4 x^4 d^3-360 A b^6 e^4 x^3 d^3-2160 a b^5 B e^4 x^3 d^3-540 a A b^5 e^4 x^2 d^3-1350 a^2 b^4 B e^4 x^2 d^3-300 a^2 A b^4 e^4 x d^3-400 a^3 b^3 B e^4 x d^3-105 a^4 A b^2 e^5 d^2-42 a^5 b B e^5 d^2-1764 b^6 B e^5 x^5 d^2-630 A b^6 e^5 x^4 d^2-3780 a b^5 B e^5 x^4 d^2-1440 a A b^5 e^5 x^3 d^2-3600 a^2 b^4 B e^5 x^3 d^2-1350 a^2 A b^4 e^5 x^2 d^2-1800 a^3 b^3 B e^5 x^2 d^2-600 a^3 A b^3 e^5 x d^2-450 a^4 b^2 B e^5 x d^2-168 a^5 A b e^6 d-28 a^6 B e^6 d-1470 b^6 B e^6 x^6 d-756 A b^6 e^6 x^5 d-4536 a b^5 B e^6 x^5 d-2520 a A b^5 e^6 x^4 d-6300 a^2 b^4 B e^6 x^4 d-3600 a^2 A b^4 e^6 x^3 d-4800 a^3 b^3 B e^6 x^3 d-2700 a^3 A b^3 e^6 x^2 d-2025 a^4 b^2 B e^6 x^2 d-1050 a^4 A b^2 e^6 x d-420 a^5 b B e^6 x d-252 a^6 A e^7-840 b^6 B e^7 x^7-630 A b^6 e^7 x^6-3780 a b^5 B e^7 x^6-3024 a A b^5 e^7 x^5-7560 a^2 b^4 B e^7 x^5-6300 a^2 A b^4 e^7 x^4-8400 a^3 b^3 B e^7 x^4-7200 a^3 A b^3 e^7 x^3-5400 a^4 b^2 B e^7 x^3-4725 a^4 A b^2 e^7 x^2-1890 a^5 b B e^7 x^2-1680 a^5 A b e^7 x-280 a^6 B e^7 x}{2520 e^8 (d+e x)^{10}}","\frac{b^2 (a+b x)^7 (-10 a B e+3 A b e+7 b B d)}{2520 e (d+e x)^7 (b d-a e)^4}+\frac{b (a+b x)^7 (-10 a B e+3 A b e+7 b B d)}{360 e (d+e x)^8 (b d-a e)^3}+\frac{(a+b x)^7 (-10 a B e+3 A b e+7 b B d)}{90 e (d+e x)^9 (b d-a e)^2}-\frac{(a+b x)^7 (B d-A e)}{10 e (d+e x)^{10} (b d-a e)}",1,"(-7*b^6*B*d^7 - 3*A*b^6*d^6*e - 18*a*b^5*B*d^6*e - 12*a*A*b^5*d^5*e^2 - 30*a^2*b^4*B*d^5*e^2 - 30*a^2*A*b^4*d^4*e^3 - 40*a^3*b^3*B*d^4*e^3 - 60*a^3*A*b^3*d^3*e^4 - 45*a^4*b^2*B*d^3*e^4 - 105*a^4*A*b^2*d^2*e^5 - 42*a^5*b*B*d^2*e^5 - 168*a^5*A*b*d*e^6 - 28*a^6*B*d*e^6 - 252*a^6*A*e^7 - 70*b^6*B*d^6*e*x - 30*A*b^6*d^5*e^2*x - 180*a*b^5*B*d^5*e^2*x - 120*a*A*b^5*d^4*e^3*x - 300*a^2*b^4*B*d^4*e^3*x - 300*a^2*A*b^4*d^3*e^4*x - 400*a^3*b^3*B*d^3*e^4*x - 600*a^3*A*b^3*d^2*e^5*x - 450*a^4*b^2*B*d^2*e^5*x - 1050*a^4*A*b^2*d*e^6*x - 420*a^5*b*B*d*e^6*x - 1680*a^5*A*b*e^7*x - 280*a^6*B*e^7*x - 315*b^6*B*d^5*e^2*x^2 - 135*A*b^6*d^4*e^3*x^2 - 810*a*b^5*B*d^4*e^3*x^2 - 540*a*A*b^5*d^3*e^4*x^2 - 1350*a^2*b^4*B*d^3*e^4*x^2 - 1350*a^2*A*b^4*d^2*e^5*x^2 - 1800*a^3*b^3*B*d^2*e^5*x^2 - 2700*a^3*A*b^3*d*e^6*x^2 - 2025*a^4*b^2*B*d*e^6*x^2 - 4725*a^4*A*b^2*e^7*x^2 - 1890*a^5*b*B*e^7*x^2 - 840*b^6*B*d^4*e^3*x^3 - 360*A*b^6*d^3*e^4*x^3 - 2160*a*b^5*B*d^3*e^4*x^3 - 1440*a*A*b^5*d^2*e^5*x^3 - 3600*a^2*b^4*B*d^2*e^5*x^3 - 3600*a^2*A*b^4*d*e^6*x^3 - 4800*a^3*b^3*B*d*e^6*x^3 - 7200*a^3*A*b^3*e^7*x^3 - 5400*a^4*b^2*B*e^7*x^3 - 1470*b^6*B*d^3*e^4*x^4 - 630*A*b^6*d^2*e^5*x^4 - 3780*a*b^5*B*d^2*e^5*x^4 - 2520*a*A*b^5*d*e^6*x^4 - 6300*a^2*b^4*B*d*e^6*x^4 - 6300*a^2*A*b^4*e^7*x^4 - 8400*a^3*b^3*B*e^7*x^4 - 1764*b^6*B*d^2*e^5*x^5 - 756*A*b^6*d*e^6*x^5 - 4536*a*b^5*B*d*e^6*x^5 - 3024*a*A*b^5*e^7*x^5 - 7560*a^2*b^4*B*e^7*x^5 - 1470*b^6*B*d*e^6*x^6 - 630*A*b^6*e^7*x^6 - 3780*a*b^5*B*e^7*x^6 - 840*b^6*B*e^7*x^7)/(2520*e^8*(d + e*x)^10)","B",1
1071,1,914,235,0.3567748,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^{12}} \, dx","IntegrateAlgebraic[((a + b*x)^6*(A + B*x))/(d + e*x)^12,x]","\frac{-7 b^6 B d^7-4 A b^6 e d^6-24 a b^5 B e d^6-77 b^6 B e x d^6-20 a A b^5 e^2 d^5-50 a^2 b^4 B e^2 d^5-385 b^6 B e^2 x^2 d^5-44 A b^6 e^2 x d^5-264 a b^5 B e^2 x d^5-60 a^2 A b^4 e^3 d^4-80 a^3 b^3 B e^3 d^4-1155 b^6 B e^3 x^3 d^4-220 A b^6 e^3 x^2 d^4-1320 a b^5 B e^3 x^2 d^4-220 a A b^5 e^3 x d^4-550 a^2 b^4 B e^3 x d^4-140 a^3 A b^3 e^4 d^3-105 a^4 b^2 B e^4 d^3-2310 b^6 B e^4 x^4 d^3-660 A b^6 e^4 x^3 d^3-3960 a b^5 B e^4 x^3 d^3-1100 a A b^5 e^4 x^2 d^3-2750 a^2 b^4 B e^4 x^2 d^3-660 a^2 A b^4 e^4 x d^3-880 a^3 b^3 B e^4 x d^3-280 a^4 A b^2 e^5 d^2-112 a^5 b B e^5 d^2-3234 b^6 B e^5 x^5 d^2-1320 A b^6 e^5 x^4 d^2-7920 a b^5 B e^5 x^4 d^2-3300 a A b^5 e^5 x^3 d^2-8250 a^2 b^4 B e^5 x^3 d^2-3300 a^2 A b^4 e^5 x^2 d^2-4400 a^3 b^3 B e^5 x^2 d^2-1540 a^3 A b^3 e^5 x d^2-1155 a^4 b^2 B e^5 x d^2-504 a^5 A b e^6 d-84 a^6 B e^6 d-3234 b^6 B e^6 x^6 d-1848 A b^6 e^6 x^5 d-11088 a b^5 B e^6 x^5 d-6600 a A b^5 e^6 x^4 d-16500 a^2 b^4 B e^6 x^4 d-9900 a^2 A b^4 e^6 x^3 d-13200 a^3 b^3 B e^6 x^3 d-7700 a^3 A b^3 e^6 x^2 d-5775 a^4 b^2 B e^6 x^2 d-3080 a^4 A b^2 e^6 x d-1232 a^5 b B e^6 x d-840 a^6 A e^7-2310 b^6 B e^7 x^7-1848 A b^6 e^7 x^6-11088 a b^5 B e^7 x^6-9240 a A b^5 e^7 x^5-23100 a^2 b^4 B e^7 x^5-19800 a^2 A b^4 e^7 x^4-26400 a^3 b^3 B e^7 x^4-23100 a^3 A b^3 e^7 x^3-17325 a^4 b^2 B e^7 x^3-15400 a^4 A b^2 e^7 x^2-6160 a^5 b B e^7 x^2-5544 a^5 A b e^7 x-924 a^6 B e^7 x}{9240 e^8 (d+e x)^{11}}","\frac{b^3 (a+b x)^7 (-11 a B e+4 A b e+7 b B d)}{9240 e (d+e x)^7 (b d-a e)^5}+\frac{b^2 (a+b x)^7 (-11 a B e+4 A b e+7 b B d)}{1320 e (d+e x)^8 (b d-a e)^4}+\frac{b (a+b x)^7 (-11 a B e+4 A b e+7 b B d)}{330 e (d+e x)^9 (b d-a e)^3}+\frac{(a+b x)^7 (-11 a B e+4 A b e+7 b B d)}{110 e (d+e x)^{10} (b d-a e)^2}-\frac{(a+b x)^7 (B d-A e)}{11 e (d+e x)^{11} (b d-a e)}",1,"(-7*b^6*B*d^7 - 4*A*b^6*d^6*e - 24*a*b^5*B*d^6*e - 20*a*A*b^5*d^5*e^2 - 50*a^2*b^4*B*d^5*e^2 - 60*a^2*A*b^4*d^4*e^3 - 80*a^3*b^3*B*d^4*e^3 - 140*a^3*A*b^3*d^3*e^4 - 105*a^4*b^2*B*d^3*e^4 - 280*a^4*A*b^2*d^2*e^5 - 112*a^5*b*B*d^2*e^5 - 504*a^5*A*b*d*e^6 - 84*a^6*B*d*e^6 - 840*a^6*A*e^7 - 77*b^6*B*d^6*e*x - 44*A*b^6*d^5*e^2*x - 264*a*b^5*B*d^5*e^2*x - 220*a*A*b^5*d^4*e^3*x - 550*a^2*b^4*B*d^4*e^3*x - 660*a^2*A*b^4*d^3*e^4*x - 880*a^3*b^3*B*d^3*e^4*x - 1540*a^3*A*b^3*d^2*e^5*x - 1155*a^4*b^2*B*d^2*e^5*x - 3080*a^4*A*b^2*d*e^6*x - 1232*a^5*b*B*d*e^6*x - 5544*a^5*A*b*e^7*x - 924*a^6*B*e^7*x - 385*b^6*B*d^5*e^2*x^2 - 220*A*b^6*d^4*e^3*x^2 - 1320*a*b^5*B*d^4*e^3*x^2 - 1100*a*A*b^5*d^3*e^4*x^2 - 2750*a^2*b^4*B*d^3*e^4*x^2 - 3300*a^2*A*b^4*d^2*e^5*x^2 - 4400*a^3*b^3*B*d^2*e^5*x^2 - 7700*a^3*A*b^3*d*e^6*x^2 - 5775*a^4*b^2*B*d*e^6*x^2 - 15400*a^4*A*b^2*e^7*x^2 - 6160*a^5*b*B*e^7*x^2 - 1155*b^6*B*d^4*e^3*x^3 - 660*A*b^6*d^3*e^4*x^3 - 3960*a*b^5*B*d^3*e^4*x^3 - 3300*a*A*b^5*d^2*e^5*x^3 - 8250*a^2*b^4*B*d^2*e^5*x^3 - 9900*a^2*A*b^4*d*e^6*x^3 - 13200*a^3*b^3*B*d*e^6*x^3 - 23100*a^3*A*b^3*e^7*x^3 - 17325*a^4*b^2*B*e^7*x^3 - 2310*b^6*B*d^3*e^4*x^4 - 1320*A*b^6*d^2*e^5*x^4 - 7920*a*b^5*B*d^2*e^5*x^4 - 6600*a*A*b^5*d*e^6*x^4 - 16500*a^2*b^4*B*d*e^6*x^4 - 19800*a^2*A*b^4*e^7*x^4 - 26400*a^3*b^3*B*e^7*x^4 - 3234*b^6*B*d^2*e^5*x^5 - 1848*A*b^6*d*e^6*x^5 - 11088*a*b^5*B*d*e^6*x^5 - 9240*a*A*b^5*e^7*x^5 - 23100*a^2*b^4*B*e^7*x^5 - 3234*b^6*B*d*e^6*x^6 - 1848*A*b^6*e^7*x^6 - 11088*a*b^5*B*e^7*x^6 - 2310*b^6*B*e^7*x^7)/(9240*e^8*(d + e*x)^11)","B",1
1072,1,914,292,0.3717746,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^{13}} \, dx","IntegrateAlgebraic[((a + b*x)^6*(A + B*x))/(d + e*x)^13,x]","\frac{-7 b^6 B d^7-5 A b^6 e d^6-30 a b^5 B e d^6-84 b^6 B e x d^6-30 a A b^5 e^2 d^5-75 a^2 b^4 B e^2 d^5-462 b^6 B e^2 x^2 d^5-60 A b^6 e^2 x d^5-360 a b^5 B e^2 x d^5-105 a^2 A b^4 e^3 d^4-140 a^3 b^3 B e^3 d^4-1540 b^6 B e^3 x^3 d^4-330 A b^6 e^3 x^2 d^4-1980 a b^5 B e^3 x^2 d^4-360 a A b^5 e^3 x d^4-900 a^2 b^4 B e^3 x d^4-280 a^3 A b^3 e^4 d^3-210 a^4 b^2 B e^4 d^3-3465 b^6 B e^4 x^4 d^3-1100 A b^6 e^4 x^3 d^3-6600 a b^5 B e^4 x^3 d^3-1980 a A b^5 e^4 x^2 d^3-4950 a^2 b^4 B e^4 x^2 d^3-1260 a^2 A b^4 e^4 x d^3-1680 a^3 b^3 B e^4 x d^3-630 a^4 A b^2 e^5 d^2-252 a^5 b B e^5 d^2-5544 b^6 B e^5 x^5 d^2-2475 A b^6 e^5 x^4 d^2-14850 a b^5 B e^5 x^4 d^2-6600 a A b^5 e^5 x^3 d^2-16500 a^2 b^4 B e^5 x^3 d^2-6930 a^2 A b^4 e^5 x^2 d^2-9240 a^3 b^3 B e^5 x^2 d^2-3360 a^3 A b^3 e^5 x d^2-2520 a^4 b^2 B e^5 x d^2-1260 a^5 A b e^6 d-210 a^6 B e^6 d-6468 b^6 B e^6 x^6 d-3960 A b^6 e^6 x^5 d-23760 a b^5 B e^6 x^5 d-14850 a A b^5 e^6 x^4 d-37125 a^2 b^4 B e^6 x^4 d-23100 a^2 A b^4 e^6 x^3 d-30800 a^3 b^3 B e^6 x^3 d-18480 a^3 A b^3 e^6 x^2 d-13860 a^4 b^2 B e^6 x^2 d-7560 a^4 A b^2 e^6 x d-3024 a^5 b B e^6 x d-2310 a^6 A e^7-5544 b^6 B e^7 x^7-4620 A b^6 e^7 x^6-27720 a b^5 B e^7 x^6-23760 a A b^5 e^7 x^5-59400 a^2 b^4 B e^7 x^5-51975 a^2 A b^4 e^7 x^4-69300 a^3 b^3 B e^7 x^4-61600 a^3 A b^3 e^7 x^3-46200 a^4 b^2 B e^7 x^3-41580 a^4 A b^2 e^7 x^2-16632 a^5 b B e^7 x^2-15120 a^5 A b e^7 x-2520 a^6 B e^7 x}{27720 e^8 (d+e x)^{12}}","\frac{b^5 (-6 a B e-A b e+7 b B d)}{6 e^8 (d+e x)^6}-\frac{3 b^4 (b d-a e) (-5 a B e-2 A b e+7 b B d)}{7 e^8 (d+e x)^7}+\frac{5 b^3 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{8 e^8 (d+e x)^8}-\frac{5 b^2 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{9 e^8 (d+e x)^9}+\frac{3 b (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{10 e^8 (d+e x)^{10}}-\frac{(b d-a e)^5 (-a B e-6 A b e+7 b B d)}{11 e^8 (d+e x)^{11}}+\frac{(b d-a e)^6 (B d-A e)}{12 e^8 (d+e x)^{12}}-\frac{b^6 B}{5 e^8 (d+e x)^5}",1,"(-7*b^6*B*d^7 - 5*A*b^6*d^6*e - 30*a*b^5*B*d^6*e - 30*a*A*b^5*d^5*e^2 - 75*a^2*b^4*B*d^5*e^2 - 105*a^2*A*b^4*d^4*e^3 - 140*a^3*b^3*B*d^4*e^3 - 280*a^3*A*b^3*d^3*e^4 - 210*a^4*b^2*B*d^3*e^4 - 630*a^4*A*b^2*d^2*e^5 - 252*a^5*b*B*d^2*e^5 - 1260*a^5*A*b*d*e^6 - 210*a^6*B*d*e^6 - 2310*a^6*A*e^7 - 84*b^6*B*d^6*e*x - 60*A*b^6*d^5*e^2*x - 360*a*b^5*B*d^5*e^2*x - 360*a*A*b^5*d^4*e^3*x - 900*a^2*b^4*B*d^4*e^3*x - 1260*a^2*A*b^4*d^3*e^4*x - 1680*a^3*b^3*B*d^3*e^4*x - 3360*a^3*A*b^3*d^2*e^5*x - 2520*a^4*b^2*B*d^2*e^5*x - 7560*a^4*A*b^2*d*e^6*x - 3024*a^5*b*B*d*e^6*x - 15120*a^5*A*b*e^7*x - 2520*a^6*B*e^7*x - 462*b^6*B*d^5*e^2*x^2 - 330*A*b^6*d^4*e^3*x^2 - 1980*a*b^5*B*d^4*e^3*x^2 - 1980*a*A*b^5*d^3*e^4*x^2 - 4950*a^2*b^4*B*d^3*e^4*x^2 - 6930*a^2*A*b^4*d^2*e^5*x^2 - 9240*a^3*b^3*B*d^2*e^5*x^2 - 18480*a^3*A*b^3*d*e^6*x^2 - 13860*a^4*b^2*B*d*e^6*x^2 - 41580*a^4*A*b^2*e^7*x^2 - 16632*a^5*b*B*e^7*x^2 - 1540*b^6*B*d^4*e^3*x^3 - 1100*A*b^6*d^3*e^4*x^3 - 6600*a*b^5*B*d^3*e^4*x^3 - 6600*a*A*b^5*d^2*e^5*x^3 - 16500*a^2*b^4*B*d^2*e^5*x^3 - 23100*a^2*A*b^4*d*e^6*x^3 - 30800*a^3*b^3*B*d*e^6*x^3 - 61600*a^3*A*b^3*e^7*x^3 - 46200*a^4*b^2*B*e^7*x^3 - 3465*b^6*B*d^3*e^4*x^4 - 2475*A*b^6*d^2*e^5*x^4 - 14850*a*b^5*B*d^2*e^5*x^4 - 14850*a*A*b^5*d*e^6*x^4 - 37125*a^2*b^4*B*d*e^6*x^4 - 51975*a^2*A*b^4*e^7*x^4 - 69300*a^3*b^3*B*e^7*x^4 - 5544*b^6*B*d^2*e^5*x^5 - 3960*A*b^6*d*e^6*x^5 - 23760*a*b^5*B*d*e^6*x^5 - 23760*a*A*b^5*e^7*x^5 - 59400*a^2*b^4*B*e^7*x^5 - 6468*b^6*B*d*e^6*x^6 - 4620*A*b^6*e^7*x^6 - 27720*a*b^5*B*e^7*x^6 - 5544*b^6*B*e^7*x^7)/(27720*e^8*(d + e*x)^12)","B",1
1073,1,914,292,0.3671022,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^{14}} \, dx","IntegrateAlgebraic[((a + b*x)^6*(A + B*x))/(d + e*x)^14,x]","\frac{-7 b^6 B d^7-6 A b^6 e d^6-36 a b^5 B e d^6-91 b^6 B e x d^6-42 a A b^5 e^2 d^5-105 a^2 b^4 B e^2 d^5-546 b^6 B e^2 x^2 d^5-78 A b^6 e^2 x d^5-468 a b^5 B e^2 x d^5-168 a^2 A b^4 e^3 d^4-224 a^3 b^3 B e^3 d^4-2002 b^6 B e^3 x^3 d^4-468 A b^6 e^3 x^2 d^4-2808 a b^5 B e^3 x^2 d^4-546 a A b^5 e^3 x d^4-1365 a^2 b^4 B e^3 x d^4-504 a^3 A b^3 e^4 d^3-378 a^4 b^2 B e^4 d^3-5005 b^6 B e^4 x^4 d^3-1716 A b^6 e^4 x^3 d^3-10296 a b^5 B e^4 x^3 d^3-3276 a A b^5 e^4 x^2 d^3-8190 a^2 b^4 B e^4 x^2 d^3-2184 a^2 A b^4 e^4 x d^3-2912 a^3 b^3 B e^4 x d^3-1260 a^4 A b^2 e^5 d^2-504 a^5 b B e^5 d^2-9009 b^6 B e^5 x^5 d^2-4290 A b^6 e^5 x^4 d^2-25740 a b^5 B e^5 x^4 d^2-12012 a A b^5 e^5 x^3 d^2-30030 a^2 b^4 B e^5 x^3 d^2-13104 a^2 A b^4 e^5 x^2 d^2-17472 a^3 b^3 B e^5 x^2 d^2-6552 a^3 A b^3 e^5 x d^2-4914 a^4 b^2 B e^5 x d^2-2772 a^5 A b e^6 d-462 a^6 B e^6 d-12012 b^6 B e^6 x^6 d-7722 A b^6 e^6 x^5 d-46332 a b^5 B e^6 x^5 d-30030 a A b^5 e^6 x^4 d-75075 a^2 b^4 B e^6 x^4 d-48048 a^2 A b^4 e^6 x^3 d-64064 a^3 b^3 B e^6 x^3 d-39312 a^3 A b^3 e^6 x^2 d-29484 a^4 b^2 B e^6 x^2 d-16380 a^4 A b^2 e^6 x d-6552 a^5 b B e^6 x d-5544 a^6 A e^7-12012 b^6 B e^7 x^7-10296 A b^6 e^7 x^6-61776 a b^5 B e^7 x^6-54054 a A b^5 e^7 x^5-135135 a^2 b^4 B e^7 x^5-120120 a^2 A b^4 e^7 x^4-160160 a^3 b^3 B e^7 x^4-144144 a^3 A b^3 e^7 x^3-108108 a^4 b^2 B e^7 x^3-98280 a^4 A b^2 e^7 x^2-39312 a^5 b B e^7 x^2-36036 a^5 A b e^7 x-6006 a^6 B e^7 x}{72072 e^8 (d+e x)^{13}}","\frac{b^5 (-6 a B e-A b e+7 b B d)}{7 e^8 (d+e x)^7}-\frac{3 b^4 (b d-a e) (-5 a B e-2 A b e+7 b B d)}{8 e^8 (d+e x)^8}+\frac{5 b^3 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{9 e^8 (d+e x)^9}-\frac{b^2 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{2 e^8 (d+e x)^{10}}+\frac{3 b (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{11 e^8 (d+e x)^{11}}-\frac{(b d-a e)^5 (-a B e-6 A b e+7 b B d)}{12 e^8 (d+e x)^{12}}+\frac{(b d-a e)^6 (B d-A e)}{13 e^8 (d+e x)^{13}}-\frac{b^6 B}{6 e^8 (d+e x)^6}",1,"(-7*b^6*B*d^7 - 6*A*b^6*d^6*e - 36*a*b^5*B*d^6*e - 42*a*A*b^5*d^5*e^2 - 105*a^2*b^4*B*d^5*e^2 - 168*a^2*A*b^4*d^4*e^3 - 224*a^3*b^3*B*d^4*e^3 - 504*a^3*A*b^3*d^3*e^4 - 378*a^4*b^2*B*d^3*e^4 - 1260*a^4*A*b^2*d^2*e^5 - 504*a^5*b*B*d^2*e^5 - 2772*a^5*A*b*d*e^6 - 462*a^6*B*d*e^6 - 5544*a^6*A*e^7 - 91*b^6*B*d^6*e*x - 78*A*b^6*d^5*e^2*x - 468*a*b^5*B*d^5*e^2*x - 546*a*A*b^5*d^4*e^3*x - 1365*a^2*b^4*B*d^4*e^3*x - 2184*a^2*A*b^4*d^3*e^4*x - 2912*a^3*b^3*B*d^3*e^4*x - 6552*a^3*A*b^3*d^2*e^5*x - 4914*a^4*b^2*B*d^2*e^5*x - 16380*a^4*A*b^2*d*e^6*x - 6552*a^5*b*B*d*e^6*x - 36036*a^5*A*b*e^7*x - 6006*a^6*B*e^7*x - 546*b^6*B*d^5*e^2*x^2 - 468*A*b^6*d^4*e^3*x^2 - 2808*a*b^5*B*d^4*e^3*x^2 - 3276*a*A*b^5*d^3*e^4*x^2 - 8190*a^2*b^4*B*d^3*e^4*x^2 - 13104*a^2*A*b^4*d^2*e^5*x^2 - 17472*a^3*b^3*B*d^2*e^5*x^2 - 39312*a^3*A*b^3*d*e^6*x^2 - 29484*a^4*b^2*B*d*e^6*x^2 - 98280*a^4*A*b^2*e^7*x^2 - 39312*a^5*b*B*e^7*x^2 - 2002*b^6*B*d^4*e^3*x^3 - 1716*A*b^6*d^3*e^4*x^3 - 10296*a*b^5*B*d^3*e^4*x^3 - 12012*a*A*b^5*d^2*e^5*x^3 - 30030*a^2*b^4*B*d^2*e^5*x^3 - 48048*a^2*A*b^4*d*e^6*x^3 - 64064*a^3*b^3*B*d*e^6*x^3 - 144144*a^3*A*b^3*e^7*x^3 - 108108*a^4*b^2*B*e^7*x^3 - 5005*b^6*B*d^3*e^4*x^4 - 4290*A*b^6*d^2*e^5*x^4 - 25740*a*b^5*B*d^2*e^5*x^4 - 30030*a*A*b^5*d*e^6*x^4 - 75075*a^2*b^4*B*d*e^6*x^4 - 120120*a^2*A*b^4*e^7*x^4 - 160160*a^3*b^3*B*e^7*x^4 - 9009*b^6*B*d^2*e^5*x^5 - 7722*A*b^6*d*e^6*x^5 - 46332*a*b^5*B*d*e^6*x^5 - 54054*a*A*b^5*e^7*x^5 - 135135*a^2*b^4*B*e^7*x^5 - 12012*b^6*B*d*e^6*x^6 - 10296*A*b^6*e^7*x^6 - 61776*a*b^5*B*e^7*x^6 - 12012*b^6*B*e^7*x^7)/(72072*e^8*(d + e*x)^13)","B",1
1074,1,914,292,0.3605912,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^{15}} \, dx","IntegrateAlgebraic[((a + b*x)^6*(A + B*x))/(d + e*x)^15,x]","\frac{-b^6 B d^7-A b^6 e d^6-6 a b^5 B e d^6-14 b^6 B e x d^6-8 a A b^5 e^2 d^5-20 a^2 b^4 B e^2 d^5-91 b^6 B e^2 x^2 d^5-14 A b^6 e^2 x d^5-84 a b^5 B e^2 x d^5-36 a^2 A b^4 e^3 d^4-48 a^3 b^3 B e^3 d^4-364 b^6 B e^3 x^3 d^4-91 A b^6 e^3 x^2 d^4-546 a b^5 B e^3 x^2 d^4-112 a A b^5 e^3 x d^4-280 a^2 b^4 B e^3 x d^4-120 a^3 A b^3 e^4 d^3-90 a^4 b^2 B e^4 d^3-1001 b^6 B e^4 x^4 d^3-364 A b^6 e^4 x^3 d^3-2184 a b^5 B e^4 x^3 d^3-728 a A b^5 e^4 x^2 d^3-1820 a^2 b^4 B e^4 x^2 d^3-504 a^2 A b^4 e^4 x d^3-672 a^3 b^3 B e^4 x d^3-330 a^4 A b^2 e^5 d^2-132 a^5 b B e^5 d^2-2002 b^6 B e^5 x^5 d^2-1001 A b^6 e^5 x^4 d^2-6006 a b^5 B e^5 x^4 d^2-2912 a A b^5 e^5 x^3 d^2-7280 a^2 b^4 B e^5 x^3 d^2-3276 a^2 A b^4 e^5 x^2 d^2-4368 a^3 b^3 B e^5 x^2 d^2-1680 a^3 A b^3 e^5 x d^2-1260 a^4 b^2 B e^5 x d^2-792 a^5 A b e^6 d-132 a^6 B e^6 d-3003 b^6 B e^6 x^6 d-2002 A b^6 e^6 x^5 d-12012 a b^5 B e^6 x^5 d-8008 a A b^5 e^6 x^4 d-20020 a^2 b^4 B e^6 x^4 d-13104 a^2 A b^4 e^6 x^3 d-17472 a^3 b^3 B e^6 x^3 d-10920 a^3 A b^3 e^6 x^2 d-8190 a^4 b^2 B e^6 x^2 d-4620 a^4 A b^2 e^6 x d-1848 a^5 b B e^6 x d-1716 a^6 A e^7-3432 b^6 B e^7 x^7-3003 A b^6 e^7 x^6-18018 a b^5 B e^7 x^6-16016 a A b^5 e^7 x^5-40040 a^2 b^4 B e^7 x^5-36036 a^2 A b^4 e^7 x^4-48048 a^3 b^3 B e^7 x^4-43680 a^3 A b^3 e^7 x^3-32760 a^4 b^2 B e^7 x^3-30030 a^4 A b^2 e^7 x^2-12012 a^5 b B e^7 x^2-11088 a^5 A b e^7 x-1848 a^6 B e^7 x}{24024 e^8 (d+e x)^{14}}","\frac{b^5 (-6 a B e-A b e+7 b B d)}{8 e^8 (d+e x)^8}-\frac{b^4 (b d-a e) (-5 a B e-2 A b e+7 b B d)}{3 e^8 (d+e x)^9}+\frac{b^3 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{2 e^8 (d+e x)^{10}}-\frac{5 b^2 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{11 e^8 (d+e x)^{11}}+\frac{b (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{4 e^8 (d+e x)^{12}}-\frac{(b d-a e)^5 (-a B e-6 A b e+7 b B d)}{13 e^8 (d+e x)^{13}}+\frac{(b d-a e)^6 (B d-A e)}{14 e^8 (d+e x)^{14}}-\frac{b^6 B}{7 e^8 (d+e x)^7}",1,"(-(b^6*B*d^7) - A*b^6*d^6*e - 6*a*b^5*B*d^6*e - 8*a*A*b^5*d^5*e^2 - 20*a^2*b^4*B*d^5*e^2 - 36*a^2*A*b^4*d^4*e^3 - 48*a^3*b^3*B*d^4*e^3 - 120*a^3*A*b^3*d^3*e^4 - 90*a^4*b^2*B*d^3*e^4 - 330*a^4*A*b^2*d^2*e^5 - 132*a^5*b*B*d^2*e^5 - 792*a^5*A*b*d*e^6 - 132*a^6*B*d*e^6 - 1716*a^6*A*e^7 - 14*b^6*B*d^6*e*x - 14*A*b^6*d^5*e^2*x - 84*a*b^5*B*d^5*e^2*x - 112*a*A*b^5*d^4*e^3*x - 280*a^2*b^4*B*d^4*e^3*x - 504*a^2*A*b^4*d^3*e^4*x - 672*a^3*b^3*B*d^3*e^4*x - 1680*a^3*A*b^3*d^2*e^5*x - 1260*a^4*b^2*B*d^2*e^5*x - 4620*a^4*A*b^2*d*e^6*x - 1848*a^5*b*B*d*e^6*x - 11088*a^5*A*b*e^7*x - 1848*a^6*B*e^7*x - 91*b^6*B*d^5*e^2*x^2 - 91*A*b^6*d^4*e^3*x^2 - 546*a*b^5*B*d^4*e^3*x^2 - 728*a*A*b^5*d^3*e^4*x^2 - 1820*a^2*b^4*B*d^3*e^4*x^2 - 3276*a^2*A*b^4*d^2*e^5*x^2 - 4368*a^3*b^3*B*d^2*e^5*x^2 - 10920*a^3*A*b^3*d*e^6*x^2 - 8190*a^4*b^2*B*d*e^6*x^2 - 30030*a^4*A*b^2*e^7*x^2 - 12012*a^5*b*B*e^7*x^2 - 364*b^6*B*d^4*e^3*x^3 - 364*A*b^6*d^3*e^4*x^3 - 2184*a*b^5*B*d^3*e^4*x^3 - 2912*a*A*b^5*d^2*e^5*x^3 - 7280*a^2*b^4*B*d^2*e^5*x^3 - 13104*a^2*A*b^4*d*e^6*x^3 - 17472*a^3*b^3*B*d*e^6*x^3 - 43680*a^3*A*b^3*e^7*x^3 - 32760*a^4*b^2*B*e^7*x^3 - 1001*b^6*B*d^3*e^4*x^4 - 1001*A*b^6*d^2*e^5*x^4 - 6006*a*b^5*B*d^2*e^5*x^4 - 8008*a*A*b^5*d*e^6*x^4 - 20020*a^2*b^4*B*d*e^6*x^4 - 36036*a^2*A*b^4*e^7*x^4 - 48048*a^3*b^3*B*e^7*x^4 - 2002*b^6*B*d^2*e^5*x^5 - 2002*A*b^6*d*e^6*x^5 - 12012*a*b^5*B*d*e^6*x^5 - 16016*a*A*b^5*e^7*x^5 - 40040*a^2*b^4*B*e^7*x^5 - 3003*b^6*B*d*e^6*x^6 - 3003*A*b^6*e^7*x^6 - 18018*a*b^5*B*e^7*x^6 - 3432*b^6*B*e^7*x^7)/(24024*e^8*(d + e*x)^14)","B",1
1075,1,5047,464,3.6650804,"\int (a+b x)^{10} (A+B x) (d+e x)^{13} \, dx","IntegrateAlgebraic[(a + b*x)^10*(A + B*x)*(d + e*x)^13,x]","\text{Result too large to show}","-\frac{b^9 (d+e x)^{24} (-10 a B e-A b e+11 b B d)}{24 e^{12}}+\frac{5 b^8 (d+e x)^{23} (b d-a e) (-9 a B e-2 A b e+11 b B d)}{23 e^{12}}-\frac{15 b^7 (d+e x)^{22} (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{22 e^{12}}+\frac{10 b^6 (d+e x)^{21} (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{7 e^{12}}-\frac{21 b^5 (d+e x)^{20} (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{10 e^{12}}+\frac{42 b^4 (d+e x)^{19} (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{19 e^{12}}-\frac{5 b^3 (d+e x)^{18} (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{3 e^{12}}+\frac{15 b^2 (d+e x)^{17} (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{17 e^{12}}-\frac{5 b (d+e x)^{16} (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{16 e^{12}}+\frac{(d+e x)^{15} (b d-a e)^9 (-a B e-10 A b e+11 b B d)}{15 e^{12}}-\frac{(d+e x)^{14} (b d-a e)^{10} (B d-A e)}{14 e^{12}}+\frac{b^{10} B (d+e x)^{25}}{25 e^{12}}",1,"Result too large to show","B",1
1076,1,4671,464,3.5007386,"\int (a+b x)^{10} (A+B x) (d+e x)^{12} \, dx","IntegrateAlgebraic[(a + b*x)^10*(A + B*x)*(d + e*x)^12,x]","\text{Result too large to show}","-\frac{b^9 (d+e x)^{23} (-10 a B e-A b e+11 b B d)}{23 e^{12}}+\frac{5 b^8 (d+e x)^{22} (b d-a e) (-9 a B e-2 A b e+11 b B d)}{22 e^{12}}-\frac{5 b^7 (d+e x)^{21} (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{7 e^{12}}+\frac{3 b^6 (d+e x)^{20} (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{2 e^{12}}-\frac{42 b^5 (d+e x)^{19} (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{19 e^{12}}+\frac{7 b^4 (d+e x)^{18} (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{3 e^{12}}-\frac{30 b^3 (d+e x)^{17} (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{17 e^{12}}+\frac{15 b^2 (d+e x)^{16} (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{16 e^{12}}-\frac{b (d+e x)^{15} (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{3 e^{12}}+\frac{(d+e x)^{14} (b d-a e)^9 (-a B e-10 A b e+11 b B d)}{14 e^{12}}-\frac{(d+e x)^{13} (b d-a e)^{10} (B d-A e)}{13 e^{12}}+\frac{b^{10} B (d+e x)^{24}}{24 e^{12}}",1,"(356948592*a^10*A*d^12*x + 1784742960*a^9*A*b*d^12*x^2 + 178474296*a^10*B*d^12*x^2 + 2141691552*a^10*A*d^11*e*x^2 + 5354228880*a^8*A*b^2*d^12*x^3 + 1189828640*a^9*b*B*d^12*x^3 + 14277943680*a^9*A*b*d^11*e*x^3 + 1427794368*a^10*B*d^11*e*x^3 + 7852869024*a^10*A*d^10*e^2*x^3 + 10708457760*a^7*A*b^3*d^12*x^4 + 4015671660*a^8*b^2*B*d^12*x^4 + 48188059920*a^8*A*b^2*d^11*e*x^4 + 10708457760*a^9*b*B*d^11*e*x^4 + 58896517680*a^9*A*b*d^10*e^2*x^4 + 5889651768*a^10*B*d^10*e^2*x^4 + 19632172560*a^10*A*d^9*e^3*x^4 + 14991840864*a^6*A*b^4*d^12*x^5 + 8566766208*a^7*b^3*B*d^12*x^5 + 102801194496*a^7*A*b^3*d^11*e*x^5 + 38550447936*a^8*b^2*B*d^11*e*x^5 + 212027463648*a^8*A*b^2*d^10*e^2*x^5 + 47117214144*a^9*b*B*d^10*e^2*x^5 + 157057380480*a^9*A*b*d^9*e^3*x^5 + 15705738048*a^10*B*d^9*e^3*x^5 + 35337910608*a^10*A*d^8*e^4*x^5 + 14991840864*a^5*A*b^5*d^12*x^6 + 12493200720*a^6*b^4*B*d^12*x^6 + 149918408640*a^6*A*b^4*d^11*e*x^6 + 85667662080*a^7*b^3*B*d^11*e*x^6 + 471172141440*a^7*A*b^3*d^10*e^2*x^6 + 176689553040*a^8*b^2*B*d^10*e^2*x^6 + 588965176800*a^8*A*b^2*d^9*e^3*x^6 + 130881150400*a^9*b*B*d^9*e^3*x^6 + 294482588400*a^9*A*b*d^8*e^4*x^6 + 29448258840*a^10*B*d^8*e^4*x^6 + 47117214144*a^10*A*d^7*e^5*x^6 + 10708457760*a^4*A*b^6*d^12*x^7 + 12850149312*a^5*b^5*B*d^12*x^7 + 154201791744*a^5*A*b^5*d^11*e*x^7 + 128501493120*a^6*b^4*B*d^11*e*x^7 + 706758212160*a^6*A*b^4*d^10*e^2*x^7 + 403861835520*a^7*b^3*B*d^10*e^2*x^7 + 1346206118400*a^7*A*b^3*d^9*e^3*x^7 + 504827294400*a^8*b^2*B*d^9*e^3*x^7 + 1135861412400*a^8*A*b^2*d^8*e^4*x^7 + 252413647200*a^9*b*B*d^8*e^4*x^7 + 403861835520*a^9*A*b*d^7*e^5*x^7 + 40386183552*a^10*B*d^7*e^5*x^7 + 47117214144*a^10*A*d^6*e^6*x^7 + 5354228880*a^3*A*b^7*d^12*x^8 + 9369900540*a^4*b^6*B*d^12*x^8 + 112438806480*a^4*A*b^6*d^11*e*x^8 + 134926567776*a^5*b^5*B*d^11*e*x^8 + 742096122768*a^5*A*b^5*d^10*e^2*x^8 + 618413435640*a^6*b^4*B*d^10*e^2*x^8 + 2061378118800*a^6*A*b^4*d^9*e^3*x^8 + 1177930353600*a^7*b^3*B*d^9*e^3*x^8 + 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1077,1,4295,461,2.9828958,"\int (a+b x)^{10} (A+B x) (d+e x)^{11} \, dx","IntegrateAlgebraic[(a + b*x)^10*(A + B*x)*(d + e*x)^11,x]","\text{Result too large to show}","-\frac{b^9 (d+e x)^{22} (-10 a B e-A b e+11 b B d)}{22 e^{12}}+\frac{5 b^8 (d+e x)^{21} (b d-a e) (-9 a B e-2 A b e+11 b B d)}{21 e^{12}}-\frac{3 b^7 (d+e x)^{20} (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{4 e^{12}}+\frac{30 b^6 (d+e x)^{19} (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{19 e^{12}}-\frac{7 b^5 (d+e x)^{18} (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{3 e^{12}}+\frac{42 b^4 (d+e x)^{17} (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{17 e^{12}}-\frac{15 b^3 (d+e x)^{16} (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{8 e^{12}}+\frac{b^2 (d+e x)^{15} (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{e^{12}}-\frac{5 b (d+e x)^{14} (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{14 e^{12}}+\frac{(d+e x)^{13} (b d-a e)^9 (-a B e-10 A b e+11 b B d)}{13 e^{12}}-\frac{(d+e x)^{12} (b d-a e)^{10} (B d-A e)}{12 e^{12}}+\frac{b^{10} B (d+e x)^{23}}{23 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4417238826*a^2*b^8*B*d*e^10*x^20 + 401567166*a^2*A*b^8*e^11*x^20 + 1070845776*a^3*b^7*B*e^11*x^20 + 467432680*b^10*B*d^2*e^9*x^21 + 93486536*A*b^10*d*e^10*x^21 + 934865360*a*b^9*B*d*e^10*x^21 + 84987760*a*A*b^9*e^11*x^21 + 382444920*a^2*b^8*B*e^11*x^21 + 89237148*b^10*B*d*e^10*x^22 + 8112468*A*b^10*e^11*x^22 + 81124680*a*b^9*B*e^11*x^22 + 7759752*b^10*B*e^11*x^23)/178474296","B",1
1078,1,3919,460,2.7030171,"\int (a+b x)^{10} (A+B x) (d+e x)^{10} \, dx","IntegrateAlgebraic[(a + b*x)^10*(A + B*x)*(d + e*x)^10,x]","\text{Result too large to show}","\frac{e^9 (a+b x)^{21} (-11 a B e+A b e+10 b B d)}{21 b^{12}}+\frac{e^8 (a+b x)^{20} (b d-a e) (-11 a B e+2 A b e+9 b B d)}{4 b^{12}}+\frac{15 e^7 (a+b x)^{19} (b d-a e)^2 (-11 a B e+3 A b e+8 b B d)}{19 b^{12}}+\frac{5 e^6 (a+b x)^{18} (b d-a e)^3 (-11 a B e+4 A b e+7 b B d)}{3 b^{12}}+\frac{42 e^5 (a+b x)^{17} (b d-a e)^4 (-11 a B e+5 A b e+6 b B d)}{17 b^{12}}+\frac{21 e^4 (a+b x)^{16} (b d-a e)^5 (-11 a B e+6 A b e+5 b B d)}{8 b^{12}}+\frac{2 e^3 (a+b x)^{15} (b d-a e)^6 (-11 a B e+7 A b e+4 b B d)}{b^{12}}+\frac{15 e^2 (a+b x)^{14} (b d-a e)^7 (-11 a B e+8 A b e+3 b B d)}{14 b^{12}}+\frac{5 e (a+b x)^{13} (b d-a e)^8 (-11 a B e+9 A b e+2 b B d)}{13 b^{12}}+\frac{(a+b x)^{12} (b d-a e)^9 (-11 a B e+10 A b e+b B d)}{12 b^{12}}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)^{10}}{11 b^{12}}+\frac{B e^{10} (a+b x)^{22}}{22 b^{12}}",1,"(7759752*a^10*A*d^10*x + 38798760*a^9*A*b*d^10*x^2 + 3879876*a^10*B*d^10*x^2 + 38798760*a^10*A*d^9*e*x^2 + 116396280*a^8*A*b^2*d^10*x^3 + 25865840*a^9*b*B*d^10*x^3 + 258658400*a^9*A*b*d^9*e*x^3 + 25865840*a^10*B*d^9*e*x^3 + 116396280*a^10*A*d^8*e^2*x^3 + 232792560*a^7*A*b^3*d^10*x^4 + 87297210*a^8*b^2*B*d^10*x^4 + 872972100*a^8*A*b^2*d^9*e*x^4 + 193993800*a^9*b*B*d^9*e*x^4 + 872972100*a^9*A*b*d^8*e^2*x^4 + 87297210*a^10*B*d^8*e^2*x^4 + 232792560*a^10*A*d^7*e^3*x^4 + 325909584*a^6*A*b^4*d^10*x^5 + 186234048*a^7*b^3*B*d^10*x^5 + 1862340480*a^7*A*b^3*d^9*e*x^5 + 698377680*a^8*b^2*B*d^9*e*x^5 + 3142699560*a^8*A*b^2*d^8*e^2*x^5 + 698377680*a^9*b*B*d^8*e^2*x^5 + 1862340480*a^9*A*b*d^7*e^3*x^5 + 186234048*a^10*B*d^7*e^3*x^5 + 325909584*a^10*A*d^6*e^4*x^5 + 325909584*a^5*A*b^5*d^10*x^6 + 271591320*a^6*b^4*B*d^10*x^6 + 2715913200*a^6*A*b^4*d^9*e*x^6 + 1551950400*a^7*b^3*B*d^9*e*x^6 + 6983776800*a^7*A*b^3*d^8*e^2*x^6 + 2618916300*a^8*b^2*B*d^8*e^2*x^6 + 6983776800*a^8*A*b^2*d^7*e^3*x^6 + 1551950400*a^9*b*B*d^7*e^3*x^6 + 2715913200*a^9*A*b*d^6*e^4*x^6 + 271591320*a^10*B*d^6*e^4*x^6 + 325909584*a^10*A*d^5*e^5*x^6 + 232792560*a^4*A*b^6*d^10*x^7 + 279351072*a^5*b^5*B*d^10*x^7 + 2793510720*a^5*A*b^5*d^9*e*x^7 + 2327925600*a^6*b^4*B*d^9*e*x^7 + 10475665200*a^6*A*b^4*d^8*e^2*x^7 + 5986094400*a^7*b^3*B*d^8*e^2*x^7 + 15962918400*a^7*A*b^3*d^7*e^3*x^7 + 5986094400*a^8*b^2*B*d^7*e^3*x^7 + 10475665200*a^8*A*b^2*d^6*e^4*x^7 + 2327925600*a^9*b*B*d^6*e^4*x^7 + 2793510720*a^9*A*b*d^5*e^5*x^7 + 279351072*a^10*B*d^5*e^5*x^7 + 232792560*a^10*A*d^4*e^6*x^7 + 116396280*a^3*A*b^7*d^10*x^8 + 203693490*a^4*b^6*B*d^10*x^8 + 2036934900*a^4*A*b^6*d^9*e*x^8 + 2444321880*a^5*b^5*B*d^9*e*x^8 + 10999448460*a^5*A*b^5*d^8*e^2*x^8 + 9166207050*a^6*b^4*B*d^8*e^2*x^8 + 24443218800*a^6*A*b^4*d^7*e^3*x^8 + 13967553600*a^7*b^3*B*d^7*e^3*x^8 + 24443218800*a^7*A*b^3*d^6*e^4*x^8 + 9166207050*a^8*b^2*B*d^6*e^4*x^8 + 10999448460*a^8*A*b^2*d^5*e^5*x^8 + 2444321880*a^9*b*B*d^5*e^5*x^8 + 2036934900*a^9*A*b*d^4*e^6*x^8 + 203693490*a^10*B*d^4*e^6*x^8 + 116396280*a^10*A*d^3*e^7*x^8 + 38798760*a^2*A*b^8*d^10*x^9 + 103463360*a^3*b^7*B*d^10*x^9 + 1034633600*a^3*A*b^7*d^9*e*x^9 + 1810608800*a^4*b^6*B*d^9*e*x^9 + 8147739600*a^4*A*b^6*d^8*e^2*x^9 + 9777287520*a^5*b^5*B*d^8*e^2*x^9 + 26072766720*a^5*A*b^5*d^7*e^3*x^9 + 21727305600*a^6*b^4*B*d^7*e^3*x^9 + 38022784800*a^6*A*b^4*d^6*e^4*x^9 + 21727305600*a^7*b^3*B*d^6*e^4*x^9 + 26072766720*a^7*A*b^3*d^5*e^5*x^9 + 9777287520*a^8*b^2*B*d^5*e^5*x^9 + 8147739600*a^8*A*b^2*d^4*e^6*x^9 + 1810608800*a^9*b*B*d^4*e^6*x^9 + 1034633600*a^9*A*b*d^3*e^7*x^9 + 103463360*a^10*B*d^3*e^7*x^9 + 38798760*a^10*A*d^2*e^8*x^9 + 7759752*a*A*b^9*d^10*x^10 + 34918884*a^2*b^8*B*d^10*x^10 + 349188840*a^2*A*b^8*d^9*e*x^10 + 931170240*a^3*b^7*B*d^9*e*x^10 + 4190266080*a^3*A*b^7*d^8*e^2*x^10 + 7332965640*a^4*b^6*B*d^8*e^2*x^10 + 19554575040*a^4*A*b^6*d^7*e^3*x^10 + 23465490048*a^5*b^5*B*d^7*e^3*x^10 + 41064607584*a^5*A*b^5*d^6*e^4*x^10 + 34220506320*a^6*b^4*B*d^6*e^4*x^10 + 41064607584*a^6*A*b^4*d^5*e^5*x^10 + 23465490048*a^7*b^3*B*d^5*e^5*x^10 + 19554575040*a^7*A*b^3*d^4*e^6*x^10 + 7332965640*a^8*b^2*B*d^4*e^6*x^10 + 4190266080*a^8*A*b^2*d^3*e^7*x^10 + 931170240*a^9*b*B*d^3*e^7*x^10 + 349188840*a^9*A*b*d^2*e^8*x^10 + 34918884*a^10*B*d^2*e^8*x^10 + 7759752*a^10*A*d*e^9*x^10 + 705432*A*b^10*d^10*x^11 + 7054320*a*b^9*B*d^10*x^11 + 70543200*a*A*b^9*d^9*e*x^11 + 317444400*a^2*b^8*B*d^9*e*x^11 + 1428499800*a^2*A*b^8*d^8*e^2*x^11 + 3809332800*a^3*b^7*B*d^8*e^2*x^11 + 10158220800*a^3*A*b^7*d^7*e^3*x^11 + 17776886400*a^4*b^6*B*d^7*e^3*x^11 + 31109551200*a^4*A*b^6*d^6*e^4*x^11 + 37331461440*a^5*b^5*B*d^6*e^4*x^11 + 44797753728*a^5*A*b^5*d^5*e^5*x^11 + 37331461440*a^6*b^4*B*d^5*e^5*x^11 + 31109551200*a^6*A*b^4*d^4*e^6*x^11 + 17776886400*a^7*b^3*B*d^4*e^6*x^11 + 10158220800*a^7*A*b^3*d^3*e^7*x^11 + 3809332800*a^8*b^2*B*d^3*e^7*x^11 + 1428499800*a^8*A*b^2*d^2*e^8*x^11 + 317444400*a^9*b*B*d^2*e^8*x^11 + 70543200*a^9*A*b*d*e^9*x^11 + 7054320*a^10*B*d*e^9*x^11 + 705432*a^10*A*e^10*x^11 + 646646*b^10*B*d^10*x^12 + 6466460*A*b^10*d^9*e*x^12 + 64664600*a*b^9*B*d^9*e*x^12 + 290990700*a*A*b^9*d^8*e^2*x^12 + 1309458150*a^2*b^8*B*d^8*e^2*x^12 + 3491888400*a^2*A*b^8*d^7*e^3*x^12 + 9311702400*a^3*b^7*B*d^7*e^3*x^12 + 16295479200*a^3*A*b^7*d^6*e^4*x^12 + 28517088600*a^4*b^6*B*d^6*e^4*x^12 + 34220506320*a^4*A*b^6*d^5*e^5*x^12 + 41064607584*a^5*b^5*B*d^5*e^5*x^12 + 34220506320*a^5*A*b^5*d^4*e^6*x^12 + 28517088600*a^6*b^4*B*d^4*e^6*x^12 + 16295479200*a^6*A*b^4*d^3*e^7*x^12 + 9311702400*a^7*b^3*B*d^3*e^7*x^12 + 3491888400*a^7*A*b^3*d^2*e^8*x^12 + 1309458150*a^8*b^2*B*d^2*e^8*x^12 + 290990700*a^8*A*b^2*d*e^9*x^12 + 64664600*a^9*b*B*d*e^9*x^12 + 6466460*a^9*A*b*e^10*x^12 + 646646*a^10*B*e^10*x^12 + 5969040*b^10*B*d^9*e*x^13 + 26860680*A*b^10*d^8*e^2*x^13 + 268606800*a*b^9*B*d^8*e^2*x^13 + 716284800*a*A*b^9*d^7*e^3*x^13 + 3223281600*a^2*b^8*B*d^7*e^3*x^13 + 5640742800*a^2*A*b^8*d^6*e^4*x^13 + 15041980800*a^3*b^7*B*d^6*e^4*x^13 + 18050376960*a^3*A*b^7*d^5*e^5*x^13 + 31588159680*a^4*b^6*B*d^5*e^5*x^13 + 26323466400*a^4*A*b^6*d^4*e^6*x^13 + 31588159680*a^5*b^5*B*d^4*e^6*x^13 + 18050376960*a^5*A*b^5*d^3*e^7*x^13 + 15041980800*a^6*b^4*B*d^3*e^7*x^13 + 5640742800*a^6*A*b^4*d^2*e^8*x^13 + 3223281600*a^7*b^3*B*d^2*e^8*x^13 + 716284800*a^7*A*b^3*d*e^9*x^13 + 268606800*a^8*b^2*B*d*e^9*x^13 + 26860680*a^8*A*b^2*e^10*x^13 + 5969040*a^9*b*B*e^10*x^13 + 24942060*b^10*B*d^8*e^2*x^14 + 66512160*A*b^10*d^7*e^3*x^14 + 665121600*a*b^9*B*d^7*e^3*x^14 + 1163962800*a*A*b^9*d^6*e^4*x^14 + 5237832600*a^2*b^8*B*d^6*e^4*x^14 + 6285399120*a^2*A*b^8*d^5*e^5*x^14 + 16761064320*a^3*b^7*B*d^5*e^5*x^14 + 13967553600*a^3*A*b^7*d^4*e^6*x^14 + 24443218800*a^4*b^6*B*d^4*e^6*x^14 + 13967553600*a^4*A*b^6*d^3*e^7*x^14 + 16761064320*a^5*b^5*B*d^3*e^7*x^14 + 6285399120*a^5*A*b^5*d^2*e^8*x^14 + 5237832600*a^6*b^4*B*d^2*e^8*x^14 + 1163962800*a^6*A*b^4*d*e^9*x^14 + 665121600*a^7*b^3*B*d*e^9*x^14 + 66512160*a^7*A*b^3*e^10*x^14 + 24942060*a^8*b^2*B*e^10*x^14 + 62078016*b^10*B*d^7*e^3*x^15 + 108636528*A*b^10*d^6*e^4*x^15 + 1086365280*a*b^9*B*d^6*e^4*x^15 + 1303638336*a*A*b^9*d^5*e^5*x^15 + 5866372512*a^2*b^8*B*d^5*e^5*x^15 + 4888643760*a^2*A*b^8*d^4*e^6*x^15 + 13036383360*a^3*b^7*B*d^4*e^6*x^15 + 7449361920*a^3*A*b^7*d^3*e^7*x^15 + 13036383360*a^4*b^6*B*d^3*e^7*x^15 + 4888643760*a^4*A*b^6*d^2*e^8*x^15 + 5866372512*a^5*b^5*B*d^2*e^8*x^15 + 1303638336*a^5*A*b^5*d*e^9*x^15 + 1086365280*a^6*b^4*B*d*e^9*x^15 + 108636528*a^6*A*b^4*e^10*x^15 + 62078016*a^7*b^3*B*e^10*x^15 + 101846745*b^10*B*d^6*e^4*x^16 + 122216094*A*b^10*d^5*e^5*x^16 + 1222160940*a*b^9*B*d^5*e^5*x^16 + 1018467450*a*A*b^9*d^4*e^6*x^16 + 4583103525*a^2*b^8*B*d^4*e^6*x^16 + 2618916300*a^2*A*b^8*d^3*e^7*x^16 + 6983776800*a^3*b^7*B*d^3*e^7*x^16 + 2618916300*a^3*A*b^7*d^2*e^8*x^16 + 4583103525*a^4*b^6*B*d^2*e^8*x^16 + 1018467450*a^4*A*b^6*d*e^9*x^16 + 1222160940*a^5*b^5*B*d*e^9*x^16 + 122216094*a^5*A*b^5*e^10*x^16 + 101846745*a^6*b^4*B*e^10*x^16 + 115026912*b^10*B*d^5*e^5*x^17 + 95855760*A*b^10*d^4*e^6*x^17 + 958557600*a*b^9*B*d^4*e^6*x^17 + 547747200*a*A*b^9*d^3*e^7*x^17 + 2464862400*a^2*b^8*B*d^3*e^7*x^17 + 924323400*a^2*A*b^8*d^2*e^8*x^17 + 2464862400*a^3*b^7*B*d^2*e^8*x^17 + 547747200*a^3*A*b^7*d*e^9*x^17 + 958557600*a^4*b^6*B*d*e^9*x^17 + 95855760*a^4*A*b^6*e^10*x^17 + 115026912*a^5*b^5*B*e^10*x^17 + 90530440*b^10*B*d^4*e^6*x^18 + 51731680*A*b^10*d^3*e^7*x^18 + 517316800*a*b^9*B*d^3*e^7*x^18 + 193993800*a*A*b^9*d^2*e^8*x^18 + 872972100*a^2*b^8*B*d^2*e^8*x^18 + 193993800*a^2*A*b^8*d*e^9*x^18 + 517316800*a^3*b^7*B*d*e^9*x^18 + 51731680*a^3*A*b^7*e^10*x^18 + 90530440*a^4*b^6*B*e^10*x^18 + 49008960*b^10*B*d^3*e^7*x^19 + 18378360*A*b^10*d^2*e^8*x^19 + 183783600*a*b^9*B*d^2*e^8*x^19 + 40840800*a*A*b^9*d*e^9*x^19 + 183783600*a^2*b^8*B*d*e^9*x^19 + 18378360*a^2*A*b^8*e^10*x^19 + 49008960*a^3*b^7*B*e^10*x^19 + 17459442*b^10*B*d^2*e^8*x^20 + 3879876*A*b^10*d*e^9*x^20 + 38798760*a*b^9*B*d*e^9*x^20 + 3879876*a*A*b^9*e^10*x^20 + 17459442*a^2*b^8*B*e^10*x^20 + 3695120*b^10*B*d*e^9*x^21 + 369512*A*b^10*e^10*x^21 + 3695120*a*b^9*B*e^10*x^21 + 352716*b^10*B*e^10*x^22)/7759752","B",1
1079,1,3543,415,2.398194,"\int (a+b x)^{10} (A+B x) (d+e x)^9 \, dx","IntegrateAlgebraic[(a + b*x)^10*(A + B*x)*(d + e*x)^9,x]","\text{Result too large to show}","\frac{e^8 (a+b x)^{20} (-10 a B e+A b e+9 b B d)}{20 b^{11}}+\frac{9 e^7 (a+b x)^{19} (b d-a e) (-5 a B e+A b e+4 b B d)}{19 b^{11}}+\frac{2 e^6 (a+b x)^{18} (b d-a e)^2 (-10 a B e+3 A b e+7 b B d)}{3 b^{11}}+\frac{42 e^5 (a+b x)^{17} (b d-a e)^3 (-5 a B e+2 A b e+3 b B d)}{17 b^{11}}+\frac{63 e^4 (a+b x)^{16} (b d-a e)^4 (-2 a B e+A b e+b B d)}{8 b^{11}}+\frac{14 e^3 (a+b x)^{15} (b d-a e)^5 (-5 a B e+3 A b e+2 b B d)}{5 b^{11}}+\frac{6 e^2 (a+b x)^{14} (b d-a e)^6 (-10 a B e+7 A b e+3 b B d)}{7 b^{11}}+\frac{9 e (a+b x)^{13} (b d-a e)^7 (-5 a B e+4 A b e+b B d)}{13 b^{11}}+\frac{(a+b x)^{12} (b d-a e)^8 (-10 a B e+9 A b e+b B d)}{12 b^{11}}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)^9}{11 b^{11}}+\frac{B e^9 (a+b x)^{21}}{21 b^{11}}",1,"(38798760*a^10*A*d^9*x + 193993800*a^9*A*b*d^9*x^2 + 19399380*a^10*B*d^9*x^2 + 174594420*a^10*A*d^8*e*x^2 + 581981400*a^8*A*b^2*d^9*x^3 + 129329200*a^9*b*B*d^9*x^3 + 1163962800*a^9*A*b*d^8*e*x^3 + 116396280*a^10*B*d^8*e*x^3 + 465585120*a^10*A*d^7*e^2*x^3 + 1163962800*a^7*A*b^3*d^9*x^4 + 436486050*a^8*b^2*B*d^9*x^4 + 3928374450*a^8*A*b^2*d^8*e*x^4 + 872972100*a^9*b*B*d^8*e*x^4 + 3491888400*a^9*A*b*d^7*e^2*x^4 + 349188840*a^10*B*d^7*e^2*x^4 + 814773960*a^10*A*d^6*e^3*x^4 + 1629547920*a^6*A*b^4*d^9*x^5 + 931170240*a^7*b^3*B*d^9*x^5 + 8380532160*a^7*A*b^3*d^8*e*x^5 + 3142699560*a^8*b^2*B*d^8*e*x^5 + 12570798240*a^8*A*b^2*d^7*e^2*x^5 + 2793510720*a^9*b*B*d^7*e^2*x^5 + 6518191680*a^9*A*b*d^6*e^3*x^5 + 651819168*a^10*B*d^6*e^3*x^5 + 977728752*a^10*A*d^5*e^4*x^5 + 1629547920*a^5*A*b^5*d^9*x^6 + 1357956600*a^6*b^4*B*d^9*x^6 + 12221609400*a^6*A*b^4*d^8*e*x^6 + 6983776800*a^7*b^3*B*d^8*e*x^6 + 27935107200*a^7*A*b^3*d^7*e^2*x^6 + 10475665200*a^8*b^2*B*d^7*e^2*x^6 + 24443218800*a^8*A*b^2*d^6*e^3*x^6 + 5431826400*a^9*b*B*d^6*e^3*x^6 + 8147739600*a^9*A*b*d^5*e^4*x^6 + 814773960*a^10*B*d^5*e^4*x^6 + 814773960*a^10*A*d^4*e^5*x^6 + 1163962800*a^4*A*b^6*d^9*x^7 + 1396755360*a^5*b^5*B*d^9*x^7 + 12570798240*a^5*A*b^5*d^8*e*x^7 + 10475665200*a^6*b^4*B*d^8*e*x^7 + 41902660800*a^6*A*b^4*d^7*e^2*x^7 + 23944377600*a^7*b^3*B*d^7*e^2*x^7 + 55870214400*a^7*A*b^3*d^6*e^3*x^7 + 20951330400*a^8*b^2*B*d^6*e^3*x^7 + 31426995600*a^8*A*b^2*d^5*e^4*x^7 + 6983776800*a^9*b*B*d^5*e^4*x^7 + 6983776800*a^9*A*b*d^4*e^5*x^7 + 698377680*a^10*B*d^4*e^5*x^7 + 465585120*a^10*A*d^3*e^6*x^7 + 581981400*a^3*A*b^7*d^9*x^8 + 1018467450*a^4*b^6*B*d^9*x^8 + 9166207050*a^4*A*b^6*d^8*e*x^8 + 10999448460*a^5*b^5*B*d^8*e*x^8 + 43997793840*a^5*A*b^5*d^7*e^2*x^8 + 36664828200*a^6*b^4*B*d^7*e^2*x^8 + 85551265800*a^6*A*b^4*d^6*e^3*x^8 + 48886437600*a^7*b^3*B*d^6*e^3*x^8 + 73329656400*a^7*A*b^3*d^5*e^4*x^8 + 27498621150*a^8*b^2*B*d^5*e^4*x^8 + 27498621150*a^8*A*b^2*d^4*e^5*x^8 + 6110804700*a^9*b*B*d^4*e^5*x^8 + 4073869800*a^9*A*b*d^3*e^6*x^8 + 407386980*a^10*B*d^3*e^6*x^8 + 174594420*a^10*A*d^2*e^7*x^8 + 193993800*a^2*A*b^8*d^9*x^9 + 517316800*a^3*b^7*B*d^9*x^9 + 4655851200*a^3*A*b^7*d^8*e*x^9 + 8147739600*a^4*b^6*B*d^8*e*x^9 + 32590958400*a^4*A*b^6*d^7*e^2*x^9 + 39109150080*a^5*b^5*B*d^7*e^2*x^9 + 91254683520*a^5*A*b^5*d^6*e^3*x^9 + 76045569600*a^6*b^4*B*d^6*e^3*x^9 + 114068354400*a^6*A*b^4*d^5*e^4*x^9 + 65181916800*a^7*b^3*B*d^5*e^4*x^9 + 65181916800*a^7*A*b^3*d^4*e^5*x^9 + 24443218800*a^8*b^2*B*d^4*e^5*x^9 + 16295479200*a^8*A*b^2*d^3*e^6*x^9 + 3621217600*a^9*b*B*d^3*e^6*x^9 + 1551950400*a^9*A*b*d^2*e^7*x^9 + 155195040*a^10*B*d^2*e^7*x^9 + 38798760*a^10*A*d*e^8*x^9 + 38798760*a*A*b^9*d^9*x^10 + 174594420*a^2*b^8*B*d^9*x^10 + 1571349780*a^2*A*b^8*d^8*e*x^10 + 4190266080*a^3*b^7*B*d^8*e*x^10 + 16761064320*a^3*A*b^7*d^7*e^2*x^10 + 29331862560*a^4*b^6*B*d^7*e^2*x^10 + 68441012640*a^4*A*b^6*d^6*e^3*x^10 + 82129215168*a^5*b^5*B*d^6*e^3*x^10 + 123193822752*a^5*A*b^5*d^5*e^4*x^10 + 102661518960*a^6*b^4*B*d^5*e^4*x^10 + 102661518960*a^6*A*b^4*d^4*e^5*x^10 + 58663725120*a^7*b^3*B*d^4*e^5*x^10 + 39109150080*a^7*A*b^3*d^3*e^6*x^10 + 14665931280*a^8*b^2*B*d^3*e^6*x^10 + 6285399120*a^8*A*b^2*d^2*e^7*x^10 + 1396755360*a^9*b*B*d^2*e^7*x^10 + 349188840*a^9*A*b*d*e^8*x^10 + 34918884*a^10*B*d*e^8*x^10 + 3879876*a^10*A*e^9*x^10 + 3527160*A*b^10*d^9*x^11 + 35271600*a*b^9*B*d^9*x^11 + 317444400*a*A*b^9*d^8*e*x^11 + 1428499800*a^2*b^8*B*d^8*e*x^11 + 5713999200*a^2*A*b^8*d^7*e^2*x^11 + 15237331200*a^3*b^7*B*d^7*e^2*x^11 + 35553772800*a^3*A*b^7*d^6*e^3*x^11 + 62219102400*a^4*b^6*B*d^6*e^3*x^11 + 93328653600*a^4*A*b^6*d^5*e^4*x^11 + 111994384320*a^5*b^5*B*d^5*e^4*x^11 + 111994384320*a^5*A*b^5*d^4*e^5*x^11 + 93328653600*a^6*b^4*B*d^4*e^5*x^11 + 62219102400*a^6*A*b^4*d^3*e^6*x^11 + 35553772800*a^7*b^3*B*d^3*e^6*x^11 + 15237331200*a^7*A*b^3*d^2*e^7*x^11 + 5713999200*a^8*b^2*B*d^2*e^7*x^11 + 1428499800*a^8*A*b^2*d*e^8*x^11 + 317444400*a^9*b*B*d*e^8*x^11 + 35271600*a^9*A*b*e^9*x^11 + 3527160*a^10*B*e^9*x^11 + 3233230*b^10*B*d^9*x^12 + 29099070*A*b^10*d^8*e*x^12 + 290990700*a*b^9*B*d^8*e*x^12 + 1163962800*a*A*b^9*d^7*e^2*x^12 + 5237832600*a^2*b^8*B*d^7*e^2*x^12 + 12221609400*a^2*A*b^8*d^6*e^3*x^12 + 32590958400*a^3*b^7*B*d^6*e^3*x^12 + 48886437600*a^3*A*b^7*d^5*e^4*x^12 + 85551265800*a^4*b^6*B*d^5*e^4*x^12 + 85551265800*a^4*A*b^6*d^4*e^5*x^12 + 102661518960*a^5*b^5*B*d^4*e^5*x^12 + 68441012640*a^5*A*b^5*d^3*e^6*x^12 + 57034177200*a^6*b^4*B*d^3*e^6*x^12 + 24443218800*a^6*A*b^4*d^2*e^7*x^12 + 13967553600*a^7*b^3*B*d^2*e^7*x^12 + 3491888400*a^7*A*b^3*d*e^8*x^12 + 1309458150*a^8*b^2*B*d*e^8*x^12 + 145495350*a^8*A*b^2*e^9*x^12 + 32332300*a^9*b*B*e^9*x^12 + 26860680*b^10*B*d^8*e*x^13 + 107442720*A*b^10*d^7*e^2*x^13 + 1074427200*a*b^9*B*d^7*e^2*x^13 + 2506996800*a*A*b^9*d^6*e^3*x^13 + 11281485600*a^2*b^8*B*d^6*e^3*x^13 + 16922228400*a^2*A*b^8*d^5*e^4*x^13 + 45125942400*a^3*b^7*B*d^5*e^4*x^13 + 45125942400*a^3*A*b^7*d^4*e^5*x^13 + 78970399200*a^4*b^6*B*d^4*e^5*x^13 + 52646932800*a^4*A*b^6*d^3*e^6*x^13 + 63176319360*a^5*b^5*B*d^3*e^6*x^13 + 27075565440*a^5*A*b^5*d^2*e^7*x^13 + 22562971200*a^6*b^4*B*d^2*e^7*x^13 + 5640742800*a^6*A*b^4*d*e^8*x^13 + 3223281600*a^7*b^3*B*d*e^8*x^13 + 358142400*a^7*A*b^3*e^9*x^13 + 134303400*a^8*b^2*B*e^9*x^13 + 99768240*b^10*B*d^7*e^2*x^14 + 232792560*A*b^10*d^6*e^3*x^14 + 2327925600*a*b^9*B*d^6*e^3*x^14 + 3491888400*a*A*b^9*d^5*e^4*x^14 + 15713497800*a^2*b^8*B*d^5*e^4*x^14 + 15713497800*a^2*A*b^8*d^4*e^5*x^14 + 41902660800*a^3*b^7*B*d^4*e^5*x^14 + 27935107200*a^3*A*b^7*d^3*e^6*x^14 + 48886437600*a^4*b^6*B*d^3*e^6*x^14 + 20951330400*a^4*A*b^6*d^2*e^7*x^14 + 25141596480*a^5*b^5*B*d^2*e^7*x^14 + 6285399120*a^5*A*b^5*d*e^8*x^14 + 5237832600*a^6*b^4*B*d*e^8*x^14 + 581981400*a^6*A*b^4*e^9*x^14 + 332560800*a^7*b^3*B*e^9*x^14 + 217273056*b^10*B*d^6*e^3*x^15 + 325909584*A*b^10*d^5*e^4*x^15 + 3259095840*a*b^9*B*d^5*e^4*x^15 + 3259095840*a*A*b^9*d^4*e^5*x^15 + 14665931280*a^2*b^8*B*d^4*e^5*x^15 + 9777287520*a^2*A*b^8*d^3*e^6*x^15 + 26072766720*a^3*b^7*B*d^3*e^6*x^15 + 11174042880*a^3*A*b^7*d^2*e^7*x^15 + 19554575040*a^4*b^6*B*d^2*e^7*x^15 + 4888643760*a^4*A*b^6*d*e^8*x^15 + 5866372512*a^5*b^5*B*d*e^8*x^15 + 651819168*a^5*A*b^5*e^9*x^15 + 543182640*a^6*b^4*B*e^9*x^15 + 305540235*b^10*B*d^5*e^4*x^16 + 305540235*A*b^10*d^4*e^5*x^16 + 3055402350*a*b^9*B*d^4*e^5*x^16 + 2036934900*a*A*b^9*d^3*e^6*x^16 + 9166207050*a^2*b^8*B*d^3*e^6*x^16 + 3928374450*a^2*A*b^8*d^2*e^7*x^16 + 10475665200*a^3*b^7*B*d^2*e^7*x^16 + 2618916300*a^3*A*b^7*d*e^8*x^16 + 4583103525*a^4*b^6*B*d*e^8*x^16 + 509233725*a^4*A*b^6*e^9*x^16 + 611080470*a^5*b^5*B*e^9*x^16 + 287567280*b^10*B*d^4*e^5*x^17 + 191711520*A*b^10*d^3*e^6*x^17 + 1917115200*a*b^9*B*d^3*e^6*x^17 + 821620800*a*A*b^9*d^2*e^7*x^17 + 3697293600*a^2*b^8*B*d^2*e^7*x^17 + 924323400*a^2*A*b^8*d*e^8*x^17 + 2464862400*a^3*b^7*B*d*e^8*x^17 + 273873600*a^3*A*b^7*e^9*x^17 + 479278800*a^4*b^6*B*e^9*x^17 + 181060880*b^10*B*d^3*e^6*x^18 + 77597520*A*b^10*d^2*e^7*x^18 + 775975200*a*b^9*B*d^2*e^7*x^18 + 193993800*a*A*b^9*d*e^8*x^18 + 872972100*a^2*b^8*B*d*e^8*x^18 + 96996900*a^2*A*b^8*e^9*x^18 + 258658400*a^3*b^7*B*e^9*x^18 + 73513440*b^10*B*d^2*e^7*x^19 + 18378360*A*b^10*d*e^8*x^19 + 183783600*a*b^9*B*d*e^8*x^19 + 20420400*a*A*b^9*e^9*x^19 + 91891800*a^2*b^8*B*e^9*x^19 + 17459442*b^10*B*d*e^8*x^20 + 1939938*A*b^10*e^9*x^20 + 19399380*a*b^9*B*e^9*x^20 + 1847560*b^10*B*e^9*x^21)/38798760","B",1
1080,1,3167,372,1.9986157,"\int (a+b x)^{10} (A+B x) (d+e x)^8 \, dx","IntegrateAlgebraic[(a + b*x)^10*(A + B*x)*(d + e*x)^8,x]","\text{Result too large to show}","\frac{e^7 (a+b x)^{19} (-9 a B e+A b e+8 b B d)}{19 b^{10}}+\frac{2 e^6 (a+b x)^{18} (b d-a e) (-9 a B e+2 A b e+7 b B d)}{9 b^{10}}+\frac{28 e^5 (a+b x)^{17} (b d-a e)^2 (-3 a B e+A b e+2 b B d)}{17 b^{10}}+\frac{7 e^4 (a+b x)^{16} (b d-a e)^3 (-9 a B e+4 A b e+5 b B d)}{8 b^{10}}+\frac{14 e^3 (a+b x)^{15} (b d-a e)^4 (-9 a B e+5 A b e+4 b B d)}{15 b^{10}}+\frac{2 e^2 (a+b x)^{14} (b d-a e)^5 (-3 a B e+2 A b e+b B d)}{b^{10}}+\frac{4 e (a+b x)^{13} (b d-a e)^6 (-9 a B e+7 A b e+2 b B d)}{13 b^{10}}+\frac{(a+b x)^{12} (b d-a e)^7 (-9 a B e+8 A b e+b B d)}{12 b^{10}}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)^8}{11 b^{10}}+\frac{B e^8 (a+b x)^{20}}{20 b^{10}}",1,"(16628040*a^10*A*d^8*x + 83140200*a^9*A*b*d^8*x^2 + 8314020*a^10*B*d^8*x^2 + 66512160*a^10*A*d^7*e*x^2 + 249420600*a^8*A*b^2*d^8*x^3 + 55426800*a^9*b*B*d^8*x^3 + 443414400*a^9*A*b*d^7*e*x^3 + 44341440*a^10*B*d^7*e*x^3 + 155195040*a^10*A*d^6*e^2*x^3 + 498841200*a^7*A*b^3*d^8*x^4 + 187065450*a^8*b^2*B*d^8*x^4 + 1496523600*a^8*A*b^2*d^7*e*x^4 + 332560800*a^9*b*B*d^7*e*x^4 + 1163962800*a^9*A*b*d^6*e^2*x^4 + 116396280*a^10*B*d^6*e^2*x^4 + 232792560*a^10*A*d^5*e^3*x^4 + 698377680*a^6*A*b^4*d^8*x^5 + 399072960*a^7*b^3*B*d^8*x^5 + 3192583680*a^7*A*b^3*d^7*e*x^5 + 1197218880*a^8*b^2*B*d^7*e*x^5 + 4190266080*a^8*A*b^2*d^6*e^2*x^5 + 931170240*a^9*b*B*d^6*e^2*x^5 + 1862340480*a^9*A*b*d^5*e^3*x^5 + 186234048*a^10*B*d^5*e^3*x^5 + 232792560*a^10*A*d^4*e^4*x^5 + 698377680*a^5*A*b^5*d^8*x^6 + 581981400*a^6*b^4*B*d^8*x^6 + 4655851200*a^6*A*b^4*d^7*e*x^6 + 2660486400*a^7*b^3*B*d^7*e*x^6 + 9311702400*a^7*A*b^3*d^6*e^2*x^6 + 3491888400*a^8*b^2*B*d^6*e^2*x^6 + 6983776800*a^8*A*b^2*d^5*e^3*x^6 + 1551950400*a^9*b*B*d^5*e^3*x^6 + 1939938000*a^9*A*b*d^4*e^4*x^6 + 193993800*a^10*B*d^4*e^4*x^6 + 155195040*a^10*A*d^3*e^5*x^6 + 498841200*a^4*A*b^6*d^8*x^7 + 598609440*a^5*b^5*B*d^8*x^7 + 4788875520*a^5*A*b^5*d^7*e*x^7 + 3990729600*a^6*b^4*B*d^7*e*x^7 + 13967553600*a^6*A*b^4*d^6*e^2*x^7 + 7981459200*a^7*b^3*B*d^6*e^2*x^7 + 15962918400*a^7*A*b^3*d^5*e^3*x^7 + 5986094400*a^8*b^2*B*d^5*e^3*x^7 + 7482618000*a^8*A*b^2*d^4*e^4*x^7 + 1662804000*a^9*b*B*d^4*e^4*x^7 + 1330243200*a^9*A*b*d^3*e^5*x^7 + 133024320*a^10*B*d^3*e^5*x^7 + 66512160*a^10*A*d^2*e^6*x^7 + 249420600*a^3*A*b^7*d^8*x^8 + 436486050*a^4*b^6*B*d^8*x^8 + 3491888400*a^4*A*b^6*d^7*e*x^8 + 4190266080*a^5*b^5*B*d^7*e*x^8 + 14665931280*a^5*A*b^5*d^6*e^2*x^8 + 12221609400*a^6*b^4*B*d^6*e^2*x^8 + 24443218800*a^6*A*b^4*d^5*e^3*x^8 + 13967553600*a^7*b^3*B*d^5*e^3*x^8 + 17459442000*a^7*A*b^3*d^4*e^4*x^8 + 6547290750*a^8*b^2*B*d^4*e^4*x^8 + 5237832600*a^8*A*b^2*d^3*e^5*x^8 + 1163962800*a^9*b*B*d^3*e^5*x^8 + 581981400*a^9*A*b*d^2*e^6*x^8 + 58198140*a^10*B*d^2*e^6*x^8 + 16628040*a^10*A*d*e^7*x^8 + 83140200*a^2*A*b^8*d^8*x^9 + 221707200*a^3*b^7*B*d^8*x^9 + 1773657600*a^3*A*b^7*d^7*e*x^9 + 3103900800*a^4*b^6*B*d^7*e*x^9 + 10863652800*a^4*A*b^6*d^6*e^2*x^9 + 13036383360*a^5*b^5*B*d^6*e^2*x^9 + 26072766720*a^5*A*b^5*d^5*e^3*x^9 + 21727305600*a^6*b^4*B*d^5*e^3*x^9 + 27159132000*a^6*A*b^4*d^4*e^4*x^9 + 15519504000*a^7*b^3*B*d^4*e^4*x^9 + 12415603200*a^7*A*b^3*d^3*e^5*x^9 + 4655851200*a^8*b^2*B*d^3*e^5*x^9 + 2327925600*a^8*A*b^2*d^2*e^6*x^9 + 517316800*a^9*b*B*d^2*e^6*x^9 + 147804800*a^9*A*b*d*e^7*x^9 + 14780480*a^10*B*d*e^7*x^9 + 1847560*a^10*A*e^8*x^9 + 16628040*a*A*b^9*d^8*x^10 + 74826180*a^2*b^8*B*d^8*x^10 + 598609440*a^2*A*b^8*d^7*e*x^10 + 1596291840*a^3*b^7*B*d^7*e*x^10 + 5587021440*a^3*A*b^7*d^6*e^2*x^10 + 9777287520*a^4*b^6*B*d^6*e^2*x^10 + 19554575040*a^4*A*b^6*d^5*e^3*x^10 + 23465490048*a^5*b^5*B*d^5*e^3*x^10 + 29331862560*a^5*A*b^5*d^4*e^4*x^10 + 24443218800*a^6*b^4*B*d^4*e^4*x^10 + 19554575040*a^6*A*b^4*d^3*e^5*x^10 + 11174042880*a^7*b^3*B*d^3*e^5*x^10 + 5587021440*a^7*A*b^3*d^2*e^6*x^10 + 2095133040*a^8*b^2*B*d^2*e^6*x^10 + 598609440*a^8*A*b^2*d*e^7*x^10 + 133024320*a^9*b*B*d*e^7*x^10 + 16628040*a^9*A*b*e^8*x^10 + 1662804*a^10*B*e^8*x^10 + 1511640*A*b^10*d^8*x^11 + 15116400*a*b^9*B*d^8*x^11 + 120931200*a*A*b^9*d^7*e*x^11 + 544190400*a^2*b^8*B*d^7*e*x^11 + 1904666400*a^2*A*b^8*d^6*e^2*x^11 + 5079110400*a^3*b^7*B*d^6*e^2*x^11 + 10158220800*a^3*A*b^7*d^5*e^3*x^11 + 17776886400*a^4*b^6*B*d^5*e^3*x^11 + 22221108000*a^4*A*b^6*d^4*e^4*x^11 + 26665329600*a^5*b^5*B*d^4*e^4*x^11 + 21332263680*a^5*A*b^5*d^3*e^5*x^11 + 17776886400*a^6*b^4*B*d^3*e^5*x^11 + 8888443200*a^6*A*b^4*d^2*e^6*x^11 + 5079110400*a^7*b^3*B*d^2*e^6*x^11 + 1451174400*a^7*A*b^3*d*e^7*x^11 + 544190400*a^8*b^2*B*d*e^7*x^11 + 68023800*a^8*A*b^2*e^8*x^11 + 15116400*a^9*b*B*e^8*x^11 + 1385670*b^10*B*d^8*x^12 + 11085360*A*b^10*d^7*e*x^12 + 110853600*a*b^9*B*d^7*e*x^12 + 387987600*a*A*b^9*d^6*e^2*x^12 + 1745944200*a^2*b^8*B*d^6*e^2*x^12 + 3491888400*a^2*A*b^8*d^5*e^3*x^12 + 9311702400*a^3*b^7*B*d^5*e^3*x^12 + 11639628000*a^3*A*b^7*d^4*e^4*x^12 + 20369349000*a^4*b^6*B*d^4*e^4*x^12 + 16295479200*a^4*A*b^6*d^3*e^5*x^12 + 19554575040*a^5*b^5*B*d^3*e^5*x^12 + 9777287520*a^5*A*b^5*d^2*e^6*x^12 + 8147739600*a^6*b^4*B*d^2*e^6*x^12 + 2327925600*a^6*A*b^4*d*e^7*x^12 + 1330243200*a^7*b^3*B*d*e^7*x^12 + 166280400*a^7*A*b^3*e^8*x^12 + 62355150*a^8*b^2*B*e^8*x^12 + 10232640*b^10*B*d^7*e*x^13 + 35814240*A*b^10*d^6*e^2*x^13 + 358142400*a*b^9*B*d^6*e^2*x^13 + 716284800*a*A*b^9*d^5*e^3*x^13 + 3223281600*a^2*b^8*B*d^5*e^3*x^13 + 4029102000*a^2*A*b^8*d^4*e^4*x^13 + 10744272000*a^3*b^7*B*d^4*e^4*x^13 + 8595417600*a^3*A*b^7*d^3*e^5*x^13 + 15041980800*a^4*b^6*B*d^3*e^5*x^13 + 7520990400*a^4*A*b^6*d^2*e^6*x^13 + 9025188480*a^5*b^5*B*d^2*e^6*x^13 + 2578625280*a^5*A*b^5*d*e^7*x^13 + 2148854400*a^6*b^4*B*d*e^7*x^13 + 268606800*a^6*A*b^4*e^8*x^13 + 153489600*a^7*b^3*B*e^8*x^13 + 33256080*b^10*B*d^6*e^2*x^14 + 66512160*A*b^10*d^5*e^3*x^14 + 665121600*a*b^9*B*d^5*e^3*x^14 + 831402000*a*A*b^9*d^4*e^4*x^14 + 3741309000*a^2*b^8*B*d^4*e^4*x^14 + 2993047200*a^2*A*b^8*d^3*e^5*x^14 + 7981459200*a^3*b^7*B*d^3*e^5*x^14 + 3990729600*a^3*A*b^7*d^2*e^6*x^14 + 6983776800*a^4*b^6*B*d^2*e^6*x^14 + 1995364800*a^4*A*b^6*d*e^7*x^14 + 2394437760*a^5*b^5*B*d*e^7*x^14 + 299304720*a^5*A*b^5*e^8*x^14 + 249420600*a^6*b^4*B*e^8*x^14 + 62078016*b^10*B*d^5*e^3*x^15 + 77597520*A*b^10*d^4*e^4*x^15 + 775975200*a*b^9*B*d^4*e^4*x^15 + 620780160*a*A*b^9*d^3*e^5*x^15 + 2793510720*a^2*b^8*B*d^3*e^5*x^15 + 1396755360*a^2*A*b^8*d^2*e^6*x^15 + 3724680960*a^3*b^7*B*d^2*e^6*x^15 + 1064194560*a^3*A*b^7*d*e^7*x^15 + 1862340480*a^4*b^6*B*d*e^7*x^15 + 232792560*a^4*A*b^6*e^8*x^15 + 279351072*a^5*b^5*B*e^8*x^15 + 72747675*b^10*B*d^4*e^4*x^16 + 58198140*A*b^10*d^3*e^5*x^16 + 581981400*a*b^9*B*d^3*e^5*x^16 + 290990700*a*A*b^9*d^2*e^6*x^16 + 1309458150*a^2*b^8*B*d^2*e^6*x^16 + 374130900*a^2*A*b^8*d*e^7*x^16 + 997682400*a^3*b^7*B*d*e^7*x^16 + 124710300*a^3*A*b^7*e^8*x^16 + 218243025*a^4*b^6*B*e^8*x^16 + 54774720*b^10*B*d^3*e^5*x^17 + 27387360*A*b^10*d^2*e^6*x^17 + 273873600*a*b^9*B*d^2*e^6*x^17 + 78249600*a*A*b^9*d*e^7*x^17 + 352123200*a^2*b^8*B*d*e^7*x^17 + 44015400*a^2*A*b^8*e^8*x^17 + 117374400*a^3*b^7*B*e^8*x^17 + 25865840*b^10*B*d^2*e^6*x^18 + 7390240*A*b^10*d*e^7*x^18 + 73902400*a*b^9*B*d*e^7*x^18 + 9237800*a*A*b^9*e^8*x^18 + 41570100*a^2*b^8*B*e^8*x^18 + 7001280*b^10*B*d*e^7*x^19 + 875160*A*b^10*e^8*x^19 + 8751600*a*b^9*B*e^8*x^19 + 831402*b^10*B*e^8*x^20)/16628040","B",1
1081,1,2791,329,1.7970227,"\int (a+b x)^{10} (A+B x) (d+e x)^7 \, dx","IntegrateAlgebraic[(a + b*x)^10*(A + B*x)*(d + e*x)^7,x]","\text{Result too large to show}","\frac{e^6 (a+b x)^{18} (-8 a B e+A b e+7 b B d)}{18 b^9}+\frac{7 e^5 (a+b x)^{17} (b d-a e) (-4 a B e+A b e+3 b B d)}{17 b^9}+\frac{7 e^4 (a+b x)^{16} (b d-a e)^2 (-8 a B e+3 A b e+5 b B d)}{16 b^9}+\frac{7 e^3 (a+b x)^{15} (b d-a e)^3 (-2 a B e+A b e+b B d)}{3 b^9}+\frac{e^2 (a+b x)^{14} (b d-a e)^4 (-8 a B e+5 A b e+3 b B d)}{2 b^9}+\frac{7 e (a+b x)^{13} (b d-a e)^5 (-4 a B e+3 A b e+b B d)}{13 b^9}+\frac{(a+b x)^{12} (b d-a e)^6 (-8 a B e+7 A b e+b B d)}{12 b^9}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)^7}{11 b^9}+\frac{B e^7 (a+b x)^{19}}{19 b^9}",1,"(6651216*a^10*A*d^7*x + 33256080*a^9*A*b*d^7*x^2 + 3325608*a^10*B*d^7*x^2 + 23279256*a^10*A*d^6*e*x^2 + 99768240*a^8*A*b^2*d^7*x^3 + 22170720*a^9*b*B*d^7*x^3 + 155195040*a^9*A*b*d^6*e*x^3 + 15519504*a^10*B*d^6*e*x^3 + 46558512*a^10*A*d^5*e^2*x^3 + 199536480*a^7*A*b^3*d^7*x^4 + 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1082,1,2415,290,1.4760683,"\int (a+b x)^{10} (A+B x) (d+e x)^6 \, dx","IntegrateAlgebraic[(a + b*x)^10*(A + B*x)*(d + e*x)^6,x]","\text{Result too large to show}","\frac{e^5 (a+b x)^{17} (-7 a B e+A b e+6 b B d)}{17 b^8}+\frac{3 e^4 (a+b x)^{16} (b d-a e) (-7 a B e+2 A b e+5 b B d)}{16 b^8}+\frac{e^3 (a+b x)^{15} (b d-a e)^2 (-7 a B e+3 A b e+4 b B d)}{3 b^8}+\frac{5 e^2 (a+b x)^{14} (b d-a e)^3 (-7 a B e+4 A b e+3 b B d)}{14 b^8}+\frac{3 e (a+b x)^{13} (b d-a e)^4 (-7 a B e+5 A b e+2 b B d)}{13 b^8}+\frac{(a+b x)^{12} (b d-a e)^5 (-7 a B e+6 A b e+b B d)}{12 b^8}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)^6}{11 b^8}+\frac{B e^6 (a+b x)^{18}}{18 b^8}",1,"(2450448*a^10*A*d^6*x + 12252240*a^9*A*b*d^6*x^2 + 1225224*a^10*B*d^6*x^2 + 7351344*a^10*A*d^5*e*x^2 + 36756720*a^8*A*b^2*d^6*x^3 + 8168160*a^9*b*B*d^6*x^3 + 49008960*a^9*A*b*d^5*e*x^3 + 4900896*a^10*B*d^5*e*x^3 + 12252240*a^10*A*d^4*e^2*x^3 + 73513440*a^7*A*b^3*d^6*x^4 + 27567540*a^8*b^2*B*d^6*x^4 + 165405240*a^8*A*b^2*d^5*e*x^4 + 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1225224*A*b^10*d^5*e*x^12 + 12252240*a*b^9*B*d^5*e*x^12 + 30630600*a*A*b^9*d^4*e^2*x^12 + 137837700*a^2*b^8*B*d^4*e^2*x^12 + 183783600*a^2*A*b^8*d^3*e^3*x^12 + 490089600*a^3*b^7*B*d^3*e^3*x^12 + 367567200*a^3*A*b^7*d^2*e^4*x^12 + 643242600*a^4*b^6*B*d^2*e^4*x^12 + 257297040*a^4*A*b^6*d*e^5*x^12 + 308756448*a^5*b^5*B*d*e^5*x^12 + 51459408*a^5*A*b^5*e^6*x^12 + 42882840*a^6*b^4*B*e^6*x^12 + 1130976*b^10*B*d^5*e*x^13 + 2827440*A*b^10*d^4*e^2*x^13 + 28274400*a*b^9*B*d^4*e^2*x^13 + 37699200*a*A*b^9*d^3*e^3*x^13 + 169646400*a^2*b^8*B*d^3*e^3*x^13 + 127234800*a^2*A*b^8*d^2*e^4*x^13 + 339292800*a^3*b^7*B*d^2*e^4*x^13 + 135717120*a^3*A*b^7*d*e^5*x^13 + 237504960*a^4*b^6*B*d*e^5*x^13 + 39584160*a^4*A*b^6*e^6*x^13 + 47500992*a^5*b^5*B*e^6*x^13 + 2625480*b^10*B*d^4*e^2*x^14 + 3500640*A*b^10*d^3*e^3*x^14 + 35006400*a*b^9*B*d^3*e^3*x^14 + 26254800*a*A*b^9*d^2*e^4*x^14 + 118146600*a^2*b^8*B*d^2*e^4*x^14 + 47258640*a^2*A*b^8*d*e^5*x^14 + 126023040*a^3*b^7*B*d*e^5*x^14 + 21003840*a^3*A*b^7*e^6*x^14 + 36756720*a^4*b^6*B*e^6*x^14 + 3267264*b^10*B*d^3*e^3*x^15 + 2450448*A*b^10*d^2*e^4*x^15 + 24504480*a*b^9*B*d^2*e^4*x^15 + 9801792*a*A*b^9*d*e^5*x^15 + 44108064*a^2*b^8*B*d*e^5*x^15 + 7351344*a^2*A*b^8*e^6*x^15 + 19603584*a^3*b^7*B*e^6*x^15 + 2297295*b^10*B*d^2*e^4*x^16 + 918918*A*b^10*d*e^5*x^16 + 9189180*a*b^9*B*d*e^5*x^16 + 1531530*a*A*b^9*e^6*x^16 + 6891885*a^2*b^8*B*e^6*x^16 + 864864*b^10*B*d*e^5*x^17 + 144144*A*b^10*e^6*x^17 + 1441440*a*b^9*B*e^6*x^17 + 136136*b^10*B*e^6*x^18)/2450448","B",1
1083,1,2039,243,1.1917707,"\int (a+b x)^{10} (A+B x) (d+e x)^5 \, dx","IntegrateAlgebraic[(a + b*x)^10*(A + B*x)*(d + e*x)^5,x]","\text{Result too large to show}","\frac{e^4 (a+b x)^{16} (-6 a B e+A b e+5 b B d)}{16 b^7}+\frac{e^3 (a+b x)^{15} (b d-a e) (-3 a B e+A b e+2 b B d)}{3 b^7}+\frac{5 e^2 (a+b x)^{14} (b d-a e)^2 (-2 a B e+A b e+b B d)}{7 b^7}+\frac{5 e (a+b x)^{13} (b d-a e)^3 (-3 a B e+2 A b e+b B d)}{13 b^7}+\frac{(a+b x)^{12} (b d-a e)^4 (-6 a B e+5 A b e+b B d)}{12 b^7}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)^5}{11 b^7}+\frac{B e^5 (a+b x)^{17}}{17 b^7}",1,"(816816*a^10*A*d^5*x + 4084080*a^9*A*b*d^5*x^2 + 408408*a^10*B*d^5*x^2 + 2042040*a^10*A*d^4*e*x^2 + 12252240*a^8*A*b^2*d^5*x^3 + 2722720*a^9*b*B*d^5*x^3 + 13613600*a^9*A*b*d^4*e*x^3 + 1361360*a^10*B*d^4*e*x^3 + 2722720*a^10*A*d^3*e^2*x^3 + 24504480*a^7*A*b^3*d^5*x^4 + 9189180*a^8*b^2*B*d^5*x^4 + 45945900*a^8*A*b^2*d^4*e*x^4 + 10210200*a^9*b*B*d^4*e*x^4 + 20420400*a^9*A*b*d^3*e^2*x^4 + 2042040*a^10*B*d^3*e^2*x^4 + 2042040*a^10*A*d^2*e^3*x^4 + 34306272*a^6*A*b^4*d^5*x^5 + 19603584*a^7*b^3*B*d^5*x^5 + 98017920*a^7*A*b^3*d^4*e*x^5 + 36756720*a^8*b^2*B*d^4*e*x^5 + 73513440*a^8*A*b^2*d^3*e^2*x^5 + 16336320*a^9*b*B*d^3*e^2*x^5 + 16336320*a^9*A*b*d^2*e^3*x^5 + 1633632*a^10*B*d^2*e^3*x^5 + 816816*a^10*A*d*e^4*x^5 + 34306272*a^5*A*b^5*d^5*x^6 + 28588560*a^6*b^4*B*d^5*x^6 + 142942800*a^6*A*b^4*d^4*e*x^6 + 81681600*a^7*b^3*B*d^4*e*x^6 + 163363200*a^7*A*b^3*d^3*e^2*x^6 + 61261200*a^8*b^2*B*d^3*e^2*x^6 + 61261200*a^8*A*b^2*d^2*e^3*x^6 + 13613600*a^9*b*B*d^2*e^3*x^6 + 6806800*a^9*A*b*d*e^4*x^6 + 680680*a^10*B*d*e^4*x^6 + 136136*a^10*A*e^5*x^6 + 24504480*a^4*A*b^6*d^5*x^7 + 29405376*a^5*b^5*B*d^5*x^7 + 147026880*a^5*A*b^5*d^4*e*x^7 + 122522400*a^6*b^4*B*d^4*e*x^7 + 245044800*a^6*A*b^4*d^3*e^2*x^7 + 140025600*a^7*b^3*B*d^3*e^2*x^7 + 140025600*a^7*A*b^3*d^2*e^3*x^7 + 52509600*a^8*b^2*B*d^2*e^3*x^7 + 26254800*a^8*A*b^2*d*e^4*x^7 + 5834400*a^9*b*B*d*e^4*x^7 + 1166880*a^9*A*b*e^5*x^7 + 116688*a^10*B*e^5*x^7 + 12252240*a^3*A*b^7*d^5*x^8 + 21441420*a^4*b^6*B*d^5*x^8 + 107207100*a^4*A*b^6*d^4*e*x^8 + 128648520*a^5*b^5*B*d^4*e*x^8 + 257297040*a^5*A*b^5*d^3*e^2*x^8 + 214414200*a^6*b^4*B*d^3*e^2*x^8 + 214414200*a^6*A*b^4*d^2*e^3*x^8 + 122522400*a^7*b^3*B*d^2*e^3*x^8 + 61261200*a^7*A*b^3*d*e^4*x^8 + 22972950*a^8*b^2*B*d*e^4*x^8 + 4594590*a^8*A*b^2*e^5*x^8 + 1021020*a^9*b*B*e^5*x^8 + 4084080*a^2*A*b^8*d^5*x^9 + 10890880*a^3*b^7*B*d^5*x^9 + 54454400*a^3*A*b^7*d^4*e*x^9 + 95295200*a^4*b^6*B*d^4*e*x^9 + 190590400*a^4*A*b^6*d^3*e^2*x^9 + 228708480*a^5*b^5*B*d^3*e^2*x^9 + 228708480*a^5*A*b^5*d^2*e^3*x^9 + 190590400*a^6*b^4*B*d^2*e^3*x^9 + 95295200*a^6*A*b^4*d*e^4*x^9 + 54454400*a^7*b^3*B*d*e^4*x^9 + 10890880*a^7*A*b^3*e^5*x^9 + 4084080*a^8*b^2*B*e^5*x^9 + 816816*a*A*b^9*d^5*x^10 + 3675672*a^2*b^8*B*d^5*x^10 + 18378360*a^2*A*b^8*d^4*e*x^10 + 49008960*a^3*b^7*B*d^4*e*x^10 + 98017920*a^3*A*b^7*d^3*e^2*x^10 + 171531360*a^4*b^6*B*d^3*e^2*x^10 + 171531360*a^4*A*b^6*d^2*e^3*x^10 + 205837632*a^5*b^5*B*d^2*e^3*x^10 + 102918816*a^5*A*b^5*d*e^4*x^10 + 85765680*a^6*b^4*B*d*e^4*x^10 + 17153136*a^6*A*b^4*e^5*x^10 + 9801792*a^7*b^3*B*e^5*x^10 + 74256*A*b^10*d^5*x^11 + 742560*a*b^9*B*d^5*x^11 + 3712800*a*A*b^9*d^4*e*x^11 + 16707600*a^2*b^8*B*d^4*e*x^11 + 33415200*a^2*A*b^8*d^3*e^2*x^11 + 89107200*a^3*b^7*B*d^3*e^2*x^11 + 89107200*a^3*A*b^7*d^2*e^3*x^11 + 155937600*a^4*b^6*B*d^2*e^3*x^11 + 77968800*a^4*A*b^6*d*e^4*x^11 + 93562560*a^5*b^5*B*d*e^4*x^11 + 18712512*a^5*A*b^5*e^5*x^11 + 15593760*a^6*b^4*B*e^5*x^11 + 68068*b^10*B*d^5*x^12 + 340340*A*b^10*d^4*e*x^12 + 3403400*a*b^9*B*d^4*e*x^12 + 6806800*a*A*b^9*d^3*e^2*x^12 + 30630600*a^2*b^8*B*d^3*e^2*x^12 + 30630600*a^2*A*b^8*d^2*e^3*x^12 + 81681600*a^3*b^7*B*d^2*e^3*x^12 + 40840800*a^3*A*b^7*d*e^4*x^12 + 71471400*a^4*b^6*B*d*e^4*x^12 + 14294280*a^4*A*b^6*e^5*x^12 + 17153136*a^5*b^5*B*e^5*x^12 + 314160*b^10*B*d^4*e*x^13 + 628320*A*b^10*d^3*e^2*x^13 + 6283200*a*b^9*B*d^3*e^2*x^13 + 6283200*a*A*b^9*d^2*e^3*x^13 + 28274400*a^2*b^8*B*d^2*e^3*x^13 + 14137200*a^2*A*b^8*d*e^4*x^13 + 37699200*a^3*b^7*B*d*e^4*x^13 + 7539840*a^3*A*b^7*e^5*x^13 + 13194720*a^4*b^6*B*e^5*x^13 + 583440*b^10*B*d^3*e^2*x^14 + 583440*A*b^10*d^2*e^3*x^14 + 5834400*a*b^9*B*d^2*e^3*x^14 + 2917200*a*A*b^9*d*e^4*x^14 + 13127400*a^2*b^8*B*d*e^4*x^14 + 2625480*a^2*A*b^8*e^5*x^14 + 7001280*a^3*b^7*B*e^5*x^14 + 544544*b^10*B*d^2*e^3*x^15 + 272272*A*b^10*d*e^4*x^15 + 2722720*a*b^9*B*d*e^4*x^15 + 544544*a*A*b^9*e^5*x^15 + 2450448*a^2*b^8*B*e^5*x^15 + 255255*b^10*B*d*e^4*x^16 + 51051*A*b^10*e^5*x^16 + 510510*a*b^9*B*e^5*x^16 + 48048*b^10*B*e^5*x^17)/816816","B",1
1084,1,1663,204,1.5690301,"\int (a+b x)^{10} (A+B x) (d+e x)^4 \, dx","IntegrateAlgebraic[(a + b*x)^10*(A + B*x)*(d + e*x)^4,x]","\frac{15015 b^{10} B e^4 x^{16}+16016 A b^{10} e^4 x^{15}+160160 a b^9 B e^4 x^{15}+64064 b^{10} B d e^3 x^{15}+171600 a A b^9 e^4 x^{14}+772200 a^2 b^8 B e^4 x^{14}+68640 A b^{10} d e^3 x^{14}+686400 a b^9 B d e^3 x^{14}+102960 b^{10} B d^2 e^2 x^{14}+831600 a^2 A b^8 e^4 x^{13}+2217600 a^3 b^7 B e^4 x^{13}+739200 a A b^9 d e^3 x^{13}+3326400 a^2 b^8 B d e^3 x^{13}+110880 A b^{10} d^2 e^2 x^{13}+1108800 a b^9 B d^2 e^2 x^{13}+73920 b^{10} B d^3 e x^{13}+20020 b^{10} B d^4 x^{12}+2402400 a^3 A b^7 e^4 x^{12}+4204200 a^4 b^6 B e^4 x^{12}+3603600 a^2 A b^8 d e^3 x^{12}+9609600 a^3 b^7 B d e^3 x^{12}+1201200 a A b^9 d^2 e^2 x^{12}+5405400 a^2 b^8 B d^2 e^2 x^{12}+80080 A b^{10} d^3 e x^{12}+800800 a b^9 B d^3 e x^{12}+21840 A b^{10} d^4 x^{11}+218400 a b^9 B d^4 x^{11}+4586400 a^4 A b^6 e^4 x^{11}+5503680 a^5 b^5 B e^4 x^{11}+10483200 a^3 A b^7 d e^3 x^{11}+18345600 a^4 b^6 B d e^3 x^{11}+5896800 a^2 A b^8 d^2 e^2 x^{11}+15724800 a^3 b^7 B d^2 e^2 x^{11}+873600 a A b^9 d^3 e x^{11}+3931200 a^2 b^8 B d^3 e x^{11}+240240 a A b^9 d^4 x^{10}+1081080 a^2 b^8 B d^4 x^{10}+6054048 a^5 A b^5 e^4 x^{10}+5045040 a^6 b^4 B e^4 x^{10}+20180160 a^4 A b^6 d e^3 x^{10}+24216192 a^5 b^5 B d e^3 x^{10}+17297280 a^3 A b^7 d^2 e^2 x^{10}+30270240 a^4 b^6 B d^2 e^2 x^{10}+4324320 a^2 A b^8 d^3 e x^{10}+11531520 a^3 b^7 B d^3 e x^{10}+1201200 a^2 A b^8 d^4 x^9+3203200 a^3 b^7 B d^4 x^9+5605600 a^6 A b^4 e^4 x^9+3203200 a^7 b^3 B e^4 x^9+26906880 a^5 A b^5 d e^3 x^9+22422400 a^6 b^4 B d e^3 x^9+33633600 a^4 A b^6 d^2 e^2 x^9+40360320 a^5 b^5 B d^2 e^2 x^9+12812800 a^3 A b^7 d^3 e x^9+22422400 a^4 b^6 B d^3 e x^9+3603600 a^3 A b^7 d^4 x^8+6306300 a^4 b^6 B d^4 x^8+3603600 a^7 A b^3 e^4 x^8+1351350 a^8 b^2 B e^4 x^8+25225200 a^6 A b^4 d e^3 x^8+14414400 a^7 b^3 B d e^3 x^8+45405360 a^5 A b^5 d^2 e^2 x^8+37837800 a^6 b^4 B d^2 e^2 x^8+25225200 a^4 A b^6 d^3 e x^8+30270240 a^5 b^5 B d^3 e x^8+7207200 a^4 A b^6 d^4 x^7+8648640 a^5 b^5 B d^4 x^7+1544400 a^8 A b^2 e^4 x^7+343200 a^9 b B e^4 x^7+16473600 a^7 A b^3 d e^3 x^7+6177600 a^8 b^2 B d e^3 x^7+43243200 a^6 A b^4 d^2 e^2 x^7+24710400 a^7 b^3 B d^2 e^2 x^7+34594560 a^5 A b^5 d^3 e x^7+28828800 a^6 b^4 B d^3 e x^7+10090080 a^5 A b^5 d^4 x^6+8408400 a^6 b^4 B d^4 x^6+400400 a^9 A b e^4 x^6+40040 a^{10} B e^4 x^6+7207200 a^8 A b^2 d e^3 x^6+1601600 a^9 b B d e^3 x^6+28828800 a^7 A b^3 d^2 e^2 x^6+10810800 a^8 b^2 B d^2 e^2 x^6+33633600 a^6 A b^4 d^3 e x^6+19219200 a^7 b^3 B d^3 e x^6+10090080 a^6 A b^4 d^4 x^5+5765760 a^7 b^3 B d^4 x^5+48048 a^{10} A e^4 x^5+1921920 a^9 A b d e^3 x^5+192192 a^{10} B d e^3 x^5+12972960 a^8 A b^2 d^2 e^2 x^5+2882880 a^9 b B d^2 e^2 x^5+23063040 a^7 A b^3 d^3 e x^5+8648640 a^8 b^2 B d^3 e x^5+7207200 a^7 A b^3 d^4 x^4+2702700 a^8 b^2 B d^4 x^4+240240 a^{10} A d e^3 x^4+3603600 a^9 A b d^2 e^2 x^4+360360 a^{10} B d^2 e^2 x^4+10810800 a^8 A b^2 d^3 e x^4+2402400 a^9 b B d^3 e x^4+3603600 a^8 A b^2 d^4 x^3+800800 a^9 b B d^4 x^3+480480 a^{10} A d^2 e^2 x^3+3203200 a^9 A b d^3 e x^3+320320 a^{10} B d^3 e x^3+1201200 a^9 A b d^4 x^2+120120 a^{10} B d^4 x^2+480480 a^{10} A d^3 e x^2+240240 a^{10} A d^4 x}{240240}","\frac{e^3 (a+b x)^{15} (-5 a B e+A b e+4 b B d)}{15 b^6}+\frac{e^2 (a+b x)^{14} (b d-a e) (-5 a B e+2 A b e+3 b B d)}{7 b^6}+\frac{2 e (a+b x)^{13} (b d-a e)^2 (-5 a B e+3 A b e+2 b B d)}{13 b^6}+\frac{(a+b x)^{12} (b d-a e)^3 (-5 a B e+4 A b e+b B d)}{12 b^6}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)^4}{11 b^6}+\frac{B e^4 (a+b x)^{16}}{16 b^6}",1,"(240240*a^10*A*d^4*x + 1201200*a^9*A*b*d^4*x^2 + 120120*a^10*B*d^4*x^2 + 480480*a^10*A*d^3*e*x^2 + 3603600*a^8*A*b^2*d^4*x^3 + 800800*a^9*b*B*d^4*x^3 + 3203200*a^9*A*b*d^3*e*x^3 + 320320*a^10*B*d^3*e*x^3 + 480480*a^10*A*d^2*e^2*x^3 + 7207200*a^7*A*b^3*d^4*x^4 + 2702700*a^8*b^2*B*d^4*x^4 + 10810800*a^8*A*b^2*d^3*e*x^4 + 2402400*a^9*b*B*d^3*e*x^4 + 3603600*a^9*A*b*d^2*e^2*x^4 + 360360*a^10*B*d^2*e^2*x^4 + 240240*a^10*A*d*e^3*x^4 + 10090080*a^6*A*b^4*d^4*x^5 + 5765760*a^7*b^3*B*d^4*x^5 + 23063040*a^7*A*b^3*d^3*e*x^5 + 8648640*a^8*b^2*B*d^3*e*x^5 + 12972960*a^8*A*b^2*d^2*e^2*x^5 + 2882880*a^9*b*B*d^2*e^2*x^5 + 1921920*a^9*A*b*d*e^3*x^5 + 192192*a^10*B*d*e^3*x^5 + 48048*a^10*A*e^4*x^5 + 10090080*a^5*A*b^5*d^4*x^6 + 8408400*a^6*b^4*B*d^4*x^6 + 33633600*a^6*A*b^4*d^3*e*x^6 + 19219200*a^7*b^3*B*d^3*e*x^6 + 28828800*a^7*A*b^3*d^2*e^2*x^6 + 10810800*a^8*b^2*B*d^2*e^2*x^6 + 7207200*a^8*A*b^2*d*e^3*x^6 + 1601600*a^9*b*B*d*e^3*x^6 + 400400*a^9*A*b*e^4*x^6 + 40040*a^10*B*e^4*x^6 + 7207200*a^4*A*b^6*d^4*x^7 + 8648640*a^5*b^5*B*d^4*x^7 + 34594560*a^5*A*b^5*d^3*e*x^7 + 28828800*a^6*b^4*B*d^3*e*x^7 + 43243200*a^6*A*b^4*d^2*e^2*x^7 + 24710400*a^7*b^3*B*d^2*e^2*x^7 + 16473600*a^7*A*b^3*d*e^3*x^7 + 6177600*a^8*b^2*B*d*e^3*x^7 + 1544400*a^8*A*b^2*e^4*x^7 + 343200*a^9*b*B*e^4*x^7 + 3603600*a^3*A*b^7*d^4*x^8 + 6306300*a^4*b^6*B*d^4*x^8 + 25225200*a^4*A*b^6*d^3*e*x^8 + 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10483200*a^3*A*b^7*d*e^3*x^11 + 18345600*a^4*b^6*B*d*e^3*x^11 + 4586400*a^4*A*b^6*e^4*x^11 + 5503680*a^5*b^5*B*e^4*x^11 + 20020*b^10*B*d^4*x^12 + 80080*A*b^10*d^3*e*x^12 + 800800*a*b^9*B*d^3*e*x^12 + 1201200*a*A*b^9*d^2*e^2*x^12 + 5405400*a^2*b^8*B*d^2*e^2*x^12 + 3603600*a^2*A*b^8*d*e^3*x^12 + 9609600*a^3*b^7*B*d*e^3*x^12 + 2402400*a^3*A*b^7*e^4*x^12 + 4204200*a^4*b^6*B*e^4*x^12 + 73920*b^10*B*d^3*e*x^13 + 110880*A*b^10*d^2*e^2*x^13 + 1108800*a*b^9*B*d^2*e^2*x^13 + 739200*a*A*b^9*d*e^3*x^13 + 3326400*a^2*b^8*B*d*e^3*x^13 + 831600*a^2*A*b^8*e^4*x^13 + 2217600*a^3*b^7*B*e^4*x^13 + 102960*b^10*B*d^2*e^2*x^14 + 68640*A*b^10*d*e^3*x^14 + 686400*a*b^9*B*d*e^3*x^14 + 171600*a*A*b^9*e^4*x^14 + 772200*a^2*b^8*B*e^4*x^14 + 64064*b^10*B*d*e^3*x^15 + 16016*A*b^10*e^4*x^15 + 160160*a*b^9*B*e^4*x^15 + 15015*b^10*B*e^4*x^16)/240240","B",1
1085,1,1287,159,1.2279336,"\int (a+b x)^{10} (A+B x) (d+e x)^3 \, dx","IntegrateAlgebraic[(a + b*x)^10*(A + B*x)*(d + e*x)^3,x]","\frac{4004 b^{10} B e^3 x^{15}+4290 A b^{10} e^3 x^{14}+42900 a b^9 B e^3 x^{14}+12870 b^{10} B d e^2 x^{14}+46200 a A b^9 e^3 x^{13}+207900 a^2 b^8 B e^3 x^{13}+13860 A b^{10} d e^2 x^{13}+138600 a b^9 B d e^2 x^{13}+13860 b^{10} B d^2 e x^{13}+5005 b^{10} B d^3 x^{12}+225225 a^2 A b^8 e^3 x^{12}+600600 a^3 b^7 B e^3 x^{12}+150150 a A b^9 d e^2 x^{12}+675675 a^2 b^8 B d e^2 x^{12}+15015 A b^{10} d^2 e x^{12}+150150 a b^9 B d^2 e x^{12}+5460 A b^{10} d^3 x^{11}+54600 a b^9 B d^3 x^{11}+655200 a^3 A b^7 e^3 x^{11}+1146600 a^4 b^6 B e^3 x^{11}+737100 a^2 A b^8 d e^2 x^{11}+1965600 a^3 b^7 B d e^2 x^{11}+163800 a A b^9 d^2 e x^{11}+737100 a^2 b^8 B d^2 e x^{11}+60060 a A b^9 d^3 x^{10}+270270 a^2 b^8 B d^3 x^{10}+1261260 a^4 A b^6 e^3 x^{10}+1513512 a^5 b^5 B e^3 x^{10}+2162160 a^3 A b^7 d e^2 x^{10}+3783780 a^4 b^6 B d e^2 x^{10}+810810 a^2 A b^8 d^2 e x^{10}+2162160 a^3 b^7 B d^2 e x^{10}+300300 a^2 A b^8 d^3 x^9+800800 a^3 b^7 B d^3 x^9+1681680 a^5 A b^5 e^3 x^9+1401400 a^6 b^4 B e^3 x^9+4204200 a^4 A b^6 d e^2 x^9+5045040 a^5 b^5 B d e^2 x^9+2402400 a^3 A b^7 d^2 e x^9+4204200 a^4 b^6 B d^2 e x^9+900900 a^3 A b^7 d^3 x^8+1576575 a^4 b^6 B d^3 x^8+1576575 a^6 A b^4 e^3 x^8+900900 a^7 b^3 B e^3 x^8+5675670 a^5 A b^5 d e^2 x^8+4729725 a^6 b^4 B d e^2 x^8+4729725 a^4 A b^6 d^2 e x^8+5675670 a^5 b^5 B d^2 e x^8+1801800 a^4 A b^6 d^3 x^7+2162160 a^5 b^5 B d^3 x^7+1029600 a^7 A b^3 e^3 x^7+386100 a^8 b^2 B e^3 x^7+5405400 a^6 A b^4 d e^2 x^7+3088800 a^7 b^3 B d e^2 x^7+6486480 a^5 A b^5 d^2 e x^7+5405400 a^6 b^4 B d^2 e x^7+2522520 a^5 A b^5 d^3 x^6+2102100 a^6 b^4 B d^3 x^6+450450 a^8 A b^2 e^3 x^6+100100 a^9 b B e^3 x^6+3603600 a^7 A b^3 d e^2 x^6+1351350 a^8 b^2 B d e^2 x^6+6306300 a^6 A b^4 d^2 e x^6+3603600 a^7 b^3 B d^2 e x^6+2522520 a^6 A b^4 d^3 x^5+1441440 a^7 b^3 B d^3 x^5+120120 a^9 A b e^3 x^5+12012 a^{10} B e^3 x^5+1621620 a^8 A b^2 d e^2 x^5+360360 a^9 b B d e^2 x^5+4324320 a^7 A b^3 d^2 e x^5+1621620 a^8 b^2 B d^2 e x^5+1801800 a^7 A b^3 d^3 x^4+675675 a^8 b^2 B d^3 x^4+15015 a^{10} A e^3 x^4+450450 a^9 A b d e^2 x^4+45045 a^{10} B d e^2 x^4+2027025 a^8 A b^2 d^2 e x^4+450450 a^9 b B d^2 e x^4+900900 a^8 A b^2 d^3 x^3+200200 a^9 b B d^3 x^3+60060 a^{10} A d e^2 x^3+600600 a^9 A b d^2 e x^3+60060 a^{10} B d^2 e x^3+300300 a^9 A b d^3 x^2+30030 a^{10} B d^3 x^2+90090 a^{10} A d^2 e x^2+60060 a^{10} A d^3 x}{60060}","\frac{e^2 (a+b x)^{14} (-4 a B e+A b e+3 b B d)}{14 b^5}+\frac{3 e (a+b x)^{13} (b d-a e) (-2 a B e+A b e+b B d)}{13 b^5}+\frac{(a+b x)^{12} (b d-a e)^2 (-4 a B e+3 A b e+b B d)}{12 b^5}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)^3}{11 b^5}+\frac{B e^3 (a+b x)^{15}}{15 b^5}",1,"(60060*a^10*A*d^3*x + 300300*a^9*A*b*d^3*x^2 + 30030*a^10*B*d^3*x^2 + 90090*a^10*A*d^2*e*x^2 + 900900*a^8*A*b^2*d^3*x^3 + 200200*a^9*b*B*d^3*x^3 + 600600*a^9*A*b*d^2*e*x^3 + 60060*a^10*B*d^2*e*x^3 + 60060*a^10*A*d*e^2*x^3 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5675670*a^5*A*b^5*d*e^2*x^8 + 4729725*a^6*b^4*B*d*e^2*x^8 + 1576575*a^6*A*b^4*e^3*x^8 + 900900*a^7*b^3*B*e^3*x^8 + 300300*a^2*A*b^8*d^3*x^9 + 800800*a^3*b^7*B*d^3*x^9 + 2402400*a^3*A*b^7*d^2*e*x^9 + 4204200*a^4*b^6*B*d^2*e*x^9 + 4204200*a^4*A*b^6*d*e^2*x^9 + 5045040*a^5*b^5*B*d*e^2*x^9 + 1681680*a^5*A*b^5*e^3*x^9 + 1401400*a^6*b^4*B*e^3*x^9 + 60060*a*A*b^9*d^3*x^10 + 270270*a^2*b^8*B*d^3*x^10 + 810810*a^2*A*b^8*d^2*e*x^10 + 2162160*a^3*b^7*B*d^2*e*x^10 + 2162160*a^3*A*b^7*d*e^2*x^10 + 3783780*a^4*b^6*B*d*e^2*x^10 + 1261260*a^4*A*b^6*e^3*x^10 + 1513512*a^5*b^5*B*e^3*x^10 + 5460*A*b^10*d^3*x^11 + 54600*a*b^9*B*d^3*x^11 + 163800*a*A*b^9*d^2*e*x^11 + 737100*a^2*b^8*B*d^2*e*x^11 + 737100*a^2*A*b^8*d*e^2*x^11 + 1965600*a^3*b^7*B*d*e^2*x^11 + 655200*a^3*A*b^7*e^3*x^11 + 1146600*a^4*b^6*B*e^3*x^11 + 5005*b^10*B*d^3*x^12 + 15015*A*b^10*d^2*e*x^12 + 150150*a*b^9*B*d^2*e*x^12 + 150150*a*A*b^9*d*e^2*x^12 + 675675*a^2*b^8*B*d*e^2*x^12 + 225225*a^2*A*b^8*e^3*x^12 + 600600*a^3*b^7*B*e^3*x^12 + 13860*b^10*B*d^2*e*x^13 + 13860*A*b^10*d*e^2*x^13 + 138600*a*b^9*B*d*e^2*x^13 + 46200*a*A*b^9*e^3*x^13 + 207900*a^2*b^8*B*e^3*x^13 + 12870*b^10*B*d*e^2*x^14 + 4290*A*b^10*e^3*x^14 + 42900*a*b^9*B*e^3*x^14 + 4004*b^10*B*e^3*x^15)/60060","B",1
1086,1,911,118,0.8941132,"\int (a+b x)^{10} (A+B x) (d+e x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^10*(A + B*x)*(d + e*x)^2,x]","\frac{858 b^{10} B e^2 x^{14}+924 A b^{10} e^2 x^{13}+9240 a b^9 B e^2 x^{13}+1848 b^{10} B d e x^{13}+1001 b^{10} B d^2 x^{12}+10010 a A b^9 e^2 x^{12}+45045 a^2 b^8 B e^2 x^{12}+2002 A b^{10} d e x^{12}+20020 a b^9 B d e x^{12}+1092 A b^{10} d^2 x^{11}+10920 a b^9 B d^2 x^{11}+49140 a^2 A b^8 e^2 x^{11}+131040 a^3 b^7 B e^2 x^{11}+21840 a A b^9 d e x^{11}+98280 a^2 b^8 B d e x^{11}+12012 a A b^9 d^2 x^{10}+54054 a^2 b^8 B d^2 x^{10}+144144 a^3 A b^7 e^2 x^{10}+252252 a^4 b^6 B e^2 x^{10}+108108 a^2 A b^8 d e x^{10}+288288 a^3 b^7 B d e x^{10}+60060 a^2 A b^8 d^2 x^9+160160 a^3 b^7 B d^2 x^9+280280 a^4 A b^6 e^2 x^9+336336 a^5 b^5 B e^2 x^9+320320 a^3 A b^7 d e x^9+560560 a^4 b^6 B d e x^9+180180 a^3 A b^7 d^2 x^8+315315 a^4 b^6 B d^2 x^8+378378 a^5 A b^5 e^2 x^8+315315 a^6 b^4 B e^2 x^8+630630 a^4 A b^6 d e x^8+756756 a^5 b^5 B d e x^8+360360 a^4 A b^6 d^2 x^7+432432 a^5 b^5 B d^2 x^7+360360 a^6 A b^4 e^2 x^7+205920 a^7 b^3 B e^2 x^7+864864 a^5 A b^5 d e x^7+720720 a^6 b^4 B d e x^7+504504 a^5 A b^5 d^2 x^6+420420 a^6 b^4 B d^2 x^6+240240 a^7 A b^3 e^2 x^6+90090 a^8 b^2 B e^2 x^6+840840 a^6 A b^4 d e x^6+480480 a^7 b^3 B d e x^6+504504 a^6 A b^4 d^2 x^5+288288 a^7 b^3 B d^2 x^5+108108 a^8 A b^2 e^2 x^5+24024 a^9 b B e^2 x^5+576576 a^7 A b^3 d e x^5+216216 a^8 b^2 B d e x^5+360360 a^7 A b^3 d^2 x^4+135135 a^8 b^2 B d^2 x^4+30030 a^9 A b e^2 x^4+3003 a^{10} B e^2 x^4+270270 a^8 A b^2 d e x^4+60060 a^9 b B d e x^4+180180 a^8 A b^2 d^2 x^3+40040 a^9 b B d^2 x^3+4004 a^{10} A e^2 x^3+80080 a^9 A b d e x^3+8008 a^{10} B d e x^3+60060 a^9 A b d^2 x^2+6006 a^{10} B d^2 x^2+12012 a^{10} A d e x^2+12012 a^{10} A d^2 x}{12012}","\frac{e (a+b x)^{13} (-3 a B e+A b e+2 b B d)}{13 b^4}+\frac{(a+b x)^{12} (b d-a e) (-3 a B e+2 A b e+b B d)}{12 b^4}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)^2}{11 b^4}+\frac{B e^2 (a+b x)^{14}}{14 b^4}",1,"(12012*a^10*A*d^2*x + 60060*a^9*A*b*d^2*x^2 + 6006*a^10*B*d^2*x^2 + 12012*a^10*A*d*e*x^2 + 180180*a^8*A*b^2*d^2*x^3 + 40040*a^9*b*B*d^2*x^3 + 80080*a^9*A*b*d*e*x^3 + 8008*a^10*B*d*e*x^3 + 4004*a^10*A*e^2*x^3 + 360360*a^7*A*b^3*d^2*x^4 + 135135*a^8*b^2*B*d^2*x^4 + 270270*a^8*A*b^2*d*e*x^4 + 60060*a^9*b*B*d*e*x^4 + 30030*a^9*A*b*e^2*x^4 + 3003*a^10*B*e^2*x^4 + 504504*a^6*A*b^4*d^2*x^5 + 288288*a^7*b^3*B*d^2*x^5 + 576576*a^7*A*b^3*d*e*x^5 + 216216*a^8*b^2*B*d*e*x^5 + 108108*a^8*A*b^2*e^2*x^5 + 24024*a^9*b*B*e^2*x^5 + 504504*a^5*A*b^5*d^2*x^6 + 420420*a^6*b^4*B*d^2*x^6 + 840840*a^6*A*b^4*d*e*x^6 + 480480*a^7*b^3*B*d*e*x^6 + 240240*a^7*A*b^3*e^2*x^6 + 90090*a^8*b^2*B*e^2*x^6 + 360360*a^4*A*b^6*d^2*x^7 + 432432*a^5*b^5*B*d^2*x^7 + 864864*a^5*A*b^5*d*e*x^7 + 720720*a^6*b^4*B*d*e*x^7 + 360360*a^6*A*b^4*e^2*x^7 + 205920*a^7*b^3*B*e^2*x^7 + 180180*a^3*A*b^7*d^2*x^8 + 315315*a^4*b^6*B*d^2*x^8 + 630630*a^4*A*b^6*d*e*x^8 + 756756*a^5*b^5*B*d*e*x^8 + 378378*a^5*A*b^5*e^2*x^8 + 315315*a^6*b^4*B*e^2*x^8 + 60060*a^2*A*b^8*d^2*x^9 + 160160*a^3*b^7*B*d^2*x^9 + 320320*a^3*A*b^7*d*e*x^9 + 560560*a^4*b^6*B*d*e*x^9 + 280280*a^4*A*b^6*e^2*x^9 + 336336*a^5*b^5*B*e^2*x^9 + 12012*a*A*b^9*d^2*x^10 + 54054*a^2*b^8*B*d^2*x^10 + 108108*a^2*A*b^8*d*e*x^10 + 288288*a^3*b^7*B*d*e*x^10 + 144144*a^3*A*b^7*e^2*x^10 + 252252*a^4*b^6*B*e^2*x^10 + 1092*A*b^10*d^2*x^11 + 10920*a*b^9*B*d^2*x^11 + 21840*a*A*b^9*d*e*x^11 + 98280*a^2*b^8*B*d*e*x^11 + 49140*a^2*A*b^8*e^2*x^11 + 131040*a^3*b^7*B*e^2*x^11 + 1001*b^10*B*d^2*x^12 + 2002*A*b^10*d*e*x^12 + 20020*a*b^9*B*d*e*x^12 + 10010*a*A*b^9*e^2*x^12 + 45045*a^2*b^8*B*e^2*x^12 + 1848*b^10*B*d*e*x^13 + 924*A*b^10*e^2*x^13 + 9240*a*b^9*B*e^2*x^13 + 858*b^10*B*e^2*x^14)/12012","B",1
1087,1,535,75,0.4076901,"\int (a+b x)^{10} (A+B x) (d+e x) \, dx","IntegrateAlgebraic[(a + b*x)^10*(A + B*x)*(d + e*x),x]","\frac{1716 a^{10} A d x+858 a^{10} A e x^2+858 a^{10} B d x^2+572 a^{10} B e x^3+8580 a^9 A b d x^2+5720 a^9 A b e x^3+5720 a^9 b B d x^3+4290 a^9 b B e x^4+25740 a^8 A b^2 d x^3+19305 a^8 A b^2 e x^4+19305 a^8 b^2 B d x^4+15444 a^8 b^2 B e x^5+51480 a^7 A b^3 d x^4+41184 a^7 A b^3 e x^5+41184 a^7 b^3 B d x^5+34320 a^7 b^3 B e x^6+72072 a^6 A b^4 d x^5+60060 a^6 A b^4 e x^6+60060 a^6 b^4 B d x^6+51480 a^6 b^4 B e x^7+72072 a^5 A b^5 d x^6+61776 a^5 A b^5 e x^7+61776 a^5 b^5 B d x^7+54054 a^5 b^5 B e x^8+51480 a^4 A b^6 d x^7+45045 a^4 A b^6 e x^8+45045 a^4 b^6 B d x^8+40040 a^4 b^6 B e x^9+25740 a^3 A b^7 d x^8+22880 a^3 A b^7 e x^9+22880 a^3 b^7 B d x^9+20592 a^3 b^7 B e x^{10}+8580 a^2 A b^8 d x^9+7722 a^2 A b^8 e x^{10}+7722 a^2 b^8 B d x^{10}+7020 a^2 b^8 B e x^{11}+1716 a A b^9 d x^{10}+1560 a A b^9 e x^{11}+1560 a b^9 B d x^{11}+1430 a b^9 B e x^{12}+156 A b^{10} d x^{11}+143 A b^{10} e x^{12}+143 b^{10} B d x^{12}+132 b^{10} B e x^{13}}{1716}","\frac{(a+b x)^{12} (-2 a B e+A b e+b B d)}{12 b^3}+\frac{(a+b x)^{11} (A b-a B) (b d-a e)}{11 b^3}+\frac{B e (a+b x)^{13}}{13 b^3}",1,"(1716*a^10*A*d*x + 8580*a^9*A*b*d*x^2 + 858*a^10*B*d*x^2 + 858*a^10*A*e*x^2 + 25740*a^8*A*b^2*d*x^3 + 5720*a^9*b*B*d*x^3 + 5720*a^9*A*b*e*x^3 + 572*a^10*B*e*x^3 + 51480*a^7*A*b^3*d*x^4 + 19305*a^8*b^2*B*d*x^4 + 19305*a^8*A*b^2*e*x^4 + 4290*a^9*b*B*e*x^4 + 72072*a^6*A*b^4*d*x^5 + 41184*a^7*b^3*B*d*x^5 + 41184*a^7*A*b^3*e*x^5 + 15444*a^8*b^2*B*e*x^5 + 72072*a^5*A*b^5*d*x^6 + 60060*a^6*b^4*B*d*x^6 + 60060*a^6*A*b^4*e*x^6 + 34320*a^7*b^3*B*e*x^6 + 51480*a^4*A*b^6*d*x^7 + 61776*a^5*b^5*B*d*x^7 + 61776*a^5*A*b^5*e*x^7 + 51480*a^6*b^4*B*e*x^7 + 25740*a^3*A*b^7*d*x^8 + 45045*a^4*b^6*B*d*x^8 + 45045*a^4*A*b^6*e*x^8 + 54054*a^5*b^5*B*e*x^8 + 8580*a^2*A*b^8*d*x^9 + 22880*a^3*b^7*B*d*x^9 + 22880*a^3*A*b^7*e*x^9 + 40040*a^4*b^6*B*e*x^9 + 1716*a*A*b^9*d*x^10 + 7722*a^2*b^8*B*d*x^10 + 7722*a^2*A*b^8*e*x^10 + 20592*a^3*b^7*B*e*x^10 + 156*A*b^10*d*x^11 + 1560*a*b^9*B*d*x^11 + 1560*a*A*b^9*e*x^11 + 7020*a^2*b^8*B*e*x^11 + 143*b^10*B*d*x^12 + 143*A*b^10*e*x^12 + 1430*a*b^9*B*e*x^12 + 132*b^10*B*e*x^13)/1716","B",1
1088,1,243,38,0.0006695,"\int (a+b x)^{10} (A+B x) \, dx","IntegrateAlgebraic[(a + b*x)^10*(A + B*x),x]","\frac{1}{132} x \left(132 a^{10} A+66 a^{10} B x+660 a^9 A b x+440 a^9 b B x^2+1980 a^8 A b^2 x^2+1485 a^8 b^2 B x^3+3960 a^7 A b^3 x^3+3168 a^7 b^3 B x^4+5544 a^6 A b^4 x^4+4620 a^6 b^4 B x^5+5544 a^5 A b^5 x^5+4752 a^5 b^5 B x^6+3960 a^4 A b^6 x^6+3465 a^4 b^6 B x^7+1980 a^3 A b^7 x^7+1760 a^3 b^7 B x^8+660 a^2 A b^8 x^8+594 a^2 b^8 B x^9+132 a A b^9 x^9+120 a b^9 B x^{10}+12 A b^{10} x^{10}+11 b^{10} B x^{11}\right)","\frac{(a+b x)^{11} (A b-a B)}{11 b^2}+\frac{B (a+b x)^{12}}{12 b^2}",1,"(x*(132*a^10*A + 660*a^9*A*b*x + 66*a^10*B*x + 1980*a^8*A*b^2*x^2 + 440*a^9*b*B*x^2 + 3960*a^7*A*b^3*x^3 + 1485*a^8*b^2*B*x^3 + 5544*a^6*A*b^4*x^4 + 3168*a^7*b^3*B*x^4 + 5544*a^5*A*b^5*x^5 + 4620*a^6*b^4*B*x^5 + 3960*a^4*A*b^6*x^6 + 4752*a^5*b^5*B*x^6 + 1980*a^3*A*b^7*x^7 + 3465*a^4*b^6*B*x^7 + 660*a^2*A*b^8*x^8 + 1760*a^3*b^7*B*x^8 + 132*a*A*b^9*x^9 + 594*a^2*b^8*B*x^9 + 12*A*b^10*x^10 + 120*a*b^9*B*x^10 + 11*b^10*B*x^11))/132","B",1
1089,1,1954,348,1.803889,"\int \frac{(a+b x)^{10} (A+B x)}{d+e x} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x),x]","\frac{2520 b^{10} B e^{10} x^{11}+2772 A b^{10} e^{10} x^{10}+27720 a b^9 B e^{10} x^{10}-2772 b^{10} B d e^9 x^{10}+30800 a A b^9 e^{10} x^9+138600 a^2 b^8 B e^{10} x^9-3080 A b^{10} d e^9 x^9-30800 a b^9 B d e^9 x^9+3080 b^{10} B d^2 e^8 x^9+155925 a^2 A b^8 e^{10} x^8+415800 a^3 b^7 B e^{10} x^8-34650 a A b^9 d e^9 x^8-155925 a^2 b^8 B d e^9 x^8+3465 A b^{10} d^2 e^8 x^8+34650 a b^9 B d^2 e^8 x^8-3465 b^{10} B d^3 e^7 x^8+475200 a^3 A b^7 e^{10} x^7+831600 a^4 b^6 B e^{10} x^7-178200 a^2 A b^8 d e^9 x^7-475200 a^3 b^7 B d e^9 x^7+39600 a A b^9 d^2 e^8 x^7+178200 a^2 b^8 B d^2 e^8 x^7-3960 A b^{10} d^3 e^7 x^7-39600 a b^9 B d^3 e^7 x^7+3960 b^{10} B d^4 e^6 x^7+970200 a^4 A b^6 e^{10} x^6+1164240 a^5 b^5 B e^{10} x^6-554400 a^3 A b^7 d e^9 x^6-970200 a^4 b^6 B d e^9 x^6+207900 a^2 A b^8 d^2 e^8 x^6+554400 a^3 b^7 B d^2 e^8 x^6-46200 a A b^9 d^3 e^7 x^6-207900 a^2 b^8 B d^3 e^7 x^6+4620 A b^{10} d^4 e^6 x^6+46200 a b^9 B d^4 e^6 x^6-4620 b^{10} B d^5 e^5 x^6+1397088 a^5 A b^5 e^{10} x^5+1164240 a^6 b^4 B e^{10} x^5-1164240 a^4 A b^6 d e^9 x^5-1397088 a^5 b^5 B d e^9 x^5+665280 a^3 A b^7 d^2 e^8 x^5+1164240 a^4 b^6 B d^2 e^8 x^5-249480 a^2 A b^8 d^3 e^7 x^5-665280 a^3 b^7 B d^3 e^7 x^5+55440 a A b^9 d^4 e^6 x^5+249480 a^2 b^8 B d^4 e^6 x^5-5544 A b^{10} d^5 e^5 x^5-55440 a b^9 B d^5 e^5 x^5+5544 b^{10} B d^6 e^4 x^5+1455300 a^6 A b^4 e^{10} x^4+831600 a^7 b^3 B e^{10} x^4-1746360 a^5 A b^5 d e^9 x^4-1455300 a^6 b^4 B d e^9 x^4+1455300 a^4 A b^6 d^2 e^8 x^4+1746360 a^5 b^5 B d^2 e^8 x^4-831600 a^3 A b^7 d^3 e^7 x^4-1455300 a^4 b^6 B d^3 e^7 x^4+311850 a^2 A b^8 d^4 e^6 x^4+831600 a^3 b^7 B d^4 e^6 x^4-69300 a A b^9 d^5 e^5 x^4-311850 a^2 b^8 B d^5 e^5 x^4+6930 A b^{10} d^6 e^4 x^4+69300 a b^9 B d^6 e^4 x^4-6930 b^{10} B d^7 e^3 x^4+1108800 a^7 A b^3 e^{10} x^3+415800 a^8 b^2 B e^{10} x^3-1940400 a^6 A b^4 d e^9 x^3-1108800 a^7 b^3 B d e^9 x^3+2328480 a^5 A b^5 d^2 e^8 x^3+1940400 a^6 b^4 B d^2 e^8 x^3-1940400 a^4 A b^6 d^3 e^7 x^3-2328480 a^5 b^5 B d^3 e^7 x^3+1108800 a^3 A b^7 d^4 e^6 x^3+1940400 a^4 b^6 B d^4 e^6 x^3-415800 a^2 A b^8 d^5 e^5 x^3-1108800 a^3 b^7 B d^5 e^5 x^3+92400 a A b^9 d^6 e^4 x^3+415800 a^2 b^8 B d^6 e^4 x^3-9240 A b^{10} d^7 e^3 x^3-92400 a b^9 B d^7 e^3 x^3+9240 b^{10} B d^8 e^2 x^3+623700 a^8 A b^2 e^{10} x^2+138600 a^9 b B e^{10} x^2-1663200 a^7 A b^3 d e^9 x^2-623700 a^8 b^2 B d e^9 x^2+2910600 a^6 A b^4 d^2 e^8 x^2+1663200 a^7 b^3 B d^2 e^8 x^2-3492720 a^5 A b^5 d^3 e^7 x^2-2910600 a^6 b^4 B d^3 e^7 x^2+2910600 a^4 A b^6 d^4 e^6 x^2+3492720 a^5 b^5 B d^4 e^6 x^2-1663200 a^3 A b^7 d^5 e^5 x^2-2910600 a^4 b^6 B d^5 e^5 x^2+623700 a^2 A b^8 d^6 e^4 x^2+1663200 a^3 b^7 B d^6 e^4 x^2-138600 a A b^9 d^7 e^3 x^2-623700 a^2 b^8 B d^7 e^3 x^2+13860 A b^{10} d^8 e^2 x^2+138600 a b^9 B d^8 e^2 x^2-13860 b^{10} B d^9 e x^2+27720 b^{10} B d^{10} x+277200 a^9 A b e^{10} x+27720 a^{10} B e^{10} x-1247400 a^8 A b^2 d e^9 x-277200 a^9 b B d e^9 x+3326400 a^7 A b^3 d^2 e^8 x+1247400 a^8 b^2 B d^2 e^8 x-5821200 a^6 A b^4 d^3 e^7 x-3326400 a^7 b^3 B d^3 e^7 x+6985440 a^5 A b^5 d^4 e^6 x+5821200 a^6 b^4 B d^4 e^6 x-5821200 a^4 A b^6 d^5 e^5 x-6985440 a^5 b^5 B d^5 e^5 x+3326400 a^3 A b^7 d^6 e^4 x+5821200 a^4 b^6 B d^6 e^4 x-1247400 a^2 A b^8 d^7 e^3 x-3326400 a^3 b^7 B d^7 e^3 x+277200 a A b^9 d^8 e^2 x+1247400 a^2 b^8 B d^8 e^2 x-27720 A b^{10} d^9 e x-277200 a b^9 B d^9 e x}{27720 e^{11}}-\frac{(b d-a e)^{10} (B d-A e) \log (d+e x)}{e^{12}}","-\frac{(b d-a e)^{10} (B d-A e) \log (d+e x)}{e^{12}}+\frac{b x (b d-a e)^9 (B d-A e)}{e^{11}}-\frac{(a+b x)^2 (b d-a e)^8 (B d-A e)}{2 e^{10}}+\frac{(a+b x)^3 (b d-a e)^7 (B d-A e)}{3 e^9}-\frac{(a+b x)^4 (b d-a e)^6 (B d-A e)}{4 e^8}+\frac{(a+b x)^5 (b d-a e)^5 (B d-A e)}{5 e^7}-\frac{(a+b x)^6 (b d-a e)^4 (B d-A e)}{6 e^6}+\frac{(a+b x)^7 (b d-a e)^3 (B d-A e)}{7 e^5}-\frac{(a+b x)^8 (b d-a e)^2 (B d-A e)}{8 e^4}+\frac{(a+b x)^9 (b d-a e) (B d-A e)}{9 e^3}-\frac{(a+b x)^{10} (B d-A e)}{10 e^2}+\frac{B (a+b x)^{11}}{11 b e}",1,"(27720*b^10*B*d^10*x - 27720*A*b^10*d^9*e*x - 277200*a*b^9*B*d^9*e*x + 277200*a*A*b^9*d^8*e^2*x + 1247400*a^2*b^8*B*d^8*e^2*x - 1247400*a^2*A*b^8*d^7*e^3*x - 3326400*a^3*b^7*B*d^7*e^3*x + 3326400*a^3*A*b^7*d^6*e^4*x + 5821200*a^4*b^6*B*d^6*e^4*x - 5821200*a^4*A*b^6*d^5*e^5*x - 6985440*a^5*b^5*B*d^5*e^5*x + 6985440*a^5*A*b^5*d^4*e^6*x + 5821200*a^6*b^4*B*d^4*e^6*x - 5821200*a^6*A*b^4*d^3*e^7*x - 3326400*a^7*b^3*B*d^3*e^7*x + 3326400*a^7*A*b^3*d^2*e^8*x + 1247400*a^8*b^2*B*d^2*e^8*x - 1247400*a^8*A*b^2*d*e^9*x - 277200*a^9*b*B*d*e^9*x + 277200*a^9*A*b*e^10*x + 27720*a^10*B*e^10*x - 13860*b^10*B*d^9*e*x^2 + 13860*A*b^10*d^8*e^2*x^2 + 138600*a*b^9*B*d^8*e^2*x^2 - 138600*a*A*b^9*d^7*e^3*x^2 - 623700*a^2*b^8*B*d^7*e^3*x^2 + 623700*a^2*A*b^8*d^6*e^4*x^2 + 1663200*a^3*b^7*B*d^6*e^4*x^2 - 1663200*a^3*A*b^7*d^5*e^5*x^2 - 2910600*a^4*b^6*B*d^5*e^5*x^2 + 2910600*a^4*A*b^6*d^4*e^6*x^2 + 3492720*a^5*b^5*B*d^4*e^6*x^2 - 3492720*a^5*A*b^5*d^3*e^7*x^2 - 2910600*a^6*b^4*B*d^3*e^7*x^2 + 2910600*a^6*A*b^4*d^2*e^8*x^2 + 1663200*a^7*b^3*B*d^2*e^8*x^2 - 1663200*a^7*A*b^3*d*e^9*x^2 - 623700*a^8*b^2*B*d*e^9*x^2 + 623700*a^8*A*b^2*e^10*x^2 + 138600*a^9*b*B*e^10*x^2 + 9240*b^10*B*d^8*e^2*x^3 - 9240*A*b^10*d^7*e^3*x^3 - 92400*a*b^9*B*d^7*e^3*x^3 + 92400*a*A*b^9*d^6*e^4*x^3 + 415800*a^2*b^8*B*d^6*e^4*x^3 - 415800*a^2*A*b^8*d^5*e^5*x^3 - 1108800*a^3*b^7*B*d^5*e^5*x^3 + 1108800*a^3*A*b^7*d^4*e^6*x^3 + 1940400*a^4*b^6*B*d^4*e^6*x^3 - 1940400*a^4*A*b^6*d^3*e^7*x^3 - 2328480*a^5*b^5*B*d^3*e^7*x^3 + 2328480*a^5*A*b^5*d^2*e^8*x^3 + 1940400*a^6*b^4*B*d^2*e^8*x^3 - 1940400*a^6*A*b^4*d*e^9*x^3 - 1108800*a^7*b^3*B*d*e^9*x^3 + 1108800*a^7*A*b^3*e^10*x^3 + 415800*a^8*b^2*B*e^10*x^3 - 6930*b^10*B*d^7*e^3*x^4 + 6930*A*b^10*d^6*e^4*x^4 + 69300*a*b^9*B*d^6*e^4*x^4 - 69300*a*A*b^9*d^5*e^5*x^4 - 311850*a^2*b^8*B*d^5*e^5*x^4 + 311850*a^2*A*b^8*d^4*e^6*x^4 + 831600*a^3*b^7*B*d^4*e^6*x^4 - 831600*a^3*A*b^7*d^3*e^7*x^4 - 1455300*a^4*b^6*B*d^3*e^7*x^4 + 1455300*a^4*A*b^6*d^2*e^8*x^4 + 1746360*a^5*b^5*B*d^2*e^8*x^4 - 1746360*a^5*A*b^5*d*e^9*x^4 - 1455300*a^6*b^4*B*d*e^9*x^4 + 1455300*a^6*A*b^4*e^10*x^4 + 831600*a^7*b^3*B*e^10*x^4 + 5544*b^10*B*d^6*e^4*x^5 - 5544*A*b^10*d^5*e^5*x^5 - 55440*a*b^9*B*d^5*e^5*x^5 + 55440*a*A*b^9*d^4*e^6*x^5 + 249480*a^2*b^8*B*d^4*e^6*x^5 - 249480*a^2*A*b^8*d^3*e^7*x^5 - 665280*a^3*b^7*B*d^3*e^7*x^5 + 665280*a^3*A*b^7*d^2*e^8*x^5 + 1164240*a^4*b^6*B*d^2*e^8*x^5 - 1164240*a^4*A*b^6*d*e^9*x^5 - 1397088*a^5*b^5*B*d*e^9*x^5 + 1397088*a^5*A*b^5*e^10*x^5 + 1164240*a^6*b^4*B*e^10*x^5 - 4620*b^10*B*d^5*e^5*x^6 + 4620*A*b^10*d^4*e^6*x^6 + 46200*a*b^9*B*d^4*e^6*x^6 - 46200*a*A*b^9*d^3*e^7*x^6 - 207900*a^2*b^8*B*d^3*e^7*x^6 + 207900*a^2*A*b^8*d^2*e^8*x^6 + 554400*a^3*b^7*B*d^2*e^8*x^6 - 554400*a^3*A*b^7*d*e^9*x^6 - 970200*a^4*b^6*B*d*e^9*x^6 + 970200*a^4*A*b^6*e^10*x^6 + 1164240*a^5*b^5*B*e^10*x^6 + 3960*b^10*B*d^4*e^6*x^7 - 3960*A*b^10*d^3*e^7*x^7 - 39600*a*b^9*B*d^3*e^7*x^7 + 39600*a*A*b^9*d^2*e^8*x^7 + 178200*a^2*b^8*B*d^2*e^8*x^7 - 178200*a^2*A*b^8*d*e^9*x^7 - 475200*a^3*b^7*B*d*e^9*x^7 + 475200*a^3*A*b^7*e^10*x^7 + 831600*a^4*b^6*B*e^10*x^7 - 3465*b^10*B*d^3*e^7*x^8 + 3465*A*b^10*d^2*e^8*x^8 + 34650*a*b^9*B*d^2*e^8*x^8 - 34650*a*A*b^9*d*e^9*x^8 - 155925*a^2*b^8*B*d*e^9*x^8 + 155925*a^2*A*b^8*e^10*x^8 + 415800*a^3*b^7*B*e^10*x^8 + 3080*b^10*B*d^2*e^8*x^9 - 3080*A*b^10*d*e^9*x^9 - 30800*a*b^9*B*d*e^9*x^9 + 30800*a*A*b^9*e^10*x^9 + 138600*a^2*b^8*B*e^10*x^9 - 2772*b^10*B*d*e^9*x^10 + 2772*A*b^10*e^10*x^10 + 27720*a*b^9*B*e^10*x^10 + 2520*b^10*B*e^10*x^11)/(27720*e^11) - ((b*d - a*e)^10*(B*d - A*e)*Log[d + e*x])/e^12","B",1
1090,1,2505,445,1.3559156,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^2} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^2,x]","\text{Result too large to show}","-\frac{b^9 (d+e x)^9 (-10 a B e-A b e+11 b B d)}{9 e^{12}}+\frac{5 b^8 (d+e x)^8 (b d-a e) (-9 a B e-2 A b e+11 b B d)}{8 e^{12}}-\frac{15 b^7 (d+e x)^7 (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{7 e^{12}}+\frac{5 b^6 (d+e x)^6 (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{e^{12}}-\frac{42 b^5 (d+e x)^5 (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{5 e^{12}}+\frac{21 b^4 (d+e x)^4 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{2 e^{12}}-\frac{10 b^3 (d+e x)^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{e^{12}}+\frac{15 b^2 (d+e x)^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{2 e^{12}}+\frac{(b d-a e)^{10} (B d-A e)}{e^{12} (d+e x)}+\frac{(b d-a e)^9 \log (d+e x) (-a B e-10 A b e+11 b B d)}{e^{12}}-\frac{5 b x (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{e^{11}}+\frac{b^{10} B (d+e x)^{10}}{10 e^{12}}",1,"(2520*b^10*B*d^11 - 2520*A*b^10*d^10*e - 25200*a*b^9*B*d^10*e + 25200*a*A*b^9*d^9*e^2 + 113400*a^2*b^8*B*d^9*e^2 - 113400*a^2*A*b^8*d^8*e^3 - 302400*a^3*b^7*B*d^8*e^3 + 302400*a^3*A*b^7*d^7*e^4 + 529200*a^4*b^6*B*d^7*e^4 - 529200*a^4*A*b^6*d^6*e^5 - 635040*a^5*b^5*B*d^6*e^5 + 635040*a^5*A*b^5*d^5*e^6 + 529200*a^6*b^4*B*d^5*e^6 - 529200*a^6*A*b^4*d^4*e^7 - 302400*a^7*b^3*B*d^4*e^7 + 302400*a^7*A*b^3*d^3*e^8 + 113400*a^8*b^2*B*d^3*e^8 - 113400*a^8*A*b^2*d^2*e^9 - 25200*a^9*b*B*d^2*e^9 + 25200*a^9*A*b*d*e^10 + 2520*a^10*B*d*e^10 - 2520*a^10*A*e^11 - 25200*b^10*B*d^10*e*x + 22680*A*b^10*d^9*e^2*x + 226800*a*b^9*B*d^9*e^2*x - 201600*a*A*b^9*d^8*e^3*x - 907200*a^2*b^8*B*d^8*e^3*x + 793800*a^2*A*b^8*d^7*e^4*x + 2116800*a^3*b^7*B*d^7*e^4*x - 1814400*a^3*A*b^7*d^6*e^5*x - 3175200*a^4*b^6*B*d^6*e^5*x + 2646000*a^4*A*b^6*d^5*e^6*x + 3175200*a^5*b^5*B*d^5*e^6*x - 2540160*a^5*A*b^5*d^4*e^7*x - 2116800*a^6*b^4*B*d^4*e^7*x + 1587600*a^6*A*b^4*d^3*e^8*x + 907200*a^7*b^3*B*d^3*e^8*x - 604800*a^7*A*b^3*d^2*e^9*x - 226800*a^8*b^2*B*d^2*e^9*x + 113400*a^8*A*b^2*d*e^10*x + 25200*a^9*b*B*d*e^10*x - 13860*b^10*B*d^9*e^2*x^2 + 12600*A*b^10*d^8*e^3*x^2 + 126000*a*b^9*B*d^8*e^3*x^2 - 113400*a*A*b^9*d^7*e^4*x^2 - 510300*a^2*b^8*B*d^7*e^4*x^2 + 453600*a^2*A*b^8*d^6*e^5*x^2 + 1209600*a^3*b^7*B*d^6*e^5*x^2 - 1058400*a^3*A*b^7*d^5*e^6*x^2 - 1852200*a^4*b^6*B*d^5*e^6*x^2 + 1587600*a^4*A*b^6*d^4*e^7*x^2 + 1905120*a^5*b^5*B*d^4*e^7*x^2 - 1587600*a^5*A*b^5*d^3*e^8*x^2 - 1323000*a^6*b^4*B*d^3*e^8*x^2 + 1058400*a^6*A*b^4*d^2*e^9*x^2 + 604800*a^7*b^3*B*d^2*e^9*x^2 - 453600*a^7*A*b^3*d*e^10*x^2 - 170100*a^8*b^2*B*d*e^10*x^2 + 113400*a^8*A*b^2*e^11*x^2 + 25200*a^9*b*B*e^11*x^2 + 4620*b^10*B*d^8*e^3*x^3 - 4200*A*b^10*d^7*e^4*x^3 - 42000*a*b^9*B*d^7*e^4*x^3 + 37800*a*A*b^9*d^6*e^5*x^3 + 170100*a^2*b^8*B*d^6*e^5*x^3 - 151200*a^2*A*b^8*d^5*e^6*x^3 - 403200*a^3*b^7*B*d^5*e^6*x^3 + 352800*a^3*A*b^7*d^4*e^7*x^3 + 617400*a^4*b^6*B*d^4*e^7*x^3 - 529200*a^4*A*b^6*d^3*e^8*x^3 - 635040*a^5*b^5*B*d^3*e^8*x^3 + 529200*a^5*A*b^5*d^2*e^9*x^3 + 441000*a^6*b^4*B*d^2*e^9*x^3 - 352800*a^6*A*b^4*d*e^10*x^3 - 201600*a^7*b^3*B*d*e^10*x^3 + 151200*a^7*A*b^3*e^11*x^3 + 56700*a^8*b^2*B*e^11*x^3 - 2310*b^10*B*d^7*e^4*x^4 + 2100*A*b^10*d^6*e^5*x^4 + 21000*a*b^9*B*d^6*e^5*x^4 - 18900*a*A*b^9*d^5*e^6*x^4 - 85050*a^2*b^8*B*d^5*e^6*x^4 + 75600*a^2*A*b^8*d^4*e^7*x^4 + 201600*a^3*b^7*B*d^4*e^7*x^4 - 176400*a^3*A*b^7*d^3*e^8*x^4 - 308700*a^4*b^6*B*d^3*e^8*x^4 + 264600*a^4*A*b^6*d^2*e^9*x^4 + 317520*a^5*b^5*B*d^2*e^9*x^4 - 264600*a^5*A*b^5*d*e^10*x^4 - 220500*a^6*b^4*B*d*e^10*x^4 + 176400*a^6*A*b^4*e^11*x^4 + 100800*a^7*b^3*B*e^11*x^4 + 1386*b^10*B*d^6*e^5*x^5 - 1260*A*b^10*d^5*e^6*x^5 - 12600*a*b^9*B*d^5*e^6*x^5 + 11340*a*A*b^9*d^4*e^7*x^5 + 51030*a^2*b^8*B*d^4*e^7*x^5 - 45360*a^2*A*b^8*d^3*e^8*x^5 - 120960*a^3*b^7*B*d^3*e^8*x^5 + 105840*a^3*A*b^7*d^2*e^9*x^5 + 185220*a^4*b^6*B*d^2*e^9*x^5 - 158760*a^4*A*b^6*d*e^10*x^5 - 190512*a^5*b^5*B*d*e^10*x^5 + 158760*a^5*A*b^5*e^11*x^5 + 132300*a^6*b^4*B*e^11*x^5 - 924*b^10*B*d^5*e^6*x^6 + 840*A*b^10*d^4*e^7*x^6 + 8400*a*b^9*B*d^4*e^7*x^6 - 7560*a*A*b^9*d^3*e^8*x^6 - 34020*a^2*b^8*B*d^3*e^8*x^6 + 30240*a^2*A*b^8*d^2*e^9*x^6 + 80640*a^3*b^7*B*d^2*e^9*x^6 - 70560*a^3*A*b^7*d*e^10*x^6 - 123480*a^4*b^6*B*d*e^10*x^6 + 105840*a^4*A*b^6*e^11*x^6 + 127008*a^5*b^5*B*e^11*x^6 + 660*b^10*B*d^4*e^7*x^7 - 600*A*b^10*d^3*e^8*x^7 - 6000*a*b^9*B*d^3*e^8*x^7 + 5400*a*A*b^9*d^2*e^9*x^7 + 24300*a^2*b^8*B*d^2*e^9*x^7 - 21600*a^2*A*b^8*d*e^10*x^7 - 57600*a^3*b^7*B*d*e^10*x^7 + 50400*a^3*A*b^7*e^11*x^7 + 88200*a^4*b^6*B*e^11*x^7 - 495*b^10*B*d^3*e^8*x^8 + 450*A*b^10*d^2*e^9*x^8 + 4500*a*b^9*B*d^2*e^9*x^8 - 4050*a*A*b^9*d*e^10*x^8 - 18225*a^2*b^8*B*d*e^10*x^8 + 16200*a^2*A*b^8*e^11*x^8 + 43200*a^3*b^7*B*e^11*x^8 + 385*b^10*B*d^2*e^9*x^9 - 350*A*b^10*d*e^10*x^9 - 3500*a*b^9*B*d*e^10*x^9 + 3150*a*A*b^9*e^11*x^9 + 14175*a^2*b^8*B*e^11*x^9 - 308*b^10*B*d*e^10*x^10 + 280*A*b^10*e^11*x^10 + 2800*a*b^9*B*e^11*x^10 + 252*b^10*B*e^11*x^11)/(2520*e^12*(d + e*x)) + ((11*b^10*B*d^10 - 10*A*b^10*d^9*e - 100*a*b^9*B*d^9*e + 90*a*A*b^9*d^8*e^2 + 405*a^2*b^8*B*d^8*e^2 - 360*a^2*A*b^8*d^7*e^3 - 960*a^3*b^7*B*d^7*e^3 + 840*a^3*A*b^7*d^6*e^4 + 1470*a^4*b^6*B*d^6*e^4 - 1260*a^4*A*b^6*d^5*e^5 - 1512*a^5*b^5*B*d^5*e^5 + 1260*a^5*A*b^5*d^4*e^6 + 1050*a^6*b^4*B*d^4*e^6 - 840*a^6*A*b^4*d^3*e^7 - 480*a^7*b^3*B*d^3*e^7 + 360*a^7*A*b^3*d^2*e^8 + 135*a^8*b^2*B*d^2*e^8 - 90*a^8*A*b^2*d*e^9 - 20*a^9*b*B*d*e^9 + 10*a^9*A*b*e^10 + a^10*B*e^10)*Log[d + e*x])/e^12","B",1
1091,1,2475,445,1.431868,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^3} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^3,x]","\text{Result too large to show}","-\frac{b^9 (d+e x)^8 (-10 a B e-A b e+11 b B d)}{8 e^{12}}+\frac{5 b^8 (d+e x)^7 (b d-a e) (-9 a B e-2 A b e+11 b B d)}{7 e^{12}}-\frac{5 b^7 (d+e x)^6 (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{2 e^{12}}+\frac{6 b^6 (d+e x)^5 (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{e^{12}}-\frac{21 b^5 (d+e x)^4 (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{2 e^{12}}+\frac{14 b^4 (d+e x)^3 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{e^{12}}-\frac{15 b^3 (d+e x)^2 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{e^{12}}+\frac{15 b^2 x (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{e^{11}}-\frac{(b d-a e)^9 (-a B e-10 A b e+11 b B d)}{e^{12} (d+e x)}+\frac{(b d-a e)^{10} (B d-A e)}{2 e^{12} (d+e x)^2}-\frac{5 b (b d-a e)^8 \log (d+e x) (-2 a B e-9 A b e+11 b B d)}{e^{12}}+\frac{b^{10} B (d+e x)^9}{9 e^{12}}",1,"(-5292*b^10*B*d^11 + 4788*A*b^10*d^10*e + 47880*a*b^9*B*d^10*e - 42840*a*A*b^9*d^9*e^2 - 192780*a^2*b^8*B*d^9*e^2 + 170100*a^2*A*b^8*d^8*e^3 + 453600*a^3*b^7*B*d^8*e^3 - 393120*a^3*A*b^7*d^7*e^4 - 687960*a^4*b^6*B*d^7*e^4 + 582120*a^4*A*b^6*d^6*e^5 + 698544*a^5*b^5*B*d^6*e^5 - 571536*a^5*A*b^5*d^5*e^6 - 476280*a^6*b^4*B*d^5*e^6 + 370440*a^6*A*b^4*d^4*e^7 + 211680*a^7*b^3*B*d^4*e^7 - 151200*a^7*A*b^3*d^3*e^8 - 56700*a^8*b^2*B*d^3*e^8 + 34020*a^8*A*b^2*d^2*e^9 + 7560*a^9*b*B*d^2*e^9 - 2520*a^9*A*b*d*e^10 - 252*a^10*B*d*e^10 - 252*a^10*A*e^11 + 17136*b^10*B*d^10*e*x - 13104*A*b^10*d^9*e^2*x - 131040*a*b^9*B*d^9*e^2*x + 95760*a*A*b^9*d^8*e^3*x + 430920*a^2*b^8*B*d^8*e^3*x - 294840*a^2*A*b^8*d^7*e^4*x - 786240*a^3*b^7*B*d^7*e^4*x + 483840*a^3*A*b^7*d^6*e^5*x + 846720*a^4*b^6*B*d^6*e^5*x - 423360*a^4*A*b^6*d^5*e^6*x - 508032*a^5*b^5*B*d^5*e^6*x + 127008*a^5*A*b^5*d^4*e^7*x + 105840*a^6*b^4*B*d^4*e^7*x + 105840*a^6*A*b^4*d^3*e^8*x + 60480*a^7*b^3*B*d^3*e^8*x - 120960*a^7*A*b^3*d^2*e^9*x - 45360*a^8*b^2*B*d^2*e^9*x + 45360*a^8*A*b^2*d*e^10*x + 10080*a^9*b*B*d*e^10*x - 5040*a^9*A*b*e^11*x - 504*a^10*B*e^11*x + 36288*b^10*B*d^9*e^2*x^2 - 29232*A*b^10*d^8*e^3*x^2 - 292320*a*b^9*B*d^8*e^3*x^2 + 229320*a*A*b^9*d^7*e^4*x^2 + 1031940*a^2*b^8*B*d^7*e^4*x^2 - 782460*a^2*A*b^8*d^6*e^5*x^2 - 2086560*a^3*b^7*B*d^6*e^5*x^2 + 1512000*a^3*A*b^7*d^5*e^6*x^2 + 2646000*a^4*b^6*B*d^5*e^6*x^2 - 1799280*a^4*A*b^6*d^4*e^7*x^2 - 2159136*a^5*b^5*B*d^4*e^7*x^2 + 1333584*a^5*A*b^5*d^3*e^8*x^2 + 1111320*a^6*b^4*B*d^3*e^8*x^2 - 582120*a^6*A*b^4*d^2*e^9*x^2 - 332640*a^7*b^3*B*d^2*e^9*x^2 + 120960*a^7*A*b^3*d*e^10*x^2 + 45360*a^8*b^2*B*d*e^10*x^2 + 9240*b^10*B*d^8*e^3*x^3 - 7560*A*b^10*d^7*e^4*x^3 - 75600*a*b^9*B*d^7*e^4*x^3 + 60480*a*A*b^9*d^6*e^5*x^3 + 272160*a^2*b^8*B*d^6*e^5*x^3 - 211680*a^2*A*b^8*d^5*e^6*x^3 - 564480*a^3*b^7*B*d^5*e^6*x^3 + 423360*a^3*A*b^7*d^4*e^7*x^3 + 740880*a^4*b^6*B*d^4*e^7*x^3 - 529200*a^4*A*b^6*d^3*e^8*x^3 - 635040*a^5*b^5*B*d^3*e^8*x^3 + 423360*a^5*A*b^5*d^2*e^9*x^3 + 352800*a^6*b^4*B*d^2*e^9*x^3 - 211680*a^6*A*b^4*d*e^10*x^3 - 120960*a^7*b^3*B*d*e^10*x^3 + 60480*a^7*A*b^3*e^11*x^3 + 22680*a^8*b^2*B*e^11*x^3 - 2310*b^10*B*d^7*e^4*x^4 + 1890*A*b^10*d^6*e^5*x^4 + 18900*a*b^9*B*d^6*e^5*x^4 - 15120*a*A*b^9*d^5*e^6*x^4 - 68040*a^2*b^8*B*d^5*e^6*x^4 + 52920*a^2*A*b^8*d^4*e^7*x^4 + 141120*a^3*b^7*B*d^4*e^7*x^4 - 105840*a^3*A*b^7*d^3*e^8*x^4 - 185220*a^4*b^6*B*d^3*e^8*x^4 + 132300*a^4*A*b^6*d^2*e^9*x^4 + 158760*a^5*b^5*B*d^2*e^9*x^4 - 105840*a^5*A*b^5*d*e^10*x^4 - 88200*a^6*b^4*B*d*e^10*x^4 + 52920*a^6*A*b^4*e^11*x^4 + 30240*a^7*b^3*B*e^11*x^4 + 924*b^10*B*d^6*e^5*x^5 - 756*A*b^10*d^5*e^6*x^5 - 7560*a*b^9*B*d^5*e^6*x^5 + 6048*a*A*b^9*d^4*e^7*x^5 + 27216*a^2*b^8*B*d^4*e^7*x^5 - 21168*a^2*A*b^8*d^3*e^8*x^5 - 56448*a^3*b^7*B*d^3*e^8*x^5 + 42336*a^3*A*b^7*d^2*e^9*x^5 + 74088*a^4*b^6*B*d^2*e^9*x^5 - 52920*a^4*A*b^6*d*e^10*x^5 - 63504*a^5*b^5*B*d*e^10*x^5 + 42336*a^5*A*b^5*e^11*x^5 + 35280*a^6*b^4*B*e^11*x^5 - 462*b^10*B*d^5*e^6*x^6 + 378*A*b^10*d^4*e^7*x^6 + 3780*a*b^9*B*d^4*e^7*x^6 - 3024*a*A*b^9*d^3*e^8*x^6 - 13608*a^2*b^8*B*d^3*e^8*x^6 + 10584*a^2*A*b^8*d^2*e^9*x^6 + 28224*a^3*b^7*B*d^2*e^9*x^6 - 21168*a^3*A*b^7*d*e^10*x^6 - 37044*a^4*b^6*B*d*e^10*x^6 + 26460*a^4*A*b^6*e^11*x^6 + 31752*a^5*b^5*B*e^11*x^6 + 264*b^10*B*d^4*e^7*x^7 - 216*A*b^10*d^3*e^8*x^7 - 2160*a*b^9*B*d^3*e^8*x^7 + 1728*a*A*b^9*d^2*e^9*x^7 + 7776*a^2*b^8*B*d^2*e^9*x^7 - 6048*a^2*A*b^8*d*e^10*x^7 - 16128*a^3*b^7*B*d*e^10*x^7 + 12096*a^3*A*b^7*e^11*x^7 + 21168*a^4*b^6*B*e^11*x^7 - 165*b^10*B*d^3*e^8*x^8 + 135*A*b^10*d^2*e^9*x^8 + 1350*a*b^9*B*d^2*e^9*x^8 - 1080*a*A*b^9*d*e^10*x^8 - 4860*a^2*b^8*B*d*e^10*x^8 + 3780*a^2*A*b^8*e^11*x^8 + 10080*a^3*b^7*B*e^11*x^8 + 110*b^10*B*d^2*e^9*x^9 - 90*A*b^10*d*e^10*x^9 - 900*a*b^9*B*d*e^10*x^9 + 720*a*A*b^9*e^11*x^9 + 3240*a^2*b^8*B*e^11*x^9 - 77*b^10*B*d*e^10*x^10 + 63*A*b^10*e^11*x^10 + 630*a*b^9*B*e^11*x^10 + 56*b^10*B*e^11*x^11)/(504*e^12*(d + e*x)^2) - (5*(11*b^10*B*d^9 - 9*A*b^10*d^8*e - 90*a*b^9*B*d^8*e + 72*a*A*b^9*d^7*e^2 + 324*a^2*b^8*B*d^7*e^2 - 252*a^2*A*b^8*d^6*e^3 - 672*a^3*b^7*B*d^6*e^3 + 504*a^3*A*b^7*d^5*e^4 + 882*a^4*b^6*B*d^5*e^4 - 630*a^4*A*b^6*d^4*e^5 - 756*a^5*b^5*B*d^4*e^5 + 504*a^5*A*b^5*d^3*e^6 + 420*a^6*b^4*B*d^3*e^6 - 252*a^6*A*b^4*d^2*e^7 - 144*a^7*b^3*B*d^2*e^7 + 72*a^7*A*b^3*d*e^8 + 27*a^8*b^2*B*d*e^8 - 9*a^8*A*b^2*e^9 - 2*a^9*b*B*e^9)*Log[d + e*x])/e^12","B",1
1092,1,2445,445,1.0812713,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^4} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^4,x]","\text{Result too large to show}","-\frac{b^9 (d+e x)^7 (-10 a B e-A b e+11 b B d)}{7 e^{12}}+\frac{5 b^8 (d+e x)^6 (b d-a e) (-9 a B e-2 A b e+11 b B d)}{6 e^{12}}-\frac{3 b^7 (d+e x)^5 (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{e^{12}}+\frac{15 b^6 (d+e x)^4 (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{2 e^{12}}-\frac{14 b^5 (d+e x)^3 (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{e^{12}}+\frac{21 b^4 (d+e x)^2 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{e^{12}}-\frac{30 b^3 x (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{e^{11}}+\frac{15 b^2 (b d-a e)^7 \log (d+e x) (-3 a B e-8 A b e+11 b B d)}{e^{12}}+\frac{5 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{e^{12} (d+e x)}-\frac{(b d-a e)^9 (-a B e-10 A b e+11 b B d)}{2 e^{12} (d+e x)^2}+\frac{(b d-a e)^{10} (B d-A e)}{3 e^{12} (d+e x)^3}+\frac{b^{10} B (d+e x)^8}{8 e^{12}}",1,"(8372*b^10*B*d^11 - 6776*A*b^10*d^10*e - 67760*a*b^9*B*d^10*e + 53480*a*A*b^9*d^9*e^2 + 240660*a^2*b^8*B*d^9*e^2 - 183960*a^2*A*b^8*d^8*e^3 - 490560*a^3*b^7*B*d^8*e^3 + 359520*a^3*A*b^7*d^7*e^4 + 629160*a^4*b^6*B*d^7*e^4 - 435120*a^4*A*b^6*d^6*e^5 - 522144*a^5*b^5*B*d^6*e^5 + 331632*a^5*A*b^5*d^5*e^6 + 276360*a^6*b^4*B*d^5*e^6 - 152880*a^6*A*b^4*d^4*e^7 - 87360*a^7*b^3*B*d^4*e^7 + 36960*a^7*A*b^3*d^3*e^8 + 13860*a^8*b^2*B*d^3*e^8 - 2520*a^8*A*b^2*d^2*e^9 - 560*a^9*b*B*d^2*e^9 - 280*a^9*A*b*d*e^10 - 28*a^10*B*d*e^10 - 56*a^10*A*e^11 - 2604*b^10*B*d^10*e*x - 168*A*b^10*d^9*e^2*x - 1680*a*b^9*B*d^9*e^2*x + 19320*a*A*b^9*d^8*e^3*x + 86940*a^2*b^8*B*d^8*e^3*x - 128520*a^2*A*b^8*d^7*e^4*x - 342720*a^3*b^7*B*d^7*e^4*x + 372960*a^3*A*b^7*d^6*e^5*x + 652680*a^4*b^6*B*d^6*e^5*x - 599760*a^4*A*b^6*d^5*e^6*x - 719712*a^5*b^5*B*d^5*e^6*x + 571536*a^5*A*b^5*d^4*e^7*x + 476280*a^6*b^4*B*d^4*e^7*x - 317520*a^6*A*b^4*d^3*e^8*x - 181440*a^7*b^3*B*d^3*e^8*x + 90720*a^7*A*b^3*d^2*e^9*x + 34020*a^8*b^2*B*d^2*e^9*x - 7560*a^8*A*b^2*d*e^10*x - 1680*a^9*b*B*d*e^10*x - 840*a^9*A*b*e^11*x - 84*a^10*B*e^11*x - 44184*b^10*B*d^9*e^2*x^2 + 30072*A*b^10*d^8*e^3*x^2 + 300720*a*b^9*B*d^8*e^3*x^2 - 192360*a*A*b^9*d^7*e^4*x^2 - 865620*a^2*b^8*B*d^7*e^4*x^2 + 506520*a^2*A*b^8*d^6*e^5*x^2 + 1350720*a^3*b^7*B*d^6*e^5*x^2 - 685440*a^3*A*b^7*d^5*e^6*x^2 - 1199520*a^4*b^6*B*d^5*e^6*x^2 + 458640*a^4*A*b^6*d^4*e^7*x^2 + 550368*a^5*b^5*B*d^4*e^7*x^2 - 63504*a^5*A*b^5*d^3*e^8*x^2 - 52920*a^6*b^4*B*d^3*e^8*x^2 - 105840*a^6*A*b^4*d^2*e^9*x^2 - 60480*a^7*b^3*B*d^2*e^9*x^2 + 60480*a^7*A*b^3*d*e^10*x^2 + 22680*a^8*b^2*B*d*e^10*x^2 - 7560*a^8*A*b^2*e^11*x^2 - 1680*a^9*b*B*e^11*x^2 - 42448*b^10*B*d^8*e^3*x^3 + 30184*A*b^10*d^7*e^4*x^3 + 301840*a*b^9*B*d^7*e^4*x^3 - 205240*a*A*b^9*d^6*e^5*x^3 - 923580*a^2*b^8*B*d^6*e^5*x^3 + 592200*a^2*A*b^8*d^5*e^6*x^3 + 1579200*a^3*b^7*B*d^5*e^6*x^3 - 934080*a^3*A*b^7*d^4*e^7*x^3 - 1634640*a^4*b^6*B*d^4*e^7*x^3 + 858480*a^4*A*b^6*d^3*e^8*x^3 + 1030176*a^5*b^5*B*d^3*e^8*x^3 - 444528*a^5*A*b^5*d^2*e^9*x^3 - 370440*a^6*b^4*B*d^2*e^9*x^3 + 105840*a^6*A*b^4*d*e^10*x^3 + 60480*a^7*b^3*B*d*e^10*x^3 - 6930*b^10*B*d^7*e^4*x^4 + 5040*A*b^10*d^6*e^5*x^4 + 50400*a*b^9*B*d^6*e^5*x^4 - 35280*a*A*b^9*d^5*e^6*x^4 - 158760*a^2*b^8*B*d^5*e^6*x^4 + 105840*a^2*A*b^8*d^4*e^7*x^4 + 282240*a^3*b^7*B*d^4*e^7*x^4 - 176400*a^3*A*b^7*d^3*e^8*x^4 - 308700*a^4*b^6*B*d^3*e^8*x^4 + 176400*a^4*A*b^6*d^2*e^9*x^4 + 211680*a^5*b^5*B*d^2*e^9*x^4 - 105840*a^5*A*b^5*d*e^10*x^4 - 88200*a^6*b^4*B*d*e^10*x^4 + 35280*a^6*A*b^4*e^11*x^4 + 20160*a^7*b^3*B*e^11*x^4 + 1386*b^10*B*d^6*e^5*x^5 - 1008*A*b^10*d^5*e^6*x^5 - 10080*a*b^9*B*d^5*e^6*x^5 + 7056*a*A*b^9*d^4*e^7*x^5 + 31752*a^2*b^8*B*d^4*e^7*x^5 - 21168*a^2*A*b^8*d^3*e^8*x^5 - 56448*a^3*b^7*B*d^3*e^8*x^5 + 35280*a^3*A*b^7*d^2*e^9*x^5 + 61740*a^4*b^6*B*d^2*e^9*x^5 - 35280*a^4*A*b^6*d*e^10*x^5 - 42336*a^5*b^5*B*d*e^10*x^5 + 21168*a^5*A*b^5*e^11*x^5 + 17640*a^6*b^4*B*e^11*x^5 - 462*b^10*B*d^5*e^6*x^6 + 336*A*b^10*d^4*e^7*x^6 + 3360*a*b^9*B*d^4*e^7*x^6 - 2352*a*A*b^9*d^3*e^8*x^6 - 10584*a^2*b^8*B*d^3*e^8*x^6 + 7056*a^2*A*b^8*d^2*e^9*x^6 + 18816*a^3*b^7*B*d^2*e^9*x^6 - 11760*a^3*A*b^7*d*e^10*x^6 - 20580*a^4*b^6*B*d*e^10*x^6 + 11760*a^4*A*b^6*e^11*x^6 + 14112*a^5*b^5*B*e^11*x^6 + 198*b^10*B*d^4*e^7*x^7 - 144*A*b^10*d^3*e^8*x^7 - 1440*a*b^9*B*d^3*e^8*x^7 + 1008*a*A*b^9*d^2*e^9*x^7 + 4536*a^2*b^8*B*d^2*e^9*x^7 - 3024*a^2*A*b^8*d*e^10*x^7 - 8064*a^3*b^7*B*d*e^10*x^7 + 5040*a^3*A*b^7*e^11*x^7 + 8820*a^4*b^6*B*e^11*x^7 - 99*b^10*B*d^3*e^8*x^8 + 72*A*b^10*d^2*e^9*x^8 + 720*a*b^9*B*d^2*e^9*x^8 - 504*a*A*b^9*d*e^10*x^8 - 2268*a^2*b^8*B*d*e^10*x^8 + 1512*a^2*A*b^8*e^11*x^8 + 4032*a^3*b^7*B*e^11*x^8 + 55*b^10*B*d^2*e^9*x^9 - 40*A*b^10*d*e^10*x^9 - 400*a*b^9*B*d*e^10*x^9 + 280*a*A*b^9*e^11*x^9 + 1260*a^2*b^8*B*e^11*x^9 - 33*b^10*B*d*e^10*x^10 + 24*A*b^10*e^11*x^10 + 240*a*b^9*B*e^11*x^10 + 21*b^10*B*e^11*x^11)/(168*e^12*(d + e*x)^3) + (15*(11*b^10*B*d^8 - 8*A*b^10*d^7*e - 80*a*b^9*B*d^7*e + 56*a*A*b^9*d^6*e^2 + 252*a^2*b^8*B*d^6*e^2 - 168*a^2*A*b^8*d^5*e^3 - 448*a^3*b^7*B*d^5*e^3 + 280*a^3*A*b^7*d^4*e^4 + 490*a^4*b^6*B*d^4*e^4 - 280*a^4*A*b^6*d^3*e^5 - 336*a^5*b^5*B*d^3*e^5 + 168*a^5*A*b^5*d^2*e^6 + 140*a^6*b^4*B*d^2*e^6 - 56*a^6*A*b^4*d*e^7 - 32*a^7*b^3*B*d*e^7 + 8*a^7*A*b^3*e^8 + 3*a^8*b^2*B*e^8)*Log[d + e*x])/e^12","B",1
1093,1,2415,444,1.0387213,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^5} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^5,x]","\text{Result too large to show}","-\frac{b^9 (d+e x)^6 (-10 a B e-A b e+11 b B d)}{6 e^{12}}+\frac{b^8 (d+e x)^5 (b d-a e) (-9 a B e-2 A b e+11 b B d)}{e^{12}}-\frac{15 b^7 (d+e x)^4 (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{4 e^{12}}+\frac{10 b^6 (d+e x)^3 (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{e^{12}}-\frac{21 b^5 (d+e x)^2 (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{e^{12}}+\frac{42 b^4 x (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{e^{11}}-\frac{30 b^3 (b d-a e)^6 \log (d+e x) (-4 a B e-7 A b e+11 b B d)}{e^{12}}-\frac{15 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{e^{12} (d+e x)}+\frac{5 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{2 e^{12} (d+e x)^2}-\frac{(b d-a e)^9 (-a B e-10 A b e+11 b B d)}{3 e^{12} (d+e x)^3}+\frac{(b d-a e)^{10} (B d-A e)}{4 e^{12} (d+e x)^4}+\frac{b^{10} B (d+e x)^7}{7 e^{12}}",1,"(-11837*b^10*B*d^11 + 8449*A*b^10*d^10*e + 84490*a*b^9*B*d^10*e - 57750*a*A*b^9*d^9*e^2 - 259875*a^2*b^8*B*d^9*e^2 + 167895*a^2*A*b^8*d^8*e^3 + 447720*a^3*b^7*B*d^8*e^3 - 267960*a^3*A*b^7*d^7*e^4 - 468930*a^4*b^6*B*d^7*e^4 + 251370*a^4*A*b^6*d^6*e^5 + 301644*a^5*b^5*B*d^6*e^5 - 135828*a^5*A*b^5*d^5*e^6 - 113190*a^6*b^4*B*d^5*e^6 + 36750*a^6*A*b^4*d^4*e^7 + 21000*a^7*b^3*B*d^4*e^7 - 2520*a^7*A*b^3*d^3*e^8 - 945*a^8*b^2*B*d^3*e^8 - 315*a^8*A*b^2*d^2*e^9 - 70*a^9*b*B*d^2*e^9 - 70*a^9*A*b*d*e^10 - 7*a^10*B*d*e^10 - 21*a^10*A*e^11 - 19628*b^10*B*d^10*e*x + 16156*A*b^10*d^9*e^2*x + 161560*a*b^9*B*d^9*e^2*x - 125160*a*A*b^9*d^8*e^3*x - 563220*a^2*b^8*B*d^8*e^3*x + 406980*a^2*A*b^8*d^7*e^4*x + 1085280*a^3*b^7*B*d^7*e^4*x - 719040*a^3*A*b^7*d^6*e^5*x - 1258320*a^4*b^6*B*d^6*e^5*x + 740880*a^4*A*b^6*d^5*e^6*x + 889056*a^5*b^5*B*d^5*e^6*x - 437472*a^5*A*b^5*d^4*e^7*x - 364560*a^6*b^4*B*d^4*e^7*x + 129360*a^6*A*b^4*d^3*e^8*x + 73920*a^7*b^3*B*d^3*e^8*x - 10080*a^7*A*b^3*d^2*e^9*x - 3780*a^8*b^2*B*d^2*e^9*x - 1260*a^8*A*b^2*d*e^10*x - 280*a^9*b*B*d*e^10*x - 280*a^9*A*b*e^11*x - 28*a^10*B*e^11*x + 25998*b^10*B*d^9*e^2*x^2 - 11046*A*b^10*d^8*e^3*x^2 - 110460*a*b^9*B*d^8*e^3*x^2 + 23940*a*A*b^9*d^7*e^4*x^2 + 107730*a^2*b^8*B*d^7*e^4*x^2 + 81270*a^2*A*b^8*d^6*e^5*x^2 + 216720*a^3*b^7*B*d^6*e^5*x^2 - 372960*a^3*A*b^7*d^5*e^6*x^2 - 652680*a^4*b^6*B*d^5*e^6*x^2 + 582120*a^4*A*b^6*d^4*e^7*x^2 + 698544*a^5*b^5*B*d^4*e^7*x^2 - 444528*a^5*A*b^5*d^3*e^8*x^2 - 370440*a^6*b^4*B*d^3*e^8*x^2 + 158760*a^6*A*b^4*d^2*e^9*x^2 + 90720*a^7*b^3*B*d^2*e^9*x^2 - 15120*a^7*A*b^3*d*e^10*x^2 - 5670*a^8*b^2*B*d*e^10*x^2 - 1890*a^8*A*b^2*e^11*x^2 - 420*a^9*b*B*e^11*x^2 + 72772*b^10*B*d^8*e^3*x^3 - 42644*A*b^10*d^7*e^4*x^3 - 426440*a*b^9*B*d^7*e^4*x^3 + 227640*a*A*b^9*d^6*e^5*x^3 + 1024380*a^2*b^8*B*d^6*e^5*x^3 - 475020*a^2*A*b^8*d^5*e^6*x^3 - 1266720*a^3*b^7*B*d^5*e^6*x^3 + 456960*a^3*A*b^7*d^4*e^7*x^3 + 799680*a^4*b^6*B*d^4*e^7*x^3 - 141120*a^4*A*b^6*d^3*e^8*x^3 - 169344*a^5*b^5*B*d^3*e^8*x^3 - 84672*a^5*A*b^5*d^2*e^9*x^3 - 70560*a^6*b^4*B*d^2*e^9*x^3 + 70560*a^6*A*b^4*d*e^10*x^3 + 40320*a^7*b^3*B*d*e^10*x^3 - 10080*a^7*A*b^3*e^11*x^3 - 3780*a^8*b^2*B*e^11*x^3 + 45913*b^10*B*d^7*e^4*x^4 - 28301*A*b^10*d^6*e^5*x^4 - 283010*a*b^9*B*d^6*e^5*x^4 + 162750*a*A*b^9*d^5*e^6*x^4 + 732375*a^2*b^8*B*d^5*e^6*x^4 - 383355*a^2*A*b^8*d^4*e^7*x^4 - 1022280*a^3*b^7*B*d^4*e^7*x^4 + 467040*a^3*A*b^7*d^3*e^8*x^4 + 817320*a^4*b^6*B*d^3*e^8*x^4 - 299880*a^4*A*b^6*d^2*e^9*x^4 - 359856*a^5*b^5*B*d^2*e^9*x^4 + 84672*a^5*A*b^5*d*e^10*x^4 + 70560*a^6*b^4*B*d*e^10*x^4 + 5544*b^10*B*d^6*e^5*x^5 - 3528*A*b^10*d^5*e^6*x^5 - 35280*a*b^9*B*d^5*e^6*x^5 + 21168*a*A*b^9*d^4*e^7*x^5 + 95256*a^2*b^8*B*d^4*e^7*x^5 - 52920*a^2*A*b^8*d^3*e^8*x^5 - 141120*a^3*b^7*B*d^3*e^8*x^5 + 70560*a^3*A*b^7*d^2*e^9*x^5 + 123480*a^4*b^6*B*d^2*e^9*x^5 - 52920*a^4*A*b^6*d*e^10*x^5 - 63504*a^5*b^5*B*d*e^10*x^5 + 21168*a^5*A*b^5*e^11*x^5 + 17640*a^6*b^4*B*e^11*x^5 - 924*b^10*B*d^5*e^6*x^6 + 588*A*b^10*d^4*e^7*x^6 + 5880*a*b^9*B*d^4*e^7*x^6 - 3528*a*A*b^9*d^3*e^8*x^6 - 15876*a^2*b^8*B*d^3*e^8*x^6 + 8820*a^2*A*b^8*d^2*e^9*x^6 + 23520*a^3*b^7*B*d^2*e^9*x^6 - 11760*a^3*A*b^7*d*e^10*x^6 - 20580*a^4*b^6*B*d*e^10*x^6 + 8820*a^4*A*b^6*e^11*x^6 + 10584*a^5*b^5*B*e^11*x^6 + 264*b^10*B*d^4*e^7*x^7 - 168*A*b^10*d^3*e^8*x^7 - 1680*a*b^9*B*d^3*e^8*x^7 + 1008*a*A*b^9*d^2*e^9*x^7 + 4536*a^2*b^8*B*d^2*e^9*x^7 - 2520*a^2*A*b^8*d*e^10*x^7 - 6720*a^3*b^7*B*d*e^10*x^7 + 3360*a^3*A*b^7*e^11*x^7 + 5880*a^4*b^6*B*e^11*x^7 - 99*b^10*B*d^3*e^8*x^8 + 63*A*b^10*d^2*e^9*x^8 + 630*a*b^9*B*d^2*e^9*x^8 - 378*a*A*b^9*d*e^10*x^8 - 1701*a^2*b^8*B*d*e^10*x^8 + 945*a^2*A*b^8*e^11*x^8 + 2520*a^3*b^7*B*e^11*x^8 + 44*b^10*B*d^2*e^9*x^9 - 28*A*b^10*d*e^10*x^9 - 280*a*b^9*B*d*e^10*x^9 + 168*a*A*b^9*e^11*x^9 + 756*a^2*b^8*B*e^11*x^9 - 22*b^10*B*d*e^10*x^10 + 14*A*b^10*e^11*x^10 + 140*a*b^9*B*e^11*x^10 + 12*b^10*B*e^11*x^11)/(84*e^12*(d + e*x)^4) - (30*(11*b^10*B*d^7 - 7*A*b^10*d^6*e - 70*a*b^9*B*d^6*e + 42*a*A*b^9*d^5*e^2 + 189*a^2*b^8*B*d^5*e^2 - 105*a^2*A*b^8*d^4*e^3 - 280*a^3*b^7*B*d^4*e^3 + 140*a^3*A*b^7*d^3*e^4 + 245*a^4*b^6*B*d^3*e^4 - 105*a^4*A*b^6*d^2*e^5 - 126*a^5*b^5*B*d^2*e^5 + 42*a^5*A*b^5*d*e^6 + 35*a^6*b^4*B*d*e^6 - 7*a^6*A*b^4*e^7 - 4*a^7*b^3*B*e^7)*Log[d + e*x])/e^12","B",1
1094,1,2385,447,1.0518507,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^6} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^6,x]","\text{Result too large to show}","-\frac{b^9 (d+e x)^5 (-10 a B e-A b e+11 b B d)}{5 e^{12}}+\frac{5 b^8 (d+e x)^4 (b d-a e) (-9 a B e-2 A b e+11 b B d)}{4 e^{12}}-\frac{5 b^7 (d+e x)^3 (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{e^{12}}+\frac{15 b^6 (d+e x)^2 (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{e^{12}}-\frac{42 b^5 x (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{e^{11}}+\frac{42 b^4 (b d-a e)^5 \log (d+e x) (-5 a B e-6 A b e+11 b B d)}{e^{12}}+\frac{30 b^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{e^{12} (d+e x)}-\frac{15 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{2 e^{12} (d+e x)^2}+\frac{5 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{3 e^{12} (d+e x)^3}-\frac{(b d-a e)^9 (-a B e-10 A b e+11 b B d)}{4 e^{12} (d+e x)^4}+\frac{(b d-a e)^{10} (B d-A e)}{5 e^{12} (d+e x)^5}+\frac{b^{10} B (d+e x)^6}{6 e^{12}}",1,"(15797*b^10*B*d^11 - 9762*A*b^10*d^10*e - 97620*a*b^9*B*d^10*e + 56370*a*A*b^9*d^9*e^2 + 253665*a^2*b^8*B*d^9*e^2 - 133740*a^2*A*b^8*d^8*e^3 - 356640*a^3*b^7*B*d^8*e^3 + 165240*a^3*A*b^7*d^7*e^4 + 289170*a^4*b^6*B*d^7*e^4 - 109620*a^4*A*b^6*d^6*e^5 - 131544*a^5*b^5*B*d^6*e^5 + 34524*a^5*A*b^5*d^5*e^6 + 28770*a^6*b^4*B*d^5*e^6 - 2520*a^6*A*b^4*d^4*e^7 - 1440*a^7*b^3*B*d^4*e^7 - 360*a^7*A*b^3*d^3*e^8 - 135*a^8*b^2*B*d^3*e^8 - 90*a^8*A*b^2*d^2*e^9 - 20*a^9*b*B*d^2*e^9 - 30*a^9*A*b*d*e^10 - 3*a^10*B*d*e^10 - 12*a^10*A*e^11 + 51265*b^10*B*d^10*e*x - 33690*A*b^10*d^9*e^2*x - 336900*a*b^9*B*d^9*e^2*x + 206250*a*A*b^9*d^8*e^3*x + 928125*a^2*b^8*B*d^8*e^3*x - 517500*a^2*A*b^8*d^7*e^4*x - 1380000*a^3*b^7*B*d^7*e^4*x + 675000*a^3*A*b^7*d^6*e^5*x + 1181250*a^4*b^6*B*d^6*e^5*x - 472500*a^4*A*b^6*d^5*e^6*x - 567000*a^5*b^5*B*d^5*e^6*x + 157500*a^5*A*b^5*d^4*e^7*x + 131250*a^6*b^4*B*d^4*e^7*x - 12600*a^6*A*b^4*d^3*e^8*x - 7200*a^7*b^3*B*d^3*e^8*x - 1800*a^7*A*b^3*d^2*e^9*x - 675*a^8*b^2*B*d^2*e^9*x - 450*a^8*A*b^2*d*e^10*x - 100*a^9*b*B*d*e^10*x - 150*a^9*A*b*e^11*x - 15*a^10*B*e^11*x + 33230*b^10*B*d^9*e^2*x^2 - 29580*A*b^10*d^8*e^3*x^2 - 295800*a*b^9*B*d^8*e^3*x^2 + 223500*a*A*b^9*d^7*e^4*x^2 + 1005750*a^2*b^8*B*d^7*e^4*x^2 - 657000*a^2*A*b^8*d^6*e^5*x^2 - 1752000*a^3*b^7*B*d^6*e^5*x^2 + 972000*a^3*A*b^7*d^5*e^6*x^2 + 1701000*a^4*b^6*B*d^5*e^6*x^2 - 756000*a^4*A*b^6*d^4*e^7*x^2 - 907200*a^5*b^5*B*d^4*e^7*x^2 + 277200*a^5*A*b^5*d^3*e^8*x^2 + 231000*a^6*b^4*B*d^3*e^8*x^2 - 25200*a^6*A*b^4*d^2*e^9*x^2 - 14400*a^7*b^3*B*d^2*e^9*x^2 - 3600*a^7*A*b^3*d*e^10*x^2 - 1350*a^8*b^2*B*d*e^10*x^2 - 900*a^8*A*b^2*e^11*x^2 - 200*a^9*b*B*e^11*x^2 - 59170*b^10*B*d^8*e^3*x^3 + 20820*A*b^10*d^7*e^4*x^3 + 208200*a*b^9*B*d^7*e^4*x^3 - 28500*a*A*b^9*d^6*e^5*x^3 - 128250*a^2*b^8*B*d^6*e^5*x^3 - 153000*a^2*A*b^8*d^5*e^6*x^3 - 408000*a^3*b^7*B*d^5*e^6*x^3 + 468000*a^3*A*b^7*d^4*e^7*x^3 + 819000*a^4*b^6*B*d^4*e^7*x^3 - 504000*a^4*A*b^6*d^3*e^8*x^3 - 604800*a^5*b^5*B*d^3*e^8*x^3 + 226800*a^5*A*b^5*d^2*e^9*x^3 + 189000*a^6*b^4*B*d^2*e^9*x^3 - 25200*a^6*A*b^4*d*e^10*x^3 - 14400*a^7*b^3*B*d*e^10*x^3 - 3600*a^7*A*b^3*e^11*x^3 - 1350*a^8*b^2*B*e^11*x^3 - 98885*b^10*B*d^7*e^4*x^4 + 48210*A*b^10*d^6*e^5*x^4 + 482100*a*b^9*B*d^6*e^5*x^4 - 203250*a*A*b^9*d^5*e^6*x^4 - 914625*a^2*b^8*B*d^5*e^6*x^4 + 301500*a^2*A*b^8*d^4*e^7*x^4 + 804000*a^3*b^7*B*d^4*e^7*x^4 - 144000*a^3*A*b^7*d^3*e^8*x^4 - 252000*a^4*b^6*B*d^3*e^8*x^4 - 63000*a^4*A*b^6*d^2*e^9*x^4 - 75600*a^5*b^5*B*d^2*e^9*x^4 + 75600*a^5*A*b^5*d*e^10*x^4 + 63000*a^6*b^4*B*d*e^10*x^4 - 12600*a^6*A*b^4*e^11*x^4 - 7200*a^7*b^3*B*e^11*x^4 - 47497*b^10*B*d^6*e^5*x^5 + 24762*A*b^10*d^5*e^6*x^5 + 247620*a*b^9*B*d^5*e^6*x^5 - 116250*a*A*b^9*d^4*e^7*x^5 - 523125*a^2*b^8*B*d^4*e^7*x^5 + 211500*a^2*A*b^8*d^3*e^8*x^5 + 564000*a^3*b^7*B*d^3*e^8*x^5 - 180000*a^3*A*b^7*d^2*e^9*x^5 - 315000*a^4*b^6*B*d^2*e^9*x^5 + 63000*a^4*A*b^6*d*e^10*x^5 + 75600*a^5*b^5*B*d*e^10*x^5 - 4620*b^10*B*d^5*e^6*x^6 + 2520*A*b^10*d^4*e^7*x^6 + 25200*a*b^9*B*d^4*e^7*x^6 - 12600*a*A*b^9*d^3*e^8*x^6 - 56700*a^2*b^8*B*d^3*e^8*x^6 + 25200*a^2*A*b^8*d^2*e^9*x^6 + 67200*a^3*b^7*B*d^2*e^9*x^6 - 25200*a^3*A*b^7*d*e^10*x^6 - 44100*a^4*b^6*B*d*e^10*x^6 + 12600*a^4*A*b^6*e^11*x^6 + 15120*a^5*b^5*B*e^11*x^6 + 660*b^10*B*d^4*e^7*x^7 - 360*A*b^10*d^3*e^8*x^7 - 3600*a*b^9*B*d^3*e^8*x^7 + 1800*a*A*b^9*d^2*e^9*x^7 + 8100*a^2*b^8*B*d^2*e^9*x^7 - 3600*a^2*A*b^8*d*e^10*x^7 - 9600*a^3*b^7*B*d*e^10*x^7 + 3600*a^3*A*b^7*e^11*x^7 + 6300*a^4*b^6*B*e^11*x^7 - 165*b^10*B*d^3*e^8*x^8 + 90*A*b^10*d^2*e^9*x^8 + 900*a*b^9*B*d^2*e^9*x^8 - 450*a*A*b^9*d*e^10*x^8 - 2025*a^2*b^8*B*d*e^10*x^8 + 900*a^2*A*b^8*e^11*x^8 + 2400*a^3*b^7*B*e^11*x^8 + 55*b^10*B*d^2*e^9*x^9 - 30*A*b^10*d*e^10*x^9 - 300*a*b^9*B*d*e^10*x^9 + 150*a*A*b^9*e^11*x^9 + 675*a^2*b^8*B*e^11*x^9 - 22*b^10*B*d*e^10*x^10 + 12*A*b^10*e^11*x^10 + 120*a*b^9*B*e^11*x^10 + 10*b^10*B*e^11*x^11)/(60*e^12*(d + e*x)^5) + (42*(11*b^10*B*d^6 - 6*A*b^10*d^5*e - 60*a*b^9*B*d^5*e + 30*a*A*b^9*d^4*e^2 + 135*a^2*b^8*B*d^4*e^2 - 60*a^2*A*b^8*d^3*e^3 - 160*a^3*b^7*B*d^3*e^3 + 60*a^3*A*b^7*d^2*e^4 + 105*a^4*b^6*B*d^2*e^4 - 30*a^4*A*b^6*d*e^5 - 36*a^5*b^5*B*d*e^5 + 6*a^5*A*b^5*e^6 + 5*a^6*b^4*B*e^6)*Log[d + e*x])/e^12","B",1
1095,1,2355,447,1.1008151,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^7} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^7,x]","\text{Result too large to show}","-\frac{b^9 (d+e x)^4 (-10 a B e-A b e+11 b B d)}{4 e^{12}}+\frac{5 b^8 (d+e x)^3 (b d-a e) (-9 a B e-2 A b e+11 b B d)}{3 e^{12}}-\frac{15 b^7 (d+e x)^2 (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{2 e^{12}}+\frac{30 b^6 x (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{e^{11}}-\frac{42 b^5 (b d-a e)^4 \log (d+e x) (-6 a B e-5 A b e+11 b B d)}{e^{12}}-\frac{42 b^4 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{e^{12} (d+e x)}+\frac{15 b^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{e^{12} (d+e x)^2}-\frac{5 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{e^{12} (d+e x)^3}+\frac{5 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{4 e^{12} (d+e x)^4}-\frac{(b d-a e)^9 (-a B e-10 A b e+11 b B d)}{5 e^{12} (d+e x)^5}+\frac{(b d-a e)^{10} (B d-A e)}{6 e^{12} (d+e x)^6}+\frac{b^{10} B (d+e x)^5}{5 e^{12}}",1,"(-20417*b^10*B*d^11 + 10655*A*b^10*d^10*e + 106550*a*b^9*B*d^10*e - 50180*a*A*b^9*d^9*e^2 - 225810*a^2*b^8*B*d^9*e^2 + 92070*a^2*A*b^8*d^8*e^3 + 245520*a^3*b^7*B*d^8*e^3 - 80280*a^3*A*b^7*d^7*e^4 - 140490*a^4*b^6*B*d^7*e^4 + 30870*a^4*A*b^6*d^6*e^5 + 37044*a^5*b^5*B*d^6*e^5 - 2520*a^5*A*b^5*d^5*e^6 - 2100*a^6*b^4*B*d^5*e^6 - 420*a^6*A*b^4*d^4*e^7 - 240*a^7*b^3*B*d^4*e^7 - 120*a^7*A*b^3*d^3*e^8 - 45*a^8*b^2*B*d^3*e^8 - 45*a^8*A*b^2*d^2*e^9 - 10*a^9*b*B*d^2*e^9 - 20*a^9*A*b*d*e^10 - 2*a^10*B*d*e^10 - 10*a^10*A*e^11 - 94782*b^10*B*d^10*e*x + 51330*A*b^10*d^9*e^2*x + 513300*a*b^9*B*d^9*e^2*x - 250680*a*A*b^9*d^8*e^3*x - 1128060*a^2*b^8*B*d^8*e^3*x + 476820*a^2*A*b^8*d^7*e^4*x + 1271520*a^3*b^7*B*d^7*e^4*x - 431280*a^3*A*b^7*d^6*e^5*x - 754740*a^4*b^6*B*d^6*e^5*x + 172620*a^4*A*b^6*d^5*e^6*x + 207144*a^5*b^5*B*d^5*e^6*x - 15120*a^5*A*b^5*d^4*e^7*x - 12600*a^6*b^4*B*d^4*e^7*x - 2520*a^6*A*b^4*d^3*e^8*x - 1440*a^7*b^3*B*d^3*e^8*x - 720*a^7*A*b^3*d^2*e^9*x - 270*a^8*b^2*B*d^2*e^9*x - 270*a^8*A*b^2*d*e^10*x - 60*a^9*b*B*d*e^10*x - 120*a^9*A*b*e^11*x - 12*a^10*B*e^11*x - 153795*b^10*B*d^9*e^2*x^2 + 90525*A*b^10*d^8*e^3*x^2 + 905250*a*b^9*B*d^8*e^3*x^2 - 475500*a*A*b^9*d^7*e^4*x^2 - 2139750*a^2*b^8*B*d^7*e^4*x^2 + 965250*a^2*A*b^8*d^6*e^5*x^2 + 2574000*a^3*b^7*B*d^6*e^5*x^2 - 927000*a^3*A*b^7*d^5*e^6*x^2 - 1622250*a^4*b^6*B*d^5*e^6*x^2 + 393750*a^4*A*b^6*d^4*e^7*x^2 + 472500*a^5*b^5*B*d^4*e^7*x^2 - 37800*a^5*A*b^5*d^3*e^8*x^2 - 31500*a^6*b^4*B*d^3*e^8*x^2 - 6300*a^6*A*b^4*d^2*e^9*x^2 - 3600*a^7*b^3*B*d^2*e^9*x^2 - 1800*a^7*A*b^3*d*e^10*x^2 - 675*a^8*b^2*B*d*e^10*x^2 - 675*a^8*A*b^2*e^11*x^2 - 150*a^9*b*B*e^11*x^2 - 66460*b^10*B*d^8*e^3*x^3 + 57700*A*b^10*d^7*e^4*x^3 + 577000*a*b^9*B*d^7*e^4*x^3 - 382000*a*A*b^9*d^6*e^5*x^3 - 1719000*a^2*b^8*B*d^6*e^5*x^3 + 909000*a^2*A*b^8*d^5*e^6*x^3 + 2424000*a^3*b^7*B*d^5*e^6*x^3 - 984000*a^3*A*b^7*d^4*e^7*x^3 - 1722000*a^4*b^6*B*d^4*e^7*x^3 + 462000*a^4*A*b^6*d^3*e^8*x^3 + 554400*a^5*b^5*B*d^3*e^8*x^3 - 50400*a^5*A*b^5*d^2*e^9*x^3 - 42000*a^6*b^4*B*d^2*e^9*x^3 - 8400*a^6*A*b^4*d*e^10*x^3 - 4800*a^7*b^3*B*d*e^10*x^3 - 2400*a^7*A*b^3*e^11*x^3 - 900*a^8*b^2*B*e^11*x^3 + 88755*b^10*B*d^7*e^4*x^4 - 19725*A*b^10*d^6*e^5*x^4 - 197250*a*b^9*B*d^6*e^5*x^4 - 34500*a*A*b^9*d^5*e^6*x^4 - 155250*a^2*b^8*B*d^5*e^6*x^4 + 303750*a^2*A*b^8*d^4*e^7*x^4 + 810000*a^3*b^7*B*d^4*e^7*x^4 - 486000*a^3*A*b^7*d^3*e^8*x^4 - 850500*a^4*b^6*B*d^3*e^8*x^4 + 283500*a^4*A*b^6*d^2*e^9*x^4 + 340200*a^5*b^5*B*d^2*e^9*x^4 - 37800*a^5*A*b^5*d*e^10*x^4 - 31500*a^6*b^4*B*d*e^10*x^4 - 6300*a^6*A*b^4*e^11*x^4 - 3600*a^7*b^3*B*e^11*x^4 + 118662*b^10*B*d^6*e^5*x^5 - 45690*A*b^10*d^5*e^6*x^5 - 456900*a*b^9*B*d^5*e^6*x^5 + 137400*a*A*b^9*d^4*e^7*x^5 + 618300*a^2*b^8*B*d^4*e^7*x^5 - 105300*a^2*A*b^8*d^3*e^8*x^5 - 280800*a^3*b^7*B*d^3*e^8*x^5 - 43200*a^3*A*b^7*d^2*e^9*x^5 - 75600*a^4*b^6*B*d^2*e^9*x^5 + 75600*a^4*A*b^6*d*e^10*x^5 + 90720*a^5*b^5*B*d*e^10*x^5 - 15120*a^5*A*b^5*e^11*x^5 - 12600*a^6*b^4*B*e^11*x^5 + 47497*b^10*B*d^5*e^6*x^6 - 20215*A*b^10*d^4*e^7*x^6 - 202150*a*b^9*B*d^4*e^7*x^6 + 73300*a*A*b^9*d^3*e^8*x^6 + 329850*a^2*b^8*B*d^3*e^8*x^6 - 93150*a^2*A*b^8*d^2*e^9*x^6 - 248400*a^3*b^7*B*d^2*e^9*x^6 + 43200*a^3*A*b^7*d*e^10*x^6 + 75600*a^4*b^6*B*d*e^10*x^6 + 3960*b^10*B*d^4*e^7*x^7 - 1800*A*b^10*d^3*e^8*x^7 - 18000*a*b^9*B*d^3*e^8*x^7 + 7200*a*A*b^9*d^2*e^9*x^7 + 32400*a^2*b^8*B*d^2*e^9*x^7 - 10800*a^2*A*b^8*d*e^10*x^7 - 28800*a^3*b^7*B*d*e^10*x^7 + 7200*a^3*A*b^7*e^11*x^7 + 12600*a^4*b^6*B*e^11*x^7 - 495*b^10*B*d^3*e^8*x^8 + 225*A*b^10*d^2*e^9*x^8 + 2250*a*b^9*B*d^2*e^9*x^8 - 900*a*A*b^9*d*e^10*x^8 - 4050*a^2*b^8*B*d*e^10*x^8 + 1350*a^2*A*b^8*e^11*x^8 + 3600*a^3*b^7*B*e^11*x^8 + 110*b^10*B*d^2*e^9*x^9 - 50*A*b^10*d*e^10*x^9 - 500*a*b^9*B*d*e^10*x^9 + 200*a*A*b^9*e^11*x^9 + 900*a^2*b^8*B*e^11*x^9 - 33*b^10*B*d*e^10*x^10 + 15*A*b^10*e^11*x^10 + 150*a*b^9*B*e^11*x^10 + 12*b^10*B*e^11*x^11)/(60*e^12*(d + e*x)^6) - (42*(11*b^10*B*d^5 - 5*A*b^10*d^4*e - 50*a*b^9*B*d^4*e + 20*a*A*b^9*d^3*e^2 + 90*a^2*b^8*B*d^3*e^2 - 30*a^2*A*b^8*d^2*e^3 - 80*a^3*b^7*B*d^2*e^3 + 20*a^3*A*b^7*d*e^4 + 35*a^4*b^6*B*d*e^4 - 5*a^4*A*b^6*e^5 - 6*a^5*b^5*B*e^5)*Log[d + e*x])/e^12","B",1
1096,1,2325,444,1.7138931,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^8} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^8,x]","\text{Result too large to show}","-\frac{b^9 (d+e x)^3 (-10 a B e-A b e+11 b B d)}{3 e^{12}}+\frac{5 b^8 (d+e x)^2 (b d-a e) (-9 a B e-2 A b e+11 b B d)}{2 e^{12}}-\frac{15 b^7 x (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{e^{11}}+\frac{30 b^6 (b d-a e)^3 \log (d+e x) (-7 a B e-4 A b e+11 b B d)}{e^{12}}+\frac{42 b^5 (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{e^{12} (d+e x)}-\frac{21 b^4 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{e^{12} (d+e x)^2}+\frac{10 b^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{e^{12} (d+e x)^3}-\frac{15 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{4 e^{12} (d+e x)^4}+\frac{b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{e^{12} (d+e x)^5}-\frac{(b d-a e)^9 (-a B e-10 A b e+11 b B d)}{6 e^{12} (d+e x)^6}+\frac{(b d-a e)^{10} (B d-A e)}{7 e^{12} (d+e x)^7}+\frac{b^{10} B (d+e x)^4}{4 e^{12}}",1,"(25961*b^10*B*d^11 - 11044*A*b^10*d^10*e - 110440*a*b^9*B*d^10*e + 40188*a*A*b^9*d^9*e^2 + 180846*a^2*b^8*B*d^9*e^2 - 51948*a^2*A*b^8*d^8*e^3 - 138528*a^3*b^7*B*d^8*e^3 + 26136*a^3*A*b^7*d^7*e^4 + 45738*a^4*b^6*B*d^7*e^4 - 2520*a^4*A*b^6*d^6*e^5 - 3024*a^5*b^5*B*d^6*e^5 - 504*a^5*A*b^5*d^5*e^6 - 420*a^6*b^4*B*d^5*e^6 - 168*a^6*A*b^4*d^4*e^7 - 96*a^7*b^3*B*d^4*e^7 - 72*a^7*A*b^3*d^3*e^8 - 27*a^8*b^2*B*d^3*e^8 - 36*a^8*A*b^2*d^2*e^9 - 8*a^9*b*B*d^2*e^9 - 20*a^9*A*b*d*e^10 - 2*a^10*B*d*e^10 - 12*a^10*A*e^11 + 154007*b^10*B*d^10*e*x - 67228*A*b^10*d^9*e^2*x - 672280*a*b^9*B*d^9*e^2*x + 251076*a*A*b^9*d^8*e^3*x + 1129842*a^2*b^8*B*d^8*e^3*x - 333396*a^2*A*b^8*d^7*e^4*x - 889056*a^3*b^7*B*d^7*e^4*x + 172872*a^3*A*b^7*d^6*e^5*x + 302526*a^4*b^6*B*d^6*e^5*x - 17640*a^4*A*b^6*d^5*e^6*x - 21168*a^5*b^5*B*d^5*e^6*x - 3528*a^5*A*b^5*d^4*e^7*x - 2940*a^6*b^4*B*d^4*e^7*x - 1176*a^6*A*b^4*d^3*e^8*x - 672*a^7*b^3*B*d^3*e^8*x - 504*a^7*A*b^3*d^2*e^9*x - 189*a^8*b^2*B*d^2*e^9*x - 252*a^8*A*b^2*d*e^10*x - 56*a^9*b*B*d*e^10*x - 140*a^9*A*b*e^11*x - 14*a^10*B*e^11*x + 365001*b^10*B*d^9*e^2*x^2 - 166404*A*b^10*d^8*e^3*x^2 - 1664040*a*b^9*B*d^8*e^3*x^2 + 647388*a*A*b^9*d^7*e^4*x^2 + 2913246*a^2*b^8*B*d^7*e^4*x^2 - 894348*a^2*A*b^8*d^6*e^5*x^2 - 2384928*a^3*b^7*B*d^6*e^5*x^2 + 483336*a^3*A*b^7*d^5*e^6*x^2 + 845838*a^4*b^6*B*d^5*e^6*x^2 - 52920*a^4*A*b^6*d^4*e^7*x^2 - 63504*a^5*b^5*B*d^4*e^7*x^2 - 10584*a^5*A*b^5*d^3*e^8*x^2 - 8820*a^6*b^4*B*d^3*e^8*x^2 - 3528*a^6*A*b^4*d^2*e^9*x^2 - 2016*a^7*b^3*B*d^2*e^9*x^2 - 1512*a^7*A*b^3*d*e^10*x^2 - 567*a^8*b^2*B*d*e^10*x^2 - 756*a^8*A*b^2*e^11*x^2 - 168*a^9*b*B*e^11*x^2 + 414295*b^10*B*d^8*e^3*x^3 - 206780*A*b^10*d^7*e^4*x^3 - 2067800*a*b^9*B*d^7*e^4*x^3 + 867300*a*A*b^9*d^6*e^5*x^3 + 3902850*a^2*b^8*B*d^6*e^5*x^3 - 1278900*a^2*A*b^8*d^5*e^6*x^3 - 3410400*a^3*b^7*B*d^5*e^6*x^3 + 735000*a^3*A*b^7*d^4*e^7*x^3 + 1286250*a^4*b^6*B*d^4*e^7*x^3 - 88200*a^4*A*b^6*d^3*e^8*x^3 - 105840*a^5*b^5*B*d^3*e^8*x^3 - 17640*a^5*A*b^5*d^2*e^9*x^3 - 14700*a^6*b^4*B*d^2*e^9*x^3 - 5880*a^6*A*b^4*d*e^10*x^3 - 3360*a^7*b^3*B*d*e^10*x^3 - 2520*a^7*A*b^3*e^11*x^3 - 945*a^8*b^2*B*e^11*x^3 + 171745*b^10*B*d^7*e^4*x^4 - 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17640*a^4*A*b^6*e^11*x^6 - 21168*a^5*b^5*B*e^11*x^6 - 45913*b^10*B*d^4*e^7*x^7 + 15092*A*b^10*d^3*e^8*x^7 + 150920*a*b^9*B*d^3*e^8*x^7 - 38220*a*A*b^9*d^2*e^9*x^7 - 171990*a^2*b^8*B*d^2*e^9*x^7 + 26460*a^2*A*b^8*d*e^10*x^7 + 70560*a^3*b^7*B*d*e^10*x^7 - 3465*b^10*B*d^3*e^8*x^8 + 1260*A*b^10*d^2*e^9*x^8 + 12600*a*b^9*B*d^2*e^9*x^8 - 3780*a*A*b^9*d*e^10*x^8 - 17010*a^2*b^8*B*d*e^10*x^8 + 3780*a^2*A*b^8*e^11*x^8 + 10080*a^3*b^7*B*e^11*x^8 + 385*b^10*B*d^2*e^9*x^9 - 140*A*b^10*d*e^10*x^9 - 1400*a*b^9*B*d*e^10*x^9 + 420*a*A*b^9*e^11*x^9 + 1890*a^2*b^8*B*e^11*x^9 - 77*b^10*B*d*e^10*x^10 + 28*A*b^10*e^11*x^10 + 280*a*b^9*B*e^11*x^10 + 21*b^10*B*e^11*x^11)/(84*e^12*(d + e*x)^7) + (30*(11*b^10*B*d^4 - 4*A*b^10*d^3*e - 40*a*b^9*B*d^3*e + 12*a*A*b^9*d^2*e^2 + 54*a^2*b^8*B*d^2*e^2 - 12*a^2*A*b^8*d*e^3 - 32*a^3*b^7*B*d*e^3 + 4*a^3*A*b^7*e^4 + 7*a^4*b^6*B*e^4)*Log[d + e*x])/e^12","B",1
1097,1,2295,445,1.6297488,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^9} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^9,x]","\text{Result too large to show}","-\frac{b^9 (d+e x)^2 (-10 a B e-A b e+11 b B d)}{2 e^{12}}+\frac{5 b^8 x (b d-a e) (-9 a B e-2 A b e+11 b B d)}{e^{11}}-\frac{15 b^7 (b d-a e)^2 \log (d+e x) (-8 a B e-3 A b e+11 b B d)}{e^{12}}-\frac{30 b^6 (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{e^{12} (d+e x)}+\frac{21 b^5 (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{e^{12} (d+e x)^2}-\frac{14 b^4 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{e^{12} (d+e x)^3}+\frac{15 b^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{2 e^{12} (d+e x)^4}-\frac{3 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{e^{12} (d+e x)^5}+\frac{5 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{6 e^{12} (d+e x)^6}-\frac{(b d-a e)^9 (-a B e-10 A b e+11 b B d)}{7 e^{12} (d+e x)^7}+\frac{(b d-a e)^{10} (B d-A e)}{8 e^{12} (d+e x)^8}+\frac{b^{10} B (d+e x)^3}{3 e^{12}}",1,"(-32891*b^10*B*d^11 + 10803*A*b^10*d^10*e + 108030*a*b^9*B*d^10*e - 27654*a*A*b^9*d^9*e^2 - 124443*a^2*b^8*B*d^9*e^2 + 20547*a^2*A*b^8*d^8*e^3 + 54792*a^3*b^7*B*d^8*e^3 - 2520*a^3*A*b^7*d^7*e^4 - 4410*a^4*b^6*B*d^7*e^4 - 630*a^4*A*b^6*d^6*e^5 - 756*a^5*b^5*B*d^6*e^5 - 252*a^5*A*b^5*d^5*e^6 - 210*a^6*b^4*B*d^5*e^6 - 126*a^6*A*b^4*d^4*e^7 - 72*a^7*b^3*B*d^4*e^7 - 72*a^7*A*b^3*d^3*e^8 - 27*a^8*b^2*B*d^3*e^8 - 45*a^8*A*b^2*d^2*e^9 - 10*a^9*b*B*d^2*e^9 - 30*a^9*A*b*d*e^10 - 3*a^10*B*d*e^10 - 21*a^10*A*e^11 - 235408*b^10*B*d^10*e*x + 78864*A*b^10*d^9*e^2*x + 788640*a*b^9*B*d^9*e^2*x - 206112*a*A*b^9*d^8*e^3*x - 927504*a^2*b^8*B*d^8*e^3*x + 156816*a^2*A*b^8*d^7*e^4*x + 418176*a^3*b^7*B*d^7*e^4*x - 20160*a^3*A*b^7*d^6*e^5*x - 35280*a^4*b^6*B*d^6*e^5*x - 5040*a^4*A*b^6*d^5*e^6*x - 6048*a^5*b^5*B*d^5*e^6*x - 2016*a^5*A*b^5*d^4*e^7*x - 1680*a^6*b^4*B*d^4*e^7*x - 1008*a^6*A*b^4*d^3*e^8*x - 576*a^7*b^3*B*d^3*e^8*x - 576*a^7*A*b^3*d^2*e^9*x - 216*a^8*b^2*B*d^2*e^9*x - 360*a^8*A*b^2*d*e^10*x - 80*a^9*b*B*d*e^10*x - 240*a^9*A*b*e^11*x - 24*a^10*B*e^11*x - 713048*b^10*B*d^9*e^2*x^2 + 245784*A*b^10*d^8*e^3*x^2 + 2457840*a*b^9*B*d^8*e^3*x^2 - 660912*a*A*b^9*d^7*e^4*x^2 - 2974104*a^2*b^8*B*d^7*e^4*x^2 + 518616*a^2*A*b^8*d^6*e^5*x^2 + 1382976*a^3*b^7*B*d^6*e^5*x^2 - 70560*a^3*A*b^7*d^5*e^6*x^2 - 123480*a^4*b^6*B*d^5*e^6*x^2 - 17640*a^4*A*b^6*d^4*e^7*x^2 - 21168*a^5*b^5*B*d^4*e^7*x^2 - 7056*a^5*A*b^5*d^3*e^8*x^2 - 5880*a^6*b^4*B*d^3*e^8*x^2 - 3528*a^6*A*b^4*d^2*e^9*x^2 - 2016*a^7*b^3*B*d^2*e^9*x^2 - 2016*a^7*A*b^3*d*e^10*x^2 - 756*a^8*b^2*B*d*e^10*x^2 - 1260*a^8*A*b^2*e^11*x^2 - 280*a^9*b*B*e^11*x^2 - 1167376*b^10*B*d^8*e^3*x^3 + 421008*A*b^10*d^7*e^4*x^3 + 4210080*a*b^9*B*d^7*e^4*x^3 - 1180704*a*A*b^9*d^6*e^5*x^3 - 5313168*a^2*b^8*B*d^6*e^5*x^3 + 966672*a^2*A*b^8*d^5*e^6*x^3 + 2577792*a^3*b^7*B*d^5*e^6*x^3 - 141120*a^3*A*b^7*d^4*e^7*x^3 - 246960*a^4*b^6*B*d^4*e^7*x^3 - 35280*a^4*A*b^6*d^3*e^8*x^3 - 42336*a^5*b^5*B*d^3*e^8*x^3 - 14112*a^5*A*b^5*d^2*e^9*x^3 - 11760*a^6*b^4*B*d^2*e^9*x^3 - 7056*a^6*A*b^4*d*e^10*x^3 - 4032*a^7*b^3*B*d*e^10*x^3 - 4032*a^7*A*b^3*e^11*x^3 - 1512*a^8*b^2*B*e^11*x^3 - 1071140*b^10*B*d^7*e^4*x^4 + 420420*A*b^10*d^6*e^5*x^4 + 4204200*a*b^9*B*d^6*e^5*x^4 - 1264200*a*A*b^9*d^5*e^6*x^4 - 5688900*a^2*b^8*B*d^5*e^6*x^4 + 1102500*a^2*A*b^8*d^4*e^7*x^4 + 2940000*a^3*b^7*B*d^4*e^7*x^4 - 176400*a^3*A*b^7*d^3*e^8*x^4 - 308700*a^4*b^6*B*d^3*e^8*x^4 - 44100*a^4*A*b^6*d^2*e^9*x^4 - 52920*a^5*b^5*B*d^2*e^9*x^4 - 17640*a^5*A*b^5*d*e^10*x^4 - 14700*a^6*b^4*B*d*e^10*x^4 - 8820*a^6*A*b^4*e^11*x^4 - 5040*a^7*b^3*B*e^11*x^4 - 468832*b^10*B*d^6*e^5*x^5 + 230496*A*b^10*d^5*e^6*x^5 + 2304960*a*b^9*B*d^5*e^6*x^5 - 799680*a*A*b^9*d^4*e^7*x^5 - 3598560*a^2*b^8*B*d^4*e^7*x^5 + 776160*a^2*A*b^8*d^3*e^8*x^5 + 2069760*a^3*b^7*B*d^3*e^8*x^5 - 141120*a^3*A*b^7*d^2*e^9*x^5 - 246960*a^4*b^6*B*d^2*e^9*x^5 - 35280*a^4*A*b^6*d*e^10*x^5 - 42336*a^5*b^5*B*d*e^10*x^5 - 14112*a^5*A*b^5*e^11*x^5 - 11760*a^6*b^4*B*e^11*x^5 + 24304*b^10*B*d^5*e^6*x^6 + 44688*A*b^10*d^4*e^7*x^6 + 446880*a*b^9*B*d^4*e^7*x^6 - 258720*a*A*b^9*d^3*e^8*x^6 - 1164240*a^2*b^8*B*d^3*e^8*x^6 + 317520*a^2*A*b^8*d^2*e^9*x^6 + 846720*a^3*b^7*B*d^2*e^9*x^6 - 70560*a^3*A*b^7*d*e^10*x^6 - 123480*a^4*b^6*B*d*e^10*x^6 - 17640*a^4*A*b^6*e^11*x^6 - 21168*a^5*b^5*B*e^11*x^6 + 117824*b^10*B*d^4*e^7*x^7 - 17472*A*b^10*d^3*e^8*x^7 - 174720*a*b^9*B*d^3*e^8*x^7 - 13440*a*A*b^9*d^2*e^9*x^7 - 60480*a^2*b^8*B*d^2*e^9*x^7 + 60480*a^2*A*b^8*d*e^10*x^7 + 161280*a^3*b^7*B*d*e^10*x^7 - 20160*a^3*A*b^7*e^11*x^7 - 35280*a^4*b^6*B*e^11*x^7 + 42448*b^10*B*d^3*e^8*x^8 - 9744*A*b^10*d^2*e^9*x^8 - 97440*a*b^9*B*d^2*e^9*x^8 + 13440*a*A*b^9*d*e^10*x^8 + 60480*a^2*b^8*B*d*e^10*x^8 + 3080*b^10*B*d^2*e^9*x^9 - 840*A*b^10*d*e^10*x^9 - 8400*a*b^9*B*d*e^10*x^9 + 1680*a*A*b^9*e^11*x^9 + 7560*a^2*b^8*B*e^11*x^9 - 308*b^10*B*d*e^10*x^10 + 84*A*b^10*e^11*x^10 + 840*a*b^9*B*e^11*x^10 + 56*b^10*B*e^11*x^11)/(168*e^12*(d + e*x)^8) - (15*(11*b^10*B*d^3 - 3*A*b^10*d^2*e - 30*a*b^9*B*d^2*e + 6*a*A*b^9*d*e^2 + 27*a^2*b^8*B*d*e^2 - 3*a^2*A*b^8*e^3 - 8*a^3*b^7*B*e^3)*Log[d + e*x])/e^12","B",1
1098,1,2267,441,1.8217658,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{10}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^10,x]","\text{Result too large to show}","-\frac{b^9 x (-10 a B e-A b e+10 b B d)}{e^{11}}+\frac{5 b^8 (b d-a e) \log (d+e x) (-9 a B e-2 A b e+11 b B d)}{e^{12}}+\frac{15 b^7 (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{e^{12} (d+e x)}-\frac{15 b^6 (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{e^{12} (d+e x)^2}+\frac{14 b^5 (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{e^{12} (d+e x)^3}-\frac{21 b^4 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{2 e^{12} (d+e x)^4}+\frac{6 b^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{e^{12} (d+e x)^5}-\frac{5 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{2 e^{12} (d+e x)^6}+\frac{5 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{7 e^{12} (d+e x)^7}-\frac{(b d-a e)^9 (-a B e-10 A b e+11 b B d)}{8 e^{12} (d+e x)^8}+\frac{(b d-a e)^{10} (B d-A e)}{9 e^{12} (d+e x)^9}+\frac{b^{10} B x^2}{2 e^{10}}",1,"(42131*b^10*B*d^11 - 9722*A*b^10*d^10*e - 97220*a*b^9*B*d^10*e + 14258*a*A*b^9*d^9*e^2 + 64161*a^2*b^8*B*d^9*e^2 - 2520*a^2*A*b^8*d^8*e^3 - 6720*a^3*b^7*B*d^8*e^3 - 840*a^3*A*b^7*d^7*e^4 - 1470*a^4*b^6*B*d^7*e^4 - 420*a^4*A*b^6*d^6*e^5 - 504*a^5*b^5*B*d^6*e^5 - 252*a^5*A*b^5*d^5*e^6 - 210*a^6*b^4*B*d^5*e^6 - 168*a^6*A*b^4*d^4*e^7 - 96*a^7*b^3*B*d^4*e^7 - 120*a^7*A*b^3*d^3*e^8 - 45*a^8*b^2*B*d^3*e^8 - 90*a^8*A*b^2*d^2*e^9 - 20*a^9*b*B*d^2*e^9 - 70*a^9*A*b*d*e^10 - 7*a^10*B*d*e^10 - 56*a^10*A*e^11 + 351459*b^10*B*d^10*e*x - 82458*A*b^10*d^9*e^2*x - 824580*a*b^9*B*d^9*e^2*x + 123282*a*A*b^9*d^8*e^3*x + 554769*a^2*b^8*B*d^8*e^3*x - 22680*a^2*A*b^8*d^7*e^4*x - 60480*a^3*b^7*B*d^7*e^4*x - 7560*a^3*A*b^7*d^6*e^5*x - 13230*a^4*b^6*B*d^6*e^5*x - 3780*a^4*A*b^6*d^5*e^6*x - 4536*a^5*b^5*B*d^5*e^6*x - 2268*a^5*A*b^5*d^4*e^7*x - 1890*a^6*b^4*B*d^4*e^7*x - 1512*a^6*A*b^4*d^3*e^8*x - 864*a^7*b^3*B*d^3*e^8*x - 1080*a^7*A*b^3*d^2*e^9*x - 405*a^8*b^2*B*d^2*e^9*x - 810*a^8*A*b^2*d*e^10*x - 180*a^9*b*B*d*e^10*x - 630*a^9*A*b*e^11*x - 63*a^10*B*e^11*x + 1281096*b^10*B*d^9*e^2*x^2 - 307152*A*b^10*d^8*e^3*x^2 - 3071520*a*b^9*B*d^8*e^3*x^2 + 470448*a*A*b^9*d^7*e^4*x^2 + 2117016*a^2*b^8*B*d^7*e^4*x^2 - 90720*a^2*A*b^8*d^6*e^5*x^2 - 241920*a^3*b^7*B*d^6*e^5*x^2 - 30240*a^3*A*b^7*d^5*e^6*x^2 - 52920*a^4*b^6*B*d^5*e^6*x^2 - 15120*a^4*A*b^6*d^4*e^7*x^2 - 18144*a^5*b^5*B*d^4*e^7*x^2 - 9072*a^5*A*b^5*d^3*e^8*x^2 - 7560*a^6*b^4*B*d^3*e^8*x^2 - 6048*a^6*A*b^4*d^2*e^9*x^2 - 3456*a^7*b^3*B*d^2*e^9*x^2 - 4320*a^7*A*b^3*d*e^10*x^2 - 1620*a^8*b^2*B*d*e^10*x^2 - 3240*a^8*A*b^2*e^11*x^2 - 720*a^9*b*B*e^11*x^2 + 2656584*b^10*B*d^8*e^3*x^3 - 656208*A*b^10*d^7*e^4*x^3 - 6562080*a*b^9*B*d^7*e^4*x^3 + 1037232*a*A*b^9*d^6*e^5*x^3 + 4667544*a^2*b^8*B*d^6*e^5*x^3 - 211680*a^2*A*b^8*d^5*e^6*x^3 - 564480*a^3*b^7*B*d^5*e^6*x^3 - 70560*a^3*A*b^7*d^4*e^7*x^3 - 123480*a^4*b^6*B*d^4*e^7*x^3 - 35280*a^4*A*b^6*d^3*e^8*x^3 - 42336*a^5*b^5*B*d^3*e^8*x^3 - 21168*a^5*A*b^5*d^2*e^9*x^3 - 17640*a^6*b^4*B*d^2*e^9*x^3 - 14112*a^6*A*b^4*d*e^10*x^3 - 8064*a^7*b^3*B*d*e^10*x^3 - 10080*a^7*A*b^3*e^11*x^3 - 3780*a^8*b^2*B*e^11*x^3 + 3402756*b^10*B*d^7*e^4*x^4 - 878472*A*b^10*d^6*e^5*x^4 - 8784720*a*b^9*B*d^6*e^5*x^4 + 1450008*a*A*b^9*d^5*e^6*x^4 + 6525036*a^2*b^8*B*d^5*e^6*x^4 - 317520*a^2*A*b^8*d^4*e^7*x^4 - 846720*a^3*b^7*B*d^4*e^7*x^4 - 105840*a^3*A*b^7*d^3*e^8*x^4 - 185220*a^4*b^6*B*d^3*e^8*x^4 - 52920*a^4*A*b^6*d^2*e^9*x^4 - 63504*a^5*b^5*B*d^2*e^9*x^4 - 31752*a^5*A*b^5*d*e^10*x^4 - 26460*a^6*b^4*B*d*e^10*x^4 - 21168*a^6*A*b^4*e^11*x^4 - 12096*a^7*b^3*B*e^11*x^4 + 2704212*b^10*B*d^6*e^5*x^5 - 751464*A*b^10*d^5*e^6*x^5 - 7514640*a*b^9*B*d^5*e^6*x^5 + 1323000*a*A*b^9*d^4*e^7*x^5 + 5953500*a^2*b^8*B*d^4*e^7*x^5 - 317520*a^2*A*b^8*d^3*e^8*x^5 - 846720*a^3*b^7*B*d^3*e^8*x^5 - 105840*a^3*A*b^7*d^2*e^9*x^5 - 185220*a^4*b^6*B*d^2*e^9*x^5 - 52920*a^4*A*b^6*d*e^10*x^5 - 63504*a^5*b^5*B*d*e^10*x^5 - 31752*a^5*A*b^5*e^11*x^5 - 26460*a^6*b^4*B*e^11*x^5 + 1220688*b^10*B*d^5*e^6*x^6 - 395136*A*b^10*d^4*e^7*x^6 - 3951360*a*b^9*B*d^4*e^7*x^6 + 776160*a*A*b^9*d^3*e^8*x^6 + 3492720*a^2*b^8*B*d^3*e^8*x^6 - 211680*a^2*A*b^8*d^2*e^9*x^6 - 564480*a^3*b^7*B*d^2*e^9*x^6 - 70560*a^3*A*b^7*d*e^10*x^6 - 123480*a^4*b^6*B*d*e^10*x^6 - 35280*a^4*A*b^6*e^11*x^6 - 42336*a^5*b^5*B*e^11*x^6 + 190512*b^10*B*d^4*e^7*x^7 - 108864*A*b^10*d^3*e^8*x^7 - 1088640*a*b^9*B*d^3*e^8*x^7 + 272160*a*A*b^9*d^2*e^9*x^7 + 1224720*a^2*b^8*B*d^2*e^9*x^7 - 90720*a^2*A*b^8*d*e^10*x^7 - 241920*a^3*b^7*B*d*e^10*x^7 - 30240*a^3*A*b^7*e^11*x^7 - 52920*a^4*b^6*B*e^11*x^7 - 77112*b^10*B*d^3*e^8*x^8 - 4536*A*b^10*d^2*e^9*x^8 - 45360*a*b^9*B*d^2*e^9*x^8 + 45360*a*A*b^9*d*e^10*x^8 + 204120*a^2*b^8*B*d*e^10*x^8 - 22680*a^2*A*b^8*e^11*x^8 - 60480*a^3*b^7*B*e^11*x^8 - 36288*b^10*B*d^2*e^9*x^9 + 4536*A*b^10*d*e^10*x^9 + 45360*a*b^9*B*d*e^10*x^9 - 2772*b^10*B*d*e^10*x^10 + 504*A*b^10*e^11*x^10 + 5040*a*b^9*B*e^11*x^10 + 252*b^10*B*e^11*x^11)/(504*e^12*(d + e*x)^9) + (5*(11*b^10*B*d^2 - 2*A*b^10*d*e - 20*a*b^9*B*d*e + 2*a*A*b^9*e^2 + 9*a^2*b^8*B*e^2)*Log[d + e*x])/e^12","B",1
1099,1,2242,446,1.8823271,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{11}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^11,x]","\text{Result too large to show}","-\frac{b^9 \log (d+e x) (-10 a B e-A b e+11 b B d)}{e^{12}}-\frac{5 b^8 (b d-a e) (-9 a B e-2 A b e+11 b B d)}{e^{12} (d+e x)}+\frac{15 b^7 (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{2 e^{12} (d+e x)^2}-\frac{10 b^6 (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{e^{12} (d+e x)^3}+\frac{21 b^5 (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{2 e^{12} (d+e x)^4}-\frac{42 b^4 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{5 e^{12} (d+e x)^5}+\frac{5 b^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{e^{12} (d+e x)^6}-\frac{15 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{7 e^{12} (d+e x)^7}+\frac{5 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{8 e^{12} (d+e x)^8}-\frac{(b d-a e)^9 (-a B e-10 A b e+11 b B d)}{9 e^{12} (d+e x)^9}+\frac{(b d-a e)^{10} (B d-A e)}{10 e^{12} (d+e x)^{10}}+\frac{b^{10} B x}{e^{11}}",1,"(-55991*b^10*B*d^11 + 7381*A*b^10*d^10*e + 73810*a*b^9*B*d^10*e - 2520*a*A*b^9*d^9*e^2 - 11340*a^2*b^8*B*d^9*e^2 - 1260*a^2*A*b^8*d^8*e^3 - 3360*a^3*b^7*B*d^8*e^3 - 840*a^3*A*b^7*d^7*e^4 - 1470*a^4*b^6*B*d^7*e^4 - 630*a^4*A*b^6*d^6*e^5 - 756*a^5*b^5*B*d^6*e^5 - 504*a^5*A*b^5*d^5*e^6 - 420*a^6*b^4*B*d^5*e^6 - 420*a^6*A*b^4*d^4*e^7 - 240*a^7*b^3*B*d^4*e^7 - 360*a^7*A*b^3*d^3*e^8 - 135*a^8*b^2*B*d^3*e^8 - 315*a^8*A*b^2*d^2*e^9 - 70*a^9*b*B*d^2*e^9 - 280*a^9*A*b*d*e^10 - 28*a^10*B*d*e^10 - 252*a^10*A*e^11 - 532190*b^10*B*d^10*e*x + 71290*A*b^10*d^9*e^2*x + 712900*a*b^9*B*d^9*e^2*x - 25200*a*A*b^9*d^8*e^3*x - 113400*a^2*b^8*B*d^8*e^3*x - 12600*a^2*A*b^8*d^7*e^4*x - 33600*a^3*b^7*B*d^7*e^4*x - 8400*a^3*A*b^7*d^6*e^5*x - 14700*a^4*b^6*B*d^6*e^5*x - 6300*a^4*A*b^6*d^5*e^6*x - 7560*a^5*b^5*B*d^5*e^6*x - 5040*a^5*A*b^5*d^4*e^7*x - 4200*a^6*b^4*B*d^4*e^7*x - 4200*a^6*A*b^4*d^3*e^8*x - 2400*a^7*b^3*B*d^3*e^8*x - 3600*a^7*A*b^3*d^2*e^9*x - 1350*a^8*b^2*B*d^2*e^9*x - 3150*a^8*A*b^2*d*e^10*x - 700*a^9*b*B*d*e^10*x - 2800*a^9*A*b*e^11*x - 280*a^10*B*e^11*x - 2256255*b^10*B*d^9*e^2*x^2 + 308205*A*b^10*d^8*e^3*x^2 + 3082050*a*b^9*B*d^8*e^3*x^2 - 113400*a*A*b^9*d^7*e^4*x^2 - 510300*a^2*b^8*B*d^7*e^4*x^2 - 56700*a^2*A*b^8*d^6*e^5*x^2 - 151200*a^3*b^7*B*d^6*e^5*x^2 - 37800*a^3*A*b^7*d^5*e^6*x^2 - 66150*a^4*b^6*B*d^5*e^6*x^2 - 28350*a^4*A*b^6*d^4*e^7*x^2 - 34020*a^5*b^5*B*d^4*e^7*x^2 - 22680*a^5*A*b^5*d^3*e^8*x^2 - 18900*a^6*b^4*B*d^3*e^8*x^2 - 18900*a^6*A*b^4*d^2*e^9*x^2 - 10800*a^7*b^3*B*d^2*e^9*x^2 - 16200*a^7*A*b^3*d*e^10*x^2 - 6075*a^8*b^2*B*d*e^10*x^2 - 14175*a^8*A*b^2*e^11*x^2 - 3150*a^9*b*B*e^11*x^2 - 5600880*b^10*B*d^8*e^3*x^3 + 784080*A*b^10*d^7*e^4*x^3 + 7840800*a*b^9*B*d^7*e^4*x^3 - 302400*a*A*b^9*d^6*e^5*x^3 - 1360800*a^2*b^8*B*d^6*e^5*x^3 - 151200*a^2*A*b^8*d^5*e^6*x^3 - 403200*a^3*b^7*B*d^5*e^6*x^3 - 100800*a^3*A*b^7*d^4*e^7*x^3 - 176400*a^4*b^6*B*d^4*e^7*x^3 - 75600*a^4*A*b^6*d^3*e^8*x^3 - 90720*a^5*b^5*B*d^3*e^8*x^3 - 60480*a^5*A*b^5*d^2*e^9*x^3 - 50400*a^6*b^4*B*d^2*e^9*x^3 - 50400*a^6*A*b^4*d*e^10*x^3 - 28800*a^7*b^3*B*d*e^10*x^3 - 43200*a^7*A*b^3*e^11*x^3 - 16200*a^8*b^2*B*e^11*x^3 - 8969940*b^10*B*d^7*e^4*x^4 + 1296540*A*b^10*d^6*e^5*x^4 + 12965400*a*b^9*B*d^6*e^5*x^4 - 529200*a*A*b^9*d^5*e^6*x^4 - 2381400*a^2*b^8*B*d^5*e^6*x^4 - 264600*a^2*A*b^8*d^4*e^7*x^4 - 705600*a^3*b^7*B*d^4*e^7*x^4 - 176400*a^3*A*b^7*d^3*e^8*x^4 - 308700*a^4*b^6*B*d^3*e^8*x^4 - 132300*a^4*A*b^6*d^2*e^9*x^4 - 158760*a^5*b^5*B*d^2*e^9*x^4 - 105840*a^5*A*b^5*d*e^10*x^4 - 88200*a^6*b^4*B*d*e^10*x^4 - 88200*a^6*A*b^4*e^11*x^4 - 50400*a^7*b^3*B*e^11*x^4 - 9599688*b^10*B*d^6*e^5*x^5 + 1450008*A*b^10*d^5*e^6*x^5 + 14500080*a*b^9*B*d^5*e^6*x^5 - 635040*a*A*b^9*d^4*e^7*x^5 - 2857680*a^2*b^8*B*d^4*e^7*x^5 - 317520*a^2*A*b^8*d^3*e^8*x^5 - 846720*a^3*b^7*B*d^3*e^8*x^5 - 211680*a^3*A*b^7*d^2*e^9*x^5 - 370440*a^4*b^6*B*d^2*e^9*x^5 - 158760*a^4*A*b^6*d*e^10*x^5 - 190512*a^5*b^5*B*d*e^10*x^5 - 127008*a^5*A*b^5*e^11*x^5 - 105840*a^6*b^4*B*e^11*x^5 - 6835500*b^10*B*d^5*e^6*x^6 + 1102500*A*b^10*d^4*e^7*x^6 + 11025000*a*b^9*B*d^4*e^7*x^6 - 529200*a*A*b^9*d^3*e^8*x^6 - 2381400*a^2*b^8*B*d^3*e^8*x^6 - 264600*a^2*A*b^8*d^2*e^9*x^6 - 705600*a^3*b^7*B*d^2*e^9*x^6 - 176400*a^3*A*b^7*d*e^10*x^6 - 308700*a^4*b^6*B*d*e^10*x^6 - 132300*a^4*A*b^6*e^11*x^6 - 158760*a^5*b^5*B*e^11*x^6 - 3074400*b^10*B*d^4*e^7*x^7 + 554400*A*b^10*d^3*e^8*x^7 + 5544000*a*b^9*B*d^3*e^8*x^7 - 302400*a*A*b^9*d^2*e^9*x^7 - 1360800*a^2*b^8*B*d^2*e^9*x^7 - 151200*a^2*A*b^8*d*e^10*x^7 - 403200*a^3*b^7*B*d*e^10*x^7 - 100800*a^3*A*b^7*e^11*x^7 - 176400*a^4*b^6*B*e^11*x^7 - 737100*b^10*B*d^3*e^8*x^8 + 170100*A*b^10*d^2*e^9*x^8 + 1701000*a*b^9*B*d^2*e^9*x^8 - 113400*a*A*b^9*d*e^10*x^8 - 510300*a^2*b^8*B*d*e^10*x^8 - 56700*a^2*A*b^8*e^11*x^8 - 151200*a^3*b^7*B*e^11*x^8 - 25200*b^10*B*d^2*e^9*x^9 + 25200*A*b^10*d*e^10*x^9 + 252000*a*b^9*B*d*e^10*x^9 - 25200*a*A*b^9*e^11*x^9 - 113400*a^2*b^8*B*e^11*x^9 + 25200*b^10*B*d*e^10*x^10 + 2520*b^10*B*e^11*x^11)/(2520*e^12*(d + e*x)^10) + ((-11*b^10*B*d + A*b^10*e + 10*a*b^9*B*e)*Log[d + e*x])/e^12","B",1
1100,1,2237,321,3.1846651,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{12}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^12,x]","\text{Result too large to show}","-\frac{(a+b x)^{11} (B d-A e)}{11 e (d+e x)^{11} (b d-a e)}+\frac{10 b^9 B (b d-a e)}{e^{12} (d+e x)}-\frac{45 b^8 B (b d-a e)^2}{2 e^{12} (d+e x)^2}+\frac{40 b^7 B (b d-a e)^3}{e^{12} (d+e x)^3}-\frac{105 b^6 B (b d-a e)^4}{2 e^{12} (d+e x)^4}+\frac{252 b^5 B (b d-a e)^5}{5 e^{12} (d+e x)^5}-\frac{35 b^4 B (b d-a e)^6}{e^{12} (d+e x)^6}+\frac{120 b^3 B (b d-a e)^7}{7 e^{12} (d+e x)^7}-\frac{45 b^2 B (b d-a e)^8}{8 e^{12} (d+e x)^8}+\frac{10 b B (b d-a e)^9}{9 e^{12} (d+e x)^9}-\frac{B (b d-a e)^{10}}{10 e^{12} (d+e x)^{10}}+\frac{b^{10} B \log (d+e x)}{e^{12}}",1,"(83711*b^10*B*d^11 - 2520*A*b^10*d^10*e - 25200*a*b^9*B*d^10*e - 2520*a*A*b^9*d^9*e^2 - 11340*a^2*b^8*B*d^9*e^2 - 2520*a^2*A*b^8*d^8*e^3 - 6720*a^3*b^7*B*d^8*e^3 - 2520*a^3*A*b^7*d^7*e^4 - 4410*a^4*b^6*B*d^7*e^4 - 2520*a^4*A*b^6*d^6*e^5 - 3024*a^5*b^5*B*d^6*e^5 - 2520*a^5*A*b^5*d^5*e^6 - 2100*a^6*b^4*B*d^5*e^6 - 2520*a^6*A*b^4*d^4*e^7 - 1440*a^7*b^3*B*d^4*e^7 - 2520*a^7*A*b^3*d^3*e^8 - 945*a^8*b^2*B*d^3*e^8 - 2520*a^8*A*b^2*d^2*e^9 - 560*a^9*b*B*d^2*e^9 - 2520*a^9*A*b*d*e^10 - 252*a^10*B*d*e^10 - 2520*a^10*A*e^11 + 893101*b^10*B*d^10*e*x - 27720*A*b^10*d^9*e^2*x - 277200*a*b^9*B*d^9*e^2*x - 27720*a*A*b^9*d^8*e^3*x - 124740*a^2*b^8*B*d^8*e^3*x - 27720*a^2*A*b^8*d^7*e^4*x - 73920*a^3*b^7*B*d^7*e^4*x - 27720*a^3*A*b^7*d^6*e^5*x - 48510*a^4*b^6*B*d^6*e^5*x - 27720*a^4*A*b^6*d^5*e^6*x - 33264*a^5*b^5*B*d^5*e^6*x - 27720*a^5*A*b^5*d^4*e^7*x - 23100*a^6*b^4*B*d^4*e^7*x - 27720*a^6*A*b^4*d^3*e^8*x - 15840*a^7*b^3*B*d^3*e^8*x - 27720*a^7*A*b^3*d^2*e^9*x - 10395*a^8*b^2*B*d^2*e^9*x - 27720*a^8*A*b^2*d*e^10*x - 6160*a^9*b*B*d*e^10*x - 27720*a^9*A*b*e^11*x - 2772*a^10*B*e^11*x + 4313045*b^10*B*d^9*e^2*x^2 - 138600*A*b^10*d^8*e^3*x^2 - 1386000*a*b^9*B*d^8*e^3*x^2 - 138600*a*A*b^9*d^7*e^4*x^2 - 623700*a^2*b^8*B*d^7*e^4*x^2 - 138600*a^2*A*b^8*d^6*e^5*x^2 - 369600*a^3*b^7*B*d^6*e^5*x^2 - 138600*a^3*A*b^7*d^5*e^6*x^2 - 242550*a^4*b^6*B*d^5*e^6*x^2 - 138600*a^4*A*b^6*d^4*e^7*x^2 - 166320*a^5*b^5*B*d^4*e^7*x^2 - 138600*a^5*A*b^5*d^3*e^8*x^2 - 115500*a^6*b^4*B*d^3*e^8*x^2 - 138600*a^6*A*b^4*d^2*e^9*x^2 - 79200*a^7*b^3*B*d^2*e^9*x^2 - 138600*a^7*A*b^3*d*e^10*x^2 - 51975*a^8*b^2*B*d*e^10*x^2 - 138600*a^8*A*b^2*e^11*x^2 - 30800*a^9*b*B*e^11*x^2 + 12430935*b^10*B*d^8*e^3*x^3 - 415800*A*b^10*d^7*e^4*x^3 - 4158000*a*b^9*B*d^7*e^4*x^3 - 415800*a*A*b^9*d^6*e^5*x^3 - 1871100*a^2*b^8*B*d^6*e^5*x^3 - 415800*a^2*A*b^8*d^5*e^6*x^3 - 1108800*a^3*b^7*B*d^5*e^6*x^3 - 415800*a^3*A*b^7*d^4*e^7*x^3 - 727650*a^4*b^6*B*d^4*e^7*x^3 - 415800*a^4*A*b^6*d^3*e^8*x^3 - 498960*a^5*b^5*B*d^3*e^8*x^3 - 415800*a^5*A*b^5*d^2*e^9*x^3 - 346500*a^6*b^4*B*d^2*e^9*x^3 - 415800*a^6*A*b^4*d*e^10*x^3 - 237600*a^7*b^3*B*d*e^10*x^3 - 415800*a^7*A*b^3*e^11*x^3 - 155925*a^8*b^2*B*e^11*x^3 + 23718420*b^10*B*d^7*e^4*x^4 - 831600*A*b^10*d^6*e^5*x^4 - 8316000*a*b^9*B*d^6*e^5*x^4 - 831600*a*A*b^9*d^5*e^6*x^4 - 3742200*a^2*b^8*B*d^5*e^6*x^4 - 831600*a^2*A*b^8*d^4*e^7*x^4 - 2217600*a^3*b^7*B*d^4*e^7*x^4 - 831600*a^3*A*b^7*d^3*e^8*x^4 - 1455300*a^4*b^6*B*d^3*e^8*x^4 - 831600*a^4*A*b^6*d^2*e^9*x^4 - 997920*a^5*b^5*B*d^2*e^9*x^4 - 831600*a^5*A*b^5*d*e^10*x^4 - 693000*a^6*b^4*B*d*e^10*x^4 - 831600*a^6*A*b^4*e^11*x^4 - 475200*a^7*b^3*B*e^11*x^4 + 31376268*b^10*B*d^6*e^5*x^5 - 1164240*A*b^10*d^5*e^6*x^5 - 11642400*a*b^9*B*d^5*e^6*x^5 - 1164240*a*A*b^9*d^4*e^7*x^5 - 5239080*a^2*b^8*B*d^4*e^7*x^5 - 1164240*a^2*A*b^8*d^3*e^8*x^5 - 3104640*a^3*b^7*B*d^3*e^8*x^5 - 1164240*a^3*A*b^7*d^2*e^9*x^5 - 2037420*a^4*b^6*B*d^2*e^9*x^5 - 1164240*a^4*A*b^6*d*e^10*x^5 - 1397088*a^5*b^5*B*d*e^10*x^5 - 1164240*a^5*A*b^5*e^11*x^5 - 970200*a^6*b^4*B*e^11*x^5 + 29241828*b^10*B*d^5*e^6*x^6 - 1164240*A*b^10*d^4*e^7*x^6 - 11642400*a*b^9*B*d^4*e^7*x^6 - 1164240*a*A*b^9*d^3*e^8*x^6 - 5239080*a^2*b^8*B*d^3*e^8*x^6 - 1164240*a^2*A*b^8*d^2*e^9*x^6 - 3104640*a^3*b^7*B*d^2*e^9*x^6 - 1164240*a^3*A*b^7*d*e^10*x^6 - 2037420*a^4*b^6*B*d*e^10*x^6 - 1164240*a^4*A*b^6*e^11*x^6 - 1397088*a^5*b^5*B*e^11*x^6 + 19057500*b^10*B*d^4*e^7*x^7 - 831600*A*b^10*d^3*e^8*x^7 - 8316000*a*b^9*B*d^3*e^8*x^7 - 831600*a*A*b^9*d^2*e^9*x^7 - 3742200*a^2*b^8*B*d^2*e^9*x^7 - 831600*a^2*A*b^8*d*e^10*x^7 - 2217600*a^3*b^7*B*d*e^10*x^7 - 831600*a^3*A*b^7*e^11*x^7 - 1455300*a^4*b^6*B*e^11*x^7 + 8385300*b^10*B*d^3*e^8*x^8 - 415800*A*b^10*d^2*e^9*x^8 - 4158000*a*b^9*B*d^2*e^9*x^8 - 415800*a*A*b^9*d*e^10*x^8 - 1871100*a^2*b^8*B*d*e^10*x^8 - 415800*a^2*A*b^8*e^11*x^8 - 1108800*a^3*b^7*B*e^11*x^8 + 2286900*b^10*B*d^2*e^9*x^9 - 138600*A*b^10*d*e^10*x^9 - 1386000*a*b^9*B*d*e^10*x^9 - 138600*a*A*b^9*e^11*x^9 - 623700*a^2*b^8*B*e^11*x^9 + 304920*b^10*B*d*e^10*x^10 - 27720*A*b^10*e^11*x^10 - 277200*a*b^9*B*e^11*x^10)/(27720*e^12*(d + e*x)^11) + (b^10*B*Log[d + e*x])/e^12","B",1
1101,1,2234,86,0.9727447,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{13}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^13,x]","\text{Result too large to show}","\frac{(a+b x)^{11} (-12 a B e+A b e+11 b B d)}{132 e (d+e x)^{11} (b d-a e)^2}-\frac{(a+b x)^{11} (B d-A e)}{12 e (d+e x)^{12} (b d-a e)}",1,"(-11*b^10*B*d^11 - A*b^10*d^10*e - 10*a*b^9*B*d^10*e - 2*a*A*b^9*d^9*e^2 - 9*a^2*b^8*B*d^9*e^2 - 3*a^2*A*b^8*d^8*e^3 - 8*a^3*b^7*B*d^8*e^3 - 4*a^3*A*b^7*d^7*e^4 - 7*a^4*b^6*B*d^7*e^4 - 5*a^4*A*b^6*d^6*e^5 - 6*a^5*b^5*B*d^6*e^5 - 6*a^5*A*b^5*d^5*e^6 - 5*a^6*b^4*B*d^5*e^6 - 7*a^6*A*b^4*d^4*e^7 - 4*a^7*b^3*B*d^4*e^7 - 8*a^7*A*b^3*d^3*e^8 - 3*a^8*b^2*B*d^3*e^8 - 9*a^8*A*b^2*d^2*e^9 - 2*a^9*b*B*d^2*e^9 - 10*a^9*A*b*d*e^10 - a^10*B*d*e^10 - 11*a^10*A*e^11 - 132*b^10*B*d^10*e*x - 12*A*b^10*d^9*e^2*x - 120*a*b^9*B*d^9*e^2*x - 24*a*A*b^9*d^8*e^3*x - 108*a^2*b^8*B*d^8*e^3*x - 36*a^2*A*b^8*d^7*e^4*x - 96*a^3*b^7*B*d^7*e^4*x - 48*a^3*A*b^7*d^6*e^5*x - 84*a^4*b^6*B*d^6*e^5*x - 60*a^4*A*b^6*d^5*e^6*x - 72*a^5*b^5*B*d^5*e^6*x - 72*a^5*A*b^5*d^4*e^7*x - 60*a^6*b^4*B*d^4*e^7*x - 84*a^6*A*b^4*d^3*e^8*x - 48*a^7*b^3*B*d^3*e^8*x - 96*a^7*A*b^3*d^2*e^9*x - 36*a^8*b^2*B*d^2*e^9*x - 108*a^8*A*b^2*d*e^10*x - 24*a^9*b*B*d*e^10*x - 120*a^9*A*b*e^11*x - 12*a^10*B*e^11*x - 726*b^10*B*d^9*e^2*x^2 - 66*A*b^10*d^8*e^3*x^2 - 660*a*b^9*B*d^8*e^3*x^2 - 132*a*A*b^9*d^7*e^4*x^2 - 594*a^2*b^8*B*d^7*e^4*x^2 - 198*a^2*A*b^8*d^6*e^5*x^2 - 528*a^3*b^7*B*d^6*e^5*x^2 - 264*a^3*A*b^7*d^5*e^6*x^2 - 462*a^4*b^6*B*d^5*e^6*x^2 - 330*a^4*A*b^6*d^4*e^7*x^2 - 396*a^5*b^5*B*d^4*e^7*x^2 - 396*a^5*A*b^5*d^3*e^8*x^2 - 330*a^6*b^4*B*d^3*e^8*x^2 - 462*a^6*A*b^4*d^2*e^9*x^2 - 264*a^7*b^3*B*d^2*e^9*x^2 - 528*a^7*A*b^3*d*e^10*x^2 - 198*a^8*b^2*B*d*e^10*x^2 - 594*a^8*A*b^2*e^11*x^2 - 132*a^9*b*B*e^11*x^2 - 2420*b^10*B*d^8*e^3*x^3 - 220*A*b^10*d^7*e^4*x^3 - 2200*a*b^9*B*d^7*e^4*x^3 - 440*a*A*b^9*d^6*e^5*x^3 - 1980*a^2*b^8*B*d^6*e^5*x^3 - 660*a^2*A*b^8*d^5*e^6*x^3 - 1760*a^3*b^7*B*d^5*e^6*x^3 - 880*a^3*A*b^7*d^4*e^7*x^3 - 1540*a^4*b^6*B*d^4*e^7*x^3 - 1100*a^4*A*b^6*d^3*e^8*x^3 - 1320*a^5*b^5*B*d^3*e^8*x^3 - 1320*a^5*A*b^5*d^2*e^9*x^3 - 1100*a^6*b^4*B*d^2*e^9*x^3 - 1540*a^6*A*b^4*d*e^10*x^3 - 880*a^7*b^3*B*d*e^10*x^3 - 1760*a^7*A*b^3*e^11*x^3 - 660*a^8*b^2*B*e^11*x^3 - 5445*b^10*B*d^7*e^4*x^4 - 495*A*b^10*d^6*e^5*x^4 - 4950*a*b^9*B*d^6*e^5*x^4 - 990*a*A*b^9*d^5*e^6*x^4 - 4455*a^2*b^8*B*d^5*e^6*x^4 - 1485*a^2*A*b^8*d^4*e^7*x^4 - 3960*a^3*b^7*B*d^4*e^7*x^4 - 1980*a^3*A*b^7*d^3*e^8*x^4 - 3465*a^4*b^6*B*d^3*e^8*x^4 - 2475*a^4*A*b^6*d^2*e^9*x^4 - 2970*a^5*b^5*B*d^2*e^9*x^4 - 2970*a^5*A*b^5*d*e^10*x^4 - 2475*a^6*b^4*B*d*e^10*x^4 - 3465*a^6*A*b^4*e^11*x^4 - 1980*a^7*b^3*B*e^11*x^4 - 8712*b^10*B*d^6*e^5*x^5 - 792*A*b^10*d^5*e^6*x^5 - 7920*a*b^9*B*d^5*e^6*x^5 - 1584*a*A*b^9*d^4*e^7*x^5 - 7128*a^2*b^8*B*d^4*e^7*x^5 - 2376*a^2*A*b^8*d^3*e^8*x^5 - 6336*a^3*b^7*B*d^3*e^8*x^5 - 3168*a^3*A*b^7*d^2*e^9*x^5 - 5544*a^4*b^6*B*d^2*e^9*x^5 - 3960*a^4*A*b^6*d*e^10*x^5 - 4752*a^5*b^5*B*d*e^10*x^5 - 4752*a^5*A*b^5*e^11*x^5 - 3960*a^6*b^4*B*e^11*x^5 - 10164*b^10*B*d^5*e^6*x^6 - 924*A*b^10*d^4*e^7*x^6 - 9240*a*b^9*B*d^4*e^7*x^6 - 1848*a*A*b^9*d^3*e^8*x^6 - 8316*a^2*b^8*B*d^3*e^8*x^6 - 2772*a^2*A*b^8*d^2*e^9*x^6 - 7392*a^3*b^7*B*d^2*e^9*x^6 - 3696*a^3*A*b^7*d*e^10*x^6 - 6468*a^4*b^6*B*d*e^10*x^6 - 4620*a^4*A*b^6*e^11*x^6 - 5544*a^5*b^5*B*e^11*x^6 - 8712*b^10*B*d^4*e^7*x^7 - 792*A*b^10*d^3*e^8*x^7 - 7920*a*b^9*B*d^3*e^8*x^7 - 1584*a*A*b^9*d^2*e^9*x^7 - 7128*a^2*b^8*B*d^2*e^9*x^7 - 2376*a^2*A*b^8*d*e^10*x^7 - 6336*a^3*b^7*B*d*e^10*x^7 - 3168*a^3*A*b^7*e^11*x^7 - 5544*a^4*b^6*B*e^11*x^7 - 5445*b^10*B*d^3*e^8*x^8 - 495*A*b^10*d^2*e^9*x^8 - 4950*a*b^9*B*d^2*e^9*x^8 - 990*a*A*b^9*d*e^10*x^8 - 4455*a^2*b^8*B*d*e^10*x^8 - 1485*a^2*A*b^8*e^11*x^8 - 3960*a^3*b^7*B*e^11*x^8 - 2420*b^10*B*d^2*e^9*x^9 - 220*A*b^10*d*e^10*x^9 - 2200*a*b^9*B*d*e^10*x^9 - 440*a*A*b^9*e^11*x^9 - 1980*a^2*b^8*B*e^11*x^9 - 726*b^10*B*d*e^10*x^10 - 66*A*b^10*e^11*x^10 - 660*a*b^9*B*e^11*x^10 - 132*b^10*B*e^11*x^11)/(132*e^12*(d + e*x)^12)","B",1
1102,1,2234,135,1.0135218,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{14}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^14,x]","\text{Result too large to show}","\frac{b (a+b x)^{11} (-13 a B e+2 A b e+11 b B d)}{1716 e (d+e x)^{11} (b d-a e)^3}+\frac{(a+b x)^{11} (-13 a B e+2 A b e+11 b B d)}{156 e (d+e x)^{12} (b d-a e)^2}-\frac{(a+b x)^{11} (B d-A e)}{13 e (d+e x)^{13} (b d-a e)}",1,"(-11*b^10*B*d^11 - 2*A*b^10*d^10*e - 20*a*b^9*B*d^10*e - 6*a*A*b^9*d^9*e^2 - 27*a^2*b^8*B*d^9*e^2 - 12*a^2*A*b^8*d^8*e^3 - 32*a^3*b^7*B*d^8*e^3 - 20*a^3*A*b^7*d^7*e^4 - 35*a^4*b^6*B*d^7*e^4 - 30*a^4*A*b^6*d^6*e^5 - 36*a^5*b^5*B*d^6*e^5 - 42*a^5*A*b^5*d^5*e^6 - 35*a^6*b^4*B*d^5*e^6 - 56*a^6*A*b^4*d^4*e^7 - 32*a^7*b^3*B*d^4*e^7 - 72*a^7*A*b^3*d^3*e^8 - 27*a^8*b^2*B*d^3*e^8 - 90*a^8*A*b^2*d^2*e^9 - 20*a^9*b*B*d^2*e^9 - 110*a^9*A*b*d*e^10 - 11*a^10*B*d*e^10 - 132*a^10*A*e^11 - 143*b^10*B*d^10*e*x - 26*A*b^10*d^9*e^2*x - 260*a*b^9*B*d^9*e^2*x - 78*a*A*b^9*d^8*e^3*x - 351*a^2*b^8*B*d^8*e^3*x - 156*a^2*A*b^8*d^7*e^4*x - 416*a^3*b^7*B*d^7*e^4*x - 260*a^3*A*b^7*d^6*e^5*x - 455*a^4*b^6*B*d^6*e^5*x - 390*a^4*A*b^6*d^5*e^6*x - 468*a^5*b^5*B*d^5*e^6*x - 546*a^5*A*b^5*d^4*e^7*x - 455*a^6*b^4*B*d^4*e^7*x - 728*a^6*A*b^4*d^3*e^8*x - 416*a^7*b^3*B*d^3*e^8*x - 936*a^7*A*b^3*d^2*e^9*x - 351*a^8*b^2*B*d^2*e^9*x - 1170*a^8*A*b^2*d*e^10*x - 260*a^9*b*B*d*e^10*x - 1430*a^9*A*b*e^11*x - 143*a^10*B*e^11*x - 858*b^10*B*d^9*e^2*x^2 - 156*A*b^10*d^8*e^3*x^2 - 1560*a*b^9*B*d^8*e^3*x^2 - 468*a*A*b^9*d^7*e^4*x^2 - 2106*a^2*b^8*B*d^7*e^4*x^2 - 936*a^2*A*b^8*d^6*e^5*x^2 - 2496*a^3*b^7*B*d^6*e^5*x^2 - 1560*a^3*A*b^7*d^5*e^6*x^2 - 2730*a^4*b^6*B*d^5*e^6*x^2 - 2340*a^4*A*b^6*d^4*e^7*x^2 - 2808*a^5*b^5*B*d^4*e^7*x^2 - 3276*a^5*A*b^5*d^3*e^8*x^2 - 2730*a^6*b^4*B*d^3*e^8*x^2 - 4368*a^6*A*b^4*d^2*e^9*x^2 - 2496*a^7*b^3*B*d^2*e^9*x^2 - 5616*a^7*A*b^3*d*e^10*x^2 - 2106*a^8*b^2*B*d*e^10*x^2 - 7020*a^8*A*b^2*e^11*x^2 - 1560*a^9*b*B*e^11*x^2 - 3146*b^10*B*d^8*e^3*x^3 - 572*A*b^10*d^7*e^4*x^3 - 5720*a*b^9*B*d^7*e^4*x^3 - 1716*a*A*b^9*d^6*e^5*x^3 - 7722*a^2*b^8*B*d^6*e^5*x^3 - 3432*a^2*A*b^8*d^5*e^6*x^3 - 9152*a^3*b^7*B*d^5*e^6*x^3 - 5720*a^3*A*b^7*d^4*e^7*x^3 - 10010*a^4*b^6*B*d^4*e^7*x^3 - 8580*a^4*A*b^6*d^3*e^8*x^3 - 10296*a^5*b^5*B*d^3*e^8*x^3 - 12012*a^5*A*b^5*d^2*e^9*x^3 - 10010*a^6*b^4*B*d^2*e^9*x^3 - 16016*a^6*A*b^4*d*e^10*x^3 - 9152*a^7*b^3*B*d*e^10*x^3 - 20592*a^7*A*b^3*e^11*x^3 - 7722*a^8*b^2*B*e^11*x^3 - 7865*b^10*B*d^7*e^4*x^4 - 1430*A*b^10*d^6*e^5*x^4 - 14300*a*b^9*B*d^6*e^5*x^4 - 4290*a*A*b^9*d^5*e^6*x^4 - 19305*a^2*b^8*B*d^5*e^6*x^4 - 8580*a^2*A*b^8*d^4*e^7*x^4 - 22880*a^3*b^7*B*d^4*e^7*x^4 - 14300*a^3*A*b^7*d^3*e^8*x^4 - 25025*a^4*b^6*B*d^3*e^8*x^4 - 21450*a^4*A*b^6*d^2*e^9*x^4 - 25740*a^5*b^5*B*d^2*e^9*x^4 - 30030*a^5*A*b^5*d*e^10*x^4 - 25025*a^6*b^4*B*d*e^10*x^4 - 40040*a^6*A*b^4*e^11*x^4 - 22880*a^7*b^3*B*e^11*x^4 - 14157*b^10*B*d^6*e^5*x^5 - 2574*A*b^10*d^5*e^6*x^5 - 25740*a*b^9*B*d^5*e^6*x^5 - 7722*a*A*b^9*d^4*e^7*x^5 - 34749*a^2*b^8*B*d^4*e^7*x^5 - 15444*a^2*A*b^8*d^3*e^8*x^5 - 41184*a^3*b^7*B*d^3*e^8*x^5 - 25740*a^3*A*b^7*d^2*e^9*x^5 - 45045*a^4*b^6*B*d^2*e^9*x^5 - 38610*a^4*A*b^6*d*e^10*x^5 - 46332*a^5*b^5*B*d*e^10*x^5 - 54054*a^5*A*b^5*e^11*x^5 - 45045*a^6*b^4*B*e^11*x^5 - 18876*b^10*B*d^5*e^6*x^6 - 3432*A*b^10*d^4*e^7*x^6 - 34320*a*b^9*B*d^4*e^7*x^6 - 10296*a*A*b^9*d^3*e^8*x^6 - 46332*a^2*b^8*B*d^3*e^8*x^6 - 20592*a^2*A*b^8*d^2*e^9*x^6 - 54912*a^3*b^7*B*d^2*e^9*x^6 - 34320*a^3*A*b^7*d*e^10*x^6 - 60060*a^4*b^6*B*d*e^10*x^6 - 51480*a^4*A*b^6*e^11*x^6 - 61776*a^5*b^5*B*e^11*x^6 - 18876*b^10*B*d^4*e^7*x^7 - 3432*A*b^10*d^3*e^8*x^7 - 34320*a*b^9*B*d^3*e^8*x^7 - 10296*a*A*b^9*d^2*e^9*x^7 - 46332*a^2*b^8*B*d^2*e^9*x^7 - 20592*a^2*A*b^8*d*e^10*x^7 - 54912*a^3*b^7*B*d*e^10*x^7 - 34320*a^3*A*b^7*e^11*x^7 - 60060*a^4*b^6*B*e^11*x^7 - 14157*b^10*B*d^3*e^8*x^8 - 2574*A*b^10*d^2*e^9*x^8 - 25740*a*b^9*B*d^2*e^9*x^8 - 7722*a*A*b^9*d*e^10*x^8 - 34749*a^2*b^8*B*d*e^10*x^8 - 15444*a^2*A*b^8*e^11*x^8 - 41184*a^3*b^7*B*e^11*x^8 - 7865*b^10*B*d^2*e^9*x^9 - 1430*A*b^10*d*e^10*x^9 - 14300*a*b^9*B*d*e^10*x^9 - 4290*a*A*b^9*e^11*x^9 - 19305*a^2*b^8*B*e^11*x^9 - 3146*b^10*B*d*e^10*x^10 - 572*A*b^10*e^11*x^10 - 5720*a*b^9*B*e^11*x^10 - 858*b^10*B*e^11*x^11)/(1716*e^12*(d + e*x)^13)","B",1
1103,1,2234,185,0.9898792,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{15}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^15,x]","\text{Result too large to show}","\frac{b^2 (a+b x)^{11} (-14 a B e+3 A b e+11 b B d)}{12012 e (d+e x)^{11} (b d-a e)^4}+\frac{b (a+b x)^{11} (-14 a B e+3 A b e+11 b B d)}{1092 e (d+e x)^{12} (b d-a e)^3}+\frac{(a+b x)^{11} (-14 a B e+3 A b e+11 b B d)}{182 e (d+e x)^{13} (b d-a e)^2}-\frac{(a+b x)^{11} (B d-A e)}{14 e (d+e x)^{14} (b d-a e)}",1,"(-11*b^10*B*d^11 - 3*A*b^10*d^10*e - 30*a*b^9*B*d^10*e - 12*a*A*b^9*d^9*e^2 - 54*a^2*b^8*B*d^9*e^2 - 30*a^2*A*b^8*d^8*e^3 - 80*a^3*b^7*B*d^8*e^3 - 60*a^3*A*b^7*d^7*e^4 - 105*a^4*b^6*B*d^7*e^4 - 105*a^4*A*b^6*d^6*e^5 - 126*a^5*b^5*B*d^6*e^5 - 168*a^5*A*b^5*d^5*e^6 - 140*a^6*b^4*B*d^5*e^6 - 252*a^6*A*b^4*d^4*e^7 - 144*a^7*b^3*B*d^4*e^7 - 360*a^7*A*b^3*d^3*e^8 - 135*a^8*b^2*B*d^3*e^8 - 495*a^8*A*b^2*d^2*e^9 - 110*a^9*b*B*d^2*e^9 - 660*a^9*A*b*d*e^10 - 66*a^10*B*d*e^10 - 858*a^10*A*e^11 - 154*b^10*B*d^10*e*x - 42*A*b^10*d^9*e^2*x - 420*a*b^9*B*d^9*e^2*x - 168*a*A*b^9*d^8*e^3*x - 756*a^2*b^8*B*d^8*e^3*x - 420*a^2*A*b^8*d^7*e^4*x - 1120*a^3*b^7*B*d^7*e^4*x - 840*a^3*A*b^7*d^6*e^5*x - 1470*a^4*b^6*B*d^6*e^5*x - 1470*a^4*A*b^6*d^5*e^6*x - 1764*a^5*b^5*B*d^5*e^6*x - 2352*a^5*A*b^5*d^4*e^7*x - 1960*a^6*b^4*B*d^4*e^7*x - 3528*a^6*A*b^4*d^3*e^8*x - 2016*a^7*b^3*B*d^3*e^8*x - 5040*a^7*A*b^3*d^2*e^9*x - 1890*a^8*b^2*B*d^2*e^9*x - 6930*a^8*A*b^2*d*e^10*x - 1540*a^9*b*B*d*e^10*x - 9240*a^9*A*b*e^11*x - 924*a^10*B*e^11*x - 1001*b^10*B*d^9*e^2*x^2 - 273*A*b^10*d^8*e^3*x^2 - 2730*a*b^9*B*d^8*e^3*x^2 - 1092*a*A*b^9*d^7*e^4*x^2 - 4914*a^2*b^8*B*d^7*e^4*x^2 - 2730*a^2*A*b^8*d^6*e^5*x^2 - 7280*a^3*b^7*B*d^6*e^5*x^2 - 5460*a^3*A*b^7*d^5*e^6*x^2 - 9555*a^4*b^6*B*d^5*e^6*x^2 - 9555*a^4*A*b^6*d^4*e^7*x^2 - 11466*a^5*b^5*B*d^4*e^7*x^2 - 15288*a^5*A*b^5*d^3*e^8*x^2 - 12740*a^6*b^4*B*d^3*e^8*x^2 - 22932*a^6*A*b^4*d^2*e^9*x^2 - 13104*a^7*b^3*B*d^2*e^9*x^2 - 32760*a^7*A*b^3*d*e^10*x^2 - 12285*a^8*b^2*B*d*e^10*x^2 - 45045*a^8*A*b^2*e^11*x^2 - 10010*a^9*b*B*e^11*x^2 - 4004*b^10*B*d^8*e^3*x^3 - 1092*A*b^10*d^7*e^4*x^3 - 10920*a*b^9*B*d^7*e^4*x^3 - 4368*a*A*b^9*d^6*e^5*x^3 - 19656*a^2*b^8*B*d^6*e^5*x^3 - 10920*a^2*A*b^8*d^5*e^6*x^3 - 29120*a^3*b^7*B*d^5*e^6*x^3 - 21840*a^3*A*b^7*d^4*e^7*x^3 - 38220*a^4*b^6*B*d^4*e^7*x^3 - 38220*a^4*A*b^6*d^3*e^8*x^3 - 45864*a^5*b^5*B*d^3*e^8*x^3 - 61152*a^5*A*b^5*d^2*e^9*x^3 - 50960*a^6*b^4*B*d^2*e^9*x^3 - 91728*a^6*A*b^4*d*e^10*x^3 - 52416*a^7*b^3*B*d*e^10*x^3 - 131040*a^7*A*b^3*e^11*x^3 - 49140*a^8*b^2*B*e^11*x^3 - 11011*b^10*B*d^7*e^4*x^4 - 3003*A*b^10*d^6*e^5*x^4 - 30030*a*b^9*B*d^6*e^5*x^4 - 12012*a*A*b^9*d^5*e^6*x^4 - 54054*a^2*b^8*B*d^5*e^6*x^4 - 30030*a^2*A*b^8*d^4*e^7*x^4 - 80080*a^3*b^7*B*d^4*e^7*x^4 - 60060*a^3*A*b^7*d^3*e^8*x^4 - 105105*a^4*b^6*B*d^3*e^8*x^4 - 105105*a^4*A*b^6*d^2*e^9*x^4 - 126126*a^5*b^5*B*d^2*e^9*x^4 - 168168*a^5*A*b^5*d*e^10*x^4 - 140140*a^6*b^4*B*d*e^10*x^4 - 252252*a^6*A*b^4*e^11*x^4 - 144144*a^7*b^3*B*e^11*x^4 - 22022*b^10*B*d^6*e^5*x^5 - 6006*A*b^10*d^5*e^6*x^5 - 60060*a*b^9*B*d^5*e^6*x^5 - 24024*a*A*b^9*d^4*e^7*x^5 - 108108*a^2*b^8*B*d^4*e^7*x^5 - 60060*a^2*A*b^8*d^3*e^8*x^5 - 160160*a^3*b^7*B*d^3*e^8*x^5 - 120120*a^3*A*b^7*d^2*e^9*x^5 - 210210*a^4*b^6*B*d^2*e^9*x^5 - 210210*a^4*A*b^6*d*e^10*x^5 - 252252*a^5*b^5*B*d*e^10*x^5 - 336336*a^5*A*b^5*e^11*x^5 - 280280*a^6*b^4*B*e^11*x^5 - 33033*b^10*B*d^5*e^6*x^6 - 9009*A*b^10*d^4*e^7*x^6 - 90090*a*b^9*B*d^4*e^7*x^6 - 36036*a*A*b^9*d^3*e^8*x^6 - 162162*a^2*b^8*B*d^3*e^8*x^6 - 90090*a^2*A*b^8*d^2*e^9*x^6 - 240240*a^3*b^7*B*d^2*e^9*x^6 - 180180*a^3*A*b^7*d*e^10*x^6 - 315315*a^4*b^6*B*d*e^10*x^6 - 315315*a^4*A*b^6*e^11*x^6 - 378378*a^5*b^5*B*e^11*x^6 - 37752*b^10*B*d^4*e^7*x^7 - 10296*A*b^10*d^3*e^8*x^7 - 102960*a*b^9*B*d^3*e^8*x^7 - 41184*a*A*b^9*d^2*e^9*x^7 - 185328*a^2*b^8*B*d^2*e^9*x^7 - 102960*a^2*A*b^8*d*e^10*x^7 - 274560*a^3*b^7*B*d*e^10*x^7 - 205920*a^3*A*b^7*e^11*x^7 - 360360*a^4*b^6*B*e^11*x^7 - 33033*b^10*B*d^3*e^8*x^8 - 9009*A*b^10*d^2*e^9*x^8 - 90090*a*b^9*B*d^2*e^9*x^8 - 36036*a*A*b^9*d*e^10*x^8 - 162162*a^2*b^8*B*d*e^10*x^8 - 90090*a^2*A*b^8*e^11*x^8 - 240240*a^3*b^7*B*e^11*x^8 - 22022*b^10*B*d^2*e^9*x^9 - 6006*A*b^10*d*e^10*x^9 - 60060*a*b^9*B*d*e^10*x^9 - 24024*a*A*b^9*e^11*x^9 - 108108*a^2*b^8*B*e^11*x^9 - 11011*b^10*B*d*e^10*x^10 - 3003*A*b^10*e^11*x^10 - 30030*a*b^9*B*e^11*x^10 - 4004*b^10*B*e^11*x^11)/(12012*e^12*(d + e*x)^14)","B",1
1104,1,2234,235,1.0863849,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{16}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^16,x]","\text{Result too large to show}","\frac{b^3 (a+b x)^{11} (-15 a B e+4 A b e+11 b B d)}{60060 e (d+e x)^{11} (b d-a e)^5}+\frac{b^2 (a+b x)^{11} (-15 a B e+4 A b e+11 b B d)}{5460 e (d+e x)^{12} (b d-a e)^4}+\frac{b (a+b x)^{11} (-15 a B e+4 A b e+11 b B d)}{910 e (d+e x)^{13} (b d-a e)^3}+\frac{(a+b x)^{11} (-15 a B e+4 A b e+11 b B d)}{210 e (d+e x)^{14} (b d-a e)^2}-\frac{(a+b x)^{11} (B d-A e)}{15 e (d+e x)^{15} (b d-a e)}",1,"(-11*b^10*B*d^11 - 4*A*b^10*d^10*e - 40*a*b^9*B*d^10*e - 20*a*A*b^9*d^9*e^2 - 90*a^2*b^8*B*d^9*e^2 - 60*a^2*A*b^8*d^8*e^3 - 160*a^3*b^7*B*d^8*e^3 - 140*a^3*A*b^7*d^7*e^4 - 245*a^4*b^6*B*d^7*e^4 - 280*a^4*A*b^6*d^6*e^5 - 336*a^5*b^5*B*d^6*e^5 - 504*a^5*A*b^5*d^5*e^6 - 420*a^6*b^4*B*d^5*e^6 - 840*a^6*A*b^4*d^4*e^7 - 480*a^7*b^3*B*d^4*e^7 - 1320*a^7*A*b^3*d^3*e^8 - 495*a^8*b^2*B*d^3*e^8 - 1980*a^8*A*b^2*d^2*e^9 - 440*a^9*b*B*d^2*e^9 - 2860*a^9*A*b*d*e^10 - 286*a^10*B*d*e^10 - 4004*a^10*A*e^11 - 165*b^10*B*d^10*e*x - 60*A*b^10*d^9*e^2*x - 600*a*b^9*B*d^9*e^2*x - 300*a*A*b^9*d^8*e^3*x - 1350*a^2*b^8*B*d^8*e^3*x - 900*a^2*A*b^8*d^7*e^4*x - 2400*a^3*b^7*B*d^7*e^4*x - 2100*a^3*A*b^7*d^6*e^5*x - 3675*a^4*b^6*B*d^6*e^5*x - 4200*a^4*A*b^6*d^5*e^6*x - 5040*a^5*b^5*B*d^5*e^6*x - 7560*a^5*A*b^5*d^4*e^7*x - 6300*a^6*b^4*B*d^4*e^7*x - 12600*a^6*A*b^4*d^3*e^8*x - 7200*a^7*b^3*B*d^3*e^8*x - 19800*a^7*A*b^3*d^2*e^9*x - 7425*a^8*b^2*B*d^2*e^9*x - 29700*a^8*A*b^2*d*e^10*x - 6600*a^9*b*B*d*e^10*x - 42900*a^9*A*b*e^11*x - 4290*a^10*B*e^11*x - 1155*b^10*B*d^9*e^2*x^2 - 420*A*b^10*d^8*e^3*x^2 - 4200*a*b^9*B*d^8*e^3*x^2 - 2100*a*A*b^9*d^7*e^4*x^2 - 9450*a^2*b^8*B*d^7*e^4*x^2 - 6300*a^2*A*b^8*d^6*e^5*x^2 - 16800*a^3*b^7*B*d^6*e^5*x^2 - 14700*a^3*A*b^7*d^5*e^6*x^2 - 25725*a^4*b^6*B*d^5*e^6*x^2 - 29400*a^4*A*b^6*d^4*e^7*x^2 - 35280*a^5*b^5*B*d^4*e^7*x^2 - 52920*a^5*A*b^5*d^3*e^8*x^2 - 44100*a^6*b^4*B*d^3*e^8*x^2 - 88200*a^6*A*b^4*d^2*e^9*x^2 - 50400*a^7*b^3*B*d^2*e^9*x^2 - 138600*a^7*A*b^3*d*e^10*x^2 - 51975*a^8*b^2*B*d*e^10*x^2 - 207900*a^8*A*b^2*e^11*x^2 - 46200*a^9*b*B*e^11*x^2 - 5005*b^10*B*d^8*e^3*x^3 - 1820*A*b^10*d^7*e^4*x^3 - 18200*a*b^9*B*d^7*e^4*x^3 - 9100*a*A*b^9*d^6*e^5*x^3 - 40950*a^2*b^8*B*d^6*e^5*x^3 - 27300*a^2*A*b^8*d^5*e^6*x^3 - 72800*a^3*b^7*B*d^5*e^6*x^3 - 63700*a^3*A*b^7*d^4*e^7*x^3 - 111475*a^4*b^6*B*d^4*e^7*x^3 - 127400*a^4*A*b^6*d^3*e^8*x^3 - 152880*a^5*b^5*B*d^3*e^8*x^3 - 229320*a^5*A*b^5*d^2*e^9*x^3 - 191100*a^6*b^4*B*d^2*e^9*x^3 - 382200*a^6*A*b^4*d*e^10*x^3 - 218400*a^7*b^3*B*d*e^10*x^3 - 600600*a^7*A*b^3*e^11*x^3 - 225225*a^8*b^2*B*e^11*x^3 - 15015*b^10*B*d^7*e^4*x^4 - 5460*A*b^10*d^6*e^5*x^4 - 54600*a*b^9*B*d^6*e^5*x^4 - 27300*a*A*b^9*d^5*e^6*x^4 - 122850*a^2*b^8*B*d^5*e^6*x^4 - 81900*a^2*A*b^8*d^4*e^7*x^4 - 218400*a^3*b^7*B*d^4*e^7*x^4 - 191100*a^3*A*b^7*d^3*e^8*x^4 - 334425*a^4*b^6*B*d^3*e^8*x^4 - 382200*a^4*A*b^6*d^2*e^9*x^4 - 458640*a^5*b^5*B*d^2*e^9*x^4 - 687960*a^5*A*b^5*d*e^10*x^4 - 573300*a^6*b^4*B*d*e^10*x^4 - 1146600*a^6*A*b^4*e^11*x^4 - 655200*a^7*b^3*B*e^11*x^4 - 33033*b^10*B*d^6*e^5*x^5 - 12012*A*b^10*d^5*e^6*x^5 - 120120*a*b^9*B*d^5*e^6*x^5 - 60060*a*A*b^9*d^4*e^7*x^5 - 270270*a^2*b^8*B*d^4*e^7*x^5 - 180180*a^2*A*b^8*d^3*e^8*x^5 - 480480*a^3*b^7*B*d^3*e^8*x^5 - 420420*a^3*A*b^7*d^2*e^9*x^5 - 735735*a^4*b^6*B*d^2*e^9*x^5 - 840840*a^4*A*b^6*d*e^10*x^5 - 1009008*a^5*b^5*B*d*e^10*x^5 - 1513512*a^5*A*b^5*e^11*x^5 - 1261260*a^6*b^4*B*e^11*x^5 - 55055*b^10*B*d^5*e^6*x^6 - 20020*A*b^10*d^4*e^7*x^6 - 200200*a*b^9*B*d^4*e^7*x^6 - 100100*a*A*b^9*d^3*e^8*x^6 - 450450*a^2*b^8*B*d^3*e^8*x^6 - 300300*a^2*A*b^8*d^2*e^9*x^6 - 800800*a^3*b^7*B*d^2*e^9*x^6 - 700700*a^3*A*b^7*d*e^10*x^6 - 1226225*a^4*b^6*B*d*e^10*x^6 - 1401400*a^4*A*b^6*e^11*x^6 - 1681680*a^5*b^5*B*e^11*x^6 - 70785*b^10*B*d^4*e^7*x^7 - 25740*A*b^10*d^3*e^8*x^7 - 257400*a*b^9*B*d^3*e^8*x^7 - 128700*a*A*b^9*d^2*e^9*x^7 - 579150*a^2*b^8*B*d^2*e^9*x^7 - 386100*a^2*A*b^8*d*e^10*x^7 - 1029600*a^3*b^7*B*d*e^10*x^7 - 900900*a^3*A*b^7*e^11*x^7 - 1576575*a^4*b^6*B*e^11*x^7 - 70785*b^10*B*d^3*e^8*x^8 - 25740*A*b^10*d^2*e^9*x^8 - 257400*a*b^9*B*d^2*e^9*x^8 - 128700*a*A*b^9*d*e^10*x^8 - 579150*a^2*b^8*B*d*e^10*x^8 - 386100*a^2*A*b^8*e^11*x^8 - 1029600*a^3*b^7*B*e^11*x^8 - 55055*b^10*B*d^2*e^9*x^9 - 20020*A*b^10*d*e^10*x^9 - 200200*a*b^9*B*d*e^10*x^9 - 100100*a*A*b^9*e^11*x^9 - 450450*a^2*b^8*B*e^11*x^9 - 33033*b^10*B*d*e^10*x^10 - 12012*A*b^10*e^11*x^10 - 120120*a*b^9*B*e^11*x^10 - 15015*b^10*B*e^11*x^11)/(60060*e^12*(d + e*x)^15)","B",1
1105,1,2234,285,1.0384207,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{17}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^17,x]","\text{Result too large to show}","\frac{b^4 (a+b x)^{11} (-16 a B e+5 A b e+11 b B d)}{240240 e (d+e x)^{11} (b d-a e)^6}+\frac{b^3 (a+b x)^{11} (-16 a B e+5 A b e+11 b B d)}{21840 e (d+e x)^{12} (b d-a e)^5}+\frac{b^2 (a+b x)^{11} (-16 a B e+5 A b e+11 b B d)}{3640 e (d+e x)^{13} (b d-a e)^4}+\frac{b (a+b x)^{11} (-16 a B e+5 A b e+11 b B d)}{840 e (d+e x)^{14} (b d-a e)^3}+\frac{(a+b x)^{11} (-16 a B e+5 A b e+11 b B d)}{240 e (d+e x)^{15} (b d-a e)^2}-\frac{(a+b x)^{11} (B d-A e)}{16 e (d+e x)^{16} (b d-a e)}",1,"(-11*b^10*B*d^11 - 5*A*b^10*d^10*e - 50*a*b^9*B*d^10*e - 30*a*A*b^9*d^9*e^2 - 135*a^2*b^8*B*d^9*e^2 - 105*a^2*A*b^8*d^8*e^3 - 280*a^3*b^7*B*d^8*e^3 - 280*a^3*A*b^7*d^7*e^4 - 490*a^4*b^6*B*d^7*e^4 - 630*a^4*A*b^6*d^6*e^5 - 756*a^5*b^5*B*d^6*e^5 - 1260*a^5*A*b^5*d^5*e^6 - 1050*a^6*b^4*B*d^5*e^6 - 2310*a^6*A*b^4*d^4*e^7 - 1320*a^7*b^3*B*d^4*e^7 - 3960*a^7*A*b^3*d^3*e^8 - 1485*a^8*b^2*B*d^3*e^8 - 6435*a^8*A*b^2*d^2*e^9 - 1430*a^9*b*B*d^2*e^9 - 10010*a^9*A*b*d*e^10 - 1001*a^10*B*d*e^10 - 15015*a^10*A*e^11 - 176*b^10*B*d^10*e*x - 80*A*b^10*d^9*e^2*x - 800*a*b^9*B*d^9*e^2*x - 480*a*A*b^9*d^8*e^3*x - 2160*a^2*b^8*B*d^8*e^3*x - 1680*a^2*A*b^8*d^7*e^4*x - 4480*a^3*b^7*B*d^7*e^4*x - 4480*a^3*A*b^7*d^6*e^5*x - 7840*a^4*b^6*B*d^6*e^5*x - 10080*a^4*A*b^6*d^5*e^6*x - 12096*a^5*b^5*B*d^5*e^6*x - 20160*a^5*A*b^5*d^4*e^7*x - 16800*a^6*b^4*B*d^4*e^7*x - 36960*a^6*A*b^4*d^3*e^8*x - 21120*a^7*b^3*B*d^3*e^8*x - 63360*a^7*A*b^3*d^2*e^9*x - 23760*a^8*b^2*B*d^2*e^9*x - 102960*a^8*A*b^2*d*e^10*x - 22880*a^9*b*B*d*e^10*x - 160160*a^9*A*b*e^11*x - 16016*a^10*B*e^11*x - 1320*b^10*B*d^9*e^2*x^2 - 600*A*b^10*d^8*e^3*x^2 - 6000*a*b^9*B*d^8*e^3*x^2 - 3600*a*A*b^9*d^7*e^4*x^2 - 16200*a^2*b^8*B*d^7*e^4*x^2 - 12600*a^2*A*b^8*d^6*e^5*x^2 - 33600*a^3*b^7*B*d^6*e^5*x^2 - 33600*a^3*A*b^7*d^5*e^6*x^2 - 58800*a^4*b^6*B*d^5*e^6*x^2 - 75600*a^4*A*b^6*d^4*e^7*x^2 - 90720*a^5*b^5*B*d^4*e^7*x^2 - 151200*a^5*A*b^5*d^3*e^8*x^2 - 126000*a^6*b^4*B*d^3*e^8*x^2 - 277200*a^6*A*b^4*d^2*e^9*x^2 - 158400*a^7*b^3*B*d^2*e^9*x^2 - 475200*a^7*A*b^3*d*e^10*x^2 - 178200*a^8*b^2*B*d*e^10*x^2 - 772200*a^8*A*b^2*e^11*x^2 - 171600*a^9*b*B*e^11*x^2 - 6160*b^10*B*d^8*e^3*x^3 - 2800*A*b^10*d^7*e^4*x^3 - 28000*a*b^9*B*d^7*e^4*x^3 - 16800*a*A*b^9*d^6*e^5*x^3 - 75600*a^2*b^8*B*d^6*e^5*x^3 - 58800*a^2*A*b^8*d^5*e^6*x^3 - 156800*a^3*b^7*B*d^5*e^6*x^3 - 156800*a^3*A*b^7*d^4*e^7*x^3 - 274400*a^4*b^6*B*d^4*e^7*x^3 - 352800*a^4*A*b^6*d^3*e^8*x^3 - 423360*a^5*b^5*B*d^3*e^8*x^3 - 705600*a^5*A*b^5*d^2*e^9*x^3 - 588000*a^6*b^4*B*d^2*e^9*x^3 - 1293600*a^6*A*b^4*d*e^10*x^3 - 739200*a^7*b^3*B*d*e^10*x^3 - 2217600*a^7*A*b^3*e^11*x^3 - 831600*a^8*b^2*B*e^11*x^3 - 20020*b^10*B*d^7*e^4*x^4 - 9100*A*b^10*d^6*e^5*x^4 - 91000*a*b^9*B*d^6*e^5*x^4 - 54600*a*A*b^9*d^5*e^6*x^4 - 245700*a^2*b^8*B*d^5*e^6*x^4 - 191100*a^2*A*b^8*d^4*e^7*x^4 - 509600*a^3*b^7*B*d^4*e^7*x^4 - 509600*a^3*A*b^7*d^3*e^8*x^4 - 891800*a^4*b^6*B*d^3*e^8*x^4 - 1146600*a^4*A*b^6*d^2*e^9*x^4 - 1375920*a^5*b^5*B*d^2*e^9*x^4 - 2293200*a^5*A*b^5*d*e^10*x^4 - 1911000*a^6*b^4*B*d*e^10*x^4 - 4204200*a^6*A*b^4*e^11*x^4 - 2402400*a^7*b^3*B*e^11*x^4 - 48048*b^10*B*d^6*e^5*x^5 - 21840*A*b^10*d^5*e^6*x^5 - 218400*a*b^9*B*d^5*e^6*x^5 - 131040*a*A*b^9*d^4*e^7*x^5 - 589680*a^2*b^8*B*d^4*e^7*x^5 - 458640*a^2*A*b^8*d^3*e^8*x^5 - 1223040*a^3*b^7*B*d^3*e^8*x^5 - 1223040*a^3*A*b^7*d^2*e^9*x^5 - 2140320*a^4*b^6*B*d^2*e^9*x^5 - 2751840*a^4*A*b^6*d*e^10*x^5 - 3302208*a^5*b^5*B*d*e^10*x^5 - 5503680*a^5*A*b^5*e^11*x^5 - 4586400*a^6*b^4*B*e^11*x^5 - 88088*b^10*B*d^5*e^6*x^6 - 40040*A*b^10*d^4*e^7*x^6 - 400400*a*b^9*B*d^4*e^7*x^6 - 240240*a*A*b^9*d^3*e^8*x^6 - 1081080*a^2*b^8*B*d^3*e^8*x^6 - 840840*a^2*A*b^8*d^2*e^9*x^6 - 2242240*a^3*b^7*B*d^2*e^9*x^6 - 2242240*a^3*A*b^7*d*e^10*x^6 - 3923920*a^4*b^6*B*d*e^10*x^6 - 5045040*a^4*A*b^6*e^11*x^6 - 6054048*a^5*b^5*B*e^11*x^6 - 125840*b^10*B*d^4*e^7*x^7 - 57200*A*b^10*d^3*e^8*x^7 - 572000*a*b^9*B*d^3*e^8*x^7 - 343200*a*A*b^9*d^2*e^9*x^7 - 1544400*a^2*b^8*B*d^2*e^9*x^7 - 1201200*a^2*A*b^8*d*e^10*x^7 - 3203200*a^3*b^7*B*d*e^10*x^7 - 3203200*a^3*A*b^7*e^11*x^7 - 5605600*a^4*b^6*B*e^11*x^7 - 141570*b^10*B*d^3*e^8*x^8 - 64350*A*b^10*d^2*e^9*x^8 - 643500*a*b^9*B*d^2*e^9*x^8 - 386100*a*A*b^9*d*e^10*x^8 - 1737450*a^2*b^8*B*d*e^10*x^8 - 1351350*a^2*A*b^8*e^11*x^8 - 3603600*a^3*b^7*B*e^11*x^8 - 125840*b^10*B*d^2*e^9*x^9 - 57200*A*b^10*d*e^10*x^9 - 572000*a*b^9*B*d*e^10*x^9 - 343200*a*A*b^9*e^11*x^9 - 1544400*a^2*b^8*B*e^11*x^9 - 88088*b^10*B*d*e^10*x^10 - 40040*A*b^10*e^11*x^10 - 400400*a*b^9*B*e^11*x^10 - 48048*b^10*B*e^11*x^11)/(240240*e^12*(d + e*x)^16)","B",1
1106,1,2234,335,1.0176255,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{18}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^18,x]","\text{Result too large to show}","\frac{b^5 (a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{816816 e (d+e x)^{11} (b d-a e)^7}+\frac{b^4 (a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{74256 e (d+e x)^{12} (b d-a e)^6}+\frac{b^3 (a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{12376 e (d+e x)^{13} (b d-a e)^5}+\frac{b^2 (a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{2856 e (d+e x)^{14} (b d-a e)^4}+\frac{b (a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{816 e (d+e x)^{15} (b d-a e)^3}+\frac{(a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{272 e (d+e x)^{16} (b d-a e)^2}-\frac{(a+b x)^{11} (B d-A e)}{17 e (d+e x)^{17} (b d-a e)}",1,"(-11*b^10*B*d^11 - 6*A*b^10*d^10*e - 60*a*b^9*B*d^10*e - 42*a*A*b^9*d^9*e^2 - 189*a^2*b^8*B*d^9*e^2 - 168*a^2*A*b^8*d^8*e^3 - 448*a^3*b^7*B*d^8*e^3 - 504*a^3*A*b^7*d^7*e^4 - 882*a^4*b^6*B*d^7*e^4 - 1260*a^4*A*b^6*d^6*e^5 - 1512*a^5*b^5*B*d^6*e^5 - 2772*a^5*A*b^5*d^5*e^6 - 2310*a^6*b^4*B*d^5*e^6 - 5544*a^6*A*b^4*d^4*e^7 - 3168*a^7*b^3*B*d^4*e^7 - 10296*a^7*A*b^3*d^3*e^8 - 3861*a^8*b^2*B*d^3*e^8 - 18018*a^8*A*b^2*d^2*e^9 - 4004*a^9*b*B*d^2*e^9 - 30030*a^9*A*b*d*e^10 - 3003*a^10*B*d*e^10 - 48048*a^10*A*e^11 - 187*b^10*B*d^10*e*x - 102*A*b^10*d^9*e^2*x - 1020*a*b^9*B*d^9*e^2*x - 714*a*A*b^9*d^8*e^3*x - 3213*a^2*b^8*B*d^8*e^3*x - 2856*a^2*A*b^8*d^7*e^4*x - 7616*a^3*b^7*B*d^7*e^4*x - 8568*a^3*A*b^7*d^6*e^5*x - 14994*a^4*b^6*B*d^6*e^5*x - 21420*a^4*A*b^6*d^5*e^6*x - 25704*a^5*b^5*B*d^5*e^6*x - 47124*a^5*A*b^5*d^4*e^7*x - 39270*a^6*b^4*B*d^4*e^7*x - 94248*a^6*A*b^4*d^3*e^8*x - 53856*a^7*b^3*B*d^3*e^8*x - 175032*a^7*A*b^3*d^2*e^9*x - 65637*a^8*b^2*B*d^2*e^9*x - 306306*a^8*A*b^2*d*e^10*x - 68068*a^9*b*B*d*e^10*x - 510510*a^9*A*b*e^11*x - 51051*a^10*B*e^11*x - 1496*b^10*B*d^9*e^2*x^2 - 816*A*b^10*d^8*e^3*x^2 - 8160*a*b^9*B*d^8*e^3*x^2 - 5712*a*A*b^9*d^7*e^4*x^2 - 25704*a^2*b^8*B*d^7*e^4*x^2 - 22848*a^2*A*b^8*d^6*e^5*x^2 - 60928*a^3*b^7*B*d^6*e^5*x^2 - 68544*a^3*A*b^7*d^5*e^6*x^2 - 119952*a^4*b^6*B*d^5*e^6*x^2 - 171360*a^4*A*b^6*d^4*e^7*x^2 - 205632*a^5*b^5*B*d^4*e^7*x^2 - 376992*a^5*A*b^5*d^3*e^8*x^2 - 314160*a^6*b^4*B*d^3*e^8*x^2 - 753984*a^6*A*b^4*d^2*e^9*x^2 - 430848*a^7*b^3*B*d^2*e^9*x^2 - 1400256*a^7*A*b^3*d*e^10*x^2 - 525096*a^8*b^2*B*d*e^10*x^2 - 2450448*a^8*A*b^2*e^11*x^2 - 544544*a^9*b*B*e^11*x^2 - 7480*b^10*B*d^8*e^3*x^3 - 4080*A*b^10*d^7*e^4*x^3 - 40800*a*b^9*B*d^7*e^4*x^3 - 28560*a*A*b^9*d^6*e^5*x^3 - 128520*a^2*b^8*B*d^6*e^5*x^3 - 114240*a^2*A*b^8*d^5*e^6*x^3 - 304640*a^3*b^7*B*d^5*e^6*x^3 - 342720*a^3*A*b^7*d^4*e^7*x^3 - 599760*a^4*b^6*B*d^4*e^7*x^3 - 856800*a^4*A*b^6*d^3*e^8*x^3 - 1028160*a^5*b^5*B*d^3*e^8*x^3 - 1884960*a^5*A*b^5*d^2*e^9*x^3 - 1570800*a^6*b^4*B*d^2*e^9*x^3 - 3769920*a^6*A*b^4*d*e^10*x^3 - 2154240*a^7*b^3*B*d*e^10*x^3 - 7001280*a^7*A*b^3*e^11*x^3 - 2625480*a^8*b^2*B*e^11*x^3 - 26180*b^10*B*d^7*e^4*x^4 - 14280*A*b^10*d^6*e^5*x^4 - 142800*a*b^9*B*d^6*e^5*x^4 - 99960*a*A*b^9*d^5*e^6*x^4 - 449820*a^2*b^8*B*d^5*e^6*x^4 - 399840*a^2*A*b^8*d^4*e^7*x^4 - 1066240*a^3*b^7*B*d^4*e^7*x^4 - 1199520*a^3*A*b^7*d^3*e^8*x^4 - 2099160*a^4*b^6*B*d^3*e^8*x^4 - 2998800*a^4*A*b^6*d^2*e^9*x^4 - 3598560*a^5*b^5*B*d^2*e^9*x^4 - 6597360*a^5*A*b^5*d*e^10*x^4 - 5497800*a^6*b^4*B*d*e^10*x^4 - 13194720*a^6*A*b^4*e^11*x^4 - 7539840*a^7*b^3*B*e^11*x^4 - 68068*b^10*B*d^6*e^5*x^5 - 37128*A*b^10*d^5*e^6*x^5 - 371280*a*b^9*B*d^5*e^6*x^5 - 259896*a*A*b^9*d^4*e^7*x^5 - 1169532*a^2*b^8*B*d^4*e^7*x^5 - 1039584*a^2*A*b^8*d^3*e^8*x^5 - 2772224*a^3*b^7*B*d^3*e^8*x^5 - 3118752*a^3*A*b^7*d^2*e^9*x^5 - 5457816*a^4*b^6*B*d^2*e^9*x^5 - 7796880*a^4*A*b^6*d*e^10*x^5 - 9356256*a^5*b^5*B*d*e^10*x^5 - 17153136*a^5*A*b^5*e^11*x^5 - 14294280*a^6*b^4*B*e^11*x^5 - 136136*b^10*B*d^5*e^6*x^6 - 74256*A*b^10*d^4*e^7*x^6 - 742560*a*b^9*B*d^4*e^7*x^6 - 519792*a*A*b^9*d^3*e^8*x^6 - 2339064*a^2*b^8*B*d^3*e^8*x^6 - 2079168*a^2*A*b^8*d^2*e^9*x^6 - 5544448*a^3*b^7*B*d^2*e^9*x^6 - 6237504*a^3*A*b^7*d*e^10*x^6 - 10915632*a^4*b^6*B*d*e^10*x^6 - 15593760*a^4*A*b^6*e^11*x^6 - 18712512*a^5*b^5*B*e^11*x^6 - 213928*b^10*B*d^4*e^7*x^7 - 116688*A*b^10*d^3*e^8*x^7 - 1166880*a*b^9*B*d^3*e^8*x^7 - 816816*a*A*b^9*d^2*e^9*x^7 - 3675672*a^2*b^8*B*d^2*e^9*x^7 - 3267264*a^2*A*b^8*d*e^10*x^7 - 8712704*a^3*b^7*B*d*e^10*x^7 - 9801792*a^3*A*b^7*e^11*x^7 - 17153136*a^4*b^6*B*e^11*x^7 - 267410*b^10*B*d^3*e^8*x^8 - 145860*A*b^10*d^2*e^9*x^8 - 1458600*a*b^9*B*d^2*e^9*x^8 - 1021020*a*A*b^9*d*e^10*x^8 - 4594590*a^2*b^8*B*d*e^10*x^8 - 4084080*a^2*A*b^8*e^11*x^8 - 10890880*a^3*b^7*B*e^11*x^8 - 267410*b^10*B*d^2*e^9*x^9 - 145860*A*b^10*d*e^10*x^9 - 1458600*a*b^9*B*d*e^10*x^9 - 1021020*a*A*b^9*e^11*x^9 - 4594590*a^2*b^8*B*e^11*x^9 - 213928*b^10*B*d*e^10*x^10 - 116688*A*b^10*e^11*x^10 - 1166880*a*b^9*B*e^11*x^10 - 136136*b^10*B*e^11*x^11)/(816816*e^12*(d + e*x)^17)","B",1
1107,1,2234,385,1.0446504,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{19}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^19,x]","\text{Result too large to show}","\frac{b^6 (a+b x)^{11} (-18 a B e+7 A b e+11 b B d)}{2450448 e (d+e x)^{11} (b d-a e)^8}+\frac{b^5 (a+b x)^{11} (-18 a B e+7 A b e+11 b B d)}{222768 e (d+e x)^{12} (b d-a e)^7}+\frac{b^4 (a+b x)^{11} (-18 a B e+7 A b e+11 b B d)}{37128 e (d+e x)^{13} (b d-a e)^6}+\frac{b^3 (a+b x)^{11} (-18 a B e+7 A b e+11 b B d)}{8568 e (d+e x)^{14} (b d-a e)^5}+\frac{b^2 (a+b x)^{11} (-18 a B e+7 A b e+11 b B d)}{2448 e (d+e x)^{15} (b d-a e)^4}+\frac{b (a+b x)^{11} (-18 a B e+7 A b e+11 b B d)}{816 e (d+e x)^{16} (b d-a e)^3}+\frac{(a+b x)^{11} (-18 a B e+7 A b e+11 b B d)}{306 e (d+e x)^{17} (b d-a e)^2}-\frac{(a+b x)^{11} (B d-A e)}{18 e (d+e x)^{18} (b d-a e)}",1,"(-11*b^10*B*d^11 - 7*A*b^10*d^10*e - 70*a*b^9*B*d^10*e - 56*a*A*b^9*d^9*e^2 - 252*a^2*b^8*B*d^9*e^2 - 252*a^2*A*b^8*d^8*e^3 - 672*a^3*b^7*B*d^8*e^3 - 840*a^3*A*b^7*d^7*e^4 - 1470*a^4*b^6*B*d^7*e^4 - 2310*a^4*A*b^6*d^6*e^5 - 2772*a^5*b^5*B*d^6*e^5 - 5544*a^5*A*b^5*d^5*e^6 - 4620*a^6*b^4*B*d^5*e^6 - 12012*a^6*A*b^4*d^4*e^7 - 6864*a^7*b^3*B*d^4*e^7 - 24024*a^7*A*b^3*d^3*e^8 - 9009*a^8*b^2*B*d^3*e^8 - 45045*a^8*A*b^2*d^2*e^9 - 10010*a^9*b*B*d^2*e^9 - 80080*a^9*A*b*d*e^10 - 8008*a^10*B*d*e^10 - 136136*a^10*A*e^11 - 198*b^10*B*d^10*e*x - 126*A*b^10*d^9*e^2*x - 1260*a*b^9*B*d^9*e^2*x - 1008*a*A*b^9*d^8*e^3*x - 4536*a^2*b^8*B*d^8*e^3*x - 4536*a^2*A*b^8*d^7*e^4*x - 12096*a^3*b^7*B*d^7*e^4*x - 15120*a^3*A*b^7*d^6*e^5*x - 26460*a^4*b^6*B*d^6*e^5*x - 41580*a^4*A*b^6*d^5*e^6*x - 49896*a^5*b^5*B*d^5*e^6*x - 99792*a^5*A*b^5*d^4*e^7*x - 83160*a^6*b^4*B*d^4*e^7*x - 216216*a^6*A*b^4*d^3*e^8*x - 123552*a^7*b^3*B*d^3*e^8*x - 432432*a^7*A*b^3*d^2*e^9*x - 162162*a^8*b^2*B*d^2*e^9*x - 810810*a^8*A*b^2*d*e^10*x - 180180*a^9*b*B*d*e^10*x - 1441440*a^9*A*b*e^11*x - 144144*a^10*B*e^11*x - 1683*b^10*B*d^9*e^2*x^2 - 1071*A*b^10*d^8*e^3*x^2 - 10710*a*b^9*B*d^8*e^3*x^2 - 8568*a*A*b^9*d^7*e^4*x^2 - 38556*a^2*b^8*B*d^7*e^4*x^2 - 38556*a^2*A*b^8*d^6*e^5*x^2 - 102816*a^3*b^7*B*d^6*e^5*x^2 - 128520*a^3*A*b^7*d^5*e^6*x^2 - 224910*a^4*b^6*B*d^5*e^6*x^2 - 353430*a^4*A*b^6*d^4*e^7*x^2 - 424116*a^5*b^5*B*d^4*e^7*x^2 - 848232*a^5*A*b^5*d^3*e^8*x^2 - 706860*a^6*b^4*B*d^3*e^8*x^2 - 1837836*a^6*A*b^4*d^2*e^9*x^2 - 1050192*a^7*b^3*B*d^2*e^9*x^2 - 3675672*a^7*A*b^3*d*e^10*x^2 - 1378377*a^8*b^2*B*d*e^10*x^2 - 6891885*a^8*A*b^2*e^11*x^2 - 1531530*a^9*b*B*e^11*x^2 - 8976*b^10*B*d^8*e^3*x^3 - 5712*A*b^10*d^7*e^4*x^3 - 57120*a*b^9*B*d^7*e^4*x^3 - 45696*a*A*b^9*d^6*e^5*x^3 - 205632*a^2*b^8*B*d^6*e^5*x^3 - 205632*a^2*A*b^8*d^5*e^6*x^3 - 548352*a^3*b^7*B*d^5*e^6*x^3 - 685440*a^3*A*b^7*d^4*e^7*x^3 - 1199520*a^4*b^6*B*d^4*e^7*x^3 - 1884960*a^4*A*b^6*d^3*e^8*x^3 - 2261952*a^5*b^5*B*d^3*e^8*x^3 - 4523904*a^5*A*b^5*d^2*e^9*x^3 - 3769920*a^6*b^4*B*d^2*e^9*x^3 - 9801792*a^6*A*b^4*d*e^10*x^3 - 5601024*a^7*b^3*B*d*e^10*x^3 - 19603584*a^7*A*b^3*e^11*x^3 - 7351344*a^8*b^2*B*e^11*x^3 - 33660*b^10*B*d^7*e^4*x^4 - 21420*A*b^10*d^6*e^5*x^4 - 214200*a*b^9*B*d^6*e^5*x^4 - 171360*a*A*b^9*d^5*e^6*x^4 - 771120*a^2*b^8*B*d^5*e^6*x^4 - 771120*a^2*A*b^8*d^4*e^7*x^4 - 2056320*a^3*b^7*B*d^4*e^7*x^4 - 2570400*a^3*A*b^7*d^3*e^8*x^4 - 4498200*a^4*b^6*B*d^3*e^8*x^4 - 7068600*a^4*A*b^6*d^2*e^9*x^4 - 8482320*a^5*b^5*B*d^2*e^9*x^4 - 16964640*a^5*A*b^5*d*e^10*x^4 - 14137200*a^6*b^4*B*d*e^10*x^4 - 36756720*a^6*A*b^4*e^11*x^4 - 21003840*a^7*b^3*B*e^11*x^4 - 94248*b^10*B*d^6*e^5*x^5 - 59976*A*b^10*d^5*e^6*x^5 - 599760*a*b^9*B*d^5*e^6*x^5 - 479808*a*A*b^9*d^4*e^7*x^5 - 2159136*a^2*b^8*B*d^4*e^7*x^5 - 2159136*a^2*A*b^8*d^3*e^8*x^5 - 5757696*a^3*b^7*B*d^3*e^8*x^5 - 7197120*a^3*A*b^7*d^2*e^9*x^5 - 12594960*a^4*b^6*B*d^2*e^9*x^5 - 19792080*a^4*A*b^6*d*e^10*x^5 - 23750496*a^5*b^5*B*d*e^10*x^5 - 47500992*a^5*A*b^5*e^11*x^5 - 39584160*a^6*b^4*B*e^11*x^5 - 204204*b^10*B*d^5*e^6*x^6 - 129948*A*b^10*d^4*e^7*x^6 - 1299480*a*b^9*B*d^4*e^7*x^6 - 1039584*a*A*b^9*d^3*e^8*x^6 - 4678128*a^2*b^8*B*d^3*e^8*x^6 - 4678128*a^2*A*b^8*d^2*e^9*x^6 - 12475008*a^3*b^7*B*d^2*e^9*x^6 - 15593760*a^3*A*b^7*d*e^10*x^6 - 27289080*a^4*b^6*B*d*e^10*x^6 - 42882840*a^4*A*b^6*e^11*x^6 - 51459408*a^5*b^5*B*e^11*x^6 - 350064*b^10*B*d^4*e^7*x^7 - 222768*A*b^10*d^3*e^8*x^7 - 2227680*a*b^9*B*d^3*e^8*x^7 - 1782144*a*A*b^9*d^2*e^9*x^7 - 8019648*a^2*b^8*B*d^2*e^9*x^7 - 8019648*a^2*A*b^8*d*e^10*x^7 - 21385728*a^3*b^7*B*d*e^10*x^7 - 26732160*a^3*A*b^7*e^11*x^7 - 46781280*a^4*b^6*B*e^11*x^7 - 481338*b^10*B*d^3*e^8*x^8 - 306306*A*b^10*d^2*e^9*x^8 - 3063060*a*b^9*B*d^2*e^9*x^8 - 2450448*a*A*b^9*d*e^10*x^8 - 11027016*a^2*b^8*B*d*e^10*x^8 - 11027016*a^2*A*b^8*e^11*x^8 - 29405376*a^3*b^7*B*e^11*x^8 - 534820*b^10*B*d^2*e^9*x^9 - 340340*A*b^10*d*e^10*x^9 - 3403400*a*b^9*B*d*e^10*x^9 - 2722720*a*A*b^9*e^11*x^9 - 12252240*a^2*b^8*B*e^11*x^9 - 481338*b^10*B*d*e^10*x^10 - 306306*A*b^10*e^11*x^10 - 3063060*a*b^9*B*e^11*x^10 - 350064*b^10*B*e^11*x^11)/(2450448*e^12*(d + e*x)^18)","B",1
1108,1,2234,460,1.0330177,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{20}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^20,x]","\text{Result too large to show}","\frac{b^9 (-10 a B e-A b e+11 b B d)}{9 e^{12} (d+e x)^9}-\frac{b^8 (b d-a e) (-9 a B e-2 A b e+11 b B d)}{2 e^{12} (d+e x)^{10}}+\frac{15 b^7 (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{11 e^{12} (d+e x)^{11}}-\frac{5 b^6 (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{2 e^{12} (d+e x)^{12}}+\frac{42 b^5 (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{13 e^{12} (d+e x)^{13}}-\frac{3 b^4 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{e^{12} (d+e x)^{14}}+\frac{2 b^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{e^{12} (d+e x)^{15}}-\frac{15 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{16 e^{12} (d+e x)^{16}}+\frac{5 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{17 e^{12} (d+e x)^{17}}-\frac{(b d-a e)^9 (-a B e-10 A b e+11 b B d)}{18 e^{12} (d+e x)^{18}}+\frac{(b d-a e)^{10} (B d-A e)}{19 e^{12} (d+e x)^{19}}-\frac{b^{10} B}{8 e^{12} (d+e x)^8}",1,"(-11*b^10*B*d^11 - 8*A*b^10*d^10*e - 80*a*b^9*B*d^10*e - 72*a*A*b^9*d^9*e^2 - 324*a^2*b^8*B*d^9*e^2 - 360*a^2*A*b^8*d^8*e^3 - 960*a^3*b^7*B*d^8*e^3 - 1320*a^3*A*b^7*d^7*e^4 - 2310*a^4*b^6*B*d^7*e^4 - 3960*a^4*A*b^6*d^6*e^5 - 4752*a^5*b^5*B*d^6*e^5 - 10296*a^5*A*b^5*d^5*e^6 - 8580*a^6*b^4*B*d^5*e^6 - 24024*a^6*A*b^4*d^4*e^7 - 13728*a^7*b^3*B*d^4*e^7 - 51480*a^7*A*b^3*d^3*e^8 - 19305*a^8*b^2*B*d^3*e^8 - 102960*a^8*A*b^2*d^2*e^9 - 22880*a^9*b*B*d^2*e^9 - 194480*a^9*A*b*d*e^10 - 19448*a^10*B*d*e^10 - 350064*a^10*A*e^11 - 209*b^10*B*d^10*e*x - 152*A*b^10*d^9*e^2*x - 1520*a*b^9*B*d^9*e^2*x - 1368*a*A*b^9*d^8*e^3*x - 6156*a^2*b^8*B*d^8*e^3*x - 6840*a^2*A*b^8*d^7*e^4*x - 18240*a^3*b^7*B*d^7*e^4*x - 25080*a^3*A*b^7*d^6*e^5*x - 43890*a^4*b^6*B*d^6*e^5*x - 75240*a^4*A*b^6*d^5*e^6*x - 90288*a^5*b^5*B*d^5*e^6*x - 195624*a^5*A*b^5*d^4*e^7*x - 163020*a^6*b^4*B*d^4*e^7*x - 456456*a^6*A*b^4*d^3*e^8*x - 260832*a^7*b^3*B*d^3*e^8*x - 978120*a^7*A*b^3*d^2*e^9*x - 366795*a^8*b^2*B*d^2*e^9*x - 1956240*a^8*A*b^2*d*e^10*x - 434720*a^9*b*B*d*e^10*x - 3695120*a^9*A*b*e^11*x - 369512*a^10*B*e^11*x - 1881*b^10*B*d^9*e^2*x^2 - 1368*A*b^10*d^8*e^3*x^2 - 13680*a*b^9*B*d^8*e^3*x^2 - 12312*a*A*b^9*d^7*e^4*x^2 - 55404*a^2*b^8*B*d^7*e^4*x^2 - 61560*a^2*A*b^8*d^6*e^5*x^2 - 164160*a^3*b^7*B*d^6*e^5*x^2 - 225720*a^3*A*b^7*d^5*e^6*x^2 - 395010*a^4*b^6*B*d^5*e^6*x^2 - 677160*a^4*A*b^6*d^4*e^7*x^2 - 812592*a^5*b^5*B*d^4*e^7*x^2 - 1760616*a^5*A*b^5*d^3*e^8*x^2 - 1467180*a^6*b^4*B*d^3*e^8*x^2 - 4108104*a^6*A*b^4*d^2*e^9*x^2 - 2347488*a^7*b^3*B*d^2*e^9*x^2 - 8803080*a^7*A*b^3*d*e^10*x^2 - 3301155*a^8*b^2*B*d*e^10*x^2 - 17606160*a^8*A*b^2*e^11*x^2 - 3912480*a^9*b*B*e^11*x^2 - 10659*b^10*B*d^8*e^3*x^3 - 7752*A*b^10*d^7*e^4*x^3 - 77520*a*b^9*B*d^7*e^4*x^3 - 69768*a*A*b^9*d^6*e^5*x^3 - 313956*a^2*b^8*B*d^6*e^5*x^3 - 348840*a^2*A*b^8*d^5*e^6*x^3 - 930240*a^3*b^7*B*d^5*e^6*x^3 - 1279080*a^3*A*b^7*d^4*e^7*x^3 - 2238390*a^4*b^6*B*d^4*e^7*x^3 - 3837240*a^4*A*b^6*d^3*e^8*x^3 - 4604688*a^5*b^5*B*d^3*e^8*x^3 - 9976824*a^5*A*b^5*d^2*e^9*x^3 - 8314020*a^6*b^4*B*d^2*e^9*x^3 - 23279256*a^6*A*b^4*d*e^10*x^3 - 13302432*a^7*b^3*B*d*e^10*x^3 - 49884120*a^7*A*b^3*e^11*x^3 - 18706545*a^8*b^2*B*e^11*x^3 - 42636*b^10*B*d^7*e^4*x^4 - 31008*A*b^10*d^6*e^5*x^4 - 310080*a*b^9*B*d^6*e^5*x^4 - 279072*a*A*b^9*d^5*e^6*x^4 - 1255824*a^2*b^8*B*d^5*e^6*x^4 - 1395360*a^2*A*b^8*d^4*e^7*x^4 - 3720960*a^3*b^7*B*d^4*e^7*x^4 - 5116320*a^3*A*b^7*d^3*e^8*x^4 - 8953560*a^4*b^6*B*d^3*e^8*x^4 - 15348960*a^4*A*b^6*d^2*e^9*x^4 - 18418752*a^5*b^5*B*d^2*e^9*x^4 - 39907296*a^5*A*b^5*d*e^10*x^4 - 33256080*a^6*b^4*B*d*e^10*x^4 - 93117024*a^6*A*b^4*e^11*x^4 - 53209728*a^7*b^3*B*e^11*x^4 - 127908*b^10*B*d^6*e^5*x^5 - 93024*A*b^10*d^5*e^6*x^5 - 930240*a*b^9*B*d^5*e^6*x^5 - 837216*a*A*b^9*d^4*e^7*x^5 - 3767472*a^2*b^8*B*d^4*e^7*x^5 - 4186080*a^2*A*b^8*d^3*e^8*x^5 - 11162880*a^3*b^7*B*d^3*e^8*x^5 - 15348960*a^3*A*b^7*d^2*e^9*x^5 - 26860680*a^4*b^6*B*d^2*e^9*x^5 - 46046880*a^4*A*b^6*d*e^10*x^5 - 55256256*a^5*b^5*B*d*e^10*x^5 - 119721888*a^5*A*b^5*e^11*x^5 - 99768240*a^6*b^4*B*e^11*x^5 - 298452*b^10*B*d^5*e^6*x^6 - 217056*A*b^10*d^4*e^7*x^6 - 2170560*a*b^9*B*d^4*e^7*x^6 - 1953504*a*A*b^9*d^3*e^8*x^6 - 8790768*a^2*b^8*B*d^3*e^8*x^6 - 9767520*a^2*A*b^8*d^2*e^9*x^6 - 26046720*a^3*b^7*B*d^2*e^9*x^6 - 35814240*a^3*A*b^7*d*e^10*x^6 - 62674920*a^4*b^6*B*d*e^10*x^6 - 107442720*a^4*A*b^6*e^11*x^6 - 128931264*a^5*b^5*B*e^11*x^6 - 554268*b^10*B*d^4*e^7*x^7 - 403104*A*b^10*d^3*e^8*x^7 - 4031040*a*b^9*B*d^3*e^8*x^7 - 3627936*a*A*b^9*d^2*e^9*x^7 - 16325712*a^2*b^8*B*d^2*e^9*x^7 - 18139680*a^2*A*b^8*d*e^10*x^7 - 48372480*a^3*b^7*B*d*e^10*x^7 - 66512160*a^3*A*b^7*e^11*x^7 - 116396280*a^4*b^6*B*e^11*x^7 - 831402*b^10*B*d^3*e^8*x^8 - 604656*A*b^10*d^2*e^9*x^8 - 6046560*a*b^9*B*d^2*e^9*x^8 - 5441904*a*A*b^9*d*e^10*x^8 - 24488568*a^2*b^8*B*d*e^10*x^8 - 27209520*a^2*A*b^8*e^11*x^8 - 72558720*a^3*b^7*B*e^11*x^8 - 1016158*b^10*B*d^2*e^9*x^9 - 739024*A*b^10*d*e^10*x^9 - 7390240*a*b^9*B*d*e^10*x^9 - 6651216*a*A*b^9*e^11*x^9 - 29930472*a^2*b^8*B*e^11*x^9 - 1016158*b^10*B*d*e^10*x^10 - 739024*A*b^10*e^11*x^10 - 7390240*a*b^9*B*e^11*x^10 - 831402*b^10*B*e^11*x^11)/(6651216*e^12*(d + e*x)^19)","B",1
1109,1,2234,462,1.0057987,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{21}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^21,x]","\text{Result too large to show}","\frac{b^9 (-10 a B e-A b e+11 b B d)}{10 e^{12} (d+e x)^{10}}-\frac{5 b^8 (b d-a e) (-9 a B e-2 A b e+11 b B d)}{11 e^{12} (d+e x)^{11}}+\frac{5 b^7 (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{4 e^{12} (d+e x)^{12}}-\frac{30 b^6 (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{13 e^{12} (d+e x)^{13}}+\frac{3 b^5 (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{e^{12} (d+e x)^{14}}-\frac{14 b^4 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{5 e^{12} (d+e x)^{15}}+\frac{15 b^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{8 e^{12} (d+e x)^{16}}-\frac{15 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{17 e^{12} (d+e x)^{17}}+\frac{5 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{18 e^{12} (d+e x)^{18}}-\frac{(b d-a e)^9 (-a B e-10 A b e+11 b B d)}{19 e^{12} (d+e x)^{19}}+\frac{(b d-a e)^{10} (B d-A e)}{20 e^{12} (d+e x)^{20}}-\frac{b^{10} B}{9 e^{12} (d+e x)^9}",1,"(-11*b^10*B*d^11 - 9*A*b^10*d^10*e - 90*a*b^9*B*d^10*e - 90*a*A*b^9*d^9*e^2 - 405*a^2*b^8*B*d^9*e^2 - 495*a^2*A*b^8*d^8*e^3 - 1320*a^3*b^7*B*d^8*e^3 - 1980*a^3*A*b^7*d^7*e^4 - 3465*a^4*b^6*B*d^7*e^4 - 6435*a^4*A*b^6*d^6*e^5 - 7722*a^5*b^5*B*d^6*e^5 - 18018*a^5*A*b^5*d^5*e^6 - 15015*a^6*b^4*B*d^5*e^6 - 45045*a^6*A*b^4*d^4*e^7 - 25740*a^7*b^3*B*d^4*e^7 - 102960*a^7*A*b^3*d^3*e^8 - 38610*a^8*b^2*B*d^3*e^8 - 218790*a^8*A*b^2*d^2*e^9 - 48620*a^9*b*B*d^2*e^9 - 437580*a^9*A*b*d*e^10 - 43758*a^10*B*d*e^10 - 831402*a^10*A*e^11 - 220*b^10*B*d^10*e*x - 180*A*b^10*d^9*e^2*x - 1800*a*b^9*B*d^9*e^2*x - 1800*a*A*b^9*d^8*e^3*x - 8100*a^2*b^8*B*d^8*e^3*x - 9900*a^2*A*b^8*d^7*e^4*x - 26400*a^3*b^7*B*d^7*e^4*x - 39600*a^3*A*b^7*d^6*e^5*x - 69300*a^4*b^6*B*d^6*e^5*x - 128700*a^4*A*b^6*d^5*e^6*x - 154440*a^5*b^5*B*d^5*e^6*x - 360360*a^5*A*b^5*d^4*e^7*x - 300300*a^6*b^4*B*d^4*e^7*x - 900900*a^6*A*b^4*d^3*e^8*x - 514800*a^7*b^3*B*d^3*e^8*x - 2059200*a^7*A*b^3*d^2*e^9*x - 772200*a^8*b^2*B*d^2*e^9*x - 4375800*a^8*A*b^2*d*e^10*x - 972400*a^9*b*B*d*e^10*x - 8751600*a^9*A*b*e^11*x - 875160*a^10*B*e^11*x - 2090*b^10*B*d^9*e^2*x^2 - 1710*A*b^10*d^8*e^3*x^2 - 17100*a*b^9*B*d^8*e^3*x^2 - 17100*a*A*b^9*d^7*e^4*x^2 - 76950*a^2*b^8*B*d^7*e^4*x^2 - 94050*a^2*A*b^8*d^6*e^5*x^2 - 250800*a^3*b^7*B*d^6*e^5*x^2 - 376200*a^3*A*b^7*d^5*e^6*x^2 - 658350*a^4*b^6*B*d^5*e^6*x^2 - 1222650*a^4*A*b^6*d^4*e^7*x^2 - 1467180*a^5*b^5*B*d^4*e^7*x^2 - 3423420*a^5*A*b^5*d^3*e^8*x^2 - 2852850*a^6*b^4*B*d^3*e^8*x^2 - 8558550*a^6*A*b^4*d^2*e^9*x^2 - 4890600*a^7*b^3*B*d^2*e^9*x^2 - 19562400*a^7*A*b^3*d*e^10*x^2 - 7335900*a^8*b^2*B*d*e^10*x^2 - 41570100*a^8*A*b^2*e^11*x^2 - 9237800*a^9*b*B*e^11*x^2 - 12540*b^10*B*d^8*e^3*x^3 - 10260*A*b^10*d^7*e^4*x^3 - 102600*a*b^9*B*d^7*e^4*x^3 - 102600*a*A*b^9*d^6*e^5*x^3 - 461700*a^2*b^8*B*d^6*e^5*x^3 - 564300*a^2*A*b^8*d^5*e^6*x^3 - 1504800*a^3*b^7*B*d^5*e^6*x^3 - 2257200*a^3*A*b^7*d^4*e^7*x^3 - 3950100*a^4*b^6*B*d^4*e^7*x^3 - 7335900*a^4*A*b^6*d^3*e^8*x^3 - 8803080*a^5*b^5*B*d^3*e^8*x^3 - 20540520*a^5*A*b^5*d^2*e^9*x^3 - 17117100*a^6*b^4*B*d^2*e^9*x^3 - 51351300*a^6*A*b^4*d*e^10*x^3 - 29343600*a^7*b^3*B*d*e^10*x^3 - 117374400*a^7*A*b^3*e^11*x^3 - 44015400*a^8*b^2*B*e^11*x^3 - 53295*b^10*B*d^7*e^4*x^4 - 43605*A*b^10*d^6*e^5*x^4 - 436050*a*b^9*B*d^6*e^5*x^4 - 436050*a*A*b^9*d^5*e^6*x^4 - 1962225*a^2*b^8*B*d^5*e^6*x^4 - 2398275*a^2*A*b^8*d^4*e^7*x^4 - 6395400*a^3*b^7*B*d^4*e^7*x^4 - 9593100*a^3*A*b^7*d^3*e^8*x^4 - 16787925*a^4*b^6*B*d^3*e^8*x^4 - 31177575*a^4*A*b^6*d^2*e^9*x^4 - 37413090*a^5*b^5*B*d^2*e^9*x^4 - 87297210*a^5*A*b^5*d*e^10*x^4 - 72747675*a^6*b^4*B*d*e^10*x^4 - 218243025*a^6*A*b^4*e^11*x^4 - 124710300*a^7*b^3*B*e^11*x^4 - 170544*b^10*B*d^6*e^5*x^5 - 139536*A*b^10*d^5*e^6*x^5 - 1395360*a*b^9*B*d^5*e^6*x^5 - 1395360*a*A*b^9*d^4*e^7*x^5 - 6279120*a^2*b^8*B*d^4*e^7*x^5 - 7674480*a^2*A*b^8*d^3*e^8*x^5 - 20465280*a^3*b^7*B*d^3*e^8*x^5 - 30697920*a^3*A*b^7*d^2*e^9*x^5 - 53721360*a^4*b^6*B*d^2*e^9*x^5 - 99768240*a^4*A*b^6*d*e^10*x^5 - 119721888*a^5*b^5*B*d*e^10*x^5 - 279351072*a^5*A*b^5*e^11*x^5 - 232792560*a^6*b^4*B*e^11*x^5 - 426360*b^10*B*d^5*e^6*x^6 - 348840*A*b^10*d^4*e^7*x^6 - 3488400*a*b^9*B*d^4*e^7*x^6 - 3488400*a*A*b^9*d^3*e^8*x^6 - 15697800*a^2*b^8*B*d^3*e^8*x^6 - 19186200*a^2*A*b^8*d^2*e^9*x^6 - 51163200*a^3*b^7*B*d^2*e^9*x^6 - 76744800*a^3*A*b^7*d*e^10*x^6 - 134303400*a^4*b^6*B*d*e^10*x^6 - 249420600*a^4*A*b^6*e^11*x^6 - 299304720*a^5*b^5*B*e^11*x^6 - 852720*b^10*B*d^4*e^7*x^7 - 697680*A*b^10*d^3*e^8*x^7 - 6976800*a*b^9*B*d^3*e^8*x^7 - 6976800*a*A*b^9*d^2*e^9*x^7 - 31395600*a^2*b^8*B*d^2*e^9*x^7 - 38372400*a^2*A*b^8*d*e^10*x^7 - 102326400*a^3*b^7*B*d*e^10*x^7 - 153489600*a^3*A*b^7*e^11*x^7 - 268606800*a^4*b^6*B*e^11*x^7 - 1385670*b^10*B*d^3*e^8*x^8 - 1133730*A*b^10*d^2*e^9*x^8 - 11337300*a*b^9*B*d^2*e^9*x^8 - 11337300*a*A*b^9*d*e^10*x^8 - 51017850*a^2*b^8*B*d*e^10*x^8 - 62355150*a^2*A*b^8*e^11*x^8 - 166280400*a^3*b^7*B*e^11*x^8 - 1847560*b^10*B*d^2*e^9*x^9 - 1511640*A*b^10*d*e^10*x^9 - 15116400*a*b^9*B*d*e^10*x^9 - 15116400*a*A*b^9*e^11*x^9 - 68023800*a^2*b^8*B*e^11*x^9 - 2032316*b^10*B*d*e^10*x^10 - 1662804*A*b^10*e^11*x^10 - 16628040*a*b^9*B*e^11*x^10 - 1847560*b^10*B*e^11*x^11)/(16628040*e^12*(d + e*x)^20)","B",1
1110,1,2234,464,1.0342254,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{22}} \, dx","IntegrateAlgebraic[((a + b*x)^10*(A + B*x))/(d + e*x)^22,x]","\text{Result too large to show}","\frac{b^9 (-10 a B e-A b e+11 b B d)}{11 e^{12} (d+e x)^{11}}-\frac{5 b^8 (b d-a e) (-9 a B e-2 A b e+11 b B d)}{12 e^{12} (d+e x)^{12}}+\frac{15 b^7 (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{13 e^{12} (d+e x)^{13}}-\frac{15 b^6 (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{7 e^{12} (d+e x)^{14}}+\frac{14 b^5 (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{5 e^{12} (d+e x)^{15}}-\frac{21 b^4 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{8 e^{12} (d+e x)^{16}}+\frac{30 b^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{17 e^{12} (d+e x)^{17}}-\frac{5 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{6 e^{12} (d+e x)^{18}}+\frac{5 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{19 e^{12} (d+e x)^{19}}-\frac{(b d-a e)^9 (-a B e-10 A b e+11 b B d)}{20 e^{12} (d+e x)^{20}}+\frac{(b d-a e)^{10} (B d-A e)}{21 e^{12} (d+e x)^{21}}-\frac{b^{10} B}{10 e^{12} (d+e x)^{10}}",1,"(-11*b^10*B*d^11 - 10*A*b^10*d^10*e - 100*a*b^9*B*d^10*e - 110*a*A*b^9*d^9*e^2 - 495*a^2*b^8*B*d^9*e^2 - 660*a^2*A*b^8*d^8*e^3 - 1760*a^3*b^7*B*d^8*e^3 - 2860*a^3*A*b^7*d^7*e^4 - 5005*a^4*b^6*B*d^7*e^4 - 10010*a^4*A*b^6*d^6*e^5 - 12012*a^5*b^5*B*d^6*e^5 - 30030*a^5*A*b^5*d^5*e^6 - 25025*a^6*b^4*B*d^5*e^6 - 80080*a^6*A*b^4*d^4*e^7 - 45760*a^7*b^3*B*d^4*e^7 - 194480*a^7*A*b^3*d^3*e^8 - 72930*a^8*b^2*B*d^3*e^8 - 437580*a^8*A*b^2*d^2*e^9 - 97240*a^9*b*B*d^2*e^9 - 923780*a^9*A*b*d*e^10 - 92378*a^10*B*d*e^10 - 1847560*a^10*A*e^11 - 231*b^10*B*d^10*e*x - 210*A*b^10*d^9*e^2*x - 2100*a*b^9*B*d^9*e^2*x - 2310*a*A*b^9*d^8*e^3*x - 10395*a^2*b^8*B*d^8*e^3*x - 13860*a^2*A*b^8*d^7*e^4*x - 36960*a^3*b^7*B*d^7*e^4*x - 60060*a^3*A*b^7*d^6*e^5*x - 105105*a^4*b^6*B*d^6*e^5*x - 210210*a^4*A*b^6*d^5*e^6*x - 252252*a^5*b^5*B*d^5*e^6*x - 630630*a^5*A*b^5*d^4*e^7*x - 525525*a^6*b^4*B*d^4*e^7*x - 1681680*a^6*A*b^4*d^3*e^8*x - 960960*a^7*b^3*B*d^3*e^8*x - 4084080*a^7*A*b^3*d^2*e^9*x - 1531530*a^8*b^2*B*d^2*e^9*x - 9189180*a^8*A*b^2*d*e^10*x - 2042040*a^9*b*B*d*e^10*x - 19399380*a^9*A*b*e^11*x - 1939938*a^10*B*e^11*x - 2310*b^10*B*d^9*e^2*x^2 - 2100*A*b^10*d^8*e^3*x^2 - 21000*a*b^9*B*d^8*e^3*x^2 - 23100*a*A*b^9*d^7*e^4*x^2 - 103950*a^2*b^8*B*d^7*e^4*x^2 - 138600*a^2*A*b^8*d^6*e^5*x^2 - 369600*a^3*b^7*B*d^6*e^5*x^2 - 600600*a^3*A*b^7*d^5*e^6*x^2 - 1051050*a^4*b^6*B*d^5*e^6*x^2 - 2102100*a^4*A*b^6*d^4*e^7*x^2 - 2522520*a^5*b^5*B*d^4*e^7*x^2 - 6306300*a^5*A*b^5*d^3*e^8*x^2 - 5255250*a^6*b^4*B*d^3*e^8*x^2 - 16816800*a^6*A*b^4*d^2*e^9*x^2 - 9609600*a^7*b^3*B*d^2*e^9*x^2 - 40840800*a^7*A*b^3*d*e^10*x^2 - 15315300*a^8*b^2*B*d*e^10*x^2 - 91891800*a^8*A*b^2*e^11*x^2 - 20420400*a^9*b*B*e^11*x^2 - 14630*b^10*B*d^8*e^3*x^3 - 13300*A*b^10*d^7*e^4*x^3 - 133000*a*b^9*B*d^7*e^4*x^3 - 146300*a*A*b^9*d^6*e^5*x^3 - 658350*a^2*b^8*B*d^6*e^5*x^3 - 877800*a^2*A*b^8*d^5*e^6*x^3 - 2340800*a^3*b^7*B*d^5*e^6*x^3 - 3803800*a^3*A*b^7*d^4*e^7*x^3 - 6656650*a^4*b^6*B*d^4*e^7*x^3 - 13313300*a^4*A*b^6*d^3*e^8*x^3 - 15975960*a^5*b^5*B*d^3*e^8*x^3 - 39939900*a^5*A*b^5*d^2*e^9*x^3 - 33283250*a^6*b^4*B*d^2*e^9*x^3 - 106506400*a^6*A*b^4*d*e^10*x^3 - 60860800*a^7*b^3*B*d*e^10*x^3 - 258658400*a^7*A*b^3*e^11*x^3 - 96996900*a^8*b^2*B*e^11*x^3 - 65835*b^10*B*d^7*e^4*x^4 - 59850*A*b^10*d^6*e^5*x^4 - 598500*a*b^9*B*d^6*e^5*x^4 - 658350*a*A*b^9*d^5*e^6*x^4 - 2962575*a^2*b^8*B*d^5*e^6*x^4 - 3950100*a^2*A*b^8*d^4*e^7*x^4 - 10533600*a^3*b^7*B*d^4*e^7*x^4 - 17117100*a^3*A*b^7*d^3*e^8*x^4 - 29954925*a^4*b^6*B*d^3*e^8*x^4 - 59909850*a^4*A*b^6*d^2*e^9*x^4 - 71891820*a^5*b^5*B*d^2*e^9*x^4 - 179729550*a^5*A*b^5*d*e^10*x^4 - 149774625*a^6*b^4*B*d*e^10*x^4 - 479278800*a^6*A*b^4*e^11*x^4 - 273873600*a^7*b^3*B*e^11*x^4 - 223839*b^10*B*d^6*e^5*x^5 - 203490*A*b^10*d^5*e^6*x^5 - 2034900*a*b^9*B*d^5*e^6*x^5 - 2238390*a*A*b^9*d^4*e^7*x^5 - 10072755*a^2*b^8*B*d^4*e^7*x^5 - 13430340*a^2*A*b^8*d^3*e^8*x^5 - 35814240*a^3*b^7*B*d^3*e^8*x^5 - 58198140*a^3*A*b^7*d^2*e^9*x^5 - 101846745*a^4*b^6*B*d^2*e^9*x^5 - 203693490*a^4*A*b^6*d*e^10*x^5 - 244432188*a^5*b^5*B*d*e^10*x^5 - 611080470*a^5*A*b^5*e^11*x^5 - 509233725*a^6*b^4*B*e^11*x^5 - 596904*b^10*B*d^5*e^6*x^6 - 542640*A*b^10*d^4*e^7*x^6 - 5426400*a*b^9*B*d^4*e^7*x^6 - 5969040*a*A*b^9*d^3*e^8*x^6 - 26860680*a^2*b^8*B*d^3*e^8*x^6 - 35814240*a^2*A*b^8*d^2*e^9*x^6 - 95504640*a^3*b^7*B*d^2*e^9*x^6 - 155195040*a^3*A*b^7*d*e^10*x^6 - 271591320*a^4*b^6*B*d*e^10*x^6 - 543182640*a^4*A*b^6*e^11*x^6 - 651819168*a^5*b^5*B*e^11*x^6 - 1279080*b^10*B*d^4*e^7*x^7 - 1162800*A*b^10*d^3*e^8*x^7 - 11628000*a*b^9*B*d^3*e^8*x^7 - 12790800*a*A*b^9*d^2*e^9*x^7 - 57558600*a^2*b^8*B*d^2*e^9*x^7 - 76744800*a^2*A*b^8*d*e^10*x^7 - 204652800*a^3*b^7*B*d*e^10*x^7 - 332560800*a^3*A*b^7*e^11*x^7 - 581981400*a^4*b^6*B*e^11*x^7 - 2238390*b^10*B*d^3*e^8*x^8 - 2034900*A*b^10*d^2*e^9*x^8 - 20349000*a*b^9*B*d^2*e^9*x^8 - 22383900*a*A*b^9*d*e^10*x^8 - 100727550*a^2*b^8*B*d*e^10*x^8 - 134303400*a^2*A*b^8*e^11*x^8 - 358142400*a^3*b^7*B*e^11*x^8 - 3233230*b^10*B*d^2*e^9*x^9 - 2939300*A*b^10*d*e^10*x^9 - 29393000*a*b^9*B*d*e^10*x^9 - 32332300*a*A*b^9*e^11*x^9 - 145495350*a^2*b^8*B*e^11*x^9 - 3879876*b^10*B*d*e^10*x^10 - 3527160*A*b^10*e^11*x^10 - 35271600*a*b^9*B*e^11*x^10 - 3879876*b^10*B*e^11*x^11)/(38798760*e^12*(d + e*x)^21)","B",1
1111,1,515,187,0.3352896,"\int \frac{(A+B x) (d+e x)^5}{a+b x} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^5)/(a + b*x),x]","\frac{x \left(-60 a^5 B e^5+60 a^4 A b e^5+300 a^4 b B d e^4+30 a^4 b B e^5 x-300 a^3 A b^2 d e^4-30 a^3 A b^2 e^5 x-600 a^3 b^2 B d^2 e^3-150 a^3 b^2 B d e^4 x-20 a^3 b^2 B e^5 x^2+600 a^2 A b^3 d^2 e^3+150 a^2 A b^3 d e^4 x+20 a^2 A b^3 e^5 x^2+600 a^2 b^3 B d^3 e^2+300 a^2 b^3 B d^2 e^3 x+100 a^2 b^3 B d e^4 x^2+15 a^2 b^3 B e^5 x^3-600 a A b^4 d^3 e^2-300 a A b^4 d^2 e^3 x-100 a A b^4 d e^4 x^2-15 a A b^4 e^5 x^3-300 a b^4 B d^4 e-300 a b^4 B d^3 e^2 x-200 a b^4 B d^2 e^3 x^2-75 a b^4 B d e^4 x^3-12 a b^4 B e^5 x^4+300 A b^5 d^4 e+300 A b^5 d^3 e^2 x+200 A b^5 d^2 e^3 x^2+75 A b^5 d e^4 x^3+12 A b^5 e^5 x^4+60 b^5 B d^5+150 b^5 B d^4 e x+200 b^5 B d^3 e^2 x^2+150 b^5 B d^2 e^3 x^3+60 b^5 B d e^4 x^4+10 b^5 B e^5 x^5\right)}{60 b^6}+\frac{(A b-a B) (b d-a e)^5 \log (a+b x)}{b^7}","\frac{(A b-a B) (b d-a e)^5 \log (a+b x)}{b^7}+\frac{e x (A b-a B) (b d-a e)^4}{b^6}+\frac{(d+e x)^2 (A b-a B) (b d-a e)^3}{2 b^5}+\frac{(d+e x)^3 (A b-a B) (b d-a e)^2}{3 b^4}+\frac{(d+e x)^4 (A b-a B) (b d-a e)}{4 b^3}+\frac{(d+e x)^5 (A b-a B)}{5 b^2}+\frac{B (d+e x)^6}{6 b e}",1,"(x*(60*b^5*B*d^5 + 300*A*b^5*d^4*e - 300*a*b^4*B*d^4*e - 600*a*A*b^4*d^3*e^2 + 600*a^2*b^3*B*d^3*e^2 + 600*a^2*A*b^3*d^2*e^3 - 600*a^3*b^2*B*d^2*e^3 - 300*a^3*A*b^2*d*e^4 + 300*a^4*b*B*d*e^4 + 60*a^4*A*b*e^5 - 60*a^5*B*e^5 + 150*b^5*B*d^4*e*x + 300*A*b^5*d^3*e^2*x - 300*a*b^4*B*d^3*e^2*x - 300*a*A*b^4*d^2*e^3*x + 300*a^2*b^3*B*d^2*e^3*x + 150*a^2*A*b^3*d*e^4*x - 150*a^3*b^2*B*d*e^4*x - 30*a^3*A*b^2*e^5*x + 30*a^4*b*B*e^5*x + 200*b^5*B*d^3*e^2*x^2 + 200*A*b^5*d^2*e^3*x^2 - 200*a*b^4*B*d^2*e^3*x^2 - 100*a*A*b^4*d*e^4*x^2 + 100*a^2*b^3*B*d*e^4*x^2 + 20*a^2*A*b^3*e^5*x^2 - 20*a^3*b^2*B*e^5*x^2 + 150*b^5*B*d^2*e^3*x^3 + 75*A*b^5*d*e^4*x^3 - 75*a*b^4*B*d*e^4*x^3 - 15*a*A*b^4*e^5*x^3 + 15*a^2*b^3*B*e^5*x^3 + 60*b^5*B*d*e^4*x^4 + 12*A*b^5*e^5*x^4 - 12*a*b^4*B*e^5*x^4 + 10*b^5*B*e^5*x^5))/(60*b^6) + ((A*b - a*B)*(b*d - a*e)^5*Log[a + b*x])/b^7","B",1
1112,1,347,155,0.2353866,"\int \frac{(A+B x) (d+e x)^4}{a+b x} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^4)/(a + b*x),x]","\frac{x \left(60 a^4 B e^4-60 a^3 A b e^4-240 a^3 b B d e^3-30 a^3 b B e^4 x+240 a^2 A b^2 d e^3+30 a^2 A b^2 e^4 x+360 a^2 b^2 B d^2 e^2+120 a^2 b^2 B d e^3 x+20 a^2 b^2 B e^4 x^2-360 a A b^3 d^2 e^2-120 a A b^3 d e^3 x-20 a A b^3 e^4 x^2-240 a b^3 B d^3 e-180 a b^3 B d^2 e^2 x-80 a b^3 B d e^3 x^2-15 a b^3 B e^4 x^3+240 A b^4 d^3 e+180 A b^4 d^2 e^2 x+80 A b^4 d e^3 x^2+15 A b^4 e^4 x^3+60 b^4 B d^4+120 b^4 B d^3 e x+120 b^4 B d^2 e^2 x^2+60 b^4 B d e^3 x^3+12 b^4 B e^4 x^4\right)}{60 b^5}+\frac{(A b-a B) (b d-a e)^4 \log (a+b x)}{b^6}","\frac{(A b-a B) (b d-a e)^4 \log (a+b x)}{b^6}+\frac{e x (A b-a B) (b d-a e)^3}{b^5}+\frac{(d+e x)^2 (A b-a B) (b d-a e)^2}{2 b^4}+\frac{(d+e x)^3 (A b-a B) (b d-a e)}{3 b^3}+\frac{(d+e x)^4 (A b-a B)}{4 b^2}+\frac{B (d+e x)^5}{5 b e}",1,"(x*(60*b^4*B*d^4 + 240*A*b^4*d^3*e - 240*a*b^3*B*d^3*e - 360*a*A*b^3*d^2*e^2 + 360*a^2*b^2*B*d^2*e^2 + 240*a^2*A*b^2*d*e^3 - 240*a^3*b*B*d*e^3 - 60*a^3*A*b*e^4 + 60*a^4*B*e^4 + 120*b^4*B*d^3*e*x + 180*A*b^4*d^2*e^2*x - 180*a*b^3*B*d^2*e^2*x - 120*a*A*b^3*d*e^3*x + 120*a^2*b^2*B*d*e^3*x + 30*a^2*A*b^2*e^4*x - 30*a^3*b*B*e^4*x + 120*b^4*B*d^2*e^2*x^2 + 80*A*b^4*d*e^3*x^2 - 80*a*b^3*B*d*e^3*x^2 - 20*a*A*b^3*e^4*x^2 + 20*a^2*b^2*B*e^4*x^2 + 60*b^4*B*d*e^3*x^3 + 15*A*b^4*e^4*x^3 - 15*a*b^3*B*e^4*x^3 + 12*b^4*B*e^4*x^4))/(60*b^5) + ((A*b - a*B)*(b*d - a*e)^4*Log[a + b*x])/b^6","B",1
1113,1,215,123,0.1531673,"\int \frac{(A+B x) (d+e x)^3}{a+b x} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^3)/(a + b*x),x]","\frac{x \left(-12 a^3 B e^3+12 a^2 A b e^3+36 a^2 b B d e^2+6 a^2 b B e^3 x-36 a A b^2 d e^2-6 a A b^2 e^3 x-36 a b^2 B d^2 e-18 a b^2 B d e^2 x-4 a b^2 B e^3 x^2+36 A b^3 d^2 e+18 A b^3 d e^2 x+4 A b^3 e^3 x^2+12 b^3 B d^3+18 b^3 B d^2 e x+12 b^3 B d e^2 x^2+3 b^3 B e^3 x^3\right)}{12 b^4}+\frac{(A b-a B) (b d-a e)^3 \log (a+b x)}{b^5}","\frac{(A b-a B) (b d-a e)^3 \log (a+b x)}{b^5}+\frac{e x (A b-a B) (b d-a e)^2}{b^4}+\frac{(d+e x)^2 (A b-a B) (b d-a e)}{2 b^3}+\frac{(d+e x)^3 (A b-a B)}{3 b^2}+\frac{B (d+e x)^4}{4 b e}",1,"(x*(12*b^3*B*d^3 + 36*A*b^3*d^2*e - 36*a*b^2*B*d^2*e - 36*a*A*b^2*d*e^2 + 36*a^2*b*B*d*e^2 + 12*a^2*A*b*e^3 - 12*a^3*B*e^3 + 18*b^3*B*d^2*e*x + 18*A*b^3*d*e^2*x - 18*a*b^2*B*d*e^2*x - 6*a*A*b^2*e^3*x + 6*a^2*b*B*e^3*x + 12*b^3*B*d*e^2*x^2 + 4*A*b^3*e^3*x^2 - 4*a*b^2*B*e^3*x^2 + 3*b^3*B*e^3*x^3))/(12*b^4) + ((A*b - a*B)*(b*d - a*e)^3*Log[a + b*x])/b^5","A",1
1114,1,119,91,0.093228,"\int \frac{(A+B x) (d+e x)^2}{a+b x} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^2)/(a + b*x),x]","\frac{x \left(6 a^2 B e^2-6 a A b e^2-12 a b B d e-3 a b B e^2 x+12 A b^2 d e+3 A b^2 e^2 x+6 b^2 B d^2+6 b^2 B d e x+2 b^2 B e^2 x^2\right)}{6 b^3}+\frac{(A b-a B) (b d-a e)^2 \log (a+b x)}{b^4}","\frac{(A b-a B) (b d-a e)^2 \log (a+b x)}{b^4}+\frac{e x (A b-a B) (b d-a e)}{b^3}+\frac{(d+e x)^2 (A b-a B)}{2 b^2}+\frac{B (d+e x)^3}{3 b e}",1,"(x*(6*b^2*B*d^2 + 12*A*b^2*d*e - 12*a*b*B*d*e - 6*a*A*b*e^2 + 6*a^2*B*e^2 + 6*b^2*B*d*e*x + 3*A*b^2*e^2*x - 3*a*b*B*e^2*x + 2*b^2*B*e^2*x^2))/(6*b^3) + ((A*b - a*B)*(b*d - a*e)^2*Log[a + b*x])/b^4","A",1
1115,1,65,59,0.0379547,"\int \frac{(A+B x) (d+e x)}{a+b x} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x))/(a + b*x),x]","\frac{\log (a+b x) \left(a^2 B e-a A b e-a b B d+A b^2 d\right)}{b^3}+\frac{x (-2 a B e+2 A b e+2 b B d+b B e x)}{2 b^2}","\frac{(A b-a B) (b d-a e) \log (a+b x)}{b^3}+\frac{B x (b d-a e)}{b^2}+\frac{e (A+B x)^2}{2 b B}",1,"(x*(2*b*B*d + 2*A*b*e - 2*a*B*e + b*B*e*x))/(2*b^2) + ((A*b^2*d - a*b*B*d - a*A*b*e + a^2*B*e)*Log[a + b*x])/b^3","A",1
1116,1,25,25,0.0005757,"\int \frac{A+B x}{a+b x} \, dx","IntegrateAlgebraic[(A + B*x)/(a + b*x),x]","\frac{(A b-a B) \log (a+b x)}{b^2}+\frac{B x}{b}","\frac{(A b-a B) \log (a+b x)}{b^2}+\frac{B x}{b}",1,"(B*x)/b + ((A*b - a*B)*Log[a + b*x])/b^2","A",1
1117,1,58,57,0.040267,"\int \frac{A+B x}{(a+b x) (d+e x)} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)*(d + e*x)),x]","\frac{(A b-a B) \log (a+b x)}{b (b d-a e)}-\frac{(B d-A e) \log (d+e x)}{e (a e-b d)}","\frac{(A b-a B) \log (a+b x)}{b (b d-a e)}+\frac{(B d-A e) \log (d+e x)}{e (b d-a e)}",1,"((A*b - a*B)*Log[a + b*x])/(b*(b*d - a*e)) - ((B*d - A*e)*Log[d + e*x])/(e*(-(b*d) + a*e))","A",1
1118,1,80,82,0.1069219,"\int \frac{A+B x}{(a+b x) (d+e x)^2} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)*(d + e*x)^2),x]","\frac{B d-A e}{e (d+e x) (a e-b d)}+\frac{(A b-a B) \log (a+b x)}{(b d-a e)^2}+\frac{(a B-A b) \log (d+e x)}{(b d-a e)^2}","-\frac{B d-A e}{e (d+e x) (b d-a e)}+\frac{(A b-a B) \log (a+b x)}{(b d-a e)^2}-\frac{(A b-a B) \log (d+e x)}{(b d-a e)^2}",1,"(B*d - A*e)/(e*(-(b*d) + a*e)*(d + e*x)) + ((A*b - a*B)*Log[a + b*x])/(b*d - a*e)^2 + ((-(A*b) + a*B)*Log[d + e*x])/(b*d - a*e)^2","A",1
1119,1,124,112,0.1518133,"\int \frac{A+B x}{(a+b x) (d+e x)^3} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)*(d + e*x)^3),x]","\frac{\left(A b^2-a b B\right) \log (a+b x)}{(b d-a e)^3}+\frac{\left(a b B-A b^2\right) \log (d+e x)}{(b d-a e)^3}+\frac{-a A e^2-a B d e-2 a B e^2 x+3 A b d e+2 A b e^2 x-b B d^2}{2 e (d+e x)^2 (a e-b d)^2}","\frac{A b-a B}{(d+e x) (b d-a e)^2}+\frac{A e-B d}{2 e (d+e x)^2 (b d-a e)}+\frac{b (A b-a B) \log (a+b x)}{(b d-a e)^3}-\frac{b (A b-a B) \log (d+e x)}{(b d-a e)^3}",1,"(-(b*B*d^2) + 3*A*b*d*e - a*B*d*e - a*A*e^2 + 2*A*b*e^2*x - 2*a*B*e^2*x)/(2*e*(-(b*d) + a*e)^2*(d + e*x)^2) + ((A*b^2 - a*b*B)*Log[a + b*x])/(b*d - a*e)^3 + ((-(A*b^2) + a*b*B)*Log[d + e*x])/(b*d - a*e)^3","A",1
1120,1,205,146,0.2774636,"\int \frac{A+B x}{(a+b x) (d+e x)^4} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)*(d + e*x)^4),x]","\frac{-2 a^2 A e^3-a^2 B d e^2-3 a^2 B e^3 x+7 a A b d e^2+3 a A b e^3 x+5 a b B d^2 e+15 a b B d e^2 x+6 a b B e^3 x^2-11 A b^2 d^2 e-15 A b^2 d e^2 x-6 A b^2 e^3 x^2+2 b^2 B d^3}{6 e (d+e x)^3 (a e-b d)^3}+\frac{\left(A b^3-a b^2 B\right) \log (a+b x)}{(b d-a e)^4}+\frac{\left(a b^2 B-A b^3\right) \log (d+e x)}{(b d-a e)^4}","\frac{b^2 (A b-a B) \log (a+b x)}{(b d-a e)^4}-\frac{b^2 (A b-a B) \log (d+e x)}{(b d-a e)^4}+\frac{b (A b-a B)}{(d+e x) (b d-a e)^3}+\frac{A b-a B}{2 (d+e x)^2 (b d-a e)^2}+\frac{A e-B d}{3 e (d+e x)^3 (b d-a e)}",1,"(2*b^2*B*d^3 - 11*A*b^2*d^2*e + 5*a*b*B*d^2*e + 7*a*A*b*d*e^2 - a^2*B*d*e^2 - 2*a^2*A*e^3 - 15*A*b^2*d*e^2*x + 15*a*b*B*d*e^2*x + 3*a*A*b*e^3*x - 3*a^2*B*e^3*x - 6*A*b^2*e^3*x^2 + 6*a*b*B*e^3*x^2)/(6*e*(-(b*d) + a*e)^3*(d + e*x)^3) + ((A*b^3 - a*b^2*B)*Log[a + b*x])/(b*d - a*e)^4 + ((-(A*b^3) + a*b^2*B)*Log[d + e*x])/(b*d - a*e)^4","A",1
1121,1,322,178,0.2106549,"\int \frac{A+B x}{(a+b x) (d+e x)^5} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)*(d + e*x)^5),x]","\frac{-3 a^3 A e^4-a^3 B d e^3-4 a^3 B e^4 x+13 a^2 A b d e^3+4 a^2 A b e^4 x+5 a^2 b B d^2 e^2+20 a^2 b B d e^3 x+6 a^2 b B e^4 x^2-23 a A b^2 d^2 e^2-20 a A b^2 d e^3 x-6 a A b^2 e^4 x^2-13 a b^2 B d^3 e-52 a b^2 B d^2 e^2 x-42 a b^2 B d e^3 x^2-12 a b^2 B e^4 x^3+25 A b^3 d^3 e+52 A b^3 d^2 e^2 x+42 A b^3 d e^3 x^2+12 A b^3 e^4 x^3-3 b^3 B d^4}{12 e (d+e x)^4 (a e-b d)^4}+\frac{\left(A b^4-a b^3 B\right) \log (a+b x)}{(b d-a e)^5}+\frac{\left(a b^3 B-A b^4\right) \log (d+e x)}{(b d-a e)^5}","\frac{b^3 (A b-a B) \log (a+b x)}{(b d-a e)^5}-\frac{b^3 (A b-a B) \log (d+e x)}{(b d-a e)^5}+\frac{b^2 (A b-a B)}{(d+e x) (b d-a e)^4}+\frac{b (A b-a B)}{2 (d+e x)^2 (b d-a e)^3}+\frac{A b-a B}{3 (d+e x)^3 (b d-a e)^2}+\frac{A e-B d}{4 e (d+e x)^4 (b d-a e)}",1,"(-3*b^3*B*d^4 + 25*A*b^3*d^3*e - 13*a*b^2*B*d^3*e - 23*a*A*b^2*d^2*e^2 + 5*a^2*b*B*d^2*e^2 + 13*a^2*A*b*d*e^3 - a^3*B*d*e^3 - 3*a^3*A*e^4 + 52*A*b^3*d^2*e^2*x - 52*a*b^2*B*d^2*e^2*x - 20*a*A*b^2*d*e^3*x + 20*a^2*b*B*d*e^3*x + 4*a^2*A*b*e^4*x - 4*a^3*B*e^4*x + 42*A*b^3*d*e^3*x^2 - 42*a*b^2*B*d*e^3*x^2 - 6*a*A*b^2*e^4*x^2 + 6*a^2*b*B*e^4*x^2 + 12*A*b^3*e^4*x^3 - 12*a*b^2*B*e^4*x^3)/(12*e*(-(b*d) + a*e)^4*(d + e*x)^4) + ((A*b^4 - a*b^3*B)*Log[a + b*x])/(b*d - a*e)^5 + ((-(A*b^4) + a*b^3*B)*Log[d + e*x])/(b*d - a*e)^5","A",1
1122,1,795,227,0.4708982,"\int \frac{(A+B x) (d+e x)^5}{(a+b x)^2} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^5)/(a + b*x)^2,x]","\frac{-60 B e^5 a^6+60 A b e^5 a^5+300 b B d e^4 a^5+300 b B e^5 x a^5-300 A b^2 d e^4 a^4-600 b^2 B d^2 e^3 a^4+180 b^2 B e^5 x^2 a^4-240 A b^2 e^5 x a^4-1200 b^2 B d e^4 x a^4+600 A b^3 d^2 e^3 a^3-60 b^3 B e^5 x^3 a^3+600 b^3 B d^3 e^2 a^3-150 A b^3 e^5 x^2 a^3-750 b^3 B d e^4 x^2 a^3+900 A b^3 d e^4 x a^3+1800 b^3 B d^2 e^3 x a^3+30 b^4 B e^5 x^4 a^2+50 A b^4 e^5 x^3 a^2+250 b^4 B d e^4 x^3 a^2-600 A b^4 d^3 e^2 a^2+600 A b^4 d e^4 x^2 a^2+1200 b^4 B d^2 e^3 x^2 a^2-300 b^4 B d^4 e a^2-1200 A b^4 d^2 e^3 x a^2-1200 b^4 B d^3 e^2 x a^2+60 b^5 B d^5 a-18 b^5 B e^5 x^5 a-25 A b^5 e^5 x^4 a-125 b^5 B d e^4 x^4 a-200 A b^5 d e^4 x^3 a-400 b^5 B d^2 e^3 x^3 a-900 A b^5 d^2 e^3 x^2 a-900 b^5 B d^3 e^2 x^2 a+300 A b^5 d^4 e a+600 A b^5 d^3 e^2 x a+300 b^5 B d^4 e x a+12 b^6 B e^5 x^6-60 A b^6 d^5+15 A b^6 e^5 x^5+75 b^6 B d e^4 x^5+100 A b^6 d e^4 x^4+200 b^6 B d^2 e^3 x^4+300 A b^6 d^2 e^3 x^3+300 b^6 B d^3 e^2 x^3+600 A b^6 d^3 e^2 x^2+300 b^6 B d^4 e x^2}{60 b^7 (a+b x)}+\frac{\left(B d^5 b^5+5 A d^4 e b^5-20 a A d^3 e^2 b^4-10 a B d^4 e b^4+30 a^2 A d^2 e^3 b^3+30 a^2 B d^3 e^2 b^3-20 a^3 A d e^4 b^2-40 a^3 B d^2 e^3 b^2+5 a^4 A e^5 b+25 a^4 B d e^4 b-6 a^5 B e^5\right) \log (a+b x)}{b^7}","\frac{e^4 (a+b x)^4 (-6 a B e+A b e+5 b B d)}{4 b^7}+\frac{5 e^3 (a+b x)^3 (b d-a e) (-3 a B e+A b e+2 b B d)}{3 b^7}+\frac{5 e^2 (a+b x)^2 (b d-a e)^2 (-2 a B e+A b e+b B d)}{b^7}-\frac{(A b-a B) (b d-a e)^5}{b^7 (a+b x)}+\frac{(b d-a e)^4 \log (a+b x) (-6 a B e+5 A b e+b B d)}{b^7}+\frac{5 e x (b d-a e)^3 (-3 a B e+2 A b e+b B d)}{b^6}+\frac{B e^5 (a+b x)^5}{5 b^7}",1,"(-60*A*b^6*d^5 + 60*a*b^5*B*d^5 + 300*a*A*b^5*d^4*e - 300*a^2*b^4*B*d^4*e - 600*a^2*A*b^4*d^3*e^2 + 600*a^3*b^3*B*d^3*e^2 + 600*a^3*A*b^3*d^2*e^3 - 600*a^4*b^2*B*d^2*e^3 - 300*a^4*A*b^2*d*e^4 + 300*a^5*b*B*d*e^4 + 60*a^5*A*b*e^5 - 60*a^6*B*e^5 + 300*a*b^5*B*d^4*e*x + 600*a*A*b^5*d^3*e^2*x - 1200*a^2*b^4*B*d^3*e^2*x - 1200*a^2*A*b^4*d^2*e^3*x + 1800*a^3*b^3*B*d^2*e^3*x + 900*a^3*A*b^3*d*e^4*x - 1200*a^4*b^2*B*d*e^4*x - 240*a^4*A*b^2*e^5*x + 300*a^5*b*B*e^5*x + 300*b^6*B*d^4*e*x^2 + 600*A*b^6*d^3*e^2*x^2 - 900*a*b^5*B*d^3*e^2*x^2 - 900*a*A*b^5*d^2*e^3*x^2 + 1200*a^2*b^4*B*d^2*e^3*x^2 + 600*a^2*A*b^4*d*e^4*x^2 - 750*a^3*b^3*B*d*e^4*x^2 - 150*a^3*A*b^3*e^5*x^2 + 180*a^4*b^2*B*e^5*x^2 + 300*b^6*B*d^3*e^2*x^3 + 300*A*b^6*d^2*e^3*x^3 - 400*a*b^5*B*d^2*e^3*x^3 - 200*a*A*b^5*d*e^4*x^3 + 250*a^2*b^4*B*d*e^4*x^3 + 50*a^2*A*b^4*e^5*x^3 - 60*a^3*b^3*B*e^5*x^3 + 200*b^6*B*d^2*e^3*x^4 + 100*A*b^6*d*e^4*x^4 - 125*a*b^5*B*d*e^4*x^4 - 25*a*A*b^5*e^5*x^4 + 30*a^2*b^4*B*e^5*x^4 + 75*b^6*B*d*e^4*x^5 + 15*A*b^6*e^5*x^5 - 18*a*b^5*B*e^5*x^5 + 12*b^6*B*e^5*x^6)/(60*b^7*(a + b*x)) + ((b^5*B*d^5 + 5*A*b^5*d^4*e - 10*a*b^4*B*d^4*e - 20*a*A*b^4*d^3*e^2 + 30*a^2*b^3*B*d^3*e^2 + 30*a^2*A*b^3*d^2*e^3 - 40*a^3*b^2*B*d^2*e^3 - 20*a^3*A*b^2*d*e^4 + 25*a^4*b*B*d*e^4 + 5*a^4*A*b*e^5 - 6*a^5*B*e^5)*Log[a + b*x])/b^7","B",1
1123,1,561,187,0.3384334,"\int \frac{(A+B x) (d+e x)^4}{(a+b x)^2} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^4)/(a + b*x)^2,x]","\frac{\log (a+b x) \left(5 a^4 B e^4-4 a^3 A b e^4-16 a^3 b B d e^3+12 a^2 A b^2 d e^3+18 a^2 b^2 B d^2 e^2-12 a A b^3 d^2 e^2-8 a b^3 B d^3 e+4 A b^4 d^3 e+b^4 B d^4\right)}{b^6}+\frac{12 a^5 B e^4-12 a^4 A b e^4-48 a^4 b B d e^3-48 a^4 b B e^4 x+48 a^3 A b^2 d e^3+36 a^3 A b^2 e^4 x+72 a^3 b^2 B d^2 e^2+144 a^3 b^2 B d e^3 x-30 a^3 b^2 B e^4 x^2-72 a^2 A b^3 d^2 e^2-96 a^2 A b^3 d e^3 x+24 a^2 A b^3 e^4 x^2-48 a^2 b^3 B d^3 e-144 a^2 b^3 B d^2 e^2 x+96 a^2 b^3 B d e^3 x^2+10 a^2 b^3 B e^4 x^3+48 a A b^4 d^3 e+72 a A b^4 d^2 e^2 x-72 a A b^4 d e^3 x^2-8 a A b^4 e^4 x^3+12 a b^4 B d^4+48 a b^4 B d^3 e x-108 a b^4 B d^2 e^2 x^2-32 a b^4 B d e^3 x^3-5 a b^4 B e^4 x^4-12 A b^5 d^4+72 A b^5 d^2 e^2 x^2+24 A b^5 d e^3 x^3+4 A b^5 e^4 x^4+48 b^5 B d^3 e x^2+36 b^5 B d^2 e^2 x^3+16 b^5 B d e^3 x^4+3 b^5 B e^4 x^5}{12 b^6 (a+b x)}","\frac{e^3 (a+b x)^3 (-5 a B e+A b e+4 b B d)}{3 b^6}+\frac{e^2 (a+b x)^2 (b d-a e) (-5 a B e+2 A b e+3 b B d)}{b^6}-\frac{(A b-a B) (b d-a e)^4}{b^6 (a+b x)}+\frac{(b d-a e)^3 \log (a+b x) (-5 a B e+4 A b e+b B d)}{b^6}+\frac{2 e x (b d-a e)^2 (-5 a B e+3 A b e+2 b B d)}{b^5}+\frac{B e^4 (a+b x)^4}{4 b^6}",1,"(-12*A*b^5*d^4 + 12*a*b^4*B*d^4 + 48*a*A*b^4*d^3*e - 48*a^2*b^3*B*d^3*e - 72*a^2*A*b^3*d^2*e^2 + 72*a^3*b^2*B*d^2*e^2 + 48*a^3*A*b^2*d*e^3 - 48*a^4*b*B*d*e^3 - 12*a^4*A*b*e^4 + 12*a^5*B*e^4 + 48*a*b^4*B*d^3*e*x + 72*a*A*b^4*d^2*e^2*x - 144*a^2*b^3*B*d^2*e^2*x - 96*a^2*A*b^3*d*e^3*x + 144*a^3*b^2*B*d*e^3*x + 36*a^3*A*b^2*e^4*x - 48*a^4*b*B*e^4*x + 48*b^5*B*d^3*e*x^2 + 72*A*b^5*d^2*e^2*x^2 - 108*a*b^4*B*d^2*e^2*x^2 - 72*a*A*b^4*d*e^3*x^2 + 96*a^2*b^3*B*d*e^3*x^2 + 24*a^2*A*b^3*e^4*x^2 - 30*a^3*b^2*B*e^4*x^2 + 36*b^5*B*d^2*e^2*x^3 + 24*A*b^5*d*e^3*x^3 - 32*a*b^4*B*d*e^3*x^3 - 8*a*A*b^4*e^4*x^3 + 10*a^2*b^3*B*e^4*x^3 + 16*b^5*B*d*e^3*x^4 + 4*A*b^5*e^4*x^4 - 5*a*b^4*B*e^4*x^4 + 3*b^5*B*e^4*x^5)/(12*b^6*(a + b*x)) + ((b^4*B*d^4 + 4*A*b^4*d^3*e - 8*a*b^3*B*d^3*e - 12*a*A*b^3*d^2*e^2 + 18*a^2*b^2*B*d^2*e^2 + 12*a^2*A*b^2*d*e^3 - 16*a^3*b*B*d*e^3 - 4*a^3*A*b*e^4 + 5*a^4*B*e^4)*Log[a + b*x])/b^6","B",1
1124,1,363,145,0.2306122,"\int \frac{(A+B x) (d+e x)^3}{(a+b x)^2} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^3)/(a + b*x)^2,x]","\frac{\log (a+b x) \left(-4 a^3 B e^3+3 a^2 A b e^3+9 a^2 b B d e^2-6 a A b^2 d e^2-6 a b^2 B d^2 e+3 A b^3 d^2 e+b^3 B d^3\right)}{b^5}+\frac{-6 a^4 B e^3+6 a^3 A b e^3+18 a^3 b B d e^2+18 a^3 b B e^3 x-18 a^2 A b^2 d e^2-12 a^2 A b^2 e^3 x-18 a^2 b^2 B d^2 e-36 a^2 b^2 B d e^2 x+12 a^2 b^2 B e^3 x^2+18 a A b^3 d^2 e+18 a A b^3 d e^2 x-9 a A b^3 e^3 x^2+6 a b^3 B d^3+18 a b^3 B d^2 e x-27 a b^3 B d e^2 x^2-4 a b^3 B e^3 x^3-6 A b^4 d^3+18 A b^4 d e^2 x^2+3 A b^4 e^3 x^3+18 b^4 B d^2 e x^2+9 b^4 B d e^2 x^3+2 b^4 B e^3 x^4}{6 b^5 (a+b x)}","\frac{e^2 (a+b x)^2 (-4 a B e+A b e+3 b B d)}{2 b^5}-\frac{(A b-a B) (b d-a e)^3}{b^5 (a+b x)}+\frac{(b d-a e)^2 \log (a+b x) (-4 a B e+3 A b e+b B d)}{b^5}+\frac{3 e x (b d-a e) (-2 a B e+A b e+b B d)}{b^4}+\frac{B e^3 (a+b x)^3}{3 b^5}",1,"(-6*A*b^4*d^3 + 6*a*b^3*B*d^3 + 18*a*A*b^3*d^2*e - 18*a^2*b^2*B*d^2*e - 18*a^2*A*b^2*d*e^2 + 18*a^3*b*B*d*e^2 + 6*a^3*A*b*e^3 - 6*a^4*B*e^3 + 18*a*b^3*B*d^2*e*x + 18*a*A*b^3*d*e^2*x - 36*a^2*b^2*B*d*e^2*x - 12*a^2*A*b^2*e^3*x + 18*a^3*b*B*e^3*x + 18*b^4*B*d^2*e*x^2 + 18*A*b^4*d*e^2*x^2 - 27*a*b^3*B*d*e^2*x^2 - 9*a*A*b^3*e^3*x^2 + 12*a^2*b^2*B*e^3*x^2 + 9*b^4*B*d*e^2*x^3 + 3*A*b^4*e^3*x^3 - 4*a*b^3*B*e^3*x^3 + 2*b^4*B*e^3*x^4)/(6*b^5*(a + b*x)) + ((b^3*B*d^3 + 3*A*b^3*d^2*e - 6*a*b^2*B*d^2*e - 6*a*A*b^2*d*e^2 + 9*a^2*b*B*d*e^2 + 3*a^2*A*b*e^3 - 4*a^3*B*e^3)*Log[a + b*x])/b^5","B",1
1125,1,202,99,0.133181,"\int \frac{(A+B x) (d+e x)^2}{(a+b x)^2} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^2)/(a + b*x)^2,x]","\frac{\log (a+b x) \left(3 a^2 B e^2-2 a A b e^2-4 a b B d e+2 A b^2 d e+b^2 B d^2\right)}{b^4}+\frac{2 a^3 B e^2-2 a^2 A b e^2-4 a^2 b B d e-4 a^2 b B e^2 x+4 a A b^2 d e+2 a A b^2 e^2 x+2 a b^2 B d^2+4 a b^2 B d e x-3 a b^2 B e^2 x^2-2 A b^3 d^2+2 A b^3 e^2 x^2+4 b^3 B d e x^2+b^3 B e^2 x^3}{2 b^4 (a+b x)}","-\frac{(A b-a B) (b d-a e)^2}{b^4 (a+b x)}+\frac{(b d-a e) \log (a+b x) (-3 a B e+2 A b e+b B d)}{b^4}+\frac{e x (-2 a B e+A b e+2 b B d)}{b^3}+\frac{B e^2 x^2}{2 b^2}",1,"(-2*A*b^3*d^2 + 2*a*b^2*B*d^2 + 4*a*A*b^2*d*e - 4*a^2*b*B*d*e - 2*a^2*A*b*e^2 + 2*a^3*B*e^2 + 4*a*b^2*B*d*e*x + 2*a*A*b^2*e^2*x - 4*a^2*b*B*e^2*x + 4*b^3*B*d*e*x^2 + 2*A*b^3*e^2*x^2 - 3*a*b^2*B*e^2*x^2 + b^3*B*e^2*x^3)/(2*b^4*(a + b*x)) + ((b^2*B*d^2 + 2*A*b^2*d*e - 4*a*b*B*d*e - 2*a*A*b*e^2 + 3*a^2*B*e^2)*Log[a + b*x])/b^4","B",1
1126,1,76,60,0.0727469,"\int \frac{(A+B x) (d+e x)}{(a+b x)^2} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x))/(a + b*x)^2,x]","\frac{a^2 (-B) e+a A b e+a b B d+a b B e x-A b^2 d+b^2 B e x^2}{b^3 (a+b x)}+\frac{\log (a+b x) (-2 a B e+A b e+b B d)}{b^3}","-\frac{(A b-a B) (b d-a e)}{b^3 (a+b x)}+\frac{\log (a+b x) (-2 a B e+A b e+b B d)}{b^3}+\frac{B e x}{b^2}",1,"(-(A*b^2*d) + a*b*B*d + a*A*b*e - a^2*B*e + a*b*B*e*x + b^2*B*e*x^2)/(b^3*(a + b*x)) + ((b*B*d + A*b*e - 2*a*B*e)*Log[a + b*x])/b^3","A",1
1127,1,31,32,0.000636,"\int \frac{A+B x}{(a+b x)^2} \, dx","IntegrateAlgebraic[(A + B*x)/(a + b*x)^2,x]","\frac{a B-A b}{b^2 (a+b x)}+\frac{B \log (a+b x)}{b^2}","\frac{B \log (a+b x)}{b^2}-\frac{A b-a B}{b^2 (a+b x)}",1,"(-(A*b) + a*B)/(b^2*(a + b*x)) + (B*Log[a + b*x])/b^2","A",1
1128,1,80,82,0.0873812,"\int \frac{A+B x}{(a+b x)^2 (d+e x)} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^2*(d + e*x)),x]","\frac{a B-A b}{b (a+b x) (b d-a e)}+\frac{\log (a+b x) (B d-A e)}{(b d-a e)^2}+\frac{(A e-B d) \log (d+e x)}{(b d-a e)^2}","-\frac{A b-a B}{b (a+b x) (b d-a e)}+\frac{\log (a+b x) (B d-A e)}{(b d-a e)^2}-\frac{(B d-A e) \log (d+e x)}{(b d-a e)^2}",1,"(-(A*b) + a*B)/(b*(b*d - a*e)*(a + b*x)) + ((B*d - A*e)*Log[a + b*x])/(b*d - a*e)^2 + ((-(B*d) + A*e)*Log[d + e*x])/(b*d - a*e)^2","A",1
1129,1,122,117,0.162093,"\int \frac{A+B x}{(a+b x)^2 (d+e x)^2} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^2*(d + e*x)^2),x]","\frac{-a A e+2 a B d+a B e x-A b d-2 A b e x+b B d x}{(a+b x) (d+e x) (b d-a e)^2}+\frac{\log (a+b x) (a B e-2 A b e+b B d)}{(b d-a e)^3}+\frac{\log (d+e x) (-a B e+2 A b e-b B d)}{(b d-a e)^3}","-\frac{A b-a B}{(a+b x) (b d-a e)^2}+\frac{B d-A e}{(d+e x) (b d-a e)^2}+\frac{\log (a+b x) (a B e-2 A b e+b B d)}{(b d-a e)^3}-\frac{\log (d+e x) (a B e-2 A b e+b B d)}{(b d-a e)^3}",1,"(-(A*b*d) + 2*a*B*d - a*A*e + b*B*d*x - 2*A*b*e*x + a*B*e*x)/((b*d - a*e)^2*(a + b*x)*(d + e*x)) + ((b*B*d - 2*A*b*e + a*B*e)*Log[a + b*x])/(b*d - a*e)^3 + ((-(b*B*d) + 2*A*b*e - a*B*e)*Log[d + e*x])/(b*d - a*e)^3","A",1
1130,1,224,157,0.2058176,"\int \frac{A+B x}{(a+b x)^2 (d+e x)^3} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^2*(d + e*x)^3),x]","\frac{a^2 A e^2+a^2 B d e+2 a^2 B e^2 x-5 a A b d e-3 a A b e^2 x+5 a b B d^2+7 a b B d e x+4 a b B e^2 x^2-2 A b^2 d^2-9 A b^2 d e x-6 A b^2 e^2 x^2+3 b^2 B d^2 x+2 b^2 B d e x^2}{2 (a+b x) (d+e x)^2 (b d-a e)^3}+\frac{\log (a+b x) \left(2 a b B e-3 A b^2 e+b^2 B d\right)}{(b d-a e)^4}+\frac{\log (d+e x) \left(-2 a b B e+3 A b^2 e+b^2 (-B) d\right)}{(b d-a e)^4}","-\frac{b (A b-a B)}{(a+b x) (b d-a e)^3}+\frac{a B e-2 A b e+b B d}{(d+e x) (b d-a e)^3}+\frac{B d-A e}{2 (d+e x)^2 (b d-a e)^2}+\frac{b \log (a+b x) (2 a B e-3 A b e+b B d)}{(b d-a e)^4}-\frac{b \log (d+e x) (2 a B e-3 A b e+b B d)}{(b d-a e)^4}",1,"(-2*A*b^2*d^2 + 5*a*b*B*d^2 - 5*a*A*b*d*e + a^2*B*d*e + a^2*A*e^2 + 3*b^2*B*d^2*x - 9*A*b^2*d*e*x + 7*a*b*B*d*e*x - 3*a*A*b*e^2*x + 2*a^2*B*e^2*x + 2*b^2*B*d*e*x^2 - 6*A*b^2*e^2*x^2 + 4*a*b*B*e^2*x^2)/(2*(b*d - a*e)^3*(a + b*x)*(d + e*x)^2) + ((b^2*B*d - 3*A*b^2*e + 2*a*b*B*e)*Log[a + b*x])/(b*d - a*e)^4 + ((-(b^2*B*d) + 3*A*b^2*e - 2*a*b*B*e)*Log[d + e*x])/(b*d - a*e)^4","A",1
1131,1,362,200,0.2865757,"\int \frac{A+B x}{(a+b x)^2 (d+e x)^4} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^2*(d + e*x)^4),x]","\frac{-2 a^3 A e^3-a^3 B d e^2-3 a^3 B e^3 x+10 a^2 A b d e^2+4 a^2 A b e^3 x+8 a^2 b B d^2 e+23 a^2 b B d e^2 x+9 a^2 b B e^3 x^2-26 a A b^2 d^2 e-32 a A b^2 d e^2 x-12 a A b^2 e^3 x^2+17 a b^2 B d^3+41 a b^2 B d^2 e x+48 a b^2 B d e^2 x^2+18 a b^2 B e^3 x^3-6 A b^3 d^3-44 A b^3 d^2 e x-60 A b^3 d e^2 x^2-24 A b^3 e^3 x^3+11 b^3 B d^3 x+15 b^3 B d^2 e x^2+6 b^3 B d e^2 x^3}{6 (a+b x) (d+e x)^3 (b d-a e)^4}+\frac{\log (a+b x) \left(3 a b^2 B e-4 A b^3 e+b^3 B d\right)}{(b d-a e)^5}+\frac{\log (d+e x) \left(-3 a b^2 B e+4 A b^3 e+b^3 (-B) d\right)}{(b d-a e)^5}","-\frac{b^2 (A b-a B)}{(a+b x) (b d-a e)^4}+\frac{b^2 \log (a+b x) (3 a B e-4 A b e+b B d)}{(b d-a e)^5}-\frac{b^2 \log (d+e x) (3 a B e-4 A b e+b B d)}{(b d-a e)^5}+\frac{b (2 a B e-3 A b e+b B d)}{(d+e x) (b d-a e)^4}+\frac{a B e-2 A b e+b B d}{2 (d+e x)^2 (b d-a e)^3}+\frac{B d-A e}{3 (d+e x)^3 (b d-a e)^2}",1,"(-6*A*b^3*d^3 + 17*a*b^2*B*d^3 - 26*a*A*b^2*d^2*e + 8*a^2*b*B*d^2*e + 10*a^2*A*b*d*e^2 - a^3*B*d*e^2 - 2*a^3*A*e^3 + 11*b^3*B*d^3*x - 44*A*b^3*d^2*e*x + 41*a*b^2*B*d^2*e*x - 32*a*A*b^2*d*e^2*x + 23*a^2*b*B*d*e^2*x + 4*a^2*A*b*e^3*x - 3*a^3*B*e^3*x + 15*b^3*B*d^2*e*x^2 - 60*A*b^3*d*e^2*x^2 + 48*a*b^2*B*d*e^2*x^2 - 12*a*A*b^2*e^3*x^2 + 9*a^2*b*B*e^3*x^2 + 6*b^3*B*d*e^2*x^3 - 24*A*b^3*e^3*x^3 + 18*a*b^2*B*e^3*x^3)/(6*(b*d - a*e)^4*(a + b*x)*(d + e*x)^3) + ((b^3*B*d - 4*A*b^3*e + 3*a*b^2*B*e)*Log[a + b*x])/(b*d - a*e)^5 + ((-(b^3*B*d) + 4*A*b^3*e - 3*a*b^2*B*e)*Log[d + e*x])/(b*d - a*e)^5","A",1
1132,1,529,239,0.3851872,"\int \frac{A+B x}{(a+b x)^2 (d+e x)^5} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^2*(d + e*x)^5),x]","\frac{3 a^4 A e^4+a^4 B d e^3+4 a^4 B e^4 x-17 a^3 A b d e^3-5 a^3 A b e^4 x-7 a^3 b B d^2 e^2-27 a^3 b B d e^3 x-8 a^3 b B e^4 x^2+43 a^2 A b^2 d^2 e^2+35 a^2 A b^2 d e^3 x+10 a^2 A b^2 e^4 x^2+29 a^2 b^2 B d^3 e+109 a^2 b^2 B d^2 e^2 x+86 a^2 b^2 B d e^3 x^2+24 a^2 b^2 B e^4 x^3-77 a A b^3 d^3 e-145 a A b^3 d^2 e^2 x-110 a A b^3 d e^3 x^2-30 a A b^3 e^4 x^3+37 a b^3 B d^4+129 a b^3 B d^3 e x+230 a b^3 B d^2 e^2 x^2+174 a b^3 B d e^3 x^3+48 a b^3 B e^4 x^4-12 A b^4 d^4-125 A b^4 d^3 e x-260 A b^4 d^2 e^2 x^2-210 A b^4 d e^3 x^3-60 A b^4 e^4 x^4+25 b^4 B d^4 x+52 b^4 B d^3 e x^2+42 b^4 B d^2 e^2 x^3+12 b^4 B d e^3 x^4}{12 (a+b x) (d+e x)^4 (b d-a e)^5}+\frac{\log (a+b x) \left(4 a b^3 B e-5 A b^4 e+b^4 B d\right)}{(b d-a e)^6}+\frac{\log (d+e x) \left(-4 a b^3 B e+5 A b^4 e+b^4 (-B) d\right)}{(b d-a e)^6}","-\frac{b^3 (A b-a B)}{(a+b x) (b d-a e)^5}+\frac{b^3 \log (a+b x) (4 a B e-5 A b e+b B d)}{(b d-a e)^6}-\frac{b^3 \log (d+e x) (4 a B e-5 A b e+b B d)}{(b d-a e)^6}+\frac{b^2 (3 a B e-4 A b e+b B d)}{(d+e x) (b d-a e)^5}+\frac{b (2 a B e-3 A b e+b B d)}{2 (d+e x)^2 (b d-a e)^4}+\frac{a B e-2 A b e+b B d}{3 (d+e x)^3 (b d-a e)^3}+\frac{B d-A e}{4 (d+e x)^4 (b d-a e)^2}",1,"(-12*A*b^4*d^4 + 37*a*b^3*B*d^4 - 77*a*A*b^3*d^3*e + 29*a^2*b^2*B*d^3*e + 43*a^2*A*b^2*d^2*e^2 - 7*a^3*b*B*d^2*e^2 - 17*a^3*A*b*d*e^3 + a^4*B*d*e^3 + 3*a^4*A*e^4 + 25*b^4*B*d^4*x - 125*A*b^4*d^3*e*x + 129*a*b^3*B*d^3*e*x - 145*a*A*b^3*d^2*e^2*x + 109*a^2*b^2*B*d^2*e^2*x + 35*a^2*A*b^2*d*e^3*x - 27*a^3*b*B*d*e^3*x - 5*a^3*A*b*e^4*x + 4*a^4*B*e^4*x + 52*b^4*B*d^3*e*x^2 - 260*A*b^4*d^2*e^2*x^2 + 230*a*b^3*B*d^2*e^2*x^2 - 110*a*A*b^3*d*e^3*x^2 + 86*a^2*b^2*B*d*e^3*x^2 + 10*a^2*A*b^2*e^4*x^2 - 8*a^3*b*B*e^4*x^2 + 42*b^4*B*d^2*e^2*x^3 - 210*A*b^4*d*e^3*x^3 + 174*a*b^3*B*d*e^3*x^3 - 30*a*A*b^3*e^4*x^3 + 24*a^2*b^2*B*e^4*x^3 + 12*b^4*B*d*e^3*x^4 - 60*A*b^4*e^4*x^4 + 48*a*b^3*B*e^4*x^4)/(12*(b*d - a*e)^5*(a + b*x)*(d + e*x)^4) + ((b^4*B*d - 5*A*b^4*e + 4*a*b^3*B*e)*Log[a + b*x])/(b*d - a*e)^6 + ((-(b^4*B*d) + 5*A*b^4*e - 4*a*b^3*B*e)*Log[d + e*x])/(b*d - a*e)^6","B",1
1133,1,764,230,0.3341352,"\int \frac{(A+B x) (d+e x)^5}{(a+b x)^3} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^5)/(a + b*x)^3,x]","\frac{5 \log (a+b x) \left(3 a^4 B e^5-2 a^3 A b e^5-10 a^3 b B d e^4+6 a^2 A b^2 d e^4+12 a^2 b^2 B d^2 e^3-6 a A b^3 d^2 e^3-6 a b^3 B d^3 e^2+2 A b^4 d^3 e^2+b^4 B d^4 e\right)}{b^7}+\frac{66 a^6 B e^5-54 a^5 A b e^5-270 a^5 b B d e^4-48 a^5 b B e^5 x+210 a^4 A b^2 d e^4+12 a^4 A b^2 e^5 x+420 a^4 b^2 B d^2 e^3+60 a^4 b^2 B d e^4 x-204 a^4 b^2 B e^5 x^2-300 a^3 A b^3 d^2 e^3+60 a^3 A b^3 d e^4 x+126 a^3 A b^3 e^5 x^2-300 a^3 b^3 B d^3 e^2+120 a^3 b^3 B d^2 e^3 x+630 a^3 b^3 B d e^4 x^2-60 a^3 b^3 B e^5 x^3+180 a^2 A b^4 d^3 e^2-240 a^2 A b^4 d^2 e^3 x-330 a^2 A b^4 d e^4 x^2+40 a^2 A b^4 e^5 x^3+90 a^2 b^4 B d^4 e-240 a^2 b^4 B d^3 e^2 x-660 a^2 b^4 B d^2 e^3 x^2+200 a^2 b^4 B d e^4 x^3+15 a^2 b^4 B e^5 x^4-30 a A b^5 d^4 e+240 a A b^5 d^3 e^2 x+240 a A b^5 d^2 e^3 x^2-120 a A b^5 d e^4 x^3-10 a A b^5 e^5 x^4-6 a b^5 B d^5+120 a b^5 B d^4 e x+240 a b^5 B d^3 e^2 x^2-240 a b^5 B d^2 e^3 x^3-50 a b^5 B d e^4 x^4-6 a b^5 B e^5 x^5-6 A b^6 d^5-60 A b^6 d^4 e x+120 A b^6 d^2 e^3 x^3+30 A b^6 d e^4 x^4+4 A b^6 e^5 x^5-12 b^6 B d^5 x+120 b^6 B d^3 e^2 x^3+60 b^6 B d^2 e^3 x^4+20 b^6 B d e^4 x^5+3 b^6 B e^5 x^6}{12 b^7 (a+b x)^2}","\frac{e^4 (a+b x)^3 (-6 a B e+A b e+5 b B d)}{3 b^7}+\frac{5 e^3 (a+b x)^2 (b d-a e) (-3 a B e+A b e+2 b B d)}{2 b^7}-\frac{(b d-a e)^4 (-6 a B e+5 A b e+b B d)}{b^7 (a+b x)}-\frac{(A b-a B) (b d-a e)^5}{2 b^7 (a+b x)^2}+\frac{5 e (b d-a e)^3 \log (a+b x) (-3 a B e+2 A b e+b B d)}{b^7}+\frac{10 e^2 x (b d-a e)^2 (-2 a B e+A b e+b B d)}{b^6}+\frac{B e^5 (a+b x)^4}{4 b^7}",1,"(-6*A*b^6*d^5 - 6*a*b^5*B*d^5 - 30*a*A*b^5*d^4*e + 90*a^2*b^4*B*d^4*e + 180*a^2*A*b^4*d^3*e^2 - 300*a^3*b^3*B*d^3*e^2 - 300*a^3*A*b^3*d^2*e^3 + 420*a^4*b^2*B*d^2*e^3 + 210*a^4*A*b^2*d*e^4 - 270*a^5*b*B*d*e^4 - 54*a^5*A*b*e^5 + 66*a^6*B*e^5 - 12*b^6*B*d^5*x - 60*A*b^6*d^4*e*x + 120*a*b^5*B*d^4*e*x + 240*a*A*b^5*d^3*e^2*x - 240*a^2*b^4*B*d^3*e^2*x - 240*a^2*A*b^4*d^2*e^3*x + 120*a^3*b^3*B*d^2*e^3*x + 60*a^3*A*b^3*d*e^4*x + 60*a^4*b^2*B*d*e^4*x + 12*a^4*A*b^2*e^5*x - 48*a^5*b*B*e^5*x + 240*a*b^5*B*d^3*e^2*x^2 + 240*a*A*b^5*d^2*e^3*x^2 - 660*a^2*b^4*B*d^2*e^3*x^2 - 330*a^2*A*b^4*d*e^4*x^2 + 630*a^3*b^3*B*d*e^4*x^2 + 126*a^3*A*b^3*e^5*x^2 - 204*a^4*b^2*B*e^5*x^2 + 120*b^6*B*d^3*e^2*x^3 + 120*A*b^6*d^2*e^3*x^3 - 240*a*b^5*B*d^2*e^3*x^3 - 120*a*A*b^5*d*e^4*x^3 + 200*a^2*b^4*B*d*e^4*x^3 + 40*a^2*A*b^4*e^5*x^3 - 60*a^3*b^3*B*e^5*x^3 + 60*b^6*B*d^2*e^3*x^4 + 30*A*b^6*d*e^4*x^4 - 50*a*b^5*B*d*e^4*x^4 - 10*a*A*b^5*e^5*x^4 + 15*a^2*b^4*B*e^5*x^4 + 20*b^6*B*d*e^4*x^5 + 4*A*b^6*e^5*x^5 - 6*a*b^5*B*e^5*x^5 + 3*b^6*B*e^5*x^6)/(12*b^7*(a + b*x)^2) + (5*(b^4*B*d^4*e + 2*A*b^4*d^3*e^2 - 6*a*b^3*B*d^3*e^2 - 6*a*A*b^3*d^2*e^3 + 12*a^2*b^2*B*d^2*e^3 + 6*a^2*A*b^2*d*e^4 - 10*a^3*b*B*d*e^4 - 2*a^3*A*b*e^5 + 3*a^4*B*e^5)*Log[a + b*x])/b^7","B",1
1134,1,531,191,0.2454043,"\int \frac{(A+B x) (d+e x)^4}{(a+b x)^3} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^4)/(a + b*x)^3,x]","\frac{2 \log (a+b x) \left(-5 a^3 B e^4+3 a^2 A b e^4+12 a^2 b B d e^3-6 a A b^2 d e^3-9 a b^2 B d^2 e^2+3 A b^3 d^2 e^2+2 b^3 B d^3 e\right)}{b^6}+\frac{-27 a^5 B e^4+21 a^4 A b e^4+84 a^4 b B d e^3+6 a^4 b B e^4 x-60 a^3 A b^2 d e^3+6 a^3 A b^2 e^4 x-90 a^3 b^2 B d^2 e^2+24 a^3 b^2 B d e^3 x+63 a^3 b^2 B e^4 x^2+54 a^2 A b^3 d^2 e^2-48 a^2 A b^3 d e^3 x-33 a^2 A b^3 e^4 x^2+36 a^2 b^3 B d^3 e-72 a^2 b^3 B d^2 e^2 x-132 a^2 b^3 B d e^3 x^2+20 a^2 b^3 B e^4 x^3-12 a A b^4 d^3 e+72 a A b^4 d^2 e^2 x+48 a A b^4 d e^3 x^2-12 a A b^4 e^4 x^3-3 a b^4 B d^4+48 a b^4 B d^3 e x+72 a b^4 B d^2 e^2 x^2-48 a b^4 B d e^3 x^3-5 a b^4 B e^4 x^4-3 A b^5 d^4-24 A b^5 d^3 e x+24 A b^5 d e^3 x^3+3 A b^5 e^4 x^4-6 b^5 B d^4 x+36 b^5 B d^2 e^2 x^3+12 b^5 B d e^3 x^4+2 b^5 B e^4 x^5}{6 b^6 (a+b x)^2}","\frac{e^3 (a+b x)^2 (-5 a B e+A b e+4 b B d)}{2 b^6}-\frac{(b d-a e)^3 (-5 a B e+4 A b e+b B d)}{b^6 (a+b x)}-\frac{(A b-a B) (b d-a e)^4}{2 b^6 (a+b x)^2}+\frac{2 e (b d-a e)^2 \log (a+b x) (-5 a B e+3 A b e+2 b B d)}{b^6}+\frac{2 e^2 x (b d-a e) (-5 a B e+2 A b e+3 b B d)}{b^5}+\frac{B e^4 (a+b x)^3}{3 b^6}",1,"(-3*A*b^5*d^4 - 3*a*b^4*B*d^4 - 12*a*A*b^4*d^3*e + 36*a^2*b^3*B*d^3*e + 54*a^2*A*b^3*d^2*e^2 - 90*a^3*b^2*B*d^2*e^2 - 60*a^3*A*b^2*d*e^3 + 84*a^4*b*B*d*e^3 + 21*a^4*A*b*e^4 - 27*a^5*B*e^4 - 6*b^5*B*d^4*x - 24*A*b^5*d^3*e*x + 48*a*b^4*B*d^3*e*x + 72*a*A*b^4*d^2*e^2*x - 72*a^2*b^3*B*d^2*e^2*x - 48*a^2*A*b^3*d*e^3*x + 24*a^3*b^2*B*d*e^3*x + 6*a^3*A*b^2*e^4*x + 6*a^4*b*B*e^4*x + 72*a*b^4*B*d^2*e^2*x^2 + 48*a*A*b^4*d*e^3*x^2 - 132*a^2*b^3*B*d*e^3*x^2 - 33*a^2*A*b^3*e^4*x^2 + 63*a^3*b^2*B*e^4*x^2 + 36*b^5*B*d^2*e^2*x^3 + 24*A*b^5*d*e^3*x^3 - 48*a*b^4*B*d*e^3*x^3 - 12*a*A*b^4*e^4*x^3 + 20*a^2*b^3*B*e^4*x^3 + 12*b^5*B*d*e^3*x^4 + 3*A*b^5*e^4*x^4 - 5*a*b^4*B*e^4*x^4 + 2*b^5*B*e^4*x^5)/(6*b^6*(a + b*x)^2) + (2*(2*b^3*B*d^3*e + 3*A*b^3*d^2*e^2 - 9*a*b^2*B*d^2*e^2 - 6*a*A*b^2*d*e^3 + 12*a^2*b*B*d*e^3 + 3*a^2*A*b*e^4 - 5*a^3*B*e^4)*Log[a + b*x])/b^6","B",1
1135,1,332,141,0.2325067,"\int \frac{(A+B x) (d+e x)^3}{(a+b x)^3} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^3)/(a + b*x)^3,x]","\frac{3 \log (a+b x) \left(2 a^2 B e^3-a A b e^3-3 a b B d e^2+A b^2 d e^2+b^2 B d^2 e\right)}{b^5}+\frac{7 a^4 B e^3-5 a^3 A b e^3-15 a^3 b B d e^2+2 a^3 b B e^3 x+9 a^2 A b^2 d e^2-4 a^2 A b^2 e^3 x+9 a^2 b^2 B d^2 e-12 a^2 b^2 B d e^2 x-11 a^2 b^2 B e^3 x^2-3 a A b^3 d^2 e+12 a A b^3 d e^2 x+4 a A b^3 e^3 x^2-a b^3 B d^3+12 a b^3 B d^2 e x+12 a b^3 B d e^2 x^2-4 a b^3 B e^3 x^3-A b^4 d^3-6 A b^4 d^2 e x+2 A b^4 e^3 x^3-2 b^4 B d^3 x+6 b^4 B d e^2 x^3+b^4 B e^3 x^4}{2 b^5 (a+b x)^2}","-\frac{(b d-a e)^2 (-4 a B e+3 A b e+b B d)}{b^5 (a+b x)}-\frac{(A b-a B) (b d-a e)^3}{2 b^5 (a+b x)^2}+\frac{3 e (b d-a e) \log (a+b x) (-2 a B e+A b e+b B d)}{b^5}+\frac{e^2 x (-3 a B e+A b e+3 b B d)}{b^4}+\frac{B e^3 x^2}{2 b^3}",1,"(-(A*b^4*d^3) - a*b^3*B*d^3 - 3*a*A*b^3*d^2*e + 9*a^2*b^2*B*d^2*e + 9*a^2*A*b^2*d*e^2 - 15*a^3*b*B*d*e^2 - 5*a^3*A*b*e^3 + 7*a^4*B*e^3 - 2*b^4*B*d^3*x - 6*A*b^4*d^2*e*x + 12*a*b^3*B*d^2*e*x + 12*a*A*b^3*d*e^2*x - 12*a^2*b^2*B*d*e^2*x - 4*a^2*A*b^2*e^3*x + 2*a^3*b*B*e^3*x + 12*a*b^3*B*d*e^2*x^2 + 4*a*A*b^3*e^3*x^2 - 11*a^2*b^2*B*e^3*x^2 + 6*b^4*B*d*e^2*x^3 + 2*A*b^4*e^3*x^3 - 4*a*b^3*B*e^3*x^3 + b^4*B*e^3*x^4)/(2*b^5*(a + b*x)^2) + (3*(b^2*B*d^2*e + A*b^2*d*e^2 - 3*a*b*B*d*e^2 - a*A*b*e^3 + 2*a^2*B*e^3)*Log[a + b*x])/b^5","B",1
1136,1,178,103,0.1333146,"\int \frac{(A+B x) (d+e x)^2}{(a+b x)^3} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^2)/(a + b*x)^3,x]","\frac{-5 a^3 B e^2+3 a^2 A b e^2+6 a^2 b B d e-4 a^2 b B e^2 x-2 a A b^2 d e+4 a A b^2 e^2 x-a b^2 B d^2+8 a b^2 B d e x+4 a b^2 B e^2 x^2-A b^3 d^2-4 A b^3 d e x-2 b^3 B d^2 x+2 b^3 B e^2 x^3}{2 b^4 (a+b x)^2}+\frac{\log (a+b x) \left(-3 a B e^2+A b e^2+2 b B d e\right)}{b^4}","-\frac{(b d-a e) (-3 a B e+2 A b e+b B d)}{b^4 (a+b x)}-\frac{(A b-a B) (b d-a e)^2}{2 b^4 (a+b x)^2}+\frac{e \log (a+b x) (-3 a B e+A b e+2 b B d)}{b^4}+\frac{B e^2 x}{b^3}",1,"(-(A*b^3*d^2) - a*b^2*B*d^2 - 2*a*A*b^2*d*e + 6*a^2*b*B*d*e + 3*a^2*A*b*e^2 - 5*a^3*B*e^2 - 2*b^3*B*d^2*x - 4*A*b^3*d*e*x + 8*a*b^2*B*d*e*x + 4*a*A*b^2*e^2*x - 4*a^2*b*B*e^2*x + 4*a*b^2*B*e^2*x^2 + 2*b^3*B*e^2*x^3)/(2*b^4*(a + b*x)^2) + ((2*b*B*d*e + A*b*e^2 - 3*a*B*e^2)*Log[a + b*x])/b^4","A",1
1137,1,77,69,0.0648177,"\int \frac{(A+B x) (d+e x)}{(a+b x)^3} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x))/(a + b*x)^3,x]","\frac{3 a^2 B e-a A b e-a b B d+4 a b B e x-A b^2 d-2 A b^2 e x-2 b^2 B d x}{2 b^3 (a+b x)^2}+\frac{B e \log (a+b x)}{b^3}","-\frac{(A b-a B) (b d-a e)}{2 b^3 (a+b x)^2}-\frac{-2 a B e+A b e+b B d}{b^3 (a+b x)}+\frac{B e \log (a+b x)}{b^3}",1,"(-(A*b^2*d) - a*b*B*d - a*A*b*e + 3*a^2*B*e - 2*b^2*B*d*x - 2*A*b^2*e*x + 4*a*b*B*e*x)/(2*b^3*(a + b*x)^2) + (B*e*Log[a + b*x])/b^3","A",1
1138,1,28,28,0.0006008,"\int \frac{A+B x}{(a+b x)^3} \, dx","IntegrateAlgebraic[(A + B*x)/(a + b*x)^3,x]","\frac{-a B-A b-2 b B x}{2 b^2 (a+b x)^2}","-\frac{(A+B x)^2}{2 (a+b x)^2 (A b-a B)}",1,"(-(A*b) - a*B - 2*b*B*x)/(2*b^2*(a + b*x)^2)","A",1
1139,1,124,113,0.1096711,"\int \frac{A+B x}{(a+b x)^3 (d+e x)} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^3*(d + e*x)),x]","\frac{a^2 (-B) e+3 a A b e-a b B d-A b^2 d+2 A b^2 e x-2 b^2 B d x}{2 b (a+b x)^2 (b d-a e)^2}+\frac{\log (a+b x) \left(A e^2-B d e\right)}{(b d-a e)^3}+\frac{\left(B d e-A e^2\right) \log (d+e x)}{(b d-a e)^3}","\frac{a B-A b}{2 b (a+b x)^2 (b d-a e)}-\frac{B d-A e}{(a+b x) (b d-a e)^2}-\frac{e \log (a+b x) (B d-A e)}{(b d-a e)^3}+\frac{e (B d-A e) \log (d+e x)}{(b d-a e)^3}",1,"(-(A*b^2*d) - a*b*B*d + 3*a*A*b*e - a^2*B*e - 2*b^2*B*d*x + 2*A*b^2*e*x)/(2*b*(b*d - a*e)^2*(a + b*x)^2) + ((-(B*d*e) + A*e^2)*Log[a + b*x])/(b*d - a*e)^3 + ((B*d*e - A*e^2)*Log[d + e*x])/(b*d - a*e)^3","A",1
1140,1,226,158,0.1846944,"\int \frac{A+B x}{(a+b x)^3 (d+e x)^2} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^3*(d + e*x)^2),x]","\frac{2 a^2 A e^2-5 a^2 B d e-3 a^2 B e^2 x+5 a A b d e+9 a A b e^2 x-a b B d^2-7 a b B d e x-2 a b B e^2 x^2-A b^2 d^2+3 A b^2 d e x+6 A b^2 e^2 x^2-2 b^2 B d^2 x-4 b^2 B d e x^2}{2 (a+b x)^2 (d+e x) (b d-a e)^3}+\frac{\log (a+b x) \left(-a B e^2+3 A b e^2-2 b B d e\right)}{(b d-a e)^4}+\frac{\log (d+e x) \left(a B e^2-3 A b e^2+2 b B d e\right)}{(b d-a e)^4}","-\frac{A b-a B}{2 (a+b x)^2 (b d-a e)^2}-\frac{a B e-2 A b e+b B d}{(a+b x) (b d-a e)^3}-\frac{e (B d-A e)}{(d+e x) (b d-a e)^3}-\frac{e \log (a+b x) (a B e-3 A b e+2 b B d)}{(b d-a e)^4}+\frac{e \log (d+e x) (a B e-3 A b e+2 b B d)}{(b d-a e)^4}",1,"(-(A*b^2*d^2) - a*b*B*d^2 + 5*a*A*b*d*e - 5*a^2*B*d*e + 2*a^2*A*e^2 - 2*b^2*B*d^2*x + 3*A*b^2*d*e*x - 7*a*b*B*d*e*x + 9*a*A*b*e^2*x - 3*a^2*B*e^2*x - 4*b^2*B*d*e*x^2 + 6*A*b^2*e^2*x^2 - 2*a*b*B*e^2*x^2)/(2*(b*d - a*e)^3*(a + b*x)^2*(d + e*x)) + ((-2*b*B*d*e + 3*A*b*e^2 - a*B*e^2)*Log[a + b*x])/(b*d - a*e)^4 + ((2*b*B*d*e - 3*A*b*e^2 + a*B*e^2)*Log[d + e*x])/(b*d - a*e)^4","A",1
1141,1,367,199,0.2865241,"\int \frac{A+B x}{(a+b x)^3 (d+e x)^3} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^3*(d + e*x)^3),x]","\frac{a^3 (-A) e^3-a^3 B d e^2-2 a^3 B e^3 x+7 a^2 A b d e^2+4 a^2 A b e^3 x-10 a^2 b B d^2 e-16 a^2 b B d e^2 x-9 a^2 b B e^3 x^2+7 a A b^2 d^2 e+28 a A b^2 d e^2 x+18 a A b^2 e^3 x^2-a b^2 B d^3-16 a b^2 B d^2 e x-18 a b^2 B d e^2 x^2-6 a b^2 B e^3 x^3-A b^3 d^3+4 A b^3 d^2 e x+18 A b^3 d e^2 x^2+12 A b^3 e^3 x^3-2 b^3 B d^3 x-9 b^3 B d^2 e x^2-6 b^3 B d e^2 x^3}{2 (a+b x)^2 (d+e x)^2 (b d-a e)^4}-\frac{3 \log (a+b x) \left(a b B e^2-2 A b^2 e^2+b^2 B d e\right)}{(b d-a e)^5}+\frac{3 \log (d+e x) \left(a b B e^2-2 A b^2 e^2+b^2 B d e\right)}{(b d-a e)^5}","-\frac{b (A b-a B)}{2 (a+b x)^2 (b d-a e)^3}-\frac{b (2 a B e-3 A b e+b B d)}{(a+b x) (b d-a e)^4}-\frac{e (a B e-3 A b e+2 b B d)}{(d+e x) (b d-a e)^4}-\frac{e (B d-A e)}{2 (d+e x)^2 (b d-a e)^3}-\frac{3 b e \log (a+b x) (a B e-2 A b e+b B d)}{(b d-a e)^5}+\frac{3 b e \log (d+e x) (a B e-2 A b e+b B d)}{(b d-a e)^5}",1,"(-(A*b^3*d^3) - a*b^2*B*d^3 + 7*a*A*b^2*d^2*e - 10*a^2*b*B*d^2*e + 7*a^2*A*b*d*e^2 - a^3*B*d*e^2 - a^3*A*e^3 - 2*b^3*B*d^3*x + 4*A*b^3*d^2*e*x - 16*a*b^2*B*d^2*e*x + 28*a*A*b^2*d*e^2*x - 16*a^2*b*B*d*e^2*x + 4*a^2*A*b*e^3*x - 2*a^3*B*e^3*x - 9*b^3*B*d^2*e*x^2 + 18*A*b^3*d*e^2*x^2 - 18*a*b^2*B*d*e^2*x^2 + 18*a*A*b^2*e^3*x^2 - 9*a^2*b*B*e^3*x^2 - 6*b^3*B*d*e^2*x^3 + 12*A*b^3*e^3*x^3 - 6*a*b^2*B*e^3*x^3)/(2*(b*d - a*e)^4*(a + b*x)^2*(d + e*x)^2) - (3*(b^2*B*d*e - 2*A*b^2*e^2 + a*b*B*e^2)*Log[a + b*x])/(b*d - a*e)^5 + (3*(b^2*B*d*e - 2*A*b^2*e^2 + a*b*B*e^2)*Log[d + e*x])/(b*d - a*e)^5","A",1
1142,1,542,248,0.3901315,"\int \frac{A+B x}{(a+b x)^3 (d+e x)^4} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^3*(d + e*x)^4),x]","\frac{2 a^4 A e^4+a^4 B d e^3+3 a^4 B e^4 x-13 a^3 A b d e^3-5 a^3 A b e^4 x-11 a^3 b B d^2 e^2-31 a^3 b B d e^3 x-12 a^3 b B e^4 x^2+47 a^2 A b^2 d^2 e^2+55 a^2 A b^2 d e^3 x+20 a^2 A b^2 e^4 x^2-47 a^2 b^2 B d^3 e-127 a^2 b^2 B d^2 e^2 x-146 a^2 b^2 B d e^3 x^2-54 a^2 b^2 B e^4 x^3+27 a A b^3 d^3 e+175 a A b^3 d^2 e^2 x+230 a A b^3 d e^3 x^2+90 a A b^3 e^4 x^3-3 a b^3 B d^4-79 a b^3 B d^3 e x-158 a b^3 B d^2 e^2 x^2-126 a b^3 B d e^3 x^3-36 a b^3 B e^4 x^4-3 A b^4 d^4+15 A b^4 d^3 e x+110 A b^4 d^2 e^2 x^2+150 A b^4 d e^3 x^3+60 A b^4 e^4 x^4-6 b^4 B d^4 x-44 b^4 B d^3 e x^2-60 b^4 B d^2 e^2 x^3-24 b^4 B d e^3 x^4}{6 (a+b x)^2 (d+e x)^3 (b d-a e)^5}-\frac{2 \log (a+b x) \left(3 a b^2 B e^2-5 A b^3 e^2+2 b^3 B d e\right)}{(b d-a e)^6}+\frac{2 \log (d+e x) \left(3 a b^2 B e^2-5 A b^3 e^2+2 b^3 B d e\right)}{(b d-a e)^6}","-\frac{b^2 (3 a B e-4 A b e+b B d)}{(a+b x) (b d-a e)^5}-\frac{b^2 (A b-a B)}{2 (a+b x)^2 (b d-a e)^4}-\frac{2 b^2 e \log (a+b x) (3 a B e-5 A b e+2 b B d)}{(b d-a e)^6}+\frac{2 b^2 e \log (d+e x) (3 a B e-5 A b e+2 b B d)}{(b d-a e)^6}-\frac{3 b e (a B e-2 A b e+b B d)}{(d+e x) (b d-a e)^5}-\frac{e (a B e-3 A b e+2 b B d)}{2 (d+e x)^2 (b d-a e)^4}-\frac{e (B d-A e)}{3 (d+e x)^3 (b d-a e)^3}",1,"(-3*A*b^4*d^4 - 3*a*b^3*B*d^4 + 27*a*A*b^3*d^3*e - 47*a^2*b^2*B*d^3*e + 47*a^2*A*b^2*d^2*e^2 - 11*a^3*b*B*d^2*e^2 - 13*a^3*A*b*d*e^3 + a^4*B*d*e^3 + 2*a^4*A*e^4 - 6*b^4*B*d^4*x + 15*A*b^4*d^3*e*x - 79*a*b^3*B*d^3*e*x + 175*a*A*b^3*d^2*e^2*x - 127*a^2*b^2*B*d^2*e^2*x + 55*a^2*A*b^2*d*e^3*x - 31*a^3*b*B*d*e^3*x - 5*a^3*A*b*e^4*x + 3*a^4*B*e^4*x - 44*b^4*B*d^3*e*x^2 + 110*A*b^4*d^2*e^2*x^2 - 158*a*b^3*B*d^2*e^2*x^2 + 230*a*A*b^3*d*e^3*x^2 - 146*a^2*b^2*B*d*e^3*x^2 + 20*a^2*A*b^2*e^4*x^2 - 12*a^3*b*B*e^4*x^2 - 60*b^4*B*d^2*e^2*x^3 + 150*A*b^4*d*e^3*x^3 - 126*a*b^3*B*d*e^3*x^3 + 90*a*A*b^3*e^4*x^3 - 54*a^2*b^2*B*e^4*x^3 - 24*b^4*B*d*e^3*x^4 + 60*A*b^4*e^4*x^4 - 36*a*b^3*B*e^4*x^4)/(6*(b*d - a*e)^5*(a + b*x)^2*(d + e*x)^3) - (2*(2*b^3*B*d*e - 5*A*b^3*e^2 + 3*a*b^2*B*e^2)*Log[a + b*x])/(b*d - a*e)^6 + (2*(2*b^3*B*d*e - 5*A*b^3*e^2 + 3*a*b^2*B*e^2)*Log[d + e*x])/(b*d - a*e)^6","B",1
1143,1,58,34,0.010823,"\int (1-2 x) (2+3 x)^8 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x),x]","\frac{1}{330} \left(-1968300 x^{11}-11763873 x^{10}-30498930 x^9-43944120 x^8-36352800 x^7-13638240 x^6+4124736 x^5+8110080 x^4+4702720 x^3+1478400 x^2+253440 x\right)","-\frac{10}{297} (3 x+2)^{11}+\frac{37}{270} (3 x+2)^{10}-\frac{7}{243} (3 x+2)^9",1,"(253440*x + 1478400*x^2 + 4702720*x^3 + 8110080*x^4 + 4124736*x^5 - 13638240*x^6 - 36352800*x^7 - 43944120*x^8 - 30498930*x^9 - 11763873*x^10 - 1968300*x^11)/330","A",1
1144,1,53,34,0.0099766,"\int (1-2 x) (2+3 x)^7 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^7*(3 + 5*x),x]","\frac{1}{24} \left(-52488 x^{10}-277992 x^9-623295 x^8-742608 x^7-450576 x^6-36288 x^5+155232 x^4+124160 x^3+46848 x^2+9216 x\right)","-\frac{1}{27} (3 x+2)^{10}+\frac{37}{243} (3 x+2)^9-\frac{7}{216} (3 x+2)^8",1,"(9216*x + 46848*x^2 + 124160*x^3 + 155232*x^4 - 36288*x^5 - 450576*x^6 - 742608*x^7 - 623295*x^8 - 277992*x^9 - 52488*x^10)/24","A",1
1145,1,48,34,0.0098313,"\int (1-2 x) (2+3 x)^6 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^6*(3 + 5*x),x]","\frac{1}{24} \left(-19440 x^9-89667 x^8-169128 x^7-157248 x^6-54432 x^5+30240 x^4+42112 x^3+19968 x^2+4608 x\right)","-\frac{10}{243} (3 x+2)^9+\frac{37}{216} (3 x+2)^8-\frac{1}{27} (3 x+2)^7",1,"(4608*x + 19968*x^2 + 42112*x^3 + 30240*x^4 - 54432*x^5 - 157248*x^6 - 169128*x^7 - 89667*x^8 - 19440*x^9)/24","A",1
1146,1,43,34,0.0086401,"\int (1-2 x) (2+3 x)^5 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^5*(3 + 5*x),x]","\frac{1}{84} \left(-25515 x^8-100116 x^7-152334 x^6-98280 x^5+2520 x^4+44800 x^3+28896 x^2+8064 x\right)","-\frac{5}{108} (3 x+2)^8+\frac{37}{189} (3 x+2)^7-\frac{7}{162} (3 x+2)^6",1,"(8064*x + 28896*x^2 + 44800*x^3 + 2520*x^4 - 98280*x^5 - 152334*x^6 - 100116*x^7 - 25515*x^8)/84","A",1
1147,1,38,34,0.006748,"\int (1-2 x) (2+3 x)^4 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x),x]","\frac{1}{210} \left(-24300 x^7-78435 x^6-89586 x^5-27720 x^4+27440 x^3+28560 x^2+10080 x\right)","-\frac{10}{189} (3 x+2)^7+\frac{37}{162} (3 x+2)^6-\frac{7}{135} (3 x+2)^5",1,"(10080*x + 28560*x^2 + 27440*x^3 - 27720*x^4 - 89586*x^5 - 78435*x^6 - 24300*x^7)/210","A",1
1148,1,33,34,0.006652,"\int (1-2 x) (2+3 x)^3 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x),x]","\frac{1}{60} \left(-2700 x^6-6804 x^5-4995 x^4+920 x^3+3000 x^2+1440 x\right)","-\frac{5}{81} (3 x+2)^6+\frac{37}{135} (3 x+2)^5-\frac{7}{108} (3 x+2)^4",1,"(1440*x + 3000*x^2 + 920*x^3 - 4995*x^4 - 6804*x^5 - 2700*x^6)/60","A",1
1149,1,28,28,0.0058979,"\int (1-2 x) (2+3 x)^2 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x),x]","\frac{1}{12} \left(-216 x^5-387 x^4-100 x^3+192 x^2+144 x\right)","-18 x^5-\frac{129 x^4}{4}-\frac{25 x^3}{3}+16 x^2+12 x",1,"(144*x + 192*x^2 - 100*x^3 - 387*x^4 - 216*x^5)/12","A",1
1150,1,20,25,0.0065834,"\int (1-2 x) (2+3 x) (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)*(3 + 5*x),x]","-\frac{1}{6} x \left(45 x^3+46 x^2-21 x-36\right)","-\frac{15 x^4}{2}-\frac{23 x^3}{3}+\frac{7 x^2}{2}+6 x",1,"-1/6*(x*(-36 - 21*x + 46*x^2 + 45*x^3))","A",1
1151,1,15,18,0.00512,"\int (1-2 x) (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)*(3 + 5*x),x]","-\frac{1}{6} x \left(20 x^2+3 x-18\right)","-\frac{10 x^3}{3}-\frac{x^2}{2}+3 x",1,"-1/6*(x*(-18 + 3*x + 20*x^2))","A",1
1152,1,21,23,0.0102986,"\int \frac{(1-2 x) (3+5 x)}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x))/(2 + 3*x),x]","-\frac{1}{9} x (15 x-17)-\frac{7}{27} \log (3 x+2)","-\frac{5 x^2}{3}+\frac{17 x}{9}-\frac{7}{27} \log (3 x+2)",1,"-1/9*(x*(-17 + 15*x)) - (7*Log[2 + 3*x])/27","A",1
1153,1,32,27,0.0169376,"\int \frac{(1-2 x) (3+5 x)}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x))/(2 + 3*x)^2,x]","\frac{-90 x^2-60 x+7}{27 (3 x+2)}+\frac{37}{27} \log (3 x+2)","-\frac{10 x}{9}+\frac{7}{27 (3 x+2)}+\frac{37}{27} \log (3 x+2)",1,"(7 - 60*x - 90*x^2)/(27*(2 + 3*x)) + (37*Log[2 + 3*x])/27","A",1
1154,1,27,33,0.0162458,"\int \frac{(1-2 x) (3+5 x)}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x))/(2 + 3*x)^3,x]","\frac{-74 x-47}{18 (3 x+2)^2}-\frac{10}{27} \log (3 x+2)","-\frac{37}{27 (3 x+2)}+\frac{7}{54 (3 x+2)^2}-\frac{10}{27} \log (3 x+2)",1,"(-47 - 74*x)/(18*(2 + 3*x)^2) - (10*Log[2 + 3*x])/27","A",1
1155,1,21,34,0.0101799,"\int \frac{(1-2 x) (3+5 x)}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x))/(2 + 3*x)^4,x]","\frac{540 x^2+387 x+32}{162 (3 x+2)^3}","\frac{10}{27 (3 x+2)}-\frac{37}{54 (3 x+2)^2}+\frac{7}{81 (3 x+2)^3}",1,"(32 + 387*x + 540*x^2)/(162*(2 + 3*x)^3)","A",1
1156,1,21,34,0.0086675,"\int \frac{(1-2 x) (3+5 x)}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x))/(2 + 3*x)^5,x]","\frac{540 x^2+276 x-35}{324 (3 x+2)^4}","\frac{5}{27 (3 x+2)^2}-\frac{37}{81 (3 x+2)^3}+\frac{7}{108 (3 x+2)^4}",1,"(-35 + 276*x + 540*x^2)/(324*(2 + 3*x)^4)","A",1
1157,1,21,34,0.0103965,"\int \frac{(1-2 x) (3+5 x)}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x))/(2 + 3*x)^6,x]","\frac{1800 x^2+735 x-226}{1620 (3 x+2)^5}","\frac{10}{81 (3 x+2)^3}-\frac{37}{108 (3 x+2)^4}+\frac{7}{135 (3 x+2)^5}",1,"(-226 + 735*x + 1800*x^2)/(1620*(2 + 3*x)^5)","A",1
1158,1,63,45,0.0105026,"\int (1-2 x) (2+3 x)^8 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x)^2,x]","\frac{1}{330} \left(-9021375 x^{12}-59377050 x^{11}-172536804 x^{10}-286803990 x^9-290875860 x^8-167508000 x^7-23728320 x^6+44814528 x^5+41965440 x^4+19036160 x^3+5068800 x^2+760320 x\right)","-\frac{25}{486} (3 x+2)^{12}+\frac{65}{297} (3 x+2)^{11}-\frac{4}{45} (3 x+2)^{10}+\frac{7}{729} (3 x+2)^9",1,"(760320*x + 5068800*x^2 + 19036160*x^3 + 41965440*x^4 + 44814528*x^5 - 23728320*x^6 - 167508000*x^7 - 290875860*x^8 - 286803990*x^9 - 172536804*x^10 - 59377050*x^11 - 9021375*x^12)/330","A",1
1159,1,58,45,0.0110298,"\int (1-2 x) (2+3 x)^7 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^7*(3 + 5*x)^2,x]","\frac{1}{264} \left(-2624400 x^{11}-15492708 x^{10}-39645936 x^9-56306745 x^8-45747504 x^7-16532208 x^6+5632704 x^5+10244256 x^4+5815040 x^3+1799424 x^2+304128 x\right)","-\frac{50}{891} (3 x+2)^{11}+\frac{13}{54} (3 x+2)^{10}-\frac{8}{81} (3 x+2)^9+\frac{7}{648} (3 x+2)^8",1,"(304128*x + 1799424*x^2 + 5815040*x^3 + 10244256*x^4 + 5632704*x^5 - 16532208*x^6 - 45747504*x^7 - 56306745*x^8 - 39645936*x^9 - 15492708*x^10 - 2624400*x^11)/264","A",1
1160,1,53,45,0.0095555,"\int (1-2 x) (2+3 x)^6 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)^2,x]","\frac{1}{3} \left(-10935 x^{10}-57105 x^9-126117 x^8-147663 x^7-87318 x^6-5292 x^5+31080 x^4+24112 x^3+8928 x^2+1728 x\right)","-\frac{5}{81} (3 x+2)^{10}+\frac{65}{243} (3 x+2)^9-\frac{1}{9} (3 x+2)^8+\frac{1}{81} (3 x+2)^7",1,"(1728*x + 8928*x^2 + 24112*x^3 + 31080*x^4 - 5292*x^5 - 87318*x^6 - 147663*x^7 - 126117*x^8 - 57105*x^9 - 10935*x^10)/3","A",1
1161,1,48,45,0.0088214,"\int (1-2 x) (2+3 x)^5 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)^2,x]","\frac{1}{168} \left(-226800 x^9-1029105 x^8-1906416 x^7-1733004 x^6-569520 x^5+351120 x^4+461440 x^3+213696 x^2+48384 x\right)","-\frac{50}{729} (3 x+2)^9+\frac{65}{216} (3 x+2)^8-\frac{8}{63} (3 x+2)^7+\frac{7}{486} (3 x+2)^6",1,"(48384*x + 213696*x^2 + 461440*x^3 + 351120*x^4 - 569520*x^5 - 1733004*x^6 - 1906416*x^7 - 1029105*x^8 - 226800*x^9)/168","A",1
1162,1,43,45,0.0071514,"\int (1-2 x) (2+3 x)^4 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^2,x]","\frac{1}{420} \left(-212625 x^8-818100 x^7-1217160 x^6-759276 x^5+39480 x^4+355040 x^3+221760 x^2+60480 x\right)","-\frac{25}{324} (3 x+2)^8+\frac{65}{189} (3 x+2)^7-\frac{4}{27} (3 x+2)^6+\frac{7}{405} (3 x+2)^5",1,"(60480*x + 221760*x^2 + 355040*x^3 + 39480*x^4 - 759276*x^5 - 1217160*x^6 - 818100*x^7 - 212625*x^8)/420","A",1
1163,1,38,44,0.006675,"\int (1-2 x) (2+3 x)^3 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^2,x]","\frac{1}{420} \left(-81000 x^7-255150 x^6-282744 x^5-80745 x^4+89320 x^3+88200 x^2+30240 x\right)","-\frac{1350 x^7}{7}-\frac{1215 x^6}{2}-\frac{3366 x^5}{5}-\frac{769 x^4}{4}+\frac{638 x^3}{3}+210 x^2+72 x",1,"(30240*x + 88200*x^2 + 89320*x^3 - 80745*x^4 - 282744*x^5 - 255150*x^6 - 81000*x^7)/420","A",1
1164,1,33,31,0.006098,"\int (1-2 x) (2+3 x)^2 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^2,x]","\frac{1}{3} \left(-225 x^6-549 x^5-384 x^4+85 x^3+234 x^2+108 x\right)","-75 x^6-183 x^5-128 x^4+\frac{85 x^3}{3}+78 x^2+36 x",1,"(108*x + 234*x^2 + 85*x^3 - 384*x^4 - 549*x^5 - 225*x^6)/3","A",1
1165,1,25,30,0.005191,"\int (1-2 x) (2+3 x) (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^2,x]","-\frac{1}{12} x \left(360 x^4+615 x^3+136 x^2-306 x-216\right)","-30 x^5-\frac{205 x^4}{4}-\frac{34 x^3}{3}+\frac{51 x^2}{2}+18 x",1,"-1/12*(x*(-216 - 306*x + 136*x^2 + 615*x^3 + 360*x^4))","A",1
1166,1,20,23,0.005313,"\int (1-2 x) (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)*(3 + 5*x)^2,x]","-\frac{1}{6} x \left(75 x^3+70 x^2-36 x-54\right)","-\frac{25 x^4}{2}-\frac{35 x^3}{3}+6 x^2+9 x",1,"-1/6*(x*(-54 - 36*x + 70*x^2 + 75*x^3))","A",1
1167,1,26,30,0.0156037,"\int \frac{(1-2 x) (3+5 x)^2}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x),x]","\frac{7}{81} \log (3 x+2)-\frac{1}{54} x \left(300 x^2+15 x-236\right)","-\frac{50 x^3}{9}-\frac{5 x^2}{18}+\frac{118 x}{27}+\frac{7}{81} \log (3 x+2)",1,"-1/54*(x*(-236 + 15*x + 300*x^2)) + (7*Log[2 + 3*x])/81","A",1
1168,1,37,34,0.0171524,"\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^2,x]","\frac{-225 x^3+135 x^2+480 x+191}{27 (3 x+2)}-\frac{8}{9} \log (3 x+2)","-\frac{25 x^2}{9}+\frac{95 x}{27}-\frac{7}{81 (3 x+2)}-\frac{8}{9} \log (3 x+2)",1,"(191 + 480*x + 135*x^2 - 225*x^3)/(27*(2 + 3*x)) - (8*Log[2 + 3*x])/9","A",1
1169,1,37,38,0.0320634,"\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^3,x]","\frac{-900 x^3-1800 x^2-1056 x-173}{54 (3 x+2)^2}+\frac{65}{27} \log (3 x+2)","-\frac{50 x}{27}+\frac{8}{9 (3 x+2)}-\frac{7}{162 (3 x+2)^2}+\frac{65}{27} \log (3 x+2)",1,"(-173 - 1056*x - 1800*x^2 - 900*x^3)/(54*(2 + 3*x)^2) + (65*Log[2 + 3*x])/27","A",1
1170,1,32,44,0.0209802,"\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^4,x]","\frac{-5265 x^2-6696 x-2131}{243 (3 x+2)^3}-\frac{50}{81} \log (3 x+2)","-\frac{65}{27 (3 x+2)}+\frac{4}{9 (3 x+2)^2}-\frac{7}{243 (3 x+2)^3}-\frac{50}{81} \log (3 x+2)",1,"(-2131 - 6696*x - 5265*x^2)/(243*(2 + 3*x)^3) - (50*Log[2 + 3*x])/81","A",1
1171,1,26,37,0.0126822,"\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^5,x]","\frac{600 x^3+810 x^2+312 x+25}{36 (3 x+2)^4}","\frac{3 (5 x+3)^3}{4 (3 x+2)^3}+\frac{7 (5 x+3)^3}{12 (3 x+2)^4}",1,"(25 + 312*x + 810*x^2 + 600*x^3)/(36*(2 + 3*x)^4)","A",1
1172,1,26,45,0.0135418,"\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^6,x]","\frac{3375 x^3+3825 x^2+870 x-127}{405 (3 x+2)^5}","\frac{25}{81 (3 x+2)^2}-\frac{65}{81 (3 x+2)^3}+\frac{2}{9 (3 x+2)^4}-\frac{7}{405 (3 x+2)^5}",1,"(-127 + 870*x + 3825*x^2 + 3375*x^3)/(405*(2 + 3*x)^5)","A",1
1173,1,26,45,0.0136638,"\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^7,x]","\frac{27000 x^3+27675 x^2+3492 x-2042}{4860 (3 x+2)^6}","\frac{50}{243 (3 x+2)^3}-\frac{65}{108 (3 x+2)^4}+\frac{8}{45 (3 x+2)^5}-\frac{7}{486 (3 x+2)^6}",1,"(-2042 + 3492*x + 27675*x^2 + 27000*x^3)/(4860*(2 + 3*x)^6)","A",1
1174,1,26,45,0.0133827,"\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^8} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^8,x]","\frac{225 x^3+216 x^2+12 x-22}{54 (3 x+2)^7}","\frac{25}{162 (3 x+2)^4}-\frac{13}{27 (3 x+2)^5}+\frac{4}{27 (3 x+2)^6}-\frac{1}{81 (3 x+2)^7}",1,"(-22 + 12*x + 216*x^2 + 225*x^3)/(54*(2 + 3*x)^7)","A",1
1175,1,68,56,0.0111798,"\int (1-2 x) (2+3 x)^8 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x)^3,x]","\frac{-360855000 x^{13}-2593144125 x^{12}-8340707700 x^{11}-15671312514 x^{10}-18661010940 x^9-13914117360 x^8-5236545600 x^7+1001366080 x^6+2619979648 x^5+1709776640 x^4+641372160 x^3+148262400 x^2+19768320 x}{2860}","-\frac{250 (3 x+2)^{13}}{3159}+\frac{1025 (3 x+2)^{12}}{2916}-\frac{185}{891} (3 x+2)^{11}+\frac{107 (3 x+2)^{10}}{2430}-\frac{7 (3 x+2)^9}{2187}",1,"(19768320*x + 148262400*x^2 + 641372160*x^3 + 1709776640*x^4 + 2619979648*x^5 + 1001366080*x^6 - 5236545600*x^7 - 13914117360*x^8 - 18661010940*x^9 - 15671312514*x^10 - 8340707700*x^11 - 2593144125*x^12 - 360855000*x^13)/2860","A",1
1176,1,63,56,0.0105059,"\int (1-2 x) (2+3 x)^7 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^7*(3 + 5*x)^3,x]","\frac{1}{88} \left(-4009500 x^{12}-26098200 x^{11}-74961612 x^{10}-123063336 x^9-123021855 x^8-69364944 x^7-8709008 x^6+19291712 x^5+17513056 x^4+7814400 x^3+2052864 x^2+304128 x\right)","-\frac{125 (3 x+2)^{12}}{1458}+\frac{1025 (3 x+2)^{11}}{2673}-\frac{37}{162} (3 x+2)^{10}+\frac{107 (3 x+2)^9}{2187}-\frac{7 (3 x+2)^8}{1944}",1,"(304128*x + 2052864*x^2 + 7814400*x^3 + 17513056*x^4 + 19291712*x^5 - 8709008*x^6 - 69364944*x^7 - 123021855*x^8 - 123063336*x^9 - 74961612*x^10 - 26098200*x^11 - 4009500*x^12)/88","A",1
1177,1,58,56,0.0097802,"\int (1-2 x) (2+3 x)^6 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)^3,x]","\frac{1}{88} \left(-1458000 x^{11}-8500140 x^{10}-21467160 x^9-30048381 x^8-23971464 x^7-8330784 x^6+3181024 x^5+5387360 x^4+2994816 x^3+912384 x^2+152064 x\right)","-\frac{250 (3 x+2)^{11}}{2673}+\frac{205}{486} (3 x+2)^{10}-\frac{185}{729} (3 x+2)^9+\frac{107 (3 x+2)^8}{1944}-\frac{1}{243} (3 x+2)^7",1,"(152064*x + 912384*x^2 + 2994816*x^3 + 5387360*x^4 + 3181024*x^5 - 8330784*x^6 - 23971464*x^7 - 30048381*x^8 - 21467160*x^9 - 8500140*x^10 - 1458000*x^11)/88","A",1
1178,1,53,56,0.0092419,"\int (1-2 x) (2+3 x)^5 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)^3,x]","\frac{1}{56} \left(-340200 x^{10}-1751400 x^9-3809295 x^8-4382136 x^7-2524004 x^6-101360 x^5+927920 x^4+698880 x^3+254016 x^2+48384 x\right)","-\frac{25}{243} (3 x+2)^{10}+\frac{1025 (3 x+2)^9}{2187}-\frac{185}{648} (3 x+2)^8+\frac{107 (3 x+2)^7}{1701}-\frac{7 (3 x+2)^6}{1458}",1,"(48384*x + 254016*x^2 + 698880*x^3 + 927920*x^4 - 101360*x^5 - 2524004*x^6 - 4382136*x^7 - 3809295*x^8 - 1751400*x^9 - 340200*x^10)/56","A",1
1179,1,48,56,0.0085037,"\int (1-2 x) (2+3 x)^4 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^3,x]","\frac{1}{280} \left(-630000 x^9-2811375 x^8-5113800 x^7-4543420 x^6-1413272 x^5+966560 x^4+1202880 x^3+544320 x^2+120960 x\right)","-\frac{250 (3 x+2)^9}{2187}+\frac{1025 (3 x+2)^8}{1944}-\frac{185}{567} (3 x+2)^7+\frac{107 (3 x+2)^6}{1458}-\frac{7 (3 x+2)^5}{1215}",1,"(120960*x + 544320*x^2 + 1202880*x^3 + 966560*x^4 - 1413272*x^5 - 4543420*x^6 - 5113800*x^7 - 2811375*x^8 - 630000*x^9)/280","A",1
1180,1,43,49,0.006998,"\int (1-2 x) (2+3 x)^3 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^3,x]","\frac{1}{140} \left(-118125 x^8-445500 x^7-647850 x^6-390404 x^5+30905 x^4+187320 x^3+113400 x^2+30240 x\right)","-\frac{3375 x^8}{4}-\frac{22275 x^7}{7}-\frac{9255 x^6}{2}-\frac{13943 x^5}{5}+\frac{883 x^4}{4}+1338 x^3+810 x^2+216 x",1,"(30240*x + 113400*x^2 + 187320*x^3 + 30905*x^4 - 390404*x^5 - 647850*x^6 - 445500*x^7 - 118125*x^8)/140","A",1
1181,1,38,40,0.0063683,"\int (1-2 x) (2+3 x)^2 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^3,x]","\frac{1}{28} \left(-9000 x^7-27650 x^6-29708 x^5-7777 x^4+9660 x^3+9072 x^2+3024 x\right)","-\frac{2250 x^7}{7}-\frac{1975 x^6}{2}-1061 x^5-\frac{1111 x^4}{4}+345 x^3+324 x^2+108 x",1,"(3024*x + 9072*x^2 + 9660*x^3 - 7777*x^4 - 29708*x^5 - 27650*x^6 - 9000*x^7)/28","A",1
1182,1,33,34,0.0066395,"\int (1-2 x) (2+3 x) (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^3,x]","\frac{1}{4} \left(-500 x^6-1180 x^5-785 x^4+204 x^3+486 x^2+216 x\right)","-\frac{1}{125} (5 x+3)^6+\frac{31}{625} (5 x+3)^5+\frac{11}{500} (5 x+3)^4",1,"(216*x + 486*x^2 + 204*x^3 - 785*x^4 - 1180*x^5 - 500*x^6)/4","A",1
1183,1,25,23,0.0060791,"\int (1-2 x) (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)*(3 + 5*x)^3,x]","-\frac{1}{4} x \left(200 x^4+325 x^3+60 x^2-162 x-108\right)","\frac{11}{100} (5 x+3)^4-\frac{2}{125} (5 x+3)^5",1,"-1/4*(x*(-108 - 162*x + 60*x^2 + 325*x^3 + 200*x^4))","A",1
1184,1,31,37,0.0185935,"\int \frac{(1-2 x) (3+5 x)^3}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x),x]","-\frac{1}{162} x \left(3375 x^3+2850 x^2-1635 x-2194\right)-\frac{7}{243} \log (3 x+2)","-\frac{125 x^4}{6}-\frac{475 x^3}{27}+\frac{545 x^2}{54}+\frac{1097 x}{81}-\frac{7}{243} \log (3 x+2)",1,"-1/162*(x*(-2194 - 1635*x + 2850*x^2 + 3375*x^3)) - (7*Log[2 + 3*x])/243","A",1
1185,1,42,41,0.0203736,"\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^2,x]","\frac{-40500 x^4-24975 x^3+28080 x^2+22740 x+3322}{1458 (3 x+2)}+\frac{107}{243} \log (3 x+2)","-\frac{250 x^3}{27}+\frac{25 x^2}{54}+\frac{55 x}{9}+\frac{7}{243 (3 x+2)}+\frac{107}{243} \log (3 x+2)",1,"(3322 + 22740*x + 28080*x^2 - 24975*x^3 - 40500*x^4)/(1458*(2 + 3*x)) + (107*Log[2 + 3*x])/243","A",1
1186,1,42,45,0.0207447,"\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^3,x]","\frac{-2250 x^4+150 x^3+6300 x^2+5462 x+1331}{54 (3 x+2)^2}-\frac{185}{81} \log (3 x+2)","-\frac{125 x^2}{27}+\frac{175 x}{27}-\frac{107}{243 (3 x+2)}+\frac{7}{486 (3 x+2)^2}-\frac{185}{81} \log (3 x+2)",1,"(1331 + 5462*x + 6300*x^2 + 150*x^3 - 2250*x^4)/(54*(2 + 3*x)^2) - (185*Log[2 + 3*x])/81","A",1
1187,1,42,49,0.0296695,"\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^4,x]","\frac{-121500 x^4-324000 x^3-294030 x^2-105003 x-11308}{1458 (3 x+2)^3}+\frac{1025}{243} \log (3 x+2)","-\frac{250 x}{81}+\frac{185}{81 (3 x+2)}-\frac{107}{486 (3 x+2)^2}+\frac{7}{729 (3 x+2)^3}+\frac{1025}{243} \log (3 x+2)",1,"(-11308 - 105003*x - 294030*x^2 - 324000*x^3 - 121500*x^4)/(1458*(2 + 3*x)^3) + (1025*Log[2 + 3*x])/243","A",1
1188,1,37,55,0.0218027,"\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^5,x]","\frac{-332100 x^3-634230 x^2-404124 x-85915}{2916 (3 x+2)^4}-\frac{250}{243} \log (3 x+2)","-\frac{1025}{243 (3 x+2)}+\frac{185}{162 (3 x+2)^2}-\frac{107}{729 (3 x+2)^3}+\frac{7}{972 (3 x+2)^4}-\frac{250}{243} \log (3 x+2)",1,"(-85915 - 404124*x - 634230*x^2 - 332100*x^3)/(2916*(2 + 3*x)^4) - (250*Log[2 + 3*x])/243","A",1
1189,1,31,37,0.0138789,"\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^6,x]","\frac{405000 x^4+803250 x^3+559800 x^2+153795 x+11758}{4860 (3 x+2)^5}","\frac{5 (5 x+3)^4}{12 (3 x+2)^4}+\frac{7 (5 x+3)^4}{15 (3 x+2)^5}",1,"(11758 + 153795*x + 559800*x^2 + 803250*x^3 + 405000*x^4)/(4860*(2 + 3*x)^5)","A",1
1190,1,31,55,0.0138974,"\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^7,x]","\frac{607500 x^4+1066500 x^3+587925 x^2+78048 x-13198}{14580 (3 x+2)^6}","\frac{29 (5 x+3)^4}{36 (3 x+2)^4}+\frac{29 (5 x+3)^4}{45 (3 x+2)^5}+\frac{7 (5 x+3)^4}{18 (3 x+2)^6}",1,"(-13198 + 78048*x + 587925*x^2 + 1066500*x^3 + 607500*x^4)/(14580*(2 + 3*x)^6)","A",1
1191,1,31,56,0.0135457,"\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^8} \, dx","IntegrateAlgebraic[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^8,x]","\frac{81000 x^4+132975 x^3+61938 x^2+642 x-3688}{2916 (3 x+2)^7}","\frac{250}{729 (3 x+2)^3}-\frac{1025}{972 (3 x+2)^4}+\frac{37}{81 (3 x+2)^5}-\frac{107}{1458 (3 x+2)^6}+\frac{1}{243 (3 x+2)^7}",1,"(-3688 + 642*x + 61938*x^2 + 132975*x^3 + 81000*x^4)/(2916*(2 + 3*x)^7)","A",1
1192,1,55,18,0.0121112,"\int (5-2 x)^6 (2+3 x)^3 (-16+33 x) \, dx","IntegrateAlgebraic[(5 - 2*x)^6*(2 + 3*x)^3*(-16 + 33*x),x]","\frac{1}{2} x \left(10368 x^{10}-153792 x^9+904608 x^8-2512752 x^7+2470808 x^6+2994460 x^5-7632450 x^4-98125 x^3+7975000 x^2-75000 x-4000000\right)","-\frac{1}{2} (5-2 x)^7 (3 x+2)^4",1,"(x*(-4000000 - 75000*x + 7975000*x^2 - 98125*x^3 - 7632450*x^4 + 2994460*x^5 + 2470808*x^6 - 2512752*x^7 + 904608*x^8 - 153792*x^9 + 10368*x^10))/2","B",1
1193,1,46,58,0.0253217,"\int \frac{(1-2 x) (2+3 x)^6}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^6)/(3 + 5*x),x]","\frac{11 \log (5 x+3)}{390625}-\frac{x \left(91125000 x^6+308306250 x^5+373369500 x^4+133410375 x^3-106728300 x^2-124444530 x-46666564\right)}{2187500}","-\frac{1458 x^7}{35}-\frac{7047 x^6}{50}-\frac{106677 x^5}{625}-\frac{152469 x^4}{2500}+\frac{152469 x^3}{3125}+\frac{1777779 x^2}{31250}+\frac{1666663 x}{78125}+\frac{11 \log (5 x+3)}{390625}",1,"-1/2187500*(x*(-46666564 - 124444530*x - 106728300*x^2 + 133410375*x^3 + 373369500*x^4 + 308306250*x^5 + 91125000*x^6)) + (11*Log[3 + 5*x])/390625","A",1
1194,1,41,51,0.021587,"\int \frac{(1-2 x) (2+3 x)^5}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^5)/(3 + 5*x),x]","\frac{11 \log (5 x+3)}{78125}-\frac{x \left(1012500 x^5+2713500 x^4+2183625 x^3-246900 x^2-1277790 x-666652\right)}{62500}","-\frac{81 x^6}{5}-\frac{5427 x^5}{125}-\frac{17469 x^4}{500}+\frac{2469 x^3}{625}+\frac{127779 x^2}{6250}+\frac{166663 x}{15625}+\frac{11 \log (5 x+3)}{78125}",1,"-1/62500*(x*(-666652 - 1277790*x - 246900*x^2 + 2183625*x^3 + 2713500*x^4 + 1012500*x^5)) + (11*Log[3 + 5*x])/78125","A",1
1195,1,36,44,0.0208446,"\int \frac{(1-2 x) (2+3 x)^4}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^4)/(3 + 5*x),x]","\frac{11 \log (5 x+3)}{15625}-\frac{x \left(81000 x^4+158625 x^3+53100 x^2-77790 x-66652\right)}{12500}","-\frac{162 x^5}{25}-\frac{1269 x^4}{100}-\frac{531 x^3}{125}+\frac{7779 x^2}{1250}+\frac{16663 x}{3125}+\frac{11 \log (5 x+3)}{15625}",1,"-1/12500*(x*(-66652 - 77790*x + 53100*x^2 + 158625*x^3 + 81000*x^4)) + (11*Log[3 + 5*x])/15625","A",1
1196,1,35,37,0.0186463,"\int \frac{(1-2 x) (2+3 x)^3}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^3)/(3 + 5*x),x]","\frac{-3375 x^4-4050 x^3+1395 x^2+3326 x+1056}{1250}+\frac{11 \log (5 x+3)}{3125}","-\frac{27 x^4}{10}-\frac{81 x^3}{25}+\frac{279 x^2}{250}+\frac{1663 x}{625}+\frac{11 \log (5 x+3)}{3125}",1,"(1056 + 3326*x + 1395*x^2 - 4050*x^3 - 3375*x^4)/1250 + (11*Log[3 + 5*x])/3125","A",1
1197,1,26,30,0.0149557,"\int \frac{(1-2 x) (2+3 x)^2}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^2)/(3 + 5*x),x]","\frac{11}{625} \log (5 x+3)-\frac{1}{250} x \left(300 x^2+105 x-326\right)","-\frac{6 x^3}{5}-\frac{21 x^2}{50}+\frac{163 x}{125}+\frac{11}{625} \log (5 x+3)",1,"-1/250*(x*(-326 + 105*x + 300*x^2)) + (11*Log[3 + 5*x])/625","A",1
1198,1,21,23,0.0099613,"\int \frac{(1-2 x) (2+3 x)}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x))/(3 + 5*x),x]","\frac{11}{125} \log (5 x+3)-\frac{1}{25} x (15 x-13)","-\frac{3 x^2}{5}+\frac{13 x}{25}+\frac{11}{125} \log (5 x+3)",1,"-1/25*(x*(-13 + 15*x)) + (11*Log[3 + 5*x])/125","A",1
1199,1,16,16,0.0063019,"\int \frac{1-2 x}{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)/(3 + 5*x),x]","\frac{11}{25} \log (5 x+3)-\frac{2 x}{5}","\frac{11}{25} \log (5 x+3)-\frac{2 x}{5}",1,"(-2*x)/5 + (11*Log[3 + 5*x])/25","A",1
1200,1,21,21,0.0092385,"\int \frac{1-2 x}{(2+3 x) (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)*(3 + 5*x)),x]","\frac{11}{5} \log (5 x+3)-\frac{7}{3} \log (3 x+2)","\frac{11}{5} \log (5 x+3)-\frac{7}{3} \log (3 x+2)",1,"(-7*Log[2 + 3*x])/3 + (11*Log[3 + 5*x])/5","A",1
1201,1,28,28,0.0237441,"\int \frac{1-2 x}{(2+3 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)^2*(3 + 5*x)),x]","\frac{7}{3 (3 x+2)}-11 \log (3 x+2)+11 \log (5 x+3)","\frac{7}{3 (3 x+2)}-11 \log (3 x+2)+11 \log (5 x+3)",1,"7/(3*(2 + 3*x)) - 11*Log[2 + 3*x] + 11*Log[3 + 5*x]","A",1
1202,1,33,37,0.0317556,"\int \frac{1-2 x}{(2+3 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)^3*(3 + 5*x)),x]","\frac{198 x+139}{6 (3 x+2)^2}-55 \log (3 x+2)+55 \log (5 x+3)","\frac{11}{3 x+2}+\frac{7}{6 (3 x+2)^2}-55 \log (3 x+2)+55 \log (5 x+3)",1,"(139 + 198*x)/(6*(2 + 3*x)^2) - 55*Log[2 + 3*x] + 55*Log[3 + 5*x]","A",1
1203,1,38,48,0.038525,"\int \frac{1-2 x}{(2+3 x)^4 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)^4*(3 + 5*x)),x]","\frac{8910 x^2+12177 x+4172}{18 (3 x+2)^3}-275 \log (3 x+2)+275 \log (5 x+3)","\frac{55}{3 x+2}+\frac{11}{2 (3 x+2)^2}+\frac{7}{9 (3 x+2)^3}-275 \log (3 x+2)+275 \log (5 x+3)",1,"(4172 + 12177*x + 8910*x^2)/(18*(2 + 3*x)^3) - 275*Log[2 + 3*x] + 275*Log[3 + 5*x]","A",1
1204,1,43,59,0.042021,"\int \frac{1-2 x}{(2+3 x)^5 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)^5*(3 + 5*x)),x]","\frac{89100 x^3+181170 x^2+122892 x+27815}{12 (3 x+2)^4}-1375 \log (3 x+2)+1375 \log (5 x+3)","\frac{275}{3 x+2}+\frac{55}{2 (3 x+2)^2}+\frac{11}{3 (3 x+2)^3}+\frac{7}{12 (3 x+2)^4}-1375 \log (3 x+2)+1375 \log (5 x+3)",1,"(27815 + 122892*x + 181170*x^2 + 89100*x^3)/(12*(2 + 3*x)^4) - 1375*Log[2 + 3*x] + 1375*Log[3 + 5*x]","A",1
1205,1,48,70,0.0499032,"\int \frac{1-2 x}{(2+3 x)^6 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)^6*(3 + 5*x)),x]","\frac{2227500 x^4+6014250 x^3+6091800 x^2+2743565 x+463586}{20 (3 x+2)^5}-6875 \log (3 x+2)+6875 \log (5 x+3)","\frac{1375}{3 x+2}+\frac{275}{2 (3 x+2)^2}+\frac{55}{3 (3 x+2)^3}+\frac{11}{4 (3 x+2)^4}+\frac{7}{15 (3 x+2)^5}-6875 \log (3 x+2)+6875 \log (5 x+3)",1,"(463586 + 2743565*x + 6091800*x^2 + 6014250*x^3 + 2227500*x^4)/(20*(2 + 3*x)^5) - 6875*Log[2 + 3*x] + 6875*Log[3 + 5*x]","A",1
1206,1,53,81,0.0717706,"\int \frac{1-2 x}{(2+3 x)^7 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)^7*(3 + 5*x)),x]","\frac{300712500 x^5+1012398750 x^4+1363675500 x^3+918643275 x^2+309504888 x+41722762}{180 (3 x+2)^6}-34375 \log (3 x+2)+34375 \log (5 x+3)","\frac{6875}{3 x+2}+\frac{1375}{2 (3 x+2)^2}+\frac{275}{3 (3 x+2)^3}+\frac{55}{4 (3 x+2)^4}+\frac{11}{5 (3 x+2)^5}+\frac{7}{18 (3 x+2)^6}-34375 \log (3 x+2)+34375 \log (5 x+3)",1,"(41722762 + 309504888*x + 918643275*x^2 + 1363675500*x^3 + 1012398750*x^4 + 300712500*x^5)/(180*(2 + 3*x)^6) - 34375*Log[2 + 3*x] + 34375*Log[3 + 5*x]","A",1
1207,1,62,69,0.0490863,"\int \frac{(1-2 x) (2+3 x)^7}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^7)/(3 + 5*x)^2,x]","\frac{-6834375000 x^8-27755156250 x^7-43662543750 x^6-28920898125 x^5+1358398125 x^4+14907422250 x^3+9916639950 x^2+2877266160 x+326378932}{54687500 (5 x+3)}+\frac{229 \log (5 x+3)}{1953125}","-\frac{4374 x^7}{175}-\frac{21627 x^6}{250}-\frac{336798 x^5}{3125}-\frac{513783 x^4}{12500}+\frac{92592 x^3}{3125}+\frac{5740767 x^2}{156250}+\frac{5555478 x}{390625}-\frac{11}{1953125 (5 x+3)}+\frac{229 \log (5 x+3)}{1953125}",1,"(326378932 + 2877266160*x + 9916639950*x^2 + 14907422250*x^3 + 1358398125*x^4 - 28920898125*x^5 - 43662543750*x^6 - 27755156250*x^7 - 6834375000*x^8)/(54687500*(3 + 5*x)) + (229*Log[3 + 5*x])/1953125","A",1
1208,1,57,62,0.0290612,"\int \frac{(1-2 x) (2+3 x)^6}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^6)/(3 + 5*x)^2,x]","\frac{-94921875 x^7-318937500 x^6-377409375 x^5-114778125 x^4+137733750 x^3+145829250 x^2+53832870 x+7302662}{1953125 (5 x+3)}+\frac{196 \log (5 x+3)}{390625}","-\frac{243 x^6}{25}-\frac{16767 x^5}{625}-\frac{14094 x^4}{625}+\frac{5553 x^3}{3125}+\frac{40743 x^2}{3125}+\frac{555489 x}{78125}-\frac{11}{390625 (5 x+3)}+\frac{196 \log (5 x+3)}{390625}",1,"(7302662 + 53832870*x + 145829250*x^2 + 137733750*x^3 - 114778125*x^4 - 377409375*x^5 - 318937500*x^6 - 94921875*x^7)/(1953125*(3 + 5*x)) + (196*Log[3 + 5*x])/390625","A",1
1209,1,52,55,0.030025,"\int \frac{(1-2 x) (2+3 x)^5}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^5)/(3 + 5*x)^2,x]","\frac{-6075000 x^6-16048125 x^5-12076875 x^4+3242250 x^3+9163950 x^2+3330000 x-44}{312500 (5 x+3)}+\frac{163 \log (5 x+3)}{78125}","-\frac{486 x^5}{125}-\frac{3969 x^4}{500}-\frac{1854 x^3}{625}+\frac{24093 x^2}{6250}+\frac{444 x}{125}-\frac{11}{78125 (5 x+3)}+\frac{163 \log (5 x+3)}{78125}",1,"(-44 + 3330000*x + 9163950*x^2 + 3242250*x^3 - 12076875*x^4 - 16048125*x^5 - 6075000*x^6)/(312500*(3 + 5*x)) + (163*Log[3 + 5*x])/78125","A",1
1210,1,47,48,0.0260973,"\int \frac{(1-2 x) (2+3 x)^4}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^4)/(3 + 5*x)^2,x]","\frac{-50625 x^5-95625 x^4-20250 x^3+66450 x^2+51795 x+11233}{6250 (5 x+3)}+\frac{26 \log (5 x+3)}{3125}","-\frac{81 x^4}{50}-\frac{261 x^3}{125}+\frac{378 x^2}{625}+\frac{5511 x}{3125}-\frac{11}{15625 (5 x+3)}+\frac{26 \log (5 x+3)}{3125}",1,"(11233 + 51795*x + 66450*x^2 - 20250*x^3 - 95625*x^4 - 50625*x^5)/(6250*(3 + 5*x)) + (26*Log[3 + 5*x])/3125","A",1
1211,1,42,41,0.0223933,"\int \frac{(1-2 x) (2+3 x)^3}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^3)/(3 + 5*x)^2,x]","\frac{-67500 x^4-70875 x^3+60075 x^2+92680 x+27354}{18750 (5 x+3)}+\frac{97 \log (5 x+3)}{3125}","-\frac{18 x^3}{25}-\frac{81 x^2}{250}+\frac{522 x}{625}-\frac{11}{3125 (5 x+3)}+\frac{97 \log (5 x+3)}{3125}",1,"(27354 + 92680*x + 60075*x^2 - 70875*x^3 - 67500*x^4)/(18750*(3 + 5*x)) + (97*Log[3 + 5*x])/3125","A",1
1212,1,37,34,0.0218693,"\int \frac{(1-2 x) (2+3 x)^2}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^2)/(3 + 5*x)^2,x]","\frac{-1125 x^3+150 x^2+1545 x+619}{625 (5 x+3)}+\frac{64}{625} \log (5 x+3)","-\frac{9 x^2}{25}+\frac{33 x}{125}-\frac{11}{625 (5 x+3)}+\frac{64}{625} \log (5 x+3)",1,"(619 + 1545*x + 150*x^2 - 1125*x^3)/(625*(3 + 5*x)) + (64*Log[3 + 5*x])/625","A",1
1213,1,32,27,0.017105,"\int \frac{(1-2 x) (2+3 x)}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x))/(3 + 5*x)^2,x]","\frac{-150 x^2-90 x-11}{125 (5 x+3)}+\frac{31}{125} \log (5 x+3)","-\frac{6 x}{25}-\frac{11}{125 (5 x+3)}+\frac{31}{125} \log (5 x+3)",1,"(-11 - 90*x - 150*x^2)/(125*(3 + 5*x)) + (31*Log[3 + 5*x])/125","A",1
1214,1,22,22,0.0092783,"\int \frac{1-2 x}{(3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)/(3 + 5*x)^2,x]","-\frac{11}{25 (5 x+3)}-\frac{2}{25} \log (5 x+3)","-\frac{11}{25 (5 x+3)}-\frac{2}{25} \log (5 x+3)",1,"-11/(25*(3 + 5*x)) - (2*Log[3 + 5*x])/25","A",1
1215,1,28,28,0.0227516,"\int \frac{1-2 x}{(2+3 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)*(3 + 5*x)^2),x]","-\frac{11}{5 (5 x+3)}+7 \log (3 x+2)-7 \log (5 x+3)","-\frac{11}{5 (5 x+3)}+7 \log (3 x+2)-7 \log (5 x+3)",1,"-11/(5*(3 + 5*x)) + 7*Log[2 + 3*x] - 7*Log[3 + 5*x]","A",1
1216,1,35,35,0.0276065,"\int \frac{1-2 x}{(2+3 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{-68 x-43}{15 x^2+19 x+6}+68 \log (3 x+2)-68 \log (5 x+3)","-\frac{7}{3 x+2}-\frac{11}{5 x+3}+68 \log (3 x+2)-68 \log (5 x+3)",1,"(-43 - 68*x)/(6 + 19*x + 15*x^2) + 68*Log[2 + 3*x] - 68*Log[3 + 5*x]","A",1
1217,1,45,46,0.0326116,"\int \frac{1-2 x}{(2+3 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)^3*(3 + 5*x)^2),x]","\frac{-3030 x^2-3939 x-1277}{2 (3 x+2)^2 (5 x+3)}+505 \log (3 x+2)-505 \log (5 x+3)","-\frac{68}{3 x+2}-\frac{55}{5 x+3}-\frac{7}{2 (3 x+2)^2}+505 \log (3 x+2)-505 \log (5 x+3)",1,"(-1277 - 3939*x - 3030*x^2)/(2*(2 + 3*x)^2*(3 + 5*x)) + 505*Log[2 + 3*x] - 505*Log[3 + 5*x]","A",1
1218,1,50,55,0.0350775,"\int \frac{1-2 x}{(2+3 x)^4 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)^4*(3 + 5*x)^2),x]","\frac{-90450 x^3-177885 x^2-116513 x-25413}{3 (3 x+2)^3 (5 x+3)}+3350 \log (3 x+2)-3350 \log (5 x+3)","-\frac{505}{3 x+2}-\frac{275}{5 x+3}-\frac{34}{(3 x+2)^2}-\frac{7}{3 (3 x+2)^3}+3350 \log (3 x+2)-3350 \log (5 x+3)",1,"(-25413 - 116513*x - 177885*x^2 - 90450*x^3)/(3*(2 + 3*x)^3*(3 + 5*x)) + 3350*Log[2 + 3*x] - 3350*Log[3 + 5*x]","A",1
1219,1,55,68,0.0489044,"\int \frac{1-2 x}{(2+3 x)^5 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)^5*(3 + 5*x)^2),x]","\frac{-6763500 x^4-17810550 x^3-17580090 x^2-7708553 x-1266855}{12 (3 x+2)^4 (5 x+3)}+20875 \log (3 x+2)-20875 \log (5 x+3)","-\frac{3350}{3 x+2}-\frac{1375}{5 x+3}-\frac{505}{2 (3 x+2)^2}-\frac{68}{3 (3 x+2)^3}-\frac{7}{4 (3 x+2)^4}+20875 \log (3 x+2)-20875 \log (5 x+3)",1,"(-1266855 - 7708553*x - 17580090*x^2 - 17810550*x^3 - 6763500*x^4)/(12*(2 + 3*x)^4*(3 + 5*x)) + 20875*Log[2 + 3*x] - 20875*Log[3 + 5*x]","A",1
1220,1,60,75,0.0560507,"\int \frac{1-2 x}{(2+3 x)^6 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)^6*(3 + 5*x)^2),x]","\frac{-151875000 x^5-501187500 x^4-661387500 x^3-436271250 x^2-143844850 x-18964893}{15 (3 x+2)^5 (5 x+3)}+125000 \log (3 x+2)-125000 \log (5 x+3)","-\frac{20875}{3 x+2}-\frac{6875}{5 x+3}-\frac{1675}{(3 x+2)^2}-\frac{505}{3 (3 x+2)^3}-\frac{17}{(3 x+2)^4}-\frac{7}{5 (3 x+2)^5}+125000 \log (3 x+2)-125000 \log (5 x+3)",1,"(-18964893 - 143844850*x - 436271250*x^2 - 661387500*x^3 - 501187500*x^4 - 151875000*x^5)/(15*(2 + 3*x)^5*(3 + 5*x)) + 125000*Log[2 + 3*x] - 125000*Log[3 + 5*x]","A",1
1221,1,65,90,0.066335,"\int \frac{1-2 x}{(2+3 x)^7 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)^7*(3 + 5*x)^2),x]","\frac{-3538687500 x^6-14036793750 x^5-23195441250 x^4-20438672625 x^3-10128331755 x^2-2676272018 x-294588002}{20 (3 x+2)^6 (5 x+3)}+728125 \log (3 x+2)-728125 \log (5 x+3)","-\frac{125000}{3 x+2}-\frac{34375}{5 x+3}-\frac{20875}{2 (3 x+2)^2}-\frac{3350}{3 (3 x+2)^3}-\frac{505}{4 (3 x+2)^4}-\frac{68}{5 (3 x+2)^5}-\frac{7}{6 (3 x+2)^6}+728125 \log (3 x+2)-728125 \log (5 x+3)",1,"(-294588002 - 2676272018*x - 10128331755*x^2 - 20438672625*x^3 - 23195441250*x^4 - 14036793750*x^5 - 3538687500*x^6)/(20*(2 + 3*x)^6*(3 + 5*x)) + 728125*Log[2 + 3*x] - 728125*Log[3 + 5*x]","A",1
1222,1,62,73,0.0389661,"\int \frac{(1-2 x) (2+3 x)^7}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^7)/(3 + 5*x)^3,x]","\frac{-227812500 x^8-920362500 x^7-1425650625 x^6-887969250 x^5+150703875 x^4+583310700 x^3+372626040 x^2+107200136 x+12167374}{1562500 (5 x+3)^2}+\frac{2037 \log (5 x+3)}{1953125}","-\frac{729 x^6}{125}-\frac{51759 x^5}{3125}-\frac{181521 x^4}{12500}+\frac{2052 x^3}{3125}+\frac{129654 x^2}{15625}+\frac{1851147 x}{390625}-\frac{229}{1953125 (5 x+3)}-\frac{11}{3906250 (5 x+3)^2}+\frac{2037 \log (5 x+3)}{1953125}",1,"(12167374 + 107200136*x + 372626040*x^2 + 583310700*x^3 + 150703875*x^4 - 887969250*x^5 - 1425650625*x^6 - 920362500*x^7 - 227812500*x^8)/(1562500*(3 + 5*x)^2) + (2037*Log[3 + 5*x])/1953125","A",1
1223,1,57,66,0.0292057,"\int \frac{(1-2 x) (2+3 x)^6}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^6)/(3 + 5*x)^3,x]","\frac{-455625000 x^7-1514953125 x^6-1725806250 x^5-364415625 x^4+874597500 x^3+834723225 x^2+302537270 x+40891591}{7812500 (5 x+3)^2}+\frac{1449 \log (5 x+3)}{390625}","-\frac{1458 x^5}{625}-\frac{12393 x^4}{2500}-\frac{6399 x^3}{3125}+\frac{297 x^2}{125}+\frac{36936 x}{15625}-\frac{196}{390625 (5 x+3)}-\frac{11}{781250 (5 x+3)^2}+\frac{1449 \log (5 x+3)}{390625}",1,"(40891591 + 302537270*x + 834723225*x^2 + 874597500*x^3 - 364415625*x^4 - 1725806250*x^5 - 1514953125*x^6 - 455625000*x^7)/(7812500*(3 + 5*x)^2) + (1449*Log[3 + 5*x])/390625","A",1
1224,1,52,59,0.0277412,"\int \frac{(1-2 x) (2+3 x)^5}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^5)/(3 + 5*x)^3,x]","\frac{-3796875 x^6-9787500 x^5-6412500 x^4+4140000 x^3+7579975 x^2+3653570 x+604711}{156250 (5 x+3)^2}+\frac{192 \log (5 x+3)}{15625}","-\frac{243 x^4}{250}-\frac{837 x^3}{625}+\frac{1971 x^2}{6250}+\frac{3636 x}{3125}-\frac{163}{78125 (5 x+3)}-\frac{11}{156250 (5 x+3)^2}+\frac{192 \log (5 x+3)}{15625}",1,"(604711 + 3653570*x + 7579975*x^2 + 4140000*x^3 - 6412500*x^4 - 9787500*x^5 - 3796875*x^6)/(156250*(3 + 5*x)^2) + (192*Log[3 + 5*x])/15625","A",1
1225,1,47,52,0.0270261,"\int \frac{(1-2 x) (2+3 x)^4}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^4)/(3 + 5*x)^3,x]","\frac{-67500 x^5-118125 x^4+13500 x^3+133650 x^2+87220 x+17192}{6250 (5 x+3)^2}+\frac{114 \log (5 x+3)}{3125}","-\frac{54 x^3}{125}-\frac{297 x^2}{1250}+\frac{1647 x}{3125}-\frac{26}{3125 (5 x+3)}-\frac{11}{31250 (5 x+3)^2}+\frac{114 \log (5 x+3)}{3125}",1,"(17192 + 87220*x + 133650*x^2 + 13500*x^3 - 118125*x^4 - 67500*x^5)/(6250*(3 + 5*x)^2) + (114*Log[3 + 5*x])/3125","A",1
1226,1,42,45,0.0228672,"\int \frac{(1-2 x) (2+3 x)^3}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^3)/(3 + 5*x)^3,x]","\frac{-33750 x^4-20250 x^3+40650 x^2+40520 x+9667}{6250 (5 x+3)^2}+\frac{279 \log (5 x+3)}{3125}","-\frac{27 x^2}{125}+\frac{81 x}{625}-\frac{97}{3125 (5 x+3)}-\frac{11}{6250 (5 x+3)^2}+\frac{279 \log (5 x+3)}{3125}",1,"(9667 + 40520*x + 40650*x^2 - 20250*x^3 - 33750*x^4)/(6250*(3 + 5*x)^2) + (279*Log[3 + 5*x])/3125","A",1
1227,1,37,38,0.0274436,"\int \frac{(1-2 x) (2+3 x)^2}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^2)/(3 + 5*x)^3,x]","\frac{-900 x^3-1680 x^2-1172 x-295}{250 (5 x+3)^2}+\frac{87}{625} \log (5 x+3)","-\frac{18 x}{125}-\frac{64}{625 (5 x+3)}-\frac{11}{1250 (5 x+3)^2}+\frac{87}{625} \log (5 x+3)",1,"(-295 - 1172*x - 1680*x^2 - 900*x^3)/(250*(3 + 5*x)^2) + (87*Log[3 + 5*x])/625","A",1
1228,1,27,33,0.0143977,"\int \frac{(1-2 x) (2+3 x)}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x))/(3 + 5*x)^3,x]","\frac{-310 x-197}{250 (5 x+3)^2}-\frac{6}{125} \log (5 x+3)","-\frac{31}{125 (5 x+3)}-\frac{11}{250 (5 x+3)^2}-\frac{6}{125} \log (5 x+3)",1,"(-197 - 310*x)/(250*(3 + 5*x)^2) - (6*Log[3 + 5*x])/125","A",1
1229,1,16,18,0.0062557,"\int \frac{1-2 x}{(3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)/(3 + 5*x)^3,x]","\frac{20 x+1}{50 (5 x+3)^2}","-\frac{(1-2 x)^2}{22 (5 x+3)^2}",1,"(1 + 20*x)/(50*(3 + 5*x)^2)","A",1
1230,1,33,37,0.0244655,"\int \frac{1-2 x}{(2+3 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)*(3 + 5*x)^3),x]","\frac{350 x+199}{10 (5 x+3)^2}-21 \log (3 x+2)+21 \log (5 x+3)","\frac{7}{5 x+3}-\frac{11}{10 (5 x+3)^2}-21 \log (3 x+2)+21 \log (5 x+3)",1,"(199 + 350*x)/(10*(3 + 5*x)^2) - 21*Log[2 + 3*x] + 21*Log[3 + 5*x]","A",1
1231,1,45,46,0.0321094,"\int \frac{1-2 x}{(2+3 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{3090 x^2+3811 x+1172}{2 (3 x+2) (5 x+3)^2}-309 \log (3 x+2)+309 \log (5 x+3)","\frac{21}{3 x+2}+\frac{68}{5 x+3}-\frac{11}{2 (5 x+3)^2}-309 \log (3 x+2)+309 \log (5 x+3)",1,"(1172 + 3811*x + 3090*x^2)/(2*(2 + 3*x)*(3 + 5*x)^2) - 309*Log[2 + 3*x] + 309*Log[3 + 5*x]","A",1
1232,1,50,57,0.0483086,"\int \frac{1-2 x}{(2+3 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{91800 x^3+174420 x^2+110296 x+23213}{2 (3 x+2)^2 (5 x+3)^2}-3060 \log (3 x+2)+3060 \log (5 x+3)","\frac{309}{3 x+2}+\frac{505}{5 x+3}+\frac{21}{2 (3 x+2)^2}-\frac{55}{2 (5 x+3)^2}-3060 \log (3 x+2)+3060 \log (5 x+3)",1,"(23213 + 110296*x + 174420*x^2 + 91800*x^3)/(2*(2 + 3*x)^2*(3 + 5*x)^2) - 3060*Log[2 + 3*x] + 3060*Log[3 + 5*x]","A",1
1233,1,55,66,0.0433422,"\int \frac{1-2 x}{(2+3 x)^4 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)^4*(3 + 5*x)^3),x]","\frac{2281500 x^4+5855850 x^3+5631080 x^2+2404363 x+384608}{2 (3 x+2)^3 (5 x+3)^2}-25350 \log (3 x+2)+25350 \log (5 x+3)","\frac{3060}{3 x+2}+\frac{3350}{5 x+3}+\frac{309}{2 (3 x+2)^2}-\frac{275}{2 (5 x+3)^2}+\frac{7}{(3 x+2)^3}-25350 \log (3 x+2)+25350 \log (5 x+3)",1,"(384608 + 2404363*x + 5631080*x^2 + 5855850*x^3 + 2281500*x^4)/(2*(2 + 3*x)^3*(3 + 5*x)^2) - 25350*Log[2 + 3*x] + 25350*Log[3 + 5*x]","A",1
1234,1,60,75,0.0531712,"\int \frac{1-2 x}{(2+3 x)^5 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)^5*(3 + 5*x)^3),x]","\frac{102262500 x^5+330648750 x^4+427381500 x^3+276035525 x^2+89085434 x+11492725}{4 (3 x+2)^4 (5 x+3)^2}-189375 \log (3 x+2)+189375 \log (5 x+3)","\frac{25350}{3 x+2}+\frac{20875}{5 x+3}+\frac{1530}{(3 x+2)^2}-\frac{1375}{2 (5 x+3)^2}+\frac{103}{(3 x+2)^3}+\frac{21}{4 (3 x+2)^4}-189375 \log (3 x+2)+189375 \log (5 x+3)",1,"(11492725 + 89085434*x + 276035525*x^2 + 427381500*x^3 + 330648750*x^4 + 102262500*x^5)/(4*(2 + 3*x)^4*(3 + 5*x)^2) - 189375*Log[2 + 3*x] + 189375*Log[3 + 5*x]","A",1
1235,1,65,86,0.0588547,"\int \frac{1-2 x}{(2+3 x)^6 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)/((2 + 3*x)^6*(3 + 5*x)^3),x]","\frac{10707187500 x^6+41758031250 x^5+67828050000 x^4+58733814375 x^3+28595335800 x^2+7421662135 x+802214966}{20 (3 x+2)^5 (5 x+3)^2}-1321875 \log (3 x+2)+1321875 \log (5 x+3)","\frac{189375}{3 x+2}+\frac{125000}{5 x+3}+\frac{12675}{(3 x+2)^2}-\frac{6875}{2 (5 x+3)^2}+\frac{1020}{(3 x+2)^3}+\frac{309}{4 (3 x+2)^4}+\frac{21}{5 (3 x+2)^5}-1321875 \log (3 x+2)+1321875 \log (5 x+3)",1,"(802214966 + 7421662135*x + 28595335800*x^2 + 58733814375*x^3 + 67828050000*x^4 + 41758031250*x^5 + 10707187500*x^6)/(20*(2 + 3*x)^5*(3 + 5*x)^2) - 1321875*Log[2 + 3*x] + 1321875*Log[3 + 5*x]","A",1
1236,1,63,45,0.010846,"\int (1-2 x)^2 (2+3 x)^8 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x),x]","\frac{1}{330} \left(3608550 x^{12}+19420560 x^{11}+43134201 x^{10}+47623950 x^9+19673280 x^8-12972960 x^7-20512800 x^6-8851392 x^5+1056000 x^4+2731520 x^3+1224960 x^2+253440 x\right)","\frac{5}{243} (3 x+2)^{12}-\frac{16}{99} (3 x+2)^{11}+\frac{91}{270} (3 x+2)^{10}-\frac{49}{729} (3 x+2)^9",1,"(253440*x + 1224960*x^2 + 2731520*x^3 + 1056000*x^4 - 8851392*x^5 - 20512800*x^6 - 12972960*x^7 + 19673280*x^8 + 47623950*x^9 + 43134201*x^10 + 19420560*x^11 + 3608550*x^12)/330","A",1
1237,1,58,45,0.009807,"\int (1-2 x)^2 (2+3 x)^7 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x),x]","\frac{5248800 x^{11}+24634368 x^{10}+45654840 x^9+37194795 x^8+1639440 x^7-21455280 x^6-15656256 x^5-1705440 x^4+3393280 x^3+2069760 x^2+506880 x}{1320}","\frac{20}{891} (3 x+2)^{11}-\frac{8}{45} (3 x+2)^{10}+\frac{91}{243} (3 x+2)^9-\frac{49}{648} (3 x+2)^8",1,"(506880*x + 2069760*x^2 + 3393280*x^3 - 1705440*x^4 - 15656256*x^5 - 21455280*x^6 + 1639440*x^7 + 37194795*x^8 + 45654840*x^9 + 24634368*x^10 + 5248800*x^11)/1320","A",1
1238,1,53,45,0.0096217,"\int (1-2 x)^2 (2+3 x)^6 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x),x]","\frac{1}{24} \left(34992 x^{10}+139968 x^9+206307 x^8+100440 x^7-66528 x^6-102816 x^5-32928 x^4+15488 x^3+15360 x^2+4608 x\right)","\frac{2}{81} (3 x+2)^{10}-\frac{16}{81} (3 x+2)^9+\frac{91}{216} (3 x+2)^8-\frac{7}{81} (3 x+2)^7",1,"(4608*x + 15360*x^2 + 15488*x^3 - 32928*x^4 - 102816*x^5 - 66528*x^6 + 100440*x^7 + 206307*x^8 + 139968*x^9 + 34992*x^10)/24","A",1
1239,1,48,45,0.0087411,"\int (1-2 x)^2 (2+3 x)^5 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x),x]","\frac{1}{6} \left(3240 x^9+10692 x^8+11502 x^7+819 x^6-7308 x^5-4620 x^4+448 x^3+1488 x^2+576 x\right)","\frac{20}{729} (3 x+2)^9-\frac{2}{9} (3 x+2)^8+\frac{13}{27} (3 x+2)^7-\frac{49}{486} (3 x+2)^6",1,"(576*x + 1488*x^2 + 448*x^3 - 4620*x^4 - 7308*x^5 + 819*x^6 + 11502*x^7 + 10692*x^8 + 3240*x^9)/6","A",1
1240,1,43,45,0.0075463,"\int (1-2 x)^2 (2+3 x)^4 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x),x]","\frac{1}{210} \left(42525 x^8+110160 x^7+70875 x^6-45234 x^5-68880 x^4-10640 x^3+18480 x^2+10080 x\right)","\frac{5}{162} (3 x+2)^8-\frac{16}{63} (3 x+2)^7+\frac{91}{162} (3 x+2)^6-\frac{49}{405} (3 x+2)^5",1,"(10080*x + 18480*x^2 - 10640*x^3 - 68880*x^4 - 45234*x^5 + 70875*x^6 + 110160*x^7 + 42525*x^8)/210","A",1
1241,1,38,42,0.0063221,"\int (1-2 x)^2 (2+3 x)^3 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x),x]","\frac{1}{420} \left(32400 x^7+60480 x^6+8316 x^5-44625 x^4-21560 x^3+10920 x^2+10080 x\right)","\frac{540 x^7}{7}+144 x^6+\frac{99 x^5}{5}-\frac{425 x^4}{4}-\frac{154 x^3}{3}+26 x^2+24 x",1,"(10080*x + 10920*x^2 - 21560*x^3 - 44625*x^4 + 8316*x^5 + 60480*x^6 + 32400*x^7)/420","A",1
1242,1,33,35,0.0064549,"\int (1-2 x)^2 (2+3 x)^2 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x),x]","\frac{1}{60} \left(1800 x^6+2016 x^5-1185 x^4-1780 x^3+240 x^2+720 x\right)","30 x^6+\frac{168 x^5}{5}-\frac{79 x^4}{4}-\frac{89 x^3}{3}+4 x^2+12 x",1,"(720*x + 240*x^2 - 1780*x^3 - 1185*x^4 + 2016*x^5 + 1800*x^6)/60","A",1
1243,1,25,28,0.0054767,"\int (1-2 x)^2 (2+3 x) (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)*(3 + 5*x),x]","\frac{1}{6} x \left(72 x^4+24 x^3-74 x^2-15 x+36\right)","12 x^5+4 x^4-\frac{37 x^3}{3}-\frac{5 x^2}{2}+6 x",1,"(x*(36 - 15*x - 74*x^2 + 24*x^3 + 72*x^4))/6","A",1
1244,1,23,23,0.0044875,"\int (1-2 x)^2 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(3 + 5*x),x]","\frac{1}{6} \left(30 x^4-16 x^3-21 x^2+18 x\right)","5 x^4-\frac{8 x^3}{3}-\frac{7 x^2}{2}+3 x",1,"(18*x - 21*x^2 - 16*x^3 + 30*x^4)/6","A",1
1245,1,26,30,0.0157709,"\int \frac{(1-2 x)^2 (3+5 x)}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x),x]","\frac{1}{27} x \left(60 x^2-96 x+65\right)-\frac{49}{81} \log (3 x+2)","\frac{20 x^3}{9}-\frac{32 x^2}{9}+\frac{65 x}{27}-\frac{49}{81} \log (3 x+2)",1,"(x*(65 - 96*x + 60*x^2))/27 - (49*Log[2 + 3*x])/81","A",1
1246,1,37,34,0.0210564,"\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^2,x]","\frac{540 x^3-1512 x^2-447 x+632}{162 (3 x+2)}+\frac{91}{27} \log (3 x+2)","\frac{10 x^2}{9}-\frac{104 x}{27}+\frac{49}{81 (3 x+2)}+\frac{91}{27} \log (3 x+2)",1,"(632 - 447*x - 1512*x^2 + 540*x^3)/(162*(2 + 3*x)) + (91*Log[2 + 3*x])/27","A",1
1247,1,37,38,0.0222516,"\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^3,x]","\frac{1080 x^3+900 x^2-1878 x-1283}{162 (3 x+2)^2}-\frac{16}{9} \log (3 x+2)","\frac{20 x}{27}-\frac{91}{27 (3 x+2)}+\frac{49}{162 (3 x+2)^2}-\frac{16}{9} \log (3 x+2)",1,"(-1283 - 1878*x + 900*x^2 + 1080*x^3)/(162*(2 + 3*x)^2) - (16*Log[2 + 3*x])/9","A",1
1248,1,32,44,0.0215984,"\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^4,x]","\frac{7776 x^2+7911 x+1916}{486 (3 x+2)^3}+\frac{20}{81} \log (3 x+2)","\frac{16}{9 (3 x+2)}-\frac{91}{54 (3 x+2)^2}+\frac{49}{243 (3 x+2)^3}+\frac{20}{81} \log (3 x+2)",1,"(1916 + 7911*x + 7776*x^2)/(486*(2 + 3*x)^3) + (20*Log[2 + 3*x])/81","A",1
1249,1,26,37,0.0162335,"\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^5,x]","\frac{-2160 x^3-1728 x^2-516 x-167}{324 (3 x+2)^4}","\frac{(1-2 x)^3}{84 (3 x+2)^4}-\frac{23 (1-2 x)^3}{294 (3 x+2)^3}",1,"(-167 - 516*x - 1728*x^2 - 2160*x^3)/(324*(2 + 3*x)^4)","A",1
1250,1,26,45,0.0153216,"\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^6,x]","\frac{-1800 x^3-720 x^2+75 x-98}{540 (3 x+2)^5}","-\frac{10}{81 (3 x+2)^2}+\frac{16}{27 (3 x+2)^3}-\frac{91}{108 (3 x+2)^4}+\frac{49}{405 (3 x+2)^5}",1,"(-98 + 75*x - 720*x^2 - 1800*x^3)/(540*(2 + 3*x)^5)","A",1
1251,1,26,45,0.016414,"\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^7,x]","\frac{-5400 x^3-1080 x^2+846 x-311}{2430 (3 x+2)^6}","-\frac{20}{243 (3 x+2)^3}+\frac{4}{9 (3 x+2)^4}-\frac{91}{135 (3 x+2)^5}+\frac{49}{486 (3 x+2)^6}",1,"(-311 + 846*x - 1080*x^2 - 5400*x^3)/(2430*(2 + 3*x)^6)","A",1
1252,1,26,45,0.0152226,"\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^8} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^8,x]","\frac{-1350 x^3-108 x^2+291 x-88}{810 (3 x+2)^7}","-\frac{5}{81 (3 x+2)^4}+\frac{16}{45 (3 x+2)^5}-\frac{91}{162 (3 x+2)^6}+\frac{7}{81 (3 x+2)^7}",1,"(-88 + 291*x - 108*x^2 - 1350*x^3)/(810*(2 + 3*x)^7)","A",1
1253,1,68,56,0.0117141,"\int (1-2 x)^2 (2+3 x)^8 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x)^2,x]","\frac{108256500 x^{13}+648937575 x^{12}+1653120495 x^{11}+2234117457 x^{10}+1497006225 x^9+14710410 x^8-824400720 x^7-639724800 x^6-145146144 x^5+87172800 x^4+79805440 x^3+28005120 x^2+4942080 x}{2145}","\frac{100 (3 x+2)^{13}}{3159}-\frac{185}{729} (3 x+2)^{12}+\frac{503}{891} (3 x+2)^{11}-\frac{259 (3 x+2)^{10}}{1215}+\frac{49 (3 x+2)^9}{2187}",1,"(4942080*x + 28005120*x^2 + 79805440*x^3 + 87172800*x^4 - 145146144*x^5 - 639724800*x^6 - 824400720*x^7 + 14710410*x^8 + 1497006225*x^9 + 2234117457*x^10 + 1653120495*x^11 + 648937575*x^12 + 108256500*x^13)/2145","A",1
1254,1,63,56,0.0108922,"\int (1-2 x)^2 (2+3 x)^7 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x)^2,x]","\frac{24057000 x^{12}+127720800 x^{11}+279349884 x^{10}+302274720 x^9+118756935 x^8-87032880 x^7-129600240 x^6-53790528 x^5+7608480 x^4+17079040 x^3+7476480 x^2+1520640 x}{1320}","\frac{25}{729} (3 x+2)^{12}-\frac{740 (3 x+2)^{11}}{2673}+\frac{503}{810} (3 x+2)^{10}-\frac{518 (3 x+2)^9}{2187}+\frac{49 (3 x+2)^8}{1944}",1,"(1520640*x + 7476480*x^2 + 17079040*x^3 + 7608480*x^4 - 53790528*x^5 - 129600240*x^6 - 87032880*x^7 + 118756935*x^8 + 302274720*x^9 + 279349884*x^10 + 127720800*x^11 + 24057000*x^12)/1320","A",1
1255,1,58,56,0.0097695,"\int (1-2 x)^2 (2+3 x)^6 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x)^2,x]","\frac{1}{132} \left(874800 x^{11}+4041576 x^{10}+7352532 x^9+5820903 x^8+89100 x^7-3453912 x^6-2420880 x^5-223872 x^4+537152 x^3+316800 x^2+76032 x\right)","\frac{100 (3 x+2)^{11}}{2673}-\frac{74}{243} (3 x+2)^{10}+\frac{503}{729} (3 x+2)^9-\frac{259}{972} (3 x+2)^8+\frac{7}{243} (3 x+2)^7",1,"(76032*x + 316800*x^2 + 537152*x^3 - 223872*x^4 - 2420880*x^5 - 3453912*x^6 + 89100*x^7 + 5820903*x^8 + 7352532*x^9 + 4041576*x^10 + 874800*x^11)/132","A",1
1256,1,53,56,0.0089198,"\int (1-2 x)^2 (2+3 x)^5 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x)^2,x]","\frac{1}{24} \left(58320 x^{10}+228960 x^9+329589 x^8+152064 x^7-111972 x^6-161616 x^5-48720 x^4+25216 x^3+23616 x^2+6912 x\right)","\frac{10}{243} (3 x+2)^{10}-\frac{740 (3 x+2)^9}{2187}+\frac{503}{648} (3 x+2)^8-\frac{74}{243} (3 x+2)^7+\frac{49 (3 x+2)^6}{1458}",1,"(6912*x + 23616*x^2 + 25216*x^3 - 48720*x^4 - 161616*x^5 - 111972*x^6 + 152064*x^7 + 329589*x^8 + 228960*x^9 + 58320*x^10)/24","A",1
1257,1,48,56,0.0091819,"\int (1-2 x)^2 (2+3 x)^4 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^2,x]","\frac{1}{210} \left(189000 x^9+609525 x^8+634230 x^7+24150 x^6-411222 x^5-246540 x^4+29680 x^3+80640 x^2+30240 x\right)","\frac{100 (3 x+2)^9}{2187}-\frac{185}{486} (3 x+2)^8+\frac{503}{567} (3 x+2)^7-\frac{259}{729} (3 x+2)^6+\frac{49 (3 x+2)^5}{1215}",1,"(30240*x + 80640*x^2 + 29680*x^3 - 246540*x^4 - 411222*x^5 + 24150*x^6 + 634230*x^7 + 609525*x^8 + 189000*x^9)/210","A",1
1258,1,43,51,0.0089561,"\int (1-2 x)^2 (2+3 x)^3 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x)^2,x]","\frac{1}{420} \left(141750 x^8+356400 x^7+216090 x^6-153552 x^5-214725 x^4-28280 x^3+57960 x^2+30240 x\right)","\frac{675 x^8}{2}+\frac{5940 x^7}{7}+\frac{1029 x^6}{2}-\frac{1828 x^5}{5}-\frac{2045 x^4}{4}-\frac{202 x^3}{3}+138 x^2+72 x",1,"(30240*x + 57960*x^2 - 28280*x^3 - 214725*x^4 - 153552*x^5 + 216090*x^6 + 356400*x^7 + 141750*x^8)/420","A",1
1259,1,38,42,0.0075223,"\int (1-2 x)^2 (2+3 x)^2 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x)^2,x]","\frac{1}{210} \left(27000 x^7+48300 x^6+4578 x^5-35805 x^4-15890 x^3+8820 x^2+7560 x\right)","\frac{900 x^7}{7}+230 x^6+\frac{109 x^5}{5}-\frac{341 x^4}{2}-\frac{227 x^3}{3}+42 x^2+36 x",1,"(7560*x + 8820*x^2 - 15890*x^3 - 35805*x^4 + 4578*x^5 + 48300*x^6 + 27000*x^7)/210","A",1
1260,1,30,35,0.0061914,"\int (1-2 x)^2 (2+3 x) (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)*(3 + 5*x)^2,x]","\frac{1}{12} x \left(600 x^5+624 x^4-411 x^3-544 x^2+90 x+216\right)","50 x^6+52 x^5-\frac{137 x^4}{4}-\frac{136 x^3}{3}+\frac{15 x^2}{2}+18 x",1,"(x*(216 + 90*x - 544*x^2 - 411*x^3 + 624*x^4 + 600*x^5))/12","A",1
1261,1,28,26,0.0054395,"\int (1-2 x)^2 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(3 + 5*x)^2,x]","\frac{1}{3} \left(60 x^5+15 x^4-59 x^3-9 x^2+27 x\right)","20 x^5+5 x^4-\frac{59 x^3}{3}-3 x^2+9 x",1,"(27*x - 9*x^2 - 59*x^3 + 15*x^4 + 60*x^5)/3","A",1
1262,1,31,37,0.0158816,"\int \frac{(1-2 x)^2 (3+5 x)^2}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x),x]","\frac{1}{162} x \left(1350 x^3-840 x^2-753 x+680\right)+\frac{49}{243} \log (3 x+2)","\frac{25 x^4}{3}-\frac{140 x^3}{27}-\frac{251 x^2}{54}+\frac{340 x}{81}+\frac{49}{243} \log (3 x+2)",1,"(x*(680 - 753*x - 840*x^2 + 1350*x^3))/162 + (49*Log[2 + 3*x])/243","A",1
1263,1,42,41,0.0208503,"\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^2,x]","\frac{8100 x^4-8370 x^3+2403 x^2+23964 x+10681}{729 (3 x+2)}-\frac{518}{243} \log (3 x+2)","\frac{100 x^3}{27}-\frac{170 x^2}{27}+\frac{143 x}{27}-\frac{49}{243 (3 x+2)}-\frac{518}{243} \log (3 x+2)",1,"(10681 + 23964*x + 2403*x^2 - 8370*x^3 + 8100*x^4)/(729*(2 + 3*x)) - (518*Log[2 + 3*x])/243","A",1
1264,1,42,45,0.0263717,"\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^3,x]","\frac{900 x^4-2040 x^3-6480 x^2-4508 x-913}{54 (3 x+2)^2}+\frac{503}{81} \log (3 x+2)","\frac{50 x^2}{27}-\frac{20 x}{3}+\frac{518}{243 (3 x+2)}-\frac{49}{486 (3 x+2)^2}+\frac{503}{81} \log (3 x+2)",1,"(-913 - 4508*x - 6480*x^2 - 2040*x^3 + 900*x^4)/(54*(2 + 3*x)^2) + (503*Log[2 + 3*x])/81","A",1
1265,1,42,49,0.0239123,"\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^4,x]","\frac{24300 x^4+64800 x^3+24057 x^2-23193 x-11803}{729 (3 x+2)^3}-\frac{740}{243} \log (3 x+2)","\frac{100 x}{81}-\frac{503}{81 (3 x+2)}+\frac{259}{243 (3 x+2)^2}-\frac{49}{729 (3 x+2)^3}-\frac{740}{243} \log (3 x+2)",1,"(-11803 - 23193*x + 24057*x^2 + 64800*x^3 + 24300*x^4)/(729*(2 + 3*x)^3) - (740*Log[2 + 3*x])/243","A",1
1266,1,37,55,0.0214216,"\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^5,x]","\frac{239760 x^3+398034 x^2+217248 x+38821}{2916 (3 x+2)^4}+\frac{100}{243} \log (3 x+2)","\frac{740}{243 (3 x+2)}-\frac{503}{162 (3 x+2)^2}+\frac{518}{729 (3 x+2)^3}-\frac{49}{972 (3 x+2)^4}+\frac{100}{243} \log (3 x+2)",1,"(38821 + 217248*x + 398034*x^2 + 239760*x^3)/(2916*(2 + 3*x)^4) + (100*Log[2 + 3*x])/243","A",1
1267,1,31,56,0.0174119,"\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^6,x]","\frac{-81000 x^4-116100 x^3-61470 x^2-19275 x-4028}{2430 (3 x+2)^5}","-\frac{100}{243 (3 x+2)}+\frac{370}{243 (3 x+2)^2}-\frac{503}{243 (3 x+2)^3}+\frac{259}{486 (3 x+2)^4}-\frac{49}{1215 (3 x+2)^5}",1,"(-4028 - 19275*x - 61470*x^2 - 116100*x^3 - 81000*x^4)/(2430*(2 + 3*x)^5)","A",1
1268,1,31,56,0.0155238,"\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^7,x]","\frac{-243000 x^4-248400 x^3-52515 x^2-8172 x-8198}{14580 (3 x+2)^6}","-\frac{50}{243 (3 x+2)^2}+\frac{740}{729 (3 x+2)^3}-\frac{503}{324 (3 x+2)^4}+\frac{518}{1215 (3 x+2)^5}-\frac{49}{1458 (3 x+2)^6}",1,"(-8198 - 8172*x - 52515*x^2 - 248400*x^3 - 243000*x^4)/(14580*(2 + 3*x)^6)","A",1
1269,1,31,56,0.0162741,"\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^8} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^8,x]","\frac{-40500 x^4-33075 x^3+1107 x^2+1461 x-1423}{3645 (3 x+2)^7}","-\frac{100}{729 (3 x+2)^3}+\frac{185}{243 (3 x+2)^4}-\frac{503}{405 (3 x+2)^5}+\frac{259}{729 (3 x+2)^6}-\frac{7}{243 (3 x+2)^7}",1,"(-1423 + 1461*x + 1107*x^2 - 33075*x^3 - 40500*x^4)/(3645*(2 + 3*x)^7)","A",1
1270,1,83,67,0.0139281,"\int (1-2 x)^2 (2+3 x)^{10} (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^10*(3 + 5*x)^3,x]","\frac{22165518375 x^{16}+176536039680 x^{15}+629838482130 x^{14}+1309694931468 x^{13}+1708811507403 x^{12}+1347446190636 x^{11}+432956972448 x^{10}-315167252400 x^9-481842977616 x^8-265315729536 x^7-42551821312 x^6+38267733504 x^5+31761649920 x^4+12020456448 x^3+2656862208 x^2+332107776 x}{12012}","\frac{125 (3 x+2)^{16}}{2916}-\frac{760 (3 x+2)^{15}}{2187}+\frac{8285 (3 x+2)^{14}}{10206}-\frac{4099 (3 x+2)^{13}}{9477}+\frac{763 (3 x+2)^{12}}{8748}-\frac{49 (3 x+2)^{11}}{8019}",1,"(332107776*x + 2656862208*x^2 + 12020456448*x^3 + 31761649920*x^4 + 38267733504*x^5 - 42551821312*x^6 - 265315729536*x^7 - 481842977616*x^8 - 315167252400*x^9 + 432956972448*x^10 + 1347446190636*x^11 + 1708811507403*x^12 + 1309694931468*x^13 + 629838482130*x^14 + 176536039680*x^15 + 22165518375*x^16)/12012","A",1
1271,1,78,67,0.0126964,"\int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^9*(3 + 5*x)^3,x]","\frac{39405366000 x^{15}+287096238000 x^{14}+924358950900 x^{13}+1697134383945 x^{12}+1872650461500 x^{11}+1097041011066 x^{10}-10850799960 x^9-582800498280 x^8-473757672960 x^7-147413506240 x^6+32827162368 x^5+52368476160 x^4+24031687680 x^3+6019453440 x^2+830269440 x}{60060}","\frac{100 (3 x+2)^{15}}{2187}-\frac{1900 (3 x+2)^{14}}{5103}+\frac{8285 (3 x+2)^{13}}{9477}-\frac{4099 (3 x+2)^{12}}{8748}+\frac{763 (3 x+2)^{11}}{8019}-\frac{49 (3 x+2)^{10}}{7290}",1,"(830269440*x + 6019453440*x^2 + 24031687680*x^3 + 52368476160*x^4 + 32827162368*x^5 - 147413506240*x^6 - 473757672960*x^7 - 582800498280*x^8 - 10850799960*x^9 + 1097041011066*x^10 + 1872650461500*x^11 + 1697134383945*x^12 + 924358950900*x^13 + 287096238000*x^14 + 39405366000*x^15)/60060","A",1
1272,1,73,67,0.012153,"\int (1-2 x)^2 (2+3 x)^8 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x)^3,x]","\frac{14073345000 x^{14}+92956248000 x^{13}+266661219825 x^{12}+423204343380 x^{11}+376288650738 x^{10}+127579151700 x^9-99753413760 x^8-146016636480 x^7-70670600000 x^6-2428922496 x^5+15702086400 x^4+9317468160 x^3+2698375680 x^2+415134720 x}{60060}","\frac{250 (3 x+2)^{14}}{5103}-\frac{3800 (3 x+2)^{13}}{9477}+\frac{8285 (3 x+2)^{12}}{8748}-\frac{4099 (3 x+2)^{11}}{8019}+\frac{763 (3 x+2)^{10}}{7290}-\frac{49 (3 x+2)^9}{6561}",1,"(415134720*x + 2698375680*x^2 + 9317468160*x^3 + 15702086400*x^4 - 2428922496*x^5 - 70670600000*x^6 - 146016636480*x^7 - 99753413760*x^8 + 127579151700*x^9 + 376288650738*x^10 + 423204343380*x^11 + 266661219825*x^12 + 92956248000*x^13 + 14073345000*x^14)/60060","A",1
1273,1,68,67,0.0116251,"\int (1-2 x)^2 (2+3 x)^7 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x)^3,x]","\frac{1443420000 x^{13}+8548254000 x^{12}+21488149800 x^{11}+28577716596 x^{10}+18650225880 x^9-318474585 x^8-10614867120 x^7-7968062960 x^6-1702189632 x^5+1129333920 x^4+990063360 x^3+341003520 x^2+59304960 x}{17160}","\frac{500 (3 x+2)^{13}}{9477}-\frac{950 (3 x+2)^{12}}{2187}+\frac{8285 (3 x+2)^{11}}{8019}-\frac{4099 (3 x+2)^{10}}{7290}+\frac{763 (3 x+2)^9}{6561}-\frac{49 (3 x+2)^8}{5832}",1,"(59304960*x + 341003520*x^2 + 990063360*x^3 + 1129333920*x^4 - 1702189632*x^5 - 7968062960*x^6 - 10614867120*x^7 - 318474585*x^8 + 18650225880*x^9 + 28577716596*x^10 + 21488149800*x^11 + 8548254000*x^12 + 1443420000*x^13)/17160","A",1
1274,1,63,67,0.0108055,"\int (1-2 x)^2 (2+3 x)^6 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x)^3,x]","\frac{1}{264} \left(8019000 x^{12}+41990400 x^{11}+90422244 x^{10}+95856552 x^9+35705043 x^8-29070360 x^7-40897472 x^6-16316256 x^5+2685408 x^4+5334912 x^3+2280960 x^2+456192 x\right)","\frac{125 (3 x+2)^{12}}{2187}-\frac{3800 (3 x+2)^{11}}{8019}+\frac{1657 (3 x+2)^{10}}{1458}-\frac{4099 (3 x+2)^9}{6561}+\frac{763 (3 x+2)^8}{5832}-\frac{7}{729} (3 x+2)^7",1,"(456192*x + 2280960*x^2 + 5334912*x^3 + 2685408*x^4 - 16316256*x^5 - 40897472*x^6 - 29070360*x^7 + 35705043*x^8 + 95856552*x^9 + 90422244*x^10 + 41990400*x^11 + 8019000*x^12)/264","A",1
1275,1,58,67,0.0099403,"\int (1-2 x)^2 (2+3 x)^5 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x)^3,x]","\frac{1}{264} \left(2916000 x^{11}+13258080 x^{10}+23668920 x^9+18194517 x^8-260568 x^7-11102476 x^6-7477008 x^5-567600 x^4+1698048 x^3+969408 x^2+228096 x\right)","\frac{500 (3 x+2)^{11}}{8019}-\frac{380}{729} (3 x+2)^{10}+\frac{8285 (3 x+2)^9}{6561}-\frac{4099 (3 x+2)^8}{5832}+\frac{109}{729} (3 x+2)^7-\frac{49 (3 x+2)^6}{4374}",1,"(228096*x + 969408*x^2 + 1698048*x^3 - 567600*x^4 - 7477008*x^5 - 11102476*x^6 - 260568*x^7 + 18194517*x^8 + 23668920*x^9 + 13258080*x^10 + 2916000*x^11)/264","A",1
1276,1,53,67,0.0096336,"\int (1-2 x)^2 (2+3 x)^4 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^3,x]","\frac{1}{840} \left(3402000 x^{10}+13104000 x^9+18413325 x^8+8024760 x^7-6563900 x^6-8879304 x^5-2513280 x^4+1431360 x^3+1270080 x^2+362880 x\right)","\frac{50}{729} (3 x+2)^{10}-\frac{3800 (3 x+2)^9}{6561}+\frac{8285 (3 x+2)^8}{5832}-\frac{4099 (3 x+2)^7}{5103}+\frac{763 (3 x+2)^6}{4374}-\frac{49 (3 x+2)^5}{3645}",1,"(362880*x + 1270080*x^2 + 1431360*x^3 - 2513280*x^4 - 8879304*x^5 - 6563900*x^6 + 8024760*x^7 + 18413325*x^8 + 13104000*x^9 + 3402000*x^10)/840","A",1
1277,1,48,52,0.008799,"\int (1-2 x)^2 (2+3 x)^3 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x)^3,x]","\frac{1}{420} \left(630000 x^9+1984500 x^8+1995300 x^7+8470 x^6-1319556 x^5-750225 x^4+108360 x^3+249480 x^2+90720 x\right)","1500 x^9+4725 x^8+\frac{33255 x^7}{7}+\frac{121 x^6}{6}-\frac{15709 x^5}{5}-\frac{7145 x^4}{4}+258 x^3+594 x^2+216 x",1,"(90720*x + 249480*x^2 + 108360*x^3 - 750225*x^4 - 1319556*x^5 + 8470*x^6 + 1995300*x^7 + 1984500*x^8 + 630000*x^9)/420","A",1
1278,1,43,49,0.0084287,"\int (1-2 x)^2 (2+3 x)^2 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x)^3,x]","\frac{1}{420} \left(236250 x^8+576000 x^7+327950 x^6-258972 x^5-334005 x^4-36540 x^3+90720 x^2+45360 x\right)","\frac{1125 x^8}{2}+\frac{9600 x^7}{7}+\frac{4685 x^6}{6}-\frac{3083 x^5}{5}-\frac{3181 x^4}{4}-87 x^3+216 x^2+108 x",1,"(45360*x + 90720*x^2 - 36540*x^3 - 334005*x^4 - 258972*x^5 + 327950*x^6 + 576000*x^7 + 236250*x^8)/420","A",1
1279,1,38,42,0.0064854,"\int (1-2 x)^2 (2+3 x) (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(2 + 3*x)*(3 + 5*x)^3,x]","\frac{1}{84} \left(18000 x^7+30800 x^6+1596 x^5-22911 x^4-9324 x^3+5670 x^2+4536 x\right)","\frac{1500 x^7}{7}+\frac{1100 x^6}{3}+19 x^5-\frac{1091 x^4}{4}-111 x^3+\frac{135 x^2}{2}+54 x",1,"(4536*x + 5670*x^2 - 9324*x^3 - 22911*x^4 + 1596*x^5 + 30800*x^6 + 18000*x^7)/84","A",1
1280,1,33,34,0.0064691,"\int (1-2 x)^2 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^2*(3 + 5*x)^3,x]","\frac{1}{12} \left(1000 x^6+960 x^5-705 x^4-828 x^3+162 x^2+324 x\right)","\frac{2}{375} (5 x+3)^6-\frac{44}{625} (5 x+3)^5+\frac{121}{500} (5 x+3)^4",1,"(324*x + 162*x^2 - 828*x^3 - 705*x^4 + 960*x^5 + 1000*x^6)/12","A",1
1281,1,36,44,0.0176514,"\int \frac{(1-2 x)^2 (3+5 x)^3}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x),x]","\frac{1}{486} x \left(16200 x^4+2700 x^3-15090 x^2-1677 x+6610\right)-\frac{49}{729} \log (3 x+2)","\frac{100 x^5}{3}+\frac{50 x^4}{9}-\frac{2515 x^3}{81}-\frac{559 x^2}{162}+\frac{3305 x}{243}-\frac{49}{729} \log (3 x+2)",1,"(x*(6610 - 1677*x - 15090*x^2 + 2700*x^3 + 16200*x^4))/486 - (49*Log[2 + 3*x])/729","A",1
1282,1,47,48,0.0386267,"\int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^2,x]","\frac{182250 x^5-8100 x^4-160515 x^3+19224 x^2+50052 x+3158}{4374 (3 x+2)}+\frac{763}{729} \log (3 x+2)","\frac{125 x^4}{9}-\frac{800 x^3}{81}-\frac{305 x^2}{54}+\frac{1271 x}{243}+\frac{49}{729 (3 x+2)}+\frac{763}{729} \log (3 x+2)",1,"(3158 + 50052*x + 19224*x^2 - 160515*x^3 - 8100*x^4 + 182250*x^5)/(4374*(2 + 3*x)) + (763*Log[2 + 3*x])/729","A",1
1283,1,47,52,0.039041,"\int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^3,x]","\frac{243000 x^5-113400 x^4-40230 x^3+941940 x^2+921426 x+238271}{4374 (3 x+2)^2}-\frac{4099}{729} \log (3 x+2)","\frac{500 x^3}{81}-\frac{100 x^2}{9}+\frac{895 x}{81}-\frac{763}{729 (3 x+2)}+\frac{49}{1458 (3 x+2)^2}-\frac{4099}{729} \log (3 x+2)",1,"(238271 + 921426*x + 941940*x^2 - 40230*x^3 - 113400*x^4 + 243000*x^5)/(4374*(2 + 3*x)^2) - (4099*Log[2 + 3*x])/729","A",1
1284,1,47,56,0.0460302,"\int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^4,x]","\frac{364500 x^5-631800 x^4-3304800 x^3-3623454 x^2-1540539 x-222904}{4374 (3 x+2)^3}+\frac{8285}{729} \log (3 x+2)","\frac{250 x^2}{81}-\frac{2800 x}{243}+\frac{4099}{729 (3 x+2)}-\frac{763}{1458 (3 x+2)^2}+\frac{49}{2187 (3 x+2)^3}+\frac{8285}{729} \log (3 x+2)",1,"(-222904 - 1540539*x - 3623454*x^2 - 3304800*x^3 - 631800*x^4 + 364500*x^5)/(4374*(2 + 3*x)^3) + (8285*Log[2 + 3*x])/729","A",1
1285,1,47,60,0.0432466,"\int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^5,x]","\frac{1458000 x^5+4860000 x^4+3795660 x^3-827334 x^2-1853148 x-510941}{8748 (3 x+2)^4}-\frac{3800}{729} \log (3 x+2)","\frac{500 x}{243}-\frac{8285}{729 (3 x+2)}+\frac{4099}{1458 (3 x+2)^2}-\frac{763}{2187 (3 x+2)^3}+\frac{49}{2916 (3 x+2)^4}-\frac{3800}{729} \log (3 x+2)",1,"(-510941 - 1853148*x - 827334*x^2 + 3795660*x^3 + 4860000*x^4 + 1458000*x^5)/(8748*(2 + 3*x)^4) - (3800*Log[2 + 3*x])/729","A",1
1286,1,42,66,0.0436175,"\int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^6,x]","\frac{18468000 x^4+42537150 x^3+36564120 x^2+13889625 x+1965218}{43740 (3 x+2)^5}+\frac{500}{729} \log (3 x+2)","\frac{3800}{729 (3 x+2)}-\frac{8285}{1458 (3 x+2)^2}+\frac{4099}{2187 (3 x+2)^3}-\frac{763}{2916 (3 x+2)^4}+\frac{49}{3645 (3 x+2)^5}+\frac{500}{729} \log (3 x+2)",1,"(1965218 + 13889625*x + 36564120*x^2 + 42537150*x^3 + 18468000*x^4)/(43740*(2 + 3*x)^5) + (500*Log[2 + 3*x])/729","A",1
1287,1,36,67,0.0327913,"\int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^7,x]","\frac{-7290000 x^5-15066000 x^4-12249900 x^3-5370435 x^2-1510848 x-233482}{43740 (3 x+2)^6}","-\frac{500}{729 (3 x+2)}+\frac{1900}{729 (3 x+2)^2}-\frac{8285}{2187 (3 x+2)^3}+\frac{4099}{2916 (3 x+2)^4}-\frac{763}{3645 (3 x+2)^5}+\frac{49}{4374 (3 x+2)^6}",1,"(-233482 - 1510848*x - 5370435*x^2 - 12249900*x^3 - 15066000*x^4 - 7290000*x^5)/(43740*(2 + 3*x)^6)","A",1
1288,1,36,67,0.0317178,"\int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^8} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^8,x]","\frac{-3645000 x^5-5994000 x^4-3139425 x^3-652158 x^2-210534 x-76288}{43740 (3 x+2)^7}","-\frac{250}{729 (3 x+2)^2}+\frac{3800}{2187 (3 x+2)^3}-\frac{8285}{2916 (3 x+2)^4}+\frac{4099}{3645 (3 x+2)^5}-\frac{763}{4374 (3 x+2)^6}+\frac{7}{729 (3 x+2)^7}",1,"(-76288 - 210534*x - 652158*x^2 - 3139425*x^3 - 5994000*x^4 - 3645000*x^5)/(43740*(2 + 3*x)^7)","A",1
