1,1,27,21,0.0143175,"\int \frac{x^2}{(-1+x)^2 (1+x)^2} \, dx","Integrate[x^2/((-1 + x)^2*(1 + x)^2),x]","\frac{1}{4} \left(-\frac{2 x}{x^2-1}+\log (1-x)-\log (x+1)\right)","\frac{x}{2 \left(1-x^2\right)}-\frac{1}{2} \tanh ^{-1}(x)",1,"((-2*x)/(-1 + x^2) + Log[1 - x] - Log[1 + x])/4","A",1
2,1,47,55,0.0042212,"\int x^2 (a+b x) (a c-b c x)^3 \, dx","Integrate[x^2*(a + b*x)*(a*c - b*c*x)^3,x]","c^3 \left(\frac{a^4 x^3}{3}-\frac{1}{2} a^3 b x^4+\frac{1}{3} a b^3 x^6-\frac{1}{7} b^4 x^7\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,"c^3*((a^4*x^3)/3 - (a^3*b*x^4)/2 + (a*b^3*x^6)/3 - (b^4*x^7)/7)","A",1
3,1,47,55,0.0040264,"\int x (a+b x) (a c-b c x)^3 \, dx","Integrate[x*(a + b*x)*(a*c - b*c*x)^3,x]","c^3 \left(\frac{a^4 x^2}{2}-\frac{2}{3} a^3 b x^3+\frac{2}{5} a b^3 x^5-\frac{1}{6} b^4 x^6\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,"c^3*((a^4*x^2)/2 - (2*a^3*b*x^3)/3 + (2*a*b^3*x^5)/5 - (b^4*x^6)/6)","A",1
4,1,40,38,0.0024565,"\int (a+b x) (a c-b c x)^3 \, dx","Integrate[(a + b*x)*(a*c - b*c*x)^3,x]","c^3 \left(a^4 x-a^3 b x^2+\frac{1}{2} a b^3 x^4-\frac{1}{5} b^4 x^5\right)","\frac{c^3 (a-b x)^5}{5 b}-\frac{a c^3 (a-b x)^4}{2 b}",1,"c^3*(a^4*x - a^3*b*x^2 + (a*b^3*x^4)/2 - (b^4*x^5)/5)","A",1
5,1,48,47,0.0151539,"\int \frac{(a+b x) (a c-b c x)^3}{x} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^3)/x,x]","c^3 \left(a^4 \log (-b x)+\frac{1}{12} \left(19 a^4-24 a^3 b x+8 a b^3 x^3-3 b^4 x^4\right)\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*Log[-(b*x)])","A",1
6,1,39,47,0.0087724,"\int \frac{(a+b x) (a c-b c x)^3}{x^2} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^3)/x^2,x]","c^3 \left(-\frac{a^4}{x}-2 a^3 b \log (x)+a b^3 x^2-\frac{b^4 x^3}{3}\right)","-\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,"c^3*(-(a^4/x) + a*b^3*x^2 - (b^4*x^3)/3 - 2*a^3*b*Log[x])","A",1
7,1,41,18,0.006966,"\int \frac{(a+b x) (a c-b c x)^3}{x^3} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^3)/x^3,x]","c^3 \left(-\frac{a^4}{2 x^2}+\frac{2 a^3 b}{x}+2 a b^3 x-\frac{b^4 x^2}{2}\right)","-\frac{c^3 (a-b x)^4}{2 x^2}",1,"c^3*(-1/2*a^4/x^2 + (2*a^3*b)/x + 2*a*b^3*x - (b^4*x^2)/2)","B",1
8,1,37,45,0.0126902,"\int \frac{(a+b x) (a c-b c x)^3}{x^4} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^3)/x^4,x]","c^3 \left(-\frac{a^4}{3 x^3}+\frac{a^3 b}{x^2}+2 a b^3 \log (x)-b^4 x\right)","-\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,"c^3*(-1/3*a^4/x^3 + (a^3*b)/x^2 - b^4*x + 2*a*b^3*Log[x])","A",1
9,1,42,50,0.008932,"\int \frac{(a+b x) (a c-b c x)^3}{x^5} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^3)/x^5,x]","c^3 \left(-\frac{a^4}{4 x^4}+\frac{2 a^3 b}{3 x^3}-\frac{2 a b^3}{x}-b^4 \log (x)\right)","-\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,"c^3*(-1/4*a^4/x^4 + (2*a^3*b)/(3*x^3) - (2*a*b^3)/x - b^4*Log[x])","A",1
10,1,42,50,0.0062308,"\int \frac{(a+b x) (a c-b c x)^3}{x^6} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^3)/x^6,x]","c^3 \left(-\frac{a^4}{5 x^5}+\frac{a^3 b}{2 x^4}-\frac{a b^3}{x^2}+\frac{b^4}{x}\right)","-\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,"c^3*(-1/5*a^4/x^5 + (a^3*b)/(2*x^4) - (a*b^3)/x^2 + b^4/x)","A",1
11,1,47,55,0.007833,"\int \frac{(a+b x) (a c-b c x)^3}{x^7} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^3)/x^7,x]","c^3 \left(-\frac{a^4}{6 x^6}+\frac{2 a^3 b}{5 x^5}-\frac{2 a b^3}{3 x^3}+\frac{b^4}{2 x^2}\right)","-\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,"c^3*(-1/6*a^4/x^6 + (2*a^3*b)/(5*x^5) - (2*a*b^3)/(3*x^3) + b^4/(2*x^2))","A",1
12,1,47,55,0.0090451,"\int \frac{(a+b x) (a c-b c x)^3}{x^8} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^3)/x^8,x]","c^3 \left(-\frac{a^4}{7 x^7}+\frac{a^3 b}{3 x^6}-\frac{a b^3}{2 x^4}+\frac{b^4}{3 x^3}\right)","-\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,"c^3*(-1/7*a^4/x^7 + (a^3*b)/(3*x^6) - (a*b^3)/(2*x^4) + b^4/(3*x^3))","A",1
13,1,87,87,0.0049317,"\int x^4 (a+b x) (a c-b c x)^4 \, dx","Integrate[x^4*(a + b*x)*(a*c - b*c*x)^4,x]","\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}","\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,"(a^5*c^4*x^5)/5 - (a^4*b*c^4*x^6)/2 + (2*a^3*b^2*c^4*x^7)/7 + (a^2*b^3*c^4*x^8)/4 - (a*b^4*c^4*x^9)/3 + (b^5*c^4*x^10)/10","A",1
14,1,87,87,0.0039523,"\int x^3 (a+b x) (a c-b c x)^4 \, dx","Integrate[x^3*(a + b*x)*(a*c - b*c*x)^4,x]","\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","\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,"(a^5*c^4*x^4)/4 - (3*a^4*b*c^4*x^5)/5 + (a^3*b^2*c^4*x^6)/3 + (2*a^2*b^3*c^4*x^7)/7 - (3*a*b^4*c^4*x^8)/8 + (b^5*c^4*x^9)/9","A",1
15,1,87,80,0.0040549,"\int x^2 (a+b x) (a c-b c x)^4 \, dx","Integrate[x^2*(a + b*x)*(a*c - b*c*x)^4,x]","\frac{1}{3} a^5 c^4 x^3-\frac{3}{4} a^4 b c^4 x^4+\frac{2}{5} a^3 b^2 c^4 x^5+\frac{1}{3} a^2 b^3 c^4 x^6-\frac{3}{7} a b^4 c^4 x^7+\frac{1}{8} b^5 c^4 x^8","-\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,"(a^5*c^4*x^3)/3 - (3*a^4*b*c^4*x^4)/4 + (2*a^3*b^2*c^4*x^5)/5 + (a^2*b^3*c^4*x^6)/3 - (3*a*b^4*c^4*x^7)/7 + (b^5*c^4*x^8)/8","A",1
16,1,85,59,0.0043025,"\int x (a+b x) (a c-b c x)^4 \, dx","Integrate[x*(a + b*x)*(a*c - b*c*x)^4,x]","\frac{1}{2} a^5 c^4 x^2-a^4 b c^4 x^3+\frac{1}{2} a^3 b^2 c^4 x^4+\frac{2}{5} a^2 b^3 c^4 x^5-\frac{1}{2} a b^4 c^4 x^6+\frac{1}{7} b^5 c^4 x^7","-\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,"(a^5*c^4*x^2)/2 - a^4*b*c^4*x^3 + (a^3*b^2*c^4*x^4)/2 + (2*a^2*b^3*c^4*x^5)/5 - (a*b^4*c^4*x^6)/2 + (b^5*c^4*x^7)/7","A",1
17,1,68,38,0.0035505,"\int (a+b x) (a c-b c x)^4 \, dx","Integrate[(a + b*x)*(a*c - b*c*x)^4,x]","c^4 \left(a^5 x-\frac{3}{2} a^4 b x^2+\frac{2}{3} a^3 b^2 x^3+\frac{1}{2} a^2 b^3 x^4-\frac{3}{5} a b^4 x^5+\frac{b^5 x^6}{6}\right)","\frac{c^4 (a-b x)^6}{6 b}-\frac{2 a c^4 (a-b x)^5}{5 b}",1,"c^4*(a^5*x - (3*a^4*b*x^2)/2 + (2*a^3*b^2*x^3)/3 + (a^2*b^3*x^4)/2 - (3*a*b^4*x^5)/5 + (b^5*x^6)/6)","A",1
18,1,70,76,0.0286144,"\int \frac{(a+b x) (a c-b c x)^4}{x} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^4)/x,x]","\frac{1}{60} c^4 \left(60 a^5 \log (-b c x)+113 a^5-180 a^4 b x+60 a^3 b^2 x^2+40 a^2 b^3 x^3-45 a b^4 x^4+12 b^5 x^5\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,"(c^4*(113*a^5 - 180*a^4*b*x + 60*a^3*b^2*x^2 + 40*a^2*b^3*x^3 - 45*a*b^4*x^4 + 12*b^5*x^5 + 60*a^5*Log[-(b*c*x)]))/60","A",1
19,1,73,73,0.0105174,"\int \frac{(a+b x) (a c-b c x)^4}{x^2} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^4)/x^2,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","-\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,"-((a^5*c^4)/x) + 2*a^3*b^2*c^4*x + a^2*b^3*c^4*x^2 - a*b^4*c^4*x^3 + (b^5*c^4*x^4)/4 - 3*a^4*b*c^4*Log[x]","A",1
20,1,78,78,0.0121109,"\int \frac{(a+b x) (a c-b c x)^4}{x^3} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^4)/x^3,x]","-\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","-\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,"-1/2*(a^5*c^4)/x^2 + (3*a^4*b*c^4)/x + 2*a^2*b^3*c^4*x - (3*a*b^4*c^4*x^2)/2 + (b^5*c^4*x^3)/3 + 2*a^3*b^2*c^4*Log[x]","A",1
21,1,78,78,0.0102205,"\int \frac{(a+b x) (a c-b c x)^4}{x^4} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^4)/x^4,x]","-\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","-\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,"-1/3*(a^5*c^4)/x^3 + (3*a^4*b*c^4)/(2*x^2) - (2*a^3*b^2*c^4)/x - 3*a*b^4*c^4*x + (b^5*c^4*x^2)/2 + 2*a^2*b^3*c^4*Log[x]","A",1