1289,1,56,72,0.023667,"\int \frac{(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^7)/(3 + 5*x),x]","\frac{x \left(10631250000 x^8+36677812500 x^7+42054187500 x^6+5704256250 x^5-25605814500 x^4-18005014125 x^3+929011300 x^2+5638889830 x+2333332204\right)}{54687500}+\frac{121 \log (5 x+3)}{9765625}","\frac{972 x^9}{5}+\frac{16767 x^8}{25}+\frac{672867 x^7}{875}+\frac{130383 x^6}{1250}-\frac{7315947 x^5}{15625}-\frac{20577159 x^4}{62500}+\frac{1327159 x^3}{78125}+\frac{80555569 x^2}{781250}+\frac{83333293 x}{1953125}+\frac{121 \log (5 x+3)}{9765625}",1,"(x*(2333332204 + 5638889830*x + 929011300*x^2 - 18005014125*x^3 - 25605814500*x^4 + 5704256250*x^5 + 42054187500*x^6 + 36677812500*x^7 + 10631250000*x^8))/54687500 + (121*Log[3 + 5*x])/9765625","A",1
1290,1,51,65,0.0226339,"\int \frac{(1-2 x)^2 (2+3 x)^6}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^6)/(3 + 5*x),x]","\frac{x \left(797343750 x^7+2187000000 x^6+1569881250 x^5-799564500 x^4-1467514125 x^3-295988700 x^2+388889830 x+233332204\right)}{10937500}+\frac{121 \log (5 x+3)}{1953125}","\frac{729 x^8}{10}+\frac{34992 x^7}{175}+\frac{35883 x^6}{250}-\frac{228447 x^5}{3125}-\frac{1677159 x^4}{12500}-\frac{422841 x^3}{15625}+\frac{5555569 x^2}{156250}+\frac{8333293 x}{390625}+\frac{121 \log (5 x+3)}{1953125}",1,"(x*(233332204 + 388889830*x - 295988700*x^2 - 1467514125*x^3 - 799564500*x^4 + 1569881250*x^5 + 2187000000*x^6 + 797343750*x^7))/10937500 + (121*Log[3 + 5*x])/1953125","A",1
1291,1,46,58,0.0197954,"\int \frac{(1-2 x)^2 (2+3 x)^5}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^5)/(3 + 5*x),x]","\frac{x \left(60750000 x^6+122850000 x^5+27310500 x^4-89389125 x^3-50988700 x^2+21389830 x+23332204\right)}{2187500}+\frac{121 \log (5 x+3)}{390625}","\frac{972 x^7}{35}+\frac{1404 x^6}{25}+\frac{7803 x^5}{625}-\frac{102159 x^4}{2500}-\frac{72841 x^3}{3125}+\frac{305569 x^2}{31250}+\frac{833293 x}{78125}+\frac{121 \log (5 x+3)}{390625}",1,"(x*(23332204 + 21389830*x - 50988700*x^2 - 89389125*x^3 + 27310500*x^4 + 122850000*x^5 + 60750000*x^6))/2187500 + (121*Log[3 + 5*x])/390625","A",1
1292,1,41,51,0.0185522,"\int \frac{(1-2 x)^2 (2+3 x)^4}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^4)/(3 + 5*x),x]","\frac{x \left(675000 x^5+864000 x^4-394875 x^3-784100 x^2+55690 x+333172\right)}{62500}+\frac{121 \log (5 x+3)}{78125}","\frac{54 x^6}{5}+\frac{1728 x^5}{125}-\frac{3159 x^4}{500}-\frac{7841 x^3}{625}+\frac{5569 x^2}{6250}+\frac{83293 x}{15625}+\frac{121 \log (5 x+3)}{78125}",1,"(x*(333172 + 55690*x - 784100*x^2 - 394875*x^3 + 864000*x^4 + 675000*x^5))/62500 + (121*Log[3 + 5*x])/78125","A",1
1293,1,36,44,0.0179141,"\int \frac{(1-2 x)^2 (2+3 x)^3}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^3)/(3 + 5*x),x]","\frac{x \left(27000 x^4+13500 x^3-29550 x^2-9655 x+16586\right)}{6250}+\frac{121 \log (5 x+3)}{15625}","\frac{108 x^5}{25}+\frac{54 x^4}{25}-\frac{591 x^3}{125}-\frac{1931 x^2}{1250}+\frac{8293 x}{3125}+\frac{121 \log (5 x+3)}{15625}",1,"(x*(16586 - 9655*x - 29550*x^2 + 13500*x^3 + 27000*x^4))/6250 + (121*Log[3 + 5*x])/15625","A",1
1294,1,35,37,0.017036,"\int \frac{(1-2 x)^2 (2+3 x)^2}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^2)/(3 + 5*x),x]","\frac{2250 x^4-800 x^3-2155 x^2+1586 x+1263}{1250}+\frac{121 \log (5 x+3)}{3125}","\frac{9 x^4}{5}-\frac{16 x^3}{25}-\frac{431 x^2}{250}+\frac{793 x}{625}+\frac{121 \log (5 x+3)}{3125}",1,"(1263 + 1586*x - 2155*x^2 - 800*x^3 + 2250*x^4)/1250 + (121*Log[3 + 5*x])/3125","A",1
1295,1,26,30,0.0155678,"\int \frac{(1-2 x)^2 (2+3 x)}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x))/(3 + 5*x),x]","\frac{1}{125} x \left(100 x^2-140 x+43\right)+\frac{121}{625} \log (5 x+3)","\frac{4 x^3}{5}-\frac{28 x^2}{25}+\frac{43 x}{125}+\frac{121}{625} \log (5 x+3)",1,"(x*(43 - 140*x + 100*x^2))/125 + (121*Log[3 + 5*x])/625","A",1
1296,1,21,23,0.0099306,"\int \frac{(1-2 x)^2}{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/(3 + 5*x),x]","\frac{2}{25} x (5 x-16)+\frac{121}{125} \log (5 x+3)","\frac{2 x^2}{5}-\frac{32 x}{25}+\frac{121}{125} \log (5 x+3)",1,"(2*x*(-16 + 5*x))/25 + (121*Log[3 + 5*x])/125","A",1
1297,1,26,26,0.0145351,"\int \frac{(1-2 x)^2}{(2+3 x) (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)*(3 + 5*x)),x]","\frac{4 x}{15}-\frac{49}{9} \log (3 x+2)+\frac{121}{25} \log (5 x+3)","\frac{4 x}{15}-\frac{49}{9} \log (3 x+2)+\frac{121}{25} \log (5 x+3)",1,"(4*x)/15 - (49*Log[2 + 3*x])/9 + (121*Log[3 + 5*x])/25","A",1
1298,1,32,32,0.0261621,"\int \frac{(1-2 x)^2}{(2+3 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^2*(3 + 5*x)),x]","\frac{49}{9 (3 x+2)}-\frac{217}{9} \log (3 x+2)+\frac{121}{5} \log (5 x+3)","\frac{49}{9 (3 x+2)}-\frac{217}{9} \log (3 x+2)+\frac{121}{5} \log (5 x+3)",1,"49/(9*(2 + 3*x)) - (217*Log[2 + 3*x])/9 + (121*Log[3 + 5*x])/5","A",1
1299,1,33,39,0.0278936,"\int \frac{(1-2 x)^2}{(2+3 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^3*(3 + 5*x)),x]","\frac{7 (186 x+131)}{18 (3 x+2)^2}-121 \log (3 x+2)+121 \log (5 x+3)","\frac{217}{9 (3 x+2)}+\frac{49}{18 (3 x+2)^2}-121 \log (3 x+2)+121 \log (5 x+3)",1,"(7*(131 + 186*x))/(18*(2 + 3*x)^2) - 121*Log[2 + 3*x] + 121*Log[3 + 5*x]","A",1
1300,1,38,48,0.040539,"\int \frac{(1-2 x)^2}{(2+3 x)^4 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^4*(3 + 5*x)),x]","\frac{58806 x^2+80361 x+27536}{54 (3 x+2)^3}-605 \log (3 x+2)+605 \log (5 x+3)","\frac{121}{3 x+2}+\frac{217}{18 (3 x+2)^2}+\frac{49}{27 (3 x+2)^3}-605 \log (3 x+2)+605 \log (5 x+3)",1,"(27536 + 80361*x + 58806*x^2)/(54*(2 + 3*x)^3) - 605*Log[2 + 3*x] + 605*Log[3 + 5*x]","A",1
1301,1,43,59,0.0481938,"\int \frac{(1-2 x)^2}{(2+3 x)^5 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^5*(3 + 5*x)),x]","\frac{1764180 x^3+3587166 x^2+2433252 x+550739}{108 (3 x+2)^4}-3025 \log (3 x+2)+3025 \log (5 x+3)","\frac{605}{3 x+2}+\frac{121}{2 (3 x+2)^2}+\frac{217}{27 (3 x+2)^3}+\frac{49}{36 (3 x+2)^4}-3025 \log (3 x+2)+3025 \log (5 x+3)",1,"(550739 + 2433252*x + 3587166*x^2 + 1764180*x^3)/(108*(2 + 3*x)^4) - 3025*Log[2 + 3*x] + 3025*Log[3 + 5*x]","A",1
1302,1,48,70,0.060777,"\int \frac{(1-2 x)^2}{(2+3 x)^6 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^6*(3 + 5*x)),x]","\frac{44104500 x^4+119082150 x^3+120617640 x^2+54322575 x+9179006}{180 (3 x+2)^5}-15125 \log (3 x+2)+15125 \log (5 x+3)","\frac{3025}{3 x+2}+\frac{605}{2 (3 x+2)^2}+\frac{121}{3 (3 x+2)^3}+\frac{217}{36 (3 x+2)^4}+\frac{49}{45 (3 x+2)^5}-15125 \log (3 x+2)+15125 \log (5 x+3)",1,"(9179006 + 54322575*x + 120617640*x^2 + 119082150*x^3 + 44104500*x^4)/(180*(2 + 3*x)^5) - 15125*Log[2 + 3*x] + 15125*Log[3 + 5*x]","A",1
1303,1,53,81,0.0931116,"\int \frac{(1-2 x)^2}{(2+3 x)^7 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^7*(3 + 5*x)),x]","\frac{1984702500 x^5+6681831750 x^4+9000258300 x^3+6063045615 x^2+2042732232 x+275370238}{540 (3 x+2)^6}-75625 \log (3 x+2)+75625 \log (5 x+3)","\frac{15125}{3 x+2}+\frac{3025}{2 (3 x+2)^2}+\frac{605}{3 (3 x+2)^3}+\frac{121}{4 (3 x+2)^4}+\frac{217}{45 (3 x+2)^5}+\frac{49}{54 (3 x+2)^6}-75625 \log (3 x+2)+75625 \log (5 x+3)",1,"(275370238 + 2042732232*x + 6063045615*x^2 + 9000258300*x^3 + 6681831750*x^4 + 1984702500*x^5)/(540*(2 + 3*x)^6) - 75625*Log[2 + 3*x] + 75625*Log[3 + 5*x]","A",1
1304,1,58,92,0.1012305,"\int \frac{(1-2 x)^2}{(2+3 x)^8 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^8*(3 + 5*x)),x]","\frac{29770537500 x^6+120074501250 x^5+201822192000 x^4+180948267225 x^3+91271440062 x^2+24557875626 x+2753702432}{540 (3 x+2)^7}-378125 \log (3 x+2)+378125 \log (5 x+3)","\frac{75625}{3 x+2}+\frac{15125}{2 (3 x+2)^2}+\frac{3025}{3 (3 x+2)^3}+\frac{605}{4 (3 x+2)^4}+\frac{121}{5 (3 x+2)^5}+\frac{217}{54 (3 x+2)^6}+\frac{7}{9 (3 x+2)^7}-378125 \log (3 x+2)+378125 \log (5 x+3)",1,"(2753702432 + 24557875626*x + 91271440062*x^2 + 180948267225*x^3 + 201822192000*x^4 + 120074501250*x^5 + 29770537500*x^6)/(540*(2 + 3*x)^7) - 378125*Log[2 + 3*x] + 378125*Log[3 + 5*x]","A",1
1305,1,67,76,0.0395431,"\int \frac{(1-2 x)^2 (2+3 x)^7}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^7)/(3 + 5*x)^2,x]","\frac{299003906250 x^9+1022308593750 x^8+1142289843750 x^7+94742156250 x^6-757103878125 x^5-483208621875 x^4+74537846250 x^3+189581876750 x^2+74994343395 x+9997654777}{1367187500 (5 x+3)}+\frac{2497 \log (5 x+3)}{9765625}","\frac{2187 x^8}{50}+\frac{107892 x^7}{875}+\frac{116397 x^6}{1250}-\frac{656424 x^5}{15625}-\frac{213867 x^4}{2500}-\frac{1512378 x^3}{78125}+\frac{17592879 x^2}{781250}+\frac{27776932 x}{1953125}-\frac{121}{9765625 (5 x+3)}+\frac{2497 \log (5 x+3)}{9765625}",1,"(9997654777 + 74994343395*x + 189581876750*x^2 + 74537846250*x^3 - 483208621875*x^4 - 757103878125*x^5 + 94742156250*x^6 + 1142289843750*x^7 + 1022308593750*x^8 + 299003906250*x^9)/(1367187500*(3 + 5*x)) + (2497*Log[3 + 5*x])/9765625","A",1
1306,1,62,69,0.0447613,"\int \frac{(1-2 x)^2 (2+3 x)^6}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^6)/(3 + 5*x)^2,x]","\frac{11390625000 x^8+30754687500 x^7+20677781250 x^6-13442034375 x^5-21011090625 x^4-2349191250 x^3+7291044250 x^2+3997343145 x+648854027}{136718750 (5 x+3)}+\frac{2134 \log (5 x+3)}{1953125}","\frac{2916 x^7}{175}+\frac{4374 x^6}{125}+\frac{28917 x^5}{3125}-\frac{157599 x^4}{6250}-\frac{48771 x^3}{3125}+\frac{463086 x^2}{78125}+\frac{2777053 x}{390625}-\frac{121}{1953125 (5 x+3)}+\frac{2134 \log (5 x+3)}{1953125}",1,"(648854027 + 3997343145*x + 7291044250*x^2 - 2349191250*x^3 - 21011090625*x^4 - 13442034375*x^5 + 20677781250*x^6 + 30754687500*x^7 + 11390625000*x^8)/(136718750*(3 + 5*x)) + (2134*Log[3 + 5*x])/1953125","A",1
1307,1,57,62,0.0414349,"\int \frac{(1-2 x)^2 (2+3 x)^5}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^5)/(3 + 5*x)^2,x]","\frac{253125000 x^7+496125000 x^6+70284375 x^5-398409375 x^4-178158750 x^3+145685750 x^2+126267855 x+25866973}{7812500 (5 x+3)}+\frac{1771 \log (5 x+3)}{390625}","\frac{162 x^6}{25}+\frac{5508 x^5}{625}-\frac{8721 x^4}{2500}-\frac{25332 x^3}{3125}+\frac{1893 x^2}{6250}+\frac{277174 x}{78125}-\frac{121}{390625 (5 x+3)}+\frac{1771 \log (5 x+3)}{390625}",1,"(25866973 + 126267855*x + 145685750*x^2 - 178158750*x^3 - 398409375*x^4 + 70284375*x^5 + 496125000*x^6 + 253125000*x^7)/(7812500*(3 + 5*x)) + (1771*Log[3 + 5*x])/390625","A",1
1308,1,52,55,0.0403433,"\int \frac{(1-2 x)^2 (2+3 x)^4}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^4)/(3 + 5*x)^2,x]","\frac{5062500 x^6+5990625 x^5-3881250 x^4-5655000 x^3+2054000 x^2+3698835 x+990421}{390625 (5 x+3)}+\frac{1408 \log (5 x+3)}{78125}","\frac{324 x^5}{125}+\frac{189 x^4}{125}-\frac{1809 x^3}{625}-\frac{3621 x^2}{3125}+\frac{5459 x}{3125}-\frac{121}{78125 (5 x+3)}+\frac{1408 \log (5 x+3)}{78125}",1,"(990421 + 3698835*x + 2054000*x^2 - 5655000*x^3 - 3881250*x^4 + 5990625*x^5 + 5062500*x^6)/(390625*(3 + 5*x)) + (1408*Log[3 + 5*x])/78125","A",1
1309,1,47,48,0.0385443,"\int \frac{(1-2 x)^2 (2+3 x)^3}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^3)/(3 + 5*x)^2,x]","\frac{33750 x^5+11250 x^4-41625 x^3+2425 x^2+35715 x+12683}{6250 (5 x+3)}+\frac{209 \log (5 x+3)}{3125}","\frac{27 x^4}{25}-\frac{36 x^3}{125}-\frac{1449 x^2}{1250}+\frac{2416 x}{3125}-\frac{121}{15625 (5 x+3)}+\frac{209 \log (5 x+3)}{3125}",1,"(12683 + 35715*x + 2425*x^2 - 41625*x^3 + 11250*x^4 + 33750*x^5)/(6250*(3 + 5*x)) + (209*Log[3 + 5*x])/3125","A",1
1310,1,42,41,0.02514,"\int \frac{(1-2 x)^2 (2+3 x)^2}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^2)/(3 + 5*x)^2,x]","\frac{1500 x^4-1050 x^3-985 x^2+1248 x+658}{625 (5 x+3)}+\frac{682 \log (5 x+3)}{3125}","\frac{12 x^3}{25}-\frac{78 x^2}{125}+\frac{37 x}{625}-\frac{121}{3125 (5 x+3)}+\frac{682 \log (5 x+3)}{3125}",1,"(658 + 1248*x - 985*x^2 - 1050*x^3 + 1500*x^4)/(625*(3 + 5*x)) + (682*Log[3 + 5*x])/3125","A",1
1311,1,37,34,0.0214401,"\int \frac{(1-2 x)^2 (2+3 x)}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x))/(3 + 5*x)^2,x]","\frac{1500 x^3-3700 x^2-835 x+913}{1250 (5 x+3)}+\frac{319}{625} \log (5 x+3)","\frac{6 x^2}{25}-\frac{92 x}{125}-\frac{121}{625 (5 x+3)}+\frac{319}{625} \log (5 x+3)",1,"(913 - 835*x - 3700*x^2 + 1500*x^3)/(1250*(3 + 5*x)) + (319*Log[3 + 5*x])/625","A",1
1312,1,32,27,0.0172828,"\int \frac{(1-2 x)^2}{(3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/(3 + 5*x)^2,x]","\frac{100 x^2+10 x-151}{125 (5 x+3)}-\frac{44}{125} \log (5 x+3)","\frac{4 x}{25}-\frac{121}{125 (5 x+3)}-\frac{44}{125} \log (5 x+3)",1,"(-151 + 10*x + 100*x^2)/(125*(3 + 5*x)) - (44*Log[3 + 5*x])/125","A",1
1313,1,32,32,0.0279414,"\int \frac{(1-2 x)^2}{(2+3 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)*(3 + 5*x)^2),x]","-\frac{121}{25 (5 x+3)}+\frac{49}{3} \log (3 x+2)-\frac{407}{25} \log (5 x+3)","-\frac{121}{25 (5 x+3)}+\frac{49}{3} \log (3 x+2)-\frac{407}{25} \log (5 x+3)",1,"-121/(25*(3 + 5*x)) + (49*Log[2 + 3*x])/3 - (407*Log[3 + 5*x])/25","A",1
1314,1,38,39,0.0448096,"\int \frac{(1-2 x)^2}{(2+3 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{-2314 x-1461}{15 \left(15 x^2+19 x+6\right)}+154 \log (3 x+2)-154 \log (5 x+3)","-\frac{49}{3 (3 x+2)}-\frac{121}{5 (5 x+3)}+154 \log (3 x+2)-154 \log (5 x+3)",1,"(-1461 - 2314*x)/(15*(6 + 19*x + 15*x^2)) + 154*Log[2 + 3*x] - 154*Log[3 + 5*x]","A",1
1315,1,45,46,0.038091,"\int \frac{(1-2 x)^2}{(2+3 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^3*(3 + 5*x)^2),x]","\frac{-20394 x^2-26513 x-8595}{6 (3 x+2)^2 (5 x+3)}+1133 \log (3 x+2)-1133 \log (5 x+3)","-\frac{154}{3 x+2}-\frac{121}{5 x+3}-\frac{49}{6 (3 x+2)^2}+1133 \log (3 x+2)-1133 \log (5 x+3)",1,"(-8595 - 26513*x - 20394*x^2)/(6*(2 + 3*x)^2*(3 + 5*x)) + 1133*Log[2 + 3*x] - 1133*Log[3 + 5*x]","A",1
1316,1,50,55,0.04774,"\int \frac{(1-2 x)^2}{(2+3 x)^4 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^4*(3 + 5*x)^2),x]","\frac{-605880 x^3-1191564 x^2-780464 x-170229}{9 (3 x+2)^3 (5 x+3)}+7480 \log (3 x+2)-7480 \log (5 x+3)","-\frac{1133}{3 x+2}-\frac{605}{5 x+3}-\frac{77}{(3 x+2)^2}-\frac{49}{9 (3 x+2)^3}+7480 \log (3 x+2)-7480 \log (5 x+3)",1,"(-170229 - 780464*x - 1191564*x^2 - 605880*x^3)/(9*(2 + 3*x)^3*(3 + 5*x)) + 7480*Log[2 + 3*x] - 7480*Log[3 + 5*x]","A",1
1317,1,55,68,0.1017278,"\int \frac{(1-2 x)^2}{(2+3 x)^5 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^5*(3 + 5*x)^2),x]","\frac{-5019300 x^4-13217490 x^3-13046462 x^2-5720639 x-940153}{4 (3 x+2)^4 (5 x+3)}+46475 \log (3 x+2)-46475 \log (5 x+3)","-\frac{7480}{3 x+2}-\frac{3025}{5 x+3}-\frac{1133}{2 (3 x+2)^2}-\frac{154}{3 (3 x+2)^3}-\frac{49}{12 (3 x+2)^4}+46475 \log (3 x+2)-46475 \log (5 x+3)",1,"(-940153 - 5720639*x - 13046462*x^2 - 13217490*x^3 - 5019300*x^4)/(4*(2 + 3*x)^4*(3 + 5*x)) + 46475*Log[2 + 3*x] - 46475*Log[3 + 5*x]","A",1
1318,1,60,77,0.0897493,"\int \frac{(1-2 x)^2}{(2+3 x)^6 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^6*(3 + 5*x)^2),x]","\frac{-674932500 x^5-2227277250 x^4-2939206050 x^3-1938789435 x^2-639246515 x-84279984}{30 (3 x+2)^5 (5 x+3)}+277750 \log (3 x+2)-277750 \log (5 x+3)","-\frac{46475}{3 x+2}-\frac{15125}{5 x+3}-\frac{3740}{(3 x+2)^2}-\frac{1133}{3 (3 x+2)^3}-\frac{77}{2 (3 x+2)^4}-\frac{49}{15 (3 x+2)^5}+277750 \log (3 x+2)-277750 \log (5 x+3)",1,"(-84279984 - 639246515*x - 1938789435*x^2 - 2939206050*x^3 - 2227277250*x^4 - 674932500*x^5)/(30*(2 + 3*x)^5*(3 + 5*x)) + 277750*Log[2 + 3*x] - 277750*Log[3 + 5*x]","A",1
1319,1,65,90,0.1312798,"\int \frac{(1-2 x)^2}{(2+3 x)^7 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^7*(3 + 5*x)^2),x]","\frac{-70667437500 x^6-280314168750 x^5-463211966250 x^4-408159415125 x^3-202262350455 x^2-53445037346 x-5882909754}{180 (3 x+2)^6 (5 x+3)}+1615625 \log (3 x+2)-1615625 \log (5 x+3)","-\frac{277750}{3 x+2}-\frac{75625}{5 x+3}-\frac{46475}{2 (3 x+2)^2}-\frac{7480}{3 (3 x+2)^3}-\frac{1133}{4 (3 x+2)^4}-\frac{154}{5 (3 x+2)^5}-\frac{49}{18 (3 x+2)^6}+1615625 \log (3 x+2)-1615625 \log (5 x+3)",1,"(-5882909754 - 53445037346*x - 202262350455*x^2 - 408159415125*x^3 - 463211966250*x^4 - 280314168750*x^5 - 70667437500*x^6)/(180*(2 + 3*x)^6*(3 + 5*x)) + 1615625*Log[2 + 3*x] - 1615625*Log[3 + 5*x]","A",1
1320,1,70,97,0.1074202,"\int \frac{(1-2 x)^2}{(2+3 x)^8 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^8*(3 + 5*x)^2),x]","\frac{-100738687500 x^7-466755918750 x^6-926721303750 x^5-1022059900125 x^4-676227617505 x^3-268408563588 x^2-59178013234 x-5590850403}{15 (3 x+2)^7 (5 x+3)}+9212500 \log (3 x+2)-9212500 \log (5 x+3)","-\frac{1615625}{3 x+2}-\frac{378125}{5 x+3}-\frac{138875}{(3 x+2)^2}-\frac{46475}{3 (3 x+2)^3}-\frac{1870}{(3 x+2)^4}-\frac{1133}{5 (3 x+2)^5}-\frac{77}{3 (3 x+2)^6}-\frac{7}{3 (3 x+2)^7}+9212500 \log (3 x+2)-9212500 \log (5 x+3)",1,"(-5590850403 - 59178013234*x - 268408563588*x^2 - 676227617505*x^3 - 1022059900125*x^4 - 926721303750*x^5 - 466755918750*x^6 - 100738687500*x^7)/(15*(2 + 3*x)^7*(3 + 5*x)) + 9212500*Log[2 + 3*x] - 9212500*Log[3 + 5*x]","A",1
1321,1,72,87,0.0438217,"\int \frac{(1-2 x)^2 (2+3 x)^8}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^8)/(3 + 5*x)^3,x]","\frac{448505859375 x^{10}+1836738281250 x^9+2748937500000 x^8+1294582500000 x^7-1049233500000 x^6-1497169800000 x^5-372682800000 x^4+369438720000 x^3+310701230325 x^2+92853841190 x+10358007077}{683593750 (5 x+3)^2}+\frac{5888 \log (5 x+3)}{9765625}","\frac{6561 x^8}{250}+\frac{332424 x^7}{4375}+\frac{376407 x^6}{6250}-\frac{74601 x^5}{3125}-\frac{1700919 x^4}{31250}-\frac{5350194 x^3}{390625}+\frac{55559043 x^2}{3906250}+\frac{92582457 x}{9765625}-\frac{572}{9765625 (5 x+3)}-\frac{121}{97656250 (5 x+3)^2}+\frac{5888 \log (5 x+3)}{9765625}",1,"(10358007077 + 92853841190*x + 310701230325*x^2 + 369438720000*x^3 - 372682800000*x^4 - 1497169800000*x^5 - 1049233500000*x^6 + 1294582500000*x^7 + 2748937500000*x^8 + 1836738281250*x^9 + 448505859375*x^10)/(683593750*(3 + 5*x)^2) + (5888*Log[3 + 5*x])/9765625","A",1
1322,1,67,80,0.0400139,"\int \frac{(1-2 x)^2 (2+3 x)^7}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^7)/(3 + 5*x)^3,x]","\frac{341718750000 x^9+1154250000000 x^8+1244084062500 x^7+11543765625 x^6-909633768750 x^5-496018096875 x^4+179818432500 x^3+275860261575 x^2+103624499690 x+13601177777}{1367187500 (5 x+3)^2}+\frac{21949 \log (5 x+3)}{9765625}","\frac{8748 x^7}{875}+\frac{13608 x^6}{625}+\frac{104247 x^5}{15625}-\frac{193833 x^4}{12500}-\frac{162612 x^3}{15625}+\frac{1390203 x^2}{390625}+\frac{9251661 x}{1953125}-\frac{2497}{9765625 (5 x+3)}-\frac{121}{19531250 (5 x+3)^2}+\frac{21949 \log (5 x+3)}{9765625}",1,"(13601177777 + 103624499690*x + 275860261575*x^2 + 179818432500*x^3 - 496018096875*x^4 - 909633768750*x^5 + 11543765625*x^6 + 1244084062500*x^7 + 1154250000000*x^8 + 341718750000*x^9)/(1367187500*(3 + 5*x)^2) + (21949*Log[3 + 5*x])/9765625","A",1
1323,1,62,73,0.0471617,"\int \frac{(1-2 x)^2 (2+3 x)^6}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^6)/(3 + 5*x)^3,x]","\frac{3796875000 x^8+10023750000 x^7+6086390625 x^6-5334918750 x^5-6763246875 x^4+481792500 x^3+3528738675 x^2+1743814610 x+274543613}{39062500 (5 x+3)^2}+\frac{15547 \log (5 x+3)}{1953125}","\frac{486 x^6}{125}+\frac{17496 x^5}{3125}-\frac{23571 x^4}{12500}-\frac{16299 x^3}{3125}+\frac{189 x^2}{15625}+\frac{920502 x}{390625}-\frac{2134}{1953125 (5 x+3)}-\frac{121}{3906250 (5 x+3)^2}+\frac{15547 \log (5 x+3)}{1953125}",1,"(274543613 + 1743814610*x + 3528738675*x^2 + 481792500*x^3 - 6763246875*x^4 - 5334918750*x^5 + 6086390625*x^6 + 10023750000*x^7 + 3796875000*x^8)/(39062500*(3 + 5*x)^2) + (15547*Log[3 + 5*x])/1953125","A",1
1324,1,57,66,0.0429376,"\int \frac{(1-2 x)^2 (2+3 x)^5}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^5)/(3 + 5*x)^3,x]","\frac{151875000 x^7+283500000 x^6+4331250 x^5-252590625 x^4-50032500 x^3+161774550 x^2+109699660 x+20870428}{3906250 (5 x+3)^2}+\frac{10234 \log (5 x+3)}{390625}","\frac{972 x^5}{625}+\frac{648 x^4}{625}-\frac{5499 x^3}{3125}-\frac{5301 x^2}{6250}+\frac{17796 x}{15625}-\frac{1771}{390625 (5 x+3)}-\frac{121}{781250 (5 x+3)^2}+\frac{10234 \log (5 x+3)}{390625}",1,"(20870428 + 109699660*x + 161774550*x^2 - 50032500*x^3 - 252590625*x^4 + 4331250*x^5 + 283500000*x^6 + 151875000*x^7)/(3906250*(3 + 5*x)^2) + (10234*Log[3 + 5*x])/390625","A",1
1325,1,52,59,0.0439743,"\int \frac{(1-2 x)^2 (2+3 x)^4}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^4)/(3 + 5*x)^3,x]","\frac{506250 x^6+517500 x^5-523125 x^4-394500 x^3+553500 x^2+536320 x+121714}{31250 (5 x+3)^2}+\frac{1202 \log (5 x+3)}{15625}","\frac{81 x^4}{125}-\frac{72 x^3}{625}-\frac{4779 x^2}{6250}+\frac{1419 x}{3125}-\frac{1408}{78125 (5 x+3)}-\frac{121}{156250 (5 x+3)^2}+\frac{1202 \log (5 x+3)}{15625}",1,"(121714 + 536320*x + 553500*x^2 - 394500*x^3 - 523125*x^4 + 517500*x^5 + 506250*x^6)/(31250*(3 + 5*x)^2) + (1202*Log[3 + 5*x])/15625","A",1
1326,1,42,52,0.0413808,"\int \frac{(1-2 x)^2 (2+3 x)^3}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^3)/(3 + 5*x)^3,x]","\frac{45000 x^5-56250 x^3-4050 x^2+24640 x+7567}{6250 (5 x+3)^2}+\frac{23}{125} \log (5 x+3)","\frac{36 x^3}{125}-\frac{216 x^2}{625}-\frac{153 x}{3125}-\frac{209}{3125 (5 x+3)}-\frac{121}{31250 (5 x+3)^2}+\frac{23}{125} \log (5 x+3)",1,"(7567 + 24640*x - 4050*x^2 - 56250*x^3 + 45000*x^5)/(6250*(3 + 5*x)^2) + (23*Log[3 + 5*x])/125","A",1
1327,1,42,45,0.0252397,"\int \frac{(1-2 x)^2 (2+3 x)^2}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x)^2)/(3 + 5*x)^3,x]","\frac{4500 x^4-7800 x^3-23760 x^2-17564 x-4277}{1250 (5 x+3)^2}+\frac{829 \log (5 x+3)}{3125}","\frac{18 x^2}{125}-\frac{264 x}{625}-\frac{682}{3125 (5 x+3)}-\frac{121}{6250 (5 x+3)^2}+\frac{829 \log (5 x+3)}{3125}",1,"(-4277 - 17564*x - 23760*x^2 - 7800*x^3 + 4500*x^4)/(1250*(3 + 5*x)^2) + (829*Log[3 + 5*x])/3125","A",1
1328,1,37,38,0.0264994,"\int \frac{(1-2 x)^2 (2+3 x)}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^2*(2 + 3*x))/(3 + 5*x)^3,x]","\frac{600 x^3+420 x^2-782 x-515}{250 (5 x+3)^2}-\frac{128}{625} \log (5 x+3)","\frac{12 x}{125}-\frac{319}{625 (5 x+3)}-\frac{121}{1250 (5 x+3)^2}-\frac{128}{625} \log (5 x+3)",1,"(-515 - 782*x + 420*x^2 + 600*x^3)/(250*(3 + 5*x)^2) - (128*Log[3 + 5*x])/625","A",1
1329,1,27,33,0.0182852,"\int \frac{(1-2 x)^2}{(3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/(3 + 5*x)^3,x]","\frac{11 (40 x+13)}{250 (5 x+3)^2}+\frac{4}{125} \log (5 x+3)","\frac{44}{125 (5 x+3)}-\frac{121}{250 (5 x+3)^2}+\frac{4}{125} \log (5 x+3)",1,"(11*(13 + 40*x))/(250*(3 + 5*x)^2) + (4*Log[3 + 5*x])/125","A",1
1330,1,33,39,0.0280091,"\int \frac{(1-2 x)^2}{(2+3 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)*(3 + 5*x)^3),x]","\frac{11 (370 x+211)}{50 (5 x+3)^2}-49 \log (3 x+2)+49 \log (5 x+3)","\frac{407}{25 (5 x+3)}-\frac{121}{50 (5 x+3)^2}-49 \log (3 x+2)+49 \log (5 x+3)",1,"(11*(211 + 370*x))/(50*(3 + 5*x)^2) - 49*Log[2 + 3*x] + 49*Log[3 + 5*x]","A",1
1331,1,45,46,0.0374047,"\int \frac{(1-2 x)^2}{(2+3 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{35350 x^2+43597 x+13408}{10 (3 x+2) (5 x+3)^2}-707 \log (3 x+2)+707 \log (5 x+3)","\frac{49}{3 x+2}+\frac{154}{5 x+3}-\frac{121}{10 (5 x+3)^2}-707 \log (3 x+2)+707 \log (5 x+3)",1,"(13408 + 43597*x + 35350*x^2)/(10*(2 + 3*x)*(3 + 5*x)^2) - 707*Log[2 + 3*x] + 707*Log[3 + 5*x]","A",1
1332,1,50,57,0.0412537,"\int \frac{(1-2 x)^2}{(2+3 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{208020 x^3+395238 x^2+249932 x+52601}{2 (3 x+2)^2 (5 x+3)^2}-6934 \log (3 x+2)+6934 \log (5 x+3)","\frac{707}{3 x+2}+\frac{1133}{5 x+3}+\frac{49}{2 (3 x+2)^2}-\frac{121}{2 (5 x+3)^2}-6934 \log (3 x+2)+6934 \log (5 x+3)",1,"(52601 + 249932*x + 395238*x^2 + 208020*x^3)/(2*(2 + 3*x)^2*(3 + 5*x)^2) - 6934*Log[2 + 3*x] + 6934*Log[3 + 5*x]","A",1
1333,1,55,68,0.0659298,"\int \frac{(1-2 x)^2}{(2+3 x)^4 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^4*(3 + 5*x)^3),x]","\frac{15419700 x^4+39577230 x^3+38058104 x^2+16250079 x+2599404}{6 (3 x+2)^3 (5 x+3)^2}-57110 \log (3 x+2)+57110 \log (5 x+3)","\frac{6934}{3 x+2}+\frac{7480}{5 x+3}+\frac{707}{2 (3 x+2)^2}-\frac{605}{2 (5 x+3)^2}+\frac{49}{3 (3 x+2)^3}-57110 \log (3 x+2)+57110 \log (5 x+3)",1,"(2599404 + 16250079*x + 38058104*x^2 + 39577230*x^3 + 15419700*x^4)/(6*(2 + 3*x)^3*(3 + 5*x)^2) - 57110*Log[2 + 3*x] + 57110*Log[3 + 5*x]","A",1
1334,1,60,77,0.0751816,"\int \frac{(1-2 x)^2}{(2+3 x)^5 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^5*(3 + 5*x)^3),x]","\frac{688459500 x^5+2226019050 x^4+2877250740 x^3+1858347679 x^2+599747838 x+77372211}{12 (3 x+2)^4 (5 x+3)^2}-424975 \log (3 x+2)+424975 \log (5 x+3)","\frac{57110}{3 x+2}+\frac{46475}{5 x+3}+\frac{3467}{(3 x+2)^2}-\frac{3025}{2 (5 x+3)^2}+\frac{707}{3 (3 x+2)^3}+\frac{49}{4 (3 x+2)^4}-424975 \log (3 x+2)+424975 \log (5 x+3)",1,"(77372211 + 599747838*x + 1858347679*x^2 + 2877250740*x^3 + 2226019050*x^4 + 688459500*x^5)/(12*(2 + 3*x)^4*(3 + 5*x)^2) - 424975*Log[2 + 3*x] + 424975*Log[3 + 5*x]","A",1
1335,1,65,88,0.0929639,"\int \frac{(1-2 x)^2}{(2+3 x)^6 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^6*(3 + 5*x)^3),x]","\frac{71882437500 x^6+280341506250 x^5+455361930000 x^4+394308004875 x^3+191974077080 x^2+49825144515 x+5385650262}{60 (3 x+2)^5 (5 x+3)^2}-2958125 \log (3 x+2)+2958125 \log (5 x+3)","\frac{424975}{3 x+2}+\frac{277750}{5 x+3}+\frac{28555}{(3 x+2)^2}-\frac{15125}{2 (5 x+3)^2}+\frac{6934}{3 (3 x+2)^3}+\frac{707}{4 (3 x+2)^4}+\frac{49}{5 (3 x+2)^5}-2958125 \log (3 x+2)+2958125 \log (5 x+3)",1,"(5385650262 + 49825144515*x + 191974077080*x^2 + 394308004875*x^3 + 455361930000*x^4 + 280341506250*x^5 + 71882437500*x^6)/(60*(2 + 3*x)^5*(3 + 5*x)^2) - 2958125*Log[2 + 3*x] + 2958125*Log[3 + 5*x]","A",1
1336,1,70,101,0.1036309,"\int \frac{(1-2 x)^2}{(2+3 x)^7 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^7*(3 + 5*x)^3),x]","\frac{238595625000 x^7+1089586687500 x^6+2131807725000 x^5+2316445391250 x^4+1509746867100 x^3+590188362770 x^2+128130976648 x+11917538647}{10 (3 x+2)^6 (5 x+3)^2}-19637500 \log (3 x+2)+19637500 \log (5 x+3)","\frac{2958125}{3 x+2}+\frac{1615625}{5 x+3}+\frac{424975}{2 (3 x+2)^2}-\frac{75625}{2 (5 x+3)^2}+\frac{57110}{3 (3 x+2)^3}+\frac{3467}{2 (3 x+2)^4}+\frac{707}{5 (3 x+2)^5}+\frac{49}{6 (3 x+2)^6}-19637500 \log (3 x+2)+19637500 \log (5 x+3)",1,"(11917538647 + 128130976648*x + 590188362770*x^2 + 1509746867100*x^3 + 2316445391250*x^4 + 2131807725000*x^5 + 1089586687500*x^6 + 238595625000*x^7)/(10*(2 + 3*x)^6*(3 + 5*x)^2) - 19637500*Log[2 + 3*x] + 19637500*Log[3 + 5*x]","A",1
1337,1,75,110,0.1191941,"\int \frac{(1-2 x)^2}{(2+3 x)^8 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^2/((2 + 3*x)^8*(3 + 5*x)^3),x]","\frac{4586321250000 x^8+24001747875000 x^7+54940731300000 x^6+71845684942500 x^5+58705292494800 x^4+30691745453460 x^3+10026079791288 x^2+1871049429619 x+152720488888}{10 (3 x+2)^7 (5 x+3)^2}-125825000 \log (3 x+2)+125825000 \log (5 x+3)","\frac{19637500}{3 x+2}+\frac{9212500}{5 x+3}+\frac{2958125}{2 (3 x+2)^2}-\frac{378125}{2 (5 x+3)^2}+\frac{424975}{3 (3 x+2)^3}+\frac{28555}{2 (3 x+2)^4}+\frac{6934}{5 (3 x+2)^5}+\frac{707}{6 (3 x+2)^6}+\frac{7}{(3 x+2)^7}-125825000 \log (3 x+2)+125825000 \log (5 x+3)",1,"(152720488888 + 1871049429619*x + 10026079791288*x^2 + 30691745453460*x^3 + 58705292494800*x^4 + 71845684942500*x^5 + 54940731300000*x^6 + 24001747875000*x^7 + 4586321250000*x^8)/(10*(2 + 3*x)^7*(3 + 5*x)^2) - 125825000*Log[2 + 3*x] + 125825000*Log[3 + 5*x]","A",1
1338,1,68,56,0.0119816,"\int (1-2 x)^3 (2+3 x)^8 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^8*(3 + 5*x),x]","\frac{-28868400 x^{13}-138648510 x^{12}-255689460 x^{11}-184551939 x^{10}+54813330 x^9+183629160 x^8+96164640 x^7-24962080 x^6-45677632 x^5-13178880 x^4+4759040 x^3+4209920 x^2+1098240 x}{1430}","-\frac{40 (3 x+2)^{13}}{3159}+\frac{107}{729} (3 x+2)^{12}-\frac{518}{891} (3 x+2)^{11}+\frac{2009 (3 x+2)^{10}}{2430}-\frac{343 (3 x+2)^9}{2187}",1,"(1098240*x + 4209920*x^2 + 4759040*x^3 - 13178880*x^4 - 45677632*x^5 - 24962080*x^6 + 96164640*x^7 + 183629160*x^8 + 54813330*x^9 - 184551939*x^10 - 255689460*x^11 - 138648510*x^12 - 28868400*x^13)/1430","A",1
1339,1,63,56,0.0107677,"\int (1-2 x)^3 (2+3 x)^7 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^7*(3 + 5*x),x]","\frac{1}{440} \left(-3207600 x^{12}-13180320 x^{11}-19181448 x^{10}-6823080 x^9+11441925 x^8+12806640 x^7+1546160 x^6-4309184 x^5-2265120 x^4+211200 x^3+520960 x^2+168960 x\right)","-\frac{10}{729} (3 x+2)^{12}+\frac{428 (3 x+2)^{11}}{2673}-\frac{259}{405} (3 x+2)^{10}+\frac{2009 (3 x+2)^9}{2187}-\frac{343 (3 x+2)^8}{1944}",1,"(168960*x + 520960*x^2 + 211200*x^3 - 2265120*x^4 - 4309184*x^5 + 1546160*x^6 + 12806640*x^7 + 11441925*x^8 - 6823080*x^9 - 19181448*x^10 - 13180320*x^11 - 3207600*x^12)/440","A",1
1340,1,58,56,0.0094824,"\int (1-2 x)^3 (2+3 x)^6 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x),x]","\frac{1}{440} \left(-1166400 x^{11}-3977424 x^{10}-4158000 x^9+559845 x^8+3932280 x^7+1921920 x^6-919072 x^5-1029600 x^4-91520 x^3+197120 x^2+84480 x\right)","-\frac{40 (3 x+2)^{11}}{2673}+\frac{214 (3 x+2)^{10}}{1215}-\frac{518}{729} (3 x+2)^9+\frac{2009 (3 x+2)^8}{1944}-\frac{49}{243} (3 x+2)^7",1,"(84480*x + 197120*x^2 - 91520*x^3 - 1029600*x^4 - 919072*x^5 + 1921920*x^6 + 3932280*x^7 + 559845*x^8 - 4158000*x^9 - 3977424*x^10 - 1166400*x^11)/440","A",1
1341,1,53,56,0.009442,"\int (1-2 x)^3 (2+3 x)^5 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^5*(3 + 5*x),x]","\frac{1}{4} \left(-3888 x^{10}-10512 x^9-6291 x^8+6732 x^7+8666 x^6+56 x^5-3528 x^4-1024 x^3+608 x^2+384 x\right)","-\frac{4}{243} (3 x+2)^{10}+\frac{428 (3 x+2)^9}{2187}-\frac{259}{324} (3 x+2)^8+\frac{287}{243} (3 x+2)^7-\frac{343 (3 x+2)^6}{1458}",1,"(384*x + 608*x^2 - 1024*x^3 - 3528*x^4 + 56*x^5 + 8666*x^6 + 6732*x^7 - 6291*x^8 - 10512*x^9 - 3888*x^10)/4","A",1
1342,1,48,56,0.0091716,"\int (1-2 x)^3 (2+3 x)^4 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x),x]","\frac{1}{10} \left(-3600 x^9-7155 x^8-540 x^7+6965 x^6+3094 x^5-2520 x^4-1680 x^3+400 x^2+480 x\right)","-\frac{40 (3 x+2)^9}{2187}+\frac{107}{486} (3 x+2)^8-\frac{74}{81} (3 x+2)^7+\frac{2009 (3 x+2)^6}{1458}-\frac{343 (3 x+2)^5}{1215}",1,"(480*x + 400*x^2 - 1680*x^3 - 2520*x^4 + 3094*x^5 + 6965*x^6 - 540*x^7 - 7155*x^8 - 3600*x^9)/10","A",1
1343,1,43,45,0.0074963,"\int (1-2 x)^3 (2+3 x)^3 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x),x]","\frac{1}{140} \left(-18900 x^8-23760 x^7+15540 x^6+26572 x^5-4095 x^4-12040 x^3+280 x^2+3360 x\right)","-135 x^8-\frac{1188 x^7}{7}+111 x^6+\frac{949 x^5}{5}-\frac{117 x^4}{4}-86 x^3+2 x^2+24 x",1,"(3360*x + 280*x^2 - 12040*x^3 - 4095*x^4 + 26572*x^5 + 15540*x^6 - 23760*x^7 - 18900*x^8)/140","A",1
1344,1,38,40,0.0064456,"\int (1-2 x)^3 (2+3 x)^2 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x),x]","\frac{1}{140} \left(-7200 x^7-3640 x^6+9128 x^5+3465 x^4-4900 x^3-1120 x^2+1680 x\right)","-\frac{360 x^7}{7}-26 x^6+\frac{326 x^5}{5}+\frac{99 x^4}{4}-35 x^3-8 x^2+12 x",1,"(1680*x - 1120*x^2 - 4900*x^3 + 3465*x^4 + 9128*x^5 - 3640*x^6 - 7200*x^7)/140","A",1
1345,1,33,34,0.0058488,"\int (1-2 x)^3 (2+3 x) (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)*(3 + 5*x),x]","\frac{1}{10} \left(-200 x^6+56 x^5+225 x^4-90 x^3-85 x^2+60 x\right)","-\frac{5}{16} (1-2 x)^6+\frac{17}{10} (1-2 x)^5-\frac{77}{32} (1-2 x)^4",1,"(60*x - 85*x^2 - 90*x^3 + 225*x^4 + 56*x^5 - 200*x^6)/10","A",1
1346,1,28,23,0.0054342,"\int (1-2 x)^3 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(3 + 5*x),x]","\frac{1}{2} \left(-16 x^5+18 x^4+4 x^3-13 x^2+6 x\right)","\frac{1}{4} (1-2 x)^5-\frac{11}{16} (1-2 x)^4",1,"(6*x - 13*x^2 + 4*x^3 + 18*x^4 - 16*x^5)/2","A",1
1347,1,31,37,0.0193167,"\int \frac{(1-2 x)^3 (3+5 x)}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x),x]","-\frac{1}{81} x \left(270 x^3-564 x^2+483 x-293\right)-\frac{343}{243} \log (3 x+2)","-\frac{10 x^4}{3}+\frac{188 x^3}{27}-\frac{161 x^2}{27}+\frac{293 x}{81}-\frac{343}{243} \log (3 x+2)",1,"-1/81*(x*(-293 + 483*x - 564*x^2 + 270*x^3)) - (343*Log[2 + 3*x])/243","A",1
1348,1,42,41,0.0236022,"\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^2,x]","\frac{-2160 x^4+5796 x^3-10620 x^2-4113 x+4808}{486 (3 x+2)}+\frac{2009}{243} \log (3 x+2)","-\frac{40 x^3}{27}+\frac{134 x^2}{27}-\frac{286 x}{27}+\frac{343}{243 (3 x+2)}+\frac{2009}{243} \log (3 x+2)",1,"(4808 - 4113*x - 10620*x^2 + 5796*x^3 - 2160*x^4)/(486*(2 + 3*x)) + (2009*Log[2 + 3*x])/243","A",1
1349,1,42,45,0.0274878,"\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^3,x]","\frac{-3240 x^4+14472 x^3+15030 x^2-15150 x-11509}{486 (3 x+2)^2}-\frac{518}{81} \log (3 x+2)","-\frac{20 x^2}{27}+\frac{116 x}{27}-\frac{2009}{243 (3 x+2)}+\frac{343}{486 (3 x+2)^2}-\frac{518}{81} \log (3 x+2)",1,"(-11509 - 15150*x + 15030*x^2 + 14472*x^3 - 3240*x^4)/(486*(2 + 3*x)^2) - (518*Log[2 + 3*x])/81","A",1
1350,1,42,49,0.0244029,"\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^4,x]","\frac{-19440 x^4-51840 x^3+32076 x^2+70767 x+22088}{1458 (3 x+2)^3}+\frac{428}{243} \log (3 x+2)","-\frac{40 x}{81}+\frac{518}{81 (3 x+2)}-\frac{2009}{486 (3 x+2)^2}+\frac{343}{729 (3 x+2)^3}+\frac{428}{243} \log (3 x+2)",1,"(22088 + 70767*x + 32076*x^2 - 51840*x^3 - 19440*x^4)/(1458*(2 + 3*x)^3) + (428*Log[2 + 3*x])/243","A",1
1351,1,37,55,0.0262147,"\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^5,x]","\frac{-138672 x^3-193428 x^2-97116 x-18835}{2916 (3 x+2)^4}-\frac{40}{243} \log (3 x+2)","-\frac{428}{243 (3 x+2)}+\frac{259}{81 (3 x+2)^2}-\frac{2009}{729 (3 x+2)^3}+\frac{343}{972 (3 x+2)^4}-\frac{40}{243} \log (3 x+2)",1,"(-18835 - 97116*x - 193428*x^2 - 138672*x^3)/(2916*(2 + 3*x)^4) - (40*Log[2 + 3*x])/243","A",1
1352,1,31,37,0.0158115,"\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^6,x]","\frac{64800 x^4+57240 x^3+34920 x^2+16905 x+1282}{4860 (3 x+2)^5}","\frac{(1-2 x)^4}{105 (3 x+2)^5}-\frac{173 (1-2 x)^4}{2940 (3 x+2)^4}",1,"(1282 + 16905*x + 34920*x^2 + 57240*x^3 + 64800*x^4)/(4860*(2 + 3*x)^5)","A",1
1353,1,31,55,0.016518,"\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^7,x]","\frac{48600 x^4+14040 x^3+3375 x^2+7218 x-413}{7290 (3 x+2)^6}","-\frac{103 (1-2 x)^4}{30870 (3 x+2)^4}-\frac{103 (1-2 x)^4}{2205 (3 x+2)^5}+\frac{(1-2 x)^4}{126 (3 x+2)^6}",1,"(-413 + 7218*x + 3375*x^2 + 14040*x^3 + 48600*x^4)/(7290*(2 + 3*x)^6)","A",1
1354,1,31,56,0.0151039,"\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^8} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^8,x]","\frac{32400 x^4-270 x^3-3024 x^2+4593 x-604}{7290 (3 x+2)^7}","\frac{40}{729 (3 x+2)^3}-\frac{107}{243 (3 x+2)^4}+\frac{518}{405 (3 x+2)^5}-\frac{2009}{1458 (3 x+2)^6}+\frac{49}{243 (3 x+2)^7}",1,"(-604 + 4593*x - 3024*x^2 - 270*x^3 + 32400*x^4)/(7290*(2 + 3*x)^7)","A",1
1355,1,73,67,0.0123792,"\int (1-2 x)^3 (2+3 x)^8 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^8*(3 + 5*x)^2,x]","\frac{-2814669000 x^{14}-15256949400 x^{13}-33344966655 x^{12}-33724757430 x^{11}-6446912472 x^{10}+20591961390 x^9+20403763380 x^8+3811785120 x^7-5569403840 x^6-3984716736 x^5-455495040 x^4+594513920 x^3+322882560 x^2+69189120 x}{30030}","-\frac{100 (3 x+2)^{14}}{5103}+\frac{2180 (3 x+2)^{13}}{9477}-\frac{4099 (3 x+2)^{12}}{4374}+\frac{11599 (3 x+2)^{11}}{8019}-\frac{1862 (3 x+2)^{10}}{3645}+\frac{343 (3 x+2)^9}{6561}",1,"(69189120*x + 322882560*x^2 + 594513920*x^3 - 455495040*x^4 - 3984716736*x^5 - 5569403840*x^6 + 3811785120*x^7 + 20403763380*x^8 + 20591961390*x^9 - 6446912472*x^10 - 33724757430*x^11 - 33344966655*x^12 - 15256949400*x^13 - 2814669000*x^14)/30030","A",1
1356,1,68,67,0.0116543,"\int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^7*(3 + 5*x)^2,x]","\frac{-577368000 x^{13}-2731271400 x^{12}-4942445040 x^{11}-3441679956 x^{10}+1184966640 x^9+3523838175 x^8+1756806480 x^7-519341680 x^6-857533248 x^5-234131040 x^4+92435200 x^3+77425920 x^2+19768320 x}{17160}","-\frac{200 (3 x+2)^{13}}{9477}+\frac{545 (3 x+2)^{12}}{2187}-\frac{8198 (3 x+2)^{11}}{8019}+\frac{11599 (3 x+2)^{10}}{7290}-\frac{3724 (3 x+2)^9}{6561}+\frac{343 (3 x+2)^8}{5832}",1,"(19768320*x + 77425920*x^2 + 92435200*x^3 - 234131040*x^4 - 857533248*x^5 - 519341680*x^6 + 1756806480*x^7 + 3523838175*x^8 + 1184966640*x^9 - 3441679956*x^10 - 4942445040*x^11 - 2731271400*x^12 - 577368000*x^13)/17160","A",1
1357,1,63,67,0.0111329,"\int (1-2 x)^3 (2+3 x)^6 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^2,x]","\frac{1}{330} \left(-4009500 x^{12}-16183800 x^{11}-22982454 x^{10}-7489350 x^9+14162445 x^8+15025230 x^7+1452220 x^6-5156712 x^5-2574000 x^4+286880 x^3+601920 x^2+190080 x\right)","-\frac{50 (3 x+2)^{12}}{2187}+\frac{2180 (3 x+2)^{11}}{8019}-\frac{4099 (3 x+2)^{10}}{3645}+\frac{11599 (3 x+2)^9}{6561}-\frac{931 (3 x+2)^8}{1458}+\frac{49}{729} (3 x+2)^7",1,"(190080*x + 601920*x^2 + 286880*x^3 - 2574000*x^4 - 5156712*x^5 + 1452220*x^6 + 15025230*x^7 + 14162445*x^8 - 7489350*x^9 - 22982454*x^10 - 16183800*x^11 - 4009500*x^12)/330","A",1
1358,1,58,67,0.0104814,"\int (1-2 x)^3 (2+3 x)^5 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^5*(3 + 5*x)^2,x]","\frac{1}{264} \left(-1166400 x^{11}-3891888 x^{10}-3926736 x^9+698247 x^8+3784176 x^7+1731268 x^6-920304 x^5-951984 x^4-68992 x^3+183744 x^2+76032 x\right)","-\frac{200 (3 x+2)^{11}}{8019}+\frac{218}{729} (3 x+2)^{10}-\frac{8198 (3 x+2)^9}{6561}+\frac{11599 (3 x+2)^8}{5832}-\frac{532}{729} (3 x+2)^7+\frac{343 (3 x+2)^6}{4374}",1,"(76032*x + 183744*x^2 - 68992*x^3 - 951984*x^4 - 920304*x^5 + 1731268*x^6 + 3784176*x^7 + 698247*x^8 - 3926736*x^9 - 3891888*x^10 - 1166400*x^11)/264","A",1
1359,1,53,67,0.0103997,"\int (1-2 x)^3 (2+3 x)^4 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^2,x]","\frac{1}{60} \left(-97200 x^{10}-255600 x^9-142965 x^8+169380 x^7+202720 x^6-4788 x^5-83160 x^4-22240 x^3+14400 x^2+8640 x\right)","-\frac{20}{729} (3 x+2)^{10}+\frac{2180 (3 x+2)^9}{6561}-\frac{4099 (3 x+2)^8}{2916}+\frac{1657}{729} (3 x+2)^7-\frac{1862 (3 x+2)^6}{2187}+\frac{343 (3 x+2)^5}{3645}",1,"(8640*x + 14400*x^2 - 22240*x^3 - 83160*x^4 - 4788*x^5 + 202720*x^6 + 169380*x^7 - 142965*x^8 - 255600*x^9 - 97200*x^10)/60","A",1
1360,1,48,56,0.0090946,"\int (1-2 x)^3 (2+3 x)^3 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^2,x]","\frac{1}{420} \left(-252000 x^9-481950 x^8-14040 x^7+472010 x^6+190008 x^5-172305 x^4-105560 x^3+27720 x^2+30240 x\right)","-600 x^9-\frac{2295 x^8}{2}-\frac{234 x^7}{7}+\frac{6743 x^6}{6}+\frac{2262 x^5}{5}-\frac{1641 x^4}{4}-\frac{754 x^3}{3}+66 x^2+72 x",1,"(30240*x + 27720*x^2 - 105560*x^3 - 172305*x^4 + 190008*x^5 + 472010*x^6 - 14040*x^7 - 481950*x^8 - 252000*x^9)/420","A",1
1361,1,43,47,0.0076936,"\int (1-2 x)^3 (2+3 x)^2 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)^2,x]","\frac{1}{105} \left(-23625 x^8-27900 x^7+20335 x^6+30933 x^5-5985 x^4-13825 x^3+630 x^2+3780 x\right)","-225 x^8-\frac{1860 x^7}{7}+\frac{581 x^6}{3}+\frac{1473 x^5}{5}-57 x^4-\frac{395 x^3}{3}+6 x^2+36 x",1,"(3780*x + 630*x^2 - 13825*x^3 - 5985*x^4 + 30933*x^5 + 20335*x^6 - 27900*x^7 - 23625*x^8)/105","A",1
1362,1,38,46,0.0068573,"\int (1-2 x)^3 (2+3 x) (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)*(3 + 5*x)^2,x]","\frac{1}{420} \left(-36000 x^7-15400 x^6+44856 x^5+14175 x^4-23240 x^3-4410 x^2+7560 x\right)","-\frac{600 x^7}{7}-\frac{110 x^6}{3}+\frac{534 x^5}{5}+\frac{135 x^4}{4}-\frac{166 x^3}{3}-\frac{21 x^2}{2}+18 x",1,"(7560*x - 4410*x^2 - 23240*x^3 + 14175*x^4 + 44856*x^5 - 15400*x^6 - 36000*x^7)/420","A",1
1363,1,30,34,0.0072984,"\int (1-2 x)^3 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(3 + 5*x)^2,x]","-\frac{1}{6} x \left(200 x^5-72 x^4-207 x^3+94 x^2+72 x-54\right)","-\frac{25}{48} (1-2 x)^6+\frac{11}{4} (1-2 x)^5-\frac{121}{32} (1-2 x)^4",1,"-1/6*(x*(-54 + 72*x + 94*x^2 - 207*x^3 - 72*x^4 + 200*x^5))","A",1
1364,1,36,44,0.0187131,"\int \frac{(1-2 x)^3 (3+5 x)^2}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x),x]","\frac{343}{729} \log (3 x+2)-\frac{1}{486} x \left(6480 x^4-7830 x^3-492 x^2+4299 x-1844\right)","-\frac{40 x^5}{3}+\frac{145 x^4}{9}+\frac{82 x^3}{81}-\frac{1433 x^2}{162}+\frac{922 x}{243}+\frac{343}{729} \log (3 x+2)",1,"-1/486*(x*(-1844 + 4299*x - 492*x^2 - 7830*x^3 + 6480*x^4)) + (343*Log[2 + 3*x])/729","A",1
1365,1,47,48,0.0399934,"\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^2,x]","\frac{-36450 x^5+55080 x^4-23139 x^3+12015 x^2+148152 x+69863}{2187 (3 x+2)}-\frac{3724}{729} \log (3 x+2)","-\frac{50 x^4}{9}+\frac{980 x^3}{81}-\frac{313 x^2}{27}+\frac{2323 x}{243}-\frac{343}{729 (3 x+2)}-\frac{3724}{729} \log (3 x+2)",1,"(69863 + 148152*x + 12015*x^2 - 23139*x^3 + 55080*x^4 - 36450*x^5)/(2187*(2 + 3*x)) - (3724*Log[2 + 3*x])/729","A",1
1366,1,47,52,0.0421165,"\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^3,x]","\frac{-97200 x^5+205740 x^4-347436 x^3-1531512 x^2-1171896 x-258005}{4374 (3 x+2)^2}+\frac{11599}{729} \log (3 x+2)","-\frac{200 x^3}{81}+\frac{230 x^2}{27}-\frac{1546 x}{81}+\frac{3724}{729 (3 x+2)}-\frac{343}{1458 (3 x+2)^2}+\frac{11599}{729} \log (3 x+2)",1,"(-258005 - 1171896*x - 1531512*x^2 - 347436*x^3 + 205740*x^4 - 97200*x^5)/(4374*(2 + 3*x)^2) + (11599*Log[2 + 3*x])/729","A",1
1367,1,47,56,0.0424711,"\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^4,x]","\frac{-72900 x^5+286740 x^4+1088640 x^3+883467 x^2+155034 x-33319}{2187 (3 x+2)^3}-\frac{8198}{729} \log (3 x+2)","-\frac{100 x^2}{81}+\frac{1780 x}{243}-\frac{11599}{729 (3 x+2)}+\frac{1862}{729 (3 x+2)^2}-\frac{343}{2187 (3 x+2)^3}-\frac{8198}{729} \log (3 x+2)",1,"(-33319 + 155034*x + 883467*x^2 + 1088640*x^3 + 286740*x^4 - 72900*x^5)/(2187*(2 + 3*x)^3) - (8198*Log[2 + 3*x])/729","A",1
1368,1,47,60,0.040997,"\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^5,x]","\frac{-583200 x^5-1944000 x^4+64152 x^3+2957958 x^2+2175096 x+460595}{8748 (3 x+2)^4}+\frac{2180}{729} \log (3 x+2)","-\frac{200 x}{243}+\frac{8198}{729 (3 x+2)}-\frac{11599}{1458 (3 x+2)^2}+\frac{3724}{2187 (3 x+2)^3}-\frac{343}{2916 (3 x+2)^4}+\frac{2180}{729} \log (3 x+2)",1,"(460595 + 2175096*x + 2957958*x^2 + 64152*x^3 - 1944000*x^4 - 583200*x^5)/(8748*(2 + 3*x)^4) + (2180*Log[2 + 3*x])/729","A",1
1369,1,42,66,0.0446461,"\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^6,x]","\frac{-2648700 x^4-5403105 x^3-4264965 x^2-1579785 x-236399}{10935 (3 x+2)^5}-\frac{200}{729} \log (3 x+2)","-\frac{2180}{729 (3 x+2)}+\frac{4099}{729 (3 x+2)^2}-\frac{11599}{2187 (3 x+2)^3}+\frac{931}{729 (3 x+2)^4}-\frac{343}{3645 (3 x+2)^5}-\frac{200}{729} \log (3 x+2)",1,"(-236399 - 1579785*x - 4264965*x^2 - 5403105*x^3 - 2648700*x^4)/(10935*(2 + 3*x)^5) - (200*Log[2 + 3*x])/729","A",1
1370,1,36,67,0.030881,"\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^7,x]","\frac{2916000 x^5+4422600 x^4+3260520 x^3+1801575 x^2+550404 x+39286}{43740 (3 x+2)^6}","\frac{200}{729 (3 x+2)}-\frac{1090}{729 (3 x+2)^2}+\frac{8198}{2187 (3 x+2)^3}-\frac{11599}{2916 (3 x+2)^4}+\frac{3724}{3645 (3 x+2)^5}-\frac{343}{4374 (3 x+2)^6}",1,"(39286 + 550404*x + 1801575*x^2 + 3260520*x^3 + 4422600*x^4 + 2916000*x^5)/(43740*(2 + 3*x)^6)","A",1
1371,1,36,67,0.0307206,"\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^8} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^8,x]","\frac{729000 x^5+664200 x^4+191295 x^3+145044 x^2+61392 x-3526}{21870 (3 x+2)^7}","\frac{100}{729 (3 x+2)^2}-\frac{2180}{2187 (3 x+2)^3}+\frac{4099}{1458 (3 x+2)^4}-\frac{11599}{3645 (3 x+2)^5}+\frac{1862}{2187 (3 x+2)^6}-\frac{49}{729 (3 x+2)^7}",1,"(-3526 + 61392*x + 145044*x^2 + 191295*x^3 + 664200*x^4 + 729000*x^5)/(21870*(2 + 3*x)^7)","A",1
1372,1,73,78,0.012058,"\int (1-2 x)^3 (2+3 x)^7 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^7*(3 + 5*x)^3,x]","\frac{-6254820000 x^{14}-33455268000 x^{13}-71975603700 x^{12}-71099781480 x^{11}-11649609972 x^{10}+44838273480 x^9+42600933375 x^8+7104228560 x^7-11972520560 x^6-8187955776 x^5-830109280 x^4+1249248000 x^3+657296640 x^2+138378240 x}{40040}","-\frac{500 (3 x+2)^{14}}{15309}+\frac{3700 (3 x+2)^{13}}{9477}-\frac{7195 (3 x+2)^{12}}{4374}+\frac{66193 (3 x+2)^{11}}{24057}-\frac{10073 (3 x+2)^{10}}{7290}+\frac{1813 (3 x+2)^9}{6561}-\frac{343 (3 x+2)^8}{17496}",1,"(138378240*x + 657296640*x^2 + 1249248000*x^3 - 830109280*x^4 - 8187955776*x^5 - 11972520560*x^6 + 7104228560*x^7 + 42600933375*x^8 + 44838273480*x^9 - 11649609972*x^10 - 71099781480*x^11 - 71975603700*x^12 - 33455268000*x^13 - 6254820000*x^14)/40040","A",1
1373,1,68,78,0.0111016,"\int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^3,x]","\frac{-320760000 x^{13}-1494207000 x^{12}-2652296400 x^{11}-1779256908 x^{10}+701586600 x^9+1875860415 x^8+889191160 x^7-296913760 x^6-446613024 x^5-115200800 x^4+49695360 x^3+39536640 x^2+9884160 x}{5720}","-\frac{1000 (3 x+2)^{13}}{28431}+\frac{925 (3 x+2)^{12}}{2187}-\frac{14390 (3 x+2)^{11}}{8019}+\frac{66193 (3 x+2)^{10}}{21870}-\frac{10073 (3 x+2)^9}{6561}+\frac{1813 (3 x+2)^8}{5832}-\frac{49 (3 x+2)^7}{2187}",1,"(9884160*x + 39536640*x^2 + 49695360*x^3 - 115200800*x^4 - 446613024*x^5 - 296913760*x^6 + 889191160*x^7 + 1875860415*x^8 + 701586600*x^9 - 1779256908*x^10 - 2652296400*x^11 - 1494207000*x^12 - 320760000*x^13)/5720","A",1
1374,1,63,78,0.0105684,"\int (1-2 x)^3 (2+3 x)^5 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^5*(3 + 5*x)^3,x]","\frac{1}{88} \left(-1782000 x^{12}-7063200 x^{11}-9781992 x^{10}-2892296 x^9+6216837 x^8+6257416 x^7+453068 x^6-2189616 x^5-1038224 x^4+135168 x^3+247104 x^2+76032 x\right)","-\frac{250 (3 x+2)^{12}}{6561}+\frac{3700 (3 x+2)^{11}}{8019}-\frac{1439}{729} (3 x+2)^{10}+\frac{66193 (3 x+2)^9}{19683}-\frac{10073 (3 x+2)^8}{5832}+\frac{259}{729} (3 x+2)^7-\frac{343 (3 x+2)^6}{13122}",1,"(76032*x + 247104*x^2 + 135168*x^3 - 1038224*x^4 - 2189616*x^5 + 453068*x^6 + 6257416*x^7 + 6216837*x^8 - 2892296*x^9 - 9781992*x^10 - 7063200*x^11 - 1782000*x^12)/88","A",1
1375,1,58,62,0.0099841,"\int (1-2 x)^3 (2+3 x)^4 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^3,x]","\frac{1}{440} \left(-3240000 x^{11}-10573200 x^{10}-10282800 x^9+2289045 x^8+10097560 x^7+4313540 x^6-2544696 x^5-2441120 x^4-137280 x^3+475200 x^2+190080 x\right)","-\frac{81000 x^{11}}{11}-24030 x^{10}-23370 x^9+\frac{41619 x^8}{8}+22949 x^7+\frac{19607 x^6}{2}-\frac{28917 x^5}{5}-5548 x^4-312 x^3+1080 x^2+432 x",1,"(190080*x + 475200*x^2 - 137280*x^3 - 2441120*x^4 - 2544696*x^5 + 4313540*x^6 + 10097560*x^7 + 2289045*x^8 - 10282800*x^9 - 10573200*x^10 - 3240000*x^11)/440","A",1
1376,1,53,59,0.0100388,"\int (1-2 x)^3 (2+3 x)^3 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^3,x]","\frac{1}{140} \left(-378000 x^{10}-966000 x^9-502425 x^8+660260 x^7+735910 x^6-39732 x^5-304255 x^4-74760 x^3+52920 x^2+30240 x\right)","-2700 x^{10}-6900 x^9-\frac{14355 x^8}{4}+\frac{33013 x^7}{7}+\frac{10513 x^6}{2}-\frac{1419 x^5}{5}-\frac{8693 x^4}{4}-534 x^3+378 x^2+216 x",1,"(30240*x + 52920*x^2 - 74760*x^3 - 304255*x^4 - 39732*x^5 + 735910*x^6 + 660260*x^7 - 502425*x^8 - 966000*x^9 - 378000*x^10)/140","A",1
1377,1,48,54,0.008857,"\int (1-2 x)^3 (2+3 x)^2 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)^3,x]","\frac{1}{140} \left(-140000 x^9-257250 x^8+4600 x^7+253190 x^6+91812 x^5-93065 x^4-52500 x^3+15120 x^2+15120 x\right)","-1000 x^9-\frac{3675 x^8}{2}+\frac{230 x^7}{7}+\frac{3617 x^6}{2}+\frac{3279 x^5}{5}-\frac{2659 x^4}{4}-375 x^3+108 x^2+108 x",1,"(15120*x + 15120*x^2 - 52500*x^3 - 93065*x^4 + 91812*x^5 + 253190*x^6 + 4600*x^7 - 257250*x^8 - 140000*x^9)/140","A",1
1378,1,43,47,0.0074585,"\int (1-2 x)^3 (2+3 x) (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)*(3 + 5*x)^3,x]","\frac{1}{140} \left(-52500 x^8-58000 x^7+46900 x^6+63756 x^5-14875 x^4-28140 x^3+1890 x^2+7560 x\right)","-375 x^8-\frac{2900 x^7}{7}+335 x^6+\frac{2277 x^5}{5}-\frac{425 x^4}{4}-201 x^3+\frac{27 x^2}{2}+54 x",1,"(7560*x + 1890*x^2 - 28140*x^3 - 14875*x^4 + 63756*x^5 + 46900*x^6 - 58000*x^7 - 52500*x^8)/140","A",1
1379,1,38,40,0.0069992,"\int (1-2 x)^3 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^3*(3 + 5*x)^3,x]","\frac{1}{28} \left(-4000 x^7-1400 x^6+4872 x^5+1253 x^4-2436 x^3-378 x^2+756 x\right)","-\frac{1000 x^7}{7}-50 x^6+174 x^5+\frac{179 x^4}{4}-87 x^3-\frac{27 x^2}{2}+27 x",1,"(756*x - 378*x^2 - 2436*x^3 + 1253*x^4 + 4872*x^5 - 1400*x^6 - 4000*x^7)/28","A",1
1380,1,41,51,0.0200661,"\int \frac{(1-2 x)^3 (3+5 x)^3}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x),x]","-\frac{x \left(81000 x^5-35640 x^4-76005 x^3+38562 x^2+24861 x-20026\right)}{1458}-\frac{343 \log (3 x+2)}{2187}","-\frac{500 x^6}{9}+\frac{220 x^5}{9}+\frac{2815 x^4}{54}-\frac{6427 x^3}{243}-\frac{8287 x^2}{486}+\frac{10013 x}{729}-\frac{343 \log (3 x+2)}{2187}",1,"-1/1458*(x*(-20026 + 24861*x + 38562*x^2 - 76005*x^3 - 35640*x^4 + 81000*x^5)) - (343*Log[2 + 3*x])/2187","A",1
1381,1,52,55,0.0236303,"\int \frac{(1-2 x)^3 (3+5 x)^3}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^2,x]","\frac{-291600 x^6+182250 x^5+220320 x^4-163269 x^3-54000 x^2-3588 x-20002}{4374 (3 x+2)}+\frac{1813}{729} \log (3 x+2)","-\frac{200 x^5}{9}+\frac{775 x^4}{27}-\frac{190 x^3}{81}-\frac{5287 x^2}{486}+\frac{2287 x}{729}+\frac{343}{2187 (3 x+2)}+\frac{1813}{729} \log (3 x+2)",1,"(-20002 - 3588*x - 54000*x^2 - 163269*x^3 + 220320*x^4 + 182250*x^5 - 291600*x^6)/(4374*(2 + 3*x)) + (1813*Log[2 + 3*x])/729","A",1
1382,1,52,59,0.0272217,"\int \frac{(1-2 x)^3 (3+5 x)^3}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^3,x]","\frac{-364500 x^6+340200 x^5+67230 x^4+81702 x^3+2072124 x^2+2076942 x+551755}{4374 (3 x+2)^2}-\frac{10073}{729} \log (3 x+2)","-\frac{250 x^4}{27}+\frac{1700 x^3}{81}-\frac{1795 x^2}{81}+\frac{16253 x}{729}-\frac{1813}{729 (3 x+2)}+\frac{343}{4374 (3 x+2)^2}-\frac{10073}{729} \log (3 x+2)",1,"(551755 + 2076942*x + 2072124*x^2 + 81702*x^3 + 67230*x^4 + 340200*x^5 - 364500*x^6)/(4374*(2 + 3*x)^2) - (10073*Log[2 + 3*x])/729","A",1
1383,1,52,63,0.0297199,"\int \frac{(1-2 x)^3 (3+5 x)^3}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^4,x]","\frac{-162000 x^6+251100 x^5-414180 x^4-3180480 x^3-3851166 x^2-1766567 x-279268}{1458 (3 x+2)^3}+\frac{66193 \log (3 x+2)}{2187}","-\frac{1000 x^3}{243}+\frac{3550 x^2}{243}-\frac{24970 x}{729}+\frac{10073}{729 (3 x+2)}-\frac{1813}{1458 (3 x+2)^2}+\frac{343}{6561 (3 x+2)^3}+\frac{66193 \log (3 x+2)}{2187}",1,"(-279268 - 1766567*x - 3851166*x^2 - 3180480*x^3 - 414180*x^4 + 251100*x^5 - 162000*x^6)/(1458*(2 + 3*x)^3) + (66193*Log[2 + 3*x])/2187","A",1
1384,1,52,67,0.0287757,"\int \frac{(1-2 x)^3 (3+5 x)^3}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^5,x]","\frac{-1458000 x^6+4957200 x^5+26244000 x^4+32163156 x^3+13894254 x^2+675708 x-597785}{8748 (3 x+2)^4}-\frac{14390}{729} \log (3 x+2)","-\frac{500 x^2}{243}+\frac{9100 x}{729}-\frac{66193}{2187 (3 x+2)}+\frac{10073}{1458 (3 x+2)^2}-\frac{1813}{2187 (3 x+2)^3}+\frac{343}{8748 (3 x+2)^4}-\frac{14390}{729} \log (3 x+2)",1,"(-597785 + 675708*x + 13894254*x^2 + 32163156*x^3 + 26244000*x^4 + 4957200*x^5 - 1458000*x^6)/(8748*(2 + 3*x)^4) - (14390*Log[2 + 3*x])/729","A",1
1385,1,52,71,0.0350249,"\int \frac{(1-2 x)^3 (3+5 x)^3}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^6,x]","\frac{-14580000 x^6-58320000 x^5-27264600 x^4+82222290 x^3+109363320 x^2+49872855 x+7991782}{43740 (3 x+2)^5}+\frac{3700}{729} \log (3 x+2)","-\frac{1000 x}{729}+\frac{14390}{729 (3 x+2)}-\frac{66193}{4374 (3 x+2)^2}+\frac{10073}{2187 (3 x+2)^3}-\frac{1813}{2916 (3 x+2)^4}+\frac{343}{10935 (3 x+2)^5}+\frac{3700}{729} \log (3 x+2)",1,"(7991782 + 49872855*x + 109363320*x^2 + 82222290*x^3 - 27264600*x^4 - 58320000*x^5 - 14580000*x^6)/(43740*(2 + 3*x)^5) + (3700*Log[2 + 3*x])/729","A",1
1386,1,47,77,0.0251158,"\int \frac{(1-2 x)^3 (3+5 x)^3}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^7,x]","\frac{-53946000 x^5-144852300 x^4-158427540 x^3-89062425 x^2-25975248 x-3165082}{43740 (3 x+2)^6}-\frac{1000 \log (3 x+2)}{2187}","-\frac{3700}{729 (3 x+2)}+\frac{7195}{729 (3 x+2)^2}-\frac{66193}{6561 (3 x+2)^3}+\frac{10073}{2916 (3 x+2)^4}-\frac{1813}{3645 (3 x+2)^5}+\frac{343}{13122 (3 x+2)^6}-\frac{1000 \log (3 x+2)}{2187}",1,"(-3165082 - 25975248*x - 89062425*x^2 - 158427540*x^3 - 144852300*x^4 - 53946000*x^5)/(43740*(2 + 3*x)^6) - (1000*Log[2 + 3*x])/2187","A",1
1387,1,41,78,0.0175433,"\int \frac{(1-2 x)^3 (3+5 x)^3}{(2+3 x)^8} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^8,x]","\frac{14580000 x^6+31347000 x^5+30601800 x^4+19748745 x^3+8660574 x^2+1990182 x+133304}{43740 (3 x+2)^7}","\frac{1000}{2187 (3 x+2)}-\frac{1850}{729 (3 x+2)^2}+\frac{14390}{2187 (3 x+2)^3}-\frac{66193}{8748 (3 x+2)^4}+\frac{10073}{3645 (3 x+2)^5}-\frac{1813}{4374 (3 x+2)^6}+\frac{49}{2187 (3 x+2)^7}",1,"(133304 + 1990182*x + 8660574*x^2 + 19748745*x^3 + 30601800*x^4 + 31347000*x^5 + 14580000*x^6)/(43740*(2 + 3*x)^7)","A",1
1388,1,56,72,0.0244152,"\int \frac{(1-2 x)^3 (2+3 x)^6}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x)^6)/(3 + 5*x),x]","\frac{1331 \log (5 x+3)}{9765625}-\frac{x \left(21262500000 x^8+45448593750 x^7+7563375000 x^6-43537331250 x^5-23226871500 x^4+15352966125 x^3+12217627100 x^2-2333364390 x-3499962732\right)}{164062500}","-\frac{648 x^9}{5}-\frac{13851 x^8}{50}-\frac{40338 x^7}{875}+\frac{331713 x^6}{1250}+\frac{2212083 x^5}{15625}-\frac{5848749 x^4}{62500}-\frac{17453753 x^3}{234375}+\frac{11111259 x^2}{781250}+\frac{41666223 x}{1953125}+\frac{1331 \log (5 x+3)}{9765625}",1,"-1/164062500*(x*(-3499962732 - 2333364390*x + 12217627100*x^2 + 15352966125*x^3 - 23226871500*x^4 - 43537331250*x^5 + 7563375000*x^6 + 45448593750*x^7 + 21262500000*x^8)) + (1331*Log[3 + 5*x])/9765625","A",1
1389,1,51,65,0.0220899,"\int \frac{(1-2 x)^3 (2+3 x)^5}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x)^5)/(3 + 5*x),x]","\frac{1331 \log (5 x+3)}{1953125}-\frac{x \left(1594687500 x^7+2247750000 x^6-1159987500 x^5-2554996500 x^4+193591125 x^3+1192627100 x^2+29135610 x-349962732\right)}{32812500}","-\frac{243 x^8}{5}-\frac{11988 x^7}{175}+\frac{4419 x^6}{125}+\frac{243333 x^5}{3125}-\frac{73749 x^4}{12500}-\frac{1703753 x^3}{46875}-\frac{138741 x^2}{156250}+\frac{4166223 x}{390625}+\frac{1331 \log (5 x+3)}{1953125}",1,"-1/32812500*(x*(-349962732 + 29135610*x + 1192627100*x^2 + 193591125*x^3 - 2554996500*x^4 - 1159987500*x^5 + 2247750000*x^6 + 1594687500*x^7)) + (1331*Log[3 + 5*x])/1953125","A",1
1390,1,46,58,0.0203588,"\int \frac{(1-2 x)^3 (2+3 x)^4}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x)^4)/(3 + 5*x),x]","\frac{1331 \log (5 x+3)}{390625}-\frac{x \left(121500000 x^6+80325000 x^5-157059000 x^4-82033875 x^3+90127100 x^2+29135610 x-34962732\right)}{6562500}","-\frac{648 x^7}{35}-\frac{306 x^6}{25}+\frac{14958 x^5}{625}+\frac{31251 x^4}{2500}-\frac{128753 x^3}{9375}-\frac{138741 x^2}{31250}+\frac{416223 x}{78125}+\frac{1331 \log (5 x+3)}{390625}",1,"-1/6562500*(x*(-34962732 + 29135610*x + 90127100*x^2 - 82033875*x^3 - 157059000*x^4 + 80325000*x^5 + 121500000*x^6)) + (1331*Log[3 + 5*x])/390625","A",1
1391,1,41,51,0.0201134,"\int \frac{(1-2 x)^3 (2+3 x)^3}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x)^3)/(3 + 5*x),x]","\frac{1331 \log (5 x+3)}{78125}-\frac{x \left(675000 x^5-81000 x^4-867375 x^3+250150 x^2+393615 x-247338\right)}{93750}","-\frac{36 x^6}{5}+\frac{108 x^5}{125}+\frac{2313 x^4}{250}-\frac{5003 x^3}{1875}-\frac{26241 x^2}{6250}+\frac{41223 x}{15625}+\frac{1331 \log (5 x+3)}{78125}",1,"-1/93750*(x*(-247338 + 393615*x + 250150*x^2 - 867375*x^3 - 81000*x^4 + 675000*x^5)) + (1331*Log[3 + 5*x])/78125","A",1
1392,1,36,44,0.0182254,"\int \frac{(1-2 x)^3 (2+3 x)^2}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x)^2)/(3 + 5*x),x]","\frac{1331 \log (5 x+3)}{15625}-\frac{x \left(54000 x^4-51750 x^3-31100 x^2+56115 x-22338\right)}{18750}","-\frac{72 x^5}{25}+\frac{69 x^4}{25}+\frac{622 x^3}{375}-\frac{3741 x^2}{1250}+\frac{3723 x}{3125}+\frac{1331 \log (5 x+3)}{15625}",1,"-1/18750*(x*(-22338 + 56115*x - 31100*x^2 - 51750*x^3 + 54000*x^4)) + (1331*Log[3 + 5*x])/15625","A",1
1393,1,35,37,0.0194996,"\int \frac{(1-2 x)^3 (2+3 x)}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x))/(3 + 5*x),x]","\frac{-2250 x^4+4300 x^3-2745 x^2-81 x+2160}{1875}+\frac{1331 \log (5 x+3)}{3125}","-\frac{6 x^4}{5}+\frac{172 x^3}{75}-\frac{183 x^2}{125}-\frac{27 x}{625}+\frac{1331 \log (5 x+3)}{3125}",1,"(2160 - 81*x - 2745*x^2 + 4300*x^3 - 2250*x^4)/1875 + (1331*Log[3 + 5*x])/3125","A",1
1394,1,26,30,0.0131577,"\int \frac{(1-2 x)^3}{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/(3 + 5*x),x]","\frac{1331}{625} \log (5 x+3)-\frac{2}{375} x \left(100 x^2-315 x+603\right)","-\frac{8 x^3}{15}+\frac{42 x^2}{25}-\frac{402 x}{125}+\frac{1331}{625} \log (5 x+3)",1,"(-2*x*(603 - 315*x + 100*x^2))/375 + (1331*Log[3 + 5*x])/625","A",1
1395,1,35,33,0.0203435,"\int \frac{(1-2 x)^3}{(2+3 x) (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)*(3 + 5*x)),x]","-\frac{4}{225} \left(15 x^2-83 x-62\right)-\frac{343}{27} \log (3 x+2)+\frac{1331}{125} \log (5 x+3)","-\frac{4 x^2}{15}+\frac{332 x}{225}-\frac{343}{27} \log (3 x+2)+\frac{1331}{125} \log (5 x+3)",1,"(-4*(-62 - 83*x + 15*x^2))/225 - (343*Log[2 + 3*x])/27 + (1331*Log[3 + 5*x])/125","A",1
1396,1,42,37,0.0295699,"\int \frac{(1-2 x)^3}{(2+3 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^2*(3 + 5*x)),x]","\frac{-72 x^2-48 x+1715}{135 (3 x+2)}-\frac{1421}{27} \log (3 x+2)+\frac{1331}{25} \log (5 x+3)","-\frac{8 x}{45}+\frac{343}{27 (3 x+2)}-\frac{1421}{27} \log (3 x+2)+\frac{1331}{25} \log (5 x+3)",1,"(1715 - 48*x - 72*x^2)/(135*(2 + 3*x)) - (1421*Log[2 + 3*x])/27 + (1331*Log[3 + 5*x])/25","A",1
1397,1,37,43,0.0355192,"\int \frac{(1-2 x)^3}{(2+3 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^3*(3 + 5*x)),x]","\frac{49 (58 x+41)}{18 (3 x+2)^2}-\frac{7189}{27} \log (3 x+2)+\frac{1331}{5} \log (5 x+3)","\frac{1421}{27 (3 x+2)}+\frac{343}{54 (3 x+2)^2}-\frac{7189}{27} \log (3 x+2)+\frac{1331}{5} \log (5 x+3)",1,"(49*(41 + 58*x))/(18*(2 + 3*x)^2) - (7189*Log[2 + 3*x])/27 + (1331*Log[3 + 5*x])/5","A",1
1398,1,38,50,0.0400069,"\int \frac{(1-2 x)^3}{(2+3 x)^4 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^4*(3 + 5*x)),x]","\frac{7 \left(55458 x^2+75771 x+25964\right)}{162 (3 x+2)^3}-1331 \log (3 x+2)+1331 \log (5 x+3)","\frac{7189}{27 (3 x+2)}+\frac{1421}{54 (3 x+2)^2}+\frac{343}{81 (3 x+2)^3}-1331 \log (3 x+2)+1331 \log (5 x+3)",1,"(7*(25964 + 75771*x + 55458*x^2))/(162*(2 + 3*x)^3) - 1331*Log[2 + 3*x] + 1331*Log[3 + 5*x]","A",1
1399,1,43,59,0.0482723,"\int \frac{(1-2 x)^3}{(2+3 x)^5 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^5*(3 + 5*x)),x]","\frac{11643588 x^3+23675382 x^2+16059444 x+3634885}{324 (3 x+2)^4}-6655 \log (3 x+2)+6655 \log (5 x+3)","\frac{1331}{3 x+2}+\frac{7189}{54 (3 x+2)^2}+\frac{1421}{81 (3 x+2)^3}+\frac{343}{108 (3 x+2)^4}-6655 \log (3 x+2)+6655 \log (5 x+3)",1,"(3634885 + 16059444*x + 23675382*x^2 + 11643588*x^3)/(324*(2 + 3*x)^4) - 6655*Log[2 + 3*x] + 6655*Log[3 + 5*x]","A",1
1400,1,48,70,0.0671574,"\int \frac{(1-2 x)^3}{(2+3 x)^6 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^6*(3 + 5*x)),x]","\frac{873269100 x^4+2357826570 x^3+2388229560 x^2+1075586865 x+181744346}{1620 (3 x+2)^5}-33275 \log (3 x+2)+33275 \log (5 x+3)","\frac{6655}{3 x+2}+\frac{1331}{2 (3 x+2)^2}+\frac{7189}{81 (3 x+2)^3}+\frac{1421}{108 (3 x+2)^4}+\frac{343}{135 (3 x+2)^5}-33275 \log (3 x+2)+33275 \log (5 x+3)",1,"(181744346 + 1075586865*x + 2388229560*x^2 + 2357826570*x^3 + 873269100*x^4)/(1620*(2 + 3*x)^5) - 33275*Log[2 + 3*x] + 33275*Log[3 + 5*x]","A",1
1401,1,53,81,0.0924321,"\int \frac{(1-2 x)^3}{(2+3 x)^7 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^7*(3 + 5*x)),x]","\frac{13099036500 x^5+44100089550 x^4+59401704780 x^3+40016101275 x^2+13482032616 x+1817443594}{1620 (3 x+2)^6}-166375 \log (3 x+2)+166375 \log (5 x+3)","\frac{33275}{3 x+2}+\frac{6655}{2 (3 x+2)^2}+\frac{1331}{3 (3 x+2)^3}+\frac{7189}{108 (3 x+2)^4}+\frac{1421}{135 (3 x+2)^5}+\frac{343}{162 (3 x+2)^6}-166375 \log (3 x+2)+166375 \log (5 x+3)",1,"(1817443594 + 13482032616*x + 40016101275*x^2 + 59401704780*x^3 + 44100089550*x^4 + 13099036500*x^5)/(1620*(2 + 3*x)^6) - 166375*Log[2 + 3*x] + 166375*Log[3 + 5*x]","A",1
1402,1,58,92,0.1058448,"\int \frac{(1-2 x)^3}{(2+3 x)^8 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^8*(3 + 5*x)),x]","\frac{196485547500 x^6+792491708250 x^5+1332026467200 x^4+1194258563685 x^3+602391504582 x^2+162081979026 x+18174436072}{1620 (3 x+2)^7}-831875 \log (3 x+2)+831875 \log (5 x+3)","\frac{166375}{3 x+2}+\frac{33275}{2 (3 x+2)^2}+\frac{6655}{3 (3 x+2)^3}+\frac{1331}{4 (3 x+2)^4}+\frac{7189}{135 (3 x+2)^5}+\frac{1421}{162 (3 x+2)^6}+\frac{49}{27 (3 x+2)^7}-831875 \log (3 x+2)+831875 \log (5 x+3)",1,"(18174436072 + 162081979026*x + 602391504582*x^2 + 1194258563685*x^3 + 1332026467200*x^4 + 792491708250*x^5 + 196485547500*x^6)/(1620*(2 + 3*x)^7) - 831875*Log[2 + 3*x] + 831875*Log[3 + 5*x]","A",1
1403,1,67,76,0.0466779,"\int \frac{(1-2 x)^3 (2+3 x)^6}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x)^6)/(3 + 5*x)^2,x]","\frac{-49833984375 x^9-103939453125 x^8-10979296875 x^7+104830031250 x^6+47772112500 x^5-42029925000 x^4-26126590000 x^3+10934112000 x^2+10818777780 x+2118706028}{341796875 (5 x+3)}+\frac{23232 \log (5 x+3)}{9765625}","-\frac{729 x^8}{25}-\frac{37908 x^7}{875}+\frac{12231 x^6}{625}+\frac{774981 x^5}{15625}-\frac{5643 x^4}{3125}-\frac{1836723 x^3}{78125}-\frac{461623 x^2}{390625}+\frac{13880997 x}{1953125}-\frac{1331}{9765625 (5 x+3)}+\frac{23232 \log (5 x+3)}{9765625}",1,"(2118706028 + 10818777780*x + 10934112000*x^2 - 26126590000*x^3 - 42029925000*x^4 + 47772112500*x^5 + 104830031250*x^6 - 10979296875*x^7 - 103939453125*x^8 - 49833984375*x^9)/(341796875*(3 + 5*x)) + (23232*Log[3 + 5*x])/9765625","A",1
1404,1,62,69,0.0428419,"\int \frac{(1-2 x)^3 (2+3 x)^5}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x)^5)/(3 + 5*x)^2,x]","\frac{-15187500000 x^8-20334375000 x^7+12946500000 x^6+23662603125 x^5-4521978125 x^4-11417376250 x^3+2176277250 x^2+4982083965 x+1247330759}{273437500 (5 x+3)}+\frac{19239 \log (5 x+3)}{1953125}","-\frac{1944 x^7}{175}-\frac{1026 x^6}{125}+\frac{44982 x^5}{3125}+\frac{108387 x^4}{12500}-\frac{26594 x^3}{3125}-\frac{507023 x^2}{156250}+\frac{1382328 x}{390625}-\frac{1331}{1953125 (5 x+3)}+\frac{19239 \log (5 x+3)}{1953125}",1,"(1247330759 + 4982083965*x + 2176277250*x^2 - 11417376250*x^3 - 4521978125*x^4 + 23662603125*x^5 + 12946500000*x^6 - 20334375000*x^7 - 15187500000*x^8)/(273437500*(3 + 5*x)) + (19239*Log[3 + 5*x])/1953125","A",1
1405,1,57,62,0.0454978,"\int \frac{(1-2 x)^3 (2+3 x)^4}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x)^4)/(3 + 5*x)^2,x]","\frac{-84375000 x^7-47250000 x^6+116353125 x^5+42240625 x^4-72563750 x^3-635250 x^2+44216865 x+14487499}{3906250 (5 x+3)}+\frac{15246 \log (5 x+3)}{390625}","-\frac{108 x^6}{25}+\frac{108 x^5}{625}+\frac{7317 x^4}{1250}-\frac{4217 x^3}{3125}-\frac{1816 x^2}{625}+\frac{133659 x}{78125}-\frac{1331}{390625 (5 x+3)}+\frac{15246 \log (5 x+3)}{390625}",1,"(14487499 + 44216865*x - 635250*x^2 - 72563750*x^3 + 42240625*x^4 + 116353125*x^5 - 47250000*x^6 - 84375000*x^7)/(3906250*(3 + 5*x)) + (15246*Log[3 + 5*x])/390625","A",1
1406,1,52,55,0.0252212,"\int \frac{(1-2 x)^3 (2+3 x)^3}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x)^3)/(3 + 5*x)^2,x]","\frac{-6750000 x^6+1856250 x^5+8456250 x^4-4600625 x^3-2031375 x^2+5485095 x+2378647}{781250 (5 x+3)}+\frac{11253 \log (5 x+3)}{78125}","-\frac{216 x^5}{125}+\frac{189 x^4}{125}+\frac{786 x^3}{625}-\frac{12077 x^2}{6250}+\frac{1998 x}{3125}-\frac{1331}{78125 (5 x+3)}+\frac{11253 \log (5 x+3)}{78125}",1,"(2378647 + 5485095*x - 2031375*x^2 - 4600625*x^3 + 8456250*x^4 + 1856250*x^5 - 6750000*x^6)/(781250*(3 + 5*x)) + (11253*Log[3 + 5*x])/78125","A",1
1407,1,47,48,0.0380606,"\int \frac{(1-2 x)^3 (2+3 x)^2}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x)^2)/(3 + 5*x)^2,x]","\frac{-11250 x^5+13750 x^4+1625 x^3-12300 x^2+2655 x+3449}{3125 (5 x+3)}+\frac{1452 \log (5 x+3)}{3125}","-\frac{18 x^4}{25}+\frac{164 x^3}{125}-\frac{427 x^2}{625}-\frac{1179 x}{3125}-\frac{1331}{15625 (5 x+3)}+\frac{1452 \log (5 x+3)}{3125}",1,"(3449 + 2655*x - 12300*x^2 + 1625*x^3 + 13750*x^4 - 11250*x^5)/(3125*(3 + 5*x)) + (1452*Log[3 + 5*x])/3125","A",1
1408,1,42,41,0.0238551,"\int \frac{(1-2 x)^3 (2+3 x)}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x))/(3 + 5*x)^2,x]","\frac{-10000 x^4+24500 x^3-36600 x^2-11865 x+9983}{6250 (5 x+3)}+\frac{3267 \log (5 x+3)}{3125}","-\frac{8 x^3}{25}+\frac{122 x^2}{125}-\frac{1098 x}{625}-\frac{1331}{3125 (5 x+3)}+\frac{3267 \log (5 x+3)}{3125}",1,"(9983 - 11865*x - 36600*x^2 + 24500*x^3 - 10000*x^4)/(6250*(3 + 5*x)) + (3267*Log[3 + 5*x])/3125","A",1
1409,1,37,34,0.018641,"\int \frac{(1-2 x)^3}{(3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/(3 + 5*x)^2,x]","\frac{-500 x^3+2400 x^2+395 x-2066}{625 (5 x+3)}-\frac{726}{625} \log (5 x+3)","-\frac{4 x^2}{25}+\frac{108 x}{125}-\frac{1331}{625 (5 x+3)}-\frac{726}{625} \log (5 x+3)",1,"(-2066 + 395*x + 2400*x^2 - 500*x^3)/(625*(3 + 5*x)) - (726*Log[3 + 5*x])/625","A",1
1410,1,42,37,0.0304967,"\int \frac{(1-2 x)^3}{(2+3 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)*(3 + 5*x)^2),x]","\frac{-200 x^2-120 x-3993}{375 (5 x+3)}+\frac{343}{9} \log (3 x+2)-\frac{4719}{125} \log (5 x+3)","-\frac{8 x}{75}-\frac{1331}{125 (5 x+3)}+\frac{343}{9} \log (3 x+2)-\frac{4719}{125} \log (5 x+3)",1,"(-3993 - 120*x - 200*x^2)/(375*(3 + 5*x)) + (343*Log[2 + 3*x])/9 - (4719*Log[3 + 5*x])/125","A",1
1411,1,44,43,0.0413773,"\int \frac{(1-2 x)^3}{(2+3 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{-78812 x-49683}{225 (3 x+2) (5 x+3)}+\frac{3136}{9} \log (3 x+2)-\frac{8712}{25} \log (5 x+3)","-\frac{343}{9 (3 x+2)}-\frac{1331}{25 (5 x+3)}+\frac{3136}{9} \log (3 x+2)-\frac{8712}{25} \log (5 x+3)",1,"(-49683 - 78812*x)/(225*(2 + 3*x)*(3 + 5*x)) + (3136*Log[2 + 3*x])/9 - (8712*Log[3 + 5*x])/25","A",1
1412,1,45,50,0.0489052,"\int \frac{(1-2 x)^3}{(2+3 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^3*(3 + 5*x)^2),x]","\frac{-686022 x^2-891911 x-289137}{90 (3 x+2)^2 (5 x+3)}+2541 \log (3 x+2)-2541 \log (5 x+3)","-\frac{3136}{9 (3 x+2)}-\frac{1331}{5 (5 x+3)}-\frac{343}{18 (3 x+2)^2}+2541 \log (3 x+2)-2541 \log (5 x+3)",1,"(-289137 - 891911*x - 686022*x^2)/(90*(2 + 3*x)^2*(3 + 5*x)) + 2541*Log[2 + 3*x] - 2541*Log[3 + 5*x]","A",1
1413,1,50,57,0.0436718,"\int \frac{(1-2 x)^3}{(2+3 x)^4 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^4*(3 + 5*x)^2),x]","\frac{-4057614 x^3-7979967 x^2-5226815 x-1140033}{27 (3 x+2)^3 (5 x+3)}+16698 \log (3 x+2)-16698 \log (5 x+3)","-\frac{2541}{3 x+2}-\frac{1331}{5 x+3}-\frac{1568}{9 (3 x+2)^2}-\frac{343}{27 (3 x+2)^3}+16698 \log (3 x+2)-16698 \log (5 x+3)",1,"(-1140033 - 5226815*x - 7979967*x^2 - 4057614*x^3)/(27*(2 + 3*x)^3*(3 + 5*x)) + 16698*Log[2 + 3*x] - 16698*Log[3 + 5*x]","A",1
1414,1,55,68,0.052884,"\int \frac{(1-2 x)^3}{(2+3 x)^5 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^5*(3 + 5*x)^2),x]","\frac{-301674780 x^4-794410254 x^3-784130946 x^2-343827337 x-56505975}{108 (3 x+2)^4 (5 x+3)}+103455 \log (3 x+2)-103455 \log (5 x+3)","-\frac{16698}{3 x+2}-\frac{6655}{5 x+3}-\frac{2541}{2 (3 x+2)^2}-\frac{3136}{27 (3 x+2)^3}-\frac{343}{36 (3 x+2)^4}+103455 \log (3 x+2)-103455 \log (5 x+3)",1,"(-56505975 - 343827337*x - 784130946*x^2 - 794410254*x^3 - 301674780*x^4)/(108*(2 + 3*x)^4*(3 + 5*x)) + 103455*Log[2 + 3*x] - 103455*Log[3 + 5*x]","A",1
1415,1,60,75,0.0834223,"\int \frac{(1-2 x)^3}{(2+3 x)^6 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^6*(3 + 5*x)^2),x]","\frac{-2249329500 x^5-7422787350 x^4-9795413430 x^3-6461351715 x^2-2130399775 x-280877649}{45 (3 x+2)^5 (5 x+3)}+617100 \log (3 x+2)-617100 \log (5 x+3)","-\frac{103455}{3 x+2}-\frac{33275}{5 x+3}-\frac{8349}{(3 x+2)^2}-\frac{847}{(3 x+2)^3}-\frac{784}{9 (3 x+2)^4}-\frac{343}{45 (3 x+2)^5}+617100 \log (3 x+2)-617100 \log (5 x+3)",1,"(-280877649 - 2130399775*x - 6461351715*x^2 - 9795413430*x^3 - 7422787350*x^4 - 2249329500*x^5)/(45*(2 + 3*x)^5*(3 + 5*x)) + 617100*Log[2 + 3*x] - 617100*Log[3 + 5*x]","A",1
1416,1,65,88,0.1130501,"\int \frac{(1-2 x)^3}{(2+3 x)^7 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^7*(3 + 5*x)^2),x]","\frac{-470374492500 x^6-1865818820250 x^5-3083217691950 x^4-2716778541015 x^3-1346292632205 x^2-355739265638 x-39157648662}{540 (3 x+2)^6 (5 x+3)}+3584625 \log (3 x+2)-3584625 \log (5 x+3)","-\frac{617100}{3 x+2}-\frac{166375}{5 x+3}-\frac{103455}{2 (3 x+2)^2}-\frac{5566}{(3 x+2)^3}-\frac{2541}{4 (3 x+2)^4}-\frac{3136}{45 (3 x+2)^5}-\frac{343}{54 (3 x+2)^6}+3584625 \log (3 x+2)-3584625 \log (5 x+3)",1,"(-39157648662 - 355739265638*x - 1346292632205*x^2 - 2716778541015*x^3 - 3083217691950*x^4 - 1865818820250*x^5 - 470374492500*x^6)/(540*(2 + 3*x)^6*(3 + 5*x)) + 3584625*Log[2 + 3*x] - 3584625*Log[3 + 5*x]","A",1
1417,1,70,97,0.1489118,"\int \frac{(1-2 x)^3}{(2+3 x)^8 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^8*(3 + 5*x)^2),x]","\frac{-4019022562500 x^7-18621471206250 x^6-36972030521250 x^5-40775613627375 x^4-26978454053595 x^3-10708299857748 x^2-2360937751874 x-223049897418}{270 (3 x+2)^7 (5 x+3)}+20418750 \log (3 x+2)-20418750 \log (5 x+3)","-\frac{3584625}{3 x+2}-\frac{831875}{5 x+3}-\frac{308550}{(3 x+2)^2}-\frac{34485}{(3 x+2)^3}-\frac{8349}{2 (3 x+2)^4}-\frac{2541}{5 (3 x+2)^5}-\frac{1568}{27 (3 x+2)^6}-\frac{49}{9 (3 x+2)^7}+20418750 \log (3 x+2)-20418750 \log (5 x+3)",1,"(-223049897418 - 2360937751874*x - 10708299857748*x^2 - 26978454053595*x^3 - 40775613627375*x^4 - 36972030521250*x^5 - 18621471206250*x^6 - 4019022562500*x^7)/(270*(2 + 3*x)^7*(3 + 5*x)) + 20418750*Log[2 + 3*x] - 20418750*Log[3 + 5*x]","A",1
1418,1,72,87,0.043117,"\int \frac{(1-2 x)^3 (2+3 x)^7}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x)^7)/(3 + 5*x)^3,x]","\frac{-598007812500 x^{10}-1651640625000 x^9-972000000000 x^8+1176752812500 x^7+1425913453125 x^6-126252393750 x^5-660465159375 x^4-73008617500 x^3+229405636575 x^2+117985377690 x+17925405377}{1367187500 (5 x+3)^2}+\frac{47289 \log (5 x+3)}{9765625}","-\frac{2187 x^8}{125}-\frac{119556 x^7}{4375}+\frac{33291 x^6}{3125}+\frac{491913 x^5}{15625}+\frac{6507 x^4}{62500}-\frac{5918904 x^3}{390625}-\frac{2300646 x^2}{1953125}+\frac{46214407 x}{9765625}-\frac{1089}{1953125 (5 x+3)}-\frac{1331}{97656250 (5 x+3)^2}+\frac{47289 \log (5 x+3)}{9765625}",1,"(17925405377 + 117985377690*x + 229405636575*x^2 - 73008617500*x^3 - 660465159375*x^4 - 126252393750*x^5 + 1425913453125*x^6 + 1176752812500*x^7 - 972000000000*x^8 - 1651640625000*x^9 - 598007812500*x^10)/(1367187500*(3 + 5*x)^2) + (47289*Log[3 + 5*x])/9765625","A",1
1419,1,67,80,0.0475884,"\int \frac{(1-2 x)^3 (2+3 x)^6}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x)^6)/(3 + 5*x)^3,x]","\frac{-227812500000 x^9-459421875000 x^8-10783125000 x^7+489359390625 x^6+170737481250 x^5-221653096875 x^4-80532567500 x^3+104273484075 x^2+73328526690 x+13353609877}{1367187500 (5 x+3)^2}+\frac{166749 \log (5 x+3)}{9765625}","-\frac{5832 x^7}{875}-\frac{3402 x^6}{625}+\frac{134622 x^5}{15625}+\frac{74223 x^4}{12500}-\frac{81747 x^3}{15625}-\frac{915777 x^2}{390625}+\frac{4571416 x}{1953125}-\frac{23232}{9765625 (5 x+3)}-\frac{1331}{19531250 (5 x+3)^2}+\frac{166749 \log (5 x+3)}{9765625}",1,"(13353609877 + 73328526690*x + 104273484075*x^2 - 80532567500*x^3 - 221653096875*x^4 + 170737481250*x^5 + 489359390625*x^6 - 10783125000*x^7 - 459421875000*x^8 - 227812500000*x^9)/(1367187500*(3 + 5*x)^2) + (166749*Log[3 + 5*x])/9765625","A",1
1420,1,62,73,0.0456166,"\int \frac{(1-2 x)^3 (2+3 x)^5}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x)^5)/(3 + 5*x)^3,x]","\frac{-1265625000 x^8-1569375000 x^7+1278703125 x^6+1828837500 x^5-692475000 x^4-744310000 x^3+711123525 x^2+698557830 x+151973789}{19531250 (5 x+3)^2}+\frac{109032 \log (5 x+3)}{1953125}","-\frac{324 x^6}{125}-\frac{324 x^5}{3125}+\frac{22977 x^4}{6250}-\frac{393 x^3}{625}-\frac{62097 x^2}{31250}+\frac{424432 x}{390625}-\frac{19239}{1953125 (5 x+3)}-\frac{1331}{3906250 (5 x+3)^2}+\frac{109032 \log (5 x+3)}{1953125}",1,"(151973789 + 698557830*x + 711123525*x^2 - 744310000*x^3 - 692475000*x^4 + 1828837500*x^5 + 1278703125*x^6 - 1569375000*x^7 - 1265625000*x^8)/(19531250*(3 + 5*x)^2) + (109032*Log[3 + 5*x])/1953125","A",1
1421,1,57,66,0.043592,"\int \frac{(1-2 x)^3 (2+3 x)^4}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x)^4)/(3 + 5*x)^3,x]","\frac{-101250000 x^7-41343750 x^6+148050000 x^5+15815625 x^4-81707500 x^3+53587800 x^2+83293560 x+21586298}{3906250 (5 x+3)^2}+\frac{63294 \log (5 x+3)}{390625}","-\frac{648 x^5}{625}+\frac{513 x^4}{625}+\frac{2826 x^3}{3125}-\frac{7617 x^2}{6250}+\frac{4691 x}{15625}-\frac{15246}{390625 (5 x+3)}-\frac{1331}{781250 (5 x+3)^2}+\frac{63294 \log (5 x+3)}{390625}",1,"(21586298 + 83293560*x + 53587800*x^2 - 81707500*x^3 + 15815625*x^4 + 148050000*x^5 - 41343750*x^6 - 101250000*x^7)/(3906250*(3 + 5*x)^2) + (63294*Log[3 + 5*x])/390625","A",1
1422,1,52,59,0.0255241,"\int \frac{(1-2 x)^3 (2+3 x)^3}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x)^3)/(3 + 5*x)^3,x]","\frac{-337500 x^6+180000 x^5+348750 x^4-393250 x^3-416250 x^2-70080 x+7139}{31250 (5 x+3)^2}+\frac{5907 \log (5 x+3)}{15625}","-\frac{54 x^4}{125}+\frac{468 x^3}{625}-\frac{927 x^2}{3125}-\frac{1303 x}{3125}-\frac{11253}{78125 (5 x+3)}-\frac{1331}{156250 (5 x+3)^2}+\frac{5907 \log (5 x+3)}{15625}",1,"(7139 - 70080*x - 416250*x^2 - 393250*x^3 + 348750*x^4 + 180000*x^5 - 337500*x^6)/(31250*(3 + 5*x)^2) + (5907*Log[3 + 5*x])/15625","A",1
1423,1,47,52,0.045772,"\int \frac{(1-2 x)^3 (2+3 x)^2}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x)^2)/(3 + 5*x)^3,x]","\frac{-30000 x^5+52500 x^4-53500 x^3-274500 x^2-221340 x-54943}{6250 (5 x+3)^2}+\frac{1551 \log (5 x+3)}{3125}","-\frac{24 x^3}{125}+\frac{354 x^2}{625}-\frac{2978 x}{3125}-\frac{1452}{3125 (5 x+3)}-\frac{1331}{31250 (5 x+3)^2}+\frac{1551 \log (5 x+3)}{3125}",1,"(-54943 - 221340*x - 274500*x^2 - 53500*x^3 + 52500*x^4 - 30000*x^5)/(6250*(3 + 5*x)^2) + (1551*Log[3 + 5*x])/3125","A",1
1424,1,42,45,0.0278437,"\int \frac{(1-2 x)^3 (2+3 x)}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^3*(2 + 3*x))/(3 + 5*x)^3,x]","\frac{-15000 x^4+61000 x^3+53650 x^2-47130 x-33803}{6250 (5 x+3)^2}-\frac{2046 \log (5 x+3)}{3125}","-\frac{12 x^2}{125}+\frac{316 x}{625}-\frac{3267}{3125 (5 x+3)}-\frac{1331}{6250 (5 x+3)^2}-\frac{2046 \log (5 x+3)}{3125}",1,"(-33803 - 47130*x + 53650*x^2 + 61000*x^3 - 15000*x^4)/(6250*(3 + 5*x)^2) - (2046*Log[3 + 5*x])/3125","A",1
1425,1,37,38,0.0246775,"\int \frac{(1-2 x)^3}{(3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/(3 + 5*x)^3,x]","\frac{-400 x^3-280 x^2+1548 x+677}{250 (5 x+3)^2}+\frac{132}{625} \log (5 x+3)","-\frac{8 x}{125}+\frac{726}{625 (5 x+3)}-\frac{1331}{1250 (5 x+3)^2}+\frac{132}{625} \log (5 x+3)",1,"(677 + 1548*x - 280*x^2 - 400*x^3)/(250*(3 + 5*x)^2) + (132*Log[3 + 5*x])/625","A",1
1426,1,37,43,0.0344579,"\int \frac{(1-2 x)^3}{(2+3 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)*(3 + 5*x)^3),x]","\frac{121 (390 x+223)}{250 (5 x+3)^2}-\frac{343}{3} \log (3 x+2)+\frac{14289}{125} \log (5 x+3)","\frac{4719}{125 (5 x+3)}-\frac{1331}{250 (5 x+3)^2}-\frac{343}{3} \log (3 x+2)+\frac{14289}{125} \log (5 x+3)",1,"(121*(223 + 390*x))/(250*(3 + 5*x)^2) - (343*Log[2 + 3*x])/3 + (14289*Log[3 + 5*x])/125","A",1
1427,1,45,50,0.0383209,"\int \frac{(1-2 x)^3}{(2+3 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{1212830 x^2+1495689 x+459996}{150 (3 x+2) (5 x+3)^2}-1617 \log (3 x+2)+1617 \log (5 x+3)","\frac{343}{3 (3 x+2)}+\frac{8712}{25 (5 x+3)}-\frac{1331}{50 (5 x+3)^2}-1617 \log (3 x+2)+1617 \log (5 x+3)",1,"(459996 + 1495689*x + 1212830*x^2)/(150*(2 + 3*x)*(3 + 5*x)^2) - 1617*Log[2 + 3*x] + 1617*Log[3 + 5*x]","A",1
1428,1,50,57,0.0452256,"\int \frac{(1-2 x)^3}{(2+3 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{7068600 x^3+13430348 x^2+8492784 x+1787403}{30 (3 x+2)^2 (5 x+3)^2}-15708 \log (3 x+2)+15708 \log (5 x+3)","\frac{1617}{3 x+2}+\frac{2541}{5 x+3}+\frac{343}{6 (3 x+2)^2}-\frac{1331}{10 (5 x+3)^2}-15708 \log (3 x+2)+15708 \log (5 x+3)",1,"(1787403 + 8492784*x + 13430348*x^2 + 7068600*x^3)/(30*(2 + 3*x)^2*(3 + 5*x)^2) - 15708*Log[2 + 3*x] + 15708*Log[3 + 5*x]","A",1
1429,1,55,68,0.04907,"\int \frac{(1-2 x)^3}{(2+3 x)^4 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^4*(3 + 5*x)^3),x]","\frac{104193540 x^4+267430086 x^3+257165096 x^2+109804551 x+17564616}{18 (3 x+2)^3 (5 x+3)^2}-128634 \log (3 x+2)+128634 \log (5 x+3)","\frac{15708}{3 x+2}+\frac{16698}{5 x+3}+\frac{1617}{2 (3 x+2)^2}-\frac{1331}{2 (5 x+3)^2}+\frac{343}{9 (3 x+2)^3}-128634 \log (3 x+2)+128634 \log (5 x+3)",1,"(17564616 + 109804551*x + 257165096*x^2 + 267430086*x^3 + 104193540*x^4)/(18*(2 + 3*x)^3*(3 + 5*x)^2) - 128634*Log[2 + 3*x] + 128634*Log[3 + 5*x]","A",1
1430,1,60,75,0.0549459,"\int \frac{(1-2 x)^3}{(2+3 x)^5 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^5*(3 + 5*x)^3),x]","\frac{1544726700 x^5+4994616330 x^4+6455813364 x^3+4169655991 x^2+1345680462 x+173603415}{12 (3 x+2)^4 (5 x+3)^2}-953535 \log (3 x+2)+953535 \log (5 x+3)","\frac{128634}{3 x+2}+\frac{103455}{5 x+3}+\frac{7854}{(3 x+2)^2}-\frac{6655}{2 (5 x+3)^2}+\frac{539}{(3 x+2)^3}+\frac{343}{12 (3 x+2)^4}-953535 \log (3 x+2)+953535 \log (5 x+3)",1,"(173603415 + 1345680462*x + 4169655991*x^2 + 6455813364*x^3 + 4994616330*x^4 + 1544726700*x^5)/(12*(2 + 3*x)^4*(3 + 5*x)^2) - 953535*Log[2 + 3*x] + 953535*Log[3 + 5*x]","A",1
1431,1,65,86,0.0920046,"\int \frac{(1-2 x)^3}{(2+3 x)^6 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^6*(3 + 5*x)^3),x]","\frac{160841092500 x^6+627280260750 x^5+1018898535600 x^4+882286862985 x^3+429553050280 x^2+111486629505 x+12050702538}{60 (3 x+2)^5 (5 x+3)^2}-6618975 \log (3 x+2)+6618975 \log (5 x+3)","\frac{953535}{3 x+2}+\frac{617100}{5 x+3}+\frac{64317}{(3 x+2)^2}-\frac{33275}{2 (5 x+3)^2}+\frac{5236}{(3 x+2)^3}+\frac{1617}{4 (3 x+2)^4}+\frac{343}{15 (3 x+2)^5}-6618975 \log (3 x+2)+6618975 \log (5 x+3)",1,"(12050702538 + 111486629505*x + 429553050280*x^2 + 882286862985*x^3 + 1018898535600*x^4 + 627280260750*x^5 + 160841092500*x^6)/(60*(2 + 3*x)^5*(3 + 5*x)^2) - 6618975*Log[2 + 3*x] + 6618975*Log[3 + 5*x]","A",1
1432,1,70,97,0.1408586,"\int \frac{(1-2 x)^3}{(2+3 x)^7 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^7*(3 + 5*x)^3),x]","\frac{4794860812500 x^7+21896531043750 x^6+42841193422500 x^5+46551705341625 x^4+30340145968110 x^3+11860532030465 x^2+2574943269792 x+239497011063}{90 (3 x+2)^6 (5 x+3)^2}-43848750 \log (3 x+2)+43848750 \log (5 x+3)","\frac{6618975}{3 x+2}+\frac{3584625}{5 x+3}+\frac{953535}{2 (3 x+2)^2}-\frac{166375}{2 (5 x+3)^2}+\frac{42878}{(3 x+2)^3}+\frac{3927}{(3 x+2)^4}+\frac{1617}{5 (3 x+2)^5}+\frac{343}{18 (3 x+2)^6}-43848750 \log (3 x+2)+43848750 \log (5 x+3)",1,"(239497011063 + 2574943269792*x + 11860532030465*x^2 + 30340145968110*x^3 + 46551705341625*x^4 + 42841193422500*x^5 + 21896531043750*x^6 + 4794860812500*x^7)/(90*(2 + 3*x)^6*(3 + 5*x)^2) - 43848750*Log[2 + 3*x] + 43848750*Log[3 + 5*x]","A",1
1433,1,75,110,0.1398499,"\int \frac{(1-2 x)^3}{(2+3 x)^8 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^3/((2 + 3*x)^8*(3 + 5*x)^3),x]","\frac{30672675000000 x^8+160520332500000 x^7+367435926000000 x^6+480493891350000 x^5+392612784696000 x^4+205262100529200 x^3+67053019228048 x^2+12513316868859 x+1021373267628}{30 (3 x+2)^7 (5 x+3)^2}-280500000 \log (3 x+2)+280500000 \log (5 x+3)","\frac{43848750}{3 x+2}+\frac{20418750}{5 x+3}+\frac{6618975}{2 (3 x+2)^2}-\frac{831875}{2 (5 x+3)^2}+\frac{317845}{(3 x+2)^3}+\frac{64317}{2 (3 x+2)^4}+\frac{15708}{5 (3 x+2)^5}+\frac{539}{2 (3 x+2)^6}+\frac{49}{3 (3 x+2)^7}-280500000 \log (3 x+2)+280500000 \log (5 x+3)",1,"(1021373267628 + 12513316868859*x + 67053019228048*x^2 + 205262100529200*x^3 + 392612784696000*x^4 + 480493891350000*x^5 + 367435926000000*x^6 + 160520332500000*x^7 + 30672675000000*x^8)/(30*(2 + 3*x)^7*(3 + 5*x)^2) - 280500000*Log[2 + 3*x] + 280500000*Log[3 + 5*x]","A",1
1434,1,56,72,0.0271819,"\int \frac{(2+3 x)^8 (3+5 x)}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^8*(3 + 5*x))/(1 - 2*x),x]","-\frac{x \left(4665600 x^8+33767280 x^7+113140800 x^6+234375120 x^5+340354224 x^4+377226990 x^3+347822580 x^2+301663095 x+315097975\right)}{2560}-\frac{63412811 \log (2 x-1)}{1024}","-\frac{3645 x^9}{2}-\frac{422091 x^8}{32}-\frac{353565 x^7}{8}-\frac{2929689 x^6}{32}-\frac{21272139 x^5}{160}-\frac{37722699 x^4}{256}-\frac{17391129 x^3}{128}-\frac{60332619 x^2}{512}-\frac{63019595 x}{512}-\frac{63412811 \log (1-2 x)}{1024}",1,"-1/2560*(x*(315097975 + 301663095*x + 347822580*x^2 + 377226990*x^3 + 340354224*x^4 + 234375120*x^5 + 113140800*x^6 + 33767280*x^7 + 4665600*x^8)) - (63412811*Log[-1 + 2*x])/1024","A",1
1435,1,51,65,0.0234412,"\int \frac{(2+3 x)^7 (3+5 x)}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^7*(3 + 5*x))/(1 - 2*x),x]","-\frac{x \left(6123600 x^7+40357440 x^6+122608080 x^5+230038704 x^4+304650990 x^3+315996660 x^2+292692855 x+313623415\right)}{8960}-\frac{9058973}{512} \log (2 x-1)","-\frac{10935 x^8}{16}-\frac{126117 x^7}{28}-\frac{218943 x^6}{16}-\frac{2053917 x^5}{80}-\frac{4352157 x^4}{128}-\frac{2257119 x^3}{64}-\frac{8362653 x^2}{256}-\frac{8960669 x}{256}-\frac{9058973}{512} \log (1-2 x)",1,"-1/8960*(x*(313623415 + 292692855*x + 315996660*x^2 + 304650990*x^3 + 230038704*x^4 + 122608080*x^5 + 40357440*x^6 + 6123600*x^7)) - (9058973*Log[-1 + 2*x])/512","A",1
1436,1,46,58,0.02279,"\int \frac{(2+3 x)^6 (3+5 x)}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x),x]","-\frac{x \left(1166400 x^6+6940080 x^5+18969552 x^4+32116770 x^3+39151980 x^2+39847185 x+44434705\right)}{4480}-\frac{1294139}{256} \log (2 x-1)","-\frac{3645 x^7}{14}-\frac{12393 x^6}{8}-\frac{169371 x^5}{40}-\frac{458811 x^4}{64}-\frac{279657 x^3}{32}-\frac{1138491 x^2}{128}-\frac{1269563 x}{128}-\frac{1294139}{256} \log (1-2 x)",1,"-1/4480*(x*(44434705 + 39847185*x + 39151980*x^2 + 32116770*x^3 + 18969552*x^4 + 6940080*x^5 + 1166400*x^6)) - (1294139*Log[-1 + 2*x])/256","A",1
1437,1,41,51,0.0207223,"\int \frac{(2+3 x)^5 (3+5 x)}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^5*(3 + 5*x))/(1 - 2*x),x]","-\frac{1}{320} x \left(32400 x^5+172368 x^4+420930 x^3+645420 x^2+752865 x+893665\right)-\frac{184877}{128} \log (2 x-1)","-\frac{405 x^6}{4}-\frac{10773 x^5}{20}-\frac{42093 x^4}{32}-\frac{32271 x^3}{16}-\frac{150573 x^2}{64}-\frac{178733 x}{64}-\frac{184877}{128} \log (1-2 x)",1,"-1/320*(x*(893665 + 752865*x + 645420*x^2 + 420930*x^3 + 172368*x^4 + 32400*x^5)) - (184877*Log[-1 + 2*x])/128","A",1
1438,1,36,44,0.0206869,"\int \frac{(2+3 x)^4 (3+5 x)}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x),x]","-\frac{1}{32} x \left(1296 x^4+6102 x^3+13284 x^2+18987 x+24875\right)-\frac{26411}{64} \log (2 x-1)","-\frac{81 x^5}{2}-\frac{3051 x^4}{16}-\frac{3321 x^3}{8}-\frac{18987 x^2}{32}-\frac{24875 x}{32}-\frac{26411}{64} \log (1-2 x)",1,"-1/32*(x*(24875 + 18987*x + 13284*x^2 + 6102*x^3 + 1296*x^4)) - (26411*Log[-1 + 2*x])/64","A",1
1439,1,31,37,0.0176277,"\int \frac{(2+3 x)^3 (3+5 x)}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x),x]","-\frac{1}{16} x \left(270 x^3+1116 x^2+2205 x+3389\right)-\frac{3773}{32} \log (2 x-1)","-\frac{135 x^4}{8}-\frac{279 x^3}{4}-\frac{2205 x^2}{16}-\frac{3389 x}{16}-\frac{3773}{32} \log (1-2 x)",1,"-1/16*(x*(3389 + 2205*x + 1116*x^2 + 270*x^3)) - (3773*Log[-1 + 2*x])/32","A",1
1440,1,26,30,0.0156531,"\int \frac{(2+3 x)^2 (3+5 x)}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x))/(1 - 2*x),x]","-\frac{1}{8} x \left(60 x^2+219 x+443\right)-\frac{539}{16} \log (2 x-1)","-\frac{15 x^3}{2}-\frac{219 x^2}{8}-\frac{443 x}{8}-\frac{539}{16} \log (1-2 x)",1,"-1/8*(x*(443 + 219*x + 60*x^2)) - (539*Log[-1 + 2*x])/16","A",1
1441,1,21,23,0.0090602,"\int \frac{(2+3 x) (3+5 x)}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x))/(1 - 2*x),x]","-\frac{1}{4} x (15 x+53)-\frac{77}{8} \log (2 x-1)","-\frac{15 x^2}{4}-\frac{53 x}{4}-\frac{77}{8} \log (1-2 x)",1,"-1/4*(x*(53 + 15*x)) - (77*Log[-1 + 2*x])/8","A",1
1442,1,16,16,0.0063213,"\int \frac{3+5 x}{1-2 x} \, dx","IntegrateAlgebraic[(3 + 5*x)/(1 - 2*x),x]","-\frac{5 x}{2}-\frac{11}{4} \log (2 x-1)","-\frac{5 x}{2}-\frac{11}{4} \log (1-2 x)",1,"(-5*x)/2 - (11*Log[-1 + 2*x])/4","A",1
1443,1,21,21,0.008333,"\int \frac{3+5 x}{(1-2 x) (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)),x]","-\frac{11}{14} \log (2 x-1)-\frac{1}{21} \log (3 x+2)","-\frac{11}{14} \log (1-2 x)-\frac{1}{21} \log (3 x+2)",1,"(-11*Log[-1 + 2*x])/14 - Log[2 + 3*x]/21","A",1
1444,1,28,32,0.0260456,"\int \frac{3+5 x}{(1-2 x) (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^2),x]","\frac{1}{21 (3 x+2)}+\frac{22}{49} \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)","\frac{1}{21 (3 x+2)}-\frac{11}{49} \log (1-2 x)+\frac{11}{49} \log (3 x+2)",1,"1/(21*(2 + 3*x)) + (22*ArcTanh[(3 + x)/(1 + 5*x)])/49","A",1
1445,1,33,43,0.0287043,"\int \frac{3+5 x}{(1-2 x) (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^3),x]","\frac{-198 x-125}{294 (3 x+2)^2}+\frac{44}{343} \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)","-\frac{11}{49 (3 x+2)}+\frac{1}{42 (3 x+2)^2}-\frac{22}{343} \log (1-2 x)+\frac{22}{343} \log (3 x+2)",1,"(-125 - 198*x)/(294*(2 + 3*x)^2) + (44*ArcTanh[(3 + x)/(1 + 5*x)])/343","A",1
1446,1,38,54,0.0340687,"\int \frac{3+5 x}{(1-2 x) (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^4),x]","\frac{-3564 x^2-6831 x-2872}{6174 (3 x+2)^3}+\frac{88 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{2401}","-\frac{22}{343 (3 x+2)}-\frac{11}{98 (3 x+2)^2}+\frac{1}{63 (3 x+2)^3}-\frac{44 \log (1-2 x)}{2401}+\frac{44 \log (3 x+2)}{2401}",1,"(-2872 - 6831*x - 3564*x^2)/(6174*(2 + 3*x)^3) + (88*ArcTanh[(3 + x)/(1 + 5*x)])/2401","A",1
1447,1,43,65,0.0444089,"\int \frac{3+5 x}{(1-2 x) (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^5),x]","\frac{-4752 x^3-12276 x^2-12188 x-3963}{9604 (3 x+2)^4}+\frac{176 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{16807}","-\frac{44}{2401 (3 x+2)}-\frac{11}{343 (3 x+2)^2}-\frac{11}{147 (3 x+2)^3}+\frac{1}{84 (3 x+2)^4}-\frac{88 \log (1-2 x)}{16807}+\frac{88 \log (3 x+2)}{16807}",1,"(-3963 - 12188*x - 12276*x^2 - 4752*x^3)/(9604*(2 + 3*x)^4) + (176*ArcTanh[(3 + x)/(1 + 5*x)])/16807","A",1
1448,1,48,76,0.0545911,"\int \frac{3+5 x}{(1-2 x) (2+3 x)^6} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^6),x]","\frac{-427680 x^4-1389960 x^3-1833480 x^2-1268025 x-348226}{1008420 (3 x+2)^5}+\frac{352 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{117649}","-\frac{88}{16807 (3 x+2)}-\frac{22}{2401 (3 x+2)^2}-\frac{22}{1029 (3 x+2)^3}-\frac{11}{196 (3 x+2)^4}+\frac{1}{105 (3 x+2)^5}-\frac{176 \log (1-2 x)}{117649}+\frac{176 \log (3 x+2)}{117649}",1,"(-348226 - 1268025*x - 1833480*x^2 - 1389960*x^3 - 427680*x^4)/(1008420*(2 + 3*x)^5) + (352*ArcTanh[(3 + x)/(1 + 5*x)])/117649","A",1
1449,1,53,87,0.0842259,"\int \frac{3+5 x}{(1-2 x) (2+3 x)^7} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^7),x]","\frac{-3849120 x^5-15075720 x^4-24841080 x^3-22413105 x^2-12254814 x-3013741}{10588410 (3 x+2)^6}+\frac{704 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{823543}","-\frac{176}{117649 (3 x+2)}-\frac{44}{16807 (3 x+2)^2}-\frac{44}{7203 (3 x+2)^3}-\frac{11}{686 (3 x+2)^4}-\frac{11}{245 (3 x+2)^5}+\frac{1}{126 (3 x+2)^6}-\frac{352 \log (1-2 x)}{823543}+\frac{352 \log (3 x+2)}{823543}",1,"(-3013741 - 12254814*x - 22413105*x^2 - 24841080*x^3 - 15075720*x^4 - 3849120*x^5)/(10588410*(2 + 3*x)^6) + (704*ArcTanh[(3 + x)/(1 + 5*x)])/823543","A",1
1450,1,58,98,0.0715082,"\int \frac{3+5 x}{(1-2 x) (2+3 x)^8} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^8),x]","\frac{-7698240 x^6-35283600 x^5-69783120 x^4-77947650 x^3-54393768 x^2-25308459 x-5811068}{24706290 (3 x+2)^7}+\frac{1408 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{5764801}","-\frac{352}{823543 (3 x+2)}-\frac{88}{117649 (3 x+2)^2}-\frac{88}{50421 (3 x+2)^3}-\frac{11}{2401 (3 x+2)^4}-\frac{22}{1715 (3 x+2)^5}-\frac{11}{294 (3 x+2)^6}+\frac{1}{147 (3 x+2)^7}-\frac{704 \log (1-2 x)}{5764801}+\frac{704 \log (3 x+2)}{5764801}",1,"(-5811068 - 25308459*x - 54393768*x^2 - 77947650*x^3 - 69783120*x^4 - 35283600*x^5 - 7698240*x^6)/(24706290*(2 + 3*x)^7) + (1408*ArcTanh[(3 + x)/(1 + 5*x)])/5764801","A",1
1451,1,61,79,0.0257383,"\int \frac{(2+3 x)^8 (3+5 x)^2}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^8*(3 + 5*x)^2)/(1 - 2*x),x]","-\frac{x \left(41990400 x^9+328147200 x^8+1192585680 x^7+2687774400 x^6+4242535920 x^5+5059941264 x^4+4872031290 x^3+4098022780 x^2+3385468445 x+3475908125\right)}{5120}-\frac{697540921 \log (2 x-1)}{2048}","-\frac{32805 x^{10}}{4}-\frac{256365 x^9}{4}-\frac{14907321 x^8}{64}-\frac{8399295 x^7}{16}-\frac{53031699 x^6}{64}-\frac{316246329 x^5}{320}-\frac{487203129 x^4}{512}-\frac{204901139 x^3}{256}-\frac{677093689 x^2}{1024}-\frac{695181625 x}{1024}-\frac{697540921 \log (1-2 x)}{2048}",1,"-1/5120*(x*(3475908125 + 3385468445*x + 4098022780*x^2 + 4872031290*x^3 + 5059941264*x^4 + 4242535920*x^5 + 2687774400*x^6 + 1192585680*x^7 + 328147200*x^8 + 41990400*x^9)) - (697540921*Log[-1 + 2*x])/2048","A",1
1452,1,56,72,0.0230454,"\int \frac{(2+3 x)^7 (3+5 x)^2}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^7*(3 + 5*x)^2)/(1 - 2*x),x]","-\frac{x \left(54432000 x^8+389869200 x^7+1293071040 x^6+2652637680 x^5+3817440144 x^4+4197880890 x^3+3847265660 x^2+3324274205 x+3467060765\right)}{17920}-\frac{99648703 \log (2 x-1)}{1024}","-\frac{6075 x^9}{2}-\frac{696195 x^8}{32}-\frac{4040847 x^7}{56}-\frac{4736853 x^6}{32}-\frac{34084287 x^5}{160}-\frac{59969727 x^4}{256}-\frac{27480469 x^3}{128}-\frac{94979263 x^2}{512}-\frac{99058879 x}{512}-\frac{99648703 \log (1-2 x)}{1024}",1,"-1/17920*(x*(3467060765 + 3324274205*x + 3847265660*x^2 + 4197880890*x^3 + 3817440144*x^4 + 2652637680*x^5 + 1293071040*x^6 + 389869200*x^7 + 54432000*x^8)) - (99648703*Log[-1 + 2*x])/1024","A",1
1453,1,51,65,0.0230843,"\int \frac{(2+3 x)^6 (3+5 x)^2}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^6*(3 + 5*x)^2)/(1 - 2*x),x]","-\frac{x \left(10206000 x^7+66484800 x^6+199720080 x^5+370751472 x^4+486340470 x^3+500559780 x^2+461256635 x+493082555\right)}{8960}-\frac{14235529}{512} \log (2 x-1)","-\frac{18225 x^8}{16}-\frac{207765 x^7}{28}-\frac{356643 x^6}{16}-\frac{3310281 x^5}{80}-\frac{6947721 x^4}{128}-\frac{3575427 x^3}{64}-\frac{13178761 x^2}{256}-\frac{14088073 x}{256}-\frac{14235529}{512} \log (1-2 x)",1,"-1/8960*(x*(493082555 + 461256635*x + 500559780*x^2 + 486340470*x^3 + 370751472*x^4 + 199720080*x^5 + 66484800*x^6 + 10206000*x^7)) - (14235529*Log[-1 + 2*x])/512","A",1
1454,1,46,58,0.0207065,"\int \frac{(2+3 x)^5 (3+5 x)^2}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^5*(3 + 5*x)^2)/(1 - 2*x),x]","-\frac{x \left(1944000 x^6+11415600 x^5+30811536 x^4+51563610 x^3+62241340 x^2+62898605 x+69887405\right)}{4480}-\frac{2033647}{256} \log (2 x-1)","-\frac{6075 x^7}{14}-\frac{20385 x^6}{8}-\frac{275103 x^5}{40}-\frac{736623 x^4}{64}-\frac{444581 x^3}{32}-\frac{1797103 x^2}{128}-\frac{1996783 x}{128}-\frac{2033647}{256} \log (1-2 x)",1,"-1/4480*(x*(69887405 + 62898605*x + 62241340*x^2 + 51563610*x^3 + 30811536*x^4 + 11415600*x^5 + 1944000*x^6)) - (2033647*Log[-1 + 2*x])/256","A",1
1455,1,41,51,0.0190109,"\int \frac{(2+3 x)^4 (3+5 x)^2}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x),x]","-\frac{1}{64} x \left(10800 x^5+56592 x^4+136242 x^3+206284 x^2+238297 x+281305\right)-\frac{290521}{128} \log (2 x-1)","-\frac{675 x^6}{4}-\frac{3537 x^5}{4}-\frac{68121 x^4}{32}-\frac{51571 x^3}{16}-\frac{238297 x^2}{64}-\frac{281305 x}{64}-\frac{290521}{128} \log (1-2 x)",1,"-1/64*(x*(281305 + 238297*x + 206284*x^2 + 136242*x^3 + 56592*x^4 + 10800*x^5)) - (290521*Log[-1 + 2*x])/128","A",1
1456,1,36,44,0.0178111,"\int \frac{(2+3 x)^3 (3+5 x)^2}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^2)/(1 - 2*x),x]","-\frac{1}{32} x \left(2160 x^4+9990 x^3+21396 x^2+30175 x+39199\right)-\frac{41503}{64} \log (2 x-1)","-\frac{135 x^5}{2}-\frac{4995 x^4}{16}-\frac{5349 x^3}{8}-\frac{30175 x^2}{32}-\frac{39199 x}{32}-\frac{41503}{64} \log (1-2 x)",1,"-1/32*(x*(39199 + 30175*x + 21396*x^2 + 9990*x^3 + 2160*x^4)) - (41503*Log[-1 + 2*x])/64","A",1
1457,1,31,37,0.0156564,"\int \frac{(2+3 x)^2 (3+5 x)^2}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x),x]","-\frac{1}{16} x \left(450 x^3+1820 x^2+3529 x+5353\right)-\frac{5929}{32} \log (2 x-1)","-\frac{225 x^4}{8}-\frac{455 x^3}{4}-\frac{3529 x^2}{16}-\frac{5353 x}{16}-\frac{5929}{32} \log (1-2 x)",1,"-1/16*(x*(5353 + 3529*x + 1820*x^2 + 450*x^3)) - (5929*Log[-1 + 2*x])/32","A",1
1458,1,26,30,0.0156889,"\int \frac{(2+3 x) (3+5 x)^2}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^2)/(1 - 2*x),x]","-\frac{1}{8} x \left(100 x^2+355 x+703\right)-\frac{847}{16} \log (2 x-1)","-\frac{25 x^3}{2}-\frac{355 x^2}{8}-\frac{703 x}{8}-\frac{847}{16} \log (1-2 x)",1,"-1/8*(x*(703 + 355*x + 100*x^2)) - (847*Log[-1 + 2*x])/16","A",1
1459,1,25,23,0.0114419,"\int \frac{(3+5 x)^2}{1-2 x} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/(1 - 2*x),x]","-\frac{5}{16} \left(20 x^2+68 x-39\right)-\frac{121}{8} \log (2 x-1)","-\frac{25 x^2}{4}-\frac{85 x}{4}-\frac{121}{8} \log (1-2 x)",1,"(-5*(-39 + 68*x + 20*x^2))/16 - (121*Log[-1 + 2*x])/8","A",1
1460,1,26,26,0.0184793,"\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)),x]","-\frac{25 x}{6}-\frac{121}{28} \log (2 x-1)+\frac{1}{63} \log (3 x+2)","-\frac{25 x}{6}-\frac{121}{28} \log (1-2 x)+\frac{1}{63} \log (3 x+2)",1,"(-25*x)/6 - (121*Log[-1 + 2*x])/28 + Log[2 + 3*x]/63","A",1
1461,1,32,32,0.0293133,"\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^2),x]","-\frac{1}{63 (3 x+2)}-\frac{121}{98} \log (2 x-1)-\frac{68}{441} \log (3 x+2)","-\frac{1}{63 (3 x+2)}-\frac{121}{98} \log (1-2 x)-\frac{68}{441} \log (3 x+2)",1,"-1/63*1/(2 + 3*x) - (121*Log[-1 + 2*x])/98 - (68*Log[2 + 3*x])/441","A",1
1462,1,33,43,0.0296631,"\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^3),x]","\frac{408 x+265}{882 (3 x+2)^2}+\frac{242}{343} \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)","\frac{68}{441 (3 x+2)}-\frac{1}{126 (3 x+2)^2}-\frac{121}{343} \log (1-2 x)+\frac{121}{343} \log (3 x+2)",1,"(265 + 408*x)/(882*(2 + 3*x)^2) + (242*ArcTanh[(3 + x)/(1 + 5*x)])/343","A",1
1463,1,38,54,0.0372685,"\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^4),x]","\frac{-29403 x^2-37062 x-11689}{9261 (3 x+2)^3}+\frac{484 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{2401}","-\frac{121}{343 (3 x+2)}+\frac{34}{441 (3 x+2)^2}-\frac{1}{189 (3 x+2)^3}-\frac{242 \log (1-2 x)}{2401}+\frac{242 \log (3 x+2)}{2401}",1,"(-11689 - 37062*x - 29403*x^2)/(9261*(2 + 3*x)^3) + (484*ArcTanh[(3 + x)/(1 + 5*x)])/2401","A",1
1464,1,43,65,0.0493711,"\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^5),x]","\frac{-705672 x^3-1822986 x^2-1449768 x-366413}{259308 (3 x+2)^4}+\frac{968 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{16807}","-\frac{242}{2401 (3 x+2)}-\frac{121}{686 (3 x+2)^2}+\frac{68}{1323 (3 x+2)^3}-\frac{1}{252 (3 x+2)^4}-\frac{484 \log (1-2 x)}{16807}+\frac{484 \log (3 x+2)}{16807}",1,"(-366413 - 1449768*x - 1822986*x^2 - 705672*x^3)/(259308*(2 + 3*x)^4) + (968*ArcTanh[(3 + x)/(1 + 5*x)])/16807","A",1
1465,1,48,76,0.0709187,"\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^6} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^6),x]","\frac{-1764180 x^4-5733585 x^3-7563105 x^2-4442775 x-953231}{756315 (3 x+2)^5}+\frac{1936 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{117649}","-\frac{484}{16807 (3 x+2)}-\frac{121}{2401 (3 x+2)^2}-\frac{121}{1029 (3 x+2)^3}+\frac{17}{441 (3 x+2)^4}-\frac{1}{315 (3 x+2)^5}-\frac{968 \log (1-2 x)}{117649}+\frac{968 \log (3 x+2)}{117649}",1,"(-953231 - 4442775*x - 7563105*x^2 - 5733585*x^3 - 1764180*x^4)/(756315*(2 + 3*x)^5) + (1936*ArcTanh[(3 + x)/(1 + 5*x)])/117649","A",1
1466,1,53,87,0.0781343,"\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^7} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^7),x]","\frac{-127020960 x^5-497498760 x^4-819755640 x^3-739632465 x^2-351466812 x-67099978}{63530460 (3 x+2)^6}+\frac{3872 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{823543}","-\frac{968}{117649 (3 x+2)}-\frac{242}{16807 (3 x+2)^2}-\frac{242}{7203 (3 x+2)^3}-\frac{121}{1372 (3 x+2)^4}+\frac{68}{2205 (3 x+2)^5}-\frac{1}{378 (3 x+2)^6}-\frac{1936 \log (1-2 x)}{823543}+\frac{1936 \log (3 x+2)}{823543}",1,"(-67099978 - 351466812*x - 739632465*x^2 - 819755640*x^3 - 497498760*x^4 - 127020960*x^5)/(63530460*(2 + 3*x)^6) + (3872*ArcTanh[(3 + x)/(1 + 5*x)])/823543","A",1
1467,1,58,98,0.0893113,"\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^8} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^8),x]","\frac{-381062880 x^6-1746538200 x^5-3454264440 x^4-3858408675 x^3-2692491516 x^2-1098354408 x-193528666}{222356610 (3 x+2)^7}+\frac{7744 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{5764801}","-\frac{1936}{823543 (3 x+2)}-\frac{484}{117649 (3 x+2)^2}-\frac{484}{50421 (3 x+2)^3}-\frac{121}{4802 (3 x+2)^4}-\frac{121}{1715 (3 x+2)^5}+\frac{34}{1323 (3 x+2)^6}-\frac{1}{441 (3 x+2)^7}-\frac{3872 \log (1-2 x)}{5764801}+\frac{3872 \log (3 x+2)}{5764801}",1,"(-193528666 - 1098354408*x - 2692491516*x^2 - 3858408675*x^3 - 3454264440*x^4 - 1746538200*x^5 - 381062880*x^6)/(222356610*(2 + 3*x)^7) + (7744*ArcTanh[(3 + x)/(1 + 5*x)])/5764801","A",1
1468,1,61,79,0.0253043,"\int \frac{(2+3 x)^7 (3+5 x)^3}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^7*(3 + 5*x)^3)/(1 - 2*x),x]","-\frac{x \left(1469664000 x^9+11376288000 x^8+40960760400 x^7+91485961920 x^6+143183481840 x^5+169463063952 x^4+162125333370 x^3+135736265980 x^2+111842847165 x+114722662845\right)}{107520}-\frac{1096135733 \log (2 x-1)}{2048}","-\frac{54675 x^{10}}{4}-\frac{423225 x^9}{4}-\frac{24381405 x^8}{64}-\frac{95297877 x^7}{112}-\frac{85228263 x^6}{64}-\frac{504354357 x^5}{320}-\frac{772025397 x^4}{512}-\frac{969544757 x^3}{768}-\frac{1065169973 x^2}{1024}-\frac{1092596789 x}{1024}-\frac{1096135733 \log (1-2 x)}{2048}",1,"-1/107520*(x*(114722662845 + 111842847165*x + 135736265980*x^2 + 162125333370*x^3 + 169463063952*x^4 + 143183481840*x^5 + 91485961920*x^6 + 40960760400*x^7 + 11376288000*x^8 + 1469664000*x^9)) - (1096135733*Log[-1 + 2*x])/2048","A",1
1469,1,56,72,0.0229444,"\int \frac{(2+3 x)^6 (3+5 x)^3}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^6*(3 + 5*x)^3)/(1 - 2*x),x]","-\frac{x \left(272160000 x^8+1928934000 x^7+6332385600 x^6+12863748240 x^5+18345697776 x^4+20016723510 x^3+18235208740 x^2+15698857755 x+16349138715\right)}{53760}-\frac{156590819 \log (2 x-1)}{1024}","-\frac{10125 x^9}{2}-\frac{1148175 x^8}{32}-\frac{6596235 x^7}{56}-\frac{7656993 x^6}{32}-\frac{54600291 x^5}{160}-\frac{95317731 x^4}{256}-\frac{130251491 x^3}{384}-\frac{149512931 x^2}{512}-\frac{155706083 x}{512}-\frac{156590819 \log (1-2 x)}{1024}",1,"-1/53760*(x*(16349138715 + 15698857755*x + 18235208740*x^2 + 20016723510*x^3 + 18345697776*x^4 + 12863748240*x^5 + 6332385600*x^6 + 1928934000*x^7 + 272160000*x^8)) - (156590819*Log[-1 + 2*x])/1024","A",1
1470,1,51,65,0.0219794,"\int \frac{(2+3 x)^5 (3+5 x)^3}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^5*(3 + 5*x)^3)/(1 - 2*x),x]","-\frac{x \left(51030000 x^7+328536000 x^6+975769200 x^5+1792134288 x^4+2328575130 x^3+2378316220 x^2+2180485965 x+2325637965\right)}{26880}-\frac{22370117}{512} \log (2 x-1)","-\frac{30375 x^8}{16}-\frac{342225 x^7}{28}-\frac{580815 x^6}{16}-\frac{5333733 x^5}{80}-\frac{11088453 x^4}{128}-\frac{16987973 x^3}{192}-\frac{20766533 x^2}{256}-\frac{22148933 x}{256}-\frac{22370117}{512} \log (1-2 x)",1,"-1/26880*(x*(2325637965 + 2180485965*x + 2378316220*x^2 + 2328575130*x^3 + 1792134288*x^4 + 975769200*x^5 + 328536000*x^6 + 51030000*x^7)) - (22370117*Log[-1 + 2*x])/512","A",1
1471,1,46,58,0.0205255,"\int \frac{(2+3 x)^4 (3+5 x)^3}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x),x]","-\frac{x \left(1944000 x^6+11264400 x^5+30019248 x^4+49656222 x^3+59353364 x^2+59562447 x+65949135\right)}{2688}-\frac{3195731}{256} \log (2 x-1)","-\frac{10125 x^7}{14}-\frac{33525 x^6}{8}-\frac{89343 x^5}{8}-\frac{1182291 x^4}{64}-\frac{2119763 x^3}{96}-\frac{2836307 x^2}{128}-\frac{3140435 x}{128}-\frac{3195731}{256} \log (1-2 x)",1,"-1/2688*(x*(65949135 + 59562447*x + 59353364*x^2 + 49656222*x^3 + 30019248*x^4 + 11264400*x^5 + 1944000*x^6)) - (3195731*Log[-1 + 2*x])/256","A",1
1472,1,41,51,0.0183459,"\int \frac{(2+3 x)^3 (3+5 x)^3}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^3)/(1 - 2*x),x]","-\frac{1}{192} x \left(54000 x^5+278640 x^4+661230 x^3+988628 x^2+1131135 x+1328127\right)-\frac{456533}{128} \log (2 x-1)","-\frac{1125 x^6}{4}-\frac{5805 x^5}{4}-\frac{110205 x^4}{32}-\frac{247157 x^3}{48}-\frac{377045 x^2}{64}-\frac{442709 x}{64}-\frac{456533}{128} \log (1-2 x)",1,"-1/192*(x*(1328127 + 1131135*x + 988628*x^2 + 661230*x^3 + 278640*x^4 + 54000*x^5)) - (456533*Log[-1 + 2*x])/128","A",1
1473,1,36,44,0.018565,"\int \frac{(2+3 x)^2 (3+5 x)^3}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^3)/(1 - 2*x),x]","-\frac{1}{96} x \left(10800 x^4+49050 x^3+103340 x^2+143817 x+185289\right)-\frac{65219}{64} \log (2 x-1)","-\frac{225 x^5}{2}-\frac{8175 x^4}{16}-\frac{25835 x^3}{24}-\frac{47939 x^2}{32}-\frac{61763 x}{32}-\frac{65219}{64} \log (1-2 x)",1,"-1/96*(x*(185289 + 143817*x + 103340*x^2 + 49050*x^3 + 10800*x^4)) - (65219*Log[-1 + 2*x])/64","A",1
1474,1,31,37,0.0176451,"\int \frac{(2+3 x) (3+5 x)^3}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^3)/(1 - 2*x),x]","-\frac{1}{48} x \left(2250 x^3+8900 x^2+16935 x+25359\right)-\frac{9317}{32} \log (2 x-1)","-\frac{375 x^4}{8}-\frac{2225 x^3}{12}-\frac{5645 x^2}{16}-\frac{8453 x}{16}-\frac{9317}{32} \log (1-2 x)",1,"-1/48*(x*(25359 + 16935*x + 8900*x^2 + 2250*x^3)) - (9317*Log[-1 + 2*x])/32","A",1
1475,1,30,30,0.0143165,"\int \frac{(3+5 x)^3}{1-2 x} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/(1 - 2*x),x]","-\frac{5}{96} \left(400 x^3+1380 x^2+2676 x-1733\right)-\frac{1331}{16} \log (2 x-1)","-\frac{125 x^3}{6}-\frac{575 x^2}{8}-\frac{1115 x}{8}-\frac{1331}{16} \log (1-2 x)",1,"(-5*(-1733 + 2676*x + 1380*x^2 + 400*x^3))/96 - (1331*Log[-1 + 2*x])/16","A",1
1476,1,35,33,0.0225104,"\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)),x]","-\frac{25}{36} \left(15 x^2+49 x+24\right)-\frac{1331}{56} \log (2 x-1)-\frac{1}{189} \log (3 x+2)","-\frac{125 x^2}{12}-\frac{1225 x}{36}-\frac{1331}{56} \log (1-2 x)-\frac{1}{189} \log (3 x+2)",1,"(-25*(24 + 49*x + 15*x^2))/36 - (1331*Log[-1 + 2*x])/56 - Log[2 + 3*x]/189","A",1
1477,1,42,37,0.0326258,"\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^2),x]","\frac{-15750 x^2-2625 x+5254}{756 (3 x+2)}-\frac{1331}{196} \log (2 x-1)+\frac{103 \log (3 x+2)}{1323}","-\frac{125 x}{18}+\frac{1}{189 (3 x+2)}-\frac{1331}{196} \log (1-2 x)+\frac{103 \log (3 x+2)}{1323}",1,"(5254 - 2625*x - 15750*x^2)/(756*(2 + 3*x)) - (1331*Log[-1 + 2*x])/196 + (103*Log[2 + 3*x])/1323","A",1
1478,1,37,43,0.0336508,"\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^3),x]","\frac{-206 x-135}{882 (3 x+2)^2}-\frac{1331}{686} \log (2 x-1)-\frac{3469 \log (3 x+2)}{9261}","-\frac{103}{1323 (3 x+2)}+\frac{1}{378 (3 x+2)^2}-\frac{1331}{686} \log (1-2 x)-\frac{3469 \log (3 x+2)}{9261}",1,"(-135 - 206*x)/(882*(2 + 3*x)^2) - (1331*Log[-1 + 2*x])/686 - (3469*Log[2 + 3*x])/9261","A",1
1479,1,38,54,0.0394901,"\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^4),x]","\frac{187326 x^2+243279 x+79028}{55566 (3 x+2)^3}+\frac{2662 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{2401}","\frac{3469}{9261 (3 x+2)}-\frac{103}{2646 (3 x+2)^2}+\frac{1}{567 (3 x+2)^3}-\frac{1331 \log (1-2 x)}{2401}+\frac{1331 \log (3 x+2)}{2401}",1,"(79028 + 243279*x + 187326*x^2)/(55566*(2 + 3*x)^3) + (2662*ArcTanh[(3 + x)/(1 + 5*x)])/2401","A",1
1480,1,43,65,0.0534297,"\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^5),x]","\frac{-11643588 x^3-21975894 x^2-13836972 x-2906507}{777924 (3 x+2)^4}+\frac{5324 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{16807}","-\frac{1331}{2401 (3 x+2)}+\frac{3469}{18522 (3 x+2)^2}-\frac{103}{3969 (3 x+2)^3}+\frac{1}{756 (3 x+2)^4}-\frac{2662 \log (1-2 x)}{16807}+\frac{2662 \log (3 x+2)}{16807}",1,"(-2906507 - 13836972*x - 21975894*x^2 - 11643588*x^3)/(777924*(2 + 3*x)^4) + (5324*ArcTanh[(3 + x)/(1 + 5*x)])/16807","A",1
1481,1,48,76,0.0765553,"\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^6} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^6),x]","\frac{-349307640 x^4-1135249830 x^3-1308416040 x^2-646472325 x-116805778}{27227340 (3 x+2)^5}+\frac{10648 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{117649}","-\frac{2662}{16807 (3 x+2)}-\frac{1331}{4802 (3 x+2)^2}+\frac{3469}{27783 (3 x+2)^3}-\frac{103}{5292 (3 x+2)^4}+\frac{1}{945 (3 x+2)^5}-\frac{5324 \log (1-2 x)}{117649}+\frac{5324 \log (3 x+2)}{117649}",1,"(-116805778 - 646472325*x - 1308416040*x^2 - 1135249830*x^3 - 349307640*x^4)/(27227340*(2 + 3*x)^5) + (10648*ArcTanh[(3 + x)/(1 + 5*x)])/117649","A",1
1482,1,53,87,0.0771538,"\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^7} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^7),x]","\frac{-2095845840 x^5-8208729540 x^4-13525968060 x^3-11211272235 x^2-4581535248 x-733614062}{190591380 (3 x+2)^6}+\frac{21296 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{823543}","-\frac{5324}{117649 (3 x+2)}-\frac{1331}{16807 (3 x+2)^2}-\frac{1331}{7203 (3 x+2)^3}+\frac{3469}{37044 (3 x+2)^4}-\frac{103}{6615 (3 x+2)^5}+\frac{1}{1134 (3 x+2)^6}-\frac{10648 \log (1-2 x)}{823543}+\frac{10648 \log (3 x+2)}{823543}",1,"(-733614062 - 4581535248*x - 11211272235*x^2 - 13525968060*x^3 - 8208729540*x^4 - 2095845840*x^5)/(190591380*(2 + 3*x)^6) + (21296*ArcTanh[(3 + x)/(1 + 5*x)])/823543","A",1
1483,1,58,98,0.0994146,"\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^8} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^8),x]","\frac{-12575075040 x^6-57635760600 x^5-113990726520 x^4-127327486275 x^3-83293304778 x^2-29451465714 x-4309941128}{1334139660 (3 x+2)^7}+\frac{42592 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{5764801}","-\frac{10648}{823543 (3 x+2)}-\frac{2662}{117649 (3 x+2)^2}-\frac{2662}{50421 (3 x+2)^3}-\frac{1331}{9604 (3 x+2)^4}+\frac{3469}{46305 (3 x+2)^5}-\frac{103}{7938 (3 x+2)^6}+\frac{1}{1323 (3 x+2)^7}-\frac{21296 \log (1-2 x)}{5764801}+\frac{21296 \log (3 x+2)}{5764801}",1,"(-4309941128 - 29451465714*x - 83293304778*x^2 - 127327486275*x^3 - 113990726520*x^4 - 57635760600*x^5 - 12575075040*x^6)/(1334139660*(2 + 3*x)^7) + (42592*ArcTanh[(3 + x)/(1 + 5*x)])/5764801","A",1
1484,1,96,104,0.1108614,"\int \frac{(a+b x)^3}{(c+d x) (e+f x)} \, dx","IntegrateAlgebraic[(a + b*x)^3/((c + d*x)*(e + f*x)),x]","\frac{b^2 x (6 a d f-2 b c f-2 b d e+b d f x)}{2 d^2 f^2}+\frac{(a d-b c)^3 \log (c+d x)}{d^3 (d e-c f)}+\frac{(a f-b e)^3 \log (e+f x)}{f^3 (c f-d e)}","-\frac{b^2 x (-3 a d f+b c f+b d e)}{d^2 f^2}-\frac{(b c-a d)^3 \log (c+d x)}{d^3 (d e-c f)}+\frac{(b e-a f)^3 \log (e+f x)}{f^3 (d e-c f)}+\frac{b^3 x^2}{2 d f}",1,"(b^2*x*(-2*b*d*e - 2*b*c*f + 6*a*d*f + b*d*f*x))/(2*d^2*f^2) + ((-(b*c) + a*d)^3*Log[c + d*x])/(d^3*(d*e - c*f)) + ((-(b*e) + a*f)^3*Log[e + f*x])/(f^3*(-(d*e) + c*f))","A",1
1485,1,56,68,0.0370976,"\int \frac{(2+3 x)^8}{(1-2 x) (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^8/((1 - 2*x)*(3 + 5*x)),x]","-\frac{9 x \left(729000000 x^6+4450950000 x^5+12472866000 x^4+21611819250 x^3+26874857100 x^2+27751862985 x+31180998793\right)}{70000000}-\frac{5764801 \log (2 x-1)}{2816}+\frac{\log (5 x+3)}{4296875}","-\frac{6561 x^7}{70}-\frac{114453 x^6}{200}-\frac{8018271 x^5}{5000}-\frac{111146499 x^4}{40000}-\frac{345533877 x^3}{100000}-\frac{7136193339 x^2}{2000000}-\frac{40089855591 x}{10000000}-\frac{5764801 \log (1-2 x)}{2816}+\frac{\log (5 x+3)}{4296875}",1,"(-9*x*(31180998793 + 27751862985*x + 26874857100*x^2 + 21611819250*x^3 + 12472866000*x^4 + 4450950000*x^5 + 729000000*x^6))/70000000 - (5764801*Log[-1 + 2*x])/2816 + Log[3 + 5*x]/4296875","A",1
1486,1,55,61,0.0354202,"\int \frac{(2+3 x)^7}{(1-2 x) (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^7/((1 - 2*x)*(3 + 5*x)),x]","-\frac{3 \left(12150000 x^6+66582000 x^5+167244750 x^4+262991700 x^3+312898095 x^2+375712911 x+163998254\right)}{1000000}-\frac{823543 \log (2 x-1)}{1408}+\frac{\log (5 x+3)}{859375}","-\frac{729 x^6}{20}-\frac{99873 x^5}{500}-\frac{2006937 x^4}{4000}-\frac{7889751 x^3}{10000}-\frac{187738857 x^2}{200000}-\frac{1127138733 x}{1000000}-\frac{823543 \log (1-2 x)}{1408}+\frac{\log (5 x+3)}{859375}",1,"(-3*(163998254 + 375712911*x + 312898095*x^2 + 262991700*x^3 + 167244750*x^4 + 66582000*x^5 + 12150000*x^6))/1000000 - (823543*Log[-1 + 2*x])/1408 + Log[3 + 5*x]/859375","A",1
1487,1,50,54,0.0281875,"\int \frac{(2+3 x)^6}{(1-2 x) (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)*(3 + 5*x)),x]","-\frac{27 \left(54000 x^5+263250 x^4+591900 x^3+869165 x^2+1158877 x+516778\right)}{100000}-\frac{117649}{704} \log (2 x-1)+\frac{\log (5 x+3)}{171875}","-\frac{729 x^5}{50}-\frac{28431 x^4}{400}-\frac{159813 x^3}{1000}-\frac{4693491 x^2}{20000}-\frac{31289679 x}{100000}-\frac{117649}{704} \log (1-2 x)+\frac{\log (5 x+3)}{171875}",1,"(-27*(516778 + 1158877*x + 869165*x^2 + 591900*x^3 + 263250*x^4 + 54000*x^5))/100000 - (117649*Log[-1 + 2*x])/704 + Log[3 + 5*x]/171875","A",1
1488,1,45,47,0.0242514,"\int \frac{(2+3 x)^5}{(1-2 x) (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)*(3 + 5*x)),x]","\frac{-60750 x^4-261900 x^3-537165 x^2-848277 x-392378}{10000}-\frac{16807}{352} \log (2 x-1)+\frac{\log (5 x+3)}{34375}","-\frac{243 x^4}{40}-\frac{2619 x^3}{100}-\frac{107433 x^2}{2000}-\frac{848277 x}{10000}-\frac{16807}{352} \log (1-2 x)+\frac{\log (5 x+3)}{34375}",1,"(-392378 - 848277*x - 537165*x^2 - 261900*x^3 - 60750*x^4)/10000 - (16807*Log[-1 + 2*x])/352 + Log[3 + 5*x]/34375","A",1
1489,1,40,40,0.0283352,"\int \frac{(2+3 x)^4}{(1-2 x) (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)*(3 + 5*x)),x]","\frac{-2700 x^3-10395 x^2-21951 x-10814}{1000}-\frac{2401}{176} \log (2 x-1)+\frac{\log (5 x+3)}{6875}","-\frac{27 x^3}{10}-\frac{2079 x^2}{200}-\frac{21951 x}{1000}-\frac{2401}{176} \log (1-2 x)+\frac{\log (5 x+3)}{6875}",1,"(-10814 - 21951*x - 10395*x^2 - 2700*x^3)/1000 - (2401*Log[-1 + 2*x])/176 + Log[3 + 5*x]/6875","A",1
1490,1,35,33,0.0220775,"\int \frac{(2+3 x)^3}{(1-2 x) (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)*(3 + 5*x)),x]","-\frac{3}{100} \left(45 x^2+171 x+94\right)-\frac{343}{88} \log (2 x-1)+\frac{\log (5 x+3)}{1375}","-\frac{27 x^2}{20}-\frac{513 x}{100}-\frac{343}{88} \log (1-2 x)+\frac{\log (5 x+3)}{1375}",1,"(-3*(94 + 171*x + 45*x^2))/100 - (343*Log[-1 + 2*x])/88 + Log[3 + 5*x]/1375","A",1
1491,1,26,26,0.017397,"\int \frac{(2+3 x)^2}{(1-2 x) (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)*(3 + 5*x)),x]","-\frac{9 x}{10}-\frac{49}{44} \log (2 x-1)+\frac{1}{275} \log (5 x+3)","-\frac{9 x}{10}-\frac{49}{44} \log (1-2 x)+\frac{1}{275} \log (5 x+3)",1,"(-9*x)/10 - (49*Log[-1 + 2*x])/44 + Log[3 + 5*x]/275","A",1
1492,1,21,21,0.0085054,"\int \frac{2+3 x}{(1-2 x) (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)*(3 + 5*x)),x]","\frac{1}{55} \log (5 x+3)-\frac{7}{22} \log (2 x-1)","\frac{1}{55} \log (5 x+3)-\frac{7}{22} \log (1-2 x)",1,"(-7*Log[-1 + 2*x])/22 + Log[3 + 5*x]/55","A",1
1493,1,21,21,0.0084591,"\int \frac{1}{(1-2 x) (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(3 + 5*x)),x]","\frac{1}{11} \log (5 x+3)-\frac{1}{11} \log (2 x-1)","\frac{1}{11} \log (5 x+3)-\frac{1}{11} \log (1-2 x)",1,"-1/11*Log[-1 + 2*x] + Log[3 + 5*x]/11","A",1
1494,1,31,31,0.0120376,"\int \frac{1}{(1-2 x) (2+3 x) (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)*(3 + 5*x)),x]","-\frac{2}{77} \log (2 x-1)-\frac{3}{7} \log (3 x+2)+\frac{5}{11} \log (5 x+3)","-\frac{2}{77} \log (1-2 x)-\frac{3}{7} \log (3 x+2)+\frac{5}{11} \log (5 x+3)",1,"(-2*Log[-1 + 2*x])/77 - (3*Log[2 + 3*x])/7 + (5*Log[3 + 5*x])/11","A",1
1495,1,42,42,0.0303364,"\int \frac{1}{(1-2 x) (2+3 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)),x]","\frac{3}{7 (3 x+2)}-\frac{4}{539} \log (2 x-1)-\frac{111}{49} \log (3 x+2)+\frac{25}{11} \log (5 x+3)","\frac{3}{7 (3 x+2)}-\frac{4}{539} \log (1-2 x)-\frac{111}{49} \log (3 x+2)+\frac{25}{11} \log (5 x+3)",1,"3/(7*(2 + 3*x)) - (4*Log[-1 + 2*x])/539 - (111*Log[2 + 3*x])/49 + (25*Log[3 + 5*x])/11","A",1
1496,1,47,53,0.0333097,"\int \frac{1}{(1-2 x) (2+3 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)),x]","\frac{3 (222 x+155)}{98 (3 x+2)^2}-\frac{8 \log (2 x-1)}{3773}-\frac{3897}{343} \log (3 x+2)+\frac{125}{11} \log (5 x+3)","\frac{111}{49 (3 x+2)}+\frac{3}{14 (3 x+2)^2}-\frac{8 \log (1-2 x)}{3773}-\frac{3897}{343} \log (3 x+2)+\frac{125}{11} \log (5 x+3)",1,"(3*(155 + 222*x))/(98*(2 + 3*x)^2) - (8*Log[-1 + 2*x])/3773 - (3897*Log[2 + 3*x])/343 + (125*Log[3 + 5*x])/11","A",1
1497,1,52,64,0.0637105,"\int \frac{1}{(1-2 x) (2+3 x)^4 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)),x]","\frac{70146 x^2+95859 x+32828}{686 (3 x+2)^3}-\frac{16 \log (2 x-1)}{26411}-\frac{136419 \log (3 x+2)}{2401}+\frac{625}{11} \log (5 x+3)","\frac{3897}{343 (3 x+2)}+\frac{111}{98 (3 x+2)^2}+\frac{1}{7 (3 x+2)^3}-\frac{16 \log (1-2 x)}{26411}-\frac{136419 \log (3 x+2)}{2401}+\frac{625}{11} \log (5 x+3)",1,"(32828 + 95859*x + 70146*x^2)/(686*(2 + 3*x)^3) - (16*Log[-1 + 2*x])/26411 - (136419*Log[2 + 3*x])/2401 + (625*Log[3 + 5*x])/11","A",1
1498,1,57,75,0.0850353,"\int \frac{1}{(1-2 x) (2+3 x)^5 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)),x]","\frac{14733252 x^3+29957526 x^2+20320788 x+4599173}{9604 (3 x+2)^4}-\frac{32 \log (2 x-1)}{184877}-\frac{4774713 \log (3 x+2)}{16807}+\frac{3125}{11} \log (5 x+3)","\frac{136419}{2401 (3 x+2)}+\frac{3897}{686 (3 x+2)^2}+\frac{37}{49 (3 x+2)^3}+\frac{3}{28 (3 x+2)^4}-\frac{32 \log (1-2 x)}{184877}-\frac{4774713 \log (3 x+2)}{16807}+\frac{3125}{11} \log (5 x+3)",1,"(4599173 + 20320788*x + 29957526*x^2 + 14733252*x^3)/(9604*(2 + 3*x)^4) - (32*Log[-1 + 2*x])/184877 - (4774713*Log[2 + 3*x])/16807 + (3125*Log[3 + 5*x])/11","A",1
1499,1,62,86,0.0911793,"\int \frac{1}{(1-2 x) (2+3 x)^6 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)),x]","\frac{27 \left(286482780 x^4+773503410 x^3+783477080 x^2+352854525 x+59622386\right)}{336140 (3 x+2)^5}-\frac{64 \log (2 x-1)}{1294139}-\frac{167115051 \log (3 x+2)}{117649}+\frac{15625}{11} \log (5 x+3)","\frac{4774713}{16807 (3 x+2)}+\frac{136419}{4802 (3 x+2)^2}+\frac{1299}{343 (3 x+2)^3}+\frac{111}{196 (3 x+2)^4}+\frac{3}{35 (3 x+2)^5}-\frac{64 \log (1-2 x)}{1294139}-\frac{167115051 \log (3 x+2)}{117649}+\frac{15625}{11} \log (5 x+3)",1,"(27*(59622386 + 352854525*x + 783477080*x^2 + 773503410*x^3 + 286482780*x^4))/(336140*(2 + 3*x)^5) - (64*Log[-1 + 2*x])/1294139 - (167115051*Log[2 + 3*x])/117649 + (15625*Log[3 + 5*x])/11","A",1
1500,1,67,97,0.0662097,"\int \frac{1}{(1-2 x) (2+3 x)^7 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)^7*(3 + 5*x)),x]","\frac{3 \left(270726382620 x^5+911445482970 x^4+1227693992580 x^3+827038992105 x^2+278642000664 x+37562284366\right)}{2352980 (3 x+2)^6}-\frac{128 \log (2 x-1)}{9058973}-\frac{5849026977 \log (3 x+2)}{823543}+\frac{78125}{11} \log (5 x+3)","\frac{167115051}{117649 (3 x+2)}+\frac{4774713}{33614 (3 x+2)^2}+\frac{45473}{2401 (3 x+2)^3}+\frac{3897}{1372 (3 x+2)^4}+\frac{111}{245 (3 x+2)^5}+\frac{1}{14 (3 x+2)^6}-\frac{128 \log (1-2 x)}{9058973}-\frac{5849026977 \log (3 x+2)}{823543}+\frac{78125}{11} \log (5 x+3)",1,"(3*(37562284366 + 278642000664*x + 827038992105*x^2 + 1227693992580*x^3 + 911445482970*x^4 + 270726382620*x^5))/(2352980*(2 + 3*x)^6) - (128*Log[-1 + 2*x])/9058973 - (5849026977*Log[2 + 3*x])/823543 + (78125*Log[3 + 5*x])/11","A",1
1501,1,67,72,0.0767984,"\int \frac{(2+3 x)^8}{(1-2 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^8/((1 - 2*x)*(3 + 5*x)^2),x]","\frac{-30071250000 x^7-185238900000 x^6-526176708750 x^5-933671103750 x^4-1221880534875 x^3-1473460896600 x^2-1020969414135 x-258172943554}{275000000 (5 x+3)}-\frac{5764801 \log (2 x-1)}{15488}+\frac{266 \log (5 x+3)}{47265625}","-\frac{2187 x^6}{100}-\frac{303993 x^5}{2500}-\frac{6194313 x^4}{20000}-\frac{24660207 x^3}{50000}-\frac{118543581 x^2}{200000}-\frac{3579885909 x}{5000000}-\frac{1}{4296875 (5 x+3)}-\frac{5764801 \log (1-2 x)}{15488}+\frac{266 \log (5 x+3)}{47265625}",1,"(-258172943554 - 1020969414135*x - 1473460896600*x^2 - 1221880534875*x^3 - 933671103750*x^4 - 526176708750*x^5 - 185238900000*x^6 - 30071250000*x^7)/(275000000*(3 + 5*x)) - (5764801*Log[-1 + 2*x])/15488 + (266*Log[3 + 5*x])/47265625","A",1
1502,1,62,65,0.0448278,"\int \frac{(2+3 x)^7}{(1-2 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^7/((1 - 2*x)*(3 + 5*x)^2),x]","\frac{-9622800000 x^6-53486730000 x^5-137632770000 x^4-227660301000 x^3-315671083200 x^2+35641061775 x+99978641969}{220000000 (5 x+3)}-\frac{823543 \log (2 x-1)}{7744}+\frac{233 \log (5 x+3)}{9453125}","-\frac{2187 x^5}{250}-\frac{86751 x^4}{2000}-\frac{495477 x^3}{5000}-\frac{14750667 x^2}{100000}-\frac{19846971 x}{100000}-\frac{1}{859375 (5 x+3)}-\frac{823543 \log (1-2 x)}{7744}+\frac{233 \log (5 x+3)}{9453125}",1,"(99978641969 + 35641061775*x - 315671083200*x^2 - 227660301000*x^3 - 137632770000*x^4 - 53486730000*x^5 - 9622800000*x^6)/(220000000*(3 + 5*x)) - (823543*Log[-1 + 2*x])/7744 + (233*Log[3 + 5*x])/9453125","A",1
1503,1,57,58,0.0461184,"\int \frac{(2+3 x)^6}{(1-2 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)*(3 + 5*x)^2),x]","\frac{-50118750 x^5-250593750 x^4-593071875 x^3-1014255000 x^2-442679985 x-16}{2750000 (5 x+3)}-\frac{117649 \log (2 x-1)}{3872}+\frac{8 \log (5 x+3)}{75625}","-\frac{729 x^4}{200}-\frac{8019 x^3}{500}-\frac{335097 x^2}{10000}-\frac{2682909 x}{50000}-\frac{1}{171875 (5 x+3)}-\frac{117649 \log (1-2 x)}{3872}+\frac{8 \log (5 x+3)}{75625}",1,"(-16 - 442679985*x - 1014255000*x^2 - 593071875*x^3 - 250593750*x^4 - 50118750*x^5)/(2750000*(3 + 5*x)) - (117649*Log[-1 + 2*x])/3872 + (8*Log[3 + 5*x])/75625","A",1
1504,1,52,51,0.0322154,"\int \frac{(2+3 x)^5}{(1-2 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)*(3 + 5*x)^2),x]","\frac{-8910000 x^4-40540500 x^3-97059600 x^2+2318085 x+28730263}{1100000 (5 x+3)}-\frac{16807 \log (2 x-1)}{1936}+\frac{167 \log (5 x+3)}{378125}","-\frac{81 x^3}{50}-\frac{6399 x^2}{1000}-\frac{69039 x}{5000}-\frac{1}{34375 (5 x+3)}-\frac{16807 \log (1-2 x)}{1936}+\frac{167 \log (5 x+3)}{378125}",1,"(28730263 + 2318085*x - 97059600*x^2 - 40540500*x^3 - 8910000*x^4)/(1100000*(3 + 5*x)) - (16807*Log[-1 + 2*x])/1936 + (167*Log[3 + 5*x])/378125","A",1
1505,1,47,44,0.0371038,"\int \frac{(2+3 x)^4}{(1-2 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)*(3 + 5*x)^2),x]","\frac{-445500 x^3-2019600 x^2-1162755 x-66841}{110000 (5 x+3)}-\frac{2401}{968} \log (2 x-1)+\frac{134 \log (5 x+3)}{75625}","-\frac{81 x^2}{100}-\frac{1593 x}{500}-\frac{1}{6875 (5 x+3)}-\frac{2401}{968} \log (1-2 x)+\frac{134 \log (5 x+3)}{75625}",1,"(-66841 - 1162755*x - 2019600*x^2 - 445500*x^3)/(110000*(3 + 5*x)) - (2401*Log[-1 + 2*x])/968 + (134*Log[3 + 5*x])/75625","A",1
1506,1,42,37,0.0301093,"\int \frac{(2+3 x)^3}{(1-2 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)*(3 + 5*x)^2),x]","\frac{-14850 x^2-1485 x+4451}{5500 (5 x+3)}-\frac{343}{484} \log (2 x-1)+\frac{101 \log (5 x+3)}{15125}","-\frac{27 x}{50}-\frac{1}{1375 (5 x+3)}-\frac{343}{484} \log (1-2 x)+\frac{101 \log (5 x+3)}{15125}",1,"(4451 - 1485*x - 14850*x^2)/(5500*(3 + 5*x)) - (343*Log[-1 + 2*x])/484 + (101*Log[3 + 5*x])/15125","A",1
1507,1,32,32,0.0252014,"\int \frac{(2+3 x)^2}{(1-2 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)*(3 + 5*x)^2),x]","-\frac{1}{275 (5 x+3)}-\frac{49}{242} \log (2 x-1)+\frac{68 \log (5 x+3)}{3025}","-\frac{1}{275 (5 x+3)}-\frac{49}{242} \log (1-2 x)+\frac{68 \log (5 x+3)}{3025}",1,"-1/275*1/(3 + 5*x) - (49*Log[-1 + 2*x])/242 + (68*Log[3 + 5*x])/3025","A",1
1508,1,32,32,0.0230136,"\int \frac{2+3 x}{(1-2 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)*(3 + 5*x)^2),x]","-\frac{1}{55 (5 x+3)}-\frac{7}{121} \log (2 x-1)+\frac{7}{121} \log (5 x+3)","-\frac{1}{55 (5 x+3)}-\frac{7}{121} \log (1-2 x)+\frac{7}{121} \log (5 x+3)",1,"-1/55*1/(3 + 5*x) - (7*Log[-1 + 2*x])/121 + (7*Log[3 + 5*x])/121","A",1
1509,1,32,32,0.02001,"\int \frac{1}{(1-2 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(3 + 5*x)^2),x]","-\frac{1}{11 (5 x+3)}-\frac{2}{121} \log (2 x-1)+\frac{2}{121} \log (5 x+3)","-\frac{1}{11 (5 x+3)}-\frac{2}{121} \log (1-2 x)+\frac{2}{121} \log (5 x+3)",1,"-1/11*1/(3 + 5*x) - (2*Log[-1 + 2*x])/121 + (2*Log[3 + 5*x])/121","A",1
1510,1,42,42,0.0309875,"\int \frac{1}{(1-2 x) (2+3 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)*(3 + 5*x)^2),x]","-\frac{5}{11 (5 x+3)}-\frac{4}{847} \log (2 x-1)+\frac{9}{7} \log (3 x+2)-\frac{155}{121} \log (5 x+3)","-\frac{5}{11 (5 x+3)}-\frac{4}{847} \log (1-2 x)+\frac{9}{7} \log (3 x+2)-\frac{155}{121} \log (5 x+3)",1,"-5/(11*(3 + 5*x)) - (4*Log[-1 + 2*x])/847 + (9*Log[2 + 3*x])/7 - (155*Log[3 + 5*x])/121","A",1
1511,1,54,53,0.0374631,"\int \frac{1}{(1-2 x) (2+3 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{-1020 x-647}{77 (3 x+2) (5 x+3)}-\frac{8 \log (2 x-1)}{5929}+\frac{648}{49} \log (3 x+2)-\frac{1600}{121} \log (5 x+3)","-\frac{9}{7 (3 x+2)}-\frac{25}{11 (5 x+3)}-\frac{8 \log (1-2 x)}{5929}+\frac{648}{49} \log (3 x+2)-\frac{1600}{121} \log (5 x+3)",1,"(-647 - 1020*x)/(77*(2 + 3*x)*(3 + 5*x)) - (8*Log[-1 + 2*x])/5929 + (648*Log[2 + 3*x])/49 - (1600*Log[3 + 5*x])/121","A",1
1512,1,59,64,0.040038,"\int \frac{1}{(1-2 x) (2+3 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^2),x]","\frac{-324090 x^2-421329 x-136615}{1078 (3 x+2)^2 (5 x+3)}-\frac{16 \log (2 x-1)}{41503}+\frac{34371}{343} \log (3 x+2)-\frac{12125}{121} \log (5 x+3)","-\frac{648}{49 (3 x+2)}-\frac{125}{11 (5 x+3)}-\frac{9}{14 (3 x+2)^2}-\frac{16 \log (1-2 x)}{41503}+\frac{34371}{343} \log (3 x+2)-\frac{12125}{121} \log (5 x+3)",1,"(-136615 - 421329*x - 324090*x^2)/(1078*(2 + 3*x)^2*(3 + 5*x)) - (16*Log[-1 + 2*x])/41503 + (34371*Log[2 + 3*x])/343 - (12125*Log[3 + 5*x])/121","A",1
1513,1,64,75,0.101371,"\int \frac{1}{(1-2 x) (2+3 x)^4 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^2),x]","\frac{-22801770 x^3-44843517 x^2-29372133 x-6406511}{3773 (3 x+2)^3 (5 x+3)}-\frac{32 \log (2 x-1)}{290521}+\frac{1612242 \log (3 x+2)}{2401}-\frac{81250}{121} \log (5 x+3)","-\frac{34371}{343 (3 x+2)}-\frac{625}{11 (5 x+3)}-\frac{324}{49 (3 x+2)^2}-\frac{3}{7 (3 x+2)^3}-\frac{32 \log (1-2 x)}{290521}+\frac{1612242 \log (3 x+2)}{2401}-\frac{81250}{121} \log (5 x+3)",1,"(-6406511 - 29372133*x - 44843517*x^2 - 22801770*x^3)/(3773*(2 + 3*x)^3*(3 + 5*x)) - (32*Log[-1 + 2*x])/290521 + (1612242*Log[2 + 3*x])/2401 - (81250*Log[3 + 5*x])/121","A",1
1514,1,69,86,0.0575367,"\int \frac{1}{(1-2 x) (2+3 x)^5 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)^2),x]","\frac{-12007729980 x^4-31620356478 x^3-31211205714 x^2-13685553417 x-2249141207}{105644 (3 x+2)^4 (5 x+3)}-\frac{64 \log (2 x-1)}{2033647}+\frac{70752609 \log (3 x+2)}{16807}-\frac{509375}{121} \log (5 x+3)","-\frac{1612242}{2401 (3 x+2)}-\frac{3125}{11 (5 x+3)}-\frac{34371}{686 (3 x+2)^2}-\frac{216}{49 (3 x+2)^3}-\frac{9}{28 (3 x+2)^4}-\frac{64 \log (1-2 x)}{2033647}+\frac{70752609 \log (3 x+2)}{16807}-\frac{509375}{121} \log (5 x+3)",1,"(-2249141207 - 13685553417*x - 31211205714*x^2 - 31620356478*x^3 - 12007729980*x^4)/(105644*(2 + 3*x)^4*(3 + 5*x)) - (64*Log[-1 + 2*x])/2033647 + (70752609*Log[2 + 3*x])/16807 - (509375*Log[3 + 5*x])/121","A",1
1515,1,74,97,0.0667371,"\int \frac{1}{(1-2 x) (2+3 x)^6 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)^2),x]","\frac{-1895084756100 x^5-6253779701610 x^4-8252743193370 x^3-5443759671885 x^2-1794885176145 x-236642515057}{924385 (3 x+2)^5 (5 x+3)}-\frac{128 \log (2 x-1)}{14235529}+\frac{2977686468 \log (3 x+2)}{117649}-\frac{3062500}{121} \log (5 x+3)","-\frac{70752609}{16807 (3 x+2)}-\frac{15625}{11 (5 x+3)}-\frac{806121}{2401 (3 x+2)^2}-\frac{11457}{343 (3 x+2)^3}-\frac{162}{49 (3 x+2)^4}-\frac{9}{35 (3 x+2)^5}-\frac{128 \log (1-2 x)}{14235529}+\frac{2977686468 \log (3 x+2)}{117649}-\frac{3062500}{121} \log (5 x+3)",1,"(-236642515057 - 1794885176145*x - 5443759671885*x^2 - 8252743193370*x^3 - 6253779701610*x^4 - 1895084756100*x^5)/(924385*(2 + 3*x)^5*(3 + 5*x)) - (128*Log[-1 + 2*x])/14235529 + (2977686468*Log[2 + 3*x])/117649 - (3062500*Log[3 + 5*x])/121","A",1
1516,1,67,76,0.0880815,"\int \frac{(2+3 x)^8}{(1-2 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^8/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{-198470250000 x^7-1238785143750 x^6-3594663765000 x^5-6651748805625 x^4-9800947319625 x^3-9104864236875 x^2-4271731670735 x-767506044662}{1512500000 (5 x+3)^2}-\frac{5764801 \log (2 x-1)}{85184}+\frac{31024 \log (5 x+3)}{519921875}","-\frac{6561 x^5}{1250}-\frac{264627 x^4}{10000}-\frac{1535517 x^3}{25000}-\frac{9268263 x^2}{100000}-\frac{62934003 x}{500000}-\frac{266}{47265625 (5 x+3)}-\frac{1}{8593750 (5 x+3)^2}-\frac{5764801 \log (1-2 x)}{85184}+\frac{31024 \log (5 x+3)}{519921875}",1,"(-767506044662 - 4271731670735*x - 9104864236875*x^2 - 9800947319625*x^3 - 6651748805625*x^4 - 3594663765000*x^5 - 1238785143750*x^6 - 198470250000*x^7)/(1512500000*(3 + 5*x)^2) - (5764801*Log[-1 + 2*x])/85184 + (31024*Log[3 + 5*x])/519921875","A",1
1517,1,62,69,0.0500553,"\int \frac{(2+3 x)^7}{(1-2 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^7/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{-66156750000 x^6-376358400000 x^5-1012198275000 x^4-1891740015000 x^3-746752646475 x^2+485450731630 x+256487424349}{1210000000 (5 x+3)^2}-\frac{823543 \log (2 x-1)}{42592}+\frac{4667 \log (5 x+3)}{20796875}","-\frac{2187 x^4}{1000}-\frac{24543 x^3}{2500}-\frac{1044657 x^2}{50000}-\frac{339309 x}{10000}-\frac{233}{9453125 (5 x+3)}-\frac{1}{1718750 (5 x+3)^2}-\frac{823543 \log (1-2 x)}{42592}+\frac{4667 \log (5 x+3)}{20796875}",1,"(256487424349 + 485450731630*x - 746752646475*x^2 - 1891740015000*x^3 - 1012198275000*x^4 - 376358400000*x^5 - 66156750000*x^6)/(1210000000*(3 + 5*x)^2) - (823543*Log[-1 + 2*x])/42592 + (4667*Log[3 + 5*x])/20796875","A",1
1518,1,57,62,0.0559652,"\int \frac{(2+3 x)^6}{(1-2 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{-1470150000 x^5-7718287500 x^4-20802622500 x^3-9661090725 x^2+5157548230 x+2965126159}{60500000 (5 x+3)^2}-\frac{117649 \log (2 x-1)}{21296}+\frac{3347 \log (5 x+3)}{4159375}","-\frac{243 x^3}{250}-\frac{19683 x^2}{5000}-\frac{216999 x}{25000}-\frac{8}{75625 (5 x+3)}-\frac{1}{343750 (5 x+3)^2}-\frac{117649 \log (1-2 x)}{21296}+\frac{3347 \log (5 x+3)}{4159375}",1,"(2965126159 + 5157548230*x - 9661090725*x^2 - 20802622500*x^3 - 7718287500*x^4 - 1470150000*x^5)/(60500000*(3 + 5*x)^2) - (117649*Log[-1 + 2*x])/21296 + (3347*Log[3 + 5*x])/4159375","A",1
1519,1,52,55,0.0367147,"\int \frac{(2+3 x)^5}{(1-2 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{-73507500 x^4-387139500 x^3-217337175 x^2+93782210 x+60415061}{6050000 (5 x+3)^2}-\frac{16807 \log (2 x-1)}{10648}+\frac{11224 \log (5 x+3)}{4159375}","-\frac{243 x^2}{500}-\frac{4941 x}{2500}-\frac{167}{378125 (5 x+3)}-\frac{1}{68750 (5 x+3)^2}-\frac{16807 \log (1-2 x)}{10648}+\frac{11224 \log (5 x+3)}{4159375}",1,"(60415061 + 93782210*x - 217337175*x^2 - 387139500*x^3 - 73507500*x^4)/(6050000*(3 + 5*x)^2) - (16807*Log[-1 + 2*x])/10648 + (11224*Log[3 + 5*x])/4159375","A",1
1520,1,47,48,0.0344433,"\int \frac{(2+3 x)^4}{(1-2 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{-490050 x^3-343035 x^2+117076 x+87883}{60500 (5 x+3)^2}-\frac{2401 \log (2 x-1)}{5324}+\frac{6802 \log (5 x+3)}{831875}","-\frac{81 x}{250}-\frac{134}{75625 (5 x+3)}-\frac{1}{13750 (5 x+3)^2}-\frac{2401 \log (1-2 x)}{5324}+\frac{6802 \log (5 x+3)}{831875}",1,"(87883 + 117076*x - 343035*x^2 - 490050*x^3)/(60500*(3 + 5*x)^2) - (2401*Log[-1 + 2*x])/5324 + (6802*Log[3 + 5*x])/831875","A",1
1521,1,37,43,0.0297373,"\int \frac{(2+3 x)^3}{(1-2 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{-1010 x-617}{30250 (5 x+3)^2}-\frac{343 \log (2 x-1)}{2662}+\frac{3469 \log (5 x+3)}{166375}","-\frac{101}{15125 (5 x+3)}-\frac{1}{2750 (5 x+3)^2}-\frac{343 \log (1-2 x)}{2662}+\frac{3469 \log (5 x+3)}{166375}",1,"(-617 - 1010*x)/(30250*(3 + 5*x)^2) - (343*Log[-1 + 2*x])/2662 + (3469*Log[3 + 5*x])/166375","A",1
1522,1,37,43,0.0307576,"\int \frac{(2+3 x)^2}{(1-2 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{-680 x-419}{6050 (5 x+3)^2}-\frac{49 \log (2 x-1)}{1331}+\frac{49 \log (5 x+3)}{1331}","-\frac{68}{3025 (5 x+3)}-\frac{1}{550 (5 x+3)^2}-\frac{49 \log (1-2 x)}{1331}+\frac{49 \log (5 x+3)}{1331}",1,"(-419 - 680*x)/(6050*(3 + 5*x)^2) - (49*Log[-1 + 2*x])/1331 + (49*Log[3 + 5*x])/1331","A",1
1523,1,37,43,0.0278996,"\int \frac{2+3 x}{(1-2 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{-350 x-221}{1210 (5 x+3)^2}-\frac{14 \log (2 x-1)}{1331}+\frac{14 \log (5 x+3)}{1331}","-\frac{7}{121 (5 x+3)}-\frac{1}{110 (5 x+3)^2}-\frac{14 \log (1-2 x)}{1331}+\frac{14 \log (5 x+3)}{1331}",1,"(-221 - 350*x)/(1210*(3 + 5*x)^2) - (14*Log[-1 + 2*x])/1331 + (14*Log[3 + 5*x])/1331","A",1
1524,1,37,43,0.0245041,"\int \frac{1}{(1-2 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{-20 x-23}{242 (5 x+3)^2}-\frac{4 \log (2 x-1)}{1331}+\frac{4 \log (5 x+3)}{1331}","-\frac{2}{121 (5 x+3)}-\frac{1}{22 (5 x+3)^2}-\frac{4 \log (1-2 x)}{1331}+\frac{4 \log (5 x+3)}{1331}",1,"(-23 - 20*x)/(242*(3 + 5*x)^2) - (4*Log[-1 + 2*x])/1331 + (4*Log[3 + 5*x])/1331","A",1
1525,1,47,53,0.047527,"\int \frac{1}{(1-2 x) (2+3 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)*(3 + 5*x)^3),x]","\frac{25 (62 x+35)}{242 (5 x+3)^2}-\frac{8 \log (2 x-1)}{9317}-\frac{27}{7} \log (3 x+2)+\frac{5135 \log (5 x+3)}{1331}","\frac{155}{121 (5 x+3)}-\frac{5}{22 (5 x+3)^2}-\frac{8 \log (1-2 x)}{9317}-\frac{27}{7} \log (3 x+2)+\frac{5135 \log (5 x+3)}{1331}",1,"(25*(35 + 62*x))/(242*(3 + 5*x)^2) - (8*Log[-1 + 2*x])/9317 - (27*Log[2 + 3*x])/7 + (5135*Log[3 + 5*x])/1331","A",1
1526,1,59,64,0.0415338,"\int \frac{1}{(1-2 x) (2+3 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{499350 x^2+615845 x+189356}{1694 (3 x+2) (5 x+3)^2}-\frac{16 \log (2 x-1)}{65219}-\frac{2889}{49} \log (3 x+2)+\frac{78475 \log (5 x+3)}{1331}","\frac{27}{7 (3 x+2)}+\frac{1600}{121 (5 x+3)}-\frac{25}{22 (5 x+3)^2}-\frac{16 \log (1-2 x)}{65219}-\frac{2889}{49} \log (3 x+2)+\frac{78475 \log (5 x+3)}{1331}",1,"(189356 + 615845*x + 499350*x^2)/(1694*(2 + 3*x)*(3 + 5*x)^2) - (16*Log[-1 + 2*x])/65219 - (2889*Log[2 + 3*x])/49 + (78475*Log[3 + 5*x])/1331","A",1
1527,1,64,75,0.0459341,"\int \frac{1}{(1-2 x) (2+3 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{105906600 x^3+201222420 x^2+127244576 x+26779805}{11858 (3 x+2)^2 (5 x+3)^2}-\frac{32 \log (2 x-1)}{456533}-\frac{204228}{343} \log (3 x+2)+\frac{792500 \log (5 x+3)}{1331}","\frac{2889}{49 (3 x+2)}+\frac{12125}{121 (5 x+3)}+\frac{27}{14 (3 x+2)^2}-\frac{125}{22 (5 x+3)^2}-\frac{32 \log (1-2 x)}{456533}-\frac{204228}{343} \log (3 x+2)+\frac{792500 \log (5 x+3)}{1331}",1,"(26779805 + 127244576*x + 201222420*x^2 + 105906600*x^3)/(11858*(2 + 3*x)^2*(3 + 5*x)^2) - (32*Log[-1 + 2*x])/456533 - (204228*Log[2 + 3*x])/343 + (792500*Log[3 + 5*x])/1331","A",1
1528,1,69,86,0.053972,"\int \frac{1}{(1-2 x) (2+3 x)^4 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^3),x]","\frac{18644777100 x^4+47854927170 x^3+46018070136 x^2+19648830809 x+3143075528}{83006 (3 x+2)^3 (5 x+3)^2}-\frac{64 \log (2 x-1)}{3195731}-\frac{11984706 \log (3 x+2)}{2401}+\frac{6643750 \log (5 x+3)}{1331}","\frac{204228}{343 (3 x+2)}+\frac{81250}{121 (5 x+3)}+\frac{2889}{98 (3 x+2)^2}-\frac{625}{22 (5 x+3)^2}+\frac{9}{7 (3 x+2)^3}-\frac{64 \log (1-2 x)}{3195731}-\frac{11984706 \log (3 x+2)}{2401}+\frac{6643750 \log (5 x+3)}{1331}",1,"(3143075528 + 19648830809*x + 46018070136*x^2 + 47854927170*x^3 + 18644777100*x^4)/(83006*(2 + 3*x)^3*(3 + 5*x)^2) - (64*Log[-1 + 2*x])/3195731 - (11984706*Log[2 + 3*x])/2401 + (6643750*Log[3 + 5*x])/1331","A",1
1529,1,74,97,0.061824,"\int \frac{1}{(1-2 x) (2+3 x)^5 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)^3),x]","\frac{5896678637700 x^5+19065927586590 x^4+24643748766492 x^3+15916809968421 x^2+5136860261578 x+662695553413}{1162084 (3 x+2)^4 (5 x+3)^2}-\frac{128 \log (2 x-1)}{22370117}-\frac{631722537 \log (3 x+2)}{16807}+\frac{50028125 \log (5 x+3)}{1331}","\frac{11984706}{2401 (3 x+2)}+\frac{509375}{121 (5 x+3)}+\frac{102114}{343 (3 x+2)^2}-\frac{3125}{22 (5 x+3)^2}+\frac{963}{49 (3 x+2)^3}+\frac{27}{28 (3 x+2)^4}-\frac{128 \log (1-2 x)}{22370117}-\frac{631722537 \log (3 x+2)}{16807}+\frac{50028125 \log (5 x+3)}{1331}",1,"(662695553413 + 5136860261578*x + 15916809968421*x^2 + 24643748766492*x^3 + 19065927586590*x^4 + 5896678637700*x^5)/(1162084*(2 + 3*x)^4*(3 + 5*x)^2) - (128*Log[-1 + 2*x])/22370117 - (631722537*Log[2 + 3*x])/16807 + (50028125*Log[3 + 5*x])/1331","A",1
1530,1,99,103,0.0774588,"\int \frac{(c+d x)^4}{(a-b x) (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^4/((a - b*x)*(a + b*x)),x]","-\frac{d^2 x \left(3 a^2 d^2+18 b^2 c^2+6 b^2 c d x+b^2 d^2 x^2\right)}{3 b^4}+\frac{(a d-b c)^4 \log (a+b x)}{2 a b^5}-\frac{(a d+b c)^4 \log (a-b x)}{2 a b^5}","-\frac{d^2 x \left(a^2 d^2+6 b^2 c^2\right)}{b^4}-\frac{(a d+b c)^4 \log (a-b x)}{2 a b^5}+\frac{(b c-a d)^4 \log (a+b x)}{2 a b^5}-\frac{2 c d^3 x^2}{b^2}-\frac{d^4 x^3}{3 b^2}",1,"-1/3*(d^2*x*(18*b^2*c^2 + 3*a^2*d^2 + 6*b^2*c*d*x + b^2*d^2*x^2))/b^4 - ((b*c + a*d)^4*Log[a - b*x])/(2*a*b^5) + ((-(b*c) + a*d)^4*Log[a + b*x])/(2*a*b^5)","A",1
1531,1,71,76,0.0512167,"\int \frac{(c+d x)^3}{(a-b x) (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^3/((a - b*x)*(a + b*x)),x]","-\frac{(a d-b c)^3 \log (a+b x)}{2 a b^4}-\frac{(a d+b c)^3 \log (a-b x)}{2 a b^4}-\frac{d^2 x (6 c+d x)}{2 b^2}","-\frac{(a d+b c)^3 \log (a-b x)}{2 a b^4}+\frac{(b c-a d)^3 \log (a+b x)}{2 a b^4}-\frac{3 c d^2 x}{b^2}-\frac{d^3 x^2}{2 b^2}",1,"-1/2*(d^2*x*(6*c + d*x))/b^2 - ((b*c + a*d)^3*Log[a - b*x])/(2*a*b^4) - ((-(b*c) + a*d)^3*Log[a + b*x])/(2*a*b^4)","A",1
1532,1,62,62,0.0370783,"\int \frac{(c+d x)^2}{(a-b x) (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)^2/((a - b*x)*(a + b*x)),x]","-\frac{(a d+b c)^2 \log (a-b x)}{2 a b^3}+\frac{(a d-b c)^2 \log (a+b x)}{2 a b^3}-\frac{d^2 x}{b^2}","-\frac{(a d+b c)^2 \log (a-b x)}{2 a b^3}+\frac{(b c-a d)^2 \log (a+b x)}{2 a b^3}-\frac{d^2 x}{b^2}",1,"-((d^2*x)/b^2) - ((b*c + a*d)^2*Log[a - b*x])/(2*a*b^3) + ((-(b*c) + a*d)^2*Log[a + b*x])/(2*a*b^3)","A",1
1533,1,37,49,0.0146292,"\int \frac{c+d x}{(a-b x) (a+b x)} \, dx","IntegrateAlgebraic[(c + d*x)/((a - b*x)*(a + b*x)),x]","\frac{c \tanh ^{-1}\left(\frac{b x}{a}\right)}{a b}-\frac{d \log \left(a^2-b^2 x^2\right)}{2 b^2}","\frac{(b c-a d) \log (a+b x)}{2 a b^2}-\frac{(a d+b c) \log (a-b x)}{2 a b^2}",1,"(c*ArcTanh[(b*x)/a])/(a*b) - (d*Log[a^2 - b^2*x^2])/(2*b^2)","A",1
1534,1,14,14,0.007521,"\int \frac{1}{(a-b x) (a+b x)} \, dx","IntegrateAlgebraic[1/((a - b*x)*(a + b*x)),x]","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{a b}","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{a b}",1,"ArcTanh[(b*x)/a]/(a*b)","A",1
1535,1,75,74,0.0574071,"\int \frac{1}{(a-b x) (a+b x) (c+d x)} \, dx","IntegrateAlgebraic[1/((a - b*x)*(a + b*x)*(c + d*x)),x]","-\frac{\log (a-b x)}{2 a (a d+b c)}-\frac{\log (a+b x)}{2 a (a d-b c)}-\frac{d \log (c+d x)}{(b c-a d) (a d+b c)}","-\frac{d \log (c+d x)}{b^2 c^2-a^2 d^2}-\frac{\log (a-b x)}{2 a (a d+b c)}+\frac{\log (a+b x)}{2 a (b c-a d)}",1,"-1/2*Log[a - b*x]/(a*(b*c + a*d)) - Log[a + b*x]/(2*a*(-(b*c) + a*d)) - (d*Log[c + d*x])/((b*c - a*d)*(b*c + a*d))","A",1
1536,1,109,107,0.2354776,"\int \frac{1}{(a-b x) (a+b x) (c+d x)^2} \, dx","IntegrateAlgebraic[1/((a - b*x)*(a + b*x)*(c + d*x)^2),x]","-\frac{2 b^2 c d \log (c+d x)}{(b c-a d)^2 (a d+b c)^2}+\frac{d}{(c+d x) (b c-a d) (a d+b c)}-\frac{b \log (a-b x)}{2 a (a d+b c)^2}+\frac{b \log (a+b x)}{2 a (a d-b c)^2}","\frac{d}{(c+d x) \left(b^2 c^2-a^2 d^2\right)}-\frac{2 b^2 c d \log (c+d x)}{\left(b^2 c^2-a^2 d^2\right)^2}-\frac{b \log (a-b x)}{2 a (a d+b c)^2}+\frac{b \log (a+b x)}{2 a (b c-a d)^2}",1,"d/((b*c - a*d)*(b*c + a*d)*(c + d*x)) - (b*Log[a - b*x])/(2*a*(b*c + a*d)^2) + (b*Log[a + b*x])/(2*a*(-(b*c) + a*d)^2) - (2*b^2*c*d*Log[c + d*x])/((b*c - a*d)^2*(b*c + a*d)^2)","A",1
1537,1,156,161,0.3330153,"\int \frac{1}{(a-b x) (a+b x) (c+d x)^3} \, dx","IntegrateAlgebraic[1/((a - b*x)*(a + b*x)*(c + d*x)^3),x]","\frac{-a^2 d^3+5 b^2 c^2 d+4 b^2 c d^2 x}{2 (c+d x)^2 \left(b^2 c^2-a^2 d^2\right)^2}+\frac{\left(-a^2 b^2 d^3-3 b^4 c^2 d\right) \log (c+d x)}{\left(b^2 c^2-a^2 d^2\right)^3}-\frac{b^2 \log (a-b x)}{2 a (a d+b c)^3}-\frac{b^2 \log (a+b x)}{2 a (a d-b c)^3}","\frac{2 b^2 c d}{(c+d x) \left(b^2 c^2-a^2 d^2\right)^2}+\frac{d}{2 (c+d x)^2 \left(b^2 c^2-a^2 d^2\right)}-\frac{b^2 d \left(a^2 d^2+3 b^2 c^2\right) \log (c+d x)}{\left(b^2 c^2-a^2 d^2\right)^3}-\frac{b^2 \log (a-b x)}{2 a (a d+b c)^3}+\frac{b^2 \log (a+b x)}{2 a (b c-a d)^3}",1,"(5*b^2*c^2*d - a^2*d^3 + 4*b^2*c*d^2*x)/(2*(b^2*c^2 - a^2*d^2)^2*(c + d*x)^2) - (b^2*Log[a - b*x])/(2*a*(b*c + a*d)^3) - (b^2*Log[a + b*x])/(2*a*(-(b*c) + a*d)^3) + ((-3*b^4*c^2*d - a^2*b^2*d^3)*Log[c + d*x])/(b^2*c^2 - a^2*d^2)^3","A",1
1538,1,67,76,0.0274222,"\int \frac{(2+3 x)^8 (3+5 x)}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^8*(3 + 5*x))/(1 - 2*x)^2,x]","\frac{587865600 x^9+4364202240 x^8+15171909120 x^7+33250113792 x^6+52899666624 x^5+68649225120 x^4+84833995680 x^3+136389333360 x^2-259057842186 x+60471800653}{286720 (2 x-1)}+\frac{246239357 \log (2 x-1)}{1024}","\frac{32805 x^8}{32}+\frac{56862 x^7}{7}+\frac{976617 x^6}{32}+\frac{5859459 x^5}{80}+\frac{32991057 x^4}{256}+\frac{5892813 x^3}{32}+\frac{122887143 x^2}{512}+\frac{91609881 x}{256}+\frac{63412811}{1024 (1-2 x)}+\frac{246239357 \log (1-2 x)}{1024}",1,"(60471800653 - 259057842186*x + 136389333360*x^2 + 84833995680*x^3 + 68649225120*x^4 + 52899666624*x^5 + 33250113792*x^6 + 15171909120*x^7 + 4364202240*x^8 + 587865600*x^9)/(286720*(-1 + 2*x)) + (246239357*Log[-1 + 2*x])/1024","A",1
1539,1,62,69,0.0241919,"\int \frac{(2+3 x)^7 (3+5 x)}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^7*(3 + 5*x))/(1 - 2*x)^2,x]","\frac{27993600 x^8+190667520 x^7+608985216 x^6+1239108192 x^5+1890599760 x^4+2567975760 x^3+4297526520 x^2-7692818118 x+1648903399}{35840 (2 x-1)}+\frac{15647317}{256} \log (2 x-1)","\frac{10935 x^7}{28}+\frac{11421 x^6}{4}+\frac{793881 x^5}{80}+\frac{1423899 x^4}{64}+\frac{2399985 x^3}{64}+\frac{873207 x^2}{16}+\frac{22333965 x}{256}+\frac{9058973}{512 (1-2 x)}+\frac{15647317}{256} \log (1-2 x)",1,"(1648903399 - 7692818118*x + 4297526520*x^2 + 2567975760*x^3 + 1890599760*x^4 + 1239108192*x^5 + 608985216*x^6 + 190667520*x^7 + 27993600*x^8)/(35840*(-1 + 2*x)) + (15647317*Log[-1 + 2*x])/256","A",1
1540,1,57,62,0.0227243,"\int \frac{(2+3 x)^6 (3+5 x)}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x)^2,x]","\frac{1555200 x^7+9673344 x^6+28405728 x^5+54545040 x^4+84957840 x^3+151398360 x^2-253249902 x+47812811}{5120 (2 x-1)}+\frac{3916031}{256} \log (2 x-1)","\frac{1215 x^6}{8}+\frac{5103 x^5}{5}+\frac{210195 x^4}{64}+\frac{111501 x^3}{16}+\frac{1507977 x^2}{128}+\frac{661617 x}{32}+\frac{1294139}{256 (1-2 x)}+\frac{3916031}{256} \log (1-2 x)",1,"(47812811 - 253249902*x + 151398360*x^2 + 84957840*x^3 + 54545040*x^4 + 28405728*x^5 + 9673344*x^6 + 1555200*x^7)/(5120*(-1 + 2*x)) + (3916031*Log[-1 + 2*x])/256","A",1
1541,1,52,55,0.0225053,"\int \frac{(2+3 x)^5 (3+5 x)}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^5*(3 + 5*x))/(1 - 2*x)^2,x]","\frac{1944 x^6+11016 x^5+30060 x^4+57420 x^3+113010 x^2-174912 x+26663}{16 (2 x-1)}+\frac{60025}{16} \log (2 x-1)","\frac{243 x^5}{4}+\frac{2997 x^4}{8}+\frac{18027 x^3}{16}+\frac{75447 x^2}{32}+\frac{301467 x}{64}+\frac{184877}{128 (1-2 x)}+\frac{60025}{16} \log (1-2 x)",1,"(26663 - 174912*x + 113010*x^2 + 57420*x^3 + 30060*x^4 + 11016*x^5 + 1944*x^6)/(16*(-1 + 2*x)) + (60025*Log[-1 + 2*x])/16","A",1
1542,1,47,46,0.0204999,"\int \frac{(2+3 x)^4 (3+5 x)}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x)^2,x]","\frac{12960 x^5+67248 x^4+177840 x^3+411144 x^2-582198 x+55831}{256 (2 x-1)}+\frac{57281}{64} \log (2 x-1)","\frac{405 x^4}{16}+144 x^3+\frac{13419 x^2}{32}+\frac{16203 x}{16}+\frac{26411}{64 (1-2 x)}+\frac{57281}{64} \log (1-2 x)",1,"(55831 - 582198*x + 411144*x^2 + 177840*x^3 + 67248*x^4 + 12960*x^5)/(256*(-1 + 2*x)) + (57281*Log[-1 + 2*x])/64","A",1
1543,1,42,41,0.0196,"\int \frac{(2+3 x)^3 (3+5 x)}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x)^2,x]","\frac{720 x^4+3528 x^3+10764 x^2-13770 x-65}{32 (2 x-1)}+\frac{3283}{16} \log (2 x-1)","\frac{45 x^3}{4}+\frac{243 x^2}{4}+\frac{3177 x}{16}+\frac{3773}{32 (1-2 x)}+\frac{3283}{16} \log (1-2 x)",1,"(-65 - 13770*x + 10764*x^2 + 3528*x^3 + 720*x^4)/(32*(-1 + 2*x)) + (3283*Log[-1 + 2*x])/16","A",1
1544,1,37,32,0.0190615,"\int \frac{(2+3 x)^2 (3+5 x)}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x))/(1 - 2*x)^2,x]","\frac{360 x^3+1932 x^2-2202 x-505}{32 (2 x-1)}+\frac{707}{16} \log (2 x-1)","\frac{45 x^2}{8}+33 x+\frac{539}{16 (1-2 x)}+\frac{707}{16} \log (1-2 x)",1,"(-505 - 2202*x + 1932*x^2 + 360*x^3)/(32*(-1 + 2*x)) + (707*Log[-1 + 2*x])/16","A",1
1545,1,32,27,0.0183321,"\int \frac{(2+3 x) (3+5 x)}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x))/(1 - 2*x)^2,x]","\frac{60 x^2-30 x-77}{8 (2 x-1)}+\frac{17}{2} \log (2 x-1)","\frac{15 x}{4}+\frac{77}{8 (1-2 x)}+\frac{17}{2} \log (1-2 x)",1,"(-77 - 30*x + 60*x^2)/(8*(-1 + 2*x)) + (17*Log[-1 + 2*x])/2","A",1
1546,1,22,22,0.0112539,"\int \frac{3+5 x}{(1-2 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)/(1 - 2*x)^2,x]","\frac{5}{4} \log (2 x-1)-\frac{11}{4 (2 x-1)}","\frac{11}{4 (1-2 x)}+\frac{5}{4} \log (1-2 x)",1,"-11/(4*(-1 + 2*x)) + (5*Log[-1 + 2*x])/4","A",1
1547,1,28,32,0.0239688,"\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)),x]","-\frac{11}{14 (2 x-1)}-\frac{2}{49} \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)","\frac{11}{14 (1-2 x)}+\frac{1}{49} \log (1-2 x)-\frac{1}{49} \log (3 x+2)",1,"-11/(14*(-1 + 2*x)) - (2*ArcTanh[(3 + x)/(1 + 5*x)])/49","A",1
1548,1,36,43,0.0277009,"\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^2),x]","\frac{-31 x-23}{49 \left(6 x^2+x-2\right)}+\frac{62}{343} \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)","\frac{11}{49 (1-2 x)}+\frac{1}{49 (3 x+2)}-\frac{31}{343} \log (1-2 x)+\frac{31}{343} \log (3 x+2)",1,"(-23 - 31*x)/(49*(-2 + x + 6*x^2)) + (62*ArcTanh[(3 + x)/(1 + 5*x)])/343","A",1
1549,1,45,54,0.0432987,"\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^3),x]","\frac{-768 x^2-576 x-59}{686 (2 x-1) (3 x+2)^2}+\frac{256 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{2401}","\frac{22}{343 (1-2 x)}-\frac{31}{343 (3 x+2)}+\frac{1}{98 (3 x+2)^2}-\frac{128 \log (1-2 x)}{2401}+\frac{128 \log (3 x+2)}{2401}",1,"(-59 - 576*x - 768*x^2)/(686*(-1 + 2*x)*(2 + 3*x)^2) + (256*ArcTanh[(3 + x)/(1 + 5*x)])/2401","A",1
1550,1,50,65,0.0478071,"\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^4),x]","\frac{-20952 x^3-29682 x^2-6887 x+2164}{14406 (2 x-1) (3 x+2)^3}+\frac{776 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{16807}","\frac{44}{2401 (1-2 x)}-\frac{128}{2401 (3 x+2)}-\frac{31}{686 (3 x+2)^2}+\frac{1}{147 (3 x+2)^3}-\frac{388 \log (1-2 x)}{16807}+\frac{388 \log (3 x+2)}{16807}",1,"(2164 - 6887*x - 29682*x^2 - 20952*x^3)/(14406*(-1 + 2*x)*(2 + 3*x)^3) + (776*ArcTanh[(3 + x)/(1 + 5*x)])/16807","A",1
1551,1,55,76,0.0725602,"\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^5),x]","\frac{-336960 x^4-702000 x^3-429000 x^2+9230 x+52979}{201684 (2 x-1) (3 x+2)^4}+\frac{2080 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{117649}","\frac{88}{16807 (1-2 x)}-\frac{388}{16807 (3 x+2)}-\frac{64}{2401 (3 x+2)^2}-\frac{31}{1029 (3 x+2)^3}+\frac{1}{196 (3 x+2)^4}-\frac{1040 \log (1-2 x)}{117649}+\frac{1040 \log (3 x+2)}{117649}",1,"(52979 + 9230*x - 429000*x^2 - 702000*x^3 - 336960*x^4)/(201684*(-1 + 2*x)*(2 + 3*x)^4) + (2080*ArcTanh[(3 + x)/(1 + 5*x)])/117649","A",1
1552,1,60,87,0.0683274,"\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^6} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^6),x]","\frac{-12674880 x^5-34855920 x^4-33741000 x^3-10410810 x^2+3488689 x+2104258}{7058940 (2 x-1) (3 x+2)^5}+\frac{5216 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{823543}","\frac{176}{117649 (1-2 x)}-\frac{1040}{117649 (3 x+2)}-\frac{194}{16807 (3 x+2)^2}-\frac{128}{7203 (3 x+2)^3}-\frac{31}{1372 (3 x+2)^4}+\frac{1}{245 (3 x+2)^5}-\frac{2608 \log (1-2 x)}{823543}+\frac{2608 \log (3 x+2)}{823543}",1,"(2104258 + 3488689*x - 10410810*x^2 - 33741000*x^3 - 34855920*x^4 - 12674880*x^5)/(7058940*(-1 + 2*x)*(2 + 3*x)^5) + (5216*ArcTanh[(3 + x)/(1 + 5*x)])/823543","A",1
1553,1,65,98,0.0642263,"\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^7} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^7),x]","\frac{-311040 x^6-1062720 x^5-1398240 x^4-807480 x^3-84708 x^2+132772 x+49131}{168070 (2 x-1) (3 x+2)^6}+\frac{256 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{117649}","\frac{352}{823543 (1-2 x)}-\frac{2608}{823543 (3 x+2)}-\frac{520}{117649 (3 x+2)^2}-\frac{388}{50421 (3 x+2)^3}-\frac{32}{2401 (3 x+2)^4}-\frac{31}{1715 (3 x+2)^5}+\frac{1}{294 (3 x+2)^6}-\frac{128 \log (1-2 x)}{117649}+\frac{128 \log (3 x+2)}{117649}",1,"(49131 + 132772*x - 84708*x^2 - 807480*x^3 - 1398240*x^4 - 1062720*x^5 - 311040*x^6)/(168070*(-1 + 2*x)*(2 + 3*x)^6) + (256*ArcTanh[(3 + x)/(1 + 5*x)])/117649","A",1
1554,1,72,81,0.0338272,"\int \frac{(2+3 x)^8 (3+5 x)^2}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^8*(3 + 5*x)^2)/(1 - 2*x)^2,x]","\frac{2612736000 x^{10}+20836569600 x^9+77907121920 x^8+183016143360 x^7+307848957696 x^6+406896098112 x^5+466727825760 x^4+538127987040 x^3+842130532880 x^2-1689637297718 x+420890769939}{286720 (2 x-1)}+\frac{1512848491 \log (2 x-1)}{1024}","\frac{18225 x^9}{4}+\frac{1235655 x^8}{32}+\frac{17378631 x^7}{112}+396738 x^6+\frac{235268793 x^5}{320}+\frac{275757561 x^4}{256}+\frac{346239417 x^3}{256}+\frac{413355417 x^2}{256}+\frac{2330515357 x}{1024}+\frac{697540921}{2048 (1-2 x)}+\frac{1512848491 \log (1-2 x)}{1024}",1,"(420890769939 - 1689637297718*x + 842130532880*x^2 + 538127987040*x^3 + 466727825760*x^4 + 406896098112*x^5 + 307848957696*x^6 + 183016143360*x^7 + 77907121920*x^8 + 20836569600*x^9 + 2612736000*x^10)/(286720*(-1 + 2*x)) + (1512848491*Log[-1 + 2*x])/1024","A",1
1555,1,67,76,0.027965,"\int \frac{(2+3 x)^7 (3+5 x)^2}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^7*(3 + 5*x)^2)/(1 - 2*x)^2,x]","\frac{979776000 x^9+7199020800 x^8+24778068480 x^7+53792895744 x^6+84861822528 x^5+109373775840 x^4+134542057440 x^3+215855484880 x^2-411248888662 x+96389258691}{286720 (2 x-1)}+\frac{389535839 \log (2 x-1)}{1024}","\frac{54675 x^8}{32}+\frac{375435 x^7}{28}+\frac{1597239 x^6}{32}+\frac{4750569 x^5}{40}+\frac{53086563 x^4}{256}+\frac{18842715 x^3}{64}+\frac{195497697 x^2}{512}+\frac{9077405 x}{16}+\frac{99648703}{1024 (1-2 x)}+\frac{389535839 \log (1-2 x)}{1024}",1,"(96389258691 - 411248888662*x + 215855484880*x^2 + 134542057440*x^3 + 109373775840*x^4 + 84861822528*x^5 + 53792895744*x^6 + 24778068480*x^7 + 7199020800*x^8 + 979776000*x^9)/(286720*(-1 + 2*x)) + (389535839*Log[-1 + 2*x])/1024","A",1
1556,1,62,69,0.0312936,"\int \frac{(2+3 x)^6 (3+5 x)^2}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^6*(3 + 5*x)^2)/(1 - 2*x)^2,x]","\frac{23328000 x^8+157075200 x^7+496202112 x^6+999450144 x^5+1511863920 x^4+2040862320 x^3+3404640680 x^2-6115223546 x+1318304553}{17920 (2 x-1)}+\frac{12386759}{128} \log (2 x-1)","\frac{18225 x^7}{28}+\frac{37665 x^6}{8}+\frac{1295919 x^5}{80}+\frac{575775 x^4}{16}+\frac{3851307 x^3}{64}+\frac{11140101 x^2}{128}+\frac{35458963 x}{256}+\frac{14235529}{512 (1-2 x)}+\frac{12386759}{128} \log (1-2 x)",1,"(1318304553 - 6115223546*x + 3404640680*x^2 + 2040862320*x^3 + 1511863920*x^4 + 999450144*x^5 + 496202112*x^6 + 157075200*x^7 + 23328000*x^8)/(17920*(-1 + 2*x)) + (12386759*Log[-1 + 2*x])/128","A",1
1557,1,57,62,0.0250002,"\int \frac{(2+3 x)^5 (3+5 x)^2}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^5*(3 + 5*x)^2)/(1 - 2*x)^2,x]","\frac{518400 x^7+3182976 x^6+9233568 x^5+17540400 x^4+27094320 x^3+48055240 x^2-80685178 x+15368793}{1024 (2 x-1)}+\frac{6206585}{256} \log (2 x-1)","\frac{2025 x^6}{8}+\frac{6723 x^5}{4}+\frac{342333 x^4}{64}+\frac{89913 x^3}{8}+\frac{2412699 x^2}{128}+\frac{2104901 x}{64}+\frac{2033647}{256 (1-2 x)}+\frac{6206585}{256} \log (1-2 x)",1,"(15368793 - 80685178*x + 48055240*x^2 + 27094320*x^3 + 17540400*x^4 + 9233568*x^5 + 3182976*x^6 + 518400*x^7)/(1024*(-1 + 2*x)) + (6206585*Log[-1 + 2*x])/256","A",1
1558,1,52,55,0.0268515,"\int \frac{(2+3 x)^4 (3+5 x)^2}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^2,x]","\frac{51840 x^6+289440 x^5+779184 x^4+1471920 x^3+2876552 x^2-4470254 x+692403}{256 (2 x-1)}+\frac{381073}{64} \log (2 x-1)","\frac{405 x^5}{4}+\frac{9855 x^4}{16}+\frac{29277 x^3}{16}+\frac{15159 x^2}{4}+\frac{480841 x}{64}+\frac{290521}{128 (1-2 x)}+\frac{381073}{64} \log (1-2 x)",1,"(692403 - 4470254*x + 2876552*x^2 + 1471920*x^3 + 779184*x^4 + 289440*x^5 + 51840*x^6)/(256*(-1 + 2*x)) + (381073*Log[-1 + 2*x])/64","A",1
1559,1,47,48,0.0226604,"\int \frac{(2+3 x)^3 (3+5 x)^2}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^2)/(1 - 2*x)^2,x]","\frac{21600 x^5+110160 x^4+286992 x^3+656536 x^2-933610 x+93225}{256 (2 x-1)}+\frac{91091}{64} \log (2 x-1)","\frac{675 x^4}{16}+\frac{945 x^3}{4}+\frac{21717 x^2}{32}+\frac{12973 x}{8}+\frac{41503}{64 (1-2 x)}+\frac{91091}{64} \log (1-2 x)",1,"(93225 - 933610*x + 656536*x^2 + 286992*x^3 + 110160*x^4 + 21600*x^5)/(256*(-1 + 2*x)) + (91091*Log[-1 + 2*x])/64","A",1
1560,1,42,41,0.0226461,"\int \frac{(2+3 x)^2 (3+5 x)^2}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x)^2,x]","\frac{300 x^4+1440 x^3+4324 x^2-5554 x+15}{8 (2 x-1)}+\frac{1309}{4} \log (2 x-1)","\frac{75 x^3}{4}+\frac{795 x^2}{8}+\frac{5119 x}{16}+\frac{5929}{32 (1-2 x)}+\frac{1309}{4} \log (1-2 x)",1,"(15 - 5554*x + 4324*x^2 + 1440*x^3 + 300*x^4)/(8*(-1 + 2*x)) + (1309*Log[-1 + 2*x])/4","A",1
1561,1,37,34,0.0189305,"\int \frac{(2+3 x) (3+5 x)^2}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^2)/(1 - 2*x)^2,x]","\frac{600 x^3+3140 x^2-3590 x-759}{32 (2 x-1)}+\frac{1133}{16} \log (2 x-1)","\frac{75 x^2}{8}+\frac{215 x}{4}+\frac{847}{16 (1-2 x)}+\frac{1133}{16} \log (1-2 x)",1,"(-759 - 3590*x + 3140*x^2 + 600*x^3)/(32*(-1 + 2*x)) + (1133*Log[-1 + 2*x])/16","A",1
1562,1,32,27,0.019427,"\int \frac{(3+5 x)^2}{(1-2 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/(1 - 2*x)^2,x]","\frac{100 x^2-50 x-121}{8 (2 x-1)}+\frac{55}{4} \log (2 x-1)","\frac{25 x}{4}+\frac{121}{8 (1-2 x)}+\frac{55}{4} \log (1-2 x)",1,"(-121 - 50*x + 100*x^2)/(8*(-1 + 2*x)) + (55*Log[-1 + 2*x])/4","A",1
1563,1,32,32,0.023665,"\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)),x]","-\frac{121}{28 (2 x-1)}+\frac{407}{196} \log (2 x-1)+\frac{1}{147} \log (3 x+2)","\frac{121}{28 (1-2 x)}+\frac{407}{196} \log (1-2 x)+\frac{1}{147} \log (3 x+2)",1,"-121/(28*(-1 + 2*x)) + (407*Log[-1 + 2*x])/196 + Log[2 + 3*x]/147","A",1
1564,1,36,43,0.040076,"\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^2),x]","\frac{-1093 x-724}{294 \left(6 x^2+x-2\right)}-\frac{44}{343} \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)","\frac{121}{98 (1-2 x)}-\frac{1}{147 (3 x+2)}+\frac{22}{343} \log (1-2 x)-\frac{22}{343} \log (3 x+2)",1,"(-724 - 1093*x)/(294*(-2 + x + 6*x^2)) - (44*ArcTanh[(3 + x)/(1 + 5*x)])/343","A",1
1565,1,45,54,0.0421558,"\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^3),x]","\frac{-5742 x^2-8594 x-3161}{2058 (2 x-1) (3 x+2)^2}+\frac{638 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{2401}","\frac{121}{343 (1-2 x)}+\frac{22}{343 (3 x+2)}-\frac{1}{294 (3 x+2)^2}-\frac{319 \log (1-2 x)}{2401}+\frac{319 \log (3 x+2)}{2401}",1,"(-3161 - 8594*x - 5742*x^2)/(2058*(-1 + 2*x)*(2 + 3*x)^2) + (638*ArcTanh[(3 + x)/(1 + 5*x)])/2401","A",1
1566,1,50,65,0.0582251,"\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^4),x]","\frac{-110484 x^3-156519 x^2-66329 x-7277}{21609 (2 x-1) (3 x+2)^3}+\frac{2728 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{16807}","\frac{242}{2401 (1-2 x)}-\frac{319}{2401 (3 x+2)}+\frac{11}{343 (3 x+2)^2}-\frac{1}{441 (3 x+2)^3}-\frac{1364 \log (1-2 x)}{16807}+\frac{1364 \log (3 x+2)}{16807}",1,"(-7277 - 66329*x - 156519*x^2 - 110484*x^3)/(21609*(-1 + 2*x)*(2 + 3*x)^3) + (2728*ArcTanh[(3 + x)/(1 + 5*x)])/16807","A",1
1567,1,55,76,0.0629229,"\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^5),x]","\frac{-1354320 x^4-2821500 x^3-1724250 x^2-172990 x+83327}{201684 (2 x-1) (3 x+2)^4}+\frac{8360 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{117649}","\frac{484}{16807 (1-2 x)}-\frac{1364}{16807 (3 x+2)}-\frac{319}{4802 (3 x+2)^2}+\frac{22}{1029 (3 x+2)^3}-\frac{1}{588 (3 x+2)^4}-\frac{4180 \log (1-2 x)}{117649}+\frac{4180 \log (3 x+2)}{117649}",1,"(83327 - 172990*x - 1724250*x^2 - 2821500*x^3 - 1354320*x^4)/(201684*(-1 + 2*x)*(2 + 3*x)^4) + (8360*ArcTanh[(3 + x)/(1 + 5*x)])/117649","A",1
1568,1,60,87,0.0909082,"\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^6} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^6),x]","\frac{-9123840 x^5-25090560 x^4-24288000 x^3-7494080 x^2+1530877 x+913244}{1176490 (2 x-1) (3 x+2)^5}+\frac{22528 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{823543}","\frac{968}{117649 (1-2 x)}-\frac{4180}{117649 (3 x+2)}-\frac{682}{16807 (3 x+2)^2}-\frac{319}{7203 (3 x+2)^3}+\frac{11}{686 (3 x+2)^4}-\frac{1}{735 (3 x+2)^5}-\frac{11264 \log (1-2 x)}{823543}+\frac{11264 \log (3 x+2)}{823543}",1,"(913244 + 1530877*x - 7494080*x^2 - 24288000*x^3 - 25090560*x^4 - 9123840*x^5)/(1176490*(-1 + 2*x)*(2 + 3*x)^5) + (22528*ArcTanh[(3 + x)/(1 + 5*x)])/823543","A",1
1569,1,65,98,0.0885931,"\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^7} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^7),x]","\frac{-177059520 x^6-604953360 x^5-795948120 x^4-459657990 x^3-48220029 x^2+60874336 x+18979078}{21176820 (2 x-1) (3 x+2)^6}+\frac{8096 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{823543}","\frac{1936}{823543 (1-2 x)}-\frac{11264}{823543 (3 x+2)}-\frac{2090}{117649 (3 x+2)^2}-\frac{1364}{50421 (3 x+2)^3}-\frac{319}{9604 (3 x+2)^4}+\frac{22}{1715 (3 x+2)^5}-\frac{1}{882 (3 x+2)^6}-\frac{4048 \log (1-2 x)}{823543}+\frac{4048 \log (3 x+2)}{823543}",1,"(18979078 + 60874336*x - 48220029*x^2 - 459657990*x^3 - 795948120*x^4 - 604953360*x^5 - 177059520*x^6)/(21176820*(-1 + 2*x)*(2 + 3*x)^6) + (8096*ArcTanh[(3 + x)/(1 + 5*x)])/823543","A",1
1570,1,70,109,0.1284779,"\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^8} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^8),x]","\frac{-746729280 x^7-3049144560 x^6-5057708040 x^5-4176440730 x^4-1495734471 x^3+183177225 x^2+327016403 x+76539293}{86472015 (2 x-1) (3 x+2)^7}+\frac{136576 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{40353607}","\frac{3872}{5764801 (1-2 x)}-\frac{4048}{823543 (3 x+2)}-\frac{5632}{823543 (3 x+2)^2}-\frac{4180}{352947 (3 x+2)^3}-\frac{341}{16807 (3 x+2)^4}-\frac{319}{12005 (3 x+2)^5}+\frac{11}{1029 (3 x+2)^6}-\frac{1}{1029 (3 x+2)^7}-\frac{68288 \log (1-2 x)}{40353607}+\frac{68288 \log (3 x+2)}{40353607}",1,"(76539293 + 327016403*x + 183177225*x^2 - 1495734471*x^3 - 4176440730*x^4 - 5057708040*x^5 - 3049144560*x^6 - 746729280*x^7)/(86472015*(-1 + 2*x)*(2 + 3*x)^7) + (136576*ArcTanh[(3 + x)/(1 + 5*x)])/40353607","A",1
1571,1,77,90,0.0314548,"\int \frac{(2+3 x)^8 (3+5 x)^3}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^8*(3 + 5*x)^3)/(1 - 2*x)^2,x]","\frac{36770371407 \log (2 x-1)}{4096}+\frac{47029248000 x^{11}+401490432000 x^{10}+1610338060800 x^9+4056416029440 x^8+7272841720320 x^7+10063991169792 x^6+11574822095424 x^5+12129460157920 x^4+13335647616480 x^3+20524026494160 x^2-43208575854086 x+11304620315803}{1146880 (2 x-1)}","\frac{164025 x^{10}}{8}+\frac{370575 x^9}{2}+\frac{101721015 x^8}{128}+\frac{242570133 x^7}{112}+\frac{544462047 x^6}{128}+\frac{260574273 x^5}{40}+\frac{8502681987 x^4}{1024}+\frac{2416569641 x^3}{256}+\frac{21573106793 x^2}{2048}+\frac{7277894263 x}{512}+\frac{7672950131}{4096 (1-2 x)}+\frac{36770371407 \log (1-2 x)}{4096}",1,"(11304620315803 - 43208575854086*x + 20524026494160*x^2 + 13335647616480*x^3 + 12129460157920*x^4 + 11574822095424*x^5 + 10063991169792*x^6 + 7272841720320*x^7 + 4056416029440*x^8 + 1610338060800*x^9 + 401490432000*x^10 + 47029248000*x^11)/(1146880*(-1 + 2*x)) + (36770371407*Log[-1 + 2*x])/4096","A",1
1572,1,72,83,0.031198,"\int \frac{(2+3 x)^7 (3+5 x)^3}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^7*(3 + 5*x)^3)/(1 - 2*x)^2,x]","\frac{1088640000 x^{10}+8600256000 x^9+31861382400 x^8+74191887360 x^7+123787657728 x^6+162468222336 x^5+185355446080 x^4+213008156480 x^3+332899764960 x^2-669744799994 x+167338715917}{71680 (2 x-1)}+\frac{298946109}{128} \log (2 x-1)","\frac{30375 x^9}{4}+\frac{127575 x^8}{2}+\frac{28463805 x^7}{112}+\frac{20626947 x^6}{32}+\frac{379446471 x^5}{320}+\frac{220950207 x^4}{128}+\frac{551942075 x^3}{256}+\frac{1312685491 x^2}{512}+\frac{3690540955 x}{1024}+\frac{1096135733}{2048 (1-2 x)}+\frac{298946109}{128} \log (1-2 x)",1,"(167338715917 - 669744799994*x + 332899764960*x^2 + 213008156480*x^3 + 185355446080*x^4 + 162468222336*x^5 + 123787657728*x^6 + 74191887360*x^7 + 31861382400*x^8 + 8600256000*x^9 + 1088640000*x^10)/(71680*(-1 + 2*x)) + (298946109*Log[-1 + 2*x])/128","A",1
1573,1,67,76,0.0279583,"\int \frac{(2+3 x)^6 (3+5 x)^3}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^6*(3 + 5*x)^3)/(1 - 2*x)^2,x]","\frac{1632960000 x^9+11873952000 x^8+40459046400 x^7+87008414976 x^6+136105970112 x^5+174226352160 x^4+213352163360 x^3+341601057840 x^2-652800288858 x+153617806869}{286720 (2 x-1)}+\frac{616195041 \log (2 x-1)}{1024}","\frac{91125 x^8}{32}+\frac{309825 x^7}{14}+\frac{2611845 x^6}{32}+\frac{15403257 x^5}{80}+\frac{85406805 x^4}{256}+\frac{7530189 x^3}{16}+\frac{310976027 x^2}{512}+\frac{230244479 x}{256}+\frac{156590819}{1024 (1-2 x)}+\frac{616195041 \log (1-2 x)}{1024}",1,"(153617806869 - 652800288858*x + 341601057840*x^2 + 213352163360*x^3 + 174226352160*x^4 + 136105970112*x^5 + 87008414976*x^6 + 40459046400*x^7 + 11873952000*x^8 + 1632960000*x^9)/(286720*(-1 + 2*x)) + (616195041*Log[-1 + 2*x])/1024","A",1
1574,1,62,69,0.0271757,"\int \frac{(2+3 x)^5 (3+5 x)^3}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^5*(3 + 5*x)^3)/(1 - 2*x)^2,x]","\frac{15552000 x^8+103507200 x^7+323374464 x^6+644755104 x^5+966981680 x^4+1297354800 x^3+2157631560 x^2-3888550282 x+843009185}{7168 (2 x-1)}+\frac{39220335}{256} \log (2 x-1)","\frac{30375 x^7}{28}+\frac{15525 x^6}{2}+\frac{423009 x^5}{16}+\frac{3724389 x^4}{64}+\frac{6179077 x^3}{64}+\frac{8881301 x^2}{64}+\frac{56291737 x}{256}+\frac{22370117}{512 (1-2 x)}+\frac{39220335}{256} \log (1-2 x)",1,"(843009185 - 3888550282*x + 2157631560*x^2 + 1297354800*x^3 + 966981680*x^4 + 644755104*x^5 + 323374464*x^6 + 103507200*x^7 + 15552000*x^8)/(7168*(-1 + 2*x)) + (39220335*Log[-1 + 2*x])/256","A",1
1575,1,57,62,0.0248058,"\int \frac{(2+3 x)^4 (3+5 x)^3}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x)^2,x]","\frac{864000 x^7+5235840 x^6+15003360 x^5+28195088 x^4+43194640 x^3+76256664 x^2-128514958 x+24691451}{1024 (2 x-1)}+\frac{9836211}{256} \log (2 x-1)","\frac{3375 x^6}{8}+\frac{5535 x^5}{2}+\frac{557415 x^4}{64}+\frac{289951 x^3}{16}+\frac{3859469 x^2}{128}+\frac{209243 x}{4}+\frac{3195731}{256 (1-2 x)}+\frac{9836211}{256} \log (1-2 x)",1,"(24691451 - 128514958*x + 76256664*x^2 + 43194640*x^3 + 28195088*x^4 + 15003360*x^5 + 5235840*x^6 + 864000*x^7)/(1024*(-1 + 2*x)) + (9836211*Log[-1 + 2*x])/256","A",1
1576,1,52,55,0.0224218,"\int \frac{(2+3 x)^3 (3+5 x)^3}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^3)/(1 - 2*x)^2,x]","\frac{43200 x^6+237600 x^5+630960 x^4+1178768 x^3+2287704 x^2-3569610 x+561465}{128 (2 x-1)}+\frac{302379}{32} \log (2 x-1)","\frac{675 x^5}{4}+\frac{2025 x^4}{2}+\frac{47535 x^3}{16}+\frac{194881 x^2}{32}+\frac{766807 x}{64}+\frac{456533}{128 (1-2 x)}+\frac{302379}{32} \log (1-2 x)",1,"(561465 - 3569610*x + 2287704*x^2 + 1178768*x^3 + 630960*x^4 + 237600*x^5 + 43200*x^6)/(128*(-1 + 2*x)) + (302379*Log[-1 + 2*x])/32","A",1
1577,1,47,48,0.0223087,"\int \frac{(2+3 x)^2 (3+5 x)^3}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^3)/(1 - 2*x)^2,x]","\frac{36000 x^5+180400 x^4+462960 x^3+1048104 x^2-1496774 x+155215}{256 (2 x-1)}+\frac{144837}{64} \log (2 x-1)","\frac{1125 x^4}{16}+\frac{775 x^3}{2}+\frac{35135 x^2}{32}+\frac{41537 x}{16}+\frac{65219}{64 (1-2 x)}+\frac{144837}{64} \log (1-2 x)",1,"(155215 - 1496774*x + 1048104*x^2 + 462960*x^3 + 180400*x^4 + 36000*x^5)/(256*(-1 + 2*x)) + (144837*Log[-1 + 2*x])/64","A",1
1578,1,42,41,0.0198887,"\int \frac{(2+3 x) (3+5 x)^3}{(1-2 x)^2} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^3)/(1 - 2*x)^2,x]","\frac{2000 x^4+9400 x^3+27780 x^2-35830 x+353}{32 (2 x-1)}+\frac{8349}{16} \log (2 x-1)","\frac{125 x^3}{4}+\frac{325 x^2}{2}+\frac{8245 x}{16}+\frac{9317}{32 (1-2 x)}+\frac{8349}{16} \log (1-2 x)",1,"(353 - 35830*x + 27780*x^2 + 9400*x^3 + 2000*x^4)/(32*(-1 + 2*x)) + (8349*Log[-1 + 2*x])/16","A",1
1579,1,37,34,0.0160914,"\int \frac{(3+5 x)^3}{(1-2 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/(1 - 2*x)^2,x]","\frac{1000 x^3+5100 x^2-5850 x-1137}{32 (2 x-1)}+\frac{1815}{16} \log (2 x-1)","\frac{125 x^2}{8}+\frac{175 x}{2}+\frac{1331}{16 (1-2 x)}+\frac{1815}{16} \log (1-2 x)",1,"(-1137 - 5850*x + 5100*x^2 + 1000*x^3)/(32*(-1 + 2*x)) + (1815*Log[-1 + 2*x])/16","A",1
1580,1,42,37,0.0310258,"\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)),x]","\frac{10500 x^2+1750 x-15479}{504 (2 x-1)}+\frac{1089}{49} \log (2 x-1)-\frac{1}{441} \log (3 x+2)","\frac{125 x}{12}+\frac{1331}{56 (1-2 x)}+\frac{1089}{49} \log (1-2 x)-\frac{1}{441} \log (3 x+2)",1,"(-15479 + 1750*x + 10500*x^2)/(504*(-1 + 2*x)) + (1089*Log[-1 + 2*x])/49 - Log[2 + 3*x]/441","A",1
1581,1,40,43,0.0354377,"\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^2),x]","\frac{-35929 x-23962}{1764 \left(6 x^2+x-2\right)}+\frac{4719 \log (2 x-1)}{1372}+\frac{101 \log (3 x+2)}{3087}","\frac{1331}{196 (1-2 x)}+\frac{1}{441 (3 x+2)}+\frac{4719 \log (1-2 x)}{1372}+\frac{101 \log (3 x+2)}{3087}",1,"(-23962 - 35929*x)/(1764*(-2 + x + 6*x^2)) + (4719*Log[-1 + 2*x])/1372 + (101*Log[2 + 3*x])/3087","A",1
1582,1,45,54,0.0478677,"\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^3),x]","\frac{-109023 x^2-143936 x-47519}{6174 (2 x-1) (3 x+2)^2}-\frac{726 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{2401}","\frac{1331}{686 (1-2 x)}-\frac{101}{3087 (3 x+2)}+\frac{1}{882 (3 x+2)^2}+\frac{363 \log (1-2 x)}{2401}-\frac{363 \log (3 x+2)}{2401}",1,"(-47519 - 143936*x - 109023*x^2)/(6174*(-1 + 2*x)*(2 + 3*x)^2) - (726*ArcTanh[(3 + x)/(1 + 5*x)])/2401","A",1
1583,1,50,65,0.0634025,"\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^4),x]","\frac{-1587762 x^3-3599892 x^2-2667797 x-649256}{129654 (2 x-1) (3 x+2)^3}+\frac{6534 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{16807}","\frac{1331}{2401 (1-2 x)}+\frac{363}{2401 (3 x+2)}-\frac{101}{6174 (3 x+2)^2}+\frac{1}{1323 (3 x+2)^3}-\frac{3267 \log (1-2 x)}{16807}+\frac{3267 \log (3 x+2)}{16807}",1,"(-649256 - 2667797*x - 3599892*x^2 - 1587762*x^3)/(129654*(-1 + 2*x)*(2 + 3*x)^3) + (6534*ArcTanh[(3 + x)/(1 + 5*x)])/16807","A",1
1584,1,55,76,0.0728478,"\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^5),x]","\frac{-42340320 x^4-88209000 x^3-66510750 x^2-21109490 x-2287541}{1815156 (2 x-1) (3 x+2)^4}+\frac{29040 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{117649}","\frac{2662}{16807 (1-2 x)}-\frac{3267}{16807 (3 x+2)}+\frac{363}{4802 (3 x+2)^2}-\frac{101}{9261 (3 x+2)^3}+\frac{1}{1764 (3 x+2)^4}-\frac{14520 \log (1-2 x)}{117649}+\frac{14520 \log (3 x+2)}{117649}",1,"(-2287541 - 21109490*x - 66510750*x^2 - 88209000*x^3 - 42340320*x^4)/(1815156*(-1 + 2*x)*(2 + 3*x)^4) + (29040*ArcTanh[(3 + x)/(1 + 5*x)])/117649","A",1
1585,1,60,87,0.0955706,"\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^6} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^6),x]","\frac{-656274960 x^5-1804756140 x^4-1747028250 x^3-649342770 x^2-25985087 x+23684986}{21176820 (2 x-1) (3 x+2)^5}+\frac{90024 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{823543}","\frac{5324}{117649 (1-2 x)}-\frac{14520}{117649 (3 x+2)}-\frac{3267}{33614 (3 x+2)^2}+\frac{121}{2401 (3 x+2)^3}-\frac{101}{12348 (3 x+2)^4}+\frac{1}{2205 (3 x+2)^5}-\frac{45012 \log (1-2 x)}{823543}+\frac{45012 \log (3 x+2)}{823543}",1,"(23684986 - 25985087*x - 649342770*x^2 - 1747028250*x^3 - 1804756140*x^4 - 656274960*x^5)/(21176820*(-1 + 2*x)*(2 + 3*x)^5) + (90024*ArcTanh[(3 + x)/(1 + 5*x)])/823543","A",1
1586,1,65,98,0.09509,"\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^7} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^7),x]","\frac{-2286377280 x^6-7811789040 x^5-10278112680 x^4-5935583610 x^3-887377581 x^2+461259404 x+145404842}{63530460 (2 x-1) (3 x+2)^6}+\frac{34848 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{823543}","\frac{10648}{823543 (1-2 x)}-\frac{45012}{823543 (3 x+2)}-\frac{7260}{117649 (3 x+2)^2}-\frac{1089}{16807 (3 x+2)^3}+\frac{363}{9604 (3 x+2)^4}-\frac{101}{15435 (3 x+2)^5}+\frac{1}{2646 (3 x+2)^6}-\frac{17424 \log (1-2 x)}{823543}+\frac{17424 \log (3 x+2)}{823543}",1,"(145404842 + 461259404*x - 887377581*x^2 - 5935583610*x^3 - 10278112680*x^4 - 7811789040*x^5 - 2286377280*x^6)/(63530460*(-1 + 2*x)*(2 + 3*x)^6) + (34848*ArcTanh[(3 + x)/(1 + 5*x)])/823543","A",1
1587,1,70,109,0.1084819,"\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^8} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^8),x]","\frac{-121177995840 x^7-494810149680 x^6-820756518120 x^5-677745912690 x^4-242725322763 x^3+18916696050 x^2+39853850134 x+8381276704}{3112992540 (2 x-1) (3 x+2)^7}+\frac{615648 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{40353607}","\frac{21296}{5764801 (1-2 x)}-\frac{17424}{823543 (3 x+2)}-\frac{22506}{823543 (3 x+2)^2}-\frac{4840}{117649 (3 x+2)^3}-\frac{3267}{67228 (3 x+2)^4}+\frac{363}{12005 (3 x+2)^5}-\frac{101}{18522 (3 x+2)^6}+\frac{1}{3087 (3 x+2)^7}-\frac{307824 \log (1-2 x)}{40353607}+\frac{307824 \log (3 x+2)}{40353607}",1,"(8381276704 + 39853850134*x + 18916696050*x^2 - 242725322763*x^3 - 677745912690*x^4 - 820756518120*x^5 - 494810149680*x^6 - 121177995840*x^7)/(3112992540*(-1 + 2*x)*(2 + 3*x)^7) + (615648*ArcTanh[(3 + x)/(1 + 5*x)])/40353607","A",1
1588,1,67,72,0.066022,"\int \frac{(2+3 x)^8}{(1-2 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^8/((1 - 2*x)^2*(3 + 5*x)),x]","\frac{4811400000 x^7+30696732000 x^6+92338785000 x^5+181163198700 x^4+286954408620 x^3+516371761026 x^2-359375507568 x-90075015625}{44000000 (2 x-1)}+\frac{188591347 \log (2 x-1)}{30976}+\frac{\log (5 x+3)}{9453125}","\frac{2187 x^6}{40}+\frac{94041 x^5}{250}+\frac{9899091 x^4}{8000}+\frac{26773659 x^3}{10000}+\frac{1839811401 x^2}{400000}+\frac{2041906293 x}{250000}+\frac{5764801}{2816 (1-2 x)}+\frac{188591347 \log (1-2 x)}{30976}+\frac{\log (5 x+3)}{9453125}",1,"(-90075015625 - 359375507568*x + 516371761026*x^2 + 286954408620*x^3 + 181163198700*x^4 + 92338785000*x^5 + 30696732000*x^6 + 4811400000*x^7)/(44000000*(-1 + 2*x)) + (188591347*Log[-1 + 2*x])/30976 + Log[3 + 5*x]/9453125","A",1
1589,1,62,65,0.0416601,"\int \frac{(2+3 x)^7}{(1-2 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^7/((1 - 2*x)^2*(3 + 5*x)),x]","\frac{4811400000 x^6+28066500000 x^5+78666390000 x^4+153656514000 x^3+306816622200 x^2-14798867886 x-158719988357}{110000000 (2 x-1)}+\frac{5764801 \log (2 x-1)}{3872}+\frac{\log (5 x+3)}{1890625}","\frac{2187 x^5}{100}+\frac{13851 x^4}{100}+\frac{853659 x^3}{2000}+\frac{18237069 x^2}{20000}+\frac{370109547 x}{200000}+\frac{823543}{1408 (1-2 x)}+\frac{5764801 \log (1-2 x)}{3872}+\frac{\log (5 x+3)}{1890625}",1,"(-158719988357 - 14798867886*x + 306816622200*x^2 + 153656514000*x^3 + 78666390000*x^4 + 28066500000*x^5 + 4811400000*x^6)/(110000000*(-1 + 2*x)) + (5764801*Log[-1 + 2*x])/3872 + Log[3 + 5*x]/1890625","A",1
1590,1,57,58,0.0340204,"\int \frac{(2+3 x)^6}{(1-2 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)^2*(3 + 5*x)),x]","\frac{8019000 x^5+43035300 x^4+117237780 x^3+276893694 x^2-6823872 x-156937135}{440000 (2 x-1)}+\frac{2739541 \log (2 x-1)}{7744}+\frac{\log (5 x+3)}{378125}","\frac{729 x^4}{80}+\frac{2673 x^3}{50}+\frac{639819 x^2}{4000}+\frac{3946293 x}{10000}+\frac{117649}{704 (1-2 x)}+\frac{2739541 \log (1-2 x)}{7744}+\frac{\log (5 x+3)}{378125}",1,"(-156937135 - 6823872*x + 276893694*x^2 + 117237780*x^3 + 43035300*x^4 + 8019000*x^5)/(440000*(-1 + 2*x)) + (2739541*Log[-1 + 2*x])/7744 + Log[3 + 5*x]/378125","A",1
1591,1,52,51,0.0324946,"\int \frac{(2+3 x)^5}{(1-2 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^2*(3 + 5*x)),x]","\frac{356400 x^4+1817640 x^3+5724972 x^2-3361446 x-2100875}{44000 (2 x-1)}+\frac{156065 \log (2 x-1)}{1936}+\frac{\log (5 x+3)}{75625}","\frac{81 x^3}{20}+\frac{567 x^2}{25}+\frac{152793 x}{2000}+\frac{16807}{352 (1-2 x)}+\frac{156065 \log (1-2 x)}{1936}+\frac{\log (5 x+3)}{75625}",1,"(-2100875 - 3361446*x + 5724972*x^2 + 1817640*x^3 + 356400*x^4)/(44000*(-1 + 2*x)) + (156065*Log[-1 + 2*x])/1936 + Log[3 + 5*x]/75625","A",1
1592,1,47,44,0.0309662,"\int \frac{(2+3 x)^4}{(1-2 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^2*(3 + 5*x)),x]","\frac{17820 x^3+100386 x^2-54648 x-60025}{4400 (2 x-1)}+\frac{33271 \log (2 x-1)}{1936}+\frac{\log (5 x+3)}{15125}","\frac{81 x^2}{40}+\frac{621 x}{50}+\frac{2401}{176 (1-2 x)}+\frac{33271 \log (1-2 x)}{1936}+\frac{\log (5 x+3)}{15125}",1,"(-60025 - 54648*x + 100386*x^2 + 17820*x^3)/(4400*(-1 + 2*x)) + (33271*Log[-1 + 2*x])/1936 + Log[3 + 5*x]/15125","A",1
1593,1,42,37,0.029673,"\int \frac{(2+3 x)^3}{(1-2 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^2*(3 + 5*x)),x]","\frac{5940 x^2+594 x-10357}{2200 (2 x-1)}+\frac{392}{121} \log (2 x-1)+\frac{\log (5 x+3)}{3025}","\frac{27 x}{20}+\frac{343}{88 (1-2 x)}+\frac{392}{121} \log (1-2 x)+\frac{\log (5 x+3)}{3025}",1,"(-10357 + 594*x + 5940*x^2)/(2200*(-1 + 2*x)) + (392*Log[-1 + 2*x])/121 + Log[3 + 5*x]/3025","A",1
1594,1,32,32,0.0213593,"\int \frac{(2+3 x)^2}{(1-2 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^2*(3 + 5*x)),x]","-\frac{49}{44 (2 x-1)}+\frac{217}{484} \log (2 x-1)+\frac{1}{605} \log (5 x+3)","\frac{49}{44 (1-2 x)}+\frac{217}{484} \log (1-2 x)+\frac{1}{605} \log (5 x+3)",1,"-49/(44*(-1 + 2*x)) + (217*Log[-1 + 2*x])/484 + Log[3 + 5*x]/605","A",1
1595,1,32,32,0.022702,"\int \frac{2+3 x}{(1-2 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^2*(3 + 5*x)),x]","-\frac{7}{22 (2 x-1)}-\frac{1}{121} \log (2 x-1)+\frac{1}{121} \log (5 x+3)","\frac{7}{22 (1-2 x)}-\frac{1}{121} \log (1-2 x)+\frac{1}{121} \log (5 x+3)",1,"-7/(22*(-1 + 2*x)) - Log[-1 + 2*x]/121 + Log[3 + 5*x]/121","A",1
1596,1,32,32,0.0186392,"\int \frac{1}{(1-2 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(3 + 5*x)),x]","-\frac{1}{11 (2 x-1)}-\frac{5}{121} \log (2 x-1)+\frac{5}{121} \log (5 x+3)","\frac{1}{11 (1-2 x)}-\frac{5}{121} \log (1-2 x)+\frac{5}{121} \log (5 x+3)",1,"-1/11*1/(-1 + 2*x) - (5*Log[-1 + 2*x])/121 + (5*Log[3 + 5*x])/121","A",1
1597,1,42,42,0.0326472,"\int \frac{1}{(1-2 x)^2 (2+3 x) (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(2 + 3*x)*(3 + 5*x)),x]","-\frac{2}{77 (2 x-1)}-\frac{136 \log (2 x-1)}{5929}-\frac{9}{49} \log (3 x+2)+\frac{25}{121} \log (5 x+3)","\frac{2}{77 (1-2 x)}-\frac{136 \log (1-2 x)}{5929}-\frac{9}{49} \log (3 x+2)+\frac{25}{121} \log (5 x+3)",1,"-2/(77*(-1 + 2*x)) - (136*Log[-1 + 2*x])/5929 - (9*Log[2 + 3*x])/49 + (25*Log[3 + 5*x])/121","A",1
1598,1,50,53,0.0429599,"\int \frac{1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x)),x]","\frac{186 x-107}{539 \left(6 x^2+x-2\right)}-\frac{404 \log (2 x-1)}{41503}-\frac{351}{343} \log (3 x+2)+\frac{125}{121} \log (5 x+3)","\frac{4}{539 (1-2 x)}+\frac{9}{49 (3 x+2)}-\frac{404 \log (1-2 x)}{41503}-\frac{351}{343} \log (3 x+2)+\frac{125}{121} \log (5 x+3)",1,"(-107 + 186*x)/(539*(-2 + x + 6*x^2)) - (404*Log[-1 + 2*x])/41503 - (351*Log[2 + 3*x])/343 + (125*Log[3 + 5*x])/121","A",1
1599,1,59,64,0.0605099,"\int \frac{1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x)),x]","\frac{46188 x^2+8916 x-16201}{7546 (2 x-1) (3 x+2)^2}-\frac{1072 \log (2 x-1)}{290521}-\frac{12393 \log (3 x+2)}{2401}+\frac{625}{121} \log (5 x+3)","\frac{8}{3773 (1-2 x)}+\frac{351}{343 (3 x+2)}+\frac{9}{98 (3 x+2)^2}-\frac{1072 \log (1-2 x)}{290521}-\frac{12393 \log (3 x+2)}{2401}+\frac{625}{121} \log (5 x+3)",1,"(-16201 + 8916*x + 46188*x^2)/(7546*(-1 + 2*x)*(2 + 3*x)^2) - (1072*Log[-1 + 2*x])/290521 - (12393*Log[2 + 3*x])/2401 + (625*Log[3 + 5*x])/121","A",1
1600,1,64,75,0.0717976,"\int \frac{1}{(1-2 x)^2 (2+3 x)^4 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)),x]","\frac{4906764 x^3+4250124 x^2-1058241 x-1148128}{52822 (2 x-1) (3 x+2)^3}-\frac{2672 \log (2 x-1)}{2033647}-\frac{434043 \log (3 x+2)}{16807}+\frac{3125}{121} \log (5 x+3)","\frac{16}{26411 (1-2 x)}+\frac{12393}{2401 (3 x+2)}+\frac{351}{686 (3 x+2)^2}+\frac{3}{49 (3 x+2)^3}-\frac{2672 \log (1-2 x)}{2033647}-\frac{434043 \log (3 x+2)}{16807}+\frac{3125}{121} \log (5 x+3)",1,"(-1148128 - 1058241*x + 4250124*x^2 + 4906764*x^3)/(52822*(-1 + 2*x)*(2 + 3*x)^3) - (2672*Log[-1 + 2*x])/2033647 - (434043*Log[2 + 3*x])/16807 + (3125*Log[3 + 5*x])/121","A",1
1601,1,69,86,0.1074144,"\int \frac{1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x)),x]","\frac{1031275800 x^4+1581255000 x^3+373875750 x^2-389284050 x-160957733}{739508 (2 x-1) (3 x+2)^4}-\frac{6400 \log (2 x-1)}{14235529}-\frac{15192225 \log (3 x+2)}{117649}+\frac{15625}{121} \log (5 x+3)","\frac{32}{184877 (1-2 x)}+\frac{434043}{16807 (3 x+2)}+\frac{12393}{4802 (3 x+2)^2}+\frac{117}{343 (3 x+2)^3}+\frac{9}{196 (3 x+2)^4}-\frac{6400 \log (1-2 x)}{14235529}-\frac{15192225 \log (3 x+2)}{117649}+\frac{15625}{121} \log (5 x+3)",1,"(-160957733 - 389284050*x + 373875750*x^2 + 1581255000*x^3 + 1031275800*x^4)/(739508*(-1 + 2*x)*(2 + 3*x)^4) - (6400*Log[-1 + 2*x])/14235529 - (15192225*Log[2 + 3*x])/117649 + (15625*Log[3 + 5*x])/121","A",1
1602,1,74,97,0.0719536,"\int \frac{1}{(1-2 x)^2 (2+3 x)^6 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x)),x]","\frac{541450587960 x^5+1191190085640 x^4+749805990750 x^3-73492321230 x^2-220760702913 x-56342700586}{25882780 (2 x-1) (3 x+2)^5}-\frac{14912 \log (2 x-1)}{99648703}-\frac{531729603 \log (3 x+2)}{823543}+\frac{78125}{121} \log (5 x+3)","\frac{64}{1294139 (1-2 x)}+\frac{15192225}{117649 (3 x+2)}+\frac{434043}{33614 (3 x+2)^2}+\frac{4131}{2401 (3 x+2)^3}+\frac{351}{1372 (3 x+2)^4}+\frac{9}{245 (3 x+2)^5}-\frac{14912 \log (1-2 x)}{99648703}-\frac{531729603 \log (3 x+2)}{823543}+\frac{78125}{121} \log (5 x+3)",1,"(-56342700586 - 220760702913*x - 73492321230*x^2 + 749805990750*x^3 + 1191190085640*x^4 + 541450587960*x^5)/(25882780*(-1 + 2*x)*(2 + 3*x)^5) - (14912*Log[-1 + 2*x])/99648703 - (531729603*Log[2 + 3*x])/823543 + (78125*Log[3 + 5*x])/121","A",1
1603,1,70,76,0.0683418,"\int \frac{(2+3 x)^8}{(1-2 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^8/((1 - 2*x)^2*(3 + 5*x)^2),x]","\frac{158776200000 x^7+1034691570000 x^6+3231830745000 x^5+6871128264000 x^4+13763527638300 x^3+1030931307450 x^2-6292591105631 x-1856788880647}{1210000000 \left(10 x^2+x-3\right)}+\frac{79883671 \log (2 x-1)}{85184}+\frac{268 \log (5 x+3)}{103984375}","\frac{6561 x^5}{500}+\frac{168399 x^4}{2000}+\frac{2626101 x^3}{10000}+\frac{14171517 x^2}{25000}+\frac{231915717 x}{200000}+\frac{5764801}{15488 (1-2 x)}-\frac{1}{9453125 (5 x+3)}+\frac{79883671 \log (1-2 x)}{85184}+\frac{268 \log (5 x+3)}{103984375}",1,"(-1856788880647 - 6292591105631*x + 1030931307450*x^2 + 13763527638300*x^3 + 6871128264000*x^4 + 3231830745000*x^5 + 1034691570000*x^6 + 158776200000*x^7)/(1210000000*(-3 + x + 10*x^2)) + (79883671*Log[-1 + 2*x])/85184 + (268*Log[3 + 5*x])/103984375","A",1
1604,1,65,69,0.0477975,"\int \frac{(2+3 x)^7}{(1-2 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^7/((1 - 2*x)^2*(3 + 5*x)^2),x]","\frac{6615675000 x^6+40061587500 x^5+121434390000 x^4+298090064250 x^3+149859391770 x^2-138137255083 x-85375648901}{121000000 \left(10 x^2+x-3\right)}+\frac{18941489 \log (2 x-1)}{85184}+\frac{47 \log (5 x+3)}{4159375}","\frac{2187 x^4}{400}+\frac{16281 x^3}{500}+\frac{1974861 x^2}{20000}+\frac{6156243 x}{25000}+\frac{823543}{7744 (1-2 x)}-\frac{1}{1890625 (5 x+3)}+\frac{18941489 \log (1-2 x)}{85184}+\frac{47 \log (5 x+3)}{4159375}",1,"(-85375648901 - 138137255083*x + 149859391770*x^2 + 298090064250*x^3 + 121434390000*x^4 + 40061587500*x^5 + 6615675000*x^6)/(121000000*(-3 + x + 10*x^2)) + (18941489*Log[-1 + 2*x])/85184 + (47*Log[3 + 5*x])/4159375","A",1
1605,1,60,62,0.0430483,"\int \frac{(2+3 x)^6}{(1-2 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)^2*(3 + 5*x)^2),x]","\frac{294030000 x^5+1705374000 x^4+5810032800 x^3+3232946970 x^2-3241191719 x-2051761483}{12100000 \left(10 x^2+x-3\right)}+\frac{67228 \log (2 x-1)}{1331}+\frac{202 \log (5 x+3)}{4159375}","\frac{243 x^3}{100}+\frac{13851 x^2}{1000}+\frac{473607 x}{10000}+\frac{117649}{3872 (1-2 x)}-\frac{1}{378125 (5 x+3)}+\frac{67228 \log (1-2 x)}{1331}+\frac{202 \log (5 x+3)}{4159375}",1,"(-2051761483 - 3241191719*x + 3232946970*x^2 + 5810032800*x^3 + 1705374000*x^4 + 294030000*x^5)/(12100000*(-3 + x + 10*x^2)) + (67228*Log[-1 + 2*x])/1331 + (202*Log[3 + 5*x])/4159375","A",1
1606,1,55,55,0.0388684,"\int \frac{(2+3 x)^5}{(1-2 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^2*(3 + 5*x)^2),x]","\frac{14701500 x^4+93599550 x^3+59688090 x^2-74672167 x-47978789}{1210000 \left(10 x^2+x-3\right)}+\frac{228095 \log (2 x-1)}{21296}+\frac{169 \log (5 x+3)}{831875}","\frac{243 x^2}{200}+\frac{3807 x}{500}+\frac{16807}{1936 (1-2 x)}-\frac{1}{75625 (5 x+3)}+\frac{228095 \log (1-2 x)}{21296}+\frac{169 \log (5 x+3)}{831875}",1,"(-47978789 - 74672167*x + 59688090*x^2 + 93599550*x^3 + 14701500*x^4)/(1210000*(-3 + x + 10*x^2)) + (228095*Log[-1 + 2*x])/21296 + (169*Log[3 + 5*x])/831875","A",1
1607,1,50,48,0.0396669,"\int \frac{(2+3 x)^4}{(1-2 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^2*(3 + 5*x)^2),x]","\frac{980100 x^3+751410 x^2-1729331 x-1096387}{121000 \left(10 x^2+x-3\right)}+\frac{10633 \log (2 x-1)}{5324}+\frac{136 \log (5 x+3)}{166375}","\frac{81 x}{100}+\frac{2401}{968 (1-2 x)}-\frac{1}{15125 (5 x+3)}+\frac{10633 \log (1-2 x)}{5324}+\frac{136 \log (5 x+3)}{166375}",1,"(-1096387 - 1729331*x + 751410*x^2 + 980100*x^3)/(121000*(-3 + x + 10*x^2)) + (10633*Log[-1 + 2*x])/5324 + (136*Log[3 + 5*x])/166375","A",1
1608,1,40,43,0.0309846,"\int \frac{(2+3 x)^3}{(1-2 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^2*(3 + 5*x)^2),x]","\frac{-42883 x-25721}{12100 \left(10 x^2+x-3\right)}+\frac{1421 \log (2 x-1)}{5324}+\frac{103 \log (5 x+3)}{33275}","\frac{343}{484 (1-2 x)}-\frac{1}{3025 (5 x+3)}+\frac{1421 \log (1-2 x)}{5324}+\frac{103 \log (5 x+3)}{33275}",1,"(-25721 - 42883*x)/(12100*(-3 + x + 10*x^2)) + (1421*Log[-1 + 2*x])/5324 + (103*Log[3 + 5*x])/33275","A",1
1609,1,40,43,0.0357641,"\int \frac{(2+3 x)^2}{(1-2 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^2*(3 + 5*x)^2),x]","\frac{-1229 x-733}{1210 \left(10 x^2+x-3\right)}-\frac{14 \log (2 x-1)}{1331}+\frac{14 \log (5 x+3)}{1331}","\frac{49}{242 (1-2 x)}-\frac{1}{605 (5 x+3)}-\frac{14 \log (1-2 x)}{1331}+\frac{14 \log (5 x+3)}{1331}",1,"(-733 - 1229*x)/(1210*(-3 + x + 10*x^2)) - (14*Log[-1 + 2*x])/1331 + (14*Log[3 + 5*x])/1331","A",1
1610,1,40,43,0.0248288,"\int \frac{2+3 x}{(1-2 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^2*(3 + 5*x)^2),x]","\frac{-37 x-20}{121 \left(10 x^2+x-3\right)}-\frac{37 \log (2 x-1)}{1331}+\frac{37 \log (5 x+3)}{1331}","\frac{7}{121 (1-2 x)}-\frac{1}{121 (5 x+3)}-\frac{37 \log (1-2 x)}{1331}+\frac{37 \log (5 x+3)}{1331}",1,"(-20 - 37*x)/(121*(-3 + x + 10*x^2)) - (37*Log[-1 + 2*x])/1331 + (37*Log[3 + 5*x])/1331","A",1
1611,1,40,43,0.0240832,"\int \frac{1}{(1-2 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(3 + 5*x)^2),x]","\frac{-20 x-1}{121 \left(10 x^2+x-3\right)}-\frac{20 \log (2 x-1)}{1331}+\frac{20 \log (5 x+3)}{1331}","\frac{2}{121 (1-2 x)}-\frac{5}{121 (5 x+3)}-\frac{20 \log (1-2 x)}{1331}+\frac{20 \log (5 x+3)}{1331}",1,"(-1 - 20*x)/(121*(-3 + x + 10*x^2)) - (20*Log[-1 + 2*x])/1331 + (20*Log[3 + 5*x])/1331","A",1
1612,1,50,53,0.043403,"\int \frac{1}{(1-2 x)^2 (2+3 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(2 + 3*x)*(3 + 5*x)^2),x]","\frac{163-370 x}{847 \left(10 x^2+x-3\right)}-\frac{412 \log (2 x-1)}{65219}+\frac{27}{49} \log (3 x+2)-\frac{725 \log (5 x+3)}{1331}","\frac{4}{847 (1-2 x)}-\frac{25}{121 (5 x+3)}-\frac{412 \log (1-2 x)}{65219}+\frac{27}{49} \log (3 x+2)-\frac{725 \log (5 x+3)}{1331}",1,"(163 - 370*x)/(847*(-3 + x + 10*x^2)) - (412*Log[-1 + 2*x])/65219 + (27*Log[2 + 3*x])/49 - (725*Log[3 + 5*x])/1331","A",1
1613,1,66,64,0.0711826,"\int \frac{1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{-69540 x^2-9544 x+22003}{5929 (2 x-1) (3 x+2) (5 x+3)}-\frac{1088 \log (2 x-1)}{456533}+\frac{1998}{343} \log (3 x+2)-\frac{7750 \log (5 x+3)}{1331}","\frac{8}{5929 (1-2 x)}-\frac{27}{49 (3 x+2)}-\frac{125}{121 (5 x+3)}-\frac{1088 \log (1-2 x)}{456533}+\frac{1998}{343} \log (3 x+2)-\frac{7750 \log (5 x+3)}{1331}",1,"(22003 - 9544*x - 69540*x^2)/(5929*(-1 + 2*x)*(2 + 3*x)*(3 + 5*x)) - (1088*Log[-1 + 2*x])/456533 + (1998*Log[2 + 3*x])/343 - (7750*Log[3 + 5*x])/1331","A",1
1614,1,67,75,0.0912336,"\int \frac{1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x)^2),x]","\frac{-22224420 x^3-17783592 x^2+5074951 x+4684319}{83006 (3 x+2)^2 \left(10 x^2+x-3\right)}-\frac{2704 \log (2 x-1)}{3195731}+\frac{107109 \log (3 x+2)}{2401}-\frac{59375 \log (5 x+3)}{1331}","\frac{16}{41503 (1-2 x)}-\frac{1998}{343 (3 x+2)}-\frac{625}{121 (5 x+3)}-\frac{27}{98 (3 x+2)^2}-\frac{2704 \log (1-2 x)}{3195731}+\frac{107109 \log (3 x+2)}{2401}-\frac{59375 \log (5 x+3)}{1331}",1,"(4684319 + 5074951*x - 17783592*x^2 - 22224420*x^3)/(83006*(2 + 3*x)^2*(-3 + x + 10*x^2)) - (2704*Log[-1 + 2*x])/3195731 + (107109*Log[2 + 3*x])/2401 - (59375*Log[3 + 5*x])/1331","A",1
1615,1,72,86,0.1151068,"\int \frac{1}{(1-2 x)^2 (2+3 x)^4 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^2),x]","\frac{-1571590080 x^4-2305013328 x^3-479067048 x^2+570653522 x+220783501}{290521 (3 x+2)^3 \left(10 x^2+x-3\right)}-\frac{6464 \log (2 x-1)}{22370117}+\frac{5050944 \log (3 x+2)}{16807}-\frac{400000 \log (5 x+3)}{1331}","\frac{32}{290521 (1-2 x)}-\frac{107109}{2401 (3 x+2)}-\frac{3125}{121 (5 x+3)}-\frac{999}{343 (3 x+2)^2}-\frac{9}{49 (3 x+2)^3}-\frac{6464 \log (1-2 x)}{22370117}+\frac{5050944 \log (3 x+2)}{16807}-\frac{400000 \log (5 x+3)}{1331}",1,"(220783501 + 570653522*x - 479067048*x^2 - 2305013328*x^3 - 1571590080*x^4)/(290521*(2 + 3*x)^3*(-3 + x + 10*x^2)) - (6464*Log[-1 + 2*x])/22370117 + (5050944*Log[2 + 3*x])/16807 - (400000*Log[3 + 5*x])/1331","A",1
1616,1,77,97,0.1355918,"\int \frac{1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x)^2),x]","\frac{-830228340600 x^5-1771154199360 x^4-1064845635750 x^3+132753874800 x^2+317609203475 x+77754195847}{8134588 (3 x+2)^4 \left(10 x^2+x-3\right)}-\frac{15040 \log (2 x-1)}{156590819}+\frac{222359715 \log (3 x+2)}{117649}-\frac{2515625 \log (5 x+3)}{1331}","\frac{64}{2033647 (1-2 x)}-\frac{5050944}{16807 (3 x+2)}-\frac{15625}{121 (5 x+3)}-\frac{107109}{4802 (3 x+2)^2}-\frac{666}{343 (3 x+2)^3}-\frac{27}{196 (3 x+2)^4}-\frac{15040 \log (1-2 x)}{156590819}+\frac{222359715 \log (3 x+2)}{117649}-\frac{2515625 \log (5 x+3)}{1331}",1,"(77754195847 + 317609203475*x + 132753874800*x^2 - 1064845635750*x^3 - 1771154199360*x^4 - 830228340600*x^5)/(8134588*(2 + 3*x)^4*(-3 + x + 10*x^2)) - (15040*Log[-1 + 2*x])/156590819 + (222359715*Log[2 + 3*x])/117649 - (2515625*Log[3 + 5*x])/1331","A",1
1617,1,74,80,0.0956518,"\int \frac{(2+3 x)^8}{(1-2 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^8/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{1091586375000 x^7+7362143662500 x^6+24633465862500 x^5+63530731316250 x^4+56533202658900 x^3-8413491954495 x^2-29145604680906 x-8878349145317}{6655000000 (2 x-1) (5 x+3)^2}+\frac{130943337 \log (2 x-1)}{937024}+\frac{6312 \log (5 x+3)}{228765625}","\frac{6561 x^4}{2000}+\frac{12393 x^3}{625}+\frac{6093711 x^2}{100000}+\frac{7680987 x}{50000}+\frac{5764801}{85184 (1-2 x)}-\frac{268}{103984375 (5 x+3)}-\frac{1}{18906250 (5 x+3)^2}+\frac{130943337 \log (1-2 x)}{937024}+\frac{6312 \log (5 x+3)}{228765625}",1,"(-8878349145317 - 29145604680906*x - 8413491954495*x^2 + 56533202658900*x^3 + 63530731316250*x^4 + 24633465862500*x^5 + 7362143662500*x^6 + 1091586375000*x^7)/(6655000000*(-1 + 2*x)*(3 + 5*x)^2) + (130943337*Log[-1 + 2*x])/937024 + (6312*Log[3 + 5*x])/228765625","A",1
1618,1,69,73,0.0520902,"\int \frac{(2+3 x)^7}{(1-2 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^7/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{48514950000 x^6+315347175000 x^5+1161933052500 x^4+42644641050 x^3-1002031406415 x^2-426293494632 x-14162188399}{665500000 (2 x-1) (5 x+3)^2}+\frac{7411887 \log (2 x-1)}{234256}+\frac{4761 \log (5 x+3)}{45753125}","\frac{729 x^3}{500}+\frac{21141 x^2}{2500}+\frac{1467477 x}{50000}+\frac{823543}{42592 (1-2 x)}-\frac{47}{4159375 (5 x+3)}-\frac{1}{3781250 (5 x+3)^2}+\frac{7411887 \log (1-2 x)}{234256}+\frac{4761 \log (5 x+3)}{45753125}",1,"(-14162188399 - 426293494632*x - 1002031406415*x^2 + 42644641050*x^3 + 1161933052500*x^4 + 315347175000*x^5 + 48514950000*x^6)/(665500000*(-1 + 2*x)*(3 + 5*x)^2) + (7411887*Log[-1 + 2*x])/234256 + (4761*Log[3 + 5*x])/45753125","A",1
1619,1,64,66,0.0624544,"\int \frac{(2+3 x)^6}{(1-2 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{4851495000 x^5+34445614500 x^4+3832681050 x^3-38424246735 x^2-23631078696 x-3604958287}{133100000 (2 x-1) (5 x+3)^2}+\frac{1563051 \log (2 x-1)}{234256}+\frac{17139 \log (5 x+3)}{45753125}","\frac{729 x^2}{1000}+\frac{2916 x}{625}+\frac{117649}{21296 (1-2 x)}-\frac{202}{4159375 (5 x+3)}-\frac{1}{756250 (5 x+3)^2}+\frac{1563051 \log (1-2 x)}{234256}+\frac{17139 \log (5 x+3)}{45753125}",1,"(-3604958287 - 23631078696*x - 38424246735*x^2 + 3832681050*x^3 + 34445614500*x^4 + 4851495000*x^5)/(133100000*(-1 + 2*x)*(3 + 5*x)^2) + (1563051*Log[-1 + 2*x])/234256 + (17139*Log[3 + 5*x])/45753125","A",1
1620,1,59,59,0.0551535,"\int \frac{(2+3 x)^5}{(1-2 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{16171650 x^4+3234330 x^3-35803563 x^2-32483568 x-7998079}{665500 (2 x-1) (5 x+3)^2}+\frac{36015 \log (2 x-1)}{29282}+\frac{11562 \log (5 x+3)}{9150625}","\frac{243 x}{500}+\frac{16807}{10648 (1-2 x)}-\frac{169}{831875 (5 x+3)}-\frac{1}{151250 (5 x+3)^2}+\frac{36015 \log (1-2 x)}{29282}+\frac{11562 \log (5 x+3)}{9150625}",1,"(-7998079 - 32483568*x - 35803563*x^2 + 3234330*x^3 + 16171650*x^4)/(665500*(-1 + 2*x)*(3 + 5*x)^2) + (36015*Log[-1 + 2*x])/29282 + (11562*Log[3 + 5*x])/9150625","A",1
1621,1,49,54,0.0467689,"\int \frac{(2+3 x)^4}{(1-2 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{-7508565 x^2-9004338 x-2699471}{665500 (2 x-1) (5 x+3)^2}+\frac{9261 \log (2 x-1)}{58564}+\frac{7074 \log (5 x+3)}{1830125}","\frac{2401}{5324 (1-2 x)}-\frac{136}{166375 (5 x+3)}-\frac{1}{30250 (5 x+3)^2}+\frac{9261 \log (1-2 x)}{58564}+\frac{7074 \log (5 x+3)}{1830125}",1,"(-2699471 - 9004338*x - 7508565*x^2)/(665500*(-1 + 2*x)*(3 + 5*x)^2) + (9261*Log[-1 + 2*x])/58564 + (7074*Log[3 + 5*x])/1830125","A",1
1622,1,49,54,0.040634,"\int \frac{(2+3 x)^3}{(1-2 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{-216435 x^2-257478 x-76546}{66550 (2 x-1) (5 x+3)^2}-\frac{147 \log (2 x-1)}{14641}+\frac{147 \log (5 x+3)}{14641}","\frac{343}{2662 (1-2 x)}-\frac{103}{33275 (5 x+3)}-\frac{1}{6050 (5 x+3)^2}-\frac{147 \log (1-2 x)}{14641}+\frac{147 \log (5 x+3)}{14641}",1,"(-76546 - 257478*x - 216435*x^2)/(66550*(-1 + 2*x)*(3 + 5*x)^2) - (147*Log[-1 + 2*x])/14641 + (147*Log[3 + 5*x])/14641","A",1
1623,1,49,54,0.0400029,"\int \frac{(2+3 x)^2}{(1-2 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{-13650 x^2-14862 x-3979}{13310 (2 x-1) (5 x+3)^2}-\frac{273 \log (2 x-1)}{14641}+\frac{273 \log (5 x+3)}{14641}","\frac{49}{1331 (1-2 x)}-\frac{14}{1331 (5 x+3)}-\frac{1}{1210 (5 x+3)^2}-\frac{273 \log (1-2 x)}{14641}+\frac{273 \log (5 x+3)}{14641}",1,"(-3979 - 14862*x - 13650*x^2)/(13310*(-1 + 2*x)*(3 + 5*x)^2) - (273*Log[-1 + 2*x])/14641 + (273*Log[3 + 5*x])/14641","A",1
1624,1,49,54,0.0379619,"\int \frac{2+3 x}{(1-2 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{-1440 x^2-936 x-19}{2662 (2 x-1) (5 x+3)^2}-\frac{144 \log (2 x-1)}{14641}+\frac{144 \log (5 x+3)}{14641}","\frac{14}{1331 (1-2 x)}-\frac{37}{1331 (5 x+3)}-\frac{1}{242 (5 x+3)^2}-\frac{144 \log (1-2 x)}{14641}+\frac{144 \log (5 x+3)}{14641}",1,"(-19 - 936*x - 1440*x^2)/(2662*(-1 + 2*x)*(3 + 5*x)^2) - (144*Log[-1 + 2*x])/14641 + (144*Log[3 + 5*x])/14641","A",1
1625,1,49,54,0.0357935,"\int \frac{1}{(1-2 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{-600 x^2-390 x+103}{2662 (2 x-1) (5 x+3)^2}-\frac{60 \log (2 x-1)}{14641}+\frac{60 \log (5 x+3)}{14641}","\frac{4}{1331 (1-2 x)}-\frac{20}{1331 (5 x+3)}-\frac{5}{242 (5 x+3)^2}-\frac{60 \log (1-2 x)}{14641}+\frac{60 \log (5 x+3)}{14641}",1,"(103 - 390*x - 600*x^2)/(2662*(-1 + 2*x)*(3 + 5*x)^2) - (60*Log[-1 + 2*x])/14641 + (60*Log[3 + 5*x])/14641","A",1
1626,1,59,64,0.0468318,"\int \frac{1}{(1-2 x)^2 (2+3 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(2 + 3*x)*(3 + 5*x)^3),x]","\frac{101100 x^2+5820 x-28669}{18634 (2 x-1) (5 x+3)^2}-\frac{1104 \log (2 x-1)}{717409}-\frac{81}{49} \log (3 x+2)+\frac{24225 \log (5 x+3)}{14641}","\frac{8}{9317 (1-2 x)}+\frac{725}{1331 (5 x+3)}-\frac{25}{242 (5 x+3)^2}-\frac{1104 \log (1-2 x)}{717409}-\frac{81}{49} \log (3 x+2)+\frac{24225 \log (5 x+3)}{14641}",1,"(-28669 + 5820*x + 101100*x^2)/(18634*(-1 + 2*x)*(3 + 5*x)^2) - (1104*Log[-1 + 2*x])/717409 - (81*Log[2 + 3*x])/49 + (24225*Log[3 + 5*x])/14641","A",1
1627,1,67,75,0.0814626,"\int \frac{1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{33563700 x^3+24606540 x^2-7974123 x-6363424}{130438 (5 x+3)^2 \left(6 x^2+x-2\right)}-\frac{2736 \log (2 x-1)}{5021863}-\frac{8829}{343} \log (3 x+2)+\frac{376875 \log (5 x+3)}{14641}","\frac{16}{65219 (1-2 x)}+\frac{81}{49 (3 x+2)}+\frac{7750}{1331 (5 x+3)}-\frac{125}{242 (5 x+3)^2}-\frac{2736 \log (1-2 x)}{5021863}-\frac{8829}{343} \log (3 x+2)+\frac{376875 \log (5 x+3)}{14641}",1,"(-6363424 - 7974123*x + 24606540*x^2 + 33563700*x^3)/(130438*(3 + 5*x)^2*(-2 + x + 6*x^2)) - (2736*Log[-1 + 2*x])/5021863 - (8829*Log[2 + 3*x])/343 + (376875*Log[3 + 5*x])/14641","A",1
1628,1,76,86,0.1382997,"\int \frac{1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{7191217800 x^4+10067655960 x^3+1808383578 x^2-2501680914 x-909187261}{913066 (2 x-1) (3 x+2)^2 (5 x+3)^2}-\frac{6528 \log (2 x-1)}{35153041}-\frac{630342 \log (3 x+2)}{2401}+\frac{3843750 \log (5 x+3)}{14641}","\frac{32}{456533 (1-2 x)}+\frac{8829}{343 (3 x+2)}+\frac{59375}{1331 (5 x+3)}+\frac{81}{98 (3 x+2)^2}-\frac{625}{242 (5 x+3)^2}-\frac{6528 \log (1-2 x)}{35153041}-\frac{630342 \log (3 x+2)}{2401}+\frac{3843750 \log (5 x+3)}{14641}",1,"(-909187261 - 2501680914*x + 1808383578*x^2 + 10067655960*x^3 + 7191217800*x^4)/(913066*(-1 + 2*x)*(2 + 3*x)^2*(3 + 5*x)^2) - (6528*Log[-1 + 2*x])/35153041 - (630342*Log[2 + 3*x])/2401 + (3843750*Log[3 + 5*x])/14641","A",1
1629,1,81,97,0.115577,"\int \frac{1}{(1-2 x)^2 (2+3 x)^4 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^3),x]","\frac{1273702595400 x^5+2632318355880 x^4+1509100957674 x^3-229550032266 x^2-456430279071 x-107358241468}{6391462 (2 x-1) (3 x+2)^3 (5 x+3)^2}-\frac{15168 \log (2 x-1)}{246071287}-\frac{37214802 \log (3 x+2)}{16807}+\frac{32418750 \log (5 x+3)}{14641}","\frac{64}{3195731 (1-2 x)}+\frac{630342}{2401 (3 x+2)}+\frac{400000}{1331 (5 x+3)}+\frac{8829}{686 (3 x+2)^2}-\frac{3125}{242 (5 x+3)^2}+\frac{27}{49 (3 x+2)^3}-\frac{15168 \log (1-2 x)}{246071287}-\frac{37214802 \log (3 x+2)}{16807}+\frac{32418750 \log (5 x+3)}{14641}",1,"(-107358241468 - 456430279071*x - 229550032266*x^2 + 1509100957674*x^3 + 2632318355880*x^4 + 1273702595400*x^5)/(6391462*(-1 + 2*x)*(2 + 3*x)^3*(3 + 5*x)^2) - (15168*Log[-1 + 2*x])/246071287 - (37214802*Log[2 + 3*x])/16807 + (32418750*Log[3 + 5*x])/14641","A",1
1630,1,67,80,0.0335335,"\int \frac{(2+3 x)^8 (3+5 x)}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^8*(3 + 5*x))/(1 - 2*x)^3,x]","\frac{-83980800 x^9-644319360 x^8-2354821632 x^7-5596371648 x^6-10256718528 x^5-17427054960 x^4-38900302560 x^3+104409393876 x^2-44728559236 x+3752427799}{35840 (2 x-1)^2}-\frac{106237047}{256} \log (2 x-1)","-\frac{32805 x^7}{56}-\frac{162567 x^6}{32}-\frac{213597 x^5}{10}-\frac{7568235 x^4}{128}-\frac{16042509 x^3}{128}-\frac{118841283 x^2}{512}-\frac{120864213 x}{256}-\frac{246239357}{1024 (1-2 x)}+\frac{63412811}{2048 (1-2 x)^2}-\frac{106237047}{256} \log (1-2 x)",1,"(3752427799 - 44728559236*x + 104409393876*x^2 - 38900302560*x^3 - 17427054960*x^4 - 10256718528*x^5 - 5596371648*x^6 - 2354821632*x^7 - 644319360*x^8 - 83980800*x^9)/(35840*(-1 + 2*x)^2) - (106237047*Log[-1 + 2*x])/256","A",1
1631,1,62,73,0.0291928,"\int \frac{(2+3 x)^7 (3+5 x)}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^7*(3 + 5*x))/(1 - 2*x)^3,x]","\frac{-4665600 x^8-33219072 x^7-113980608 x^6-263003328 x^5-512613360 x^4-1218762720 x^3+3056516316 x^2-1152760076 x+52207049}{5120 (2 x-1)^2}-\frac{23647449}{256} \log (2 x-1)","-\frac{3645 x^6}{16}-\frac{147987 x^5}{80}-\frac{235467 x^4}{32}-\frac{631611 x^3}{32}-\frac{10989621 x^2}{256}-\frac{24960933 x}{256}-\frac{15647317}{256 (1-2 x)}+\frac{9058973}{1024 (1-2 x)^2}-\frac{23647449}{256} \log (1-2 x)",1,"(52207049 - 1152760076*x + 3056516316*x^2 - 1218762720*x^3 - 512613360*x^4 - 263003328*x^5 - 113980608*x^6 - 33219072*x^7 - 4665600*x^8)/(5120*(-1 + 2*x)^2) - (23647449*Log[-1 + 2*x])/256","A",1
1632,1,57,66,0.0278422,"\int \frac{(2+3 x)^6 (3+5 x)}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x)^3,x]","\frac{-373248 x^7-2472768 x^6-8112960 x^5-19403280 x^4-50971680 x^3+118266804 x^2-35968388 x-1114981}{1024 (2 x-1)^2}-\frac{5078115}{256} \log (2 x-1)","-\frac{729 x^5}{8}-\frac{44469 x^4}{64}-\frac{10611 x^3}{4}-\frac{461835 x^2}{64}-\frac{2431647 x}{128}-\frac{3916031}{256 (1-2 x)}+\frac{1294139}{512 (1-2 x)^2}-\frac{5078115}{256} \log (1-2 x)",1,"(-1114981 - 35968388*x + 118266804*x^2 - 50971680*x^3 - 19403280*x^4 - 8112960*x^5 - 2472768*x^6 - 373248*x^7)/(1024*(-1 + 2*x)^2) - (5078115*Log[-1 + 2*x])/256","A",1
1633,1,52,59,0.0271222,"\int \frac{(2+3 x)^5 (3+5 x)}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^5*(3 + 5*x))/(1 - 2*x)^3,x]","\frac{-77760 x^6-485568 x^5-1609200 x^4-4969440 x^3+10547820 x^2-2008220 x-524947}{512 (2 x-1)^2}-\frac{519645}{128} \log (2 x-1)","-\frac{1215 x^4}{32}-\frac{4401 x^3}{16}-\frac{16821 x^2}{16}-\frac{109089 x}{32}-\frac{60025}{16 (1-2 x)}+\frac{184877}{256 (1-2 x)^2}-\frac{519645}{128} \log (1-2 x)",1,"(-524947 - 2008220*x + 10547820*x^2 - 4969440*x^3 - 1609200*x^4 - 485568*x^5 - 77760*x^6)/(512*(-1 + 2*x)^2) - (519645*Log[-1 + 2*x])/128","A",1
1634,1,47,50,0.0260412,"\int \frac{(2+3 x)^4 (3+5 x)}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x)^3,x]","\frac{-2160 x^5-13284 x^4-54216 x^3+103950 x^2+1310 x-12365}{32 (2 x-1)^2}-\frac{24843}{32} \log (2 x-1)","-\frac{135 x^3}{8}-\frac{3861 x^2}{32}-540 x-\frac{57281}{64 (1-2 x)}+\frac{26411}{128 (1-2 x)^2}-\frac{24843}{32} \log (1-2 x)",1,"(-12365 + 1310*x + 103950*x^2 - 54216*x^3 - 13284*x^4 - 2160*x^5)/(32*(-1 + 2*x)^2) - (24843*Log[-1 + 2*x])/32","A",1
1635,1,42,45,0.0223456,"\int \frac{(2+3 x)^3 (3+5 x)}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x)^3,x]","\frac{-1080 x^4-7776 x^3+13284 x^2+6220 x-3505}{32 (2 x-1)^2}-\frac{1071}{8} \log (2 x-1)","-\frac{135 x^2}{16}-\frac{1107 x}{16}-\frac{3283}{16 (1-2 x)}+\frac{3773}{64 (1-2 x)^2}-\frac{1071}{8} \log (1-2 x)",1,"(-3505 + 6220*x + 13284*x^2 - 7776*x^3 - 1080*x^4)/(32*(-1 + 2*x)^2) - (1071*Log[-1 + 2*x])/8","A",1
1636,1,37,38,0.0312251,"\int \frac{(2+3 x)^2 (3+5 x)}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x))/(1 - 2*x)^3,x]","\frac{-720 x^3+1080 x^2+2288 x-785}{32 (2 x-1)^2}-\frac{309}{16} \log (2 x-1)","-\frac{45 x}{8}-\frac{707}{16 (1-2 x)}+\frac{539}{32 (1-2 x)^2}-\frac{309}{16} \log (1-2 x)",1,"(-785 + 2288*x + 1080*x^2 - 720*x^3)/(32*(-1 + 2*x)^2) - (309*Log[-1 + 2*x])/16","A",1
1637,1,27,33,0.0131038,"\int \frac{(2+3 x) (3+5 x)}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x))/(1 - 2*x)^3,x]","\frac{272 x-59}{16 (2 x-1)^2}-\frac{15}{8} \log (2 x-1)","-\frac{17}{2 (1-2 x)}+\frac{77}{16 (1-2 x)^2}-\frac{15}{8} \log (1-2 x)",1,"(-59 + 272*x)/(16*(-1 + 2*x)^2) - (15*Log[-1 + 2*x])/8","A",1
1638,1,16,18,0.0067346,"\int \frac{3+5 x}{(1-2 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)/(1 - 2*x)^3,x]","\frac{20 x+1}{8 (2 x-1)^2}","\frac{(5 x+3)^2}{22 (1-2 x)^2}",1,"(1 + 20*x)/(8*(-1 + 2*x)^2)","A",1
1639,1,33,43,0.0296899,"\int \frac{3+5 x}{(1-2 x)^3 (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)),x]","\frac{8 x+73}{196 (2 x-1)^2}-\frac{6}{343} \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)","-\frac{1}{49 (1-2 x)}+\frac{11}{28 (1-2 x)^2}+\frac{3}{343} \log (1-2 x)-\frac{3}{343} \log (3 x+2)",1,"(73 + 8*x)/(196*(-1 + 2*x)^2) - (6*ArcTanh[(3 + x)/(1 + 5*x)])/343","A",1
1640,1,45,54,0.0530636,"\int \frac{3+5 x}{(1-2 x)^3 (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)^2),x]","\frac{-348 x^2+145 x+284}{686 (2 x-1)^2 (3 x+2)}+\frac{174 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{2401}","\frac{31}{343 (1-2 x)}+\frac{3}{343 (3 x+2)}+\frac{11}{98 (1-2 x)^2}-\frac{87 \log (1-2 x)}{2401}+\frac{87 \log (3 x+2)}{2401}",1,"(284 + 145*x - 348*x^2)/(686*(-1 + 2*x)^2*(2 + 3*x)) + (174*ArcTanh[(3 + x)/(1 + 5*x)])/2401","A",1
1641,1,46,65,0.0384183,"\int \frac{3+5 x}{(1-2 x)^3 (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)^3),x]","\frac{-6696 x^3-1674 x^2+3658 x+1313}{4802 \left(6 x^2+x-2\right)^2}+\frac{1116 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{16807}","\frac{128}{2401 (1-2 x)}-\frac{87}{2401 (3 x+2)}+\frac{11}{343 (1-2 x)^2}+\frac{3}{686 (3 x+2)^2}-\frac{558 \log (1-2 x)}{16807}+\frac{558 \log (3 x+2)}{16807}",1,"(1313 + 3658*x - 1674*x^2 - 6696*x^3)/(4802*(-2 + x + 6*x^2)^2) + (1116*ArcTanh[(3 + x)/(1 + 5*x)])/16807","A",1
1642,1,55,76,0.0527916,"\int \frac{3+5 x}{(1-2 x)^3 (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)^4),x]","\frac{-82080 x^4-75240 x^3+31160 x^2+33725 x+3088}{33614 (2 x-1)^2 (3 x+2)^3}+\frac{4560 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{117649}","\frac{388}{16807 (1-2 x)}-\frac{558}{16807 (3 x+2)}+\frac{22}{2401 (1-2 x)^2}-\frac{87}{4802 (3 x+2)^2}+\frac{1}{343 (3 x+2)^3}-\frac{2280 \log (1-2 x)}{117649}+\frac{2280 \log (3 x+2)}{117649}",1,"(3088 + 33725*x + 31160*x^2 - 75240*x^3 - 82080*x^4)/(33614*(-1 + 2*x)^2*(2 + 3*x)^3) + (4560*ArcTanh[(3 + x)/(1 + 5*x)])/117649","A",1
1643,1,60,87,0.0820449,"\int \frac{3+5 x}{(1-2 x)^3 (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)^5),x]","\frac{-1658880 x^5-2626560 x^4-384000 x^3+1101440 x^2+403584 x-28275}{470596 (2 x-1)^2 (3 x+2)^4}+\frac{15360 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{823543}","\frac{1040}{117649 (1-2 x)}-\frac{2280}{117649 (3 x+2)}+\frac{44}{16807 (1-2 x)^2}-\frac{279}{16807 (3 x+2)^2}-\frac{29}{2401 (3 x+2)^3}+\frac{3}{1372 (3 x+2)^4}-\frac{7680 \log (1-2 x)}{823543}+\frac{7680 \log (3 x+2)}{823543}",1,"(-28275 + 403584*x + 1101440*x^2 - 384000*x^3 - 2626560*x^4 - 1658880*x^5)/(470596*(-1 + 2*x)^2*(2 + 3*x)^4) + (15360*ArcTanh[(3 + x)/(1 + 5*x)])/823543","A",1
1644,1,65,98,0.0792395,"\int \frac{3+5 x}{(1-2 x)^3 (2+3 x)^6} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)^6),x]","\frac{-10730880 x^6-24144480 x^5-13811040 x^4+5468940 x^3+7360644 x^2+1134751 x-381394}{2352980 (2 x-1)^2 (3 x+2)^5}+\frac{6624 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{823543}","\frac{2608}{823543 (1-2 x)}-\frac{7680}{823543 (3 x+2)}+\frac{88}{117649 (1-2 x)^2}-\frac{1140}{117649 (3 x+2)^2}-\frac{186}{16807 (3 x+2)^3}-\frac{87}{9604 (3 x+2)^4}+\frac{3}{1715 (3 x+2)^5}-\frac{3312 \log (1-2 x)}{823543}+\frac{3312 \log (3 x+2)}{823543}",1,"(-381394 + 1134751*x + 7360644*x^2 + 5468940*x^3 - 13811040*x^4 - 24144480*x^5 - 10730880*x^6)/(2352980*(-1 + 2*x)^2*(2 + 3*x)^5) + (6624*ArcTanh[(3 + x)/(1 + 5*x)])/823543","A",1
1645,1,67,80,0.0355087,"\int \frac{(2+3 x)^7 (3+5 x)^2}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^7*(3 + 5*x)^2)/(1 - 2*x)^3,x]","\frac{-34992000 x^9-265744800 x^8-961797888 x^7-2265332832 x^6-4120214112 x^5-6962248440 x^4-15497514480 x^3+41720946264 x^2-17964456304 x+1533057471}{8960 (2 x-1)^2}-\frac{84589631}{128} \log (2 x-1)","-\frac{54675 x^7}{56}-\frac{268515 x^6}{32}-\frac{2798631 x^5}{80}-\frac{12299769 x^4}{128}-\frac{25895367 x^3}{128}-\frac{190742391 x^2}{512}-\frac{48280011 x}{64}-\frac{389535839}{1024 (1-2 x)}+\frac{99648703}{2048 (1-2 x)^2}-\frac{84589631}{128} \log (1-2 x)",1,"(1533057471 - 17964456304*x + 41720946264*x^2 - 15497514480*x^3 - 6962248440*x^4 - 4120214112*x^5 - 2265332832*x^6 - 961797888*x^7 - 265744800*x^8 - 34992000*x^9)/(8960*(-1 + 2*x)^2) - (84589631*Log[-1 + 2*x])/128","A",1
1646,1,62,73,0.0334495,"\int \frac{(2+3 x)^6 (3+5 x)^2}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^6*(3 + 5*x)^2)/(1 - 2*x)^3,x]","\frac{-777600 x^8-5474304 x^7-18584640 x^6-42481728 x^5-82201680 x^4-194631840 x^3+489708252 x^2-186131948 x+8887005}{512 (2 x-1)^2}-\frac{18859855}{128} \log (2 x-1)","-\frac{6075 x^6}{16}-\frac{48843 x^5}{16}-\frac{770067 x^4}{64}-\frac{1024389 x^3}{32}-\frac{17700255 x^2}{256}-\frac{39980457 x}{256}-\frac{12386759}{128 (1-2 x)}+\frac{14235529}{1024 (1-2 x)^2}-\frac{18859855}{128} \log (1-2 x)",1,"(8887005 - 186131948*x + 489708252*x^2 - 194631840*x^3 - 82201680*x^4 - 42481728*x^5 - 18584640*x^6 - 5474304*x^7 - 777600*x^8)/(512*(-1 + 2*x)^2) - (18859855*Log[-1 + 2*x])/128","A",1
1647,1,57,66,0.0317229,"\int \frac{(2+3 x)^5 (3+5 x)^2}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^5*(3 + 5*x)^2)/(1 - 2*x)^3,x]","\frac{-622080 x^7-4069440 x^6-13197888 x^5-31266000 x^4-81639840 x^3+190079460 x^2-58608500 x-1508337}{1024 (2 x-1)^2}-\frac{8117095}{256} \log (2 x-1)","-\frac{1215 x^5}{8}-\frac{73305 x^4}{64}-\frac{69273 x^3}{16}-\frac{747297 x^2}{64}-\frac{3907293 x}{128}-\frac{6206585}{256 (1-2 x)}+\frac{2033647}{512 (1-2 x)^2}-\frac{8117095}{256} \log (1-2 x)",1,"(-1508337 - 58608500*x + 190079460*x^2 - 81639840*x^3 - 31266000*x^4 - 13197888*x^5 - 4069440*x^6 - 622080*x^7)/(1024*(-1 + 2*x)^2) - (8117095*Log[-1 + 2*x])/256","A",1
1648,1,52,59,0.0297858,"\int \frac{(2+3 x)^4 (3+5 x)^2}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^3,x]","\frac{-129600 x^6-797760 x^5-2611152 x^4-7993248 x^3+17025300 x^2-3354020 x-808965}{512 (2 x-1)^2}-\frac{832951}{128} \log (2 x-1)","-\frac{2025 x^4}{32}-\frac{7245 x^3}{16}-\frac{54783 x^2}{32}-\frac{176055 x}{32}-\frac{381073}{64 (1-2 x)}+\frac{290521}{256 (1-2 x)^2}-\frac{832951}{128} \log (1-2 x)",1,"(-808965 - 3354020*x + 17025300*x^2 - 7993248*x^3 - 2611152*x^4 - 797760*x^5 - 129600*x^6)/(512*(-1 + 2*x)^2) - (832951*Log[-1 + 2*x])/128","A",1
1649,1,47,52,0.0278033,"\int \frac{(2+3 x)^3 (3+5 x)^2}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^2)/(1 - 2*x)^3,x]","\frac{-1800 x^5-10890 x^4-43884 x^3+84411 x^2+55 x-9720}{16 (2 x-1)^2}-\frac{39977}{32} \log (2 x-1)","-\frac{225 x^3}{8}-\frac{6345 x^2}{32}-\frac{14031 x}{16}-\frac{91091}{64 (1-2 x)}+\frac{41503}{128 (1-2 x)^2}-\frac{39977}{32} \log (1-2 x)",1,"(-9720 + 55*x + 84411*x^2 - 43884*x^3 - 10890*x^4 - 1800*x^5)/(16*(-1 + 2*x)^2) - (39977*Log[-1 + 2*x])/32","A",1
1650,1,42,45,0.0240508,"\int \frac{(2+3 x)^2 (3+5 x)^2}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x)^3,x]","\frac{-450 x^4-3180 x^3+5445 x^2+2401 x-1395}{8 (2 x-1)^2}-\frac{3467}{16} \log (2 x-1)","-\frac{225 x^2}{16}-\frac{1815 x}{16}-\frac{1309}{4 (1-2 x)}+\frac{5929}{64 (1-2 x)^2}-\frac{3467}{16} \log (1-2 x)",1,"(-1395 + 2401*x + 5445*x^2 - 3180*x^3 - 450*x^4)/(8*(-1 + 2*x)^2) - (3467*Log[-1 + 2*x])/16","A",1
1651,1,37,38,0.0301273,"\int \frac{(2+3 x) (3+5 x)^2}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^2)/(1 - 2*x)^3,x]","\frac{-1200 x^3+1800 x^2+3632 x-1269}{32 (2 x-1)^2}-\frac{505}{16} \log (2 x-1)","-\frac{75 x}{8}-\frac{1133}{16 (1-2 x)}+\frac{847}{32 (1-2 x)^2}-\frac{505}{16} \log (1-2 x)",1,"(-1269 + 3632*x + 1800*x^2 - 1200*x^3)/(32*(-1 + 2*x)^2) - (505*Log[-1 + 2*x])/16","A",1
1652,1,27,33,0.0147192,"\int \frac{(3+5 x)^2}{(1-2 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/(1 - 2*x)^3,x]","\frac{11 (40 x-9)}{16 (2 x-1)^2}-\frac{25}{8} \log (2 x-1)","-\frac{55}{4 (1-2 x)}+\frac{121}{16 (1-2 x)^2}-\frac{25}{8} \log (1-2 x)",1,"(11*(-9 + 40*x))/(16*(-1 + 2*x)^2) - (25*Log[-1 + 2*x])/8","A",1
1653,1,33,43,0.036306,"\int \frac{(3+5 x)^2}{(1-2 x)^3 (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)),x]","\frac{11 (148 x+3)}{392 (2 x-1)^2}+\frac{2}{343} \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)","-\frac{407}{196 (1-2 x)}+\frac{121}{56 (1-2 x)^2}-\frac{1}{343} \log (1-2 x)+\frac{1}{343} \log (3 x+2)",1,"(11*(3 + 148*x))/(392*(-1 + 2*x)^2) + (2*ArcTanh[(3 + x)/(1 + 5*x)])/343","A",1
1654,1,45,54,0.0566443,"\int \frac{(3+5 x)^2}{(1-2 x)^3 (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^2),x]","\frac{512 x^2+2645 x+1514}{1372 (2 x-1)^2 (3 x+2)}-\frac{128 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{2401}","-\frac{22}{343 (1-2 x)}-\frac{1}{343 (3 x+2)}+\frac{121}{196 (1-2 x)^2}+\frac{64 \log (1-2 x)}{2401}-\frac{64 \log (3 x+2)}{2401}",1,"(1514 + 2645*x + 512*x^2)/(1372*(-1 + 2*x)^2*(2 + 3*x)) - (128*ArcTanh[(3 + x)/(1 + 5*x)])/2401","A",1
1655,1,46,65,0.0446163,"\int \frac{(3+5 x)^2}{(1-2 x)^3 (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^3),x]","\frac{-9948 x^3-2487 x^2+12104 x+6189}{4802 \left(6 x^2+x-2\right)^2}+\frac{1658 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{16807}","\frac{319}{2401 (1-2 x)}+\frac{64}{2401 (3 x+2)}+\frac{121}{686 (1-2 x)^2}-\frac{1}{686 (3 x+2)^2}-\frac{829 \log (1-2 x)}{16807}+\frac{829 \log (3 x+2)}{16807}",1,"(6189 + 12104*x - 2487*x^2 - 9948*x^3)/(4802*(-2 + x + 6*x^2)^2) + (1658*ArcTanh[(3 + x)/(1 + 5*x)])/16807","A",1
1656,1,55,76,0.0741485,"\int \frac{(3+5 x)^2}{(1-2 x)^3 (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^4),x]","\frac{-310500 x^4-284625 x^3+117875 x^2+180100 x+44411}{50421 (2 x-1)^2 (3 x+2)^3}+\frac{11500 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{117649}","\frac{1364}{16807 (1-2 x)}-\frac{829}{16807 (3 x+2)}+\frac{121}{2401 (1-2 x)^2}+\frac{32}{2401 (3 x+2)^2}-\frac{1}{1029 (3 x+2)^3}-\frac{5750 \log (1-2 x)}{117649}+\frac{5750 \log (3 x+2)}{117649}",1,"(44411 + 180100*x + 117875*x^2 - 284625*x^3 - 310500*x^4)/(50421*(-1 + 2*x)^2*(2 + 3*x)^3) + (11500*ArcTanh[(3 + x)/(1 + 5*x)])/117649","A",1
1657,1,60,87,0.0835436,"\int \frac{(3+5 x)^2}{(1-2 x)^3 (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^5),x]","\frac{-15577920 x^5-24665040 x^4-3606000 x^3+10343210 x^2+4966396 x+460595}{1411788 (2 x-1)^2 (3 x+2)^4}+\frac{48080 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{823543}","\frac{4180}{117649 (1-2 x)}-\frac{5750}{117649 (3 x+2)}+\frac{242}{16807 (1-2 x)^2}-\frac{829}{33614 (3 x+2)^2}+\frac{64}{7203 (3 x+2)^3}-\frac{1}{1372 (3 x+2)^4}-\frac{24040 \log (1-2 x)}{823543}+\frac{24040 \log (3 x+2)}{823543}",1,"(460595 + 4966396*x + 10343210*x^2 - 3606000*x^3 - 24665040*x^4 - 15577920*x^5)/(1411788*(-1 + 2*x)^2*(2 + 3*x)^4) + (48080*ArcTanh[(3 + x)/(1 + 5*x)])/823543","A",1
1658,1,65,98,0.1018691,"\int \frac{(3+5 x)^2}{(1-2 x)^3 (2+3 x)^6} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^6),x]","\frac{-28421280 x^6-63947880 x^5-36579240 x^4+14484765 x^3+19495039 x^2+4230956 x-258089}{1764735 (2 x-1)^2 (3 x+2)^5}+\frac{23392 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{823543}","\frac{11264}{823543 (1-2 x)}-\frac{24040}{823543 (3 x+2)}+\frac{484}{117649 (1-2 x)^2}-\frac{2875}{117649 (3 x+2)^2}-\frac{829}{50421 (3 x+2)^3}+\frac{16}{2401 (3 x+2)^4}-\frac{1}{1715 (3 x+2)^5}-\frac{11696 \log (1-2 x)}{823543}+\frac{11696 \log (3 x+2)}{823543}",1,"(-258089 + 4230956*x + 19495039*x^2 + 14484765*x^3 - 36579240*x^4 - 63947880*x^5 - 28421280*x^6)/(1764735*(-1 + 2*x)^2*(2 + 3*x)^5) + (23392*ArcTanh[(3 + x)/(1 + 5*x)])/823543","A",1
1659,1,67,80,0.0378209,"\int \frac{(2+3 x)^6 (3+5 x)^3}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^6*(3 + 5*x)^3)/(1 - 2*x)^3,x]","\frac{-23328000 x^9-175348800 x^8-628425216 x^7-1466857728 x^6-2647685376 x^5-4449695040 x^4-9877535360 x^3+26671311588 x^2-11541996324 x+1001301969}{3584 (2 x-1)^2}-\frac{33674025}{32} \log (2 x-1)","-\frac{91125 x^7}{56}-\frac{443475 x^6}{32}-\frac{229149 x^5}{4}-\frac{19986237 x^4}{128}-\frac{41793093 x^3}{128}-\frac{306103815 x^2}{512}-\frac{308539921 x}{256}-\frac{616195041}{1024 (1-2 x)}+\frac{156590819}{2048 (1-2 x)^2}-\frac{33674025}{32} \log (1-2 x)",1,"(1001301969 - 11541996324*x + 26671311588*x^2 - 9877535360*x^3 - 4449695040*x^4 - 2647685376*x^5 - 1466857728*x^6 - 628425216*x^7 - 175348800*x^8 - 23328000*x^9)/(3584*(-1 + 2*x)^2) - (33674025*Log[-1 + 2*x])/32","A",1
1660,1,62,73,0.0344624,"\int \frac{(2+3 x)^5 (3+5 x)^3}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^5*(3 + 5*x)^3)/(1 - 2*x)^3,x]","\frac{-2592000 x^8-18040320 x^7-60592320 x^6-137206464 x^5-263583600 x^4-621559520 x^3+1569001020 x^2-600903660 x+30126129}{1024 (2 x-1)^2}-\frac{60160485}{256} \log (2 x-1)","-\frac{10125 x^6}{16}-\frac{80595 x^5}{16}-\frac{629505 x^4}{32}-\frac{1661133 x^3}{32}-\frac{28504029 x^2}{256}-\frac{64029233 x}{256}-\frac{39220335}{256 (1-2 x)}+\frac{22370117}{1024 (1-2 x)^2}-\frac{60160485}{256} \log (1-2 x)",1,"(30126129 - 600903660*x + 1569001020*x^2 - 621559520*x^3 - 263583600*x^4 - 137206464*x^5 - 60592320*x^6 - 18040320*x^7 - 2592000*x^8)/(1024*(-1 + 2*x)^2) - (60160485*Log[-1 + 2*x])/256","A",1
1661,1,57,64,0.0309886,"\int \frac{(2+3 x)^4 (3+5 x)^3}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x)^3,x]","\frac{-1036800 x^7-6696000 x^6-21464640 x^5-50369232 x^4-130737568 x^3+305448900 x^2-95444820 x-1974585}{1024 (2 x-1)^2}-\frac{12973191}{256} \log (2 x-1)","-\frac{2025 x^5}{8}-\frac{120825 x^4}{64}-7065 x^3-\frac{1208973 x^2}{64}-\frac{6277415 x}{128}-\frac{9836211}{256 (1-2 x)}+\frac{3195731}{512 (1-2 x)^2}-\frac{12973191}{256} \log (1-2 x)",1,"(-1974585 - 95444820*x + 305448900*x^2 - 130737568*x^3 - 50369232*x^4 - 21464640*x^5 - 6696000*x^6 - 1036800*x^7)/(1024*(-1 + 2*x)^2) - (12973191*Log[-1 + 2*x])/256","A",1
1662,1,52,59,0.0290982,"\int \frac{(2+3 x)^3 (3+5 x)^3}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^3)/(1 - 2*x)^3,x]","\frac{-216000 x^6-1310400 x^5-4235760 x^4-12853984 x^3+27475116 x^2-5590620 x-1244595}{512 (2 x-1)^2}-\frac{1334949}{128} \log (2 x-1)","-\frac{3375 x^4}{32}-\frac{11925 x^3}{16}-\frac{44595 x^2}{16}-\frac{284071 x}{32}-\frac{302379}{32 (1-2 x)}+\frac{456533}{256 (1-2 x)^2}-\frac{1334949}{128} \log (1-2 x)",1,"(-1244595 - 5590620*x + 27475116*x^2 - 12853984*x^3 - 4235760*x^4 - 1310400*x^5 - 216000*x^6)/(512*(-1 + 2*x)^2) - (1334949*Log[-1 + 2*x])/128","A",1
1663,1,47,52,0.0296416,"\int \frac{(2+3 x)^2 (3+5 x)^3}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^3)/(1 - 2*x)^3,x]","\frac{-3000 x^5-17850 x^4-71020 x^3+137055 x^2-1509 x-15270}{16 (2 x-1)^2}-\frac{64317}{32} \log (2 x-1)","-\frac{375 x^3}{8}-\frac{10425 x^2}{32}-\frac{5695 x}{4}-\frac{144837}{64 (1-2 x)}+\frac{65219}{128 (1-2 x)^2}-\frac{64317}{32} \log (1-2 x)",1,"(-15270 - 1509*x + 137055*x^2 - 71020*x^3 - 17850*x^4 - 3000*x^5)/(16*(-1 + 2*x)^2) - (64317*Log[-1 + 2*x])/32","A",1
1664,1,42,45,0.0224715,"\int \frac{(2+3 x) (3+5 x)^3}{(1-2 x)^3} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^3)/(1 - 2*x)^3,x]","\frac{-3000 x^4-20800 x^3+35700 x^2+14796 x-8877}{32 (2 x-1)^2}-\frac{2805}{8} \log (2 x-1)","-\frac{375 x^2}{16}-\frac{2975 x}{16}-\frac{8349}{16 (1-2 x)}+\frac{9317}{64 (1-2 x)^2}-\frac{2805}{8} \log (1-2 x)",1,"(-8877 + 14796*x + 35700*x^2 - 20800*x^3 - 3000*x^4)/(32*(-1 + 2*x)^2) - (2805*Log[-1 + 2*x])/8","A",1
1665,1,37,38,0.0282129,"\int \frac{(3+5 x)^3}{(1-2 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/(1 - 2*x)^3,x]","\frac{-2000 x^3+3000 x^2+5760 x-2049}{32 (2 x-1)^2}-\frac{825}{16} \log (2 x-1)","-\frac{125 x}{8}-\frac{1815}{16 (1-2 x)}+\frac{1331}{32 (1-2 x)^2}-\frac{825}{16} \log (1-2 x)",1,"(-2049 + 5760*x + 3000*x^2 - 2000*x^3)/(32*(-1 + 2*x)^2) - (825*Log[-1 + 2*x])/16","A",1
1666,1,37,43,0.0330833,"\int \frac{(3+5 x)^3}{(1-2 x)^3 (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^3*(2 + 3*x)),x]","\frac{121 (288 x-67)}{784 (2 x-1)^2}-\frac{14289 \log (2 x-1)}{2744}-\frac{\log (3 x+2)}{1029}","-\frac{1089}{49 (1-2 x)}+\frac{1331}{112 (1-2 x)^2}-\frac{14289 \log (1-2 x)}{2744}-\frac{\log (3 x+2)}{1029}",1,"(121*(-67 + 288*x))/(784*(-1 + 2*x)^2) - (14289*Log[-1 + 2*x])/2744 - Log[2 + 3*x]/1029","A",1
1667,1,45,54,0.0537777,"\int \frac{(3+5 x)^3}{(1-2 x)^3 (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^3*(2 + 3*x)^2),x]","\frac{169916 x^2+112135 x-718}{8232 (2 x-1)^2 (3 x+2)}+\frac{66 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{2401}","-\frac{4719}{1372 (1-2 x)}+\frac{1}{1029 (3 x+2)}+\frac{1331}{392 (1-2 x)^2}-\frac{33 \log (1-2 x)}{2401}+\frac{33 \log (3 x+2)}{2401}",1,"(-718 + 112135*x + 169916*x^2)/(8232*(-1 + 2*x)^2*(2 + 3*x)) + (66*ArcTanh[(3 + x)/(1 + 5*x)])/2401","A",1
1668,1,46,65,0.0445205,"\int \frac{(3+5 x)^3}{(1-2 x)^3 (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^3*(2 + 3*x)^3),x]","\frac{73656 x^3+318539 x^2+319912 x+93602}{28812 \left(6 x^2+x-2\right)^2}-\frac{2046 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{16807}","-\frac{363}{2401 (1-2 x)}-\frac{33}{2401 (3 x+2)}+\frac{1331}{1372 (1-2 x)^2}+\frac{1}{2058 (3 x+2)^2}+\frac{1023 \log (1-2 x)}{16807}-\frac{1023 \log (3 x+2)}{16807}",1,"(93602 + 319912*x + 318539*x^2 + 73656*x^3)/(28812*(-2 + x + 6*x^2)^2) - (2046*ArcTanh[(3 + x)/(1 + 5*x)])/16807","A",1
1669,1,55,76,0.0799612,"\int \frac{(3+5 x)^3}{(1-2 x)^3 (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^3*(2 + 3*x)^4),x]","\frac{-2512620 x^4-2303235 x^3+3054740 x^2+4131175 x+1210868}{302526 (2 x-1)^2 (3 x+2)^3}+\frac{15510 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{117649}","\frac{3267}{16807 (1-2 x)}+\frac{1023}{16807 (3 x+2)}+\frac{1331}{4802 (1-2 x)^2}-\frac{33}{4802 (3 x+2)^2}+\frac{1}{3087 (3 x+2)^3}-\frac{7755 \log (1-2 x)}{117649}+\frac{7755 \log (3 x+2)}{117649}",1,"(1210868 + 4131175*x + 3054740*x^2 - 2303235*x^3 - 2512620*x^4)/(302526*(-1 + 2*x)^2*(2 + 3*x)^3) + (15510*ArcTanh[(3 + x)/(1 + 5*x)])/117649","A",1
1670,1,60,87,0.0810772,"\int \frac{(3+5 x)^3}{(1-2 x)^3 (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^3*(2 + 3*x)^5),x]","\frac{-38277360 x^5-60605820 x^4-8860500 x^3+32767930 x^2+21371408 x+3991495}{1411788 (2 x-1)^2 (3 x+2)^4}+\frac{118140 \tanh ^{-1}\left(\frac{x+3}{5 x+1}\right)}{823543}","\frac{14520}{117649 (1-2 x)}-\frac{7755}{117649 (3 x+2)}+\frac{1331}{16807 (1-2 x)^2}+\frac{1023}{33614 (3 x+2)^2}-\frac{11}{2401 (3 x+2)^3}+\frac{1}{4116 (3 x+2)^4}-\frac{59070 \log (1-2 x)}{823543}+\frac{59070 \log (3 x+2)}{823543}",1,"(3991495 + 21371408*x + 32767930*x^2 - 8860500*x^3 - 60605820*x^4 - 38277360*x^5)/(1411788*(-1 + 2*x)^2*(2 + 3*x)^4) + (118140*ArcTanh[(3 + x)/(1 + 5*x)])/823543","A",1
1671,1,67,76,0.0557757,"\int \frac{(2+3 x)^8}{(1-2 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^8/((1 - 2*x)^3*(3 + 5*x)),x]","\frac{-25404192000 x^7-172536804000 x^6-579192055200 x^5-1411803862920 x^4-3754570373136 x^3+4566498586056 x^2+1528849714256 x-1129331321655}{193600000 (2 x-1)^2}-\frac{2644396573 \log (2 x-1)}{340736}+\frac{\log (5 x+3)}{20796875}","-\frac{6561 x^5}{200}-\frac{408969 x^4}{1600}-\frac{124416 x^3}{125}-\frac{110180817 x^2}{40000}-\frac{2941619571 x}{400000}-\frac{188591347}{30976 (1-2 x)}+\frac{5764801}{5632 (1-2 x)^2}-\frac{2644396573 \log (1-2 x)}{340736}+\frac{\log (5 x+3)}{20796875}",1,"(-1129331321655 + 1528849714256*x + 4566498586056*x^2 - 3754570373136*x^3 - 1411803862920*x^4 - 579192055200*x^5 - 172536804000*x^6 - 25404192000*x^7)/(193600000*(-1 + 2*x)^2) - (2644396573*Log[-1 + 2*x])/340736 + Log[3 + 5*x]/20796875","A",1
1672,1,62,69,0.0497022,"\int \frac{(2+3 x)^7}{(1-2 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^7/((1 - 2*x)^3*(3 + 5*x)),x]","\frac{-1058508000 x^6-6797973600 x^5-23090763960 x^4-72578051568 x^3+42333890544 x^2+83615877112 x-35985148011}{19360000 (2 x-1)^2}-\frac{269063263 \log (2 x-1)}{170368}+\frac{\log (5 x+3)}{4159375}","-\frac{2187 x^4}{160}-\frac{40581 x^3}{400}-\frac{792423 x^2}{2000}-\frac{26161299 x}{20000}-\frac{5764801}{3872 (1-2 x)}+\frac{823543}{2816 (1-2 x)^2}-\frac{269063263 \log (1-2 x)}{170368}+\frac{\log (5 x+3)}{4159375}",1,"(-35985148011 + 83615877112*x + 42333890544*x^2 - 72578051568*x^3 - 23090763960*x^4 - 6797973600*x^5 - 1058508000*x^6)/(19360000*(-1 + 2*x)^2) - (269063263*Log[-1 + 2*x])/170368 + Log[3 + 5*x]/4159375","A",1
1673,1,57,62,0.0406656,"\int \frac{(2+3 x)^6}{(1-2 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)^3*(3 + 5*x)),x]","\frac{-235224000 x^5-1493672400 x^4-6252253920 x^3+3308307948 x^2+9050078692 x-3661042443}{9680000 (2 x-1)^2}-\frac{12761315 \log (2 x-1)}{42592}+\frac{\log (5 x+3)}{831875}","-\frac{243 x^3}{40}-\frac{35721 x^2}{800}-\frac{102303 x}{500}-\frac{2739541}{7744 (1-2 x)}+\frac{117649}{1408 (1-2 x)^2}-\frac{12761315 \log (1-2 x)}{42592}+\frac{\log (5 x+3)}{831875}",1,"(-3661042443 + 9050078692*x + 3308307948*x^2 - 6252253920*x^3 - 1493672400*x^4 - 235224000*x^5)/(9680000*(-1 + 2*x)^2) - (12761315*Log[-1 + 2*x])/42592 + Log[3 + 5*x]/831875","A",1
1674,1,52,55,0.0439134,"\int \frac{(2+3 x)^5}{(1-2 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^3*(3 + 5*x)),x]","\frac{-11761200 x^4-87816960 x^3+41124996 x^2+186683324 x-68801091}{968000 (2 x-1)^2}-\frac{543655 \log (2 x-1)}{10648}+\frac{\log (5 x+3)}{166375}","-\frac{243 x^2}{80}-\frac{10287 x}{400}-\frac{156065}{1936 (1-2 x)}+\frac{16807}{704 (1-2 x)^2}-\frac{543655 \log (1-2 x)}{10648}+\frac{\log (5 x+3)}{166375}",1,"(-68801091 + 186683324*x + 41124996*x^2 - 87816960*x^3 - 11761200*x^4)/(968000*(-1 + 2*x)^2) - (543655*Log[-1 + 2*x])/10648 + Log[3 + 5*x]/166375","A",1
1675,1,47,48,0.0410945,"\int \frac{(2+3 x)^4}{(1-2 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^3*(3 + 5*x)),x]","\frac{-784080 x^3+313632 x^2+3601528 x-1120887}{96800 (2 x-1)^2}-\frac{153811 \log (2 x-1)}{21296}+\frac{\log (5 x+3)}{33275}","-\frac{81 x}{40}-\frac{33271}{1936 (1-2 x)}+\frac{2401}{352 (1-2 x)^2}-\frac{153811 \log (1-2 x)}{21296}+\frac{\log (5 x+3)}{33275}",1,"(-1120887 + 3601528*x + 313632*x^2 - 784080*x^3)/(96800*(-1 + 2*x)^2) - (153811*Log[-1 + 2*x])/21296 + Log[3 + 5*x]/33275","A",1
1676,1,37,43,0.0313931,"\int \frac{(2+3 x)^3}{(1-2 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^3*(3 + 5*x)),x]","\frac{49 (256 x-51)}{1936 (2 x-1)^2}-\frac{7189 \log (2 x-1)}{10648}+\frac{\log (5 x+3)}{6655}","-\frac{392}{121 (1-2 x)}+\frac{343}{176 (1-2 x)^2}-\frac{7189 \log (1-2 x)}{10648}+\frac{\log (5 x+3)}{6655}",1,"(49*(-51 + 256*x))/(1936*(-1 + 2*x)^2) - (7189*Log[-1 + 2*x])/10648 + Log[3 + 5*x]/6655","A",1
1677,1,37,43,0.032034,"\int \frac{(2+3 x)^2}{(1-2 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^3*(3 + 5*x)),x]","\frac{7 (124 x+15)}{968 (2 x-1)^2}-\frac{\log (2 x-1)}{1331}+\frac{\log (5 x+3)}{1331}","-\frac{217}{484 (1-2 x)}+\frac{49}{88 (1-2 x)^2}-\frac{\log (1-2 x)}{1331}+\frac{\log (5 x+3)}{1331}",1,"(7*(15 + 124*x))/(968*(-1 + 2*x)^2) - Log[-1 + 2*x]/1331 + Log[3 + 5*x]/1331","A",1
1678,1,37,43,0.0263523,"\int \frac{2+3 x}{(1-2 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^3*(3 + 5*x)),x]","\frac{81-8 x}{484 (2 x-1)^2}-\frac{5 \log (2 x-1)}{1331}+\frac{5 \log (5 x+3)}{1331}","\frac{1}{121 (1-2 x)}+\frac{7}{44 (1-2 x)^2}-\frac{5 \log (1-2 x)}{1331}+\frac{5 \log (5 x+3)}{1331}",1,"(81 - 8*x)/(484*(-1 + 2*x)^2) - (5*Log[-1 + 2*x])/1331 + (5*Log[3 + 5*x])/1331","A",1
1679,1,37,43,0.0227175,"\int \frac{1}{(1-2 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^3*(3 + 5*x)),x]","\frac{21-20 x}{242 (2 x-1)^2}-\frac{25 \log (2 x-1)}{1331}+\frac{25 \log (5 x+3)}{1331}","\frac{5}{121 (1-2 x)}+\frac{1}{22 (1-2 x)^2}-\frac{25 \log (1-2 x)}{1331}+\frac{25 \log (5 x+3)}{1331}",1,"(21 - 20*x)/(242*(-1 + 2*x)^2) - (25*Log[-1 + 2*x])/1331 + (25*Log[3 + 5*x])/1331","A",1
1680,1,47,53,0.0391806,"\int \frac{1}{(1-2 x)^3 (2+3 x) (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^3*(2 + 3*x)*(3 + 5*x)),x]","\frac{213-272 x}{5929 (2 x-1)^2}-\frac{6938 \log (2 x-1)}{456533}-\frac{27}{343} \log (3 x+2)+\frac{125 \log (5 x+3)}{1331}","\frac{136}{5929 (1-2 x)}+\frac{1}{77 (1-2 x)^2}-\frac{6938 \log (1-2 x)}{456533}-\frac{27}{343} \log (3 x+2)+\frac{125 \log (5 x+3)}{1331}",1,"(213 - 272*x)/(5929*(-1 + 2*x)^2) - (6938*Log[-1 + 2*x])/456533 - (27*Log[2 + 3*x])/343 + (125*Log[3 + 5*x])/1331","A",1
1681,1,59,64,0.0736016,"\int \frac{1}{(1-2 x)^3 (2+3 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)),x]","\frac{10644 x^2-13010 x+4383}{41503 (2 x-1)^2 (3 x+2)}-\frac{27208 \log (2 x-1)}{3195731}-\frac{1107 \log (3 x+2)}{2401}+\frac{625 \log (5 x+3)}{1331}","\frac{404}{41503 (1-2 x)}+\frac{27}{343 (3 x+2)}+\frac{2}{539 (1-2 x)^2}-\frac{27208 \log (1-2 x)}{3195731}-\frac{1107 \log (3 x+2)}{2401}+\frac{625 \log (5 x+3)}{1331}",1,"(4383 - 13010*x + 10644*x^2)/(41503*(-1 + 2*x)^2*(2 + 3*x)) - (27208*Log[-1 + 2*x])/3195731 - (1107*Log[2 + 3*x])/2401 + (625*Log[3 + 5*x])/1331","A",1
1682,1,60,75,0.0748804,"\int \frac{1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)),x]","\frac{3176136 x^3-1006716 x^2-1414978 x+569697}{581042 \left(6 x^2+x-2\right)^2}-\frac{89792 \log (2 x-1)}{22370117}-\frac{39393 \log (3 x+2)}{16807}+\frac{3125 \log (5 x+3)}{1331}","\frac{1072}{290521 (1-2 x)}+\frac{1107}{2401 (3 x+2)}+\frac{4}{3773 (1-2 x)^2}+\frac{27}{686 (3 x+2)^2}-\frac{89792 \log (1-2 x)}{22370117}-\frac{39393 \log (3 x+2)}{16807}+\frac{3125 \log (5 x+3)}{1331}",1,"(569697 - 1414978*x - 1006716*x^2 + 3176136*x^3)/(581042*(-2 + x + 6*x^2)^2) - (89792*Log[-1 + 2*x])/22370117 - (39393*Log[2 + 3*x])/16807 + (3125*Log[3 + 5*x])/1331","A",1
1683,1,69,86,0.1068096,"\int \frac{1}{(1-2 x)^3 (2+3 x)^4 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)),x]","\frac{342903240 x^4+125249220 x^3-222614730 x^2-43096225 x+40167012}{4067294 (2 x-1)^2 (3 x+2)^3}-\frac{267760 \log (2 x-1)}{156590819}-\frac{1380915 \log (3 x+2)}{117649}+\frac{15625 \log (5 x+3)}{1331}","\frac{2672}{2033647 (1-2 x)}+\frac{39393}{16807 (3 x+2)}+\frac{8}{26411 (1-2 x)^2}+\frac{1107}{4802 (3 x+2)^2}+\frac{9}{343 (3 x+2)^3}-\frac{267760 \log (1-2 x)}{156590819}-\frac{1380915 \log (3 x+2)}{117649}+\frac{15625 \log (5 x+3)}{1331}",1,"(40167012 - 43096225*x - 222614730*x^2 + 125249220*x^3 + 342903240*x^4)/(4067294*(-1 + 2*x)^2*(2 + 3*x)^3) - (267760*Log[-1 + 2*x])/156590819 - (1380915*Log[2 + 3*x])/117649 + (15625*Log[3 + 5*x])/1331","A",1
1684,1,74,80,0.0650835,"\int \frac{(2+3 x)^8}{(1-2 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^8/((1 - 2*x)^3*(3 + 5*x)^2),x]","\frac{-873269100000 x^7-6209913600000 x^6-22962125835000 x^5-73729463247000 x^4+34440579007560 x^3+79486494609816 x^2-142510638861 x-13226392063531}{5324000000 (2 x-1)^2 (5 x+3)}-\frac{1845559863 \log (2 x-1)}{1874048}+\frac{54 \log (5 x+3)}{45753125}","-\frac{6561 x^4}{800}-\frac{123201 x^3}{2000}-\frac{4863159 x^2}{20000}-\frac{81001863 x}{100000}-\frac{79883671}{85184 (1-2 x)}-\frac{1}{20796875 (5 x+3)}+\frac{5764801}{30976 (1-2 x)^2}-\frac{1845559863 \log (1-2 x)}{1874048}+\frac{54 \log (5 x+3)}{45753125}",1,"(-13226392063531 - 142510638861*x + 79486494609816*x^2 + 34440579007560*x^3 - 73729463247000*x^4 - 22962125835000*x^5 - 6209913600000*x^6 - 873269100000*x^7)/(5324000000*(-1 + 2*x)^2*(3 + 5*x)) - (1845559863*Log[-1 + 2*x])/1874048 + (54*Log[3 + 5*x])/45753125","A",1
1685,1,69,73,0.0603316,"\int \frac{(2+3 x)^7}{(1-2 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^7/((1 - 2*x)^3*(3 + 5*x)^2),x]","\frac{-4851495000 x^6-34203039750 x^5-151415158950 x^4+172378468845 x^3+163837494156 x^2-25343933346 x-19763981131}{66550000 (2 x-1)^2 (5 x+3)}-\frac{87177909 \log (2 x-1)}{468512}+\frac{237 \log (5 x+3)}{45753125}","-\frac{729 x^3}{200}-\frac{108621 x^2}{4000}-\frac{1258983 x}{10000}-\frac{18941489}{85184 (1-2 x)}-\frac{1}{4159375 (5 x+3)}+\frac{823543}{15488 (1-2 x)^2}-\frac{87177909 \log (1-2 x)}{468512}+\frac{237 \log (5 x+3)}{45753125}",1,"(-19763981131 - 25343933346*x + 163837494156*x^2 + 172378468845*x^3 - 151415158950*x^4 - 34203039750*x^5 - 4851495000*x^6)/(66550000*(-1 + 2*x)^2*(3 + 5*x)) - (87177909*Log[-1 + 2*x])/468512 + (237*Log[3 + 5*x])/45753125","A",1
1686,1,64,66,0.0528279,"\int \frac{(2+3 x)^6}{(1-2 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)^3*(3 + 5*x)^2),x]","\frac{-242574750 x^5-1989112950 x^4+858714615 x^3+4079421228 x^2+549966942 x-714202733}{6655000 (2 x-1)^2 (5 x+3)}-\frac{7383075 \log (2 x-1)}{234256}+\frac{204 \log (5 x+3)}{9150625}","-\frac{729 x^2}{400}-\frac{31347 x}{2000}-\frac{67228}{1331 (1-2 x)}-\frac{1}{831875 (5 x+3)}+\frac{117649}{7744 (1-2 x)^2}-\frac{7383075 \log (1-2 x)}{234256}+\frac{204 \log (5 x+3)}{9150625}",1,"(-714202733 + 549966942*x + 4079421228*x^2 + 858714615*x^3 - 1989112950*x^4 - 242574750*x^5)/(6655000*(-1 + 2*x)^2*(3 + 5*x)) - (7383075*Log[-1 + 2*x])/234256 + (204*Log[3 + 5*x])/9150625","A",1
1687,1,59,59,0.0480957,"\int \frac{(2+3 x)^5}{(1-2 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^3*(3 + 5*x)^2),x]","\frac{-129373200 x^4+116435880 x^3+589643352 x^2+130525713 x-92039417}{5324000 (2 x-1)^2 (5 x+3)}-\frac{1034145 \log (2 x-1)}{234256}+\frac{171 \log (5 x+3)}{1830125}","-\frac{243 x}{200}-\frac{228095}{21296 (1-2 x)}-\frac{1}{166375 (5 x+3)}+\frac{16807}{3872 (1-2 x)^2}-\frac{1034145 \log (1-2 x)}{234256}+\frac{171 \log (5 x+3)}{1830125}",1,"(-92039417 + 130525713*x + 589643352*x^2 + 116435880*x^3 - 129373200*x^4)/(5324000*(-1 + 2*x)^2*(3 + 5*x)) - (1034145*Log[-1 + 2*x])/234256 + (171*Log[3 + 5*x])/1830125","A",1
1688,1,49,54,0.0431429,"\int \frac{(2+3 x)^4}{(1-2 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^3*(3 + 5*x)^2),x]","\frac{10632936 x^2+4364739 x-1209091}{532400 (2 x-1)^2 (5 x+3)}-\frac{47481 \log (2 x-1)}{117128}+\frac{138 \log (5 x+3)}{366025}","-\frac{10633}{5324 (1-2 x)}-\frac{1}{33275 (5 x+3)}+\frac{2401}{1936 (1-2 x)^2}-\frac{47481 \log (1-2 x)}{117128}+\frac{138 \log (5 x+3)}{366025}",1,"(-1209091 + 4364739*x + 10632936*x^2)/(532400*(-1 + 2*x)^2*(3 + 5*x)) - (47481*Log[-1 + 2*x])/117128 + (138*Log[3 + 5*x])/366025","A",1
1689,1,49,54,0.0521807,"\int \frac{(2+3 x)^3}{(1-2 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^3*(3 + 5*x)^2),x]","\frac{142068 x^2+108567 x+13957}{53240 (2 x-1)^2 (5 x+3)}-\frac{21 \log (2 x-1)}{14641}+\frac{21 \log (5 x+3)}{14641}","-\frac{1421}{5324 (1-2 x)}-\frac{1}{6655 (5 x+3)}+\frac{343}{968 (1-2 x)^2}-\frac{21 \log (1-2 x)}{14641}+\frac{21 \log (5 x+3)}{14641}",1,"(13957 + 108567*x + 142068*x^2)/(53240*(-1 + 2*x)^2*(3 + 5*x)) - (21*Log[-1 + 2*x])/14641 + (21*Log[3 + 5*x])/14641","A",1
1690,1,49,54,0.047993,"\int \frac{(2+3 x)^2}{(1-2 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^3*(3 + 5*x)^2),x]","\frac{-576 x^2+2655 x+1781}{5324 (2 x-1)^2 (5 x+3)}-\frac{72 \log (2 x-1)}{14641}+\frac{72 \log (5 x+3)}{14641}","\frac{14}{1331 (1-2 x)}-\frac{1}{1331 (5 x+3)}+\frac{49}{484 (1-2 x)^2}-\frac{72 \log (1-2 x)}{14641}+\frac{72 \log (5 x+3)}{14641}",1,"(1781 + 2655*x - 576*x^2)/(5324*(-1 + 2*x)^2*(3 + 5*x)) - (72*Log[-1 + 2*x])/14641 + (72*Log[3 + 5*x])/14641","A",1
1691,1,49,54,0.0323039,"\int \frac{2+3 x}{(1-2 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^3*(3 + 5*x)^2),x]","\frac{-780 x^2+351 x+443}{2662 (2 x-1)^2 (5 x+3)}-\frac{195 \log (2 x-1)}{14641}+\frac{195 \log (5 x+3)}{14641}","\frac{37}{1331 (1-2 x)}-\frac{5}{1331 (5 x+3)}+\frac{7}{242 (1-2 x)^2}-\frac{195 \log (1-2 x)}{14641}+\frac{195 \log (5 x+3)}{14641}",1,"(443 + 351*x - 780*x^2)/(2662*(-1 + 2*x)^2*(3 + 5*x)) - (195*Log[-1 + 2*x])/14641 + (195*Log[3 + 5*x])/14641","A",1
1692,1,49,54,0.0305625,"\int \frac{1}{(1-2 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^3*(3 + 5*x)^2),x]","\frac{-300 x^2+135 x+68}{1331 (2 x-1)^2 (5 x+3)}-\frac{150 \log (2 x-1)}{14641}+\frac{150 \log (5 x+3)}{14641}","\frac{20}{1331 (1-2 x)}-\frac{25}{1331 (5 x+3)}+\frac{1}{121 (1-2 x)^2}-\frac{150 \log (1-2 x)}{14641}+\frac{150 \log (5 x+3)}{14641}",1,"(68 + 135*x - 300*x^2)/(1331*(-1 + 2*x)^2*(3 + 5*x)) - (150*Log[-1 + 2*x])/14641 + (150*Log[3 + 5*x])/14641","A",1
1693,1,59,64,0.0458568,"\int \frac{1}{(1-2 x)^3 (2+3 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^3*(2 + 3*x)*(3 + 5*x)^2),x]","\frac{-28620 x^2+24858 x-4427}{65219 (2 x-1)^2 (5 x+3)}-\frac{28296 \log (2 x-1)}{5021863}+\frac{81}{343} \log (3 x+2)-\frac{3375 \log (5 x+3)}{14641}","\frac{412}{65219 (1-2 x)}-\frac{125}{1331 (5 x+3)}+\frac{2}{847 (1-2 x)^2}-\frac{28296 \log (1-2 x)}{5021863}+\frac{81}{343} \log (3 x+2)-\frac{3375 \log (5 x+3)}{14641}",1,"(-4427 + 24858*x - 28620*x^2)/(65219*(-1 + 2*x)^2*(3 + 5*x)) - (28296*Log[-1 + 2*x])/5021863 + (81*Log[2 + 3*x])/343 - (3375*Log[3 + 5*x])/14641","A",1
1694,1,71,75,0.0869505,"\int \frac{1}{(1-2 x)^3 (2+3 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{-4761360 x^3+1699584 x^2+1840020 x-743807}{456533 (2 x-1)^2 (3 x+2) (5 x+3)}-\frac{92496 \log (2 x-1)}{35153041}+\frac{6156 \log (3 x+2)}{2401}-\frac{37500 \log (5 x+3)}{14641}","\frac{1088}{456533 (1-2 x)}-\frac{81}{343 (3 x+2)}-\frac{625}{1331 (5 x+3)}+\frac{4}{5929 (1-2 x)^2}-\frac{92496 \log (1-2 x)}{35153041}+\frac{6156 \log (3 x+2)}{2401}-\frac{37500 \log (5 x+3)}{14641}",1,"(-743807 + 1840020*x + 1699584*x^2 - 4761360*x^3)/(456533*(-1 + 2*x)^2*(2 + 3*x)*(3 + 5*x)) - (92496*Log[-1 + 2*x])/35153041 + (6156*Log[2 + 3*x])/2401 - (37500*Log[3 + 5*x])/14641","A",1
1695,1,72,86,0.0791213,"\int \frac{1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^2),x]","\frac{-1523948040 x^4-458007084 x^3+957482214 x^2+147486147 x-160532983}{6391462 (5 x+3) \left(6 x^2+x-2\right)^2}-\frac{274224 \log (2 x-1)}{246071287}+\frac{333639 \log (3 x+2)}{16807}-\frac{290625 \log (5 x+3)}{14641}","\frac{2704}{3195731 (1-2 x)}-\frac{6156}{2401 (3 x+2)}-\frac{3125}{1331 (5 x+3)}+\frac{8}{41503 (1-2 x)^2}-\frac{81}{686 (3 x+2)^2}-\frac{274224 \log (1-2 x)}{246071287}+\frac{333639 \log (3 x+2)}{16807}-\frac{290625 \log (5 x+3)}{14641}",1,"(-160532983 + 147486147*x + 957482214*x^2 - 458007084*x^3 - 1523948040*x^4)/(6391462*(3 + 5*x)*(-2 + x + 6*x^2)^2) - (274224*Log[-1 + 2*x])/246071287 + (333639*Log[2 + 3*x])/16807 - (290625*Log[3 + 5*x])/14641","A",1
1696,1,81,97,0.162098,"\int \frac{1}{(1-2 x)^3 (2+3 x)^4 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^2),x]","\frac{-108296789400 x^5-104690324340 x^4+46403447130 x^3+55829767905 x^2-4446481815 x-7606921499}{22370117 (2 x-1)^2 (3 x+2)^3 (5 x+3)}-\frac{761760 \log (2 x-1)}{1722499009}+\frac{15820110 \log (3 x+2)}{117649}-\frac{1968750 \log (5 x+3)}{14641}","\frac{6464}{22370117 (1-2 x)}-\frac{333639}{16807 (3 x+2)}-\frac{15625}{1331 (5 x+3)}+\frac{16}{290521 (1-2 x)^2}-\frac{3078}{2401 (3 x+2)^2}-\frac{27}{343 (3 x+2)^3}-\frac{761760 \log (1-2 x)}{1722499009}+\frac{15820110 \log (3 x+2)}{117649}-\frac{1968750 \log (5 x+3)}{14641}",1,"(-7606921499 - 4446481815*x + 55829767905*x^2 + 46403447130*x^3 - 104690324340*x^4 - 108296789400*x^5)/(22370117*(-1 + 2*x)^2*(2 + 3*x)^3*(3 + 5*x)) - (761760*Log[-1 + 2*x])/1722499009 + (15820110*Log[2 + 3*x])/117649 - (1968750*Log[3 + 5*x])/14641","A",1
1697,1,75,91,0.0612379,"\int \frac{(2+3 x)^9}{(1-2 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^9/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{-144089401500000 x^8-1123897331700000 x^7-4502793796875000 x^6-14903967293820000 x^5-8450955823285800 x^4+15846035365304040 x^3+12213049363361937 x^2-1867950230356442 x-1977372328510687}{292820000000 \left(10 x^2+x-3\right)^2}-\frac{12657032367 \log (2 x-1)}{20614528}+\frac{8202 \log (5 x+3)}{2516421875}","-\frac{19683 x^4}{4000}-\frac{373977 x^3}{10000}-\frac{7459857 x^2}{50000}-\frac{50150097 x}{100000}-\frac{17294403}{29282 (1-2 x)}-\frac{303}{1143828125 (5 x+3)}+\frac{40353607}{340736 (1-2 x)^2}-\frac{1}{207968750 (5 x+3)^2}-\frac{12657032367 \log (1-2 x)}{20614528}+\frac{8202 \log (5 x+3)}{2516421875}",1,"(-1977372328510687 - 1867950230356442*x + 12213049363361937*x^2 + 15846035365304040*x^3 - 8450955823285800*x^4 - 14903967293820000*x^5 - 4502793796875000*x^6 - 1123897331700000*x^7 - 144089401500000*x^8)/(292820000000*(-3 + x + 10*x^2)^2) - (12657032367*Log[-1 + 2*x])/20614528 + (8202*Log[3 + 5*x])/2516421875","A",1
1698,1,70,84,0.0517739,"\int \frac{(2+3 x)^8}{(1-2 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^8/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{-6403973400000 x^7-49630793850000 x^6-232677700200000 x^5-148045752548100 x^4+314407515766380 x^3+254889143270829 x^2-31893783102814 x-39754322426279}{29282000000 \left(10 x^2+x-3\right)^2}-\frac{595421589 \log (2 x-1)}{5153632}+\frac{1284 \log (5 x+3)}{100656875}","-\frac{2187 x^3}{1000}-\frac{330237 x^2}{20000}-\frac{242028 x}{3125}-\frac{130943337}{937024 (1-2 x)}-\frac{54}{45753125 (5 x+3)}+\frac{5764801}{170368 (1-2 x)^2}-\frac{1}{41593750 (5 x+3)^2}-\frac{595421589 \log (1-2 x)}{5153632}+\frac{1284 \log (5 x+3)}{100656875}",1,"(-39754322426279 - 31893783102814*x + 254889143270829*x^2 + 314407515766380*x^3 - 148045752548100*x^4 - 232677700200000*x^5 - 49630793850000*x^6 - 6403973400000*x^7)/(29282000000*(-3 + x + 10*x^2)^2) - (595421589*Log[-1 + 2*x])/5153632 + (1284*Log[3 + 5*x])/100656875","A",1
1699,1,65,77,0.0479775,"\int \frac{(2+3 x)^7}{(1-2 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^7/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{-320198670000 x^6-2860441452000 x^5-2092320420300 x^4+5957126547060 x^3+5105353973121 x^2-410862940766 x-734029874011}{2928200000 \left(10 x^2+x-3\right)^2}-\frac{25059237 \log (2 x-1)}{1288408}+\frac{24279 \log (5 x+3)}{503284375}","-\frac{2187 x^2}{2000}-\frac{95499 x}{10000}-\frac{7411887}{234256 (1-2 x)}-\frac{237}{45753125 (5 x+3)}+\frac{823543}{85184 (1-2 x)^2}-\frac{1}{8318750 (5 x+3)^2}-\frac{25059237 \log (1-2 x)}{1288408}+\frac{24279 \log (5 x+3)}{503284375}",1,"(-734029874011 - 410862940766*x + 5105353973121*x^2 + 5957126547060*x^3 - 2092320420300*x^4 - 2860441452000*x^5 - 320198670000*x^6)/(2928200000*(-3 + x + 10*x^2)^2) - (25059237*Log[-1 + 2*x])/1288408 + (24279*Log[3 + 5*x])/503284375","A",1
1700,1,60,70,0.0477194,"\int \frac{(2+3 x)^6}{(1-2 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{-4269315600 x^5-3700073520 x^4+21487765512 x^3+19656314001 x^2-49588250 x-2317121263}{58564000 \left(10 x^2+x-3\right)^2}-\frac{6950895 \log (2 x-1)}{2576816}+\frac{17547 \log (5 x+3)}{100656875}","-\frac{729 x}{1000}-\frac{1563051}{234256 (1-2 x)}-\frac{204}{9150625 (5 x+3)}+\frac{117649}{42592 (1-2 x)^2}-\frac{1}{1663750 (5 x+3)^2}-\frac{6950895 \log (1-2 x)}{2576816}+\frac{17547 \log (5 x+3)}{100656875}",1,"(-2317121263 - 49588250*x + 19656314001*x^2 + 21487765512*x^3 - 3700073520*x^4 - 4269315600*x^5)/(58564000*(-3 + x + 10*x^2)^2) - (6950895*Log[-1 + 2*x])/2576816 + (17547*Log[3 + 5*x])/100656875","A",1
1701,1,50,65,0.0429799,"\int \frac{(2+3 x)^5}{(1-2 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{1800695280 x^3+1838287161 x^2+261128254 x-116156671}{29282000 \left(10 x^2+x-3\right)^2}-\frac{313845 \log (2 x-1)}{1288408}+\frac{11904 \log (5 x+3)}{20131375}","-\frac{36015}{29282 (1-2 x)}-\frac{171}{1830125 (5 x+3)}+\frac{16807}{21296 (1-2 x)^2}-\frac{1}{332750 (5 x+3)^2}-\frac{313845 \log (1-2 x)}{1288408}+\frac{11904 \log (5 x+3)}{20131375}",1,"(-116156671 + 261128254*x + 1838287161*x^2 + 1800695280*x^3)/(29282000*(-3 + x + 10*x^2)^2) - (313845*Log[-1 + 2*x])/1288408 + (11904*Log[3 + 5*x])/20131375","A",1
1702,1,50,65,0.0403361,"\int \frac{(2+3 x)^4}{(1-2 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{23130420 x^3+32722281 x^2+14259554 x+1771669}{2928200 \left(10 x^2+x-3\right)^2}-\frac{294 \log (2 x-1)}{161051}+\frac{294 \log (5 x+3)}{161051}","-\frac{9261}{58564 (1-2 x)}-\frac{138}{366025 (5 x+3)}+\frac{2401}{10648 (1-2 x)^2}-\frac{1}{66550 (5 x+3)^2}-\frac{294 \log (1-2 x)}{161051}+\frac{294 \log (5 x+3)}{161051}",1,"(1771669 + 14259554*x + 32722281*x^2 + 23130420*x^3)/(2928200*(-3 + x + 10*x^2)^2) - (294*Log[-1 + 2*x])/161051 + (294*Log[3 + 5*x])/161051","A",1
1703,1,50,65,0.0402517,"\int \frac{(2+3 x)^3}{(1-2 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{-155400 x^3+371997 x^2+604258 x+194963}{292820 \left(10 x^2+x-3\right)^2}-\frac{777 \log (2 x-1)}{161051}+\frac{777 \log (5 x+3)}{161051}","\frac{147}{14641 (1-2 x)}-\frac{21}{14641 (5 x+3)}+\frac{343}{5324 (1-2 x)^2}-\frac{1}{13310 (5 x+3)^2}-\frac{777 \log (1-2 x)}{161051}+\frac{777 \log (5 x+3)}{161051}",1,"(194963 + 604258*x + 371997*x^2 - 155400*x^3)/(292820*(-3 + x + 10*x^2)^2) - (777*Log[-1 + 2*x])/161051 + (777*Log[3 + 5*x])/161051","A",1
1704,1,50,65,0.0414461,"\int \frac{(2+3 x)^2}{(1-2 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{-30180 x^3-4527 x^2+23774 x+9322}{29282 \left(10 x^2+x-3\right)^2}-\frac{1509 \log (2 x-1)}{161051}+\frac{1509 \log (5 x+3)}{161051}","\frac{273}{14641 (1-2 x)}-\frac{72}{14641 (5 x+3)}+\frac{49}{2662 (1-2 x)^2}-\frac{1}{2662 (5 x+3)^2}-\frac{1509 \log (1-2 x)}{161051}+\frac{1509 \log (5 x+3)}{161051}",1,"(9322 + 23774*x - 4527*x^2 - 30180*x^3)/(29282*(-3 + x + 10*x^2)^2) - (1509*Log[-1 + 2*x])/161051 + (1509*Log[3 + 5*x])/161051","A",1
1705,1,50,65,0.0339175,"\int \frac{2+3 x}{(1-2 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{-22200 x^3-3330 x^2+11026 x+2753}{29282 \left(10 x^2+x-3\right)^2}-\frac{1110 \log (2 x-1)}{161051}+\frac{1110 \log (5 x+3)}{161051}","\frac{144}{14641 (1-2 x)}-\frac{195}{14641 (5 x+3)}+\frac{7}{1331 (1-2 x)^2}-\frac{5}{2662 (5 x+3)^2}-\frac{1110 \log (1-2 x)}{161051}+\frac{1110 \log (5 x+3)}{161051}",1,"(2753 + 11026*x - 3330*x^2 - 22200*x^3)/(29282*(-3 + x + 10*x^2)^2) - (1110*Log[-1 + 2*x])/161051 + (1110*Log[3 + 5*x])/161051","A",1
1706,1,50,65,0.0311401,"\int \frac{1}{(1-2 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{-12000 x^3-1800 x^2+5960 x+301}{29282 \left(10 x^2+x-3\right)^2}-\frac{600 \log (2 x-1)}{161051}+\frac{600 \log (5 x+3)}{161051}","\frac{60}{14641 (1-2 x)}-\frac{150}{14641 (5 x+3)}+\frac{2}{1331 (1-2 x)^2}-\frac{25}{2662 (5 x+3)^2}-\frac{600 \log (1-2 x)}{161051}+\frac{600 \log (5 x+3)}{161051}",1,"(301 + 5960*x - 1800*x^2 - 12000*x^3)/(29282*(-3 + x + 10*x^2)^2) - (600*Log[-1 + 2*x])/161051 + (600*Log[3 + 5*x])/161051","A",1
1707,1,60,75,0.0789473,"\int \frac{1}{(1-2 x)^3 (2+3 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^3*(2 + 3*x)*(3 + 5*x)^3),x]","\frac{6504600 x^3-2977380 x^2-2000774 x+950291}{1434818 \left(10 x^2+x-3\right)^2}-\frac{95232 \log (2 x-1)}{55240493}-\frac{243}{343} \log (3 x+2)+\frac{114375 \log (5 x+3)}{161051}","\frac{1104}{717409 (1-2 x)}+\frac{3375}{14641 (5 x+3)}+\frac{4}{9317 (1-2 x)^2}-\frac{125}{2662 (5 x+3)^2}-\frac{95232 \log (1-2 x)}{55240493}-\frac{243}{343} \log (3 x+2)+\frac{114375 \log (5 x+3)}{161051}",1,"(950291 - 2000774*x - 2977380*x^2 + 6504600*x^3)/(1434818*(-3 + x + 10*x^2)^2) - (95232*Log[-1 + 2*x])/55240493 - (243*Log[2 + 3*x])/343 + (114375*Log[3 + 5*x])/161051","A",1
1708,1,72,86,0.0858466,"\int \frac{1}{(1-2 x)^3 (2+3 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{2254231800 x^4+524583660 x^3-1362222102 x^2-159141275 x+213794156}{10043726 (3 x+2) \left(10 x^2+x-3\right)^2}-\frac{280752 \log (2 x-1)}{386683451}-\frac{26973 \log (3 x+2)}{2401}+\frac{1809375 \log (5 x+3)}{161051}","\frac{2736}{5021863 (1-2 x)}+\frac{243}{343 (3 x+2)}+\frac{37500}{14641 (5 x+3)}+\frac{8}{65219 (1-2 x)^2}-\frac{625}{2662 (5 x+3)^2}-\frac{280752 \log (1-2 x)}{386683451}-\frac{26973 \log (3 x+2)}{2401}+\frac{1809375 \log (5 x+3)}{161051}",1,"(213794156 - 159141275*x - 1362222102*x^2 + 524583660*x^3 + 2254231800*x^4)/(10043726*(2 + 3*x)*(-3 + x + 10*x^2)^2) - (280752*Log[-1 + 2*x])/386683451 - (26973*Log[2 + 3*x])/2401 + (1809375*Log[3 + 5*x])/161051","A",1
1709,1,81,97,0.1737616,"\int \frac{1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{488145765600 x^5+439319535120 x^4-218954328504 x^3-231191334456 x^2+23195310772 x+30858356237}{70306082 (2 x-1)^2 (3 x+2)^2 (5 x+3)^2}-\frac{776928 \log (2 x-1)}{2706784157}-\frac{1944972 \log (3 x+2)}{16807}+\frac{18637500 \log (5 x+3)}{161051}","\frac{6528}{35153041 (1-2 x)}+\frac{26973}{2401 (3 x+2)}+\frac{290625}{14641 (5 x+3)}+\frac{16}{456533 (1-2 x)^2}+\frac{243}{686 (3 x+2)^2}-\frac{3125}{2662 (5 x+3)^2}-\frac{776928 \log (1-2 x)}{2706784157}-\frac{1944972 \log (3 x+2)}{16807}+\frac{18637500 \log (5 x+3)}{161051}",1,"(30858356237 + 23195310772*x - 231191334456*x^2 - 218954328504*x^3 + 439319535120*x^4 + 488145765600*x^5)/(70306082*(-1 + 2*x)^2*(2 + 3*x)^2*(3 + 5*x)^2) - (776928*Log[-1 + 2*x])/2706784157 - (1944972*Log[2 + 3*x])/16807 + (18637500*Log[3 + 5*x])/161051","A",1
1710,1,82,108,0.1363485,"\int \frac{1}{(1-2 x)^3 (2+3 x)^4 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^3),x]","\frac{86993245890000 x^6+136289326113000 x^5+13177709631900 x^4-67213599053550 x^3-23334840827100 x^2+8254486652965 x+3666255393392}{492142574 (3 x+2)^3 \left(10 x^2+x-3\right)^2}-\frac{2054400 \log (2 x-1)}{18947489099}-\frac{115534350 \log (3 x+2)}{117649}+\frac{158156250 \log (5 x+3)}{161051}","\frac{15168}{246071287 (1-2 x)}+\frac{1944972}{16807 (3 x+2)}+\frac{1968750}{14641 (5 x+3)}+\frac{32}{3195731 (1-2 x)^2}+\frac{26973}{4802 (3 x+2)^2}-\frac{15625}{2662 (5 x+3)^2}+\frac{81}{343 (3 x+2)^3}-\frac{2054400 \log (1-2 x)}{18947489099}-\frac{115534350 \log (3 x+2)}{117649}+\frac{158156250 \log (5 x+3)}{161051}",1,"(3666255393392 + 8254486652965*x - 23334840827100*x^2 - 67213599053550*x^3 + 13177709631900*x^4 + 136289326113000*x^5 + 86993245890000*x^6)/(492142574*(2 + 3*x)^3*(-3 + x + 10*x^2)^2) - (2054400*Log[-1 + 2*x])/18947489099 - (115534350*Log[2 + 3*x])/117649 + (158156250*Log[3 + 5*x])/161051","A",1
1711,1,995,361,0.5409386,"\int (a+b x)^3 (c+d x)^3 (e+f x)^3 \, dx","IntegrateAlgebraic[(a + b*x)^3*(c + d*x)^3*(e + f*x)^3,x]","\frac{1}{840} \left(84 b^3 d^3 f^3 x^{10}+280 a b^2 d^3 f^3 x^9+280 b^3 c d^2 f^3 x^9+280 b^3 d^3 e f^2 x^9+315 a^2 b d^3 f^3 x^8+945 a b^2 c d^2 f^3 x^8+315 b^3 c^2 d f^3 x^8+945 a b^2 d^3 e f^2 x^8+945 b^3 c d^2 e f^2 x^8+315 b^3 d^3 e^2 f x^8+120 b^3 d^3 e^3 x^7+120 b^3 c^3 f^3 x^7+120 a^3 d^3 f^3 x^7+1080 a^2 b c d^2 f^3 x^7+1080 a b^2 c^2 d f^3 x^7+1080 a^2 b d^3 e f^2 x^7+3240 a b^2 c d^2 e f^2 x^7+1080 b^3 c^2 d e f^2 x^7+1080 a b^2 d^3 e^2 f x^7+1080 b^3 c d^2 e^2 f x^7+420 a b^2 d^3 e^3 x^6+420 b^3 c d^2 e^3 x^6+420 a b^2 c^3 f^3 x^6+420 a^3 c d^2 f^3 x^6+1260 a^2 b c^2 d f^3 x^6+420 b^3 c^3 e f^2 x^6+420 a^3 d^3 e f^2 x^6+3780 a^2 b c d^2 e f^2 x^6+3780 a b^2 c^2 d e f^2 x^6+1260 a^2 b d^3 e^2 f x^6+3780 a b^2 c d^2 e^2 f x^6+1260 b^3 c^2 d e^2 f x^6+504 a^2 b d^3 e^3 x^5+1512 a b^2 c d^2 e^3 x^5+504 b^3 c^2 d e^3 x^5+504 a^2 b c^3 f^3 x^5+504 a^3 c^2 d f^3 x^5+1512 a b^2 c^3 e f^2 x^5+1512 a^3 c d^2 e f^2 x^5+4536 a^2 b c^2 d e f^2 x^5+504 b^3 c^3 e^2 f x^5+504 a^3 d^3 e^2 f x^5+4536 a^2 b c d^2 e^2 f x^5+4536 a b^2 c^2 d e^2 f x^5+210 b^3 c^3 e^3 x^4+210 a^3 d^3 e^3 x^4+1890 a^2 b c d^2 e^3 x^4+1890 a b^2 c^2 d e^3 x^4+210 a^3 c^3 f^3 x^4+1890 a^2 b c^3 e f^2 x^4+1890 a^3 c^2 d e f^2 x^4+1890 a b^2 c^3 e^2 f x^4+1890 a^3 c d^2 e^2 f x^4+5670 a^2 b c^2 d e^2 f x^4+840 a b^2 c^3 e^3 x^3+840 a^3 c d^2 e^3 x^3+2520 a^2 b c^2 d e^3 x^3+840 a^3 c^3 e f^2 x^3+2520 a^2 b c^3 e^2 f x^3+2520 a^3 c^2 d e^2 f x^3+1260 a^2 b c^3 e^3 x^2+1260 a^3 c^2 d e^3 x^2+1260 a^3 c^3 e^2 f x^2+840 a^3 c^3 e^3 x\right)","\frac{3 d f (a+b x)^8 \left(5 a^2 d^2 f^2-5 a b d f (c f+d e)+b^2 \left(c^2 f^2+3 c d e f+d^2 e^2\right)\right)}{8 b^7}+\frac{(a+b x)^7 (-2 a d f+b c f+b d e) \left(10 a^2 d^2 f^2-10 a b d f (c f+d e)+b^2 \left(c^2 f^2+8 c d e f+d^2 e^2\right)\right)}{7 b^7}+\frac{(a+b x)^6 (b c-a d) (b e-a f) \left(5 a^2 d^2 f^2-5 a b d f (c f+d e)+b^2 \left(c^2 f^2+3 c d e f+d^2 e^2\right)\right)}{2 b^7}+\frac{d^2 f^2 (a+b x)^9 (-2 a d f+b c f+b d e)}{3 b^7}+\frac{3 (a+b x)^5 (b c-a d)^2 (b e-a f)^2 (-2 a d f+b c f+b d e)}{5 b^7}+\frac{(a+b x)^4 (b c-a d)^3 (b e-a f)^3}{4 b^7}+\frac{d^3 f^3 (a+b x)^{10}}{10 b^7}",1,"(840*a^3*c^3*e^3*x + 1260*a^2*b*c^3*e^3*x^2 + 1260*a^3*c^2*d*e^3*x^2 + 1260*a^3*c^3*e^2*f*x^2 + 840*a*b^2*c^3*e^3*x^3 + 2520*a^2*b*c^2*d*e^3*x^3 + 840*a^3*c*d^2*e^3*x^3 + 2520*a^2*b*c^3*e^2*f*x^3 + 2520*a^3*c^2*d*e^2*f*x^3 + 840*a^3*c^3*e*f^2*x^3 + 210*b^3*c^3*e^3*x^4 + 1890*a*b^2*c^2*d*e^3*x^4 + 1890*a^2*b*c*d^2*e^3*x^4 + 210*a^3*d^3*e^3*x^4 + 1890*a*b^2*c^3*e^2*f*x^4 + 5670*a^2*b*c^2*d*e^2*f*x^4 + 1890*a^3*c*d^2*e^2*f*x^4 + 1890*a^2*b*c^3*e*f^2*x^4 + 1890*a^3*c^2*d*e*f^2*x^4 + 210*a^3*c^3*f^3*x^4 + 504*b^3*c^2*d*e^3*x^5 + 1512*a*b^2*c*d^2*e^3*x^5 + 504*a^2*b*d^3*e^3*x^5 + 504*b^3*c^3*e^2*f*x^5 + 4536*a*b^2*c^2*d*e^2*f*x^5 + 4536*a^2*b*c*d^2*e^2*f*x^5 + 504*a^3*d^3*e^2*f*x^5 + 1512*a*b^2*c^3*e*f^2*x^5 + 4536*a^2*b*c^2*d*e*f^2*x^5 + 1512*a^3*c*d^2*e*f^2*x^5 + 504*a^2*b*c^3*f^3*x^5 + 504*a^3*c^2*d*f^3*x^5 + 420*b^3*c*d^2*e^3*x^6 + 420*a*b^2*d^3*e^3*x^6 + 1260*b^3*c^2*d*e^2*f*x^6 + 3780*a*b^2*c*d^2*e^2*f*x^6 + 1260*a^2*b*d^3*e^2*f*x^6 + 420*b^3*c^3*e*f^2*x^6 + 3780*a*b^2*c^2*d*e*f^2*x^6 + 3780*a^2*b*c*d^2*e*f^2*x^6 + 420*a^3*d^3*e*f^2*x^6 + 420*a*b^2*c^3*f^3*x^6 + 1260*a^2*b*c^2*d*f^3*x^6 + 420*a^3*c*d^2*f^3*x^6 + 120*b^3*d^3*e^3*x^7 + 1080*b^3*c*d^2*e^2*f*x^7 + 1080*a*b^2*d^3*e^2*f*x^7 + 1080*b^3*c^2*d*e*f^2*x^7 + 3240*a*b^2*c*d^2*e*f^2*x^7 + 1080*a^2*b*d^3*e*f^2*x^7 + 120*b^3*c^3*f^3*x^7 + 1080*a*b^2*c^2*d*f^3*x^7 + 1080*a^2*b*c*d^2*f^3*x^7 + 120*a^3*d^3*f^3*x^7 + 315*b^3*d^3*e^2*f*x^8 + 945*b^3*c*d^2*e*f^2*x^8 + 945*a*b^2*d^3*e*f^2*x^8 + 315*b^3*c^2*d*f^3*x^8 + 945*a*b^2*c*d^2*f^3*x^8 + 315*a^2*b*d^3*f^3*x^8 + 280*b^3*d^3*e*f^2*x^9 + 280*b^3*c*d^2*f^3*x^9 + 280*a*b^2*d^3*f^3*x^9 + 84*b^3*d^3*f^3*x^10)/840","B",1
1712,1,354,193,0.1937717,"\int (a+b x)^2 (c+d x)^2 (e+f x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^2*(c + d*x)^2*(e + f*x)^2,x]","\frac{1}{210} \left(210 a^2 c^2 e^2 x+210 a^2 c^2 e f x^2+70 a^2 c^2 f^2 x^3+210 a^2 c d e^2 x^2+280 a^2 c d e f x^3+105 a^2 c d f^2 x^4+70 a^2 d^2 e^2 x^3+105 a^2 d^2 e f x^4+42 a^2 d^2 f^2 x^5+210 a b c^2 e^2 x^2+280 a b c^2 e f x^3+105 a b c^2 f^2 x^4+280 a b c d e^2 x^3+420 a b c d e f x^4+168 a b c d f^2 x^5+105 a b d^2 e^2 x^4+168 a b d^2 e f x^5+70 a b d^2 f^2 x^6+70 b^2 c^2 e^2 x^3+105 b^2 c^2 e f x^4+42 b^2 c^2 f^2 x^5+105 b^2 c d e^2 x^4+168 b^2 c d e f x^5+70 b^2 c d f^2 x^6+42 b^2 d^2 e^2 x^5+70 b^2 d^2 e f x^6+30 b^2 d^2 f^2 x^7\right)","\frac{(a+b x)^5 \left(6 a^2 d^2 f^2-6 a b d f (c f+d e)+b^2 \left(c^2 f^2+4 c d e f+d^2 e^2\right)\right)}{5 b^5}+\frac{d f (a+b x)^6 (-2 a d f+b c f+b d e)}{3 b^5}+\frac{(a+b x)^4 (b c-a d) (b e-a f) (-2 a d f+b c f+b d e)}{2 b^5}+\frac{(a+b x)^3 (b c-a d)^2 (b e-a f)^2}{3 b^5}+\frac{d^2 f^2 (a+b x)^7}{7 b^5}",1,"(210*a^2*c^2*e^2*x + 210*a*b*c^2*e^2*x^2 + 210*a^2*c*d*e^2*x^2 + 210*a^2*c^2*e*f*x^2 + 70*b^2*c^2*e^2*x^3 + 280*a*b*c*d*e^2*x^3 + 70*a^2*d^2*e^2*x^3 + 280*a*b*c^2*e*f*x^3 + 280*a^2*c*d*e*f*x^3 + 70*a^2*c^2*f^2*x^3 + 105*b^2*c*d*e^2*x^4 + 105*a*b*d^2*e^2*x^4 + 105*b^2*c^2*e*f*x^4 + 420*a*b*c*d*e*f*x^4 + 105*a^2*d^2*e*f*x^4 + 105*a*b*c^2*f^2*x^4 + 105*a^2*c*d*f^2*x^4 + 42*b^2*d^2*e^2*x^5 + 168*b^2*c*d*e*f*x^5 + 168*a*b*d^2*e*f*x^5 + 42*b^2*c^2*f^2*x^5 + 168*a*b*c*d*f^2*x^5 + 42*a^2*d^2*f^2*x^5 + 70*b^2*d^2*e*f*x^6 + 70*b^2*c*d*f^2*x^6 + 70*a*b*d^2*f^2*x^6 + 30*b^2*d^2*f^2*x^7)/210","A",1
1713,1,61,56,0.0436985,"\int (a+b x) (c+d x) (e+f x) \, dx","IntegrateAlgebraic[(a + b*x)*(c + d*x)*(e + f*x),x]","\frac{1}{12} x \left(12 a c e+6 a c f x+6 a d e x+4 a d f x^2+6 b c e x+4 b c f x^2+4 b d e x^2+3 b d f x^3\right)","\frac{1}{3} x^3 (a d f+b c f+b d e)+\frac{1}{2} x^2 (a c f+a d e+b c e)+a c e x+\frac{1}{4} b d f x^4",1,"(x*(12*a*c*e + 6*b*c*e*x + 6*a*d*e*x + 6*a*c*f*x + 4*b*d*e*x^2 + 4*b*c*f*x^2 + 4*a*d*f*x^2 + 3*b*d*f*x^3))/12","A",1
1714,1,85,86,0.0824497,"\int \frac{1}{(a+b x) (c+d x) (e+f x)} \, dx","IntegrateAlgebraic[1/((a + b*x)*(c + d*x)*(e + f*x)),x]","\frac{b \log (a+b x)}{(b c-a d) (b e-a f)}+\frac{d \log (c+d x)}{(b c-a d) (c f-d e)}+\frac{f \log (e+f x)}{(b e-a f) (d e-c f)}","\frac{b \log (a+b x)}{(b c-a d) (b e-a f)}-\frac{d \log (c+d x)}{(b c-a d) (d e-c f)}+\frac{f \log (e+f x)}{(b e-a f) (d e-c f)}",1,"(b*Log[a + b*x])/((b*c - a*d)*(b*e - a*f)) + (d*Log[c + d*x])/((b*c - a*d)*(-(d*e) + c*f)) + (f*Log[e + f*x])/((b*e - a*f)*(d*e - c*f))","A",1
1715,1,521,234,0.8016006,"\int \frac{1}{(a+b x)^2 (c+d x)^2 (e+f x)^2} \, dx","IntegrateAlgebraic[1/((a + b*x)^2*(c + d*x)^2*(e + f*x)^2),x]","\frac{-a^3 c d^2 f^3-a^3 d^3 e f^2-2 a^3 d^3 f^3 x+2 a^2 b c^2 d f^3+a^2 b c d^2 f^3 x+2 a^2 b d^3 e^2 f+a^2 b d^3 e f^2 x-2 a^2 b d^3 f^3 x^2-a b^2 c^3 f^3+a b^2 c^2 d f^3 x+2 a b^2 c d^2 f^3 x^2-a b^2 d^3 e^3+a b^2 d^3 e^2 f x+2 a b^2 d^3 e f^2 x^2-b^3 c^3 e f^2-2 b^3 c^3 f^3 x+2 b^3 c^2 d e^2 f+b^3 c^2 d e f^2 x-2 b^3 c^2 d f^3 x^2+b^3 (-c) d^2 e^3+b^3 c d^2 e^2 f x+2 b^3 c d^2 e f^2 x^2-2 b^3 d^3 e^3 x-2 b^3 d^3 e^2 f x^2}{(a+b x) (c+d x) (e+f x) (b c-a d)^2 (b e-a f)^2 (c f-d e)^2}-\frac{2 \log (a+b x) \left(-2 a b^3 d f+b^4 c f+b^4 d e\right)}{(b c-a d)^3 (b e-a f)^3}-\frac{2 \log (c+d x) \left(a d^4 f-2 b c d^3 f+b d^4 e\right)}{(b c-a d)^3 (c f-d e)^3}+\frac{2 \log (e+f x) \left(-a d f^4-b c f^4+2 b d e f^3\right)}{(b e-a f)^3 (d e-c f)^3}","-\frac{b^3}{(a+b x) (b c-a d)^2 (b e-a f)^2}-\frac{2 b^3 \log (a+b x) (-2 a d f+b c f+b d e)}{(b c-a d)^3 (b e-a f)^3}-\frac{d^3}{(c+d x) (b c-a d)^2 (d e-c f)^2}+\frac{2 d^3 \log (c+d x) (a d f-2 b c f+b d e)}{(b c-a d)^3 (d e-c f)^3}-\frac{f^3}{(e+f x) (b e-a f)^2 (d e-c f)^2}+\frac{2 f^3 \log (e+f x) (-a d f-b c f+2 b d e)}{(b e-a f)^3 (d e-c f)^3}",1,"(-(b^3*c*d^2*e^3) - a*b^2*d^3*e^3 + 2*b^3*c^2*d*e^2*f + 2*a^2*b*d^3*e^2*f - b^3*c^3*e*f^2 - a^3*d^3*e*f^2 - a*b^2*c^3*f^3 + 2*a^2*b*c^2*d*f^3 - a^3*c*d^2*f^3 - 2*b^3*d^3*e^3*x + b^3*c*d^2*e^2*f*x + a*b^2*d^3*e^2*f*x + b^3*c^2*d*e*f^2*x + a^2*b*d^3*e*f^2*x - 2*b^3*c^3*f^3*x + a*b^2*c^2*d*f^3*x + a^2*b*c*d^2*f^3*x - 2*a^3*d^3*f^3*x - 2*b^3*d^3*e^2*f*x^2 + 2*b^3*c*d^2*e*f^2*x^2 + 2*a*b^2*d^3*e*f^2*x^2 - 2*b^3*c^2*d*f^3*x^2 + 2*a*b^2*c*d^2*f^3*x^2 - 2*a^2*b*d^3*f^3*x^2)/((b*c - a*d)^2*(b*e - a*f)^2*(-(d*e) + c*f)^2*(a + b*x)*(c + d*x)*(e + f*x)) - (2*(b^4*d*e + b^4*c*f - 2*a*b^3*d*f)*Log[a + b*x])/((b*c - a*d)^3*(b*e - a*f)^3) - (2*(b*d^4*e - 2*b*c*d^3*f + a*d^4*f)*Log[c + d*x])/((b*c - a*d)^3*(-(d*e) + c*f)^3) + (2*(2*b*d*e*f^3 - b*c*f^4 - a*d*f^4)*Log[e + f*x])/((b*e - a*f)^3*(d*e - c*f)^3)","B",1
1716,1,4340,495,3.8230107,"\int \frac{1}{(a+b x)^3 (c+d x)^3 (e+f x)^3} \, dx","IntegrateAlgebraic[1/((a + b*x)^3*(c + d*x)^3*(e + f*x)^3),x]","\text{Result too large to show}","\frac{3 f^5 \log (e+f x) \left(2 a^2 d^2 f^2-a b d f (7 d e-3 c f)+b^2 \left(2 c^2 f^2-7 c d e f+7 d^2 e^2\right)\right)}{(b e-a f)^5 (d e-c f)^5}-\frac{3 d^5 \log (c+d x) \left(2 a^2 d^2 f^2+a b d f (3 d e-7 c f)+b^2 \left(7 c^2 f^2-7 c d e f+2 d^2 e^2\right)\right)}{(b c-a d)^5 (d e-c f)^5}+\frac{3 b^5 \log (a+b x) \left(7 a^2 d^2 f^2-7 a b d f (c f+d e)+b^2 \left(2 c^2 f^2+3 c d e f+2 d^2 e^2\right)\right)}{(b c-a d)^5 (b e-a f)^5}+\frac{3 b^5 (-2 a d f+b c f+b d e)}{(a+b x) (b c-a d)^4 (b e-a f)^4}-\frac{b^5}{2 (a+b x)^2 (b c-a d)^3 (b e-a f)^3}+\frac{3 d^5 (a d f-2 b c f+b d e)}{(c+d x) (b c-a d)^4 (d e-c f)^4}+\frac{d^5}{2 (c+d x)^2 (b c-a d)^3 (d e-c f)^3}-\frac{3 f^5 (-a d f-b c f+2 b d e)}{(e+f x) (b e-a f)^4 (d e-c f)^4}-\frac{f^5}{2 (e+f x)^2 (b e-a f)^3 (d e-c f)^3}",1,"(-(b^7*c^3*d^4*e^7) + 7*a*b^6*c^2*d^5*e^7 + 7*a^2*b^5*c*d^6*e^7 - a^3*b^4*d^7*e^7 + 4*b^7*c^4*d^3*e^6*f - 21*a*b^6*c^3*d^4*e^6*f - 26*a^2*b^5*c^2*d^5*e^6*f - 21*a^3*b^4*c*d^6*e^6*f + 4*a^4*b^3*d^7*e^6*f - 6*b^7*c^5*d^2*e^5*f^2 + 14*a*b^6*c^4*d^3*e^5*f^2 + 52*a^2*b^5*c^3*d^4*e^5*f^2 + 52*a^3*b^4*c^2*d^5*e^5*f^2 + 14*a^4*b^3*c*d^6*e^5*f^2 - 6*a^5*b^2*d^7*e^5*f^2 + 4*b^7*c^6*d*e^4*f^3 + 14*a*b^6*c^5*d^2*e^4*f^3 - 78*a^2*b^5*c^4*d^3*e^4*f^3 - 78*a^4*b^3*c^2*d^5*e^4*f^3 + 14*a^5*b^2*c*d^6*e^4*f^3 + 4*a^6*b*d^7*e^4*f^3 - b^7*c^7*e^3*f^4 - 21*a*b^6*c^6*d*e^3*f^4 + 52*a^2*b^5*c^5*d^2*e^3*f^4 + 52*a^5*b^2*c^2*d^5*e^3*f^4 - 21*a^6*b*c*d^6*e^3*f^4 - a^7*d^7*e^3*f^4 + 7*a*b^6*c^7*e^2*f^5 - 26*a^2*b^5*c^6*d*e^2*f^5 + 52*a^3*b^4*c^5*d^2*e^2*f^5 - 78*a^4*b^3*c^4*d^3*e^2*f^5 + 52*a^5*b^2*c^3*d^4*e^2*f^5 - 26*a^6*b*c^2*d^5*e^2*f^5 + 7*a^7*c*d^6*e^2*f^5 + 7*a^2*b^5*c^7*e*f^6 - 21*a^3*b^4*c^6*d*e*f^6 + 14*a^4*b^3*c^5*d^2*e*f^6 + 14*a^5*b^2*c^4*d^3*e*f^6 - 21*a^6*b*c^3*d^4*e*f^6 + 7*a^7*c^2*d^5*e*f^6 - a^3*b^4*c^7*f^7 + 4*a^4*b^3*c^6*d*f^7 - 6*a^5*b^2*c^5*d^2*f^7 + 4*a^6*b*c^4*d^3*f^7 - a^7*c^3*d^4*f^7 + 4*b^7*c^2*d^5*e^7*x + 28*a*b^6*c*d^6*e^7*x + 4*a^2*b^5*d^7*e^7*x - 12*b^7*c^3*d^4*e^6*f*x - 66*a*b^6*c^2*d^5*e^6*f*x - 66*a^2*b^5*c*d^6*e^6*f*x - 12*a^3*b^4*d^7*e^6*f*x + 8*b^7*c^4*d^3*e^5*f^2*x + 34*a*b^6*c^3*d^4*e^5*f^2*x + 156*a^2*b^5*c^2*d^5*e^5*f^2*x + 34*a^3*b^4*c*d^6*e^5*f^2*x + 8*a^4*b^3*d^7*e^5*f^2*x + 8*b^7*c^5*d^2*e^4*f^3*x - 16*a*b^6*c^4*d^3*e^4*f^3*x - 52*a^2*b^5*c^3*d^4*e^4*f^3*x - 52*a^3*b^4*c^2*d^5*e^4*f^3*x - 16*a^4*b^3*c*d^6*e^4*f^3*x + 8*a^5*b^2*d^7*e^4*f^3*x - 12*b^7*c^6*d*e^3*f^4*x + 34*a*b^6*c^5*d^2*e^3*f^4*x - 52*a^2*b^5*c^4*d^3*e^3*f^4*x - 52*a^4*b^3*c^2*d^5*e^3*f^4*x + 34*a^5*b^2*c*d^6*e^3*f^4*x - 12*a^6*b*d^7*e^3*f^4*x + 4*b^7*c^7*e^2*f^5*x - 66*a*b^6*c^6*d*e^2*f^5*x + 156*a^2*b^5*c^5*d^2*e^2*f^5*x - 52*a^3*b^4*c^4*d^3*e^2*f^5*x - 52*a^4*b^3*c^3*d^4*e^2*f^5*x + 156*a^5*b^2*c^2*d^5*e^2*f^5*x - 66*a^6*b*c*d^6*e^2*f^5*x + 4*a^7*d^7*e^2*f^5*x + 28*a*b^6*c^7*e*f^6*x - 66*a^2*b^5*c^6*d*e*f^6*x + 34*a^3*b^4*c^5*d^2*e*f^6*x - 16*a^4*b^3*c^4*d^3*e*f^6*x + 34*a^5*b^2*c^3*d^4*e*f^6*x - 66*a^6*b*c^2*d^5*e*f^6*x + 28*a^7*c*d^6*e*f^6*x + 4*a^2*b^5*c^7*f^7*x - 12*a^3*b^4*c^6*d*f^7*x + 8*a^4*b^3*c^5*d^2*f^7*x + 8*a^5*b^2*c^4*d^3*f^7*x - 12*a^6*b*c^3*d^4*f^7*x + 4*a^7*c^2*d^5*f^7*x + 18*b^7*c*d^6*e^7*x^2 + 18*a*b^6*d^7*e^7*x^2 - 37*b^7*c^2*d^5*e^6*f*x^2 - 34*a*b^6*c*d^6*e^6*f*x^2 - 37*a^2*b^5*d^7*e^6*f*x^2 - 3*b^7*c^3*d^4*e^5*f^2*x^2 + 9*a*b^6*c^2*d^5*e^5*f^2*x^2 + 9*a^2*b^5*c*d^6*e^5*f^2*x^2 - 3*a^3*b^4*d^7*e^5*f^2*x^2 + 32*b^7*c^4*d^3*e^4*f^3*x^2 + a*b^6*c^3*d^4*e^4*f^3*x^2 + 234*a^2*b^5*c^2*d^5*e^4*f^3*x^2 + a^3*b^4*c*d^6*e^4*f^3*x^2 + 32*a^4*b^3*d^7*e^4*f^3*x^2 - 3*b^7*c^5*d^2*e^3*f^4*x^2 + a*b^6*c^4*d^3*e^3*f^4*x^2 - 208*a^2*b^5*c^3*d^4*e^3*f^4*x^2 - 208*a^3*b^4*c^2*d^5*e^3*f^4*x^2 + a^4*b^3*c*d^6*e^3*f^4*x^2 - 3*a^5*b^2*d^7*e^3*f^4*x^2 - 37*b^7*c^6*d*e^2*f^5*x^2 + 9*a*b^6*c^5*d^2*e^2*f^5*x^2 + 234*a^2*b^5*c^4*d^3*e^2*f^5*x^2 - 208*a^3*b^4*c^3*d^4*e^2*f^5*x^2 + 234*a^4*b^3*c^2*d^5*e^2*f^5*x^2 + 9*a^5*b^2*c*d^6*e^2*f^5*x^2 - 37*a^6*b*d^7*e^2*f^5*x^2 + 18*b^7*c^7*e*f^6*x^2 - 34*a*b^6*c^6*d*e*f^6*x^2 + 9*a^2*b^5*c^5*d^2*e*f^6*x^2 + a^3*b^4*c^4*d^3*e*f^6*x^2 + a^4*b^3*c^3*d^4*e*f^6*x^2 + 9*a^5*b^2*c^2*d^5*e*f^6*x^2 - 34*a^6*b*c*d^6*e*f^6*x^2 + 18*a^7*d^7*e*f^6*x^2 + 18*a*b^6*c^7*f^7*x^2 - 37*a^2*b^5*c^6*d*f^7*x^2 - 3*a^3*b^4*c^5*d^2*f^7*x^2 + 32*a^4*b^3*c^4*d^3*f^7*x^2 - 3*a^5*b^2*c^3*d^4*f^7*x^2 - 37*a^6*b*c^2*d^5*f^7*x^2 + 18*a^7*c*d^6*f^7*x^2 + 12*b^7*d^7*e^7*x^3 + 6*b^7*c*d^6*e^6*f*x^3 + 6*a*b^6*d^7*e^6*f*x^3 - 74*b^7*c^2*d^5*e^5*f^2*x^3 - 56*a*b^6*c*d^6*e^5*f^2*x^3 - 74*a^2*b^5*d^7*e^5*f^2*x^3 + 38*b^7*c^3*d^4*e^4*f^3*x^3 + 172*a*b^6*c^2*d^5*e^4*f^3*x^3 + 172*a^2*b^5*c*d^6*e^4*f^3*x^3 + 38*a^3*b^4*d^7*e^4*f^3*x^3 + 38*b^7*c^4*d^3*e^3*f^4*x^3 - 136*a*b^6*c^3*d^4*e^3*f^4*x^3 - 104*a^2*b^5*c^2*d^5*e^3*f^4*x^3 - 136*a^3*b^4*c*d^6*e^3*f^4*x^3 + 38*a^4*b^3*d^7*e^3*f^4*x^3 - 74*b^7*c^5*d^2*e^2*f^5*x^3 + 172*a*b^6*c^4*d^3*e^2*f^5*x^3 - 104*a^2*b^5*c^3*d^4*e^2*f^5*x^3 - 104*a^3*b^4*c^2*d^5*e^2*f^5*x^3 + 172*a^4*b^3*c*d^6*e^2*f^5*x^3 - 74*a^5*b^2*d^7*e^2*f^5*x^3 + 6*b^7*c^6*d*e*f^6*x^3 - 56*a*b^6*c^5*d^2*e*f^6*x^3 + 172*a^2*b^5*c^4*d^3*e*f^6*x^3 - 136*a^3*b^4*c^3*d^4*e*f^6*x^3 + 172*a^4*b^3*c^2*d^5*e*f^6*x^3 - 56*a^5*b^2*c*d^6*e*f^6*x^3 + 6*a^6*b*d^7*e*f^6*x^3 + 12*b^7*c^7*f^7*x^3 + 6*a*b^6*c^6*d*f^7*x^3 - 74*a^2*b^5*c^5*d^2*f^7*x^3 + 38*a^3*b^4*c^4*d^3*f^7*x^3 + 38*a^4*b^3*c^3*d^4*f^7*x^3 - 74*a^5*b^2*c^2*d^5*f^7*x^3 + 6*a^6*b*c*d^6*f^7*x^3 + 12*a^7*d^7*f^7*x^3 + 24*b^7*d^7*e^6*f*x^4 - 42*b^7*c*d^6*e^5*f^2*x^4 - 42*a*b^6*d^7*e^5*f^2*x^4 - 21*b^7*c^2*d^5*e^4*f^3*x^4 + 102*a*b^6*c*d^6*e^4*f^3*x^4 - 21*a^2*b^5*d^7*e^4*f^3*x^4 + 42*b^7*c^3*d^4*e^3*f^4*x^4 + 18*a*b^6*c^2*d^5*e^3*f^4*x^4 + 18*a^2*b^5*c*d^6*e^3*f^4*x^4 + 42*a^3*b^4*d^7*e^3*f^4*x^4 - 21*b^7*c^4*d^3*e^2*f^5*x^4 + 18*a*b^6*c^3*d^4*e^2*f^5*x^4 - 234*a^2*b^5*c^2*d^5*e^2*f^5*x^4 + 18*a^3*b^4*c*d^6*e^2*f^5*x^4 - 21*a^4*b^3*d^7*e^2*f^5*x^4 - 42*b^7*c^5*d^2*e*f^6*x^4 + 102*a*b^6*c^4*d^3*e*f^6*x^4 + 18*a^2*b^5*c^3*d^4*e*f^6*x^4 + 18*a^3*b^4*c^2*d^5*e*f^6*x^4 + 102*a^4*b^3*c*d^6*e*f^6*x^4 - 42*a^5*b^2*d^7*e*f^6*x^4 + 24*b^7*c^6*d*f^7*x^4 - 42*a*b^6*c^5*d^2*f^7*x^4 - 21*a^2*b^5*c^4*d^3*f^7*x^4 + 42*a^3*b^4*c^3*d^4*f^7*x^4 - 21*a^4*b^3*c^2*d^5*f^7*x^4 - 42*a^5*b^2*c*d^6*f^7*x^4 + 24*a^6*b*d^7*f^7*x^4 + 12*b^7*d^7*e^5*f^2*x^5 - 30*b^7*c*d^6*e^4*f^3*x^5 - 30*a*b^6*d^7*e^4*f^3*x^5 + 12*b^7*c^2*d^5*e^3*f^4*x^5 + 96*a*b^6*c*d^6*e^3*f^4*x^5 + 12*a^2*b^5*d^7*e^3*f^4*x^5 + 12*b^7*c^3*d^4*e^2*f^5*x^5 - 72*a*b^6*c^2*d^5*e^2*f^5*x^5 - 72*a^2*b^5*c*d^6*e^2*f^5*x^5 + 12*a^3*b^4*d^7*e^2*f^5*x^5 - 30*b^7*c^4*d^3*e*f^6*x^5 + 96*a*b^6*c^3*d^4*e*f^6*x^5 - 72*a^2*b^5*c^2*d^5*e*f^6*x^5 + 96*a^3*b^4*c*d^6*e*f^6*x^5 - 30*a^4*b^3*d^7*e*f^6*x^5 + 12*b^7*c^5*d^2*f^7*x^5 - 30*a*b^6*c^4*d^3*f^7*x^5 + 12*a^2*b^5*c^3*d^4*f^7*x^5 + 12*a^3*b^4*c^2*d^5*f^7*x^5 - 30*a^4*b^3*c*d^6*f^7*x^5 + 12*a^5*b^2*d^7*f^7*x^5)/(2*(b*c - a*d)^4*(b*e - a*f)^4*(-(d*e) + c*f)^4*(a + b*x)^2*(c + d*x)^2*(e + f*x)^2) + (3*(2*b^7*d^2*e^2 + 3*b^7*c*d*e*f - 7*a*b^6*d^2*e*f + 2*b^7*c^2*f^2 - 7*a*b^6*c*d*f^2 + 7*a^2*b^5*d^2*f^2)*Log[a + b*x])/((b*c - a*d)^5*(b*e - a*f)^5) + (3*(2*b^2*d^7*e^2 - 7*b^2*c*d^6*e*f + 3*a*b*d^7*e*f + 7*b^2*c^2*d^5*f^2 - 7*a*b*c*d^6*f^2 + 2*a^2*d^7*f^2)*Log[c + d*x])/((b*c - a*d)^5*(-(d*e) + c*f)^5) + (3*(7*b^2*d^2*e^2*f^5 - 7*b^2*c*d*e*f^6 - 7*a*b*d^2*e*f^6 + 2*b^2*c^2*f^7 + 3*a*b*c*d*f^7 + 2*a^2*d^2*f^7)*Log[e + f*x])/((b*e - a*f)^5*(d*e - c*f)^5)","B",1
1717,1,202,170,0.4806206,"\int \frac{(c+d x)^{3/2}}{(a+b x)^2 (e+f x)} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/((a + b*x)^2*(e + f*x)),x]","\frac{\left(3 b d e \sqrt{a d-b c}-2 b c f \sqrt{a d-b c}-a d f \sqrt{a d-b c}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{b^{3/2} (b e-a f)^2}+\frac{\sqrt{c+d x} (a d-b c)}{b (a+b x) (b e-a f)}+\frac{2 (d e-c f)^{3/2} \tan ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d e-c f}}\right)}{\sqrt{f} (a f-b e)^2}","-\frac{\sqrt{b c-a d} (-a d f-2 b c f+3 b d e) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{3/2} (b e-a f)^2}-\frac{\sqrt{c+d x} (b c-a d)}{b (a+b x) (b e-a f)}+\frac{2 (d e-c f)^{3/2} \tan ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d e-c f}}\right)}{\sqrt{f} (b e-a f)^2}",1,"((-(b*c) + a*d)*Sqrt[c + d*x])/(b*(b*e - a*f)*(a + b*x)) + ((3*b*d*Sqrt[-(b*c) + a*d]*e - 2*b*c*Sqrt[-(b*c) + a*d]*f - a*d*Sqrt[-(b*c) + a*d]*f)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(b^(3/2)*(b*e - a*f)^2) + (2*(d*e - c*f)^(3/2)*ArcTan[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[d*e - c*f]])/(Sqrt[f]*(-(b*e) + a*f)^2)","A",1
1718,1,280,83,0.062725,"\int (a+b x) (A+B x) (d+e x)^{7/2} \, dx","IntegrateAlgebraic[(a + b*x)*(A + B*x)*(d + e*x)^(7/2),x]","\frac{2 \sqrt{d+e x} \left(143 a A d^4 e^2+572 a A d^3 e^3 x+858 a A d^2 e^4 x^2+572 a A d e^5 x^3+143 a A e^6 x^4-26 a B d^5 e+13 a B d^4 e^2 x+312 a B d^3 e^3 x^2+598 a B d^2 e^4 x^3+442 a B d e^5 x^4+117 a B e^6 x^5-26 A b d^5 e+13 A b d^4 e^2 x+312 A b d^3 e^3 x^2+598 A b d^2 e^4 x^3+442 A b d e^5 x^4+117 A b e^6 x^5+8 b B d^6-4 b B d^5 e x+3 b B d^4 e^2 x^2+212 b B d^3 e^3 x^3+458 b B d^2 e^4 x^4+360 b B d e^5 x^5+99 b B e^6 x^6\right)}{1287 e^3}","-\frac{2 (d+e x)^{11/2} (-a B e-A b e+2 b B d)}{11 e^3}+\frac{2 (d+e x)^{9/2} (b d-a e) (B d-A e)}{9 e^3}+\frac{2 b B (d+e x)^{13/2}}{13 e^3}",1,"(2*Sqrt[d + e*x]*(8*b*B*d^6 - 26*A*b*d^5*e - 26*a*B*d^5*e + 143*a*A*d^4*e^2 - 4*b*B*d^5*e*x + 13*A*b*d^4*e^2*x + 13*a*B*d^4*e^2*x + 572*a*A*d^3*e^3*x + 3*b*B*d^4*e^2*x^2 + 312*A*b*d^3*e^3*x^2 + 312*a*B*d^3*e^3*x^2 + 858*a*A*d^2*e^4*x^2 + 212*b*B*d^3*e^3*x^3 + 598*A*b*d^2*e^4*x^3 + 598*a*B*d^2*e^4*x^3 + 572*a*A*d*e^5*x^3 + 458*b*B*d^2*e^4*x^4 + 442*A*b*d*e^5*x^4 + 442*a*B*d*e^5*x^4 + 143*a*A*e^6*x^4 + 360*b*B*d*e^5*x^5 + 117*A*b*e^6*x^5 + 117*a*B*e^6*x^5 + 99*b*B*e^6*x^6))/(1287*e^3)","B",1
1719,1,228,83,0.0536108,"\int (a+b x) (A+B x) (d+e x)^{5/2} \, dx","IntegrateAlgebraic[(a + b*x)*(A + B*x)*(d + e*x)^(5/2),x]","\frac{2 \sqrt{d+e x} \left(99 a A d^3 e^2+297 a A d^2 e^3 x+297 a A d e^4 x^2+99 a A e^5 x^3-22 a B d^4 e+11 a B d^3 e^2 x+165 a B d^2 e^3 x^2+209 a B d e^4 x^3+77 a B e^5 x^4-22 A b d^4 e+11 A b d^3 e^2 x+165 A b d^2 e^3 x^2+209 A b d e^4 x^3+77 A b e^5 x^4+8 b B d^5-4 b B d^4 e x+3 b B d^3 e^2 x^2+113 b B d^2 e^3 x^3+161 b B d e^4 x^4+63 b B e^5 x^5\right)}{693 e^3}","-\frac{2 (d+e x)^{9/2} (-a B e-A b e+2 b B d)}{9 e^3}+\frac{2 (d+e x)^{7/2} (b d-a e) (B d-A e)}{7 e^3}+\frac{2 b B (d+e x)^{11/2}}{11 e^3}",1,"(2*Sqrt[d + e*x]*(8*b*B*d^5 - 22*A*b*d^4*e - 22*a*B*d^4*e + 99*a*A*d^3*e^2 - 4*b*B*d^4*e*x + 11*A*b*d^3*e^2*x + 11*a*B*d^3*e^2*x + 297*a*A*d^2*e^3*x + 3*b*B*d^3*e^2*x^2 + 165*A*b*d^2*e^3*x^2 + 165*a*B*d^2*e^3*x^2 + 297*a*A*d*e^4*x^2 + 113*b*B*d^2*e^3*x^3 + 209*A*b*d*e^4*x^3 + 209*a*B*d*e^4*x^3 + 99*a*A*e^5*x^3 + 161*b*B*d*e^4*x^4 + 77*A*b*e^5*x^4 + 77*a*B*e^5*x^4 + 63*b*B*e^5*x^5))/(693*e^3)","B",1
1720,1,176,83,0.0498444,"\int (a+b x) (A+B x) (d+e x)^{3/2} \, dx","IntegrateAlgebraic[(a + b*x)*(A + B*x)*(d + e*x)^(3/2),x]","\frac{2 \sqrt{d+e x} \left(63 a A d^2 e^2+126 a A d e^3 x+63 a A e^4 x^2-18 a B d^3 e+9 a B d^2 e^2 x+72 a B d e^3 x^2+45 a B e^4 x^3-18 A b d^3 e+9 A b d^2 e^2 x+72 A b d e^3 x^2+45 A b e^4 x^3+8 b B d^4-4 b B d^3 e x+3 b B d^2 e^2 x^2+50 b B d e^3 x^3+35 b B e^4 x^4\right)}{315 e^3}","-\frac{2 (d+e x)^{7/2} (-a B e-A b e+2 b B d)}{7 e^3}+\frac{2 (d+e x)^{5/2} (b d-a e) (B d-A e)}{5 e^3}+\frac{2 b B (d+e x)^{9/2}}{9 e^3}",1,"(2*Sqrt[d + e*x]*(8*b*B*d^4 - 18*A*b*d^3*e - 18*a*B*d^3*e + 63*a*A*d^2*e^2 - 4*b*B*d^3*e*x + 9*A*b*d^2*e^2*x + 9*a*B*d^2*e^2*x + 126*a*A*d*e^3*x + 3*b*B*d^2*e^2*x^2 + 72*A*b*d*e^3*x^2 + 72*a*B*d*e^3*x^2 + 63*a*A*e^4*x^2 + 50*b*B*d*e^3*x^3 + 45*A*b*e^4*x^3 + 45*a*B*e^4*x^3 + 35*b*B*e^4*x^4))/(315*e^3)","B",1
1721,1,124,83,0.0440428,"\int (a+b x) (A+B x) \sqrt{d+e x} \, dx","IntegrateAlgebraic[(a + b*x)*(A + B*x)*Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(35 a A d e^2+35 a A e^3 x-14 a B d^2 e+7 a B d e^2 x+21 a B e^3 x^2-14 A b d^2 e+7 A b d e^2 x+21 A b e^3 x^2+8 b B d^3-4 b B d^2 e x+3 b B d e^2 x^2+15 b B e^3 x^3\right)}{105 e^3}","-\frac{2 (d+e x)^{5/2} (-a B e-A b e+2 b B d)}{5 e^3}+\frac{2 (d+e x)^{3/2} (b d-a e) (B d-A e)}{3 e^3}+\frac{2 b B (d+e x)^{7/2}}{7 e^3}",1,"(2*Sqrt[d + e*x]*(8*b*B*d^3 - 14*A*b*d^2*e - 14*a*B*d^2*e + 35*a*A*d*e^2 - 4*b*B*d^2*e*x + 7*A*b*d*e^2*x + 7*a*B*d*e^2*x + 35*a*A*e^3*x + 3*b*B*d*e^2*x^2 + 21*A*b*e^3*x^2 + 21*a*B*e^3*x^2 + 15*b*B*e^3*x^3))/(105*e^3)","A",1
1722,1,76,81,0.0433658,"\int \frac{(a+b x) (A+B x)}{\sqrt{d+e x}} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(15 a A e^2-10 a B d e+5 a B e^2 x-10 A b d e+5 A b e^2 x+8 b B d^2-4 b B d e x+3 b B e^2 x^2\right)}{15 e^3}","-\frac{2 (d+e x)^{3/2} (-a B e-A b e+2 b B d)}{3 e^3}+\frac{2 \sqrt{d+e x} (b d-a e) (B d-A e)}{e^3}+\frac{2 b B (d+e x)^{5/2}}{5 e^3}",1,"(2*Sqrt[d + e*x]*(8*b*B*d^2 - 10*A*b*d*e - 10*a*B*d*e + 15*a*A*e^2 - 4*b*B*d*e*x + 5*A*b*e^2*x + 5*a*B*e^2*x + 3*b*B*e^2*x^2))/(15*e^3)","A",1
1723,1,76,79,0.0454078,"\int \frac{(a+b x) (A+B x)}{(d+e x)^{3/2}} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/(d + e*x)^(3/2),x]","-\frac{2 \left(3 a A e^2-6 a B d e-3 a B e^2 x-6 A b d e-3 A b e^2 x+8 b B d^2+4 b B d e x-b B e^2 x^2\right)}{3 e^3 \sqrt{d+e x}}","-\frac{2 \sqrt{d+e x} (-a B e-A b e+2 b B d)}{e^3}-\frac{2 (b d-a e) (B d-A e)}{e^3 \sqrt{d+e x}}+\frac{2 b B (d+e x)^{3/2}}{3 e^3}",1,"(-2*(8*b*B*d^2 - 6*A*b*d*e - 6*a*B*d*e + 3*a*A*e^2 + 4*b*B*d*e*x - 3*A*b*e^2*x - 3*a*B*e^2*x - b*B*e^2*x^2))/(3*e^3*Sqrt[d + e*x])","A",1
1724,1,76,79,0.0505167,"\int \frac{(a+b x) (A+B x)}{(d+e x)^{5/2}} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/(d + e*x)^(5/2),x]","\frac{2 \left(-a A e^2-2 a B d e-3 a B e^2 x-2 A b d e-3 A b e^2 x+8 b B d^2+12 b B d e x+3 b B e^2 x^2\right)}{3 e^3 (d+e x)^{3/2}}","\frac{2 (-a B e-A b e+2 b B d)}{e^3 \sqrt{d+e x}}-\frac{2 (b d-a e) (B d-A e)}{3 e^3 (d+e x)^{3/2}}+\frac{2 b B \sqrt{d+e x}}{e^3}",1,"(2*(8*b*B*d^2 - 2*A*b*d*e - 2*a*B*d*e - a*A*e^2 + 12*b*B*d*e*x - 3*A*b*e^2*x - 3*a*B*e^2*x + 3*b*B*e^2*x^2))/(3*e^3*(d + e*x)^(3/2))","A",1
1725,1,76,81,0.0476553,"\int \frac{(a+b x) (A+B x)}{(d+e x)^{7/2}} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/(d + e*x)^(7/2),x]","-\frac{2 \left(3 a A e^2+2 a B d e+5 a B e^2 x+2 A b d e+5 A b e^2 x+8 b B d^2+20 b B d e x+15 b B e^2 x^2\right)}{15 e^3 (d+e x)^{5/2}}","\frac{2 (-a B e-A b e+2 b B d)}{3 e^3 (d+e x)^{3/2}}-\frac{2 (b d-a e) (B d-A e)}{5 e^3 (d+e x)^{5/2}}-\frac{2 b B}{e^3 \sqrt{d+e x}}",1,"(-2*(8*b*B*d^2 + 2*A*b*d*e + 2*a*B*d*e + 3*a*A*e^2 + 20*b*B*d*e*x + 5*A*b*e^2*x + 5*a*B*e^2*x + 15*b*B*e^2*x^2))/(15*e^3*(d + e*x)^(5/2))","A",1
1726,1,520,128,0.0882503,"\int (a+b x)^2 (A+B x) (d+e x)^{7/2} \, dx","IntegrateAlgebraic[(a + b*x)^2*(A + B*x)*(d + e*x)^(7/2),x]","-\frac{2 \sqrt{d+e x} \left(-715 a^2 A d^4 e^3-2860 a^2 A d^3 e^4 x-4290 a^2 A d^2 e^5 x^2-2860 a^2 A d e^6 x^3-715 a^2 A e^7 x^4+130 a^2 B d^5 e^2-65 a^2 B d^4 e^3 x-1560 a^2 B d^3 e^4 x^2-2990 a^2 B d^2 e^5 x^3-2210 a^2 B d e^6 x^4-585 a^2 B e^7 x^5+260 a A b d^5 e^2-130 a A b d^4 e^3 x-3120 a A b d^3 e^4 x^2-5980 a A b d^2 e^5 x^3-4420 a A b d e^6 x^4-1170 a A b e^7 x^5-80 a b B d^6 e+40 a b B d^5 e^2 x-30 a b B d^4 e^3 x^2-2120 a b B d^3 e^4 x^3-4580 a b B d^2 e^5 x^4-3600 a b B d e^6 x^5-990 a b B e^7 x^6-40 A b^2 d^6 e+20 A b^2 d^5 e^2 x-15 A b^2 d^4 e^3 x^2-1060 A b^2 d^3 e^4 x^3-2290 A b^2 d^2 e^5 x^4-1800 A b^2 d e^6 x^5-495 A b^2 e^7 x^6+16 b^2 B d^7-8 b^2 B d^6 e x+6 b^2 B d^5 e^2 x^2-5 b^2 B d^4 e^3 x^3-800 b^2 B d^3 e^4 x^4-1854 b^2 B d^2 e^5 x^5-1518 b^2 B d e^6 x^6-429 b^2 B e^7 x^7\right)}{6435 e^4}","-\frac{2 b (d+e x)^{13/2} (-2 a B e-A b e+3 b B d)}{13 e^4}+\frac{2 (d+e x)^{11/2} (b d-a e) (-a B e-2 A b e+3 b B d)}{11 e^4}-\frac{2 (d+e x)^{9/2} (b d-a e)^2 (B d-A e)}{9 e^4}+\frac{2 b^2 B (d+e x)^{15/2}}{15 e^4}",1,"(-2*Sqrt[d + e*x]*(16*b^2*B*d^7 - 40*A*b^2*d^6*e - 80*a*b*B*d^6*e + 260*a*A*b*d^5*e^2 + 130*a^2*B*d^5*e^2 - 715*a^2*A*d^4*e^3 - 8*b^2*B*d^6*e*x + 20*A*b^2*d^5*e^2*x + 40*a*b*B*d^5*e^2*x - 130*a*A*b*d^4*e^3*x - 65*a^2*B*d^4*e^3*x - 2860*a^2*A*d^3*e^4*x + 6*b^2*B*d^5*e^2*x^2 - 15*A*b^2*d^4*e^3*x^2 - 30*a*b*B*d^4*e^3*x^2 - 3120*a*A*b*d^3*e^4*x^2 - 1560*a^2*B*d^3*e^4*x^2 - 4290*a^2*A*d^2*e^5*x^2 - 5*b^2*B*d^4*e^3*x^3 - 1060*A*b^2*d^3*e^4*x^3 - 2120*a*b*B*d^3*e^4*x^3 - 5980*a*A*b*d^2*e^5*x^3 - 2990*a^2*B*d^2*e^5*x^3 - 2860*a^2*A*d*e^6*x^3 - 800*b^2*B*d^3*e^4*x^4 - 2290*A*b^2*d^2*e^5*x^4 - 4580*a*b*B*d^2*e^5*x^4 - 4420*a*A*b*d*e^6*x^4 - 2210*a^2*B*d*e^6*x^4 - 715*a^2*A*e^7*x^4 - 1854*b^2*B*d^2*e^5*x^5 - 1800*A*b^2*d*e^6*x^5 - 3600*a*b*B*d*e^6*x^5 - 1170*a*A*b*e^7*x^5 - 585*a^2*B*e^7*x^5 - 1518*b^2*B*d*e^6*x^6 - 495*A*b^2*e^7*x^6 - 990*a*b*B*e^7*x^6 - 429*b^2*B*e^7*x^7))/(6435*e^4)","B",1
1727,1,432,128,0.0760506,"\int (a+b x)^2 (A+B x) (d+e x)^{5/2} \, dx","IntegrateAlgebraic[(a + b*x)^2*(A + B*x)*(d + e*x)^(5/2),x]","-\frac{2 \sqrt{d+e x} \left(-1287 a^2 A d^3 e^3-3861 a^2 A d^2 e^4 x-3861 a^2 A d e^5 x^2-1287 a^2 A e^6 x^3+286 a^2 B d^4 e^2-143 a^2 B d^3 e^3 x-2145 a^2 B d^2 e^4 x^2-2717 a^2 B d e^5 x^3-1001 a^2 B e^6 x^4+572 a A b d^4 e^2-286 a A b d^3 e^3 x-4290 a A b d^2 e^4 x^2-5434 a A b d e^5 x^3-2002 a A b e^6 x^4-208 a b B d^5 e+104 a b B d^4 e^2 x-78 a b B d^3 e^3 x^2-2938 a b B d^2 e^4 x^3-4186 a b B d e^5 x^4-1638 a b B e^6 x^5-104 A b^2 d^5 e+52 A b^2 d^4 e^2 x-39 A b^2 d^3 e^3 x^2-1469 A b^2 d^2 e^4 x^3-2093 A b^2 d e^5 x^4-819 A b^2 e^6 x^5+48 b^2 B d^6-24 b^2 B d^5 e x+18 b^2 B d^4 e^2 x^2-15 b^2 B d^3 e^3 x^3-1113 b^2 B d^2 e^4 x^4-1701 b^2 B d e^5 x^5-693 b^2 B e^6 x^6\right)}{9009 e^4}","-\frac{2 b (d+e x)^{11/2} (-2 a B e-A b e+3 b B d)}{11 e^4}+\frac{2 (d+e x)^{9/2} (b d-a e) (-a B e-2 A b e+3 b B d)}{9 e^4}-\frac{2 (d+e x)^{7/2} (b d-a e)^2 (B d-A e)}{7 e^4}+\frac{2 b^2 B (d+e x)^{13/2}}{13 e^4}",1,"(-2*Sqrt[d + e*x]*(48*b^2*B*d^6 - 104*A*b^2*d^5*e - 208*a*b*B*d^5*e + 572*a*A*b*d^4*e^2 + 286*a^2*B*d^4*e^2 - 1287*a^2*A*d^3*e^3 - 24*b^2*B*d^5*e*x + 52*A*b^2*d^4*e^2*x + 104*a*b*B*d^4*e^2*x - 286*a*A*b*d^3*e^3*x - 143*a^2*B*d^3*e^3*x - 3861*a^2*A*d^2*e^4*x + 18*b^2*B*d^4*e^2*x^2 - 39*A*b^2*d^3*e^3*x^2 - 78*a*b*B*d^3*e^3*x^2 - 4290*a*A*b*d^2*e^4*x^2 - 2145*a^2*B*d^2*e^4*x^2 - 3861*a^2*A*d*e^5*x^2 - 15*b^2*B*d^3*e^3*x^3 - 1469*A*b^2*d^2*e^4*x^3 - 2938*a*b*B*d^2*e^4*x^3 - 5434*a*A*b*d*e^5*x^3 - 2717*a^2*B*d*e^5*x^3 - 1287*a^2*A*e^6*x^3 - 1113*b^2*B*d^2*e^4*x^4 - 2093*A*b^2*d*e^5*x^4 - 4186*a*b*B*d*e^5*x^4 - 2002*a*A*b*e^6*x^4 - 1001*a^2*B*e^6*x^4 - 1701*b^2*B*d*e^5*x^5 - 819*A*b^2*e^6*x^5 - 1638*a*b*B*e^6*x^5 - 693*b^2*B*e^6*x^6))/(9009*e^4)","B",1
1728,1,344,128,0.0667678,"\int (a+b x)^2 (A+B x) (d+e x)^{3/2} \, dx","IntegrateAlgebraic[(a + b*x)^2*(A + B*x)*(d + e*x)^(3/2),x]","-\frac{2 \sqrt{d+e x} \left(-693 a^2 A d^2 e^3-1386 a^2 A d e^4 x-693 a^2 A e^5 x^2+198 a^2 B d^3 e^2-99 a^2 B d^2 e^3 x-792 a^2 B d e^4 x^2-495 a^2 B e^5 x^3+396 a A b d^3 e^2-198 a A b d^2 e^3 x-1584 a A b d e^4 x^2-990 a A b e^5 x^3-176 a b B d^4 e+88 a b B d^3 e^2 x-66 a b B d^2 e^3 x^2-1100 a b B d e^4 x^3-770 a b B e^5 x^4-88 A b^2 d^4 e+44 A b^2 d^3 e^2 x-33 A b^2 d^2 e^3 x^2-550 A b^2 d e^4 x^3-385 A b^2 e^5 x^4+48 b^2 B d^5-24 b^2 B d^4 e x+18 b^2 B d^3 e^2 x^2-15 b^2 B d^2 e^3 x^3-420 b^2 B d e^4 x^4-315 b^2 B e^5 x^5\right)}{3465 e^4}","-\frac{2 b (d+e x)^{9/2} (-2 a B e-A b e+3 b B d)}{9 e^4}+\frac{2 (d+e x)^{7/2} (b d-a e) (-a B e-2 A b e+3 b B d)}{7 e^4}-\frac{2 (d+e x)^{5/2} (b d-a e)^2 (B d-A e)}{5 e^4}+\frac{2 b^2 B (d+e x)^{11/2}}{11 e^4}",1,"(-2*Sqrt[d + e*x]*(48*b^2*B*d^5 - 88*A*b^2*d^4*e - 176*a*b*B*d^4*e + 396*a*A*b*d^3*e^2 + 198*a^2*B*d^3*e^2 - 693*a^2*A*d^2*e^3 - 24*b^2*B*d^4*e*x + 44*A*b^2*d^3*e^2*x + 88*a*b*B*d^3*e^2*x - 198*a*A*b*d^2*e^3*x - 99*a^2*B*d^2*e^3*x - 1386*a^2*A*d*e^4*x + 18*b^2*B*d^3*e^2*x^2 - 33*A*b^2*d^2*e^3*x^2 - 66*a*b*B*d^2*e^3*x^2 - 1584*a*A*b*d*e^4*x^2 - 792*a^2*B*d*e^4*x^2 - 693*a^2*A*e^5*x^2 - 15*b^2*B*d^2*e^3*x^3 - 550*A*b^2*d*e^4*x^3 - 1100*a*b*B*d*e^4*x^3 - 990*a*A*b*e^5*x^3 - 495*a^2*B*e^5*x^3 - 420*b^2*B*d*e^4*x^4 - 385*A*b^2*e^5*x^4 - 770*a*b*B*e^5*x^4 - 315*b^2*B*e^5*x^5))/(3465*e^4)","B",1
1729,1,256,128,0.0619911,"\int (a+b x)^2 (A+B x) \sqrt{d+e x} \, dx","IntegrateAlgebraic[(a + b*x)^2*(A + B*x)*Sqrt[d + e*x],x]","-\frac{2 \sqrt{d+e x} \left(-105 a^2 A d e^3-105 a^2 A e^4 x+42 a^2 B d^2 e^2-21 a^2 B d e^3 x-63 a^2 B e^4 x^2+84 a A b d^2 e^2-42 a A b d e^3 x-126 a A b e^4 x^2-48 a b B d^3 e+24 a b B d^2 e^2 x-18 a b B d e^3 x^2-90 a b B e^4 x^3-24 A b^2 d^3 e+12 A b^2 d^2 e^2 x-9 A b^2 d e^3 x^2-45 A b^2 e^4 x^3+16 b^2 B d^4-8 b^2 B d^3 e x+6 b^2 B d^2 e^2 x^2-5 b^2 B d e^3 x^3-35 b^2 B e^4 x^4\right)}{315 e^4}","-\frac{2 b (d+e x)^{7/2} (-2 a B e-A b e+3 b B d)}{7 e^4}+\frac{2 (d+e x)^{5/2} (b d-a e) (-a B e-2 A b e+3 b B d)}{5 e^4}-\frac{2 (d+e x)^{3/2} (b d-a e)^2 (B d-A e)}{3 e^4}+\frac{2 b^2 B (d+e x)^{9/2}}{9 e^4}",1,"(-2*Sqrt[d + e*x]*(16*b^2*B*d^4 - 24*A*b^2*d^3*e - 48*a*b*B*d^3*e + 84*a*A*b*d^2*e^2 + 42*a^2*B*d^2*e^2 - 105*a^2*A*d*e^3 - 8*b^2*B*d^3*e*x + 12*A*b^2*d^2*e^2*x + 24*a*b*B*d^2*e^2*x - 42*a*A*b*d*e^3*x - 21*a^2*B*d*e^3*x - 105*a^2*A*e^4*x + 6*b^2*B*d^2*e^2*x^2 - 9*A*b^2*d*e^3*x^2 - 18*a*b*B*d*e^3*x^2 - 126*a*A*b*e^4*x^2 - 63*a^2*B*e^4*x^2 - 5*b^2*B*d*e^3*x^3 - 45*A*b^2*e^4*x^3 - 90*a*b*B*e^4*x^3 - 35*b^2*B*e^4*x^4))/(315*e^4)","A",1
1730,1,172,126,0.0823292,"\int \frac{(a+b x)^2 (A+B x)}{\sqrt{d+e x}} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/Sqrt[d + e*x],x]","-\frac{2 \sqrt{d+e x} \left(-105 a^2 A e^3+70 a^2 B d e^2-35 a^2 B e^3 x+140 a A b d e^2-70 a A b e^3 x-112 a b B d^2 e+56 a b B d e^2 x-42 a b B e^3 x^2-56 A b^2 d^2 e+28 A b^2 d e^2 x-21 A b^2 e^3 x^2+48 b^2 B d^3-24 b^2 B d^2 e x+18 b^2 B d e^2 x^2-15 b^2 B e^3 x^3\right)}{105 e^4}","-\frac{2 b (d+e x)^{5/2} (-2 a B e-A b e+3 b B d)}{5 e^4}+\frac{2 (d+e x)^{3/2} (b d-a e) (-a B e-2 A b e+3 b B d)}{3 e^4}-\frac{2 \sqrt{d+e x} (b d-a e)^2 (B d-A e)}{e^4}+\frac{2 b^2 B (d+e x)^{7/2}}{7 e^4}",1,"(-2*Sqrt[d + e*x]*(48*b^2*B*d^3 - 56*A*b^2*d^2*e - 112*a*b*B*d^2*e + 140*a*A*b*d*e^2 + 70*a^2*B*d*e^2 - 105*a^2*A*e^3 - 24*b^2*B*d^2*e*x + 28*A*b^2*d*e^2*x + 56*a*b*B*d*e^2*x - 70*a*A*b*e^3*x - 35*a^2*B*e^3*x + 18*b^2*B*d*e^2*x^2 - 21*A*b^2*e^3*x^2 - 42*a*b*B*e^3*x^2 - 15*b^2*B*e^3*x^3))/(105*e^4)","A",1
1731,1,172,124,0.0777869,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^{3/2}} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/(d + e*x)^(3/2),x]","\frac{2 \left(-15 a^2 A e^3+30 a^2 B d e^2+15 a^2 B e^3 x+60 a A b d e^2+30 a A b e^3 x-80 a b B d^2 e-40 a b B d e^2 x+10 a b B e^3 x^2-40 A b^2 d^2 e-20 A b^2 d e^2 x+5 A b^2 e^3 x^2+48 b^2 B d^3+24 b^2 B d^2 e x-6 b^2 B d e^2 x^2+3 b^2 B e^3 x^3\right)}{15 e^4 \sqrt{d+e x}}","-\frac{2 b (d+e x)^{3/2} (-2 a B e-A b e+3 b B d)}{3 e^4}+\frac{2 \sqrt{d+e x} (b d-a e) (-a B e-2 A b e+3 b B d)}{e^4}+\frac{2 (b d-a e)^2 (B d-A e)}{e^4 \sqrt{d+e x}}+\frac{2 b^2 B (d+e x)^{5/2}}{5 e^4}",1,"(2*(48*b^2*B*d^3 - 40*A*b^2*d^2*e - 80*a*b*B*d^2*e + 60*a*A*b*d*e^2 + 30*a^2*B*d*e^2 - 15*a^2*A*e^3 + 24*b^2*B*d^2*e*x - 20*A*b^2*d*e^2*x - 40*a*b*B*d*e^2*x + 30*a*A*b*e^3*x + 15*a^2*B*e^3*x - 6*b^2*B*d*e^2*x^2 + 5*A*b^2*e^3*x^2 + 10*a*b*B*e^3*x^2 + 3*b^2*B*e^3*x^3))/(15*e^4*Sqrt[d + e*x])","A",1
1732,1,171,124,0.082275,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^{5/2}} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/(d + e*x)^(5/2),x]","-\frac{2 \left(a^2 A e^3+2 a^2 B d e^2+3 a^2 B e^3 x+4 a A b d e^2+6 a A b e^3 x-16 a b B d^2 e-24 a b B d e^2 x-6 a b B e^3 x^2-8 A b^2 d^2 e-12 A b^2 d e^2 x-3 A b^2 e^3 x^2+16 b^2 B d^3+24 b^2 B d^2 e x+6 b^2 B d e^2 x^2-b^2 B e^3 x^3\right)}{3 e^4 (d+e x)^{3/2}}","-\frac{2 b \sqrt{d+e x} (-2 a B e-A b e+3 b B d)}{e^4}-\frac{2 (b d-a e) (-a B e-2 A b e+3 b B d)}{e^4 \sqrt{d+e x}}+\frac{2 (b d-a e)^2 (B d-A e)}{3 e^4 (d+e x)^{3/2}}+\frac{2 b^2 B (d+e x)^{3/2}}{3 e^4}",1,"(-2*(16*b^2*B*d^3 - 8*A*b^2*d^2*e - 16*a*b*B*d^2*e + 4*a*A*b*d*e^2 + 2*a^2*B*d*e^2 + a^2*A*e^3 + 24*b^2*B*d^2*e*x - 12*A*b^2*d*e^2*x - 24*a*b*B*d*e^2*x + 6*a*A*b*e^3*x + 3*a^2*B*e^3*x + 6*b^2*B*d*e^2*x^2 - 3*A*b^2*e^3*x^2 - 6*a*b*B*e^3*x^2 - b^2*B*e^3*x^3))/(3*e^4*(d + e*x)^(3/2))","A",1
1733,1,172,124,0.0864285,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^{7/2}} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/(d + e*x)^(7/2),x]","\frac{2 \left(-3 a^2 A e^3-2 a^2 B d e^2-5 a^2 B e^3 x-4 a A b d e^2-10 a A b e^3 x-16 a b B d^2 e-40 a b B d e^2 x-30 a b B e^3 x^2-8 A b^2 d^2 e-20 A b^2 d e^2 x-15 A b^2 e^3 x^2+48 b^2 B d^3+120 b^2 B d^2 e x+90 b^2 B d e^2 x^2+15 b^2 B e^3 x^3\right)}{15 e^4 (d+e x)^{5/2}}","\frac{2 b (-2 a B e-A b e+3 b B d)}{e^4 \sqrt{d+e x}}-\frac{2 (b d-a e) (-a B e-2 A b e+3 b B d)}{3 e^4 (d+e x)^{3/2}}+\frac{2 (b d-a e)^2 (B d-A e)}{5 e^4 (d+e x)^{5/2}}+\frac{2 b^2 B \sqrt{d+e x}}{e^4}",1,"(2*(48*b^2*B*d^3 - 8*A*b^2*d^2*e - 16*a*b*B*d^2*e - 4*a*A*b*d*e^2 - 2*a^2*B*d*e^2 - 3*a^2*A*e^3 + 120*b^2*B*d^2*e*x - 20*A*b^2*d*e^2*x - 40*a*b*B*d*e^2*x - 10*a*A*b*e^3*x - 5*a^2*B*e^3*x + 90*b^2*B*d*e^2*x^2 - 15*A*b^2*e^3*x^2 - 30*a*b*B*e^3*x^2 + 15*b^2*B*e^3*x^3))/(15*e^4*(d + e*x)^(5/2))","A",1
1734,1,796,173,0.1244781,"\int (a+b x)^3 (A+B x) (d+e x)^{7/2} \, dx","IntegrateAlgebraic[(a + b*x)^3*(A + B*x)*(d + e*x)^(7/2),x]","\frac{2 \sqrt{d+e x} \left(128 b^3 B d^8-272 A b^3 e d^7-816 a b^2 B e d^7-64 b^3 B e x d^7+2040 a A b^2 e^2 d^6+2040 a^2 b B e^2 d^6+48 b^3 B e^2 x^2 d^6+136 A b^3 e^2 x d^6+408 a b^2 B e^2 x d^6-6630 a^2 A b e^3 d^5-2210 a^3 B e^3 d^5-40 b^3 B e^3 x^3 d^5-102 A b^3 e^3 x^2 d^5-306 a b^2 B e^3 x^2 d^5-1020 a A b^2 e^3 x d^5-1020 a^2 b B e^3 x d^5+12155 a^3 A e^4 d^4+35 b^3 B e^4 x^4 d^4+85 A b^3 e^4 x^3 d^4+255 a b^2 B e^4 x^3 d^4+765 a A b^2 e^4 x^2 d^4+765 a^2 b B e^4 x^2 d^4+3315 a^2 A b e^4 x d^4+1105 a^3 B e^4 x d^4+10908 b^3 B e^5 x^5 d^3+13600 A b^3 e^5 x^4 d^3+40800 a b^2 B e^5 x^4 d^3+54060 a A b^2 e^5 x^3 d^3+54060 a^2 b B e^5 x^3 d^3+79560 a^2 A b e^5 x^2 d^3+26520 a^3 B e^5 x^2 d^3+48620 a^3 A e^5 x d^3+26466 b^3 B e^6 x^6 d^2+31518 A b^3 e^6 x^5 d^2+94554 a b^2 B e^6 x^5 d^2+116790 a A b^2 e^6 x^4 d^2+116790 a^2 b B e^6 x^4 d^2+152490 a^2 A b e^6 x^3 d^2+50830 a^3 B e^6 x^3 d^2+72930 a^3 A e^6 x^2 d^2+22308 b^3 B e^7 x^7 d+25806 A b^3 e^7 x^6 d+77418 a b^2 B e^7 x^6 d+91800 a A b^2 e^7 x^5 d+91800 a^2 b B e^7 x^5 d+112710 a^2 A b e^7 x^4 d+37570 a^3 B e^7 x^4 d+48620 a^3 A e^7 x^3 d+6435 b^3 B e^8 x^8+7293 A b^3 e^8 x^7+21879 a b^2 B e^8 x^7+25245 a A b^2 e^8 x^6+25245 a^2 b B e^8 x^6+29835 a^2 A b e^8 x^5+9945 a^3 B e^8 x^5+12155 a^3 A e^8 x^4\right)}{109395 e^5}","-\frac{2 b^2 (d+e x)^{15/2} (-3 a B e-A b e+4 b B d)}{15 e^5}+\frac{6 b (d+e x)^{13/2} (b d-a e) (-a B e-A b e+2 b B d)}{13 e^5}-\frac{2 (d+e x)^{11/2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{11 e^5}+\frac{2 (d+e x)^{9/2} (b d-a e)^3 (B d-A e)}{9 e^5}+\frac{2 b^3 B (d+e x)^{17/2}}{17 e^5}",1,"(2*Sqrt[d + e*x]*(128*b^3*B*d^8 - 272*A*b^3*d^7*e - 816*a*b^2*B*d^7*e + 2040*a*A*b^2*d^6*e^2 + 2040*a^2*b*B*d^6*e^2 - 6630*a^2*A*b*d^5*e^3 - 2210*a^3*B*d^5*e^3 + 12155*a^3*A*d^4*e^4 - 64*b^3*B*d^7*e*x + 136*A*b^3*d^6*e^2*x + 408*a*b^2*B*d^6*e^2*x - 1020*a*A*b^2*d^5*e^3*x - 1020*a^2*b*B*d^5*e^3*x + 3315*a^2*A*b*d^4*e^4*x + 1105*a^3*B*d^4*e^4*x + 48620*a^3*A*d^3*e^5*x + 48*b^3*B*d^6*e^2*x^2 - 102*A*b^3*d^5*e^3*x^2 - 306*a*b^2*B*d^5*e^3*x^2 + 765*a*A*b^2*d^4*e^4*x^2 + 765*a^2*b*B*d^4*e^4*x^2 + 79560*a^2*A*b*d^3*e^5*x^2 + 26520*a^3*B*d^3*e^5*x^2 + 72930*a^3*A*d^2*e^6*x^2 - 40*b^3*B*d^5*e^3*x^3 + 85*A*b^3*d^4*e^4*x^3 + 255*a*b^2*B*d^4*e^4*x^3 + 54060*a*A*b^2*d^3*e^5*x^3 + 54060*a^2*b*B*d^3*e^5*x^3 + 152490*a^2*A*b*d^2*e^6*x^3 + 50830*a^3*B*d^2*e^6*x^3 + 48620*a^3*A*d*e^7*x^3 + 35*b^3*B*d^4*e^4*x^4 + 13600*A*b^3*d^3*e^5*x^4 + 40800*a*b^2*B*d^3*e^5*x^4 + 116790*a*A*b^2*d^2*e^6*x^4 + 116790*a^2*b*B*d^2*e^6*x^4 + 112710*a^2*A*b*d*e^7*x^4 + 37570*a^3*B*d*e^7*x^4 + 12155*a^3*A*e^8*x^4 + 10908*b^3*B*d^3*e^5*x^5 + 31518*A*b^3*d^2*e^6*x^5 + 94554*a*b^2*B*d^2*e^6*x^5 + 91800*a*A*b^2*d*e^7*x^5 + 91800*a^2*b*B*d*e^7*x^5 + 29835*a^2*A*b*e^8*x^5 + 9945*a^3*B*e^8*x^5 + 26466*b^3*B*d^2*e^6*x^6 + 25806*A*b^3*d*e^7*x^6 + 77418*a*b^2*B*d*e^7*x^6 + 25245*a*A*b^2*e^8*x^6 + 25245*a^2*b*B*e^8*x^6 + 22308*b^3*B*d*e^7*x^7 + 7293*A*b^3*e^8*x^7 + 21879*a*b^2*B*e^8*x^7 + 6435*b^3*B*e^8*x^8))/(109395*e^5)","B",1
1735,1,672,173,0.107302,"\int (a+b x)^3 (A+B x) (d+e x)^{5/2} \, dx","IntegrateAlgebraic[(a + b*x)^3*(A + B*x)*(d + e*x)^(5/2),x]","\frac{2 \sqrt{d+e x} \left(6435 a^3 A d^3 e^4+19305 a^3 A d^2 e^5 x+19305 a^3 A d e^6 x^2+6435 a^3 A e^7 x^3-1430 a^3 B d^4 e^3+715 a^3 B d^3 e^4 x+10725 a^3 B d^2 e^5 x^2+13585 a^3 B d e^6 x^3+5005 a^3 B e^7 x^4-4290 a^2 A b d^4 e^3+2145 a^2 A b d^3 e^4 x+32175 a^2 A b d^2 e^5 x^2+40755 a^2 A b d e^6 x^3+15015 a^2 A b e^7 x^4+1560 a^2 b B d^5 e^2-780 a^2 b B d^4 e^3 x+585 a^2 b B d^3 e^4 x^2+22035 a^2 b B d^2 e^5 x^3+31395 a^2 b B d e^6 x^4+12285 a^2 b B e^7 x^5+1560 a A b^2 d^5 e^2-780 a A b^2 d^4 e^3 x+585 a A b^2 d^3 e^4 x^2+22035 a A b^2 d^2 e^5 x^3+31395 a A b^2 d e^6 x^4+12285 a A b^2 e^7 x^5-720 a b^2 B d^6 e+360 a b^2 B d^5 e^2 x-270 a b^2 B d^4 e^3 x^2+225 a b^2 B d^3 e^4 x^3+16695 a b^2 B d^2 e^5 x^4+25515 a b^2 B d e^6 x^5+10395 a b^2 B e^7 x^6-240 A b^3 d^6 e+120 A b^3 d^5 e^2 x-90 A b^3 d^4 e^3 x^2+75 A b^3 d^3 e^4 x^3+5565 A b^3 d^2 e^5 x^4+8505 A b^3 d e^6 x^5+3465 A b^3 e^7 x^6+128 b^3 B d^7-64 b^3 B d^6 e x+48 b^3 B d^5 e^2 x^2-40 b^3 B d^4 e^3 x^3+35 b^3 B d^3 e^4 x^4+4473 b^3 B d^2 e^5 x^5+7161 b^3 B d e^6 x^6+3003 b^3 B e^7 x^7\right)}{45045 e^5}","-\frac{2 b^2 (d+e x)^{13/2} (-3 a B e-A b e+4 b B d)}{13 e^5}+\frac{6 b (d+e x)^{11/2} (b d-a e) (-a B e-A b e+2 b B d)}{11 e^5}-\frac{2 (d+e x)^{9/2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{9 e^5}+\frac{2 (d+e x)^{7/2} (b d-a e)^3 (B d-A e)}{7 e^5}+\frac{2 b^3 B (d+e x)^{15/2}}{15 e^5}",1,"(2*Sqrt[d + e*x]*(128*b^3*B*d^7 - 240*A*b^3*d^6*e - 720*a*b^2*B*d^6*e + 1560*a*A*b^2*d^5*e^2 + 1560*a^2*b*B*d^5*e^2 - 4290*a^2*A*b*d^4*e^3 - 1430*a^3*B*d^4*e^3 + 6435*a^3*A*d^3*e^4 - 64*b^3*B*d^6*e*x + 120*A*b^3*d^5*e^2*x + 360*a*b^2*B*d^5*e^2*x - 780*a*A*b^2*d^4*e^3*x - 780*a^2*b*B*d^4*e^3*x + 2145*a^2*A*b*d^3*e^4*x + 715*a^3*B*d^3*e^4*x + 19305*a^3*A*d^2*e^5*x + 48*b^3*B*d^5*e^2*x^2 - 90*A*b^3*d^4*e^3*x^2 - 270*a*b^2*B*d^4*e^3*x^2 + 585*a*A*b^2*d^3*e^4*x^2 + 585*a^2*b*B*d^3*e^4*x^2 + 32175*a^2*A*b*d^2*e^5*x^2 + 10725*a^3*B*d^2*e^5*x^2 + 19305*a^3*A*d*e^6*x^2 - 40*b^3*B*d^4*e^3*x^3 + 75*A*b^3*d^3*e^4*x^3 + 225*a*b^2*B*d^3*e^4*x^3 + 22035*a*A*b^2*d^2*e^5*x^3 + 22035*a^2*b*B*d^2*e^5*x^3 + 40755*a^2*A*b*d*e^6*x^3 + 13585*a^3*B*d*e^6*x^3 + 6435*a^3*A*e^7*x^3 + 35*b^3*B*d^3*e^4*x^4 + 5565*A*b^3*d^2*e^5*x^4 + 16695*a*b^2*B*d^2*e^5*x^4 + 31395*a*A*b^2*d*e^6*x^4 + 31395*a^2*b*B*d*e^6*x^4 + 15015*a^2*A*b*e^7*x^4 + 5005*a^3*B*e^7*x^4 + 4473*b^3*B*d^2*e^5*x^5 + 8505*A*b^3*d*e^6*x^5 + 25515*a*b^2*B*d*e^6*x^5 + 12285*a*A*b^2*e^7*x^5 + 12285*a^2*b*B*e^7*x^5 + 7161*b^3*B*d*e^6*x^6 + 3465*A*b^3*e^7*x^6 + 10395*a*b^2*B*e^7*x^6 + 3003*b^3*B*e^7*x^7))/(45045*e^5)","B",1
1736,1,548,173,0.0996647,"\int (a+b x)^3 (A+B x) (d+e x)^{3/2} \, dx","IntegrateAlgebraic[(a + b*x)^3*(A + B*x)*(d + e*x)^(3/2),x]","\frac{2 \sqrt{d+e x} \left(3003 a^3 A d^2 e^4+6006 a^3 A d e^5 x+3003 a^3 A e^6 x^2-858 a^3 B d^3 e^3+429 a^3 B d^2 e^4 x+3432 a^3 B d e^5 x^2+2145 a^3 B e^6 x^3-2574 a^2 A b d^3 e^3+1287 a^2 A b d^2 e^4 x+10296 a^2 A b d e^5 x^2+6435 a^2 A b e^6 x^3+1144 a^2 b B d^4 e^2-572 a^2 b B d^3 e^3 x+429 a^2 b B d^2 e^4 x^2+7150 a^2 b B d e^5 x^3+5005 a^2 b B e^6 x^4+1144 a A b^2 d^4 e^2-572 a A b^2 d^3 e^3 x+429 a A b^2 d^2 e^4 x^2+7150 a A b^2 d e^5 x^3+5005 a A b^2 e^6 x^4-624 a b^2 B d^5 e+312 a b^2 B d^4 e^2 x-234 a b^2 B d^3 e^3 x^2+195 a b^2 B d^2 e^4 x^3+5460 a b^2 B d e^5 x^4+4095 a b^2 B e^6 x^5-208 A b^3 d^5 e+104 A b^3 d^4 e^2 x-78 A b^3 d^3 e^3 x^2+65 A b^3 d^2 e^4 x^3+1820 A b^3 d e^5 x^4+1365 A b^3 e^6 x^5+128 b^3 B d^6-64 b^3 B d^5 e x+48 b^3 B d^4 e^2 x^2-40 b^3 B d^3 e^3 x^3+35 b^3 B d^2 e^4 x^4+1470 b^3 B d e^5 x^5+1155 b^3 B e^6 x^6\right)}{15015 e^5}","-\frac{2 b^2 (d+e x)^{11/2} (-3 a B e-A b e+4 b B d)}{11 e^5}+\frac{2 b (d+e x)^{9/2} (b d-a e) (-a B e-A b e+2 b B d)}{3 e^5}-\frac{2 (d+e x)^{7/2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{7 e^5}+\frac{2 (d+e x)^{5/2} (b d-a e)^3 (B d-A e)}{5 e^5}+\frac{2 b^3 B (d+e x)^{13/2}}{13 e^5}",1,"(2*Sqrt[d + e*x]*(128*b^3*B*d^6 - 208*A*b^3*d^5*e - 624*a*b^2*B*d^5*e + 1144*a*A*b^2*d^4*e^2 + 1144*a^2*b*B*d^4*e^2 - 2574*a^2*A*b*d^3*e^3 - 858*a^3*B*d^3*e^3 + 3003*a^3*A*d^2*e^4 - 64*b^3*B*d^5*e*x + 104*A*b^3*d^4*e^2*x + 312*a*b^2*B*d^4*e^2*x - 572*a*A*b^2*d^3*e^3*x - 572*a^2*b*B*d^3*e^3*x + 1287*a^2*A*b*d^2*e^4*x + 429*a^3*B*d^2*e^4*x + 6006*a^3*A*d*e^5*x + 48*b^3*B*d^4*e^2*x^2 - 78*A*b^3*d^3*e^3*x^2 - 234*a*b^2*B*d^3*e^3*x^2 + 429*a*A*b^2*d^2*e^4*x^2 + 429*a^2*b*B*d^2*e^4*x^2 + 10296*a^2*A*b*d*e^5*x^2 + 3432*a^3*B*d*e^5*x^2 + 3003*a^3*A*e^6*x^2 - 40*b^3*B*d^3*e^3*x^3 + 65*A*b^3*d^2*e^4*x^3 + 195*a*b^2*B*d^2*e^4*x^3 + 7150*a*A*b^2*d*e^5*x^3 + 7150*a^2*b*B*d*e^5*x^3 + 6435*a^2*A*b*e^6*x^3 + 2145*a^3*B*e^6*x^3 + 35*b^3*B*d^2*e^4*x^4 + 1820*A*b^3*d*e^5*x^4 + 5460*a*b^2*B*d*e^5*x^4 + 5005*a*A*b^2*e^6*x^4 + 5005*a^2*b*B*e^6*x^4 + 1470*b^3*B*d*e^5*x^5 + 1365*A*b^3*e^6*x^5 + 4095*a*b^2*B*e^6*x^5 + 1155*b^3*B*e^6*x^6))/(15015*e^5)","B",1
1737,1,424,173,0.087171,"\int (a+b x)^3 (A+B x) \sqrt{d+e x} \, dx","IntegrateAlgebraic[(a + b*x)^3*(A + B*x)*Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(1155 a^3 A d e^4+1155 a^3 A e^5 x-462 a^3 B d^2 e^3+231 a^3 B d e^4 x+693 a^3 B e^5 x^2-1386 a^2 A b d^2 e^3+693 a^2 A b d e^4 x+2079 a^2 A b e^5 x^2+792 a^2 b B d^3 e^2-396 a^2 b B d^2 e^3 x+297 a^2 b B d e^4 x^2+1485 a^2 b B e^5 x^3+792 a A b^2 d^3 e^2-396 a A b^2 d^2 e^3 x+297 a A b^2 d e^4 x^2+1485 a A b^2 e^5 x^3-528 a b^2 B d^4 e+264 a b^2 B d^3 e^2 x-198 a b^2 B d^2 e^3 x^2+165 a b^2 B d e^4 x^3+1155 a b^2 B e^5 x^4-176 A b^3 d^4 e+88 A b^3 d^3 e^2 x-66 A b^3 d^2 e^3 x^2+55 A b^3 d e^4 x^3+385 A b^3 e^5 x^4+128 b^3 B d^5-64 b^3 B d^4 e x+48 b^3 B d^3 e^2 x^2-40 b^3 B d^2 e^3 x^3+35 b^3 B d e^4 x^4+315 b^3 B e^5 x^5\right)}{3465 e^5}","-\frac{2 b^2 (d+e x)^{9/2} (-3 a B e-A b e+4 b B d)}{9 e^5}+\frac{6 b (d+e x)^{7/2} (b d-a e) (-a B e-A b e+2 b B d)}{7 e^5}-\frac{2 (d+e x)^{5/2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{5 e^5}+\frac{2 (d+e x)^{3/2} (b d-a e)^3 (B d-A e)}{3 e^5}+\frac{2 b^3 B (d+e x)^{11/2}}{11 e^5}",1,"(2*Sqrt[d + e*x]*(128*b^3*B*d^5 - 176*A*b^3*d^4*e - 528*a*b^2*B*d^4*e + 792*a*A*b^2*d^3*e^2 + 792*a^2*b*B*d^3*e^2 - 1386*a^2*A*b*d^2*e^3 - 462*a^3*B*d^2*e^3 + 1155*a^3*A*d*e^4 - 64*b^3*B*d^4*e*x + 88*A*b^3*d^3*e^2*x + 264*a*b^2*B*d^3*e^2*x - 396*a*A*b^2*d^2*e^3*x - 396*a^2*b*B*d^2*e^3*x + 693*a^2*A*b*d*e^4*x + 231*a^3*B*d*e^4*x + 1155*a^3*A*e^5*x + 48*b^3*B*d^3*e^2*x^2 - 66*A*b^3*d^2*e^3*x^2 - 198*a*b^2*B*d^2*e^3*x^2 + 297*a*A*b^2*d*e^4*x^2 + 297*a^2*b*B*d*e^4*x^2 + 2079*a^2*A*b*e^5*x^2 + 693*a^3*B*e^5*x^2 - 40*b^3*B*d^2*e^3*x^3 + 55*A*b^3*d*e^4*x^3 + 165*a*b^2*B*d*e^4*x^3 + 1485*a*A*b^2*e^5*x^3 + 1485*a^2*b*B*e^5*x^3 + 35*b^3*B*d*e^4*x^4 + 385*A*b^3*e^5*x^4 + 1155*a*b^2*B*e^5*x^4 + 315*b^3*B*e^5*x^5))/(3465*e^5)","B",1
1738,1,304,171,0.0764738,"\int \frac{(a+b x)^3 (A+B x)}{\sqrt{d+e x}} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(315 a^3 A e^4-210 a^3 B d e^3+105 a^3 B e^4 x-630 a^2 A b d e^3+315 a^2 A b e^4 x+504 a^2 b B d^2 e^2-252 a^2 b B d e^3 x+189 a^2 b B e^4 x^2+504 a A b^2 d^2 e^2-252 a A b^2 d e^3 x+189 a A b^2 e^4 x^2-432 a b^2 B d^3 e+216 a b^2 B d^2 e^2 x-162 a b^2 B d e^3 x^2+135 a b^2 B e^4 x^3-144 A b^3 d^3 e+72 A b^3 d^2 e^2 x-54 A b^3 d e^3 x^2+45 A b^3 e^4 x^3+128 b^3 B d^4-64 b^3 B d^3 e x+48 b^3 B d^2 e^2 x^2-40 b^3 B d e^3 x^3+35 b^3 B e^4 x^4\right)}{315 e^5}","-\frac{2 b^2 (d+e x)^{7/2} (-3 a B e-A b e+4 b B d)}{7 e^5}+\frac{6 b (d+e x)^{5/2} (b d-a e) (-a B e-A b e+2 b B d)}{5 e^5}-\frac{2 (d+e x)^{3/2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{3 e^5}+\frac{2 \sqrt{d+e x} (b d-a e)^3 (B d-A e)}{e^5}+\frac{2 b^3 B (d+e x)^{9/2}}{9 e^5}",1,"(2*Sqrt[d + e*x]*(128*b^3*B*d^4 - 144*A*b^3*d^3*e - 432*a*b^2*B*d^3*e + 504*a*A*b^2*d^2*e^2 + 504*a^2*b*B*d^2*e^2 - 630*a^2*A*b*d*e^3 - 210*a^3*B*d*e^3 + 315*a^3*A*e^4 - 64*b^3*B*d^3*e*x + 72*A*b^3*d^2*e^2*x + 216*a*b^2*B*d^2*e^2*x - 252*a*A*b^2*d*e^3*x - 252*a^2*b*B*d*e^3*x + 315*a^2*A*b*e^4*x + 105*a^3*B*e^4*x + 48*b^3*B*d^2*e^2*x^2 - 54*A*b^3*d*e^3*x^2 - 162*a*b^2*B*d*e^3*x^2 + 189*a*A*b^2*e^4*x^2 + 189*a^2*b*B*e^4*x^2 - 40*b^3*B*d*e^3*x^3 + 45*A*b^3*e^4*x^3 + 135*a*b^2*B*e^4*x^3 + 35*b^3*B*e^4*x^4))/(315*e^5)","A",1
1739,1,304,167,0.1152634,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^{3/2}} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/(d + e*x)^(3/2),x]","-\frac{2 \left(35 a^3 A e^4-70 a^3 B d e^3-35 a^3 B e^4 x-210 a^2 A b d e^3-105 a^2 A b e^4 x+280 a^2 b B d^2 e^2+140 a^2 b B d e^3 x-35 a^2 b B e^4 x^2+280 a A b^2 d^2 e^2+140 a A b^2 d e^3 x-35 a A b^2 e^4 x^2-336 a b^2 B d^3 e-168 a b^2 B d^2 e^2 x+42 a b^2 B d e^3 x^2-21 a b^2 B e^4 x^3-112 A b^3 d^3 e-56 A b^3 d^2 e^2 x+14 A b^3 d e^3 x^2-7 A b^3 e^4 x^3+128 b^3 B d^4+64 b^3 B d^3 e x-16 b^3 B d^2 e^2 x^2+8 b^3 B d e^3 x^3-5 b^3 B e^4 x^4\right)}{35 e^5 \sqrt{d+e x}}","-\frac{2 b^2 (d+e x)^{5/2} (-3 a B e-A b e+4 b B d)}{5 e^5}+\frac{2 b (d+e x)^{3/2} (b d-a e) (-a B e-A b e+2 b B d)}{e^5}-\frac{2 \sqrt{d+e x} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{e^5}-\frac{2 (b d-a e)^3 (B d-A e)}{e^5 \sqrt{d+e x}}+\frac{2 b^3 B (d+e x)^{7/2}}{7 e^5}",1,"(-2*(128*b^3*B*d^4 - 112*A*b^3*d^3*e - 336*a*b^2*B*d^3*e + 280*a*A*b^2*d^2*e^2 + 280*a^2*b*B*d^2*e^2 - 210*a^2*A*b*d*e^3 - 70*a^3*B*d*e^3 + 35*a^3*A*e^4 + 64*b^3*B*d^3*e*x - 56*A*b^3*d^2*e^2*x - 168*a*b^2*B*d^2*e^2*x + 140*a*A*b^2*d*e^3*x + 140*a^2*b*B*d*e^3*x - 105*a^2*A*b*e^4*x - 35*a^3*B*e^4*x - 16*b^3*B*d^2*e^2*x^2 + 14*A*b^3*d*e^3*x^2 + 42*a*b^2*B*d*e^3*x^2 - 35*a*A*b^2*e^4*x^2 - 35*a^2*b*B*e^4*x^2 + 8*b^3*B*d*e^3*x^3 - 7*A*b^3*e^4*x^3 - 21*a*b^2*B*e^4*x^3 - 5*b^3*B*e^4*x^4))/(35*e^5*Sqrt[d + e*x])","A",1