22,1,72,72,0.0160879,"\int \frac{(a+b x) (a c-b c x)^4}{x^5} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^4)/x^5,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","-\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,"-1/4*(a^5*c^4)/x^4 + (a^4*b*c^4)/x^3 - (a^3*b^2*c^4)/x^2 - (2*a^2*b^3*c^4)/x + b^5*c^4*x - 3*a*b^4*c^4*Log[x]","A",1
23,1,79,79,0.0085158,"\int \frac{(a+b x) (a c-b c x)^4}{x^6} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^4)/x^6,x]","-\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)","-\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,"-1/5*(a^5*c^4)/x^5 + (3*a^4*b*c^4)/(4*x^4) - (2*a^3*b^2*c^4)/(3*x^3) - (a^2*b^3*c^4)/x^2 + (3*a*b^4*c^4)/x + b^5*c^4*Log[x]","A",1
24,1,85,41,0.0130452,"\int \frac{(a+b x) (a c-b c x)^4}{x^7} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^4)/x^7,x]","-\frac{a^5 c^4}{6 x^6}+\frac{3 a^4 b c^4}{5 x^5}-\frac{a^3 b^2 c^4}{2 x^4}-\frac{2 a^2 b^3 c^4}{3 x^3}+\frac{3 a b^4 c^4}{2 x^2}-\frac{b^5 c^4}{x}","-\frac{c^4 (a-b x)^5}{6 x^6}-\frac{7 b c^4 (a-b x)^5}{30 a x^5}",1,"-1/6*(a^5*c^4)/x^6 + (3*a^4*b*c^4)/(5*x^5) - (a^3*b^2*c^4)/(2*x^4) - (2*a^2*b^3*c^4)/(3*x^3) + (3*a*b^4*c^4)/(2*x^2) - (b^5*c^4)/x","B",1
25,1,84,84,0.0095753,"\int \frac{(a+b x) (a c-b c x)^4}{x^8} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^4)/x^8,x]","-\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}","-\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,"-1/7*(a^5*c^4)/x^7 + (a^4*b*c^4)/(2*x^6) - (2*a^3*b^2*c^4)/(5*x^5) - (a^2*b^3*c^4)/(2*x^4) + (a*b^4*c^4)/x^3 - (b^5*c^4)/(2*x^2)","A",1
26,1,87,87,0.0098557,"\int \frac{(a+b x) (a c-b c x)^4}{x^9} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^4)/x^9,x]","-\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}","-\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,"-1/8*(a^5*c^4)/x^8 + (3*a^4*b*c^4)/(7*x^7) - (a^3*b^2*c^4)/(3*x^6) - (2*a^2*b^3*c^4)/(5*x^5) + (3*a*b^4*c^4)/(4*x^4) - (b^5*c^4)/(3*x^3)","A",1
27,1,73,87,0.0052508,"\int x^4 (a+b x) (a c-b c x)^5 \, dx","Integrate[x^4*(a + b*x)*(a*c - b*c*x)^5,x]","c^5 \left(\frac{a^6 x^5}{5}-\frac{2}{3} a^5 b x^6+\frac{5}{7} a^4 b^2 x^7-\frac{5}{9} a^2 b^4 x^9+\frac{2}{5} a b^5 x^{10}-\frac{1}{11} b^6 x^{11}\right)","\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,"c^5*((a^6*x^5)/5 - (2*a^5*b*x^6)/3 + (5*a^4*b^2*x^7)/7 - (5*a^2*b^4*x^9)/9 + (2*a*b^5*x^10)/5 - (b^6*x^11)/11)","A",1
28,1,73,87,0.0038323,"\int x^3 (a+b x) (a c-b c x)^5 \, dx","Integrate[x^3*(a + b*x)*(a*c - b*c*x)^5,x]","c^5 \left(\frac{a^6 x^4}{4}-\frac{4}{5} a^5 b x^5+\frac{5}{6} a^4 b^2 x^6-\frac{5}{8} a^2 b^4 x^8+\frac{4}{9} a b^5 x^9-\frac{1}{10} b^6 x^{10}\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,"c^5*((a^6*x^4)/4 - (4*a^5*b*x^5)/5 + (5*a^4*b^2*x^6)/6 - (5*a^2*b^4*x^8)/8 + (4*a*b^5*x^9)/9 - (b^6*x^10)/10)","A",1
29,1,68,80,0.0046462,"\int x^2 (a+b x) (a c-b c x)^5 \, dx","Integrate[x^2*(a + b*x)*(a*c - b*c*x)^5,x]","c^5 \left(\frac{a^6 x^3}{3}-a^5 b x^4+a^4 b^2 x^5-\frac{5}{7} a^2 b^4 x^7+\frac{1}{2} a b^5 x^8-\frac{1}{9} b^6 x^9\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,"c^5*((a^6*x^3)/3 - a^5*b*x^4 + a^4*b^2*x^5 - (5*a^2*b^4*x^7)/7 + (a*b^5*x^8)/2 - (b^6*x^9)/9)","A",1
30,1,73,59,0.0031647,"\int x (a+b x) (a c-b c x)^5 \, dx","Integrate[x*(a + b*x)*(a*c - b*c*x)^5,x]","c^5 \left(\frac{a^6 x^2}{2}-\frac{4}{3} a^5 b x^3+\frac{5}{4} a^4 b^2 x^4-\frac{5}{6} a^2 b^4 x^6+\frac{4}{7} a b^5 x^7-\frac{1}{8} b^6 x^8\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,"c^5*((a^6*x^2)/2 - (4*a^5*b*x^3)/3 + (5*a^4*b^2*x^4)/4 - (5*a^2*b^4*x^6)/6 + (4*a*b^5*x^7)/7 - (b^6*x^8)/8)","A",1
31,1,64,38,0.0065419,"\int (a+b x) (a c-b c x)^5 \, dx","Integrate[(a + b*x)*(a*c - b*c*x)^5,x]","c^5 \left(a^6 x-2 a^5 b x^2+\frac{5}{3} a^4 b^2 x^3-a^2 b^4 x^5+\frac{2}{3} a b^5 x^6-\frac{1}{7} b^6 x^7\right)","\frac{c^5 (a-b x)^7}{7 b}-\frac{a c^5 (a-b x)^6}{3 b}",1,"c^5*(a^6*x - 2*a^5*b*x^2 + (5*a^4*b^2*x^3)/3 - a^2*b^4*x^5 + (2*a*b^5*x^6)/3 - (b^6*x^7)/7)","A",1
32,1,75,79,0.016277,"\int \frac{(a+b x) (a c-b c x)^5}{x} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^5)/x,x]","c^5 \left(a^6 \log (-b x)+\frac{127 a^6}{60}-4 a^5 b x+\frac{5}{2} a^4 b^2 x^2-\frac{5}{4} a^2 b^4 x^4+\frac{4}{5} a b^5 x^5-\frac{b^6 x^6}{6}\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,"c^5*((127*a^6)/60 - 4*a^5*b*x + (5*a^4*b^2*x^2)/2 - (5*a^2*b^4*x^4)/4 + (4*a*b^5*x^5)/5 - (b^6*x^6)/6 + a^6*Log[-(b*x)])","A",1
33,1,61,75,0.0091727,"\int \frac{(a+b x) (a c-b c x)^5}{x^2} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^5)/x^2,x]","c^5 \left(-\frac{a^6}{x}-4 a^5 b \log (x)+5 a^4 b^2 x-\frac{5}{3} a^2 b^4 x^3+a b^5 x^4-\frac{b^6 x^5}{5}\right)","-\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,"c^5*(-(a^6/x) + 5*a^4*b^2*x - (5*a^2*b^4*x^3)/3 + a*b^5*x^4 - (b^6*x^5)/5 - 4*a^5*b*Log[x])","A",1
34,1,68,82,0.0091996,"\int \frac{(a+b x) (a c-b c x)^5}{x^3} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^5)/x^3,x]","c^5 \left(-\frac{a^6}{2 x^2}+\frac{4 a^5 b}{x}+5 a^4 b^2 \log (x)-\frac{5}{2} a^2 b^4 x^2+\frac{4}{3} a b^5 x^3-\frac{b^6 x^4}{4}\right)","-\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,"c^5*(-1/2*a^6/x^2 + (4*a^5*b)/x - (5*a^2*b^4*x^2)/2 + (4*a*b^5*x^3)/3 - (b^6*x^4)/4 + 5*a^4*b^2*Log[x])","A",1
35,1,63,18,0.0152335,"\int \frac{(a+b x) (a c-b c x)^5}{x^4} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^5)/x^4,x]","c^5 \left(-\frac{a^6}{3 x^3}+\frac{2 a^5 b}{x^2}-\frac{5 a^4 b^2}{x}-5 a^2 b^4 x+2 a b^5 x^2-\frac{b^6 x^3}{3}\right)","-\frac{c^5 (a-b x)^6}{3 x^3}",1,"c^5*(-1/3*a^6/x^3 + (2*a^5*b)/x^2 - (5*a^4*b^2)/x - 5*a^2*b^4*x + 2*a*b^5*x^2 - (b^6*x^3)/3)","B",1
36,1,66,80,0.0126653,"\int \frac{(a+b x) (a c-b c x)^5}{x^5} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^5)/x^5,x]","c^5 \left(-\frac{a^6}{4 x^4}+\frac{4 a^5 b}{3 x^3}-\frac{5 a^4 b^2}{2 x^2}-5 a^2 b^4 \log (x)+4 a b^5 x-\frac{b^6 x^2}{2}\right)","-\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,"c^5*(-1/4*a^6/x^4 + (4*a^5*b)/(3*x^3) - (5*a^4*b^2)/(2*x^2) + 4*a*b^5*x - (b^6*x^2)/2 - 5*a^2*b^4*Log[x])","A",1
37,1,61,75,0.0138506,"\int \frac{(a+b x) (a c-b c x)^5}{x^6} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^5)/x^6,x]","c^5 \left(-\frac{a^6}{5 x^5}+\frac{a^5 b}{x^4}-\frac{5 a^4 b^2}{3 x^3}+\frac{5 a^2 b^4}{x}+4 a b^5 \log (x)-b^6 x\right)","-\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,"c^5*(-1/5*a^6/x^5 + (a^5*b)/x^4 - (5*a^4*b^2)/(3*x^3) + (5*a^2*b^4)/x - b^6*x + 4*a*b^5*Log[x])","A",1
38,1,68,82,0.009083,"\int \frac{(a+b x) (a c-b c x)^5}{x^7} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^5)/x^7,x]","c^5 \left(-\frac{a^6}{6 x^6}+\frac{4 a^5 b}{5 x^5}-\frac{5 a^4 b^2}{4 x^4}+\frac{5 a^2 b^4}{2 x^2}-\frac{4 a b^5}{x}-b^6 \log (x)\right)","-\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,"c^5*(-1/6*a^6/x^6 + (4*a^5*b)/(5*x^5) - (5*a^4*b^2)/(4*x^4) + (5*a^2*b^4)/(2*x^2) - (4*a*b^5)/x - b^6*Log[x])","A",1
39,1,66,41,0.0089514,"\int \frac{(a+b x) (a c-b c x)^5}{x^8} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^5)/x^8,x]","c^5 \left(-\frac{a^6}{7 x^7}+\frac{2 a^5 b}{3 x^6}-\frac{a^4 b^2}{x^5}+\frac{5 a^2 b^4}{3 x^3}-\frac{2 a b^5}{x^2}+\frac{b^6}{x}\right)","-\frac{c^5 (a-b x)^6}{7 x^7}-\frac{4 b c^5 (a-b x)^6}{21 a x^6}",1,"c^5*(-1/7*a^6/x^7 + (2*a^5*b)/(3*x^6) - (a^4*b^2)/x^5 + (5*a^2*b^4)/(3*x^3) - (2*a*b^5)/x^2 + b^6/x)","A",1
40,1,73,65,0.0086433,"\int \frac{(a+b x) (a c-b c x)^5}{x^9} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^5)/x^9,x]","c^5 \left(-\frac{a^6}{8 x^8}+\frac{4 a^5 b}{7 x^7}-\frac{5 a^4 b^2}{6 x^6}+\frac{5 a^2 b^4}{4 x^4}-\frac{4 a b^5}{3 x^3}+\frac{b^6}{2 x^2}\right)","-\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,"c^5*(-1/8*a^6/x^8 + (4*a^5*b)/(7*x^7) - (5*a^4*b^2)/(6*x^6) + (5*a^2*b^4)/(4*x^4) - (4*a*b^5)/(3*x^3) + b^6/(2*x^2))","A",1
41,1,68,82,0.0070931,"\int \frac{(a+b x) (a c-b c x)^5}{x^{10}} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^5)/x^10,x]","c^5 \left(-\frac{a^6}{9 x^9}+\frac{a^5 b}{2 x^8}-\frac{5 a^4 b^2}{7 x^7}+\frac{a^2 b^4}{x^5}-\frac{a b^5}{x^4}+\frac{b^6}{3 x^3}\right)","-\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,"c^5*(-1/9*a^6/x^9 + (a^5*b)/(2*x^8) - (5*a^4*b^2)/(7*x^7) + (a^2*b^4)/x^5 - (a*b^5)/x^4 + b^6/(3*x^3))","A",1
42,1,73,87,0.0093446,"\int \frac{(a+b x) (a c-b c x)^5}{x^{11}} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^5)/x^11,x]","c^5 \left(-\frac{a^6}{10 x^{10}}+\frac{4 a^5 b}{9 x^9}-\frac{5 a^4 b^2}{8 x^8}+\frac{5 a^2 b^4}{6 x^6}-\frac{4 a b^5}{5 x^5}+\frac{b^6}{4 x^4}\right)","-\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,"c^5*(-1/10*a^6/x^10 + (4*a^5*b)/(9*x^9) - (5*a^4*b^2)/(8*x^8) + (5*a^2*b^4)/(6*x^6) - (4*a*b^5)/(5*x^5) + b^6/(4*x^4))","A",1
43,1,73,87,0.0069387,"\int \frac{(a+b x) (a c-b c x)^5}{x^{12}} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^5)/x^12,x]","c^5 \left(-\frac{a^6}{11 x^{11}}+\frac{2 a^5 b}{5 x^{10}}-\frac{5 a^4 b^2}{9 x^9}+\frac{5 a^2 b^4}{7 x^7}-\frac{2 a b^5}{3 x^6}+\frac{b^6}{5 x^5}\right)","-\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,"c^5*(-1/11*a^6/x^11 + (2*a^5*b)/(5*x^10) - (5*a^4*b^2)/(9*x^9) + (5*a^2*b^4)/(7*x^7) - (2*a*b^5)/(3*x^6) + b^6/(5*x^5))","A",1
44,1,113,113,0.0149681,"\int \frac{(a+b x) (a c-b c x)^6}{x^8} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^6)/x^8,x]","-\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)","-\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,"-1/7*(a^7*c^6)/x^7 + (5*a^6*b*c^6)/(6*x^6) - (9*a^5*b^2*c^6)/(5*x^5) + (5*a^4*b^3*c^6)/(4*x^4) + (5*a^3*b^4*c^6)/(3*x^3) - (9*a^2*b^5*c^6)/(2*x^2) + (5*a*b^6*c^6)/x + b^7*c^6*Log[x]","A",1
45,1,112,41,0.0155095,"\int \frac{(a+b x) (a c-b c x)^6}{x^9} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^6)/x^9,x]","-\frac{a^7 c^6}{8 x^8}+\frac{5 a^6 b c^6}{7 x^7}-\frac{3 a^5 b^2 c^6}{2 x^6}+\frac{a^4 b^3 c^6}{x^5}+\frac{5 a^3 b^4 c^6}{4 x^4}-\frac{3 a^2 b^5 c^6}{x^3}+\frac{5 a b^6 c^6}{2 x^2}-\frac{b^7 c^6}{x}","-\frac{c^6 (a-b x)^7}{8 x^8}-\frac{9 b c^6 (a-b x)^7}{56 a x^7}",1,"-1/8*(a^7*c^6)/x^8 + (5*a^6*b*c^6)/(7*x^7) - (3*a^5*b^2*c^6)/(2*x^6) + (a^4*b^3*c^6)/x^5 + (5*a^3*b^4*c^6)/(4*x^4) - (3*a^2*b^5*c^6)/x^3 + (5*a*b^6*c^6)/(2*x^2) - (b^7*c^6)/x","B",1
46,1,116,65,0.0102597,"\int \frac{(a+b x) (a c-b c x)^6}{x^{10}} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^6)/x^10,x]","-\frac{a^7 c^6}{9 x^9}+\frac{5 a^6 b c^6}{8 x^8}-\frac{9 a^5 b^2 c^6}{7 x^7}+\frac{5 a^4 b^3 c^6}{6 x^6}+\frac{a^3 b^4 c^6}{x^5}-\frac{9 a^2 b^5 c^6}{4 x^4}+\frac{5 a b^6 c^6}{3 x^3}-\frac{b^7 c^6}{2 x^2}","-\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,"-1/9*(a^7*c^6)/x^9 + (5*a^6*b*c^6)/(8*x^8) - (9*a^5*b^2*c^6)/(7*x^7) + (5*a^4*b^3*c^6)/(6*x^6) + (a^3*b^4*c^6)/x^5 - (9*a^2*b^5*c^6)/(4*x^4) + (5*a*b^6*c^6)/(3*x^3) - (b^7*c^6)/(2*x^2)","A",1
47,1,119,89,0.013094,"\int \frac{(a+b x) (a c-b c x)^6}{x^{11}} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^6)/x^11,x]","-\frac{a^7 c^6}{10 x^{10}}+\frac{5 a^6 b c^6}{9 x^9}-\frac{9 a^5 b^2 c^6}{8 x^8}+\frac{5 a^4 b^3 c^6}{7 x^7}+\frac{5 a^3 b^4 c^6}{6 x^6}-\frac{9 a^2 b^5 c^6}{5 x^5}+\frac{5 a b^6 c^6}{4 x^4}-\frac{b^7 c^6}{3 x^3}","-\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,"-1/10*(a^7*c^6)/x^10 + (5*a^6*b*c^6)/(9*x^9) - (9*a^5*b^2*c^6)/(8*x^8) + (5*a^4*b^3*c^6)/(7*x^7) + (5*a^3*b^4*c^6)/(6*x^6) - (9*a^2*b^5*c^6)/(5*x^5) + (5*a*b^6*c^6)/(4*x^4) - (b^7*c^6)/(3*x^3)","A",1
48,1,114,114,0.0150549,"\int \frac{(a+b x) (a c-b c x)^6}{x^{12}} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^6)/x^12,x]","-\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}","-\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,"-1/11*(a^7*c^6)/x^11 + (a^6*b*c^6)/(2*x^10) - (a^5*b^2*c^6)/x^9 + (5*a^4*b^3*c^6)/(8*x^8) + (5*a^3*b^4*c^6)/(7*x^7) - (3*a^2*b^5*c^6)/(2*x^6) + (a*b^6*c^6)/x^5 - (b^7*c^6)/(4*x^4)","A",1
49,1,119,119,0.0100887,"\int \frac{(a+b x) (a c-b c x)^6}{x^{13}} \, dx","Integrate[((a + b*x)*(a*c - b*c*x)^6)/x^13,x]","-\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}","-\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,"-1/12*(a^7*c^6)/x^12 + (5*a^6*b*c^6)/(11*x^11) - (9*a^5*b^2*c^6)/(10*x^10) + (5*a^4*b^3*c^6)/(9*x^9) + (5*a^3*b^4*c^6)/(8*x^8) - (9*a^2*b^5*c^6)/(7*x^7) + (5*a*b^6*c^6)/(6*x^6) - (b^7*c^6)/(5*x^5)","A",1
50,1,85,106,0.0640083,"\int \frac{(e x)^{5/2}}{(a+b x) (a c-b c x)} \, dx","Integrate[(e*x)^(5/2)/((a + b*x)*(a*c - b*c*x)),x]","-\frac{(e x)^{5/2} \left(3 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)-3 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+2 b^{3/2} x^{3/2}\right)}{3 b^{7/2} c x^{5/2}}","-\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,"-1/3*((e*x)^(5/2)*(2*b^(3/2)*x^(3/2) + 3*a^(3/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]] - 3*a^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(b^(7/2)*c*x^(5/2))","A",1
51,1,80,103,0.0440224,"\int \frac{(e x)^{3/2}}{(a+b x) (a c-b c x)} \, dx","Integrate[(e*x)^(3/2)/((a + b*x)*(a*c - b*c*x)),x]","\frac{(e x)^{3/2} \left(\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)-2 \sqrt{b} \sqrt{x}\right)}{b^{5/2} c x^{3/2}}","\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,"((e*x)^(3/2)*(-2*Sqrt[b]*Sqrt[x] + Sqrt[a]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]] + Sqrt[a]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(b^(5/2)*c*x^(3/2))","A",1
52,1,63,88,0.0248974,"\int \frac{\sqrt{e x}}{(a+b x) (a c-b c x)} \, dx","Integrate[Sqrt[e*x]/((a + b*x)*(a*c - b*c*x)),x]","\frac{\sqrt{e x} \left(\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)-\tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)\right)}{\sqrt{a} b^{3/2} c \sqrt{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}",1,"(Sqrt[e*x]*(-ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]] + ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(Sqrt[a]*b^(3/2)*c*Sqrt[x])","A",1
53,1,61,87,0.0406981,"\int \frac{1}{\sqrt{e x} (a+b x) (a c-b c x)} \, dx","Integrate[1/(Sqrt[e*x]*(a + b*x)*(a*c - b*c*x)),x]","\frac{\sqrt{x} \left(\tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)\right)}{a^{3/2} \sqrt{b} c \sqrt{e 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}}",1,"(Sqrt[x]*(ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]] + ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(a^(3/2)*Sqrt[b]*c*Sqrt[e*x])","A",1
54,1,34,106,0.0162897,"\int \frac{1}{(e x)^{3/2} (a+b x) (a c-b c x)} \, dx","Integrate[1/((e*x)^(3/2)*(a + b*x)*(a*c - b*c*x)),x]","-\frac{2 x \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};\frac{b^2 x^2}{a^2}\right)}{a^2 c (e x)^{3/2}}","-\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*x*Hypergeometric2F1[-1/4, 1, 3/4, (b^2*x^2)/a^2])/(a^2*c*(e*x)^(3/2))","C",1