1740,1,304,169,0.1212257,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^{5/2}} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/(d + e*x)^(5/2),x]","\frac{2 \left(-5 a^3 A e^4-10 a^3 B d e^3-15 a^3 B e^4 x-30 a^2 A b d e^3-45 a^2 A b e^4 x+120 a^2 b B d^2 e^2+180 a^2 b B d e^3 x+45 a^2 b B e^4 x^2+120 a A b^2 d^2 e^2+180 a A b^2 d e^3 x+45 a A b^2 e^4 x^2-240 a b^2 B d^3 e-360 a b^2 B d^2 e^2 x-90 a b^2 B d e^3 x^2+15 a b^2 B e^4 x^3-80 A b^3 d^3 e-120 A b^3 d^2 e^2 x-30 A b^3 d e^3 x^2+5 A b^3 e^4 x^3+128 b^3 B d^4+192 b^3 B d^3 e x+48 b^3 B d^2 e^2 x^2-8 b^3 B d e^3 x^3+3 b^3 B e^4 x^4\right)}{15 e^5 (d+e x)^{3/2}}","-\frac{2 b^2 (d+e x)^{3/2} (-3 a B e-A b e+4 b B d)}{3 e^5}+\frac{6 b \sqrt{d+e x} (b d-a e) (-a B e-A b e+2 b B d)}{e^5}+\frac{2 (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{e^5 \sqrt{d+e x}}-\frac{2 (b d-a e)^3 (B d-A e)}{3 e^5 (d+e x)^{3/2}}+\frac{2 b^3 B (d+e x)^{5/2}}{5 e^5}",1,"(2*(128*b^3*B*d^4 - 80*A*b^3*d^3*e - 240*a*b^2*B*d^3*e + 120*a*A*b^2*d^2*e^2 + 120*a^2*b*B*d^2*e^2 - 30*a^2*A*b*d*e^3 - 10*a^3*B*d*e^3 - 5*a^3*A*e^4 + 192*b^3*B*d^3*e*x - 120*A*b^3*d^2*e^2*x - 360*a*b^2*B*d^2*e^2*x + 180*a*A*b^2*d*e^3*x + 180*a^2*b*B*d*e^3*x - 45*a^2*A*b*e^4*x - 15*a^3*B*e^4*x + 48*b^3*B*d^2*e^2*x^2 - 30*A*b^3*d*e^3*x^2 - 90*a*b^2*B*d*e^3*x^2 + 45*a*A*b^2*e^4*x^2 + 45*a^2*b*B*e^4*x^2 - 8*b^3*B*d*e^3*x^3 + 5*A*b^3*e^4*x^3 + 15*a*b^2*B*e^4*x^3 + 3*b^3*B*e^4*x^4))/(15*e^5*(d + e*x)^(3/2))","A",1
1741,1,304,169,0.1274802,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^{7/2}} \, dx","IntegrateAlgebraic[((a + b*x)^3*(A + B*x))/(d + e*x)^(7/2),x]","-\frac{2 \left(3 a^3 A e^4+2 a^3 B d e^3+5 a^3 B e^4 x+6 a^2 A b d e^3+15 a^2 A b e^4 x+24 a^2 b B d^2 e^2+60 a^2 b B d e^3 x+45 a^2 b B e^4 x^2+24 a A b^2 d^2 e^2+60 a A b^2 d e^3 x+45 a A b^2 e^4 x^2-144 a b^2 B d^3 e-360 a b^2 B d^2 e^2 x-270 a b^2 B d e^3 x^2-45 a b^2 B e^4 x^3-48 A b^3 d^3 e-120 A b^3 d^2 e^2 x-90 A b^3 d e^3 x^2-15 A b^3 e^4 x^3+128 b^3 B d^4+320 b^3 B d^3 e x+240 b^3 B d^2 e^2 x^2+40 b^3 B d e^3 x^3-5 b^3 B e^4 x^4\right)}{15 e^5 (d+e x)^{5/2}}","-\frac{2 b^2 \sqrt{d+e x} (-3 a B e-A b e+4 b B d)}{e^5}-\frac{6 b (b d-a e) (-a B e-A b e+2 b B d)}{e^5 \sqrt{d+e x}}+\frac{2 (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{3 e^5 (d+e x)^{3/2}}-\frac{2 (b d-a e)^3 (B d-A e)}{5 e^5 (d+e x)^{5/2}}+\frac{2 b^3 B (d+e x)^{3/2}}{3 e^5}",1,"(-2*(128*b^3*B*d^4 - 48*A*b^3*d^3*e - 144*a*b^2*B*d^3*e + 24*a*A*b^2*d^2*e^2 + 24*a^2*b*B*d^2*e^2 + 6*a^2*A*b*d*e^3 + 2*a^3*B*d*e^3 + 3*a^3*A*e^4 + 320*b^3*B*d^3*e*x - 120*A*b^3*d^2*e^2*x - 360*a*b^2*B*d^2*e^2*x + 60*a*A*b^2*d*e^3*x + 60*a^2*b*B*d*e^3*x + 15*a^2*A*b*e^4*x + 5*a^3*B*e^4*x + 240*b^3*B*d^2*e^2*x^2 - 90*A*b^3*d*e^3*x^2 - 270*a*b^2*B*d*e^3*x^2 + 45*a*A*b^2*e^4*x^2 + 45*a^2*b*B*e^4*x^2 + 40*b^3*B*d*e^3*x^3 - 15*A*b^3*e^4*x^3 - 45*a*b^2*B*e^4*x^3 - 5*b^3*B*e^4*x^4))/(15*e^5*(d + e*x)^(5/2))","A",1
1742,1,395,198,0.3176784,"\int \frac{(A+B x) (d+e x)^{7/2}}{a+b x} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^(7/2))/(a + b*x),x]","\frac{2 \sqrt{d+e x} \left(315 a^4 B e^4-315 a^3 A b e^4-1050 a^3 b B d e^3-105 a^3 b B e^4 x+1050 a^2 A b^2 d e^3+105 a^2 A b^2 e^4 x+1218 a^2 b^2 B d^2 e^2+336 a^2 b^2 B d e^3 x+63 a^2 b^2 B e^4 x^2-1218 a A b^3 d^2 e^2-336 a A b^3 d e^3 x-63 a A b^3 e^4 x^2-528 a b^3 B d^3 e-366 a b^3 B d^2 e^2 x-198 a b^3 B d e^3 x^2-45 a b^3 B e^4 x^3+528 A b^4 d^3 e+366 A b^4 d^2 e^2 x+198 A b^4 d e^3 x^2+45 A b^4 e^4 x^3+35 b^4 B d^4+140 b^4 B d^3 e x+210 b^4 B d^2 e^2 x^2+140 b^4 B d e^3 x^3+35 b^4 B e^4 x^4\right)}{315 b^5 e}-\frac{2 (A b-a B) (a e-b d)^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{b^{11/2}}","-\frac{2 (A b-a B) (b d-a e)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{11/2}}+\frac{2 \sqrt{d+e x} (A b-a B) (b d-a e)^3}{b^5}+\frac{2 (d+e x)^{3/2} (A b-a B) (b d-a e)^2}{3 b^4}+\frac{2 (d+e x)^{5/2} (A b-a B) (b d-a e)}{5 b^3}+\frac{2 (d+e x)^{7/2} (A b-a B)}{7 b^2}+\frac{2 B (d+e x)^{9/2}}{9 b e}",1,"(2*Sqrt[d + e*x]*(35*b^4*B*d^4 + 528*A*b^4*d^3*e - 528*a*b^3*B*d^3*e - 1218*a*A*b^3*d^2*e^2 + 1218*a^2*b^2*B*d^2*e^2 + 1050*a^2*A*b^2*d*e^3 - 1050*a^3*b*B*d*e^3 - 315*a^3*A*b*e^4 + 315*a^4*B*e^4 + 140*b^4*B*d^3*e*x + 366*A*b^4*d^2*e^2*x - 366*a*b^3*B*d^2*e^2*x - 336*a*A*b^3*d*e^3*x + 336*a^2*b^2*B*d*e^3*x + 105*a^2*A*b^2*e^4*x - 105*a^3*b*B*e^4*x + 210*b^4*B*d^2*e^2*x^2 + 198*A*b^4*d*e^3*x^2 - 198*a*b^3*B*d*e^3*x^2 - 63*a*A*b^3*e^4*x^2 + 63*a^2*b^2*B*e^4*x^2 + 140*b^4*B*d*e^3*x^3 + 45*A*b^4*e^4*x^3 - 45*a*b^3*B*e^4*x^3 + 35*b^4*B*e^4*x^4))/(315*b^5*e) - (2*(A*b - a*B)*(-(b*d) + a*e)^(7/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/b^(11/2)","A",1
1743,1,263,164,0.2250464,"\int \frac{(A+B x) (d+e x)^{5/2}}{a+b x} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^(5/2))/(a + b*x),x]","\frac{2 \sqrt{d+e x} \left(-105 a^3 B e^3+105 a^2 A b e^3+245 a^2 b B d e^2+35 a^2 b B e^3 x-245 a A b^2 d e^2-35 a A b^2 e^3 x-161 a b^2 B d^2 e-77 a b^2 B d e^2 x-21 a b^2 B e^3 x^2+161 A b^3 d^2 e+77 A b^3 d e^2 x+21 A b^3 e^3 x^2+15 b^3 B d^3+45 b^3 B d^2 e x+45 b^3 B d e^2 x^2+15 b^3 B e^3 x^3\right)}{105 b^4 e}+\frac{2 (A b-a B) (a e-b d)^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{b^{9/2}}","-\frac{2 (A b-a B) (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{9/2}}+\frac{2 \sqrt{d+e x} (A b-a B) (b d-a e)^2}{b^4}+\frac{2 (d+e x)^{3/2} (A b-a B) (b d-a e)}{3 b^3}+\frac{2 (d+e x)^{5/2} (A b-a B)}{5 b^2}+\frac{2 B (d+e x)^{7/2}}{7 b e}",1,"(2*Sqrt[d + e*x]*(15*b^3*B*d^3 + 161*A*b^3*d^2*e - 161*a*b^2*B*d^2*e - 245*a*A*b^2*d*e^2 + 245*a^2*b*B*d*e^2 + 105*a^2*A*b*e^3 - 105*a^3*B*e^3 + 45*b^3*B*d^2*e*x + 77*A*b^3*d*e^2*x - 77*a*b^2*B*d*e^2*x - 35*a*A*b^2*e^3*x + 35*a^2*b*B*e^3*x + 45*b^3*B*d*e^2*x^2 + 21*A*b^3*e^3*x^2 - 21*a*b^2*B*e^3*x^2 + 15*b^3*B*e^3*x^3))/(105*b^4*e) + (2*(A*b - a*B)*(-(b*d) + a*e)^(5/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/b^(9/2)","A",1
1744,1,167,130,0.1602438,"\int \frac{(A+B x) (d+e x)^{3/2}}{a+b x} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^(3/2))/(a + b*x),x]","\frac{2 \sqrt{d+e x} \left(15 a^2 B e^2-15 a A b e^2-20 a b B d e-5 a b B e^2 x+20 A b^2 d e+5 A b^2 e^2 x+3 b^2 B d^2+6 b^2 B d e x+3 b^2 B e^2 x^2\right)}{15 b^3 e}-\frac{2 (A b-a B) (a e-b d)^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{b^{7/2}}","-\frac{2 (A b-a B) (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{7/2}}+\frac{2 \sqrt{d+e x} (A b-a B) (b d-a e)}{b^3}+\frac{2 (d+e x)^{3/2} (A b-a B)}{3 b^2}+\frac{2 B (d+e x)^{5/2}}{5 b e}",1,"(2*Sqrt[d + e*x]*(3*b^2*B*d^2 + 20*A*b^2*d*e - 20*a*b*B*d*e - 15*a*A*b*e^2 + 15*a^2*B*e^2 + 6*b^2*B*d*e*x + 5*A*b^2*e^2*x - 5*a*b*B*e^2*x + 3*b^2*B*e^2*x^2))/(15*b^3*e) - (2*(A*b - a*B)*(-(b*d) + a*e)^(3/2)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/b^(7/2)","A",1
1745,1,105,98,0.1468685,"\int \frac{(A+B x) \sqrt{d+e x}}{a+b x} \, dx","IntegrateAlgebraic[((A + B*x)*Sqrt[d + e*x])/(a + b*x),x]","\frac{2 (A b-a B) \sqrt{a e-b d} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{b^{5/2}}+\frac{2 \sqrt{d+e x} (-3 a B e+3 A b e+b B d+b B e x)}{3 b^2 e}","-\frac{2 (A b-a B) \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2}}+\frac{2 \sqrt{d+e x} (A b-a B)}{b^2}+\frac{2 B (d+e x)^{3/2}}{3 b e}",1,"(2*Sqrt[d + e*x]*(b*B*d + 3*A*b*e - 3*a*B*e + b*B*e*x))/(3*b^2*e) + (2*(A*b - a*B)*Sqrt[-(b*d) + a*e]*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/b^(5/2)","A",1
1746,1,84,74,0.0865299,"\int \frac{A+B x}{(a+b x) \sqrt{d+e x}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)*Sqrt[d + e*x]),x]","\frac{2 B \sqrt{d+e x}}{b e}-\frac{2 (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{b^{3/2} \sqrt{a e-b d}}","\frac{2 B \sqrt{d+e x}}{b e}-\frac{2 (A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2} \sqrt{b d-a e}}",1,"(2*B*Sqrt[d + e*x])/(b*e) - (2*(A*b - a*B)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/(b^(3/2)*Sqrt[-(b*d) + a*e])","A",1
1747,1,98,88,0.1523021,"\int \frac{A+B x}{(a+b x) (d+e x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)*(d + e*x)^(3/2)),x]","\frac{2 (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{\sqrt{b} (a e-b d)^{3/2}}-\frac{2 (A e-B d)}{e \sqrt{d+e x} (a e-b d)}","-\frac{2 (B d-A e)}{e \sqrt{d+e x} (b d-a e)}-\frac{2 (A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} (b d-a e)^{3/2}}",1,"(-2*(-(B*d) + A*e))/(e*(-(b*d) + a*e)*Sqrt[d + e*x]) + (2*(A*b - a*B)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/(Sqrt[b]*(-(b*d) + a*e)^(3/2))","A",1
1748,1,139,119,0.1968874,"\int \frac{A+B x}{(a+b x) (d+e x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)*(d + e*x)^(5/2)),x]","\frac{2 \left(-a A e^2-2 a B d e-3 a B e^2 x+4 A b d e+3 A b e^2 x-b B d^2\right)}{3 e (d+e x)^{3/2} (a e-b d)^2}-\frac{2 \left(A b^{3/2}-a \sqrt{b} B\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{(a e-b d)^{5/2}}","\frac{2 (A b-a B)}{\sqrt{d+e x} (b d-a e)^2}-\frac{2 (B d-A e)}{3 e (d+e x)^{3/2} (b d-a e)}-\frac{2 \sqrt{b} (A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{5/2}}",1,"(2*(-(b*B*d^2) + 4*A*b*d*e - 2*a*B*d*e - a*A*e^2 + 3*A*b*e^2*x - 3*a*B*e^2*x))/(3*e*(-(b*d) + a*e)^2*(d + e*x)^(3/2)) - (2*(A*b^(3/2) - a*Sqrt[b]*B)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/(-(b*d) + a*e)^(5/2)","A",1
1749,1,216,151,0.3130051,"\int \frac{A+B x}{(a+b x) (d+e x)^{7/2}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)*(d + e*x)^(7/2)),x]","\frac{2 \left(A b^{5/2}-a b^{3/2} B\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{(a e-b d)^{7/2}}-\frac{2 \left(3 a^2 A e^3+2 a^2 B d e^2+5 a^2 B e^3 x-11 a A b d e^2-5 a A b e^3 x-14 a b B d^2 e-35 a b B d e^2 x-15 a b B e^3 x^2+23 A b^2 d^2 e+35 A b^2 d e^2 x+15 A b^2 e^3 x^2-3 b^2 B d^3\right)}{15 e (d+e x)^{5/2} (a e-b d)^3}","-\frac{2 b^{3/2} (A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{7/2}}+\frac{2 b (A b-a B)}{\sqrt{d+e x} (b d-a e)^3}+\frac{2 (A b-a B)}{3 (d+e x)^{3/2} (b d-a e)^2}-\frac{2 (B d-A e)}{5 e (d+e x)^{5/2} (b d-a e)}",1,"(-2*(-3*b^2*B*d^3 + 23*A*b^2*d^2*e - 14*a*b*B*d^2*e - 11*a*A*b*d*e^2 + 2*a^2*B*d*e^2 + 3*a^2*A*e^3 + 35*A*b^2*d*e^2*x - 35*a*b*B*d*e^2*x - 5*a*A*b*e^3*x + 5*a^2*B*e^3*x + 15*A*b^2*e^3*x^2 - 15*a*b*B*e^3*x^2))/(15*e*(-(b*d) + a*e)^3*(d + e*x)^(5/2)) + (2*(A*b^(5/2) - a*b^(3/2)*B)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/(-(b*d) + a*e)^(7/2)","A",1
1750,1,408,256,0.4144375,"\int \frac{(A+B x) (d+e x)^{7/2}}{(a+b x)^2} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^(7/2))/(a + b*x)^2,x]","\frac{\sqrt{d+e x} \left(-945 a^4 B e^3+735 a^3 A b e^3+2415 a^3 b B d e^2-630 a^3 b B e^3 x-1715 a^2 A b^2 d e^2+490 a^2 A b^2 e^3 x-1939 a^2 b^2 B d^2 e+1652 a^2 b^2 B d e^2 x+126 a^2 b^2 B e^3 x^2+1127 a A b^3 d^2 e-1176 a A b^3 d e^2 x-98 a A b^3 e^3 x^2+457 a b^3 B d^3-1380 a b^3 B d^2 e x-316 a b^3 B d e^2 x^2-54 a b^3 B e^3 x^3-105 A b^4 d^3+812 A b^4 d^2 e x+224 A b^4 d e^2 x^2+42 A b^4 e^3 x^3+352 b^4 B d^3 x+244 b^4 B d^2 e x^2+132 b^4 B d e^2 x^3+30 b^4 B e^3 x^4\right)}{105 b^5 (a+b x)}+\frac{\left(7 A b e (a e-b d)^{5/2}+2 b B d (a e-b d)^{5/2}-9 a B e (a e-b d)^{5/2}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{b^{11/2}}","-\frac{(b d-a e)^{5/2} (-9 a B e+7 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{11/2}}+\frac{\sqrt{d+e x} (b d-a e)^2 (-9 a B e+7 A b e+2 b B d)}{b^5}+\frac{(d+e x)^{3/2} (b d-a e) (-9 a B e+7 A b e+2 b B d)}{3 b^4}+\frac{(d+e x)^{5/2} (-9 a B e+7 A b e+2 b B d)}{5 b^3}+\frac{(d+e x)^{7/2} (-9 a B e+7 A b e+2 b B d)}{7 b^2 (b d-a e)}-\frac{(d+e x)^{9/2} (A b-a B)}{b (a+b x) (b d-a e)}",1,"(Sqrt[d + e*x]*(-105*A*b^4*d^3 + 457*a*b^3*B*d^3 + 1127*a*A*b^3*d^2*e - 1939*a^2*b^2*B*d^2*e - 1715*a^2*A*b^2*d*e^2 + 2415*a^3*b*B*d*e^2 + 735*a^3*A*b*e^3 - 945*a^4*B*e^3 + 352*b^4*B*d^3*x + 812*A*b^4*d^2*e*x - 1380*a*b^3*B*d^2*e*x - 1176*a*A*b^3*d*e^2*x + 1652*a^2*b^2*B*d*e^2*x + 490*a^2*A*b^2*e^3*x - 630*a^3*b*B*e^3*x + 244*b^4*B*d^2*e*x^2 + 224*A*b^4*d*e^2*x^2 - 316*a*b^3*B*d*e^2*x^2 - 98*a*A*b^3*e^3*x^2 + 126*a^2*b^2*B*e^3*x^2 + 132*b^4*B*d*e^2*x^3 + 42*A*b^4*e^3*x^3 - 54*a*b^3*B*e^3*x^3 + 30*b^4*B*e^3*x^4))/(105*b^5*(a + b*x)) + ((2*b*B*d*(-(b*d) + a*e)^(5/2) + 7*A*b*e*(-(b*d) + a*e)^(5/2) - 9*a*B*e*(-(b*d) + a*e)^(5/2))*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/b^(11/2)","A",1
1751,1,276,214,0.2962917,"\int \frac{(A+B x) (d+e x)^{5/2}}{(a+b x)^2} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^(5/2))/(a + b*x)^2,x]","\frac{\sqrt{d+e x} \left(105 a^3 B e^2-75 a^2 A b e^2-170 a^2 b B d e+70 a^2 b B e^2 x+100 a A b^2 d e-50 a A b^2 e^2 x+61 a b^2 B d^2-118 a b^2 B d e x-14 a b^2 B e^2 x^2-15 A b^3 d^2+70 A b^3 d e x+10 A b^3 e^2 x^2+46 b^3 B d^2 x+22 b^3 B d e x^2+6 b^3 B e^2 x^3\right)}{15 b^4 (a+b x)}+\frac{\left(-5 A b e (a e-b d)^{3/2}-2 b B d (a e-b d)^{3/2}+7 a B e (a e-b d)^{3/2}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{b^{9/2}}","-\frac{(b d-a e)^{3/2} (-7 a B e+5 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{9/2}}+\frac{\sqrt{d+e x} (b d-a e) (-7 a B e+5 A b e+2 b B d)}{b^4}+\frac{(d+e x)^{3/2} (-7 a B e+5 A b e+2 b B d)}{3 b^3}+\frac{(d+e x)^{5/2} (-7 a B e+5 A b e+2 b B d)}{5 b^2 (b d-a e)}-\frac{(d+e x)^{7/2} (A b-a B)}{b (a+b x) (b d-a e)}",1,"(Sqrt[d + e*x]*(-15*A*b^3*d^2 + 61*a*b^2*B*d^2 + 100*a*A*b^2*d*e - 170*a^2*b*B*d*e - 75*a^2*A*b*e^2 + 105*a^3*B*e^2 + 46*b^3*B*d^2*x + 70*A*b^3*d*e*x - 118*a*b^2*B*d*e*x - 50*a*A*b^2*e^2*x + 70*a^2*b*B*e^2*x + 22*b^3*B*d*e*x^2 + 10*A*b^3*e^2*x^2 - 14*a*b^2*B*e^2*x^2 + 6*b^3*B*e^2*x^3))/(15*b^4*(a + b*x)) + ((-2*b*B*d*(-(b*d) + a*e)^(3/2) - 5*A*b*e*(-(b*d) + a*e)^(3/2) + 7*a*B*e*(-(b*d) + a*e)^(3/2))*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/b^(9/2)","A",1
1752,1,180,174,0.2031232,"\int \frac{(A+B x) (d+e x)^{3/2}}{(a+b x)^2} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^(3/2))/(a + b*x)^2,x]","\frac{\sqrt{d+e x} \left(-15 a^2 B e+9 a A b e+11 a b B d-10 a b B e x-3 A b^2 d+6 A b^2 e x+8 b^2 B d x+2 b^2 B e x^2\right)}{3 b^3 (a+b x)}+\frac{\left(3 A b e \sqrt{a e-b d}+2 b B d \sqrt{a e-b d}-5 a B e \sqrt{a e-b d}\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{b^{7/2}}","-\frac{\sqrt{b d-a e} (-5 a B e+3 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{7/2}}+\frac{\sqrt{d+e x} (-5 a B e+3 A b e+2 b B d)}{b^3}+\frac{(d+e x)^{3/2} (-5 a B e+3 A b e+2 b B d)}{3 b^2 (b d-a e)}-\frac{(d+e x)^{5/2} (A b-a B)}{b (a+b x) (b d-a e)}",1,"(Sqrt[d + e*x]*(-3*A*b^2*d + 11*a*b*B*d + 9*a*A*b*e - 15*a^2*B*e + 8*b^2*B*d*x + 6*A*b^2*e*x - 10*a*b*B*e*x + 2*b^2*B*e*x^2))/(3*b^3*(a + b*x)) + ((2*b*B*d*Sqrt[-(b*d) + a*e] + 3*A*b*e*Sqrt[-(b*d) + a*e] - 5*a*B*e*Sqrt[-(b*d) + a*e])*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/b^(7/2)","A",1
1753,1,107,140,0.1431724,"\int \frac{(A+B x) \sqrt{d+e x}}{(a+b x)^2} \, dx","IntegrateAlgebraic[((A + B*x)*Sqrt[d + e*x])/(a + b*x)^2,x]","\frac{(3 a B e-A b e-2 b B d) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{b^{5/2} \sqrt{a e-b d}}+\frac{\sqrt{d+e x} (3 a B-A b+2 b B x)}{b^2 (a+b x)}","-\frac{(-3 a B e+A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2} \sqrt{b d-a e}}+\frac{\sqrt{d+e x} (-3 a B e+A b e+2 b B d)}{b^2 (b d-a e)}-\frac{(d+e x)^{3/2} (A b-a B)}{b (a+b x) (b d-a e)}",1,"((-(A*b) + 3*a*B + 2*b*B*x)*Sqrt[d + e*x])/(b^2*(a + b*x)) + ((-2*b*B*d - A*b*e + 3*a*B*e)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/(b^(5/2)*Sqrt[-(b*d) + a*e])","A",1
1754,1,111,103,0.1582682,"\int \frac{A+B x}{(a+b x)^2 \sqrt{d+e x}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^2*Sqrt[d + e*x]),x]","\frac{(-a B e-A b e+2 b B d) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{b^{3/2} (a e-b d)^{3/2}}+\frac{\sqrt{d+e x} (a B-A b)}{b (a+b x) (b d-a e)}","-\frac{(-a B e-A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2} (b d-a e)^{3/2}}-\frac{\sqrt{d+e x} (A b-a B)}{b (a+b x) (b d-a e)}",1,"((-(A*b) + a*B)*Sqrt[d + e*x])/(b*(b*d - a*e)*(a + b*x)) + ((2*b*B*d - A*b*e - a*B*e)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/(b^(3/2)*(-(b*d) + a*e)^(3/2))","A",1
1755,1,133,140,0.2854712,"\int \frac{A+B x}{(a+b x)^2 (d+e x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^2*(d + e*x)^(3/2)),x]","\frac{-2 a A e+3 a B d+a B e x-A b d-3 A b e x+2 b B d x}{(a+b x) \sqrt{d+e x} (b d-a e)^2}+\frac{(-a B e+3 A b e-2 b B d) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{\sqrt{b} (a e-b d)^{5/2}}","-\frac{A b-a B}{b (a+b x) \sqrt{d+e x} (b d-a e)}+\frac{a B e-3 A b e+2 b B d}{b \sqrt{d+e x} (b d-a e)^2}-\frac{(a B e-3 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} (b d-a e)^{5/2}}",1,"(-(A*b*d) + 3*a*B*d - 2*a*A*e + 2*b*B*d*x - 3*A*b*e*x + a*B*e*x)/((b*d - a*e)^2*(a + b*x)*Sqrt[d + e*x]) + ((-2*b*B*d + 3*A*b*e - a*B*e)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/(Sqrt[b]*(-(b*d) + a*e)^(5/2))","A",1
1756,1,233,181,0.4733566,"\int \frac{A+B x}{(a+b x)^2 (d+e x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^2*(d + e*x)^(5/2)),x]","\frac{2 a^2 A e^2+4 a^2 B d e+6 a^2 B e^2 x-14 a A b d e-10 a A b e^2 x+11 a b B d^2+16 a b B d e x+9 a b B e^2 x^2-3 A b^2 d^2-20 A b^2 d e x-15 A b^2 e^2 x^2+8 b^2 B d^2 x+6 b^2 B d e x^2}{3 (a+b x) (d+e x)^{3/2} (b d-a e)^3}+\frac{\left(3 a \sqrt{b} B e-5 A b^{3/2} e+2 b^{3/2} B d\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{(a e-b d)^{7/2}}","-\frac{A b-a B}{b (a+b x) (d+e x)^{3/2} (b d-a e)}+\frac{3 a B e-5 A b e+2 b B d}{\sqrt{d+e x} (b d-a e)^3}+\frac{3 a B e-5 A b e+2 b B d}{3 b (d+e x)^{3/2} (b d-a e)^2}-\frac{\sqrt{b} (3 a B e-5 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{7/2}}",1,"(-3*A*b^2*d^2 + 11*a*b*B*d^2 - 14*a*A*b*d*e + 4*a^2*B*d*e + 2*a^2*A*e^2 + 8*b^2*B*d^2*x - 20*A*b^2*d*e*x + 16*a*b*B*d*e*x - 10*a*A*b*e^2*x + 6*a^2*B*e^2*x + 6*b^2*B*d*e*x^2 - 15*A*b^2*e^2*x^2 + 9*a*b*B*e^2*x^2)/(3*(b*d - a*e)^3*(a + b*x)*(d + e*x)^(3/2)) + ((2*b^(3/2)*B*d - 5*A*b^(3/2)*e + 3*a*Sqrt[b]*B*e)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/(-(b*d) + a*e)^(7/2)","A",1
1757,1,365,221,0.5473684,"\int \frac{A+B x}{(a+b x)^2 (d+e x)^{7/2}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^2*(d + e*x)^(7/2)),x]","\frac{-6 a^3 A e^3-4 a^3 B d e^2-10 a^3 B e^3 x+32 a^2 A b d e^2+14 a^2 A b e^3 x+48 a^2 b B d^2 e+116 a^2 b B d e^2 x+50 a^2 b B e^3 x^2-116 a A b^2 d^2 e-168 a A b^2 d e^2 x-70 a A b^2 e^3 x^2+61 a b^2 B d^3+163 a b^2 B d^2 e x+195 a b^2 B d e^2 x^2+75 a b^2 B e^3 x^3-15 A b^3 d^3-161 A b^3 d^2 e x-245 A b^3 d e^2 x^2-105 A b^3 e^3 x^3+46 b^3 B d^3 x+70 b^3 B d^2 e x^2+30 b^3 B d e^2 x^3}{15 (a+b x) (d+e x)^{5/2} (b d-a e)^4}+\frac{\left(-5 a b^{3/2} B e+7 A b^{5/2} e-2 b^{5/2} B d\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{(a e-b d)^{9/2}}","-\frac{b^{3/2} (5 a B e-7 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{9/2}}+\frac{b (5 a B e-7 A b e+2 b B d)}{\sqrt{d+e x} (b d-a e)^4}+\frac{5 a B e-7 A b e+2 b B d}{3 (d+e x)^{3/2} (b d-a e)^3}+\frac{5 a B e-7 A b e+2 b B d}{5 b (d+e x)^{5/2} (b d-a e)^2}-\frac{A b-a B}{b (a+b x) (d+e x)^{5/2} (b d-a e)}",1,"(-15*A*b^3*d^3 + 61*a*b^2*B*d^3 - 116*a*A*b^2*d^2*e + 48*a^2*b*B*d^2*e + 32*a^2*A*b*d*e^2 - 4*a^3*B*d*e^2 - 6*a^3*A*e^3 + 46*b^3*B*d^3*x - 161*A*b^3*d^2*e*x + 163*a*b^2*B*d^2*e*x - 168*a*A*b^2*d*e^2*x + 116*a^2*b*B*d*e^2*x + 14*a^2*A*b*e^3*x - 10*a^3*B*e^3*x + 70*b^3*B*d^2*e*x^2 - 245*A*b^3*d*e^2*x^2 + 195*a*b^2*B*d*e^2*x^2 - 70*a*A*b^2*e^3*x^2 + 50*a^2*b*B*e^3*x^2 + 30*b^3*B*d*e^2*x^3 - 105*A*b^3*e^3*x^3 + 75*a*b^2*B*e^3*x^3)/(15*(b*d - a*e)^4*(a + b*x)*(d + e*x)^(5/2)) + ((-2*b^(5/2)*B*d + 7*A*b^(5/2)*e - 5*a*b^(3/2)*B*e)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/(-(b*d) + a*e)^(9/2)","A",1
1758,1,392,274,0.4882675,"\int \frac{(A+B x) (d+e x)^{7/2}}{(a+b x)^3} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^(7/2))/(a + b*x)^3,x]","\frac{\sqrt{d+e x} \left(945 a^4 B e^3-525 a^3 A b e^3-1680 a^3 b B d e^2+1575 a^3 b B e^3 x+700 a^2 A b^2 d e^2-875 a^2 A b^2 e^3 x+749 a^2 b^2 B d^2 e-2842 a^2 b^2 B d e^2 x+504 a^2 b^2 B e^3 x^2-105 a A b^3 d^2 e+1190 a A b^3 d e^2 x-280 a A b^3 e^3 x^2-30 a b^3 B d^3+1303 a b^3 B d^2 e x-944 a b^3 B d e^2 x^2-72 a b^3 B e^3 x^3-30 A b^4 d^3-195 A b^4 d^2 e x+400 A b^4 d e^2 x^2+40 A b^4 e^3 x^3-60 b^4 B d^3 x+464 b^4 B d^2 e x^2+128 b^4 B d e^2 x^3+24 b^4 B e^3 x^4\right)}{60 b^5 (a+b x)^2}-\frac{7 (a e-b d)^{3/2} \left(-9 a B e^2+5 A b e^2+4 b B d e\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{4 b^{11/2}}","-\frac{7 e (b d-a e)^{3/2} (-9 a B e+5 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{11/2}}+\frac{7 e \sqrt{d+e x} (b d-a e) (-9 a B e+5 A b e+4 b B d)}{4 b^5}+\frac{7 e (d+e x)^{3/2} (-9 a B e+5 A b e+4 b B d)}{12 b^4}+\frac{7 e (d+e x)^{5/2} (-9 a B e+5 A b e+4 b B d)}{20 b^3 (b d-a e)}-\frac{(d+e x)^{7/2} (-9 a B e+5 A b e+4 b B d)}{4 b^2 (a+b x) (b d-a e)}-\frac{(d+e x)^{9/2} (A b-a B)}{2 b (a+b x)^2 (b d-a e)}",1,"(Sqrt[d + e*x]*(-30*A*b^4*d^3 - 30*a*b^3*B*d^3 - 105*a*A*b^3*d^2*e + 749*a^2*b^2*B*d^2*e + 700*a^2*A*b^2*d*e^2 - 1680*a^3*b*B*d*e^2 - 525*a^3*A*b*e^3 + 945*a^4*B*e^3 - 60*b^4*B*d^3*x - 195*A*b^4*d^2*e*x + 1303*a*b^3*B*d^2*e*x + 1190*a*A*b^3*d*e^2*x - 2842*a^2*b^2*B*d*e^2*x - 875*a^2*A*b^2*e^3*x + 1575*a^3*b*B*e^3*x + 464*b^4*B*d^2*e*x^2 + 400*A*b^4*d*e^2*x^2 - 944*a*b^3*B*d*e^2*x^2 - 280*a*A*b^3*e^3*x^2 + 504*a^2*b^2*B*e^3*x^2 + 128*b^4*B*d*e^2*x^3 + 40*A*b^4*e^3*x^3 - 72*a*b^3*B*e^3*x^3 + 24*b^4*B*e^3*x^4))/(60*b^5*(a + b*x)^2) - (7*(-(b*d) + a*e)^(3/2)*(4*b*B*d*e + 5*A*b*e^2 - 9*a*B*e^2)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/(4*b^(11/2))","A",1
1759,1,260,233,0.3174055,"\int \frac{(A+B x) (d+e x)^{5/2}}{(a+b x)^3} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^(5/2))/(a + b*x)^3,x]","\frac{\sqrt{d+e x} \left(-105 a^3 B e^2+45 a^2 A b e^2+95 a^2 b B d e-175 a^2 b B e^2 x-15 a A b^2 d e+75 a A b^2 e^2 x-6 a b^2 B d^2+163 a b^2 B d e x-56 a b^2 B e^2 x^2-6 A b^3 d^2-27 A b^3 d e x+24 A b^3 e^2 x^2-12 b^3 B d^2 x+56 b^3 B d e x^2+8 b^3 B e^2 x^3\right)}{12 b^4 (a+b x)^2}+\frac{5 \sqrt{a e-b d} \left(-7 a B e^2+3 A b e^2+4 b B d e\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{4 b^{9/2}}","-\frac{5 e \sqrt{b d-a e} (-7 a B e+3 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{9/2}}+\frac{5 e \sqrt{d+e x} (-7 a B e+3 A b e+4 b B d)}{4 b^4}+\frac{5 e (d+e x)^{3/2} (-7 a B e+3 A b e+4 b B d)}{12 b^3 (b d-a e)}-\frac{(d+e x)^{5/2} (-7 a B e+3 A b e+4 b B d)}{4 b^2 (a+b x) (b d-a e)}-\frac{(d+e x)^{7/2} (A b-a B)}{2 b (a+b x)^2 (b d-a e)}",1,"(Sqrt[d + e*x]*(-6*A*b^3*d^2 - 6*a*b^2*B*d^2 - 15*a*A*b^2*d*e + 95*a^2*b*B*d*e + 45*a^2*A*b*e^2 - 105*a^3*B*e^2 - 12*b^3*B*d^2*x - 27*A*b^3*d*e*x + 163*a*b^2*B*d*e*x + 75*a*A*b^2*e^2*x - 175*a^2*b*B*e^2*x + 56*b^3*B*d*e*x^2 + 24*A*b^3*e^2*x^2 - 56*a*b^2*B*e^2*x^2 + 8*b^3*B*e^2*x^3))/(12*b^4*(a + b*x)^2) + (5*Sqrt[-(b*d) + a*e]*(4*b*B*d*e + 3*A*b*e^2 - 7*a*B*e^2)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/(4*b^(9/2))","A",1
1760,1,163,197,0.222178,"\int \frac{(A+B x) (d+e x)^{3/2}}{(a+b x)^3} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^(3/2))/(a + b*x)^3,x]","\frac{\sqrt{d+e x} \left(15 a^2 B e-3 a A b e-2 a b B d+25 a b B e x-2 A b^2 d-5 A b^2 e x-4 b^2 B d x+8 b^2 B e x^2\right)}{4 b^3 (a+b x)^2}-\frac{3 \left(-5 a B e^2+A b e^2+4 b B d e\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{4 b^{7/2} \sqrt{a e-b d}}","-\frac{3 e (-5 a B e+A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{7/2} \sqrt{b d-a e}}+\frac{3 e \sqrt{d+e x} (-5 a B e+A b e+4 b B d)}{4 b^3 (b d-a e)}-\frac{(d+e x)^{3/2} (-5 a B e+A b e+4 b B d)}{4 b^2 (a+b x) (b d-a e)}-\frac{(d+e x)^{5/2} (A b-a B)}{2 b (a+b x)^2 (b d-a e)}",1,"(Sqrt[d + e*x]*(-2*A*b^2*d - 2*a*b*B*d - 3*a*A*b*e + 15*a^2*B*e - 4*b^2*B*d*x - 5*A*b^2*e*x + 25*a*b*B*e*x + 8*b^2*B*e*x^2))/(4*b^3*(a + b*x)^2) - (3*(4*b*B*d*e + A*b*e^2 - 5*a*B*e^2)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/(4*b^(7/2)*Sqrt[-(b*d) + a*e])","A",1
1761,1,163,157,0.3560335,"\int \frac{(A+B x) \sqrt{d+e x}}{(a+b x)^3} \, dx","IntegrateAlgebraic[((A + B*x)*Sqrt[d + e*x])/(a + b*x)^3,x]","\frac{\sqrt{d+e x} \left(3 a^2 B e+a A b e-2 a b B d+5 a b B e x-2 A b^2 d-A b^2 e x-4 b^2 B d x\right)}{4 b^2 (a+b x)^2 (b d-a e)}+\frac{\left(-3 a B e^2-A b e^2+4 b B d e\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{4 b^{5/2} (a e-b d)^{3/2}}","-\frac{e (-3 a B e-A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{5/2} (b d-a e)^{3/2}}-\frac{\sqrt{d+e x} (-3 a B e-A b e+4 b B d)}{4 b^2 (a+b x) (b d-a e)}-\frac{(d+e x)^{3/2} (A b-a B)}{2 b (a+b x)^2 (b d-a e)}",1,"(Sqrt[d + e*x]*(-2*A*b^2*d - 2*a*b*B*d + a*A*b*e + 3*a^2*B*e - 4*b^2*B*d*x - A*b^2*e*x + 5*a*b*B*e*x))/(4*b^2*(b*d - a*e)*(a + b*x)^2) + ((4*b*B*d*e - A*b*e^2 - 3*a*B*e^2)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/(4*b^(5/2)*(-(b*d) + a*e)^(3/2))","A",1
1762,1,163,157,0.3784566,"\int \frac{A+B x}{(a+b x)^3 \sqrt{d+e x}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^3*Sqrt[d + e*x]),x]","\frac{\sqrt{d+e x} \left(a^2 (-B) e+5 a A b e-2 a b B d+a b B e x-2 A b^2 d+3 A b^2 e x-4 b^2 B d x\right)}{4 b (a+b x)^2 (b d-a e)^2}+\frac{\left(-a B e^2-3 A b e^2+4 b B d e\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{4 b^{3/2} (a e-b d)^{5/2}}","\frac{e (-a B e-3 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{3/2} (b d-a e)^{5/2}}-\frac{\sqrt{d+e x} (A b-a B)}{2 b (a+b x)^2 (b d-a e)}-\frac{\sqrt{d+e x} (-a B e-3 A b e+4 b B d)}{4 b (a+b x) (b d-a e)^2}",1,"(Sqrt[d + e*x]*(-2*A*b^2*d - 2*a*b*B*d + 5*a*A*b*e - a^2*B*e - 4*b^2*B*d*x + 3*A*b^2*e*x + a*b*B*e*x))/(4*b*(b*d - a*e)^2*(a + b*x)^2) + ((4*b*B*d*e - 3*A*b*e^2 - a*B*e^2)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/(4*b^(3/2)*(-(b*d) + a*e)^(5/2))","A",1
1763,1,232,197,0.4810747,"\int \frac{A+B x}{(a+b x)^3 (d+e x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^3*(d + e*x)^(3/2)),x]","\frac{8 a^2 A e^2-13 a^2 B d e-5 a^2 B e^2 x+9 a A b d e+25 a A b e^2 x-2 a b B d^2-21 a b B d e x-3 a b B e^2 x^2-2 A b^2 d^2+5 A b^2 d e x+15 A b^2 e^2 x^2-4 b^2 B d^2 x-12 b^2 B d e x^2}{4 (a+b x)^2 \sqrt{d+e x} (b d-a e)^3}-\frac{3 \left(a B e^2-5 A b e^2+4 b B d e\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{4 \sqrt{b} (a e-b d)^{7/2}}","-\frac{A b-a B}{2 b (a+b x)^2 \sqrt{d+e x} (b d-a e)}-\frac{3 e (a B e-5 A b e+4 b B d)}{4 b \sqrt{d+e x} (b d-a e)^3}-\frac{a B e-5 A b e+4 b B d}{4 b (a+b x) \sqrt{d+e x} (b d-a e)^2}+\frac{3 e (a B e-5 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 \sqrt{b} (b d-a e)^{7/2}}",1,"(-2*A*b^2*d^2 - 2*a*b*B*d^2 + 9*a*A*b*d*e - 13*a^2*B*d*e + 8*a^2*A*e^2 - 4*b^2*B*d^2*x + 5*A*b^2*d*e*x - 21*a*b*B*d*e*x + 25*a*A*b*e^2*x - 5*a^2*B*e^2*x - 12*b^2*B*d*e*x^2 + 15*A*b^2*e^2*x^2 - 3*a*b*B*e^2*x^2)/(4*(b*d - a*e)^3*(a + b*x)^2*Sqrt[d + e*x]) - (3*(4*b*B*d*e - 5*A*b*e^2 + a*B*e^2)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/(4*Sqrt[b]*(-(b*d) + a*e)^(7/2))","A",1
1764,1,373,240,0.6149632,"\int \frac{A+B x}{(a+b x)^3 (d+e x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^3*(d + e*x)^(5/2)),x]","\frac{-8 a^3 A e^3-16 a^3 B d e^2-24 a^3 B e^3 x+80 a^2 A b d e^2+56 a^2 A b e^3 x-83 a^2 b B d^2 e-134 a^2 b B d e^2 x-75 a^2 b B e^3 x^2+39 a A b^2 d^2 e+238 a A b^2 d e^2 x+175 a A b^2 e^3 x^2-6 a b^2 B d^3-145 a b^2 B d^2 e x-160 a b^2 B d e^2 x^2-45 a b^2 B e^3 x^3-6 A b^3 d^3+21 A b^3 d^2 e x+140 A b^3 d e^2 x^2+105 A b^3 e^3 x^3-12 b^3 B d^3 x-80 b^3 B d^2 e x^2-60 b^3 B d e^2 x^3}{12 (a+b x)^2 (d+e x)^{3/2} (b d-a e)^4}+\frac{5 \left(3 a \sqrt{b} B e^2-7 A b^{3/2} e^2+4 b^{3/2} B d e\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{4 (a e-b d)^{9/2}}","-\frac{A b-a B}{2 b (a+b x)^2 (d+e x)^{3/2} (b d-a e)}-\frac{5 e (3 a B e-7 A b e+4 b B d)}{4 \sqrt{d+e x} (b d-a e)^4}-\frac{5 e (3 a B e-7 A b e+4 b B d)}{12 b (d+e x)^{3/2} (b d-a e)^3}-\frac{3 a B e-7 A b e+4 b B d}{4 b (a+b x) (d+e x)^{3/2} (b d-a e)^2}+\frac{5 \sqrt{b} e (3 a B e-7 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 (b d-a e)^{9/2}}",1,"(-6*A*b^3*d^3 - 6*a*b^2*B*d^3 + 39*a*A*b^2*d^2*e - 83*a^2*b*B*d^2*e + 80*a^2*A*b*d*e^2 - 16*a^3*B*d*e^2 - 8*a^3*A*e^3 - 12*b^3*B*d^3*x + 21*A*b^3*d^2*e*x - 145*a*b^2*B*d^2*e*x + 238*a*A*b^2*d*e^2*x - 134*a^2*b*B*d*e^2*x + 56*a^2*A*b*e^3*x - 24*a^3*B*e^3*x - 80*b^3*B*d^2*e*x^2 + 140*A*b^3*d*e^2*x^2 - 160*a*b^2*B*d*e^2*x^2 + 175*a*A*b^2*e^3*x^2 - 75*a^2*b*B*e^3*x^2 - 60*b^3*B*d*e^2*x^3 + 105*A*b^3*e^3*x^3 - 45*a*b^2*B*e^3*x^3)/(12*(b*d - a*e)^4*(a + b*x)^2*(d + e*x)^(3/2)) + (5*(4*b^(3/2)*B*d*e - 7*A*b^(3/2)*e^2 + 3*a*Sqrt[b]*B*e^2)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/(4*(-(b*d) + a*e)^(9/2))","A",1
1765,1,541,281,0.8245322,"\int \frac{A+B x}{(a+b x)^3 (d+e x)^{7/2}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^3*(d + e*x)^(7/2)),x]","\frac{24 a^4 A e^4+16 a^4 B d e^3+40 a^4 B e^4 x-168 a^3 A b d e^3-72 a^3 A b e^4 x-272 a^3 b B d^2 e^2-648 a^3 b B d e^3 x-280 a^3 b B e^4 x^2+864 a^2 A b^2 d^2 e^2+1224 a^2 A b^2 d e^3 x+504 a^2 A b^2 e^4 x^2-659 a^2 b^2 B d^3 e-1929 a^2 b^2 B d^2 e^2 x-2289 a^2 b^2 B d e^3 x^2-875 a^2 b^2 B e^4 x^3+255 a A b^3 d^3 e+2493 a A b^3 d^2 e^2 x+3717 a A b^3 d e^3 x^2+1575 a A b^3 e^4 x^3-30 a b^3 B d^4-1183 a b^3 B d^3 e x-2457 a b^3 B d^2 e^2 x^2-1925 a b^3 B d e^3 x^3-525 a b^3 B e^4 x^4-30 A b^4 d^4+135 A b^4 d^3 e x+1449 A b^4 d^2 e^2 x^2+2205 A b^4 d e^3 x^3+945 A b^4 e^4 x^4-60 b^4 B d^4 x-644 b^4 B d^3 e x^2-980 b^4 B d^2 e^2 x^3-420 b^4 B d e^3 x^4}{60 (a+b x)^2 (d+e x)^{5/2} (b d-a e)^5}-\frac{7 \left(5 a b^{3/2} B e^2-9 A b^{5/2} e^2+4 b^{5/2} B d e\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x} \sqrt{a e-b d}}{b d-a e}\right)}{4 (a e-b d)^{11/2}}","\frac{7 b^{3/2} e (5 a B e-9 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 (b d-a e)^{11/2}}-\frac{7 b e (5 a B e-9 A b e+4 b B d)}{4 \sqrt{d+e x} (b d-a e)^5}-\frac{7 e (5 a B e-9 A b e+4 b B d)}{12 (d+e x)^{3/2} (b d-a e)^4}-\frac{7 e (5 a B e-9 A b e+4 b B d)}{20 b (d+e x)^{5/2} (b d-a e)^3}-\frac{5 a B e-9 A b e+4 b B d}{4 b (a+b x) (d+e x)^{5/2} (b d-a e)^2}-\frac{A b-a B}{2 b (a+b x)^2 (d+e x)^{5/2} (b d-a e)}",1,"(-30*A*b^4*d^4 - 30*a*b^3*B*d^4 + 255*a*A*b^3*d^3*e - 659*a^2*b^2*B*d^3*e + 864*a^2*A*b^2*d^2*e^2 - 272*a^3*b*B*d^2*e^2 - 168*a^3*A*b*d*e^3 + 16*a^4*B*d*e^3 + 24*a^4*A*e^4 - 60*b^4*B*d^4*x + 135*A*b^4*d^3*e*x - 1183*a*b^3*B*d^3*e*x + 2493*a*A*b^3*d^2*e^2*x - 1929*a^2*b^2*B*d^2*e^2*x + 1224*a^2*A*b^2*d*e^3*x - 648*a^3*b*B*d*e^3*x - 72*a^3*A*b*e^4*x + 40*a^4*B*e^4*x - 644*b^4*B*d^3*e*x^2 + 1449*A*b^4*d^2*e^2*x^2 - 2457*a*b^3*B*d^2*e^2*x^2 + 3717*a*A*b^3*d*e^3*x^2 - 2289*a^2*b^2*B*d*e^3*x^2 + 504*a^2*A*b^2*e^4*x^2 - 280*a^3*b*B*e^4*x^2 - 980*b^4*B*d^2*e^2*x^3 + 2205*A*b^4*d*e^3*x^3 - 1925*a*b^3*B*d*e^3*x^3 + 1575*a*A*b^3*e^4*x^3 - 875*a^2*b^2*B*e^4*x^3 - 420*b^4*B*d*e^3*x^4 + 945*A*b^4*e^4*x^4 - 525*a*b^3*B*e^4*x^4)/(60*(b*d - a*e)^5*(a + b*x)^2*(d + e*x)^(5/2)) - (7*(4*b^(5/2)*B*d*e - 9*A*b^(5/2)*e^2 + 5*a*b^(3/2)*B*e^2)*ArcTan[(Sqrt[b]*Sqrt[-(b*d) + a*e]*Sqrt[d + e*x])/(b*d - a*e)])/(4*(-(b*d) + a*e)^(11/2))","A",1
1766,1,263,164,0.2450102,"\int \frac{(a+b x) (e+f x)^{5/2}}{c+d x} \, dx","IntegrateAlgebraic[((a + b*x)*(e + f*x)^(5/2))/(c + d*x),x]","\frac{2 (a d-b c) (c f-d e)^{5/2} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{d^{9/2}}-\frac{2 \sqrt{e+f x} \left(-105 a c^2 d f^3+245 a c d^2 e f^2+35 a c d^2 f^3 x-161 a d^3 e^2 f-77 a d^3 e f^2 x-21 a d^3 f^3 x^2+105 b c^3 f^3-245 b c^2 d e f^2-35 b c^2 d f^3 x+161 b c d^2 e^2 f+77 b c d^2 e f^2 x+21 b c d^2 f^3 x^2-15 b d^3 e^3-45 b d^3 e^2 f x-45 b d^3 e f^2 x^2-15 b d^3 f^3 x^3\right)}{105 d^4 f}","\frac{2 (b c-a d) (d e-c f)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{d^{9/2}}-\frac{2 \sqrt{e+f x} (b c-a d) (d e-c f)^2}{d^4}-\frac{2 (e+f x)^{3/2} (b c-a d) (d e-c f)}{3 d^3}-\frac{2 (e+f x)^{5/2} (b c-a d)}{5 d^2}+\frac{2 b (e+f x)^{7/2}}{7 d f}",1,"(-2*Sqrt[e + f*x]*(-15*b*d^3*e^3 + 161*b*c*d^2*e^2*f - 161*a*d^3*e^2*f - 245*b*c^2*d*e*f^2 + 245*a*c*d^2*e*f^2 + 105*b*c^3*f^3 - 105*a*c^2*d*f^3 - 45*b*d^3*e^2*f*x + 77*b*c*d^2*e*f^2*x - 77*a*d^3*e*f^2*x - 35*b*c^2*d*f^3*x + 35*a*c*d^2*f^3*x - 45*b*d^3*e*f^2*x^2 + 21*b*c*d^2*f^3*x^2 - 21*a*d^3*f^3*x^2 - 15*b*d^3*f^3*x^3))/(105*d^4*f) + (2*(-(b*c) + a*d)*(-(d*e) + c*f)^(5/2)*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/d^(9/2)","A",1
1767,1,167,130,0.1687473,"\int \frac{(a+b x) (e+f x)^{3/2}}{c+d x} \, dx","IntegrateAlgebraic[((a + b*x)*(e + f*x)^(3/2))/(c + d*x),x]","\frac{2 \sqrt{e+f x} \left(-15 a c d f^2+20 a d^2 e f+5 a d^2 f^2 x+15 b c^2 f^2-20 b c d e f-5 b c d f^2 x+3 b d^2 e^2+6 b d^2 e f x+3 b d^2 f^2 x^2\right)}{15 d^3 f}-\frac{2 (a d-b c) (c f-d e)^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{d^{7/2}}","\frac{2 (b c-a d) (d e-c f)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{d^{7/2}}-\frac{2 \sqrt{e+f x} (b c-a d) (d e-c f)}{d^3}-\frac{2 (e+f x)^{3/2} (b c-a d)}{3 d^2}+\frac{2 b (e+f x)^{5/2}}{5 d f}",1,"(2*Sqrt[e + f*x]*(3*b*d^2*e^2 - 20*b*c*d*e*f + 20*a*d^2*e*f + 15*b*c^2*f^2 - 15*a*c*d*f^2 + 6*b*d^2*e*f*x - 5*b*c*d*f^2*x + 5*a*d^2*f^2*x + 3*b*d^2*f^2*x^2))/(15*d^3*f) - (2*(-(b*c) + a*d)*(-(d*e) + c*f)^(3/2)*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/d^(7/2)","A",1
1768,1,107,98,0.1582259,"\int \frac{(a+b x) \sqrt{e+f x}}{c+d x} \, dx","IntegrateAlgebraic[((a + b*x)*Sqrt[e + f*x])/(c + d*x),x]","\frac{2 (a d-b c) \sqrt{c f-d e} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{d^{5/2}}-\frac{2 \sqrt{e+f x} (-3 a d f+3 b c f-b d e-b d f x)}{3 d^2 f}","\frac{2 (b c-a d) \sqrt{d e-c f} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{d^{5/2}}-\frac{2 \sqrt{e+f x} (b c-a d)}{d^2}+\frac{2 b (e+f x)^{3/2}}{3 d f}",1,"(-2*Sqrt[e + f*x]*(-(b*d*e) + 3*b*c*f - 3*a*d*f - b*d*f*x))/(3*d^2*f) + (2*(-(b*c) + a*d)*Sqrt[-(d*e) + c*f]*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/d^(5/2)","A",1
1769,1,84,74,0.0879269,"\int \frac{a+b x}{(c+d x) \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(a + b*x)/((c + d*x)*Sqrt[e + f*x]),x]","\frac{2 b \sqrt{e+f x}}{d f}-\frac{2 (a d-b c) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{d^{3/2} \sqrt{c f-d e}}","\frac{2 (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{d^{3/2} \sqrt{d e-c f}}+\frac{2 b \sqrt{e+f x}}{d f}",1,"(2*b*Sqrt[e + f*x])/(d*f) - (2*(-(b*c) + a*d)*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/(d^(3/2)*Sqrt[-(d*e) + c*f])","A",1
1770,1,98,88,0.153931,"\int \frac{a+b x}{(c+d x) (e+f x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)/((c + d*x)*(e + f*x)^(3/2)),x]","\frac{2 (a d-b c) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{\sqrt{d} (c f-d e)^{3/2}}-\frac{2 (a f-b e)}{f \sqrt{e+f x} (c f-d e)}","\frac{2 (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{\sqrt{d} (d e-c f)^{3/2}}-\frac{2 (b e-a f)}{f \sqrt{e+f x} (d e-c f)}",1,"(-2*(-(b*e) + a*f))/(f*(-(d*e) + c*f)*Sqrt[e + f*x]) + (2*(-(b*c) + a*d)*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/(Sqrt[d]*(-(d*e) + c*f)^(3/2))","A",1
1771,1,137,119,0.2018944,"\int \frac{a+b x}{(c+d x) (e+f x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)/((c + d*x)*(e + f*x)^(5/2)),x]","-\frac{2 \left(a d^{3/2}-b c \sqrt{d}\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{(c f-d e)^{5/2}}-\frac{2 \left(a c f^2-4 a d e f-3 a d f^2 x+2 b c e f+3 b c f^2 x+b d e^2\right)}{3 f (e+f x)^{3/2} (c f-d e)^2}","-\frac{2 (b c-a d)}{\sqrt{e+f x} (d e-c f)^2}-\frac{2 (b e-a f)}{3 f (e+f x)^{3/2} (d e-c f)}+\frac{2 \sqrt{d} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{(d e-c f)^{5/2}}",1,"(-2*(b*d*e^2 + 2*b*c*e*f - 4*a*d*e*f + a*c*f^2 + 3*b*c*f^2*x - 3*a*d*f^2*x))/(3*f*(-(d*e) + c*f)^2*(e + f*x)^(3/2)) - (2*(-(b*c*Sqrt[d]) + a*d^(3/2))*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/(-(d*e) + c*f)^(5/2)","A",1
1772,1,216,151,0.3262657,"\int \frac{a+b x}{(c+d x) (e+f x)^{7/2}} \, dx","IntegrateAlgebraic[(a + b*x)/((c + d*x)*(e + f*x)^(7/2)),x]","\frac{2 \left(a d^{5/2}-b c d^{3/2}\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{(c f-d e)^{7/2}}-\frac{2 \left(3 a c^2 f^3-11 a c d e f^2-5 a c d f^3 x+23 a d^2 e^2 f+35 a d^2 e f^2 x+15 a d^2 f^3 x^2+2 b c^2 e f^2+5 b c^2 f^3 x-14 b c d e^2 f-35 b c d e f^2 x-15 b c d f^3 x^2-3 b d^2 e^3\right)}{15 f (e+f x)^{5/2} (c f-d e)^3}","\frac{2 d^{3/2} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{(d e-c f)^{7/2}}-\frac{2 d (b c-a d)}{\sqrt{e+f x} (d e-c f)^3}-\frac{2 (b c-a d)}{3 (e+f x)^{3/2} (d e-c f)^2}-\frac{2 (b e-a f)}{5 f (e+f x)^{5/2} (d e-c f)}",1,"(-2*(-3*b*d^2*e^3 - 14*b*c*d*e^2*f + 23*a*d^2*e^2*f + 2*b*c^2*e*f^2 - 11*a*c*d*e*f^2 + 3*a*c^2*f^3 - 35*b*c*d*e*f^2*x + 35*a*d^2*e*f^2*x + 5*b*c^2*f^3*x - 5*a*c*d*f^3*x - 15*b*c*d*f^3*x^2 + 15*a*d^2*f^3*x^2))/(15*f*(-(d*e) + c*f)^3*(e + f*x)^(5/2)) + (2*(-(b*c*d^(3/2)) + a*d^(5/2))*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/(-(d*e) + c*f)^(7/2)","A",1
1773,1,333,185,0.4508908,"\int \frac{a+b x}{(c+d x) (e+f x)^{9/2}} \, dx","IntegrateAlgebraic[(a + b*x)/((c + d*x)*(e + f*x)^(9/2)),x]","-\frac{2 \left(15 a c^3 f^4-66 a c^2 d e f^3-21 a c^2 d f^4 x+122 a c d^2 e^2 f^2+112 a c d^2 e f^3 x+35 a c d^2 f^4 x^2-176 a d^3 e^3 f-406 a d^3 e^2 f^2 x-350 a d^3 e f^3 x^2-105 a d^3 f^4 x^3+6 b c^3 e f^3+21 b c^3 f^4 x-32 b c^2 d e^2 f^2-112 b c^2 d e f^3 x-35 b c^2 d f^4 x^2+116 b c d^2 e^3 f+406 b c d^2 e^2 f^2 x+350 b c d^2 e f^3 x^2+105 b c d^2 f^4 x^3+15 b d^3 e^4\right)}{105 f (e+f x)^{7/2} (c f-d e)^4}-\frac{2 \left(a d^{7/2}-b c d^{5/2}\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{(c f-d e)^{9/2}}","\frac{2 d^{5/2} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{(d e-c f)^{9/2}}-\frac{2 d^2 (b c-a d)}{\sqrt{e+f x} (d e-c f)^4}-\frac{2 d (b c-a d)}{3 (e+f x)^{3/2} (d e-c f)^3}-\frac{2 (b c-a d)}{5 (e+f x)^{5/2} (d e-c f)^2}-\frac{2 (b e-a f)}{7 f (e+f x)^{7/2} (d e-c f)}",1,"(-2*(15*b*d^3*e^4 + 116*b*c*d^2*e^3*f - 176*a*d^3*e^3*f - 32*b*c^2*d*e^2*f^2 + 122*a*c*d^2*e^2*f^2 + 6*b*c^3*e*f^3 - 66*a*c^2*d*e*f^3 + 15*a*c^3*f^4 + 406*b*c*d^2*e^2*f^2*x - 406*a*d^3*e^2*f^2*x - 112*b*c^2*d*e*f^3*x + 112*a*c*d^2*e*f^3*x + 21*b*c^3*f^4*x - 21*a*c^2*d*f^4*x + 350*b*c*d^2*e*f^3*x^2 - 350*a*d^3*e*f^3*x^2 - 35*b*c^2*d*f^4*x^2 + 35*a*c*d^2*f^4*x^2 + 105*b*c*d^2*f^4*x^3 - 105*a*d^3*f^4*x^3))/(105*f*(-(d*e) + c*f)^4*(e + f*x)^(7/2)) - (2*(-(b*c*d^(5/2)) + a*d^(7/2))*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/(-(d*e) + c*f)^(9/2)","A",1
1774,1,529,208,0.3878166,"\int \frac{(a+b x)^2 (e+f x)^{5/2}}{c+d x} \, dx","IntegrateAlgebraic[((a + b*x)^2*(e + f*x)^(5/2))/(c + d*x),x]","\frac{2 \left(a^2 d^2-2 a b c d+b^2 c^2\right) (c f-d e)^{5/2} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{d^{11/2}}+\frac{2 \sqrt{e+f x} \left(315 a^2 c^2 d^2 f^4-735 a^2 c d^3 e f^3-105 a^2 c d^3 f^4 x+483 a^2 d^4 e^2 f^2+231 a^2 d^4 e f^3 x+63 a^2 d^4 f^4 x^2-630 a b c^3 d f^4+1470 a b c^2 d^2 e f^3+210 a b c^2 d^2 f^4 x-966 a b c d^3 e^2 f^2-462 a b c d^3 e f^3 x-126 a b c d^3 f^4 x^2+90 a b d^4 e^3 f+270 a b d^4 e^2 f^2 x+270 a b d^4 e f^3 x^2+90 a b d^4 f^4 x^3+315 b^2 c^4 f^4-735 b^2 c^3 d e f^3-105 b^2 c^3 d f^4 x+483 b^2 c^2 d^2 e^2 f^2+231 b^2 c^2 d^2 e f^3 x+63 b^2 c^2 d^2 f^4 x^2-45 b^2 c d^3 e^3 f-135 b^2 c d^3 e^2 f^2 x-135 b^2 c d^3 e f^3 x^2-45 b^2 c d^3 f^4 x^3-10 b^2 d^4 e^4+5 b^2 d^4 e^3 f x+75 b^2 d^4 e^2 f^2 x^2+95 b^2 d^4 e f^3 x^3+35 b^2 d^4 f^4 x^4\right)}{315 d^5 f^2}","-\frac{2 (b c-a d)^2 (d e-c f)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{d^{11/2}}+\frac{2 \sqrt{e+f x} (b c-a d)^2 (d e-c f)^2}{d^5}+\frac{2 (e+f x)^{3/2} (b c-a d)^2 (d e-c f)}{3 d^4}+\frac{2 (e+f x)^{5/2} (b c-a d)^2}{5 d^3}-\frac{2 b (e+f x)^{7/2} (-2 a d f+b c f+b d e)}{7 d^2 f^2}+\frac{2 b^2 (e+f x)^{9/2}}{9 d f^2}",1,"(2*Sqrt[e + f*x]*(-10*b^2*d^4*e^4 - 45*b^2*c*d^3*e^3*f + 90*a*b*d^4*e^3*f + 483*b^2*c^2*d^2*e^2*f^2 - 966*a*b*c*d^3*e^2*f^2 + 483*a^2*d^4*e^2*f^2 - 735*b^2*c^3*d*e*f^3 + 1470*a*b*c^2*d^2*e*f^3 - 735*a^2*c*d^3*e*f^3 + 315*b^2*c^4*f^4 - 630*a*b*c^3*d*f^4 + 315*a^2*c^2*d^2*f^4 + 5*b^2*d^4*e^3*f*x - 135*b^2*c*d^3*e^2*f^2*x + 270*a*b*d^4*e^2*f^2*x + 231*b^2*c^2*d^2*e*f^3*x - 462*a*b*c*d^3*e*f^3*x + 231*a^2*d^4*e*f^3*x - 105*b^2*c^3*d*f^4*x + 210*a*b*c^2*d^2*f^4*x - 105*a^2*c*d^3*f^4*x + 75*b^2*d^4*e^2*f^2*x^2 - 135*b^2*c*d^3*e*f^3*x^2 + 270*a*b*d^4*e*f^3*x^2 + 63*b^2*c^2*d^2*f^4*x^2 - 126*a*b*c*d^3*f^4*x^2 + 63*a^2*d^4*f^4*x^2 + 95*b^2*d^4*e*f^3*x^3 - 45*b^2*c*d^3*f^4*x^3 + 90*a*b*d^4*f^4*x^3 + 35*b^2*d^4*f^4*x^4))/(315*d^5*f^2) + (2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(-(d*e) + c*f)^(5/2)*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/d^(11/2)","B",1
1775,1,338,172,0.2747066,"\int \frac{(a+b x)^2 (e+f x)^{3/2}}{c+d x} \, dx","IntegrateAlgebraic[((a + b*x)^2*(e + f*x)^(3/2))/(c + d*x),x]","-\frac{2 \left(a^2 d^2-2 a b c d+b^2 c^2\right) (c f-d e)^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{d^{9/2}}-\frac{2 \sqrt{e+f x} \left(105 a^2 c d^2 f^3-140 a^2 d^3 e f^2-35 a^2 d^3 f^3 x-210 a b c^2 d f^3+280 a b c d^2 e f^2+70 a b c d^2 f^3 x-42 a b d^3 e^2 f-84 a b d^3 e f^2 x-42 a b d^3 f^3 x^2+105 b^2 c^3 f^3-140 b^2 c^2 d e f^2-35 b^2 c^2 d f^3 x+21 b^2 c d^2 e^2 f+42 b^2 c d^2 e f^2 x+21 b^2 c d^2 f^3 x^2+6 b^2 d^3 e^3-3 b^2 d^3 e^2 f x-24 b^2 d^3 e f^2 x^2-15 b^2 d^3 f^3 x^3\right)}{105 d^4 f^2}","-\frac{2 (b c-a d)^2 (d e-c f)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{d^{9/2}}+\frac{2 \sqrt{e+f x} (b c-a d)^2 (d e-c f)}{d^4}+\frac{2 (e+f x)^{3/2} (b c-a d)^2}{3 d^3}-\frac{2 b (e+f x)^{5/2} (-2 a d f+b c f+b d e)}{5 d^2 f^2}+\frac{2 b^2 (e+f x)^{7/2}}{7 d f^2}",1,"(-2*Sqrt[e + f*x]*(6*b^2*d^3*e^3 + 21*b^2*c*d^2*e^2*f - 42*a*b*d^3*e^2*f - 140*b^2*c^2*d*e*f^2 + 280*a*b*c*d^2*e*f^2 - 140*a^2*d^3*e*f^2 + 105*b^2*c^3*f^3 - 210*a*b*c^2*d*f^3 + 105*a^2*c*d^2*f^3 - 3*b^2*d^3*e^2*f*x + 42*b^2*c*d^2*e*f^2*x - 84*a*b*d^3*e*f^2*x - 35*b^2*c^2*d*f^3*x + 70*a*b*c*d^2*f^3*x - 35*a^2*d^3*f^3*x - 24*b^2*d^3*e*f^2*x^2 + 21*b^2*c*d^2*f^3*x^2 - 42*a*b*d^3*f^3*x^2 - 15*b^2*d^3*f^3*x^3))/(105*d^4*f^2) - (2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(-(d*e) + c*f)^(3/2)*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/d^(9/2)","A",1
1776,1,205,138,0.2657325,"\int \frac{(a+b x)^2 \sqrt{e+f x}}{c+d x} \, dx","IntegrateAlgebraic[((a + b*x)^2*Sqrt[e + f*x])/(c + d*x),x]","\frac{2 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \sqrt{c f-d e} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{d^{7/2}}+\frac{2 \sqrt{e+f x} \left(15 a^2 d^2 f^2-30 a b c d f^2+10 a b d^2 e f+10 a b d^2 f^2 x+15 b^2 c^2 f^2-5 b^2 c d e f-5 b^2 c d f^2 x-2 b^2 d^2 e^2+b^2 d^2 e f x+3 b^2 d^2 f^2 x^2\right)}{15 d^3 f^2}","-\frac{2 (b c-a d)^2 \sqrt{d e-c f} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{d^{7/2}}+\frac{2 \sqrt{e+f x} (b c-a d)^2}{d^3}-\frac{2 b (e+f x)^{3/2} (-2 a d f+b c f+b d e)}{3 d^2 f^2}+\frac{2 b^2 (e+f x)^{5/2}}{5 d f^2}",1,"(2*Sqrt[e + f*x]*(-2*b^2*d^2*e^2 - 5*b^2*c*d*e*f + 10*a*b*d^2*e*f + 15*b^2*c^2*f^2 - 30*a*b*c*d*f^2 + 15*a^2*d^2*f^2 + b^2*d^2*e*f*x - 5*b^2*c*d*f^2*x + 10*a*b*d^2*f^2*x + 3*b^2*d^2*f^2*x^2))/(15*d^3*f^2) + (2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*Sqrt[-(d*e) + c*f]*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/d^(7/2)","A",1
1777,1,127,112,0.1323057,"\int \frac{(a+b x)^2}{(c+d x) \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(a + b*x)^2/((c + d*x)*Sqrt[e + f*x]),x]","-\frac{2 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{d^{5/2} \sqrt{c f-d e}}-\frac{2 \sqrt{e+f x} \left(-6 a b d f+3 b^2 c f+2 b^2 d e-b^2 d f x\right)}{3 d^2 f^2}","-\frac{2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{d^{5/2} \sqrt{d e-c f}}-\frac{2 b \sqrt{e+f x} (-2 a d f+b c f+b d e)}{d^2 f^2}+\frac{2 b^2 (e+f x)^{3/2}}{3 d f^2}",1,"(-2*Sqrt[e + f*x]*(2*b^2*d*e + 3*b^2*c*f - 6*a*b*d*f - b^2*d*f*x))/(3*d^2*f^2) - (2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/(d^(5/2)*Sqrt[-(d*e) + c*f])","A",1
1778,1,157,112,0.1916255,"\int \frac{(a+b x)^2}{(c+d x) (e+f x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/((c + d*x)*(e + f*x)^(3/2)),x]","\frac{2 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{d^{3/2} (c f-d e)^{3/2}}+\frac{2 \left(a^2 d f^2-2 a b d e f-b^2 c e f-b^2 c f^2 x+2 b^2 d e^2+b^2 d e f x\right)}{d f^2 \sqrt{e+f x} (d e-c f)}","-\frac{2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{d^{3/2} (d e-c f)^{3/2}}+\frac{2 (b e-a f)^2}{f^2 \sqrt{e+f x} (d e-c f)}+\frac{2 b^2 \sqrt{e+f x}}{d f^2}",1,"(2*(2*b^2*d*e^2 - b^2*c*e*f - 2*a*b*d*e*f + a^2*d*f^2 + b^2*d*e*f*x - b^2*c*f^2*x))/(d*f^2*(d*e - c*f)*Sqrt[e + f*x]) + (2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/(d^(3/2)*(-(d*e) + c*f)^(3/2))","A",1
1779,1,202,140,0.2540946,"\int \frac{(a+b x)^2}{(c+d x) (e+f x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/((c + d*x)*(e + f*x)^(5/2)),x]","-\frac{2 \left(a^2 d^2-2 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{\sqrt{d} (c f-d e)^{5/2}}-\frac{2 \left(a^2 c f^3-4 a^2 d e f^2-3 a^2 d f^3 x+4 a b c e f^2+6 a b c f^3 x+2 a b d e^2 f-5 b^2 c e^2 f-6 b^2 c e f^2 x+2 b^2 d e^3+3 b^2 d e^2 f x\right)}{3 f^2 (e+f x)^{3/2} (c f-d e)^2}","-\frac{2 (b e-a f) (a d f-2 b c f+b d e)}{f^2 \sqrt{e+f x} (d e-c f)^2}+\frac{2 (b e-a f)^2}{3 f^2 (e+f x)^{3/2} (d e-c f)}-\frac{2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{\sqrt{d} (d e-c f)^{5/2}}",1,"(-2*(2*b^2*d*e^3 - 5*b^2*c*e^2*f + 2*a*b*d*e^2*f + 4*a*b*c*e*f^2 - 4*a^2*d*e*f^2 + a^2*c*f^3 + 3*b^2*d*e^2*f*x - 6*b^2*c*e*f^2*x + 6*a*b*c*f^3*x - 3*a^2*d*f^3*x))/(3*f^2*(-(d*e) + c*f)^2*(e + f*x)^(3/2)) - (2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/(Sqrt[d]*(-(d*e) + c*f)^(5/2))","A",1
1780,1,344,173,0.3759092,"\int \frac{(a+b x)^2}{(c+d x) (e+f x)^{7/2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/((c + d*x)*(e + f*x)^(7/2)),x]","\frac{2 \left(a^2 d^{5/2}-2 a b c d^{3/2}+b^2 c^2 \sqrt{d}\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{(c f-d e)^{7/2}}-\frac{2 \left(3 a^2 c^2 f^4-11 a^2 c d e f^3-5 a^2 c d f^4 x+23 a^2 d^2 e^2 f^2+35 a^2 d^2 e f^3 x+15 a^2 d^2 f^4 x^2+4 a b c^2 e f^3+10 a b c^2 f^4 x-28 a b c d e^2 f^2-70 a b c d e f^3 x-30 a b c d f^4 x^2-6 a b d^2 e^3 f+8 b^2 c^2 e^2 f^2+20 b^2 c^2 e f^3 x+15 b^2 c^2 f^4 x^2+9 b^2 c d e^3 f+15 b^2 c d e^2 f^2 x-2 b^2 d^2 e^4-5 b^2 d^2 e^3 f x\right)}{15 f^2 (e+f x)^{5/2} (c f-d e)^3}","-\frac{2 (b e-a f) (a d f-2 b c f+b d e)}{3 f^2 (e+f x)^{3/2} (d e-c f)^2}+\frac{2 (b e-a f)^2}{5 f^2 (e+f x)^{5/2} (d e-c f)}+\frac{2 (b c-a d)^2}{\sqrt{e+f x} (d e-c f)^3}-\frac{2 \sqrt{d} (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{(d e-c f)^{7/2}}",1,"(-2*(-2*b^2*d^2*e^4 + 9*b^2*c*d*e^3*f - 6*a*b*d^2*e^3*f + 8*b^2*c^2*e^2*f^2 - 28*a*b*c*d*e^2*f^2 + 23*a^2*d^2*e^2*f^2 + 4*a*b*c^2*e*f^3 - 11*a^2*c*d*e*f^3 + 3*a^2*c^2*f^4 - 5*b^2*d^2*e^3*f*x + 15*b^2*c*d*e^2*f^2*x + 20*b^2*c^2*e*f^3*x - 70*a*b*c*d*e*f^3*x + 35*a^2*d^2*e*f^3*x + 10*a*b*c^2*f^4*x - 5*a^2*c*d*f^4*x + 15*b^2*c^2*f^4*x^2 - 30*a*b*c*d*f^4*x^2 + 15*a^2*d^2*f^4*x^2))/(15*f^2*(-(d*e) + c*f)^3*(e + f*x)^(5/2)) + (2*(b^2*c^2*Sqrt[d] - 2*a*b*c*d^(3/2) + a^2*d^(5/2))*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/(-(d*e) + c*f)^(7/2)","A",1
1781,1,539,207,0.5674043,"\int \frac{(a+b x)^2}{(c+d x) (e+f x)^{9/2}} \, dx","IntegrateAlgebraic[(a + b*x)^2/((c + d*x)*(e + f*x)^(9/2)),x]","-\frac{2 \left(a^2 d^{7/2}-2 a b c d^{5/2}+b^2 c^2 d^{3/2}\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{(c f-d e)^{9/2}}-\frac{2 \left(15 a^2 c^3 f^5-66 a^2 c^2 d e f^4-21 a^2 c^2 d f^5 x+122 a^2 c d^2 e^2 f^3+112 a^2 c d^2 e f^4 x+35 a^2 c d^2 f^5 x^2-176 a^2 d^3 e^3 f^2-406 a^2 d^3 e^2 f^3 x-350 a^2 d^3 e f^4 x^2-105 a^2 d^3 f^5 x^3+12 a b c^3 e f^4+42 a b c^3 f^5 x-64 a b c^2 d e^2 f^3-224 a b c^2 d e f^4 x-70 a b c^2 d f^5 x^2+232 a b c d^2 e^3 f^2+812 a b c d^2 e^2 f^3 x+700 a b c d^2 e f^4 x^2+210 a b c d^2 f^5 x^3+30 a b d^3 e^4 f+8 b^2 c^3 e^2 f^3+28 b^2 c^3 e f^4 x+35 b^2 c^3 f^5 x^2-80 b^2 c^2 d e^3 f^2-280 b^2 c^2 d e^2 f^3 x-350 b^2 c^2 d e f^4 x^2-105 b^2 c^2 d f^5 x^3-39 b^2 c d^2 e^4 f-84 b^2 c d^2 e^3 f^2 x+6 b^2 d^3 e^5+21 b^2 d^3 e^4 f x\right)}{105 f^2 (e+f x)^{7/2} (c f-d e)^4}","-\frac{2 d^{3/2} (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{(d e-c f)^{9/2}}-\frac{2 (b e-a f) (a d f-2 b c f+b d e)}{5 f^2 (e+f x)^{5/2} (d e-c f)^2}+\frac{2 (b e-a f)^2}{7 f^2 (e+f x)^{7/2} (d e-c f)}+\frac{2 d (b c-a d)^2}{\sqrt{e+f x} (d e-c f)^4}+\frac{2 (b c-a d)^2}{3 (e+f x)^{3/2} (d e-c f)^3}",1,"(-2*(6*b^2*d^3*e^5 - 39*b^2*c*d^2*e^4*f + 30*a*b*d^3*e^4*f - 80*b^2*c^2*d*e^3*f^2 + 232*a*b*c*d^2*e^3*f^2 - 176*a^2*d^3*e^3*f^2 + 8*b^2*c^3*e^2*f^3 - 64*a*b*c^2*d*e^2*f^3 + 122*a^2*c*d^2*e^2*f^3 + 12*a*b*c^3*e*f^4 - 66*a^2*c^2*d*e*f^4 + 15*a^2*c^3*f^5 + 21*b^2*d^3*e^4*f*x - 84*b^2*c*d^2*e^3*f^2*x - 280*b^2*c^2*d*e^2*f^3*x + 812*a*b*c*d^2*e^2*f^3*x - 406*a^2*d^3*e^2*f^3*x + 28*b^2*c^3*e*f^4*x - 224*a*b*c^2*d*e*f^4*x + 112*a^2*c*d^2*e*f^4*x + 42*a*b*c^3*f^5*x - 21*a^2*c^2*d*f^5*x - 350*b^2*c^2*d*e*f^4*x^2 + 700*a*b*c*d^2*e*f^4*x^2 - 350*a^2*d^3*e*f^4*x^2 + 35*b^2*c^3*f^5*x^2 - 70*a*b*c^2*d*f^5*x^2 + 35*a^2*c*d^2*f^5*x^2 - 105*b^2*c^2*d*f^5*x^3 + 210*a*b*c*d^2*f^5*x^3 - 105*a^2*d^3*f^5*x^3))/(105*f^2*(-(d*e) + c*f)^4*(e + f*x)^(7/2)) - (2*(b^2*c^2*d^(3/2) - 2*a*b*c*d^(5/2) + a^2*d^(7/2))*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/(-(d*e) + c*f)^(9/2)","B",1
1782,1,915,280,0.606476,"\int \frac{(a+b x)^3 (e+f x)^{5/2}}{c+d x} \, dx","IntegrateAlgebraic[((a + b*x)^3*(e + f*x)^(5/2))/(c + d*x),x]","\frac{2 \left(-b^3 c^3+3 a b^2 d c^2-3 a^2 b d^2 c+a^3 d^3\right) (c f-d e)^{5/2} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{c f-d e} \sqrt{e+f x}}{d e-c f}\right)}{d^{13/2}}-\frac{2 \sqrt{e+f x} \left(-40 b^3 e^5 d^5-315 b^3 f^5 x^5 d^5-1155 a b^2 f^5 x^4 d^5-805 b^3 e f^4 x^4 d^5-5313 a^3 e^2 f^3 d^5-1485 a^2 b f^5 x^3 d^5-3135 a b^2 e f^4 x^3 d^5-565 b^3 e^2 f^3 x^3 d^5-1485 a^2 b e^3 f^2 d^5-693 a^3 f^5 x^2 d^5-4455 a^2 b e f^4 x^2 d^5-2475 a b^2 e^2 f^3 x^2 d^5-15 b^3 e^3 f^2 x^2 d^5+330 a b^2 e^4 f d^5-2541 a^3 e f^4 x d^5-4455 a^2 b e^2 f^3 x d^5-165 a b^2 e^3 f^2 x d^5+20 b^3 e^4 f x d^5+8085 a^3 c e f^4 d^4+385 b^3 c f^5 x^4 d^4+15939 a^2 b c e^2 f^3 d^4+1485 a b^2 c f^5 x^3 d^4+1045 b^3 c e f^4 x^3 d^4+1485 a b^2 c e^3 f^2 d^4+2079 a^2 b c f^5 x^2 d^4+4455 a b^2 c e f^4 x^2 d^4+825 b^3 c e^2 f^3 x^2 d^4-110 b^3 c e^4 f d^4+1155 a^3 c f^5 x d^4+7623 a^2 b c e f^4 x d^4+4455 a b^2 c e^2 f^3 x d^4+55 b^3 c e^3 f^2 x d^4-3465 a^3 c^2 f^5 d^3-24255 a^2 b c^2 e f^4 d^3-15939 a b^2 c^2 e^2 f^3 d^3-495 b^3 c^2 f^5 x^3 d^3-495 b^3 c^2 e^3 f^2 d^3-2079 a b^2 c^2 f^5 x^2 d^3-1485 b^3 c^2 e f^4 x^2 d^3-3465 a^2 b c^2 f^5 x d^3-7623 a b^2 c^2 e f^4 x d^3-1485 b^3 c^2 e^2 f^3 x d^3+10395 a^2 b c^3 f^5 d^2+24255 a b^2 c^3 e f^4 d^2+5313 b^3 c^3 e^2 f^3 d^2+693 b^3 c^3 f^5 x^2 d^2+3465 a b^2 c^3 f^5 x d^2+2541 b^3 c^3 e f^4 x d^2-10395 a b^2 c^4 f^5 d-8085 b^3 c^4 e f^4 d-1155 b^3 c^4 f^5 x d+3465 b^3 c^5 f^5\right)}{3465 d^6 f^3}","\frac{2 b (e+f x)^{7/2} \left(3 a^2 d^2 f^2-3 a b d f (c f+d e)+b^2 \left(c^2 f^2+c d e f+d^2 e^2\right)\right)}{7 d^3 f^3}-\frac{2 b^2 (e+f x)^{9/2} (-3 a d f+b c f+2 b d e)}{9 d^2 f^3}+\frac{2 (b c-a d)^3 (d e-c f)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{d^{13/2}}-\frac{2 \sqrt{e+f x} (b c-a d)^3 (d e-c f)^2}{d^6}-\frac{2 (e+f x)^{3/2} (b c-a d)^3 (d e-c f)}{3 d^5}-\frac{2 (e+f x)^{5/2} (b c-a d)^3}{5 d^4}+\frac{2 b^3 (e+f x)^{11/2}}{11 d f^3}",1,"(-2*Sqrt[e + f*x]*(-40*b^3*d^5*e^5 - 110*b^3*c*d^4*e^4*f + 330*a*b^2*d^5*e^4*f - 495*b^3*c^2*d^3*e^3*f^2 + 1485*a*b^2*c*d^4*e^3*f^2 - 1485*a^2*b*d^5*e^3*f^2 + 5313*b^3*c^3*d^2*e^2*f^3 - 15939*a*b^2*c^2*d^3*e^2*f^3 + 15939*a^2*b*c*d^4*e^2*f^3 - 5313*a^3*d^5*e^2*f^3 - 8085*b^3*c^4*d*e*f^4 + 24255*a*b^2*c^3*d^2*e*f^4 - 24255*a^2*b*c^2*d^3*e*f^4 + 8085*a^3*c*d^4*e*f^4 + 3465*b^3*c^5*f^5 - 10395*a*b^2*c^4*d*f^5 + 10395*a^2*b*c^3*d^2*f^5 - 3465*a^3*c^2*d^3*f^5 + 20*b^3*d^5*e^4*f*x + 55*b^3*c*d^4*e^3*f^2*x - 165*a*b^2*d^5*e^3*f^2*x - 1485*b^3*c^2*d^3*e^2*f^3*x + 4455*a*b^2*c*d^4*e^2*f^3*x - 4455*a^2*b*d^5*e^2*f^3*x + 2541*b^3*c^3*d^2*e*f^4*x - 7623*a*b^2*c^2*d^3*e*f^4*x + 7623*a^2*b*c*d^4*e*f^4*x - 2541*a^3*d^5*e*f^4*x - 1155*b^3*c^4*d*f^5*x + 3465*a*b^2*c^3*d^2*f^5*x - 3465*a^2*b*c^2*d^3*f^5*x + 1155*a^3*c*d^4*f^5*x - 15*b^3*d^5*e^3*f^2*x^2 + 825*b^3*c*d^4*e^2*f^3*x^2 - 2475*a*b^2*d^5*e^2*f^3*x^2 - 1485*b^3*c^2*d^3*e*f^4*x^2 + 4455*a*b^2*c*d^4*e*f^4*x^2 - 4455*a^2*b*d^5*e*f^4*x^2 + 693*b^3*c^3*d^2*f^5*x^2 - 2079*a*b^2*c^2*d^3*f^5*x^2 + 2079*a^2*b*c*d^4*f^5*x^2 - 693*a^3*d^5*f^5*x^2 - 565*b^3*d^5*e^2*f^3*x^3 + 1045*b^3*c*d^4*e*f^4*x^3 - 3135*a*b^2*d^5*e*f^4*x^3 - 495*b^3*c^2*d^3*f^5*x^3 + 1485*a*b^2*c*d^4*f^5*x^3 - 1485*a^2*b*d^5*f^5*x^3 - 805*b^3*d^5*e*f^4*x^4 + 385*b^3*c*d^4*f^5*x^4 - 1155*a*b^2*d^5*f^5*x^4 - 315*b^3*d^5*f^5*x^5))/(3465*d^6*f^3) + (2*(-(b^3*c^3) + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*(-(d*e) + c*f)^(5/2)*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/d^(13/2)","B",1
1783,1,606,244,0.4189116,"\int \frac{(a+b x)^3 (e+f x)^{3/2}}{c+d x} \, dx","IntegrateAlgebraic[((a + b*x)^3*(e + f*x)^(3/2))/(c + d*x),x]","\frac{2 \sqrt{e+f x} \left(-315 a^3 c d^3 f^4+420 a^3 d^4 e f^3+105 a^3 d^4 f^4 x+945 a^2 b c^2 d^2 f^4-1260 a^2 b c d^3 e f^3-315 a^2 b c d^3 f^4 x+189 a^2 b d^4 e^2 f^2+378 a^2 b d^4 e f^3 x+189 a^2 b d^4 f^4 x^2-945 a b^2 c^3 d f^4+1260 a b^2 c^2 d^2 e f^3+315 a b^2 c^2 d^2 f^4 x-189 a b^2 c d^3 e^2 f^2-378 a b^2 c d^3 e f^3 x-189 a b^2 c d^3 f^4 x^2-54 a b^2 d^4 e^3 f+27 a b^2 d^4 e^2 f^2 x+216 a b^2 d^4 e f^3 x^2+135 a b^2 d^4 f^4 x^3+315 b^3 c^4 f^4-420 b^3 c^3 d e f^3-105 b^3 c^3 d f^4 x+63 b^3 c^2 d^2 e^2 f^2+126 b^3 c^2 d^2 e f^3 x+63 b^3 c^2 d^2 f^4 x^2+18 b^3 c d^3 e^3 f-9 b^3 c d^3 e^2 f^2 x-72 b^3 c d^3 e f^3 x^2-45 b^3 c d^3 f^4 x^3+8 b^3 d^4 e^4-4 b^3 d^4 e^3 f x+3 b^3 d^4 e^2 f^2 x^2+50 b^3 d^4 e f^3 x^3+35 b^3 d^4 f^4 x^4\right)}{315 d^5 f^3}-\frac{2 \left(a^3 d^3-3 a^2 b c d^2+3 a b^2 c^2 d-b^3 c^3\right) (c f-d e)^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{d^{11/2}}","\frac{2 b (e+f x)^{5/2} \left(3 a^2 d^2 f^2-3 a b d f (c f+d e)+b^2 \left(c^2 f^2+c d e f+d^2 e^2\right)\right)}{5 d^3 f^3}-\frac{2 b^2 (e+f x)^{7/2} (-3 a d f+b c f+2 b d e)}{7 d^2 f^3}+\frac{2 (b c-a d)^3 (d e-c f)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{d^{11/2}}-\frac{2 \sqrt{e+f x} (b c-a d)^3 (d e-c f)}{d^5}-\frac{2 (e+f x)^{3/2} (b c-a d)^3}{3 d^4}+\frac{2 b^3 (e+f x)^{9/2}}{9 d f^3}",1,"(2*Sqrt[e + f*x]*(8*b^3*d^4*e^4 + 18*b^3*c*d^3*e^3*f - 54*a*b^2*d^4*e^3*f + 63*b^3*c^2*d^2*e^2*f^2 - 189*a*b^2*c*d^3*e^2*f^2 + 189*a^2*b*d^4*e^2*f^2 - 420*b^3*c^3*d*e*f^3 + 1260*a*b^2*c^2*d^2*e*f^3 - 1260*a^2*b*c*d^3*e*f^3 + 420*a^3*d^4*e*f^3 + 315*b^3*c^4*f^4 - 945*a*b^2*c^3*d*f^4 + 945*a^2*b*c^2*d^2*f^4 - 315*a^3*c*d^3*f^4 - 4*b^3*d^4*e^3*f*x - 9*b^3*c*d^3*e^2*f^2*x + 27*a*b^2*d^4*e^2*f^2*x + 126*b^3*c^2*d^2*e*f^3*x - 378*a*b^2*c*d^3*e*f^3*x + 378*a^2*b*d^4*e*f^3*x - 105*b^3*c^3*d*f^4*x + 315*a*b^2*c^2*d^2*f^4*x - 315*a^2*b*c*d^3*f^4*x + 105*a^3*d^4*f^4*x + 3*b^3*d^4*e^2*f^2*x^2 - 72*b^3*c*d^3*e*f^3*x^2 + 216*a*b^2*d^4*e*f^3*x^2 + 63*b^3*c^2*d^2*f^4*x^2 - 189*a*b^2*c*d^3*f^4*x^2 + 189*a^2*b*d^4*f^4*x^2 + 50*b^3*d^4*e*f^3*x^3 - 45*b^3*c*d^3*f^4*x^3 + 135*a*b^2*d^4*f^4*x^3 + 35*b^3*d^4*f^4*x^4))/(315*d^5*f^3) - (2*(-(b^3*c^3) + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*(-(d*e) + c*f)^(3/2)*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/d^(11/2)","B",1
1784,1,379,210,0.7120381,"\int \frac{(a+b x)^3 \sqrt{e+f x}}{c+d x} \, dx","IntegrateAlgebraic[((a + b*x)^3*Sqrt[e + f*x])/(c + d*x),x]","\frac{2 \left(a^3 d^3-3 a^2 b c d^2+3 a b^2 c^2 d-b^3 c^3\right) \sqrt{c f-d e} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{d^{9/2}}-\frac{2 \sqrt{e+f x} \left(-105 a^3 d^3 f^3+315 a^2 b c d^2 f^3-105 a^2 b d^3 e f^2-105 a^2 b d^3 f^3 x-315 a b^2 c^2 d f^3+105 a b^2 c d^2 e f^2+105 a b^2 c d^2 f^3 x+42 a b^2 d^3 e^2 f-21 a b^2 d^3 e f^2 x-63 a b^2 d^3 f^3 x^2+105 b^3 c^3 f^3-35 b^3 c^2 d e f^2-35 b^3 c^2 d f^3 x-14 b^3 c d^2 e^2 f+7 b^3 c d^2 e f^2 x+21 b^3 c d^2 f^3 x^2-8 b^3 d^3 e^3+4 b^3 d^3 e^2 f x-3 b^3 d^3 e f^2 x^2-15 b^3 d^3 f^3 x^3\right)}{105 d^4 f^3}","\frac{2 b (e+f x)^{3/2} \left(3 a^2 d^2 f^2-3 a b d f (c f+d e)+b^2 \left(c^2 f^2+c d e f+d^2 e^2\right)\right)}{3 d^3 f^3}-\frac{2 b^2 (e+f x)^{5/2} (-3 a d f+b c f+2 b d e)}{5 d^2 f^3}+\frac{2 (b c-a d)^3 \sqrt{d e-c f} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{d^{9/2}}-\frac{2 \sqrt{e+f x} (b c-a d)^3}{d^4}+\frac{2 b^3 (e+f x)^{7/2}}{7 d f^3}",1,"(-2*Sqrt[e + f*x]*(-8*b^3*d^3*e^3 - 14*b^3*c*d^2*e^2*f + 42*a*b^2*d^3*e^2*f - 35*b^3*c^2*d*e*f^2 + 105*a*b^2*c*d^2*e*f^2 - 105*a^2*b*d^3*e*f^2 + 105*b^3*c^3*f^3 - 315*a*b^2*c^2*d*f^3 + 315*a^2*b*c*d^2*f^3 - 105*a^3*d^3*f^3 + 4*b^3*d^3*e^2*f*x + 7*b^3*c*d^2*e*f^2*x - 21*a*b^2*d^3*e*f^2*x - 35*b^3*c^2*d*f^3*x + 105*a*b^2*c*d^2*f^3*x - 105*a^2*b*d^3*f^3*x - 3*b^3*d^3*e*f^2*x^2 + 21*b^3*c*d^2*f^3*x^2 - 63*a*b^2*d^3*f^3*x^2 - 15*b^3*d^3*f^3*x^3))/(105*d^4*f^3) + (2*(-(b^3*c^3) + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*Sqrt[-(d*e) + c*f]*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/d^(9/2)","A",1
1785,1,228,184,0.2024938,"\int \frac{(a+b x)^3}{(c+d x) \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(a + b*x)^3/((c + d*x)*Sqrt[e + f*x]),x]","\frac{2 \sqrt{e+f x} \left(45 a^2 b d^2 f^2-45 a b^2 c d f^2-30 a b^2 d^2 e f+15 a b^2 d^2 f^2 x+15 b^3 c^2 f^2+10 b^3 c d e f-5 b^3 c d f^2 x+8 b^3 d^2 e^2-4 b^3 d^2 e f x+3 b^3 d^2 f^2 x^2\right)}{15 d^3 f^3}-\frac{2 \left(a^3 d^3-3 a^2 b c d^2+3 a b^2 c^2 d-b^3 c^3\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{d^{7/2} \sqrt{c f-d e}}","\frac{2 b \sqrt{e+f x} \left(3 a^2 d^2 f^2-3 a b d f (c f+d e)+b^2 \left(c^2 f^2+c d e f+d^2 e^2\right)\right)}{d^3 f^3}-\frac{2 b^2 (e+f x)^{3/2} (-3 a d f+b c f+2 b d e)}{3 d^2 f^3}+\frac{2 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{d^{7/2} \sqrt{d e-c f}}+\frac{2 b^3 (e+f x)^{5/2}}{5 d f^3}",1,"(2*Sqrt[e + f*x]*(8*b^3*d^2*e^2 + 10*b^3*c*d*e*f - 30*a*b^2*d^2*e*f + 15*b^3*c^2*f^2 - 45*a*b^2*c*d*f^2 + 45*a^2*b*d^2*f^2 - 4*b^3*d^2*e*f*x - 5*b^3*c*d*f^2*x + 15*a*b^2*d^2*f^2*x + 3*b^3*d^2*f^2*x^2))/(15*d^3*f^3) - (2*(-(b^3*c^3) + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/(d^(7/2)*Sqrt[-(d*e) + c*f])","A",1
1786,1,296,149,0.303387,"\int \frac{(a+b x)^3}{(c+d x) (e+f x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x)^3/((c + d*x)*(e + f*x)^(3/2)),x]","\frac{2 \left(3 a^3 d^2 f^3-9 a^2 b d^2 e f^2-9 a b^2 c d e f^2-9 a b^2 c d f^3 x+18 a b^2 d^2 e^2 f+9 a b^2 d^2 e f^2 x+3 b^3 c^2 e f^2+3 b^3 c^2 f^3 x+2 b^3 c d e^2 f+b^3 c d e f^2 x-b^3 c d f^3 x^2-8 b^3 d^2 e^3-4 b^3 d^2 e^2 f x+b^3 d^2 e f^2 x^2\right)}{3 d^2 f^3 \sqrt{e+f x} (d e-c f)}+\frac{2 \left(a^3 d^3-3 a^2 b c d^2+3 a b^2 c^2 d-b^3 c^3\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{d^{5/2} (c f-d e)^{3/2}}","-\frac{2 b^2 \sqrt{e+f x} (-3 a d f+b c f+2 b d e)}{d^2 f^3}+\frac{2 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{d^{5/2} (d e-c f)^{3/2}}-\frac{2 (b e-a f)^3}{f^3 \sqrt{e+f x} (d e-c f)}+\frac{2 b^3 (e+f x)^{3/2}}{3 d f^3}",1,"(2*(-8*b^3*d^2*e^3 + 2*b^3*c*d*e^2*f + 18*a*b^2*d^2*e^2*f + 3*b^3*c^2*e*f^2 - 9*a*b^2*c*d*e*f^2 - 9*a^2*b*d^2*e*f^2 + 3*a^3*d^2*f^3 - 4*b^3*d^2*e^2*f*x + b^3*c*d*e*f^2*x + 9*a*b^2*d^2*e*f^2*x + 3*b^3*c^2*f^3*x - 9*a*b^2*c*d*f^3*x + b^3*d^2*e*f^2*x^2 - b^3*c*d*f^3*x^2))/(3*d^2*f^3*(d*e - c*f)*Sqrt[e + f*x]) + (2*(-(b^3*c^3) + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/(d^(5/2)*(-(d*e) + c*f)^(3/2))","A",1
1787,1,373,163,0.3690406,"\int \frac{(a+b x)^3}{(c+d x) (e+f x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x)^3/((c + d*x)*(e + f*x)^(5/2)),x]","-\frac{2 \left(a^3 c d f^4-4 a^3 d^2 e f^3-3 a^3 d^2 f^4 x+6 a^2 b c d e f^3+9 a^2 b c d f^4 x+3 a^2 b d^2 e^2 f^2-15 a b^2 c d e^2 f^2-18 a b^2 c d e f^3 x+6 a b^2 d^2 e^3 f+9 a b^2 d^2 e^2 f^2 x-3 b^3 c^2 e^2 f^2-6 b^3 c^2 e f^3 x-3 b^3 c^2 f^4 x^2+14 b^3 c d e^3 f+21 b^3 c d e^2 f^2 x+6 b^3 c d e f^3 x^2-8 b^3 d^2 e^4-12 b^3 d^2 e^3 f x-3 b^3 d^2 e^2 f^2 x^2\right)}{3 d f^3 (e+f x)^{3/2} (d e-c f)^2}-\frac{2 \left(a^3 d^3-3 a^2 b c d^2+3 a b^2 c^2 d-b^3 c^3\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{d^{3/2} (c f-d e)^{5/2}}","\frac{2 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{d^{3/2} (d e-c f)^{5/2}}+\frac{2 (b e-a f)^2 (a d f-3 b c f+2 b d e)}{f^3 \sqrt{e+f x} (d e-c f)^2}-\frac{2 (b e-a f)^3}{3 f^3 (e+f x)^{3/2} (d e-c f)}+\frac{2 b^3 \sqrt{e+f x}}{d f^3}",1,"(-2*(-8*b^3*d^2*e^4 + 14*b^3*c*d*e^3*f + 6*a*b^2*d^2*e^3*f - 3*b^3*c^2*e^2*f^2 - 15*a*b^2*c*d*e^2*f^2 + 3*a^2*b*d^2*e^2*f^2 + 6*a^2*b*c*d*e*f^3 - 4*a^3*d^2*e*f^3 + a^3*c*d*f^4 - 12*b^3*d^2*e^3*f*x + 21*b^3*c*d*e^2*f^2*x + 9*a*b^2*d^2*e^2*f^2*x - 6*b^3*c^2*e*f^3*x - 18*a*b^2*c*d*e*f^3*x + 9*a^2*b*c*d*f^4*x - 3*a^3*d^2*f^4*x - 3*b^3*d^2*e^2*f^2*x^2 + 6*b^3*c*d*e*f^3*x^2 - 3*b^3*c^2*f^4*x^2))/(3*d*f^3*(d*e - c*f)^2*(e + f*x)^(3/2)) - (2*(-(b^3*c^3) + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/(d^(3/2)*(-(d*e) + c*f)^(5/2))","B",1
1788,1,505,227,0.5194824,"\int \frac{(a+b x)^3}{(c+d x) (e+f x)^{7/2}} \, dx","IntegrateAlgebraic[(a + b*x)^3/((c + d*x)*(e + f*x)^(7/2)),x]","\frac{2 \left(a^3 d^3-3 a^2 b c d^2+3 a b^2 c^2 d-b^3 c^3\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{\sqrt{d} (c f-d e)^{7/2}}-\frac{2 \left(3 a^3 c^2 f^5-11 a^3 c d e f^4-5 a^3 c d f^5 x+23 a^3 d^2 e^2 f^3+35 a^3 d^2 e f^4 x+15 a^3 d^2 f^5 x^2+6 a^2 b c^2 e f^4+15 a^2 b c^2 f^5 x-42 a^2 b c d e^2 f^3-105 a^2 b c d e f^4 x-45 a^2 b c d f^5 x^2-9 a^2 b d^2 e^3 f^2+24 a b^2 c^2 e^2 f^3+60 a b^2 c^2 e f^4 x+45 a b^2 c^2 f^5 x^2+27 a b^2 c d e^3 f^2+45 a b^2 c d e^2 f^3 x-6 a b^2 d^2 e^4 f-15 a b^2 d^2 e^3 f^2 x-33 b^3 c^2 e^3 f^2-75 b^3 c^2 e^2 f^3 x-45 b^3 c^2 e f^4 x^2+26 b^3 c d e^4 f+65 b^3 c d e^3 f^2 x+45 b^3 c d e^2 f^3 x^2-8 b^3 d^2 e^5-20 b^3 d^2 e^4 f x-15 b^3 d^2 e^3 f^2 x^2\right)}{15 f^3 (e+f x)^{5/2} (c f-d e)^3}","-\frac{2 (b e-a f) \left(a^2 d^2 f^2+a b d f (d e-3 c f)+b^2 \left(3 c^2 f^2-3 c d e f+d^2 e^2\right)\right)}{f^3 \sqrt{e+f x} (d e-c f)^3}+\frac{2 (b e-a f)^2 (a d f-3 b c f+2 b d e)}{3 f^3 (e+f x)^{3/2} (d e-c f)^2}-\frac{2 (b e-a f)^3}{5 f^3 (e+f x)^{5/2} (d e-c f)}+\frac{2 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{\sqrt{d} (d e-c f)^{7/2}}",1,"(-2*(-8*b^3*d^2*e^5 + 26*b^3*c*d*e^4*f - 6*a*b^2*d^2*e^4*f - 33*b^3*c^2*e^3*f^2 + 27*a*b^2*c*d*e^3*f^2 - 9*a^2*b*d^2*e^3*f^2 + 24*a*b^2*c^2*e^2*f^3 - 42*a^2*b*c*d*e^2*f^3 + 23*a^3*d^2*e^2*f^3 + 6*a^2*b*c^2*e*f^4 - 11*a^3*c*d*e*f^4 + 3*a^3*c^2*f^5 - 20*b^3*d^2*e^4*f*x + 65*b^3*c*d*e^3*f^2*x - 15*a*b^2*d^2*e^3*f^2*x - 75*b^3*c^2*e^2*f^3*x + 45*a*b^2*c*d*e^2*f^3*x + 60*a*b^2*c^2*e*f^4*x - 105*a^2*b*c*d*e*f^4*x + 35*a^3*d^2*e*f^4*x + 15*a^2*b*c^2*f^5*x - 5*a^3*c*d*f^5*x - 15*b^3*d^2*e^3*f^2*x^2 + 45*b^3*c*d*e^2*f^3*x^2 - 45*b^3*c^2*e*f^4*x^2 + 45*a*b^2*c^2*f^5*x^2 - 45*a^2*b*c*d*f^5*x^2 + 15*a^3*d^2*f^5*x^2))/(15*f^3*(-(d*e) + c*f)^3*(e + f*x)^(5/2)) + (2*(-(b^3*c^3) + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/(Sqrt[d]*(-(d*e) + c*f)^(7/2))","B",1
1789,1,789,260,0.7281673,"\int \frac{(a+b x)^3}{(c+d x) (e+f x)^{9/2}} \, dx","IntegrateAlgebraic[(a + b*x)^3/((c + d*x)*(e + f*x)^(9/2)),x]","-\frac{2 \left(a^3 d^{7/2}-3 a^2 b c d^{5/2}+3 a b^2 c^2 d^{3/2}-b^3 c^3 \sqrt{d}\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{(c f-d e)^{9/2}}-\frac{2 \left(15 a^3 c^3 f^6-66 a^3 c^2 d e f^5-21 a^3 c^2 d f^6 x+122 a^3 c d^2 e^2 f^4+112 a^3 c d^2 e f^5 x+35 a^3 c d^2 f^6 x^2-176 a^3 d^3 e^3 f^3-406 a^3 d^3 e^2 f^4 x-350 a^3 d^3 e f^5 x^2-105 a^3 d^3 f^6 x^3+18 a^2 b c^3 e f^5+63 a^2 b c^3 f^6 x-96 a^2 b c^2 d e^2 f^4-336 a^2 b c^2 d e f^5 x-105 a^2 b c^2 d f^6 x^2+348 a^2 b c d^2 e^3 f^3+1218 a^2 b c d^2 e^2 f^4 x+1050 a^2 b c d^2 e f^5 x^2+315 a^2 b c d^2 f^6 x^3+45 a^2 b d^3 e^4 f^2+24 a b^2 c^3 e^2 f^4+84 a b^2 c^3 e f^5 x+105 a b^2 c^3 f^6 x^2-240 a b^2 c^2 d e^3 f^3-840 a b^2 c^2 d e^2 f^4 x-1050 a b^2 c^2 d e f^5 x^2-315 a b^2 c^2 d f^6 x^3-117 a b^2 c d^2 e^4 f^2-252 a b^2 c d^2 e^3 f^3 x+18 a b^2 d^3 e^5 f+63 a b^2 d^3 e^4 f^2 x+48 b^3 c^3 e^3 f^3+168 b^3 c^3 e^2 f^4 x+210 b^3 c^3 e f^5 x^2+105 b^3 c^3 f^6 x^3+87 b^3 c^2 d e^4 f^2+252 b^3 c^2 d e^3 f^3 x+210 b^3 c^2 d e^2 f^4 x^2-38 b^3 c d^2 e^5 f-133 b^3 c d^2 e^4 f^2 x-140 b^3 c d^2 e^3 f^3 x^2+8 b^3 d^3 e^6+28 b^3 d^3 e^5 f x+35 b^3 d^3 e^4 f^2 x^2\right)}{105 f^3 (e+f x)^{7/2} (c f-d e)^4}","-\frac{2 (b e-a f) \left(a^2 d^2 f^2+a b d f (d e-3 c f)+b^2 \left(3 c^2 f^2-3 c d e f+d^2 e^2\right)\right)}{3 f^3 (e+f x)^{3/2} (d e-c f)^3}+\frac{2 (b e-a f)^2 (a d f-3 b c f+2 b d e)}{5 f^3 (e+f x)^{5/2} (d e-c f)^2}-\frac{2 (b e-a f)^3}{7 f^3 (e+f x)^{7/2} (d e-c f)}-\frac{2 (b c-a d)^3}{\sqrt{e+f x} (d e-c f)^4}+\frac{2 \sqrt{d} (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{(d e-c f)^{9/2}}",1,"(-2*(8*b^3*d^3*e^6 - 38*b^3*c*d^2*e^5*f + 18*a*b^2*d^3*e^5*f + 87*b^3*c^2*d*e^4*f^2 - 117*a*b^2*c*d^2*e^4*f^2 + 45*a^2*b*d^3*e^4*f^2 + 48*b^3*c^3*e^3*f^3 - 240*a*b^2*c^2*d*e^3*f^3 + 348*a^2*b*c*d^2*e^3*f^3 - 176*a^3*d^3*e^3*f^3 + 24*a*b^2*c^3*e^2*f^4 - 96*a^2*b*c^2*d*e^2*f^4 + 122*a^3*c*d^2*e^2*f^4 + 18*a^2*b*c^3*e*f^5 - 66*a^3*c^2*d*e*f^5 + 15*a^3*c^3*f^6 + 28*b^3*d^3*e^5*f*x - 133*b^3*c*d^2*e^4*f^2*x + 63*a*b^2*d^3*e^4*f^2*x + 252*b^3*c^2*d*e^3*f^3*x - 252*a*b^2*c*d^2*e^3*f^3*x + 168*b^3*c^3*e^2*f^4*x - 840*a*b^2*c^2*d*e^2*f^4*x + 1218*a^2*b*c*d^2*e^2*f^4*x - 406*a^3*d^3*e^2*f^4*x + 84*a*b^2*c^3*e*f^5*x - 336*a^2*b*c^2*d*e*f^5*x + 112*a^3*c*d^2*e*f^5*x + 63*a^2*b*c^3*f^6*x - 21*a^3*c^2*d*f^6*x + 35*b^3*d^3*e^4*f^2*x^2 - 140*b^3*c*d^2*e^3*f^3*x^2 + 210*b^3*c^2*d*e^2*f^4*x^2 + 210*b^3*c^3*e*f^5*x^2 - 1050*a*b^2*c^2*d*e*f^5*x^2 + 1050*a^2*b*c*d^2*e*f^5*x^2 - 350*a^3*d^3*e*f^5*x^2 + 105*a*b^2*c^3*f^6*x^2 - 105*a^2*b*c^2*d*f^6*x^2 + 35*a^3*c*d^2*f^6*x^2 + 105*b^3*c^3*f^6*x^3 - 315*a*b^2*c^2*d*f^6*x^3 + 315*a^2*b*c*d^2*f^6*x^3 - 105*a^3*d^3*f^6*x^3))/(105*f^3*(-(d*e) + c*f)^4*(e + f*x)^(7/2)) - (2*(-(b^3*c^3*Sqrt[d]) + 3*a*b^2*c^2*d^(3/2) - 3*a^2*b*c*d^(5/2) + a^3*d^(7/2))*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/(-(d*e) + c*f)^(9/2)","B",1
1790,1,53,105,0.0174345,"\int \sqrt{1-2 x} (2+3 x)^6 (3+5 x) \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^6*(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(15637050 x^8+80999919 x^7+181983186 x^6+229582836 x^5+173491920 x^4+72883440 x^3+5339712 x^2-16666112 x-23667392\right)}{36465}","\frac{3645 (1-2 x)^{17/2}}{2176}-\frac{19683}{640} (1-2 x)^{15/2}+\frac{409941 (1-2 x)^{13/2}}{1664}-\frac{1580985 (1-2 x)^{11/2}}{1408}+\frac{406455}{128} (1-2 x)^{9/2}-\frac{725445}{128} (1-2 x)^{7/2}+\frac{3916031}{640} (1-2 x)^{5/2}-\frac{1294139}{384} (1-2 x)^{3/2}",1,"(Sqrt[1 - 2*x]*(-23667392 - 16666112*x + 5339712*x^2 + 72883440*x^3 + 173491920*x^4 + 229582836*x^5 + 181983186*x^6 + 80999919*x^7 + 15637050*x^8))/36465","A",1
1791,1,48,92,0.014593,"\int \sqrt{1-2 x} (2+3 x)^5 (3+5 x) \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^5*(3 + 5*x),x]","\frac{1}{33} \sqrt{1-2 x} \left(5346 x^7+24057 x^6+45765 x^5+46875 x^4+26220 x^3+5172 x^2-4120 x-7288\right)","-\frac{81}{64} (1-2 x)^{15/2}+\frac{81}{4} (1-2 x)^{13/2}-\frac{97335}{704} (1-2 x)^{11/2}+\frac{4165}{8} (1-2 x)^{9/2}-\frac{74235}{64} (1-2 x)^{7/2}+\frac{12005}{8} (1-2 x)^{5/2}-\frac{184877}{192} (1-2 x)^{3/2}",1,"(Sqrt[1 - 2*x]*(-7288 - 4120*x + 5172*x^2 + 26220*x^3 + 46875*x^4 + 45765*x^5 + 24057*x^6 + 5346*x^7))/33","A",1
1792,1,43,79,0.0144673,"\int \sqrt{1-2 x} (2+3 x)^4 (3+5 x) \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(133650 x^6+509895 x^5+791640 x^4+614160 x^3+200328 x^2-60928 x-163888\right)}{2145}","\frac{405}{416} (1-2 x)^{13/2}-\frac{4671}{352} (1-2 x)^{11/2}+\frac{1197}{16} (1-2 x)^{9/2}-\frac{3549}{16} (1-2 x)^{7/2}+\frac{57281}{160} (1-2 x)^{5/2}-\frac{26411}{96} (1-2 x)^{3/2}",1,"(Sqrt[1 - 2*x]*(-163888 - 60928*x + 200328*x^2 + 614160*x^3 + 791640*x^4 + 509895*x^5 + 133650*x^6))/2145","A",1
1793,1,38,66,0.0114026,"\int \sqrt{1-2 x} (2+3 x)^3 (3+5 x) \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x),x]","\frac{1}{165} \sqrt{1-2 x} \left(4050 x^5+12645 x^4+15075 x^3+7527 x^2-482 x-4442\right)","-\frac{135}{176} (1-2 x)^{11/2}+\frac{69}{8} (1-2 x)^{9/2}-\frac{153}{4} (1-2 x)^{7/2}+\frac{3283}{40} (1-2 x)^{5/2}-\frac{3773}{48} (1-2 x)^{3/2}",1,"(Sqrt[1 - 2*x]*(-4442 - 482*x + 7527*x^2 + 15075*x^3 + 12645*x^4 + 4050*x^5))/165","A",1
1794,1,33,53,0.0102018,"\int \sqrt{1-2 x} (2+3 x)^2 (3+5 x) \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x),x]","\frac{1}{105} \sqrt{1-2 x} \left(1050 x^4+2535 x^3+2046 x^2+244 x-1016\right)","\frac{5}{8} (1-2 x)^{9/2}-\frac{309}{56} (1-2 x)^{7/2}+\frac{707}{40} (1-2 x)^{5/2}-\frac{539}{24} (1-2 x)^{3/2}",1,"(Sqrt[1 - 2*x]*(-1016 + 244*x + 2046*x^2 + 2535*x^3 + 1050*x^4))/105","A",1
1795,1,28,40,0.0090012,"\int \sqrt{1-2 x} (2+3 x) (3+5 x) \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x),x]","\frac{1}{105} \sqrt{1-2 x} \left(450 x^3+753 x^2+257 x-373\right)","-\frac{15}{28} (1-2 x)^{7/2}+\frac{17}{5} (1-2 x)^{5/2}-\frac{77}{12} (1-2 x)^{3/2}",1,"(Sqrt[1 - 2*x]*(-373 + 257*x + 753*x^2 + 450*x^3))/105","A",1
1796,1,23,27,0.0076908,"\int \sqrt{1-2 x} (3+5 x) \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(3 + 5*x),x]","\frac{1}{3} \sqrt{1-2 x} \left(6 x^2+5 x-4\right)","\frac{1}{2} (1-2 x)^{5/2}-\frac{11}{6} (1-2 x)^{3/2}",1,"(Sqrt[1 - 2*x]*(-4 + 5*x + 6*x^2))/3","A",1
1797,1,48,56,0.0545585,"\int \frac{\sqrt{1-2 x} (3+5 x)}{2+3 x} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x))/(2 + 3*x),x]","\frac{1}{9} \sqrt{1-2 x} (10 x-7)+\frac{2}{9} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","-\frac{5}{9} (1-2 x)^{3/2}-\frac{2}{9} \sqrt{1-2 x}+\frac{2}{9} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-7 + 10*x))/9 + (2*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/9","A",1
1798,1,51,59,0.0813132,"\int \frac{\sqrt{1-2 x} (3+5 x)}{(2+3 x)^2} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x))/(2 + 3*x)^2,x]","\frac{\sqrt{1-2 x} (10 x+7)}{3 (3 x+2)}-\frac{8 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{\sqrt{21}}","\frac{(1-2 x)^{3/2}}{21 (3 x+2)}+\frac{8}{7} \sqrt{1-2 x}-\frac{8 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{\sqrt{21}}",1,"(Sqrt[1 - 2*x]*(7 + 10*x))/(3*(2 + 3*x)) - (8*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/Sqrt[21]","A",1
1799,1,53,68,0.0994147,"\int \frac{\sqrt{1-2 x} (3+5 x)}{(2+3 x)^3} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x))/(2 + 3*x)^3,x]","\frac{\sqrt{1-2 x} (-71 x-45)}{42 (3 x+2)^2}+\frac{23 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{21 \sqrt{21}}","\frac{(1-2 x)^{3/2}}{42 (3 x+2)^2}-\frac{23 \sqrt{1-2 x}}{42 (3 x+2)}+\frac{23 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{21 \sqrt{21}}",1,"((-45 - 71*x)*Sqrt[1 - 2*x])/(42*(2 + 3*x)^2) + (23*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(21*Sqrt[21])","A",1
1800,1,58,88,0.0915858,"\int \frac{\sqrt{1-2 x} (3+5 x)}{(2+3 x)^4} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x))/(2 + 3*x)^4,x]","\frac{\sqrt{1-2 x} \left(153 x^2-167 x-163\right)}{441 (3 x+2)^3}+\frac{34 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{441 \sqrt{21}}","\frac{(1-2 x)^{3/2}}{63 (3 x+2)^3}+\frac{17 \sqrt{1-2 x}}{441 (3 x+2)}-\frac{17 \sqrt{1-2 x}}{63 (3 x+2)^2}+\frac{34 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{441 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-163 - 167*x + 153*x^2))/(441*(2 + 3*x)^3) + (34*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(441*Sqrt[21])","A",1
1801,1,65,110,0.1119565,"\int \frac{\sqrt{1-2 x} (3+5 x)}{(2+3 x)^5} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x))/(2 + 3*x)^5,x]","\frac{\sqrt{1-2 x} \left(1215 x^3+3375 x^2-1726 x-2062\right)}{8232 (3 x+2)^4}+\frac{5 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1372}","\frac{(1-2 x)^{3/2}}{84 (3 x+2)^4}+\frac{15 \sqrt{1-2 x}}{2744 (3 x+2)}+\frac{5 \sqrt{1-2 x}}{392 (3 x+2)^2}-\frac{5 \sqrt{1-2 x}}{28 (3 x+2)^3}+\frac{5 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1372}",1,"(Sqrt[1 - 2*x]*(-2062 - 1726*x + 3375*x^2 + 1215*x^3))/(8232*(2 + 3*x)^4) + (5*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/1372","A",1
1802,1,68,128,0.1217376,"\int \frac{\sqrt{1-2 x} (3+5 x)}{(2+3 x)^6} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x))/(2 + 3*x)^6,x]","\frac{\sqrt{1-2 x} \left(405 x^4+1395 x^3+2004 x^2-864 x-1019\right)}{5145 (3 x+2)^5}+\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1029 \sqrt{21}}","\frac{(1-2 x)^{3/2}}{105 (3 x+2)^5}+\frac{\sqrt{1-2 x}}{1029 (3 x+2)}+\frac{\sqrt{1-2 x}}{441 (3 x+2)^2}+\frac{2 \sqrt{1-2 x}}{315 (3 x+2)^3}-\frac{2 \sqrt{1-2 x}}{15 (3 x+2)^4}+\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1029 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-1019 - 864*x + 2004*x^2 + 1395*x^3 + 405*x^4))/(5145*(2 + 3*x)^5) + (2*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(1029*Sqrt[21])","A",1
1803,1,48,92,0.0155128,"\int \sqrt{1-2 x} (2+3 x)^4 (3+5 x)^2 \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(579150 x^7+2561625 x^6+4787910 x^5+4814245 x^4+2635780 x^3+493524 x^2-426024 x-734904\right)}{2145}","-\frac{135}{64} (1-2 x)^{15/2}+\frac{13905}{416} (1-2 x)^{13/2}-\frac{159111}{704} (1-2 x)^{11/2}+\frac{40453}{48} (1-2 x)^{9/2}-\frac{118993}{64} (1-2 x)^{7/2}+\frac{381073}{160} (1-2 x)^{5/2}-\frac{290521}{192} (1-2 x)^{3/2}",1,"(Sqrt[1 - 2*x]*(-734904 - 426024*x + 493524*x^2 + 2635780*x^3 + 4814245*x^4 + 4787910*x^5 + 2561625*x^6 + 579150*x^7))/2145","A",1
1804,1,43,79,0.0127466,"\int \sqrt{1-2 x} (2+3 x)^3 (3+5 x)^2 \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(222750 x^6+832275 x^5+1264605 x^4+958275 x^3+301263 x^2-99458 x-253898\right)}{2145}","\frac{675}{416} (1-2 x)^{13/2}-\frac{7695}{352} (1-2 x)^{11/2}+\frac{1949}{16} (1-2 x)^{9/2}-\frac{5711}{16} (1-2 x)^{7/2}+\frac{91091}{160} (1-2 x)^{5/2}-\frac{41503}{96} (1-2 x)^{3/2}",1,"(Sqrt[1 - 2*x]*(-253898 - 99458*x + 301263*x^2 + 958275*x^3 + 1264605*x^4 + 832275*x^5 + 222750*x^6))/2145","A",1
1805,1,38,66,0.0127415,"\int \sqrt{1-2 x} (2+3 x)^2 (3+5 x)^2 \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(47250 x^5+143675 x^4+166580 x^3+80313 x^2-6518 x-48098\right)}{1155}","-\frac{225}{176} (1-2 x)^{11/2}+\frac{85}{6} (1-2 x)^{9/2}-\frac{3467}{56} (1-2 x)^{7/2}+\frac{1309}{10} (1-2 x)^{5/2}-\frac{5929}{48} (1-2 x)^{3/2}",1,"(Sqrt[1 - 2*x]*(-48098 - 6518*x + 80313*x^2 + 166580*x^3 + 143675*x^4 + 47250*x^5))/1155","A",1
1806,1,33,53,0.0102852,"\int \sqrt{1-2 x} (2+3 x) (3+5 x)^2 \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^2,x]","\frac{1}{105} \sqrt{1-2 x} \left(1750 x^4+4075 x^3+3159 x^2+321 x-1569\right)","\frac{25}{24} (1-2 x)^{9/2}-\frac{505}{56} (1-2 x)^{7/2}+\frac{1133}{40} (1-2 x)^{5/2}-\frac{847}{24} (1-2 x)^{3/2}",1,"(Sqrt[1 - 2*x]*(-1569 + 321*x + 3159*x^2 + 4075*x^3 + 1750*x^4))/105","A",1
1807,1,28,40,0.0086568,"\int \sqrt{1-2 x} (3+5 x)^2 \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(3 + 5*x)^2,x]","\frac{1}{21} \sqrt{1-2 x} \left(150 x^3+237 x^2+74 x-115\right)","-\frac{25}{28} (1-2 x)^{7/2}+\frac{11}{2} (1-2 x)^{5/2}-\frac{121}{12} (1-2 x)^{3/2}",1,"(Sqrt[1 - 2*x]*(-115 + 74*x + 237*x^2 + 150*x^3))/21","A",1
1808,1,53,69,0.0557257,"\int \frac{\sqrt{1-2 x} (3+5 x)^2}{2+3 x} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^2)/(2 + 3*x),x]","\frac{1}{27} \sqrt{1-2 x} \left(90 x^2+65 x-53\right)-\frac{2}{27} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","\frac{5}{6} (1-2 x)^{5/2}-\frac{155}{54} (1-2 x)^{3/2}+\frac{2}{27} \sqrt{1-2 x}-\frac{2}{27} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-53 + 65*x + 90*x^2))/27 - (2*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/27","A",1
1809,1,58,74,0.0942601,"\int \frac{\sqrt{1-2 x} (3+5 x)^2}{(2+3 x)^2} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^2)/(2 + 3*x)^2,x]","\frac{\sqrt{1-2 x} \left(150 x^2-35 x-91\right)}{27 (3 x+2)}+\frac{142 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{27 \sqrt{21}}","-\frac{(1-2 x)^{3/2}}{63 (3 x+2)}-\frac{25}{27} (1-2 x)^{3/2}-\frac{142}{189} \sqrt{1-2 x}+\frac{142 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{27 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-91 - 35*x + 150*x^2))/(27*(2 + 3*x)) + (142*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(27*Sqrt[21])","A",1
1810,1,58,81,0.0909076,"\int \frac{\sqrt{1-2 x} (3+5 x)^2}{(2+3 x)^3} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^2)/(2 + 3*x)^3,x]","\frac{\sqrt{1-2 x} \left(2100 x^2+2941 x+1025\right)}{126 (3 x+2)^2}-\frac{863 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{63 \sqrt{21}}","\frac{139 (1-2 x)^{3/2}}{882 (3 x+2)}-\frac{(1-2 x)^{3/2}}{126 (3 x+2)^2}+\frac{863}{441} \sqrt{1-2 x}-\frac{863 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{63 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(1025 + 2941*x + 2100*x^2))/(126*(2 + 3*x)^2) - (863*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(63*Sqrt[21])","A",1
1811,1,58,88,0.0992808,"\int \frac{\sqrt{1-2 x} (3+5 x)^2}{(2+3 x)^4} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^2)/(2 + 3*x)^4,x]","\frac{\sqrt{1-2 x} \left(-22671 x^2-28751 x-9124\right)}{2646 (3 x+2)^3}+\frac{2381 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1323 \sqrt{21}}","\frac{23 (1-2 x)^{3/2}}{294 (3 x+2)^2}-\frac{(1-2 x)^{3/2}}{189 (3 x+2)^3}-\frac{2381 \sqrt{1-2 x}}{2646 (3 x+2)}+\frac{2381 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1323 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-9124 - 28751*x - 22671*x^2))/(2646*(2 + 3*x)^3) + (2381*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(1323*Sqrt[21])","A",1
1812,1,63,108,0.1042819,"\int \frac{\sqrt{1-2 x} (3+5 x)^2}{(2+3 x)^5} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^2)/(2 + 3*x)^5,x]","\frac{\sqrt{1-2 x} \left(124875 x^3-64725 x^2-225262 x-85094\right)}{74088 (3 x+2)^4}+\frac{4625 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{37044 \sqrt{21}}","\frac{275 (1-2 x)^{3/2}}{5292 (3 x+2)^3}-\frac{(1-2 x)^{3/2}}{252 (3 x+2)^4}+\frac{4625 \sqrt{1-2 x}}{74088 (3 x+2)}-\frac{4625 \sqrt{1-2 x}}{10584 (3 x+2)^2}+\frac{4625 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{37044 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-85094 - 225262*x - 64725*x^2 + 124875*x^3))/(74088*(2 + 3*x)^4) + (4625*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(37044*Sqrt[21])","A",1
1813,1,68,128,0.1148555,"\int \frac{\sqrt{1-2 x} (3+5 x)^2}{(2+3 x)^6} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^2)/(2 + 3*x)^6,x]","\frac{\sqrt{1-2 x} \left(12555 x^4+43245 x^3+3324 x^2-33434 x-13564\right)}{17640 (3 x+2)^5}+\frac{31 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1764 \sqrt{21}}","\frac{7 (1-2 x)^{3/2}}{180 (3 x+2)^4}-\frac{(1-2 x)^{3/2}}{315 (3 x+2)^5}+\frac{31 \sqrt{1-2 x}}{3528 (3 x+2)}+\frac{31 \sqrt{1-2 x}}{1512 (3 x+2)^2}-\frac{31 \sqrt{1-2 x}}{108 (3 x+2)^3}+\frac{31 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1764 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-13564 - 33434*x + 3324*x^2 + 43245*x^3 + 12555*x^4))/(17640*(2 + 3*x)^5) + (31*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(1764*Sqrt[21])","A",1
1814,1,73,148,0.1438384,"\int \frac{\sqrt{1-2 x} (3+5 x)^2}{(2+3 x)^7} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^2)/(2 + 3*x)^7,x]","\frac{\sqrt{1-2 x} \left(1959795 x^5+8056935 x^4+14197626 x^3+1791558 x^2-7772840 x-3136864\right)}{5186160 (3 x+2)^6}+\frac{1613 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{518616 \sqrt{21}}","\frac{137 (1-2 x)^{3/2}}{4410 (3 x+2)^5}-\frac{(1-2 x)^{3/2}}{378 (3 x+2)^6}+\frac{1613 \sqrt{1-2 x}}{1037232 (3 x+2)}+\frac{1613 \sqrt{1-2 x}}{444528 (3 x+2)^2}+\frac{1613 \sqrt{1-2 x}}{158760 (3 x+2)^3}-\frac{1613 \sqrt{1-2 x}}{7560 (3 x+2)^4}+\frac{1613 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{518616 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-3136864 - 7772840*x + 1791558*x^2 + 14197626*x^3 + 8056935*x^4 + 1959795*x^5))/(5186160*(2 + 3*x)^6) + (1613*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(518616*Sqrt[21])","A",1
1815,1,53,105,0.0168153,"\int \sqrt{1-2 x} (2+3 x)^4 (3+5 x)^3 \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(130308750 x^8+655308225 x^7+1428673950 x^6+1747511955 x^5+1277595710 x^4+514265240 x^3+26582592 x^2-124054192 x-171312832\right)}{109395}","\frac{10125 (1-2 x)^{17/2}}{2176}-\frac{10755}{128} (1-2 x)^{15/2}+\frac{1101465 (1-2 x)^{13/2}}{1664}-\frac{4177401 (1-2 x)^{11/2}}{1408}+\frac{9504551 (1-2 x)^{9/2}}{1152}-\frac{1853313}{128} (1-2 x)^{7/2}+\frac{9836211}{640} (1-2 x)^{5/2}-\frac{3195731}{384} (1-2 x)^{3/2}",1,"(Sqrt[1 - 2*x]*(-171312832 - 124054192*x + 26582592*x^2 + 514265240*x^3 + 1277595710*x^4 + 1747511955*x^5 + 1428673950*x^6 + 655308225*x^7 + 130308750*x^8))/109395","A",1
1816,1,48,92,0.0149374,"\int \sqrt{1-2 x} (2+3 x)^3 (3+5 x)^3 \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(2895750 x^7+12585375 x^6+23107275 x^5+22806620 x^4+12220625 x^3+2166357 x^2-2030662 x-3420622\right)}{6435}","-\frac{225}{64} (1-2 x)^{15/2}+\frac{11475}{208} (1-2 x)^{13/2}-\frac{260055}{704} (1-2 x)^{11/2}+\frac{98209}{72} (1-2 x)^{9/2}-\frac{190707}{64} (1-2 x)^{7/2}+\frac{302379}{80} (1-2 x)^{5/2}-\frac{456533}{192} (1-2 x)^{3/2}",1,"(Sqrt[1 - 2*x]*(-3420622 - 2030662*x + 2166357*x^2 + 12220625*x^3 + 22806620*x^4 + 23107275*x^5 + 12585375*x^6 + 2895750*x^7))/6435","A",1
1817,1,43,79,0.0142645,"\int \sqrt{1-2 x} (2+3 x)^2 (3+5 x)^3 \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(7796250 x^6+28515375 x^5+42393400 x^4+31374085 x^3+9500136 x^2-3396296 x-8261156\right)}{45045}","\frac{1125}{416} (1-2 x)^{13/2}-\frac{12675}{352} (1-2 x)^{11/2}+\frac{28555}{144} (1-2 x)^{9/2}-\frac{64317}{112} (1-2 x)^{7/2}+\frac{144837}{160} (1-2 x)^{5/2}-\frac{65219}{96} (1-2 x)^{3/2}",1,"(Sqrt[1 - 2*x]*(-8261156 - 3396296*x + 9500136*x^2 + 31374085*x^3 + 42393400*x^4 + 28515375*x^5 + 7796250*x^6))/45045","A",1
1818,1,38,66,0.0113808,"\int \sqrt{1-2 x} (2+3 x) (3+5 x)^3 \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(236250 x^5+699125 x^4+788075 x^3+366816 x^2-36121 x-223231\right)}{3465}","-\frac{375}{176} (1-2 x)^{11/2}+\frac{1675}{72} (1-2 x)^{9/2}-\frac{2805}{28} (1-2 x)^{7/2}+\frac{8349}{40} (1-2 x)^{5/2}-\frac{9317}{48} (1-2 x)^{3/2}",1,"(Sqrt[1 - 2*x]*(-223231 - 36121*x + 366816*x^2 + 788075*x^3 + 699125*x^4 + 236250*x^5))/3465","A",1
1819,1,33,53,0.0099797,"\int \sqrt{1-2 x} (3+5 x)^3 \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(3 + 5*x)^3,x]","\frac{1}{63} \sqrt{1-2 x} \left(1750 x^4+3925 x^3+2922 x^2+247 x-1454\right)","\frac{125}{72} (1-2 x)^{9/2}-\frac{825}{56} (1-2 x)^{7/2}+\frac{363}{8} (1-2 x)^{5/2}-\frac{1331}{24} (1-2 x)^{3/2}",1,"(Sqrt[1 - 2*x]*(-1454 + 247*x + 2922*x^2 + 3925*x^3 + 1750*x^4))/63","A",1
1820,1,58,82,0.0582785,"\int \frac{\sqrt{1-2 x} (3+5 x)^3}{2+3 x} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^3)/(2 + 3*x),x]","\frac{1}{567} \sqrt{1-2 x} \left(6750 x^3+10035 x^2+2875 x-4804\right)+\frac{2}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","-\frac{125}{84} (1-2 x)^{7/2}+\frac{80}{9} (1-2 x)^{5/2}-\frac{5135}{324} (1-2 x)^{3/2}-\frac{2}{81} \sqrt{1-2 x}+\frac{2}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-4804 + 2875*x + 10035*x^2 + 6750*x^3))/567 + (2*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/81","A",1
1821,1,63,93,0.0952636,"\int \frac{\sqrt{1-2 x} (3+5 x)^3}{(2+3 x)^2} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^3)/(2 + 3*x)^2,x]","\frac{\sqrt{1-2 x} \left(1350 x^3+1725 x^2-110 x-439\right)}{81 (3 x+2)}-\frac{212 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{81 \sqrt{21}}","-\frac{\sqrt{1-2 x} (5 x+3)^3}{3 (3 x+2)}+\frac{7}{9} \sqrt{1-2 x} (5 x+3)^2-\frac{2}{81} \sqrt{1-2 x} (170 x+211)-\frac{212 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{81 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-439 - 110*x + 1725*x^2 + 1350*x^3))/(81*(2 + 3*x)) - (212*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(81*Sqrt[21])","A",1
1822,1,63,100,0.1030862,"\int \frac{\sqrt{1-2 x} (3+5 x)^3}{(2+3 x)^3} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^3)/(2 + 3*x)^3,x]","\frac{\sqrt{1-2 x} \left(31500 x^3+7350 x^2-32833 x-15815\right)}{1134 (3 x+2)^2}+\frac{7559 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{567 \sqrt{21}}","-\frac{\sqrt{1-2 x} (5 x+3)^3}{6 (3 x+2)^2}-\frac{53 \sqrt{1-2 x} (5 x+3)^2}{63 (3 x+2)}+\frac{5 \sqrt{1-2 x} (2815 x+323)}{1134}+\frac{7559 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{567 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-15815 - 32833*x + 7350*x^2 + 31500*x^3))/(1134*(2 + 3*x)^2) + (7559*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(567*Sqrt[21])","A",1
1823,1,63,107,0.1019417,"\int \frac{\sqrt{1-2 x} (3+5 x)^3}{(2+3 x)^4} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^3)/(2 + 3*x)^4,x]","\frac{\sqrt{1-2 x} \left(330750 x^3+695043 x^2+484618 x+112187\right)}{3969 (3 x+2)^3}-\frac{92996 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{3969 \sqrt{21}}","-\frac{\sqrt{1-2 x} (5 x+3)^3}{9 (3 x+2)^3}-\frac{53 \sqrt{1-2 x} (5 x+3)^2}{189 (3 x+2)^2}+\frac{2 \sqrt{1-2 x} (26075 x+18016)}{3969 (3 x+2)}-\frac{92996 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{3969 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(112187 + 484618*x + 695043*x^2 + 330750*x^3))/(3969*(2 + 3*x)^3) - (92996*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(3969*Sqrt[21])","A",1
1824,1,63,107,0.1049139,"\int \frac{\sqrt{1-2 x} (3+5 x)^3}{(2+3 x)^5} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^3)/(2 + 3*x)^5,x]","\frac{\sqrt{1-2 x} \left(-9646695 x^3-18358575 x^2-11657098 x-2469626\right)}{222264 (3 x+2)^4}+\frac{328715 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{111132 \sqrt{21}}","-\frac{\sqrt{1-2 x} (5 x+3)^3}{12 (3 x+2)^4}-\frac{53 \sqrt{1-2 x} (5 x+3)^2}{378 (3 x+2)^3}-\frac{5 \sqrt{1-2 x} (110981 x+70429)}{222264 (3 x+2)^2}+\frac{328715 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{111132 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-2469626 - 11657098*x - 18358575*x^2 - 9646695*x^3))/(222264*(2 + 3*x)^4) + (328715*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(111132*Sqrt[21])","A",1
1825,1,68,127,0.1221967,"\int \frac{\sqrt{1-2 x} (3+5 x)^3}{(2+3 x)^6} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^3)/(2 + 3*x)^6,x]","\frac{\sqrt{1-2 x} \left(4550985 x^4+240615 x^3-10100352 x^2-8471518 x-1984928\right)}{555660 (3 x+2)^5}+\frac{11237 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{55566 \sqrt{21}}","-\frac{\sqrt{1-2 x} (5 x+3)^3}{15 (3 x+2)^5}-\frac{53 \sqrt{1-2 x} (5 x+3)^2}{630 (3 x+2)^4}-\frac{\sqrt{1-2 x} (59665 x+37224)}{79380 (3 x+2)^3}+\frac{11237 \sqrt{1-2 x}}{111132 (3 x+2)}+\frac{11237 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{55566 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-1984928 - 8471518*x - 10100352*x^2 + 240615*x^3 + 4550985*x^4))/(555660*(2 + 3*x)^5) + (11237*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(55566*Sqrt[21])","A",1
1826,1,73,147,0.1279661,"\int \frac{\sqrt{1-2 x} (3+5 x)^3}{(2+3 x)^7} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^3)/(2 + 3*x)^7,x]","\frac{\sqrt{1-2 x} \left(53407755 x^5+219565215 x^4+127601514 x^3-139462938 x^2-150340360 x-36741296\right)}{15558480 (3 x+2)^6}+\frac{43957 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1555848 \sqrt{21}}","-\frac{\sqrt{1-2 x} (5 x+3)^3}{18 (3 x+2)^6}-\frac{53 \sqrt{1-2 x} (5 x+3)^2}{945 (3 x+2)^5}-\frac{\sqrt{1-2 x} (160029 x+98995)}{476280 (3 x+2)^4}+\frac{43957 \sqrt{1-2 x}}{3111696 (3 x+2)}+\frac{43957 \sqrt{1-2 x}}{1333584 (3 x+2)^2}+\frac{43957 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1555848 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-36741296 - 150340360*x - 139462938*x^2 + 127601514*x^3 + 219565215*x^4 + 53407755*x^5))/(15558480*(2 + 3*x)^6) + (43957*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(1555848*Sqrt[21])","A",1
1827,1,78,167,0.1464669,"\int \frac{\sqrt{1-2 x} (3+5 x)^3}{(2+3 x)^8} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^3)/(2 + 3*x)^8,x]","\frac{\sqrt{1-2 x} \left(86448465 x^6+413031555 x^5+863203932 x^4+473987484 x^3-306463011 x^2-361589428 x-88036937\right)}{47647845 (3 x+2)^7}+\frac{47434 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{9529569 \sqrt{21}}","-\frac{\sqrt{1-2 x} (5 x+3)^3}{21 (3 x+2)^7}-\frac{53 \sqrt{1-2 x} (5 x+3)^2}{1323 (3 x+2)^6}-\frac{2 \sqrt{1-2 x} (88099 x+54227)}{972405 (3 x+2)^5}+\frac{23717 \sqrt{1-2 x}}{9529569 (3 x+2)}+\frac{23717 \sqrt{1-2 x}}{4084101 (3 x+2)^2}+\frac{47434 \sqrt{1-2 x}}{2917215 (3 x+2)^3}+\frac{47434 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{9529569 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-88036937 - 361589428*x - 306463011*x^2 + 473987484*x^3 + 863203932*x^4 + 413031555*x^5 + 86448465*x^6))/(47647845*(2 + 3*x)^7) + (47434*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(9529569*Sqrt[21])","A",1
1828,1,63,95,0.0664479,"\int \frac{\sqrt{1-2 x} (2+3 x)^4}{3+5 x} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^4)/(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(78750 x^4+203625 x^3+177930 x^2+27865 x-88776\right)}{21875}-\frac{2 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125}","\frac{9}{40} (1-2 x)^{9/2}-\frac{2889 (1-2 x)^{7/2}}{1400}+\frac{34371 (1-2 x)^{5/2}}{5000}-\frac{45473 (1-2 x)^{3/2}}{5000}+\frac{2 \sqrt{1-2 x}}{3125}-\frac{2 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125}",1,"(Sqrt[1 - 2*x]*(-88776 + 27865*x + 177930*x^2 + 203625*x^3 + 78750*x^4))/21875 - (2*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/3125","A",1
1829,1,58,82,0.0584981,"\int \frac{\sqrt{1-2 x} (2+3 x)^3}{3+5 x} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^3)/(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(6750 x^3+12555 x^2+5115 x-6526\right)}{4375}-\frac{2}{625} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{27}{140} (1-2 x)^{7/2}+\frac{162}{125} (1-2 x)^{5/2}-\frac{1299}{500} (1-2 x)^{3/2}+\frac{2}{625} \sqrt{1-2 x}-\frac{2}{625} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-6526 + 5115*x + 12555*x^2 + 6750*x^3))/4375 - (2*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/625","A",1
1830,1,53,69,0.0541676,"\int \frac{\sqrt{1-2 x} (2+3 x)^2}{3+5 x} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^2)/(3 + 5*x),x]","\frac{1}{125} \sqrt{1-2 x} \left(90 x^2+95 x-68\right)-\frac{2}{125} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{9}{50} (1-2 x)^{5/2}-\frac{37}{50} (1-2 x)^{3/2}+\frac{2}{125} \sqrt{1-2 x}-\frac{2}{125} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-68 + 95*x + 90*x^2))/125 - (2*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/125","A",1
1831,1,48,56,0.0477479,"\int \frac{\sqrt{1-2 x} (2+3 x)}{3+5 x} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x))/(3 + 5*x),x]","\frac{1}{25} \sqrt{1-2 x} (10 x-3)-\frac{2}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{1}{5} (1-2 x)^{3/2}+\frac{2}{25} \sqrt{1-2 x}-\frac{2}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-3 + 10*x))/25 - (2*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/25","A",1
1832,1,43,43,0.0373217,"\int \frac{\sqrt{1-2 x}}{3+5 x} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/(3 + 5*x),x]","\frac{2}{5} \sqrt{1-2 x}-\frac{2}{5} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{2}{5} \sqrt{1-2 x}-\frac{2}{5} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(2*Sqrt[1 - 2*x])/5 - (2*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/5","A",1
1833,1,55,55,0.0881809,"\int \frac{\sqrt{1-2 x}}{(2+3 x) (3+5 x)} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)*(3 + 5*x)),x]","2 \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-2 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","2 \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-2 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"2*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - 2*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1834,1,68,68,0.1182516,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^2*(3 + 5*x)),x]","\frac{\sqrt{1-2 x}}{3 x+2}+\frac{68 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{\sqrt{21}}-2 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{\sqrt{1-2 x}}{3 x+2}+\frac{68 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{\sqrt{21}}-2 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"Sqrt[1 - 2*x]/(2 + 3*x) + (68*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/Sqrt[21] - 2*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1835,1,80,95,0.119239,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^3*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} (207 x+145)}{14 (3 x+2)^2}+\frac{793}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-10 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{69 \sqrt{1-2 x}}{14 (3 x+2)}+\frac{\sqrt{1-2 x}}{2 (3 x+2)^2}+\frac{793}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-10 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(145 + 207*x))/(14*(2 + 3*x)^2) + (793*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/7 - 10*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1836,1,83,113,0.1288585,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^4 (3+5 x)} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^4*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(10863 x^2+14848 x+5087\right)}{49 (3 x+2)^3}+\frac{83264 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{49 \sqrt{21}}-50 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{1207 \sqrt{1-2 x}}{49 (3 x+2)}+\frac{52 \sqrt{1-2 x}}{21 (3 x+2)^2}+\frac{\sqrt{1-2 x}}{3 (3 x+2)^3}+\frac{83264 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{49 \sqrt{21}}-50 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(5087 + 14848*x + 10863*x^2))/(49*(2 + 3*x)^3) + (83264*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(49*Sqrt[21]) - 50*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1837,1,88,133,0.15968,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^5 (3+5 x)} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^5*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(9124785 x^3+18555225 x^2+12587542 x+2849254\right)}{2744 (3 x+2)^4}+\frac{11656955 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1372 \sqrt{21}}-250 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{337955 \sqrt{1-2 x}}{2744 (3 x+2)}+\frac{14555 \sqrt{1-2 x}}{1176 (3 x+2)^2}+\frac{139 \sqrt{1-2 x}}{84 (3 x+2)^3}+\frac{\sqrt{1-2 x}}{4 (3 x+2)^4}+\frac{11656955 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1372 \sqrt{21}}-250 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(2849254 + 12587542*x + 18555225*x^2 + 9124785*x^3))/(2744*(2 + 3*x)^4) + (11656955*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(1372*Sqrt[21]) - 250*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1838,1,73,133,0.1099346,"\int \frac{\sqrt{1-2 x} (2+3 x)^5}{(3+5 x)^2} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^5)/(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(1181250 x^5+3864375 x^4+4760100 x^3+2225760 x^2-1133340 x-862072\right)}{109375 (5 x+3)}-\frac{328 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15625 \sqrt{55}}","-\frac{\sqrt{1-2 x} (3 x+2)^5}{5 (5 x+3)}+\frac{11}{75} \sqrt{1-2 x} (3 x+2)^4+\frac{64 \sqrt{1-2 x} (3 x+2)^3}{2625}-\frac{172 \sqrt{1-2 x} (3 x+2)^2}{3125}-\frac{4 \sqrt{1-2 x} (3625 x+10998)}{15625}-\frac{328 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15625 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-862072 - 1133340*x + 2225760*x^2 + 4760100*x^3 + 3864375*x^4 + 1181250*x^5))/(109375*(3 + 5*x)) - (328*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(15625*Sqrt[55])","A",1
1839,1,68,113,0.108706,"\int \frac{\sqrt{1-2 x} (2+3 x)^4}{(3+5 x)^2} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^4)/(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(101250 x^4+258525 x^3+206415 x^2-52485 x-63088\right)}{21875 (5 x+3)}-\frac{262 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125 \sqrt{55}}","-\frac{\sqrt{1-2 x} (3 x+2)^4}{5 (5 x+3)}+\frac{27}{175} \sqrt{1-2 x} (3 x+2)^3+\frac{12}{625} \sqrt{1-2 x} (3 x+2)^2-\frac{3 \sqrt{1-2 x} (375 x+1256)}{3125}-\frac{262 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-63088 - 52485*x + 206415*x^2 + 258525*x^3 + 101250*x^4))/(21875*(3 + 5*x)) - (262*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(3125*Sqrt[55])","A",1
1840,1,63,88,0.0929059,"\int \frac{\sqrt{1-2 x} (2+3 x)^3}{(3+5 x)^2} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^3)/(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(1350 x^3+2385 x^2-90 x-622\right)}{625 (5 x+3)}-\frac{196 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{625 \sqrt{55}}","-\frac{\sqrt{1-2 x} (3 x+2)^3}{5 (5 x+3)}+\frac{21}{125} \sqrt{1-2 x} (3 x+2)^2-\frac{294}{625} \sqrt{1-2 x}-\frac{196 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{625 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-622 - 90*x + 2385*x^2 + 1350*x^3))/(625*(3 + 5*x)) - (196*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(625*Sqrt[55])","A",1
1841,1,58,74,0.1068409,"\int \frac{\sqrt{1-2 x} (2+3 x)^2}{(3+5 x)^2} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^2)/(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(30 x^2+15 x-2\right)}{25 (5 x+3)}-\frac{26 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{25 \sqrt{55}}","-\frac{(1-2 x)^{3/2}}{275 (5 x+3)}-\frac{3}{25} (1-2 x)^{3/2}+\frac{26}{275} \sqrt{1-2 x}-\frac{26 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{25 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-2 + 15*x + 30*x^2))/(25*(3 + 5*x)) - (26*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(25*Sqrt[55])","A",1
1842,1,53,61,0.0748029,"\int \frac{\sqrt{1-2 x} (2+3 x)}{(3+5 x)^2} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x))/(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} (30 x+17)}{25 (5 x+3)}-\frac{64 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{25 \sqrt{55}}","-\frac{(1-2 x)^{3/2}}{55 (5 x+3)}+\frac{64}{275} \sqrt{1-2 x}-\frac{64 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{25 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(17 + 30*x))/(25*(3 + 5*x)) - (64*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(25*Sqrt[55])","A",1
1843,1,48,48,0.0653793,"\int \frac{\sqrt{1-2 x}}{(3+5 x)^2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/(3 + 5*x)^2,x]","\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{5 \sqrt{55}}-\frac{\sqrt{1-2 x}}{5 (5 x+3)}","\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{5 \sqrt{55}}-\frac{\sqrt{1-2 x}}{5 (5 x+3)}",1,"-1/5*Sqrt[1 - 2*x]/(3 + 5*x) + (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(5*Sqrt[55])","A",1
1844,1,68,69,0.1145293,"\int \frac{\sqrt{1-2 x}}{(2+3 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x}}{-5 x-3}-2 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{68 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{\sqrt{55}}","-\frac{\sqrt{1-2 x}}{5 x+3}-2 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{68 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{\sqrt{55}}",1,"Sqrt[1 - 2*x]/(-3 - 5*x) - 2*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] + (68*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/Sqrt[55]","A",1
1845,1,82,97,0.1120125,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} (-30 x-19)}{15 x^2+19 x+6}-138 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+134 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{10 \sqrt{1-2 x}}{5 x+3}+\frac{\sqrt{1-2 x}}{(3 x+2) (5 x+3)}-138 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+134 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"((-19 - 30*x)*Sqrt[1 - 2*x])/(6 + 19*x + 15*x^2) - 138*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] + 134*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1846,1,94,131,0.1486817,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^3*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-9405 x^2-12228 x-3965\right)}{14 (3 x+2)^2 (5 x+3)}-\frac{7209}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+1000 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{1045 \sqrt{1-2 x}}{14 (5 x+3)}+\frac{52 \sqrt{1-2 x}}{7 (3 x+2) (5 x+3)}+\frac{\sqrt{1-2 x}}{2 (3 x+2)^2 (5 x+3)}-\frac{7209}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+1000 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-3965 - 12228*x - 9405*x^2))/(14*(2 + 3*x)^2*(3 + 5*x)) - (7209*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/7 + 1000*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1847,1,99,158,0.1636369,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^4 (3+5 x)^2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^4*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-1313415 x^3-2583264 x^2-1692159 x-369116\right)}{98 (3 x+2)^3 (5 x+3)}-\frac{335579}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+6650 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{48645 \sqrt{1-2 x}}{98 (5 x+3)}+\frac{7261 \sqrt{1-2 x}}{147 (3 x+2) (5 x+3)}+\frac{139 \sqrt{1-2 x}}{42 (3 x+2)^2 (5 x+3)}+\frac{\sqrt{1-2 x}}{3 (3 x+2)^3 (5 x+3)}-\frac{335579}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+6650 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-369116 - 1692159*x - 2583264*x^2 - 1313415*x^3))/(98*(2 + 3*x)^3*(3 + 5*x)) - (335579*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/49 + 6650*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1848,1,68,120,0.1143062,"\int \frac{\sqrt{1-2 x} (2+3 x)^4}{(3+5 x)^3} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^4)/(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(445500 x^4+1103850 x^3+506880 x^2-200305 x-121976\right)}{68750 (5 x+3)^2}-\frac{12803 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{34375 \sqrt{55}}","-\frac{\sqrt{1-2 x} (3 x+2)^4}{10 (5 x+3)^2}-\frac{131 \sqrt{1-2 x} (3 x+2)^3}{550 (5 x+3)}+\frac{1428 \sqrt{1-2 x} (3 x+2)^2}{6875}-\frac{21 (704-375 x) \sqrt{1-2 x}}{68750}-\frac{12803 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{34375 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-121976 - 200305*x + 506880*x^2 + 1103850*x^3 + 445500*x^4))/(68750*(3 + 5*x)^2) - (12803*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(34375*Sqrt[55])","A",1
1849,1,63,100,0.1052795,"\int \frac{\sqrt{1-2 x} (2+3 x)^3}{(3+5 x)^3} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^3)/(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(9900 x^3+12870 x^2+4555 x+236\right)}{2750 (5 x+3)^2}-\frac{1267 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1375 \sqrt{55}}","-\frac{\sqrt{1-2 x} (3 x+2)^3}{10 (5 x+3)^2}-\frac{49 \sqrt{1-2 x} (3 x+2)^2}{275 (5 x+3)}+\frac{21 \sqrt{1-2 x} (75 x+44)}{2750}-\frac{1267 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1375 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(236 + 4555*x + 12870*x^2 + 9900*x^3))/(2750*(3 + 5*x)^2) - (1267*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(1375*Sqrt[55])","A",1
1850,1,58,81,0.0932284,"\int \frac{\sqrt{1-2 x} (2+3 x)^2}{(3+5 x)^3} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^2)/(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(1980 x^2+2245 x+632\right)}{550 (5 x+3)^2}-\frac{409 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{275 \sqrt{55}}","-\frac{133 (1-2 x)^{3/2}}{6050 (5 x+3)}-\frac{(1-2 x)^{3/2}}{550 (5 x+3)^2}+\frac{409 \sqrt{1-2 x}}{3025}-\frac{409 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{275 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(632 + 2245*x + 1980*x^2))/(550*(3 + 5*x)^2) - (409*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(275*Sqrt[55])","A",1
1851,1,53,68,0.0838796,"\int \frac{\sqrt{1-2 x} (2+3 x)}{(3+5 x)^3} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x))/(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} (-325 x-206)}{550 (5 x+3)^2}+\frac{67 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{275 \sqrt{55}}","-\frac{(1-2 x)^{3/2}}{110 (5 x+3)^2}-\frac{67 \sqrt{1-2 x}}{550 (5 x+3)}+\frac{67 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{275 \sqrt{55}}",1,"((-206 - 325*x)*Sqrt[1 - 2*x])/(550*(3 + 5*x)^2) + (67*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(275*Sqrt[55])","A",1
1852,1,53,68,0.0874718,"\int \frac{\sqrt{1-2 x}}{(3+5 x)^3} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} (5 x-8)}{110 (5 x+3)^2}+\frac{\tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{55 \sqrt{55}}","\frac{\sqrt{1-2 x}}{110 (5 x+3)}-\frac{\sqrt{1-2 x}}{10 (5 x+3)^2}+\frac{\tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{55 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-8 + 5*x))/(110*(3 + 5*x)^2) + ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]/(55*Sqrt[55])","A",1
1853,1,78,93,0.1236723,"\int \frac{\sqrt{1-2 x}}{(2+3 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)*(3 + 5*x)^3),x]","\frac{5 \sqrt{1-2 x} (67 x+38)}{22 (5 x+3)^2}+6 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{2243 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{11 \sqrt{55}}","\frac{67 \sqrt{1-2 x}}{22 (5 x+3)}-\frac{\sqrt{1-2 x}}{2 (5 x+3)^2}+6 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{2243 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{11 \sqrt{55}}",1,"(5*Sqrt[1 - 2*x]*(38 + 67*x))/(22*(3 + 5*x)^2) + 6*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - (2243*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(11*Sqrt[55])","A",1
1854,1,94,121,0.1371187,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(14925 x^2+18410 x+5662\right)}{22 (3 x+2) (5 x+3)^2}+624 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{6665}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{995 \sqrt{1-2 x}}{22 (5 x+3)}-\frac{15 \sqrt{1-2 x}}{2 (5 x+3)^2}+\frac{\sqrt{1-2 x}}{(3 x+2) (5 x+3)^2}+624 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{6665}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(5662 + 18410*x + 14925*x^2))/(22*(2 + 3*x)*(3 + 5*x)^2) + 624*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - (6665*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/11","A",1
1855,1,99,153,0.1530466,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(3118950 x^3+5926515 x^2+3748007 x+788875\right)}{154 \left(15 x^2+19 x+6\right)^2}+\frac{43467}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{66325}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{34655 \sqrt{1-2 x}}{77 (5 x+3)}-\frac{1045 \sqrt{1-2 x}}{14 (5 x+3)^2}+\frac{139 \sqrt{1-2 x}}{14 (3 x+2) (5 x+3)^2}+\frac{\sqrt{1-2 x}}{2 (3 x+2)^2 (5 x+3)^2}+\frac{43467}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{66325}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(788875 + 3748007*x + 5926515*x^2 + 3118950*x^3))/(154*(6 + 19*x + 15*x^2)^2) + (43467*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/7 - (66325*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/11","A",1
1856,1,106,180,0.177442,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^4 (3+5 x)^3} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^4*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(544203225 x^4+1396877220 x^3+1343346156 x^2+573620246 x+91763734\right)}{1078 (3 x+2)^3 (5 x+3)^2}+\frac{2528082}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{551075}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{4031135 \sqrt{1-2 x}}{1078 (5 x+3)}-\frac{182335 \sqrt{1-2 x}}{294 (5 x+3)^2}+\frac{4042 \sqrt{1-2 x}}{49 (3 x+2) (5 x+3)^2}+\frac{29 \sqrt{1-2 x}}{7 (3 x+2)^2 (5 x+3)^2}+\frac{\sqrt{1-2 x}}{3 (3 x+2)^3 (5 x+3)^2}+\frac{2528082}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{551075}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(91763734 + 573620246*x + 1343346156*x^2 + 1396877220*x^3 + 544203225*x^4))/(1078*(2 + 3*x)^3*(3 + 5*x)^2) + (2528082*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/49 - (551075*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/11","A",1
1857,1,58,105,0.0176252,"\int (1-2 x)^{3/2} (2+3 x)^6 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^6*(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(-177219900 x^9-806871780 x^8-1489122063 x^7-1322260632 x^6-372044232 x^5+342957860 x^4+377036800 x^3+136800176 x^2-7336416 x-51677856\right)}{230945}","\frac{3645 (1-2 x)^{19/2}}{2432}-\frac{59049 (1-2 x)^{17/2}}{2176}+\frac{136647}{640} (1-2 x)^{15/2}-\frac{1580985 (1-2 x)^{13/2}}{1664}+\frac{3658095 (1-2 x)^{11/2}}{1408}-\frac{564235}{128} (1-2 x)^{9/2}+\frac{559433}{128} (1-2 x)^{7/2}-\frac{1294139}{640} (1-2 x)^{5/2}",1,"(Sqrt[1 - 2*x]*(-51677856 - 7336416*x + 136800176*x^2 + 377036800*x^3 + 342957860*x^4 - 372044232*x^5 - 1322260632*x^6 - 1489122063*x^7 - 806871780*x^8 - 177219900*x^9))/230945","A",1
1858,1,53,92,0.0150809,"\int (1-2 x)^{3/2} (2+3 x)^5 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^5*(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(-10424700 x^8-40216176 x^7-59295159 x^6-35057799 x^5+5198095 x^4+19014940 x^3+9775332 x^2+488008 x-3012632\right)}{36465}","-\frac{1215 (1-2 x)^{17/2}}{1088}+\frac{351}{20} (1-2 x)^{15/2}-\frac{97335}{832} (1-2 x)^{13/2}+\frac{37485}{88} (1-2 x)^{11/2}-\frac{173215}{192} (1-2 x)^{9/2}+\frac{8575}{8} (1-2 x)^{7/2}-\frac{184877}{320} (1-2 x)^{5/2}",1,"(Sqrt[1 - 2*x]*(-3012632 + 488008*x + 9775332*x^2 + 19014940*x^3 + 5198095*x^4 - 35057799*x^5 - 59295159*x^6 - 40216176*x^7 - 10424700*x^8))/36465","A",1
1859,1,48,79,0.0143793,"\int (1-2 x)^{3/2} (2+3 x)^4 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(-231660 x^7-730620 x^6-793395 x^5-184090 x^4+296840 x^3+243312 x^2+36368 x-66592\right)}{2145}","\frac{27}{32} (1-2 x)^{15/2}-\frac{4671}{416} (1-2 x)^{13/2}+\frac{10773}{176} (1-2 x)^{11/2}-\frac{8281}{48} (1-2 x)^{9/2}+\frac{8183}{32} (1-2 x)^{7/2}-\frac{26411}{160} (1-2 x)^{5/2}",1,"(Sqrt[1 - 2*x]*(-66592 + 36368*x + 243312*x^2 + 296840*x^3 - 184090*x^4 - 793395*x^5 - 730620*x^6 - 231660*x^7))/2145","A",1
1860,1,43,66,0.0116649,"\int (1-2 x)^{3/2} (2+3 x)^3 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x),x]","\frac{1}{715} \sqrt{1-2 x} \left(-29700 x^6-72360 x^5-48065 x^4+15945 x^3+31589 x^2+8666 x-8494\right)","-\frac{135}{208} (1-2 x)^{13/2}+\frac{621}{88} (1-2 x)^{11/2}-\frac{119}{4} (1-2 x)^{9/2}+\frac{469}{8} (1-2 x)^{7/2}-\frac{3773}{80} (1-2 x)^{5/2}",1,"(Sqrt[1 - 2*x]*(-8494 + 8666*x + 31589*x^2 + 15945*x^3 - 48065*x^4 - 72360*x^5 - 29700*x^6))/715","A",1
1861,1,38,53,0.0106262,"\int (1-2 x)^{3/2} (2+3 x)^2 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x),x]","\frac{1}{165} \sqrt{1-2 x} \left(-2700 x^5-4580 x^4-755 x^3+2484 x^2+1216 x-764\right)","\frac{45}{88} (1-2 x)^{11/2}-\frac{103}{24} (1-2 x)^{9/2}+\frac{101}{8} (1-2 x)^{7/2}-\frac{539}{40} (1-2 x)^{5/2}",1,"(Sqrt[1 - 2*x]*(-764 + 1216*x + 2484*x^2 - 755*x^3 - 4580*x^4 - 2700*x^5))/165","A",1
1862,1,33,40,0.0099604,"\int (1-2 x)^{3/2} (2+3 x) (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x),x]","\frac{1}{105} \sqrt{1-2 x} \left(-700 x^4-640 x^3+393 x^2+437 x-193\right)","-\frac{5}{12} (1-2 x)^{9/2}+\frac{17}{7} (1-2 x)^{7/2}-\frac{77}{20} (1-2 x)^{5/2}",1,"(Sqrt[1 - 2*x]*(-193 + 437*x + 393*x^2 - 640*x^3 - 700*x^4))/105","A",1
1863,1,28,27,0.0086753,"\int (1-2 x)^{3/2} (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(3 + 5*x),x]","\frac{1}{35} \sqrt{1-2 x} \left(-100 x^3-4 x^2+79 x-26\right)","\frac{5}{14} (1-2 x)^{7/2}-\frac{11}{10} (1-2 x)^{5/2}",1,"(Sqrt[1 - 2*x]*(-26 + 79*x - 4*x^2 - 100*x^3))/35","A",1
1864,1,53,69,0.0549936,"\int \frac{(1-2 x)^{3/2} (3+5 x)}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x),x]","\frac{1}{27} \sqrt{1-2 x} \left(-36 x^2+40 x-25\right)+\frac{14}{27} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","-\frac{1}{3} (1-2 x)^{5/2}-\frac{2}{27} (1-2 x)^{3/2}-\frac{14}{27} \sqrt{1-2 x}+\frac{14}{27} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-25 + 40*x - 36*x^2))/27 + (14*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/27","A",1
1865,1,60,76,0.0881673,"\int \frac{(1-2 x)^{3/2} (3+5 x)}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x)^2,x]","\frac{\sqrt{1-2 x} \left(-60 x^2+212 x+175\right)}{27 (3 x+2)}-\frac{76}{27} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","\frac{(1-2 x)^{5/2}}{21 (3 x+2)}+\frac{76}{189} (1-2 x)^{3/2}+\frac{76}{27} \sqrt{1-2 x}-\frac{76}{27} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(175 + 212*x - 60*x^2))/(27*(2 + 3*x)) - (76*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/27","A",1
1866,1,58,81,0.0902864,"\int \frac{(1-2 x)^{3/2} (3+5 x)}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x)^3,x]","\frac{\sqrt{1-2 x} \left(-120 x^2-235 x-101\right)}{18 (3 x+2)^2}+\frac{71 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{9 \sqrt{21}}","\frac{(1-2 x)^{5/2}}{42 (3 x+2)^2}-\frac{71 (1-2 x)^{3/2}}{126 (3 x+2)}-\frac{71}{63} \sqrt{1-2 x}+\frac{71 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{9 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-101 - 235*x - 120*x^2))/(18*(2 + 3*x)^2) + (71*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(9*Sqrt[21])","A",1
1867,1,58,88,0.0912712,"\int \frac{(1-2 x)^{3/2} (3+5 x)}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x)^4,x]","\frac{\sqrt{1-2 x} \left(792 x^2+664 x+107\right)}{189 (3 x+2)^3}-\frac{104 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{189 \sqrt{21}}","\frac{(1-2 x)^{5/2}}{63 (3 x+2)^3}-\frac{52 (1-2 x)^{3/2}}{189 (3 x+2)^2}+\frac{52 \sqrt{1-2 x}}{189 (3 x+2)}-\frac{104 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{189 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(107 + 664*x + 792*x^2))/(189*(2 + 3*x)^3) - (104*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(189*Sqrt[21])","A",1
1868,1,63,108,0.1081823,"\int \frac{(1-2 x)^{3/2} (3+5 x)}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x)^5,x]","\frac{\sqrt{1-2 x} \left(-3699 x^3+13245 x^2+7990 x-970\right)}{10584 (3 x+2)^4}-\frac{137 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{5292 \sqrt{21}}","\frac{(1-2 x)^{5/2}}{84 (3 x+2)^4}-\frac{137 (1-2 x)^{3/2}}{756 (3 x+2)^3}-\frac{137 \sqrt{1-2 x}}{10584 (3 x+2)}+\frac{137 \sqrt{1-2 x}}{1512 (3 x+2)^2}-\frac{137 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{5292 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-970 + 7990*x + 13245*x^2 - 3699*x^3))/(10584*(2 + 3*x)^4) - (137*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(5292*Sqrt[21])","A",1
1869,1,68,128,0.1134038,"\int \frac{(1-2 x)^{3/2} (3+5 x)}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x)^6,x]","\frac{\sqrt{1-2 x} \left(-6885 x^4-23715 x^3+48252 x^2+23998 x-7912\right)}{61740 (3 x+2)^5}-\frac{17 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{6174 \sqrt{21}}","\frac{(1-2 x)^{5/2}}{105 (3 x+2)^5}-\frac{17 (1-2 x)^{3/2}}{126 (3 x+2)^4}-\frac{17 \sqrt{1-2 x}}{12348 (3 x+2)}-\frac{17 \sqrt{1-2 x}}{5292 (3 x+2)^2}+\frac{17 \sqrt{1-2 x}}{378 (3 x+2)^3}-\frac{17 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{6174 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-7912 + 23998*x + 48252*x^2 - 23715*x^3 - 6885*x^4))/(61740*(2 + 3*x)^5) - (17*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(6174*Sqrt[21])","A",1
1870,1,53,92,0.0164629,"\int (1-2 x)^{3/2} (2+3 x)^4 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(-52123500 x^8-197142660 x^7-284055255 x^6-161801280 x^5+29120005 x^4+90028420 x^3+44740356 x^2+1821784 x-13931096\right)}{109395}","-\frac{2025 (1-2 x)^{17/2}}{1088}+\frac{927}{32} (1-2 x)^{15/2}-\frac{159111}{832} (1-2 x)^{13/2}+\frac{121359}{176} (1-2 x)^{11/2}-\frac{832951}{576} (1-2 x)^{9/2}+\frac{54439}{32} (1-2 x)^{7/2}-\frac{290521}{320} (1-2 x)^{5/2}",1,"(Sqrt[1 - 2*x]*(-13931096 + 1821784*x + 44740356*x^2 + 90028420*x^3 + 29120005*x^4 - 161801280*x^5 - 284055255*x^6 - 197142660*x^7 - 52123500*x^8))/109395","A",1
1871,1,48,79,0.0133229,"\int (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(-1158300 x^7-3564000 x^6-3749895 x^5-776255 x^4+1436365 x^3+1121793 x^2+155842 x-307478\right)}{6435}","\frac{45}{32} (1-2 x)^{15/2}-\frac{7695}{416} (1-2 x)^{13/2}+\frac{17541}{176} (1-2 x)^{11/2}-\frac{39977}{144} (1-2 x)^{9/2}+\frac{13013}{32} (1-2 x)^{7/2}-\frac{41503}{160} (1-2 x)^{5/2}",1,"(Sqrt[1 - 2*x]*(-307478 + 155842*x + 1121793*x^2 + 1436365*x^3 - 776255*x^4 - 3749895*x^5 - 3564000*x^6 - 1158300*x^7))/6435","A",1
1872,1,43,66,0.0127983,"\int (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(-445500 x^6-1050300 x^5-661435 x^4+248990 x^3+441543 x^2+114182 x-117478\right)}{6435}","-\frac{225}{208} (1-2 x)^{13/2}+\frac{255}{22} (1-2 x)^{11/2}-\frac{3467}{72} (1-2 x)^{9/2}+\frac{187}{2} (1-2 x)^{7/2}-\frac{5929}{80} (1-2 x)^{5/2}",1,"(Sqrt[1 - 2*x]*(-117478 + 114182*x + 441543*x^2 + 248990*x^3 - 661435*x^4 - 1050300*x^5 - 445500*x^6))/6435","A",1
1873,1,38,53,0.0103983,"\int (1-2 x)^{3/2} (2+3 x) (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(-94500 x^5-152600 x^4-19385 x^3+82617 x^2+37753 x-24617\right)}{3465}","\frac{75}{88} (1-2 x)^{11/2}-\frac{505}{72} (1-2 x)^{9/2}+\frac{1133}{56} (1-2 x)^{7/2}-\frac{847}{40} (1-2 x)^{5/2}",1,"(Sqrt[1 - 2*x]*(-24617 + 37753*x + 82617*x^2 - 19385*x^3 - 152600*x^4 - 94500*x^5))/3465","A",1
1874,1,33,40,0.0090339,"\int (1-2 x)^{3/2} (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(3 + 5*x)^2,x]","\frac{1}{315} \sqrt{1-2 x} \left(-3500 x^4-2900 x^3+1977 x^2+1948 x-887\right)","-\frac{25}{36} (1-2 x)^{9/2}+\frac{55}{14} (1-2 x)^{7/2}-\frac{121}{20} (1-2 x)^{5/2}",1,"(Sqrt[1 - 2*x]*(-887 + 1948*x + 1977*x^2 - 2900*x^3 - 3500*x^4))/315","A",1
1875,1,58,82,0.0599303,"\int \frac{(1-2 x)^{3/2} (3+5 x)^2}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x),x]","\frac{1}{567} \sqrt{1-2 x} \left(-2700 x^3+144 x^2+1853 x-527\right)-\frac{14}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","\frac{25}{42} (1-2 x)^{7/2}-\frac{31}{18} (1-2 x)^{5/2}+\frac{2}{81} (1-2 x)^{3/2}+\frac{14}{81} \sqrt{1-2 x}-\frac{14}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-527 + 1853*x + 144*x^2 - 2700*x^3))/567 - (14*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/81","A",1
1876,1,65,89,0.0979097,"\int \frac{(1-2 x)^{3/2} (3+5 x)^2}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^2,x]","\frac{\sqrt{1-2 x} \left(-540 x^3+300 x^2-187 x-425\right)}{81 (3 x+2)}+\frac{146}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","-\frac{(1-2 x)^{5/2}}{63 (3 x+2)}-\frac{5}{9} (1-2 x)^{5/2}-\frac{146}{567} (1-2 x)^{3/2}-\frac{146}{81} \sqrt{1-2 x}+\frac{146}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-425 - 187*x + 300*x^2 - 540*x^3))/(81*(2 + 3*x)) + (146*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/81","A",1
1877,1,63,94,0.1091514,"\int \frac{(1-2 x)^{3/2} (3+5 x)^2}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^3,x]","\frac{\sqrt{1-2 x} \left(-1800 x^3+5520 x^2+10195 x+3803\right)}{162 (3 x+2)^2}-\frac{2873 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{81 \sqrt{21}}","\frac{47 (1-2 x)^{5/2}}{294 (3 x+2)}-\frac{(1-2 x)^{5/2}}{126 (3 x+2)^2}+\frac{2873 (1-2 x)^{3/2}}{3969}+\frac{2873}{567} \sqrt{1-2 x}-\frac{2873 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{81 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(3803 + 10195*x + 5520*x^2 - 1800*x^3))/(162*(2 + 3*x)^2) - (2873*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(81*Sqrt[21])","A",1
1878,1,63,101,0.1074236,"\int \frac{(1-2 x)^{3/2} (3+5 x)^2}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^4,x]","\frac{\sqrt{1-2 x} \left(-37800 x^3-100809 x^2-82493 x-21424\right)}{1134 (3 x+2)^3}+\frac{7559 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{567 \sqrt{21}}","\frac{209 (1-2 x)^{5/2}}{2646 (3 x+2)^2}-\frac{(1-2 x)^{5/2}}{189 (3 x+2)^3}-\frac{7559 (1-2 x)^{3/2}}{7938 (3 x+2)}-\frac{7559 \sqrt{1-2 x}}{3969}+\frac{7559 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{567 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-21424 - 82493*x - 100809*x^2 - 37800*x^3))/(1134*(2 + 3*x)^3) + (7559*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(567*Sqrt[21])","A",1
1879,1,63,108,0.1068488,"\int \frac{(1-2 x)^{3/2} (3+5 x)^2}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^5,x]","\frac{\sqrt{1-2 x} \left(668979 x^3+988035 x^2+453730 x+60890\right)}{31752 (3 x+2)^4}-\frac{14423 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{15876 \sqrt{21}}","\frac{277 (1-2 x)^{5/2}}{5292 (3 x+2)^3}-\frac{(1-2 x)^{5/2}}{252 (3 x+2)^4}-\frac{14423 (1-2 x)^{3/2}}{31752 (3 x+2)^2}+\frac{14423 \sqrt{1-2 x}}{31752 (3 x+2)}-\frac{14423 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{15876 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(60890 + 453730*x + 988035*x^2 + 668979*x^3))/(31752*(2 + 3*x)^4) - (14423*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(15876*Sqrt[21])","A",1
1880,1,68,128,0.1247222,"\int \frac{(1-2 x)^{3/2} (3+5 x)^2}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^6,x]","\frac{\sqrt{1-2 x} \left(-1900665 x^4+5801265 x^3+8540988 x^2+2143262 x-292028\right)}{1111320 (3 x+2)^5}-\frac{4693 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{111132 \sqrt{21}}","\frac{23 (1-2 x)^{5/2}}{588 (3 x+2)^4}-\frac{(1-2 x)^{5/2}}{315 (3 x+2)^5}-\frac{4693 (1-2 x)^{3/2}}{15876 (3 x+2)^3}-\frac{4693 \sqrt{1-2 x}}{222264 (3 x+2)}+\frac{4693 \sqrt{1-2 x}}{31752 (3 x+2)^2}-\frac{4693 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{111132 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-292028 + 2143262*x + 8540988*x^2 + 5801265*x^3 - 1900665*x^4))/(1111320*(2 + 3*x)^5) - (4693*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(111132*Sqrt[21])","A",1
1881,1,73,148,0.1399119,"\int \frac{(1-2 x)^{3/2} (3+5 x)^2}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^7,x]","\frac{\sqrt{1-2 x} \left(-1204065 x^5-4950045 x^4+6094818 x^3+9658494 x^2+1262200 x-858112\right)}{2222640 (3 x+2)^6}-\frac{991 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{222264 \sqrt{21}}","\frac{59 (1-2 x)^{5/2}}{1890 (3 x+2)^5}-\frac{(1-2 x)^{5/2}}{378 (3 x+2)^6}-\frac{991 (1-2 x)^{3/2}}{4536 (3 x+2)^4}-\frac{991 \sqrt{1-2 x}}{444528 (3 x+2)}-\frac{991 \sqrt{1-2 x}}{190512 (3 x+2)^2}+\frac{991 \sqrt{1-2 x}}{13608 (3 x+2)^3}-\frac{991 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{222264 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-858112 + 1262200*x + 9658494*x^2 + 6094818*x^3 - 4950045*x^4 - 1204065*x^5))/(2222640*(2 + 3*x)^6) - (991*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(222264*Sqrt[21])","A",1
1882,1,58,105,0.0181811,"\int (1-2 x)^{3/2} (2+3 x)^4 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(-1476832500 x^9-6503854500 x^8-11568656385 x^7-9793273050 x^6-2388733575 x^5+2741637820 x^4+2751200080 x^3+942365544 x^2-70133984 x-369438704\right)}{692835}","\frac{10125 (1-2 x)^{19/2}}{2432}-\frac{161325 (1-2 x)^{17/2}}{2176}+\frac{73431}{128} (1-2 x)^{15/2}-\frac{4177401 (1-2 x)^{13/2}}{1664}+\frac{9504551 (1-2 x)^{11/2}}{1408}-\frac{4324397}{384} (1-2 x)^{9/2}+\frac{1405173}{128} (1-2 x)^{7/2}-\frac{3195731}{640} (1-2 x)^{5/2}",1,"(Sqrt[1 - 2*x]*(-369438704 - 70133984*x + 942365544*x^2 + 2751200080*x^3 + 2741637820*x^4 - 2388733575*x^5 - 9793273050*x^6 - 11568656385*x^7 - 6503854500*x^8 - 1476832500*x^9))/692835","A",1
1883,1,53,92,0.0155667,"\int (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(-28957500 x^8-107335800 x^7-151076475 x^6-82806465 x^5+17644040 x^4+47302655 x^3+22736811 x^2+717734 x-7158706\right)}{36465}","-\frac{3375 (1-2 x)^{17/2}}{1088}+\frac{765}{16} (1-2 x)^{15/2}-\frac{260055}{832} (1-2 x)^{13/2}+\frac{98209}{88} (1-2 x)^{11/2}-\frac{444983}{192} (1-2 x)^{9/2}+\frac{43197}{16} (1-2 x)^{7/2}-\frac{456533}{320} (1-2 x)^{5/2}",1,"(Sqrt[1 - 2*x]*(-7158706 + 717734*x + 22736811*x^2 + 47302655*x^3 + 17644040*x^4 - 82806465*x^5 - 151076475*x^6 - 107335800*x^7 - 28957500*x^8))/36465","A",1
1884,1,48,79,0.0136906,"\int (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^3,x]","\frac{1}{165} \sqrt{1-2 x} \left(-49500 x^7-148500 x^6-151275 x^5-27520 x^4+59255 x^3+44166 x^2+5684 x-12136\right)","\frac{75}{32} (1-2 x)^{15/2}-\frac{975}{32} (1-2 x)^{13/2}+\frac{28555}{176} (1-2 x)^{11/2}-\frac{21439}{48} (1-2 x)^{9/2}+\frac{20691}{32} (1-2 x)^{7/2}-\frac{65219}{160} (1-2 x)^{5/2}",1,"(Sqrt[1 - 2*x]*(-12136 + 5684*x + 44166*x^2 + 59255*x^3 - 27520*x^4 - 151275*x^5 - 148500*x^6 - 49500*x^7))/165","A",1
1885,1,43,66,0.0117401,"\int (1-2 x)^{3/2} (2+3 x) (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(-1732500 x^6-3948000 x^5-2351825 x^4+996295 x^3+1597776 x^2+389509 x-421301\right)}{15015}","-\frac{375}{208} (1-2 x)^{13/2}+\frac{1675}{88} (1-2 x)^{11/2}-\frac{935}{12} (1-2 x)^{9/2}+\frac{8349}{56} (1-2 x)^{7/2}-\frac{9317}{80} (1-2 x)^{5/2}",1,"(Sqrt[1 - 2*x]*(-421301 + 389509*x + 1597776*x^2 + 996295*x^3 - 2351825*x^4 - 3948000*x^5 - 1732500*x^6))/15015","A",1
1886,1,38,53,0.0106426,"\int (1-2 x)^{3/2} (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(-52500 x^5-80500 x^4-7225 x^3+43482 x^2+18593 x-12592\right)}{1155}","\frac{125}{88} (1-2 x)^{11/2}-\frac{275}{24} (1-2 x)^{9/2}+\frac{1815}{56} (1-2 x)^{7/2}-\frac{1331}{40} (1-2 x)^{5/2}",1,"(Sqrt[1 - 2*x]*(-12592 + 18593*x + 43482*x^2 - 7225*x^3 - 80500*x^4 - 52500*x^5))/1155","A",1
1887,1,63,95,0.0683072,"\int \frac{(1-2 x)^{3/2} (3+5 x)^3}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x),x]","\frac{\sqrt{1-2 x} \left(-31500 x^4-23400 x^3+17649 x^2+15679 x-7456\right)}{1701}+\frac{14}{243} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","-\frac{125}{108} (1-2 x)^{9/2}+\frac{400}{63} (1-2 x)^{7/2}-\frac{1027}{108} (1-2 x)^{5/2}-\frac{2}{243} (1-2 x)^{3/2}-\frac{14}{243} \sqrt{1-2 x}+\frac{14}{243} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-7456 + 15679*x + 17649*x^2 - 23400*x^3 - 31500*x^4))/1701 + (14*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/243","A",1
1888,1,70,108,0.1150192,"\int \frac{(1-2 x)^{3/2} (3+5 x)^3}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^2,x]","\frac{\sqrt{1-2 x} \left(-1500 x^4-780 x^3+1005 x^2+442 x-85\right)}{63 (3 x+2)}-\frac{8}{9} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","-\frac{(1-2 x)^{3/2} (5 x+3)^3}{3 (3 x+2)}+\frac{5}{7} (1-2 x)^{3/2} (5 x+3)^2-\frac{10}{63} (1-2 x)^{3/2} (27 x+22)+\frac{8}{9} \sqrt{1-2 x}-\frac{8}{9} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-85 + 442*x + 1005*x^2 - 780*x^3 - 1500*x^4))/(63*(2 + 3*x)) - (8*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/9","A",1
1889,1,63,118,0.1171609,"\int \frac{(1-2 x)^{3/2} (3+5 x)^3}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^3,x]","\frac{\sqrt{1-2 x} \left(-1800 x^4-570 x^2-2965 x-1367\right)}{54 (3 x+2)^2}+\frac{887 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{27 \sqrt{21}}","\frac{6 \sqrt{1-2 x} (5 x+3)^3}{3 x+2}-\frac{(1-2 x)^{3/2} (5 x+3)^3}{6 (3 x+2)^2}-\frac{31}{3} \sqrt{1-2 x} (5 x+3)^2+\frac{1}{54} \sqrt{1-2 x} (1715 x+367)+\frac{887 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{27 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-1367 - 2965*x - 570*x^2 - 1800*x^4))/(54*(2 + 3*x)^2) + (887*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(27*Sqrt[21])","A",1
1890,1,68,125,0.1198987,"\int \frac{(1-2 x)^{3/2} (3+5 x)^3}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^4,x]","\frac{\sqrt{1-2 x} \left(-31500 x^4+81900 x^3+259614 x^2+199243 x+47939\right)}{567 (3 x+2)^3}-\frac{36038 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{567 \sqrt{21}}","\frac{2 \sqrt{1-2 x} (5 x+3)^3}{(3 x+2)^2}-\frac{(1-2 x)^{3/2} (5 x+3)^3}{9 (3 x+2)^3}+\frac{251 \sqrt{1-2 x} (5 x+3)^2}{63 (3 x+2)}-\frac{5}{567} \sqrt{1-2 x} (7265 x+2323)-\frac{36038 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{567 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(47939 + 199243*x + 259614*x^2 + 81900*x^3 - 31500*x^4))/(567*(2 + 3*x)^3) - (36038*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(567*Sqrt[21])","A",1
1891,1,68,131,0.1201352,"\int \frac{(1-2 x)^{3/2} (3+5 x)^3}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^5,x]","\frac{\sqrt{1-2 x} \left(-196000 x^4-661639 x^3-788415 x^2-401850 x-74810\right)}{1176 (3 x+2)^4}+\frac{13243 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{588 \sqrt{21}}","\frac{\sqrt{1-2 x} (5 x+3)^3}{(3 x+2)^3}-\frac{(1-2 x)^{3/2} (5 x+3)^3}{12 (3 x+2)^4}+\frac{13 \sqrt{1-2 x} (5 x+3)^2}{56 (3 x+2)^2}-\frac{\sqrt{1-2 x} (26775 x+18187)}{1176 (3 x+2)}+\frac{13243 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{588 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-74810 - 401850*x - 788415*x^2 - 661639*x^3 - 196000*x^4))/(1176*(2 + 3*x)^4) + (13243*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(588*Sqrt[21])","A",1
1892,1,68,134,0.1372212,"\int \frac{(1-2 x)^{3/2} (3+5 x)^3}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^6,x]","\frac{\sqrt{1-2 x} \left(4904370 x^4+10375830 x^3+7992771 x^2+2619854 x+300049\right)}{46305 (3 x+2)^5}-\frac{13892 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{9261 \sqrt{21}}","\frac{3 \sqrt{1-2 x} (5 x+3)^3}{5 (3 x+2)^4}-\frac{(1-2 x)^{3/2} (5 x+3)^3}{15 (3 x+2)^5}-\frac{67 \sqrt{1-2 x} (5 x+3)^2}{315 (3 x+2)^3}-\frac{2 \sqrt{1-2 x} (15074 x+9529)}{9261 (3 x+2)^2}-\frac{13892 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{9261 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(300049 + 2619854*x + 7992771*x^2 + 10375830*x^3 + 4904370*x^4))/(46305*(2 + 3*x)^5) - (13892*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(9261*Sqrt[21])","A",1
1893,1,73,154,0.1501508,"\int \frac{(1-2 x)^{3/2} (3+5 x)^3}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^7,x]","\frac{\sqrt{1-2 x} \left(-18605295 x^5+46991565 x^4+122053374 x^3+75153042 x^2+10947400 x-1660816\right)}{2222640 (3 x+2)^6}-\frac{15313 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{222264 \sqrt{21}}","\frac{2 \sqrt{1-2 x} (5 x+3)^3}{5 (3 x+2)^5}-\frac{(1-2 x)^{3/2} (5 x+3)^3}{18 (3 x+2)^6}-\frac{653 \sqrt{1-2 x} (5 x+3)^2}{2520 (3 x+2)^4}-\frac{\sqrt{1-2 x} (664915 x+413424)}{317520 (3 x+2)^3}-\frac{15313 \sqrt{1-2 x}}{444528 (3 x+2)}-\frac{15313 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{222264 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-1660816 + 10947400*x + 75153042*x^2 + 122053374*x^3 + 46991565*x^4 - 18605295*x^5))/(2222640*(2 + 3*x)^6) - (15313*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(222264*Sqrt[21])","A",1
1894,1,78,174,0.156062,"\int \frac{(1-2 x)^{3/2} (3+5 x)^3}{(2+3 x)^8} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^8,x]","\frac{\sqrt{1-2 x} \left(-15925005 x^6-76086135 x^5+42669876 x^4+182748162 x^3+98441652 x^2-606784 x-7033976\right)}{6050520 (3 x+2)^7}-\frac{4369 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{605052 \sqrt{21}}","\frac{2 \sqrt{1-2 x} (5 x+3)^3}{7 (3 x+2)^6}-\frac{(1-2 x)^{3/2} (5 x+3)^3}{21 (3 x+2)^7}-\frac{173 \sqrt{1-2 x} (5 x+3)^2}{735 (3 x+2)^5}-\frac{\sqrt{1-2 x} (237807 x+146585)}{185220 (3 x+2)^4}-\frac{4369 \sqrt{1-2 x}}{1210104 (3 x+2)}-\frac{4369 \sqrt{1-2 x}}{518616 (3 x+2)^2}-\frac{4369 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{605052 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-7033976 - 606784*x + 98441652*x^2 + 182748162*x^3 + 42669876*x^4 - 76086135*x^5 - 15925005*x^6))/(6050520*(2 + 3*x)^7) - (4369*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(605052*Sqrt[21])","A",1
1895,1,78,134,0.0723437,"\int \frac{(1-2 x)^{3/2} (2+3 x)^6}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^6)/(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(-45608062500 x^7-150857437500 x^6-174123928125 x^5-49094797500 x^4+61883481375 x^3+56176961670 x^2+9645684935 x-15379193944\right)}{1173046875}-\frac{22 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{390625}","\frac{243}{800} (1-2 x)^{15/2}-\frac{43011 (1-2 x)^{13/2}}{10400}+\frac{507627 (1-2 x)^{11/2}}{22000}-\frac{665817 (1-2 x)^{9/2}}{10000}+\frac{70752609 (1-2 x)^{7/2}}{700000}-\frac{167115051 (1-2 x)^{5/2}}{2500000}+\frac{2 (1-2 x)^{3/2}}{234375}+\frac{22 \sqrt{1-2 x}}{390625}-\frac{22 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{390625}",1,"(Sqrt[1 - 2*x]*(-15379193944 + 9645684935*x + 56176961670*x^2 + 61883481375*x^3 - 49094797500*x^4 - 174123928125*x^5 - 150857437500*x^6 - 45608062500*x^7))/1173046875 - (22*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/390625","A",1
1896,1,73,121,0.0644436,"\int \frac{(1-2 x)^{3/2} (2+3 x)^5}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^5)/(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(-3508312500 x^6-9100350000 x^5-6683000625 x^4+1659418875 x^3+4276774170 x^2+1321809935 x-1180568944\right)}{234609375}-\frac{22 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{78125}","-\frac{243 (1-2 x)^{13/2}}{1040}+\frac{5751 (1-2 x)^{11/2}}{2200}-\frac{5673}{500} (1-2 x)^{9/2}+\frac{806121 (1-2 x)^{7/2}}{35000}-\frac{4774713 (1-2 x)^{5/2}}{250000}+\frac{2 (1-2 x)^{3/2}}{46875}+\frac{22 \sqrt{1-2 x}}{78125}-\frac{22 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{78125}",1,"(Sqrt[1 - 2*x]*(-1180568944 + 1321809935*x + 4276774170*x^2 + 1659418875*x^3 - 6683000625*x^4 - 9100350000*x^5 - 3508312500*x^6))/234609375 - (22*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/78125","A",1
1897,1,68,108,0.069223,"\int \frac{(1-2 x)^{3/2} (2+3 x)^4}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^4)/(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(-21262500 x^5-39532500 x^4-9559125 x^3+21433590 x^2+12144995 x-7095688\right)}{3609375}-\frac{22 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15625}","\frac{81}{440} (1-2 x)^{11/2}-\frac{321}{200} (1-2 x)^{9/2}+\frac{34371 (1-2 x)^{7/2}}{7000}-\frac{136419 (1-2 x)^{5/2}}{25000}+\frac{2 (1-2 x)^{3/2}}{9375}+\frac{22 \sqrt{1-2 x}}{15625}-\frac{22 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15625}",1,"(Sqrt[1 - 2*x]*(-7095688 + 12144995*x + 21433590*x^2 - 9559125*x^3 - 39532500*x^4 - 21262500*x^5))/3609375 - (22*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/15625","A",1
1898,1,63,95,0.0647775,"\int \frac{(1-2 x)^{3/2} (2+3 x)^3}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^3)/(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(-157500 x^4-171000 x^3+83565 x^2+123295 x-50858\right)}{65625}-\frac{22 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125}","-\frac{3}{20} (1-2 x)^{9/2}+\frac{162}{175} (1-2 x)^{7/2}-\frac{3897 (1-2 x)^{5/2}}{2500}+\frac{2 (1-2 x)^{3/2}}{1875}+\frac{22 \sqrt{1-2 x}}{3125}-\frac{22 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125}",1,"(Sqrt[1 - 2*x]*(-50858 + 123295*x + 83565*x^2 - 171000*x^3 - 157500*x^4))/65625 - (22*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/3125","A",1
1899,1,58,82,0.0591819,"\int \frac{(1-2 x)^{3/2} (2+3 x)^2}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^2)/(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(-13500 x^3-3060 x^2+13045 x-3608\right)}{13125}-\frac{22}{625} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{9}{70} (1-2 x)^{7/2}-\frac{111}{250} (1-2 x)^{5/2}+\frac{2}{375} (1-2 x)^{3/2}+\frac{22}{625} \sqrt{1-2 x}-\frac{22}{625} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-3608 + 13045*x - 3060*x^2 - 13500*x^3))/13125 - (22*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/625","A",1
1900,1,53,69,0.0545135,"\int \frac{(1-2 x)^{3/2} (2+3 x)}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x))/(3 + 5*x),x]","\frac{1}{375} \sqrt{1-2 x} \left(-180 x^2+160 x+31\right)-\frac{22}{125} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{3}{25} (1-2 x)^{5/2}+\frac{2}{75} (1-2 x)^{3/2}+\frac{22}{125} \sqrt{1-2 x}-\frac{22}{125} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(31 + 160*x - 180*x^2))/375 - (22*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/125","A",1
1901,1,48,56,0.043395,"\int \frac{(1-2 x)^{3/2}}{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/(3 + 5*x),x]","-\frac{4}{75} \sqrt{1-2 x} (5 x-19)-\frac{22}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{2}{15} (1-2 x)^{3/2}+\frac{22}{25} \sqrt{1-2 x}-\frac{22}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(-4*Sqrt[1 - 2*x]*(-19 + 5*x))/75 - (22*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/25","A",1
1902,1,72,72,0.0841826,"\int \frac{(1-2 x)^{3/2}}{(2+3 x) (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)*(3 + 5*x)),x]","-\frac{4}{15} \sqrt{1-2 x}+\frac{14}{3} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{22}{5} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{4}{15} \sqrt{1-2 x}+\frac{14}{3} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{22}{5} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(-4*Sqrt[1 - 2*x])/15 + (14*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/3 - (22*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/5","A",1
1903,1,77,77,0.1238311,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^2*(3 + 5*x)),x]","\frac{7 \sqrt{1-2 x}}{3 (3 x+2)}+\frac{64}{3} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-22 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{7 \sqrt{1-2 x}}{3 (3 x+2)}+\frac{64}{3} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-22 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(7*Sqrt[1 - 2*x])/(3*(2 + 3*x)) + (64*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/3 - 22*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1904,1,78,93,0.1241382,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^3*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} (195 x+137)}{6 (3 x+2)^2}+\frac{2243 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{3 \sqrt{21}}-22 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{65 \sqrt{1-2 x}}{6 (3 x+2)}+\frac{7 \sqrt{1-2 x}}{6 (3 x+2)^2}+\frac{2243 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{3 \sqrt{21}}-22 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(137 + 195*x))/(6*(2 + 3*x)^2) + (2243*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(3*Sqrt[21]) - 22*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1905,1,83,113,0.1293733,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^4 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^4*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(10242 x^2+13999 x+4797\right)}{21 (3 x+2)^3}+\frac{78506 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{21 \sqrt{21}}-110 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{1138 \sqrt{1-2 x}}{21 (3 x+2)}+\frac{49 \sqrt{1-2 x}}{9 (3 x+2)^2}+\frac{7 \sqrt{1-2 x}}{9 (3 x+2)^3}+\frac{78506 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{21 \sqrt{21}}-110 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(4797 + 13999*x + 10242*x^2))/(21*(2 + 3*x)^3) + (78506*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(21*Sqrt[21]) - 110*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1906,1,88,133,0.1608778,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^5 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^5*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(8603361 x^3+17494905 x^2+11868230 x+2686470\right)}{1176 (3 x+2)^4}+\frac{10990843 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{588 \sqrt{21}}-550 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{318643 \sqrt{1-2 x}}{1176 (3 x+2)}+\frac{13723 \sqrt{1-2 x}}{504 (3 x+2)^2}+\frac{131 \sqrt{1-2 x}}{36 (3 x+2)^3}+\frac{7 \sqrt{1-2 x}}{12 (3 x+2)^4}+\frac{10990843 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{588 \sqrt{21}}-550 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(2686470 + 11868230*x + 17494905*x^2 + 8603361*x^3))/(1176*(2 + 3*x)^4) + (10990843*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(588*Sqrt[21]) - 550*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1907,1,93,153,0.1681444,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^6 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^6*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(1129191435 x^4+3049001415 x^3+3088510878 x^2+1391064622 x+235067382\right)}{10290 (3 x+2)^5}+\frac{96169877 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1029 \sqrt{21}}-2750 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{2788127 \sqrt{1-2 x}}{2058 (3 x+2)}+\frac{120077 \sqrt{1-2 x}}{882 (3 x+2)^2}+\frac{5732 \sqrt{1-2 x}}{315 (3 x+2)^3}+\frac{41 \sqrt{1-2 x}}{15 (3 x+2)^4}+\frac{7 \sqrt{1-2 x}}{15 (3 x+2)^5}+\frac{96169877 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1029 \sqrt{21}}-2750 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(235067382 + 1391064622*x + 3088510878*x^2 + 3049001415*x^3 + 1129191435*x^4))/(10290*(2 + 3*x)^5) + (96169877*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(1029*Sqrt[21]) - 2750*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1908,1,80,148,0.1193853,"\int \frac{(1-2 x)^{3/2} (2+3 x)^5}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^5)/(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(-106312500 x^6-270112500 x^5-181738125 x^4+76760550 x^3+135193430 x^2+2532130 x-23061496\right)}{6015625 (5 x+3)}-\frac{324 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{78125}","-\frac{(1-2 x)^{3/2} (3 x+2)^5}{5 (5 x+3)}+\frac{39}{275} (1-2 x)^{3/2} (3 x+2)^4+\frac{38 (1-2 x)^{3/2} (3 x+2)^3}{4125}-\frac{4016 (1-2 x)^{3/2} (3 x+2)^2}{48125}-\frac{2 (1-2 x)^{3/2} (204777 x+298462)}{515625}+\frac{324 \sqrt{1-2 x}}{78125}-\frac{324 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{78125}",1,"(Sqrt[1 - 2*x]*(-23061496 + 2532130*x + 135193430*x^2 + 76760550*x^3 - 181738125*x^4 - 270112500*x^5 - 106312500*x^6))/(6015625*(3 + 5*x)) - (324*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/78125","A",1
1909,1,75,128,0.1122952,"\int \frac{(1-2 x)^{3/2} (2+3 x)^4}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^4)/(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(-787500 x^5-1395000 x^4-157275 x^3+924335 x^2+143235 x-161312\right)}{109375 (5 x+3)}-\frac{258 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15625}","-\frac{(1-2 x)^{3/2} (3 x+2)^4}{5 (5 x+3)}+\frac{11}{75} (1-2 x)^{3/2} (3 x+2)^3-\frac{2}{875} (1-2 x)^{3/2} (3 x+2)^2-\frac{(1-2 x)^{3/2} (3663 x+5678)}{9375}+\frac{258 \sqrt{1-2 x}}{15625}-\frac{258 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15625}",1,"(Sqrt[1 - 2*x]*(-161312 + 143235*x + 924335*x^2 - 157275*x^3 - 1395000*x^4 - 787500*x^5))/(109375*(3 + 5*x)) - (258*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/15625","A",1
1910,1,70,108,0.099904,"\int \frac{(1-2 x)^{3/2} (2+3 x)^3}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^3)/(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(-67500 x^4-62100 x^3+57165 x^2+27640 x-8738\right)}{21875 (5 x+3)}-\frac{192 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125}","-\frac{(1-2 x)^{3/2} (3 x+2)^3}{5 (5 x+3)}+\frac{27}{175} (1-2 x)^{3/2} (3 x+2)^2-\frac{6}{625} (1-2 x)^{3/2} (9 x+29)+\frac{192 \sqrt{1-2 x}}{3125}-\frac{192 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125}",1,"(Sqrt[1 - 2*x]*(-8738 + 27640*x + 57165*x^2 - 62100*x^3 - 67500*x^4))/(21875*(3 + 5*x)) - (192*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/3125","A",1
1911,1,65,89,0.1008909,"\int \frac{(1-2 x)^{3/2} (2+3 x)^2}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^2)/(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(-900 x^3+160 x^2+935 x+298\right)}{625 (5 x+3)}-\frac{126}{625} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{(1-2 x)^{5/2}}{275 (5 x+3)}-\frac{9}{125} (1-2 x)^{5/2}+\frac{42 (1-2 x)^{3/2}}{1375}+\frac{126}{625} \sqrt{1-2 x}-\frac{126}{625} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(298 + 935*x + 160*x^2 - 900*x^3))/(625*(3 + 5*x)) - (126*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/625","A",1
1912,1,60,76,0.0853109,"\int \frac{(1-2 x)^{3/2} (2+3 x)}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x))/(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(-20 x^2+60 x+41\right)}{25 (5 x+3)}-\frac{12}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{(1-2 x)^{5/2}}{55 (5 x+3)}+\frac{4}{55} (1-2 x)^{3/2}+\frac{12}{25} \sqrt{1-2 x}-\frac{12}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(41 + 60*x - 20*x^2))/(25*(3 + 5*x)) - (12*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/25","A",1
1913,1,55,63,0.0687914,"\int \frac{(1-2 x)^{3/2}}{(3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} (-20 x-23)}{25 (5 x+3)}+\frac{6}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{(1-2 x)^{3/2}}{5 (5 x+3)}-\frac{6}{25} \sqrt{1-2 x}+\frac{6}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"((-23 - 20*x)*Sqrt[1 - 2*x])/(25*(3 + 5*x)) + (6*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/25","A",1
1914,1,77,77,0.1190999,"\int \frac{(1-2 x)^{3/2}}{(2+3 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)*(3 + 5*x)^2),x]","-\frac{11 \sqrt{1-2 x}}{5 (5 x+3)}-14 \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{72}{5} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{11 \sqrt{1-2 x}}{5 (5 x+3)}-14 \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{72}{5} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(-11*Sqrt[1 - 2*x])/(5*(3 + 5*x)) - 14*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] + (72*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/5","A",1
1915,1,82,102,0.1133997,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} (-68 x-43)}{15 x^2+19 x+6}-134 \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+138 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{68 \sqrt{1-2 x}}{3 (5 x+3)}+\frac{7 \sqrt{1-2 x}}{3 (3 x+2) (5 x+3)}-134 \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+138 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"((-43 - 68*x)*Sqrt[1 - 2*x])/(6 + 19*x + 15*x^2) - 134*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] + 138*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1916,1,90,127,0.1490087,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^3*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-3015 x^2-3920 x-1271\right)}{2 (3 x+2)^2 (5 x+3)}-2311 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+204 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{335 \sqrt{1-2 x}}{2 (5 x+3)}+\frac{50 \sqrt{1-2 x}}{3 (3 x+2) (5 x+3)}+\frac{7 \sqrt{1-2 x}}{6 (3 x+2)^2 (5 x+3)}-2311 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+204 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-1271 - 3920*x - 3015*x^2))/(2*(2 + 3*x)^2*(3 + 5*x)) - 2311*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] + 204*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1917,1,95,154,0.1627477,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^4 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^4*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-418995 x^3-824092 x^2-539819 x-117752\right)}{14 (3 x+2)^3 (5 x+3)}-\frac{321161 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{7 \sqrt{21}}+1350 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{46555 \sqrt{1-2 x}}{42 (5 x+3)}+\frac{6949 \sqrt{1-2 x}}{63 (3 x+2) (5 x+3)}+\frac{133 \sqrt{1-2 x}}{18 (3 x+2)^2 (5 x+3)}+\frac{7 \sqrt{1-2 x}}{9 (3 x+2)^3 (5 x+3)}-\frac{321161 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{7 \sqrt{21}}+1350 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-117752 - 539819*x - 824092*x^2 - 418995*x^3))/(14*(2 + 3*x)^3*(3 + 5*x)) - (321161*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(7*Sqrt[21]) + 1350*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1918,1,100,181,0.1902355,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^5 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^5*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-218994705 x^4-576721848 x^3-569295605 x^2-249642200 x-41029970\right)}{392 (3 x+2)^4 (5 x+3)}-\frac{55953383 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{196 \sqrt{21}}+8400 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{8110915 \sqrt{1-2 x}}{1176 (5 x+3)}+\frac{302668 \sqrt{1-2 x}}{441 (3 x+2) (5 x+3)}+\frac{23173 \sqrt{1-2 x}}{504 (3 x+2)^2 (5 x+3)}+\frac{83 \sqrt{1-2 x}}{18 (3 x+2)^3 (5 x+3)}+\frac{7 \sqrt{1-2 x}}{12 (3 x+2)^4 (5 x+3)}-\frac{55953383 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{196 \sqrt{21}}+8400 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-41029970 - 249642200*x - 569295605*x^2 - 576721848*x^3 - 218994705*x^4))/(392*(2 + 3*x)^4*(3 + 5*x)) - (55953383*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(196*Sqrt[21]) + 8400*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1919,1,73,140,0.1365813,"\int \frac{(1-2 x)^{3/2} (2+3 x)^4}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^4)/(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(-2025000 x^5-3267000 x^4+496350 x^3+2120880 x^2+489445 x-96776\right)}{218750 (5 x+3)^2}-\frac{12279 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15625 \sqrt{55}}","-\frac{129 \sqrt{1-2 x} (3 x+2)^4}{50 (5 x+3)}-\frac{(1-2 x)^{3/2} (3 x+2)^4}{10 (5 x+3)^2}+\frac{2643 \sqrt{1-2 x} (3 x+2)^3}{1750}+\frac{1404 \sqrt{1-2 x} (3 x+2)^2}{3125}+\frac{9 \sqrt{1-2 x} (1375 x+32)}{31250}-\frac{12279 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15625 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-96776 + 489445*x + 2120880*x^2 + 496350*x^3 - 3267000*x^4 - 2025000*x^5))/(218750*(3 + 5*x)^2) - (12279*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(15625*Sqrt[55])","A",1
1920,1,68,120,0.1122513,"\int \frac{(1-2 x)^{3/2} (2+3 x)^3}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^3)/(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(-27000 x^4-14400 x^3+37530 x^2+36295 x+8644\right)}{6250 (5 x+3)^2}-\frac{5943 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125 \sqrt{55}}","-\frac{48 \sqrt{1-2 x} (3 x+2)^3}{25 (5 x+3)}-\frac{(1-2 x)^{3/2} (3 x+2)^3}{10 (5 x+3)^2}+\frac{693}{625} \sqrt{1-2 x} (3 x+2)^2+\frac{63 \sqrt{1-2 x} (125 x+92)}{6250}-\frac{5943 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(8644 + 36295*x + 37530*x^2 - 14400*x^3 - 27000*x^4))/(6250*(3 + 5*x)^2) - (5943*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(3125*Sqrt[55])","A",1
1921,1,63,94,0.1033052,"\int \frac{(1-2 x)^{3/2} (2+3 x)^2}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^2)/(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(-600 x^3+1320 x^2+2105 x+656\right)}{250 (5 x+3)^2}-\frac{357 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{125 \sqrt{55}}","-\frac{131 (1-2 x)^{5/2}}{6050 (5 x+3)}-\frac{(1-2 x)^{5/2}}{550 (5 x+3)^2}+\frac{119 (1-2 x)^{3/2}}{3025}+\frac{357 \sqrt{1-2 x}}{1375}-\frac{357 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{125 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(656 + 2105*x + 1320*x^2 - 600*x^3))/(250*(3 + 5*x)^2) - (357*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(125*Sqrt[55])","A",1
1922,1,58,81,0.0933782,"\int \frac{(1-2 x)^{3/2} (2+3 x)}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x))/(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(-120 x^2-205 x-82\right)}{50 (5 x+3)^2}+\frac{39 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{25 \sqrt{55}}","-\frac{(1-2 x)^{5/2}}{110 (5 x+3)^2}-\frac{13 (1-2 x)^{3/2}}{110 (5 x+3)}-\frac{39}{275} \sqrt{1-2 x}+\frac{39 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{25 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-82 - 205*x - 120*x^2))/(50*(3 + 5*x)^2) + (39*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(25*Sqrt[55])","A",1
1923,1,53,68,0.1012147,"\int \frac{(1-2 x)^{3/2}}{(3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} (25 x+4)}{50 (5 x+3)^2}-\frac{3 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{25 \sqrt{55}}","-\frac{(1-2 x)^{3/2}}{10 (5 x+3)^2}+\frac{3 \sqrt{1-2 x}}{50 (5 x+3)}-\frac{3 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{25 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(4 + 25*x))/(50*(3 + 5*x)^2) - (3*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(25*Sqrt[55])","A",1
1924,1,78,93,0.1245135,"\int \frac{(1-2 x)^{3/2}}{(2+3 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} (355 x+202)}{10 (5 x+3)^2}+14 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{2379 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{5 \sqrt{55}}","\frac{71 \sqrt{1-2 x}}{10 (5 x+3)}-\frac{11 \sqrt{1-2 x}}{10 (5 x+3)^2}+14 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{2379 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{5 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(202 + 355*x))/(10*(3 + 5*x)^2) + 14*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - (2379*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(5*Sqrt[55])","A",1
1925,1,88,118,0.1386894,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(3105 x^2+3830 x+1178\right)}{2 (3 x+2) (5 x+3)^2}+204 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{6933 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{\sqrt{55}}","\frac{207 \sqrt{1-2 x}}{2 (5 x+3)}-\frac{103 \sqrt{1-2 x}}{6 (5 x+3)^2}+\frac{7 \sqrt{1-2 x}}{3 (3 x+2) (5 x+3)^2}+204 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{6933 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{\sqrt{55}}",1,"(Sqrt[1 - 2*x]*(1178 + 3830*x + 3105*x^2))/(2*(2 + 3*x)*(3 + 5*x)^2) + 204*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - (6933*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/Sqrt[55]","A",1
1926,1,95,147,0.1488898,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(91800 x^3+174435 x^2+110315 x+23219\right)}{2 \left(15 x^2+19 x+6\right)^2}+14073 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-13665 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{1020 \sqrt{1-2 x}}{5 x+3}-\frac{1015 \sqrt{1-2 x}}{6 (5 x+3)^2}+\frac{45 \sqrt{1-2 x}}{2 (3 x+2) (5 x+3)^2}+\frac{7 \sqrt{1-2 x}}{6 (3 x+2)^2 (5 x+3)^2}+14073 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-13665 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(23219 + 110315*x + 174435*x^2 + 91800*x^3))/(2*(6 + 19*x + 15*x^2)^2) + 14073*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - 13665*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1927,1,104,178,0.1765659,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^4 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^4*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(15923925 x^4+40874010 x^3+39307638 x^2+16784696 x+2685098\right)}{14 (3 x+2)^3 (5 x+3)^2}+\frac{813716}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-112875 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{117955 \sqrt{1-2 x}}{14 (5 x+3)}-\frac{176065 \sqrt{1-2 x}}{126 (5 x+3)^2}+\frac{1301 \sqrt{1-2 x}}{7 (3 x+2) (5 x+3)^2}+\frac{28 \sqrt{1-2 x}}{3 (3 x+2)^2 (5 x+3)^2}+\frac{7 \sqrt{1-2 x}}{9 (3 x+2)^3 (5 x+3)^2}+\frac{813716}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-112875 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(2685098 + 16784696*x + 39307638*x^2 + 40874010*x^3 + 15923925*x^4))/(14*(2 + 3*x)^3*(3 + 5*x)^2) + (813716*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/7 - 112875*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1928,1,63,105,0.0175036,"\int (1-2 x)^{5/2} (2+3 x)^6 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^6*(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(4040613720 x^{10}+15971057388 x^9+23013359226 x^8+10299128697 x^7-8457459318 x^6-11546145324 x^5-3037739768 x^4+2155110064 x^3+1656222432 x^2+235056064 x-323646080\right)}{2909907}","\frac{1215}{896} (1-2 x)^{21/2}-\frac{59049 (1-2 x)^{19/2}}{2432}+\frac{409941 (1-2 x)^{17/2}}{2176}-\frac{105399}{128} (1-2 x)^{15/2}+\frac{3658095 (1-2 x)^{13/2}}{1664}-\frac{5078115 (1-2 x)^{11/2}}{1408}+\frac{3916031 (1-2 x)^{9/2}}{1152}-\frac{184877}{128} (1-2 x)^{7/2}",1,"(Sqrt[1 - 2*x]*(-323646080 + 235056064*x + 1656222432*x^2 + 2155110064*x^3 - 3037739768*x^4 - 11546145324*x^5 - 8457459318*x^6 + 10299128697*x^7 + 23013359226*x^8 + 15971057388*x^9 + 4040613720*x^10))/2909907","A",1
1929,1,58,92,0.0154775,"\int (1-2 x)^{5/2} (2+3 x)^5 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^5*(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(212663880 x^9+690949116 x^8+717196194 x^7+9461529 x^6-486084375 x^5-273280105 x^4+53353244 x^3+95863620 x^2+21784712 x-18122584\right)}{415701}","-\frac{1215 (1-2 x)^{19/2}}{1216}+\frac{1053}{68} (1-2 x)^{17/2}-\frac{6489}{64} (1-2 x)^{15/2}+\frac{37485}{104} (1-2 x)^{13/2}-\frac{519645}{704} (1-2 x)^{11/2}+\frac{60025}{72} (1-2 x)^{9/2}-\frac{26411}{64} (1-2 x)^{7/2}",1,"(Sqrt[1 - 2*x]*(-18122584 + 21784712*x + 95863620*x^2 + 53353244*x^3 - 273280105*x^4 - 486084375*x^5 + 9461529*x^6 + 717196194*x^7 + 690949116*x^8 + 212663880*x^9))/415701","A",1
1930,1,53,79,0.0150341,"\int (1-2 x)^{5/2} (2+3 x)^4 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^4*(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(20849400 x^8+52864812 x^7+31646538 x^6-24298407 x^5-32302900 x^4-2705920 x^3+9403464 x^2+3351776 x-1899184\right)}{109395}","\frac{405}{544} (1-2 x)^{17/2}-\frac{1557}{160} (1-2 x)^{15/2}+\frac{10773}{208} (1-2 x)^{13/2}-\frac{24843}{176} (1-2 x)^{11/2}+\frac{57281}{288} (1-2 x)^{9/2}-\frac{3773}{32} (1-2 x)^{7/2}",1,"(Sqrt[1 - 2*x]*(-1899184 + 3351776*x + 9403464*x^2 - 2705920*x^3 - 32302900*x^4 - 24298407*x^5 + 31646538*x^6 + 52864812*x^7 + 20849400*x^8))/109395","A",1
1931,1,48,66,0.0125259,"\int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(92664 x^7+167508 x^6+13446 x^5-128237 x^4-51767 x^3+35349 x^2+21850 x-9038\right)}{1287}","-\frac{9}{16} (1-2 x)^{15/2}+\frac{621}{104} (1-2 x)^{13/2}-\frac{1071}{44} (1-2 x)^{11/2}+\frac{3283}{72} (1-2 x)^{9/2}-\frac{539}{16} (1-2 x)^{7/2}",1,"(Sqrt[1 - 2*x]*(-9038 + 21850*x + 35349*x^2 - 51767*x^3 - 128237*x^4 + 13446*x^5 + 167508*x^6 + 92664*x^7))/1287","A",1
1932,1,43,53,0.0109733,"\int (1-2 x)^{5/2} (2+3 x)^2 (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(35640 x^6+37692 x^5-25678 x^4-32875 x^3+7302 x^2+11732 x-3712\right)}{1287}","\frac{45}{104} (1-2 x)^{13/2}-\frac{309}{88} (1-2 x)^{11/2}+\frac{707}{72} (1-2 x)^{9/2}-\frac{77}{8} (1-2 x)^{7/2}",1,"(Sqrt[1 - 2*x]*(-3712 + 11732*x + 7302*x^2 - 32875*x^3 - 25678*x^4 + 37692*x^5 + 35640*x^6))/1287","A",1
1933,1,38,40,0.0103603,"\int (1-2 x)^{5/2} (2+3 x) (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x),x]","\frac{1}{99} \sqrt{1-2 x} \left(1080 x^5+292 x^4-1106 x^3-129 x^2+475 x-119\right)","-\frac{15}{44} (1-2 x)^{11/2}+\frac{17}{9} (1-2 x)^{9/2}-\frac{11}{4} (1-2 x)^{7/2}",1,"(Sqrt[1 - 2*x]*(-119 + 475*x - 129*x^2 - 1106*x^3 + 292*x^4 + 1080*x^5))/99","A",1
1934,1,33,27,0.008651,"\int (1-2 x)^{5/2} (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(3 + 5*x),x]","\frac{1}{63} \sqrt{1-2 x} \left(280 x^4-164 x^3-174 x^2+157 x-32\right)","\frac{5}{18} (1-2 x)^{9/2}-\frac{11}{14} (1-2 x)^{7/2}",1,"(Sqrt[1 - 2*x]*(-32 + 157*x - 174*x^2 - 164*x^3 + 280*x^4))/63","A",1
1935,1,58,82,0.0700131,"\int \frac{(1-2 x)^{5/2} (3+5 x)}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x),x]","\frac{\sqrt{1-2 x} \left(5400 x^3-8604 x^2+5534 x-4721\right)}{2835}+\frac{98}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","-\frac{5}{21} (1-2 x)^{7/2}-\frac{2}{45} (1-2 x)^{5/2}-\frac{14}{81} (1-2 x)^{3/2}-\frac{98}{81} \sqrt{1-2 x}+\frac{98}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-4721 + 5534*x - 8604*x^2 + 5400*x^3))/2835 + (98*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/81","A",1
1936,1,65,89,0.0916341,"\int \frac{(1-2 x)^{5/2} (3+5 x)}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^2,x]","\frac{\sqrt{1-2 x} \left(216 x^3-516 x^2+1474 x+1325\right)}{81 (3 x+2)}-\frac{560}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","\frac{(1-2 x)^{7/2}}{21 (3 x+2)}+\frac{16}{63} (1-2 x)^{5/2}+\frac{80}{81} (1-2 x)^{3/2}+\frac{560}{81} \sqrt{1-2 x}-\frac{560}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(1325 + 1474*x - 516*x^2 + 216*x^3))/(81*(2 + 3*x)) - (560*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/81","A",1
1937,1,65,96,0.1025828,"\int \frac{(1-2 x)^{5/2} (3+5 x)}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^3,x]","\frac{\sqrt{1-2 x} \left(720 x^3-4584 x^2-8731 x-3521\right)}{162 (3 x+2)^2}+\frac{365}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","\frac{(1-2 x)^{7/2}}{42 (3 x+2)^2}-\frac{73 (1-2 x)^{5/2}}{126 (3 x+2)}-\frac{365}{567} (1-2 x)^{3/2}-\frac{365}{81} \sqrt{1-2 x}+\frac{365}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-3521 - 8731*x - 4584*x^2 + 720*x^3))/(162*(2 + 3*x)^2) + (365*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/81","A",1
1938,1,63,101,0.0953918,"\int \frac{(1-2 x)^{5/2} (3+5 x)}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^4,x]","\frac{\sqrt{1-2 x} \left(1080 x^3+3627 x^2+2983 x+713\right)}{81 (3 x+2)^3}-\frac{530 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{81 \sqrt{21}}","\frac{(1-2 x)^{7/2}}{63 (3 x+2)^3}-\frac{53 (1-2 x)^{5/2}}{189 (3 x+2)^2}+\frac{265 (1-2 x)^{3/2}}{567 (3 x+2)}+\frac{530}{567} \sqrt{1-2 x}-\frac{530 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{81 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(713 + 2983*x + 3627*x^2 + 1080*x^3))/(81*(2 + 3*x)^3) - (530*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(81*Sqrt[21])","A",1
1939,1,63,108,0.1026395,"\int \frac{(1-2 x)^{5/2} (3+5 x)}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^5,x]","\frac{\sqrt{1-2 x} \left(-41715 x^3-43971 x^2-18394 x-4394\right)}{4536 (3 x+2)^4}+\frac{695 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{2268 \sqrt{21}}","\frac{(1-2 x)^{7/2}}{84 (3 x+2)^4}-\frac{139 (1-2 x)^{5/2}}{756 (3 x+2)^3}+\frac{695 (1-2 x)^{3/2}}{4536 (3 x+2)^2}-\frac{695 \sqrt{1-2 x}}{4536 (3 x+2)}+\frac{695 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{2268 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-4394 - 18394*x - 43971*x^2 - 41715*x^3))/(4536*(2 + 3*x)^4) + (695*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(2268*Sqrt[21])","A",1
1940,1,68,128,0.1179144,"\int \frac{(1-2 x)^{5/2} (3+5 x)}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^6,x]","\frac{\sqrt{1-2 x} \left(17415 x^4-116415 x^3-53772 x^2+3322 x-7018\right)}{39690 (3 x+2)^5}+\frac{43 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{3969 \sqrt{21}}","\frac{(1-2 x)^{7/2}}{105 (3 x+2)^5}-\frac{43 (1-2 x)^{5/2}}{315 (3 x+2)^4}+\frac{43 (1-2 x)^{3/2}}{567 (3 x+2)^3}+\frac{43 \sqrt{1-2 x}}{7938 (3 x+2)}-\frac{43 \sqrt{1-2 x}}{1134 (3 x+2)^2}+\frac{43 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{3969 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-7018 + 3322*x - 53772*x^2 - 116415*x^3 + 17415*x^4))/(39690*(2 + 3*x)^5) + (43*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(3969*Sqrt[21])","A",1
1941,1,73,148,0.1208231,"\int \frac{(1-2 x)^{5/2} (3+5 x)}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^7,x]","\frac{\sqrt{1-2 x} \left(49815 x^5+204795 x^4-824526 x^3-176850 x^2+154312 x-51904\right)}{444528 (3 x+2)^6}+\frac{205 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{222264 \sqrt{21}}","\frac{(1-2 x)^{7/2}}{126 (3 x+2)^6}-\frac{41 (1-2 x)^{5/2}}{378 (3 x+2)^5}+\frac{205 (1-2 x)^{3/2}}{4536 (3 x+2)^4}+\frac{205 \sqrt{1-2 x}}{444528 (3 x+2)}+\frac{205 \sqrt{1-2 x}}{190512 (3 x+2)^2}-\frac{205 \sqrt{1-2 x}}{13608 (3 x+2)^3}+\frac{205 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{222264 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-51904 + 154312*x - 176850*x^2 - 824526*x^3 + 204795*x^4 + 49815*x^5))/(444528*(2 + 3*x)^6) + (205*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(222264*Sqrt[21])","A",1
1942,1,58,92,0.0162213,"\int (1-2 x)^{5/2} (2+3 x)^4 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^4*(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(1772199000 x^9+5625863100 x^8+5641824474 x^7-121581999 x^6-3896813214 x^5-2072749175 x^4+461747860 x^3+739308228 x^2+160311352 x-138993368\right)}{2078505}","-\frac{2025 (1-2 x)^{19/2}}{1216}+\frac{13905}{544} (1-2 x)^{17/2}-\frac{53037}{320} (1-2 x)^{15/2}+\frac{121359}{208} (1-2 x)^{13/2}-\frac{832951}{704} (1-2 x)^{11/2}+\frac{381073}{288} (1-2 x)^{9/2}-\frac{41503}{64} (1-2 x)^{7/2}",1,"(Sqrt[1 - 2*x]*(-138993368 + 160311352*x + 739308228*x^2 + 461747860*x^3 - 2072749175*x^4 - 3896813214*x^5 - 121581999*x^6 + 5641824474*x^7 + 5625863100*x^8 + 1772199000*x^9))/2078505","A",1
1943,1,53,79,0.013547,"\int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(6949800 x^8+17096508 x^7+9599634 x^6-8175663 x^5-10040957 x^4-608627 x^3+2934177 x^2+993442 x-581846\right)}{21879}","\frac{675}{544} (1-2 x)^{17/2}-\frac{513}{32} (1-2 x)^{15/2}+\frac{17541}{208} (1-2 x)^{13/2}-\frac{39977}{176} (1-2 x)^{11/2}+\frac{91091}{288} (1-2 x)^{9/2}-\frac{5929}{32} (1-2 x)^{7/2}",1,"(Sqrt[1 - 2*x]*(-581846 + 993442*x + 2934177*x^2 - 608627*x^3 - 10040957*x^4 - 8175663*x^5 + 9599634*x^6 + 17096508*x^7 + 6949800*x^8))/21879","A",1
1944,1,48,66,0.0133843,"\int (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(154440 x^7+267300 x^6+9846 x^5-205169 x^4-75320 x^3+56481 x^2+32506 x-13826\right)}{1287}","-\frac{15}{16} (1-2 x)^{15/2}+\frac{255}{26} (1-2 x)^{13/2}-\frac{3467}{88} (1-2 x)^{11/2}+\frac{1309}{18} (1-2 x)^{9/2}-\frac{847}{16} (1-2 x)^{7/2}",1,"(Sqrt[1 - 2*x]*(-13826 + 32506*x + 56481*x^2 - 75320*x^3 - 205169*x^4 + 9846*x^5 + 267300*x^6 + 154440*x^7))/1287","A",1
1945,1,43,53,0.0108671,"\int (1-2 x)^{5/2} (2+3 x) (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(59400 x^6+58140 x^5-44062 x^4-49999 x^3+12729 x^2+17495 x-5671\right)}{1287}","\frac{75}{104} (1-2 x)^{13/2}-\frac{505}{88} (1-2 x)^{11/2}+\frac{1133}{72} (1-2 x)^{9/2}-\frac{121}{8} (1-2 x)^{7/2}",1,"(Sqrt[1 - 2*x]*(-5671 + 17495*x + 12729*x^2 - 49999*x^3 - 44062*x^4 + 58140*x^5 + 59400*x^6))/1287","A",1
1946,1,38,40,0.0095636,"\int (1-2 x)^{5/2} (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(3 + 5*x)^2,x]","\frac{1}{693} \sqrt{1-2 x} \left(12600 x^5+2380 x^4-12302 x^3-867 x^2+4966 x-1271\right)","-\frac{25}{44} (1-2 x)^{11/2}+\frac{55}{18} (1-2 x)^{9/2}-\frac{121}{28} (1-2 x)^{7/2}",1,"(Sqrt[1 - 2*x]*(-1271 + 4966*x - 867*x^2 - 12302*x^3 + 2380*x^4 + 12600*x^5))/693","A",1
1947,1,63,95,0.0657081,"\int \frac{(1-2 x)^{5/2} (3+5 x)^2}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x),x]","\frac{\sqrt{1-2 x} \left(63000 x^4-42300 x^3-30546 x^2+29791 x-2479\right)}{8505}-\frac{98}{243} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","\frac{25}{54} (1-2 x)^{9/2}-\frac{155}{126} (1-2 x)^{7/2}+\frac{2}{135} (1-2 x)^{5/2}+\frac{14}{243} (1-2 x)^{3/2}+\frac{98}{243} \sqrt{1-2 x}-\frac{98}{243} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-2479 + 29791*x - 30546*x^2 - 42300*x^3 + 63000*x^4))/8505 - (98*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/243","A",1
1948,1,70,102,0.1228198,"\int \frac{(1-2 x)^{5/2} (3+5 x)^2}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^2,x]","\frac{\sqrt{1-2 x} \left(5400 x^4-5508 x^3+1002 x^2-4471 x-6239\right)}{567 (3 x+2)}+\frac{350}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","-\frac{(1-2 x)^{7/2}}{63 (3 x+2)}-\frac{25}{63} (1-2 x)^{7/2}-\frac{10}{63} (1-2 x)^{5/2}-\frac{50}{81} (1-2 x)^{3/2}-\frac{350}{81} \sqrt{1-2 x}+\frac{350}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-6239 - 4471*x + 1002*x^2 - 5508*x^3 + 5400*x^4))/(567*(2 + 3*x)) + (350*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/81","A",1
1949,1,70,109,0.1155195,"\int \frac{(1-2 x)^{5/2} (3+5 x)^2}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^3,x]","\frac{\sqrt{1-2 x} \left(2160 x^4-3960 x^3+12828 x^2+25987 x+10007\right)}{162 (3 x+2)^2}-\frac{1055}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","\frac{143 (1-2 x)^{7/2}}{882 (3 x+2)}-\frac{(1-2 x)^{7/2}}{126 (3 x+2)^2}+\frac{211}{441} (1-2 x)^{5/2}+\frac{1055}{567} (1-2 x)^{3/2}+\frac{1055}{81} \sqrt{1-2 x}-\frac{1055}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(10007 + 25987*x + 12828*x^2 - 3960*x^3 + 2160*x^4))/(162*(2 + 3*x)^2) - (1055*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/81","A",1
1950,1,68,114,0.122883,"\int \frac{(1-2 x)^{5/2} (3+5 x)^2}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^4,x]","\frac{\sqrt{1-2 x} \left(3600 x^4-21240 x^3-61353 x^2-48697 x-12212\right)}{162 (3 x+2)^3}+\frac{4435 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{81 \sqrt{21}}","\frac{211 (1-2 x)^{7/2}}{2646 (3 x+2)^2}-\frac{(1-2 x)^{7/2}}{189 (3 x+2)^3}-\frac{887 (1-2 x)^{5/2}}{882 (3 x+2)}-\frac{4435 (1-2 x)^{3/2}}{3969}-\frac{4435}{567} \sqrt{1-2 x}+\frac{4435 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{81 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-12212 - 48697*x - 61353*x^2 - 21240*x^3 + 3600*x^4))/(162*(2 + 3*x)^3) + (4435*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(81*Sqrt[21])","A",1
1951,1,68,121,0.1145092,"\int \frac{(1-2 x)^{5/2} (3+5 x)^2}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^5,x]","\frac{\sqrt{1-2 x} \left(302400 x^4+1231065 x^3+1526937 x^2+762598 x+134558\right)}{4536 (3 x+2)^4}-\frac{24965 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{2268 \sqrt{21}}","\frac{31 (1-2 x)^{7/2}}{588 (3 x+2)^3}-\frac{(1-2 x)^{7/2}}{252 (3 x+2)^4}-\frac{4993 (1-2 x)^{5/2}}{10584 (3 x+2)^2}+\frac{24965 (1-2 x)^{3/2}}{31752 (3 x+2)}+\frac{24965 \sqrt{1-2 x}}{15876}-\frac{24965 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{2268 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(134558 + 762598*x + 1526937*x^2 + 1231065*x^3 + 302400*x^4))/(4536*(2 + 3*x)^4) - (24965*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(2268*Sqrt[21])","A",1
1952,1,68,128,0.1205385,"\int \frac{(1-2 x)^{5/2} (3+5 x)^2}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^6,x]","\frac{\sqrt{1-2 x} \left(-7323345 x^4-12406455 x^3-8277204 x^2-2919346 x-503276\right)}{158760 (3 x+2)^5}+\frac{8051 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{15876 \sqrt{21}}","\frac{347 (1-2 x)^{7/2}}{8820 (3 x+2)^4}-\frac{(1-2 x)^{7/2}}{315 (3 x+2)^5}-\frac{8051 (1-2 x)^{5/2}}{26460 (3 x+2)^3}+\frac{8051 (1-2 x)^{3/2}}{31752 (3 x+2)^2}-\frac{8051 \sqrt{1-2 x}}{31752 (3 x+2)}+\frac{8051 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{15876 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-503276 - 2919346*x - 8277204*x^2 - 12406455*x^3 - 7323345*x^4))/(158760*(2 + 3*x)^5) + (8051*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(15876*Sqrt[21])","A",1
1953,1,73,148,0.1425241,"\int \frac{(1-2 x)^{5/2} (3+5 x)^2}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^7,x]","\frac{\sqrt{1-2 x} \left(319545 x^5-1979115 x^4-2360850 x^3-587502 x^2-106808 x-81568\right)}{148176 (3 x+2)^6}+\frac{1315 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{74088 \sqrt{21}}","\frac{83 (1-2 x)^{7/2}}{2646 (3 x+2)^5}-\frac{(1-2 x)^{7/2}}{378 (3 x+2)^6}-\frac{263 (1-2 x)^{5/2}}{1176 (3 x+2)^4}+\frac{1315 (1-2 x)^{3/2}}{10584 (3 x+2)^3}+\frac{1315 \sqrt{1-2 x}}{148176 (3 x+2)}-\frac{1315 \sqrt{1-2 x}}{21168 (3 x+2)^2}+\frac{1315 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{74088 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-81568 - 106808*x - 587502*x^2 - 2360850*x^3 - 1979115*x^4 + 319545*x^5))/(148176*(2 + 3*x)^6) + (1315*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(74088*Sqrt[21])","A",1
1954,1,78,168,0.1483764,"\int \frac{(1-2 x)^{5/2} (3+5 x)^2}{(2+3 x)^8} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^8,x]","\frac{\sqrt{1-2 x} \left(1702215 x^6+8132805 x^5-24492348 x^4-23950566 x^3+1405308 x^2+1415408 x-1107536\right)}{3111696 (3 x+2)^7}+\frac{2335 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1555848 \sqrt{21}}","\frac{23 (1-2 x)^{7/2}}{882 (3 x+2)^6}-\frac{(1-2 x)^{7/2}}{441 (3 x+2)^7}-\frac{467 (1-2 x)^{5/2}}{2646 (3 x+2)^5}+\frac{2335 (1-2 x)^{3/2}}{31752 (3 x+2)^4}+\frac{2335 \sqrt{1-2 x}}{3111696 (3 x+2)}+\frac{2335 \sqrt{1-2 x}}{1333584 (3 x+2)^2}-\frac{2335 \sqrt{1-2 x}}{95256 (3 x+2)^3}+\frac{2335 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1555848 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-1107536 + 1415408*x + 1405308*x^2 - 23950566*x^3 - 24492348*x^4 + 8132805*x^5 + 1702215*x^6))/(3111696*(2 + 3*x)^7) + (2335*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(1555848*Sqrt[21])","A",1
1955,1,63,105,0.0189299,"\int (1-2 x)^{5/2} (2+3 x)^4 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^4*(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(1700595000 x^{10}+6471211500 x^9+8880844050 x^8+3513142893 x^7-3556515018 x^6-4297543173 x^5-970928350 x^4+842946920 x^3+588303696 x^2+74758064 x-115708576\right)}{440895}","\frac{3375}{896} (1-2 x)^{21/2}-\frac{161325 (1-2 x)^{19/2}}{2432}+\frac{1101465 (1-2 x)^{17/2}}{2176}-\frac{1392467}{640} (1-2 x)^{15/2}+\frac{9504551 (1-2 x)^{13/2}}{1664}-\frac{1179381}{128} (1-2 x)^{11/2}+\frac{3278737}{384} (1-2 x)^{9/2}-\frac{456533}{128} (1-2 x)^{7/2}",1,"(Sqrt[1 - 2*x]*(-115708576 + 74758064*x + 588303696*x^2 + 842946920*x^3 - 970928350*x^4 - 4297543173*x^5 - 3556515018*x^6 + 3513142893*x^7 + 8880844050*x^8 + 6471211500*x^9 + 1700595000*x^10))/440895","A",1
1956,1,58,92,0.0165884,"\int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^3,x]","\frac{1}{741} \sqrt{1-2 x} \left(1053000 x^9+3264300 x^8+3159234 x^7-180615 x^6-2223099 x^5-1118224 x^4+281231 x^3+406155 x^2+84038 x-76018\right)","-\frac{3375 (1-2 x)^{19/2}}{1216}+\frac{675}{16} (1-2 x)^{17/2}-\frac{17337}{64} (1-2 x)^{15/2}+\frac{98209}{104} (1-2 x)^{13/2}-\frac{121359}{64} (1-2 x)^{11/2}+\frac{100793}{48} (1-2 x)^{9/2}-\frac{65219}{64} (1-2 x)^{7/2}",1,"(Sqrt[1 - 2*x]*(-76018 + 84038*x + 406155*x^2 + 281231*x^3 - 1118224*x^4 - 2223099*x^5 - 180615*x^6 + 3159234*x^7 + 3264300*x^8 + 1053000*x^9))/741","A",1
1957,1,53,79,0.0143752,"\int (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^3,x]","\frac{1}{221} \sqrt{1-2 x} \left(117000 x^8+278980 x^7+146310 x^6-138201 x^5-157296 x^4-5935 x^3+46164 x^2+14864 x-9004\right)","\frac{1125}{544} (1-2 x)^{17/2}-\frac{845}{32} (1-2 x)^{15/2}+\frac{28555}{208} (1-2 x)^{13/2}-\frac{5847}{16} (1-2 x)^{11/2}+\frac{16093}{32} (1-2 x)^{9/2}-\frac{9317}{32} (1-2 x)^{7/2}",1,"(Sqrt[1 - 2*x]*(-9004 + 14864*x + 46164*x^2 - 5935*x^3 - 157296*x^4 - 138201*x^5 + 146310*x^6 + 278980*x^7 + 117000*x^8))/221","A",1
1958,1,48,66,0.0126736,"\int (1-2 x)^{5/2} (2+3 x) (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^3,x]","\frac{1}{39} \sqrt{1-2 x} \left(7800 x^7+12900 x^6-90 x^5-9917 x^4-3299 x^3+2724 x^2+1465 x-641\right)","-\frac{25}{16} (1-2 x)^{15/2}+\frac{1675}{104} (1-2 x)^{13/2}-\frac{255}{4} (1-2 x)^{11/2}+\frac{2783}{24} (1-2 x)^{9/2}-\frac{1331}{16} (1-2 x)^{7/2}",1,"(Sqrt[1 - 2*x]*(-641 + 1465*x + 2724*x^2 - 3299*x^3 - 9917*x^4 - 90*x^5 + 12900*x^6 + 7800*x^7))/39","A",1
1959,1,43,53,0.0109113,"\int (1-2 x)^{5/2} (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(3 + 5*x)^3,x]","\frac{1}{273} \sqrt{1-2 x} \left(21000 x^6+18900 x^5-15890 x^4-16061 x^3+4614 x^2+5533 x-1838\right)","\frac{125}{104} (1-2 x)^{13/2}-\frac{75}{8} (1-2 x)^{11/2}+\frac{605}{24} (1-2 x)^{9/2}-\frac{1331}{56} (1-2 x)^{7/2}",1,"(Sqrt[1 - 2*x]*(-1838 + 5533*x + 4614*x^2 - 16061*x^3 - 15890*x^4 + 18900*x^5 + 21000*x^6))/273","A",1
1960,1,68,108,0.0628622,"\int \frac{(1-2 x)^{5/2} (3+5 x)^3}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x),x]","\frac{\sqrt{1-2 x} \left(8505000 x^5+913500 x^4-7838550 x^3-249219 x^2+3024349 x-830656\right)}{280665}+\frac{98}{729} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","-\frac{125}{132} (1-2 x)^{11/2}+\frac{400}{81} (1-2 x)^{9/2}-\frac{5135}{756} (1-2 x)^{7/2}-\frac{2}{405} (1-2 x)^{5/2}-\frac{14}{729} (1-2 x)^{3/2}-\frac{98}{729} \sqrt{1-2 x}+\frac{98}{729} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-830656 + 3024349*x - 249219*x^2 - 7838550*x^3 + 913500*x^4 + 8505000*x^5))/280665 + (98*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/729","A",1
1961,1,75,121,0.1077745,"\int \frac{(1-2 x)^{5/2} (3+5 x)^3}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^2,x]","\frac{\sqrt{1-2 x} \left(189000 x^5-17100 x^4-159714 x^3+25275 x^2+65558 x+13759\right)}{5103 (3 x+2)}-\frac{1540}{729} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","-\frac{(1-2 x)^{5/2} (5 x+3)^3}{3 (3 x+2)}+\frac{55}{81} (1-2 x)^{5/2} (5 x+3)^2+\frac{220}{729} (1-2 x)^{3/2}-\frac{22}{567} (1-2 x)^{5/2} (100 x+69)+\frac{1540}{729} \sqrt{1-2 x}-\frac{1540}{729} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(13759 + 65558*x + 25275*x^2 - 159714*x^3 - 17100*x^4 + 189000*x^5))/(5103*(2 + 3*x)) - (1540*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/729","A",1
1962,1,75,135,0.1435221,"\int \frac{(1-2 x)^{5/2} (3+5 x)^3}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^3,x]","\frac{\sqrt{1-2 x} \left(54000 x^5-24120 x^4-17460 x^3-67962 x^2-152833 x-64943\right)}{1134 (3 x+2)^2}+\frac{935}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","\frac{55 (1-2 x)^{3/2} (5 x+3)^3}{9 (3 x+2)}-\frac{(1-2 x)^{5/2} (5 x+3)^3}{6 (3 x+2)^2}-\frac{220}{21} (1-2 x)^{3/2} (5 x+3)^2+\frac{55 (1-2 x)^{3/2} (603 x+209)}{1134}-\frac{935}{81} \sqrt{1-2 x}+\frac{935}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-64943 - 152833*x - 67962*x^2 - 17460*x^3 - 24120*x^4 + 54000*x^5))/(1134*(2 + 3*x)^2) + (935*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/81","A",1
1963,1,73,147,0.1052336,"\int \frac{(1-2 x)^{5/2} (3+5 x)^3}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^4,x]","\frac{\sqrt{1-2 x} \left(16200 x^5-20700 x^4+87030 x^3+289719 x^2+229336 x+56141\right)}{243 (3 x+2)^3}-\frac{41360 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{243 \sqrt{21}}","-\frac{275 \sqrt{1-2 x} (5 x+3)^3}{9 (3 x+2)}+\frac{55 (1-2 x)^{3/2} (5 x+3)^3}{27 (3 x+2)^2}-\frac{(1-2 x)^{5/2} (5 x+3)^3}{9 (3 x+2)^3}+\frac{1441}{27} \sqrt{1-2 x} (5 x+3)^2-\frac{22}{243} \sqrt{1-2 x} (1885 x+578)-\frac{41360 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{243 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(56141 + 229336*x + 289719*x^2 + 87030*x^3 - 20700*x^4 + 16200*x^5))/(243*(2 + 3*x)^3) - (41360*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(243*Sqrt[21])","A",1
1964,1,73,154,0.127247,"\int \frac{(1-2 x)^{5/2} (3+5 x)^3}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^5,x]","\frac{\sqrt{1-2 x} \left(1512000 x^5-8215200 x^4-32946525 x^3-39158517 x^2-19526798 x-3553918\right)}{13608 (3 x+2)^4}+\frac{645865 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{6804 \sqrt{21}}","-\frac{55 \sqrt{1-2 x} (5 x+3)^3}{24 (3 x+2)^2}+\frac{55 (1-2 x)^{3/2} (5 x+3)^3}{54 (3 x+2)^3}-\frac{(1-2 x)^{5/2} (5 x+3)^3}{12 (3 x+2)^4}-\frac{2255 \sqrt{1-2 x} (5 x+3)^2}{378 (3 x+2)}+\frac{275 \sqrt{1-2 x} (4595 x+1123)}{13608}+\frac{645865 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{6804 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-3553918 - 19526798*x - 39158517*x^2 - 32946525*x^3 - 8215200*x^4 + 1512000*x^5))/(13608*(2 + 3*x)^4) + (645865*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(6804*Sqrt[21])","A",1
1965,1,73,161,0.1445113,"\int \frac{(1-2 x)^{5/2} (3+5 x)^3}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^6,x]","\frac{\sqrt{1-2 x} \left(26460000 x^5+126578745 x^4+207486855 x^3+157178184 x^2+56745266 x+7933096\right)}{79380 (3 x+2)^5}-\frac{146971 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{7938 \sqrt{21}}","\frac{11 \sqrt{1-2 x} (5 x+3)^3}{9 (3 x+2)^3}+\frac{11 (1-2 x)^{3/2} (5 x+3)^3}{18 (3 x+2)^4}-\frac{(1-2 x)^{5/2} (5 x+3)^3}{15 (3 x+2)^5}-\frac{209 \sqrt{1-2 x} (5 x+3)^2}{756 (3 x+2)^2}-\frac{11 \sqrt{1-2 x} (6475 x+3911)}{15876 (3 x+2)}-\frac{146971 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{7938 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(7933096 + 56745266*x + 157178184*x^2 + 207486855*x^3 + 126578745*x^4 + 26460000*x^5))/(79380*(2 + 3*x)^5) - (146971*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(7938*Sqrt[21])","A",1
1966,1,73,162,0.144288,"\int \frac{(1-2 x)^{5/2} (3+5 x)^3}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^7,x]","\frac{\sqrt{1-2 x} \left(-308539125 x^5-720187425 x^4-687940758 x^3-352611738 x^2-102558856 x-13847024\right)}{1333584 (3 x+2)^6}+\frac{559625 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{666792 \sqrt{21}}","\frac{11 (1-2 x)^{3/2} (5 x+3)^3}{27 (3 x+2)^5}-\frac{(1-2 x)^{5/2} (5 x+3)^3}{18 (3 x+2)^6}+\frac{559625 \sqrt{1-2 x}}{1333584 (3 x+2)}-\frac{559625 \sqrt{1-2 x}}{190512 (3 x+2)^2}+\frac{33275 (1-2 x)^{3/2}}{95256 (3 x+2)^3}-\frac{121 (1-2 x)^{3/2}}{4536 (3 x+2)^4}+\frac{559625 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{666792 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-13847024 - 102558856*x - 352611738*x^2 - 687940758*x^3 - 720187425*x^4 - 308539125*x^5))/(1333584*(2 + 3*x)^6) + (559625*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(666792*Sqrt[21])","A",1
1967,1,78,181,0.1618913,"\int \frac{(1-2 x)^{5/2} (3+5 x)^3}{(2+3 x)^8} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^8,x]","\frac{\sqrt{1-2 x} \left(24738615 x^6-141112395 x^5-283697388 x^4-164222766 x^3-39606312 x^2-12384752 x-4005436\right)}{2333772 (3 x+2)^7}+\frac{33935 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1166886 \sqrt{21}}","\frac{11 \sqrt{1-2 x} (5 x+3)^3}{7 (3 x+2)^5}+\frac{55 (1-2 x)^{3/2} (5 x+3)^3}{189 (3 x+2)^6}-\frac{(1-2 x)^{5/2} (5 x+3)^3}{21 (3 x+2)^7}-\frac{3223 \sqrt{1-2 x} (5 x+3)^2}{2646 (3 x+2)^4}-\frac{11 \sqrt{1-2 x} (301765 x+187704)}{333396 (3 x+2)^3}+\frac{33935 \sqrt{1-2 x}}{2333772 (3 x+2)}+\frac{33935 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1166886 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-4005436 - 12384752*x - 39606312*x^2 - 164222766*x^3 - 283697388*x^4 - 141112395*x^5 + 24738615*x^6))/(2333772*(2 + 3*x)^7) + (33935*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(1166886*Sqrt[21])","A",1
1968,1,73,121,0.07219,"\int \frac{(1-2 x)^{5/2} (2+3 x)^4}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^4)/(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(2338875000 x^6+2842087500 x^5-1540428750 x^4-2556079875 x^3+399578370 x^2+960784285 x-289133384\right)}{234609375}-\frac{242 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{78125}","\frac{81}{520} (1-2 x)^{13/2}-\frac{2889 (1-2 x)^{11/2}}{2200}+\frac{3819 (1-2 x)^{9/2}}{1000}-\frac{136419 (1-2 x)^{7/2}}{35000}+\frac{2 (1-2 x)^{5/2}}{15625}+\frac{22 (1-2 x)^{3/2}}{46875}+\frac{242 \sqrt{1-2 x}}{78125}-\frac{242 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{78125}",1,"(Sqrt[1 - 2*x]*(-289133384 + 960784285*x + 399578370*x^2 - 2556079875*x^3 - 1540428750*x^4 + 2842087500*x^5 + 2338875000*x^6))/234609375 - (242*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/78125","A",1
1969,1,68,108,0.0655094,"\int \frac{(1-2 x)^{5/2} (2+3 x)^3}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(14175000 x^5+6142500 x^4-15572250 x^3-3564885 x^2+7726195 x-1796318\right)}{3609375}-\frac{242 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15625}","-\frac{27}{220} (1-2 x)^{11/2}+\frac{18}{25} (1-2 x)^{9/2}-\frac{3897 (1-2 x)^{7/2}}{3500}+\frac{2 (1-2 x)^{5/2}}{3125}+\frac{22 (1-2 x)^{3/2}}{9375}+\frac{242 \sqrt{1-2 x}}{15625}-\frac{242 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15625}",1,"(Sqrt[1 - 2*x]*(-1796318 + 7726195*x - 3564885*x^2 - 15572250*x^3 + 6142500*x^4 + 14175000*x^5))/3609375 - (242*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/15625","A",1
1970,1,63,95,0.0610834,"\int \frac{(1-2 x)^{5/2} (2+3 x)^2}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^2)/(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(105000 x^4-43500 x^3-91410 x^2+69995 x-8188\right)}{65625}-\frac{242 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125}","\frac{1}{10} (1-2 x)^{9/2}-\frac{111}{350} (1-2 x)^{7/2}+\frac{2}{625} (1-2 x)^{5/2}+\frac{22 (1-2 x)^{3/2}}{1875}+\frac{242 \sqrt{1-2 x}}{3125}-\frac{242 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125}",1,"(Sqrt[1 - 2*x]*(-8188 + 69995*x - 91410*x^2 - 43500*x^3 + 105000*x^4))/65625 - (242*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/3125","A",1
1971,1,58,82,0.0564608,"\int \frac{(1-2 x)^{5/2} (2+3 x)}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x))/(3 + 5*x),x]","\frac{\sqrt{1-2 x} \left(9000 x^3-12660 x^2+4370 x+4937\right)}{13125}-\frac{242}{625} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{3}{35} (1-2 x)^{7/2}+\frac{2}{125} (1-2 x)^{5/2}+\frac{22}{375} (1-2 x)^{3/2}+\frac{242}{625} \sqrt{1-2 x}-\frac{242}{625} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(4937 + 4370*x - 12660*x^2 + 9000*x^3))/13125 - (242*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/625","A",1
1972,1,53,69,0.0504766,"\int \frac{(1-2 x)^{5/2}}{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/(3 + 5*x),x]","\frac{2}{375} \sqrt{1-2 x} \left(60 x^2-170 x+433\right)-\frac{242}{125} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{2}{25} (1-2 x)^{5/2}+\frac{22}{75} (1-2 x)^{3/2}+\frac{242}{125} \sqrt{1-2 x}-\frac{242}{125} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(2*Sqrt[1 - 2*x]*(433 - 170*x + 60*x^2))/375 - (242*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/125","A",1
1973,1,77,85,0.0827582,"\int \frac{(1-2 x)^{5/2}}{(2+3 x) (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)*(3 + 5*x)),x]","\frac{4}{225} \sqrt{1-2 x} (10 x-73)+\frac{98}{9} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{242}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{4}{45} (1-2 x)^{3/2}-\frac{272}{225} \sqrt{1-2 x}+\frac{98}{9} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{242}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(4*Sqrt[1 - 2*x]*(-73 + 10*x))/225 + (98*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/9 - (242*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/25","A",1
1974,1,84,92,0.1354964,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^2*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} (8 x+87)}{15 (3 x+2)}+\frac{140}{3} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{242}{5} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{7 (1-2 x)^{3/2}}{3 (3 x+2)}+\frac{26}{15} \sqrt{1-2 x}+\frac{140}{3} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{242}{5} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(87 + 8*x))/(15*(2 + 3*x)) + (140*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/3 - (242*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/5","A",1
1975,1,80,95,0.1296851,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^3*(3 + 5*x)),x]","\frac{7 \sqrt{1-2 x} (61 x+43)}{6 (3 x+2)^2}+235 \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-242 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{7 (1-2 x)^{3/2}}{6 (3 x+2)^2}+\frac{49 \sqrt{1-2 x}}{2 (3 x+2)}+235 \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-242 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(7*Sqrt[1 - 2*x]*(43 + 61*x))/(6*(2 + 3*x)^2) + 235*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - 242*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1976,1,83,113,0.1319467,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^4 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^4*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(9657 x^2+13198 x+4523\right)}{9 (3 x+2)^3}+\frac{74020 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{9 \sqrt{21}}-242 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{7 (1-2 x)^{3/2}}{9 (3 x+2)^3}+\frac{1073 \sqrt{1-2 x}}{9 (3 x+2)}+\frac{112 \sqrt{1-2 x}}{9 (3 x+2)^2}+\frac{74020 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{9 \sqrt{21}}-242 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(4523 + 13198*x + 9657*x^2))/(9*(2 + 3*x)^3) + (74020*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(9*Sqrt[21]) - 242*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1977,1,88,133,0.1595677,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^5 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^5*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(2703915 x^3+5498403 x^2+3730002 x+844322\right)}{168 (3 x+2)^4}+\frac{3454265 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{84 \sqrt{21}}-1210 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{7 (1-2 x)^{3/2}}{12 (3 x+2)^4}+\frac{100145 \sqrt{1-2 x}}{168 (3 x+2)}+\frac{4313 \sqrt{1-2 x}}{72 (3 x+2)^2}+\frac{301 \sqrt{1-2 x}}{36 (3 x+2)^3}+\frac{3454265 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{84 \sqrt{21}}-1210 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(844322 + 3730002*x + 5498403*x^2 + 2703915*x^3))/(168*(2 + 3*x)^4) + (3454265*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(84*Sqrt[21]) - 1210*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1978,1,93,153,0.1781878,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^6 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^6*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(709777485 x^4+1916515215 x^3+1941349752 x^2+874383298 x+147756688\right)}{2940 (3 x+2)^5}+\frac{20149879 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{98 \sqrt{21}}-6050 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{7 (1-2 x)^{3/2}}{15 (3 x+2)^5}+\frac{584179 \sqrt{1-2 x}}{196 (3 x+2)}+\frac{25159 \sqrt{1-2 x}}{84 (3 x+2)^2}+\frac{1201 \sqrt{1-2 x}}{30 (3 x+2)^3}+\frac{63 \sqrt{1-2 x}}{10 (3 x+2)^4}+\frac{20149879 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{98 \sqrt{21}}-6050 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(147756688 + 874383298*x + 1941349752*x^2 + 1916515215*x^3 + 709777485*x^4))/(2940*(2 + 3*x)^5) + (20149879*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(98*Sqrt[21]) - 6050*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1979,1,98,173,0.2266534,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^7 (3+5 x)} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^7*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(178863925005 x^5+602204446665 x^4+811194684822 x^3+546491397114 x^2+184131053992 x+24823128464\right)}{49392 (3 x+2)^6}+\frac{25388847535 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{24696 \sqrt{21}}-30250 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{7 (1-2 x)^{3/2}}{18 (3 x+2)^6}+\frac{736065535 \sqrt{1-2 x}}{49392 (3 x+2)}+\frac{31700335 \sqrt{1-2 x}}{21168 (3 x+2)^2}+\frac{302651 \sqrt{1-2 x}}{1512 (3 x+2)^3}+\frac{2165 \sqrt{1-2 x}}{72 (3 x+2)^4}+\frac{91 \sqrt{1-2 x}}{18 (3 x+2)^5}+\frac{25388847535 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{24696 \sqrt{21}}-30250 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(24823128464 + 184131053992*x + 546491397114*x^2 + 811194684822*x^3 + 602204446665*x^4 + 178863925005*x^5))/(49392*(2 + 3*x)^6) + (25388847535*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(24696*Sqrt[21]) - 30250*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1980,1,80,141,0.1353618,"\int \frac{(1-2 x)^{5/2} (2+3 x)^4}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^4)/(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(212625000 x^6+237037500 x^5-173598750 x^4-214071975 x^3+85482115 x^2+50081215 x-15982128\right)}{18046875 (5 x+3)}-\frac{2794 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{78125}","-\frac{(1-2 x)^{5/2} (3 x+2)^4}{5 (5 x+3)}+\frac{39}{275} (1-2 x)^{5/2} (3 x+2)^3-\frac{32 (1-2 x)^{5/2} (3 x+2)^2}{4125}+\frac{254 (1-2 x)^{3/2}}{46875}-\frac{(1-2 x)^{5/2} (1110975 x+1347116)}{3609375}+\frac{2794 \sqrt{1-2 x}}{78125}-\frac{2794 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{78125}",1,"(Sqrt[1 - 2*x]*(-15982128 + 50081215*x + 85482115*x^2 - 214071975*x^3 - 173598750*x^4 + 237037500*x^5 + 212625000*x^6))/(18046875*(3 + 5*x)) - (2794*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/78125","A",1
1981,1,75,121,0.1107425,"\int \frac{(1-2 x)^{5/2} (2+3 x)^3}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(1575000 x^5+427500 x^4-1858950 x^3+152105 x^2+680930 x+16794\right)}{328125 (5 x+3)}-\frac{2068 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15625}","-\frac{(1-2 x)^{5/2} (3 x+2)^3}{5 (5 x+3)}+\frac{11}{75} (1-2 x)^{5/2} (3 x+2)^2+\frac{188 (1-2 x)^{3/2}}{9375}-\frac{2 (1-2 x)^{5/2} (2850 x+6191)}{65625}+\frac{2068 \sqrt{1-2 x}}{15625}-\frac{2068 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15625}",1,"(Sqrt[1 - 2*x]*(16794 + 680930*x + 152105*x^2 - 1858950*x^3 + 427500*x^4 + 1575000*x^5))/(328125*(3 + 5*x)) - (2068*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/15625","A",1
1982,1,70,102,0.1189991,"\int \frac{(1-2 x)^{5/2} (2+3 x)^2}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^2)/(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(135000 x^4-96300 x^3-75130 x^2+173795 x+90486\right)}{65625 (5 x+3)}-\frac{1342 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125}","-\frac{(1-2 x)^{7/2}}{275 (5 x+3)}-\frac{9}{175} (1-2 x)^{7/2}+\frac{122 (1-2 x)^{5/2}}{6875}+\frac{122 (1-2 x)^{3/2}}{1875}+\frac{1342 \sqrt{1-2 x}}{3125}-\frac{1342 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125}",1,"(Sqrt[1 - 2*x]*(90486 + 173795*x - 75130*x^2 - 96300*x^3 + 135000*x^4))/(65625*(3 + 5*x)) - (1342*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/3125","A",1
1983,1,65,89,0.08739,"\int \frac{(1-2 x)^{5/2} (2+3 x)}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x))/(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(1800 x^3-3820 x^2+8630 x+6579\right)}{1875 (5 x+3)}-\frac{616}{625} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{(1-2 x)^{7/2}}{55 (5 x+3)}+\frac{56 (1-2 x)^{5/2}}{1375}+\frac{56}{375} (1-2 x)^{3/2}+\frac{616}{625} \sqrt{1-2 x}-\frac{616}{625} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(6579 + 8630*x - 3820*x^2 + 1800*x^3))/(1875*(3 + 5*x)) - (616*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/625","A",1
1984,1,60,76,0.0777792,"\int \frac{(1-2 x)^{5/2}}{(3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(40 x^2-260 x-243\right)}{75 (5 x+3)}+\frac{22}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{(1-2 x)^{5/2}}{5 (5 x+3)}-\frac{2}{15} (1-2 x)^{3/2}-\frac{22}{25} \sqrt{1-2 x}+\frac{22}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-243 - 260*x + 40*x^2))/(75*(3 + 5*x)) + (22*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/25","A",1
1985,1,84,92,0.1234613,"\int \frac{(1-2 x)^{5/2}}{(2+3 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} (40 x-339)}{75 (5 x+3)}-\frac{98}{3} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{836}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{11 (1-2 x)^{3/2}}{5 (5 x+3)}-\frac{58}{75} \sqrt{1-2 x}-\frac{98}{3} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{836}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-339 + 40*x))/(75*(3 + 5*x)) - (98*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/3 + (836*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/25","A",1
1986,1,89,106,0.1264997,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} (-2314 x-1461)}{15 \left(15 x^2+19 x+6\right)}-\frac{910}{3} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{1562}{5} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{7 (1-2 x)^{3/2}}{3 (3 x+2) (5 x+3)}-\frac{748 \sqrt{1-2 x}}{15 (5 x+3)}-\frac{910}{3} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{1562}{5} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"((-1461 - 2314*x)*Sqrt[1 - 2*x])/(15*(6 + 19*x + 15*x^2)) - (910*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/3 + (1562*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/5","A",1
1987,1,94,131,0.1503437,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^3*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-20289 x^2-26380 x-8553\right)}{6 (3 x+2)^2 (5 x+3)}-\frac{6665}{3} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+2288 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{7 (1-2 x)^{3/2}}{6 (3 x+2)^2 (5 x+3)}+\frac{343 \sqrt{1-2 x}}{9 (3 x+2) (5 x+3)}-\frac{6763 \sqrt{1-2 x}}{18 (5 x+3)}-\frac{6665}{3} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+2288 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-8553 - 26380*x - 20289*x^2))/(6*(2 + 3*x)^2*(3 + 5*x)) - (6665*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/3 + 2288*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1988,1,95,154,0.1625825,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^4 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^4*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-400905 x^3-788512 x^2-516513 x-112668\right)}{6 (3 x+2)^3 (5 x+3)}-\frac{307295 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{3 \sqrt{21}}+3014 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{7 (1-2 x)^{3/2}}{9 (3 x+2)^3 (5 x+3)}+\frac{6649 \sqrt{1-2 x}}{27 (3 x+2) (5 x+3)}+\frac{917 \sqrt{1-2 x}}{54 (3 x+2)^2 (5 x+3)}-\frac{44545 \sqrt{1-2 x}}{18 (5 x+3)}-\frac{307295 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{3 \sqrt{21}}+3014 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-112668 - 516513*x - 788512*x^2 - 400905*x^3))/(6*(2 + 3*x)^3*(3 + 5*x)) - (307295*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(3*Sqrt[21]) + 3014*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1989,1,100,181,0.1864071,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^5 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^5*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-208938825 x^4-550239720 x^3-543154477 x^2-238179048 x-39145938\right)}{168 (3 x+2)^4 (5 x+3)}-\frac{53384095 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{84 \sqrt{21}}+18700 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{7 (1-2 x)^{3/2}}{12 (3 x+2)^4 (5 x+3)}+\frac{288770 \sqrt{1-2 x}}{189 (3 x+2) (5 x+3)}+\frac{22109 \sqrt{1-2 x}}{216 (3 x+2)^2 (5 x+3)}+\frac{287 \sqrt{1-2 x}}{27 (3 x+2)^3 (5 x+3)}-\frac{7738475 \sqrt{1-2 x}}{504 (5 x+3)}-\frac{53384095 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{84 \sqrt{21}}+18700 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-39145938 - 238179048*x - 543154477*x^2 - 550239720*x^3 - 208938825*x^4))/(168*(2 + 3*x)^4*(3 + 5*x)) - (53384095*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(84*Sqrt[21]) + 18700*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1990,1,105,208,0.2008435,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^6 (3+5 x)^2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^6*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-130986207675 x^5-432275892930 x^4-570477768855 x^3-376323861626 x^2-124085884254 x-16360698684\right)}{5880 (3 x+2)^5 (5 x+3)}-\frac{2231141147 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{588 \sqrt{21}}+111650 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{7 (1-2 x)^{3/2}}{15 (3 x+2)^5 (5 x+3)}+\frac{12068887 \sqrt{1-2 x}}{1323 (3 x+2) (5 x+3)}+\frac{924025 \sqrt{1-2 x}}{1512 (3 x+2)^2 (5 x+3)}+\frac{16549 \sqrt{1-2 x}}{270 (3 x+2)^3 (5 x+3)}+\frac{1379 \sqrt{1-2 x}}{180 (3 x+2)^4 (5 x+3)}-\frac{323422735 \sqrt{1-2 x}}{3528 (5 x+3)}-\frac{2231141147 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{588 \sqrt{21}}+111650 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-16360698684 - 124085884254*x - 376323861626*x^2 - 570477768855*x^3 - 432275892930*x^4 - 130986207675*x^5))/(5880*(2 + 3*x)^5*(3 + 5*x)) - (2231141147*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(588*Sqrt[21]) + 111650*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1991,1,80,155,0.135133,"\int \frac{(1-2 x)^{5/2} (2+3 x)^4}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^4)/(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(15750000 x^6+15075000 x^5-16051500 x^4-11139550 x^3+9372960 x^2+6891315 x+871208\right)}{1093750 (5 x+3)^2}-\frac{11763 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{78125}","-\frac{127 (1-2 x)^{3/2} (3 x+2)^4}{50 (5 x+3)}-\frac{(1-2 x)^{5/2} (3 x+2)^4}{10 (5 x+3)^2}+\frac{1117}{750} (1-2 x)^{3/2} (3 x+2)^3+\frac{1903 (1-2 x)^{3/2} (3 x+2)^2}{4375}+\frac{(1-2 x)^{3/2} (24939 x+734)}{93750}+\frac{11763 \sqrt{1-2 x}}{78125}-\frac{11763 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{78125}",1,"(Sqrt[1 - 2*x]*(871208 + 6891315*x + 9372960*x^2 - 11139550*x^3 - 16051500*x^4 + 15075000*x^5 + 15750000*x^6))/(1093750*(3 + 5*x)^2) - (11763*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/78125","A",1
1992,1,75,135,0.1326067,"\int \frac{(1-2 x)^{5/2} (2+3 x)^3}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(1350000 x^5-27000 x^4-1506900 x^3+1651030 x^2+2637795 x+770444\right)}{218750 (5 x+3)^2}-\frac{5559 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15625}","-\frac{47 (1-2 x)^{3/2} (3 x+2)^3}{25 (5 x+3)}-\frac{(1-2 x)^{5/2} (3 x+2)^3}{10 (5 x+3)^2}+\frac{954}{875} (1-2 x)^{3/2} (3 x+2)^2+\frac{3 (1-2 x)^{3/2} (2403 x+1618)}{6250}+\frac{5559 \sqrt{1-2 x}}{15625}-\frac{5559 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15625}",1,"(Sqrt[1 - 2*x]*(770444 + 2637795*x + 1651030*x^2 - 1506900*x^3 - 27000*x^4 + 1350000*x^5))/(218750*(3 + 5*x)^2) - (5559*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/15625","A",1
1993,1,70,109,0.0923889,"\int \frac{(1-2 x)^{5/2} (2+3 x)^2}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^2)/(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(18000 x^4-25400 x^3+51980 x^2+98595 x+32504\right)}{6250 (5 x+3)^2}-\frac{1533 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125}","-\frac{129 (1-2 x)^{7/2}}{6050 (5 x+3)}-\frac{(1-2 x)^{7/2}}{550 (5 x+3)^2}+\frac{1533 (1-2 x)^{5/2}}{75625}+\frac{511 (1-2 x)^{3/2}}{6875}+\frac{1533 \sqrt{1-2 x}}{3125}-\frac{1533 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125}",1,"(Sqrt[1 - 2*x]*(32504 + 98595*x + 51980*x^2 - 25400*x^3 + 18000*x^4))/(6250*(3 + 5*x)^2) - (1533*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/3125","A",1
1994,1,65,96,0.0855316,"\int \frac{(1-2 x)^{5/2} (2+3 x)}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x))/(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(400 x^3-2280 x^2-3795 x-1394\right)}{250 (5 x+3)^2}+\frac{63}{125} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{(1-2 x)^{7/2}}{110 (5 x+3)^2}-\frac{63 (1-2 x)^{5/2}}{550 (5 x+3)}-\frac{21}{275} (1-2 x)^{3/2}-\frac{63}{125} \sqrt{1-2 x}+\frac{63}{125} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-1394 - 3795*x - 2280*x^2 + 400*x^3))/(250*(3 + 5*x)^2) + (63*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/125","A",1
1995,1,60,83,0.0986126,"\int \frac{(1-2 x)^{5/2}}{(3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/(3 + 5*x)^3,x]","\frac{\sqrt{1-2 x} \left(80 x^2+195 x+64\right)}{50 (5 x+3)^2}-\frac{3}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{(1-2 x)^{5/2}}{10 (5 x+3)^2}+\frac{(1-2 x)^{3/2}}{10 (5 x+3)}+\frac{3}{25} \sqrt{1-2 x}-\frac{3}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(64 + 195*x + 80*x^2))/(50*(3 + 5*x)^2) - (3*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/25","A",1
1996,1,82,97,0.1259204,"\int \frac{(1-2 x)^{5/2}}{(2+3 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)*(3 + 5*x)^3),x]","\frac{11 \sqrt{1-2 x} (375 x+214)}{50 (5 x+3)^2}+98 \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{2523}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{11 (1-2 x)^{3/2}}{10 (5 x+3)^2}+\frac{803 \sqrt{1-2 x}}{50 (5 x+3)}+98 \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{2523}{25} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(11*Sqrt[1 - 2*x]*(214 + 375*x))/(50*(3 + 5*x)^2) + 98*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - (2523*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/25","A",1
1997,1,94,124,0.138676,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(35515 x^2+43806 x+13474\right)}{10 (3 x+2) (5 x+3)^2}+1400 \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{7209}{5} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{7 (1-2 x)^{3/2}}{3 (3 x+2) (5 x+3)^2}+\frac{7103 \sqrt{1-2 x}}{30 (5 x+3)}-\frac{1133 \sqrt{1-2 x}}{30 (5 x+3)^2}+1400 \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{7209}{5} \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(13474 + 43806*x + 35515*x^2))/(10*(2 + 3*x)*(3 + 5*x)^2) + 1400*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - (7209*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/5","A",1
1998,1,93,145,0.1565711,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(207990 x^3+395215 x^2+249939 x+52607\right)}{2 \left(15 x^2+19 x+6\right)^2}+4555 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-14073 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{7 (1-2 x)^{3/2}}{6 (3 x+2)^2 (5 x+3)^2}+\frac{2311 \sqrt{1-2 x}}{5 x+3}+\frac{931 \sqrt{1-2 x}}{18 (3 x+2) (5 x+3)^2}-\frac{6899 \sqrt{1-2 x}}{18 (5 x+3)^2}+4555 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-14073 \sqrt{\frac{11}{5}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(52607 + 249939*x + 395215*x^2 + 207990*x^3))/(2*(6 + 19*x + 15*x^2)^2) + 4555*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - 14073*Sqrt[11/5]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
1999,1,98,172,0.1800952,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^4 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^4*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(5124375 x^4+13153400 x^3+12649336 x^2+5401374 x+864074\right)}{2 (3 x+2)^3 (5 x+3)^2}+\frac{785570 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{\sqrt{21}}-23115 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{7 (1-2 x)^{3/2}}{9 (3 x+2)^3 (5 x+3)^2}+\frac{113875 \sqrt{1-2 x}}{6 (5 x+3)}+\frac{1256 \sqrt{1-2 x}}{3 (3 x+2) (5 x+3)^2}+\frac{581 \sqrt{1-2 x}}{27 (3 x+2)^2 (5 x+3)^2}-\frac{169975 \sqrt{1-2 x}}{54 (5 x+3)^2}+\frac{785570 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{\sqrt{21}}-23115 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(864074 + 5401374*x + 12649336*x^2 + 13153400*x^3 + 5124375*x^4))/(2*(2 + 3*x)^3*(3 + 5*x)^2) + (785570*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/Sqrt[21] - 23115*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
2000,1,105,201,0.2155074,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^5 (3+5 x)^3} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^5*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(3196931625 x^5+10337268075 x^4+13362164665 x^3+8630749831 x^2+2785562634 x+359378534\right)}{56 (3 x+2)^4 (5 x+3)^2}+\frac{163363895 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{28 \sqrt{21}}-171675 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{7 (1-2 x)^{3/2}}{12 (3 x+2)^4 (5 x+3)^2}+\frac{23680975 \sqrt{1-2 x}}{168 (5 x+3)}+\frac{522385 \sqrt{1-2 x}}{168 (3 x+2) (5 x+3)^2}+\frac{11243 \sqrt{1-2 x}}{72 (3 x+2)^2 (5 x+3)^2}+\frac{1393 \sqrt{1-2 x}}{108 (3 x+2)^3 (5 x+3)^2}-\frac{8836825 \sqrt{1-2 x}}{378 (5 x+3)^2}+\frac{163363895 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{28 \sqrt{21}}-171675 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(359378534 + 2785562634*x + 8630749831*x^2 + 13362164665*x^3 + 10337268075*x^4 + 3196931625*x^5))/(56*(2 + 3*x)^4*(3 + 5*x)^2) + (163363895*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(28*Sqrt[21]) - 171675*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
2001,1,43,92,0.0148327,"\int \frac{(2+3 x)^5 (3+5 x)}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^5*(3 + 5*x))/Sqrt[1 - 2*x],x]","\frac{1}{429} \sqrt{1-2 x} \left(-40095 x^6-208251 x^5-488925 x^4-698580 x^3-707436 x^2-597464 x-638648\right)","-\frac{1215}{832} (1-2 x)^{13/2}+\frac{1053}{44} (1-2 x)^{11/2}-\frac{10815}{64} (1-2 x)^{9/2}+\frac{5355}{8} (1-2 x)^{7/2}-\frac{103929}{64} (1-2 x)^{5/2}+\frac{60025}{24} (1-2 x)^{3/2}-\frac{184877}{64} \sqrt{1-2 x}",1,"(Sqrt[1 - 2*x]*(-638648 - 597464*x - 707436*x^2 - 698580*x^3 - 488925*x^4 - 208251*x^5 - 40095*x^6))/429","A",1
2002,1,38,79,0.0136872,"\int \frac{(2+3 x)^4 (3+5 x)}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x))/Sqrt[1 - 2*x],x]","\frac{1}{165} \sqrt{1-2 x} \left(-6075 x^5-27630 x^4-56520 x^3-71136 x^2-67664 x-75584\right)","\frac{405}{352} (1-2 x)^{11/2}-\frac{519}{32} (1-2 x)^{9/2}+\frac{1539}{16} (1-2 x)^{7/2}-\frac{24843}{80} (1-2 x)^{5/2}+\frac{57281}{96} (1-2 x)^{3/2}-\frac{26411}{32} \sqrt{1-2 x}",1,"(Sqrt[1 - 2*x]*(-75584 - 67664*x - 71136*x^2 - 56520*x^3 - 27630*x^4 - 6075*x^5))/165","A",1
2003,1,33,66,0.0114962,"\int \frac{(2+3 x)^3 (3+5 x)}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x))/Sqrt[1 - 2*x],x]","\frac{1}{105} \sqrt{1-2 x} \left(-1575 x^4-6165 x^3-10881 x^2-12434 x-14954\right)","-\frac{15}{16} (1-2 x)^{9/2}+\frac{621}{56} (1-2 x)^{7/2}-\frac{1071}{20} (1-2 x)^{5/2}+\frac{3283}{24} (1-2 x)^{3/2}-\frac{3773}{16} \sqrt{1-2 x}",1,"(Sqrt[1 - 2*x]*(-14954 - 12434*x - 10881*x^2 - 6165*x^3 - 1575*x^4))/105","A",1
2004,1,28,53,0.0102026,"\int \frac{(2+3 x)^2 (3+5 x)}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x))/Sqrt[1 - 2*x],x]","\frac{1}{105} \sqrt{1-2 x} \left(-675 x^3-2232 x^2-3448 x-4708\right)","\frac{45}{56} (1-2 x)^{7/2}-\frac{309}{40} (1-2 x)^{5/2}+\frac{707}{24} (1-2 x)^{3/2}-\frac{539}{8} \sqrt{1-2 x}",1,"(Sqrt[1 - 2*x]*(-4708 - 3448*x - 2232*x^2 - 675*x^3))/105","A",1
2005,1,23,40,0.0093439,"\int \frac{(2+3 x) (3+5 x)}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x))/Sqrt[1 - 2*x],x]","\frac{1}{3} \sqrt{1-2 x} \left(-9 x^2-25 x-43\right)","-\frac{3}{4} (1-2 x)^{5/2}+\frac{17}{3} (1-2 x)^{3/2}-\frac{77}{4} \sqrt{1-2 x}",1,"(Sqrt[1 - 2*x]*(-43 - 25*x - 9*x^2))/3","A",1
2006,1,18,27,0.007406,"\int \frac{3+5 x}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[(3 + 5*x)/Sqrt[1 - 2*x],x]","\frac{1}{3} (-5 x-14) \sqrt{1-2 x}","\frac{5}{6} (1-2 x)^{3/2}-\frac{11}{2} \sqrt{1-2 x}",1,"((-14 - 5*x)*Sqrt[1 - 2*x])/3","A",1
2007,1,41,41,0.0408622,"\int \frac{3+5 x}{\sqrt{1-2 x} (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)/(Sqrt[1 - 2*x]*(2 + 3*x)),x]","\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{3 \sqrt{21}}-\frac{5}{3} \sqrt{1-2 x}","\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{3 \sqrt{21}}-\frac{5}{3} \sqrt{1-2 x}",1,"(-5*Sqrt[1 - 2*x])/3 + (2*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(3*Sqrt[21])","A",1
2008,1,48,48,0.0664632,"\int \frac{3+5 x}{\sqrt{1-2 x} (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)/(Sqrt[1 - 2*x]*(2 + 3*x)^2),x]","\frac{\sqrt{1-2 x}}{21 (3 x+2)}-\frac{68 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{21 \sqrt{21}}","\frac{\sqrt{1-2 x}}{21 (3 x+2)}-\frac{68 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{21 \sqrt{21}}",1,"Sqrt[1 - 2*x]/(21*(2 + 3*x)) - (68*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(21*Sqrt[21])","A",1
2009,1,53,68,0.0824201,"\int \frac{3+5 x}{\sqrt{1-2 x} (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)/(Sqrt[1 - 2*x]*(2 + 3*x)^3),x]","\frac{(-201 x-127) \sqrt{1-2 x}}{294 (3 x+2)^2}-\frac{67 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{147 \sqrt{21}}","-\frac{67 \sqrt{1-2 x}}{294 (3 x+2)}+\frac{\sqrt{1-2 x}}{42 (3 x+2)^2}-\frac{67 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{147 \sqrt{21}}",1,"((-127 - 201*x)*Sqrt[1 - 2*x])/(294*(2 + 3*x)^2) - (67*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(147*Sqrt[21])","A",1
2010,1,58,88,0.0904236,"\int \frac{3+5 x}{\sqrt{1-2 x} (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)/(Sqrt[1 - 2*x]*(2 + 3*x)^4),x]","\frac{\sqrt{1-2 x} \left(-450 x^2-950 x-417\right)}{1029 (3 x+2)^3}-\frac{100 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1029 \sqrt{21}}","-\frac{50 \sqrt{1-2 x}}{1029 (3 x+2)}-\frac{50 \sqrt{1-2 x}}{441 (3 x+2)^2}+\frac{\sqrt{1-2 x}}{63 (3 x+2)^3}-\frac{100 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1029 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-417 - 950*x - 450*x^2))/(1029*(2 + 3*x)^3) - (100*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(1029*Sqrt[21])","A",1
2011,1,63,108,0.0988366,"\int \frac{3+5 x}{\sqrt{1-2 x} (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)/(Sqrt[1 - 2*x]*(2 + 3*x)^5),x]","\frac{\sqrt{1-2 x} \left(-2565 x^3-7125 x^2-7942 x-2790\right)}{8232 (3 x+2)^4}-\frac{95 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{4116 \sqrt{21}}","-\frac{95 \sqrt{1-2 x}}{8232 (3 x+2)}-\frac{95 \sqrt{1-2 x}}{3528 (3 x+2)^2}-\frac{19 \sqrt{1-2 x}}{252 (3 x+2)^3}+\frac{\sqrt{1-2 x}}{84 (3 x+2)^4}-\frac{95 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{4116 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-2790 - 7942*x - 7125*x^2 - 2565*x^3))/(8232*(2 + 3*x)^4) - (95*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(4116*Sqrt[21])","A",1
2012,1,48,105,0.0165256,"\int \frac{(2+3 x)^5 (3+5 x)^2}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^5*(3 + 5*x)^2)/Sqrt[1 - 2*x],x]","\frac{1}{429} \sqrt{1-2 x} \left(-173745 x^7-1002375 x^6-2632743 x^5-4212525 x^4-4694340 x^3-4058988 x^2-3152152 x-3275704\right)","\frac{405}{128} (1-2 x)^{15/2}-\frac{97605 (1-2 x)^{13/2}}{1664}+\frac{672003 (1-2 x)^{11/2}}{1408}-\frac{285565}{128} (1-2 x)^{9/2}+\frac{842415}{128} (1-2 x)^{7/2}-\frac{1623419}{128} (1-2 x)^{5/2}+\frac{6206585}{384} (1-2 x)^{3/2}-\frac{2033647}{128} \sqrt{1-2 x}",1,"(Sqrt[1 - 2*x]*(-3275704 - 3152152*x - 4058988*x^2 - 4694340*x^3 - 4212525*x^4 - 2632743*x^5 - 1002375*x^6 - 173745*x^7))/429","A",1
2013,1,43,92,0.0149395,"\int \frac{(2+3 x)^4 (3+5 x)^2}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^2)/Sqrt[1 - 2*x],x]","\frac{\sqrt{1-2 x} \left(-334125 x^6-1709100 x^5-3954645 x^4-5576580 x^3-5587044 x^2-4685656 x-4994536\right)}{2145}","-\frac{2025}{832} (1-2 x)^{13/2}+\frac{13905}{352} (1-2 x)^{11/2}-\frac{17679}{64} (1-2 x)^{9/2}+\frac{17337}{16} (1-2 x)^{7/2}-\frac{832951}{320} (1-2 x)^{5/2}+\frac{381073}{96} (1-2 x)^{3/2}-\frac{290521}{64} \sqrt{1-2 x}",1,"(Sqrt[1 - 2*x]*(-4994536 - 4685656*x - 5587044*x^2 - 5576580*x^3 - 3954645*x^4 - 1709100*x^5 - 334125*x^6))/2145","A",1
2014,1,38,79,0.0139293,"\int \frac{(2+3 x)^3 (3+5 x)^2}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^2)/Sqrt[1 - 2*x],x]","\frac{\sqrt{1-2 x} \left(-70875 x^5-316575 x^4-636795 x^3-790023 x^2-743822 x-826982\right)}{1155}","\frac{675}{352} (1-2 x)^{11/2}-\frac{855}{32} (1-2 x)^{9/2}+\frac{17541}{112} (1-2 x)^{7/2}-\frac{39977}{80} (1-2 x)^{5/2}+\frac{91091}{96} (1-2 x)^{3/2}-\frac{41503}{32} \sqrt{1-2 x}",1,"(Sqrt[1 - 2*x]*(-826982 - 743822*x - 790023*x^2 - 636795*x^3 - 316575*x^4 - 70875*x^5))/1155","A",1
2015,1,33,66,0.0125564,"\int \frac{(2+3 x)^2 (3+5 x)^2}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^2)/Sqrt[1 - 2*x],x]","\frac{1}{105} \sqrt{1-2 x} \left(-2625 x^4-10050 x^3-17391 x^2-19574 x-23354\right)","-\frac{25}{16} (1-2 x)^{9/2}+\frac{255}{14} (1-2 x)^{7/2}-\frac{3467}{40} (1-2 x)^{5/2}+\frac{1309}{6} (1-2 x)^{3/2}-\frac{5929}{16} \sqrt{1-2 x}",1,"(Sqrt[1 - 2*x]*(-23354 - 19574*x - 17391*x^2 - 10050*x^3 - 2625*x^4))/105","A",1
2016,1,28,53,0.009962,"\int \frac{(2+3 x) (3+5 x)^2}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^2)/Sqrt[1 - 2*x],x]","\frac{1}{21} \sqrt{1-2 x} \left(-225 x^3-723 x^2-1091 x-1469\right)","\frac{75}{56} (1-2 x)^{7/2}-\frac{101}{8} (1-2 x)^{5/2}+\frac{1133}{24} (1-2 x)^{3/2}-\frac{847}{8} \sqrt{1-2 x}",1,"(Sqrt[1 - 2*x]*(-1469 - 1091*x - 723*x^2 - 225*x^3))/21","A",1
2017,1,23,40,0.0087273,"\int \frac{(3+5 x)^2}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/Sqrt[1 - 2*x],x]","\frac{1}{3} \sqrt{1-2 x} \left(-15 x^2-40 x-67\right)","-\frac{5}{4} (1-2 x)^{5/2}+\frac{55}{6} (1-2 x)^{3/2}-\frac{121}{4} \sqrt{1-2 x}",1,"(Sqrt[1 - 2*x]*(-67 - 40*x - 15*x^2))/3","A",1
2018,1,46,54,0.0520043,"\int \frac{(3+5 x)^2}{\sqrt{1-2 x} (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/(Sqrt[1 - 2*x]*(2 + 3*x)),x]","-\frac{5}{9} \sqrt{1-2 x} (5 x+13)-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{9 \sqrt{21}}","\frac{25}{18} (1-2 x)^{3/2}-\frac{155}{18} \sqrt{1-2 x}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{9 \sqrt{21}}",1,"(-5*Sqrt[1 - 2*x]*(13 + 5*x))/9 - (2*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(9*Sqrt[21])","A",1
2019,1,53,61,0.0837343,"\int \frac{(3+5 x)^2}{\sqrt{1-2 x} (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/(Sqrt[1 - 2*x]*(2 + 3*x)^2),x]","\frac{\sqrt{1-2 x} (-175 x-117)}{21 (3 x+2)}+\frac{46 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{21 \sqrt{21}}","-\frac{25}{9} \sqrt{1-2 x}-\frac{\sqrt{1-2 x}}{63 (3 x+2)}+\frac{46 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{21 \sqrt{21}}",1,"((-117 - 175*x)*Sqrt[1 - 2*x])/(21*(2 + 3*x)) + (46*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(21*Sqrt[21])","A",1
2020,1,53,68,0.1066012,"\int \frac{(3+5 x)^2}{\sqrt{1-2 x} (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/(Sqrt[1 - 2*x]*(2 + 3*x)^3),x]","\frac{\sqrt{1-2 x} (137 x+89)}{294 (3 x+2)^2}-\frac{257 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{49 \sqrt{21}}","\frac{137 \sqrt{1-2 x}}{882 (3 x+2)}-\frac{\sqrt{1-2 x}}{126 (3 x+2)^2}-\frac{257 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{49 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(89 + 137*x))/(294*(2 + 3*x)^2) - (257*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(49*Sqrt[21])","A",1
2021,1,58,88,0.0962573,"\int \frac{(3+5 x)^2}{\sqrt{1-2 x} (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/(Sqrt[1 - 2*x]*(2 + 3*x)^4),x]","\frac{\sqrt{1-2 x} \left(-20205 x^2-25505 x-8056\right)}{6174 (3 x+2)^3}-\frac{2245 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{3087 \sqrt{21}}","-\frac{2245 \sqrt{1-2 x}}{6174 (3 x+2)}+\frac{205 \sqrt{1-2 x}}{2646 (3 x+2)^2}-\frac{\sqrt{1-2 x}}{189 (3 x+2)^3}-\frac{2245 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{3087 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-8056 - 25505*x - 20205*x^2))/(6174*(2 + 3*x)^3) - (2245*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(3087*Sqrt[21])","A",1
2022,1,63,108,0.0952566,"\int \frac{(3+5 x)^2}{\sqrt{1-2 x} (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/(Sqrt[1 - 2*x]*(2 + 3*x)^5),x]","\frac{\sqrt{1-2 x} \left(-17145 x^3-47625 x^2-39366 x-10190\right)}{8232 (3 x+2)^4}-\frac{635 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{4116 \sqrt{21}}","-\frac{635 \sqrt{1-2 x}}{8232 (3 x+2)}-\frac{635 \sqrt{1-2 x}}{3528 (3 x+2)^2}+\frac{13 \sqrt{1-2 x}}{252 (3 x+2)^3}-\frac{\sqrt{1-2 x}}{252 (3 x+2)^4}-\frac{635 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{4116 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-10190 - 39366*x - 47625*x^2 - 17145*x^3))/(8232*(2 + 3*x)^4) - (635*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(4116*Sqrt[21])","A",1
2023,1,70,130,0.1397444,"\int \frac{(3+5 x)^2}{\sqrt{1-2 x} (2+3 x)^6} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/(Sqrt[1 - 2*x]*(2 + 3*x)^6),x]","\frac{\sqrt{1-2 x} \left(-426465 x^4-1468935 x^3-2110212 x^2-1327058 x-298748\right)}{288120 (3 x+2)^5}-\frac{117 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{9604}","-\frac{351 \sqrt{1-2 x}}{19208 (3 x+2)}-\frac{117 \sqrt{1-2 x}}{2744 (3 x+2)^2}-\frac{117 \sqrt{1-2 x}}{980 (3 x+2)^3}+\frac{341 \sqrt{1-2 x}}{8820 (3 x+2)^4}-\frac{\sqrt{1-2 x}}{315 (3 x+2)^5}-\frac{117 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{9604}",1,"(Sqrt[1 - 2*x]*(-298748 - 1327058*x - 2110212*x^2 - 1468935*x^3 - 426465*x^4))/(288120*(2 + 3*x)^5) - (117*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/9604","A",1
2024,1,48,105,0.0180019,"\int \frac{(2+3 x)^4 (3+5 x)^3}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^3)/Sqrt[1 - 2*x],x]","\frac{\sqrt{1-2 x} \left(-1447875 x^7-8241750 x^6-21369825 x^5-33786160 x^4-37260640 x^3-31962552 x^2-24706048 x-25632688\right)}{2145}","\frac{675}{128} (1-2 x)^{15/2}-\frac{161325 (1-2 x)^{13/2}}{1664}+\frac{1101465 (1-2 x)^{11/2}}{1408}-\frac{1392467}{384} (1-2 x)^{9/2}+\frac{1357793}{128} (1-2 x)^{7/2}-\frac{12973191}{640} (1-2 x)^{5/2}+\frac{3278737}{128} (1-2 x)^{3/2}-\frac{3195731}{128} \sqrt{1-2 x}",1,"(Sqrt[1 - 2*x]*(-25632688 - 24706048*x - 31962552*x^2 - 37260640*x^3 - 33786160*x^4 - 21369825*x^5 - 8241750*x^6 - 1447875*x^7))/2145","A",1
2025,1,43,92,0.0151422,"\int \frac{(2+3 x)^3 (3+5 x)^3}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^3)/Sqrt[1 - 2*x],x]","\frac{\sqrt{1-2 x} \left(-1299375 x^6-6544125 x^5-14921900 x^4-20766885 x^3-20586249 x^2-17147586 x-18228666\right)}{5005}","-\frac{3375}{832} (1-2 x)^{13/2}+\frac{11475}{176} (1-2 x)^{11/2}-\frac{28895}{64} (1-2 x)^{9/2}+\frac{98209}{56} (1-2 x)^{7/2}-\frac{1334949}{320} (1-2 x)^{5/2}+\frac{100793}{16} (1-2 x)^{3/2}-\frac{456533}{64} \sqrt{1-2 x}",1,"(Sqrt[1 - 2*x]*(-18228666 - 17147586*x - 20586249*x^2 - 20766885*x^3 - 14921900*x^4 - 6544125*x^5 - 1299375*x^6))/5005","A",1
2026,1,38,79,0.0130903,"\int \frac{(2+3 x)^2 (3+5 x)^3}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^3)/Sqrt[1 - 2*x],x]","\frac{\sqrt{1-2 x} \left(-118125 x^5-518000 x^4-1024475 x^3-1252938 x^2-1167932 x-1292672\right)}{1155}","\frac{1125}{352} (1-2 x)^{11/2}-\frac{4225}{96} (1-2 x)^{9/2}+\frac{28555}{112} (1-2 x)^{7/2}-\frac{64317}{80} (1-2 x)^{5/2}+\frac{48279}{32} (1-2 x)^{3/2}-\frac{65219}{32} \sqrt{1-2 x}",1,"(Sqrt[1 - 2*x]*(-1292672 - 1167932*x - 1252938*x^2 - 1024475*x^3 - 518000*x^4 - 118125*x^5))/1155","A",1
2027,1,33,66,0.01142,"\int \frac{(2+3 x) (3+5 x)^3}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^3)/Sqrt[1 - 2*x],x]","\frac{1}{21} \sqrt{1-2 x} \left(-875 x^4-3275 x^3-5556 x^2-6161 x-7295\right)","-\frac{125}{48} (1-2 x)^{9/2}+\frac{1675}{56} (1-2 x)^{7/2}-\frac{561}{4} (1-2 x)^{5/2}+\frac{2783}{8} (1-2 x)^{3/2}-\frac{9317}{16} \sqrt{1-2 x}",1,"(Sqrt[1 - 2*x]*(-7295 - 6161*x - 5556*x^2 - 3275*x^3 - 875*x^4))/21","A",1
2028,1,28,53,0.010025,"\int \frac{(3+5 x)^3}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/Sqrt[1 - 2*x],x]","\frac{1}{7} \sqrt{1-2 x} \left(-125 x^3-390 x^2-575 x-764\right)","\frac{125}{56} (1-2 x)^{7/2}-\frac{165}{8} (1-2 x)^{5/2}+\frac{605}{8} (1-2 x)^{3/2}-\frac{1331}{8} \sqrt{1-2 x}",1,"(Sqrt[1 - 2*x]*(-764 - 575*x - 390*x^2 - 125*x^3))/7","A",1
2029,1,51,67,0.0553811,"\int \frac{(3+5 x)^3}{\sqrt{1-2 x} (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/(Sqrt[1 - 2*x]*(2 + 3*x)),x]","\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{27 \sqrt{21}}-\frac{5}{27} \sqrt{1-2 x} \left(45 x^2+115 x+188\right)","-\frac{25}{12} (1-2 x)^{5/2}+\frac{400}{27} (1-2 x)^{3/2}-\frac{5135}{108} \sqrt{1-2 x}+\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{27 \sqrt{21}}",1,"(-5*Sqrt[1 - 2*x]*(188 + 115*x + 45*x^2))/27 + (2*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(27*Sqrt[21])","A",1
2030,1,58,73,0.0894857,"\int \frac{(3+5 x)^3}{\sqrt{1-2 x} (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/(Sqrt[1 - 2*x]*(2 + 3*x)^2),x]","\frac{\sqrt{1-2 x} \left(-2625 x^2-8050 x-4199\right)}{189 (3 x+2)}-\frac{208 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{189 \sqrt{21}}","\frac{\sqrt{1-2 x} (5 x+3)^2}{21 (3 x+2)}-\frac{10}{189} \sqrt{1-2 x} (95 x+214)-\frac{208 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{189 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-4199 - 8050*x - 2625*x^2))/(189*(2 + 3*x)) - (208*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(189*Sqrt[21])","A",1
2031,1,58,80,0.0893027,"\int \frac{(3+5 x)^3}{\sqrt{1-2 x} (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/(Sqrt[1 - 2*x]*(2 + 3*x)^3),x]","\frac{\sqrt{1-2 x} \left(-36750 x^2-49207 x-16469\right)}{882 (3 x+2)^2}+\frac{2381 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{441 \sqrt{21}}","\frac{\sqrt{1-2 x} (5 x+3)^2}{42 (3 x+2)^2}-\frac{\sqrt{1-2 x} (12425 x+8329)}{882 (3 x+2)}+\frac{2381 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{441 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-16469 - 49207*x - 36750*x^2))/(882*(2 + 3*x)^2) + (2381*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(441*Sqrt[21])","A",1
2032,1,58,80,0.0919104,"\int \frac{(3+5 x)^3}{\sqrt{1-2 x} (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/(Sqrt[1 - 2*x]*(2 + 3*x)^4),x]","\frac{\sqrt{1-2 x} \left(31680 x^2+41155 x+13373\right)}{9261 (3 x+2)^3}-\frac{78710 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{9261 \sqrt{21}}","\frac{\sqrt{1-2 x} (5 x+3)^2}{63 (3 x+2)^3}+\frac{5 \sqrt{1-2 x} (1867 x+1205)}{9261 (3 x+2)^2}-\frac{78710 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{9261 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(13373 + 41155*x + 31680*x^2))/(9261*(2 + 3*x)^3) - (78710*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(9261*Sqrt[21])","A",1
2033,1,63,100,0.1094156,"\int \frac{(3+5 x)^3}{\sqrt{1-2 x} (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/(Sqrt[1 - 2*x]*(2 + 3*x)^5),x]","\frac{\sqrt{1-2 x} \left(-1160865 x^3-2195625 x^2-1385462 x-291670\right)}{74088 (3 x+2)^4}-\frac{42995 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{37044 \sqrt{21}}","\frac{\sqrt{1-2 x} (5 x+3)^2}{84 (3 x+2)^4}+\frac{\sqrt{1-2 x} (4955 x+3168)}{10584 (3 x+2)^3}-\frac{42995 \sqrt{1-2 x}}{74088 (3 x+2)}-\frac{42995 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{37044 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-291670 - 1385462*x - 2195625*x^2 - 1160865*x^3))/(74088*(2 + 3*x)^4) - (42995*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(37044*Sqrt[21])","A",1
2034,1,68,120,0.1265101,"\int \frac{(3+5 x)^3}{\sqrt{1-2 x} (2+3 x)^6} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/(Sqrt[1 - 2*x]*(2 + 3*x)^6),x]","\frac{\sqrt{1-2 x} \left(-2143665 x^4-7383735 x^3-8806422 x^2-4450198 x-816938\right)}{216090 (3 x+2)^5}-\frac{5293 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{21609 \sqrt{21}}","\frac{\sqrt{1-2 x} (5 x+3)^2}{105 (3 x+2)^5}+\frac{\sqrt{1-2 x} (1971 x+1255)}{6615 (3 x+2)^4}-\frac{5293 \sqrt{1-2 x}}{43218 (3 x+2)}-\frac{5293 \sqrt{1-2 x}}{18522 (3 x+2)^2}-\frac{5293 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{21609 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-816938 - 4450198*x - 8806422*x^2 - 7383735*x^3 - 2143665*x^4))/(216090*(2 + 3*x)^5) - (5293*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(21609*Sqrt[21])","A",1
2035,1,185,132,0.2812296,"\int \frac{(a+b x)^2}{(c+d x)^2 \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(a + b*x)^2/((c + d*x)^2*Sqrt[e + f*x]),x]","\frac{\sqrt{e+f x} \left(-a^2 d^2 f+2 a b c d f-3 b^2 c^2 f+2 b^2 c d e-2 b^2 c d f x+2 b^2 d^2 e x\right)}{d^2 f (c+d x) (d e-c f)}+\frac{\left(-a^2 d^2 f-2 a b c d f+4 a b d^2 e+3 b^2 c^2 f-4 b^2 c d e\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x} \sqrt{c f-d e}}{d e-c f}\right)}{d^{5/2} (c f-d e)^{3/2}}","\frac{(b c-a d) (-a d f-3 b c f+4 b d e) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{d^{5/2} (d e-c f)^{3/2}}-\frac{\sqrt{e+f x} (b c-a d)^2}{d^2 (c+d x) (d e-c f)}+\frac{2 b^2 \sqrt{e+f x}}{d^2 f}",1,"(Sqrt[e + f*x]*(2*b^2*c*d*e - 3*b^2*c^2*f + 2*a*b*c*d*f - a^2*d^2*f + 2*b^2*d^2*e*x - 2*b^2*c*d*f*x))/(d^2*f*(d*e - c*f)*(c + d*x)) + ((-4*b^2*c*d*e + 4*a*b*d^2*e + 3*b^2*c^2*f - 2*a*b*c*d*f - a^2*d^2*f)*ArcTan[(Sqrt[d]*Sqrt[-(d*e) + c*f]*Sqrt[e + f*x])/(d*e - c*f)])/(d^(5/2)*(-(d*e) + c*f)^(3/2))","A",1
2036,1,61,93,0.0684387,"\int \frac{(2+3 x)^5}{\sqrt{1-2 x} (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/(Sqrt[1 - 2*x]*(3 + 5*x)),x]","-\frac{3 \sqrt{1-2 x} \left(39375 x^4+160875 x^3+295290 x^2+348095 x+425872\right)}{21875}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125 \sqrt{55}}","-\frac{27}{80} (1-2 x)^{9/2}+\frac{5751 (1-2 x)^{7/2}}{1400}-\frac{51057 (1-2 x)^{5/2}}{2500}+\frac{268707 (1-2 x)^{3/2}}{5000}-\frac{4774713 \sqrt{1-2 x}}{50000}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125 \sqrt{55}}",1,"(-3*Sqrt[1 - 2*x]*(425872 + 348095*x + 295290*x^2 + 160875*x^3 + 39375*x^4))/21875 - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(3125*Sqrt[55])","A",1
2037,1,56,80,0.0586883,"\int \frac{(2+3 x)^4}{\sqrt{1-2 x} (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/(Sqrt[1 - 2*x]*(3 + 5*x)),x]","-\frac{3 \sqrt{1-2 x} \left(3375 x^3+11790 x^2+19095 x+26872\right)}{4375}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{625 \sqrt{55}}","\frac{81}{280} (1-2 x)^{7/2}-\frac{2889 (1-2 x)^{5/2}}{1000}+\frac{11457 (1-2 x)^{3/2}}{1000}-\frac{136419 \sqrt{1-2 x}}{5000}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{625 \sqrt{55}}",1,"(-3*Sqrt[1 - 2*x]*(26872 + 19095*x + 11790*x^2 + 3375*x^3))/4375 - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(625*Sqrt[55])","A",1
2038,1,51,67,0.0556783,"\int \frac{(2+3 x)^3}{\sqrt{1-2 x} (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/(Sqrt[1 - 2*x]*(3 + 5*x)),x]","-\frac{9}{125} \sqrt{1-2 x} \left(15 x^2+45 x+82\right)-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{125 \sqrt{55}}","-\frac{27}{100} (1-2 x)^{5/2}+\frac{54}{25} (1-2 x)^{3/2}-\frac{3897}{500} \sqrt{1-2 x}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{125 \sqrt{55}}",1,"(-9*Sqrt[1 - 2*x]*(82 + 45*x + 15*x^2))/125 - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(125*Sqrt[55])","A",1
2039,1,46,54,0.0508304,"\int \frac{(2+3 x)^2}{\sqrt{1-2 x} (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/(Sqrt[1 - 2*x]*(3 + 5*x)),x]","-\frac{3}{25} \sqrt{1-2 x} (5 x+16)-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{25 \sqrt{55}}","\frac{3}{10} (1-2 x)^{3/2}-\frac{111}{50} \sqrt{1-2 x}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{25 \sqrt{55}}",1,"(-3*Sqrt[1 - 2*x]*(16 + 5*x))/25 - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(25*Sqrt[55])","A",1
2040,1,41,41,0.0409061,"\int \frac{2+3 x}{\sqrt{1-2 x} (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)/(Sqrt[1 - 2*x]*(3 + 5*x)),x]","-\frac{3}{5} \sqrt{1-2 x}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{5 \sqrt{55}}","-\frac{3}{5} \sqrt{1-2 x}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{5 \sqrt{55}}",1,"(-3*Sqrt[1 - 2*x])/5 - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(5*Sqrt[55])","A",1
2041,1,25,25,0.0366526,"\int \frac{1}{\sqrt{1-2 x} (3+5 x)} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(3 + 5*x)),x]","-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{\sqrt{55}}","-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{\sqrt{55}}",1,"(-2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/Sqrt[55]","A",1
2042,1,55,55,0.0755371,"\int \frac{1}{\sqrt{1-2 x} (2+3 x) (3+5 x)} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)),x]","2 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-2 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","2 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-2 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"2*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - 2*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
2043,1,77,77,0.1262987,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)),x]","\frac{3 \sqrt{1-2 x}}{7 (3 x+2)}+\frac{72}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-10 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{3 \sqrt{1-2 x}}{7 (3 x+2)}+\frac{72}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-10 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(3*Sqrt[1 - 2*x])/(7*(2 + 3*x)) + (72*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/7 - 10*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
2044,1,82,97,0.1248902,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)),x]","\frac{9 \sqrt{1-2 x} (73 x+51)}{98 (3 x+2)^2}+\frac{2523}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-50 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{219 \sqrt{1-2 x}}{98 (3 x+2)}+\frac{3 \sqrt{1-2 x}}{14 (3 x+2)^2}+\frac{2523}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-50 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(9*Sqrt[1 - 2*x]*(51 + 73*x))/(98*(2 + 3*x)^2) + (2523*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/49 - 50*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
2045,1,87,117,0.1340959,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^4 (3+5 x)} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)),x]","\frac{3 \sqrt{1-2 x} \left(11520 x^2+15745 x+5393\right)}{343 (3 x+2)^3}+\frac{88310}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-250 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{3840 \sqrt{1-2 x}}{343 (3 x+2)}+\frac{55 \sqrt{1-2 x}}{49 (3 x+2)^2}+\frac{\sqrt{1-2 x}}{7 (3 x+2)^3}+\frac{88310}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-250 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(3*Sqrt[1 - 2*x]*(5393 + 15745*x + 11520*x^2))/(343*(2 + 3*x)^3) + (88310*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 - 250*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
2046,1,92,137,0.1634857,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^5 (3+5 x)} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^5*(3 + 5*x)),x]","\frac{3 \sqrt{1-2 x} \left(28215 x^3+57375 x^2+38922 x+8810\right)}{56 (3 x+2)^4}+\frac{36045}{28} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-1250 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{3135 \sqrt{1-2 x}}{56 (3 x+2)}+\frac{45 \sqrt{1-2 x}}{8 (3 x+2)^2}+\frac{3 \sqrt{1-2 x}}{4 (3 x+2)^3}+\frac{3 \sqrt{1-2 x}}{28 (3 x+2)^4}+\frac{36045}{28} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-1250 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(3*Sqrt[1 - 2*x]*(8810 + 38922*x + 57375*x^2 + 28215*x^3))/(56*(2 + 3*x)^4) + (36045*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/28 - 1250*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]","A",1
2047,1,73,133,0.1140592,"\int \frac{(2+3 x)^6}{\sqrt{1-2 x} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/(Sqrt[1 - 2*x]*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-19490625 x^5-92998125 x^4-200942775 x^3-273540465 x^2-334366065 x-135011752\right)}{1203125 (5 x+3)}-\frac{398 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{171875 \sqrt{55}}","-\frac{\sqrt{1-2 x} (3 x+2)^5}{55 (5 x+3)}-\frac{8}{275} \sqrt{1-2 x} (3 x+2)^4-\frac{1717 \sqrt{1-2 x} (3 x+2)^3}{9625}-\frac{26352 \sqrt{1-2 x} (3 x+2)^2}{34375}-\frac{3 \sqrt{1-2 x} (615875 x+1847824)}{171875}-\frac{398 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{171875 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-135011752 - 334366065*x - 273540465*x^2 - 200942775*x^3 - 92998125*x^4 - 19490625*x^5))/(1203125*(3 + 5*x)) - (398*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(171875*Sqrt[55])","A",1
2048,1,68,113,0.0964327,"\int \frac{(2+3 x)^5}{\sqrt{1-2 x} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/(Sqrt[1 - 2*x]*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-1670625 x^4-6994350 x^3-13532310 x^2-20175210 x-8527768\right)}{240625 (5 x+3)}-\frac{332 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{34375 \sqrt{55}}","-\frac{\sqrt{1-2 x} (3 x+2)^4}{55 (5 x+3)}-\frac{78 \sqrt{1-2 x} (3 x+2)^3}{1925}-\frac{1668 \sqrt{1-2 x} (3 x+2)^2}{6875}-\frac{6 \sqrt{1-2 x} (19875 x+59708)}{34375}-\frac{332 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{34375 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-8527768 - 20175210*x - 13532310*x^2 - 6994350*x^3 - 1670625*x^4))/(240625*(3 + 5*x)) - (332*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(34375*Sqrt[55])","A",1
2049,1,63,93,0.0967119,"\int \frac{(2+3 x)^4}{\sqrt{1-2 x} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/(Sqrt[1 - 2*x]*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-22275 x^3-82665 x^2-171765 x-78112\right)}{6875 (5 x+3)}-\frac{266 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{6875 \sqrt{55}}","-\frac{\sqrt{1-2 x} (3 x+2)^3}{55 (5 x+3)}-\frac{84 \sqrt{1-2 x} (3 x+2)^2}{1375}-\frac{21 \sqrt{1-2 x} (375 x+1144)}{6875}-\frac{266 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{6875 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-78112 - 171765*x - 82665*x^2 - 22275*x^3))/(6875*(3 + 5*x)) - (266*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(6875*Sqrt[55])","A",1
2050,1,58,73,0.0983761,"\int \frac{(2+3 x)^3}{\sqrt{1-2 x} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/(Sqrt[1 - 2*x]*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-99 x^2-396 x-202\right)}{55 (5 x+3)}-\frac{8 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{55 \sqrt{55}}","-\frac{\sqrt{1-2 x} (3 x+2)^2}{55 (5 x+3)}-\frac{6}{55} \sqrt{1-2 x} (3 x+11)-\frac{8 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{55 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-202 - 396*x - 99*x^2))/(55*(3 + 5*x)) - (8*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(55*Sqrt[55])","A",1
2051,1,53,61,0.0803567,"\int \frac{(2+3 x)^2}{\sqrt{1-2 x} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/(Sqrt[1 - 2*x]*(3 + 5*x)^2),x]","\frac{(-495 x-298) \sqrt{1-2 x}}{275 (5 x+3)}-\frac{134 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{275 \sqrt{55}}","-\frac{9}{25} \sqrt{1-2 x}-\frac{\sqrt{1-2 x}}{275 (5 x+3)}-\frac{134 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{275 \sqrt{55}}",1,"((-298 - 495*x)*Sqrt[1 - 2*x])/(275*(3 + 5*x)) - (134*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(275*Sqrt[55])","A",1
2052,1,48,48,0.0613706,"\int \frac{2+3 x}{\sqrt{1-2 x} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)/(Sqrt[1 - 2*x]*(3 + 5*x)^2),x]","-\frac{\sqrt{1-2 x}}{55 (5 x+3)}-\frac{68 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{55 \sqrt{55}}","-\frac{\sqrt{1-2 x}}{55 (5 x+3)}-\frac{68 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{55 \sqrt{55}}",1,"-1/55*Sqrt[1 - 2*x]/(3 + 5*x) - (68*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(55*Sqrt[55])","A",1
2053,1,48,48,0.0619169,"\int \frac{1}{\sqrt{1-2 x} (3+5 x)^2} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(3 + 5*x)^2),x]","-\frac{\sqrt{1-2 x}}{11 (5 x+3)}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{11 \sqrt{55}}","-\frac{\sqrt{1-2 x}}{11 (5 x+3)}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{11 \sqrt{55}}",1,"-1/11*Sqrt[1 - 2*x]/(3 + 5*x) - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(11*Sqrt[55])","A",1
2054,1,77,77,0.1157712,"\int \frac{1}{\sqrt{1-2 x} (2+3 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^2),x]","-\frac{5 \sqrt{1-2 x}}{11 (5 x+3)}-6 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{64}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{5 \sqrt{1-2 x}}{11 (5 x+3)}-6 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{64}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(-5*Sqrt[1 - 2*x])/(11*(3 + 5*x)) - 6*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] + (64*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/11","A",1
2055,1,89,106,0.1094608,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} (-1020 x-647)}{77 \left(15 x^2+19 x+6\right)}-\frac{426}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{650}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{340 \sqrt{1-2 x}}{77 (5 x+3)}+\frac{3 \sqrt{1-2 x}}{7 (3 x+2) (5 x+3)}-\frac{426}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{650}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"((-647 - 1020*x)*Sqrt[1 - 2*x])/(77*(6 + 19*x + 15*x^2)) - (426*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/7 + (650*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/11","A",1
2056,1,96,133,0.1476697,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-322605 x^2-419448 x-136021\right)}{1078 (3 x+2)^2 (5 x+3)}-\frac{22479}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{4900}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{35845 \sqrt{1-2 x}}{1078 (5 x+3)}+\frac{162 \sqrt{1-2 x}}{49 (3 x+2) (5 x+3)}+\frac{3 \sqrt{1-2 x}}{14 (3 x+2)^2 (5 x+3)}-\frac{22479}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{4900}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-136021 - 419448*x - 322605*x^2))/(1078*(2 + 3*x)^2*(3 + 5*x)) - (22479*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/49 + (4900*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/11","A",1
2057,1,101,160,0.1589694,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^4 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-45278325 x^3-89054820 x^2-58335165 x-12724912\right)}{7546 (3 x+2)^3 (5 x+3)}-\frac{1051695}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{32750}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{1676975 \sqrt{1-2 x}}{7546 (5 x+3)}+\frac{7585 \sqrt{1-2 x}}{343 (3 x+2) (5 x+3)}+\frac{145 \sqrt{1-2 x}}{98 (3 x+2)^2 (5 x+3)}+\frac{\sqrt{1-2 x}}{7 (3 x+2)^3 (5 x+3)}-\frac{1051695}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{32750}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-12724912 - 58335165*x - 89054820*x^2 - 45278325*x^3))/(7546*(2 + 3*x)^3*(3 + 5*x)) - (1051695*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 + (32750*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/11","A",1
2058,1,73,140,0.1389617,"\int \frac{(2+3 x)^6}{\sqrt{1-2 x} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/(Sqrt[1 - 2*x]*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(-551306250 x^5-2690374500 x^4-6078090150 x^3-9876010320 x^2-7254126105 x-1804176536\right)}{26468750 (5 x+3)^2}-\frac{33069 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1890625 \sqrt{55}}","-\frac{\sqrt{1-2 x} (3 x+2)^5}{110 (5 x+3)^2}-\frac{117 \sqrt{1-2 x} (3 x+2)^4}{3025 (5 x+3)}-\frac{927 \sqrt{1-2 x} (3 x+2)^3}{211750}-\frac{56556 \sqrt{1-2 x} (3 x+2)^2}{378125}-\frac{9 \sqrt{1-2 x} (934875 x+2815648)}{3781250}-\frac{33069 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1890625 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-1804176536 - 7254126105*x - 9876010320*x^2 - 6078090150*x^3 - 2690374500*x^4 - 551306250*x^5))/(26468750*(3 + 5*x)^2) - (33069*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(1890625*Sqrt[55])","A",1
2059,1,68,120,0.1138307,"\int \frac{(2+3 x)^5}{\sqrt{1-2 x} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/(Sqrt[1 - 2*x]*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(-7350750 x^4-32506650 x^3-76970520 x^2-63610155 x-16525496\right)}{756250 (5 x+3)^2}-\frac{22113 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{378125 \sqrt{55}}","-\frac{\sqrt{1-2 x} (3 x+2)^4}{110 (5 x+3)^2}-\frac{201 \sqrt{1-2 x} (3 x+2)^3}{6050 (5 x+3)}-\frac{1512 \sqrt{1-2 x} (3 x+2)^2}{75625}-\frac{189 \sqrt{1-2 x} (2875 x+8976)}{756250}-\frac{22113 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{378125 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-16525496 - 63610155*x - 76970520*x^2 - 32506650*x^3 - 7350750*x^4))/(756250*(3 + 5*x)^2) - (22113*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(378125*Sqrt[55])","A",1
2060,1,63,100,0.1135626,"\int \frac{(2+3 x)^4}{\sqrt{1-2 x} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/(Sqrt[1 - 2*x]*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(-163350 x^3-784080 x^2-764745 x-211864\right)}{30250 (5 x+3)^2}-\frac{2667 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15125 \sqrt{55}}","-\frac{\sqrt{1-2 x} (3 x+2)^3}{110 (5 x+3)^2}-\frac{84 \sqrt{1-2 x} (3 x+2)^2}{3025 (5 x+3)}-\frac{63 \sqrt{1-2 x} (75 x+352)}{30250}-\frac{2667 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15125 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-211864 - 764745*x - 784080*x^2 - 163350*x^3))/(30250*(3 + 5*x)^2) - (2667*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(15125*Sqrt[55])","A",1
2061,1,58,80,0.0976359,"\int \frac{(2+3 x)^3}{\sqrt{1-2 x} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/(Sqrt[1 - 2*x]*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(-32670 x^2-39405 x-11884\right)}{6050 (5 x+3)^2}-\frac{1347 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3025 \sqrt{55}}","-\frac{\sqrt{1-2 x} (3 x+2)^2}{110 (5 x+3)^2}-\frac{9 \sqrt{1-2 x} (715 x+432)}{6050 (5 x+3)}-\frac{1347 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3025 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-11884 - 39405*x - 32670*x^2))/(6050*(3 + 5*x)^2) - (1347*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(3025*Sqrt[55])","A",1
2062,1,53,68,0.0912418,"\int \frac{(2+3 x)^2}{\sqrt{1-2 x} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/(Sqrt[1 - 2*x]*(3 + 5*x)^3),x]","\frac{(-675 x-416) \sqrt{1-2 x}}{6050 (5 x+3)^2}-\frac{2313 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3025 \sqrt{55}}","-\frac{27 \sqrt{1-2 x}}{1210 (5 x+3)}-\frac{\sqrt{1-2 x}}{550 (5 x+3)^2}-\frac{2313 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3025 \sqrt{55}}",1,"((-416 - 675*x)*Sqrt[1 - 2*x])/(6050*(3 + 5*x)^2) - (2313*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(3025*Sqrt[55])","A",1
2063,1,53,68,0.0930432,"\int \frac{2+3 x}{\sqrt{1-2 x} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)/(Sqrt[1 - 2*x]*(3 + 5*x)^3),x]","\frac{(-345 x-218) \sqrt{1-2 x}}{1210 (5 x+3)^2}-\frac{69 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{605 \sqrt{55}}","-\frac{69 \sqrt{1-2 x}}{1210 (5 x+3)}-\frac{\sqrt{1-2 x}}{110 (5 x+3)^2}-\frac{69 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{605 \sqrt{55}}",1,"((-218 - 345*x)*Sqrt[1 - 2*x])/(1210*(3 + 5*x)^2) - (69*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(605*Sqrt[55])","A",1
2064,1,53,68,0.0865918,"\int \frac{1}{\sqrt{1-2 x} (3+5 x)^3} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(3 + 5*x)^3),x]","-\frac{5 \sqrt{1-2 x} (3 x+4)}{242 (5 x+3)^2}-\frac{3 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{121 \sqrt{55}}","-\frac{3 \sqrt{1-2 x}}{242 (5 x+3)}-\frac{\sqrt{1-2 x}}{22 (5 x+3)^2}-\frac{3 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{121 \sqrt{55}}",1,"(-5*Sqrt[1 - 2*x]*(4 + 3*x))/(242*(3 + 5*x)^2) - (3*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(121*Sqrt[55])","A",1
2065,1,82,97,0.1213761,"\int \frac{1}{\sqrt{1-2 x} (2+3 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^3),x]","\frac{5 \sqrt{1-2 x} (315 x+178)}{242 (5 x+3)^2}+18 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{2115}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{315 \sqrt{1-2 x}}{242 (5 x+3)}-\frac{5 \sqrt{1-2 x}}{22 (5 x+3)^2}+18 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{2115}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(5*Sqrt[1 - 2*x]*(178 + 315*x))/(242*(3 + 5*x)^2) + 18*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - (2115*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/121","A",1
2066,1,96,126,0.1369548,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(501975 x^2+619170 x+190406\right)}{1694 (3 x+2) (5 x+3)^2}+\frac{1908}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{32025}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{33465 \sqrt{1-2 x}}{1694 (5 x+3)}-\frac{505 \sqrt{1-2 x}}{154 (5 x+3)^2}+\frac{3 \sqrt{1-2 x}}{7 (3 x+2) (5 x+3)^2}+\frac{1908}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{32025}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(190406 + 619170*x + 501975*x^2))/(1694*(2 + 3*x)*(3 + 5*x)^2) + (1908*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/7 - (32025*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/121","A",1
2067,1,99,153,0.146531,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(105937200 x^3+201297915 x^2+127303347 x+26794499\right)}{11858 \left(15 x^2+19 x+6\right)^2}+\frac{134217}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{321825}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{1177080 \sqrt{1-2 x}}{5929 (5 x+3)}-\frac{35495 \sqrt{1-2 x}}{1078 (5 x+3)^2}+\frac{429 \sqrt{1-2 x}}{98 (3 x+2) (5 x+3)^2}+\frac{3 \sqrt{1-2 x}}{14 (3 x+2)^2 (5 x+3)^2}+\frac{134217}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{321825}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(26794499 + 127303347*x + 201297915*x^2 + 105937200*x^3))/(11858*(6 + 19*x + 15*x^2)^2) + (134217*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/49 - (321825*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/121","A",1
2068,1,106,180,0.1860256,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^4 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(18594329625 x^4+47728484550 x^3+45899434890 x^2+19599448500 x+3135381218\right)}{83006 (3 x+2)^3 (5 x+3)^2}+\frac{7852680}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{2689875}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{137735775 \sqrt{1-2 x}}{83006 (5 x+3)}-\frac{2076675 \sqrt{1-2 x}}{7546 (5 x+3)^2}+\frac{12555 \sqrt{1-2 x}}{343 (3 x+2) (5 x+3)^2}+\frac{90 \sqrt{1-2 x}}{49 (3 x+2)^2 (5 x+3)^2}+\frac{\sqrt{1-2 x}}{7 (3 x+2)^3 (5 x+3)^2}+\frac{7852680}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{2689875}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(3135381218 + 19599448500*x + 45899434890*x^2 + 47728484550*x^3 + 18594329625*x^4))/(83006*(2 + 3*x)^3*(3 + 5*x)^2) + (7852680*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 - (2689875*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/121","A",1
2069,1,60,118,0.0223273,"\int \frac{(2+3 x)^7 (3+5 x)}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^7*(3 + 5*x))/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(104247 x^8+697653 x^7+2168775 x^6+4220622 x^5+5949090 x^4+6921432 x^3+8106616 x^2+16881328 x-16936240\right)}{143 (2 x-1)}","-\frac{729}{256} (1-2 x)^{15/2}+\frac{101331 (1-2 x)^{13/2}}{1664}-\frac{821583 (1-2 x)^{11/2}}{1408}+\frac{422919}{128} (1-2 x)^{9/2}-\frac{787185}{64} (1-2 x)^{7/2}+\frac{4084101}{128} (1-2 x)^{5/2}-\frac{7882483}{128} (1-2 x)^{3/2}+\frac{15647317}{128} \sqrt{1-2 x}+\frac{9058973}{256 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-16936240 + 16881328*x + 8106616*x^2 + 6921432*x^3 + 5949090*x^4 + 4220622*x^5 + 2168775*x^6 + 697653*x^7 + 104247*x^8))/(143*(-1 + 2*x))","A",1
2070,1,55,105,0.0214795,"\int \frac{(2+3 x)^6 (3+5 x)}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(40095 x^7+243486 x^6+687420 x^5+1230120 x^4+1663632 x^3+2109792 x^2+4512448 x-4539904\right)}{143 (2 x-1)}","\frac{3645 (1-2 x)^{13/2}}{1664}-\frac{59049 (1-2 x)^{11/2}}{1408}+\frac{45549}{128} (1-2 x)^{9/2}-\frac{225855}{128} (1-2 x)^{7/2}+\frac{731619}{128} (1-2 x)^{5/2}-\frac{1692705}{128} (1-2 x)^{3/2}+\frac{3916031}{128} \sqrt{1-2 x}+\frac{1294139}{128 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-4539904 + 4512448*x + 2109792*x^2 + 1663632*x^3 + 1230120*x^4 + 687420*x^5 + 243486*x^6 + 40095*x^7))/(143*(-1 + 2*x))","A",1
2071,1,50,92,0.019385,"\int \frac{(2+3 x)^5 (3+5 x)}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^5*(3 + 5*x))/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(1215 x^6+6651 x^5+17055 x^4+28692 x^3+41012 x^2+91704 x-92760\right)}{11 (2 x-1)}","-\frac{1215}{704} (1-2 x)^{11/2}+\frac{117}{4} (1-2 x)^{9/2}-\frac{13905}{64} (1-2 x)^{7/2}+\frac{7497}{8} (1-2 x)^{5/2}-\frac{173215}{64} (1-2 x)^{3/2}+\frac{60025}{8} \sqrt{1-2 x}+\frac{184877}{64 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-92760 + 91704*x + 41012*x^2 + 28692*x^3 + 17055*x^4 + 6651*x^5 + 1215*x^6))/(11*(-1 + 2*x))","A",1
2072,1,45,79,0.0148272,"\int \frac{(2+3 x)^4 (3+5 x)}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(1575 x^5+7740 x^4+18288 x^3+31448 x^2+75776 x-77456\right)}{35 (2 x-1)}","\frac{45}{32} (1-2 x)^{9/2}-\frac{4671}{224} (1-2 x)^{7/2}+\frac{10773}{80} (1-2 x)^{5/2}-\frac{8281}{16} (1-2 x)^{3/2}+\frac{57281}{32} \sqrt{1-2 x}+\frac{26411}{32 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-77456 + 75776*x + 31448*x^2 + 18288*x^3 + 7740*x^4 + 1575*x^5))/(35*(-1 + 2*x))","A",1
2073,1,40,66,0.0131422,"\int \frac{(2+3 x)^3 (3+5 x)}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(675 x^4+2997 x^3+6987 x^2+19154 x-19994\right)}{35 (2 x-1)}","-\frac{135}{112} (1-2 x)^{7/2}+\frac{621}{40} (1-2 x)^{5/2}-\frac{357}{4} (1-2 x)^{3/2}+\frac{3283}{8} \sqrt{1-2 x}+\frac{3773}{16 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-19994 + 19154*x + 6987*x^2 + 2997*x^3 + 675*x^4))/(35*(-1 + 2*x))","A",1
2074,1,32,53,0.0118319,"\int \frac{(2+3 x)^2 (3+5 x)}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x))/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(9 x^3+38 x^2+132 x-144\right)}{2 x-1}","\frac{9}{8} (1-2 x)^{5/2}-\frac{103}{8} (1-2 x)^{3/2}+\frac{707}{8} \sqrt{1-2 x}+\frac{539}{8 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-144 + 132*x + 38*x^2 + 9*x^3))/(-1 + 2*x)","A",1
2075,1,27,38,0.0110173,"\int \frac{(2+3 x) (3+5 x)}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x))/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(5 x^2+29 x-35\right)}{2 x-1}","-\frac{5}{4} (1-2 x)^{3/2}+17 \sqrt{1-2 x}+\frac{77}{4 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-35 + 29*x + 5*x^2))/(-1 + 2*x)","A",1
2076,1,22,27,0.0084567,"\int \frac{3+5 x}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} (5 x-8)}{2 x-1}","\frac{5}{2} \sqrt{1-2 x}+\frac{11}{2 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-8 + 5*x))/(-1 + 2*x)","A",1
2077,1,48,41,0.0468627,"\int \frac{3+5 x}{(1-2 x)^{3/2} (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)),x]","\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{7 \sqrt{21}}-\frac{11 \sqrt{1-2 x}}{7 (2 x-1)}","\frac{11}{7 \sqrt{1-2 x}}+\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{7 \sqrt{21}}",1,"(-11*Sqrt[1 - 2*x])/(7*(-1 + 2*x)) + (2*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(7*Sqrt[21])","A",1
2078,1,56,61,0.0799036,"\int \frac{3+5 x}{(1-2 x)^{3/2} (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^2),x]","\frac{(-64 x-45) \sqrt{1-2 x}}{49 \left(6 x^2+x-2\right)}-\frac{64 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{49 \sqrt{21}}","\frac{64}{147 \sqrt{1-2 x}}+\frac{1}{21 \sqrt{1-2 x} (3 x+2)}-\frac{64 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{49 \sqrt{21}}",1,"((-45 - 64*x)*Sqrt[1 - 2*x])/(49*(-2 + x + 6*x^2)) - (64*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(49*Sqrt[21])","A",1
2079,1,67,83,0.1036424,"\int \frac{3+5 x}{(1-2 x)^{3/2} (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^3),x]","\frac{\sqrt{1-2 x} \left(-1170 x^2-1105 x-233\right)}{686 (2 x-1) (3 x+2)^2}-\frac{65}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","\frac{65}{343 \sqrt{1-2 x}}-\frac{65}{294 \sqrt{1-2 x} (3 x+2)}+\frac{1}{42 \sqrt{1-2 x} (3 x+2)^2}-\frac{65}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-233 - 1105*x - 1170*x^2))/(686*(-1 + 2*x)*(2 + 3*x)^2) - (65*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343","A",1
2080,1,70,101,0.1201261,"\int \frac{3+5 x}{(1-2 x)^{3/2} (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^4),x]","\frac{\sqrt{1-2 x} \left(-90 x^3-145 x^2-57 x-1\right)}{49 (2 x-1) (3 x+2)^3}-\frac{10 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{49 \sqrt{21}}","\frac{10}{147 \sqrt{1-2 x}}-\frac{5}{63 \sqrt{1-2 x} (3 x+2)}-\frac{1}{9 \sqrt{1-2 x} (3 x+2)^2}+\frac{1}{63 \sqrt{1-2 x} (3 x+2)^3}-\frac{10 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{49 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-1 - 57*x - 145*x^2 - 90*x^3))/(49*(-1 + 2*x)*(2 + 3*x)^3) - (10*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(49*Sqrt[21])","A",1
2081,1,75,121,0.1150643,"\int \frac{3+5 x}{(1-2 x)^{3/2} (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^5),x]","\frac{\sqrt{1-2 x} \left(-35370 x^4-80565 x^3-60391 x^2-10742 x+2566\right)}{19208 (2 x-1) (3 x+2)^4}-\frac{655 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{9604 \sqrt{21}}","\frac{655}{28812 \sqrt{1-2 x}}-\frac{655}{24696 \sqrt{1-2 x} (3 x+2)}-\frac{131}{3528 \sqrt{1-2 x} (3 x+2)^2}-\frac{131}{1764 \sqrt{1-2 x} (3 x+2)^3}+\frac{1}{84 \sqrt{1-2 x} (3 x+2)^4}-\frac{655 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{9604 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(2566 - 10742*x - 60391*x^2 - 80565*x^3 - 35370*x^4))/(19208*(-1 + 2*x)*(2 + 3*x)^4) - (655*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(9604*Sqrt[21])","A",1
2082,1,82,143,0.1324349,"\int \frac{3+5 x}{(1-2 x)^{3/2} (2+3 x)^6} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^6),x]","\frac{\sqrt{1-2 x} \left(-298890 x^5-880065 x^4-964197 x^3-430992 x^2-8774 x+32894\right)}{168070 (2 x-1) (3 x+2)^5}-\frac{123 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{16807}","\frac{123}{16807 \sqrt{1-2 x}}-\frac{41}{4802 \sqrt{1-2 x} (3 x+2)}-\frac{41}{3430 \sqrt{1-2 x} (3 x+2)^2}-\frac{41}{1715 \sqrt{1-2 x} (3 x+2)^3}-\frac{41}{735 \sqrt{1-2 x} (3 x+2)^4}+\frac{1}{105 \sqrt{1-2 x} (3 x+2)^5}-\frac{123 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{16807}",1,"(Sqrt[1 - 2*x]*(32894 - 8774*x - 430992*x^2 - 964197*x^3 - 880065*x^4 - 298890*x^5))/(168070*(-1 + 2*x)*(2 + 3*x)^5) - (123*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/16807","A",1
2083,1,55,105,0.0235195,"\int \frac{(2+3 x)^5 (3+5 x)^2}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^5*(3 + 5*x)^2)/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(200475 x^7+1201635 x^6+3350637 x^5+5928885 x^4+7945164 x^3+10015804 x^2+21370088 x-21493640\right)}{429 (2 x-1)}","\frac{6075 (1-2 x)^{13/2}}{1664}-\frac{97605 (1-2 x)^{11/2}}{1408}+\frac{74667}{128} (1-2 x)^{9/2}-\frac{367155}{128} (1-2 x)^{7/2}+\frac{1179381}{128} (1-2 x)^{5/2}-\frac{8117095}{384} (1-2 x)^{3/2}+\frac{6206585}{128} \sqrt{1-2 x}+\frac{2033647}{128 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-21493640 + 21370088*x + 10015804*x^2 + 7945164*x^3 + 5928885*x^4 + 3350637*x^5 + 1201635*x^6 + 200475*x^7))/(429*(-1 + 2*x))","A",1
2084,1,50,92,0.0259502,"\int \frac{(2+3 x)^4 (3+5 x)^2}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(212625 x^6+1146600 x^5+2899485 x^4+4819932 x^3+6831172 x^2+15214664 x-15380984\right)}{1155 (2 x-1)}","-\frac{2025}{704} (1-2 x)^{11/2}+\frac{1545}{32} (1-2 x)^{9/2}-\frac{159111}{448} (1-2 x)^{7/2}+\frac{121359}{80} (1-2 x)^{5/2}-\frac{832951}{192} (1-2 x)^{3/2}+\frac{381073}{32} \sqrt{1-2 x}+\frac{290521}{64 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-15380984 + 15214664*x + 6831172*x^2 + 4819932*x^3 + 2899485*x^4 + 1146600*x^5 + 212625*x^6))/(1155*(-1 + 2*x))","A",1
2085,1,45,79,0.0152529,"\int \frac{(2+3 x)^3 (3+5 x)^2}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^2)/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(7875 x^5+38025 x^4+88443 x^3+150253 x^2+359726 x-367286\right)}{105 (2 x-1)}","\frac{75}{32} (1-2 x)^{9/2}-\frac{7695}{224} (1-2 x)^{7/2}+\frac{17541}{80} (1-2 x)^{5/2}-\frac{39977}{48} (1-2 x)^{3/2}+\frac{91091}{32} \sqrt{1-2 x}+\frac{41503}{32 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-367286 + 359726*x + 150253*x^2 + 88443*x^3 + 38025*x^4 + 7875*x^5))/(105*(-1 + 2*x))","A",1
2086,1,40,66,0.0142297,"\int \frac{(2+3 x)^2 (3+5 x)^2}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(675 x^4+2934 x^3+6721 x^2+18230 x-18986\right)}{21 (2 x-1)}","-\frac{225}{112} (1-2 x)^{7/2}+\frac{51}{2} (1-2 x)^{5/2}-\frac{3467}{24} (1-2 x)^{3/2}+\frac{1309}{2} \sqrt{1-2 x}+\frac{5929}{16 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-18986 + 18230*x + 6721*x^2 + 2934*x^3 + 675*x^4))/(21*(-1 + 2*x))","A",1
2087,1,35,53,0.0127901,"\int \frac{(2+3 x) (3+5 x)^2}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^2)/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(45 x^3+185 x^2+631 x-685\right)}{3 (2 x-1)}","\frac{15}{8} (1-2 x)^{5/2}-\frac{505}{24} (1-2 x)^{3/2}+\frac{1133}{8} \sqrt{1-2 x}+\frac{847}{8 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-685 + 631*x + 185*x^2 + 45*x^3))/(3*(-1 + 2*x))","A",1
2088,1,30,40,0.0101937,"\int \frac{(3+5 x)^2}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(25 x^2+140 x-167\right)}{3 (2 x-1)}","-\frac{25}{12} (1-2 x)^{3/2}+\frac{55}{2} \sqrt{1-2 x}+\frac{121}{4 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-167 + 140*x + 25*x^2))/(3*(-1 + 2*x))","A",1
2089,1,53,54,0.057736,"\int \frac{(3+5 x)^2}{(1-2 x)^{3/2} (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^(3/2)*(2 + 3*x)),x]","\frac{\sqrt{1-2 x} (175 x-269)}{21 (2 x-1)}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{21 \sqrt{21}}","\frac{25}{6} \sqrt{1-2 x}+\frac{121}{14 \sqrt{1-2 x}}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{21 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-269 + 175*x))/(21*(-1 + 2*x)) - (2*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(21*Sqrt[21])","A",1
2090,1,56,68,0.0867665,"\int \frac{(3+5 x)^2}{(1-2 x)^{3/2} (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^(3/2)*(2 + 3*x)^2),x]","\frac{\sqrt{1-2 x} (-1091 x-725)}{147 \left(6 x^2+x-2\right)}+\frac{134 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{147 \sqrt{21}}","-\frac{1091 \sqrt{1-2 x}}{294 (3 x+2)}+\frac{121}{14 \sqrt{1-2 x} (3 x+2)}+\frac{134 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{147 \sqrt{21}}",1,"((-725 - 1091*x)*Sqrt[1 - 2*x])/(147*(-2 + x + 6*x^2)) + (134*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(147*Sqrt[21])","A",1
2091,1,65,88,0.1064247,"\int \frac{(3+5 x)^2}{(1-2 x)^{3/2} (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^(3/2)*(2 + 3*x)^3),x]","\frac{\sqrt{1-2 x} \left(-12270 x^2-17305 x-6067\right)}{2058 (2 x-1) (3 x+2)^2}-\frac{2045 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1029 \sqrt{21}}","-\frac{2045 \sqrt{1-2 x}}{2058 (3 x+2)}-\frac{545 \sqrt{1-2 x}}{147 (3 x+2)^2}+\frac{121}{14 \sqrt{1-2 x} (3 x+2)^2}-\frac{2045 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1029 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-6067 - 17305*x - 12270*x^2))/(2058*(-1 + 2*x)*(2 + 3*x)^2) - (2045*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(1029*Sqrt[21])","A",1
2092,1,70,108,0.1150812,"\int \frac{(3+5 x)^2}{(1-2 x)^{3/2} (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^(3/2)*(2 + 3*x)^4),x]","\frac{\sqrt{1-2 x} \left(-16290 x^3-26245 x^2-13747 x-2316\right)}{2058 (2 x-1) (3 x+2)^3}-\frac{905 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1029 \sqrt{21}}","-\frac{905 \sqrt{1-2 x}}{2058 (3 x+2)}-\frac{905 \sqrt{1-2 x}}{882 (3 x+2)^2}-\frac{467 \sqrt{1-2 x}}{126 (3 x+2)^3}+\frac{121}{14 \sqrt{1-2 x} (3 x+2)^3}-\frac{905 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1029 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-2316 - 13747*x - 26245*x^2 - 16290*x^3))/(2058*(-1 + 2*x)*(2 + 3*x)^3) - (905*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(1029*Sqrt[21])","A",1
2093,1,75,128,0.1136497,"\int \frac{(3+5 x)^2}{(1-2 x)^{3/2} (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^(3/2)*(2 + 3*x)^5),x]","\frac{\sqrt{1-2 x} \left(-493830 x^4-1124835 x^3-843169 x^2-218578 x-6486\right)}{57624 (2 x-1) (3 x+2)^4}-\frac{9145 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{28812 \sqrt{21}}","-\frac{9145 \sqrt{1-2 x}}{57624 (3 x+2)}-\frac{9145 \sqrt{1-2 x}}{24696 (3 x+2)^2}-\frac{1829 \sqrt{1-2 x}}{1764 (3 x+2)^3}-\frac{2179 \sqrt{1-2 x}}{588 (3 x+2)^4}+\frac{121}{14 \sqrt{1-2 x} (3 x+2)^4}-\frac{9145 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{28812 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-6486 - 218578*x - 843169*x^2 - 1124835*x^3 - 493830*x^4))/(57624*(-1 + 2*x)*(2 + 3*x)^4) - (9145*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(28812*Sqrt[21])","A",1
2094,1,55,105,0.0226359,"\int \frac{(2+3 x)^4 (3+5 x)^3}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(3898125 x^7+23058000 x^6+63495075 x^5+111095730 x^4+147527176 x^3+184884496 x^2+393552752 x-395714912\right)}{5005 (2 x-1)}","\frac{10125 (1-2 x)^{13/2}}{1664}-\frac{161325 (1-2 x)^{11/2}}{1408}+\frac{122385}{128} (1-2 x)^{9/2}-\frac{4177401}{896} (1-2 x)^{7/2}+\frac{9504551}{640} (1-2 x)^{5/2}-\frac{4324397}{128} (1-2 x)^{3/2}+\frac{9836211}{128} \sqrt{1-2 x}+\frac{3195731}{128 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-395714912 + 393552752*x + 184884496*x^2 + 147527176*x^3 + 111095730*x^4 + 63495075*x^5 + 23058000*x^6 + 3898125*x^7))/(5005*(-1 + 2*x))","A",1
2095,1,50,92,0.0193588,"\int \frac{(2+3 x)^3 (3+5 x)^3}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^3)/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(118125 x^6+627375 x^5+1564350 x^4+2569643 x^3+3611453 x^2+8012926 x-8096086\right)}{385 (2 x-1)}","-\frac{3375}{704} (1-2 x)^{11/2}+\frac{1275}{16} (1-2 x)^{9/2}-\frac{260055}{448} (1-2 x)^{7/2}+\frac{98209}{40} (1-2 x)^{5/2}-\frac{444983}{64} (1-2 x)^{3/2}+\frac{302379}{16} \sqrt{1-2 x}+\frac{456533}{64 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-8096086 + 8012926*x + 3611453*x^2 + 2569643*x^3 + 1564350*x^4 + 627375*x^5 + 118125*x^6))/(385*(-1 + 2*x))","A",1
2096,1,45,79,0.0147381,"\int \frac{(2+3 x)^2 (3+5 x)^3}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^3)/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(875 x^5+4150 x^4+9501 x^3+15948 x^2+37944 x-38700\right)}{7 (2 x-1)}","\frac{125}{32} (1-2 x)^{9/2}-\frac{12675}{224} (1-2 x)^{7/2}+\frac{5711}{16} (1-2 x)^{5/2}-\frac{21439}{16} (1-2 x)^{3/2}+\frac{144837}{32} \sqrt{1-2 x}+\frac{65219}{32 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-38700 + 37944*x + 15948*x^2 + 9501*x^3 + 4150*x^4 + 875*x^5))/(7*(-1 + 2*x))","A",1
2097,1,40,66,0.0131379,"\int \frac{(2+3 x) (3+5 x)^3}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^3)/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(375 x^4+1595 x^3+3590 x^2+9637 x-10015\right)}{7 (2 x-1)}","-\frac{375}{112} (1-2 x)^{7/2}+\frac{335}{8} (1-2 x)^{5/2}-\frac{935}{4} (1-2 x)^{3/2}+\frac{8349}{8} \sqrt{1-2 x}+\frac{9317}{16 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-10015 + 9637*x + 3590*x^2 + 1595*x^3 + 375*x^4))/(7*(-1 + 2*x))","A",1
2098,1,32,53,0.0104941,"\int \frac{(3+5 x)^3}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \left(25 x^3+100 x^2+335 x-362\right)}{2 x-1}","\frac{25}{8} (1-2 x)^{5/2}-\frac{275}{8} (1-2 x)^{3/2}+\frac{1815}{8} \sqrt{1-2 x}+\frac{1331}{8 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-362 + 335*x + 100*x^2 + 25*x^3))/(-1 + 2*x)","A",1
2099,1,58,67,0.0639391,"\int \frac{(3+5 x)^3}{(1-2 x)^{3/2} (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^(3/2)*(2 + 3*x)),x]","\frac{\sqrt{1-2 x} \left(875 x^2+4725 x-5576\right)}{63 (2 x-1)}+\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{63 \sqrt{21}}","-\frac{125}{36} (1-2 x)^{3/2}+\frac{400}{9} \sqrt{1-2 x}+\frac{1331}{28 \sqrt{1-2 x}}+\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{63 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-5576 + 4725*x + 875*x^2))/(63*(-1 + 2*x)) + (2*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(63*Sqrt[21])","A",1
2100,1,61,80,0.0845373,"\int \frac{(3+5 x)^3}{(1-2 x)^{3/2} (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^(3/2)*(2 + 3*x)^2),x]","\frac{\sqrt{1-2 x} \left(6125 x^2-4968 x-6035\right)}{147 \left(6 x^2+x-2\right)}-\frac{68 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{147 \sqrt{21}}","\frac{11 (5 x+3)^2}{7 \sqrt{1-2 x} (3 x+2)}+\frac{2 \sqrt{1-2 x} (2975 x+1978)}{147 (3 x+2)}-\frac{68 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{147 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-6035 - 4968*x + 6125*x^2))/(147*(-2 + x + 6*x^2)) - (68*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(147*Sqrt[21])","A",1
2101,1,65,80,0.1025891,"\int \frac{(3+5 x)^3}{(1-2 x)^{3/2} (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^(3/2)*(2 + 3*x)^3),x]","\frac{\sqrt{1-2 x} \left(-72280 x^2-95895 x-31811\right)}{2058 (2 x-1) (3 x+2)^2}+\frac{2245 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1029 \sqrt{21}}","\frac{11 (5 x+3)^2}{7 \sqrt{1-2 x} (3 x+2)^2}+\frac{5 \sqrt{1-2 x} (857 x+541)}{2058 (3 x+2)^2}+\frac{2245 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1029 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-31811 - 95895*x - 72280*x^2))/(2058*(-1 + 2*x)*(2 + 3*x)^2) + (2245*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(1029*Sqrt[21])","A",1
2102,1,70,100,0.1073747,"\int \frac{(3+5 x)^3}{(1-2 x)^{3/2} (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^(3/2)*(2 + 3*x)^4),x]","\frac{\sqrt{1-2 x} \left(-83880 x^3-178015 x^2-125154 x-29177\right)}{3087 (2 x-1) (3 x+2)^3}-\frac{9320 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{3087 \sqrt{21}}","\frac{11 (5 x+3)^2}{7 \sqrt{1-2 x} (3 x+2)^3}+\frac{2 \sqrt{1-2 x} (470 x+297)}{441 (3 x+2)^3}-\frac{4660 \sqrt{1-2 x}}{3087 (3 x+2)}-\frac{9320 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{3087 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-29177 - 125154*x - 178015*x^2 - 83880*x^3))/(3087*(-1 + 2*x)*(2 + 3*x)^3) - (9320*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(3087*Sqrt[21])","A",1
2103,1,75,120,0.1156052,"\int \frac{(3+5 x)^3}{(1-2 x)^{3/2} (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^(3/2)*(2 + 3*x)^5),x]","\frac{\sqrt{1-2 x} \left(-2115990 x^4-4819755 x^3-4093057 x^2-1534434 x-213998\right)}{57624 (2 x-1) (3 x+2)^4}-\frac{39185 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{28812 \sqrt{21}}","\frac{11 (5 x+3)^2}{7 \sqrt{1-2 x} (3 x+2)^4}+\frac{\sqrt{1-2 x} (3789 x+2395)}{1764 (3 x+2)^4}-\frac{39185 \sqrt{1-2 x}}{57624 (3 x+2)}-\frac{39185 \sqrt{1-2 x}}{24696 (3 x+2)^2}-\frac{39185 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{28812 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-213998 - 1534434*x - 4093057*x^2 - 4819755*x^3 - 2115990*x^4))/(57624*(-1 + 2*x)*(2 + 3*x)^4) - (39185*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(28812*Sqrt[21])","A",1
2104,1,73,106,0.091543,"\int \frac{(2+3 x)^6}{(1-2 x)^{3/2} (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)^(3/2)*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(3898125 x^5+19824750 x^4+48323385 x^3+85159800 x^2+207964053 x-213097384\right)}{240625 (2 x-1)}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{34375 \sqrt{55}}","\frac{81}{160} (1-2 x)^{9/2}-\frac{43011 (1-2 x)^{7/2}}{5600}+\frac{507627 (1-2 x)^{5/2}}{10000}-\frac{1997451 (1-2 x)^{3/2}}{10000}+\frac{70752609 \sqrt{1-2 x}}{100000}+\frac{117649}{352 \sqrt{1-2 x}}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{34375 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-213097384 + 207964053*x + 85159800*x^2 + 48323385*x^3 + 19824750*x^4 + 3898125*x^5))/(240625*(-1 + 2*x)) - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(34375*Sqrt[55])","A",1
2105,1,68,93,0.0774913,"\int \frac{(2+3 x)^5}{(1-2 x)^{3/2} (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^(3/2)*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(334125 x^4+1545885 x^3+3732300 x^2+10459053 x-10972384\right)}{48125 (2 x-1)}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{6875 \sqrt{55}}","-\frac{243}{560} (1-2 x)^{7/2}+\frac{5751 (1-2 x)^{5/2}}{1000}-\frac{17019}{500} (1-2 x)^{3/2}+\frac{806121 \sqrt{1-2 x}}{5000}+\frac{16807}{176 \sqrt{1-2 x}}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{6875 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-10972384 + 10459053*x + 3732300*x^2 + 1545885*x^3 + 334125*x^4))/(48125*(-1 + 2*x)) - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(6875*Sqrt[55])","A",1
2106,1,63,80,0.063734,"\int \frac{(2+3 x)^4}{(1-2 x)^{3/2} (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^(3/2)*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(4455 x^3+19800 x^2+71379 x-78712\right)}{1375 (2 x-1)}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1375 \sqrt{55}}","\frac{81}{200} (1-2 x)^{5/2}-\frac{963}{200} (1-2 x)^{3/2}+\frac{34371 \sqrt{1-2 x}}{1000}+\frac{2401}{88 \sqrt{1-2 x}}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1375 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-78712 + 71379*x + 19800*x^2 + 4455*x^3))/(1375*(-1 + 2*x)) - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(1375*Sqrt[55])","A",1
2107,1,58,67,0.0707724,"\int \frac{(2+3 x)^3}{(1-2 x)^{3/2} (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(495 x^2+3069 x-3802\right)}{275 (2 x-1)}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{275 \sqrt{55}}","-\frac{9}{20} (1-2 x)^{3/2}+\frac{162}{25} \sqrt{1-2 x}+\frac{343}{44 \sqrt{1-2 x}}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{275 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-3802 + 3069*x + 495*x^2))/(275*(-1 + 2*x)) - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(275*Sqrt[55])","A",1
2108,1,53,54,0.063726,"\int \frac{(2+3 x)^2}{(1-2 x)^{3/2} (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^(3/2)*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} (99 x-172)}{55 (2 x-1)}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{55 \sqrt{55}}","\frac{9}{10} \sqrt{1-2 x}+\frac{49}{22 \sqrt{1-2 x}}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{55 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-172 + 99*x))/(55*(-1 + 2*x)) - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(55*Sqrt[55])","A",1
2109,1,48,41,0.0466801,"\int \frac{2+3 x}{(1-2 x)^{3/2} (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^(3/2)*(3 + 5*x)),x]","-\frac{7 \sqrt{1-2 x}}{11 (2 x-1)}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{11 \sqrt{55}}","\frac{7}{11 \sqrt{1-2 x}}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{11 \sqrt{55}}",1,"(-7*Sqrt[1 - 2*x])/(11*(-1 + 2*x)) - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(11*Sqrt[55])","A",1
2110,1,50,43,0.0441334,"\int \frac{1}{(1-2 x)^{3/2} (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(3 + 5*x)),x]","-\frac{2 \sqrt{1-2 x}}{11 (2 x-1)}-\frac{2}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{2}{11 \sqrt{1-2 x}}-\frac{2}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(-2*Sqrt[1 - 2*x])/(11*(-1 + 2*x)) - (2*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/11","A",1
2111,1,79,72,0.09322,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x) (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)),x]","-\frac{4 \sqrt{1-2 x}}{77 (2 x-1)}+\frac{6}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{10}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{4}{77 \sqrt{1-2 x}}+\frac{6}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{10}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(-4*Sqrt[1 - 2*x])/(77*(-1 + 2*x)) + (6*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/7 - (10*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/11","A",1
2112,1,87,92,0.1381556,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} (174 x-115)}{539 \left(6 x^2+x-2\right)}+\frac{228}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{50}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{58}{539 \sqrt{1-2 x}}+\frac{3}{7 \sqrt{1-2 x} (3 x+2)}+\frac{228}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{50}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-115 + 174*x))/(539*(-2 + x + 6*x^2)) + (228*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/49 - (50*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/11","A",1
2113,1,96,112,0.1364873,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(45450 x^2+8625 x-16067\right)}{7546 (2 x-1) (3 x+2)^2}+\frac{8025}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{250}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{2525}{3773 \sqrt{1-2 x}}+\frac{225}{98 \sqrt{1-2 x} (3 x+2)}+\frac{3}{14 \sqrt{1-2 x} (3 x+2)^2}+\frac{8025}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{250}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-16067 + 8625*x + 45450*x^2))/(7546*(-1 + 2*x)*(2 + 3*x)^2) + (8025*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 - (250*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/11","A",1
2114,1,101,132,0.1469188,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^4 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(345330 x^3+299115 x^2-74556 x-80863\right)}{3773 (2 x-1) (3 x+2)^3}+\frac{40140}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{1250}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{12790}{3773 \sqrt{1-2 x}}+\frac{565}{49 \sqrt{1-2 x} (3 x+2)}+\frac{8}{7 \sqrt{1-2 x} (3 x+2)^2}+\frac{1}{7 \sqrt{1-2 x} (3 x+2)^3}+\frac{40140}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{1250}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(-80863 - 74556*x + 299115*x^2 + 345330*x^3))/(3773*(-1 + 2*x)*(2 + 3*x)^3) + (40140*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 - (1250*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/11","A",1
2115,1,76,140,0.1113984,"\int \frac{(2+3 x)^6}{(1-2 x)^{3/2} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)^(3/2)*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(55130625 x^5+293294925 x^4+795400155 x^3+2195407665 x^2-818846961 x-1143572552\right)}{2646875 \left(10 x^2+x-3\right)}-\frac{402 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{378125 \sqrt{55}}","\frac{7 (3 x+2)^5}{11 \sqrt{1-2 x} (5 x+3)}-\frac{36 \sqrt{1-2 x} (3 x+2)^4}{605 (5 x+3)}+\frac{14517 \sqrt{1-2 x} (3 x+2)^3}{21175}+\frac{217152 \sqrt{1-2 x} (3 x+2)^2}{75625}+\frac{9 \sqrt{1-2 x} (1688625 x+5065808)}{378125}-\frac{402 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{378125 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-1143572552 - 818846961*x + 2195407665*x^2 + 795400155*x^3 + 293294925*x^4 + 55130625*x^5))/(2646875*(-3 + x + 10*x^2)) - (402*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(378125*Sqrt[55])","A",1
2116,1,71,120,0.0863681,"\int \frac{(2+3 x)^5}{(1-2 x)^{3/2} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^(3/2)*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(735075 x^4+3789720 x^3+14309460 x^2-6264264 x-8186648\right)}{75625 \left(10 x^2+x-3\right)}-\frac{336 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{75625 \sqrt{55}}","\frac{7 (3 x+2)^4}{11 \sqrt{1-2 x} (5 x+3)}-\frac{36 \sqrt{1-2 x} (3 x+2)^3}{605 (5 x+3)}+\frac{10836 \sqrt{1-2 x} (3 x+2)^2}{15125}+\frac{504 \sqrt{1-2 x} (1500 x+4499)}{75625}-\frac{336 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{75625 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-8186648 - 6264264*x + 14309460*x^2 + 3789720*x^3 + 735075*x^4))/(75625*(-3 + x + 10*x^2)) - (336*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(75625*Sqrt[55])","A",1
2117,1,66,100,0.0993193,"\int \frac{(2+3 x)^4}{(1-2 x)^{3/2} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^(3/2)*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(16335 x^3+114345 x^2-68661 x-78832\right)}{3025 \left(10 x^2+x-3\right)}-\frac{54 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3025 \sqrt{55}}","\frac{7 (3 x+2)^3}{11 \sqrt{1-2 x} (5 x+3)}-\frac{36 \sqrt{1-2 x} (3 x+2)^2}{605 (5 x+3)}+\frac{27 \sqrt{1-2 x} (265 x+792)}{3025}-\frac{54 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3025 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-78832 - 68661*x + 114345*x^2 + 16335*x^3))/(3025*(-3 + x + 10*x^2)) - (54*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(3025*Sqrt[55])","A",1
2118,1,61,80,0.0799038,"\int \frac{(2+3 x)^3}{(1-2 x)^{3/2} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(16335 x^2-19806 x-17762\right)}{3025 \left(10 x^2+x-3\right)}-\frac{204 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3025 \sqrt{55}}","\frac{7 (3 x+2)^2}{11 \sqrt{1-2 x} (5 x+3)}+\frac{18 \sqrt{1-2 x} (935 x+559)}{3025 (5 x+3)}-\frac{204 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3025 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-17762 - 19806*x + 16335*x^2))/(3025*(-3 + x + 10*x^2)) - (204*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(3025*Sqrt[55])","A",1
2119,1,56,68,0.081449,"\int \frac{(2+3 x)^2}{(1-2 x)^{3/2} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^(3/2)*(3 + 5*x)^2),x]","\frac{(-1227 x-734) \sqrt{1-2 x}}{605 \left(10 x^2+x-3\right)}-\frac{138 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{605 \sqrt{55}}","-\frac{1227 \sqrt{1-2 x}}{1210 (5 x+3)}+\frac{49}{22 \sqrt{1-2 x} (5 x+3)}-\frac{138 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{605 \sqrt{55}}",1,"((-734 - 1227*x)*Sqrt[1 - 2*x])/(605*(-3 + x + 10*x^2)) - (138*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(605*Sqrt[55])","A",1
2120,1,56,61,0.0740776,"\int \frac{2+3 x}{(1-2 x)^{3/2} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^(3/2)*(3 + 5*x)^2),x]","\frac{(-72 x-41) \sqrt{1-2 x}}{121 \left(10 x^2+x-3\right)}-\frac{72 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{121 \sqrt{55}}","\frac{72}{605 \sqrt{1-2 x}}-\frac{1}{55 \sqrt{1-2 x} (5 x+3)}-\frac{72 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{121 \sqrt{55}}",1,"((-41 - 72*x)*Sqrt[1 - 2*x])/(121*(-3 + x + 10*x^2)) - (72*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(121*Sqrt[55])","A",1
2121,1,58,63,0.0795886,"\int \frac{1}{(1-2 x)^{3/2} (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(3 + 5*x)^2),x]","\frac{(-30 x-7) \sqrt{1-2 x}}{121 \left(10 x^2+x-3\right)}-\frac{6}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{6}{121 \sqrt{1-2 x}}-\frac{1}{11 \sqrt{1-2 x} (5 x+3)}-\frac{6}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"((-7 - 30*x)*Sqrt[1 - 2*x])/(121*(-3 + x + 10*x^2)) - (6*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/121","A",1
2122,1,87,92,0.1331466,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} (151-390 x)}{847 \left(10 x^2+x-3\right)}-\frac{18}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{300}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{78}{847 \sqrt{1-2 x}}-\frac{5}{11 \sqrt{1-2 x} (5 x+3)}-\frac{18}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{300}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"((151 - 390*x)*Sqrt[1 - 2*x])/(847*(-3 + x + 10*x^2)) - (18*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/7 + (300*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/121","A",1
2123,1,101,119,0.1302147,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-69660 x^2-9696 x+21955\right)}{5929 (2 x-1) \left(15 x^2+19 x+6\right)}-\frac{1314}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{3150}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{4644}{5929 \sqrt{1-2 x}}-\frac{340}{77 \sqrt{1-2 x} (5 x+3)}+\frac{3}{7 \sqrt{1-2 x} (3 x+2) (5 x+3)}-\frac{1314}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{3150}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(21955 - 9696*x - 69660*x^2))/(5929*(-1 + 2*x)*(6 + 19*x + 15*x^2)) - (1314*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/49 + (3150*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/121","A",1
2124,1,104,146,0.1616759,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-22127850 x^3-17711235 x^2+5050290 x+4664333\right)}{83006 (3 x+2)^2 \left(10 x^2+x-3\right)}-\frac{70065}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{24000}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{245865}{41503 \sqrt{1-2 x}}-\frac{36175}{1078 \sqrt{1-2 x} (5 x+3)}+\frac{165}{49 \sqrt{1-2 x} (3 x+2) (5 x+3)}+\frac{3}{14 \sqrt{1-2 x} (3 x+2)^2 (5 x+3)}-\frac{70065}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{24000}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(4664333 + 5050290*x - 17711235*x^2 - 22127850*x^3))/(83006*(2 + 3*x)^2*(-3 + x + 10*x^2)) - (70065*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 + (24000*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/121","A",1
2125,1,80,147,0.1555344,"\int \frac{(2+3 x)^6}{(1-2 x)^{3/2} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)^(3/2)*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(242574750 x^5+1423105200 x^4+5682717810 x^3+762244410 x^2-4150263077 x-1702670584\right)}{8318750 (2 x-1) (5 x+3)^2}-\frac{33873 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{4159375 \sqrt{55}}","\frac{7 (3 x+2)^5}{11 \sqrt{1-2 x} (5 x+3)^2}-\frac{71 \sqrt{1-2 x} (3 x+2)^4}{1210 (5 x+3)^2}-\frac{2721 \sqrt{1-2 x} (3 x+2)^3}{66550 (5 x+3)}+\frac{377748 \sqrt{1-2 x} (3 x+2)^2}{831875}+\frac{63 \sqrt{1-2 x} (831375 x+2492512)}{8318750}-\frac{33873 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{4159375 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-1702670584 - 4150263077*x + 762244410*x^2 + 5682717810*x^3 + 1423105200*x^4 + 242574750*x^5))/(8318750*(-1 + 2*x)*(3 + 5*x)^2) - (33873*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(4159375*Sqrt[55])","A",1
2126,1,75,127,0.1086642,"\int \frac{(2+3 x)^5}{(1-2 x)^{3/2} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^(3/2)*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(5390550 x^4+42046290 x^3-764310 x^2-41668993 x-16342856\right)}{332750 (2 x-1) (5 x+3)^2}-\frac{4557 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{166375 \sqrt{55}}","\frac{7 (3 x+2)^4}{11 \sqrt{1-2 x} (5 x+3)^2}-\frac{71 \sqrt{1-2 x} (3 x+2)^3}{1210 (5 x+3)^2}-\frac{1344 \sqrt{1-2 x} (3 x+2)^2}{33275 (5 x+3)}+\frac{441 \sqrt{1-2 x} (1125 x+3344)}{332750}-\frac{4557 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{166375 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-16342856 - 41668993*x - 764310*x^2 + 42046290*x^3 + 5390550*x^4))/(332750*(-1 + 2*x)*(3 + 5*x)^2) - (4557*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(166375*Sqrt[55])","A",1
2127,1,70,107,0.1135227,"\int \frac{(2+3 x)^4}{(1-2 x)^{3/2} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^(3/2)*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(215622 x^3-149298 x^2-411911 x-146824\right)}{13310 (2 x-1) (5 x+3)^2}-\frac{111 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331 \sqrt{55}}","\frac{7 (3 x+2)^3}{11 \sqrt{1-2 x} (5 x+3)^2}-\frac{71 \sqrt{1-2 x} (3 x+2)^2}{1210 (5 x+3)^2}+\frac{9 \sqrt{1-2 x} (5093 x+3044)}{13310 (5 x+3)}-\frac{111 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-146824 - 411911*x - 149298*x^2 + 215622*x^3))/(13310*(-1 + 2*x)*(3 + 5*x)^2) - (111*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(1331*Sqrt[55])","A",1
2128,1,65,80,0.0965001,"\int \frac{(2+3 x)^3}{(1-2 x)^{3/2} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(-430800 x^2-514727 x-153724\right)}{66550 (2 x-1) (5 x+3)^2}-\frac{7143 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{33275 \sqrt{55}}","\frac{7 (3 x+2)^2}{11 \sqrt{1-2 x} (5 x+3)^2}-\frac{\sqrt{1-2 x} (24825 x+15676)}{66550 (5 x+3)^2}-\frac{7143 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{33275 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-153724 - 514727*x - 430800*x^2))/(66550*(-1 + 2*x)*(3 + 5*x)^2) - (7143*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(33275*Sqrt[55])","A",1
2129,1,65,88,0.1021986,"\int \frac{(2+3 x)^2}{(1-2 x)^{3/2} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^(3/2)*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(-25890 x^2-29561 x-8392\right)}{13310 (2 x-1) (5 x+3)^2}-\frac{2589 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{6655 \sqrt{55}}","-\frac{2589 \sqrt{1-2 x}}{13310 (5 x+3)}-\frac{613 \sqrt{1-2 x}}{605 (5 x+3)^2}+\frac{49}{22 \sqrt{1-2 x} (5 x+3)^2}-\frac{2589 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{6655 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-8392 - 29561*x - 25890*x^2))/(13310*(-1 + 2*x)*(3 + 5*x)^2) - (2589*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(6655*Sqrt[55])","A",1
2130,1,65,81,0.0998098,"\int \frac{2+3 x}{(1-2 x)^{3/2} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^(3/2)*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(-2130 x^2-1775 x-274\right)}{2662 (2 x-1) (5 x+3)^2}-\frac{213 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331 \sqrt{55}}","\frac{213}{6655 \sqrt{1-2 x}}-\frac{71}{1210 \sqrt{1-2 x} (5 x+3)}-\frac{1}{110 \sqrt{1-2 x} (5 x+3)^2}-\frac{213 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-274 - 1775*x - 2130*x^2))/(2662*(-1 + 2*x)*(3 + 5*x)^2) - (213*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(1331*Sqrt[55])","A",1
2131,1,67,83,0.0949499,"\int \frac{1}{(1-2 x)^{3/2} (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(-750 x^2-625 x+16\right)}{2662 (2 x-1) (5 x+3)^2}-\frac{15 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}","\frac{15}{1331 \sqrt{1-2 x}}-\frac{5}{242 \sqrt{1-2 x} (5 x+3)}-\frac{1}{22 \sqrt{1-2 x} (5 x+3)^2}-\frac{15 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}",1,"(Sqrt[1 - 2*x]*(16 - 625*x - 750*x^2))/(2662*(-1 + 2*x)*(3 + 5*x)^2) - (15*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1331","A",1
2132,1,96,112,0.1395857,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(102450 x^2+5515 x-29338\right)}{18634 (2 x-1) (5 x+3)^2}+\frac{54}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{9975 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}","-\frac{2049}{9317 \sqrt{1-2 x}}+\frac{305}{242 \sqrt{1-2 x} (5 x+3)}-\frac{5}{22 \sqrt{1-2 x} (5 x+3)^2}+\frac{54}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{9975 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}",1,"(Sqrt[1 - 2*x]*(-29338 + 5515*x + 102450*x^2))/(18634*(-1 + 2*x)*(3 + 5*x)^2) + (54*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/7 - (9975*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1331","A",1
2133,1,104,139,0.1513786,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(33745050 x^3+24742935 x^2-8019782 x-6400750\right)}{130438 (5 x+3)^2 \left(6 x^2+x-2\right)}+\frac{5832}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{153825 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}","-\frac{224967}{65219 \sqrt{1-2 x}}+\frac{33115}{1694 \sqrt{1-2 x} (5 x+3)}-\frac{505}{154 \sqrt{1-2 x} (5 x+3)^2}+\frac{3}{7 \sqrt{1-2 x} (3 x+2) (5 x+3)^2}+\frac{5832}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{153825 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}",1,"(Sqrt[1 - 2*x]*(-6400750 - 8019782*x + 24742935*x^2 + 33745050*x^3))/(130438*(3 + 5*x)^2*(-2 + x + 6*x^2)) + (5832*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/49 - (153825*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1331","A",1
2134,1,111,166,0.165245,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(7194325500 x^4+10073172600 x^3+1810042755 x^2-2503057145 x-909821467\right)}{913066 (2 x-1) \left(15 x^2+19 x+6\right)^2}+\frac{414315}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{1561125 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}","-\frac{15987390}{456533 \sqrt{1-2 x}}+\frac{1176400}{5929 \sqrt{1-2 x} (5 x+3)}-\frac{35825}{1078 \sqrt{1-2 x} (5 x+3)^2}+\frac{435}{98 \sqrt{1-2 x} (3 x+2) (5 x+3)^2}+\frac{3}{14 \sqrt{1-2 x} (3 x+2)^2 (5 x+3)^2}+\frac{414315}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{1561125 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}",1,"(Sqrt[1 - 2*x]*(-909821467 - 2503057145*x + 1810042755*x^2 + 10073172600*x^3 + 7194325500*x^4))/(913066*(-1 + 2*x)*(6 + 19*x + 15*x^2)^2) + (414315*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 - (1561125*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1331","A",1
2135,1,50,92,0.0198015,"\int \frac{(2+3 x)^5 (3+5 x)}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^5*(3 + 5*x))/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \left(-2835 x^6-16767 x^5-49653 x^4-114084 x^3-412812 x^2+844104 x-280696\right)}{21 (2 x-1)^2}","-\frac{135}{64} (1-2 x)^{9/2}+\frac{1053}{28} (1-2 x)^{7/2}-\frac{19467}{64} (1-2 x)^{5/2}+\frac{12495}{8} (1-2 x)^{3/2}-\frac{519645}{64} \sqrt{1-2 x}-\frac{60025}{8 \sqrt{1-2 x}}+\frac{184877}{192 (1-2 x)^{3/2}}",1,"(Sqrt[1 - 2*x]*(-280696 + 844104*x - 412812*x^2 - 114084*x^3 - 49653*x^4 - 16767*x^5 - 2835*x^6))/(21*(-1 + 2*x)^2)","A",1
2136,1,45,79,0.0148049,"\int \frac{(2+3 x)^4 (3+5 x)}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \left(-6075 x^5-33858 x^4-105624 x^3-435312 x^2+909264 x-301408\right)}{105 (2 x-1)^2}","\frac{405}{224} (1-2 x)^{7/2}-\frac{4671}{160} (1-2 x)^{5/2}+\frac{3591}{16} (1-2 x)^{3/2}-\frac{24843}{16} \sqrt{1-2 x}-\frac{57281}{32 \sqrt{1-2 x}}+\frac{26411}{96 (1-2 x)^{3/2}}",1,"(Sqrt[1 - 2*x]*(-301408 + 909264*x - 435312*x^2 - 105624*x^3 - 33858*x^4 - 6075*x^5))/(105*(-1 + 2*x)^2)","A",1
2137,1,40,66,0.0132805,"\int \frac{(2+3 x)^3 (3+5 x)}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \left(-81 x^4-459 x^3-2403 x^2+5250 x-1726\right)}{3 (2 x-1)^2}","-\frac{27}{16} (1-2 x)^{5/2}+\frac{207}{8} (1-2 x)^{3/2}-\frac{1071}{4} \sqrt{1-2 x}-\frac{3283}{8 \sqrt{1-2 x}}+\frac{3773}{48 (1-2 x)^{3/2}}",1,"(Sqrt[1 - 2*x]*(-1726 + 5250*x - 2403*x^2 - 459*x^3 - 81*x^4))/(3*(-1 + 2*x)^2)","A",1
2138,1,35,53,0.0123478,"\int \frac{(2+3 x)^2 (3+5 x)}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x))/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \left(-45 x^3-396 x^2+960 x-308\right)}{3 (2 x-1)^2}","\frac{15}{8} (1-2 x)^{3/2}-\frac{309}{8} \sqrt{1-2 x}-\frac{707}{8 \sqrt{1-2 x}}+\frac{539}{24 (1-2 x)^{3/2}}",1,"(Sqrt[1 - 2*x]*(-308 + 960*x - 396*x^2 - 45*x^3))/(3*(-1 + 2*x)^2)","A",1
2139,1,30,38,0.0115343,"\int \frac{(2+3 x) (3+5 x)}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x))/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \left(-45 x^2+147 x-43\right)}{3 (2 x-1)^2}","-\frac{15}{4} \sqrt{1-2 x}-\frac{17}{\sqrt{1-2 x}}+\frac{77}{12 (1-2 x)^{3/2}}",1,"(Sqrt[1 - 2*x]*(-43 + 147*x - 45*x^2))/(3*(-1 + 2*x)^2)","A",1
2140,1,25,27,0.0098085,"\int \frac{3+5 x}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} (15 x-2)}{3 (2 x-1)^2}","\frac{11}{6 (1-2 x)^{3/2}}-\frac{5}{2 \sqrt{1-2 x}}",1,"(Sqrt[1 - 2*x]*(-2 + 15*x))/(3*(-1 + 2*x)^2)","A",1
2141,1,55,56,0.056823,"\int \frac{3+5 x}{(1-2 x)^{5/2} (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)),x]","\frac{\sqrt{1-2 x} (12 x+71)}{147 (2 x-1)^2}+\frac{2}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","-\frac{2}{49 \sqrt{1-2 x}}+\frac{11}{21 (1-2 x)^{3/2}}+\frac{2}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(71 + 12*x))/(147*(-1 + 2*x)^2) + (2*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/49","A",1
2142,1,67,76,0.0993884,"\int \frac{3+5 x}{(1-2 x)^{5/2} (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^2),x]","\frac{\sqrt{1-2 x} \left(-1080 x^2+240 x+689\right)}{1029 (2 x-1)^2 (3 x+2)}-\frac{60}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","\frac{60}{343 \sqrt{1-2 x}}+\frac{1}{21 (1-2 x)^{3/2} (3 x+2)}+\frac{20}{147 (1-2 x)^{3/2}}-\frac{60}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(689 + 240*x - 1080*x^2))/(1029*(-1 + 2*x)^2*(2 + 3*x)) - (60*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343","A",1
2143,1,68,96,0.1089714,"\int \frac{3+5 x}{(1-2 x)^{5/2} (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^3),x]","\frac{\sqrt{1-2 x} \left(-4860 x^3-2160 x^2+2277 x+1087\right)}{2058 \left(6 x^2+x-2\right)^2}-\frac{45}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","\frac{45}{343 \sqrt{1-2 x}}-\frac{3}{14 (1-2 x)^{3/2} (3 x+2)}+\frac{5}{49 (1-2 x)^{3/2}}+\frac{1}{42 (1-2 x)^{3/2} (3 x+2)^2}-\frac{45}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(1087 + 2277*x - 2160*x^2 - 4860*x^3))/(2058*(-2 + x + 6*x^2)^2) - (45*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343","A",1
2144,1,77,116,0.1099648,"\int \frac{3+5 x}{(1-2 x)^{5/2} (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]","\frac{\sqrt{1-2 x} \left(-25920 x^4-28800 x^3+4464 x^2+11280 x+2237\right)}{7203 (2 x-1)^2 (3 x+2)^3}-\frac{160 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{2401}","\frac{160}{2401 \sqrt{1-2 x}}-\frac{16}{147 (1-2 x)^{3/2} (3 x+2)}+\frac{160}{3087 (1-2 x)^{3/2}}-\frac{16}{147 (1-2 x)^{3/2} (3 x+2)^2}+\frac{1}{63 (1-2 x)^{3/2} (3 x+2)^3}-\frac{160 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{2401}",1,"(Sqrt[1 - 2*x]*(2237 + 11280*x + 4464*x^2 - 28800*x^3 - 25920*x^4))/(7203*(-1 + 2*x)^2*(2 + 3*x)^3) - (160*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/2401","A",1
2145,1,82,136,0.1287572,"\int \frac{3+5 x}{(1-2 x)^{5/2} (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^5),x]","\frac{\sqrt{1-2 x} \left(-1880820 x^5-3343680 x^4-1069281 x^3+1034451 x^2+611202 x+48490\right)}{403368 (2 x-1)^2 (3 x+2)^4}-\frac{1935 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{67228}","\frac{1935}{67228 \sqrt{1-2 x}}-\frac{129}{2744 (1-2 x)^{3/2} (3 x+2)}+\frac{215}{9604 (1-2 x)^{3/2}}-\frac{129}{2744 (1-2 x)^{3/2} (3 x+2)^2}-\frac{43}{588 (1-2 x)^{3/2} (3 x+2)^3}+\frac{1}{84 (1-2 x)^{3/2} (3 x+2)^4}-\frac{1935 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{67228}",1,"(Sqrt[1 - 2*x]*(48490 + 611202*x + 1034451*x^2 - 1069281*x^3 - 3343680*x^4 - 1880820*x^5))/(403368*(-1 + 2*x)^2*(2 + 3*x)^4) - (1935*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/67228","A",1
2146,1,55,105,0.0239224,"\int \frac{(2+3 x)^5 (3+5 x)^2}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^5*(3 + 5*x)^2)/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \left(-127575 x^7-806085 x^6-2456001 x^5-5121279 x^4-9702012 x^3-32450916 x^2+65622552 x-21852008\right)}{231 (2 x-1)^2}","\frac{6075 (1-2 x)^{11/2}}{1408}-\frac{10845}{128} (1-2 x)^{9/2}+\frac{672003}{896} (1-2 x)^{7/2}-\frac{514017}{128} (1-2 x)^{5/2}+\frac{1965635}{128} (1-2 x)^{3/2}-\frac{8117095}{128} \sqrt{1-2 x}-\frac{6206585}{128 \sqrt{1-2 x}}+\frac{2033647}{384 (1-2 x)^{3/2}}",1,"(Sqrt[1 - 2*x]*(-21852008 + 65622552*x - 32450916*x^2 - 9702012*x^3 - 5121279*x^4 - 2456001*x^5 - 806085*x^6 - 127575*x^7))/(231*(-1 + 2*x)^2)","A",1
2147,1,50,92,0.0266282,"\int \frac{(2+3 x)^4 (3+5 x)^2}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \left(-23625 x^6-137700 x^5-402489 x^4-915492 x^3-3294996 x^2+6731112 x-2238664\right)}{105 (2 x-1)^2}","-\frac{225}{64} (1-2 x)^{9/2}+\frac{13905}{224} (1-2 x)^{7/2}-\frac{159111}{320} (1-2 x)^{5/2}+\frac{40453}{16} (1-2 x)^{3/2}-\frac{832951}{64} \sqrt{1-2 x}-\frac{381073}{32 \sqrt{1-2 x}}+\frac{290521}{192 (1-2 x)^{3/2}}",1,"(Sqrt[1 - 2*x]*(-2238664 + 6731112*x - 3294996*x^2 - 915492*x^3 - 402489*x^4 - 137700*x^5 - 23625*x^6))/(105*(-1 + 2*x)^2)","A",1
2148,1,45,79,0.0155532,"\int \frac{(2+3 x)^3 (3+5 x)^2}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^2)/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \left(-2025 x^5-11097 x^4-34137 x^3-139497 x^2+290838 x-96442\right)}{21 (2 x-1)^2}","\frac{675}{224} (1-2 x)^{7/2}-\frac{1539}{32} (1-2 x)^{5/2}+\frac{5847}{16} (1-2 x)^{3/2}-\frac{39977}{16} \sqrt{1-2 x}-\frac{91091}{32 \sqrt{1-2 x}}+\frac{41503}{96 (1-2 x)^{3/2}}",1,"(Sqrt[1 - 2*x]*(-96442 + 290838*x - 139497*x^2 - 34137*x^3 - 11097*x^4 - 2025*x^5))/(21*(-1 + 2*x)^2)","A",1
2149,1,40,66,0.0147938,"\int \frac{(2+3 x)^2 (3+5 x)^2}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \left(-135 x^4-750 x^3-3873 x^2+8430 x-2774\right)}{3 (2 x-1)^2}","-\frac{45}{16} (1-2 x)^{5/2}+\frac{85}{2} (1-2 x)^{3/2}-\frac{3467}{8} \sqrt{1-2 x}-\frac{1309}{2 \sqrt{1-2 x}}+\frac{5929}{48 (1-2 x)^{3/2}}",1,"(Sqrt[1 - 2*x]*(-2774 + 8430*x - 3873*x^2 - 750*x^3 - 135*x^4))/(3*(-1 + 2*x)^2)","A",1
2150,1,35,53,0.0123541,"\int \frac{(2+3 x) (3+5 x)^2}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^2)/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \left(-75 x^3-645 x^2+1551 x-499\right)}{3 (2 x-1)^2}","\frac{25}{8} (1-2 x)^{3/2}-\frac{505}{8} \sqrt{1-2 x}-\frac{1133}{8 \sqrt{1-2 x}}+\frac{847}{24 (1-2 x)^{3/2}}",1,"(Sqrt[1 - 2*x]*(-499 + 1551*x - 645*x^2 - 75*x^3))/(3*(-1 + 2*x)^2)","A",1
2151,1,30,40,0.0102423,"\int \frac{(3+5 x)^2}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \left(-75 x^2+240 x-71\right)}{3 (2 x-1)^2}","-\frac{25}{4} \sqrt{1-2 x}-\frac{55}{2 \sqrt{1-2 x}}+\frac{121}{12 (1-2 x)^{3/2}}",1,"(Sqrt[1 - 2*x]*(-71 + 240*x - 75*x^2))/(3*(-1 + 2*x)^2)","A",1
2152,1,53,54,0.0562966,"\int \frac{(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)),x]","\frac{11 \sqrt{1-2 x} (111 x-17)}{147 (2 x-1)^2}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{49 \sqrt{21}}","-\frac{407}{98 \sqrt{1-2 x}}+\frac{121}{42 (1-2 x)^{3/2}}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{49 \sqrt{21}}",1,"(11*Sqrt[1 - 2*x]*(-17 + 111*x))/(147*(-1 + 2*x)^2) - (2*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(49*Sqrt[21])","A",1
2153,1,65,81,0.0997291,"\int \frac{(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)^2),x]","\frac{\sqrt{1-2 x} \left(780 x^2+2685 x+1427\right)}{1029 (2 x-1)^2 (3 x+2)}+\frac{130 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{343 \sqrt{21}}","-\frac{130}{1029 \sqrt{1-2 x}}-\frac{365}{294 \sqrt{1-2 x} (3 x+2)}+\frac{121}{42 (1-2 x)^{3/2} (3 x+2)}+\frac{130 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{343 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(1427 + 2685*x + 780*x^2))/(1029*(-1 + 2*x)^2*(2 + 3*x)) + (130*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(343*Sqrt[21])","A",1
2154,1,68,103,0.1140488,"\int \frac{(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)^3),x]","\frac{\sqrt{1-2 x} \left(-9180 x^3-4080 x^2+7731 x+4231\right)}{2058 \left(6 x^2+x-2\right)^2}-\frac{85}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)","\frac{85}{343 \sqrt{1-2 x}}-\frac{85}{294 \sqrt{1-2 x} (3 x+2)}-\frac{26}{21 \sqrt{1-2 x} (3 x+2)^2}+\frac{121}{42 (1-2 x)^{3/2} (3 x+2)^2}-\frac{85}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(4231 + 7731*x - 4080*x^2 - 9180*x^3))/(2058*(-2 + x + 6*x^2)^2) - (85*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343","A",1
2155,1,75,121,0.1177549,"\int \frac{(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]","\frac{\sqrt{1-2 x} \left(-152820 x^4-169800 x^3+26319 x^2+83655 x+23872\right)}{14406 (2 x-1)^2 (3 x+2)^3}-\frac{1415 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{2401 \sqrt{21}}","\frac{1415}{7203 \sqrt{1-2 x}}-\frac{1415}{6174 \sqrt{1-2 x} (3 x+2)}-\frac{283}{882 \sqrt{1-2 x} (3 x+2)^2}-\frac{1091}{882 \sqrt{1-2 x} (3 x+2)^3}+\frac{121}{42 (1-2 x)^{3/2} (3 x+2)^3}-\frac{1415 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{2401 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(23872 + 83655*x + 26319*x^2 - 169800*x^3 - 152820*x^4))/(14406*(-1 + 2*x)^2*(2 + 3*x)^3) - (1415*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(2401*Sqrt[21])","A",1
2156,1,80,141,0.137379,"\int \frac{(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)^5),x]","\frac{\sqrt{1-2 x} \left(-6630660 x^5-11787840 x^4-3769653 x^3+3646863 x^2+2528226 x+401410\right)}{403368 (2 x-1)^2 (3 x+2)^4}-\frac{20465 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{67228 \sqrt{21}}","\frac{20465}{201684 \sqrt{1-2 x}}-\frac{20465}{172872 \sqrt{1-2 x} (3 x+2)}-\frac{4093}{24696 \sqrt{1-2 x} (3 x+2)^2}-\frac{4093}{12348 \sqrt{1-2 x} (3 x+2)^3}-\frac{727}{588 \sqrt{1-2 x} (3 x+2)^4}+\frac{121}{42 (1-2 x)^{3/2} (3 x+2)^4}-\frac{20465 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{67228 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(401410 + 2528226*x + 3646863*x^2 - 3769653*x^3 - 11787840*x^4 - 6630660*x^5))/(403368*(-1 + 2*x)^2*(2 + 3*x)^4) - (20465*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(67228*Sqrt[21])","A",1
2157,1,60,118,0.0244603,"\int \frac{(2+3 x)^5 (3+5 x)^3}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^5*(3 + 5*x)^3)/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \left(-7016625 x^8-47670525 x^7-153878760 x^6-324478899 x^5-540496701 x^4-905206628 x^3-2892917004 x^2+5818266408 x-1938557272\right)}{3003 (2 x-1)^2}","-\frac{30375 (1-2 x)^{13/2}}{3328}+\frac{277425 (1-2 x)^{11/2}}{1408}-\frac{246315}{128} (1-2 x)^{9/2}+\frac{10121229}{896} (1-2 x)^{7/2}-\frac{2887773}{64} (1-2 x)^{5/2}+\frac{52725715}{384} (1-2 x)^{3/2}-\frac{60160485}{128} \sqrt{1-2 x}-\frac{39220335}{128 \sqrt{1-2 x}}+\frac{22370117}{768 (1-2 x)^{3/2}}",1,"(Sqrt[1 - 2*x]*(-1938557272 + 5818266408*x - 2892917004*x^2 - 905206628*x^3 - 540496701*x^4 - 324478899*x^5 - 153878760*x^6 - 47670525*x^7 - 7016625*x^8))/(3003*(-1 + 2*x)^2)","A",1
2158,1,55,105,0.0240023,"\int \frac{(2+3 x)^4 (3+5 x)^3}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \left(-1063125 x^7-6630750 x^6-19961775 x^5-41201532 x^4-77493296 x^3-258342648 x^2+522173856 x-173891632\right)}{1155 (2 x-1)^2}","\frac{10125 (1-2 x)^{11/2}}{1408}-\frac{17925}{128} (1-2 x)^{9/2}+\frac{1101465}{896} (1-2 x)^{7/2}-\frac{4177401}{640} (1-2 x)^{5/2}+\frac{9504551}{384} (1-2 x)^{3/2}-\frac{12973191}{128} \sqrt{1-2 x}-\frac{9836211}{128 \sqrt{1-2 x}}+\frac{3195731}{384 (1-2 x)^{3/2}}",1,"(Sqrt[1 - 2*x]*(-173891632 + 522173856*x - 258342648*x^2 - 77493296*x^3 - 41201532*x^4 - 19961775*x^5 - 6630750*x^6 - 1063125*x^7))/(1155*(-1 + 2*x)^2)","A",1
2159,1,50,92,0.0202245,"\int \frac{(2+3 x)^3 (3+5 x)^3}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^3)/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \left(-7875 x^6-45225 x^5-130464 x^4-293785 x^3-1051833 x^2+2146758 x-714074\right)}{21 (2 x-1)^2}","-\frac{375}{64} (1-2 x)^{9/2}+\frac{11475}{112} (1-2 x)^{7/2}-\frac{52011}{64} (1-2 x)^{5/2}+\frac{98209}{24} (1-2 x)^{3/2}-\frac{1334949}{64} \sqrt{1-2 x}-\frac{302379}{16 \sqrt{1-2 x}}+\frac{456533}{192 (1-2 x)^{3/2}}",1,"(Sqrt[1 - 2*x]*(-714074 + 2146758*x - 1051833*x^2 - 293785*x^3 - 130464*x^4 - 45225*x^5 - 7875*x^6))/(21*(-1 + 2*x)^2)","A",1
2160,1,45,79,0.0156581,"\int \frac{(2+3 x)^2 (3+5 x)^3}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^3)/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \left(-3375 x^5-18180 x^4-55145 x^3-223458 x^2+465060 x-154264\right)}{21 (2 x-1)^2}","\frac{1125}{224} (1-2 x)^{7/2}-\frac{2535}{32} (1-2 x)^{5/2}+\frac{28555}{48} (1-2 x)^{3/2}-\frac{64317}{16} \sqrt{1-2 x}-\frac{144837}{32 \sqrt{1-2 x}}+\frac{65219}{96 (1-2 x)^{3/2}}",1,"(Sqrt[1 - 2*x]*(-154264 + 465060*x - 223458*x^2 - 55145*x^3 - 18180*x^4 - 3375*x^5))/(21*(-1 + 2*x)^2)","A",1
2161,1,40,66,0.0142182,"\int \frac{(2+3 x) (3+5 x)^3}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^3)/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \left(-225 x^4-1225 x^3-6240 x^2+13533 x-4457\right)}{3 (2 x-1)^2}","-\frac{75}{16} (1-2 x)^{5/2}+\frac{1675}{24} (1-2 x)^{3/2}-\frac{2805}{4} \sqrt{1-2 x}-\frac{8349}{8 \sqrt{1-2 x}}+\frac{9317}{48 (1-2 x)^{3/2}}",1,"(Sqrt[1 - 2*x]*(-4457 + 13533*x - 6240*x^2 - 1225*x^3 - 225*x^4))/(3*(-1 + 2*x)^2)","A",1
2162,1,35,53,0.0111723,"\int \frac{(3+5 x)^3}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \left(-125 x^3-1050 x^2+2505 x-808\right)}{3 (2 x-1)^2}","\frac{125}{24} (1-2 x)^{3/2}-\frac{825}{8} \sqrt{1-2 x}-\frac{1815}{8 \sqrt{1-2 x}}+\frac{1331}{24 (1-2 x)^{3/2}}",1,"(Sqrt[1 - 2*x]*(-808 + 2505*x - 1050*x^2 - 125*x^3))/(3*(-1 + 2*x)^2)","A",1
2163,1,58,67,0.0705688,"\int \frac{(3+5 x)^3}{(1-2 x)^{5/2} (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)),x]","\frac{\sqrt{1-2 x} \left(-6125 x^2+19193 x-5736\right)}{147 (2 x-1)^2}+\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{147 \sqrt{21}}","-\frac{125}{12} \sqrt{1-2 x}-\frac{2178}{49 \sqrt{1-2 x}}+\frac{1331}{84 (1-2 x)^{3/2}}+\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{147 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-5736 + 19193*x - 6125*x^2))/(147*(-1 + 2*x)^2) + (2*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(147*Sqrt[21])","A",1
2164,1,65,80,0.0986812,"\int \frac{(3+5 x)^3}{(1-2 x)^{5/2} (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)^2),x]","\frac{\sqrt{1-2 x} \left(42475 x^2+21050 x-4839\right)}{1029 (2 x-1)^2 (3 x+2)}-\frac{200 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1029 \sqrt{21}}","\frac{11 (5 x+3)^2}{21 (1-2 x)^{3/2} (3 x+2)}-\frac{10 (1450 x+969)}{1029 \sqrt{1-2 x} (3 x+2)}-\frac{200 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1029 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(-4839 + 21050*x + 42475*x^2))/(1029*(-1 + 2*x)^2*(2 + 3*x)) - (200*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(1029*Sqrt[21])","A",1
2165,1,66,100,0.1152215,"\int \frac{(3+5 x)^3}{(1-2 x)^{5/2} (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)^3),x]","\frac{\sqrt{1-2 x} \left(10860 x^3+33410 x^2+29593 x+8103\right)}{2058 \left(6 x^2+x-2\right)^2}+\frac{905 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1029 \sqrt{21}}","\frac{11 (5 x+3)^2}{21 (1-2 x)^{3/2} (3 x+2)^2}-\frac{720 x+487}{294 \sqrt{1-2 x} (3 x+2)^2}+\frac{905 \sqrt{1-2 x}}{2058 (3 x+2)}+\frac{905 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1029 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(8103 + 29593*x + 33410*x^2 + 10860*x^3))/(2058*(-2 + x + 6*x^2)^2) + (905*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(1029*Sqrt[21])","A",1
2166,1,75,120,0.1108984,"\int \frac{(3+5 x)^3}{(1-2 x)^{5/2} (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]","\frac{\sqrt{1-2 x} \left(-135180 x^4-150200 x^3+83306 x^2+150295 x+45383\right)}{7203 (2 x-1)^2 (3 x+2)^3}-\frac{7510 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{7203 \sqrt{21}}","\frac{11 (5 x+3)^2}{21 (1-2 x)^{3/2} (3 x+2)^3}+\frac{2 (2027 x+1346)}{441 \sqrt{1-2 x} (3 x+2)^3}-\frac{3755 \sqrt{1-2 x}}{7203 (3 x+2)}-\frac{3755 \sqrt{1-2 x}}{3087 (3 x+2)^2}-\frac{7510 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{7203 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(45383 + 150295*x + 83306*x^2 - 150200*x^3 - 135180*x^4))/(7203*(-1 + 2*x)^2*(2 + 3*x)^3) - (7510*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(7203*Sqrt[21])","A",1
2167,1,80,140,0.1292204,"\int \frac{(3+5 x)^3}{(1-2 x)^{5/2} (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)^5),x]","\frac{\sqrt{1-2 x} \left(-19184580 x^5-34105920 x^4-10906789 x^3+12952519 x^2+10307138 x+2094250\right)}{403368 (2 x-1)^2 (3 x+2)^4}-\frac{177635 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{201684 \sqrt{21}}","\frac{11 (5 x+3)^2}{21 (1-2 x)^{3/2} (3 x+2)^4}+\frac{85754 x+57069}{4116 \sqrt{1-2 x} (3 x+2)^4}-\frac{177635 \sqrt{1-2 x}}{403368 (3 x+2)}-\frac{177635 \sqrt{1-2 x}}{172872 (3 x+2)^2}-\frac{35527 \sqrt{1-2 x}}{12348 (3 x+2)^3}-\frac{177635 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{201684 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(2094250 + 10307138*x + 12952519*x^2 - 10906789*x^3 - 34105920*x^4 - 19184580*x^5))/(403368*(-1 + 2*x)^2*(2 + 3*x)^4) - (177635*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(201684*Sqrt[21])","A",1
2168,1,85,160,0.1458646,"\int \frac{(3+5 x)^3}{(1-2 x)^{5/2} (2+3 x)^6} \, dx","IntegrateAlgebraic[(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)^6),x]","\frac{\sqrt{1-2 x} \left(-132413940 x^6-323678520 x^5-232214817 x^4+22641149 x^3+99751837 x^2+42553376 x+5615203\right)}{1764735 (2 x-1)^2 (3 x+2)^5}-\frac{163474 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{352947 \sqrt{21}}","\frac{11 (5 x+3)^2}{21 (1-2 x)^{3/2} (3 x+2)^5}+\frac{2 (83544 x+55633)}{5145 \sqrt{1-2 x} (3 x+2)^5}-\frac{81737 \sqrt{1-2 x}}{352947 (3 x+2)}-\frac{81737 \sqrt{1-2 x}}{151263 (3 x+2)^2}-\frac{163474 \sqrt{1-2 x}}{108045 (3 x+2)^3}-\frac{163474 \sqrt{1-2 x}}{36015 (3 x+2)^4}-\frac{163474 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{352947 \sqrt{21}}",1,"(Sqrt[1 - 2*x]*(5615203 + 42553376*x + 99751837*x^2 + 22641149*x^3 - 232214817*x^4 - 323678520*x^5 - 132413940*x^6))/(1764735*(-1 + 2*x)^2*(2 + 3*x)^5) - (163474*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(352947*Sqrt[21])","A",1
2169,1,73,106,0.0883113,"\int \frac{(2+3 x)^6}{(1-2 x)^{5/2} (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)^(5/2)*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(-33078375 x^5-190531440 x^4-611141355 x^3-2562785082 x^2+5374023537 x-1780047848\right)}{1588125 (2 x-1)^2}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{75625 \sqrt{55}}","\frac{729 (1-2 x)^{7/2}}{1120}-\frac{43011 (1-2 x)^{5/2}}{4000}+\frac{169209 (1-2 x)^{3/2}}{2000}-\frac{5992353 \sqrt{1-2 x}}{10000}-\frac{2739541}{3872 \sqrt{1-2 x}}+\frac{117649}{1056 (1-2 x)^{3/2}}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{75625 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-1780047848 + 5374023537*x - 2562785082*x^2 - 611141355*x^3 - 190531440*x^4 - 33078375*x^5))/(1588125*(-1 + 2*x)^2) - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(75625*Sqrt[55])","A",1
2170,1,68,93,0.0809937,"\int \frac{(2+3 x)^5}{(1-2 x)^{5/2} (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(-441045 x^4-2597265 x^3-13976226 x^2+30775791 x-10097264\right)}{45375 (2 x-1)^2}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15125 \sqrt{55}}","-\frac{243}{400} (1-2 x)^{5/2}+\frac{1917}{200} (1-2 x)^{3/2}-\frac{51057}{500} \sqrt{1-2 x}-\frac{156065}{968 \sqrt{1-2 x}}+\frac{16807}{528 (1-2 x)^{3/2}}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15125 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-10097264 + 30775791*x - 13976226*x^2 - 2597265*x^3 - 441045*x^4))/(45375*(-1 + 2*x)^2) - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(15125*Sqrt[55])","A",1
2171,1,63,80,0.0765752,"\int \frac{(2+3 x)^4}{(1-2 x)^{5/2} (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^(5/2)*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(-49005 x^3-450846 x^2+1111431 x-354344\right)}{9075 (2 x-1)^2}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3025 \sqrt{55}}","\frac{27}{40} (1-2 x)^{3/2}-\frac{2889}{200} \sqrt{1-2 x}-\frac{33271}{968 \sqrt{1-2 x}}+\frac{2401}{264 (1-2 x)^{3/2}}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3025 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-354344 + 1111431*x - 450846*x^2 - 49005*x^3))/(9075*(-1 + 2*x)^2) - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(3025*Sqrt[55])","A",1
2172,1,58,67,0.0709809,"\int \frac{(2+3 x)^3}{(1-2 x)^{5/2} (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^(5/2)*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(-9801 x^2+33321 x-9494\right)}{1815 (2 x-1)^2}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{605 \sqrt{55}}","-\frac{27}{20} \sqrt{1-2 x}-\frac{784}{121 \sqrt{1-2 x}}+\frac{343}{132 (1-2 x)^{3/2}}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{605 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-9494 + 33321*x - 9801*x^2))/(1815*(-1 + 2*x)^2) - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(605*Sqrt[55])","A",1
2173,1,53,54,0.0690864,"\int \frac{(2+3 x)^2}{(1-2 x)^{5/2} (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^(5/2)*(3 + 5*x)),x]","\frac{7 \sqrt{1-2 x} (93 x-8)}{363 (2 x-1)^2}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{121 \sqrt{55}}","-\frac{217}{242 \sqrt{1-2 x}}+\frac{49}{66 (1-2 x)^{3/2}}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{121 \sqrt{55}}",1,"(7*Sqrt[1 - 2*x]*(-8 + 93*x))/(363*(-1 + 2*x)^2) - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(121*Sqrt[55])","A",1
2174,1,55,56,0.0545149,"\int \frac{2+3 x}{(1-2 x)^{5/2} (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^(5/2)*(3 + 5*x)),x]","\frac{(83-12 x) \sqrt{1-2 x}}{363 (2 x-1)^2}-\frac{2}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{2}{121 \sqrt{1-2 x}}+\frac{7}{33 (1-2 x)^{3/2}}-\frac{2}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"((83 - 12*x)*Sqrt[1 - 2*x])/(363*(-1 + 2*x)^2) - (2*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/121","A",1
2175,1,55,56,0.0523718,"\int \frac{1}{(1-2 x)^{5/2} (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(3 + 5*x)),x]","-\frac{4 \sqrt{1-2 x} (15 x-13)}{363 (2 x-1)^2}-\frac{10}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{10}{121 \sqrt{1-2 x}}+\frac{2}{33 (1-2 x)^{3/2}}-\frac{10}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(-4*Sqrt[1 - 2*x]*(-13 + 15*x))/(363*(-1 + 2*x)^2) - (10*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/121","A",1
2176,1,84,85,0.1119696,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x) (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)),x]","-\frac{4 \sqrt{1-2 x} (408 x-281)}{17787 (2 x-1)^2}+\frac{18}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{50}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","\frac{272}{5929 \sqrt{1-2 x}}+\frac{4}{231 (1-2 x)^{3/2}}+\frac{18}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{50}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(-4*Sqrt[1 - 2*x]*(-281 + 408*x))/(17787*(-1 + 2*x)^2) + (18*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/49 - (50*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/121","A",1
2177,1,96,105,0.1362355,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^2 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(24660 x^2-39780 x+15881\right)}{124509 (2 x-1)^2 (3 x+2)}+\frac{720}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{250}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{1370}{41503 \sqrt{1-2 x}}+\frac{3}{7 (1-2 x)^{3/2} (3 x+2)}-\frac{190}{1617 (1-2 x)^{3/2}}+\frac{720}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{250}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(15881 - 39780*x + 24660*x^2))/(124509*(-1 + 2*x)^2*(2 + 3*x)) + (720*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 - (250*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/121","A",1
2178,1,97,125,0.1400967,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^3 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(1327860 x^3-438840 x^2-594687 x+245383\right)}{249018 \left(6 x^2+x-2\right)^2}+\frac{3645}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{1250}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{12295}{41503 \sqrt{1-2 x}}+\frac{33}{14 (1-2 x)^{3/2} (3 x+2)}-\frac{1115}{1617 (1-2 x)^{3/2}}+\frac{3}{14 (1-2 x)^{3/2} (3 x+2)^2}+\frac{3645}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{1250}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(245383 - 594687*x - 438840*x^2 + 1327860*x^3))/(249018*(-2 + x + 6*x^2)^2) + (3645*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 - (1250*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/121","A",1
2179,1,106,145,0.1540149,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^4 (3+5 x)} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^4*(3 + 5*x)),x]","\frac{\sqrt{1-2 x} \left(72358920 x^4+26376300 x^3-47036214 x^2-9083055 x+8496203\right)}{871563 (2 x-1)^2 (3 x+2)^3}+\frac{127710 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{2401}-\frac{6250}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)","-\frac{446660}{290521 \sqrt{1-2 x}}+\frac{582}{49 (1-2 x)^{3/2} (3 x+2)}-\frac{39520}{11319 (1-2 x)^{3/2}}+\frac{57}{49 (1-2 x)^{3/2} (3 x+2)^2}+\frac{1}{7 (1-2 x)^{3/2} (3 x+2)^3}+\frac{127710 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{2401}-\frac{6250}{121} \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)",1,"(Sqrt[1 - 2*x]*(8496203 - 9083055*x - 47036214*x^2 + 26376300*x^3 + 72358920*x^4))/(871563*(-1 + 2*x)^2*(2 + 3*x)^3) + (127710*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/2401 - (6250*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/121","A",1
2180,1,80,140,0.1331809,"\int \frac{(2+3 x)^6}{(1-2 x)^{5/2} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-72772425 x^5-480298005 x^4-2644064775 x^3+3837745731 x^2+1434109759 x-1035652776\right)}{2495625 (2 x-1)^2 (5 x+3)}-\frac{406 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{831875 \sqrt{55}}","\frac{7 (3 x+2)^5}{33 (1-2 x)^{3/2} (5 x+3)}-\frac{38 (3 x+2)^4}{1815 \sqrt{1-2 x} (5 x+3)}-\frac{10283 (3 x+2)^3}{6655 \sqrt{1-2 x}}-\frac{463344 \sqrt{1-2 x} (3 x+2)^2}{166375}-\frac{21 \sqrt{1-2 x} (1544625 x+4633904)}{831875}-\frac{406 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{831875 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-1035652776 + 1434109759*x + 3837745731*x^2 - 2644064775*x^3 - 480298005*x^4 - 72772425*x^5))/(2495625*(-1 + 2*x)^2*(3 + 5*x)) - (406*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(831875*Sqrt[55])","A",1
2181,1,75,120,0.0974999,"\int \frac{(2+3 x)^5}{(1-2 x)^{5/2} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-1617165 x^4-16171650 x^3+28677318 x^2+10671002 x-7204728\right)}{99825 (2 x-1)^2 (5 x+3)}-\frac{68 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{33275 \sqrt{55}}","\frac{7 (3 x+2)^4}{33 (1-2 x)^{3/2} (5 x+3)}-\frac{38 (3 x+2)^3}{1815 \sqrt{1-2 x} (5 x+3)}-\frac{7588 (3 x+2)^2}{6655 \sqrt{1-2 x}}-\frac{6 \sqrt{1-2 x} (38025 x+114092)}{33275}-\frac{68 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{33275 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-7204728 + 10671002*x + 28677318*x^2 - 16171650*x^3 - 1617165*x^4))/(99825*(-1 + 2*x)^2*(3 + 5*x)) - (68*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(33275*Sqrt[55])","A",1
2182,1,70,100,0.1146017,"\int \frac{(2+3 x)^4}{(1-2 x)^{5/2} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-1617165 x^3+4634229 x^2+1790101 x-943584\right)}{99825 (2 x-1)^2 (5 x+3)}-\frac{274 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{33275 \sqrt{55}}","\frac{7 (3 x+2)^3}{33 (1-2 x)^{3/2} (5 x+3)}-\frac{38 (3 x+2)^2}{1815 \sqrt{1-2 x} (5 x+3)}-\frac{3 (40912-24739 x)}{33275 \sqrt{1-2 x}}-\frac{274 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{33275 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-943584 + 1790101*x + 4634229*x^2 - 1617165*x^3))/(99825*(-1 + 2*x)^2*(3 + 5*x)) - (274*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(33275*Sqrt[55])","A",1
2183,1,65,80,0.096291,"\int \frac{(2+3 x)^3}{(1-2 x)^{5/2} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(106563 x^2+57832 x-3678\right)}{19965 (2 x-1)^2 (5 x+3)}-\frac{208 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{6655 \sqrt{55}}","\frac{7 (3 x+2)^2}{33 (1-2 x)^{3/2} (5 x+3)}-\frac{2 (17112 x+10309)}{19965 \sqrt{1-2 x} (5 x+3)}-\frac{208 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{6655 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-3678 + 57832*x + 106563*x^2))/(19965*(-1 + 2*x)^2*(3 + 5*x)) - (208*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(6655*Sqrt[55])","A",1
2184,1,65,81,0.1008005,"\int \frac{(2+3 x)^2}{(1-2 x)^{5/2} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-852 x^2+2623 x+1866\right)}{3993 (2 x-1)^2 (5 x+3)}-\frac{142 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331 \sqrt{55}}","\frac{142}{6655 \sqrt{1-2 x}}-\frac{1231}{3630 \sqrt{1-2 x} (5 x+3)}+\frac{49}{66 (1-2 x)^{3/2} (5 x+3)}-\frac{142 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(1866 + 2623*x - 852*x^2))/(3993*(-1 + 2*x)^2*(3 + 5*x)) - (142*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(1331*Sqrt[55])","A",1
2185,1,67,76,0.0806289,"\int \frac{2+3 x}{(1-2 x)^{5/2} (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-2280 x^2+608 x+1113\right)}{3993 (2 x-1)^2 (5 x+3)}-\frac{76 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}","\frac{76}{1331 \sqrt{1-2 x}}-\frac{1}{55 (1-2 x)^{3/2} (5 x+3)}+\frac{76}{1815 (1-2 x)^{3/2}}-\frac{76 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}",1,"(Sqrt[1 - 2*x]*(1113 + 608*x - 2280*x^2))/(3993*(-1 + 2*x)^2*(3 + 5*x)) - (76*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1331","A",1
2186,1,67,76,0.0963753,"\int \frac{1}{(1-2 x)^{5/2} (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-1500 x^2+400 x+417\right)}{3993 (2 x-1)^2 (5 x+3)}-\frac{50 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}","\frac{50}{1331 \sqrt{1-2 x}}-\frac{1}{11 (1-2 x)^{3/2} (5 x+3)}+\frac{10}{363 (1-2 x)^{3/2}}-\frac{50 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}",1,"(Sqrt[1 - 2*x]*(417 + 400*x - 1500*x^2))/(3993*(-1 + 2*x)^2*(3 + 5*x)) - (50*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1331","A",1
2187,1,96,105,0.1384298,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-98220 x^2+74108 x-9111\right)}{195657 (2 x-1)^2 (5 x+3)}-\frac{54}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{1400 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}","\frac{3274}{65219 \sqrt{1-2 x}}-\frac{5}{11 (1-2 x)^{3/2} (5 x+3)}+\frac{218}{2541 (1-2 x)^{3/2}}-\frac{54}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{1400 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}",1,"(Sqrt[1 - 2*x]*(-9111 + 74108*x - 98220*x^2))/(195657*(-1 + 2*x)^2*(3 + 5*x)) - (54*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/49 + (1400*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1331","A",1
2188,1,106,132,0.1314283,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-14382000 x^3+5028300 x^2+5548760 x-2209989\right)}{1369599 (2 x-1)^2 \left(15 x^2+19 x+6\right)}-\frac{4050}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{15250 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}","\frac{159800}{456533 \sqrt{1-2 x}}+\frac{3}{7 (1-2 x)^{3/2} (3 x+2) (5 x+3)}-\frac{340}{77 (1-2 x)^{3/2} (5 x+3)}+\frac{13900}{17787 (1-2 x)^{3/2}}-\frac{4050}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{15250 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}",1,"(Sqrt[1 - 2*x]*(-2209989 + 5548760*x + 5028300*x^2 - 14382000*x^3))/(1369599*(-1 + 2*x)^2*(6 + 19*x + 15*x^2)) - (4050*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 + (15250*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1331","A",1
2189,1,109,159,0.1778096,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^2} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^2),x]","\frac{\sqrt{1-2 x} \left(-92936700 x^4-27977220 x^3+58371045 x^2+9008764 x-9784671\right)}{391314 (5 x+3) \left(6 x^2+x-2\right)^2}-\frac{4455}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{117500 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}","\frac{172105}{65219 \sqrt{1-2 x}}+\frac{24}{7 (1-2 x)^{3/2} (3 x+2) (5 x+3)}-\frac{745}{22 (1-2 x)^{3/2} (5 x+3)}+\frac{3}{14 (1-2 x)^{3/2} (3 x+2)^2 (5 x+3)}+\frac{15185}{2541 (1-2 x)^{3/2}}-\frac{4455}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{117500 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1331}",1,"(Sqrt[1 - 2*x]*(-9784671 + 9008764*x + 58371045*x^2 - 27977220*x^3 - 92936700*x^4))/(391314*(3 + 5*x)*(-2 + x + 6*x^2)^2) - (4455*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/49 + (117500*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1331","A",1
2190,1,76,147,0.1266116,"\int \frac{(2+3 x)^6}{(1-2 x)^{5/2} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(-533664450 x^5-5763576060 x^4+6510290070 x^3+9509366452 x^2-253794537 x-1463964312\right)}{10980750 \left(10 x^2+x-3\right)^2}-\frac{6937 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1830125 \sqrt{55}}","\frac{7 (3 x+2)^5}{33 (1-2 x)^{3/2} (5 x+3)^2}-\frac{73 (3 x+2)^4}{3630 \sqrt{1-2 x} (5 x+3)^2}-\frac{3269 (3 x+2)^3}{199650 \sqrt{1-2 x} (5 x+3)}-\frac{256172 (3 x+2)^2}{366025 \sqrt{1-2 x}}-\frac{21 \sqrt{1-2 x} (736875 x+2211616)}{3660250}-\frac{6937 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1830125 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-1463964312 - 253794537*x + 9509366452*x^2 + 6510290070*x^3 - 5763576060*x^4 - 533664450*x^5))/(10980750*(-3 + x + 10*x^2)^2) - (6937*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(1830125*Sqrt[55])","A",1
2191,1,71,127,0.1111064,"\int \frac{(2+3 x)^5}{(1-2 x)^{5/2} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(-106732890 x^4+248761830 x^3+309826828 x^2+10907307 x-37428168\right)}{2196150 \left(10 x^2+x-3\right)^2}-\frac{4693 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{366025 \sqrt{55}}","\frac{7 (3 x+2)^4}{33 (1-2 x)^{3/2} (5 x+3)^2}-\frac{73 (3 x+2)^3}{3630 \sqrt{1-2 x} (5 x+3)^2}-\frac{317 (3 x+2)^2}{19965 \sqrt{1-2 x} (5 x+3)}-\frac{3 (544568-333311 x)}{732050 \sqrt{1-2 x}}-\frac{4693 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{366025 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-37428168 + 10907307*x + 309826828*x^2 + 248761830*x^3 - 106732890*x^4))/(2196150*(-3 + x + 10*x^2)^2) - (4693*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(366025*Sqrt[55])","A",1
2192,1,66,107,0.127723,"\int \frac{(2+3 x)^4}{(1-2 x)^{5/2} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(34712250 x^3+40823468 x^2+11479257 x-311208\right)}{2196150 \left(10 x^2+x-3\right)^2}-\frac{14423 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{366025 \sqrt{55}}","\frac{7 (3 x+2)^3}{33 (1-2 x)^{3/2} (5 x+3)^2}-\frac{73 (3 x+2)^2}{3630 \sqrt{1-2 x} (5 x+3)^2}-\frac{2133933 x+1287116}{2196150 \sqrt{1-2 x} (5 x+3)}-\frac{14423 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{366025 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(-311208 + 11479257*x + 40823468*x^2 + 34712250*x^3))/(2196150*(-3 + x + 10*x^2)^2) - (14423*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(366025*Sqrt[55])","A",1
2193,1,66,100,0.1122082,"\int \frac{(2+3 x)^3}{(1-2 x)^{5/2} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(-453540 x^3+639434 x^2+1242261 x+417036\right)}{439230 \left(10 x^2+x-3\right)^2}-\frac{7559 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{73205 \sqrt{55}}","\frac{7 (3 x+2)^2}{33 (1-2 x)^{3/2} (5 x+3)^2}+\frac{17296 x+10217}{39930 \sqrt{1-2 x} (5 x+3)^2}-\frac{7559 \sqrt{1-2 x}}{146410 (5 x+3)}-\frac{7559 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{73205 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(417036 + 1242261*x + 639434*x^2 - 453540*x^3))/(439230*(-3 + x + 10*x^2)^2) - (7559*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(73205*Sqrt[55])","A",1
2194,1,66,101,0.1079942,"\int \frac{(2+3 x)^2}{(1-2 x)^{5/2} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(-172380 x^3-57460 x^2+107127 x+47568\right)}{87846 \left(10 x^2+x-3\right)^2}-\frac{2873 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{14641 \sqrt{55}}","\frac{2873}{73205 \sqrt{1-2 x}}-\frac{2873}{39930 \sqrt{1-2 x} (5 x+3)}-\frac{614}{1815 \sqrt{1-2 x} (5 x+3)^2}+\frac{49}{66 (1-2 x)^{3/2} (5 x+3)^2}-\frac{2873 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{14641 \sqrt{55}}",1,"(Sqrt[1 - 2*x]*(47568 + 107127*x - 57460*x^2 - 172380*x^3))/(87846*(-3 + x + 10*x^2)^2) - (2873*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(14641*Sqrt[55])","A",1
2195,1,68,96,0.1087732,"\int \frac{2+3 x}{(1-2 x)^{5/2} (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(-109500 x^3-36500 x^2+47961 x+17466\right)}{87846 \left(10 x^2+x-3\right)^2}-\frac{365 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{14641}","\frac{365}{14641 \sqrt{1-2 x}}-\frac{73}{1210 (1-2 x)^{3/2} (5 x+3)}+\frac{73}{3993 (1-2 x)^{3/2}}-\frac{1}{110 (1-2 x)^{3/2} (5 x+3)^2}-\frac{365 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{14641}",1,"(Sqrt[1 - 2*x]*(17466 + 47961*x - 36500*x^2 - 109500*x^3))/(87846*(-3 + x + 10*x^2)^2) - (365*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/14641","A",1
2196,1,68,96,0.108469,"\int \frac{1}{(1-2 x)^{5/2} (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(-52500 x^3-17500 x^2+22995 x+4764\right)}{87846 \left(10 x^2+x-3\right)^2}-\frac{175 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{14641}","\frac{175}{14641 \sqrt{1-2 x}}-\frac{7}{242 (1-2 x)^{3/2} (5 x+3)}+\frac{35}{3993 (1-2 x)^{3/2}}-\frac{1}{22 (1-2 x)^{3/2} (5 x+3)^2}-\frac{175 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{14641}",1,"(Sqrt[1 - 2*x]*(4764 + 22995*x - 17500*x^2 - 52500*x^3))/(87846*(-3 + x + 10*x^2)^2) - (175*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/14641","A",1
2197,1,97,125,0.1465225,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(19550100 x^3-9295580 x^2-6032979 x+2971158\right)}{4304454 \left(10 x^2+x-3\right)^2}+\frac{162}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{47075 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{14641}","-\frac{65167}{717409 \sqrt{1-2 x}}+\frac{295}{242 (1-2 x)^{3/2} (5 x+3)}-\frac{5969}{27951 (1-2 x)^{3/2}}-\frac{5}{22 (1-2 x)^{3/2} (5 x+3)^2}+\frac{162}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{47075 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{14641}",1,"(Sqrt[1 - 2*x]*(2971158 - 6032979*x - 9295580*x^2 + 19550100*x^3))/(4304454*(-3 + x + 10*x^2)^2) + (162*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/49 - (47075*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/14641","A",1
2198,1,109,152,0.1666688,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(6798820500 x^4+1580768100 x^3-4110847595 x^2-479695050 x+645558882\right)}{30131178 (3 x+2) \left(10 x^2+x-3\right)^2}+\frac{17820}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{738625 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{14641}","-\frac{7554245}{5021863 \sqrt{1-2 x}}+\frac{32765}{1694 (1-2 x)^{3/2} (5 x+3)}-\frac{667615}{195657 (1-2 x)^{3/2}}+\frac{3}{7 (1-2 x)^{3/2} (3 x+2) (5 x+3)^2}-\frac{505}{154 (1-2 x)^{3/2} (5 x+3)^2}+\frac{17820}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{738625 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{14641}",1,"(Sqrt[1 - 2*x]*(645558882 - 479695050*x - 4110847595*x^2 + 1580768100*x^3 + 6798820500*x^4))/(30131178*(2 + 3*x)*(-3 + x + 10*x^2)^2) + (17820*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 - (738625*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/14641","A",1
2199,1,116,179,0.1760258,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^3} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(209324196000 x^5+188418548700 x^4-93885376440 x^3-99160158305 x^2+9944654283 x+13236365823\right)}{30131178 (2 x-1)^2 \left(15 x^2+19 x+6\right)^2}+\frac{182655}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{7570625 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{14641}","-\frac{77527480}{5021863 \sqrt{1-2 x}}+\frac{167960}{847 (1-2 x)^{3/2} (5 x+3)}-\frac{6845810}{195657 (1-2 x)^{3/2}}+\frac{9}{2 (1-2 x)^{3/2} (3 x+2) (5 x+3)^2}-\frac{5165}{154 (1-2 x)^{3/2} (5 x+3)^2}+\frac{3}{14 (1-2 x)^{3/2} (3 x+2)^2 (5 x+3)^2}+\frac{182655}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{7570625 \sqrt{\frac{5}{11}} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{14641}",1,"(Sqrt[1 - 2*x]*(13236365823 + 9944654283*x - 99160158305*x^2 - 93885376440*x^3 + 188418548700*x^4 + 209324196000*x^5))/(30131178*(-1 + 2*x)^2*(6 + 19*x + 15*x^2)^2) + (182655*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 - (7570625*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/14641","A",1
2200,-1,0,304,180.0342175,"\int \sqrt{a+b x} (A+B x) (d+e x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*(A + B*x)*(d + e*x)^(5/2),x]","\text{\$Aborted}","\frac{(b d-a e)^4 (7 a B e-10 A b e+3 b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{128 b^{9/2} e^{5/2}}-\frac{\sqrt{a+b x} \sqrt{d+e x} (b d-a e)^3 (7 a B e-10 A b e+3 b B d)}{128 b^4 e^2}-\frac{(a+b x)^{3/2} \sqrt{d+e x} (b d-a e)^2 (7 a B e-10 A b e+3 b B d)}{64 b^4 e}-\frac{(a+b x)^{3/2} (d+e x)^{3/2} (b d-a e) (7 a B e-10 A b e+3 b B d)}{48 b^3 e}-\frac{(a+b x)^{3/2} (d+e x)^{5/2} (7 a B e-10 A b e+3 b B d)}{40 b^2 e}+\frac{B (a+b x)^{3/2} (d+e x)^{7/2}}{5 b e}",1,"$Aborted","F",-1
2201,-1,0,250,180.0195922,"\int \sqrt{a+b x} (A+B x) (d+e x)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*(A + B*x)*(d + e*x)^(3/2),x]","\text{\$Aborted}","\frac{(b d-a e)^3 (5 a B e-8 A b e+3 b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{64 b^{7/2} e^{5/2}}-\frac{\sqrt{a+b x} \sqrt{d+e x} (b d-a e)^2 (5 a B e-8 A b e+3 b B d)}{64 b^3 e^2}-\frac{(a+b x)^{3/2} \sqrt{d+e x} (b d-a e) (5 a B e-8 A b e+3 b B d)}{32 b^3 e}-\frac{(a+b x)^{3/2} (d+e x)^{3/2} (5 a B e-8 A b e+3 b B d)}{24 b^2 e}+\frac{B (a+b x)^{3/2} (d+e x)^{5/2}}{4 b e}",1,"$Aborted","F",-1
2202,-1,0,196,180.0530064,"\int \sqrt{a+b x} (A+B x) \sqrt{d+e x} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*(A + B*x)*Sqrt[d + e*x],x]","\text{\$Aborted}","-\frac{(b d-a e)^2 (2 A b e-B (a e+b d)) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{8 b^{5/2} e^{5/2}}+\frac{\sqrt{a+b x} \sqrt{d+e x} (b d-a e) (2 A b e-B (a e+b d))}{8 b^2 e^2}+\frac{(a+b x)^{3/2} \sqrt{d+e x} (2 A b e-B (a e+b d))}{4 b^2 e}+\frac{B (a+b x)^{3/2} (d+e x)^{3/2}}{3 b e}",1,"$Aborted","F",-1
2203,1,1802,140,15.3891286,"\int \frac{\sqrt{a+b x} (A+B x)}{\sqrt{d+e x}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/Sqrt[d + e*x],x]","\frac{\left(-4 B \sqrt{a+b x} b^4-\frac{4 B d \sqrt{a+b x} b^4}{e}-\frac{B d^2 \sqrt{a+b x} b^4}{2 e^2}+\frac{4 \sqrt{a+b} B \sqrt{d+e} \sqrt{d+e x} b^4}{e}+\frac{2 \sqrt{a+b} B d \sqrt{d+e} \sqrt{d+e x} b^4}{e^2}-\frac{2 \sqrt{a+b} B d b^4}{e}-\frac{3 \sqrt{a+b} B d^2 b^4}{2 e^2}+2 a \sqrt{a+b} B b^3-4 a B \sqrt{a+b x} b^3-\frac{3 a B d \sqrt{a+b x} b^3}{e}+\frac{2 a \sqrt{a+b} B \sqrt{d+e} \sqrt{d+e x} b^3}{e}+\frac{a \sqrt{a+b} B d b^3}{e}+\frac{1}{2} a^2 \sqrt{a+b} B b^2-\frac{1}{2} a^2 B \sqrt{a+b x} b^2\right) \left(\sqrt{d+e}-\sqrt{d+e x}\right)^7}{\left(-d b+\sqrt{d+e} \sqrt{d+e x} b+a e-\sqrt{a+b} e \sqrt{a+b x}\right)^4}+\frac{\left(-4 \sqrt{a+b} B b^3-12 B \sqrt{a+b x} b^3-\frac{12 B d \sqrt{a+b x} b^3}{e}-\frac{3 B d^2 \sqrt{a+b x} b^3}{2 e^2}+\frac{16 \sqrt{a+b} B \sqrt{d+e} \sqrt{d+e x} b^3}{e}+\frac{8 \sqrt{a+b} B d \sqrt{d+e} \sqrt{d+e x} b^3}{e^2}-\frac{12 \sqrt{a+b} B d b^3}{e}-\frac{13 \sqrt{a+b} B d^2 b^3}{2 e^2}+4 a \sqrt{a+b} B b^2-12 a B \sqrt{a+b x} b^2-\frac{9 a B d \sqrt{a+b x} b^2}{e}+\frac{8 a \sqrt{a+b} B \sqrt{d+e} \sqrt{d+e x} b^2}{e}+\frac{a \sqrt{a+b} B d b^2}{e}+\frac{3}{2} a^2 \sqrt{a+b} B b-\frac{3}{2} a^2 B \sqrt{a+b x} b\right) \left(\sqrt{d+e}-\sqrt{d+e x}\right)^5}{\left(-d b+\sqrt{d+e} \sqrt{d+e x} b+a e-\sqrt{a+b} e \sqrt{a+b x}\right)^3}+\frac{\left(\frac{5}{4} \sqrt{a+b} B a^2-\frac{5}{4} B \sqrt{a+b x} a^2+A b \sqrt{a+b} a-A b \sqrt{a+b x} a-10 b B \sqrt{a+b x} a-\frac{13 b B d \sqrt{a+b x} a}{2 e}+\frac{10 b \sqrt{a+b} B \sqrt{d+e} \sqrt{d+e x} a}{e}-\frac{7 b \sqrt{a+b} B d a}{2 e}-10 b^2 \sqrt{a+b} B-2 A b^2 \sqrt{a+b x}-10 b^2 B \sqrt{a+b x}-\frac{A b^2 d \sqrt{a+b x}}{e}-\frac{8 b^2 B d \sqrt{a+b x}}{e}-\frac{b^2 B d^2 \sqrt{a+b x}}{4 e^2}+\frac{20 b^2 \sqrt{a+b} B \sqrt{d+e} \sqrt{d+e x}}{e}+\frac{2 A b^2 \sqrt{a+b} \sqrt{d+e} \sqrt{d+e x}}{e}+\frac{8 b^2 \sqrt{a+b} B d \sqrt{d+e} \sqrt{d+e x}}{e^2}-\frac{20 b^2 \sqrt{a+b} B d}{e}-\frac{A b^2 \sqrt{a+b} d}{e}-\frac{31 b^2 \sqrt{a+b} B d^2}{4 e^2}\right) \left(\sqrt{d+e}-\sqrt{d+e x}\right)^3}{\left(-d b+\sqrt{d+e} \sqrt{d+e x} b+a e-\sqrt{a+b} e \sqrt{a+b x}\right)^2}+\frac{\left(\frac{\sqrt{d+e x}}{4 b e^2}-\frac{\sqrt{d+e}}{4 b e^2}\right) \left(3 \sqrt{a+b} B d^2 b^2+24 \sqrt{a+b} B e^2 b^2+8 A \sqrt{a+b} e^2 b^2+32 \sqrt{a+b} B d e b^2+12 A \sqrt{a+b} d e b^2-3 B d^2 \sqrt{a+b x} b^2+8 A e^2 \sqrt{a+b x} b^2+8 B e^2 \sqrt{a+b x} b^2+4 A d e \sqrt{a+b x} b^2-32 \sqrt{a+b} B e \sqrt{d+e} \sqrt{d+e x} b^2-16 A \sqrt{a+b} e \sqrt{d+e} \sqrt{d+e x} b^2+8 a \sqrt{a+b} B e^2 b-4 a A \sqrt{a+b} e^2 b+14 a \sqrt{a+b} B d e b+4 a A e^2 \sqrt{a+b x} b+8 a B e^2 \sqrt{a+b x} b+2 a B d e \sqrt{a+b x} b-16 a \sqrt{a+b} B e \sqrt{d+e} \sqrt{d+e x} b-a^2 \sqrt{a+b} B e^2+a^2 B e^2 \sqrt{a+b x}\right)}{-d b+\sqrt{d+e} \sqrt{d+e x} b+a e-\sqrt{a+b} e \sqrt{a+b x}}+\left(-\frac{B a^2}{2 b^{3/2} \sqrt{e}}+\frac{2 A a}{\sqrt{b} \sqrt{e}}-\frac{B d a}{\sqrt{b} e^{3/2}}-\frac{2 A \sqrt{b} d}{e^{3/2}}+\frac{3 \sqrt{b} B d^2}{2 e^{5/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{a+b} \sqrt{e}-\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \left(\sqrt{d+e}-\sqrt{d+e x}\right)}\right)","\frac{(b d-a e) (a B e-4 A b e+3 b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{4 b^{3/2} e^{5/2}}-\frac{\sqrt{a+b x} \sqrt{d+e x} (a B e-4 A b e+3 b B d)}{4 b e^2}+\frac{B (a+b x)^{3/2} \sqrt{d+e x}}{2 b e}",1,"((Sqrt[d + e] - Sqrt[d + e*x])^3*(a*A*b*Sqrt[a + b] + (5*a^2*Sqrt[a + b]*B)/4 - 10*b^2*Sqrt[a + b]*B - (31*b^2*Sqrt[a + b]*B*d^2)/(4*e^2) - (A*b^2*Sqrt[a + b]*d)/e - (7*a*b*Sqrt[a + b]*B*d)/(2*e) - (20*b^2*Sqrt[a + b]*B*d)/e - a*A*b*Sqrt[a + b*x] - 2*A*b^2*Sqrt[a + b*x] - (5*a^2*B*Sqrt[a + b*x])/4 - 10*a*b*B*Sqrt[a + b*x] - 10*b^2*B*Sqrt[a + b*x] - (b^2*B*d^2*Sqrt[a + b*x])/(4*e^2) - (A*b^2*d*Sqrt[a + b*x])/e - (13*a*b*B*d*Sqrt[a + b*x])/(2*e) - (8*b^2*B*d*Sqrt[a + b*x])/e + (8*b^2*Sqrt[a + b]*B*d*Sqrt[d + e]*Sqrt[d + e*x])/e^2 + (2*A*b^2*Sqrt[a + b]*Sqrt[d + e]*Sqrt[d + e*x])/e + (10*a*b*Sqrt[a + b]*B*Sqrt[d + e]*Sqrt[d + e*x])/e + (20*b^2*Sqrt[a + b]*B*Sqrt[d + e]*Sqrt[d + e*x])/e))/(-(b*d) + a*e - Sqrt[a + b]*e*Sqrt[a + b*x] + b*Sqrt[d + e]*Sqrt[d + e*x])^2 + ((Sqrt[d + e] - Sqrt[d + e*x])^5*((3*a^2*b*Sqrt[a + b]*B)/2 + 4*a*b^2*Sqrt[a + b]*B - 4*b^3*Sqrt[a + b]*B - (13*b^3*Sqrt[a + b]*B*d^2)/(2*e^2) + (a*b^2*Sqrt[a + b]*B*d)/e - (12*b^3*Sqrt[a + b]*B*d)/e - (3*a^2*b*B*Sqrt[a + b*x])/2 - 12*a*b^2*B*Sqrt[a + b*x] - 12*b^3*B*Sqrt[a + b*x] - (3*b^3*B*d^2*Sqrt[a + b*x])/(2*e^2) - (9*a*b^2*B*d*Sqrt[a + b*x])/e - (12*b^3*B*d*Sqrt[a + b*x])/e + (8*b^3*Sqrt[a + b]*B*d*Sqrt[d + e]*Sqrt[d + e*x])/e^2 + (8*a*b^2*Sqrt[a + b]*B*Sqrt[d + e]*Sqrt[d + e*x])/e + (16*b^3*Sqrt[a + b]*B*Sqrt[d + e]*Sqrt[d + e*x])/e))/(-(b*d) + a*e - Sqrt[a + b]*e*Sqrt[a + b*x] + b*Sqrt[d + e]*Sqrt[d + e*x])^3 + ((Sqrt[d + e] - Sqrt[d + e*x])^7*((a^2*b^2*Sqrt[a + b]*B)/2 + 2*a*b^3*Sqrt[a + b]*B - (3*b^4*Sqrt[a + b]*B*d^2)/(2*e^2) + (a*b^3*Sqrt[a + b]*B*d)/e - (2*b^4*Sqrt[a + b]*B*d)/e - (a^2*b^2*B*Sqrt[a + b*x])/2 - 4*a*b^3*B*Sqrt[a + b*x] - 4*b^4*B*Sqrt[a + b*x] - (b^4*B*d^2*Sqrt[a + b*x])/(2*e^2) - (3*a*b^3*B*d*Sqrt[a + b*x])/e - (4*b^4*B*d*Sqrt[a + b*x])/e + (2*b^4*Sqrt[a + b]*B*d*Sqrt[d + e]*Sqrt[d + e*x])/e^2 + (2*a*b^3*Sqrt[a + b]*B*Sqrt[d + e]*Sqrt[d + e*x])/e + (4*b^4*Sqrt[a + b]*B*Sqrt[d + e]*Sqrt[d + e*x])/e))/(-(b*d) + a*e - Sqrt[a + b]*e*Sqrt[a + b*x] + b*Sqrt[d + e]*Sqrt[d + e*x])^4 + ((-1/4*Sqrt[d + e]/(b*e^2) + Sqrt[d + e*x]/(4*b*e^2))*(3*b^2*Sqrt[a + b]*B*d^2 + 12*A*b^2*Sqrt[a + b]*d*e + 14*a*b*Sqrt[a + b]*B*d*e + 32*b^2*Sqrt[a + b]*B*d*e - 4*a*A*b*Sqrt[a + b]*e^2 + 8*A*b^2*Sqrt[a + b]*e^2 - a^2*Sqrt[a + b]*B*e^2 + 8*a*b*Sqrt[a + b]*B*e^2 + 24*b^2*Sqrt[a + b]*B*e^2 - 3*b^2*B*d^2*Sqrt[a + b*x] + 4*A*b^2*d*e*Sqrt[a + b*x] + 2*a*b*B*d*e*Sqrt[a + b*x] + 4*a*A*b*e^2*Sqrt[a + b*x] + 8*A*b^2*e^2*Sqrt[a + b*x] + a^2*B*e^2*Sqrt[a + b*x] + 8*a*b*B*e^2*Sqrt[a + b*x] + 8*b^2*B*e^2*Sqrt[a + b*x] - 16*A*b^2*Sqrt[a + b]*e*Sqrt[d + e]*Sqrt[d + e*x] - 16*a*b*Sqrt[a + b]*B*e*Sqrt[d + e]*Sqrt[d + e*x] - 32*b^2*Sqrt[a + b]*B*e*Sqrt[d + e]*Sqrt[d + e*x]))/(-(b*d) + a*e - Sqrt[a + b]*e*Sqrt[a + b*x] + b*Sqrt[d + e]*Sqrt[d + e*x]) + ((3*Sqrt[b]*B*d^2)/(2*e^(5/2)) - (2*A*Sqrt[b]*d)/e^(3/2) - (a*B*d)/(Sqrt[b]*e^(3/2)) + (2*a*A)/(Sqrt[b]*Sqrt[e]) - (a^2*B)/(2*b^(3/2)*Sqrt[e]))*ArcTanh[(Sqrt[a + b]*Sqrt[e] - Sqrt[e]*Sqrt[a + b*x])/(Sqrt[b]*(Sqrt[d + e] - Sqrt[d + e*x]))]","B",1
2204,-1,0,148,180.0381924,"\int \frac{\sqrt{a+b x} (A+B x)}{(d+e x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/(d + e*x)^(3/2),x]","\text{\$Aborted}","-\frac{(-a B e-2 A b e+3 b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{\sqrt{b} e^{5/2}}+\frac{\sqrt{a+b x} \sqrt{d+e x} (-a B e-2 A b e+3 b B d)}{e^2 (b d-a e)}-\frac{2 (a+b x)^{3/2} (B d-A e)}{e \sqrt{d+e x} (b d-a e)}",1,"$Aborted","F",-1
2205,-1,0,111,180.5419372,"\int \frac{\sqrt{a+b x} (A+B x)}{(d+e x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/(d + e*x)^(5/2),x]","\text{\$Aborted}","-\frac{2 (a+b x)^{3/2} (B d-A e)}{3 e (d+e x)^{3/2} (b d-a e)}+\frac{2 \sqrt{b} B \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{e^{5/2}}-\frac{2 B \sqrt{a+b x}}{e^2 \sqrt{d+e x}}",1,"$Aborted","F",-1
2206,-1,0,95,180.0195835,"\int \frac{\sqrt{a+b x} (A+B x)}{(d+e x)^{7/2}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/(d + e*x)^(7/2),x]","\text{\$Aborted}","\frac{2 (a+b x)^{3/2} (-5 a B e+2 A b e+3 b B d)}{15 e (d+e x)^{3/2} (b d-a e)^2}-\frac{2 (a+b x)^{3/2} (B d-A e)}{5 e (d+e x)^{5/2} (b d-a e)}",1,"$Aborted","F",-1
2207,-1,0,147,180.050193,"\int \frac{\sqrt{a+b x} (A+B x)}{(d+e x)^{9/2}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/(d + e*x)^(9/2),x]","\text{\$Aborted}","\frac{4 b (a+b x)^{3/2} (-7 a B e+4 A b e+3 b B d)}{105 e (d+e x)^{3/2} (b d-a e)^3}+\frac{2 (a+b x)^{3/2} (-7 a B e+4 A b e+3 b B d)}{35 e (d+e x)^{5/2} (b d-a e)^2}-\frac{2 (a+b x)^{3/2} (B d-A e)}{7 e (d+e x)^{7/2} (b d-a e)}",1,"$Aborted","F",-1
2208,-1,0,198,180.5210329,"\int \frac{\sqrt{a+b x} (A+B x)}{(d+e x)^{11/2}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/(d + e*x)^(11/2),x]","\text{\$Aborted}","\frac{16 b^2 (a+b x)^{3/2} (-3 a B e+2 A b e+b B d)}{315 e (d+e x)^{3/2} (b d-a e)^4}+\frac{8 b (a+b x)^{3/2} (-3 a B e+2 A b e+b B d)}{105 e (d+e x)^{5/2} (b d-a e)^3}+\frac{2 (a+b x)^{3/2} (-3 a B e+2 A b e+b B d)}{21 e (d+e x)^{7/2} (b d-a e)^2}-\frac{2 (a+b x)^{3/2} (B d-A e)}{9 e (d+e x)^{9/2} (b d-a e)}",1,"$Aborted","F",-1
2209,-1,0,255,181.2135741,"\int \frac{\sqrt{a+b x} (A+B x)}{(d+e x)^{13/2}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/(d + e*x)^(13/2),x]","\text{\$Aborted}","\frac{32 b^3 (a+b x)^{3/2} (-11 a B e+8 A b e+3 b B d)}{3465 e (d+e x)^{3/2} (b d-a e)^5}+\frac{16 b^2 (a+b x)^{3/2} (-11 a B e+8 A b e+3 b B d)}{1155 e (d+e x)^{5/2} (b d-a e)^4}+\frac{4 b (a+b x)^{3/2} (-11 a B e+8 A b e+3 b B d)}{231 e (d+e x)^{7/2} (b d-a e)^3}+\frac{2 (a+b x)^{3/2} (-11 a B e+8 A b e+3 b B d)}{99 e (d+e x)^{9/2} (b d-a e)^2}-\frac{2 (a+b x)^{3/2} (B d-A e)}{11 e (d+e x)^{11/2} (b d-a e)}",1,"$Aborted","F",-1
2210,-1,0,309,183.0032364,"\int \frac{\sqrt{a+b x} (A+B x)}{(d+e x)^{15/2}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/(d + e*x)^(15/2),x]","\text{\$Aborted}","\frac{256 b^4 (a+b x)^{3/2} (-13 a B e+10 A b e+3 b B d)}{45045 e (d+e x)^{3/2} (b d-a e)^6}+\frac{128 b^3 (a+b x)^{3/2} (-13 a B e+10 A b e+3 b B d)}{15015 e (d+e x)^{5/2} (b d-a e)^5}+\frac{32 b^2 (a+b x)^{3/2} (-13 a B e+10 A b e+3 b B d)}{3003 e (d+e x)^{7/2} (b d-a e)^4}+\frac{16 b (a+b x)^{3/2} (-13 a B e+10 A b e+3 b B d)}{1287 e (d+e x)^{9/2} (b d-a e)^3}+\frac{2 (a+b x)^{3/2} (-13 a B e+10 A b e+3 b B d)}{143 e (d+e x)^{11/2} (b d-a e)^2}-\frac{2 (a+b x)^{3/2} (B d-A e)}{13 e (d+e x)^{13/2} (b d-a e)}",1,"$Aborted","F",-1
2211,-1,0,358,180.0661644,"\int (a+b x)^{3/2} (A+B x) (d+e x)^{5/2} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)*(A + B*x)*(d + e*x)^(5/2),x]","\text{\$Aborted}","-\frac{(b d-a e)^5 (7 a B e-12 A b e+5 b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{512 b^{9/2} e^{7/2}}+\frac{\sqrt{a+b x} \sqrt{d+e x} (b d-a e)^4 (7 a B e-12 A b e+5 b B d)}{512 b^4 e^3}-\frac{(a+b x)^{3/2} \sqrt{d+e x} (b d-a e)^3 (7 a B e-12 A b e+5 b B d)}{768 b^4 e^2}-\frac{(a+b x)^{5/2} \sqrt{d+e x} (b d-a e)^2 (7 a B e-12 A b e+5 b B d)}{192 b^4 e}-\frac{(a+b x)^{5/2} (d+e x)^{3/2} (b d-a e) (7 a B e-12 A b e+5 b B d)}{96 b^3 e}-\frac{(a+b x)^{5/2} (d+e x)^{5/2} (7 a B e-12 A b e+5 b B d)}{60 b^2 e}+\frac{B (a+b x)^{5/2} (d+e x)^{7/2}}{6 b e}",1,"$Aborted","F",-1
2212,-1,0,304,180.0331196,"\int (a+b x)^{3/2} (A+B x) (d+e x)^{3/2} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)*(A + B*x)*(d + e*x)^(3/2),x]","\text{\$Aborted}","\frac{3 (b d-a e)^4 (2 A b e-B (a e+b d)) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{128 b^{7/2} e^{7/2}}-\frac{3 \sqrt{a+b x} \sqrt{d+e x} (b d-a e)^3 (2 A b e-B (a e+b d))}{128 b^3 e^3}+\frac{(a+b x)^{3/2} \sqrt{d+e x} (b d-a e)^2 (2 A b e-B (a e+b d))}{64 b^3 e^2}+\frac{(a+b x)^{5/2} \sqrt{d+e x} (b d-a e) (2 A b e-B (a e+b d))}{16 b^3 e}+\frac{(a+b x)^{5/2} (d+e x)^{3/2} (2 A b e-B (a e+b d))}{8 b^2 e}+\frac{B (a+b x)^{5/2} (d+e x)^{5/2}}{5 b e}",1,"$Aborted","F",-1
2213,-1,0,250,180.0171106,"\int (a+b x)^{3/2} (A+B x) \sqrt{d+e x} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)*(A + B*x)*Sqrt[d + e*x],x]","\text{\$Aborted}","-\frac{(b d-a e)^3 (3 a B e-8 A b e+5 b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{64 b^{5/2} e^{7/2}}+\frac{\sqrt{a+b x} \sqrt{d+e x} (b d-a e)^2 (3 a B e-8 A b e+5 b B d)}{64 b^2 e^3}-\frac{(a+b x)^{3/2} \sqrt{d+e x} (b d-a e) (3 a B e-8 A b e+5 b B d)}{96 b^2 e^2}-\frac{(a+b x)^{5/2} \sqrt{d+e x} (3 a B e-8 A b e+5 b B d)}{24 b^2 e}+\frac{B (a+b x)^{5/2} (d+e x)^{3/2}}{4 b e}",1,"$Aborted","F",-1
2214,-1,0,193,180.0111751,"\int \frac{(a+b x)^{3/2} (A+B x)}{\sqrt{d+e x}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/Sqrt[d + e*x],x]","\text{\$Aborted}","-\frac{(b d-a e)^2 (a B e-6 A b e+5 b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{8 b^{3/2} e^{7/2}}+\frac{\sqrt{a+b x} \sqrt{d+e x} (b d-a e) (a B e-6 A b e+5 b B d)}{8 b e^3}-\frac{(a+b x)^{3/2} \sqrt{d+e x} (a B e-6 A b e+5 b B d)}{12 b e^2}+\frac{B (a+b x)^{5/2} \sqrt{d+e x}}{3 b e}",1,"$Aborted","F",-1
2215,-1,0,202,180.1564787,"\int \frac{(a+b x)^{3/2} (A+B x)}{(d+e x)^{3/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(3/2),x]","\text{\$Aborted}","\frac{3 (b d-a e) (-a B e-4 A b e+5 b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{4 \sqrt{b} e^{7/2}}-\frac{3 \sqrt{a+b x} \sqrt{d+e x} (-a B e-4 A b e+5 b B d)}{4 e^3}+\frac{(a+b x)^{3/2} \sqrt{d+e x} (-a B e-4 A b e+5 b B d)}{2 e^2 (b d-a e)}-\frac{2 (a+b x)^{5/2} (B d-A e)}{e \sqrt{d+e x} (b d-a e)}",1,"$Aborted","F",-1
2216,-1,0,202,180.008091,"\int \frac{(a+b x)^{3/2} (A+B x)}{(d+e x)^{5/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(5/2),x]","\text{\$Aborted}","-\frac{\sqrt{b} (-3 a B e-2 A b e+5 b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{e^{7/2}}+\frac{b \sqrt{a+b x} \sqrt{d+e x} (-3 a B e-2 A b e+5 b B d)}{e^3 (b d-a e)}-\frac{2 (a+b x)^{3/2} (-3 a B e-2 A b e+5 b B d)}{3 e^2 \sqrt{d+e x} (b d-a e)}-\frac{2 (a+b x)^{5/2} (B d-A e)}{3 e (d+e x)^{3/2} (b d-a e)}",1,"$Aborted","F",-1
2217,-1,0,138,180.0165513,"\int \frac{(a+b x)^{3/2} (A+B x)}{(d+e x)^{7/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(7/2),x]","\text{\$Aborted}","-\frac{2 (a+b x)^{5/2} (B d-A e)}{5 e (d+e x)^{5/2} (b d-a e)}+\frac{2 b^{3/2} B \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{e^{7/2}}-\frac{2 b B \sqrt{a+b x}}{e^3 \sqrt{d+e x}}-\frac{2 B (a+b x)^{3/2}}{3 e^2 (d+e x)^{3/2}}",1,"$Aborted","F",-1
2218,-1,0,95,180.2036743,"\int \frac{(a+b x)^{3/2} (A+B x)}{(d+e x)^{9/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(9/2),x]","\text{\$Aborted}","\frac{2 (a+b x)^{5/2} (-7 a B e+2 A b e+5 b B d)}{35 e (d+e x)^{5/2} (b d-a e)^2}-\frac{2 (a+b x)^{5/2} (B d-A e)}{7 e (d+e x)^{7/2} (b d-a e)}",1,"$Aborted","F",-1
2219,-1,0,147,180.6462356,"\int \frac{(a+b x)^{3/2} (A+B x)}{(d+e x)^{11/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(11/2),x]","\text{\$Aborted}","\frac{4 b (a+b x)^{5/2} (-9 a B e+4 A b e+5 b B d)}{315 e (d+e x)^{5/2} (b d-a e)^3}+\frac{2 (a+b x)^{5/2} (-9 a B e+4 A b e+5 b B d)}{63 e (d+e x)^{7/2} (b d-a e)^2}-\frac{2 (a+b x)^{5/2} (B d-A e)}{9 e (d+e x)^{9/2} (b d-a e)}",1,"$Aborted","F",-1
2220,-1,0,201,181.5811408,"\int \frac{(a+b x)^{3/2} (A+B x)}{(d+e x)^{13/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(13/2),x]","\text{\$Aborted}","\frac{16 b^2 (a+b x)^{5/2} (-11 a B e+6 A b e+5 b B d)}{3465 e (d+e x)^{5/2} (b d-a e)^4}+\frac{8 b (a+b x)^{5/2} (-11 a B e+6 A b e+5 b B d)}{693 e (d+e x)^{7/2} (b d-a e)^3}+\frac{2 (a+b x)^{5/2} (-11 a B e+6 A b e+5 b B d)}{99 e (d+e x)^{9/2} (b d-a e)^2}-\frac{2 (a+b x)^{5/2} (B d-A e)}{11 e (d+e x)^{11/2} (b d-a e)}",1,"$Aborted","F",-1
2221,-1,0,255,180.9505134,"\int \frac{(a+b x)^{3/2} (A+B x)}{(d+e x)^{15/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(15/2),x]","\text{\$Aborted}","\frac{32 b^3 (a+b x)^{5/2} (-13 a B e+8 A b e+5 b B d)}{15015 e (d+e x)^{5/2} (b d-a e)^5}+\frac{16 b^2 (a+b x)^{5/2} (-13 a B e+8 A b e+5 b B d)}{3003 e (d+e x)^{7/2} (b d-a e)^4}+\frac{4 b (a+b x)^{5/2} (-13 a B e+8 A b e+5 b B d)}{429 e (d+e x)^{9/2} (b d-a e)^3}+\frac{2 (a+b x)^{5/2} (-13 a B e+8 A b e+5 b B d)}{143 e (d+e x)^{11/2} (b d-a e)^2}-\frac{2 (a+b x)^{5/2} (B d-A e)}{13 e (d+e x)^{13/2} (b d-a e)}",1,"$Aborted","F",-1
2222,-1,0,304,180.3113703,"\int \frac{(a+b x)^{3/2} (A+B x)}{(d+e x)^{17/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(17/2),x]","\text{\$Aborted}","\frac{256 b^4 (a+b x)^{5/2} (-3 a B e+2 A b e+b B d)}{45045 e (d+e x)^{5/2} (b d-a e)^6}+\frac{128 b^3 (a+b x)^{5/2} (-3 a B e+2 A b e+b B d)}{9009 e (d+e x)^{7/2} (b d-a e)^5}+\frac{32 b^2 (a+b x)^{5/2} (-3 a B e+2 A b e+b B d)}{1287 e (d+e x)^{9/2} (b d-a e)^4}+\frac{16 b (a+b x)^{5/2} (-3 a B e+2 A b e+b B d)}{429 e (d+e x)^{11/2} (b d-a e)^3}+\frac{2 (a+b x)^{5/2} (-3 a B e+2 A b e+b B d)}{39 e (d+e x)^{13/2} (b d-a e)^2}-\frac{2 (a+b x)^{5/2} (B d-A e)}{15 e (d+e x)^{15/2} (b d-a e)}",1,"$Aborted","F",-1
2223,-1,0,412,180.1191496,"\int (a+b x)^{5/2} (A+B x) (d+e x)^{5/2} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)*(A + B*x)*(d + e*x)^(5/2),x]","\text{\$Aborted}","-\frac{5 (b d-a e)^6 (2 A b e-B (a e+b d)) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{1024 b^{9/2} e^{9/2}}+\frac{5 \sqrt{a+b x} \sqrt{d+e x} (b d-a e)^5 (2 A b e-B (a e+b d))}{1024 b^4 e^4}-\frac{5 (a+b x)^{3/2} \sqrt{d+e x} (b d-a e)^4 (2 A b e-B (a e+b d))}{1536 b^4 e^3}+\frac{(a+b x)^{5/2} \sqrt{d+e x} (b d-a e)^3 (2 A b e-B (a e+b d))}{384 b^4 e^2}+\frac{(a+b x)^{7/2} \sqrt{d+e x} (b d-a e)^2 (2 A b e-B (a e+b d))}{64 b^4 e}+\frac{(a+b x)^{7/2} (d+e x)^{3/2} (b d-a e) (2 A b e-B (a e+b d))}{24 b^3 e}+\frac{(a+b x)^{7/2} (d+e x)^{5/2} (2 A b e-B (a e+b d))}{12 b^2 e}+\frac{B (a+b x)^{7/2} (d+e x)^{7/2}}{7 b e}",1,"$Aborted","F",-1
2224,-1,0,358,180.063507,"\int (a+b x)^{5/2} (A+B x) (d+e x)^{3/2} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)*(A + B*x)*(d + e*x)^(3/2),x]","\text{\$Aborted}","\frac{(b d-a e)^5 (5 a B e-12 A b e+7 b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{512 b^{7/2} e^{9/2}}-\frac{\sqrt{a+b x} \sqrt{d+e x} (b d-a e)^4 (5 a B e-12 A b e+7 b B d)}{512 b^3 e^4}+\frac{(a+b x)^{3/2} \sqrt{d+e x} (b d-a e)^3 (5 a B e-12 A b e+7 b B d)}{768 b^3 e^3}-\frac{(a+b x)^{5/2} \sqrt{d+e x} (b d-a e)^2 (5 a B e-12 A b e+7 b B d)}{960 b^3 e^2}-\frac{(a+b x)^{7/2} \sqrt{d+e x} (b d-a e) (5 a B e-12 A b e+7 b B d)}{160 b^3 e}-\frac{(a+b x)^{7/2} (d+e x)^{3/2} (5 a B e-12 A b e+7 b B d)}{60 b^2 e}+\frac{B (a+b x)^{7/2} (d+e x)^{5/2}}{6 b e}",1,"$Aborted","F",-1
2225,-1,0,304,180.0317482,"\int (a+b x)^{5/2} (A+B x) \sqrt{d+e x} \, dx","IntegrateAlgebraic[(a + b*x)^(5/2)*(A + B*x)*Sqrt[d + e*x],x]","\text{\$Aborted}","\frac{(b d-a e)^4 (3 a B e-10 A b e+7 b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{128 b^{5/2} e^{9/2}}-\frac{\sqrt{a+b x} \sqrt{d+e x} (b d-a e)^3 (3 a B e-10 A b e+7 b B d)}{128 b^2 e^4}+\frac{(a+b x)^{3/2} \sqrt{d+e x} (b d-a e)^2 (3 a B e-10 A b e+7 b B d)}{192 b^2 e^3}-\frac{(a+b x)^{5/2} \sqrt{d+e x} (b d-a e) (3 a B e-10 A b e+7 b B d)}{240 b^2 e^2}-\frac{(a+b x)^{7/2} \sqrt{d+e x} (3 a B e-10 A b e+7 b B d)}{40 b^2 e}+\frac{B (a+b x)^{7/2} (d+e x)^{3/2}}{5 b e}",1,"$Aborted","F",-1
2226,-1,0,246,180.0221698,"\int \frac{(a+b x)^{5/2} (A+B x)}{\sqrt{d+e x}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/Sqrt[d + e*x],x]","\text{\$Aborted}","\frac{5 (b d-a e)^3 (a B e-8 A b e+7 b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{64 b^{3/2} e^{9/2}}-\frac{5 \sqrt{a+b x} \sqrt{d+e x} (b d-a e)^2 (a B e-8 A b e+7 b B d)}{64 b e^4}+\frac{5 (a+b x)^{3/2} \sqrt{d+e x} (b d-a e) (a B e-8 A b e+7 b B d)}{96 b e^3}-\frac{(a+b x)^{5/2} \sqrt{d+e x} (a B e-8 A b e+7 b B d)}{24 b e^2}+\frac{B (a+b x)^{7/2} \sqrt{d+e x}}{4 b e}",1,"$Aborted","F",-1
2227,-1,0,253,180.0272238,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{3/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(3/2),x]","\text{\$Aborted}","-\frac{5 (b d-a e)^2 (-a B e-6 A b e+7 b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{8 \sqrt{b} e^{9/2}}+\frac{5 \sqrt{a+b x} \sqrt{d+e x} (b d-a e) (-a B e-6 A b e+7 b B d)}{8 e^4}-\frac{5 (a+b x)^{3/2} \sqrt{d+e x} (-a B e-6 A b e+7 b B d)}{12 e^3}+\frac{(a+b x)^{5/2} \sqrt{d+e x} (-a B e-6 A b e+7 b B d)}{3 e^2 (b d-a e)}-\frac{2 (a+b x)^{7/2} (B d-A e)}{e \sqrt{d+e x} (b d-a e)}",1,"$Aborted","F",-1
2228,-1,0,257,180.0479038,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{5/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(5/2),x]","\text{\$Aborted}","\frac{5 \sqrt{b} (b d-a e) (-3 a B e-4 A b e+7 b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{4 e^{9/2}}-\frac{5 b \sqrt{a+b x} \sqrt{d+e x} (-3 a B e-4 A b e+7 b B d)}{4 e^4}+\frac{5 b (a+b x)^{3/2} \sqrt{d+e x} (-3 a B e-4 A b e+7 b B d)}{6 e^3 (b d-a e)}-\frac{2 (a+b x)^{5/2} (-3 a B e-4 A b e+7 b B d)}{3 e^2 \sqrt{d+e x} (b d-a e)}-\frac{2 (a+b x)^{7/2} (B d-A e)}{3 e (d+e x)^{3/2} (b d-a e)}",1,"$Aborted","F",-1
2229,-1,0,256,180.0217183,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{7/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(7/2),x]","\text{\$Aborted}","-\frac{b^{3/2} (-5 a B e-2 A b e+7 b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{e^{9/2}}+\frac{b^2 \sqrt{a+b x} \sqrt{d+e x} (-5 a B e-2 A b e+7 b B d)}{e^4 (b d-a e)}-\frac{2 b (a+b x)^{3/2} (-5 a B e-2 A b e+7 b B d)}{3 e^3 \sqrt{d+e x} (b d-a e)}-\frac{2 (a+b x)^{5/2} (-5 a B e-2 A b e+7 b B d)}{15 e^2 (d+e x)^{3/2} (b d-a e)}-\frac{2 (a+b x)^{7/2} (B d-A e)}{5 e (d+e x)^{5/2} (b d-a e)}",1,"$Aborted","F",-1
2230,-1,0,167,180.1761251,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{9/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(9/2),x]","\text{\$Aborted}","-\frac{2 (a+b x)^{7/2} (B d-A e)}{7 e (d+e x)^{7/2} (b d-a e)}+\frac{2 b^{5/2} B \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{e^{9/2}}-\frac{2 b^2 B \sqrt{a+b x}}{e^4 \sqrt{d+e x}}-\frac{2 b B (a+b x)^{3/2}}{3 e^3 (d+e x)^{3/2}}-\frac{2 B (a+b x)^{5/2}}{5 e^2 (d+e x)^{5/2}}",1,"$Aborted","F",-1
2231,-1,0,95,180.7458448,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{11/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(11/2),x]","\text{\$Aborted}","\frac{2 (a+b x)^{7/2} (-9 a B e+2 A b e+7 b B d)}{63 e (d+e x)^{7/2} (b d-a e)^2}-\frac{2 (a+b x)^{7/2} (B d-A e)}{9 e (d+e x)^{9/2} (b d-a e)}",1,"$Aborted","F",-1
2232,-1,0,147,181.5815685,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{13/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(13/2),x]","\text{\$Aborted}","\frac{4 b (a+b x)^{7/2} (-11 a B e+4 A b e+7 b B d)}{693 e (d+e x)^{7/2} (b d-a e)^3}+\frac{2 (a+b x)^{7/2} (-11 a B e+4 A b e+7 b B d)}{99 e (d+e x)^{9/2} (b d-a e)^2}-\frac{2 (a+b x)^{7/2} (B d-A e)}{11 e (d+e x)^{11/2} (b d-a e)}",1,"$Aborted","F",-1
2233,-1,0,201,180.1511019,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{15/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(15/2),x]","\text{\$Aborted}","\frac{16 b^2 (a+b x)^{7/2} (-13 a B e+6 A b e+7 b B d)}{9009 e (d+e x)^{7/2} (b d-a e)^4}+\frac{8 b (a+b x)^{7/2} (-13 a B e+6 A b e+7 b B d)}{1287 e (d+e x)^{9/2} (b d-a e)^3}+\frac{2 (a+b x)^{7/2} (-13 a B e+6 A b e+7 b B d)}{143 e (d+e x)^{11/2} (b d-a e)^2}-\frac{2 (a+b x)^{7/2} (B d-A e)}{13 e (d+e x)^{13/2} (b d-a e)}",1,"$Aborted","F",-1
2234,-1,0,255,180.3769697,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{17/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(17/2),x]","\text{\$Aborted}","\frac{32 b^3 (a+b x)^{7/2} (-15 a B e+8 A b e+7 b B d)}{45045 e (d+e x)^{7/2} (b d-a e)^5}+\frac{16 b^2 (a+b x)^{7/2} (-15 a B e+8 A b e+7 b B d)}{6435 e (d+e x)^{9/2} (b d-a e)^4}+\frac{4 b (a+b x)^{7/2} (-15 a B e+8 A b e+7 b B d)}{715 e (d+e x)^{11/2} (b d-a e)^3}+\frac{2 (a+b x)^{7/2} (-15 a B e+8 A b e+7 b B d)}{195 e (d+e x)^{13/2} (b d-a e)^2}-\frac{2 (a+b x)^{7/2} (B d-A e)}{15 e (d+e x)^{15/2} (b d-a e)}",1,"$Aborted","F",-1
2235,-1,0,309,180.199035,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{19/2}} \, dx","IntegrateAlgebraic[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(19/2),x]","\text{\$Aborted}","\frac{256 b^4 (a+b x)^{7/2} (-17 a B e+10 A b e+7 b B d)}{765765 e (d+e x)^{7/2} (b d-a e)^6}+\frac{128 b^3 (a+b x)^{7/2} (-17 a B e+10 A b e+7 b B d)}{109395 e (d+e x)^{9/2} (b d-a e)^5}+\frac{32 b^2 (a+b x)^{7/2} (-17 a B e+10 A b e+7 b B d)}{12155 e (d+e x)^{11/2} (b d-a e)^4}+\frac{16 b (a+b x)^{7/2} (-17 a B e+10 A b e+7 b B d)}{3315 e (d+e x)^{13/2} (b d-a e)^3}+\frac{2 (a+b x)^{7/2} (-17 a B e+10 A b e+7 b B d)}{255 e (d+e x)^{15/2} (b d-a e)^2}-\frac{2 (a+b x)^{7/2} (B d-A e)}{17 e (d+e x)^{17/2} (b d-a e)}",1,"$Aborted","F",-1
2236,-1,0,246,180.0163207,"\int \frac{(A+B x) (d+e x)^{5/2}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^(5/2))/Sqrt[a + b*x],x]","\text{\$Aborted}","-\frac{5 (b d-a e)^3 (7 a B e-8 A b e+b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{64 b^{9/2} e^{3/2}}-\frac{5 \sqrt{a+b x} \sqrt{d+e x} (b d-a e)^2 (7 a B e-8 A b e+b B d)}{64 b^4 e}-\frac{5 \sqrt{a+b x} (d+e x)^{3/2} (b d-a e) (7 a B e-8 A b e+b B d)}{96 b^3 e}-\frac{\sqrt{a+b x} (d+e x)^{5/2} (7 a B e-8 A b e+b B d)}{24 b^2 e}+\frac{B \sqrt{a+b x} (d+e x)^{7/2}}{4 b e}",1,"$Aborted","F",-1
2237,-1,0,193,180.0151513,"\int \frac{(A+B x) (d+e x)^{3/2}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^(3/2))/Sqrt[a + b*x],x]","\text{\$Aborted}","-\frac{(b d-a e)^2 (5 a B e-6 A b e+b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{8 b^{7/2} e^{3/2}}-\frac{\sqrt{a+b x} \sqrt{d+e x} (b d-a e) (5 a B e-6 A b e+b B d)}{8 b^3 e}-\frac{\sqrt{a+b x} (d+e x)^{3/2} (5 a B e-6 A b e+b B d)}{12 b^2 e}+\frac{B \sqrt{a+b x} (d+e x)^{5/2}}{3 b e}",1,"$Aborted","F",-1
2238,1,1705,140,14.1676947,"\int \frac{(A+B x) \sqrt{d+e x}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[((A + B*x)*Sqrt[d + e*x])/Sqrt[a + b*x],x]","\frac{\left(-2 \sqrt{a+b} B d b^3-4 B d \sqrt{a+b x} b^3-4 B e \sqrt{a+b x} b^3-\frac{B d^2 \sqrt{a+b x} b^3}{2 e}+4 \sqrt{a+b} B \sqrt{d+e} \sqrt{d+e x} b^3+\frac{2 \sqrt{a+b} B d \sqrt{d+e} \sqrt{d+e x} b^3}{e}-\frac{3 \sqrt{a+b} B d^2 b^3}{2 e}+a \sqrt{a+b} B d b^2+2 a \sqrt{a+b} B e b^2-3 a B d \sqrt{a+b x} b^2-4 a B e \sqrt{a+b x} b^2+2 a \sqrt{a+b} B \sqrt{d+e} \sqrt{d+e x} b^2+\frac{1}{2} a^2 \sqrt{a+b} B e b-\frac{1}{2} a^2 B e \sqrt{a+b x} b\right) \left(\sqrt{d+e}-\sqrt{d+e x}\right)^7}{\left(-d b+\sqrt{d+e} \sqrt{d+e x} b+a e-\sqrt{a+b} e \sqrt{a+b x}\right)^4}+\frac{\left(\frac{3}{2} \sqrt{a+b} B e a^2-\frac{3}{2} B e \sqrt{a+b x} a^2+b \sqrt{a+b} B d a+4 b \sqrt{a+b} B e a-9 b B d \sqrt{a+b x} a-12 b B e \sqrt{a+b x} a+8 b \sqrt{a+b} B \sqrt{d+e} \sqrt{d+e x} a-12 b^2 \sqrt{a+b} B d-4 b^2 \sqrt{a+b} B e-12 b^2 B d \sqrt{a+b x}-12 b^2 B e \sqrt{a+b x}-\frac{3 b^2 B d^2 \sqrt{a+b x}}{2 e}+16 b^2 \sqrt{a+b} B \sqrt{d+e} \sqrt{d+e x}+\frac{8 b^2 \sqrt{a+b} B d \sqrt{d+e} \sqrt{d+e x}}{e}-\frac{13 b^2 \sqrt{a+b} B d^2}{2 e}\right) \left(\sqrt{d+e}-\sqrt{d+e x}\right)^5}{\left(-d b+\sqrt{d+e} \sqrt{d+e x} b+a e-\sqrt{a+b} e \sqrt{a+b x}\right)^3}+\frac{\left(\frac{\sqrt{a+b} B e a^2}{4 b}-\frac{B e \sqrt{a+b x} a^2}{4 b}-\frac{3}{2} \sqrt{a+b} B d a+A \sqrt{a+b} e a-\frac{13}{2} B d \sqrt{a+b x} a-A e \sqrt{a+b x} a-8 B e \sqrt{a+b x} a+8 \sqrt{a+b} B \sqrt{d+e} \sqrt{d+e x} a-20 b \sqrt{a+b} B d-A b \sqrt{a+b} d-10 b \sqrt{a+b} B e-A b d \sqrt{a+b x}-10 b B d \sqrt{a+b x}-2 A b e \sqrt{a+b x}-10 b B e \sqrt{a+b x}-\frac{5 b B d^2 \sqrt{a+b x}}{4 e}+20 b \sqrt{a+b} B \sqrt{d+e} \sqrt{d+e x}+2 A b \sqrt{a+b} \sqrt{d+e} \sqrt{d+e x}+\frac{10 b \sqrt{a+b} B d \sqrt{d+e} \sqrt{d+e x}}{e}-\frac{35 b \sqrt{a+b} B d^2}{4 e}\right) \left(\sqrt{d+e}-\sqrt{d+e x}\right)^3}{\left(-d b+\sqrt{d+e} \sqrt{d+e x} b+a e-\sqrt{a+b} e \sqrt{a+b x}\right)^2}+\frac{\left(\frac{\sqrt{d+e}}{4 b^2 e}-\frac{\sqrt{d+e x}}{4 b^2 e}\right) \left(-15 \sqrt{a+b} B d^2 b^2-24 \sqrt{a+b} B e^2 b^2-8 A \sqrt{a+b} e^2 b^2-40 \sqrt{a+b} B d e b^2-12 A \sqrt{a+b} d e b^2-B d^2 \sqrt{a+b x} b^2-8 A e^2 \sqrt{a+b x} b^2-8 B e^2 \sqrt{a+b x} b^2-4 A d e \sqrt{a+b x} b^2-8 B d e \sqrt{a+b x} b^2+16 \sqrt{a+b} B d \sqrt{d+e} \sqrt{d+e x} b^2+32 \sqrt{a+b} B e \sqrt{d+e} \sqrt{d+e x} b^2+16 A \sqrt{a+b} e \sqrt{d+e} \sqrt{d+e x} b^2+4 a A \sqrt{a+b} e^2 b+2 a \sqrt{a+b} B d e b-4 a A e^2 \sqrt{a+b x} b-2 a B d e \sqrt{a+b x} b-3 a^2 \sqrt{a+b} B e^2+3 a^2 B e^2 \sqrt{a+b x}\right)}{-d b+\sqrt{d+e} \sqrt{d+e x} b+a e-\sqrt{a+b} e \sqrt{a+b x}}+\left(\frac{3 B \sqrt{e} a^2}{2 b^{5/2}}-\frac{2 A \sqrt{e} a}{b^{3/2}}-\frac{B d a}{b^{3/2} \sqrt{e}}+\frac{2 A d}{\sqrt{b} \sqrt{e}}-\frac{B d^2}{2 \sqrt{b} e^{3/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{a+b} \sqrt{e}-\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \left(\sqrt{d+e}-\sqrt{d+e x}\right)}\right)","-\frac{(b d-a e) (3 a B e-4 A b e+b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{4 b^{5/2} e^{3/2}}-\frac{\sqrt{a+b x} \sqrt{d+e x} (3 a B e-4 A b e+b B d)}{4 b^2 e}+\frac{B \sqrt{a+b x} (d+e x)^{3/2}}{2 b e}",1,"((Sqrt[d + e] - Sqrt[d + e*x])^3*(-(A*b*Sqrt[a + b]*d) - (3*a*Sqrt[a + b]*B*d)/2 - 20*b*Sqrt[a + b]*B*d - (35*b*Sqrt[a + b]*B*d^2)/(4*e) + a*A*Sqrt[a + b]*e + (a^2*Sqrt[a + b]*B*e)/(4*b) - 10*b*Sqrt[a + b]*B*e - A*b*d*Sqrt[a + b*x] - (13*a*B*d*Sqrt[a + b*x])/2 - 10*b*B*d*Sqrt[a + b*x] - (5*b*B*d^2*Sqrt[a + b*x])/(4*e) - a*A*e*Sqrt[a + b*x] - 2*A*b*e*Sqrt[a + b*x] - 8*a*B*e*Sqrt[a + b*x] - (a^2*B*e*Sqrt[a + b*x])/(4*b) - 10*b*B*e*Sqrt[a + b*x] + 2*A*b*Sqrt[a + b]*Sqrt[d + e]*Sqrt[d + e*x] + 8*a*Sqrt[a + b]*B*Sqrt[d + e]*Sqrt[d + e*x] + 20*b*Sqrt[a + b]*B*Sqrt[d + e]*Sqrt[d + e*x] + (10*b*Sqrt[a + b]*B*d*Sqrt[d + e]*Sqrt[d + e*x])/e))/(-(b*d) + a*e - Sqrt[a + b]*e*Sqrt[a + b*x] + b*Sqrt[d + e]*Sqrt[d + e*x])^2 + ((Sqrt[d + e] - Sqrt[d + e*x])^5*(a*b*Sqrt[a + b]*B*d - 12*b^2*Sqrt[a + b]*B*d - (13*b^2*Sqrt[a + b]*B*d^2)/(2*e) + (3*a^2*Sqrt[a + b]*B*e)/2 + 4*a*b*Sqrt[a + b]*B*e - 4*b^2*Sqrt[a + b]*B*e - 9*a*b*B*d*Sqrt[a + b*x] - 12*b^2*B*d*Sqrt[a + b*x] - (3*b^2*B*d^2*Sqrt[a + b*x])/(2*e) - (3*a^2*B*e*Sqrt[a + b*x])/2 - 12*a*b*B*e*Sqrt[a + b*x] - 12*b^2*B*e*Sqrt[a + b*x] + 8*a*b*Sqrt[a + b]*B*Sqrt[d + e]*Sqrt[d + e*x] + 16*b^2*Sqrt[a + b]*B*Sqrt[d + e]*Sqrt[d + e*x] + (8*b^2*Sqrt[a + b]*B*d*Sqrt[d + e]*Sqrt[d + e*x])/e))/(-(b*d) + a*e - Sqrt[a + b]*e*Sqrt[a + b*x] + b*Sqrt[d + e]*Sqrt[d + e*x])^3 + ((Sqrt[d + e] - Sqrt[d + e*x])^7*(a*b^2*Sqrt[a + b]*B*d - 2*b^3*Sqrt[a + b]*B*d - (3*b^3*Sqrt[a + b]*B*d^2)/(2*e) + (a^2*b*Sqrt[a + b]*B*e)/2 + 2*a*b^2*Sqrt[a + b]*B*e - 3*a*b^2*B*d*Sqrt[a + b*x] - 4*b^3*B*d*Sqrt[a + b*x] - (b^3*B*d^2*Sqrt[a + b*x])/(2*e) - (a^2*b*B*e*Sqrt[a + b*x])/2 - 4*a*b^2*B*e*Sqrt[a + b*x] - 4*b^3*B*e*Sqrt[a + b*x] + 2*a*b^2*Sqrt[a + b]*B*Sqrt[d + e]*Sqrt[d + e*x] + 4*b^3*Sqrt[a + b]*B*Sqrt[d + e]*Sqrt[d + e*x] + (2*b^3*Sqrt[a + b]*B*d*Sqrt[d + e]*Sqrt[d + e*x])/e))/(-(b*d) + a*e - Sqrt[a + b]*e*Sqrt[a + b*x] + b*Sqrt[d + e]*Sqrt[d + e*x])^4 + ((Sqrt[d + e]/(4*b^2*e) - Sqrt[d + e*x]/(4*b^2*e))*(-15*b^2*Sqrt[a + b]*B*d^2 - 12*A*b^2*Sqrt[a + b]*d*e + 2*a*b*Sqrt[a + b]*B*d*e - 40*b^2*Sqrt[a + b]*B*d*e + 4*a*A*b*Sqrt[a + b]*e^2 - 8*A*b^2*Sqrt[a + b]*e^2 - 3*a^2*Sqrt[a + b]*B*e^2 - 24*b^2*Sqrt[a + b]*B*e^2 - b^2*B*d^2*Sqrt[a + b*x] - 4*A*b^2*d*e*Sqrt[a + b*x] - 2*a*b*B*d*e*Sqrt[a + b*x] - 8*b^2*B*d*e*Sqrt[a + b*x] - 4*a*A*b*e^2*Sqrt[a + b*x] - 8*A*b^2*e^2*Sqrt[a + b*x] + 3*a^2*B*e^2*Sqrt[a + b*x] - 8*b^2*B*e^2*Sqrt[a + b*x] + 16*b^2*Sqrt[a + b]*B*d*Sqrt[d + e]*Sqrt[d + e*x] + 16*A*b^2*Sqrt[a + b]*e*Sqrt[d + e]*Sqrt[d + e*x] + 32*b^2*Sqrt[a + b]*B*e*Sqrt[d + e]*Sqrt[d + e*x]))/(-(b*d) + a*e - Sqrt[a + b]*e*Sqrt[a + b*x] + b*Sqrt[d + e]*Sqrt[d + e*x]) + (-1/2*(B*d^2)/(Sqrt[b]*e^(3/2)) + (2*A*d)/(Sqrt[b]*Sqrt[e]) - (a*B*d)/(b^(3/2)*Sqrt[e]) - (2*a*A*Sqrt[e])/b^(3/2) + (3*a^2*B*Sqrt[e])/(2*b^(5/2)))*ArcTanh[(Sqrt[a + b]*Sqrt[e] - Sqrt[e]*Sqrt[a + b*x])/(Sqrt[b]*(Sqrt[d + e] - Sqrt[d + e*x]))]","B",1
2239,1,373,84,1.3397,"\int \frac{A+B x}{\sqrt{a+b x} \sqrt{d+e x}} \, dx","IntegrateAlgebraic[(A + B*x)/(Sqrt[a + b*x]*Sqrt[d + e*x]),x]","\frac{\left(\sqrt{d+e}-\sqrt{d+e x}\right) \left(\frac{B \sqrt{a+b}}{b e}-\frac{B \sqrt{a+b x}}{b e}\right) \left(a^2 e^2+b d e \sqrt{a+b} \sqrt{a+b x}+a b e \sqrt{d+e} \sqrt{d+e x}-2 b e \sqrt{a+b} \sqrt{d+e} \sqrt{a+b x} \sqrt{d+e x}+a b e^2 x-a e^2 \sqrt{a+b} \sqrt{a+b x}+a b e^2+b^2 d^2+b^2 d e x-b^2 d \sqrt{d+e} \sqrt{d+e x}+b^2 d e+2 b^2 e^2 x\right)}{\left(-e \sqrt{a+b} \sqrt{a+b x}+a e+b \sqrt{d+e} \sqrt{d+e x}+b (-d)\right)^2}+\left(-\frac{2 a B}{b^{3/2} \sqrt{e}}+\frac{4 A}{\sqrt{b} \sqrt{e}}-\frac{2 B d}{\sqrt{b} e^{3/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b}-\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \left(\sqrt{d+e}-\sqrt{d+e x}\right)}\right)","\frac{(2 A b e-B (a e+b d)) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{b^{3/2} e^{3/2}}+\frac{B \sqrt{a+b x} \sqrt{d+e x}}{b e}",1,"(((Sqrt[a + b]*B)/(b*e) - (B*Sqrt[a + b*x])/(b*e))*(Sqrt[d + e] - Sqrt[d + e*x])*(b^2*d^2 + b^2*d*e + a^2*e^2 + a*b*e^2 + b^2*d*e*x + a*b*e^2*x + 2*b^2*e^2*x + b*Sqrt[a + b]*d*e*Sqrt[a + b*x] - a*Sqrt[a + b]*e^2*Sqrt[a + b*x] - b^2*d*Sqrt[d + e]*Sqrt[d + e*x] + a*b*e*Sqrt[d + e]*Sqrt[d + e*x] - 2*b*Sqrt[a + b]*e*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x]))/(-(b*d) + a*e - Sqrt[a + b]*e*Sqrt[a + b*x] + b*Sqrt[d + e]*Sqrt[d + e*x])^2 + ((-2*B*d)/(Sqrt[b]*e^(3/2)) + (4*A)/(Sqrt[b]*Sqrt[e]) - (2*a*B)/(b^(3/2)*Sqrt[e]))*ArcTanh[(Sqrt[a + b]*Sqrt[e] - Sqrt[e]*Sqrt[a + b*x])/(Sqrt[b]*(Sqrt[d + e] - Sqrt[d + e*x]))]","B",1
2240,1,661,85,10.1748549,"\int \frac{A+B x}{\sqrt{a+b x} (d+e x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(Sqrt[a + b*x]*(d + e*x)^(3/2)),x]","\frac{\sqrt{a+b} \left(2 \sqrt{d+e} (A e-B d) \left(6 a d e+2 a e^2 x+4 a e^2+2 b d^2+5 b d e x+5 b d e+b e^2 x^2+5 b e^2 x+2 b e^2\right)+2 \sqrt{d+e x} (A e-B d) \left(-6 a d e-6 a e^2-2 b d^2-4 b d e x-6 b d e-4 b e^2 x-4 b e^2\right)\right)+2 \sqrt{d+e} \sqrt{a+b x} (A e-B d) \left(-6 a d e-2 a e^2 x-4 a e^2-2 b d^2-2 b d e x-8 b d e-4 b e^2 x-4 b e^2\right)+2 \sqrt{a+b x} \sqrt{d+e x} (A e-B d) \left(6 a d e+6 a e^2+2 b d^2+b d e x+9 b d e+b e^2 x+7 b e^2\right)}{e (d+e)^{3/2} \sqrt{d+e x} \left(4 a^2 e^2-2 a b d e+2 a b e^2 x+4 a b e^2-2 b^2 d^2-2 b^2 d e x-4 b^2 d e\right)+e (d+e) \left(-2 a^2 d e^2-2 a^2 e^3 x+2 a b d^2 e+a b d e^2 x-a b d e^2-a b e^3 x^2-a b e^3 x+2 b^2 d^3+3 b^2 d^2 e x+5 b^2 d^2 e+b^2 d e^2 x^2+5 b^2 d e^2 x+2 b^2 d e^2+2 b^2 e^3 x\right)+\sqrt{a+b} \sqrt{a+b x} \left(e (d+e) \left(2 a d e^2+2 a e^3 x-2 b d^2 e-2 b d e^2 x\right)+e (d+e)^{3/2} \sqrt{d+e x} \left(-4 a e^2+2 b d e-2 b e^2\right)\right)}+\frac{4 B \tanh ^{-1}\left(\frac{\frac{\sqrt{e} \sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b}}}{\sqrt{d+e}-\sqrt{d+e x}}\right)}{\sqrt{b} e^{3/2}}","\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{\sqrt{b} e^{3/2}}-\frac{2 \sqrt{a+b x} (B d-A e)}{e \sqrt{d+e x} (b d-a e)}",1,"(2*Sqrt[d + e]*(-(B*d) + A*e)*Sqrt[a + b*x]*(-2*b*d^2 - 6*a*d*e - 8*b*d*e - 4*a*e^2 - 4*b*e^2 - 2*b*d*e*x - 2*a*e^2*x - 4*b*e^2*x) + 2*(-(B*d) + A*e)*Sqrt[a + b*x]*Sqrt[d + e*x]*(2*b*d^2 + 6*a*d*e + 9*b*d*e + 6*a*e^2 + 7*b*e^2 + b*d*e*x + b*e^2*x) + Sqrt[a + b]*(2*(-(B*d) + A*e)*Sqrt[d + e*x]*(-2*b*d^2 - 6*a*d*e - 6*b*d*e - 6*a*e^2 - 4*b*e^2 - 4*b*d*e*x - 4*b*e^2*x) + 2*Sqrt[d + e]*(-(B*d) + A*e)*(2*b*d^2 + 6*a*d*e + 5*b*d*e + 4*a*e^2 + 2*b*e^2 + 5*b*d*e*x + 2*a*e^2*x + 5*b*e^2*x + b*e^2*x^2)))/(e*(d + e)^(3/2)*Sqrt[d + e*x]*(-2*b^2*d^2 - 2*a*b*d*e - 4*b^2*d*e + 4*a^2*e^2 + 4*a*b*e^2 - 2*b^2*d*e*x + 2*a*b*e^2*x) + e*(d + e)*(2*b^2*d^3 + 2*a*b*d^2*e + 5*b^2*d^2*e - 2*a^2*d*e^2 - a*b*d*e^2 + 2*b^2*d*e^2 + 3*b^2*d^2*e*x + a*b*d*e^2*x + 5*b^2*d*e^2*x - 2*a^2*e^3*x - a*b*e^3*x + 2*b^2*e^3*x + b^2*d*e^2*x^2 - a*b*e^3*x^2) + Sqrt[a + b]*Sqrt[a + b*x]*(e*(d + e)^(3/2)*(2*b*d*e - 4*a*e^2 - 2*b*e^2)*Sqrt[d + e*x] + e*(d + e)*(-2*b*d^2*e + 2*a*d*e^2 - 2*b*d*e^2*x + 2*a*e^3*x))) + (4*B*ArcTanh[((Sqrt[a + b]*Sqrt[e])/Sqrt[b] - (Sqrt[e]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[d + e] - Sqrt[d + e*x])])/(Sqrt[b]*e^(3/2))","B",1
2241,1,2286,94,7.2150854,"\int \frac{A+B x}{\sqrt{a+b x} (d+e x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(Sqrt[a + b*x]*(d + e*x)^(5/2)),x]","\text{Result too large to show}","\frac{2 \sqrt{a+b x} (-3 a B e+2 A b e+b B d)}{3 e \sqrt{d+e x} (b d-a e)^2}-\frac{2 \sqrt{a+b x} (B d-A e)}{3 e (d+e x)^{3/2} (b d-a e)}",1,"((-1/6*1/(d + e)^(3/2) + Sqrt[a + b*x]/(6*Sqrt[a + b]*(d + e)^(3/2)))*(Sqrt[d + e] - Sqrt[d + e*x])^6*((24*A*b^2*Sqrt[a + b]*d^3 - 16*a*A*b*Sqrt[a + b]*d^2*e + 28*A*b^2*Sqrt[a + b]*d^2*e + 16*a^2*A*Sqrt[a + b]*d*e^2 + 8*A*b^2*Sqrt[a + b]*d*e^2 + 8*a^2*A*Sqrt[a + b]*e^3 + 4*a*A*b*Sqrt[a + b]*e^3 + 28*A*b^2*Sqrt[a + b]*d^2*e*x + 40*A*b^2*Sqrt[a + b]*d*e^2*x + 8*a^2*A*Sqrt[a + b]*e^3*x + 8*a*A*b*Sqrt[a + b]*e^3*x + 12*A*b^2*Sqrt[a + b]*e^3*x + 8*A*b^2*Sqrt[a + b]*d*e^2*x^2 + 4*a*A*b*Sqrt[a + b]*e^3*x^2 + 12*A*b^2*Sqrt[a + b]*e^3*x^2 + 16*a*A*b*d^2*e*Sqrt[a + b*x] + 16*A*b^2*d^2*e*Sqrt[a + b*x] - 16*a^2*A*d*e^2*Sqrt[a + b*x] - 8*a*A*b*d*e^2*Sqrt[a + b*x] + 8*A*b^2*d*e^2*Sqrt[a + b*x] - 8*a^2*A*e^3*Sqrt[a + b*x] - 8*a*A*b*e^3*Sqrt[a + b*x] + 8*a*A*b*d*e^2*x*Sqrt[a + b*x] + 8*A*b^2*d*e^2*x*Sqrt[a + b*x] - 8*a^2*A*e^3*x*Sqrt[a + b*x] - 8*a*A*b*e^3*x*Sqrt[a + b*x] - 24*A*b^2*Sqrt[a + b]*d^2*Sqrt[d + e]*Sqrt[d + e*x] + 16*a*A*b*Sqrt[a + b]*d*e*Sqrt[d + e]*Sqrt[d + e*x] - 16*A*b^2*Sqrt[a + b]*d*e*Sqrt[d + e]*Sqrt[d + e*x] + 8*a^2*A*Sqrt[a + b]*e^2*Sqrt[d + e]*Sqrt[d + e*x] + 16*a*A*b*Sqrt[a + b]*e^2*Sqrt[d + e]*Sqrt[d + e*x] - 16*A*b^2*Sqrt[a + b]*d*e*Sqrt[d + e]*x*Sqrt[d + e*x] + 16*a*A*b*Sqrt[a + b]*e^2*Sqrt[d + e]*x*Sqrt[d + e*x] - 16*a*A*b*d*e*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 16*A*b^2*d*e*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 8*a^2*A*e^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 20*a*A*b*e^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 12*A*b^2*e^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 12*a*A*b*e^2*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 12*A*b^2*e^2*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x])/(Sqrt[d + e] - Sqrt[d + e*x])^4 + (-8*a*b*Sqrt[a + b]*B*d^3 + 8*b^2*Sqrt[a + b]*B*d^3 + 8*a^2*Sqrt[a + b]*B*d^2*e - 12*a*b*Sqrt[a + b]*B*d^2*e + 4*b^2*Sqrt[a + b]*B*d^2*e + 16*a^2*Sqrt[a + b]*B*d*e^2 + 8*a*b*Sqrt[a + b]*B*d*e^2 + 8*b^2*Sqrt[a + b]*B*d^3*x - 12*a*b*Sqrt[a + b]*B*d^2*e*x + 32*b^2*Sqrt[a + b]*B*d^2*e*x + 16*a^2*Sqrt[a + b]*B*d*e^2*x - 8*a*b*Sqrt[a + b]*B*d*e^2*x + 24*b^2*Sqrt[a + b]*B*d*e^2*x + 24*a^2*Sqrt[a + b]*B*e^3*x + 12*a*b*Sqrt[a + b]*B*e^3*x + 4*b^2*Sqrt[a + b]*B*d^2*e*x^2 + 8*a*b*Sqrt[a + b]*B*d*e^2*x^2 + 24*b^2*Sqrt[a + b]*B*d*e^2*x^2 + 12*a*b*Sqrt[a + b]*B*e^3*x^2 + 24*b^2*Sqrt[a + b]*B*e^3*x^2 + 8*a*b*B*d^3*Sqrt[a + b*x] + 8*b^2*B*d^3*Sqrt[a + b*x] - 8*a^2*B*d^2*e*Sqrt[a + b*x] + 8*a*b*B*d^2*e*Sqrt[a + b*x] + 16*b^2*B*d^2*e*Sqrt[a + b*x] - 16*a^2*B*d*e^2*Sqrt[a + b*x] - 16*a*b*B*d*e^2*Sqrt[a + b*x] + 16*a*b*B*d^2*e*x*Sqrt[a + b*x] + 16*b^2*B*d^2*e*x*Sqrt[a + b*x] - 16*a^2*B*d*e^2*x*Sqrt[a + b*x] + 8*a*b*B*d*e^2*x*Sqrt[a + b*x] + 24*b^2*B*d*e^2*x*Sqrt[a + b*x] - 24*a^2*B*e^3*x*Sqrt[a + b*x] - 24*a*b*B*e^3*x*Sqrt[a + b*x] + 8*a*b*Sqrt[a + b]*B*d^2*Sqrt[d + e]*Sqrt[d + e*x] - 8*b^2*Sqrt[a + b]*B*d^2*Sqrt[d + e]*Sqrt[d + e*x] - 8*a^2*Sqrt[a + b]*B*d*e*Sqrt[d + e]*Sqrt[d + e*x] + 8*a*b*Sqrt[a + b]*B*d*e*Sqrt[d + e]*Sqrt[d + e*x] - 8*b^2*Sqrt[a + b]*B*d^2*Sqrt[d + e]*x*Sqrt[d + e*x] + 8*a*b*Sqrt[a + b]*B*d*e*Sqrt[d + e]*x*Sqrt[d + e*x] - 24*b^2*Sqrt[a + b]*B*d*e*Sqrt[d + e]*x*Sqrt[d + e*x] + 24*a*b*Sqrt[a + b]*B*e^2*Sqrt[d + e]*x*Sqrt[d + e*x] - 8*a*b*B*d^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 8*b^2*B*d^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] + 8*a^2*B*d*e*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 4*a*b*B*d*e*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 12*b^2*B*d*e*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 12*a*b*B*d*e*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 12*b^2*B*d*e*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 24*a*b*B*e^2*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 24*b^2*B*e^2*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x])/(Sqrt[d + e] - Sqrt[d + e*x])^4))/((-Sqrt[d + e] + Sqrt[d + e*x])*(b*d*Sqrt[d + e] + b*e*Sqrt[d + e]*x - b*d*Sqrt[d + e*x] + a*e*Sqrt[d + e*x] - Sqrt[a + b]*e*Sqrt[a + b*x]*Sqrt[d + e*x])^3)","B",1
2242,1,13746,145,60.665313,"\int \frac{A+B x}{\sqrt{a+b x} (d+e x)^{7/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(Sqrt[a + b*x]*(d + e*x)^(7/2)),x]","\text{Result too large to show}","-\frac{2 \sqrt{a+b x} (B d-A e)}{5 e (d+e x)^{5/2} (b d-a e)}+\frac{4 b \sqrt{a+b x} (-5 a B e+4 A b e+b B d)}{15 e \sqrt{d+e x} (b d-a e)^3}+\frac{2 \sqrt{a+b x} (-5 a B e+4 A b e+b B d)}{15 e (d+e x)^{3/2} (b d-a e)^2}",1,"Result too large to show","B",1
2243,-1,0,198,180.0371918,"\int \frac{A+B x}{\sqrt{a+b x} (d+e x)^{9/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(Sqrt[a + b*x]*(d + e*x)^(9/2)),x]","\text{\$Aborted}","\frac{16 b^2 \sqrt{a+b x} (-7 a B e+6 A b e+b B d)}{105 e \sqrt{d+e x} (b d-a e)^4}+\frac{8 b \sqrt{a+b x} (-7 a B e+6 A b e+b B d)}{105 e (d+e x)^{3/2} (b d-a e)^3}+\frac{2 \sqrt{a+b x} (-7 a B e+6 A b e+b B d)}{35 e (d+e x)^{5/2} (b d-a e)^2}-\frac{2 \sqrt{a+b x} (B d-A e)}{7 e (d+e x)^{7/2} (b d-a e)}",1,"$Aborted","F",-1
2244,-1,0,251,180.3788308,"\int \frac{A+B x}{\sqrt{a+b x} (d+e x)^{11/2}} \, dx","IntegrateAlgebraic[(A + B*x)/(Sqrt[a + b*x]*(d + e*x)^(11/2)),x]","\text{\$Aborted}","\frac{32 b^3 \sqrt{a+b x} (-9 a B e+8 A b e+b B d)}{315 e \sqrt{d+e x} (b d-a e)^5}+\frac{16 b^2 \sqrt{a+b x} (-9 a B e+8 A b e+b B d)}{315 e (d+e x)^{3/2} (b d-a e)^4}+\frac{4 b \sqrt{a+b x} (-9 a B e+8 A b e+b B d)}{105 e (d+e x)^{5/2} (b d-a e)^3}+\frac{2 \sqrt{a+b x} (-9 a B e+8 A b e+b B d)}{63 e (d+e x)^{7/2} (b d-a e)^2}-\frac{2 \sqrt{a+b x} (B d-A e)}{9 e (d+e x)^{9/2} (b d-a e)}",1,"$Aborted","F",-1
2245,-1,0,249,180.0163489,"\int \frac{(A+B x) (d+e x)^{5/2}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^(5/2))/(a + b*x)^(3/2),x]","\text{\$Aborted}","\frac{5 (b d-a e)^2 (-7 a B e+6 A b e+b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{8 b^{9/2} \sqrt{e}}+\frac{5 \sqrt{a+b x} \sqrt{d+e x} (b d-a e) (-7 a B e+6 A b e+b B d)}{8 b^4}+\frac{5 \sqrt{a+b x} (d+e x)^{3/2} (-7 a B e+6 A b e+b B d)}{12 b^3}+\frac{\sqrt{a+b x} (d+e x)^{5/2} (-7 a B e+6 A b e+b B d)}{3 b^2 (b d-a e)}-\frac{2 (d+e x)^{7/2} (A b-a B)}{b \sqrt{a+b x} (b d-a e)}",1,"$Aborted","F",-1
2246,-1,0,199,180.1911541,"\int \frac{(A+B x) (d+e x)^{3/2}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^(3/2))/(a + b*x)^(3/2),x]","\text{\$Aborted}","\frac{3 (b d-a e) (-5 a B e+4 A b e+b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{4 b^{7/2} \sqrt{e}}+\frac{3 \sqrt{a+b x} \sqrt{d+e x} (-5 a B e+4 A b e+b B d)}{4 b^3}+\frac{\sqrt{a+b x} (d+e x)^{3/2} (-5 a B e+4 A b e+b B d)}{2 b^2 (b d-a e)}-\frac{2 (d+e x)^{5/2} (A b-a B)}{b \sqrt{a+b x} (b d-a e)}",1,"$Aborted","F",-1
2247,-1,0,145,180.2847158,"\int \frac{(A+B x) \sqrt{d+e x}}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[((A + B*x)*Sqrt[d + e*x])/(a + b*x)^(3/2),x]","\text{\$Aborted}","\frac{(-3 a B e+2 A b e+b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{b^{5/2} \sqrt{e}}+\frac{\sqrt{a+b x} \sqrt{d+e x} (-3 a B e+2 A b e+b B d)}{b^2 (b d-a e)}-\frac{2 (d+e x)^{3/2} (A b-a B)}{b \sqrt{a+b x} (b d-a e)}",1,"$Aborted","F",-1
2248,1,859,85,26.4197132,"\int \frac{A+B x}{(a+b x)^{3/2} \sqrt{d+e x}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^(3/2)*Sqrt[d + e*x]),x]","\frac{\left(-\frac{2 B a^2}{b (a+b)^{3/2}}-\frac{2 B a}{(a+b)^{3/2}}+\frac{2 B \sqrt{a+b x} a}{b (a+b)}+\frac{2 A a}{(a+b)^{3/2}}-\frac{2 A \sqrt{a+b x}}{a+b}+\frac{2 A b}{(a+b)^{3/2}}\right) \left(\sqrt{d+e}-\sqrt{d+e x}\right) \left(-e a^2-2 b d a-3 b e a-b e x a+\sqrt{a+b} e \sqrt{a+b x} a+2 b \sqrt{d+e} \sqrt{d+e x} a-2 b^2 d-2 b^2 e-b^2 e x+b \sqrt{a+b} d \sqrt{a+b x}+2 b \sqrt{a+b} e \sqrt{a+b x}+2 b^2 \sqrt{d+e} \sqrt{d+e x}-b \sqrt{a+b} \sqrt{d+e} \sqrt{a+b x} \sqrt{d+e x}\right)}{-2 e^2 a^3-5 b e^2 a^2-2 b d e a^2-3 b e^2 x a^2+2 \sqrt{a+b} e^2 \sqrt{a+b x} a^2+2 b e \sqrt{d+e} \sqrt{d+e x} a^2+2 b^2 d^2 a-2 b^2 e^2 a-b^2 e^2 x^2 a+b^2 d e a-5 b^2 e^2 x a-b^2 d e x a+4 b \sqrt{a+b} e^2 \sqrt{a+b x} a+2 b \sqrt{a+b} d e \sqrt{a+b x} a+2 b \sqrt{a+b} e^2 x \sqrt{a+b x} a+2 b^2 e \sqrt{d+e} x \sqrt{d+e x} a-2 b^2 d \sqrt{d+e} \sqrt{d+e x} a-2 b \sqrt{a+b} e \sqrt{d+e} \sqrt{a+b x} \sqrt{d+e x} a+b^3 d e x^2+2 b^3 d^2 x-2 b^3 e^2 x+b^3 d e x-4 b^2 \sqrt{a+b} d^2 \sqrt{a+b x}-4 b^2 \sqrt{a+b} d e \sqrt{a+b x}-2 b^2 \sqrt{a+b} d e x \sqrt{a+b x}-2 b^3 d \sqrt{d+e} x \sqrt{d+e x}+4 b^2 \sqrt{a+b} d \sqrt{d+e} \sqrt{a+b x} \sqrt{d+e x}+2 b^2 \sqrt{a+b} e \sqrt{d+e} \sqrt{a+b x} \sqrt{d+e x}}+\frac{4 B \tanh ^{-1}\left(\frac{\frac{\sqrt{a+b} \sqrt{e}}{\sqrt{b}}-\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b}}}{\sqrt{d+e}-\sqrt{d+e x}}\right)}{b^{3/2} \sqrt{e}}","\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{b^{3/2} \sqrt{e}}-\frac{2 \sqrt{d+e x} (A b-a B)}{b \sqrt{a+b x} (b d-a e)}",1,"(((2*a*A)/(a + b)^(3/2) + (2*A*b)/(a + b)^(3/2) - (2*a*B)/(a + b)^(3/2) - (2*a^2*B)/(b*(a + b)^(3/2)) - (2*A*Sqrt[a + b*x])/(a + b) + (2*a*B*Sqrt[a + b*x])/(b*(a + b)))*(Sqrt[d + e] - Sqrt[d + e*x])*(-2*a*b*d - 2*b^2*d - a^2*e - 3*a*b*e - 2*b^2*e - a*b*e*x - b^2*e*x + b*Sqrt[a + b]*d*Sqrt[a + b*x] + a*Sqrt[a + b]*e*Sqrt[a + b*x] + 2*b*Sqrt[a + b]*e*Sqrt[a + b*x] + 2*a*b*Sqrt[d + e]*Sqrt[d + e*x] + 2*b^2*Sqrt[d + e]*Sqrt[d + e*x] - b*Sqrt[a + b]*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x]))/(2*a*b^2*d^2 - 2*a^2*b*d*e + a*b^2*d*e - 2*a^3*e^2 - 5*a^2*b*e^2 - 2*a*b^2*e^2 + 2*b^3*d^2*x - a*b^2*d*e*x + b^3*d*e*x - 3*a^2*b*e^2*x - 5*a*b^2*e^2*x - 2*b^3*e^2*x + b^3*d*e*x^2 - a*b^2*e^2*x^2 - 4*b^2*Sqrt[a + b]*d^2*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*d*e*Sqrt[a + b*x] - 4*b^2*Sqrt[a + b]*d*e*Sqrt[a + b*x] + 2*a^2*Sqrt[a + b]*e^2*Sqrt[a + b*x] + 4*a*b*Sqrt[a + b]*e^2*Sqrt[a + b*x] - 2*b^2*Sqrt[a + b]*d*e*x*Sqrt[a + b*x] + 2*a*b*Sqrt[a + b]*e^2*x*Sqrt[a + b*x] - 2*a*b^2*d*Sqrt[d + e]*Sqrt[d + e*x] + 2*a^2*b*e*Sqrt[d + e]*Sqrt[d + e*x] - 2*b^3*d*Sqrt[d + e]*x*Sqrt[d + e*x] + 2*a*b^2*e*Sqrt[d + e]*x*Sqrt[d + e*x] + 4*b^2*Sqrt[a + b]*d*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 2*a*b*Sqrt[a + b]*e*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] + 2*b^2*Sqrt[a + b]*e*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x]) + (4*B*ArcTanh[((Sqrt[a + b]*Sqrt[e])/Sqrt[b] - (Sqrt[e]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[d + e] - Sqrt[d + e*x])])/(b^(3/2)*Sqrt[e])","B",1
2249,1,425,89,2.9023268,"\int \frac{A+B x}{(a+b x)^{3/2} (d+e x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^(3/2)*(d + e*x)^(3/2)),x]","\frac{\left(\sqrt{d+e}-\sqrt{d+e x}\right)^4 \left(\frac{1}{\sqrt{d+e}}-\frac{\sqrt{a+b x}}{\sqrt{a+b} \sqrt{d+e}}\right) \left(\frac{-2 A e \sqrt{a+b} \sqrt{a+b x}+2 a A e-2 A b \sqrt{d+e} \sqrt{d+e x}+2 A b d+2 A b e x+2 A b e}{\left(\sqrt{d+e}-\sqrt{d+e x}\right)^2}+\frac{-2 B \sqrt{a+b} \sqrt{d+e} \sqrt{a+b x} \sqrt{d+e x}+2 B d \sqrt{a+b} \sqrt{a+b x}+2 a B \sqrt{d+e} \sqrt{d+e x}-2 a B d+2 b B e x}{\left(\sqrt{d+e}-\sqrt{d+e x}\right)^2}\right)}{\left(\sqrt{d+e x}-\sqrt{d+e}\right) \left(-e \sqrt{a+b} \sqrt{a+b x} \sqrt{d+e x}+a e \sqrt{d+e x}-b d \sqrt{d+e x}+b e x \sqrt{d+e}+b d \sqrt{d+e}\right) \left(b \sqrt{d+e} \sqrt{a+b x} \sqrt{d+e x}-b d \sqrt{a+b x}+b e x \left(-\sqrt{a+b}\right)+a e \sqrt{a+b x}-a e \sqrt{a+b}\right)}","\frac{2 \sqrt{d+e x} (a B e-2 A b e+b B d)}{e \sqrt{a+b x} (b d-a e)^2}-\frac{2 (B d-A e)}{e \sqrt{a+b x} \sqrt{d+e x} (b d-a e)}",1,"((1/Sqrt[d + e] - Sqrt[a + b*x]/(Sqrt[a + b]*Sqrt[d + e]))*(Sqrt[d + e] - Sqrt[d + e*x])^4*((2*A*b*d + 2*a*A*e + 2*A*b*e + 2*A*b*e*x - 2*A*Sqrt[a + b]*e*Sqrt[a + b*x] - 2*A*b*Sqrt[d + e]*Sqrt[d + e*x])/(Sqrt[d + e] - Sqrt[d + e*x])^2 + (-2*a*B*d + 2*b*B*e*x + 2*Sqrt[a + b]*B*d*Sqrt[a + b*x] + 2*a*B*Sqrt[d + e]*Sqrt[d + e*x] - 2*Sqrt[a + b]*B*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x])/(Sqrt[d + e] - Sqrt[d + e*x])^2))/((-Sqrt[d + e] + Sqrt[d + e*x])*(b*d*Sqrt[d + e] + b*e*Sqrt[d + e]*x - b*d*Sqrt[d + e*x] + a*e*Sqrt[d + e*x] - Sqrt[a + b]*e*Sqrt[a + b*x]*Sqrt[d + e*x])*(-(a*Sqrt[a + b]*e) - b*Sqrt[a + b]*e*x - b*d*Sqrt[a + b*x] + a*e*Sqrt[a + b*x] + b*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x]))","B",1
2250,1,3729,139,34.1460688,"\int \frac{A+B x}{(a+b x)^{3/2} (d+e x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^(3/2)*(d + e*x)^(5/2)),x]","\text{Result too large to show}","-\frac{2 (A b-a B)}{b \sqrt{a+b x} (d+e x)^{3/2} (b d-a e)}+\frac{4 \sqrt{a+b x} (3 a B e-4 A b e+b B d)}{3 \sqrt{d+e x} (b d-a e)^3}+\frac{2 \sqrt{a+b x} (3 a B e-4 A b e+b B d)}{3 b (d+e x)^{3/2} (b d-a e)^2}",1,"((1/(12*(d + e)^(3/2)) - Sqrt[a + b*x]/(12*Sqrt[a + b]*(d + e)^(3/2)))*(Sqrt[d + e] - Sqrt[d + e*x])^8*((96*A*b^3*d^4 + 48*a*A*b^2*d^3*e + 216*A*b^3*d^3*e - 112*a^2*A*b*d^2*e^2 - 40*a*A*b^2*d^2*e^2 + 144*A*b^3*d^2*e^2 + 64*a^3*A*d*e^3 - 16*a^2*A*b*d*e^3 - 56*a*A*b^2*d*e^3 + 24*A*b^3*d*e^3 + 32*a^3*A*e^4 + 40*a^2*A*b*e^4 + 8*a*A*b^2*e^4 + 216*A*b^3*d^3*e*x - 40*a*A*b^2*d^2*e^2*x + 320*A*b^3*d^2*e^2*x - 16*a^2*A*b*d*e^3*x + 160*A*b^3*d*e^3*x + 32*a^3*A*e^4*x + 32*A*b^3*e^4*x + 144*A*b^3*d^2*e^2*x^2 - 56*a*A*b^2*d*e^3*x^2 + 160*A*b^3*d*e^3*x^2 + 40*a^2*A*b*e^4*x^2 + 32*A*b^3*e^4*x^2 + 24*A*b^3*d*e^3*x^3 + 8*a*A*b^2*e^4*x^3 + 32*A*b^3*e^4*x^3 - 48*A*b^2*Sqrt[a + b]*d^3*e*Sqrt[a + b*x] + 112*a*A*b*Sqrt[a + b]*d^2*e^2*Sqrt[a + b*x] - 16*A*b^2*Sqrt[a + b]*d^2*e^2*Sqrt[a + b*x] - 64*a^2*A*Sqrt[a + b]*d*e^3*Sqrt[a + b*x] + 48*a*A*b*Sqrt[a + b]*d*e^3*Sqrt[a + b*x] + 24*A*b^2*Sqrt[a + b]*d*e^3*Sqrt[a + b*x] - 32*a^2*A*Sqrt[a + b]*e^4*Sqrt[a + b*x] - 24*a*A*b*Sqrt[a + b]*e^4*Sqrt[a + b*x] - 16*A*b^2*Sqrt[a + b]*d^2*e^2*x*Sqrt[a + b*x] + 48*a*A*b*Sqrt[a + b]*d*e^3*x*Sqrt[a + b*x] - 32*A*b^2*Sqrt[a + b]*d*e^3*x*Sqrt[a + b*x] - 32*a^2*A*Sqrt[a + b]*e^4*x*Sqrt[a + b*x] + 32*a*A*b*Sqrt[a + b]*e^4*x*Sqrt[a + b*x] + 24*A*b^2*Sqrt[a + b]*d*e^3*x^2*Sqrt[a + b*x] - 24*a*A*b*Sqrt[a + b]*e^4*x^2*Sqrt[a + b*x] - 96*A*b^3*d^3*Sqrt[d + e]*Sqrt[d + e*x] - 48*a*A*b^2*d^2*e*Sqrt[d + e]*Sqrt[d + e*x] - 168*A*b^3*d^2*e*Sqrt[d + e]*Sqrt[d + e*x] + 112*a^2*A*b*d*e^2*Sqrt[d + e]*Sqrt[d + e*x] + 64*a*A*b^2*d*e^2*Sqrt[d + e]*Sqrt[d + e*x] - 72*A*b^3*d*e^2*Sqrt[d + e]*Sqrt[d + e*x] + 32*a^3*A*e^3*Sqrt[d + e]*Sqrt[d + e*x] + 104*a^2*A*b*e^3*Sqrt[d + e]*Sqrt[d + e*x] + 72*a*A*b^2*e^3*Sqrt[d + e]*Sqrt[d + e*x] - 168*A*b^3*d^2*e*Sqrt[d + e]*x*Sqrt[d + e*x] + 64*a*A*b^2*d*e^2*Sqrt[d + e]*x*Sqrt[d + e*x] - 128*A*b^3*d*e^2*Sqrt[d + e]*x*Sqrt[d + e*x] + 104*a^2*A*b*e^3*Sqrt[d + e]*x*Sqrt[d + e*x] + 128*a*A*b^2*e^3*Sqrt[d + e]*x*Sqrt[d + e*x] - 72*A*b^3*d*e^2*Sqrt[d + e]*x^2*Sqrt[d + e*x] + 72*a*A*b^2*e^3*Sqrt[d + e]*x^2*Sqrt[d + e*x] + 48*A*b^2*Sqrt[a + b]*d^2*e*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 112*a*A*b*Sqrt[a + b]*d*e^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 8*A*b^2*Sqrt[a + b]*d*e^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 32*a^2*A*Sqrt[a + b]*e^3*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 88*a*A*b*Sqrt[a + b]*e^3*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 32*A*b^2*Sqrt[a + b]*e^3*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 8*A*b^2*Sqrt[a + b]*d*e^2*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 88*a*A*b*Sqrt[a + b]*e^3*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 32*A*b^2*Sqrt[a + b]*e^3*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 32*A*b^2*Sqrt[a + b]*e^3*Sqrt[d + e]*x^2*Sqrt[a + b*x]*Sqrt[d + e*x])/(Sqrt[d + e] - Sqrt[d + e*x])^6 + (-96*a*b^2*B*d^4 + 64*a^2*b*B*d^3*e - 104*a*b^2*B*d^3*e + 32*a^3*B*d^2*e^2 + 88*a^2*b*B*d^2*e^2 - 16*a*b^2*B*d^2*e^2 + 64*a^3*B*d*e^3 + 80*a^2*b*B*d*e^3 + 16*a*b^2*B*d*e^3 - 104*a*b^2*B*d^3*e*x + 112*b^3*B*d^3*e*x + 88*a^2*b*B*d^2*e^2*x - 144*a*b^2*B*d^2*e^2*x + 128*b^3*B*d^2*e^2*x + 64*a^3*B*d*e^3*x + 192*a^2*b*B*d*e^3*x + 24*a*b^2*B*d*e^3*x + 40*b^3*B*d*e^3*x + 96*a^3*B*e^4*x + 120*a^2*b*B*e^4*x + 24*a*b^2*B*e^4*x - 16*a*b^2*B*d^2*e^2*x^2 + 128*b^3*B*d^2*e^2*x^2 + 80*a^2*b*B*d*e^3*x^2 + 24*a*b^2*B*d*e^3*x^2 + 160*b^3*B*d*e^3*x^2 + 120*a^2*b*B*e^4*x^2 + 96*a*b^2*B*e^4*x^2 + 48*b^3*B*e^4*x^2 + 16*a*b^2*B*d*e^3*x^3 + 40*b^3*B*d*e^3*x^3 + 24*a*b^2*B*e^4*x^3 + 48*b^3*B*e^4*x^3 + 96*b^2*Sqrt[a + b]*B*d^4*Sqrt[a + b*x] - 64*a*b*Sqrt[a + b]*B*d^3*e*Sqrt[a + b*x] + 136*b^2*Sqrt[a + b]*B*d^3*e*Sqrt[a + b*x] - 32*a^2*Sqrt[a + b]*B*d^2*e^2*Sqrt[a + b*x] - 72*a*b*Sqrt[a + b]*B*d^2*e^2*Sqrt[a + b*x] + 48*b^2*Sqrt[a + b]*B*d^2*e^2*Sqrt[a + b*x] - 64*a^2*Sqrt[a + b]*B*d*e^3*Sqrt[a + b*x] - 48*a*b*Sqrt[a + b]*B*d*e^3*Sqrt[a + b*x] + 136*b^2*Sqrt[a + b]*B*d^3*e*x*Sqrt[a + b*x] - 72*a*b*Sqrt[a + b]*B*d^2*e^2*x*Sqrt[a + b*x] + 224*b^2*Sqrt[a + b]*B*d^2*e^2*x*Sqrt[a + b*x] - 64*a^2*Sqrt[a + b]*B*d*e^3*x*Sqrt[a + b*x] - 128*a*b*Sqrt[a + b]*B*d*e^3*x*Sqrt[a + b*x] + 72*b^2*Sqrt[a + b]*B*d*e^3*x*Sqrt[a + b*x] - 96*a^2*Sqrt[a + b]*B*e^4*x*Sqrt[a + b*x] - 72*a*b*Sqrt[a + b]*B*e^4*x*Sqrt[a + b*x] + 48*b^2*Sqrt[a + b]*B*d^2*e^2*x^2*Sqrt[a + b*x] - 48*a*b*Sqrt[a + b]*B*d*e^3*x^2*Sqrt[a + b*x] + 72*b^2*Sqrt[a + b]*B*d*e^3*x^2*Sqrt[a + b*x] - 72*a*b*Sqrt[a + b]*B*e^4*x^2*Sqrt[a + b*x] + 96*a*b^2*B*d^3*Sqrt[d + e]*Sqrt[d + e*x] - 64*a^2*b*B*d^2*e*Sqrt[d + e]*Sqrt[d + e*x] + 56*a*b^2*B*d^2*e*Sqrt[d + e]*Sqrt[d + e*x] - 32*a^3*B*d*e^2*Sqrt[d + e]*Sqrt[d + e*x] - 56*a^2*b*B*d*e^2*Sqrt[d + e]*Sqrt[d + e*x] + 56*a*b^2*B*d^2*e*Sqrt[d + e]*x*Sqrt[d + e*x] - 112*b^3*B*d^2*e*Sqrt[d + e]*x*Sqrt[d + e*x] - 56*a^2*b*B*d*e^2*Sqrt[d + e]*x*Sqrt[d + e*x] + 64*a*b^2*B*d*e^2*Sqrt[d + e]*x*Sqrt[d + e*x] - 72*b^3*B*d*e^2*Sqrt[d + e]*x*Sqrt[d + e*x] + 48*a^2*b*B*e^3*Sqrt[d + e]*x*Sqrt[d + e*x] + 72*a*b^2*B*e^3*Sqrt[d + e]*x*Sqrt[d + e*x] - 72*b^3*B*d*e^2*Sqrt[d + e]*x^2*Sqrt[d + e*x] + 72*a*b^2*B*e^3*Sqrt[d + e]*x^2*Sqrt[d + e*x] - 96*b^2*Sqrt[a + b]*B*d^3*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] + 64*a*b*Sqrt[a + b]*B*d^2*e*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 88*b^2*Sqrt[a + b]*B*d^2*e*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] + 32*a^2*Sqrt[a + b]*B*d*e^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] + 40*a*b*Sqrt[a + b]*B*d*e^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 16*b^2*Sqrt[a + b]*B*d*e^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 88*b^2*Sqrt[a + b]*B*d^2*e*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] + 40*a*b*Sqrt[a + b]*B*d*e^2*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 112*b^2*Sqrt[a + b]*B*d*e^2*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 48*a*b*Sqrt[a + b]*B*e^3*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 48*b^2*Sqrt[a + b]*B*e^3*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 16*b^2*Sqrt[a + b]*B*d*e^2*Sqrt[d + e]*x^2*Sqrt[a + b*x]*Sqrt[d + e*x] - 48*b^2*Sqrt[a + b]*B*e^3*Sqrt[d + e]*x^2*Sqrt[a + b*x]*Sqrt[d + e*x])/(Sqrt[d + e] - Sqrt[d + e*x])^6))/((-Sqrt[d + e] + Sqrt[d + e*x])*(b*d*Sqrt[d + e] + b*e*Sqrt[d + e]*x - b*d*Sqrt[d + e*x] + a*e*Sqrt[d + e*x] - Sqrt[a + b]*e*Sqrt[a + b*x]*Sqrt[d + e*x])^3*(-(a*Sqrt[a + b]*e) - b*Sqrt[a + b]*e*x - b*d*Sqrt[a + b*x] + a*e*Sqrt[a + b*x] + b*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x]))","B",1
2251,-1,0,187,180.0245034,"\int \frac{A+B x}{(a+b x)^{3/2} (d+e x)^{7/2}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^(3/2)*(d + e*x)^(7/2)),x]","\text{\$Aborted}","-\frac{2 (A b-a B)}{b \sqrt{a+b x} (d+e x)^{5/2} (b d-a e)}+\frac{16 b \sqrt{a+b x} (5 a B e-6 A b e+b B d)}{15 \sqrt{d+e x} (b d-a e)^4}+\frac{8 \sqrt{a+b x} (5 a B e-6 A b e+b B d)}{15 (d+e x)^{3/2} (b d-a e)^3}+\frac{2 \sqrt{a+b x} (5 a B e-6 A b e+b B d)}{5 b (d+e x)^{5/2} (b d-a e)^2}",1,"$Aborted","F",-1
2252,-1,0,237,180.0401143,"\int \frac{A+B x}{(a+b x)^{3/2} (d+e x)^{9/2}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^(3/2)*(d + e*x)^(9/2)),x]","\text{\$Aborted}","\frac{32 b^2 \sqrt{a+b x} (7 a B e-8 A b e+b B d)}{35 \sqrt{d+e x} (b d-a e)^5}+\frac{16 b \sqrt{a+b x} (7 a B e-8 A b e+b B d)}{35 (d+e x)^{3/2} (b d-a e)^4}+\frac{12 \sqrt{a+b x} (7 a B e-8 A b e+b B d)}{35 (d+e x)^{5/2} (b d-a e)^3}+\frac{2 \sqrt{a+b x} (7 a B e-8 A b e+b B d)}{7 b (d+e x)^{7/2} (b d-a e)^2}-\frac{2 (A b-a B)}{b \sqrt{a+b x} (d+e x)^{7/2} (b d-a e)}",1,"$Aborted","F",-1
2253,-1,0,302,180.0546497,"\int \frac{(A+B x) (d+e x)^{7/2}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^(7/2))/(a + b*x)^(5/2),x]","\text{\$Aborted}","\frac{35 \sqrt{e} (b d-a e)^2 (-3 a B e+2 A b e+b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{8 b^{11/2}}+\frac{35 e \sqrt{a+b x} \sqrt{d+e x} (b d-a e) (-3 a B e+2 A b e+b B d)}{8 b^5}+\frac{35 e \sqrt{a+b x} (d+e x)^{3/2} (-3 a B e+2 A b e+b B d)}{12 b^4}+\frac{7 e \sqrt{a+b x} (d+e x)^{5/2} (-3 a B e+2 A b e+b B d)}{3 b^3 (b d-a e)}-\frac{2 (d+e x)^{7/2} (-3 a B e+2 A b e+b B d)}{b^2 \sqrt{a+b x} (b d-a e)}-\frac{2 (d+e x)^{9/2} (A b-a B)}{3 b (a+b x)^{3/2} (b d-a e)}",1,"$Aborted","F",-1
2254,-1,0,257,180.0665236,"\int \frac{(A+B x) (d+e x)^{5/2}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^(5/2))/(a + b*x)^(5/2),x]","\text{\$Aborted}","\frac{5 \sqrt{e} (b d-a e) (-7 a B e+4 A b e+3 b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{4 b^{9/2}}+\frac{5 e \sqrt{a+b x} \sqrt{d+e x} (-7 a B e+4 A b e+3 b B d)}{4 b^4}+\frac{5 e \sqrt{a+b x} (d+e x)^{3/2} (-7 a B e+4 A b e+3 b B d)}{6 b^3 (b d-a e)}-\frac{2 (d+e x)^{5/2} (-7 a B e+4 A b e+3 b B d)}{3 b^2 \sqrt{a+b x} (b d-a e)}-\frac{2 (d+e x)^{7/2} (A b-a B)}{3 b (a+b x)^{3/2} (b d-a e)}",1,"$Aborted","F",-1
2255,-1,0,201,180.0040865,"\int \frac{(A+B x) (d+e x)^{3/2}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^(3/2))/(a + b*x)^(5/2),x]","\text{\$Aborted}","\frac{\sqrt{e} (-5 a B e+2 A b e+3 b B d) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{b^{7/2}}+\frac{e \sqrt{a+b x} \sqrt{d+e x} (-5 a B e+2 A b e+3 b B d)}{b^3 (b d-a e)}-\frac{2 (d+e x)^{3/2} (-5 a B e+2 A b e+3 b B d)}{3 b^2 \sqrt{a+b x} (b d-a e)}-\frac{2 (d+e x)^{5/2} (A b-a B)}{3 b (a+b x)^{3/2} (b d-a e)}",1,"$Aborted","F",-1
2256,1,5039,111,83.3787958,"\int \frac{(A+B x) \sqrt{d+e x}}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[((A + B*x)*Sqrt[d + e*x])/(a + b*x)^(5/2),x]","\text{Result too large to show}","-\frac{2 (d+e x)^{3/2} (A b-a B)}{3 b (a+b x)^{3/2} (b d-a e)}+\frac{2 B \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{b^{5/2}}-\frac{2 B \sqrt{d+e x}}{b^2 \sqrt{a+b x}}",1,"Result too large to show","B",1
2257,1,3009,95,10.5777637,"\int \frac{A+B x}{(a+b x)^{5/2} \sqrt{d+e x}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^(5/2)*Sqrt[d + e*x]),x]","\text{Result too large to show}","-\frac{2 \sqrt{d+e x} (A b-a B)}{3 b (a+b x)^{3/2} (b d-a e)}-\frac{2 \sqrt{d+e x} (-a B e-2 A b e+3 b B d)}{3 b \sqrt{a+b x} (b d-a e)^2}",1,"((1/(6*(a + b)*Sqrt[d + e]) - Sqrt[a + b*x]/(6*(a + b)^(3/2)*Sqrt[d + e]))*(Sqrt[d + e] - Sqrt[d + e*x])^6*((4*a^2*B*e*Sqrt[d + e]*(Sqrt[a + b] - Sqrt[a + b*x])^2)/(Sqrt[d + e] - Sqrt[d + e*x])^2 + (24*a*A*b^2*d^2*Sqrt[d + e] + 8*a^2*A*b*d*e*Sqrt[d + e] + 28*a*A*b^2*d*e*Sqrt[d + e] + 24*a^3*A*e^2*Sqrt[d + e] + 28*a^2*A*b*e^2*Sqrt[d + e] + 8*a*A*b^2*e^2*Sqrt[d + e] + 28*a*A*b^2*d*e*Sqrt[d + e]*x + 28*a^2*A*b*e^2*Sqrt[d + e]*x + 40*a*A*b^2*e^2*Sqrt[d + e]*x + 8*a*A*b^2*e^2*Sqrt[d + e]*x^2 - 8*a*A*b*Sqrt[a + b]*d*e*Sqrt[d + e]*Sqrt[a + b*x] - 24*a^2*A*Sqrt[a + b]*e^2*Sqrt[d + e]*Sqrt[a + b*x] - 16*a*A*b*Sqrt[a + b]*e^2*Sqrt[d + e]*Sqrt[a + b*x] - 16*a*A*b*Sqrt[a + b]*e^2*Sqrt[d + e]*x*Sqrt[a + b*x] - 24*a*A*b^2*d^2*Sqrt[d + e*x] - 8*a^2*A*b*d*e*Sqrt[d + e*x] - 40*a*A*b^2*d*e*Sqrt[d + e*x] - 8*a^2*A*b*e^2*Sqrt[d + e*x] - 16*a*A*b^2*e^2*Sqrt[d + e*x] - 16*a*A*b^2*d*e*x*Sqrt[d + e*x] - 16*a*A*b^2*e^2*x*Sqrt[d + e*x] + 8*a*A*b*Sqrt[a + b]*d*e*Sqrt[a + b*x]*Sqrt[d + e*x] + 8*a*A*b*Sqrt[a + b]*e^2*Sqrt[a + b*x]*Sqrt[d + e*x])/(Sqrt[d + e] - Sqrt[d + e*x])^4 + (-8*a*A*b^2*d^2*Sqrt[d + e] + 8*A*b^3*d^2*Sqrt[d + e] - 24*a^2*A*b*d*e*Sqrt[d + e] - 28*a*A*b^2*d*e*Sqrt[d + e] + 4*A*b^3*d*e*Sqrt[d + e] + 8*A*b^3*d^2*Sqrt[d + e]*x - 28*a*A*b^2*d*e*Sqrt[d + e]*x + 8*A*b^3*d*e*Sqrt[d + e]*x + 12*A*b^3*e^2*Sqrt[d + e]*x + 4*A*b^3*d*e*Sqrt[d + e]*x^2 + 12*A*b^3*e^2*Sqrt[d + e]*x^2 + 8*A*b^2*Sqrt[a + b]*d^2*Sqrt[d + e]*Sqrt[a + b*x] + 24*a*A*b*Sqrt[a + b]*d*e*Sqrt[d + e]*Sqrt[a + b*x] + 16*A*b^2*Sqrt[a + b]*d*e*Sqrt[d + e]*Sqrt[a + b*x] + 16*A*b^2*Sqrt[a + b]*d*e*Sqrt[d + e]*x*Sqrt[a + b*x] + 8*a*A*b^2*d^2*Sqrt[d + e*x] - 8*A*b^3*d^2*Sqrt[d + e*x] + 24*a^2*A*b*d*e*Sqrt[d + e*x] + 32*a*A*b^2*d*e*Sqrt[d + e*x] - 8*A*b^3*d*e*Sqrt[d + e*x] + 24*a^2*A*b*e^2*Sqrt[d + e*x] + 24*a*A*b^2*e^2*Sqrt[d + e*x] - 8*A*b^3*d^2*x*Sqrt[d + e*x] + 24*a*A*b^2*d*e*x*Sqrt[d + e*x] - 8*A*b^3*d*e*x*Sqrt[d + e*x] + 24*a*A*b^2*e^2*x*Sqrt[d + e*x] - 8*A*b^2*Sqrt[a + b]*d^2*Sqrt[a + b*x]*Sqrt[d + e*x] - 24*a*A*b*Sqrt[a + b]*d*e*Sqrt[a + b*x]*Sqrt[d + e*x] - 20*A*b^2*Sqrt[a + b]*d*e*Sqrt[a + b*x]*Sqrt[d + e*x] - 24*a*A*b*Sqrt[a + b]*e^2*Sqrt[a + b*x]*Sqrt[d + e*x] - 12*A*b^2*Sqrt[a + b]*e^2*Sqrt[a + b*x]*Sqrt[d + e*x] - 12*A*b^2*Sqrt[a + b]*d*e*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 12*A*b^2*Sqrt[a + b]*e^2*x*Sqrt[a + b*x]*Sqrt[d + e*x])/(Sqrt[d + e] - Sqrt[d + e*x])^4 + (8*a^2*b*B*d^2*Sqrt[d + e] + 16*a*b^2*B*d^2*Sqrt[d + e] - 24*a^3*B*d*e*Sqrt[d + e] + 28*a^2*b*B*d*e*Sqrt[d + e] + 32*a*b^2*B*d*e*Sqrt[d + e] + 24*a^2*b*B*e^2*Sqrt[d + e] + 12*a*b^2*B*e^2*Sqrt[d + e] + 16*a*b^2*B*d^2*Sqrt[d + e]*x - 20*a^2*b*B*d*e*Sqrt[d + e]*x + 40*a*b^2*B*d*e*Sqrt[d + e]*x + 24*a^2*b*B*e^2*Sqrt[d + e]*x + 36*a*b^2*B*e^2*Sqrt[d + e]*x + 8*a*b^2*B*d*e*Sqrt[d + e]*x^2 + 24*a*b^2*B*e^2*Sqrt[d + e]*x^2 - 8*a*b*Sqrt[a + b]*B*d^2*Sqrt[d + e]*Sqrt[a + b*x] + 24*a^2*Sqrt[a + b]*B*d*e*Sqrt[d + e]*Sqrt[a + b*x] - 40*a*b*Sqrt[a + b]*B*d*e*Sqrt[d + e]*Sqrt[a + b*x] - 24*a*b*Sqrt[a + b]*B*e^2*Sqrt[d + e]*Sqrt[a + b*x] + 8*a*b*Sqrt[a + b]*B*d*e*Sqrt[d + e]*x*Sqrt[a + b*x] - 24*a*b*Sqrt[a + b]*B*e^2*Sqrt[d + e]*x*Sqrt[a + b*x] - 8*a^2*b*B*d^2*Sqrt[d + e*x] - 16*a*b^2*B*d^2*Sqrt[d + e*x] + 24*a^3*B*d*e*Sqrt[d + e*x] - 32*a^2*b*B*d*e*Sqrt[d + e*x] - 40*a*b^2*B*d*e*Sqrt[d + e*x] + 24*a^3*B*e^2*Sqrt[d + e*x] - 24*a^2*b*B*e^2*Sqrt[d + e*x] - 24*a*b^2*B*e^2*Sqrt[d + e*x] - 16*a*b^2*B*d^2*x*Sqrt[d + e*x] + 24*a^2*b*B*d*e*x*Sqrt[d + e*x] - 40*a*b^2*B*d*e*x*Sqrt[d + e*x] + 24*a^2*b*B*e^2*x*Sqrt[d + e*x] - 24*a*b^2*B*e^2*x*Sqrt[d + e*x] + 8*a*b*Sqrt[a + b]*B*d^2*Sqrt[a + b*x]*Sqrt[d + e*x] - 24*a^2*Sqrt[a + b]*B*d*e*Sqrt[a + b*x]*Sqrt[d + e*x] + 44*a*b*Sqrt[a + b]*B*d*e*Sqrt[a + b*x]*Sqrt[d + e*x] - 24*a^2*Sqrt[a + b]*B*e^2*Sqrt[a + b*x]*Sqrt[d + e*x] + 36*a*b*Sqrt[a + b]*B*e^2*Sqrt[a + b*x]*Sqrt[d + e*x] - 12*a*b*Sqrt[a + b]*B*d*e*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 12*a*b*Sqrt[a + b]*B*e^2*x*Sqrt[a + b*x]*Sqrt[d + e*x])/(Sqrt[d + e] - Sqrt[d + e*x])^4 + (-48*a^2*b*B*d*e*Sqrt[d + e] - 24*a*b^2*B*d*e*Sqrt[d + e] - 24*a^2*b*B*e^2*Sqrt[d + e] - 12*a*b^2*B*e^2*Sqrt[d + e] + 24*b^3*B*d^2*Sqrt[d + e]*x - 48*a*b^2*B*d*e*Sqrt[d + e]*x + 12*b^3*B*d*e*Sqrt[d + e]*x - 12*a*b^2*B*e^2*Sqrt[d + e]*x + 12*b^3*B*d*e*Sqrt[d + e]*x^2 + 24*b^3*B*e^2*Sqrt[d + e]*x^2 + 48*a*b*Sqrt[a + b]*B*d*e*Sqrt[d + e]*Sqrt[a + b*x] + 24*a*b*Sqrt[a + b]*B*e^2*Sqrt[d + e]*Sqrt[a + b*x] + 24*b^2*Sqrt[a + b]*B*d*e*Sqrt[d + e]*x*Sqrt[a + b*x] + 48*a^2*b*B*d*e*Sqrt[d + e*x] + 24*a*b^2*B*d*e*Sqrt[d + e*x] + 48*a^2*b*B*e^2*Sqrt[d + e*x] + 24*a*b^2*B*e^2*Sqrt[d + e*x] - 24*b^3*B*d^2*x*Sqrt[d + e*x] + 48*a*b^2*B*d*e*x*Sqrt[d + e*x] - 24*b^3*B*d*e*x*Sqrt[d + e*x] + 48*a*b^2*B*e^2*x*Sqrt[d + e*x] - 48*a*b*Sqrt[a + b]*B*d*e*Sqrt[a + b*x]*Sqrt[d + e*x] - 48*a*b*Sqrt[a + b]*B*e^2*Sqrt[a + b*x]*Sqrt[d + e*x] - 24*b^2*Sqrt[a + b]*B*d*e*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 24*b^2*Sqrt[a + b]*B*e^2*x*Sqrt[a + b*x]*Sqrt[d + e*x])/(Sqrt[d + e] - Sqrt[d + e*x])^4))/((-Sqrt[d + e] + Sqrt[d + e*x])*(-(a*Sqrt[a + b]*e) - b*Sqrt[a + b]*e*x - b*d*Sqrt[a + b*x] + a*e*Sqrt[a + b*x] + b*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x])^3)","B",1
2258,1,3768,139,75.6384231,"\int \frac{A+B x}{(a+b x)^{5/2} (d+e x)^{3/2}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^(5/2)*(d + e*x)^(3/2)),x]","\text{Result too large to show}","-\frac{2 (B d-A e)}{e (a+b x)^{3/2} \sqrt{d+e x} (b d-a e)}-\frac{4 \sqrt{d+e x} (a B e-4 A b e+3 b B d)}{3 \sqrt{a+b x} (b d-a e)^3}+\frac{2 \sqrt{d+e x} (a B e-4 A b e+3 b B d)}{3 e (a+b x)^{3/2} (b d-a e)^2}",1,"((1/(12*(a + b)*Sqrt[d + e]) - Sqrt[a + b*x]/(12*(a + b)^(3/2)*Sqrt[d + e]))*(Sqrt[d + e] - Sqrt[d + e*x])^8*((-24*a*A*(-(b*d) - a*e - b*e - b*e*x + Sqrt[a + b]*e*Sqrt[a + b*x] + b*Sqrt[d + e]*Sqrt[d + e*x])^3)/(Sqrt[d + e] - Sqrt[d + e*x])^6 + ((-24*b^2*B*d - 24*a*b*B*e - 24*b^2*B*e - 24*b^2*B*e*x + 24*b*Sqrt[a + b]*B*e*Sqrt[a + b*x] + 24*b^2*B*Sqrt[d + e]*Sqrt[d + e*x])*(4*a^2*d*e + 2*a*b*d*e + 2*a^2*e^2 + a*b*e^2 - 2*b^2*d^2*x + 4*a*b*d*e*x - b^2*d*e*x + a*b*e^2*x - b^2*d*e*x^2 - 2*b^2*e^2*x^2 - 4*a*Sqrt[a + b]*d*e*Sqrt[a + b*x] - 2*a*Sqrt[a + b]*e^2*Sqrt[a + b*x] - 2*b*Sqrt[a + b]*d*e*x*Sqrt[a + b*x] - 4*a^2*e*Sqrt[d + e]*Sqrt[d + e*x] - 2*a*b*e*Sqrt[d + e]*Sqrt[d + e*x] + 2*b^2*d*Sqrt[d + e]*x*Sqrt[d + e*x] - 4*a*b*e*Sqrt[d + e]*x*Sqrt[d + e*x] + 4*a*Sqrt[a + b]*e*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] + 2*b*Sqrt[a + b]*e*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x]))/(Sqrt[d + e] - Sqrt[d + e*x])^6 + (-32*a*A*b^3*d^3 + 32*A*b^4*d^3 - 256*a^2*A*b^2*d^2*e - 232*a*A*b^3*d^2*e + 40*A*b^4*d^2*e - 96*a^3*A*b*d*e^2 - 328*a^2*A*b^2*d*e^2 - 200*a*A*b^3*d*e^2 + 8*A*b^4*d*e^2 + 32*A*b^4*d^3*x - 232*a*A*b^3*d^2*e*x - 328*a^2*A*b^2*d*e^2*x - 432*a*A*b^3*d*e^2*x - 112*a^2*A*b^2*e^3*x - 56*a*A*b^3*e^3*x + 32*A*b^4*e^3*x + 40*A*b^4*d^2*e*x^2 - 200*a*A*b^3*d*e^2*x^2 - 56*a*A*b^3*e^3*x^2 + 32*A*b^4*e^3*x^2 + 8*A*b^4*d*e^2*x^3 + 32*A*b^4*e^3*x^3 + 32*A*b^3*Sqrt[a + b]*d^3*Sqrt[a + b*x] + 256*a*A*b^2*Sqrt[a + b]*d^2*e*Sqrt[a + b*x] + 104*A*b^3*Sqrt[a + b]*d^2*e*Sqrt[a + b*x] + 96*a^2*A*b*Sqrt[a + b]*d*e^2*Sqrt[a + b*x] + 280*a*A*b^2*Sqrt[a + b]*d*e^2*Sqrt[a + b*x] + 72*A*b^3*Sqrt[a + b]*d*e^2*Sqrt[a + b*x] + 104*A*b^3*Sqrt[a + b]*d^2*e*x*Sqrt[a + b*x] + 280*a*A*b^2*Sqrt[a + b]*d*e^2*x*Sqrt[a + b*x] + 128*A*b^3*Sqrt[a + b]*d*e^2*x*Sqrt[a + b*x] + 112*a*A*b^2*Sqrt[a + b]*e^3*x*Sqrt[a + b*x] + 72*A*b^3*Sqrt[a + b]*d*e^2*x^2*Sqrt[a + b*x] + 32*a*A*b^3*d^2*Sqrt[d + e]*Sqrt[d + e*x] - 32*A*b^4*d^2*Sqrt[d + e]*Sqrt[d + e*x] + 256*a^2*A*b^2*d*e*Sqrt[d + e]*Sqrt[d + e*x] + 216*a*A*b^3*d*e*Sqrt[d + e]*Sqrt[d + e*x] - 24*A*b^4*d*e*Sqrt[d + e]*Sqrt[d + e*x] + 96*a^3*A*b*e^2*Sqrt[d + e]*Sqrt[d + e*x] + 200*a^2*A*b^2*e^2*Sqrt[d + e]*Sqrt[d + e*x] + 96*a*A*b^3*e^2*Sqrt[d + e]*Sqrt[d + e*x] - 32*A*b^4*d^2*Sqrt[d + e]*x*Sqrt[d + e*x] + 216*a*A*b^3*d*e*Sqrt[d + e]*x*Sqrt[d + e*x] + 32*A*b^4*d*e*Sqrt[d + e]*x*Sqrt[d + e*x] + 200*a^2*A*b^2*e^2*Sqrt[d + e]*x*Sqrt[d + e*x] + 208*a*A*b^3*e^2*Sqrt[d + e]*x*Sqrt[d + e*x] - 24*A*b^4*d*e*Sqrt[d + e]*x^2*Sqrt[d + e*x] + 96*a*A*b^3*e^2*Sqrt[d + e]*x^2*Sqrt[d + e*x] - 32*A*b^3*Sqrt[a + b]*d^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 256*a*A*b^2*Sqrt[a + b]*d*e*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 88*A*b^3*Sqrt[a + b]*d*e*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 96*a^2*A*b*Sqrt[a + b]*e^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 152*a*A*b^2*Sqrt[a + b]*e^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 32*A*b^3*Sqrt[a + b]*e^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 88*A*b^3*Sqrt[a + b]*d*e*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 152*a*A*b^2*Sqrt[a + b]*e^2*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 32*A*b^3*Sqrt[a + b]*e^2*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 32*A*b^3*Sqrt[a + b]*e^2*Sqrt[d + e]*x^2*Sqrt[a + b*x]*Sqrt[d + e*x])/(Sqrt[d + e] - Sqrt[d + e*x])^6 + (32*a^2*b^2*B*d^3 + 64*a*b^3*B*d^3 + 64*a^3*b*B*d^2*e + 280*a^2*b^2*B*d^2*e + 176*a*b^3*B*d^2*e - 96*a^4*B*d*e^2 + 88*a^3*b*B*d*e^2 + 368*a^2*b^2*B*d*e^2 + 136*a*b^3*B*d*e^2 + 96*a^3*b*B*e^3 + 120*a^2*b^2*B*e^3 + 24*a*b^3*B*e^3 + 64*a*b^3*B*d^3*x + 88*a^2*b^2*B*d^2*e*x + 336*a*b^3*B*d^2*e*x - 104*a^3*b*B*d*e^2*x + 288*a^2*b^2*B*d*e^2*x + 456*a*b^3*B*d*e^2*x + 112*a^3*b*B*e^3*x + 344*a^2*b^2*B*e^3*x + 184*a*b^3*B*e^3*x + 80*a*b^3*B*d^2*e*x^2 - 16*a^2*b^2*B*d*e^2*x^2 + 240*a*b^3*B*d*e^2*x^2 + 128*a^2*b^2*B*e^3*x^2 + 232*a*b^3*B*e^3*x^2 + 16*a*b^3*B*d*e^2*x^3 + 40*a*b^3*B*e^3*x^3 - 32*a*b^2*Sqrt[a + b]*B*d^3*Sqrt[a + b*x] - 64*a^2*b*Sqrt[a + b]*B*d^2*e*Sqrt[a + b*x] - 248*a*b^2*Sqrt[a + b]*B*d^2*e*Sqrt[a + b*x] + 96*a^3*Sqrt[a + b]*B*d*e^2*Sqrt[a + b*x] - 136*a^2*b*Sqrt[a + b]*B*d*e^2*Sqrt[a + b*x] - 288*a*b^2*Sqrt[a + b]*B*d*e^2*Sqrt[a + b*x] - 96*a^2*b*Sqrt[a + b]*B*e^3*Sqrt[a + b*x] - 72*a*b^2*Sqrt[a + b]*B*e^3*Sqrt[a + b*x] - 56*a*b^2*Sqrt[a + b]*B*d^2*e*x*Sqrt[a + b*x] + 56*a^2*b*Sqrt[a + b]*B*d*e^2*x*Sqrt[a + b*x] - 272*a*b^2*Sqrt[a + b]*B*d*e^2*x*Sqrt[a + b*x] - 112*a^2*b*Sqrt[a + b]*B*e^3*x*Sqrt[a + b*x] - 240*a*b^2*Sqrt[a + b]*B*e^3*x*Sqrt[a + b*x] - 72*a*b^2*Sqrt[a + b]*B*e^3*x^2*Sqrt[a + b*x] - 32*a^2*b^2*B*d^2*Sqrt[d + e]*Sqrt[d + e*x] - 64*a*b^3*B*d^2*Sqrt[d + e]*Sqrt[d + e*x] - 64*a^3*b*B*d*e*Sqrt[d + e]*Sqrt[d + e*x] - 264*a^2*b^2*B*d*e*Sqrt[d + e]*Sqrt[d + e*x] - 144*a*b^3*B*d*e*Sqrt[d + e]*Sqrt[d + e*x] + 96*a^4*B*e^2*Sqrt[d + e]*Sqrt[d + e*x] - 56*a^3*b*B*e^2*Sqrt[d + e]*Sqrt[d + e*x] - 240*a^2*b^2*B*e^2*Sqrt[d + e]*Sqrt[d + e*x] - 72*a*b^3*B*e^2*Sqrt[d + e]*Sqrt[d + e*x] - 64*a*b^3*B*d^2*Sqrt[d + e]*x*Sqrt[d + e*x] - 72*a^2*b^2*B*d*e*Sqrt[d + e]*x*Sqrt[d + e*x] - 272*a*b^3*B*d*e*Sqrt[d + e]*x*Sqrt[d + e*x] + 136*a^3*b*B*e^2*Sqrt[d + e]*x*Sqrt[d + e*x] - 112*a^2*b^2*B*e^2*Sqrt[d + e]*x*Sqrt[d + e*x] - 240*a*b^3*B*e^2*Sqrt[d + e]*x*Sqrt[d + e*x] - 48*a*b^3*B*d*e*Sqrt[d + e]*x^2*Sqrt[d + e*x] + 48*a^2*b^2*B*e^2*Sqrt[d + e]*x^2*Sqrt[d + e*x] - 72*a*b^3*B*e^2*Sqrt[d + e]*x^2*Sqrt[d + e*x] + 32*a*b^2*Sqrt[a + b]*B*d^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] + 64*a^2*b*Sqrt[a + b]*B*d*e*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] + 232*a*b^2*Sqrt[a + b]*B*d*e*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] - 96*a^3*Sqrt[a + b]*B*e^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] + 104*a^2*b*Sqrt[a + b]*B*e^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] + 176*a*b^2*Sqrt[a + b]*B*e^2*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x] + 40*a*b^2*Sqrt[a + b]*B*d*e*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 88*a^2*b*Sqrt[a + b]*B*e^2*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] + 128*a*b^2*Sqrt[a + b]*B*e^2*Sqrt[d + e]*x*Sqrt[a + b*x]*Sqrt[d + e*x] - 16*a*b^2*Sqrt[a + b]*B*e^2*Sqrt[d + e]*x^2*Sqrt[a + b*x]*Sqrt[d + e*x])/(Sqrt[d + e] - Sqrt[d + e*x])^6))/((-Sqrt[d + e] + Sqrt[d + e*x])*(b*d*Sqrt[d + e] + b*e*Sqrt[d + e]*x - b*d*Sqrt[d + e*x] + a*e*Sqrt[d + e*x] - Sqrt[a + b]*e*Sqrt[a + b*x]*Sqrt[d + e*x])*(-(a*Sqrt[a + b]*e) - b*Sqrt[a + b]*e*x - b*d*Sqrt[a + b*x] + a*e*Sqrt[a + b*x] + b*Sqrt[d + e]*Sqrt[a + b*x]*Sqrt[d + e*x])^3)","B",1
2259,-1,0,186,180.0885162,"\int \frac{A+B x}{(a+b x)^{5/2} (d+e x)^{5/2}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^(5/2)*(d + e*x)^(5/2)),x]","\text{\$Aborted}","-\frac{2 (B d-A e)}{3 e (a+b x)^{3/2} (d+e x)^{3/2} (b d-a e)}-\frac{16 e \sqrt{a+b x} (a B e-2 A b e+b B d)}{3 \sqrt{d+e x} (b d-a e)^4}-\frac{8 (a B e-2 A b e+b B d)}{3 \sqrt{a+b x} \sqrt{d+e x} (b d-a e)^3}+\frac{2 (a B e-2 A b e+b B d)}{3 e (a+b x)^{3/2} \sqrt{d+e x} (b d-a e)^2}",1,"$Aborted","F",-1
2260,-1,0,246,180.226379,"\int \frac{A+B x}{(a+b x)^{5/2} (d+e x)^{7/2}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^(5/2)*(d + e*x)^(7/2)),x]","\text{\$Aborted}","-\frac{2 (A b-a B)}{3 b (a+b x)^{3/2} (d+e x)^{5/2} (b d-a e)}-\frac{32 b e \sqrt{a+b x} (5 a B e-8 A b e+3 b B d)}{15 \sqrt{d+e x} (b d-a e)^5}-\frac{16 e \sqrt{a+b x} (5 a B e-8 A b e+3 b B d)}{15 (d+e x)^{3/2} (b d-a e)^4}-\frac{4 e \sqrt{a+b x} (5 a B e-8 A b e+3 b B d)}{5 b (d+e x)^{5/2} (b d-a e)^3}-\frac{2 (5 a B e-8 A b e+3 b B d)}{3 b \sqrt{a+b x} (d+e x)^{5/2} (b d-a e)^2}",1,"$Aborted","F",-1
2261,-1,0,298,180.4413637,"\int \frac{A+B x}{(a+b x)^{5/2} (d+e x)^{9/2}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^(5/2)*(d + e*x)^(9/2)),x]","\text{\$Aborted}","-\frac{256 b^2 e \sqrt{a+b x} (7 a B e-10 A b e+3 b B d)}{105 \sqrt{d+e x} (b d-a e)^6}-\frac{128 b e \sqrt{a+b x} (7 a B e-10 A b e+3 b B d)}{105 (d+e x)^{3/2} (b d-a e)^5}-\frac{32 e \sqrt{a+b x} (7 a B e-10 A b e+3 b B d)}{35 (d+e x)^{5/2} (b d-a e)^4}-\frac{16 e \sqrt{a+b x} (7 a B e-10 A b e+3 b B d)}{21 b (d+e x)^{7/2} (b d-a e)^3}-\frac{2 (7 a B e-10 A b e+3 b B d)}{3 b \sqrt{a+b x} (d+e x)^{7/2} (b d-a e)^2}-\frac{2 (A b-a B)}{3 b (a+b x)^{3/2} (d+e x)^{7/2} (b d-a e)}",1,"$Aborted","F",-1
2262,1,486,157,2.8902261,"\int \sqrt{1-2 x} (2+3 x)^4 \sqrt{3+5 x} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^4*Sqrt[3 + 5*x],x]","\frac{4122385421 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{25600000 \sqrt{10}}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-16349029200000000000 x^{11}+581021860428000000000 x^{10}+16502013912753450000000 x^9+37332279528133337500000 x^8-64392554271377501687500 x^7-290002197537375574796875 x^6-328017671559331007215000 x^5-81554594238170363309750 x^4+143451621763564750342000 x^3+159536154910220928260240 x^2-2032192942788100645760 x-52034935500405878496608\right)+\sqrt{5 x+3} \left(326834481600000000000 x^{11}+3955494912336000000000 x^{10}-30336495142951800000000 x^9-171458379580533870000000 x^8-218910356808572398750000 x^7+77328957275096505687500 x^6+377021240697031114538750 x^5+280177954113685043655250 x^4-8922822498272477515600 x^3-187338998266366595844800 x^2-49993538372170895309280 x+52034935500405878496608\right)+\sqrt{3} \left(-18145296000000000000 x^{12}-2445965825760000000000 x^{11}+1556376256242000000000 x^{10}+118156260704987700000000 x^9+333977257845519532500000 x^8+223151070464967556875000 x^7-312151430880599744434375 x^6-590572414576113262260000 x^5-308367729889209889359750 x^4+132754373031030407395600 x^3+247062134549392668670800 x^2+6630059811182923645440 x+\sqrt{1-2 x} \left(87316574400000000000 x^{11}-6376174641936000000000 x^{10}-43308944270875800000000 x^9-25558916903088690000000 x^8+226892260965400973250000 x^7+522551356742496809062500 x^6+415673875564239128636250 x^5+2917351079601263445250 x^4-262171246108719062601200 x^3-175903482786798098207040 x^2+45395671503776072309600 x+52034935500405878496608\right)-52034935500405878496608\right)}{51200000 \sqrt{3} \sqrt{5 x+3} \left(25265212500 x^5-1941218400000 x^4-5284290066000 x^3+24057375117600 x^2+13825440024000 x-16748592098304\right)+\sqrt{1-2 x} \left(51200000 \left(-236425406250 x^5-2220611593750 x^4+28520358020000 x^3+52011357156000 x^2-49788771586400 x-50183931760160\right)+51200000 \sqrt{3} \sqrt{5 x+3} \left(2625187500 x^5+345183000000 x^4-1378186950000 x^3-13912170444000 x^2+2687092123200 x+16725373086720\right)\right)+51200000 \left(-23653109375 x^6+916525237500 x^5+21026153381250 x^4-17065853944000 x^3-123670456765200 x^2+301410173760 x+50253588794912\right)}","-\frac{1}{20} (1-2 x)^{3/2} (5 x+3)^{3/2} (3 x+2)^3-\frac{333 (1-2 x)^{3/2} (5 x+3)^{3/2} (3 x+2)^2}{2000}-\frac{7 (1-2 x)^{3/2} (5 x+3)^{3/2} (140652 x+231223)}{640000}-\frac{34069301 (1-2 x)^{3/2} \sqrt{5 x+3}}{5120000}+\frac{374762311 \sqrt{1-2 x} \sqrt{5 x+3}}{51200000}+\frac{4122385421 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{51200000 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-52034935500405878496608 - 2032192942788100645760*x + 159536154910220928260240*x^2 + 143451621763564750342000*x^3 - 81554594238170363309750*x^4 - 328017671559331007215000*x^5 - 290002197537375574796875*x^6 - 64392554271377501687500*x^7 + 37332279528133337500000*x^8 + 16502013912753450000000*x^9 + 581021860428000000000*x^10 - 16349029200000000000*x^11) + Sqrt[3 + 5*x]*(52034935500405878496608 - 49993538372170895309280*x - 187338998266366595844800*x^2 - 8922822498272477515600*x^3 + 280177954113685043655250*x^4 + 377021240697031114538750*x^5 + 77328957275096505687500*x^6 - 218910356808572398750000*x^7 - 171458379580533870000000*x^8 - 30336495142951800000000*x^9 + 3955494912336000000000*x^10 + 326834481600000000000*x^11) + Sqrt[3]*(-52034935500405878496608 + 6630059811182923645440*x + 247062134549392668670800*x^2 + 132754373031030407395600*x^3 - 308367729889209889359750*x^4 - 590572414576113262260000*x^5 - 312151430880599744434375*x^6 + 223151070464967556875000*x^7 + 333977257845519532500000*x^8 + 118156260704987700000000*x^9 + 1556376256242000000000*x^10 - 2445965825760000000000*x^11 - 18145296000000000000*x^12 + Sqrt[1 - 2*x]*(52034935500405878496608 + 45395671503776072309600*x - 175903482786798098207040*x^2 - 262171246108719062601200*x^3 + 2917351079601263445250*x^4 + 415673875564239128636250*x^5 + 522551356742496809062500*x^6 + 226892260965400973250000*x^7 - 25558916903088690000000*x^8 - 43308944270875800000000*x^9 - 6376174641936000000000*x^10 + 87316574400000000000*x^11)))/(51200000*Sqrt[3]*Sqrt[3 + 5*x]*(-16748592098304 + 13825440024000*x + 24057375117600*x^2 - 5284290066000*x^3 - 1941218400000*x^4 + 25265212500*x^5) + 51200000*(50253588794912 + 301410173760*x - 123670456765200*x^2 - 17065853944000*x^3 + 21026153381250*x^4 + 916525237500*x^5 - 23653109375*x^6) + Sqrt[1 - 2*x]*(51200000*(-50183931760160 - 49788771586400*x + 52011357156000*x^2 + 28520358020000*x^3 - 2220611593750*x^4 - 236425406250*x^5) + 51200000*Sqrt[3]*Sqrt[3 + 5*x]*(16725373086720 + 2687092123200*x - 13912170444000*x^2 - 1378186950000*x^3 + 345183000000*x^4 + 2625187500*x^5))) + (4122385421*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(25600000*Sqrt[10])","B",1
2263,1,426,128,2.6407604,"\int \sqrt{1-2 x} (2+3 x)^3 \sqrt{3+5 x} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^3*Sqrt[3 + 5*x],x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(1529301600000000 x^9+174068838270000000 x^8+120640199758500000 x^7-3269284108322562500 x^6-7757075698173828125 x^5-4927596619494131125 x^4+2634270124663392900 x^3+5310458552522966020 x^2+477015766266239040 x-1777169668842683984\right)+\sqrt{5 x+3} \left(18934344000000000 x^9-675169832700000000 x^8-3329662787715000000 x^7-1708864965424375000 x^6+7203981924786968750 x^5+10150791729283995625 x^4+2286201967685691000 x^3-5674123889355109100 x^2-2250590101933323920 x+1777169668842683984\right)+\sqrt{3} \left(-5704560000000000 x^{10}+102142917000000000 x^9+2553518994450000000 x^8+5431933228141250000 x^7-1876824300620312500 x^6-14353560772149009375 x^5-12900397422247338125 x^4+1152758304900041500 x^3+8169113384251432500 x^2+\sqrt{1-2 x} \left(-43815816000000000 x^9-465342480900000000 x^8+1210664446893000000 x^7+8112879287926875000 x^6+11881437171471243750 x^5+3955331558371290625 x^4-6387554314029053000 x^3-6326888767983177020 x^2+1004539624149539280 x+1777169668842683984\right)+769034711517545600 x-1777169668842683984\right)}{1280000 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right)+\sqrt{1-2 x} \left(1280000 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right)+1280000 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right)\right)+1280000 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right)}+\frac{39142411 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{640000 \sqrt{10}}","-\frac{3}{50} (1-2 x)^{3/2} (5 x+3)^{3/2} (3 x+2)^2-\frac{21 (1-2 x)^{3/2} (5 x+3)^{3/2} (444 x+731)}{16000}-\frac{323491 (1-2 x)^{3/2} \sqrt{5 x+3}}{128000}+\frac{3558401 \sqrt{1-2 x} \sqrt{5 x+3}}{1280000}+\frac{39142411 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{1280000 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-1777169668842683984 + 477015766266239040*x + 5310458552522966020*x^2 + 2634270124663392900*x^3 - 4927596619494131125*x^4 - 7757075698173828125*x^5 - 3269284108322562500*x^6 + 120640199758500000*x^7 + 174068838270000000*x^8 + 1529301600000000*x^9) + Sqrt[3 + 5*x]*(1777169668842683984 - 2250590101933323920*x - 5674123889355109100*x^2 + 2286201967685691000*x^3 + 10150791729283995625*x^4 + 7203981924786968750*x^5 - 1708864965424375000*x^6 - 3329662787715000000*x^7 - 675169832700000000*x^8 + 18934344000000000*x^9) + Sqrt[3]*(-1777169668842683984 + 769034711517545600*x + 8169113384251432500*x^2 + 1152758304900041500*x^3 - 12900397422247338125*x^4 - 14353560772149009375*x^5 - 1876824300620312500*x^6 + 5431933228141250000*x^7 + 2553518994450000000*x^8 + 102142917000000000*x^9 - 5704560000000000*x^10 + Sqrt[1 - 2*x]*(1777169668842683984 + 1004539624149539280*x - 6326888767983177020*x^2 - 6387554314029053000*x^3 + 3955331558371290625*x^4 + 11881437171471243750*x^5 + 8112879287926875000*x^6 + 1210664446893000000*x^7 - 465342480900000000*x^8 - 43815816000000000*x^9)))/(1280000*Sqrt[3]*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 1280000*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(1280000*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 1280000*Sqrt[3]*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (39142411*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(640000*Sqrt[10])","B",1
2264,1,366,121,2.2647347,"\int \sqrt{1-2 x} (2+3 x)^2 \sqrt{3+5 x} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^2*Sqrt[3 + 5*x],x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-246258000000 x^7+1854558100000 x^6+40024288377500 x^5+65750053451375 x^4+512030827800 x^3-64295946246840 x^2-17592507176480 x+22854086456696\right)+\sqrt{5 x+3} \left(2792592000000 x^7+20733776800000 x^6-23955782620000 x^5-112734170329000 x^4-72554717192100 x^3+55247810172500 x^2+40114417096600 x-22854086456696\right)+\sqrt{3} \left(-171360000000 x^8-15639896000000 x^7-18640477400000 x^6+91424672070000 x^5+175658675096375 x^4+47392130690600 x^3-97010195802200 x^2+\sqrt{1-2 x} \left(1284624000000 x^7-20395751200000 x^6-85568737100000 x^5-78228969599000 x^4+40293154240900 x^3+87212819963940 x^2-1529818516600 x-22854086456696\right)-20992091403520 x+22854086456696\right)}{12800 \sqrt{3} \sqrt{5 x+3} \left(8921000 x^3-162998000 x^2-220512160 x+287530496\right)+\sqrt{1-2 x} \left(12800 \left(-48482500 x^3-297203500 x^2+794989800 x+852279560\right)+12800 \sqrt{3} \sqrt{5 x+3} \left(595000 x^3+53178000 x^2-36412000 x-283051520\right)\right)+12800 \left(-8550625 x^4+79738000 x^3+1253327000 x^2-32289760 x-865716488\right)}+\frac{158873 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{6400 \sqrt{10}}","-\frac{3}{40} (3 x+2) (5 x+3)^{3/2} (1-2 x)^{3/2}-\frac{37}{160} (5 x+3)^{3/2} (1-2 x)^{3/2}-\frac{1313 \sqrt{5 x+3} (1-2 x)^{3/2}}{1280}+\frac{14443 \sqrt{5 x+3} \sqrt{1-2 x}}{12800}+\frac{158873 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{12800 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(22854086456696 - 17592507176480*x - 64295946246840*x^2 + 512030827800*x^3 + 65750053451375*x^4 + 40024288377500*x^5 + 1854558100000*x^6 - 246258000000*x^7) + Sqrt[3 + 5*x]*(-22854086456696 + 40114417096600*x + 55247810172500*x^2 - 72554717192100*x^3 - 112734170329000*x^4 - 23955782620000*x^5 + 20733776800000*x^6 + 2792592000000*x^7) + Sqrt[3]*(22854086456696 - 20992091403520*x - 97010195802200*x^2 + 47392130690600*x^3 + 175658675096375*x^4 + 91424672070000*x^5 - 18640477400000*x^6 - 15639896000000*x^7 - 171360000000*x^8 + Sqrt[1 - 2*x]*(-22854086456696 - 1529818516600*x + 87212819963940*x^2 + 40293154240900*x^3 - 78228969599000*x^4 - 85568737100000*x^5 - 20395751200000*x^6 + 1284624000000*x^7)))/(12800*Sqrt[3]*Sqrt[3 + 5*x]*(287530496 - 220512160*x - 162998000*x^2 + 8921000*x^3) + 12800*(-865716488 - 32289760*x + 1253327000*x^2 + 79738000*x^3 - 8550625*x^4) + Sqrt[1 - 2*x]*(12800*(852279560 + 794989800*x - 297203500*x^2 - 48482500*x^3) + 12800*Sqrt[3]*Sqrt[3 + 5*x]*(-283051520 - 36412000*x + 53178000*x^2 + 595000*x^3))) + (158873*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(6400*Sqrt[10])","B",1
2265,1,306,94,1.8835464,"\int \sqrt{1-2 x} (2+3 x) \sqrt{3+5 x} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)*Sqrt[3 + 5*x],x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(35900000 x^5+2418017500 x^4+2208392875 x^3-3785024225 x^2-2891839600 x+1438507532\right)+\sqrt{5 x+3} \left(627000000 x^5-4194025000 x^4-8424814750 x^3+761036375 x^2+4171001340 x-1438507532\right)+\sqrt{3} \left(-234000000 x^6+511950000 x^5+10093852500 x^4+9974654125 x^3-4993759725 x^2+\sqrt{1-2 x} \left(-917400000 x^5-4624455000 x^4-616728750 x^3+6898414875 x^2+1639718740 x-1438507532\right)-2918880480 x+1438507532\right)}{800 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right)+\sqrt{1-2 x} \left(800 \left(-391875 x^2+2827000 x+3481060\right)+800 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right)\right)+800 \left(44875 x^3+2976525 x^2-279060 x-3667684\right)}+\frac{4477 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{400 \sqrt{10}}","-\frac{1}{10} (5 x+3)^{3/2} (1-2 x)^{3/2}-\frac{37}{80} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{407}{800} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{4477 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{800 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1438507532 - 2891839600*x - 3785024225*x^2 + 2208392875*x^3 + 2418017500*x^4 + 35900000*x^5) + Sqrt[3 + 5*x]*(-1438507532 + 4171001340*x + 761036375*x^2 - 8424814750*x^3 - 4194025000*x^4 + 627000000*x^5) + Sqrt[3]*(1438507532 - 2918880480*x - 4993759725*x^2 + 9974654125*x^3 + 10093852500*x^4 + 511950000*x^5 - 234000000*x^6 + Sqrt[1 - 2*x]*(-1438507532 + 1639718740*x + 6898414875*x^2 - 616728750*x^3 - 4624455000*x^4 - 917400000*x^5)))/(800*Sqrt[3]*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 800*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(800*(3481060 + 2827000*x - 391875*x^2) + 800*Sqrt[3]*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (4477*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(400*Sqrt[10])","B",1
2266,1,246,72,1.5350441,"\int \sqrt{1-2 x} \sqrt{3+5 x} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*Sqrt[3 + 5*x],x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-59500 x^3+33425 x^2+333360 x+29282\right)+\sqrt{5 x+3} \left(286000 x^3+430100 x^2-252670 x-29282\right)+\sqrt{3} \left(-20000 x^4-851000 x^3-124275 x^2+\sqrt{1-2 x} \left(198000 x^3-381700 x^2-332970 x-29282\right)+252280 x+29282\right)}{40 \left(-2975 x^2+1820 x+16562\right)+40 \sqrt{3} \sqrt{5 x+3} (1980 x-5104)+\sqrt{1-2 x} \left(40 (-7150 x-13970)+40 \sqrt{3} \sqrt{5 x+3} (100 x+4240)\right)}+\frac{121 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{20 \sqrt{10}}","-\frac{1}{4} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{11}{40} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{121 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{40 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(29282 + 333360*x + 33425*x^2 - 59500*x^3) + Sqrt[3 + 5*x]*(-29282 - 252670*x + 430100*x^2 + 286000*x^3) + Sqrt[3]*(29282 + 252280*x - 124275*x^2 - 851000*x^3 - 20000*x^4 + Sqrt[1 - 2*x]*(-29282 - 332970*x - 381700*x^2 + 198000*x^3)))/(40*Sqrt[3]*Sqrt[3 + 5*x]*(-5104 + 1980*x) + 40*(16562 + 1820*x - 2975*x^2) + Sqrt[1 - 2*x]*(40*(-13970 - 7150*x) + 40*Sqrt[3]*Sqrt[3 + 5*x]*(4240 + 100*x))) + (121*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(20*Sqrt[10])","B",1
2267,1,376,84,1.4990541,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{2+3 x} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x),x]","\frac{7}{9} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{\left(\frac{1}{3}-\frac{1}{3} \sqrt{1-2 x}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right) \left(10 x-55 \sqrt{1-2 x}+20 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}-22 \sqrt{3} \sqrt{5 x+3}+61\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}+\frac{37}{9} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{1}{3} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{37 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{9 \sqrt{10}}+\frac{2}{9} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"((1/3 - Sqrt[1 - 2*x]/3)*(Sqrt[3] - Sqrt[3 + 5*x])*(61 - 55*Sqrt[1 - 2*x] + 10*x - 22*Sqrt[3]*Sqrt[3 + 5*x] + 20*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2 + (37*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/9 + (7*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ])/9","C",1
2268,1,469,91,1.6553529,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^2} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^2,x]","\frac{37}{9} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{185}{18} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{3} \left(185 x^2-263 x+\sqrt{1-2 x} (385 x+242)-242\right)+\sqrt{1-2 x} \sqrt{5 x+3} (-100 x-242)+(242-22 x) \sqrt{5 x+3}}{6 (5 x+91) (3 x+2)-132 \sqrt{3} \sqrt{5 x+3} (3 x+2)+\sqrt{1-2 x} \left(60 \sqrt{3} (3 x+2) \sqrt{5 x+3}-330 (3 x+2)\right)}-\frac{4}{9} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{\sqrt{1-2 x} \sqrt{5 x+3}}{3 (3 x+2)}-\frac{2}{9} \sqrt{10} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{37 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{9 \sqrt{7}}",1,"((242 - 22*x)*Sqrt[3 + 5*x] + (-242 - 100*x)*Sqrt[1 - 2*x]*Sqrt[3 + 5*x] + Sqrt[3]*(-242 - 263*x + 185*x^2 + Sqrt[1 - 2*x]*(242 + 385*x)))/(-132*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x] + 6*(2 + 3*x)*(91 + 5*x) + Sqrt[1 - 2*x]*(-330*(2 + 3*x) + 60*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x])) - (4*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/9 + (37*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/9 - (185*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/18","C",1
2269,1,479,93,1.8157341,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^3} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^3,x]","\frac{121}{28} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{605}{56} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-796400 x^3-722590 x^2+901010 x+585640\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(96575 x^3-598240 x^2-1418394 x-585640\right)+\sqrt{3} \left(170875 x^4+1689100 x^3+200790 x^2+\sqrt{1-2 x} \left(-44550 x^3+1584110 x^2+1939344 x+585640\right)-1421960 x-585640\right)}{28 \left(2975 x^2-1820 x-16562\right) (3 x+2)^2+28 \sqrt{3} (5104-1980 x) \sqrt{5 x+3} (3 x+2)^2+\sqrt{1-2 x} \left(28 (7150 x+13970) (3 x+2)^2+28 \sqrt{3} (-100 x-4240) \sqrt{5 x+3} (3 x+2)^2\right)}","\frac{\sqrt{1-2 x} (5 x+3)^{3/2}}{2 (3 x+2)^2}-\frac{11 \sqrt{1-2 x} \sqrt{5 x+3}}{28 (3 x+2)}-\frac{121 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{28 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(585640 + 901010*x - 722590*x^2 - 796400*x^3) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-585640 - 1418394*x - 598240*x^2 + 96575*x^3) + Sqrt[3]*(-585640 - 1421960*x + 200790*x^2 + 1689100*x^3 + 170875*x^4 + Sqrt[1 - 2*x]*(585640 + 1939344*x + 1584110*x^2 - 44550*x^3)))/(28*Sqrt[3]*(5104 - 1980*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 28*(2 + 3*x)^2*(-16562 - 1820*x + 2975*x^2) + Sqrt[1 - 2*x]*(28*Sqrt[3]*(-4240 - 100*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 28*(2 + 3*x)^2*(13970 + 7150*x))) + (121*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/28 - (605*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/56","C",1
2270,1,539,122,2.1416496,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^4} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^4,x]","\frac{4477}{392} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{22385}{784} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-1046972850 x^5-38328790445 x^4-54207367522 x^3+3653991836 x^2+33112294424 x+11678130112\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(647237125 x^5+10136969025 x^4-7921969790 x^3-49511194708 x^2-44269992408 x-11678130112\right)+\sqrt{3} \left(-787902750 x^6+18954079800 x^5+77089867830 x^4+59967838792 x^3-26844636456 x^2+\sqrt{1-2 x} \left(-6247131000 x^5-10591279050 x^4+36415043280 x^3+82174212648 x^2+54176059168 x+11678130112\right)-43018361184 x-11678130112\right)}{392 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right) (3 x+2)^3+\sqrt{1-2 x} \left(392 \left(-391875 x^2+2827000 x+3481060\right) (3 x+2)^3+392 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right) (3 x+2)^3\right)+392 \left(44875 x^3+2976525 x^2-279060 x-3667684\right) (3 x+2)^3}","\frac{37 \sqrt{1-2 x} (5 x+3)^{3/2}}{28 (3 x+2)^2}+\frac{(1-2 x)^{3/2} (5 x+3)^{3/2}}{7 (3 x+2)^3}-\frac{407 \sqrt{1-2 x} \sqrt{5 x+3}}{392 (3 x+2)}-\frac{4477 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{392 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(11678130112 + 33112294424*x + 3653991836*x^2 - 54207367522*x^3 - 38328790445*x^4 - 1046972850*x^5) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-11678130112 - 44269992408*x - 49511194708*x^2 - 7921969790*x^3 + 10136969025*x^4 + 647237125*x^5) + Sqrt[3]*(-11678130112 - 43018361184*x - 26844636456*x^2 + 59967838792*x^3 + 77089867830*x^4 + 18954079800*x^5 - 787902750*x^6 + Sqrt[1 - 2*x]*(11678130112 + 54176059168*x + 82174212648*x^2 + 36415043280*x^3 - 10591279050*x^4 - 6247131000*x^5)))/(392*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 392*(2 + 3*x)^3*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(392*(2 + 3*x)^3*(3481060 + 2827000*x - 391875*x^2) + 392*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (4477*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/392 - (22385*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/784","C",1
2271,1,599,151,2.6053409,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^5} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^5,x]","\frac{794365 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{21952}-\frac{3971825 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{43904}+\frac{\sqrt{5 x+3} \left(-262378877178000 x^7-138901179246500 x^6+6891777289172380 x^5+13997494878147352 x^4+6619343531804872 x^3-4037752301390368 x^2-4373284959362528 x-1019346788867968\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(10663894505625 x^7-611145262799000 x^6-3599622983415500 x^5-2803962567771440 x^4+5540177790962920 x^3+9768231631398720 x^2+5378547464871264 x+1019346788867968\right)+\sqrt{3} \left(36889108569375 x^8+849869037082000 x^7-2872169012175000 x^6-16047594769339440 x^5-19906308806279512 x^4-4492624174328832 x^3+7319590382502208 x^2+\sqrt{1-2 x} \left(62245278232500 x^7+2590555524243500 x^6+6272316570918200 x^5+297990052364840 x^4-12089534245838720 x^3-13891064021267840 x^2-6231278676427904 x-1019346788867968\right)+5226016170919168 x+1019346788867968\right)}{21952 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^4+\sqrt{1-2 x} \left(21952 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^4+21952 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^4\right)+21952 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^4}","\frac{625115 \sqrt{1-2 x} \sqrt{5 x+3}}{197568 (3 x+2)}+\frac{6005 \sqrt{1-2 x} \sqrt{5 x+3}}{14112 (3 x+2)^2}+\frac{37 \sqrt{1-2 x} \sqrt{5 x+3}}{504 (3 x+2)^3}-\frac{\sqrt{1-2 x} \sqrt{5 x+3}}{12 (3 x+2)^4}-\frac{794365 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{21952 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-1019346788867968 - 4373284959362528*x - 4037752301390368*x^2 + 6619343531804872*x^3 + 13997494878147352*x^4 + 6891777289172380*x^5 - 138901179246500*x^6 - 262378877178000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1019346788867968 + 5378547464871264*x + 9768231631398720*x^2 + 5540177790962920*x^3 - 2803962567771440*x^4 - 3599622983415500*x^5 - 611145262799000*x^6 + 10663894505625*x^7) + Sqrt[3]*(1019346788867968 + 5226016170919168*x + 7319590382502208*x^2 - 4492624174328832*x^3 - 19906308806279512*x^4 - 16047594769339440*x^5 - 2872169012175000*x^6 + 849869037082000*x^7 + 36889108569375*x^8 + Sqrt[1 - 2*x]*(-1019346788867968 - 6231278676427904*x - 13891064021267840*x^2 - 12089534245838720*x^3 + 297990052364840*x^4 + 6272316570918200*x^5 + 2590555524243500*x^6 + 62245278232500*x^7)))/(21952*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 21952*(2 + 3*x)^4*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(21952*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 21952*(2 + 3*x)^4*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) + (794365*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/21952 - (3971825*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/43904","C",1
2272,1,659,180,3.1082494,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^6} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^6,x]","\frac{5591773 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{43904}-\frac{27958865 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{87808}+\frac{\sqrt{5 x+3} \left(-668905136878275000 x^9-32358334563155143125 x^8-68628562305329972550 x^7+160660536726840346240 x^6+563476655448867555472 x^5+513922521287561344640 x^4+58109313388048792320 x^3-172426513345037110720 x^2-100598931535483300480 x-17402473091744271872\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(122639048879765625 x^9+3638862298847671875 x^8-31824220555950731250 x^7-193569717360314119000 x^6-284186589596842796800 x^5-23177560716607219040 x^4+300684915661579785600 x^3+298024361216763399488 x^2+117929380014361606272 x+17402473091744271872\right)+\sqrt{3} \left(-92914225319896875 x^{10}+10969877375698359375 x^9+85850094571157287500 x^8+26080472689230673000 x^7-493529389702860867800 x^6-945883974258344658672 x^5-598078107961437802240 x^4+55625961733470649280 x^3+250179662222264766720 x^2+\sqrt{1-2 x} \left(-1690961615397140625 x^9+1400329572103687500 x^8+128758002575578200000 x^7+391846389544405125000 x^6+350955893258085918000 x^5-152981465654145103360 x^4-513048227052288389440 x^3-390231182870139643648 x^2-132443073301231832832 x-17402473091744271872\right)+115112624822353527040 x+17402473091744271872\right)}{219520 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right) (3 x+2)^5+\sqrt{1-2 x} \left(219520 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right) (3 x+2)^5+219520 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right) (3 x+2)^5\right)+219520 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right) (3 x+2)^5}","\frac{1466281 \sqrt{1-2 x} \sqrt{5 x+3}}{131712 (3 x+2)}+\frac{14023 \sqrt{1-2 x} \sqrt{5 x+3}}{9408 (3 x+2)^2}+\frac{403 \sqrt{1-2 x} \sqrt{5 x+3}}{1680 (3 x+2)^3}+\frac{37 \sqrt{1-2 x} \sqrt{5 x+3}}{840 (3 x+2)^4}-\frac{\sqrt{1-2 x} \sqrt{5 x+3}}{15 (3 x+2)^5}-\frac{5591773 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{43904 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-17402473091744271872 - 100598931535483300480*x - 172426513345037110720*x^2 + 58109313388048792320*x^3 + 513922521287561344640*x^4 + 563476655448867555472*x^5 + 160660536726840346240*x^6 - 68628562305329972550*x^7 - 32358334563155143125*x^8 - 668905136878275000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(17402473091744271872 + 117929380014361606272*x + 298024361216763399488*x^2 + 300684915661579785600*x^3 - 23177560716607219040*x^4 - 284186589596842796800*x^5 - 193569717360314119000*x^6 - 31824220555950731250*x^7 + 3638862298847671875*x^8 + 122639048879765625*x^9) + Sqrt[3]*(17402473091744271872 + 115112624822353527040*x + 250179662222264766720*x^2 + 55625961733470649280*x^3 - 598078107961437802240*x^4 - 945883974258344658672*x^5 - 493529389702860867800*x^6 + 26080472689230673000*x^7 + 85850094571157287500*x^8 + 10969877375698359375*x^9 - 92914225319896875*x^10 + Sqrt[1 - 2*x]*(-17402473091744271872 - 132443073301231832832*x - 390231182870139643648*x^2 - 513048227052288389440*x^3 - 152981465654145103360*x^4 + 350955893258085918000*x^5 + 391846389544405125000*x^6 + 128758002575578200000*x^7 + 1400329572103687500*x^8 - 1690961615397140625*x^9)))/(219520*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 219520*(2 + 3*x)^5*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(219520*(2 + 3*x)^5*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 219520*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (5591773*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/43904 - (27958865*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/87808","C",1
2273,1,719,209,3.7239235,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^7} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^7,x]","\frac{588912203 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{1229312}-\frac{2944561015 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2458624}+\frac{\sqrt{5 x+3} \left(-37200439395389612925000 x^{11}+192697427150305146506250 x^{10}+6571773373105837639388250 x^9+18929941212735194944057800 x^8+3409155969890821643187200 x^7-51342598616417444771528192 x^6-77877571657167743266655168 x^5-38886238674268173399228160 x^4+7334437019082920439869440 x^3+16093628349164126481712640 x^2+6458374598072276543324672 x+887305122083331816122368\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(686715902464214390625 x^{11}-159708470429535736500000 x^{10}-1507921332270252266193750 x^9+1533312294933783367333000 x^8+23304123086954140153641600 x^7+48725488322723501998932160 x^6+34455453834998503086510080 x^5-11605644138848383888442880 x^4-35155237056582559058107648 x^3-23862726132030287845417984 x^2-7344586017490106845309440 x-887305122083331816122368\right)+\sqrt{3} \left(4022201189697088921875 x^{12}+138876249855166796362500 x^{11}-2572639026698095531481250 x^{10}-18047984800642658019279000 x^9-27332936822727481578844200 x^8+22456351037868323659899360 x^7+103599375139568903311368832 x^6+109807851424828713709459968 x^5+36756877101078867605352960 x^4-18759368998966674557770240 x^3-21167065461207019498329600 x^2-7197918199174011390093312 x+\sqrt{1-2 x} \left(15892616308611960843750 x^{11}+894249779238870847031250 x^{10}+2197390771244516812470000 x^9-12078005774548688817249000 x^8-53507678533871554077122400 x^7-76306192689706925162458560 x^6-31985781911837081280353280 x^5+34476784253673536292869120 x^4+52746439226089180179795968 x^3+29674795426286997780355584 x^2+8084129618591841692078080 x+887305122083331816122368\right)-887305122083331816122368\right)}{6146560 \sqrt{3} \sqrt{5 x+3} \left(-25265212500 x^5+1941218400000 x^4+5284290066000 x^3-24057375117600 x^2-13825440024000 x+16748592098304\right) (3 x+2)^6+\sqrt{1-2 x} \left(6146560 \sqrt{3} \sqrt{5 x+3} \left(-2625187500 x^5-345183000000 x^4+1378186950000 x^3+13912170444000 x^2-2687092123200 x-16725373086720\right) (3 x+2)^6+6146560 \left(236425406250 x^5+2220611593750 x^4-28520358020000 x^3-52011357156000 x^2+49788771586400 x+50183931760160\right) (3 x+2)^6\right)+6146560 \left(23653109375 x^6-916525237500 x^5-21026153381250 x^4+17065853944000 x^3+123670456765200 x^2-301410173760 x-50253588794912\right) (3 x+2)^6}","\frac{463266973 \sqrt{1-2 x} \sqrt{5 x+3}}{11063808 (3 x+2)}+\frac{4429459 \sqrt{1-2 x} \sqrt{5 x+3}}{790272 (3 x+2)^2}+\frac{126799 \sqrt{1-2 x} \sqrt{5 x+3}}{141120 (3 x+2)^3}+\frac{10921 \sqrt{1-2 x} \sqrt{5 x+3}}{70560 (3 x+2)^4}+\frac{37 \sqrt{1-2 x} \sqrt{5 x+3}}{1260 (3 x+2)^5}-\frac{\sqrt{1-2 x} \sqrt{5 x+3}}{18 (3 x+2)^6}-\frac{588912203 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1229312 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(887305122083331816122368 + 6458374598072276543324672*x + 16093628349164126481712640*x^2 + 7334437019082920439869440*x^3 - 38886238674268173399228160*x^4 - 77877571657167743266655168*x^5 - 51342598616417444771528192*x^6 + 3409155969890821643187200*x^7 + 18929941212735194944057800*x^8 + 6571773373105837639388250*x^9 + 192697427150305146506250*x^10 - 37200439395389612925000*x^11) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-887305122083331816122368 - 7344586017490106845309440*x - 23862726132030287845417984*x^2 - 35155237056582559058107648*x^3 - 11605644138848383888442880*x^4 + 34455453834998503086510080*x^5 + 48725488322723501998932160*x^6 + 23304123086954140153641600*x^7 + 1533312294933783367333000*x^8 - 1507921332270252266193750*x^9 - 159708470429535736500000*x^10 + 686715902464214390625*x^11) + Sqrt[3]*(-887305122083331816122368 - 7197918199174011390093312*x - 21167065461207019498329600*x^2 - 18759368998966674557770240*x^3 + 36756877101078867605352960*x^4 + 109807851424828713709459968*x^5 + 103599375139568903311368832*x^6 + 22456351037868323659899360*x^7 - 27332936822727481578844200*x^8 - 18047984800642658019279000*x^9 - 2572639026698095531481250*x^10 + 138876249855166796362500*x^11 + 4022201189697088921875*x^12 + Sqrt[1 - 2*x]*(887305122083331816122368 + 8084129618591841692078080*x + 29674795426286997780355584*x^2 + 52746439226089180179795968*x^3 + 34476784253673536292869120*x^4 - 31985781911837081280353280*x^5 - 76306192689706925162458560*x^6 - 53507678533871554077122400*x^7 - 12078005774548688817249000*x^8 + 2197390771244516812470000*x^9 + 894249779238870847031250*x^10 + 15892616308611960843750*x^11)))/(6146560*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(16748592098304 - 13825440024000*x - 24057375117600*x^2 + 5284290066000*x^3 + 1941218400000*x^4 - 25265212500*x^5) + 6146560*(2 + 3*x)^6*(-50253588794912 - 301410173760*x + 123670456765200*x^2 + 17065853944000*x^3 - 21026153381250*x^4 - 916525237500*x^5 + 23653109375*x^6) + Sqrt[1 - 2*x]*(6146560*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(-16725373086720 - 2687092123200*x + 13912170444000*x^2 + 1378186950000*x^3 - 345183000000*x^4 - 2625187500*x^5) + 6146560*(2 + 3*x)^6*(50183931760160 + 49788771586400*x - 52011357156000*x^2 - 28520358020000*x^3 + 2220611593750*x^4 + 236425406250*x^5))) + (588912203*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/1229312 - (2944561015*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2458624","C",1
2274,1,1331,179,14.2474299,"\int \sqrt{1-2 x} (2+3 x)^4 (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^(3/2),x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{28} \left(\frac{70224051139 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}{102400000 \sqrt{10} \left(\sqrt{3}-\sqrt{5 x+3}\right)^{28}}+\frac{\left(-\frac{11241651139 \sqrt{1-2 x}}{204800000}-\frac{4224}{5} \sqrt{3} \sqrt{5 x+3}+\frac{530286771139}{204800000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{13}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{27}}+\frac{\left(-\frac{2395240268861 \sqrt{1-2 x}}{307200000}-\frac{4672}{5} \sqrt{3} \sqrt{5 x+3}+\frac{3256383308861}{307200000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{25}}+\frac{\left(-\frac{39147440307139 \sqrt{1-2 x}}{384000000}+\frac{11252224}{125} \sqrt{3} \sqrt{5 x+3}-\frac{64553056076861}{384000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{11}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{23}}+\frac{\left(-\frac{145657984844861 \sqrt{1-2 x}}{448000000}+\frac{556827808}{625} \sqrt{3} \sqrt{5 x+3}-\frac{1051744533478339}{448000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{21}}+\frac{\left(\frac{273864148522687 \sqrt{1-2 x}}{168000000}+\frac{11983210752 \sqrt{3} \sqrt{5 x+3}}{3125}-\frac{2206516378605247}{168000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{19}}+\frac{\left(\frac{287034691309411 \sqrt{1-2 x}}{16800000}+\frac{25793441856 \sqrt{3} \sqrt{5 x+3}}{3125}-\frac{703031321562979}{16800000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{17}}+\frac{\left(\frac{94146993008337 \sqrt{1-2 x}}{1400000}+\frac{104368146816 \sqrt{3} \sqrt{5 x+3}}{21875}-\frac{114185677197009}{1400000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{15}}+\frac{\left(\frac{79134060494949 \sqrt{1-2 x}}{500000}-\frac{69029035296 \sqrt{3} \sqrt{5 x+3}}{3125}-\frac{46000123552869}{500000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{13}}+\frac{\left(\frac{7770801866283 \sqrt{1-2 x}}{31250}-\frac{221637143808 \sqrt{3} \sqrt{5 x+3}}{3125}-\frac{1121687552043}{31250}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{11}}+\frac{\left(\frac{4246986515247 \sqrt{1-2 x}}{15625}-\frac{338594283648 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{831927739473}{15625}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}+\frac{\left(\frac{912245009148 \sqrt{1-2 x}}{4375}-\frac{314679769344 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{2047050110484}{21875}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}+\frac{\left(\frac{2392069293576 \sqrt{1-2 x}}{21875}-\frac{180922108032 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{1407294975096}{21875}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{\frac{120211972992 \sqrt{1-2 x}}{21875}-\frac{59296375296 \sqrt{3} \sqrt{5 x+3}}{21875}+\frac{57677152896}{21875}}{\sqrt{3}-\sqrt{5 x+3}}+\frac{\left(-\frac{5184 \sqrt{1-2 x}}{4375}-\frac{10368 \sqrt{3} \sqrt{5 x+3}}{21875}+\frac{57024}{21875}\right) \left(-150728747 \sqrt{1-2 x}+80068408 \sqrt{3} \sqrt{5 x+3}-89476477\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}","-\frac{3}{70} (1-2 x)^{3/2} (5 x+3)^{5/2} (3 x+2)^3-\frac{403 (1-2 x)^{3/2} (5 x+3)^{5/2} (3 x+2)^2}{2800}-\frac{52760369 (1-2 x)^{3/2} (5 x+3)^{3/2}}{7680000}-\frac{(1-2 x)^{3/2} (5 x+3)^{5/2} (874608 x+1480103)}{640000}-\frac{580364059 (1-2 x)^{3/2} \sqrt{5 x+3}}{20480000}+\frac{6384004649 \sqrt{1-2 x} \sqrt{5 x+3}}{204800000}+\frac{70224051139 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{204800000 \sqrt{10}}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^28*((57677152896/21875 + (120211972992*Sqrt[1 - 2*x])/21875 - (59296375296*Sqrt[3]*Sqrt[3 + 5*x])/21875)/(Sqrt[3] - Sqrt[3 + 5*x]) + ((1407294975096/21875 + (2392069293576*Sqrt[1 - 2*x])/21875 - (180922108032*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^5 + ((2047050110484/21875 + (912245009148*Sqrt[1 - 2*x])/4375 - (314679769344*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^7 + ((831927739473/15625 + (4246986515247*Sqrt[1 - 2*x])/15625 - (338594283648*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^9 + ((-1121687552043/31250 + (7770801866283*Sqrt[1 - 2*x])/31250 - (221637143808*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^11 + ((-46000123552869/500000 + (79134060494949*Sqrt[1 - 2*x])/500000 - (69029035296*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^13 + ((3256383308861/307200000 - (2395240268861*Sqrt[1 - 2*x])/307200000 - (4672*Sqrt[3]*Sqrt[3 + 5*x])/5)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12)/(Sqrt[3] - Sqrt[3 + 5*x])^25 + ((530286771139/204800000 - (11241651139*Sqrt[1 - 2*x])/204800000 - (4224*Sqrt[3]*Sqrt[3 + 5*x])/5)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^13)/(Sqrt[3] - Sqrt[3 + 5*x])^27 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^11*(-64553056076861/384000000 - (39147440307139*Sqrt[1 - 2*x])/384000000 + (11252224*Sqrt[3]*Sqrt[3 + 5*x])/125))/(Sqrt[3] - Sqrt[3 + 5*x])^23 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^10*(-1051744533478339/448000000 - (145657984844861*Sqrt[1 - 2*x])/448000000 + (556827808*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^21 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^9*(-2206516378605247/168000000 + (273864148522687*Sqrt[1 - 2*x])/168000000 + (11983210752*Sqrt[3]*Sqrt[3 + 5*x])/3125))/(Sqrt[3] - Sqrt[3 + 5*x])^19 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^7*(-114185677197009/1400000 + (94146993008337*Sqrt[1 - 2*x])/1400000 + (104368146816*Sqrt[3]*Sqrt[3 + 5*x])/21875))/(Sqrt[3] - Sqrt[3 + 5*x])^15 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^8*(-703031321562979/16800000 + (287034691309411*Sqrt[1 - 2*x])/16800000 + (25793441856*Sqrt[3]*Sqrt[3 + 5*x])/3125))/(Sqrt[3] - Sqrt[3 + 5*x])^17 + ((57024/21875 - (5184*Sqrt[1 - 2*x])/4375 - (10368*Sqrt[3]*Sqrt[3 + 5*x])/21875)*(-89476477 - 150728747*Sqrt[1 - 2*x] + 80068408*Sqrt[3]*Sqrt[3 + 5*x]))/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (70224051139*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(102400000*Sqrt[10]*(Sqrt[3] - Sqrt[3 + 5*x])^28)))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14","B",1
2275,1,1157,150,9.2249368,"\int \sqrt{1-2 x} (2+3 x)^3 (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^(3/2),x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{24} \left(\frac{1269748711 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}{5120000 \sqrt{10} \left(\sqrt{3}-\sqrt{5 x+3}\right)^{24}}+\frac{\left(\frac{204811289 \sqrt{1-2 x}}{10240000}-336 \sqrt{3} \sqrt{5 x+3}+\frac{10117108711}{10240000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{11}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{23}}+\frac{\left(-\frac{29843467289 \sqrt{1-2 x}}{15360000}-\frac{50416}{25} \sqrt{3} \sqrt{5 x+3}+\frac{122770238489}{15360000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{21}}+\frac{\left(-\frac{647264654311 \sqrt{1-2 x}}{19200000}+\frac{1037648}{125} \sqrt{3} \sqrt{5 x+3}+\frac{169116455911}{19200000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{19}}+\frac{\left(-\frac{617427004127 \sqrt{1-2 x}}{3200000}+\frac{97811792}{625} \sqrt{3} \sqrt{5 x+3}-\frac{884962120993}{3200000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{17}}+\frac{\left(-\frac{513504311051 \sqrt{1-2 x}}{1200000}+\frac{511956144}{625} \sqrt{3} \sqrt{5 x+3}-\frac{2435363078389}{1200000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{15}}+\frac{\left(\frac{23414061313 \sqrt{1-2 x}}{120000}+\frac{1476578064}{625} \sqrt{3} \sqrt{5 x+3}-\frac{873923026177}{120000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{13}}+\frac{\left(\frac{33034692411 \sqrt{1-2 x}}{10000}+\frac{541943424}{125} \sqrt{3} \sqrt{5 x+3}-\frac{163101114171}{10000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{11}}+\frac{\left(\frac{210707897121 \sqrt{1-2 x}}{25000}+\frac{3349706112}{625} \sqrt{3} \sqrt{5 x+3}-\frac{612672630561}{25000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}+\frac{\left(\frac{35525652894 \sqrt{1-2 x}}{3125}+\frac{569208384}{125} \sqrt{3} \sqrt{5 x+3}-\frac{78216281694}{3125}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}+\frac{\left(\frac{27876736332 \sqrt{1-2 x}}{3125}+\frac{1633732416}{625} \sqrt{3} \sqrt{5 x+3}-\frac{52382722572}{3125}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{\frac{435974112}{625} \sqrt{1-2 x}+\frac{96774912}{625} \sqrt{3} \sqrt{5 x+3}-\frac{726298848}{625}}{\sqrt{3}-\sqrt{5 x+3}}+\frac{\left(\frac{144}{125} \sqrt{1-2 x}+\frac{288}{625} \sqrt{3} \sqrt{5 x+3}-\frac{1584}{625}\right) \left(16651789 \sqrt{1-2 x}+4032288 \sqrt{3} \sqrt{5 x+3}-28748653\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}","-\frac{1}{20} (1-2 x)^{3/2} (3 x+2)^2 (5 x+3)^{5/2}-\frac{7 (1-2 x)^{3/2} (2256 x+3821) (5 x+3)^{5/2}}{32000}-\frac{953981 (1-2 x)^{3/2} (5 x+3)^{3/2}}{384000}-\frac{10493791 (1-2 x)^{3/2} \sqrt{5 x+3}}{1024000}+\frac{115431701 \sqrt{1-2 x} \sqrt{5 x+3}}{10240000}+\frac{1269748711 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{10240000 \sqrt{10}}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^24*(((122770238489/15360000 - (29843467289*Sqrt[1 - 2*x])/15360000 - (50416*Sqrt[3]*Sqrt[3 + 5*x])/25)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^10)/(Sqrt[3] - Sqrt[3 + 5*x])^21 + ((10117108711/10240000 + (204811289*Sqrt[1 - 2*x])/10240000 - 336*Sqrt[3]*Sqrt[3 + 5*x])*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^11)/(Sqrt[3] - Sqrt[3 + 5*x])^23 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^9*(169116455911/19200000 - (647264654311*Sqrt[1 - 2*x])/19200000 + (1037648*Sqrt[3]*Sqrt[3 + 5*x])/125))/(Sqrt[3] - Sqrt[3 + 5*x])^19 + (-726298848/625 + (435974112*Sqrt[1 - 2*x])/625 + (96774912*Sqrt[3]*Sqrt[3 + 5*x])/625)/(Sqrt[3] - Sqrt[3 + 5*x]) + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^8*(-884962120993/3200000 - (617427004127*Sqrt[1 - 2*x])/3200000 + (97811792*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^17 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^7*(-2435363078389/1200000 - (513504311051*Sqrt[1 - 2*x])/1200000 + (511956144*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^15 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^6*(-873923026177/120000 + (23414061313*Sqrt[1 - 2*x])/120000 + (1476578064*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^13 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2*(-52382722572/3125 + (27876736332*Sqrt[1 - 2*x])/3125 + (1633732416*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^5 + ((-1584/625 + (144*Sqrt[1 - 2*x])/125 + (288*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-28748653 + 16651789*Sqrt[1 - 2*x] + 4032288*Sqrt[3]*Sqrt[3 + 5*x]))/(Sqrt[3] - Sqrt[3 + 5*x])^3 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^5*(-163101114171/10000 + (33034692411*Sqrt[1 - 2*x])/10000 + (541943424*Sqrt[3]*Sqrt[3 + 5*x])/125))/(Sqrt[3] - Sqrt[3 + 5*x])^11 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^3*(-78216281694/3125 + (35525652894*Sqrt[1 - 2*x])/3125 + (569208384*Sqrt[3]*Sqrt[3 + 5*x])/125))/(Sqrt[3] - Sqrt[3 + 5*x])^7 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^4*(-612672630561/25000 + (210707897121*Sqrt[1 - 2*x])/25000 + (3349706112*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^9 + (1269748711*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(5120000*Sqrt[10]*(Sqrt[3] - Sqrt[3 + 5*x])^24)))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12","B",1
2276,1,426,143,2.4847757,"\int \sqrt{1-2 x} (2+3 x)^2 (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^(3/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(1529301600000000 x^9+173941396470000000 x^8+106225973528500000 x^7-3268975433078812500 x^6-7483499590885640625 x^5-4475215286839443625 x^4+2683830929872986900 x^3+4957581048612598420 x^2+392581058644255040 x-1666555890392275344\right)+\sqrt{5 x+3} \left(18934344000000000 x^9-676747694700000000 x^8-3272265642415000000 x^7-1472461185421875000 x^6+7171585337889843750 x^5+9540002858614958125 x^4+1874625743835911000 x^3-5355322475391043100 x^2-2056019950073600720 x+1666555890392275344\right)+\sqrt{3} \left(-5704560000000000 x^{10}+102618297000000000 x^9+2544665735450000000 x^8+5225453057066250000 x^7-2180481490911562500 x^6-13958102815316946875 x^5-11924893613558150625 x^4+1399435163845471500 x^3+7649209849787802500 x^2+\sqrt{1-2 x} \left(-43815816000000000 x^9-461691162900000000 x^8+1246821137793000000 x^7+7985689704510375000 x^6+11292722215560018750 x^5+3395647848752713125 x^4-6205140654166289000 x^3-5864765934083861420 x^2+996718929417016080 x+1666555890392275344\right)+666719962012329600 x-1666555890392275344\right)}{768000 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right)+\sqrt{1-2 x} \left(768000 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right)+768000 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right)\right)+768000 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right)}+\frac{11988317 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{128000 \sqrt{10}}","-\frac{153}{800} (1-2 x)^{3/2} (5 x+3)^{5/2}-\frac{3}{50} (1-2 x)^{3/2} (3 x+2) (5 x+3)^{5/2}-\frac{9007 (1-2 x)^{3/2} (5 x+3)^{3/2}}{9600}-\frac{99077 (1-2 x)^{3/2} \sqrt{5 x+3}}{25600}+\frac{1089847 \sqrt{1-2 x} \sqrt{5 x+3}}{256000}+\frac{11988317 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{256000 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-1666555890392275344 + 392581058644255040*x + 4957581048612598420*x^2 + 2683830929872986900*x^3 - 4475215286839443625*x^4 - 7483499590885640625*x^5 - 3268975433078812500*x^6 + 106225973528500000*x^7 + 173941396470000000*x^8 + 1529301600000000*x^9) + Sqrt[3 + 5*x]*(1666555890392275344 - 2056019950073600720*x - 5355322475391043100*x^2 + 1874625743835911000*x^3 + 9540002858614958125*x^4 + 7171585337889843750*x^5 - 1472461185421875000*x^6 - 3272265642415000000*x^7 - 676747694700000000*x^8 + 18934344000000000*x^9) + Sqrt[3]*(-1666555890392275344 + 666719962012329600*x + 7649209849787802500*x^2 + 1399435163845471500*x^3 - 11924893613558150625*x^4 - 13958102815316946875*x^5 - 2180481490911562500*x^6 + 5225453057066250000*x^7 + 2544665735450000000*x^8 + 102618297000000000*x^9 - 5704560000000000*x^10 + Sqrt[1 - 2*x]*(1666555890392275344 + 996718929417016080*x - 5864765934083861420*x^2 - 6205140654166289000*x^3 + 3395647848752713125*x^4 + 11292722215560018750*x^5 + 7985689704510375000*x^6 + 1246821137793000000*x^7 - 461691162900000000*x^8 - 43815816000000000*x^9)))/(768000*Sqrt[3]*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 768000*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(768000*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 768000*Sqrt[3]*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (11988317*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(128000*Sqrt[10])","B",1
2277,1,366,116,2.2355698,"\int \sqrt{1-2 x} (2+3 x) (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^(3/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-1231290000000 x^7+9382238500000 x^6+199212979687500 x^5+311633746666875 x^4-13205400469000 x^3-305385946008600 x^2-77064011228320 x+108700531119576\right)+\sqrt{5 x+3} \left(13962960000000 x^7+102427732000000 x^6-128038927500000 x^5-546362495085000 x^4-324511167392500 x^3+269545598752100 x^2+184287226017400 x-108700531119576\right)+\sqrt{3} \left(-856800000000 x^8-78123320000000 x^7-86309923000000 x^6+460085889150000 x^5+833694767451875 x^4+196303370173000 x^3-462561508191800 x^2+\sqrt{1-2 x} \left(6423120000000 x^7-102549700000000 x^6-418339597500000 x^5-360286531275000 x^4+209695052924500 x^3+408705599894900 x^2-13863341267160 x-108700531119576\right)-93359873521920 x+108700531119576\right)}{38400 \sqrt{3} \sqrt{5 x+3} \left(8921000 x^3-162998000 x^2-220512160 x+287530496\right)+\sqrt{1-2 x} \left(38400 \left(-48482500 x^3-297203500 x^2+794989800 x+852279560\right)+38400 \sqrt{3} \sqrt{5 x+3} \left(595000 x^3+53178000 x^2-36412000 x-283051520\right)\right)+38400 \left(-8550625 x^4+79738000 x^3+1253327000 x^2-32289760 x-865716488\right)}+\frac{240911 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{6400 \sqrt{10}}","-\frac{3}{40} (1-2 x)^{3/2} (5 x+3)^{5/2}-\frac{181}{480} (1-2 x)^{3/2} (5 x+3)^{3/2}-\frac{1991 (1-2 x)^{3/2} \sqrt{5 x+3}}{1280}+\frac{21901 \sqrt{1-2 x} \sqrt{5 x+3}}{12800}+\frac{240911 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{12800 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(108700531119576 - 77064011228320*x - 305385946008600*x^2 - 13205400469000*x^3 + 311633746666875*x^4 + 199212979687500*x^5 + 9382238500000*x^6 - 1231290000000*x^7) + Sqrt[3 + 5*x]*(-108700531119576 + 184287226017400*x + 269545598752100*x^2 - 324511167392500*x^3 - 546362495085000*x^4 - 128038927500000*x^5 + 102427732000000*x^6 + 13962960000000*x^7) + Sqrt[3]*(108700531119576 - 93359873521920*x - 462561508191800*x^2 + 196303370173000*x^3 + 833694767451875*x^4 + 460085889150000*x^5 - 86309923000000*x^6 - 78123320000000*x^7 - 856800000000*x^8 + Sqrt[1 - 2*x]*(-108700531119576 - 13863341267160*x + 408705599894900*x^2 + 209695052924500*x^3 - 360286531275000*x^4 - 418339597500000*x^5 - 102549700000000*x^6 + 6423120000000*x^7)))/(38400*Sqrt[3]*Sqrt[3 + 5*x]*(287530496 - 220512160*x - 162998000*x^2 + 8921000*x^3) + 38400*(-865716488 - 32289760*x + 1253327000*x^2 + 79738000*x^3 - 8550625*x^4) + Sqrt[1 - 2*x]*(38400*(852279560 + 794989800*x - 297203500*x^2 - 48482500*x^3) + 38400*Sqrt[3]*Sqrt[3 + 5*x]*(-283051520 - 36412000*x + 53178000*x^2 + 595000*x^3))) + (240911*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(6400*Sqrt[10])","B",1
2278,1,306,94,1.7895675,"\int \sqrt{1-2 x} (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(3 + 5*x)^(3/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(35900000 x^5+2414427500 x^4+1970091375 x^3-3774956525 x^2-2596145840 x+1466852508\right)+\sqrt{5 x+3} \left(627000000 x^5-4256725000 x^4-7944279750 x^3+1118781675 x^2+3918458060 x-1466852508\right)+\sqrt{3} \left(-234000000 x^6+535350000 x^5+10019842500 x^4+9044327625 x^3-5119890825 x^2+\sqrt{1-2 x} \left(-917400000 x^5-4532715000 x^4-243729750 x^3+6625732575 x^2+1325362500 x-1466852508\right)-2647674720 x+1466852508\right)}{480 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right)+\sqrt{1-2 x} \left(480 \left(-391875 x^2+2827000 x+3481060\right)+480 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right)\right)+480 \left(44875 x^3+2976525 x^2-279060 x-3667684\right)}+\frac{1331 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{80 \sqrt{10}}","-\frac{1}{6} (5 x+3)^{3/2} (1-2 x)^{3/2}-\frac{11}{16} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{121}{160} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{1331 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{160 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1466852508 - 2596145840*x - 3774956525*x^2 + 1970091375*x^3 + 2414427500*x^4 + 35900000*x^5) + Sqrt[3 + 5*x]*(-1466852508 + 3918458060*x + 1118781675*x^2 - 7944279750*x^3 - 4256725000*x^4 + 627000000*x^5) + Sqrt[3]*(1466852508 - 2647674720*x - 5119890825*x^2 + 9044327625*x^3 + 10019842500*x^4 + 535350000*x^5 - 234000000*x^6 + Sqrt[1 - 2*x]*(-1466852508 + 1325362500*x + 6625732575*x^2 - 243729750*x^3 - 4532715000*x^4 - 917400000*x^5)))/(480*Sqrt[3]*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 480*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(480*(3481060 + 2827000*x - 391875*x^2) + 480*Sqrt[3]*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (1331*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(80*Sqrt[10])","B",1
2279,1,444,106,1.8654981,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{2+3 x} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x),x]","-\frac{7}{27} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{5 \sqrt{1-2 x} \sqrt{5 x+3} \left(-35700 x^3+24815 x^2+196624 x-29282\right)+5 \sqrt{5 x+3} \left(171600 x^3+235180 x^2-194370 x+29282\right)+\sqrt{3} \left(5 \sqrt{1-2 x} \left(118800 x^3-244860 x^2-157014 x+29282\right)+5 \left(-12000 x^4-509000 x^3-1805 x^2+154760 x-29282\right)\right)}{72 \left(-2975 x^2+1820 x+16562\right)+72 \sqrt{3} \sqrt{5 x+3} (1980 x-5104)+\sqrt{1-2 x} \left(72 (-7150 x-13970)+72 \sqrt{3} \sqrt{5 x+3} (100 x+4240)\right)}+\frac{793 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{108 \sqrt{10}}","\frac{1}{6} \sqrt{1-2 x} (5 x+3)^{3/2}-\frac{41}{72} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{793 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{216 \sqrt{10}}-\frac{2}{27} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(5*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-29282 + 196624*x + 24815*x^2 - 35700*x^3) + 5*Sqrt[3 + 5*x]*(29282 - 194370*x + 235180*x^2 + 171600*x^3) + Sqrt[3]*(5*Sqrt[1 - 2*x]*(29282 - 157014*x - 244860*x^2 + 118800*x^3) + 5*(-29282 + 154760*x - 1805*x^2 - 509000*x^3 - 12000*x^4)))/(72*Sqrt[3]*Sqrt[3 + 5*x]*(-5104 + 1980*x) + 72*(16562 + 1820*x - 2975*x^2) + Sqrt[1 - 2*x]*(72*(-13970 - 7150*x) + 72*Sqrt[3]*Sqrt[3 + 5*x]*(4240 + 100*x))) + (793*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(108*Sqrt[10]) - (7*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ])/27","C",1
2280,1,529,115,2.0195779,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^2} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^2,x]","-\frac{107}{27} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{535}{54} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-429000 x^3-1134320 x^2+336336 x+644204\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(89250 x^3+950 x^2-963260 x-644204\right)+\sqrt{3} \left(30000 x^4+1395175 x^3+1058590 x^2+\sqrt{1-2 x} \left(-297000 x^3+605550 x^2+1508430 x+644204\right)-881506 x-644204\right)}{18 \left(2975 x^2-1820 x-16562\right) (3 x+2)+18 \sqrt{3} (5104-1980 x) \sqrt{5 x+3} (3 x+2)+\sqrt{1-2 x} \left(18 (7150 x+13970) (3 x+2)+18 \sqrt{3} (-100 x-4240) \sqrt{5 x+3} (3 x+2)\right)}+\frac{41}{27} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{\sqrt{1-2 x} (5 x+3)^{3/2}}{3 (3 x+2)}+\frac{10}{9} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{41}{27} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)+\frac{107 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{27 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(644204 + 336336*x - 1134320*x^2 - 429000*x^3) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-644204 - 963260*x + 950*x^2 + 89250*x^3) + Sqrt[3]*(-644204 - 881506*x + 1058590*x^2 + 1395175*x^3 + 30000*x^4 + Sqrt[1 - 2*x]*(644204 + 1508430*x + 605550*x^2 - 297000*x^3)))/(18*Sqrt[3]*(5104 - 1980*x)*(2 + 3*x)*Sqrt[3 + 5*x] + 18*(2 + 3*x)*(-16562 - 1820*x + 2975*x^2) + Sqrt[1 - 2*x]*(18*Sqrt[3]*(-4240 - 100*x)*(2 + 3*x)*Sqrt[3 + 5*x] + 18*(2 + 3*x)*(13970 + 7150*x))) + (41*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/27 - (107*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/27 + (535*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/54","C",1
2281,1,537,120,2.1191266,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^3} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^3,x]","\frac{4091}{756} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{20455 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{1512}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-1350225 x^3+9991720 x^2+22489622 x+9955880\right)+\sqrt{5 x+3} \left(12137400 x^3+10246610 x^2-13948110 x-9955880\right)+\sqrt{3} \left(-2806875 x^4-24549700 x^3-3027310 x^2+\sqrt{1-2 x} \left(-212850 x^3-25011030 x^2-31468272 x-9955880\right)+22926760 x+9955880\right)}{252 \left(2975 x^2-1820 x-16562\right) (3 x+2)^2+252 \sqrt{3} (5104-1980 x) \sqrt{5 x+3} (3 x+2)^2+\sqrt{1-2 x} \left(252 (7150 x+13970) (3 x+2)^2+252 \sqrt{3} (-100 x-4240) \sqrt{5 x+3} (3 x+2)^2\right)}-\frac{20}{27} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{\sqrt{1-2 x} (5 x+3)^{3/2}}{6 (3 x+2)^2}-\frac{107 \sqrt{1-2 x} \sqrt{5 x+3}}{252 (3 x+2)}-\frac{10}{27} \sqrt{10} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{4091 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{756 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(9955880 + 22489622*x + 9991720*x^2 - 1350225*x^3) + Sqrt[3 + 5*x]*(-9955880 - 13948110*x + 10246610*x^2 + 12137400*x^3) + Sqrt[3]*(9955880 + 22926760*x - 3027310*x^2 - 24549700*x^3 - 2806875*x^4 + Sqrt[1 - 2*x]*(-9955880 - 31468272*x - 25011030*x^2 - 212850*x^3)))/(252*Sqrt[3]*(5104 - 1980*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 252*(2 + 3*x)^2*(-16562 - 1820*x + 2975*x^2) + Sqrt[1 - 2*x]*(252*Sqrt[3]*(-4240 - 100*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 252*(2 + 3*x)^2*(13970 + 7150*x))) - (20*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/27 + (4091*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/756 - (20455*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/1512","C",1
2282,1,539,122,2.1390383,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^4} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^4,x]","\frac{1331}{392} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{6655}{784} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(530679125 x^5+12322917725 x^4-2894843910 x^3-41297926772 x^2-34802067512 x-8163353088\right)+\sqrt{5 x+3} \left(634637850 x^5-36510185305 x^4-51458677578 x^3+4276130364 x^2+26806302776 x+8163353088\right)+\sqrt{3} \left(-1060753500 x^6+14580426450 x^5+75066052170 x^4+55573802808 x^3-23833176744 x^2+\sqrt{1-2 x} \left(-6366335250 x^5-16638538950 x^4+26992054320 x^3+67574235432 x^2+41660986752 x+8163353088\right)-33665222016 x-8163353088\right)}{1176 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right) (3 x+2)^3+\sqrt{1-2 x} \left(1176 \left(-391875 x^2+2827000 x+3481060\right) (3 x+2)^3+1176 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right) (3 x+2)^3\right)+1176 \left(44875 x^3+2976525 x^2-279060 x-3667684\right) (3 x+2)^3}","\frac{\sqrt{1-2 x} (5 x+3)^{5/2}}{3 (3 x+2)^3}-\frac{11 \sqrt{1-2 x} (5 x+3)^{3/2}}{84 (3 x+2)^2}-\frac{121 \sqrt{1-2 x} \sqrt{5 x+3}}{392 (3 x+2)}-\frac{1331 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{392 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-8163353088 - 34802067512*x - 41297926772*x^2 - 2894843910*x^3 + 12322917725*x^4 + 530679125*x^5) + Sqrt[3 + 5*x]*(8163353088 + 26806302776*x + 4276130364*x^2 - 51458677578*x^3 - 36510185305*x^4 + 634637850*x^5) + Sqrt[3]*(-8163353088 - 33665222016*x - 23833176744*x^2 + 55573802808*x^3 + 75066052170*x^4 + 14580426450*x^5 - 1060753500*x^6 + Sqrt[1 - 2*x]*(8163353088 + 41660986752*x + 67574235432*x^2 + 26992054320*x^3 - 16638538950*x^4 - 6366335250*x^5)))/(1176*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 1176*(2 + 3*x)^3*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(1176*(2 + 3*x)^3*(3481060 + 2827000*x - 391875*x^2) + 1176*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (1331*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/392 - (6655*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/784","C",1
2283,1,599,151,2.5735577,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^5} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^5,x]","\frac{153065 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{21952}-\frac{765325 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{43904}+\frac{\sqrt{5 x+3} \left(-151565278062000 x^7-128362227933500 x^6+3847944634774020 x^5+8044095358093608 x^4+3860581712759288 x^3-2299434996059872 x^2-2472620820852512 x-563273403910272\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(6472858869375 x^7-341834209961000 x^6-2085545937484500 x^5-1740743586378960 x^4+3042617825276120 x^3+5529924360780480 x^2+3028994684721056 x+563273403910272\right)+\sqrt{3} \left(20788001480625 x^8+506639323678000 x^7-1527966634585000 x^6-9084959019335760 x^5-11486859558206248 x^4-2649965215728128 x^3+4160812637079232 x^2+\sqrt{1-2 x} \left(31369134967500 x^7+1478278315596500 x^6+3689437508281800 x^5+402892501206360 x^4-6750971675592320 x^3-7856551500856960 x^2-3499993800479616 x-563273403910272\right)+2943619936611072 x+563273403910272\right)}{65856 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^4+\sqrt{1-2 x} \left(65856 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^4+65856 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^4\right)+65856 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^4}","\frac{115 \sqrt{1-2 x} (5 x+3)^{5/2}}{168 (3 x+2)^3}+\frac{3 (1-2 x)^{3/2} (5 x+3)^{5/2}}{28 (3 x+2)^4}-\frac{1265 \sqrt{1-2 x} (5 x+3)^{3/2}}{4704 (3 x+2)^2}-\frac{13915 \sqrt{1-2 x} \sqrt{5 x+3}}{21952 (3 x+2)}-\frac{153065 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{21952 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-563273403910272 - 2472620820852512*x - 2299434996059872*x^2 + 3860581712759288*x^3 + 8044095358093608*x^4 + 3847944634774020*x^5 - 128362227933500*x^6 - 151565278062000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(563273403910272 + 3028994684721056*x + 5529924360780480*x^2 + 3042617825276120*x^3 - 1740743586378960*x^4 - 2085545937484500*x^5 - 341834209961000*x^6 + 6472858869375*x^7) + Sqrt[3]*(563273403910272 + 2943619936611072*x + 4160812637079232*x^2 - 2649965215728128*x^3 - 11486859558206248*x^4 - 9084959019335760*x^5 - 1527966634585000*x^6 + 506639323678000*x^7 + 20788001480625*x^8 + Sqrt[1 - 2*x]*(-563273403910272 - 3499993800479616*x - 7856551500856960*x^2 - 6750971675592320*x^3 + 402892501206360*x^4 + 3689437508281800*x^5 + 1478278315596500*x^6 + 31369134967500*x^7)))/(65856*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 65856*(2 + 3*x)^4*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(65856*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 65856*(2 + 3*x)^4*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) + (153065*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/21952 - (765325*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/43904","C",1
2284,1,659,180,3.0677164,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^6} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^6,x]","\frac{783959 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{43904}-\frac{3919795 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{87808}+\frac{\sqrt{5 x+3} \left(-277334440591725000 x^9-13578612778851388125 x^8-29013393329422704950 x^7+66797970657074405760 x^6+235929896462105050128 x^5+215829648983108927360 x^4+24687122419641383680 x^3-72277580858185785280 x^2-42148581828443643520 x-7265719198860553728\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(51359860561640625 x^9+1537148336101546875 x^8-13269614126839581250 x^7-81146831832780831000 x^6-119543589200893843200 x^5-10430695666762052960 x^4+125662901512032470400 x^3+124871267274579067712 x^2+49384918799983692928 x+7265719198860553728\right)+\sqrt{3} \left(-39377360837446875 x^{10}+4590348007813359375 x^9+36107883992338337500 x^8+11519846084328477000 x^7-206062171463619322200 x^6-396449257775730306928 x^5-251376936477216149760 x^4+22985192475672054720 x^3+104864028714576129280 x^2+\sqrt{1-2 x} \left(-710485409803640625 x^9+535711368486937500 x^8+53868107548599300000 x^7+164461477909579125000 x^6+148004420481556782000 x^5-63109463466905264640 x^4-214643238339916682560 x^3-163492741334336119552 x^2-55444430192784154368 x-7265719198860553728\right)+48208093221244104960 x+7265719198860553728\right)}{658560 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right) (3 x+2)^5+\sqrt{1-2 x} \left(658560 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right) (3 x+2)^5+658560 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right) (3 x+2)^5\right)+658560 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right) (3 x+2)^5}","-\frac{\sqrt{1-2 x} (5 x+3)^{3/2}}{15 (3 x+2)^5}+\frac{1852307 \sqrt{1-2 x} \sqrt{5 x+3}}{1185408 (3 x+2)}+\frac{17981 \sqrt{1-2 x} \sqrt{5 x+3}}{84672 (3 x+2)^2}+\frac{641 \sqrt{1-2 x} \sqrt{5 x+3}}{15120 (3 x+2)^3}-\frac{107 \sqrt{1-2 x} \sqrt{5 x+3}}{2520 (3 x+2)^4}-\frac{783959 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{43904 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-7265719198860553728 - 42148581828443643520*x - 72277580858185785280*x^2 + 24687122419641383680*x^3 + 215829648983108927360*x^4 + 235929896462105050128*x^5 + 66797970657074405760*x^6 - 29013393329422704950*x^7 - 13578612778851388125*x^8 - 277334440591725000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(7265719198860553728 + 49384918799983692928*x + 124871267274579067712*x^2 + 125662901512032470400*x^3 - 10430695666762052960*x^4 - 119543589200893843200*x^5 - 81146831832780831000*x^6 - 13269614126839581250*x^7 + 1537148336101546875*x^8 + 51359860561640625*x^9) + Sqrt[3]*(7265719198860553728 + 48208093221244104960*x + 104864028714576129280*x^2 + 22985192475672054720*x^3 - 251376936477216149760*x^4 - 396449257775730306928*x^5 - 206062171463619322200*x^6 + 11519846084328477000*x^7 + 36107883992338337500*x^8 + 4590348007813359375*x^9 - 39377360837446875*x^10 + Sqrt[1 - 2*x]*(-7265719198860553728 - 55444430192784154368*x - 163492741334336119552*x^2 - 214643238339916682560*x^3 - 63109463466905264640*x^4 + 148004420481556782000*x^5 + 164461477909579125000*x^6 + 53868107548599300000*x^7 + 535711368486937500*x^8 - 710485409803640625*x^9)))/(658560*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 658560*(2 + 3*x)^5*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(658560*(2 + 3*x)^5*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 658560*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (783959*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/43904 - (3919795*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/87808","C",1
2285,1,719,209,3.910486,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^7} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^7,x]","\frac{64645339 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{1229312}-\frac{323226695 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2458624}+\frac{\sqrt{5 x+3} \left(-12248598909286666575000 x^{11}+63251550475093035618750 x^{10}+2162850999443893421016750 x^9+6233241892625621506954200 x^8+1130251199864953700300800 x^7-16890102588440034574207488 x^6-25631130718854238293663552 x^5-12803752086721065034794240 x^4+2411173355529536614748160 x^3+5296979575860053374824960 x^2+2125594860326749697566208 x+291886454613260045924352\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(226461333918978421875 x^{11}-52557239596469773500000 x^{10}-496613035791134609681250 x^9+502998548654770159487000 x^8+7667984777102534649622400 x^7+16038900228465192731634240 x^6+11347856059847676200581120 x^5-3811872514210774912248320 x^4-11567621963655474869167872 x^3-7853767932196754633010176 x^2-2417123001410133381455360 x-291886454613260045924352\right)+\sqrt{3} \left(1323758736424850765625 x^{12}+45768472496143226887500 x^{11}-846327226291926824643750 x^{10}-5941090213666497510381000 x^9-9003674373876498093223800 x^8+7376864262903469047515040 x^7+34087802816665077110552448 x^6+36143648208607128213130752 x^5+12105250645701964132861440 x^4-6171500049009092207439360 x^3-6966812637831421162406400 x^2-2368873759751341402503168 x+\sqrt{1-2 x} \left(5225016411521363531250 x^{11}+294388893984878256093750 x^{10}+724379276448401871330000 x^9-3971963384828532326211000 x^8-17609258337236512696173600 x^7-25120908531305218785003840 x^6-10540579278328801393105920 x^5+11336981880465452882119680 x^4+17357294327738433008996352 x^3+9766581298984483823832576 x^2+2660401900834725086392320 x+291886454613260045924352\right)-291886454613260045924352\right)}{18439680 \sqrt{3} \sqrt{5 x+3} \left(-25265212500 x^5+1941218400000 x^4+5284290066000 x^3-24057375117600 x^2-13825440024000 x+16748592098304\right) (3 x+2)^6+\sqrt{1-2 x} \left(18439680 \sqrt{3} \sqrt{5 x+3} \left(-2625187500 x^5-345183000000 x^4+1378186950000 x^3+13912170444000 x^2-2687092123200 x-16725373086720\right) (3 x+2)^6+18439680 \left(236425406250 x^5+2220611593750 x^4-28520358020000 x^3-52011357156000 x^2+49788771586400 x+50183931760160\right) (3 x+2)^6\right)+18439680 \left(23653109375 x^6-916525237500 x^5-21026153381250 x^4+17065853944000 x^3+123670456765200 x^2-301410173760 x-50253588794912\right) (3 x+2)^6}","-\frac{\sqrt{1-2 x} (5 x+3)^{3/2}}{18 (3 x+2)^6}+\frac{152571047 \sqrt{1-2 x} \sqrt{5 x+3}}{33191424 (3 x+2)}+\frac{1460201 \sqrt{1-2 x} \sqrt{5 x+3}}{2370816 (3 x+2)^2}+\frac{42461 \sqrt{1-2 x} \sqrt{5 x+3}}{423360 (3 x+2)^3}+\frac{4619 \sqrt{1-2 x} \sqrt{5 x+3}}{211680 (3 x+2)^4}-\frac{107 \sqrt{1-2 x} \sqrt{5 x+3}}{3780 (3 x+2)^5}-\frac{64645339 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1229312 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(291886454613260045924352 + 2125594860326749697566208*x + 5296979575860053374824960*x^2 + 2411173355529536614748160*x^3 - 12803752086721065034794240*x^4 - 25631130718854238293663552*x^5 - 16890102588440034574207488*x^6 + 1130251199864953700300800*x^7 + 6233241892625621506954200*x^8 + 2162850999443893421016750*x^9 + 63251550475093035618750*x^10 - 12248598909286666575000*x^11) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-291886454613260045924352 - 2417123001410133381455360*x - 7853767932196754633010176*x^2 - 11567621963655474869167872*x^3 - 3811872514210774912248320*x^4 + 11347856059847676200581120*x^5 + 16038900228465192731634240*x^6 + 7667984777102534649622400*x^7 + 502998548654770159487000*x^8 - 496613035791134609681250*x^9 - 52557239596469773500000*x^10 + 226461333918978421875*x^11) + Sqrt[3]*(-291886454613260045924352 - 2368873759751341402503168*x - 6966812637831421162406400*x^2 - 6171500049009092207439360*x^3 + 12105250645701964132861440*x^4 + 36143648208607128213130752*x^5 + 34087802816665077110552448*x^6 + 7376864262903469047515040*x^7 - 9003674373876498093223800*x^8 - 5941090213666497510381000*x^9 - 846327226291926824643750*x^10 + 45768472496143226887500*x^11 + 1323758736424850765625*x^12 + Sqrt[1 - 2*x]*(291886454613260045924352 + 2660401900834725086392320*x + 9766581298984483823832576*x^2 + 17357294327738433008996352*x^3 + 11336981880465452882119680*x^4 - 10540579278328801393105920*x^5 - 25120908531305218785003840*x^6 - 17609258337236512696173600*x^7 - 3971963384828532326211000*x^8 + 724379276448401871330000*x^9 + 294388893984878256093750*x^10 + 5225016411521363531250*x^11)))/(18439680*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(16748592098304 - 13825440024000*x - 24057375117600*x^2 + 5284290066000*x^3 + 1941218400000*x^4 - 25265212500*x^5) + 18439680*(2 + 3*x)^6*(-50253588794912 - 301410173760*x + 123670456765200*x^2 + 17065853944000*x^3 - 21026153381250*x^4 - 916525237500*x^5 + 23653109375*x^6) + Sqrt[1 - 2*x]*(18439680*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(-16725373086720 - 2687092123200*x + 13912170444000*x^2 + 1378186950000*x^3 - 345183000000*x^4 - 2625187500*x^5) + 18439680*(2 + 3*x)^6*(50183931760160 + 49788771586400*x - 52011357156000*x^2 - 28520358020000*x^3 + 2220611593750*x^4 + 236425406250*x^5))) + (64645339*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/1229312 - (323226695*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2458624","C",1
2286,1,1503,201,21.2389916,"\int \sqrt{1-2 x} (2+3 x)^4 (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^(5/2),x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{32} \left(\frac{1988505613369 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{16}}{655360000 \sqrt{10} \left(\sqrt{3}-\sqrt{5 x+3}\right)^{32}}+\frac{\left(-\frac{856043533369 \sqrt{1-2 x}}{1310720000}-\frac{15552}{5} \sqrt{3} \sqrt{5 x+3}+\frac{13086633997369}{1310720000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{15}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{31}}+\frac{\left(-\frac{78189809650631 \sqrt{1-2 x}}{1966080000}+\frac{96384}{5} \sqrt{3} \sqrt{5 x+3}-\frac{35509383181369}{1966080000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{29}}+\frac{\left(-\frac{872104420160569 \sqrt{1-2 x}}{2457600000}+\frac{82524032}{125} \sqrt{3} \sqrt{5 x+3}-\frac{3995361044876231}{2457600000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{13}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{27}}+\frac{\left(\frac{3318991748314169 \sqrt{1-2 x}}{2867200000}+\frac{2994736544}{625} \sqrt{3} \sqrt{5 x+3}-\frac{44534233119306809}{2867200000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{25}}+\frac{\left(\frac{33725489555096557 \sqrt{1-2 x}}{1075200000}+\frac{32872960576 \sqrt{3} \sqrt{5 x+3}}{3125}-\frac{67656696477959149}{1075200000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{11}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{23}}+\frac{\left(\frac{104669788845888893 \sqrt{1-2 x}}{537600000}-\frac{136832695168 \sqrt{3} \sqrt{5 x+3}}{3125}-\frac{6810196440092953}{107520000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{21}}+\frac{\left(\frac{5640800025557443 \sqrt{1-2 x}}{8960000}-\frac{342233809664}{875} \sqrt{3} \sqrt{5 x+3}+\frac{4872622607320637}{8960000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{19}}+\frac{\left(\frac{3609292572945599 \sqrt{1-2 x}}{3200000}-\frac{883771209376}{625} \sqrt{3} \sqrt{5 x+3}+\frac{9965433203069761}{3200000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{17}}+\frac{\left(\frac{145569261553713 \sqrt{1-2 x}}{200000}-\frac{2012691475776}{625} \sqrt{3} \sqrt{5 x+3}+\frac{1786614555191247}{200000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{15}}+\frac{\left(-\frac{158578033641603 \sqrt{1-2 x}}{100000}-\frac{15999882278592 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{338913346477287}{20000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{13}}+\frac{\left(-\frac{892935892646523 \sqrt{1-2 x}}{175000}-\frac{18453908865024 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{798638516394111}{35000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{11}}+\frac{\left(-\frac{126012222262701 \sqrt{1-2 x}}{17500}-\frac{3121406520192}{625} \sqrt{3} \sqrt{5 x+3}+\frac{388210369958829}{17500}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}+\frac{\left(-\frac{26929361840706 \sqrt{1-2 x}}{4375}-\frac{1912944847104}{625} \sqrt{3} \sqrt{5 x+3}+\frac{13420240725978}{875}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}+\frac{\left(-\frac{14302389370788 \sqrt{1-2 x}}{4375}-\frac{5693954717952 \sqrt{3} \sqrt{5 x+3}}{4375}+\frac{31384253524644}{4375}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{-\frac{414669821472 \sqrt{1-2 x}}{3125}-\frac{135036066816 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{163955604384}{625}}{\sqrt{3}-\sqrt{5 x+3}}+\frac{\left(-\frac{1296}{625} \sqrt{1-2 x}-\frac{2592 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{14256}{3125}\right) \left(2399709615 \sqrt{1-2 x}+833555968 \sqrt{3} \sqrt{5 x+3}-4900377519\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{16}}","-\frac{3}{80} (1-2 x)^{3/2} (3 x+2)^3 (5 x+3)^{7/2}-\frac{1419 (1-2 x)^{3/2} (3 x+2)^2 (5 x+3)^{7/2}}{11200}-\frac{3 (1-2 x)^{3/2} (522420 x+899099) (5 x+3)^{7/2}}{1280000}-\frac{135817609 (1-2 x)^{3/2} (5 x+3)^{5/2}}{20480000}-\frac{1493993699 (1-2 x)^{3/2} (5 x+3)^{3/2}}{49152000}-\frac{16433930689 (1-2 x)^{3/2} \sqrt{5 x+3}}{131072000}+\frac{180773237579 \sqrt{1-2 x} \sqrt{5 x+3}}{1310720000}+\frac{1988505613369 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{1310720000 \sqrt{10}}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^32*((163955604384/625 - (414669821472*Sqrt[1 - 2*x])/3125 - (135036066816*Sqrt[3]*Sqrt[3 + 5*x])/3125)/(Sqrt[3] - Sqrt[3 + 5*x]) + ((31384253524644/4375 - (14302389370788*Sqrt[1 - 2*x])/4375 - (5693954717952*Sqrt[3]*Sqrt[3 + 5*x])/4375)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^5 + ((13420240725978/875 - (26929361840706*Sqrt[1 - 2*x])/4375 - (1912944847104*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^7 + ((388210369958829/17500 - (126012222262701*Sqrt[1 - 2*x])/17500 - (3121406520192*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^9 + ((798638516394111/35000 - (892935892646523*Sqrt[1 - 2*x])/175000 - (18453908865024*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^11 + ((338913346477287/20000 - (158578033641603*Sqrt[1 - 2*x])/100000 - (15999882278592*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^13 + ((1786614555191247/200000 + (145569261553713*Sqrt[1 - 2*x])/200000 - (2012691475776*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^7)/(Sqrt[3] - Sqrt[3 + 5*x])^15 + ((9965433203069761/3200000 + (3609292572945599*Sqrt[1 - 2*x])/3200000 - (883771209376*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^8)/(Sqrt[3] - Sqrt[3 + 5*x])^17 + ((4872622607320637/8960000 + (5640800025557443*Sqrt[1 - 2*x])/8960000 - (342233809664*Sqrt[3]*Sqrt[3 + 5*x])/875)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^9)/(Sqrt[3] - Sqrt[3 + 5*x])^19 + ((-6810196440092953/107520000 + (104669788845888893*Sqrt[1 - 2*x])/537600000 - (136832695168*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^10)/(Sqrt[3] - Sqrt[3 + 5*x])^21 + ((13086633997369/1310720000 - (856043533369*Sqrt[1 - 2*x])/1310720000 - (15552*Sqrt[3]*Sqrt[3 + 5*x])/5)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^15)/(Sqrt[3] - Sqrt[3 + 5*x])^31 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14*(-35509383181369/1966080000 - (78189809650631*Sqrt[1 - 2*x])/1966080000 + (96384*Sqrt[3]*Sqrt[3 + 5*x])/5))/(Sqrt[3] - Sqrt[3 + 5*x])^29 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^13*(-3995361044876231/2457600000 - (872104420160569*Sqrt[1 - 2*x])/2457600000 + (82524032*Sqrt[3]*Sqrt[3 + 5*x])/125))/(Sqrt[3] - Sqrt[3 + 5*x])^27 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12*(-44534233119306809/2867200000 + (3318991748314169*Sqrt[1 - 2*x])/2867200000 + (2994736544*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^25 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^11*(-67656696477959149/1075200000 + (33725489555096557*Sqrt[1 - 2*x])/1075200000 + (32872960576*Sqrt[3]*Sqrt[3 + 5*x])/3125))/(Sqrt[3] - Sqrt[3 + 5*x])^23 + ((14256/3125 - (1296*Sqrt[1 - 2*x])/625 - (2592*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-4900377519 + 2399709615*Sqrt[1 - 2*x] + 833555968*Sqrt[3]*Sqrt[3 + 5*x]))/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (1988505613369*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^16*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(655360000*Sqrt[10]*(Sqrt[3] - Sqrt[3 + 5*x])^32)))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^16","B",1
2287,1,1329,172,13.9050789,"\int \sqrt{1-2 x} (2+3 x)^3 (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^(5/2),x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{28} \left(\frac{4343003753 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}{4096000 \sqrt{10} \left(\sqrt{3}-\sqrt{5 x+3}\right)^{28}}+\frac{\left(-\frac{804059753 \sqrt{1-2 x}}{8192000}-1296 \sqrt{3} \sqrt{5 x+3}+\frac{32654555753}{8192000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{13}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{27}}+\frac{\left(-\frac{151724426647 \sqrt{1-2 x}}{12288000}-\frac{22128}{25} \sqrt{3} \sqrt{5 x+3}+\frac{184353490327}{12288000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{25}}+\frac{\left(-\frac{2437225445993 \sqrt{1-2 x}}{15360000}+\frac{18407824}{125} \sqrt{3} \sqrt{5 x+3}-\frac{4348634793367}{15360000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{11}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{23}}+\frac{\left(-\frac{8558001915287 \sqrt{1-2 x}}{17920000}+\frac{895442416}{625} \sqrt{3} \sqrt{5 x+3}-\frac{68464372939369}{17920000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{21}}+\frac{\left(\frac{19216151282141 \sqrt{1-2 x}}{6720000}+\frac{3823751536}{625} \sqrt{3} \sqrt{5 x+3}-\frac{142555080827357}{6720000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{19}}+\frac{\left(\frac{95459699197549 \sqrt{1-2 x}}{3360000}+\frac{8105621264}{625} \sqrt{3} \sqrt{5 x+3}-\frac{226187158943341}{3360000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{17}}+\frac{\left(\frac{31074007206943 \sqrt{1-2 x}}{280000}+\frac{28466708992 \sqrt{3} \sqrt{5 x+3}}{4375}-\frac{36539615333407}{280000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{15}}+\frac{\left(\frac{5219415260431 \sqrt{1-2 x}}{20000}-\frac{24126247136}{625} \sqrt{3} \sqrt{5 x+3}-\frac{23226364283}{160}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{13}}+\frac{\left(\frac{513316704033 \sqrt{1-2 x}}{1250}-\frac{74827728576}{625} \sqrt{3} \sqrt{5 x+3}-\frac{64350332577}{1250}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{11}}+\frac{\left(\frac{281273985261}{625} \sqrt{1-2 x}-\frac{113409338688}{625} \sqrt{3} \sqrt{5 x+3}+\frac{58954030803}{625}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}+\frac{\left(\frac{1514813347476 \sqrt{1-2 x}}{4375}-\frac{105086806272}{625} \sqrt{3} \sqrt{5 x+3}+\frac{692009584236}{4375}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}+\frac{\left(\frac{796339158264 \sqrt{1-2 x}}{4375}-\frac{60339627648}{625} \sqrt{3} \sqrt{5 x+3}+\frac{470793022344}{4375}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{\frac{40070657664 \sqrt{1-2 x}}{4375}-\frac{19765458432 \sqrt{3} \sqrt{5 x+3}}{4375}+\frac{19225717632}{4375}}{\sqrt{3}-\sqrt{5 x+3}}+\frac{\left(-\frac{1728}{875} \sqrt{1-2 x}-\frac{3456 \sqrt{3} \sqrt{5 x+3}}{4375}+\frac{19008}{4375}\right) \left(-150728747 \sqrt{1-2 x}+80068408 \sqrt{3} \sqrt{5 x+3}-89476477\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}","-\frac{3}{70} (1-2 x)^{3/2} (3 x+2)^2 (5 x+3)^{7/2}-\frac{3 (1-2 x)^{3/2} (1140 x+1963) (5 x+3)^{7/2}}{8000}-\frac{296633 (1-2 x)^{3/2} (5 x+3)^{5/2}}{128000}-\frac{3262963 (1-2 x)^{3/2} (5 x+3)^{3/2}}{307200}-\frac{35892593 (1-2 x)^{3/2} \sqrt{5 x+3}}{819200}+\frac{394818523 \sqrt{1-2 x} \sqrt{5 x+3}}{8192000}+\frac{4343003753 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{8192000 \sqrt{10}}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^28*((19225717632/4375 + (40070657664*Sqrt[1 - 2*x])/4375 - (19765458432*Sqrt[3]*Sqrt[3 + 5*x])/4375)/(Sqrt[3] - Sqrt[3 + 5*x]) + ((470793022344/4375 + (796339158264*Sqrt[1 - 2*x])/4375 - (60339627648*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^5 + ((692009584236/4375 + (1514813347476*Sqrt[1 - 2*x])/4375 - (105086806272*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^7 + ((58954030803/625 + (281273985261*Sqrt[1 - 2*x])/625 - (113409338688*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^9 + ((-64350332577/1250 + (513316704033*Sqrt[1 - 2*x])/1250 - (74827728576*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^11 + ((-23226364283/160 + (5219415260431*Sqrt[1 - 2*x])/20000 - (24126247136*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^13 + ((184353490327/12288000 - (151724426647*Sqrt[1 - 2*x])/12288000 - (22128*Sqrt[3]*Sqrt[3 + 5*x])/25)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12)/(Sqrt[3] - Sqrt[3 + 5*x])^25 + ((32654555753/8192000 - (804059753*Sqrt[1 - 2*x])/8192000 - 1296*Sqrt[3]*Sqrt[3 + 5*x])*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^13)/(Sqrt[3] - Sqrt[3 + 5*x])^27 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^11*(-4348634793367/15360000 - (2437225445993*Sqrt[1 - 2*x])/15360000 + (18407824*Sqrt[3]*Sqrt[3 + 5*x])/125))/(Sqrt[3] - Sqrt[3 + 5*x])^23 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^10*(-68464372939369/17920000 - (8558001915287*Sqrt[1 - 2*x])/17920000 + (895442416*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^21 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^9*(-142555080827357/6720000 + (19216151282141*Sqrt[1 - 2*x])/6720000 + (3823751536*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^19 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^7*(-36539615333407/280000 + (31074007206943*Sqrt[1 - 2*x])/280000 + (28466708992*Sqrt[3]*Sqrt[3 + 5*x])/4375))/(Sqrt[3] - Sqrt[3 + 5*x])^15 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^8*(-226187158943341/3360000 + (95459699197549*Sqrt[1 - 2*x])/3360000 + (8105621264*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^17 + ((19008/4375 - (1728*Sqrt[1 - 2*x])/875 - (3456*Sqrt[3]*Sqrt[3 + 5*x])/4375)*(-89476477 - 150728747*Sqrt[1 - 2*x] + 80068408*Sqrt[3]*Sqrt[3 + 5*x]))/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (4343003753*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(4096000*Sqrt[10]*(Sqrt[3] - Sqrt[3 + 5*x])^28)))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14","B",1
2288,1,486,165,2.9521127,"\int \sqrt{1-2 x} (2+3 x)^2 (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^(5/2),x]","\frac{15651229 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{40960 \sqrt{10}}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-217987056000000000 x^{11}+7781836068000000000 x^{10}+218761558265310000000 x^9+463492954922036500000 x^8-912816683904895662500 x^7-3687449430240944360625 x^6-3882538870129603165000 x^5-752249794910808602050 x^4+1783181565722403792720 x^3+1825862540643315972272 x^2-49471139162674901632 x-604905104236359963168\right)+\sqrt{5 x+3} \left(4357793088000000000 x^{11}+52042685270400000000 x^{10}-412409609389800000000 x^9-2215502686933866000000 x^8-2604783917574528250000 x^7+1262966594242966222500 x^6+4671399077133650804250 x^5+3145906320921415080150 x^4-262517692210684170480 x^3-2175279050538559394880 x^2-555362793311883861920 x+604905104236359963168\right)+\sqrt{3} \left(-241937280000000000 x^{12}-32574167712000000000 x^{11}+25941130729200000000 x^{10}+1568258743683420000000 x^9+4205993486991613500000 x^8+2445519790998839025000 x^7-4234355865327033793125 x^6-7108834011712534236000 x^5-3348349075885410323250 x^4+1709110589518299320880 x^3+2848005636266708260080 x^2+51267224061531809280 x+\sqrt{1-2 x} \left(1164220992000000000 x^{11}-85201937251200000000 x^{10}-563712395839560000000 x^9-258540151167606000000 x^8+3018288385229005350000 x^7+6483584022281964427500 x^6+4778719522230819024750 x^5-260379463067574874650 x^4-3148481610088191529680 x^3-1994552866922613784512 x^2+553566708413026954272 x+604905104236359963168\right)-604905104236359963168\right)}{245760 \sqrt{3} \sqrt{5 x+3} \left(25265212500 x^5-1941218400000 x^4-5284290066000 x^3+24057375117600 x^2+13825440024000 x-16748592098304\right)+\sqrt{1-2 x} \left(245760 \left(-236425406250 x^5-2220611593750 x^4+28520358020000 x^3+52011357156000 x^2-49788771586400 x-50183931760160\right)+245760 \sqrt{3} \sqrt{5 x+3} \left(2625187500 x^5+345183000000 x^4-1378186950000 x^3-13912170444000 x^2+2687092123200 x+16725373086720\right)\right)+245760 \left(-23653109375 x^6+916525237500 x^5+21026153381250 x^4-17065853944000 x^3-123670456765200 x^2+301410173760 x+50253588794912\right)}","-\frac{13}{80} (1-2 x)^{3/2} (5 x+3)^{7/2}-\frac{1}{20} (1-2 x)^{3/2} (3 x+2) (5 x+3)^{7/2}-\frac{1069 (1-2 x)^{3/2} (5 x+3)^{5/2}}{1280}-\frac{11759 (1-2 x)^{3/2} (5 x+3)^{3/2}}{3072}-\frac{129349 (1-2 x)^{3/2} \sqrt{5 x+3}}{8192}+\frac{1422839 \sqrt{1-2 x} \sqrt{5 x+3}}{81920}+\frac{15651229 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{81920 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-604905104236359963168 - 49471139162674901632*x + 1825862540643315972272*x^2 + 1783181565722403792720*x^3 - 752249794910808602050*x^4 - 3882538870129603165000*x^5 - 3687449430240944360625*x^6 - 912816683904895662500*x^7 + 463492954922036500000*x^8 + 218761558265310000000*x^9 + 7781836068000000000*x^10 - 217987056000000000*x^11) + Sqrt[3 + 5*x]*(604905104236359963168 - 555362793311883861920*x - 2175279050538559394880*x^2 - 262517692210684170480*x^3 + 3145906320921415080150*x^4 + 4671399077133650804250*x^5 + 1262966594242966222500*x^6 - 2604783917574528250000*x^7 - 2215502686933866000000*x^8 - 412409609389800000000*x^9 + 52042685270400000000*x^10 + 4357793088000000000*x^11) + Sqrt[3]*(-604905104236359963168 + 51267224061531809280*x + 2848005636266708260080*x^2 + 1709110589518299320880*x^3 - 3348349075885410323250*x^4 - 7108834011712534236000*x^5 - 4234355865327033793125*x^6 + 2445519790998839025000*x^7 + 4205993486991613500000*x^8 + 1568258743683420000000*x^9 + 25941130729200000000*x^10 - 32574167712000000000*x^11 - 241937280000000000*x^12 + Sqrt[1 - 2*x]*(604905104236359963168 + 553566708413026954272*x - 1994552866922613784512*x^2 - 3148481610088191529680*x^3 - 260379463067574874650*x^4 + 4778719522230819024750*x^5 + 6483584022281964427500*x^6 + 3018288385229005350000*x^7 - 258540151167606000000*x^8 - 563712395839560000000*x^9 - 85201937251200000000*x^10 + 1164220992000000000*x^11)))/(245760*Sqrt[3]*Sqrt[3 + 5*x]*(-16748592098304 + 13825440024000*x + 24057375117600*x^2 - 5284290066000*x^3 - 1941218400000*x^4 + 25265212500*x^5) + 245760*(50253588794912 + 301410173760*x - 123670456765200*x^2 - 17065853944000*x^3 + 21026153381250*x^4 + 916525237500*x^5 - 23653109375*x^6) + Sqrt[1 - 2*x]*(245760*(-50183931760160 - 49788771586400*x + 52011357156000*x^2 + 28520358020000*x^3 - 2220611593750*x^4 - 236425406250*x^5) + 245760*Sqrt[3]*Sqrt[3 + 5*x]*(16725373086720 + 2687092123200*x - 13912170444000*x^2 - 1378186950000*x^3 + 345183000000*x^4 + 2625187500*x^5))) + (15651229*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(40960*Sqrt[10])","B",1
2289,1,426,138,2.5366661,"\int \sqrt{1-2 x} (2+3 x) (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^(5/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(509767200000000 x^9+57937984890000000 x^8+30607691819500000 x^7-1089131403223687500 x^6-2403644288952684375 x^5-1348895315264185375 x^4+904168604152380300 x^3+1540724530986723340 x^2+106205772242536640 x-520444592089508592\right)+\sqrt{5 x+3} \left(6311448000000000 x^9-226108518900000000 x^8-1071576080905000000 x^7-413755763953125000 x^6+2374049750816906250 x^5+2982203423840306875 x^4+501893311796657000 x^3-1681919092563119300 x^2-625753187045462960 x+520444592089508592\right)+\sqrt{3} \left(-1901520000000000 x^{10}+34364559000000000 x^9+845256740150000000 x^8+1673264118663750000 x^7-822135005460937500 x^6-4516508292015828125 x^5-3666290178085854375 x^4+534621063917020500 x^3+2384554926054393500 x^2+\sqrt{1-2 x} \left(-14605272000000000 x^9-152679948300000000 x^8+427551089031000000 x^7+2618511975044625000 x^6+3572557910114531250 x^5+959452645928431875 x^4-2003666820903671000 x^3-1810259286334933940 x^2+327642953639345520 x+520444592089508592\right)+191904461163580800 x-520444592089508592\right)}{153600 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right)+\sqrt{1-2 x} \left(153600 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right)+153600 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right)\right)+153600 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right)}+\frac{3674891 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{25600 \sqrt{10}}","-\frac{3}{50} (1-2 x)^{3/2} (5 x+3)^{7/2}-\frac{251}{800} (1-2 x)^{3/2} (5 x+3)^{5/2}-\frac{2761 (1-2 x)^{3/2} (5 x+3)^{3/2}}{1920}-\frac{30371 (1-2 x)^{3/2} \sqrt{5 x+3}}{5120}+\frac{334081 \sqrt{1-2 x} \sqrt{5 x+3}}{51200}+\frac{3674891 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{51200 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-520444592089508592 + 106205772242536640*x + 1540724530986723340*x^2 + 904168604152380300*x^3 - 1348895315264185375*x^4 - 2403644288952684375*x^5 - 1089131403223687500*x^6 + 30607691819500000*x^7 + 57937984890000000*x^8 + 509767200000000*x^9) + Sqrt[3 + 5*x]*(520444592089508592 - 625753187045462960*x - 1681919092563119300*x^2 + 501893311796657000*x^3 + 2982203423840306875*x^4 + 2374049750816906250*x^5 - 413755763953125000*x^6 - 1071576080905000000*x^7 - 226108518900000000*x^8 + 6311448000000000*x^9) + Sqrt[3]*(-520444592089508592 + 191904461163580800*x + 2384554926054393500*x^2 + 534621063917020500*x^3 - 3666290178085854375*x^4 - 4516508292015828125*x^5 - 822135005460937500*x^6 + 1673264118663750000*x^7 + 845256740150000000*x^8 + 34364559000000000*x^9 - 1901520000000000*x^10 + Sqrt[1 - 2*x]*(520444592089508592 + 327642953639345520*x - 1810259286334933940*x^2 - 2003666820903671000*x^3 + 959452645928431875*x^4 + 3572557910114531250*x^5 + 2618511975044625000*x^6 + 427551089031000000*x^7 - 152679948300000000*x^8 - 14605272000000000*x^9)))/(153600*Sqrt[3]*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 153600*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(153600*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 153600*Sqrt[3]*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (3674891*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(25600*Sqrt[10])","B",1
2290,1,366,116,2.143946,"\int \sqrt{1-2 x} (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(3 + 5*x)^(5/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-82086000000 x^7+632779100000 x^6+13219571512500 x^5+19641249565125 x^4-1824098603000 x^3-19282871238120 x^2-4485510755168 x+6868058547240\right)+\sqrt{5 x+3} \left(930864000000 x^7+6745772000000 x^6-9078321780000 x^5-35223276627000 x^4-19241846079500 x^3+17435721505180 x^2+11266182241160 x-6868058547240\right)+\sqrt{3} \left(-57120000000 x^8-5203144000000 x^7-5295005000000 x^6+30824439810000 x^5+52630788716125 x^4+10636338332600 x^3-29305043137480 x^2+\sqrt{1-2 x} \left(428208000000 x^7-6874709600000 x^6-27251894340000 x^5-22028952693000 x^4+14388906339500 x^3+25481309861260 x^2-1258194805032 x-6868058547240\right)-5522476680960 x+6868058547240\right)}{1536 \sqrt{3} \sqrt{5 x+3} \left(8921000 x^3-162998000 x^2-220512160 x+287530496\right)+\sqrt{1-2 x} \left(1536 \left(-48482500 x^3-297203500 x^2+794989800 x+852279560\right)+1536 \sqrt{3} \sqrt{5 x+3} \left(595000 x^3+53178000 x^2-36412000 x-283051520\right)\right)+1536 \left(-8550625 x^4+79738000 x^3+1253327000 x^2-32289760 x-865716488\right)}+\frac{14641 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{256 \sqrt{10}}","-\frac{1}{8} (1-2 x)^{3/2} (5 x+3)^{5/2}-\frac{55}{96} (1-2 x)^{3/2} (5 x+3)^{3/2}-\frac{605}{256} (1-2 x)^{3/2} \sqrt{5 x+3}+\frac{1331}{512} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{14641 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{512 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(6868058547240 - 4485510755168*x - 19282871238120*x^2 - 1824098603000*x^3 + 19641249565125*x^4 + 13219571512500*x^5 + 632779100000*x^6 - 82086000000*x^7) + Sqrt[3 + 5*x]*(-6868058547240 + 11266182241160*x + 17435721505180*x^2 - 19241846079500*x^3 - 35223276627000*x^4 - 9078321780000*x^5 + 6745772000000*x^6 + 930864000000*x^7) + Sqrt[3]*(6868058547240 - 5522476680960*x - 29305043137480*x^2 + 10636338332600*x^3 + 52630788716125*x^4 + 30824439810000*x^5 - 5295005000000*x^6 - 5203144000000*x^7 - 57120000000*x^8 + Sqrt[1 - 2*x]*(-6868058547240 - 1258194805032*x + 25481309861260*x^2 + 14388906339500*x^3 - 22028952693000*x^4 - 27251894340000*x^5 - 6874709600000*x^6 + 428208000000*x^7)))/(1536*Sqrt[3]*Sqrt[3 + 5*x]*(287530496 - 220512160*x - 162998000*x^2 + 8921000*x^3) + 1536*(-865716488 - 32289760*x + 1253327000*x^2 + 79738000*x^3 - 8550625*x^4) + Sqrt[1 - 2*x]*(1536*(852279560 + 794989800*x - 297203500*x^2 - 48482500*x^3) + 1536*Sqrt[3]*Sqrt[3 + 5*x]*(-283051520 - 36412000*x + 53178000*x^2 + 595000*x^3))) + (14641*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(256*Sqrt[10])","B",1
2291,1,500,130,2.2871915,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{2+3 x} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x),x]","\frac{7}{81} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(107700000 x^5+7232512500 x^4+5196805625 x^3-11196609675 x^2-6919588560 x+4258832644\right)+\sqrt{5 x+3} \left(1881000000 x^5-12958275000 x^4-22366154250 x^3+4214095325 x^2+10790212180 x-4258832644\right)+\sqrt{3} \left(-702000000 x^6+1676250000 x^5+29828137500 x^4+24373511375 x^3-15272261775 x^2+\sqrt{1-2 x} \left(-2752200000 x^5-13322925000 x^4+351111750 x^3+18899246025 x^2+3240550940 x-4258832644\right)-7111174560 x+4258832644\right)}{864 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right)+\sqrt{1-2 x} \left(864 \left(-391875 x^2+2827000 x+3481060\right)+864 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right)\right)+864 \left(44875 x^3+2976525 x^2-279060 x-3667684\right)}+\frac{6553 \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{1296}","\frac{1}{9} \sqrt{1-2 x} (5 x+3)^{5/2}-\frac{5}{24} \sqrt{1-2 x} (5 x+3)^{3/2}-\frac{925}{864} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{6553 \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{2592}+\frac{2}{81} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(4258832644 - 6919588560*x - 11196609675*x^2 + 5196805625*x^3 + 7232512500*x^4 + 107700000*x^5) + Sqrt[3 + 5*x]*(-4258832644 + 10790212180*x + 4214095325*x^2 - 22366154250*x^3 - 12958275000*x^4 + 1881000000*x^5) + Sqrt[3]*(4258832644 - 7111174560*x - 15272261775*x^2 + 24373511375*x^3 + 29828137500*x^4 + 1676250000*x^5 - 702000000*x^6 + Sqrt[1 - 2*x]*(-4258832644 + 3240550940*x + 18899246025*x^2 + 351111750*x^3 - 13322925000*x^4 - 2752200000*x^5)))/(864*Sqrt[3]*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 864*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(864*(3481060 + 2827000*x - 391875*x^2) + 864*Sqrt[3]*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (6553*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/1296 + (7*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ])/81","C",1
2292,1,591,137,2.5439351,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^2} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^2,x]","\frac{59}{27} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{295}{54} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(13462500 x^5+899015625 x^4+309993875 x^3-1258876650 x^2-233047740 x+325967224\right)+\sqrt{5 x+3} \left(235125000 x^5-1707956250 x^4-2045306175 x^3+958005290 x^2+519512884 x-325967224\right)+\sqrt{3} \left(-87750000 x^6+242437500 x^5+3611179875 x^4+1567252775 x^3-1561315410 x^2+\sqrt{1-2 x} \left(-344025000 x^5-1536356250 x^4+555608625 x^3+1610236650 x^2-51820780 x-325967224\right)-234644364 x+325967224\right)}{72 \sqrt{3} (3 x+2) \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right)+\sqrt{1-2 x} \left(72 (3 x+2) \left(-391875 x^2+2827000 x+3481060\right)+72 \sqrt{3} (3 x+2) \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right)\right)+72 (3 x+2) \left(44875 x^3+2976525 x^2-279060 x-3667684\right)}+\frac{155}{108} \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{\sqrt{1-2 x} (5 x+3)^{5/2}}{3 (3 x+2)}+\frac{5}{6} \sqrt{1-2 x} (5 x+3)^{3/2}-\frac{95}{72} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{155}{216} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{59 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{27 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(325967224 - 233047740*x - 1258876650*x^2 + 309993875*x^3 + 899015625*x^4 + 13462500*x^5) + Sqrt[3 + 5*x]*(-325967224 + 519512884*x + 958005290*x^2 - 2045306175*x^3 - 1707956250*x^4 + 235125000*x^5) + Sqrt[3]*(325967224 - 234644364*x - 1561315410*x^2 + 1567252775*x^3 + 3611179875*x^4 + 242437500*x^5 - 87750000*x^6 + Sqrt[1 - 2*x]*(-325967224 - 51820780*x + 1610236650*x^2 + 555608625*x^3 - 1536356250*x^4 - 344025000*x^5)))/(72*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 72*(2 + 3*x)*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(72*(2 + 3*x)*(3481060 + 2827000*x - 391875*x^2) + 72*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (155*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/108 + (59*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/27 - (295*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/54","C",1
2293,1,597,144,2.5973704,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^3} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^3,x]","-\frac{2119}{252} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{10595}{504} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(31412500 x^5+2205218875 x^4+2765806475 x^3-4947164440 x^2-7924390876 x-2692772720\right)+\sqrt{5 x+3} \left(548625000 x^5-4006079000 x^4-11672272425 x^3-4015403260 x^2+5262286700 x+2692772720\right)+\sqrt{3} \left(-204750000 x^6+392285625 x^5+11567231625 x^4+16154437850 x^3+566356260 x^2+\sqrt{1-2 x} \left(-802725000 x^5-4750131375 x^4-689302350 x^3+10624902420 x^2+10178638976 x+2692772720\right)-7516534800 x-2692772720\right)}{84 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right) (3 x+2)^2+\sqrt{1-2 x} \left(84 \left(-391875 x^2+2827000 x+3481060\right) (3 x+2)^2+84 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right) (3 x+2)^2\right)+84 \left(44875 x^3+2976525 x^2-279060 x-3667684\right) (3 x+2)^2}+\frac{25}{9} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{\sqrt{1-2 x} (5 x+3)^{5/2}}{6 (3 x+2)^2}-\frac{59 \sqrt{1-2 x} (5 x+3)^{3/2}}{84 (3 x+2)}+\frac{215}{84} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{25}{9} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)+\frac{2119 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{252 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-2692772720 - 7924390876*x - 4947164440*x^2 + 2765806475*x^3 + 2205218875*x^4 + 31412500*x^5) + Sqrt[3 + 5*x]*(2692772720 + 5262286700*x - 4015403260*x^2 - 11672272425*x^3 - 4006079000*x^4 + 548625000*x^5) + Sqrt[3]*(-2692772720 - 7516534800*x + 566356260*x^2 + 16154437850*x^3 + 11567231625*x^4 + 392285625*x^5 - 204750000*x^6 + Sqrt[1 - 2*x]*(2692772720 + 10178638976*x + 10624902420*x^2 - 689302350*x^3 - 4750131375*x^4 - 802725000*x^5)))/(84*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 84*(2 + 3*x)^2*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(84*(2 + 3*x)^2*(3481060 + 2827000*x - 391875*x^2) + 84*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (25*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/9 - (2119*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/252 + (10595*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/504","C",1
2294,1,597,149,2.6756262,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^4} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^4,x]","\frac{250433 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{31752}-\frac{1252165 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{63504}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-20693086125 x^5-356914258425 x^4+227665232830 x^3+1588339205556 x^2+1398310596696 x+361795273664\right)+\sqrt{5 x+3} \left(21235356450 x^5+1268122086165 x^4+1782648624834 x^3-132734100092 x^2-1051274917528 x-361795273664\right)+\sqrt{3} \left(28589766750 x^6-598500930600 x^5-2560642113510 x^4-1954585058024 x^3+874314200232 x^2+\sqrt{1-2 x} \left(209927817000 x^5+402315125850 x^4-1146790019760 x^3-2624058663336 x^2-1704749616416 x-361795273664\right)+1357713937248 x+361795273664\right)}{10584 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right) (3 x+2)^3+\sqrt{1-2 x} \left(10584 \left(-391875 x^2+2827000 x+3481060\right) (3 x+2)^3+10584 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right) (3 x+2)^3\right)+10584 \left(44875 x^3+2976525 x^2-279060 x-3667684\right) (3 x+2)^3}-\frac{100}{81} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{\sqrt{1-2 x} (5 x+3)^{5/2}}{9 (3 x+2)^3}-\frac{59 \sqrt{1-2 x} (5 x+3)^{3/2}}{252 (3 x+2)^2}-\frac{6401 \sqrt{1-2 x} \sqrt{5 x+3}}{10584 (3 x+2)}-\frac{50}{81} \sqrt{10} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{250433 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{31752 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(361795273664 + 1398310596696*x + 1588339205556*x^2 + 227665232830*x^3 - 356914258425*x^4 - 20693086125*x^5) + Sqrt[3 + 5*x]*(-361795273664 - 1051274917528*x - 132734100092*x^2 + 1782648624834*x^3 + 1268122086165*x^4 + 21235356450*x^5) + Sqrt[3]*(361795273664 + 1357713937248*x + 874314200232*x^2 - 1954585058024*x^3 - 2560642113510*x^4 - 598500930600*x^5 + 28589766750*x^6 + Sqrt[1 - 2*x]*(-361795273664 - 1704749616416*x - 2624058663336*x^2 - 1146790019760*x^3 + 402315125850*x^4 + 209927817000*x^5)))/(10584*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 10584*(2 + 3*x)^3*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(10584*(2 + 3*x)^3*(3481060 + 2827000*x - 391875*x^2) + 10584*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) - (100*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/81 + (250433*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/31752 - (1252165*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/63504","C",1
2295,1,599,151,2.6804605,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^5} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^5,x]","\frac{73205 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{21952}-\frac{366025 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{43904}+\frac{\sqrt{5 x+3} \left(-93268807566000 x^7-346106646495500 x^6+1783702682599860 x^5+3961199845659144 x^4+1673143534444184 x^3-1059920197907296 x^2-938218607174816 x-181008068858496\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(6009759001875 x^7-141736167893000 x^6-1289128957138500 x^5-1255462867940880 x^4+1182349293849080 x^3+2264255238267840 x^2+1119274135263008 x+181008068858496\right)+\sqrt{3} \left(9414736573125 x^8+410789243854000 x^7-337466874085000 x^6-4394664992689680 x^5-5508117033966664 x^4-1068112719970304 x^3+1780337596643776 x^2+\sqrt{1-2 x} \left(-10419125722500 x^7+812476593054500 x^6+2348179964519400 x^5+791326242087480 x^4-2729528166231680 x^3-3135541206244480 x^2-1270103155145088 x-181008068858496\right)+1089047627056896 x+181008068858496\right)}{65856 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^4+\sqrt{1-2 x} \left(65856 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^4+65856 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^4\right)+65856 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^4}","\frac{\sqrt{1-2 x} (5 x+3)^{7/2}}{4 (3 x+2)^4}-\frac{11 \sqrt{1-2 x} (5 x+3)^{5/2}}{168 (3 x+2)^3}-\frac{605 \sqrt{1-2 x} (5 x+3)^{3/2}}{4704 (3 x+2)^2}-\frac{6655 \sqrt{1-2 x} \sqrt{5 x+3}}{21952 (3 x+2)}-\frac{73205 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{21952 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-181008068858496 - 938218607174816*x - 1059920197907296*x^2 + 1673143534444184*x^3 + 3961199845659144*x^4 + 1783702682599860*x^5 - 346106646495500*x^6 - 93268807566000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(181008068858496 + 1119274135263008*x + 2264255238267840*x^2 + 1182349293849080*x^3 - 1255462867940880*x^4 - 1289128957138500*x^5 - 141736167893000*x^6 + 6009759001875*x^7) + Sqrt[3]*(181008068858496 + 1089047627056896*x + 1780337596643776*x^2 - 1068112719970304*x^3 - 5508117033966664*x^4 - 4394664992689680*x^5 - 337466874085000*x^6 + 410789243854000*x^7 + 9414736573125*x^8 + Sqrt[1 - 2*x]*(-181008068858496 - 1270103155145088*x - 3135541206244480*x^2 - 2729528166231680*x^3 + 791326242087480*x^4 + 2348179964519400*x^5 + 812476593054500*x^6 - 10419125722500*x^7)))/(65856*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 65856*(2 + 3*x)^4*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(65856*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 65856*(2 + 3*x)^4*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) + (73205*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/21952 - (366025*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/43904","C",1
2296,1,659,180,3.2248402,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^6} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^6,x]","\frac{248897 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{43904}-\frac{1244485 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{87808}+\frac{\sqrt{5 x+3} \left(-72553591991925000 x^9-4263086778715276875 x^8-10076189338900105850 x^7+18412769691332734080 x^6+72531931744611917424 x^5+67850447235367786880 x^4+7944529451050973440 x^3-22233852884858866240 x^2-12697474929258444160 x-2121832391922676224\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(15680263417734375 x^9+526722342751828125 x^8-3792640823835868750 x^7-25189242290666073000 x^6-38865529263529305600 x^5-5503934045272107680 x^4+37797423283649347200 x^3+38003898219004373696 x^2+14812542500854474624 x+2121832391922676224\right)+\sqrt{3} \left(-14041507030903125 x^{10}+1385091597766640625 x^9+11701581386334512500 x^8+6178174824409791000 x^7-60864848713094562600 x^6-122943742375500311824 x^5-79127564323806286080 x^4+6778304057313053760 x^3+32075916735309418240 x^2+\sqrt{1-2 x} \left(-227010169331859375 x^9-58280979196687500 x^8+16206615393665400000 x^7+51973560288951675000 x^6+49267026539433186000 x^5-16462147987834053120 x^4-64926783710191564480 x^3-49609610935368284416 x^2-16581828717040038144 x-2121832391922676224\right)+14466761145444007680 x+2121832391922676224\right)}{658560 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right) (3 x+2)^5+\sqrt{1-2 x} \left(658560 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right) (3 x+2)^5+658560 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right) (3 x+2)^5\right)+658560 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right) (3 x+2)^5}","\frac{17 \sqrt{1-2 x} (5 x+3)^{7/2}}{40 (3 x+2)^4}+\frac{3 (1-2 x)^{3/2} (5 x+3)^{7/2}}{35 (3 x+2)^5}-\frac{187 \sqrt{1-2 x} (5 x+3)^{5/2}}{1680 (3 x+2)^3}-\frac{2057 \sqrt{1-2 x} (5 x+3)^{3/2}}{9408 (3 x+2)^2}-\frac{22627 \sqrt{1-2 x} \sqrt{5 x+3}}{43904 (3 x+2)}-\frac{248897 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{43904 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-2121832391922676224 - 12697474929258444160*x - 22233852884858866240*x^2 + 7944529451050973440*x^3 + 67850447235367786880*x^4 + 72531931744611917424*x^5 + 18412769691332734080*x^6 - 10076189338900105850*x^7 - 4263086778715276875*x^8 - 72553591991925000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(2121832391922676224 + 14812542500854474624*x + 38003898219004373696*x^2 + 37797423283649347200*x^3 - 5503934045272107680*x^4 - 38865529263529305600*x^5 - 25189242290666073000*x^6 - 3792640823835868750*x^7 + 526722342751828125*x^8 + 15680263417734375*x^9) + Sqrt[3]*(2121832391922676224 + 14466761145444007680*x + 32075916735309418240*x^2 + 6778304057313053760*x^3 - 79127564323806286080*x^4 - 122943742375500311824*x^5 - 60864848713094562600*x^6 + 6178174824409791000*x^7 + 11701581386334512500*x^8 + 1385091597766640625*x^9 - 14041507030903125*x^10 + Sqrt[1 - 2*x]*(-2121832391922676224 - 16581828717040038144*x - 49609610935368284416*x^2 - 64926783710191564480*x^3 - 16462147987834053120*x^4 + 49267026539433186000*x^5 + 51973560288951675000*x^6 + 16206615393665400000*x^7 - 58280979196687500*x^8 - 227010169331859375*x^9)))/(658560*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 658560*(2 + 3*x)^5*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(658560*(2 + 3*x)^5*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 658560*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (248897*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/43904 - (1244485*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/87808","C",1
2297,1,719,209,3.6534835,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^7} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^7,x]","\frac{15036307 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{1229312}-\frac{75181535 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2458624}+\frac{\sqrt{5 x+3} \left(-2845865697628092975000 x^{11}+13957481251842921168750 x^{10}+498857956527875697942750 x^9+1449862319768234921544600 x^8+293071637806499472870400 x^7-3869263526714585164306944 x^6-5920505035774575241824576 x^5-2972964427677710539941120 x^4+551598832627415206318080 x^3+1222835770791349279572480 x^2+489436334304850088482304 x+66812892767177024894976\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(53945901817802296875 x^{11}-12104781929878405500000 x^{10}-115822086416781477731250 x^9+109777649576746958231000 x^8+1762134106258731084771200 x^7+3711241801284543376173120 x^6+2649907495761596909762560 x^5-854506222528543005340160 x^4-2662598450413425747361536 x^3-1811030905726071268133888 x^2-556171216347725445025280 x-66812892767177024894976\right)+\sqrt{3} \left(305349288307564640625 x^{12}+10792506709256220787500 x^{11}-193845725320225958493750 x^{10}-1375179745401041467653000 x^9-2108017953658436615369400 x^8+1647956618236550594063520 x^7+7838036750833195238423424 x^6+8359699658634126244978176 x^5+2816106214401613458654720 x^4-1419958082073778876423680 x^3-1607470325208801775219200 x^2-545122494366039275894784 x+\sqrt{1-2 x} \left(1184744908031760281250 x^{11}+68205322781629682343750 x^{10}+171602769464457478290000 x^9-904398643171891354443000 x^8-4059064947405466403776800 x^7-5826251249118651581017920 x^6-2482268189292991985064960 x^5+2585523070596349961763840 x^4+3997931465991996853579776 x^3+2251286611267794894233088 x^2+611857376408914632437760 x+66812892767177024894976\right)-66812892767177024894976\right)}{18439680 \sqrt{3} \sqrt{5 x+3} \left(-25265212500 x^5+1941218400000 x^4+5284290066000 x^3-24057375117600 x^2-13825440024000 x+16748592098304\right) (3 x+2)^6+\sqrt{1-2 x} \left(18439680 \sqrt{3} \sqrt{5 x+3} \left(-2625187500 x^5-345183000000 x^4+1378186950000 x^3+13912170444000 x^2-2687092123200 x-16725373086720\right) (3 x+2)^6+18439680 \left(236425406250 x^5+2220611593750 x^4-28520358020000 x^3-52011357156000 x^2+49788771586400 x+50183931760160\right) (3 x+2)^6\right)+18439680 \left(23653109375 x^6-916525237500 x^5-21026153381250 x^4+17065853944000 x^3+123670456765200 x^2-301410173760 x-50253588794912\right) (3 x+2)^6}","-\frac{\sqrt{1-2 x} (5 x+3)^{5/2}}{18 (3 x+2)^6}-\frac{59 \sqrt{1-2 x} (5 x+3)^{3/2}}{1260 (3 x+2)^5}+\frac{106751933 \sqrt{1-2 x} \sqrt{5 x+3}}{99574272 (3 x+2)}+\frac{1057139 \sqrt{1-2 x} \sqrt{5 x+3}}{7112448 (3 x+2)^2}+\frac{47279 \sqrt{1-2 x} \sqrt{5 x+3}}{1270080 (3 x+2)^3}-\frac{6533 \sqrt{1-2 x} \sqrt{5 x+3}}{211680 (3 x+2)^4}-\frac{15036307 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1229312 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(66812892767177024894976 + 489436334304850088482304*x + 1222835770791349279572480*x^2 + 551598832627415206318080*x^3 - 2972964427677710539941120*x^4 - 5920505035774575241824576*x^5 - 3869263526714585164306944*x^6 + 293071637806499472870400*x^7 + 1449862319768234921544600*x^8 + 498857956527875697942750*x^9 + 13957481251842921168750*x^10 - 2845865697628092975000*x^11) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-66812892767177024894976 - 556171216347725445025280*x - 1811030905726071268133888*x^2 - 2662598450413425747361536*x^3 - 854506222528543005340160*x^4 + 2649907495761596909762560*x^5 + 3711241801284543376173120*x^6 + 1762134106258731084771200*x^7 + 109777649576746958231000*x^8 - 115822086416781477731250*x^9 - 12104781929878405500000*x^10 + 53945901817802296875*x^11) + Sqrt[3]*(-66812892767177024894976 - 545122494366039275894784*x - 1607470325208801775219200*x^2 - 1419958082073778876423680*x^3 + 2816106214401613458654720*x^4 + 8359699658634126244978176*x^5 + 7838036750833195238423424*x^6 + 1647956618236550594063520*x^7 - 2108017953658436615369400*x^8 - 1375179745401041467653000*x^9 - 193845725320225958493750*x^10 + 10792506709256220787500*x^11 + 305349288307564640625*x^12 + Sqrt[1 - 2*x]*(66812892767177024894976 + 611857376408914632437760*x + 2251286611267794894233088*x^2 + 3997931465991996853579776*x^3 + 2585523070596349961763840*x^4 - 2482268189292991985064960*x^5 - 5826251249118651581017920*x^6 - 4059064947405466403776800*x^7 - 904398643171891354443000*x^8 + 171602769464457478290000*x^9 + 68205322781629682343750*x^10 + 1184744908031760281250*x^11)))/(18439680*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(16748592098304 - 13825440024000*x - 24057375117600*x^2 + 5284290066000*x^3 + 1941218400000*x^4 - 25265212500*x^5) + 18439680*(2 + 3*x)^6*(-50253588794912 - 301410173760*x + 123670456765200*x^2 + 17065853944000*x^3 - 21026153381250*x^4 - 916525237500*x^5 + 23653109375*x^6) + Sqrt[1 - 2*x]*(18439680*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(-16725373086720 - 2687092123200*x + 13912170444000*x^2 + 1378186950000*x^3 - 345183000000*x^4 - 2625187500*x^5) + 18439680*(2 + 3*x)^6*(50183931760160 + 49788771586400*x - 52011357156000*x^2 - 28520358020000*x^3 + 2220611593750*x^4 + 236425406250*x^5))) + (15036307*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/1229312 - (75181535*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2458624","C",1
2298,1,779,238,4.5518927,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^8} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^8,x]","\frac{3735929329 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{120472576}-\frac{18679646645 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{240945152}+\frac{\sqrt{5 x+3} \left(-75625042670844486521625000 x^{13}-4750384931905715910169621875 x^{12}-5589133119110303842570548750 x^{11}+165060671642860723823863275000 x^{10}+617169736261515105769647536000 x^9+659043002221834190676389864960 x^8-420474900908149828362621557888 x^7-1604791703898137818237365861824 x^6-1431718443732285996471050382208 x^5-367145522212458216280373492480 x^4+258346083050513131784565368320 x^3+233669196370258822722911515648 x^2+71619675264557248094861686784 x+8149999862842896476648153088\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(7075123003354849144453125 x^{13}+258279526614287159030671875 x^{12}-9450948292455287078124468750 x^{11}-73603800622630855222486995000 x^{10}-91203042839917517278693900000 x^9+332367810123619099264517611200 x^8+1130054246426659269452422412480 x^7+1320450572999587497395639310400 x^6+471422153632466409260011827840 x^5-451937157404451147851912012032 x^4-619151034404208471126582500864 x^3-317449647795520883983752305664 x^2-79766718018460626745664018432 x-8149999862842896476648153088\right)+\sqrt{3} \left(-2788890401919452559609375 x^{14}+1301415616793841619295671875 x^{13}+14064529551463095225090075000 x^{12}-48651605133970058329697692500 x^{11}-502072396127199554900998465000 x^{10}-1124272551478167294838584760400 x^9-585336219612857817588609403520 x^8+1389359662753799844220887567808 x^7+2644526092444871676671672497664 x^6+1778487464296300441895846948608 x^5+214715068349938391158727764480 x^4-430559276709272523915583682560 x^3-290521450276447068886460090368 x^2-78411572135986390992068481024 x+\sqrt{1-2 x} \left(-118573954860404055939609375 x^{13}+1301525240202465521122687500 x^{12}+43378626453218549564659087500 x^{11}+154348621951661111731062405000 x^{10}-17285735791521351773194730000 x^9-970399532745785145452326081600 x^8-2041321443105231815682698364480 x^7-1762322401398142910511181216000 x^6-239108427000507756525042753280 x^5+878303074215979376747516861952 x^4+858351834355604213387883997184 x^3+381091334315688674856302823424 x^2+86558614889889769642870812672 x+8149999862842896476648153088\right)-8149999862842896476648153088\right)}{1807088640 \sqrt{3} \sqrt{5 x+3} \left(-5663973218750 x^6-52303209612500 x^5+1428846604955000 x^4+2194696763160000 x^3-7555736895916000 x^2-3365532949972160 x+4051435671804928\right) (3 x+2)^7+\sqrt{1-2 x} \left(1807088640 \left(-3042263984375 x^6+486365726000000 x^5+1796810007300000 x^4-11790948756840000 x^3-17392813876790000 x^2+12117692004316800 x+12149682333912640\right) (3 x+2)^7+1807088640 \sqrt{3} \sqrt{5 x+3} \left(223405156250 x^6-14941831687500 x^5-390402719125000 x^4+702446326920000 x^3+4956682106340000 x^2-666120123963200 x-4049763902970880\right) (3 x+2)^7\right)+1807088640 \left(905821796875 x^7+135547777203125 x^6-996207107350000 x^5-11461663884510000 x^4+5424159101550000 x^3+35265969543725200 x^2-26521579595840 x-12154697640414784\right) (3 x+2)^7}","-\frac{\sqrt{1-2 x} (5 x+3)^{5/2}}{21 (3 x+2)^7}-\frac{59 \sqrt{1-2 x} (5 x+3)^{3/2}}{1764 (3 x+2)^6}+\frac{8818415317 \sqrt{1-2 x} \sqrt{5 x+3}}{3252759552 (3 x+2)}+\frac{84539611 \sqrt{1-2 x} \sqrt{5 x+3}}{232339968 (3 x+2)^2}+\frac{2524471 \sqrt{1-2 x} \sqrt{5 x+3}}{41489280 (3 x+2)^3}+\frac{369409 \sqrt{1-2 x} \sqrt{5 x+3}}{20744640 (3 x+2)^4}-\frac{6577 \sqrt{1-2 x} \sqrt{5 x+3}}{370440 (3 x+2)^5}-\frac{3735929329 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{120472576 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(8149999862842896476648153088 + 71619675264557248094861686784*x + 233669196370258822722911515648*x^2 + 258346083050513131784565368320*x^3 - 367145522212458216280373492480*x^4 - 1431718443732285996471050382208*x^5 - 1604791703898137818237365861824*x^6 - 420474900908149828362621557888*x^7 + 659043002221834190676389864960*x^8 + 617169736261515105769647536000*x^9 + 165060671642860723823863275000*x^10 - 5589133119110303842570548750*x^11 - 4750384931905715910169621875*x^12 - 75625042670844486521625000*x^13) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-8149999862842896476648153088 - 79766718018460626745664018432*x - 317449647795520883983752305664*x^2 - 619151034404208471126582500864*x^3 - 451937157404451147851912012032*x^4 + 471422153632466409260011827840*x^5 + 1320450572999587497395639310400*x^6 + 1130054246426659269452422412480*x^7 + 332367810123619099264517611200*x^8 - 91203042839917517278693900000*x^9 - 73603800622630855222486995000*x^10 - 9450948292455287078124468750*x^11 + 258279526614287159030671875*x^12 + 7075123003354849144453125*x^13) + Sqrt[3]*(-8149999862842896476648153088 - 78411572135986390992068481024*x - 290521450276447068886460090368*x^2 - 430559276709272523915583682560*x^3 + 214715068349938391158727764480*x^4 + 1778487464296300441895846948608*x^5 + 2644526092444871676671672497664*x^6 + 1389359662753799844220887567808*x^7 - 585336219612857817588609403520*x^8 - 1124272551478167294838584760400*x^9 - 502072396127199554900998465000*x^10 - 48651605133970058329697692500*x^11 + 14064529551463095225090075000*x^12 + 1301415616793841619295671875*x^13 - 2788890401919452559609375*x^14 + Sqrt[1 - 2*x]*(8149999862842896476648153088 + 86558614889889769642870812672*x + 381091334315688674856302823424*x^2 + 858351834355604213387883997184*x^3 + 878303074215979376747516861952*x^4 - 239108427000507756525042753280*x^5 - 1762322401398142910511181216000*x^6 - 2041321443105231815682698364480*x^7 - 970399532745785145452326081600*x^8 - 17285735791521351773194730000*x^9 + 154348621951661111731062405000*x^10 + 43378626453218549564659087500*x^11 + 1301525240202465521122687500*x^12 - 118573954860404055939609375*x^13)))/(1807088640*Sqrt[3]*(2 + 3*x)^7*Sqrt[3 + 5*x]*(4051435671804928 - 3365532949972160*x - 7555736895916000*x^2 + 2194696763160000*x^3 + 1428846604955000*x^4 - 52303209612500*x^5 - 5663973218750*x^6) + 1807088640*(2 + 3*x)^7*(-12154697640414784 - 26521579595840*x + 35265969543725200*x^2 + 5424159101550000*x^3 - 11461663884510000*x^4 - 996207107350000*x^5 + 135547777203125*x^6 + 905821796875*x^7) + Sqrt[1 - 2*x]*(1807088640*(2 + 3*x)^7*(12149682333912640 + 12117692004316800*x - 17392813876790000*x^2 - 11790948756840000*x^3 + 1796810007300000*x^4 + 486365726000000*x^5 - 3042263984375*x^6) + 1807088640*Sqrt[3]*(2 + 3*x)^7*Sqrt[3 + 5*x]*(-4049763902970880 - 666120123963200*x + 4956682106340000*x^2 + 702446326920000*x^3 - 390402719125000*x^4 - 14941831687500*x^5 + 223405156250*x^6))) + (3735929329*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/120472576 - (18679646645*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/240945152","C",1
2299,1,436,119,8.7576187,"\int \frac{\sqrt{a+b x}}{\sqrt{c+d x} (e+f x)} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(Sqrt[c + d*x]*(e + f*x)),x]","\frac{(a f-b e) \text{RootSum}\left[\text{$\#$1}^4 d^2 e+\text{$\#$1}^4 d^2 f-4 \text{$\#$1}^3 d f \sqrt{a+b} \sqrt{c+d}+4 \text{$\#$1}^2 a d f+4 \text{$\#$1}^2 b c f-2 \text{$\#$1}^2 b d e+6 \text{$\#$1}^2 b d f-4 \text{$\#$1} b f \sqrt{a+b} \sqrt{c+d}+b^2 e+b^2 f\&,\frac{-\text{$\#$1}^2 d \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)+\text{$\#$1}^2 d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)+b \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)-b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{\text{$\#$1}^3 d^2 e+\text{$\#$1}^3 d^2 f-3 \text{$\#$1}^2 d f \sqrt{a+b} \sqrt{c+d}+2 \text{$\#$1} a d f+2 \text{$\#$1} b c f-\text{$\#$1} b d e+3 \text{$\#$1} b d f-b f \sqrt{a+b} \sqrt{c+d}}\&\right]}{f}+\frac{4 \sqrt{b} \tanh ^{-1}\left(\frac{\frac{\sqrt{d} \sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b}}}{\sqrt{c+d}-\sqrt{c+d x}}\right)}{\sqrt{d} f}","\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{d} f}-\frac{2 \sqrt{b e-a f} \tanh ^{-1}\left(\frac{\sqrt{a+b x} \sqrt{d e-c f}}{\sqrt{c+d x} \sqrt{b e-a f}}\right)}{f \sqrt{d e-c f}}",1,"(4*Sqrt[b]*ArcTanh[((Sqrt[a + b]*Sqrt[d])/Sqrt[b] - (Sqrt[d]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[c + d] - Sqrt[c + d*x])])/(Sqrt[d]*f) + ((-(b*e) + a*f)*RootSum[b^2*e + b^2*f - 4*b*Sqrt[a + b]*Sqrt[c + d]*f*#1 - 2*b*d*e*#1^2 + 4*b*c*f*#1^2 + 4*a*d*f*#1^2 + 6*b*d*f*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*f*#1^3 + d^2*e*#1^4 + d^2*f*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]*f) - b*d*e*#1 + 2*b*c*f*#1 + 2*a*d*f*#1 + 3*b*d*f*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*f*#1^2 + d^2*e*#1^3 + d^2*f*#1^3) & ])/f","C",1
2300,1,436,119,2.331579,"\int \frac{\sqrt{c+d x}}{\sqrt{a+b x} (e+f x)} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(Sqrt[a + b*x]*(e + f*x)),x]","\frac{(c f-d e) \text{RootSum}\left[\text{$\#$1}^4 d^2 e+\text{$\#$1}^4 d^2 f-4 \text{$\#$1}^3 d f \sqrt{a+b} \sqrt{c+d}+4 \text{$\#$1}^2 a d f+4 \text{$\#$1}^2 b c f-2 \text{$\#$1}^2 b d e+6 \text{$\#$1}^2 b d f-4 \text{$\#$1} b f \sqrt{a+b} \sqrt{c+d}+b^2 e+b^2 f\&,\frac{-\text{$\#$1}^2 d \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)+\text{$\#$1}^2 d \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)+b \log \left(\text{$\#$1} \sqrt{c+d x}+\text{$\#$1} \left(-\sqrt{c+d}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)-b \log \left(\sqrt{c+d}-\sqrt{c+d x}\right)}{\text{$\#$1}^3 d^2 e+\text{$\#$1}^3 d^2 f-3 \text{$\#$1}^2 d f \sqrt{a+b} \sqrt{c+d}+2 \text{$\#$1} a d f+2 \text{$\#$1} b c f-\text{$\#$1} b d e+3 \text{$\#$1} b d f-b f \sqrt{a+b} \sqrt{c+d}}\&\right]}{f}+\frac{4 \sqrt{d} \tanh ^{-1}\left(\frac{\frac{\sqrt{d} \sqrt{a+b}}{\sqrt{b}}-\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b}}}{\sqrt{c+d}-\sqrt{c+d x}}\right)}{\sqrt{b} f}","\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b} \sqrt{c+d x}}\right)}{\sqrt{b} f}-\frac{2 \sqrt{d e-c f} \tanh ^{-1}\left(\frac{\sqrt{a+b x} \sqrt{d e-c f}}{\sqrt{c+d x} \sqrt{b e-a f}}\right)}{f \sqrt{b e-a f}}",1,"(4*Sqrt[d]*ArcTanh[((Sqrt[a + b]*Sqrt[d])/Sqrt[b] - (Sqrt[d]*Sqrt[a + b*x])/Sqrt[b])/(Sqrt[c + d] - Sqrt[c + d*x])])/(Sqrt[b]*f) + ((-(d*e) + c*f)*RootSum[b^2*e + b^2*f - 4*b*Sqrt[a + b]*Sqrt[c + d]*f*#1 - 2*b*d*e*#1^2 + 4*b*c*f*#1^2 + 4*a*d*f*#1^2 + 6*b*d*f*#1^2 - 4*Sqrt[a + b]*d*Sqrt[c + d]*f*#1^3 + d^2*e*#1^4 + d^2*f*#1^4 & , (-(b*Log[Sqrt[c + d] - Sqrt[c + d*x]]) + b*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1] + d*Log[Sqrt[c + d] - Sqrt[c + d*x]]*#1^2 - d*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[c + d]*#1 + Sqrt[c + d*x]*#1]*#1^2)/(-(b*Sqrt[a + b]*Sqrt[c + d]*f) - b*d*e*#1 + 2*b*c*f*#1 + 2*a*d*f*#1 + 3*b*d*f*#1 - 3*Sqrt[a + b]*d*Sqrt[c + d]*f*#1^2 + d^2*e*#1^3 + d^2*f*#1^3) & ])/f","C",1
2301,1,366,106,2.2376068,"\int \frac{\sqrt{1-2 x} (2+3 x)^3}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^3)/Sqrt[3 + 5*x],x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-738774000000 x^7+5498005500000 x^6+120611375572500 x^5+207580107564125 x^4+11969458822600 x^3-202369977582760 x^2-60001433411680 x+71662746224872\right)+\sqrt{5 x+3} \left(8377776000000 x^7+62946021600000 x^6-66836870100000 x^5-348154602235000 x^4-241990324937900 x^3+168726386810300 x^2+130547505974600 x-71662746224872\right)+\sqrt{3} \left(-514080000000 x^8-46965384000000 x^7-60061480200000 x^6+272086797170000 x^5+553899202115125 x^4+168950343313400 x^3-303788185400200 x^2+\sqrt{1-2 x} \left(3853872000000 x^7-60844687200000 x^6-262374407460000 x^5-253800976781000 x^4+114601770906700 x^3+278383679766060 x^2+22775620120 x-71662746224872\right)-70568848183040 x+71662746224872\right)}{64000 \sqrt{3} \sqrt{5 x+3} \left(8921000 x^3-162998000 x^2-220512160 x+287530496\right)+\sqrt{1-2 x} \left(64000 \left(-48482500 x^3-297203500 x^2+794989800 x+852279560\right)+64000 \sqrt{3} \sqrt{5 x+3} \left(595000 x^3+53178000 x^2-36412000 x-283051520\right)\right)+64000 \left(-8550625 x^4+79738000 x^3+1253327000 x^2-32289760 x-865716488\right)}+\frac{525371 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{32000 \sqrt{10}}","-\frac{3}{40} (1-2 x)^{3/2} \sqrt{5 x+3} (3 x+2)^2-\frac{21 (1-2 x)^{3/2} \sqrt{5 x+3} (216 x+335)}{6400}+\frac{47761 \sqrt{1-2 x} \sqrt{5 x+3}}{64000}+\frac{525371 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{64000 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(71662746224872 - 60001433411680*x - 202369977582760*x^2 + 11969458822600*x^3 + 207580107564125*x^4 + 120611375572500*x^5 + 5498005500000*x^6 - 738774000000*x^7) + Sqrt[3 + 5*x]*(-71662746224872 + 130547505974600*x + 168726386810300*x^2 - 241990324937900*x^3 - 348154602235000*x^4 - 66836870100000*x^5 + 62946021600000*x^6 + 8377776000000*x^7) + Sqrt[3]*(71662746224872 - 70568848183040*x - 303788185400200*x^2 + 168950343313400*x^3 + 553899202115125*x^4 + 272086797170000*x^5 - 60061480200000*x^6 - 46965384000000*x^7 - 514080000000*x^8 + Sqrt[1 - 2*x]*(-71662746224872 + 22775620120*x + 278383679766060*x^2 + 114601770906700*x^3 - 253800976781000*x^4 - 262374407460000*x^5 - 60844687200000*x^6 + 3853872000000*x^7)))/(64000*Sqrt[3]*Sqrt[3 + 5*x]*(287530496 - 220512160*x - 162998000*x^2 + 8921000*x^3) + 64000*(-865716488 - 32289760*x + 1253327000*x^2 + 79738000*x^3 - 8550625*x^4) + Sqrt[1 - 2*x]*(64000*(852279560 + 794989800*x - 297203500*x^2 - 48482500*x^3) + 64000*Sqrt[3]*Sqrt[3 + 5*x]*(-283051520 - 36412000*x + 53178000*x^2 + 595000*x^3))) + (525371*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(32000*Sqrt[10])","B",1
2302,1,306,99,1.9063398,"\int \frac{\sqrt{1-2 x} (2+3 x)^2}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^2)/Sqrt[3 + 5*x],x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(21540000 x^5+1452964500 x^4+1468303825 x^3-2257443795 x^2-1916166480 x+800745572\right)+\sqrt{5 x+3} \left(376200000 x^5-2478795000 x^4-5338193850 x^3+198877525 x^2+2612620340 x-800745572\right)+\sqrt{3} \left(-140400000 x^6+293130000 x^5+6098845500 x^4+6549289975 x^3-2827416375 x^2+\sqrt{1-2 x} \left(-550440000 x^5-2829717000 x^4-601175850 x^3+4270677345 x^2+1213951420 x-800745572\right)-1910405280 x+800745572\right)}{800 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right)+\sqrt{1-2 x} \left(800 \left(-391875 x^2+2827000 x+3481060\right)+800 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right)\right)+800 \left(44875 x^3+2976525 x^2-279060 x-3667684\right)}+\frac{3047 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{400 \sqrt{10}}","-\frac{1}{10} (3 x+2) \sqrt{5 x+3} (1-2 x)^{3/2}-\frac{23}{80} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{277}{800} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{3047 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{800 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(800745572 - 1916166480*x - 2257443795*x^2 + 1468303825*x^3 + 1452964500*x^4 + 21540000*x^5) + Sqrt[3 + 5*x]*(-800745572 + 2612620340*x + 198877525*x^2 - 5338193850*x^3 - 2478795000*x^4 + 376200000*x^5) + Sqrt[3]*(800745572 - 1910405280*x - 2827416375*x^2 + 6549289975*x^3 + 6098845500*x^4 + 293130000*x^5 - 140400000*x^6 + Sqrt[1 - 2*x]*(-800745572 + 1213951420*x + 4270677345*x^2 - 601175850*x^3 - 2829717000*x^4 - 550440000*x^5)))/(800*Sqrt[3]*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 800*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(800*(3481060 + 2827000*x - 391875*x^2) + 800*Sqrt[3]*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (3047*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(400*Sqrt[10])","B",1
2303,1,246,72,1.5929985,"\int \frac{\sqrt{1-2 x} (2+3 x)}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x))/Sqrt[3 + 5*x],x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-178500 x^3+76475 x^2+1017040 x+322102\right)+\sqrt{5 x+3} \left(858000 x^3+1404700 x^2-544170 x-322102\right)+\sqrt{3} \left(-60000 x^4-2561000 x^3-736625 x^2+\sqrt{1-2 x} \left(594000 x^3-1065900 x^2-1212750 x-322102\right)+739880 x+322102\right)}{200 \left(-2975 x^2+1820 x+16562\right)+200 \sqrt{3} \sqrt{5 x+3} (1980 x-5104)+\sqrt{1-2 x} \left(200 (-7150 x-13970)+200 \sqrt{3} \sqrt{5 x+3} (100 x+4240)\right)}+\frac{451 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{100 \sqrt{10}}","-\frac{3}{20} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{41}{200} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{451 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{200 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(322102 + 1017040*x + 76475*x^2 - 178500*x^3) + Sqrt[3 + 5*x]*(-322102 - 544170*x + 1404700*x^2 + 858000*x^3) + Sqrt[3]*(322102 + 739880*x - 736625*x^2 - 2561000*x^3 - 60000*x^4 + Sqrt[1 - 2*x]*(-322102 - 1212750*x - 1065900*x^2 + 594000*x^3)))/(200*Sqrt[3]*Sqrt[3 + 5*x]*(-5104 + 1980*x) + 200*(16562 + 1820*x - 2975*x^2) + Sqrt[1 - 2*x]*(200*(-13970 - 7150*x) + 200*Sqrt[3]*Sqrt[3 + 5*x]*(4240 + 100*x))) + (451*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(100*Sqrt[10])","B",1
2304,1,184,50,1.2431952,"\int \frac{\sqrt{1-2 x}}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/Sqrt[3 + 5*x],x]","\frac{\left(\frac{1}{5}-\frac{1}{5} \sqrt{1-2 x}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right) \left(10 x-55 \sqrt{1-2 x}+20 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}-22 \sqrt{3} \sqrt{5 x+3}+61\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}+\frac{11}{5} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{1}{5} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{11 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{5 \sqrt{10}}",1,"((1/5 - Sqrt[1 - 2*x]/5)*(Sqrt[3] - Sqrt[3 + 5*x])*(61 - 55*Sqrt[1 - 2*x] + 10*x - 22*Sqrt[3]*Sqrt[3 + 5*x] + 20*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2 + (11*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/5","B",1
2305,1,253,64,1.3296968,"\int \frac{\sqrt{1-2 x}}{(2+3 x) \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)*Sqrt[3 + 5*x]),x]","-\frac{7}{3} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]-\frac{4}{3} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{2}{3} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{2}{3} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(-4*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/3 - (7*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ])/3","C",1
2306,1,409,59,1.4438164,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^2 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^2*Sqrt[3 + 5*x]),x]","11 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{55}{2} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{3} \left(-185 x^2+263 x+(-385 x-242) \sqrt{1-2 x}+242\right)+\sqrt{5 x+3} (22 x-242)+\sqrt{1-2 x} \sqrt{5 x+3} (100 x+242)}{2 (5 x+91) (3 x+2)-44 \sqrt{3} \sqrt{5 x+3} (3 x+2)+\sqrt{1-2 x} \left(20 \sqrt{3} (3 x+2) \sqrt{5 x+3}-110 (3 x+2)\right)}","\frac{\sqrt{1-2 x} \sqrt{5 x+3}}{3 x+2}-\frac{11 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{\sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-242 + 22*x) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(242 + 100*x) + Sqrt[3]*(242 + (-242 - 385*x)*Sqrt[1 - 2*x] + 263*x - 185*x^2))/(-44*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x] + 2*(2 + 3*x)*(91 + 5*x) + Sqrt[1 - 2*x]*(-110*(2 + 3*x) + 20*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x])) + 11*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ] - (55*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2","C",1
2307,1,479,93,1.8467309,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^3 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^3*Sqrt[3 + 5*x]),x]","\frac{1177}{28} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{5885}{56} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-7359000 x^3-5911070 x^2+8542050 x+6442040\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(770775 x^3-6402280 x^2-13979258 x-6442040\right)+\sqrt{3} \left(1781625 x^4+14415100 x^3+1822570 x^2+\sqrt{1-2 x} \left(480150 x^3+15506370 x^2+19832208 x+6442040\right)-14395000 x-6442040\right)}{28 \left(2975 x^2-1820 x-16562\right) (3 x+2)^2+28 \sqrt{3} (5104-1980 x) \sqrt{5 x+3} (3 x+2)^2+\sqrt{1-2 x} \left(28 (7150 x+13970) (3 x+2)^2+28 \sqrt{3} (-100 x-4240) \sqrt{5 x+3} (3 x+2)^2\right)}","\frac{3 \sqrt{5 x+3} (1-2 x)^{3/2}}{14 (3 x+2)^2}+\frac{107 \sqrt{5 x+3} \sqrt{1-2 x}}{28 (3 x+2)}-\frac{1177 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{28 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(6442040 + 8542050*x - 5911070*x^2 - 7359000*x^3) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-6442040 - 13979258*x - 6402280*x^2 + 770775*x^3) + Sqrt[3]*(-6442040 - 14395000*x + 1822570*x^2 + 14415100*x^3 + 1781625*x^4 + Sqrt[1 - 2*x]*(6442040 + 19832208*x + 15506370*x^2 + 480150*x^3)))/(28*Sqrt[3]*(5104 - 1980*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 28*(2 + 3*x)^2*(-16562 - 1820*x + 2975*x^2) + Sqrt[1 - 2*x]*(28*Sqrt[3]*(-4240 - 100*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 28*(2 + 3*x)^2*(13970 + 7150*x))) + (1177*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/28 - (5885*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/56","C",1
2308,1,539,122,2.1332607,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^4 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^4*Sqrt[3 + 5*x]),x]","\frac{68959}{392} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{344795}{784} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-17524341450 x^5-594571304415 x^4-831654218934 x^3+61363000292 x^2+512007542728 x+183221924864\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(10091839875 x^5+154775277675 x^4-130313909530 x^3-771057112236 x^2-686662057416 x-183221924864\right)+\sqrt{3} \left(-11951860500 x^6+296690374350 x^5+1191238833510 x^4+914710283624 x^3-418213881432 x^2+\sqrt{1-2 x} \left(-96406620750 x^5-157246763850 x^4+576126141360 x^3+1276322630616 x^2+842216203136 x+183221924864\right)-667561688448 x-183221924864\right)}{392 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right) (3 x+2)^3+\sqrt{1-2 x} \left(392 \left(-391875 x^2+2827000 x+3481060\right) (3 x+2)^3+392 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right) (3 x+2)^3\right)+392 \left(44875 x^3+2976525 x^2-279060 x-3667684\right) (3 x+2)^3}","\frac{18083 \sqrt{1-2 x} \sqrt{5 x+3}}{1176 (3 x+2)}+\frac{173 \sqrt{1-2 x} \sqrt{5 x+3}}{84 (3 x+2)^2}+\frac{\sqrt{1-2 x} \sqrt{5 x+3}}{3 (3 x+2)^3}-\frac{68959 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{392 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(183221924864 + 512007542728*x + 61363000292*x^2 - 831654218934*x^3 - 594571304415*x^4 - 17524341450*x^5) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-183221924864 - 686662057416*x - 771057112236*x^2 - 130313909530*x^3 + 154775277675*x^4 + 10091839875*x^5) + Sqrt[3]*(-183221924864 - 667561688448*x - 418213881432*x^2 + 914710283624*x^3 + 1191238833510*x^4 + 296690374350*x^5 - 11951860500*x^6 + Sqrt[1 - 2*x]*(183221924864 + 842216203136*x + 1276322630616*x^2 + 576126141360*x^3 - 157246763850*x^4 - 96406620750*x^5)))/(392*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 392*(2 + 3*x)^3*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(392*(2 + 3*x)^3*(3481060 + 2827000*x - 391875*x^2) + 392*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (68959*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/392 - (344795*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/784","C",1
2309,1,599,151,2.5317274,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^5 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^5*Sqrt[3 + 5*x]),x]","\frac{16925425 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{21952}-\frac{84627125 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{43904}+\frac{\sqrt{5 x+3} \left(-5593251970746000 x^7-2882397080920500 x^6+147136254189243660 x^5+298516605889203064 x^4+140930219855548904 x^3-86199093016278176 x^2-93259200114387296 x-21772194890965376\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(226809473608125 x^7-13046511576123000 x^6-76725995957653500 x^5-59581086140378480 x^4+118447636215030920 x^3+208427636428824640 x^2+114728209877134048 x+21772194890965376\right)+\sqrt{3} \left(787245037891875 x^8+18091119162474000 x^7-61439189608395000 x^6-342439211256996080 x^5-424383489938952184 x^4-95480399537498624 x^3+156167319163349056 x^2+\sqrt{1-2 x} \left(1334504362702500 x^7+55253682801949500 x^6+133611700279325400 x^5+5934739084351880 x^4-258217841465499520 x^3-296357215215684480 x^2-132942216790438528 x-21772194890965376\right)+111473207027691776 x+21772194890965376\right)}{21952 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^4+\sqrt{1-2 x} \left(21952 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^4+21952 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^4\right)+21952 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^4}","\frac{1479375 \sqrt{1-2 x} \sqrt{5 x+3}}{21952 (3 x+2)}+\frac{14145 \sqrt{1-2 x} \sqrt{5 x+3}}{1568 (3 x+2)^2}+\frac{81 \sqrt{1-2 x} \sqrt{5 x+3}}{56 (3 x+2)^3}+\frac{\sqrt{1-2 x} \sqrt{5 x+3}}{4 (3 x+2)^4}-\frac{16925425 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{21952 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-21772194890965376 - 93259200114387296*x - 86199093016278176*x^2 + 140930219855548904*x^3 + 298516605889203064*x^4 + 147136254189243660*x^5 - 2882397080920500*x^6 - 5593251970746000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(21772194890965376 + 114728209877134048*x + 208427636428824640*x^2 + 118447636215030920*x^3 - 59581086140378480*x^4 - 76725995957653500*x^5 - 13046511576123000*x^6 + 226809473608125*x^7) + Sqrt[3]*(21772194890965376 + 111473207027691776*x + 156167319163349056*x^2 - 95480399537498624*x^3 - 424383489938952184*x^4 - 342439211256996080*x^5 - 61439189608395000*x^6 + 18091119162474000*x^7 + 787245037891875*x^8 + Sqrt[1 - 2*x]*(-21772194890965376 - 132942216790438528*x - 296357215215684480*x^2 - 258217841465499520*x^3 + 5934739084351880*x^4 + 133611700279325400*x^5 + 55253682801949500*x^6 + 1334504362702500*x^7)))/(21952*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 21952*(2 + 3*x)^4*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(21952*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 21952*(2 + 3*x)^4*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) + (16925425*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/21952 - (84627125*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/43904","C",1
2310,1,344,113,2.3324559,"\int \frac{\sqrt{1-2 x} (2+3 x)^3}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^3)/(3 + 5*x)^(3/2),x]","\frac{47601000000 x^7+789382125000 x^6-2011620791250 x^5-7547160902625 x^4-3441877183725 x^3+2798499984900 x^2+\sqrt{3} \sqrt{5 x+3} \left(-97297200000 x^6-7837830000 x^5+1299363565500 x^4+1448598033575 x^3-554196196400 x^2-417945548020 x+139216349624\right)+\sqrt{1-2 x} \left(74636100000 x^6+2093215162500 x^5+3517345495125 x^4-885649242225 x^3-3402328202460 x^2+\sqrt{3} \sqrt{5 x+3} \left(4379400000 x^6-199176435000 x^5-785512896750 x^4-290380241525 x^3+857878325520 x^2+290961655100 x-139216349624\right)-535085653740 x+417649048872\right)+916037332500 x-417649048872}{12000 \sqrt{1-2 x} \sqrt{5 x+3} \left(-1101875 x^3-16812750 x^2+68422100 x+77141440\right)+12000 \sqrt{5 x+3} \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right)+\sqrt{3} \left(12000 \sqrt{1-2 x} \left(11261250 x^3-7257250 x^2-135935800 x-76516440\right)+12000 \left(1013750 x^4-47347500 x^3-123624450 x^2+74349280 x+78755928\right)\right)}+\frac{10409 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{2000 \sqrt{10}}","-\frac{2 \sqrt{1-2 x} (3 x+2)^3}{5 \sqrt{5 x+3}}+\frac{7}{25} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2-\frac{7 (73-60 x) \sqrt{1-2 x} \sqrt{5 x+3}}{4000}+\frac{10409 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{4000 \sqrt{10}}",1,"(-417649048872 + 916037332500*x + 2798499984900*x^2 - 3441877183725*x^3 - 7547160902625*x^4 - 2011620791250*x^5 + 789382125000*x^6 + 47601000000*x^7 + Sqrt[3]*Sqrt[3 + 5*x]*(139216349624 - 417945548020*x - 554196196400*x^2 + 1448598033575*x^3 + 1299363565500*x^4 - 7837830000*x^5 - 97297200000*x^6) + Sqrt[1 - 2*x]*(417649048872 - 535085653740*x - 3402328202460*x^2 - 885649242225*x^3 + 3517345495125*x^4 + 2093215162500*x^5 + 74636100000*x^6 + Sqrt[3]*Sqrt[3 + 5*x]*(-139216349624 + 290961655100*x + 857878325520*x^2 - 290380241525*x^3 - 785512896750*x^4 - 199176435000*x^5 + 4379400000*x^6)))/(12000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(77141440 + 68422100*x - 16812750*x^2 - 1101875*x^3) + 12000*Sqrt[3 + 5*x]*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3) + Sqrt[3]*(12000*Sqrt[1 - 2*x]*(-76516440 - 135935800*x - 7257250*x^2 + 11261250*x^3) + 12000*(78755928 + 74349280*x - 123624450*x^2 - 47347500*x^3 + 1013750*x^4))) + (10409*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(2000*Sqrt[10])","B",1
2311,1,284,94,1.9003703,"\int \frac{\sqrt{1-2 x} (2+3 x)^2}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^2)/(3 + 5*x)^(3/2),x]","\frac{-12825000 x^5+228746250 x^4+442262625 x^3+104746275 x^2+\sqrt{3} \sqrt{5 x+3} \left(-5940000 x^4-110583000 x^3-48417875 x^2+32482450 x+19970324\right)+\sqrt{1-2 x} \left(-88357500 x^4-62877375 x^3+189655785 x^2+\sqrt{3} \sqrt{5 x+3} \left(3753000 x^4+35861850 x^3-28918445 x^2-55817190 x-19970324\right)+221433630 x+59910972\right)-151429410 x-59910972}{600 \sqrt{5 x+3} \left(-163625 x^2+33550 x+343904\right)+600 \sqrt{1-2 x} \sqrt{5 x+3} \left(11875 x^2-216750 x-312800\right)+\sqrt{3} \left(600 \sqrt{1-2 x} \left(27500 x^2+517000 x+300300\right)+600 \left(34750 x^3+321050 x^2-372220 x-331404\right)\right)}+\frac{317 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{100 \sqrt{10}}","-\frac{9}{100} \sqrt{5 x+3} (1-2 x)^{3/2}-\frac{2 (1-2 x)^{3/2}}{275 \sqrt{5 x+3}}+\frac{317 \sqrt{5 x+3} \sqrt{1-2 x}}{2200}+\frac{317 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{200 \sqrt{10}}",1,"(-59910972 - 151429410*x + 104746275*x^2 + 442262625*x^3 + 228746250*x^4 - 12825000*x^5 + Sqrt[3]*Sqrt[3 + 5*x]*(19970324 + 32482450*x - 48417875*x^2 - 110583000*x^3 - 5940000*x^4) + Sqrt[1 - 2*x]*(59910972 + 221433630*x + 189655785*x^2 - 62877375*x^3 - 88357500*x^4 + Sqrt[3]*Sqrt[3 + 5*x]*(-19970324 - 55817190*x - 28918445*x^2 + 35861850*x^3 + 3753000*x^4)))/(600*Sqrt[3 + 5*x]*(343904 + 33550*x - 163625*x^2) + 600*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-312800 - 216750*x + 11875*x^2) + Sqrt[3]*(600*Sqrt[1 - 2*x]*(300300 + 517000*x + 27500*x^2) + 600*(-331404 - 372220*x + 321050*x^2 + 34750*x^3))) + (317*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(100*Sqrt[10])","B",1
2312,1,226,72,1.5949399,"\int \frac{\sqrt{1-2 x} (2+3 x)}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x))/(3 + 5*x)^(3/2),x]","\frac{29250 x^3+120075 x^2+\sqrt{3} \sqrt{5 x+3} \left(-29700 x^2+2145 x+18634\right)+\sqrt{1-2 x} \left(7425 x^2+\sqrt{3} \sqrt{5 x+3} \left(4050 x^2-21715 x-18634\right)+113355 x+55902\right)-54645 x-55902}{\sqrt{3} \left(75 \left(450 x^2-2100 x-1422\right)+75 \sqrt{1-2 x} (1650 x+990)\right)+75 \sqrt{1-2 x} \sqrt{5 x+3} (-325 x-1240)+75 \sqrt{5 x+3} (165 x+1672)}+\frac{29}{25} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{2 (1-2 x)^{3/2}}{55 \sqrt{5 x+3}}+\frac{29}{275} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{29 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{25 \sqrt{10}}",1,"(-55902 - 54645*x + 120075*x^2 + 29250*x^3 + Sqrt[3]*Sqrt[3 + 5*x]*(18634 + 2145*x - 29700*x^2) + Sqrt[1 - 2*x]*(55902 + 113355*x + 7425*x^2 + Sqrt[3]*Sqrt[3 + 5*x]*(-18634 - 21715*x + 4050*x^2)))/(75*(-1240 - 325*x)*Sqrt[1 - 2*x]*Sqrt[3 + 5*x] + 75*Sqrt[3 + 5*x]*(1672 + 165*x) + Sqrt[3]*(75*Sqrt[1 - 2*x]*(990 + 1650*x) + 75*(-1422 - 2100*x + 450*x^2))) + (29*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/25","B",1
2313,1,151,52,1.2430795,"\int \frac{\sqrt{1-2 x}}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/(3 + 5*x)^(3/2),x]","\frac{\sqrt{3} \left(22 \sqrt{1-2 x}-22\right)-22 \sqrt{1-2 x} \sqrt{5 x+3}+22 \sqrt{5 x+3}}{\sqrt{3} \sqrt{5 x+3} \left(25 \sqrt{1-2 x}-55\right)+5 (30 x+18)}-\frac{4}{5} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{2 \sqrt{1-2 x}}{5 \sqrt{5 x+3}}-\frac{2}{5} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"(Sqrt[3]*(-22 + 22*Sqrt[1 - 2*x]) + 22*Sqrt[3 + 5*x] - 22*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(Sqrt[3]*(-55 + 25*Sqrt[1 - 2*x])*Sqrt[3 + 5*x] + 5*(18 + 30*x)) - (4*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/5","B",1
2314,1,270,53,1.2632779,"\int \frac{\sqrt{1-2 x}}{(2+3 x) (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)*(3 + 5*x)^(3/2)),x]","7 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{\left(22 \sqrt{1-2 x}-22\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)}{30 x+5 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{3} \sqrt{5 x+3}+18}","2 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-\frac{2 \sqrt{1-2 x}}{\sqrt{5 x+3}}",1,"((-22 + 22*Sqrt[1 - 2*x])*(Sqrt[3] - Sqrt[3 + 5*x]))/(18 + 30*x - 11*Sqrt[3]*Sqrt[3 + 5*x] + 5*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]) + 7*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ]","C",1
2315,1,449,84,1.8261746,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^2 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^2*(3 + 5*x)^(3/2)),x]","-103 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{515}{2} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(3975 x^2+239050 x+154396\right)+\sqrt{5 x+3} \left(163845 x^2-129294 x-154396\right)+\sqrt{3} \left(-97650 x^3-75050 x^2+\sqrt{1-2 x} \left(-158400 x^2-341880 x-154396\right)+232124 x+154396\right)}{2 (3 x+2) \left(1350 x^2-6300 x-4266\right)+2 \sqrt{3} (3 x+2) \sqrt{5 x+3} (165 x+1672)+\sqrt{1-2 x} \left(2 (4950 x+2970) (3 x+2)+2 \sqrt{3} (-325 x-1240) \sqrt{5 x+3} (3 x+2)\right)}","\frac{3 (1-2 x)^{3/2}}{7 (3 x+2) \sqrt{5 x+3}}-\frac{103 \sqrt{1-2 x}}{7 \sqrt{5 x+3}}+\frac{103 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{\sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(154396 + 239050*x + 3975*x^2) + Sqrt[3 + 5*x]*(-154396 - 129294*x + 163845*x^2) + Sqrt[3]*(154396 + 232124*x - 75050*x^2 - 97650*x^3 + Sqrt[1 - 2*x]*(-154396 - 341880*x - 158400*x^2)))/(2*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(1672 + 165*x) + 2*(2 + 3*x)*(-4266 - 6300*x + 1350*x^2) + Sqrt[1 - 2*x]*(2*Sqrt[3]*(-1240 - 325*x)*(2 + 3*x)*Sqrt[3 + 5*x] + 2*(2 + 3*x)*(2970 + 4950*x))) - 103*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ] + (515*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2","C",1
2316,1,519,115,2.1689792,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^3 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^3*(3 + 5*x)^(3/2)),x]","-\frac{17951}{28} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{89755}{56} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-760564125 x^4-316744800 x^3+15586292320 x^2+20075261844 x+6506460400\right)+\sqrt{5 x+3} \left(4495033125 x^4+18960620250 x^3+4112478700 x^2-14127294500 x-6506460400\right)+\sqrt{3} \left(-230737500 x^5-18097738125 x^4-24747218125 x^3+5812757550 x^2+\sqrt{1-2 x} \left(3225976875 x^4-8322043125 x^3-30243722190 x^2-25272866344 x-6506460400\right)+19324899000 x+6506460400\right)}{28 \sqrt{3} \sqrt{5 x+3} \left(-163625 x^2+33550 x+343904\right) (3 x+2)^2+\sqrt{1-2 x} \left(28 \sqrt{3} \sqrt{5 x+3} \left(11875 x^2-216750 x-312800\right) (3 x+2)^2+28 \left(82500 x^2+1551000 x+900900\right) (3 x+2)^2\right)+28 \left(104250 x^3+963150 x^2-1116660 x-994212\right) (3 x+2)^2}","-\frac{2615 \sqrt{1-2 x}}{28 \sqrt{5 x+3}}+\frac{173 \sqrt{1-2 x}}{28 (3 x+2) \sqrt{5 x+3}}+\frac{\sqrt{1-2 x}}{2 (3 x+2)^2 \sqrt{5 x+3}}+\frac{17951 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{28 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(6506460400 + 20075261844*x + 15586292320*x^2 - 316744800*x^3 - 760564125*x^4) + Sqrt[3 + 5*x]*(-6506460400 - 14127294500*x + 4112478700*x^2 + 18960620250*x^3 + 4495033125*x^4) + Sqrt[3]*(6506460400 + 19324899000*x + 5812757550*x^2 - 24747218125*x^3 - 18097738125*x^4 - 230737500*x^5 + Sqrt[1 - 2*x]*(-6506460400 - 25272866344*x - 30243722190*x^2 - 8322043125*x^3 + 3225976875*x^4)))/(28*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(343904 + 33550*x - 163625*x^2) + 28*(2 + 3*x)^2*(-994212 - 1116660*x + 963150*x^2 + 104250*x^3) + Sqrt[1 - 2*x]*(28*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(-312800 - 216750*x + 11875*x^2) + 28*(2 + 3*x)^2*(900900 + 1551000*x + 82500*x^2))) - (17951*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/28 + (89755*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/56","C",1
2317,1,579,144,2.5214927,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^4 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^4*(3 + 5*x)^(3/2)),x]","-\frac{1463447}{392} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{7317235}{784} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(2622670447500 x^6+264383933769000 x^5+465390886645350 x^4-653374583049220 x^3-1759102850488488 x^2-1181427108597968 x-256716819475072\right)+\sqrt{5 x+3} \left(58581172707750 x^6-523776305641050 x^5-2008006608949110 x^4-1548360718304972 x^3+512680674307736 x^2+931265179426384 x+256716819475072\right)+\sqrt{3} \left(-18319015676250 x^7+39572591383125 x^6+1703465401242825 x^5+3306114877150620 x^4+1362656151594992 x^3-1203865855053656 x^2+\sqrt{1-2 x} \left(-82475247999375 x^6-645691997498625 x^5-279745648320600 x^4+1792427140336360 x^3+2656926955960728 x^2+1393528441910528 x+256716819475072\right)-1143366512738944 x-256716819475072\right)}{392 \sqrt{3} \sqrt{5 x+3} \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (3 x+2)^3+\sqrt{1-2 x} \left(392 \sqrt{3} \sqrt{5 x+3} \left(-1101875 x^3-16812750 x^2+68422100 x+77141440\right) (3 x+2)^3+392 \left(33783750 x^3-21771750 x^2-407807400 x-229549320\right) (3 x+2)^3\right)+392 \left(3041250 x^4-142042500 x^3-370873350 x^2+223047840 x+236267784\right) (3 x+2)^3}","-\frac{639565 \sqrt{1-2 x}}{1176 \sqrt{5 x+3}}+\frac{14101 \sqrt{1-2 x}}{392 (3 x+2) \sqrt{5 x+3}}+\frac{81 \sqrt{1-2 x}}{28 (3 x+2)^2 \sqrt{5 x+3}}+\frac{\sqrt{1-2 x}}{3 (3 x+2)^3 \sqrt{5 x+3}}+\frac{1463447 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{392 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-256716819475072 - 1181427108597968*x - 1759102850488488*x^2 - 653374583049220*x^3 + 465390886645350*x^4 + 264383933769000*x^5 + 2622670447500*x^6) + Sqrt[3 + 5*x]*(256716819475072 + 931265179426384*x + 512680674307736*x^2 - 1548360718304972*x^3 - 2008006608949110*x^4 - 523776305641050*x^5 + 58581172707750*x^6) + Sqrt[3]*(-256716819475072 - 1143366512738944*x - 1203865855053656*x^2 + 1362656151594992*x^3 + 3306114877150620*x^4 + 1703465401242825*x^5 + 39572591383125*x^6 - 18319015676250*x^7 + Sqrt[1 - 2*x]*(256716819475072 + 1393528441910528*x + 2656926955960728*x^2 + 1792427140336360*x^3 - 279745648320600*x^4 - 645691997498625*x^5 - 82475247999375*x^6)))/(392*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3) + 392*(2 + 3*x)^3*(236267784 + 223047840*x - 370873350*x^2 - 142042500*x^3 + 3041250*x^4) + Sqrt[1 - 2*x]*(392*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(77141440 + 68422100*x - 16812750*x^2 - 1101875*x^3) + 392*(2 + 3*x)^3*(-229549320 - 407807400*x - 21771750*x^2 + 33783750*x^3))) - (1463447*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/392 + (7317235*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/784","C",1
2318,1,414,142,2.770865,"\int \frac{\sqrt{1-2 x} (2+3 x)^4}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^4)/(3 + 5*x)^(5/2),x]","\frac{-145235025000000 x^9+14507792094375000 x^8+84722024806031250 x^7+13615340893846875 x^6-303681341586330000 x^5-307933466824990125 x^4+12394330305018300 x^3+92622594170646900 x^2+\sqrt{3} \sqrt{5 x+3} \left(-343533960000000 x^8-12326734629000000 x^7-18556048194750000 x^6+41116221855658125 x^5+83618044018686375 x^4+14995371994772400 x^3-25790953563094500 x^2-5264847727051000 x+2252856963436464\right)+\sqrt{1-2 x} \left(-2468428627500000 x^8+2156134185562500 x^7+112323130538540625 x^6+254191628559453750 x^5+111886050494926125 x^4-118114723303483500 x^3-95423653702054260 x^2+\sqrt{3} \sqrt{5 x+3} \left(67217445000000 x^8+1532837408625000 x^7-10812571589643750 x^6-48446210042249375 x^5-43606996262408375 x^4+17277041588012400 x^3+28522424002030420 x^2+3089484456640840 x-2252856963436464\right)-3681367351956360 x+6758570890309392\right)+10207457163186840 x-6758570890309392}{540000 \left(-846511875 x^4+2876857500 x^3+32771841300 x^2-464036760 x-18959828096\right) (5 x+3)^{3/2}+540000 \sqrt{1-2 x} \left(24903125 x^4-2538047500 x^3-9400717500 x^2+18053298200 x+18798584960\right) (5 x+3)^{3/2}+\sqrt{3} \left(540000 \sqrt{1-2 x} (5 x+3) \left(294525000 x^4+10148490000 x^3+1543311000 x^2-33942744000 x-18767334960\right)+540000 (5 x+3) \left(115256250 x^5+2406453750 x^4-23245830000 x^3-39836473200 x^2+16519101840 x+18928578096\right)\right)}+\frac{35511 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{10000 \sqrt{10}}","-\frac{2 \sqrt{1-2 x} (3 x+2)^4}{15 (5 x+3)^{3/2}}-\frac{524 \sqrt{1-2 x} (3 x+2)^3}{825 \sqrt{5 x+3}}+\frac{623 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2}{1375}+\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} (8940 x+2563)}{220000}+\frac{35511 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{20000 \sqrt{10}}",1,"(-6758570890309392 + 10207457163186840*x + 92622594170646900*x^2 + 12394330305018300*x^3 - 307933466824990125*x^4 - 303681341586330000*x^5 + 13615340893846875*x^6 + 84722024806031250*x^7 + 14507792094375000*x^8 - 145235025000000*x^9 + Sqrt[3]*Sqrt[3 + 5*x]*(2252856963436464 - 5264847727051000*x - 25790953563094500*x^2 + 14995371994772400*x^3 + 83618044018686375*x^4 + 41116221855658125*x^5 - 18556048194750000*x^6 - 12326734629000000*x^7 - 343533960000000*x^8) + Sqrt[1 - 2*x]*(6758570890309392 - 3681367351956360*x - 95423653702054260*x^2 - 118114723303483500*x^3 + 111886050494926125*x^4 + 254191628559453750*x^5 + 112323130538540625*x^6 + 2156134185562500*x^7 - 2468428627500000*x^8 + Sqrt[3]*Sqrt[3 + 5*x]*(-2252856963436464 + 3089484456640840*x + 28522424002030420*x^2 + 17277041588012400*x^3 - 43606996262408375*x^4 - 48446210042249375*x^5 - 10812571589643750*x^6 + 1532837408625000*x^7 + 67217445000000*x^8)))/(540000*(3 + 5*x)^(3/2)*(-18959828096 - 464036760*x + 32771841300*x^2 + 2876857500*x^3 - 846511875*x^4) + 540000*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)*(18798584960 + 18053298200*x - 9400717500*x^2 - 2538047500*x^3 + 24903125*x^4) + Sqrt[3]*(540000*Sqrt[1 - 2*x]*(3 + 5*x)*(-18767334960 - 33942744000*x + 1543311000*x^2 + 10148490000*x^3 + 294525000*x^4) + 540000*(3 + 5*x)*(18928578096 + 16519101840*x - 39836473200*x^2 - 23245830000*x^3 + 2406453750*x^4 + 115256250*x^5))) + (35511*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(10000*Sqrt[10])","B",1
2319,1,354,113,2.3822847,"\int \frac{\sqrt{1-2 x} (2+3 x)^3}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^3)/(3 + 5*x)^(5/2),x]","\frac{160653375000 x^7+2636050331250 x^6-7137419803125 x^5-23449972981500 x^4-16282432964925 x^3+2525769805200 x^2+\sqrt{3} \sqrt{5 x+3} \left(-328378050000 x^6+31013482500 x^5+4199579085625 x^4+4869208126475 x^3+246180711700 x^2-1549747455740 x-491799506088\right)+\sqrt{1-2 x} \left(251896837500 x^6+7020519226875 x^5+10972354065750 x^4-690109854225 x^3-11171962499280 x^2+\sqrt{3} \sqrt{5 x+3} \left(14780475000 x^6-674807051250 x^5-2529872972125 x^4-1050251592225 x^3+2202280431460 x^2+2062915036580 x+491799506088\right)-7436134187460 x-1475398518264\right)+5896631444940 x+1475398518264}{27000 \sqrt{1-2 x} \left(-1101875 x^3-16812750 x^2+68422100 x+77141440\right) (5 x+3)^{3/2}+27000 \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (5 x+3)^{3/2}+\sqrt{3} \left(27000 \sqrt{1-2 x} (5 x+3) \left(11261250 x^3-7257250 x^2-135935800 x-76516440\right)+27000 (5 x+3) \left(1013750 x^4-47347500 x^3-123624450 x^2+74349280 x+78755928\right)\right)}+\frac{1071 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{500 \sqrt{10}}","-\frac{2 \sqrt{1-2 x} (3 x+2)^3}{15 (5 x+3)^{3/2}}-\frac{392 \sqrt{1-2 x} (3 x+2)^2}{825 \sqrt{5 x+3}}+\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} (1740 x+1243)}{11000}+\frac{1071 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{1000 \sqrt{10}}",1,"(1475398518264 + 5896631444940*x + 2525769805200*x^2 - 16282432964925*x^3 - 23449972981500*x^4 - 7137419803125*x^5 + 2636050331250*x^6 + 160653375000*x^7 + Sqrt[3]*Sqrt[3 + 5*x]*(-491799506088 - 1549747455740*x + 246180711700*x^2 + 4869208126475*x^3 + 4199579085625*x^4 + 31013482500*x^5 - 328378050000*x^6) + Sqrt[1 - 2*x]*(-1475398518264 - 7436134187460*x - 11171962499280*x^2 - 690109854225*x^3 + 10972354065750*x^4 + 7020519226875*x^5 + 251896837500*x^6 + Sqrt[3]*Sqrt[3 + 5*x]*(491799506088 + 2062915036580*x + 2202280431460*x^2 - 1050251592225*x^3 - 2529872972125*x^4 - 674807051250*x^5 + 14780475000*x^6)))/(27000*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)*(77141440 + 68422100*x - 16812750*x^2 - 1101875*x^3) + 27000*(3 + 5*x)^(3/2)*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3) + Sqrt[3]*(27000*Sqrt[1 - 2*x]*(3 + 5*x)*(-76516440 - 135935800*x - 7257250*x^2 + 11261250*x^3) + 27000*(3 + 5*x)*(78755928 + 74349280*x - 123624450*x^2 - 47347500*x^3 + 1013750*x^4))) + (1071*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(500*Sqrt[10])","B",1
2320,1,296,94,1.9538454,"\int \frac{\sqrt{1-2 x} (2+3 x)^2}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^2)/(3 + 5*x)^(5/2),x]","\frac{-5771250 x^5+105619875 x^4+227014050 x^3+24035025 x^2+\sqrt{3} \sqrt{5 x+3} \left(-2673000 x^4-54202225 x^3-22225225 x^2+23132230 x+10365828\right)+\sqrt{1-2 x} \left(-39760875 x^4-26852100 x^3+126223647 x^2+\sqrt{3} \sqrt{5 x+3} \left(1688850 x^4+16488995 x^3-18473619 x^2-34104586 x-10365828\right)+128959578 x+31097484\right)-96042510 x-31097484}{135 \left(-163625 x^2+33550 x+343904\right) (5 x+3)^{3/2}+135 \sqrt{1-2 x} \left(11875 x^2-216750 x-312800\right) (5 x+3)^{3/2}+\sqrt{3} \left(135 \sqrt{1-2 x} (5 x+3) \left(27500 x^2+517000 x+300300\right)+135 (5 x+3) \left(34750 x^3+321050 x^2-372220 x-331404\right)\right)}+\frac{3}{5} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{12 (1-2 x)^{3/2}}{275 \sqrt{5 x+3}}-\frac{2 (1-2 x)^{3/2}}{825 (5 x+3)^{3/2}}+\frac{3}{55} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{3 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{5 \sqrt{10}}",1,"(-31097484 - 96042510*x + 24035025*x^2 + 227014050*x^3 + 105619875*x^4 - 5771250*x^5 + Sqrt[3]*Sqrt[3 + 5*x]*(10365828 + 23132230*x - 22225225*x^2 - 54202225*x^3 - 2673000*x^4) + Sqrt[1 - 2*x]*(31097484 + 128959578*x + 126223647*x^2 - 26852100*x^3 - 39760875*x^4 + Sqrt[3]*Sqrt[3 + 5*x]*(-10365828 - 34104586*x - 18473619*x^2 + 16488995*x^3 + 1688850*x^4)))/(135*(3 + 5*x)^(3/2)*(343904 + 33550*x - 163625*x^2) + 135*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)*(-312800 - 216750*x + 11875*x^2) + Sqrt[3]*(135*Sqrt[1 - 2*x]*(3 + 5*x)*(300300 + 517000*x + 27500*x^2) + 135*(3 + 5*x)*(-331404 - 372220*x + 321050*x^2 + 34750*x^3))) + (3*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/5","B",1
2321,1,244,74,1.6899264,"\int \frac{\sqrt{1-2 x} (2+3 x)}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x))/(3 + 5*x)^(5/2),x]","\frac{-2 \sqrt{3} \sqrt{5 x+3} \left(-239250 x^2+210980 x+219252\right)+\sqrt{1-2 x} \left(-2 \sqrt{3} \sqrt{5 x+3} \left(-8900 x^2-362840 x-219252\right)-2 \left(744975 x^2+1519650 x+657756\right)\right)-2 \left(443250 x^3+262125 x^2-1064070 x-657756\right)}{\sqrt{3} \left(675 (5 x+3) \left(450 x^2-2100 x-1422\right)+675 \sqrt{1-2 x} (5 x+3) (1650 x+990)\right)+675 (165 x+1672) (5 x+3)^{3/2}+675 (-325 x-1240) \sqrt{1-2 x} (5 x+3)^{3/2}}-\frac{12}{25} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{2 (1-2 x)^{3/2}}{165 (5 x+3)^{3/2}}-\frac{6 \sqrt{1-2 x}}{25 \sqrt{5 x+3}}-\frac{6}{25} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"(-2*Sqrt[3]*Sqrt[3 + 5*x]*(219252 + 210980*x - 239250*x^2) - 2*(-657756 - 1064070*x + 262125*x^2 + 443250*x^3) + Sqrt[1 - 2*x]*(-2*Sqrt[3]*Sqrt[3 + 5*x]*(-219252 - 362840*x - 8900*x^2) - 2*(657756 + 1519650*x + 744975*x^2)))/(675*(-1240 - 325*x)*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2) + 675*(3 + 5*x)^(3/2)*(1672 + 165*x) + Sqrt[3]*(675*Sqrt[1 - 2*x]*(3 + 5*x)*(990 + 1650*x) + 675*(3 + 5*x)*(-1422 - 2100*x + 450*x^2))) - (12*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/25","B",1
2322,1,258,22,1.3065181,"\int \frac{\sqrt{1-2 x}}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/(3 + 5*x)^(5/2),x]","\frac{\left(\frac{1}{54}-\frac{1}{54} \sqrt{1-2 x}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^6 \left(\frac{225 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4}-\frac{90 \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}-\frac{56 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{36 \sqrt{1-2 x}-36}{\sqrt{3}-\sqrt{5 x+3}}+36 \sqrt{3}\right)}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(10 \sqrt{3} x+5 \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{5 x+3}+6 \sqrt{3}\right)^3}","-\frac{2 (1-2 x)^{3/2}}{33 (5 x+3)^{3/2}}",1,"((1/54 - Sqrt[1 - 2*x]/54)*(Sqrt[3] - Sqrt[3 + 5*x])^6*(36*Sqrt[3] + (225*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^4 - (90*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 - (56*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^2 + (-36 + 36*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x])))/((-Sqrt[3] + Sqrt[3 + 5*x])*(6*Sqrt[3] + 10*Sqrt[3]*x - 11*Sqrt[3 + 5*x] + 5*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3)","B",1
2323,1,374,75,1.6749209,"\int \frac{\sqrt{1-2 x}}{(2+3 x) (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)*(3 + 5*x)^(5/2)),x]","\frac{2 \sqrt{3} \sqrt{5 x+3} \left(-250800 x^2+213730 x+211992\right)+\sqrt{1-2 x} \left(2 \sqrt{3} \sqrt{5 x+3} \left(-5950 x^2-364810 x-211992\right)+2 \left(725175 x^2+1518660 x+635976\right)\right)+2 \left(447750 x^3+317025 x^2-1065420 x-635976\right)}{\sqrt{3} \left(27 (5 x+3) \left(450 x^2-2100 x-1422\right)+27 \sqrt{1-2 x} (5 x+3) (1650 x+990)\right)+27 (165 x+1672) (5 x+3)^{3/2}+27 (-325 x-1240) \sqrt{1-2 x} (5 x+3)^{3/2}}-21 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]","-\frac{10 (1-2 x)^{3/2}}{33 (5 x+3)^{3/2}}+\frac{6 \sqrt{1-2 x}}{\sqrt{5 x+3}}-6 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(2*Sqrt[3]*Sqrt[3 + 5*x]*(211992 + 213730*x - 250800*x^2) + 2*(-635976 - 1065420*x + 317025*x^2 + 447750*x^3) + Sqrt[1 - 2*x]*(2*Sqrt[3]*Sqrt[3 + 5*x]*(-211992 - 364810*x - 5950*x^2) + 2*(635976 + 1518660*x + 725175*x^2)))/(27*(-1240 - 325*x)*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2) + 27*(3 + 5*x)^(3/2)*(1672 + 165*x) + Sqrt[3]*(27*Sqrt[1 - 2*x]*(3 + 5*x)*(990 + 1650*x) + 27*(3 + 5*x)*(-1422 - 2100*x + 450*x^2))) - 21*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ]","C",1
2324,1,517,103,2.181188,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^2 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^2*(3 + 5*x)^(5/2)),x]","519 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{2595}{2} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{600153750 x^5+47049800250 x^4+61282285350 x^3-17337803610 x^2+\sqrt{3} \sqrt{5 x+3} \left(-3898475625 x^4-16185599375 x^3-2644827020 x^2+11874881348 x+5078552952\right)+\sqrt{1-2 x} \left(-8394581250 x^4+22210485000 x^3+76873927350 x^2+\sqrt{3} \sqrt{5 x+3} \left(659664375 x^4+231249625 x^3-13506684300 x^2-16517667260 x-5078552952\right)+61724009160 x+15235658856\right)-47795651424 x-15235658856}{54 (3 x+2) \left(-163625 x^2+33550 x+343904\right) (5 x+3)^{3/2}+54 \sqrt{1-2 x} (3 x+2) \left(11875 x^2-216750 x-312800\right) (5 x+3)^{3/2}+\sqrt{3} \left(54 \sqrt{1-2 x} (3 x+2) (5 x+3) \left(27500 x^2+517000 x+300300\right)+54 (3 x+2) (5 x+3) \left(34750 x^3+321050 x^2-372220 x-331404\right)\right)}","\frac{2495 \sqrt{1-2 x}}{33 \sqrt{5 x+3}}-\frac{25 \sqrt{1-2 x}}{3 (5 x+3)^{3/2}}+\frac{\sqrt{1-2 x}}{(3 x+2) (5 x+3)^{3/2}}-\frac{519 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{\sqrt{7}}",1,"(-15235658856 - 47795651424*x - 17337803610*x^2 + 61282285350*x^3 + 47049800250*x^4 + 600153750*x^5 + Sqrt[3]*Sqrt[3 + 5*x]*(5078552952 + 11874881348*x - 2644827020*x^2 - 16185599375*x^3 - 3898475625*x^4) + Sqrt[1 - 2*x]*(15235658856 + 61724009160*x + 76873927350*x^2 + 22210485000*x^3 - 8394581250*x^4 + Sqrt[3]*Sqrt[3 + 5*x]*(-5078552952 - 16517667260*x - 13506684300*x^2 + 231249625*x^3 + 659664375*x^4)))/(54*(2 + 3*x)*(3 + 5*x)^(3/2)*(343904 + 33550*x - 163625*x^2) + 54*Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^(3/2)*(-312800 - 216750*x + 11875*x^2) + Sqrt[3]*(54*Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)*(300300 + 517000*x + 27500*x^2) + 54*(2 + 3*x)*(3 + 5*x)*(-331404 - 372220*x + 321050*x^2 + 34750*x^3))) + 519*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ] - (2595*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2","C",1