55,1,36,107,0.0169986,"\int \frac{1}{(e x)^{5/2} (a+b x) (a c-b c x)} \, dx","Integrate[1/((e*x)^(5/2)*(a + b*x)*(a*c - b*c*x)),x]","-\frac{2 x \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};\frac{b^2 x^2}{a^2}\right)}{3 a^2 c (e x)^{5/2}}","\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*x*Hypergeometric2F1[-3/4, 1, 1/4, (b^2*x^2)/a^2])/(3*a^2*c*(e*x)^(5/2))","C",1
56,1,100,156,0.0832027,"\int (e x)^m (2-2 a x)^3 (1+a x)^4 \, dx","Integrate[(e*x)^m*(2 - 2*a*x)^3*(1 + a*x)^4,x]","8 x \left(-\frac{a^7 x^7}{m+8}-\frac{a^6 x^6}{m+7}+\frac{3 a^5 x^5}{m+6}+\frac{3 a^4 x^4}{m+5}-\frac{3 a^3 x^3}{m+4}-\frac{3 a^2 x^2}{m+3}+\frac{a x}{m+2}+\frac{1}{m+1}\right) (e x)^m","-\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,"8*x*(e*x)^m*((1 + m)^(-1) + (a*x)/(2 + m) - (3*a^2*x^2)/(3 + m) - (3*a^3*x^3)/(4 + m) + (3*a^4*x^4)/(5 + m) + (3*a^5*x^5)/(6 + m) - (a^6*x^6)/(7 + m) - (a^7*x^7)/(8 + m))","A",1
57,1,72,116,0.0464697,"\int (e x)^m (2-2 a x)^2 (1+a x)^3 \, dx","Integrate[(e*x)^m*(2 - 2*a*x)^2*(1 + a*x)^3,x]","4 x \left(\frac{a^5 x^5}{m+6}+\frac{a^4 x^4}{m+5}-\frac{2 a^3 x^3}{m+4}-\frac{2 a^2 x^2}{m+3}+\frac{a x}{m+2}+\frac{1}{m+1}\right) (e x)^m","\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,"4*x*(e*x)^m*((1 + m)^(-1) + (a*x)/(2 + m) - (2*a^2*x^2)/(3 + m) - (2*a^3*x^3)/(4 + m) + (a^4*x^4)/(5 + m) + (a^5*x^5)/(6 + m))","A",1
58,1,83,76,0.0899537,"\int (e x)^m (2-2 a x) (1+a x)^2 \, dx","Integrate[(e*x)^m*(2 - 2*a*x)*(1 + a*x)^2,x]","\frac{\left(\frac{2 (2 m+5) x \left(m \left(3 a^2 x^2+8 a x+5\right)+2 a^2 x^2+(a m x+m)^2+6 a x+6\right)}{(m+1) (m+2) (m+3)}-2 x (a x+1)^3\right) (e x)^m}{m+4}","-\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,"((e*x)^m*(-2*x*(1 + a*x)^3 + (2*(5 + 2*m)*x*(6 + 6*a*x + 2*a^2*x^2 + (m + a*m*x)^2 + m*(5 + 8*a*x + 3*a^2*x^2)))/((1 + m)*(2 + m)*(3 + m))))/(4 + m)","A",1
59,1,77,86,0.0387618,"\int \frac{(e x)^m}{(2-2 a x)^2 (1+a x)} \, dx","Integrate[(e*x)^m/((2 - 2*a*x)^2*(1 + a*x)),x]","\frac{x (e x)^m \left(a (m+1) x \, _2F_1\left(2,\frac{m}{2}+1;\frac{m}{2}+2;a^2 x^2\right)+(m+2) \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)\right)}{4 (m+1) (m+2)}","\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,"(x*(e*x)^m*(a*(1 + m)*x*Hypergeometric2F1[2, 1 + m/2, 2 + m/2, a^2*x^2] + (2 + m)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, a^2*x^2]))/(4*(1 + m)*(2 + m))","A",1
60,1,77,86,0.0341219,"\int \frac{(e x)^m}{(2-2 a x)^3 (1+a x)^2} \, dx","Integrate[(e*x)^m/((2 - 2*a*x)^3*(1 + a*x)^2),x]","\frac{x (e x)^m \left(a (m+1) x \, _2F_1\left(3,\frac{m}{2}+1;\frac{m}{2}+2;a^2 x^2\right)+(m+2) \, _2F_1\left(3,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)\right)}{8 (m+1) (m+2)}","\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,"(x*(e*x)^m*(a*(1 + m)*x*Hypergeometric2F1[3, 1 + m/2, 2 + m/2, a^2*x^2] + (2 + m)*Hypergeometric2F1[3, (1 + m)/2, (3 + m)/2, a^2*x^2]))/(8*(1 + m)*(2 + m))","A",1
61,1,77,86,0.0354723,"\int \frac{(e x)^m}{(2-2 a x)^4 (1+a x)^3} \, dx","Integrate[(e*x)^m/((2 - 2*a*x)^4*(1 + a*x)^3),x]","\frac{x (e x)^m \left(a (m+1) x \, _2F_1\left(4,\frac{m}{2}+1;\frac{m}{2}+2;a^2 x^2\right)+(m+2) \, _2F_1\left(4,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)\right)}{16 (m+1) (m+2)}","\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,"(x*(e*x)^m*(a*(1 + m)*x*Hypergeometric2F1[4, 1 + m/2, 2 + m/2, a^2*x^2] + (2 + m)*Hypergeometric2F1[4, (1 + m)/2, (3 + m)/2, a^2*x^2]))/(16*(1 + m)*(2 + m))","A",1
62,1,122,197,0.107651,"\int (e x)^m (a+b x)^4 (a d-b d x)^3 \, dx","Integrate[(e*x)^m*(a + b*x)^4*(a*d - b*d*x)^3,x]","d^3 x (e x)^m \left(\frac{a^7}{m+1}+\frac{a^6 b x}{m+2}-\frac{3 a^5 b^2 x^2}{m+3}-\frac{3 a^4 b^3 x^3}{m+4}+\frac{3 a^3 b^4 x^4}{m+5}+\frac{3 a^2 b^5 x^5}{m+6}-\frac{a b^6 x^6}{m+7}-\frac{b^7 x^7}{m+8}\right)","\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,"d^3*x*(e*x)^m*(a^7/(1 + m) + (a^6*b*x)/(2 + m) - (3*a^5*b^2*x^2)/(3 + m) - (3*a^4*b^3*x^3)/(4 + m) + (3*a^3*b^4*x^4)/(5 + m) + (3*a^2*b^5*x^5)/(6 + m) - (a*b^6*x^6)/(7 + m) - (b^7*x^7)/(8 + m))","A",1
63,1,88,143,0.069339,"\int (e x)^m (a+b x)^3 (a d-b d x)^2 \, dx","Integrate[(e*x)^m*(a + b*x)^3*(a*d - b*d*x)^2,x]","d^2 x (e x)^m \left(\frac{a^5}{m+1}+\frac{a^4 b x}{m+2}-\frac{2 a^3 b^2 x^2}{m+3}-\frac{2 a^2 b^3 x^3}{m+4}+\frac{a b^4 x^4}{m+5}+\frac{b^5 x^5}{m+6}\right)","\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,"d^2*x*(e*x)^m*(a^5/(1 + m) + (a^4*b*x)/(2 + m) - (2*a^3*b^2*x^2)/(3 + m) - (2*a^2*b^3*x^3)/(4 + m) + (a*b^4*x^4)/(5 + m) + (b^5*x^5)/(6 + m))","A",1
64,1,87,85,0.1017372,"\int (e x)^m (a+b x)^2 (a d-b d x) \, dx","Integrate[(e*x)^m*(a + b*x)^2*(a*d - b*d*x),x]","\frac{d (e x)^m \left(\frac{a (2 m+5) x \left(a^2 \left(m^2+5 m+6\right)+2 a b \left(m^2+4 m+3\right) x+b^2 \left(m^2+3 m+2\right) x^2\right)}{(m+1) (m+2) (m+3)}-x (a+b x)^3\right)}{m+4}","\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,"(d*(e*x)^m*(-(x*(a + b*x)^3) + (a*(5 + 2*m)*x*(a^2*(6 + 5*m + m^2) + 2*a*b*(3 + 4*m + m^2)*x + b^2*(2 + 3*m + m^2)*x^2))/((1 + m)*(2 + m)*(3 + m))))/(4 + m)","A",1
65,1,87,98,0.0463278,"\int \frac{(e x)^m}{(a+b x) (a d-b d x)^2} \, dx","Integrate[(e*x)^m/((a + b*x)*(a*d - b*d*x)^2),x]","\frac{x (e x)^m \left(b (m+1) x \, _2F_1\left(2,\frac{m}{2}+1;\frac{m}{2}+2;\frac{b^2 x^2}{a^2}\right)+a (m+2) \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};\frac{b^2 x^2}{a^2}\right)\right)}{a^4 d^2 (m+1) (m+2)}","\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,"(x*(e*x)^m*(b*(1 + m)*x*Hypergeometric2F1[2, 1 + m/2, 2 + m/2, (b^2*x^2)/a^2] + a*(2 + m)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, (b^2*x^2)/a^2]))/(a^4*d^2*(1 + m)*(2 + m))","A",1
66,1,87,98,0.0478565,"\int \frac{(e x)^m}{(a+b x)^2 (a d-b d x)^3} \, dx","Integrate[(e*x)^m/((a + b*x)^2*(a*d - b*d*x)^3),x]","\frac{x (e x)^m \left(b (m+1) x \, _2F_1\left(3,\frac{m}{2}+1;\frac{m}{2}+2;\frac{b^2 x^2}{a^2}\right)+a (m+2) \, _2F_1\left(3,\frac{m+1}{2};\frac{m+3}{2};\frac{b^2 x^2}{a^2}\right)\right)}{a^6 d^3 (m+1) (m+2)}","\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,"(x*(e*x)^m*(b*(1 + m)*x*Hypergeometric2F1[3, 1 + m/2, 2 + m/2, (b^2*x^2)/a^2] + a*(2 + m)*Hypergeometric2F1[3, (1 + m)/2, (3 + m)/2, (b^2*x^2)/a^2]))/(a^6*d^3*(1 + m)*(2 + m))","A",1
67,1,87,98,0.0377485,"\int \frac{(e x)^m}{(a+b x)^3 (a d-b d x)^4} \, dx","Integrate[(e*x)^m/((a + b*x)^3*(a*d - b*d*x)^4),x]","\frac{x (e x)^m \left(b (m+1) x \, _2F_1\left(4,\frac{m}{2}+1;\frac{m}{2}+2;\frac{b^2 x^2}{a^2}\right)+a (m+2) \, _2F_1\left(4,\frac{m+1}{2};\frac{m+3}{2};\frac{b^2 x^2}{a^2}\right)\right)}{a^8 d^4 (m+1) (m+2)}","\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,"(x*(e*x)^m*(b*(1 + m)*x*Hypergeometric2F1[4, 1 + m/2, 2 + m/2, (b^2*x^2)/a^2] + a*(2 + m)*Hypergeometric2F1[4, (1 + m)/2, (3 + m)/2, (b^2*x^2)/a^2]))/(a^8*d^4*(1 + m)*(2 + m))","A",1
68,1,96,145,0.1317217,"\int (e x)^m (a+b x) (a c-b c x)^4 \, dx","Integrate[(e*x)^m*(a + b*x)*(a*c - b*c*x)^4,x]","\frac{c^4 x (e x)^m \left(a (2 m+7) \left(\frac{a^4}{m+1}-\frac{4 a^3 b x}{m+2}+\frac{6 a^2 b^2 x^2}{m+3}-\frac{4 a b^3 x^3}{m+4}+\frac{b^4 x^4}{m+5}\right)+(b x-a)^5\right)}{m+6}","\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,"(c^4*x*(e*x)^m*((-a + b*x)^5 + a*(7 + 2*m)*(a^4/(1 + m) - (4*a^3*b*x)/(2 + m) + (6*a^2*b^2*x^2)/(3 + m) - (4*a*b^3*x^3)/(4 + m) + (b^4*x^4)/(5 + m))))/(6 + m)","A",1