2325,1,587,137,2.6301724,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^3 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^3*(3 + 5*x)^(5/2)),x]","\frac{126513}{28} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{632565}{56} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{71264297812500 x^7-158688749221875 x^6-6613340524282500 x^5-12428547938017875 x^4-4732130295242550 x^3+4657382439707940 x^2+\sqrt{3} \sqrt{5 x+3} \left(-75964150040625 x^6+684255656555625 x^5+2555177495967250 x^4+1866652668311750 x^3-704553055096880 x^2-1136772505881320 x-299601010774560\right)+\sqrt{1-2 x} \left(320842643034375 x^6+2490472847362500 x^5+935087716938375 x^4-6943246496424150 x^3-9890763000864900 x^2+\sqrt{3} \sqrt{5 x+3} \left(-3400838128125 x^6-342606885920625 x^5-580783730392000 x^4+872336548459350 x^3+2207855333183560 x^2+1428723853390088 x+299601010774560\right)-5028769445231664 x-898803032323680\right)+4152915402705360 x+898803032323680}{756 \sqrt{1-2 x} (5 x+3)^{3/2} \left(-1101875 x^3-16812750 x^2+68422100 x+77141440\right) (3 x+2)^2+756 (5 x+3)^{3/2} \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (3 x+2)^2+\sqrt{3} \left(756 \sqrt{1-2 x} (5 x+3) \left(11261250 x^3-7257250 x^2-135935800 x-76516440\right) (3 x+2)^2+756 (5 x+3) \left(1013750 x^4-47347500 x^3-123624450 x^2+74349280 x+78755928\right) (3 x+2)^2\right)}","\frac{608185 \sqrt{1-2 x}}{924 \sqrt{5 x+3}}-\frac{6095 \sqrt{1-2 x}}{84 (5 x+3)^{3/2}}+\frac{243 \sqrt{1-2 x}}{28 (3 x+2) (5 x+3)^{3/2}}+\frac{\sqrt{1-2 x}}{2 (3 x+2)^2 (5 x+3)^{3/2}}-\frac{126513 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{28 \sqrt{7}}",1,"(898803032323680 + 4152915402705360*x + 4657382439707940*x^2 - 4732130295242550*x^3 - 12428547938017875*x^4 - 6613340524282500*x^5 - 158688749221875*x^6 + 71264297812500*x^7 + Sqrt[3]*Sqrt[3 + 5*x]*(-299601010774560 - 1136772505881320*x - 704553055096880*x^2 + 1866652668311750*x^3 + 2555177495967250*x^4 + 684255656555625*x^5 - 75964150040625*x^6) + Sqrt[1 - 2*x]*(-898803032323680 - 5028769445231664*x - 9890763000864900*x^2 - 6943246496424150*x^3 + 935087716938375*x^4 + 2490472847362500*x^5 + 320842643034375*x^6 + Sqrt[3]*Sqrt[3 + 5*x]*(299601010774560 + 1428723853390088*x + 2207855333183560*x^2 + 872336548459350*x^3 - 580783730392000*x^4 - 342606885920625*x^5 - 3400838128125*x^6)))/(756*Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^(3/2)*(77141440 + 68422100*x - 16812750*x^2 - 1101875*x^3) + 756*(2 + 3*x)^2*(3 + 5*x)^(3/2)*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3) + Sqrt[3]*(756*Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)*(-76516440 - 135935800*x - 7257250*x^2 + 11261250*x^3) + 756*(2 + 3*x)^2*(3 + 5*x)*(78755928 + 74349280*x - 123624450*x^2 - 47347500*x^3 + 1013750*x^4))) + (126513*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/28 - (632565*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/56","C",1
2326,1,647,166,3.0930161,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^4 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^4*(3 + 5*x)^(5/2)),x]","\frac{13246251}{392} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{66231255}{784} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{432394474643156250 x^9+53352633496057396875 x^8+92619640078708623750 x^7-574939098670127576625 x^6-1612574522371066053150 x^5-1326140439142074608700 x^4-29914152438333697632 x^3+528020531112124544976 x^2+\sqrt{3} \sqrt{5 x+3} \left(-2744862761133900000 x^8-28246715446022865000 x^7+39461417818079103000 x^6+286633361672028934200 x^5+352214950606728223080 x^4+81965325488462627904 x^3-114383908255166198352 x^2-80202095175626402528 x-15182645340392454144\right)+\sqrt{1-2 x} \left(-3953882984434453125 x^8+79004740287447562500 x^7+462578357365368316875 x^6+608521158040073429250 x^5-171503887693081254300 x^4-993819004145829108720 x^3-869705789227100633808 x^2+\sqrt{3} \sqrt{5 x+3} \left(218505856308468750 x^8-1892875150413450000 x^7-61868567390387006250 x^6-145214660029181702500 x^5-40645903825977088000 x^4+180016895510980222560 x^3+215745256811659620656 x^2+95269403790049731296 x+15182645340392454144\right)-323697765630567829248 x-45547936021177362432\right)+278495839787297842944 x+45547936021177362432}{10584 (5 x+3)^{3/2} \left(-846511875 x^4+2876857500 x^3+32771841300 x^2-464036760 x-18959828096\right) (3 x+2)^3+10584 \sqrt{1-2 x} (5 x+3)^{3/2} \left(24903125 x^4-2538047500 x^3-9400717500 x^2+18053298200 x+18798584960\right) (3 x+2)^3+\sqrt{3} \left(10584 \sqrt{1-2 x} (5 x+3) \left(294525000 x^4+10148490000 x^3+1543311000 x^2-33942744000 x-18767334960\right) (3 x+2)^3+10584 (5 x+3) \left(115256250 x^5+2406453750 x^4-23245830000 x^3-39836473200 x^2+16519101840 x+18928578096\right) (3 x+2)^3\right)}","\frac{63678595 \sqrt{1-2 x}}{12936 \sqrt{5 x+3}}-\frac{638165 \sqrt{1-2 x}}{1176 (5 x+3)^{3/2}}+\frac{25441 \sqrt{1-2 x}}{392 (3 x+2) (5 x+3)^{3/2}}+\frac{313 \sqrt{1-2 x}}{84 (3 x+2)^2 (5 x+3)^{3/2}}+\frac{\sqrt{1-2 x}}{3 (3 x+2)^3 (5 x+3)^{3/2}}-\frac{13246251 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{392 \sqrt{7}}",1,"(45547936021177362432 + 278495839787297842944*x + 528020531112124544976*x^2 - 29914152438333697632*x^3 - 1326140439142074608700*x^4 - 1612574522371066053150*x^5 - 574939098670127576625*x^6 + 92619640078708623750*x^7 + 53352633496057396875*x^8 + 432394474643156250*x^9 + Sqrt[3]*Sqrt[3 + 5*x]*(-15182645340392454144 - 80202095175626402528*x - 114383908255166198352*x^2 + 81965325488462627904*x^3 + 352214950606728223080*x^4 + 286633361672028934200*x^5 + 39461417818079103000*x^6 - 28246715446022865000*x^7 - 2744862761133900000*x^8) + Sqrt[1 - 2*x]*(-45547936021177362432 - 323697765630567829248*x - 869705789227100633808*x^2 - 993819004145829108720*x^3 - 171503887693081254300*x^4 + 608521158040073429250*x^5 + 462578357365368316875*x^6 + 79004740287447562500*x^7 - 3953882984434453125*x^8 + Sqrt[3]*Sqrt[3 + 5*x]*(15182645340392454144 + 95269403790049731296*x + 215745256811659620656*x^2 + 180016895510980222560*x^3 - 40645903825977088000*x^4 - 145214660029181702500*x^5 - 61868567390387006250*x^6 - 1892875150413450000*x^7 + 218505856308468750*x^8)))/(10584*(2 + 3*x)^3*(3 + 5*x)^(3/2)*(-18959828096 - 464036760*x + 32771841300*x^2 + 2876857500*x^3 - 846511875*x^4) + 10584*Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^(3/2)*(18798584960 + 18053298200*x - 9400717500*x^2 - 2538047500*x^3 + 24903125*x^4) + Sqrt[3]*(10584*Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)*(-18767334960 - 33942744000*x + 1543311000*x^2 + 10148490000*x^3 + 294525000*x^4) + 10584*(2 + 3*x)^3*(3 + 5*x)*(18928578096 + 16519101840*x - 39836473200*x^2 - 23245830000*x^3 + 2406453750*x^4 + 115256250*x^5))) + (13246251*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/392 - (66231255*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/784","C",1
2327,1,486,150,2.9647661,"\int (1-2 x)^{3/2} (2+3 x)^3 \sqrt{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^3*Sqrt[3 + 5*x],x]","\frac{452517373 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{12800000 \sqrt{10}}+\frac{\sqrt{5 x+3} \left(-326834481600000000000 x^{11}-3497926638096000000000 x^{10}+35555034148939800000000 x^9+125324945699738070000000 x^8+10763884241318023750000 x^7-236730710398379271937500 x^6-144988309264500249363750 x^5+118721248749262974729750 x^4+111240981387845436771600 x^3-30562914548166287707200 x^2-26291434589969748437920 x+8175572879984254881312\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(16349029200000000000 x^{11}-603910501308000000000 x^{10}-15672618481140450000000 x^9-14806842376746587500000 x^8+100906995074782427937500 x^7+173234158559342498859375 x^6+203114002670754115000 x^5-148269026695196804005250 x^4-59914867797558245262000 x^3+44914480463362938397360 x^2+18142898482948649983360 x-8175572879984254881312\right)+\sqrt{3} \left(18145296000000000000 x^{12}+2420562411360000000000 x^{11}-4963009530762000000000 x^{10}-113599963087409700000000 x^9-171568156468898482500000 x^8+131119557635208380625000 x^7+369662014708021211746875 x^6+82654961895620125860000 x^5-211731921484966909355250 x^4-97391698129565447451600 x^3+55342119508441926121200 x^2+19475424835971150620160 x+\sqrt{1-2 x} \left(-87316574400000000000 x^{11}+6498417846096000000000 x^{10}+34297035137263800000000 x^9-28793785401257910000000 x^8-224329644911097668250000 x^7-203506929947998307812500 x^6+97859417617140821688750 x^5+205935316986635285139750 x^4+31250206440721095313200 x^3-62900206313775942682560 x^2-11326888728950052165600 x+8175572879984254881312\right)-8175572879984254881312\right)}{76800000 \sqrt{3} \sqrt{5 x+3} \left(25265212500 x^5-1941218400000 x^4-5284290066000 x^3+24057375117600 x^2+13825440024000 x-16748592098304\right)+\sqrt{1-2 x} \left(76800000 \left(-236425406250 x^5-2220611593750 x^4+28520358020000 x^3+52011357156000 x^2-49788771586400 x-50183931760160\right)+76800000 \sqrt{3} \sqrt{5 x+3} \left(2625187500 x^5+345183000000 x^4-1378186950000 x^3-13912170444000 x^2+2687092123200 x+16725373086720\right)\right)+76800000 \left(-23653109375 x^6+916525237500 x^5+21026153381250 x^4-17065853944000 x^3-123670456765200 x^2+301410173760 x+50253588794912\right)}","-\frac{1}{20} (3 x+2)^2 (5 x+3)^{3/2} (1-2 x)^{5/2}-\frac{(5 x+3)^{3/2} (63120 x+88987) (1-2 x)^{5/2}}{160000}-\frac{339983 \sqrt{5 x+3} (1-2 x)^{5/2}}{384000}+\frac{3739813 \sqrt{5 x+3} (1-2 x)^{3/2}}{7680000}+\frac{41137943 \sqrt{5 x+3} \sqrt{1-2 x}}{25600000}+\frac{452517373 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{25600000 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(8175572879984254881312 - 26291434589969748437920*x - 30562914548166287707200*x^2 + 111240981387845436771600*x^3 + 118721248749262974729750*x^4 - 144988309264500249363750*x^5 - 236730710398379271937500*x^6 + 10763884241318023750000*x^7 + 125324945699738070000000*x^8 + 35555034148939800000000*x^9 - 3497926638096000000000*x^10 - 326834481600000000000*x^11) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-8175572879984254881312 + 18142898482948649983360*x + 44914480463362938397360*x^2 - 59914867797558245262000*x^3 - 148269026695196804005250*x^4 + 203114002670754115000*x^5 + 173234158559342498859375*x^6 + 100906995074782427937500*x^7 - 14806842376746587500000*x^8 - 15672618481140450000000*x^9 - 603910501308000000000*x^10 + 16349029200000000000*x^11) + Sqrt[3]*(-8175572879984254881312 + 19475424835971150620160*x + 55342119508441926121200*x^2 - 97391698129565447451600*x^3 - 211731921484966909355250*x^4 + 82654961895620125860000*x^5 + 369662014708021211746875*x^6 + 131119557635208380625000*x^7 - 171568156468898482500000*x^8 - 113599963087409700000000*x^9 - 4963009530762000000000*x^10 + 2420562411360000000000*x^11 + 18145296000000000000*x^12 + Sqrt[1 - 2*x]*(8175572879984254881312 - 11326888728950052165600*x - 62900206313775942682560*x^2 + 31250206440721095313200*x^3 + 205935316986635285139750*x^4 + 97859417617140821688750*x^5 - 203506929947998307812500*x^6 - 224329644911097668250000*x^7 - 28793785401257910000000*x^8 + 34297035137263800000000*x^9 + 6498417846096000000000*x^10 - 87316574400000000000*x^11)))/(76800000*Sqrt[3]*Sqrt[3 + 5*x]*(-16748592098304 + 13825440024000*x + 24057375117600*x^2 - 5284290066000*x^3 - 1941218400000*x^4 + 25265212500*x^5) + 76800000*(50253588794912 + 301410173760*x - 123670456765200*x^2 - 17065853944000*x^3 + 21026153381250*x^4 + 916525237500*x^5 - 23653109375*x^6) + Sqrt[1 - 2*x]*(76800000*(-50183931760160 - 49788771586400*x + 52011357156000*x^2 + 28520358020000*x^3 - 2220611593750*x^4 - 236425406250*x^5) + 76800000*Sqrt[3]*Sqrt[3 + 5*x]*(16725373086720 + 2687092123200*x - 13912170444000*x^2 - 1378186950000*x^3 + 345183000000*x^4 + 2625187500*x^5))) + (452517373*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(12800000*Sqrt[10])","B",1
2328,1,426,143,2.565388,"\int (1-2 x)^{3/2} (2+3 x)^2 \sqrt{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^2*Sqrt[3 + 5*x],x]","\frac{\sqrt{5 x+3} \left(-18934344000000000 x^9+702782417700000000 x^8+2325212744965000000 x^7-2428201184619375000 x^6-6637041654087281250 x^5+538013507424160625 x^4+4916381949685459000 x^3+95099144983954100 x^2-1154387555611832080 x+158571454039467216\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-1529301600000000 x^9-171838606770000000 x^8+131608759266500000 x^7+3263882291556937500 x^6+2969493820630546875 x^5-2989076701962900125 x^4-3501584215831287900 x^3+864897765908466980 x^2+1000591617118480960 x-158571454039467216\right)+\sqrt{3} \left(5704560000000000 x^{10}-110462067000000000 x^9-2398586961950000000 x^8-1818530234328750000 x^7+7190825130717187500 x^6+7433046527587915625 x^5-4170919229813443125 x^4-5469603336445066500 x^3+929198468862092500 x^2+\sqrt{1-2 x} \left(43815816000000000 x^9+401444415900000000 x^8-1843406537643000000 x^7-5887061578138125000 x^6-1578925443024806250 x^5+5839133359953815625 x^4+3195315266430683000 x^3-1760260825254845980 x^2-867677466330383280 x+158571454039467216\right)+1021473404823734400 x-158571454039467216\right)}{1920000 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right)+\sqrt{1-2 x} \left(1920000 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right)+1920000 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right)\right)+1920000 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right)}+\frac{5487713 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{320000 \sqrt{10}}","-\frac{3}{50} (3 x+2) (5 x+3)^{3/2} (1-2 x)^{5/2}-\frac{567 (5 x+3)^{3/2} (1-2 x)^{5/2}}{4000}-\frac{4123 \sqrt{5 x+3} (1-2 x)^{5/2}}{9600}+\frac{45353 \sqrt{5 x+3} (1-2 x)^{3/2}}{192000}+\frac{498883 \sqrt{5 x+3} \sqrt{1-2 x}}{640000}+\frac{5487713 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{640000 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(158571454039467216 - 1154387555611832080*x + 95099144983954100*x^2 + 4916381949685459000*x^3 + 538013507424160625*x^4 - 6637041654087281250*x^5 - 2428201184619375000*x^6 + 2325212744965000000*x^7 + 702782417700000000*x^8 - 18934344000000000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-158571454039467216 + 1000591617118480960*x + 864897765908466980*x^2 - 3501584215831287900*x^3 - 2989076701962900125*x^4 + 2969493820630546875*x^5 + 3263882291556937500*x^6 + 131608759266500000*x^7 - 171838606770000000*x^8 - 1529301600000000*x^9) + Sqrt[3]*(-158571454039467216 + 1021473404823734400*x + 929198468862092500*x^2 - 5469603336445066500*x^3 - 4170919229813443125*x^4 + 7433046527587915625*x^5 + 7190825130717187500*x^6 - 1818530234328750000*x^7 - 2398586961950000000*x^8 - 110462067000000000*x^9 + 5704560000000000*x^10 + Sqrt[1 - 2*x]*(158571454039467216 - 867677466330383280*x - 1760260825254845980*x^2 + 3195315266430683000*x^3 + 5839133359953815625*x^4 - 1578925443024806250*x^5 - 5887061578138125000*x^6 - 1843406537643000000*x^7 + 401444415900000000*x^8 + 43815816000000000*x^9)))/(1920000*Sqrt[3]*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 1920000*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(1920000*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 1920000*Sqrt[3]*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (5487713*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(320000*Sqrt[10])","B",1
2329,1,366,116,2.1786264,"\int (1-2 x)^{3/2} (2+3 x) \sqrt{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)*Sqrt[3 + 5*x],x]","\frac{\sqrt{5 x+3} \left(-2792592000000 x^7-16389744800000 x^6+52865833020000 x^5+52154922369000 x^4-61363747795900 x^3-31820727786100 x^2+16882591033000 x+3359432383032\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(246258000000 x^7-2237626100000 x^6-36844670677500 x^5-5842231386375 x^4+54667410300200 x^3+7967697957240 x^2-20552329112800 x-3359432383032\right)+\sqrt{3} \left(171360000000 x^8+15373336000000 x^7-5483146600000 x^6-101793522870000 x^5-19563546991375 x^4+94908360789400 x^3+18297047935000 x^2+\sqrt{1-2 x} \left(-1284624000000 x^7+22394055200000 x^6+52304429100000 x^5-29775138921000 x^4-69095640260900 x^3+8541929772860 x^2+23279688911160 x+3359432383032\right)-19609950831360 x-3359432383032\right)}{19200 \sqrt{3} \sqrt{5 x+3} \left(8921000 x^3-162998000 x^2-220512160 x+287530496\right)+\sqrt{1-2 x} \left(19200 \left(-48482500 x^3-297203500 x^2+794989800 x+852279560\right)+19200 \sqrt{3} \sqrt{5 x+3} \left(595000 x^3+53178000 x^2-36412000 x-283051520\right)\right)+19200 \left(-8550625 x^4+79738000 x^3+1253327000 x^2-32289760 x-865716488\right)}+\frac{30613 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{3200 \sqrt{10}}","-\frac{3}{40} (5 x+3)^{3/2} (1-2 x)^{5/2}-\frac{23}{96} \sqrt{5 x+3} (1-2 x)^{5/2}+\frac{253 \sqrt{5 x+3} (1-2 x)^{3/2}}{1920}+\frac{2783 \sqrt{5 x+3} \sqrt{1-2 x}}{6400}+\frac{30613 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{6400 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(3359432383032 + 16882591033000*x - 31820727786100*x^2 - 61363747795900*x^3 + 52154922369000*x^4 + 52865833020000*x^5 - 16389744800000*x^6 - 2792592000000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-3359432383032 - 20552329112800*x + 7967697957240*x^2 + 54667410300200*x^3 - 5842231386375*x^4 - 36844670677500*x^5 - 2237626100000*x^6 + 246258000000*x^7) + Sqrt[3]*(-3359432383032 - 19609950831360*x + 18297047935000*x^2 + 94908360789400*x^3 - 19563546991375*x^4 - 101793522870000*x^5 - 5483146600000*x^6 + 15373336000000*x^7 + 171360000000*x^8 + Sqrt[1 - 2*x]*(3359432383032 + 23279688911160*x + 8541929772860*x^2 - 69095640260900*x^3 - 29775138921000*x^4 + 52304429100000*x^5 + 22394055200000*x^6 - 1284624000000*x^7)))/(19200*Sqrt[3]*Sqrt[3 + 5*x]*(287530496 - 220512160*x - 162998000*x^2 + 8921000*x^3) + 19200*(-865716488 - 32289760*x + 1253327000*x^2 + 79738000*x^3 - 8550625*x^4) + Sqrt[1 - 2*x]*(19200*(852279560 + 794989800*x - 297203500*x^2 - 48482500*x^3) + 19200*Sqrt[3]*Sqrt[3 + 5*x]*(-283051520 - 36412000*x + 53178000*x^2 + 595000*x^3))) + (30613*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(3200*Sqrt[10])","B",1
2330,1,306,94,1.7445433,"\int (1-2 x)^{3/2} \sqrt{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*Sqrt[3 + 5*x],x]","\frac{\sqrt{5 x+3} \left(-627000000 x^5+5291275000 x^4+15452250 x^3-7021579125 x^2+248506060 x+1934544612\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-35900000 x^5-2355192500 x^4+1961883375 x^3+3608839475 x^2-2282801200 x-1934544612\right)+\sqrt{3} \left(234000000 x^6-921450000 x^5-8798677500 x^4+6306059625 x^3+7201053975 x^2+\sqrt{1-2 x} \left(917400000 x^5+3019005000 x^4-5910753750 x^3-2126474625 x^2+3861515460 x+1934544612\right)-1827220320 x-1934544612\right)}{1200 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right)+\sqrt{1-2 x} \left(1200 \left(-391875 x^2+2827000 x+3481060\right)+1200 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right)\right)+1200 \left(44875 x^3+2976525 x^2-279060 x-3667684\right)}+\frac{1331 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{200 \sqrt{10}}","-\frac{1}{6} \sqrt{5 x+3} (1-2 x)^{5/2}+\frac{11}{120} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{121}{400} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{1331 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{400 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(1934544612 + 248506060*x - 7021579125*x^2 + 15452250*x^3 + 5291275000*x^4 - 627000000*x^5) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-1934544612 - 2282801200*x + 3608839475*x^2 + 1961883375*x^3 - 2355192500*x^4 - 35900000*x^5) + Sqrt[3]*(-1934544612 - 1827220320*x + 7201053975*x^2 + 6306059625*x^3 - 8798677500*x^4 - 921450000*x^5 + 234000000*x^6 + Sqrt[1 - 2*x]*(1934544612 + 3861515460*x - 2126474625*x^2 - 5910753750*x^3 + 3019005000*x^4 + 917400000*x^5)))/(1200*Sqrt[3]*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 1200*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(1200*(3481060 + 2827000*x - 391875*x^2) + 1200*Sqrt[3]*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (1331*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(200*Sqrt[10])","B",1
2331,1,438,106,1.8080336,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x),x]","\frac{49}{27} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-858000 x^3+711700 x^2+4500210 x-4011634\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(178500 x^3-516775 x^2-703280 x+4011634\right)+\sqrt{3} \left(60000 x^4+2413000 x^3-5993675 x^2+\sqrt{1-2 x} \left(-594000 x^3+2531100 x^2-2743290 x-4011634\right)-1053640 x+4011634\right)}{180 \left(-2975 x^2+1820 x+16562\right)+180 \sqrt{3} \sqrt{5 x+3} (1980 x-5104)+\sqrt{1-2 x} \left(180 (-7150 x-13970)+180 \sqrt{3} \sqrt{5 x+3} (100 x+4240)\right)}+\frac{4091 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{270 \sqrt{10}}","\frac{1}{6} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{107}{180} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{4091 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{540 \sqrt{10}}+\frac{14}{27} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[3 + 5*x]*(-4011634 + 4500210*x + 711700*x^2 - 858000*x^3) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(4011634 - 703280*x - 516775*x^2 + 178500*x^3) + Sqrt[3]*(4011634 - 1053640*x - 5993675*x^2 + 2413000*x^3 + 60000*x^4 + Sqrt[1 - 2*x]*(-4011634 - 2743290*x + 2531100*x^2 - 594000*x^3)))/(180*Sqrt[3]*Sqrt[3 + 5*x]*(-5104 + 1980*x) + 180*(16562 + 1820*x - 2975*x^2) + Sqrt[1 - 2*x]*(180*(-13970 - 7150*x) + 180*Sqrt[3]*Sqrt[3 + 5*x]*(4240 + 100*x))) + (4091*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(270*Sqrt[10]) + (49*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ])/27","C",1
2332,1,531,115,2.1307186,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^2,x]","\frac{287}{27} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{1435}{54} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-35700 x^3-33710 x^2+665144 x+644204\right)+\sqrt{5 x+3} \left(171600 x^3+760100 x^2-84876 x-644204\right)+\sqrt{3} \left(-12000 x^4-630175 x^3-987670 x^2+\sqrt{1-2 x} \left(118800 x^3-253110 x^2-1232814 x-644204\right)+652546 x+644204\right)}{18 \left(2975 x^2-1820 x-16562\right) (3 x+2)+18 \sqrt{3} (5104-1980 x) \sqrt{5 x+3} (3 x+2)+\sqrt{1-2 x} \left(18 (7150 x+13970) (3 x+2)+18 \sqrt{3} (-100 x-4240) \sqrt{5 x+3} (3 x+2)\right)}-\frac{214}{27} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{\sqrt{5 x+3} (1-2 x)^{3/2}}{3 (3 x+2)}-\frac{4}{9} \sqrt{5 x+3} \sqrt{1-2 x}-\frac{107}{27} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{41}{27} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(644204 + 665144*x - 33710*x^2 - 35700*x^3) + Sqrt[3 + 5*x]*(-644204 - 84876*x + 760100*x^2 + 171600*x^3) + Sqrt[3]*(644204 + 652546*x - 987670*x^2 - 630175*x^3 - 12000*x^4 + Sqrt[1 - 2*x]*(-644204 - 1232814*x - 253110*x^2 + 118800*x^3)))/(18*Sqrt[3]*(5104 - 1980*x)*(2 + 3*x)*Sqrt[3 + 5*x] + 18*(2 + 3*x)*(-16562 - 1820*x + 2975*x^2) + Sqrt[1 - 2*x]*(18*Sqrt[3]*(-4240 - 100*x)*(2 + 3*x)*Sqrt[3 + 5*x] + 18*(2 + 3*x)*(13970 + 7150*x))) - (214*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/27 + (287*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/27 - (1435*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/54","C",1
2333,1,537,120,2.0251236,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^3,x]","\frac{793}{108} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{3965}{216} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-2946240 x^3-2629418 x^2+3345606 x+2225432\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(350325 x^3-2263120 x^2-5297150 x-2225432\right)+\sqrt{3} \left(643725 x^4+6180580 x^3+740938 x^2+\sqrt{1-2 x} \left(-113850 x^3+5909970 x^2+7283760 x+2225432\right)-5332216 x-2225432\right)}{36 \left(2975 x^2-1820 x-16562\right) (3 x+2)^2+36 \sqrt{3} (5104-1980 x) \sqrt{5 x+3} (3 x+2)^2+\sqrt{1-2 x} \left(36 (7150 x+13970) (3 x+2)^2+36 \sqrt{3} (-100 x-4240) \sqrt{5 x+3} (3 x+2)^2\right)}+\frac{8}{27} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{\sqrt{5 x+3} (1-2 x)^{3/2}}{6 (3 x+2)^2}+\frac{41 \sqrt{5 x+3} \sqrt{1-2 x}}{36 (3 x+2)}+\frac{4}{27} \sqrt{10} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{793 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{108 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(2225432 + 3345606*x - 2629418*x^2 - 2946240*x^3) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-2225432 - 5297150*x - 2263120*x^2 + 350325*x^3) + Sqrt[3]*(-2225432 - 5332216*x + 740938*x^2 + 6180580*x^3 + 643725*x^4 + Sqrt[1 - 2*x]*(2225432 + 7283760*x + 5909970*x^2 - 113850*x^3)))/(36*Sqrt[3]*(5104 - 1980*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 36*(2 + 3*x)^2*(-16562 - 1820*x + 2975*x^2) + Sqrt[1 - 2*x]*(36*Sqrt[3]*(-4240 - 100*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 36*(2 + 3*x)^2*(13970 + 7150*x))) + (8*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/27 + (793*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/108 - (3965*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/216","C",1
2334,1,539,122,2.1457339,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^4,x]","\frac{1331}{56} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{6655}{112} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-1023410850 x^5-34052277545 x^4-48169307802 x^3+3200841996 x^2+29688374584 x+10544331072\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(579927625 x^5+8853546925 x^4-7303866150 x^3-44322102052 x^2-39751588984 x-10544331072\right)+\sqrt{3} \left(-682265250 x^6+17037822300 x^5+68395243830 x^4+53365459272 x^3-23948761416 x^2+\sqrt{1-2 x} \left(-5526361500 x^5-9035289450 x^4+32791780560 x^3+73617158472 x^2+48699656544 x+10544331072\right)-38636442144 x-10544331072\right)}{168 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right) (3 x+2)^3+\sqrt{1-2 x} \left(168 \left(-391875 x^2+2827000 x+3481060\right) (3 x+2)^3+168 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right) (3 x+2)^3\right)+168 \left(44875 x^3+2976525 x^2-279060 x-3667684\right) (3 x+2)^3}","\frac{11 \sqrt{1-2 x} (5 x+3)^{3/2}}{4 (3 x+2)^2}+\frac{(1-2 x)^{3/2} (5 x+3)^{3/2}}{3 (3 x+2)^3}-\frac{121 \sqrt{1-2 x} \sqrt{5 x+3}}{56 (3 x+2)}-\frac{1331 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{56 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(10544331072 + 29688374584*x + 3200841996*x^2 - 48169307802*x^3 - 34052277545*x^4 - 1023410850*x^5) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-10544331072 - 39751588984*x - 44322102052*x^2 - 7303866150*x^3 + 8853546925*x^4 + 579927625*x^5) + Sqrt[3]*(-10544331072 - 38636442144*x - 23948761416*x^2 + 53365459272*x^3 + 68395243830*x^4 + 17037822300*x^5 - 682265250*x^6 + Sqrt[1 - 2*x]*(10544331072 + 48699656544*x + 73617158472*x^2 + 32791780560*x^3 - 9035289450*x^4 - 5526361500*x^5)))/(168*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 168*(2 + 3*x)^3*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(168*(2 + 3*x)^3*(3481060 + 2827000*x - 391875*x^2) + 168*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (1331*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/56 - (6655*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/112","C",1
2335,1,599,151,2.5527071,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^5,x]","\frac{240911 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{3136}-\frac{1204555 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{6272}+\frac{\sqrt{5 x+3} \left(-238724925450000 x^7-123628984550500 x^6+6278078893518300 x^5+12737975436076440 x^4+6020490660686920 x^3-3675627312964640 x^2-3982090343350240 x-928911349280640\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(9684651455625 x^7-556689292927000 x^6-3274756187935500 x^5-2544265073248560 x^4+5049732327177832 x^3+8894051288988480 x^2+4898116484894560 x+928911349280640\right)+\sqrt{3} \left(33593273709375 x^8+772354273610000 x^7-2620732689503000 x^6-14611448838558000 x^5-18112413471166040 x^4-4084476209182720 x^3+6663567352811840 x^2+\sqrt{1-2 x} \left(56895883192500 x^7+2358050733395500 x^6+5703073480678200 x^5+257939620732200 x^4-11012933907471232 x^3-12648343134289280 x^2-5675205963461760 x-928911349280640\right)+4759179821917440 x+928911349280640\right)}{9408 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^4+\sqrt{1-2 x} \left(9408 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^4+9408 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^4\right)+9408 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^4}","\frac{3 (5 x+3)^{3/2} (1-2 x)^{5/2}}{28 (3 x+2)^4}+\frac{181 (5 x+3)^{3/2} (1-2 x)^{3/2}}{168 (3 x+2)^3}+\frac{1991 (5 x+3)^{3/2} \sqrt{1-2 x}}{224 (3 x+2)^2}-\frac{21901 \sqrt{5 x+3} \sqrt{1-2 x}}{3136 (3 x+2)}-\frac{240911 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{3136 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-928911349280640 - 3982090343350240*x - 3675627312964640*x^2 + 6020490660686920*x^3 + 12737975436076440*x^4 + 6278078893518300*x^5 - 123628984550500*x^6 - 238724925450000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(928911349280640 + 4898116484894560*x + 8894051288988480*x^2 + 5049732327177832*x^3 - 2544265073248560*x^4 - 3274756187935500*x^5 - 556689292927000*x^6 + 9684651455625*x^7) + Sqrt[3]*(928911349280640 + 4759179821917440*x + 6663567352811840*x^2 - 4084476209182720*x^3 - 18112413471166040*x^4 - 14611448838558000*x^5 - 2620732689503000*x^6 + 772354273610000*x^7 + 33593273709375*x^8 + Sqrt[1 - 2*x]*(-928911349280640 - 5675205963461760*x - 12648343134289280*x^2 - 11012933907471232*x^3 + 257939620732200*x^4 + 5703073480678200*x^5 + 2358050733395500*x^6 + 56895883192500*x^7)))/(9408*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 9408*(2 + 3*x)^4*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(9408*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 9408*(2 + 3*x)^4*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) + (240911*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/3136 - (1204555*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/6272","C",1
2336,1,659,180,3.1629661,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^6,x]","\frac{11988317 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{43904}-\frac{59941585 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{87808}+\frac{\sqrt{5 x+3} \left(-4303840127159925000 x^9-208133563005283389375 x^8-441343153883408736850 x^7+1033640354134316522880 x^6+3624573967377683846064 x^5+3305556780904661303680 x^4+373646619393265475840 x^3-1109103955733970616640 x^2-647093515402812325760 x-111950034725967972864\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(788873778381796875 x^9+23401631837954015625 x^8-204732010018538993750 x^7-1245101401844960853000 x^6-1827814055658804921600 x^5-148799622462902824480 x^4+1934255282761613596800 x^3+1917012277120806809536 x^2+758579940574793124224 x+111950034725967972864\right)+\sqrt{3} \left(-597482942776340625 x^{10}+70565051476483828125 x^9+552167470572702762500 x^8+167523181315191051000 x^7-3174869103453433998600 x^6-6084254526994782624464 x^5-3846764737954603034880 x^4+357937270450637463360 x^3+1609240159181117008640 x^2+\sqrt{1-2 x} \left(-10876152497699671875 x^9+9027890628489562500 x^8+828255573979376400000 x^7+2520401579829242175000 x^6+2257107127310744346000 x^5-984433887930595576320 x^4-3300261003209136697280 x^3-2510128710409187200256 x^2-851946511711016434944 x-111950034725967972864\right)+740460086539035636480 x+111950034725967972864\right)}{658560 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right) (3 x+2)^5+\sqrt{1-2 x} \left(658560 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right) (3 x+2)^5+658560 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right) (3 x+2)^5\right)+658560 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right) (3 x+2)^5}","-\frac{\sqrt{5 x+3} (1-2 x)^{3/2}}{15 (3 x+2)^5}+\frac{28291441 \sqrt{5 x+3} \sqrt{1-2 x}}{1185408 (3 x+2)}+\frac{270463 \sqrt{5 x+3} \sqrt{1-2 x}}{84672 (3 x+2)^2}+\frac{7723 \sqrt{5 x+3} \sqrt{1-2 x}}{15120 (3 x+2)^3}+\frac{41 \sqrt{5 x+3} \sqrt{1-2 x}}{360 (3 x+2)^4}-\frac{11988317 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{43904 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-111950034725967972864 - 647093515402812325760*x - 1109103955733970616640*x^2 + 373646619393265475840*x^3 + 3305556780904661303680*x^4 + 3624573967377683846064*x^5 + 1033640354134316522880*x^6 - 441343153883408736850*x^7 - 208133563005283389375*x^8 - 4303840127159925000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(111950034725967972864 + 758579940574793124224*x + 1917012277120806809536*x^2 + 1934255282761613596800*x^3 - 148799622462902824480*x^4 - 1827814055658804921600*x^5 - 1245101401844960853000*x^6 - 204732010018538993750*x^7 + 23401631837954015625*x^8 + 788873778381796875*x^9) + Sqrt[3]*(111950034725967972864 + 740460086539035636480*x + 1609240159181117008640*x^2 + 357937270450637463360*x^3 - 3846764737954603034880*x^4 - 6084254526994782624464*x^5 - 3174869103453433998600*x^6 + 167523181315191051000*x^7 + 552167470572702762500*x^8 + 70565051476483828125*x^9 - 597482942776340625*x^10 + Sqrt[1 - 2*x]*(-111950034725967972864 - 851946511711016434944*x - 2510128710409187200256*x^2 - 3300261003209136697280*x^3 - 984433887930595576320*x^4 + 2257107127310744346000*x^5 + 2520401579829242175000*x^6 + 828255573979376400000*x^7 + 9027890628489562500*x^8 - 10876152497699671875*x^9)))/(658560*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 658560*(2 + 3*x)^5*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(658560*(2 + 3*x)^5*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 658560*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (11988317*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/43904 - (59941585*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/87808","C",1
2337,1,1331,172,14.0267808,"\int (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(3/2),x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{28} \left(\frac{6219452877 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}{51200000 \sqrt{10} \left(\sqrt{3}-\sqrt{5 x+3}\right)^{28}}+\frac{\left(\frac{8526147123 \sqrt{1-2 x}}{102400000}-\frac{1104}{5} \sqrt{3} \sqrt{5 x+3}+\frac{59303612877}{102400000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{13}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{27}}+\frac{\left(\frac{34021950959 \sqrt{1-2 x}}{51200000}-\frac{102064}{25} \sqrt{3} \sqrt{5 x+3}+\frac{593059265041}{51200000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{25}}+\frac{\left(-\frac{684565054959 \sqrt{1-2 x}}{64000000}-\frac{5080304}{125} \sqrt{3} \sqrt{5 x+3}+\frac{8487911998959}{64000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{11}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{23}}+\frac{\left(-\frac{52293749059123 \sqrt{1-2 x}}{224000000}-\frac{142991024}{625} \sqrt{3} \sqrt{5 x+3}+\frac{206037698063923}{224000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{21}}+\frac{\left(-\frac{58386806770853 \sqrt{1-2 x}}{28000000}-\frac{2015985488 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{112576496688293}{28000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{19}}+\frac{\left(-\frac{30617977918449 \sqrt{1-2 x}}{2800000}+\frac{31116176 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{30534337637361}{2800000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{17}}+\frac{\left(-\frac{25986664575649 \sqrt{1-2 x}}{700000}+\frac{151714800256 \sqrt{3} \sqrt{5 x+3}}{21875}+\frac{11422043751073}{700000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{15}}+\frac{\left(-\frac{21461502565493 \sqrt{1-2 x}}{250000}+\frac{85099261504 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{1037679804533}{250000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{13}}+\frac{\left(-\frac{2175801338331 \sqrt{1-2 x}}{15625}+\frac{180961918272 \sqrt{3} \sqrt{5 x+3}}{3125}-\frac{538627435749}{15625}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{11}}+\frac{\left(-\frac{2506095752958 \sqrt{1-2 x}}{15625}+\frac{244789733952 \sqrt{3} \sqrt{5 x+3}}{3125}-\frac{1165750256322}{15625}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}+\frac{\left(-\frac{568998331704 \sqrt{1-2 x}}{4375}+\frac{216560756736 \sqrt{3} \sqrt{5 x+3}}{3125}-\frac{1702784232936}{21875}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}+\frac{\left(-\frac{1559108309904 \sqrt{1-2 x}}{21875}+\frac{121743779328 \sqrt{3} \sqrt{5 x+3}}{3125}-\frac{997511055984}{21875}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{-\frac{80141315328 \sqrt{1-2 x}}{21875}+\frac{39530916864 \sqrt{3} \sqrt{5 x+3}}{21875}-\frac{38451435264}{21875}}{\sqrt{3}-\sqrt{5 x+3}}+\frac{\left(\frac{3456 \sqrt{1-2 x}}{4375}+\frac{6912 \sqrt{3} \sqrt{5 x+3}}{21875}-\frac{38016}{21875}\right) \left(-150728747 \sqrt{1-2 x}+80068408 \sqrt{3} \sqrt{5 x+3}-89476477\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}","-\frac{3}{70} (3 x+2)^2 (5 x+3)^{5/2} (1-2 x)^{5/2}-\frac{141599 (5 x+3)^{3/2} (1-2 x)^{5/2}}{128000}-\frac{3 (5 x+3)^{5/2} (33300 x+49829) (1-2 x)^{5/2}}{280000}-\frac{1557589 \sqrt{5 x+3} (1-2 x)^{5/2}}{512000}+\frac{17133479 \sqrt{5 x+3} (1-2 x)^{3/2}}{10240000}+\frac{565404807 \sqrt{5 x+3} \sqrt{1-2 x}}{102400000}+\frac{6219452877 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{102400000 \sqrt{10}}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^28*(((112576496688293/28000000 - (58386806770853*Sqrt[1 - 2*x])/28000000 - (2015985488*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^9)/(Sqrt[3] - Sqrt[3 + 5*x])^19 + ((206037698063923/224000000 - (52293749059123*Sqrt[1 - 2*x])/224000000 - (142991024*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^10)/(Sqrt[3] - Sqrt[3 + 5*x])^21 + ((8487911998959/64000000 - (684565054959*Sqrt[1 - 2*x])/64000000 - (5080304*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^11)/(Sqrt[3] - Sqrt[3 + 5*x])^23 + ((593059265041/51200000 + (34021950959*Sqrt[1 - 2*x])/51200000 - (102064*Sqrt[3]*Sqrt[3 + 5*x])/25)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12)/(Sqrt[3] - Sqrt[3 + 5*x])^25 + ((59303612877/102400000 + (8526147123*Sqrt[1 - 2*x])/102400000 - (1104*Sqrt[3]*Sqrt[3 + 5*x])/5)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^13)/(Sqrt[3] - Sqrt[3 + 5*x])^27 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^8*(30534337637361/2800000 - (30617977918449*Sqrt[1 - 2*x])/2800000 + (31116176*Sqrt[3]*Sqrt[3 + 5*x])/3125))/(Sqrt[3] - Sqrt[3 + 5*x])^17 + (-38451435264/21875 - (80141315328*Sqrt[1 - 2*x])/21875 + (39530916864*Sqrt[3]*Sqrt[3 + 5*x])/21875)/(Sqrt[3] - Sqrt[3 + 5*x]) + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^7*(11422043751073/700000 - (25986664575649*Sqrt[1 - 2*x])/700000 + (151714800256*Sqrt[3]*Sqrt[3 + 5*x])/21875))/(Sqrt[3] - Sqrt[3 + 5*x])^15 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^6*(1037679804533/250000 - (21461502565493*Sqrt[1 - 2*x])/250000 + (85099261504*Sqrt[3]*Sqrt[3 + 5*x])/3125))/(Sqrt[3] - Sqrt[3 + 5*x])^13 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2*(-997511055984/21875 - (1559108309904*Sqrt[1 - 2*x])/21875 + (121743779328*Sqrt[3]*Sqrt[3 + 5*x])/3125))/(Sqrt[3] - Sqrt[3 + 5*x])^5 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^5*(-538627435749/15625 - (2175801338331*Sqrt[1 - 2*x])/15625 + (180961918272*Sqrt[3]*Sqrt[3 + 5*x])/3125))/(Sqrt[3] - Sqrt[3 + 5*x])^11 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^3*(-1702784232936/21875 - (568998331704*Sqrt[1 - 2*x])/4375 + (216560756736*Sqrt[3]*Sqrt[3 + 5*x])/3125))/(Sqrt[3] - Sqrt[3 + 5*x])^7 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^4*(-1165750256322/15625 - (2506095752958*Sqrt[1 - 2*x])/15625 + (244789733952*Sqrt[3]*Sqrt[3 + 5*x])/3125))/(Sqrt[3] - Sqrt[3 + 5*x])^9 + ((-38016/21875 + (3456*Sqrt[1 - 2*x])/4375 + (6912*Sqrt[3]*Sqrt[3 + 5*x])/21875)*(-89476477 - 150728747*Sqrt[1 - 2*x] + 80068408*Sqrt[3]*Sqrt[3 + 5*x]))/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (6219452877*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(51200000*Sqrt[10]*(Sqrt[3] - Sqrt[3 + 5*x])^28)))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14","B",1
2338,1,486,165,2.9709918,"\int (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2),x]","\frac{136205223 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{2560000 \sqrt{10}}+\frac{\sqrt{5 x+3} \left(-36314942400000000000 x^{11}-385753319952000000000 x^{10}+3979456187592600000000 x^9+13586805686769590000000 x^8+334488099519763750000 x^7-25713642043173642937500 x^6-14348302668460741983750 x^5+13092137107454993205750 x^4+11206276983555684637200 x^3-3398815847085878542400 x^2-2672653918772653620640 x+874286504995982927904\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(1816558800000000000 x^{11}-67246491516000000000 x^{10}-1735924118859650000000 x^9-1510017826126387500000 x^8+11240761202058014937500 x^7+18315188603600249609375 x^6-819668506556263245000 x^5-15736900723895232169250 x^4-5804141231087287534000 x^3+4792692166736479347120 x^2+1801065866666514421120 x-874286504995982927904\right)+\sqrt{3} \left(2016144000000000000 x^{12}+268790087520000000000 x^{11}-572839704234000000000 x^{10}-12561915245100900000000 x^9-18096697613708602500000 x^8+15357927197472350625000 x^7+39207688773363028696875 x^6+7199266456493352420000 x^5-22553301086301079439250 x^4-9566938261349709397200 x^3+5932645721789885180400 x^2+1943779181826782430720 x+\sqrt{1-2 x} \left(-9701841600000000000 x^{11}+722822574672000000000 x^{10}+3752431329708600000000 x^9-3460149654693270000000 x^8-24466375615017080250000 x^7-20935551076204076812500 x^6+11373448923442252308750 x^5+21440678688732204255750 x^4+2698011570428484644400 x^3-6599896015236151235520 x^2-1072191129720643231200 x+874286504995982927904\right)-874286504995982927904\right)}{5120000 \sqrt{3} \sqrt{5 x+3} \left(25265212500 x^5-1941218400000 x^4-5284290066000 x^3+24057375117600 x^2+13825440024000 x-16748592098304\right)+\sqrt{1-2 x} \left(5120000 \left(-236425406250 x^5-2220611593750 x^4+28520358020000 x^3+52011357156000 x^2-49788771586400 x-50183931760160\right)+5120000 \sqrt{3} \sqrt{5 x+3} \left(2625187500 x^5+345183000000 x^4-1378186950000 x^3-13912170444000 x^2+2687092123200 x+16725373086720\right)\right)+5120000 \left(-23653109375 x^6+916525237500 x^5+21026153381250 x^4-17065853944000 x^3-123670456765200 x^2+301410173760 x+50253588794912\right)}","-\frac{1}{20} (3 x+2) (5 x+3)^{5/2} (1-2 x)^{5/2}-\frac{259 (5 x+3)^{5/2} (1-2 x)^{5/2}}{2000}-\frac{3101 (5 x+3)^{3/2} (1-2 x)^{5/2}}{6400}-\frac{34111 \sqrt{5 x+3} (1-2 x)^{5/2}}{25600}+\frac{375221 \sqrt{5 x+3} (1-2 x)^{3/2}}{512000}+\frac{12382293 \sqrt{5 x+3} \sqrt{1-2 x}}{5120000}+\frac{136205223 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{5120000 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(874286504995982927904 - 2672653918772653620640*x - 3398815847085878542400*x^2 + 11206276983555684637200*x^3 + 13092137107454993205750*x^4 - 14348302668460741983750*x^5 - 25713642043173642937500*x^6 + 334488099519763750000*x^7 + 13586805686769590000000*x^8 + 3979456187592600000000*x^9 - 385753319952000000000*x^10 - 36314942400000000000*x^11) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-874286504995982927904 + 1801065866666514421120*x + 4792692166736479347120*x^2 - 5804141231087287534000*x^3 - 15736900723895232169250*x^4 - 819668506556263245000*x^5 + 18315188603600249609375*x^6 + 11240761202058014937500*x^7 - 1510017826126387500000*x^8 - 1735924118859650000000*x^9 - 67246491516000000000*x^10 + 1816558800000000000*x^11) + Sqrt[3]*(-874286504995982927904 + 1943779181826782430720*x + 5932645721789885180400*x^2 - 9566938261349709397200*x^3 - 22553301086301079439250*x^4 + 7199266456493352420000*x^5 + 39207688773363028696875*x^6 + 15357927197472350625000*x^7 - 18096697613708602500000*x^8 - 12561915245100900000000*x^9 - 572839704234000000000*x^10 + 268790087520000000000*x^11 + 2016144000000000000*x^12 + Sqrt[1 - 2*x]*(874286504995982927904 - 1072191129720643231200*x - 6599896015236151235520*x^2 + 2698011570428484644400*x^3 + 21440678688732204255750*x^4 + 11373448923442252308750*x^5 - 20935551076204076812500*x^6 - 24466375615017080250000*x^7 - 3460149654693270000000*x^8 + 3752431329708600000000*x^9 + 722822574672000000000*x^10 - 9701841600000000000*x^11)))/(5120000*Sqrt[3]*Sqrt[3 + 5*x]*(-16748592098304 + 13825440024000*x + 24057375117600*x^2 - 5284290066000*x^3 - 1941218400000*x^4 + 25265212500*x^5) + 5120000*(50253588794912 + 301410173760*x - 123670456765200*x^2 - 17065853944000*x^3 + 21026153381250*x^4 + 916525237500*x^5 - 23653109375*x^6) + Sqrt[1 - 2*x]*(5120000*(-50183931760160 - 49788771586400*x + 52011357156000*x^2 + 28520358020000*x^3 - 2220611593750*x^4 - 236425406250*x^5) + 5120000*Sqrt[3]*Sqrt[3 + 5*x]*(16725373086720 + 2687092123200*x - 13912170444000*x^2 - 1378186950000*x^3 + 345183000000*x^4 + 2625187500*x^5))) + (136205223*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(2560000*Sqrt[10])","B",1
2339,1,426,138,2.5494571,"\int (1-2 x)^{3/2} (2+3 x) (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(3/2),x]","\frac{\sqrt{5 x+3} \left(-2103816000000000 x^9+78262253300000000 x^8+251706794185000000 x^7-285936883546875000 x^6-700717093633906250 x^5+93818601725633125 x^4+509102878218671000 x^3-6896498265383100 x^2-119142984036400720 x+19425678530371344\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-169922400000000 x^9-19079018330000000 x^8+16202749188500000 x^7+360144891493687500 x^6+301509102266984375 x^5-336005353497898625 x^4-353960152788409100 x^3+101338825033877620 x^2+100198269433003840 x-19425678530371344\right)+\sqrt{3} \left(633840000000000 x^{10}-12326383000000000 x^9-265443802550000000 x^8-180710087583750000 x^7+798238131850937500 x^6+756443208677928125 x^5-475612252689125625 x^4-552991739132588500 x^3+113647655960342500 x^2+\sqrt{1-2 x} \left(4868424000000000 x^9+44199233100000000 x^8-208209266727000000 x^7-634222062824625000 x^6-136597080474731250 x^5+628547288130788125 x^4+311965255966551000 x^3-192225042199964620 x^2-83932525631652720 x+19425678530371344\right)+102877240235049600 x-19425678530371344\right)}{128000 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right)+\sqrt{1-2 x} \left(128000 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right)+128000 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right)\right)+128000 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right)}+\frac{1625151 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{64000 \sqrt{10}}","-\frac{3}{50} (5 x+3)^{5/2} (1-2 x)^{5/2}-\frac{37}{160} (5 x+3)^{3/2} (1-2 x)^{5/2}-\frac{407}{640} \sqrt{5 x+3} (1-2 x)^{5/2}+\frac{4477 \sqrt{5 x+3} (1-2 x)^{3/2}}{12800}+\frac{147741 \sqrt{5 x+3} \sqrt{1-2 x}}{128000}+\frac{1625151 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{128000 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(19425678530371344 - 119142984036400720*x - 6896498265383100*x^2 + 509102878218671000*x^3 + 93818601725633125*x^4 - 700717093633906250*x^5 - 285936883546875000*x^6 + 251706794185000000*x^7 + 78262253300000000*x^8 - 2103816000000000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-19425678530371344 + 100198269433003840*x + 101338825033877620*x^2 - 353960152788409100*x^3 - 336005353497898625*x^4 + 301509102266984375*x^5 + 360144891493687500*x^6 + 16202749188500000*x^7 - 19079018330000000*x^8 - 169922400000000*x^9) + Sqrt[3]*(-19425678530371344 + 102877240235049600*x + 113647655960342500*x^2 - 552991739132588500*x^3 - 475612252689125625*x^4 + 756443208677928125*x^5 + 798238131850937500*x^6 - 180710087583750000*x^7 - 265443802550000000*x^8 - 12326383000000000*x^9 + 633840000000000*x^10 + Sqrt[1 - 2*x]*(19425678530371344 - 83932525631652720*x - 192225042199964620*x^2 + 311965255966551000*x^3 + 628547288130788125*x^4 - 136597080474731250*x^5 - 634222062824625000*x^6 - 208209266727000000*x^7 + 44199233100000000*x^8 + 4868424000000000*x^9)))/(128000*Sqrt[3]*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 128000*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(128000*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 128000*Sqrt[3]*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (1625151*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(64000*Sqrt[10])","B",1
2340,1,366,116,2.0299259,"\int (1-2 x)^{3/2} (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2),x]","\frac{\sqrt{5 x+3} \left(-1551440000000 x^7-8967508000000 x^6+30046351500000 x^5+25680993965000 x^4-33716629567500 x^3-14374946188900 x^2+9262932331400 x+1034067241944\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(136810000000 x^7-1255286500000 x^6-20347039687500 x^5-1541243426875 x^4+28992975061000 x^3+2542843429400 x^2-10456623559520 x-1034067241944\right)+\sqrt{3} \left(95200000000 x^8+8532280000000 x^7-3797213000000 x^6-55555364350000 x^5-6624263891875 x^4+49662977283000 x^3+6700993158200 x^2+\sqrt{1-2 x} \left(-713680000000 x^7+12504580000000 x^6+27890989500000 x^5-18014187125000 x^4-35235504540500 x^3+6088728853900 x^2+11281222823640 x+1034067241944\right)-10087531595520 x-1034067241944\right)}{6400 \sqrt{3} \sqrt{5 x+3} \left(8921000 x^3-162998000 x^2-220512160 x+287530496\right)+\sqrt{1-2 x} \left(6400 \left(-48482500 x^3-297203500 x^2+794989800 x+852279560\right)+6400 \sqrt{3} \sqrt{5 x+3} \left(595000 x^3+53178000 x^2-36412000 x-283051520\right)\right)+6400 \left(-8550625 x^4+79738000 x^3+1253327000 x^2-32289760 x-865716488\right)}+\frac{43923 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{3200 \sqrt{10}}","-\frac{1}{8} (5 x+3)^{3/2} (1-2 x)^{5/2}-\frac{11}{32} \sqrt{5 x+3} (1-2 x)^{5/2}+\frac{121}{640} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{3993 \sqrt{5 x+3} \sqrt{1-2 x}}{6400}+\frac{43923 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{6400 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(1034067241944 + 9262932331400*x - 14374946188900*x^2 - 33716629567500*x^3 + 25680993965000*x^4 + 30046351500000*x^5 - 8967508000000*x^6 - 1551440000000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-1034067241944 - 10456623559520*x + 2542843429400*x^2 + 28992975061000*x^3 - 1541243426875*x^4 - 20347039687500*x^5 - 1255286500000*x^6 + 136810000000*x^7) + Sqrt[3]*(-1034067241944 - 10087531595520*x + 6700993158200*x^2 + 49662977283000*x^3 - 6624263891875*x^4 - 55555364350000*x^5 - 3797213000000*x^6 + 8532280000000*x^7 + 95200000000*x^8 + Sqrt[1 - 2*x]*(1034067241944 + 11281222823640*x + 6088728853900*x^2 - 35235504540500*x^3 - 18014187125000*x^4 + 27890989500000*x^5 + 12504580000000*x^6 - 713680000000*x^7)))/(6400*Sqrt[3]*Sqrt[3 + 5*x]*(287530496 - 220512160*x - 162998000*x^2 + 8921000*x^3) + 6400*(-865716488 - 32289760*x + 1253327000*x^2 + 79738000*x^3 - 8550625*x^4) + Sqrt[1 - 2*x]*(6400*(852279560 + 794989800*x - 297203500*x^2 - 48482500*x^3) + 6400*Sqrt[3]*Sqrt[3 + 5*x]*(-283051520 - 36412000*x + 53178000*x^2 + 595000*x^3))) + (43923*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(3200*Sqrt[10])","B",1
2341,1,498,128,2.2292251,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x),x]","-\frac{49}{81} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-1881000000 x^5+16061925000 x^4-1834148250 x^3-18366975275 x^2+5134960820 x+1920372124\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-107700000 x^5-7054807500 x^4+6575424625 x^3+9080321325 x^2-7416419280 x-1920372124\right)+\sqrt{3} \left(702000000 x^6-2834550000 x^5-26010202500 x^4+21157768375 x^3+13829985225 x^2+\sqrt{1-2 x} \left(2752200000 x^5+8781795000 x^4-18209078250 x^3-2763042975 x^2+8895802300 x+1920372124\right)-6614343840 x-1920372124\right)}{2160 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right)+\sqrt{1-2 x} \left(2160 \left(-391875 x^2+2827000 x+3481060\right)+2160 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right)\right)+2160 \left(44875 x^3+2976525 x^2-279060 x-3667684\right)}+\frac{19573 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{3240 \sqrt{10}}","\frac{1}{9} (1-2 x)^{3/2} (5 x+3)^{3/2}+\frac{37}{180} \sqrt{1-2 x} (5 x+3)^{3/2}-\frac{1781 \sqrt{1-2 x} \sqrt{5 x+3}}{2160}+\frac{19573 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{6480 \sqrt{10}}-\frac{14}{81} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[3 + 5*x]*(1920372124 + 5134960820*x - 18366975275*x^2 - 1834148250*x^3 + 16061925000*x^4 - 1881000000*x^5) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-1920372124 - 7416419280*x + 9080321325*x^2 + 6575424625*x^3 - 7054807500*x^4 - 107700000*x^5) + Sqrt[3]*(-1920372124 - 6614343840*x + 13829985225*x^2 + 21157768375*x^3 - 26010202500*x^4 - 2834550000*x^5 + 702000000*x^6 + Sqrt[1 - 2*x]*(1920372124 + 8895802300*x - 2763042975*x^2 - 18209078250*x^3 + 8781795000*x^4 + 2752200000*x^5)))/(2160*Sqrt[3]*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 2160*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(2160*(3481060 + 2827000*x - 391875*x^2) + 2160*Sqrt[3]*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (19573*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(3240*Sqrt[10]) - (49*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ])/81","C",1
2342,1,589,135,2.4560493,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^2,x]","-\frac{259}{27} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{1295}{54} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-47025000 x^5+445046250 x^4-413032125 x^3-1730538590 x^2+251285276 x+751141864\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-2692500 x^5-173879625 x^4+347987725 x^3+469351590 x^2-989052420 x-751141864\right)+\sqrt{3} \left(17550000 x^6-87097500 x^5-619987125 x^4+1742592775 x^3+1792844910 x^2+\sqrt{1-2 x} \left(68805000 x^5+155900250 x^4-886907175 x^3+87627210 x^2+1619483140 x+751141864\right)-881715996 x-751141864\right)}{36 \sqrt{3} (3 x+2) \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right)+\sqrt{1-2 x} \left(36 (3 x+2) \left(-391875 x^2+2827000 x+3481060\right)+36 \sqrt{3} (3 x+2) \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right)\right)+36 (3 x+2) \left(44875 x^3+2976525 x^2-279060 x-3667684\right)}+\frac{1649 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{54 \sqrt{10}}","-\frac{1}{3} \sqrt{1-2 x} (5 x+3)^{3/2}-\frac{(1-2 x)^{3/2} (5 x+3)^{3/2}}{3 (3 x+2)}+\frac{107}{36} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{1649 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{108 \sqrt{10}}+\frac{37}{27} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[3 + 5*x]*(751141864 + 251285276*x - 1730538590*x^2 - 413032125*x^3 + 445046250*x^4 - 47025000*x^5) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-751141864 - 989052420*x + 469351590*x^2 + 347987725*x^3 - 173879625*x^4 - 2692500*x^5) + Sqrt[3]*(-751141864 - 881715996*x + 1792844910*x^2 + 1742592775*x^3 - 619987125*x^4 - 87097500*x^5 + 17550000*x^6 + Sqrt[1 - 2*x]*(751141864 + 1619483140*x + 87627210*x^2 - 886907175*x^3 + 155900250*x^4 + 68805000*x^5)))/(36*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 36*(2 + 3*x)*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(36*(2 + 3*x)*(3481060 + 2827000*x - 391875*x^2) + 36*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (1649*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(54*Sqrt[10]) - (259*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/27 + (1295*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/54","C",1
2343,1,597,142,2.5569876,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^3,x]","\frac{1649}{108} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{8245}{216} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-94050000 x^5+721386600 x^4+3711820695 x^3+1984652252 x^2-1945755284 x-1218833968\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-5385000 x^5-406624125 x^4-933910525 x^3+1482326400 x^2+3127326660 x+1218833968\right)+\sqrt{3} \left(35100000 x^6-29224125 x^5-2838556425 x^4-5694152830 x^3-822923532 x^2+\sqrt{1-2 x} \left(137610000 x^5+1099902375 x^4+455170650 x^3-3641177100 x^2-4155500800 x-1218833968\right)+2973929424 x+1218833968\right)}{36 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right) (3 x+2)^2+\sqrt{1-2 x} \left(36 \left(-391875 x^2+2827000 x+3481060\right) (3 x+2)^2+36 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right) (3 x+2)^2\right)+36 \left(44875 x^3+2976525 x^2-279060 x-3667684\right) (3 x+2)^2}-\frac{74}{27} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{37 \sqrt{1-2 x} (5 x+3)^{3/2}}{12 (3 x+2)}-\frac{(1-2 x)^{3/2} (5 x+3)^{3/2}}{6 (3 x+2)^2}-\frac{205}{36} \sqrt{1-2 x} \sqrt{5 x+3}-\frac{37}{27} \sqrt{10} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{1649 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{108 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-1218833968 - 1945755284*x + 1984652252*x^2 + 3711820695*x^3 + 721386600*x^4 - 94050000*x^5) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1218833968 + 3127326660*x + 1482326400*x^2 - 933910525*x^3 - 406624125*x^4 - 5385000*x^5) + Sqrt[3]*(1218833968 + 2973929424*x - 822923532*x^2 - 5694152830*x^3 - 2838556425*x^4 - 29224125*x^5 + 35100000*x^6 + Sqrt[1 - 2*x]*(-1218833968 - 4155500800*x - 3641177100*x^2 + 455170650*x^3 + 1099902375*x^4 + 137610000*x^5)))/(36*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 36*(2 + 3*x)^2*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(36*(2 + 3*x)^2*(3481060 + 2827000*x - 391875*x^2) + 36*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) - (74*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/27 + (1649*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/108 - (8245*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/216","C",1
2344,1,597,149,2.6429507,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^4,x]","\frac{19573 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{4536}-\frac{97865 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{9072}+\frac{\sqrt{5 x+3} \left(581669550 x^5-175735786215 x^4-247420180854 x^3+19680145892 x^2+135896394568 x+43764642944\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(2683525875 x^5+55251353475 x^4-21197714650 x^3-207576376044 x^2-178343596488 x-43764642944\right)+\sqrt{3} \left(-4634118000 x^6+75441830850 x^5+358652096910 x^4+268885045544 x^3-117374654232 x^2+\sqrt{1-2 x} \left(-30003509250 x^5-70052731650 x^4+141879811920 x^3+341084760984 x^2+215255340608 x+43764642944\right)-172808138688 x-43764642944\right)}{1512 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right) (3 x+2)^3+\sqrt{1-2 x} \left(1512 \left(-391875 x^2+2827000 x+3481060\right) (3 x+2)^3+1512 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right) (3 x+2)^3\right)+1512 \left(44875 x^3+2976525 x^2-279060 x-3667684\right) (3 x+2)^3}+\frac{40}{81} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{37 \sqrt{1-2 x} (5 x+3)^{3/2}}{36 (3 x+2)^2}-\frac{(1-2 x)^{3/2} (5 x+3)^{3/2}}{9 (3 x+2)^3}-\frac{661 \sqrt{1-2 x} \sqrt{5 x+3}}{1512 (3 x+2)}+\frac{20}{81} \sqrt{10} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{19573 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{4536 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(43764642944 + 135896394568*x + 19680145892*x^2 - 247420180854*x^3 - 175735786215*x^4 + 581669550*x^5) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-43764642944 - 178343596488*x - 207576376044*x^2 - 21197714650*x^3 + 55251353475*x^4 + 2683525875*x^5) + Sqrt[3]*(-43764642944 - 172808138688*x - 117374654232*x^2 + 268885045544*x^3 + 358652096910*x^4 + 75441830850*x^5 - 4634118000*x^6 + Sqrt[1 - 2*x]*(43764642944 + 215255340608*x + 341084760984*x^2 + 141879811920*x^3 - 70052731650*x^4 - 30003509250*x^5)))/(1512*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 1512*(2 + 3*x)^3*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(1512*(2 + 3*x)^3*(3481060 + 2827000*x - 391875*x^2) + 1512*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (40*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/81 + (19573*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/4536 - (97865*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/9072","C",1
2345,1,599,151,2.5656318,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^5,x]","\frac{43923 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{3136}-\frac{219615 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{6272}+\frac{\sqrt{5 x+3} \left(-14101718510000 x^7-6854963945500 x^6+369142720164900 x^5+767263326168680 x^4+372572493061560 x^3-220704233912800 x^2-241165636333600 x-55561821955200\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(563637424375 x^7-33111466417000 x^6-193930927600500 x^5-158450035374160 x^4+296229499907992 x^3+536196738019520 x^2+296003745346720 x+55561821955200\right)+\sqrt{3} \left(1998462315625 x^8+45251943550000 x^7-153644754593000 x^6-868049706926800 x^5-1098468772117480 x^4-257270399362560 x^3+401983464900800 x^2+\sqrt{1-2 x} \left(3484749867500 x^7+139391507480500 x^6+341785263448200 x^5+27134905039000 x^4-655253639038592 x^3-763342705685120 x^2-342473576142720 x-55561821955200\right)+287635467129600 x+55561821955200\right)}{3136 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^4+\sqrt{1-2 x} \left(3136 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^4+3136 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^4\right)+3136 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^4}","\frac{11 \sqrt{1-2 x} (5 x+3)^{5/2}}{8 (3 x+2)^3}+\frac{(1-2 x)^{3/2} (5 x+3)^{5/2}}{4 (3 x+2)^4}-\frac{121 \sqrt{1-2 x} (5 x+3)^{3/2}}{224 (3 x+2)^2}-\frac{3993 \sqrt{1-2 x} \sqrt{5 x+3}}{3136 (3 x+2)}-\frac{43923 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{3136 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-55561821955200 - 241165636333600*x - 220704233912800*x^2 + 372572493061560*x^3 + 767263326168680*x^4 + 369142720164900*x^5 - 6854963945500*x^6 - 14101718510000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(55561821955200 + 296003745346720*x + 536196738019520*x^2 + 296229499907992*x^3 - 158450035374160*x^4 - 193930927600500*x^5 - 33111466417000*x^6 + 563637424375*x^7) + Sqrt[3]*(55561821955200 + 287635467129600*x + 401983464900800*x^2 - 257270399362560*x^3 - 1098468772117480*x^4 - 868049706926800*x^5 - 153644754593000*x^6 + 45251943550000*x^7 + 1998462315625*x^8 + Sqrt[1 - 2*x]*(-55561821955200 - 342473576142720*x - 763342705685120*x^2 - 655253639038592*x^3 + 27134905039000*x^4 + 341785263448200*x^5 + 139391507480500*x^6 + 3484749867500*x^7)))/(3136*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 3136*(2 + 3*x)^4*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(3136*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 3136*(2 + 3*x)^4*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) + (43923*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/3136 - (219615*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/6272","C",1
2346,1,659,180,3.127769,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^6,x]","\frac{1625151 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{43904}-\frac{8125755 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{87808}+\frac{\sqrt{5 x+3} \left(-193704777501675000 x^9-9389237800662314375 x^8-19932996529723302850 x^7+46530142523010199680 x^6+163344333172928781104 x^5+149228349622897508480 x^4+17044619180930218240 x^3-50039045578021727040 x^2-29215963350290879360 x-5045283093574715904\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(35573195956171875 x^9+1057012467440890625 x^8-9225364916504243750 x^7-56149111038617133000 x^6-82483228178851577600 x^5-6915318949589224480 x^4+87113138004337232000 x^3+86505076238824066496 x^2+34240601453207444864 x+5045283093574715904\right)+\sqrt{3} \left(-27004530343340625 x^{10}+3181576326027578125 x^9+24918904076203512500 x^8+7624130485252911000 x^7-142996945911574894600 x^6-274336956718802183504 x^5-173792744840117671680 x^4+15952033941184432960 x^3+72623498825981239040 x^2+\sqrt{1-2 x} \left(-490754611278421875 x^9+400625800783312500 x^8+37342396816484100000 x^7+113675275761831135000 x^6+101967638147883882000 x^5-44085320144019320320 x^4-148748136954580025280 x^3-113280062187130716416 x^2-38448338312436374784 x-5045283093574715904\right)+33423700209519809280 x+5045283093574715904\right)}{219520 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right) (3 x+2)^5+\sqrt{1-2 x} \left(219520 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right) (3 x+2)^5+219520 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right) (3 x+2)^5\right)+219520 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right) (3 x+2)^5}","\frac{407 \sqrt{1-2 x} (5 x+3)^{5/2}}{112 (3 x+2)^3}+\frac{37 (1-2 x)^{3/2} (5 x+3)^{5/2}}{56 (3 x+2)^4}+\frac{3 (1-2 x)^{5/2} (5 x+3)^{5/2}}{35 (3 x+2)^5}-\frac{4477 \sqrt{1-2 x} (5 x+3)^{3/2}}{3136 (3 x+2)^2}-\frac{147741 \sqrt{1-2 x} \sqrt{5 x+3}}{43904 (3 x+2)}-\frac{1625151 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{43904 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-5045283093574715904 - 29215963350290879360*x - 50039045578021727040*x^2 + 17044619180930218240*x^3 + 149228349622897508480*x^4 + 163344333172928781104*x^5 + 46530142523010199680*x^6 - 19932996529723302850*x^7 - 9389237800662314375*x^8 - 193704777501675000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(5045283093574715904 + 34240601453207444864*x + 86505076238824066496*x^2 + 87113138004337232000*x^3 - 6915318949589224480*x^4 - 82483228178851577600*x^5 - 56149111038617133000*x^6 - 9225364916504243750*x^7 + 1057012467440890625*x^8 + 35573195956171875*x^9) + Sqrt[3]*(5045283093574715904 + 33423700209519809280*x + 72623498825981239040*x^2 + 15952033941184432960*x^3 - 173792744840117671680*x^4 - 274336956718802183504*x^5 - 142996945911574894600*x^6 + 7624130485252911000*x^7 + 24918904076203512500*x^8 + 3181576326027578125*x^9 - 27004530343340625*x^10 + Sqrt[1 - 2*x]*(-5045283093574715904 - 38448338312436374784*x - 113280062187130716416*x^2 - 148748136954580025280*x^3 - 44085320144019320320*x^4 + 101967638147883882000*x^5 + 113675275761831135000*x^6 + 37342396816484100000*x^7 + 400625800783312500*x^8 - 490754611278421875*x^9)))/(219520*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 219520*(2 + 3*x)^5*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(219520*(2 + 3*x)^5*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 219520*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (1625151*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/43904 - (8125755*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/87808","C",1
2347,1,719,209,3.8479841,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^7,x]","\frac{19457889 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{175616}-\frac{97289445 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{351232}+\frac{\sqrt{5 x+3} \left(-1228979586732353775000 x^{11}+6360496121165119518750 x^{10}+217082334103115011764750 x^9+625389868374717778413400 x^8+112824951646680873881600 x^7-1695739061137249618930176 x^6-2572394550817594959491904 x^5-1284717562843583755265280 x^4+242092469005429260472320 x^3+531629559932170367275520 x^2+213358769476043299964416 x+29305954430585775765504\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(22696979709268171875 x^{11}-5275429254299149500000 x^{10}-49819992579703978581250 x^9+50604083200466455599000 x^8+769748231767718275964800 x^7+1609575418195695555196480 x^6+1138348587302868994160640 x^5-383062716297727981181440 x^4-1161129949517936876820224 x^3-788279861359163413588992 x^2-242628672217295393390080 x-29305954430585775765504\right)+\sqrt{3} \left(132863309752935515625 x^{12}+4589220800372029087500 x^{11}-84970552748292791943750 x^{10}-596206027233613235037000 x^9-903089354336424817092600 x^8+741424701480619603186080 x^7+3421807214110947216564096 x^6+3627245056927715789090304 x^5+1214528996894460748039680 x^4-619491279761451966942720 x^3-699238079673600278438400 x^2-237784441605073113102336 x+\sqrt{1-2 x} \left(524816102006395031250 x^{11}+29541592269241918593750 x^{10}+72618728590509577410000 x^9-398883809016857836947000 x^8-1767463922045625779527200 x^7-2520738012820191461647680 x^6-1056969863647912679562240 x^5+1138435757561212207426560 x^4+1742232139744178756112384 x^3+980284010155178402606592 x^2+267054344346325206528000 x+29305954430585775765504\right)-29305954430585775765504\right)}{878080 \sqrt{3} \sqrt{5 x+3} \left(-25265212500 x^5+1941218400000 x^4+5284290066000 x^3-24057375117600 x^2-13825440024000 x+16748592098304\right) (3 x+2)^6+\sqrt{1-2 x} \left(878080 \sqrt{3} \sqrt{5 x+3} \left(-2625187500 x^5-345183000000 x^4+1378186950000 x^3+13912170444000 x^2-2687092123200 x-16725373086720\right) (3 x+2)^6+878080 \left(236425406250 x^5+2220611593750 x^4-28520358020000 x^3-52011357156000 x^2+49788771586400 x+50183931760160\right) (3 x+2)^6\right)+878080 \left(23653109375 x^6-916525237500 x^5-21026153381250 x^4+17065853944000 x^3+123670456765200 x^2-301410173760 x-50253588794912\right) (3 x+2)^6}","\frac{37 \sqrt{1-2 x} (5 x+3)^{3/2}}{180 (3 x+2)^5}-\frac{(1-2 x)^{3/2} (5 x+3)^{3/2}}{18 (3 x+2)^6}+\frac{137752591 \sqrt{1-2 x} \sqrt{5 x+3}}{14224896 (3 x+2)}+\frac{1316353 \sqrt{1-2 x} \sqrt{5 x+3}}{1016064 (3 x+2)^2}+\frac{37333 \sqrt{1-2 x} \sqrt{5 x+3}}{181440 (3 x+2)^3}-\frac{7591 \sqrt{1-2 x} \sqrt{5 x+3}}{30240 (3 x+2)^4}-\frac{19457889 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{175616 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(29305954430585775765504 + 213358769476043299964416*x + 531629559932170367275520*x^2 + 242092469005429260472320*x^3 - 1284717562843583755265280*x^4 - 2572394550817594959491904*x^5 - 1695739061137249618930176*x^6 + 112824951646680873881600*x^7 + 625389868374717778413400*x^8 + 217082334103115011764750*x^9 + 6360496121165119518750*x^10 - 1228979586732353775000*x^11) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-29305954430585775765504 - 242628672217295393390080*x - 788279861359163413588992*x^2 - 1161129949517936876820224*x^3 - 383062716297727981181440*x^4 + 1138348587302868994160640*x^5 + 1609575418195695555196480*x^6 + 769748231767718275964800*x^7 + 50604083200466455599000*x^8 - 49819992579703978581250*x^9 - 5275429254299149500000*x^10 + 22696979709268171875*x^11) + Sqrt[3]*(-29305954430585775765504 - 237784441605073113102336*x - 699238079673600278438400*x^2 - 619491279761451966942720*x^3 + 1214528996894460748039680*x^4 + 3627245056927715789090304*x^5 + 3421807214110947216564096*x^6 + 741424701480619603186080*x^7 - 903089354336424817092600*x^8 - 596206027233613235037000*x^9 - 84970552748292791943750*x^10 + 4589220800372029087500*x^11 + 132863309752935515625*x^12 + Sqrt[1 - 2*x]*(29305954430585775765504 + 267054344346325206528000*x + 980284010155178402606592*x^2 + 1742232139744178756112384*x^3 + 1138435757561212207426560*x^4 - 1056969863647912679562240*x^5 - 2520738012820191461647680*x^6 - 1767463922045625779527200*x^7 - 398883809016857836947000*x^8 + 72618728590509577410000*x^9 + 29541592269241918593750*x^10 + 524816102006395031250*x^11)))/(878080*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(16748592098304 - 13825440024000*x - 24057375117600*x^2 + 5284290066000*x^3 + 1941218400000*x^4 - 25265212500*x^5) + 878080*(2 + 3*x)^6*(-50253588794912 - 301410173760*x + 123670456765200*x^2 + 17065853944000*x^3 - 21026153381250*x^4 - 916525237500*x^5 + 23653109375*x^6) + Sqrt[1 - 2*x]*(878080*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(-16725373086720 - 2687092123200*x + 13912170444000*x^2 + 1378186950000*x^3 - 345183000000*x^4 - 2625187500*x^5) + 878080*(2 + 3*x)^6*(50183931760160 + 49788771586400*x - 52011357156000*x^2 - 28520358020000*x^3 + 2220611593750*x^4 + 236425406250*x^5))) + (19457889*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/175616 - (97289445*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/351232","C",1
2348,1,779,238,4.4930802,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^8} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^8,x]","\frac{6219452877 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{17210368}-\frac{31097264385 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{34420736}+\frac{\sqrt{5 x+3} \left(-42120654046094658832875000 x^{13}-2637814853661382807103278125 x^{12}-3067996363135992834615011250 x^{11}+91818302037896514986573525000 x^{10}+342853862074965559618923216000 x^9+365508493838016335849173429760 x^8-234778395302584706190943763328 x^7-892416173699824142285499834944 x^6-795419127382616275079529374848 x^5-203664053895616725607988225280 x^4+143664346584193119784096504320 x^3+129852245101314257031689817088 x^2+39813181341547243459792635904 x+4535349639403684768789782528\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(3931766254948807540546875 x^{13}+142893715052900036125828125 x^{12}-5256691923213117583598531250 x^{11}-40871981931632483778452845000 x^{10}-50468448988170719530454900000 x^9+185129456335633648699722747200 x^8+628227632950615426746528898880 x^7+733411121162334749472581412800 x^6+261215914577071184117841837440 x^5-251652641800896146311921123072 x^4-344200209829582369937491730944 x^3-176432416690466593492031366144 x^2-44346868030317921435700160512 x-4535349639403684768789782528\right)+\sqrt{3} \left(-1538580181331981754140625 x^{14}+723377982478691496959578125 x^{13}+7799633954130826909299825000 x^{12}-27135977182043390957901467500 x^{11}-279093525743077805676414415000 x^{10}-624277856106184419542352212400 x^9-323819481440356247383736181120 x^8+773709004485664967606605622848 x^7+1470134390675762589788181737984 x^6+987856433607215084890373845248 x^5+118872570363098947459124385280 x^4-239362092503623305509879285760 x^3-161454582647464302009020561408 x^2-43592768895897584933784121344 x+\sqrt{1-2 x} \left(-65814788838607177846640625 x^{13}+726642123407324539265812500 x^{12}+24105652369782799207296712500 x^{11}+85642793890805637321808555000 x^{10}-10087359403303265548556630000 x^9-539915658122736704887063409600 x^8-1134467699591285957647261842880 x^7-978472233495741641777997254400 x^6-131737732018612652320651239680 x^5+488694270520130468924117115392 x^4+477140223530518656194146801664 x^3+211812955998772807615951714304 x^2+48126455584668262909691645952 x+4535349639403684768789782528\right)-4535349639403684768789782528\right)}{86051840 \sqrt{3} \sqrt{5 x+3} \left(-5663973218750 x^6-52303209612500 x^5+1428846604955000 x^4+2194696763160000 x^3-7555736895916000 x^2-3365532949972160 x+4051435671804928\right) (3 x+2)^7+\sqrt{1-2 x} \left(86051840 \left(-3042263984375 x^6+486365726000000 x^5+1796810007300000 x^4-11790948756840000 x^3-17392813876790000 x^2+12117692004316800 x+12149682333912640\right) (3 x+2)^7+86051840 \sqrt{3} \sqrt{5 x+3} \left(223405156250 x^6-14941831687500 x^5-390402719125000 x^4+702446326920000 x^3+4956682106340000 x^2-666120123963200 x-4049763902970880\right) (3 x+2)^7\right)+86051840 \left(905821796875 x^7+135547777203125 x^6-996207107350000 x^5-11461663884510000 x^4+5424159101550000 x^3+35265969543725200 x^2-26521579595840 x-12154697640414784\right) (3 x+2)^7}","\frac{37 \sqrt{1-2 x} (5 x+3)^{3/2}}{252 (3 x+2)^6}-\frac{(1-2 x)^{3/2} (5 x+3)^{3/2}}{21 (3 x+2)^7}+\frac{14677525921 \sqrt{1-2 x} \sqrt{5 x+3}}{464679936 (3 x+2)}+\frac{140331343 \sqrt{1-2 x} \sqrt{5 x+3}}{33191424 (3 x+2)^2}+\frac{4014523 \sqrt{1-2 x} \sqrt{5 x+3}}{5927040 (3 x+2)^3}+\frac{341917 \sqrt{1-2 x} \sqrt{5 x+3}}{2963520 (3 x+2)^4}-\frac{9901 \sqrt{1-2 x} \sqrt{5 x+3}}{52920 (3 x+2)^5}-\frac{6219452877 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{17210368 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(4535349639403684768789782528 + 39813181341547243459792635904*x + 129852245101314257031689817088*x^2 + 143664346584193119784096504320*x^3 - 203664053895616725607988225280*x^4 - 795419127382616275079529374848*x^5 - 892416173699824142285499834944*x^6 - 234778395302584706190943763328*x^7 + 365508493838016335849173429760*x^8 + 342853862074965559618923216000*x^9 + 91818302037896514986573525000*x^10 - 3067996363135992834615011250*x^11 - 2637814853661382807103278125*x^12 - 42120654046094658832875000*x^13) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-4535349639403684768789782528 - 44346868030317921435700160512*x - 176432416690466593492031366144*x^2 - 344200209829582369937491730944*x^3 - 251652641800896146311921123072*x^4 + 261215914577071184117841837440*x^5 + 733411121162334749472581412800*x^6 + 628227632950615426746528898880*x^7 + 185129456335633648699722747200*x^8 - 50468448988170719530454900000*x^9 - 40871981931632483778452845000*x^10 - 5256691923213117583598531250*x^11 + 142893715052900036125828125*x^12 + 3931766254948807540546875*x^13) + Sqrt[3]*(-4535349639403684768789782528 - 43592768895897584933784121344*x - 161454582647464302009020561408*x^2 - 239362092503623305509879285760*x^3 + 118872570363098947459124385280*x^4 + 987856433607215084890373845248*x^5 + 1470134390675762589788181737984*x^6 + 773709004485664967606605622848*x^7 - 323819481440356247383736181120*x^8 - 624277856106184419542352212400*x^9 - 279093525743077805676414415000*x^10 - 27135977182043390957901467500*x^11 + 7799633954130826909299825000*x^12 + 723377982478691496959578125*x^13 - 1538580181331981754140625*x^14 + Sqrt[1 - 2*x]*(4535349639403684768789782528 + 48126455584668262909691645952*x + 211812955998772807615951714304*x^2 + 477140223530518656194146801664*x^3 + 488694270520130468924117115392*x^4 - 131737732018612652320651239680*x^5 - 978472233495741641777997254400*x^6 - 1134467699591285957647261842880*x^7 - 539915658122736704887063409600*x^8 - 10087359403303265548556630000*x^9 + 85642793890805637321808555000*x^10 + 24105652369782799207296712500*x^11 + 726642123407324539265812500*x^12 - 65814788838607177846640625*x^13)))/(86051840*Sqrt[3]*(2 + 3*x)^7*Sqrt[3 + 5*x]*(4051435671804928 - 3365532949972160*x - 7555736895916000*x^2 + 2194696763160000*x^3 + 1428846604955000*x^4 - 52303209612500*x^5 - 5663973218750*x^6) + 86051840*(2 + 3*x)^7*(-12154697640414784 - 26521579595840*x + 35265969543725200*x^2 + 5424159101550000*x^3 - 11461663884510000*x^4 - 996207107350000*x^5 + 135547777203125*x^6 + 905821796875*x^7) + Sqrt[1 - 2*x]*(86051840*(2 + 3*x)^7*(12149682333912640 + 12117692004316800*x - 17392813876790000*x^2 - 11790948756840000*x^3 + 1796810007300000*x^4 + 486365726000000*x^5 - 3042263984375*x^6) + 86051840*Sqrt[3]*(2 + 3*x)^7*Sqrt[3 + 5*x]*(-4049763902970880 - 666120123963200*x + 4956682106340000*x^2 + 702446326920000*x^3 - 390402719125000*x^4 - 14941831687500*x^5 + 223405156250*x^6))) + (6219452877*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/17210368 - (31097264385*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/34420736","C",1
2349,1,1503,194,20.9909055,"\int (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(5/2),x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{32} \left(\frac{147858829437 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{16}}{327680000 \sqrt{10} \left(\sqrt{3}-\sqrt{5 x+3}\right)^{32}}+\frac{\left(\frac{135256690563 \sqrt{1-2 x}}{655360000}-\frac{4752}{5} \sqrt{3} \sqrt{5 x+3}+\frac{1733305741437}{655360000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{15}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{31}}+\frac{\left(-\frac{752874363521 \sqrt{1-2 x}}{327680000}-\frac{372912}{25} \sqrt{3} \sqrt{5 x+3}+\frac{15416370862721}{327680000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{29}}+\frac{\left(-\frac{54749092177279 \sqrt{1-2 x}}{409600000}-\frac{12064432}{125} \sqrt{3} \sqrt{5 x+3}+\frac{173347284510079}{409600000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{13}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{27}}+\frac{\left(-\frac{2703824273624963 \sqrt{1-2 x}}{1433600000}+\frac{92874608}{625} \sqrt{3} \sqrt{5 x+3}+\frac{2064728091086723}{1433600000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{25}}+\frac{\left(-\frac{2551604981899733 \sqrt{1-2 x}}{179200000}+\frac{22695127536 \sqrt{3} \sqrt{5 x+3}}{3125}-\frac{1352683198373419}{179200000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{11}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{23}}+\frac{\left(-\frac{5690261921695717 \sqrt{1-2 x}}{89600000}+\frac{185787378192 \sqrt{3} \sqrt{5 x+3}}{3125}-\frac{2058085040173471}{17920000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{21}}+\frac{\left(-\frac{720170406126609 \sqrt{1-2 x}}{4480000}+\frac{1207201686528 \sqrt{3} \sqrt{5 x+3}}{4375}-\frac{2988353174887407}{4480000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{19}}+\frac{\left(-\frac{228806675701413 \sqrt{1-2 x}}{1600000}+\frac{21315449184}{25} \sqrt{3} \sqrt{5 x+3}-\frac{3863759567626587}{1600000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{17}}+\frac{\left(\frac{47296030901589 \sqrt{1-2 x}}{100000}+\frac{233439256768}{125} \sqrt{3} \sqrt{5 x+3}-\frac{607550247144789}{100000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{15}}+\frac{\left(\frac{105363821795921 \sqrt{1-2 x}}{50000}+\frac{9343479234368 \sqrt{3} \sqrt{5 x+3}}{3125}-\frac{110770165009117}{10000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{13}}+\frac{\left(\frac{368336587097721 \sqrt{1-2 x}}{87500}+\frac{11076593170176 \sqrt{3} \sqrt{5 x+3}}{3125}-\frac{259754082678501}{17500}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{11}}+\frac{\left(\frac{45720323492799 \sqrt{1-2 x}}{8750}+\frac{1940145215616}{625} \sqrt{3} \sqrt{5 x+3}-\frac{127206422548671}{8750}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}+\frac{\left(\frac{18560646201708 \sqrt{1-2 x}}{4375}+\frac{1229177161728}{625} \sqrt{3} \sqrt{5 x+3}-\frac{44373366597996}{4375}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}+\frac{\left(\frac{9628424448408 \sqrt{1-2 x}}{4375}+\frac{749970081792}{875} \sqrt{3} \sqrt{5 x+3}-\frac{20877975675288}{4375}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{\frac{276446547648 \sqrt{1-2 x}}{3125}+\frac{90024044544 \sqrt{3} \sqrt{5 x+3}}{3125}-\frac{109303736256}{625}}{\sqrt{3}-\sqrt{5 x+3}}+\frac{\left(\frac{864}{625} \sqrt{1-2 x}+\frac{1728 \sqrt{3} \sqrt{5 x+3}}{3125}-\frac{9504}{3125}\right) \left(2399709615 \sqrt{1-2 x}+833555968 \sqrt{3} \sqrt{5 x+3}-4900377519\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{16}}","-\frac{3}{80} (1-2 x)^{5/2} (3 x+2)^2 (5 x+3)^{7/2}-\frac{9 (1-2 x)^{5/2} (16120 x+25043) (5 x+3)^{7/2}}{448000}-\frac{306029 (1-2 x)^{5/2} (5 x+3)^{5/2}}{256000}-\frac{3366319 (1-2 x)^{5/2} (5 x+3)^{3/2}}{819200}-\frac{37029509 (1-2 x)^{5/2} \sqrt{5 x+3}}{3276800}+\frac{407324599 (1-2 x)^{3/2} \sqrt{5 x+3}}{65536000}+\frac{13441711767 \sqrt{1-2 x} \sqrt{5 x+3}}{655360000}+\frac{147858829437 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{655360000 \sqrt{10}}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^32*(((173347284510079/409600000 - (54749092177279*Sqrt[1 - 2*x])/409600000 - (12064432*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^13)/(Sqrt[3] - Sqrt[3 + 5*x])^27 + ((15416370862721/327680000 - (752874363521*Sqrt[1 - 2*x])/327680000 - (372912*Sqrt[3]*Sqrt[3 + 5*x])/25)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14)/(Sqrt[3] - Sqrt[3 + 5*x])^29 + ((1733305741437/655360000 + (135256690563*Sqrt[1 - 2*x])/655360000 - (4752*Sqrt[3]*Sqrt[3 + 5*x])/5)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^15)/(Sqrt[3] - Sqrt[3 + 5*x])^31 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12*(2064728091086723/1433600000 - (2703824273624963*Sqrt[1 - 2*x])/1433600000 + (92874608*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^25 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^11*(-1352683198373419/179200000 - (2551604981899733*Sqrt[1 - 2*x])/179200000 + (22695127536*Sqrt[3]*Sqrt[3 + 5*x])/3125))/(Sqrt[3] - Sqrt[3 + 5*x])^23 + (-109303736256/625 + (276446547648*Sqrt[1 - 2*x])/3125 + (90024044544*Sqrt[3]*Sqrt[3 + 5*x])/3125)/(Sqrt[3] - Sqrt[3 + 5*x]) + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^10*(-2058085040173471/17920000 - (5690261921695717*Sqrt[1 - 2*x])/89600000 + (185787378192*Sqrt[3]*Sqrt[3 + 5*x])/3125))/(Sqrt[3] - Sqrt[3 + 5*x])^21 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^9*(-2988353174887407/4480000 - (720170406126609*Sqrt[1 - 2*x])/4480000 + (1207201686528*Sqrt[3]*Sqrt[3 + 5*x])/4375))/(Sqrt[3] - Sqrt[3 + 5*x])^19 + ((-9504/3125 + (864*Sqrt[1 - 2*x])/625 + (1728*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-4900377519 + 2399709615*Sqrt[1 - 2*x] + 833555968*Sqrt[3]*Sqrt[3 + 5*x]))/(Sqrt[3] - Sqrt[3 + 5*x])^3 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^8*(-3863759567626587/1600000 - (228806675701413*Sqrt[1 - 2*x])/1600000 + (21315449184*Sqrt[3]*Sqrt[3 + 5*x])/25))/(Sqrt[3] - Sqrt[3 + 5*x])^17 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2*(-20877975675288/4375 + (9628424448408*Sqrt[1 - 2*x])/4375 + (749970081792*Sqrt[3]*Sqrt[3 + 5*x])/875))/(Sqrt[3] - Sqrt[3 + 5*x])^5 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^7*(-607550247144789/100000 + (47296030901589*Sqrt[1 - 2*x])/100000 + (233439256768*Sqrt[3]*Sqrt[3 + 5*x])/125))/(Sqrt[3] - Sqrt[3 + 5*x])^15 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^3*(-44373366597996/4375 + (18560646201708*Sqrt[1 - 2*x])/4375 + (1229177161728*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^7 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^6*(-110770165009117/10000 + (105363821795921*Sqrt[1 - 2*x])/50000 + (9343479234368*Sqrt[3]*Sqrt[3 + 5*x])/3125))/(Sqrt[3] - Sqrt[3 + 5*x])^13 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^4*(-127206422548671/8750 + (45720323492799*Sqrt[1 - 2*x])/8750 + (1940145215616*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^9 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^5*(-259754082678501/17500 + (368336587097721*Sqrt[1 - 2*x])/87500 + (11076593170176*Sqrt[3]*Sqrt[3 + 5*x])/3125))/(Sqrt[3] - Sqrt[3 + 5*x])^11 + (147858829437*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^16*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(327680000*Sqrt[10]*(Sqrt[3] - Sqrt[3 + 5*x])^32)))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^16","B",1
2350,1,1331,187,14.2788702,"\int (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2),x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{28} \left(\frac{378308799 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}{2048000 \sqrt{10} \left(\sqrt{3}-\sqrt{5 x+3}\right)^{28}}+\frac{\left(\frac{506427201 \sqrt{1-2 x}}{4096000}-\frac{1728}{5} \sqrt{3} \sqrt{5 x+3}+\frac{3740305599}{4096000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{13}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{27}}+\frac{\left(\frac{1777610133 \sqrt{1-2 x}}{2048000}-\frac{31848}{5} \sqrt{3} \sqrt{5 x+3}+\frac{37357212267}{2048000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{25}}+\frac{\left(-\frac{49203883413 \sqrt{1-2 x}}{2560000}-\frac{7878272}{125} \sqrt{3} \sqrt{5 x+3}+\frac{533244915093}{2560000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{11}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{23}}+\frac{\left(-\frac{3493334218561 \sqrt{1-2 x}}{8960000}-\frac{218681144}{625} \sqrt{3} \sqrt{5 x+3}+\frac{12898372859713}{8960000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{21}}+\frac{\left(-\frac{3842448149639 \sqrt{1-2 x}}{1120000}-\frac{587702544}{625} \sqrt{3} \sqrt{5 x+3}+\frac{7001937026183}{1120000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{19}}+\frac{\left(-\frac{10032195630391 \sqrt{1-2 x}}{560000}+\frac{250043664}{625} \sqrt{3} \sqrt{5 x+3}+\frac{9360078261559}{560000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{17}}+\frac{\left(-\frac{8514972952071 \sqrt{1-2 x}}{140000}+\frac{53817994752 \sqrt{3} \sqrt{5 x+3}}{4375}+\frac{3348445455879}{140000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{15}}+\frac{\left(-\frac{1409607110007 \sqrt{1-2 x}}{10000}+\frac{28987464864}{625} \sqrt{3} \sqrt{5 x+3}+\frac{3641759307}{2000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{13}}+\frac{\left(-\frac{143403137241}{625} \sqrt{1-2 x}+\frac{60893934784}{625} \sqrt{3} \sqrt{5 x+3}-\frac{39278667111}{625}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{11}}+\frac{\left(-\frac{165818224714}{625} \sqrt{1-2 x}+\frac{81947797952}{625} \sqrt{3} \sqrt{5 x+3}-\frac{80025169142}{625}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}+\frac{\left(-\frac{944600552104 \sqrt{1-2 x}}{4375}+\frac{72315952128}{625} \sqrt{3} \sqrt{5 x+3}-\frac{574034442584}{4375}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}+\frac{\left(-\frac{519024588016 \sqrt{1-2 x}}{4375}+\frac{40602765312}{625} \sqrt{3} \sqrt{5 x+3}-\frac{333633483536}{4375}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{-\frac{26713771776 \sqrt{1-2 x}}{4375}+\frac{13176972288 \sqrt{3} \sqrt{5 x+3}}{4375}-\frac{12817145088}{4375}}{\sqrt{3}-\sqrt{5 x+3}}+\frac{\left(\frac{1152}{875} \sqrt{1-2 x}+\frac{2304 \sqrt{3} \sqrt{5 x+3}}{4375}-\frac{12672}{4375}\right) \left(-150728747 \sqrt{1-2 x}+80068408 \sqrt{3} \sqrt{5 x+3}-89476477\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}","-\frac{47}{400} (1-2 x)^{5/2} (5 x+3)^{7/2}-\frac{3}{70} (1-2 x)^{5/2} (3 x+2) (5 x+3)^{7/2}-\frac{783 (1-2 x)^{5/2} (5 x+3)^{5/2}}{1600}-\frac{8613 (1-2 x)^{5/2} (5 x+3)^{3/2}}{5120}-\frac{94743 (1-2 x)^{5/2} \sqrt{5 x+3}}{20480}+\frac{1042173 (1-2 x)^{3/2} \sqrt{5 x+3}}{409600}+\frac{34391709 \sqrt{1-2 x} \sqrt{5 x+3}}{4096000}+\frac{378308799 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{4096000 \sqrt{10}}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^28*(((7001937026183/1120000 - (3842448149639*Sqrt[1 - 2*x])/1120000 - (587702544*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^9)/(Sqrt[3] - Sqrt[3 + 5*x])^19 + ((12898372859713/8960000 - (3493334218561*Sqrt[1 - 2*x])/8960000 - (218681144*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^10)/(Sqrt[3] - Sqrt[3 + 5*x])^21 + ((533244915093/2560000 - (49203883413*Sqrt[1 - 2*x])/2560000 - (7878272*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^11)/(Sqrt[3] - Sqrt[3 + 5*x])^23 + ((37357212267/2048000 + (1777610133*Sqrt[1 - 2*x])/2048000 - (31848*Sqrt[3]*Sqrt[3 + 5*x])/5)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12)/(Sqrt[3] - Sqrt[3 + 5*x])^25 + ((3740305599/4096000 + (506427201*Sqrt[1 - 2*x])/4096000 - (1728*Sqrt[3]*Sqrt[3 + 5*x])/5)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^13)/(Sqrt[3] - Sqrt[3 + 5*x])^27 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^8*(9360078261559/560000 - (10032195630391*Sqrt[1 - 2*x])/560000 + (250043664*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^17 + (-12817145088/4375 - (26713771776*Sqrt[1 - 2*x])/4375 + (13176972288*Sqrt[3]*Sqrt[3 + 5*x])/4375)/(Sqrt[3] - Sqrt[3 + 5*x]) + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^7*(3348445455879/140000 - (8514972952071*Sqrt[1 - 2*x])/140000 + (53817994752*Sqrt[3]*Sqrt[3 + 5*x])/4375))/(Sqrt[3] - Sqrt[3 + 5*x])^15 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^6*(3641759307/2000 - (1409607110007*Sqrt[1 - 2*x])/10000 + (28987464864*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^13 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2*(-333633483536/4375 - (519024588016*Sqrt[1 - 2*x])/4375 + (40602765312*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^5 + ((-12672/4375 + (1152*Sqrt[1 - 2*x])/875 + (2304*Sqrt[3]*Sqrt[3 + 5*x])/4375)*(-89476477 - 150728747*Sqrt[1 - 2*x] + 80068408*Sqrt[3]*Sqrt[3 + 5*x]))/(Sqrt[3] - Sqrt[3 + 5*x])^3 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^5*(-39278667111/625 - (143403137241*Sqrt[1 - 2*x])/625 + (60893934784*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^11 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^3*(-574034442584/4375 - (944600552104*Sqrt[1 - 2*x])/4375 + (72315952128*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^7 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^4*(-80025169142/625 - (165818224714*Sqrt[1 - 2*x])/625 + (81947797952*Sqrt[3]*Sqrt[3 + 5*x])/625))/(Sqrt[3] - Sqrt[3 + 5*x])^9 + (378308799*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(2048000*Sqrt[10]*(Sqrt[3] - Sqrt[3 + 5*x])^28)))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14","B",1
2351,1,1157,160,9.2800543,"\int (1-2 x)^{3/2} (2+3 x) (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(5/2),x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{24} \left(\frac{8213601 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}{102400 \sqrt{10} \left(\sqrt{3}-\sqrt{5 x+3}\right)^{24}}+\frac{\left(\frac{13904799 \sqrt{1-2 x}}{204800}-108 \sqrt{3} \sqrt{5 x+3}+\frac{52450401}{204800}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{11}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{23}}+\frac{\left(\frac{108168907 \sqrt{1-2 x}}{102400}-\frac{52404}{25} \sqrt{3} \sqrt{5 x+3}+\frac{107154289}{20480}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{21}}+\frac{\left(\frac{734873909 \sqrt{1-2 x}}{128000}-\frac{2843104}{125} \sqrt{3} \sqrt{5 x+3}+\frac{7999141579}{128000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{19}}+\frac{\left(-\frac{182301097 \sqrt{1-2 x}}{64000}-\frac{3800632}{25} \sqrt{3} \sqrt{5 x+3}+\frac{29371154857}{64000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{17}}+\frac{\left(-\frac{1975290207 \sqrt{1-2 x}}{8000}-\frac{81864816}{125} \sqrt{3} \sqrt{5 x+3}+\frac{17693334879}{8000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{15}}+\frac{\left(-\frac{6414657423 \sqrt{1-2 x}}{4000}-\frac{233954448}{125} \sqrt{3} \sqrt{5 x+3}+\frac{28874284431}{4000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{13}}+\frac{\left(-\frac{5331764319 \sqrt{1-2 x}}{1000}-\frac{455507328}{125} \sqrt{3} \sqrt{5 x+3}+\frac{16263940191}{1000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{11}}+\frac{\left(-\frac{5322094377}{500} \sqrt{1-2 x}-\frac{613907808}{125} \sqrt{3} \sqrt{5 x+3}+\frac{12688988073}{500}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}+\frac{\left(-\frac{1654363452}{125} \sqrt{1-2 x}-\frac{113982976}{25} \sqrt{3} \sqrt{5 x+3}+\frac{3364108092}{125}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}+\frac{\left(-\frac{1255731736}{125} \sqrt{1-2 x}-\frac{350543872}{125} \sqrt{3} \sqrt{5 x+3}+\frac{2307363352}{125}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{-\frac{96883136}{125} \sqrt{1-2 x}-\frac{21505536}{125} \sqrt{3} \sqrt{5 x+3}+\frac{161399744}{125}}{\sqrt{3}-\sqrt{5 x+3}}+\frac{\left(-\frac{32}{25} \sqrt{1-2 x}-\frac{64}{125} \sqrt{3} \sqrt{5 x+3}+\frac{352}{125}\right) \left(16651789 \sqrt{1-2 x}+4032288 \sqrt{3} \sqrt{5 x+3}-28748653\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}","-\frac{1}{20} (1-2 x)^{5/2} (5 x+3)^{7/2}-\frac{17}{80} (1-2 x)^{5/2} (5 x+3)^{5/2}-\frac{187}{256} (1-2 x)^{5/2} (5 x+3)^{3/2}-\frac{2057 (1-2 x)^{5/2} \sqrt{5 x+3}}{1024}+\frac{22627 (1-2 x)^{3/2} \sqrt{5 x+3}}{20480}+\frac{746691 \sqrt{1-2 x} \sqrt{5 x+3}}{204800}+\frac{8213601 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{204800 \sqrt{10}}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^24*((161399744/125 - (96883136*Sqrt[1 - 2*x])/125 - (21505536*Sqrt[3]*Sqrt[3 + 5*x])/125)/(Sqrt[3] - Sqrt[3 + 5*x]) + ((2307363352/125 - (1255731736*Sqrt[1 - 2*x])/125 - (350543872*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^5 + ((3364108092/125 - (1654363452*Sqrt[1 - 2*x])/125 - (113982976*Sqrt[3]*Sqrt[3 + 5*x])/25)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^7 + ((12688988073/500 - (5322094377*Sqrt[1 - 2*x])/500 - (613907808*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^9 + ((16263940191/1000 - (5331764319*Sqrt[1 - 2*x])/1000 - (455507328*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^11 + ((28874284431/4000 - (6414657423*Sqrt[1 - 2*x])/4000 - (233954448*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^13 + ((17693334879/8000 - (1975290207*Sqrt[1 - 2*x])/8000 - (81864816*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^7)/(Sqrt[3] - Sqrt[3 + 5*x])^15 + ((29371154857/64000 - (182301097*Sqrt[1 - 2*x])/64000 - (3800632*Sqrt[3]*Sqrt[3 + 5*x])/25)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^8)/(Sqrt[3] - Sqrt[3 + 5*x])^17 + ((7999141579/128000 + (734873909*Sqrt[1 - 2*x])/128000 - (2843104*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^9)/(Sqrt[3] - Sqrt[3 + 5*x])^19 + ((107154289/20480 + (108168907*Sqrt[1 - 2*x])/102400 - (52404*Sqrt[3]*Sqrt[3 + 5*x])/25)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^10)/(Sqrt[3] - Sqrt[3 + 5*x])^21 + ((52450401/204800 + (13904799*Sqrt[1 - 2*x])/204800 - 108*Sqrt[3]*Sqrt[3 + 5*x])*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^11)/(Sqrt[3] - Sqrt[3 + 5*x])^23 + ((352/125 - (32*Sqrt[1 - 2*x])/25 - (64*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-28748653 + 16651789*Sqrt[1 - 2*x] + 4032288*Sqrt[3]*Sqrt[3 + 5*x]))/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (8213601*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(102400*Sqrt[10]*(Sqrt[3] - Sqrt[3 + 5*x])^24)))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12","B",1
2352,1,426,138,2.4600382,"\int (1-2 x)^{3/2} (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2),x]","\frac{\sqrt{5 x+3} \left(-701272000000000 x^9+26145857100000000 x^8+81680344295000000 x^7-100489162503125000 x^6-221043820115593750 x^5+41210585940156875 x^4+157494113751777000 x^3-6949989387047300 x^2-36712149594768560 x+6808885206857712\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-56640800000000 x^9-6354952710000000 x^8+5927014739500000 x^7+119165667831312500 x^6+91143964224065625 x^5-112558497180795375 x^4-106892154673371700 x^3+34804823498033740 x^2+30048261794229440 x-6808885206857712\right)+\sqrt{3} \left(211280000000000 x^{10}-4126401000000000 x^9-88124415850000000 x^8-53153509636250000 x^7+265230879614062500 x^6+229605750520421875 x^5-160958999004304375 x^4-167187761540299500 x^3+40121871050433500 x^2+\sqrt{1-2 x} \left(1622808000000000 x^9+14597843700000000 x^8-70519840809000000 x^7-204686642205375000 x^6-33263779107968750 x^5+202243708194281875 x^4+90880490192569000 x^3-62400047437012340 x^2-24350772897889680 x+6808885206857712\right)+31014660698428800 x-6808885206857712\right)}{25600 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right)+\sqrt{1-2 x} \left(25600 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right)+25600 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right)\right)+25600 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right)}+\frac{483153 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{12800 \sqrt{10}}","-\frac{1}{10} (5 x+3)^{5/2} (1-2 x)^{5/2}-\frac{11}{32} (5 x+3)^{3/2} (1-2 x)^{5/2}-\frac{121}{128} \sqrt{5 x+3} (1-2 x)^{5/2}+\frac{1331 \sqrt{5 x+3} (1-2 x)^{3/2}}{2560}+\frac{43923 \sqrt{5 x+3} \sqrt{1-2 x}}{25600}+\frac{483153 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{25600 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(6808885206857712 - 36712149594768560*x - 6949989387047300*x^2 + 157494113751777000*x^3 + 41210585940156875*x^4 - 221043820115593750*x^5 - 100489162503125000*x^6 + 81680344295000000*x^7 + 26145857100000000*x^8 - 701272000000000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-6808885206857712 + 30048261794229440*x + 34804823498033740*x^2 - 106892154673371700*x^3 - 112558497180795375*x^4 + 91143964224065625*x^5 + 119165667831312500*x^6 + 5927014739500000*x^7 - 6354952710000000*x^8 - 56640800000000*x^9) + Sqrt[3]*(-6808885206857712 + 31014660698428800*x + 40121871050433500*x^2 - 167187761540299500*x^3 - 160958999004304375*x^4 + 229605750520421875*x^5 + 265230879614062500*x^6 - 53153509636250000*x^7 - 88124415850000000*x^8 - 4126401000000000*x^9 + 211280000000000*x^10 + Sqrt[1 - 2*x]*(6808885206857712 - 24350772897889680*x - 62400047437012340*x^2 + 90880490192569000*x^3 + 202243708194281875*x^4 - 33263779107968750*x^5 - 204686642205375000*x^6 - 70519840809000000*x^7 + 14597843700000000*x^8 + 1622808000000000*x^9)))/(25600*Sqrt[3]*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 25600*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(25600*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 25600*Sqrt[3]*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (483153*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(12800*Sqrt[10])","B",1
2353,1,558,150,2.7150007,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x),x]","\frac{49}{243} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-8377776000000 x^7-47679852000000 x^6+165828628020000 x^5+120640735523000 x^4-177594734520500 x^3-63255550406620 x^2+45982254247160 x+4096826933672\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(738774000000 x^7-6844215900000 x^6-109207449712500 x^5+805031988875 x^4+148302303355000 x^3+6062006751080 x^2-50857856414368 x-4096826933672\right)+\sqrt{3} \left(514080000000 x^8+46028616000000 x^7-24555891000000 x^6-294218936290000 x^5-14040150570125 x^4+249998976710600 x^3+24851128571720 x^2+\sqrt{1-2 x} \left(-3853872000000 x^7+67867298400000 x^6+144275142660000 x^5-104544226523000 x^4-173501467947500 x^3+36224298660660 x^2+54090760629928 x+4096826933672\right)-49215158462720 x-4096826933672\right)}{20736 \sqrt{3} \sqrt{5 x+3} \left(8921000 x^3-162998000 x^2-220512160 x+287530496\right)+\sqrt{1-2 x} \left(20736 \left(-48482500 x^3-297203500 x^2+794989800 x+852279560\right)+20736 \sqrt{3} \sqrt{5 x+3} \left(595000 x^3+53178000 x^2-36412000 x-283051520\right)\right)+20736 \left(-8550625 x^4+79738000 x^3+1253327000 x^2-32289760 x-865716488\right)}+\frac{648919 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{31104 \sqrt{10}}","\frac{1}{12} (1-2 x)^{3/2} (5 x+3)^{5/2}+\frac{23}{216} \sqrt{1-2 x} (5 x+3)^{5/2}-\frac{53}{192} \sqrt{1-2 x} (5 x+3)^{3/2}-\frac{15863 \sqrt{1-2 x} \sqrt{5 x+3}}{20736}+\frac{648919 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{62208 \sqrt{10}}+\frac{14}{243} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[3 + 5*x]*(4096826933672 + 45982254247160*x - 63255550406620*x^2 - 177594734520500*x^3 + 120640735523000*x^4 + 165828628020000*x^5 - 47679852000000*x^6 - 8377776000000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-4096826933672 - 50857856414368*x + 6062006751080*x^2 + 148302303355000*x^3 + 805031988875*x^4 - 109207449712500*x^5 - 6844215900000*x^6 + 738774000000*x^7) + Sqrt[3]*(-4096826933672 - 49215158462720*x + 24851128571720*x^2 + 249998976710600*x^3 - 14040150570125*x^4 - 294218936290000*x^5 - 24555891000000*x^6 + 46028616000000*x^7 + 514080000000*x^8 + Sqrt[1 - 2*x]*(4096826933672 + 54090760629928*x + 36224298660660*x^2 - 173501467947500*x^3 - 104544226523000*x^4 + 144275142660000*x^5 + 67867298400000*x^6 - 3853872000000*x^7)))/(20736*Sqrt[3]*Sqrt[3 + 5*x]*(287530496 - 220512160*x - 162998000*x^2 + 8921000*x^3) + 20736*(-865716488 - 32289760*x + 1253327000*x^2 + 79738000*x^3 - 8550625*x^4) + Sqrt[1 - 2*x]*(20736*(852279560 + 794989800*x - 297203500*x^2 - 48482500*x^3) + 20736*Sqrt[3]*Sqrt[3 + 5*x]*(-283051520 - 36412000*x + 53178000*x^2 + 595000*x^3))) + (648919*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(31104*Sqrt[10]) + (49*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ])/243","C",1
2354,1,651,159,3.1117011,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^2,x]","\frac{1267}{243} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{6335}{486} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-61564500000 x^7+590017762500 x^6+8905680065625 x^5-2848081467250 x^4-10341835991000 x^3+2635441704560 x^2+2008123974344 x-1251855865040\right)+\sqrt{5 x+3} \left(698148000000 x^7+3750301500000 x^6-14943775935000 x^5-4856481371500 x^4+14340499442500 x^3-848914689040 x^2-3196427648920 x+1251855865040\right)+\sqrt{3} \left(-42840000000 x^8-3822033000000 x^7+3262754250000 x^6+23065375360625 x^5-5783918635250 x^4-15410275379800 x^3+4057701658640 x^2+\sqrt{1-2 x} \left(321156000000 x^7-5758199700000 x^6-10149789705000 x^5+11296841891500 x^4+9421979198500 x^3-4839195403680 x^2-950130545144 x+1251855865040\right)+2138434219720 x-1251855865040\right)}{1296 \sqrt{3} (3 x+2) \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right)+\sqrt{1-2 x} \left(1296 \sqrt{3} (3 x+2) \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right)+1296 (3 x+2) \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right)\right)+1296 (3 x+2) \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right)}-\frac{43 \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{1944}","-\frac{8}{27} \sqrt{1-2 x} (5 x+3)^{5/2}-\frac{(1-2 x)^{3/2} (5 x+3)^{5/2}}{3 (3 x+2)}+\frac{25}{12} \sqrt{1-2 x} (5 x+3)^{3/2}-\frac{3065 \sqrt{1-2 x} \sqrt{5 x+3}}{1296}-\frac{43 \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{3888}-\frac{181}{243} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-1251855865040 + 2008123974344*x + 2635441704560*x^2 - 10341835991000*x^3 - 2848081467250*x^4 + 8905680065625*x^5 + 590017762500*x^6 - 61564500000*x^7) + Sqrt[3 + 5*x]*(1251855865040 - 3196427648920*x - 848914689040*x^2 + 14340499442500*x^3 - 4856481371500*x^4 - 14943775935000*x^5 + 3750301500000*x^6 + 698148000000*x^7) + Sqrt[3]*(-1251855865040 + 2138434219720*x + 4057701658640*x^2 - 15410275379800*x^3 - 5783918635250*x^4 + 23065375360625*x^5 + 3262754250000*x^6 - 3822033000000*x^7 - 42840000000*x^8 + Sqrt[1 - 2*x]*(1251855865040 - 950130545144*x - 4839195403680*x^2 + 9421979198500*x^3 + 11296841891500*x^4 - 10149789705000*x^5 - 5758199700000*x^6 + 321156000000*x^7)))/(1296*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 1296*(2 + 3*x)*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(1296*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 1296*(2 + 3*x)*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) - (43*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/1944 + (1267*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/243 - (6335*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/486","C",1
2355,1,659,166,3.5120094,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^3,x]","-\frac{6829}{324} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{34145}{648} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-7695562500 x^7+81127134375 x^6+1061256785625 x^5-2077763017000 x^4-4872240455000 x^3+2061292432280 x^2+5896998706760 x+2112721131136\right)+\sqrt{5 x+3} \left(87268500000 x^7+385155375000 x^6-2659879678500 x^5+755382914000 x^4+10331821509460 x^3+4763203714544 x^2-3796590280648 x-2112721131136\right)+\sqrt{3} \left(-5355000000 x^8-472622250000 x^7+905868007500 x^6+3788418164000 x^5-7193544863000 x^4-15014860037680 x^3-2342605088704 x^2+\sqrt{1-2 x} \left(40144500000 x^7-758246775000 x^6-568043190000 x^5+5742200563000 x^4+4602854911600 x^3-6235094954880 x^2-7660463191040 x-2112721131136\right)+5560054764928 x+2112721131136\right)}{108 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^2+\sqrt{1-2 x} \left(108 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^2+108 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^2\right)+108 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^2}+\frac{1945}{162} \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{181 \sqrt{1-2 x} (5 x+3)^{5/2}}{36 (3 x+2)}-\frac{(1-2 x)^{3/2} (5 x+3)^{5/2}}{6 (3 x+2)^2}-\frac{35}{4} \sqrt{1-2 x} (5 x+3)^{3/2}+\frac{185}{27} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{1945}{324} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)+\frac{6829 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{324 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(2112721131136 + 5896998706760*x + 2061292432280*x^2 - 4872240455000*x^3 - 2077763017000*x^4 + 1061256785625*x^5 + 81127134375*x^6 - 7695562500*x^7) + Sqrt[3 + 5*x]*(-2112721131136 - 3796590280648*x + 4763203714544*x^2 + 10331821509460*x^3 + 755382914000*x^4 - 2659879678500*x^5 + 385155375000*x^6 + 87268500000*x^7) + Sqrt[3]*(2112721131136 + 5560054764928*x - 2342605088704*x^2 - 15014860037680*x^3 - 7193544863000*x^4 + 3788418164000*x^5 + 905868007500*x^6 - 472622250000*x^7 - 5355000000*x^8 + Sqrt[1 - 2*x]*(-2112721131136 - 7660463191040*x - 6235094954880*x^2 + 4602854911600*x^3 + 5742200563000*x^4 - 568043190000*x^5 - 758246775000*x^6 + 40144500000*x^7)))/(108*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 108*(2 + 3*x)^2*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(108*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 108*(2 + 3*x)^2*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) + (1945*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/162 - (6829*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/324 + (34145*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/648","C",1
2356,1,657,171,3.5770339,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^4,x]","\frac{326717 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{13608}-\frac{1633585 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{27216}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-646427250000 x^7+4048357895625 x^6+158434177985250 x^5+434423750875000 x^4+50120068746800 x^3-634379811145208 x^2-548831831855216 x-134473328099968\right)+\sqrt{5 x+3} \left(7330554000000 x^7+76163516517000 x^6-74685648922500 x^5-876708512139020 x^4-964953521903008 x^3+31083104853064 x^2+415580180291056 x+134473328099968\right)+\sqrt{3} \left(-449820000000 x^8-44216913558750 x^7-114097511890500 x^6+542493032344000 x^5+1607679569614160 x^4+1044829035089488 x^3-329747737005344 x^2+\sqrt{1-2 x} \left(3372138000000 x^7-59628736200000 x^6-438428866326000 x^5-575074319749600 x^4+325949866169840 x^3+1044371609184288 x^2+661177061521856 x+134473328099968\right)-527925409957696 x-134473328099968\right)}{4536 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^3+\sqrt{1-2 x} \left(4536 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^3+4536 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^3\right)+4536 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^3}-\frac{1150}{243} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{181 \sqrt{1-2 x} (5 x+3)^{5/2}}{108 (3 x+2)^2}-\frac{(1-2 x)^{3/2} (5 x+3)^{5/2}}{9 (3 x+2)^3}+\frac{331 \sqrt{1-2 x} (5 x+3)^{3/2}}{168 (3 x+2)}-\frac{39745 \sqrt{1-2 x} \sqrt{5 x+3}}{4536}-\frac{575}{243} \sqrt{10} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{326717 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{13608 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-134473328099968 - 548831831855216*x - 634379811145208*x^2 + 50120068746800*x^3 + 434423750875000*x^4 + 158434177985250*x^5 + 4048357895625*x^6 - 646427250000*x^7) + Sqrt[3 + 5*x]*(134473328099968 + 415580180291056*x + 31083104853064*x^2 - 964953521903008*x^3 - 876708512139020*x^4 - 74685648922500*x^5 + 76163516517000*x^6 + 7330554000000*x^7) + Sqrt[3]*(-134473328099968 - 527925409957696*x - 329747737005344*x^2 + 1044829035089488*x^3 + 1607679569614160*x^4 + 542493032344000*x^5 - 114097511890500*x^6 - 44216913558750*x^7 - 449820000000*x^8 + Sqrt[1 - 2*x]*(134473328099968 + 661177061521856*x + 1044371609184288*x^2 + 325949866169840*x^3 - 575074319749600*x^4 - 438428866326000*x^5 - 59628736200000*x^6 + 3372138000000*x^7)))/(4536*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 4536*(2 + 3*x)^3*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(4536*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 4536*(2 + 3*x)^3*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) - (1150*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/243 + (326717*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/13608 - (1633585*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/27216","C",1
2357,1,657,178,3.2706422,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^5,x]","\frac{1922677 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{762048}-\frac{9613385 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{1524096}+\frac{\sqrt{5 x+3} \left(-1638746771310000 x^7-4040937577891500 x^6+35896784572852500 x^5+76692664708386760 x^4+34202731152675800 x^3-21234127261482080 x^2-20762692995762080 x-4430815218980480\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(90290754466875 x^7-3010491056301000 x^6-22588890927166500 x^5-20353995465345680 x^4+26162304872954936 x^3+48168008340575680 x^2+25159929242091040 x+4430815218980480\right)+\sqrt{3} \left(190920986578125 x^8+6468552624270000 x^7-10609786025469000 x^6-86248874399334800 x^5-107786872024506760 x^4-22523317734118400 x^3+36992532445804480 x^2+\sqrt{1-2 x} \left(41357910577500 x^7+15020073725266500 x^6+40487347299042600 x^5+9300707222833400 x^4-58766153671198336 x^3-67598586459338880 x^2-28860084653741440 x-4430815218980480\right)+24462848407412480 x+4430815218980480\right)}{254016 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^4+\sqrt{1-2 x} \left(254016 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^4+254016 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^4\right)+254016 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^4}+\frac{200}{243} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{181 \sqrt{1-2 x} (5 x+3)^{5/2}}{216 (3 x+2)^3}-\frac{(1-2 x)^{3/2} (5 x+3)^{5/2}}{12 (3 x+2)^4}-\frac{871 \sqrt{1-2 x} (5 x+3)^{3/2}}{6048 (3 x+2)^2}-\frac{77269 \sqrt{1-2 x} \sqrt{5 x+3}}{254016 (3 x+2)}+\frac{100}{243} \sqrt{10} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{1922677 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{762048 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-4430815218980480 - 20762692995762080*x - 21234127261482080*x^2 + 34202731152675800*x^3 + 76692664708386760*x^4 + 35896784572852500*x^5 - 4040937577891500*x^6 - 1638746771310000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(4430815218980480 + 25159929242091040*x + 48168008340575680*x^2 + 26162304872954936*x^3 - 20353995465345680*x^4 - 22588890927166500*x^5 - 3010491056301000*x^6 + 90290754466875*x^7) + Sqrt[3]*(4430815218980480 + 24462848407412480*x + 36992532445804480*x^2 - 22523317734118400*x^3 - 107786872024506760*x^4 - 86248874399334800*x^5 - 10609786025469000*x^6 + 6468552624270000*x^7 + 190920986578125*x^8 + Sqrt[1 - 2*x]*(-4430815218980480 - 28860084653741440*x - 67598586459338880*x^2 - 58766153671198336*x^3 + 9300707222833400*x^4 + 40487347299042600*x^5 + 15020073725266500*x^6 + 41357910577500*x^7)))/(254016*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 254016*(2 + 3*x)^4*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(254016*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 254016*(2 + 3*x)^4*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) + (200*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/243 + (1922677*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/762048 - (9613385*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/1524096","C",1
2358,1,659,180,3.2600191,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^6,x]","\frac{483153 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{43904}-\frac{2415765 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{87808}+\frac{\sqrt{5 x+3} \left(-57753934095275000 x^9-2634531273696155625 x^8-5710115573934211550 x^7+12582922303020333440 x^6+47051838858296519632 x^5+44414360853893683840 x^4+5508601445013553920 x^3-14721895094514224320 x^2-8574668027794506880 x-1455629848545388032\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(10112487821328125 x^9+288421876447359375 x^8-2602705011662856250 x^7-15916866143839139000 x^6-24344211036285580800 x^5-3031166738956681440 x^4+25084928204874313600 x^3+25395992275209071168 x^2+10025021162465667712 x+1455629848545388032\right)+\sqrt{3} \left(-7228490686334375 x^{10}+905504109565546875 x^9+6982542628166537500 x^8+2658553759537613000 x^7-40097982542448751800 x^6-79956280312221318832 x^5-52051328588694429440 x^4+4196589335568895680 x^3+21359827698389720320 x^2+\sqrt{1-2 x} \left(-137267331644953125 x^9+143455958874937500 x^8+10485553064474400000 x^7+32711210100542985000 x^6+30723201723271574000 x^5-11531758117566184960 x^4-43180686403858315840 x^3-33243404710060534528 x^2-11238898255003491072 x-1455629848545388032\right)+9788545120332330240 x+1455629848545388032\right)}{219520 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right) (3 x+2)^5+\sqrt{1-2 x} \left(219520 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right) (3 x+2)^5+219520 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right) (3 x+2)^5\right)+219520 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right) (3 x+2)^5}","\frac{33 \sqrt{1-2 x} (5 x+3)^{7/2}}{40 (3 x+2)^4}+\frac{(1-2 x)^{3/2} (5 x+3)^{7/2}}{5 (3 x+2)^5}-\frac{121 \sqrt{1-2 x} (5 x+3)^{5/2}}{560 (3 x+2)^3}-\frac{1331 \sqrt{1-2 x} (5 x+3)^{3/2}}{3136 (3 x+2)^2}-\frac{43923 \sqrt{1-2 x} \sqrt{5 x+3}}{43904 (3 x+2)}-\frac{483153 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{43904 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-1455629848545388032 - 8574668027794506880*x - 14721895094514224320*x^2 + 5508601445013553920*x^3 + 44414360853893683840*x^4 + 47051838858296519632*x^5 + 12582922303020333440*x^6 - 5710115573934211550*x^7 - 2634531273696155625*x^8 - 57753934095275000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1455629848545388032 + 10025021162465667712*x + 25395992275209071168*x^2 + 25084928204874313600*x^3 - 3031166738956681440*x^4 - 24344211036285580800*x^5 - 15916866143839139000*x^6 - 2602705011662856250*x^7 + 288421876447359375*x^8 + 10112487821328125*x^9) + Sqrt[3]*(1455629848545388032 + 9788545120332330240*x + 21359827698389720320*x^2 + 4196589335568895680*x^3 - 52051328588694429440*x^4 - 79956280312221318832*x^5 - 40097982542448751800*x^6 + 2658553759537613000*x^7 + 6982542628166537500*x^8 + 905504109565546875*x^9 - 7228490686334375*x^10 + Sqrt[1 - 2*x]*(-1455629848545388032 - 11238898255003491072*x - 33243404710060534528*x^2 - 43180686403858315840*x^3 - 11531758117566184960*x^4 + 30723201723271574000*x^5 + 32711210100542985000*x^6 + 10485553064474400000*x^7 + 143455958874937500*x^8 - 137267331644953125*x^9)))/(219520*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 219520*(2 + 3*x)^5*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(219520*(2 + 3*x)^5*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 219520*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (483153*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/43904 - (2415765*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/87808","C",1
2359,1,719,209,3.8035562,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^7,x]","\frac{4348377 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{175616}-\frac{21741885 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{351232}+\frac{\sqrt{5 x+3} \left(-273782204696608575000 x^{11}+1404260622015683368750 x^{10}+48296274386442984046750 x^9+139279759955580985666200 x^8+25854119892305448268800 x^7-375968887623345563847168 x^6-572500704911386636030272 x^5-287234543729647829751040 x^4+53391462790800182005760 x^3+118508027800784705487360 x^2+47550625648413191935488 x+6510795305072491395072\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(5079738707297796875 x^{11}-1173354917300253500000 x^{10}-11105414376034169931250 x^9+11160300729983132407000 x^8+171020492364009548566400 x^7+358145686149307698456640 x^6+254452066524133684971520 x^5-83939343013619211665920 x^4-258210779804099590053632 x^3-175679409163525573856256 x^2-54053618992231753059840 x-6510795305072491395072\right)+\sqrt{3} \left(29559075029032640625 x^{12}+1025130784177756387500 x^{11}-18882306749873158893750 x^{10}-132700116727995425541000 x^9-201395904365816366191800 x^8+163272410646424563169440 x^7+759833369267908540537728 x^6+808155964246821959081472 x^5+272063265610093511370240 x^4-137515809611467604712960 x^3-155869771353326083699200 x^2-52977163444515268098048 x+\sqrt{1-2 x} \left(116397585686622281250 x^{11}+6577716253097132343750 x^{10}+16227625488929402130000 x^9-88516474692317436171000 x^8-392883457325578155789600 x^7-561506898914024751378240 x^6-237312737587346161720320 x^5+251815804701455305006080 x^4+387718188183051569344512 x^3+218461188877790753005056 x^2+59480156788333829222400 x+6510795305072491395072\right)-6510795305072491395072\right)}{878080 \sqrt{3} \sqrt{5 x+3} \left(-25265212500 x^5+1941218400000 x^4+5284290066000 x^3-24057375117600 x^2-13825440024000 x+16748592098304\right) (3 x+2)^6+\sqrt{1-2 x} \left(878080 \sqrt{3} \sqrt{5 x+3} \left(-2625187500 x^5-345183000000 x^4+1378186950000 x^3+13912170444000 x^2-2687092123200 x-16725373086720\right) (3 x+2)^6+878080 \left(236425406250 x^5+2220611593750 x^4-28520358020000 x^3-52011357156000 x^2+49788771586400 x+50183931760160\right) (3 x+2)^6\right)+878080 \left(23653109375 x^6-916525237500 x^5-21026153381250 x^4+17065853944000 x^3+123670456765200 x^2-301410173760 x-50253588794912\right) (3 x+2)^6}","\frac{297 \sqrt{1-2 x} (5 x+3)^{7/2}}{160 (3 x+2)^4}+\frac{9 (1-2 x)^{3/2} (5 x+3)^{7/2}}{20 (3 x+2)^5}+\frac{(1-2 x)^{5/2} (5 x+3)^{7/2}}{14 (3 x+2)^6}-\frac{1089 \sqrt{1-2 x} (5 x+3)^{5/2}}{2240 (3 x+2)^3}-\frac{11979 \sqrt{1-2 x} (5 x+3)^{3/2}}{12544 (3 x+2)^2}-\frac{395307 \sqrt{1-2 x} \sqrt{5 x+3}}{175616 (3 x+2)}-\frac{4348377 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{175616 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(6510795305072491395072 + 47550625648413191935488*x + 118508027800784705487360*x^2 + 53391462790800182005760*x^3 - 287234543729647829751040*x^4 - 572500704911386636030272*x^5 - 375968887623345563847168*x^6 + 25854119892305448268800*x^7 + 139279759955580985666200*x^8 + 48296274386442984046750*x^9 + 1404260622015683368750*x^10 - 273782204696608575000*x^11) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-6510795305072491395072 - 54053618992231753059840*x - 175679409163525573856256*x^2 - 258210779804099590053632*x^3 - 83939343013619211665920*x^4 + 254452066524133684971520*x^5 + 358145686149307698456640*x^6 + 171020492364009548566400*x^7 + 11160300729983132407000*x^8 - 11105414376034169931250*x^9 - 1173354917300253500000*x^10 + 5079738707297796875*x^11) + Sqrt[3]*(-6510795305072491395072 - 52977163444515268098048*x - 155869771353326083699200*x^2 - 137515809611467604712960*x^3 + 272063265610093511370240*x^4 + 808155964246821959081472*x^5 + 759833369267908540537728*x^6 + 163272410646424563169440*x^7 - 201395904365816366191800*x^8 - 132700116727995425541000*x^9 - 18882306749873158893750*x^10 + 1025130784177756387500*x^11 + 29559075029032640625*x^12 + Sqrt[1 - 2*x]*(6510795305072491395072 + 59480156788333829222400*x + 218461188877790753005056*x^2 + 387718188183051569344512*x^3 + 251815804701455305006080*x^4 - 237312737587346161720320*x^5 - 561506898914024751378240*x^6 - 392883457325578155789600*x^7 - 88516474692317436171000*x^8 + 16227625488929402130000*x^9 + 6577716253097132343750*x^10 + 116397585686622281250*x^11)))/(878080*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(16748592098304 - 13825440024000*x - 24057375117600*x^2 + 5284290066000*x^3 + 1941218400000*x^4 - 25265212500*x^5) + 878080*(2 + 3*x)^6*(-50253588794912 - 301410173760*x + 123670456765200*x^2 + 17065853944000*x^3 - 21026153381250*x^4 - 916525237500*x^5 + 23653109375*x^6) + Sqrt[1 - 2*x]*(878080*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(-16725373086720 - 2687092123200*x + 13912170444000*x^2 + 1378186950000*x^3 - 345183000000*x^4 - 2625187500*x^5) + 878080*(2 + 3*x)^6*(50183931760160 + 49788771586400*x - 52011357156000*x^2 - 28520358020000*x^3 + 2220611593750*x^4 + 236425406250*x^5))) + (4348377*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/175616 - (21741885*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/351232","C",1
2360,1,779,238,4.8425552,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^8} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^8,x]","\frac{1104970911 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{17210368}-\frac{5524854555 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{34420736}+\frac{\sqrt{5 x+3} \left(-7473807602197774501125000 x^{13}-468468787243594039159709375 x^{12}-546706439249090022982983750 x^{11}+16298370156936023071391575000 x^{10}+60881406392779047287698288000 x^9+64931150584517497768687879680 x^8-41626150273919128190467903104 x^7-158401801496487193018980582592 x^6-141237757754048585358878382464 x^5-36197795387810501945399863040 x^4+25496151601253328411478965760 x^3+23059146245009253966641398784 x^2+7069887319115824563893327872 x+804950171118012603919048704\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(698109502006256587265625 x^{13}+25405143359359525379359375 x^{12}-933119154690207423774343750 x^{11}-7258685316521881173882335000 x^{10}-8971686278920958580720700000 x^9+32849842661000593820321329600 x^8+111528530254347483683833211840 x^7+130233242347820938736679086400 x^6+46428462901495586484507425920 x^5-44640445908939832797649495296 x^4-61106218195436504816104084992 x^3-31330087853989274691743419392 x^2-7874543871378377890140092416 x-804950171118012603919048704\right)+\sqrt{3} \left(-273776836415454490546875 x^{14}+128431953068426206761859375 x^{13}+1385724471382738495954975000 x^{12}-4813092353068251337963102500 x^{11}-49550736532037624245239845000 x^{10}-110866981248631007679773133200 x^9-57565105844261970583839788160 x^8+137277073601364414980337462464 x^7+260975989581098174447289933312 x^6+175431357578241806080091089664 x^5+21153556630325637579109143040 x^4-42490061414160886730684487680 x^3-28671127854893301310191724544 x^2-7740701997345147567159201792 x+\sqrt{1-2 x} \left(-11689970882995773655546875 x^{13}+128843858316014300242437500 x^{12}+4280153699611719223508637500 x^{11}+15213107702479885783207865000 x^{10}-1767436600653965604915090000 x^9-95831241088345387410827412800 x^8-201416292744672528678944683840 x^7-173773972925738429239034195200 x^6-23470100773723546508953066240 x^5+86720492390747482320608237056 x^4+84713124447552888279058941952 x^3+37612639459723095640499382272 x^2+8545358549607700893405966336 x+804950171118012603919048704\right)-804950171118012603919048704\right)}{86051840 \sqrt{3} \sqrt{5 x+3} \left(-5663973218750 x^6-52303209612500 x^5+1428846604955000 x^4+2194696763160000 x^3-7555736895916000 x^2-3365532949972160 x+4051435671804928\right) (3 x+2)^7+\sqrt{1-2 x} \left(86051840 \left(-3042263984375 x^6+486365726000000 x^5+1796810007300000 x^4-11790948756840000 x^3-17392813876790000 x^2+12117692004316800 x+12149682333912640\right) (3 x+2)^7+86051840 \sqrt{3} \sqrt{5 x+3} \left(223405156250 x^6-14941831687500 x^5-390402719125000 x^4+702446326920000 x^3+4956682106340000 x^2-666120123963200 x-4049763902970880\right) (3 x+2)^7\right)+86051840 \left(905821796875 x^7+135547777203125 x^6-996207107350000 x^5-11461663884510000 x^4+5424159101550000 x^3+35265969543725200 x^2-26521579595840 x-12154697640414784\right) (3 x+2)^7}","\frac{181 \sqrt{1-2 x} (5 x+3)^{5/2}}{756 (3 x+2)^6}-\frac{(1-2 x)^{3/2} (5 x+3)^{5/2}}{21 (3 x+2)^7}-\frac{12421 \sqrt{1-2 x} (5 x+3)^{3/2}}{52920 (3 x+2)^5}+\frac{23466191827 \sqrt{1-2 x} \sqrt{5 x+3}}{4182119424 (3 x+2)}+\frac{224018941 \sqrt{1-2 x} \sqrt{5 x+3}}{298722816 (3 x+2)^2}+\frac{6249601 \sqrt{1-2 x} \sqrt{5 x+3}}{53343360 (3 x+2)^3}-\frac{1289227 \sqrt{1-2 x} \sqrt{5 x+3}}{8890560 (3 x+2)^4}-\frac{1104970911 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{17210368 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(804950171118012603919048704 + 7069887319115824563893327872*x + 23059146245009253966641398784*x^2 + 25496151601253328411478965760*x^3 - 36197795387810501945399863040*x^4 - 141237757754048585358878382464*x^5 - 158401801496487193018980582592*x^6 - 41626150273919128190467903104*x^7 + 64931150584517497768687879680*x^8 + 60881406392779047287698288000*x^9 + 16298370156936023071391575000*x^10 - 546706439249090022982983750*x^11 - 468468787243594039159709375*x^12 - 7473807602197774501125000*x^13) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-804950171118012603919048704 - 7874543871378377890140092416*x - 31330087853989274691743419392*x^2 - 61106218195436504816104084992*x^3 - 44640445908939832797649495296*x^4 + 46428462901495586484507425920*x^5 + 130233242347820938736679086400*x^6 + 111528530254347483683833211840*x^7 + 32849842661000593820321329600*x^8 - 8971686278920958580720700000*x^9 - 7258685316521881173882335000*x^10 - 933119154690207423774343750*x^11 + 25405143359359525379359375*x^12 + 698109502006256587265625*x^13) + Sqrt[3]*(-804950171118012603919048704 - 7740701997345147567159201792*x - 28671127854893301310191724544*x^2 - 42490061414160886730684487680*x^3 + 21153556630325637579109143040*x^4 + 175431357578241806080091089664*x^5 + 260975989581098174447289933312*x^6 + 137277073601364414980337462464*x^7 - 57565105844261970583839788160*x^8 - 110866981248631007679773133200*x^9 - 49550736532037624245239845000*x^10 - 4813092353068251337963102500*x^11 + 1385724471382738495954975000*x^12 + 128431953068426206761859375*x^13 - 273776836415454490546875*x^14 + Sqrt[1 - 2*x]*(804950171118012603919048704 + 8545358549607700893405966336*x + 37612639459723095640499382272*x^2 + 84713124447552888279058941952*x^3 + 86720492390747482320608237056*x^4 - 23470100773723546508953066240*x^5 - 173773972925738429239034195200*x^6 - 201416292744672528678944683840*x^7 - 95831241088345387410827412800*x^8 - 1767436600653965604915090000*x^9 + 15213107702479885783207865000*x^10 + 4280153699611719223508637500*x^11 + 128843858316014300242437500*x^12 - 11689970882995773655546875*x^13)))/(86051840*Sqrt[3]*(2 + 3*x)^7*Sqrt[3 + 5*x]*(4051435671804928 - 3365532949972160*x - 7555736895916000*x^2 + 2194696763160000*x^3 + 1428846604955000*x^4 - 52303209612500*x^5 - 5663973218750*x^6) + 86051840*(2 + 3*x)^7*(-12154697640414784 - 26521579595840*x + 35265969543725200*x^2 + 5424159101550000*x^3 - 11461663884510000*x^4 - 996207107350000*x^5 + 135547777203125*x^6 + 905821796875*x^7) + Sqrt[1 - 2*x]*(86051840*(2 + 3*x)^7*(12149682333912640 + 12117692004316800*x - 17392813876790000*x^2 - 11790948756840000*x^3 + 1796810007300000*x^4 + 486365726000000*x^5 - 3042263984375*x^6) + 86051840*Sqrt[3]*(2 + 3*x)^7*Sqrt[3 + 5*x]*(-4049763902970880 - 666120123963200*x + 4956682106340000*x^2 + 702446326920000*x^3 - 390402719125000*x^4 - 14941831687500*x^5 + 223405156250*x^6))) + (1104970911*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/17210368 - (5524854555*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/34420736","C",1
2361,1,426,128,2.5306569,"\int \frac{(1-2 x)^{3/2} (2+3 x)^3}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^3)/Sqrt[3 + 5*x],x]","\frac{\sqrt{5 x+3} \left(-18934344000000000 x^9+701204555700000000 x^8+2384924087865000000 x^7-2277529111116875000 x^6-6959381057851406250 x^5+193582835531023125 x^4+5250139561744319000 x^3+291032558862948100 x^2-1232282946349779280 x+130492635663408656\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-1529301600000000 x^9-171966048570000000 x^8+117381447676500000 x^7+3285206702970687500 x^6+3228499076607234375 x^5-2933661261506912625 x^4-3832349661832973900 x^3+792626878581456180 x^2+1107039032913431360 x-130492635663408656\right)+\sqrt{3} \left(5704560000000000 x^{10}-109986687000000000 x^9-2408137444950000000 x^8-2011558872803750000 x^7+7181184218475937500 x^6+8073032287241478125 x^5-4012836664885355625 x^4-5989351986309476500 x^3+789252843965742500 x^2+\sqrt{1-2 x} \left(43815816000000000 x^9+405095733900000000 x^8-1812605113143000000 x^7-6063695921534625000 x^6-1946583820883831250 x^5+6004994425207298125 x^4+3618223627566823000 x^3-1767694655603815180 x^2-997447471917882480 x+130492635663408656\right)+1122691385354230400 x-130492635663408656\right)}{3200000 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right)+\sqrt{1-2 x} \left(3200000 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right)+3200000 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right)\right)+3200000 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right)}+\frac{18648399 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{1600000 \sqrt{10}}","-\frac{3 \sqrt{5 x+3} (11580 x+14629) (1-2 x)^{5/2}}{80000}-\frac{3}{50} (3 x+2)^2 \sqrt{5 x+3} (1-2 x)^{5/2}+\frac{51373 \sqrt{5 x+3} (1-2 x)^{3/2}}{320000}+\frac{1695309 \sqrt{5 x+3} \sqrt{1-2 x}}{3200000}+\frac{18648399 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{3200000 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(130492635663408656 - 1232282946349779280*x + 291032558862948100*x^2 + 5250139561744319000*x^3 + 193582835531023125*x^4 - 6959381057851406250*x^5 - 2277529111116875000*x^6 + 2384924087865000000*x^7 + 701204555700000000*x^8 - 18934344000000000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-130492635663408656 + 1107039032913431360*x + 792626878581456180*x^2 - 3832349661832973900*x^3 - 2933661261506912625*x^4 + 3228499076607234375*x^5 + 3285206702970687500*x^6 + 117381447676500000*x^7 - 171966048570000000*x^8 - 1529301600000000*x^9) + Sqrt[3]*(-130492635663408656 + 1122691385354230400*x + 789252843965742500*x^2 - 5989351986309476500*x^3 - 4012836664885355625*x^4 + 8073032287241478125*x^5 + 7181184218475937500*x^6 - 2011558872803750000*x^7 - 2408137444950000000*x^8 - 109986687000000000*x^9 + 5704560000000000*x^10 + Sqrt[1 - 2*x]*(130492635663408656 - 997447471917882480*x - 1767694655603815180*x^2 + 3618223627566823000*x^3 + 6004994425207298125*x^4 - 1946583820883831250*x^5 - 6063695921534625000*x^6 - 1812605113143000000*x^7 + 405095733900000000*x^8 + 43815816000000000*x^9)))/(3200000*Sqrt[3]*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 3200000*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(3200000*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 3200000*Sqrt[3]*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (18648399*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(1600000*Sqrt[10])","B",1
2362,1,366,121,2.1758678,"\int \frac{(1-2 x)^{3/2} (2+3 x)^2}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^2)/Sqrt[3 + 5*x],x]","\frac{\sqrt{5 x+3} \left(-2792592000000 x^7-16637975200000 x^6+51623410300000 x^5+57997668465000 x^4-61239236296700 x^3-38841550562100 x^2+16008983669800 x+5801408755384\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(246258000000 x^7-2215736500000 x^6-37062480957500 x^5-8935343796375 x^4+56871484037800 x^3+12144182614520 x^2-22139008175840 x-5801408755384\right)+\sqrt{3} \left(171360000000 x^8+15388568000000 x^7-4129786600000 x^6-103454376790000 x^5-27581202553375 x^4+99864601138200 x^3+26843406837400 x^2+\sqrt{1-2 x} \left(-1284624000000 x^7+22279866400000 x^6+54393658220000 x^5-26898404313000 x^4-74820459228900 x^3+4885889344380 x^2+26897089951160 x+5801408755384\right)-20767065445120 x-5801408755384\right)}{32000 \sqrt{3} \sqrt{5 x+3} \left(8921000 x^3-162998000 x^2-220512160 x+287530496\right)+\sqrt{1-2 x} \left(32000 \left(-48482500 x^3-297203500 x^2+794989800 x+852279560\right)+32000 \sqrt{3} \sqrt{5 x+3} \left(595000 x^3+53178000 x^2-36412000 x-283051520\right)\right)+32000 \left(-8550625 x^4+79738000 x^3+1253327000 x^2-32289760 x-865716488\right)}+\frac{109263 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{16000 \sqrt{10}}","-\frac{3}{40} (3 x+2) \sqrt{5 x+3} (1-2 x)^{5/2}-\frac{119}{800} \sqrt{5 x+3} (1-2 x)^{5/2}+\frac{301 \sqrt{5 x+3} (1-2 x)^{3/2}}{3200}+\frac{9933 \sqrt{5 x+3} \sqrt{1-2 x}}{32000}+\frac{109263 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{32000 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(5801408755384 + 16008983669800*x - 38841550562100*x^2 - 61239236296700*x^3 + 57997668465000*x^4 + 51623410300000*x^5 - 16637975200000*x^6 - 2792592000000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-5801408755384 - 22139008175840*x + 12144182614520*x^2 + 56871484037800*x^3 - 8935343796375*x^4 - 37062480957500*x^5 - 2215736500000*x^6 + 246258000000*x^7) + Sqrt[3]*(-5801408755384 - 20767065445120*x + 26843406837400*x^2 + 99864601138200*x^3 - 27581202553375*x^4 - 103454376790000*x^5 - 4129786600000*x^6 + 15388568000000*x^7 + 171360000000*x^8 + Sqrt[1 - 2*x]*(5801408755384 + 26897089951160*x + 4885889344380*x^2 - 74820459228900*x^3 - 26898404313000*x^4 + 54393658220000*x^5 + 22279866400000*x^6 - 1284624000000*x^7)))/(32000*Sqrt[3]*Sqrt[3 + 5*x]*(287530496 - 220512160*x - 162998000*x^2 + 8921000*x^3) + 32000*(-865716488 - 32289760*x + 1253327000*x^2 + 79738000*x^3 - 8550625*x^4) + Sqrt[1 - 2*x]*(32000*(852279560 + 794989800*x - 297203500*x^2 - 48482500*x^3) + 32000*Sqrt[3]*Sqrt[3 + 5*x]*(-283051520 - 36412000*x + 53178000*x^2 + 595000*x^3))) + (109263*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(16000*Sqrt[10])","B",1
2363,1,306,94,1.8457382,"\int \frac{(1-2 x)^{3/2} (2+3 x)}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x))/Sqrt[3 + 5*x],x]","\frac{\sqrt{5 x+3} \left(-125400000 x^5+1045715000 x^4+126785450 x^3-1569800925 x^2-229092820 x+630675716\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-7180000 x^5-471756500 x^4+346295975 x^3+831643915 x^2-417477040 x-630675716\right)+\sqrt{3} \left(46800000 x^6-179610000 x^5-1784833500 x^4+1109805425 x^3+1927368975 x^2+\sqrt{1-2 x} \left(183480000 x^5+622149000 x^4-1147916550 x^3-655726665 x^2+937717220 x+630675716\right)-291147360 x-630675716\right)}{400 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right)+\sqrt{1-2 x} \left(400 \left(-391875 x^2+2827000 x+3481060\right)+400 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right)\right)+400 \left(44875 x^3+2976525 x^2-279060 x-3667684\right)}+\frac{1089 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{200 \sqrt{10}}","-\frac{1}{10} \sqrt{5 x+3} (1-2 x)^{5/2}+\frac{3}{40} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{99}{400} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{1089 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{400 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(630675716 - 229092820*x - 1569800925*x^2 + 126785450*x^3 + 1045715000*x^4 - 125400000*x^5) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-630675716 - 417477040*x + 831643915*x^2 + 346295975*x^3 - 471756500*x^4 - 7180000*x^5) + Sqrt[3]*(-630675716 - 291147360*x + 1927368975*x^2 + 1109805425*x^3 - 1784833500*x^4 - 179610000*x^5 + 46800000*x^6 + Sqrt[1 - 2*x]*(630675716 + 937717220*x - 655726665*x^2 - 1147916550*x^3 + 622149000*x^4 + 183480000*x^5)))/(400*Sqrt[3]*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 400*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(400*(3481060 + 2827000*x - 391875*x^2) + 400*Sqrt[3]*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (1089*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(200*Sqrt[10])","B",1
2364,1,246,72,1.5257904,"\int \frac{(1-2 x)^{3/2}}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/Sqrt[3 + 5*x],x]","\frac{\sqrt{5 x+3} \left(-286000 x^3+199100 x^2+1428790 x-1259126\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(59500 x^3-164325 x^2-240080 x+1259126\right)+\sqrt{3} \left(20000 x^4+807000 x^3-1876625 x^2+\sqrt{1-2 x} \left(-198000 x^3+817300 x^2-843150 x-1259126\right)-345560 x+1259126\right)}{100 \left(-2975 x^2+1820 x+16562\right)+100 \sqrt{3} \sqrt{5 x+3} (1980 x-5104)+\sqrt{1-2 x} \left(100 (-7150 x-13970)+100 \sqrt{3} \sqrt{5 x+3} (100 x+4240)\right)}+\frac{363 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{50 \sqrt{10}}","\frac{1}{10} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{33}{100} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{363 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{100 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(-1259126 + 1428790*x + 199100*x^2 - 286000*x^3) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1259126 - 240080*x - 164325*x^2 + 59500*x^3) + Sqrt[3]*(1259126 - 345560*x - 1876625*x^2 + 807000*x^3 + 20000*x^4 + Sqrt[1 - 2*x]*(-1259126 - 843150*x + 817300*x^2 - 198000*x^3)))/(100*Sqrt[3]*Sqrt[3 + 5*x]*(-5104 + 1980*x) + 100*(16562 + 1820*x - 2975*x^2) + Sqrt[1 - 2*x]*(100*(-13970 - 7150*x) + 100*Sqrt[3]*Sqrt[3 + 5*x]*(4240 + 100*x))) + (363*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(50*Sqrt[10])","B",1
2365,1,376,86,1.4949075,"\int \frac{(1-2 x)^{3/2}}{(2+3 x) \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)*Sqrt[3 + 5*x]),x]","-\frac{49}{9} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{\left(\frac{2}{15} \sqrt{1-2 x}-\frac{2}{15}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right) \left(10 x-55 \sqrt{1-2 x}+20 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}-22 \sqrt{3} \sqrt{5 x+3}+61\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}-\frac{206}{45} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{2}{15} \sqrt{1-2 x} \sqrt{5 x+3}-\frac{103}{45} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{14}{9} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"((-2/15 + (2*Sqrt[1 - 2*x])/15)*(Sqrt[3] - Sqrt[3 + 5*x])*(61 - 55*Sqrt[1 - 2*x] + 10*x - 22*Sqrt[3]*Sqrt[3 + 5*x] + 20*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2 - (206*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/45 - (49*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ])/9","C",1
2366,1,477,93,1.652357,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^2 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^2*Sqrt[3 + 5*x]),x]","\frac{203}{9} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{1015}{18} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{3} \left(-7 \left(185 x^2-263 x-242\right)-7 \sqrt{1-2 x} (385 x+242)\right)-7 \sqrt{1-2 x} \sqrt{5 x+3} (-100 x-242)-7 (242-22 x) \sqrt{5 x+3}}{6 (5 x+91) (3 x+2)-132 \sqrt{3} \sqrt{5 x+3} (3 x+2)+\sqrt{1-2 x} \left(60 \sqrt{3} (3 x+2) \sqrt{5 x+3}-330 (3 x+2)\right)}+\frac{8}{9} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{7 \sqrt{1-2 x} \sqrt{5 x+3}}{3 (3 x+2)}+\frac{4}{9} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{29}{9} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(-7*(242 - 22*x)*Sqrt[3 + 5*x] - 7*(-242 - 100*x)*Sqrt[1 - 2*x]*Sqrt[3 + 5*x] + Sqrt[3]*(-7*Sqrt[1 - 2*x]*(242 + 385*x) - 7*(-242 - 263*x + 185*x^2)))/(-132*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x] + 6*(2 + 3*x)*(91 + 5*x) + Sqrt[1 - 2*x]*(-330*(2 + 3*x) + 60*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x])) + (8*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/9 + (203*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/9 - (1015*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/18","C",1
2367,1,479,93,1.8340825,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^3 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^3*Sqrt[3 + 5*x]),x]","\frac{363}{4} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{1815}{8} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-2267320 x^3-1816474 x^2+2633158 x+1991176\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(236725 x^3-1977960 x^2-4312430 x-1991176\right)+\sqrt{3} \left(550175 x^4+4433940 x^3+561334 x^2+\sqrt{1-2 x} \left(153450 x^3+4782910 x^2+6122160 x+1991176\right)-4442888 x-1991176\right)}{4 \left(2975 x^2-1820 x-16562\right) (3 x+2)^2+4 \sqrt{3} (5104-1980 x) \sqrt{5 x+3} (3 x+2)^2+\sqrt{1-2 x} \left(4 (7150 x+13970) (3 x+2)^2+4 \sqrt{3} (-100 x-4240) \sqrt{5 x+3} (3 x+2)^2\right)}","\frac{\sqrt{5 x+3} (1-2 x)^{3/2}}{2 (3 x+2)^2}+\frac{33 \sqrt{5 x+3} \sqrt{1-2 x}}{4 (3 x+2)}-\frac{363 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{4 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(1991176 + 2633158*x - 1816474*x^2 - 2267320*x^3) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-1991176 - 4312430*x - 1977960*x^2 + 236725*x^3) + Sqrt[3]*(-1991176 - 4442888*x + 561334*x^2 + 4433940*x^3 + 550175*x^4 + Sqrt[1 - 2*x]*(1991176 + 6122160*x + 4782910*x^2 + 153450*x^3)))/(4*Sqrt[3]*(5104 - 1980*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 4*(2 + 3*x)^2*(-16562 - 1820*x + 2975*x^2) + Sqrt[1 - 2*x]*(4*Sqrt[3]*(-4240 - 100*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 4*(2 + 3*x)^2*(13970 + 7150*x))) + (363*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/4 - (1815*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/8","C",1
2368,1,539,122,2.1405634,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^4 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^4*Sqrt[3 + 5*x]),x]","\frac{21417}{56} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{107085}{112} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-5447823150 x^5-184675050505 x^4-258279476378 x^3+19076714844 x^2+159024525176 x+56916711808\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(3134736125 x^5+48064403325 x^4-40503116150 x^3-239503024148 x^2-213278361336 x-56916711808\right)+\sqrt{3} \left(-3711276000 x^6+92162455950 x^5+369984212370 x^4+284053641208 x^3-129904669224 x^2+\sqrt{1-2 x} \left(-29942244750 x^5-48815195550 x^4+178987356240 x^3+396434300328 x^2+261600746176 x+56916711808\right)-207346910016 x-56916711808\right)}{56 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right) (3 x+2)^3+\sqrt{1-2 x} \left(56 \left(-391875 x^2+2827000 x+3481060\right) (3 x+2)^3+56 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right) (3 x+2)^3\right)+56 \left(44875 x^3+2976525 x^2-279060 x-3667684\right) (3 x+2)^3}","\frac{\sqrt{5 x+3} (1-2 x)^{5/2}}{7 (3 x+2)^3}+\frac{59 \sqrt{5 x+3} (1-2 x)^{3/2}}{28 (3 x+2)^2}+\frac{1947 \sqrt{5 x+3} \sqrt{1-2 x}}{56 (3 x+2)}-\frac{21417 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{56 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(56916711808 + 159024525176*x + 19076714844*x^2 - 258279476378*x^3 - 184675050505*x^4 - 5447823150*x^5) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-56916711808 - 213278361336*x - 239503024148*x^2 - 40503116150*x^3 + 48064403325*x^4 + 3134736125*x^5) + Sqrt[3]*(-56916711808 - 207346910016*x - 129904669224*x^2 + 284053641208*x^3 + 369984212370*x^4 + 92162455950*x^5 - 3711276000*x^6 + Sqrt[1 - 2*x]*(56916711808 + 261600746176*x + 396434300328*x^2 + 178987356240*x^3 - 48815195550*x^4 - 29942244750*x^5)))/(56*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 56*(2 + 3*x)^3*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(56*(2 + 3*x)^3*(3481060 + 2827000*x - 391875*x^2) + 56*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (21417*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/56 - (107085*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/112","C",1
2369,1,599,151,2.5397075,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^5 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^5*Sqrt[3 + 5*x]),x]","\frac{5274027 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{3136}-\frac{26370135 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{6272}+\frac{\sqrt{5 x+3} \left(-1742886112110000 x^7-897959015189500 x^6+45849006900095300 x^5+93019647857855400 x^4+43914106609926520 x^3-26860414816465120 x^2-29060132323986720 x-6784441434939520\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(70673612019375 x^7-4065409623193000 x^6-23908191701924500 x^5-18565257783103440 x^4+36909818365240408 x^3+64947643927264960 x^2+35750091820535200 x+6784441434939520\right)+\sqrt{3} \left(245311919990625 x^8+5637216363230000 x^7-19145335647657000 x^6-106706746693950800 x^5-132240164906169000 x^4-29751404187537920 x^3+48662895143766720 x^2+\sqrt{1-2 x} \left(415858783807500 x^7+17217411422084500 x^6+41633830569449800 x^5+1848175709232600 x^4-80463348217966208 x^3-92347063980856960 x^2-41425766495484800 x-6784441434939520\right)+34735806998936320 x+6784441434939520\right)}{3136 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^4+\sqrt{1-2 x} \left(3136 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^4+3136 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^4\right)+3136 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^4}","\frac{4148797 \sqrt{1-2 x} \sqrt{5 x+3}}{28224 (3 x+2)}+\frac{39667 \sqrt{1-2 x} \sqrt{5 x+3}}{2016 (3 x+2)^2}+\frac{227 \sqrt{1-2 x} \sqrt{5 x+3}}{72 (3 x+2)^3}+\frac{7 \sqrt{1-2 x} \sqrt{5 x+3}}{12 (3 x+2)^4}-\frac{5274027 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{3136 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-6784441434939520 - 29060132323986720*x - 26860414816465120*x^2 + 43914106609926520*x^3 + 93019647857855400*x^4 + 45849006900095300*x^5 - 897959015189500*x^6 - 1742886112110000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(6784441434939520 + 35750091820535200*x + 64947643927264960*x^2 + 36909818365240408*x^3 - 18565257783103440*x^4 - 23908191701924500*x^5 - 4065409623193000*x^6 + 70673612019375*x^7) + Sqrt[3]*(6784441434939520 + 34735806998936320*x + 48662895143766720*x^2 - 29751404187537920*x^3 - 132240164906169000*x^4 - 106706746693950800*x^5 - 19145335647657000*x^6 + 5637216363230000*x^7 + 245311919990625*x^8 + Sqrt[1 - 2*x]*(-6784441434939520 - 41425766495484800*x - 92347063980856960*x^2 - 80463348217966208*x^3 + 1848175709232600*x^4 + 41633830569449800*x^5 + 17217411422084500*x^6 + 415858783807500*x^7)))/(3136*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 3136*(2 + 3*x)^4*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(3136*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 3136*(2 + 3*x)^4*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) + (5274027*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/3136 - (26370135*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/6272","C",1
2370,1,659,180,3.0752374,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^6 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^6*Sqrt[3 + 5*x]),x]","\frac{333216939 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{43904}-\frac{1666084695 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{87808}+\frac{\sqrt{5 x+3} \left(-39882729208402575000 x^9-1928463877173083641875 x^8-4088939203514371900650 x^7+9578122649604170837120 x^6+33584511801567110781936 x^5+30628008977184874696320 x^4+3460855321635632124160 x^3-10276936095880583863360 x^2-5995474411364403194240 x-1037334344352786715136\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(7309488164424609375 x^9+216811713928842703125 x^8-1897080478700496318750 x^7-11536631344608478097000 x^6-16935289846273177958400 x^5-1377699139074753666720 x^4+17923308041960075638400 x^3+17762504858085838774464 x^2+7028510475576268667776 x+1037334344352786715136\right)+\sqrt{3} \left(-5535358739307253125 x^{10}+653842300251721640625 x^9+5115984079517150362500 x^8+1551319177104542699000 x^7-29418353016126615551400 x^6-56375132003072967003536 x^5-35641878717190756965120 x^4+3318169893426429336640 x^3+14910780980562799471360 x^2+\sqrt{1-2 x} \left(-100771675340782359375 x^9+83731065265008562500 x^8+7674465574024791300000 x^7+23352802388751752235000 x^6+20912374350448945650000 x^5-9123279579706255828480 x^4-30580457186813368457920 x^3-23257907325850858943744 x^2-7893649958776507597056 x-1037334344352786715136\right)+6860613894564642123520 x+1037334344352786715136\right)}{219520 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right) (3 x+2)^5+\sqrt{1-2 x} \left(219520 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right) (3 x+2)^5+219520 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right) (3 x+2)^5\right)+219520 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right) (3 x+2)^5}","\frac{87374783 \sqrt{1-2 x} \sqrt{5 x+3}}{131712 (3 x+2)}+\frac{835409 \sqrt{1-2 x} \sqrt{5 x+3}}{9408 (3 x+2)^2}+\frac{23909 \sqrt{1-2 x} \sqrt{5 x+3}}{1680 (3 x+2)^3}+\frac{293 \sqrt{1-2 x} \sqrt{5 x+3}}{120 (3 x+2)^4}+\frac{7 \sqrt{1-2 x} \sqrt{5 x+3}}{15 (3 x+2)^5}-\frac{333216939 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{43904 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-1037334344352786715136 - 5995474411364403194240*x - 10276936095880583863360*x^2 + 3460855321635632124160*x^3 + 30628008977184874696320*x^4 + 33584511801567110781936*x^5 + 9578122649604170837120*x^6 - 4088939203514371900650*x^7 - 1928463877173083641875*x^8 - 39882729208402575000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1037334344352786715136 + 7028510475576268667776*x + 17762504858085838774464*x^2 + 17923308041960075638400*x^3 - 1377699139074753666720*x^4 - 16935289846273177958400*x^5 - 11536631344608478097000*x^6 - 1897080478700496318750*x^7 + 216811713928842703125*x^8 + 7309488164424609375*x^9) + Sqrt[3]*(1037334344352786715136 + 6860613894564642123520*x + 14910780980562799471360*x^2 + 3318169893426429336640*x^3 - 35641878717190756965120*x^4 - 56375132003072967003536*x^5 - 29418353016126615551400*x^6 + 1551319177104542699000*x^7 + 5115984079517150362500*x^8 + 653842300251721640625*x^9 - 5535358739307253125*x^10 + Sqrt[1 - 2*x]*(-1037334344352786715136 - 7893649958776507597056*x - 23257907325850858943744*x^2 - 30580457186813368457920*x^3 - 9123279579706255828480*x^4 + 20912374350448945650000*x^5 + 23352802388751752235000*x^6 + 7674465574024791300000*x^7 + 83731065265008562500*x^8 - 100771675340782359375*x^9)))/(219520*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 219520*(2 + 3*x)^5*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(219520*(2 + 3*x)^5*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 219520*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (333216939*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/43904 - (1666084695*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/87808","C",1
2371,1,404,135,2.696273,"\int \frac{(1-2 x)^{3/2} (2+3 x)^3}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^3)/(3 + 5*x)^(3/2),x]","\frac{64548900000000 x^9-6545268855000000 x^8-27841377243375000 x^7+41900453786343750 x^6+104176662589231875 x^5-21330314444953125 x^4-85897759221234600 x^3-14359942435508100 x^2+\sqrt{3} \sqrt{5 x+3} \left(152681760000000 x^8+5248253736000000 x^7+190061526600000 x^6-23532949989450000 x^5-7751235577969125 x^4+21436550414033700 x^3+7725866693519700 x^2-4341938674894920 x-1764989869248848\right)+\sqrt{1-2 x} \left(1097079390000000 x^8-2613043273500000 x^7-46992868677562500 x^6-40903192320148125 x^5+56104632045829125 x^4+57587698491265800 x^3-11975952215820780 x^2+\sqrt{3} \sqrt{5 x+3} \left(-29874420000000 x^8-636200487000000 x^7+5792769672975000 x^6+13412679071208750 x^5-5378710747004875 x^4-17376600341032900 x^3-456377075864340 x^2+6144233137990040 x+1764989869248848\right)-22866863727717240 x-5294969607746544\right)+17459980338431880 x+5294969607746544}{480000 \sqrt{5 x+3} \left(-846511875 x^4+2876857500 x^3+32771841300 x^2-464036760 x-18959828096\right)+480000 \sqrt{1-2 x} \sqrt{5 x+3} \left(24903125 x^4-2538047500 x^3-9400717500 x^2+18053298200 x+18798584960\right)+\sqrt{3} \left(480000 \sqrt{1-2 x} \left(294525000 x^4+10148490000 x^3+1543311000 x^2-33942744000 x-18767334960\right)+480000 \left(115256250 x^5+2406453750 x^4-23245830000 x^3-39836473200 x^2+16519101840 x+18928578096\right)\right)}+\frac{390621 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{80000 \sqrt{10}}","-\frac{2 (1-2 x)^{3/2} (3 x+2)^3}{5 \sqrt{5 x+3}}+\frac{27}{100} (1-2 x)^{3/2} \sqrt{5 x+3} (3 x+2)^2-\frac{63 (35-8 x) (1-2 x)^{3/2} \sqrt{5 x+3}}{16000}+\frac{35511 \sqrt{1-2 x} \sqrt{5 x+3}}{160000}+\frac{390621 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{160000 \sqrt{10}}",1,"(5294969607746544 + 17459980338431880*x - 14359942435508100*x^2 - 85897759221234600*x^3 - 21330314444953125*x^4 + 104176662589231875*x^5 + 41900453786343750*x^6 - 27841377243375000*x^7 - 6545268855000000*x^8 + 64548900000000*x^9 + Sqrt[3]*Sqrt[3 + 5*x]*(-1764989869248848 - 4341938674894920*x + 7725866693519700*x^2 + 21436550414033700*x^3 - 7751235577969125*x^4 - 23532949989450000*x^5 + 190061526600000*x^6 + 5248253736000000*x^7 + 152681760000000*x^8) + Sqrt[1 - 2*x]*(-5294969607746544 - 22866863727717240*x - 11975952215820780*x^2 + 57587698491265800*x^3 + 56104632045829125*x^4 - 40903192320148125*x^5 - 46992868677562500*x^6 - 2613043273500000*x^7 + 1097079390000000*x^8 + Sqrt[3]*Sqrt[3 + 5*x]*(1764989869248848 + 6144233137990040*x - 456377075864340*x^2 - 17376600341032900*x^3 - 5378710747004875*x^4 + 13412679071208750*x^5 + 5792769672975000*x^6 - 636200487000000*x^7 - 29874420000000*x^8)))/(480000*Sqrt[3 + 5*x]*(-18959828096 - 464036760*x + 32771841300*x^2 + 2876857500*x^3 - 846511875*x^4) + 480000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(18798584960 + 18053298200*x - 9400717500*x^2 - 2538047500*x^3 + 24903125*x^4) + Sqrt[3]*(480000*Sqrt[1 - 2*x]*(-18767334960 - 33942744000*x + 1543311000*x^2 + 10148490000*x^3 + 294525000*x^4) + 480000*(18928578096 + 16519101840*x - 39836473200*x^2 - 23245830000*x^3 + 2406453750*x^4 + 115256250*x^5))) + (390621*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(80000*Sqrt[10])","B",1
2372,1,344,116,2.3270701,"\int \frac{(1-2 x)^{3/2} (2+3 x)^2}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^2)/(3 + 5*x)^(3/2),x]","\frac{-15867000000 x^7-235360125000 x^6+1105791251250 x^5+962272574625 x^4-1741459014675 x^3-1554243831300 x^2+\sqrt{3} \sqrt{5 x+3} \left(32432400000 x^6-54144090000 x^5-386139253500 x^4+208039595225 x^3+502754282800 x^2-53803810060 x-159171212728\right)+\sqrt{1-2 x} \left(-24878700000 x^6-654200662500 x^5+9046912875 x^4+1318866483825 x^3+264590797020 x^2+\sqrt{3} \sqrt{5 x+3} \left(-1459800000 x^6+68946795000 x^5+143330904750 x^4-253365944075 x^3-207264372240 x^2+214549756100 x+159171212728\right)-1042895737620 x-477513638184\right)+560657899500 x+477513638184}{6000 \sqrt{1-2 x} \sqrt{5 x+3} \left(-1101875 x^3-16812750 x^2+68422100 x+77141440\right)+6000 \sqrt{5 x+3} \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right)+\sqrt{3} \left(6000 \sqrt{1-2 x} \left(11261250 x^3-7257250 x^2-135935800 x-76516440\right)+6000 \left(1013750 x^4-47347500 x^3-123624450 x^2+74349280 x+78755928\right)\right)}+\frac{3927 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{1000 \sqrt{10}}","-\frac{3}{50} \sqrt{5 x+3} (1-2 x)^{5/2}-\frac{2 (1-2 x)^{5/2}}{275 \sqrt{5 x+3}}+\frac{119 \sqrt{5 x+3} (1-2 x)^{3/2}}{2200}+\frac{357 \sqrt{5 x+3} \sqrt{1-2 x}}{2000}+\frac{3927 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{2000 \sqrt{10}}",1,"(477513638184 + 560657899500*x - 1554243831300*x^2 - 1741459014675*x^3 + 962272574625*x^4 + 1105791251250*x^5 - 235360125000*x^6 - 15867000000*x^7 + Sqrt[3]*Sqrt[3 + 5*x]*(-159171212728 - 53803810060*x + 502754282800*x^2 + 208039595225*x^3 - 386139253500*x^4 - 54144090000*x^5 + 32432400000*x^6) + Sqrt[1 - 2*x]*(-477513638184 - 1042895737620*x + 264590797020*x^2 + 1318866483825*x^3 + 9046912875*x^4 - 654200662500*x^5 - 24878700000*x^6 + Sqrt[3]*Sqrt[3 + 5*x]*(159171212728 + 214549756100*x - 207264372240*x^2 - 253365944075*x^3 + 143330904750*x^4 + 68946795000*x^5 - 1459800000*x^6)))/(6000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(77141440 + 68422100*x - 16812750*x^2 - 1101875*x^3) + 6000*Sqrt[3 + 5*x]*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3) + Sqrt[3]*(6000*Sqrt[1 - 2*x]*(-76516440 - 135935800*x - 7257250*x^2 + 11261250*x^3) + 6000*(78755928 + 74349280*x - 123624450*x^2 - 47347500*x^3 + 1013750*x^4))) + (3927*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(1000*Sqrt[10])","B",1
2373,1,284,94,1.8795498,"\int \frac{(1-2 x)^{3/2} (2+3 x)}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x))/(3 + 5*x)^(3/2),x]","\frac{855000 x^5-17244750 x^4+8358525 x^3+57404175 x^2+\sqrt{3} \sqrt{5 x+3} \left(396000 x^4+6448200 x^3-15696175 x^2-950950 x+7086244\right)+\sqrt{1-2 x} \left(5890500 x^4-9552675 x^3-15161619 x^2+\sqrt{3} \sqrt{5 x+3} \left(-250200 x^4-1806990 x^3+7398863 x^2-6036798 x-7086244\right)+35707254 x+21258732\right)-14744010 x-21258732}{60 \sqrt{5 x+3} \left(-163625 x^2+33550 x+343904\right)+60 \sqrt{1-2 x} \sqrt{5 x+3} \left(11875 x^2-216750 x-312800\right)+\sqrt{3} \left(60 \sqrt{1-2 x} \left(27500 x^2+517000 x+300300\right)+60 \left(34750 x^3+321050 x^2-372220 x-331404\right)\right)}+\frac{33 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{10 \sqrt{10}}","-\frac{2 (1-2 x)^{5/2}}{55 \sqrt{5 x+3}}+\frac{1}{22} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{3}{20} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{33 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{20 \sqrt{10}}",1,"(-21258732 - 14744010*x + 57404175*x^2 + 8358525*x^3 - 17244750*x^4 + 855000*x^5 + Sqrt[3]*Sqrt[3 + 5*x]*(7086244 - 950950*x - 15696175*x^2 + 6448200*x^3 + 396000*x^4) + Sqrt[1 - 2*x]*(21258732 + 35707254*x - 15161619*x^2 - 9552675*x^3 + 5890500*x^4 + Sqrt[3]*Sqrt[3 + 5*x]*(-7086244 - 6036798*x + 7398863*x^2 - 1806990*x^3 - 250200*x^4)))/(60*Sqrt[3 + 5*x]*(343904 + 33550*x - 163625*x^2) + 60*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-312800 - 216750*x + 11875*x^2) + Sqrt[3]*(60*Sqrt[1 - 2*x]*(300300 + 517000*x + 27500*x^2) + 60*(-331404 - 372220*x + 321050*x^2 + 34750*x^3))) + (33*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(10*Sqrt[10])","B",1
2374,1,234,74,1.5505585,"\int \frac{(1-2 x)^{3/2}}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/(3 + 5*x)^(3/2),x]","\frac{-2 \sqrt{3} \sqrt{5 x+3} \left(-9900 x^2-20460 x+37268\right)+\sqrt{1-2 x} \left(-2 \sqrt{3} \sqrt{5 x+3} \left(1350 x^2-7880 x-37268\right)-2 \left(2475 x^2+101310 x+111804\right)\right)-2 \left(9750 x^3+78525 x^2-16290 x-111804\right)}{\sqrt{3} \left(75 \left(450 x^2-2100 x-1422\right)+75 \sqrt{1-2 x} (1650 x+990)\right)+75 \sqrt{1-2 x} \sqrt{5 x+3} (-325 x-1240)+75 \sqrt{5 x+3} (165 x+1672)}-\frac{66}{25} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{2 (1-2 x)^{3/2}}{5 \sqrt{5 x+3}}-\frac{6}{25} \sqrt{5 x+3} \sqrt{1-2 x}-\frac{33}{25} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"(-2*Sqrt[3]*Sqrt[3 + 5*x]*(37268 - 20460*x - 9900*x^2) - 2*(-111804 - 16290*x + 78525*x^2 + 9750*x^3) + Sqrt[1 - 2*x]*(-2*Sqrt[3]*Sqrt[3 + 5*x]*(-37268 - 7880*x + 1350*x^2) - 2*(111804 + 101310*x + 2475*x^2)))/(75*(-1240 - 325*x)*Sqrt[1 - 2*x]*Sqrt[3 + 5*x] + 75*Sqrt[3 + 5*x]*(1672 + 165*x) + Sqrt[3]*(75*Sqrt[1 - 2*x]*(990 + 1650*x) + 75*(-1422 - 2100*x + 450*x^2))) - (66*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/25","B",1
2375,1,336,86,1.4451244,"\int \frac{(1-2 x)^{3/2}}{(2+3 x) (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)*(3 + 5*x)^(3/2)),x]","\frac{49}{3} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{\left(\frac{242}{5} \sqrt{1-2 x}-\frac{242}{5}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)}{30 x+5 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{3} \sqrt{5 x+3}+18}+\frac{8}{15} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{22 \sqrt{1-2 x}}{5 \sqrt{5 x+3}}+\frac{4}{15} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)+\frac{14}{3} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"((-242/5 + (242*Sqrt[1 - 2*x])/5)*(Sqrt[3] - Sqrt[3 + 5*x]))/(18 + 30*x - 11*Sqrt[3]*Sqrt[3 + 5*x] + 5*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]) + (8*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/15 + (49*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ])/3","C",1
2376,1,449,79,1.8733207,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^2 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^2*(3 + 5*x)^(3/2)),x]","-231 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{1155}{2} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(8835 x^2+536194 x+346060\right)+\sqrt{5 x+3} \left(367785 x^2-290070 x-346060\right)+\sqrt{3} \left(-219050 x^3-168810 x^2+\sqrt{1-2 x} \left(-355080 x^2-766744 x-346060\right)+520620 x+346060\right)}{2 (3 x+2) \left(1350 x^2-6300 x-4266\right)+2 \sqrt{3} (3 x+2) \sqrt{5 x+3} (165 x+1672)+\sqrt{1-2 x} \left(2 (4950 x+2970) (3 x+2)+2 \sqrt{3} (-325 x-1240) \sqrt{5 x+3} (3 x+2)\right)}","\frac{(1-2 x)^{3/2}}{(3 x+2) \sqrt{5 x+3}}-\frac{33 \sqrt{1-2 x}}{\sqrt{5 x+3}}+33 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(346060 + 536194*x + 8835*x^2) + Sqrt[3 + 5*x]*(-346060 - 290070*x + 367785*x^2) + Sqrt[3]*(346060 + 520620*x - 168810*x^2 - 219050*x^3 + Sqrt[1 - 2*x]*(-346060 - 766744*x - 355080*x^2)))/(2*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(1672 + 165*x) + 2*(2 + 3*x)*(-4266 - 6300*x + 1350*x^2) + Sqrt[1 - 2*x]*(2*Sqrt[3]*(-1240 - 325*x)*(2 + 3*x)*Sqrt[3 + 5*x] + 2*(2 + 3*x)*(2970 + 4950*x))) - 231*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ] + (1155*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2","C",1
2377,1,519,115,2.1255485,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^3 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^3*(3 + 5*x)^(3/2)),x]","-\frac{5709}{4} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{28545}{8} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-241882875 x^4-100816200 x^3+4956777040 x^2+6384526620 x+2069183248\right)+\sqrt{5 x+3} \left(1429522875 x^4+6030108150 x^3+1308073492 x^2-4492936844 x-2069183248\right)+\sqrt{3} \left(-73369500 x^5-5755604975 x^4-7870533735 x^3+1848456778 x^2+\sqrt{1-2 x} \left(1025990625 x^4-2646491375 x^3-9618261290 x^2-8037475160 x-2069183248\right)+6145885384 x+2069183248\right)}{4 \sqrt{3} \sqrt{5 x+3} \left(-163625 x^2+33550 x+343904\right) (3 x+2)^2+\sqrt{1-2 x} \left(4 \sqrt{3} \sqrt{5 x+3} \left(11875 x^2-216750 x-312800\right) (3 x+2)^2+4 \left(82500 x^2+1551000 x+900900\right) (3 x+2)^2\right)+4 \left(104250 x^3+963150 x^2-1116660 x-994212\right) (3 x+2)^2}","\frac{3 (1-2 x)^{5/2}}{14 (3 x+2)^2 \sqrt{5 x+3}}+\frac{173 (1-2 x)^{3/2}}{28 (3 x+2) \sqrt{5 x+3}}-\frac{5709 \sqrt{1-2 x}}{28 \sqrt{5 x+3}}+\frac{5709 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{4 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(2069183248 + 6384526620*x + 4956777040*x^2 - 100816200*x^3 - 241882875*x^4) + Sqrt[3 + 5*x]*(-2069183248 - 4492936844*x + 1308073492*x^2 + 6030108150*x^3 + 1429522875*x^4) + Sqrt[3]*(2069183248 + 6145885384*x + 1848456778*x^2 - 7870533735*x^3 - 5755604975*x^4 - 73369500*x^5 + Sqrt[1 - 2*x]*(-2069183248 - 8037475160*x - 9618261290*x^2 - 2646491375*x^3 + 1025990625*x^4)))/(4*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(343904 + 33550*x - 163625*x^2) + 4*(2 + 3*x)^2*(-994212 - 1116660*x + 963150*x^2 + 104250*x^3) + Sqrt[1 - 2*x]*(4*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(-312800 - 216750*x + 11875*x^2) + 4*(2 + 3*x)^2*(900900 + 1551000*x + 82500*x^2))) - (5709*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/4 + (28545*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/8","C",1
2378,1,579,144,2.5626133,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^4 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^4*(3 + 5*x)^(3/2)),x]","-\frac{463881}{56} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{2319405}{112} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(831323700000 x^6+83803904073000 x^5+147519093712650 x^4-207104518795420 x^3-557596366997784 x^2-374486413262768 x-81373437380224\right)+\sqrt{5 x+3} \left(18568990266750 x^6-166025242117350 x^5-636493807226970 x^4-490796917872404 x^3+162507878881832 x^2+295190708650288 x+81373437380224\right)+\sqrt{3} \left(-5806727658750 x^7+12543396916875 x^6+539960584015775 x^5+1047965904071540 x^4+431933171796144 x^3-381598499847272 x^2+\sqrt{1-2 x} \left(-26142812705625 x^6-204670372974375 x^5-88674169568600 x^4+568158684755640 x^3+842186884723624 x^2+441717753996288 x+81373437380224\right)-362422049383808 x-81373437380224\right)}{56 \sqrt{3} \sqrt{5 x+3} \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (3 x+2)^3+\sqrt{1-2 x} \left(56 \sqrt{3} \sqrt{5 x+3} \left(-1101875 x^3-16812750 x^2+68422100 x+77141440\right) (3 x+2)^3+56 \left(33783750 x^3-21771750 x^2-407807400 x-229549320\right) (3 x+2)^3\right)+56 \left(3041250 x^4-142042500 x^3-370873350 x^2+223047840 x+236267784\right) (3 x+2)^3}","-\frac{608185 \sqrt{1-2 x}}{504 \sqrt{5 x+3}}+\frac{13409 \sqrt{1-2 x}}{168 (3 x+2) \sqrt{5 x+3}}+\frac{77 \sqrt{1-2 x}}{12 (3 x+2)^2 \sqrt{5 x+3}}+\frac{7 \sqrt{1-2 x}}{9 (3 x+2)^3 \sqrt{5 x+3}}+\frac{463881 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{56 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-81373437380224 - 374486413262768*x - 557596366997784*x^2 - 207104518795420*x^3 + 147519093712650*x^4 + 83803904073000*x^5 + 831323700000*x^6) + Sqrt[3 + 5*x]*(81373437380224 + 295190708650288*x + 162507878881832*x^2 - 490796917872404*x^3 - 636493807226970*x^4 - 166025242117350*x^5 + 18568990266750*x^6) + Sqrt[3]*(-81373437380224 - 362422049383808*x - 381598499847272*x^2 + 431933171796144*x^3 + 1047965904071540*x^4 + 539960584015775*x^5 + 12543396916875*x^6 - 5806727658750*x^7 + Sqrt[1 - 2*x]*(81373437380224 + 441717753996288*x + 842186884723624*x^2 + 568158684755640*x^3 - 88674169568600*x^4 - 204670372974375*x^5 - 26142812705625*x^6)))/(56*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3) + 56*(2 + 3*x)^3*(236267784 + 223047840*x - 370873350*x^2 - 142042500*x^3 + 3041250*x^4) + Sqrt[1 - 2*x]*(56*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(77141440 + 68422100*x - 16812750*x^2 - 1101875*x^3) + 56*(2 + 3*x)^3*(-229549320 - 407807400*x - 21771750*x^2 + 33783750*x^3))) - (463881*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/56 + (2319405*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/112","C",1
2379,1,639,173,2.9909983,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^5 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^5*(3 + 5*x)^(3/2)),x]","-\frac{145708761 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{3136}+\frac{728543805 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{6272}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-160237638941821875 x^8+1377427025098766250 x^7+45469239922152157500 x^6+109456072229580556800 x^5+35127173098627667840 x^4-133217411486231708944 x^3-166291056729689779200 x^2-75565084924425455680 x-12371047637885981440\right)+\sqrt{5 x+3} \left(2012899731476596875 x^8+20848451011098232500 x^7-27637955348069731500 x^6-212907325441534059600 x^5-270678490084679901840 x^4-69894801547935231120 x^3+85746501504660363840 x^2+63288015521081144640 x+12371047637885981440\right)+\sqrt{3} \left(-105696477963000000 x^9-13048802479854928125 x^8-23505571644358314375 x^7+139550486960912991500 x^6+404148460947947413800 x^5+344468579425777072440 x^4+16742977187445515920 x^3-134242617114593963040 x^2+\sqrt{1-2 x} \left(966504599642896875 x^8-19247841021252999375 x^7-114400867385504254500 x^6-155492242408991683800 x^5+36052148651586446280 x^4+249251112124195828944 x^3+224999849897618637600 x^2+85856077677872106880 x+12371047637885981440\right)-73579008274527795840 x-12371047637885981440\right)}{3136 \sqrt{3} \sqrt{5 x+3} \left(-846511875 x^4+2876857500 x^3+32771841300 x^2-464036760 x-18959828096\right) (3 x+2)^4+\sqrt{1-2 x} \left(3136 \sqrt{3} \sqrt{5 x+3} \left(24903125 x^4-2538047500 x^3-9400717500 x^2+18053298200 x+18798584960\right) (3 x+2)^4+3136 \left(883575000 x^4+30445470000 x^3+4629933000 x^2-101828232000 x-56302004880\right) (3 x+2)^4\right)+3136 \left(345768750 x^5+7219361250 x^4-69737490000 x^3-119509419600 x^2+49557305520 x+56785734288\right) (3 x+2)^4}","-\frac{63678595 \sqrt{1-2 x}}{9408 \sqrt{5 x+3}}+\frac{1403963 \sqrt{1-2 x}}{3136 (3 x+2) \sqrt{5 x+3}}+\frac{8063 \sqrt{1-2 x}}{224 (3 x+2)^2 \sqrt{5 x+3}}+\frac{33 \sqrt{1-2 x}}{8 (3 x+2)^3 \sqrt{5 x+3}}+\frac{7 \sqrt{1-2 x}}{12 (3 x+2)^4 \sqrt{5 x+3}}+\frac{145708761 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{3136 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-12371047637885981440 - 75565084924425455680*x - 166291056729689779200*x^2 - 133217411486231708944*x^3 + 35127173098627667840*x^4 + 109456072229580556800*x^5 + 45469239922152157500*x^6 + 1377427025098766250*x^7 - 160237638941821875*x^8) + Sqrt[3 + 5*x]*(12371047637885981440 + 63288015521081144640*x + 85746501504660363840*x^2 - 69894801547935231120*x^3 - 270678490084679901840*x^4 - 212907325441534059600*x^5 - 27637955348069731500*x^6 + 20848451011098232500*x^7 + 2012899731476596875*x^8) + Sqrt[3]*(-12371047637885981440 - 73579008274527795840*x - 134242617114593963040*x^2 + 16742977187445515920*x^3 + 344468579425777072440*x^4 + 404148460947947413800*x^5 + 139550486960912991500*x^6 - 23505571644358314375*x^7 - 13048802479854928125*x^8 - 105696477963000000*x^9 + Sqrt[1 - 2*x]*(12371047637885981440 + 85856077677872106880*x + 224999849897618637600*x^2 + 249251112124195828944*x^3 + 36052148651586446280*x^4 - 155492242408991683800*x^5 - 114400867385504254500*x^6 - 19247841021252999375*x^7 + 966504599642896875*x^8)))/(3136*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-18959828096 - 464036760*x + 32771841300*x^2 + 2876857500*x^3 - 846511875*x^4) + 3136*(2 + 3*x)^4*(56785734288 + 49557305520*x - 119509419600*x^2 - 69737490000*x^3 + 7219361250*x^4 + 345768750*x^5) + Sqrt[1 - 2*x]*(3136*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(18798584960 + 18053298200*x - 9400717500*x^2 - 2538047500*x^3 + 24903125*x^4) + 3136*(2 + 3*x)^4*(-56302004880 - 101828232000*x + 4629933000*x^2 + 30445470000*x^3 + 883575000*x^4))) - (145708761*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/3136 + (728543805*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/6272","C",1
2380,1,414,142,2.7849439,"\int \frac{(1-2 x)^{3/2} (2+3 x)^3}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^3)/(3 + 5*x)^(5/2),x]","\frac{48411675000000 x^9-4920651129375000 x^8-19703665836281250 x^7+37412950183228125 x^6+77714407563210000 x^5-41788185308422875 x^4-108777728647979100 x^3-19038080016681300 x^2+\sqrt{3} \sqrt{5 x+3} \left(114511320000000 x^8+3908516733000000 x^7-829900343250000 x^6-18595377922213125 x^5-2916556227663375 x^4+25780430779765200 x^3+10974302606866500 x^2-7051696172653000 x-3527980198855728\right)+\sqrt{1-2 x} \left(822809542500000 x^8-2158628094562500 x^7-34923371459315625 x^6-22022558064663750 x^5+61652529058390875 x^4+56480207114479500 x^3-26988987353527980 x^2+\sqrt{3} \sqrt{5 x+3} \left(-22405815000000 x^8-471735626625000 x^7+4464036780693750 x^6+9111679402114375 x^5-7452222818422625 x^4-17425910422114800 x^3+1417729327219660 x^2+10589743506083320 x+3527980198855728\right)-40595034249764280 x-10583940596567184\right)+29980892249473320 x+10583940596567184}{270000 \left(-846511875 x^4+2876857500 x^3+32771841300 x^2-464036760 x-18959828096\right) (5 x+3)^{3/2}+270000 \sqrt{1-2 x} \left(24903125 x^4-2538047500 x^3-9400717500 x^2+18053298200 x+18798584960\right) (5 x+3)^{3/2}+\sqrt{3} \left(270000 \sqrt{1-2 x} (5 x+3) \left(294525000 x^4+10148490000 x^3+1543311000 x^2-33942744000 x-18767334960\right)+270000 (5 x+3) \left(115256250 x^5+2406453750 x^4-23245830000 x^3-39836473200 x^2+16519101840 x+18928578096\right)\right)}+\frac{13153 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{5000 \sqrt{10}}","-\frac{128 \sqrt{1-2 x} (3 x+2)^3}{25 \sqrt{5 x+3}}-\frac{2 (1-2 x)^{3/2} (3 x+2)^3}{15 (5 x+3)^{3/2}}+\frac{378}{125} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2+\frac{21 \sqrt{1-2 x} \sqrt{5 x+3} (1140 x+853)}{10000}+\frac{13153 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{10000 \sqrt{10}}",1,"(10583940596567184 + 29980892249473320*x - 19038080016681300*x^2 - 108777728647979100*x^3 - 41788185308422875*x^4 + 77714407563210000*x^5 + 37412950183228125*x^6 - 19703665836281250*x^7 - 4920651129375000*x^8 + 48411675000000*x^9 + Sqrt[3]*Sqrt[3 + 5*x]*(-3527980198855728 - 7051696172653000*x + 10974302606866500*x^2 + 25780430779765200*x^3 - 2916556227663375*x^4 - 18595377922213125*x^5 - 829900343250000*x^6 + 3908516733000000*x^7 + 114511320000000*x^8) + Sqrt[1 - 2*x]*(-10583940596567184 - 40595034249764280*x - 26988987353527980*x^2 + 56480207114479500*x^3 + 61652529058390875*x^4 - 22022558064663750*x^5 - 34923371459315625*x^6 - 2158628094562500*x^7 + 822809542500000*x^8 + Sqrt[3]*Sqrt[3 + 5*x]*(3527980198855728 + 10589743506083320*x + 1417729327219660*x^2 - 17425910422114800*x^3 - 7452222818422625*x^4 + 9111679402114375*x^5 + 4464036780693750*x^6 - 471735626625000*x^7 - 22405815000000*x^8)))/(270000*(3 + 5*x)^(3/2)*(-18959828096 - 464036760*x + 32771841300*x^2 + 2876857500*x^3 - 846511875*x^4) + 270000*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)*(18798584960 + 18053298200*x - 9400717500*x^2 - 2538047500*x^3 + 24903125*x^4) + Sqrt[3]*(270000*Sqrt[1 - 2*x]*(3 + 5*x)*(-18767334960 - 33942744000*x + 1543311000*x^2 + 10148490000*x^3 + 294525000*x^4) + 270000*(3 + 5*x)*(18928578096 + 16519101840*x - 39836473200*x^2 - 23245830000*x^3 + 2406453750*x^4 + 115256250*x^5))) + (13153*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(5000*Sqrt[10])","B",1
2381,1,354,116,2.4043531,"\int \frac{(1-2 x)^{3/2} (2+3 x)^2}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^2)/(3 + 5*x)^(5/2),x]","\frac{-53551125000 x^7-753730818750 x^6+4359219346875 x^5-22174879500 x^4-10083560793525 x^3-2752327484400 x^2+\sqrt{3} \sqrt{5 x+3} \left(109459350000 x^6-265742977500 x^5-1171763429375 x^4+2056556330675 x^3+1431810018100 x^2-807106907420 x-421390585704\right)+\sqrt{1-2 x} \left(-83965612500 x^6-2144253313125 x^5+1874475429750 x^4+4821734767575 x^3-2620597269840 x^2+\sqrt{3} \sqrt{5 x+3} \left(-4926825000 x^6+236431608750 x^5+303338214875 x^4-1341615358425 x^3+4594325380 x^2+1231564471940 x+421390585704\right)-4750737692580 x-1264171757112\right)+3477364999020 x+1264171757112}{13500 \sqrt{1-2 x} \left(-1101875 x^3-16812750 x^2+68422100 x+77141440\right) (5 x+3)^{3/2}+13500 \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (5 x+3)^{3/2}+\sqrt{3} \left(13500 \sqrt{1-2 x} (5 x+3) \left(11261250 x^3-7257250 x^2-135935800 x-76516440\right)+13500 (5 x+3) \left(1013750 x^4-47347500 x^3-123624450 x^2+74349280 x+78755928\right)\right)}+\frac{343 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{250 \sqrt{10}}","-\frac{388 (1-2 x)^{5/2}}{9075 \sqrt{5 x+3}}-\frac{2 (1-2 x)^{5/2}}{825 (5 x+3)^{3/2}}+\frac{343 \sqrt{5 x+3} (1-2 x)^{3/2}}{18150}+\frac{343 \sqrt{5 x+3} \sqrt{1-2 x}}{5500}+\frac{343 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{500 \sqrt{10}}",1,"(1264171757112 + 3477364999020*x - 2752327484400*x^2 - 10083560793525*x^3 - 22174879500*x^4 + 4359219346875*x^5 - 753730818750*x^6 - 53551125000*x^7 + Sqrt[3]*Sqrt[3 + 5*x]*(-421390585704 - 807106907420*x + 1431810018100*x^2 + 2056556330675*x^3 - 1171763429375*x^4 - 265742977500*x^5 + 109459350000*x^6) + Sqrt[1 - 2*x]*(-1264171757112 - 4750737692580*x - 2620597269840*x^2 + 4821734767575*x^3 + 1874475429750*x^4 - 2144253313125*x^5 - 83965612500*x^6 + Sqrt[3]*Sqrt[3 + 5*x]*(421390585704 + 1231564471940*x + 4594325380*x^2 - 1341615358425*x^3 + 303338214875*x^4 + 236431608750*x^5 - 4926825000*x^6)))/(13500*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)*(77141440 + 68422100*x - 16812750*x^2 - 1101875*x^3) + 13500*(3 + 5*x)^(3/2)*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3) + Sqrt[3]*(13500*Sqrt[1 - 2*x]*(3 + 5*x)*(-76516440 - 135935800*x - 7257250*x^2 + 11261250*x^3) + 13500*(3 + 5*x)*(78755928 + 74349280*x - 123624450*x^2 - 47347500*x^3 + 1013750*x^4))) + (343*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(250*Sqrt[10])","B",1
2382,1,304,96,1.9589752,"\int \frac{(1-2 x)^{3/2} (2+3 x)}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x))/(3 + 5*x)^(5/2),x]","\frac{2 \sqrt{3} \sqrt{5 x+3} \left(4455000 x^4+152931625 x^3+244358125 x^2-135585010 x-141080676\right)+\sqrt{1-2 x} \left(2 \sqrt{3} \sqrt{5 x+3} \left(-2814750 x^4-37720325 x^3+38334315 x^2+266354710 x+141080676\right)+2 \left(66268125 x^4+169830375 x^3-659744745 x^2-1139334570 x-423242028\right)\right)+2 \left(9618750 x^5-187434375 x^4-1105575375 x^3-502825575 x^2+747025470 x+423242028\right)}{675 \left(-163625 x^2+33550 x+343904\right) (5 x+3)^{3/2}+675 \sqrt{1-2 x} \left(11875 x^2-216750 x-312800\right) (5 x+3)^{3/2}+\sqrt{3} \left(675 \sqrt{1-2 x} (5 x+3) \left(27500 x^2+517000 x+300300\right)+675 (5 x+3) \left(34750 x^3+321050 x^2-372220 x-331404\right)\right)}-\frac{38}{25} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{2 (1-2 x)^{5/2}}{165 (5 x+3)^{3/2}}-\frac{38 (1-2 x)^{3/2}}{165 \sqrt{5 x+3}}-\frac{38}{275} \sqrt{5 x+3} \sqrt{1-2 x}-\frac{19}{25} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"(2*Sqrt[3]*Sqrt[3 + 5*x]*(-141080676 - 135585010*x + 244358125*x^2 + 152931625*x^3 + 4455000*x^4) + 2*(423242028 + 747025470*x - 502825575*x^2 - 1105575375*x^3 - 187434375*x^4 + 9618750*x^5) + Sqrt[1 - 2*x]*(2*Sqrt[3]*Sqrt[3 + 5*x]*(141080676 + 266354710*x + 38334315*x^2 - 37720325*x^3 - 2814750*x^4) + 2*(-423242028 - 1139334570*x - 659744745*x^2 + 169830375*x^3 + 66268125*x^4)))/(675*(3 + 5*x)^(3/2)*(343904 + 33550*x - 163625*x^2) + 675*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)*(-312800 - 216750*x + 11875*x^2) + Sqrt[3]*(675*Sqrt[1 - 2*x]*(3 + 5*x)*(300300 + 517000*x + 27500*x^2) + 675*(3 + 5*x)*(-331404 - 372220*x + 321050*x^2 + 34750*x^3))) - (38*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/25","B",1
2383,1,244,74,1.6226766,"\int \frac{(1-2 x)^{3/2}}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/(3 + 5*x)^(5/2),x]","\frac{22 \sqrt{3} \sqrt{5 x+3} \left(-20625 x^2+14245 x+9438\right)+\sqrt{1-2 x} \left(22 \sqrt{3} \sqrt{5 x+3} \left(1025 x^2-23035 x-9438\right)+22 \left(34650 x^2+91575 x+28314\right)\right)+22 \left(29250 x^3+45000 x^2-65205 x-28314\right)}{\sqrt{3} \left(675 (5 x+3) \left(450 x^2-2100 x-1422\right)+675 \sqrt{1-2 x} (5 x+3) (1650 x+990)\right)+675 (165 x+1672) (5 x+3)^{3/2}+675 (-325 x-1240) \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{8}{25} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{2 (1-2 x)^{3/2}}{15 (5 x+3)^{3/2}}+\frac{4 \sqrt{1-2 x}}{25 \sqrt{5 x+3}}+\frac{4}{25} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"(22*Sqrt[3]*Sqrt[3 + 5*x]*(9438 + 14245*x - 20625*x^2) + 22*(-28314 - 65205*x + 45000*x^2 + 29250*x^3) + Sqrt[1 - 2*x]*(22*Sqrt[3]*Sqrt[3 + 5*x]*(-9438 - 23035*x + 1025*x^2) + 22*(28314 + 91575*x + 34650*x^2)))/(675*(-1240 - 325*x)*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2) + 675*(3 + 5*x)^(3/2)*(1672 + 165*x) + Sqrt[3]*(675*Sqrt[1 - 2*x]*(3 + 5*x)*(990 + 1650*x) + 675*(3 + 5*x)*(-1422 - 2100*x + 450*x^2))) + (8*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/25","B",1
2384,1,374,75,1.672639,"\int \frac{(1-2 x)^{3/2}}{(2+3 x) (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)*(3 + 5*x)^(5/2)),x]","\frac{22 \sqrt{3} \sqrt{5 x+3} \left(-53130 x^2+45320 x+45012\right)+\sqrt{1-2 x} \left(22 \sqrt{3} \sqrt{5 x+3} \left(-1280 x^2-77372 x-45012\right)+22 \left(153945 x^2+322146 x+135036\right)\right)+22 \left(94950 x^3+66915 x^2-225990 x-135036\right)}{\sqrt{3} \left(27 (5 x+3) \left(450 x^2-2100 x-1422\right)+27 \sqrt{1-2 x} (5 x+3) (1650 x+990)\right)+27 (165 x+1672) (5 x+3)^{3/2}+27 (-325 x-1240) \sqrt{1-2 x} (5 x+3)^{3/2}}-49 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]","-\frac{2 (1-2 x)^{3/2}}{3 (5 x+3)^{3/2}}+\frac{14 \sqrt{1-2 x}}{\sqrt{5 x+3}}-14 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(22*Sqrt[3]*Sqrt[3 + 5*x]*(45012 + 45320*x - 53130*x^2) + 22*(-135036 - 225990*x + 66915*x^2 + 94950*x^3) + Sqrt[1 - 2*x]*(22*Sqrt[3]*Sqrt[3 + 5*x]*(-45012 - 77372*x - 1280*x^2) + 22*(135036 + 322146*x + 153945*x^2)))/(27*(-1240 - 325*x)*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2) + 27*(3 + 5*x)^(3/2)*(1672 + 165*x) + Sqrt[3]*(27*Sqrt[1 - 2*x]*(3 + 5*x)*(990 + 1650*x) + 27*(3 + 5*x)*(-1422 - 2100*x + 450*x^2))) - 49*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ]","C",1
2385,1,517,104,2.204925,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^2 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^2*(3 + 5*x)^(5/2)),x]","1183 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{5915}{2} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{1368168750 x^5+107245526250 x^4+139684152750 x^3-39522328050 x^2+\sqrt{3} \sqrt{5 x+3} \left(-8886343125 x^4-36893115875 x^3-6027741500 x^2+27067447220 x+11576345880\right)+\sqrt{1-2 x} \left(-19134101250 x^4+50629029000 x^3+175228490910 x^2+\sqrt{3} \sqrt{5 x+3} \left(1503634875 x^4+526701925 x^3-30787749180 x^2-37650393548 x-11576345880\right)+140694370344 x+34729037640\right)-108945531360 x-34729037640}{54 (3 x+2) \left(-163625 x^2+33550 x+343904\right) (5 x+3)^{3/2}+54 \sqrt{1-2 x} (3 x+2) \left(11875 x^2-216750 x-312800\right) (5 x+3)^{3/2}+\sqrt{3} \left(54 \sqrt{1-2 x} (3 x+2) (5 x+3) \left(27500 x^2+517000 x+300300\right)+54 (3 x+2) (5 x+3) \left(34750 x^3+321050 x^2-372220 x-331404\right)\right)}","\frac{3 (1-2 x)^{5/2}}{7 (3 x+2) (5 x+3)^{3/2}}-\frac{169 (1-2 x)^{3/2}}{21 (5 x+3)^{3/2}}+\frac{169 \sqrt{1-2 x}}{\sqrt{5 x+3}}-169 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(-34729037640 - 108945531360*x - 39522328050*x^2 + 139684152750*x^3 + 107245526250*x^4 + 1368168750*x^5 + Sqrt[3]*Sqrt[3 + 5*x]*(11576345880 + 27067447220*x - 6027741500*x^2 - 36893115875*x^3 - 8886343125*x^4) + Sqrt[1 - 2*x]*(34729037640 + 140694370344*x + 175228490910*x^2 + 50629029000*x^3 - 19134101250*x^4 + Sqrt[3]*Sqrt[3 + 5*x]*(-11576345880 - 37650393548*x - 30787749180*x^2 + 526701925*x^3 + 1503634875*x^4)))/(54*(2 + 3*x)*(3 + 5*x)^(3/2)*(343904 + 33550*x - 163625*x^2) + 54*Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^(3/2)*(-312800 - 216750*x + 11875*x^2) + Sqrt[3]*(54*Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)*(300300 + 517000*x + 27500*x^2) + 54*(2 + 3*x)*(3 + 5*x)*(-331404 - 372220*x + 321050*x^2 + 34750*x^3))) + 1183*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ] - (5915*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2","C",1
2386,1,587,137,2.6190582,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^3 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^3*(3 + 5*x)^(5/2)),x]","\frac{40787}{4} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{203935}{8} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{22975171762500 x^7-51160814420625 x^6-2132101869724500 x^5-4006887990797025 x^4-1525607744261490 x^3+1501512869942988 x^2+\sqrt{3} \sqrt{5 x+3} \left(-24490347564375 x^6+220600104792375 x^5+823773800091550 x^4+601797058978610 x^3-227144048266256 x^2-366488478468728 x-96589644086496\right)+\sqrt{1-2 x} \left(103437779878125 x^6+802912882117500 x^5+301464600562125 x^4-2238463217180850 x^3-3188723058131820 x^2+\sqrt{3} \sqrt{5 x+3} \left(-1096413271875 x^6-110454373059375 x^5-187240853275000 x^4+281236601765250 x^3+711799534868440 x^2+460611902071640 x+96589644086496\right)-1621244985806160 x-289768932259488\right)+1338874714997424 x+289768932259488}{108 \sqrt{1-2 x} (5 x+3)^{3/2} \left(-1101875 x^3-16812750 x^2+68422100 x+77141440\right) (3 x+2)^2+108 (5 x+3)^{3/2} \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (3 x+2)^2+\sqrt{3} \left(108 \sqrt{1-2 x} (5 x+3) \left(11261250 x^3-7257250 x^2-135935800 x-76516440\right) (3 x+2)^2+108 (5 x+3) \left(1013750 x^4-47347500 x^3-123624450 x^2+74349280 x+78755928\right) (3 x+2)^2\right)}","\frac{17825 \sqrt{1-2 x}}{12 \sqrt{5 x+3}}-\frac{655 \sqrt{1-2 x}}{4 (5 x+3)^{3/2}}+\frac{235 \sqrt{1-2 x}}{12 (3 x+2) (5 x+3)^{3/2}}+\frac{7 \sqrt{1-2 x}}{6 (3 x+2)^2 (5 x+3)^{3/2}}-\frac{40787 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{4 \sqrt{7}}",1,"(289768932259488 + 1338874714997424*x + 1501512869942988*x^2 - 1525607744261490*x^3 - 4006887990797025*x^4 - 2132101869724500*x^5 - 51160814420625*x^6 + 22975171762500*x^7 + Sqrt[3]*Sqrt[3 + 5*x]*(-96589644086496 - 366488478468728*x - 227144048266256*x^2 + 601797058978610*x^3 + 823773800091550*x^4 + 220600104792375*x^5 - 24490347564375*x^6) + Sqrt[1 - 2*x]*(-289768932259488 - 1621244985806160*x - 3188723058131820*x^2 - 2238463217180850*x^3 + 301464600562125*x^4 + 802912882117500*x^5 + 103437779878125*x^6 + Sqrt[3]*Sqrt[3 + 5*x]*(96589644086496 + 460611902071640*x + 711799534868440*x^2 + 281236601765250*x^3 - 187240853275000*x^4 - 110454373059375*x^5 - 1096413271875*x^6)))/(108*Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^(3/2)*(77141440 + 68422100*x - 16812750*x^2 - 1101875*x^3) + 108*(2 + 3*x)^2*(3 + 5*x)^(3/2)*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3) + Sqrt[3]*(108*Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)*(-76516440 - 135935800*x - 7257250*x^2 + 11261250*x^3) + 108*(2 + 3*x)^2*(3 + 5*x)*(78755928 + 74349280*x - 123624450*x^2 - 47347500*x^3 + 1013750*x^4))) + (40787*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/4 - (203935*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/8","C",1
2387,1,647,166,3.1392166,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^4 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^4*(3 + 5*x)^(5/2)),x]","\frac{4246733}{56} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{21233665}{112} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{138625199837718750 x^9+17104794070124278125 x^8+29693747572774391250 x^7-184324839683640726375 x^6-516989584348191184050 x^5-425159126230970031300 x^4-9590432367169803744 x^3+169282791273336491952 x^2+\sqrt{3} \sqrt{5 x+3} \left(-879999932283862500 x^8-9055864739352667500 x^7+12651288257605536000 x^6+91894335516424643400 x^5+112919716332716783160 x^4+26277988580381659968 x^3-36671353606304653104 x^2-25712701209430527776 x-4867539261177635328\right)+\sqrt{1-2 x} \left(-1267610318458171875 x^8+25328831989746037500 x^7+148302100252646938125 x^6+195091188832698864750 x^5-54983970796243688100 x^4-318617268091327648080 x^3-278826701032588073904 x^2+\sqrt{3} \sqrt{5 x+3} \left(70052730286218750 x^8-606853787893762500 x^7-19834993318168608750 x^6-46555655405733389500 x^5-13031027623397216800 x^4+57713217569427772320 x^3+69167687867699659088 x^2+30543263630632153376 x+4867539261177635328\right)-103777139966903048448 x-14602617783532905984\right)+89285452703298171648 x+14602617783532905984}{1512 (5 x+3)^{3/2} \left(-846511875 x^4+2876857500 x^3+32771841300 x^2-464036760 x-18959828096\right) (3 x+2)^3+1512 \sqrt{1-2 x} (5 x+3)^{3/2} \left(24903125 x^4-2538047500 x^3-9400717500 x^2+18053298200 x+18798584960\right) (3 x+2)^3+\sqrt{3} \left(1512 \sqrt{1-2 x} (5 x+3) \left(294525000 x^4+10148490000 x^3+1543311000 x^2-33942744000 x-18767334960\right) (3 x+2)^3+1512 (5 x+3) \left(115256250 x^5+2406453750 x^4-23245830000 x^3-39836473200 x^2+16519101840 x+18928578096\right) (3 x+2)^3\right)}","\frac{618645 \sqrt{1-2 x}}{56 \sqrt{5 x+3}}-\frac{204595 \sqrt{1-2 x}}{168 (5 x+3)^{3/2}}+\frac{24469 \sqrt{1-2 x}}{168 (3 x+2) (5 x+3)^{3/2}}+\frac{301 \sqrt{1-2 x}}{36 (3 x+2)^2 (5 x+3)^{3/2}}+\frac{7 \sqrt{1-2 x}}{9 (3 x+2)^3 (5 x+3)^{3/2}}-\frac{4246733 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{56 \sqrt{7}}",1,"(14602617783532905984 + 89285452703298171648*x + 169282791273336491952*x^2 - 9590432367169803744*x^3 - 425159126230970031300*x^4 - 516989584348191184050*x^5 - 184324839683640726375*x^6 + 29693747572774391250*x^7 + 17104794070124278125*x^8 + 138625199837718750*x^9 + Sqrt[3]*Sqrt[3 + 5*x]*(-4867539261177635328 - 25712701209430527776*x - 36671353606304653104*x^2 + 26277988580381659968*x^3 + 112919716332716783160*x^4 + 91894335516424643400*x^5 + 12651288257605536000*x^6 - 9055864739352667500*x^7 - 879999932283862500*x^8) + Sqrt[1 - 2*x]*(-14602617783532905984 - 103777139966903048448*x - 278826701032588073904*x^2 - 318617268091327648080*x^3 - 54983970796243688100*x^4 + 195091188832698864750*x^5 + 148302100252646938125*x^6 + 25328831989746037500*x^7 - 1267610318458171875*x^8 + Sqrt[3]*Sqrt[3 + 5*x]*(4867539261177635328 + 30543263630632153376*x + 69167687867699659088*x^2 + 57713217569427772320*x^3 - 13031027623397216800*x^4 - 46555655405733389500*x^5 - 19834993318168608750*x^6 - 606853787893762500*x^7 + 70052730286218750*x^8)))/(1512*(2 + 3*x)^3*(3 + 5*x)^(3/2)*(-18959828096 - 464036760*x + 32771841300*x^2 + 2876857500*x^3 - 846511875*x^4) + 1512*Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^(3/2)*(18798584960 + 18053298200*x - 9400717500*x^2 - 2538047500*x^3 + 24903125*x^4) + Sqrt[3]*(1512*Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)*(-18767334960 - 33942744000*x + 1543311000*x^2 + 10148490000*x^3 + 294525000*x^4) + 1512*(2 + 3*x)^3*(3 + 5*x)*(18928578096 + 16519101840*x - 39836473200*x^2 - 23245830000*x^3 + 2406453750*x^4 + 115256250*x^5))) + (4246733*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/56 - (21233665*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/112","C",1
2388,1,1331,172,14.0499407,"\int (1-2 x)^{5/2} (2+3 x)^3 \sqrt{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^3*Sqrt[3 + 5*x],x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{28} \left(\frac{3735929329 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}{128000000 \sqrt{10} \left(\sqrt{3}-\sqrt{5 x+3}\right)^{28}}+\frac{\left(\frac{8552070671 \sqrt{1-2 x}}{256000000}-\frac{16}{5} \sqrt{3} \sqrt{5 x+3}-\frac{6094470671}{256000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{13}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{27}}+\frac{\left(\frac{308887929329 \sqrt{1-2 x}}{384000000}-\frac{3632}{25} \sqrt{3} \sqrt{5 x+3}-\frac{141525369329}{384000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{25}}+\frac{\left(\frac{5199822470671 \sqrt{1-2 x}}{480000000}-\frac{377072}{125} \sqrt{3} \sqrt{5 x+3}-\frac{855953030671}{480000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{11}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{23}}+\frac{\left(\frac{57233754489329 \sqrt{1-2 x}}{560000000}-\frac{23022032}{625} \sqrt{3} \sqrt{5 x+3}+\frac{4649467526671}{560000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{21}}+\frac{\left(\frac{142134492375557 \sqrt{1-2 x}}{210000000}-\frac{910100752 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{41341819227643}{210000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{19}}+\frac{\left(\frac{66932003722193 \sqrt{1-2 x}}{21000000}-\frac{24352425136 \sqrt{3} \sqrt{5 x+3}}{15625}+\frac{31256974426159}{21000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{17}}+\frac{\left(\frac{18800296999723 \sqrt{1-2 x}}{1750000}-\frac{126107018368 \sqrt{3} \sqrt{5 x+3}}{21875}+\frac{11465387408597}{1750000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{15}}+\frac{\left(\frac{16256455262279 \sqrt{1-2 x}}{625000}-\frac{232387931168 \sqrt{3} \sqrt{5 x+3}}{15625}+\frac{11630096477881}{625000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{13}}+\frac{\left(\frac{3536730124146 \sqrt{1-2 x}}{78125}-\frac{419014744704 \sqrt{3} \sqrt{5 x+3}}{15625}+\frac{2748491046414}{78125}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{11}}+\frac{\left(\frac{4391501486868 \sqrt{1-2 x}}{78125}-\frac{104883435648 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{3474756186732}{78125}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}+\frac{\left(\frac{5320713244176 \sqrt{1-2 x}}{109375}-\frac{445895801856 \sqrt{3} \sqrt{5 x+3}}{15625}+\frac{161723943792}{4375}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}+\frac{\left(\frac{610215321312 \sqrt{1-2 x}}{21875}-\frac{49123321344 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{421374426912}{21875}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{\frac{160282630656 \sqrt{1-2 x}}{109375}-\frac{79061833728 \sqrt{3} \sqrt{5 x+3}}{109375}+\frac{76902870528}{109375}}{\sqrt{3}-\sqrt{5 x+3}}+\frac{\left(-\frac{6912 \sqrt{1-2 x}}{21875}-\frac{13824 \sqrt{3} \sqrt{5 x+3}}{109375}+\frac{76032}{109375}\right) \left(-150728747 \sqrt{1-2 x}+80068408 \sqrt{3} \sqrt{5 x+3}-89476477\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}","-\frac{3}{70} (3 x+2)^2 (5 x+3)^{3/2} (1-2 x)^{7/2}-\frac{3 (5 x+3)^{3/2} (26700 x+33857) (1-2 x)^{7/2}}{280000}-\frac{255169 \sqrt{5 x+3} (1-2 x)^{7/2}}{640000}+\frac{2806859 \sqrt{5 x+3} (1-2 x)^{5/2}}{19200000}+\frac{30875449 \sqrt{5 x+3} (1-2 x)^{3/2}}{76800000}+\frac{339629939 \sqrt{5 x+3} \sqrt{1-2 x}}{256000000}+\frac{3735929329 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{256000000 \sqrt{10}}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^28*((76902870528/109375 + (160282630656*Sqrt[1 - 2*x])/109375 - (79061833728*Sqrt[3]*Sqrt[3 + 5*x])/109375)/(Sqrt[3] - Sqrt[3 + 5*x]) + ((421374426912/21875 + (610215321312*Sqrt[1 - 2*x])/21875 - (49123321344*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^5 + ((161723943792/4375 + (5320713244176*Sqrt[1 - 2*x])/109375 - (445895801856*Sqrt[3]*Sqrt[3 + 5*x])/15625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^7 + ((3474756186732/78125 + (4391501486868*Sqrt[1 - 2*x])/78125 - (104883435648*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^9 + ((2748491046414/78125 + (3536730124146*Sqrt[1 - 2*x])/78125 - (419014744704*Sqrt[3]*Sqrt[3 + 5*x])/15625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^11 + ((11630096477881/625000 + (16256455262279*Sqrt[1 - 2*x])/625000 - (232387931168*Sqrt[3]*Sqrt[3 + 5*x])/15625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^13 + ((11465387408597/1750000 + (18800296999723*Sqrt[1 - 2*x])/1750000 - (126107018368*Sqrt[3]*Sqrt[3 + 5*x])/21875)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^7)/(Sqrt[3] - Sqrt[3 + 5*x])^15 + ((31256974426159/21000000 + (66932003722193*Sqrt[1 - 2*x])/21000000 - (24352425136*Sqrt[3]*Sqrt[3 + 5*x])/15625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^8)/(Sqrt[3] - Sqrt[3 + 5*x])^17 + ((41341819227643/210000000 + (142134492375557*Sqrt[1 - 2*x])/210000000 - (910100752*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^9)/(Sqrt[3] - Sqrt[3 + 5*x])^19 + ((4649467526671/560000000 + (57233754489329*Sqrt[1 - 2*x])/560000000 - (23022032*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^10)/(Sqrt[3] - Sqrt[3 + 5*x])^21 + ((-855953030671/480000000 + (5199822470671*Sqrt[1 - 2*x])/480000000 - (377072*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^11)/(Sqrt[3] - Sqrt[3 + 5*x])^23 + ((-141525369329/384000000 + (308887929329*Sqrt[1 - 2*x])/384000000 - (3632*Sqrt[3]*Sqrt[3 + 5*x])/25)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12)/(Sqrt[3] - Sqrt[3 + 5*x])^25 + ((-6094470671/256000000 + (8552070671*Sqrt[1 - 2*x])/256000000 - (16*Sqrt[3]*Sqrt[3 + 5*x])/5)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^13)/(Sqrt[3] - Sqrt[3 + 5*x])^27 + ((76032/109375 - (6912*Sqrt[1 - 2*x])/21875 - (13824*Sqrt[3]*Sqrt[3 + 5*x])/109375)*(-89476477 - 150728747*Sqrt[1 - 2*x] + 80068408*Sqrt[3]*Sqrt[3 + 5*x]))/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (3735929329*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(128000000*Sqrt[10]*(Sqrt[3] - Sqrt[3 + 5*x])^28)))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14","B",1
2389,1,486,165,2.9222713,"\int (1-2 x)^{5/2} (2+3 x)^2 \sqrt{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^2*Sqrt[3 + 5*x],x]","\frac{105254149 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{6400000 \sqrt{10}}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-5449676400000000000 x^{11}+208933047396000000000 x^{10}+4936614593859150000000 x^9-2161697200470887500000 x^8-35151490196742430562500 x^7-8759529612629360765625 x^6+44149723608892967995000 x^5+10707641180917266856750 x^4-24814358254487753406000 x^3-4586696205169004538320 x^2+5229983656225567799680 x+934390672375701867744\right)+\sqrt{5 x+3} \left(108944827200000000000 x^{11}+1013452787952000000000 x^{10}-13368762029442600000000 x^9-24020097206844090000000 x^8+41640738102461533750000 x^7+47947300075530258562500 x^6-44149810860562417353750 x^5-34370330020440782288250 x^4+23495855996476458790800 x^3+10341801957094041086400 x^2-4288559509269301324960 x-934390672375701867744\right)+\sqrt{3} \left(-6048432000000000000 x^{12}-798386332320000000000 x^{11}+2777532053094000000000 x^{10}+34700753387043900000000 x^9+6451764140759977500000 x^8-85133610873652314375000 x^7-25262579707442341978125 x^6+76640801460009690180000 x^5+19522738863488669106750 x^4-33390080991750217630800 x^3-7082243097538378304400 x^2+5066429551935250798080 x+\sqrt{1-2 x} \left(29105524800000000000 x^{11}-2206887016752000000000 x^{10}-8368951554750600000000 x^9+23292037164478170000000 x^8+50671672777359537750000 x^7-20171683213276660312500 x^6-58879271586443726921250 x^5+7008612268053344841750 x^4+30230527976470580391600 x^3+543406074130255110720 x^2-6007853698891517272800 x-934390672375701867744\right)+934390672375701867744\right)}{38400000 \sqrt{3} \sqrt{5 x+3} \left(25265212500 x^5-1941218400000 x^4-5284290066000 x^3+24057375117600 x^2+13825440024000 x-16748592098304\right)+\sqrt{1-2 x} \left(38400000 \left(-236425406250 x^5-2220611593750 x^4+28520358020000 x^3+52011357156000 x^2-49788771586400 x-50183931760160\right)+38400000 \sqrt{3} \sqrt{5 x+3} \left(2625187500 x^5+345183000000 x^4-1378186950000 x^3-13912170444000 x^2+2687092123200 x+16725373086720\right)\right)+38400000 \left(-23653109375 x^6+916525237500 x^5+21026153381250 x^4-17065853944000 x^3-123670456765200 x^2+301410173760 x+50253588794912\right)}","-\frac{1}{20} (3 x+2) (5 x+3)^{3/2} (1-2 x)^{7/2}-\frac{193 (5 x+3)^{3/2} (1-2 x)^{7/2}}{2000}-\frac{7189 \sqrt{5 x+3} (1-2 x)^{7/2}}{32000}+\frac{79079 \sqrt{5 x+3} (1-2 x)^{5/2}}{960000}+\frac{869869 \sqrt{5 x+3} (1-2 x)^{3/2}}{3840000}+\frac{9568559 \sqrt{5 x+3} \sqrt{1-2 x}}{12800000}+\frac{105254149 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{12800000 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(934390672375701867744 + 5229983656225567799680*x - 4586696205169004538320*x^2 - 24814358254487753406000*x^3 + 10707641180917266856750*x^4 + 44149723608892967995000*x^5 - 8759529612629360765625*x^6 - 35151490196742430562500*x^7 - 2161697200470887500000*x^8 + 4936614593859150000000*x^9 + 208933047396000000000*x^10 - 5449676400000000000*x^11) + Sqrt[3 + 5*x]*(-934390672375701867744 - 4288559509269301324960*x + 10341801957094041086400*x^2 + 23495855996476458790800*x^3 - 34370330020440782288250*x^4 - 44149810860562417353750*x^5 + 47947300075530258562500*x^6 + 41640738102461533750000*x^7 - 24020097206844090000000*x^8 - 13368762029442600000000*x^9 + 1013452787952000000000*x^10 + 108944827200000000000*x^11) + Sqrt[3]*(934390672375701867744 + 5066429551935250798080*x - 7082243097538378304400*x^2 - 33390080991750217630800*x^3 + 19522738863488669106750*x^4 + 76640801460009690180000*x^5 - 25262579707442341978125*x^6 - 85133610873652314375000*x^7 + 6451764140759977500000*x^8 + 34700753387043900000000*x^9 + 2777532053094000000000*x^10 - 798386332320000000000*x^11 - 6048432000000000000*x^12 + Sqrt[1 - 2*x]*(-934390672375701867744 - 6007853698891517272800*x + 543406074130255110720*x^2 + 30230527976470580391600*x^3 + 7008612268053344841750*x^4 - 58879271586443726921250*x^5 - 20171683213276660312500*x^6 + 50671672777359537750000*x^7 + 23292037164478170000000*x^8 - 8368951554750600000000*x^9 - 2206887016752000000000*x^10 + 29105524800000000000*x^11)))/(38400000*Sqrt[3]*Sqrt[3 + 5*x]*(-16748592098304 + 13825440024000*x + 24057375117600*x^2 - 5284290066000*x^3 - 1941218400000*x^4 + 25265212500*x^5) + 38400000*(50253588794912 + 301410173760*x - 123670456765200*x^2 - 17065853944000*x^3 + 21026153381250*x^4 + 916525237500*x^5 - 23653109375*x^6) + Sqrt[1 - 2*x]*(38400000*(-50183931760160 - 49788771586400*x + 52011357156000*x^2 + 28520358020000*x^3 - 2220611593750*x^4 - 236425406250*x^5) + 38400000*Sqrt[3]*Sqrt[3 + 5*x]*(16725373086720 + 2687092123200*x - 13912170444000*x^2 - 1378186950000*x^3 + 345183000000*x^4 + 2625187500*x^5))) + (105254149*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(6400000*Sqrt[10])","B",1
2390,1,426,138,2.5715032,"\int (1-2 x)^{5/2} (2+3 x) \sqrt{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)*Sqrt[3 + 5*x],x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(509767200000000 x^9+56536125090000000 x^8-126796156430500000 x^7-956254199855437500 x^6+502988144451328125 x^5+1200359197843727125 x^4-675805165680605700 x^3-563350601782006660 x^2+242844748918943680 x+147705125627425872\right)+\sqrt{5 x+3} \left(6311448000000000 x^9-243465000900000000 x^8-425936597405000000 x^7+1656579870804375000 x^6+283918318300031250 x^5-1966402299762855625 x^4+312199616789797000 x^3+885111456344360300 x^2-94124893954038640 x-147705125627425872\right)+\sqrt{3} \left(-1901520000000000 x^{10}+39593739000000000 x^9+743571343150000000 x^8-514636690661250000 x^7-2357963703229687500 x^6+1168487446142309375 x^5+2029587502205158125 x^4-1050752045986969500 x^3-855910359176472500 x^2+\sqrt{1-2 x} \left(-14605272000000000 x^9-112515450300000000 x^8+792250546131000000 x^7+917819618533125000 x^6-1512743211713043750 x^5-883499147120390625 x^4+1196058027124829000 x^3+410380176596489660 x^2-365768469155340240 x-147705125627425872\right)+217048614190435200 x+147705125627425872\right)}{960000 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right)+\sqrt{1-2 x} \left(960000 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right)+960000 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right)\right)+960000 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right)}+\frac{1742279 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{160000 \sqrt{10}}","-\frac{3}{50} (5 x+3)^{3/2} (1-2 x)^{7/2}-\frac{119}{800} \sqrt{5 x+3} (1-2 x)^{7/2}+\frac{1309 \sqrt{5 x+3} (1-2 x)^{5/2}}{24000}+\frac{14399 \sqrt{5 x+3} (1-2 x)^{3/2}}{96000}+\frac{158389 \sqrt{5 x+3} \sqrt{1-2 x}}{320000}+\frac{1742279 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{320000 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(147705125627425872 + 242844748918943680*x - 563350601782006660*x^2 - 675805165680605700*x^3 + 1200359197843727125*x^4 + 502988144451328125*x^5 - 956254199855437500*x^6 - 126796156430500000*x^7 + 56536125090000000*x^8 + 509767200000000*x^9) + Sqrt[3 + 5*x]*(-147705125627425872 - 94124893954038640*x + 885111456344360300*x^2 + 312199616789797000*x^3 - 1966402299762855625*x^4 + 283918318300031250*x^5 + 1656579870804375000*x^6 - 425936597405000000*x^7 - 243465000900000000*x^8 + 6311448000000000*x^9) + Sqrt[3]*(147705125627425872 + 217048614190435200*x - 855910359176472500*x^2 - 1050752045986969500*x^3 + 2029587502205158125*x^4 + 1168487446142309375*x^5 - 2357963703229687500*x^6 - 514636690661250000*x^7 + 743571343150000000*x^8 + 39593739000000000*x^9 - 1901520000000000*x^10 + Sqrt[1 - 2*x]*(-147705125627425872 - 365768469155340240*x + 410380176596489660*x^2 + 1196058027124829000*x^3 - 883499147120390625*x^4 - 1512743211713043750*x^5 + 917819618533125000*x^6 + 792250546131000000*x^7 - 112515450300000000*x^8 - 14605272000000000*x^9)))/(960000*Sqrt[3]*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 960000*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(960000*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 960000*Sqrt[3]*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (1742279*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(160000*Sqrt[10])","B",1
2391,1,366,116,2.0021567,"\int (1-2 x)^{5/2} \sqrt{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*Sqrt[3 + 5*x],x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-82086000000 x^7+873564700000 x^6+10998227992500 x^5-15949216642875 x^4-3755481489400 x^3+17122482756120 x^2-3243262745440 x-7619172066264\right)+\sqrt{5 x+3} \left(930864000000 x^7+4015237600000 x^6-24724609140000 x^5+17201636397000 x^4+16523997581300 x^3-24077067840100 x^2-4406538798200 x+7619172066264\right)+\sqrt{3} \left(-57120000000 x^8-5035592000000 x^7+9713430200000 x^6+23466949890000 x^5-38044737587875 x^4+534722870200 x^3+30273335481400 x^2+\sqrt{1-2 x} \left(428208000000 x^7-8130786400000 x^6-5181029700000 x^5+25385700747000 x^4-10053223759700 x^3-16951039215220 x^2+9585449363160 x+7619172066264\right)-1935647819520 x-7619172066264\right)}{9600 \sqrt{3} \sqrt{5 x+3} \left(8921000 x^3-162998000 x^2-220512160 x+287530496\right)+\sqrt{1-2 x} \left(9600 \left(-48482500 x^3-297203500 x^2+794989800 x+852279560\right)+9600 \sqrt{3} \sqrt{5 x+3} \left(595000 x^3+53178000 x^2-36412000 x-283051520\right)\right)+9600 \left(-8550625 x^4+79738000 x^3+1253327000 x^2-32289760 x-865716488\right)}+\frac{14641 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{1600 \sqrt{10}}","-\frac{1}{8} \sqrt{5 x+3} (1-2 x)^{7/2}+\frac{11}{240} \sqrt{5 x+3} (1-2 x)^{5/2}+\frac{121}{960} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{1331 \sqrt{5 x+3} \sqrt{1-2 x}}{3200}+\frac{14641 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{3200 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-7619172066264 - 3243262745440*x + 17122482756120*x^2 - 3755481489400*x^3 - 15949216642875*x^4 + 10998227992500*x^5 + 873564700000*x^6 - 82086000000*x^7) + Sqrt[3 + 5*x]*(7619172066264 - 4406538798200*x - 24077067840100*x^2 + 16523997581300*x^3 + 17201636397000*x^4 - 24724609140000*x^5 + 4015237600000*x^6 + 930864000000*x^7) + Sqrt[3]*(-7619172066264 - 1935647819520*x + 30273335481400*x^2 + 534722870200*x^3 - 38044737587875*x^4 + 23466949890000*x^5 + 9713430200000*x^6 - 5035592000000*x^7 - 57120000000*x^8 + Sqrt[1 - 2*x]*(7619172066264 + 9585449363160*x - 16951039215220*x^2 - 10053223759700*x^3 + 25385700747000*x^4 - 5181029700000*x^5 - 8130786400000*x^6 + 428208000000*x^7)))/(9600*Sqrt[3]*Sqrt[3 + 5*x]*(287530496 - 220512160*x - 162998000*x^2 + 8921000*x^3) + 9600*(-865716488 - 32289760*x + 1253327000*x^2 + 79738000*x^3 - 8550625*x^4) + Sqrt[1 - 2*x]*(9600*(852279560 + 794989800*x - 297203500*x^2 - 48482500*x^3) + 9600*Sqrt[3]*Sqrt[3 + 5*x]*(-283051520 - 36412000*x + 53178000*x^2 + 595000*x^3))) + (14641*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(1600*Sqrt[10])","B",1
2392,1,498,128,2.2359083,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x),x]","\frac{343}{81} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(107700000 x^5+6877102500 x^4-17956703875 x^3+19731930825 x^2+16788678000 x-62153446124\right)+\sqrt{5 x+3} \left(1881000000 x^5-19165575000 x^4+32862480750 x^3-26146099375 x^2-77560764380 x+62153446124\right)+\sqrt{3} \left(-702000000 x^6+3992850000 x^5+19644007500 x^4-58110995125 x^3+114427430325 x^2+\sqrt{1-2 x} \left(-2752200000 x^5-4240665000 x^4+26076558750 x^3-56907241875 x^2+35468475020 x+62153446124\right)+25303611360 x-62153446124\right)}{5400 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right)+\sqrt{1-2 x} \left(5400 \left(-391875 x^2+2827000 x+3481060\right)+5400 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right)\right)+5400 \left(44875 x^3+2976525 x^2-279060 x-3667684\right)}+\frac{250433 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{8100 \sqrt{10}}","\frac{1}{9} \sqrt{5 x+3} (1-2 x)^{5/2}+\frac{59}{180} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{6401 \sqrt{5 x+3} \sqrt{1-2 x}}{5400}+\frac{250433 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{16200 \sqrt{10}}+\frac{98}{81} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-62153446124 + 16788678000*x + 19731930825*x^2 - 17956703875*x^3 + 6877102500*x^4 + 107700000*x^5) + Sqrt[3 + 5*x]*(62153446124 - 77560764380*x - 26146099375*x^2 + 32862480750*x^3 - 19165575000*x^4 + 1881000000*x^5) + Sqrt[3]*(-62153446124 + 25303611360*x + 114427430325*x^2 - 58110995125*x^3 + 19644007500*x^4 + 3992850000*x^5 - 702000000*x^6 + Sqrt[1 - 2*x]*(62153446124 + 35468475020*x - 56907241875*x^2 + 26076558750*x^3 - 4240665000*x^4 - 2752200000*x^5)))/(5400*Sqrt[3]*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 5400*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(5400*(3481060 + 2827000*x - 391875*x^2) + 5400*Sqrt[3]*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (250433*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(8100*Sqrt[10]) + (343*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ])/81","C",1
2393,1,589,135,2.5661219,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^2,x]","\frac{245}{9} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{1225}{18} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(897500 x^5+55985375 x^4-261200675 x^3-356182040 x^2+950668636 x+822004304\right)+\sqrt{5 x+3} \left(15675000 x^5-182833750 x^4+423727425 x^3+1586376220 x^2-150001676 x-822004304\right)+\sqrt{3} \left(-5850000 x^6+41902500 x^5+183478500 x^4-1529963600 x^3-1775411040 x^2+\sqrt{1-2 x} \left(-22935000 x^5-1509750 x^4+638183700 x^3-129151440 x^2-1642818056 x-822004304\right)+842151096 x+822004304\right)}{30 \sqrt{3} (3 x+2) \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right)+\sqrt{1-2 x} \left(30 (3 x+2) \left(-391875 x^2+2827000 x+3481060\right)+30 \sqrt{3} (3 x+2) \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right)\right)+30 (3 x+2) \left(44875 x^3+2976525 x^2-279060 x-3667684\right)}-\frac{2119 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{45 \sqrt{10}}","-\frac{\sqrt{5 x+3} (1-2 x)^{5/2}}{3 (3 x+2)}-\frac{1}{3} \sqrt{5 x+3} (1-2 x)^{3/2}-\frac{43}{30} \sqrt{5 x+3} \sqrt{1-2 x}-\frac{2119 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{90 \sqrt{10}}-\frac{35}{9} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(822004304 + 950668636*x - 356182040*x^2 - 261200675*x^3 + 55985375*x^4 + 897500*x^5) + Sqrt[3 + 5*x]*(-822004304 - 150001676*x + 1586376220*x^2 + 423727425*x^3 - 182833750*x^4 + 15675000*x^5) + Sqrt[3]*(822004304 + 842151096*x - 1775411040*x^2 - 1529963600*x^3 + 183478500*x^4 + 41902500*x^5 - 5850000*x^6 + Sqrt[1 - 2*x]*(-822004304 - 1642818056*x - 129151440*x^2 + 638183700*x^3 - 1509750*x^4 - 22935000*x^5)))/(30*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 30*(2 + 3*x)*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(30*(2 + 3*x)*(3481060 + 2827000*x - 391875*x^2) + 30*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) - (2119*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(45*Sqrt[10]) + (245*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/9 - (1225*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/18","C",1
2394,1,599,144,2.6117908,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^3,x]","\frac{1085}{108} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{5425}{216} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(2154000 x^5+208989075 x^4+1199749295 x^3-1595341992 x^2-4150246380 x-1672353584\right)+\sqrt{5 x+3} \left(37620000 x^5-314625300 x^4-4378603845 x^3-2970523996 x^2+2536181692 x+1672353584\right)+\sqrt{3} \left(-14040000 x^6-58300875 x^5+2507900325 x^4+7269548450 x^3+1495335636 x^2+\sqrt{1-2 x} \left(-55044000 x^5-927969075 x^4-874581510 x^3+4435105092 x^2+5563395200 x+1672353584\right)-3949330512 x-1672353584\right)}{36 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right) (3 x+2)^2+\sqrt{1-2 x} \left(36 \left(-391875 x^2+2827000 x+3481060\right) (3 x+2)^2+36 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right) (3 x+2)^2\right)+36 \left(44875 x^3+2976525 x^2-279060 x-3667684\right) (3 x+2)^2}+\frac{236}{27} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{\sqrt{5 x+3} (1-2 x)^{5/2}}{6 (3 x+2)^2}+\frac{5 \sqrt{5 x+3} (1-2 x)^{3/2}}{4 (3 x+2)}+\frac{19}{18} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{118}{27} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{155}{108} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-1672353584 - 4150246380*x - 1595341992*x^2 + 1199749295*x^3 + 208989075*x^4 + 2154000*x^5) + Sqrt[3 + 5*x]*(1672353584 + 2536181692*x - 2970523996*x^2 - 4378603845*x^3 - 314625300*x^4 + 37620000*x^5) + Sqrt[3]*(-1672353584 - 3949330512*x + 1495335636*x^2 + 7269548450*x^3 + 2507900325*x^4 - 58300875*x^5 - 14040000*x^6 + Sqrt[1 - 2*x]*(1672353584 + 5563395200*x + 4435105092*x^2 - 874581510*x^3 - 927969075*x^4 - 55044000*x^5)))/(36*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 36*(2 + 3*x)^2*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(36*(2 + 3*x)^2*(3481060 + 2827000*x - 391875*x^2) + 36*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (236*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/27 + (1085*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/108 - (5425*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/216","C",1
2395,1,597,149,2.6513754,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^4,x]","\frac{32765}{648} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{163825 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{1296}+\frac{\sqrt{5 x+3} \left(-2928028950 x^5-86277254415 x^4-122112031734 x^3+7929230452 x^2+76210179848 x+27324556864\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(1487022375 x^5+21885669675 x^4-19448209130 x^3-113506724316 x^2-102249146184 x-27324556864\right)+\sqrt{3} \left(-1665029250 x^6+43881735600 x^5+172966427010 x^4+135583153624 x^3-61033659192 x^2+\sqrt{1-2 x} \left(-13917222000 x^5-21553948350 x^4+84646475760 x^3+188740833336 x^2+125450151904 x+27324556864\right)-99411185568 x-27324556864\right)}{216 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right) (3 x+2)^3+\sqrt{1-2 x} \left(216 \left(-391875 x^2+2827000 x+3481060\right) (3 x+2)^3+216 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right) (3 x+2)^3\right)+216 \left(44875 x^3+2976525 x^2-279060 x-3667684\right) (3 x+2)^3}-\frac{16}{81} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{\sqrt{5 x+3} (1-2 x)^{5/2}}{9 (3 x+2)^3}+\frac{5 \sqrt{5 x+3} (1-2 x)^{3/2}}{12 (3 x+2)^2}+\frac{925 \sqrt{5 x+3} \sqrt{1-2 x}}{216 (3 x+2)}-\frac{8}{81} \sqrt{10} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{32765 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{648 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(27324556864 + 76210179848*x + 7929230452*x^2 - 122112031734*x^3 - 86277254415*x^4 - 2928028950*x^5) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-27324556864 - 102249146184*x - 113506724316*x^2 - 19448209130*x^3 + 21885669675*x^4 + 1487022375*x^5) + Sqrt[3]*(-27324556864 - 99411185568*x - 61033659192*x^2 + 135583153624*x^3 + 172966427010*x^4 + 43881735600*x^5 - 1665029250*x^6 + Sqrt[1 - 2*x]*(27324556864 + 125450151904*x + 188740833336*x^2 + 84646475760*x^3 - 21553948350*x^4 - 13917222000*x^5)))/(216*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 216*(2 + 3*x)^3*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(216*(2 + 3*x)^3*(3481060 + 2827000*x - 391875*x^2) + 216*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) - (16*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/81 + (32765*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/648 - (163825*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/1296","C",1
2396,1,599,151,2.6096801,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^5,x]","\frac{73205}{448} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{366025}{896} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-72610396254000 x^7-37679687039500 x^6+1909828900220340 x^5+3871832852566536 x^4+1828284637405336 x^3-1117362143975264 x^2-1210171427395744 x-282418683153024\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(2947124041875 x^7-169283240677000 x^6-995963785762500 x^5-772463302671120 x^4+1536276531414520 x^3+2703353821450176 x^2+1488664538907424 x+282418683153024\right)+\sqrt{3} \left(10215292483125 x^8+234982438526000 x^7-797319744485000 x^6-4443361113787920 x^5-5504163872860616 x^4-1239589025852416 x^3+2025352574043584 x^2+\sqrt{1-2 x} \left(17284177597500 x^7+717205972070500 x^6+1733802763050600 x^5+76415039937720 x^4-3348878604227200 x^3-3844334806944896 x^2-1724926404034944 x-282418683153024\right)+1446433292523264 x+282418683153024\right)}{1344 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^4+\sqrt{1-2 x} \left(1344 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^4+1344 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^4\right)+1344 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^4}","\frac{(5 x+3)^{3/2} (1-2 x)^{5/2}}{4 (3 x+2)^4}+\frac{55 (5 x+3)^{3/2} (1-2 x)^{3/2}}{24 (3 x+2)^3}+\frac{605 (5 x+3)^{3/2} \sqrt{1-2 x}}{32 (3 x+2)^2}-\frac{6655 \sqrt{5 x+3} \sqrt{1-2 x}}{448 (3 x+2)}-\frac{73205 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{448 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-282418683153024 - 1210171427395744*x - 1117362143975264*x^2 + 1828284637405336*x^3 + 3871832852566536*x^4 + 1909828900220340*x^5 - 37679687039500*x^6 - 72610396254000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(282418683153024 + 1488664538907424*x + 2703353821450176*x^2 + 1536276531414520*x^3 - 772463302671120*x^4 - 995963785762500*x^5 - 169283240677000*x^6 + 2947124041875*x^7) + Sqrt[3]*(282418683153024 + 1446433292523264*x + 2025352574043584*x^2 - 1239589025852416*x^3 - 5504163872860616*x^4 - 4443361113787920*x^5 - 797319744485000*x^6 + 234982438526000*x^7 + 10215292483125*x^8 + Sqrt[1 - 2*x]*(-282418683153024 - 1724926404034944*x - 3844334806944896*x^2 - 3348878604227200*x^3 + 76415039937720*x^4 + 1733802763050600*x^5 + 717205972070500*x^6 + 17284177597500*x^7)))/(1344*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 1344*(2 + 3*x)^4*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(1344*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 1344*(2 + 3*x)^4*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) + (73205*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/448 - (366025*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/896","C",1
2397,1,659,180,3.2062455,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^6,x]","\frac{3674891 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{6272}-\frac{18374455 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{12544}+\frac{\sqrt{5 x+3} \left(-1319428935249975000 x^9-63803821892975525625 x^8-135290763243975893950 x^7+316881801152554872960 x^6+1111149932631912846288 x^5+1013307271206111122560 x^4+114509859949723969280 x^3-339997406845872754880 x^2-198363796837976865920 x-34319390954977125888\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(241833496756078125 x^9+7173596440367109375 x^8-62762854877282956250 x^7-381692021544653331000 x^6-560315864090678419200 x^5-45580112382697020640 x^4+592975122352906462080 x^3+587660131168455157312 x^2+232541021074385134208 x+34319390954977125888\right)+\sqrt{3} \left(-183151005385134375 x^{10}+21632174522433046875 x^9+169266535766928837500 x^8+51343148901588117000 x^7-973302241786237846200 x^6-1865165087332279879088 x^5-1179190161384569352960 x^4+109759936323140157120 x^3+493311450229611418880 x^2+\sqrt{1-2 x} \left(-3334089994486453125 x^9+2768658345962437500 x^8+253907340939263880000 x^7+772639020672876489000 x^6+691896359186596700400 x^5-301836024182069583360 x^4-1011725206102086386240 x^3-769478155467950711552 x^2-261163474255616072448 x-34319390954977125888\right)+226986250019207804160 x+34319390954977125888\right)}{94080 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right) (3 x+2)^5+\sqrt{1-2 x} \left(94080 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right) (3 x+2)^5+94080 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right) (3 x+2)^5\right)+94080 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right) (3 x+2)^5}","\frac{3 (5 x+3)^{3/2} (1-2 x)^{7/2}}{35 (3 x+2)^5}+\frac{251 (5 x+3)^{3/2} (1-2 x)^{5/2}}{280 (3 x+2)^4}+\frac{2761 (5 x+3)^{3/2} (1-2 x)^{3/2}}{336 (3 x+2)^3}+\frac{30371 (5 x+3)^{3/2} \sqrt{1-2 x}}{448 (3 x+2)^2}-\frac{334081 \sqrt{5 x+3} \sqrt{1-2 x}}{6272 (3 x+2)}-\frac{3674891 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{6272 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-34319390954977125888 - 198363796837976865920*x - 339997406845872754880*x^2 + 114509859949723969280*x^3 + 1013307271206111122560*x^4 + 1111149932631912846288*x^5 + 316881801152554872960*x^6 - 135290763243975893950*x^7 - 63803821892975525625*x^8 - 1319428935249975000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(34319390954977125888 + 232541021074385134208*x + 587660131168455157312*x^2 + 592975122352906462080*x^3 - 45580112382697020640*x^4 - 560315864090678419200*x^5 - 381692021544653331000*x^6 - 62762854877282956250*x^7 + 7173596440367109375*x^8 + 241833496756078125*x^9) + Sqrt[3]*(34319390954977125888 + 226986250019207804160*x + 493311450229611418880*x^2 + 109759936323140157120*x^3 - 1179190161384569352960*x^4 - 1865165087332279879088*x^5 - 973302241786237846200*x^6 + 51343148901588117000*x^7 + 169266535766928837500*x^8 + 21632174522433046875*x^9 - 183151005385134375*x^10 + Sqrt[1 - 2*x]*(-34319390954977125888 - 261163474255616072448*x - 769478155467950711552*x^2 - 1011725206102086386240*x^3 - 301836024182069583360*x^4 + 691896359186596700400*x^5 + 772639020672876489000*x^6 + 253907340939263880000*x^7 + 2768658345962437500*x^8 - 3334089994486453125*x^9)))/(94080*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 94080*(2 + 3*x)^5*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(94080*(2 + 3*x)^5*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 94080*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (3674891*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/6272 - (18374455*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/12544","C",1
2398,1,719,209,3.8171591,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^7,x]","\frac{391280725 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{175616}-\frac{1956403625 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{351232}+\frac{\sqrt{5 x+3} \left(-14829948127209518325000 x^{11}+76825060296758910056250 x^{10}+2619867111186284863274250 x^9+7546406247115910123512200 x^8+1358816972374327190348800 x^7-20468200957685747738807808 x^6-31046252320074745853533632 x^5-15501978748176378199484160 x^4+2924017606416354479370240 x^3+6415784379990743955985920 x^2+2574653200666375770157568 x+353732579296382531807232\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(273747837153538265625 x^{11}-63668657544452932500000 x^{10}-601128866725667172243750 x^9+611313757163954815037000 x^8+9290347299196430029174400 x^7+19424554992344343907343040 x^6+13735569949090520291676160 x^5-4626907950476346774156800 x^4-14014886947360321996387584 x^3-9512969052037990364693504 x^2-2927949711031147220392448 x-353732579296382531807232\right)+\sqrt{3} \left(1603468622412091546875 x^{12}+55361641067922594262500 x^{11}-1025605659012394058831250 x^{10}-7194869979672643584471000 x^9-10896144532587592735405800 x^8+8952760257887308631804640 x^7+41300642284266950045847168 x^6+43775278108192738217298432 x^5+14653005467586684540264960 x^4-7478611173482054768970240 x^3-8438325585890743718684160 x^2-2869479258112652879996928 x+\sqrt{1-2 x} \left(6335837688630090093750 x^{11}+356494148365145134781250 x^{10}+875961797572443143430000 x^9-4815048344915892781401000 x^8-21331104229424673642261600 x^7-30419580543980181501435840 x^6-12750837049722931670184960 x^5+13744671512714741882680320 x^4+21027689388015827817467904 x^3+11829972924607924669254144 x^2+3222775768477424330231808 x+353732579296382531807232\right)-353732579296382531807232\right)}{526848 \sqrt{3} \sqrt{5 x+3} \left(-25265212500 x^5+1941218400000 x^4+5284290066000 x^3-24057375117600 x^2-13825440024000 x+16748592098304\right) (3 x+2)^6+\sqrt{1-2 x} \left(526848 \sqrt{3} \sqrt{5 x+3} \left(-2625187500 x^5-345183000000 x^4+1378186950000 x^3+13912170444000 x^2-2687092123200 x-16725373086720\right) (3 x+2)^6+526848 \left(236425406250 x^5+2220611593750 x^4-28520358020000 x^3-52011357156000 x^2+49788771586400 x+50183931760160\right) (3 x+2)^6\right)+526848 \left(23653109375 x^6-916525237500 x^5-21026153381250 x^4+17065853944000 x^3+123670456765200 x^2-301410173760 x-50253588794912\right) (3 x+2)^6}","-\frac{\sqrt{5 x+3} (1-2 x)^{5/2}}{18 (3 x+2)^6}+\frac{\sqrt{5 x+3} (1-2 x)^{3/2}}{12 (3 x+2)^5}+\frac{2770202075 \sqrt{5 x+3} \sqrt{1-2 x}}{14224896 (3 x+2)}+\frac{26486645 \sqrt{5 x+3} \sqrt{1-2 x}}{1016064 (3 x+2)^2}+\frac{151621 \sqrt{5 x+3} \sqrt{1-2 x}}{36288 (3 x+2)^3}+\frac{647 \sqrt{5 x+3} \sqrt{1-2 x}}{864 (3 x+2)^4}-\frac{391280725 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{175616 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(353732579296382531807232 + 2574653200666375770157568*x + 6415784379990743955985920*x^2 + 2924017606416354479370240*x^3 - 15501978748176378199484160*x^4 - 31046252320074745853533632*x^5 - 20468200957685747738807808*x^6 + 1358816972374327190348800*x^7 + 7546406247115910123512200*x^8 + 2619867111186284863274250*x^9 + 76825060296758910056250*x^10 - 14829948127209518325000*x^11) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-353732579296382531807232 - 2927949711031147220392448*x - 9512969052037990364693504*x^2 - 14014886947360321996387584*x^3 - 4626907950476346774156800*x^4 + 13735569949090520291676160*x^5 + 19424554992344343907343040*x^6 + 9290347299196430029174400*x^7 + 611313757163954815037000*x^8 - 601128866725667172243750*x^9 - 63668657544452932500000*x^10 + 273747837153538265625*x^11) + Sqrt[3]*(-353732579296382531807232 - 2869479258112652879996928*x - 8438325585890743718684160*x^2 - 7478611173482054768970240*x^3 + 14653005467586684540264960*x^4 + 43775278108192738217298432*x^5 + 41300642284266950045847168*x^6 + 8952760257887308631804640*x^7 - 10896144532587592735405800*x^8 - 7194869979672643584471000*x^9 - 1025605659012394058831250*x^10 + 55361641067922594262500*x^11 + 1603468622412091546875*x^12 + Sqrt[1 - 2*x]*(353732579296382531807232 + 3222775768477424330231808*x + 11829972924607924669254144*x^2 + 21027689388015827817467904*x^3 + 13744671512714741882680320*x^4 - 12750837049722931670184960*x^5 - 30419580543980181501435840*x^6 - 21331104229424673642261600*x^7 - 4815048344915892781401000*x^8 + 875961797572443143430000*x^9 + 356494148365145134781250*x^10 + 6335837688630090093750*x^11)))/(526848*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(16748592098304 - 13825440024000*x - 24057375117600*x^2 + 5284290066000*x^3 + 1941218400000*x^4 - 25265212500*x^5) + 526848*(2 + 3*x)^6*(-50253588794912 - 301410173760*x + 123670456765200*x^2 + 17065853944000*x^3 - 21026153381250*x^4 - 916525237500*x^5 + 23653109375*x^6) + Sqrt[1 - 2*x]*(526848*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(-16725373086720 - 2687092123200*x + 13912170444000*x^2 + 1378186950000*x^3 - 345183000000*x^4 - 2625187500*x^5) + 526848*(2 + 3*x)^6*(50183931760160 + 49788771586400*x - 52011357156000*x^2 - 28520358020000*x^3 + 2220611593750*x^4 + 236425406250*x^5))) + (391280725*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/175616 - (1956403625*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/351232","C",1
2399,1,1503,194,21.1364869,"\int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^(3/2),x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{32} \left(\frac{355329559167 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{16}}{4096000000 \sqrt{10} \left(\sqrt{3}-\sqrt{5 x+3}\right)^{32}}+\frac{\left(\frac{824318440833 \sqrt{1-2 x}}{8192000000}-\frac{528}{5} \sqrt{3} \sqrt{5 x+3}+\frac{1770907159167}{8192000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{15}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{31}}+\frac{\left(\frac{9752235186389 \sqrt{1-2 x}}{4096000000}-\frac{75376}{25} \sqrt{3} \sqrt{5 x+3}+\frac{27296576333611}{4096000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{29}}+\frac{\left(\frac{153262011213611 \sqrt{1-2 x}}{5120000000}-\frac{6350896}{125} \sqrt{3} \sqrt{5 x+3}+\frac{627136089266389}{5120000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{13}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{27}}+\frac{\left(\frac{4315421533719167 \sqrt{1-2 x}}{17920000000}-\frac{351730096}{625} \sqrt{3} \sqrt{5 x+3}+\frac{25938994403816833}{17920000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{25}}+\frac{\left(\frac{2481946917828537 \sqrt{1-2 x}}{2240000000}-\frac{13513219088 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{26576879409006663}{2240000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{11}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{23}}+\frac{\left(\frac{301497808048693 \sqrt{1-2 x}}{224000000}-\frac{371232478448 \sqrt{3} \sqrt{5 x+3}}{15625}+\frac{15664468625042891}{224000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{21}}+\frac{\left(-\frac{972800934681179 \sqrt{1-2 x}}{56000000}-\frac{10403154062464 \sqrt{3} \sqrt{5 x+3}}{109375}+\frac{16952045574625883}{56000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{19}}+\frac{\left(-\frac{2633191073019703 \sqrt{1-2 x}}{20000000}-\frac{4392770419456 \sqrt{3} \sqrt{5 x+3}}{15625}+\frac{19501429483730743}{20000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{17}}+\frac{\left(-\frac{619421190054201 \sqrt{1-2 x}}{1250000}-\frac{9681381737408 \sqrt{3} \sqrt{5 x+3}}{15625}+\frac{2942952807032121}{1250000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{15}}+\frac{\left(-\frac{747355535239909 \sqrt{1-2 x}}{625000}-\frac{15994271395264 \sqrt{3} \sqrt{5 x+3}}{15625}+\frac{2666668102671589}{625000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{13}}+\frac{\left(-\frac{430926403585161 \sqrt{1-2 x}}{218750}-\frac{19771018016256 \sqrt{3} \sqrt{5 x+3}}{15625}+\frac{1261309160267913}{218750}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{11}}+\frac{\left(-\frac{245751808872939 \sqrt{1-2 x}}{109375}-\frac{18062270583552 \sqrt{3} \sqrt{5 x+3}}{15625}+\frac{625059491127531}{109375}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}+\frac{\left(-\frac{191336566063032 \sqrt{1-2 x}}{109375}-\frac{11856931531776 \sqrt{3} \sqrt{5 x+3}}{15625}+\frac{440332128230328}{109375}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}+\frac{\left(-\frac{97165798952688 \sqrt{1-2 x}}{109375}-\frac{37063664004096 \sqrt{3} \sqrt{5 x+3}}{109375}+\frac{208356790964976}{109375}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{-\frac{552893095296 \sqrt{1-2 x}}{15625}-\frac{180048089088 \sqrt{3} \sqrt{5 x+3}}{15625}+\frac{218607472512}{3125}}{\sqrt{3}-\sqrt{5 x+3}}+\frac{\left(-\frac{1728 \sqrt{1-2 x}}{3125}-\frac{3456 \sqrt{3} \sqrt{5 x+3}}{15625}+\frac{19008}{15625}\right) \left(2399709615 \sqrt{1-2 x}+833555968 \sqrt{3} \sqrt{5 x+3}-4900377519\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{16}}","-\frac{3}{80} (3 x+2)^2 (5 x+3)^{5/2} (1-2 x)^{7/2}-\frac{735439 (5 x+3)^{3/2} (1-2 x)^{7/2}}{1280000}-\frac{9 (5 x+3)^{5/2} (13480 x+18399) (1-2 x)^{7/2}}{448000}-\frac{24269487 \sqrt{5 x+3} (1-2 x)^{7/2}}{20480000}+\frac{88988119 \sqrt{5 x+3} (1-2 x)^{5/2}}{204800000}+\frac{978869309 \sqrt{5 x+3} (1-2 x)^{3/2}}{819200000}+\frac{32302687197 \sqrt{5 x+3} \sqrt{1-2 x}}{8192000000}+\frac{355329559167 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{8192000000 \sqrt{10}}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^32*((218607472512/3125 - (552893095296*Sqrt[1 - 2*x])/15625 - (180048089088*Sqrt[3]*Sqrt[3 + 5*x])/15625)/(Sqrt[3] - Sqrt[3 + 5*x]) + ((208356790964976/109375 - (97165798952688*Sqrt[1 - 2*x])/109375 - (37063664004096*Sqrt[3]*Sqrt[3 + 5*x])/109375)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^5 + ((440332128230328/109375 - (191336566063032*Sqrt[1 - 2*x])/109375 - (11856931531776*Sqrt[3]*Sqrt[3 + 5*x])/15625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^7 + ((625059491127531/109375 - (245751808872939*Sqrt[1 - 2*x])/109375 - (18062270583552*Sqrt[3]*Sqrt[3 + 5*x])/15625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^9 + ((1261309160267913/218750 - (430926403585161*Sqrt[1 - 2*x])/218750 - (19771018016256*Sqrt[3]*Sqrt[3 + 5*x])/15625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^11 + ((2666668102671589/625000 - (747355535239909*Sqrt[1 - 2*x])/625000 - (15994271395264*Sqrt[3]*Sqrt[3 + 5*x])/15625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^13 + ((2942952807032121/1250000 - (619421190054201*Sqrt[1 - 2*x])/1250000 - (9681381737408*Sqrt[3]*Sqrt[3 + 5*x])/15625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^7)/(Sqrt[3] - Sqrt[3 + 5*x])^15 + ((19501429483730743/20000000 - (2633191073019703*Sqrt[1 - 2*x])/20000000 - (4392770419456*Sqrt[3]*Sqrt[3 + 5*x])/15625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^8)/(Sqrt[3] - Sqrt[3 + 5*x])^17 + ((16952045574625883/56000000 - (972800934681179*Sqrt[1 - 2*x])/56000000 - (10403154062464*Sqrt[3]*Sqrt[3 + 5*x])/109375)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^9)/(Sqrt[3] - Sqrt[3 + 5*x])^19 + ((15664468625042891/224000000 + (301497808048693*Sqrt[1 - 2*x])/224000000 - (371232478448*Sqrt[3]*Sqrt[3 + 5*x])/15625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^10)/(Sqrt[3] - Sqrt[3 + 5*x])^21 + ((26576879409006663/2240000000 + (2481946917828537*Sqrt[1 - 2*x])/2240000000 - (13513219088*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^11)/(Sqrt[3] - Sqrt[3 + 5*x])^23 + ((25938994403816833/17920000000 + (4315421533719167*Sqrt[1 - 2*x])/17920000000 - (351730096*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12)/(Sqrt[3] - Sqrt[3 + 5*x])^25 + ((627136089266389/5120000000 + (153262011213611*Sqrt[1 - 2*x])/5120000000 - (6350896*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^13)/(Sqrt[3] - Sqrt[3 + 5*x])^27 + ((27296576333611/4096000000 + (9752235186389*Sqrt[1 - 2*x])/4096000000 - (75376*Sqrt[3]*Sqrt[3 + 5*x])/25)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14)/(Sqrt[3] - Sqrt[3 + 5*x])^29 + ((1770907159167/8192000000 + (824318440833*Sqrt[1 - 2*x])/8192000000 - (528*Sqrt[3]*Sqrt[3 + 5*x])/5)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^15)/(Sqrt[3] - Sqrt[3 + 5*x])^31 + ((19008/15625 - (1728*Sqrt[1 - 2*x])/3125 - (3456*Sqrt[3]*Sqrt[3 + 5*x])/15625)*(-4900377519 + 2399709615*Sqrt[1 - 2*x] + 833555968*Sqrt[3]*Sqrt[3 + 5*x]))/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (355329559167*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^16*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(4096000000*Sqrt[10]*(Sqrt[3] - Sqrt[3 + 5*x])^32)))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^16","B",1
2400,1,1331,187,14.1542734,"\int (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2),x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{28} \left(\frac{1104970911 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}{25600000 \sqrt{10} \left(\sqrt{3}-\sqrt{5 x+3}\right)^{28}}+\frac{\left(\frac{2581429089 \sqrt{1-2 x}}{51200000}-\frac{48}{5} \sqrt{3} \sqrt{5 x+3}-\frac{1106869089}{51200000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{13}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{27}}+\frac{\left(\frac{31579843637 \sqrt{1-2 x}}{25600000}-\frac{8024}{25} \sqrt{3} \sqrt{5 x+3}-\frac{6930115637}{25600000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{25}}+\frac{\left(\frac{540231996363 \sqrt{1-2 x}}{32000000}-\frac{147088}{25} \sqrt{3} \sqrt{5 x+3}+\frac{24585923637}{32000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{11}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{23}}+\frac{\left(\frac{18051124298911 \sqrt{1-2 x}}{112000000}-\frac{42133256}{625} \sqrt{3} \sqrt{5 x+3}+\frac{4599714126689}{112000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{21}}+\frac{\left(\frac{15086775853721 \sqrt{1-2 x}}{14000000}-\frac{1606251328 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{6501241994599}{14000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{19}}+\frac{\left(\frac{7164544980373 \sqrt{1-2 x}}{1400000}-\frac{8409250304 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{4137487428203}{1400000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{17}}+\frac{\left(\frac{6085371495173 \sqrt{1-2 x}}{350000}-\frac{214767013504 \sqrt{3} \sqrt{5 x+3}}{21875}+\frac{4223445153019}{350000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{15}}+\frac{\left(\frac{5302358015401 \sqrt{1-2 x}}{125000}-\frac{78469393696 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{4113969228119}{125000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{13}}+\frac{\left(\frac{1161734295534 \sqrt{1-2 x}}{15625}-\frac{140706616448 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{948864951186}{15625}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{11}}+\frac{\left(\frac{1451136042412 \sqrt{1-2 x}}{15625}-\frac{175485854848 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{1181151780308}{15625}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}+\frac{\left(\frac{353222215984 \sqrt{1-2 x}}{4375}-\frac{148890000384 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{1360578928144}{21875}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}+\frac{\left(\frac{1015669171616 \sqrt{1-2 x}}{21875}-\frac{81915213312 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{704550307936}{21875}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{\frac{53427543552 \sqrt{1-2 x}}{21875}-\frac{26353944576 \sqrt{3} \sqrt{5 x+3}}{21875}+\frac{25634290176}{21875}}{\sqrt{3}-\sqrt{5 x+3}}+\frac{\left(-\frac{2304 \sqrt{1-2 x}}{4375}-\frac{4608 \sqrt{3} \sqrt{5 x+3}}{21875}+\frac{25344}{21875}\right) \left(-150728747 \sqrt{1-2 x}+80068408 \sqrt{3} \sqrt{5 x+3}-89476477\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}","-\frac{3}{70} (3 x+2) (5 x+3)^{5/2} (1-2 x)^{7/2}-\frac{263 (5 x+3)^{5/2} (1-2 x)^{7/2}}{2800}-\frac{2287 (5 x+3)^{3/2} (1-2 x)^{7/2}}{8000}-\frac{75471 \sqrt{5 x+3} (1-2 x)^{7/2}}{128000}+\frac{276727 \sqrt{5 x+3} (1-2 x)^{5/2}}{1280000}+\frac{3043997 \sqrt{5 x+3} (1-2 x)^{3/2}}{5120000}+\frac{100451901 \sqrt{5 x+3} \sqrt{1-2 x}}{51200000}+\frac{1104970911 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{51200000 \sqrt{10}}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^28*((25634290176/21875 + (53427543552*Sqrt[1 - 2*x])/21875 - (26353944576*Sqrt[3]*Sqrt[3 + 5*x])/21875)/(Sqrt[3] - Sqrt[3 + 5*x]) + ((704550307936/21875 + (1015669171616*Sqrt[1 - 2*x])/21875 - (81915213312*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^5 + ((1360578928144/21875 + (353222215984*Sqrt[1 - 2*x])/4375 - (148890000384*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^7 + ((1181151780308/15625 + (1451136042412*Sqrt[1 - 2*x])/15625 - (175485854848*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^9 + ((948864951186/15625 + (1161734295534*Sqrt[1 - 2*x])/15625 - (140706616448*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^11 + ((4113969228119/125000 + (5302358015401*Sqrt[1 - 2*x])/125000 - (78469393696*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^13 + ((4223445153019/350000 + (6085371495173*Sqrt[1 - 2*x])/350000 - (214767013504*Sqrt[3]*Sqrt[3 + 5*x])/21875)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^7)/(Sqrt[3] - Sqrt[3 + 5*x])^15 + ((4137487428203/1400000 + (7164544980373*Sqrt[1 - 2*x])/1400000 - (8409250304*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^8)/(Sqrt[3] - Sqrt[3 + 5*x])^17 + ((6501241994599/14000000 + (15086775853721*Sqrt[1 - 2*x])/14000000 - (1606251328*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^9)/(Sqrt[3] - Sqrt[3 + 5*x])^19 + ((4599714126689/112000000 + (18051124298911*Sqrt[1 - 2*x])/112000000 - (42133256*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^10)/(Sqrt[3] - Sqrt[3 + 5*x])^21 + ((24585923637/32000000 + (540231996363*Sqrt[1 - 2*x])/32000000 - (147088*Sqrt[3]*Sqrt[3 + 5*x])/25)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^11)/(Sqrt[3] - Sqrt[3 + 5*x])^23 + ((-6930115637/25600000 + (31579843637*Sqrt[1 - 2*x])/25600000 - (8024*Sqrt[3]*Sqrt[3 + 5*x])/25)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12)/(Sqrt[3] - Sqrt[3 + 5*x])^25 + ((-1106869089/51200000 + (2581429089*Sqrt[1 - 2*x])/51200000 - (48*Sqrt[3]*Sqrt[3 + 5*x])/5)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^13)/(Sqrt[3] - Sqrt[3 + 5*x])^27 + ((25344/21875 - (2304*Sqrt[1 - 2*x])/4375 - (4608*Sqrt[3]*Sqrt[3 + 5*x])/21875)*(-89476477 - 150728747*Sqrt[1 - 2*x] + 80068408*Sqrt[3]*Sqrt[3 + 5*x]))/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (1104970911*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(25600000*Sqrt[10]*(Sqrt[3] - Sqrt[3 + 5*x])^28)))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14","B",1
2401,1,486,160,2.9675437,"\int (1-2 x)^{5/2} (2+3 x) (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^(3/2),x]","\frac{30438639 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{1280000 \sqrt{10}}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-605519600000000000 x^{11}+23263224612000000000 x^{10}+546616110497550000000 x^9-282530392643287500000 x^8-3851835937289904562500 x^7-700453432266457265625 x^6+4753476947668002715000 x^5+893556258823310784750 x^4-2586530123228299902000 x^3-374971388532404773840 x^2+528961344614219852160 x+72048172129000597728\right)+\sqrt{5 x+3} \left(12104980800000000000 x^{11}+111637466864000000000 x^{10}-1493638034748200000000 x^9-2543274563355130000000 x^8+4738772805637653750000 x^7+4852797055158180562500 x^6-4950767607009082113750 x^5-3330071187615745240250 x^4+2531855105760405299600 x^3+945960821286428516800 x^2-456196617987199631520 x-72048172129000597728\right)+\sqrt{3} \left(-672048000000000000 x^{12}-88655828640000000000 x^{11}+315667667238000000000 x^{10}+3825202270266300000000 x^9+432472549248217500000 x^8-9281612313193254375000 x^7-2167013029021070878125 x^6+8186108181369765060000 x^5+1676622522384184074750 x^4-3463402849041182379600 x^3-589786000328106982800 x^2+516156395072564712960 x+\sqrt{1-2 x} \left(3233947200000000000 x^{11}-245468384304000000000 x^{10}-910056094840200000000 x^9+2646278497444890000000 x^8+5373655802192361750000 x^7-2487807704804542312500 x^6-6132022858693698161250 x^5+987012626992443009750 x^4+3066611719756750849200 x^3-41760338259631527360 x^2-588921121699584933600 x-72048172129000597728\right)+72048172129000597728\right)}{2560000 \sqrt{3} \sqrt{5 x+3} \left(25265212500 x^5-1941218400000 x^4-5284290066000 x^3+24057375117600 x^2+13825440024000 x-16748592098304\right)+\sqrt{1-2 x} \left(2560000 \left(-236425406250 x^5-2220611593750 x^4+28520358020000 x^3+52011357156000 x^2-49788771586400 x-50183931760160\right)+2560000 \sqrt{3} \sqrt{5 x+3} \left(2625187500 x^5+345183000000 x^4-1378186950000 x^3-13912170444000 x^2+2687092123200 x+16725373086720\right)\right)+2560000 \left(-23653109375 x^6+916525237500 x^5+21026153381250 x^4-17065853944000 x^3-123670456765200 x^2+301410173760 x+50253588794912\right)}","-\frac{1}{20} (5 x+3)^{5/2} (1-2 x)^{7/2}-\frac{63}{400} (5 x+3)^{3/2} (1-2 x)^{7/2}-\frac{2079 \sqrt{5 x+3} (1-2 x)^{7/2}}{6400}+\frac{7623 \sqrt{5 x+3} (1-2 x)^{5/2}}{64000}+\frac{83853 \sqrt{5 x+3} (1-2 x)^{3/2}}{256000}+\frac{2767149 \sqrt{5 x+3} \sqrt{1-2 x}}{2560000}+\frac{30438639 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{2560000 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(72048172129000597728 + 528961344614219852160*x - 374971388532404773840*x^2 - 2586530123228299902000*x^3 + 893556258823310784750*x^4 + 4753476947668002715000*x^5 - 700453432266457265625*x^6 - 3851835937289904562500*x^7 - 282530392643287500000*x^8 + 546616110497550000000*x^9 + 23263224612000000000*x^10 - 605519600000000000*x^11) + Sqrt[3 + 5*x]*(-72048172129000597728 - 456196617987199631520*x + 945960821286428516800*x^2 + 2531855105760405299600*x^3 - 3330071187615745240250*x^4 - 4950767607009082113750*x^5 + 4852797055158180562500*x^6 + 4738772805637653750000*x^7 - 2543274563355130000000*x^8 - 1493638034748200000000*x^9 + 111637466864000000000*x^10 + 12104980800000000000*x^11) + Sqrt[3]*(72048172129000597728 + 516156395072564712960*x - 589786000328106982800*x^2 - 3463402849041182379600*x^3 + 1676622522384184074750*x^4 + 8186108181369765060000*x^5 - 2167013029021070878125*x^6 - 9281612313193254375000*x^7 + 432472549248217500000*x^8 + 3825202270266300000000*x^9 + 315667667238000000000*x^10 - 88655828640000000000*x^11 - 672048000000000000*x^12 + Sqrt[1 - 2*x]*(-72048172129000597728 - 588921121699584933600*x - 41760338259631527360*x^2 + 3066611719756750849200*x^3 + 987012626992443009750*x^4 - 6132022858693698161250*x^5 - 2487807704804542312500*x^6 + 5373655802192361750000*x^7 + 2646278497444890000000*x^8 - 910056094840200000000*x^9 - 245468384304000000000*x^10 + 3233947200000000000*x^11)))/(2560000*Sqrt[3]*Sqrt[3 + 5*x]*(-16748592098304 + 13825440024000*x + 24057375117600*x^2 - 5284290066000*x^3 - 1941218400000*x^4 + 25265212500*x^5) + 2560000*(50253588794912 + 301410173760*x - 123670456765200*x^2 - 17065853944000*x^3 + 21026153381250*x^4 + 916525237500*x^5 - 23653109375*x^6) + Sqrt[1 - 2*x]*(2560000*(-50183931760160 - 49788771586400*x + 52011357156000*x^2 + 28520358020000*x^3 - 2220611593750*x^4 - 236425406250*x^5) + 2560000*Sqrt[3]*Sqrt[3 + 5*x]*(16725373086720 + 2687092123200*x - 13912170444000*x^2 - 1378186950000*x^3 + 345183000000*x^4 + 2625187500*x^5))) + (30438639*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(1280000*Sqrt[10])","B",1
2402,1,426,138,2.5097433,"\int (1-2 x)^{5/2} (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(56640800000000 x^9+6277071610000000 x^8-14607637404500000 x^7-104602283832687500 x^6+63280688547265625 x^5+121744256425476625 x^4-76168133552245300 x^3-51720873529263540 x^2+25245900482505920 x+12314259202967568\right)+\sqrt{5 x+3} \left(701272000000000 x^9-27110106100000000 x^8-45018657145000000 x^7+185907484296875000 x^6+14322837036406250 x^5-205182944461763125 x^4+43918839546593000 x^3+83694073813720700 x^2-12823794291754160 x-12314259202967568\right)+\sqrt{3} \left(-211280000000000 x^{10}+4416911000000000 x^9+82236363350000000 x^8-63719063076250000 x^7-251230668065937500 x^6+142337013621221875 x^5+200915092785135625 x^4-115668738273995500 x^3-77070635600702500 x^2+\sqrt{1-2 x} \left(-1622808000000000 x^9-12366482700000000 x^8+88946247159000000 x^7+93794893058625000 x^6-169167808221568750 x^5-82254808680598125 x^4+125400329446073000 x^3+34763098047910540 x^2-35490365261020560 x-12314259202967568\right)+23068259070268800 x+12314259202967568\right)}{64000 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right)+\sqrt{1-2 x} \left(64000 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right)+64000 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right)\right)+64000 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right)}+\frac{483153 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{32000 \sqrt{10}}","-\frac{1}{10} (5 x+3)^{3/2} (1-2 x)^{7/2}-\frac{33}{160} \sqrt{5 x+3} (1-2 x)^{7/2}+\frac{121 \sqrt{5 x+3} (1-2 x)^{5/2}}{1600}+\frac{1331 \sqrt{5 x+3} (1-2 x)^{3/2}}{6400}+\frac{43923 \sqrt{5 x+3} \sqrt{1-2 x}}{64000}+\frac{483153 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{64000 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(12314259202967568 + 25245900482505920*x - 51720873529263540*x^2 - 76168133552245300*x^3 + 121744256425476625*x^4 + 63280688547265625*x^5 - 104602283832687500*x^6 - 14607637404500000*x^7 + 6277071610000000*x^8 + 56640800000000*x^9) + Sqrt[3 + 5*x]*(-12314259202967568 - 12823794291754160*x + 83694073813720700*x^2 + 43918839546593000*x^3 - 205182944461763125*x^4 + 14322837036406250*x^5 + 185907484296875000*x^6 - 45018657145000000*x^7 - 27110106100000000*x^8 + 701272000000000*x^9) + Sqrt[3]*(12314259202967568 + 23068259070268800*x - 77070635600702500*x^2 - 115668738273995500*x^3 + 200915092785135625*x^4 + 142337013621221875*x^5 - 251230668065937500*x^6 - 63719063076250000*x^7 + 82236363350000000*x^8 + 4416911000000000*x^9 - 211280000000000*x^10 + Sqrt[1 - 2*x]*(-12314259202967568 - 35490365261020560*x + 34763098047910540*x^2 + 125400329446073000*x^3 - 82254808680598125*x^4 - 169167808221568750*x^5 + 93794893058625000*x^6 + 88946247159000000*x^7 - 12366482700000000*x^8 - 1622808000000000*x^9)))/(64000*Sqrt[3]*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 64000*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(64000*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 64000*Sqrt[3]*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (483153*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(32000*Sqrt[10])","B",1
2403,1,558,150,2.6104129,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x),x]","-\frac{343}{243} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-3693870000000 x^7+39638755500000 x^6+491045669062500 x^5-757064245699375 x^4-60081153887000 x^3+602411157078200 x^2-208363359508960 x-102204599589752\right)+\sqrt{5 x+3} \left(41888880000000 x^7+176962236000000 x^6-1124355358500000 x^5+884818453145000 x^4+518780798222500 x^3-869177866575700 x^2+103189107012200 x+102204599589752\right)+\sqrt{3} \left(-2570400000000 x^8-226373160000000 x^7+456982071000000 x^6+994242107450000 x^5-1722596388944375 x^4+249945917399000 x^3+810818701952600 x^2+\sqrt{1-2 x} \left(19269360000000 x^7-367598220000000 x^6-198639160500000 x^5+1122299456575000 x^4-516038827386500 x^3-457097428395300 x^2+292843212812920 x+102204599589752\right)-187668960316160 x-102204599589752\right)}{259200 \sqrt{3} \sqrt{5 x+3} \left(8921000 x^3-162998000 x^2-220512160 x+287530496\right)+\sqrt{1-2 x} \left(259200 \left(-48482500 x^3-297203500 x^2+794989800 x+852279560\right)+259200 \sqrt{3} \sqrt{5 x+3} \left(595000 x^3+53178000 x^2-36412000 x-283051520\right)\right)+259200 \left(-8550625 x^4+79738000 x^3+1253327000 x^2-32289760 x-865716488\right)}+\frac{1922677 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{388800 \sqrt{10}}","\frac{1}{12} (5 x+3)^{3/2} (1-2 x)^{5/2}+\frac{181 (5 x+3)^{3/2} (1-2 x)^{3/2}}{1080}+\frac{7093 (5 x+3)^{3/2} \sqrt{1-2 x}}{21600}-\frac{390869 \sqrt{5 x+3} \sqrt{1-2 x}}{259200}+\frac{1922677 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{777600 \sqrt{10}}-\frac{98}{243} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-102204599589752 - 208363359508960*x + 602411157078200*x^2 - 60081153887000*x^3 - 757064245699375*x^4 + 491045669062500*x^5 + 39638755500000*x^6 - 3693870000000*x^7) + Sqrt[3 + 5*x]*(102204599589752 + 103189107012200*x - 869177866575700*x^2 + 518780798222500*x^3 + 884818453145000*x^4 - 1124355358500000*x^5 + 176962236000000*x^6 + 41888880000000*x^7) + Sqrt[3]*(-102204599589752 - 187668960316160*x + 810818701952600*x^2 + 249945917399000*x^3 - 1722596388944375*x^4 + 994242107450000*x^5 + 456982071000000*x^6 - 226373160000000*x^7 - 2570400000000*x^8 + Sqrt[1 - 2*x]*(102204599589752 + 292843212812920*x - 457097428395300*x^2 - 516038827386500*x^3 + 1122299456575000*x^4 - 198639160500000*x^5 - 367598220000000*x^6 + 19269360000000*x^7)))/(259200*Sqrt[3]*Sqrt[3 + 5*x]*(287530496 - 220512160*x - 162998000*x^2 + 8921000*x^3) + 259200*(-865716488 - 32289760*x + 1253327000*x^2 + 79738000*x^3 - 8550625*x^4) + Sqrt[1 - 2*x]*(259200*(852279560 + 794989800*x - 297203500*x^2 - 48482500*x^3) + 259200*Sqrt[3]*Sqrt[3 + 5*x]*(-283051520 - 36412000*x + 53178000*x^2 + 595000*x^3))) + (1922677*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(388800*Sqrt[10]) - (343*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ])/243","C",1
2404,1,649,157,3.0505931,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^2,x]","-\frac{5635}{243} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{28175}{486} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-698148000000 x^7-2598357300000 x^6+19413456645000 x^5-31790678397500 x^4+17463297542900 x^3+100581638462800 x^2-8704201098296 x-37243569420464\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(61564500000 x^7-691599187500 x^6-7780625131875 x^5+16203118354750 x^4-22831888799800 x^3-38463008387600 x^2+45693548319976 x+37243569420464\right)+\sqrt{3} \left(42840000000 x^8+3751347000000 x^7-9463668750000 x^6-7888032974375 x^5+44079318662750 x^4-93139220624600 x^3-106566931009520 x^2+\sqrt{1-2 x} \left(-321156000000 x^7+6288107100000 x^6-141685005000 x^5-13227117260500 x^4+59804122746500 x^3+13564720957920 x^2-76788980128696 x-37243569420464\right)+39799632907016 x+37243569420464\right)}{3240 \sqrt{3} (3 x+2) \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right)+\sqrt{1-2 x} \left(3240 \sqrt{3} (3 x+2) \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right)+3240 (3 x+2) \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right)\right)+3240 (3 x+2) \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right)}+\frac{326717 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{4860 \sqrt{10}}","-\frac{(5 x+3)^{3/2} (1-2 x)^{5/2}}{3 (3 x+2)}-\frac{8}{27} (5 x+3)^{3/2} (1-2 x)^{3/2}-\frac{247}{270} (5 x+3)^{3/2} \sqrt{1-2 x}+\frac{24251 \sqrt{5 x+3} \sqrt{1-2 x}}{3240}+\frac{326717 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{9720 \sqrt{10}}+\frac{805}{243} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[3 + 5*x]*(-37243569420464 - 8704201098296*x + 100581638462800*x^2 + 17463297542900*x^3 - 31790678397500*x^4 + 19413456645000*x^5 - 2598357300000*x^6 - 698148000000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(37243569420464 + 45693548319976*x - 38463008387600*x^2 - 22831888799800*x^3 + 16203118354750*x^4 - 7780625131875*x^5 - 691599187500*x^6 + 61564500000*x^7) + Sqrt[3]*(37243569420464 + 39799632907016*x - 106566931009520*x^2 - 93139220624600*x^3 + 44079318662750*x^4 - 7888032974375*x^5 - 9463668750000*x^6 + 3751347000000*x^7 + 42840000000*x^8 + Sqrt[1 - 2*x]*(-37243569420464 - 76788980128696*x + 13564720957920*x^2 + 59804122746500*x^3 - 13227117260500*x^4 - 141685005000*x^5 + 6288107100000*x^6 - 321156000000*x^7)))/(3240*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 3240*(2 + 3*x)*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(3240*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 3240*(2 + 3*x)*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) + (326717*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(4860*Sqrt[10]) - (5635*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/243 + (28175*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/486","C",1
2405,1,657,164,3.4245482,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^3,x]","\frac{13615}{324} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{68075}{648} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-34907400000 x^7-77265870000 x^6+1785471435000 x^5-1601501828300 x^4-11855123017540 x^3-6048499117496 x^2+4613398937752 x+2791810066144\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(3078225000 x^7-39222948750 x^6-376260744375 x^5+2409157686100 x^4+5133991579880 x^3-2520733106480 x^2-7382576738168 x-2791810066144\right)+\sqrt{3} \left(2142000000 x^8+184336500000 x^7-819376359375 x^6-2312113005500 x^5+8845199381300 x^4+17666240253520 x^3+3197526067336 x^2+\sqrt{1-2 x} \left(-16057800000 x^7+338625870000 x^6-419326924500 x^5-6225778091500 x^4-4781854289080 x^3+7684617865320 x^2+9714348668288 x+2791810066144\right)-6945170867872 x-2791810066144\right)}{108 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^2+\sqrt{1-2 x} \left(108 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^2+108 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^2\right)+108 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^2}-\frac{6829 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{81 \sqrt{10}}","-\frac{(5 x+3)^{3/2} (1-2 x)^{5/2}}{6 (3 x+2)^2}+\frac{115 (5 x+3)^{3/2} (1-2 x)^{3/2}}{36 (3 x+2)}+\frac{41}{18} (5 x+3)^{3/2} \sqrt{1-2 x}-\frac{1649}{108} \sqrt{5 x+3} \sqrt{1-2 x}-\frac{6829 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{162 \sqrt{10}}-\frac{1945}{324} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[3 + 5*x]*(2791810066144 + 4613398937752*x - 6048499117496*x^2 - 11855123017540*x^3 - 1601501828300*x^4 + 1785471435000*x^5 - 77265870000*x^6 - 34907400000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-2791810066144 - 7382576738168*x - 2520733106480*x^2 + 5133991579880*x^3 + 2409157686100*x^4 - 376260744375*x^5 - 39222948750*x^6 + 3078225000*x^7) + Sqrt[3]*(-2791810066144 - 6945170867872*x + 3197526067336*x^2 + 17666240253520*x^3 + 8845199381300*x^4 - 2312113005500*x^5 - 819376359375*x^6 + 184336500000*x^7 + 2142000000*x^8 + Sqrt[1 - 2*x]*(2791810066144 + 9714348668288*x + 7684617865320*x^2 - 4781854289080*x^3 - 6225778091500*x^4 - 419326924500*x^5 + 338625870000*x^6 - 16057800000*x^7)))/(108*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 108*(2 + 3*x)^2*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(108*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 108*(2 + 3*x)^2*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) - (6829*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(81*Sqrt[10]) + (13615*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/324 - (68075*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/648","C",1
2406,1,657,171,3.6313192,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^4,x]","-\frac{215 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{1944}+\frac{1075 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{3888}+\frac{\sqrt{5 x+3} \left(-418888800000 x^7-6618978993000 x^6+1035443095500 x^5+103732095138980 x^4+128720270226592 x^3-1147508459416 x^2-54689465529424 x-17670031278592\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(36938700000 x^7-112906306875 x^6-13514936655750 x^5-53082016307800 x^4-11673796895120 x^3+80466890139368 x^2+72200251295312 x+17670031278592\right)+\sqrt{3} \left(25704000000 x^8+2801545485000 x^7+14968645917000 x^6-53197447489000 x^5-200186021987840 x^4-141767697915712 x^3+40473372345536 x^2+\sqrt{1-2 x} \left(-192693600000 x^7+3559387755000 x^6+46035406329000 x^5+74676338572000 x^4-35240416133120 x^3-134422110913728 x^2-86962312777472 x-17670031278592\right)+69451527011584 x+17670031278592\right)}{648 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^3+\sqrt{1-2 x} \left(648 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^3+648 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^3\right)+648 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^3}+\frac{724}{243} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{(5 x+3)^{3/2} (1-2 x)^{5/2}}{9 (3 x+2)^3}+\frac{115 (5 x+3)^{3/2} (1-2 x)^{3/2}}{108 (3 x+2)^2}+\frac{365 (5 x+3)^{3/2} \sqrt{1-2 x}}{216 (3 x+2)}-\frac{845}{648} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{362}{243} \sqrt{10} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)+\frac{215 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1944 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-17670031278592 - 54689465529424*x - 1147508459416*x^2 + 128720270226592*x^3 + 103732095138980*x^4 + 1035443095500*x^5 - 6618978993000*x^6 - 418888800000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(17670031278592 + 72200251295312*x + 80466890139368*x^2 - 11673796895120*x^3 - 53082016307800*x^4 - 13514936655750*x^5 - 112906306875*x^6 + 36938700000*x^7) + Sqrt[3]*(17670031278592 + 69451527011584*x + 40473372345536*x^2 - 141767697915712*x^3 - 200186021987840*x^4 - 53197447489000*x^5 + 14968645917000*x^6 + 2801545485000*x^7 + 25704000000*x^8 + Sqrt[1 - 2*x]*(-17670031278592 - 86962312777472*x - 134422110913728*x^2 - 35240416133120*x^3 + 74676338572000*x^4 + 46035406329000*x^5 + 3559387755000*x^6 - 192693600000*x^7)))/(648*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 648*(2 + 3*x)^3*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(648*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 648*(2 + 3*x)^3*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) + (724*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/243 - (215*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/1944 + (1075*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/3888","C",1
2407,1,657,178,3.2977046,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^5,x]","\frac{3244595 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{108864}-\frac{16222975 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{217728}+\frac{\sqrt{5 x+3} \left(-265346789994000 x^7+56402922295500 x^6+7346074129177740 x^5+15149894119986296 x^4+7530189400357096 x^3-4405120511238304 x^2-4952948456620384 x-1161255797832064\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(9189126748125 x^7-670895270427000 x^6-3646133561077500 x^5-2870599731076720 x^4+6046167847774600 x^3+10897579339835456 x^2+6097699389135584 x+1161255797832064\right)+\sqrt{3} \left(39965370001875 x^8+782353612986000 x^7-3305082979755000 x^6-17169558287803120 x^5-21804626625933176 x^4-5262322581822976 x^3+8119491495285824 x^2+\sqrt{1-2 x} \left(86348466022500 x^7+2690219591845500 x^6+6387313575264600 x^5+159308169830920 x^4-13322819572599680 x^3-15569747938478976 x^2-7069251058162304 x-1161255797832064\right)+5924500125647104 x+1161255797832064\right)}{36288 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^4+\sqrt{1-2 x} \left(36288 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^4+36288 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^4\right)+36288 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^4}-\frac{80}{243} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{(5 x+3)^{3/2} (1-2 x)^{5/2}}{12 (3 x+2)^4}+\frac{115 (5 x+3)^{3/2} (1-2 x)^{3/2}}{216 (3 x+2)^3}+\frac{2675 (5 x+3)^{3/2} \sqrt{1-2 x}}{864 (3 x+2)^2}-\frac{97235 \sqrt{5 x+3} \sqrt{1-2 x}}{36288 (3 x+2)}-\frac{40}{243} \sqrt{10} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{3244595 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{108864 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-1161255797832064 - 4952948456620384*x - 4405120511238304*x^2 + 7530189400357096*x^3 + 15149894119986296*x^4 + 7346074129177740*x^5 + 56402922295500*x^6 - 265346789994000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1161255797832064 + 6097699389135584*x + 10897579339835456*x^2 + 6046167847774600*x^3 - 2870599731076720*x^4 - 3646133561077500*x^5 - 670895270427000*x^6 + 9189126748125*x^7) + Sqrt[3]*(1161255797832064 + 5924500125647104*x + 8119491495285824*x^2 - 5262322581822976*x^3 - 21804626625933176*x^4 - 17169558287803120*x^5 - 3305082979755000*x^6 + 782353612986000*x^7 + 39965370001875*x^8 + Sqrt[1 - 2*x]*(-1161255797832064 - 7069251058162304*x - 15569747938478976*x^2 - 13322819572599680*x^3 + 159308169830920*x^4 + 6387313575264600*x^5 + 2690219591845500*x^6 + 86348466022500*x^7)))/(36288*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 36288*(2 + 3*x)^4*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(36288*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 36288*(2 + 3*x)^4*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) - (80*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/243 + (3244595*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/108864 - (16222975*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/217728","C",1
2408,1,659,180,3.191275,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^6,x]","\frac{483153 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{6272}-\frac{2415765 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{12544}+\frac{\sqrt{5 x+3} \left(-57578419552225000 x^9-2800358664568375625 x^8-5938363733688225950 x^7+13904734947059186560 x^6+48648113919589244368 x^5+44362374975545292160 x^4+5042103088577294080 x^3-14885306033406015680 x^2-8692178879931733120 x-1502481552349459968\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(10602290853578125 x^9+315722668255859375 x^8-2750674401663456250 x^7-16737328261060291000 x^6-24532202511279891200 x^5-2000176427644803040 x^4+25944990332513169280 x^3+25736110116475616832 x^2+10188473533152873088 x+1502481552349459968\right)+\sqrt{3} \left(-8074081497259375 x^{10}+948180896204921875 x^9+7432653130911587500 x^8+2244237937677337000 x^7-42650583998355038200 x^6-81651256093782325168 x^5-51646215316111586560 x^4+4773691276625456320 x^3+21603966619686119680 x^2+\sqrt{1-2 x} \left(-146393316022078125 x^9+117713482596187500 x^8+11137007395782180000 x^7+33857303233687329000 x^6+30291360462290844400 x^5-13196428724259432960 x^4-44281946676933247040 x^3-33702682132523337472 x^2-11441540712194089728 x-1502481552349459968\right)+9945246058972949760 x+1502481552349459968\right)}{31360 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right) (3 x+2)^5+\sqrt{1-2 x} \left(31360 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right) (3 x+2)^5+31360 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right) (3 x+2)^5\right)+31360 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right) (3 x+2)^5}","\frac{121 \sqrt{1-2 x} (5 x+3)^{5/2}}{16 (3 x+2)^3}+\frac{11 (1-2 x)^{3/2} (5 x+3)^{5/2}}{8 (3 x+2)^4}+\frac{(1-2 x)^{5/2} (5 x+3)^{5/2}}{5 (3 x+2)^5}-\frac{1331 \sqrt{1-2 x} (5 x+3)^{3/2}}{448 (3 x+2)^2}-\frac{43923 \sqrt{1-2 x} \sqrt{5 x+3}}{6272 (3 x+2)}-\frac{483153 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{6272 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-1502481552349459968 - 8692178879931733120*x - 14885306033406015680*x^2 + 5042103088577294080*x^3 + 44362374975545292160*x^4 + 48648113919589244368*x^5 + 13904734947059186560*x^6 - 5938363733688225950*x^7 - 2800358664568375625*x^8 - 57578419552225000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1502481552349459968 + 10188473533152873088*x + 25736110116475616832*x^2 + 25944990332513169280*x^3 - 2000176427644803040*x^4 - 24532202511279891200*x^5 - 16737328261060291000*x^6 - 2750674401663456250*x^7 + 315722668255859375*x^8 + 10602290853578125*x^9) + Sqrt[3]*(1502481552349459968 + 9945246058972949760*x + 21603966619686119680*x^2 + 4773691276625456320*x^3 - 51646215316111586560*x^4 - 81651256093782325168*x^5 - 42650583998355038200*x^6 + 2244237937677337000*x^7 + 7432653130911587500*x^8 + 948180896204921875*x^9 - 8074081497259375*x^10 + Sqrt[1 - 2*x]*(-1502481552349459968 - 11441540712194089728*x - 33702682132523337472*x^2 - 44281946676933247040*x^3 - 13196428724259432960*x^4 + 30291360462290844400*x^5 + 33857303233687329000*x^6 + 11137007395782180000*x^7 + 117713482596187500*x^8 - 146393316022078125*x^9)))/(31360*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 31360*(2 + 3*x)^5*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(31360*(2 + 3*x)^5*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 31360*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (483153*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/6272 - (2415765*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/12544","C",1
2409,1,719,209,4.0385014,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^7,x]","\frac{41068005 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{175616}-\frac{205340025 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{351232}+\frac{\sqrt{5 x+3} \left(-518848441786506975000 x^{11}+2686277443551397918750 x^{10}+91652525054455166452750 x^9+264029161288429343648600 x^8+47574649133155148646400 x^7-716047675890522187221504 x^6-1086053545966830851294016 x^5-542296964152805025936640 x^4+102249369339124860047360 x^3+224436364146092185162240 x^2+90073808517585996629504 x+12373756325051942025216\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(9580291975494171875 x^{11}-2227320478507605500000 x^{10}-21032363584987016981250 x^9+21372972549806589871000 x^8+325007582588675277539200 x^7+679561529114161428409920 x^6+480517213091331662632960 x^5-161832447729910774786560 x^4-490240315403564258596608 x^3-332788786264949856070656 x^2-102432326256231432846848 x-12373756325051942025216\right)+\sqrt{3} \left(56095130288969015625 x^{12}+1937246689429472287500 x^{11}-35876458669258975743750 x^{10}-251714642644550189373000 x^9-381247643558761610225400 x^8+313165075799758660348320 x^7+1444808504667384092045184 x^6+1531335347908449190473216 x^5+512627697384755248227840 x^4-261574898326121457077760 x^3-295195173348118035816960 x^2-100386981230670948317184 x+\sqrt{1-2 x} \left(221607278027884031250 x^{11}+12472083298218673593750 x^{10}+30654030540709861890000 x^9-168427557992032053363000 x^8-746253449114029090528800 x^7-1064204173727762263014720 x^6-446081720998093886069760 x^5+480766468950816946867200 x^4+735564686432794527141888 x^3+413848069358055236906496 x^2+112745498969316384534528 x+12373756325051942025216\right)-12373756325051942025216\right)}{175616 \sqrt{3} \sqrt{5 x+3} \left(-25265212500 x^5+1941218400000 x^4+5284290066000 x^3-24057375117600 x^2-13825440024000 x+16748592098304\right) (3 x+2)^6+\sqrt{1-2 x} \left(175616 \sqrt{3} \sqrt{5 x+3} \left(-2625187500 x^5-345183000000 x^4+1378186950000 x^3+13912170444000 x^2-2687092123200 x-16725373086720\right) (3 x+2)^6+175616 \left(236425406250 x^5+2220611593750 x^4-28520358020000 x^3-52011357156000 x^2+49788771586400 x+50183931760160\right) (3 x+2)^6\right)+175616 \left(23653109375 x^6-916525237500 x^5-21026153381250 x^4+17065853944000 x^3+123670456765200 x^2-301410173760 x-50253588794912\right) (3 x+2)^6}","\frac{(5 x+3)^{5/2} (1-2 x)^{7/2}}{14 (3 x+2)^6}+\frac{17 (5 x+3)^{5/2} (1-2 x)^{5/2}}{28 (3 x+2)^5}+\frac{935 (5 x+3)^{5/2} (1-2 x)^{3/2}}{224 (3 x+2)^4}+\frac{10285 (5 x+3)^{5/2} \sqrt{1-2 x}}{448 (3 x+2)^3}-\frac{113135 (5 x+3)^{3/2} \sqrt{1-2 x}}{12544 (3 x+2)^2}-\frac{3733455 \sqrt{5 x+3} \sqrt{1-2 x}}{175616 (3 x+2)}-\frac{41068005 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{175616 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(12373756325051942025216 + 90073808517585996629504*x + 224436364146092185162240*x^2 + 102249369339124860047360*x^3 - 542296964152805025936640*x^4 - 1086053545966830851294016*x^5 - 716047675890522187221504*x^6 + 47574649133155148646400*x^7 + 264029161288429343648600*x^8 + 91652525054455166452750*x^9 + 2686277443551397918750*x^10 - 518848441786506975000*x^11) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-12373756325051942025216 - 102432326256231432846848*x - 332788786264949856070656*x^2 - 490240315403564258596608*x^3 - 161832447729910774786560*x^4 + 480517213091331662632960*x^5 + 679561529114161428409920*x^6 + 325007582588675277539200*x^7 + 21372972549806589871000*x^8 - 21032363584987016981250*x^9 - 2227320478507605500000*x^10 + 9580291975494171875*x^11) + Sqrt[3]*(-12373756325051942025216 - 100386981230670948317184*x - 295195173348118035816960*x^2 - 261574898326121457077760*x^3 + 512627697384755248227840*x^4 + 1531335347908449190473216*x^5 + 1444808504667384092045184*x^6 + 313165075799758660348320*x^7 - 381247643558761610225400*x^8 - 251714642644550189373000*x^9 - 35876458669258975743750*x^10 + 1937246689429472287500*x^11 + 56095130288969015625*x^12 + Sqrt[1 - 2*x]*(12373756325051942025216 + 112745498969316384534528*x + 413848069358055236906496*x^2 + 735564686432794527141888*x^3 + 480766468950816946867200*x^4 - 446081720998093886069760*x^5 - 1064204173727762263014720*x^6 - 746253449114029090528800*x^7 - 168427557992032053363000*x^8 + 30654030540709861890000*x^9 + 12472083298218673593750*x^10 + 221607278027884031250*x^11)))/(175616*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(16748592098304 - 13825440024000*x - 24057375117600*x^2 + 5284290066000*x^3 + 1941218400000*x^4 - 25265212500*x^5) + 175616*(2 + 3*x)^6*(-50253588794912 - 301410173760*x + 123670456765200*x^2 + 17065853944000*x^3 - 21026153381250*x^4 - 916525237500*x^5 + 23653109375*x^6) + Sqrt[1 - 2*x]*(175616*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(-16725373086720 - 2687092123200*x + 13912170444000*x^2 + 1378186950000*x^3 - 345183000000*x^4 - 2625187500*x^5) + 175616*(2 + 3*x)^6*(50183931760160 + 49788771586400*x - 52011357156000*x^2 - 28520358020000*x^3 + 2220611593750*x^4 + 236425406250*x^5))) + (41068005*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/175616 - (205340025*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/351232","C",1
2410,1,779,238,4.7202969,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^8} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^8,x]","\frac{1891543995 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2458624}-\frac{9457719975 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{4917248}+\frac{\sqrt{5 x+3} \left(-2562169024586546846625000 x^{13}-160451576090217273141809375 x^{12}-186597412091415663627423750 x^{11}+5585169040588512106911575000 x^{10}+20855026685937503207044336000 x^9+22232749320280826850305896960 x^8-14281771701603391495539689088 x^7-54284424615457663880585925824 x^6-48383627918289610600897522048 x^5-12388051440435217015983261440 x^4+8738945766992100918869163520 x^3+7898608020711076110944601088 x^2+2421744114964503022456756224 x+275879689664025755707711488\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(239161198859567827265625 x^{13}+8691546164932464837859375 x^{12}-319756416262650734697343750 x^{11}-2486139603513791766944095000 x^{10}-3069768950354491415277500000 x^9+11261281910685536846036043200 x^8+38213982296846141296252294080 x^7+44611747703371659238428784960 x^6+15888675054541667727584259200 x^5-15307989531382731107633333504 x^4-20937084981340188912458290688 x^3-10731979473640879880164903936 x^2-2697522631947087885785266176 x-275879689664025755707711488\right)+\sqrt{3} \left(-93581876124690801796875 x^{14}+44001679435021451731609375 x^{13}+474425854586706394345075000 x^{12}-1650683224550518844919942500 x^{11}-16976727486341603508286165000 x^{10}-37973271169547237712036160400 x^9-19696480480887970171733819520 x^8+47064256583654776078354211008 x^7+89425864675835383650145252864 x^6+60088903168702184695051029248 x^5+7230235204191069410812285440 x^4-14560016541208769069413160960 x^3-9820903733784689825593387008 x^2-2651651736343903652213182464 x+\sqrt{1-2 x} \left(-4003329916906785194296875 x^{13}+44202146519134521893937500 x^{12}+1466296392390784873332837500 x^{11}+5209397242250869936991305000 x^{10}-613863315628731370424530000 x^9-32842341469562359879634529600 x^8-69007497771513145581497090880 x^7-59517980700581035434742293760 x^6-8012427718041669042910042880 x^5+29726834233942515391566124544 x^4+29023521199660568237585696768 x^3+12884098497526026814254114816 x^2+2927430253326488515541692416 x+275879689664025755707711488\right)-275879689664025755707711488\right)}{2458624 \sqrt{3} \sqrt{5 x+3} \left(-5663973218750 x^6-52303209612500 x^5+1428846604955000 x^4+2194696763160000 x^3-7555736895916000 x^2-3365532949972160 x+4051435671804928\right) (3 x+2)^7+\sqrt{1-2 x} \left(2458624 \left(-3042263984375 x^6+486365726000000 x^5+1796810007300000 x^4-11790948756840000 x^3-17392813876790000 x^2+12117692004316800 x+12149682333912640\right) (3 x+2)^7+2458624 \sqrt{3} \sqrt{5 x+3} \left(223405156250 x^6-14941831687500 x^5-390402719125000 x^4+702446326920000 x^3+4956682106340000 x^2-666120123963200 x-4049763902970880\right) (3 x+2)^7\right)+2458624 \left(905821796875 x^7+135547777203125 x^6-996207107350000 x^5-11461663884510000 x^4+5424159101550000 x^3+35265969543725200 x^2-26521579595840 x-12154697640414784\right) (3 x+2)^7}","-\frac{(5 x+3)^{3/2} (1-2 x)^{5/2}}{21 (3 x+2)^7}+\frac{115 (5 x+3)^{3/2} (1-2 x)^{3/2}}{756 (3 x+2)^6}+\frac{1921 (5 x+3)^{3/2} \sqrt{1-2 x}}{1512 (3 x+2)^5}+\frac{40175505215 \sqrt{5 x+3} \sqrt{1-2 x}}{597445632 (3 x+2)}+\frac{384136145 \sqrt{5 x+3} \sqrt{1-2 x}}{42674688 (3 x+2)^2}+\frac{2199649 \sqrt{5 x+3} \sqrt{1-2 x}}{1524096 (3 x+2)^3}-\frac{443563 \sqrt{5 x+3} \sqrt{1-2 x}}{254016 (3 x+2)^4}-\frac{1891543995 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2458624 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(275879689664025755707711488 + 2421744114964503022456756224*x + 7898608020711076110944601088*x^2 + 8738945766992100918869163520*x^3 - 12388051440435217015983261440*x^4 - 48383627918289610600897522048*x^5 - 54284424615457663880585925824*x^6 - 14281771701603391495539689088*x^7 + 22232749320280826850305896960*x^8 + 20855026685937503207044336000*x^9 + 5585169040588512106911575000*x^10 - 186597412091415663627423750*x^11 - 160451576090217273141809375*x^12 - 2562169024586546846625000*x^13) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-275879689664025755707711488 - 2697522631947087885785266176*x - 10731979473640879880164903936*x^2 - 20937084981340188912458290688*x^3 - 15307989531382731107633333504*x^4 + 15888675054541667727584259200*x^5 + 44611747703371659238428784960*x^6 + 38213982296846141296252294080*x^7 + 11261281910685536846036043200*x^8 - 3069768950354491415277500000*x^9 - 2486139603513791766944095000*x^10 - 319756416262650734697343750*x^11 + 8691546164932464837859375*x^12 + 239161198859567827265625*x^13) + Sqrt[3]*(-275879689664025755707711488 - 2651651736343903652213182464*x - 9820903733784689825593387008*x^2 - 14560016541208769069413160960*x^3 + 7230235204191069410812285440*x^4 + 60088903168702184695051029248*x^5 + 89425864675835383650145252864*x^6 + 47064256583654776078354211008*x^7 - 19696480480887970171733819520*x^8 - 37973271169547237712036160400*x^9 - 16976727486341603508286165000*x^10 - 1650683224550518844919942500*x^11 + 474425854586706394345075000*x^12 + 44001679435021451731609375*x^13 - 93581876124690801796875*x^14 + Sqrt[1 - 2*x]*(275879689664025755707711488 + 2927430253326488515541692416*x + 12884098497526026814254114816*x^2 + 29023521199660568237585696768*x^3 + 29726834233942515391566124544*x^4 - 8012427718041669042910042880*x^5 - 59517980700581035434742293760*x^6 - 69007497771513145581497090880*x^7 - 32842341469562359879634529600*x^8 - 613863315628731370424530000*x^9 + 5209397242250869936991305000*x^10 + 1466296392390784873332837500*x^11 + 44202146519134521893937500*x^12 - 4003329916906785194296875*x^13)))/(2458624*Sqrt[3]*(2 + 3*x)^7*Sqrt[3 + 5*x]*(4051435671804928 - 3365532949972160*x - 7555736895916000*x^2 + 2194696763160000*x^3 + 1428846604955000*x^4 - 52303209612500*x^5 - 5663973218750*x^6) + 2458624*(2 + 3*x)^7*(-12154697640414784 - 26521579595840*x + 35265969543725200*x^2 + 5424159101550000*x^3 - 11461663884510000*x^4 - 996207107350000*x^5 + 135547777203125*x^6 + 905821796875*x^7) + Sqrt[1 - 2*x]*(2458624*(2 + 3*x)^7*(12149682333912640 + 12117692004316800*x - 17392813876790000*x^2 - 11790948756840000*x^3 + 1796810007300000*x^4 + 486365726000000*x^5 - 3042263984375*x^6) + 2458624*Sqrt[3]*(2 + 3*x)^7*Sqrt[3 + 5*x]*(-4049763902970880 - 666120123963200*x + 4956682106340000*x^2 + 702446326920000*x^3 - 390402719125000*x^4 - 14941831687500*x^5 + 223405156250*x^6))) + (1891543995*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2458624 - (9457719975*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/4917248","C",1
2411,1,1675,216,31.2744098,"\int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^(5/2),x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{36} \left(\frac{932023556783 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{18}}{3276800000 \sqrt{10} \left(\sqrt{3}-\sqrt{5 x+3}\right)^{36}}+\frac{\left(\frac{1899131643217 \sqrt{1-2 x}}{6553600000}-\frac{3024}{5} \sqrt{3} \sqrt{5 x+3}+\frac{9991720196783}{6553600000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{17}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{35}}+\frac{\left(\frac{50477239556783 \sqrt{1-2 x}}{9830400000}-\frac{419568}{25} \sqrt{3} \sqrt{5 x+3}+\frac{444465312507217}{9830400000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{16}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{33}}+\frac{\left(\frac{224144814843217 \sqrt{1-2 x}}{12288000000}-\frac{34054128}{125} \sqrt{3} \sqrt{5 x+3}+\frac{9818826181892783}{12288000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{15}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{31}}+\frac{\left(-\frac{9059944002299217 \sqrt{1-2 x}}{14336000000}-\frac{1787113488}{625} \sqrt{3} \sqrt{5 x+3}+\frac{132036227029345617}{14336000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{29}}+\frac{\left(-\frac{70738088889567461 \sqrt{1-2 x}}{5376000000}-\frac{12616121616}{625} \sqrt{3} \sqrt{5 x+3}+\frac{396294583966124261}{5376000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{13}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{27}}+\frac{\left(-\frac{72526446305951537 \sqrt{1-2 x}}{537600000}-\frac{1496798010864 \sqrt{3} \sqrt{5 x+3}}{15625}+\frac{1135123697744624629}{2688000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{25}}+\frac{\left(-\frac{200733304036177527 \sqrt{1-2 x}}{224000000}-\frac{31405366385664 \sqrt{3} \sqrt{5 x+3}}{109375}+\frac{393687875109697143}{224000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{11}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{23}}+\frac{\left(-\frac{13371364329849083 \sqrt{1-2 x}}{3200000}-\frac{6033418106208 \sqrt{3} \sqrt{5 x+3}}{15625}+\frac{85391482071516391}{16000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{21}}+\frac{\left(-\frac{14205141028792969 \sqrt{1-2 x}}{1000000}+\frac{2560593044544 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{11746971706030729}{1000000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{19}}+\frac{\left(-\frac{18001192862387701 \sqrt{1-2 x}}{500000}+\frac{18450350387136 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{9145024676562421}{500000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{17}}+\frac{\left(-\frac{36199565617661963 \sqrt{1-2 x}}{525000}+\frac{260999585480448 \sqrt{3} \sqrt{5 x+3}}{15625}+\frac{49454037006164023}{2625000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{15}}+\frac{\left(-\frac{131752681780770389 \sqrt{1-2 x}}{1312500}+\frac{470371709215104 \sqrt{3} \sqrt{5 x+3}}{15625}+\frac{13219011058564181}{1312500}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{13}}+\frac{\left(-\frac{12120677984306502 \sqrt{1-2 x}}{109375}+\frac{589194535850496 \sqrt{3} \sqrt{5 x+3}}{15625}-\frac{252407268553914}{109375}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{11}}+\frac{\left(-\frac{2002440869253372 \sqrt{1-2 x}}{21875}+\frac{731045542169088 \sqrt{3} \sqrt{5 x+3}}{21875}-\frac{190695757253892}{21875}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}+\frac{\left(-\frac{171746421747024 \sqrt{1-2 x}}{3125}+\frac{64511024873472 \sqrt{3} \sqrt{5 x+3}}{3125}-\frac{21786652873392}{3125}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}+\frac{\left(-\frac{14177411714016}{625} \sqrt{1-2 x}+\frac{132415158454272 \sqrt{3} \sqrt{5 x+3}}{15625}-\frac{42810182512416}{15625}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{-\frac{10585485809664 \sqrt{1-2 x}}{15625}+\frac{3611598741504 \sqrt{3} \sqrt{5 x+3}}{15625}-\frac{249310414848}{15625}}{\sqrt{3}-\sqrt{5 x+3}}+\frac{\left(\frac{3072 \sqrt{1-2 x}}{3125}+\frac{6144 \sqrt{3} \sqrt{5 x+3}}{15625}-\frac{33792}{15625}\right) \left(-29289267377 \sqrt{1-2 x}+10580855688 \sqrt{3} \sqrt{5 x+3}-2453299687\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{18}}","-\frac{1}{30} (3 x+2)^2 (5 x+3)^{7/2} (1-2 x)^{7/2}-\frac{526103 (5 x+3)^{5/2} (1-2 x)^{7/2}}{768000}-\frac{5787133 (5 x+3)^{3/2} (1-2 x)^{7/2}}{3072000}-\frac{(5 x+3)^{7/2} (170940 x+245011) (1-2 x)^{7/2}}{672000}-\frac{63658463 \sqrt{5 x+3} (1-2 x)^{7/2}}{16384000}+\frac{700243093 \sqrt{5 x+3} (1-2 x)^{5/2}}{491520000}+\frac{7702674023 \sqrt{5 x+3} (1-2 x)^{3/2}}{1966080000}+\frac{84729414253 \sqrt{5 x+3} \sqrt{1-2 x}}{6553600000}+\frac{932023556783 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{6553600000 \sqrt{10}}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^36*(((85391482071516391/16000000 - (13371364329849083*Sqrt[1 - 2*x])/3200000 - (6033418106208*Sqrt[3]*Sqrt[3 + 5*x])/15625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^10)/(Sqrt[3] - Sqrt[3 + 5*x])^21 + ((393687875109697143/224000000 - (200733304036177527*Sqrt[1 - 2*x])/224000000 - (31405366385664*Sqrt[3]*Sqrt[3 + 5*x])/109375)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^11)/(Sqrt[3] - Sqrt[3 + 5*x])^23 + ((1135123697744624629/2688000000 - (72526446305951537*Sqrt[1 - 2*x])/537600000 - (1496798010864*Sqrt[3]*Sqrt[3 + 5*x])/15625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12)/(Sqrt[3] - Sqrt[3 + 5*x])^25 + ((396294583966124261/5376000000 - (70738088889567461*Sqrt[1 - 2*x])/5376000000 - (12616121616*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^13)/(Sqrt[3] - Sqrt[3 + 5*x])^27 + ((132036227029345617/14336000000 - (9059944002299217*Sqrt[1 - 2*x])/14336000000 - (1787113488*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14)/(Sqrt[3] - Sqrt[3 + 5*x])^29 + ((9818826181892783/12288000000 + (224144814843217*Sqrt[1 - 2*x])/12288000000 - (34054128*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^15)/(Sqrt[3] - Sqrt[3 + 5*x])^31 + ((444465312507217/9830400000 + (50477239556783*Sqrt[1 - 2*x])/9830400000 - (419568*Sqrt[3]*Sqrt[3 + 5*x])/25)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^16)/(Sqrt[3] - Sqrt[3 + 5*x])^33 + ((9991720196783/6553600000 + (1899131643217*Sqrt[1 - 2*x])/6553600000 - (3024*Sqrt[3]*Sqrt[3 + 5*x])/5)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^17)/(Sqrt[3] - Sqrt[3 + 5*x])^35 + (-249310414848/15625 - (10585485809664*Sqrt[1 - 2*x])/15625 + (3611598741504*Sqrt[3]*Sqrt[3 + 5*x])/15625)/(Sqrt[3] - Sqrt[3 + 5*x]) + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^9*(11746971706030729/1000000 - (14205141028792969*Sqrt[1 - 2*x])/1000000 + (2560593044544*Sqrt[3]*Sqrt[3 + 5*x])/3125))/(Sqrt[3] - Sqrt[3 + 5*x])^19 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^8*(9145024676562421/500000 - (18001192862387701*Sqrt[1 - 2*x])/500000 + (18450350387136*Sqrt[3]*Sqrt[3 + 5*x])/3125))/(Sqrt[3] - Sqrt[3 + 5*x])^17 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2*(-42810182512416/15625 - (14177411714016*Sqrt[1 - 2*x])/625 + (132415158454272*Sqrt[3]*Sqrt[3 + 5*x])/15625))/(Sqrt[3] - Sqrt[3 + 5*x])^5 + ((-33792/15625 + (3072*Sqrt[1 - 2*x])/3125 + (6144*Sqrt[3]*Sqrt[3 + 5*x])/15625)*(-2453299687 - 29289267377*Sqrt[1 - 2*x] + 10580855688*Sqrt[3]*Sqrt[3 + 5*x]))/(Sqrt[3] - Sqrt[3 + 5*x])^3 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^7*(49454037006164023/2625000 - (36199565617661963*Sqrt[1 - 2*x])/525000 + (260999585480448*Sqrt[3]*Sqrt[3 + 5*x])/15625))/(Sqrt[3] - Sqrt[3 + 5*x])^15 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^3*(-21786652873392/3125 - (171746421747024*Sqrt[1 - 2*x])/3125 + (64511024873472*Sqrt[3]*Sqrt[3 + 5*x])/3125))/(Sqrt[3] - Sqrt[3 + 5*x])^7 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^6*(13219011058564181/1312500 - (131752681780770389*Sqrt[1 - 2*x])/1312500 + (470371709215104*Sqrt[3]*Sqrt[3 + 5*x])/15625))/(Sqrt[3] - Sqrt[3 + 5*x])^13 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^4*(-190695757253892/21875 - (2002440869253372*Sqrt[1 - 2*x])/21875 + (731045542169088*Sqrt[3]*Sqrt[3 + 5*x])/21875))/(Sqrt[3] - Sqrt[3 + 5*x])^9 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^5*(-252407268553914/109375 - (12120677984306502*Sqrt[1 - 2*x])/109375 + (589194535850496*Sqrt[3]*Sqrt[3 + 5*x])/15625))/(Sqrt[3] - Sqrt[3 + 5*x])^11 + (932023556783*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^18*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(3276800000*Sqrt[10]*(Sqrt[3] - Sqrt[3 + 5*x])^36)))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^18","B",1
2412,1,1503,209,20.9687843,"\int (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2),x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{32} \left(\frac{21331366001 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{16}}{163840000 \sqrt{10} \left(\sqrt{3}-\sqrt{5 x+3}\right)^{32}}+\frac{\left(\frac{49447513999 \sqrt{1-2 x}}{327680000}-\frac{864}{5} \sqrt{3} \sqrt{5 x+3}+\frac{120421798001}{327680000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{15}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{31}}+\frac{\left(\frac{1748336038001 \sqrt{1-2 x}}{491520000}-\frac{122952}{25} \sqrt{3} \sqrt{5 x+3}+\frac{5503668006799}{491520000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{29}}+\frac{\left(\frac{27194917465999 \sqrt{1-2 x}}{614400000}-\frac{2067936}{25} \sqrt{3} \sqrt{5 x+3}+\frac{125269867942001}{614400000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{13}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{27}}+\frac{\left(\frac{249185703743601 \sqrt{1-2 x}}{716800000}-\frac{572172408}{625} \sqrt{3} \sqrt{5 x+3}+\frac{1719453570117519}{716800000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{25}}+\frac{\left(\frac{399834018101893 \sqrt{1-2 x}}{268800000}-\frac{21986614704 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{5273767933035899}{268800000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{11}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{23}}+\frac{\left(\frac{72232368676757 \sqrt{1-2 x}}{134400000}-\frac{120941076048 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{3106413805468079}{26880000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{21}}+\frac{\left(-\frac{77835521501781 \sqrt{1-2 x}}{2240000}-\frac{679225803264 \sqrt{3} \sqrt{5 x+3}}{4375}+\frac{224225271063057}{448000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{19}}+\frac{\left(-\frac{186857768634169 \sqrt{1-2 x}}{800000}-\frac{287620068384}{625} \sqrt{3} \sqrt{5 x+3}+\frac{1291318831228729}{800000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{17}}+\frac{\left(-\frac{42533929252183 \sqrt{1-2 x}}{50000}-\frac{636045008064}{625} \sqrt{3} \sqrt{5 x+3}+\frac{195184731187543}{50000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{15}}+\frac{\left(-\frac{50597641571947 \sqrt{1-2 x}}{25000}-\frac{5272928513472 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{7085917035811}{1000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{13}}+\frac{\left(-\frac{434458625745001 \sqrt{1-2 x}}{131250}-\frac{6540709338624 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{10068704019293}{1050}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{11}}+\frac{\left(-\frac{49353495608911 \sqrt{1-2 x}}{13125}-\frac{1198690358016}{625} \sqrt{3} \sqrt{5 x+3}+\frac{124870988163919}{13125}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}+\frac{\left(-\frac{12778923006408 \sqrt{1-2 x}}{4375}-\frac{157741034496}{125} \sqrt{3} \sqrt{5 x+3}+\frac{29341731628488}{4375}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}+\frac{\left(-\frac{6481281766416 \sqrt{1-2 x}}{4375}-\frac{2469154003968 \sqrt{3} \sqrt{5 x+3}}{4375}+\frac{2777748755664}{875}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{-\frac{184297698432 \sqrt{1-2 x}}{3125}-\frac{60016029696 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{72869157504}{625}}{\sqrt{3}-\sqrt{5 x+3}}+\frac{\left(-\frac{576}{625} \sqrt{1-2 x}-\frac{1152 \sqrt{3} \sqrt{5 x+3}}{3125}+\frac{6336}{3125}\right) \left(2399709615 \sqrt{1-2 x}+833555968 \sqrt{3} \sqrt{5 x+3}-4900377519\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{16}}","-\frac{3}{80} (3 x+2) (5 x+3)^{7/2} (1-2 x)^{7/2}-\frac{999 (5 x+3)^{7/2} (1-2 x)^{7/2}}{11200}-\frac{12041 (5 x+3)^{5/2} (1-2 x)^{7/2}}{38400}-\frac{132451 (5 x+3)^{3/2} (1-2 x)^{7/2}}{153600}-\frac{1456961 \sqrt{5 x+3} (1-2 x)^{7/2}}{819200}+\frac{16026571 \sqrt{5 x+3} (1-2 x)^{5/2}}{24576000}+\frac{176292281 \sqrt{5 x+3} (1-2 x)^{3/2}}{98304000}+\frac{1939215091 \sqrt{5 x+3} \sqrt{1-2 x}}{327680000}+\frac{21331366001 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{327680000 \sqrt{10}}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^32*((72869157504/625 - (184297698432*Sqrt[1 - 2*x])/3125 - (60016029696*Sqrt[3]*Sqrt[3 + 5*x])/3125)/(Sqrt[3] - Sqrt[3 + 5*x]) + ((2777748755664/875 - (6481281766416*Sqrt[1 - 2*x])/4375 - (2469154003968*Sqrt[3]*Sqrt[3 + 5*x])/4375)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^5 + ((29341731628488/4375 - (12778923006408*Sqrt[1 - 2*x])/4375 - (157741034496*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^7 + ((124870988163919/13125 - (49353495608911*Sqrt[1 - 2*x])/13125 - (1198690358016*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^9 + ((10068704019293/1050 - (434458625745001*Sqrt[1 - 2*x])/131250 - (6540709338624*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^11 + ((7085917035811/1000 - (50597641571947*Sqrt[1 - 2*x])/25000 - (5272928513472*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^13 + ((195184731187543/50000 - (42533929252183*Sqrt[1 - 2*x])/50000 - (636045008064*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^7)/(Sqrt[3] - Sqrt[3 + 5*x])^15 + ((1291318831228729/800000 - (186857768634169*Sqrt[1 - 2*x])/800000 - (287620068384*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^8)/(Sqrt[3] - Sqrt[3 + 5*x])^17 + ((224225271063057/448000 - (77835521501781*Sqrt[1 - 2*x])/2240000 - (679225803264*Sqrt[3]*Sqrt[3 + 5*x])/4375)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^9)/(Sqrt[3] - Sqrt[3 + 5*x])^19 + ((3106413805468079/26880000 + (72232368676757*Sqrt[1 - 2*x])/134400000 - (120941076048*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^10)/(Sqrt[3] - Sqrt[3 + 5*x])^21 + ((5273767933035899/268800000 + (399834018101893*Sqrt[1 - 2*x])/268800000 - (21986614704*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^11)/(Sqrt[3] - Sqrt[3 + 5*x])^23 + ((1719453570117519/716800000 + (249185703743601*Sqrt[1 - 2*x])/716800000 - (572172408*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12)/(Sqrt[3] - Sqrt[3 + 5*x])^25 + ((125269867942001/614400000 + (27194917465999*Sqrt[1 - 2*x])/614400000 - (2067936*Sqrt[3]*Sqrt[3 + 5*x])/25)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^13)/(Sqrt[3] - Sqrt[3 + 5*x])^27 + ((5503668006799/491520000 + (1748336038001*Sqrt[1 - 2*x])/491520000 - (122952*Sqrt[3]*Sqrt[3 + 5*x])/25)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14)/(Sqrt[3] - Sqrt[3 + 5*x])^29 + ((120421798001/327680000 + (49447513999*Sqrt[1 - 2*x])/327680000 - (864*Sqrt[3]*Sqrt[3 + 5*x])/5)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^15)/(Sqrt[3] - Sqrt[3 + 5*x])^31 + ((6336/3125 - (576*Sqrt[1 - 2*x])/625 - (1152*Sqrt[3]*Sqrt[3 + 5*x])/3125)*(-4900377519 + 2399709615*Sqrt[1 - 2*x] + 833555968*Sqrt[3]*Sqrt[3 + 5*x]))/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (21331366001*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^16*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(163840000*Sqrt[10]*(Sqrt[3] - Sqrt[3 + 5*x])^32)))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^16","B",1
2413,1,1331,182,13.8232432,"\int (1-2 x)^{5/2} (2+3 x) (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^(5/2),x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{28} \left(\frac{65547757 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}{1024000 \sqrt{10} \left(\sqrt{3}-\sqrt{5 x+3}\right)^{28}}+\frac{\left(\frac{155636243 \sqrt{1-2 x}}{2048000}-\frac{108}{5} \sqrt{3} \sqrt{5 x+3}-\frac{22925843}{2048000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{13}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{27}}+\frac{\left(\frac{5794213357 \sqrt{1-2 x}}{3072000}-\frac{16116}{25} \sqrt{3} \sqrt{5 x+3}+\frac{146788883}{3072000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{25}}+\frac{\left(\frac{100645057043 \sqrt{1-2 x}}{3840000}-\frac{1381728}{125} \sqrt{3} \sqrt{5 x+3}+\frac{26694995437}{3840000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{11}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{23}}+\frac{\left(\frac{1134668893677 \sqrt{1-2 x}}{4480000}-\frac{75916104}{625} \sqrt{3} \sqrt{5 x+3}+\frac{497831006739}{4480000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{21}}+\frac{\left(\frac{2874555948209 \sqrt{1-2 x}}{1680000}-\frac{563287824}{625} \sqrt{3} \sqrt{5 x+3}+\frac{1667797064527}{1680000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{19}}+\frac{\left(\frac{6889013493121 \sqrt{1-2 x}}{840000}-\frac{2896164336}{625} \sqrt{3} \sqrt{5 x+3}+\frac{4788321109631}{840000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{17}}+\frac{\left(\frac{1967469478587 \sqrt{1-2 x}}{70000}-\frac{73078428288 \sqrt{3} \sqrt{5 x+3}}{4375}+\frac{1540295079237}{70000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{15}}+\frac{\left(\frac{345686834539 \sqrt{1-2 x}}{5000}-\frac{26487234336}{625} \sqrt{3} \sqrt{5 x+3}+\frac{11600271581}{200}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{13}}+\frac{\left(\frac{76301184554}{625} \sqrt{1-2 x}-\frac{47244963456}{625} \sqrt{3} \sqrt{5 x+3}+\frac{65433705814}{625}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{11}}+\frac{\left(\frac{95895279556}{625} \sqrt{1-2 x}-\frac{58721543808}{625} \sqrt{3} \sqrt{5 x+3}+\frac{80269351868}{625}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}+\frac{\left(\frac{1758651078448 \sqrt{1-2 x}}{13125}-\frac{49716022272}{625} \sqrt{3} \sqrt{5 x+3}+\frac{1373458324688}{13125}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}+\frac{\left(\frac{1014312807712 \sqrt{1-2 x}}{13125}-\frac{27319408128}{625} \sqrt{3} \sqrt{5 x+3}+\frac{706809904352}{13125}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{\frac{17809181184 \sqrt{1-2 x}}{4375}-\frac{8784648192 \sqrt{3} \sqrt{5 x+3}}{4375}+\frac{8544763392}{4375}}{\sqrt{3}-\sqrt{5 x+3}}+\frac{\left(-\frac{768}{875} \sqrt{1-2 x}-\frac{1536 \sqrt{3} \sqrt{5 x+3}}{4375}+\frac{8448}{4375}\right) \left(-150728747 \sqrt{1-2 x}+80068408 \sqrt{3} \sqrt{5 x+3}-89476477\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{14}}","-\frac{3}{70} (5 x+3)^{7/2} (1-2 x)^{7/2}-\frac{37}{240} (5 x+3)^{5/2} (1-2 x)^{7/2}-\frac{407}{960} (5 x+3)^{3/2} (1-2 x)^{7/2}-\frac{4477 \sqrt{5 x+3} (1-2 x)^{7/2}}{5120}+\frac{49247 \sqrt{5 x+3} (1-2 x)^{5/2}}{153600}+\frac{541717 \sqrt{5 x+3} (1-2 x)^{3/2}}{614400}+\frac{5958887 \sqrt{5 x+3} \sqrt{1-2 x}}{2048000}+\frac{65547757 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{2048000 \sqrt{10}}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^28*((8544763392/4375 + (17809181184*Sqrt[1 - 2*x])/4375 - (8784648192*Sqrt[3]*Sqrt[3 + 5*x])/4375)/(Sqrt[3] - Sqrt[3 + 5*x]) + ((706809904352/13125 + (1014312807712*Sqrt[1 - 2*x])/13125 - (27319408128*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^5 + ((1373458324688/13125 + (1758651078448*Sqrt[1 - 2*x])/13125 - (49716022272*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^7 + ((80269351868/625 + (95895279556*Sqrt[1 - 2*x])/625 - (58721543808*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^9 + ((65433705814/625 + (76301184554*Sqrt[1 - 2*x])/625 - (47244963456*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^11 + ((11600271581/200 + (345686834539*Sqrt[1 - 2*x])/5000 - (26487234336*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^13 + ((1540295079237/70000 + (1967469478587*Sqrt[1 - 2*x])/70000 - (73078428288*Sqrt[3]*Sqrt[3 + 5*x])/4375)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^7)/(Sqrt[3] - Sqrt[3 + 5*x])^15 + ((4788321109631/840000 + (6889013493121*Sqrt[1 - 2*x])/840000 - (2896164336*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^8)/(Sqrt[3] - Sqrt[3 + 5*x])^17 + ((1667797064527/1680000 + (2874555948209*Sqrt[1 - 2*x])/1680000 - (563287824*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^9)/(Sqrt[3] - Sqrt[3 + 5*x])^19 + ((497831006739/4480000 + (1134668893677*Sqrt[1 - 2*x])/4480000 - (75916104*Sqrt[3]*Sqrt[3 + 5*x])/625)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^10)/(Sqrt[3] - Sqrt[3 + 5*x])^21 + ((26694995437/3840000 + (100645057043*Sqrt[1 - 2*x])/3840000 - (1381728*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^11)/(Sqrt[3] - Sqrt[3 + 5*x])^23 + ((146788883/3072000 + (5794213357*Sqrt[1 - 2*x])/3072000 - (16116*Sqrt[3]*Sqrt[3 + 5*x])/25)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12)/(Sqrt[3] - Sqrt[3 + 5*x])^25 + ((-22925843/2048000 + (155636243*Sqrt[1 - 2*x])/2048000 - (108*Sqrt[3]*Sqrt[3 + 5*x])/5)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^13)/(Sqrt[3] - Sqrt[3 + 5*x])^27 + ((8448/4375 - (768*Sqrt[1 - 2*x])/875 - (1536*Sqrt[3]*Sqrt[3 + 5*x])/4375)*(-89476477 - 150728747*Sqrt[1 - 2*x] + 80068408*Sqrt[3]*Sqrt[3 + 5*x]))/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (65547757*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(1024000*Sqrt[10]*(Sqrt[3] - Sqrt[3 + 5*x])^28)))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^14","B",1
2414,1,486,160,2.8876508,"\int (1-2 x)^{5/2} (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2),x]","\frac{1771561 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{51200 \sqrt{10}}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-121103920000000000 x^{11}+4662333236000000000 x^{10}+108943090309350000000 x^9-64942094406557500000 x^8-758913900282333812500 x^7-87043168043349478125 x^6+917071879686902295000 x^5+125208501734537895750 x^4-483142945305461679600 x^3-52930233566179736080 x^2+96034398834356328320 x+9641553262411077216\right)+\sqrt{5 x+3} \left(2420996160000000000 x^{11}+22133813680000000000 x^{10}-300355473270600000000 x^9-483407614614210000000 x^8+967952704405568750000 x^7+875762073456277012500 x^6-991201369657648668750 x^5-575168569213649925250 x^4+486810386349594133200 x^3+154899819218053905600 x^2-86261958645334065440 x-9641553262411077216\right)+\sqrt{3} \left(-134409600000000000 x^{12}-17720412960000000000 x^{11}+64543236318000000000 x^{10}+758836322808300000000 x^9+30230359962247500000 x^8-1816597565875153875000 x^7-312269500477669340625 x^6+1566603952602663060000 x^5+248412378342208761750 x^4-644069845737339373200 x^3-86176880471585787600 x^2+94281906524166213120 x+\sqrt{1-2 x} \left(646789440000000000 x^{11}-49145420016000000000 x^{10}-178041424789800000000 x^9+540576181610850000000 x^8+1022758678491684750000 x^7-541951019911849762500 x^6-1144753473972898226250 x^5+231842027215679388750 x^4+558657243383905446000 x^3-23921725497963184320 x^2-104054346713188476000 x-9641553262411077216\right)+9641553262411077216\right)}{307200 \sqrt{3} \sqrt{5 x+3} \left(25265212500 x^5-1941218400000 x^4-5284290066000 x^3+24057375117600 x^2+13825440024000 x-16748592098304\right)+\sqrt{1-2 x} \left(307200 \left(-236425406250 x^5-2220611593750 x^4+28520358020000 x^3+52011357156000 x^2-49788771586400 x-50183931760160\right)+307200 \sqrt{3} \sqrt{5 x+3} \left(2625187500 x^5+345183000000 x^4-1378186950000 x^3-13912170444000 x^2+2687092123200 x+16725373086720\right)\right)+307200 \left(-23653109375 x^6+916525237500 x^5+21026153381250 x^4-17065853944000 x^3-123670456765200 x^2+301410173760 x+50253588794912\right)}","-\frac{1}{12} (5 x+3)^{5/2} (1-2 x)^{7/2}-\frac{11}{48} (5 x+3)^{3/2} (1-2 x)^{7/2}-\frac{121}{256} \sqrt{5 x+3} (1-2 x)^{7/2}+\frac{1331 \sqrt{5 x+3} (1-2 x)^{5/2}}{7680}+\frac{14641 \sqrt{5 x+3} (1-2 x)^{3/2}}{30720}+\frac{161051 \sqrt{5 x+3} \sqrt{1-2 x}}{102400}+\frac{1771561 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{102400 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(9641553262411077216 + 96034398834356328320*x - 52930233566179736080*x^2 - 483142945305461679600*x^3 + 125208501734537895750*x^4 + 917071879686902295000*x^5 - 87043168043349478125*x^6 - 758913900282333812500*x^7 - 64942094406557500000*x^8 + 108943090309350000000*x^9 + 4662333236000000000*x^10 - 121103920000000000*x^11) + Sqrt[3 + 5*x]*(-9641553262411077216 - 86261958645334065440*x + 154899819218053905600*x^2 + 486810386349594133200*x^3 - 575168569213649925250*x^4 - 991201369657648668750*x^5 + 875762073456277012500*x^6 + 967952704405568750000*x^7 - 483407614614210000000*x^8 - 300355473270600000000*x^9 + 22133813680000000000*x^10 + 2420996160000000000*x^11) + Sqrt[3]*(9641553262411077216 + 94281906524166213120*x - 86176880471585787600*x^2 - 644069845737339373200*x^3 + 248412378342208761750*x^4 + 1566603952602663060000*x^5 - 312269500477669340625*x^6 - 1816597565875153875000*x^7 + 30230359962247500000*x^8 + 758836322808300000000*x^9 + 64543236318000000000*x^10 - 17720412960000000000*x^11 - 134409600000000000*x^12 + Sqrt[1 - 2*x]*(-9641553262411077216 - 104054346713188476000*x - 23921725497963184320*x^2 + 558657243383905446000*x^3 + 231842027215679388750*x^4 - 1144753473972898226250*x^5 - 541951019911849762500*x^6 + 1022758678491684750000*x^7 + 540576181610850000000*x^8 - 178041424789800000000*x^9 - 49145420016000000000*x^10 + 646789440000000000*x^11)))/(307200*Sqrt[3]*Sqrt[3 + 5*x]*(-16748592098304 + 13825440024000*x + 24057375117600*x^2 - 5284290066000*x^3 - 1941218400000*x^4 + 25265212500*x^5) + 307200*(50253588794912 + 301410173760*x - 123670456765200*x^2 - 17065853944000*x^3 + 21026153381250*x^4 + 916525237500*x^5 - 23653109375*x^6) + Sqrt[1 - 2*x]*(307200*(-50183931760160 - 49788771586400*x + 52011357156000*x^2 + 28520358020000*x^3 - 2220611593750*x^4 - 236425406250*x^5) + 307200*Sqrt[3]*Sqrt[3 + 5*x]*(16725373086720 + 2687092123200*x - 13912170444000*x^2 - 1378186950000*x^3 + 345183000000*x^4 + 2625187500*x^5))) + (1771561*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(51200*Sqrt[10])","B",1
2415,1,618,172,3.1763254,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{2+3 x} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x),x]","\frac{343}{729} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(4587904800000000 x^9+508060475010000000 x^8-1225237867174500000 x^7-8335583483384437500 x^6+5708443081089278125 x^5+8886853079050269125 x^4-6127344149696207300 x^3-3565089265906735940 x^2+1844497097266688960 x+898520943037493072\right)+\sqrt{5 x+3} \left(56803032000000000 x^9-2200652180100000000 x^8-3459172317645000000 x^7+15190691288334375000 x^6-228225981988468750 x^5-15433959842106925625 x^4+3988950420800213000 x^3+5901502485078896300 x^2-938095808255894640 x-898520943037493072\right)+\sqrt{3} \left(-17113680000000000 x^{10}+359195931000000000 x^9+6630022006350000000 x^8-5687855904401250000 x^7-19434048569954687500 x^6+12415012885785359375 x^5+14386868834863748125 x^4-9052046149073665500 x^3-5416358944711568500 x^2+\sqrt{1-2 x} \left(-131447448000000000 x^9-990731144700000000 x^8+7278063439779000000 x^7+6928911417619125000 x^6-13725671135792343750 x^5-5449237029318300625 x^4+9544677139550861000 x^3+2325884037900204540 x^2-2591991829928141520 x-898520943037493072\right)+1685590540917347200 x+898520943037493072\right)}{3110400 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right)+\sqrt{1-2 x} \left(3110400 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right)+3110400 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right)\right)+3110400 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right)}+\frac{109715471 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{4665600 \sqrt{10}}","\frac{1}{15} (1-2 x)^{5/2} (5 x+3)^{5/2}+\frac{37}{360} (1-2 x)^{3/2} (5 x+3)^{5/2}+\frac{4783 \sqrt{1-2 x} (5 x+3)^{5/2}}{32400}-\frac{14557 \sqrt{1-2 x} (5 x+3)^{3/2}}{28800}-\frac{1994287 \sqrt{1-2 x} \sqrt{5 x+3}}{3110400}+\frac{109715471 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{9331200 \sqrt{10}}+\frac{98}{729} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(898520943037493072 + 1844497097266688960*x - 3565089265906735940*x^2 - 6127344149696207300*x^3 + 8886853079050269125*x^4 + 5708443081089278125*x^5 - 8335583483384437500*x^6 - 1225237867174500000*x^7 + 508060475010000000*x^8 + 4587904800000000*x^9) + Sqrt[3 + 5*x]*(-898520943037493072 - 938095808255894640*x + 5901502485078896300*x^2 + 3988950420800213000*x^3 - 15433959842106925625*x^4 - 228225981988468750*x^5 + 15190691288334375000*x^6 - 3459172317645000000*x^7 - 2200652180100000000*x^8 + 56803032000000000*x^9) + Sqrt[3]*(898520943037493072 + 1685590540917347200*x - 5416358944711568500*x^2 - 9052046149073665500*x^3 + 14386868834863748125*x^4 + 12415012885785359375*x^5 - 19434048569954687500*x^6 - 5687855904401250000*x^7 + 6630022006350000000*x^8 + 359195931000000000*x^9 - 17113680000000000*x^10 + Sqrt[1 - 2*x]*(-898520943037493072 - 2591991829928141520*x + 2325884037900204540*x^2 + 9544677139550861000*x^3 - 5449237029318300625*x^4 - 13725671135792343750*x^5 + 6928911417619125000*x^6 + 7278063439779000000*x^7 - 990731144700000000*x^8 - 131447448000000000*x^9)))/(3110400*Sqrt[3]*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 3110400*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(3110400*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 3110400*Sqrt[3]*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (109715471*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(4665600*Sqrt[10]) + (343*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ])/729","C",1
2416,1,709,179,3.5064661,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^2,x]","\frac{9065}{729} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{45325 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{1458}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(57348810000000 x^9+6336020479500000 x^8-16935995821087500 x^7-99021113800209375 x^6+94044586642654375 x^5+74128589936876450 x^4-65963099873831660 x^3+8899971358111432 x^2-590203094997616 x-18948014918919328\right)+\sqrt{5 x+3} \left(710037900000000 x^9-27690592545000000 x^8-36032065447125000 x^7+195471357548156250 x^6-55450613423115625 x^5-141386175155975750 x^4+68523357630368300 x^3-17879337636705160 x^2-18213713025600048 x+18948014918919328\right)+\sqrt{3} \left(-213921000000000 x^{10}+4544914950000000 x^9+81679572363750000 x^8-91474974722437500 x^7-209094987801053125 x^6+187608347313126875 x^5+91271033465880250 x^4-66412624486829100 x^3+39868668571725800 x^2+\sqrt{1-2 x} \left(-1643093100000000 x^9-11961955665000000 x^8+93834962899425000 x^7+61073300405081250 x^6-173554859002160625 x^5-23131933618609750 x^4+64608878661031100 x^3-15196099432217352 x^2+16403488287847056 x+18948014918919328\right)+2400427832750608 x-18948014918919328\right)}{31104 \sqrt{3} (3 x+2) \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right)+\sqrt{1-2 x} \left(31104 (3 x+2) \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right)+31104 \sqrt{3} (3 x+2) \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right)\right)+31104 (3 x+2) \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right)}-\frac{660959 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{46656 \sqrt{10}}","-\frac{5}{18} (1-2 x)^{3/2} (5 x+3)^{5/2}-\frac{247}{324} \sqrt{1-2 x} (5 x+3)^{5/2}-\frac{(1-2 x)^{5/2} (5 x+3)^{5/2}}{3 (3 x+2)}+\frac{1453}{288} \sqrt{1-2 x} (5 x+3)^{3/2}-\frac{155777 \sqrt{1-2 x} \sqrt{5 x+3}}{31104}-\frac{660959 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{93312 \sqrt{10}}-\frac{1295}{729} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-18948014918919328 - 590203094997616*x + 8899971358111432*x^2 - 65963099873831660*x^3 + 74128589936876450*x^4 + 94044586642654375*x^5 - 99021113800209375*x^6 - 16935995821087500*x^7 + 6336020479500000*x^8 + 57348810000000*x^9) + Sqrt[3 + 5*x]*(18948014918919328 - 18213713025600048*x - 17879337636705160*x^2 + 68523357630368300*x^3 - 141386175155975750*x^4 - 55450613423115625*x^5 + 195471357548156250*x^6 - 36032065447125000*x^7 - 27690592545000000*x^8 + 710037900000000*x^9) + Sqrt[3]*(-18948014918919328 + 2400427832750608*x + 39868668571725800*x^2 - 66412624486829100*x^3 + 91271033465880250*x^4 + 187608347313126875*x^5 - 209094987801053125*x^6 - 91474974722437500*x^7 + 81679572363750000*x^8 + 4544914950000000*x^9 - 213921000000000*x^10 + Sqrt[1 - 2*x]*(18948014918919328 + 16403488287847056*x - 15196099432217352*x^2 + 64608878661031100*x^3 - 23131933618609750*x^4 - 173554859002160625*x^5 + 61073300405081250*x^6 + 93834962899425000*x^7 - 11961955665000000*x^8 - 1643093100000000*x^9)))/(31104*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 31104*(2 + 3*x)*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(31104*(2 + 3*x)*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 31104*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) - (660959*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(46656*Sqrt[10]) + (9065*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/729 - (45325*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/1458","C",1
2417,1,719,188,3.8519558,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^3,x]","-\frac{153545 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2916}+\frac{767725 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{5832}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(4779067500000 x^9+525545796937500 x^8-1676566878028125 x^7-6793072426996875 x^6+13040936520741250 x^5-25362338608530400 x^4-70344566516392280 x^3+9532845991780096 x^2+59943154039259744 x+22079595815545664\right)+\sqrt{5 x+3} \left(59169825000000 x^9-2337956094375000 x^8-1741319861531250 x^7+14800498650815625 x^6-34774391347176250 x^5-5933727478078400 x^4+118020506251790120 x^3+60911164371343616 x^2-37909943359133472 x-22079595815545664\right)+\sqrt{3} \left(-17826750000000 x^{10}+387903881250000 x^9+6589244014687500 x^8-10721999497753125 x^7+380885598490625 x^6+58996268298965000 x^5-66851320715564000 x^4-175489446386305200 x^3-37030129676421856 x^2+\sqrt{1-2 x} \left(-136924425000000 x^9-926465698125000 x^8+8157060537243750 x^7-1219224282890625 x^6-8491828422990000 x^5+76484405205725000 x^4+76793406315362000 x^3-51782381045140416 x^2-78350308677214464 x-22079595815545664\right)+56317097997088192 x+22079595815545664\right)}{1944 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right) (3 x+2)^2+\sqrt{1-2 x} \left(1944 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right) (3 x+2)^2+1944 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right) (3 x+2)^2\right)+1944 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right) (3 x+2)^2}+\frac{81733 \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{2916}","\frac{575}{162} \sqrt{1-2 x} (5 x+3)^{5/2}+\frac{185 (1-2 x)^{3/2} (5 x+3)^{5/2}}{36 (3 x+2)}-\frac{(1-2 x)^{5/2} (5 x+3)^{5/2}}{6 (3 x+2)^2}-\frac{785}{36} \sqrt{1-2 x} (5 x+3)^{3/2}+\frac{34145 \sqrt{1-2 x} \sqrt{5 x+3}}{1944}+\frac{81733 \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{5832}+\frac{21935 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2916}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(22079595815545664 + 59943154039259744*x + 9532845991780096*x^2 - 70344566516392280*x^3 - 25362338608530400*x^4 + 13040936520741250*x^5 - 6793072426996875*x^6 - 1676566878028125*x^7 + 525545796937500*x^8 + 4779067500000*x^9) + Sqrt[3 + 5*x]*(-22079595815545664 - 37909943359133472*x + 60911164371343616*x^2 + 118020506251790120*x^3 - 5933727478078400*x^4 - 34774391347176250*x^5 + 14800498650815625*x^6 - 1741319861531250*x^7 - 2337956094375000*x^8 + 59169825000000*x^9) + Sqrt[3]*(22079595815545664 + 56317097997088192*x - 37030129676421856*x^2 - 175489446386305200*x^3 - 66851320715564000*x^4 + 58996268298965000*x^5 + 380885598490625*x^6 - 10721999497753125*x^7 + 6589244014687500*x^8 + 387903881250000*x^9 - 17826750000000*x^10 + Sqrt[1 - 2*x]*(-22079595815545664 - 78350308677214464*x - 51782381045140416*x^2 + 76793406315362000*x^3 + 76484405205725000*x^4 - 8491828422990000*x^5 - 1219224282890625*x^6 + 8157060537243750*x^7 - 926465698125000*x^8 - 136924425000000*x^9)))/(1944*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 1944*(2 + 3*x)^2*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(1944*(2 + 3*x)^2*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 1944*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (81733*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/2916 - (153545*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2916 + (767725*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/5832","C",1
2418,1,719,195,4.3001914,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^4} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^4,x]","\frac{408665 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{5832}-\frac{2043325 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{11664}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(7168601250000 x^9+777267101812500 x^8-3938811751284375 x^7-17975669841909375 x^6+87293409950221250 x^5+257781894548419900 x^4+95759212114247480 x^3-199537265425774096 x^2-185635932116073824 x-44813229729830144\right)+\sqrt{5 x+3} \left(88754737500000 x^9-3643764361875000 x^8+2714755405518750 x^7+94681032168958125 x^6+38217614660976850 x^5-354200143672489180 x^4-402692190086434424 x^3-7149060916015568 x^2+140931939451103328 x+44813229729830144\right)+\sqrt{3} \left(-26740125000000 x^{10}+623080181250000 x^9+9347864306418750 x^8-49103539208850000 x^7-165213890084881250 x^6+146559969058571500 x^5+659729596895294600 x^4+444537586465085664 x^3-94644368025935072 x^2+\sqrt{1-2 x} \left(-205386637500000 x^9-1073060814375000 x^8+18269540569912500 x^7-7587668636831250 x^6-251699245291642500 x^5-366375155120843000 x^4+19048535988116800 x^3+338601663984366816 x^2+222997932620098944 x+44813229729830144\right)-178293939955128448 x-44813229729830144\right)}{1944 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right) (3 x+2)^3+\sqrt{1-2 x} \left(1944 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right) (3 x+2)^3+1944 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right) (3 x+2)^3\right)+1944 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right) (3 x+2)^3}-\frac{21935}{729} \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{10385 \sqrt{1-2 x} (5 x+3)^{5/2}}{648 (3 x+2)}+\frac{185 (1-2 x)^{3/2} (5 x+3)^{5/2}}{108 (3 x+2)^2}-\frac{(1-2 x)^{5/2} (5 x+3)^{5/2}}{9 (3 x+2)^3}+\frac{2075}{72} \sqrt{1-2 x} (5 x+3)^{3/2}-\frac{48625 \sqrt{1-2 x} \sqrt{5 x+3}}{1944}-\frac{21935 \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{1458}-\frac{408665 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{5832 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-44813229729830144 - 185635932116073824*x - 199537265425774096*x^2 + 95759212114247480*x^3 + 257781894548419900*x^4 + 87293409950221250*x^5 - 17975669841909375*x^6 - 3938811751284375*x^7 + 777267101812500*x^8 + 7168601250000*x^9) + Sqrt[3 + 5*x]*(44813229729830144 + 140931939451103328*x - 7149060916015568*x^2 - 402692190086434424*x^3 - 354200143672489180*x^4 + 38217614660976850*x^5 + 94681032168958125*x^6 + 2714755405518750*x^7 - 3643764361875000*x^8 + 88754737500000*x^9) + Sqrt[3]*(-44813229729830144 - 178293939955128448*x - 94644368025935072*x^2 + 444537586465085664*x^3 + 659729596895294600*x^4 + 146559969058571500*x^5 - 165213890084881250*x^6 - 49103539208850000*x^7 + 9347864306418750*x^8 + 623080181250000*x^9 - 26740125000000*x^10 + Sqrt[1 - 2*x]*(44813229729830144 + 222997932620098944*x + 338601663984366816*x^2 + 19048535988116800*x^3 - 366375155120843000*x^4 - 251699245291642500*x^5 - 7587668636831250*x^6 + 18269540569912500*x^7 - 1073060814375000*x^8 - 205386637500000*x^9)))/(1944*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 1944*(2 + 3*x)^3*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(1944*(2 + 3*x)^3*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 1944*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) - (21935*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/729 + (408665*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/5832 - (2043325*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/11664","C",1
2419,1,717,200,4.0641448,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^5} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^5,x]","-\frac{3304795 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{326592}+\frac{16523975 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{653184}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(802883340000000 x^9+102274278531328125 x^8+459089493269165625 x^7-4557363715547250000 x^6-19861379559769391000 x^5-18447044202375996400 x^4+8654085407451327040 x^3+22141876355586562048 x^2+11908698462134829632 x+2113618735799428352\right)+\sqrt{5 x+3} \left(9940530600000000 x^9-396763812809100000 x^8-4771243178113850625 x^7-6216863337943282200 x^6+20375716616430953360 x^5+43472878906030895728 x^4+20013674865992237408 x^3-9250522373163049792 x^2-9800312155104812352 x-2113618735799428352\right)+\sqrt{3} \left(-2994894000000000 x^{10}+42528075799303125 x^9+2302730117243615625 x^8+10713275143770468750 x^7-1782675995590625500 x^6-49199052731849081200 x^5-61139946404742429968 x^4-15100545538702527648 x^3+16680741372070036352 x^2+\sqrt{1-2 x} \left(-23003303400000000 x^9-408670964996765625 x^8+586355827218356250 x^7+15658058942507272500 x^6+34674812063845338000 x^5+16096849153260774800 x^4-23576386338312707680 x^3-31329929010143563008 x^2-13670892475092686592 x-2113618735799428352\right)+11562506168062669312 x+2113618735799428352\right)}{108864 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right) (3 x+2)^4+\sqrt{1-2 x} \left(108864 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right) (3 x+2)^4+108864 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right) (3 x+2)^4\right)+108864 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right) (3 x+2)^4}+\frac{3700}{729} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{1165 \sqrt{1-2 x} (5 x+3)^{5/2}}{2592 (3 x+2)^2}+\frac{185 (1-2 x)^{3/2} (5 x+3)^{5/2}}{216 (3 x+2)^3}-\frac{(1-2 x)^{5/2} (5 x+3)^{5/2}}{12 (3 x+2)^4}-\frac{3485 \sqrt{1-2 x} (5 x+3)^{3/2}}{4032 (3 x+2)}+\frac{249575 \sqrt{1-2 x} \sqrt{5 x+3}}{108864}+\frac{1850}{729} \sqrt{10} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)+\frac{3304795 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{326592 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(2113618735799428352 + 11908698462134829632*x + 22141876355586562048*x^2 + 8654085407451327040*x^3 - 18447044202375996400*x^4 - 19861379559769391000*x^5 - 4557363715547250000*x^6 + 459089493269165625*x^7 + 102274278531328125*x^8 + 802883340000000*x^9) + Sqrt[3 + 5*x]*(-2113618735799428352 - 9800312155104812352*x - 9250522373163049792*x^2 + 20013674865992237408*x^3 + 43472878906030895728*x^4 + 20375716616430953360*x^5 - 6216863337943282200*x^6 - 4771243178113850625*x^7 - 396763812809100000*x^8 + 9940530600000000*x^9) + Sqrt[3]*(2113618735799428352 + 11562506168062669312*x + 16680741372070036352*x^2 - 15100545538702527648*x^3 - 61139946404742429968*x^4 - 49199052731849081200*x^5 - 1782675995590625500*x^6 + 10713275143770468750*x^7 + 2302730117243615625*x^8 + 42528075799303125*x^9 - 2994894000000000*x^10 + Sqrt[1 - 2*x]*(-2113618735799428352 - 13670892475092686592*x - 31329929010143563008*x^2 - 23576386338312707680*x^3 + 16096849153260774800*x^4 + 34674812063845338000*x^5 + 15658058942507272500*x^6 + 586355827218356250*x^7 - 408670964996765625*x^8 - 23003303400000000*x^9)))/(108864*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 108864*(2 + 3*x)^4*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(108864*(2 + 3*x)^4*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 108864*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (3700*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/729 - (3304795*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/326592 + (16523975*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/653184","C",1
2420,1,717,207,4.6467338,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^6} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^6,x]","\frac{109715471 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{4572288}-\frac{548577355 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{9144576}+\frac{\sqrt{5 x+3} \left(-3877428024877275000 x^9-102922944074752168125 x^8-162075700694799650550 x^7+630498677183315360640 x^6+2127120385619418827792 x^5+2076193396553804007040 x^4+299722269840820555520 x^3-704900393243545385920 x^2-429313985499796721280 x-75015726412445384192\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(448366511346890625 x^9+6637686711828046875 x^8-133348026005360981250 x^7-666816715411338879000 x^6-1009011472099117452800 x^5-90646018401293553760 x^4+1199251252257522113920 x^3+1241607043445255833408 x^2+503999005529666079872 x+75015726412445384192\right)+\sqrt{3} \left(-101039514765271875 x^{10}+41588354535780234375 x^9+242405825655750787500 x^8-29040495604228647000 x^7-1867505744040615995800 x^6-3652370982089483642992 x^5-2467585978417285840640 x^4+159976211179318342080 x^3+1036455491468568561920 x^2+\sqrt{1-2 x} \left(-4988862687295265625 x^9+27881714808393187500 x^8+466853643287368920000 x^7+1362259692111185901000 x^6+1266509714463369063600 x^5-601897061562291658240 x^4-2080193663749965079360 x^3-1635453069288920141568 x^2-566565521800453900032 x-75015726412445384192\right)+491880501770584541440 x+75015726412445384192\right)}{7620480 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right) (3 x+2)^5+\sqrt{1-2 x} \left(7620480 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right) (3 x+2)^5+7620480 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right) (3 x+2)^5\right)+7620480 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right) (3 x+2)^5}-\frac{400}{729} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{2543 \sqrt{1-2 x} (5 x+3)^{5/2}}{1296 (3 x+2)^3}+\frac{37 (1-2 x)^{3/2} (5 x+3)^{5/2}}{72 (3 x+2)^4}-\frac{(1-2 x)^{5/2} (5 x+3)^{5/2}}{15 (3 x+2)^5}-\frac{32453 \sqrt{1-2 x} (5 x+3)^{3/2}}{36288 (3 x+2)^2}-\frac{3248687 \sqrt{1-2 x} \sqrt{5 x+3}}{1524096 (3 x+2)}-\frac{200}{729} \sqrt{10} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{109715471 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{4572288 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-75015726412445384192 - 429313985499796721280*x - 704900393243545385920*x^2 + 299722269840820555520*x^3 + 2076193396553804007040*x^4 + 2127120385619418827792*x^5 + 630498677183315360640*x^6 - 162075700694799650550*x^7 - 102922944074752168125*x^8 - 3877428024877275000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(75015726412445384192 + 503999005529666079872*x + 1241607043445255833408*x^2 + 1199251252257522113920*x^3 - 90646018401293553760*x^4 - 1009011472099117452800*x^5 - 666816715411338879000*x^6 - 133348026005360981250*x^7 + 6637686711828046875*x^8 + 448366511346890625*x^9) + Sqrt[3]*(75015726412445384192 + 491880501770584541440*x + 1036455491468568561920*x^2 + 159976211179318342080*x^3 - 2467585978417285840640*x^4 - 3652370982089483642992*x^5 - 1867505744040615995800*x^6 - 29040495604228647000*x^7 + 242405825655750787500*x^8 + 41588354535780234375*x^9 - 101039514765271875*x^10 + Sqrt[1 - 2*x]*(-75015726412445384192 - 566565521800453900032*x - 1635453069288920141568*x^2 - 2080193663749965079360*x^3 - 601897061562291658240*x^4 + 1266509714463369063600*x^5 + 1362259692111185901000*x^6 + 466853643287368920000*x^7 + 27881714808393187500*x^8 - 4988862687295265625*x^9)))/(7620480*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 7620480*(2 + 3*x)^5*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(7620480*(2 + 3*x)^5*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 7620480*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) - (400*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/729 + (109715471*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/4572288 - (548577355*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/9144576","C",1
2421,1,719,209,3.9208716,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^7} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^7,x]","\frac{8857805 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{175616}-\frac{44289025 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{351232}+\frac{\sqrt{5 x+3} \left(-337518810060700125000 x^{11}+1709698259672955406250 x^{10}+59474165937044476736250 x^9+171029726500990559037000 x^8+30293169208235426944000 x^7-462477104229889683770880 x^6-700978165071322266025920 x^5-350700401318403303284480 x^4+65627424792618982993920 x^3+145042873008551987504640 x^2+58240966819557869642240 x+7987873672387939461120\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(6313431239096640625 x^{11}-1442763838762296500000 x^{10}-13694863370316150093750 x^9+13820082595691458165000 x^8+210466103916164961040000 x^7+439032054076855826193600 x^6+310360196493994842531840 x^5-103978464872468293178880 x^4-316403429026312025419008 x^3-215085245285369965356032 x^2-66219133501066928671232 x-7987873672387939461120\right)+\sqrt{3} \left(36355227109936171875 x^{12}+1269495165776448562500 x^{11}-23222125783985773781250 x^{10}-163297546425338563935000 x^9-246500139881482820313000 x^8+202863436259042341394400 x^7+932738016821127162276480 x^6+988797397764181755640320 x^5+331890727411131924410880 x^4-168578583002764301253120 x^3-190799545474201622115840 x^2-64898616916839485859840 x+\sqrt{1-2 x} \left(142370187790457343750 x^{11}+8103415494744488531250 x^{10}+19994879907273748950000 x^9-109164157467672679185000 x^8-482698379085388981020000 x^7-687369074955221017444800 x^6-288470390576940726359040 x^5+309746593517625507640320 x^4+474950767788205290835968 x^3+267491478689235482491392 x^2+72876783598348544888832 x+7987873672387939461120\right)-7987873672387939461120\right)}{526848 \sqrt{3} \sqrt{5 x+3} \left(-25265212500 x^5+1941218400000 x^4+5284290066000 x^3-24057375117600 x^2-13825440024000 x+16748592098304\right) (3 x+2)^6+\sqrt{1-2 x} \left(526848 \sqrt{3} \sqrt{5 x+3} \left(-2625187500 x^5-345183000000 x^4+1378186950000 x^3+13912170444000 x^2-2687092123200 x-16725373086720\right) (3 x+2)^6+526848 \left(236425406250 x^5+2220611593750 x^4-28520358020000 x^3-52011357156000 x^2+49788771586400 x+50183931760160\right) (3 x+2)^6\right)+526848 \left(23653109375 x^6-916525237500 x^5-21026153381250 x^4+17065853944000 x^3+123670456765200 x^2-301410173760 x-50253588794912\right) (3 x+2)^6}","\frac{121 \sqrt{1-2 x} (5 x+3)^{7/2}}{32 (3 x+2)^4}+\frac{11 (1-2 x)^{3/2} (5 x+3)^{7/2}}{12 (3 x+2)^5}+\frac{(1-2 x)^{5/2} (5 x+3)^{7/2}}{6 (3 x+2)^6}-\frac{1331 \sqrt{1-2 x} (5 x+3)^{5/2}}{1344 (3 x+2)^3}-\frac{73205 \sqrt{1-2 x} (5 x+3)^{3/2}}{37632 (3 x+2)^2}-\frac{805255 \sqrt{1-2 x} \sqrt{5 x+3}}{175616 (3 x+2)}-\frac{8857805 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{175616 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(7987873672387939461120 + 58240966819557869642240*x + 145042873008551987504640*x^2 + 65627424792618982993920*x^3 - 350700401318403303284480*x^4 - 700978165071322266025920*x^5 - 462477104229889683770880*x^6 + 30293169208235426944000*x^7 + 171029726500990559037000*x^8 + 59474165937044476736250*x^9 + 1709698259672955406250*x^10 - 337518810060700125000*x^11) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-7987873672387939461120 - 66219133501066928671232*x - 215085245285369965356032*x^2 - 316403429026312025419008*x^3 - 103978464872468293178880*x^4 + 310360196493994842531840*x^5 + 439032054076855826193600*x^6 + 210466103916164961040000*x^7 + 13820082595691458165000*x^8 - 13694863370316150093750*x^9 - 1442763838762296500000*x^10 + 6313431239096640625*x^11) + Sqrt[3]*(-7987873672387939461120 - 64898616916839485859840*x - 190799545474201622115840*x^2 - 168578583002764301253120*x^3 + 331890727411131924410880*x^4 + 988797397764181755640320*x^5 + 932738016821127162276480*x^6 + 202863436259042341394400*x^7 - 246500139881482820313000*x^8 - 163297546425338563935000*x^9 - 23222125783985773781250*x^10 + 1269495165776448562500*x^11 + 36355227109936171875*x^12 + Sqrt[1 - 2*x]*(7987873672387939461120 + 72876783598348544888832*x + 267491478689235482491392*x^2 + 474950767788205290835968*x^3 + 309746593517625507640320*x^4 - 288470390576940726359040*x^5 - 687369074955221017444800*x^6 - 482698379085388981020000*x^7 - 109164157467672679185000*x^8 + 19994879907273748950000*x^9 + 8103415494744488531250*x^10 + 142370187790457343750*x^11)))/(526848*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(16748592098304 - 13825440024000*x - 24057375117600*x^2 + 5284290066000*x^3 + 1941218400000*x^4 - 25265212500*x^5) + 526848*(2 + 3*x)^6*(-50253588794912 - 301410173760*x + 123670456765200*x^2 + 17065853944000*x^3 - 21026153381250*x^4 - 916525237500*x^5 + 23653109375*x^6) + Sqrt[1 - 2*x]*(526848*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(-16725373086720 - 2687092123200*x + 13912170444000*x^2 + 1378186950000*x^3 - 345183000000*x^4 - 2625187500*x^5) + 526848*(2 + 3*x)^6*(50183931760160 + 49788771586400*x - 52011357156000*x^2 - 28520358020000*x^3 + 2220611593750*x^4 + 236425406250*x^5))) + (8857805*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/175616 - (44289025*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/351232","C",1
2422,1,779,238,4.7417271,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^8} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^8,x]","\frac{327738785 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2458624}-\frac{1638693925 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{4917248}+\frac{\sqrt{5 x+3} \left(-1331047303611819457125000 x^{13}-83402622116040900062534375 x^{12}-97212811922564277811313750 x^{11}+2902272650080831285906175000 x^{10}+10840081748340503070429424000 x^9+11557133925487569484694576640 x^8-7421184039484497565049956992 x^7-28207999309167940886071310016 x^6-25141650392243244776439324032 x^5-6439534202275838261168623360 x^4+4539854549525055840397626880 x^3+4104795251796067587472417792 x^2+1258632445295492817958639616 x+143343174628734040106606592\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(124297428535205851640625 x^{13}+4521029236456117096984375 x^{12}-166156082015332272628593750 x^{11}-1292307249559327071638855000 x^{10}-1596687011543033099169500000 x^9+5851481152000178108893348800 x^8+19860135744485174415211062720 x^7+23184021288743896114552031040 x^6+8258138156551627626371664000 x^5-7952232575812104780927769856 x^4-10879132694182066315988444672 x^3-5577305469353336800311880704 x^2-1401923187654690171901097984 x-143343174628734040106606592\right)+\sqrt{3} \left(-48704368557269341171875 x^{14}+22867688595470661946984375 x^{13}+246668619777325334698175000 x^{12}-857294673593381219541482500 x^{11}-8823134439485212212999485000 x^{10}-19738562213436961351847203600 x^9-10239526237350765482852503680 x^8+24456342570558702240649582272 x^7+46468179893073548461642661376 x^6+31225545014123723259455320832 x^5+3760432501088625069166543360 x^4-7564944576303452689493923840 x^3-5103866746085832421845379072 x^2-1378089174588850351380811776 x+\sqrt{1-2 x} \left(-2081094579393767311171875 x^{13}+22952461947443864657937500 x^{12}+762072198390070455155537500 x^{11}+2708296238219389332149745000 x^{10}-316754378025286118456770000 x^9-17067485340114040021017326400 x^8-35863121794406883761214745920 x^7-30930786492775756974064170240 x^6-4167025301289477287142859520 x^5+15444199892110152425544623616 x^4+15081550023438305094554273792 x^3+6695789999378511929636890624 x^2+1521379916948047705323270144 x+143343174628734040106606592\right)-143343174628734040106606592\right)}{7375872 \sqrt{3} \sqrt{5 x+3} \left(-5663973218750 x^6-52303209612500 x^5+1428846604955000 x^4+2194696763160000 x^3-7555736895916000 x^2-3365532949972160 x+4051435671804928\right) (3 x+2)^7+\sqrt{1-2 x} \left(7375872 \left(-3042263984375 x^6+486365726000000 x^5+1796810007300000 x^4-11790948756840000 x^3-17392813876790000 x^2+12117692004316800 x+12149682333912640\right) (3 x+2)^7+7375872 \sqrt{3} \sqrt{5 x+3} \left(223405156250 x^6-14941831687500 x^5-390402719125000 x^4+702446326920000 x^3+4956682106340000 x^2-666120123963200 x-4049763902970880\right) (3 x+2)^7\right)+7375872 \left(905821796875 x^7+135547777203125 x^6-996207107350000 x^5-11461663884510000 x^4+5424159101550000 x^3+35265969543725200 x^2-26521579595840 x-12154697640414784\right) (3 x+2)^7}","\frac{4477 \sqrt{1-2 x} (5 x+3)^{7/2}}{448 (3 x+2)^4}+\frac{407 (1-2 x)^{3/2} (5 x+3)^{7/2}}{168 (3 x+2)^5}+\frac{37 (1-2 x)^{5/2} (5 x+3)^{7/2}}{84 (3 x+2)^6}+\frac{3 (1-2 x)^{7/2} (5 x+3)^{7/2}}{49 (3 x+2)^7}-\frac{49247 \sqrt{1-2 x} (5 x+3)^{5/2}}{18816 (3 x+2)^3}-\frac{2708585 \sqrt{1-2 x} (5 x+3)^{3/2}}{526848 (3 x+2)^2}-\frac{29794435 \sqrt{1-2 x} \sqrt{5 x+3}}{2458624 (3 x+2)}-\frac{327738785 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2458624 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(143343174628734040106606592 + 1258632445295492817958639616*x + 4104795251796067587472417792*x^2 + 4539854549525055840397626880*x^3 - 6439534202275838261168623360*x^4 - 25141650392243244776439324032*x^5 - 28207999309167940886071310016*x^6 - 7421184039484497565049956992*x^7 + 11557133925487569484694576640*x^8 + 10840081748340503070429424000*x^9 + 2902272650080831285906175000*x^10 - 97212811922564277811313750*x^11 - 83402622116040900062534375*x^12 - 1331047303611819457125000*x^13) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-143343174628734040106606592 - 1401923187654690171901097984*x - 5577305469353336800311880704*x^2 - 10879132694182066315988444672*x^3 - 7952232575812104780927769856*x^4 + 8258138156551627626371664000*x^5 + 23184021288743896114552031040*x^6 + 19860135744485174415211062720*x^7 + 5851481152000178108893348800*x^8 - 1596687011543033099169500000*x^9 - 1292307249559327071638855000*x^10 - 166156082015332272628593750*x^11 + 4521029236456117096984375*x^12 + 124297428535205851640625*x^13) + Sqrt[3]*(-143343174628734040106606592 - 1378089174588850351380811776*x - 5103866746085832421845379072*x^2 - 7564944576303452689493923840*x^3 + 3760432501088625069166543360*x^4 + 31225545014123723259455320832*x^5 + 46468179893073548461642661376*x^6 + 24456342570558702240649582272*x^7 - 10239526237350765482852503680*x^8 - 19738562213436961351847203600*x^9 - 8823134439485212212999485000*x^10 - 857294673593381219541482500*x^11 + 246668619777325334698175000*x^12 + 22867688595470661946984375*x^13 - 48704368557269341171875*x^14 + Sqrt[1 - 2*x]*(143343174628734040106606592 + 1521379916948047705323270144*x + 6695789999378511929636890624*x^2 + 15081550023438305094554273792*x^3 + 15444199892110152425544623616*x^4 - 4167025301289477287142859520*x^5 - 30930786492775756974064170240*x^6 - 35863121794406883761214745920*x^7 - 17067485340114040021017326400*x^8 - 316754378025286118456770000*x^9 + 2708296238219389332149745000*x^10 + 762072198390070455155537500*x^11 + 22952461947443864657937500*x^12 - 2081094579393767311171875*x^13)))/(7375872*Sqrt[3]*(2 + 3*x)^7*Sqrt[3 + 5*x]*(4051435671804928 - 3365532949972160*x - 7555736895916000*x^2 + 2194696763160000*x^3 + 1428846604955000*x^4 - 52303209612500*x^5 - 5663973218750*x^6) + 7375872*(2 + 3*x)^7*(-12154697640414784 - 26521579595840*x + 35265969543725200*x^2 + 5424159101550000*x^3 - 11461663884510000*x^4 - 996207107350000*x^5 + 135547777203125*x^6 + 905821796875*x^7) + Sqrt[1 - 2*x]*(7375872*(2 + 3*x)^7*(12149682333912640 + 12117692004316800*x - 17392813876790000*x^2 - 11790948756840000*x^3 + 1796810007300000*x^4 + 486365726000000*x^5 - 3042263984375*x^6) + 7375872*Sqrt[3]*(2 + 3*x)^7*Sqrt[3 + 5*x]*(-4049763902970880 - 666120123963200*x + 4956682106340000*x^2 + 702446326920000*x^3 - 390402719125000*x^4 - 14941831687500*x^5 + 223405156250*x^6))) + (327738785*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2458624 - (1638693925*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/4917248","C",1
2423,1,839,267,5.8168573,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^9} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^9,x]","\frac{\sqrt{5 x+3} \left(-131879141368451272950907500000 x^{15}+2839418789303887047644231625000 x^{14}+87789180302622349941479903825000 x^{13}+262542279672244650488827992850000 x^{12}-738551176415301061379442825730000 x^{11}-4579850864141546773303209174684800 x^{10}-7734370946053196446696089546687360 x^9-3192014454361406381697254974912896 x^8+6770405650692156567601539065413248 x^7+11033279642073993682365836857119232 x^6+6366878072133812858416390874333696 x^5+363729203111049333793202742353920 x^4-1586494633393942988937610623432704 x^3-934595800867656668084661327290368 x^2-232148493142271225641444893171712 x-22585995918604662363806442356736\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(818022215272474847598046875 x^{15}-908022556247633877969105000000 x^{14}-10416665037415872212929269312500 x^{13}+83562871152666528414440150250000 x^{12}+771481948388101419092008298150000 x^{11}+1727116393596907699683472133264000 x^{10}+38718213297575275225239979780800 x^9-5835211712471239123216898452757760 x^8-10506533772398461290071556857900160 x^7-7875390771745405479253499568291840 x^6-852528280220438808868946116014592 x^5+3298202282075320814498270399080448 x^4+2925046173990223693589746767022080 x^3+1200562100911028912166343322845184 x^2+254732025507129529322246268854272 x+22585995918604662363806442356736\right)+\sqrt{3} \left(12374040200426216186389453125 x^{16}+423691912075625238458985000000 x^{15}-30766039888378572567923584000000 x^{14}-262744423936177615907400176700000 x^{13}-149969259380281236220317385800000 x^{12}+3012491523464378174905948985328000 x^{11}+9605674701053007212184079467110400 x^{10}+11027804271605192767622749310039040 x^9-88456659882296611897248664047744 x^8-14097866728732207932669612620433408 x^7-15963686039749966472415254258829312 x^6-7012457585253473365982852447748096 x^5+694209768601592366917504680038400 x^4+2291251879167633043977511431634944 x^3+1120209897438184054742877056892928 x^2+250970289656206377194616928468992 x+\sqrt{1-2 x} \left(85903966159050131929546875000 x^{15}+5961542058014338861219378125000 x^{14}+1037062642671622470697208250000 x^{13}-417291908160389073736938945250000 x^{12}-1858574839254528920956465903000000 x^{11}-2358519166260346307390697659640000 x^{10}+2806710422305048226264534233392000 x^9+12466973893161543016633196794738560 x^8+16377418924744114157228126214696960 x^7+9166916080918188676529870743193600 x^6-1158883337206041718140034007400448 x^5-5385784676862088465741655794434048 x^4-3843600077358611924572437649408000 x^3-1404995941034036151475226865516544 x^2-273553822021064680875418304151552 x-22585995918604662363806442356736\right)+22585995918604662363806442356736\right)}{826097664 \sqrt{3} \sqrt{5 x+3} \left(-37171901250000 x^7+15172614638500000 x^6+48893843935200000 x^5-745683451048800000 x^4-779154494418080000 x^3+2242423760579059200 x^2+816076994481239040 x-980317832225898496\right) (3 x+2)^8+826097664 \left(62492437890625 x^8-6770478145000000 x^7-196992069589500000 x^6+638594105804400000 x^5+4962095357691300000 x^4-1578419941107136000 x^3-9786297447342252800 x^2+2251097121029120 x+2940973027927695488\right) (3 x+2)^8+\sqrt{1-2 x} \left(826097664 \sqrt{3} \sqrt{5 x+3} \left(-10175243750000 x^7-1679546817500000 x^6+21097160796000000 x^5+264747438084000000 x^4-281640167973600000 x^3-1598594601059136000 x^2+162615878437964800 x+980197464869847040\right) (3 x+2)^8+826097664 \left(988351203125000 x^7+8768813934375000 x^6-449445803870250000 x^5-1038239639951250000 x^4+4168896450367000000 x^3+5408235606946920000 x^2-2938048328738512000 x-2940611925859541120\right) (3 x+2)^8\right)}+\frac{106656830005 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(-\sqrt{5 x+3} \text{$\#$1}+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{275365888}-\frac{533284150025 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\sqrt{3}-\sqrt{5 x+3}\right) \text{$\#$1}^2-\log \left(-\sqrt{5 x+3} \text{$\#$1}+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right) \text{$\#$1}^2}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{550731776}","\frac{47365 \sqrt{1-2 x} (5 x+3)^{5/2}}{36288 (3 x+2)^6}+\frac{185 (1-2 x)^{3/2} (5 x+3)^{5/2}}{1008 (3 x+2)^7}-\frac{(1-2 x)^{5/2} (5 x+3)^{5/2}}{24 (3 x+2)^8}-\frac{720833 \sqrt{1-2 x} (5 x+3)^{3/2}}{508032 (3 x+2)^5}+\frac{6796051494355 \sqrt{1-2 x} \sqrt{5 x+3}}{200741732352 (3 x+2)}+\frac{64983635965 \sqrt{1-2 x} \sqrt{5 x+3}}{14338695168 (3 x+2)^2}+\frac{372439373 \sqrt{1-2 x} \sqrt{5 x+3}}{512096256 (3 x+2)^3}-\frac{75045071 \sqrt{1-2 x} \sqrt{5 x+3}}{85349376 (3 x+2)^4}-\frac{106656830005 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{275365888 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-22585995918604662363806442356736 - 232148493142271225641444893171712*x - 934595800867656668084661327290368*x^2 - 1586494633393942988937610623432704*x^3 + 363729203111049333793202742353920*x^4 + 6366878072133812858416390874333696*x^5 + 11033279642073993682365836857119232*x^6 + 6770405650692156567601539065413248*x^7 - 3192014454361406381697254974912896*x^8 - 7734370946053196446696089546687360*x^9 - 4579850864141546773303209174684800*x^10 - 738551176415301061379442825730000*x^11 + 262542279672244650488827992850000*x^12 + 87789180302622349941479903825000*x^13 + 2839418789303887047644231625000*x^14 - 131879141368451272950907500000*x^15) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(22585995918604662363806442356736 + 254732025507129529322246268854272*x + 1200562100911028912166343322845184*x^2 + 2925046173990223693589746767022080*x^3 + 3298202282075320814498270399080448*x^4 - 852528280220438808868946116014592*x^5 - 7875390771745405479253499568291840*x^6 - 10506533772398461290071556857900160*x^7 - 5835211712471239123216898452757760*x^8 + 38718213297575275225239979780800*x^9 + 1727116393596907699683472133264000*x^10 + 771481948388101419092008298150000*x^11 + 83562871152666528414440150250000*x^12 - 10416665037415872212929269312500*x^13 - 908022556247633877969105000000*x^14 + 818022215272474847598046875*x^15) + Sqrt[3]*(22585995918604662363806442356736 + 250970289656206377194616928468992*x + 1120209897438184054742877056892928*x^2 + 2291251879167633043977511431634944*x^3 + 694209768601592366917504680038400*x^4 - 7012457585253473365982852447748096*x^5 - 15963686039749966472415254258829312*x^6 - 14097866728732207932669612620433408*x^7 - 88456659882296611897248664047744*x^8 + 11027804271605192767622749310039040*x^9 + 9605674701053007212184079467110400*x^10 + 3012491523464378174905948985328000*x^11 - 149969259380281236220317385800000*x^12 - 262744423936177615907400176700000*x^13 - 30766039888378572567923584000000*x^14 + 423691912075625238458985000000*x^15 + 12374040200426216186389453125*x^16 + Sqrt[1 - 2*x]*(-22585995918604662363806442356736 - 273553822021064680875418304151552*x - 1404995941034036151475226865516544*x^2 - 3843600077358611924572437649408000*x^3 - 5385784676862088465741655794434048*x^4 - 1158883337206041718140034007400448*x^5 + 9166916080918188676529870743193600*x^6 + 16377418924744114157228126214696960*x^7 + 12466973893161543016633196794738560*x^8 + 2806710422305048226264534233392000*x^9 - 2358519166260346307390697659640000*x^10 - 1858574839254528920956465903000000*x^11 - 417291908160389073736938945250000*x^12 + 1037062642671622470697208250000*x^13 + 5961542058014338861219378125000*x^14 + 85903966159050131929546875000*x^15)))/(826097664*Sqrt[3]*(2 + 3*x)^8*Sqrt[3 + 5*x]*(-980317832225898496 + 816076994481239040*x + 2242423760579059200*x^2 - 779154494418080000*x^3 - 745683451048800000*x^4 + 48893843935200000*x^5 + 15172614638500000*x^6 - 37171901250000*x^7) + 826097664*(2 + 3*x)^8*(2940973027927695488 + 2251097121029120*x - 9786297447342252800*x^2 - 1578419941107136000*x^3 + 4962095357691300000*x^4 + 638594105804400000*x^5 - 196992069589500000*x^6 - 6770478145000000*x^7 + 62492437890625*x^8) + Sqrt[1 - 2*x]*(826097664*Sqrt[3]*(2 + 3*x)^8*Sqrt[3 + 5*x]*(980197464869847040 + 162615878437964800*x - 1598594601059136000*x^2 - 281640167973600000*x^3 + 264747438084000000*x^4 + 21097160796000000*x^5 - 1679546817500000*x^6 - 10175243750000*x^7) + 826097664*(2 + 3*x)^8*(-2940611925859541120 - 2938048328738512000*x + 5408235606946920000*x^2 + 4168896450367000000*x^3 - 1038239639951250000*x^4 - 449445803870250000*x^5 + 8768813934375000*x^6 + 988351203125000*x^7))) + (106656830005*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/275365888 - (533284150025*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/550731776","C",1
2424,1,546,179,3.570876,"\int \frac{(1-2 x)^{5/2} (2+3 x)^4}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^4)/Sqrt[3 + 5*x],x]","\frac{12679836719 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{640000000 \sqrt{10}}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(225397449360000000000000 x^{13}+34010997412734000000000000 x^{12}-205767728213856660000000000 x^{11}-3182878056846909138750000000 x^{10}-2113241758717190638062500000 x^9+12439525364503768708056562500 x^8+13334917663934625690089828125 x^7-10109070845912452848889684375 x^6-14514237740930028774228637500 x^5+3170160967605249715275505000 x^4+6828826062707650084137520400 x^3-330431690544304107255295920 x^2-1199349699378106147058003200 x+22375315675788955465253184\right)+\sqrt{5 x+3} \left(1514025263520000000000000 x^{13}-240906988090692000000000000 x^{12}-1078263456516088920000000000 x^{11}+5489068962631109872500000000 x^{10}+14361952512600127574425000000 x^9-6109698214326057809376875000 x^8-26574994330213970456411406250 x^7-674264960601658492782821875 x^6+20110546105406796641882087500 x^5+2841913725280957134206399000 x^4-7773262287088094465187402400 x^3-863149579778480360110030000 x^2+1221228597150147975985245760 x-22375315675788955465253184\right)+\sqrt{3} \left(-555903518400000000000000 x^{14}+36428044698360000000000000 x^{13}+1022170849035008400000000000 x^{12}-461500249672694295000000000 x^{11}-15503047065705172373750000000 x^{10}-15176560335612278440993750000 x^9+24687537184344881624165937500 x^8+31829057773565355172047921875 x^7-13579118589223697730534321875 x^6-24528017112156642913715162500 x^5+2964643127593886461085993000 x^4+8926342454605147737941868400 x^3-162848202655003197079151600 x^2-1202543836467921437576701440 x+\sqrt{1-2 x} \left(-7046888919840000000000000 x^{13}-78129880464636000000000000 x^{12}+1656039211987323240000000000 x^{11}+6024354835626465277500000000 x^{10}-3962648132608633972075000000 x^9-23744945572008908059113125000 x^8-9241973779791133095854906250 x^7+21678965998954341612427440625 x^6+13953285665590741870381712500 x^5-8613022622581738839312681000 x^4-6979178250570316311326352800 x^3+1338158393882017064817608720 x^2+1180664938695879608649458880 x-22375315675788955465253184\right)+22375315675788955465253184\right)}{26880000000 \sqrt{3} \sqrt{5 x+3} \left(-5663973218750 x^6-52303209612500 x^5+1428846604955000 x^4+2194696763160000 x^3-7555736895916000 x^2-3365532949972160 x+4051435671804928\right)+\sqrt{1-2 x} \left(26880000000 \left(-3042263984375 x^6+486365726000000 x^5+1796810007300000 x^4-11790948756840000 x^3-17392813876790000 x^2+12117692004316800 x+12149682333912640\right)+26880000000 \sqrt{3} \sqrt{5 x+3} \left(223405156250 x^6-14941831687500 x^5-390402719125000 x^4+702446326920000 x^3+4956682106340000 x^2-666120123963200 x-4049763902970880\right)\right)+26880000000 \left(905821796875 x^7+135547777203125 x^6-996207107350000 x^5-11461663884510000 x^4+5424159101550000 x^3+35265969543725200 x^2-26521579595840 x-12154697640414784\right)}","-\frac{\sqrt{5 x+3} (11603280 x+12923401) (1-2 x)^{7/2}}{22400000}-\frac{3}{70} (3 x+2)^3 \sqrt{5 x+3} (1-2 x)^{7/2}-\frac{271 (3 x+2)^2 \sqrt{5 x+3} (1-2 x)^{7/2}}{2800}+\frac{9526549 \sqrt{5 x+3} (1-2 x)^{5/2}}{96000000}+\frac{104792039 \sqrt{5 x+3} (1-2 x)^{3/2}}{384000000}+\frac{1152712429 \sqrt{5 x+3} \sqrt{1-2 x}}{1280000000}+\frac{12679836719 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{1280000000 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(22375315675788955465253184 - 1199349699378106147058003200*x - 330431690544304107255295920*x^2 + 6828826062707650084137520400*x^3 + 3170160967605249715275505000*x^4 - 14514237740930028774228637500*x^5 - 10109070845912452848889684375*x^6 + 13334917663934625690089828125*x^7 + 12439525364503768708056562500*x^8 - 2113241758717190638062500000*x^9 - 3182878056846909138750000000*x^10 - 205767728213856660000000000*x^11 + 34010997412734000000000000*x^12 + 225397449360000000000000*x^13) + Sqrt[3 + 5*x]*(-22375315675788955465253184 + 1221228597150147975985245760*x - 863149579778480360110030000*x^2 - 7773262287088094465187402400*x^3 + 2841913725280957134206399000*x^4 + 20110546105406796641882087500*x^5 - 674264960601658492782821875*x^6 - 26574994330213970456411406250*x^7 - 6109698214326057809376875000*x^8 + 14361952512600127574425000000*x^9 + 5489068962631109872500000000*x^10 - 1078263456516088920000000000*x^11 - 240906988090692000000000000*x^12 + 1514025263520000000000000*x^13) + Sqrt[3]*(22375315675788955465253184 - 1202543836467921437576701440*x - 162848202655003197079151600*x^2 + 8926342454605147737941868400*x^3 + 2964643127593886461085993000*x^4 - 24528017112156642913715162500*x^5 - 13579118589223697730534321875*x^6 + 31829057773565355172047921875*x^7 + 24687537184344881624165937500*x^8 - 15176560335612278440993750000*x^9 - 15503047065705172373750000000*x^10 - 461500249672694295000000000*x^11 + 1022170849035008400000000000*x^12 + 36428044698360000000000000*x^13 - 555903518400000000000000*x^14 + Sqrt[1 - 2*x]*(-22375315675788955465253184 + 1180664938695879608649458880*x + 1338158393882017064817608720*x^2 - 6979178250570316311326352800*x^3 - 8613022622581738839312681000*x^4 + 13953285665590741870381712500*x^5 + 21678965998954341612427440625*x^6 - 9241973779791133095854906250*x^7 - 23744945572008908059113125000*x^8 - 3962648132608633972075000000*x^9 + 6024354835626465277500000000*x^10 + 1656039211987323240000000000*x^11 - 78129880464636000000000000*x^12 - 7046888919840000000000000*x^13)))/(26880000000*Sqrt[3]*Sqrt[3 + 5*x]*(4051435671804928 - 3365532949972160*x - 7555736895916000*x^2 + 2194696763160000*x^3 + 1428846604955000*x^4 - 52303209612500*x^5 - 5663973218750*x^6) + 26880000000*(-12154697640414784 - 26521579595840*x + 35265969543725200*x^2 + 5424159101550000*x^3 - 11461663884510000*x^4 - 996207107350000*x^5 + 135547777203125*x^6 + 905821796875*x^7) + Sqrt[1 - 2*x]*(26880000000*(12149682333912640 + 12117692004316800*x - 17392813876790000*x^2 - 11790948756840000*x^3 + 1796810007300000*x^4 + 486365726000000*x^5 - 3042263984375*x^6) + 26880000000*Sqrt[3]*Sqrt[3 + 5*x]*(-4049763902970880 - 666120123963200*x + 4956682106340000*x^2 + 702446326920000*x^3 - 390402719125000*x^4 - 14941831687500*x^5 + 223405156250*x^6))) + (12679836719*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(640000000*Sqrt[10])","B",1
2425,1,486,150,2.9336642,"\int \frac{(1-2 x)^{5/2} (2+3 x)^3}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^3)/Sqrt[3 + 5*x],x]","\frac{368012183 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{32000000 \sqrt{10}}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-16349029200000000000 x^{11}+625491219852000000000 x^{10}+14860943586193050000000 x^9-5337505433330562500000 x^8-106817678969832590187500 x^7-33842176532414947921875 x^6+136094353057958183465000 x^5+40888780833858789352250 x^4-78951993927927121002000 x^3-18250099911739847123440 x^2+17150723692720379922560 x+4007116126352328774048\right)+\sqrt{5 x+3} \left(326834481600000000000 x^{11}+3066505122384000000000 x^{10}-39882166341910200000000 x^9-75435469523056830000000 x^8+121600923056156431250000 x^7+156649276246991754187500 x^6-130115961208998790451250 x^5-117194896131414789162750 x^4+71855119080861997623600 x^3+37588968884807789908800 x^2-13120760483285222340320 x-4007116126352328774048\right)+\sqrt{3} \left(-18145296000000000000 x^{12}-2396610620640000000000 x^{11}+8142044334498000000000 x^{10}+104908289418177300000000 x^9+27115309965616792500000 x^8-259623738976798198125000 x^7-93951218264414473659375 x^6+238058157082366782060000 x^5+73577310761768193302250 x^4-106767016980119031903600 x^3-28012825690276967914800 x^2+16457461469502006735360 x+\sqrt{1-2 x} \left(87316574400000000000 x^{11}-6613675724304000000000 x^{10}-25641612657322200000000 x^9+68257612447887390000000 x^8+158847289155648299250000 x^7-53199785859854021437500 x^6-187700125271242387773750 x^5+14339180966494925747250 x^4+99117768251408949517200 x^3+5318216495089883394240 x^2-20487424678937164317600 x-4007116126352328774048\right)+4007116126352328774048\right)}{192000000 \sqrt{3} \sqrt{5 x+3} \left(25265212500 x^5-1941218400000 x^4-5284290066000 x^3+24057375117600 x^2+13825440024000 x-16748592098304\right)+\sqrt{1-2 x} \left(192000000 \left(-236425406250 x^5-2220611593750 x^4+28520358020000 x^3+52011357156000 x^2-49788771586400 x-50183931760160\right)+192000000 \sqrt{3} \sqrt{5 x+3} \left(2625187500 x^5+345183000000 x^4-1378186950000 x^3-13912170444000 x^2+2687092123200 x+16725373086720\right)\right)+192000000 \left(-23653109375 x^6+916525237500 x^5+21026153381250 x^4-17065853944000 x^3-123670456765200 x^2+301410173760 x+50253588794912\right)}","-\frac{\sqrt{5 x+3} (47280 x+52951) (1-2 x)^{7/2}}{160000}-\frac{1}{20} (3 x+2)^2 \sqrt{5 x+3} (1-2 x)^{7/2}+\frac{276493 \sqrt{5 x+3} (1-2 x)^{5/2}}{4800000}+\frac{3041423 \sqrt{5 x+3} (1-2 x)^{3/2}}{19200000}+\frac{33455653 \sqrt{5 x+3} \sqrt{1-2 x}}{64000000}+\frac{368012183 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{64000000 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(4007116126352328774048 + 17150723692720379922560*x - 18250099911739847123440*x^2 - 78951993927927121002000*x^3 + 40888780833858789352250*x^4 + 136094353057958183465000*x^5 - 33842176532414947921875*x^6 - 106817678969832590187500*x^7 - 5337505433330562500000*x^8 + 14860943586193050000000*x^9 + 625491219852000000000*x^10 - 16349029200000000000*x^11) + Sqrt[3 + 5*x]*(-4007116126352328774048 - 13120760483285222340320*x + 37588968884807789908800*x^2 + 71855119080861997623600*x^3 - 117194896131414789162750*x^4 - 130115961208998790451250*x^5 + 156649276246991754187500*x^6 + 121600923056156431250000*x^7 - 75435469523056830000000*x^8 - 39882166341910200000000*x^9 + 3066505122384000000000*x^10 + 326834481600000000000*x^11) + Sqrt[3]*(4007116126352328774048 + 16457461469502006735360*x - 28012825690276967914800*x^2 - 106767016980119031903600*x^3 + 73577310761768193302250*x^4 + 238058157082366782060000*x^5 - 93951218264414473659375*x^6 - 259623738976798198125000*x^7 + 27115309965616792500000*x^8 + 104908289418177300000000*x^9 + 8142044334498000000000*x^10 - 2396610620640000000000*x^11 - 18145296000000000000*x^12 + Sqrt[1 - 2*x]*(-4007116126352328774048 - 20487424678937164317600*x + 5318216495089883394240*x^2 + 99117768251408949517200*x^3 + 14339180966494925747250*x^4 - 187700125271242387773750*x^5 - 53199785859854021437500*x^6 + 158847289155648299250000*x^7 + 68257612447887390000000*x^8 - 25641612657322200000000*x^9 - 6613675724304000000000*x^10 + 87316574400000000000*x^11)))/(192000000*Sqrt[3]*Sqrt[3 + 5*x]*(-16748592098304 + 13825440024000*x + 24057375117600*x^2 - 5284290066000*x^3 - 1941218400000*x^4 + 25265212500*x^5) + 192000000*(50253588794912 + 301410173760*x - 123670456765200*x^2 - 17065853944000*x^3 + 21026153381250*x^4 + 916525237500*x^5 - 23653109375*x^6) + Sqrt[1 - 2*x]*(192000000*(-50183931760160 - 49788771586400*x + 52011357156000*x^2 + 28520358020000*x^3 - 2220611593750*x^4 - 236425406250*x^5) + 192000000*Sqrt[3]*Sqrt[3 + 5*x]*(16725373086720 + 2687092123200*x - 13912170444000*x^2 - 1378186950000*x^3 + 345183000000*x^4 + 2625187500*x^5))) + (368012183*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(32000000*Sqrt[10])","B",1
2426,1,426,143,2.6022326,"\int \frac{(1-2 x)^{5/2} (2+3 x)^2}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^2)/Sqrt[3 + 5*x],x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(1529301600000000 x^9+169735817070000000 x^8-366359400501500000 x^7-2912029503230062500 x^6+1304092902984796875 x^5+3903431469486693875 x^4-1956045643196531100 x^3-2057367406804145180 x^2+755790743498200640 x+621871957244433456\right)+\sqrt{5 x+3} \left(18934344000000000 x^9-728817140700000000 x^8-1339975587115000000 x^7+4914290397410625000 x^6+1318441491979218750 x^5-6221119593660929375 x^4+590618649285731000 x^3+3137802184019446900 x^2-130886391564296720 x-621871957244433456\right)+\sqrt{3} \left(-5704560000000000 x^{10}+118305837000000000 x^9+2241003992450000000 x^8-1366442300508750000 x^7-7349900182697812500 x^6+3126718506695865625 x^5+6779281551126886875 x^4-3106249386317698500 x^3-3238301279651867500 x^2+\sqrt{1-2 x} \left(-43815816000000000 x^9-341197668900000000 x^8+2351630041893000000 x^7+2972594912095875000 x^6-4487437791649106250 x^5-3102425783271354375 x^4+3782672692315627000 x^3+1637602624496854180 x^2-1273527625863353520 x-621871957244433456\right)+648623273929449600 x+621871957244433456\right)}{4800000 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right)+\sqrt{1-2 x} \left(4800000 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right)+4800000 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right)\right)+4800000 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right)}+\frac{6531217 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{800000 \sqrt{10}}","-\frac{3}{50} (3 x+2) \sqrt{5 x+3} (1-2 x)^{7/2}-\frac{369 \sqrt{5 x+3} (1-2 x)^{7/2}}{4000}+\frac{4907 \sqrt{5 x+3} (1-2 x)^{5/2}}{120000}+\frac{53977 \sqrt{5 x+3} (1-2 x)^{3/2}}{480000}+\frac{593747 \sqrt{5 x+3} \sqrt{1-2 x}}{1600000}+\frac{6531217 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{1600000 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(621871957244433456 + 755790743498200640*x - 2057367406804145180*x^2 - 1956045643196531100*x^3 + 3903431469486693875*x^4 + 1304092902984796875*x^5 - 2912029503230062500*x^6 - 366359400501500000*x^7 + 169735817070000000*x^8 + 1529301600000000*x^9) + Sqrt[3 + 5*x]*(-621871957244433456 - 130886391564296720*x + 3137802184019446900*x^2 + 590618649285731000*x^3 - 6221119593660929375*x^4 + 1318441491979218750*x^5 + 4914290397410625000*x^6 - 1339975587115000000*x^7 - 728817140700000000*x^8 + 18934344000000000*x^9) + Sqrt[3]*(621871957244433456 + 648623273929449600*x - 3238301279651867500*x^2 - 3106249386317698500*x^3 + 6779281551126886875*x^4 + 3126718506695865625*x^5 - 7349900182697812500*x^6 - 1366442300508750000*x^7 + 2241003992450000000*x^8 + 118305837000000000*x^9 - 5704560000000000*x^10 + Sqrt[1 - 2*x]*(-621871957244433456 - 1273527625863353520*x + 1637602624496854180*x^2 + 3782672692315627000*x^3 - 3102425783271354375*x^4 - 4487437791649106250*x^5 + 2972594912095875000*x^6 + 2351630041893000000*x^7 - 341197668900000000*x^8 - 43815816000000000*x^9)))/(4800000*Sqrt[3]*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 4800000*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(4800000*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 4800000*Sqrt[3]*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (6531217*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(800000*Sqrt[10])","B",1
2427,1,366,116,2.1604406,"\int \frac{(1-2 x)^{5/2} (2+3 x)}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x))/Sqrt[3 + 5*x],x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-246258000000 x^7+2598804500000 x^6+33250801057500 x^5-45194123378625 x^4-18300193629800 x^3+60944298887880 x^2-5627875427360 x-36933177760776\right)+\sqrt{5 x+3} \left(2792592000000 x^7+12293943200000 x^6-73365807900000 x^5+44250388215000 x^4+63418187532700 x^3-84022848017900 x^2-31297112525800 x+36933177760776\right)+\sqrt{3} \left(-171360000000 x^8-15122008000000 x^7+27813586600000 x^6+74389433190000 x^5-112727769781625 x^4-13130395034200 x^3+122717873954600 x^2+\sqrt{1-2 x} \left(1284624000000 x^7-24278170400000 x^6-17832148620000 x^5+77241259953000 x^4-25363872711100 x^3-68866596842780 x^2+36407428248840 x+36933177760776\right)+517559704320 x-36933177760776\right)}{48000 \sqrt{3} \sqrt{5 x+3} \left(8921000 x^3-162998000 x^2-220512160 x+287530496\right)+\sqrt{1-2 x} \left(48000 \left(-48482500 x^3-297203500 x^2+794989800 x+852279560\right)+48000 \sqrt{3} \sqrt{5 x+3} \left(595000 x^3+53178000 x^2-36412000 x-283051520\right)\right)+48000 \left(-8550625 x^4+79738000 x^3+1253327000 x^2-32289760 x-865716488\right)}+\frac{65219 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{8000 \sqrt{10}}","-\frac{3}{40} \sqrt{5 x+3} (1-2 x)^{7/2}+\frac{49 \sqrt{5 x+3} (1-2 x)^{5/2}}{1200}+\frac{539 \sqrt{5 x+3} (1-2 x)^{3/2}}{4800}+\frac{5929 \sqrt{5 x+3} \sqrt{1-2 x}}{16000}+\frac{65219 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{16000 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-36933177760776 - 5627875427360*x + 60944298887880*x^2 - 18300193629800*x^3 - 45194123378625*x^4 + 33250801057500*x^5 + 2598804500000*x^6 - 246258000000*x^7) + Sqrt[3 + 5*x]*(36933177760776 - 31297112525800*x - 84022848017900*x^2 + 63418187532700*x^3 + 44250388215000*x^4 - 73365807900000*x^5 + 12293943200000*x^6 + 2792592000000*x^7) + Sqrt[3]*(-36933177760776 + 517559704320*x + 122717873954600*x^2 - 13130395034200*x^3 - 112727769781625*x^4 + 74389433190000*x^5 + 27813586600000*x^6 - 15122008000000*x^7 - 171360000000*x^8 + Sqrt[1 - 2*x]*(36933177760776 + 36407428248840*x - 68866596842780*x^2 - 25363872711100*x^3 + 77241259953000*x^4 - 17832148620000*x^5 - 24278170400000*x^6 + 1284624000000*x^7)))/(48000*Sqrt[3]*Sqrt[3 + 5*x]*(287530496 - 220512160*x - 162998000*x^2 + 8921000*x^3) + 48000*(-865716488 - 32289760*x + 1253327000*x^2 + 79738000*x^3 - 8550625*x^4) + Sqrt[1 - 2*x]*(48000*(852279560 + 794989800*x - 297203500*x^2 - 48482500*x^3) + 48000*Sqrt[3]*Sqrt[3 + 5*x]*(-283051520 - 36412000*x + 53178000*x^2 + 595000*x^3))) + (65219*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(8000*Sqrt[10])","B",1
2428,1,306,94,1.7632841,"\int \frac{(1-2 x)^{5/2}}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/Sqrt[3 + 5*x],x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(7180000 x^5+459191500 x^4-1152708225 x^3+1091186435 x^2+1101433040 x-3635243172\right)+\sqrt{5 x+3} \left(125400000 x^5-1265165000 x^4+2037877050 x^3-1326188325 x^2-4649802740 x+3635243172\right)+\sqrt{3} \left(-46800000 x^6+261510000 x^5+1345618500 x^4-3759419175 x^3+6597899175 x^2+\sqrt{1-2 x} \left(-183480000 x^5-301059000 x^4+1747015050 x^3-3376828785 x^2+1957030020 x+3635243172\right)+1591339680 x-3635243172\right)}{600 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right)+\sqrt{1-2 x} \left(600 \left(-391875 x^2+2827000 x+3481060\right)+600 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right)\right)+600 \left(44875 x^3+2976525 x^2-279060 x-3667684\right)}+\frac{1331 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{100 \sqrt{10}}","\frac{1}{15} \sqrt{5 x+3} (1-2 x)^{5/2}+\frac{11}{60} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{121}{200} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{1331 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{200 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-3635243172 + 1101433040*x + 1091186435*x^2 - 1152708225*x^3 + 459191500*x^4 + 7180000*x^5) + Sqrt[3 + 5*x]*(3635243172 - 4649802740*x - 1326188325*x^2 + 2037877050*x^3 - 1265165000*x^4 + 125400000*x^5) + Sqrt[3]*(-3635243172 + 1591339680*x + 6597899175*x^2 - 3759419175*x^3 + 1345618500*x^4 + 261510000*x^5 - 46800000*x^6 + Sqrt[1 - 2*x]*(3635243172 + 1957030020*x - 3376828785*x^2 + 1747015050*x^3 - 301059000*x^4 - 183480000*x^5)))/(600*Sqrt[3]*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 600*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(600*(3481060 + 2827000*x - 391875*x^2) + 600*Sqrt[3]*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (1331*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(100*Sqrt[10])","B",1
2429,1,438,106,1.837473,"\int \frac{(1-2 x)^{5/2}}{(2+3 x) \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)*Sqrt[3 + 5*x]),x]","-\frac{343}{27} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-178500 x^3+909475 x^2+423440 x-7876858\right)+\sqrt{5 x+3} \left(858000 x^3-2599300 x^2-8028570 x+7876858\right)+\sqrt{3} \left(-60000 x^4-2281000 x^3+11996375 x^2+\sqrt{1-2 x} \left(594000 x^3-3837900 x^2+6271650 x+7876858\right)+1333480 x-7876858\right)}{450 \left(-2975 x^2+1820 x+16562\right)+450 \sqrt{3} \sqrt{5 x+3} (1980 x-5104)+\sqrt{1-2 x} \left(450 (-7150 x-13970)+450 \sqrt{3} \sqrt{5 x+3} (100 x+4240)\right)}-\frac{17687 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{675 \sqrt{10}}","-\frac{1}{15} \sqrt{5 x+3} (1-2 x)^{3/2}-\frac{239}{450} \sqrt{5 x+3} \sqrt{1-2 x}-\frac{17687 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{1350 \sqrt{10}}-\frac{98}{27} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-7876858 + 423440*x + 909475*x^2 - 178500*x^3) + Sqrt[3 + 5*x]*(7876858 - 8028570*x - 2599300*x^2 + 858000*x^3) + Sqrt[3]*(-7876858 + 1333480*x + 11996375*x^2 - 2281000*x^3 - 60000*x^4 + Sqrt[1 - 2*x]*(7876858 + 6271650*x - 3837900*x^2 + 594000*x^3)))/(450*Sqrt[3]*Sqrt[3 + 5*x]*(-5104 + 1980*x) + 450*(16562 + 1820*x - 2975*x^2) + Sqrt[1 - 2*x]*(450*(-13970 - 7150*x) + 450*Sqrt[3]*Sqrt[3 + 5*x]*(4240 + 100*x))) - (17687*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(675*Sqrt[10]) - (343*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ])/27","C",1
2430,1,531,115,2.1290311,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^2 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^2*Sqrt[3 + 5*x]),x]","\frac{1225}{27} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{6125}{54} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-343200 x^3-12243220 x^2-1568292 x+14816692\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(71400 x^3+1233970 x^2-11124688 x-14816692\right)+\sqrt{3} \left(24000 x^4+3784025 x^3+21723530 x^2+\sqrt{1-2 x} \left(-237600 x^3+887370 x^2+24496098 x+14816692\right)-11803118 x-14816692\right)}{90 \left(2975 x^2-1820 x-16562\right) (3 x+2)+90 \sqrt{3} (5104-1980 x) \sqrt{5 x+3} (3 x+2)+\sqrt{1-2 x} \left(90 (7150 x+13970) (3 x+2)+90 \sqrt{3} (-100 x-4240) \sqrt{5 x+3} (3 x+2)\right)}+\frac{692}{135} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{7 \sqrt{5 x+3} (1-2 x)^{3/2}}{3 (3 x+2)}+\frac{74}{45} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{346}{135} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{175}{27} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[3 + 5*x]*(14816692 - 1568292*x - 12243220*x^2 - 343200*x^3) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-14816692 - 11124688*x + 1233970*x^2 + 71400*x^3) + Sqrt[3]*(-14816692 - 11803118*x + 21723530*x^2 + 3784025*x^3 + 24000*x^4 + Sqrt[1 - 2*x]*(14816692 + 24496098*x + 887370*x^2 - 237600*x^3)))/(90*Sqrt[3]*(5104 - 1980*x)*(2 + 3*x)*Sqrt[3 + 5*x] + 90*(2 + 3*x)*(-16562 - 1820*x + 2975*x^2) + Sqrt[1 - 2*x]*(90*Sqrt[3]*(-4240 - 100*x)*(2 + 3*x)*Sqrt[3 + 5*x] + 90*(2 + 3*x)*(13970 + 7150*x))) + (692*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/135 + (1225*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/27 - (6125*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/54","C",1
2431,1,545,122,2.1353562,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^3 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^3*Sqrt[3 + 5*x]),x]","\frac{21245}{108} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{106225}{216} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{7 \sqrt{5 x+3} \left(-6244920 x^3-4987774 x^2+7256898 x+5505016\right)+7 \sqrt{1-2 x} \sqrt{5 x+3} \left(649575 x^3-5465480 x^2-11895322 x-5505016\right)+\sqrt{3} \left(7 \sqrt{1-2 x} \left(440550 x^3+13191090 x^2+16900752 x+5505016\right)+7 \left(1519425 x^4+12188540 x^3+1545434 x^2-12262328 x-5505016\right)\right)}{36 \left(2975 x^2-1820 x-16562\right) (3 x+2)^2+36 \sqrt{3} (5104-1980 x) \sqrt{5 x+3} (3 x+2)^2+\sqrt{1-2 x} \left(36 (7150 x+13970) (3 x+2)^2+36 \sqrt{3} (-100 x-4240) \sqrt{5 x+3} (3 x+2)^2\right)}-\frac{16}{27} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{7 \sqrt{5 x+3} (1-2 x)^{3/2}}{6 (3 x+2)^2}+\frac{637 \sqrt{5 x+3} \sqrt{1-2 x}}{36 (3 x+2)}-\frac{8}{27} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{3035}{108} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(7*Sqrt[3 + 5*x]*(5505016 + 7256898*x - 4987774*x^2 - 6244920*x^3) + 7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-5505016 - 11895322*x - 5465480*x^2 + 649575*x^3) + Sqrt[3]*(7*Sqrt[1 - 2*x]*(5505016 + 16900752*x + 13191090*x^2 + 440550*x^3) + 7*(-5505016 - 12262328*x + 1545434*x^2 + 12188540*x^3 + 1519425*x^4)))/(36*Sqrt[3]*(5104 - 1980*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 36*(2 + 3*x)^2*(-16562 - 1820*x + 2975*x^2) + Sqrt[1 - 2*x]*(36*Sqrt[3]*(-4240 - 100*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 36*(2 + 3*x)^2*(13970 + 7150*x))) - (16*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/27 + (21245*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/108 - (106225*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/216","C",1
2432,1,539,122,2.1396353,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^4 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^4*Sqrt[3 + 5*x]),x]","\frac{6655}{8} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{33275}{16} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-5078038350 x^5-172176346045 x^4-240768117282 x^3+17803711596 x^2+148240930904 x+53061795072\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(2922469625 x^5+44811949025 x^4-37771288590 x^3-223284445508 x^2-198819507032 x-53061795072\right)+\sqrt{3} \left(-3460216500 x^6+85922440050 x^5+344933957730 x^4+264772549752 x^3-121113044616 x^2+\sqrt{1-2 x} \left(-27915467250 x^5-45509453550 x^4+166885691280 x^3+369574216968 x^2+243869294592 x+53061795072\right)-193290718464 x-53061795072\right)}{24 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right) (3 x+2)^3+\sqrt{1-2 x} \left(24 \left(-391875 x^2+2827000 x+3481060\right) (3 x+2)^3+24 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right) (3 x+2)^3\right)+24 \left(44875 x^3+2976525 x^2-279060 x-3667684\right) (3 x+2)^3}","\frac{\sqrt{5 x+3} (1-2 x)^{5/2}}{3 (3 x+2)^3}+\frac{55 \sqrt{5 x+3} (1-2 x)^{3/2}}{12 (3 x+2)^2}+\frac{605 \sqrt{5 x+3} \sqrt{1-2 x}}{8 (3 x+2)}-\frac{6655 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{8 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(53061795072 + 148240930904*x + 17803711596*x^2 - 240768117282*x^3 - 172176346045*x^4 - 5078038350*x^5) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-53061795072 - 198819507032*x - 223284445508*x^2 - 37771288590*x^3 + 44811949025*x^4 + 2922469625*x^5) + Sqrt[3]*(-53061795072 - 193290718464*x - 121113044616*x^2 + 264772549752*x^3 + 344933957730*x^4 + 85922440050*x^5 - 3460216500*x^6 + Sqrt[1 - 2*x]*(53061795072 + 243869294592*x + 369574216968*x^2 + 166885691280*x^3 - 45509453550*x^4 - 27915467250*x^5)))/(24*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 24*(2 + 3*x)^3*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(24*(2 + 3*x)^3*(3481060 + 2827000*x - 391875*x^2) + 24*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (6655*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/8 - (33275*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/16","C",1
2433,1,599,151,2.5660437,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^5 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^5*Sqrt[3 + 5*x]),x]","\frac{1643785}{448} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{8218925}{896} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-1629651195678000 x^7-839582558061500 x^6+42870316283317380 x^5+86976355098202152 x^4+41060701051605752 x^3-25115498123354848 x^2-27172005314424608 x-6343678418698368\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(66081711249375 x^7-3801289685129000 x^6-22354880393932500 x^5-17358999334169040 x^4+34512129754245080 x^3+60728118486336192 x^2+33427337060224928 x+6343678418698368\right)+\sqrt{3} \left(229374480350625 x^8+5270955183982000 x^7-17901560314105000 x^6-99774278377807440 x^5-123648588998892712 x^4-27817925307725312 x^3+45501383001105088 x^2+\sqrt{1-2 x} \left(388844231407500 x^7+16098813584628500 x^6+38928864623728200 x^5+1727826261806040 x^4-75236132096512640 x^3-86347326431420032 x^2-38734282354973568 x-6343678418698368\right)+32478950609173248 x+6343678418698368\right)}{1344 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^4+\sqrt{1-2 x} \left(1344 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^4+1344 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^4\right)+1344 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^4}","\frac{3 \sqrt{5 x+3} (1-2 x)^{7/2}}{28 (3 x+2)^4}+\frac{247 \sqrt{5 x+3} (1-2 x)^{5/2}}{168 (3 x+2)^3}+\frac{13585 \sqrt{5 x+3} (1-2 x)^{3/2}}{672 (3 x+2)^2}+\frac{149435 \sqrt{5 x+3} \sqrt{1-2 x}}{448 (3 x+2)}-\frac{1643785 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{448 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-6343678418698368 - 27172005314424608*x - 25115498123354848*x^2 + 41060701051605752*x^3 + 86976355098202152*x^4 + 42870316283317380*x^5 - 839582558061500*x^6 - 1629651195678000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(6343678418698368 + 33427337060224928*x + 60728118486336192*x^2 + 34512129754245080*x^3 - 17358999334169040*x^4 - 22354880393932500*x^5 - 3801289685129000*x^6 + 66081711249375*x^7) + Sqrt[3]*(6343678418698368 + 32478950609173248*x + 45501383001105088*x^2 - 27817925307725312*x^3 - 123648588998892712*x^4 - 99774278377807440*x^5 - 17901560314105000*x^6 + 5270955183982000*x^7 + 229374480350625*x^8 + Sqrt[1 - 2*x]*(-6343678418698368 - 38734282354973568*x - 86347326431420032*x^2 - 75236132096512640*x^3 + 1727826261806040*x^4 + 38928864623728200*x^5 + 16098813584628500*x^6 + 388844231407500*x^7)))/(1344*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 1344*(2 + 3*x)^4*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(1344*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 1344*(2 + 3*x)^4*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) + (1643785*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/448 - (8218925*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/896","C",1
2434,1,659,180,3.0758613,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^6 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^6*Sqrt[3 + 5*x]),x]","\frac{104040277 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{6272}-\frac{520201385 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{12544}+\frac{\sqrt{5 x+3} \left(-37357782389227575000 x^9-1806372594877176954375 x^8-3830065925948784435650 x^7+8971736192247685845120 x^6+31458278329055979660336 x^5+28688948076722615496320 x^4+3241740925005409404160 x^3-9626305235788323607360 x^2-5615899101263419450240 x-971660951262572161536\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(6846724624835671875 x^9+203085237027882890625 x^8-1776976907916551443750 x^7-10806246616239710157000 x^6-15863112480448493222400 x^5-1290470638415459010080 x^4+16788590137690264824960 x^3+16637961021788316169664 x^2+6583533880367636565376 x+971660951262572161536\right)+\sqrt{3} \left(-5184910643188190625 x^{10}+612447594438681328125 x^9+4792089705226301612500 x^8+1453099613766272199000 x^7-27555883180722041291400 x^6-52806024201354809881936 x^5-33385384805468164965120 x^4+3108106626919168376640 x^3+13966779772577432815360 x^2+\sqrt{1-2 x} \left(-94391799464297671875 x^9+78430553499665812500 x^8+7188595794138838860000 x^7+21874333590547123983000 x^6+19588403980291249078800 x^5-8545695952984150033920 x^4-28644416147383511020480 x^3-21785448123778856306944 x^2-7393901589034363366656 x-971660951262572161536\right)+6426266809930146251520 x+971660951262572161536\right)}{94080 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right) (3 x+2)^5+\sqrt{1-2 x} \left(94080 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right) (3 x+2)^5+94080 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right) (3 x+2)^5\right)+94080 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right) (3 x+2)^5}","\frac{7 \sqrt{5 x+3} (1-2 x)^{3/2}}{15 (3 x+2)^5}+\frac{245529161 \sqrt{5 x+3} \sqrt{1-2 x}}{169344 (3 x+2)}+\frac{2347559 \sqrt{5 x+3} \sqrt{1-2 x}}{12096 (3 x+2)^2}+\frac{67187 \sqrt{5 x+3} \sqrt{1-2 x}}{2160 (3 x+2)^3}+\frac{2023 \sqrt{5 x+3} \sqrt{1-2 x}}{360 (3 x+2)^4}-\frac{104040277 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{6272 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-971660951262572161536 - 5615899101263419450240*x - 9626305235788323607360*x^2 + 3241740925005409404160*x^3 + 28688948076722615496320*x^4 + 31458278329055979660336*x^5 + 8971736192247685845120*x^6 - 3830065925948784435650*x^7 - 1806372594877176954375*x^8 - 37357782389227575000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(971660951262572161536 + 6583533880367636565376*x + 16637961021788316169664*x^2 + 16788590137690264824960*x^3 - 1290470638415459010080*x^4 - 15863112480448493222400*x^5 - 10806246616239710157000*x^6 - 1776976907916551443750*x^7 + 203085237027882890625*x^8 + 6846724624835671875*x^9) + Sqrt[3]*(971660951262572161536 + 6426266809930146251520*x + 13966779772577432815360*x^2 + 3108106626919168376640*x^3 - 33385384805468164965120*x^4 - 52806024201354809881936*x^5 - 27555883180722041291400*x^6 + 1453099613766272199000*x^7 + 4792089705226301612500*x^8 + 612447594438681328125*x^9 - 5184910643188190625*x^10 + Sqrt[1 - 2*x]*(-971660951262572161536 - 7393901589034363366656*x - 21785448123778856306944*x^2 - 28644416147383511020480*x^3 - 8545695952984150033920*x^4 + 19588403980291249078800*x^5 + 21874333590547123983000*x^6 + 7188595794138838860000*x^7 + 78430553499665812500*x^8 - 94391799464297671875*x^9)))/(94080*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 94080*(2 + 3*x)^5*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(94080*(2 + 3*x)^5*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 94080*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (104040277*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/6272 - (520201385*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/12544","C",1
2435,1,719,209,3.6804182,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^7 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^7*Sqrt[3 + 5*x]),x]","\frac{13391796605 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{175616}-\frac{66958983025 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{351232}+\frac{\sqrt{5 x+3} \left(-507563436454273066725000 x^{11}+2629419742469623432106250 x^{10}+89666635657491847893980250 x^9+258279981143704108362054600 x^8+46504735949039477735014400 x^7-700538289193443197489862144 x^6-1062577419161908675077514176 x^5-530565526272852426381653760 x^4+100077068180935131264675840 x^3+219584856553717540163520000 x^2+88118959996250529958019584 x+12106751473621230337714176\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(9369106966942643390625 x^{11}-2179101651818768356500000 x^{10}-20573955901531693571793750 x^9+20922925464629681970661000 x^8+317968429755709949598275200 x^7+664817175443318388156361920 x^6+470107323317887232623493120 x^5-158359484095557275441159680 x^4-479669440645397812010753280 x^3-325587825306594974228030464 x^2-100210786150524105993366016 x-12106751473621230337714176\right)+\sqrt{3} \left(54879743451522409171875 x^{12}+1894775534460414985162500 x^{11}-35102083018066960843181250 x^{10}-246248799392079394230303000 x^9-372925943533144885873439400 x^8+306416555950398483803735520 x^7+1413541514941701007971498624 x^6+1498236786278863170075326976 x^5+501508553222427703956226560 x^4-255961468339424515541015040 x^3-288807452167579762927941120 x^2-98209593531491180239448064 x+\sqrt{1-2 x} \left(216849177105822734343750 x^{11}+12201225658857036335531250 x^{10}+29980122954283896234390000 x^9-164798722489229658162993000 x^8-730070825143083013957672800 x^7-1041127979291484106596995520 x^6-436403860815978863361438720 x^5+470421388051297225212257280 x^4+719687470411657545495244800 x^3+404888616689574802021906944 x^2+110301419685764756274794496 x+12106751473621230337714176\right)-12106751473621230337714176\right)}{526848 \sqrt{3} \sqrt{5 x+3} \left(-25265212500 x^5+1941218400000 x^4+5284290066000 x^3-24057375117600 x^2-13825440024000 x+16748592098304\right) (3 x+2)^6+\sqrt{1-2 x} \left(526848 \sqrt{3} \sqrt{5 x+3} \left(-2625187500 x^5-345183000000 x^4+1378186950000 x^3+13912170444000 x^2-2687092123200 x-16725373086720\right) (3 x+2)^6+526848 \left(236425406250 x^5+2220611593750 x^4-28520358020000 x^3-52011357156000 x^2+49788771586400 x+50183931760160\right) (3 x+2)^6\right)+526848 \left(23653109375 x^6-916525237500 x^5-21026153381250 x^4+17065853944000 x^3+123670456765200 x^2-301410173760 x-50253588794912\right) (3 x+2)^6}","\frac{7 \sqrt{5 x+3} (1-2 x)^{3/2}}{18 (3 x+2)^6}+\frac{31603880465 \sqrt{5 x+3} \sqrt{1-2 x}}{4741632 (3 x+2)}+\frac{302171615 \sqrt{5 x+3} \sqrt{1-2 x}}{338688 (3 x+2)^2}+\frac{1729615 \sqrt{5 x+3} \sqrt{1-2 x}}{12096 (3 x+2)^3}+\frac{21199 \sqrt{5 x+3} \sqrt{1-2 x}}{864 (3 x+2)^4}+\frac{497 \sqrt{5 x+3} \sqrt{1-2 x}}{108 (3 x+2)^5}-\frac{13391796605 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{175616 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(12106751473621230337714176 + 88118959996250529958019584*x + 219584856553717540163520000*x^2 + 100077068180935131264675840*x^3 - 530565526272852426381653760*x^4 - 1062577419161908675077514176*x^5 - 700538289193443197489862144*x^6 + 46504735949039477735014400*x^7 + 258279981143704108362054600*x^8 + 89666635657491847893980250*x^9 + 2629419742469623432106250*x^10 - 507563436454273066725000*x^11) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-12106751473621230337714176 - 100210786150524105993366016*x - 325587825306594974228030464*x^2 - 479669440645397812010753280*x^3 - 158359484095557275441159680*x^4 + 470107323317887232623493120*x^5 + 664817175443318388156361920*x^6 + 317968429755709949598275200*x^7 + 20922925464629681970661000*x^8 - 20573955901531693571793750*x^9 - 2179101651818768356500000*x^10 + 9369106966942643390625*x^11) + Sqrt[3]*(-12106751473621230337714176 - 98209593531491180239448064*x - 288807452167579762927941120*x^2 - 255961468339424515541015040*x^3 + 501508553222427703956226560*x^4 + 1498236786278863170075326976*x^5 + 1413541514941701007971498624*x^6 + 306416555950398483803735520*x^7 - 372925943533144885873439400*x^8 - 246248799392079394230303000*x^9 - 35102083018066960843181250*x^10 + 1894775534460414985162500*x^11 + 54879743451522409171875*x^12 + Sqrt[1 - 2*x]*(12106751473621230337714176 + 110301419685764756274794496*x + 404888616689574802021906944*x^2 + 719687470411657545495244800*x^3 + 470421388051297225212257280*x^4 - 436403860815978863361438720*x^5 - 1041127979291484106596995520*x^6 - 730070825143083013957672800*x^7 - 164798722489229658162993000*x^8 + 29980122954283896234390000*x^9 + 12201225658857036335531250*x^10 + 216849177105822734343750*x^11)))/(526848*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(16748592098304 - 13825440024000*x - 24057375117600*x^2 + 5284290066000*x^3 + 1941218400000*x^4 - 25265212500*x^5) + 526848*(2 + 3*x)^6*(-50253588794912 - 301410173760*x + 123670456765200*x^2 + 17065853944000*x^3 - 21026153381250*x^4 - 916525237500*x^5 + 23653109375*x^6) + Sqrt[1 - 2*x]*(526848*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(-16725373086720 - 2687092123200*x + 13912170444000*x^2 + 1378186950000*x^3 - 345183000000*x^4 - 2625187500*x^5) + 526848*(2 + 3*x)^6*(50183931760160 + 49788771586400*x - 52011357156000*x^2 - 28520358020000*x^3 + 2220611593750*x^4 + 236425406250*x^5))) + (13391796605*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/175616 - (66958983025*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/351232","C",1
2436,1,524,186,3.7632514,"\int \frac{(1-2 x)^{5/2} (2+3 x)^4}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^4)/(3 + 5*x)^(3/2),x]","\frac{1298595837 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{160000000 \sqrt{10}}+\frac{-819277740000000000000 x^{13}+364115396626200000000000 x^{12}+2203404711894337500000000 x^{11}-16611533145978947625000000 x^{10}-42727749467608938065625000 x^9+25800678448135925817656250 x^8+89145369855537007332515625 x^7-8578782336024169532765625 x^6-73718750030448450150221250 x^5-2931573080137383253869000 x^4+30230013785397490706643600 x^3+4927633054023752077042800 x^2-4433370333043949481253920 x+\sqrt{3} \sqrt{5 x+3} \left(-7784331984000000000000 x^{12}-377309091725280000000000 x^{11}+710230257745866000000000 x^{10}+8956129029372825300000000 x^9+3000820835457224422500000 x^8-19734609127088532373125000 x^7-8260204417006021376771875 x^6+17513641845302002817738750 x^5+6337928514617692431439000 x^4-7714310374787694268219200 x^3-2485249061880957507964400 x^2+1167620359037742478188320 x+372104574052148193675584\right)+\sqrt{1-2 x} \left(-35068667634000000000000 x^{12}+444602288293020000000000 x^{11}+8069866314887198250000000 x^{10}+3899733617848813387500000 x^9-42050536019107509867187500 x^8-40450582146944358319734375 x^7+41057616249609765778603125 x^6+47854031267821761155208750 x^5-18302345610088871934339000 x^4-25566337073212064179974000 x^3+1210448227856818300207440 x^2+5552335569379316134787040 x+\sqrt{3} \sqrt{5 x+3} \left(762650316000000000000 x^{12}+20421164220120000000000 x^{11}-795884687535433500000000 x^{10}-2592126762137941125000000 x^9+4991277360594758008125000 x^8+12606598001639509997906250 x^7-3227088174847306166178125 x^6-14255385992540497151201250 x^5+449740726275028499485000 x^4+7475190246141592552130400 x^3+750128251614041973473520 x^2-1540608771149531362699360 x-372104574052148193675584\right)+1116313722156444581026752\right)-1116313722156444581026752}{960000000 \sqrt{5 x+3} \left(-3382394640625 x^6+46839566881250 x^5+721064958542500 x^4-436816644264000 x^3-2966115478898000 x^2+4019894758880 x+1105183793314304\right)+960000000 \sqrt{1-2 x} \sqrt{5 x+3} \left(39509921875 x^6-17586049031250 x^5-94425179937500 x^4+841225686360000 x^3+1360283516838000 x^2-1099312389138400 x-1104347908897280\right)+\sqrt{3} \left(960000000 \sqrt{1-2 x} \left(1877009062500 x^6+90847846375000 x^5-175063626237500 x^4-2024055290400000 x^3-831988612312000 x^2+2020474709052800 x+1104269783897280\right)+960000000 \left(367790468750 x^7+9638528906250 x^6-388916755537500 x^5-1017871743627500 x^4+2573340308796000 x^3+3351687890666400 x^2-925956910020800 x-1105105668314304\right)\right)}","-\frac{2 (1-2 x)^{5/2} (3 x+2)^4}{5 \sqrt{5 x+3}}+\frac{13}{50} (1-2 x)^{5/2} \sqrt{5 x+3} (3 x+2)^3+\frac{111 (1-2 x)^{5/2} \sqrt{5 x+3} (3 x+2)^2}{5000}-\frac{(1-2 x)^{5/2} \sqrt{5 x+3} (1990620 x+2725981)}{8000000}+\frac{3577399 (1-2 x)^{3/2} \sqrt{5 x+3}}{32000000}+\frac{118054167 \sqrt{1-2 x} \sqrt{5 x+3}}{320000000}+\frac{1298595837 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{320000000 \sqrt{10}}",1,"(-1116313722156444581026752 - 4433370333043949481253920*x + 4927633054023752077042800*x^2 + 30230013785397490706643600*x^3 - 2931573080137383253869000*x^4 - 73718750030448450150221250*x^5 - 8578782336024169532765625*x^6 + 89145369855537007332515625*x^7 + 25800678448135925817656250*x^8 - 42727749467608938065625000*x^9 - 16611533145978947625000000*x^10 + 2203404711894337500000000*x^11 + 364115396626200000000000*x^12 - 819277740000000000000*x^13 + Sqrt[3]*Sqrt[3 + 5*x]*(372104574052148193675584 + 1167620359037742478188320*x - 2485249061880957507964400*x^2 - 7714310374787694268219200*x^3 + 6337928514617692431439000*x^4 + 17513641845302002817738750*x^5 - 8260204417006021376771875*x^6 - 19734609127088532373125000*x^7 + 3000820835457224422500000*x^8 + 8956129029372825300000000*x^9 + 710230257745866000000000*x^10 - 377309091725280000000000*x^11 - 7784331984000000000000*x^12) + Sqrt[1 - 2*x]*(1116313722156444581026752 + 5552335569379316134787040*x + 1210448227856818300207440*x^2 - 25566337073212064179974000*x^3 - 18302345610088871934339000*x^4 + 47854031267821761155208750*x^5 + 41057616249609765778603125*x^6 - 40450582146944358319734375*x^7 - 42050536019107509867187500*x^8 + 3899733617848813387500000*x^9 + 8069866314887198250000000*x^10 + 444602288293020000000000*x^11 - 35068667634000000000000*x^12 + Sqrt[3]*Sqrt[3 + 5*x]*(-372104574052148193675584 - 1540608771149531362699360*x + 750128251614041973473520*x^2 + 7475190246141592552130400*x^3 + 449740726275028499485000*x^4 - 14255385992540497151201250*x^5 - 3227088174847306166178125*x^6 + 12606598001639509997906250*x^7 + 4991277360594758008125000*x^8 - 2592126762137941125000000*x^9 - 795884687535433500000000*x^10 + 20421164220120000000000*x^11 + 762650316000000000000*x^12)))/(960000000*Sqrt[3 + 5*x]*(1105183793314304 + 4019894758880*x - 2966115478898000*x^2 - 436816644264000*x^3 + 721064958542500*x^4 + 46839566881250*x^5 - 3382394640625*x^6) + 960000000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-1104347908897280 - 1099312389138400*x + 1360283516838000*x^2 + 841225686360000*x^3 - 94425179937500*x^4 - 17586049031250*x^5 + 39509921875*x^6) + Sqrt[3]*(960000000*Sqrt[1 - 2*x]*(1104269783897280 + 2020474709052800*x - 831988612312000*x^2 - 2024055290400000*x^3 - 175063626237500*x^4 + 90847846375000*x^5 + 1877009062500*x^6) + 960000000*(-1105105668314304 - 925956910020800*x + 3351687890666400*x^2 + 2573340308796000*x^3 - 1017871743627500*x^4 - 388916755537500*x^5 + 9638528906250*x^6 + 367790468750*x^7))) + (1298595837*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(160000000*Sqrt[10])","B",1
2437,1,464,157,3.2070032,"\int \frac{(1-2 x)^{5/2} (2+3 x)^3}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(3 + 5*x)^(3/2),x]","\frac{24319911 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{4000000 \sqrt{10}}+\frac{742805640000000000 x^{11}+18329900224500000000 x^{10}-377464198779675000000 x^9-774010879088131875000 x^8+1546787291972070468750 x^7+1720796601608944846875 x^6-1979321835458680531875 x^5-1341043162498298822250 x^4+1311090724372551837300 x^3+788883206039058890400 x^2+\sqrt{3} \sqrt{5 x+3} \left(-2070755280000000000 x^{10}+15676532883000000000 x^9+204399898244190000000 x^8-98761172145611250000 x^7-572416282165107187500 x^6+211368313376937784375 x^5+531814405372666666250 x^4-207815207794673821100 x^3-278306016925453972400 x^2+41815932183411546160 x+55596544273189305056\right)+\sqrt{1-2 x} \left(2775682404000000000 x^{10}+115272201879450000000 x^9-94175025094012500000 x^8-1235896603773007687500 x^7-239160368095101234375 x^6+1767717994717992508125 x^5+227937913863718880250 x^4-1281280563657914658300 x^3-271851958050475799040 x^2+\sqrt{3} \sqrt{5 x+3} \left(39689352000000000 x^{10}-8336803977900000000 x^9-37636760612565000000 x^8+189547881692336625000 x^7+239782454595077156250 x^6-331821132359521488125 x^5-250394153608506209250 x^4+283286525242692745700 x^3+152395803212355519280 x^2-97518974839689138960 x-55596544273189305056\right)+431591285410634429520 x+166789632819567915168\right)-264482157441801651120 x-166789632819567915168}{24000000 \sqrt{1-2 x} \sqrt{5 x+3} \left(-3582203125 x^5-88889062500 x^4+1803368312500 x^3+3864602795000 x^2-4498159242000 x-4559963226880\right)+24000000 \sqrt{5 x+3} \left(26771628125 x^5+1102102787500 x^4-1277247746500 x^3-10194890840200 x^2+44616484880 x+4571572732672\right)+\sqrt{3} \left(24000000 \sqrt{1-2 x} \left(49931406250 x^5-341178406250 x^4-5136237645000 x^3-1756271561000 x^2+8312451514400 x+4558400726880\right)+24000000 \left(1914031250 x^6-401590362500 x^5-1908507943750 x^4+8285194844000 x^3+11815417982200 x^2-3870145845440 x-4570010232672\right)\right)}","-\frac{2 (1-2 x)^{5/2} (3 x+2)^3}{5 \sqrt{5 x+3}}+\frac{33}{125} (1-2 x)^{5/2} \sqrt{5 x+3} (3 x+2)^2-\frac{9 (2127-460 x) (1-2 x)^{5/2} \sqrt{5 x+3}}{200000}+\frac{66997 (1-2 x)^{3/2} \sqrt{5 x+3}}{800000}+\frac{2210901 \sqrt{1-2 x} \sqrt{5 x+3}}{8000000}+\frac{24319911 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{8000000 \sqrt{10}}",1,"(-166789632819567915168 - 264482157441801651120*x + 788883206039058890400*x^2 + 1311090724372551837300*x^3 - 1341043162498298822250*x^4 - 1979321835458680531875*x^5 + 1720796601608944846875*x^6 + 1546787291972070468750*x^7 - 774010879088131875000*x^8 - 377464198779675000000*x^9 + 18329900224500000000*x^10 + 742805640000000000*x^11 + Sqrt[3]*Sqrt[3 + 5*x]*(55596544273189305056 + 41815932183411546160*x - 278306016925453972400*x^2 - 207815207794673821100*x^3 + 531814405372666666250*x^4 + 211368313376937784375*x^5 - 572416282165107187500*x^6 - 98761172145611250000*x^7 + 204399898244190000000*x^8 + 15676532883000000000*x^9 - 2070755280000000000*x^10) + Sqrt[1 - 2*x]*(166789632819567915168 + 431591285410634429520*x - 271851958050475799040*x^2 - 1281280563657914658300*x^3 + 227937913863718880250*x^4 + 1767717994717992508125*x^5 - 239160368095101234375*x^6 - 1235896603773007687500*x^7 - 94175025094012500000*x^8 + 115272201879450000000*x^9 + 2775682404000000000*x^10 + Sqrt[3]*Sqrt[3 + 5*x]*(-55596544273189305056 - 97518974839689138960*x + 152395803212355519280*x^2 + 283286525242692745700*x^3 - 250394153608506209250*x^4 - 331821132359521488125*x^5 + 239782454595077156250*x^6 + 189547881692336625000*x^7 - 37636760612565000000*x^8 - 8336803977900000000*x^9 + 39689352000000000*x^10)))/(24000000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-4559963226880 - 4498159242000*x + 3864602795000*x^2 + 1803368312500*x^3 - 88889062500*x^4 - 3582203125*x^5) + 24000000*Sqrt[3 + 5*x]*(4571572732672 + 44616484880*x - 10194890840200*x^2 - 1277247746500*x^3 + 1102102787500*x^4 + 26771628125*x^5) + Sqrt[3]*(24000000*Sqrt[1 - 2*x]*(4558400726880 + 8312451514400*x - 1756271561000*x^2 - 5136237645000*x^3 - 341178406250*x^4 + 49931406250*x^5) + 24000000*(-4570010232672 - 3870145845440*x + 11815417982200*x^2 + 8285194844000*x^3 - 1908507943750*x^4 - 401590362500*x^5 + 1914031250*x^6))) + (24319911*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(4000000*Sqrt[10])","B",1
2438,1,404,138,2.7290369,"\int \frac{(1-2 x)^{5/2} (2+3 x)^2}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^2)/(3 + 5*x)^(3/2),x]","\frac{-21516300000000 x^9+2215226085000000 x^8+5855098576125000 x^7-25188814940531250 x^6-1267783491485625 x^5+36409287960909375 x^4-17821965535153800 x^3-34650014569749300 x^2+\sqrt{3} \sqrt{5 x+3} \left(-50893920000000 x^8-1670249592000000 x^7+2583412741800000 x^6+5423825389950000 x^5-8365074730538625 x^4-1658415812073900 x^3+10321401093884100 x^2+215633550801240 x-3006817168400144\right)+\sqrt{1-2 x} \left(-365693130000000 x^8+1439870404500000 x^7+13773705517687500 x^6-9143608593425625 x^5-18124999864401375 x^4+20920676356727400 x^3+14423004643542660 x^2+\sqrt{3} \sqrt{5 x+3} \left(9958140000000 x^8+196576389000000 x^7-2246218127325000 x^6-1165113632486250 x^5+5753749535956625 x^4-1857815527683700 x^3-6082842487558020 x^2+2789330960840120 x+3006817168400144\right)-15883958631645720 x-9020451505200432\right)+6869065096721640 x+9020451505200432}{240000 \sqrt{5 x+3} \left(-846511875 x^4+2876857500 x^3+32771841300 x^2-464036760 x-18959828096\right)+240000 \sqrt{1-2 x} \sqrt{5 x+3} \left(24903125 x^4-2538047500 x^3-9400717500 x^2+18053298200 x+18798584960\right)+\sqrt{3} \left(240000 \sqrt{1-2 x} \left(294525000 x^4+10148490000 x^3+1543311000 x^2-33942744000 x-18767334960\right)+240000 \left(115256250 x^5+2406453750 x^4-23245830000 x^3-39836473200 x^2+16519101840 x+18928578096\right)\right)}+\frac{236313 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{40000 \sqrt{10}}","-\frac{9}{200} \sqrt{5 x+3} (1-2 x)^{7/2}-\frac{2 (1-2 x)^{7/2}}{275 \sqrt{5 x+3}}+\frac{651 \sqrt{5 x+3} (1-2 x)^{5/2}}{22000}+\frac{651 \sqrt{5 x+3} (1-2 x)^{3/2}}{8000}+\frac{21483 \sqrt{5 x+3} \sqrt{1-2 x}}{80000}+\frac{236313 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{80000 \sqrt{10}}",1,"(9020451505200432 + 6869065096721640*x - 34650014569749300*x^2 - 17821965535153800*x^3 + 36409287960909375*x^4 - 1267783491485625*x^5 - 25188814940531250*x^6 + 5855098576125000*x^7 + 2215226085000000*x^8 - 21516300000000*x^9 + Sqrt[3]*Sqrt[3 + 5*x]*(-3006817168400144 + 215633550801240*x + 10321401093884100*x^2 - 1658415812073900*x^3 - 8365074730538625*x^4 + 5423825389950000*x^5 + 2583412741800000*x^6 - 1670249592000000*x^7 - 50893920000000*x^8) + Sqrt[1 - 2*x]*(-9020451505200432 - 15883958631645720*x + 14423004643542660*x^2 + 20920676356727400*x^3 - 18124999864401375*x^4 - 9143608593425625*x^5 + 13773705517687500*x^6 + 1439870404500000*x^7 - 365693130000000*x^8 + Sqrt[3]*Sqrt[3 + 5*x]*(3006817168400144 + 2789330960840120*x - 6082842487558020*x^2 - 1857815527683700*x^3 + 5753749535956625*x^4 - 1165113632486250*x^5 - 2246218127325000*x^6 + 196576389000000*x^7 + 9958140000000*x^8)))/(240000*Sqrt[3 + 5*x]*(-18959828096 - 464036760*x + 32771841300*x^2 + 2876857500*x^3 - 846511875*x^4) + 240000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(18798584960 + 18053298200*x - 9400717500*x^2 - 2538047500*x^3 + 24903125*x^4) + Sqrt[3]*(240000*Sqrt[1 - 2*x]*(-18767334960 - 33942744000*x + 1543311000*x^2 + 10148490000*x^3 + 294525000*x^4) + 240000*(18928578096 + 16519101840*x - 39836473200*x^2 - 23245830000*x^3 + 2406453750*x^4 + 115256250*x^5))) + (236313*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(40000*Sqrt[10])","B",1
2439,1,344,116,2.3369213,"\int \frac{(1-2 x)^{5/2} (2+3 x)}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x))/(3 + 5*x)^(3/2),x]","\frac{5289000000 x^7+69197625000 x^6-492083996250 x^5+530504608875 x^4-30229157025 x^3-1384317801900 x^2+\sqrt{3} \sqrt{5 x+3} \left(-10810800000 x^6+36966930000 x^5+68908339500 x^4-237974523325 x^3+372902160400 x^2+46203177020 x-147011218024\right)+\sqrt{1-2 x} \left(8292900000 x^6+203554312500 x^5-362984766375 x^4+174365270475 x^3+540231622260 x^2+\sqrt{3} \sqrt{5 x+3} \left(486600000 x^6-23833815000 x^5-6287775750 x^4+106429326775 x^3-212545155120 x^2+99455763500 x+147011218024\right)-664763148060 x-441033654072\right)+227786326500 x+441033654072}{3000 \sqrt{1-2 x} \sqrt{5 x+3} \left(-1101875 x^3-16812750 x^2+68422100 x+77141440\right)+3000 \sqrt{5 x+3} \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right)+\sqrt{3} \left(3000 \sqrt{1-2 x} \left(11261250 x^3-7257250 x^2-135935800 x-76516440\right)+3000 \left(1013750 x^4-47347500 x^3-123624450 x^2+74349280 x+78755928\right)\right)}+\frac{2541 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{500 \sqrt{10}}","-\frac{2 (1-2 x)^{7/2}}{55 \sqrt{5 x+3}}+\frac{7}{275} \sqrt{5 x+3} (1-2 x)^{5/2}+\frac{7}{100} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{231 \sqrt{5 x+3} \sqrt{1-2 x}}{1000}+\frac{2541 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{1000 \sqrt{10}}",1,"(441033654072 + 227786326500*x - 1384317801900*x^2 - 30229157025*x^3 + 530504608875*x^4 - 492083996250*x^5 + 69197625000*x^6 + 5289000000*x^7 + Sqrt[3]*Sqrt[3 + 5*x]*(-147011218024 + 46203177020*x + 372902160400*x^2 - 237974523325*x^3 + 68908339500*x^4 + 36966930000*x^5 - 10810800000*x^6) + Sqrt[1 - 2*x]*(-441033654072 - 664763148060*x + 540231622260*x^2 + 174365270475*x^3 - 362984766375*x^4 + 203554312500*x^5 + 8292900000*x^6 + Sqrt[3]*Sqrt[3 + 5*x]*(147011218024 + 99455763500*x - 212545155120*x^2 + 106429326775*x^3 - 6287775750*x^4 - 23833815000*x^5 + 486600000*x^6)))/(3000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(77141440 + 68422100*x - 16812750*x^2 - 1101875*x^3) + 3000*Sqrt[3 + 5*x]*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3) + Sqrt[3]*(3000*Sqrt[1 - 2*x]*(-76516440 - 135935800*x - 7257250*x^2 + 11261250*x^3) + 3000*(78755928 + 74349280*x - 123624450*x^2 - 47347500*x^3 + 1013750*x^4))) + (2541*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(500*Sqrt[10])","B",1
2440,1,284,94,1.8065449,"\int \frac{(1-2 x)^{5/2}}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/(3 + 5*x)^(3/2),x]","\frac{-1425000 x^5+32066250 x^4-80595375 x^3-453351225 x^2+\sqrt{3} \sqrt{5 x+3} \left(-660000 x^4-9207000 x^3+79110625 x^2+59509450 x-95986396\right)+\sqrt{1-2 x} \left(-9817500 x^4+38828625 x^3+73933365 x^2+\sqrt{3} \sqrt{5 x+3} \left(417000 x^4+2038650 x^3-25013105 x^2+30313170 x+95986396\right)-323474250 x-287959188\right)+54006390 x+287959188}{150 \sqrt{5 x+3} \left(-163625 x^2+33550 x+343904\right)+150 \sqrt{1-2 x} \sqrt{5 x+3} \left(11875 x^2-216750 x-312800\right)+\sqrt{3} \left(150 \sqrt{1-2 x} \left(27500 x^2+517000 x+300300\right)+150 \left(34750 x^3+321050 x^2-372220 x-331404\right)\right)}-\frac{363 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{25 \sqrt{10}}","-\frac{2 (1-2 x)^{5/2}}{5 \sqrt{5 x+3}}-\frac{1}{5} \sqrt{5 x+3} (1-2 x)^{3/2}-\frac{33}{50} \sqrt{5 x+3} \sqrt{1-2 x}-\frac{363 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{50 \sqrt{10}}",1,"(287959188 + 54006390*x - 453351225*x^2 - 80595375*x^3 + 32066250*x^4 - 1425000*x^5 + Sqrt[3]*Sqrt[3 + 5*x]*(-95986396 + 59509450*x + 79110625*x^2 - 9207000*x^3 - 660000*x^4) + Sqrt[1 - 2*x]*(-287959188 - 323474250*x + 73933365*x^2 + 38828625*x^3 - 9817500*x^4 + Sqrt[3]*Sqrt[3 + 5*x]*(95986396 + 30313170*x - 25013105*x^2 + 2038650*x^3 + 417000*x^4)))/(150*Sqrt[3 + 5*x]*(343904 + 33550*x - 163625*x^2) + 150*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-312800 - 216750*x + 11875*x^2) + Sqrt[3]*(150*Sqrt[1 - 2*x]*(300300 + 517000*x + 27500*x^2) + 150*(-331404 - 372220*x + 321050*x^2 + 34750*x^3))) - (363*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(25*Sqrt[10])","B",1
2441,1,426,108,1.8823264,"\int \frac{(1-2 x)^{5/2}}{(2+3 x) (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)*(3 + 5*x)^(3/2)),x]","\frac{343}{9} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{2 \sqrt{3} \sqrt{5 x+3} \left(-6600 x^2+219285 x-316778\right)+\sqrt{1-2 x} \left(2 \sqrt{3} \sqrt{5 x+3} \left(900 x^2+1805 x+316778\right)+2 \left(1650 x^2-631235 x-950334\right)\right)+2 \left(6500 x^3-371150 x^2-32035 x+950334\right)}{\sqrt{3} \left(75 \left(450 x^2-2100 x-1422\right)+75 \sqrt{1-2 x} (1650 x+990)\right)+75 \sqrt{1-2 x} \sqrt{5 x+3} (-325 x-1240)+75 \sqrt{5 x+3} (165 x+1672)}+\frac{676}{225} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{22 (1-2 x)^{3/2}}{5 \sqrt{5 x+3}}-\frac{128}{75} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{338}{225} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)+\frac{98}{9} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(2*Sqrt[3]*Sqrt[3 + 5*x]*(-316778 + 219285*x - 6600*x^2) + 2*(950334 - 32035*x - 371150*x^2 + 6500*x^3) + Sqrt[1 - 2*x]*(2*Sqrt[3]*Sqrt[3 + 5*x]*(316778 + 1805*x + 900*x^2) + 2*(-950334 - 631235*x + 1650*x^2)))/(75*(-1240 - 325*x)*Sqrt[1 - 2*x]*Sqrt[3 + 5*x] + 75*Sqrt[3 + 5*x]*(1672 + 165*x) + Sqrt[3]*(75*Sqrt[1 - 2*x]*(990 + 1650*x) + 75*(-1422 - 2100*x + 450*x^2))) + (676*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/225 + (343*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ])/9","C",1
2442,1,511,115,2.2087412,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^2 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^2*(3 + 5*x)^(3/2)),x]","-\frac{4655}{9} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{23275}{18} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(294705 x^2+18054342 x+11643588\right)+\sqrt{5 x+3} \left(12393315 x^2-9769122 x-11643588\right)+\sqrt{3} \left(-7376350 x^3-5700230 x^2+\sqrt{1-2 x} \left(-11948640 x^2-25813832 x-11643588\right)+17528612 x+11643588\right)}{30 (3 x+2) \left(1350 x^2-6300 x-4266\right)+30 \sqrt{3} (3 x+2) \sqrt{5 x+3} (165 x+1672)+\sqrt{1-2 x} \left(30 (4950 x+2970) (3 x+2)+30 \sqrt{3} (-325 x-1240) \sqrt{5 x+3} (3 x+2)\right)}-\frac{16}{45} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{7 (1-2 x)^{3/2}}{3 (3 x+2) \sqrt{5 x+3}}-\frac{1111 \sqrt{1-2 x}}{15 \sqrt{5 x+3}}-\frac{8}{45} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)+\frac{665}{9} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(11643588 + 18054342*x + 294705*x^2) + Sqrt[3 + 5*x]*(-11643588 - 9769122*x + 12393315*x^2) + Sqrt[3]*(11643588 + 17528612*x - 5700230*x^2 - 7376350*x^3 + Sqrt[1 - 2*x]*(-11643588 - 25813832*x - 11948640*x^2)))/(30*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(1672 + 165*x) + 30*(2 + 3*x)*(-4266 - 6300*x + 1350*x^2) + Sqrt[1 - 2*x]*(30*Sqrt[3]*(-1240 - 325*x)*(2 + 3*x)*Sqrt[3 + 5*x] + 30*(2 + 3*x)*(2970 + 4950*x))) - (16*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/45 - (4655*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/9 + (23275*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/18","C",1
2443,1,519,115,2.1462331,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^3 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^3*(3 + 5*x)^(3/2)),x]","-\frac{12705}{4} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{63525}{8} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-538284075 x^4-224342640 x^3+11030666368 x^2+14208372012 x+4604770192\right)+\sqrt{5 x+3} \left(3181261875 x^4+13419362550 x^3+2911420468 x^2-9998798876 x-4604770192\right)+\sqrt{3} \left(-163280500 x^5-12808466275 x^4-17515350515 x^3+4113249362 x^2+\sqrt{1-2 x} \left(2283219125 x^4-5889402475 x^3-21404492978 x^2-17886859672 x-4604770192\right)+13677286536 x+4604770192\right)}{4 \sqrt{3} \sqrt{5 x+3} \left(-163625 x^2+33550 x+343904\right) (3 x+2)^2+\sqrt{1-2 x} \left(4 \sqrt{3} \sqrt{5 x+3} \left(11875 x^2-216750 x-312800\right) (3 x+2)^2+4 \left(82500 x^2+1551000 x+900900\right) (3 x+2)^2\right)+4 \left(104250 x^3+963150 x^2-1116660 x-994212\right) (3 x+2)^2}","\frac{(1-2 x)^{5/2}}{2 (3 x+2)^2 \sqrt{5 x+3}}+\frac{55 (1-2 x)^{3/2}}{4 (3 x+2) \sqrt{5 x+3}}-\frac{1815 \sqrt{1-2 x}}{4 \sqrt{5 x+3}}+\frac{1815}{4} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(4604770192 + 14208372012*x + 11030666368*x^2 - 224342640*x^3 - 538284075*x^4) + Sqrt[3 + 5*x]*(-4604770192 - 9998798876*x + 2911420468*x^2 + 13419362550*x^3 + 3181261875*x^4) + Sqrt[3]*(4604770192 + 13677286536*x + 4113249362*x^2 - 17515350515*x^3 - 12808466275*x^4 - 163280500*x^5 + Sqrt[1 - 2*x]*(-4604770192 - 17886859672*x - 21404492978*x^2 - 5889402475*x^3 + 2283219125*x^4)))/(4*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(343904 + 33550*x - 163625*x^2) + 4*(2 + 3*x)^2*(-994212 - 1116660*x + 963150*x^2 + 104250*x^3) + Sqrt[1 - 2*x]*(4*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(-312800 - 216750*x + 11875*x^2) + 4*(2 + 3*x)^2*(900900 + 1551000*x + 82500*x^2))) - (12705*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/4 + (63525*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/8","C",1
2444,1,579,144,2.5651236,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^4 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^4*(3 + 5*x)^(3/2)),x]","-\frac{147015}{8} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{735075}{16} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(263465902500 x^6+26559449181000 x^5+46752328333350 x^4-65636273047300 x^3-176715447183528 x^2-118683703604432 x-25789166204032\right)+\sqrt{5 x+3} \left(5884957212750 x^6-52617324733050 x^5-201719988718710 x^4-155545243785932 x^3+51502445524376 x^2+93553017043024 x+25789166204032\right)+\sqrt{3} \left(-1840290126250 x^7+3975285153125 x^6+171126309910825 x^5+332125261609020 x^4+136890066296752 x^3-120937522225496 x^2+\sqrt{1-2 x} \left(-8285276759375 x^6-64864917126625 x^5-28103002974200 x^4+180062832140840 x^3+266908993102488 x^2+139990905857792 x+25789166204032\right)-114860219296384 x-25789166204032\right)}{8 \sqrt{3} \sqrt{5 x+3} \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (3 x+2)^3+\sqrt{1-2 x} \left(8 \sqrt{3} \sqrt{5 x+3} \left(-1101875 x^3-16812750 x^2+68422100 x+77141440\right) (3 x+2)^3+8 \left(33783750 x^3-21771750 x^2-407807400 x-229549320\right) (3 x+2)^3\right)+8 \left(3041250 x^4-142042500 x^3-370873350 x^2+223047840 x+236267784\right) (3 x+2)^3}","\frac{(1-2 x)^{7/2}}{7 (3 x+2)^3 \sqrt{5 x+3}}+\frac{81 (1-2 x)^{5/2}}{28 (3 x+2)^2 \sqrt{5 x+3}}+\frac{4455 (1-2 x)^{3/2}}{56 (3 x+2) \sqrt{5 x+3}}-\frac{147015 \sqrt{1-2 x}}{56 \sqrt{5 x+3}}+\frac{147015 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{8 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-25789166204032 - 118683703604432*x - 176715447183528*x^2 - 65636273047300*x^3 + 46752328333350*x^4 + 26559449181000*x^5 + 263465902500*x^6) + Sqrt[3 + 5*x]*(25789166204032 + 93553017043024*x + 51502445524376*x^2 - 155545243785932*x^3 - 201719988718710*x^4 - 52617324733050*x^5 + 5884957212750*x^6) + Sqrt[3]*(-25789166204032 - 114860219296384*x - 120937522225496*x^2 + 136890066296752*x^3 + 332125261609020*x^4 + 171126309910825*x^5 + 3975285153125*x^6 - 1840290126250*x^7 + Sqrt[1 - 2*x]*(25789166204032 + 139990905857792*x + 266908993102488*x^2 + 180062832140840*x^3 - 28103002974200*x^4 - 64864917126625*x^5 - 8285276759375*x^6)))/(8*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3) + 8*(2 + 3*x)^3*(236267784 + 223047840*x - 370873350*x^2 - 142042500*x^3 + 3041250*x^4) + Sqrt[1 - 2*x]*(8*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(77141440 + 68422100*x - 16812750*x^2 - 1101875*x^3) + 8*(2 + 3*x)^3*(-229549320 - 407807400*x - 21771750*x^2 + 33783750*x^3))) - (147015*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/8 + (735075*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/16","C",1
2445,1,639,173,3.0189539,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^5 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^5*(3 + 5*x)^(3/2)),x]","-\frac{46095555}{448} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{230477775}{896} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-50691822933740625 x^8+435754508350848750 x^7+14384376989014612500 x^6+34626869717486966400 x^5+11112624251633601920 x^4-42143862208631228080 x^3-52606843936978593792 x^2-23905319393113878208 x-3913630579604508928\right)+\sqrt{5 x+3} \left(636788923620485625 x^8+6595491650423197500 x^7-8743377353699052900 x^6-67354088360945134320 x^5-85630229762831983152 x^4-22111503315569912112 x^3+27126249040950890688 x^2+20021419192924298688 x+3913630579604508928\right)+\sqrt{3} \left(-33437503188300000 x^9-4128041233938539375 x^8-7436083062514668125 x^7+44147356386067708100 x^6+127853991255208429880 x^5+108974022076200129512 x^4+5296711496595399472 x^3-42468191059865407328 x^2+\sqrt{1-2 x} \left(305757642056315625 x^8-6089131797181723125 x^7-36191175073794295500 x^6-49190598472866477000 x^5+11405239427864461080 x^4+78851589260785222640 x^3+71179607509342760032 x^2+27160916262742635648 x+3913630579604508928\right)-23277016062553056128 x-3913630579604508928\right)}{448 \sqrt{3} \sqrt{5 x+3} \left(-846511875 x^4+2876857500 x^3+32771841300 x^2-464036760 x-18959828096\right) (3 x+2)^4+\sqrt{1-2 x} \left(448 \sqrt{3} \sqrt{5 x+3} \left(24903125 x^4-2538047500 x^3-9400717500 x^2+18053298200 x+18798584960\right) (3 x+2)^4+448 \left(883575000 x^4+30445470000 x^3+4629933000 x^2-101828232000 x-56302004880\right) (3 x+2)^4\right)+448 \left(345768750 x^5+7219361250 x^4-69737490000 x^3-119509419600 x^2+49557305520 x+56785734288\right) (3 x+2)^4}","\frac{7 (1-2 x)^{3/2}}{12 (3 x+2)^4 \sqrt{5 x+3}}+\frac{3997345 \sqrt{1-2 x}}{4032 (3 x+2) \sqrt{5 x+3}}+\frac{22957 \sqrt{1-2 x}}{288 (3 x+2)^2 \sqrt{5 x+3}}+\frac{2051 \sqrt{1-2 x}}{216 (3 x+2)^3 \sqrt{5 x+3}}-\frac{181304825 \sqrt{1-2 x}}{12096 \sqrt{5 x+3}}+\frac{46095555 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{448 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-3913630579604508928 - 23905319393113878208*x - 52606843936978593792*x^2 - 42143862208631228080*x^3 + 11112624251633601920*x^4 + 34626869717486966400*x^5 + 14384376989014612500*x^6 + 435754508350848750*x^7 - 50691822933740625*x^8) + Sqrt[3 + 5*x]*(3913630579604508928 + 20021419192924298688*x + 27126249040950890688*x^2 - 22111503315569912112*x^3 - 85630229762831983152*x^4 - 67354088360945134320*x^5 - 8743377353699052900*x^6 + 6595491650423197500*x^7 + 636788923620485625*x^8) + Sqrt[3]*(-3913630579604508928 - 23277016062553056128*x - 42468191059865407328*x^2 + 5296711496595399472*x^3 + 108974022076200129512*x^4 + 127853991255208429880*x^5 + 44147356386067708100*x^6 - 7436083062514668125*x^7 - 4128041233938539375*x^8 - 33437503188300000*x^9 + Sqrt[1 - 2*x]*(3913630579604508928 + 27160916262742635648*x + 71179607509342760032*x^2 + 78851589260785222640*x^3 + 11405239427864461080*x^4 - 49190598472866477000*x^5 - 36191175073794295500*x^6 - 6089131797181723125*x^7 + 305757642056315625*x^8)))/(448*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-18959828096 - 464036760*x + 32771841300*x^2 + 2876857500*x^3 - 846511875*x^4) + 448*(2 + 3*x)^4*(56785734288 + 49557305520*x - 119509419600*x^2 - 69737490000*x^3 + 7219361250*x^4 + 345768750*x^5) + Sqrt[1 - 2*x]*(448*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(18798584960 + 18053298200*x - 9400717500*x^2 - 2538047500*x^3 + 24903125*x^4) + 448*(2 + 3*x)^4*(-56302004880 - 101828232000*x + 4629933000*x^2 + 30445470000*x^3 + 883575000*x^4))) - (46095555*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/448 + (230477775*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/896","C",1
2446,1,699,202,3.9752576,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^6 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^6*(3 + 5*x)^(3/2)),x]","-\frac{3538809681 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{6272}+\frac{17694048405 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{12544}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(1447041499930835578125 x^{10}+209949806715334632843750 x^9+222669638489869988906250 x^8-6480775235917322099467500 x^7-20471769208930472301708000 x^6-19986055834258423988583040 x^5+2966650903864286927545920 x^4+20331450932529364264675840 x^3+16161240133328254797824384 x^2+5533442583198965794711296 x+727098642968333575064576\right)+\sqrt{5 x+3} \left(21339398741915500228125 x^{10}-893920202455229221387500 x^9-5896153568525262422910750 x^8-4491439461406435896590100 x^7+19898637033096620626927440 x^6+42173922651770491621034336 x^5+27738499983574231431733120 x^4-1237062694398888099761920 x^3-10290541881308384585127040 x^2-4807987293550845443480320 x-727098642968333575064576\right)+\sqrt{3} \left(-5644978066841619937500 x^{11}+115038127818785326303125 x^{10}+3892388221271859875840625 x^9+10797785031982203064465750 x^8-3934750877871630238996400 x^7-46765806458885953386603720 x^6-63934803683476280106105936 x^5-29114983090263408965119520 x^4+8354724112084264155333120 x^3+14045470404787223296685440 x^2+\sqrt{1-2 x} \left(-46964835866868101015625 x^{10}-640156868034125958140625 x^9+2100405344814604195046250 x^8+18202524384153359673742000 x^7+35504793010306714344846200 x^6+21312808901616434963915440 x^5-15675448416765557441308320 x^4-32089872184456329958872960 x^3-20520493555900631302075264 x^2-6139136943392681273931776 x-727098642968333575064576\right)+5413681653744560922700800 x+727098642968333575064576\right)}{31360 \sqrt{3} \sqrt{5 x+3} \left(26771628125 x^5+1102102787500 x^4-1277247746500 x^3-10194890840200 x^2+44616484880 x+4571572732672\right) (3 x+2)^5+\sqrt{1-2 x} \left(31360 \sqrt{3} \sqrt{5 x+3} \left(-3582203125 x^5-88889062500 x^4+1803368312500 x^3+3864602795000 x^2-4498159242000 x-4559963226880\right) (3 x+2)^5+31360 \left(149794218750 x^5-1023535218750 x^4-15408712935000 x^3-5268814683000 x^2+24937354543200 x+13675202180640\right) (3 x+2)^5\right)+31360 \left(5742093750 x^6-1204771087500 x^5-5725523831250 x^4+24855584532000 x^3+35446253946600 x^2-11610437536320 x-13710030698016\right) (3 x+2)^5}","\frac{7 (1-2 x)^{3/2}}{15 (3 x+2)^5 \sqrt{5 x+3}}+\frac{102293609 \sqrt{1-2 x}}{18816 (3 x+2) \sqrt{5 x+3}}+\frac{587477 \sqrt{1-2 x}}{1344 (3 x+2)^2 \sqrt{5 x+3}}+\frac{12023 \sqrt{1-2 x}}{240 (3 x+2)^3 \sqrt{5 x+3}}+\frac{2513 \sqrt{1-2 x}}{360 (3 x+2)^4 \sqrt{5 x+3}}-\frac{4639661185 \sqrt{1-2 x}}{56448 \sqrt{5 x+3}}+\frac{3538809681 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{6272 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(727098642968333575064576 + 5533442583198965794711296*x + 16161240133328254797824384*x^2 + 20331450932529364264675840*x^3 + 2966650903864286927545920*x^4 - 19986055834258423988583040*x^5 - 20471769208930472301708000*x^6 - 6480775235917322099467500*x^7 + 222669638489869988906250*x^8 + 209949806715334632843750*x^9 + 1447041499930835578125*x^10) + Sqrt[3 + 5*x]*(-727098642968333575064576 - 4807987293550845443480320*x - 10290541881308384585127040*x^2 - 1237062694398888099761920*x^3 + 27738499983574231431733120*x^4 + 42173922651770491621034336*x^5 + 19898637033096620626927440*x^6 - 4491439461406435896590100*x^7 - 5896153568525262422910750*x^8 - 893920202455229221387500*x^9 + 21339398741915500228125*x^10) + Sqrt[3]*(727098642968333575064576 + 5413681653744560922700800*x + 14045470404787223296685440*x^2 + 8354724112084264155333120*x^3 - 29114983090263408965119520*x^4 - 63934803683476280106105936*x^5 - 46765806458885953386603720*x^6 - 3934750877871630238996400*x^7 + 10797785031982203064465750*x^8 + 3892388221271859875840625*x^9 + 115038127818785326303125*x^10 - 5644978066841619937500*x^11 + Sqrt[1 - 2*x]*(-727098642968333575064576 - 6139136943392681273931776*x - 20520493555900631302075264*x^2 - 32089872184456329958872960*x^3 - 15675448416765557441308320*x^4 + 21312808901616434963915440*x^5 + 35504793010306714344846200*x^6 + 18202524384153359673742000*x^7 + 2100405344814604195046250*x^8 - 640156868034125958140625*x^9 - 46964835866868101015625*x^10)))/(31360*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(4571572732672 + 44616484880*x - 10194890840200*x^2 - 1277247746500*x^3 + 1102102787500*x^4 + 26771628125*x^5) + 31360*(2 + 3*x)^5*(-13710030698016 - 11610437536320*x + 35446253946600*x^2 + 24855584532000*x^3 - 5725523831250*x^4 - 1204771087500*x^5 + 5742093750*x^6) + Sqrt[1 - 2*x]*(31360*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(-4559963226880 - 4498159242000*x + 3864602795000*x^2 + 1803368312500*x^3 - 88889062500*x^4 - 3582203125*x^5) + 31360*(2 + 3*x)^5*(13675202180640 + 24937354543200*x - 5268814683000*x^2 - 15408712935000*x^3 - 1023535218750*x^4 + 149794218750*x^5))) - (3538809681*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/6272 + (17694048405*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/12544","C",1
2447,1,534,193,10.1931197,"\int \frac{(1-2 x)^{5/2} (2+3 x)^4}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^4)/(3 + 5*x)^(5/2),x]","\frac{88296593 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{20000000 \sqrt{10}}+\frac{-1106024949000000000000 x^{13}+491693116876537500000000 x^{12}+2913600415980886875000000 x^{11}-22812324297367666640625000 x^{10}-54948750407601746561718750 x^9+43108007167525915817109375 x^8+115777537735180509824343750 x^7-34389809605545988772840625 x^6-109306452827214757305633750 x^5+14060663796347077542111000 x^4+65940943943291815689544800 x^3+11370164148854456776258800 x^2-12894067556040431805455520 x+\sqrt{3} \sqrt{5 x+3} \left(-10508848178400000000000 x^{12}-508062425180310000000000 x^{11}+1022426874809554500000000 x^{10}+11988485460357811762500000 x^9+2460355845234462264375000 x^8-27471495871568394961046875 x^7-6772744124406799705684375 x^6+27528789319011007134786250 x^5+6433755470656328678721000 x^4-16372704381229174658279600 x^3-5914991281426867362751600 x^2+3133278422503582561582880 x+1397624665787389273282752\right)+\sqrt{1-2 x} \left(-47342701305900000000000 x^{12}+606091474607726250000000 x^{11}+10821458083026027937500000 x^{10}+3885636633474400045312500 x^9-57739318413743309658046875 x^8-46561233829766064632437500 x^7+65256071726993334270290625 x^6+56305872760327055438306250 x^5-46504778717212986051387000 x^4-47425856560949165993284800 x^3+7831508424773373872117520 x^2+17088767114924974944134880 x+\sqrt{3} \sqrt{5 x+3} \left(1029577926600000000000 x^{12}+27440732437942500000000 x^{11}-1077903635508923625000000 x^{10}-3366817807605701146875000 x^9+7213534911150122110781250 x^8+16188026340392699193765625 x^7-7099147771723778929228125 x^6-19007345555247751296803750 x^5+4884345173041983017607000 x^4+14077509093644398025158800 x^3+679684953483700553203760 x^2-4531511608798430274476000 x-1397624665787389273282752\right)+4192873997362167819848256\right)-4192873997362167819848256}{1080000000 \left(-3382394640625 x^6+46839566881250 x^5+721064958542500 x^4-436816644264000 x^3-2966115478898000 x^2+4019894758880 x+1105183793314304\right) (5 x+3)^{3/2}+1080000000 \sqrt{1-2 x} \left(39509921875 x^6-17586049031250 x^5-94425179937500 x^4+841225686360000 x^3+1360283516838000 x^2-1099312389138400 x-1104347908897280\right) (5 x+3)^{3/2}+\sqrt{3} \left(1080000000 \sqrt{1-2 x} (5 x+3) \left(1877009062500 x^6+90847846375000 x^5-175063626237500 x^4-2024055290400000 x^3-831988612312000 x^2+2020474709052800 x+1104269783897280\right)+1080000000 (5 x+3) \left(367790468750 x^7+9638528906250 x^6-388916755537500 x^5-1017871743627500 x^4+2573340308796000 x^3+3351687890666400 x^2-925956910020800 x-1105105668314304\right)\right)}","-\frac{508 (1-2 x)^{3/2} (3 x+2)^4}{75 \sqrt{5 x+3}}-\frac{2 (1-2 x)^{5/2} (3 x+2)^4}{15 (5 x+3)^{3/2}}+\frac{2514}{625} (1-2 x)^{3/2} \sqrt{5 x+3} (3 x+2)^3+\frac{23991 (1-2 x)^{3/2} \sqrt{5 x+3} (3 x+2)^2}{25000}+\frac{21 (1-2 x)^{3/2} \sqrt{5 x+3} (118392 x+64435)}{4000000}+\frac{8026963 \sqrt{1-2 x} \sqrt{5 x+3}}{40000000}+\frac{88296593 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{40000000 \sqrt{10}}",1,"(-4192873997362167819848256 - 12894067556040431805455520*x + 11370164148854456776258800*x^2 + 65940943943291815689544800*x^3 + 14060663796347077542111000*x^4 - 109306452827214757305633750*x^5 - 34389809605545988772840625*x^6 + 115777537735180509824343750*x^7 + 43108007167525915817109375*x^8 - 54948750407601746561718750*x^9 - 22812324297367666640625000*x^10 + 2913600415980886875000000*x^11 + 491693116876537500000000*x^12 - 1106024949000000000000*x^13 + Sqrt[3]*Sqrt[3 + 5*x]*(1397624665787389273282752 + 3133278422503582561582880*x - 5914991281426867362751600*x^2 - 16372704381229174658279600*x^3 + 6433755470656328678721000*x^4 + 27528789319011007134786250*x^5 - 6772744124406799705684375*x^6 - 27471495871568394961046875*x^7 + 2460355845234462264375000*x^8 + 11988485460357811762500000*x^9 + 1022426874809554500000000*x^10 - 508062425180310000000000*x^11 - 10508848178400000000000*x^12) + Sqrt[1 - 2*x]*(4192873997362167819848256 + 17088767114924974944134880*x + 7831508424773373872117520*x^2 - 47425856560949165993284800*x^3 - 46504778717212986051387000*x^4 + 56305872760327055438306250*x^5 + 65256071726993334270290625*x^6 - 46561233829766064632437500*x^7 - 57739318413743309658046875*x^8 + 3885636633474400045312500*x^9 + 10821458083026027937500000*x^10 + 606091474607726250000000*x^11 - 47342701305900000000000*x^12 + Sqrt[3]*Sqrt[3 + 5*x]*(-1397624665787389273282752 - 4531511608798430274476000*x + 679684953483700553203760*x^2 + 14077509093644398025158800*x^3 + 4884345173041983017607000*x^4 - 19007345555247751296803750*x^5 - 7099147771723778929228125*x^6 + 16188026340392699193765625*x^7 + 7213534911150122110781250*x^8 - 3366817807605701146875000*x^9 - 1077903635508923625000000*x^10 + 27440732437942500000000*x^11 + 1029577926600000000000*x^12)))/(1080000000*(3 + 5*x)^(3/2)*(1105183793314304 + 4019894758880*x - 2966115478898000*x^2 - 436816644264000*x^3 + 721064958542500*x^4 + 46839566881250*x^5 - 3382394640625*x^6) + 1080000000*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)*(-1104347908897280 - 1099312389138400*x + 1360283516838000*x^2 + 841225686360000*x^3 - 94425179937500*x^4 - 17586049031250*x^5 + 39509921875*x^6) + Sqrt[3]*(1080000000*Sqrt[1 - 2*x]*(3 + 5*x)*(1104269783897280 + 2020474709052800*x - 831988612312000*x^2 - 2024055290400000*x^3 - 175063626237500*x^4 + 90847846375000*x^5 + 1877009062500*x^6) + 1080000000*(3 + 5*x)*(-1105105668314304 - 925956910020800*x + 3351687890666400*x^2 + 2573340308796000*x^3 - 1017871743627500*x^4 - 388916755537500*x^5 + 9638528906250*x^6 + 367790468750*x^7))) + (88296593*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(20000000*Sqrt[10])","B",1
2448,1,474,164,3.4493487,"\int \frac{(1-2 x)^{5/2} (2+3 x)^3}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(3 + 5*x)^(5/2),x]","\frac{766843 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{200000 \sqrt{10}}+\frac{417828172500000000 x^{11}+10221780389625000000 x^{10}-214503110171071875000 x^9-389836406176763906250 x^8+960533095630541953125 x^7+690309036530794106250 x^6-1616803777456909704375 x^5-253909988132285789250 x^4+1817410844369910576300 x^3+582320687108875825200 x^2+\sqrt{3} \sqrt{5 x+3} \left(-1164799845000000000 x^{10}+9065569713750000000 x^9+113069054973228750000 x^8-80139175948637437500 x^7-304296726013426953125 x^6+241710955177306071875 x^5+297825206764950510250 x^4-374328605025814660100 x^3-257471895555562608800 x^2+102569385697175679920 x+63599422509159610656\right)+\sqrt{1-2 x} \left(1561321352250000000 x^{10}+64508832769837500000 x^9-66709118552824687500 x^8-681619274342784421875 x^7+36349336967842387500 x^6+1008275014796739298125 x^5-498762202021794537750 x^4-1234465543075485101700 x^3+169437774369251966160 x^2+\sqrt{3} \sqrt{5 x+3} \left(22325260500000000 x^{10}-4694196355425000000 x^9-20173554911829375000 x^8+110998010525323781250 x^7+110011706130878490625 x^6-223007353181486743125 x^5-53755655420522412250 x^4+322567860574297319500 x^3+59876805921144655680 x^2-166160073440562752720 x-63599422509159610656\right)+657475249810993534800 x+190798267527478831968\right)-466703186580832316400 x-190798267527478831968}{10800000 \sqrt{1-2 x} \left(-3582203125 x^5-88889062500 x^4+1803368312500 x^3+3864602795000 x^2-4498159242000 x-4559963226880\right) (5 x+3)^{3/2}+10800000 \left(26771628125 x^5+1102102787500 x^4-1277247746500 x^3-10194890840200 x^2+44616484880 x+4571572732672\right) (5 x+3)^{3/2}+\sqrt{3} \left(10800000 \sqrt{1-2 x} (5 x+3) \left(49931406250 x^5-341178406250 x^4-5136237645000 x^3-1756271561000 x^2+8312451514400 x+4558400726880\right)+10800000 (5 x+3) \left(1914031250 x^6-401590362500 x^5-1908507943750 x^4+8285194844000 x^3+11815417982200 x^2-3870145845440 x-4570010232672\right)\right)}","-\frac{376 (1-2 x)^{3/2} (3 x+2)^3}{75 \sqrt{5 x+3}}-\frac{2 (1-2 x)^{5/2} (3 x+2)^3}{15 (5 x+3)^{3/2}}+\frac{741}{250} (1-2 x)^{3/2} \sqrt{5 x+3} (3 x+2)^2+\frac{21 (1-2 x)^{3/2} \sqrt{5 x+3} (4392 x+3185)}{40000}+\frac{69713 \sqrt{1-2 x} \sqrt{5 x+3}}{400000}+\frac{766843 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{400000 \sqrt{10}}",1,"(-190798267527478831968 - 466703186580832316400*x + 582320687108875825200*x^2 + 1817410844369910576300*x^3 - 253909988132285789250*x^4 - 1616803777456909704375*x^5 + 690309036530794106250*x^6 + 960533095630541953125*x^7 - 389836406176763906250*x^8 - 214503110171071875000*x^9 + 10221780389625000000*x^10 + 417828172500000000*x^11 + Sqrt[3]*Sqrt[3 + 5*x]*(63599422509159610656 + 102569385697175679920*x - 257471895555562608800*x^2 - 374328605025814660100*x^3 + 297825206764950510250*x^4 + 241710955177306071875*x^5 - 304296726013426953125*x^6 - 80139175948637437500*x^7 + 113069054973228750000*x^8 + 9065569713750000000*x^9 - 1164799845000000000*x^10) + Sqrt[1 - 2*x]*(190798267527478831968 + 657475249810993534800*x + 169437774369251966160*x^2 - 1234465543075485101700*x^3 - 498762202021794537750*x^4 + 1008275014796739298125*x^5 + 36349336967842387500*x^6 - 681619274342784421875*x^7 - 66709118552824687500*x^8 + 64508832769837500000*x^9 + 1561321352250000000*x^10 + Sqrt[3]*Sqrt[3 + 5*x]*(-63599422509159610656 - 166160073440562752720*x + 59876805921144655680*x^2 + 322567860574297319500*x^3 - 53755655420522412250*x^4 - 223007353181486743125*x^5 + 110011706130878490625*x^6 + 110998010525323781250*x^7 - 20173554911829375000*x^8 - 4694196355425000000*x^9 + 22325260500000000*x^10)))/(10800000*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)*(-4559963226880 - 4498159242000*x + 3864602795000*x^2 + 1803368312500*x^3 - 88889062500*x^4 - 3582203125*x^5) + 10800000*(3 + 5*x)^(3/2)*(4571572732672 + 44616484880*x - 10194890840200*x^2 - 1277247746500*x^3 + 1102102787500*x^4 + 26771628125*x^5) + Sqrt[3]*(10800000*Sqrt[1 - 2*x]*(3 + 5*x)*(4558400726880 + 8312451514400*x - 1756271561000*x^2 - 5136237645000*x^3 - 341178406250*x^4 + 49931406250*x^5) + 10800000*(3 + 5*x)*(-4570010232672 - 3870145845440*x + 11815417982200*x^2 + 8285194844000*x^3 - 1908507943750*x^4 - 401590362500*x^5 + 1914031250*x^6))) + (766843*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(200000*Sqrt[10])","B",1
2449,1,414,138,2.8244082,"\int \frac{(1-2 x)^{5/2} (2+3 x)^2}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^2)/(3 + 5*x)^(5/2),x]","\frac{-16137225000000 x^9+1668457186875000 x^8+3656325243656250 x^7-19717354443065625 x^6+10837419610230000 x^5+13798148140011375 x^4-30354502324209300 x^3-12125269927899900 x^2+\sqrt{3} \sqrt{5 x+3} \left(-38170440000000 x^8-1236040641000000 x^7+2459187398250000 x^6+2359826600360625 x^5-6910073016070125 x^4+5198098708479600 x^3+5461465692919500 x^2-2214898420999000 x-1203458774323344\right)+\sqrt{1-2 x} \left(-274269847500000 x^8+1199514931312500 x^7+9681964591303125 x^6-10675005084191250 x^5-2313453709227375 x^4+19539237796798500 x^3-2912516899425540 x^2+\sqrt{3} \sqrt{5 x+3} \left(7468605000000 x^8+144175150125000 x^7-1744130873418750 x^6-40909190256875 x^5+3507998832452125 x^4-4506759122600400 x^3-1453597974193820 x^2+3420154008208360 x+1203458774323344\right)-13270153663558440 x-3610376322970032\right)+9654386901930360 x+3610376322970032}{135000 \left(-846511875 x^4+2876857500 x^3+32771841300 x^2-464036760 x-18959828096\right) (5 x+3)^{3/2}+135000 \sqrt{1-2 x} \left(24903125 x^4-2538047500 x^3-9400717500 x^2+18053298200 x+18798584960\right) (5 x+3)^{3/2}+\sqrt{3} \left(135000 \sqrt{1-2 x} (5 x+3) \left(294525000 x^4+10148490000 x^3+1543311000 x^2-33942744000 x-18767334960\right)+135000 (5 x+3) \left(115256250 x^5+2406453750 x^4-23245830000 x^3-39836473200 x^2+16519101840 x+18928578096\right)\right)}+\frac{3619 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{2500 \sqrt{10}}","-\frac{76 (1-2 x)^{7/2}}{1815 \sqrt{5 x+3}}-\frac{2 (1-2 x)^{7/2}}{825 (5 x+3)^{3/2}}+\frac{329 \sqrt{5 x+3} (1-2 x)^{5/2}}{45375}+\frac{329 \sqrt{5 x+3} (1-2 x)^{3/2}}{16500}+\frac{329 \sqrt{5 x+3} \sqrt{1-2 x}}{5000}+\frac{3619 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{5000 \sqrt{10}}",1,"(3610376322970032 + 9654386901930360*x - 12125269927899900*x^2 - 30354502324209300*x^3 + 13798148140011375*x^4 + 10837419610230000*x^5 - 19717354443065625*x^6 + 3656325243656250*x^7 + 1668457186875000*x^8 - 16137225000000*x^9 + Sqrt[3]*Sqrt[3 + 5*x]*(-1203458774323344 - 2214898420999000*x + 5461465692919500*x^2 + 5198098708479600*x^3 - 6910073016070125*x^4 + 2359826600360625*x^5 + 2459187398250000*x^6 - 1236040641000000*x^7 - 38170440000000*x^8) + Sqrt[1 - 2*x]*(-3610376322970032 - 13270153663558440*x - 2912516899425540*x^2 + 19539237796798500*x^3 - 2313453709227375*x^4 - 10675005084191250*x^5 + 9681964591303125*x^6 + 1199514931312500*x^7 - 274269847500000*x^8 + Sqrt[3]*Sqrt[3 + 5*x]*(1203458774323344 + 3420154008208360*x - 1453597974193820*x^2 - 4506759122600400*x^3 + 3507998832452125*x^4 - 40909190256875*x^5 - 1744130873418750*x^6 + 144175150125000*x^7 + 7468605000000*x^8)))/(135000*(3 + 5*x)^(3/2)*(-18959828096 - 464036760*x + 32771841300*x^2 + 2876857500*x^3 - 846511875*x^4) + 135000*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)*(18798584960 + 18053298200*x - 9400717500*x^2 - 2538047500*x^3 + 24903125*x^4) + Sqrt[3]*(135000*Sqrt[1 - 2*x]*(3 + 5*x)*(-18767334960 - 33942744000*x + 1543311000*x^2 + 10148490000*x^3 + 294525000*x^4) + 135000*(3 + 5*x)*(18928578096 + 16519101840*x - 39836473200*x^2 - 23245830000*x^3 + 2406453750*x^4 + 115256250*x^5))) + (3619*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(2500*Sqrt[10])","B",1
2450,1,354,116,2.4020378,"\int \frac{(1-2 x)^{5/2} (2+3 x)}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x))/(3 + 5*x)^(5/2),x]","\frac{17850375000 x^7+209592731250 x^6-2253780628125 x^5+3251627919000 x^4+21113373330675 x^3+9390590296800 x^2+\sqrt{3} \sqrt{5 x+3} \left(-36486450000 x^6+173716042500 x^5+457541940625 x^4-3515656946725 x^3-4023969418700 x^2+1740778143940 x+1733734629528\right)+\sqrt{1-2 x} \left(27988537500 x^6+649444516875 x^5-3123086100750 x^4-7123167989025 x^3+7029370080480 x^2+\sqrt{3} \sqrt{5 x+3} \left(1642275000 x^6-82642511250 x^5+86581125875 x^4+1681264956975 x^3-41974080860 x^2-3440890220380 x-1733734629528\right)+14628856922460 x+5201203888584\right)-9528520693140 x-5201203888584}{6750 \sqrt{1-2 x} \left(-1101875 x^3-16812750 x^2+68422100 x+77141440\right) (5 x+3)^{3/2}+6750 \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (5 x+3)^{3/2}+\sqrt{3} \left(6750 \sqrt{1-2 x} (5 x+3) \left(11261250 x^3-7257250 x^2-135935800 x-76516440\right)+6750 (5 x+3) \left(1013750 x^4-47347500 x^3-123624450 x^2+74349280 x+78755928\right)\right)}-\frac{1001 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{125 \sqrt{10}}","-\frac{2 (1-2 x)^{7/2}}{165 (5 x+3)^{3/2}}-\frac{182 (1-2 x)^{5/2}}{825 \sqrt{5 x+3}}-\frac{91}{825} \sqrt{5 x+3} (1-2 x)^{3/2}-\frac{91}{250} \sqrt{5 x+3} \sqrt{1-2 x}-\frac{1001 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{250 \sqrt{10}}",1,"(-5201203888584 - 9528520693140*x + 9390590296800*x^2 + 21113373330675*x^3 + 3251627919000*x^4 - 2253780628125*x^5 + 209592731250*x^6 + 17850375000*x^7 + Sqrt[3]*Sqrt[3 + 5*x]*(1733734629528 + 1740778143940*x - 4023969418700*x^2 - 3515656946725*x^3 + 457541940625*x^4 + 173716042500*x^5 - 36486450000*x^6) + Sqrt[1 - 2*x]*(5201203888584 + 14628856922460*x + 7029370080480*x^2 - 7123167989025*x^3 - 3123086100750*x^4 + 649444516875*x^5 + 27988537500*x^6 + Sqrt[3]*Sqrt[3 + 5*x]*(-1733734629528 - 3440890220380*x - 41974080860*x^2 + 1681264956975*x^3 + 86581125875*x^4 - 82642511250*x^5 + 1642275000*x^6)))/(6750*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)*(77141440 + 68422100*x - 16812750*x^2 - 1101875*x^3) + 6750*(3 + 5*x)^(3/2)*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3) + Sqrt[3]*(6750*Sqrt[1 - 2*x]*(3 + 5*x)*(-76516440 - 135935800*x - 7257250*x^2 + 11261250*x^3) + 6750*(3 + 5*x)*(78755928 + 74349280*x - 123624450*x^2 - 47347500*x^3 + 1013750*x^4))) - (1001*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(125*Sqrt[10])","B",1
2451,1,304,96,1.9428115,"\int \frac{(1-2 x)^{5/2}}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/(3 + 5*x)^(5/2),x]","\frac{-2 \sqrt{3} \sqrt{5 x+3} \left(2970000 x^4+136010875 x^3+339257875 x^2-176532730 x-152676348\right)+\sqrt{1-2 x} \left(-2 \sqrt{3} \sqrt{5 x+3} \left(-1876500 x^4-32785925 x^3+5018385 x^2+321137590 x+152676348\right)-2 \left(44178750 x^4+238152750 x^3-666084705 x^2-1335372390 x-458029044\right)\right)-2 \left(6412500 x^5-120817500 x^4-1260246000 x^3-718524975 x^2+901557810 x+458029044\right)}{675 \left(-163625 x^2+33550 x+343904\right) (5 x+3)^{3/2}+675 \sqrt{1-2 x} \left(11875 x^2-216750 x-312800\right) (5 x+3)^{3/2}+\sqrt{3} \left(675 \sqrt{1-2 x} (5 x+3) \left(27500 x^2+517000 x+300300\right)+675 (5 x+3) \left(34750 x^3+321050 x^2-372220 x-331404\right)\right)}+\frac{44}{25} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{2 (1-2 x)^{5/2}}{15 (5 x+3)^{3/2}}+\frac{4 (1-2 x)^{3/2}}{15 \sqrt{5 x+3}}+\frac{4}{25} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{22}{25} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"(-2*Sqrt[3]*Sqrt[3 + 5*x]*(-152676348 - 176532730*x + 339257875*x^2 + 136010875*x^3 + 2970000*x^4) - 2*(458029044 + 901557810*x - 718524975*x^2 - 1260246000*x^3 - 120817500*x^4 + 6412500*x^5) + Sqrt[1 - 2*x]*(-2*Sqrt[3]*Sqrt[3 + 5*x]*(152676348 + 321137590*x + 5018385*x^2 - 32785925*x^3 - 1876500*x^4) - 2*(-458029044 - 1335372390*x - 666084705*x^2 + 238152750*x^3 + 44178750*x^4)))/(675*(3 + 5*x)^(3/2)*(343904 + 33550*x - 163625*x^2) + 675*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)*(-312800 - 216750*x + 11875*x^2) + Sqrt[3]*(675*Sqrt[1 - 2*x]*(3 + 5*x)*(300300 + 517000*x + 27500*x^2) + 675*(3 + 5*x)*(-331404 - 372220*x + 321050*x^2 + 34750*x^3))) + (44*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/25","B",1
2452,1,436,108,2.0471783,"\int \frac{(1-2 x)^{5/2}}{(2+3 x) (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)*(3 + 5*x)^(5/2)),x]","-\frac{343}{3} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{242 \sqrt{3} \sqrt{5 x+3} \left(-280500 x^2+239470 x+238128\right)+\sqrt{1-2 x} \left(242 \sqrt{3} \sqrt{5 x+3} \left(-6850 x^2-408910 x-238128\right)+242 \left(814275 x^2+1702800 x+714384\right)\right)+242 \left(501750 x^3+352125 x^2-1194480 x-714384\right)}{\sqrt{3} \left(675 (5 x+3) \left(450 x^2-2100 x-1422\right)+675 \sqrt{1-2 x} (5 x+3) (1650 x+990)\right)+675 (165 x+1672) (5 x+3)^{3/2}+675 (-325 x-1240) \sqrt{1-2 x} (5 x+3)^{3/2}}-\frac{16}{75} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{22 (1-2 x)^{3/2}}{15 (5 x+3)^{3/2}}+\frac{814 \sqrt{1-2 x}}{25 \sqrt{5 x+3}}-\frac{8}{75} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{98}{3} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(242*Sqrt[3]*Sqrt[3 + 5*x]*(238128 + 239470*x - 280500*x^2) + 242*(-714384 - 1194480*x + 352125*x^2 + 501750*x^3) + Sqrt[1 - 2*x]*(242*Sqrt[3]*Sqrt[3 + 5*x]*(-238128 - 408910*x - 6850*x^2) + 242*(714384 + 1702800*x + 814275*x^2)))/(675*(-1240 - 325*x)*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2) + 675*(3 + 5*x)^(3/2)*(1672 + 165*x) + Sqrt[3]*(675*Sqrt[1 - 2*x]*(3 + 5*x)*(990 + 1650*x) + 675*(3 + 5*x)*(-1422 - 2100*x + 450*x^2))) - (16*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/75 - (343*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ])/3","C",1
2453,1,517,101,2.1981547,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^2 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^2*(3 + 5*x)^(5/2)),x]","2695 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{13475}{2} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{3116823750 x^5+244320296250 x^4+318215314950 x^3-90041348010 x^2+\sqrt{3} \sqrt{5 x+3} \left(-20244266625 x^4-84047571575 x^3-13730002220 x^2+61662245348 x+26372423352\right)+\sqrt{1-2 x} \left(-43590269250 x^4+115341091800 x^3+399193630374 x^2+\sqrt{3} \sqrt{5 x+3} \left(3425488575 x^4+1199939665 x^3-70139255148 x^2-85771479452 x-26372423352\right)+320516921736 x+79117270056\right)-248189219424 x-79117270056}{54 (3 x+2) \left(-163625 x^2+33550 x+343904\right) (5 x+3)^{3/2}+54 \sqrt{1-2 x} (3 x+2) \left(11875 x^2-216750 x-312800\right) (5 x+3)^{3/2}+\sqrt{3} \left(54 \sqrt{1-2 x} (3 x+2) (5 x+3) \left(27500 x^2+517000 x+300300\right)+54 (3 x+2) (5 x+3) \left(34750 x^3+321050 x^2-372220 x-331404\right)\right)}","\frac{(1-2 x)^{5/2}}{(3 x+2) (5 x+3)^{3/2}}-\frac{55 (1-2 x)^{3/2}}{3 (5 x+3)^{3/2}}+\frac{385 \sqrt{1-2 x}}{\sqrt{5 x+3}}-385 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(-79117270056 - 248189219424*x - 90041348010*x^2 + 318215314950*x^3 + 244320296250*x^4 + 3116823750*x^5 + Sqrt[3]*Sqrt[3 + 5*x]*(26372423352 + 61662245348*x - 13730002220*x^2 - 84047571575*x^3 - 20244266625*x^4) + Sqrt[1 - 2*x]*(79117270056 + 320516921736*x + 399193630374*x^2 + 115341091800*x^3 - 43590269250*x^4 + Sqrt[3]*Sqrt[3 + 5*x]*(-26372423352 - 85771479452*x - 70139255148*x^2 + 1199939665*x^3 + 3425488575*x^4)))/(54*(2 + 3*x)*(3 + 5*x)^(3/2)*(343904 + 33550*x - 163625*x^2) + 54*Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^(3/2)*(-312800 - 216750*x + 11875*x^2) + Sqrt[3]*(54*Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)*(300300 + 517000*x + 27500*x^2) + 54*(2 + 3*x)*(3 + 5*x)*(-331404 - 372220*x + 321050*x^2 + 34750*x^3))) + 2695*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ] - (13475*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2","C",1
2454,1,587,137,2.6222119,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^3 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^3*(3 + 5*x)^(5/2)),x]","\frac{92015}{4} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{460075}{8} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{51831735637500 x^7-115418485468125 x^6-4809999123775500 x^5-9039496242664125 x^4-3441751962138090 x^3+3387398269472412 x^2+\sqrt{3} \sqrt{5 x+3} \left(-55249942584375 x^6+497671544283375 x^5+1858424853773950 x^4+1357647437440250 x^3-512435256910544 x^2-826793726507672 x-217905234327264\right)+\sqrt{1-2 x} \left(233354536655625 x^6+1811362543105500 x^5+680100054150825 x^4-5049950946828810 x^3-7193725231408188 x^2+\sqrt{3} \sqrt{5 x+3} \left(-2473498186875 x^6-249183862926375 x^5-422413213020400 x^4+634467066066090 x^3+1605812449781176 x^2+1039135179087224 x+217905234327264\right)-3657510374954832 x-653715702981792\right)+3020486017216176 x+653715702981792}{108 \sqrt{1-2 x} (5 x+3)^{3/2} \left(-1101875 x^3-16812750 x^2+68422100 x+77141440\right) (3 x+2)^2+108 (5 x+3)^{3/2} \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (3 x+2)^2+\sqrt{3} \left(108 \sqrt{1-2 x} (5 x+3) \left(11261250 x^3-7257250 x^2-135935800 x-76516440\right) (3 x+2)^2+108 (5 x+3) \left(1013750 x^4-47347500 x^3-123624450 x^2+74349280 x+78755928\right) (3 x+2)^2\right)}","\frac{3 (1-2 x)^{7/2}}{14 (3 x+2)^2 (5 x+3)^{3/2}}+\frac{239 (1-2 x)^{5/2}}{28 (3 x+2) (5 x+3)^{3/2}}-\frac{13145 (1-2 x)^{3/2}}{84 (5 x+3)^{3/2}}+\frac{13145 \sqrt{1-2 x}}{4 \sqrt{5 x+3}}-\frac{13145}{4} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)",1,"(653715702981792 + 3020486017216176*x + 3387398269472412*x^2 - 3441751962138090*x^3 - 9039496242664125*x^4 - 4809999123775500*x^5 - 115418485468125*x^6 + 51831735637500*x^7 + Sqrt[3]*Sqrt[3 + 5*x]*(-217905234327264 - 826793726507672*x - 512435256910544*x^2 + 1357647437440250*x^3 + 1858424853773950*x^4 + 497671544283375*x^5 - 55249942584375*x^6) + Sqrt[1 - 2*x]*(-653715702981792 - 3657510374954832*x - 7193725231408188*x^2 - 5049950946828810*x^3 + 680100054150825*x^4 + 1811362543105500*x^5 + 233354536655625*x^6 + Sqrt[3]*Sqrt[3 + 5*x]*(217905234327264 + 1039135179087224*x + 1605812449781176*x^2 + 634467066066090*x^3 - 422413213020400*x^4 - 249183862926375*x^5 - 2473498186875*x^6)))/(108*Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^(3/2)*(77141440 + 68422100*x - 16812750*x^2 - 1101875*x^3) + 108*(2 + 3*x)^2*(3 + 5*x)^(3/2)*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3) + Sqrt[3]*(108*Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)*(-76516440 - 135935800*x - 7257250*x^2 + 11261250*x^3) + 108*(2 + 3*x)^2*(3 + 5*x)*(78755928 + 74349280*x - 123624450*x^2 - 47347500*x^3 + 1013750*x^4))) + (92015*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/4 - (460075*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/8","C",1
2455,1,647,166,3.213328,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^4 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^4*(3 + 5*x)^(5/2)),x]","\frac{1361195}{8} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{6805975}{16} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{44433200584406250 x^9+5482558111705396875 x^8+9517664387726673750 x^7-59081194577575796625 x^6-165709417500516405150 x^5-136275222753994635900 x^4-3073996372026043872 x^3+54259802905461694416 x^2+\sqrt{3} \sqrt{5 x+3} \left(-282064244465025000 x^8-2902654303570890000 x^7+4055086916880813000 x^6+29454668548941814200 x^5+36193882667659159080 x^4+8422819654097496384 x^3-11754180288285847632 x^2-8241629605085574368 x-1560180570075393024\right)+\sqrt{1-2 x} \left(-406304047609453125 x^8+8118589155196162500 x^7+47534912212079716875 x^6+62532104424441077250 x^5-17623880269997175900 x^4-102125621465484320880 x^3-89371646217368391888 x^2+\sqrt{3} \sqrt{5 x+3} \left(22453831490343750 x^8-194513385733875000 x^7-6357662290638056250 x^6-14922371129300342500 x^5-4176803369199630400 x^4+18498677943806429280 x^3+22170151349206492976 x^2+9789958076168478944 x+1560180570075393024\right)-33263434605131419392 x-4680541710226179072\right)+28618449191882705664 x+4680541710226179072}{216 (5 x+3)^{3/2} \left(-846511875 x^4+2876857500 x^3+32771841300 x^2-464036760 x-18959828096\right) (3 x+2)^3+216 \sqrt{1-2 x} (5 x+3)^{3/2} \left(24903125 x^4-2538047500 x^3-9400717500 x^2+18053298200 x+18798584960\right) (3 x+2)^3+\sqrt{3} \left(216 \sqrt{1-2 x} (5 x+3) \left(294525000 x^4+10148490000 x^3+1543311000 x^2-33942744000 x-18767334960\right) (3 x+2)^3+216 (5 x+3) \left(115256250 x^5+2406453750 x^4-23245830000 x^3-39836473200 x^2+16519101840 x+18928578096\right) (3 x+2)^3\right)}","\frac{7 (1-2 x)^{3/2}}{9 (3 x+2)^3 (5 x+3)^{3/2}}+\frac{1784635 \sqrt{1-2 x}}{72 \sqrt{5 x+3}}+\frac{7843 \sqrt{1-2 x}}{24 (3 x+2) (5 x+3)^{3/2}}+\frac{77 \sqrt{1-2 x}}{4 (3 x+2)^2 (5 x+3)^{3/2}}-\frac{196735 \sqrt{1-2 x}}{72 (5 x+3)^{3/2}}-\frac{1361195 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{8 \sqrt{7}}",1,"(4680541710226179072 + 28618449191882705664*x + 54259802905461694416*x^2 - 3073996372026043872*x^3 - 136275222753994635900*x^4 - 165709417500516405150*x^5 - 59081194577575796625*x^6 + 9517664387726673750*x^7 + 5482558111705396875*x^8 + 44433200584406250*x^9 + Sqrt[3]*Sqrt[3 + 5*x]*(-1560180570075393024 - 8241629605085574368*x - 11754180288285847632*x^2 + 8422819654097496384*x^3 + 36193882667659159080*x^4 + 29454668548941814200*x^5 + 4055086916880813000*x^6 - 2902654303570890000*x^7 - 282064244465025000*x^8) + Sqrt[1 - 2*x]*(-4680541710226179072 - 33263434605131419392*x - 89371646217368391888*x^2 - 102125621465484320880*x^3 - 17623880269997175900*x^4 + 62532104424441077250*x^5 + 47534912212079716875*x^6 + 8118589155196162500*x^7 - 406304047609453125*x^8 + Sqrt[3]*Sqrt[3 + 5*x]*(1560180570075393024 + 9789958076168478944*x + 22170151349206492976*x^2 + 18498677943806429280*x^3 - 4176803369199630400*x^4 - 14922371129300342500*x^5 - 6357662290638056250*x^6 - 194513385733875000*x^7 + 22453831490343750*x^8)))/(216*(2 + 3*x)^3*(3 + 5*x)^(3/2)*(-18959828096 - 464036760*x + 32771841300*x^2 + 2876857500*x^3 - 846511875*x^4) + 216*Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^(3/2)*(18798584960 + 18053298200*x - 9400717500*x^2 - 2538047500*x^3 + 24903125*x^4) + Sqrt[3]*(216*Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)*(-18767334960 - 33942744000*x + 1543311000*x^2 + 10148490000*x^3 + 294525000*x^4) + 216*(2 + 3*x)^3*(3 + 5*x)*(18928578096 + 16519101840*x - 39836473200*x^2 - 23245830000*x^3 + 2406453750*x^4 + 115256250*x^5))) + (1361195*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/8 - (6805975*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/16","C",1
2456,1,707,195,5.4624813,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^5 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^5*(3 + 5*x)^(5/2)),x]","\frac{519421265}{448} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{2597106325}{896} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{7457053977972306562500 x^{11}-152463275657890291265625 x^{10}-5131408500354905272293750 x^9-13928130238520812092755625 x^8+5924884416113615668981500 x^7+60946720923668311622101200 x^6+80893924795965054826272360 x^5+35206788432662329938061152 x^4-11431185948685414226268768 x^3-17555358136615017326223168 x^2+\sqrt{3} \sqrt{5 x+3} \left(-9396496450364266546875 x^{10}+394251297603046255040625 x^9+2569626887689013995755000 x^8+1822427699488918323623250 x^7-8790385169332465531098200 x^6-17967668267844327998495200 x^5-11378209855233844197733664 x^4+801646954313905825254976 x^3+4323693979469422164318976 x^2+1953440174359346102731136 x+288150657478024846619136\right)+\sqrt{1-2 x} \left(62040863782372109765625 x^{10}+841515470605486261406250 x^9-2828268955482933986409375 x^8-23824934126091870625507500 x^7-45446175028265183955948000 x^6-25998156040585862064934200 x^5+21146858268574661650415520 x^4+40717454834462491688935200 x^3+25397302037824786652565312 x^2+\sqrt{3} \sqrt{5 x+3} \left(-637183845561346171875 x^{10}-92405889761612298328125 x^9-91914460112599315593750 x^8+2856162562848184245843750 x^7+8822569389624628456315000 x^6+8327527398549288916059600 x^5-1577664001820654389342240 x^4-8684678236395033406974080 x^3-6698180104481847486359424 x^2-2240939567633245946819456 x-288150657478024846619136\right)+7442932389582543707006208 x+864451972434074539857408\right)-6580434209760844174741248 x-864451972434074539857408}{12096 \sqrt{1-2 x} (5 x+3)^{3/2} \left(-3582203125 x^5-88889062500 x^4+1803368312500 x^3+3864602795000 x^2-4498159242000 x-4559963226880\right) (3 x+2)^4+12096 (5 x+3)^{3/2} \left(26771628125 x^5+1102102787500 x^4-1277247746500 x^3-10194890840200 x^2+44616484880 x+4571572732672\right) (3 x+2)^4+\sqrt{3} \left(12096 \sqrt{1-2 x} (5 x+3) \left(49931406250 x^5-341178406250 x^4-5136237645000 x^3-1756271561000 x^2+8312451514400 x+4558400726880\right) (3 x+2)^4+12096 (5 x+3) \left(1914031250 x^6-401590362500 x^5-1908507943750 x^4+8285194844000 x^3+11815417982200 x^2-3870145845440 x-4570010232672\right) (3 x+2)^4\right)}","\frac{7 (1-2 x)^{3/2}}{12 (3 x+2)^4 (5 x+3)^{3/2}}+\frac{227000875 \sqrt{1-2 x}}{1344 \sqrt{5 x+3}}+\frac{2992825 \sqrt{1-2 x}}{1344 (3 x+2) (5 x+3)^{3/2}}+\frac{36817 \sqrt{1-2 x}}{288 (3 x+2)^2 (5 x+3)^{3/2}}+\frac{847 \sqrt{1-2 x}}{72 (3 x+2)^3 (5 x+3)^{3/2}}-\frac{25024175 \sqrt{1-2 x}}{1344 (5 x+3)^{3/2}}-\frac{519421265 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{448 \sqrt{7}}",1,"(-864451972434074539857408 - 6580434209760844174741248*x - 17555358136615017326223168*x^2 - 11431185948685414226268768*x^3 + 35206788432662329938061152*x^4 + 80893924795965054826272360*x^5 + 60946720923668311622101200*x^6 + 5924884416113615668981500*x^7 - 13928130238520812092755625*x^8 - 5131408500354905272293750*x^9 - 152463275657890291265625*x^10 + 7457053977972306562500*x^11 + Sqrt[3]*Sqrt[3 + 5*x]*(288150657478024846619136 + 1953440174359346102731136*x + 4323693979469422164318976*x^2 + 801646954313905825254976*x^3 - 11378209855233844197733664*x^4 - 17967668267844327998495200*x^5 - 8790385169332465531098200*x^6 + 1822427699488918323623250*x^7 + 2569626887689013995755000*x^8 + 394251297603046255040625*x^9 - 9396496450364266546875*x^10) + Sqrt[1 - 2*x]*(864451972434074539857408 + 7442932389582543707006208*x + 25397302037824786652565312*x^2 + 40717454834462491688935200*x^3 + 21146858268574661650415520*x^4 - 25998156040585862064934200*x^5 - 45446175028265183955948000*x^6 - 23824934126091870625507500*x^7 - 2828268955482933986409375*x^8 + 841515470605486261406250*x^9 + 62040863782372109765625*x^10 + Sqrt[3]*Sqrt[3 + 5*x]*(-288150657478024846619136 - 2240939567633245946819456*x - 6698180104481847486359424*x^2 - 8684678236395033406974080*x^3 - 1577664001820654389342240*x^4 + 8327527398549288916059600*x^5 + 8822569389624628456315000*x^6 + 2856162562848184245843750*x^7 - 91914460112599315593750*x^8 - 92405889761612298328125*x^9 - 637183845561346171875*x^10)))/(12096*Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^(3/2)*(-4559963226880 - 4498159242000*x + 3864602795000*x^2 + 1803368312500*x^3 - 88889062500*x^4 - 3582203125*x^5) + 12096*(2 + 3*x)^4*(3 + 5*x)^(3/2)*(4571572732672 + 44616484880*x - 10194890840200*x^2 - 1277247746500*x^3 + 1102102787500*x^4 + 26771628125*x^5) + Sqrt[3]*(12096*Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)*(4558400726880 + 8312451514400*x - 1756271561000*x^2 - 5136237645000*x^3 - 341178406250*x^4 + 49931406250*x^5) + 12096*(2 + 3*x)^4*(3 + 5*x)*(-4570010232672 - 3870145845440*x + 11815417982200*x^2 + 8285194844000*x^3 - 1908507943750*x^4 - 401590362500*x^5 + 1914031250*x^6))) + (519421265*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/448 - (2597106325*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/896","C",1
2457,1,767,224,8.023856,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^6 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^6*(3 + 5*x)^(5/2)),x]","\frac{46975917593 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{6272}-\frac{234879587965 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{12544}+\frac{309898706068731774881250000 x^{13}+51190426516327390485637734375 x^{12}-31574504373012290620156781250 x^{11}-3682662933301579046473492078125 x^{10}-12673524216155044050869881792500 x^9-10644660479521065250796995747500 x^8+16826926468954065858415183919400 x^7+42768378429494319686006977199760 x^6+34254957467247254373067625456736 x^5+6762379264159173461868564270720 x^4-7511315207212530635599334983680 x^3-5920988504715573773408919264000 x^2-1723875338829078080001323458560 x+\sqrt{3} \sqrt{5 x+3} \left(-2064647012369678791753359375 x^{12}-31043759388739171827357515625 x^{11}+280797813148046285935250550000 x^{10}+1986756310973111549468843317500 x^9+3192703476344309192378404219500 x^8-1018202833420110351523822855400 x^7-8061221888427001293358895278160 x^6-8774535680285130199978233807712 x^5-2982831606129312770947624319040 x^4+1366368652452712429184309106560 x^3+1560483768134258741055068089600 x^2+522074652389200357912359938560 x+63065308976242683755697457152\right)+\sqrt{1-2 x} \left(-1762389540326171994458203125 x^{12}+144184298054826825065515781250 x^{11}+1201462663855520115468027984375 x^{10}+695464574993914783715625825000 x^9-10001796079358373049248807532500 x^8-27810907247748454016001131889000 x^7-29248736650867084166004792464400 x^6-6748686580533532006267833690720 x^5+14591054854348083056041019953920 x^4+16463848071095443162399086923520 x^3+7925964841656088238527348571904 x^2+1912944042500451980321563785216 x+\sqrt{3} \sqrt{5 x+3} \left(96839259737767398235546875 x^{12}-3859683130123317965993203125 x^{11}-138789767418653112133541343750 x^{10}-379018958054554079511789487500 x^9+875728564711299856904749867500 x^8+4696545750797620525015814903000 x^7+6887651340266448627600715095600 x^6+3262593253211172972736719153440 x^5-2253130049868654552522416322240 x^4-3859245367037001974654190614400 x^3-2176294093020980713713922212608 x^2-585097553612991658019106714112 x-63065308976242683755697457152\right)+189195926928728051267092371456\right)-189195926928728051267092371456}{846720 (5 x+3)^{3/2} \left(-3382394640625 x^6+46839566881250 x^5+721064958542500 x^4-436816644264000 x^3-2966115478898000 x^2+4019894758880 x+1105183793314304\right) (3 x+2)^5+846720 \sqrt{1-2 x} (5 x+3)^{3/2} \left(39509921875 x^6-17586049031250 x^5-94425179937500 x^4+841225686360000 x^3+1360283516838000 x^2-1099312389138400 x-1104347908897280\right) (3 x+2)^5+\sqrt{3} \left(846720 \sqrt{1-2 x} (5 x+3) \left(1877009062500 x^6+90847846375000 x^5-175063626237500 x^4-2024055290400000 x^3-831988612312000 x^2+2020474709052800 x+1104269783897280\right) (3 x+2)^5+846720 (5 x+3) \left(367790468750 x^7+9638528906250 x^6-388916755537500 x^5-1017871743627500 x^4+2573340308796000 x^3+3351687890666400 x^2-925956910020800 x-1105105668314304\right) (3 x+2)^5\right)}","\frac{7 (1-2 x)^{3/2}}{15 (3 x+2)^5 (5 x+3)^{3/2}}+\frac{20529722435 \sqrt{1-2 x}}{18816 \sqrt{5 x+3}}+\frac{270667969 \sqrt{1-2 x}}{18816 (3 x+2) (5 x+3)^{3/2}}+\frac{3329689 \sqrt{1-2 x}}{4032 (3 x+2)^2 (5 x+3)^{3/2}}+\frac{53009 \sqrt{1-2 x}}{720 (3 x+2)^3 (5 x+3)^{3/2}}+\frac{1001 \sqrt{1-2 x}}{120 (3 x+2)^4 (5 x+3)^{3/2}}-\frac{754386765 \sqrt{1-2 x}}{6272 (5 x+3)^{3/2}}-\frac{46975917593 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{6272 \sqrt{7}}",1,"(-189195926928728051267092371456 - 1723875338829078080001323458560*x - 5920988504715573773408919264000*x^2 - 7511315207212530635599334983680*x^3 + 6762379264159173461868564270720*x^4 + 34254957467247254373067625456736*x^5 + 42768378429494319686006977199760*x^6 + 16826926468954065858415183919400*x^7 - 10644660479521065250796995747500*x^8 - 12673524216155044050869881792500*x^9 - 3682662933301579046473492078125*x^10 - 31574504373012290620156781250*x^11 + 51190426516327390485637734375*x^12 + 309898706068731774881250000*x^13 + Sqrt[3]*Sqrt[3 + 5*x]*(63065308976242683755697457152 + 522074652389200357912359938560*x + 1560483768134258741055068089600*x^2 + 1366368652452712429184309106560*x^3 - 2982831606129312770947624319040*x^4 - 8774535680285130199978233807712*x^5 - 8061221888427001293358895278160*x^6 - 1018202833420110351523822855400*x^7 + 3192703476344309192378404219500*x^8 + 1986756310973111549468843317500*x^9 + 280797813148046285935250550000*x^10 - 31043759388739171827357515625*x^11 - 2064647012369678791753359375*x^12) + Sqrt[1 - 2*x]*(189195926928728051267092371456 + 1912944042500451980321563785216*x + 7925964841656088238527348571904*x^2 + 16463848071095443162399086923520*x^3 + 14591054854348083056041019953920*x^4 - 6748686580533532006267833690720*x^5 - 29248736650867084166004792464400*x^6 - 27810907247748454016001131889000*x^7 - 10001796079358373049248807532500*x^8 + 695464574993914783715625825000*x^9 + 1201462663855520115468027984375*x^10 + 144184298054826825065515781250*x^11 - 1762389540326171994458203125*x^12 + Sqrt[3]*Sqrt[3 + 5*x]*(-63065308976242683755697457152 - 585097553612991658019106714112*x - 2176294093020980713713922212608*x^2 - 3859245367037001974654190614400*x^3 - 2253130049868654552522416322240*x^4 + 3262593253211172972736719153440*x^5 + 6887651340266448627600715095600*x^6 + 4696545750797620525015814903000*x^7 + 875728564711299856904749867500*x^8 - 379018958054554079511789487500*x^9 - 138789767418653112133541343750*x^10 - 3859683130123317965993203125*x^11 + 96839259737767398235546875*x^12)))/(846720*(2 + 3*x)^5*(3 + 5*x)^(3/2)*(1105183793314304 + 4019894758880*x - 2966115478898000*x^2 - 436816644264000*x^3 + 721064958542500*x^4 + 46839566881250*x^5 - 3382394640625*x^6) + 846720*Sqrt[1 - 2*x]*(2 + 3*x)^5*(3 + 5*x)^(3/2)*(-1104347908897280 - 1099312389138400*x + 1360283516838000*x^2 + 841225686360000*x^3 - 94425179937500*x^4 - 17586049031250*x^5 + 39509921875*x^6) + Sqrt[3]*(846720*Sqrt[1 - 2*x]*(2 + 3*x)^5*(3 + 5*x)*(1104269783897280 + 2020474709052800*x - 831988612312000*x^2 - 2024055290400000*x^3 - 175063626237500*x^4 + 90847846375000*x^5 + 1877009062500*x^6) + 846720*(2 + 3*x)^5*(3 + 5*x)*(-1105105668314304 - 925956910020800*x + 3351687890666400*x^2 + 2573340308796000*x^3 - 1017871743627500*x^4 - 388916755537500*x^5 + 9638528906250*x^6 + 367790468750*x^7))) + (46975917593*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/6272 - (234879587965*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/12544","C",1
2458,1,426,135,2.5003128,"\int \frac{(2+3 x)^4 \sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*Sqrt[3 + 5*x])/Sqrt[1 - 2*x],x]","\frac{\sqrt{5 x+3} \left(-56803032000000000 x^9+1942671743100000000 x^8+12873479761395000000 x^7+22098873735654375000 x^6+412485301377531250 x^5-38724233403095205625 x^4-62585554215388523000 x^3-122494599402987247700 x^2-26082864421994928240 x+65328779336992208048\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-4587904800000000 x^9-528897209310000000 x^8-1129075223350500000 x^7+8636690592339562500 x^6+36490584670965078125 x^5+59262710528957237125 x^4+57735514295766506300 x^3+49599111764941162940 x^2-39378391068952493120 x-65328779336992208048\right)+\sqrt{3} \left(17113680000000000 x^{10}-281471301000000000 x^9-8086530380850000000 x^8-27820957003361250000 x^7-27829603458054687500 x^6+21345394366281559375 x^5+72318057558438108125 x^4+137845550508617950500 x^3+166677216943008527500 x^2+\sqrt{1-2 x} \left(131447448000000000 x^9+1587721637700000000 x^8-1435576098429000000 x^7-27770901757396875000 x^6-73633220548725543750 x^5-96023578316409940625 x^4-94774260201246131000 x^3-39252078700969799940 x^2+93797644877982458160 x+65328779336992208048\right)-28336389387035036800 x-65328779336992208048\right)}{2560000 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right)+\sqrt{1-2 x} \left(2560000 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right)+2560000 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right)\right)+2560000 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right)}+\frac{1067352517 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{1280000 \sqrt{10}}","-\frac{3}{50} \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^3-\frac{987 \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^2}{4000}-\frac{21 \sqrt{1-2 x} (5 x+3)^{3/2} (92040 x+194923)}{640000}-\frac{97032047 \sqrt{1-2 x} \sqrt{5 x+3}}{2560000}+\frac{1067352517 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{2560000 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(65328779336992208048 - 26082864421994928240*x - 122494599402987247700*x^2 - 62585554215388523000*x^3 - 38724233403095205625*x^4 + 412485301377531250*x^5 + 22098873735654375000*x^6 + 12873479761395000000*x^7 + 1942671743100000000*x^8 - 56803032000000000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-65328779336992208048 - 39378391068952493120*x + 49599111764941162940*x^2 + 57735514295766506300*x^3 + 59262710528957237125*x^4 + 36490584670965078125*x^5 + 8636690592339562500*x^6 - 1129075223350500000*x^7 - 528897209310000000*x^8 - 4587904800000000*x^9) + Sqrt[3]*(-65328779336992208048 - 28336389387035036800*x + 166677216943008527500*x^2 + 137845550508617950500*x^3 + 72318057558438108125*x^4 + 21345394366281559375*x^5 - 27829603458054687500*x^6 - 27820957003361250000*x^7 - 8086530380850000000*x^8 - 281471301000000000*x^9 + 17113680000000000*x^10 + Sqrt[1 - 2*x]*(65328779336992208048 + 93797644877982458160*x - 39252078700969799940*x^2 - 94774260201246131000*x^3 - 96023578316409940625*x^4 - 73633220548725543750*x^5 - 27770901757396875000*x^6 - 1435576098429000000*x^7 + 1587721637700000000*x^8 + 131447448000000000*x^9)))/(2560000*Sqrt[3]*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 2560000*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(2560000*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 2560000*Sqrt[3]*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (1067352517*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(1280000*Sqrt[10])","B",1
2459,1,366,106,2.1251432,"\int \frac{(2+3 x)^3 \sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*Sqrt[3 + 5*x])/Sqrt[1 - 2*x],x]","\frac{\sqrt{5 x+3} \left(-1675555200000 x^7-15046685280000 x^6-7533794268000 x^5+67436822413400 x^4+148451861332060 x^3+261979172312660 x^2+77781727811480 x-166848378615160\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(147754800000 x^7-882894060000 x^6-25520122246500 x^5-78186973159825 x^4-101511091829480 x^3-84505245399736 x^2+90032445680096 x+166848378615160\right)+\sqrt{3} \left(102816000000 x^8+9543873600000 x^7+25938348840000 x^6-22923506362000 x^5-153118706330825 x^4-300180344230360 x^3-382557890537560 x^2+\sqrt{1-2 x} \left(-770774400000 x^7+11038468320000 x^6+69201607860000 x^5+143817289191400 x^4+161777512323460 x^3+65463432069156 x^2-228848148171896 x-166848378615160\right)+61033974680320 x+166848378615160\right)}{5120 \sqrt{3} \sqrt{5 x+3} \left(8921000 x^3-162998000 x^2-220512160 x+287530496\right)+\sqrt{1-2 x} \left(5120 \left(-48482500 x^3-297203500 x^2+794989800 x+852279560\right)+5120 \sqrt{3} \sqrt{5 x+3} \left(595000 x^3+53178000 x^2-36412000 x-283051520\right)\right)+5120 \left(-8550625 x^4+79738000 x^3+1253327000 x^2-32289760 x-865716488\right)}+\frac{677017 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{2560 \sqrt{10}}","-\frac{3}{40} \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^2-\frac{3 \sqrt{1-2 x} (5 x+3)^{3/2} (408 x+865)}{1280}-\frac{61547 \sqrt{1-2 x} \sqrt{5 x+3}}{5120}+\frac{677017 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{5120 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(-166848378615160 + 77781727811480*x + 261979172312660*x^2 + 148451861332060*x^3 + 67436822413400*x^4 - 7533794268000*x^5 - 15046685280000*x^6 - 1675555200000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(166848378615160 + 90032445680096*x - 84505245399736*x^2 - 101511091829480*x^3 - 78186973159825*x^4 - 25520122246500*x^5 - 882894060000*x^6 + 147754800000*x^7) + Sqrt[3]*(166848378615160 + 61033974680320*x - 382557890537560*x^2 - 300180344230360*x^3 - 153118706330825*x^4 - 22923506362000*x^5 + 25938348840000*x^6 + 9543873600000*x^7 + 102816000000*x^8 + Sqrt[1 - 2*x]*(-166848378615160 - 228848148171896*x + 65463432069156*x^2 + 161777512323460*x^3 + 143817289191400*x^4 + 69201607860000*x^5 + 11038468320000*x^6 - 770774400000*x^7)))/(5120*Sqrt[3]*Sqrt[3 + 5*x]*(287530496 - 220512160*x - 162998000*x^2 + 8921000*x^3) + 5120*(-865716488 - 32289760*x + 1253327000*x^2 + 79738000*x^3 - 8550625*x^4) + Sqrt[1 - 2*x]*(5120*(852279560 + 794989800*x - 297203500*x^2 - 48482500*x^3) + 5120*Sqrt[3]*Sqrt[3 + 5*x]*(-283051520 - 36412000*x + 53178000*x^2 + 595000*x^3))) + (677017*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(2560*Sqrt[10])","B",1
2460,1,306,99,1.8226976,"\int \frac{(2+3 x)^2 \sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*Sqrt[3 + 5*x])/Sqrt[1 - 2*x],x]","\frac{\sqrt{5 x+3} \left(-1881000000 x^5+9290325000 x^4+42821781750 x^3+82490984125 x^2+37785197780 x-66617779844\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-107700000 x^5-7442527500 x^4-19575782375 x^3-18146268075 x^2+29783089200 x+66617779844\right)+\sqrt{3} \left(702000000 x^6-307350000 x^5-31300582500 x^4-88415428625 x^3-134293078575 x^2+\sqrt{1-2 x} \left(2752200000 x^5+18689715000 x^4+32670783750 x^3+13959779625 x^2-84979582820 x-66617779844\right)+17411295840 x+66617779844\right)}{1600 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right)+\sqrt{1-2 x} \left(1600 \left(-391875 x^2+2827000 x+3481060\right)+1600 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right)\right)+1600 \left(44875 x^3+2976525 x^2-279060 x-3667684\right)}+\frac{68959 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{800 \sqrt{10}}","-\frac{1}{10} \sqrt{1-2 x} (3 x+2) (5 x+3)^{3/2}-\frac{181}{400} \sqrt{1-2 x} (5 x+3)^{3/2}-\frac{6269 \sqrt{1-2 x} \sqrt{5 x+3}}{1600}+\frac{68959 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{1600 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(-66617779844 + 37785197780*x + 82490984125*x^2 + 42821781750*x^3 + 9290325000*x^4 - 1881000000*x^5) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(66617779844 + 29783089200*x - 18146268075*x^2 - 19575782375*x^3 - 7442527500*x^4 - 107700000*x^5) + Sqrt[3]*(66617779844 + 17411295840*x - 134293078575*x^2 - 88415428625*x^3 - 31300582500*x^4 - 307350000*x^5 + 702000000*x^6 + Sqrt[1 - 2*x]*(-66617779844 - 84979582820*x + 13959779625*x^2 + 32670783750*x^3 + 18689715000*x^4 + 2752200000*x^5)))/(1600*Sqrt[3]*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 1600*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(1600*(3481060 + 2827000*x - 391875*x^2) + 1600*Sqrt[3]*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (68959*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(800*Sqrt[10])","B",1
2461,1,246,72,1.5434749,"\int \frac{(2+3 x) \sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)*Sqrt[3 + 5*x])/Sqrt[1 - 2*x],x]","\frac{\sqrt{5 x+3} \left(-858000 x^3-3292300 x^2-2984190 x+4187326\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(178500 x^3+316225 x^2-1296880 x-4187326\right)+\sqrt{3} \left(60000 x^4+2693000 x^3+6739325 x^2+\sqrt{1-2 x} \left(-594000 x^3-240900 x^2+4741110 x+4187326\right)-460040 x-4187326\right)}{80 \left(-2975 x^2+1820 x+16562\right)+80 \sqrt{3} \sqrt{5 x+3} (1980 x-5104)+\sqrt{1-2 x} \left(80 (-7150 x-13970)+80 \sqrt{3} \sqrt{5 x+3} (100 x+4240)\right)}+\frac{1177 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{40 \sqrt{10}}","-\frac{3}{20} \sqrt{1-2 x} (5 x+3)^{3/2}-\frac{107}{80} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{1177 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{80 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(4187326 - 2984190*x - 3292300*x^2 - 858000*x^3) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-4187326 - 1296880*x + 316225*x^2 + 178500*x^3) + Sqrt[3]*(-4187326 - 460040*x + 6739325*x^2 + 2693000*x^3 + 60000*x^4 + Sqrt[1 - 2*x]*(4187326 + 4741110*x - 240900*x^2 - 594000*x^3)))/(80*Sqrt[3]*Sqrt[3 + 5*x]*(-5104 + 1980*x) + 80*(16562 + 1820*x - 2975*x^2) + Sqrt[1 - 2*x]*(80*(-13970 - 7150*x) + 80*Sqrt[3]*Sqrt[3 + 5*x]*(4240 + 100*x))) + (1177*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(40*Sqrt[10])","B",1
2462,1,581,50,4.8037974,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/Sqrt[1 - 2*x],x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{10} \left(-\frac{225 \left(\sqrt{1-2 x}-1\right)^6}{64 \left(\sqrt{3}-\sqrt{5 x+3}\right)^6}-\frac{15 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^5}{8 \left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{345 \left(\sqrt{1-2 x}-1\right)^4}{32 \left(\sqrt{3}-\sqrt{5 x+3}\right)^4}+\frac{21 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^3}{4 \left(\sqrt{3}-\sqrt{5 x+3}\right)^3}-\frac{69 \left(\sqrt{1-2 x}-1\right)^2}{16 \left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{\frac{3 \sqrt{3}}{10}-\frac{3}{10} \sqrt{3} \sqrt{1-2 x}}{\sqrt{3}-\sqrt{5 x+3}}+\frac{9}{40}\right) \left(\frac{\left(20-20 \sqrt{1-2 x}\right) \left(10 x-55 \sqrt{1-2 x}+20 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}-22 \sqrt{3} \sqrt{5 x+3}+61\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}-\frac{44 \sqrt{10} \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4}\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2 \left(-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5\right) \left(30 x+5 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{3} \sqrt{5 x+3}+18\right)^2}","\frac{11 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{2 \sqrt{10}}-\frac{1}{2} \sqrt{1-2 x} \sqrt{5 x+3}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^10*(9/40 - (225*(-1 + Sqrt[1 - 2*x])^6)/(64*(Sqrt[3] - Sqrt[3 + 5*x])^6) - (15*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^5)/(8*(Sqrt[3] - Sqrt[3 + 5*x])^5) + (345*(-1 + Sqrt[1 - 2*x])^4)/(32*(Sqrt[3] - Sqrt[3 + 5*x])^4) + (21*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^3)/(4*(Sqrt[3] - Sqrt[3 + 5*x])^3) - (69*(-1 + Sqrt[1 - 2*x])^2)/(16*(Sqrt[3] - Sqrt[3 + 5*x])^2) + ((3*Sqrt[3])/10 - (3*Sqrt[3]*Sqrt[1 - 2*x])/10)/(Sqrt[3] - Sqrt[3 + 5*x]))*(((20 - 20*Sqrt[1 - 2*x])*(61 - 55*Sqrt[1 - 2*x] + 10*x - 22*Sqrt[3]*Sqrt[3 + 5*x] + 20*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]))/(Sqrt[3] - Sqrt[3 + 5*x])^3 - (44*Sqrt[10]*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(Sqrt[3] - Sqrt[3 + 5*x])^4))/((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2*(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])*(18 + 30*x - 11*Sqrt[3]*Sqrt[3 + 5*x] + 5*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^2)","B",1
2463,1,589,62,3.1142438,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*(2 + 3*x)),x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^6 \left(-\frac{375 \left(\sqrt{1-2 x}-1\right)^6}{8 \left(\sqrt{3}-\sqrt{5 x+3}\right)^6}-\frac{25 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{575 \left(\sqrt{1-2 x}-1\right)^4}{4 \left(\sqrt{3}-\sqrt{5 x+3}\right)^4}+\frac{70 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}-\frac{115 \left(\sqrt{1-2 x}-1\right)^2}{2 \left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{4 \sqrt{3}-4 \sqrt{3} \sqrt{1-2 x}}{\sqrt{3}-\sqrt{5 x+3}}+3\right) \left(2 \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5}-\sqrt{5} \sqrt{1-2 x}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)-\text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]\right)}{\left(-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5\right) \left(30 x+5 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{3} \sqrt{5 x+3}+18\right)^2}","\frac{1}{3} \sqrt{10} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)+\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{3 \sqrt{7}}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^6*(3 - (375*(-1 + Sqrt[1 - 2*x])^6)/(8*(Sqrt[3] - Sqrt[3 + 5*x])^6) - (25*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^5 + (575*(-1 + Sqrt[1 - 2*x])^4)/(4*(Sqrt[3] - Sqrt[3 + 5*x])^4) + (70*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 - (115*(-1 + Sqrt[1 - 2*x])^2)/(2*(Sqrt[3] - Sqrt[3 + 5*x])^2) + (4*Sqrt[3] - 4*Sqrt[3]*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x]))*(2*Sqrt[10]*ArcTan[(Sqrt[5] - Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])] - RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ]))/((5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])*(18 + 30*x - 11*Sqrt[3]*Sqrt[3 + 5*x] + 5*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^2)","C",1
2464,1,411,64,1.4430665,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^2} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*(2 + 3*x)^2),x]","\frac{11}{7} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{55}{14} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{3} \left(185 x^2-263 x+\sqrt{1-2 x} (385 x+242)-242\right)+\sqrt{1-2 x} \sqrt{5 x+3} (-100 x-242)+(242-22 x) \sqrt{5 x+3}}{14 (5 x+91) (3 x+2)-308 \sqrt{3} \sqrt{5 x+3} (3 x+2)+\sqrt{1-2 x} \left(140 \sqrt{3} (3 x+2) \sqrt{5 x+3}-770 (3 x+2)\right)}","-\frac{\sqrt{1-2 x} \sqrt{5 x+3}}{7 (3 x+2)}-\frac{11 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{7 \sqrt{7}}",1,"((242 - 22*x)*Sqrt[3 + 5*x] + (-242 - 100*x)*Sqrt[1 - 2*x]*Sqrt[3 + 5*x] + Sqrt[3]*(-242 - 263*x + 185*x^2 + Sqrt[1 - 2*x]*(242 + 385*x)))/(-308*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x] + 14*(2 + 3*x)*(91 + 5*x) + Sqrt[1 - 2*x]*(-770*(2 + 3*x) + 140*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x])) + (11*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/7 - (55*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/14","C",1
2465,1,479,93,1.7831975,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^3} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*(2 + 3*x)^3),x]","\frac{451}{196} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{2255}{392} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-1832160 x^3-1706122 x^2+2060454 x+1288408\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(229125 x^3-1326320 x^2-3213214 x-1288408\right)+\sqrt{3} \left(381525 x^4+3954020 x^3+463802 x^2+\sqrt{1-2 x} \left(-153450 x^3+3594690 x^2+4352304 x+1288408\right)-3199544 x-1288408\right)}{196 \left(2975 x^2-1820 x-16562\right) (3 x+2)^2+196 \sqrt{3} (5104-1980 x) \sqrt{5 x+3} (3 x+2)^2+\sqrt{1-2 x} \left(196 (7150 x+13970) (3 x+2)^2+196 \sqrt{3} (-100 x-4240) \sqrt{5 x+3} (3 x+2)^2\right)}","\frac{3 \sqrt{1-2 x} (5 x+3)^{3/2}}{14 (3 x+2)^2}-\frac{41 \sqrt{1-2 x} \sqrt{5 x+3}}{196 (3 x+2)}-\frac{451 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{196 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(1288408 + 2060454*x - 1706122*x^2 - 1832160*x^3) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-1288408 - 3213214*x - 1326320*x^2 + 229125*x^3) + Sqrt[3]*(-1288408 - 3199544*x + 463802*x^2 + 3954020*x^3 + 381525*x^4 + Sqrt[1 - 2*x]*(1288408 + 4352304*x + 3594690*x^2 - 153450*x^3)))/(196*Sqrt[3]*(5104 - 1980*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 196*(2 + 3*x)^2*(-16562 - 1820*x + 2975*x^2) + Sqrt[1 - 2*x]*(196*Sqrt[3]*(-4240 - 100*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 196*(2 + 3*x)^2*(13970 + 7150*x))) + (451*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/196 - (2255*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/392","C",1
2466,1,539,122,2.1066534,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^4} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*(2 + 3*x)^4),x]","\frac{15235 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2744}-\frac{76175 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{5488}+\frac{\sqrt{5 x+3} \left(-3140086950 x^5-124765870515 x^4-176454569214 x^3+12007579012 x^2+107025458408 x+37528748224\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(2092807875 x^5+33436468575 x^4-25011141890 x^3-160208558220 x^2-142914777000 x-37528748224\right)+\sqrt{3} \left(-2615766750 x^6+61128053100 x^5+251218043010 x^4+195004569304 x^3-87096534552 x^2+\sqrt{1-2 x} \left(-20404147500 x^5-35557854750 x^4+117255840240 x^3+265754320920 x^2+174737775520 x+37528748224\right)-138848456928 x-37528748224\right)}{2744 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right) (3 x+2)^3+\sqrt{1-2 x} \left(2744 \left(-391875 x^2+2827000 x+3481060\right) (3 x+2)^3+2744 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right) (3 x+2)^3\right)+2744 \left(44875 x^3+2976525 x^2-279060 x-3667684\right) (3 x+2)^3}","\frac{3895 \sqrt{1-2 x} \sqrt{5 x+3}}{8232 (3 x+2)}+\frac{25 \sqrt{1-2 x} \sqrt{5 x+3}}{588 (3 x+2)^2}-\frac{\sqrt{1-2 x} \sqrt{5 x+3}}{21 (3 x+2)^3}-\frac{15235 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2744 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(37528748224 + 107025458408*x + 12007579012*x^2 - 176454569214*x^3 - 124765870515*x^4 - 3140086950*x^5) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-37528748224 - 142914777000*x - 160208558220*x^2 - 25011141890*x^3 + 33436468575*x^4 + 2092807875*x^5) + Sqrt[3]*(-37528748224 - 138848456928*x - 87096534552*x^2 + 195004569304*x^3 + 251218043010*x^4 + 61128053100*x^5 - 2615766750*x^6 + Sqrt[1 - 2*x]*(37528748224 + 174737775520*x + 265754320920*x^2 + 117255840240*x^3 - 35557854750*x^4 - 20404147500*x^5)))/(2744*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 2744*(2 + 3*x)^3*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(2744*(2 + 3*x)^3*(3481060 + 2827000*x - 391875*x^2) + 2744*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (15235*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2744 - (76175*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/5488","C",1
2467,1,599,151,2.5929104,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^5} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*(2 + 3*x)^5),x]","\frac{375265 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{21952}-\frac{1876325 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{43904}+\frac{\sqrt{5 x+3} \left(-123497675730000 x^7-67857011392500 x^6+3237608725332300 x^5+6583257752470520 x^4+3113933272438120 x^3-1898125490150560 x^2-2054545910681440 x-478380427550080\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(5036587678125 x^7-287054314875000 x^6-1694492438557500 x^5-1324084254089200 x^4+2600285475633160 x^3+4589917803513920 x^2+2526350610238688 x+478380427550080\right)+\sqrt{3} \left(17334369646875 x^8+400875913170000 x^7-1345626410715000 x^6-7543154710140400 x^5-9363054182120120 x^4-2114004157112320 x^3+3440138939485760 x^2+\sqrt{1-2 x} \left(29044777162500 x^7+1218412850737500 x^6+2954544305823000 x^5+149225145843400 x^4-5677843904332160 x^3-6526631139980160 x^2-2926530270697088 x-478380427550080\right)+2454725571139840 x+478380427550080\right)}{21952 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^4+\sqrt{1-2 x} \left(21952 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^4+21952 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^4\right)+21952 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^4}","\frac{32735 \sqrt{1-2 x} \sqrt{5 x+3}}{21952 (3 x+2)}+\frac{305 \sqrt{1-2 x} \sqrt{5 x+3}}{1568 (3 x+2)^2}+\frac{\sqrt{1-2 x} \sqrt{5 x+3}}{56 (3 x+2)^3}-\frac{\sqrt{1-2 x} \sqrt{5 x+3}}{28 (3 x+2)^4}-\frac{375265 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{21952 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-478380427550080 - 2054545910681440*x - 1898125490150560*x^2 + 3113933272438120*x^3 + 6583257752470520*x^4 + 3237608725332300*x^5 - 67857011392500*x^6 - 123497675730000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(478380427550080 + 2526350610238688*x + 4589917803513920*x^2 + 2600285475633160*x^3 - 1324084254089200*x^4 - 1694492438557500*x^5 - 287054314875000*x^6 + 5036587678125*x^7) + Sqrt[3]*(478380427550080 + 2454725571139840*x + 3440138939485760*x^2 - 2114004157112320*x^3 - 9363054182120120*x^4 - 7543154710140400*x^5 - 1345626410715000*x^6 + 400875913170000*x^7 + 17334369646875*x^8 + Sqrt[1 - 2*x]*(-478380427550080 - 2926530270697088*x - 6526631139980160*x^2 - 5677843904332160*x^3 + 149225145843400*x^4 + 2954544305823000*x^5 + 1218412850737500*x^6 + 29044777162500*x^7)))/(21952*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 21952*(2 + 3*x)^4*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(21952*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 21952*(2 + 3*x)^4*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) + (375265*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/21952 - (1876325*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/43904","C",1
2468,1,426,128,2.530759,"\int \frac{(2+3 x)^3 (3+5 x)^{3/2}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^(3/2))/Sqrt[1 - 2*x],x]","\frac{\sqrt{5 x+3} \left(-18934344000000000 x^9+649135109700000000 x^8+4236217227165000000 x^7+7043009743515625000 x^6-282017872412031250 x^5-12750518596931864375 x^4-19800385722989861000 x^3-38174067018689985900 x^2-8068866526802216080 x+20430349524835112016\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-1529301600000000 x^9-176171627970000000 x^8-361745938753500000 x^7+2901204706639437500 x^6+11911730936484671875 x^5+18907000258786224875 x^4+17994917628688708100 x^3+15284837494551624580 x^2-12403323808314568640 x-20430349524835112016\right)+\sqrt{3} \left(5704560000000000 x^{10}-94299147000000000 x^9-2687396347950000000 x^8-9054125528378750000 x^7-8639199698210312500 x^6+7528755987811290625 x^5+23465697942494681875 x^4+43257015399571353500 x^3+51917461702988312500 x^2+\sqrt{1-2 x} \left(43815816000000000 x^9+525589227900000000 x^8-520361885043000000 x^7-9191590797349125000 x^6-23820808582254956250 x^5-30404857845635769375 x^4-29421192959589981000 x^3-11974831090705755580 x^2+29421857554557370320 x+20430349524835112016\right)-8949667219440585600 x-20430349524835112016\right)}{512000 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right)+\sqrt{1-2 x} \left(512000 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right)+512000 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right)\right)+512000 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right)}+\frac{333216939 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{256000 \sqrt{10}}","-\frac{3}{50} \sqrt{1-2 x} (3 x+2)^2 (5 x+3)^{5/2}-\frac{3 \sqrt{1-2 x} (3900 x+7889) (5 x+3)^{5/2}}{16000}-\frac{917953 \sqrt{1-2 x} (5 x+3)^{3/2}}{128000}-\frac{30292449 \sqrt{1-2 x} \sqrt{5 x+3}}{512000}+\frac{333216939 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{512000 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(20430349524835112016 - 8068866526802216080*x - 38174067018689985900*x^2 - 19800385722989861000*x^3 - 12750518596931864375*x^4 - 282017872412031250*x^5 + 7043009743515625000*x^6 + 4236217227165000000*x^7 + 649135109700000000*x^8 - 18934344000000000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-20430349524835112016 - 12403323808314568640*x + 15284837494551624580*x^2 + 17994917628688708100*x^3 + 18907000258786224875*x^4 + 11911730936484671875*x^5 + 2901204706639437500*x^6 - 361745938753500000*x^7 - 176171627970000000*x^8 - 1529301600000000*x^9) + Sqrt[3]*(-20430349524835112016 - 8949667219440585600*x + 51917461702988312500*x^2 + 43257015399571353500*x^3 + 23465697942494681875*x^4 + 7528755987811290625*x^5 - 8639199698210312500*x^6 - 9054125528378750000*x^7 - 2687396347950000000*x^8 - 94299147000000000*x^9 + 5704560000000000*x^10 + Sqrt[1 - 2*x]*(20430349524835112016 + 29421857554557370320*x - 11974831090705755580*x^2 - 29421192959589981000*x^3 - 30404857845635769375*x^4 - 23820808582254956250*x^5 - 9191590797349125000*x^6 - 520361885043000000*x^7 + 525589227900000000*x^8 + 43815816000000000*x^9)))/(512000*Sqrt[3]*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 512000*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(512000*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 512000*Sqrt[3]*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (333216939*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(256000*Sqrt[10])","B",1
2469,1,366,121,2.1521044,"\int \frac{(2+3 x)^2 (3+5 x)^{3/2}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^(3/2))/Sqrt[1 - 2*x],x]","\frac{\sqrt{5 x+3} \left(-13962960000000 x^7-124147892000000 x^6-52349588500000 x^5+562070510485000 x^4+1187137401092500 x^3+2042622693835900 x^2+599680885062600 x-1304421807274344\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(1231290000000 x^7-7466898500000 x^6-211950757187500 x^5-633111947241875 x^4-797733444611000 x^3-645599514927400 x^2+712424218108320 x+1304421807274344\right)+\sqrt{3} \left(856800000000 x^8+79456120000000 x^7+209127163000000 x^6-206234599150000 x^5-1253263742626875 x^4-2372100456293000 x^3-2978094798280200 x^2+\sqrt{1-2 x} \left(-6423120000000 x^7+92558180000000 x^6+568175129500000 x^5+1152344120675000 x^4+1259596695615500 x^3+489437589125100 x^2-1797655501774440 x-1304421807274344\right)+485550398603520 x+1304421807274344\right)}{25600 \sqrt{3} \sqrt{5 x+3} \left(8921000 x^3-162998000 x^2-220512160 x+287530496\right)+\sqrt{1-2 x} \left(25600 \left(-48482500 x^3-297203500 x^2+794989800 x+852279560\right)+25600 \sqrt{3} \sqrt{5 x+3} \left(595000 x^3+53178000 x^2-36412000 x-283051520\right)\right)+25600 \left(-8550625 x^4+79738000 x^3+1253327000 x^2-32289760 x-865716488\right)}+\frac{5274027 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{12800 \sqrt{10}}","-\frac{3}{40} \sqrt{1-2 x} (3 x+2) (5 x+3)^{5/2}-\frac{251}{800} \sqrt{1-2 x} (5 x+3)^{5/2}-\frac{14529 \sqrt{1-2 x} (5 x+3)^{3/2}}{6400}-\frac{479457 \sqrt{1-2 x} \sqrt{5 x+3}}{25600}+\frac{5274027 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{25600 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(-1304421807274344 + 599680885062600*x + 2042622693835900*x^2 + 1187137401092500*x^3 + 562070510485000*x^4 - 52349588500000*x^5 - 124147892000000*x^6 - 13962960000000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1304421807274344 + 712424218108320*x - 645599514927400*x^2 - 797733444611000*x^3 - 633111947241875*x^4 - 211950757187500*x^5 - 7466898500000*x^6 + 1231290000000*x^7) + Sqrt[3]*(1304421807274344 + 485550398603520*x - 2978094798280200*x^2 - 2372100456293000*x^3 - 1253263742626875*x^4 - 206234599150000*x^5 + 209127163000000*x^6 + 79456120000000*x^7 + 856800000000*x^8 + Sqrt[1 - 2*x]*(-1304421807274344 - 1797655501774440*x + 489437589125100*x^2 + 1259596695615500*x^3 + 1152344120675000*x^4 + 568175129500000*x^5 + 92558180000000*x^6 - 6423120000000*x^7)))/(25600*Sqrt[3]*Sqrt[3 + 5*x]*(287530496 - 220512160*x - 162998000*x^2 + 8921000*x^3) + 25600*(-865716488 - 32289760*x + 1253327000*x^2 + 79738000*x^3 - 8550625*x^4) + Sqrt[1 - 2*x]*(25600*(852279560 + 794989800*x - 297203500*x^2 - 48482500*x^3) + 25600*Sqrt[3]*Sqrt[3 + 5*x]*(-283051520 - 36412000*x + 53178000*x^2 + 595000*x^3))) + (5274027*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(12800*Sqrt[10])","B",1
2470,1,306,94,1.8228416,"\int \frac{(2+3 x) (3+5 x)^{3/2}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^(3/2))/Sqrt[1 - 2*x],x]","\frac{\sqrt{5 x+3} \left(-627000000 x^5+3159475000 x^4+13939692250 x^3+25882250075 x^2+11637004940 x-20854816092\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-35900000 x^5-2477252500 x^4-6278582625 x^3-5486825725 x^2+9525647440 x+20854816092\right)+\sqrt{3} \left(234000000 x^6-125850000 x^5-10414117500 x^4-28357686375 x^3-41921038425 x^2+\sqrt{1-2 x} \left(917400000 x^5+6138165000 x^4+10303202250 x^3+3993164175 x^2-26801567100 x-20854816092\right)+5638914720 x+20854816092\right)}{320 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right)+\sqrt{1-2 x} \left(320 \left(-391875 x^2+2827000 x+3481060\right)+320 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right)\right)+320 \left(44875 x^3+2976525 x^2-279060 x-3667684\right)}+\frac{21417 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{160 \sqrt{10}}","-\frac{1}{10} \sqrt{1-2 x} (5 x+3)^{5/2}-\frac{59}{80} \sqrt{1-2 x} (5 x+3)^{3/2}-\frac{1947}{320} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{21417 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{320 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(-20854816092 + 11637004940*x + 25882250075*x^2 + 13939692250*x^3 + 3159475000*x^4 - 627000000*x^5) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(20854816092 + 9525647440*x - 5486825725*x^2 - 6278582625*x^3 - 2477252500*x^4 - 35900000*x^5) + Sqrt[3]*(20854816092 + 5638914720*x - 41921038425*x^2 - 28357686375*x^3 - 10414117500*x^4 - 125850000*x^5 + 234000000*x^6 + Sqrt[1 - 2*x]*(-20854816092 - 26801567100*x + 3993164175*x^2 + 10303202250*x^3 + 6138165000*x^4 + 917400000*x^5)))/(320*Sqrt[3]*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 320*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(320*(3481060 + 2827000*x - 391875*x^2) + 320*Sqrt[3]*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (21417*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(160*Sqrt[10])","B",1
2471,1,252,72,1.5256644,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/Sqrt[1 - 2*x],x]","\frac{-5 \sqrt{1-2 x} \sqrt{5 x+3} \left(-11900 x^3-19495 x^2+85328 x+263538\right)-5 \sqrt{5 x+3} \left(57200 x^3+211860 x^2+184690 x-263538\right)+\sqrt{3} \left(-5 \sqrt{1-2 x} \left(39600 x^3+10780 x^2-301818 x-263538\right)-5 \left(-4000 x^4-179000 x^3-425035 x^2+31800 x+263538\right)\right)}{16 \left(-2975 x^2+1820 x+16562\right)+16 \sqrt{3} \sqrt{5 x+3} (1980 x-5104)+\sqrt{1-2 x} \left(16 (-7150 x-13970)+16 \sqrt{3} \sqrt{5 x+3} (100 x+4240)\right)}+\frac{363 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{8 \sqrt{10}}","-\frac{1}{4} \sqrt{1-2 x} (5 x+3)^{3/2}-\frac{33}{16} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{363 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{16 \sqrt{10}}",1,"(-5*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(263538 + 85328*x - 19495*x^2 - 11900*x^3) - 5*Sqrt[3 + 5*x]*(-263538 + 184690*x + 211860*x^2 + 57200*x^3) + Sqrt[3]*(-5*Sqrt[1 - 2*x]*(-263538 - 301818*x + 10780*x^2 + 39600*x^3) - 5*(263538 + 31800*x - 425035*x^2 - 179000*x^3 - 4000*x^4)))/(16*Sqrt[3]*Sqrt[3 + 5*x]*(-5104 + 1980*x) + 16*(16562 + 1820*x - 2975*x^2) + Sqrt[1 - 2*x]*(16*(-13970 - 7150*x) + 16*Sqrt[3]*Sqrt[3 + 5*x]*(4240 + 100*x))) + (363*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(8*Sqrt[10])","B",1
2472,1,376,86,1.4763142,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)),x]","-\frac{1}{9} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{\left(\frac{5}{6} \sqrt{1-2 x}-\frac{5}{6}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right) \left(10 x-55 \sqrt{1-2 x}+20 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}-22 \sqrt{3} \sqrt{5 x+3}+61\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}+\frac{29}{9} \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{5}{6} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{29}{18} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{9 \sqrt{7}}",1,"((-5/6 + (5*Sqrt[1 - 2*x])/6)*(Sqrt[3] - Sqrt[3 + 5*x])*(61 - 55*Sqrt[1 - 2*x] + 10*x - 22*Sqrt[3]*Sqrt[3 + 5*x] + 20*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2 + (29*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/9 - RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ]/9","C",1
2473,1,469,91,1.608196,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^2),x]","-\frac{103}{63} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{515}{126} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{3} \left(-185 x^2+263 x+(-385 x-242) \sqrt{1-2 x}+242\right)+\sqrt{5 x+3} (22 x-242)+\sqrt{1-2 x} \sqrt{5 x+3} (100 x+242)}{42 (5 x+91) (3 x+2)-924 \sqrt{3} \sqrt{5 x+3} (3 x+2)+\sqrt{1-2 x} \left(420 \sqrt{3} (3 x+2) \sqrt{5 x+3}-2310 (3 x+2)\right)}+\frac{10}{9} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{\sqrt{1-2 x} \sqrt{5 x+3}}{21 (3 x+2)}+\frac{5}{9} \sqrt{10} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)+\frac{103 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{63 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-242 + 22*x) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(242 + 100*x) + Sqrt[3]*(242 + (-242 - 385*x)*Sqrt[1 - 2*x] + 263*x - 185*x^2))/(-924*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x] + 42*(2 + 3*x)*(91 + 5*x) + Sqrt[1 - 2*x]*(-2310*(2 + 3*x) + 420*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x])) + (10*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/9 - (103*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/63 + (515*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/126","C",1
2474,1,479,93,1.8185626,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^3),x]","\frac{363}{196} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{1815}{392} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-429875 x^3+3174440 x^2+7149218 x+3162456\right)+\sqrt{5 x+3} \left(3860120 x^3+3261654 x^2-4435178 x-3162456\right)+\sqrt{3} \left(-891925 x^4-7812140 x^3-962914 x^2+\sqrt{1-2 x} \left(-64350 x^3-7951130 x^2-10000848 x-3162456\right)+7286808 x+3162456\right)}{196 \left(2975 x^2-1820 x-16562\right) (3 x+2)^2+196 \sqrt{3} (5104-1980 x) \sqrt{5 x+3} (3 x+2)^2+\sqrt{1-2 x} \left(196 (7150 x+13970) (3 x+2)^2+196 \sqrt{3} (-100 x-4240) \sqrt{5 x+3} (3 x+2)^2\right)}","-\frac{\sqrt{1-2 x} (5 x+3)^{3/2}}{14 (3 x+2)^2}-\frac{33 \sqrt{1-2 x} \sqrt{5 x+3}}{196 (3 x+2)}-\frac{363 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{196 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(3162456 + 7149218*x + 3174440*x^2 - 429875*x^3) + Sqrt[3 + 5*x]*(-3162456 - 4435178*x + 3261654*x^2 + 3860120*x^3) + Sqrt[3]*(3162456 + 7286808*x - 962914*x^2 - 7812140*x^3 - 891925*x^4 + Sqrt[1 - 2*x]*(-3162456 - 10000848*x - 7951130*x^2 - 64350*x^3)))/(196*Sqrt[3]*(5104 - 1980*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 196*(2 + 3*x)^2*(-16562 - 1820*x + 2975*x^2) + Sqrt[1 - 2*x]*(196*Sqrt[3]*(-4240 - 100*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 196*(2 + 3*x)^2*(13970 + 7150*x))) + (363*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/196 - (1815*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/392","C",1
2475,1,539,122,2.1365756,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^4),x]","\frac{5445 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2744}-\frac{27225 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{5488}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(183793625 x^5+6503619225 x^4+1073190930 x^3-14701162820 x^2-11306406360 x-2040838272\right)+\sqrt{5 x+3} \left(1051546650 x^5-15458455045 x^4-21871199042 x^3+2096827436 x^2+9174868824 x+2040838272\right)+\sqrt{3} \left(-598419000 x^6+4507895550 x^5+32626549530 x^4+23087952312 x^3-9249802056 x^2+\sqrt{1-2 x} \left(-2898018750 x^5-10220817750 x^4+7643863920 x^3+23600043720 x^2+12976729920 x+2040838272\right)-10845192384 x-2040838272\right)}{2744 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right) (3 x+2)^3+\sqrt{1-2 x} \left(2744 \left(-391875 x^2+2827000 x+3481060\right) (3 x+2)^3+2744 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right) (3 x+2)^3\right)+2744 \left(44875 x^3+2976525 x^2-279060 x-3667684\right) (3 x+2)^3}","\frac{\sqrt{1-2 x} (5 x+3)^{5/2}}{7 (3 x+2)^3}-\frac{15 \sqrt{1-2 x} (5 x+3)^{3/2}}{196 (3 x+2)^2}-\frac{495 \sqrt{1-2 x} \sqrt{5 x+3}}{2744 (3 x+2)}-\frac{5445 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2744 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-2040838272 - 11306406360*x - 14701162820*x^2 + 1073190930*x^3 + 6503619225*x^4 + 183793625*x^5) + Sqrt[3 + 5*x]*(2040838272 + 9174868824*x + 2096827436*x^2 - 21871199042*x^3 - 15458455045*x^4 + 1051546650*x^5) + Sqrt[3]*(-2040838272 - 10845192384*x - 9249802056*x^2 + 23087952312*x^3 + 32626549530*x^4 + 4507895550*x^5 - 598419000*x^6 + Sqrt[1 - 2*x]*(2040838272 + 12976729920*x + 23600043720*x^2 + 7643863920*x^3 - 10220817750*x^4 - 2898018750*x^5)))/(2744*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 2744*(2 + 3*x)^3*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(2744*(2 + 3*x)^3*(3481060 + 2827000*x - 391875*x^2) + 2744*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (5445*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2744 - (27225*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/5488","C",1
2476,1,599,151,2.5222713,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^5),x]","\frac{78045 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{21952}-\frac{390225 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{43904}+\frac{\sqrt{5 x+3} \left(-23290023570000 x^7-25960614542500 x^6+577404766396700 x^5+1214180443219480 x^4+578274168897480 x^3-345309442352160 x^2-366790110341600 x-82725379355520\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(1041495965625 x^7-50935574815000 x^6-320650953527500 x^5-272556978062000 x^4+451125638575080 x^3+823968840829760 x^2+448559694134624 x+82725379355520\right)+\sqrt{3} \left(3116261634375 x^8+80144929730000 x^7-220522728495000 x^6-1368363982423600 x^5-1731025985961880 x^4-395462428295680 x^3+621788210916160 x^2+\sqrt{1-2 x} \left(4133078812500 x^7+224881868447500 x^6+569202254731000 x^5+75763171226600 x^4-1004305859230080 x^3-1168811216721280 x^2-517719797764224 x-82725379355520\right)+435950213971200 x+82725379355520\right)}{21952 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^4+\sqrt{1-2 x} \left(21952 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^4+21952 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^4\right)+21952 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^4}","\frac{57595 \sqrt{1-2 x} \sqrt{5 x+3}}{197568 (3 x+2)}+\frac{85 \sqrt{1-2 x} \sqrt{5 x+3}}{14112 (3 x+2)^2}-\frac{43 \sqrt{1-2 x} \sqrt{5 x+3}}{504 (3 x+2)^3}+\frac{\sqrt{1-2 x} \sqrt{5 x+3}}{84 (3 x+2)^4}-\frac{78045 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{21952 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-82725379355520 - 366790110341600*x - 345309442352160*x^2 + 578274168897480*x^3 + 1214180443219480*x^4 + 577404766396700*x^5 - 25960614542500*x^6 - 23290023570000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(82725379355520 + 448559694134624*x + 823968840829760*x^2 + 451125638575080*x^3 - 272556978062000*x^4 - 320650953527500*x^5 - 50935574815000*x^6 + 1041495965625*x^7) + Sqrt[3]*(82725379355520 + 435950213971200*x + 621788210916160*x^2 - 395462428295680*x^3 - 1731025985961880*x^4 - 1368363982423600*x^5 - 220522728495000*x^6 + 80144929730000*x^7 + 3116261634375*x^8 + Sqrt[1 - 2*x]*(-82725379355520 - 517719797764224*x - 1168811216721280*x^2 - 1004305859230080*x^3 + 75763171226600*x^4 + 569202254731000*x^5 + 224881868447500*x^6 + 4133078812500*x^7)))/(21952*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 21952*(2 + 3*x)^4*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(21952*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 21952*(2 + 3*x)^4*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) + (78045*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/21952 - (390225*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/43904","C",1
2477,1,659,180,3.0544849,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^6} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^6),x]","\frac{2664057 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{307328}-\frac{13320285 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{614656}+\frac{\sqrt{5 x+3} \left(-304667054086725000 x^9-15190907070981200625 x^8-32763911533483519950 x^7+73952796137921317760 x^6+263180871721745243728 x^5+240989922183524159360 x^4+27543585685329063680 x^3-80570699089090457280 x^2-46897886483879995520 x-8066500871021987328\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(57281580293203125 x^9+1736253003981234375 x^8-14715616163923706250 x^7-90652622696599931000 x^6-133955779088876243200 x^5-12213770156341979360 x^4+139895072124248214400 x^3+139070955724648112192 x^2+54932252436361490048 x+8066500871021987328\right)+\sqrt{3} \left(-44691458140884375 x^{10}+5113844570755546875 x^9+40521169499549587500 x^8+13655839140264377000 x^7-229232887338946662200 x^6-442420531123031860528 x^5-280653094814060181760 x^4+25618783596050134720 x^3+116835718212455041280 x^2+\sqrt{1-2 x} \left(-796273093636453125 x^9+516319065708187500 x^8+60023134250966700000 x^7+183944727417285945000 x^6+166115890545075174000 x^5-69626941088670282240 x^4-239010045233008272960 x^3-182036469777163941632 x^2-61659526464296479488 x-8066500871021987328\right)+53625160511814984960 x+8066500871021987328\right)}{1536640 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right) (3 x+2)^5+\sqrt{1-2 x} \left(1536640 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right) (3 x+2)^5+1536640 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right) (3 x+2)^5\right)+1536640 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right) (3 x+2)^5}","\frac{694229 \sqrt{1-2 x} \sqrt{5 x+3}}{921984 (3 x+2)}+\frac{6107 \sqrt{1-2 x} \sqrt{5 x+3}}{65856 (3 x+2)^2}-\frac{73 \sqrt{1-2 x} \sqrt{5 x+3}}{11760 (3 x+2)^3}-\frac{367 \sqrt{1-2 x} \sqrt{5 x+3}}{5880 (3 x+2)^4}+\frac{\sqrt{1-2 x} \sqrt{5 x+3}}{105 (3 x+2)^5}-\frac{2664057 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{307328 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-8066500871021987328 - 46897886483879995520*x - 80570699089090457280*x^2 + 27543585685329063680*x^3 + 240989922183524159360*x^4 + 263180871721745243728*x^5 + 73952796137921317760*x^6 - 32763911533483519950*x^7 - 15190907070981200625*x^8 - 304667054086725000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(8066500871021987328 + 54932252436361490048*x + 139070955724648112192*x^2 + 139895072124248214400*x^3 - 12213770156341979360*x^4 - 133955779088876243200*x^5 - 90652622696599931000*x^6 - 14715616163923706250*x^7 + 1736253003981234375*x^8 + 57281580293203125*x^9) + Sqrt[3]*(8066500871021987328 + 53625160511814984960*x + 116835718212455041280*x^2 + 25618783596050134720*x^3 - 280653094814060181760*x^4 - 442420531123031860528*x^5 - 229232887338946662200*x^6 + 13655839140264377000*x^7 + 40521169499549587500*x^8 + 5113844570755546875*x^9 - 44691458140884375*x^10 + Sqrt[1 - 2*x]*(-8066500871021987328 - 61659526464296479488*x - 182036469777163941632*x^2 - 239010045233008272960*x^3 - 69626941088670282240*x^4 + 166115890545075174000*x^5 + 183944727417285945000*x^6 + 60023134250966700000*x^7 + 516319065708187500*x^8 - 796273093636453125*x^9)))/(1536640*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 1536640*(2 + 3*x)^5*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(1536640*(2 + 3*x)^5*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 1536640*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (2664057*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/307328 - (13320285*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/614656","C",1
2478,1,1159,150,9.388409,"\int \frac{(2+3 x)^3 (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^(5/2))/Sqrt[1 - 2*x],x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{24} \left(\frac{2678359321 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}{409600 \sqrt{10} \left(\sqrt{3}-\sqrt{5 x+3}\right)^{24}}+\frac{\left(-\frac{2324464921 \sqrt{1-2 x}}{819200}-\frac{8208}{5} \sqrt{3} \sqrt{5 x+3}+\frac{6358861081}{819200}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{11}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{23}}+\frac{\left(-\frac{28924410599 \sqrt{1-2 x}}{1228800}+\frac{715728}{25} \sqrt{3} \sqrt{5 x+3}-\frac{76613977369}{1228800}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{21}}+\frac{\left(\frac{5489210111 \sqrt{1-2 x}}{61440}+\frac{13595856}{125} \sqrt{3} \sqrt{5 x+3}-\frac{638427888359}{1536000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{19}}+\frac{\left(\frac{265689844191 \sqrt{1-2 x}}{256000}-\frac{4795152}{25} \sqrt{3} \sqrt{5 x+3}-\frac{118382774751}{256000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{17}}+\frac{\left(\frac{298283520523 \sqrt{1-2 x}}{96000}-\frac{281446416}{125} \sqrt{3} \sqrt{5 x+3}+\frac{350169021941}{96000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{15}}+\frac{\left(\frac{155036383739 \sqrt{1-2 x}}{48000}-\frac{898196208}{125} \sqrt{3} \sqrt{5 x+3}+\frac{879685647877}{48000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{13}}+\frac{\left(-\frac{16901693991 \sqrt{1-2 x}}{4000}-\frac{1635245568}{125} \sqrt{3} \sqrt{5 x+3}+\frac{173885268519}{4000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{11}}+\frac{\left(-\frac{7321396077}{400} \sqrt{1-2 x}-\frac{1933200288}{125} \sqrt{3} \sqrt{5 x+3}+\frac{129400594209}{2000}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}+\frac{\left(-\frac{3401164431}{125} \sqrt{1-2 x}-\frac{309704256}{25} \sqrt{3} \sqrt{5 x+3}+\frac{8046728271}{125}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}+\frac{\left(-\frac{2754028998}{125} \sqrt{1-2 x}-\frac{841966272}{125} \sqrt{3} \sqrt{5 x+3}+\frac{5279927814}{125}\right) \left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{-\frac{217987056}{125} \sqrt{1-2 x}-\frac{48387456}{125} \sqrt{3} \sqrt{5 x+3}+\frac{363149424}{125}}{\sqrt{3}-\sqrt{5 x+3}}+\frac{\left(-\frac{72}{25} \sqrt{1-2 x}-\frac{144}{125} \sqrt{3} \sqrt{5 x+3}+\frac{792}{125}\right) \left(16651789 \sqrt{1-2 x}+4032288 \sqrt{3} \sqrt{5 x+3}-28748653\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^{12}}","-\frac{1}{20} \sqrt{1-2 x} (3 x+2)^2 (5 x+3)^{7/2}-\frac{\sqrt{1-2 x} (18960 x+37439) (5 x+3)^{7/2}}{32000}-\frac{2012291 \sqrt{1-2 x} (5 x+3)^{5/2}}{384000}-\frac{22135201 \sqrt{1-2 x} (5 x+3)^{3/2}}{614400}-\frac{243487211 \sqrt{1-2 x} \sqrt{5 x+3}}{819200}+\frac{2678359321 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{819200 \sqrt{10}}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^24*((363149424/125 - (217987056*Sqrt[1 - 2*x])/125 - (48387456*Sqrt[3]*Sqrt[3 + 5*x])/125)/(Sqrt[3] - Sqrt[3 + 5*x]) + ((5279927814/125 - (2754028998*Sqrt[1 - 2*x])/125 - (841966272*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^5 + ((8046728271/125 - (3401164431*Sqrt[1 - 2*x])/125 - (309704256*Sqrt[3]*Sqrt[3 + 5*x])/25)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^7 + ((129400594209/2000 - (7321396077*Sqrt[1 - 2*x])/400 - (1933200288*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^9 + ((173885268519/4000 - (16901693991*Sqrt[1 - 2*x])/4000 - (1635245568*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^11 + ((879685647877/48000 + (155036383739*Sqrt[1 - 2*x])/48000 - (898196208*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^13 + ((350169021941/96000 + (298283520523*Sqrt[1 - 2*x])/96000 - (281446416*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^7)/(Sqrt[3] - Sqrt[3 + 5*x])^15 + ((-118382774751/256000 + (265689844191*Sqrt[1 - 2*x])/256000 - (4795152*Sqrt[3]*Sqrt[3 + 5*x])/25)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^8)/(Sqrt[3] - Sqrt[3 + 5*x])^17 + ((6358861081/819200 - (2324464921*Sqrt[1 - 2*x])/819200 - (8208*Sqrt[3]*Sqrt[3 + 5*x])/5)*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^11)/(Sqrt[3] - Sqrt[3 + 5*x])^23 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^10*(-76613977369/1228800 - (28924410599*Sqrt[1 - 2*x])/1228800 + (715728*Sqrt[3]*Sqrt[3 + 5*x])/25))/(Sqrt[3] - Sqrt[3 + 5*x])^21 + ((-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^9*(-638427888359/1536000 + (5489210111*Sqrt[1 - 2*x])/61440 + (13595856*Sqrt[3]*Sqrt[3 + 5*x])/125))/(Sqrt[3] - Sqrt[3 + 5*x])^19 + ((792/125 - (72*Sqrt[1 - 2*x])/25 - (144*Sqrt[3]*Sqrt[3 + 5*x])/125)*(-28748653 + 16651789*Sqrt[1 - 2*x] + 4032288*Sqrt[3]*Sqrt[3 + 5*x]))/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (2678359321*(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(409600*Sqrt[10]*(Sqrt[3] - Sqrt[3 + 5*x])^24)))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^12","B",1
2479,1,426,143,2.5025792,"\int \frac{(2+3 x)^2 (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^(5/2))/Sqrt[1 - 2*x],x]","\frac{\sqrt{5 x+3} \left(-18934344000000000 x^9+650712971700000000 x^8+4181134279465000000 x^7+6724692683053125000 x^6-675707441867906250 x^5-12567060554742326875 x^4-18776056581323921000 x^3-35686673333313927100 x^2-7490301585266455120 x+19167669215393547024\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-1529301600000000 x^9-176044186170000000 x^8-347144797883500000 x^7+2922220176721687500 x^6+11658689145307584375 x^5+18082326831817837375 x^4+16813274853913754100 x^3+14128127863513668980 x^2-11716995651190550720 x-19167669215393547024\right)+\sqrt{3} \left(5704560000000000 x^{10}-94774527000000000 x^9-2679240312950000000 x^8-8835344244303750000 x^7-8020932201689062500 x^6+7896147235097328125 x^5+22806223409412594375 x^4+40705218224518963500 x^3+48513651899972534500 x^2+\sqrt{1-2 x} \left(43815816000000000 x^9+521937909900000000 x^8-561873842343000000 x^7-9122682163472625000 x^6-23104917932729531250 x^5-28861474417242451875 x^4-27385402467375337000 x^3-10955425546432063180 x^2+27683653184044548240 x+19167669215393547024\right)-8476355947587542400 x-19167669215393547024\right)}{307200 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right)+\sqrt{1-2 x} \left(307200 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right)+307200 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right)\right)+307200 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right)}+\frac{104040277 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{51200 \sqrt{10}}","-\frac{3}{50} \sqrt{1-2 x} (3 x+2) (5 x+3)^{7/2}-\frac{963 \sqrt{1-2 x} (5 x+3)^{7/2}}{4000}-\frac{78167 \sqrt{1-2 x} (5 x+3)^{5/2}}{48000}-\frac{859837 \sqrt{1-2 x} (5 x+3)^{3/2}}{76800}-\frac{9458207 \sqrt{1-2 x} \sqrt{5 x+3}}{102400}+\frac{104040277 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{102400 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(19167669215393547024 - 7490301585266455120*x - 35686673333313927100*x^2 - 18776056581323921000*x^3 - 12567060554742326875*x^4 - 675707441867906250*x^5 + 6724692683053125000*x^6 + 4181134279465000000*x^7 + 650712971700000000*x^8 - 18934344000000000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-19167669215393547024 - 11716995651190550720*x + 14128127863513668980*x^2 + 16813274853913754100*x^3 + 18082326831817837375*x^4 + 11658689145307584375*x^5 + 2922220176721687500*x^6 - 347144797883500000*x^7 - 176044186170000000*x^8 - 1529301600000000*x^9) + Sqrt[3]*(-19167669215393547024 - 8476355947587542400*x + 48513651899972534500*x^2 + 40705218224518963500*x^3 + 22806223409412594375*x^4 + 7896147235097328125*x^5 - 8020932201689062500*x^6 - 8835344244303750000*x^7 - 2679240312950000000*x^8 - 94774527000000000*x^9 + 5704560000000000*x^10 + Sqrt[1 - 2*x]*(19167669215393547024 + 27683653184044548240*x - 10955425546432063180*x^2 - 27385402467375337000*x^3 - 28861474417242451875*x^4 - 23104917932729531250*x^5 - 9122682163472625000*x^6 - 561873842343000000*x^7 + 521937909900000000*x^8 + 43815816000000000*x^9)))/(307200*Sqrt[3]*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 307200*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(307200*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 307200*Sqrt[3]*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (104040277*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(51200*Sqrt[10])","B",1
2480,1,366,116,2.1473391,"\int \frac{(2+3 x) (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^(5/2))/Sqrt[1 - 2*x],x]","\frac{\sqrt{5 x+3} \left(-2792592000000 x^7-24581348000000 x^6-8408334660000 x^5+112234581921000 x^4+227568894690500 x^3+382099758280460 x^2+110976541457320 x-244734391873224\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(246258000000 x^7-1515269300000 x^6-42244576837500 x^5-122948352870375 x^4-150278816407000 x^3-118251497717640 x^2+135223584114464 x+244734391873224\right)+\sqrt{3} \left(171360000000 x^8+15875992000000 x^7+40421807000000 x^6-44148077430000 x^5-245857674523375 x^4-449553838845800 x^3-556297173296360 x^2+\sqrt{1-2 x} \left(-1284624000000 x^7+18625824800000 x^6+111922619820000 x^5+221416737399000 x^4+235127433425500 x^3+87623024236220 x^2-338828027862984 x-244734391873224\right)+92627902291200 x+244734391873224\right)}{3072 \sqrt{3} \sqrt{5 x+3} \left(8921000 x^3-162998000 x^2-220512160 x+287530496\right)+\sqrt{1-2 x} \left(3072 \left(-48482500 x^3-297203500 x^2+794989800 x+852279560\right)+3072 \sqrt{3} \sqrt{5 x+3} \left(595000 x^3+53178000 x^2-36412000 x-283051520\right)\right)+3072 \left(-8550625 x^4+79738000 x^3+1253327000 x^2-32289760 x-865716488\right)}+\frac{328757 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{512 \sqrt{10}}","-\frac{3}{40} \sqrt{1-2 x} (5 x+3)^{7/2}-\frac{247}{480} \sqrt{1-2 x} (5 x+3)^{5/2}-\frac{2717}{768} \sqrt{1-2 x} (5 x+3)^{3/2}-\frac{29887 \sqrt{1-2 x} \sqrt{5 x+3}}{1024}+\frac{328757 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{1024 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(-244734391873224 + 110976541457320*x + 382099758280460*x^2 + 227568894690500*x^3 + 112234581921000*x^4 - 8408334660000*x^5 - 24581348000000*x^6 - 2792592000000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(244734391873224 + 135223584114464*x - 118251497717640*x^2 - 150278816407000*x^3 - 122948352870375*x^4 - 42244576837500*x^5 - 1515269300000*x^6 + 246258000000*x^7) + Sqrt[3]*(244734391873224 + 92627902291200*x - 556297173296360*x^2 - 449553838845800*x^3 - 245857674523375*x^4 - 44148077430000*x^5 + 40421807000000*x^6 + 15875992000000*x^7 + 171360000000*x^8 + Sqrt[1 - 2*x]*(-244734391873224 - 338828027862984*x + 87623024236220*x^2 + 235127433425500*x^3 + 221416737399000*x^4 + 111922619820000*x^5 + 18625824800000*x^6 - 1284624000000*x^7)))/(3072*Sqrt[3]*Sqrt[3 + 5*x]*(287530496 - 220512160*x - 162998000*x^2 + 8921000*x^3) + 3072*(-865716488 - 32289760*x + 1253327000*x^2 + 79738000*x^3 - 8550625*x^4) + Sqrt[1 - 2*x]*(3072*(852279560 + 794989800*x - 297203500*x^2 - 48482500*x^3) + 3072*Sqrt[3]*Sqrt[3 + 5*x]*(-283051520 - 36412000*x + 53178000*x^2 + 595000*x^3))) + (328757*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(512*Sqrt[10])","B",1
2481,1,308,96,1.73281,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/Sqrt[1 - 2*x],x]","\frac{\sqrt{5 x+3} \left(-627000000 x^5+3222175000 x^4+13597097250 x^3+24339333975 x^2+10748121340 x-19579292172\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-35900000 x^5-2473662500 x^4-6032383125 x^3-4957581025 x^2+9129675920 x+19579292172\right)+\sqrt{3} \left(234000000 x^6-149250000 x^5-10391587500 x^4-27254065875 x^3-39232985325 x^2+\sqrt{1-2 x} \left(917400000 x^5+6046425000 x^4+9728375250 x^3+3386370075 x^2-25345783980 x-19579292172\right)+5467986720 x+19579292172\right)}{192 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right)+\sqrt{1-2 x} \left(192 \left(-391875 x^2+2827000 x+3481060\right)+192 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right)\right)+192 \left(44875 x^3+2976525 x^2-279060 x-3667684\right)}+\frac{1331}{32} \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{1}{6} \sqrt{1-2 x} (5 x+3)^{5/2}-\frac{55}{48} \sqrt{1-2 x} (5 x+3)^{3/2}-\frac{605}{64} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{1331}{64} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"(Sqrt[3 + 5*x]*(-19579292172 + 10748121340*x + 24339333975*x^2 + 13597097250*x^3 + 3222175000*x^4 - 627000000*x^5) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(19579292172 + 9129675920*x - 4957581025*x^2 - 6032383125*x^3 - 2473662500*x^4 - 35900000*x^5) + Sqrt[3]*(19579292172 + 5467986720*x - 39232985325*x^2 - 27254065875*x^3 - 10391587500*x^4 - 149250000*x^5 + 234000000*x^6 + Sqrt[1 - 2*x]*(-19579292172 - 25345783980*x + 3386370075*x^2 + 9728375250*x^3 + 6046425000*x^4 + 917400000*x^5)))/(192*Sqrt[3]*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 192*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(192*(3481060 + 2827000*x - 391875*x^2) + 192*Sqrt[3]*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (1331*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/32","B",1
2482,1,446,108,1.8454151,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)),x]","\frac{1}{27} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{-5 \sqrt{1-2 x} \sqrt{5 x+3} \left(-178500 x^3-268625 x^2+1262960 x+3718814\right)-5 \sqrt{5 x+3} \left(858000 x^3+3063500 x^2+2556510 x-3718814\right)+\sqrt{3} \left(-5 \sqrt{1-2 x} \left(594000 x^3+82500 x^2-4313430 x-3718814\right)-5 \left(-60000 x^4-2677000 x^3-6011725 x^2+493960 x+3718814\right)\right)}{144 \left(-2975 x^2+1820 x+16562\right)+144 \sqrt{3} \sqrt{5 x+3} (1980 x-5104)+\sqrt{1-2 x} \left(144 (-7150 x-13970)+144 \sqrt{3} \sqrt{5 x+3} (100 x+4240)\right)}+\frac{3035}{216} \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{5}{12} \sqrt{1-2 x} (5 x+3)^{3/2}-\frac{455}{144} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{3035}{432} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)+\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{27 \sqrt{7}}",1,"(-5*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(3718814 + 1262960*x - 268625*x^2 - 178500*x^3) - 5*Sqrt[3 + 5*x]*(-3718814 + 2556510*x + 3063500*x^2 + 858000*x^3) + Sqrt[3]*(-5*Sqrt[1 - 2*x]*(-3718814 - 4313430*x + 82500*x^2 + 594000*x^3) - 5*(3718814 + 493960*x - 6011725*x^2 - 2677000*x^3 - 60000*x^4)))/(144*Sqrt[3]*Sqrt[3 + 5*x]*(-5104 + 1980*x) + 144*(16562 + 1820*x - 2975*x^2) + Sqrt[1 - 2*x]*(144*(-13970 - 7150*x) + 144*Sqrt[3]*Sqrt[3 + 5*x]*(4240 + 100*x))) + (3035*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/216 + RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ]/27","C",1
2483,1,531,115,2.0439836,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^2),x]","\frac{173}{189} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{865}{378} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-1561875 x^3+66700 x^2+16157450 x+10307264\right)+\sqrt{5 x+3} \left(7507500 x^3+19084670 x^2-6010026 x-10307264\right)+\sqrt{3} \left(-525000 x^4-24235300 x^3-17114740 x^2+\sqrt{1-2 x} \left(5197500 x^3-10569900 x^2-24823920 x-10307264\right)+14676496 x+10307264\right)}{126 \left(2975 x^2-1820 x-16562\right) (3 x+2)+126 \sqrt{3} (5104-1980 x) \sqrt{5 x+3} (3 x+2)+\sqrt{1-2 x} \left(126 (7150 x+13970) (3 x+2)+126 \sqrt{3} (-100 x-4240) \sqrt{5 x+3} (3 x+2)\right)}+\frac{125}{27} \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{\sqrt{1-2 x} (5 x+3)^{3/2}}{21 (3 x+2)}-\frac{185}{126} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{125}{54} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{173 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{189 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(10307264 + 16157450*x + 66700*x^2 - 1561875*x^3) + Sqrt[3 + 5*x]*(-10307264 - 6010026*x + 19084670*x^2 + 7507500*x^3) + Sqrt[3]*(10307264 + 14676496*x - 17114740*x^2 - 24235300*x^3 - 525000*x^4 + Sqrt[1 - 2*x]*(-10307264 - 24823920*x - 10569900*x^2 + 5197500*x^3)))/(126*Sqrt[3]*(5104 - 1980*x)*(2 + 3*x)*Sqrt[3 + 5*x] + 126*(2 + 3*x)*(-16562 - 1820*x + 2975*x^2) + Sqrt[1 - 2*x]*(126*Sqrt[3]*(-4240 - 100*x)*(2 + 3*x)*Sqrt[3 + 5*x] + 126*(2 + 3*x)*(13970 + 7150*x))) + (125*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/27 + (173*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/189 - (865*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/378","C",1
2484,1,537,120,2.0874931,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^3),x]","-\frac{17687 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{5292}+\frac{88435 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{10584}+\frac{\sqrt{5 x+3} \left(-21328560 x^3-17863802 x^2+24550614 x+17686328\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(2350125 x^3-17720320 x^2-39682094 x-17686328\right)+\sqrt{3} \left(4970025 x^4+42918820 x^3+5313682 x^2+\sqrt{1-2 x} \left(539550 x^3+44112090 x^2+55652784 x+17686328\right)-40521304 x-17686328\right)}{1764 \left(2975 x^2-1820 x-16562\right) (3 x+2)^2+1764 \sqrt{3} (5104-1980 x) \sqrt{5 x+3} (3 x+2)^2+\sqrt{1-2 x} \left(1764 (7150 x+13970) (3 x+2)^2+1764 \sqrt{3} (-100 x-4240) \sqrt{5 x+3} (3 x+2)^2\right)}+\frac{50}{27} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{\sqrt{1-2 x} (5 x+3)^{3/2}}{42 (3 x+2)^2}+\frac{239 \sqrt{1-2 x} \sqrt{5 x+3}}{1764 (3 x+2)}+\frac{25}{27} \sqrt{10} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)+\frac{17687 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{5292 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(17686328 + 24550614*x - 17863802*x^2 - 21328560*x^3) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-17686328 - 39682094*x - 17720320*x^2 + 2350125*x^3) + Sqrt[3]*(-17686328 - 40521304*x + 5313682*x^2 + 42918820*x^3 + 4970025*x^4 + Sqrt[1 - 2*x]*(17686328 + 55652784*x + 44112090*x^2 + 539550*x^3)))/(1764*Sqrt[3]*(5104 - 1980*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 1764*(2 + 3*x)^2*(-16562 - 1820*x + 2975*x^2) + Sqrt[1 - 2*x]*(1764*Sqrt[3]*(-4240 - 100*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 1764*(2 + 3*x)^2*(13970 + 7150*x))) + (50*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/27 - (17687*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/5292 + (88435*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/10584","C",1
2485,1,539,122,2.1758852,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^4),x]","\frac{6655 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2744}-\frac{33275 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{5488}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-6254289875 x^5-108341342975 x^4+68367418770 x^3+480144531980 x^2+422480476520 x+109184847552\right)+\sqrt{5 x+3} \left(6244357350 x^5+383863734595 x^4+539652073422 x^3-40234628676 x^2-317724962984 x-109184847552\right)+\sqrt{3} \left(8689272750 x^6-180777186300 x^5-775317845730 x^4-591590335992 x^3+264458859096 x^2+\sqrt{1-2 x} \left(63593557500 x^5+122530938750 x^4-346237195920 x^3-793148398680 x^2-514951224480 x-109184847552\right)+410195710944 x+109184847552\right)}{8232 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right) (3 x+2)^3+\sqrt{1-2 x} \left(8232 \left(-391875 x^2+2827000 x+3481060\right) (3 x+2)^3+8232 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right) (3 x+2)^3\right)+8232 \left(44875 x^3+2976525 x^2-279060 x-3667684\right) (3 x+2)^3}","-\frac{\sqrt{1-2 x} (5 x+3)^{5/2}}{21 (3 x+2)^3}-\frac{55 \sqrt{1-2 x} (5 x+3)^{3/2}}{588 (3 x+2)^2}-\frac{605 \sqrt{1-2 x} \sqrt{5 x+3}}{2744 (3 x+2)}-\frac{6655 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2744 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(109184847552 + 422480476520*x + 480144531980*x^2 + 68367418770*x^3 - 108341342975*x^4 - 6254289875*x^5) + Sqrt[3 + 5*x]*(-109184847552 - 317724962984*x - 40234628676*x^2 + 539652073422*x^3 + 383863734595*x^4 + 6244357350*x^5) + Sqrt[3]*(109184847552 + 410195710944*x + 264458859096*x^2 - 591590335992*x^3 - 775317845730*x^4 - 180777186300*x^5 + 8689272750*x^6 + Sqrt[1 - 2*x]*(-109184847552 - 514951224480*x - 793148398680*x^2 - 346237195920*x^3 + 122530938750*x^4 + 63593557500*x^5)))/(8232*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 8232*(2 + 3*x)^3*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(8232*(2 + 3*x)^3*(3481060 + 2827000*x - 391875*x^2) + 8232*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (6655*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2744 - (33275*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/5488","C",1
2486,1,599,151,2.5748426,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^5),x]","\frac{6655 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{3136}-\frac{33275 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{6272}+\frac{\sqrt{5 x+3} \left(-767456250000 x^7-15349224302500 x^6-13240420198500 x^5-10894440301800 x^4-15704356441400 x^3+7283098762720 x^2+18502175927840 x+6173535772800\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(143219465625 x^7+2021220065000 x^6-10982269927500 x^5-20761596010800 x^4-23281646671640 x^3-32760718322880 x^2-24464536940192 x-6173535772800\right)+\sqrt{3} \left(-78812390625 x^8+7970433050000 x^7+25898795185000 x^6+19198834050000 x^5+22174303877800 x^4+14254710348800 x^3-20360873225920 x^2+\sqrt{1-2 x} \left(-1461005287500 x^7+2122148627500 x^6+24034776051000 x^5+34694438889000 x^4+43768930240640 x^3+50856239463040 x^2+29658262584192 x+6173535772800\right)-23695901571840 x-6173535772800\right)}{9408 \sqrt{3} \sqrt{5 x+3} \left(-8921000 x^3+162998000 x^2+220512160 x-287530496\right) (3 x+2)^4+\sqrt{1-2 x} \left(9408 \sqrt{3} \sqrt{5 x+3} \left(-595000 x^3-53178000 x^2+36412000 x+283051520\right) (3 x+2)^4+9408 \left(48482500 x^3+297203500 x^2-794989800 x-852279560\right) (3 x+2)^4\right)+9408 \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (3 x+2)^4}","\frac{3 \sqrt{1-2 x} (5 x+3)^{7/2}}{28 (3 x+2)^4}-\frac{\sqrt{1-2 x} (5 x+3)^{5/2}}{24 (3 x+2)^3}-\frac{55 \sqrt{1-2 x} (5 x+3)^{3/2}}{672 (3 x+2)^2}-\frac{605 \sqrt{1-2 x} \sqrt{5 x+3}}{3136 (3 x+2)}-\frac{6655 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{3136 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(6173535772800 + 18502175927840*x + 7283098762720*x^2 - 15704356441400*x^3 - 10894440301800*x^4 - 13240420198500*x^5 - 15349224302500*x^6 - 767456250000*x^7) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-6173535772800 - 24464536940192*x - 32760718322880*x^2 - 23281646671640*x^3 - 20761596010800*x^4 - 10982269927500*x^5 + 2021220065000*x^6 + 143219465625*x^7) + Sqrt[3]*(-6173535772800 - 23695901571840*x - 20360873225920*x^2 + 14254710348800*x^3 + 22174303877800*x^4 + 19198834050000*x^5 + 25898795185000*x^6 + 7970433050000*x^7 - 78812390625*x^8 + Sqrt[1 - 2*x]*(6173535772800 + 29658262584192*x + 50856239463040*x^2 + 43768930240640*x^3 + 34694438889000*x^4 + 24034776051000*x^5 + 2122148627500*x^6 - 1461005287500*x^7)))/(9408*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-287530496 + 220512160*x + 162998000*x^2 - 8921000*x^3) + 9408*(2 + 3*x)^4*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[1 - 2*x]*(9408*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(283051520 + 36412000*x - 53178000*x^2 - 595000*x^3) + 9408*(2 + 3*x)^4*(-852279560 - 794989800*x + 297203500*x^2 + 48482500*x^3))) + (6655*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/3136 - (33275*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/6272","C",1
2487,1,659,180,3.1618698,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^6} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^6),x]","\frac{933031 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{307328}-\frac{4665155 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{614656}+\frac{\sqrt{5 x+3} \left(-173653682075775000 x^9-13024243041290518125 x^8-32870157037580742550 x^7+51256649776899642240 x^6+213711195321958144272 x^5+199314858823742400640 x^4+22444521464205336320 x^3-64558869951741302720 x^2-36214944986256164480 x-5947178391803100672\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(46348515009140625 x^9+1748078683913296875 x^8-10589419485048481250 x^7-75698717420234319000 x^6-118257543950815756800 x^5-18990033411306732640 x^4+109167913589527305600 x^3+109423592151560166208 x^2+42146086200249959552 x+5947178391803100672\right)+\sqrt{3} \left(-48305244669271875 x^{10}+4047345280732734375 x^9+36711326876647287500 x^8+23724039338613873000 x^7-176254640479281787800 x^6-362076752454745327472 x^5-231679676080710378240 x^4+20469061010566265280 x^3+92668848000425918720 x^2+\sqrt{1-2 x} \left(-705011373437765625 x^9-855684364336312500 x^8+47689833040462800000 x^7+157012138967583405000 x^6+150834835566496686000 x^5-44428917292217525760 x^4-187409075396094559040 x^3-142478777972322944768 x^2-47104658287169210112 x-5947178391803100672\right)+41173517073175415040 x+5947178391803100672\right)}{4609920 \sqrt{3} \sqrt{5 x+3} \left(-1267818750 x^4-9518685000 x^3+69310513800 x^2+56147279760 x-69301667072\right) (3 x+2)^5+\sqrt{1-2 x} \left(4609920 \left(-1369671875 x^4+51596875000 x^3+138263482500 x^2-202281464000 x-207093792400\right) (3 x+2)^5+4609920 \sqrt{3} \sqrt{5 x+3} \left(82531250 x^4-1693375000 x^3-32693775000 x^2+10413254000 x+68979180800\right) (3 x+2)^5\right)+4609920 \left(221253125 x^5+24627671875 x^4-44901737500 x^3-413522831500 x^2+3249828400 x+208061251216\right) (3 x+2)^5}","\frac{\sqrt{1-2 x} (5 x+3)^{3/2}}{105 (3 x+2)^5}+\frac{1948963 \sqrt{1-2 x} \sqrt{5 x+3}}{8297856 (3 x+2)}-\frac{12371 \sqrt{1-2 x} \sqrt{5 x+3}}{592704 (3 x+2)^2}-\frac{14831 \sqrt{1-2 x} \sqrt{5 x+3}}{105840 (3 x+2)^3}+\frac{437 \sqrt{1-2 x} \sqrt{5 x+3}}{17640 (3 x+2)^4}-\frac{933031 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{307328 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-5947178391803100672 - 36214944986256164480*x - 64558869951741302720*x^2 + 22444521464205336320*x^3 + 199314858823742400640*x^4 + 213711195321958144272*x^5 + 51256649776899642240*x^6 - 32870157037580742550*x^7 - 13024243041290518125*x^8 - 173653682075775000*x^9) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(5947178391803100672 + 42146086200249959552*x + 109423592151560166208*x^2 + 109167913589527305600*x^3 - 18990033411306732640*x^4 - 118257543950815756800*x^5 - 75698717420234319000*x^6 - 10589419485048481250*x^7 + 1748078683913296875*x^8 + 46348515009140625*x^9) + Sqrt[3]*(5947178391803100672 + 41173517073175415040*x + 92668848000425918720*x^2 + 20469061010566265280*x^3 - 231679676080710378240*x^4 - 362076752454745327472*x^5 - 176254640479281787800*x^6 + 23724039338613873000*x^7 + 36711326876647287500*x^8 + 4047345280732734375*x^9 - 48305244669271875*x^10 + Sqrt[1 - 2*x]*(-5947178391803100672 - 47104658287169210112*x - 142478777972322944768*x^2 - 187409075396094559040*x^3 - 44428917292217525760*x^4 + 150834835566496686000*x^5 + 157012138967583405000*x^6 + 47689833040462800000*x^7 - 855684364336312500*x^8 - 705011373437765625*x^9)))/(4609920*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(-69301667072 + 56147279760*x + 69310513800*x^2 - 9518685000*x^3 - 1267818750*x^4) + 4609920*(2 + 3*x)^5*(208061251216 + 3249828400*x - 413522831500*x^2 - 44901737500*x^3 + 24627671875*x^4 + 221253125*x^5) + Sqrt[1 - 2*x]*(4609920*(2 + 3*x)^5*(-207093792400 - 202281464000*x + 138263482500*x^2 + 51596875000*x^3 - 1369671875*x^4) + 4609920*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(68979180800 + 10413254000*x - 32693775000*x^2 - 1693375000*x^3 + 82531250*x^4))) + (933031*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/307328 - (4665155*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/614656","C",1
2488,1,719,209,3.7733306,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^7} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^7),x]","\frac{52573169 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{8605184}-\frac{262865845 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{17210368}+\frac{\sqrt{5 x+3} \left(-9730850615965826325000 x^{11}+44151780156608601056250 x^{10}+1688716853126673943394250 x^9+4957159570569378753880200 x^8+1099431317811841246284800 x^7-13017425638575993425776128 x^6-20012801493813732294770112 x^5-10046838927718149775722240 x^4+1865613590645970211368960 x^3+4118855169176543847912960 x^2+1643056649823105887400448 x+223466153034592680486912\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(191055659814185765625 x^{11}-40865911230237268500000 x^{10}-398040255674498553243750 x^9+344930444427860000797000 x^8+5940709848650297764854400 x^7+12591185937044722134133440 x^6+9032472612144033942149120 x^5-2838436713762861314782720 x^4-8965139993621402901779712 x^3-6092358748453197968720896 x^2-1866270295855957242780160 x-223466153034592680486912\right)+\sqrt{3} \left(1033080930304944046875 x^{12}+37684656182216352262500 x^{11}-649654977435044885831250 x^{10}-4676214854425181512311000 x^9-7252681395531753997837800 x^8+5411688264530366683926240 x^7+26431965460746262224309888 x^6+28257717633562013157837312 x^5+9513255310382784439165440 x^4-4791940003732278630812160 x^3-5410381864312051295577600 x^2-1829306764359224787806208 x+\sqrt{1-2 x} \left(3905817664059435093750 x^{11}+232277745779356225781250 x^{10}+601332753058901500230000 x^9-3013842958215043930041000 x^8-13727090593557400060821600 x^7-19790714216346194574383040 x^6-8500441376440190720209920 x^5+8667356511125137113953280 x^4+13458495699607717756833792 x^3+7569925135623373212535296 x^2+2052520410392076143185920 x+223466153034592680486912\right)-223466153034592680486912\right)}{129077760 \sqrt{3} \sqrt{5 x+3} \left(-25265212500 x^5+1941218400000 x^4+5284290066000 x^3-24057375117600 x^2-13825440024000 x+16748592098304\right) (3 x+2)^6+\sqrt{1-2 x} \left(129077760 \sqrt{3} \sqrt{5 x+3} \left(-2625187500 x^5-345183000000 x^4+1378186950000 x^3+13912170444000 x^2-2687092123200 x-16725373086720\right) (3 x+2)^6+129077760 \left(236425406250 x^5+2220611593750 x^4-28520358020000 x^3-52011357156000 x^2+49788771586400 x+50183931760160\right) (3 x+2)^6\right)+129077760 \left(23653109375 x^6-916525237500 x^5-21026153381250 x^4+17065853944000 x^3+123670456765200 x^2-301410173760 x-50253588794912\right) (3 x+2)^6}","\frac{\sqrt{1-2 x} (5 x+3)^{3/2}}{126 (3 x+2)^6}+\frac{122343637 \sqrt{1-2 x} \sqrt{5 x+3}}{232339968 (3 x+2)}+\frac{958171 \sqrt{1-2 x} \sqrt{5 x+3}}{16595712 (3 x+2)^2}-\frac{71369 \sqrt{1-2 x} \sqrt{5 x+3}}{2963520 (3 x+2)^3}-\frac{149951 \sqrt{1-2 x} \sqrt{5 x+3}}{1481760 (3 x+2)^4}+\frac{503 \sqrt{1-2 x} \sqrt{5 x+3}}{26460 (3 x+2)^5}-\frac{52573169 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{8605184 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(223466153034592680486912 + 1643056649823105887400448*x + 4118855169176543847912960*x^2 + 1865613590645970211368960*x^3 - 10046838927718149775722240*x^4 - 20012801493813732294770112*x^5 - 13017425638575993425776128*x^6 + 1099431317811841246284800*x^7 + 4957159570569378753880200*x^8 + 1688716853126673943394250*x^9 + 44151780156608601056250*x^10 - 9730850615965826325000*x^11) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-223466153034592680486912 - 1866270295855957242780160*x - 6092358748453197968720896*x^2 - 8965139993621402901779712*x^3 - 2838436713762861314782720*x^4 + 9032472612144033942149120*x^5 + 12591185937044722134133440*x^6 + 5940709848650297764854400*x^7 + 344930444427860000797000*x^8 - 398040255674498553243750*x^9 - 40865911230237268500000*x^10 + 191055659814185765625*x^11) + Sqrt[3]*(-223466153034592680486912 - 1829306764359224787806208*x - 5410381864312051295577600*x^2 - 4791940003732278630812160*x^3 + 9513255310382784439165440*x^4 + 28257717633562013157837312*x^5 + 26431965460746262224309888*x^6 + 5411688264530366683926240*x^7 - 7252681395531753997837800*x^8 - 4676214854425181512311000*x^9 - 649654977435044885831250*x^10 + 37684656182216352262500*x^11 + 1033080930304944046875*x^12 + Sqrt[1 - 2*x]*(223466153034592680486912 + 2052520410392076143185920*x + 7569925135623373212535296*x^2 + 13458495699607717756833792*x^3 + 8667356511125137113953280*x^4 - 8500441376440190720209920*x^5 - 19790714216346194574383040*x^6 - 13727090593557400060821600*x^7 - 3013842958215043930041000*x^8 + 601332753058901500230000*x^9 + 232277745779356225781250*x^10 + 3905817664059435093750*x^11)))/(129077760*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(16748592098304 - 13825440024000*x - 24057375117600*x^2 + 5284290066000*x^3 + 1941218400000*x^4 - 25265212500*x^5) + 129077760*(2 + 3*x)^6*(-50253588794912 - 301410173760*x + 123670456765200*x^2 + 17065853944000*x^3 - 21026153381250*x^4 - 916525237500*x^5 + 23653109375*x^6) + Sqrt[1 - 2*x]*(129077760*Sqrt[3]*(2 + 3*x)^6*Sqrt[3 + 5*x]*(-16725373086720 - 2687092123200*x + 13912170444000*x^2 + 1378186950000*x^3 - 345183000000*x^4 - 2625187500*x^5) + 129077760*(2 + 3*x)^6*(50183931760160 + 49788771586400*x - 52011357156000*x^2 - 28520358020000*x^3 + 2220611593750*x^4 + 236425406250*x^5))) + (52573169*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/8605184 - (262865845*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/17210368","C",1
2489,1,372,113,2.2326612,"\int \frac{(2+3 x)^4}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","\frac{-3 \sqrt{1-2 x} \sqrt{5 x+3} \left(-738774000000 x^7+4348801500000 x^6+128024201272500 x^5+402047275389125 x^4+537590974318600 x^3+460398724246040 x^2-473808337187680 x-889145204548568\right)-3 \sqrt{5 x+3} \left(8377776000000 x^7+75978117600000 x^6+44002658700000 x^5-336519233875000 x^4-772578638885900 x^3-1399509331161700 x^2-420390829665400 x+889145204548568\right)+\sqrt{3} \left(-3 \sqrt{1-2 x} \left(3853872000000 x^7-54849775200000 x^6-351076744260000 x^5-747285565301000 x^4-864856612073300 x^3-364026302170740 x^2+1213587284207320 x+889145204548568\right)-3 \left(-514080000000 x^8-47765064000000 x^7-133911760200000 x^6+105073939970000 x^5+778423491020125 x^4+1581626047081400 x^3+2047127491359800 x^2-319388117354240 x-889145204548568\right)\right)}{128000 \sqrt{3} \sqrt{5 x+3} \left(8921000 x^3-162998000 x^2-220512160 x+287530496\right)+\sqrt{1-2 x} \left(128000 \left(-48482500 x^3-297203500 x^2+794989800 x+852279560\right)+128000 \sqrt{3} \sqrt{5 x+3} \left(595000 x^3+53178000 x^2-36412000 x-283051520\right)\right)+128000 \left(-8550625 x^4+79738000 x^3+1253327000 x^2-32289760 x-865716488\right)}+\frac{10866247 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{64000 \sqrt{10}}","-\frac{3}{40} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^3-\frac{259}{800} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2-\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} (77820 x+187559)}{128000}+\frac{10866247 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{128000 \sqrt{10}}",1,"(-3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-889145204548568 - 473808337187680*x + 460398724246040*x^2 + 537590974318600*x^3 + 402047275389125*x^4 + 128024201272500*x^5 + 4348801500000*x^6 - 738774000000*x^7) - 3*Sqrt[3 + 5*x]*(889145204548568 - 420390829665400*x - 1399509331161700*x^2 - 772578638885900*x^3 - 336519233875000*x^4 + 44002658700000*x^5 + 75978117600000*x^6 + 8377776000000*x^7) + Sqrt[3]*(-3*Sqrt[1 - 2*x]*(889145204548568 + 1213587284207320*x - 364026302170740*x^2 - 864856612073300*x^3 - 747285565301000*x^4 - 351076744260000*x^5 - 54849775200000*x^6 + 3853872000000*x^7) - 3*(-889145204548568 - 319388117354240*x + 2047127491359800*x^2 + 1581626047081400*x^3 + 778423491020125*x^4 + 105073939970000*x^5 - 133911760200000*x^6 - 47765064000000*x^7 - 514080000000*x^8)))/(128000*Sqrt[3]*Sqrt[3 + 5*x]*(287530496 - 220512160*x - 162998000*x^2 + 8921000*x^3) + 128000*(-865716488 - 32289760*x + 1253327000*x^2 + 79738000*x^3 - 8550625*x^4) + Sqrt[1 - 2*x]*(128000*(852279560 + 794989800*x - 297203500*x^2 - 48482500*x^3) + 128000*Sqrt[3]*Sqrt[3 + 5*x]*(-283051520 - 36412000*x + 53178000*x^2 + 595000*x^3))) + (10866247*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(64000*Sqrt[10])","B",1
2490,1,312,84,1.9666221,"\int \frac{(2+3 x)^3}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","\frac{9 \sqrt{5 x+3} \left(-125400000 x^5+606815000 x^4+2919960450 x^3+5836713575 x^2+2724460860 x-4726524748\right)+9 \sqrt{1-2 x} \sqrt{5 x+3} \left(-7180000 x^5-496886500 x^4-1354483525 x^3-1328674385 x^2+2067164560 x+4726524748\right)+\sqrt{3} \left(9 \sqrt{1-2 x} \left(183480000 x^5+1264329000 x^4+2297910450 x^3+1073331435 x^2-5984133100 x-4726524748\right)+9 \left(46800000 x^6-15810000 x^5-2089963500 x^4-6119287075 x^3-9552589725 x^2+1192507680 x+4726524748\right)\right)}{1600 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right)+\sqrt{1-2 x} \left(1600 \left(-391875 x^2+2827000 x+3481060\right)+1600 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right)\right)+1600 \left(44875 x^3+2976525 x^2-279060 x-3667684\right)}+\frac{44437 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{800 \sqrt{10}}","-\frac{1}{10} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2-\frac{\sqrt{1-2 x} \sqrt{5 x+3} (2220 x+5363)}{1600}+\frac{44437 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{1600 \sqrt{10}}",1,"(9*Sqrt[3 + 5*x]*(-4726524748 + 2724460860*x + 5836713575*x^2 + 2919960450*x^3 + 606815000*x^4 - 125400000*x^5) + 9*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(4726524748 + 2067164560*x - 1328674385*x^2 - 1354483525*x^3 - 496886500*x^4 - 7180000*x^5) + Sqrt[3]*(9*Sqrt[1 - 2*x]*(-4726524748 - 5984133100*x + 1073331435*x^2 + 2297910450*x^3 + 1264329000*x^4 + 183480000*x^5) + 9*(4726524748 + 1192507680*x - 9552589725*x^2 - 6119287075*x^3 - 2089963500*x^4 - 15810000*x^5 + 46800000*x^6)))/(1600*Sqrt[3]*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 1600*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(1600*(3481060 + 2827000*x - 391875*x^2) + 1600*Sqrt[3]*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (44437*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(800*Sqrt[10])","B",1
2491,1,252,77,1.6121598,"\int \frac{(2+3 x)^2}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","\frac{-3 \sqrt{1-2 x} \sqrt{5 x+3} \left(-178500 x^3-340025 x^2+1313840 x+4421582\right)-3 \sqrt{5 x+3} \left(858000 x^3+3406700 x^2+3198030 x-4421582\right)+\sqrt{3} \left(-3 \sqrt{1-2 x} \left(594000 x^3+320100 x^2-4954950 x-4421582\right)-3 \left(-60000 x^4-2701000 x^3-7103125 x^2+443080 x+4421582\right)\right)}{400 \left(-2975 x^2+1820 x+16562\right)+400 \sqrt{3} \sqrt{5 x+3} (1980 x-5104)+\sqrt{1-2 x} \left(400 (-7150 x-13970)+400 \sqrt{3} \sqrt{5 x+3} (100 x+4240)\right)}+\frac{3827 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{200 \sqrt{10}}","-\frac{3}{20} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)-\frac{333}{400} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{3827 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{400 \sqrt{10}}",1,"(-3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(4421582 + 1313840*x - 340025*x^2 - 178500*x^3) - 3*Sqrt[3 + 5*x]*(-4421582 + 3198030*x + 3406700*x^2 + 858000*x^3) + Sqrt[3]*(-3*Sqrt[1 - 2*x]*(-4421582 - 4954950*x + 320100*x^2 + 594000*x^3) - 3*(4421582 + 443080*x - 7103125*x^2 - 2701000*x^3 - 60000*x^4)))/(400*Sqrt[3]*Sqrt[3 + 5*x]*(-5104 + 1980*x) + 400*(16562 + 1820*x - 2975*x^2) + Sqrt[1 - 2*x]*(400*(-13970 - 7150*x) + 400*Sqrt[3]*Sqrt[3 + 5*x]*(4240 + 100*x))) + (3827*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(200*Sqrt[10])","B",1
2492,1,182,50,1.2646623,"\int \frac{2+3 x}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","\frac{\left(\frac{3}{10} \sqrt{1-2 x}-\frac{3}{10}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right) \left(10 x-55 \sqrt{1-2 x}+20 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}-22 \sqrt{3} \sqrt{5 x+3}+61\right)}{\left(5 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{5 x+3}-11\right)^2}+\frac{37 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{5 \sqrt{10}}","\frac{37 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{10 \sqrt{10}}-\frac{3}{10} \sqrt{1-2 x} \sqrt{5 x+3}",1,"((-3/10 + (3*Sqrt[1 - 2*x])/10)*(Sqrt[3] - Sqrt[3 + 5*x])*(61 - 55*Sqrt[1 - 2*x] + 10*x - 22*Sqrt[3]*Sqrt[3 + 5*x] + 20*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]))/(-11 + 5*Sqrt[1 - 2*x] + 2*Sqrt[3]*Sqrt[3 + 5*x])^2 + (37*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(5*Sqrt[10])","B",1
2493,1,57,26,1.1404751,"\int \frac{1}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","-2 \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5}-\sqrt{5} \sqrt{1-2 x}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"-2*Sqrt[2/5]*ArcTan[(Sqrt[5] - Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])]","B",1
2494,1,188,32,1.2246374,"\int \frac{1}{\sqrt{1-2 x} (2+3 x) \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)*Sqrt[3 + 5*x]),x]","\text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{\sqrt{7}}",1,"RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (2*Log[Sqrt[3] - Sqrt[3 + 5*x]] - 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] + 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ]","C",1
2495,1,417,64,1.4713703,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^2 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^2*Sqrt[3 + 5*x]),x]","\frac{37}{7} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{185}{14} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{3} \left(-3 \left(185 x^2-263 x-242\right)-3 \sqrt{1-2 x} (385 x+242)\right)-3 \sqrt{1-2 x} \sqrt{5 x+3} (-100 x-242)-3 (242-22 x) \sqrt{5 x+3}}{14 (5 x+91) (3 x+2)-308 \sqrt{3} \sqrt{5 x+3} (3 x+2)+\sqrt{1-2 x} \left(140 \sqrt{3} (3 x+2) \sqrt{5 x+3}-770 (3 x+2)\right)}","\frac{3 \sqrt{1-2 x} \sqrt{5 x+3}}{7 (3 x+2)}-\frac{37 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{7 \sqrt{7}}",1,"(-3*(242 - 22*x)*Sqrt[3 + 5*x] - 3*(-242 - 100*x)*Sqrt[1 - 2*x]*Sqrt[3 + 5*x] + Sqrt[3]*(-3*Sqrt[1 - 2*x]*(242 + 385*x) - 3*(-242 - 263*x + 185*x^2)))/(-308*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x] + 14*(2 + 3*x)*(91 + 5*x) + Sqrt[1 - 2*x]*(-770*(2 + 3*x) + 140*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x])) + (37*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/7 - (185*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/14","C",1
2496,1,485,93,1.8747366,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^3 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^3*Sqrt[3 + 5*x]),x]","\frac{3827}{196} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{19135}{392} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{3 \sqrt{5 x+3} \left(-7916040 x^3-6372718 x^2+9184626 x+6910552\right)+3 \sqrt{1-2 x} \sqrt{5 x+3} \left(831375 x^3-6870680 x^2-15021226 x-6910552\right)+\sqrt{3} \left(3 \sqrt{1-2 x} \left(499950 x^3+16664010 x^2+21297936 x+6910552\right)+3 \left(1912725 x^4+15528380 x^3+1961138 x^2-15461336 x-6910552\right)\right)}{196 \left(2975 x^2-1820 x-16562\right) (3 x+2)^2+196 \sqrt{3} (5104-1980 x) \sqrt{5 x+3} (3 x+2)^2+\sqrt{1-2 x} \left(196 (7150 x+13970) (3 x+2)^2+196 \sqrt{3} (-100 x-4240) \sqrt{5 x+3} (3 x+2)^2\right)}","\frac{333 \sqrt{1-2 x} \sqrt{5 x+3}}{196 (3 x+2)}+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3}}{14 (3 x+2)^2}-\frac{3827 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{196 \sqrt{7}}",1,"(3*Sqrt[3 + 5*x]*(6910552 + 9184626*x - 6372718*x^2 - 7916040*x^3) + 3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-6910552 - 15021226*x - 6870680*x^2 + 831375*x^3) + Sqrt[3]*(3*Sqrt[1 - 2*x]*(6910552 + 21297936*x + 16664010*x^2 + 499950*x^3) + 3*(-6910552 - 15461336*x + 1961138*x^2 + 15528380*x^3 + 1912725*x^4)))/(196*Sqrt[3]*(5104 - 1980*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 196*(2 + 3*x)^2*(-16562 - 1820*x + 2975*x^2) + Sqrt[1 - 2*x]*(196*Sqrt[3]*(-4240 - 100*x)*(2 + 3*x)^2*Sqrt[3 + 5*x] + 196*(2 + 3*x)^2*(13970 + 7150*x))) + (3827*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/196 - (19135*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/392","C",1
2497,1,545,122,2.1749351,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^4 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^4*Sqrt[3 + 5*x]),x]","\frac{222185 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2744}-\frac{1110925 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{5488}+\frac{-9 \sqrt{1-2 x} \sqrt{5 x+3} \left(-3610101125 x^5-55394016725 x^4+46575849670 x^3+275832485300 x^2+245646480440 x+65533584512\right)-9 \sqrt{5 x+3} \left(6258910350 x^5+212722498945 x^4+297583907082 x^3-21936567356 x^2-183174898104 x-65533584512\right)+\sqrt{3} \left(-9 \sqrt{1-2 x} \left(34495353750 x^5+56310630750 x^4-206049763920 x^3-456593946600 x^2-301283259200 x-65533584512\right)-9 \left(4278249000 x^6-106125446550 x^5-426220154130 x^4-327321909752 x^3+149612918376 x^2+238811676864 x+65533584512\right)\right)}{2744 \sqrt{3} \sqrt{5 x+3} \left(-229350 x^2-783420 x+1201728\right) (3 x+2)^3+\sqrt{1-2 x} \left(2744 \left(-391875 x^2+2827000 x+3481060\right) (3 x+2)^3+2744 \sqrt{3} \sqrt{5 x+3} \left(29250 x^2-96900 x-1139520\right) (3 x+2)^3\right)+2744 \left(44875 x^3+2976525 x^2-279060 x-3667684\right) (3 x+2)^3}","\frac{19415 \sqrt{1-2 x} \sqrt{5 x+3}}{2744 (3 x+2)}+\frac{185 \sqrt{1-2 x} \sqrt{5 x+3}}{196 (3 x+2)^2}+\frac{\sqrt{1-2 x} \sqrt{5 x+3}}{7 (3 x+2)^3}-\frac{222185 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2744 \sqrt{7}}",1,"(-9*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(65533584512 + 245646480440*x + 275832485300*x^2 + 46575849670*x^3 - 55394016725*x^4 - 3610101125*x^5) - 9*Sqrt[3 + 5*x]*(-65533584512 - 183174898104*x - 21936567356*x^2 + 297583907082*x^3 + 212722498945*x^4 + 6258910350*x^5) + Sqrt[3]*(-9*Sqrt[1 - 2*x]*(-65533584512 - 301283259200*x - 456593946600*x^2 - 206049763920*x^3 + 56310630750*x^4 + 34495353750*x^5) - 9*(65533584512 + 238811676864*x + 149612918376*x^2 - 327321909752*x^3 - 426220154130*x^4 - 106125446550*x^5 + 4278249000*x^6)))/(2744*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(1201728 - 783420*x - 229350*x^2) + 2744*(2 + 3*x)^3*(-3667684 - 279060*x + 2976525*x^2 + 44875*x^3) + Sqrt[1 - 2*x]*(2744*(2 + 3*x)^3*(3481060 + 2827000*x - 391875*x^2) + 2744*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-1139520 - 96900*x + 29250*x^2))) + (222185*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2744 - (1110925*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/5488","C",1
2498,1,344,113,2.3128631,"\int \frac{(2+3 x)^4}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","\frac{-142803000000 x^7-2618051625000 x^6+1534491236250 x^5+27499071169125 x^4+79367157739425 x^3+64530030072300 x^2+\sqrt{3} \sqrt{5 x+3} \left(291891600000 x^6+534323790000 x^5-3129037411500 x^4-12103686993475 x^3-20079039318800 x^2+2217051096260 x+8958443837288\right)+\sqrt{1-2 x} \left(-223908300000 x^6-6671485012500 x^5-22099787411625 x^4-32897083536075 x^3+5772137621580 x^2+\sqrt{3} \sqrt{5 x+3} \left(-13138200000 x^6+574537455000 x^5+3369451587750 x^4+6586867690825 x^3+4182536549040 x^2-11240383725100 x-8958443837288\right)+56171588581020 x+26875331511864\right)-29101590694500 x-26875331511864}{24000 \sqrt{1-2 x} \sqrt{5 x+3} \left(-1101875 x^3-16812750 x^2+68422100 x+77141440\right)+24000 \sqrt{5 x+3} \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right)+\sqrt{3} \left(24000 \sqrt{1-2 x} \left(11261250 x^3-7257250 x^2-135935800 x-76516440\right)+24000 \left(1013750 x^4-47347500 x^3-123624450 x^2+74349280 x+78755928\right)\right)}+\frac{143283 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{4000 \sqrt{10}}","-\frac{2 \sqrt{1-2 x} (3 x+2)^3}{55 \sqrt{5 x+3}}-\frac{21}{550} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2-\frac{21 \sqrt{1-2 x} \sqrt{5 x+3} (3660 x+8987)}{88000}+\frac{143283 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{8000 \sqrt{10}}",1,"(-26875331511864 - 29101590694500*x + 64530030072300*x^2 + 79367157739425*x^3 + 27499071169125*x^4 + 1534491236250*x^5 - 2618051625000*x^6 - 142803000000*x^7 + Sqrt[3]*Sqrt[3 + 5*x]*(8958443837288 + 2217051096260*x - 20079039318800*x^2 - 12103686993475*x^3 - 3129037411500*x^4 + 534323790000*x^5 + 291891600000*x^6) + Sqrt[1 - 2*x]*(26875331511864 + 56171588581020*x + 5772137621580*x^2 - 32897083536075*x^3 - 22099787411625*x^4 - 6671485012500*x^5 - 223908300000*x^6 + Sqrt[3]*Sqrt[3 + 5*x]*(-8958443837288 - 11240383725100*x + 4182536549040*x^2 + 6586867690825*x^3 + 3369451587750*x^4 + 574537455000*x^5 - 13138200000*x^6)))/(24000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(77141440 + 68422100*x - 16812750*x^2 - 1101875*x^3) + 24000*Sqrt[3 + 5*x]*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3) + Sqrt[3]*(24000*Sqrt[1 - 2*x]*(-76516440 - 135935800*x - 7257250*x^2 + 11261250*x^3) + 24000*(78755928 + 74349280*x - 123624450*x^2 - 47347500*x^3 + 1013750*x^4))) + (143283*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(4000*Sqrt[10])","B",1
2499,1,284,84,1.9872358,"\int \frac{(2+3 x)^3}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","\frac{38475000 x^5-596463750 x^4-3035589375 x^3-3621354525 x^2+\sqrt{3} \sqrt{5 x+3} \left(17820000 x^4+373329000 x^3+1031870125 x^2-54003950 x-553488364\right)+\sqrt{1-2 x} \left(265072500 x^4+807134625 x^3-382896855 x^2+\sqrt{3} \sqrt{5 x+3} \left(-11259000 x^4-133856550 x^3-165269165 x^2+613085850 x+553488364\right)-3229722210 x-1660465092\right)+1552476510 x+1660465092}{1200 \sqrt{5 x+3} \left(-163625 x^2+33550 x+343904\right)+1200 \sqrt{1-2 x} \sqrt{5 x+3} \left(11875 x^2-216750 x-312800\right)+\sqrt{3} \left(1200 \sqrt{1-2 x} \left(27500 x^2+517000 x+300300\right)+1200 \left(34750 x^3+321050 x^2-372220 x-331404\right)\right)}+\frac{2493 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{200 \sqrt{10}}","-\frac{2 \sqrt{1-2 x} (3 x+2)^2}{55 \sqrt{5 x+3}}-\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} (300 x+979)}{4400}+\frac{2493 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{400 \sqrt{10}}",1,"(1660465092 + 1552476510*x - 3621354525*x^2 - 3035589375*x^3 - 596463750*x^4 + 38475000*x^5 + Sqrt[3]*Sqrt[3 + 5*x]*(-553488364 - 54003950*x + 1031870125*x^2 + 373329000*x^3 + 17820000*x^4) + Sqrt[1 - 2*x]*(-1660465092 - 3229722210*x - 382896855*x^2 + 807134625*x^3 + 265072500*x^4 + Sqrt[3]*Sqrt[3 + 5*x]*(553488364 + 613085850*x - 165269165*x^2 - 133856550*x^3 - 11259000*x^4)))/(1200*Sqrt[3 + 5*x]*(343904 + 33550*x - 163625*x^2) + 1200*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-312800 - 216750*x + 11875*x^2) + Sqrt[3]*(1200*Sqrt[1 - 2*x]*(300300 + 517000*x + 27500*x^2) + 1200*(-331404 - 372220*x + 321050*x^2 + 34750*x^3))) + (2493*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(200*Sqrt[10])","B",1
2500,1,224,72,1.5957429,"\int \frac{(2+3 x)^2}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","\frac{-87750 x^3-381225 x^2+\sqrt{3} \sqrt{5 x+3} \left(89100 x^2+5115 x-72842\right)+\sqrt{1-2 x} \left(-22275 x^2+\sqrt{3} \sqrt{5 x+3} \left(-12150 x^2+65495 x+72842\right)-374715 x-218526\right)+162885 x+218526}{\sqrt{3} \left(150 \left(450 x^2-2100 x-1422\right)+150 \sqrt{1-2 x} (1650 x+990)\right)+150 \sqrt{1-2 x} \sqrt{5 x+3} (-325 x-1240)+150 \sqrt{5 x+3} (165 x+1672)}+\frac{123 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{25 \sqrt{10}}","-\frac{9}{50} \sqrt{1-2 x} \sqrt{5 x+3}-\frac{2 \sqrt{1-2 x}}{275 \sqrt{5 x+3}}+\frac{123 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{50 \sqrt{10}}",1,"(218526 + 162885*x - 381225*x^2 - 87750*x^3 + Sqrt[3]*Sqrt[3 + 5*x]*(-72842 + 5115*x + 89100*x^2) + Sqrt[1 - 2*x]*(-218526 - 374715*x - 22275*x^2 + Sqrt[3]*Sqrt[3 + 5*x]*(72842 + 65495*x - 12150*x^2)))/(150*(-1240 - 325*x)*Sqrt[1 - 2*x]*Sqrt[3 + 5*x] + 150*Sqrt[3 + 5*x]*(1672 + 165*x) + Sqrt[3]*(150*Sqrt[1 - 2*x]*(990 + 1650*x) + 150*(-1422 - 2100*x + 450*x^2))) + (123*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(25*Sqrt[10])","B",1
2501,1,151,52,1.2730482,"\int \frac{2+3 x}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","\frac{\sqrt{3} \left(2 \sqrt{1-2 x}-2\right)-2 \sqrt{1-2 x} \sqrt{5 x+3}+2 \sqrt{5 x+3}}{\sqrt{3} \sqrt{5 x+3} \left(25 \sqrt{1-2 x}-55\right)+5 (30 x+18)}+\frac{6}{5} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{3}{5} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{2 \sqrt{1-2 x}}{55 \sqrt{5 x+3}}",1,"(Sqrt[3]*(-2 + 2*Sqrt[1 - 2*x]) + 2*Sqrt[3 + 5*x] - 2*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(Sqrt[3]*(-55 + 25*Sqrt[1 - 2*x])*Sqrt[3 + 5*x] + 5*(18 + 30*x)) + (6*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/5","B",1
2502,1,100,22,1.1017557,"\int \frac{1}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","\frac{\left(2-2 \sqrt{1-2 x}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^2}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(30 x+5 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{3} \sqrt{5 x+3}+18\right)}","-\frac{2 \sqrt{1-2 x}}{11 \sqrt{5 x+3}}",1,"((2 - 2*Sqrt[1 - 2*x])*(Sqrt[3] - Sqrt[3 + 5*x])^2)/((-Sqrt[3] + Sqrt[3 + 5*x])*(18 + 30*x - 11*Sqrt[3]*Sqrt[3 + 5*x] + 5*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]))","B",1
2503,1,270,55,1.2811164,"\int \frac{1}{\sqrt{1-2 x} (2+3 x) (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^(3/2)),x]","3 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{\left(10 \sqrt{1-2 x}-10\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)}{30 x+5 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{3} \sqrt{5 x+3}+18}","\frac{6 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{\sqrt{7}}-\frac{10 \sqrt{1-2 x}}{11 \sqrt{5 x+3}}",1,"((-10 + 10*Sqrt[1 - 2*x])*(Sqrt[3] - Sqrt[3 + 5*x]))/(18 + 30*x - 11*Sqrt[3]*Sqrt[3 + 5*x] + 5*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]) + 3*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ]","C",1
2504,1,451,86,1.8390398,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^2 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^(3/2)),x]","-\frac{321}{7} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{1605}{14} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(12525 x^2+746590 x+482548\right)+\sqrt{5 x+3} \left(511335 x^2-403722 x-482548\right)+\sqrt{3} \left(-304950 x^3-233750 x^2+\sqrt{1-2 x} \left(-495000 x^2-1067880 x-482548\right)+725012 x+482548\right)}{14 (3 x+2) \left(1350 x^2-6300 x-4266\right)+14 \sqrt{3} (3 x+2) \sqrt{5 x+3} (165 x+1672)+\sqrt{1-2 x} \left(14 (4950 x+2970) (3 x+2)+14 \sqrt{3} (-325 x-1240) \sqrt{5 x+3} (3 x+2)\right)}","-\frac{515 \sqrt{1-2 x}}{77 \sqrt{5 x+3}}+\frac{3 \sqrt{1-2 x}}{7 (3 x+2) \sqrt{5 x+3}}+\frac{321 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{7 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(482548 + 746590*x + 12525*x^2) + Sqrt[3 + 5*x]*(-482548 - 403722*x + 511335*x^2) + Sqrt[3]*(482548 + 725012*x - 233750*x^2 - 304950*x^3 + Sqrt[1 - 2*x]*(-482548 - 1067880*x - 495000*x^2)))/(14*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(1672 + 165*x) + 14*(2 + 3*x)*(-4266 - 6300*x + 1350*x^2) + Sqrt[1 - 2*x]*(14*Sqrt[3]*(-1240 - 325*x)*(2 + 3*x)*Sqrt[3 + 5*x] + 14*(2 + 3*x)*(2970 + 4950*x))) - (321*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/7 + (1605*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/14","C",1
2505,1,519,115,2.1550623,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^3 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^(3/2)),x]","-\frac{56421}{196} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{282105}{392} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-2390722875 x^4-994039800 x^3+48995582320 x^2+63105405564 x+20453594128\right)+\sqrt{5 x+3} \left(14130232875 x^4+59599140150 x^3+12925414612 x^2-44407746284 x-20453594128\right)+\sqrt{3} \left(-725539500 x^5-56888235975 x^4-77787716335 x^3+18273780858 x^2+\sqrt{1-2 x} \left(10139765625 x^4-26162148375 x^3-95070489690 x^2-79444396504 x-20453594128\right)+60746737224 x+20453594128\right)}{196 \sqrt{3} \sqrt{5 x+3} \left(-163625 x^2+33550 x+343904\right) (3 x+2)^2+\sqrt{1-2 x} \left(196 \sqrt{3} \sqrt{5 x+3} \left(11875 x^2-216750 x-312800\right) (3 x+2)^2+196 \left(82500 x^2+1551000 x+900900\right) (3 x+2)^2\right)+196 \left(104250 x^3+963150 x^2-1116660 x-994212\right) (3 x+2)^2}","-\frac{90415 \sqrt{1-2 x}}{2156 \sqrt{5 x+3}}+\frac{543 \sqrt{1-2 x}}{196 (3 x+2) \sqrt{5 x+3}}+\frac{3 \sqrt{1-2 x}}{14 (3 x+2)^2 \sqrt{5 x+3}}+\frac{56421 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{196 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(20453594128 + 63105405564*x + 48995582320*x^2 - 994039800*x^3 - 2390722875*x^4) + Sqrt[3 + 5*x]*(-20453594128 - 44407746284*x + 12925414612*x^2 + 59599140150*x^3 + 14130232875*x^4) + Sqrt[3]*(20453594128 + 60746737224*x + 18273780858*x^2 - 77787716335*x^3 - 56888235975*x^4 - 725539500*x^5 + Sqrt[1 - 2*x]*(-20453594128 - 79444396504*x - 95070489690*x^2 - 26162148375*x^3 + 10139765625*x^4)))/(196*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(343904 + 33550*x - 163625*x^2) + 196*(2 + 3*x)^2*(-994212 - 1116660*x + 963150*x^2 + 104250*x^3) + Sqrt[1 - 2*x]*(196*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(-312800 - 216750*x + 11875*x^2) + 196*(2 + 3*x)^2*(900900 + 1551000*x + 82500*x^2))) - (56421*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/196 + (282105*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/392","C",1
2506,1,579,144,2.5710568,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^4 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^(3/2)),x]","-\frac{4616025 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2744}+\frac{23080125 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{5488}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(8272648935000 x^6+833928284493000 x^5+1467941488519050 x^4-2060913967748380 x^3-5548633513652760 x^2-3726502708810160 x-809748616657024\right)+\sqrt{5 x+3} \left(184777462311750 x^6-1652120740081350 x^5-6333724399942170 x^4-4883881562895764 x^3+1617122202621992 x^2+2937430181536048 x+809748616657024\right)+\sqrt{3} \left(-57782382108750 x^7+124827482986875 x^6+5373138628943775 x^5+10428255350811540 x^4+4298120460654704 x^3-3797282927632232 x^2+\sqrt{1-2 x} \left(-260146879925625 x^6-2036657833662375 x^5-882361648337400 x^4+5653760458322680 x^3+8380584360974760 x^2+4395522905607680 x+809748616657024\right)-3606450378333568 x-809748616657024\right)}{2744 \sqrt{3} \sqrt{5 x+3} \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (3 x+2)^3+\sqrt{1-2 x} \left(2744 \sqrt{3} \sqrt{5 x+3} \left(-1101875 x^3-16812750 x^2+68422100 x+77141440\right) (3 x+2)^3+2744 \left(33783750 x^3-21771750 x^2-407807400 x-229549320\right) (3 x+2)^3\right)+2744 \left(3041250 x^4-142042500 x^3-370873350 x^2+223047840 x+236267784\right) (3 x+2)^3}","-\frac{7396875 \sqrt{1-2 x}}{30184 \sqrt{5 x+3}}+\frac{44475 \sqrt{1-2 x}}{2744 (3 x+2) \sqrt{5 x+3}}+\frac{255 \sqrt{1-2 x}}{196 (3 x+2)^2 \sqrt{5 x+3}}+\frac{\sqrt{1-2 x}}{7 (3 x+2)^3 \sqrt{5 x+3}}+\frac{4616025 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2744 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-809748616657024 - 3726502708810160*x - 5548633513652760*x^2 - 2060913967748380*x^3 + 1467941488519050*x^4 + 833928284493000*x^5 + 8272648935000*x^6) + Sqrt[3 + 5*x]*(809748616657024 + 2937430181536048*x + 1617122202621992*x^2 - 4883881562895764*x^3 - 6333724399942170*x^4 - 1652120740081350*x^5 + 184777462311750*x^6) + Sqrt[3]*(-809748616657024 - 3606450378333568*x - 3797282927632232*x^2 + 4298120460654704*x^3 + 10428255350811540*x^4 + 5373138628943775*x^5 + 124827482986875*x^6 - 57782382108750*x^7 + Sqrt[1 - 2*x]*(809748616657024 + 4395522905607680*x + 8380584360974760*x^2 + 5653760458322680*x^3 - 882361648337400*x^4 - 2036657833662375*x^5 - 260146879925625*x^6)))/(2744*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3) + 2744*(2 + 3*x)^3*(236267784 + 223047840*x - 370873350*x^2 - 142042500*x^3 + 3041250*x^4) + Sqrt[1 - 2*x]*(2744*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(77141440 + 68422100*x - 16812750*x^2 - 1101875*x^3) + 2744*(2 + 3*x)^3*(-229549320 - 407807400*x - 21771750*x^2 + 33783750*x^3))) - (4616025*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2744 + (23080125*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/5488","C",1
2507,1,414,142,2.8685648,"\int \frac{(2+3 x)^5}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\frac{435705075000000 x^9-42760892401875000 x^8-329220027253406250 x^7-601015310116509375 x^6+263991043179090000 x^5+3556179014282771625 x^4+4576078090891322100 x^3+573256554742950300 x^2+\sqrt{3} \sqrt{5 x+3} \left(1030601880000000 x^8+38783757177000000 x^7+123013683267750000 x^6+72489284155344375 x^5-454283754804622875 x^4-1106169841845961200 x^3-422350006098091500 x^2+356168513960303000 x+186655657734205968\right)+\sqrt{1-2 x} \left(7405285882500000 x^8+6490847737687500 x^7-329390189410528125 x^6-1399256221683498750 x^5-2741804980426499625 x^4-1425481373744554500 x^3+1811070883792033380 x^2+\sqrt{3} \sqrt{5 x+3} \left(-201652335000000 x^8-4951403812125000 x^7+23875684810368750 x^6+190780393281341875 x^5+502819665522128875 x^4+522766146307198800 x^3-216481637685451460 x^2-543211448602794920 x-186655657734205968\right)+2096498660722024680 x+559966973202617904\right)-1535369856794548920 x-559966973202617904}{1080000 \left(-846511875 x^4+2876857500 x^3+32771841300 x^2-464036760 x-18959828096\right) (5 x+3)^{3/2}+1080000 \sqrt{1-2 x} \left(24903125 x^4-2538047500 x^3-9400717500 x^2+18053298200 x+18798584960\right) (5 x+3)^{3/2}+\sqrt{3} \left(1080000 \sqrt{1-2 x} (5 x+3) \left(294525000 x^4+10148490000 x^3+1543311000 x^2-33942744000 x-18767334960\right)+1080000 (5 x+3) \left(115256250 x^5+2406453750 x^4-23245830000 x^3-39836473200 x^2+16519101840 x+18928578096\right)\right)}+\frac{462357 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{20000 \sqrt{10}}","-\frac{2 \sqrt{1-2 x} (3 x+2)^4}{165 (5 x+3)^{3/2}}-\frac{734 \sqrt{1-2 x} (3 x+2)^3}{9075 \sqrt{5 x+3}}+\frac{511 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2}{30250}-\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} (366420 x+938509)}{4840000}+\frac{462357 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{40000 \sqrt{10}}",1,"(-559966973202617904 - 1535369856794548920*x + 573256554742950300*x^2 + 4576078090891322100*x^3 + 3556179014282771625*x^4 + 263991043179090000*x^5 - 601015310116509375*x^6 - 329220027253406250*x^7 - 42760892401875000*x^8 + 435705075000000*x^9 + Sqrt[3]*Sqrt[3 + 5*x]*(186655657734205968 + 356168513960303000*x - 422350006098091500*x^2 - 1106169841845961200*x^3 - 454283754804622875*x^4 + 72489284155344375*x^5 + 123013683267750000*x^6 + 38783757177000000*x^7 + 1030601880000000*x^8) + Sqrt[1 - 2*x]*(559966973202617904 + 2096498660722024680*x + 1811070883792033380*x^2 - 1425481373744554500*x^3 - 2741804980426499625*x^4 - 1399256221683498750*x^5 - 329390189410528125*x^6 + 6490847737687500*x^7 + 7405285882500000*x^8 + Sqrt[3]*Sqrt[3 + 5*x]*(-186655657734205968 - 543211448602794920*x - 216481637685451460*x^2 + 522766146307198800*x^3 + 502819665522128875*x^4 + 190780393281341875*x^5 + 23875684810368750*x^6 - 4951403812125000*x^7 - 201652335000000*x^8)))/(1080000*(3 + 5*x)^(3/2)*(-18959828096 - 464036760*x + 32771841300*x^2 + 2876857500*x^3 - 846511875*x^4) + 1080000*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)*(18798584960 + 18053298200*x - 9400717500*x^2 - 2538047500*x^3 + 24903125*x^4) + Sqrt[3]*(1080000*Sqrt[1 - 2*x]*(3 + 5*x)*(-18767334960 - 33942744000*x + 1543311000*x^2 + 10148490000*x^3 + 294525000*x^4) + 1080000*(3 + 5*x)*(18928578096 + 16519101840*x - 39836473200*x^2 - 23245830000*x^3 + 2406453750*x^4 + 115256250*x^5))) + (462357*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(20000*Sqrt[10])","B",1
2508,1,354,113,2.4562731,"\int \frac{(2+3 x)^4}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\frac{-481960125000 x^7-9032724618750 x^6+3115080946875 x^5+142919257954500 x^4+230938196656275 x^3+36053902208400 x^2+\sqrt{3} \sqrt{5 x+3} \left(985134150000 x^6+2205605902500 x^5-14161019324375 x^4-53107251429925 x^3-24667935469100 x^2+20078726375620 x+11417604995544\right)+\sqrt{1-2 x} \left(-755690512500 x^6-22824835543125 x^5-84901421162250 x^4-52831245357825 x^3+104138918376240 x^2+\sqrt{3} \sqrt{5 x+3} \left(-44341425000 x^6+1920957828750 x^5+12474403173875 x^4+20643242744175 x^3-12514167785180 x^2-31527044829340 x-11417604995544\right)+123150861664380 x+34252814986632\right)-88805906303220 x-34252814986632}{54000 \sqrt{1-2 x} \left(-1101875 x^3-16812750 x^2+68422100 x+77141440\right) (5 x+3)^{3/2}+54000 \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (5 x+3)^{3/2}+\sqrt{3} \left(54000 \sqrt{1-2 x} (5 x+3) \left(11261250 x^3-7257250 x^2-135935800 x-76516440\right)+54000 (5 x+3) \left(1013750 x^4-47347500 x^3-123624450 x^2+74349280 x+78755928\right)\right)}+\frac{8127 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{1000 \sqrt{10}}","-\frac{2 \sqrt{1-2 x} (3 x+2)^3}{165 (5 x+3)^{3/2}}-\frac{602 \sqrt{1-2 x} (3 x+2)^2}{9075 \sqrt{5 x+3}}-\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} (1020 x+12199)}{242000}+\frac{8127 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{2000 \sqrt{10}}",1,"(-34252814986632 - 88805906303220*x + 36053902208400*x^2 + 230938196656275*x^3 + 142919257954500*x^4 + 3115080946875*x^5 - 9032724618750*x^6 - 481960125000*x^7 + Sqrt[3]*Sqrt[3 + 5*x]*(11417604995544 + 20078726375620*x - 24667935469100*x^2 - 53107251429925*x^3 - 14161019324375*x^4 + 2205605902500*x^5 + 985134150000*x^6) + Sqrt[1 - 2*x]*(34252814986632 + 123150861664380*x + 104138918376240*x^2 - 52831245357825*x^3 - 84901421162250*x^4 - 22824835543125*x^5 - 755690512500*x^6 + Sqrt[3]*Sqrt[3 + 5*x]*(-11417604995544 - 31527044829340*x - 12514167785180*x^2 + 20643242744175*x^3 + 12474403173875*x^4 + 1920957828750*x^5 - 44341425000*x^6)))/(54000*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)*(77141440 + 68422100*x - 16812750*x^2 - 1101875*x^3) + 54000*(3 + 5*x)^(3/2)*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3) + Sqrt[3]*(54000*Sqrt[1 - 2*x]*(3 + 5*x)*(-76516440 - 135935800*x - 7257250*x^2 + 11261250*x^3) + 54000*(3 + 5*x)*(78755928 + 74349280*x - 123624450*x^2 - 47347500*x^3 + 1013750*x^4))) + (8127*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(1000*Sqrt[10])","B",1
2509,1,294,84,2.0468515,"\int \frac{(2+3 x)^3}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\frac{86568750 x^5-1596530625 x^4-4224483750 x^3-884369325 x^2+\sqrt{3} \sqrt{5 x+3} \left(40095000 x^4+883007125 x^3+568286125 x^2-457107310 x-293453556\right)+\sqrt{1-2 x} \left(596413125 x^4+545424000 x^3-2394797955 x^2+\sqrt{3} \sqrt{5 x+3} \left(-25332750 x^4-258883175 x^3+284316735 x^2+747248290 x+293453556\right)-2971385010 x-880360668\right)+2100962070 x+880360668}{1350 \left(-163625 x^2+33550 x+343904\right) (5 x+3)^{3/2}+1350 \sqrt{1-2 x} \left(11875 x^2-216750 x-312800\right) (5 x+3)^{3/2}+\sqrt{3} \left(1350 \sqrt{1-2 x} (5 x+3) \left(27500 x^2+517000 x+300300\right)+1350 (5 x+3) \left(34750 x^3+321050 x^2-372220 x-331404\right)\right)}+\frac{81 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{25 \sqrt{10}}","-\frac{2 \sqrt{1-2 x} (3 x+2)^2}{165 (5 x+3)^{3/2}}-\frac{\sqrt{1-2 x} (9405 x+5831)}{18150 \sqrt{5 x+3}}+\frac{81 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{50 \sqrt{10}}",1,"(880360668 + 2100962070*x - 884369325*x^2 - 4224483750*x^3 - 1596530625*x^4 + 86568750*x^5 + Sqrt[3]*Sqrt[3 + 5*x]*(-293453556 - 457107310*x + 568286125*x^2 + 883007125*x^3 + 40095000*x^4) + Sqrt[1 - 2*x]*(-880360668 - 2971385010*x - 2394797955*x^2 + 545424000*x^3 + 596413125*x^4 + Sqrt[3]*Sqrt[3 + 5*x]*(293453556 + 747248290*x + 284316735*x^2 - 258883175*x^3 - 25332750*x^4)))/(1350*(3 + 5*x)^(3/2)*(343904 + 33550*x - 163625*x^2) + 1350*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)*(-312800 - 216750*x + 11875*x^2) + Sqrt[3]*(1350*Sqrt[1 - 2*x]*(3 + 5*x)*(300300 + 517000*x + 27500*x^2) + 1350*(3 + 5*x)*(-331404 - 372220*x + 321050*x^2 + 34750*x^3))) + (81*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(25*Sqrt[10])","B",1
2510,1,244,74,1.6801313,"\int \frac{(2+3 x)^2}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\frac{-2 \sqrt{3} \sqrt{5 x+3} \left(-45375 x^2+39655 x+40722\right)+\sqrt{1-2 x} \left(-2 \sqrt{3} \sqrt{5 x+3} \left(-1525 x^2-68065 x-40722\right)-2 \left(138600 x^2+284625 x+122166\right)\right)-2 \left(83250 x^3+51750 x^2-199395 x-122166\right)}{\sqrt{3} \left(675 (5 x+3) \left(450 x^2-2100 x-1422\right)+675 \sqrt{1-2 x} (5 x+3) (1650 x+990)\right)+675 (165 x+1672) (5 x+3)^{3/2}+675 (-325 x-1240) \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{18}{25} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{404 \sqrt{1-2 x}}{9075 \sqrt{5 x+3}}-\frac{2 \sqrt{1-2 x}}{825 (5 x+3)^{3/2}}+\frac{9}{25} \sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"(-2*Sqrt[3]*Sqrt[3 + 5*x]*(40722 + 39655*x - 45375*x^2) - 2*(-122166 - 199395*x + 51750*x^2 + 83250*x^3) + Sqrt[1 - 2*x]*(-2*Sqrt[3]*Sqrt[3 + 5*x]*(-40722 - 68065*x - 1525*x^2) - 2*(122166 + 284625*x + 138600*x^2)))/(675*(-1240 - 325*x)*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2) + 675*(3 + 5*x)^(3/2)*(1672 + 165*x) + Sqrt[3]*(675*Sqrt[1 - 2*x]*(3 + 5*x)*(990 + 1650*x) + 675*(3 + 5*x)*(-1422 - 2100*x + 450*x^2))) + (18*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/25","B",1