69,1,112,94,0.0695951,"\int (e x)^m (a+b x) (a c-b c x)^3 \, dx","Integrate[(e*x)^m*(a + b*x)*(a*c - b*c*x)^3,x]","-\frac{c^3 x (e x)^m \left(-\left(a^4 \left(m^3+11 m^2+38 m+40\right)\right)+2 a^3 b \left(m^3+10 m^2+29 m+20\right) x-2 a b^3 \left(m^3+8 m^2+17 m+10\right) x^3+b^4 \left(m^3+7 m^2+14 m+8\right) x^4\right)}{(m+1) (m+2) (m+4) (m+5)}","\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,"-((c^3*x*(e*x)^m*(-(a^4*(40 + 38*m + 11*m^2 + m^3)) + 2*a^3*b*(20 + 29*m + 10*m^2 + m^3)*x - 2*a*b^3*(10 + 17*m + 8*m^2 + m^3)*x^3 + b^4*(8 + 14*m + 7*m^2 + m^3)*x^4))/((1 + m)*(2 + m)*(4 + m)*(5 + m)))","A",1
70,1,88,93,0.0862149,"\int (e x)^m (a+b x) (a c-b c x)^2 \, dx","Integrate[(e*x)^m*(a + b*x)*(a*c - b*c*x)^2,x]","\frac{c^2 x (e x)^m \left(\frac{a (2 m+5) \left(a^2 \left(m^2+5 m+6\right)-2 a b \left(m^2+4 m+3\right) x+b^2 \left(m^2+3 m+2\right) x^2\right)}{(m+1) (m+2) (m+3)}+(b x-a)^3\right)}{m+4}","\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,"(c^2*x*(e*x)^m*((-a + b*x)^3 + (a*(5 + 2*m)*(a^2*(6 + 5*m + m^2) - 2*a*b*(3 + 4*m + m^2)*x + b^2*(2 + 3*m + m^2)*x^2))/((1 + m)*(2 + m)*(3 + m))))/(4 + m)","A",1
71,1,31,42,0.0318775,"\int (e x)^m (a+b x) (a c-b c x) \, dx","Integrate[(e*x)^m*(a + b*x)*(a*c - b*c*x),x]","c x (e x)^m \left(\frac{a^2}{m+1}-\frac{b^2 x^2}{m+3}\right)","\frac{a^2 c (e x)^{m+1}}{e (m+1)}-\frac{b^2 c (e x)^{m+3}}{e^3 (m+3)}",1,"c*x*(e*x)^m*(a^2/(1 + m) - (b^2*x^2)/(3 + m))","A",1
72,1,33,55,0.0135099,"\int \frac{(e x)^m (a+b x)}{a c-b c x} \, dx","Integrate[((e*x)^m*(a + b*x))/(a*c - b*c*x),x]","\frac{x (e x)^m \left(2 \, _2F_1\left(1,m+1;m+2;\frac{b x}{a}\right)-1\right)}{c (m+1)}","\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,"(x*(e*x)^m*(-1 + 2*Hypergeometric2F1[1, 1 + m, 2 + m, (b*x)/a]))/(c*(1 + m))","A",1
73,1,62,66,0.029806,"\int \frac{(e x)^m (a+b x)}{(a c-b c x)^2} \, dx","Integrate[((e*x)^m*(a + b*x))/(a*c - b*c*x)^2,x]","-\frac{x (e x)^m \left(2 a (m+1)-(2 m+1) (a-b x) \, _2F_1\left(1,m+1;m+2;\frac{b x}{a}\right)\right)}{a c^2 (m+1) (b x-a)}","\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,"-((x*(e*x)^m*(2*a*(1 + m) - (1 + 2*m)*(a - b*x)*Hypergeometric2F1[1, 1 + m, 2 + m, (b*x)/a]))/(a*c^2*(1 + m)*(-a + b*x)))","A",1
74,1,69,107,0.0899704,"\int \frac{(e x)^m (a c-b c x)^3}{a+b x} \, dx","Integrate[((e*x)^m*(a*c - b*c*x)^3)/(a + b*x),x]","c^3 x (e x)^m \left(\frac{8 a^2 \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{m+1}-\frac{7 a^2}{m+1}+\frac{4 a b x}{m+2}-\frac{b^2 x^2}{m+3}\right)","\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,"c^3*x*(e*x)^m*((-7*a^2)/(1 + m) + (4*a*b*x)/(2 + m) - (b^2*x^2)/(3 + m) + (8*a^2*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*x)/a)])/(1 + m))","A",1
75,1,54,78,0.0451464,"\int \frac{(e x)^m (a c-b c x)^2}{a+b x} \, dx","Integrate[((e*x)^m*(a*c - b*c*x)^2)/(a + b*x),x]","\frac{c^2 x (e x)^m \left(4 a (m+2) \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)-3 a (m+2)+b (m+1) x\right)}{(m+1) (m+2)}","\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,"(c^2*x*(e*x)^m*(-3*a*(2 + m) + b*(1 + m)*x + 4*a*(2 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*x)/a)]))/((1 + m)*(2 + m))","A",1
76,1,32,52,0.0120498,"\int \frac{(e x)^m (a c-b c x)}{a+b x} \, dx","Integrate[((e*x)^m*(a*c - b*c*x))/(a + b*x),x]","\frac{c x (e x)^m \left(2 \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)-1\right)}{m+1}","\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,"(c*x*(e*x)^m*(-1 + 2*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*x)/a)]))/(1 + m)","A",1
77,1,46,48,0.0177651,"\int \frac{(e x)^m}{(a+b x) (a c-b c x)} \, dx","Integrate[(e*x)^m/((a + b*x)*(a*c - b*c*x)),x]","\frac{x (e x)^m \, _2F_1\left(1,\frac{m+1}{2};\frac{m+1}{2}+1;\frac{b^2 x^2}{a^2}\right)}{a^2 c (m+1)}","\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,"(x*(e*x)^m*Hypergeometric2F1[1, (1 + m)/2, 1 + (1 + m)/2, (b^2*x^2)/a^2])/(a^2*c*(1 + m))","A",1
78,1,87,98,0.0509366,"\int \frac{(e x)^m}{(a+b x) (a c-b c x)^2} \, dx","Integrate[(e*x)^m/((a + b*x)*(a*c - b*c*x)^2),x]","\frac{x (e x)^m \left(b (m+1) x \, _2F_1\left(2,\frac{m}{2}+1;\frac{m}{2}+2;\frac{b^2 x^2}{a^2}\right)+a (m+2) \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};\frac{b^2 x^2}{a^2}\right)\right)}{a^4 c^2 (m+1) (m+2)}","\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,"(x*(e*x)^m*(b*(1 + m)*x*Hypergeometric2F1[2, 1 + m/2, 2 + m/2, (b^2*x^2)/a^2] + a*(2 + m)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, (b^2*x^2)/a^2]))/(a^4*c^2*(1 + m)*(2 + m))","A",1
79,1,106,151,0.1313939,"\int \frac{(e x)^m}{(a+b x) (a c-b c x)^3} \, dx","Integrate[(e*x)^m/((a + b*x)*(a*c - b*c*x)^3),x]","\frac{x (e x)^m \left(\left(2 m^2-4 m+1\right) (a-b x)^2 \, _2F_1\left(1,m+1;m+2;\frac{b x}{a}\right)+(a-b x)^2 \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)-2 a (m+1) (a (m-3)-b (m-2) x)\right)}{8 a^4 c^3 (m+1) (a-b x)^2}","\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,"(x*(e*x)^m*(-2*a*(1 + m)*(a*(-3 + m) - b*(-2 + m)*x) + (a - b*x)^2*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*x)/a)] + (1 - 4*m + 2*m^2)*(a - b*x)^2*Hypergeometric2F1[1, 1 + m, 2 + m, (b*x)/a]))/(8*a^4*c^3*(1 + m)*(a - b*x)^2)","A",1
80,1,33,33,0.0110418,"\int x^4 (a+b x) (A+B x) \, dx","Integrate[x^4*(a + b*x)*(A + B*x),x]","\frac{1}{6} x^6 (a B+A b)+\frac{1}{5} a A x^5+\frac{1}{7} b B x^7","\frac{1}{6} x^6 (a B+A b)+\frac{1}{5} a A x^5+\frac{1}{7} b B x^7",1,"(a*A*x^5)/5 + ((A*b + a*B)*x^6)/6 + (b*B*x^7)/7","A",1
81,1,33,33,0.0059119,"\int x^3 (a+b x) (A+B x) \, dx","Integrate[x^3*(a + b*x)*(A + B*x),x]","\frac{1}{5} x^5 (a B+A b)+\frac{1}{4} a A x^4+\frac{1}{6} b B x^6","\frac{1}{5} x^5 (a B+A b)+\frac{1}{4} a A x^4+\frac{1}{6} b B x^6",1,"(a*A*x^4)/4 + ((A*b + a*B)*x^5)/5 + (b*B*x^6)/6","A",1
82,1,33,33,0.0050947,"\int x^2 (a+b x) (A+B x) \, dx","Integrate[x^2*(a + b*x)*(A + B*x),x]","\frac{1}{4} x^4 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{5} b B x^5","\frac{1}{4} x^4 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{5} b B x^5",1,"(a*A*x^3)/3 + ((A*b + a*B)*x^4)/4 + (b*B*x^5)/5","A",1
83,1,29,33,0.0074681,"\int x (a+b x) (A+B x) \, dx","Integrate[x*(a + b*x)*(A + B*x),x]","\frac{1}{12} x^2 (a (6 A+4 B x)+b x (4 A+3 B x))","\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*(b*x*(4*A + 3*B*x) + a*(6*A + 4*B*x)))/12","A",1
84,1,28,28,0.0061798,"\int (a+b x) (A+B x) \, dx","Integrate[(a + b*x)*(A + B*x),x]","\frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} b B x^3","\frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} b B x^3",1,"a*A*x + ((A*b + a*B)*x^2)/2 + (b*B*x^3)/3","A",1
85,1,24,24,0.0072809,"\int \frac{(a+b x) (A+B x)}{x} \, dx","Integrate[((a + b*x)*(A + B*x))/x,x]","x (a B+A b)+a A \log (x)+\frac{1}{2} b B x^2","x (a B+A b)+a A \log (x)+\frac{1}{2} b B x^2",1,"(A*b + a*B)*x + (b*B*x^2)/2 + a*A*Log[x]","A",1
86,1,22,22,0.0099483,"\int \frac{(a+b x) (A+B x)}{x^2} \, dx","Integrate[((a + b*x)*(A + B*x))/x^2,x]","\log (x) (a B+A b)-\frac{a A}{x}+b B x","\log (x) (a B+A b)-\frac{a A}{x}+b B x",1,"-((a*A)/x) + b*B*x + (A*b + a*B)*Log[x]","A",1
87,1,28,27,0.0166722,"\int \frac{(a+b x) (A+B x)}{x^3} \, dx","Integrate[((a + b*x)*(A + B*x))/x^3,x]","\frac{-a B-A b}{x}-\frac{a A}{2 x^2}+b B \log (x)","-\frac{a B+A b}{x}-\frac{a A}{2 x^2}+b B \log (x)",1,"-1/2*(a*A)/x^2 + (-(A*b) - a*B)/x + b*B*Log[x]","A",1