2511,1,258,45,1.3319009,"\int \frac{2+3 x}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\frac{\left(\frac{1}{27}-\frac{1}{27} \sqrt{1-2 x}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^6 \left(\frac{225 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4}+\frac{855 \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}+\frac{112 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{342-342 \sqrt{1-2 x}}{\sqrt{3}-\sqrt{5 x+3}}+36 \sqrt{3}\right)}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(10 \sqrt{3} x+5 \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{5 x+3}+6 \sqrt{3}\right)^3}","-\frac{206 \sqrt{1-2 x}}{1815 \sqrt{5 x+3}}-\frac{2 \sqrt{1-2 x}}{165 (5 x+3)^{3/2}}",1,"((1/27 - Sqrt[1 - 2*x]/27)*(Sqrt[3] - Sqrt[3 + 5*x])^6*(36*Sqrt[3] + (225*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^4 + (855*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (112*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^2 + (342 - 342*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x])))/((-Sqrt[3] + Sqrt[3 + 5*x])*(6*Sqrt[3] + 10*Sqrt[3]*x - 11*Sqrt[3 + 5*x] + 5*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3)","B",1
2512,1,258,45,1.32546,"\int \frac{1}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\frac{\left(\frac{1}{54}-\frac{1}{54} \sqrt{1-2 x}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^6 \left(\frac{225 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4}+\frac{450 \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}+\frac{40 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{180-180 \sqrt{1-2 x}}{\sqrt{3}-\sqrt{5 x+3}}+36 \sqrt{3}\right)}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(10 \sqrt{3} x+5 \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{5 x+3}+6 \sqrt{3}\right)^3}","-\frac{8 \sqrt{1-2 x}}{363 \sqrt{5 x+3}}-\frac{2 \sqrt{1-2 x}}{33 (5 x+3)^{3/2}}",1,"((1/54 - Sqrt[1 - 2*x]/54)*(Sqrt[3] - Sqrt[3 + 5*x])^6*(36*Sqrt[3] + (225*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^4 + (450*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (40*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^2 + (180 - 180*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x])))/((-Sqrt[3] + Sqrt[3 + 5*x])*(6*Sqrt[3] + 10*Sqrt[3]*x - 11*Sqrt[3 + 5*x] + 5*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3)","B",1
2513,0,0,77,16.1744455,"\int \frac{1}{\sqrt{1-2 x} (2+3 x) (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^(5/2)),x]","\int \frac{1}{\sqrt{1-2 x} (2+3 x) (3+5 x)^{5/2}} \, dx","\frac{950 \sqrt{1-2 x}}{363 \sqrt{5 x+3}}-\frac{10 \sqrt{1-2 x}}{33 (5 x+3)^{3/2}}-\frac{18 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{\sqrt{7}}",1,"Could not integrate","F",-1
2514,0,0,108,20.115155,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^2 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^(5/2)),x]","\int \frac{1}{\sqrt{1-2 x} (2+3 x)^2 (3+5 x)^{5/2}} \, dx","\frac{84235 \sqrt{1-2 x}}{2541 \sqrt{5 x+3}}-\frac{845 \sqrt{1-2 x}}{231 (5 x+3)^{3/2}}+\frac{3 \sqrt{1-2 x}}{7 (3 x+2) (5 x+3)^{3/2}}-\frac{1593 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{7 \sqrt{7}}",1,"Could not integrate","F",-1
2515,0,0,137,25.048277,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^3 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^(5/2)),x]","\int \frac{1}{\sqrt{1-2 x} (2+3 x)^3 (3+5 x)^{5/2}} \, dx","\frac{20743985 \sqrt{1-2 x}}{71148 \sqrt{5 x+3}}-\frac{207895 \sqrt{1-2 x}}{6468 (5 x+3)^{3/2}}+\frac{753 \sqrt{1-2 x}}{196 (3 x+2) (5 x+3)^{3/2}}+\frac{3 \sqrt{1-2 x}}{14 (3 x+2)^2 (5 x+3)^{3/2}}-\frac{392283 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{196 \sqrt{7}}",1,"Could not integrate","F",-1
2516,0,0,166,32.7208718,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^4 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^(5/2)),x]","\int \frac{1}{\sqrt{1-2 x} (2+3 x)^4 (3+5 x)^{5/2}} \, dx","\frac{2184369575 \sqrt{1-2 x}}{996072 \sqrt{5 x+3}}-\frac{21891025 \sqrt{1-2 x}}{90552 (5 x+3)^{3/2}}+\frac{79335 \sqrt{1-2 x}}{2744 (3 x+2) (5 x+3)^{3/2}}+\frac{325 \sqrt{1-2 x}}{196 (3 x+2)^2 (5 x+3)^{3/2}}+\frac{\sqrt{1-2 x}}{7 (3 x+2)^3 (5 x+3)^{3/2}}-\frac{41307885 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2744 \sqrt{7}}",1,"Could not integrate","F",-1
2517,1,410,59,4.4121918,"\int \frac{1}{\sqrt{a+b x} (e+f x) \sqrt{2 b e-a f+b f x}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*(e + f*x)*Sqrt[2*b*e - a*f + b*f*x]),x]","\frac{\text{RootSum}\left[\text{$\#$1}^4 b e f^2+\text{$\#$1}^4 b f^3-4 \text{$\#$1}^3 f^2 \sqrt{a+b} \sqrt{-a f+2 b e+b f}+6 \text{$\#$1}^2 b e f+6 \text{$\#$1}^2 b f^2-4 \text{$\#$1} f \sqrt{a+b} \sqrt{-a f+2 b e+b f}+b e+b f\&,\frac{\text{$\#$1}^2 f \log \left(\sqrt{-a f+2 b e+b f}-\sqrt{-a f+2 b e+b f x}\right)-\text{$\#$1}^2 f \log \left(\text{$\#$1} \sqrt{-a f+2 b e+b f x}+\text{$\#$1} \left(-\sqrt{-a f+2 b e+b f}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)+\log \left(\text{$\#$1} \sqrt{-a f+2 b e+b f x}+\text{$\#$1} \left(-\sqrt{-a f+2 b e+b f}\right)-\sqrt{a+b x}+\sqrt{a+b}\right)-\log \left(\sqrt{-a f+2 b e+b f}-\sqrt{-a f+2 b e+b f x}\right)}{\text{$\#$1}^3 b e f+\text{$\#$1}^3 b f^2-3 \text{$\#$1}^2 f \sqrt{a+b} \sqrt{-a f+2 b e+b f}+3 \text{$\#$1} b e+3 \text{$\#$1} b f-\sqrt{a+b} \sqrt{-a f+2 b e+b f}}\&\right]}{f}","\frac{\tan ^{-1}\left(\frac{\sqrt{f} \sqrt{a+b x} \sqrt{-a f+2 b e+b f x}}{b e-a f}\right)}{\sqrt{f} (b e-a f)}",1,"RootSum[b*e + b*f - 4*Sqrt[a + b]*f*Sqrt[2*b*e - a*f + b*f]*#1 + 6*b*e*f*#1^2 + 6*b*f^2*#1^2 - 4*Sqrt[a + b]*f^2*Sqrt[2*b*e - a*f + b*f]*#1^3 + b*e*f^2*#1^4 + b*f^3*#1^4 & , (-Log[Sqrt[2*b*e - a*f + b*f] - Sqrt[2*b*e - a*f + b*f*x]] + Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[2*b*e - a*f + b*f]*#1 + Sqrt[2*b*e - a*f + b*f*x]*#1] + f*Log[Sqrt[2*b*e - a*f + b*f] - Sqrt[2*b*e - a*f + b*f*x]]*#1^2 - f*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[2*b*e - a*f + b*f]*#1 + Sqrt[2*b*e - a*f + b*f*x]*#1]*#1^2)/(-(Sqrt[a + b]*Sqrt[2*b*e - a*f + b*f]) + 3*b*e*#1 + 3*b*f*#1 - 3*Sqrt[a + b]*f*Sqrt[2*b*e - a*f + b*f]*#1^2 + b*e*f*#1^3 + b*f^2*#1^3) & ]/f","C",1
2518,1,466,168,3.0598489,"\int \frac{(2+3 x)^5 \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^5*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\frac{\sqrt{5 x+3} \left(-3330818884800000000 x^{10}-153537381829260000000 x^9-555235214583159000000 x^8+415074095234803125000 x^7+5437806464268601293750 x^6+12530468884341845603375 x^5+33926204664198250668550 x^4+55909512479730290448980 x^3-89220594057900043031920 x^2-62463994105829224457296 x+49208577194410337284768\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(445683384000000000 x^{10}+13256069280300000000 x^9-164735471741985000000 x^8-1451494930507138125000 x^7-4169862728913392343750 x^6-6015240694282353435625 x^5-8308013949287673387750 x^4+6454482579066000919300 x^3+78475511238865962126800 x^2+13325892412461322826160 x-49208577194410337284768\right)+\sqrt{3} \left(-238136112000000000 x^{11}+48790453955400000000 x^{10}+480995604561690000000 x^9+709166225027585250000 x^8-2908022364048554062500 x^7-12641248200147695802500 x^6-26933671976322619678875 x^5-80591902295070354841950 x^4-16885751501980039494580 x^3+158248631899485646671600 x^2+\sqrt{1-2 x} \left(-6212265840000000000 x^{10}+11826758889000000000 x^9+776902134336570000000 x^8+3741278734425746250000 x^7+7977159468071489437500 x^6+10359993785266392403125 x^5+13033929444243797498750 x^4-53488474367859062623300 x^3-106564616158374408157200 x^2+27671770093817864494480 x+49208577194410337284768\right)+21466331599550037136656 x-49208577194410337284768\right)}{5120000 \sqrt{3} \sqrt{5 x+3} \left(-19972562500 x^5+158441181250 x^4+1891194668000 x^3-1459455705400 x^2-2800561494720 x+1519466908960\right)+\sqrt{1-2 x} \left(5120000 \sqrt{3} \sqrt{5 x+3} \left(382806250 x^5-80547756250 x^4-333372935000 x^3+1857062729800 x^2+1248845958560 x-1523336744224\right)+5120000 \left(26771628125 x^5+1102102787500 x^4-1277247746500 x^3-10194890840200 x^2+44616484880 x+4571572732672\right)\right)+5120000 \left(7164406250 x^6+174195921875 x^5-3695625687500 x^4-5925837277500 x^3+12860921279000 x^2+4621767211760 x-4559963226880\right)}-\frac{35439958001 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{2560000 \sqrt{10}}","\frac{\sqrt{5 x+3} (3 x+2)^5}{\sqrt{1-2 x}}+\frac{33}{20} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^4+\frac{10389 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^3}{1600}+\frac{847637 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2}{32000}+\frac{49 \sqrt{1-2 x} \sqrt{5 x+3} (36265980 x+87394471)}{5120000}-\frac{35439958001 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{5120000 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(49208577194410337284768 - 62463994105829224457296*x - 89220594057900043031920*x^2 + 55909512479730290448980*x^3 + 33926204664198250668550*x^4 + 12530468884341845603375*x^5 + 5437806464268601293750*x^6 + 415074095234803125000*x^7 - 555235214583159000000*x^8 - 153537381829260000000*x^9 - 3330818884800000000*x^10) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-49208577194410337284768 + 13325892412461322826160*x + 78475511238865962126800*x^2 + 6454482579066000919300*x^3 - 8308013949287673387750*x^4 - 6015240694282353435625*x^5 - 4169862728913392343750*x^6 - 1451494930507138125000*x^7 - 164735471741985000000*x^8 + 13256069280300000000*x^9 + 445683384000000000*x^10) + Sqrt[3]*(-49208577194410337284768 + 21466331599550037136656*x + 158248631899485646671600*x^2 - 16885751501980039494580*x^3 - 80591902295070354841950*x^4 - 26933671976322619678875*x^5 - 12641248200147695802500*x^6 - 2908022364048554062500*x^7 + 709166225027585250000*x^8 + 480995604561690000000*x^9 + 48790453955400000000*x^10 - 238136112000000000*x^11 + Sqrt[1 - 2*x]*(49208577194410337284768 + 27671770093817864494480*x - 106564616158374408157200*x^2 - 53488474367859062623300*x^3 + 13033929444243797498750*x^4 + 10359993785266392403125*x^5 + 7977159468071489437500*x^6 + 3741278734425746250000*x^7 + 776902134336570000000*x^8 + 11826758889000000000*x^9 - 6212265840000000000*x^10)))/(5120000*Sqrt[3]*Sqrt[3 + 5*x]*(1519466908960 - 2800561494720*x - 1459455705400*x^2 + 1891194668000*x^3 + 158441181250*x^4 - 19972562500*x^5) + 5120000*(-4559963226880 + 4621767211760*x + 12860921279000*x^2 - 5925837277500*x^3 - 3695625687500*x^4 + 174195921875*x^5 + 7164406250*x^6) + Sqrt[1 - 2*x]*(5120000*Sqrt[3]*Sqrt[3 + 5*x]*(-1523336744224 + 1248845958560*x + 1857062729800*x^2 - 333372935000*x^3 - 80547756250*x^4 + 382806250*x^5) + 5120000*(4571572732672 + 44616484880*x - 10194890840200*x^2 - 1277247746500*x^3 + 1102102787500*x^4 + 26771628125*x^5))) - (35439958001*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(2560000*Sqrt[10])","B",1
2519,1,406,139,2.6967505,"\int \frac{(2+3 x)^4 \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-12909780000000 x^8+1258849071000000 x^7+10544807686275000 x^6+24613642604276250 x^5+21873467041634875 x^4-59387331469208900 x^3-607331878300772700 x^2-137740451935593320 x+530069395019703088\right)+\sqrt{5 x+3} \left(438831756000000 x^8+441934752600000 x^7-19309545847845000 x^6-80931226044561750 x^5-198074889783087075 x^4-393803990744868660 x^3+718995164547838860 x^2+665202451737040536 x-530069395019703088\right)+\sqrt{3} \left(-59748840000000 x^9-1510732458000000 x^8+5976073513350000 x^7+60555041192542500 x^6+176962117383809500 x^5+480806117230524875 x^4+157684697984416060 x^3-1452494951873307740 x^2+\sqrt{1-2 x} \left(-152681760000000 x^8-5933625192000000 x^7-25456154229000000 x^6-39700078526790000 x^5-25556968062907875 x^4+381470946998667900 x^3+901785329786493900 x^2-303478713252700920 x-530069395019703088\right)-223983286548746296 x+530069395019703088\right)}{51200 \sqrt{3} \sqrt{5 x+3} \left(-117810000 x^4-3929805000 x^3+3770256600 x^2+11623605840 x-6255778320\right)+\sqrt{1-2 x} \left(51200 \left(-846511875 x^4+2876857500 x^3+32771841300 x^2-464036760 x-18959828096\right)+51200 \sqrt{3} \sqrt{5 x+3} \left(23051250 x^4+467460000 x^3-4929642000 x^2-5009509440 x+6309526032\right)\right)+51200 \left(-49806250 x^5+5100998125 x^4+16263387500 x^3-45507313900 x^2-19543871720 x+18798584960\right)}-\frac{92108287 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{25600 \sqrt{10}}","\frac{\sqrt{5 x+3} (3 x+2)^4}{\sqrt{1-2 x}}+\frac{27}{16} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^3+\frac{2203}{320} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2+\frac{\sqrt{1-2 x} \sqrt{5 x+3} (4618500 x+11129753)}{51200}-\frac{92108287 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{51200 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(530069395019703088 - 137740451935593320*x - 607331878300772700*x^2 - 59387331469208900*x^3 + 21873467041634875*x^4 + 24613642604276250*x^5 + 10544807686275000*x^6 + 1258849071000000*x^7 - 12909780000000*x^8) + Sqrt[3 + 5*x]*(-530069395019703088 + 665202451737040536*x + 718995164547838860*x^2 - 393803990744868660*x^3 - 198074889783087075*x^4 - 80931226044561750*x^5 - 19309545847845000*x^6 + 441934752600000*x^7 + 438831756000000*x^8) + Sqrt[3]*(530069395019703088 - 223983286548746296*x - 1452494951873307740*x^2 + 157684697984416060*x^3 + 480806117230524875*x^4 + 176962117383809500*x^5 + 60555041192542500*x^6 + 5976073513350000*x^7 - 1510732458000000*x^8 - 59748840000000*x^9 + Sqrt[1 - 2*x]*(-530069395019703088 - 303478713252700920*x + 901785329786493900*x^2 + 381470946998667900*x^3 - 25556968062907875*x^4 - 39700078526790000*x^5 - 25456154229000000*x^6 - 5933625192000000*x^7 - 152681760000000*x^8)))/(51200*Sqrt[3]*Sqrt[3 + 5*x]*(-6255778320 + 11623605840*x + 3770256600*x^2 - 3929805000*x^3 - 117810000*x^4) + 51200*(18798584960 - 19543871720*x - 45507313900*x^2 + 16263387500*x^3 + 5100998125*x^4 - 49806250*x^5) + Sqrt[1 - 2*x]*(51200*(-18959828096 - 464036760*x + 32771841300*x^2 + 2876857500*x^3 - 846511875*x^4) + 51200*Sqrt[3]*Sqrt[3 + 5*x]*(6309526032 - 5009509440*x - 4929642000*x^2 + 467460000*x^3 + 23051250*x^4))) - (92108287*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(25600*Sqrt[10])","B",1
2520,1,346,110,2.3106886,"\int \frac{(2+3 x)^3 \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\frac{\sqrt{5 x+3} \left(-49757400000 x^6-1504943055000 x^5-5681769959250 x^4-13794159214825 x^3+30891237758920 x^2+42866151809228 x-35050872939544\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(15867000000 x^6+305968275000 x^5+146410886250 x^4-2788620795125 x^3-24483275727600 x^2-8418838428340 x+35050872939544\right)+\sqrt{3} \left(-14598000000 x^7+623047050000 x^6+4379805247500 x^5+13573869052500 x^4+8863212352825 x^3-77515303959160 x^2+\sqrt{1-2 x} \left(-162162000000 x^6-548197650000 x^5+771283012500 x^4+13324966626125 x^3+42569689839600 x^2-20621779958780 x-35050872939544\right)-13825533422108 x+35050872939544\right)}{3200 \sqrt{3} \sqrt{5 x+3} \left(-4504500 x^3+7857850 x^2+48208160 x-25505480\right)+\sqrt{1-2 x} \left(3200 \sqrt{3} \sqrt{5 x+3} \left(202750 x^3-9591150 x^2-18970200 x+26251976\right)+3200 \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right)\right)+3200 \left(2203750 x^4+32523625 x^3-153656950 x^2-85860780 x+77141440\right)}-\frac{1463447 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{1600 \sqrt{10}}","\frac{\sqrt{5 x+3} (3 x+2)^3}{\sqrt{1-2 x}}+\frac{7}{4} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2+\frac{\sqrt{1-2 x} \sqrt{5 x+3} (73380 x+176833)}{3200}-\frac{1463447 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{3200 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(-35050872939544 + 42866151809228*x + 30891237758920*x^2 - 13794159214825*x^3 - 5681769959250*x^4 - 1504943055000*x^5 - 49757400000*x^6) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(35050872939544 - 8418838428340*x - 24483275727600*x^2 - 2788620795125*x^3 + 146410886250*x^4 + 305968275000*x^5 + 15867000000*x^6) + Sqrt[3]*(35050872939544 - 13825533422108*x - 77515303959160*x^2 + 8863212352825*x^3 + 13573869052500*x^4 + 4379805247500*x^5 + 623047050000*x^6 - 14598000000*x^7 + Sqrt[1 - 2*x]*(-35050872939544 - 20621779958780*x + 42569689839600*x^2 + 13324966626125*x^3 + 771283012500*x^4 - 548197650000*x^5 - 162162000000*x^6)))/(3200*Sqrt[3]*Sqrt[3 + 5*x]*(-25505480 + 48208160*x + 7857850*x^2 - 4504500*x^3) + 3200*(77141440 - 85860780*x - 153656950*x^2 + 32523625*x^3 + 2203750*x^4) + Sqrt[1 - 2*x]*(3200*Sqrt[3]*Sqrt[3 + 5*x]*(26251976 - 18970200*x - 9591150*x^2 + 202750*x^3) + 3200*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3))) - (1463447*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(1600*Sqrt[10])","B",1
2521,1,286,94,1.8481384,"\int \frac{(2+3 x)^2 \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-4275000 x^4+60003750 x^3+533559025 x^2+371936730 x-1809569036\right)+\sqrt{5 x+3} \left(58905000 x^4+236304750 x^3-727053965 x^2-2068541222 x+1809569036\right)+\sqrt{3} \left(-12510000 x^5-168328500 x^4-322455700 x^3+2837223225 x^2+\sqrt{1-2 x} \left(-9900000 x^4-227865000 x^3-1275289125 x^2+1090639550 x+1809569036\right)+605964942 x-1809569036\right)}{160 \sqrt{3} \sqrt{5 x+3} \left(-11000 x^2-194700 x+100100\right)+\sqrt{1-2 x} \left(160 \left(-163625 x^2+33550 x+343904\right)+160 \sqrt{3} \sqrt{5 x+3} \left(6950 x^2+60040 x-110468\right)\right)+160 \left(-23750 x^3+445375 x^2+408850 x-312800\right)}-\frac{17951 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{80 \sqrt{10}}","\frac{9}{40} \sqrt{1-2 x} (5 x+3)^{3/2}+\frac{49 (5 x+3)^{3/2}}{22 \sqrt{1-2 x}}+\frac{17951 \sqrt{1-2 x} \sqrt{5 x+3}}{1760}-\frac{17951 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{160 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-1809569036 + 371936730*x + 533559025*x^2 + 60003750*x^3 - 4275000*x^4) + Sqrt[3 + 5*x]*(1809569036 - 2068541222*x - 727053965*x^2 + 236304750*x^3 + 58905000*x^4) + Sqrt[3]*(-1809569036 + 605964942*x + 2837223225*x^2 - 322455700*x^3 - 168328500*x^4 - 12510000*x^5 + Sqrt[1 - 2*x]*(1809569036 + 1090639550*x - 1275289125*x^2 - 227865000*x^3 - 9900000*x^4)))/(160*Sqrt[3]*Sqrt[3 + 5*x]*(100100 - 194700*x - 11000*x^2) + 160*(-312800 + 408850*x + 445375*x^2 - 23750*x^3) + Sqrt[1 - 2*x]*(160*(343904 + 33550*x - 163625*x^2) + 160*Sqrt[3]*Sqrt[3 + 5*x]*(-110468 + 60040*x + 6950*x^2))) - (17951*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(80*Sqrt[10])","B",1
2522,1,226,72,1.5425812,"\int \frac{(2+3 x) \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\frac{\sqrt{5 x+3} \left(-990 x^2-40887 x+45254\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(1950 x^2+6505 x-45254\right)+\sqrt{3} \left(-2700 x^3+31300 x^2+\sqrt{1-2 x} \left(-9900 x^2+24915 x+45254\right)+9467 x-45254\right)}{4 \left(650 x^2+2155 x-1240\right)+4 \sqrt{3} \sqrt{5 x+3} (330-660 x)+\sqrt{1-2 x} \left(4 \sqrt{3} \sqrt{5 x+3} (90 x-474)+4 (165 x+1672)\right)}-\frac{103 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{2 \sqrt{10}}","\frac{7 (5 x+3)^{3/2}}{11 \sqrt{1-2 x}}+\frac{103}{44} \sqrt{1-2 x} \sqrt{5 x+3}-\frac{103 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{4 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(45254 - 40887*x - 990*x^2) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-45254 + 6505*x + 1950*x^2) + Sqrt[3]*(-45254 + 9467*x + 31300*x^2 - 2700*x^3 + Sqrt[1 - 2*x]*(45254 + 24915*x - 9900*x^2)))/(4*Sqrt[3]*(330 - 660*x)*Sqrt[3 + 5*x] + 4*(-1240 + 2155*x + 650*x^2) + Sqrt[1 - 2*x]*(4*Sqrt[3]*Sqrt[3 + 5*x]*(-474 + 90*x) + 4*(1672 + 165*x))) - (103*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(2*Sqrt[10])","B",1
2523,1,500,47,2.9849362,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/(1 - 2*x)^(3/2),x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^8 \left(\frac{1125 \left(\sqrt{1-2 x}-1\right)^6}{16 \left(\sqrt{3}-\sqrt{5 x+3}\right)^6}+\frac{75 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^5}{2 \left(\sqrt{3}-\sqrt{5 x+3}\right)^5}-\frac{1725 \left(\sqrt{1-2 x}-1\right)^4}{8 \left(\sqrt{3}-\sqrt{5 x+3}\right)^4}-\frac{105 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}+\frac{345 \left(\sqrt{1-2 x}-1\right)^2}{4 \left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{6 \sqrt{3} \sqrt{1-2 x}-6 \sqrt{3}}{\sqrt{3}-\sqrt{5 x+3}}-\frac{9}{2}\right) \left(\frac{22-22 \sqrt{1-2 x}}{\sqrt{3}-\sqrt{5 x+3}}+\frac{\left(20 \sqrt{10} x+22 \sqrt{10} \sqrt{1-2 x}-4 \sqrt{30} \sqrt{1-2 x} \sqrt{5 x+3}-10 \sqrt{10}\right) \tan ^{-1}\left(\frac{\sqrt{5} \left(\sqrt{1-2 x}-1\right)}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}\right)}{\left(-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5\right)^2 \left(30 x+5 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{3} \sqrt{5 x+3}+18\right)^2}","\frac{\sqrt{5 x+3}}{\sqrt{1-2 x}}-\sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"((Sqrt[3] - Sqrt[3 + 5*x])^8*(-9/2 + (1125*(-1 + Sqrt[1 - 2*x])^6)/(16*(Sqrt[3] - Sqrt[3 + 5*x])^6) + (75*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^5)/(2*(Sqrt[3] - Sqrt[3 + 5*x])^5) - (1725*(-1 + Sqrt[1 - 2*x])^4)/(8*(Sqrt[3] - Sqrt[3 + 5*x])^4) - (105*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (345*(-1 + Sqrt[1 - 2*x])^2)/(4*(Sqrt[3] - Sqrt[3 + 5*x])^2) + (-6*Sqrt[3] + 6*Sqrt[3]*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x]))*((22 - 22*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x]) + ((-10*Sqrt[10] + 22*Sqrt[10]*Sqrt[1 - 2*x] + 20*Sqrt[10]*x - 4*Sqrt[30]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])*ArcTan[(Sqrt[5]*(-1 + Sqrt[1 - 2*x]))/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(Sqrt[3] - Sqrt[3 + 5*x])^2))/((5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^2*(18 + 30*x - 11*Sqrt[3]*Sqrt[3 + 5*x] + 5*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^2)","B",1
2524,1,271,57,1.2694688,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*(2 + 3*x)),x]","\frac{1}{7} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{\left(\frac{22}{7}-\frac{22}{7} \sqrt{1-2 x}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5}","\frac{2 \sqrt{5 x+3}}{7 \sqrt{1-2 x}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{7 \sqrt{7}}",1,"((22/7 - (22*Sqrt[1 - 2*x])/7)*(Sqrt[3] - Sqrt[3 + 5*x]))/(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]) + RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ]/7","C",1
2525,1,451,93,1.7946283,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)^2} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*(2 + 3*x)^2),x]","\frac{29}{49} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{145}{98} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-23760 x^2+56892 x+26620\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-7650 x^2-66520 x-26620\right)+\sqrt{3} \left(25950 x^3-32275 x^2+\sqrt{1-2 x} \left(61875 x^2+78870 x+26620\right)-69242 x-26620\right)}{98 \left(650 x^2+2155 x-1240\right) (3 x+2)+98 \sqrt{3} (330-660 x) \sqrt{5 x+3} (3 x+2)+\sqrt{1-2 x} \left(98 \sqrt{3} (3 x+2) \sqrt{5 x+3} (90 x-474)+98 (3 x+2) (165 x+1672)\right)}","\frac{4 (5 x+3)^{3/2}}{77 \sqrt{1-2 x} (3 x+2)}-\frac{29 \sqrt{1-2 x} \sqrt{5 x+3}}{539 (3 x+2)}-\frac{29 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{49 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(26620 + 56892*x - 23760*x^2) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-26620 - 66520*x - 7650*x^2) + Sqrt[3]*(-26620 - 69242*x - 32275*x^2 + 25950*x^3 + Sqrt[1 - 2*x]*(26620 + 78870*x + 61875*x^2)))/(98*Sqrt[3]*(330 - 660*x)*(2 + 3*x)*Sqrt[3 + 5*x] + 98*(2 + 3*x)*(-1240 + 2155*x + 650*x^2) + Sqrt[1 - 2*x]*(98*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(-474 + 90*x) + 98*(2 + 3*x)*(1672 + 165*x))) + (29*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/49 - (145*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/98","C",1
2526,1,519,122,2.1325862,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)^3} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*(2 + 3*x)^3),x]","\frac{1585 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{1372}-\frac{7925 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2744}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-8876700 x^4-123494715 x^3+96217438 x^2+345222504 x+136571248\right)+\sqrt{5 x+3} \left(1014750 x^4+368891325 x^3+287292610 x^2-213555320 x-136571248\right)+\sqrt{3} \left(14456250 x^5-182518125 x^4-644137000 x^3-152382360 x^2+\sqrt{1-2 x} \left(80524125 x^4+123454650 x^3-338879508 x^2-457061044 x-136571248\right)+325393860 x+136571248\right)}{1372 \sqrt{3} \sqrt{5 x+3} \left(11000 x^2+194700 x-100100\right) (3 x+2)^2+\sqrt{1-2 x} \left(1372 \sqrt{3} \sqrt{5 x+3} \left(-6950 x^2-60040 x+110468\right) (3 x+2)^2+1372 \left(163625 x^2-33550 x-343904\right) (3 x+2)^2\right)+1372 \left(23750 x^3-445375 x^2-408850 x+312800\right) (3 x+2)^2}","\frac{15 \sqrt{1-2 x} \sqrt{5 x+3}}{1372 (3 x+2)}-\frac{15 \sqrt{1-2 x} \sqrt{5 x+3}}{98 (3 x+2)^2}+\frac{2 \sqrt{5 x+3}}{7 \sqrt{1-2 x} (3 x+2)^2}-\frac{1585 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1372 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(136571248 + 345222504*x + 96217438*x^2 - 123494715*x^3 - 8876700*x^4) + Sqrt[3 + 5*x]*(-136571248 - 213555320*x + 287292610*x^2 + 368891325*x^3 + 1014750*x^4) + Sqrt[3]*(136571248 + 325393860*x - 152382360*x^2 - 644137000*x^3 - 182518125*x^4 + 14456250*x^5 + Sqrt[1 - 2*x]*(-136571248 - 457061044*x - 338879508*x^2 + 123454650*x^3 + 80524125*x^4)))/(1372*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(-100100 + 194700*x + 11000*x^2) + 1372*(2 + 3*x)^2*(312800 - 408850*x - 445375*x^2 + 23750*x^3) + Sqrt[1 - 2*x]*(1372*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(110468 - 60040*x - 6950*x^2) + 1372*(2 + 3*x)^2*(-343904 - 33550*x + 163625*x^2))) + (1585*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/1372 - (7925*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2744","C",1
2527,1,579,151,2.4856082,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)^4} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*(2 + 3*x)^4),x]","\frac{7435 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2744}-\frac{37175 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{5488}+\frac{\sqrt{5 x+3} \left(-149708616750 x^6-978534243225 x^5+798225314040 x^4+3169188183920 x^3+1250116572760 x^2-759750335872 x-391614188416\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(16362812250 x^6-53766551475 x^5-1527352321500 x^4-2011801804616 x^3+169247678568 x^2+1159392342272 x+391614188416\right)+\sqrt{3} \left(8373555000 x^7+786460396500 x^6+915479739900 x^5-2865382867890 x^4-4360823769620 x^3-761946219400 x^2+\sqrt{1-2 x} \left(-85232243250 x^6+809810382150 x^5+3014468371530 x^4+2165015585876 x^3-992693453928 x^2-1487977915952 x-391614188416\right)+1088335909552 x+391614188416\right)}{2744 \sqrt{3} \sqrt{5 x+3} \left(-4504500 x^3+7857850 x^2+48208160 x-25505480\right) (3 x+2)^3+\sqrt{1-2 x} \left(2744 \sqrt{3} \sqrt{5 x+3} \left(202750 x^3-9591150 x^2-18970200 x+26251976\right) (3 x+2)^3+2744 \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (3 x+2)^3\right)+2744 \left(2203750 x^4+32523625 x^3-153656950 x^2-85860780 x+77141440\right) (3 x+2)^3}","\frac{565 \sqrt{1-2 x} \sqrt{5 x+3}}{2744 (3 x+2)}-\frac{5 \sqrt{1-2 x} \sqrt{5 x+3}}{196 (3 x+2)^2}-\frac{\sqrt{1-2 x} \sqrt{5 x+3}}{7 (3 x+2)^3}+\frac{2 \sqrt{5 x+3}}{7 \sqrt{1-2 x} (3 x+2)^3}-\frac{7435 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2744 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-391614188416 - 759750335872*x + 1250116572760*x^2 + 3169188183920*x^3 + 798225314040*x^4 - 978534243225*x^5 - 149708616750*x^6) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(391614188416 + 1159392342272*x + 169247678568*x^2 - 2011801804616*x^3 - 1527352321500*x^4 - 53766551475*x^5 + 16362812250*x^6) + Sqrt[3]*(391614188416 + 1088335909552*x - 761946219400*x^2 - 4360823769620*x^3 - 2865382867890*x^4 + 915479739900*x^5 + 786460396500*x^6 + 8373555000*x^7 + Sqrt[1 - 2*x]*(-391614188416 - 1487977915952*x - 992693453928*x^2 + 2165015585876*x^3 + 3014468371530*x^4 + 809810382150*x^5 - 85232243250*x^6)))/(2744*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-25505480 + 48208160*x + 7857850*x^2 - 4504500*x^3) + 2744*(2 + 3*x)^3*(77141440 - 85860780*x - 153656950*x^2 + 32523625*x^3 + 2203750*x^4) + Sqrt[1 - 2*x]*(2744*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(26251976 - 18970200*x - 9591150*x^2 + 202750*x^3) + 2744*(2 + 3*x)^3*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3))) + (7435*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2744 - (37175*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/5488","C",1
2528,1,639,180,2.9924329,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)^5} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*(2 + 3*x)^5),x]","\frac{1244755 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{153664}-\frac{6223775 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{307328}+\frac{\sqrt{5 x+3} \left(-3261140099786250 x^8+68251354467058125 x^7+311471148043806300 x^6+142702228532009520 x^5-471099267123039720 x^4-496517802984067920 x^3-38258866549452384 x^2+114180302472584832 x+34605768493398784\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-176906017440000 x^8-21845342917681875 x^7-26519235004498500 x^6+250760524285489680 x^5+529195991995087976 x^4+259908216379623536 x^3-130907209672485024 x^2-149041293266360704 x-34605768493398784\right)+\sqrt{3} \left(898758195693750 x^9-8108698311039375 x^8-251042608786398750 x^7-485753172323604900 x^6+112353099597966080 x^5+847821846134607520 x^4+557977281124150640 x^3-44647463811938176 x^2+\sqrt{1-2 x} \left(5636566037581875 x^8+58516000988692500 x^7-77480160487418700 x^6-597064920599370960 x^5-757557823670935056 x^4-192654309200652816 x^3+242913829487022144 x^2+177928897469193024 x+34605768493398784\right)-143067906675417152 x-34605768493398784\right)}{153664 \sqrt{3} \sqrt{5 x+3} \left(117810000 x^4+3929805000 x^3-3770256600 x^2-11623605840 x+6255778320\right) (3 x+2)^4+\sqrt{1-2 x} \left(153664 \sqrt{3} \sqrt{5 x+3} \left(-23051250 x^4-467460000 x^3+4929642000 x^2+5009509440 x-6309526032\right) (3 x+2)^4+153664 \left(846511875 x^4-2876857500 x^3-32771841300 x^2+464036760 x+18959828096\right) (3 x+2)^4\right)+153664 \left(49806250 x^5-5100998125 x^4-16263387500 x^3+45507313900 x^2+19543871720 x-18798584960\right) (3 x+2)^4}","\frac{107245 \sqrt{1-2 x} \sqrt{5 x+3}}{153664 (3 x+2)}+\frac{835 \sqrt{1-2 x} \sqrt{5 x+3}}{10976 (3 x+2)^2}-\frac{13 \sqrt{1-2 x} \sqrt{5 x+3}}{392 (3 x+2)^3}-\frac{27 \sqrt{1-2 x} \sqrt{5 x+3}}{196 (3 x+2)^4}+\frac{2 \sqrt{5 x+3}}{7 \sqrt{1-2 x} (3 x+2)^4}-\frac{1244755 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{153664 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(34605768493398784 + 114180302472584832*x - 38258866549452384*x^2 - 496517802984067920*x^3 - 471099267123039720*x^4 + 142702228532009520*x^5 + 311471148043806300*x^6 + 68251354467058125*x^7 - 3261140099786250*x^8) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-34605768493398784 - 149041293266360704*x - 130907209672485024*x^2 + 259908216379623536*x^3 + 529195991995087976*x^4 + 250760524285489680*x^5 - 26519235004498500*x^6 - 21845342917681875*x^7 - 176906017440000*x^8) + Sqrt[3]*(-34605768493398784 - 143067906675417152*x - 44647463811938176*x^2 + 557977281124150640*x^3 + 847821846134607520*x^4 + 112353099597966080*x^5 - 485753172323604900*x^6 - 251042608786398750*x^7 - 8108698311039375*x^8 + 898758195693750*x^9 + Sqrt[1 - 2*x]*(34605768493398784 + 177928897469193024*x + 242913829487022144*x^2 - 192654309200652816*x^3 - 757557823670935056*x^4 - 597064920599370960*x^5 - 77480160487418700*x^6 + 58516000988692500*x^7 + 5636566037581875*x^8)))/(153664*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(6255778320 - 11623605840*x - 3770256600*x^2 + 3929805000*x^3 + 117810000*x^4) + 153664*(2 + 3*x)^4*(-18798584960 + 19543871720*x + 45507313900*x^2 - 16263387500*x^3 - 5100998125*x^4 + 49806250*x^5) + Sqrt[1 - 2*x]*(153664*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-6309526032 + 5009509440*x + 4929642000*x^2 - 467460000*x^3 - 23051250*x^4) + 153664*(2 + 3*x)^4*(18959828096 + 464036760*x - 32771841300*x^2 - 2876857500*x^3 + 846511875*x^4))) + (1244755*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/153664 - (6223775*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/307328","C",1
2529,1,466,161,3.2607144,"\int \frac{(2+3 x)^4 (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]","\frac{\sqrt{5 x+3} \left(-1110272961600000000 x^{10}-51086604529620000000 x^9-180861923526273000000 x^8+151620032584477875000 x^7+1796518146938721456250 x^6+4052557168067371423625 x^5+10754617210253349447850 x^4+17644160345499940694860 x^3-28219309183709607975440 x^2-19746337144226971093552 x+15547680440838324779616\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(148561128000000000 x^{10}+4406309666100000000 x^9-55273565705895000000 x^8-479072481098566875000 x^7-1352344721977836406250 x^6-1906883598434580249375 x^5-2578013908492023234250 x^4+2103306002177908995100 x^3+24834548295906739047600 x^2+4220896987364695379920 x-15547680440838324779616\right)+\sqrt{3} \left(-79378704000000000 x^{11}+16270099543800000000 x^{10}+158973114168630000000 x^9+223742542796856750000 x^8-983083416012994437500 x^7-4137161898907031417500 x^6-8634771141108564192125 x^5-25488741668791111941650 x^4-5293452792192061390060 x^3+50037855629614293011600 x^2+\sqrt{1-2 x} \left(-2070755280000000000 x^{10}+4114815903000000000 x^9+258548501159190000000 x^8+1225818532536303750000 x^7+2566554200260558062500 x^6+3254426785093362621875 x^5+4028602118746058411250 x^4-16993412566407907323100 x^3-33718221219448850572400 x^2+8732510104977919019760 x+15547680440838324779616\right)+6792930051884356693872 x-15547680440838324779616\right)}{1024000 \sqrt{3} \sqrt{5 x+3} \left(-19972562500 x^5+158441181250 x^4+1891194668000 x^3-1459455705400 x^2-2800561494720 x+1519466908960\right)+\sqrt{1-2 x} \left(1024000 \sqrt{3} \sqrt{5 x+3} \left(382806250 x^5-80547756250 x^4-333372935000 x^3+1857062729800 x^2+1248845958560 x-1523336744224\right)+1024000 \left(26771628125 x^5+1102102787500 x^4-1277247746500 x^3-10194890840200 x^2+44616484880 x+4571572732672\right)\right)+1024000 \left(7164406250 x^6+174195921875 x^5-3695625687500 x^4-5925837277500 x^3+12860921279000 x^2+4621767211760 x-4559963226880\right)}-\frac{11199264087 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{512000 \sqrt{10}}","\frac{(5 x+3)^{3/2} (3 x+2)^4}{\sqrt{1-2 x}}+\frac{33}{20} \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^3+\frac{10377 \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^2}{1600}+\frac{9 \sqrt{1-2 x} (5 x+3)^{3/2} (2253560 x+4772357)}{256000}+\frac{1018114917 \sqrt{1-2 x} \sqrt{5 x+3}}{1024000}-\frac{11199264087 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{1024000 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(15547680440838324779616 - 19746337144226971093552*x - 28219309183709607975440*x^2 + 17644160345499940694860*x^3 + 10754617210253349447850*x^4 + 4052557168067371423625*x^5 + 1796518146938721456250*x^6 + 151620032584477875000*x^7 - 180861923526273000000*x^8 - 51086604529620000000*x^9 - 1110272961600000000*x^10) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-15547680440838324779616 + 4220896987364695379920*x + 24834548295906739047600*x^2 + 2103306002177908995100*x^3 - 2578013908492023234250*x^4 - 1906883598434580249375*x^5 - 1352344721977836406250*x^6 - 479072481098566875000*x^7 - 55273565705895000000*x^8 + 4406309666100000000*x^9 + 148561128000000000*x^10) + Sqrt[3]*(-15547680440838324779616 + 6792930051884356693872*x + 50037855629614293011600*x^2 - 5293452792192061390060*x^3 - 25488741668791111941650*x^4 - 8634771141108564192125*x^5 - 4137161898907031417500*x^6 - 983083416012994437500*x^7 + 223742542796856750000*x^8 + 158973114168630000000*x^9 + 16270099543800000000*x^10 - 79378704000000000*x^11 + Sqrt[1 - 2*x]*(15547680440838324779616 + 8732510104977919019760*x - 33718221219448850572400*x^2 - 16993412566407907323100*x^3 + 4028602118746058411250*x^4 + 3254426785093362621875*x^5 + 2566554200260558062500*x^6 + 1225818532536303750000*x^7 + 258548501159190000000*x^8 + 4114815903000000000*x^9 - 2070755280000000000*x^10)))/(1024000*Sqrt[3]*Sqrt[3 + 5*x]*(1519466908960 - 2800561494720*x - 1459455705400*x^2 + 1891194668000*x^3 + 158441181250*x^4 - 19972562500*x^5) + 1024000*(-4559963226880 + 4621767211760*x + 12860921279000*x^2 - 5925837277500*x^3 - 3695625687500*x^4 + 174195921875*x^5 + 7164406250*x^6) + Sqrt[1 - 2*x]*(1024000*Sqrt[3]*Sqrt[3 + 5*x]*(-1523336744224 + 1248845958560*x + 1857062729800*x^2 - 333372935000*x^3 - 80547756250*x^4 + 382806250*x^5) + 1024000*(4571572732672 + 44616484880*x - 10194890840200*x^2 - 1277247746500*x^3 + 1102102787500*x^4 + 26771628125*x^5))) - (11199264087*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(512000*Sqrt[10])","B",1
2530,1,406,132,2.8453819,"\int \frac{(2+3 x)^3 (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-21516300000000 x^8+2099994345000000 x^7+17387455483125000 x^6+39535152405493750 x^5+32892103591088125 x^4-97746600230449500 x^3-963664335790448900 x^2-218888876921068760 x+838209998358867024\right)+\sqrt{5 x+3} \left(731386260000000 x^8+671545809000000 x^7-32223307507875000 x^6-132123393903476250 x^5-316401895701247125 x^4-622313302479115500 x^3+1139251413515583060 x^2+1052984983453366568 x-838209998358867024\right)+\sqrt{3} \left(-99581400000000 x^9-2509035750000000 x^8+10180566182250000 x^7+99971380977637500 x^6+286444480541242500 x^5+763605798867046125 x^4+247425404090379300 x^3-2300066281726762500 x^2+\sqrt{1-2 x} \left(-254469600000000 x^8-9866755800000000 x^7-41556476115000000 x^6-62687038862250000 x^5-36339868898623125 x^4+609406830881590500 x^3+1430196415021588500 x^2-478822155247778760 x-838209998358867024\right)-355273951284519048 x+838209998358867024\right)}{51200 \sqrt{3} \sqrt{5 x+3} \left(-117810000 x^4-3929805000 x^3+3770256600 x^2+11623605840 x-6255778320\right)+\sqrt{1-2 x} \left(51200 \left(-846511875 x^4+2876857500 x^3+32771841300 x^2-464036760 x-18959828096\right)+51200 \sqrt{3} \sqrt{5 x+3} \left(23051250 x^4+467460000 x^3-4929642000 x^2-5009509440 x+6309526032\right)\right)+51200 \left(-49806250 x^5+5100998125 x^4+16263387500 x^3-45507313900 x^2-19543871720 x+18798584960\right)}-\frac{145708761 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{25600 \sqrt{10}}","\frac{(5 x+3)^{3/2} (3 x+2)^3}{\sqrt{1-2 x}}+\frac{27}{16} \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^2+\frac{9 \sqrt{1-2 x} (5 x+3)^{3/2} (29320 x+62091)}{12800}+\frac{13246251 \sqrt{1-2 x} \sqrt{5 x+3}}{51200}-\frac{145708761 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{51200 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(838209998358867024 - 218888876921068760*x - 963664335790448900*x^2 - 97746600230449500*x^3 + 32892103591088125*x^4 + 39535152405493750*x^5 + 17387455483125000*x^6 + 2099994345000000*x^7 - 21516300000000*x^8) + Sqrt[3 + 5*x]*(-838209998358867024 + 1052984983453366568*x + 1139251413515583060*x^2 - 622313302479115500*x^3 - 316401895701247125*x^4 - 132123393903476250*x^5 - 32223307507875000*x^6 + 671545809000000*x^7 + 731386260000000*x^8) + Sqrt[3]*(838209998358867024 - 355273951284519048*x - 2300066281726762500*x^2 + 247425404090379300*x^3 + 763605798867046125*x^4 + 286444480541242500*x^5 + 99971380977637500*x^6 + 10180566182250000*x^7 - 2509035750000000*x^8 - 99581400000000*x^9 + Sqrt[1 - 2*x]*(-838209998358867024 - 478822155247778760*x + 1430196415021588500*x^2 + 609406830881590500*x^3 - 36339868898623125*x^4 - 62687038862250000*x^5 - 41556476115000000*x^6 - 9866755800000000*x^7 - 254469600000000*x^8)))/(51200*Sqrt[3]*Sqrt[3 + 5*x]*(-6255778320 + 11623605840*x + 3770256600*x^2 - 3929805000*x^3 - 117810000*x^4) + 51200*(18798584960 - 19543871720*x - 45507313900*x^2 + 16263387500*x^3 + 5100998125*x^4 - 49806250*x^5) + Sqrt[1 - 2*x]*(51200*(-18959828096 - 464036760*x + 32771841300*x^2 + 2876857500*x^3 - 846511875*x^4) + 51200*Sqrt[3]*Sqrt[3 + 5*x]*(6309526032 - 5009509440*x - 4929642000*x^2 + 467460000*x^3 + 23051250*x^4))) - (145708761*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(25600*Sqrt[10])","B",1
2531,1,346,116,2.4356438,"\int \frac{(2+3 x)^2 (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]","\frac{\sqrt{5 x+3} \left(-16585800000 x^6-499989105000 x^5-1843440656750 x^4-4379088774775 x^3+9822557782840 x^2+13602654387124 x-11099736704232\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(5289000000 x^6+101460525000 x^5+38503313750 x^4-928877872875 x^3-7814842173200 x^2-2693259606220 x+11099736704232\right)+\sqrt{3} \left(-4866000000 x^7+208168950000 x^6+1439260112500 x^5+4357401331500 x^4+2795396238375 x^3-24611637594760 x^2+\sqrt{1-2 x} \left(-54054000000 x^6-177327150000 x^5+276403627500 x^4+4306599017875 x^3+13565880605200 x^2-6503400043140 x-11099736704232\right)-4405994737764 x+11099736704232\right)}{640 \sqrt{3} \sqrt{5 x+3} \left(-4504500 x^3+7857850 x^2+48208160 x-25505480\right)+\sqrt{1-2 x} \left(640 \sqrt{3} \sqrt{5 x+3} \left(202750 x^3-9591150 x^2-18970200 x+26251976\right)+640 \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right)\right)+640 \left(2203750 x^4+32523625 x^3-153656950 x^2-85860780 x+77141440\right)}-\frac{463881 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{320 \sqrt{10}}","\frac{3}{20} \sqrt{1-2 x} (5 x+3)^{5/2}+\frac{49 (5 x+3)^{5/2}}{22 \sqrt{1-2 x}}+\frac{14057 \sqrt{1-2 x} (5 x+3)^{3/2}}{1760}+\frac{42171}{640} \sqrt{1-2 x} \sqrt{5 x+3}-\frac{463881 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{640 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(-11099736704232 + 13602654387124*x + 9822557782840*x^2 - 4379088774775*x^3 - 1843440656750*x^4 - 499989105000*x^5 - 16585800000*x^6) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(11099736704232 - 2693259606220*x - 7814842173200*x^2 - 928877872875*x^3 + 38503313750*x^4 + 101460525000*x^5 + 5289000000*x^6) + Sqrt[3]*(11099736704232 - 4405994737764*x - 24611637594760*x^2 + 2795396238375*x^3 + 4357401331500*x^4 + 1439260112500*x^5 + 208168950000*x^6 - 4866000000*x^7 + Sqrt[1 - 2*x]*(-11099736704232 - 6503400043140*x + 13565880605200*x^2 + 4306599017875*x^3 + 276403627500*x^4 - 177327150000*x^5 - 54054000000*x^6)))/(640*Sqrt[3]*Sqrt[3 + 5*x]*(-25505480 + 48208160*x + 7857850*x^2 - 4504500*x^3) + 640*(77141440 - 85860780*x - 153656950*x^2 + 32523625*x^3 + 2203750*x^4) + Sqrt[1 - 2*x]*(640*Sqrt[3]*Sqrt[3 + 5*x]*(26251976 - 18970200*x - 9591150*x^2 + 202750*x^3) + 640*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3))) - (463881*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(320*Sqrt[10])","B",1
2532,1,286,94,1.9259679,"\int \frac{(2+3 x) (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-1425000 x^4+20191250 x^3+172901475 x^2+120634670 x-573985764\right)+\sqrt{5 x+3} \left(19635000 x^4+76150250 x^3-232900855 x^2-659053010 x+573985764\right)+\sqrt{3} \left(-4170000 x^5-55553500 x^4-102847100 x^3+905040955 x^2+\sqrt{1-2 x} \left(-3300000 x^4-75515000 x^3-410653375 x^2+343393050 x+573985764\right)+195025290 x-573985764\right)}{32 \sqrt{3} \sqrt{5 x+3} \left(-11000 x^2-194700 x+100100\right)+\sqrt{1-2 x} \left(32 \left(-163625 x^2+33550 x+343904\right)+32 \sqrt{3} \sqrt{5 x+3} \left(6950 x^2+60040 x-110468\right)\right)+32 \left(-23750 x^3+445375 x^2+408850 x-312800\right)}-\frac{5709 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{16 \sqrt{10}}","\frac{7 (5 x+3)^{5/2}}{11 \sqrt{1-2 x}}+\frac{173}{88} \sqrt{1-2 x} (5 x+3)^{3/2}+\frac{519}{32} \sqrt{1-2 x} \sqrt{5 x+3}-\frac{5709 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{32 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-573985764 + 120634670*x + 172901475*x^2 + 20191250*x^3 - 1425000*x^4) + Sqrt[3 + 5*x]*(573985764 - 659053010*x - 232900855*x^2 + 76150250*x^3 + 19635000*x^4) + Sqrt[3]*(-573985764 + 195025290*x + 905040955*x^2 - 102847100*x^3 - 55553500*x^4 - 4170000*x^5 + Sqrt[1 - 2*x]*(573985764 + 343393050*x - 410653375*x^2 - 75515000*x^3 - 3300000*x^4)))/(32*Sqrt[3]*Sqrt[3 + 5*x]*(100100 - 194700*x - 11000*x^2) + 32*(-312800 + 408850*x + 445375*x^2 - 23750*x^3) + Sqrt[1 - 2*x]*(32*(343904 + 33550*x - 163625*x^2) + 32*Sqrt[3]*Sqrt[3 + 5*x]*(-110468 + 60040*x + 6950*x^2))) - (5709*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(16*Sqrt[10])","B",1
2533,1,228,71,1.5080037,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/(1 - 2*x)^(3/2),x]","\frac{\sqrt{5 x+3} \left(-1650 x^2-65725 x+71874\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(3250 x^2+10915 x-71874\right)+\sqrt{3} \left(-4500 x^3+50700 x^2+\sqrt{1-2 x} \left(-16500 x^2+39105 x+71874\right)+15705 x-71874\right)}{4 \left(650 x^2+2155 x-1240\right)+4 \sqrt{3} \sqrt{5 x+3} (330-660 x)+\sqrt{1-2 x} \left(4 \sqrt{3} \sqrt{5 x+3} (90 x-474)+4 (165 x+1672)\right)}-\frac{33}{2} \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{(5 x+3)^{3/2}}{\sqrt{1-2 x}}+\frac{15}{4} \sqrt{1-2 x} \sqrt{5 x+3}-\frac{33}{4} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"(Sqrt[3 + 5*x]*(71874 - 65725*x - 1650*x^2) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-71874 + 10915*x + 3250*x^2) + Sqrt[3]*(-71874 + 15705*x + 50700*x^2 - 4500*x^3 + Sqrt[1 - 2*x]*(71874 + 39105*x - 16500*x^2)))/(4*Sqrt[3]*(330 - 660*x)*Sqrt[3 + 5*x] + 4*(-1240 + 2155*x + 650*x^2) + Sqrt[1 - 2*x]*(4*Sqrt[3]*Sqrt[3 + 5*x]*(-474 + 90*x) + 4*(1672 + 165*x))) - (33*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/2","B",1
2534,1,329,86,1.4380211,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)),x]","-\frac{1}{21} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{\left(\frac{121}{7}-\frac{121}{7} \sqrt{1-2 x}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5}-\frac{5}{3} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{11 \sqrt{5 x+3}}{7 \sqrt{1-2 x}}-\frac{5}{3} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{21 \sqrt{7}}",1,"((121/7 - (121*Sqrt[1 - 2*x])/7)*(Sqrt[3] - Sqrt[3 + 5*x]))/(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]) - (5*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/3 - RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ]/21","C",1
2535,1,451,93,1.8458694,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^2),x]","-\frac{33}{49} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{165}{98} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-246180 x^2+184316 x+239580\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-5150 x^2-355640 x-239580\right)+\sqrt{3} \left(145350 x^3+121125 x^2+\sqrt{1-2 x} \left(233475 x^2+515790 x+239580\right)-344466 x-239580\right)}{98 \left(650 x^2+2155 x-1240\right) (3 x+2)+98 \sqrt{3} (330-660 x) \sqrt{5 x+3} (3 x+2)+\sqrt{1-2 x} \left(98 \sqrt{3} (3 x+2) \sqrt{5 x+3} (90 x-474)+98 (3 x+2) (165 x+1672)\right)}","\frac{2 (5 x+3)^{3/2}}{7 \sqrt{1-2 x} (3 x+2)}+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3}}{49 (3 x+2)}+\frac{33 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{49 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(239580 + 184316*x - 246180*x^2) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-239580 - 355640*x - 5150*x^2) + Sqrt[3]*(-239580 - 344466*x + 121125*x^2 + 145350*x^3 + Sqrt[1 - 2*x]*(239580 + 515790*x + 233475*x^2)))/(98*Sqrt[3]*(330 - 660*x)*(2 + 3*x)*Sqrt[3 + 5*x] + 98*(2 + 3*x)*(-1240 + 2155*x + 650*x^2) + Sqrt[1 - 2*x]*(98*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(-474 + 90*x) + 98*(2 + 3*x)*(1672 + 165*x))) - (33*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/49 + (165*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/98","C",1
2536,1,519,122,2.2288407,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^3),x]","\frac{825 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{1372}-\frac{4125 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2744}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-48858600 x^4+340796405 x^3+1352583054 x^2+1110449432 x+255104784\right)+\sqrt{5 x+3} \left(446646750 x^4+841422725 x^3-448067950 x^2-910803080 x-255104784\right)+\sqrt{3} \left(-67451250 x^5-1265305375 x^4-669343100 x^3+1170200800 x^2+\sqrt{1-2 x} \left(75664875 x^4-1215594050 x^3-2218800364 x^2-1300749252 x-255104784\right)+1101102900 x+255104784\right)}{1372 \sqrt{3} \sqrt{5 x+3} \left(11000 x^2+194700 x-100100\right) (3 x+2)^2+\sqrt{1-2 x} \left(1372 \sqrt{3} \sqrt{5 x+3} \left(-6950 x^2-60040 x+110468\right) (3 x+2)^2+1372 \left(163625 x^2-33550 x-343904\right) (3 x+2)^2\right)+1372 \left(23750 x^3-445375 x^2-408850 x+312800\right) (3 x+2)^2}","\frac{4 (5 x+3)^{5/2}}{77 \sqrt{1-2 x} (3 x+2)^2}-\frac{25 \sqrt{1-2 x} (5 x+3)^{3/2}}{1078 (3 x+2)^2}-\frac{75 \sqrt{1-2 x} \sqrt{5 x+3}}{1372 (3 x+2)}-\frac{825 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1372 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(255104784 + 1110449432*x + 1352583054*x^2 + 340796405*x^3 - 48858600*x^4) + Sqrt[3 + 5*x]*(-255104784 - 910803080*x - 448067950*x^2 + 841422725*x^3 + 446646750*x^4) + Sqrt[3]*(255104784 + 1101102900*x + 1170200800*x^2 - 669343100*x^3 - 1265305375*x^4 - 67451250*x^5 + Sqrt[1 - 2*x]*(-255104784 - 1300749252*x - 2218800364*x^2 - 1215594050*x^3 + 75664875*x^4)))/(1372*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(-100100 + 194700*x + 11000*x^2) + 1372*(2 + 3*x)^2*(312800 - 408850*x - 445375*x^2 + 23750*x^3) + Sqrt[1 - 2*x]*(1372*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(110468 - 60040*x - 6950*x^2) + 1372*(2 + 3*x)^2*(-343904 - 33550*x + 163625*x^2))) + (825*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/1372 - (4125*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2744","C",1
2537,1,579,151,2.5609019,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^4),x]","\frac{2805 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2744}-\frac{14025 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{5488}+\frac{\sqrt{5 x+3} \left(-17666360250 x^6+240084323325 x^5+895871357920 x^4+587207096960 x^3-360296408120 x^2-417747921536 x-89796883968\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-1561230750 x^6-102194461425 x^5-157871279500 x^4+405233949432 x^3+864468238264 x^2+502514915456 x+89796883968\right)+\sqrt{3} \left(6808327500 x^7-39881811750 x^6-761012927300 x^5-1430551600470 x^4-405993696060 x^3+682017285800 x^2+\sqrt{1-2 x} \left(34757761500 x^6+240582099450 x^5+12358382190 x^4-979829016452 x^3-1255424527544 x^2-575941902096 x-89796883968\right)+491174908176 x+89796883968\right)}{2744 \sqrt{3} \sqrt{5 x+3} \left(-4504500 x^3+7857850 x^2+48208160 x-25505480\right) (3 x+2)^3+\sqrt{1-2 x} \left(2744 \sqrt{3} \sqrt{5 x+3} \left(202750 x^3-9591150 x^2-18970200 x+26251976\right) (3 x+2)^3+2744 \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (3 x+2)^3\right)+2744 \left(2203750 x^4+32523625 x^3-153656950 x^2-85860780 x+77141440\right) (3 x+2)^3}","-\frac{415 \sqrt{1-2 x} \sqrt{5 x+3}}{8232 (3 x+2)}-\frac{145 \sqrt{1-2 x} \sqrt{5 x+3}}{588 (3 x+2)^2}-\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{3 (3 x+2)^3}+\frac{11 \sqrt{5 x+3}}{7 \sqrt{1-2 x} (3 x+2)^3}-\frac{2805 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2744 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-89796883968 - 417747921536*x - 360296408120*x^2 + 587207096960*x^3 + 895871357920*x^4 + 240084323325*x^5 - 17666360250*x^6) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(89796883968 + 502514915456*x + 864468238264*x^2 + 405233949432*x^3 - 157871279500*x^4 - 102194461425*x^5 - 1561230750*x^6) + Sqrt[3]*(89796883968 + 491174908176*x + 682017285800*x^2 - 405993696060*x^3 - 1430551600470*x^4 - 761012927300*x^5 - 39881811750*x^6 + 6808327500*x^7 + Sqrt[1 - 2*x]*(-89796883968 - 575941902096*x - 1255424527544*x^2 - 979829016452*x^3 + 12358382190*x^4 + 240582099450*x^5 + 34757761500*x^6)))/(2744*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-25505480 + 48208160*x + 7857850*x^2 - 4504500*x^3) + 2744*(2 + 3*x)^3*(77141440 - 85860780*x - 153656950*x^2 + 32523625*x^3 + 2203750*x^4) + Sqrt[1 - 2*x]*(2744*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(26251976 - 18970200*x - 9591150*x^2 + 202750*x^3) + 2744*(2 + 3*x)^3*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3))) + (2805*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2744 - (14025*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/5488","C",1
2538,1,639,180,3.0709356,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^5),x]","\frac{279015 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{153664}-\frac{1395075 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{307328}+\frac{\sqrt{5 x+3} \left(-484494244121250 x^8+12148928528405625 x^7+50929710684345900 x^6+11390141792565360 x^5-95937251257970760 x^4-85224464563257360 x^3+1396682873026848 x^2+22963654734010496 x+6155262106912512\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-34277126670000 x^8-3608906061414375 x^7-2665166760760500 x^6+47358615470812240 x^5+89272819031188168 x^4+32381962149763248 x^3-33879456682982432 x^2-29141736614502272 x-6155262106912512\right)+\sqrt{3} \left(146849700768750 x^9-1759399326286875 x^8-43027159895583750 x^7-73781579249075700 x^6+43473721174309440 x^5+162497827000352160 x^4+90267468952025520 x^3-18377580114246528 x^2+\sqrt{1-2 x} \left(969317793489375 x^8+9146328329902500 x^7-18085386960719100 x^6-107372532515363280 x^5-121319829926518608 x^4-12512759662350288 x^3+56013178116278592 x^2+34275544328596032 x+6155262106912512\right)-28097462448104256 x-6155262106912512\right)}{153664 \sqrt{3} \sqrt{5 x+3} \left(117810000 x^4+3929805000 x^3-3770256600 x^2-11623605840 x+6255778320\right) (3 x+2)^4+\sqrt{1-2 x} \left(153664 \sqrt{3} \sqrt{5 x+3} \left(-23051250 x^4-467460000 x^3+4929642000 x^2+5009509440 x-6309526032\right) (3 x+2)^4+153664 \left(846511875 x^4-2876857500 x^3-32771841300 x^2+464036760 x+18959828096\right) (3 x+2)^4\right)+153664 \left(49806250 x^5-5100998125 x^4-16263387500 x^3+45507313900 x^2+19543871720 x-18798584960\right) (3 x+2)^4}","\frac{16985 \sqrt{1-2 x} \sqrt{5 x+3}}{153664 (3 x+2)}-\frac{745 \sqrt{1-2 x} \sqrt{5 x+3}}{10976 (3 x+2)^2}-\frac{89 \sqrt{1-2 x} \sqrt{5 x+3}}{392 (3 x+2)^3}-\frac{131 \sqrt{1-2 x} \sqrt{5 x+3}}{196 (3 x+2)^4}+\frac{11 \sqrt{5 x+3}}{7 \sqrt{1-2 x} (3 x+2)^4}-\frac{279015 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{153664 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(6155262106912512 + 22963654734010496*x + 1396682873026848*x^2 - 85224464563257360*x^3 - 95937251257970760*x^4 + 11390141792565360*x^5 + 50929710684345900*x^6 + 12148928528405625*x^7 - 484494244121250*x^8) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-6155262106912512 - 29141736614502272*x - 33879456682982432*x^2 + 32381962149763248*x^3 + 89272819031188168*x^4 + 47358615470812240*x^5 - 2665166760760500*x^6 - 3608906061414375*x^7 - 34277126670000*x^8) + Sqrt[3]*(-6155262106912512 - 28097462448104256*x - 18377580114246528*x^2 + 90267468952025520*x^3 + 162497827000352160*x^4 + 43473721174309440*x^5 - 73781579249075700*x^6 - 43027159895583750*x^7 - 1759399326286875*x^8 + 146849700768750*x^9 + Sqrt[1 - 2*x]*(6155262106912512 + 34275544328596032*x + 56013178116278592*x^2 - 12512759662350288*x^3 - 121319829926518608*x^4 - 107372532515363280*x^5 - 18085386960719100*x^6 + 9146328329902500*x^7 + 969317793489375*x^8)))/(153664*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(6255778320 - 11623605840*x - 3770256600*x^2 + 3929805000*x^3 + 117810000*x^4) + 153664*(2 + 3*x)^4*(-18798584960 + 19543871720*x + 45507313900*x^2 - 16263387500*x^3 - 5100998125*x^4 + 49806250*x^5) + Sqrt[1 - 2*x]*(153664*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-6309526032 + 5009509440*x + 4929642000*x^2 - 467460000*x^3 - 23051250*x^4) + 153664*(2 + 3*x)^4*(18959828096 + 464036760*x - 32771841300*x^2 - 2876857500*x^3 + 846511875*x^4))) + (279015*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/153664 - (1395075*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/307328","C",1
2539,1,526,183,4.9749231,"\int \frac{(2+3 x)^4 (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-10923703200000000000 x^{12}+4803749024040000000000 x^{11}+51973706658460500000000 x^{10}-28299847451609575000000 x^9-1167972683490338551875000 x^8-4112740095288327282906250 x^7-7143078281165739601809375 x^6-8010714884995750590671250 x^5-15199744590220337471021000 x^4+5190303567908202320333600 x^3+73283927607407824699189200 x^2+9974603597193014871242400 x-35942118257080799922983616\right)+\sqrt{5 x+3} \left(935164470240000000000 x^{12}-7947073535544000000000 x^{11}-256171456558403100000000 x^{10}-1098410414440408355000000 x^9-1444895008742733065375000 x^8+1386325669702864552268750 x^7+6989292669193985836516875 x^6+9940953109477258238570750 x^5+41103981480924299767594600 x^4+55692956504563828300623520 x^3-81141754219843588055825040 x^2-45901601077607765310064992 x+35942118257080799922983616\right)+\sqrt{3} \left(-101686708800000000000 x^{13}-3208884364080000000000 x^{12}+91914518121381000000000 x^{11}+818966795366288050000000 x^{10}+2168051619538628441250000 x^9+1253433578871666874687500 x^8-5231010465262652805662500 x^7-12796274405798017882014375 x^6-26432762588444027114784750 x^5-92072783284335019283240200 x^4-14287698914719405830798720 x^3+131853442752150492063512400 x^2+15951249109814273186745312 x+\sqrt{1-2 x} \left(-518955465600000000000 x^{12}-27894024306720000000000 x^{11}-92898880019946000000000 x^{10}+472409132045093100000000 x^9+3314780395481987217500000 x^8+8449734987451492431125000 x^7+12075116245588027850521875 x^6+15854444635896206525721250 x^5+23000312778612389624833000 x^4-52504596215008305001233600 x^3-94057864819142944487024400 x^2+19975748370600477252077280 x+35942118257080799922983616\right)-35942118257080799922983616\right)}{1638400 \sqrt{3} \sqrt{5 x+3} \left(-750803625000 x^6-35513254562500 x^5+109502972507500 x^4+708907607408000 x^3-497360177600000 x^2-676171499523520 x+368089927965760\right)+\sqrt{1-2 x} \left(1638400 \left(-3382394640625 x^6+46839566881250 x^5+721064958542500 x^4-436816644264000 x^3-2966115478898000 x^2+4019894758880 x+1105183793314304\right)+1638400 \sqrt{3} \sqrt{5 x+3} \left(73558093750 x^6+1883570925000 x^5-78913493662500 x^4-156226252528000 x^3+608403813276000 x^2+305295290167680 x-368368556104768\right)\right)+1638400 \left(-79019843750 x^7+35211607984375 x^6+171264310843750 x^5-1776876552657500 x^4-1879341347316000 x^3+3558908295114800 x^2+1109383428656160 x-1104347908897280\right)}-\frac{107121749031 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{819200 \sqrt{10}}","\frac{(5 x+3)^{5/2} (3 x+2)^4}{\sqrt{1-2 x}}+\frac{13}{8} \sqrt{1-2 x} (5 x+3)^{5/2} (3 x+2)^3+\frac{999}{160} \sqrt{1-2 x} (5 x+3)^{5/2} (3 x+2)^2+\frac{295101237 \sqrt{1-2 x} (5 x+3)^{3/2}}{409600}+\frac{\sqrt{1-2 x} (5 x+3)^{5/2} (3765060 x+7611023)}{51200}+\frac{9738340821 \sqrt{1-2 x} \sqrt{5 x+3}}{1638400}-\frac{107121749031 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{1638400 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-35942118257080799922983616 + 9974603597193014871242400*x + 73283927607407824699189200*x^2 + 5190303567908202320333600*x^3 - 15199744590220337471021000*x^4 - 8010714884995750590671250*x^5 - 7143078281165739601809375*x^6 - 4112740095288327282906250*x^7 - 1167972683490338551875000*x^8 - 28299847451609575000000*x^9 + 51973706658460500000000*x^10 + 4803749024040000000000*x^11 - 10923703200000000000*x^12) + Sqrt[3 + 5*x]*(35942118257080799922983616 - 45901601077607765310064992*x - 81141754219843588055825040*x^2 + 55692956504563828300623520*x^3 + 41103981480924299767594600*x^4 + 9940953109477258238570750*x^5 + 6989292669193985836516875*x^6 + 1386325669702864552268750*x^7 - 1444895008742733065375000*x^8 - 1098410414440408355000000*x^9 - 256171456558403100000000*x^10 - 7947073535544000000000*x^11 + 935164470240000000000*x^12) + Sqrt[3]*(-35942118257080799922983616 + 15951249109814273186745312*x + 131853442752150492063512400*x^2 - 14287698914719405830798720*x^3 - 92072783284335019283240200*x^4 - 26432762588444027114784750*x^5 - 12796274405798017882014375*x^6 - 5231010465262652805662500*x^7 + 1253433578871666874687500*x^8 + 2168051619538628441250000*x^9 + 818966795366288050000000*x^10 + 91914518121381000000000*x^11 - 3208884364080000000000*x^12 - 101686708800000000000*x^13 + Sqrt[1 - 2*x]*(35942118257080799922983616 + 19975748370600477252077280*x - 94057864819142944487024400*x^2 - 52504596215008305001233600*x^3 + 23000312778612389624833000*x^4 + 15854444635896206525721250*x^5 + 12075116245588027850521875*x^6 + 8449734987451492431125000*x^7 + 3314780395481987217500000*x^8 + 472409132045093100000000*x^9 - 92898880019946000000000*x^10 - 27894024306720000000000*x^11 - 518955465600000000000*x^12)))/(1638400*Sqrt[3]*Sqrt[3 + 5*x]*(368089927965760 - 676171499523520*x - 497360177600000*x^2 + 708907607408000*x^3 + 109502972507500*x^4 - 35513254562500*x^5 - 750803625000*x^6) + 1638400*(-1104347908897280 + 1109383428656160*x + 3558908295114800*x^2 - 1879341347316000*x^3 - 1776876552657500*x^4 + 171264310843750*x^5 + 35211607984375*x^6 - 79019843750*x^7) + Sqrt[1 - 2*x]*(1638400*(1105183793314304 + 4019894758880*x - 2966115478898000*x^2 - 436816644264000*x^3 + 721064958542500*x^4 + 46839566881250*x^5 - 3382394640625*x^6) + 1638400*Sqrt[3]*Sqrt[3 + 5*x]*(-368368556104768 + 305295290167680*x + 608403813276000*x^2 - 156226252528000*x^3 - 78913493662500*x^4 + 1883570925000*x^5 + 73558093750*x^6))) - (107121749031*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(819200*Sqrt[10])","B",1
2540,1,466,154,3.2935436,"\int \frac{(2+3 x)^3 (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]","\frac{\sqrt{5 x+3} \left(-370090987200000000 x^{10}-16998027260940000000 x^9-58884555478551000000 x^8+54836788288319125000 x^7+593127429864986293750 x^6+1309829595944220935375 x^5+3408181844232253114950 x^4+5567492216463835057620 x^3-8924702845351439028080 x^2-6241780931300359574096 x+4912097720808980500128\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(49520376000000000 x^{10}+1464643190700000000 x^9-18544735681665000000 x^8-158093860884078125000 x^7-438389460690153343750 x^6-603948366101270295625 x^5-799053758827306579750 x^4+684723174887242477700 x^3+7858393860598085045200 x^2+1336701704868044784560 x-4912097720808980500128\right)+\sqrt{3} \left(-26459568000000000 x^{11}+5425571478600000000 x^{10}+52537924053210000000 x^9+70405781938617250000 x^8-331916339389312062500 x^7-1353164601783169322500 x^6-2766935681214549394875 x^5-8059678756287944827550 x^4-1658927242947376026420 x^3+15820652377992378603760 x^2+\sqrt{1-2 x} \left(-690251760000000000 x^{10}+1429126281000000000 x^9+86038095092730000000 x^8+401529074806186250000 x^7+825300989124923437500 x^6+1021273042542220703125 x^5+1243821122702406338750 x^4-5398142681317400373700 x^3-10667721976233189379600 x^2+2755768457451678548880 x+4912097720808980500128\right)+2149310768980636240656 x-4912097720808980500128\right)}{204800 \sqrt{3} \sqrt{5 x+3} \left(-19972562500 x^5+158441181250 x^4+1891194668000 x^3-1459455705400 x^2-2800561494720 x+1519466908960\right)+\sqrt{1-2 x} \left(204800 \sqrt{3} \sqrt{5 x+3} \left(382806250 x^5-80547756250 x^4-333372935000 x^3+1857062729800 x^2+1248845958560 x-1523336744224\right)+204800 \left(26771628125 x^5+1102102787500 x^4-1277247746500 x^3-10194890840200 x^2+44616484880 x+4571572732672\right)\right)+204800 \left(7164406250 x^6+174195921875 x^5-3695625687500 x^4-5925837277500 x^3+12860921279000 x^2+4621767211760 x-4559963226880\right)}-\frac{3538809681 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{102400 \sqrt{10}}","\frac{(5 x+3)^{5/2} (3 x+2)^3}{\sqrt{1-2 x}}+\frac{33}{20} \sqrt{1-2 x} (5 x+3)^{5/2} (3 x+2)^2+\frac{9748787 \sqrt{1-2 x} (5 x+3)^{3/2}}{51200}+\frac{9 \sqrt{1-2 x} (5 x+3)^{5/2} (13820 x+27937)}{6400}+\frac{321709971 \sqrt{1-2 x} \sqrt{5 x+3}}{204800}-\frac{3538809681 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{204800 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(4912097720808980500128 - 6241780931300359574096*x - 8924702845351439028080*x^2 + 5567492216463835057620*x^3 + 3408181844232253114950*x^4 + 1309829595944220935375*x^5 + 593127429864986293750*x^6 + 54836788288319125000*x^7 - 58884555478551000000*x^8 - 16998027260940000000*x^9 - 370090987200000000*x^10) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-4912097720808980500128 + 1336701704868044784560*x + 7858393860598085045200*x^2 + 684723174887242477700*x^3 - 799053758827306579750*x^4 - 603948366101270295625*x^5 - 438389460690153343750*x^6 - 158093860884078125000*x^7 - 18544735681665000000*x^8 + 1464643190700000000*x^9 + 49520376000000000*x^10) + Sqrt[3]*(-4912097720808980500128 + 2149310768980636240656*x + 15820652377992378603760*x^2 - 1658927242947376026420*x^3 - 8059678756287944827550*x^4 - 2766935681214549394875*x^5 - 1353164601783169322500*x^6 - 331916339389312062500*x^7 + 70405781938617250000*x^8 + 52537924053210000000*x^9 + 5425571478600000000*x^10 - 26459568000000000*x^11 + Sqrt[1 - 2*x]*(4912097720808980500128 + 2755768457451678548880*x - 10667721976233189379600*x^2 - 5398142681317400373700*x^3 + 1243821122702406338750*x^4 + 1021273042542220703125*x^5 + 825300989124923437500*x^6 + 401529074806186250000*x^7 + 86038095092730000000*x^8 + 1429126281000000000*x^9 - 690251760000000000*x^10)))/(204800*Sqrt[3]*Sqrt[3 + 5*x]*(1519466908960 - 2800561494720*x - 1459455705400*x^2 + 1891194668000*x^3 + 158441181250*x^4 - 19972562500*x^5) + 204800*(-4559963226880 + 4621767211760*x + 12860921279000*x^2 - 5925837277500*x^3 - 3695625687500*x^4 + 174195921875*x^5 + 7164406250*x^6) + Sqrt[1 - 2*x]*(204800*Sqrt[3]*Sqrt[3 + 5*x]*(-1523336744224 + 1248845958560*x + 1857062729800*x^2 - 333372935000*x^3 - 80547756250*x^4 + 382806250*x^5) + 204800*(4571572732672 + 44616484880*x - 10194890840200*x^2 - 1277247746500*x^3 + 1102102787500*x^4 + 26771628125*x^5))) - (3538809681*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(102400*Sqrt[10])","B",1
2541,1,406,138,2.980111,"\int \frac{(2+3 x)^2 (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-1434420000000 x^8+140127127000000 x^7+1146669348875000 x^6+2537750191946250 x^5+1965896987311875 x^4-6427772428468900 x^3-61152497200286460 x^2-13909189798767400 x+53015454522672048\right)+\sqrt{5 x+3} \left(48759084000000 x^8+40435579800000 x^7-2150502492765000 x^6-8623739459403750 x^5-20206382260576875 x^4-39325228524588820 x^3+72198657119690156 x^2+66665003126046424 x-53015454522672048\right)+\sqrt{3} \left(-6638760000000 x^9-166678938000000 x^8+693341644950000 x^7+6599698618522500 x^6+18537107884357500 x^5+48491779509702675 x^4+15519183377227740 x^3-145673481641889276 x^2+\sqrt{1-2 x} \left(-16964640000000 x^8-656275752000000 x^7-2712552697800000 x^6-3952983898710000 x^5-2030558023456875 x^4+38934666671996700 x^3+90714464152878060 x^2-30220035433667640 x-53015454522672048\right)-22535777893611384 x+53015454522672048\right)}{2048 \sqrt{3} \sqrt{5 x+3} \left(-117810000 x^4-3929805000 x^3+3770256600 x^2+11623605840 x-6255778320\right)+\sqrt{1-2 x} \left(2048 \left(-846511875 x^4+2876857500 x^3+32771841300 x^2-464036760 x-18959828096\right)+2048 \sqrt{3} \sqrt{5 x+3} \left(23051250 x^4+467460000 x^3-4929642000 x^2-5009509440 x+6309526032\right)\right)+2048 \left(-49806250 x^5+5100998125 x^4+16263387500 x^3-45507313900 x^2-19543871720 x+18798584960\right)}-\frac{9219111 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{1024 \sqrt{10}}","\frac{9}{80} \sqrt{1-2 x} (5 x+3)^{7/2}+\frac{49 (5 x+3)^{7/2}}{22 \sqrt{1-2 x}}+\frac{25397 \sqrt{1-2 x} (5 x+3)^{5/2}}{3520}+\frac{25397}{512} \sqrt{1-2 x} (5 x+3)^{3/2}+\frac{838101 \sqrt{1-2 x} \sqrt{5 x+3}}{2048}-\frac{9219111 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{2048 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(53015454522672048 - 13909189798767400*x - 61152497200286460*x^2 - 6427772428468900*x^3 + 1965896987311875*x^4 + 2537750191946250*x^5 + 1146669348875000*x^6 + 140127127000000*x^7 - 1434420000000*x^8) + Sqrt[3 + 5*x]*(-53015454522672048 + 66665003126046424*x + 72198657119690156*x^2 - 39325228524588820*x^3 - 20206382260576875*x^4 - 8623739459403750*x^5 - 2150502492765000*x^6 + 40435579800000*x^7 + 48759084000000*x^8) + Sqrt[3]*(53015454522672048 - 22535777893611384*x - 145673481641889276*x^2 + 15519183377227740*x^3 + 48491779509702675*x^4 + 18537107884357500*x^5 + 6599698618522500*x^6 + 693341644950000*x^7 - 166678938000000*x^8 - 6638760000000*x^9 + Sqrt[1 - 2*x]*(-53015454522672048 - 30220035433667640*x + 90714464152878060*x^2 + 38934666671996700*x^3 - 2030558023456875*x^4 - 3952983898710000*x^5 - 2712552697800000*x^6 - 656275752000000*x^7 - 16964640000000*x^8)))/(2048*Sqrt[3]*Sqrt[3 + 5*x]*(-6255778320 + 11623605840*x + 3770256600*x^2 - 3929805000*x^3 - 117810000*x^4) + 2048*(18798584960 - 19543871720*x - 45507313900*x^2 + 16263387500*x^3 + 5100998125*x^4 - 49806250*x^5) + Sqrt[1 - 2*x]*(2048*(-18959828096 - 464036760*x + 32771841300*x^2 + 2876857500*x^3 - 846511875*x^4) + 2048*Sqrt[3]*Sqrt[3 + 5*x]*(6309526032 - 5009509440*x - 4929642000*x^2 + 467460000*x^3 + 23051250*x^4))) - (9219111*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(1024*Sqrt[10])","B",1
2542,1,348,118,2.420524,"\int \frac{(2+3 x) (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]","\frac{\sqrt{5 x+3} \left(-5528600000 x^6-166110175000 x^5-597726379250 x^4-1389248960825 x^3+3123006064200 x^2+4315703116428 x-3514706161560\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(1763000000 x^6+33643875000 x^5+9424506250 x^4-309076325125 x^3-2493745916400 x^2-861029789940 x+3514706161560\right)+\sqrt{3} \left(-1622000000 x^7+69551850000 x^6+472840087500 x^5+1397931108500 x^4+880537420425 x^3-7813293083640 x^2+\sqrt{1-2 x} \left(-18018000000 x^6-57307250000 x^5+98330732500 x^4+1391558524125 x^3+4321892559600 x^2-2051137948860 x-3514706161560\right)-1403535377628 x+3514706161560\right)}{128 \sqrt{3} \sqrt{5 x+3} \left(-4504500 x^3+7857850 x^2+48208160 x-25505480\right)+\sqrt{1-2 x} \left(128 \sqrt{3} \sqrt{5 x+3} \left(202750 x^3-9591150 x^2-18970200 x+26251976\right)+128 \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right)\right)+128 \left(2203750 x^4+32523625 x^3-153656950 x^2-85860780 x+77141440\right)}-\frac{29403}{64} \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{7 (5 x+3)^{7/2}}{11 \sqrt{1-2 x}}+\frac{81}{44} \sqrt{1-2 x} (5 x+3)^{5/2}+\frac{405}{32} \sqrt{1-2 x} (5 x+3)^{3/2}+\frac{13365}{128} \sqrt{1-2 x} \sqrt{5 x+3}-\frac{29403}{128} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"(Sqrt[3 + 5*x]*(-3514706161560 + 4315703116428*x + 3123006064200*x^2 - 1389248960825*x^3 - 597726379250*x^4 - 166110175000*x^5 - 5528600000*x^6) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(3514706161560 - 861029789940*x - 2493745916400*x^2 - 309076325125*x^3 + 9424506250*x^4 + 33643875000*x^5 + 1763000000*x^6) + Sqrt[3]*(3514706161560 - 1403535377628*x - 7813293083640*x^2 + 880537420425*x^3 + 1397931108500*x^4 + 472840087500*x^5 + 69551850000*x^6 - 1622000000*x^7 + Sqrt[1 - 2*x]*(-3514706161560 - 2051137948860*x + 4321892559600*x^2 + 1391558524125*x^3 + 98330732500*x^4 - 57307250000*x^5 - 18018000000*x^6)))/(128*Sqrt[3]*Sqrt[3 + 5*x]*(-25505480 + 48208160*x + 7857850*x^2 - 4504500*x^3) + 128*(77141440 - 85860780*x - 153656950*x^2 + 32523625*x^3 + 2203750*x^4) + Sqrt[1 - 2*x]*(128*Sqrt[3]*Sqrt[3 + 5*x]*(26251976 - 18970200*x - 9591150*x^2 + 202750*x^3) + 128*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3))) - (29403*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/64","B",1
2543,1,288,93,1.805755,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/(1 - 2*x)^(3/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-2375000 x^4+33968750 x^3+280032925 x^2+195353810 x-910260252\right)+\sqrt{5 x+3} \left(32725000 x^4+122553750 x^3-373116425 x^2-1049611310 x+910260252\right)+\sqrt{3} \left(-6950000 x^5-91662500 x^4-163642500 x^3+1443293125 x^2+\sqrt{1-2 x} \left(-5500000 x^4-125125000 x^3-660834625 x^2+540690150 x+910260252\right)+313567350 x-910260252\right)}{32 \sqrt{3} \sqrt{5 x+3} \left(-11000 x^2-194700 x+100100\right)+\sqrt{1-2 x} \left(32 \left(-163625 x^2+33550 x+343904\right)+32 \sqrt{3} \sqrt{5 x+3} \left(6950 x^2+60040 x-110468\right)\right)+32 \left(-23750 x^3+445375 x^2+408850 x-312800\right)}-\frac{1815}{16} \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{(5 x+3)^{5/2}}{\sqrt{1-2 x}}+\frac{25}{8} \sqrt{1-2 x} (5 x+3)^{3/2}+\frac{825}{32} \sqrt{1-2 x} \sqrt{5 x+3}-\frac{1815}{32} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-910260252 + 195353810*x + 280032925*x^2 + 33968750*x^3 - 2375000*x^4) + Sqrt[3 + 5*x]*(910260252 - 1049611310*x - 373116425*x^2 + 122553750*x^3 + 32725000*x^4) + Sqrt[3]*(-910260252 + 313567350*x + 1443293125*x^2 - 163642500*x^3 - 91662500*x^4 - 6950000*x^5 + Sqrt[1 - 2*x]*(910260252 + 540690150*x - 660834625*x^2 - 125125000*x^3 - 5500000*x^4)))/(32*Sqrt[3]*Sqrt[3 + 5*x]*(100100 - 194700*x - 11000*x^2) + 32*(-312800 + 408850*x + 445375*x^2 - 23750*x^3) + Sqrt[1 - 2*x]*(32*(343904 + 33550*x - 163625*x^2) + 32*Sqrt[3]*Sqrt[3 + 5*x]*(-110468 + 60040*x + 6950*x^2))) - (1815*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/16","B",1
2544,1,420,108,1.8550162,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)),x]","\frac{1}{63} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-57750 x^2-2220515 x+2398462\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(113750 x^2+384445 x-2398462\right)+\sqrt{3} \left(-157500 x^3+1726100 x^2+\sqrt{1-2 x} \left(-577500 x^2+1288815 x+2398462\right)+547255 x-2398462\right)}{84 \left(650 x^2+2155 x-1240\right)+84 \sqrt{3} \sqrt{5 x+3} (330-660 x)+\sqrt{1-2 x} \left(84 \sqrt{3} \sqrt{5 x+3} (90 x-474)+84 (165 x+1672)\right)}-\frac{475}{18} \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{11 (5 x+3)^{3/2}}{7 \sqrt{1-2 x}}+\frac{505}{84} \sqrt{1-2 x} \sqrt{5 x+3}-\frac{475}{36} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)+\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{63 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(2398462 - 2220515*x - 57750*x^2) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-2398462 + 384445*x + 113750*x^2) + Sqrt[3]*(-2398462 + 547255*x + 1726100*x^2 - 157500*x^3 + Sqrt[1 - 2*x]*(2398462 + 1288815*x - 577500*x^2)))/(84*Sqrt[3]*(330 - 660*x)*Sqrt[3 + 5*x] + 84*(-1240 + 2155*x + 650*x^2) + Sqrt[1 - 2*x]*(84*Sqrt[3]*Sqrt[3 + 5*x]*(-474 + 90*x) + 84*(1672 + 165*x))) - (475*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/18 + RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ]/63","C",1
2545,1,509,122,2.0755701,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^2),x]","\frac{169}{441} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{845}{882} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-3946470 x^2+3169804 x+3859900\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-121900 x^2-5878280 x-3859900\right)+\sqrt{3} \left(2395650 x^3+1699925 x^2+\sqrt{1-2 x} \left(3959175 x^2+8428530 x+3859900\right)-5720054 x-3859900\right)}{294 \left(650 x^2+2155 x-1240\right) (3 x+2)+294 \sqrt{3} (330-660 x) \sqrt{5 x+3} (3 x+2)+\sqrt{1-2 x} \left(294 \sqrt{3} (3 x+2) \sqrt{5 x+3} (90 x-474)+294 (3 x+2) (165 x+1672)\right)}-\frac{25}{9} \sqrt{10} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{11 (5 x+3)^{3/2}}{7 \sqrt{1-2 x} (3 x+2)}+\frac{32 \sqrt{1-2 x} \sqrt{5 x+3}}{147 (3 x+2)}-\frac{25}{9} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)-\frac{169 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{441 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(3859900 + 3169804*x - 3946470*x^2) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-3859900 - 5878280*x - 121900*x^2) + Sqrt[3]*(-3859900 - 5720054*x + 1699925*x^2 + 2395650*x^3 + Sqrt[1 - 2*x]*(3859900 + 8428530*x + 3959175*x^2)))/(294*Sqrt[3]*(330 - 660*x)*(2 + 3*x)*Sqrt[3 + 5*x] + 294*(2 + 3*x)*(-1240 + 2155*x + 650*x^2) + Sqrt[1 - 2*x]*(294*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(-474 + 90*x) + 294*(2 + 3*x)*(1672 + 165*x))) - (25*Sqrt[10]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/9 + (169*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/441 - (845*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/882","C",1
2546,1,519,122,2.1944367,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^3),x]","-\frac{1815 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{1372}+\frac{9075 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2744}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-287146300 x^4-282108635 x^3+5736882782 x^2+7798485256 x+2620621872\right)+\sqrt{5 x+3} \left(1629047750 x^4+7362686925 x^3+2003855810 x^2-5388717400 x-2620621872\right)+\sqrt{3} \left(-64438750 x^5-6790881625 x^4-9903705600 x^3+1733158040 x^2+\sqrt{1-2 x} \left(1274634625 x^4-2820011150 x^3-11397299012 x^2-9897599316 x-2620621872\right)+7487831460 x+2620621872\right)}{1372 \sqrt{3} \sqrt{5 x+3} \left(11000 x^2+194700 x-100100\right) (3 x+2)^2+\sqrt{1-2 x} \left(1372 \sqrt{3} \sqrt{5 x+3} \left(-6950 x^2-60040 x+110468\right) (3 x+2)^2+1372 \left(163625 x^2-33550 x-343904\right) (3 x+2)^2\right)+1372 \left(23750 x^3-445375 x^2-408850 x+312800\right) (3 x+2)^2}","\frac{2 (5 x+3)^{5/2}}{7 \sqrt{1-2 x} (3 x+2)^2}+\frac{5 \sqrt{1-2 x} (5 x+3)^{3/2}}{98 (3 x+2)^2}+\frac{165 \sqrt{1-2 x} \sqrt{5 x+3}}{1372 (3 x+2)}+\frac{1815 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1372 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(2620621872 + 7798485256*x + 5736882782*x^2 - 282108635*x^3 - 287146300*x^4) + Sqrt[3 + 5*x]*(-2620621872 - 5388717400*x + 2003855810*x^2 + 7362686925*x^3 + 1629047750*x^4) + Sqrt[3]*(2620621872 + 7487831460*x + 1733158040*x^2 - 9903705600*x^3 - 6790881625*x^4 - 64438750*x^5 + Sqrt[1 - 2*x]*(-2620621872 - 9897599316*x - 11397299012*x^2 - 2820011150*x^3 + 1274634625*x^4)))/(1372*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(-100100 + 194700*x + 11000*x^2) + 1372*(2 + 3*x)^2*(312800 - 408850*x - 445375*x^2 + 23750*x^3) + Sqrt[1 - 2*x]*(1372*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(110468 - 60040*x - 6950*x^2) + 1372*(2 + 3*x)^2*(-343904 - 33550*x + 163625*x^2))) - (1815*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/1372 + (9075*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2744","C",1
2547,1,579,151,2.5675533,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^4),x]","\frac{1815 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2744}-\frac{9075 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{5488}+\frac{\sqrt{5 x+3} \left(-26404435750 x^6+2335868471475 x^5+4778389545160 x^4+1472408300880 x^3-2437663236360 x^2-1901842794368 x-381636756864\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-22157894750 x^6-683661697775 x^5+100679186500 x^4+3557507937336 x^3+4657061148872 x^2+2258536133888 x+381636756864\right)+\sqrt{3} \left(43216595000 x^7-825018551500 x^6-5510756342900 x^5-6508669262810 x^4+29599269820 x^3+3909377802200 x^2+\sqrt{1-2 x} \left(306363345750 x^6+1047841452350 x^5-1926772631630 x^4-6794078372796 x^3-6419058914312 x^2-2569605514608 x-381636756864\right)+2212912175088 x+381636756864\right)}{2744 \sqrt{3} \sqrt{5 x+3} \left(-4504500 x^3+7857850 x^2+48208160 x-25505480\right) (3 x+2)^3+\sqrt{1-2 x} \left(2744 \sqrt{3} \sqrt{5 x+3} \left(202750 x^3-9591150 x^2-18970200 x+26251976\right) (3 x+2)^3+2744 \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (3 x+2)^3\right)+2744 \left(2203750 x^4+32523625 x^3-153656950 x^2-85860780 x+77141440\right) (3 x+2)^3}","\frac{4 (5 x+3)^{7/2}}{77 \sqrt{1-2 x} (3 x+2)^3}-\frac{\sqrt{1-2 x} (5 x+3)^{5/2}}{77 (3 x+2)^3}-\frac{5 \sqrt{1-2 x} (5 x+3)^{3/2}}{196 (3 x+2)^2}-\frac{165 \sqrt{1-2 x} \sqrt{5 x+3}}{2744 (3 x+2)}-\frac{1815 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2744 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-381636756864 - 1901842794368*x - 2437663236360*x^2 + 1472408300880*x^3 + 4778389545160*x^4 + 2335868471475*x^5 - 26404435750*x^6) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(381636756864 + 2258536133888*x + 4657061148872*x^2 + 3557507937336*x^3 + 100679186500*x^4 - 683661697775*x^5 - 22157894750*x^6) + Sqrt[3]*(381636756864 + 2212912175088*x + 3909377802200*x^2 + 29599269820*x^3 - 6508669262810*x^4 - 5510756342900*x^5 - 825018551500*x^6 + 43216595000*x^7 + Sqrt[1 - 2*x]*(-381636756864 - 2569605514608*x - 6419058914312*x^2 - 6794078372796*x^3 - 1926772631630*x^4 + 1047841452350*x^5 + 306363345750*x^6)))/(2744*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-25505480 + 48208160*x + 7857850*x^2 - 4504500*x^3) + 2744*(2 + 3*x)^3*(77141440 - 85860780*x - 153656950*x^2 + 32523625*x^3 + 2203750*x^4) + Sqrt[1 - 2*x]*(2744*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(26251976 - 18970200*x - 9591150*x^2 + 202750*x^3) + 2744*(2 + 3*x)^3*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3))) + (1815*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2744 - (9075*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/5488","C",1
2548,1,639,180,3.1150335,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^5),x]","\frac{168795 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{153664}-\frac{843975 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{307328}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-43578519060000 x^8+2054420310713125 x^7+18841168694273500 x^6+25284262130818320 x^5-27282681505276376 x^4-79461594430001936 x^3-60977854858370976 x^2-19125650822464896 x-2004670536143616\right)+\sqrt{5 x+3} \left(944065178223750 x^8+2722434012973125 x^7-32769375390711300 x^6-98666037855245520 x^5-77602120148743080 x^4+12678145678307120 x^3+41732909062467744 x^2+17196188599759488 x+2004670536143616\right)+\sqrt{3} \left(-102196019756250 x^9-4047151935054375 x^8+8858617022711250 x^7+91491871045779900 x^6+159877723036993920 x^5+77440059080261280 x^4-42074871011738640 x^3-55424216320550784 x^2+\sqrt{1-2 x} \left(-67675417363125 x^8-11104335760567500 x^7-38632264544976300 x^6-17483141858585040 x^5+77033166644505456 x^4+124261174870191216 x^3+76262471427041856 x^2+20781633727584576 x+2004670536143616\right)-18852171504879168 x-2004670536143616\right)}{153664 \sqrt{3} \sqrt{5 x+3} \left(117810000 x^4+3929805000 x^3-3770256600 x^2-11623605840 x+6255778320\right) (3 x+2)^4+\sqrt{1-2 x} \left(153664 \sqrt{3} \sqrt{5 x+3} \left(-23051250 x^4-467460000 x^3+4929642000 x^2+5009509440 x-6309526032\right) (3 x+2)^4+153664 \left(846511875 x^4-2876857500 x^3-32771841300 x^2+464036760 x+18959828096\right) (3 x+2)^4\right)+153664 \left(49806250 x^5-5100998125 x^4-16263387500 x^3+45507313900 x^2+19543871720 x-18798584960\right) (3 x+2)^4}","\frac{11 (5 x+3)^{3/2}}{7 \sqrt{1-2 x} (3 x+2)^4}-\frac{167155 \sqrt{1-2 x} \sqrt{5 x+3}}{1382976 (3 x+2)}-\frac{38365 \sqrt{1-2 x} \sqrt{5 x+3}}{98784 (3 x+2)^2}-\frac{3653 \sqrt{1-2 x} \sqrt{5 x+3}}{3528 (3 x+2)^3}+\frac{131 \sqrt{1-2 x} \sqrt{5 x+3}}{588 (3 x+2)^4}-\frac{168795 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{153664 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-2004670536143616 - 19125650822464896*x - 60977854858370976*x^2 - 79461594430001936*x^3 - 27282681505276376*x^4 + 25284262130818320*x^5 + 18841168694273500*x^6 + 2054420310713125*x^7 - 43578519060000*x^8) + Sqrt[3 + 5*x]*(2004670536143616 + 17196188599759488*x + 41732909062467744*x^2 + 12678145678307120*x^3 - 77602120148743080*x^4 - 98666037855245520*x^5 - 32769375390711300*x^6 + 2722434012973125*x^7 + 944065178223750*x^8) + Sqrt[3]*(-2004670536143616 - 18852171504879168*x - 55424216320550784*x^2 - 42074871011738640*x^3 + 77440059080261280*x^4 + 159877723036993920*x^5 + 91491871045779900*x^6 + 8858617022711250*x^7 - 4047151935054375*x^8 - 102196019756250*x^9 + Sqrt[1 - 2*x]*(2004670536143616 + 20781633727584576*x + 76262471427041856*x^2 + 124261174870191216*x^3 + 77033166644505456*x^4 - 17483141858585040*x^5 - 38632264544976300*x^6 - 11104335760567500*x^7 - 67675417363125*x^8)))/(153664*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(6255778320 - 11623605840*x - 3770256600*x^2 + 3929805000*x^3 + 117810000*x^4) + 153664*(2 + 3*x)^4*(-18798584960 + 19543871720*x + 45507313900*x^2 - 16263387500*x^3 - 5100998125*x^4 + 49806250*x^5) + Sqrt[1 - 2*x]*(153664*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-6309526032 + 5009509440*x + 4929642000*x^2 - 467460000*x^3 - 23051250*x^4) + 153664*(2 + 3*x)^4*(18959828096 + 464036760*x - 32771841300*x^2 - 2876857500*x^3 + 846511875*x^4))) + (168795*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/153664 - (843975*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/307328","C",1
2549,1,699,209,3.8735402,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^6} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^6),x]","\frac{3474273 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2151296}-\frac{17371365 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{4302592}+\frac{\sqrt{5 x+3} \left(-10572411563798906250 x^{10}-97376093579115759375 x^9+823011752323226408250 x^8+3488827904141466187400 x^7+2435196900130689808520 x^6-4044547163926479148400 x^5-6287569252532035337760 x^4-1921448422194138934272 x^3+1169232844205094044288 x^2+860889015822496449536 x+150243135409538417664\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(556290226827787500 x^{10}-18830475389994103125 x^9-416867693828993396250 x^8-626487150565874825800 x^7+1987258228932739339240 x^6+5383949115774015041104 x^5+3652454139123260781280 x^4-913553677357387556480 x^3-2255260717466180037760 x^2-1011107997423044495360 x-150243135409538417664\right)+\sqrt{3} \left(674730161923218750 x^{11}+70683376294775953125 x^{10}-93027002386335843750 x^9-2799254941576542193750 x^8-5805067281782679089500 x^7-573691369644979591520 x^6+8485188303168562540800 x^5+8090485533859028697920 x^4+1202732395676426687232 x^3-1834508305779556912768 x^2+\sqrt{1-2 x} \left(-2408176604527959375 x^{10}+179199344940747862500 x^9+968590497689230094250 x^8-55511161499566576100 x^7-5333621888115493154160 x^6-8343832710628404361504 x^5-3426648122570149642880 x^4+2485164390502203393280 x^3+3045715412895266277760 x^2+1136307359451826510080 x+150243135409538417664\right)-986088377851278464256 x-150243135409538417664\right)}{10756480 \sqrt{3} \sqrt{5 x+3} \left(-19972562500 x^5+158441181250 x^4+1891194668000 x^3-1459455705400 x^2-2800561494720 x+1519466908960\right) (3 x+2)^5+\sqrt{1-2 x} \left(10756480 \sqrt{3} \sqrt{5 x+3} \left(382806250 x^5-80547756250 x^4-333372935000 x^3+1857062729800 x^2+1248845958560 x-1523336744224\right) (3 x+2)^5+10756480 \left(26771628125 x^5+1102102787500 x^4-1277247746500 x^3-10194890840200 x^2+44616484880 x+4571572732672\right) (3 x+2)^5\right)+10756480 \left(7164406250 x^6+174195921875 x^5-3695625687500 x^4-5925837277500 x^3+12860921279000 x^2+4621767211760 x-4559963226880\right) (3 x+2)^5}","\frac{11 (5 x+3)^{3/2}}{7 \sqrt{1-2 x} (3 x+2)^5}+\frac{426781 \sqrt{1-2 x} \sqrt{5 x+3}}{6453888 (3 x+2)}-\frac{55277 \sqrt{1-2 x} \sqrt{5 x+3}}{460992 (3 x+2)^2}-\frac{29297 \sqrt{1-2 x} \sqrt{5 x+3}}{82320 (3 x+2)^3}-\frac{42863 \sqrt{1-2 x} \sqrt{5 x+3}}{41160 (3 x+2)^4}+\frac{164 \sqrt{1-2 x} \sqrt{5 x+3}}{735 (3 x+2)^5}-\frac{3474273 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2151296 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(150243135409538417664 + 860889015822496449536*x + 1169232844205094044288*x^2 - 1921448422194138934272*x^3 - 6287569252532035337760*x^4 - 4044547163926479148400*x^5 + 2435196900130689808520*x^6 + 3488827904141466187400*x^7 + 823011752323226408250*x^8 - 97376093579115759375*x^9 - 10572411563798906250*x^10) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-150243135409538417664 - 1011107997423044495360*x - 2255260717466180037760*x^2 - 913553677357387556480*x^3 + 3652454139123260781280*x^4 + 5383949115774015041104*x^5 + 1987258228932739339240*x^6 - 626487150565874825800*x^7 - 416867693828993396250*x^8 - 18830475389994103125*x^9 + 556290226827787500*x^10) + Sqrt[3]*(-150243135409538417664 - 986088377851278464256*x - 1834508305779556912768*x^2 + 1202732395676426687232*x^3 + 8090485533859028697920*x^4 + 8485188303168562540800*x^5 - 573691369644979591520*x^6 - 5805067281782679089500*x^7 - 2799254941576542193750*x^8 - 93027002386335843750*x^9 + 70683376294775953125*x^10 + 674730161923218750*x^11 + Sqrt[1 - 2*x]*(150243135409538417664 + 1136307359451826510080*x + 3045715412895266277760*x^2 + 2485164390502203393280*x^3 - 3426648122570149642880*x^4 - 8343832710628404361504*x^5 - 5333621888115493154160*x^6 - 55511161499566576100*x^7 + 968590497689230094250*x^8 + 179199344940747862500*x^9 - 2408176604527959375*x^10)))/(10756480*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(1519466908960 - 2800561494720*x - 1459455705400*x^2 + 1891194668000*x^3 + 158441181250*x^4 - 19972562500*x^5) + 10756480*(2 + 3*x)^5*(-4559963226880 + 4621767211760*x + 12860921279000*x^2 - 5925837277500*x^3 - 3695625687500*x^4 + 174195921875*x^5 + 7164406250*x^6) + Sqrt[1 - 2*x]*(10756480*Sqrt[3]*(2 + 3*x)^5*Sqrt[3 + 5*x]*(-1523336744224 + 1248845958560*x + 1857062729800*x^2 - 333372935000*x^3 - 80547756250*x^4 + 382806250*x^5) + 10756480*(2 + 3*x)^5*(4571572732672 + 44616484880*x - 10194890840200*x^2 - 1277247746500*x^3 + 1102102787500*x^4 + 26771628125*x^5))) + (3474273*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2151296 - (17371365*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/4302592","C",1
2550,1,406,142,2.7319679,"\int \frac{(2+3 x)^5}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-38729340000000 x^8+3773104605000000 x^7+31971081987225000 x^6+76552169729928750 x^5+72328256488386625 x^4-180193097071465100 x^3-1913482824820252500 x^2-433230321186847160 x+1675914696244472464\right)+\sqrt{5 x+3} \left(1316495268000000 x^8+1442826059400000 x^7-57843619392735000 x^6-247754112435497250 x^5-619687974267120825 x^4-1245634526577288540 x^3+2268605152851758820 x^2+2100881840399225928 x-1675914696244472464\right)+\sqrt{3} \left(-179246520000000 x^9-4548130398000000 x^8+17529828649650000 x^7+183341563713427500 x^6+546356697699596500 x^5+1513145798436631025 x^4+502118192431159540 x^3-4585779042514559060 x^2+\sqrt{1-2 x} \left(-458045280000000 x^8-17841590712000000 x^7-77939339880600000 x^6-125521805018610000 x^5-88624219417853625 x^4+1193746210431314100 x^3+2842548574207112100 x^2-961763799949171560 x-1675914696244472464\right)-705887719263207208 x+1675914696244472464\right)}{256000 \sqrt{3} \sqrt{5 x+3} \left(-117810000 x^4-3929805000 x^3+3770256600 x^2+11623605840 x-6255778320\right)+\sqrt{1-2 x} \left(256000 \left(-846511875 x^4+2876857500 x^3+32771841300 x^2-464036760 x-18959828096\right)+256000 \sqrt{3} \sqrt{5 x+3} \left(23051250 x^4+467460000 x^3-4929642000 x^2-5009509440 x+6309526032\right)\right)+256000 \left(-49806250 x^5+5100998125 x^4+16263387500 x^3-45507313900 x^2-19543871720 x+18798584960\right)}-\frac{291096141 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{128000 \sqrt{10}}","\frac{7 \sqrt{5 x+3} (3 x+2)^4}{11 \sqrt{1-2 x}}+\frac{939}{880} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^3+\frac{76587 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2}{17600}+\frac{21 \sqrt{1-2 x} \sqrt{5 x+3} (7645620 x+18424549)}{2816000}-\frac{291096141 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{256000 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1675914696244472464 - 433230321186847160*x - 1913482824820252500*x^2 - 180193097071465100*x^3 + 72328256488386625*x^4 + 76552169729928750*x^5 + 31971081987225000*x^6 + 3773104605000000*x^7 - 38729340000000*x^8) + Sqrt[3 + 5*x]*(-1675914696244472464 + 2100881840399225928*x + 2268605152851758820*x^2 - 1245634526577288540*x^3 - 619687974267120825*x^4 - 247754112435497250*x^5 - 57843619392735000*x^6 + 1442826059400000*x^7 + 1316495268000000*x^8) + Sqrt[3]*(1675914696244472464 - 705887719263207208*x - 4585779042514559060*x^2 + 502118192431159540*x^3 + 1513145798436631025*x^4 + 546356697699596500*x^5 + 183341563713427500*x^6 + 17529828649650000*x^7 - 4548130398000000*x^8 - 179246520000000*x^9 + Sqrt[1 - 2*x]*(-1675914696244472464 - 961763799949171560*x + 2842548574207112100*x^2 + 1193746210431314100*x^3 - 88624219417853625*x^4 - 125521805018610000*x^5 - 77939339880600000*x^6 - 17841590712000000*x^7 - 458045280000000*x^8)))/(256000*Sqrt[3]*Sqrt[3 + 5*x]*(-6255778320 + 11623605840*x + 3770256600*x^2 - 3929805000*x^3 - 117810000*x^4) + 256000*(18798584960 - 19543871720*x - 45507313900*x^2 + 16263387500*x^3 + 5100998125*x^4 - 49806250*x^5) + Sqrt[1 - 2*x]*(256000*(-18959828096 - 464036760*x + 32771841300*x^2 + 2876857500*x^3 - 846511875*x^4) + 256000*Sqrt[3]*Sqrt[3 + 5*x]*(6309526032 - 5009509440*x - 4929642000*x^2 + 467460000*x^3 + 23051250*x^4))) - (291096141*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(128000*Sqrt[10])","B",1
2551,1,346,113,2.2602754,"\int \frac{(2+3 x)^4}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{\sqrt{5 x+3} \left(-5970888000 x^6-181190255400 x^5-700065765630 x^4-1736903089471 x^3+3885701741944 x^2+5402364337172 x-4426989214120\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(1904040000 x^6+36906597000 x^5+21302806950 x^4-334519422995 x^3-3067343832720 x^2-1051936126060 x+4426989214120\right)+\sqrt{3} \left(-1751760000 x^7+74590470000 x^6+532996262100 x^5+1690375501260 x^4+1122660624751 x^3-9764200786504 x^2+\sqrt{1-2 x} \left(-19459440000 x^6-67729662000 x^5+85343157900 x^4+1648792201595 x^3+5341852805520 x^2-2615854781540 x-4426989214120\right)-1734573429572 x+4426989214120\right)}{640 \sqrt{3} \sqrt{5 x+3} \left(-4504500 x^3+7857850 x^2+48208160 x-25505480\right)+\sqrt{1-2 x} \left(640 \sqrt{3} \sqrt{5 x+3} \left(202750 x^3-9591150 x^2-18970200 x+26251976\right)+640 \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right)\right)+640 \left(2203750 x^4+32523625 x^3-153656950 x^2-85860780 x+77141440\right)}-\frac{184641 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{320 \sqrt{10}}","\frac{7 \sqrt{5 x+3} (3 x+2)^3}{11 \sqrt{1-2 x}}+\frac{243}{220} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2+\frac{9 \sqrt{1-2 x} \sqrt{5 x+3} (11316 x+27269)}{7040}-\frac{184641 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{640 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(-4426989214120 + 5402364337172*x + 3885701741944*x^2 - 1736903089471*x^3 - 700065765630*x^4 - 181190255400*x^5 - 5970888000*x^6) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(4426989214120 - 1051936126060*x - 3067343832720*x^2 - 334519422995*x^3 + 21302806950*x^4 + 36906597000*x^5 + 1904040000*x^6) + Sqrt[3]*(4426989214120 - 1734573429572*x - 9764200786504*x^2 + 1122660624751*x^3 + 1690375501260*x^4 + 532996262100*x^5 + 74590470000*x^6 - 1751760000*x^7 + Sqrt[1 - 2*x]*(-4426989214120 - 2615854781540*x + 5341852805520*x^2 + 1648792201595*x^3 + 85343157900*x^4 - 67729662000*x^5 - 19459440000*x^6)))/(640*Sqrt[3]*Sqrt[3 + 5*x]*(-25505480 + 48208160*x + 7857850*x^2 - 4504500*x^3) + 640*(77141440 - 85860780*x - 153656950*x^2 + 32523625*x^3 + 2203750*x^4) + Sqrt[1 - 2*x]*(640*Sqrt[3]*Sqrt[3 + 5*x]*(26251976 - 18970200*x - 9591150*x^2 + 202750*x^3) + 640*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3))) - (184641*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(320*Sqrt[10])","B",1
2552,1,286,84,1.9573854,"\int \frac{(2+3 x)^3}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-12825000 x^4+178301250 x^3+1645907275 x^2+1145162430 x-5704660676\right)+\sqrt{5 x+3} \left(176715000 x^4+732476250 x^3-2270220095 x^2-6490981442 x+5704660676\right)+\sqrt{3} \left(-37530000 x^5-509989500 x^4-1008886300 x^3+8893577955 x^2+\sqrt{1-2 x} \left(-29700000 x^4-687555000 x^3-3958626375 x^2+3464511050 x+5704660676\right)+1881307962 x-5704660676\right)}{800 \sqrt{3} \sqrt{5 x+3} \left(-11000 x^2-194700 x+100100\right)+\sqrt{1-2 x} \left(800 \left(-163625 x^2+33550 x+343904\right)+800 \sqrt{3} \sqrt{5 x+3} \left(6950 x^2+60040 x-110468\right)\right)+800 \left(-23750 x^3+445375 x^2+408850 x-312800\right)}-\frac{56421 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{400 \sqrt{10}}","\frac{7 \sqrt{5 x+3} (3 x+2)^2}{11 \sqrt{1-2 x}}+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} (10380 x+25003)}{8800}-\frac{56421 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{800 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-5704660676 + 1145162430*x + 1645907275*x^2 + 178301250*x^3 - 12825000*x^4) + Sqrt[3 + 5*x]*(5704660676 - 6490981442*x - 2270220095*x^2 + 732476250*x^3 + 176715000*x^4) + Sqrt[3]*(-5704660676 + 1881307962*x + 8893577955*x^2 - 1008886300*x^3 - 509989500*x^4 - 37530000*x^5 + Sqrt[1 - 2*x]*(5704660676 + 3464511050*x - 3958626375*x^2 - 687555000*x^3 - 29700000*x^4)))/(800*Sqrt[3]*Sqrt[3 + 5*x]*(100100 - 194700*x - 11000*x^2) + 800*(-312800 + 408850*x + 445375*x^2 - 23750*x^3) + Sqrt[1 - 2*x]*(800*(343904 + 33550*x - 163625*x^2) + 800*Sqrt[3]*Sqrt[3 + 5*x]*(-110468 + 60040*x + 6950*x^2))) - (56421*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(400*Sqrt[10])","B",1
2553,1,226,72,1.5628284,"\int \frac{(2+3 x)^2}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{\sqrt{5 x+3} \left(-2970 x^2-127281 x+142538\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(5850 x^2+19375 x-142538\right)+\sqrt{3} \left(-8100 x^3+96700 x^2+\sqrt{1-2 x} \left(-29700 x^2+79365 x+142538\right)+28541 x-142538\right)}{20 \left(650 x^2+2155 x-1240\right)+20 \sqrt{3} \sqrt{5 x+3} (330-660 x)+\sqrt{1-2 x} \left(20 \sqrt{3} \sqrt{5 x+3} (90 x-474)+20 (165 x+1672)\right)}-\frac{321 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{10 \sqrt{10}}","\frac{9}{20} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{49 \sqrt{5 x+3}}{22 \sqrt{1-2 x}}-\frac{321 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{20 \sqrt{10}}",1,"(Sqrt[3 + 5*x]*(142538 - 127281*x - 2970*x^2) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-142538 + 19375*x + 5850*x^2) + Sqrt[3]*(-142538 + 28541*x + 96700*x^2 - 8100*x^3 + Sqrt[1 - 2*x]*(142538 + 79365*x - 29700*x^2)))/(20*Sqrt[3]*(330 - 660*x)*Sqrt[3 + 5*x] + 20*(-1240 + 2155*x + 650*x^2) + Sqrt[1 - 2*x]*(20*Sqrt[3]*Sqrt[3 + 5*x]*(-474 + 90*x) + 20*(1672 + 165*x))) - (321*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(10*Sqrt[10])","B",1
2554,1,133,48,1.2332948,"\int \frac{2+3 x}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{\left(7-7 \sqrt{1-2 x}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5}-3 \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{7 \sqrt{5 x+3}}{11 \sqrt{1-2 x}}-\frac{3 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{\sqrt{10}}",1,"((7 - 7*Sqrt[1 - 2*x])*(Sqrt[3] - Sqrt[3 + 5*x]))/(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]) - 3*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])]","B",1
2555,1,95,22,1.0951001,"\int \frac{1}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{\left(2 \sqrt{1-2 x}-2\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^2}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5\right)}","\frac{2 \sqrt{5 x+3}}{11 \sqrt{1-2 x}}",1,"((-2 + 2*Sqrt[1 - 2*x])*(Sqrt[3] - Sqrt[3 + 5*x])^2)/((-Sqrt[3] + Sqrt[3 + 5*x])*(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]))","B",1
2556,1,271,57,1.2726114,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x) \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)*Sqrt[3 + 5*x]),x]","\frac{\left(\frac{4}{7}-\frac{4}{7} \sqrt{1-2 x}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5}-\frac{3}{7} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]","\frac{4 \sqrt{5 x+3}}{77 \sqrt{1-2 x}}-\frac{6 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{7 \sqrt{7}}",1,"((4/7 - (4*Sqrt[1 - 2*x])/7)*(Sqrt[3] - Sqrt[3 + 5*x]))/(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]) - (3*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ])/7","C",1
2557,1,451,86,1.7896271,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^2 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*Sqrt[3 + 5*x]),x]","\frac{123}{49} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{615}{98} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-67320 x^2-59796 x+55660\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(18750 x^2-6520 x-55660\right)+\sqrt{3} \left(6150 x^3+157025 x^2+\sqrt{1-2 x} \left(-47025 x^2+59070 x+55660\right)+7246 x-55660\right)}{98 \left(650 x^2+2155 x-1240\right) (3 x+2)+98 \sqrt{3} (330-660 x) \sqrt{5 x+3} (3 x+2)+\sqrt{1-2 x} \left(98 \sqrt{3} (3 x+2) \sqrt{5 x+3} (90 x-474)+98 (3 x+2) (165 x+1672)\right)}","-\frac{58 \sqrt{5 x+3}}{539 \sqrt{1-2 x}}+\frac{3 \sqrt{5 x+3}}{7 \sqrt{1-2 x} (3 x+2)}-\frac{123 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{49 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(55660 - 59796*x - 67320*x^2) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-55660 - 6520*x + 18750*x^2) + Sqrt[3]*(-55660 + 7246*x + 157025*x^2 + 6150*x^3 + Sqrt[1 - 2*x]*(55660 + 59070*x - 47025*x^2)))/(98*Sqrt[3]*(330 - 660*x)*(2 + 3*x)*Sqrt[3 + 5*x] + 98*(2 + 3*x)*(-1240 + 2155*x + 650*x^2) + Sqrt[1 - 2*x]*(98*Sqrt[3]*(2 + 3*x)*Sqrt[3 + 5*x]*(-474 + 90*x) + 98*(2 + 3*x)*(1672 + 165*x))) + (123*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/49 - (615*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/98","C",1
2558,1,519,115,2.1149147,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^3 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*Sqrt[3 + 5*x]),x]","\frac{12465 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{1372}-\frac{62325 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2744}+\frac{\sqrt{5 x+3} \left(-872759250 x^4+3246867525 x^3+5151326290 x^2-371773160 x-1476047056\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-31802400 x^4-2438507355 x^3-1869886514 x^2+1969944888 x+1476047056\right)+\sqrt{3} \left(343923750 x^5-43012875 x^4-7164462100 x^3-5532559440 x^2+\sqrt{1-2 x} \left(1018821375 x^4+4281398550 x^3+870230724 x^2-3249063268 x-1476047056\right)+1650891540 x+1476047056\right)}{1372 \sqrt{3} \sqrt{5 x+3} \left(11000 x^2+194700 x-100100\right) (3 x+2)^2+\sqrt{1-2 x} \left(1372 \sqrt{3} \sqrt{5 x+3} \left(-6950 x^2-60040 x+110468\right) (3 x+2)^2+1372 \left(163625 x^2-33550 x-343904\right) (3 x+2)^2\right)+1372 \left(23750 x^3-445375 x^2-408850 x+312800\right) (3 x+2)^2}","-\frac{3895 \sqrt{5 x+3}}{7546 \sqrt{1-2 x}}+\frac{345 \sqrt{5 x+3}}{196 \sqrt{1-2 x} (3 x+2)}+\frac{3 \sqrt{5 x+3}}{14 \sqrt{1-2 x} (3 x+2)^2}-\frac{12465 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1372 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-1476047056 - 371773160*x + 5151326290*x^2 + 3246867525*x^3 - 872759250*x^4) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1476047056 + 1969944888*x - 1869886514*x^2 - 2438507355*x^3 - 31802400*x^4) + Sqrt[3]*(1476047056 + 1650891540*x - 5532559440*x^2 - 7164462100*x^3 - 43012875*x^4 + 343923750*x^5 + Sqrt[1 - 2*x]*(-1476047056 - 3249063268*x + 870230724*x^2 + 4281398550*x^3 + 1018821375*x^4)))/(1372*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(-100100 + 194700*x + 11000*x^2) + 1372*(2 + 3*x)^2*(312800 - 408850*x - 445375*x^2 + 23750*x^3) + Sqrt[1 - 2*x]*(1372*Sqrt[3]*(2 + 3*x)^2*Sqrt[3 + 5*x]*(110468 - 60040*x - 6950*x^2) + 1372*(2 + 3*x)^2*(-343904 - 33550*x + 163625*x^2))) + (12465*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/1372 - (62325*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2744","C",1
2559,1,579,144,2.4447427,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^4 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^4*Sqrt[3 + 5*x]),x]","\frac{102345 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2744}-\frac{511725 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{5488}+\frac{\sqrt{5 x+3} \left(-2301583457250 x^6-15492819070575 x^5+10504284270480 x^4+47646601867040 x^3+20550794494120 x^2-10538076655744 x-5969225185792\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(255672578250 x^6-704048138325 x^5-23350415395500 x^4-32122691405192 x^3+283088832216 x^2+16659077915264 x+5969225185792\right)+\sqrt{3} \left(121875097500 x^7+12238354739250 x^6+15501508836300 x^5-41235992480430 x^4-66641776468940 x^3-14017845609400 x^2+\sqrt{1-2 x} \left(-1363145206500 x^6+12180765262050 x^5+46704366511110 x^4+35994241380812 x^3-11959230016536 x^2-21675790153424 x-5969225185792\right)+15554788893904 x+5969225185792\right)}{2744 \sqrt{3} \sqrt{5 x+3} \left(-4504500 x^3+7857850 x^2+48208160 x-25505480\right) (3 x+2)^3+\sqrt{1-2 x} \left(2744 \sqrt{3} \sqrt{5 x+3} \left(202750 x^3-9591150 x^2-18970200 x+26251976\right) (3 x+2)^3+2744 \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (3 x+2)^3\right)+2744 \left(2203750 x^4+32523625 x^3-153656950 x^2-85860780 x+77141440\right) (3 x+2)^3}","-\frac{32735 \sqrt{5 x+3}}{15092 \sqrt{1-2 x}}+\frac{2865 \sqrt{5 x+3}}{392 \sqrt{1-2 x} (3 x+2)}+\frac{27 \sqrt{5 x+3}}{28 \sqrt{1-2 x} (3 x+2)^2}+\frac{\sqrt{5 x+3}}{7 \sqrt{1-2 x} (3 x+2)^3}-\frac{102345 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2744 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-5969225185792 - 10538076655744*x + 20550794494120*x^2 + 47646601867040*x^3 + 10504284270480*x^4 - 15492819070575*x^5 - 2301583457250*x^6) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(5969225185792 + 16659077915264*x + 283088832216*x^2 - 32122691405192*x^3 - 23350415395500*x^4 - 704048138325*x^5 + 255672578250*x^6) + Sqrt[3]*(5969225185792 + 15554788893904*x - 14017845609400*x^2 - 66641776468940*x^3 - 41235992480430*x^4 + 15501508836300*x^5 + 12238354739250*x^6 + 121875097500*x^7 + Sqrt[1 - 2*x]*(-5969225185792 - 21675790153424*x - 11959230016536*x^2 + 35994241380812*x^3 + 46704366511110*x^4 + 12180765262050*x^5 - 1363145206500*x^6)))/(2744*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-25505480 + 48208160*x + 7857850*x^2 - 4504500*x^3) + 2744*(2 + 3*x)^3*(77141440 - 85860780*x - 153656950*x^2 + 32523625*x^3 + 2203750*x^4) + Sqrt[1 - 2*x]*(2744*Sqrt[3]*(2 + 3*x)^3*Sqrt[3 + 5*x]*(26251976 - 18970200*x - 9591150*x^2 + 202750*x^3) + 2744*(2 + 3*x)^3*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3))) + (102345*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2744 - (511725*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/5488","C",1
2560,1,639,173,2.9410843,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^5 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^5*Sqrt[3 + 5*x]),x]","\frac{24922335 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{153664}-\frac{124611675 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{307328}+\frac{\sqrt{5 x+3} \left(-66119838412691250 x^8+1389268979944250625 x^7+6333556258228409100 x^6+2923582492434518640 x^5-9538220640648264840 x^4-10093589748564804240 x^3-809523618640770528 x^2+2308505039445922944 x+705132091698335488\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-3614359233330000 x^8-444126431206929375 x^7-537590464974364500 x^6+5095130871554567760 x^5+10765218817300909832 x^4+5321968665047112752 x^3-2620935150140052768 x^2-3018991075535840128 x-705132091698335488\right)+\sqrt{3} \left(18268346576418750 x^9-166118801646931875 x^8-5105167355114853750 x^7-9886926542651769300 x^6+2234398875010554560 x^5+17189881218437825440 x^4+11364152162631410480 x^3-864552375030020992 x^2+\sqrt{1-2 x} \left(114736792693854375 x^8+1188486662519722500 x^7-1575170664205455900 x^6-12136019996674656720 x^5-15429172919409949392 x^4-3983796207362309712 x^3+4888120470844108608 x^2+3607638782242786368 x+705132091698335488\right)-2897152746152869184 x-705132091698335488\right)}{153664 \sqrt{3} \sqrt{5 x+3} \left(117810000 x^4+3929805000 x^3-3770256600 x^2-11623605840 x+6255778320\right) (3 x+2)^4+\sqrt{1-2 x} \left(153664 \sqrt{3} \sqrt{5 x+3} \left(-23051250 x^4-467460000 x^3+4929642000 x^2+5009509440 x-6309526032\right) (3 x+2)^4+153664 \left(846511875 x^4-2876857500 x^3-32771841300 x^2+464036760 x+18959828096\right) (3 x+2)^4\right)+153664 \left(49806250 x^5-5100998125 x^4-16263387500 x^3+45507313900 x^2+19543871720 x-18798584960\right) (3 x+2)^4}","-\frac{7986105 \sqrt{5 x+3}}{845152 \sqrt{1-2 x}}+\frac{698295 \sqrt{5 x+3}}{21952 \sqrt{1-2 x} (3 x+2)}+\frac{6621 \sqrt{5 x+3}}{1568 \sqrt{1-2 x} (3 x+2)^2}+\frac{263 \sqrt{5 x+3}}{392 \sqrt{1-2 x} (3 x+2)^3}+\frac{3 \sqrt{5 x+3}}{28 \sqrt{1-2 x} (3 x+2)^4}-\frac{24922335 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{153664 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(705132091698335488 + 2308505039445922944*x - 809523618640770528*x^2 - 10093589748564804240*x^3 - 9538220640648264840*x^4 + 2923582492434518640*x^5 + 6333556258228409100*x^6 + 1389268979944250625*x^7 - 66119838412691250*x^8) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-705132091698335488 - 3018991075535840128*x - 2620935150140052768*x^2 + 5321968665047112752*x^3 + 10765218817300909832*x^4 + 5095130871554567760*x^5 - 537590464974364500*x^6 - 444126431206929375*x^7 - 3614359233330000*x^8) + Sqrt[3]*(-705132091698335488 - 2897152746152869184*x - 864552375030020992*x^2 + 11364152162631410480*x^3 + 17189881218437825440*x^4 + 2234398875010554560*x^5 - 9886926542651769300*x^6 - 5105167355114853750*x^7 - 166118801646931875*x^8 + 18268346576418750*x^9 + Sqrt[1 - 2*x]*(705132091698335488 + 3607638782242786368*x + 4888120470844108608*x^2 - 3983796207362309712*x^3 - 15429172919409949392*x^4 - 12136019996674656720*x^5 - 1575170664205455900*x^6 + 1188486662519722500*x^7 + 114736792693854375*x^8)))/(153664*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(6255778320 - 11623605840*x - 3770256600*x^2 + 3929805000*x^3 + 117810000*x^4) + 153664*(2 + 3*x)^4*(-18798584960 + 19543871720*x + 45507313900*x^2 - 16263387500*x^3 - 5100998125*x^4 + 49806250*x^5) + Sqrt[1 - 2*x]*(153664*Sqrt[3]*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-6309526032 + 5009509440*x + 4929642000*x^2 - 467460000*x^3 - 23051250*x^4) + 153664*(2 + 3*x)^4*(18959828096 + 464036760*x - 32771841300*x^2 - 2876857500*x^3 + 846511875*x^4))) + (24922335*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/153664 - (124611675*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/307328","C",1
2561,1,384,142,3.5558295,"\int \frac{(2+3 x)^5}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{3324483000000 x^8-14961503925000 x^7-592573174098750 x^6-2811780669790125 x^5-7944001944868125 x^4+8647158505855680 x^3+21617017496373240 x^2+\sqrt{3} \sqrt{5 x+3} \left(-3468484800000 x^7+46638183240000 x^6+345288069918000 x^5+1314397501920800 x^4+687701108821540 x^3-5613101170711540 x^2-903354212085688 x+2306252449738424\right)+\sqrt{1-2 x} \left(18849996000000 x^7+206503951500000 x^6+499665311145000 x^5-306744269848500 x^4-10344142161348600 x^3-8692178340057300 x^2+\sqrt{3} \sqrt{5 x+3} \left(-231336000000 x^7-21791802600000 x^6-88685849430000 x^5-106184004313375 x^4+1053005201714200 x^3+3213569669365400 x^2-1381044738200320 x-2306252449738424\right)+9924012615509520 x+6918757349215272\right)-3070815764651496 x-6918757349215272}{48000 \sqrt{1-2 x} \sqrt{5 x+3} \left(-8550625 x^4+79738000 x^3+1253327000 x^2-32289760 x-865716488\right)+48000 \sqrt{5 x+3} \left(96965000 x^4+545924500 x^3-1887183100 x^2-909569320 x+852279560\right)+\sqrt{3} \left(48000 \sqrt{1-2 x} \left(44605000 x^4-788227000 x^3-1591554800 x^2+776116000 x+862591488\right)+48000 \left(-5950000 x^5-532375000 x^4+312727000 x^3+3026461200 x^2+173815520 x-849154560\right)\right)}-\frac{2911419 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{8000 \sqrt{10}}","\frac{7 (3 x+2)^4}{11 \sqrt{1-2 x} \sqrt{5 x+3}}-\frac{37 \sqrt{1-2 x} (3 x+2)^3}{605 \sqrt{5 x+3}}+\frac{8463 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2}{12100}+\frac{21 \sqrt{1-2 x} \sqrt{5 x+3} (841380 x+2027201)}{1936000}-\frac{2911419 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{16000 \sqrt{10}}",1,"(-6918757349215272 - 3070815764651496*x + 21617017496373240*x^2 + 8647158505855680*x^3 - 7944001944868125*x^4 - 2811780669790125*x^5 - 592573174098750*x^6 - 14961503925000*x^7 + 3324483000000*x^8 + Sqrt[3]*Sqrt[3 + 5*x]*(2306252449738424 - 903354212085688*x - 5613101170711540*x^2 + 687701108821540*x^3 + 1314397501920800*x^4 + 345288069918000*x^5 + 46638183240000*x^6 - 3468484800000*x^7) + Sqrt[1 - 2*x]*(6918757349215272 + 9924012615509520*x - 8692178340057300*x^2 - 10344142161348600*x^3 - 306744269848500*x^4 + 499665311145000*x^5 + 206503951500000*x^6 + 18849996000000*x^7 + Sqrt[3]*Sqrt[3 + 5*x]*(-2306252449738424 - 1381044738200320*x + 3213569669365400*x^2 + 1053005201714200*x^3 - 106184004313375*x^4 - 88685849430000*x^5 - 21791802600000*x^6 - 231336000000*x^7)))/(48000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-865716488 - 32289760*x + 1253327000*x^2 + 79738000*x^3 - 8550625*x^4) + 48000*Sqrt[3 + 5*x]*(852279560 - 909569320*x - 1887183100*x^2 + 545924500*x^3 + 96965000*x^4) + Sqrt[3]*(48000*Sqrt[1 - 2*x]*(862591488 + 776116000*x - 1591554800*x^2 - 788227000*x^3 + 44605000*x^4) + 48000*(-849154560 + 173815520*x + 3026461200*x^2 + 312727000*x^3 - 532375000*x^4 - 5950000*x^5))) - (2911419*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(8000*Sqrt[10])","B",1
2562,1,324,113,2.262075,"\int \frac{(2+3 x)^4}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{436185000 x^6+31149096750 x^5+156470426175 x^4-270367191030 x^3-896581026135 x^2+\sqrt{3} \sqrt{5 x+3} \left(-2229282000 x^5-18947025900 x^4-26944426740 x^3+217293489215 x^2+39405090076 x-118690897468\right)+\sqrt{1-2 x} \left(-3809025000 x^5+8115896250 x^4+253713059325 x^3+260251699125 x^2+\sqrt{3} \sqrt{5 x+3} \left(284310000 x^5+503374500 x^4-18300447775 x^3-102047083425 x^2+75181541280 x+118690897468\right)-526395398760 x-356072692404\right)+182635504692 x+356072692404}{2400 \sqrt{5 x+3} \left(-783750 x^3+6045875 x^2+4135120 x-3481060\right)+2400 \sqrt{1-2 x} \sqrt{5 x+3} \left(-44875 x^3-2976525 x^2+279060 x+3667684\right)+\sqrt{3} \left(2400 \sqrt{1-2 x} \left(1146750 x^3+4605150 x^2-3658380 x-3605184\right)+2400 \left(292500 x^4-939750 x^3-11579850 x^2-848820 x+3418560\right)\right)}-\frac{35451 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{400 \sqrt{10}}","\frac{7 (3 x+2)^3}{11 \sqrt{1-2 x} \sqrt{5 x+3}}-\frac{37 \sqrt{1-2 x} (3 x+2)^2}{605 \sqrt{5 x+3}}+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} (72060 x+173063)}{96800}-\frac{35451 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{800 \sqrt{10}}",1,"(356072692404 + 182635504692*x - 896581026135*x^2 - 270367191030*x^3 + 156470426175*x^4 + 31149096750*x^5 + 436185000*x^6 + Sqrt[3]*Sqrt[3 + 5*x]*(-118690897468 + 39405090076*x + 217293489215*x^2 - 26944426740*x^3 - 18947025900*x^4 - 2229282000*x^5) + Sqrt[1 - 2*x]*(-356072692404 - 526395398760*x + 260251699125*x^2 + 253713059325*x^3 + 8115896250*x^4 - 3809025000*x^5 + Sqrt[3]*Sqrt[3 + 5*x]*(118690897468 + 75181541280*x - 102047083425*x^2 - 18300447775*x^3 + 503374500*x^4 + 284310000*x^5)))/(2400*Sqrt[3 + 5*x]*(-3481060 + 4135120*x + 6045875*x^2 - 783750*x^3) + 2400*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(3667684 + 279060*x - 2976525*x^2 - 44875*x^3) + Sqrt[3]*(2400*Sqrt[1 - 2*x]*(-3605184 - 3658380*x + 4605150*x^2 + 1146750*x^3) + 2400*(3418560 - 848820*x - 11579850*x^2 - 939750*x^3 + 292500*x^4))) - (35451*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(400*Sqrt[10])","B",1
2563,1,264,84,1.9986808,"\int \frac{(2+3 x)^3}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{2409750 x^4-9077775 x^3-78742755 x^2+\sqrt{3} \sqrt{5 x+3} \left(-1603800 x^3+15422000 x^2+3089262 x-14820806\right)+\sqrt{1-2 x} \left(5791500 x^3+11723250 x^2+\sqrt{3} \sqrt{5 x+3} \left(-81000 x^3-4735625 x^2+9745640 x+14820806\right)-69162060 x-44462418\right)+30657354 x+44462418}{300 \sqrt{1-2 x} \sqrt{5 x+3} \left(-2975 x^2+1820 x+16562\right)+300 \sqrt{5 x+3} \left(14300 x^2+20790 x-13970\right)+\sqrt{3} \left(300 \sqrt{1-2 x} \left(9900 x^2-19580 x-15312\right)+300 \left(-1000 x^3-42500 x^2-3940 x+12720\right)\right)}-\frac{999 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{50 \sqrt{10}}","\frac{7 (3 x+2)^2}{11 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{\sqrt{1-2 x} (50985 x+30443)}{12100 \sqrt{5 x+3}}-\frac{999 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{100 \sqrt{10}}",1,"(44462418 + 30657354*x - 78742755*x^2 - 9077775*x^3 + 2409750*x^4 + Sqrt[3]*Sqrt[3 + 5*x]*(-14820806 + 3089262*x + 15422000*x^2 - 1603800*x^3) + Sqrt[1 - 2*x]*(-44462418 - 69162060*x + 11723250*x^2 + 5791500*x^3 + Sqrt[3]*Sqrt[3 + 5*x]*(14820806 + 9745640*x - 4735625*x^2 - 81000*x^3)))/(300*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(16562 + 1820*x - 2975*x^2) + 300*Sqrt[3 + 5*x]*(-13970 + 20790*x + 14300*x^2) + Sqrt[3]*(300*Sqrt[1 - 2*x]*(-15312 - 19580*x + 9900*x^2) + 300*(12720 - 3940*x - 42500*x^2 - 1000*x^3))) - (999*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(50*Sqrt[10])","B",1
2564,1,208,72,1.5194508,"\int \frac{(2+3 x)^2}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{\sqrt{3} \left(-555 x^2+894 x+(-1225 x-733) \sqrt{1-2 x}+733\right)+\sqrt{5 x+3} (-4 x-733)+\sqrt{1-2 x} \sqrt{5 x+3} (335 x+733)}{5 \left(-300 x^2-30 x+90\right)+5 \sqrt{3} \sqrt{5 x+3} (110 x-55)+\sqrt{1-2 x} \left(5 (-330 x-198)+5 \sqrt{3} \sqrt{5 x+3} (5 x+91)\right)}-\frac{9}{5} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{1229 \sqrt{1-2 x}}{1210 \sqrt{5 x+3}}+\frac{49}{22 \sqrt{1-2 x} \sqrt{5 x+3}}-\frac{9 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{5 \sqrt{10}}",1,"((-733 - 4*x)*Sqrt[3 + 5*x] + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(733 + 335*x) + Sqrt[3]*(733 + (-733 - 1225*x)*Sqrt[1 - 2*x] + 894*x - 555*x^2))/(5*Sqrt[3]*Sqrt[3 + 5*x]*(-55 + 110*x) + 5*(90 - 30*x - 300*x^2) + Sqrt[1 - 2*x]*(5*(-198 - 330*x) + 5*Sqrt[3]*Sqrt[3 + 5*x]*(91 + 5*x))) - (9*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/5","B",1
2565,1,215,45,1.3366579,"\int \frac{2+3 x}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{-30 x^2+54 x-\frac{4}{3} \sqrt{5 x+3} \left(\sqrt{3} x+10 \sqrt{3}\right)+\frac{10}{3} \sqrt{1-2 x} \left(2 \sqrt{3} \sqrt{5 x+3} x-21 x+4 \sqrt{3} \sqrt{5 x+3}-12\right)+40}{-100 \sqrt{3} x^2-110 \sqrt{3} \sqrt{1-2 x} x+5 \sqrt{1-2 x} \sqrt{5 x+3} x+110 \sqrt{5 x+3} x-10 \sqrt{3} x-66 \sqrt{3} \sqrt{1-2 x}+91 \sqrt{1-2 x} \sqrt{5 x+3}-55 \sqrt{5 x+3}+30 \sqrt{3}}","\frac{74 \sqrt{5 x+3}}{605 \sqrt{1-2 x}}-\frac{2}{55 \sqrt{1-2 x} \sqrt{5 x+3}}",1,"(40 + 54*x - 30*x^2 - (4*Sqrt[3 + 5*x]*(10*Sqrt[3] + Sqrt[3]*x))/3 + (10*Sqrt[1 - 2*x]*(-12 - 21*x + 4*Sqrt[3]*Sqrt[3 + 5*x] + 2*Sqrt[3]*x*Sqrt[3 + 5*x]))/3)/(30*Sqrt[3] - 66*Sqrt[3]*Sqrt[1 - 2*x] - 10*Sqrt[3]*x - 110*Sqrt[3]*Sqrt[1 - 2*x]*x - 100*Sqrt[3]*x^2 - 55*Sqrt[3 + 5*x] + 91*Sqrt[1 - 2*x]*Sqrt[3 + 5*x] + 110*x*Sqrt[3 + 5*x] + 5*Sqrt[1 - 2*x]*x*Sqrt[3 + 5*x])","B",1
2566,1,209,45,1.2953721,"\int \frac{1}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4 \left(\frac{5 \left(\sqrt{1-2 x}-1\right)^3}{2 \left(\sqrt{3}-\sqrt{5 x+3}\right)^3}+\frac{1-\sqrt{1-2 x}}{\sqrt{3}-\sqrt{5 x+3}}\right)}{-300 x^2-330 \sqrt{1-2 x} x+5 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3} x+110 \sqrt{3} \sqrt{5 x+3} x-30 x-198 \sqrt{1-2 x}+91 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}-55 \sqrt{3} \sqrt{5 x+3}+90}","\frac{2}{11 \sqrt{1-2 x} \sqrt{5 x+3}}-\frac{20 \sqrt{1-2 x}}{121 \sqrt{5 x+3}}",1,"((Sqrt[3] - Sqrt[3 + 5*x])^4*((5*(-1 + Sqrt[1 - 2*x])^3)/(2*(Sqrt[3] - Sqrt[3 + 5*x])^3) + (1 - Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x])))/(90 - 198*Sqrt[1 - 2*x] - 30*x - 330*Sqrt[1 - 2*x]*x - 300*x^2 - 55*Sqrt[3]*Sqrt[3 + 5*x] + 91*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x] + 110*Sqrt[3]*x*Sqrt[3 + 5*x] + 5*Sqrt[3]*Sqrt[1 - 2*x]*x*Sqrt[3 + 5*x])","B",1
2567,0,0,79,14.1266869,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x) (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(3/2)),x]","\int \frac{1}{(1-2 x)^{3/2} (2+3 x) (3+5 x)^{3/2}} \, dx","-\frac{370 \sqrt{1-2 x}}{847 \sqrt{5 x+3}}+\frac{4}{77 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{18 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{7 \sqrt{7}}",1,"Could not integrate","F",-1
2568,0,0,108,17.4044417,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2)),x]","\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^{3/2}} \, dx","-\frac{17735 \sqrt{1-2 x}}{5929 \sqrt{5 x+3}}-\frac{58}{539 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{3}{7 \sqrt{1-2 x} (3 x+2) \sqrt{5 x+3}}+\frac{999 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{49 \sqrt{7}}",1,"Could not integrate","F",-1
2569,0,0,137,22.0472117,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(3/2)),x]","\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{3/2}} \, dx","-\frac{3125575 \sqrt{1-2 x}}{166012 \sqrt{5 x+3}}-\frac{6205}{7546 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{555}{196 \sqrt{1-2 x} (3 x+2) \sqrt{5 x+3}}+\frac{3}{14 \sqrt{1-2 x} (3 x+2)^2 \sqrt{5 x+3}}+\frac{177255 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1372 \sqrt{7}}",1,"Could not integrate","F",-1
2570,0,0,166,28.0354085,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^4 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x)^(3/2)),x]","\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^4 (3+5 x)^{3/2}} \, dx","-\frac{36657025 \sqrt{1-2 x}}{332024 \sqrt{5 x+3}}-\frac{73435}{15092 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{6525}{392 \sqrt{1-2 x} (3 x+2) \sqrt{5 x+3}}+\frac{37}{28 \sqrt{1-2 x} (3 x+2)^2 \sqrt{5 x+3}}+\frac{1}{7 \sqrt{1-2 x} (3 x+2)^3 \sqrt{5 x+3}}+\frac{2079585 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2744 \sqrt{7}}",1,"Could not integrate","F",-1
2571,1,394,142,2.8062955,"\int \frac{(2+3 x)^5}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{-11220130125000 x^8+39368446706250 x^7+2331029143730625 x^6+13117293828573000 x^5-7448506163947275 x^4-44860322060650440 x^3-15569890657969440 x^2+\sqrt{3} \sqrt{5 x+3} \left(11706136200000 x^7-145795283370000 x^6-1800774674842000 x^5-2174242269343100 x^4+8743198810265480 x^3+7021456654632860 x^2-3257398881952336 x-2444748548368632\right)+\sqrt{1-2 x} \left(-63618736500000 x^7-760039416675000 x^6-1342539646057500 x^5+14429580361993500 x^4+21726879697251300 x^3-10581954348896700 x^2+\sqrt{3} \sqrt{5 x+3} \left(780759000000 x^7+74321586450000 x^6+375962010280625 x^5-1053896104594625 x^4-5746045267057600 x^3-326234092432600 x^2+5676794184433480 x+2444748548368632\right)-23159942988284520 x-7334245645105896\right)+15901757080841088 x+7334245645105896}{108000 \left(-96965000 x^4-545924500 x^3+1887183100 x^2+909569320 x-852279560\right) (5 x+3)^{3/2}+108000 \sqrt{1-2 x} \left(8550625 x^4-79738000 x^3-1253327000 x^2+32289760 x+865716488\right) (5 x+3)^{3/2}+\sqrt{3} \left(108000 \sqrt{1-2 x} (5 x+3) \left(-44605000 x^4+788227000 x^3+1591554800 x^2-776116000 x-862591488\right)+108000 (5 x+3) \left(5950000 x^5+532375000 x^4-312727000 x^3-3026461200 x^2-173815520 x+849154560\right)\right)}-\frac{111321 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{2000 \sqrt{10}}","\frac{7 (3 x+2)^4}{11 \sqrt{1-2 x} (5 x+3)^{3/2}}-\frac{107 \sqrt{1-2 x} (3 x+2)^3}{1815 (5 x+3)^{3/2}}-\frac{4487 \sqrt{1-2 x} (3 x+2)^2}{99825 \sqrt{5 x+3}}+\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} (1078860 x+2571547)}{5324000}-\frac{111321 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{4000 \sqrt{10}}",1,"(7334245645105896 + 15901757080841088*x - 15569890657969440*x^2 - 44860322060650440*x^3 - 7448506163947275*x^4 + 13117293828573000*x^5 + 2331029143730625*x^6 + 39368446706250*x^7 - 11220130125000*x^8 + Sqrt[3]*Sqrt[3 + 5*x]*(-2444748548368632 - 3257398881952336*x + 7021456654632860*x^2 + 8743198810265480*x^3 - 2174242269343100*x^4 - 1800774674842000*x^5 - 145795283370000*x^6 + 11706136200000*x^7) + Sqrt[1 - 2*x]*(-7334245645105896 - 23159942988284520*x - 10581954348896700*x^2 + 21726879697251300*x^3 + 14429580361993500*x^4 - 1342539646057500*x^5 - 760039416675000*x^6 - 63618736500000*x^7 + Sqrt[3]*Sqrt[3 + 5*x]*(2444748548368632 + 5676794184433480*x - 326234092432600*x^2 - 5746045267057600*x^3 - 1053896104594625*x^4 + 375962010280625*x^5 + 74321586450000*x^6 + 780759000000*x^7)))/(108000*(3 + 5*x)^(3/2)*(-852279560 + 909569320*x + 1887183100*x^2 - 545924500*x^3 - 96965000*x^4) + 108000*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)*(865716488 + 32289760*x - 1253327000*x^2 - 79738000*x^3 + 8550625*x^4) + Sqrt[3]*(108000*Sqrt[1 - 2*x]*(3 + 5*x)*(-862591488 - 776116000*x + 1591554800*x^2 + 788227000*x^3 - 44605000*x^4) + 108000*(3 + 5*x)*(849154560 - 173815520*x - 3026461200*x^2 - 312727000*x^3 + 532375000*x^4 + 5950000*x^5))) - (111321*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(2000*Sqrt[10])","B",1
2572,1,334,113,2.3306218,"\int \frac{(2+3 x)^4}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{981416250 x^6+75646924875 x^5-178311448575 x^4-824742937755 x^3-223543313775 x^2+\sqrt{3} \sqrt{5 x+3} \left(-5015884500 x^5-17922689400 x^4+160023252785 x^3+123898946215 x^2-88220946088 x-61038004236\right)+\sqrt{1-2 x} \left(-8570306250 x^5+129090740625 x^4+205827811200 x^3-408613760775 x^2+\sqrt{3} \sqrt{5 x+3} \left(639697500 x^5-4097718625 x^4-65909133150 x^3+37181404275 x^2+146798592820 x+61038004236\right)-595462695300 x-183114012708\right)+419729755104 x+183114012708}{2700 \left(-783750 x^3+6045875 x^2+4135120 x-3481060\right) (5 x+3)^{3/2}+2700 \sqrt{1-2 x} \left(-44875 x^3-2976525 x^2+279060 x+3667684\right) (5 x+3)^{3/2}+\sqrt{3} \left(2700 \sqrt{1-2 x} (5 x+3) \left(1146750 x^3+4605150 x^2-3658380 x-3605184\right)+2700 (5 x+3) \left(292500 x^4-939750 x^3-11579850 x^2-848820 x+3418560\right)\right)}-\frac{621 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{50 \sqrt{10}}","\frac{7 (3 x+2)^3}{11 \sqrt{1-2 x} (5 x+3)^{3/2}}-\frac{107 \sqrt{1-2 x} (3 x+2)^2}{1815 (5 x+3)^{3/2}}+\frac{\sqrt{1-2 x} (1051875 x+627641)}{399300 \sqrt{5 x+3}}-\frac{621 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{100 \sqrt{10}}",1,"(183114012708 + 419729755104*x - 223543313775*x^2 - 824742937755*x^3 - 178311448575*x^4 + 75646924875*x^5 + 981416250*x^6 + Sqrt[3]*Sqrt[3 + 5*x]*(-61038004236 - 88220946088*x + 123898946215*x^2 + 160023252785*x^3 - 17922689400*x^4 - 5015884500*x^5) + Sqrt[1 - 2*x]*(-183114012708 - 595462695300*x - 408613760775*x^2 + 205827811200*x^3 + 129090740625*x^4 - 8570306250*x^5 + Sqrt[3]*Sqrt[3 + 5*x]*(61038004236 + 146798592820*x + 37181404275*x^2 - 65909133150*x^3 - 4097718625*x^4 + 639697500*x^5)))/(2700*(3 + 5*x)^(3/2)*(-3481060 + 4135120*x + 6045875*x^2 - 783750*x^3) + 2700*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)*(3667684 + 279060*x - 2976525*x^2 - 44875*x^3) + Sqrt[3]*(2700*Sqrt[1 - 2*x]*(3 + 5*x)*(-3605184 - 3658380*x + 4605150*x^2 + 1146750*x^3) + 2700*(3 + 5*x)*(3418560 - 848820*x - 11579850*x^2 - 939750*x^3 + 292500*x^4))) - (621*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(50*Sqrt[10])","B",1
2573,1,276,84,2.0369827,"\int \frac{(2+3 x)^3}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{15649125 x^4+119100000 x^3-1399485 x^2+\sqrt{3} \sqrt{5 x+3} \left(-21029800 x^3-13272270 x^2+24873508 x+15157626\right)+\sqrt{1-2 x} \left(5766750 x^3+133978350 x^2+\sqrt{3} \sqrt{5 x+3} \left(2127625 x^3-19167025 x^2-37531150 x-15157626\right)+154104390 x+45472878\right)-116131464 x-45472878}{675 \left(-14300 x^2-20790 x+13970\right) (5 x+3)^{3/2}+675 \sqrt{1-2 x} \left(2975 x^2-1820 x-16562\right) (5 x+3)^{3/2}+\sqrt{3} \left(675 \sqrt{1-2 x} (5 x+3) \left(-9900 x^2+19580 x+15312\right)+675 (5 x+3) \left(1000 x^3+42500 x^2+3940 x-12720\right)\right)}-\frac{27}{25} \sqrt{\frac{2}{5}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{7 (3 x+2)^2}{11 \sqrt{1-2 x} (5 x+3)^{3/2}}-\frac{\sqrt{1-2 x} (38770 x+24439)}{99825 (5 x+3)^{3/2}}-\frac{27 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{25 \sqrt{10}}",1,"(-45472878 - 116131464*x - 1399485*x^2 + 119100000*x^3 + 15649125*x^4 + Sqrt[3]*Sqrt[3 + 5*x]*(15157626 + 24873508*x - 13272270*x^2 - 21029800*x^3) + Sqrt[1 - 2*x]*(45472878 + 154104390*x + 133978350*x^2 + 5766750*x^3 + Sqrt[3]*Sqrt[3 + 5*x]*(-15157626 - 37531150*x - 19167025*x^2 + 2127625*x^3)))/(675*(3 + 5*x)^(3/2)*(13970 - 20790*x - 14300*x^2) + 675*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)*(-16562 - 1820*x + 2975*x^2) + Sqrt[3]*(675*Sqrt[1 - 2*x]*(3 + 5*x)*(15312 + 19580*x - 9900*x^2) + 675*(3 + 5*x)*(-12720 + 3940*x + 42500*x^2 + 1000*x^3))) - (27*Sqrt[2/5]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/25","B",1
2574,1,374,67,1.8740114,"\int \frac{(2+3 x)^2}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{\left(\frac{1}{27} \sqrt{1-2 x}-\frac{1}{27}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^8 \left(-\frac{1125 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^6}-\frac{6300 \left(\sqrt{1-2 x}-1\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}-\frac{2570 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4}+\frac{2622 \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}+\frac{1028 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{1008-1008 \sqrt{1-2 x}}{\sqrt{3}-\sqrt{5 x+3}}+72 \sqrt{3}\right)}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(10 \sqrt{3} x+5 \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{5 x+3}+6 \sqrt{3}\right)^3 \left(-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5\right)}","-\frac{4091 \sqrt{1-2 x}}{19965 \sqrt{5 x+3}}-\frac{3679 \sqrt{1-2 x}}{3630 (5 x+3)^{3/2}}+\frac{49}{22 (5 x+3)^{3/2} \sqrt{1-2 x}}",1,"((-1/27 + Sqrt[1 - 2*x]/27)*(Sqrt[3] - Sqrt[3 + 5*x])^8*(72*Sqrt[3] - (1125*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^6 - (6300*(-1 + Sqrt[1 - 2*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^5 - (2570*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^4 + (2622*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (1028*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^2 + (1008 - 1008*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x])))/((-Sqrt[3] + Sqrt[3 + 5*x])*(6*Sqrt[3] + 10*Sqrt[3]*x - 11*Sqrt[3 + 5*x] + 5*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3*(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]))","B",1
2575,1,374,67,1.8518901,"\int \frac{2+3 x}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{\left(\frac{1}{54} \sqrt{1-2 x}-\frac{1}{54}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^8 \left(-\frac{1125 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^6}-\frac{4275 \left(\sqrt{1-2 x}-1\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}-\frac{50 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4}+\frac{3540 \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}+\frac{20 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{684-684 \sqrt{1-2 x}}{\sqrt{3}-\sqrt{5 x+3}}+72 \sqrt{3}\right)}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(10 \sqrt{3} x+5 \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{5 x+3}+6 \sqrt{3}\right)^3 \left(-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5\right)}","-\frac{428 \sqrt{1-2 x}}{3993 \sqrt{5 x+3}}-\frac{107 \sqrt{1-2 x}}{363 (5 x+3)^{3/2}}+\frac{7}{11 (5 x+3)^{3/2} \sqrt{1-2 x}}",1,"((-1/54 + Sqrt[1 - 2*x]/54)*(Sqrt[3] - Sqrt[3 + 5*x])^8*(72*Sqrt[3] - (1125*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^6 - (4275*(-1 + Sqrt[1 - 2*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^5 - (50*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^4 + (3540*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (20*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^2 + (684 - 684*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x])))/((-Sqrt[3] + Sqrt[3 + 5*x])*(6*Sqrt[3] + 10*Sqrt[3]*x - 11*Sqrt[3 + 5*x] + 5*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3*(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]))","B",1
2576,1,374,67,1.8367268,"\int \frac{1}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{\left(\frac{1}{108} \sqrt{1-2 x}-\frac{1}{108}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^8 \left(-\frac{1125 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^6}-\frac{2250 \left(\sqrt{1-2 x}-1\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{850 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4}+\frac{3000 \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}-\frac{340 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{360-360 \sqrt{1-2 x}}{\sqrt{3}-\sqrt{5 x+3}}+72 \sqrt{3}\right)}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(10 \sqrt{3} x+5 \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{5 x+3}+6 \sqrt{3}\right)^3 \left(-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5\right)}","-\frac{160 \sqrt{1-2 x}}{3993 \sqrt{5 x+3}}-\frac{40 \sqrt{1-2 x}}{363 (5 x+3)^{3/2}}+\frac{2}{11 (5 x+3)^{3/2} \sqrt{1-2 x}}",1,"((-1/108 + Sqrt[1 - 2*x]/108)*(Sqrt[3] - Sqrt[3 + 5*x])^8*(72*Sqrt[3] - (1125*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^6 - (2250*(-1 + Sqrt[1 - 2*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^5 + (850*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^4 + (3000*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 - (340*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^2 + (360 - 360*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x])))/((-Sqrt[3] + Sqrt[3 + 5*x])*(6*Sqrt[3] + 10*Sqrt[3]*x - 11*Sqrt[3 + 5*x] + 5*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3*(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]))","B",1
2577,0,0,101,17.6655685,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x) (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(5/2)),x]","\int \frac{1}{(1-2 x)^{3/2} (2+3 x) (3+5 x)^{5/2}} \, dx","\frac{31030 \sqrt{1-2 x}}{27951 \sqrt{5 x+3}}-\frac{410 \sqrt{1-2 x}}{2541 (5 x+3)^{3/2}}+\frac{4}{77 \sqrt{1-2 x} (5 x+3)^{3/2}}-\frac{54 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{7 \sqrt{7}}",1,"Could not integrate","F",-1
2578,0,0,130,21.8491346,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2)),x]","\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^{5/2}} \, dx","\frac{2841815 \sqrt{1-2 x}}{195657 \sqrt{5 x+3}}-\frac{28705 \sqrt{1-2 x}}{17787 (5 x+3)^{3/2}}-\frac{58}{539 \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{3}{7 \sqrt{1-2 x} (3 x+2) (5 x+3)^{3/2}}-\frac{4887 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{49 \sqrt{7}}",1,"Could not integrate","F",-1
2579,0,0,159,28.0358639,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(5/2)),x]","\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{5/2}} \, dx","\frac{707286025 \sqrt{1-2 x}}{5478396 \sqrt{5 x+3}}-\frac{7090175 \sqrt{1-2 x}}{498036 (5 x+3)^{3/2}}-\frac{8515}{7546 \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{765}{196 \sqrt{1-2 x} (3 x+2) (5 x+3)^{3/2}}+\frac{3}{14 \sqrt{1-2 x} (3 x+2)^2 (5 x+3)^{3/2}}-\frac{1215945 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1372 \sqrt{7}}",1,"Could not integrate","F",-1
2580,1,426,142,2.7215076,"\int \frac{(2+3 x)^4 \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-6454890000000 x^8+623812367250000 x^7+5787576988762500 x^6+21579904943342500 x^5-10623188963496125 x^4-439917919390581900 x^3+176156766309626740 x^2+523006768851081784 x-226495493281363152\right)+\sqrt{5 x+3} \left(219415878000000 x^8+411737292450000 x^7-8372302752577500 x^6-76849302388122000 x^5-237776136317665275 x^4+764671028219815860 x^3+237132306829920348 x^2-748483862498082568 x+226495493281363152\right)+\sqrt{3} \left(-29874420000000 x^9-781340377500000 x^8+2182831742025000 x^7+31906352091547500 x^6+262593091241511750 x^5-74580792856634925 x^4-1274682817234495500 x^3+462840489412444692 x^2+\sqrt{1-2 x} \left(-76340880000000 x^8-3033186750000000 x^7-15686919359100000 x^6-47179719349166250 x^5+251190910141417125 x^4+529343455271350500 x^3-688429357184699460 x^2-334457897121820824 x+226495493281363152\right)+559934990768821608 x-226495493281363152\right)}{19200 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(117810000 x^4+3929805000 x^3-3770256600 x^2-11623605840 x+6255778320\right)+\sqrt{1-2 x} \left(19200 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-23051250 x^4-467460000 x^3+4929642000 x^2+5009509440 x-6309526032\right)+19200 (2 x-1) \left(846511875 x^4-2876857500 x^3-32771841300 x^2+464036760 x+18959828096\right)\right)+19200 (2 x-1) \left(49806250 x^5-5100998125 x^4-16263387500 x^3+45507313900 x^2+19543871720 x-18798584960\right)}+\frac{13246251 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{3200 \sqrt{10}}","\frac{\sqrt{5 x+3} (3 x+2)^4}{3 (1-2 x)^{3/2}}-\frac{299 \sqrt{5 x+3} (3 x+2)^3}{66 \sqrt{1-2 x}}-\frac{697}{88} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2-\frac{\sqrt{1-2 x} \sqrt{5 x+3} (7306140 x+17606479)}{70400}+\frac{13246251 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{6400 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-226495493281363152 + 523006768851081784*x + 176156766309626740*x^2 - 439917919390581900*x^3 - 10623188963496125*x^4 + 21579904943342500*x^5 + 5787576988762500*x^6 + 623812367250000*x^7 - 6454890000000*x^8) + Sqrt[3 + 5*x]*(226495493281363152 - 748483862498082568*x + 237132306829920348*x^2 + 764671028219815860*x^3 - 237776136317665275*x^4 - 76849302388122000*x^5 - 8372302752577500*x^6 + 411737292450000*x^7 + 219415878000000*x^8) + Sqrt[3]*(-226495493281363152 + 559934990768821608*x + 462840489412444692*x^2 - 1274682817234495500*x^3 - 74580792856634925*x^4 + 262593091241511750*x^5 + 31906352091547500*x^6 + 2182831742025000*x^7 - 781340377500000*x^8 - 29874420000000*x^9 + Sqrt[1 - 2*x]*(226495493281363152 - 334457897121820824*x - 688429357184699460*x^2 + 529343455271350500*x^3 + 251190910141417125*x^4 - 47179719349166250*x^5 - 15686919359100000*x^6 - 3033186750000000*x^7 - 76340880000000*x^8)))/(19200*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(6255778320 - 11623605840*x - 3770256600*x^2 + 3929805000*x^3 + 117810000*x^4) + 19200*(-1 + 2*x)*(-18798584960 + 19543871720*x + 45507313900*x^2 - 16263387500*x^3 - 5100998125*x^4 + 49806250*x^5) + Sqrt[1 - 2*x]*(19200*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(-6309526032 + 5009509440*x + 4929642000*x^2 - 467460000*x^3 - 23051250*x^4) + 19200*(-1 + 2*x)*(18959828096 + 464036760*x - 32771841300*x^2 - 2876857500*x^3 + 846511875*x^4))) + (13246251*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(3200*Sqrt[10])","B",1
2581,1,366,113,2.3551056,"\int \frac{(2+3 x)^3 \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-7140150000 x^6-152144527500 x^5-105999969500 x^4+9156194664375 x^3-4206241449640 x^2-20827169896436 x+8863913342328\right)+\sqrt{5 x+3} \left(22390830000 x^6+722565805500 x^5+4499422928000 x^4-18648906561725 x^3-12360839882512 x^2+29566620333932 x-8863913342328\right)+\sqrt{3} \left(6569100000 x^7-267068745000 x^6-3072506063500 x^5-192134088150 x^4+40129072899885 x^3-14986899568448 x^2+\sqrt{1-2 x} \left(72972900000 x^6+394459065000 x^5-3386869158750 x^4-14112684037375 x^3+24305840848520 x^2+13475310756996 x-8863913342328\right)-22214761194492 x+8863913342328\right)}{960 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-4504500 x^3+7857850 x^2+48208160 x-25505480\right)+\sqrt{1-2 x} \left(960 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(202750 x^3-9591150 x^2-18970200 x+26251976\right)+960 (2 x-1) \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right)\right)+960 (2 x-1) \left(2203750 x^4+32523625 x^3-153656950 x^2-85860780 x+77141440\right)}+\frac{126513 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{160 \sqrt{10}}","\frac{\sqrt{5 x+3} (3 x+2)^3}{3 (1-2 x)^{3/2}}-\frac{233 \sqrt{5 x+3} (3 x+2)^2}{66 \sqrt{1-2 x}}-\frac{\sqrt{1-2 x} \sqrt{5 x+3} (69780 x+168157)}{3520}+\frac{126513 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{320 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(8863913342328 - 20827169896436*x - 4206241449640*x^2 + 9156194664375*x^3 - 105999969500*x^4 - 152144527500*x^5 - 7140150000*x^6) + Sqrt[3 + 5*x]*(-8863913342328 + 29566620333932*x - 12360839882512*x^2 - 18648906561725*x^3 + 4499422928000*x^4 + 722565805500*x^5 + 22390830000*x^6) + Sqrt[3]*(8863913342328 - 22214761194492*x - 14986899568448*x^2 + 40129072899885*x^3 - 192134088150*x^4 - 3072506063500*x^5 - 267068745000*x^6 + 6569100000*x^7 + Sqrt[1 - 2*x]*(-8863913342328 + 13475310756996*x + 24305840848520*x^2 - 14112684037375*x^3 - 3386869158750*x^4 + 394459065000*x^5 + 72972900000*x^6)))/(960*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(-25505480 + 48208160*x + 7857850*x^2 - 4504500*x^3) + 960*(-1 + 2*x)*(77141440 - 85860780*x - 153656950*x^2 + 32523625*x^3 + 2203750*x^4) + Sqrt[1 - 2*x]*(960*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(26251976 - 18970200*x - 9591150*x^2 + 202750*x^3) + 960*(-1 + 2*x)*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3))) + (126513*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(160*Sqrt[10])","B",1
2582,1,306,94,1.9113514,"\int \frac{(2+3 x)^2 \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-1282500 x^4+41139700 x^3-44309535 x^2-360532838 x+145297284\right)+\sqrt{5 x+3} \left(17671500 x^4-133225400 x^3-232754357 x^2+500744618 x-145297284\right)+\sqrt{3} \left(-3753000 x^5-21023900 x^4+463708610 x^3-213603583 x^2+\sqrt{1-2 x} \left(-2970000 x^4-110365750 x^3+375868075 x^2+241495518 x-145297284\right)-381707298 x+145297284\right)}{24 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(11000 x^2+194700 x-100100\right)+\sqrt{1-2 x} \left(24 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-6950 x^2-60040 x+110468\right)+24 (2 x-1) \left(163625 x^2-33550 x-343904\right)\right)+24 (2 x-1) \left(23750 x^3-445375 x^2-408850 x+312800\right)}+\frac{519 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{4 \sqrt{10}}","-\frac{21 (5 x+3)^{3/2}}{11 \sqrt{1-2 x}}+\frac{49 (5 x+3)^{3/2}}{66 (1-2 x)^{3/2}}-\frac{519}{88} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{519 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{8 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(145297284 - 360532838*x - 44309535*x^2 + 41139700*x^3 - 1282500*x^4) + Sqrt[3 + 5*x]*(-145297284 + 500744618*x - 232754357*x^2 - 133225400*x^3 + 17671500*x^4) + Sqrt[3]*(145297284 - 381707298*x - 213603583*x^2 + 463708610*x^3 - 21023900*x^4 - 3753000*x^5 + Sqrt[1 - 2*x]*(-145297284 + 241495518*x + 375868075*x^2 - 110365750*x^3 - 2970000*x^4)))/(24*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(-100100 + 194700*x + 11000*x^2) + 24*(-1 + 2*x)*(312800 - 408850*x - 445375*x^2 + 23750*x^3) + Sqrt[1 - 2*x]*(24*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(110468 - 60040*x - 6950*x^2) + 24*(-1 + 2*x)*(-343904 - 33550*x + 163625*x^2))) + (519*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(4*Sqrt[10])","B",1
2583,1,246,74,1.5931467,"\int \frac{(2+3 x) \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(5120 x^2+44663 x-13794\right)+\sqrt{5 x+3} \left(16500 x^2-60401 x+13794\right)+\sqrt{3} \left(-17700 x^3+34530 x^2+\sqrt{1-2 x} \left(-41910 x^2-32043 x+13794\right)+47781 x-13794\right)}{6 \left(650 x^2+2155 x-1240\right) (2 x-1)+6 \sqrt{3} (330-660 x) \sqrt{5 x+3} (2 x-1)+\sqrt{1-2 x} \left(6 \sqrt{3} (2 x-1) \sqrt{5 x+3} (90 x-474)+6 (2 x-1) (165 x+1672)\right)}+3 \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{7 (5 x+3)^{3/2}}{33 (1-2 x)^{3/2}}-\frac{3 \sqrt{5 x+3}}{2 \sqrt{1-2 x}}+\frac{3}{2} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-13794 + 44663*x + 5120*x^2) + Sqrt[3 + 5*x]*(13794 - 60401*x + 16500*x^2) + Sqrt[3]*(-13794 + 47781*x + 34530*x^2 - 17700*x^3 + Sqrt[1 - 2*x]*(13794 - 32043*x - 41910*x^2)))/(6*Sqrt[3]*(330 - 660*x)*(-1 + 2*x)*Sqrt[3 + 5*x] + 6*(-1 + 2*x)*(-1240 + 2155*x + 650*x^2) + Sqrt[1 - 2*x]*(6*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(-474 + 90*x) + 6*(-1 + 2*x)*(1672 + 165*x))) + 3*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])]","B",1
2584,1,252,22,1.349719,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/(1 - 2*x)^(5/2),x]","\frac{\left(\frac{1}{6} \sqrt{1-2 x}-\frac{1}{6}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^6 \left(\frac{225 \left(\sqrt{1-2 x}-1\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4}-\frac{30 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}-\frac{56 \left(\sqrt{1-2 x}-1\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{12 \sqrt{3} \sqrt{1-2 x}-12 \sqrt{3}}{\sqrt{3}-\sqrt{5 x+3}}+36\right)}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5\right)^3}","\frac{2 (5 x+3)^{3/2}}{33 (1-2 x)^{3/2}}",1,"((-1/6 + Sqrt[1 - 2*x]/6)*(Sqrt[3] - Sqrt[3 + 5*x])^6*(36 + (225*(-1 + Sqrt[1 - 2*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^4 - (30*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 - (56*(-1 + Sqrt[1 - 2*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^2 + (-12*Sqrt[3] + 12*Sqrt[3]*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x])))/((-Sqrt[3] + Sqrt[3 + 5*x])*(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3)","B",1
2585,1,386,79,1.6001441,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} (2+3 x)} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/((1 - 2*x)^(5/2)*(2 + 3*x)),x]","\frac{3}{49} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{2 \sqrt{5 x+3} \left(-48840 x^2+68101 x-34122\right)+2 \sqrt{1-2 x} \sqrt{5 x+3} \left(3140 x^2-50179 x+34122\right)+\sqrt{3} \left(2 \sqrt{1-2 x} \left(23430 x^2+31119 x-34122\right)+2 \left(21900 x^3+16710 x^2-49041 x+34122\right)\right)}{147 \left(650 x^2+2155 x-1240\right) (2 x-1)+147 \sqrt{3} (330-660 x) \sqrt{5 x+3} (2 x-1)+\sqrt{1-2 x} \left(147 \sqrt{3} (2 x-1) \sqrt{5 x+3} (90 x-474)+147 (2 x-1) (165 x+1672)\right)}","\frac{4 (5 x+3)^{3/2}}{231 (1-2 x)^{3/2}}+\frac{6 \sqrt{5 x+3}}{49 \sqrt{1-2 x}}+\frac{6 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{49 \sqrt{7}}",1,"(2*Sqrt[3 + 5*x]*(-34122 + 68101*x - 48840*x^2) + 2*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(34122 - 50179*x + 3140*x^2) + Sqrt[3]*(2*Sqrt[1 - 2*x]*(-34122 + 31119*x + 23430*x^2) + 2*(34122 - 49041*x + 16710*x^2 + 21900*x^3)))/(147*Sqrt[3]*(330 - 660*x)*(-1 + 2*x)*Sqrt[3 + 5*x] + 147*(-1 + 2*x)*(-1240 + 2155*x + 650*x^2) + Sqrt[1 - 2*x]*(147*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(-474 + 90*x) + 147*(-1 + 2*x)*(1672 + 165*x))) + (3*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ])/49","C",1
2586,1,523,115,2.1337214,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} (2+3 x)^2} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/((1 - 2*x)^(5/2)*(2 + 3*x)^2),x]","\frac{75}{343} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{375}{686} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-29469300 x^4+41606990 x^3+508977522 x^2-44946208 x-190098744\right)+\sqrt{5 x+3} \left(180939000 x^4+447411800 x^3-547675150 x^2-115479320 x+190098744\right)+\sqrt{3} \left(-11197500 x^5-679250500 x^4+5962825 x^3+651248800 x^2+\sqrt{1-2 x} \left(119352750 x^4-477658775 x^3-490788232 x^2+191436828 x+190098744\right)-31011300 x-190098744\right)}{2058 \sqrt{3} \sqrt{5 x+3} \left(6 x^2+x-2\right) \left(11000 x^2+194700 x-100100\right)+\sqrt{1-2 x} \left(2058 \sqrt{3} \sqrt{5 x+3} \left(-6950 x^2-60040 x+110468\right) \left(6 x^2+x-2\right)+2058 \left(163625 x^2-33550 x-343904\right) \left(6 x^2+x-2\right)\right)+2058 \left(6 x^2+x-2\right) \left(23750 x^3-445375 x^2-408850 x+312800\right)}","\frac{850 \sqrt{5 x+3}}{11319 \sqrt{1-2 x}}-\frac{5 \sqrt{5 x+3}}{49 \sqrt{1-2 x} (3 x+2)}+\frac{2 \sqrt{5 x+3}}{21 (1-2 x)^{3/2} (3 x+2)}-\frac{75 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{343 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-190098744 - 44946208*x + 508977522*x^2 + 41606990*x^3 - 29469300*x^4) + Sqrt[3 + 5*x]*(190098744 - 115479320*x - 547675150*x^2 + 447411800*x^3 + 180939000*x^4) + Sqrt[3]*(-190098744 - 31011300*x + 651248800*x^2 + 5962825*x^3 - 679250500*x^4 - 11197500*x^5 + Sqrt[1 - 2*x]*(190098744 + 191436828*x - 490788232*x^2 - 477658775*x^3 + 119352750*x^4)))/(2058*Sqrt[3]*Sqrt[3 + 5*x]*(-2 + x + 6*x^2)*(-100100 + 194700*x + 11000*x^2) + 2058*(-2 + x + 6*x^2)*(312800 - 408850*x - 445375*x^2 + 23750*x^3) + Sqrt[1 - 2*x]*(2058*Sqrt[3]*Sqrt[3 + 5*x]*(110468 - 60040*x - 6950*x^2)*(-2 + x + 6*x^2) + 2058*(-2 + x + 6*x^2)*(-343904 - 33550*x + 163625*x^2))) + (75*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/343 - (375*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/686","C",1
2587,1,599,144,2.5474179,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} (2+3 x)^3} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/((1 - 2*x)^(5/2)*(2 + 3*x)^3),x]","\frac{765 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{1372}-\frac{3825 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2744}+\frac{\sqrt{5 x+3} \left(-32390473500 x^6+162928989300 x^5+610037163505 x^4-74060891410 x^3-469245425660 x^2+23415331984 x+95069049504\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(172602000 x^6-102344695950 x^5-158170189225 x^4+342338338278 x^3+324815183740 x^2-115588723504 x-95069049504\right)+\sqrt{3} \left(7424347500 x^7+31769845500 x^6-600748654325 x^5-688463470830 x^4+453062313510 x^3+478262110640 x^2+\sqrt{1-2 x} \left(24777002250 x^6+266513922675 x^5-13087914840 x^4-629717437778 x^3-257828834120 x^2+194004806424 x+95069049504\right)-101831414904 x-95069049504\right)}{4116 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-4504500 x^3+7857850 x^2+48208160 x-25505480\right) (3 x+2)^2+\sqrt{1-2 x} \left(4116 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(202750 x^3-9591150 x^2-18970200 x+26251976\right) (3 x+2)^2+4116 (2 x-1) \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (3 x+2)^2\right)+4116 (2 x-1) \left(2203750 x^4+32523625 x^3-153656950 x^2-85860780 x+77141440\right) (3 x+2)^2}","\frac{415 \sqrt{5 x+3}}{22638 \sqrt{1-2 x}}+\frac{5 \sqrt{5 x+3}}{196 \sqrt{1-2 x} (3 x+2)}-\frac{\sqrt{5 x+3}}{14 \sqrt{1-2 x} (3 x+2)^2}+\frac{2 \sqrt{5 x+3}}{21 (1-2 x)^{3/2} (3 x+2)^2}-\frac{765 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1372 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(95069049504 + 23415331984*x - 469245425660*x^2 - 74060891410*x^3 + 610037163505*x^4 + 162928989300*x^5 - 32390473500*x^6) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-95069049504 - 115588723504*x + 324815183740*x^2 + 342338338278*x^3 - 158170189225*x^4 - 102344695950*x^5 + 172602000*x^6) + Sqrt[3]*(-95069049504 - 101831414904*x + 478262110640*x^2 + 453062313510*x^3 - 688463470830*x^4 - 600748654325*x^5 + 31769845500*x^6 + 7424347500*x^7 + Sqrt[1 - 2*x]*(95069049504 + 194004806424*x - 257828834120*x^2 - 629717437778*x^3 - 13087914840*x^4 + 266513922675*x^5 + 24777002250*x^6)))/(4116*Sqrt[3]*(-1 + 2*x)*(2 + 3*x)^2*Sqrt[3 + 5*x]*(-25505480 + 48208160*x + 7857850*x^2 - 4504500*x^3) + 4116*(-1 + 2*x)*(2 + 3*x)^2*(77141440 - 85860780*x - 153656950*x^2 + 32523625*x^3 + 2203750*x^4) + Sqrt[1 - 2*x]*(4116*Sqrt[3]*(-1 + 2*x)*(2 + 3*x)^2*Sqrt[3 + 5*x]*(26251976 - 18970200*x - 9591150*x^2 + 202750*x^3) + 4116*(-1 + 2*x)*(2 + 3*x)^2*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3))) + (765*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/1372 - (3825*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2744","C",1
2588,1,659,173,3.0615082,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} (2+3 x)^4} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]","\frac{25365 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{19208}-\frac{126825 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{38416}+\frac{\sqrt{5 x+3} \left(-75592513507500 x^8+2747289483922500 x^7+6843916307465325 x^6-8667265361082570 x^5-15313285705822500 x^4+3135967164388080 x^3+7296101729768016 x^2-275764742598400 x-1036989382209792\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-8677494022500 x^8-702150178320000 x^7+723843881254125 x^6+9969073277935870 x^5+6467827290393244 x^4-7353932932198464 x^3-5437522847275472 x^2+1316288251863040 x+1036989382209792\right)+\sqrt{3} \left(28461103650000 x^9-528771207195000 x^8-8274195056992500 x^7-3864751610309850 x^6+20625718556843820 x^5+14991250864024800 x^4-8993513952767760 x^3-7432482410314416 x^2+\sqrt{1-2 x} \left(206172412627500 x^8+1400528938421250 x^7-6392737151628300 x^6-16250761701401040 x^5-2297327356286424 x^4+12029048339079024 x^3+4706115665934672 x^2-2181131007871200 x-1036989382209792\right)+1140607498606560 x+1036989382209792\right)}{57624 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(117810000 x^4+3929805000 x^3-3770256600 x^2-11623605840 x+6255778320\right) (3 x+2)^3+\sqrt{1-2 x} \left(57624 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-23051250 x^4-467460000 x^3+4929642000 x^2+5009509440 x-6309526032\right) (3 x+2)^3+57624 (2 x-1) \left(846511875 x^4-2876857500 x^3-32771841300 x^2+464036760 x+18959828096\right) (3 x+2)^3\right)+57624 (2 x-1) \left(49806250 x^5-5100998125 x^4-16263387500 x^3+45507313900 x^2+19543871720 x-18798584960\right) (3 x+2)^3}","-\frac{16985 \sqrt{5 x+3}}{316932 \sqrt{1-2 x}}+\frac{605 \sqrt{5 x+3}}{2744 \sqrt{1-2 x} (3 x+2)}-\frac{\sqrt{5 x+3}}{196 \sqrt{1-2 x} (3 x+2)^2}-\frac{3 \sqrt{5 x+3}}{49 \sqrt{1-2 x} (3 x+2)^3}+\frac{2 \sqrt{5 x+3}}{21 (1-2 x)^{3/2} (3 x+2)^3}-\frac{25365 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{19208 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-1036989382209792 - 275764742598400*x + 7296101729768016*x^2 + 3135967164388080*x^3 - 15313285705822500*x^4 - 8667265361082570*x^5 + 6843916307465325*x^6 + 2747289483922500*x^7 - 75592513507500*x^8) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1036989382209792 + 1316288251863040*x - 5437522847275472*x^2 - 7353932932198464*x^3 + 6467827290393244*x^4 + 9969073277935870*x^5 + 723843881254125*x^6 - 702150178320000*x^7 - 8677494022500*x^8) + Sqrt[3]*(1036989382209792 + 1140607498606560*x - 7432482410314416*x^2 - 8993513952767760*x^3 + 14991250864024800*x^4 + 20625718556843820*x^5 - 3864751610309850*x^6 - 8274195056992500*x^7 - 528771207195000*x^8 + 28461103650000*x^9 + Sqrt[1 - 2*x]*(-1036989382209792 - 2181131007871200*x + 4706115665934672*x^2 + 12029048339079024*x^3 - 2297327356286424*x^4 - 16250761701401040*x^5 - 6392737151628300*x^6 + 1400528938421250*x^7 + 206172412627500*x^8)))/(57624*Sqrt[3]*(-1 + 2*x)*(2 + 3*x)^3*Sqrt[3 + 5*x]*(6255778320 - 11623605840*x - 3770256600*x^2 + 3929805000*x^3 + 117810000*x^4) + 57624*(-1 + 2*x)*(2 + 3*x)^3*(-18798584960 + 19543871720*x + 45507313900*x^2 - 16263387500*x^3 - 5100998125*x^4 + 49806250*x^5) + Sqrt[1 - 2*x]*(57624*Sqrt[3]*(-1 + 2*x)*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-6309526032 + 5009509440*x + 4929642000*x^2 - 467460000*x^3 - 23051250*x^4) + 57624*(-1 + 2*x)*(2 + 3*x)^3*(18959828096 + 464036760*x - 32771841300*x^2 - 2876857500*x^3 + 846511875*x^4))) + (25365*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/19208 - (126825*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/38416","C",1
2589,1,486,164,3.3519042,"\int \frac{(2+3 x)^4 (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2),x]","\frac{1626211523 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{51200 \sqrt{10}}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-55710423000000000 x^{10}-1681691472450000000 x^9+19771612916321250000 x^8+187463368320728062500 x^7+628969843415900787500 x^6+2147369781541853536875 x^5-1430934007874013602750 x^4-19435327020921936701500 x^3+7697460184231194593520 x^2+15477706820138079093104 x-6747599928841431894432\right)+\sqrt{5 x+3} \left(416352360600000000 x^{10}+19376639955090000000 x^9+78551623946292750000 x^8+12541769791275037500 x^7-420601180779872785000 x^6-6117224576207960439125 x^5-10692051858247760679250 x^4+31574728909646261863700 x^3+4455510148106905105328 x^2-22216038182060474682128 x+6747599928841431894432\right)+\sqrt{3} \left(29767014000000000 x^{11}-6085618303500000000 x^{10}-62780516481172500000 x^9-124432821869441625000 x^8+155217977965468962500 x^7+2244288517301880321250 x^6+16832015589722456293625 x^5-6048099812013328438150 x^4-44842181935598081370740 x^3+16383257870182203794512 x^2+\sqrt{1-2 x} \left(776533230000000000 x^{10}-1134297499500000000 x^9-96566596300102500000 x^8-505532851104983625000 x^7-1590501702153320618750 x^6-3784492090060181699375 x^5+14135794750604575017750 x^4+20251248999127220664700 x^3-22922199505337317585840 x^2-9855954317189229597744 x+6747599928841431894432\right)+16594285679111625186768 x-6747599928841431894432\right)}{307200 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-19972562500 x^5+158441181250 x^4+1891194668000 x^3-1459455705400 x^2-2800561494720 x+1519466908960\right)+\sqrt{1-2 x} \left(307200 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(382806250 x^5-80547756250 x^4-333372935000 x^3+1857062729800 x^2+1248845958560 x-1523336744224\right)+307200 (2 x-1) \left(26771628125 x^5+1102102787500 x^4-1277247746500 x^3-10194890840200 x^2+44616484880 x+4571572732672\right)\right)+307200 (2 x-1) \left(7164406250 x^6+174195921875 x^5-3695625687500 x^4-5925837277500 x^3+12860921279000 x^2+4621767211760 x-4559963226880\right)}","\frac{(5 x+3)^{3/2} (3 x+2)^4}{3 (1-2 x)^{3/2}}-\frac{123 (5 x+3)^{3/2} (3 x+2)^3}{22 \sqrt{1-2 x}}-\frac{3315}{352} \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^2-\frac{3 \sqrt{1-2 x} (5 x+3)^{3/2} (10798680 x+22868329)}{281600}-\frac{1626211523 \sqrt{1-2 x} \sqrt{5 x+3}}{1126400}+\frac{1626211523 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{102400 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-6747599928841431894432 + 15477706820138079093104*x + 7697460184231194593520*x^2 - 19435327020921936701500*x^3 - 1430934007874013602750*x^4 + 2147369781541853536875*x^5 + 628969843415900787500*x^6 + 187463368320728062500*x^7 + 19771612916321250000*x^8 - 1681691472450000000*x^9 - 55710423000000000*x^10) + Sqrt[3 + 5*x]*(6747599928841431894432 - 22216038182060474682128*x + 4455510148106905105328*x^2 + 31574728909646261863700*x^3 - 10692051858247760679250*x^4 - 6117224576207960439125*x^5 - 420601180779872785000*x^6 + 12541769791275037500*x^7 + 78551623946292750000*x^8 + 19376639955090000000*x^9 + 416352360600000000*x^10) + Sqrt[3]*(-6747599928841431894432 + 16594285679111625186768*x + 16383257870182203794512*x^2 - 44842181935598081370740*x^3 - 6048099812013328438150*x^4 + 16832015589722456293625*x^5 + 2244288517301880321250*x^6 + 155217977965468962500*x^7 - 124432821869441625000*x^8 - 62780516481172500000*x^9 - 6085618303500000000*x^10 + 29767014000000000*x^11 + Sqrt[1 - 2*x]*(6747599928841431894432 - 9855954317189229597744*x - 22922199505337317585840*x^2 + 20251248999127220664700*x^3 + 14135794750604575017750*x^4 - 3784492090060181699375*x^5 - 1590501702153320618750*x^6 - 505532851104983625000*x^7 - 96566596300102500000*x^8 - 1134297499500000000*x^9 + 776533230000000000*x^10)))/(307200*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(1519466908960 - 2800561494720*x - 1459455705400*x^2 + 1891194668000*x^3 + 158441181250*x^4 - 19972562500*x^5) + 307200*(-1 + 2*x)*(-4559963226880 + 4621767211760*x + 12860921279000*x^2 - 5925837277500*x^3 - 3695625687500*x^4 + 174195921875*x^5 + 7164406250*x^6) + Sqrt[1 - 2*x]*(307200*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(-1523336744224 + 1248845958560*x + 1857062729800*x^2 - 333372935000*x^3 - 80547756250*x^4 + 382806250*x^5) + 307200*(-1 + 2*x)*(4571572732672 + 44616484880*x - 10194890840200*x^2 - 1277247746500*x^3 + 1102102787500*x^4 + 26771628125*x^5))) + (1626211523*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(51200*Sqrt[10])","B",1
2590,1,426,135,2.9088795,"\int \frac{(2+3 x)^3 (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-2151630000000 x^8+208152618750000 x^7+1908565335337500 x^6+6963533979317500 x^5-3532481578644875 x^4-141341730861436500 x^3+56237788621986220 x^2+167625015806324872 x-72638408388663216\right)+\sqrt{5 x+3} \left(73138626000000 x^8+129931901550000 x^7-2810160404122500 x^6-24946047626742000 x^5-76475978529433725 x^4+245216500411998060 x^3+76208293230022404 x^2-239935906089064504 x+72638408388663216\right)+\sqrt{3} \left(-9958140000000 x^9-259450978500000 x^8+754427015775000 x^7+10542995238352500 x^6+84682284752414250 x^5-23663805979045275 x^4-408872090123949780 x^3+148186511919688716 x^2+\sqrt{1-2 x} \left(-25446960000000 x^8-1008517554000000 x^7-5125894755300000 x^6-15118174558203750 x^5+80842504454971875 x^4+170195877714426300 x^3-220436993739205980 x^2-107156484018897192 x+72638408388663216\right)+179467374301636824 x-72638408388663216\right)}{3840 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(117810000 x^4+3929805000 x^3-3770256600 x^2-11623605840 x+6255778320\right)+\sqrt{1-2 x} \left(3840 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-23051250 x^4-467460000 x^3+4929642000 x^2+5009509440 x-6309526032\right)+3840 (2 x-1) \left(846511875 x^4-2876857500 x^3-32771841300 x^2+464036760 x+18959828096\right)\right)+3840 (2 x-1) \left(49806250 x^5-5100998125 x^4-16263387500 x^3+45507313900 x^2+19543871720 x-18798584960\right)}+\frac{4246733 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{640 \sqrt{10}}","\frac{(5 x+3)^{3/2} (3 x+2)^3}{3 (1-2 x)^{3/2}}-\frac{101 (5 x+3)^{3/2} (3 x+2)^2}{22 \sqrt{1-2 x}}-\frac{3 \sqrt{1-2 x} (5 x+3)^{3/2} (28200 x+59719)}{3520}-\frac{4246733 \sqrt{1-2 x} \sqrt{5 x+3}}{14080}+\frac{4246733 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{1280 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-72638408388663216 + 167625015806324872*x + 56237788621986220*x^2 - 141341730861436500*x^3 - 3532481578644875*x^4 + 6963533979317500*x^5 + 1908565335337500*x^6 + 208152618750000*x^7 - 2151630000000*x^8) + Sqrt[3 + 5*x]*(72638408388663216 - 239935906089064504*x + 76208293230022404*x^2 + 245216500411998060*x^3 - 76475978529433725*x^4 - 24946047626742000*x^5 - 2810160404122500*x^6 + 129931901550000*x^7 + 73138626000000*x^8) + Sqrt[3]*(-72638408388663216 + 179467374301636824*x + 148186511919688716*x^2 - 408872090123949780*x^3 - 23663805979045275*x^4 + 84682284752414250*x^5 + 10542995238352500*x^6 + 754427015775000*x^7 - 259450978500000*x^8 - 9958140000000*x^9 + Sqrt[1 - 2*x]*(72638408388663216 - 107156484018897192*x - 220436993739205980*x^2 + 170195877714426300*x^3 + 80842504454971875*x^4 - 15118174558203750*x^5 - 5125894755300000*x^6 - 1008517554000000*x^7 - 25446960000000*x^8)))/(3840*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(6255778320 - 11623605840*x - 3770256600*x^2 + 3929805000*x^3 + 117810000*x^4) + 3840*(-1 + 2*x)*(-18798584960 + 19543871720*x + 45507313900*x^2 - 16263387500*x^3 - 5100998125*x^4 + 49806250*x^5) + Sqrt[1 - 2*x]*(3840*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(-6309526032 + 5009509440*x + 4929642000*x^2 - 467460000*x^3 - 23051250*x^4) + 3840*(-1 + 2*x)*(18959828096 + 464036760*x - 32771841300*x^2 - 2876857500*x^3 + 846511875*x^4))) + (4246733*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(640*Sqrt[10])","B",1
2591,1,366,116,2.4337883,"\int \frac{(2+3 x)^2 (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-2380050000 x^6-50397502500 x^5-31819620500 x^4+2966611661925 x^3-1337417169400 x^2-6710355621596 x+2860872600168\right)+\sqrt{5 x+3} \left(7463610000 x^6+239860120500 x^5+1463918825600 x^4-6011257278455 x^3-4000241658160 x^2+9530717003588 x-2860872600168\right)+\sqrt{3} \left(2189700000 x^7-89314875000 x^6-1005986414500 x^5-79772808450 x^4+12947900310855 x^3-4815823839680 x^2+\sqrt{1-2 x} \left(24324300000 x^6+128243115000 x^5-1101656036250 x^4-4578511832125 x^3+7814487453080 x^2+4337601058956 x-2860872600168\right)-7157962440948 x+2860872600168\right)}{192 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-4504500 x^3+7857850 x^2+48208160 x-25505480\right)+\sqrt{1-2 x} \left(192 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(202750 x^3-9591150 x^2-18970200 x+26251976\right)+192 (2 x-1) \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right)\right)+192 (2 x-1) \left(2203750 x^4+32523625 x^3-153656950 x^2-85860780 x+77141440\right)}+\frac{40787 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{32 \sqrt{10}}","-\frac{938 (5 x+3)^{5/2}}{363 \sqrt{1-2 x}}+\frac{49 (5 x+3)^{5/2}}{66 (1-2 x)^{3/2}}-\frac{40787 \sqrt{1-2 x} (5 x+3)^{3/2}}{5808}-\frac{40787}{704} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{40787 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{64 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(2860872600168 - 6710355621596*x - 1337417169400*x^2 + 2966611661925*x^3 - 31819620500*x^4 - 50397502500*x^5 - 2380050000*x^6) + Sqrt[3 + 5*x]*(-2860872600168 + 9530717003588*x - 4000241658160*x^2 - 6011257278455*x^3 + 1463918825600*x^4 + 239860120500*x^5 + 7463610000*x^6) + Sqrt[3]*(2860872600168 - 7157962440948*x - 4815823839680*x^2 + 12947900310855*x^3 - 79772808450*x^4 - 1005986414500*x^5 - 89314875000*x^6 + 2189700000*x^7 + Sqrt[1 - 2*x]*(-2860872600168 + 4337601058956*x + 7814487453080*x^2 - 4578511832125*x^3 - 1101656036250*x^4 + 128243115000*x^5 + 24324300000*x^6)))/(192*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(-25505480 + 48208160*x + 7857850*x^2 - 4504500*x^3) + 192*(-1 + 2*x)*(77141440 - 85860780*x - 153656950*x^2 + 32523625*x^3 + 2203750*x^4) + Sqrt[1 - 2*x]*(192*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(26251976 - 18970200*x - 9591150*x^2 + 202750*x^3) + 192*(-1 + 2*x)*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3))) + (40787*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(32*Sqrt[10])","B",1
2592,1,308,96,1.9878455,"\int \frac{(2+3 x) (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-2137500 x^4+67892300 x^3-69070965 x^2-586400482 x+237711276\right)+\sqrt{5 x+3} \left(29452500 x^4-216271000 x^3-382301095 x^2+815449294 x-237711276\right)+\sqrt{3} \left(-6255000 x^5-35840500 x^4+756340150 x^3-344268725 x^2+\sqrt{1-2 x} \left(-4950000 x^4-182575250 x^3+608248025 x^2+391789002 x-237711276\right)-620837814 x+237711276\right)}{24 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(11000 x^2+194700 x-100100\right)+\sqrt{1-2 x} \left(24 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-6950 x^2-60040 x+110468\right)+24 (2 x-1) \left(163625 x^2-33550 x-343904\right)\right)+24 (2 x-1) \left(23750 x^3-445375 x^2-408850 x+312800\right)}+\frac{169}{4} \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{7 (5 x+3)^{5/2}}{33 (1-2 x)^{3/2}}-\frac{169 (5 x+3)^{3/2}}{66 \sqrt{1-2 x}}-\frac{845}{88} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{169}{8} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(237711276 - 586400482*x - 69070965*x^2 + 67892300*x^3 - 2137500*x^4) + Sqrt[3 + 5*x]*(-237711276 + 815449294*x - 382301095*x^2 - 216271000*x^3 + 29452500*x^4) + Sqrt[3]*(237711276 - 620837814*x - 344268725*x^2 + 756340150*x^3 - 35840500*x^4 - 6255000*x^5 + Sqrt[1 - 2*x]*(-237711276 + 391789002*x + 608248025*x^2 - 182575250*x^3 - 4950000*x^4)))/(24*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(-100100 + 194700*x + 11000*x^2) + 24*(-1 + 2*x)*(312800 - 408850*x - 445375*x^2 + 23750*x^3) + Sqrt[1 - 2*x]*(24*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(110468 - 60040*x - 6950*x^2) + 24*(-1 + 2*x)*(-343904 - 33550*x + 163625*x^2))) + (169*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/4","B",1
2593,1,252,74,1.5846526,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/(1 - 2*x)^(5/2),x]","\frac{-11 \sqrt{5 x+3} \left(-2640 x^2+9185 x-2178\right)-11 \sqrt{1-2 x} \sqrt{5 x+3} \left(-740 x^2-6791 x+2178\right)+\sqrt{3} \left(-11 \sqrt{1-2 x} \left(6270 x^2+4851 x-2178\right)-11 \left(2700 x^3-5010 x^2-7245 x+2178\right)\right)}{6 \left(650 x^2+2155 x-1240\right) (2 x-1)+6 \sqrt{3} (330-660 x) \sqrt{5 x+3} (2 x-1)+\sqrt{1-2 x} \left(6 \sqrt{3} (2 x-1) \sqrt{5 x+3} (90 x-474)+6 (2 x-1) (165 x+1672)\right)}+5 \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{(5 x+3)^{3/2}}{3 (1-2 x)^{3/2}}-\frac{5 \sqrt{5 x+3}}{2 \sqrt{1-2 x}}+\frac{5}{2} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"(-11*Sqrt[3 + 5*x]*(-2178 + 9185*x - 2640*x^2) - 11*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(2178 - 6791*x - 740*x^2) + Sqrt[3]*(-11*Sqrt[1 - 2*x]*(-2178 + 4851*x + 6270*x^2) - 11*(2178 - 7245*x - 5010*x^2 + 2700*x^3)))/(6*Sqrt[3]*(330 - 660*x)*(-1 + 2*x)*Sqrt[3 + 5*x] + 6*(-1 + 2*x)*(-1240 + 2155*x + 650*x^2) + Sqrt[1 - 2*x]*(6*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(-474 + 90*x) + 6*(-1 + 2*x)*(1672 + 165*x))) + 5*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])]","B",1
2594,1,386,79,1.6337339,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)),x]","\frac{22 \sqrt{5 x+3} \left(-7095 x^2-22 x-4356\right)+22 \sqrt{1-2 x} \sqrt{5 x+3} \left(2095 x^2+58 x+4356\right)+\sqrt{3} \left(22 \sqrt{1-2 x} \left(-5610 x^2-1188 x-4356\right)+22 \left(450 x^3+13080 x^2+1152 x+4356\right)\right)}{147 \left(650 x^2+2155 x-1240\right) (2 x-1)+147 \sqrt{3} (330-660 x) \sqrt{5 x+3} (2 x-1)+\sqrt{1-2 x} \left(147 \sqrt{3} (2 x-1) \sqrt{5 x+3} (90 x-474)+147 (2 x-1) (165 x+1672)\right)}-\frac{1}{49} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]","\frac{2 (5 x+3)^{3/2}}{21 (1-2 x)^{3/2}}-\frac{2 \sqrt{5 x+3}}{49 \sqrt{1-2 x}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{49 \sqrt{7}}",1,"(22*Sqrt[3 + 5*x]*(-4356 - 22*x - 7095*x^2) + 22*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(4356 + 58*x + 2095*x^2) + Sqrt[3]*(22*Sqrt[1 - 2*x]*(-4356 - 1188*x - 5610*x^2) + 22*(4356 + 1152*x + 13080*x^2 + 450*x^3)))/(147*Sqrt[3]*(330 - 660*x)*(-1 + 2*x)*Sqrt[3 + 5*x] + 147*(-1 + 2*x)*(-1240 + 2155*x + 650*x^2) + Sqrt[1 - 2*x]*(147*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(-474 + 90*x) + 147*(-1 + 2*x)*(1672 + 165*x))) - RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ]/49","C",1
2595,1,523,122,2.1920104,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^2),x]","-\frac{95}{343} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{475}{686} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-84354900 x^4-311289430 x^3+1307201946 x^2-52214944 x-707335992\right)+\sqrt{5 x+3} \left(324687000 x^4+1796408900 x^3-1317563830 x^2-556148120 x+707335992\right)+\sqrt{3} \left(32362500 x^5-1856267500 x^4-888803375 x^3+1854116080 x^2+\sqrt{1-2 x} \left(502680750 x^4-686073575 x^3-1376559976 x^2+601886604 x+707335992\right)+6476460 x-707335992\right)}{2058 \sqrt{3} \sqrt{5 x+3} \left(6 x^2+x-2\right) \left(11000 x^2+194700 x-100100\right)+\sqrt{1-2 x} \left(2058 \sqrt{3} \sqrt{5 x+3} \left(-6950 x^2-60040 x+110468\right) \left(6 x^2+x-2\right)+2058 \left(163625 x^2-33550 x-343904\right) \left(6 x^2+x-2\right)\right)+2058 \left(6 x^2+x-2\right) \left(23750 x^3-445375 x^2-408850 x+312800\right)}","\frac{4 (5 x+3)^{5/2}}{231 (1-2 x)^{3/2} (3 x+2)}+\frac{190 (5 x+3)^{3/2}}{1617 \sqrt{1-2 x} (3 x+2)}+\frac{95 \sqrt{1-2 x} \sqrt{5 x+3}}{3773 (3 x+2)}+\frac{95 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{343 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-707335992 - 52214944*x + 1307201946*x^2 - 311289430*x^3 - 84354900*x^4) + Sqrt[3 + 5*x]*(707335992 - 556148120*x - 1317563830*x^2 + 1796408900*x^3 + 324687000*x^4) + Sqrt[3]*(-707335992 + 6476460*x + 1854116080*x^2 - 888803375*x^3 - 1856267500*x^4 + 32362500*x^5 + Sqrt[1 - 2*x]*(707335992 + 601886604*x - 1376559976*x^2 - 686073575*x^3 + 502680750*x^4)))/(2058*Sqrt[3]*Sqrt[3 + 5*x]*(-2 + x + 6*x^2)*(-100100 + 194700*x + 11000*x^2) + 2058*(-2 + x + 6*x^2)*(312800 - 408850*x - 445375*x^2 + 23750*x^3) + Sqrt[1 - 2*x]*(2058*Sqrt[3]*Sqrt[3 + 5*x]*(110468 - 60040*x - 6950*x^2)*(-2 + x + 6*x^2) + 2058*(-2 + x + 6*x^2)*(-343904 - 33550*x + 163625*x^2))) - (95*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/343 + (475*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/686","C",1
2596,1,599,144,2.6066336,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^3),x]","\frac{5}{28} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{25}{56} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-1567219500 x^6+18510284100 x^5+31437783685 x^4-16151927770 x^3-24014043020 x^2+4928171248 x+5612305248\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-99801000 x^6-7671592650 x^5-1718346325 x^4+25649889486 x^3+12724010380 x^2-10269498448 x-5612305248\right)+\sqrt{3} \left(539482500 x^7-2895391500 x^6-45766573775 x^5-25665789210 x^4+36857866470 x^3+21446784080 x^2+\sqrt{1-2 x} \left(2586795750 x^6+14513377725 x^5-14525552580 x^4-38506365986 x^3-5781270440 x^2+14870794488 x+5612305248\right)-9529467288 x-5612305248\right)}{84 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-4504500 x^3+7857850 x^2+48208160 x-25505480\right) (3 x+2)^2+\sqrt{1-2 x} \left(84 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(202750 x^3-9591150 x^2-18970200 x+26251976\right) (3 x+2)^2+84 (2 x-1) \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (3 x+2)^2\right)+84 (2 x-1) \left(2203750 x^4+32523625 x^3-153656950 x^2-85860780 x+77141440\right) (3 x+2)^2}","\frac{5 \sqrt{5 x+3}}{42 \sqrt{1-2 x}}-\frac{5 \sqrt{5 x+3}}{28 \sqrt{1-2 x} (3 x+2)}-\frac{3 \sqrt{5 x+3}}{14 \sqrt{1-2 x} (3 x+2)^2}+\frac{11 \sqrt{5 x+3}}{21 (1-2 x)^{3/2} (3 x+2)^2}-\frac{5 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{28 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(5612305248 + 4928171248*x - 24014043020*x^2 - 16151927770*x^3 + 31437783685*x^4 + 18510284100*x^5 - 1567219500*x^6) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-5612305248 - 10269498448*x + 12724010380*x^2 + 25649889486*x^3 - 1718346325*x^4 - 7671592650*x^5 - 99801000*x^6) + Sqrt[3]*(-5612305248 - 9529467288*x + 21446784080*x^2 + 36857866470*x^3 - 25665789210*x^4 - 45766573775*x^5 - 2895391500*x^6 + 539482500*x^7 + Sqrt[1 - 2*x]*(5612305248 + 14870794488*x - 5781270440*x^2 - 38506365986*x^3 - 14525552580*x^4 + 14513377725*x^5 + 2586795750*x^6)))/(84*Sqrt[3]*(-1 + 2*x)*(2 + 3*x)^2*Sqrt[3 + 5*x]*(-25505480 + 48208160*x + 7857850*x^2 - 4504500*x^3) + 84*(-1 + 2*x)*(2 + 3*x)^2*(77141440 - 85860780*x - 153656950*x^2 + 32523625*x^3 + 2203750*x^4) + Sqrt[1 - 2*x]*(84*Sqrt[3]*(-1 + 2*x)*(2 + 3*x)^2*Sqrt[3 + 5*x]*(26251976 - 18970200*x - 9591150*x^2 + 202750*x^3) + 84*(-1 + 2*x)*(2 + 3*x)^2*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3))) + (5*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/28 - (25*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/56","C",1
2597,1,659,173,3.3417248,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]","\frac{9395 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{19208}-\frac{46975 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{38416}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-12759042442500 x^8+181386619852500 x^7+3558004371799875 x^6+3850277052714610 x^5-5515065553009868 x^4-7872913812549792 x^3-238108311056816 x^2+2484954642085120 x+727983338328576\right)+\sqrt{5 x+3} \left(173569029727500 x^8+1335275492017500 x^7-4664150454741525 x^6-12558980288080710 x^5-1711972365797100 x^4+8832380838153840 x^3+2985504340225968 x^2-1767878756934400 x-727983338328576\right)+\sqrt{3} \left(-10877342175000 x^9-1039563955710000 x^8-75027895008750 x^7+13084652760277950 x^6+16007192048447460 x^5-4332971351970000 x^4-11748012389034480 x^3-1751606806089168 x^2+\sqrt{1-2 x} \left(65883342195000 x^8-1795388337517500 x^7-6988629206552400 x^6-1495844760057120 x^5+11516559939212328 x^4+8737767031883472 x^3-1591238523205584 x^2-3089493486525600 x-727983338328576\right)+2372417601374880 x+727983338328576\right)}{57624 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(117810000 x^4+3929805000 x^3-3770256600 x^2-11623605840 x+6255778320\right) (3 x+2)^3+\sqrt{1-2 x} \left(57624 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-23051250 x^4-467460000 x^3+4929642000 x^2+5009509440 x-6309526032\right) (3 x+2)^3+57624 (2 x-1) \left(846511875 x^4-2876857500 x^3-32771841300 x^2+464036760 x+18959828096\right) (3 x+2)^3\right)+57624 (2 x-1) \left(49806250 x^5-5100998125 x^4-16263387500 x^3+45507313900 x^2+19543871720 x-18798584960\right) (3 x+2)^3}","\frac{465 \sqrt{5 x+3}}{9604 \sqrt{1-2 x}}-\frac{85 \sqrt{5 x+3}}{2744 \sqrt{1-2 x} (3 x+2)}-\frac{23 \sqrt{5 x+3}}{196 \sqrt{1-2 x} (3 x+2)^2}-\frac{32 \sqrt{5 x+3}}{147 \sqrt{1-2 x} (3 x+2)^3}+\frac{11 \sqrt{5 x+3}}{21 (1-2 x)^{3/2} (3 x+2)^3}-\frac{9395 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{19208 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(727983338328576 + 2484954642085120*x - 238108311056816*x^2 - 7872913812549792*x^3 - 5515065553009868*x^4 + 3850277052714610*x^5 + 3558004371799875*x^6 + 181386619852500*x^7 - 12759042442500*x^8) + Sqrt[3 + 5*x]*(-727983338328576 - 1767878756934400*x + 2985504340225968*x^2 + 8832380838153840*x^3 - 1711972365797100*x^4 - 12558980288080710*x^5 - 4664150454741525*x^6 + 1335275492017500*x^7 + 173569029727500*x^8) + Sqrt[3]*(727983338328576 + 2372417601374880*x - 1751606806089168*x^2 - 11748012389034480*x^3 - 4332971351970000*x^4 + 16007192048447460*x^5 + 13084652760277950*x^6 - 75027895008750*x^7 - 1039563955710000*x^8 - 10877342175000*x^9 + Sqrt[1 - 2*x]*(-727983338328576 - 3089493486525600*x - 1591238523205584*x^2 + 8737767031883472*x^3 + 11516559939212328*x^4 - 1495844760057120*x^5 - 6988629206552400*x^6 - 1795388337517500*x^7 + 65883342195000*x^8)))/(57624*Sqrt[3]*(-1 + 2*x)*(2 + 3*x)^3*Sqrt[3 + 5*x]*(6255778320 - 11623605840*x - 3770256600*x^2 + 3929805000*x^3 + 117810000*x^4) + 57624*(-1 + 2*x)*(2 + 3*x)^3*(-18798584960 + 19543871720*x + 45507313900*x^2 - 16263387500*x^3 - 5100998125*x^4 + 49806250*x^5) + Sqrt[1 - 2*x]*(57624*Sqrt[3]*(-1 + 2*x)*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-6309526032 + 5009509440*x + 4929642000*x^2 - 467460000*x^3 - 23051250*x^4) + 57624*(-1 + 2*x)*(2 + 3*x)^3*(18959828096 + 464036760*x - 32771841300*x^2 - 2876857500*x^3 + 846511875*x^4))) + (9395*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/19208 - (46975*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/38416","C",1
2598,1,546,186,9.5883257,"\int \frac{(2+3 x)^4 (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2),x]","\frac{46975917593 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{204800 \sqrt{10}}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-9831332880000000000 x^{12}+4319728335693000000000 x^{11}+48372084693483750000000 x^{10}-4848866666329173750000 x^9-1014313663201248642187500 x^8-3907993849287837630662500 x^7-9519088004061952714880625 x^6-36575078865857844793423750 x^5+23968001463526733853210600 x^4+179703052363685069266473600 x^3-72377501591689176361067600 x^2-108023407482526134114571168 x+47211838021200407195957184\right)+\sqrt{5 x+3} \left(841648023216000000000 x^{12}-6840255040047000000000 x^{11}-232564364047333890000000 x^{10}-1077427037972256864750000 x^9-1846654392538605372937500 x^8-1139752138285238790455000 x^7-199202249399955786441875 x^6+88648685207537505211959050 x^5+94726012465864887636844920 x^4-282848902657990951336035520 x^3-12176898529998326354662256 x^2+155215760192387961204509536 x-47211838021200407195957184\right)+\sqrt{3} \left(-91518037920000000000 x^{13}-2921933866734000000000 x^{12}+81582261450043500000000 x^{11}+765314586481543582500000 x^{10}+2278971991871195411625000 x^9+2607668266859215918037500 x^8+2972722979546008579338750 x^7-30070863852262336962110625 x^6-202058852861537806359578650 x^5+78592463423277436797717480 x^4+360336930242028824395293600 x^3-133533476929811239083455824 x^2-115874383014168598437045216 x+\sqrt{1-2 x} \left(-467059919040000000000 x^{12}-25277823262692000000000 x^{11}-93275047731036600000000 x^{10}+373841161490723355000000 x^9+3006762264906563913750000 x^8+8461371025912592081043750 x^7+27493497180732827099838125 x^6+53225135320425713300405750 x^5-154170464758067188890630600 x^4-170369205187429301099103200 x^3+178762737632728195786737040 x^2+68682030304306771347106848 x-47211838021200407195957184\right)+47211838021200407195957184\right)}{1228800 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(750803625000 x^6+35513254562500 x^5-109502972507500 x^4-708907607408000 x^3+497360177600000 x^2+676171499523520 x-368089927965760\right)+\sqrt{1-2 x} \left(1228800 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-73558093750 x^6-1883570925000 x^5+78913493662500 x^4+156226252528000 x^3-608403813276000 x^2-305295290167680 x+368368556104768\right)+1228800 (2 x-1) \left(3382394640625 x^6-46839566881250 x^5-721064958542500 x^4+436816644264000 x^3+2966115478898000 x^2-4019894758880 x-1105183793314304\right)\right)+1228800 (2 x-1) \left(79019843750 x^7-35211607984375 x^6-171264310843750 x^5+1776876552657500 x^4+1879341347316000 x^3-3558908295114800 x^2-1109383428656160 x+1104347908897280\right)}","\frac{(5 x+3)^{5/2} (3 x+2)^4}{3 (1-2 x)^{3/2}}-\frac{439 (5 x+3)^{5/2} (3 x+2)^3}{66 \sqrt{1-2 x}}-\frac{4819}{440} \sqrt{1-2 x} (5 x+3)^{5/2} (3 x+2)^2-\frac{4270537963 \sqrt{1-2 x} (5 x+3)^{3/2}}{3379200}-\frac{\sqrt{1-2 x} (5 x+3)^{5/2} (18161940 x+36714139)}{140800}-\frac{4270537963 \sqrt{1-2 x} \sqrt{5 x+3}}{409600}+\frac{46975917593 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{409600 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(47211838021200407195957184 - 108023407482526134114571168*x - 72377501591689176361067600*x^2 + 179703052363685069266473600*x^3 + 23968001463526733853210600*x^4 - 36575078865857844793423750*x^5 - 9519088004061952714880625*x^6 - 3907993849287837630662500*x^7 - 1014313663201248642187500*x^8 - 4848866666329173750000*x^9 + 48372084693483750000000*x^10 + 4319728335693000000000*x^11 - 9831332880000000000*x^12) + Sqrt[3 + 5*x]*(-47211838021200407195957184 + 155215760192387961204509536*x - 12176898529998326354662256*x^2 - 282848902657990951336035520*x^3 + 94726012465864887636844920*x^4 + 88648685207537505211959050*x^5 - 199202249399955786441875*x^6 - 1139752138285238790455000*x^7 - 1846654392538605372937500*x^8 - 1077427037972256864750000*x^9 - 232564364047333890000000*x^10 - 6840255040047000000000*x^11 + 841648023216000000000*x^12) + Sqrt[3]*(47211838021200407195957184 - 115874383014168598437045216*x - 133533476929811239083455824*x^2 + 360336930242028824395293600*x^3 + 78592463423277436797717480*x^4 - 202058852861537806359578650*x^5 - 30070863852262336962110625*x^6 + 2972722979546008579338750*x^7 + 2607668266859215918037500*x^8 + 2278971991871195411625000*x^9 + 765314586481543582500000*x^10 + 81582261450043500000000*x^11 - 2921933866734000000000*x^12 - 91518037920000000000*x^13 + Sqrt[1 - 2*x]*(-47211838021200407195957184 + 68682030304306771347106848*x + 178762737632728195786737040*x^2 - 170369205187429301099103200*x^3 - 154170464758067188890630600*x^4 + 53225135320425713300405750*x^5 + 27493497180732827099838125*x^6 + 8461371025912592081043750*x^7 + 3006762264906563913750000*x^8 + 373841161490723355000000*x^9 - 93275047731036600000000*x^10 - 25277823262692000000000*x^11 - 467059919040000000000*x^12)))/(1228800*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(-368089927965760 + 676171499523520*x + 497360177600000*x^2 - 708907607408000*x^3 - 109502972507500*x^4 + 35513254562500*x^5 + 750803625000*x^6) + 1228800*(-1 + 2*x)*(1104347908897280 - 1109383428656160*x - 3558908295114800*x^2 + 1879341347316000*x^3 + 1776876552657500*x^4 - 171264310843750*x^5 - 35211607984375*x^6 + 79019843750*x^7) + Sqrt[1 - 2*x]*(1228800*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(368368556104768 - 305295290167680*x - 608403813276000*x^2 + 156226252528000*x^3 + 78913493662500*x^4 - 1883570925000*x^5 - 73558093750*x^6) + 1228800*(-1 + 2*x)*(-1105183793314304 - 4019894758880*x + 2966115478898000*x^2 + 436816644264000*x^3 - 721064958542500*x^4 - 46839566881250*x^5 + 3382394640625*x^6))) + (46975917593*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(204800*Sqrt[10])","B",1
2599,1,486,157,3.6356865,"\int \frac{(2+3 x)^3 (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^3*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2),x]","\frac{103884253 \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)}{2048 \sqrt{10}}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-3714028200000000 x^{10}-111782628990000000 x^9+1328007996726750000 x^8+12379655563317937500 x^7+40845824389178012500 x^6+137263244244540259125 x^5-92336928383873426050 x^4-1242817100892597046340 x^3+491021351311029618960 x^2+988600712376536350864 x-431089600770701861472\right)+\sqrt{5 x+3} \left(27756824040000000 x^{10}+1289308723758000000 x^9+5122436997798450000 x^8+384093698582962500 x^7-28400653390097615000 x^6-392543330289172984075 x^5-683671508644090222190 x^4+2017543688532785179756 x^3+285175964049546839632 x^2-1419097562076504056560 x+431089600770701861472\right)+\sqrt{3} \left(1984467600000000 x^{11}-405884284020000000 x^{10}-4149270052699500000 x^9-7931257437469575000 x^8+11196573951572237500 x^7+146128936242166550750 x^6+1077601951660179871975 x^5-385963673382787023290 x^4-2865524019277230095116 x^3+1045969663317900763568 x^2+\sqrt{1-2 x} \left(51768882000000000 x^{10}-80221511700000000 x^9-6430143770473500000 x^8-33148389135060375000 x^7-102464941981473981250 x^6-241342387179305520625 x^5+904779451142718302250 x^4+1295488160451221230340 x^3-1463499381101160384080 x^2-629439155573607716304 x+431089600770701861472\right)+1059936005273575422000 x-431089600770701861472\right)}{12288 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-19972562500 x^5+158441181250 x^4+1891194668000 x^3-1459455705400 x^2-2800561494720 x+1519466908960\right)+\sqrt{1-2 x} \left(12288 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(382806250 x^5-80547756250 x^4-333372935000 x^3+1857062729800 x^2+1248845958560 x-1523336744224\right)+12288 (2 x-1) \left(26771628125 x^5+1102102787500 x^4-1277247746500 x^3-10194890840200 x^2+44616484880 x+4571572732672\right)\right)+12288 (2 x-1) \left(7164406250 x^6+174195921875 x^5-3695625687500 x^4-5925837277500 x^3+12860921279000 x^2+4621767211760 x-4559963226880\right)}","\frac{(5 x+3)^{5/2} (3 x+2)^3}{3 (1-2 x)^{3/2}}-\frac{373 (5 x+3)^{5/2} (3 x+2)^2}{66 \sqrt{1-2 x}}-\frac{9444023 \sqrt{1-2 x} (5 x+3)^{3/2}}{33792}-\frac{\sqrt{1-2 x} (5 x+3)^{5/2} (40164 x+81191)}{1408}-\frac{9444023 \sqrt{1-2 x} \sqrt{5 x+3}}{4096}+\frac{103884253 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{4096 \sqrt{10}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-431089600770701861472 + 988600712376536350864*x + 491021351311029618960*x^2 - 1242817100892597046340*x^3 - 92336928383873426050*x^4 + 137263244244540259125*x^5 + 40845824389178012500*x^6 + 12379655563317937500*x^7 + 1328007996726750000*x^8 - 111782628990000000*x^9 - 3714028200000000*x^10) + Sqrt[3 + 5*x]*(431089600770701861472 - 1419097562076504056560*x + 285175964049546839632*x^2 + 2017543688532785179756*x^3 - 683671508644090222190*x^4 - 392543330289172984075*x^5 - 28400653390097615000*x^6 + 384093698582962500*x^7 + 5122436997798450000*x^8 + 1289308723758000000*x^9 + 27756824040000000*x^10) + Sqrt[3]*(-431089600770701861472 + 1059936005273575422000*x + 1045969663317900763568*x^2 - 2865524019277230095116*x^3 - 385963673382787023290*x^4 + 1077601951660179871975*x^5 + 146128936242166550750*x^6 + 11196573951572237500*x^7 - 7931257437469575000*x^8 - 4149270052699500000*x^9 - 405884284020000000*x^10 + 1984467600000000*x^11 + Sqrt[1 - 2*x]*(431089600770701861472 - 629439155573607716304*x - 1463499381101160384080*x^2 + 1295488160451221230340*x^3 + 904779451142718302250*x^4 - 241342387179305520625*x^5 - 102464941981473981250*x^6 - 33148389135060375000*x^7 - 6430143770473500000*x^8 - 80221511700000000*x^9 + 51768882000000000*x^10)))/(12288*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(1519466908960 - 2800561494720*x - 1459455705400*x^2 + 1891194668000*x^3 + 158441181250*x^4 - 19972562500*x^5) + 12288*(-1 + 2*x)*(-4559963226880 + 4621767211760*x + 12860921279000*x^2 - 5925837277500*x^3 - 3695625687500*x^4 + 174195921875*x^5 + 7164406250*x^6) + Sqrt[1 - 2*x]*(12288*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(-1523336744224 + 1248845958560*x + 1857062729800*x^2 - 333372935000*x^3 - 80547756250*x^4 + 382806250*x^5) + 12288*(-1 + 2*x)*(4571572732672 + 44616484880*x - 10194890840200*x^2 - 1277247746500*x^3 + 1102102787500*x^4 + 26771628125*x^5))) + (103884253*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/(2048*Sqrt[10])","B",1
2600,1,428,140,2.9484296,"\int \frac{(2+3 x)^2 (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^2*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-717210000000 x^8+69455927250000 x^7+629303217562500 x^6+2245736372462500 x^5-1175176457448125 x^4-45401226932546700 x^3+17951963758771060 x^2+53712941299599928 x-23289694570566864\right)+\sqrt{5 x+3} \left(24379542000000 x^8+40872679650000 x^7-942859347457500 x^6-8095668770970000 x^5-24587774545978875 x^4+78621378572885940 x^3+24484195548061788 x^2-76897352245137160 x+23289694570566864\right)+\sqrt{3} \left(-3319380000000 x^9-86151721500000 x^8+260370225225000 x^7+3482796605467500 x^6+27300900388263750 x^5-7511701157959725 x^4-131123004406407180 x^3+47435291153377812 x^2+\sqrt{1-2 x} \left(-8482320000000 x^8-335324286000000 x^7-1674385227900000 x^6-4841112540206250 x^5+26014663830313125 x^4+54706976652982500 x^3-70571512677471300 x^2-34325267162669208 x+23289694570566864\right)+57509678108206440 x-23289694570566864\right)}{768 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(117810000 x^4+3929805000 x^3-3770256600 x^2-11623605840 x+6255778320\right)+\sqrt{1-2 x} \left(768 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-23051250 x^4-467460000 x^3+4929642000 x^2+5009509440 x-6309526032\right)+768 (2 x-1) \left(846511875 x^4-2876857500 x^3-32771841300 x^2+464036760 x+18959828096\right)\right)+768 (2 x-1) \left(49806250 x^5-5100998125 x^4-16263387500 x^3+45507313900 x^2+19543871720 x-18798584960\right)}+\frac{272239}{128} \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","-\frac{1183 (5 x+3)^{7/2}}{363 \sqrt{1-2 x}}+\frac{49 (5 x+3)^{7/2}}{66 (1-2 x)^{3/2}}-\frac{24749 \sqrt{1-2 x} (5 x+3)^{5/2}}{2904}-\frac{123745 \sqrt{1-2 x} (5 x+3)^{3/2}}{2112}-\frac{123745}{256} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{272239}{256} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-23289694570566864 + 53712941299599928*x + 17951963758771060*x^2 - 45401226932546700*x^3 - 1175176457448125*x^4 + 2245736372462500*x^5 + 629303217562500*x^6 + 69455927250000*x^7 - 717210000000*x^8) + Sqrt[3 + 5*x]*(23289694570566864 - 76897352245137160*x + 24484195548061788*x^2 + 78621378572885940*x^3 - 24587774545978875*x^4 - 8095668770970000*x^5 - 942859347457500*x^6 + 40872679650000*x^7 + 24379542000000*x^8) + Sqrt[3]*(-23289694570566864 + 57509678108206440*x + 47435291153377812*x^2 - 131123004406407180*x^3 - 7511701157959725*x^4 + 27300900388263750*x^5 + 3482796605467500*x^6 + 260370225225000*x^7 - 86151721500000*x^8 - 3319380000000*x^9 + Sqrt[1 - 2*x]*(23289694570566864 - 34325267162669208*x - 70571512677471300*x^2 + 54706976652982500*x^3 + 26014663830313125*x^4 - 4841112540206250*x^5 - 1674385227900000*x^6 - 335324286000000*x^7 - 8482320000000*x^8)))/(768*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(6255778320 - 11623605840*x - 3770256600*x^2 + 3929805000*x^3 + 117810000*x^4) + 768*(-1 + 2*x)*(-18798584960 + 19543871720*x + 45507313900*x^2 - 16263387500*x^3 - 5100998125*x^4 + 49806250*x^5) + Sqrt[1 - 2*x]*(768*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(-6309526032 + 5009509440*x + 4929642000*x^2 - 467460000*x^3 - 23051250*x^4) + 768*(-1 + 2*x)*(18959828096 + 464036760*x - 32771841300*x^2 - 2876857500*x^3 + 846511875*x^4))) + (272239*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/128","B",1
2601,1,368,118,2.4848147,"\int \frac{(2+3 x) (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-3966750000 x^6-83466937500 x^5-47103491500 x^4+4804438315275 x^3-2125926398600 x^2-10806574550116 x+4614717990168\right)+\sqrt{5 x+3} \left(12439350000 x^6+398108287500 x^5+2380248640000 x^4-9685923096025 x^3-6469854852560 x^2+15355437036412 x-4614717990168\right)+\sqrt{3} \left(3649500000 x^7-149344725000 x^6-1646509257500 x^5-156205830750 x^4+20881836345225 x^3-7735076276800 x^2+\sqrt{1-2 x} \left(40540500000 x^6+208333125000 x^5-1791695655750 x^4-7423764823475 x^3+12558517851880 x^2+6979355287476 x-4614717990168\right)-11528217773772 x+4614717990168\right)}{192 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-4504500 x^3+7857850 x^2+48208160 x-25505480\right)+\sqrt{1-2 x} \left(192 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(202750 x^3-9591150 x^2-18970200 x+26251976\right)+192 (2 x-1) \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right)\right)+192 (2 x-1) \left(2203750 x^4+32523625 x^3-153656950 x^2-85860780 x+77141440\right)}+\frac{13145}{32} \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{7 (5 x+3)^{7/2}}{33 (1-2 x)^{3/2}}-\frac{239 (5 x+3)^{5/2}}{66 \sqrt{1-2 x}}-\frac{5975}{528} \sqrt{1-2 x} (5 x+3)^{3/2}-\frac{5975}{64} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{13145}{64} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(4614717990168 - 10806574550116*x - 2125926398600*x^2 + 4804438315275*x^3 - 47103491500*x^4 - 83466937500*x^5 - 3966750000*x^6) + Sqrt[3 + 5*x]*(-4614717990168 + 15355437036412*x - 6469854852560*x^2 - 9685923096025*x^3 + 2380248640000*x^4 + 398108287500*x^5 + 12439350000*x^6) + Sqrt[3]*(4614717990168 - 11528217773772*x - 7735076276800*x^2 + 20881836345225*x^3 - 156205830750*x^4 - 1646509257500*x^5 - 149344725000*x^6 + 3649500000*x^7 + Sqrt[1 - 2*x]*(-4614717990168 + 6979355287476*x + 12558517851880*x^2 - 7423764823475*x^3 - 1791695655750*x^4 + 208333125000*x^5 + 40540500000*x^6)))/(192*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(-25505480 + 48208160*x + 7857850*x^2 - 4504500*x^3) + 192*(-1 + 2*x)*(77141440 - 85860780*x - 153656950*x^2 + 32523625*x^3 + 2203750*x^4) + Sqrt[1 - 2*x]*(192*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(26251976 - 18970200*x - 9591150*x^2 + 202750*x^3) + 192*(-1 + 2*x)*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3))) + (13145*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/32","B",1
2602,1,308,96,1.924219,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/(1 - 2*x)^(5/2),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-3562500 x^4+112020100 x^3-107488455 x^2-953137334 x+388455012\right)+\sqrt{5 x+3} \left(49087500 x^4-350933000 x^3-627298925 x^2+1326926810 x-388455012\right)+\sqrt{3} \left(-10425000 x^5-61017500 x^4+1232887250 x^3-554544775 x^2+\sqrt{1-2 x} \left(-8250000 x^4-301831750 x^3+983734675 x^2+635318574 x-388455012\right)-1009108050 x+388455012\right)}{24 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(11000 x^2+194700 x-100100\right)+\sqrt{1-2 x} \left(24 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-6950 x^2-60040 x+110468\right)+24 (2 x-1) \left(163625 x^2-33550 x-343904\right)\right)+24 (2 x-1) \left(23750 x^3-445375 x^2-408850 x+312800\right)}+\frac{275}{4} \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{(5 x+3)^{5/2}}{3 (1-2 x)^{3/2}}-\frac{25 (5 x+3)^{3/2}}{6 \sqrt{1-2 x}}-\frac{125}{8} \sqrt{1-2 x} \sqrt{5 x+3}+\frac{275}{8} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(388455012 - 953137334*x - 107488455*x^2 + 112020100*x^3 - 3562500*x^4) + Sqrt[3 + 5*x]*(-388455012 + 1326926810*x - 627298925*x^2 - 350933000*x^3 + 49087500*x^4) + Sqrt[3]*(388455012 - 1009108050*x - 554544775*x^2 + 1232887250*x^3 - 61017500*x^4 - 10425000*x^5 + Sqrt[1 - 2*x]*(-388455012 + 635318574*x + 983734675*x^2 - 301831750*x^3 - 8250000*x^4)))/(24*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(-100100 + 194700*x + 11000*x^2) + 24*(-1 + 2*x)*(312800 - 408850*x - 445375*x^2 + 23750*x^3) + Sqrt[1 - 2*x]*(24*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(110468 - 60040*x - 6950*x^2) + 24*(-1 + 2*x)*(-343904 - 33550*x + 163625*x^2))) + (275*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/4","B",1
2603,1,446,108,1.9862454,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)),x]","\frac{1}{147} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{-5 \text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)+2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{50 \text{$\#$1}^3-45 \sqrt{3} \text{$\#$1}^2+14 \text{$\#$1}+6 \sqrt{3}}\&\right]+\frac{-121 \sqrt{5 x+3} \left(-20460 x^2+68189 x-16698\right)-121 \sqrt{1-2 x} \sqrt{5 x+3} \left(-5240 x^2-50411 x+16698\right)+\sqrt{3} \left(-121 \sqrt{1-2 x} \left(45870 x^2+35871 x-16698\right)-121 \left(20100 x^3-35610 x^2-53649 x+16698\right)\right)}{294 \left(650 x^2+2155 x-1240\right) (2 x-1)+294 \sqrt{3} (330-660 x) \sqrt{5 x+3} (2 x-1)+\sqrt{1-2 x} \left(294 \sqrt{3} (2 x-1) \sqrt{5 x+3} (90 x-474)+294 (2 x-1) (165 x+1672)\right)}+\frac{25}{3} \sqrt{\frac{5}{2}} \tan ^{-1}\left(\frac{\sqrt{5} \sqrt{1-2 x}-\sqrt{5}}{\sqrt{6}-\sqrt{2} \sqrt{5 x+3}}\right)","\frac{11 (5 x+3)^{3/2}}{21 (1-2 x)^{3/2}}-\frac{407 \sqrt{5 x+3}}{98 \sqrt{1-2 x}}+\frac{25}{6} \sqrt{\frac{5}{2}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)+\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{147 \sqrt{7}}",1,"(-121*Sqrt[3 + 5*x]*(-16698 + 68189*x - 20460*x^2) - 121*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(16698 - 50411*x - 5240*x^2) + Sqrt[3]*(-121*Sqrt[1 - 2*x]*(-16698 + 35871*x + 45870*x^2) - 121*(16698 - 53649*x - 35610*x^2 + 20100*x^3)))/(294*Sqrt[3]*(330 - 660*x)*(-1 + 2*x)*Sqrt[3 + 5*x] + 294*(-1 + 2*x)*(-1240 + 2155*x + 650*x^2) + Sqrt[1 - 2*x]*(294*Sqrt[3]*(-1 + 2*x)*Sqrt[3 + 5*x]*(-474 + 90*x) + 294*(-1 + 2*x)*(1672 + 165*x))) + (25*Sqrt[5/2]*ArcTan[(-Sqrt[5] + Sqrt[5]*Sqrt[1 - 2*x])/(Sqrt[6] - Sqrt[2]*Sqrt[3 + 5*x])])/3 + RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-2*Log[Sqrt[3] - Sqrt[3 + 5*x]] + 2*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1] - 5*Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 + 5*Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(6*Sqrt[3] + 14*#1 - 45*Sqrt[3]*#1^2 + 50*#1^3) & ]/147","C",1
2604,1,523,122,2.1850712,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^2} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^2),x]","\frac{55}{343} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]-\frac{275}{686} \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]+\frac{\sqrt{5 x+3} \left(-881116500 x^4+1526884700 x^3+1272929570 x^2+1190850760 x+846484056\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-8803200 x^4-1990333990 x^3-2032892622 x^2-1750991392 x-846484056\right)+\sqrt{3} \left(308377500 x^5+457389500 x^4-2218916675 x^3-2361981920 x^2+\sqrt{1-2 x} \left(814959750 x^4+3339157525 x^3+3473653832 x^2+2341319772 x+846484056\right)-1781179140 x-846484056\right)}{2058 \sqrt{3} \sqrt{5 x+3} \left(6 x^2+x-2\right) \left(11000 x^2+194700 x-100100\right)+\sqrt{1-2 x} \left(2058 \sqrt{3} \sqrt{5 x+3} \left(-6950 x^2-60040 x+110468\right) \left(6 x^2+x-2\right)+2058 \left(163625 x^2-33550 x-343904\right) \left(6 x^2+x-2\right)\right)+2058 \left(6 x^2+x-2\right) \left(23750 x^3-445375 x^2-408850 x+312800\right)}","\frac{2 (5 x+3)^{5/2}}{21 (1-2 x)^{3/2} (3 x+2)}-\frac{10 (5 x+3)^{3/2}}{147 \sqrt{1-2 x} (3 x+2)}-\frac{5 \sqrt{1-2 x} \sqrt{5 x+3}}{343 (3 x+2)}-\frac{55 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{343 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(846484056 + 1190850760*x + 1272929570*x^2 + 1526884700*x^3 - 881116500*x^4) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-846484056 - 1750991392*x - 2032892622*x^2 - 1990333990*x^3 - 8803200*x^4) + Sqrt[3]*(-846484056 - 1781179140*x - 2361981920*x^2 - 2218916675*x^3 + 457389500*x^4 + 308377500*x^5 + Sqrt[1 - 2*x]*(846484056 + 2341319772*x + 3473653832*x^2 + 3339157525*x^3 + 814959750*x^4)))/(2058*Sqrt[3]*Sqrt[3 + 5*x]*(-2 + x + 6*x^2)*(-100100 + 194700*x + 11000*x^2) + 2058*(-2 + x + 6*x^2)*(312800 - 408850*x - 445375*x^2 + 23750*x^3) + Sqrt[1 - 2*x]*(2058*Sqrt[3]*Sqrt[3 + 5*x]*(110468 - 60040*x - 6950*x^2)*(-2 + x + 6*x^2) + 2058*(-2 + x + 6*x^2)*(-343904 - 33550*x + 163625*x^2))) + (55*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/343 - (275*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/686","C",1
2605,1,599,151,2.6170331,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^3} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^3),x]","-\frac{715 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{1372}+\frac{3575 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2744}+\frac{\sqrt{5 x+3} \left(-373925821500 x^6+1308163556700 x^5+5122457146345 x^4-814050164290 x^3-3743296448540 x^2+652466677456 x+1049501081376\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(7121088000 x^6-1030591475550 x^5-1764740859025 x^4+2277572255382 x^3+1870783036060 x^2-1658886728176 x-1049501081376\right)+\sqrt{3} \left(77161477500 x^7+556761289500 x^6-5207564553425 x^5-5512989039270 x^4+3916692341190 x^3+3506535773360 x^2+\sqrt{1-2 x} \left(220217555250 x^6+2775713284575 x^5+572464625040 x^4-4129824140882 x^3-807362110280 x^2+2521447837656 x+1049501081376\right)-1515027786936 x-1049501081376\right)}{4116 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-4504500 x^3+7857850 x^2+48208160 x-25505480\right) (3 x+2)^2+\sqrt{1-2 x} \left(4116 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(202750 x^3-9591150 x^2-18970200 x+26251976\right) (3 x+2)^2+4116 (2 x-1) \left(3455375 x^3+90602050 x^2-4344340 x-79380928\right) (3 x+2)^2\right)+4116 (2 x-1) \left(2203750 x^4+32523625 x^3-153656950 x^2-85860780 x+77141440\right) (3 x+2)^2}","\frac{4 (5 x+3)^{7/2}}{231 (1-2 x)^{3/2} (3 x+2)^2}+\frac{26 (5 x+3)^{5/2}}{231 \sqrt{1-2 x} (3 x+2)^2}+\frac{65 \sqrt{1-2 x} (5 x+3)^{3/2}}{3234 (3 x+2)^2}+\frac{65 \sqrt{1-2 x} \sqrt{5 x+3}}{1372 (3 x+2)}+\frac{715 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1372 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(1049501081376 + 652466677456*x - 3743296448540*x^2 - 814050164290*x^3 + 5122457146345*x^4 + 1308163556700*x^5 - 373925821500*x^6) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-1049501081376 - 1658886728176*x + 1870783036060*x^2 + 2277572255382*x^3 - 1764740859025*x^4 - 1030591475550*x^5 + 7121088000*x^6) + Sqrt[3]*(-1049501081376 - 1515027786936*x + 3506535773360*x^2 + 3916692341190*x^3 - 5512989039270*x^4 - 5207564553425*x^5 + 556761289500*x^6 + 77161477500*x^7 + Sqrt[1 - 2*x]*(1049501081376 + 2521447837656*x - 807362110280*x^2 - 4129824140882*x^3 + 572464625040*x^4 + 2775713284575*x^5 + 220217555250*x^6)))/(4116*Sqrt[3]*(-1 + 2*x)*(2 + 3*x)^2*Sqrt[3 + 5*x]*(-25505480 + 48208160*x + 7857850*x^2 - 4504500*x^3) + 4116*(-1 + 2*x)*(2 + 3*x)^2*(77141440 - 85860780*x - 153656950*x^2 + 32523625*x^3 + 2203750*x^4) + Sqrt[1 - 2*x]*(4116*Sqrt[3]*(-1 + 2*x)*(2 + 3*x)^2*Sqrt[3 + 5*x]*(26251976 - 18970200*x - 9591150*x^2 + 202750*x^3) + 4116*(-1 + 2*x)*(2 + 3*x)^2*(-79380928 - 4344340*x + 90602050*x^2 + 3455375*x^3))) - (715*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/1372 + (3575*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2744","C",1
2606,1,659,173,3.3169598,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^4} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]","\frac{2585 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{19208}-\frac{12925 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{38416}+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(-49548147952500 x^8+654267700620000 x^7+13225284614774625 x^6+13370404384733830 x^5-18356165136055604 x^4-25071088522949376 x^3+763563994467952 x^2+9549166367887360 x+2863038949993728\right)+\sqrt{5 x+3} \left(661167002182500 x^8+5146859490052500 x^7-16995990677284575 x^6-42230770629980130 x^5-4006642087658100 x^4+30324235036558320 x^3+9815710608693264 x^2-6727105425990400 x-2863038949993728\right)+\sqrt{3} \left(-39858087150000 x^9-4003290042255000 x^8-367917740932500 x^7+45820805356036350 x^6+52624428649144380 x^5-16879327244935200 x^4-40077976658153040 x^3-5157274625226864 x^2+\sqrt{1-2 x} \left(266571939397500 x^8-6742050137583750 x^7-25288495975244700 x^6-5389264146681360 x^5+37737827178342984 x^4+26953937423818416 x^3-7765775617015152 x^2-11927090347048800 x-2863038949993728\right)+9105029405151840 x+2863038949993728\right)}{57624 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(117810000 x^4+3929805000 x^3-3770256600 x^2-11623605840 x+6255778320\right) (3 x+2)^3+\sqrt{1-2 x} \left(57624 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-23051250 x^4-467460000 x^3+4929642000 x^2+5009509440 x-6309526032\right) (3 x+2)^3+57624 (2 x-1) \left(846511875 x^4-2876857500 x^3-32771841300 x^2+464036760 x+18959828096\right) (3 x+2)^3\right)+57624 (2 x-1) \left(49806250 x^5-5100998125 x^4-16263387500 x^3+45507313900 x^2+19543871720 x-18798584960\right) (3 x+2)^3}","\frac{11 (5 x+3)^{3/2}}{21 (1-2 x)^{3/2} (3 x+2)^3}+\frac{15755 \sqrt{5 x+3}}{86436 \sqrt{1-2 x}}-\frac{2365 \sqrt{5 x+3}}{8232 \sqrt{1-2 x} (3 x+2)}-\frac{187 \sqrt{5 x+3}}{588 \sqrt{1-2 x} (3 x+2)^2}+\frac{32 \sqrt{5 x+3}}{441 \sqrt{1-2 x} (3 x+2)^3}-\frac{2585 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{19208 \sqrt{7}}",1,"(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(2863038949993728 + 9549166367887360*x + 763563994467952*x^2 - 25071088522949376*x^3 - 18356165136055604*x^4 + 13370404384733830*x^5 + 13225284614774625*x^6 + 654267700620000*x^7 - 49548147952500*x^8) + Sqrt[3 + 5*x]*(-2863038949993728 - 6727105425990400*x + 9815710608693264*x^2 + 30324235036558320*x^3 - 4006642087658100*x^4 - 42230770629980130*x^5 - 16995990677284575*x^6 + 5146859490052500*x^7 + 661167002182500*x^8) + Sqrt[3]*(2863038949993728 + 9105029405151840*x - 5157274625226864*x^2 - 40077976658153040*x^3 - 16879327244935200*x^4 + 52624428649144380*x^5 + 45820805356036350*x^6 - 367917740932500*x^7 - 4003290042255000*x^8 - 39858087150000*x^9 + Sqrt[1 - 2*x]*(-2863038949993728 - 11927090347048800*x - 7765775617015152*x^2 + 26953937423818416*x^3 + 37737827178342984*x^4 - 5389264146681360*x^5 - 25288495975244700*x^6 - 6742050137583750*x^7 + 266571939397500*x^8)))/(57624*Sqrt[3]*(-1 + 2*x)*(2 + 3*x)^3*Sqrt[3 + 5*x]*(6255778320 - 11623605840*x - 3770256600*x^2 + 3929805000*x^3 + 117810000*x^4) + 57624*(-1 + 2*x)*(2 + 3*x)^3*(-18798584960 + 19543871720*x + 45507313900*x^2 - 16263387500*x^3 - 5100998125*x^4 + 49806250*x^5) + Sqrt[1 - 2*x]*(57624*Sqrt[3]*(-1 + 2*x)*(2 + 3*x)^3*Sqrt[3 + 5*x]*(-6309526032 + 5009509440*x + 4929642000*x^2 - 467460000*x^3 - 23051250*x^4) + 57624*(-1 + 2*x)*(2 + 3*x)^3*(18959828096 + 464036760*x - 32771841300*x^2 - 2876857500*x^3 + 846511875*x^4))) + (2585*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/19208 - (12925*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/38416","C",1
2607,1,719,202,3.6981598,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^5} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^5),x]","\frac{547745 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)-\log \left(\sqrt{3}-\sqrt{5 x+3}\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{1075648}-\frac{2738725 \text{RootSum}\left[-25 \text{$\#$1}^4+30 \sqrt{3} \text{$\#$1}^3-14 \text{$\#$1}^2-12 \sqrt{3} \text{$\#$1}-4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{3}-\sqrt{5 x+3}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1} \left(-\sqrt{5 x+3}\right)+\sqrt{3} \text{$\#$1}+\sqrt{1-2 x}-1\right)}{-50 \text{$\#$1}^3+45 \sqrt{3} \text{$\#$1}^2-14 \text{$\#$1}-6 \sqrt{3}}\&\right]}{2151296}+\frac{\sqrt{5 x+3} \left(-551212185515062500 x^{10}+62265552358624312500 x^9+228238181737298184375 x^8-287029354803879979500 x^7-1203281433730097836400 x^6-640272642882685406440 x^5+588169750631436260320 x^4+559687098092125445728 x^3-5552184899359723328 x^2-113866733431027937536 x-26537546056472225280\right)+\sqrt{1-2 x} \sqrt{5 x+3} \left(-128395118388375000 x^{10}-11356929983172093750 x^9+29468126219193365625 x^8+411500300006076199500 x^7+589603141370278632400 x^6-193837555512923714760 x^5-784988927537404715680 x^4-328945416700108080800 x^3+157302296938717419840 x^2+140261131169737250560 x+26537546056472225280\right)+\sqrt{3} \left(297508861785937500 x^{11}-12442498144667437500 x^{10}-216695020155511640625 x^9-195106492264107930000 x^8+1031668228114028449750 x^7+1804431191716765838600 x^6+322634778299433011440 x^5-1031839020269372771360 x^4-587166723056999663488 x^3+91359641915330148608 x^2+\sqrt{1-2 x} \left(3048645042094781250 x^{10}+22791965707394296875 x^9-225538242006235826250 x^8-849529868089719654750 x^7-595242212824244068600 x^6+720064834793494636160 x^5+1081524037335963307680 x^4+239027297264027729600 x^3-265085819359862272640 x^2-162356486839714104960 x-26537546056472225280\right)+135962089101004791936 x+26537546056472225280\right)}{3226944 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(-19972562500 x^5+158441181250 x^4+1891194668000 x^3-1459455705400 x^2-2800561494720 x+1519466908960\right) (3 x+2)^4+\sqrt{1-2 x} \left(3226944 \sqrt{3} (2 x-1) \sqrt{5 x+3} \left(382806250 x^5-80547756250 x^4-333372935000 x^3+1857062729800 x^2+1248845958560 x-1523336744224\right) (3 x+2)^4+3226944 (2 x-1) \left(26771628125 x^5+1102102787500 x^4-1277247746500 x^3-10194890840200 x^2+44616484880 x+4571572732672\right) (3 x+2)^4\right)+3226944 (2 x-1) \left(7164406250 x^6+174195921875 x^5-3695625687500 x^4-5925837277500 x^3+12860921279000 x^2+4621767211760 x-4559963226880\right) (3 x+2)^4}","\frac{11 (5 x+3)^{3/2}}{21 (1-2 x)^{3/2} (3 x+2)^4}+\frac{139745 \sqrt{5 x+3}}{1613472 \sqrt{1-2 x}}-\frac{14135 \sqrt{5 x+3}}{153664 \sqrt{1-2 x} (3 x+2)}-\frac{2013 \sqrt{5 x+3}}{10976 \sqrt{1-2 x} (3 x+2)^2}-\frac{2717 \sqrt{5 x+3}}{8232 \sqrt{1-2 x} (3 x+2)^3}+\frac{43 \sqrt{5 x+3}}{588 \sqrt{1-2 x} (3 x+2)^4}-\frac{547745 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1075648 \sqrt{7}}",1,"(Sqrt[3 + 5*x]*(-26537546056472225280 - 113866733431027937536*x - 5552184899359723328*x^2 + 559687098092125445728*x^3 + 588169750631436260320*x^4 - 640272642882685406440*x^5 - 1203281433730097836400*x^6 - 287029354803879979500*x^7 + 228238181737298184375*x^8 + 62265552358624312500*x^9 - 551212185515062500*x^10) + Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(26537546056472225280 + 140261131169737250560*x + 157302296938717419840*x^2 - 328945416700108080800*x^3 - 784988927537404715680*x^4 - 193837555512923714760*x^5 + 589603141370278632400*x^6 + 411500300006076199500*x^7 + 29468126219193365625*x^8 - 11356929983172093750*x^9 - 128395118388375000*x^10) + Sqrt[3]*(26537546056472225280 + 135962089101004791936*x + 91359641915330148608*x^2 - 587166723056999663488*x^3 - 1031839020269372771360*x^4 + 322634778299433011440*x^5 + 1804431191716765838600*x^6 + 1031668228114028449750*x^7 - 195106492264107930000*x^8 - 216695020155511640625*x^9 - 12442498144667437500*x^10 + 297508861785937500*x^11 + Sqrt[1 - 2*x]*(-26537546056472225280 - 162356486839714104960*x - 265085819359862272640*x^2 + 239027297264027729600*x^3 + 1081524037335963307680*x^4 + 720064834793494636160*x^5 - 595242212824244068600*x^6 - 849529868089719654750*x^7 - 225538242006235826250*x^8 + 22791965707394296875*x^9 + 3048645042094781250*x^10)))/(3226944*Sqrt[3]*(-1 + 2*x)*(2 + 3*x)^4*Sqrt[3 + 5*x]*(1519466908960 - 2800561494720*x - 1459455705400*x^2 + 1891194668000*x^3 + 158441181250*x^4 - 19972562500*x^5) + 3226944*(-1 + 2*x)*(2 + 3*x)^4*(-4559963226880 + 4621767211760*x + 12860921279000*x^2 - 5925837277500*x^3 - 3695625687500*x^4 + 174195921875*x^5 + 7164406250*x^6) + Sqrt[1 - 2*x]*(3226944*Sqrt[3]*(-1 + 2*x)*(2 + 3*x)^4*Sqrt[3 + 5*x]*(-1523336744224 + 1248845958560*x + 1857062729800*x^2 - 333372935000*x^3 - 80547756250*x^4 + 382806250*x^5) + 3226944*(-1 + 2*x)*(2 + 3*x)^4*(4571572732672 + 44616484880*x - 10194890840200*x^2 - 1277247746500*x^3 + 1102102787500*x^4 + 26771628125*x^5))) + (547745*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (-Log[Sqrt[3] - Sqrt[3 + 5*x]] + Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1])/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/1075648 - (2738725*RootSum[-4 - 12*Sqrt[3]*#1 - 14*#1^2 + 30*Sqrt[3]*#1^3 - 25*#1^4 & , (Log[Sqrt[3] - Sqrt[3 + 5*x]]*#1^2 - Log[-1 + Sqrt[1 - 2*x] + Sqrt[3]*#1 - Sqrt[3 + 5*x]*#1]*#1^2)/(-6*Sqrt[3] - 14*#1 + 45*Sqrt[3]*#1^2 - 50*#1^3) & ])/2151296","C",1
2608,0,0,142,26.6290742,"\int \frac{(2+3 x)^5}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","\int \frac{(2+3 x)^5}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","\frac{7 \sqrt{5 x+3} (3 x+2)^4}{33 (1-2 x)^{3/2}}-\frac{2051 \sqrt{5 x+3} (3 x+2)^3}{726 \sqrt{1-2 x}}-\frac{23909 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2}{4840}-\frac{\sqrt{1-2 x} \sqrt{5 x+3} (50124540 x+120791143)}{774400}+\frac{8261577 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{6400 \sqrt{10}}",1,"Could not integrate","F",-1
2609,0,0,113,21.4955001,"\int \frac{(2+3 x)^4}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","\int \frac{(2+3 x)^4}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","\frac{7 \sqrt{5 x+3} (3 x+2)^3}{33 (1-2 x)^{3/2}}-\frac{1589 \sqrt{5 x+3} (3 x+2)^2}{726 \sqrt{1-2 x}}-\frac{\sqrt{1-2 x} \sqrt{5 x+3} (2380020 x+5735477)}{193600}+\frac{392283 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{1600 \sqrt{10}}",1,"Could not integrate","F",-1
2610,0,0,84,18.163271,"\int \frac{(2+3 x)^3}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","\int \frac{(2+3 x)^3}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","\frac{7 \sqrt{5 x+3} (3 x+2)^2}{33 (1-2 x)^{3/2}}-\frac{(95621-33462 x) \sqrt{5 x+3}}{14520 \sqrt{1-2 x}}+\frac{1593 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{40 \sqrt{10}}",1,"Could not integrate","F",-1
2611,0,0,72,13.6987826,"\int \frac{(2+3 x)^2}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","\int \frac{(2+3 x)^2}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","-\frac{448 \sqrt{5 x+3}}{363 \sqrt{1-2 x}}+\frac{49 \sqrt{5 x+3}}{66 (1-2 x)^{3/2}}+\frac{9 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{2 \sqrt{10}}",1,"Could not integrate","F",-1
2612,1,252,45,1.3007691,"\int \frac{2+3 x}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","\frac{\left(\frac{1}{3} \sqrt{1-2 x}-\frac{1}{3}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^6 \left(\frac{75 \left(\sqrt{1-2 x}-1\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4}-\frac{15 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}-\frac{14 \left(\sqrt{1-2 x}-1\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{6 \sqrt{3} \sqrt{1-2 x}-6 \sqrt{3}}{\sqrt{3}-\sqrt{5 x+3}}+12\right)}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5\right)^3}","\frac{7 \sqrt{5 x+3}}{33 (1-2 x)^{3/2}}-\frac{29 \sqrt{5 x+3}}{363 \sqrt{1-2 x}}",1,"((-1/3 + Sqrt[1 - 2*x]/3)*(Sqrt[3] - Sqrt[3 + 5*x])^6*(12 + (75*(-1 + Sqrt[1 - 2*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^4 - (15*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 - (14*(-1 + Sqrt[1 - 2*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^2 + (-6*Sqrt[3] + 6*Sqrt[3]*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x])))/((-Sqrt[3] + Sqrt[3 + 5*x])*(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3)","B",1
2613,1,252,45,1.295352,"\int \frac{1}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","\frac{\left(\frac{1}{6} \sqrt{1-2 x}-\frac{1}{6}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^6 \left(\frac{75 \left(\sqrt{1-2 x}-1\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4}-\frac{60 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}+\frac{28 \left(\sqrt{1-2 x}-1\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{24 \sqrt{3} \sqrt{1-2 x}-24 \sqrt{3}}{\sqrt{3}-\sqrt{5 x+3}}+12\right)}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5\right)^3}","\frac{20 \sqrt{5 x+3}}{363 \sqrt{1-2 x}}+\frac{2 \sqrt{5 x+3}}{33 (1-2 x)^{3/2}}",1,"((-1/6 + Sqrt[1 - 2*x]/6)*(Sqrt[3] - Sqrt[3 + 5*x])^6*(12 + (75*(-1 + Sqrt[1 - 2*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^4 - (60*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (28*(-1 + Sqrt[1 - 2*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^2 + (-24*Sqrt[3] + 24*Sqrt[3]*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x])))/((-Sqrt[3] + Sqrt[3 + 5*x])*(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3)","B",1
2614,0,0,79,15.9418179,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x) \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)*Sqrt[3 + 5*x]),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x) \sqrt{3+5 x}} \, dx","\frac{676 \sqrt{5 x+3}}{17787 \sqrt{1-2 x}}+\frac{4 \sqrt{5 x+3}}{231 (1-2 x)^{3/2}}-\frac{18 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{49 \sqrt{7}}",1,"Could not integrate","F",-1
2615,0,0,108,19.1677995,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^2 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*Sqrt[3 + 5*x]),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^2 \sqrt{3+5 x}} \, dx","-\frac{4390 \sqrt{5 x+3}}{124509 \sqrt{1-2 x}}+\frac{3 \sqrt{5 x+3}}{7 (1-2 x)^{3/2} (3 x+2)}-\frac{190 \sqrt{5 x+3}}{1617 (1-2 x)^{3/2}}-\frac{405 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{343 \sqrt{7}}",1,"Could not integrate","F",-1
2616,0,0,137,23.749453,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^3 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*Sqrt[3 + 5*x]),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^3 \sqrt{3+5 x}} \, dx","-\frac{57595 \sqrt{5 x+3}}{249018 \sqrt{1-2 x}}+\frac{51 \sqrt{5 x+3}}{28 (1-2 x)^{3/2} (3 x+2)}-\frac{1735 \sqrt{5 x+3}}{3234 (1-2 x)^{3/2}}+\frac{3 \sqrt{5 x+3}}{14 (1-2 x)^{3/2} (3 x+2)^2}-\frac{5805 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1372 \sqrt{7}}",1,"Could not integrate","F",-1
2617,0,0,166,28.9936131,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^4 \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^4*Sqrt[3 + 5*x]),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^4 \sqrt{3+5 x}} \, dx","-\frac{3471145 \sqrt{5 x+3}}{3486252 \sqrt{1-2 x}}+\frac{423 \sqrt{5 x+3}}{56 (1-2 x)^{3/2} (3 x+2)}-\frac{101485 \sqrt{5 x+3}}{45276 (1-2 x)^{3/2}}+\frac{193 \sqrt{5 x+3}}{196 (1-2 x)^{3/2} (3 x+2)^2}+\frac{\sqrt{5 x+3}}{7 (1-2 x)^{3/2} (3 x+2)^3}-\frac{330255 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{19208 \sqrt{7}}",1,"Could not integrate","F",-1
2618,0,0,142,27.9321556,"\int \frac{(2+3 x)^5}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(2+3 x)^5}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","\frac{7 (3 x+2)^4}{33 (1-2 x)^{3/2} \sqrt{5 x+3}}-\frac{1561 (3 x+2)^3}{726 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{7723 \sqrt{1-2 x} (3 x+2)^2}{39930 \sqrt{5 x+3}}-\frac{\sqrt{1-2 x} \sqrt{5 x+3} (16227780 x+39109961)}{2129600}+\frac{243189 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{1600 \sqrt{10}}",1,"Could not integrate","F",-1
2619,0,0,113,22.1614718,"\int \frac{(2+3 x)^4}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(2+3 x)^4}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","\frac{7 (3 x+2)^3}{33 (1-2 x)^{3/2} \sqrt{5 x+3}}-\frac{1099 (3 x+2)^2}{726 \sqrt{1-2 x} \sqrt{5 x+3}}-\frac{\sqrt{1-2 x} (8200665 x+4898747)}{798600 \sqrt{5 x+3}}+\frac{4887 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{200 \sqrt{10}}",1,"Could not integrate","F",-1
2620,0,0,84,16.7189714,"\int \frac{(2+3 x)^3}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(2+3 x)^3}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","\frac{7 (3 x+2)^2}{33 (1-2 x)^{3/2} \sqrt{5 x+3}}-\frac{111311 x+66967}{39930 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{27 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{10 \sqrt{10}}",1,"Could not integrate","F",-1
2621,1,374,67,1.8541581,"\int \frac{(2+3 x)^2}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{\left(\frac{1}{3} \sqrt{1-2 x}-\frac{1}{3}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^8 \left(-\frac{125 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^6}-\frac{150 \left(\sqrt{1-2 x}-1\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{130 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4}-\frac{46 \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}-\frac{52 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{24-24 \sqrt{1-2 x}}{\sqrt{3}-\sqrt{5 x+3}}+8 \sqrt{3}\right)}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(10 \sqrt{3} x+5 \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{5 x+3}+6 \sqrt{3}\right) \left(-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5\right)^3}","-\frac{793 \sqrt{5 x+3}}{19965 \sqrt{1-2 x}}-\frac{1237}{3630 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{49}{66 (1-2 x)^{3/2} \sqrt{5 x+3}}",1,"((-1/3 + Sqrt[1 - 2*x]/3)*(Sqrt[3] - Sqrt[3 + 5*x])^8*(8*Sqrt[3] - (125*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^6 - (150*(-1 + Sqrt[1 - 2*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^5 + (130*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^4 - (46*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 - (52*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^2 + (24 - 24*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x])))/((-Sqrt[3] + Sqrt[3 + 5*x])*(6*Sqrt[3] + 10*Sqrt[3]*x - 11*Sqrt[3 + 5*x] + 5*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])*(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3)","B",1
2622,1,374,67,1.8396457,"\int \frac{2+3 x}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{\left(\frac{1}{6}-\frac{1}{6} \sqrt{1-2 x}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^8 \left(\frac{125 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^6}-\frac{75 \left(\sqrt{1-2 x}-1\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}-\frac{190 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4}+\frac{340 \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}+\frac{76 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{12-12 \sqrt{1-2 x}}{\sqrt{3}-\sqrt{5 x+3}}-8 \sqrt{3}\right)}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(10 \sqrt{3} x+5 \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{5 x+3}+6 \sqrt{3}\right) \left(-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5\right)^3}","\frac{164 \sqrt{5 x+3}}{3993 \sqrt{1-2 x}}+\frac{82 \sqrt{5 x+3}}{1815 (1-2 x)^{3/2}}-\frac{2}{55 (1-2 x)^{3/2} \sqrt{5 x+3}}",1,"((1/6 - Sqrt[1 - 2*x]/6)*(Sqrt[3] - Sqrt[3 + 5*x])^8*(-8*Sqrt[3] + (125*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^6 - (75*(-1 + Sqrt[1 - 2*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^5 - (190*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^4 + (340*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (76*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^2 + (12 - 12*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x])))/((-Sqrt[3] + Sqrt[3 + 5*x])*(6*Sqrt[3] + 10*Sqrt[3]*x - 11*Sqrt[3 + 5*x] + 5*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])*(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3)","B",1
2623,1,374,67,1.8324349,"\int \frac{1}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{\left(\frac{1}{12}-\frac{1}{12} \sqrt{1-2 x}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^8 \left(\frac{125 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^6}-\frac{300 \left(\sqrt{1-2 x}-1\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}-\frac{70 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4}+\frac{400 \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}+\frac{28 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{48-48 \sqrt{1-2 x}}{\sqrt{3}-\sqrt{5 x+3}}-8 \sqrt{3}\right)}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(10 \sqrt{3} x+5 \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{5 x+3}+6 \sqrt{3}\right) \left(-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5\right)^3}","-\frac{400 \sqrt{1-2 x}}{3993 \sqrt{5 x+3}}+\frac{40}{363 \sqrt{5 x+3} \sqrt{1-2 x}}+\frac{2}{33 \sqrt{5 x+3} (1-2 x)^{3/2}}",1,"((1/12 - Sqrt[1 - 2*x]/12)*(Sqrt[3] - Sqrt[3 + 5*x])^8*(-8*Sqrt[3] + (125*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^6 - (300*(-1 + Sqrt[1 - 2*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^5 - (70*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^4 + (400*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (28*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^2 + (48 - 48*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x])))/((-Sqrt[3] + Sqrt[3 + 5*x])*(6*Sqrt[3] + 10*Sqrt[3]*x - 11*Sqrt[3 + 5*x] + 5*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])*(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3)","B",1
2624,0,0,101,17.7373413,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x) (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^(3/2)),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x) (3+5 x)^{3/2}} \, dx","-\frac{42230 \sqrt{1-2 x}}{195657 \sqrt{5 x+3}}+\frac{956}{17787 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{4}{231 (1-2 x)^{3/2} \sqrt{5 x+3}}+\frac{54 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{49 \sqrt{7}}",1,"Could not integrate","F",-1
2625,0,0,130,21.7530531,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2)),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{3/2}} \, dx","-\frac{1840225 \sqrt{1-2 x}}{1369599 \sqrt{5 x+3}}-\frac{3830}{124509 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{3}{7 (1-2 x)^{3/2} (3 x+2) \sqrt{5 x+3}}-\frac{190}{1617 (1-2 x)^{3/2} \sqrt{5 x+3}}+\frac{3105 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{343 \sqrt{7}}",1,"Could not integrate","F",-1
2626,0,0,159,27.8824873,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^(3/2)),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^{3/2}} \, dx","-\frac{46307675 \sqrt{1-2 x}}{5478396 \sqrt{5 x+3}}-\frac{89945}{249018 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{81}{28 (1-2 x)^{3/2} (3 x+2) \sqrt{5 x+3}}-\frac{2725}{3234 (1-2 x)^{3/2} \sqrt{5 x+3}}+\frac{3}{14 (1-2 x)^{3/2} (3 x+2)^2 \sqrt{5 x+3}}+\frac{79515 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1372 \sqrt{7}}",1,"Could not integrate","F",-1
2627,0,0,171,43.7654748,"\int \frac{(2+3 x)^6}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^6}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","\frac{7 (3 x+2)^5}{33 (1-2 x)^{3/2} (5 x+3)^{3/2}}-\frac{511 (3 x+2)^4}{242 \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{7591 \sqrt{1-2 x} (3 x+2)^3}{39930 (5 x+3)^{3/2}}+\frac{261331 \sqrt{1-2 x} (3 x+2)^2}{2196150 \sqrt{5 x+3}}-\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} (78981180 x+190406711)}{117128000}+\frac{753543 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{8000 \sqrt{10}}",1,"Could not integrate","F",-1
2628,0,0,142,28.5221234,"\int \frac{(2+3 x)^5}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^5}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","\frac{7 (3 x+2)^4}{33 (1-2 x)^{3/2} (5 x+3)^{3/2}}-\frac{357 (3 x+2)^3}{242 \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{5281 \sqrt{1-2 x} (3 x+2)^2}{39930 (5 x+3)^{3/2}}-\frac{\sqrt{1-2 x} (55300905 x+33035947)}{8784600 \sqrt{5 x+3}}+\frac{2997 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{200 \sqrt{10}}",1,"Could not integrate","F",-1
2629,0,0,113,20.5866689,"\int \frac{(2+3 x)^4}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^4/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^4}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","\frac{7 (3 x+2)^3}{33 (1-2 x)^{3/2} (5 x+3)^{3/2}}-\frac{203 (3 x+2)^2}{242 \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{\sqrt{1-2 x} (991010 x+627287)}{2196150 (5 x+3)^{3/2}}+\frac{81 \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)}{50 \sqrt{10}}",1,"Could not integrate","F",-1
2630,1,520,96,3.4311802,"\int \frac{(2+3 x)^3}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^3/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{\left(\frac{1}{54} \sqrt{1-2 x}-\frac{1}{54}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^{12} \left(-\frac{28125 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{10}}-\frac{140625 \left(\sqrt{1-2 x}-1\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}-\frac{22250 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^8}+\frac{134100 \left(\sqrt{1-2 x}-1\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}-\frac{8220 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^6}-\frac{115092 \left(\sqrt{1-2 x}-1\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{3288 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4}+\frac{21456 \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}+\frac{1424 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{3600-3600 \sqrt{1-2 x}}{\sqrt{3}-\sqrt{5 x+3}}+288 \sqrt{3}\right)}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(10 \sqrt{3} x+5 \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{5 x+3}+6 \sqrt{3}\right)^3 \left(-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5\right)^3}","\frac{2 (3 x+2)^3}{33 (1-2 x)^{3/2} (5 x+3)^{3/2}}-\frac{8182 \sqrt{1-2 x}}{219615 \sqrt{5 x+3}}-\frac{3679 \sqrt{1-2 x}}{19965 (5 x+3)^{3/2}}+\frac{49}{121 \sqrt{1-2 x} (5 x+3)^{3/2}}",1,"((-1/54 + Sqrt[1 - 2*x]/54)*(Sqrt[3] - Sqrt[3 + 5*x])^12*(288*Sqrt[3] - (28125*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^10)/(Sqrt[3] - Sqrt[3 + 5*x])^10 - (140625*(-1 + Sqrt[1 - 2*x])^9)/(Sqrt[3] - Sqrt[3 + 5*x])^9 - (22250*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^8)/(Sqrt[3] - Sqrt[3 + 5*x])^8 + (134100*(-1 + Sqrt[1 - 2*x])^7)/(Sqrt[3] - Sqrt[3 + 5*x])^7 - (8220*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^6 - (115092*(-1 + Sqrt[1 - 2*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^5 + (3288*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^4 + (21456*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 + (1424*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^2 + (3600 - 3600*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x])))/((-Sqrt[3] + Sqrt[3 + 5*x])*(6*Sqrt[3] + 10*Sqrt[3]*x - 11*Sqrt[3 + 5*x] + 5*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3*(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3)","B",1
2631,1,520,89,3.3782757,"\int \frac{(2+3 x)^2}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^2/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{\left(\frac{1}{108} \sqrt{1-2 x}-\frac{1}{108}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^{12} \left(-\frac{28125 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{10}}-\frac{90000 \left(\sqrt{1-2 x}-1\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}+\frac{54250 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^8}+\frac{138150 \left(\sqrt{1-2 x}-1\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}-\frac{114600 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^6}-\frac{161640 \left(\sqrt{1-2 x}-1\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{45840 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4}+\frac{22104 \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}-\frac{3472 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{2304-2304 \sqrt{1-2 x}}{\sqrt{3}-\sqrt{5 x+3}}+288 \sqrt{3}\right)}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(10 \sqrt{3} x+5 \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{5 x+3}+6 \sqrt{3}\right)^3 \left(-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5\right)^3}","-\frac{3298 \sqrt{1-2 x}}{43923 \sqrt{5 x+3}}-\frac{1649 \sqrt{1-2 x}}{7986 (5 x+3)^{3/2}}+\frac{14}{121 (5 x+3)^{3/2} \sqrt{1-2 x}}+\frac{49}{66 (5 x+3)^{3/2} (1-2 x)^{3/2}}",1,"((-1/108 + Sqrt[1 - 2*x]/108)*(Sqrt[3] - Sqrt[3 + 5*x])^12*(288*Sqrt[3] - (28125*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^10)/(Sqrt[3] - Sqrt[3 + 5*x])^10 - (90000*(-1 + Sqrt[1 - 2*x])^9)/(Sqrt[3] - Sqrt[3 + 5*x])^9 + (54250*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^8)/(Sqrt[3] - Sqrt[3 + 5*x])^8 + (138150*(-1 + Sqrt[1 - 2*x])^7)/(Sqrt[3] - Sqrt[3 + 5*x])^7 - (114600*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^6 - (161640*(-1 + Sqrt[1 - 2*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^5 + (45840*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^4 + (22104*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 - (3472*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^2 + (2304 - 2304*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x])))/((-Sqrt[3] + Sqrt[3 + 5*x])*(6*Sqrt[3] + 10*Sqrt[3]*x - 11*Sqrt[3 + 5*x] + 5*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3*(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3)","B",1
2632,1,520,89,3.385721,"\int \frac{2+3 x}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{\left(\frac{1}{216} \sqrt{1-2 x}-\frac{1}{216}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^{12} \left(-\frac{28125 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^{10}}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^{10}}-\frac{39375 \left(\sqrt{1-2 x}-1\right)^9}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^9}+\frac{90250 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^8}+\frac{45000 \left(\sqrt{1-2 x}-1\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}-\frac{157800 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^6}-\frac{66600 \left(\sqrt{1-2 x}-1\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{63120 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4}+\frac{7200 \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}-\frac{5776 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{1008-1008 \sqrt{1-2 x}}{\sqrt{3}-\sqrt{5 x+3}}+288 \sqrt{3}\right)}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(10 \sqrt{3} x+5 \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{5 x+3}+6 \sqrt{3}\right)^3 \left(-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5\right)^3}","-\frac{2960 \sqrt{1-2 x}}{43923 \sqrt{5 x+3}}+\frac{296}{3993 \sqrt{5 x+3} \sqrt{1-2 x}}+\frac{74}{1815 \sqrt{5 x+3} (1-2 x)^{3/2}}-\frac{2}{165 (5 x+3)^{3/2} (1-2 x)^{3/2}}",1,"((-1/216 + Sqrt[1 - 2*x]/216)*(Sqrt[3] - Sqrt[3 + 5*x])^12*(288*Sqrt[3] - (28125*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^10)/(Sqrt[3] - Sqrt[3 + 5*x])^10 - (39375*(-1 + Sqrt[1 - 2*x])^9)/(Sqrt[3] - Sqrt[3 + 5*x])^9 + (90250*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^8)/(Sqrt[3] - Sqrt[3 + 5*x])^8 + (45000*(-1 + Sqrt[1 - 2*x])^7)/(Sqrt[3] - Sqrt[3 + 5*x])^7 - (157800*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^6 - (66600*(-1 + Sqrt[1 - 2*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^5 + (63120*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^4 + (7200*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 - (5776*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^2 + (1008 - 1008*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x])))/((-Sqrt[3] + Sqrt[3 + 5*x])*(6*Sqrt[3] + 10*Sqrt[3]*x - 11*Sqrt[3 + 5*x] + 5*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3*(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3)","B",1
2633,1,483,89,4.4159968,"\int \frac{1}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{\left(\frac{1}{432}-\frac{1}{432} \sqrt{1-2 x}\right) \left(\sqrt{3}-\sqrt{5 x+3}\right)^{12} \left(\frac{5 \left(\sqrt{1-2 x}-1\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}-2\right) \left(\frac{5625 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^8}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^8}-\frac{2250 \left(\sqrt{1-2 x}-1\right)^7}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^7}-\frac{14900 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^6}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^6}+\frac{6300 \left(\sqrt{1-2 x}-1\right)^5}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^5}+\frac{24520 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^4}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^4}-\frac{2520 \left(\sqrt{1-2 x}-1\right)^3}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^3}-\frac{2384 \sqrt{3} \left(\sqrt{1-2 x}-1\right)^2}{\left(\sqrt{3}-\sqrt{5 x+3}\right)^2}+\frac{144 \sqrt{1-2 x}-144}{\sqrt{3}-\sqrt{5 x+3}}+144 \sqrt{3}\right)}{\left(\sqrt{5 x+3}-\sqrt{3}\right) \left(10 \sqrt{3} x+5 \sqrt{1-2 x} \sqrt{5 x+3}-11 \sqrt{5 x+3}+6 \sqrt{3}\right)^3 \left(-10 x-11 \sqrt{1-2 x}+2 \sqrt{3} \sqrt{1-2 x} \sqrt{5 x+3}+5\right)^3}","-\frac{1600 \sqrt{1-2 x}}{43923 \sqrt{5 x+3}}-\frac{400 \sqrt{1-2 x}}{3993 (5 x+3)^{3/2}}+\frac{20}{121 (5 x+3)^{3/2} \sqrt{1-2 x}}+\frac{2}{33 (5 x+3)^{3/2} (1-2 x)^{3/2}}",1,"((1/432 - Sqrt[1 - 2*x]/432)*(Sqrt[3] - Sqrt[3 + 5*x])^12*(-2 + (5*(-1 + Sqrt[1 - 2*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^2)*(144*Sqrt[3] + (5625*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^8)/(Sqrt[3] - Sqrt[3 + 5*x])^8 - (2250*(-1 + Sqrt[1 - 2*x])^7)/(Sqrt[3] - Sqrt[3 + 5*x])^7 - (14900*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^6)/(Sqrt[3] - Sqrt[3 + 5*x])^6 + (6300*(-1 + Sqrt[1 - 2*x])^5)/(Sqrt[3] - Sqrt[3 + 5*x])^5 + (24520*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^4)/(Sqrt[3] - Sqrt[3 + 5*x])^4 - (2520*(-1 + Sqrt[1 - 2*x])^3)/(Sqrt[3] - Sqrt[3 + 5*x])^3 - (2384*Sqrt[3]*(-1 + Sqrt[1 - 2*x])^2)/(Sqrt[3] - Sqrt[3 + 5*x])^2 + (-144 + 144*Sqrt[1 - 2*x])/(Sqrt[3] - Sqrt[3 + 5*x])))/((-Sqrt[3] + Sqrt[3 + 5*x])*(6*Sqrt[3] + 10*Sqrt[3]*x - 11*Sqrt[3 + 5*x] + 5*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3*(5 - 11*Sqrt[1 - 2*x] - 10*x + 2*Sqrt[3]*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])^3)","B",1
2634,0,0,123,23.5266318,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x) (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^(5/2)),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x) (3+5 x)^{5/2}} \, dx","\frac{1001590 \sqrt{1-2 x}}{2152227 \sqrt{5 x+3}}-\frac{19130 \sqrt{1-2 x}}{195657 (5 x+3)^{3/2}}+\frac{412}{5929 \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{4}{231 (1-2 x)^{3/2} (5 x+3)^{3/2}}-\frac{162 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{49 \sqrt{7}}",1,"Could not integrate","F",-1
2635,0,0,152,30.6801391,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2)),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{5/2}} \, dx","\frac{95783075 \sqrt{1-2 x}}{15065589 \sqrt{5 x+3}}-\frac{985525 \sqrt{1-2 x}}{1369599 (5 x+3)^{3/2}}-\frac{1090}{41503 \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{3}{7 (1-2 x)^{3/2} (3 x+2) (5 x+3)^{3/2}}-\frac{190}{1617 (1-2 x)^{3/2} (5 x+3)^{3/2}}-\frac{14985 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{343 \sqrt{7}}",1,"Could not integrate","F",-1
2636,0,0,181,37.5622421,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^(5/2)),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^{5/2}} \, dx","\frac{3443814775 \sqrt{1-2 x}}{60262356 \sqrt{5 x+3}}-\frac{34551425 \sqrt{1-2 x}}{5478396 (5 x+3)^{3/2}}-\frac{40765}{83006 \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{111}{28 (1-2 x)^{3/2} (3 x+2) (5 x+3)^{3/2}}-\frac{3715}{3234 (1-2 x)^{3/2} (5 x+3)^{3/2}}+\frac{3}{14 (1-2 x)^{3/2} (3 x+2)^2 (5 x+3)^{3/2}}-\frac{538245 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1372 \sqrt{7}}",1,"Could not integrate","F",-1
2637,0,0,58,1.0475961,"\int \frac{1}{\sqrt{a+b x} \sqrt{c+\frac{b (-1+c) x}{a}} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*Sqrt[c + (b*(-1 + c)*x)/a]*Sqrt[e + (b*(-1 + e)*x)/a]),x]","\int \frac{1}{\sqrt{a+b x} \sqrt{c+\frac{b (-1+c) x}{a}} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","\frac{2 \sqrt{a} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c} \sqrt{a+b x}}{\sqrt{a}}\right)|\frac{1-e}{1-c}\right)}{b \sqrt{1-c}}",1,"Could not integrate","F",-1
2638,0,0,96,1.1940282,"\int \frac{1}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + (b*(-1 + e)*x)/a]),x]","\int \frac{1}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","\frac{2 \sqrt{a} \sqrt{\frac{b (c+d x)}{b c-a d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-e} \sqrt{a+b x}}{\sqrt{a}}\right)|-\frac{a d}{(b c-a d) (1-e)}\right)}{b \sqrt{1-e} \sqrt{c+d x}}",1,"Could not integrate","F",-1
2639,0,0,134,1.1475874,"\int \frac{1}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\int \frac{1}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x}} \, dx","\frac{2 \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{b \sqrt{d} \sqrt{c+d x} \sqrt{e+f x}}",1,"Could not integrate","F",-1
2640,0,0,58,1.2698923,"\int \frac{\sqrt{e+\frac{b (-1+e) x}{a}}}{\sqrt{a+b x} \sqrt{c+\frac{b (-1+c) x}{a}}} \, dx","IntegrateAlgebraic[Sqrt[e + (b*(-1 + e)*x)/a]/(Sqrt[a + b*x]*Sqrt[c + (b*(-1 + c)*x)/a]),x]","\int \frac{\sqrt{e+\frac{b (-1+e) x}{a}}}{\sqrt{a+b x} \sqrt{c+\frac{b (-1+c) x}{a}}} \, dx","\frac{2 \sqrt{a} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c} \sqrt{a+b x}}{\sqrt{a}}\right)|\frac{1-e}{1-c}\right)}{b \sqrt{1-c}}",1,"Could not integrate","F",-1
2641,0,0,96,0.9200716,"\int \frac{\sqrt{c+d x}}{\sqrt{a+b x} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/(Sqrt[a + b*x]*Sqrt[e + (b*(-1 + e)*x)/a]),x]","\int \frac{\sqrt{c+d x}}{\sqrt{a+b x} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","\frac{2 \sqrt{a} \sqrt{c+d x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-e} \sqrt{a+b x}}{\sqrt{a}}\right)|-\frac{a d}{(b c-a d) (1-e)}\right)}{b \sqrt{1-e} \sqrt{\frac{b (c+d x)}{b c-a d}}}",1,"Could not integrate","F",-1
2642,0,0,162,0.7374476,"\int \frac{\sqrt{a+b x}}{\sqrt{c+\frac{b (-1+c) x}{a}} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(Sqrt[c + (b*(-1 + c)*x)/a]*Sqrt[e + (b*(-1 + e)*x)/a]),x]","\int \frac{\sqrt{a+b x}}{\sqrt{c+\frac{b (-1+c) x}{a}} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","-\frac{2 a \sqrt{c-e} \sqrt{a+b x} \sqrt{-\frac{(1-c) (a e-b (1-e) x)}{a (c-e)}} E\left(\sin ^{-1}\left(\frac{\sqrt{1-e} \sqrt{c-\frac{b (1-c) x}{a}}}{\sqrt{c-e}}\right)|\frac{c-e}{1-e}\right)}{b (1-c) \sqrt{1-e} \sqrt{\frac{(1-c) (a+b x)}{a}} \sqrt{e-\frac{b (1-e) x}{a}}}",1,"Could not integrate","F",-1
2643,0,0,134,1.1561367,"\int \frac{\sqrt{e+f x}}{\sqrt{a+b x} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[Sqrt[e + f*x]/(Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\int \frac{\sqrt{e+f x}}{\sqrt{a+b x} \sqrt{c+d x}} \, dx","\frac{2 \sqrt{e+f x} \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{b \sqrt{d} \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}",1,"Could not integrate","F",-1
2644,0,0,101,0.8237574,"\int \frac{1}{\sqrt{-c+d x} \sqrt{c+d x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-c + d*x]*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\int \frac{1}{\sqrt{-c+d x} \sqrt{c+d x} \sqrt{e+f x}} \, dx","\frac{2 \sqrt{c} \sqrt{\frac{c-d x}{c}} \sqrt{\frac{d (e+f x)}{d e-c f}} F\left(\sin ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{2} \sqrt{c}}\right)|-\frac{2 c f}{d e-c f}\right)}{d \sqrt{d x-c} \sqrt{e+f x}}",1,"Could not integrate","F",-1
2645,0,0,191,0.395781,"\int \sqrt{1-2 x} (2+3 x)^{5/2} \sqrt{3+5 x} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x],x]","\int \sqrt{1-2 x} (2+3 x)^{5/2} \sqrt{3+5 x} \, dx","\frac{2}{45} \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^{5/2}-\frac{23 \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^{3/2}}{1575}-\frac{1244 \sqrt{1-2 x} (5 x+3)^{3/2} \sqrt{3 x+2}}{13125}-\frac{175111 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{236250}-\frac{175111 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1181250}-\frac{2911577 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{590625}",1,"Could not integrate","F",-1
2646,0,0,160,0.5535791,"\int \sqrt{1-2 x} (2+3 x)^{3/2} \sqrt{3+5 x} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x],x]","\int \sqrt{1-2 x} (2+3 x)^{3/2} \sqrt{3+5 x} \, dx","\frac{2}{35} \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{3/2}-\frac{27}{875} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{823 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{2625}-\frac{823 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{13125}-\frac{55019 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{26250}",1,"Could not integrate","F",-1
2647,0,0,129,0.2594052,"\int \sqrt{1-2 x} \sqrt{2+3 x} \sqrt{3+5 x} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x],x]","\int \sqrt{1-2 x} \sqrt{2+3 x} \sqrt{3+5 x} \, dx","\frac{2}{25} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{31}{225} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{31 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1125}-\frac{1159 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1125}",1,"Could not integrate","F",-1
2648,0,0,98,0.2254977,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{\sqrt{2+3 x}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/Sqrt[2 + 3*x],x]","\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{\sqrt{2+3 x}} \, dx","\frac{2}{9} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+\frac{2}{45} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{37}{45} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2649,0,0,98,0.5842721,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^(3/2),x]","\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^{3/2}} \, dx","-\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{3 \sqrt{3 x+2}}-\frac{2}{3} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{4}{3} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2650,0,0,129,0.4288985,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^(5/2),x]","\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^{5/2}} \, dx","\frac{74 \sqrt{1-2 x} \sqrt{5 x+3}}{63 \sqrt{3 x+2}}-\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{9 (3 x+2)^{3/2}}+\frac{4}{63} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{74}{63} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2651,0,0,160,0.5280045,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^(7/2),x]","\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^{7/2}} \, dx","\frac{4636 \sqrt{1-2 x} \sqrt{5 x+3}}{2205 \sqrt{3 x+2}}+\frac{74 \sqrt{1-2 x} \sqrt{5 x+3}}{315 (3 x+2)^{3/2}}-\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{15 (3 x+2)^{5/2}}-\frac{124 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2205}-\frac{4636 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2205}",1,"Could not integrate","F",-1
2652,0,0,191,0.668632,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^{9/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^(9/2),x]","\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^{9/2}} \, dx","\frac{220076 \sqrt{1-2 x} \sqrt{5 x+3}}{36015 \sqrt{3 x+2}}+\frac{3184 \sqrt{1-2 x} \sqrt{5 x+3}}{5145 (3 x+2)^{3/2}}+\frac{74 \sqrt{1-2 x} \sqrt{5 x+3}}{735 (3 x+2)^{5/2}}-\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{21 (3 x+2)^{7/2}}-\frac{6584 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{36015}-\frac{220076 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{36015}",1,"Could not integrate","F",-1
2653,0,0,218,0.78689,"\int \sqrt{1-2 x} (2+3 x)^{5/2} (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2),x]","\int \sqrt{1-2 x} (2+3 x)^{5/2} (3+5 x)^{3/2} \, dx","\frac{2}{55} \sqrt{1-2 x} (3 x+2)^{5/2} (5 x+3)^{5/2}-\frac{23 \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}}{2475}-\frac{543 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{9625}-\frac{342971 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{866250}-\frac{11346991 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{3898125}-\frac{11346991 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1771875 \sqrt{33}}-\frac{1508889271 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{7087500 \sqrt{33}}",1,"Could not integrate","F",-1
2654,0,0,191,0.7831178,"\int \sqrt{1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2),x]","\int \sqrt{1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2} \, dx","\frac{2}{45} \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}-\frac{3}{175} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}-\frac{1208 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{7875}-\frac{160297 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{141750}-\frac{160297 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{708750}-\frac{5327983 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{708750}",1,"Could not integrate","F",-1
2655,0,0,160,0.5423818,"\int \sqrt{1-2 x} \sqrt{2+3 x} (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2),x]","\int \sqrt{1-2 x} \sqrt{2+3 x} (3+5 x)^{3/2} \, dx","\frac{2}{35} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}-\frac{31}{525} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{2252 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{4725}-\frac{2252 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{23625}-\frac{148831 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{47250}",1,"Could not integrate","F",-1
2656,0,0,129,0.5856832,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{\sqrt{2+3 x}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/Sqrt[2 + 3*x],x]","\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{\sqrt{2+3 x}} \, dx","\frac{2}{15} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{41}{135} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{41}{675} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{974}{675} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2657,0,0,129,0.8702164,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^(3/2),x]","\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{3/2}} \, dx","-\frac{2 \sqrt{1-2 x} (5 x+3)^{3/2}}{3 \sqrt{3 x+2}}+\frac{40}{27} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+\frac{8}{27} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{49}{27} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2658,0,0,129,0.8440829,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^(5/2),x]","\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{5/2}} \, dx","-\frac{2 \sqrt{1-2 x} (5 x+3)^{3/2}}{9 (3 x+2)^{3/2}}-\frac{214 \sqrt{1-2 x} \sqrt{5 x+3}}{189 \sqrt{3 x+2}}-\frac{214}{189} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{494}{189} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2659,0,0,160,0.9121293,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^(7/2),x]","\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{7/2}} \, dx","-\frac{2 \sqrt{1-2 x} (5 x+3)^{3/2}}{15 (3 x+2)^{5/2}}+\frac{8314 \sqrt{1-2 x} \sqrt{5 x+3}}{6615 \sqrt{3 x+2}}-\frac{214 \sqrt{1-2 x} \sqrt{5 x+3}}{945 (3 x+2)^{3/2}}+\frac{824 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6615}-\frac{8314 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6615}",1,"Could not integrate","F",-1
2660,0,0,191,0.9878455,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{9/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^(9/2),x]","\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{9/2}} \, dx","-\frac{2 \sqrt{1-2 x} (5 x+3)^{3/2}}{21 (3 x+2)^{7/2}}+\frac{475592 \sqrt{1-2 x} \sqrt{5 x+3}}{324135 \sqrt{3 x+2}}+\frac{8578 \sqrt{1-2 x} \sqrt{5 x+3}}{46305 (3 x+2)^{3/2}}-\frac{214 \sqrt{1-2 x} \sqrt{5 x+3}}{2205 (3 x+2)^{5/2}}-\frac{10628 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{324135}-\frac{475592 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{324135}",1,"Could not integrate","F",-1
2661,0,0,222,1.0217416,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{11/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^(11/2),x]","\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{11/2}} \, dx","-\frac{2 \sqrt{1-2 x} (5 x+3)^{3/2}}{27 (3 x+2)^{9/2}}+\frac{22738708 \sqrt{1-2 x} \sqrt{5 x+3}}{6806835 \sqrt{3 x+2}}+\frac{332372 \sqrt{1-2 x} \sqrt{5 x+3}}{972405 (3 x+2)^{3/2}}+\frac{8842 \sqrt{1-2 x} \sqrt{5 x+3}}{138915 (3 x+2)^{5/2}}-\frac{214 \sqrt{1-2 x} \sqrt{5 x+3}}{3969 (3 x+2)^{7/2}}-\frac{673072 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6806835}-\frac{22738708 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6806835}",1,"Could not integrate","F",-1
2662,0,0,249,0.9328547,"\int \sqrt{1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2),x]","\int \sqrt{1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2} \, dx","\frac{2}{65} \sqrt{1-2 x} (3 x+2)^{5/2} (5 x+3)^{7/2}-\frac{23 \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{7/2}}{3575}-\frac{2014 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{7/2}}{53625}-\frac{564731 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{2252250}-\frac{1865989 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{1126125}-\frac{493825477 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{40540500}-\frac{493825477 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{18427500 \sqrt{33}}-\frac{16416987253 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{18427500 \sqrt{33}}",1,"Could not integrate","F",-1
2663,0,0,218,0.8191684,"\int \sqrt{1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2),x]","\int \sqrt{1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2} \, dx","\frac{2}{55} \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{7/2}-\frac{3}{275} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{7/2}-\frac{177 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{1925}-\frac{7031 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{11550}-\frac{465127 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{103950}-\frac{465127 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{47250 \sqrt{33}}-\frac{30926081 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{94500 \sqrt{33}}",1,"Could not integrate","F",-1
2664,0,0,191,0.396423,"\int \sqrt{1-2 x} \sqrt{2+3 x} (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3 + 5*x)^(5/2),x]","\int \sqrt{1-2 x} \sqrt{2+3 x} (3+5 x)^{5/2} \, dx","\frac{2}{45} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{7/2}-\frac{31}{945} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}-\frac{223}{945} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{29357 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{17010}-\frac{29357 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{85050}-\frac{488149 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{42525}",1,"Could not integrate","F",-1
2665,0,0,160,0.4118046,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{\sqrt{2+3 x}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/Sqrt[2 + 3*x],x]","\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{\sqrt{2+3 x}} \, dx","\frac{2}{21} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}-\frac{1}{7} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{131}{189} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{131}{945} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{9013 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1890}",1,"Could not integrate","F",-1
2666,0,0,156,0.8645089,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^(3/2),x]","\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{3/2}} \, dx","-\frac{2 \sqrt{1-2 x} (5 x+3)^{5/2}}{3 \sqrt{3 x+2}}+\frac{4}{3} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{1}{5} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{3}{5} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2667,0,0,160,0.9176332,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^(5/2),x]","\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{5/2}} \, dx","-\frac{2 \sqrt{1-2 x} (5 x+3)^{5/2}}{9 (3 x+2)^{3/2}}-\frac{118 \sqrt{1-2 x} (5 x+3)^{3/2}}{63 \sqrt{3 x+2}}+\frac{2470}{567} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+\frac{494}{567} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{2209}{567} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2668,0,0,160,0.9387912,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^(7/2),x]","\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{7/2}} \, dx","-\frac{2 \sqrt{1-2 x} (5 x+3)^{5/2}}{15 (3 x+2)^{5/2}}-\frac{118 \sqrt{1-2 x} (5 x+3)^{3/2}}{315 (3 x+2)^{3/2}}-\frac{12758 \sqrt{1-2 x} \sqrt{5 x+3}}{6615 \sqrt{3 x+2}}-\frac{12758 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6615}+\frac{31588 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6615}",1,"Could not integrate","F",-1
2669,0,0,191,0.9689214,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{9/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^(9/2),x]","\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{9/2}} \, dx","-\frac{2 \sqrt{1-2 x} (5 x+3)^{5/2}}{21 (3 x+2)^{7/2}}-\frac{118 \sqrt{1-2 x} (5 x+3)^{3/2}}{735 (3 x+2)^{5/2}}+\frac{173482 \sqrt{1-2 x} \sqrt{5 x+3}}{108045 \sqrt{3 x+2}}-\frac{4282 \sqrt{1-2 x} \sqrt{5 x+3}}{15435 (3 x+2)^{3/2}}+\frac{23612 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{108045}-\frac{173482 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{108045}",1,"Could not integrate","F",-1
2670,0,0,222,1.0345172,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{11/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^(11/2),x]","\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{11/2}} \, dx","-\frac{2 \sqrt{1-2 x} (5 x+3)^{5/2}}{27 (3 x+2)^{9/2}}-\frac{118 \sqrt{1-2 x} (5 x+3)^{3/2}}{1323 (3 x+2)^{7/2}}+\frac{27198452 \sqrt{1-2 x} \sqrt{5 x+3}}{20420505 \sqrt{3 x+2}}+\frac{568318 \sqrt{1-2 x} \sqrt{5 x+3}}{2917215 (3 x+2)^{3/2}}-\frac{12934 \sqrt{1-2 x} \sqrt{5 x+3}}{138915 (3 x+2)^{5/2}}-\frac{442868 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{20420505}-\frac{27198452 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{20420505}",1,"Could not integrate","F",-1
2671,0,0,249,1.1131535,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{13/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^(13/2),x]","\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{13/2}} \, dx","-\frac{2 \sqrt{1-2 x} (5 x+3)^{5/2}}{33 (3 x+2)^{11/2}}-\frac{118 \sqrt{1-2 x} (5 x+3)^{3/2}}{2079 (3 x+2)^{9/2}}+\frac{1305025844 \sqrt{1-2 x} \sqrt{5 x+3}}{524126295 \sqrt{3 x+2}}+\frac{19417096 \sqrt{1-2 x} \sqrt{5 x+3}}{74875185 (3 x+2)^{3/2}}+\frac{627806 \sqrt{1-2 x} \sqrt{5 x+3}}{10696455 (3 x+2)^{5/2}}-\frac{13022 \sqrt{1-2 x} \sqrt{5 x+3}}{305613 (3 x+2)^{7/2}}-\frac{37904696 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{47647845 \sqrt{33}}-\frac{1305025844 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{47647845 \sqrt{33}}",1,"Could not integrate","F",-1
2672,0,0,134,0.0005916,"\int \frac{\sqrt{e+f x}}{\sqrt{a+b x} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[Sqrt[e + f*x]/(Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\int \frac{\sqrt{e+f x}}{\sqrt{a+b x} \sqrt{c+d x}} \, dx","\frac{2 \sqrt{e+f x} \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{b \sqrt{d} \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}",1,"Could not integrate","F",-1
2673,0,0,184,1.8522148,"\int \frac{\sqrt{e+f x}}{(a+b x)^{3/2} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[Sqrt[e + f*x]/((a + b*x)^(3/2)*Sqrt[c + d*x]),x]","\int \frac{\sqrt{e+f x}}{(a+b x)^{3/2} \sqrt{c+d x}} \, dx","\frac{2 \sqrt{f} \sqrt{c+d x} \sqrt{a f-b e} \sqrt{\frac{b (e+f x)}{b e-a f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{a+b x}}{\sqrt{a f-b e}}\right)|\frac{d (b e-a f)}{(b c-a d) f}\right)}{b \sqrt{e+f x} (b c-a d) \sqrt{\frac{b (c+d x)}{b c-a d}}}-\frac{2 \sqrt{c+d x} \sqrt{e+f x}}{\sqrt{a+b x} (b c-a d)}",1,"Could not integrate","F",-1
2674,0,0,31,0.257773,"\int \frac{\sqrt{1-2 x}}{\sqrt{-3-5 x} \sqrt{2+3 x}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/(Sqrt[-3 - 5*x]*Sqrt[2 + 3*x]),x]","\int \frac{\sqrt{1-2 x}}{\sqrt{-3-5 x} \sqrt{2+3 x}} \, dx","\frac{2}{3} \sqrt{\frac{7}{5}} E\left(\sin ^{-1}\left(\sqrt{5} \sqrt{3 x+2}\right)|\frac{2}{35}\right)",1,"Could not integrate","F",-1
2675,0,0,158,0.4057627,"\int \frac{\sqrt{1-2 x} (2+3 x)^{5/2}}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2))/Sqrt[3 + 5*x],x]","\int \frac{\sqrt{1-2 x} (2+3 x)^{5/2}}{\sqrt{3+5 x}} \, dx","\frac{2}{35} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{5/2}-\frac{23}{875} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}-\frac{859 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{4375}-\frac{314 \sqrt{33} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{21875}-\frac{61151 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{43750}",1,"Could not integrate","F",-1
2676,0,0,127,0.6386187,"\int \frac{\sqrt{1-2 x} (2+3 x)^{3/2}}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2))/Sqrt[3 + 5*x],x]","\int \frac{\sqrt{1-2 x} (2+3 x)^{3/2}}{\sqrt{3+5 x}} \, dx","\frac{2}{25} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}-\frac{9}{125} \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}-\frac{17}{625} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{146}{625} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2677,0,0,98,0.2861145,"\int \frac{\sqrt{1-2 x} \sqrt{2+3 x}}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*Sqrt[2 + 3*x])/Sqrt[3 + 5*x],x]","\int \frac{\sqrt{1-2 x} \sqrt{2+3 x}}{\sqrt{3+5 x}} \, dx","\frac{2}{15} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{4}{75} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{31}{75} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2678,0,0,49,0.2465312,"\int \frac{\sqrt{1-2 x}}{\sqrt{2+3 x} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/(Sqrt[2 + 3*x]*Sqrt[3 + 5*x]),x]","\int \frac{\sqrt{1-2 x}}{\sqrt{2+3 x} \sqrt{3+5 x}} \, dx","\frac{2 \sqrt{\frac{7}{5}} \sqrt{-5 x-3} E\left(\sin ^{-1}\left(\sqrt{5} \sqrt{3 x+2}\right)|\frac{2}{35}\right)}{3 \sqrt{5 x+3}}",1,"Could not integrate","F",-1
2679,0,0,61,0.5927175,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^(3/2)*Sqrt[3 + 5*x]),x]","\int \frac{\sqrt{1-2 x}}{(2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{\sqrt{3 x+2}}-2 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2680,0,0,129,0.4468747,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^(5/2)*Sqrt[3 + 5*x]),x]","\int \frac{\sqrt{1-2 x}}{(2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","\frac{136 \sqrt{1-2 x} \sqrt{5 x+3}}{21 \sqrt{3 x+2}}+\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{3 (3 x+2)^{3/2}}-\frac{4}{21} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{136}{21} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2681,0,0,158,0.5673306,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^(7/2)*Sqrt[3 + 5*x]),x]","\int \frac{\sqrt{1-2 x}}{(2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","\frac{6388 \sqrt{1-2 x} \sqrt{5 x+3}}{245 \sqrt{3 x+2}}+\frac{92 \sqrt{1-2 x} \sqrt{5 x+3}}{35 (3 x+2)^{3/2}}+\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{5 (3 x+2)^{5/2}}-\frac{64}{245} \sqrt{33} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{6388}{245} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2682,0,0,189,0.6543363,"\int \frac{\sqrt{1-2 x} (2+3 x)^{7/2}}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2))/(3 + 5*x)^(3/2),x]","\int \frac{\sqrt{1-2 x} (2+3 x)^{7/2}}{(3+5 x)^{3/2}} \, dx","-\frac{2 \sqrt{1-2 x} (3 x+2)^{7/2}}{5 \sqrt{5 x+3}}+\frac{48}{175} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{5/2}+\frac{183 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{4375}-\frac{2486 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{21875}-\frac{38723 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{109375 \sqrt{33}}-\frac{203179 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{218750}",1,"Could not integrate","F",-1
2683,0,0,158,0.5176571,"\int \frac{\sqrt{1-2 x} (2+3 x)^{5/2}}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2))/(3 + 5*x)^(3/2),x]","\int \frac{\sqrt{1-2 x} (2+3 x)^{5/2}}{(3+5 x)^{3/2}} \, dx","-\frac{2 \sqrt{1-2 x} (3 x+2)^{5/2}}{5 \sqrt{5 x+3}}+\frac{36}{125} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}+\frac{13}{625} \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}-\frac{1091 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3125 \sqrt{33}}-\frac{1409 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3125}",1,"Could not integrate","F",-1
2684,0,0,127,0.6606731,"\int \frac{\sqrt{1-2 x} (2+3 x)^{3/2}}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2))/(3 + 5*x)^(3/2),x]","\int \frac{\sqrt{1-2 x} (2+3 x)^{3/2}}{(3+5 x)^{3/2}} \, dx","-\frac{2 \sqrt{1-2 x} (3 x+2)^{3/2}}{5 \sqrt{5 x+3}}+\frac{8}{25} \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}-\frac{106 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{125 \sqrt{33}}-\frac{19}{125} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2685,0,0,94,0.5738235,"\int \frac{\sqrt{1-2 x} \sqrt{2+3 x}}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*Sqrt[2 + 3*x])/(3 + 5*x)^(3/2),x]","\int \frac{\sqrt{1-2 x} \sqrt{2+3 x}}{(3+5 x)^{3/2}} \, dx","-\frac{2 \sqrt{1-2 x} \sqrt{3 x+2}}{5 \sqrt{5 x+3}}-\frac{62 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{25 \sqrt{33}}+\frac{4}{25} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2686,0,0,61,0.575244,"\int \frac{\sqrt{1-2 x}}{\sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/(Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)),x]","\int \frac{\sqrt{1-2 x}}{\sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","2 \sqrt{\frac{7}{5}} E\left(\sin ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)|\frac{33}{35}\right)-\frac{2 \sqrt{1-2 x} \sqrt{3 x+2}}{\sqrt{5 x+3}}",1,"Could not integrate","F",-1
2687,0,0,117,0.6631253,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\int \frac{\sqrt{1-2 x}}{(2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","-\frac{20 \sqrt{1-2 x} \sqrt{3 x+2}}{\sqrt{5 x+3}}+\frac{2 \sqrt{1-2 x}}{\sqrt{3 x+2} \sqrt{5 x+3}}+\frac{4 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{\sqrt{33}}+4 \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2688,0,0,158,0.6133956,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\int \frac{\sqrt{1-2 x}}{(2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","-\frac{2780 \sqrt{1-2 x} \sqrt{3 x+2}}{21 \sqrt{5 x+3}}+\frac{92 \sqrt{1-2 x}}{7 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{2 \sqrt{1-2 x}}{3 (3 x+2)^{3/2} \sqrt{5 x+3}}+\frac{184 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{7 \sqrt{33}}+\frac{556}{7} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2689,0,0,189,0.7501887,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)),x]","\int \frac{\sqrt{1-2 x}}{(2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","-\frac{116464 \sqrt{1-2 x} \sqrt{3 x+2}}{147 \sqrt{5 x+3}}+\frac{19268 \sqrt{1-2 x}}{245 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{416 \sqrt{1-2 x}}{105 (3 x+2)^{3/2} \sqrt{5 x+3}}+\frac{2 \sqrt{1-2 x}}{5 (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{38536 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{245 \sqrt{33}}+\frac{116464}{245} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2690,0,0,218,0.8009086,"\int \frac{\sqrt{1-2 x} (2+3 x)^{9/2}}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^(9/2))/(3 + 5*x)^(5/2),x]","\int \frac{\sqrt{1-2 x} (2+3 x)^{9/2}}{(3+5 x)^{5/2}} \, dx","-\frac{2 \sqrt{1-2 x} (3 x+2)^{9/2}}{15 (5 x+3)^{3/2}}-\frac{118 \sqrt{1-2 x} (3 x+2)^{7/2}}{165 \sqrt{5 x+3}}+\frac{958 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{5/2}}{1925}+\frac{5153 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{48125}-\frac{12601 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{240625}-\frac{31288 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{109375 \sqrt{33}}-\frac{1473539 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{218750 \sqrt{33}}",1,"Could not integrate","F",-1
2691,0,0,189,0.7119743,"\int \frac{\sqrt{1-2 x} (2+3 x)^{7/2}}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2))/(3 + 5*x)^(5/2),x]","\int \frac{\sqrt{1-2 x} (2+3 x)^{7/2}}{(3+5 x)^{5/2}} \, dx","-\frac{2 \sqrt{1-2 x} (3 x+2)^{7/2}}{15 (5 x+3)^{3/2}}-\frac{458 \sqrt{1-2 x} (3 x+2)^{5/2}}{825 \sqrt{5 x+3}}+\frac{2818 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{6875}+\frac{2719 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{34375}-\frac{523 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{15625}-\frac{47342 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{15625 \sqrt{33}}",1,"Could not integrate","F",-1
2692,0,0,156,0.7350556,"\int \frac{\sqrt{1-2 x} (2+3 x)^{5/2}}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2))/(3 + 5*x)^(5/2),x]","\int \frac{\sqrt{1-2 x} (2+3 x)^{5/2}}{(3+5 x)^{5/2}} \, dx","-\frac{2 \sqrt{1-2 x} (3 x+2)^{5/2}}{15 (5 x+3)^{3/2}}-\frac{326 \sqrt{1-2 x} (3 x+2)^{3/2}}{825 \sqrt{5 x+3}}+\frac{458 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{1375}-\frac{496 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{625 \sqrt{33}}-\frac{169 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{625 \sqrt{33}}",1,"Could not integrate","F",-1
2693,0,0,125,0.6885639,"\int \frac{\sqrt{1-2 x} (2+3 x)^{3/2}}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2))/(3 + 5*x)^(5/2),x]","\int \frac{\sqrt{1-2 x} (2+3 x)^{3/2}}{(3+5 x)^{5/2}} \, dx","-\frac{2 \sqrt{1-2 x} (3 x+2)^{3/2}}{15 (5 x+3)^{3/2}}-\frac{194 \sqrt{1-2 x} \sqrt{3 x+2}}{825 \sqrt{5 x+3}}-\frac{178 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{125 \sqrt{33}}+\frac{458 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{125 \sqrt{33}}",1,"Could not integrate","F",-1
2694,0,0,125,0.4332198,"\int \frac{\sqrt{1-2 x} \sqrt{2+3 x}}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[1 - 2*x]*Sqrt[2 + 3*x])/(3 + 5*x)^(5/2),x]","\int \frac{\sqrt{1-2 x} \sqrt{2+3 x}}{(3+5 x)^{5/2}} \, dx","-\frac{62 \sqrt{1-2 x} \sqrt{3 x+2}}{165 \sqrt{5 x+3}}-\frac{2 \sqrt{1-2 x} \sqrt{3 x+2}}{15 (5 x+3)^{3/2}}+\frac{8 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{25 \sqrt{33}}+\frac{62 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{25 \sqrt{33}}",1,"Could not integrate","F",-1
2695,0,0,125,0.4216779,"\int \frac{\sqrt{1-2 x}}{\sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/(Sqrt[2 + 3*x]*(3 + 5*x)^(5/2)),x]","\int \frac{\sqrt{1-2 x}}{\sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","\frac{136 \sqrt{1-2 x} \sqrt{3 x+2}}{33 \sqrt{5 x+3}}-\frac{2 \sqrt{1-2 x} \sqrt{3 x+2}}{3 (5 x+3)^{3/2}}-\frac{4 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5 \sqrt{33}}-\frac{136 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5 \sqrt{33}}",1,"Could not integrate","F",-1
2696,0,0,150,0.7538576,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\int \frac{\sqrt{1-2 x}}{(2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","\frac{2660 \sqrt{1-2 x} \sqrt{3 x+2}}{33 \sqrt{5 x+3}}-\frac{40 \sqrt{1-2 x} \sqrt{3 x+2}}{3 (5 x+3)^{3/2}}+\frac{2 \sqrt{1-2 x}}{\sqrt{3 x+2} (5 x+3)^{3/2}}-\frac{16 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{\sqrt{33}}-\frac{532 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{\sqrt{33}}",1,"Could not integrate","F",-1
2697,0,0,187,0.8324643,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\int \frac{\sqrt{1-2 x}}{(2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","\frac{184840 \sqrt{1-2 x} \sqrt{3 x+2}}{231 \sqrt{5 x+3}}-\frac{2780 \sqrt{1-2 x} \sqrt{3 x+2}}{21 (5 x+3)^{3/2}}+\frac{416 \sqrt{1-2 x}}{21 \sqrt{3 x+2} (5 x+3)^{3/2}}+\frac{2 \sqrt{1-2 x}}{3 (3 x+2)^{3/2} (5 x+3)^{3/2}}-\frac{1112 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{7 \sqrt{33}}-\frac{36968 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{7 \sqrt{33}}",1,"Could not integrate","F",-1
2698,0,0,218,0.8698884,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)),x]","\int \frac{\sqrt{1-2 x}}{(2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","\frac{10312712 \sqrt{1-2 x} \sqrt{3 x+2}}{1617 \sqrt{5 x+3}}-\frac{155104 \sqrt{1-2 x} \sqrt{3 x+2}}{147 (5 x+3)^{3/2}}+\frac{116044 \sqrt{1-2 x}}{735 \sqrt{3 x+2} (5 x+3)^{3/2}}+\frac{556 \sqrt{1-2 x}}{105 (3 x+2)^{3/2} (5 x+3)^{3/2}}+\frac{2 \sqrt{1-2 x}}{5 (3 x+2)^{5/2} (5 x+3)^{3/2}}-\frac{310208 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{245 \sqrt{33}}-\frac{10312712 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{245 \sqrt{33}}",1,"Could not integrate","F",-1
2699,0,0,218,0.7678325,"\int (1-2 x)^{3/2} (2+3 x)^{5/2} \sqrt{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x],x]","\int (1-2 x)^{3/2} (2+3 x)^{5/2} \sqrt{3+5 x} \, dx","\frac{2}{55} (1-2 x)^{3/2} (5 x+3)^{3/2} (3 x+2)^{5/2}+\frac{178 \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^{5/2}}{7425}+\frac{1103 \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^{3/2}}{259875}-\frac{124891 \sqrt{1-2 x} (5 x+3)^{3/2} \sqrt{3 x+2}}{2165625}-\frac{18177329 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{38981250}-\frac{18177329 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{17718750 \sqrt{33}}-\frac{604915631 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{17718750 \sqrt{33}}",1,"Could not integrate","F",-1
2700,0,0,191,0.9226527,"\int (1-2 x)^{3/2} (2+3 x)^{3/2} \sqrt{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x],x]","\int (1-2 x)^{3/2} (2+3 x)^{3/2} \sqrt{3+5 x} \, dx","\frac{2}{45} (1-2 x)^{3/2} (3 x+2)^{3/2} (5 x+3)^{3/2}+\frac{62 \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{3/2}}{1575}-\frac{347 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{39375}-\frac{84134 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{354375}-\frac{84134 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1771875}-\frac{5684677 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3543750}",1,"Could not integrate","F",-1
2701,0,0,160,0.5384096,"\int (1-2 x)^{3/2} \sqrt{2+3 x} \sqrt{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x],x]","\int (1-2 x)^{3/2} \sqrt{2+3 x} \sqrt{3+5 x} \, dx","\frac{2}{35} (1-2 x)^{3/2} \sqrt{3 x+2} (5 x+3)^{3/2}+\frac{194 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{2625}-\frac{2657 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{23625}-\frac{2657 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{118125}-\frac{118898 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{118125}",1,"Could not integrate","F",-1
2702,0,0,129,0.5489897,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{\sqrt{2+3 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/Sqrt[2 + 3*x],x]","\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{\sqrt{2+3 x}} \, dx","\frac{2}{15} \sqrt{3 x+2} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{214}{675} \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{412 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3375}-\frac{4157 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3375}",1,"Could not integrate","F",-1
2703,0,0,129,0.8633795,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(3/2),x]","\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^{3/2}} \, dx","-\frac{2 \sqrt{5 x+3} (1-2 x)^{3/2}}{3 \sqrt{3 x+2}}-\frac{16}{27} \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}-\frac{214}{135} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{494}{135} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2704,0,0,129,0.8153405,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(5/2),x]","\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^{5/2}} \, dx","-\frac{2 \sqrt{5 x+3} (1-2 x)^{3/2}}{9 (3 x+2)^{3/2}}+\frac{82 \sqrt{5 x+3} \sqrt{1-2 x}}{27 \sqrt{3 x+2}}+\frac{16}{27} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{98}{27} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2705,0,0,160,0.9200295,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(7/2),x]","\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^{7/2}} \, dx","-\frac{2 \sqrt{5 x+3} (1-2 x)^{3/2}}{15 (3 x+2)^{5/2}}+\frac{3896 \sqrt{5 x+3} \sqrt{1-2 x}}{945 \sqrt{3 x+2}}+\frac{82 \sqrt{5 x+3} \sqrt{1-2 x}}{135 (3 x+2)^{3/2}}-\frac{164}{945} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{3896}{945} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2706,0,0,191,0.9518956,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^{9/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(9/2),x]","\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^{9/2}} \, dx","-\frac{2 \sqrt{5 x+3} (1-2 x)^{3/2}}{21 (3 x+2)^{7/2}}+\frac{595324 \sqrt{5 x+3} \sqrt{1-2 x}}{46305 \sqrt{3 x+2}}+\frac{8516 \sqrt{5 x+3} \sqrt{1-2 x}}{6615 (3 x+2)^{3/2}}+\frac{82 \sqrt{5 x+3} \sqrt{1-2 x}}{315 (3 x+2)^{5/2}}-\frac{18016 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{46305}-\frac{595324 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{46305}",1,"Could not integrate","F",-1
2707,0,0,222,1.0130386,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^{11/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(11/2),x]","\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^{11/2}} \, dx","-\frac{2 \sqrt{5 x+3} (1-2 x)^{3/2}}{27 (3 x+2)^{9/2}}+\frac{42623864 \sqrt{5 x+3} \sqrt{1-2 x}}{972405 \sqrt{3 x+2}}+\frac{613276 \sqrt{5 x+3} \sqrt{1-2 x}}{138915 (3 x+2)^{3/2}}+\frac{13136 \sqrt{5 x+3} \sqrt{1-2 x}}{19845 (3 x+2)^{5/2}}+\frac{82 \sqrt{5 x+3} \sqrt{1-2 x}}{567 (3 x+2)^{7/2}}-\frac{1282376 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{972405}-\frac{42623864 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{972405}",1,"Could not integrate","F",-1
2708,0,0,249,1.2097696,"\int (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2),x]","\int (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{3/2} \, dx","\frac{2}{65} (1-2 x)^{3/2} (3 x+2)^{5/2} (5 x+3)^{5/2}+\frac{178 \sqrt{1-2 x} (3 x+2)^{5/2} (5 x+3)^{5/2}}{10725}+\frac{601 \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}}{160875}-\frac{18034 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{625625}-\frac{11725073 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{56306250}-\frac{776112041 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{506756250}-\frac{776112041 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{230343750 \sqrt{33}}-\frac{51601293223 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{460687500 \sqrt{33}}",1,"Could not integrate","F",-1
2709,0,0,218,1.1095516,"\int (1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2),x]","\int (1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2} \, dx","\frac{2}{55} (1-2 x)^{3/2} (3 x+2)^{3/2} (5 x+3)^{5/2}+\frac{62 \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}}{2475}-\frac{23 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{9625}-\frac{40703 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{433125}-\frac{5442127 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{7796250}-\frac{5442127 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3543750 \sqrt{33}}-\frac{90397364 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1771875 \sqrt{33}}",1,"Could not integrate","F",-1
2710,0,0,191,0.8398219,"\int (1-2 x)^{3/2} \sqrt{2+3 x} (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2),x]","\int (1-2 x)^{3/2} \sqrt{2+3 x} (3+5 x)^{3/2} \, dx","\frac{2}{45} (1-2 x)^{3/2} \sqrt{3 x+2} (5 x+3)^{5/2}+\frac{194 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{4725}-\frac{839 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{23625}-\frac{76163 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{212625}-\frac{76163 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1063125}-\frac{4971289 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2126250}",1,"Could not integrate","F",-1
2711,0,0,160,0.9069907,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{\sqrt{2+3 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/Sqrt[2 + 3*x],x]","\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{\sqrt{2+3 x}} \, dx","\frac{2}{21} (1-2 x)^{3/2} \sqrt{3 x+2} (5 x+3)^{3/2}+\frac{74}{525} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{1847 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{4725}-\frac{1847 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{23625}-\frac{29933 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{23625}",1,"Could not integrate","F",-1
2712,0,0,160,1.1642371,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(3/2),x]","\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{3/2}} \, dx","-\frac{8}{15} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{2 (1-2 x)^{3/2} (5 x+3)^{3/2}}{3 \sqrt{3 x+2}}+\frac{494}{135} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+\frac{494}{675} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{2209}{675} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2713,0,0,160,1.1799257,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(5/2),x]","\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{5/2}} \, dx","\frac{74 \sqrt{1-2 x} (5 x+3)^{3/2}}{9 \sqrt{3 x+2}}-\frac{2 (1-2 x)^{3/2} (5 x+3)^{3/2}}{9 (3 x+2)^{3/2}}-\frac{1150}{81} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{230}{81} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{592}{81} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2714,0,0,160,1.2101141,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(7/2),x]","\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{7/2}} \, dx","\frac{74 \sqrt{1-2 x} (5 x+3)^{3/2}}{45 (3 x+2)^{3/2}}-\frac{2 (1-2 x)^{3/2} (5 x+3)^{3/2}}{15 (3 x+2)^{5/2}}+\frac{988 \sqrt{1-2 x} \sqrt{5 x+3}}{945 \sqrt{3 x+2}}+\frac{988}{945} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{4418}{945} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2715,0,0,191,1.2711722,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{9/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(9/2),x]","\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{9/2}} \, dx","\frac{74 \sqrt{1-2 x} (5 x+3)^{3/2}}{105 (3 x+2)^{5/2}}-\frac{2 (1-2 x)^{3/2} (5 x+3)^{3/2}}{21 (3 x+2)^{7/2}}+\frac{119732 \sqrt{1-2 x} \sqrt{5 x+3}}{46305 \sqrt{3 x+2}}-\frac{3632 \sqrt{1-2 x} \sqrt{5 x+3}}{6615 (3 x+2)^{3/2}}-\frac{7388 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{46305}-\frac{119732 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{46305}",1,"Could not integrate","F",-1
2716,0,0,222,1.3263174,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{11/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(11/2),x]","\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{11/2}} \, dx","\frac{74 \sqrt{1-2 x} (5 x+3)^{3/2}}{189 (3 x+2)^{7/2}}-\frac{2 (1-2 x)^{3/2} (5 x+3)^{3/2}}{27 (3 x+2)^{9/2}}+\frac{19885156 \sqrt{1-2 x} \sqrt{5 x+3}}{2917215 \sqrt{3 x+2}}+\frac{280904 \sqrt{1-2 x} \sqrt{5 x+3}}{416745 (3 x+2)^{3/2}}-\frac{8252 \sqrt{1-2 x} \sqrt{5 x+3}}{19845 (3 x+2)^{5/2}}-\frac{609304 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2917215}-\frac{19885156 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2917215}",1,"Could not integrate","F",-1
2717,0,0,249,1.3945689,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{13/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(13/2),x]","\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{13/2}} \, dx","\frac{74 \sqrt{1-2 x} (5 x+3)^{3/2}}{297 (3 x+2)^{9/2}}-\frac{2 (1-2 x)^{3/2} (5 x+3)^{3/2}}{33 (3 x+2)^{11/2}}+\frac{1446357824 \sqrt{1-2 x} \sqrt{5 x+3}}{74875185 \sqrt{3 x+2}}+\frac{20799916 \sqrt{1-2 x} \sqrt{5 x+3}}{10696455 (3 x+2)^{3/2}}+\frac{442076 \sqrt{1-2 x} \sqrt{5 x+3}}{1528065 (3 x+2)^{5/2}}-\frac{12872 \sqrt{1-2 x} \sqrt{5 x+3}}{43659 (3 x+2)^{7/2}}-\frac{43537016 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6806835 \sqrt{33}}-\frac{1446357824 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6806835 \sqrt{33}}",1,"Could not integrate","F",-1
2718,0,0,280,1.2475027,"\int (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2),x]","\int (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2} \, dx","\frac{2}{75} (1-2 x)^{3/2} (3 x+2)^{5/2} (5 x+3)^{7/2}+\frac{178 \sqrt{1-2 x} (3 x+2)^{5/2} (5 x+3)^{7/2}}{14625}+\frac{2503 \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{7/2}}{804375}-\frac{199721 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{7/2}}{12065625}-\frac{57509209 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{506756250}-\frac{380132617 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{506756250}-\frac{50299451003 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{9121612500}-\frac{50299451003 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{4146187500 \sqrt{33}}-\frac{836091184171 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2073093750 \sqrt{33}}",1,"Could not integrate","F",-1
2719,0,0,249,1.2128805,"\int (1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2),x]","\int (1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{5/2} \, dx","\frac{2}{65} (1-2 x)^{3/2} (3 x+2)^{3/2} (5 x+3)^{7/2}+\frac{62 \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{7/2}}{3575}-\frac{67 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{7/2}}{160875}-\frac{160084 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{3378375}-\frac{2133359 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{6756750}-\frac{70536439 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{30405375}-\frac{70536439 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{13820625 \sqrt{33}}-\frac{9380126059 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{55282500 \sqrt{33}}",1,"Could not integrate","F",-1
2720,0,0,218,0.7532023,"\int (1-2 x)^{3/2} \sqrt{2+3 x} (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)*Sqrt[2 + 3*x]*(3 + 5*x)^(5/2),x]","\int (1-2 x)^{3/2} \sqrt{2+3 x} (3+5 x)^{5/2} \, dx","\frac{2}{55} (1-2 x)^{3/2} \sqrt{3 x+2} (5 x+3)^{7/2}+\frac{194 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{7/2}}{7425}-\frac{2377 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{155925}-\frac{22576 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{155925}-\frac{2930159 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{2806650}-\frac{2930159 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1275750 \sqrt{33}}-\frac{97540001 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1275750 \sqrt{33}}",1,"Could not integrate","F",-1
2721,0,0,191,0.8578405,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{\sqrt{2+3 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/Sqrt[2 + 3*x],x]","\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{\sqrt{2+3 x}} \, dx","\frac{2}{27} (1-2 x)^{3/2} \sqrt{3 x+2} (5 x+3)^{5/2}+\frac{46}{567} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}-\frac{499 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{2835}-\frac{11908 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{25515}-\frac{11908 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{127575}-\frac{886499 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{255150}",1,"Could not integrate","F",-1
2722,0,0,191,1.2012205,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(3/2),x]","\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{3/2}} \, dx","-\frac{32}{63} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}-\frac{2 (1-2 x)^{3/2} (5 x+3)^{5/2}}{3 \sqrt{3 x+2}}+\frac{202}{63} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{1061}{567} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{1061 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2835}-\frac{2894 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2835}",1,"Could not integrate","F",-1
2723,0,0,191,1.2530463,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(5/2),x]","\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{5/2}} \, dx","\frac{362 \sqrt{1-2 x} (5 x+3)^{5/2}}{27 \sqrt{3 x+2}}-\frac{2 (1-2 x)^{3/2} (5 x+3)^{5/2}}{9 (3 x+2)^{3/2}}-\frac{614}{27} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}+\frac{2632}{243} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+\frac{2632 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1215}-\frac{9587 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1215}",1,"Could not integrate","F",-1
2724,0,0,191,1.2475219,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(7/2),x]","\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{7/2}} \, dx","\frac{362 \sqrt{1-2 x} (5 x+3)^{5/2}}{135 (3 x+2)^{3/2}}-\frac{2 (1-2 x)^{3/2} (5 x+3)^{5/2}}{15 (3 x+2)^{5/2}}+\frac{9808 \sqrt{1-2 x} (5 x+3)^{3/2}}{945 \sqrt{3 x+2}}-\frac{43214 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{1701}-\frac{43214 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{8505}+\frac{116854 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{8505}",1,"Could not integrate","F",-1
2725,0,0,191,1.2995037,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{9/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(9/2),x]","\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{9/2}} \, dx","\frac{362 \sqrt{1-2 x} (5 x+3)^{5/2}}{315 (3 x+2)^{5/2}}-\frac{2 (1-2 x)^{3/2} (5 x+3)^{5/2}}{21 (3 x+2)^{7/2}}+\frac{2108 \sqrt{1-2 x} (5 x+3)^{3/2}}{6615 (3 x+2)^{3/2}}+\frac{249448 \sqrt{1-2 x} \sqrt{5 x+3}}{138915 \sqrt{3 x+2}}+\frac{249448 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{138915}-\frac{962678 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{138915}",1,"Could not integrate","F",-1
2726,0,0,222,1.365835,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{11/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(11/2),x]","\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{11/2}} \, dx","\frac{362 \sqrt{1-2 x} (5 x+3)^{5/2}}{567 (3 x+2)^{7/2}}-\frac{2 (1-2 x)^{3/2} (5 x+3)^{5/2}}{27 (3 x+2)^{9/2}}-\frac{1864 \sqrt{1-2 x} (5 x+3)^{3/2}}{6615 (3 x+2)^{5/2}}+\frac{17830424 \sqrt{1-2 x} \sqrt{5 x+3}}{8751645 \sqrt{3 x+2}}-\frac{558524 \sqrt{1-2 x} \sqrt{5 x+3}}{1250235 (3 x+2)^{3/2}}-\frac{1717916 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{8751645}-\frac{17830424 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{8751645}",1,"Could not integrate","F",-1
2727,0,0,249,1.3965315,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{13/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(13/2),x]","\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{13/2}} \, dx","\frac{362 \sqrt{1-2 x} (5 x+3)^{5/2}}{891 (3 x+2)^{9/2}}-\frac{2 (1-2 x)^{3/2} (5 x+3)^{5/2}}{33 (3 x+2)^{11/2}}-\frac{13292 \sqrt{1-2 x} (5 x+3)^{3/2}}{43659 (3 x+2)^{7/2}}+\frac{3316711588 \sqrt{1-2 x} \sqrt{5 x+3}}{673876665 \sqrt{3 x+2}}+\frac{45748292 \sqrt{1-2 x} \sqrt{5 x+3}}{96268095 (3 x+2)^{3/2}}-\frac{1366496 \sqrt{1-2 x} \sqrt{5 x+3}}{4584195 (3 x+2)^{5/2}}-\frac{103970992 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{61261515 \sqrt{33}}-\frac{3316711588 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{61261515 \sqrt{33}}",1,"Could not integrate","F",-1
2728,0,0,280,1.4419849,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{15/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(15/2),x]","\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{15/2}} \, dx","\frac{362 \sqrt{1-2 x} (5 x+3)^{5/2}}{1287 (3 x+2)^{11/2}}-\frac{2 (1-2 x)^{3/2} (5 x+3)^{5/2}}{39 (3 x+2)^{13/2}}-\frac{20992 \sqrt{1-2 x} (5 x+3)^{3/2}}{81081 (3 x+2)^{9/2}}+\frac{245282464136 \sqrt{1-2 x} \sqrt{5 x+3}}{20440925505 \sqrt{3 x+2}}+\frac{3523482724 \sqrt{1-2 x} \sqrt{5 x+3}}{2920132215 (3 x+2)^{3/2}}+\frac{73596464 \sqrt{1-2 x} \sqrt{5 x+3}}{417161745 (3 x+2)^{5/2}}-\frac{2174468 \sqrt{1-2 x} \sqrt{5 x+3}}{11918907 (3 x+2)^{7/2}}-\frac{7391549624 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1858265955 \sqrt{33}}-\frac{245282464136 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1858265955 \sqrt{33}}",1,"Could not integrate","F",-1
2729,0,0,191,0.8150768,"\int \frac{(1-2 x)^{3/2} (2+3 x)^{5/2}}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2))/Sqrt[3 + 5*x],x]","\int \frac{(1-2 x)^{3/2} (2+3 x)^{5/2}}{\sqrt{3+5 x}} \, dx","\frac{2}{45} (1-2 x)^{3/2} \sqrt{5 x+3} (3 x+2)^{5/2}+\frac{178 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{5/2}}{4725}+\frac{403 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{118125}-\frac{87476 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{590625}-\frac{104663 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2953125}-\frac{6515539 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5906250}",1,"Could not integrate","F",-1
2730,0,0,160,0.8891966,"\int \frac{(1-2 x)^{3/2} (2+3 x)^{3/2}}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2))/Sqrt[3 + 5*x],x]","\int \frac{(1-2 x)^{3/2} (2+3 x)^{3/2}}{\sqrt{3+5 x}} \, dx","\frac{2}{35} (1-2 x)^{3/2} \sqrt{5 x+3} (3 x+2)^{3/2}+\frac{62}{875} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}-\frac{487 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{13125}-\frac{2281 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{65625}-\frac{46159 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{65625}",1,"Could not integrate","F",-1
2731,0,0,129,0.5992655,"\int \frac{(1-2 x)^{3/2} \sqrt{2+3 x}}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*Sqrt[2 + 3*x])/Sqrt[3 + 5*x],x]","\int \frac{(1-2 x)^{3/2} \sqrt{2+3 x}}{\sqrt{3+5 x}} \, dx","\frac{2}{25} \sqrt{3 x+2} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{194 \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}}{1125}-\frac{598 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5625}-\frac{2797 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5625}",1,"Could not integrate","F",-1
2732,0,0,98,0.5814642,"\int \frac{(1-2 x)^{3/2}}{\sqrt{2+3 x} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/(Sqrt[2 + 3*x]*Sqrt[3 + 5*x]),x]","\int \frac{(1-2 x)^{3/2}}{\sqrt{2+3 x} \sqrt{3+5 x}} \, dx","-\frac{4}{45} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{202}{225} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{272}{225} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2733,0,0,98,0.9465894,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^(3/2)*Sqrt[3 + 5*x]),x]","\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","\frac{14 \sqrt{1-2 x} \sqrt{5 x+3}}{3 \sqrt{3 x+2}}+\frac{4}{15} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{74}{15} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2734,0,0,129,0.8233575,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^(5/2)*Sqrt[3 + 5*x]),x]","\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","\frac{124 \sqrt{1-2 x} \sqrt{5 x+3}}{9 \sqrt{3 x+2}}+\frac{14 \sqrt{1-2 x} \sqrt{5 x+3}}{9 (3 x+2)^{3/2}}-\frac{4}{9} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{124}{9} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2735,0,0,160,0.9809765,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^(7/2)*Sqrt[3 + 5*x]),x]","\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","\frac{17804 \sqrt{1-2 x} \sqrt{5 x+3}}{315 \sqrt{3 x+2}}+\frac{256 \sqrt{1-2 x} \sqrt{5 x+3}}{45 (3 x+2)^{3/2}}+\frac{14 \sqrt{1-2 x} \sqrt{5 x+3}}{15 (3 x+2)^{5/2}}-\frac{536}{315} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{17804}{315} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2736,0,0,191,1.0547611,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{9/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^(9/2)*Sqrt[3 + 5*x]),x]","\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{9/2} \sqrt{3+5 x}} \, dx","\frac{1255552 \sqrt{1-2 x} \sqrt{5 x+3}}{5145 \sqrt{3 x+2}}+\frac{18068 \sqrt{1-2 x} \sqrt{5 x+3}}{735 (3 x+2)^{3/2}}+\frac{388 \sqrt{1-2 x} \sqrt{5 x+3}}{105 (3 x+2)^{5/2}}+\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{3 (3 x+2)^{7/2}}-\frac{37768 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5145}-\frac{1255552 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5145}",1,"Could not integrate","F",-1
2737,0,0,222,1.0456424,"\int \frac{(1-2 x)^{3/2} (2+3 x)^{7/2}}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2))/(3 + 5*x)^(3/2),x]","\int \frac{(1-2 x)^{3/2} (2+3 x)^{7/2}}{(3+5 x)^{3/2}} \, dx","-\frac{8}{45} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{7/2}-\frac{2 (1-2 x)^{3/2} (3 x+2)^{7/2}}{5 \sqrt{5 x+3}}+\frac{958 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{5/2}}{1575}+\frac{5153 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{39375}-\frac{12601 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{196875}-\frac{31288 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{984375}-\frac{1473539 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1968750}",1,"Could not integrate","F",-1
2738,0,0,191,1.009449,"\int \frac{(1-2 x)^{3/2} (2+3 x)^{5/2}}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2))/(3 + 5*x)^(3/2),x]","\int \frac{(1-2 x)^{3/2} (2+3 x)^{5/2}}{(3+5 x)^{3/2}} \, dx","-\frac{32}{175} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{5/2}-\frac{2 (1-2 x)^{3/2} (3 x+2)^{5/2}}{5 \sqrt{5 x+3}}+\frac{2818 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{4375}+\frac{2719 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{21875}-\frac{5753 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{109375}-\frac{47342 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{109375}",1,"Could not integrate","F",-1
2739,0,0,160,0.9665073,"\int \frac{(1-2 x)^{3/2} (2+3 x)^{3/2}}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2))/(3 + 5*x)^(3/2),x]","\int \frac{(1-2 x)^{3/2} (2+3 x)^{3/2}}{(3+5 x)^{3/2}} \, dx","-\frac{24}{125} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}-\frac{2 (1-2 x)^{3/2} (3 x+2)^{3/2}}{5 \sqrt{5 x+3}}+\frac{458}{625} \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}-\frac{496 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3125}-\frac{169 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3125}",1,"Could not integrate","F",-1
2740,0,0,129,0.8359199,"\int \frac{(1-2 x)^{3/2} \sqrt{2+3 x}}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*Sqrt[2 + 3*x])/(3 + 5*x)^(3/2),x]","\int \frac{(1-2 x)^{3/2} \sqrt{2+3 x}}{(3+5 x)^{3/2}} \, dx","-\frac{2 \sqrt{3 x+2} (1-2 x)^{3/2}}{5 \sqrt{5 x+3}}-\frac{16}{75} \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}-\frac{178}{375} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{458}{375} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2741,0,0,98,0.9237358,"\int \frac{(1-2 x)^{3/2}}{\sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/(Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)),x]","\int \frac{(1-2 x)^{3/2}}{\sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","-\frac{22 \sqrt{1-2 x} \sqrt{3 x+2}}{5 \sqrt{5 x+3}}+\frac{8}{25} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{62}{25} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2742,0,0,129,0.9794903,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","-\frac{136 \sqrt{1-2 x} \sqrt{3 x+2}}{3 \sqrt{5 x+3}}+\frac{14 \sqrt{1-2 x}}{3 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{4}{5} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{136}{5} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2743,0,0,160,1.0722674,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","-\frac{2660 \sqrt{1-2 x} \sqrt{3 x+2}}{9 \sqrt{5 x+3}}+\frac{88 \sqrt{1-2 x}}{3 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{14 \sqrt{1-2 x}}{9 (3 x+2)^{3/2} \sqrt{5 x+3}}+\frac{16}{3} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{532}{3} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2744,0,0,191,1.1349929,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","-\frac{36968 \sqrt{1-2 x} \sqrt{3 x+2}}{21 \sqrt{5 x+3}}+\frac{6116 \sqrt{1-2 x}}{35 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{44 \sqrt{1-2 x}}{5 (3 x+2)^{3/2} \sqrt{5 x+3}}+\frac{14 \sqrt{1-2 x}}{15 (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{1112}{35} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{36968}{35} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2745,0,0,222,1.2103453,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{9/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^(9/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{9/2} (3+5 x)^{3/2}} \, dx","-\frac{10312712 \sqrt{1-2 x} \sqrt{3 x+2}}{1029 \sqrt{5 x+3}}+\frac{1706144 \sqrt{1-2 x}}{1715 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{12276 \sqrt{1-2 x}}{245 (3 x+2)^{3/2} \sqrt{5 x+3}}+\frac{176 \sqrt{1-2 x}}{35 (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{2 \sqrt{1-2 x}}{3 (3 x+2)^{7/2} \sqrt{5 x+3}}+\frac{310208 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1715}+\frac{10312712 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1715}",1,"Could not integrate","F",-1
2746,0,0,220,1.071,"\int \frac{(1-2 x)^{3/2} (2+3 x)^{7/2}}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2))/(3 + 5*x)^(5/2),x]","\int \frac{(1-2 x)^{3/2} (2+3 x)^{7/2}}{(3+5 x)^{5/2}} \, dx","-\frac{6 \sqrt{1-2 x} (3 x+2)^{7/2}}{\sqrt{5 x+3}}-\frac{2 (1-2 x)^{3/2} (3 x+2)^{7/2}}{15 (5 x+3)^{3/2}}+\frac{622}{175} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{5/2}+\frac{3872 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{4375}+\frac{4801 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{21875}-\frac{24369 \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{109375}-\frac{25643 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{109375}",1,"Could not integrate","F",-1
2747,0,0,191,1.0348753,"\int \frac{(1-2 x)^{3/2} (2+3 x)^{5/2}}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2))/(3 + 5*x)^(5/2),x]","\int \frac{(1-2 x)^{3/2} (2+3 x)^{5/2}}{(3+5 x)^{5/2}} \, dx","-\frac{106 \sqrt{1-2 x} (3 x+2)^{5/2}}{25 \sqrt{5 x+3}}-\frac{2 (1-2 x)^{3/2} (3 x+2)^{5/2}}{15 (5 x+3)^{3/2}}+\frac{1558}{625} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}+\frac{2264 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{3125}-\frac{8366 \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{15625}+\frac{1973 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{15625}",1,"Could not integrate","F",-1
2748,0,0,160,0.9906078,"\int \frac{(1-2 x)^{3/2} (2+3 x)^{3/2}}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2))/(3 + 5*x)^(5/2),x]","\int \frac{(1-2 x)^{3/2} (2+3 x)^{3/2}}{(3+5 x)^{5/2}} \, dx","-\frac{62 \sqrt{1-2 x} (3 x+2)^{3/2}}{25 \sqrt{5 x+3}}-\frac{2 (1-2 x)^{3/2} (3 x+2)^{3/2}}{15 (5 x+3)^{3/2}}+\frac{178}{125} \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}-\frac{582}{625} \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{496}{625} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2749,0,0,127,0.8039488,"\int \frac{(1-2 x)^{3/2} \sqrt{2+3 x}}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(3/2)*Sqrt[2 + 3*x])/(3 + 5*x)^(5/2),x]","\int \frac{(1-2 x)^{3/2} \sqrt{2+3 x}}{(3+5 x)^{5/2}} \, dx","-\frac{2 \sqrt{3 x+2} (1-2 x)^{3/2}}{15 (5 x+3)^{3/2}}-\frac{18 \sqrt{3 x+2} \sqrt{1-2 x}}{25 \sqrt{5 x+3}}+\frac{212 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{125 \sqrt{33}}+\frac{38}{125} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2750,0,0,127,0.8096119,"\int \frac{(1-2 x)^{3/2}}{\sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/(Sqrt[2 + 3*x]*(3 + 5*x)^(5/2)),x]","\int \frac{(1-2 x)^{3/2}}{\sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","\frac{148 \sqrt{1-2 x} \sqrt{3 x+2}}{15 \sqrt{5 x+3}}-\frac{22 \sqrt{1-2 x} \sqrt{3 x+2}}{15 (5 x+3)^{3/2}}-\frac{52 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{25 \sqrt{33}}-\frac{148}{25} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2751,0,0,158,1.056322,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","\frac{556 \sqrt{1-2 x} \sqrt{3 x+2}}{3 \sqrt{5 x+3}}-\frac{92 \sqrt{1-2 x} \sqrt{3 x+2}}{3 (5 x+3)^{3/2}}+\frac{14 \sqrt{1-2 x}}{3 \sqrt{3 x+2} (5 x+3)^{3/2}}-\frac{184 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5 \sqrt{33}}-\frac{556}{5} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2752,0,0,185,1.0866227,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","\frac{5440 \sqrt{1-2 x} \sqrt{3 x+2}}{3 \sqrt{5 x+3}}-\frac{300 \sqrt{1-2 x} \sqrt{3 x+2}}{(5 x+3)^{3/2}}+\frac{404 \sqrt{1-2 x}}{9 \sqrt{3 x+2} (5 x+3)^{3/2}}+\frac{14 \sqrt{1-2 x}}{9 (3 x+2)^{3/2} (5 x+3)^{3/2}}-120 \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-1088 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2753,0,0,222,1.1796626,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(3/2)/((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","\frac{301304 \sqrt{1-2 x} \sqrt{3 x+2}}{21 \sqrt{5 x+3}}-\frac{16616 \sqrt{1-2 x} \sqrt{3 x+2}}{7 (5 x+3)^{3/2}}+\frac{111884 \sqrt{1-2 x}}{315 \sqrt{3 x+2} (5 x+3)^{3/2}}+\frac{536 \sqrt{1-2 x}}{45 (3 x+2)^{3/2} (5 x+3)^{3/2}}+\frac{14 \sqrt{1-2 x}}{15 (3 x+2)^{5/2} (5 x+3)^{3/2}}-\frac{33232}{35} \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{301304}{35} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2754,0,0,249,0.9858549,"\int (1-2 x)^{5/2} (2+3 x)^{5/2} \sqrt{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x],x]","\int (1-2 x)^{5/2} (2+3 x)^{5/2} \sqrt{3+5 x} \, dx","\frac{2}{65} (1-2 x)^{5/2} (5 x+3)^{3/2} (3 x+2)^{5/2}+\frac{62 (1-2 x)^{3/2} (5 x+3)^{3/2} (3 x+2)^{5/2}}{2145}+\frac{34 \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^{5/2}}{2475}+\frac{32717 \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^{3/2}}{1126125}-\frac{445024 \sqrt{1-2 x} (5 x+3)^{3/2} \sqrt{3 x+2}}{9384375}-\frac{69808931 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{168918750}-\frac{69808931 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{76781250 \sqrt{33}}-\frac{1163388067 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{38390625 \sqrt{33}}",1,"Could not integrate","F",-1
2755,0,0,218,0.7611628,"\int (1-2 x)^{5/2} (2+3 x)^{3/2} \sqrt{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x],x]","\int (1-2 x)^{5/2} (2+3 x)^{3/2} \sqrt{3+5 x} \, dx","\frac{2}{55} (3 x+2)^{3/2} (5 x+3)^{3/2} (1-2 x)^{5/2}+\frac{106 (3 x+2)^{3/2} (5 x+3)^{3/2} (1-2 x)^{3/2}}{2475}+\frac{2866 (3 x+2)^{3/2} (5 x+3)^{3/2} \sqrt{1-2 x}}{86625}+\frac{38729 \sqrt{3 x+2} (5 x+3)^{3/2} \sqrt{1-2 x}}{2165625}-\frac{4738087 \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}}{19490625}-\frac{4738087 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{8859375 \sqrt{33}}-\frac{326256461 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{17718750 \sqrt{33}}",1,"Could not integrate","F",-1
2756,0,0,191,0.4540166,"\int (1-2 x)^{5/2} \sqrt{2+3 x} \sqrt{3+5 x} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x],x]","\int (1-2 x)^{5/2} \sqrt{2+3 x} \sqrt{3+5 x} \, dx","\frac{2}{45} \sqrt{3 x+2} (5 x+3)^{3/2} (1-2 x)^{5/2}+\frac{326 \sqrt{3 x+2} (5 x+3)^{3/2} (1-2 x)^{3/2}}{4725}+\frac{10214 \sqrt{3 x+2} (5 x+3)^{3/2} \sqrt{1-2 x}}{118125}-\frac{110717 \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}}{1063125}-\frac{110717 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5315625}-\frac{6799613 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5315625}",1,"Could not integrate","F",-1
2757,0,0,160,0.4248724,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{\sqrt{2+3 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/Sqrt[2 + 3*x],x]","\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{\sqrt{2+3 x}} \, dx","\frac{2}{21} \sqrt{3 x+2} \sqrt{5 x+3} (1-2 x)^{5/2}+\frac{118}{525} \sqrt{3 x+2} \sqrt{5 x+3} (1-2 x)^{3/2}+\frac{4282 \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}}{7875}+\frac{11806 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{39375}-\frac{86741 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{39375}",1,"Could not integrate","F",-1
2758,0,0,160,0.7461636,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(3/2),x]","\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{3/2}} \, dx","-\frac{2 \sqrt{5 x+3} (1-2 x)^{5/2}}{3 \sqrt{3 x+2}}-\frac{8}{15} \sqrt{3 x+2} \sqrt{5 x+3} (1-2 x)^{3/2}-\frac{1076}{675} \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}-\frac{12758 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3375}+\frac{31588 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3375}",1,"Could not integrate","F",-1
2759,0,0,160,0.9998787,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(5/2),x]","\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{5/2}} \, dx","-\frac{2 \sqrt{5 x+3} (1-2 x)^{5/2}}{9 (3 x+2)^{3/2}}+\frac{10 \sqrt{5 x+3} (1-2 x)^{3/2}}{3 \sqrt{3 x+2}}+\frac{196}{81} \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{988}{405} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{4418}{405} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2760,0,0,156,0.9818714,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(7/2),x]","\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{7/2}} \, dx","-\frac{2 \sqrt{5 x+3} (1-2 x)^{5/2}}{15 (3 x+2)^{5/2}}+\frac{2 \sqrt{5 x+3} (1-2 x)^{3/2}}{3 (3 x+2)^{3/2}}+\frac{8 \sqrt{5 x+3} \sqrt{1-2 x}}{\sqrt{3 x+2}}-\frac{4}{5} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{12}{5} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2761,0,0,191,1.0225136,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{9/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(9/2),x]","\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{9/2}} \, dx","-\frac{2 \sqrt{5 x+3} (1-2 x)^{5/2}}{21 (3 x+2)^{7/2}}+\frac{2 \sqrt{5 x+3} (1-2 x)^{3/2}}{7 (3 x+2)^{5/2}}+\frac{36052 \sqrt{5 x+3} \sqrt{1-2 x}}{1323 \sqrt{3 x+2}}+\frac{524 \sqrt{5 x+3} \sqrt{1-2 x}}{189 (3 x+2)^{3/2}}-\frac{1048 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1323}-\frac{36052 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1323}",1,"Could not integrate","F",-1
2762,0,0,222,1.0543694,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{11/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(11/2),x]","\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{11/2}} \, dx","-\frac{2 \sqrt{5 x+3} (1-2 x)^{5/2}}{27 (3 x+2)^{9/2}}+\frac{10 \sqrt{5 x+3} (1-2 x)^{3/2}}{63 (3 x+2)^{7/2}}+\frac{7810384 \sqrt{5 x+3} \sqrt{1-2 x}}{83349 \sqrt{3 x+2}}+\frac{112436 \sqrt{5 x+3} \sqrt{1-2 x}}{11907 (3 x+2)^{3/2}}+\frac{832 \sqrt{5 x+3} \sqrt{1-2 x}}{567 (3 x+2)^{5/2}}-\frac{234856 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{83349}-\frac{7810384 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{83349}",1,"Could not integrate","F",-1
2763,0,0,249,1.1244573,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{13/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(13/2),x]","\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{13/2}} \, dx","-\frac{2 \sqrt{5 x+3} (1-2 x)^{5/2}}{33 (3 x+2)^{11/2}}+\frac{10 \sqrt{5 x+3} (1-2 x)^{3/2}}{99 (3 x+2)^{9/2}}+\frac{247408648 \sqrt{5 x+3} \sqrt{1-2 x}}{713097 \sqrt{3 x+2}}+\frac{3560432 \sqrt{5 x+3} \sqrt{1-2 x}}{101871 (3 x+2)^{3/2}}+\frac{76492 \sqrt{5 x+3} \sqrt{1-2 x}}{14553 (3 x+2)^{5/2}}+\frac{1900 \sqrt{5 x+3} \sqrt{1-2 x}}{2079 (3 x+2)^{7/2}}-\frac{7442032 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{64827 \sqrt{33}}-\frac{247408648 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{64827 \sqrt{33}}",1,"Could not integrate","F",-1
2764,0,0,280,1.2826459,"\int (1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2),x]","\int (1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{3/2} \, dx","\frac{2}{75} (1-2 x)^{5/2} (3 x+2)^{5/2} (5 x+3)^{5/2}+\frac{62 (1-2 x)^{3/2} (3 x+2)^{5/2} (5 x+3)^{5/2}}{2925}+\frac{3698 \sqrt{1-2 x} (3 x+2)^{5/2} (5 x+3)^{5/2}}{482625}+\frac{142391 \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}}{7239375}-\frac{569519 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{28153125}-\frac{400516993 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{2533781250}-\frac{13267820528 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{11402015625}-\frac{13267820528 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5182734375 \sqrt{33}}-\frac{1764163292393 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{20730937500 \sqrt{33}}",1,"Could not integrate","F",-1
2765,0,0,249,1.2118014,"\int (1-2 x)^{5/2} (2+3 x)^{3/2} (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2),x]","\int (1-2 x)^{5/2} (2+3 x)^{3/2} (3+5 x)^{3/2} \, dx","\frac{2}{65} (1-2 x)^{5/2} (3 x+2)^{3/2} (5 x+3)^{5/2}+\frac{106 (1-2 x)^{3/2} (3 x+2)^{3/2} (5 x+3)^{5/2}}{3575}+\frac{8318 \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}}{482625}+\frac{25603 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{1876875}-\frac{6794792 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{84459375}-\frac{923943703 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{1520268750}-\frac{923943703 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{691031250 \sqrt{33}}-\frac{30660308017 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{691031250 \sqrt{33}}",1,"Could not integrate","F",-1
2766,0,0,218,0.7495219,"\int (1-2 x)^{5/2} \sqrt{2+3 x} (3+5 x)^{3/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2),x]","\int (1-2 x)^{5/2} \sqrt{2+3 x} (3+5 x)^{3/2} \, dx","\frac{2}{55} (1-2 x)^{5/2} \sqrt{3 x+2} (5 x+3)^{5/2}+\frac{326 (1-2 x)^{3/2} \sqrt{3 x+2} (5 x+3)^{5/2}}{7425}+\frac{30362 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{779625}-\frac{78797 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{3898125}-\frac{12996374 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{35083125}-\frac{12996374 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{15946875 \sqrt{33}}-\frac{829177897 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{31893750 \sqrt{33}}",1,"Could not integrate","F",-1
2767,0,0,191,0.8608119,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{\sqrt{2+3 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/Sqrt[2 + 3*x],x]","\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{\sqrt{2+3 x}} \, dx","\frac{2}{27} \sqrt{3 x+2} (5 x+3)^{3/2} (1-2 x)^{5/2}+\frac{362 \sqrt{3 x+2} (5 x+3)^{3/2} (1-2 x)^{3/2}}{2835}+\frac{14318 \sqrt{3 x+2} (5 x+3)^{3/2} \sqrt{1-2 x}}{70875}-\frac{429479 \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}}{637875}-\frac{429479 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3189375}-\frac{4457606 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3189375}",1,"Could not integrate","F",-1
2768,0,0,191,1.2222728,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(3/2),x]","\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{3/2}} \, dx","-\frac{2 (5 x+3)^{3/2} (1-2 x)^{5/2}}{3 \sqrt{3 x+2}}-\frac{32}{63} \sqrt{3 x+2} (5 x+3)^{3/2} (1-2 x)^{3/2}-\frac{2108 \sqrt{3 x+2} (5 x+3)^{3/2} \sqrt{1-2 x}}{1575}+\frac{124724 \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}}{14175}+\frac{124724 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{70875}-\frac{481339 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{70875}",1,"Could not integrate","F",-1
2769,0,0,191,1.2730693,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(5/2),x]","\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{5/2}} \, dx","-\frac{2 (5 x+3)^{3/2} (1-2 x)^{5/2}}{9 (3 x+2)^{3/2}}+\frac{230 (5 x+3)^{3/2} (1-2 x)^{3/2}}{27 \sqrt{3 x+2}}+\frac{788}{135} \sqrt{3 x+2} (5 x+3)^{3/2} \sqrt{1-2 x}-\frac{43214 \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}}{1215}-\frac{43214 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6075}+\frac{116854 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6075}",1,"Could not integrate","F",-1
2770,0,0,191,1.2730774,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(7/2),x]","\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{7/2}} \, dx","-\frac{2 (5 x+3)^{3/2} (1-2 x)^{5/2}}{15 (3 x+2)^{5/2}}+\frac{46 (5 x+3)^{3/2} (1-2 x)^{3/2}}{27 (3 x+2)^{3/2}}-\frac{316 (5 x+3)^{3/2} \sqrt{1-2 x}}{27 \sqrt{3 x+2}}+\frac{5264}{243} \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{5264 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1215}-\frac{19174 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1215}",1,"Could not integrate","F",-1
2771,0,0,191,1.3354454,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{9/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(9/2),x]","\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{9/2}} \, dx","-\frac{2 (5 x+3)^{3/2} (1-2 x)^{5/2}}{21 (3 x+2)^{7/2}}+\frac{46 (5 x+3)^{3/2} (1-2 x)^{3/2}}{63 (3 x+2)^{5/2}}+\frac{608 (5 x+3)^{3/2} \sqrt{1-2 x}}{189 (3 x+2)^{3/2}}-\frac{4244 \sqrt{5 x+3} \sqrt{1-2 x}}{3969 \sqrt{3 x+2}}-\frac{4244 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3969}-\frac{11576 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3969}",1,"Could not integrate","F",-1
2772,0,0,222,1.4026148,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{11/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(11/2),x]","\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{11/2}} \, dx","-\frac{2 (5 x+3)^{3/2} (1-2 x)^{5/2}}{27 (3 x+2)^{9/2}}+\frac{230 (5 x+3)^{3/2} (1-2 x)^{3/2}}{567 (3 x+2)^{7/2}}+\frac{1532 (5 x+3)^{3/2} \sqrt{1-2 x}}{567 (3 x+2)^{5/2}}+\frac{3545996 \sqrt{5 x+3} \sqrt{1-2 x}}{250047 \sqrt{3 x+2}}-\frac{104036 \sqrt{5 x+3} \sqrt{1-2 x}}{35721 (3 x+2)^{3/2}}-\frac{95264 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{250047}-\frac{3545996 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{250047}",1,"Could not integrate","F",-1
2773,0,0,249,1.4213915,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{13/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(13/2),x]","\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{13/2}} \, dx","-\frac{2 (5 x+3)^{3/2} (1-2 x)^{5/2}}{33 (3 x+2)^{11/2}}+\frac{230 (5 x+3)^{3/2} (1-2 x)^{3/2}}{891 (3 x+2)^{9/2}}+\frac{12280 (5 x+3)^{3/2} \sqrt{1-2 x}}{6237 (3 x+2)^{7/2}}+\frac{780320008 \sqrt{5 x+3} \sqrt{1-2 x}}{19253619 \sqrt{3 x+2}}+\frac{11243972 \sqrt{5 x+3} \sqrt{1-2 x}}{2750517 (3 x+2)^{3/2}}-\frac{325796 \sqrt{5 x+3} \sqrt{1-2 x}}{130977 (3 x+2)^{5/2}}-\frac{23441272 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1750329 \sqrt{33}}-\frac{780320008 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1750329 \sqrt{33}}",1,"Could not integrate","F",-1
2774,0,0,280,1.4441346,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{15/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(15/2),x]","\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{15/2}} \, dx","-\frac{2 (5 x+3)^{3/2} (1-2 x)^{5/2}}{39 (3 x+2)^{13/2}}+\frac{230 (5 x+3)^{3/2} (1-2 x)^{3/2}}{1287 (3 x+2)^{11/2}}+\frac{1300 (5 x+3)^{3/2} \sqrt{1-2 x}}{891 (3 x+2)^{9/2}}+\frac{75041008472 \sqrt{5 x+3} \sqrt{1-2 x}}{584026443 \sqrt{3 x+2}}+\frac{1079936248 \sqrt{5 x+3} \sqrt{1-2 x}}{83432349 (3 x+2)^{3/2}}+\frac{23210828 \sqrt{5 x+3} \sqrt{1-2 x}}{11918907 (3 x+2)^{5/2}}-\frac{3347620 \sqrt{5 x+3} \sqrt{1-2 x}}{1702701 (3 x+2)^{7/2}}-\frac{2257166048 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{53093313 \sqrt{33}}-\frac{75041008472 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{53093313 \sqrt{33}}",1,"Could not integrate","F",-1
2775,0,0,280,1.2876665,"\int (1-2 x)^{5/2} (2+3 x)^{3/2} (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2),x]","\int (1-2 x)^{5/2} (2+3 x)^{3/2} (3+5 x)^{5/2} \, dx","\frac{2}{75} (1-2 x)^{5/2} (3 x+2)^{3/2} (5 x+3)^{7/2}+\frac{106 (1-2 x)^{3/2} (3 x+2)^{3/2} (5 x+3)^{7/2}}{4875}+\frac{8038 \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{7/2}}{804375}+\frac{364267 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{7/2}}{36196875}-\frac{26534891 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{760134375}-\frac{359748241 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{1520268750}-\frac{23763809947 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{13682418750}-\frac{23763809947 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6219281250 \sqrt{33}}-\frac{1580201444291 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{12438562500 \sqrt{33}}",1,"Could not integrate","F",-1
2776,0,0,249,0.9669632,"\int (1-2 x)^{5/2} \sqrt{2+3 x} (3+5 x)^{5/2} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)*Sqrt[2 + 3*x]*(3 + 5*x)^(5/2),x]","\int (1-2 x)^{5/2} \sqrt{2+3 x} (3+5 x)^{5/2} \, dx","\frac{2}{65} (1-2 x)^{5/2} \sqrt{3 x+2} (5 x+3)^{7/2}+\frac{326 (1-2 x)^{3/2} \sqrt{3 x+2} (5 x+3)^{7/2}}{10725}+\frac{2314 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{7/2}}{111375}-\frac{121031 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{30405375}-\frac{3872003 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{30405375}-\frac{486785077 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{547296750}-\frac{486785077 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{248771250 \sqrt{33}}-\frac{8120161139 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{124385625 \sqrt{33}}",1,"Could not integrate","F",-1
2777,0,0,218,1.008715,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{\sqrt{2+3 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/Sqrt[2 + 3*x],x]","\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{\sqrt{2+3 x}} \, dx","\frac{2}{33} (1-2 x)^{5/2} \sqrt{3 x+2} (5 x+3)^{5/2}+\frac{74}{891} (1-2 x)^{3/2} \sqrt{3 x+2} (5 x+3)^{5/2}+\frac{9698 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{93555}-\frac{146963 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{467775}-\frac{1654421 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{4209975}-\frac{1654421 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1913625 \sqrt{33}}-\frac{146222113 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3827250 \sqrt{33}}",1,"Could not integrate","F",-1
2778,0,0,222,1.2986829,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(3/2),x]","\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{3/2}} \, dx","-\frac{40}{81} (1-2 x)^{3/2} \sqrt{3 x+2} (5 x+3)^{5/2}-\frac{2108 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{1701}-\frac{2 (1-2 x)^{5/2} (5 x+3)^{5/2}}{3 \sqrt{3 x+2}}+\frac{64628 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{8505}-\frac{310399 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{76545}-\frac{310399 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{382725}-\frac{25111 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{382725}",1,"Could not integrate","F",-1
2779,0,0,222,1.2943446,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(5/2),x]","\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{5/2}} \, dx","\frac{5260}{567} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}+\frac{370 (1-2 x)^{3/2} (5 x+3)^{5/2}}{27 \sqrt{3 x+2}}-\frac{2 (1-2 x)^{5/2} (5 x+3)^{5/2}}{9 (3 x+2)^{3/2}}-\frac{31298}{567} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}+\frac{135334 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{5103}+\frac{135334 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{25515}-\frac{452399 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{25515}",1,"Could not integrate","F",-1
2780,0,0,222,1.3057129,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(7/2),x]","\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{7/2}} \, dx","-\frac{6464 \sqrt{1-2 x} (5 x+3)^{5/2}}{81 \sqrt{3 x+2}}+\frac{74 (1-2 x)^{3/2} (5 x+3)^{5/2}}{27 (3 x+2)^{3/2}}-\frac{2 (1-2 x)^{5/2} (5 x+3)^{5/2}}{15 (3 x+2)^{5/2}}+\frac{11036}{81} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{48478}{729} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{48478 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3645}+\frac{136028 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3645}",1,"Could not integrate","F",-1
2781,0,0,222,1.3550158,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{9/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(9/2),x]","\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{9/2}} \, dx","-\frac{1844 \sqrt{1-2 x} (5 x+3)^{5/2}}{567 (3 x+2)^{3/2}}+\frac{74 (1-2 x)^{3/2} (5 x+3)^{5/2}}{63 (3 x+2)^{5/2}}-\frac{2 (1-2 x)^{5/2} (5 x+3)^{5/2}}{21 (3 x+2)^{7/2}}-\frac{62596 \sqrt{1-2 x} (5 x+3)^{3/2}}{3969 \sqrt{3 x+2}}+\frac{1353340 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{35721}+\frac{270668 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{35721}-\frac{904798 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{35721}",1,"Could not integrate","F",-1
2782,0,0,222,1.3956784,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{11/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(11/2),x]","\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{11/2}} \, dx","\frac{2776 \sqrt{1-2 x} (5 x+3)^{5/2}}{1701 (3 x+2)^{5/2}}+\frac{370 (1-2 x)^{3/2} (5 x+3)^{5/2}}{567 (3 x+2)^{7/2}}-\frac{2 (1-2 x)^{5/2} (5 x+3)^{5/2}}{27 (3 x+2)^{9/2}}-\frac{13316 \sqrt{1-2 x} (5 x+3)^{3/2}}{35721 (3 x+2)^{3/2}}-\frac{1241596 \sqrt{1-2 x} \sqrt{5 x+3}}{750141 \sqrt{3 x+2}}-\frac{1241596 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{750141}-\frac{100444 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{750141}",1,"Could not integrate","F",-1
2783,0,0,249,1.4668786,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{13/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(13/2),x]","\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{13/2}} \, dx","\frac{36980 \sqrt{1-2 x} (5 x+3)^{5/2}}{18711 (3 x+2)^{7/2}}+\frac{370 (1-2 x)^{3/2} (5 x+3)^{5/2}}{891 (3 x+2)^{9/2}}-\frac{2 (1-2 x)^{5/2} (5 x+3)^{5/2}}{33 (3 x+2)^{11/2}}-\frac{55772 \sqrt{1-2 x} (5 x+3)^{3/2}}{43659 (3 x+2)^{5/2}}+\frac{584888452 \sqrt{1-2 x} \sqrt{5 x+3}}{57760857 \sqrt{3 x+2}}-\frac{17089252 \sqrt{1-2 x} \sqrt{5 x+3}}{8251551 (3 x+2)^{3/2}}-\frac{13235368 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5250987 \sqrt{33}}-\frac{584888452 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5250987 \sqrt{33}}",1,"Could not integrate","F",-1
2784,0,0,280,1.4595023,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{15/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(15/2),x]","\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{15/2}} \, dx","\frac{60080 \sqrt{1-2 x} (5 x+3)^{5/2}}{34749 (3 x+2)^{9/2}}+\frac{370 (1-2 x)^{3/2} (5 x+3)^{5/2}}{1287 (3 x+2)^{11/2}}-\frac{2 (1-2 x)^{5/2} (5 x+3)^{5/2}}{39 (3 x+2)^{13/2}}-\frac{2622980 \sqrt{1-2 x} (5 x+3)^{3/2}}{1702701 (3 x+2)^{7/2}}+\frac{129922578224 \sqrt{1-2 x} \sqrt{5 x+3}}{5256237987 \sqrt{3 x+2}}+\frac{1876198516 \sqrt{1-2 x} \sqrt{5 x+3}}{750891141 (3 x+2)^{3/2}}-\frac{54281308 \sqrt{1-2 x} \sqrt{5 x+3}}{35756721 (3 x+2)^{5/2}}-\frac{3894280616 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{477839817 \sqrt{33}}-\frac{129922578224 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{477839817 \sqrt{33}}",1,"Could not integrate","F",-1
2785,0,0,311,1.4997769,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{17/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(17/2),x]","\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{17/2}} \, dx","\frac{16636 \sqrt{1-2 x} (5 x+3)^{5/2}}{11583 (3 x+2)^{11/2}}+\frac{74 (1-2 x)^{3/2} (5 x+3)^{5/2}}{351 (3 x+2)^{13/2}}-\frac{2 (1-2 x)^{5/2} (5 x+3)^{5/2}}{45 (3 x+2)^{15/2}}-\frac{1085156 \sqrt{1-2 x} (5 x+3)^{3/2}}{729729 (3 x+2)^{9/2}}+\frac{12641611554328 \sqrt{1-2 x} \sqrt{5 x+3}}{183968329545 \sqrt{3 x+2}}+\frac{181941877952 \sqrt{1-2 x} \sqrt{5 x+3}}{26281189935 (3 x+2)^{3/2}}+\frac{3914701972 \sqrt{1-2 x} \sqrt{5 x+3}}{3754455705 (3 x+2)^{5/2}}-\frac{112817764 \sqrt{1-2 x} \sqrt{5 x+3}}{107270163 (3 x+2)^{7/2}}-\frac{380220959152 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{16724393595 \sqrt{33}}-\frac{12641611554328 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{16724393595 \sqrt{33}}",1,"Could not integrate","F",-1
2786,0,0,218,1.0161592,"\int \frac{(1-2 x)^{5/2} (2+3 x)^{5/2}}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2))/Sqrt[3 + 5*x],x]","\int \frac{(1-2 x)^{5/2} (2+3 x)^{5/2}}{\sqrt{3+5 x}} \, dx","\frac{2}{55} (1-2 x)^{5/2} \sqrt{5 x+3} (3 x+2)^{5/2}+\frac{62 (1-2 x)^{3/2} \sqrt{5 x+3} (3 x+2)^{5/2}}{1485}+\frac{4258 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{5/2}}{155925}+\frac{181333 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{3898125}-\frac{2865161 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{19490625}-\frac{3963068 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{8859375 \sqrt{33}}-\frac{231061879 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{17718750 \sqrt{33}}",1,"Could not integrate","F",-1
2787,0,0,191,0.8079373,"\int \frac{(1-2 x)^{5/2} (2+3 x)^{3/2}}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2))/Sqrt[3 + 5*x],x]","\int \frac{(1-2 x)^{5/2} (2+3 x)^{3/2}}{\sqrt{3+5 x}} \, dx","\frac{2}{45} (3 x+2)^{3/2} \sqrt{5 x+3} (1-2 x)^{5/2}+\frac{106 (3 x+2)^{3/2} \sqrt{5 x+3} (1-2 x)^{3/2}}{1575}+\frac{8878 (3 x+2)^{3/2} \sqrt{5 x+3} \sqrt{1-2 x}}{118125}+\frac{21547 \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}}{1771875}-\frac{509189 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{8859375}-\frac{8024546 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{8859375}",1,"Could not integrate","F",-1
2788,0,0,160,0.4117983,"\int \frac{(1-2 x)^{5/2} \sqrt{2+3 x}}{\sqrt{3+5 x}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*Sqrt[2 + 3*x])/Sqrt[3 + 5*x],x]","\int \frac{(1-2 x)^{5/2} \sqrt{2+3 x}}{\sqrt{3+5 x}} \, dx","\frac{2}{35} \sqrt{3 x+2} \sqrt{5 x+3} (1-2 x)^{5/2}+\frac{326 \sqrt{3 x+2} \sqrt{5 x+3} (1-2 x)^{3/2}}{2625}+\frac{30922 \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}}{118125}-\frac{132824 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{590625}-\frac{408311 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{590625}",1,"Could not integrate","F",-1
2789,0,0,129,0.4118483,"\int \frac{(1-2 x)^{5/2}}{\sqrt{2+3 x} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/(Sqrt[2 + 3*x]*Sqrt[3 + 5*x]),x]","\int \frac{(1-2 x)^{5/2}}{\sqrt{2+3 x} \sqrt{3+5 x}} \, dx","-\frac{4}{75} \sqrt{3 x+2} \sqrt{5 x+3} (1-2 x)^{3/2}-\frac{1088 \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}}{3375}-\frac{34154 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{16875}+\frac{53194 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{16875}",1,"Could not integrate","F",-1
2790,0,0,129,0.8422015,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^(3/2)*Sqrt[3 + 5*x]),x]","\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","\frac{14 \sqrt{5 x+3} (1-2 x)^{3/2}}{3 \sqrt{3 x+2}}+\frac{428}{135} \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{824}{675} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{8314}{675} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2791,0,0,129,0.9851943,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^(5/2)*Sqrt[3 + 5*x]),x]","\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","\frac{14 \sqrt{5 x+3} (1-2 x)^{3/2}}{9 (3 x+2)^{3/2}}+\frac{812 \sqrt{5 x+3} \sqrt{1-2 x}}{27 \sqrt{3 x+2}}-\frac{164}{135} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{3896}{135} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2792,0,0,160,1.0154499,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^(7/2)*Sqrt[3 + 5*x]),x]","\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","\frac{14 \sqrt{5 x+3} (1-2 x)^{3/2}}{15 (3 x+2)^{5/2}}+\frac{16564 \sqrt{5 x+3} \sqrt{1-2 x}}{135 \sqrt{3 x+2}}+\frac{1736 \sqrt{5 x+3} \sqrt{1-2 x}}{135 (3 x+2)^{3/2}}-\frac{496}{135} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{16564}{135} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2793,0,0,191,1.0671392,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{9/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^(9/2)*Sqrt[3 + 5*x]),x]","\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{9/2} \sqrt{3+5 x}} \, dx","\frac{2 \sqrt{5 x+3} (1-2 x)^{3/2}}{3 (3 x+2)^{7/2}}+\frac{703480 \sqrt{5 x+3} \sqrt{1-2 x}}{1323 \sqrt{3 x+2}}+\frac{10124 \sqrt{5 x+3} \sqrt{1-2 x}}{189 (3 x+2)^{3/2}}+\frac{76 \sqrt{5 x+3} \sqrt{1-2 x}}{9 (3 x+2)^{5/2}}-\frac{21160 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1323}-\frac{703480 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1323}",1,"Could not integrate","F",-1
2794,0,0,222,1.1433076,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{11/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^(11/2)*Sqrt[3 + 5*x]),x]","\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{11/2} \sqrt{3+5 x}} \, dx","\frac{14 \sqrt{5 x+3} (1-2 x)^{3/2}}{27 (3 x+2)^{9/2}}+\frac{66055016 \sqrt{5 x+3} \sqrt{1-2 x}}{27783 \sqrt{3 x+2}}+\frac{950584 \sqrt{5 x+3} \sqrt{1-2 x}}{3969 (3 x+2)^{3/2}}+\frac{20420 \sqrt{5 x+3} \sqrt{1-2 x}}{567 (3 x+2)^{5/2}}+\frac{512 \sqrt{5 x+3} \sqrt{1-2 x}}{81 (3 x+2)^{7/2}}-\frac{1986944 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{27783}-\frac{66055016 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{27783}",1,"Could not integrate","F",-1
2795,0,0,249,1.1908093,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{13/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^(13/2)*Sqrt[3 + 5*x]),x]","\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{13/2} \sqrt{3+5 x}} \, dx","\frac{14 \sqrt{5 x+3} (1-2 x)^{3/2}}{33 (3 x+2)^{11/2}}+\frac{23204503328 \sqrt{5 x+3} \sqrt{1-2 x}}{2139291 \sqrt{3 x+2}}+\frac{333930952 \sqrt{5 x+3} \sqrt{1-2 x}}{305613 (3 x+2)^{3/2}}+\frac{7173272 \sqrt{5 x+3} \sqrt{1-2 x}}{43659 (3 x+2)^{5/2}}+\frac{171004 \sqrt{5 x+3} \sqrt{1-2 x}}{6237 (3 x+2)^{7/2}}+\frac{4508 \sqrt{5 x+3} \sqrt{1-2 x}}{891 (3 x+2)^{9/2}}-\frac{697995152 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{194481 \sqrt{33}}-\frac{23204503328 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{194481 \sqrt{33}}",1,"Could not integrate","F",-1
2796,0,0,249,1.1519227,"\int \frac{(1-2 x)^{5/2} (2+3 x)^{7/2}}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2))/(3 + 5*x)^(3/2),x]","\int \frac{(1-2 x)^{5/2} (2+3 x)^{7/2}}{(3+5 x)^{3/2}} \, dx","-\frac{48}{275} (1-2 x)^{3/2} \sqrt{5 x+3} (3 x+2)^{7/2}-\frac{2972 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{7/2}}{7425}-\frac{2 (1-2 x)^{5/2} (3 x+2)^{7/2}}{5 \sqrt{5 x+3}}+\frac{346636 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{5/2}}{259875}+\frac{2020841 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{6496875}-\frac{703672 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{32484375}-\frac{7261561 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{14765625 \sqrt{33}}-\frac{264260033 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{29531250 \sqrt{33}}",1,"Could not integrate","F",-1
2797,0,0,222,1.1493522,"\int \frac{(1-2 x)^{5/2} (2+3 x)^{5/2}}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2))/(3 + 5*x)^(3/2),x]","\int \frac{(1-2 x)^{5/2} (2+3 x)^{5/2}}{(3+5 x)^{3/2}} \, dx","-\frac{8}{45} (1-2 x)^{3/2} \sqrt{5 x+3} (3 x+2)^{5/2}-\frac{1972 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{5/2}}{4725}-\frac{2 (1-2 x)^{5/2} (3 x+2)^{5/2}}{5 \sqrt{5 x+3}}+\frac{167228 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{118125}+\frac{196499 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{590625}-\frac{299863 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2953125}-\frac{1509007 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2953125}",1,"Could not integrate","F",-1
2798,0,0,191,1.0162346,"\int \frac{(1-2 x)^{5/2} (2+3 x)^{3/2}}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2))/(3 + 5*x)^(3/2),x]","\int \frac{(1-2 x)^{5/2} (2+3 x)^{3/2}}{(3+5 x)^{3/2}} \, dx","-\frac{2 (3 x+2)^{3/2} (1-2 x)^{5/2}}{5 \sqrt{5 x+3}}-\frac{32}{175} (3 x+2)^{3/2} \sqrt{5 x+3} (1-2 x)^{3/2}-\frac{1972 (3 x+2)^{3/2} \sqrt{5 x+3} \sqrt{1-2 x}}{4375}+\frac{106772 \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}}{65625}-\frac{110014 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{328125}+\frac{53279 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{328125}",1,"Could not integrate","F",-1
2799,0,0,160,0.731046,"\int \frac{(1-2 x)^{5/2} \sqrt{2+3 x}}{(3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*Sqrt[2 + 3*x])/(3 + 5*x)^(3/2),x]","\int \frac{(1-2 x)^{5/2} \sqrt{2+3 x}}{(3+5 x)^{3/2}} \, dx","-\frac{2 \sqrt{3 x+2} (1-2 x)^{5/2}}{5 \sqrt{5 x+3}}-\frac{24}{125} \sqrt{3 x+2} \sqrt{5 x+3} (1-2 x)^{3/2}-\frac{3028 \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}}{5625}-\frac{28174 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{28125}+\frac{81164 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{28125}",1,"Could not integrate","F",-1
2800,0,0,129,0.8578332,"\int \frac{(1-2 x)^{5/2}}{\sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/(Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)),x]","\int \frac{(1-2 x)^{5/2}}{\sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","-\frac{22 \sqrt{3 x+2} (1-2 x)^{3/2}}{5 \sqrt{5 x+3}}-\frac{388}{225} \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{1196 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1125}+\frac{5594 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1125}",1,"Could not integrate","F",-1
2801,0,0,129,1.0366502,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","\frac{14 (1-2 x)^{3/2}}{3 \sqrt{3 x+2} \sqrt{5 x+3}}-\frac{1496 \sqrt{3 x+2} \sqrt{1-2 x}}{15 \sqrt{5 x+3}}+\frac{124}{75} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{4636}{75} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2802,0,0,160,1.1298912,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","\frac{14 (1-2 x)^{3/2}}{9 (3 x+2)^{3/2} \sqrt{5 x+3}}-\frac{17804 \sqrt{3 x+2} \sqrt{1-2 x}}{27 \sqrt{5 x+3}}+\frac{1792 \sqrt{1-2 x}}{27 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{536}{45} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{17804}{45} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2803,0,0,191,1.1440616,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","\frac{14 (1-2 x)^{3/2}}{15 (3 x+2)^{5/2} \sqrt{5 x+3}}-\frac{105584 \sqrt{3 x+2} \sqrt{1-2 x}}{27 \sqrt{5 x+3}}+\frac{17468 \sqrt{1-2 x}}{45 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{2716 \sqrt{1-2 x}}{135 (3 x+2)^{3/2} \sqrt{5 x+3}}+\frac{3176}{45} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{105584}{45} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2804,0,0,222,1.2297562,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{9/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^(9/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{9/2} (3+5 x)^{3/2}} \, dx","\frac{2 (1-2 x)^{3/2}}{3 (3 x+2)^{7/2} \sqrt{5 x+3}}-\frac{9795160 \sqrt{3 x+2} \sqrt{1-2 x}}{441 \sqrt{5 x+3}}+\frac{324104 \sqrt{1-2 x}}{147 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{2332 \sqrt{1-2 x}}{21 (3 x+2)^{3/2} \sqrt{5 x+3}}+\frac{104 \sqrt{1-2 x}}{9 (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{58928}{147} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{1959032}{147} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2805,0,0,253,1.2793243,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{11/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^(11/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{11/2} (3+5 x)^{3/2}} \, dx","\frac{14 (1-2 x)^{3/2}}{27 (3 x+2)^{9/2} \sqrt{5 x+3}}-\frac{3415750480 \sqrt{3 x+2} \sqrt{1-2 x}}{27783 \sqrt{5 x+3}}+\frac{113020952 \sqrt{1-2 x}}{9261 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{813208 \sqrt{1-2 x}}{1323 (3 x+2)^{3/2} \sqrt{5 x+3}}+\frac{11660 \sqrt{1-2 x}}{189 (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{652 \sqrt{1-2 x}}{81 (3 x+2)^{7/2} \sqrt{5 x+3}}+\frac{20549264 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{9261}+\frac{683150096 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{9261}",1,"Could not integrate","F",-1
2806,0,0,253,1.1273167,"\int \frac{(1-2 x)^{5/2} (2+3 x)^{7/2}}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2))/(3 + 5*x)^(5/2),x]","\int \frac{(1-2 x)^{5/2} (2+3 x)^{7/2}}{(3+5 x)^{5/2}} \, dx","-\frac{524}{225} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{7/2}-\frac{442 (1-2 x)^{3/2} (3 x+2)^{7/2}}{75 \sqrt{5 x+3}}-\frac{2 (1-2 x)^{5/2} (3 x+2)^{7/2}}{15 (5 x+3)^{3/2}}+\frac{59662 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{5/2}}{7875}+\frac{373022 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{196875}+\frac{500501 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{984375}-\frac{595387 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{4921875}-\frac{1065118 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{4921875}",1,"Could not integrate","F",-1
2807,0,0,222,1.1431996,"\int \frac{(1-2 x)^{5/2} (2+3 x)^{5/2}}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2))/(3 + 5*x)^(5/2),x]","\int \frac{(1-2 x)^{5/2} (2+3 x)^{5/2}}{(3+5 x)^{5/2}} \, dx","-\frac{284}{175} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{5/2}-\frac{62 (1-2 x)^{3/2} (3 x+2)^{5/2}}{15 \sqrt{5 x+3}}-\frac{2 (1-2 x)^{5/2} (3 x+2)^{5/2}}{15 (5 x+3)^{3/2}}+\frac{22866 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{4375}+\frac{33778 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{21875}-\frac{32836 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{109375}+\frac{49321 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{109375}",1,"Could not integrate","F",-1
2808,0,0,189,1.0182738,"\int \frac{(1-2 x)^{5/2} (2+3 x)^{3/2}}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2))/(3 + 5*x)^(5/2),x]","\int \frac{(1-2 x)^{5/2} (2+3 x)^{3/2}}{(3+5 x)^{5/2}} \, dx","-\frac{2 (3 x+2)^{3/2} (1-2 x)^{5/2}}{15 (5 x+3)^{3/2}}-\frac{178 (3 x+2)^{3/2} (1-2 x)^{3/2}}{75 \sqrt{5 x+3}}-\frac{572}{625} (3 x+2)^{3/2} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{8874 \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}}{3125}-\frac{7738 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{15625}+\frac{9206 \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{15625}",1,"Could not integrate","F",-1
2809,0,0,160,0.9375058,"\int \frac{(1-2 x)^{5/2} \sqrt{2+3 x}}{(3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[((1 - 2*x)^(5/2)*Sqrt[2 + 3*x])/(3 + 5*x)^(5/2),x]","\int \frac{(1-2 x)^{5/2} \sqrt{2+3 x}}{(3+5 x)^{5/2}} \, dx","-\frac{2 \sqrt{3 x+2} (1-2 x)^{5/2}}{15 (5 x+3)^{3/2}}-\frac{46 \sqrt{3 x+2} (1-2 x)^{3/2}}{75 \sqrt{5 x+3}}-\frac{76}{375} \sqrt{3 x+2} \sqrt{5 x+3} \sqrt{1-2 x}+\frac{992 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1875}+\frac{338 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1875}",1,"Could not integrate","F",-1
2810,0,0,127,0.9807383,"\int \frac{(1-2 x)^{5/2}}{\sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/(Sqrt[2 + 3*x]*(3 + 5*x)^(5/2)),x]","\int \frac{(1-2 x)^{5/2}}{\sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","-\frac{22 \sqrt{3 x+2} (1-2 x)^{3/2}}{15 (5 x+3)^{3/2}}+\frac{572 \sqrt{3 x+2} \sqrt{1-2 x}}{25 \sqrt{5 x+3}}-\frac{68}{125} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{584}{125} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2811,0,0,158,1.1021531,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","\frac{14 (1-2 x)^{3/2}}{3 \sqrt{3 x+2} (5 x+3)^{3/2}}+\frac{6388 \sqrt{3 x+2} \sqrt{1-2 x}}{15 \sqrt{5 x+3}}-\frac{1012 \sqrt{3 x+2} \sqrt{1-2 x}}{15 (5 x+3)^{3/2}}-\frac{64}{25} \sqrt{33} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{6388}{25} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2812,0,0,191,1.0888826,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","\frac{14 (1-2 x)^{3/2}}{9 (3 x+2)^{3/2} (5 x+3)^{3/2}}+\frac{36968 \sqrt{3 x+2} \sqrt{1-2 x}}{9 \sqrt{5 x+3}}-\frac{6116 \sqrt{3 x+2} \sqrt{1-2 x}}{9 (5 x+3)^{3/2}}+\frac{308 \sqrt{1-2 x}}{3 \sqrt{3 x+2} (5 x+3)^{3/2}}-\frac{1112}{15} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{36968}{15} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2813,0,0,222,1.2108385,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","\frac{14 (1-2 x)^{3/2}}{15 (3 x+2)^{5/2} (5 x+3)^{3/2}}+\frac{96808 \sqrt{3 x+2} \sqrt{1-2 x}}{3 \sqrt{5 x+3}}-\frac{16016 \sqrt{3 x+2} \sqrt{1-2 x}}{3 (5 x+3)^{3/2}}+\frac{35948 \sqrt{1-2 x}}{45 \sqrt{3 x+2} (5 x+3)^{3/2}}+\frac{1232 \sqrt{1-2 x}}{45 (3 x+2)^{3/2} (5 x+3)^{3/2}}-\frac{2912}{5} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{96808}{5} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2814,0,0,251,1.2536373,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{9/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(1 - 2*x)^(5/2)/((2 + 3*x)^(9/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{9/2} (3+5 x)^{5/2}} \, dx","\frac{2 (1-2 x)^{3/2}}{3 (3 x+2)^{7/2} (5 x+3)^{3/2}}+\frac{11171040 \sqrt{3 x+2} \sqrt{1-2 x}}{49 \sqrt{5 x+3}}-\frac{5544440 \sqrt{3 x+2} \sqrt{1-2 x}}{147 (5 x+3)^{3/2}}+\frac{2488904 \sqrt{1-2 x}}{441 \sqrt{3 x+2} (5 x+3)^{3/2}}+\frac{11924 \sqrt{1-2 x}}{63 (3 x+2)^{3/2} (5 x+3)^{3/2}}+\frac{44 \sqrt{1-2 x}}{3 (3 x+2)^{5/2} (5 x+3)^{3/2}}-\frac{201616}{49} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{2234208}{49} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2815,0,0,158,0.3979851,"\int \frac{(2+3 x)^{5/2} \sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(5/2)*Sqrt[3 + 5*x])/Sqrt[1 - 2*x],x]","\int \frac{(2+3 x)^{5/2} \sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","-\frac{1}{7} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{5/2}-\frac{104}{175} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}-\frac{4839 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{1750}-\frac{5057 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{8750}-\frac{56041 \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{8750}",1,"Could not integrate","F",-1
2816,0,0,127,0.5274992,"\int \frac{(2+3 x)^{3/2} \sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(3/2)*Sqrt[3 + 5*x])/Sqrt[1 - 2*x],x]","\int \frac{(2+3 x)^{3/2} \sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","-\frac{1}{5} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}-\frac{23}{25} \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}-\frac{8}{125} \sqrt{33} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{1597}{250} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2817,0,0,98,0.2413465,"\int \frac{\sqrt{2+3 x} \sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 + 3*x]*Sqrt[3 + 5*x])/Sqrt[1 - 2*x],x]","\int \frac{\sqrt{2+3 x} \sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","-\frac{1}{3} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{1}{15} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{34}{15} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2818,0,0,31,0.2669912,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} \sqrt{2+3 x}} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*Sqrt[2 + 3*x]),x]","\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} \sqrt{2+3 x}} \, dx","-\sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2819,0,0,81,0.6196838,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)),x]","\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^{3/2}} \, dx","\frac{2 \sqrt{\frac{5}{7}} \sqrt{-5 x-3} E\left(\sin ^{-1}\left(\sqrt{5} \sqrt{3 x+2}\right)|\frac{2}{35}\right)}{3 \sqrt{5 x+3}}-\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{7 \sqrt{3 x+2}}",1,"Could not integrate","F",-1
2820,0,0,129,0.4820742,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)),x]","\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^{5/2}} \, dx","\frac{62 \sqrt{1-2 x} \sqrt{5 x+3}}{147 \sqrt{3 x+2}}-\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{21 (3 x+2)^{3/2}}-\frac{8}{147} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{62}{147} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2821,0,0,158,0.6152954,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2)),x]","\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^{7/2}} \, dx","\frac{1752 \sqrt{1-2 x} \sqrt{5 x+3}}{1715 \sqrt{3 x+2}}+\frac{18 \sqrt{1-2 x} \sqrt{5 x+3}}{245 (3 x+2)^{3/2}}-\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{35 (3 x+2)^{5/2}}-\frac{68 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1715}-\frac{584 \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1715}",1,"Could not integrate","F",-1
2822,0,0,191,0.8282422,"\int \frac{(2+3 x)^{5/2} (3+5 x)^{3/2}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/Sqrt[1 - 2*x],x]","\int \frac{(2+3 x)^{5/2} (3+5 x)^{3/2}}{\sqrt{1-2 x}} \, dx","-\frac{1}{9} \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^{5/2}-\frac{137}{315} \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^{3/2}-\frac{9547 \sqrt{1-2 x} (5 x+3)^{3/2} \sqrt{3 x+2}}{5250}-\frac{663409 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{47250}-\frac{663409 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{236250}-\frac{44109377 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{472500}",1,"Could not integrate","F",-1
2823,0,0,160,0.8246687,"\int \frac{(2+3 x)^{3/2} (3+5 x)^{3/2}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/Sqrt[1 - 2*x],x]","\int \frac{(2+3 x)^{3/2} (3+5 x)^{3/2}}{\sqrt{1-2 x}} \, dx","-\frac{1}{7} \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{3/2}-\frac{102}{175} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{4721 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{1050}-\frac{4721 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5250}-\frac{78472 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2625}",1,"Could not integrate","F",-1
2824,0,0,129,0.5250374,"\int \frac{\sqrt{2+3 x} (3+5 x)^{3/2}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 + 3*x]*(3 + 5*x)^(3/2))/Sqrt[1 - 2*x],x]","\int \frac{\sqrt{2+3 x} (3+5 x)^{3/2}}{\sqrt{1-2 x}} \, dx","-\frac{1}{5} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{67}{45} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{67}{225} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{4451}{450} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2825,0,0,98,0.5854814,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} \sqrt{2+3 x}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*Sqrt[2 + 3*x]),x]","\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} \sqrt{2+3 x}} \, dx","-\frac{5}{9} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{1}{9} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{31}{9} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2826,0,0,98,0.9599826,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)),x]","\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^{3/2}} \, dx","\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{21 \sqrt{3 x+2}}+\frac{2}{21} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{37}{21} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2827,0,0,129,0.9854355,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)),x]","\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^{5/2}} \, dx","-\frac{272 \sqrt{1-2 x} \sqrt{5 x+3}}{441 \sqrt{3 x+2}}+\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{63 (3 x+2)^{3/2}}-\frac{202}{441} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{272}{441} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2828,0,0,160,1.0118962,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2)),x]","\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^{7/2}} \, dx","\frac{5594 \sqrt{1-2 x} \sqrt{5 x+3}}{15435 \sqrt{3 x+2}}-\frac{404 \sqrt{1-2 x} \sqrt{5 x+3}}{2205 (3 x+2)^{3/2}}+\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{105 (3 x+2)^{5/2}}-\frac{1196 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{15435}-\frac{5594 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{15435}",1,"Could not integrate","F",-1
2829,0,0,191,1.0968546,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^{9/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(9/2)),x]","\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^{9/2}} \, dx","\frac{184636 \sqrt{1-2 x} \sqrt{5 x+3}}{252105 \sqrt{3 x+2}}+\frac{974 \sqrt{1-2 x} \sqrt{5 x+3}}{36015 (3 x+2)^{3/2}}-\frac{536 \sqrt{1-2 x} \sqrt{5 x+3}}{5145 (3 x+2)^{5/2}}+\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{147 (3 x+2)^{7/2}}-\frac{9124 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{252105}-\frac{184636 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{252105}",1,"Could not integrate","F",-1
2830,0,0,249,1.0166822,"\int \frac{(2+3 x)^{7/2} (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2))/Sqrt[1 - 2*x],x]","\int \frac{(2+3 x)^{7/2} (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","-\frac{1}{13} \sqrt{1-2 x} (5 x+3)^{5/2} (3 x+2)^{7/2}-\frac{41}{143} \sqrt{1-2 x} (5 x+3)^{5/2} (3 x+2)^{5/2}-\frac{14303 \sqrt{1-2 x} (5 x+3)^{5/2} (3 x+2)^{3/2}}{12870}-\frac{221673 \sqrt{1-2 x} (5 x+3)^{5/2} \sqrt{3 x+2}}{50050}-\frac{138809831 \sqrt{1-2 x} (5 x+3)^{3/2} \sqrt{3 x+2}}{4504500}-\frac{2295970088 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{10135125}-\frac{2295970088 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{4606875 \sqrt{33}}-\frac{610627101631 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{36855000 \sqrt{33}}",1,"Could not integrate","F",-1
2831,0,0,218,0.958191,"\int \frac{(2+3 x)^{5/2} (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/Sqrt[1 - 2*x],x]","\int \frac{(2+3 x)^{5/2} (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","-\frac{1}{11} \sqrt{1-2 x} (3 x+2)^{5/2} (5 x+3)^{5/2}-\frac{34}{99} \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}-\frac{1053}{770} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}-\frac{329683 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{34650}-\frac{43624697 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{623700}-\frac{43624697 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{283500 \sqrt{33}}-\frac{725140729 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{141750 \sqrt{33}}",1,"Could not integrate","F",-1
2832,0,0,191,0.8746399,"\int \frac{(2+3 x)^{3/2} (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/Sqrt[1 - 2*x],x]","\int \frac{(2+3 x)^{3/2} (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","-\frac{1}{9} \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}-\frac{3}{7} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}-\frac{1877}{630} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{62092 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{2835}-\frac{62092 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{14175}-\frac{8256877 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{56700}",1,"Could not integrate","F",-1
2833,0,0,160,0.3886026,"\int \frac{\sqrt{2+3 x} (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 + 3*x]*(3 + 5*x)^(5/2))/Sqrt[1 - 2*x],x]","\int \frac{\sqrt{2+3 x} (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","-\frac{1}{7} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}-\frac{20}{21} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{2645}{378} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{529}{378} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{17587}{378} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2834,0,0,129,0.4091504,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} \sqrt{2+3 x}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*Sqrt[2 + 3*x]),x]","\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} \sqrt{2+3 x}} \, dx","-\frac{1}{3} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{62}{27} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{62}{135} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{4141}{270} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2835,0,0,129,0.9516601,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)),x]","\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{3/2}} \, dx","\frac{2 \sqrt{1-2 x} (5 x+3)^{3/2}}{21 \sqrt{3 x+2}}-\frac{205}{189} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{41}{189} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{974}{189} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2836,0,0,129,1.0293057,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)),x]","\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{5/2}} \, dx","\frac{2 \sqrt{1-2 x} (5 x+3)^{3/2}}{63 (3 x+2)^{3/2}}+\frac{412 \sqrt{1-2 x} \sqrt{5 x+3}}{1323 \sqrt{3 x+2}}+\frac{412 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1323}-\frac{4157 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1323}",1,"Could not integrate","F",-1
2837,0,0,160,1.0562148,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2)),x]","\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{7/2}} \, dx","\frac{2 \sqrt{1-2 x} (5 x+3)^{3/2}}{105 (3 x+2)^{5/2}}-\frac{53194 \sqrt{1-2 x} \sqrt{5 x+3}}{46305 \sqrt{3 x+2}}+\frac{544 \sqrt{1-2 x} \sqrt{5 x+3}}{6615 (3 x+2)^{3/2}}-\frac{34154 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{46305}+\frac{53194 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{46305}",1,"Could not integrate","F",-1
2838,0,0,191,1.1107617,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{9/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(9/2)),x]","\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{9/2}} \, dx","\frac{2 \sqrt{1-2 x} (5 x+3)^{3/2}}{147 (3 x+2)^{7/2}}+\frac{816622 \sqrt{1-2 x} \sqrt{5 x+3}}{2268945 \sqrt{3 x+2}}-\frac{101902 \sqrt{1-2 x} \sqrt{5 x+3}}{324135 (3 x+2)^{3/2}}+\frac{676 \sqrt{1-2 x} \sqrt{5 x+3}}{15435 (3 x+2)^{5/2}}-\frac{265648 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2268945}-\frac{816622 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2268945}",1,"Could not integrate","F",-1
2839,0,0,222,1.2114371,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{11/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(11/2)),x]","\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{11/2}} \, dx","\frac{2 \sqrt{1-2 x} (5 x+3)^{3/2}}{189 (3 x+2)^{9/2}}+\frac{32098184 \sqrt{1-2 x} \sqrt{5 x+3}}{47647845 \sqrt{3 x+2}}-\frac{43094 \sqrt{1-2 x} \sqrt{5 x+3}}{6806835 (3 x+2)^{3/2}}-\frac{168034 \sqrt{1-2 x} \sqrt{5 x+3}}{972405 (3 x+2)^{5/2}}+\frac{808 \sqrt{1-2 x} \sqrt{5 x+3}}{27783 (3 x+2)^{7/2}}-\frac{2036756 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{47647845}-\frac{32098184 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{47647845}",1,"Could not integrate","F",-1
2840,0,0,249,1.3246056,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{13/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(13/2)),x]","\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{13/2}} \, dx","\frac{2 \sqrt{1-2 x} (5 x+3)^{3/2}}{231 (3 x+2)^{11/2}}+\frac{924247516 \sqrt{1-2 x} \sqrt{5 x+3}}{733776813 \sqrt{3 x+2}}+\frac{11460644 \sqrt{1-2 x} \sqrt{5 x+3}}{104825259 (3 x+2)^{3/2}}-\frac{362666 \sqrt{1-2 x} \sqrt{5 x+3}}{14975037 (3 x+2)^{5/2}}-\frac{251590 \sqrt{1-2 x} \sqrt{5 x+3}}{2139291 (3 x+2)^{7/2}}+\frac{940 \sqrt{1-2 x} \sqrt{5 x+3}}{43659 (3 x+2)^{9/2}}-\frac{31704544 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{66706983 \sqrt{33}}-\frac{924247516 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{66706983 \sqrt{33}}",1,"Could not integrate","F",-1
2841,0,0,12,0.2030368,"\int \frac{1}{\sqrt{1+x} \sqrt{2+x} \sqrt{3+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 + x]*Sqrt[2 + x]*Sqrt[3 + x]),x]","\int \frac{1}{\sqrt{1+x} \sqrt{2+x} \sqrt{3+x}} \, dx","-2 F\left(\left.\sin ^{-1}\left(\frac{1}{\sqrt{x+3}}\right)\right|2\right)",1,"Could not integrate","F",-1
2842,0,0,16,0.2235698,"\int \frac{1}{\sqrt{3-x} \sqrt{1+x} \sqrt{2+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[3 - x]*Sqrt[1 + x]*Sqrt[2 + x]),x]","\int \frac{1}{\sqrt{3-x} \sqrt{1+x} \sqrt{2+x}} \, dx","2 F\left(\left.\sin ^{-1}\left(\frac{\sqrt{x+1}}{2}\right)\right|-4\right)",1,"Could not integrate","F",-1
2843,0,0,24,0.2230226,"\int \frac{1}{\sqrt{2-x} \sqrt{1+x} \sqrt{3+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[2 - x]*Sqrt[1 + x]*Sqrt[3 + x]),x]","\int \frac{1}{\sqrt{2-x} \sqrt{1+x} \sqrt{3+x}} \, dx","\sqrt{2} F\left(\sin ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{3}}\right)|-\frac{3}{2}\right)",1,"Could not integrate","F",-1
2844,0,0,18,0.2512048,"\int \frac{1}{\sqrt{2-x} \sqrt{3-x} \sqrt{1+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[2 - x]*Sqrt[3 - x]*Sqrt[1 + x]),x]","\int \frac{1}{\sqrt{2-x} \sqrt{3-x} \sqrt{1+x}} \, dx","F\left(\sin ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{3}}\right)|\frac{3}{4}\right)",1,"Could not integrate","F",-1
2845,0,0,18,0.2368565,"\int \frac{1}{\sqrt{1-x} \sqrt{2+x} \sqrt{3+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - x]*Sqrt[2 + x]*Sqrt[3 + x]),x]","\int \frac{1}{\sqrt{1-x} \sqrt{2+x} \sqrt{3+x}} \, dx","2 F\left(\left.\sin ^{-1}\left(\frac{\sqrt{x+2}}{\sqrt{3}}\right)\right|-3\right)",1,"Could not integrate","F",-1
2846,0,0,25,0.2501402,"\int \frac{1}{\sqrt{1-x} \sqrt{3-x} \sqrt{2+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - x]*Sqrt[3 - x]*Sqrt[2 + x]),x]","\int \frac{1}{\sqrt{1-x} \sqrt{3-x} \sqrt{2+x}} \, dx","\frac{2 F\left(\sin ^{-1}\left(\frac{\sqrt{x+2}}{\sqrt{3}}\right)|\frac{3}{5}\right)}{\sqrt{5}}",1,"Could not integrate","F",-1
2847,0,0,23,0.2505297,"\int \frac{1}{\sqrt{1-x} \sqrt{2-x} \sqrt{3+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - x]*Sqrt[2 - x]*Sqrt[3 + x]),x]","\int \frac{1}{\sqrt{1-x} \sqrt{2-x} \sqrt{3+x}} \, dx","\frac{2 F\left(\sin ^{-1}\left(\frac{\sqrt{x+3}}{2}\right)|\frac{4}{5}\right)}{\sqrt{5}}",1,"Could not integrate","F",-1
2848,0,0,14,0.2167019,"\int \frac{1}{\sqrt{1-x} \sqrt{2-x} \sqrt{3-x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - x]*Sqrt[2 - x]*Sqrt[3 - x]),x]","\int \frac{1}{\sqrt{1-x} \sqrt{2-x} \sqrt{3-x}} \, dx","2 F\left(\left.\sin ^{-1}\left(\frac{1}{\sqrt{3-x}}\right)\right|2\right)",1,"Could not integrate","F",-1
2849,0,0,12,0.2214469,"\int \frac{1}{\sqrt{-3+x} \sqrt{-2+x} \sqrt{-1+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-3 + x]*Sqrt[-2 + x]*Sqrt[-1 + x]),x]","\int \frac{1}{\sqrt{-3+x} \sqrt{-2+x} \sqrt{-1+x}} \, dx","-2 F\left(\left.\sin ^{-1}\left(\frac{1}{\sqrt{x-1}}\right)\right|2\right)",1,"Could not integrate","F",-1
2850,0,0,57,0.2291951,"\int \frac{1}{\sqrt{-3-x} \sqrt{-2+x} \sqrt{-1+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-3 - x]*Sqrt[-2 + x]*Sqrt[-1 + x]),x]","\int \frac{1}{\sqrt{-3-x} \sqrt{-2+x} \sqrt{-1+x}} \, dx","-\frac{\sqrt{x+3} F\left(\sin ^{-1}\left(\frac{2}{\sqrt{x+3}}\right)|\frac{5}{4}\right)}{\sqrt{-x-3}}-\frac{i K\left(-\frac{1}{4}\right) \sqrt{x+3}}{\sqrt{-x-3}}",1,"Could not integrate","F",-1
2851,0,0,41,0.2425879,"\int \frac{1}{\sqrt{-2-x} \sqrt{-3+x} \sqrt{-1+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-2 - x]*Sqrt[-3 + x]*Sqrt[-1 + x]),x]","\int \frac{1}{\sqrt{-2-x} \sqrt{-3+x} \sqrt{-1+x}} \, dx","-\frac{2 \sqrt{x+2} F\left(\sin ^{-1}\left(\frac{1}{\sqrt{\frac{x}{3}+\frac{2}{3}}}\right)|\frac{5}{3}\right)}{\sqrt{3} \sqrt{-x-2}}",1,"Could not integrate","F",-1
2852,0,0,92,0.2492169,"\int \frac{1}{\sqrt{-3-x} \sqrt{-2-x} \sqrt{-1+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-3 - x]*Sqrt[-2 - x]*Sqrt[-1 + x]),x]","\int \frac{1}{\sqrt{-3-x} \sqrt{-2-x} \sqrt{-1+x}} \, dx","-\frac{2 i K(4) \sqrt{x+2}}{\sqrt{-x-2}}+\frac{K\left(\frac{3}{4}\right) \sqrt{x+3}}{\sqrt{-x-3}}-\frac{\sqrt{x+2} \sqrt{x+3} F\left(\sin ^{-1}\left(\frac{2}{\sqrt{x+3}}\right)|\frac{1}{4}\right)}{\sqrt{-x-3} \sqrt{-x-2}}",1,"Could not integrate","F",-1
2853,0,0,41,0.2495998,"\int \frac{1}{\sqrt{-1-x} \sqrt{-3+x} \sqrt{-2+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-1 - x]*Sqrt[-3 + x]*Sqrt[-2 + x]),x]","\int \frac{1}{\sqrt{-1-x} \sqrt{-3+x} \sqrt{-2+x}} \, dx","-\frac{2 \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{1}{\sqrt{\frac{x}{3}+\frac{1}{3}}}\right)|\frac{4}{3}\right)}{\sqrt{3} \sqrt{-x-1}}",1,"Could not integrate","F",-1
2854,0,0,57,0.2516315,"\int \frac{1}{\sqrt{-3-x} \sqrt{-1-x} \sqrt{-2+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-3 - x]*Sqrt[-1 - x]*Sqrt[-2 + x]),x]","\int \frac{1}{\sqrt{-3-x} \sqrt{-1-x} \sqrt{-2+x}} \, dx","-\frac{2 \sqrt{x+1} \sqrt{x+3} F\left(\sin ^{-1}\left(\frac{1}{\sqrt{\frac{x}{5}+\frac{3}{5}}}\right)|\frac{2}{5}\right)}{\sqrt{5} \sqrt{-x-3} \sqrt{-x-1}}",1,"Could not integrate","F",-1
2855,0,0,57,0.2522009,"\int \frac{1}{\sqrt{-2-x} \sqrt{-1-x} \sqrt{-3+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-2 - x]*Sqrt[-1 - x]*Sqrt[-3 + x]),x]","\int \frac{1}{\sqrt{-2-x} \sqrt{-1-x} \sqrt{-3+x}} \, dx","-\frac{2 \sqrt{x+1} \sqrt{x+2} F\left(\sin ^{-1}\left(\frac{1}{\sqrt{\frac{x}{5}+\frac{2}{5}}}\right)|\frac{1}{5}\right)}{\sqrt{5} \sqrt{-x-2} \sqrt{-x-1}}",1,"Could not integrate","F",-1
2856,0,0,14,0.2174914,"\int \frac{1}{\sqrt{-3-x} \sqrt{-2-x} \sqrt{-1-x}} \, dx","IntegrateAlgebraic[1/(Sqrt[-3 - x]*Sqrt[-2 - x]*Sqrt[-1 - x]),x]","\int \frac{1}{\sqrt{-3-x} \sqrt{-2-x} \sqrt{-1-x}} \, dx","2 F\left(\left.\sin ^{-1}\left(\frac{1}{\sqrt{-x-1}}\right)\right|2\right)",1,"Could not integrate","F",-1
2857,0,0,204,1.8331192,"\int \frac{1}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\int \frac{1}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx","\frac{2 \sqrt{f} \sqrt{a+b x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|-\frac{b (d e-c f)}{(b c-a d) f}\right)}{\sqrt{e+f x} (b c-a d) (b e-a f) \sqrt{-\frac{d (a+b x)}{b c-a d}}}-\frac{2 b \sqrt{c+d x} \sqrt{e+f x}}{\sqrt{a+b x} (b c-a d) (b e-a f)}",1,"Could not integrate","F",-1
2858,0,0,437,1.9849893,"\int \frac{1}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(5/2)*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\int \frac{1}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx","\frac{4 b \sqrt{c+d x} \sqrt{e+f x} (-2 a d f+b c f+b d e)}{3 \sqrt{a+b x} (b c-a d)^2 (b e-a f)^2}-\frac{2 b \sqrt{c+d x} \sqrt{e+f x}}{3 (a+b x)^{3/2} (b c-a d) (b e-a f)}+\frac{2 \sqrt{d} \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} (-3 a d f+b c f+2 b d e) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b \sqrt{c+d x} \sqrt{e+f x} (a d-b c)^{3/2} (b e-a f)}-\frac{4 \sqrt{d} \sqrt{e+f x} \sqrt{\frac{b (c+d x)}{b c-a d}} (-2 a d f+b c f+b d e) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 \sqrt{c+d x} (a d-b c)^{3/2} (b e-a f)^2 \sqrt{\frac{b (e+f x)}{b e-a f}}}",1,"Could not integrate","F",-1
2859,0,0,158,0.4684644,"\int \frac{(2+3 x)^{7/2}}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(7/2)/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","\int \frac{(2+3 x)^{7/2}}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","-\frac{3}{35} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{5/2}-\frac{333}{875} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}-\frac{15553 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{8750}-\frac{178879 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{43750 \sqrt{33}}-\frac{270248 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{21875}",1,"Could not integrate","F",-1
2860,0,0,127,0.4085968,"\int \frac{(2+3 x)^{5/2}}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(5/2)/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","\int \frac{(2+3 x)^{5/2}}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","-\frac{3}{25} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}-\frac{74}{125} \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}-\frac{857 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{625 \sqrt{33}}-\frac{5161 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1250}",1,"Could not integrate","F",-1
2861,0,0,96,0.5664838,"\int \frac{(2+3 x)^{3/2}}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(3/2)/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","\int \frac{(2+3 x)^{3/2}}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","-\frac{1}{5} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{13 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{25 \sqrt{33}}-\frac{37}{25} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2862,0,0,31,0.2693446,"\int \frac{\sqrt{2+3 x}}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[Sqrt[2 + 3*x]/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","\int \frac{\sqrt{2+3 x}}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","-\sqrt{\frac{7}{5}} E\left(\sin ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)|\frac{33}{35}\right)",1,"Could not integrate","F",-1
2863,0,0,29,0.2377104,"\int \frac{1}{\sqrt{1-2 x} \sqrt{2+3 x} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]),x]","\int \frac{1}{\sqrt{1-2 x} \sqrt{2+3 x} \sqrt{3+5 x}} \, dx","-\frac{2 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{\sqrt{33}}",1,"Could not integrate","F",-1
2864,0,0,63,0.6290846,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x]),x]","\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","\frac{6 \sqrt{1-2 x} \sqrt{5 x+3}}{7 \sqrt{3 x+2}}-2 \sqrt{\frac{5}{7}} E\left(\sin ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)|\frac{33}{35}\right)",1,"Could not integrate","F",-1
2865,0,0,127,0.4799417,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x]),x]","\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","\frac{148 \sqrt{1-2 x} \sqrt{5 x+3}}{49 \sqrt{3 x+2}}+\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{7 (3 x+2)^{3/2}}-\frac{52 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{49 \sqrt{33}}-\frac{148}{49} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2866,0,0,158,0.5911015,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2)*Sqrt[3 + 5*x]),x]","\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","\frac{20644 \sqrt{1-2 x} \sqrt{5 x+3}}{1715 \sqrt{3 x+2}}+\frac{296 \sqrt{1-2 x} \sqrt{5 x+3}}{245 (3 x+2)^{3/2}}+\frac{6 \sqrt{1-2 x} \sqrt{5 x+3}}{35 (3 x+2)^{5/2}}-\frac{6856 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1715 \sqrt{33}}-\frac{20644 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1715}",1,"Could not integrate","F",-1
2867,0,0,160,0.7664431,"\int \frac{(2+3 x)^{7/2}}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(7/2)/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","\int \frac{(2+3 x)^{7/2}}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","-\frac{2 \sqrt{1-2 x} (3 x+2)^{5/2}}{55 \sqrt{5 x+3}}-\frac{69 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{1375}-\frac{2577 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{6875}-\frac{942 \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3125}-\frac{61151 \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6250}",1,"Could not integrate","F",-1
2868,0,0,129,0.7039596,"\int \frac{(2+3 x)^{5/2}}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(5/2)/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","\int \frac{(2+3 x)^{5/2}}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","-\frac{2 \sqrt{1-2 x} (3 x+2)^{3/2}}{55 \sqrt{5 x+3}}-\frac{27}{275} \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}-\frac{17}{125} \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{438}{125} \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2869,0,0,98,0.692551,"\int \frac{(2+3 x)^{3/2}}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(3/2)/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","\int \frac{(2+3 x)^{3/2}}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","-\frac{2 \sqrt{1-2 x} \sqrt{3 x+2}}{55 \sqrt{5 x+3}}-\frac{4}{25} \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{31}{25} \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2870,0,0,81,0.6296524,"\int \frac{\sqrt{2+3 x}}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[2 + 3*x]/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","\int \frac{\sqrt{2+3 x}}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","\frac{2 \sqrt{\frac{7}{5}} \sqrt{-5 x-3} E\left(\sin ^{-1}\left(\sqrt{5} \sqrt{3 x+2}\right)|\frac{2}{35}\right)}{11 \sqrt{5 x+3}}-\frac{2 \sqrt{1-2 x} \sqrt{3 x+2}}{11 \sqrt{5 x+3}}",1,"Could not integrate","F",-1
2871,0,0,63,0.633898,"\int \frac{1}{\sqrt{1-2 x} \sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)),x]","\int \frac{1}{\sqrt{1-2 x} \sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","2 \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{10 \sqrt{1-2 x} \sqrt{3 x+2}}{11 \sqrt{5 x+3}}",1,"Could not integrate","F",-1
2872,0,0,129,0.7625245,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","-\frac{680 \sqrt{1-2 x} \sqrt{3 x+2}}{77 \sqrt{5 x+3}}+\frac{6 \sqrt{1-2 x}}{7 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{4}{7} \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{136}{7} \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2873,0,0,160,0.8524357,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","-\frac{31940 \sqrt{1-2 x} \sqrt{3 x+2}}{539 \sqrt{5 x+3}}+\frac{288 \sqrt{1-2 x}}{49 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{2 \sqrt{1-2 x}}{7 (3 x+2)^{3/2} \sqrt{5 x+3}}+\frac{192}{49} \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{6388}{49} \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2874,0,0,191,0.9383283,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)),x]","\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","-\frac{1344984 \sqrt{1-2 x} \sqrt{3 x+2}}{3773 \sqrt{5 x+3}}+\frac{60684 \sqrt{1-2 x}}{1715 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{436 \sqrt{1-2 x}}{245 (3 x+2)^{3/2} \sqrt{5 x+3}}+\frac{6 \sqrt{1-2 x}}{35 (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{40456 \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1715}+\frac{1344984 \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1715}",1,"Could not integrate","F",-1
2875,0,0,187,0.800123,"\int \frac{(2+3 x)^{9/2}}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(9/2)/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^{9/2}}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","-\frac{2 \sqrt{1-2 x} (3 x+2)^{7/2}}{165 (5 x+3)^{3/2}}-\frac{668 \sqrt{1-2 x} (3 x+2)^{5/2}}{9075 \sqrt{5 x+3}}+\frac{403 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{75625}-\frac{87476 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{378125}-\frac{104663 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{171875 \sqrt{33}}-\frac{6515539 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{343750 \sqrt{33}}",1,"Could not integrate","F",-1
2876,0,0,156,0.7801272,"\int \frac{(2+3 x)^{7/2}}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(7/2)/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^{7/2}}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","-\frac{2 \sqrt{1-2 x} (3 x+2)^{5/2}}{165 (5 x+3)^{3/2}}-\frac{536 \sqrt{1-2 x} (3 x+2)^{3/2}}{9075 \sqrt{5 x+3}}-\frac{487 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{15125}-\frac{2281 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6875 \sqrt{33}}-\frac{46159 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6875 \sqrt{33}}",1,"Could not integrate","F",-1
2877,0,0,125,0.7582674,"\int \frac{(2+3 x)^{5/2}}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(5/2)/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^{5/2}}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","-\frac{2 \sqrt{1-2 x} (3 x+2)^{3/2}}{165 (5 x+3)^{3/2}}-\frac{404 \sqrt{1-2 x} \sqrt{3 x+2}}{9075 \sqrt{5 x+3}}-\frac{598 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1375 \sqrt{33}}-\frac{2797 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1375 \sqrt{33}}",1,"Could not integrate","F",-1
2878,0,0,125,0.6976682,"\int \frac{(2+3 x)^{3/2}}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(3/2)/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^{3/2}}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","-\frac{272 \sqrt{1-2 x} \sqrt{3 x+2}}{1815 \sqrt{5 x+3}}-\frac{2 \sqrt{1-2 x} \sqrt{3 x+2}}{165 (5 x+3)^{3/2}}-\frac{202 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{275 \sqrt{33}}+\frac{272 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{275 \sqrt{33}}",1,"Could not integrate","F",-1
2879,0,0,125,0.4975737,"\int \frac{\sqrt{2+3 x}}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[2 + 3*x]/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\int \frac{\sqrt{2+3 x}}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","-\frac{74 \sqrt{1-2 x} \sqrt{3 x+2}}{363 \sqrt{5 x+3}}-\frac{2 \sqrt{1-2 x} \sqrt{3 x+2}}{33 (5 x+3)^{3/2}}-\frac{4 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{55 \sqrt{33}}+\frac{74 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{55 \sqrt{33}}",1,"Could not integrate","F",-1
2880,0,0,125,0.4752231,"\int \frac{1}{\sqrt{1-2 x} \sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3 + 5*x)^(5/2)),x]","\int \frac{1}{\sqrt{1-2 x} \sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","\frac{620 \sqrt{1-2 x} \sqrt{3 x+2}}{363 \sqrt{5 x+3}}-\frac{10 \sqrt{1-2 x} \sqrt{3 x+2}}{33 (5 x+3)^{3/2}}-\frac{4 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{11 \sqrt{33}}-\frac{124 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{11 \sqrt{33}}",1,"Could not integrate","F",-1
2881,0,0,156,0.8771936,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","\frac{89020 \sqrt{1-2 x} \sqrt{3 x+2}}{2541 \sqrt{5 x+3}}-\frac{1340 \sqrt{1-2 x} \sqrt{3 x+2}}{231 (5 x+3)^{3/2}}+\frac{6 \sqrt{1-2 x}}{7 \sqrt{3 x+2} (5 x+3)^{3/2}}-\frac{536 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{77 \sqrt{33}}-\frac{17804 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{77 \sqrt{33}}",1,"Could not integrate","F",-1
2882,0,0,187,0.9390381,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","\frac{6277760 \sqrt{1-2 x} \sqrt{3 x+2}}{17787 \sqrt{5 x+3}}-\frac{94420 \sqrt{1-2 x} \sqrt{3 x+2}}{1617 (5 x+3)^{3/2}}+\frac{428 \sqrt{1-2 x}}{49 \sqrt{3 x+2} (5 x+3)^{3/2}}+\frac{2 \sqrt{1-2 x}}{7 (3 x+2)^{3/2} (5 x+3)^{3/2}}-\frac{37768 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{539 \sqrt{33}}-\frac{1255552 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{539 \sqrt{33}}",1,"Could not integrate","F",-1
2883,0,0,218,1.0010785,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)),x]","\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","\frac{352875016 \sqrt{1-2 x} \sqrt{3 x+2}}{124509 \sqrt{5 x+3}}-\frac{5307272 \sqrt{1-2 x} \sqrt{3 x+2}}{11319 (5 x+3)^{3/2}}+\frac{120324 \sqrt{1-2 x}}{1715 \sqrt{3 x+2} (5 x+3)^{3/2}}+\frac{576 \sqrt{1-2 x}}{245 (3 x+2)^{3/2} (5 x+3)^{3/2}}+\frac{6 \sqrt{1-2 x}}{35 (3 x+2)^{5/2} (5 x+3)^{3/2}}-\frac{10614544 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{18865 \sqrt{33}}-\frac{352875016 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{18865 \sqrt{33}}",1,"Could not integrate","F",-1
2884,0,0,86,0.3603931,"\int \frac{\sqrt{x}}{\sqrt{a+2 x} \sqrt{c+2 x}} \, dx","IntegrateAlgebraic[Sqrt[x]/(Sqrt[a + 2*x]*Sqrt[c + 2*x]),x]","\int \frac{\sqrt{x}}{\sqrt{a+2 x} \sqrt{c+2 x}} \, dx","\frac{\sqrt{x} \sqrt{a-c} \sqrt{-\frac{c+2 x}{a-c}} E\left(\sin ^{-1}\left(\frac{\sqrt{a+2 x}}{\sqrt{a-c}}\right)|1-\frac{c}{a}\right)}{\sqrt{2} \sqrt{-\frac{x}{a}} \sqrt{c+2 x}}",1,"Could not integrate","F",-1
2885,0,0,18,0.2212034,"\int \frac{1}{\sqrt{4-x} \sqrt{5-x} \sqrt{-3+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[4 - x]*Sqrt[5 - x]*Sqrt[-3 + x]),x]","\int \frac{1}{\sqrt{4-x} \sqrt{5-x} \sqrt{-3+x}} \, dx","\sqrt{2} F\left(\sin ^{-1}\left(\sqrt{x-3}\right)|\frac{1}{2}\right)",1,"Could not integrate","F",-1
2886,0,0,14,11.060014,"\int \frac{1}{\sqrt{4-x} \sqrt{(5-x) (-3+x)}} \, dx","IntegrateAlgebraic[1/(Sqrt[4 - x]*Sqrt[(5 - x)*(-3 + x)]),x]","\int \frac{1}{\sqrt{4-x} \sqrt{(5-x) (-3+x)}} \, dx","-2 F\left(\left.\sin ^{-1}\left(\sqrt{4-x}\right)\right|-1\right)",1,"Could not integrate","F",-1
2887,0,0,14,11.048025,"\int \frac{1}{\sqrt{4-x} \sqrt{-15+8 x-x^2}} \, dx","IntegrateAlgebraic[1/(Sqrt[4 - x]*Sqrt[-15 + 8*x - x^2]),x]","\int \frac{1}{\sqrt{4-x} \sqrt{-15+8 x-x^2}} \, dx","-2 F\left(\left.\sin ^{-1}\left(\sqrt{4-x}\right)\right|-1\right)",1,"Could not integrate","F",-1
2888,0,0,16,0.2310088,"\int \frac{1}{\sqrt{6-x} \sqrt{-2+x} \sqrt{-1+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[6 - x]*Sqrt[-2 + x]*Sqrt[-1 + x]),x]","\int \frac{1}{\sqrt{6-x} \sqrt{-2+x} \sqrt{-1+x}} \, dx","2 F\left(\left.\sin ^{-1}\left(\frac{\sqrt{x-2}}{2}\right)\right|-4\right)",1,"Could not integrate","F",-1
2889,0,0,25,12.1845644,"\int \frac{1}{\sqrt{(6-x) (-2+x)} \sqrt{-1+x}} \, dx","IntegrateAlgebraic[1/(Sqrt[(6 - x)*(-2 + x)]*Sqrt[-1 + x]),x]","\int \frac{1}{\sqrt{(6-x) (-2+x)} \sqrt{-1+x}} \, dx","-\frac{2 F\left(\sin ^{-1}\left(\frac{\sqrt{6-x}}{2}\right)|\frac{4}{5}\right)}{\sqrt{5}}",1,"Could not integrate","F",-1
2890,0,0,25,12.1496923,"\int \frac{1}{\sqrt{-1+x} \sqrt{-12+8 x-x^2}} \, dx","IntegrateAlgebraic[1/(Sqrt[-1 + x]*Sqrt[-12 + 8*x - x^2]),x]","\int \frac{1}{\sqrt{-1+x} \sqrt{-12+8 x-x^2}} \, dx","-\frac{2 F\left(\sin ^{-1}\left(\frac{\sqrt{6-x}}{2}\right)|\frac{4}{5}\right)}{\sqrt{5}}",1,"Could not integrate","F",-1
2891,0,0,186,0.9148252,"\int \frac{(2+3 x)^{7/2} \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(7/2)*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\int \frac{(2+3 x)^{7/2} \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","\frac{\sqrt{5 x+3} (3 x+2)^{7/2}}{\sqrt{1-2 x}}+\frac{12}{7} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{5/2}+\frac{2517}{350} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}+\frac{29293}{875} \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}+\frac{673523 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{8750 \sqrt{33}}+\frac{4071079 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{17500}",1,"Could not integrate","F",-1
2892,0,0,155,0.7389335,"\int \frac{(2+3 x)^{5/2} \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(5/2)*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\int \frac{(2+3 x)^{5/2} \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","\frac{\sqrt{5 x+3} (3 x+2)^{5/2}}{\sqrt{1-2 x}}+\frac{9}{5} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}+\frac{419}{50} \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}+\frac{4817 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{250 \sqrt{33}}+\frac{7279}{125} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2893,0,0,122,0.9164564,"\int \frac{(2+3 x)^{3/2} \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(3/2)*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\int \frac{(2+3 x)^{3/2} \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","\frac{\sqrt{5 x+3} (3 x+2)^{3/2}}{\sqrt{1-2 x}}+2 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}+\frac{23 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5 \sqrt{33}}+\frac{139}{10} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2894,0,0,85,0.5602146,"\int \frac{\sqrt{2+3 x} \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[2 + 3*x]*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\int \frac{\sqrt{2+3 x} \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","\frac{\sqrt{3 x+2} \sqrt{5 x+3}}{\sqrt{1-2 x}}+\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{\sqrt{33}}+\sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2895,0,0,62,0.6271083,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} \sqrt{2+3 x}} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]),x]","\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} \sqrt{2+3 x}} \, dx","\frac{2 \sqrt{3 x+2} \sqrt{5 x+3}}{7 \sqrt{1-2 x}}+\sqrt{\frac{5}{7}} E\left(\sin ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)|\frac{33}{35}\right)",1,"Could not integrate","F",-1
2896,0,0,125,0.9721466,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)),x]","\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)^{3/2}} \, dx","-\frac{12 \sqrt{1-2 x} \sqrt{5 x+3}}{49 \sqrt{3 x+2}}+\frac{2 \sqrt{5 x+3}}{7 \sqrt{1-2 x} \sqrt{3 x+2}}-\frac{62 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{49 \sqrt{33}}+\frac{4}{49} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2897,0,0,158,0.8635349,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)),x]","\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)^{5/2}} \, dx","\frac{38 \sqrt{1-2 x} \sqrt{5 x+3}}{343 \sqrt{3 x+2}}-\frac{8 \sqrt{1-2 x} \sqrt{5 x+3}}{49 (3 x+2)^{3/2}}+\frac{2 \sqrt{5 x+3}}{7 \sqrt{1-2 x} (3 x+2)^{3/2}}-\frac{212 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{343 \sqrt{33}}-\frac{38}{343} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2898,0,0,189,1.0027466,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)),x]","\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)^{7/2}} \, dx","\frac{5636 \sqrt{1-2 x} \sqrt{5 x+3}}{12005 \sqrt{3 x+2}}-\frac{26 \sqrt{1-2 x} \sqrt{5 x+3}}{1715 (3 x+2)^{3/2}}-\frac{36 \sqrt{1-2 x} \sqrt{5 x+3}}{245 (3 x+2)^{5/2}}+\frac{2 \sqrt{5 x+3}}{7 \sqrt{1-2 x} (3 x+2)^{5/2}}-\frac{4364 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{12005 \sqrt{33}}-\frac{5636 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{12005}",1,"Could not integrate","F",-1
2899,0,0,219,1.2551406,"\int \frac{(2+3 x)^{7/2} (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]","\int \frac{(2+3 x)^{7/2} (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","\frac{(5 x+3)^{3/2} (3 x+2)^{7/2}}{\sqrt{1-2 x}}+\frac{5}{3} \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^{5/2}+\frac{1397}{210} \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^{3/2}+\frac{24358}{875} \sqrt{1-2 x} (5 x+3)^{3/2} \sqrt{3 x+2}+\frac{6770629 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{31500}+\frac{6770629 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{157500}+\frac{112543103 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{78750}",1,"Could not integrate","F",-1
2900,0,0,188,1.1994251,"\int \frac{(2+3 x)^{5/2} (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]","\int \frac{(2+3 x)^{5/2} (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","\frac{(5 x+3)^{3/2} (3 x+2)^{5/2}}{\sqrt{1-2 x}}+\frac{12}{7} \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^{3/2}+\frac{2511}{350} \sqrt{1-2 x} (5 x+3)^{3/2} \sqrt{3 x+2}+\frac{9694}{175} \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}+\frac{9694}{875} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{1289089 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3500}",1,"Could not integrate","F",-1
2901,0,0,157,1.1450384,"\int \frac{(2+3 x)^{3/2} (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]","\int \frac{(2+3 x)^{3/2} (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","\frac{(3 x+2)^{3/2} (5 x+3)^{3/2}}{\sqrt{1-2 x}}+\frac{9}{5} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}+\frac{139}{10} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+\frac{139}{50} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{4621}{50} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2902,0,0,126,0.8537701,"\int \frac{\sqrt{2+3 x} (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[2 + 3*x]*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]","\int \frac{\sqrt{2+3 x} (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","\frac{\sqrt{3 x+2} (5 x+3)^{3/2}}{\sqrt{1-2 x}}+\frac{10}{3} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+\frac{2}{3} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{133}{6} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2903,0,0,98,0.9081939,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} \sqrt{2+3 x}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]),x]","\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} \sqrt{2+3 x}} \, dx","\frac{11 \sqrt{3 x+2} \sqrt{5 x+3}}{7 \sqrt{1-2 x}}+\frac{1}{7} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{34}{7} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2904,0,0,129,1.2625926,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)),x]","\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^{3/2}} \, dx","-\frac{31 \sqrt{1-2 x} \sqrt{5 x+3}}{49 \sqrt{3 x+2}}+\frac{11 \sqrt{5 x+3}}{7 \sqrt{1-2 x} \sqrt{3 x+2}}+\frac{4}{49} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{31}{49} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2905,0,0,160,1.3319954,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)),x]","\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^{5/2}} \, dx","-\frac{458 \sqrt{1-2 x} \sqrt{5 x+3}}{1029 \sqrt{3 x+2}}-\frac{97 \sqrt{1-2 x} \sqrt{5 x+3}}{147 (3 x+2)^{3/2}}+\frac{11 \sqrt{5 x+3}}{7 \sqrt{1-2 x} (3 x+2)^{3/2}}-\frac{178 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1029}+\frac{458 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1029}",1,"Could not integrate","F",-1
2906,0,0,191,1.3543245,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)),x]","\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^{7/2}} \, dx","\frac{338 \sqrt{1-2 x} \sqrt{5 x+3}}{12005 \sqrt{3 x+2}}-\frac{458 \sqrt{1-2 x} \sqrt{5 x+3}}{1715 (3 x+2)^{3/2}}-\frac{163 \sqrt{1-2 x} \sqrt{5 x+3}}{245 (3 x+2)^{5/2}}+\frac{11 \sqrt{5 x+3}}{7 \sqrt{1-2 x} (3 x+2)^{5/2}}-\frac{992 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{12005}-\frac{338 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{12005}",1,"Could not integrate","F",-1
2907,0,0,222,1.4517937,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^{9/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(9/2)),x]","\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^{9/2}} \, dx","\frac{189368 \sqrt{1-2 x} \sqrt{5 x+3}}{588245 \sqrt{3 x+2}}-\frac{5438 \sqrt{1-2 x} \sqrt{5 x+3}}{84035 (3 x+2)^{3/2}}-\frac{2818 \sqrt{1-2 x} \sqrt{5 x+3}}{12005 (3 x+2)^{5/2}}-\frac{229 \sqrt{1-2 x} \sqrt{5 x+3}}{343 (3 x+2)^{7/2}}+\frac{11 \sqrt{5 x+3}}{7 \sqrt{1-2 x} (3 x+2)^{7/2}}-\frac{23012 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{588245}-\frac{189368 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{588245}",1,"Could not integrate","F",-1
2908,0,0,246,1.2933834,"\int \frac{(2+3 x)^{7/2} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]","\int \frac{(2+3 x)^{7/2} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","\frac{(5 x+3)^{5/2} (3 x+2)^{7/2}}{\sqrt{1-2 x}}+\frac{18}{11} \sqrt{1-2 x} (5 x+3)^{5/2} (3 x+2)^{5/2}+\frac{419}{66} \sqrt{1-2 x} (5 x+3)^{5/2} (3 x+2)^{3/2}+\frac{9741}{385} \sqrt{1-2 x} (5 x+3)^{5/2} \sqrt{3 x+2}+\frac{4066493 \sqrt{1-2 x} (5 x+3)^{3/2} \sqrt{3 x+2}}{23100}+\frac{269045681 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{207900}+\frac{269045681 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{94500 \sqrt{33}}+\frac{17888580643 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{189000 \sqrt{33}}",1,"Could not integrate","F",-1
2909,0,0,219,1.2643089,"\int \frac{(2+3 x)^{5/2} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]","\int \frac{(2+3 x)^{5/2} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","\frac{(3 x+2)^{5/2} (5 x+3)^{5/2}}{\sqrt{1-2 x}}+\frac{5}{3} \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}+\frac{93}{14} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}+\frac{4853}{105} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}+\frac{1284329 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{3780}+\frac{1284329 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{18900}+\frac{42696881 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{18900}",1,"Could not integrate","F",-1
2910,0,0,188,1.195126,"\int \frac{(2+3 x)^{3/2} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]","\int \frac{(2+3 x)^{3/2} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","\frac{(3 x+2)^{3/2} (5 x+3)^{5/2}}{\sqrt{1-2 x}}+\frac{12}{7} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}+\frac{167}{14} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}+\frac{3683}{42} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+\frac{3683}{210} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{244879}{420} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2911,0,0,155,0.7269569,"\int \frac{\sqrt{2+3 x} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[2 + 3*x]*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]","\int \frac{\sqrt{2+3 x} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","\frac{\sqrt{3 x+2} (5 x+3)^{5/2}}{\sqrt{1-2 x}}+3 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}+\frac{397}{18} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+\frac{397}{90} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{6599}{45} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2912,0,0,129,0.845204,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} \sqrt{2+3 x}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]),x]","\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} \sqrt{2+3 x}} \, dx","\frac{11 \sqrt{3 x+2} (5 x+3)^{3/2}}{7 \sqrt{1-2 x}}+\frac{335}{63} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+\frac{67}{63} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{4451}{126} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2913,0,0,129,1.2803535,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)),x]","\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^{3/2}} \, dx","\frac{11 (5 x+3)^{3/2}}{7 \sqrt{1-2 x} \sqrt{3 x+2}}+\frac{31 \sqrt{1-2 x} \sqrt{5 x+3}}{147 \sqrt{3 x+2}}+\frac{31}{147} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{1159}{147} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2914,0,0,160,1.3817112,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)),x]","\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^{5/2}} \, dx","\frac{11 (5 x+3)^{3/2}}{7 \sqrt{1-2 x} (3 x+2)^{3/2}}-\frac{2797 \sqrt{1-2 x} \sqrt{5 x+3}}{3087 \sqrt{3 x+2}}+\frac{97 \sqrt{1-2 x} \sqrt{5 x+3}}{441 (3 x+2)^{3/2}}+\frac{598 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3087}+\frac{2797 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3087}",1,"Could not integrate","F",-1
2915,0,0,191,1.3924195,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)),x]","\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^{7/2}} \, dx","\frac{11 (5 x+3)^{3/2}}{7 \sqrt{1-2 x} (3 x+2)^{5/2}}-\frac{81164 \sqrt{1-2 x} \sqrt{5 x+3}}{108045 \sqrt{3 x+2}}-\frac{15601 \sqrt{1-2 x} \sqrt{5 x+3}}{15435 (3 x+2)^{3/2}}+\frac{163 \sqrt{1-2 x} \sqrt{5 x+3}}{735 (3 x+2)^{5/2}}-\frac{28174 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{108045}+\frac{81164 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{108045}",1,"Could not integrate","F",-1
2916,0,0,222,1.47781,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^{9/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(9/2)),x]","\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^{9/2}} \, dx","\frac{11 (5 x+3)^{3/2}}{7 \sqrt{1-2 x} (3 x+2)^{7/2}}-\frac{106558 \sqrt{1-2 x} \sqrt{5 x+3}}{1764735 \sqrt{3 x+2}}-\frac{106772 \sqrt{1-2 x} \sqrt{5 x+3}}{252105 (3 x+2)^{3/2}}-\frac{37117 \sqrt{1-2 x} \sqrt{5 x+3}}{36015 (3 x+2)^{5/2}}+\frac{229 \sqrt{1-2 x} \sqrt{5 x+3}}{1029 (3 x+2)^{7/2}}-\frac{220028 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1764735}+\frac{106558 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1764735}",1,"Could not integrate","F",-1
2917,0,0,253,1.5771527,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^{11/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(11/2)),x]","\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^{11/2}} \, dx","\frac{11 (5 x+3)^{3/2}}{7 \sqrt{1-2 x} (3 x+2)^{9/2}}+\frac{6036028 \sqrt{1-2 x} \sqrt{5 x+3}}{22235661 \sqrt{3 x+2}}-\frac{392998 \sqrt{1-2 x} \sqrt{5 x+3}}{3176523 (3 x+2)^{3/2}}-\frac{167228 \sqrt{1-2 x} \sqrt{5 x+3}}{453789 (3 x+2)^{5/2}}-\frac{67345 \sqrt{1-2 x} \sqrt{5 x+3}}{64827 (3 x+2)^{7/2}}+\frac{295 \sqrt{1-2 x} \sqrt{5 x+3}}{1323 (3 x+2)^{9/2}}-\frac{1199452 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{22235661}-\frac{6036028 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{22235661}",1,"Could not integrate","F",-1
2918,0,0,160,1.0169152,"\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(7/2)/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","\frac{7 \sqrt{5 x+3} (3 x+2)^{5/2}}{11 \sqrt{1-2 x}}+\frac{312}{275} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}+\frac{14517 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{2750}+\frac{5057 \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1250}+\frac{168123 \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1250}",1,"Could not integrate","F",-1
2919,0,0,129,0.8390652,"\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(5/2)/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","\frac{7 \sqrt{5 x+3} (3 x+2)^{3/2}}{11 \sqrt{1-2 x}}+\frac{69}{55} \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}+\frac{24}{25} \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{1597}{50} \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2920,0,0,98,0.9197347,"\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(3/2)/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","\frac{7 \sqrt{3 x+2} \sqrt{5 x+3}}{11 \sqrt{1-2 x}}+\frac{1}{5} \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{34}{5} \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2921,0,0,62,0.5820527,"\int \frac{\sqrt{2+3 x}}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[Sqrt[2 + 3*x]/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\int \frac{\sqrt{2+3 x}}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","\frac{2 \sqrt{3 x+2} \sqrt{5 x+3}}{11 \sqrt{1-2 x}}+\sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2922,0,0,81,0.6360428,"\int \frac{1}{(1-2 x)^{3/2} \sqrt{2+3 x} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]),x]","\int \frac{1}{(1-2 x)^{3/2} \sqrt{2+3 x} \sqrt{3+5 x}} \, dx","\frac{4 \sqrt{3 x+2} \sqrt{5 x+3}}{77 \sqrt{1-2 x}}+\frac{2 \sqrt{\frac{5}{7}} \sqrt{-5 x-3} E\left(\sin ^{-1}\left(\sqrt{5} \sqrt{3 x+2}\right)|\frac{2}{35}\right)}{11 \sqrt{5 x+3}}",1,"Could not integrate","F",-1
2923,0,0,129,1.0148005,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x]),x]","\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","\frac{186 \sqrt{1-2 x} \sqrt{5 x+3}}{539 \sqrt{3 x+2}}+\frac{4 \sqrt{5 x+3}}{77 \sqrt{1-2 x} \sqrt{3 x+2}}-\frac{8}{49} \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{62}{49} \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2924,0,0,160,0.9426618,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x]),x]","\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","\frac{5256 \sqrt{1-2 x} \sqrt{5 x+3}}{3773 \sqrt{3 x+2}}+\frac{54 \sqrt{1-2 x} \sqrt{5 x+3}}{539 (3 x+2)^{3/2}}+\frac{4 \sqrt{5 x+3}}{77 \sqrt{1-2 x} (3 x+2)^{3/2}}-\frac{68}{343} \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{1752}{343} \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2925,0,0,191,1.1307786,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)*Sqrt[3 + 5*x]),x]","\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","\frac{733812 \sqrt{1-2 x} \sqrt{5 x+3}}{132055 \sqrt{3 x+2}}+\frac{10308 \sqrt{1-2 x} \sqrt{5 x+3}}{18865 (3 x+2)^{3/2}}+\frac{138 \sqrt{1-2 x} \sqrt{5 x+3}}{2695 (3 x+2)^{5/2}}+\frac{4 \sqrt{5 x+3}}{77 \sqrt{1-2 x} (3 x+2)^{5/2}}-\frac{7536 \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{12005}-\frac{244604 \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{12005}",1,"Could not integrate","F",-1
2926,0,0,191,1.0908662,"\int \frac{(2+3 x)^{9/2}}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(9/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(2+3 x)^{9/2}}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","\frac{7 (3 x+2)^{7/2}}{11 \sqrt{1-2 x} \sqrt{5 x+3}}-\frac{37 \sqrt{1-2 x} (3 x+2)^{5/2}}{605 \sqrt{5 x+3}}+\frac{10851 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{15125}+\frac{502941 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{151250}+\frac{175111 \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{68750}+\frac{2911577 \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{34375}",1,"Could not integrate","F",-1
2927,0,0,160,1.0643937,"\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(7/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","\frac{7 (3 x+2)^{5/2}}{11 \sqrt{1-2 x} \sqrt{5 x+3}}-\frac{37 \sqrt{1-2 x} (3 x+2)^{3/2}}{605 \sqrt{5 x+3}}+\frac{2388 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{3025}+\frac{823 \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1375}+\frac{55019 \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2750}",1,"Could not integrate","F",-1
2928,0,0,129,1.0363895,"\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(5/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","\frac{7 (3 x+2)^{3/2}}{11 \sqrt{1-2 x} \sqrt{5 x+3}}-\frac{37 \sqrt{1-2 x} \sqrt{3 x+2}}{605 \sqrt{5 x+3}}+\frac{31}{275} \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{1159}{275} \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2929,0,0,129,0.9564284,"\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(3/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","-\frac{37 \sqrt{1-2 x} \sqrt{3 x+2}}{121 \sqrt{5 x+3}}+\frac{7 \sqrt{3 x+2}}{11 \sqrt{1-2 x} \sqrt{5 x+3}}-\frac{2}{55} \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{37}{55} \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2930,0,0,129,0.928515,"\int \frac{\sqrt{2+3 x}}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[2 + 3*x]/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\int \frac{\sqrt{2+3 x}}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","-\frac{20 \sqrt{1-2 x} \sqrt{3 x+2}}{121 \sqrt{5 x+3}}+\frac{2 \sqrt{3 x+2}}{11 \sqrt{1-2 x} \sqrt{5 x+3}}-\frac{2}{11} \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{4}{11} \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2931,0,0,129,0.975215,"\int \frac{1}{(1-2 x)^{3/2} \sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)),x]","\int \frac{1}{(1-2 x)^{3/2} \sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","-\frac{370 \sqrt{1-2 x} \sqrt{3 x+2}}{847 \sqrt{5 x+3}}+\frac{4 \sqrt{3 x+2}}{77 \sqrt{1-2 x} \sqrt{5 x+3}}-\frac{4}{77} \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{74}{77} \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2932,0,0,160,1.0604667,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","-\frac{23180 \sqrt{1-2 x} \sqrt{3 x+2}}{5929 \sqrt{5 x+3}}+\frac{186 \sqrt{1-2 x}}{539 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{4}{77 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{124}{539} \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)+\frac{4636}{539} \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2933,0,0,191,1.2329135,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","-\frac{1100380 \sqrt{1-2 x} \sqrt{3 x+2}}{41503 \sqrt{5 x+3}}+\frac{9876 \sqrt{1-2 x}}{3773 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{54 \sqrt{1-2 x}}{539 (3 x+2)^{3/2} \sqrt{5 x+3}}+\frac{4}{77 \sqrt{1-2 x} (3 x+2)^{3/2} \sqrt{5 x+3}}+\frac{6584 \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3773}+\frac{220076 \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3773}",1,"Could not integrate","F",-1
2934,0,0,222,1.2670959,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)),x]","\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","-\frac{46585232 \sqrt{1-2 x} \sqrt{3 x+2}}{290521 \sqrt{5 x+3}}+\frac{2101332 \sqrt{1-2 x}}{132055 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{14928 \sqrt{1-2 x}}{18865 (3 x+2)^{3/2} \sqrt{5 x+3}}+\frac{138 \sqrt{1-2 x}}{2695 (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{4}{77 \sqrt{1-2 x} (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{1400888 \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{132055}+\frac{46585232 \sqrt{\frac{3}{11}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{132055}",1,"Could not integrate","F",-1
2935,0,0,218,1.2231911,"\int \frac{(2+3 x)^{11/2}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(11/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^{11/2}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","\frac{7 (3 x+2)^{9/2}}{11 \sqrt{1-2 x} (5 x+3)^{3/2}}-\frac{107 \sqrt{1-2 x} (3 x+2)^{7/2}}{1815 (5 x+3)^{3/2}}-\frac{4553 \sqrt{1-2 x} (3 x+2)^{5/2}}{99825 \sqrt{5 x+3}}+\frac{380188 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{831875}+\frac{17427983 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{8318750}+\frac{18177329 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3781250 \sqrt{33}}+\frac{604915631 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3781250 \sqrt{33}}",1,"Could not integrate","F",-1
2936,0,0,187,1.1588504,"\int \frac{(2+3 x)^{9/2}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(9/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^{9/2}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","\frac{7 (3 x+2)^{7/2}}{11 \sqrt{1-2 x} (5 x+3)^{3/2}}-\frac{107 \sqrt{1-2 x} (3 x+2)^{5/2}}{1815 (5 x+3)^{3/2}}-\frac{4421 \sqrt{1-2 x} (3 x+2)^{3/2}}{99825 \sqrt{5 x+3}}+\frac{83093 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{166375}+\frac{84134 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{75625 \sqrt{33}}+\frac{5684677 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{151250 \sqrt{33}}",1,"Could not integrate","F",-1
2937,0,0,156,1.1285482,"\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(7/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","\frac{7 (3 x+2)^{5/2}}{11 \sqrt{1-2 x} (5 x+3)^{3/2}}-\frac{107 \sqrt{1-2 x} (3 x+2)^{3/2}}{1815 (5 x+3)^{3/2}}-\frac{4289 \sqrt{1-2 x} \sqrt{3 x+2}}{99825 \sqrt{5 x+3}}+\frac{2657 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{15125 \sqrt{33}}+\frac{118898 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{15125 \sqrt{33}}",1,"Could not integrate","F",-1
2938,0,0,156,1.1269717,"\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(5/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","\frac{7 (3 x+2)^{3/2}}{11 \sqrt{1-2 x} (5 x+3)^{3/2}}-\frac{4157 \sqrt{1-2 x} \sqrt{3 x+2}}{19965 \sqrt{5 x+3}}-\frac{107 \sqrt{1-2 x} \sqrt{3 x+2}}{1815 (5 x+3)^{3/2}}-\frac{412 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3025 \sqrt{33}}+\frac{4157 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3025 \sqrt{33}}",1,"Could not integrate","F",-1
2939,0,0,156,1.0669522,"\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(3/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","-\frac{494 \sqrt{1-2 x} \sqrt{3 x+2}}{3993 \sqrt{5 x+3}}-\frac{107 \sqrt{1-2 x} \sqrt{3 x+2}}{363 (5 x+3)^{3/2}}+\frac{7 \sqrt{3 x+2}}{11 \sqrt{1-2 x} (5 x+3)^{3/2}}-\frac{214 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{605 \sqrt{33}}+\frac{494 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{605 \sqrt{33}}",1,"Could not integrate","F",-1
2940,0,0,156,0.8432313,"\int \frac{\sqrt{2+3 x}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[2 + 3*x]/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\int \frac{\sqrt{2+3 x}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","-\frac{490 \sqrt{1-2 x} \sqrt{3 x+2}}{3993 \sqrt{5 x+3}}-\frac{40 \sqrt{1-2 x} \sqrt{3 x+2}}{363 (5 x+3)^{3/2}}+\frac{2 \sqrt{3 x+2}}{11 \sqrt{1-2 x} (5 x+3)^{3/2}}-\frac{16 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{121 \sqrt{33}}+\frac{98 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{121 \sqrt{33}}",1,"Could not integrate","F",-1
2941,0,0,156,0.925618,"\int \frac{1}{(1-2 x)^{3/2} \sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]*(3 + 5*x)^(5/2)),x]","\int \frac{1}{(1-2 x)^{3/2} \sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","\frac{19480 \sqrt{1-2 x} \sqrt{3 x+2}}{27951 \sqrt{5 x+3}}-\frac{410 \sqrt{1-2 x} \sqrt{3 x+2}}{2541 (5 x+3)^{3/2}}+\frac{4 \sqrt{3 x+2}}{77 \sqrt{1-2 x} (5 x+3)^{3/2}}-\frac{164 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{847 \sqrt{33}}-\frac{3896 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{847 \sqrt{33}}",1,"Could not integrate","F",-1
2942,0,0,187,1.2280371,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","\frac{2976620 \sqrt{1-2 x} \sqrt{3 x+2}}{195657 \sqrt{5 x+3}}-\frac{45040 \sqrt{1-2 x} \sqrt{3 x+2}}{17787 (5 x+3)^{3/2}}+\frac{186 \sqrt{1-2 x}}{539 \sqrt{3 x+2} (5 x+3)^{3/2}}+\frac{4}{77 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}-\frac{18016 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5929 \sqrt{33}}-\frac{595324 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5929 \sqrt{33}}",1,"Could not integrate","F",-1
2943,0,0,218,1.3099257,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","\frac{213119320 \sqrt{1-2 x} \sqrt{3 x+2}}{1369599 \sqrt{5 x+3}}-\frac{3205940 \sqrt{1-2 x} \sqrt{3 x+2}}{124509 (5 x+3)^{3/2}}+\frac{14496 \sqrt{1-2 x}}{3773 \sqrt{3 x+2} (5 x+3)^{3/2}}+\frac{54 \sqrt{1-2 x}}{539 (3 x+2)^{3/2} (5 x+3)^{3/2}}+\frac{4}{77 \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{3/2}}-\frac{1282376 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{41503 \sqrt{33}}-\frac{42623864 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{41503 \sqrt{33}}",1,"Could not integrate","F",-1
2944,0,0,249,1.4052412,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)),x]","\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","\frac{12071114168 \sqrt{1-2 x} \sqrt{3 x+2}}{9587193 \sqrt{5 x+3}}-\frac{181551856 \sqrt{1-2 x} \sqrt{3 x+2}}{871563 (5 x+3)^{3/2}}+\frac{4115652 \sqrt{1-2 x}}{132055 \sqrt{3 x+2} (5 x+3)^{3/2}}+\frac{19548 \sqrt{1-2 x}}{18865 (3 x+2)^{3/2} (5 x+3)^{3/2}}+\frac{138 \sqrt{1-2 x}}{2695 (3 x+2)^{5/2} (5 x+3)^{3/2}}+\frac{4}{77 \sqrt{1-2 x} (3 x+2)^{5/2} (5 x+3)^{3/2}}-\frac{363103712 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1452605 \sqrt{33}}-\frac{12071114168 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1452605 \sqrt{33}}",1,"Could not integrate","F",-1
2945,0,0,218,1.0101426,"\int \frac{(2+3 x)^{9/2} \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(9/2)*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","\int \frac{(2+3 x)^{9/2} \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","\frac{\sqrt{5 x+3} (3 x+2)^{9/2}}{3 (1-2 x)^{3/2}}-\frac{166 \sqrt{5 x+3} (3 x+2)^{7/2}}{33 \sqrt{1-2 x}}-\frac{1327}{154} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{5/2}-\frac{139163 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{3850}-\frac{6478333 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{38500}-\frac{6770629 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{17500 \sqrt{33}}-\frac{112543103 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{8750 \sqrt{33}}",1,"Could not integrate","F",-1
2946,0,0,187,0.9825406,"\int \frac{(2+3 x)^{7/2} \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(7/2)*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","\int \frac{(2+3 x)^{7/2} \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","\frac{\sqrt{5 x+3} (3 x+2)^{7/2}}{3 (1-2 x)^{3/2}}-\frac{133 \sqrt{5 x+3} (3 x+2)^{5/2}}{33 \sqrt{1-2 x}}-\frac{797}{110} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}-\frac{18551}{550} \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}-\frac{9694 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{125 \sqrt{33}}-\frac{1289089 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{500 \sqrt{33}}",1,"Could not integrate","F",-1
2947,0,0,156,0.9293195,"\int \frac{(2+3 x)^{5/2} \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(5/2)*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","\int \frac{(2+3 x)^{5/2} \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","\frac{\sqrt{5 x+3} (3 x+2)^{5/2}}{3 (1-2 x)^{3/2}}-\frac{100 \sqrt{5 x+3} (3 x+2)^{3/2}}{33 \sqrt{1-2 x}}-\frac{133}{22} \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}-\frac{139 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{10 \sqrt{33}}-\frac{4621 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{10 \sqrt{33}}",1,"Could not integrate","F",-1
2948,0,0,123,0.7963238,"\int \frac{(2+3 x)^{3/2} \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(3/2)*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","\int \frac{(2+3 x)^{3/2} \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","\frac{\sqrt{5 x+3} (3 x+2)^{3/2}}{3 (1-2 x)^{3/2}}-\frac{67 \sqrt{5 x+3} \sqrt{3 x+2}}{33 \sqrt{1-2 x}}-\frac{2 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{\sqrt{33}}-\frac{133 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2 \sqrt{33}}",1,"Could not integrate","F",-1
2949,0,0,125,0.4148755,"\int \frac{\sqrt{2+3 x} \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[2 + 3*x]*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","\int \frac{\sqrt{2+3 x} \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","-\frac{68 \sqrt{3 x+2} \sqrt{5 x+3}}{231 \sqrt{1-2 x}}+\frac{\sqrt{3 x+2} \sqrt{5 x+3}}{3 (1-2 x)^{3/2}}-\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{7 \sqrt{33}}-\frac{34 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{7 \sqrt{33}}",1,"Could not integrate","F",-1
2950,0,0,125,0.5190166,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} \sqrt{2+3 x}} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/((1 - 2*x)^(5/2)*Sqrt[2 + 3*x]),x]","\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} \sqrt{2+3 x}} \, dx","\frac{62 \sqrt{3 x+2} \sqrt{5 x+3}}{1617 \sqrt{1-2 x}}+\frac{2 \sqrt{3 x+2} \sqrt{5 x+3}}{21 (1-2 x)^{3/2}}+\frac{4 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{49 \sqrt{33}}+\frac{31 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{49 \sqrt{33}}",1,"Could not integrate","F",-1
2951,0,0,156,0.9348562,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} (2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)),x]","\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} (2+3 x)^{3/2}} \, dx","-\frac{458 \sqrt{1-2 x} \sqrt{5 x+3}}{3773 \sqrt{3 x+2}}+\frac{194 \sqrt{5 x+3}}{1617 \sqrt{1-2 x} \sqrt{3 x+2}}+\frac{2 \sqrt{5 x+3}}{21 (1-2 x)^{3/2} \sqrt{3 x+2}}-\frac{178 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{343 \sqrt{33}}+\frac{458 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{343 \sqrt{33}}",1,"Could not integrate","F",-1
2952,0,0,187,1.0722935,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} (2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)),x]","\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} (2+3 x)^{5/2}} \, dx","\frac{338 \sqrt{1-2 x} \sqrt{5 x+3}}{26411 \sqrt{3 x+2}}-\frac{458 \sqrt{1-2 x} \sqrt{5 x+3}}{3773 (3 x+2)^{3/2}}+\frac{326 \sqrt{5 x+3}}{1617 \sqrt{1-2 x} (3 x+2)^{3/2}}+\frac{2 \sqrt{5 x+3}}{21 (1-2 x)^{3/2} (3 x+2)^{3/2}}-\frac{992 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2401 \sqrt{33}}-\frac{338 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2401 \sqrt{33}}",1,"Could not integrate","F",-1
2953,0,0,220,1.1360964,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} (2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[Sqrt[3 + 5*x]/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)),x]","\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} (2+3 x)^{7/2}} \, dx","\frac{189368 \sqrt{1-2 x} \sqrt{5 x+3}}{924385 \sqrt{3 x+2}}-\frac{5438 \sqrt{1-2 x} \sqrt{5 x+3}}{132055 (3 x+2)^{3/2}}-\frac{2818 \sqrt{1-2 x} \sqrt{5 x+3}}{18865 (3 x+2)^{5/2}}+\frac{458 \sqrt{5 x+3}}{1617 \sqrt{1-2 x} (3 x+2)^{5/2}}+\frac{2 \sqrt{5 x+3}}{21 (1-2 x)^{3/2} (3 x+2)^{5/2}}-\frac{2092 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{84035}-\frac{189368 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{84035 \sqrt{33}}",1,"Could not integrate","F",-1
2954,0,0,222,1.2909847,"\int \frac{(2+3 x)^{7/2} (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2),x]","\int \frac{(2+3 x)^{7/2} (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","\frac{(5 x+3)^{3/2} (3 x+2)^{7/2}}{3 (1-2 x)^{3/2}}-\frac{56 (5 x+3)^{3/2} (3 x+2)^{5/2}}{11 \sqrt{1-2 x}}-\frac{1341}{154} \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^{3/2}-\frac{140289 \sqrt{1-2 x} (5 x+3)^{3/2} \sqrt{3 x+2}}{3850}-\frac{2166399 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{7700}-\frac{722133 \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3500}-\frac{6547351 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3500}",1,"Could not integrate","F",-1
2955,0,0,191,1.2508323,"\int \frac{(2+3 x)^{5/2} (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2),x]","\int \frac{(2+3 x)^{5/2} (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","\frac{(5 x+3)^{3/2} (3 x+2)^{5/2}}{3 (1-2 x)^{3/2}}-\frac{45 (5 x+3)^{3/2} (3 x+2)^{3/2}}{11 \sqrt{1-2 x}}-\frac{807}{110} \sqrt{1-2 x} (5 x+3)^{3/2} \sqrt{3 x+2}-\frac{6231}{110} \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}-\frac{2077}{50} \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{37663}{100} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2956,0,0,158,1.1643591,"\int \frac{(2+3 x)^{3/2} (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2),x]","\int \frac{(2+3 x)^{3/2} (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","\frac{(3 x+2)^{3/2} (5 x+3)^{3/2}}{3 (1-2 x)^{3/2}}-\frac{34 \sqrt{3 x+2} (5 x+3)^{3/2}}{11 \sqrt{1-2 x}}-\frac{225}{22} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{15}{2} \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-68 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2957,0,0,127,0.7986123,"\int \frac{\sqrt{2+3 x} (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[2 + 3*x]*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2),x]","\int \frac{\sqrt{2+3 x} (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","\frac{\sqrt{3 x+2} (5 x+3)^{3/2}}{3 (1-2 x)^{3/2}}-\frac{23 \sqrt{3 x+2} \sqrt{5 x+3}}{7 \sqrt{1-2 x}}-\frac{23 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{7 \sqrt{33}}-\frac{139}{14} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2958,0,0,127,0.8216531,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} \sqrt{2+3 x}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*Sqrt[2 + 3*x]),x]","\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} \sqrt{2+3 x}} \, dx","-\frac{74 \sqrt{3 x+2} \sqrt{5 x+3}}{147 \sqrt{1-2 x}}+\frac{11 \sqrt{3 x+2} \sqrt{5 x+3}}{21 (1-2 x)^{3/2}}-\frac{13 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{49 \sqrt{33}}-\frac{37}{49} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2959,0,0,158,1.337754,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} (2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)),x]","\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} (2+3 x)^{3/2}} \, dx","-\frac{19 \sqrt{1-2 x} \sqrt{5 x+3}}{343 \sqrt{3 x+2}}-\frac{8 \sqrt{5 x+3}}{147 \sqrt{1-2 x} \sqrt{3 x+2}}+\frac{11 \sqrt{5 x+3}}{21 (1-2 x)^{3/2} \sqrt{3 x+2}}+\frac{106 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{343 \sqrt{33}}+\frac{19}{343} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2960,0,0,191,1.3882355,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} (2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)),x]","\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} (2+3 x)^{5/2}} \, dx","-\frac{496 \sqrt{1-2 x} \sqrt{5 x+3}}{2401 \sqrt{3 x+2}}-\frac{89 \sqrt{1-2 x} \sqrt{5 x+3}}{343 (3 x+2)^{3/2}}+\frac{58 \sqrt{5 x+3}}{147 \sqrt{1-2 x} (3 x+2)^{3/2}}+\frac{11 \sqrt{5 x+3}}{21 (1-2 x)^{3/2} (3 x+2)^{3/2}}-\frac{582 \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2401}+\frac{496 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2401}",1,"Could not integrate","F",-1
2961,0,0,222,1.433646,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} (2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)),x]","\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} (2+3 x)^{7/2}} \, dx","-\frac{3946 \sqrt{1-2 x} \sqrt{5 x+3}}{84035 \sqrt{3 x+2}}-\frac{2264 \sqrt{1-2 x} \sqrt{5 x+3}}{12005 (3 x+2)^{3/2}}-\frac{779 \sqrt{1-2 x} \sqrt{5 x+3}}{1715 (3 x+2)^{5/2}}+\frac{124 \sqrt{5 x+3}}{147 \sqrt{1-2 x} (3 x+2)^{5/2}}+\frac{11 \sqrt{5 x+3}}{21 (1-2 x)^{3/2} (3 x+2)^{5/2}}-\frac{16732 \sqrt{\frac{3}{11}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{84035}+\frac{3946 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{84035}",1,"Could not integrate","F",-1
2962,0,0,253,1.3486272,"\int \frac{(2+3 x)^{7/2} (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2),x]","\int \frac{(2+3 x)^{7/2} (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","\frac{(5 x+3)^{5/2} (3 x+2)^{7/2}}{3 (1-2 x)^{3/2}}-\frac{203 (5 x+3)^{5/2} (3 x+2)^{5/2}}{33 \sqrt{1-2 x}}-\frac{225}{22} \sqrt{1-2 x} (5 x+3)^{5/2} (3 x+2)^{3/2}-\frac{6277}{154} \sqrt{1-2 x} (5 x+3)^{5/2} \sqrt{3 x+2}-\frac{1310203 \sqrt{1-2 x} (5 x+3)^{3/2} \sqrt{3 x+2}}{4620}-\frac{1313411}{630} \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}-\frac{1313411 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3150}-\frac{174654791 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{12600}",1,"Could not integrate","F",-1
2963,0,0,220,1.2802612,"\int \frac{(2+3 x)^{5/2} (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2),x]","\int \frac{(2+3 x)^{5/2} (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","\frac{(3 x+2)^{5/2} (5 x+3)^{5/2}}{3 (1-2 x)^{3/2}}-\frac{170 (3 x+2)^{3/2} (5 x+3)^{5/2}}{33 \sqrt{1-2 x}}-\frac{1355}{154} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}-\frac{28283}{462} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{12601}{28} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{12601}{140} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{69819}{70} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2964,0,0,189,1.2231241,"\int \frac{(2+3 x)^{3/2} (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2),x]","\int \frac{(2+3 x)^{3/2} (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","\frac{(3 x+2)^{3/2} (5 x+3)^{5/2}}{3 (1-2 x)^{3/2}}-\frac{137 \sqrt{3 x+2} (5 x+3)^{5/2}}{33 \sqrt{1-2 x}}-\frac{817}{66} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-91 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{91}{5} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{12101}{20} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2965,0,0,160,0.9233356,"\int \frac{\sqrt{2+3 x} (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[2 + 3*x]*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2),x]","\int \frac{\sqrt{2+3 x} (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","\frac{\sqrt{3 x+2} (5 x+3)^{5/2}}{3 (1-2 x)^{3/2}}-\frac{104 \sqrt{3 x+2} (5 x+3)^{3/2}}{21 \sqrt{1-2 x}}-\frac{695}{42} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{139}{42} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{4621}{42} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2966,0,0,127,1.0117051,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} \sqrt{2+3 x}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*Sqrt[2 + 3*x]),x]","\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} \sqrt{2+3 x}} \, dx","\frac{11 \sqrt{3 x+2} (5 x+3)^{3/2}}{21 (1-2 x)^{3/2}}-\frac{264 \sqrt{3 x+2} \sqrt{5 x+3}}{49 \sqrt{1-2 x}}-\frac{8}{49} \sqrt{33} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{1597}{98} \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2967,0,0,158,1.3934158,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^{3/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)),x]","\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^{3/2}} \, dx","\frac{11 (5 x+3)^{3/2}}{21 (1-2 x)^{3/2} \sqrt{3 x+2}}+\frac{438 \sqrt{1-2 x} \sqrt{5 x+3}}{343 \sqrt{3 x+2}}-\frac{143 \sqrt{5 x+3}}{49 \sqrt{1-2 x} \sqrt{3 x+2}}-\frac{17}{343} \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)-\frac{146}{343} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"Could not integrate","F",-1
2968,0,0,191,1.3894078,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^{5/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)),x]","\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^{5/2}} \, dx","\frac{11 (5 x+3)^{3/2}}{21 (1-2 x)^{3/2} (3 x+2)^{3/2}}-\frac{169 \sqrt{1-2 x} \sqrt{5 x+3}}{7203 \sqrt{3 x+2}}+\frac{229 \sqrt{1-2 x} \sqrt{5 x+3}}{1029 (3 x+2)^{3/2}}-\frac{22 \sqrt{5 x+3}}{49 \sqrt{1-2 x} (3 x+2)^{3/2}}+\frac{496 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{7203}+\frac{169 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{7203}",1,"Could not integrate","F",-1
2969,0,0,220,1.4349503,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^{7/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)),x]","\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^{7/2}} \, dx","\frac{11 (5 x+3)^{3/2}}{21 (1-2 x)^{3/2} (3 x+2)^{5/2}}-\frac{27618 \sqrt{1-2 x} \sqrt{5 x+3}}{84035 \sqrt{3 x+2}}-\frac{4437 \sqrt{1-2 x} \sqrt{5 x+3}}{12005 (3 x+2)^{3/2}}-\frac{1432 \sqrt{1-2 x} \sqrt{5 x+3}}{1715 (3 x+2)^{5/2}}+\frac{99 \sqrt{5 x+3}}{49 \sqrt{1-2 x} (3 x+2)^{5/2}}-\frac{7738 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{84035}+\frac{9206 \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{84035}",1,"Could not integrate","F",-1
2970,0,0,253,1.516731,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^{9/2}} \, dx","IntegrateAlgebraic[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(9/2)),x]","\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^{9/2}} \, dx","\frac{11 (5 x+3)^{3/2}}{21 (1-2 x)^{3/2} (3 x+2)^{7/2}}-\frac{98642 \sqrt{1-2 x} \sqrt{5 x+3}}{823543 \sqrt{3 x+2}}-\frac{33778 \sqrt{1-2 x} \sqrt{5 x+3}}{117649 (3 x+2)^{3/2}}-\frac{11433 \sqrt{1-2 x} \sqrt{5 x+3}}{16807 (3 x+2)^{5/2}}-\frac{4545 \sqrt{1-2 x} \sqrt{5 x+3}}{2401 (3 x+2)^{7/2}}+\frac{220 \sqrt{5 x+3}}{49 \sqrt{1-2 x} (3 x+2)^{7/2}}-\frac{65672 \sqrt{\frac{11}{3}} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{823543}+\frac{98642 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{823543}",1,"Could not integrate","F",-1
2971,0,0,187,1.0536577,"\int \frac{(2+3 x)^{9/2}}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(9/2)/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","\int \frac{(2+3 x)^{9/2}}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","\frac{7 \sqrt{5 x+3} (3 x+2)^{7/2}}{33 (1-2 x)^{3/2}}-\frac{910 \sqrt{5 x+3} (3 x+2)^{5/2}}{363 \sqrt{1-2 x}}-\frac{27271 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{6050}-\frac{317384 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{15125}-\frac{663409 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{13750 \sqrt{33}}-\frac{44109377 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{27500 \sqrt{33}}",1,"Could not integrate","F",-1
2972,0,0,156,1.0594889,"\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(7/2)/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","\frac{7 \sqrt{5 x+3} (3 x+2)^{5/2}}{33 (1-2 x)^{3/2}}-\frac{679 \sqrt{5 x+3} (3 x+2)^{3/2}}{363 \sqrt{1-2 x}}-\frac{4517 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{1210}-\frac{4721 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{550 \sqrt{33}}-\frac{78472 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{275 \sqrt{33}}",1,"Could not integrate","F",-1
2973,0,0,125,1.0150861,"\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(5/2)/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","\frac{7 \sqrt{5 x+3} (3 x+2)^{3/2}}{33 (1-2 x)^{3/2}}-\frac{448 \sqrt{5 x+3} \sqrt{3 x+2}}{363 \sqrt{1-2 x}}-\frac{67 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{55 \sqrt{33}}-\frac{4451 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{110 \sqrt{33}}",1,"Could not integrate","F",-1
2974,0,0,125,0.8317417,"\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(3/2)/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","-\frac{62 \sqrt{3 x+2} \sqrt{5 x+3}}{363 \sqrt{1-2 x}}+\frac{7 \sqrt{3 x+2} \sqrt{5 x+3}}{33 (1-2 x)^{3/2}}-\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{11 \sqrt{33}}-\frac{31 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{11 \sqrt{33}}",1,"Could not integrate","F",-1
2975,0,0,125,0.4363031,"\int \frac{\sqrt{2+3 x}}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[Sqrt[2 + 3*x]/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","\int \frac{\sqrt{2+3 x}}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","\frac{74 \sqrt{3 x+2} \sqrt{5 x+3}}{2541 \sqrt{1-2 x}}+\frac{2 \sqrt{3 x+2} \sqrt{5 x+3}}{33 (1-2 x)^{3/2}}-\frac{2 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{77 \sqrt{33}}+\frac{37 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{77 \sqrt{33}}",1,"Could not integrate","F",-1
2976,0,0,125,0.4972062,"\int \frac{1}{(1-2 x)^{5/2} \sqrt{2+3 x} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]),x]","\int \frac{1}{(1-2 x)^{5/2} \sqrt{2+3 x} \sqrt{3+5 x}} \, dx","\frac{544 \sqrt{3 x+2} \sqrt{5 x+3}}{17787 \sqrt{1-2 x}}+\frac{4 \sqrt{3 x+2} \sqrt{5 x+3}}{231 (1-2 x)^{3/2}}-\frac{202 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{539 \sqrt{33}}+\frac{272 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{539 \sqrt{33}}",1,"Could not integrate","F",-1
2977,0,0,156,0.9415921,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x]),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","\frac{5594 \sqrt{1-2 x} \sqrt{5 x+3}}{41503 \sqrt{3 x+2}}+\frac{808 \sqrt{5 x+3}}{17787 \sqrt{1-2 x} \sqrt{3 x+2}}+\frac{4 \sqrt{5 x+3}}{231 (1-2 x)^{3/2} \sqrt{3 x+2}}-\frac{1196 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3773 \sqrt{33}}-\frac{5594 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3773 \sqrt{33}}",1,"Could not integrate","F",-1
2978,0,0,187,1.1298618,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x]),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","\frac{184636 \sqrt{1-2 x} \sqrt{5 x+3}}{290521 \sqrt{3 x+2}}+\frac{974 \sqrt{1-2 x} \sqrt{5 x+3}}{41503 (3 x+2)^{3/2}}+\frac{1072 \sqrt{5 x+3}}{17787 \sqrt{1-2 x} (3 x+2)^{3/2}}+\frac{4 \sqrt{5 x+3}}{231 (1-2 x)^{3/2} (3 x+2)^{3/2}}-\frac{9124 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{26411 \sqrt{33}}-\frac{184636 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{26411 \sqrt{33}}",1,"Could not integrate","F",-1
2979,0,0,218,1.2317181,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)*Sqrt[3 + 5*x]),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","\frac{26062156 \sqrt{1-2 x} \sqrt{5 x+3}}{10168235 \sqrt{3 x+2}}+\frac{349904 \sqrt{1-2 x} \sqrt{5 x+3}}{1452605 (3 x+2)^{3/2}}-\frac{806 \sqrt{1-2 x} \sqrt{5 x+3}}{207515 (3 x+2)^{5/2}}+\frac{1336 \sqrt{5 x+3}}{17787 \sqrt{1-2 x} (3 x+2)^{5/2}}+\frac{4 \sqrt{5 x+3}}{231 (1-2 x)^{3/2} (3 x+2)^{5/2}}-\frac{837304 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{924385 \sqrt{33}}-\frac{26062156 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{924385 \sqrt{33}}",1,"Could not integrate","F",-1
2980,0,0,218,1.2397851,"\int \frac{(2+3 x)^{11/2}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(11/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(2+3 x)^{11/2}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","\frac{7 (3 x+2)^{9/2}}{33 (1-2 x)^{3/2} \sqrt{5 x+3}}-\frac{896 (3 x+2)^{7/2}}{363 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{4439 \sqrt{1-2 x} (3 x+2)^{5/2}}{19965 \sqrt{5 x+3}}-\frac{932783 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{332750}-\frac{21713939 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{1663750}-\frac{11346991 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{378125 \sqrt{33}}-\frac{1508889271 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1512500 \sqrt{33}}",1,"Could not integrate","F",-1
2981,0,0,187,1.1744694,"\int \frac{(2+3 x)^{9/2}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(9/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(2+3 x)^{9/2}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","\frac{7 (3 x+2)^{7/2}}{33 (1-2 x)^{3/2} \sqrt{5 x+3}}-\frac{665 (3 x+2)^{5/2}}{363 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{3284 \sqrt{1-2 x} (3 x+2)^{3/2}}{19965 \sqrt{5 x+3}}-\frac{153319 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{66550}-\frac{160297 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{30250 \sqrt{33}}-\frac{5327983 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{30250 \sqrt{33}}",1,"Could not integrate","F",-1
2982,0,0,156,1.114143,"\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(7/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","\frac{7 (3 x+2)^{5/2}}{33 (1-2 x)^{3/2} \sqrt{5 x+3}}-\frac{434 (3 x+2)^{3/2}}{363 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{2129 \sqrt{1-2 x} \sqrt{3 x+2}}{19965 \sqrt{5 x+3}}-\frac{2252 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3025 \sqrt{33}}-\frac{148831 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6050 \sqrt{33}}",1,"Could not integrate","F",-1
2983,0,0,156,1.1130683,"\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(5/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","\frac{7 (3 x+2)^{3/2}}{33 (1-2 x)^{3/2} \sqrt{5 x+3}}+\frac{974 \sqrt{1-2 x} \sqrt{3 x+2}}{3993 \sqrt{5 x+3}}-\frac{203 \sqrt{3 x+2}}{363 \sqrt{1-2 x} \sqrt{5 x+3}}-\frac{41 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{605 \sqrt{33}}-\frac{974 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{605 \sqrt{33}}",1,"Could not integrate","F",-1
2984,0,0,156,1.0526136,"\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(3/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","-\frac{245 \sqrt{1-2 x} \sqrt{3 x+2}}{3993 \sqrt{5 x+3}}+\frac{8 \sqrt{3 x+2}}{363 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{7 \sqrt{3 x+2}}{33 (1-2 x)^{3/2} \sqrt{5 x+3}}-\frac{8 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{121 \sqrt{33}}+\frac{49 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{121 \sqrt{33}}",1,"Could not integrate","F",-1
2985,0,0,156,0.8581392,"\int \frac{\sqrt{2+3 x}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[2 + 3*x]/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\int \frac{\sqrt{2+3 x}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","-\frac{2470 \sqrt{1-2 x} \sqrt{3 x+2}}{27951 \sqrt{5 x+3}}+\frac{214 \sqrt{3 x+2}}{2541 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{2 \sqrt{3 x+2}}{33 (1-2 x)^{3/2} \sqrt{5 x+3}}-\frac{214 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{847 \sqrt{33}}+\frac{494 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{847 \sqrt{33}}",1,"Could not integrate","F",-1
2986,0,0,156,0.9060833,"\int \frac{1}{(1-2 x)^{5/2} \sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)),x]","\int \frac{1}{(1-2 x)^{5/2} \sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","-\frac{41570 \sqrt{1-2 x} \sqrt{3 x+2}}{195657 \sqrt{5 x+3}}+\frac{824 \sqrt{3 x+2}}{17787 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{4 \sqrt{3 x+2}}{231 (1-2 x)^{3/2} \sqrt{5 x+3}}-\frac{824 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5929 \sqrt{33}}+\frac{8314 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5929 \sqrt{33}}",1,"Could not integrate","F",-1
2987,0,0,187,1.2240292,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","-\frac{2377960 \sqrt{1-2 x} \sqrt{3 x+2}}{1369599 \sqrt{5 x+3}}+\frac{5314 \sqrt{1-2 x}}{41503 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{1088}{17787 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{4}{231 (1-2 x)^{3/2} \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{10628 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{41503 \sqrt{33}}+\frac{475592 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{41503 \sqrt{33}}",1,"Could not integrate","F",-1
2988,0,0,218,1.3051562,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","-\frac{113693540 \sqrt{1-2 x} \sqrt{3 x+2}}{9587193 \sqrt{5 x+3}}+\frac{336536 \sqrt{1-2 x}}{290521 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{694 \sqrt{1-2 x}}{41503 (3 x+2)^{3/2} \sqrt{5 x+3}}+\frac{1352}{17787 \sqrt{1-2 x} (3 x+2)^{3/2} \sqrt{5 x+3}}+\frac{4}{231 (1-2 x)^{3/2} (3 x+2)^{3/2} \sqrt{5 x+3}}+\frac{673072 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{290521 \sqrt{33}}+\frac{22738708 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{290521 \sqrt{33}}",1,"Could not integrate","F",-1
2989,0,0,249,1.3733137,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","-\frac{4839325048 \sqrt{1-2 x} \sqrt{3 x+2}}{67110351 \sqrt{5 x+3}}+\frac{72709316 \sqrt{1-2 x}}{10168235 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{499564 \sqrt{1-2 x}}{1452605 (3 x+2)^{3/2} \sqrt{5 x+3}}-\frac{2206 \sqrt{1-2 x}}{207515 (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{1616}{17787 \sqrt{1-2 x} (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{4}{231 (1-2 x)^{3/2} (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{145418632 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{10168235 \sqrt{33}}+\frac{4839325048 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{10168235 \sqrt{33}}",1,"Could not integrate","F",-1
2990,0,0,249,1.2865143,"\int \frac{(2+3 x)^{13/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(13/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^{13/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","\frac{7 (3 x+2)^{11/2}}{33 (1-2 x)^{3/2} (5 x+3)^{3/2}}-\frac{294 (3 x+2)^{9/2}}{121 \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{4373 \sqrt{1-2 x} (3 x+2)^{7/2}}{19965 (5 x+3)^{3/2}}+\frac{150812 \sqrt{1-2 x} (3 x+2)^{5/2}}{1098075 \sqrt{5 x+3}}-\frac{31887029 \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^{3/2}}{18301250}-\frac{371279941 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{45753125}-\frac{776112041 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{41593750 \sqrt{33}}-\frac{51601293223 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{83187500 \sqrt{33}}",1,"Could not integrate","F",-1
2991,0,0,218,1.229256,"\int \frac{(2+3 x)^{11/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(11/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^{11/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","\frac{7 (3 x+2)^{9/2}}{33 (1-2 x)^{3/2} (5 x+3)^{3/2}}-\frac{217 (3 x+2)^{7/2}}{121 \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{3218 \sqrt{1-2 x} (3 x+2)^{5/2}}{19965 (5 x+3)^{3/2}}+\frac{110519 \sqrt{1-2 x} (3 x+2)^{3/2}}{1098075 \sqrt{5 x+3}}-\frac{5199979 \sqrt{1-2 x} \sqrt{5 x+3} \sqrt{3 x+2}}{3660250}-\frac{5442127 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1663750 \sqrt{33}}-\frac{90397364 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{831875 \sqrt{33}}",1,"Could not integrate","F",-1
2992,0,0,187,1.1637301,"\int \frac{(2+3 x)^{9/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(9/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^{9/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","\frac{7 (3 x+2)^{7/2}}{33 (1-2 x)^{3/2} (5 x+3)^{3/2}}-\frac{140 (3 x+2)^{5/2}}{121 \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{2063 \sqrt{1-2 x} (3 x+2)^{3/2}}{19965 (5 x+3)^{3/2}}+\frac{70226 \sqrt{1-2 x} \sqrt{3 x+2}}{1098075 \sqrt{5 x+3}}-\frac{76163 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{166375 \sqrt{33}}-\frac{4971289 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{332750 \sqrt{33}}",1,"Could not integrate","F",-1
2993,0,0,187,1.1534446,"\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(7/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","\frac{7 (3 x+2)^{5/2}}{33 (1-2 x)^{3/2} (5 x+3)^{3/2}}-\frac{63 (3 x+2)^{3/2}}{121 \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{29933 \sqrt{1-2 x} \sqrt{3 x+2}}{219615 \sqrt{5 x+3}}+\frac{908 \sqrt{1-2 x} \sqrt{3 x+2}}{19965 (5 x+3)^{3/2}}-\frac{1847 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{33275 \sqrt{33}}-\frac{29933 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{33275 \sqrt{33}}",1,"Could not integrate","F",-1
2994,0,0,187,1.1306532,"\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(5/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","\frac{7 (3 x+2)^{3/2}}{33 (1-2 x)^{3/2} (5 x+3)^{3/2}}-\frac{2209 \sqrt{1-2 x} \sqrt{3 x+2}}{43923 \sqrt{5 x+3}}-\frac{247 \sqrt{1-2 x} \sqrt{3 x+2}}{3993 (5 x+3)^{3/2}}+\frac{14 \sqrt{3 x+2}}{121 \sqrt{1-2 x} (5 x+3)^{3/2}}-\frac{494 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6655 \sqrt{33}}+\frac{2209 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6655 \sqrt{33}}",1,"Could not integrate","F",-1
2995,0,0,187,1.1032288,"\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(2 + 3*x)^(3/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","-\frac{2960 \sqrt{1-2 x} \sqrt{3 x+2}}{43923 \sqrt{5 x+3}}-\frac{575 \sqrt{1-2 x} \sqrt{3 x+2}}{3993 (5 x+3)^{3/2}}+\frac{26 \sqrt{3 x+2}}{121 \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{7 \sqrt{3 x+2}}{33 (1-2 x)^{3/2} (5 x+3)^{3/2}}-\frac{230 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1331 \sqrt{33}}+\frac{592 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1331 \sqrt{33}}",1,"Could not integrate","F",-1
2996,0,0,187,1.0630083,"\int \frac{\sqrt{2+3 x}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[2 + 3*x]/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\int \frac{\sqrt{2+3 x}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","-\frac{22090 \sqrt{1-2 x} \sqrt{3 x+2}}{307461 \sqrt{5 x+3}}-\frac{2470 \sqrt{1-2 x} \sqrt{3 x+2}}{27951 (5 x+3)^{3/2}}+\frac{118 \sqrt{3 x+2}}{847 \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{2 \sqrt{3 x+2}}{33 (1-2 x)^{3/2} (5 x+3)^{3/2}}-\frac{988 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{9317 \sqrt{33}}+\frac{4418 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{9317 \sqrt{33}}",1,"Could not integrate","F",-1
2997,0,0,187,1.1239065,"\int \frac{1}{(1-2 x)^{5/2} \sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*Sqrt[2 + 3*x]*(3 + 5*x)^(5/2)),x]","\int \frac{1}{(1-2 x)^{5/2} \sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","\frac{598660 \sqrt{1-2 x} \sqrt{3 x+2}}{2152227 \sqrt{5 x+3}}-\frac{18470 \sqrt{1-2 x} \sqrt{3 x+2}}{195657 (5 x+3)^{3/2}}+\frac{368 \sqrt{3 x+2}}{5929 \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{4 \sqrt{3 x+2}}{231 (1-2 x)^{3/2} (5 x+3)^{3/2}}-\frac{7388 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{65219 \sqrt{33}}-\frac{119732 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{65219 \sqrt{33}}",1,"Could not integrate","F",-1
2998,0,0,218,1.292033,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","\frac{99425780 \sqrt{1-2 x} \sqrt{3 x+2}}{15065589 \sqrt{5 x+3}}-\frac{1523260 \sqrt{1-2 x} \sqrt{3 x+2}}{1369599 (5 x+3)^{3/2}}+\frac{5034 \sqrt{1-2 x}}{41503 \sqrt{3 x+2} (5 x+3)^{3/2}}+\frac{456}{5929 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}+\frac{4}{231 (1-2 x)^{3/2} \sqrt{3 x+2} (5 x+3)^{3/2}}-\frac{609304 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{456533 \sqrt{33}}-\frac{19885156 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{456533 \sqrt{33}}",1,"Could not integrate","F",-1
2999,0,0,249,1.3449527,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","\frac{7231789120 \sqrt{1-2 x} \sqrt{3 x+2}}{105459123 \sqrt{5 x+3}}-\frac{108842540 \sqrt{1-2 x} \sqrt{3 x+2}}{9587193 (5 x+3)^{3/2}}+\frac{488436 \sqrt{1-2 x}}{290521 \sqrt{3 x+2} (5 x+3)^{3/2}}+\frac{414 \sqrt{1-2 x}}{41503 (3 x+2)^{3/2} (5 x+3)^{3/2}}+\frac{544}{5929 \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{3/2}}+\frac{4}{231 (1-2 x)^{3/2} (3 x+2)^{3/2} (5 x+3)^{3/2}}-\frac{43537016 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3195731 \sqrt{33}}-\frac{1446357824 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3195731 \sqrt{33}}",1,"Could not integrate","F",-1
3000,0,0,280,1.4397012,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)),x]","\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","\frac{412810345784 \sqrt{1-2 x} \sqrt{3 x+2}}{738213861 \sqrt{5 x+3}}-\frac{6208896328 \sqrt{1-2 x} \sqrt{3 x+2}}{67110351 (5 x+3)^{3/2}}+\frac{140700876 \sqrt{1-2 x}}{10168235 \sqrt{3 x+2} (5 x+3)^{3/2}}+\frac{649224 \sqrt{1-2 x}}{1452605 (3 x+2)^{3/2} (5 x+3)^{3/2}}-\frac{3606 \sqrt{1-2 x}}{207515 (3 x+2)^{5/2} (5 x+3)^{3/2}}+\frac{632}{5929 \sqrt{1-2 x} (3 x+2)^{5/2} (5 x+3)^{3/2}}+\frac{4}{231 (1-2 x)^{3/2} (3 x+2)^{5/2} (5 x+3)^{3/2}}-\frac{12417792656 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{111850585 \sqrt{33}}-\frac{412810345784 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{111850585 \sqrt{33}}",1,"Could not integrate","F",-1
3001,0,0,571,11.9974512,"\int \sqrt[3]{a+b x} (c+d x)^{2/3} (e+f x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^(1/3)*(c + d*x)^(2/3)*(e + f*x)^2,x]","\int \sqrt[3]{a+b x} (c+d x)^{2/3} (e+f x)^2 \, dx","\frac{(b c-a d)^2 \log (a+b x) \left(10 a^2 d^2 f^2-10 a b d f (3 d e-c f)+b^2 \left(7 c^2 f^2-24 c d e f+27 d^2 e^2\right)\right)}{486 b^{11/3} d^{10/3}}+\frac{(b c-a d)^2 \left(10 a^2 d^2 f^2-10 a b d f (3 d e-c f)+b^2 \left(7 c^2 f^2-24 c d e f+27 d^2 e^2\right)\right) \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{162 b^{11/3} d^{10/3}}+\frac{(b c-a d)^2 \left(10 a^2 d^2 f^2-10 a b d f (3 d e-c f)+b^2 \left(7 c^2 f^2-24 c d e f+27 d^2 e^2\right)\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{81 \sqrt{3} b^{11/3} d^{10/3}}+\frac{(a+b x)^{4/3} (c+d x)^{2/3} \left(10 a^2 d^2 f^2-10 a b d f (3 d e-c f)+b^2 \left(7 c^2 f^2-24 c d e f+27 d^2 e^2\right)\right)}{54 b^3 d^2}+\frac{\sqrt[3]{a+b x} (c+d x)^{2/3} (b c-a d) \left(10 a^2 d^2 f^2-10 a b d f (3 d e-c f)+b^2 \left(7 c^2 f^2-24 c d e f+27 d^2 e^2\right)\right)}{81 b^3 d^3}+\frac{f (a+b x)^{4/3} (c+d x)^{5/3} (-8 a d f-7 b c f+15 b d e)}{36 b^2 d^2}+\frac{f (a+b x)^{4/3} (c+d x)^{5/3} (e+f x)}{4 b d}",1,"Could not integrate","F",-1
3002,0,0,331,9.5988313,"\int \sqrt[3]{a+b x} (c+d x)^{2/3} (e+f x) \, dx","IntegrateAlgebraic[(a + b*x)^(1/3)*(c + d*x)^(2/3)*(e + f*x),x]","\int \sqrt[3]{a+b x} (c+d x)^{2/3} (e+f x) \, dx","\frac{(b c-a d)^2 \log (a+b x) (-5 a d f-4 b c f+9 b d e)}{162 b^{8/3} d^{7/3}}+\frac{(b c-a d)^2 (-5 a d f-4 b c f+9 b d e) \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{54 b^{8/3} d^{7/3}}+\frac{(b c-a d)^2 (-5 a d f-4 b c f+9 b d e) \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{27 \sqrt{3} b^{8/3} d^{7/3}}+\frac{\sqrt[3]{a+b x} (c+d x)^{2/3} (b c-a d) (-5 a d f-4 b c f+9 b d e)}{27 b^2 d^2}+\frac{(a+b x)^{4/3} (c+d x)^{2/3} (-5 a d f-4 b c f+9 b d e)}{18 b^2 d}+\frac{f (a+b x)^{4/3} (c+d x)^{5/3}}{3 b d}",1,"Could not integrate","F",-1
3003,0,0,219,7.5115766,"\int \sqrt[3]{a+b x} (c+d x)^{2/3} \, dx","IntegrateAlgebraic[(a + b*x)^(1/3)*(c + d*x)^(2/3),x]","\int \sqrt[3]{a+b x} (c+d x)^{2/3} \, dx","\frac{(b c-a d)^2 \log (a+b x)}{18 b^{5/3} d^{4/3}}+\frac{(b c-a d)^2 \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{6 b^{5/3} d^{4/3}}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{5/3} d^{4/3}}+\frac{\sqrt[3]{a+b x} (c+d x)^{2/3} (b c-a d)}{3 b d}+\frac{(a+b x)^{4/3} (c+d x)^{2/3}}{2 b}",1,"Could not integrate","F",-1
3004,0,0,409,12.2247498,"\int \frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{e+f x} \, dx","IntegrateAlgebraic[((a + b*x)^(1/3)*(c + d*x)^(2/3))/(e + f*x),x]","\int \frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{e+f x} \, dx","\frac{\log (a+b x) (-a d f-2 b c f+3 b d e)}{6 b^{2/3} \sqrt[3]{d} f^2}+\frac{(-a d f-2 b c f+3 b d e) \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{2 b^{2/3} \sqrt[3]{d} f^2}+\frac{(-a d f-2 b c f+3 b d e) \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3} \sqrt[3]{d} f^2}+\frac{\sqrt[3]{b e-a f} (d e-c f)^{2/3} \log (e+f x)}{2 f^2}-\frac{3 \sqrt[3]{b e-a f} (d e-c f)^{2/3} \log \left(\frac{\sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt[3]{d e-c f}}-\sqrt[3]{a+b x}\right)}{2 f^2}-\frac{\sqrt{3} \sqrt[3]{b e-a f} (d e-c f)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt{3} \sqrt[3]{a+b x} \sqrt[3]{d e-c f}}+\frac{1}{\sqrt{3}}\right)}{f^2}+\frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{f}",1,"Could not integrate","F",-1
3005,0,0,417,17.2122597,"\int \frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{(e+f x)^2} \, dx","IntegrateAlgebraic[((a + b*x)^(1/3)*(c + d*x)^(2/3))/(e + f*x)^2,x]","\int \frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{(e+f x)^2} \, dx","-\frac{3 \sqrt[3]{b} d^{2/3} \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{2 f^2}-\frac{\sqrt{3} \sqrt[3]{b} d^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{f^2}-\frac{\log (e+f x) (-2 a d f-b c f+3 b d e)}{6 f^2 (b e-a f)^{2/3} \sqrt[3]{d e-c f}}+\frac{(-2 a d f-b c f+3 b d e) \log \left(\frac{\sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt[3]{d e-c f}}-\sqrt[3]{a+b x}\right)}{2 f^2 (b e-a f)^{2/3} \sqrt[3]{d e-c f}}+\frac{(-2 a d f-b c f+3 b d e) \tan ^{-1}\left(\frac{2 \sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt{3} \sqrt[3]{a+b x} \sqrt[3]{d e-c f}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} f^2 (b e-a f)^{2/3} \sqrt[3]{d e-c f}}-\frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{f (e+f x)}-\frac{\sqrt[3]{b} d^{2/3} \log (a+b x)}{2 f^2}",1,"Could not integrate","F",-1
3006,0,0,325,29.0978848,"\int \frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{(e+f x)^3} \, dx","IntegrateAlgebraic[((a + b*x)^(1/3)*(c + d*x)^(2/3))/(e + f*x)^3,x]","\int \frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{(e+f x)^3} \, dx","-\frac{\sqrt[3]{a+b x} (c+d x)^{2/3} (b c-a d)}{6 (e+f x) (b e-a f) (d e-c f)}+\frac{\sqrt[3]{a+b x} (c+d x)^{5/3}}{2 (e+f x)^2 (d e-c f)}-\frac{(b c-a d)^2 \log (e+f x)}{18 (b e-a f)^{5/3} (d e-c f)^{4/3}}+\frac{(b c-a d)^2 \log \left(\frac{\sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt[3]{d e-c f}}-\sqrt[3]{a+b x}\right)}{6 (b e-a f)^{5/3} (d e-c f)^{4/3}}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt{3} \sqrt[3]{a+b x} \sqrt[3]{d e-c f}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} (b e-a f)^{5/3} (d e-c f)^{4/3}}",1,"Could not integrate","F",-1
3007,0,0,465,41.6605746,"\int \frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{(e+f x)^4} \, dx","IntegrateAlgebraic[((a + b*x)^(1/3)*(c + d*x)^(2/3))/(e + f*x)^4,x]","\int \frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{(e+f x)^4} \, dx","-\frac{\sqrt[3]{a+b x} (c+d x)^{2/3} (b c-a d) (-4 a d f-5 b c f+9 b d e)}{54 (e+f x) (b e-a f)^2 (d e-c f)^2}+\frac{\sqrt[3]{a+b x} (c+d x)^{5/3} (-4 a d f-5 b c f+9 b d e)}{18 (e+f x)^2 (b e-a f) (d e-c f)^2}-\frac{f (a+b x)^{4/3} (c+d x)^{5/3}}{3 (e+f x)^3 (b e-a f) (d e-c f)}-\frac{(b c-a d)^2 \log (e+f x) (-4 a d f-5 b c f+9 b d e)}{162 (b e-a f)^{8/3} (d e-c f)^{7/3}}+\frac{(b c-a d)^2 (-4 a d f-5 b c f+9 b d e) \log \left(\frac{\sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt[3]{d e-c f}}-\sqrt[3]{a+b x}\right)}{54 (b e-a f)^{8/3} (d e-c f)^{7/3}}+\frac{(b c-a d)^2 (-4 a d f-5 b c f+9 b d e) \tan ^{-1}\left(\frac{2 \sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt{3} \sqrt[3]{a+b x} \sqrt[3]{d e-c f}}+\frac{1}{\sqrt{3}}\right)}{27 \sqrt{3} (b e-a f)^{8/3} (d e-c f)^{7/3}}",1,"Could not integrate","F",-1
3008,0,0,475,10.6611374,"\int \frac{\sqrt[3]{a+b x} (e+f x)^2}{\sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[((a + b*x)^(1/3)*(e + f*x)^2)/(c + d*x)^(1/3),x]","\int \frac{\sqrt[3]{a+b x} (e+f x)^2}{\sqrt[3]{c+d x}} \, dx","\frac{\sqrt[3]{a+b x} (c+d x)^{2/3} \left(5 a^2 d^2 f^2-2 a b d f (9 d e-4 c f)+b^2 \left(14 c^2 f^2-36 c d e f+27 d^2 e^2\right)\right)}{27 b^2 d^3}+\frac{(b c-a d) \log (a+b x) \left(5 a^2 d^2 f^2-2 a b d f (9 d e-4 c f)+b^2 \left(14 c^2 f^2-36 c d e f+27 d^2 e^2\right)\right)}{162 b^{8/3} d^{10/3}}+\frac{(b c-a d) \left(5 a^2 d^2 f^2-2 a b d f (9 d e-4 c f)+b^2 \left(14 c^2 f^2-36 c d e f+27 d^2 e^2\right)\right) \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{54 b^{8/3} d^{10/3}}+\frac{(b c-a d) \left(5 a^2 d^2 f^2-2 a b d f (9 d e-4 c f)+b^2 \left(14 c^2 f^2-36 c d e f+27 d^2 e^2\right)\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{27 \sqrt{3} b^{8/3} d^{10/3}}+\frac{f (a+b x)^{4/3} (c+d x)^{2/3} (-5 a d f-7 b c f+12 b d e)}{18 b^2 d^2}+\frac{f (a+b x)^{4/3} (c+d x)^{2/3} (e+f x)}{3 b d}",1,"Could not integrate","F",-1
3009,0,0,273,8.6444596,"\int \frac{\sqrt[3]{a+b x} (e+f x)}{\sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[((a + b*x)^(1/3)*(e + f*x))/(c + d*x)^(1/3),x]","\int \frac{\sqrt[3]{a+b x} (e+f x)}{\sqrt[3]{c+d x}} \, dx","\frac{(b c-a d) \log (a+b x) (-a d f-2 b c f+3 b d e)}{18 b^{5/3} d^{7/3}}+\frac{(b c-a d) (-a d f-2 b c f+3 b d e) \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{6 b^{5/3} d^{7/3}}+\frac{(b c-a d) (-a d f-2 b c f+3 b d e) \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{5/3} d^{7/3}}+\frac{\sqrt[3]{a+b x} (c+d x)^{2/3} (-a d f-2 b c f+3 b d e)}{3 b d^2}+\frac{f (a+b x)^{4/3} (c+d x)^{2/3}}{2 b d}",1,"Could not integrate","F",-1
3010,0,0,171,0.0007072,"\int \frac{\sqrt[3]{a+b x}}{\sqrt[3]{c+d x}} \, dx","IntegrateAlgebraic[(a + b*x)^(1/3)/(c + d*x)^(1/3),x]","\int \frac{\sqrt[3]{a+b x}}{\sqrt[3]{c+d x}} \, dx","\frac{(b c-a d) \log (a+b x)}{6 b^{2/3} d^{4/3}}+\frac{(b c-a d) \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{2 b^{2/3} d^{4/3}}+\frac{(b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3} d^{4/3}}+\frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{d}",1,"Could not integrate","F",-1
3011,1,646,339,8.0696803,"\int \frac{\sqrt[3]{a+b x}}{\sqrt[3]{c+d x} (e+f x)} \, dx","IntegrateAlgebraic[(a + b*x)^(1/3)/((c + d*x)^(1/3)*(e + f*x)),x]","\frac{\sqrt[3]{b} \log \left(d^{2/3} \left(a+\frac{b (c+d x)}{d}-\frac{b c}{d}\right)^{2/3}+\sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{c+d x} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}+b^{2/3} (c+d x)^{2/3}\right)}{2 \sqrt[3]{d} f}-\frac{\sqrt[3]{b e-a f} \log \left(\sqrt[3]{c+d x} \sqrt[3]{b e-a f}+\sqrt[3]{c f-d e} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}\right)}{f \sqrt[3]{c f-d e}}+\frac{\sqrt[3]{b e-a f} \log \left((c+d x)^{2/3} (b e-a f)^{2/3}-\sqrt[3]{c+d x} \sqrt[3]{b e-a f} \sqrt[3]{c f-d e} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}+(c f-d e)^{2/3} \left(a+\frac{b (c+d x)}{d}-\frac{b c}{d}\right)^{2/3}\right)}{2 f \sqrt[3]{c f-d e}}+\frac{\sqrt{3} \sqrt[3]{b e-a f} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{c f-d e} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}}{\sqrt[3]{c f-d e} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}-2 \sqrt[3]{c+d x} \sqrt[3]{b e-a f}}\right)}{f \sqrt[3]{c f-d e}}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{b} \sqrt[3]{c+d x}-\sqrt[3]{d} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}\right)}{\sqrt[3]{d} f}+\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}}{\sqrt[3]{d} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}+2 \sqrt[3]{b} \sqrt[3]{c+d x}}\right)}{\sqrt[3]{d} f}","-\frac{\sqrt[3]{b e-a f} \log (e+f x)}{2 f \sqrt[3]{d e-c f}}+\frac{3 \sqrt[3]{b e-a f} \log \left(\frac{\sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt[3]{d e-c f}}-\sqrt[3]{a+b x}\right)}{2 f \sqrt[3]{d e-c f}}+\frac{\sqrt{3} \sqrt[3]{b e-a f} \tan ^{-1}\left(\frac{2 \sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt{3} \sqrt[3]{a+b x} \sqrt[3]{d e-c f}}+\frac{1}{\sqrt{3}}\right)}{f \sqrt[3]{d e-c f}}-\frac{3 \sqrt[3]{b} \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{2 \sqrt[3]{d} f}-\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{d} f}-\frac{\sqrt[3]{b} \log (a+b x)}{2 \sqrt[3]{d} f}",1,"(Sqrt[3]*b^(1/3)*ArcTan[(Sqrt[3]*d^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))/(2*b^(1/3)*(c + d*x)^(1/3) + d^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))])/(d^(1/3)*f) + (Sqrt[3]*(b*e - a*f)^(1/3)*ArcTan[(Sqrt[3]*(-(d*e) + c*f)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))/(-2*(b*e - a*f)^(1/3)*(c + d*x)^(1/3) + (-(d*e) + c*f)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))])/(f*(-(d*e) + c*f)^(1/3)) - (b^(1/3)*Log[b^(1/3)*(c + d*x)^(1/3) - d^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3)])/(d^(1/3)*f) - ((b*e - a*f)^(1/3)*Log[(b*e - a*f)^(1/3)*(c + d*x)^(1/3) + (-(d*e) + c*f)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3)])/(f*(-(d*e) + c*f)^(1/3)) + (b^(1/3)*Log[b^(2/3)*(c + d*x)^(2/3) + b^(1/3)*d^(1/3)*(c + d*x)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3) + d^(2/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(2/3)])/(2*d^(1/3)*f) + ((b*e - a*f)^(1/3)*Log[(b*e - a*f)^(2/3)*(c + d*x)^(2/3) - (b*e - a*f)^(1/3)*(-(d*e) + c*f)^(1/3)*(c + d*x)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3) + (-(d*e) + c*f)^(2/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(2/3)])/(2*f*(-(d*e) + c*f)^(1/3))","A",1
3012,1,462,256,10.8880294,"\int \frac{\sqrt[3]{a+b x}}{\sqrt[3]{c+d x} (e+f x)^2} \, dx","IntegrateAlgebraic[(a + b*x)^(1/3)/((c + d*x)^(1/3)*(e + f*x)^2),x]","\frac{d (c+d x)^{2/3} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}}{(d e-c f) (f (c+d x)-c f+d e)}+\frac{(b c-a d) \log \left(\sqrt[3]{c+d x} \sqrt[3]{b e-a f}+\sqrt[3]{c f-d e} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}\right)}{3 (b e-a f)^{2/3} (c f-d e)^{4/3}}+\frac{(a d-b c) \log \left((c+d x)^{2/3} (b e-a f)^{2/3}-\sqrt[3]{c+d x} \sqrt[3]{b e-a f} \sqrt[3]{c f-d e} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}+(c f-d e)^{2/3} \left(a+\frac{b (c+d x)}{d}-\frac{b c}{d}\right)^{2/3}\right)}{6 (b e-a f)^{2/3} (c f-d e)^{4/3}}+\frac{\left(\sqrt{3} a d-\sqrt{3} b c\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{c f-d e} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}}{\sqrt[3]{c f-d e} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}-2 \sqrt[3]{c+d x} \sqrt[3]{b e-a f}}\right)}{3 (b e-a f)^{2/3} (c f-d e)^{4/3}}","\frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{(e+f x) (d e-c f)}-\frac{(b c-a d) \log (e+f x)}{6 (b e-a f)^{2/3} (d e-c f)^{4/3}}+\frac{(b c-a d) \log \left(\frac{\sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt[3]{d e-c f}}-\sqrt[3]{a+b x}\right)}{2 (b e-a f)^{2/3} (d e-c f)^{4/3}}+\frac{(b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt{3} \sqrt[3]{a+b x} \sqrt[3]{d e-c f}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} (b e-a f)^{2/3} (d e-c f)^{4/3}}",1,"(d*(c + d*x)^(2/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))/((d*e - c*f)*(d*e - c*f + f*(c + d*x))) + ((-(Sqrt[3]*b*c) + Sqrt[3]*a*d)*ArcTan[(Sqrt[3]*(-(d*e) + c*f)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))/(-2*(b*e - a*f)^(1/3)*(c + d*x)^(1/3) + (-(d*e) + c*f)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))])/(3*(b*e - a*f)^(2/3)*(-(d*e) + c*f)^(4/3)) + ((b*c - a*d)*Log[(b*e - a*f)^(1/3)*(c + d*x)^(1/3) + (-(d*e) + c*f)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3)])/(3*(b*e - a*f)^(2/3)*(-(d*e) + c*f)^(4/3)) + ((-(b*c) + a*d)*Log[(b*e - a*f)^(2/3)*(c + d*x)^(2/3) - (b*e - a*f)^(1/3)*(-(d*e) + c*f)^(1/3)*(c + d*x)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3) + (-(d*e) + c*f)^(2/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(2/3)])/(6*(b*e - a*f)^(2/3)*(-(d*e) + c*f)^(4/3))","A",1
3013,0,0,386,33.3285147,"\int \frac{\sqrt[3]{a+b x}}{\sqrt[3]{c+d x} (e+f x)^3} \, dx","IntegrateAlgebraic[(a + b*x)^(1/3)/((c + d*x)^(1/3)*(e + f*x)^3),x]","\int \frac{\sqrt[3]{a+b x}}{\sqrt[3]{c+d x} (e+f x)^3} \, dx","-\frac{f (a+b x)^{4/3} (c+d x)^{2/3}}{2 (e+f x)^2 (b e-a f) (d e-c f)}+\frac{\sqrt[3]{a+b x} (c+d x)^{2/3} (-2 a d f-b c f+3 b d e)}{3 (e+f x) (b e-a f) (d e-c f)^2}-\frac{(b c-a d) \log (e+f x) (-2 a d f-b c f+3 b d e)}{18 (b e-a f)^{5/3} (d e-c f)^{7/3}}+\frac{(b c-a d) (-2 a d f-b c f+3 b d e) \log \left(\frac{\sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt[3]{d e-c f}}-\sqrt[3]{a+b x}\right)}{6 (b e-a f)^{5/3} (d e-c f)^{7/3}}+\frac{(b c-a d) (-2 a d f-b c f+3 b d e) \tan ^{-1}\left(\frac{2 \sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt{3} \sqrt[3]{a+b x} \sqrt[3]{d e-c f}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} (b e-a f)^{5/3} (d e-c f)^{7/3}}",1,"Could not integrate","F",-1
3014,0,0,591,46.7848953,"\int \frac{\sqrt[3]{a+b x}}{\sqrt[3]{c+d x} (e+f x)^4} \, dx","IntegrateAlgebraic[(a + b*x)^(1/3)/((c + d*x)^(1/3)*(e + f*x)^4),x]","\int \frac{\sqrt[3]{a+b x}}{\sqrt[3]{c+d x} (e+f x)^4} \, dx","\frac{\sqrt[3]{a+b x} (c+d x)^{2/3} \left(28 a^2 d^2 f^2-a b d f (5 c f+51 d e)+b^2 \left(-5 c^2 f^2+15 c d e f+18 d^2 e^2\right)\right)}{54 (e+f x) (b e-a f)^2 (d e-c f)^3}-\frac{(b c-a d) \log (e+f x) \left(14 a^2 d^2 f^2-4 a b d f (9 d e-2 c f)+b^2 \left(5 c^2 f^2-18 c d e f+27 d^2 e^2\right)\right)}{162 (b e-a f)^{8/3} (d e-c f)^{10/3}}+\frac{(b c-a d) \left(14 a^2 d^2 f^2-4 a b d f (9 d e-2 c f)+b^2 \left(5 c^2 f^2-18 c d e f+27 d^2 e^2\right)\right) \log \left(\frac{\sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt[3]{d e-c f}}-\sqrt[3]{a+b x}\right)}{54 (b e-a f)^{8/3} (d e-c f)^{10/3}}+\frac{(b c-a d) \left(14 a^2 d^2 f^2-4 a b d f (9 d e-2 c f)+b^2 \left(5 c^2 f^2-18 c d e f+27 d^2 e^2\right)\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt{3} \sqrt[3]{a+b x} \sqrt[3]{d e-c f}}+\frac{1}{\sqrt{3}}\right)}{27 \sqrt{3} (b e-a f)^{8/3} (d e-c f)^{10/3}}+\frac{\sqrt[3]{a+b x} (c+d x)^{2/3} (-7 a d f+b c f+6 b d e)}{18 (e+f x)^2 (b e-a f) (d e-c f)^2}+\frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{3 (e+f x)^3 (d e-c f)}",1,"Could not integrate","F",-1
3015,0,0,587,15.8001428,"\int \frac{(e+f x)^3}{\sqrt[3]{a+b x} (c+d x)^{2/3}} \, dx","IntegrateAlgebraic[(e + f*x)^3/((a + b*x)^(1/3)*(c + d*x)^(2/3)),x]","\int \frac{(e+f x)^3}{\sqrt[3]{a+b x} (c+d x)^{2/3}} \, dx","\frac{f (a+b x)^{2/3} \sqrt[3]{c+d x} \left(28 a^2 d^2 f^2+3 b d f x (-7 a d f-8 b c f+15 b d e)-a b d f (108 d e-31 c f)+b^2 \left(40 c^2 f^2-135 c d e f+144 d^2 e^2\right)\right)}{54 b^3 d^3}+\frac{\log (c+d x) \left(14 a^3 d^3 f^3-6 a^2 b d^2 f^2 (9 d e-2 c f)+3 a b^2 d f \left(5 c^2 f^2-18 c d e f+27 d^2 e^2\right)-\left(b^3 \left(-40 c^3 f^3+135 c^2 d e f^2-162 c d^2 e^2 f+81 d^3 e^3\right)\right)\right)}{162 b^{10/3} d^{11/3}}+\frac{\left(14 a^3 d^3 f^3-6 a^2 b d^2 f^2 (9 d e-2 c f)+3 a b^2 d f \left(5 c^2 f^2-18 c d e f+27 d^2 e^2\right)-\left(b^3 \left(-40 c^3 f^3+135 c^2 d e f^2-162 c d^2 e^2 f+81 d^3 e^3\right)\right)\right) \log \left(\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{b} \sqrt[3]{c+d x}}-1\right)}{54 b^{10/3} d^{11/3}}+\frac{\left(14 a^3 d^3 f^3-6 a^2 b d^2 f^2 (9 d e-2 c f)+3 a b^2 d f \left(5 c^2 f^2-18 c d e f+27 d^2 e^2\right)-\left(b^3 \left(-40 c^3 f^3+135 c^2 d e f^2-162 c d^2 e^2 f+81 d^3 e^3\right)\right)\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{27 \sqrt{3} b^{10/3} d^{11/3}}+\frac{f (a+b x)^{2/3} \sqrt[3]{c+d x} (e+f x)^2}{3 b d}",1,"Could not integrate","F",-1
3016,0,0,369,12.85392,"\int \frac{(e+f x)^2}{\sqrt[3]{a+b x} (c+d x)^{2/3}} \, dx","IntegrateAlgebraic[(e + f*x)^2/((a + b*x)^(1/3)*(c + d*x)^(2/3)),x]","\int \frac{(e+f x)^2}{\sqrt[3]{a+b x} (c+d x)^{2/3}} \, dx","-\frac{\log (c+d x) \left(2 a^2 d^2 f^2-2 a b d f (3 d e-c f)+b^2 \left(5 c^2 f^2-12 c d e f+9 d^2 e^2\right)\right)}{18 b^{7/3} d^{8/3}}-\frac{\left(2 a^2 d^2 f^2-2 a b d f (3 d e-c f)+b^2 \left(5 c^2 f^2-12 c d e f+9 d^2 e^2\right)\right) \log \left(\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{b} \sqrt[3]{c+d x}}-1\right)}{6 b^{7/3} d^{8/3}}-\frac{\left(2 a^2 d^2 f^2-2 a b d f (3 d e-c f)+b^2 \left(5 c^2 f^2-12 c d e f+9 d^2 e^2\right)\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{7/3} d^{8/3}}+\frac{f (a+b x)^{2/3} \sqrt[3]{c+d x} (-4 a d f-5 b c f+9 b d e)}{6 b^2 d^2}+\frac{f (a+b x)^{2/3} \sqrt[3]{c+d x} (e+f x)}{2 b d}",1,"Could not integrate","F",-1
3017,0,0,200,8.2439379,"\int \frac{e+f x}{\sqrt[3]{a+b x} (c+d x)^{2/3}} \, dx","IntegrateAlgebraic[(e + f*x)/((a + b*x)^(1/3)*(c + d*x)^(2/3)),x]","\int \frac{e+f x}{\sqrt[3]{a+b x} (c+d x)^{2/3}} \, dx","-\frac{\log (c+d x) (-a d f-2 b c f+3 b d e)}{6 b^{4/3} d^{5/3}}-\frac{(-a d f-2 b c f+3 b d e) \log \left(\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{b} \sqrt[3]{c+d x}}-1\right)}{2 b^{4/3} d^{5/3}}-\frac{(-a d f-2 b c f+3 b d e) \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} b^{4/3} d^{5/3}}+\frac{f (a+b x)^{2/3} \sqrt[3]{c+d x}}{b d}",1,"Could not integrate","F",-1
3018,1,263,126,0.0008123,"\int \frac{1}{\sqrt[3]{a+b x} (c+d x)^{2/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/3)*(c + d*x)^(2/3)),x]","\frac{\log \left(d^{2/3} \left(a+\frac{b (c+d x)}{d}-\frac{b c}{d}\right)^{2/3}+\sqrt[3]{b} \sqrt[3]{d} \sqrt[3]{c+d x} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}+b^{2/3} (c+d x)^{2/3}\right)}{2 \sqrt[3]{b} d^{2/3}}-\frac{\log \left(\sqrt[3]{b} \sqrt[3]{c+d x}-\sqrt[3]{d} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}\right)}{\sqrt[3]{b} d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}}{\sqrt[3]{d} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}+2 \sqrt[3]{b} \sqrt[3]{c+d x}}\right)}{\sqrt[3]{b} d^{2/3}}","-\frac{3 \log \left(\frac{\sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt[3]{b} \sqrt[3]{c+d x}}-1\right)}{2 \sqrt[3]{b} d^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x}}{\sqrt{3} \sqrt[3]{b} \sqrt[3]{c+d x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{b} d^{2/3}}-\frac{\log (c+d x)}{2 \sqrt[3]{b} d^{2/3}}",1,"-((Sqrt[3]*ArcTan[(Sqrt[3]*d^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))/(2*b^(1/3)*(c + d*x)^(1/3) + d^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))])/(b^(1/3)*d^(2/3))) - Log[b^(1/3)*(c + d*x)^(1/3) - d^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3)]/(b^(1/3)*d^(2/3)) + Log[b^(2/3)*(c + d*x)^(2/3) + b^(1/3)*d^(1/3)*(c + d*x)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3) + d^(2/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(2/3)]/(2*b^(1/3)*d^(2/3))","B",1
3019,1,366,197,4.715894,"\int \frac{1}{\sqrt[3]{a+b x} (c+d x)^{2/3} (e+f x)} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/3)*(c + d*x)^(2/3)*(e + f*x)),x]","\frac{\log \left(\sqrt[3]{c+d x} \sqrt[3]{a f-b e}+\sqrt[3]{d e-c f} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}\right)}{\sqrt[3]{a f-b e} (d e-c f)^{2/3}}-\frac{\log \left((c+d x)^{2/3} (a f-b e)^{2/3}-\sqrt[3]{c+d x} \sqrt[3]{a f-b e} \sqrt[3]{d e-c f} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}+(d e-c f)^{2/3} \left(a+\frac{b (c+d x)}{d}-\frac{b c}{d}\right)^{2/3}\right)}{2 \sqrt[3]{a f-b e} (d e-c f)^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d e-c f} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}}{\sqrt[3]{d e-c f} \sqrt[3]{a+\frac{b (c+d x)}{d}-\frac{b c}{d}}-2 \sqrt[3]{c+d x} \sqrt[3]{a f-b e}}\right)}{\sqrt[3]{a f-b e} (d e-c f)^{2/3}}","\frac{\log (e+f x)}{2 \sqrt[3]{b e-a f} (d e-c f)^{2/3}}-\frac{3 \log \left(\frac{\sqrt[3]{a+b x} \sqrt[3]{d e-c f}}{\sqrt[3]{b e-a f}}-\sqrt[3]{c+d x}\right)}{2 \sqrt[3]{b e-a f} (d e-c f)^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x} \sqrt[3]{d e-c f}}{\sqrt{3} \sqrt[3]{c+d x} \sqrt[3]{b e-a f}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{b e-a f} (d e-c f)^{2/3}}",1,"(Sqrt[3]*ArcTan[(Sqrt[3]*(d*e - c*f)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))/(-2*(-(b*e) + a*f)^(1/3)*(c + d*x)^(1/3) + (d*e - c*f)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3))])/((-(b*e) + a*f)^(1/3)*(d*e - c*f)^(2/3)) + Log[(-(b*e) + a*f)^(1/3)*(c + d*x)^(1/3) + (d*e - c*f)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3)]/((-(b*e) + a*f)^(1/3)*(d*e - c*f)^(2/3)) - Log[(-(b*e) + a*f)^(2/3)*(c + d*x)^(2/3) - (-(b*e) + a*f)^(1/3)*(d*e - c*f)^(1/3)*(c + d*x)^(1/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(1/3) + (d*e - c*f)^(2/3)*(a - (b*c)/d + (b*(c + d*x))/d)^(2/3)]/(2*(-(b*e) + a*f)^(1/3)*(d*e - c*f)^(2/3))","A",1
3020,0,0,293,31.555737,"\int \frac{1}{\sqrt[3]{a+b x} (c+d x)^{2/3} (e+f x)^2} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/3)*(c + d*x)^(2/3)*(e + f*x)^2),x]","\int \frac{1}{\sqrt[3]{a+b x} (c+d x)^{2/3} (e+f x)^2} \, dx","-\frac{f (a+b x)^{2/3} \sqrt[3]{c+d x}}{(e+f x) (b e-a f) (d e-c f)}+\frac{\log (e+f x) (-2 a d f-b c f+3 b d e)}{6 (b e-a f)^{4/3} (d e-c f)^{5/3}}-\frac{(-2 a d f-b c f+3 b d e) \log \left(\frac{\sqrt[3]{a+b x} \sqrt[3]{d e-c f}}{\sqrt[3]{b e-a f}}-\sqrt[3]{c+d x}\right)}{2 (b e-a f)^{4/3} (d e-c f)^{5/3}}-\frac{(-2 a d f-b c f+3 b d e) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x} \sqrt[3]{d e-c f}}{\sqrt{3} \sqrt[3]{c+d x} \sqrt[3]{b e-a f}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} (b e-a f)^{4/3} (d e-c f)^{5/3}}",1,"Could not integrate","F",-1
3021,0,0,477,32.3509145,"\int \frac{1}{\sqrt[3]{a+b x} (c+d x)^{2/3} (e+f x)^3} \, dx","IntegrateAlgebraic[1/((a + b*x)^(1/3)*(c + d*x)^(2/3)*(e + f*x)^3),x]","\int \frac{1}{\sqrt[3]{a+b x} (c+d x)^{2/3} (e+f x)^3} \, dx","\frac{\log (e+f x) \left(5 a^2 d^2 f^2-2 a b d f (6 d e-c f)+b^2 \left(2 c^2 f^2-6 c d e f+9 d^2 e^2\right)\right)}{18 (b e-a f)^{7/3} (d e-c f)^{8/3}}-\frac{\left(5 a^2 d^2 f^2-2 a b d f (6 d e-c f)+b^2 \left(2 c^2 f^2-6 c d e f+9 d^2 e^2\right)\right) \log \left(\frac{\sqrt[3]{a+b x} \sqrt[3]{d e-c f}}{\sqrt[3]{b e-a f}}-\sqrt[3]{c+d x}\right)}{6 (b e-a f)^{7/3} (d e-c f)^{8/3}}-\frac{\left(5 a^2 d^2 f^2-2 a b d f (6 d e-c f)+b^2 \left(2 c^2 f^2-6 c d e f+9 d^2 e^2\right)\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x} \sqrt[3]{d e-c f}}{\sqrt{3} \sqrt[3]{c+d x} \sqrt[3]{b e-a f}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} (b e-a f)^{7/3} (d e-c f)^{8/3}}-\frac{f (a+b x)^{2/3} \sqrt[3]{c+d x} (-5 a d f-4 b c f+9 b d e)}{6 (e+f x) (b e-a f)^2 (d e-c f)^2}-\frac{f (a+b x)^{2/3} \sqrt[3]{c+d x}}{2 (e+f x)^2 (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3022,0,0,1389,9.9286302,"\int \frac{(a+b x)^3}{\sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","IntegrateAlgebraic[(a + b*x)^3/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)),x]","\int \frac{(a+b x)^3}{\sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","\frac{81 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{11/3}}{224 b^{2/3} d^4 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}-\frac{27\ 3^{3/4} \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{11/3}}{56 \sqrt{2} b^{2/3} d^4 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}-\frac{81 \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} (b c-a d)^3}{112 b^{2/3} d^6 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}+\frac{9 (c+d x)^{2/3} (23 b c-39 a d-16 b d x) (b c+a d+2 b d x)^{2/3} (b c-a d)}{560 d^4}+\frac{3 (a+b x)^2 (c+d x)^{2/3} (b c+a d+2 b d x)^{2/3}}{20 d^2}",1,"Could not integrate","F",-1
3023,0,0,1373,7.9787474,"\int \frac{(a+b x)^2}{\sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","IntegrateAlgebraic[(a + b*x)^2/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)),x]","\int \frac{(a+b x)^2}{\sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","-\frac{99 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{8/3}}{224 b^{2/3} d^3 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}+\frac{33\ 3^{3/4} \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{8/3}}{56 \sqrt{2} b^{2/3} d^3 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}+\frac{99 \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} (b c-a d)^2}{112 b^{2/3} d^5 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}-\frac{45 (c+d x)^{2/3} (b c+a d+2 b d x)^{2/3} (b c-a d)}{112 d^3}+\frac{3 (a+b x) (c+d x)^{2/3} (b c+a d+2 b d x)^{2/3}}{14 d^2}",1,"Could not integrate","F",-1
3024,0,0,1326,6.264526,"\int \frac{a+b x}{\sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","IntegrateAlgebraic[(a + b*x)/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)),x]","\int \frac{a+b x}{\sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","\frac{9 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{5/3}}{16 b^{2/3} d^2 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}-\frac{3\ 3^{3/4} \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{5/3}}{4 \sqrt{2} b^{2/3} d^2 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}-\frac{9 \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} (b c-a d)}{8 b^{2/3} d^4 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}+\frac{3 (c+d x)^{2/3} (b c+a d+2 b d x)^{2/3}}{8 d^2}",1,"Could not integrate","F",-1
3025,0,0,1283,5.4361427,"\int \frac{1}{\sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","IntegrateAlgebraic[1/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)),x]","\int \frac{1}{\sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (b c-a d)^{2/3} \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right)}{4 b^{2/3} d \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}+\frac{3^{3/4} (b c-a d)^{2/3} \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right)}{\sqrt{2} b^{2/3} d \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}+\frac{3 \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2}}{2 b^{2/3} d^3 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}",1,"Could not integrate","F",-1
3026,1,364,178,1.8250085,"\int \frac{1}{(a+b x) \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)),x]","\frac{i \left(\sqrt{3}+i\right) \log \left(\sqrt[3]{b c-a d} \sqrt[3]{a d+2 b (c+d x)-b c}+\sqrt[3]{-1} b^{2/3} (c+d x)^{2/3}\right)}{4 b^{2/3} (b c-a d)^{2/3}}+\frac{\left(1-i \sqrt{3}\right) \log \left(-\sqrt[3]{-1} b^{2/3} (c+d x)^{2/3} \sqrt[3]{b c-a d} \sqrt[3]{a d+2 b (c+d x)-b c}+(b c-a d)^{2/3} (a d+2 b (c+d x)-b c)^{2/3}+(-1)^{2/3} b^{4/3} (c+d x)^{4/3}\right)}{8 b^{2/3} (b c-a d)^{2/3}}-\frac{\sqrt{\frac{1}{2} \left(-3-3 i \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b c-a d} \sqrt[3]{a d+2 b (c+d x)-b c}}{\sqrt[3]{b c-a d} \sqrt[3]{a d+2 b (c+d x)-b c}-2 \sqrt[3]{-1} b^{2/3} (c+d x)^{2/3}}\right)}{2 b^{2/3} (b c-a d)^{2/3}}","-\frac{\log (a+b x)}{2 b^{2/3} (b c-a d)^{2/3}}+\frac{3 \log \left(\frac{b^{2/3} (c+d x)^{2/3}}{\sqrt[3]{b c-a d}}-\sqrt[3]{a d+b c+2 b d x}\right)}{4 b^{2/3} (b c-a d)^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 b^{2/3} (c+d x)^{2/3}}{\sqrt{3} \sqrt[3]{b c-a d} \sqrt[3]{a d+b c+2 b d x}}+\frac{1}{\sqrt{3}}\right)}{2 b^{2/3} (b c-a d)^{2/3}}",1,"-1/2*(Sqrt[(-3 - (3*I)*Sqrt[3])/2]*ArcTan[(Sqrt[3]*(b*c - a*d)^(1/3)*(-(b*c) + a*d + 2*b*(c + d*x))^(1/3))/(-2*(-1)^(1/3)*b^(2/3)*(c + d*x)^(2/3) + (b*c - a*d)^(1/3)*(-(b*c) + a*d + 2*b*(c + d*x))^(1/3))])/(b^(2/3)*(b*c - a*d)^(2/3)) + ((I/4)*(I + Sqrt[3])*Log[(-1)^(1/3)*b^(2/3)*(c + d*x)^(2/3) + (b*c - a*d)^(1/3)*(-(b*c) + a*d + 2*b*(c + d*x))^(1/3)])/(b^(2/3)*(b*c - a*d)^(2/3)) + ((1 - I*Sqrt[3])*Log[(-1)^(2/3)*b^(4/3)*(c + d*x)^(4/3) - (-1)^(1/3)*b^(2/3)*(b*c - a*d)^(1/3)*(c + d*x)^(2/3)*(-(b*c) + a*d + 2*b*(c + d*x))^(1/3) + (b*c - a*d)^(2/3)*(-(b*c) + a*d + 2*b*(c + d*x))^(2/3)])/(8*b^(2/3)*(b*c - a*d)^(2/3))","C",0
3027,0,0,1510,20.7466969,"\int \frac{1}{(a+b x)^2 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^2*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)),x]","\int \frac{1}{(a+b x)^2 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","\frac{\sqrt{3} d \tan ^{-1}\left(\frac{2 b^{2/3} (c+d x)^{2/3}}{\sqrt{3} \sqrt[3]{b c-a d} \sqrt[3]{b c+a d+2 b d x}}+\frac{1}{\sqrt{3}}\right)}{2 b^{2/3} (b c-a d)^{5/3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} d \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right)}{2 b^{2/3} (b c-a d)^{4/3} \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}+\frac{\sqrt{2} d \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} (b c-a d)^{4/3} \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}+\frac{d \log (a+b x)}{2 b^{2/3} (b c-a d)^{5/3}}-\frac{3 d \log \left(\frac{b^{2/3} (c+d x)^{2/3}}{\sqrt[3]{b c-a d}}-\sqrt[3]{b c+a d+2 b d x}\right)}{4 b^{2/3} (b c-a d)^{5/3}}-\frac{(c+d x)^{2/3} (b c+a d+2 b d x)^{2/3}}{(b c-a d)^2 (a+b x)}+\frac{\sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2}}{b^{2/3} d (b c-a d)^2 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}",1,"Could not integrate","F",-1
3028,0,0,1558,28.0312229,"\int \frac{1}{(a+b x)^3 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^3*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)),x]","\int \frac{1}{(a+b x)^3 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","-\frac{2 \tan ^{-1}\left(\frac{2 b^{2/3} (c+d x)^{2/3}}{\sqrt{3} \sqrt[3]{b c-a d} \sqrt[3]{b c+a d+2 b d x}}+\frac{1}{\sqrt{3}}\right) d^2}{\sqrt{3} b^{2/3} (b c-a d)^{8/3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right) d^2}{b^{2/3} (b c-a d)^{7/3} \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}-\frac{2 \sqrt{2} \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right) d^2}{\sqrt[4]{3} b^{2/3} (b c-a d)^{7/3} \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}-\frac{2 \log (a+b x) d^2}{3 b^{2/3} (b c-a d)^{8/3}}+\frac{\log \left(\frac{b^{2/3} (c+d x)^{2/3}}{\sqrt[3]{b c-a d}}-\sqrt[3]{b c+a d+2 b d x}\right) d^2}{b^{2/3} (b c-a d)^{8/3}}+\frac{2 (c+d x)^{2/3} (b c+a d+2 b d x)^{2/3} d}{(b c-a d)^3 (a+b x)}-\frac{(c+d x)^{2/3} (b c+a d+2 b d x)^{2/3}}{2 (b c-a d)^2 (a+b x)^2}-\frac{2 \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2}}{b^{2/3} (b c-a d)^3 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}",1,"Could not integrate","F",-1
3029,0,0,1388,12.044682,"\int \frac{(a+b x)^3}{\sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","IntegrateAlgebraic[(a + b*x)^3/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)),x]","\int \frac{(a+b x)^3}{\sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","-\frac{81 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{8/3}}{224 b^{2/3} d^4 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}+\frac{27\ 3^{3/4} \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{8/3}}{56 \sqrt{2} b^{2/3} d^4 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}+\frac{81 \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} (b c-a d)^2}{112 b^{2/3} d^6 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}+\frac{9 (c+d x)^{2/3} (b c-7 a d-6 b d x) (b c-a d)}{112 d^4 \sqrt[3]{b c+a d+2 b d x}}+\frac{3 (a+b x)^2 (c+d x)^{2/3}}{14 d^2 \sqrt[3]{b c+a d+2 b d x}}",1,"Could not integrate","F",-1
3030,0,0,1366,11.3668919,"\int \frac{(a+b x)^2}{\sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","IntegrateAlgebraic[(a + b*x)^2/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)),x]","\int \frac{(a+b x)^2}{\sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","\frac{9 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{5/3}}{32 b^{2/3} d^3 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}-\frac{3\ 3^{3/4} \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right) (b c-a d)^{5/3}}{8 \sqrt{2} b^{2/3} d^3 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}-\frac{3 (c+d x)^{2/3} (b c-a d)}{4 d^3 \sqrt[3]{b c+a d+2 b d x}}-\frac{9 \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} (b c-a d)}{16 b^{2/3} d^5 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}+\frac{3 (c+d x)^{2/3} (b c+a d+2 b d x)^{2/3}}{16 d^3}",1,"Could not integrate","F",-1
3031,0,0,32,9.2535342,"\int \frac{a+b x}{\sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","IntegrateAlgebraic[(a + b*x)/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)),x]","\int \frac{a+b x}{\sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","\frac{3 (c+d x)^{2/3}}{2 d^2 \sqrt[3]{a d+b c+2 b d x}}",1,"Could not integrate","F",-1
3032,0,0,1333,7.3463677,"\int \frac{1}{\sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","IntegrateAlgebraic[1/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)),x]","\int \frac{1}{\sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right)}{4 b^{2/3} d \sqrt[3]{b c-a d} \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}+\frac{3^{3/4} \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right) \sqrt{\frac{(b c-a d)^{4/3}-2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))} (b c-a d)^{2/3}+4 b^{2/3} ((c+d x) (a d+b (c+2 d x)))^{2/3}}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}{\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}}\right)|-7-4 \sqrt{3}\right)}{\sqrt{2} b^{2/3} d \sqrt[3]{b c-a d} \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\frac{(b c-a d)^{2/3} \left((b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}{\left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)^2}}}-\frac{3 (c+d x)^{2/3}}{d (b c-a d) \sqrt[3]{b c+a d+2 b d x}}+\frac{3 \sqrt[3]{(c+d x) (b c+a d+2 b d x)} \sqrt{d^2 (3 b c+a d+4 b d x)^2} \sqrt{\left(4 b x d^2+(3 b c+a d) d\right)^2}}{2 b^{2/3} d^3 (b c-a d) \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x} (3 b c+a d+4 b d x) \left(\left(1+\sqrt{3}\right) (b c-a d)^{2/3}+2 \sqrt[3]{b} \sqrt[3]{(c+d x) (a d+b (c+2 d x))}\right)}",1,"Could not integrate","F",-1
3033,0,0,113,13.7329649,"\int \frac{1}{(a+b x) \sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)),x]","\int \frac{1}{(a+b x) \sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","\frac{3 (c+d x)^{2/3} \sqrt[3]{-\frac{a d+b c+2 b d x}{b c-a d}} F_1\left(\frac{2}{3};\frac{4}{3},1;\frac{5}{3};\frac{2 b (c+d x)}{b c-a d},\frac{b (c+d x)}{b c-a d}\right)}{2 (b c-a d)^2 \sqrt[3]{a d+b c+2 b d x}}",1,"Could not integrate","F",-1
3034,0,0,114,23.1243653,"\int \frac{1}{(a+b x)^2 \sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^2*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)),x]","\int \frac{1}{(a+b x)^2 \sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","-\frac{3 d (c+d x)^{2/3} \sqrt[3]{-\frac{a d+b c+2 b d x}{b c-a d}} F_1\left(\frac{2}{3};\frac{4}{3},2;\frac{5}{3};\frac{2 b (c+d x)}{b c-a d},\frac{b (c+d x)}{b c-a d}\right)}{2 (b c-a d)^3 \sqrt[3]{a d+b c+2 b d x}}",1,"Could not integrate","F",-1
3035,0,0,116,27.6649382,"\int \frac{1}{(a+b x)^3 \sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","IntegrateAlgebraic[1/((a + b*x)^3*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)),x]","\int \frac{1}{(a+b x)^3 \sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","\frac{3 d^2 (c+d x)^{2/3} \sqrt[3]{-\frac{a d+b c+2 b d x}{b c-a d}} F_1\left(\frac{2}{3};\frac{4}{3},3;\frac{5}{3};\frac{2 b (c+d x)}{b c-a d},\frac{b (c+d x)}{b c-a d}\right)}{2 (b c-a d)^4 \sqrt[3]{a d+b c+2 b d x}}",1,"Could not integrate","F",-1
3036,1,495,120,1.5068702,"\int \frac{1}{\sqrt[3]{d-3 e x} (d+e x) \sqrt[3]{d+3 e x}} \, dx","IntegrateAlgebraic[1/((d - 3*e*x)^(1/3)*(d + e*x)*(d + 3*e*x)^(1/3)),x]","-\frac{\log \left(\sqrt[3]{d-3 e x}-\sqrt[3]{2} \sqrt[3]{d+3 e x}+2^{2/3} \sqrt[3]{d}\right)}{2 d^{2/3} e}-\frac{\log \left(2 \sqrt[3]{d-3 e x}+\sqrt[3]{2} \sqrt[3]{d+3 e x}-2^{2/3} \sqrt[3]{d}\right)}{4 d^{2/3} e}+\frac{\log \left(2 \sqrt[3]{2} d^{2/3}+2\ 2^{2/3} \sqrt[3]{d} \sqrt[3]{d-3 e x}-4 \sqrt[3]{d} \sqrt[3]{d+3 e x}+4 (d-3 e x)^{2/3}+2^{2/3} (d+3 e x)^{2/3}-2 \sqrt[3]{2} \sqrt[3]{d-3 e x} \sqrt[3]{d+3 e x}\right)}{8 d^{2/3} e}+\frac{\log \left(2 \sqrt[3]{2} d^{2/3}-2^{2/3} \sqrt[3]{d} \sqrt[3]{d-3 e x}-4 \sqrt[3]{d} \sqrt[3]{d+3 e x}+(d-3 e x)^{2/3}+2^{2/3} (d+3 e x)^{2/3}+\sqrt[3]{2} \sqrt[3]{d-3 e x} \sqrt[3]{d+3 e x}\right)}{4 d^{2/3} e}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d-3 e x}}{\sqrt[3]{d-3 e x}-\sqrt[3]{2} \sqrt[3]{d+3 e x}+2^{2/3} \sqrt[3]{d}}\right)}{4 d^{2/3} e}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{d-3 e x}}{\sqrt[3]{d-3 e x}+2 \sqrt[3]{2} \sqrt[3]{d+3 e x}-2\ 2^{2/3} \sqrt[3]{d}}\right)}{2 d^{2/3} e}","\frac{\log (d+e x)}{4 d^{2/3} e}-\frac{3 \log \left(-\frac{(d-3 e x)^{2/3}}{2 \sqrt[3]{d}}-\sqrt[3]{d+3 e x}\right)}{8 d^{2/3} e}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{(d-3 e x)^{2/3}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{d+3 e x}}\right)}{4 d^{2/3} e}",1,"-1/4*(Sqrt[3]*ArcTan[(Sqrt[3]*(d - 3*e*x)^(1/3))/(2^(2/3)*d^(1/3) + (d - 3*e*x)^(1/3) - 2^(1/3)*(d + 3*e*x)^(1/3))])/(d^(2/3)*e) - (Sqrt[3]*ArcTan[(Sqrt[3]*(d - 3*e*x)^(1/3))/(-2*2^(2/3)*d^(1/3) + (d - 3*e*x)^(1/3) + 2*2^(1/3)*(d + 3*e*x)^(1/3))])/(2*d^(2/3)*e) - Log[2^(2/3)*d^(1/3) + (d - 3*e*x)^(1/3) - 2^(1/3)*(d + 3*e*x)^(1/3)]/(2*d^(2/3)*e) - Log[-(2^(2/3)*d^(1/3)) + 2*(d - 3*e*x)^(1/3) + 2^(1/3)*(d + 3*e*x)^(1/3)]/(4*d^(2/3)*e) + Log[2*2^(1/3)*d^(2/3) + 2*2^(2/3)*d^(1/3)*(d - 3*e*x)^(1/3) + 4*(d - 3*e*x)^(2/3) - 4*d^(1/3)*(d + 3*e*x)^(1/3) - 2*2^(1/3)*(d - 3*e*x)^(1/3)*(d + 3*e*x)^(1/3) + 2^(2/3)*(d + 3*e*x)^(2/3)]/(8*d^(2/3)*e) + Log[2*2^(1/3)*d^(2/3) - 2^(2/3)*d^(1/3)*(d - 3*e*x)^(1/3) + (d - 3*e*x)^(2/3) - 4*d^(1/3)*(d + 3*e*x)^(1/3) + 2^(1/3)*(d - 3*e*x)^(1/3)*(d + 3*e*x)^(1/3) + 2^(2/3)*(d + 3*e*x)^(2/3)]/(4*d^(2/3)*e)","B",1
3037,0,0,562,13.1663921,"\int \frac{(a+b x)^{4/3} (e+f x)^2}{(c+d x)^{4/3}} \, dx","IntegrateAlgebraic[((a + b*x)^(4/3)*(e + f*x)^2)/(c + d*x)^(4/3),x]","\int \frac{(a+b x)^{4/3} (e+f x)^2}{(c+d x)^{4/3}} \, dx","-\frac{4 \sqrt[3]{a+b x} (c+d x)^{2/3} \left(a^2 d^2 f^2-a b d f (9 d e-7 c f)-\left(b^2 \left(35 c^2 f^2-63 c d e f+27 d^2 e^2\right)\right)\right)}{27 b d^4}+\frac{(a+b x)^{4/3} (c+d x)^{2/3} \left(a^2 d^2 f^2-a b d f (9 d e-7 c f)-\left(b^2 \left(35 c^2 f^2-63 c d e f+27 d^2 e^2\right)\right)\right)}{9 b d^3 (b c-a d)}-\frac{2 (b c-a d) \log (a+b x) \left(a^2 d^2 f^2-a b d f (9 d e-7 c f)-\left(b^2 \left(35 c^2 f^2-63 c d e f+27 d^2 e^2\right)\right)\right)}{81 b^{5/3} d^{13/3}}-\frac{2 (b c-a d) \left(a^2 d^2 f^2-a b d f (9 d e-7 c f)-\left(b^2 \left(35 c^2 f^2-63 c d e f+27 d^2 e^2\right)\right)\right) \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{27 b^{5/3} d^{13/3}}-\frac{4 (b c-a d) \left(a^2 d^2 f^2-a b d f (9 d e-7 c f)-\left(b^2 \left(35 c^2 f^2-63 c d e f+27 d^2 e^2\right)\right)\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{27 \sqrt{3} b^{5/3} d^{13/3}}+\frac{3 (a+b x)^{7/3} (d e-c f)^2}{d^2 \sqrt[3]{c+d x} (b c-a d)}+\frac{f^2 (a+b x)^{7/3} (c+d x)^{2/3}}{3 b d^2}",1,"Could not integrate","F",-1
3038,0,0,328,10.8160892,"\int \frac{(a+b x)^{4/3} (e+f x)}{(c+d x)^{4/3}} \, dx","IntegrateAlgebraic[((a + b*x)^(4/3)*(e + f*x))/(c + d*x)^(4/3),x]","\int \frac{(a+b x)^{4/3} (e+f x)}{(c+d x)^{4/3}} \, dx","\frac{(b c-a d) \log (a+b x) (a d f-7 b c f+6 b d e)}{9 b^{2/3} d^{10/3}}+\frac{(b c-a d) (a d f-7 b c f+6 b d e) \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{3 b^{2/3} d^{10/3}}+\frac{2 (b c-a d) (a d f-7 b c f+6 b d e) \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{2/3} d^{10/3}}+\frac{2 \sqrt[3]{a+b x} (c+d x)^{2/3} (a d f-7 b c f+6 b d e)}{3 d^3}-\frac{(a+b x)^{4/3} (c+d x)^{2/3} (a d f-7 b c f+6 b d e)}{2 d^2 (b c-a d)}+\frac{3 (a+b x)^{7/3} (d e-c f)}{d \sqrt[3]{c+d x} (b c-a d)}",1,"Could not integrate","F",-1
3039,0,0,195,0.0006751,"\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3}} \, dx","IntegrateAlgebraic[(a + b*x)^(4/3)/(c + d*x)^(4/3),x]","\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3}} \, dx","\frac{2 \sqrt[3]{b} (b c-a d) \log (a+b x)}{3 d^{7/3}}+\frac{2 \sqrt[3]{b} (b c-a d) \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{d^{7/3}}+\frac{4 \sqrt[3]{b} (b c-a d) \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} d^{7/3}}+\frac{4 b \sqrt[3]{a+b x} (c+d x)^{2/3}}{d^2}-\frac{3 (a+b x)^{4/3}}{d \sqrt[3]{c+d x}}",1,"Could not integrate","F",-1
3040,0,0,380,25.5836764,"\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3} (e+f x)} \, dx","IntegrateAlgebraic[(a + b*x)^(4/3)/((c + d*x)^(4/3)*(e + f*x)),x]","\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3} (e+f x)} \, dx","-\frac{3 b^{4/3} \log \left(\frac{\sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt[3]{d} \sqrt[3]{a+b x}}-1\right)}{2 d^{4/3} f}-\frac{\sqrt{3} b^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[3]{c+d x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{a+b x}}+\frac{1}{\sqrt{3}}\right)}{d^{4/3} f}-\frac{b^{4/3} \log (a+b x)}{2 d^{4/3} f}+\frac{3 \sqrt[3]{a+b x} (b c-a d)}{d \sqrt[3]{c+d x} (d e-c f)}-\frac{(b e-a f)^{4/3} \log (e+f x)}{2 f (d e-c f)^{4/3}}+\frac{3 (b e-a f)^{4/3} \log \left(\frac{\sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt[3]{d e-c f}}-\sqrt[3]{a+b x}\right)}{2 f (d e-c f)^{4/3}}+\frac{\sqrt{3} (b e-a f)^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt{3} \sqrt[3]{a+b x} \sqrt[3]{d e-c f}}+\frac{1}{\sqrt{3}}\right)}{f (d e-c f)^{4/3}}",1,"Could not integrate","F",-1
3041,0,0,301,25.3143036,"\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3} (e+f x)^2} \, dx","IntegrateAlgebraic[(a + b*x)^(4/3)/((c + d*x)^(4/3)*(e + f*x)^2),x]","\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3} (e+f x)^2} \, dx","-\frac{3 (a+b x)^{4/3}}{\sqrt[3]{c+d x} (e+f x) (d e-c f)}+\frac{4 \sqrt[3]{a+b x} (c+d x)^{2/3} (b e-a f)}{(e+f x) (d e-c f)^2}-\frac{2 (b c-a d) \sqrt[3]{b e-a f} \log (e+f x)}{3 (d e-c f)^{7/3}}+\frac{2 (b c-a d) \sqrt[3]{b e-a f} \log \left(\frac{\sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt[3]{d e-c f}}-\sqrt[3]{a+b x}\right)}{(d e-c f)^{7/3}}+\frac{4 (b c-a d) \sqrt[3]{b e-a f} \tan ^{-1}\left(\frac{2 \sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt{3} \sqrt[3]{a+b x} \sqrt[3]{d e-c f}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} (d e-c f)^{7/3}}",1,"Could not integrate","F",-1
3042,0,0,434,32.1865563,"\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3} (e+f x)^3} \, dx","IntegrateAlgebraic[(a + b*x)^(4/3)/((c + d*x)^(4/3)*(e + f*x)^3),x]","\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3} (e+f x)^3} \, dx","\frac{3 d (a+b x)^{7/3}}{\sqrt[3]{c+d x} (e+f x)^2 (b c-a d) (d e-c f)}-\frac{(a+b x)^{4/3} (c+d x)^{2/3} (-7 a d f+b c f+6 b d e)}{2 (e+f x)^2 (b c-a d) (d e-c f)^2}+\frac{2 \sqrt[3]{a+b x} (c+d x)^{2/3} (-7 a d f+b c f+6 b d e)}{3 (e+f x) (d e-c f)^3}-\frac{(b c-a d) \log (e+f x) (-7 a d f+b c f+6 b d e)}{9 (b e-a f)^{2/3} (d e-c f)^{10/3}}+\frac{(b c-a d) (-7 a d f+b c f+6 b d e) \log \left(\frac{\sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt[3]{d e-c f}}-\sqrt[3]{a+b x}\right)}{3 (b e-a f)^{2/3} (d e-c f)^{10/3}}+\frac{2 (b c-a d) (-7 a d f+b c f+6 b d e) \tan ^{-1}\left(\frac{2 \sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt{3} \sqrt[3]{a+b x} \sqrt[3]{d e-c f}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} (b e-a f)^{2/3} (d e-c f)^{10/3}}",1,"Could not integrate","F",-1
3043,0,0,645,48.3113194,"\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3} (e+f x)^4} \, dx","IntegrateAlgebraic[(a + b*x)^(4/3)/((c + d*x)^(4/3)*(e + f*x)^4),x]","\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3} (e+f x)^4} \, dx","\frac{\sqrt[3]{a+b x} (c+d x)^{2/3} \left(140 a^2 d^2 f^2-7 a b d f (19 c f+21 d e)+b^2 \left(2 c^2 f^2+129 c d e f+9 d^2 e^2\right)\right)}{27 (e+f x) (b e-a f) (d e-c f)^4}-\frac{2 (b c-a d) \log (e+f x) \left(35 a^2 d^2 f^2-7 a b d f (c f+9 d e)+b^2 \left(-c^2 f^2+9 c d e f+27 d^2 e^2\right)\right)}{81 (b e-a f)^{5/3} (d e-c f)^{13/3}}+\frac{2 (b c-a d) \left(35 a^2 d^2 f^2-7 a b d f (c f+9 d e)+b^2 \left(-c^2 f^2+9 c d e f+27 d^2 e^2\right)\right) \log \left(\frac{\sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt[3]{d e-c f}}-\sqrt[3]{a+b x}\right)}{27 (b e-a f)^{5/3} (d e-c f)^{13/3}}+\frac{4 (b c-a d) \left(35 a^2 d^2 f^2-7 a b d f (c f+9 d e)+b^2 \left(-c^2 f^2+9 c d e f+27 d^2 e^2\right)\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{c+d x} \sqrt[3]{b e-a f}}{\sqrt{3} \sqrt[3]{a+b x} \sqrt[3]{d e-c f}}+\frac{1}{\sqrt{3}}\right)}{27 \sqrt{3} (b e-a f)^{5/3} (d e-c f)^{13/3}}+\frac{3 \sqrt[3]{a+b x} (b c-a d)}{d \sqrt[3]{c+d x} (e+f x)^3 (d e-c f)}+\frac{\sqrt[3]{a+b x} (c+d x)^{2/3} (-35 a d f+32 b c f+3 b d e)}{9 (e+f x)^2 (d e-c f)^3}+\frac{\sqrt[3]{a+b x} (c+d x)^{2/3} (-10 a d f+9 b c f+b d e)}{3 d (e+f x)^3 (d e-c f)^2}",1,"Could not integrate","F",-1
3044,0,0,266,7.3847263,"\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt[4]{e+f x}} \, dx","IntegrateAlgebraic[1/((a + b*x)*Sqrt[c + d*x]*(e + f*x)^(1/4)),x]","\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt[4]{e+f x}} \, dx","\frac{2 \sqrt[4]{d e-c f} \sqrt{-\frac{f (c+d x)}{d e-c f}} \Pi \left(-\frac{\sqrt{b} \sqrt{d e-c f}}{\sqrt{d} \sqrt{b e-a f}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{e+f x}}{\sqrt[4]{d e-c f}}\right)\right|-1\right)}{\sqrt{b} \sqrt[4]{d} \sqrt{c+d x} \sqrt{b e-a f}}-\frac{2 \sqrt[4]{d e-c f} \sqrt{-\frac{f (c+d x)}{d e-c f}} \Pi \left(\frac{\sqrt{b} \sqrt{d e-c f}}{\sqrt{d} \sqrt{b e-a f}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{e+f x}}{\sqrt[4]{d e-c f}}\right)\right|-1\right)}{\sqrt{b} \sqrt[4]{d} \sqrt{c+d x} \sqrt{b e-a f}}",1,"Could not integrate","F",-1
3045,0,0,252,47.1606595,"\int \frac{1}{(a+b x) \sqrt{c+d x} (e+f x)^{3/4}} \, dx","IntegrateAlgebraic[1/((a + b*x)*Sqrt[c + d*x]*(e + f*x)^(3/4)),x]","\int \frac{1}{(a+b x) \sqrt{c+d x} (e+f x)^{3/4}} \, dx","-\frac{2 \sqrt[4]{d e-c f} \sqrt{-\frac{f (c+d x)}{d e-c f}} \Pi \left(-\frac{\sqrt{b} \sqrt{d e-c f}}{\sqrt{d} \sqrt{b e-a f}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{e+f x}}{\sqrt[4]{d e-c f}}\right)\right|-1\right)}{\sqrt[4]{d} \sqrt{c+d x} (b e-a f)}-\frac{2 \sqrt[4]{d e-c f} \sqrt{-\frac{f (c+d x)}{d e-c f}} \Pi \left(\frac{\sqrt{b} \sqrt{d e-c f}}{\sqrt{d} \sqrt{b e-a f}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt[4]{e+f x}}{\sqrt[4]{d e-c f}}\right)\right|-1\right)}{\sqrt[4]{d} \sqrt{c+d x} (b e-a f)}",1,"Could not integrate","F",-1
3046,0,0,125,0.0578109,"\int (a+b x)^p (A+B x) (d+e x)^{-2-p} \, dx","IntegrateAlgebraic[(a + b*x)^p*(A + B*x)*(d + e*x)^(-2 - p),x]","\int (a+b x)^p (A+B x) (d+e x)^{-2-p} \, dx","-\frac{(a+b x)^{p+1} (B d-A e) (d+e x)^{-p-1}}{e (p+1) (b d-a e)}-\frac{B (a+b x)^p (d+e x)^{-p} \left(-\frac{e (a+b x)}{b d-a e}\right)^{-p} \, _2F_1\left(-p,-p;1-p;\frac{b (d+e x)}{b d-a e}\right)}{e^2 p}",1,"Could not integrate","F",-1
3047,0,0,134,0.0443538,"\int (a+b x) (c+d x)^n (e+f x)^{-n} \, dx","IntegrateAlgebraic[((a + b*x)*(c + d*x)^n)/(e + f*x)^n,x]","\int (a+b x) (c+d x)^n (e+f x)^{-n} \, dx","\frac{(c+d x)^{n+1} (e+f x)^{-n} \left(\frac{d (e+f x)}{d e-c f}\right)^n (2 a d f-b (c f (1-n)+d e (n+1))) \, _2F_1\left(n,n+1;n+2;-\frac{f (c+d x)}{d e-c f}\right)}{2 d^2 f (n+1)}+\frac{b (c+d x)^{n+1} (e+f x)^{1-n}}{2 d f}",1,"Could not integrate","F",-1
3048,0,0,152,0.0589284,"\int (a+b x) (c+d x)^{-1+n} (e+f x)^{-n} \, dx","IntegrateAlgebraic[((a + b*x)*(c + d*x)^(-1 + n))/(e + f*x)^n,x]","\int (a+b x) (c+d x)^{-1+n} (e+f x)^{-n} \, dx","-\frac{(c+d x)^{n+1} (e+f x)^{-n} \left(\frac{d (e+f x)}{d e-c f}\right)^n (a d f-b (c f (1-n)+d e n)) \, _2F_1\left(n,n+1;n+2;-\frac{f (c+d x)}{d e-c f}\right)}{d^2 n (n+1) (d e-c f)}-\frac{(b c-a d) (c+d x)^n (e+f x)^{1-n}}{d n (d e-c f)}",1,"Could not integrate","F",-1
3049,0,0,117,0.0585217,"\int (a+b x) (c+d x)^{-2+n} (e+f x)^{-n} \, dx","IntegrateAlgebraic[((a + b*x)*(c + d*x)^(-2 + n))/(e + f*x)^n,x]","\int (a+b x) (c+d x)^{-2+n} (e+f x)^{-n} \, dx","\frac{(b c-a d) (c+d x)^{n-1} (e+f x)^{1-n}}{d (1-n) (d e-c f)}+\frac{b (c+d x)^n (e+f x)^{-n} \left(\frac{d (e+f x)}{d e-c f}\right)^n \, _2F_1\left(n,n;n+1;-\frac{f (c+d x)}{d e-c f}\right)}{d^2 n}",1,"Could not integrate","F",-1
3050,0,0,123,0.1125867,"\int (a+b x) (c+d x)^{-3+n} (e+f x)^{-n} \, dx","IntegrateAlgebraic[((a + b*x)*(c + d*x)^(-3 + n))/(e + f*x)^n,x]","\int (a+b x) (c+d x)^{-3+n} (e+f x)^{-n} \, dx","\frac{(b c-a d) (c+d x)^{n-2} (e+f x)^{1-n}}{d (2-n) (d e-c f)}+\frac{(c+d x)^{n-1} (e+f x)^{1-n} (a d f+b (c f (1-n)-d e (2-n)))}{d (1-n) (2-n) (d e-c f)^2}",1,"Could not integrate","F",-1
3051,0,0,207,0.0599373,"\int (a+b x) (c+d x)^{-4+n} (e+f x)^{-n} \, dx","IntegrateAlgebraic[((a + b*x)*(c + d*x)^(-4 + n))/(e + f*x)^n,x]","\int (a+b x) (c+d x)^{-4+n} (e+f x)^{-n} \, dx","\frac{(b c-a d) (c+d x)^{n-3} (e+f x)^{1-n}}{d (3-n) (d e-c f)}+\frac{(c+d x)^{n-2} (e+f x)^{1-n} (2 a d f+b (c f (1-n)-d e (3-n)))}{d (2-n) (3-n) (d e-c f)^2}-\frac{f (c+d x)^{n-1} (e+f x)^{1-n} (2 a d f+b (c f (1-n)-d e (3-n)))}{d (1-n) (2-n) (3-n) (d e-c f)^3}",1,"Could not integrate","F",-1
3052,0,0,299,0.060215,"\int (a+b x) (c+d x)^{-5+n} (e+f x)^{-n} \, dx","IntegrateAlgebraic[((a + b*x)*(c + d*x)^(-5 + n))/(e + f*x)^n,x]","\int (a+b x) (c+d x)^{-5+n} (e+f x)^{-n} \, dx","\frac{2 f^2 (c+d x)^{n-1} (e+f x)^{1-n} (3 a d f+b (c f (1-n)-d e (4-n)))}{d (1-n) (2-n) (3-n) (4-n) (d e-c f)^4}+\frac{(b c-a d) (c+d x)^{n-4} (e+f x)^{1-n}}{d (4-n) (d e-c f)}+\frac{(c+d x)^{n-3} (e+f x)^{1-n} (3 a d f+b (c f (1-n)-d e (4-n)))}{d (3-n) (4-n) (d e-c f)^2}-\frac{2 f (c+d x)^{n-2} (e+f x)^{1-n} (3 a d f+b (c f (1-n)-d e (4-n)))}{d (2-n) (3-n) (4-n) (d e-c f)^3}",1,"Could not integrate","F",-1
3053,0,0,135,0.1158849,"\int (a+b x)^{-n} (c+d x) (e+f x)^n \, dx","IntegrateAlgebraic[((c + d*x)*(e + f*x)^n)/(a + b*x)^n,x]","\int (a+b x)^{-n} (c+d x) (e+f x)^n \, dx","\frac{(a+b x)^{-n} (e+f x)^{n+1} \left(-\frac{f (a+b x)}{b e-a f}\right)^n (b (2 c f-d e (1-n))-a d f (n+1)) \, _2F_1\left(n,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)}{2 b f^2 (n+1)}+\frac{d (a+b x)^{1-n} (e+f x)^{n+1}}{2 b f}",1,"Could not integrate","F",-1
3054,0,0,151,0.1341221,"\int (a+b x)^{-n} (c+d x) (e+f x)^{-1+n} \, dx","IntegrateAlgebraic[((c + d*x)*(e + f*x)^(-1 + n))/(a + b*x)^n,x]","\int (a+b x)^{-n} (c+d x) (e+f x)^{-1+n} \, dx","\frac{(a+b x)^{-n} (e+f x)^{n+1} \left(-\frac{f (a+b x)}{b e-a f}\right)^n (b (c f-d e (1-n))-a d f n) \, _2F_1\left(n,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)}{f^2 n (n+1) (b e-a f)}+\frac{(a+b x)^{1-n} (d e-c f) (e+f x)^n}{f n (b e-a f)}",1,"Could not integrate","F",-1
3055,0,0,118,0.1403804,"\int (a+b x)^{-n} (c+d x) (e+f x)^{-2+n} \, dx","IntegrateAlgebraic[((c + d*x)*(e + f*x)^(-2 + n))/(a + b*x)^n,x]","\int (a+b x)^{-n} (c+d x) (e+f x)^{-2+n} \, dx","\frac{d (a+b x)^{-n} (e+f x)^n \left(-\frac{f (a+b x)}{b e-a f}\right)^n \, _2F_1\left(n,n;n+1;\frac{b (e+f x)}{b e-a f}\right)}{f^2 n}-\frac{(a+b x)^{1-n} (d e-c f) (e+f x)^{n-1}}{f (1-n) (b e-a f)}",1,"Could not integrate","F",-1
3056,0,0,125,0.113705,"\int (a+b x)^{-n} (c+d x) (e+f x)^{-3+n} \, dx","IntegrateAlgebraic[((c + d*x)*(e + f*x)^(-3 + n))/(a + b*x)^n,x]","\int (a+b x)^{-n} (c+d x) (e+f x)^{-3+n} \, dx","-\frac{(a+b x)^{1-n} (d e-c f) (e+f x)^{n-2}}{f (2-n) (b e-a f)}-\frac{(a+b x)^{1-n} (e+f x)^{n-1} (a d f (2-n)-b (c f+d (e-e n)))}{f (1-n) (2-n) (b e-a f)^2}",1,"Could not integrate","F",-1
3057,0,0,207,0.0972041,"\int (a+b x)^{-n} (c+d x) (e+f x)^{-4+n} \, dx","IntegrateAlgebraic[((c + d*x)*(e + f*x)^(-4 + n))/(a + b*x)^n,x]","\int (a+b x)^{-n} (c+d x) (e+f x)^{-4+n} \, dx","-\frac{(a+b x)^{1-n} (d e-c f) (e+f x)^{n-3}}{f (3-n) (b e-a f)}+\frac{(a+b x)^{1-n} (e+f x)^{n-2} (b (2 c f+d e (1-n))-a d f (3-n))}{f (2-n) (3-n) (b e-a f)^2}+\frac{b (a+b x)^{1-n} (e+f x)^{n-1} (b (2 c f+d e (1-n))-a d f (3-n))}{f (1-n) (2-n) (3-n) (b e-a f)^3}",1,"Could not integrate","F",-1
3058,0,0,300,0.0593501,"\int (a+b x)^{-n} (c+d x) (e+f x)^{-5+n} \, dx","IntegrateAlgebraic[((c + d*x)*(e + f*x)^(-5 + n))/(a + b*x)^n,x]","\int (a+b x)^{-n} (c+d x) (e+f x)^{-5+n} \, dx","\frac{2 b^2 (a+b x)^{1-n} (e+f x)^{n-1} (b (3 c f+d e (1-n))-a d f (4-n))}{f (1-n) (2-n) (3-n) (4-n) (b e-a f)^4}-\frac{(a+b x)^{1-n} (d e-c f) (e+f x)^{n-4}}{f (4-n) (b e-a f)}+\frac{(a+b x)^{1-n} (e+f x)^{n-3} (b (3 c f+d e (1-n))-a d f (4-n))}{f (3-n) (4-n) (b e-a f)^2}+\frac{2 b (a+b x)^{1-n} (e+f x)^{n-2} (b (3 c f+d e (1-n))-a d f (4-n))}{f (2-n) (3-n) (4-n) (b e-a f)^3}",1,"Could not integrate","F",-1
3059,0,0,121,0.0474227,"\int (a+b x)^m (c+d x)^{-m} (e+f x)^p \, dx","IntegrateAlgebraic[((a + b*x)^m*(e + f*x)^p)/(c + d*x)^m,x]","\int (a+b x)^m (c+d x)^{-m} (e+f x)^p \, dx","\frac{(a+b x)^{m+1} (c+d x)^{-m} (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+1;m,-p;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b (m+1)}",1,"Could not integrate","F",-1
3060,0,0,188,0.036459,"\int (5-4 x)^4 (1+2 x)^{-m} (2+3 x)^m \, dx","IntegrateAlgebraic[((5 - 4*x)^4*(2 + 3*x)^m)/(1 + 2*x)^m,x]","\int (5-4 x)^4 (1+2 x)^{-m} (2+3 x)^m \, dx","\frac{2^{-m-1} \left(2 m^4-440 m^3+29050 m^2-639760 m+3528363\right) (2 x+1)^{1-m} \, _2F_1(1-m,-m;2-m;-3 (2 x+1))}{1215 (1-m)}-\frac{(3 x+2)^{m+1} \left(-2 m^3-24 \left(m^2-154 m+4359\right) x+426 m^2-25441 m+386850\right) (2 x+1)^{1-m}}{1215}-\frac{2}{15} (5-4 x)^3 (3 x+2)^{m+1} (2 x+1)^{1-m}-\frac{1}{45} (88-m) (5-4 x)^2 (3 x+2)^{m+1} (2 x+1)^{1-m}",1,"Could not integrate","F",-1
3061,0,0,432,0.1060328,"\int (a+b x)^m (c+d x)^{-m} (e+f x)^3 \, dx","IntegrateAlgebraic[((a + b*x)^m*(e + f*x)^3)/(c + d*x)^m,x]","\int (a+b x)^m (c+d x)^{-m} (e+f x)^3 \, dx","\frac{f (a+b x)^{m+1} (c+d x)^{1-m} \left(a^2 d^2 f^2 \left(m^2-5 m+6\right)-2 a b d f \left(6 d e (2-m)-c f \left(3-m^2\right)\right)-2 b d f x (a d f (3-m)-b (6 d e-c f (m+3)))+b^2 \left(c^2 f^2 \left(m^2+5 m+6\right)-12 c d e f (m+2)+30 d^2 e^2\right)\right)}{24 b^3 d^3}-\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(a^3 d^3 f^3 \left(-m^3+6 m^2-11 m+6\right)-3 a^2 b d^2 f^2 \left(m^2-3 m+2\right) (4 d e-c f (m+1))+3 a b^2 d f (1-m) \left(c^2 f^2 \left(m^2+3 m+2\right)-8 c d e f (m+1)+12 d^2 e^2\right)-\left(b^3 \left(-c^3 f^3 \left(m^3+6 m^2+11 m+6\right)+12 c^2 d e f^2 \left(m^2+3 m+2\right)-36 c d^2 e^2 f (m+1)+24 d^3 e^3\right)\right)\right) \, _2F_1\left(m,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{24 b^4 d^3 (m+1)}+\frac{f (e+f x)^2 (a+b x)^{m+1} (c+d x)^{1-m}}{4 b d}",1,"Could not integrate","F",-1
3062,0,0,250,0.1111915,"\int (a+b x)^m (c+d x)^{-m} (e+f x)^2 \, dx","IntegrateAlgebraic[((a + b*x)^m*(e + f*x)^2)/(c + d*x)^m,x]","\int (a+b x)^m (c+d x)^{-m} (e+f x)^2 \, dx","\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(a^2 d^2 f^2 \left(m^2-3 m+2\right)-2 a b d f (1-m) (3 d e-c f (m+1))+b^2 \left(c^2 f^2 \left(m^2+3 m+2\right)-6 c d e f (m+1)+6 d^2 e^2\right)\right) \, _2F_1\left(m,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{6 b^3 d^2 (m+1)}-\frac{f (a+b x)^{m+1} (c+d x)^{1-m} (a d f (2-m)-b (4 d e-c f (m+2)))}{6 b^2 d^2}+\frac{f (e+f x) (a+b x)^{m+1} (c+d x)^{1-m}}{3 b d}",1,"Could not integrate","F",-1
3063,0,0,135,0.0449986,"\int (a+b x)^m (c+d x)^{-m} (e+f x) \, dx","IntegrateAlgebraic[((a + b*x)^m*(e + f*x))/(c + d*x)^m,x]","\int (a+b x)^m (c+d x)^{-m} (e+f x) \, dx","\frac{f (a+b x)^{m+1} (c+d x)^{1-m}}{2 b d}-\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m (a d f (1-m)-b (2 d e-c f (m+1))) \, _2F_1\left(m,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{2 b^2 d (m+1)}",1,"Could not integrate","F",-1
3064,0,0,72,0.0254047,"\int (a+b x)^m (c+d x)^{-m} \, dx","IntegrateAlgebraic[(a + b*x)^m/(c + d*x)^m,x]","\int (a+b x)^m (c+d x)^{-m} \, dx","\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{b (m+1)}",1,"Could not integrate","F",-1
3065,0,0,128,0.0634741,"\int \frac{(a+b x)^m (c+d x)^{-m}}{e+f x} \, dx","IntegrateAlgebraic[(a + b*x)^m/((c + d*x)^m*(e + f*x)),x]","\int \frac{(a+b x)^m (c+d x)^{-m}}{e+f x} \, dx","\frac{(a+b x)^m (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m,m;m+1;-\frac{d (a+b x)}{b c-a d}\right)}{f m}-\frac{(a+b x)^m (c+d x)^{-m} \, _2F_1\left(1,m;m+1;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{f m}",1,"Could not integrate","F",-1
3066,0,0,83,0.104305,"\int \frac{(a+b x)^m (c+d x)^{-m}}{(e+f x)^2} \, dx","IntegrateAlgebraic[(a + b*x)^m/((c + d*x)^m*(e + f*x)^2),x]","\int \frac{(a+b x)^m (c+d x)^{-m}}{(e+f x)^2} \, dx","\frac{(b c-a d) (a+b x)^{m+1} (c+d x)^{-m-1} \, _2F_1\left(2,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{(m+1) (b e-a f)^2}",1,"Could not integrate","F",-1
3067,0,0,174,0.1138647,"\int \frac{(a+b x)^m (c+d x)^{-m}}{(e+f x)^3} \, dx","IntegrateAlgebraic[(a + b*x)^m/((c + d*x)^m*(e + f*x)^3),x]","\int \frac{(a+b x)^m (c+d x)^{-m}}{(e+f x)^3} \, dx","\frac{(b c-a d) (a+b x)^{m+1} (c+d x)^{-m-1} (b (2 d e-c f (1-m))-a d f (m+1)) \, _2F_1\left(2,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{2 (m+1) (b e-a f)^3 (d e-c f)}-\frac{f (a+b x)^{m+1} (c+d x)^{1-m}}{2 (e+f x)^2 (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3068,0,0,309,0.0674535,"\int \frac{(a+b x)^m (c+d x)^{-m}}{(e+f x)^4} \, dx","IntegrateAlgebraic[(a + b*x)^m/((c + d*x)^m*(e + f*x)^4),x]","\int \frac{(a+b x)^m (c+d x)^{-m}}{(e+f x)^4} \, dx","-\frac{(b c-a d) (a+b x)^{m+1} (c+d x)^{-m-1} \left(-a^2 d^2 f^2 \left(m^2+3 m+2\right)+2 a b d f (m+1) (3 d e-c f (1-m))-\left(b^2 \left(c^2 f^2 \left(m^2-3 m+2\right)-6 c d e f (1-m)+6 d^2 e^2\right)\right)\right) \, _2F_1\left(2,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{6 (m+1) (b e-a f)^4 (d e-c f)^2}-\frac{f (a+b x)^{m+1} (c+d x)^{1-m} (b (4 d e-c f (2-m))-a d f (m+2))}{6 (e+f x)^2 (b e-a f)^2 (d e-c f)^2}-\frac{f (a+b x)^{m+1} (c+d x)^{1-m}}{3 (e+f x)^3 (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3069,0,0,179,0.0377886,"\int \frac{(1+2 x)^{-m} (2+3 x)^m}{(5-4 x)^5} \, dx","IntegrateAlgebraic[(2 + 3*x)^m/((5 - 4*x)^5*(1 + 2*x)^m),x]","\int \frac{(1+2 x)^{-m} (2+3 x)^m}{(5-4 x)^5} \, dx","\frac{\left(m^3+132 m^2+4358 m+32010\right) (3 x+2)^{m-1} (2 x+1)^{1-m} \, _2F_1\left(2,1-m;2-m;\frac{23 (2 x+1)}{14 (3 x+2)}\right)}{2453889228 (1-m)}+\frac{\left(2 m^2+220 m+4359\right) (3 x+2)^{m+1} (2 x+1)^{1-m}}{25039686 (5-4 x)^2}+\frac{(m+66) (3 x+2)^{m+1} (2 x+1)^{1-m}}{77763 (5-4 x)^3}+\frac{(3 x+2)^{m+1} (2 x+1)^{1-m}}{322 (5-4 x)^4}",1,"Could not integrate","F",-1
3070,0,0,130,0.0613012,"\int (a+b x)^m (c+d x)^{-1-m} (e+f x)^p \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-1 - m)*(e + f*x)^p,x]","\int (a+b x)^m (c+d x)^{-1-m} (e+f x)^p \, dx","\frac{(a+b x)^{m+1} (c+d x)^{-m} (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+1;m+1,-p;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{(m+1) (b c-a d)}",1,"Could not integrate","F",-1
3071,0,0,142,0.0877302,"\int (5-4 x)^3 (1+2 x)^{-1-m} (2+3 x)^m \, dx","IntegrateAlgebraic[(5 - 4*x)^3*(1 + 2*x)^(-1 - m)*(2 + 3*x)^m,x]","\int (5-4 x)^3 (1+2 x)^{-1-m} (2+3 x)^m \, dx","\frac{2^{-m-1} \left(-4 m^3+390 m^2-8324 m+27783\right) (2 x+1)^{1-m} \, _2F_1(1-m,-m;2-m;-3 (2 x+1))}{27 (1-m) m}-\frac{(3 x+2)^{m+1} \left(4 m^2-4 (109-2 m) m x-512 m+9261\right) (2 x+1)^{-m}}{27 m}-\frac{2}{9} (5-4 x)^2 (3 x+2)^{m+1} (2 x+1)^{-m}",1,"Could not integrate","F",-1
3072,0,0,121,0.0927677,"\int (5-4 x)^2 (1+2 x)^{-1-m} (2+3 x)^m \, dx","IntegrateAlgebraic[(5 - 4*x)^2*(1 + 2*x)^(-1 - m)*(2 + 3*x)^m,x]","\int (5-4 x)^2 (1+2 x)^{-1-m} (2+3 x)^m \, dx","\frac{2^{-m-1} \left(2 m^2-86 m+441\right) (2 x+1)^{1-m} \, _2F_1(1-m,-m;2-m;-3 (2 x+1))}{3 (1-m) m}-\frac{1}{3} (5-4 x) (3 x+2)^{m+1} (2 x+1)^{-m}-\frac{7 (21-m) (3 x+2)^{m+1} (2 x+1)^{-m}}{3 m}",1,"Could not integrate","F",-1
3073,0,0,152,0.1076608,"\int (a+b x)^m (c+d x)^{-1-m} (e+f x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-1 - m)*(e + f*x),x]","\int (a+b x)^m (c+d x)^{-1-m} (e+f x) \, dx","\frac{(a+b x)^{m+1} (d e-c f) (c+d x)^{-m}}{d m (b c-a d)}-\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m (a d f m+b (d e-c f (m+1))) \, _2F_1\left(m,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{b d m (m+1) (b c-a d)}",1,"Could not integrate","F",-1
3074,0,0,75,0.0318971,"\int (a+b x)^m (c+d x)^{-1-m} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-1 - m),x]","\int (a+b x)^m (c+d x)^{-1-m} \, dx","-\frac{(a+b x)^m (c+d x)^{-m} \left(-\frac{d (a+b x)}{b c-a d}\right)^{-m} \, _2F_1\left(-m,-m;1-m;\frac{b (c+d x)}{b c-a d}\right)}{d m}",1,"Could not integrate","F",-1
3075,0,0,72,0.145032,"\int \frac{(a+b x)^m (c+d x)^{-1-m}}{e+f x} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(-1 - m))/(e + f*x),x]","\int \frac{(a+b x)^m (c+d x)^{-1-m}}{e+f x} \, dx","-\frac{(a+b x)^m (c+d x)^{-m} \, _2F_1\left(1,-m;1-m;\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{m (d e-c f)}",1,"Could not integrate","F",-1
3076,0,0,158,0.0692333,"\int \frac{(a+b x)^m (c+d x)^{-1-m}}{(e+f x)^2} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(-1 - m))/(e + f*x)^2,x]","\int \frac{(a+b x)^m (c+d x)^{-1-m}}{(e+f x)^2} \, dx","\frac{(a+b x)^{m+1} (c+d x)^{-m-1} (a d f (m+1)-b (c f m+d e)) \, _2F_1\left(2,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{m (m+1) (b e-a f)^2 (d e-c f)}+\frac{d (a+b x)^{m+1} (c+d x)^{-m}}{m (e+f x) (b c-a d) (d e-c f)}",1,"Could not integrate","F",-1
3077,0,0,283,0.0722134,"\int \frac{(a+b x)^m (c+d x)^{-1-m}}{(e+f x)^3} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(-1 - m))/(e + f*x)^3,x]","\int \frac{(a+b x)^m (c+d x)^{-1-m}}{(e+f x)^3} \, dx","\frac{(a+b x)^m (c+d x)^{-m} \left(-a^2 d^2 f^2 \left(m^2+3 m+2\right)+2 a b d f (m+1) (c f m+2 d e)-\left(b^2 \left(-c^2 f^2 (1-m) m+4 c d e f m+2 d^2 e^2\right)\right)\right) \, _2F_1\left(1,-m;1-m;\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{2 m (b e-a f)^2 (d e-c f)^3}-\frac{f (a+b x)^{m+1} (c+d x)^{-m} (b (3 d e-c f (1-m))-a d f (m+2))}{2 (e+f x) (b e-a f)^2 (d e-c f)^2}-\frac{f (a+b x)^{m+1} (c+d x)^{-m}}{2 (e+f x)^2 (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3078,0,0,498,0.072558,"\int \frac{(a+b x)^m (c+d x)^{-1-m}}{(e+f x)^4} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(-1 - m))/(e + f*x)^4,x]","\int \frac{(a+b x)^m (c+d x)^{-1-m}}{(e+f x)^4} \, dx","-\frac{f (a+b x)^{m+1} (c+d x)^{-m} \left(a^2 d^2 f^2 \left(m^2+5 m+6\right)-a b d f \left(d e (8 m+15)-c f \left(-2 m^2-2 m+3\right)\right)+b^2 \left(c^2 f^2 \left(m^2-3 m+2\right)-c d e f (7-8 m)+11 d^2 e^2\right)\right)}{6 (e+f x) (b e-a f)^3 (d e-c f)^3}+\frac{(a+b x)^m (c+d x)^{-m} \left(a^3 d^3 f^3 \left(m^3+6 m^2+11 m+6\right)-3 a^2 b d^2 f^2 \left(m^2+3 m+2\right) (c f m+3 d e)+3 a b^2 d f (m+1) \left(-c^2 f^2 (1-m) m+6 c d e f m+6 d^2 e^2\right)-\left(b^3 \left(c^3 f^3 m \left(m^2-3 m+2\right)-9 c^2 d e f^2 (1-m) m+18 c d^2 e^2 f m+6 d^3 e^3\right)\right)\right) \, _2F_1\left(1,-m;1-m;\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{6 m (b e-a f)^3 (d e-c f)^4}-\frac{f (a+b x)^{m+1} (c+d x)^{-m} (b (5 d e-c f (2-m))-a d f (m+3))}{6 (e+f x)^2 (b e-a f)^2 (d e-c f)^2}-\frac{f (a+b x)^{m+1} (c+d x)^{-m}}{3 (e+f x)^3 (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3079,0,0,131,0.0612048,"\int (a+b x)^m (c+d x)^{-2-m} (e+f x)^p \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-2 - m)*(e + f*x)^p,x]","\int (a+b x)^m (c+d x)^{-2-m} (e+f x)^p \, dx","\frac{b (a+b x)^{m+1} (c+d x)^{-m} (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+1;m+2,-p;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{(m+1) (b c-a d)^2}",1,"Could not integrate","F",-1
3080,0,0,132,0.1048741,"\int (5-4 x)^3 (1+2 x)^{-2-m} (2+3 x)^m \, dx","IntegrateAlgebraic[(5 - 4*x)^3*(1 + 2*x)^(-2 - m)*(2 + 3*x)^m,x]","\int (5-4 x)^3 (1+2 x)^{-2-m} (2+3 x)^m \, dx","\frac{2^{-m} \left(2 m^2-128 m+1323\right) (2 x+1)^{-m} \, _2F_1(-m,-m;1-m;-3 (2 x+1))}{9 m}-\frac{(3 x+2)^{m+1} \left(4 m^2-8 (43-m) (m+1) x-315 m+2768\right) (2 x+1)^{-m-1}}{9 (m+1)}-\frac{1}{3} (5-4 x)^2 (3 x+2)^{m+1} (2 x+1)^{-m-1}",1,"Could not integrate","F",-1
3081,0,0,204,0.1228988,"\int (a+b x)^m (c+d x)^{-2-m} (e+f x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-2 - m)*(e + f*x)^2,x]","\int (a+b x)^m (c+d x)^{-2-m} (e+f x)^2 \, dx","-\frac{f (a+b x)^m (c+d x)^{-m} \left(-\frac{d (a+b x)}{b c-a d}\right)^{-m} (a d f m+b (2 d e-c f (m+2))) \, _2F_1\left(-m,-m;1-m;\frac{b (c+d x)}{b c-a d}\right)}{b d^3 m}+\frac{(a+b x)^{m+1} (d e-c f) (c+d x)^{-m-1} (a d f (m+1)+b (d e-c f (m+2)))}{b d^2 (m+1) (b c-a d)}+\frac{f (e+f x) (a+b x)^{m+1} (c+d x)^{-m-1}}{b d}",1,"Could not integrate","F",-1
3082,0,0,124,0.0559041,"\int (a+b x)^m (c+d x)^{-2-m} (e+f x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-2 - m)*(e + f*x),x]","\int (a+b x)^m (c+d x)^{-2-m} (e+f x) \, dx","\frac{(a+b x)^{m+1} (d e-c f) (c+d x)^{-m-1}}{d (m+1) (b c-a d)}-\frac{f (a+b x)^m (c+d x)^{-m} \left(-\frac{d (a+b x)}{b c-a d}\right)^{-m} \, _2F_1\left(-m,-m;1-m;\frac{b (c+d x)}{b c-a d}\right)}{d^2 m}",1,"Could not integrate","F",-1
3083,0,0,36,0.0320767,"\int (a+b x)^m (c+d x)^{-2-m} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-2 - m),x]","\int (a+b x)^m (c+d x)^{-2-m} \, dx","\frac{(a+b x)^{m+1} (c+d x)^{-m-1}}{(m+1) (b c-a d)}",1,"Could not integrate","F",-1
3084,0,0,120,0.0822575,"\int \frac{(a+b x)^m (c+d x)^{-2-m}}{e+f x} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(-2 - m))/(e + f*x),x]","\int \frac{(a+b x)^m (c+d x)^{-2-m}}{e+f x} \, dx","\frac{f (a+b x)^m (c+d x)^{-m} \, _2F_1\left(1,-m;1-m;\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{m (d e-c f)^2}+\frac{d (a+b x)^{m+1} (c+d x)^{-m-1}}{(m+1) (b c-a d) (d e-c f)}",1,"Could not integrate","F",-1
3085,0,0,233,0.1270093,"\int \frac{(a+b x)^m (c+d x)^{-2-m}}{(e+f x)^2} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(-2 - m))/(e + f*x)^2,x]","\int \frac{(a+b x)^m (c+d x)^{-2-m}}{(e+f x)^2} \, dx","-\frac{f (a+b x)^m (c+d x)^{-m} (a d f (m+2)-b (c f m+2 d e)) \, _2F_1\left(1,-m;1-m;\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{m (b e-a f) (d e-c f)^3}-\frac{d (a+b x)^{m+1} (c+d x)^{-m-1} (a d f (m+2)-b (c f (m+1)+d e))}{(m+1) (b c-a d) (b e-a f) (d e-c f)^2}-\frac{f (a+b x)^{m+1} (c+d x)^{-m-1}}{(e+f x) (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3086,0,0,432,0.1430041,"\int \frac{(a+b x)^m (c+d x)^{-2-m}}{(e+f x)^3} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(-2 - m))/(e + f*x)^3,x]","\int \frac{(a+b x)^m (c+d x)^{-2-m}}{(e+f x)^3} \, dx","-\frac{f (a+b x)^m (c+d x)^{-m} \left(-a^2 d^2 f^2 \left(m^2+5 m+6\right)+2 a b d f (m+2) (c f m+3 d e)-\left(b^2 \left(-c^2 f^2 (1-m) m+6 c d e f m+6 d^2 e^2\right)\right)\right) \, _2F_1\left(1,-m;1-m;\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{2 m (b e-a f)^2 (d e-c f)^4}+\frac{d (a+b x)^{m+1} (c+d x)^{-m-1} \left(a^2 d^2 f^2 \left(m^2+5 m+6\right)-a b d f \left(c f \left(2 m^2+5 m+3\right)+d e (5 m+9)\right)+b^2 \left(-c^2 f^2 \left(1-m^2\right)+5 c d e f (m+1)+2 d^2 e^2\right)\right)}{2 (m+1) (b c-a d) (b e-a f)^2 (d e-c f)^3}-\frac{f (a+b x)^{m+1} (c+d x)^{-m-1} (b (4 d e-c f (1-m))-a d f (m+3))}{2 (e+f x) (b e-a f)^2 (d e-c f)^2}-\frac{f (a+b x)^{m+1} (c+d x)^{-m-1}}{2 (e+f x)^2 (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3087,0,0,133,0.0630969,"\int (a+b x)^m (c+d x)^{-3-m} (e+f x)^p \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-3 - m)*(e + f*x)^p,x]","\int (a+b x)^m (c+d x)^{-3-m} (e+f x)^p \, dx","\frac{b^2 (a+b x)^{m+1} (c+d x)^{-m} (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+1;m+3,-p;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{(m+1) (b c-a d)^3}",1,"Could not integrate","F",-1
3088,0,0,188,0.0843085,"\int (5-4 x)^4 (1+2 x)^{-3-m} (2+3 x)^m \, dx","IntegrateAlgebraic[(5 - 4*x)^4*(1 + 2*x)^(-3 - m)*(2 + 3*x)^m,x]","\int (5-4 x)^4 (1+2 x)^{-3-m} (2+3 x)^m \, dx","-\frac{2^{2-m} \left(m^2-85 m+1323\right) (2 x+1)^{-m} \, _2F_1(-m,-m;1-m;-3 (2 x+1))}{9 m}+\frac{7 (3 x+2)^{m+1} \left(2 \left(8 m^3-530 m^2+1882 m+15209\right) x+3 \left(-2 m^3+108 m^2+485 m+4638\right)\right) (2 x+1)^{-m-2}}{9 \left(m^2+3 m+2\right)}-\frac{1}{3} (5-4 x)^3 (3 x+2)^{m+1} (2 x+1)^{-m-2}-\frac{1}{9} (107-2 m) (5-4 x)^2 (3 x+2)^{m+1} (2 x+1)^{-m-2}",1,"Could not integrate","F",-1
3089,0,0,139,0.0394566,"\int (5-4 x)^3 (1+2 x)^{-3-m} (2+3 x)^m \, dx","IntegrateAlgebraic[(5 - 4*x)^3*(1 + 2*x)^(-3 - m)*(2 + 3*x)^m,x]","\int (5-4 x)^3 (1+2 x)^{-3-m} (2+3 x)^m \, dx","-\frac{2^{1-m} (63-2 m) (2 x+1)^{-m} \, _2F_1(-m,-m;1-m;-3 (2 x+1))}{3 m}+\frac{7 (3 x+2)^{m+1} \left(2 \left(-8 m^2+102 m+677\right) x+3 \left(2 m^2-m+186\right)\right) (2 x+1)^{-m-2}}{3 \left(m^2+3 m+2\right)}-\frac{2}{3} (5-4 x)^2 (3 x+2)^{m+1} (2 x+1)^{-m-2}",1,"Could not integrate","F",-1
3090,0,0,205,0.0650758,"\int (a+b x)^m (c+d x)^{-3-m} (e+f x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-3 - m)*(e + f*x)^2,x]","\int (a+b x)^m (c+d x)^{-3-m} (e+f x)^2 \, dx","-\frac{f^2 (a+b x)^m (c+d x)^{-m} \left(-\frac{d (a+b x)}{b c-a d}\right)^{-m} \, _2F_1\left(-m,-m;1-m;\frac{b (c+d x)}{b c-a d}\right)}{d^3 m}+\frac{(a+b x)^{m+1} (d e-c f)^2 (c+d x)^{-m-2}}{d^2 (m+2) (b c-a d)}-\frac{(a+b x)^{m+1} (d e-c f) (c+d x)^{-m-1} (2 a d f (m+2)-b (c f (2 m+3)+d e))}{d^2 (m+1) (m+2) (b c-a d)^2}",1,"Could not integrate","F",-1
3091,0,0,114,0.1301365,"\int (a+b x)^m (c+d x)^{-3-m} (e+f x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-3 - m)*(e + f*x),x]","\int (a+b x)^m (c+d x)^{-3-m} (e+f x) \, dx","\frac{(a+b x)^{m+1} (d e-c f) (c+d x)^{-m-2}}{d (m+2) (b c-a d)}-\frac{(a+b x)^{m+1} (c+d x)^{-m-1} (a d f (m+2)-b (c f (m+1)+d e))}{d (m+1) (m+2) (b c-a d)^2}",1,"Could not integrate","F",-1
3092,0,0,79,0.0322996,"\int (a+b x)^m (c+d x)^{-3-m} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-3 - m),x]","\int (a+b x)^m (c+d x)^{-3-m} \, dx","\frac{(a+b x)^{m+1} (c+d x)^{-m-2}}{(m+2) (b c-a d)}+\frac{b (a+b x)^{m+1} (c+d x)^{-m-1}}{(m+1) (m+2) (b c-a d)^2}",1,"Could not integrate","F",-1
3093,0,0,196,0.1386761,"\int \frac{(a+b x)^m (c+d x)^{-3-m}}{e+f x} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(-3 - m))/(e + f*x),x]","\int \frac{(a+b x)^m (c+d x)^{-3-m}}{e+f x} \, dx","-\frac{f^2 (a+b x)^m (c+d x)^{-m} \, _2F_1\left(1,-m;1-m;\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{m (d e-c f)^3}+\frac{d (a+b x)^{m+1} (c+d x)^{-m-2}}{(m+2) (b c-a d) (d e-c f)}+\frac{d (a+b x)^{m+1} (c+d x)^{-m-1} (a d f (m+2)+b (d e-c f (m+3)))}{(m+1) (m+2) (b c-a d)^2 (d e-c f)^2}",1,"Could not integrate","F",-1
3094,0,0,384,0.0698212,"\int \frac{(a+b x)^m (c+d x)^{-3-m}}{(e+f x)^2} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(-3 - m))/(e + f*x)^2,x]","\int \frac{(a+b x)^m (c+d x)^{-3-m}}{(e+f x)^2} \, dx","-\frac{d (a+b x)^{m+1} (c+d x)^{-m-1} \left(a^2 d^2 f^2 \left(m^2+5 m+6\right)-a b d f \left(c f \left(2 m^2+8 m+9\right)+d e (2 m+3)\right)-\left(b^2 \left(-c^2 f^2 \left(m^2+3 m+2\right)-c d e f (2 m+5)+d^2 e^2\right)\right)\right)}{(m+1) (m+2) (b c-a d)^2 (b e-a f) (d e-c f)^3}+\frac{f^2 (a+b x)^m (c+d x)^{-m} (a d f (m+3)-b (c f m+3 d e)) \, _2F_1\left(1,-m;1-m;\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{m (b e-a f) (d e-c f)^4}-\frac{d (a+b x)^{m+1} (c+d x)^{-m-2} (a d f (m+3)-b (c f (m+2)+d e))}{(m+2) (b c-a d) (b e-a f) (d e-c f)^2}-\frac{f (a+b x)^{m+1} (c+d x)^{-m-2}}{(e+f x) (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3095,0,0,133,0.0628441,"\int (a+b x)^m (c+d x)^{-4-m} (e+f x)^p \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-4 - m)*(e + f*x)^p,x]","\int (a+b x)^m (c+d x)^{-4-m} (e+f x)^p \, dx","\frac{b^3 (a+b x)^{m+1} (c+d x)^{-m} (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+1;m+4,-p;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{(m+1) (b c-a d)^4}",1,"Could not integrate","F",-1
3096,0,0,333,0.1242963,"\int (5-4 x)^4 (1+2 x)^{-4-m} (2+3 x)^m \, dx","IntegrateAlgebraic[(5 - 4*x)^4*(1 + 2*x)^(-4 - m)*(2 + 3*x)^m,x]","\int (5-4 x)^4 (1+2 x)^{-4-m} (2+3 x)^m \, dx","\frac{2^{3-m} (42-m) (2 x+1)^{-m} \, _2F_1(-m,-m;1-m;-3 (2 x+1))}{3 m}+\frac{14 (15-2 m) \left(2 m^2+52 m+579\right) (3 x+2)^{m+1} (2 x+1)^{-m-2}}{9 (m+2) (m+3)}-\frac{14 (15-2 m) \left(2 m^2+52 m+579\right) (3 x+2)^{m+1} (2 x+1)^{-m-1}}{3 (m+3) \left(m^2+3 m+2\right)}-\frac{2}{3} (5-4 x)^3 (3 x+2)^{m+1} (2 x+1)^{-m-3}-\frac{49 (15-2 m) (2 m+27) (3 x+2)^{m+1} (2 x+1)^{-m-3}}{9 (m+3)}+\frac{14}{9} (15-2 m) (5-4 x) (3 x+2)^{m+1} (2 x+1)^{-m-3}+\frac{196 (42-m) (3 x+2)^{m+1} (2 x+1)^{-m-2}}{3 (m+2)}-\frac{28 (42-m) (4 m+29) (3 x+2)^{m+1} (2 x+1)^{-m-1}}{3 (m+1) (m+2)}",1,"Could not integrate","F",-1
3097,0,0,406,0.067993,"\int (a+b x)^m (c+d x)^{-4-m} (e+f x)^3 \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-4 - m)*(e + f*x)^3,x]","\int (a+b x)^m (c+d x)^{-4-m} (e+f x)^3 \, dx","\frac{2 b^2 (a+b x)^{m+1} (d e-c f)^3 (c+d x)^{-m-1}}{d^3 (m+1) (m+2) (m+3) (b c-a d)^3}-\frac{f^3 (a+b x)^m (c+d x)^{-m} \left(-\frac{d (a+b x)}{b c-a d}\right)^{-m} \, _2F_1\left(-m,-m;1-m;\frac{b (c+d x)}{b c-a d}\right)}{d^4 m}+\frac{3 f^2 (a+b x)^{m+1} (d e-c f) (c+d x)^{-m-1}}{d^3 (m+1) (b c-a d)}+\frac{(a+b x)^{m+1} (d e-c f)^3 (c+d x)^{-m-3}}{d^3 (m+3) (b c-a d)}+\frac{3 f (a+b x)^{m+1} (d e-c f)^2 (c+d x)^{-m-2}}{d^3 (m+2) (b c-a d)}+\frac{2 b (a+b x)^{m+1} (d e-c f)^3 (c+d x)^{-m-2}}{d^3 (m+2) (m+3) (b c-a d)^2}+\frac{3 b f (a+b x)^{m+1} (d e-c f)^2 (c+d x)^{-m-1}}{d^3 (m+1) (m+2) (b c-a d)^2}",1,"Could not integrate","F",-1
3098,0,0,353,0.0658158,"\int (a+b x)^m (c+d x)^{-4-m} (e+f x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-4 - m)*(e + f*x)^2,x]","\int (a+b x)^m (c+d x)^{-4-m} (e+f x)^2 \, dx","\frac{(a+b x)^{m+1} (c+d x)^{-m-2} \left(a^2 d^2 f^2 \left(m^2+5 m+6\right)-2 a b d f (m+3) (c f (m+1)+d e)+b^2 \left(c^2 f^2 \left(m^2+3 m+2\right)+2 c d e f (m+1)+2 d^2 e^2\right)\right)}{b d^2 (m+2) (m+3) (b c-a d)^2}+\frac{(a+b x)^{m+1} (c+d x)^{-m-1} \left(a^2 d^2 f^2 \left(m^2+5 m+6\right)-2 a b d f (m+3) (c f (m+1)+d e)+b^2 \left(c^2 f^2 \left(m^2+3 m+2\right)+2 c d e f (m+1)+2 d^2 e^2\right)\right)}{d^2 (m+1) (m+2) (m+3) (b c-a d)^3}-\frac{(a+b x)^{m+1} (d e-c f) (c+d x)^{-m-3} (a d f (m+3)-b (c f (m+2)+d e))}{b d^2 (m+3) (b c-a d)}-\frac{f (e+f x) (a+b x)^{m+1} (c+d x)^{-m-3}}{b d}",1,"Could not integrate","F",-1
3099,0,0,188,0.113391,"\int (a+b x)^m (c+d x)^{-4-m} (e+f x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-4 - m)*(e + f*x),x]","\int (a+b x)^m (c+d x)^{-4-m} (e+f x) \, dx","\frac{(a+b x)^{m+1} (d e-c f) (c+d x)^{-m-3}}{d (m+3) (b c-a d)}-\frac{(a+b x)^{m+1} (c+d x)^{-m-2} (a d f (m+3)-b (c f (m+1)+2 d e))}{d (m+2) (m+3) (b c-a d)^2}-\frac{b (a+b x)^{m+1} (c+d x)^{-m-1} (a d f (m+3)-b (c f (m+1)+2 d e))}{d (m+1) (m+2) (m+3) (b c-a d)^3}",1,"Could not integrate","F",-1
3100,0,0,130,0.032338,"\int (a+b x)^m (c+d x)^{-4-m} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-4 - m),x]","\int (a+b x)^m (c+d x)^{-4-m} \, dx","\frac{2 b^2 (a+b x)^{m+1} (c+d x)^{-m-1}}{(m+1) (m+2) (m+3) (b c-a d)^3}+\frac{(a+b x)^{m+1} (c+d x)^{-m-3}}{(m+3) (b c-a d)}+\frac{2 b (a+b x)^{m+1} (c+d x)^{-m-2}}{(m+2) (m+3) (b c-a d)^2}",1,"Could not integrate","F",-1
3101,0,0,330,0.1477537,"\int \frac{(a+b x)^m (c+d x)^{-4-m}}{e+f x} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(-4 - m))/(e + f*x),x]","\int \frac{(a+b x)^m (c+d x)^{-4-m}}{e+f x} \, dx","\frac{d (a+b x)^{m+1} (c+d x)^{-m-1} \left(a^2 d^2 f^2 \left(m^2+5 m+6\right)+a b d f (m+3) (d e-c f (2 m+5))+b^2 \left(c^2 f^2 \left(m^2+6 m+11\right)-c d e f (m+7)+2 d^2 e^2\right)\right)}{(m+1) (m+2) (m+3) (b c-a d)^3 (d e-c f)^3}+\frac{f^3 (a+b x)^m (c+d x)^{-m} \, _2F_1\left(1,-m;1-m;\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{m (d e-c f)^4}+\frac{d (a+b x)^{m+1} (c+d x)^{-m-3}}{(m+3) (b c-a d) (d e-c f)}+\frac{d (a+b x)^{m+1} (c+d x)^{-m-2} (a d f (m+3)+b (2 d e-c f (m+5)))}{(m+2) (m+3) (b c-a d)^2 (d e-c f)^2}",1,"Could not integrate","F",-1
3102,0,0,634,0.130449,"\int \frac{(a+b x)^m (c+d x)^{-4-m}}{(e+f x)^2} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(-4 - m))/(e + f*x)^2,x]","\int \frac{(a+b x)^m (c+d x)^{-4-m}}{(e+f x)^2} \, dx","-\frac{d (a+b x)^{m+1} (c+d x)^{-m-2} \left(a^2 d^2 f^2 \left(m^2+7 m+12\right)-2 a b d f \left(c f \left(m^2+6 m+10\right)+d e (m+2)\right)-\left(b^2 \left(-c^2 f^2 \left(m^2+5 m+6\right)-2 c d e f (m+4)+2 d^2 e^2\right)\right)\right)}{(m+2) (m+3) (b c-a d)^2 (b e-a f) (d e-c f)^3}-\frac{d (a+b x)^{m+1} (c+d x)^{-m-1} \left(a^3 d^3 f^3 \left(m^3+9 m^2+26 m+24\right)-a^2 b d^2 f^2 (m+3) \left(c f \left(3 m^2+15 m+20\right)+d e (3 m+4)\right)-a b^2 d f \left(-c^2 f^2 \left(3 m^3+21 m^2+50 m+44\right)-2 c d e f \left(3 m^2+15 m+16\right)+2 d^2 e^2 (m+2)\right)-\left(b^3 \left(c^3 f^3 \left(m^3+6 m^2+11 m+6\right)+c^2 d e f^2 \left(3 m^2+17 m+26\right)-2 c d^2 e^2 f (m+5)+2 d^3 e^3\right)\right)\right)}{(m+1) (m+2) (m+3) (b c-a d)^3 (b e-a f) (d e-c f)^4}-\frac{f^3 (a+b x)^m (c+d x)^{-m} (a d f (m+4)-b (c f m+4 d e)) \, _2F_1\left(1,-m;1-m;\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{m (b e-a f) (d e-c f)^5}-\frac{d (a+b x)^{m+1} (c+d x)^{-m-3} (a d f (m+4)-b (c f (m+3)+d e))}{(m+3) (b c-a d) (b e-a f) (d e-c f)^2}-\frac{f (a+b x)^{m+1} (c+d x)^{-m-3}}{(e+f x) (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3103,0,0,133,0.0627719,"\int (a+b x)^m (c+d x)^{-5-m} (e+f x)^p \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-5 - m)*(e + f*x)^p,x]","\int (a+b x)^m (c+d x)^{-5-m} (e+f x)^p \, dx","\frac{b^4 (a+b x)^{m+1} (c+d x)^{-m} (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+1;m+5,-p;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{(m+1) (b c-a d)^5}",1,"Could not integrate","F",-1
3104,0,0,546,0.1013788,"\int (5-4 x)^5 (1+2 x)^{-5-m} (2+3 x)^m \, dx","IntegrateAlgebraic[(5 - 4*x)^5*(1 + 2*x)^(-5 - m)*(2 + 3*x)^m,x]","\int (5-4 x)^5 (1+2 x)^{-5-m} (2+3 x)^m \, dx","-\frac{2^{3-m} (105-2 m) (2 x+1)^{-m-3} \, _2F_1(-m-3,-m-3;-m-2;-3 (2 x+1))}{81 (m+3)}-\frac{322 (13-2 m) \left(2 m^2+52 m+579\right) (3 x+2)^{m+1} (2 x+1)^{-m-2}}{3 (m+2) (m+3) (m+4)}-\frac{48668 (105-2 m) (3 x+2)^{m+1} (2 x+1)^{-m-2}}{27 \left(m^2+5 m+6\right)}+\frac{4232 (105-2 m) (3 x+2)^{m+2} (2 x+1)^{-m-2}}{9 \left(m^2+5 m+6\right)}+\frac{322 (13-2 m) \left(2 m^2+52 m+579\right) (3 x+2)^{m+1} (2 x+1)^{-m-1}}{(m+3) (m+4) \left(m^2+3 m+2\right)}+\frac{48668 (105-2 m) (3 x+2)^{m+1} (2 x+1)^{-m-1}}{9 \left(m^3+6 m^2+11 m+6\right)}-\frac{2}{3} (5-4 x)^4 (3 x+2)^{m+1} (2 x+1)^{-m-4}-\frac{7 (13-2 m) (5-4 x)^3 (3 x+2)^{m+1} (2 x+1)^{-m-4}}{3 (m+4)}+\frac{1127 (13-2 m) (2 m+27) (3 x+2)^{m+1} (2 x+1)^{-m-3}}{3 (m+3) (m+4)}-\frac{322 (13-2 m) (5-4 x) (3 x+2)^{m+1} (2 x+1)^{-m-3}}{3 (m+4)}+\frac{24334 (105-2 m) (3 x+2)^{m+1} (2 x+1)^{-m-3}}{81 (m+3)}-\frac{4232 (105-2 m) (3 x+2)^{m+2} (2 x+1)^{-m-3}}{27 (m+3)}+\frac{736 (105-2 m) (3 x+2)^{m+3} (2 x+1)^{-m-3}}{27 (m+3)}",1,"Could not integrate","F",-1
3105,0,0,650,0.0708348,"\int (a+b x)^m (c+d x)^{-5-m} (e+f x)^4 \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-5 - m)*(e + f*x)^4,x]","\int (a+b x)^m (c+d x)^{-5-m} (e+f x)^4 \, dx","\frac{6 b^3 (a+b x)^{m+1} (d e-c f)^4 (c+d x)^{-m-1}}{d^4 (m+1) (m+2) (m+3) (m+4) (b c-a d)^4}+\frac{6 b^2 (a+b x)^{m+1} (d e-c f)^4 (c+d x)^{-m-2}}{d^4 (m+2) (m+3) (m+4) (b c-a d)^3}+\frac{8 b^2 f (a+b x)^{m+1} (d e-c f)^3 (c+d x)^{-m-1}}{d^4 (m+1) (m+2) (m+3) (b c-a d)^3}-\frac{f^4 (a+b x)^m (c+d x)^{-m} \left(-\frac{d (a+b x)}{b c-a d}\right)^{-m} \, _2F_1\left(-m,-m;1-m;\frac{b (c+d x)}{b c-a d}\right)}{d^5 m}+\frac{4 f^3 (a+b x)^{m+1} (d e-c f) (c+d x)^{-m-1}}{d^4 (m+1) (b c-a d)}+\frac{6 f^2 (a+b x)^{m+1} (d e-c f)^2 (c+d x)^{-m-2}}{d^4 (m+2) (b c-a d)}+\frac{6 b f^2 (a+b x)^{m+1} (d e-c f)^2 (c+d x)^{-m-1}}{d^4 (m+1) (m+2) (b c-a d)^2}+\frac{(a+b x)^{m+1} (d e-c f)^4 (c+d x)^{-m-4}}{d^4 (m+4) (b c-a d)}+\frac{4 f (a+b x)^{m+1} (d e-c f)^3 (c+d x)^{-m-3}}{d^4 (m+3) (b c-a d)}+\frac{3 b (a+b x)^{m+1} (d e-c f)^4 (c+d x)^{-m-3}}{d^4 (m+3) (m+4) (b c-a d)^2}+\frac{8 b f (a+b x)^{m+1} (d e-c f)^3 (c+d x)^{-m-2}}{d^4 (m+2) (m+3) (b c-a d)^2}",1,"Could not integrate","F",-1
3106,0,0,460,0.0680414,"\int (a+b x)^m (c+d x)^{-5-m} (e+f x)^3 \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-5 - m)*(e + f*x)^3,x]","\int (a+b x)^m (c+d x)^{-5-m} (e+f x)^3 \, dx","\frac{3 (b e-a f) (a+b x)^{m+1} (c+d x)^{-m-2} \left(a^2 d^2 f^2 \left(m^2+5 m+6\right)-2 a b d f (m+3) (c f (m+1)+d e)+b^2 \left(c^2 f^2 \left(m^2+3 m+2\right)+2 c d e f (m+1)+2 d^2 e^2\right)\right)}{b d^2 (m+2) (m+3) (m+4) (b c-a d)^3}+\frac{3 (b e-a f) (a+b x)^{m+1} (c+d x)^{-m-1} \left(a^2 d^2 f^2 \left(m^2+5 m+6\right)-2 a b d f (m+3) (c f (m+1)+d e)+b^2 \left(c^2 f^2 \left(m^2+3 m+2\right)+2 c d e f (m+1)+2 d^2 e^2\right)\right)}{d^2 (m+1) (m+2) (m+3) (m+4) (b c-a d)^4}-\frac{3 (b e-a f) (a+b x)^{m+1} (d e-c f) (c+d x)^{-m-3} (a d f (m+3)-b (c f (m+2)+d e))}{b d^2 (m+3) (m+4) (b c-a d)^2}+\frac{(e+f x)^3 (a+b x)^{m+1} (c+d x)^{-m-4}}{(m+4) (b c-a d)}-\frac{3 f (e+f x) (b e-a f) (a+b x)^{m+1} (c+d x)^{-m-3}}{b d (m+4) (b c-a d)}",1,"Could not integrate","F",-1
3107,0,0,494,0.1318234,"\int (a+b x)^m (c+d x)^{-5-m} (e+f x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-5 - m)*(e + f*x)^2,x]","\int (a+b x)^m (c+d x)^{-5-m} (e+f x)^2 \, dx","\frac{(a+b x)^{m+1} (c+d x)^{-m-3} \left(a^2 d^2 f^2 \left(m^2+7 m+12\right)-2 a b d f (m+4) (c f (m+1)+2 d e)+b^2 \left(c^2 f^2 \left(m^2+3 m+2\right)+4 c d e f (m+1)+6 d^2 e^2\right)\right)}{2 b d^2 (m+3) (m+4) (b c-a d)^2}+\frac{(a+b x)^{m+1} (c+d x)^{-m-2} \left(a^2 d^2 f^2 \left(m^2+7 m+12\right)-2 a b d f (m+4) (c f (m+1)+2 d e)+b^2 \left(c^2 f^2 \left(m^2+3 m+2\right)+4 c d e f (m+1)+6 d^2 e^2\right)\right)}{d^2 (m+2) (m+3) (m+4) (b c-a d)^3}+\frac{b (a+b x)^{m+1} (c+d x)^{-m-1} \left(a^2 d^2 f^2 \left(m^2+7 m+12\right)-2 a b d f (m+4) (c f (m+1)+2 d e)+b^2 \left(c^2 f^2 \left(m^2+3 m+2\right)+4 c d e f (m+1)+6 d^2 e^2\right)\right)}{d^2 (m+1) (m+2) (m+3) (m+4) (b c-a d)^4}-\frac{(a+b x)^{m+1} (d e-c f) (c+d x)^{-m-4} (a d f (m+4)-b (c f (m+2)+2 d e))}{2 b d^2 (m+4) (b c-a d)}-\frac{f (e+f x) (a+b x)^{m+1} (c+d x)^{-m-4}}{2 b d}",1,"Could not integrate","F",-1
3108,0,0,268,0.1065957,"\int (a+b x)^m (c+d x)^{-5-m} (e+f x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-5 - m)*(e + f*x),x]","\int (a+b x)^m (c+d x)^{-5-m} (e+f x) \, dx","-\frac{2 b^2 (a+b x)^{m+1} (c+d x)^{-m-1} (a d f (m+4)-b (c f (m+1)+3 d e))}{d (m+1) (m+2) (m+3) (m+4) (b c-a d)^4}+\frac{(a+b x)^{m+1} (d e-c f) (c+d x)^{-m-4}}{d (m+4) (b c-a d)}-\frac{(a+b x)^{m+1} (c+d x)^{-m-3} (a d f (m+4)-b (c f (m+1)+3 d e))}{d (m+3) (m+4) (b c-a d)^2}-\frac{2 b (a+b x)^{m+1} (c+d x)^{-m-2} (a d f (m+4)-b (c f (m+1)+3 d e))}{d (m+2) (m+3) (m+4) (b c-a d)^3}",1,"Could not integrate","F",-1
3109,0,0,185,0.0321219,"\int (a+b x)^m (c+d x)^{-5-m} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-5 - m),x]","\int (a+b x)^m (c+d x)^{-5-m} \, dx","\frac{6 b^3 (a+b x)^{m+1} (c+d x)^{-m-1}}{(m+1) (m+2) (m+3) (m+4) (b c-a d)^4}+\frac{6 b^2 (a+b x)^{m+1} (c+d x)^{-m-2}}{(m+2) (m+3) (m+4) (b c-a d)^3}+\frac{(a+b x)^{m+1} (c+d x)^{-m-4}}{(m+4) (b c-a d)}+\frac{3 b (a+b x)^{m+1} (c+d x)^{-m-3}}{(m+3) (m+4) (b c-a d)^2}",1,"Could not integrate","F",-1
3110,0,0,557,0.1403865,"\int \frac{(a+b x)^m (c+d x)^{-5-m}}{e+f x} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(-5 - m))/(e + f*x),x]","\int \frac{(a+b x)^m (c+d x)^{-5-m}}{e+f x} \, dx","\frac{d (a+b x)^{m+1} (c+d x)^{-m-2} \left(a^2 d^2 f^2 \left(m^2+7 m+12\right)+2 a b d f (m+4) (d e-c f (m+4))+b^2 \left(c^2 f^2 \left(m^2+9 m+26\right)-2 c d e f (m+10)+6 d^2 e^2\right)\right)}{(m+2) (m+3) (m+4) (b c-a d)^3 (d e-c f)^3}+\frac{d (a+b x)^{m+1} (c+d x)^{-m-1} \left(a^3 d^3 f^3 \left(m^3+9 m^2+26 m+24\right)+a^2 b d^2 f^2 \left(m^2+7 m+12\right) (d e-c f (3 m+7))+a b^2 d f (m+4) \left(c^2 f^2 \left(3 m^2+17 m+26\right)-2 c d e f (m+5)+2 d^2 e^2\right)+b^3 \left(-c^3 f^3 \left(m^3+10 m^2+35 m+50\right)+c^2 d e f^2 \left(m^2+11 m+46\right)-2 c d^2 e^2 f (m+13)+6 d^3 e^3\right)\right)}{(m+1) (m+2) (m+3) (m+4) (b c-a d)^4 (d e-c f)^4}-\frac{f^4 (a+b x)^m (c+d x)^{-m} \, _2F_1\left(1,-m;1-m;\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{m (d e-c f)^5}+\frac{d (a+b x)^{m+1} (c+d x)^{-m-4}}{(m+4) (b c-a d) (d e-c f)}+\frac{d (a+b x)^{m+1} (c+d x)^{-m-3} (a d f (m+4)+b (3 d e-c f (m+7)))}{(m+3) (m+4) (b c-a d)^2 (d e-c f)^2}",1,"Could not integrate","F",-1
3111,0,0,131,0.1166286,"\int (a+b x)^m (c+d x)^{1-m} (e+f x)^p \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(1 - m)*(e + f*x)^p,x]","\int (a+b x)^m (c+d x)^{1-m} (e+f x)^p \, dx","\frac{(b c-a d) (a+b x)^{m+1} (c+d x)^{-m} (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+1;m-1,-p;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^2 (m+1)}",1,"Could not integrate","F",-1
3112,0,0,445,0.1070538,"\int (a+b x)^m (c+d x)^{1-m} (e+f x)^3 \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(1 - m)*(e + f*x)^3,x]","\int (a+b x)^m (c+d x)^{1-m} (e+f x)^3 \, dx","\frac{f (a+b x)^{m+1} (c+d x)^{2-m} \left(a^2 d^2 f^2 \left(m^2-7 m+12\right)-a b d f \left(15 d e (3-m)-c f \left(-2 m^2+2 m+9\right)\right)-3 b d f x (a d f (4-m)-b (7 d e-c f (m+3)))+b^2 \left(c^2 f^2 \left(m^2+5 m+6\right)-15 c d e f (m+2)+48 d^2 e^2\right)\right)}{60 b^3 d^3}-\frac{(b c-a d) (a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(a^3 d^3 f^3 \left(-m^3+9 m^2-26 m+24\right)-3 a^2 b d^2 f^2 \left(m^2-5 m+6\right) (5 d e-c f (m+1))+3 a b^2 d f (2-m) \left(c^2 f^2 \left(m^2+3 m+2\right)-10 c d e f (m+1)+20 d^2 e^2\right)-\left(b^3 \left(-c^3 f^3 \left(m^3+6 m^2+11 m+6\right)+15 c^2 d e f^2 \left(m^2+3 m+2\right)-60 c d^2 e^2 f (m+1)+60 d^3 e^3\right)\right)\right) \, _2F_1\left(m-1,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{60 b^5 d^3 (m+1)}+\frac{f (e+f x)^2 (a+b x)^{m+1} (c+d x)^{2-m}}{5 b d}",1,"Could not integrate","F",-1
3113,0,0,260,0.1045151,"\int (a+b x)^m (c+d x)^{1-m} (e+f x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(1 - m)*(e + f*x)^2,x]","\int (a+b x)^m (c+d x)^{1-m} (e+f x)^2 \, dx","\frac{(b c-a d) (a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(a^2 d^2 f^2 \left(m^2-5 m+6\right)-2 a b d f (2-m) (4 d e-c f (m+1))+b^2 \left(c^2 f^2 \left(m^2+3 m+2\right)-8 c d e f (m+1)+12 d^2 e^2\right)\right) \, _2F_1\left(m-1,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{12 b^4 d^2 (m+1)}-\frac{f (a+b x)^{m+1} (c+d x)^{2-m} (a d f (3-m)-b (5 d e-c f (m+2)))}{12 b^2 d^2}+\frac{f (e+f x) (a+b x)^{m+1} (c+d x)^{2-m}}{4 b d}",1,"Could not integrate","F",-1
3114,0,0,145,0.0511708,"\int (a+b x)^m (c+d x)^{1-m} (e+f x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(1 - m)*(e + f*x),x]","\int (a+b x)^m (c+d x)^{1-m} (e+f x) \, dx","\frac{f (a+b x)^{m+1} (c+d x)^{2-m}}{3 b d}-\frac{(b c-a d) (a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m (a d f (2-m)-b (3 d e-c f (m+1))) \, _2F_1\left(m-1,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{3 b^3 d (m+1)}",1,"Could not integrate","F",-1
3115,0,0,82,0.0282901,"\int (a+b x)^m (c+d x)^{1-m} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(1 - m),x]","\int (a+b x)^m (c+d x)^{1-m} \, dx","\frac{(b c-a d) (a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m-1,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{b^2 (m+1)}",1,"Could not integrate","F",-1
3116,0,0,230,0.0760372,"\int \frac{(a+b x)^m (c+d x)^{1-m}}{e+f x} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(1 - m))/(e + f*x),x]","\int \frac{(a+b x)^m (c+d x)^{1-m}}{e+f x} \, dx","-\frac{(a+b x)^m (d e-c f) (c+d x)^{-m} \, _2F_1\left(1,-m;1-m;\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{f^2 m}+\frac{d (a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m (b (d e-c f (1-m))-a d f m) \, _2F_1\left(m,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{b f^2 m (m+1) (b c-a d)}-\frac{d (a+b x)^{m+1} (d e-c f) (c+d x)^{-m}}{f^2 m (b c-a d)}",1,"Could not integrate","F",-1
3117,0,0,190,0.0621287,"\int \frac{(a+b x)^m (c+d x)^{1-m}}{(e+f x)^2} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(1 - m))/(e + f*x)^2,x]","\int \frac{(a+b x)^m (c+d x)^{1-m}}{(e+f x)^2} \, dx","\frac{(a+b x)^m (c+d x)^{-m} (a d f (1-m)-b (d e-c f m)) \, _2F_1\left(1,m;m+1;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{f^2 m (b e-a f)}-\frac{(a+b x)^m (c+d x)^{1-m}}{f (e+f x)}+\frac{d (a+b x)^m (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m,m;m+1;-\frac{d (a+b x)}{b c-a d}\right)}{f^2 m}",1,"Could not integrate","F",-1
3118,0,0,85,0.0648448,"\int \frac{(a+b x)^m (c+d x)^{1-m}}{(e+f x)^3} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(1 - m))/(e + f*x)^3,x]","\int \frac{(a+b x)^m (c+d x)^{1-m}}{(e+f x)^3} \, dx","\frac{(b c-a d)^2 (a+b x)^{m+1} (c+d x)^{-m-1} \, _2F_1\left(3,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{(m+1) (b e-a f)^3}",1,"Could not integrate","F",-1
3119,0,0,176,0.0681706,"\int \frac{(a+b x)^m (c+d x)^{1-m}}{(e+f x)^4} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(1 - m))/(e + f*x)^4,x]","\int \frac{(a+b x)^m (c+d x)^{1-m}}{(e+f x)^4} \, dx","\frac{(b c-a d)^2 (a+b x)^{m+1} (c+d x)^{-m-1} (b (3 d e-c f (2-m))-a d f (m+1)) \, _2F_1\left(3,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{3 (m+1) (b e-a f)^4 (d e-c f)}-\frac{f (a+b x)^{m+1} (c+d x)^{2-m}}{3 (e+f x)^3 (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3120,0,0,311,0.0707927,"\int \frac{(a+b x)^m (c+d x)^{1-m}}{(e+f x)^5} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(1 - m))/(e + f*x)^5,x]","\int \frac{(a+b x)^m (c+d x)^{1-m}}{(e+f x)^5} \, dx","-\frac{(b c-a d)^2 (a+b x)^{m+1} (c+d x)^{-m-1} \left(-a^2 d^2 f^2 \left(m^2+3 m+2\right)+2 a b d f (m+1) (4 d e-c f (2-m))-\left(b^2 \left(c^2 f^2 \left(m^2-5 m+6\right)-8 c d e f (2-m)+12 d^2 e^2\right)\right)\right) \, _2F_1\left(3,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{12 (m+1) (b e-a f)^5 (d e-c f)^2}-\frac{f (a+b x)^{m+1} (c+d x)^{2-m} (b (5 d e-c f (3-m))-a d f (m+2))}{12 (e+f x)^3 (b e-a f)^2 (d e-c f)^2}-\frac{f (a+b x)^{m+1} (c+d x)^{2-m}}{4 (e+f x)^4 (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3121,0,0,542,0.0769418,"\int \frac{(a+b x)^m (c+d x)^{1-m}}{(e+f x)^6} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(1 - m))/(e + f*x)^6,x]","\int \frac{(a+b x)^m (c+d x)^{1-m}}{(e+f x)^6} \, dx","-\frac{f (a+b x)^{m+1} (c+d x)^{2-m} \left(a^2 d^2 f^2 \left(m^2+5 m+6\right)-a b d f \left(3 d e (4 m+7)-c f \left(-2 m^2+2 m+9\right)\right)+b^2 \left(c^2 f^2 \left(m^2-7 m+12\right)-3 c d e f (11-4 m)+27 d^2 e^2\right)\right)}{60 (e+f x)^3 (b e-a f)^3 (d e-c f)^3}+\frac{(b c-a d)^2 (a+b x)^{m+1} (c+d x)^{-m-1} \left(-a^3 d^3 f^3 \left(m^3+6 m^2+11 m+6\right)+3 a^2 b d^2 f^2 \left(m^2+3 m+2\right) (5 d e-c f (2-m))-3 a b^2 d f (m+1) \left(c^2 f^2 \left(m^2-5 m+6\right)-10 c d e f (2-m)+20 d^2 e^2\right)+b^3 \left(-c^3 f^3 \left(-m^3+9 m^2-26 m+24\right)+15 c^2 d e f^2 \left(m^2-5 m+6\right)-60 c d^2 e^2 f (2-m)+60 d^3 e^3\right)\right) \, _2F_1\left(3,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{60 (m+1) (b e-a f)^6 (d e-c f)^3}-\frac{f (a+b x)^{m+1} (c+d x)^{2-m} (b (7 d e-c f (4-m))-a d f (m+3))}{20 (e+f x)^4 (b e-a f)^2 (d e-c f)^2}-\frac{f (a+b x)^{m+1} (c+d x)^{2-m}}{5 (e+f x)^5 (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3122,0,0,133,0.0597959,"\int (a+b x)^m (c+d x)^{2-m} (e+f x)^p \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(2 - m)*(e + f*x)^p,x]","\int (a+b x)^m (c+d x)^{2-m} (e+f x)^p \, dx","\frac{(b c-a d)^2 (a+b x)^{m+1} (c+d x)^{-m} (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+1;m-2,-p;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^3 (m+1)}",1,"Could not integrate","F",-1
3123,0,0,447,0.0680546,"\int (a+b x)^m (c+d x)^{2-m} (e+f x)^3 \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(2 - m)*(e + f*x)^3,x]","\int (a+b x)^m (c+d x)^{2-m} (e+f x)^3 \, dx","\frac{f (a+b x)^{m+1} (c+d x)^{3-m} \left(a^2 d^2 f^2 \left(m^2-9 m+20\right)-2 a b d f \left(9 d e (4-m)-c f \left(-m^2+2 m+6\right)\right)-4 b d f x (a d f (5-m)-b (8 d e-c f (m+3)))+b^2 \left(c^2 f^2 \left(m^2+5 m+6\right)-18 c d e f (m+2)+70 d^2 e^2\right)\right)}{120 b^3 d^3}-\frac{(b c-a d)^2 (a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(a^3 d^3 f^3 \left(-m^3+12 m^2-47 m+60\right)-3 a^2 b d^2 f^2 \left(m^2-7 m+12\right) (6 d e-c f (m+1))+3 a b^2 d f (3-m) \left(c^2 f^2 \left(m^2+3 m+2\right)-12 c d e f (m+1)+30 d^2 e^2\right)-\left(b^3 \left(-c^3 f^3 \left(m^3+6 m^2+11 m+6\right)+18 c^2 d e f^2 \left(m^2+3 m+2\right)-90 c d^2 e^2 f (m+1)+120 d^3 e^3\right)\right)\right) \, _2F_1\left(m-2,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{120 b^6 d^3 (m+1)}+\frac{f (e+f x)^2 (a+b x)^{m+1} (c+d x)^{3-m}}{6 b d}",1,"Could not integrate","F",-1
3124,0,0,262,0.0651153,"\int (a+b x)^m (c+d x)^{2-m} (e+f x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(2 - m)*(e + f*x)^2,x]","\int (a+b x)^m (c+d x)^{2-m} (e+f x)^2 \, dx","\frac{(b c-a d)^2 (a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(a^2 d^2 f^2 \left(m^2-7 m+12\right)-2 a b d f (3-m) (5 d e-c f (m+1))+b^2 \left(c^2 f^2 \left(m^2+3 m+2\right)-10 c d e f (m+1)+20 d^2 e^2\right)\right) \, _2F_1\left(m-2,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{20 b^5 d^2 (m+1)}-\frac{f (a+b x)^{m+1} (c+d x)^{3-m} (a d f (4-m)-b (6 d e-c f (m+2)))}{20 b^2 d^2}+\frac{f (e+f x) (a+b x)^{m+1} (c+d x)^{3-m}}{5 b d}",1,"Could not integrate","F",-1
3125,0,0,147,0.0563191,"\int (a+b x)^m (c+d x)^{2-m} (e+f x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(2 - m)*(e + f*x),x]","\int (a+b x)^m (c+d x)^{2-m} (e+f x) \, dx","\frac{f (a+b x)^{m+1} (c+d x)^{3-m}}{4 b d}-\frac{(b c-a d)^2 (a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m (a d f (3-m)-b (4 d e-c f (m+1))) \, _2F_1\left(m-2,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{4 b^4 d (m+1)}",1,"Could not integrate","F",-1
3126,0,0,84,0.0310471,"\int (a+b x)^m (c+d x)^{2-m} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(2 - m),x]","\int (a+b x)^m (c+d x)^{2-m} \, dx","\frac{(b c-a d)^2 (a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m-2,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{b^3 (m+1)}",1,"Could not integrate","F",-1
3127,0,0,370,0.0798199,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{e+f x} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(2 - m))/(e + f*x),x]","\int \frac{(a+b x)^m (c+d x)^{2-m}}{e+f x} \, dx","\frac{d (a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(a^2 d^2 f^2 (1-m) m+2 a b d f m (d e-c f (2-m))-\left(b^2 \left(c^2 f^2 \left(m^2-3 m+2\right)-2 c d e f (2-m)+2 d^2 e^2\right)\right)\right) \, _2F_1\left(m,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{2 b^2 f^3 m (m+1) (b c-a d)}-\frac{d (a+b x)^{m+1} (c+d x)^{-m} \left(-a^2 d^2 f^2 m+2 a b c d f^2 m-\left(b^2 \left(c^2 f^2 (m+2)-4 c d e f+2 d^2 e^2\right)\right)\right)}{2 b^2 f^3 m (b c-a d)}+\frac{d^2 (a+b x)^{m+2} (c+d x)^{-m}}{2 b^2 f}+\frac{(a+b x)^m (d e-c f)^2 (c+d x)^{-m} \, _2F_1\left(1,-m;1-m;\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{f^3 m}",1,"Could not integrate","F",-1
3128,0,0,316,0.065925,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^2} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(2 - m))/(e + f*x)^2,x]","\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^2} \, dx","\frac{d^2 (a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m (b (2 d e-c f (2-m))-a d f m) \, _2F_1\left(m,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{b f^3 m (m+1) (b c-a d)}-\frac{2 d^2 (a+b x)^{m+1} (d e-c f) (c+d x)^{-m}}{f^3 m (b c-a d)}+\frac{(a+b x)^m (d e-c f) (c+d x)^{-m} (a d f (2-m)-b (2 d e-c f m)) \, _2F_1\left(1,-m;1-m;\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{f^3 m (b e-a f)}+\frac{(a+b x)^{m+1} (d e-c f)^2 (c+d x)^{-m}}{f^2 (e+f x) (b e-a f)}",1,"Could not integrate","F",-1
3129,0,0,362,0.0677575,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^3} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(2 - m))/(e + f*x)^3,x]","\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^3} \, dx","-\frac{(a+b x)^{m-1} (c+d x)^{1-m} \left(-a^2 d^2 f^2 \left(m^2-3 m+2\right)+2 a b d f (2-m) (d e-c f m)-\left(b^2 \left(-c^2 f^2 (1-m) m-2 c d e f m+2 d^2 e^2\right)\right)\right) \, _2F_1\left(1,m-1;m;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{2 f^3 (1-m) (b e-a f) (d e-c f)}+\frac{(a+b x)^{m-1} (c+d x)^{2-m} (a d f (2-m)-b (3 d e-c f (m+1)))}{2 f^2 (e+f x) (d e-c f)}+\frac{(b e-a f) (a+b x)^{m-1} (c+d x)^{2-m}}{2 f^2 (e+f x)^2}-\frac{d (b c-a d) (a+b x)^{m-1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m-1,m-1;m;-\frac{d (a+b x)}{b c-a d}\right)}{f^3 (1-m)}",1,"Could not integrate","F",-1
3130,0,0,85,0.0707439,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^4} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(2 - m))/(e + f*x)^4,x]","\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^4} \, dx","\frac{(b c-a d)^3 (a+b x)^{m+1} (c+d x)^{-m-1} \, _2F_1\left(4,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{(m+1) (b e-a f)^4}",1,"Could not integrate","F",-1
3131,0,0,176,0.0743706,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^5} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(2 - m))/(e + f*x)^5,x]","\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^5} \, dx","\frac{(b c-a d)^3 (a+b x)^{m+1} (c+d x)^{-m-1} (b (4 d e-c f (3-m))-a d f (m+1)) \, _2F_1\left(4,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{4 (m+1) (b e-a f)^5 (d e-c f)}-\frac{f (a+b x)^{m+1} (c+d x)^{3-m}}{4 (e+f x)^4 (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3132,0,0,311,0.0807111,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^6} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(2 - m))/(e + f*x)^6,x]","\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^6} \, dx","-\frac{(b c-a d)^3 (a+b x)^{m+1} (c+d x)^{-m-1} \left(-a^2 d^2 f^2 \left(m^2+3 m+2\right)+2 a b d f (m+1) (5 d e-c f (3-m))-\left(b^2 \left(c^2 f^2 \left(m^2-7 m+12\right)-10 c d e f (3-m)+20 d^2 e^2\right)\right)\right) \, _2F_1\left(4,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{20 (m+1) (b e-a f)^6 (d e-c f)^2}-\frac{f (a+b x)^{m+1} (c+d x)^{3-m} (b (6 d e-c f (4-m))-a d f (m+2))}{20 (e+f x)^4 (b e-a f)^2 (d e-c f)^2}-\frac{f (a+b x)^{m+1} (c+d x)^{3-m}}{5 (e+f x)^5 (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3133,0,0,541,0.0919275,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^7} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(2 - m))/(e + f*x)^7,x]","\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^7} \, dx","-\frac{f (a+b x)^{m+1} (c+d x)^{3-m} \left(a^2 d^2 f^2 \left(m^2+5 m+6\right)-2 a b d f \left(d e (7 m+12)-c f \left(-m^2+2 m+6\right)\right)+b^2 \left(c^2 f^2 \left(m^2-9 m+20\right)-2 c d e f (26-7 m)+38 d^2 e^2\right)\right)}{120 (e+f x)^4 (b e-a f)^3 (d e-c f)^3}+\frac{(b c-a d)^3 (a+b x)^{m+1} (c+d x)^{-m-1} \left(-a^3 d^3 f^3 \left(m^3+6 m^2+11 m+6\right)+3 a^2 b d^2 f^2 \left(m^2+3 m+2\right) (6 d e-c f (3-m))-3 a b^2 d f (m+1) \left(c^2 f^2 \left(m^2-7 m+12\right)-12 c d e f (3-m)+30 d^2 e^2\right)+b^3 \left(-c^3 f^3 \left(-m^3+12 m^2-47 m+60\right)+18 c^2 d e f^2 \left(m^2-7 m+12\right)-90 c d^2 e^2 f (3-m)+120 d^3 e^3\right)\right) \, _2F_1\left(4,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{120 (m+1) (b e-a f)^7 (d e-c f)^3}-\frac{f (a+b x)^{m+1} (c+d x)^{3-m} (b (8 d e-c f (5-m))-a d f (m+3))}{30 (e+f x)^5 (b e-a f)^2 (d e-c f)^2}-\frac{f (a+b x)^{m+1} (c+d x)^{3-m}}{6 (e+f x)^6 (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3134,0,0,488,0.0810108,"\int \frac{(a+b x)^m (c+d x)^{3-m}}{e+f x} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(3 - m))/(e + f*x),x]","\int \frac{(a+b x)^m (c+d x)^{3-m}}{e+f x} \, dx","-\frac{(b c-a d)^2 (a+b x)^{m-2} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(a^3 d^3 f^3 m \left(m^2-3 m+2\right)+3 a^2 b d^2 f^2 (1-m) m (d e-c f (3-m))+3 a b^2 d f m \left(c^2 f^2 \left(m^2-5 m+6\right)-2 c d e f (3-m)+2 d^2 e^2\right)-\left(b^3 \left(-c^3 f^3 \left(-m^3+6 m^2-11 m+6\right)+3 c^2 d e f^2 \left(m^2-5 m+6\right)-6 c d^2 e^2 f (3-m)+6 d^3 e^3\right)\right)\right) \, _2F_1\left(m-3,m-2;m-1;-\frac{d (a+b x)}{b c-a d}\right)}{6 b^3 d^2 f^4 (2-m) (3-m)}-\frac{b (a+b x)^{m-2} (c+d x)^{4-m} (b (3 d e-c f (1-m))-a d f (m+2))}{6 d^2 f^2}-\frac{(b e-a f)^3 (a+b x)^{m-3} (c+d x)^{3-m} \, _2F_1\left(1,m-3;m-2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{f^4 (3-m)}+\frac{b (b e-a f)^3 (a+b x)^{m-3} (c+d x)^{4-m}}{f^4 (3-m) (b c-a d)}+\frac{b (a+b x)^{m-1} (c+d x)^{4-m}}{3 d f}",1,"Could not integrate","F",-1
3135,0,0,397,0.0678532,"\int \frac{(a+b x)^m (c+d x)^{3-m}}{(e+f x)^2} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(3 - m))/(e + f*x)^2,x]","\int \frac{(a+b x)^m (c+d x)^{3-m}}{(e+f x)^2} \, dx","\frac{d^2 (a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(a^2 d^2 f^2 (1-m) m+2 a b d f m (2 d e-c f (3-m))-\left(b^2 \left(c^2 f^2 \left(m^2-5 m+6\right)-4 c d e f (3-m)+6 d^2 e^2\right)\right)\right) \, _2F_1\left(m,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{2 b^2 f^4 m (m+1) (b c-a d)}+\frac{d^2 (a+b x)^{m+1} (c+d x)^{1-m}}{2 b f^2}+\frac{(a+b x)^m (d e-c f)^2 (c+d x)^{-m} (a d f (3-m)-b (3 d e-c f m)) \, _2F_1\left(1,m;m+1;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{f^4 m (b e-a f)}+\frac{3 b d (a+b x)^m (d e-c f)^2 (c+d x)^{1-m}}{f^4 m (b c-a d)}-\frac{(a+b x)^m (d e-c f)^2 (c+d x)^{1-m}}{f^3 (e+f x)}",1,"Could not integrate","F",-1
3136,0,0,453,0.0692833,"\int \frac{(a+b x)^m (c+d x)^{3-m}}{(e+f x)^3} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(3 - m))/(e + f*x)^3,x]","\int \frac{(a+b x)^m (c+d x)^{3-m}}{(e+f x)^3} \, dx","\frac{(a+b x)^m (d e-c f) (c+d x)^{-m} \left(-a^2 d^2 f^2 \left(m^2-5 m+6\right)+2 a b d f (3-m) (2 d e-c f m)-\left(b^2 \left(-c^2 f^2 (1-m) m-4 c d e f m+6 d^2 e^2\right)\right)\right) \, _2F_1\left(1,-m;1-m;\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{2 f^4 m (b e-a f)^2}+\frac{d^3 (a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m (b (3 d e-c f (3-m))-a d f m) \, _2F_1\left(m,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{b f^4 m (m+1) (b c-a d)}-\frac{3 d^3 (a+b x)^{m+1} (d e-c f) (c+d x)^{-m}}{f^4 m (b c-a d)}+\frac{(a+b x)^{m+1} (d e-c f)^2 (c+d x)^{-m} (b (c f (1-m)+5 d e)-a d f (6-m))}{2 f^3 (e+f x) (b e-a f)^2}-\frac{(a+b x)^{m+1} (d e-c f)^3 (c+d x)^{-m}}{2 f^3 (e+f x)^2 (b e-a f)}",1,"Could not integrate","F",-1
3137,0,0,245,0.0998435,"\int \frac{(a+b x)^{1-n} (c+d x)^{1+n}}{b c+a d+2 b d x} \, dx","IntegrateAlgebraic[((a + b*x)^(1 - n)*(c + d*x)^(1 + n))/(b*c + a*d + 2*b*d*x),x]","\int \frac{(a+b x)^{1-n} (c+d x)^{1+n}}{b c+a d+2 b d x} \, dx","\frac{(b c-a d)^2 (a+b x)^{1-n} (c+d x)^{n-1} \, _2F_1\left(1,n-1;n;-\frac{b (c+d x)}{d (a+b x)}\right)}{8 b^3 d (1-n)}+\frac{(3-2 n) (b c-a d) (a+b x)^{2-n} (c+d x)^{n-1}}{8 b^3 (1-n)}+\frac{d (a+b x)^{3-n} (c+d x)^{n-1}}{4 b^3}-\frac{\left(1-2 n^2\right) (b c-a d)^2 (a+b x)^{-n} (c+d x)^n \left(-\frac{d (a+b x)}{b c-a d}\right)^n \, _2F_1\left(n-1,n;n+1;\frac{b (c+d x)}{b c-a d}\right)}{8 b^2 d^2 (1-n) n}",1,"Could not integrate","F",-1
3138,0,0,154,0.079649,"\int \frac{(a+b x)^{1-n} (c+d x)^{1+n}}{(b c+a d+2 b d x)^2} \, dx","IntegrateAlgebraic[((a + b*x)^(1 - n)*(c + d*x)^(1 + n))/(b*c + a*d + 2*b*d*x)^2,x]","\int \frac{(a+b x)^{1-n} (c+d x)^{1+n}}{(b c+a d+2 b d x)^2} \, dx","\frac{(a+b x)^{-n} (c+d x)^{n+1} \left(-\frac{d (a+b x)}{b c-a d}\right)^n \, _2F_1\left(n,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)}{4 b d^2 (n+1)}-\frac{(b c-a d) (a+b x)^{1-n} (c+d x)^{n-1} \, _2F_1\left(2,1-n;2-n;-\frac{d (a+b x)}{b (c+d x)}\right)}{4 b^3 d (1-n)}",1,"Could not integrate","F",-1
3139,0,0,230,0.0810737,"\int \frac{(a+b x)^{1-n} (c+d x)^{1+n}}{(b c+a d+2 b d x)^3} \, dx","IntegrateAlgebraic[((a + b*x)^(1 - n)*(c + d*x)^(1 + n))/(b*c + a*d + 2*b*d*x)^3,x]","\int \frac{(a+b x)^{1-n} (c+d x)^{1+n}}{(b c+a d+2 b d x)^3} \, dx","-\frac{\left(1-2 n^2\right) (a+b x)^{-n} (c+d x)^n \, _2F_1\left(1,n;n+1;-\frac{b (c+d x)}{d (a+b x)}\right)}{8 b^2 d^2 n}+\frac{(a+b x)^{-n} (c+d x)^n \left(-\frac{d (a+b x)}{b c-a d}\right)^n \, _2F_1\left(n,n;n+1;\frac{b (c+d x)}{b c-a d}\right)}{8 b^2 d^2 n}-\frac{(2 n+1) (a+b x)^{1-n} (c+d x)^n}{8 b^2 d (a d+b c+2 b d x)}-\frac{(b c-a d) (a+b x)^{1-n} (c+d x)^n}{8 b^2 d (a d+b c+2 b d x)^2}",1,"Could not integrate","F",-1
3140,0,0,71,0.0853546,"\int \frac{(a+b x)^{1-n} (c+d x)^{1+n}}{(b c+a d+2 b d x)^4} \, dx","IntegrateAlgebraic[((a + b*x)^(1 - n)*(c + d*x)^(1 + n))/(b*c + a*d + 2*b*d*x)^4,x]","\int \frac{(a+b x)^{1-n} (c+d x)^{1+n}}{(b c+a d+2 b d x)^4} \, dx","\frac{(a+b x)^{2-n} (c+d x)^{n-2} \, _2F_1\left(4,2-n;3-n;-\frac{d (a+b x)}{b (c+d x)}\right)}{b^4 (2-n) (b c-a d)}",1,"Could not integrate","F",-1
3141,0,0,231,0.092466,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{b c+a d+2 b d x} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(2 - m))/(b*c + a*d + 2*b*d*x),x]","\int \frac{(a+b x)^m (c+d x)^{2-m}}{b c+a d+2 b d x} \, dx","-\frac{\left(2 m^2-4 m+1\right) (b c-a d) (a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{8 b^3 m (m+1)}+\frac{(b c-a d)^2 (a+b x)^m (c+d x)^{-m} \, _2F_1\left(1,-m;1-m;-\frac{b (c+d x)}{d (a+b x)}\right)}{8 b^3 d m}+\frac{(2 m+1) (b c-a d) (a+b x)^{m+1} (c+d x)^{-m}}{8 b^3 m}+\frac{d (a+b x)^{m+2} (c+d x)^{-m}}{4 b^3}",1,"Could not integrate","F",-1
3142,0,0,144,0.074601,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(b c+a d+2 b d x)^2} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(2 - m))/(b*c + a*d + 2*b*d*x)^2,x]","\int \frac{(a+b x)^m (c+d x)^{2-m}}{(b c+a d+2 b d x)^2} \, dx","\frac{(b c-a d) (a+b x)^m (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m-1,m;m+1;-\frac{d (a+b x)}{b c-a d}\right)}{4 b^3 d m}-\frac{(b c-a d) (a+b x)^m (c+d x)^{-m} \, _2F_1\left(2,m;m+1;-\frac{d (a+b x)}{b (c+d x)}\right)}{4 b^3 d m}",1,"Could not integrate","F",-1
3143,0,0,261,0.0753635,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(b c+a d+2 b d x)^3} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(2 - m))/(b*c + a*d + 2*b*d*x)^3,x]","\int \frac{(a+b x)^m (c+d x)^{2-m}}{(b c+a d+2 b d x)^3} \, dx","-\frac{(b c-a d) (a+b x)^{m-1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m-1,m-1;m;-\frac{d (a+b x)}{b c-a d}\right)}{8 b^3 d^2 (1-m)}-\frac{\left(2 m^2-4 m+1\right) (a+b x)^{m-1} (c+d x)^{1-m} \, _2F_1\left(1,m-1;m;-\frac{d (a+b x)}{b (c+d x)}\right)}{8 b^2 d^2 (1-m)}+\frac{(1-2 m) (a+b x)^{m-1} (c+d x)^{2-m}}{8 b d^2 (a d+b c+2 b d x)}+\frac{(b c-a d) (a+b x)^{m-1} (c+d x)^{2-m}}{8 b d^2 (a d+b c+2 b d x)^2}",1,"Could not integrate","F",-1
3144,0,0,65,0.0777784,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(b c+a d+2 b d x)^4} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^(2 - m))/(b*c + a*d + 2*b*d*x)^4,x]","\int \frac{(a+b x)^m (c+d x)^{2-m}}{(b c+a d+2 b d x)^4} \, dx","\frac{(a+b x)^{m+1} (c+d x)^{-m-1} \, _2F_1\left(4,m+1;m+2;-\frac{d (a+b x)}{b (c+d x)}\right)}{b^4 (m+1) (b c-a d)}",1,"Could not integrate","F",-1
3145,0,0,139,0.0600045,"\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{n+p} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-m - n)*(e + f*x)^(n + p),x]","\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{n+p} \, dx","\frac{(a+b x)^{m+1} (c+d x)^{-m-n} (e+f x)^{n+p} \left(\frac{b (c+d x)}{b c-a d}\right)^{m+n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-n-p} F_1\left(m+1;m+n,-n-p;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b (m+1)}",1,"Could not integrate","F",-1
3146,0,0,139,0.0675585,"\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{1+n} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-m - n)*(e + f*x)^(1 + n),x]","\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{1+n} \, dx","\frac{(b e-a f) (a+b x)^{m+1} (e+f x)^n (c+d x)^{-m-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^{m+n} F_1\left(m+1;m+n,-n-1;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^2 (m+1)}",1,"Could not integrate","F",-1
3147,0,0,129,0.0535106,"\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^n \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-m - n)*(e + f*x)^n,x]","\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^n \, dx","\frac{(a+b x)^{m+1} (e+f x)^n (c+d x)^{-m-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^{m+n} F_1\left(m+1;m+n,-n;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b (m+1)}",1,"Could not integrate","F",-1
3148,0,0,138,0.0709495,"\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{-1+n} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-m - n)*(e + f*x)^(-1 + n),x]","\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{-1+n} \, dx","\frac{(a+b x)^{m+1} (e+f x)^n (c+d x)^{-m-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-n} \left(\frac{b (c+d x)}{b c-a d}\right)^{m+n} F_1\left(m+1;m+n,1-n;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{(m+1) (b e-a f)}",1,"Could not integrate","F",-1
3149,0,0,124,0.0725178,"\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{-2+n} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-m - n)*(e + f*x)^(-2 + n),x]","\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{-2+n} \, dx","\frac{(a+b x)^{m+1} (e+f x)^{n-1} (c+d x)^{-m-n} \left(\frac{(c+d x) (b e-a f)}{(e+f x) (b c-a d)}\right)^{m+n} \, _2F_1\left(m+1,m+n;m+2;-\frac{(d e-c f) (a+b x)}{(b c-a d) (e+f x)}\right)}{(m+1) (b e-a f)}",1,"Could not integrate","F",-1
3150,0,0,237,0.0732364,"\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{-3+n} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-m - n)*(e + f*x)^(-3 + n),x]","\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{-3+n} \, dx","-\frac{(a+b x)^{m+1} (e+f x)^{n-1} (c+d x)^{-m-n} (a d f (m+1)-b (d e (2-n)-c f (-m-n+1))) \left(\frac{(c+d x) (b e-a f)}{(e+f x) (b c-a d)}\right)^{m+n} \, _2F_1\left(m+1,m+n;m+2;-\frac{(d e-c f) (a+b x)}{(b c-a d) (e+f x)}\right)}{(m+1) (2-n) (b e-a f)^2 (d e-c f)}-\frac{f (a+b x)^{m+1} (e+f x)^{n-2} (c+d x)^{-m-n+1}}{(2-n) (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3151,0,0,428,0.0741292,"\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{-4+n} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-m - n)*(e + f*x)^(-4 + n),x]","\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{-4+n} \, dx","\frac{(a+b x)^{m+1} (e+f x)^{n-1} (c+d x)^{-m-n} \left(a^2 d^2 f^2 \left(m^2+3 m+2\right)-2 a b d f (m+1) (d e (3-n)-c f (-m-n+1))-\left(b^2 \left(-c^2 f^2 \left(m^2-m (3-2 n)+n^2-3 n+2\right)+2 c d e f (3-n) (-m-n+1)-d^2 e^2 \left(n^2-5 n+6\right)\right)\right)\right) \left(\frac{(c+d x) (b e-a f)}{(e+f x) (b c-a d)}\right)^{m+n} \, _2F_1\left(m+1,m+n;m+2;-\frac{(d e-c f) (a+b x)}{(b c-a d) (e+f x)}\right)}{(m+1) (2-n) (3-n) (b e-a f)^3 (d e-c f)^2}-\frac{f (a+b x)^{m+1} (e+f x)^{n-3} (c+d x)^{-m-n+1}}{(3-n) (b e-a f) (d e-c f)}+\frac{f (a+b x)^{m+1} (e+f x)^{n-2} (c+d x)^{-m-n+1} (a d f (m+2)-b (d e (4-n)-c f (-m-n+2)))}{(2-n) (3-n) (b e-a f)^2 (d e-c f)^2}",1,"Could not integrate","F",-1
3152,0,0,88,0.2101612,"\int (a+b x)^m (c+d x)^n \left(\frac{b c f+a d f+a d f m+b c f n}{b d (2+m+n)}+f x\right)^{-3-m-n} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^n*((b*c*f + a*d*f + a*d*f*m + b*c*f*n)/(b*d*(2 + m + n)) + f*x)^(-3 - m - n),x]","\int (a+b x)^m (c+d x)^n \left(\frac{b c f+a d f+a d f m+b c f n}{b d (2+m+n)}+f x\right)^{-3-m-n} \, dx","\frac{b d (m+n+2) (a+b x)^{m+1} (c+d x)^{n+1} \left(\frac{f (a d (m+1)+b c (n+1))}{b d (m+n+2)}+f x\right)^{-m-n-2}}{f (m+1) (n+1) (b c-a d)^2}",1,"Could not integrate","F",-1
3153,0,0,101,0.2153405,"\int (a+b x)^m (c+d x)^{-1-\frac{d (b e-a f) (1+m)}{b (d e-c f)}} (e+f x)^{-1+\frac{(b c-a d) f (1+m)}{b (d e-c f)}} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-1 - (d*(b*e - a*f)*(1 + m))/(b*(d*e - c*f)))*(e + f*x)^(-1 + ((b*c - a*d)*f*(1 + m))/(b*(d*e - c*f))),x]","\int (a+b x)^m (c+d x)^{-1-\frac{d (b e-a f) (1+m)}{b (d e-c f)}} (e+f x)^{-1+\frac{(b c-a d) f (1+m)}{b (d e-c f)}} \, dx","\frac{b (a+b x)^{m+1} (c+d x)^{-\frac{d (m+1) (b e-a f)}{b (d e-c f)}} (e+f x)^{\frac{f (m+1) (b c-a d)}{b (d e-c f)}}}{(m+1) (b c-a d) (b e-a f)}",1,"Could not integrate","F",-1
3154,0,0,129,0.053881,"\int (a+b x)^m (c+d x)^n (e+f x)^{-m-n} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^n*(e + f*x)^(-m - n),x]","\int (a+b x)^m (c+d x)^n (e+f x)^{-m-n} \, dx","\frac{(a+b x)^{m+1} (c+d x)^n (e+f x)^{-m-n} \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{m+n} F_1\left(m+1;-n,m+n;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b (m+1)}",1,"Could not integrate","F",-1
3155,0,0,137,0.0724157,"\int (a+b x)^m (c+d x)^n (e+f x)^{-1-m-n} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^n*(e + f*x)^(-1 - m - n),x]","\int (a+b x)^m (c+d x)^n (e+f x)^{-1-m-n} \, dx","\frac{(a+b x)^{m+1} (c+d x)^n (e+f x)^{-m-n} \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{m+n} F_1\left(m+1;-n,m+n+1;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{(m+1) (b e-a f)}",1,"Could not integrate","F",-1
3156,0,0,123,0.0742746,"\int (a+b x)^m (c+d x)^n (e+f x)^{-2-m-n} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^n*(e + f*x)^(-2 - m - n),x]","\int (a+b x)^m (c+d x)^n (e+f x)^{-2-m-n} \, dx","\frac{(a+b x)^{m+1} (c+d x)^n (e+f x)^{-m-n-1} \left(\frac{(c+d x) (b e-a f)}{(e+f x) (b c-a d)}\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{(d e-c f) (a+b x)}{(b c-a d) (e+f x)}\right)}{(m+1) (b e-a f)}",1,"Could not integrate","F",-1
3157,0,0,227,0.1491726,"\int (a+b x)^m (c+d x)^n (e+f x)^{-3-m-n} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^n*(e + f*x)^(-3 - m - n),x]","\int (a+b x)^m (c+d x)^n (e+f x)^{-3-m-n} \, dx","-\frac{(a+b x)^{m+1} (c+d x)^n (e+f x)^{-m-n-1} (a d f (m+1)+b (c f (n+1)-d e (m+n+2))) \left(\frac{(c+d x) (b e-a f)}{(e+f x) (b c-a d)}\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{(d e-c f) (a+b x)}{(b c-a d) (e+f x)}\right)}{(m+1) (m+n+2) (b e-a f)^2 (d e-c f)}-\frac{f (a+b x)^{m+1} (c+d x)^{n+1} (e+f x)^{-m-n-2}}{(m+n+2) (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3158,0,0,402,0.1155633,"\int (a+b x)^m (c+d x)^n (e+f x)^{-4-m-n} \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^n*(e + f*x)^(-4 - m - n),x]","\int (a+b x)^m (c+d x)^n (e+f x)^{-4-m-n} \, dx","\frac{(a+b x)^{m+1} (c+d x)^n (e+f x)^{-m-n-1} \left(a^2 d^2 f^2 \left(m^2+3 m+2\right)+2 a b d f (m+1) (c f (n+1)-d e (m+n+3))-\left(b^2 \left(-c^2 f^2 \left(n^2+3 n+2\right)+2 c d e f (n+1) (m+n+3)-d^2 e^2 \left(m^2+m (2 n+5)+n^2+5 n+6\right)\right)\right)\right) \left(\frac{(c+d x) (b e-a f)}{(e+f x) (b c-a d)}\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{(d e-c f) (a+b x)}{(b c-a d) (e+f x)}\right)}{(m+1) (m+n+2) (m+n+3) (b e-a f)^3 (d e-c f)^2}-\frac{f (a+b x)^{m+1} (c+d x)^{n+1} (e+f x)^{-m-n-3}}{(m+n+3) (b e-a f) (d e-c f)}+\frac{f (a+b x)^{m+1} (c+d x)^{n+1} (e+f x)^{-m-n-2} (a d f (m+2)+b (c f (n+2)-d e (m+n+4)))}{(m+n+2) (m+n+3) (b e-a f)^2 (d e-c f)^2}",1,"Could not integrate","F",-1
3159,0,0,123,0.0459709,"\int (a+b x)^m (c+d x)^n (e+f x)^p \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p,x]","\int (a+b x)^m (c+d x)^n (e+f x)^p \, dx","\frac{(a+b x)^{m+1} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+1;-n,-p;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b (m+1)}",1,"Could not integrate","F",-1
3160,0,0,259,0.050843,"\int (a+b x)^m (c+d x)^n (e+f x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^n*(e + f*x)^2,x]","\int (a+b x)^m (c+d x)^n (e+f x)^2 \, dx","\frac{(a+b x)^{m+1} (c+d x)^{n+1} (f (a d (n+1)+b c (m+1)) (b d e (m+n+4)-f (a d (n+2)+b c (m+2)))+b d (m+n+2) (a f (c f+d e (n+1))+b e (c f (m+1)-d e (m+n+3)))) \, _2F_1\left(1,m+n+2;n+2;\frac{b (c+d x)}{b c-a d}\right)}{b^2 d^2 (n+1) (m+n+2) (m+n+3) (b c-a d)}+\frac{f (a+b x)^{m+1} (c+d x)^{n+1} (b d e (m+n+4)-f (a d (n+2)+b c (m+2)))}{b^2 d^2 (m+n+2) (m+n+3)}+\frac{f (e+f x) (a+b x)^{m+1} (c+d x)^{n+1}}{b d (m+n+3)}",1,"Could not integrate","F",-1
3161,0,0,131,0.0421622,"\int (a+b x)^m (c+d x)^n (e+f x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^n*(e + f*x),x]","\int (a+b x)^m (c+d x)^n (e+f x) \, dx","\frac{f (a+b x)^{m+1} (c+d x)^{n+1}}{b d (m+n+2)}-\frac{(a+b x)^{m+1} (c+d x)^{n+1} (b d e (m+n+2)-f (a d (n+1)+b c (m+1))) \, _2F_1\left(1,m+n+2;n+2;\frac{b (c+d x)}{b c-a d}\right)}{b d (n+1) (m+n+2) (b c-a d)}",1,"Could not integrate","F",-1
3162,0,0,61,0.0006445,"\int (a+b x)^m (c+d x)^n \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^n,x]","\int (a+b x)^m (c+d x)^n \, dx","-\frac{(a+b x)^{m+1} (c+d x)^{n+1} \, _2F_1\left(1,m+n+2;n+2;\frac{b (c+d x)}{b c-a d}\right)}{(n+1) (b c-a d)}",1,"Could not integrate","F",-1
3163,0,0,100,0.1053531,"\int \frac{(a+b x)^m (c+d x)^n}{e+f x} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^n)/(e + f*x),x]","\int \frac{(a+b x)^m (c+d x)^n}{e+f x} \, dx","\frac{(a+b x)^{m+1} (c+d x)^n \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{(m+1) (b e-a f)}",1,"Could not integrate","F",-1
3164,0,0,101,0.0521533,"\int \frac{(a+b x)^m (c+d x)^n}{(e+f x)^2} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^n)/(e + f*x)^2,x]","\int \frac{(a+b x)^m (c+d x)^n}{(e+f x)^2} \, dx","\frac{b (a+b x)^{m+1} (c+d x)^n \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} F_1\left(m+1;-n,2;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{(m+1) (b e-a f)^2}",1,"Could not integrate","F",-1
3165,0,0,103,0.0565373,"\int \frac{(a+b x)^m (c+d x)^n}{(e+f x)^3} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^n)/(e + f*x)^3,x]","\int \frac{(a+b x)^m (c+d x)^n}{(e+f x)^3} \, dx","\frac{b^2 (a+b x)^{m+1} (c+d x)^n \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} F_1\left(m+1;-n,3;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{(m+1) (b e-a f)^3}",1,"Could not integrate","F",-1
3166,0,0,50,0.0616527,"\int \frac{(3+4 x)^n}{\sqrt{1-x} \sqrt{1+x}} \, dx","IntegrateAlgebraic[(3 + 4*x)^n/(Sqrt[1 - x]*Sqrt[1 + x]),x]","\int \frac{(3+4 x)^n}{\sqrt{1-x} \sqrt{1+x}} \, dx","-\sqrt{2} 7^n \sqrt{1-x} F_1\left(\frac{1}{2};\frac{1}{2},-n;\frac{3}{2};\frac{1-x}{2},\frac{4 (1-x)}{7}\right)",1,"Could not integrate","F",-1
3167,0,0,43,0.0619866,"\int \frac{(3-4 x)^n}{\sqrt{1-x} \sqrt{1+x}} \, dx","IntegrateAlgebraic[(3 - 4*x)^n/(Sqrt[1 - x]*Sqrt[1 + x]),x]","\int \frac{(3-4 x)^n}{\sqrt{1-x} \sqrt{1+x}} \, dx","\sqrt{2} 7^n \sqrt{x+1} F_1\left(\frac{1}{2};-n,\frac{1}{2};\frac{3}{2};\frac{4 (x+1)}{7},\frac{x+1}{2}\right)",1,"Could not integrate","F",-1
3168,0,0,45,0.111955,"\int \frac{(-3+4 x)^n}{\sqrt{1-x} \sqrt{1+x}} \, dx","IntegrateAlgebraic[(-3 + 4*x)^n/(Sqrt[1 - x]*Sqrt[1 + x]),x]","\int \frac{(-3+4 x)^n}{\sqrt{1-x} \sqrt{1+x}} \, dx","-\sqrt{2} \sqrt{1-x} F_1\left(\frac{1}{2};\frac{1}{2},-n;\frac{3}{2};\frac{1-x}{2},4 (1-x)\right)",1,"Could not integrate","F",-1
3169,0,0,38,0.1241715,"\int \frac{(-3-4 x)^n}{\sqrt{1-x} \sqrt{1+x}} \, dx","IntegrateAlgebraic[(-3 - 4*x)^n/(Sqrt[1 - x]*Sqrt[1 + x]),x]","\int \frac{(-3-4 x)^n}{\sqrt{1-x} \sqrt{1+x}} \, dx","\sqrt{2} \sqrt{x+1} F_1\left(\frac{1}{2};-n,\frac{1}{2};\frac{3}{2};4 (x+1),\frac{x+1}{2}\right)",1,"Could not integrate","F",-1
3170,0,0,100,8.4549149,"\int \frac{(a+b x)^{4/3}}{\sqrt{c+d x} (e+f x)} \, dx","IntegrateAlgebraic[(a + b*x)^(4/3)/(Sqrt[c + d*x]*(e + f*x)),x]","\int \frac{(a+b x)^{4/3}}{\sqrt{c+d x} (e+f x)} \, dx","\frac{3 (a+b x)^{7/3} \sqrt{\frac{b (c+d x)}{b c-a d}} F_1\left(\frac{7}{3};\frac{1}{2},1;\frac{10}{3};-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{7 \sqrt{c+d x} (b e-a f)}",1,"Could not integrate","F",-1
3171,0,0,123,2.4329872,"\int \frac{(c+d x)^{2/5} (e+f x)^{3/5}}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[((c + d*x)^(2/5)*(e + f*x)^(3/5))/Sqrt[a + b*x],x]","\int \frac{(c+d x)^{2/5} (e+f x)^{3/5}}{\sqrt{a+b x}} \, dx","\frac{2 \sqrt{a+b x} (c+d x)^{2/5} (e+f x)^{3/5} F_1\left(\frac{1}{2};-\frac{2}{5},-\frac{3}{5};\frac{3}{2};-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b \left(\frac{b (c+d x)}{b c-a d}\right)^{2/5} \left(\frac{b (e+f x)}{b e-a f}\right)^{3/5}}",1,"Could not integrate","F",-1
3172,0,0,123,0.1882176,"\int \frac{\sqrt{a+b x} (e+f x)^n}{\sqrt{c+d x}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(e + f*x)^n)/Sqrt[c + d*x],x]","\int \frac{\sqrt{a+b x} (e+f x)^n}{\sqrt{c+d x}} \, dx","\frac{2 (a+b x)^{3/2} (e+f x)^n \sqrt{\frac{b (c+d x)}{b c-a d}} \left(\frac{b (e+f x)}{b e-a f}\right)^{-n} F_1\left(\frac{3}{2};\frac{1}{2},-n;\frac{5}{2};-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{3 b \sqrt{c+d x}}",1,"Could not integrate","F",-1
3173,0,0,121,0.2367726,"\int \frac{\sqrt{c+d x} (e+f x)^n}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*(e + f*x)^n)/Sqrt[a + b*x],x]","\int \frac{\sqrt{c+d x} (e+f x)^n}{\sqrt{a+b x}} \, dx","\frac{2 \sqrt{a+b x} \sqrt{c+d x} (e+f x)^n \left(\frac{b (e+f x)}{b e-a f}\right)^{-n} F_1\left(\frac{1}{2};-\frac{1}{2},-n;\frac{3}{2};-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b \sqrt{\frac{b (c+d x)}{b c-a d}}}",1,"Could not integrate","F",-1
3174,0,0,128,0.3904492,"\int \frac{(e+f x)^n}{\sqrt{a+b x} (c+d x)^{3/2}} \, dx","IntegrateAlgebraic[(e + f*x)^n/(Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\int \frac{(e+f x)^n}{\sqrt{a+b x} (c+d x)^{3/2}} \, dx","\frac{2 \sqrt{a+b x} (e+f x)^n \sqrt{\frac{b (c+d x)}{b c-a d}} \left(\frac{b (e+f x)}{b e-a f}\right)^{-n} F_1\left(\frac{1}{2};\frac{3}{2},-n;\frac{3}{2};-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{\sqrt{c+d x} (b c-a d)}",1,"Could not integrate","F",-1
3175,0,0,121,0.4676368,"\int \frac{(e+f x)^n}{(a+b x)^{3/2} \sqrt{c+d x}} \, dx","IntegrateAlgebraic[(e + f*x)^n/((a + b*x)^(3/2)*Sqrt[c + d*x]),x]","\int \frac{(e+f x)^n}{(a+b x)^{3/2} \sqrt{c+d x}} \, dx","-\frac{2 (e+f x)^n \sqrt{\frac{b (c+d x)}{b c-a d}} \left(\frac{b (e+f x)}{b e-a f}\right)^{-n} F_1\left(-\frac{1}{2};\frac{1}{2},-n;\frac{1}{2};-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b \sqrt{a+b x} \sqrt{c+d x}}",1,"Could not integrate","F",-1
3176,0,0,100,7.003968,"\int \frac{\sqrt{a+b x} \sqrt[3]{c+d x}}{e+f x} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(c + d*x)^(1/3))/(e + f*x),x]","\int \frac{\sqrt{a+b x} \sqrt[3]{c+d x}}{e+f x} \, dx","\frac{2 (a+b x)^{3/2} \sqrt[3]{c+d x} F_1\left(\frac{3}{2};-\frac{1}{3},1;\frac{5}{2};-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{3 (b e-a f) \sqrt[3]{\frac{b (c+d x)}{b c-a d}}}",1,"Could not integrate","F",-1
3177,0,0,100,6.9997787,"\int \frac{\sqrt[3]{a+b x} \sqrt{c+d x}}{e+f x} \, dx","IntegrateAlgebraic[((a + b*x)^(1/3)*Sqrt[c + d*x])/(e + f*x),x]","\int \frac{\sqrt[3]{a+b x} \sqrt{c+d x}}{e+f x} \, dx","\frac{3 (a+b x)^{4/3} \sqrt{c+d x} F_1\left(\frac{4}{3};-\frac{1}{2},1;\frac{7}{3};-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{4 (b e-a f) \sqrt{\frac{b (c+d x)}{b c-a d}}}",1,"Could not integrate","F",-1
3178,0,0,125,1.8880539,"\int \sqrt{a+b x} \sqrt[3]{c+d x} \sqrt[4]{e+f x} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*(c + d*x)^(1/3)*(e + f*x)^(1/4),x]","\int \sqrt{a+b x} \sqrt[3]{c+d x} \sqrt[4]{e+f x} \, dx","\frac{2 (a+b x)^{3/2} \sqrt[3]{c+d x} \sqrt[4]{e+f x} F_1\left(\frac{3}{2};-\frac{1}{3},-\frac{1}{4};\frac{5}{2};-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{3 b \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \sqrt[4]{\frac{b (e+f x)}{b e-a f}}}",1,"Could not integrate","F",-1
3179,0,0,125,1.7903669,"\int \sqrt[3]{a+b x} \sqrt{c+d x} \sqrt[4]{e+f x} \, dx","IntegrateAlgebraic[(a + b*x)^(1/3)*Sqrt[c + d*x]*(e + f*x)^(1/4),x]","\int \sqrt[3]{a+b x} \sqrt{c+d x} \sqrt[4]{e+f x} \, dx","\frac{3 (a+b x)^{4/3} \sqrt{c+d x} \sqrt[4]{e+f x} F_1\left(\frac{4}{3};-\frac{1}{2},-\frac{1}{4};\frac{7}{3};-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{4 b \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt[4]{\frac{b (e+f x)}{b e-a f}}}",1,"Could not integrate","F",-1
3180,0,0,234,0.1068189,"\int (a+b x)^4 (A+B x) (d+e x)^m \, dx","IntegrateAlgebraic[(a + b*x)^4*(A + B*x)*(d + e*x)^m,x]","\int (a+b x)^4 (A+B x) (d+e x)^m \, dx","-\frac{b^3 (d+e x)^{m+5} (-4 a B e-A b e+5 b B d)}{e^6 (m+5)}+\frac{2 b^2 (b d-a e) (d+e x)^{m+4} (-3 a B e-2 A b e+5 b B d)}{e^6 (m+4)}-\frac{(b d-a e)^4 (B d-A e) (d+e x)^{m+1}}{e^6 (m+1)}+\frac{(b d-a e)^3 (d+e x)^{m+2} (-a B e-4 A b e+5 b B d)}{e^6 (m+2)}-\frac{2 b (b d-a e)^2 (d+e x)^{m+3} (-2 a B e-3 A b e+5 b B d)}{e^6 (m+3)}+\frac{b^4 B (d+e x)^{m+6}}{e^6 (m+6)}",1,"Could not integrate","F",-1
3181,0,0,186,0.0778902,"\int (a+b x)^3 (A+B x) (d+e x)^m \, dx","IntegrateAlgebraic[(a + b*x)^3*(A + B*x)*(d + e*x)^m,x]","\int (a+b x)^3 (A+B x) (d+e x)^m \, dx","-\frac{b^2 (d+e x)^{m+4} (-3 a B e-A b e+4 b B d)}{e^5 (m+4)}+\frac{(b d-a e)^3 (B d-A e) (d+e x)^{m+1}}{e^5 (m+1)}-\frac{(b d-a e)^2 (d+e x)^{m+2} (-a B e-3 A b e+4 b B d)}{e^5 (m+2)}+\frac{3 b (b d-a e) (d+e x)^{m+3} (-a B e-A b e+2 b B d)}{e^5 (m+3)}+\frac{b^3 B (d+e x)^{m+5}}{e^5 (m+5)}",1,"Could not integrate","F",-1
3182,0,0,138,0.0649917,"\int (a+b x)^2 (A+B x) (d+e x)^m \, dx","IntegrateAlgebraic[(a + b*x)^2*(A + B*x)*(d + e*x)^m,x]","\int (a+b x)^2 (A+B x) (d+e x)^m \, dx","-\frac{(b d-a e)^2 (B d-A e) (d+e x)^{m+1}}{e^4 (m+1)}+\frac{(b d-a e) (d+e x)^{m+2} (-a B e-2 A b e+3 b B d)}{e^4 (m+2)}-\frac{b (d+e x)^{m+3} (-2 a B e-A b e+3 b B d)}{e^4 (m+3)}+\frac{b^2 B (d+e x)^{m+4}}{e^4 (m+4)}",1,"Could not integrate","F",-1
3183,0,0,90,0.05007,"\int (a+b x) (A+B x) (d+e x)^m \, dx","IntegrateAlgebraic[(a + b*x)*(A + B*x)*(d + e*x)^m,x]","\int (a+b x) (A+B x) (d+e x)^m \, dx","\frac{(b d-a e) (B d-A e) (d+e x)^{m+1}}{e^3 (m+1)}-\frac{(d+e x)^{m+2} (-a B e-A b e+2 b B d)}{e^3 (m+2)}+\frac{b B (d+e x)^{m+3}}{e^3 (m+3)}",1,"Could not integrate","F",-1
3184,0,0,47,0.026935,"\int (A+B x) (d+e x)^m \, dx","IntegrateAlgebraic[(A + B*x)*(d + e*x)^m,x]","\int (A+B x) (d+e x)^m \, dx","\frac{B (d+e x)^{m+2}}{e^2 (m+2)}-\frac{(B d-A e) (d+e x)^{m+1}}{e^2 (m+1)}",1,"Could not integrate","F",-1
3185,0,0,85,0.0700375,"\int \frac{(A+B x) (d+e x)^m}{a+b x} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^m)/(a + b*x),x]","\int \frac{(A+B x) (d+e x)^m}{a+b x} \, dx","\frac{B (d+e x)^{m+1}}{b e (m+1)}-\frac{(A b-a B) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{b (m+1) (b d-a e)}",1,"Could not integrate","F",-1
3186,0,0,112,0.119486,"\int \frac{(A+B x) (d+e x)^m}{(a+b x)^2} \, dx","IntegrateAlgebraic[((A + B*x)*(d + e*x)^m)/(a + b*x)^2,x]","\int \frac{(A+B x) (d+e x)^m}{(a+b x)^2} \, dx","\frac{(d+e x)^{m+1} (a B e (m+1)-b (A e m+B d)) \, _2F_1\left(1,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{b (m+1) (b d-a e)^2}-\frac{(A b-a B) (d+e x)^{m+1}}{b (a+b x) (b d-a e)}",1,"Could not integrate","F",-1
3187,0,0,91,0.0339366,"\int (1-2 x) (2+3 x)^m (3+5 x)^3 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^m*(3 + 5*x)^3,x]","\int (1-2 x) (2+3 x)^m (3+5 x)^3 \, dx","-\frac{7 (3 x+2)^{m+1}}{243 (m+1)}+\frac{107 (3 x+2)^{m+2}}{243 (m+2)}-\frac{185 (3 x+2)^{m+3}}{81 (m+3)}+\frac{1025 (3 x+2)^{m+4}}{243 (m+4)}-\frac{250 (3 x+2)^{m+5}}{243 (m+5)}",1,"Could not integrate","F",-1
3188,0,0,73,0.0312999,"\int (1-2 x) (2+3 x)^m (3+5 x)^2 \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^m*(3 + 5*x)^2,x]","\int (1-2 x) (2+3 x)^m (3+5 x)^2 \, dx","\frac{7 (3 x+2)^{m+1}}{81 (m+1)}-\frac{8 (3 x+2)^{m+2}}{9 (m+2)}+\frac{65 (3 x+2)^{m+3}}{27 (m+3)}-\frac{50 (3 x+2)^{m+4}}{81 (m+4)}",1,"Could not integrate","F",-1
3189,0,0,55,0.0258536,"\int (1-2 x) (2+3 x)^m (3+5 x) \, dx","IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^m*(3 + 5*x),x]","\int (1-2 x) (2+3 x)^m (3+5 x) \, dx","-\frac{7 (3 x+2)^{m+1}}{27 (m+1)}+\frac{37 (3 x+2)^{m+2}}{27 (m+2)}-\frac{10 (3 x+2)^{m+3}}{27 (m+3)}",1,"Could not integrate","F",-1
3190,0,0,52,0.0394154,"\int \frac{(1-2 x) (2+3 x)^m}{3+5 x} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^m)/(3 + 5*x),x]","\int \frac{(1-2 x) (2+3 x)^m}{3+5 x} \, dx","-\frac{11 (3 x+2)^{m+1} \, _2F_1(1,m+1;m+2;5 (3 x+2))}{5 (m+1)}-\frac{2 (3 x+2)^{m+1}}{15 (m+1)}",1,"Could not integrate","F",-1
3191,0,0,59,0.1030009,"\int \frac{(1-2 x) (2+3 x)^m}{(3+5 x)^2} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^m)/(3 + 5*x)^2,x]","\int \frac{(1-2 x) (2+3 x)^m}{(3+5 x)^2} \, dx","\frac{(2-33 m) (3 x+2)^{m+1} \, _2F_1(1,m+1;m+2;5 (3 x+2))}{5 (m+1)}-\frac{11 (3 x+2)^{m+1}}{5 (5 x+3)}",1,"Could not integrate","F",-1
3192,0,0,59,0.1362776,"\int \frac{(1-2 x) (2+3 x)^m}{(3+5 x)^3} \, dx","IntegrateAlgebraic[((1 - 2*x)*(2 + 3*x)^m)/(3 + 5*x)^3,x]","\int \frac{(1-2 x) (2+3 x)^m}{(3+5 x)^3} \, dx","-\frac{3 (37-33 m) (3 x+2)^{m+1} \, _2F_1(2,m+1;m+2;5 (3 x+2))}{10 (m+1)}-\frac{11 (3 x+2)^{m+1}}{10 (5 x+3)^2}",1,"Could not integrate","F",-1
3193,0,0,90,0.0480946,"\int \frac{(2+3 x)^m (3+5 x)^3}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^m*(3 + 5*x)^3)/(1 - 2*x),x]","\int \frac{(2+3 x)^m (3+5 x)^3}{1-2 x} \, dx","\frac{1331 (3 x+2)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{2}{7} (3 x+2)\right)}{56 (m+1)}-\frac{5135 (3 x+2)^{m+1}}{216 (m+1)}-\frac{725 (3 x+2)^{m+2}}{108 (m+2)}-\frac{125 (3 x+2)^{m+3}}{54 (m+3)}",1,"Could not integrate","F",-1
3194,0,0,72,0.0465609,"\int \frac{(2+3 x)^m (3+5 x)^2}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^m*(3 + 5*x)^2)/(1 - 2*x),x]","\int \frac{(2+3 x)^m (3+5 x)^2}{1-2 x} \, dx","\frac{121 (3 x+2)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{2}{7} (3 x+2)\right)}{28 (m+1)}-\frac{155 (3 x+2)^{m+1}}{36 (m+1)}-\frac{25 (3 x+2)^{m+2}}{18 (m+2)}",1,"Could not integrate","F",-1
3195,0,0,54,0.0397164,"\int \frac{(2+3 x)^m (3+5 x)}{1-2 x} \, dx","IntegrateAlgebraic[((2 + 3*x)^m*(3 + 5*x))/(1 - 2*x),x]","\int \frac{(2+3 x)^m (3+5 x)}{1-2 x} \, dx","\frac{11 (3 x+2)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{2}{7} (3 x+2)\right)}{14 (m+1)}-\frac{5 (3 x+2)^{m+1}}{6 (m+1)}",1,"Could not integrate","F",-1
3196,0,0,69,0.0624911,"\int \frac{(2+3 x)^m}{(1-2 x) (3+5 x)} \, dx","IntegrateAlgebraic[(2 + 3*x)^m/((1 - 2*x)*(3 + 5*x)),x]","\int \frac{(2+3 x)^m}{(1-2 x) (3+5 x)} \, dx","\frac{2 (3 x+2)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{2}{7} (3 x+2)\right)}{77 (m+1)}-\frac{5 (3 x+2)^{m+1} \, _2F_1(1,m+1;m+2;5 (3 x+2))}{11 (m+1)}",1,"Could not integrate","F",-1
3197,0,0,94,0.0948636,"\int \frac{(2+3 x)^m}{(1-2 x) (3+5 x)^2} \, dx","IntegrateAlgebraic[(2 + 3*x)^m/((1 - 2*x)*(3 + 5*x)^2),x]","\int \frac{(2+3 x)^m}{(1-2 x) (3+5 x)^2} \, dx","\frac{4 (3 x+2)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{2}{7} (3 x+2)\right)}{847 (m+1)}-\frac{5 (33 m+2) (3 x+2)^{m+1} \, _2F_1(1,m+1;m+2;5 (3 x+2))}{121 (m+1)}-\frac{5 (3 x+2)^{m+1}}{11 (5 x+3)}",1,"Could not integrate","F",-1
3198,0,0,124,0.0569468,"\int \frac{(2+3 x)^m}{(1-2 x) (3+5 x)^3} \, dx","IntegrateAlgebraic[(2 + 3*x)^m/((1 - 2*x)*(3 + 5*x)^3),x]","\int \frac{(2+3 x)^m}{(1-2 x) (3+5 x)^3} \, dx","-\frac{5 \left(1089 m^2-957 m+8\right) (3 x+2)^{m+1} \, _2F_1(1,m+1;m+2;5 (3 x+2))}{2662 (m+1)}+\frac{8 (3 x+2)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{2}{7} (3 x+2)\right)}{9317 (m+1)}+\frac{5 (29-33 m) (3 x+2)^{m+1}}{242 (5 x+3)}-\frac{5 (3 x+2)^{m+1}}{22 (5 x+3)^2}",1,"Could not integrate","F",-1
3199,0,0,52,0.0368244,"\int \frac{(a+b x)^m}{(e+f x)^2} \, dx","IntegrateAlgebraic[(a + b*x)^m/(e + f*x)^2,x]","\int \frac{(a+b x)^m}{(e+f x)^2} \, dx","\frac{b (a+b x)^{m+1} \, _2F_1\left(2,m+1;m+2;-\frac{f (a+b x)}{b e-a f}\right)}{(m+1) (b e-a f)^2}",1,"Could not integrate","F",-1
3200,0,0,187,0.0996887,"\int \frac{(a+b x)^m}{(c+d x) (e+f x)^2} \, dx","IntegrateAlgebraic[(a + b*x)^m/((c + d*x)*(e + f*x)^2),x]","\int \frac{(a+b x)^m}{(c+d x) (e+f x)^2} \, dx","\frac{d^2 (a+b x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{(m+1) (b c-a d) (d e-c f)^2}+\frac{f (a+b x)^{m+1} (a d f-b (c f m+d e (1-m))) \, _2F_1\left(1,m+1;m+2;-\frac{f (a+b x)}{b e-a f}\right)}{(m+1) (b e-a f)^2 (d e-c f)^2}-\frac{f (a+b x)^{m+1}}{(e+f x) (b e-a f) (d e-c f)}",1,"Could not integrate","F",-1
3201,0,0,281,0.1202157,"\int \frac{(a+b x)^m}{(c+d x)^2 (e+f x)^2} \, dx","IntegrateAlgebraic[(a + b*x)^m/((c + d*x)^2*(e + f*x)^2),x]","\int \frac{(a+b x)^m}{(c+d x)^2 (e+f x)^2} \, dx","\frac{d^2 (a+b x)^{m+1} (2 a d f-b (c f (2-m)+d e m)) \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{(m+1) (b c-a d)^2 (d e-c f)^3}-\frac{f^2 (a+b x)^{m+1} (2 a d f-b (c f m+d e (2-m))) \, _2F_1\left(1,m+1;m+2;-\frac{f (a+b x)}{b e-a f}\right)}{(m+1) (b e-a f)^2 (d e-c f)^3}+\frac{f (a+b x)^{m+1} (-2 a d f+b c f+b d e)}{(e+f x) (b c-a d) (b e-a f) (d e-c f)^2}+\frac{d (a+b x)^{m+1}}{(c+d x) (e+f x) (b c-a d) (d e-c f)}",1,"Could not integrate","F",-1