88,1,28,31,0.0096579,"\int \frac{(a+b x) (A+B x)}{x^4} \, dx","Integrate[((a + b*x)*(A + B*x))/x^4,x]","-\frac{a (2 A+3 B x)+3 b x (A+2 B x)}{6 x^3}","-\frac{a B+A b}{2 x^2}-\frac{a A}{3 x^3}-\frac{b B}{x}",1,"-1/6*(3*b*x*(A + 2*B*x) + a*(2*A + 3*B*x))/x^3","A",1
89,1,29,33,0.0120779,"\int \frac{(a+b x) (A+B x)}{x^5} \, dx","Integrate[((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,"-1/12*(3*a*A + 4*A*b*x + 4*a*B*x + 6*b*B*x^2)/x^4","A",1
90,1,31,33,0.0119262,"\int \frac{(a+b x) (A+B x)}{x^6} \, dx","Integrate[((a + b*x)*(A + B*x))/x^6,x]","-\frac{3 a (4 A+5 B x)+5 b x (3 A+4 B x)}{60 x^5}","-\frac{a B+A b}{4 x^4}-\frac{a A}{5 x^5}-\frac{b B}{3 x^3}",1,"-1/60*(5*b*x*(3*A + 4*B*x) + 3*a*(4*A + 5*B*x))/x^5","A",1
91,1,55,55,0.0088209,"\int x^4 (a+b x)^2 (A+B x) \, dx","Integrate[x^4*(a + b*x)^2*(A + B*x),x]","\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","\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,"(a^2*A*x^5)/5 + (a*(2*A*b + a*B)*x^6)/6 + (b*(A*b + 2*a*B)*x^7)/7 + (b^2*B*x^8)/8","A",1
92,1,55,55,0.0098622,"\int x^3 (a+b x)^2 (A+B x) \, dx","Integrate[x^3*(a + b*x)^2*(A + B*x),x]","\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","\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,"(a^2*A*x^4)/4 + (a*(2*A*b + a*B)*x^5)/5 + (b*(A*b + 2*a*B)*x^6)/6 + (b^2*B*x^7)/7","A",1
93,1,50,55,0.011556,"\int x^2 (a+b x)^2 (A+B x) \, dx","Integrate[x^2*(a + b*x)^2*(A + B*x),x]","\frac{1}{60} x^3 \left(5 a^2 (4 A+3 B x)+6 a b x (5 A+4 B x)+2 b^2 x^2 (6 A+5 B x)\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*(5*a^2*(4*A + 3*B*x) + 6*a*b*x*(5*A + 4*B*x) + 2*b^2*x^2*(6*A + 5*B*x)))/60","A",1
94,1,50,55,0.0131308,"\int x (a+b x)^2 (A+B x) \, dx","Integrate[x*(a + b*x)^2*(A + B*x),x]","\frac{1}{60} x^2 \left(10 a^2 (3 A+2 B x)+10 a b x (4 A+3 B x)+3 b^2 x^2 (5 A+4 B x)\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*(10*a^2*(3*A + 2*B*x) + 10*a*b*x*(4*A + 3*B*x) + 3*b^2*x^2*(5*A + 4*B*x)))/60","A",1
95,1,46,38,0.0103147,"\int (a+b x)^2 (A+B x) \, dx","Integrate[(a + b*x)^2*(A + B*x),x]","\frac{1}{12} x \left(6 a^2 (2 A+B x)+4 a b x (3 A+2 B x)+b^2 x^2 (4 A+3 B x)\right)","\frac{(a+b x)^3 (A b-a B)}{3 b^2}+\frac{B (a+b x)^4}{4 b^2}",1,"(x*(6*a^2*(2*A + B*x) + 4*a*b*x*(3*A + 2*B*x) + b^2*x^2*(4*A + 3*B*x)))/12","A",1
96,1,43,40,0.0213561,"\int \frac{(a+b x)^2 (A+B x)}{x} \, dx","Integrate[((a + b*x)^2*(A + B*x))/x,x]","a^2 A \log (x)+a^2 B x+a b x (2 A+B x)+\frac{1}{6} b^2 x^2 (3 A+2 B 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,"a^2*B*x + a*b*x*(2*A + B*x) + (b^2*x^2*(3*A + 2*B*x))/6 + a^2*A*Log[x]","A",1
97,1,43,44,0.0316047,"\int \frac{(a+b x)^2 (A+B x)}{x^2} \, dx","Integrate[((a + b*x)^2*(A + B*x))/x^2,x]","-\frac{a^2 A}{x}+a \log (x) (a B+2 A b)+2 a b B x+\frac{1}{2} b^2 x (2 A+B x)","-\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,"-((a^2*A)/x) + 2*a*b*B*x + (b^2*x*(2*A + B*x))/2 + a*(2*A*b + a*B)*Log[x]","A",1
98,1,43,44,0.0298205,"\int \frac{(a+b x)^2 (A+B x)}{x^3} \, dx","Integrate[((a + b*x)^2*(A + B*x))/x^3,x]","-\frac{a^2 (A+2 B x)}{2 x^2}+b \log (x) (2 a B+A b)-\frac{2 a A b}{x}+b^2 B x","-\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,"(-2*a*A*b)/x + b^2*B*x - (a^2*(A + 2*B*x))/(2*x^2) + b*(A*b + 2*a*B)*Log[x]","A",1
99,1,48,49,0.0309577,"\int \frac{(a+b x)^2 (A+B x)}{x^4} \, dx","Integrate[((a + b*x)^2*(A + B*x))/x^4,x]","b^2 B \log (x)-\frac{a^2 (2 A+3 B x)+6 a b x (A+2 B x)+6 A b^2 x^2}{6 x^3}","-\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,"-1/6*(6*A*b^2*x^2 + 6*a*b*x*(A + 2*B*x) + a^2*(2*A + 3*B*x))/x^3 + b^2*B*Log[x]","A",1
100,1,47,44,0.022018,"\int \frac{(a+b x)^2 (A+B x)}{x^5} \, dx","Integrate[((a + b*x)^2*(A + B*x))/x^5,x]","-\frac{a^2 (3 A+4 B x)+4 a b x (2 A+3 B x)+6 b^2 x^2 (A+2 B x)}{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,"-1/12*(6*b^2*x^2*(A + 2*B*x) + 4*a*b*x*(2*A + 3*B*x) + a^2*(3*A + 4*B*x))/x^4","A",1
101,1,50,55,0.015668,"\int \frac{(a+b x)^2 (A+B x)}{x^6} \, dx","Integrate[((a + b*x)^2*(A + B*x))/x^6,x]","-\frac{3 a^2 (4 A+5 B x)+10 a b x (3 A+4 B x)+10 b^2 x^2 (2 A+3 B x)}{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,"-1/60*(10*b^2*x^2*(2*A + 3*B*x) + 10*a*b*x*(3*A + 4*B*x) + 3*a^2*(4*A + 5*B*x))/x^5","A",1
102,1,50,55,0.021291,"\int \frac{(a+b x)^2 (A+B x)}{x^7} \, dx","Integrate[((a + b*x)^2*(A + B*x))/x^7,x]","-\frac{2 a^2 (5 A+6 B x)+6 a b x (4 A+5 B x)+5 b^2 x^2 (3 A+4 B x)}{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,"-1/60*(5*b^2*x^2*(3*A + 4*B*x) + 6*a*b*x*(4*A + 5*B*x) + 2*a^2*(5*A + 6*B*x))/x^6","A",1
103,1,50,55,0.0237865,"\int \frac{(a+b x)^2 (A+B x)}{x^8} \, dx","Integrate[((a + b*x)^2*(A + B*x))/x^8,x]","-\frac{10 a^2 (6 A+7 B x)+28 a b x (5 A+6 B x)+21 b^2 x^2 (4 A+5 B x)}{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,"-1/420*(21*b^2*x^2*(4*A + 5*B*x) + 28*a*b*x*(5*A + 6*B*x) + 10*a^2*(6*A + 7*B*x))/x^7","A",1
104,1,75,75,0.0111201,"\int x^4 (a+b x)^3 (A+B x) \, dx","Integrate[x^4*(a + b*x)^3*(A + B*x),x]","\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","\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,"(a^3*A*x^5)/5 + (a^2*(3*A*b + a*B)*x^6)/6 + (3*a*b*(A*b + a*B)*x^7)/7 + (b^2*(A*b + 3*a*B)*x^8)/8 + (b^3*B*x^9)/9","A",1
105,1,75,75,0.0154724,"\int x^3 (a+b x)^3 (A+B x) \, dx","Integrate[x^3*(a + b*x)^3*(A + B*x),x]","\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","\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,"(a^3*A*x^4)/4 + (a^2*(3*A*b + a*B)*x^5)/5 + (a*b*(A*b + a*B)*x^6)/2 + (b^2*(A*b + 3*a*B)*x^7)/7 + (b^3*B*x^8)/8","A",1
106,1,75,75,0.014416,"\int x^2 (a+b x)^3 (A+B x) \, dx","Integrate[x^2*(a + b*x)^3*(A + B*x),x]","\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","\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,"(a^3*A*x^3)/3 + (a^2*(3*A*b + a*B)*x^4)/4 + (3*a*b*(A*b + a*B)*x^5)/5 + (b^2*(A*b + 3*a*B)*x^6)/6 + (b^3*B*x^7)/7","A",1
107,1,69,61,0.0156015,"\int x (a+b x)^3 (A+B x) \, dx","Integrate[x*(a + b*x)^3*(A + B*x),x]","\frac{1}{60} x^2 \left(10 a^3 (3 A+2 B x)+15 a^2 b x (4 A+3 B x)+9 a b^2 x^2 (5 A+4 B x)+2 b^3 x^3 (6 A+5 B x)\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*(10*a^3*(3*A + 2*B*x) + 15*a^2*b*x*(4*A + 3*B*x) + 9*a*b^2*x^2*(5*A + 4*B*x) + 2*b^3*x^3*(6*A + 5*B*x)))/60","A",1
108,1,67,38,0.0140619,"\int (a+b x)^3 (A+B x) \, dx","Integrate[(a + b*x)^3*(A + B*x),x]","a^3 A x+\frac{1}{2} a^2 x^2 (a B+3 A b)+\frac{1}{4} b^2 x^4 (3 a B+A b)+a b x^3 (a B+A b)+\frac{1}{5} b^3 B x^5","\frac{(a+b x)^4 (A b-a B)}{4 b^2}+\frac{B (a+b x)^5}{5 b^2}",1,"a^3*A*x + (a^2*(3*A*b + a*B)*x^2)/2 + a*b*(A*b + a*B)*x^3 + (b^2*(A*b + 3*a*B)*x^4)/4 + (b^3*B*x^5)/5","A",1
109,1,63,54,0.0382761,"\int \frac{(a+b x)^3 (A+B x)}{x} \, dx","Integrate[((a + b*x)^3*(A + B*x))/x,x]","a^3 A \log (x)+\frac{1}{12} x \left(12 a^3 B+18 a^2 b (2 A+B x)+6 a b^2 x (3 A+2 B x)+b^3 x^2 (4 A+3 B x)\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*(12*a^3*B + 18*a^2*b*(2*A + B*x) + 6*a*b^2*x*(3*A + 2*B*x) + b^3*x^2*(4*A + 3*B*x)))/12 + a^3*A*Log[x]","A",1
110,1,67,65,0.034704,"\int \frac{(a+b x)^3 (A+B x)}{x^2} \, dx","Integrate[((a + b*x)^3*(A + B*x))/x^2,x]","-\frac{a^3 A}{x}+\log (x) \left(a^3 B+3 a^2 A b\right)+\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","-\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,"-((a^3*A)/x) + 3*a*b*(A*b + a*B)*x + (b^2*(A*b + 3*a*B)*x^2)/2 + (b^3*B*x^3)/3 + (3*a^2*A*b + a^3*B)*Log[x]","A",1
111,1,62,65,0.0305218,"\int \frac{(a+b x)^3 (A+B x)}{x^3} \, dx","Integrate[((a + b*x)^3*(A + B*x))/x^3,x]","\frac{1}{2} \left(-\frac{a^3 (A+2 B x)}{x^2}-\frac{6 a^2 A b}{x}+6 a b \log (x) (a B+A b)+6 a b^2 B x+b^3 x (2 A+B x)\right)","-\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,"((-6*a^2*A*b)/x + 6*a*b^2*B*x + b^3*x*(2*A + B*x) - (a^3*(A + 2*B*x))/x^2 + 6*a*b*(A*b + a*B)*Log[x])/2","A",1
112,1,67,64,0.0397049,"\int \frac{(a+b x)^3 (A+B x)}{x^4} \, dx","Integrate[((a + b*x)^3*(A + B*x))/x^4,x]","b^2 \log (x) (3 a B+A b)-\frac{a^3 (2 A+3 B x)+9 a^2 b x (A+2 B x)+18 a A b^2 x^2-6 b^3 B x^4}{6 x^3}","-\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,"-1/6*(18*a*A*b^2*x^2 - 6*b^3*B*x^4 + 9*a^2*b*x*(A + 2*B*x) + a^3*(2*A + 3*B*x))/x^3 + b^2*(A*b + 3*a*B)*Log[x]","A",1
113,1,70,59,0.0296971,"\int \frac{(a+b x)^3 (A+B x)}{x^5} \, dx","Integrate[((a + b*x)^3*(A + B*x))/x^5,x]","-\frac{a^3 (3 A+4 B x)+6 a^2 b x (2 A+3 B x)+18 a b^2 x^2 (A+2 B x)+12 A b^3 x^3-12 b^3 B x^4 \log (x)}{12 x^4}","-\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,"-1/12*(12*A*b^3*x^3 + 18*a*b^2*x^2*(A + 2*B*x) + 6*a^2*b*x*(2*A + 3*B*x) + a^3*(3*A + 4*B*x) - 12*b^3*B*x^4*Log[x])/x^4","A",1
114,1,66,44,0.0251218,"\int \frac{(a+b x)^3 (A+B x)}{x^6} \, dx","Integrate[((a + b*x)^3*(A + B*x))/x^6,x]","-\frac{a^3 (4 A+5 B x)+5 a^2 b x (3 A+4 B x)+10 a b^2 x^2 (2 A+3 B x)+10 b^3 x^3 (A+2 B x)}{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,"-1/20*(10*b^3*x^3*(A + 2*B*x) + 10*a*b^2*x^2*(2*A + 3*B*x) + 5*a^2*b*x*(3*A + 4*B*x) + a^3*(4*A + 5*B*x))/x^5","A",1
115,1,69,75,0.0314532,"\int \frac{(a+b x)^3 (A+B x)}{x^7} \, dx","Integrate[((a + b*x)^3*(A + B*x))/x^7,x]","-\frac{2 a^3 (5 A+6 B x)+9 a^2 b x (4 A+5 B x)+15 a b^2 x^2 (3 A+4 B x)+10 b^3 x^3 (2 A+3 B x)}{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,"-1/60*(10*b^3*x^3*(2*A + 3*B*x) + 15*a*b^2*x^2*(3*A + 4*B*x) + 9*a^2*b*x*(4*A + 5*B*x) + 2*a^3*(5*A + 6*B*x))/x^6","A",1
116,1,69,75,0.0204489,"\int \frac{(a+b x)^3 (A+B x)}{x^8} \, dx","Integrate[((a + b*x)^3*(A + B*x))/x^8,x]","-\frac{10 a^3 (6 A+7 B x)+42 a^2 b x (5 A+6 B x)+63 a b^2 x^2 (4 A+5 B x)+35 b^3 x^3 (3 A+4 B x)}{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,"-1/420*(35*b^3*x^3*(3*A + 4*B*x) + 63*a*b^2*x^2*(4*A + 5*B*x) + 42*a^2*b*x*(5*A + 6*B*x) + 10*a^3*(6*A + 7*B*x))/x^7","A",1
117,1,69,75,0.0234423,"\int \frac{(a+b x)^3 (A+B x)}{x^9} \, dx","Integrate[((a + b*x)^3*(A + B*x))/x^9,x]","-\frac{5 a^3 (7 A+8 B x)+20 a^2 b x (6 A+7 B x)+28 a b^2 x^2 (5 A+6 B x)+14 b^3 x^3 (4 A+5 B x)}{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,"-1/280*(14*b^3*x^3*(4*A + 5*B*x) + 28*a*b^2*x^2*(5*A + 6*B*x) + 20*a^2*b*x*(6*A + 7*B*x) + 5*a^3*(7*A + 8*B*x))/x^8","A",1
118,1,69,75,0.0286752,"\int \frac{(a+b x)^3 (A+B x)}{x^{10}} \, dx","Integrate[((a + b*x)^3*(A + B*x))/x^10,x]","-\frac{35 a^3 (8 A+9 B x)+135 a^2 b x (7 A+8 B x)+180 a b^2 x^2 (6 A+7 B x)+84 b^3 x^3 (5 A+6 B x)}{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,"-1/2520*(84*b^3*x^3*(5*A + 6*B*x) + 180*a*b^2*x^2*(6*A + 7*B*x) + 135*a^2*b*x*(7*A + 8*B*x) + 35*a^3*(8*A + 9*B*x))/x^9","A",1
119,1,117,117,0.0244893,"\int x^5 (a+b x)^5 (A+B x) \, dx","Integrate[x^5*(a + b*x)^5*(A + B*x),x]","\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}","\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,"(a^5*A*x^6)/6 + (a^4*(5*A*b + a*B)*x^7)/7 + (5*a^3*b*(2*A*b + a*B)*x^8)/8 + (10*a^2*b^2*(A*b + a*B)*x^9)/9 + (a*b^3*(A*b + 2*a*B)*x^10)/2 + (b^4*(A*b + 5*a*B)*x^11)/11 + (b^5*B*x^12)/12","A",1
120,1,117,117,0.0239811,"\int x^4 (a+b x)^5 (A+B x) \, dx","Integrate[x^4*(a + b*x)^5*(A + B*x),x]","\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}","\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,"(a^5*A*x^5)/5 + (a^4*(5*A*b + a*B)*x^6)/6 + (5*a^3*b*(2*A*b + a*B)*x^7)/7 + (5*a^2*b^2*(A*b + a*B)*x^8)/4 + (5*a*b^3*(A*b + 2*a*B)*x^9)/9 + (b^4*(A*b + 5*a*B)*x^10)/10 + (b^5*B*x^11)/11","A",1
121,1,117,112,0.0232747,"\int x^3 (a+b x)^5 (A+B x) \, dx","Integrate[x^3*(a + b*x)^5*(A + B*x),x]","\frac{1}{4} a^5 A x^4+\frac{1}{5} a^4 x^5 (a B+5 A b)+\frac{5}{6} a^3 b x^6 (a B+2 A b)+\frac{10}{7} a^2 b^2 x^7 (a B+A b)+\frac{1}{9} b^4 x^9 (5 a B+A b)+\frac{5}{8} a b^3 x^8 (2 a B+A b)+\frac{1}{10} b^5 B x^{10}","-\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,"(a^5*A*x^4)/4 + (a^4*(5*A*b + a*B)*x^5)/5 + (5*a^3*b*(2*A*b + a*B)*x^6)/6 + (10*a^2*b^2*(A*b + a*B)*x^7)/7 + (5*a*b^3*(A*b + 2*a*B)*x^8)/8 + (b^4*(A*b + 5*a*B)*x^9)/9 + (b^5*B*x^10)/10","A",1
122,1,114,87,0.0292343,"\int x^2 (a+b x)^5 (A+B x) \, dx","Integrate[x^2*(a + b*x)^5*(A + B*x),x]","\frac{1}{3} a^5 A x^3+\frac{1}{4} a^4 x^4 (a B+5 A b)+a^3 b x^5 (a B+2 A b)+\frac{5}{3} a^2 b^2 x^6 (a B+A b)+\frac{1}{8} b^4 x^8 (5 a B+A b)+\frac{5}{7} a b^3 x^7 (2 a B+A b)+\frac{1}{9} b^5 B x^9","\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,"(a^5*A*x^3)/3 + (a^4*(5*A*b + a*B)*x^4)/4 + a^3*b*(2*A*b + a*B)*x^5 + (5*a^2*b^2*(A*b + a*B)*x^6)/3 + (5*a*b^3*(A*b + 2*a*B)*x^7)/7 + (b^4*(A*b + 5*a*B)*x^8)/8 + (b^5*B*x^9)/9","A",1
123,1,115,61,0.026503,"\int x (a+b x)^5 (A+B x) \, dx","Integrate[x*(a + b*x)^5*(A + B*x),x]","\frac{1}{2} a^5 A x^2+\frac{1}{3} a^4 x^3 (a B+5 A b)+\frac{5}{4} a^3 b x^4 (a B+2 A b)+2 a^2 b^2 x^5 (a B+A b)+\frac{1}{7} b^4 x^7 (5 a B+A b)+\frac{5}{6} a b^3 x^6 (2 a B+A b)+\frac{1}{8} b^5 B x^8","\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,"(a^5*A*x^2)/2 + (a^4*(5*A*b + a*B)*x^3)/3 + (5*a^3*b*(2*A*b + a*B)*x^4)/4 + 2*a^2*b^2*(A*b + a*B)*x^5 + (5*a*b^3*(A*b + 2*a*B)*x^6)/6 + (b^4*(A*b + 5*a*B)*x^7)/7 + (b^5*B*x^8)/8","A",1
124,1,109,38,0.019506,"\int (a+b x)^5 (A+B x) \, dx","Integrate[(a + b*x)^5*(A + B*x),x]","a^5 A x+\frac{1}{2} a^4 x^2 (a B+5 A b)+\frac{5}{3} a^3 b x^3 (a B+2 A b)+\frac{5}{2} a^2 b^2 x^4 (a B+A b)+\frac{1}{6} b^4 x^6 (5 a B+A b)+a b^3 x^5 (2 a B+A b)+\frac{1}{7} b^5 B x^7","\frac{(a+b x)^6 (A b-a B)}{6 b^2}+\frac{B (a+b x)^7}{7 b^2}",1,"a^5*A*x + (a^4*(5*A*b + a*B)*x^2)/2 + (5*a^3*b*(2*A*b + a*B)*x^3)/3 + (5*a^2*b^2*(A*b + a*B)*x^4)/2 + a*b^3*(A*b + 2*a*B)*x^5 + (b^4*(A*b + 5*a*B)*x^6)/6 + (b^5*B*x^7)/7","B",1
125,1,108,80,0.0445295,"\int \frac{(a+b x)^5 (A+B x)}{x} \, dx","Integrate[((a + b*x)^5*(A + B*x))/x,x]","a^5 A \log (x)+a^4 x (a B+5 A b)+\frac{5}{2} a^3 b x^2 (a B+2 A b)+\frac{10}{3} a^2 b^2 x^3 (a B+A b)+\frac{1}{5} b^4 x^5 (5 a B+A b)+\frac{5}{4} a b^3 x^4 (2 a B+A b)+\frac{1}{6} b^5 B x^6","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,"a^4*(5*A*b + a*B)*x + (5*a^3*b*(2*A*b + a*B)*x^2)/2 + (10*a^2*b^2*(A*b + a*B)*x^3)/3 + (5*a*b^3*(A*b + 2*a*B)*x^4)/4 + (b^4*(A*b + 5*a*B)*x^5)/5 + (b^5*B*x^6)/6 + a^5*A*Log[x]","A",1
126,1,107,105,0.0550421,"\int \frac{(a+b x)^5 (A+B x)}{x^2} \, dx","Integrate[((a + b*x)^5*(A + B*x))/x^2,x]","-\frac{a^5 A}{x}+5 a^3 b x (a B+2 A b)+5 a^2 b^2 x^2 (a B+A b)+\log (x) \left(a^5 B+5 a^4 A b\right)+\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","-\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,"-((a^5*A)/x) + 5*a^3*b*(2*A*b + a*B)*x + 5*a^2*b^2*(A*b + a*B)*x^2 + (5*a*b^3*(A*b + 2*a*B)*x^3)/3 + (b^4*(A*b + 5*a*B)*x^4)/4 + (b^5*B*x^5)/5 + (5*a^4*A*b + a^5*B)*Log[x]","A",1
127,1,106,108,0.0510817,"\int \frac{(a+b x)^5 (A+B x)}{x^3} \, dx","Integrate[((a + b*x)^5*(A + B*x))/x^3,x]","-\frac{a^5 (A+2 B x)}{2 x^2}-\frac{5 a^4 A b}{x}+5 a^3 b \log (x) (a B+2 A b)+10 a^3 b^2 B x+5 a^2 b^3 x (2 A+B x)+\frac{5}{6} a b^4 x^2 (3 A+2 B x)+\frac{1}{12} b^5 x^3 (4 A+3 B x)","-\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,"(-5*a^4*A*b)/x + 10*a^3*b^2*B*x + 5*a^2*b^3*x*(2*A + B*x) - (a^5*(A + 2*B*x))/(2*x^2) + (5*a*b^4*x^2*(3*A + 2*B*x))/6 + (b^5*x^3*(4*A + 3*B*x))/12 + 5*a^3*b*(2*A*b + a*B)*Log[x]","A",1
128,1,109,108,0.0340886,"\int \frac{(a+b x)^5 (A+B x)}{x^4} \, dx","Integrate[((a + b*x)^5*(A + B*x))/x^4,x]","\frac{-\left(a^5 (2 A+3 B x)\right)-15 a^4 b x (A+2 B x)-60 a^3 A b^2 x^2+60 a^2 b^2 x^3 \log (x) (a B+A b)+60 a^2 b^3 B x^4+15 a b^4 x^4 (2 A+B x)+b^5 x^5 (3 A+2 B x)}{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,"(-60*a^3*A*b^2*x^2 + 60*a^2*b^3*B*x^4 + 15*a*b^4*x^4*(2*A + B*x) - 15*a^4*b*x*(A + 2*B*x) + b^5*x^5*(3*A + 2*B*x) - a^5*(2*A + 3*B*x) + 60*a^2*b^2*(A*b + a*B)*x^3*Log[x])/(6*x^3)","A",1
129,1,106,107,0.0580231,"\int \frac{(a+b x)^5 (A+B x)}{x^5} \, dx","Integrate[((a + b*x)^5*(A + B*x))/x^5,x]","-\frac{a^5 (3 A+4 B x)}{12 x^4}-\frac{5 a^4 b (2 A+3 B x)}{6 x^3}-\frac{5 a^3 b^2 (A+2 B x)}{x^2}-\frac{10 a^2 A b^3}{x}+5 a b^3 \log (x) (2 a B+A b)+5 a b^4 B x+\frac{1}{2} b^5 x (2 A+B x)","-\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,"(-10*a^2*A*b^3)/x + 5*a*b^4*B*x + (b^5*x*(2*A + B*x))/2 - (5*a^3*b^2*(A + 2*B*x))/x^2 - (5*a^4*b*(2*A + 3*B*x))/(6*x^3) - (a^5*(3*A + 4*B*x))/(12*x^4) + 5*a*b^3*(A*b + 2*a*B)*Log[x]","A",1
130,1,106,104,0.0617865,"\int \frac{(a+b x)^5 (A+B x)}{x^6} \, dx","Integrate[((a + b*x)^5*(A + B*x))/x^6,x]","-\frac{a^5 (4 A+5 B x)}{20 x^5}-\frac{5 a^4 b (3 A+4 B x)}{12 x^4}-\frac{5 a^3 b^2 (2 A+3 B x)}{3 x^3}-\frac{5 a^2 b^3 (A+2 B x)}{x^2}+b^4 \log (x) (5 a B+A b)-\frac{5 a A b^4}{x}+b^5 B x","-\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,"(-5*a*A*b^4)/x + b^5*B*x - (5*a^2*b^3*(A + 2*B*x))/x^2 - (5*a^3*b^2*(2*A + 3*B*x))/(3*x^3) - (5*a^4*b*(3*A + 4*B*x))/(12*x^4) - (a^5*(4*A + 5*B*x))/(20*x^5) + b^4*(A*b + 5*a*B)*Log[x]","A",1
131,1,109,85,0.044479,"\int \frac{(a+b x)^5 (A+B x)}{x^7} \, dx","Integrate[((a + b*x)^5*(A + B*x))/x^7,x]","-\frac{2 a^5 (5 A+6 B x)+15 a^4 b x (4 A+5 B x)+50 a^3 b^2 x^2 (3 A+4 B x)+100 a^2 b^3 x^3 (2 A+3 B x)+150 a b^4 x^4 (A+2 B x)+60 A b^5 x^5-60 b^5 B x^6 \log (x)}{60 x^6}","-\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,"-1/60*(60*A*b^5*x^5 + 150*a*b^4*x^4*(A + 2*B*x) + 100*a^2*b^3*x^3*(2*A + 3*B*x) + 50*a^3*b^2*x^2*(3*A + 4*B*x) + 15*a^4*b*x*(4*A + 5*B*x) + 2*a^5*(5*A + 6*B*x) - 60*b^5*B*x^6*Log[x])/x^6","A",1
132,1,104,44,0.0304208,"\int \frac{(a+b x)^5 (A+B x)}{x^8} \, dx","Integrate[((a + b*x)^5*(A + B*x))/x^8,x]","-\frac{a^5 (6 A+7 B x)+7 a^4 b x (5 A+6 B x)+21 a^3 b^2 x^2 (4 A+5 B x)+35 a^2 b^3 x^3 (3 A+4 B x)+35 a b^4 x^4 (2 A+3 B x)+21 b^5 x^5 (A+2 B x)}{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,"-1/42*(21*b^5*x^5*(A + 2*B*x) + 35*a*b^4*x^4*(2*A + 3*B*x) + 35*a^2*b^3*x^3*(3*A + 4*B*x) + 21*a^3*b^2*x^2*(4*A + 5*B*x) + 7*a^4*b*x*(5*A + 6*B*x) + a^5*(6*A + 7*B*x))/x^7","B",1
133,1,107,70,0.0333581,"\int \frac{(a+b x)^5 (A+B x)}{x^9} \, dx","Integrate[((a + b*x)^5*(A + B*x))/x^9,x]","-\frac{3 a^5 (7 A+8 B x)+20 a^4 b x (6 A+7 B x)+56 a^3 b^2 x^2 (5 A+6 B x)+84 a^2 b^3 x^3 (4 A+5 B x)+70 a b^4 x^4 (3 A+4 B x)+28 b^5 x^5 (2 A+3 B x)}{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,"-1/168*(28*b^5*x^5*(2*A + 3*B*x) + 70*a*b^4*x^4*(3*A + 4*B*x) + 84*a^2*b^3*x^3*(4*A + 5*B*x) + 56*a^3*b^2*x^2*(5*A + 6*B*x) + 20*a^4*b*x*(6*A + 7*B*x) + 3*a^5*(7*A + 8*B*x))/x^8","A",1
134,1,107,115,0.0331801,"\int \frac{(a+b x)^5 (A+B x)}{x^{10}} \, dx","Integrate[((a + b*x)^5*(A + B*x))/x^10,x]","-\frac{7 a^5 (8 A+9 B x)+45 a^4 b x (7 A+8 B x)+120 a^3 b^2 x^2 (6 A+7 B x)+168 a^2 b^3 x^3 (5 A+6 B x)+126 a b^4 x^4 (4 A+5 B x)+42 b^5 x^5 (3 A+4 B x)}{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,"-1/504*(42*b^5*x^5*(3*A + 4*B*x) + 126*a*b^4*x^4*(4*A + 5*B*x) + 168*a^2*b^3*x^3*(5*A + 6*B*x) + 120*a^3*b^2*x^2*(6*A + 7*B*x) + 45*a^4*b*x*(7*A + 8*B*x) + 7*a^5*(8*A + 9*B*x))/x^9","A",1
135,1,107,117,0.0387995,"\int \frac{(a+b x)^5 (A+B x)}{x^{11}} \, dx","Integrate[((a + b*x)^5*(A + B*x))/x^11,x]","-\frac{28 a^5 (9 A+10 B x)+175 a^4 b x (8 A+9 B x)+450 a^3 b^2 x^2 (7 A+8 B x)+600 a^2 b^3 x^3 (6 A+7 B x)+420 a b^4 x^4 (5 A+6 B x)+126 b^5 x^5 (4 A+5 B x)}{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,"-1/2520*(126*b^5*x^5*(4*A + 5*B*x) + 420*a*b^4*x^4*(5*A + 6*B*x) + 600*a^2*b^3*x^3*(6*A + 7*B*x) + 450*a^3*b^2*x^2*(7*A + 8*B*x) + 175*a^4*b*x*(8*A + 9*B*x) + 28*a^5*(9*A + 10*B*x))/x^10","A",1
136,1,107,117,0.0389024,"\int \frac{(a+b x)^5 (A+B x)}{x^{12}} \, dx","Integrate[((a + b*x)^5*(A + B*x))/x^12,x]","-\frac{126 a^5 (10 A+11 B x)+770 a^4 b x (9 A+10 B x)+1925 a^3 b^2 x^2 (8 A+9 B x)+2475 a^2 b^3 x^3 (7 A+8 B x)+1650 a b^4 x^4 (6 A+7 B x)+462 b^5 x^5 (5 A+6 B x)}{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,"-1/13860*(462*b^5*x^5*(5*A + 6*B*x) + 1650*a*b^4*x^4*(6*A + 7*B*x) + 2475*a^2*b^3*x^3*(7*A + 8*B*x) + 1925*a^3*b^2*x^2*(8*A + 9*B*x) + 770*a^4*b*x*(9*A + 10*B*x) + 126*a^5*(10*A + 11*B*x))/x^11","A",1
137,1,229,229,0.0537652,"\int x^{10} (a+b x)^{10} (A+B x) \, dx","Integrate[x^10*(a + b*x)^10*(A + B*x),x]","\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}","\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,"(a^10*A*x^11)/11 + (a^9*(10*A*b + a*B)*x^12)/12 + (5*a^8*b*(9*A*b + 2*a*B)*x^13)/13 + (15*a^7*b^2*(8*A*b + 3*a*B)*x^14)/14 + 2*a^6*b^3*(7*A*b + 4*a*B)*x^15 + (21*a^5*b^4*(6*A*b + 5*a*B)*x^16)/8 + (42*a^4*b^5*(5*A*b + 6*a*B)*x^17)/17 + (5*a^3*b^6*(4*A*b + 7*a*B)*x^18)/3 + (15*a^2*b^7*(3*A*b + 8*a*B)*x^19)/19 + (a*b^8*(2*A*b + 9*a*B)*x^20)/4 + (b^9*(A*b + 10*a*B)*x^21)/21 + (b^10*B*x^22)/22","A",1
138,1,231,231,0.0458528,"\int x^9 (a+b x)^{10} (A+B x) \, dx","Integrate[x^9*(a + b*x)^10*(A + B*x),x]","\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}","\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,"(a^10*A*x^10)/10 + (a^9*(10*A*b + a*B)*x^11)/11 + (5*a^8*b*(9*A*b + 2*a*B)*x^12)/12 + (15*a^7*b^2*(8*A*b + 3*a*B)*x^13)/13 + (15*a^6*b^3*(7*A*b + 4*a*B)*x^14)/7 + (14*a^5*b^4*(6*A*b + 5*a*B)*x^15)/5 + (21*a^4*b^5*(5*A*b + 6*a*B)*x^16)/8 + (30*a^3*b^6*(4*A*b + 7*a*B)*x^17)/17 + (5*a^2*b^7*(3*A*b + 8*a*B)*x^18)/6 + (5*a*b^8*(2*A*b + 9*a*B)*x^19)/19 + (b^9*(A*b + 10*a*B)*x^20)/20 + (b^10*B*x^21)/21","A",1
139,1,229,240,0.0454347,"\int x^8 (a+b x)^{10} (A+B x) \, dx","Integrate[x^8*(a + b*x)^10*(A + B*x),x]","\frac{1}{9} a^{10} A x^9+\frac{1}{10} a^9 x^{10} (a B+10 A b)+\frac{5}{11} a^8 b x^{11} (2 a B+9 A b)+\frac{5}{4} a^7 b^2 x^{12} (3 a B+8 A b)+\frac{30}{13} a^6 b^3 x^{13} (4 a B+7 A b)+3 a^5 b^4 x^{14} (5 a B+6 A b)+\frac{14}{5} a^4 b^5 x^{15} (6 a B+5 A b)+\frac{15}{8} a^3 b^6 x^{16} (7 a B+4 A b)+\frac{15}{17} a^2 b^7 x^{17} (8 a B+3 A b)+\frac{1}{19} b^9 x^{19} (10 a B+A b)+\frac{5}{18} a b^8 x^{18} (9 a B+2 A b)+\frac{1}{20} b^{10} B x^{20}","\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,"(a^10*A*x^9)/9 + (a^9*(10*A*b + a*B)*x^10)/10 + (5*a^8*b*(9*A*b + 2*a*B)*x^11)/11 + (5*a^7*b^2*(8*A*b + 3*a*B)*x^12)/4 + (30*a^6*b^3*(7*A*b + 4*a*B)*x^13)/13 + 3*a^5*b^4*(6*A*b + 5*a*B)*x^14 + (14*a^4*b^5*(5*A*b + 6*a*B)*x^15)/5 + (15*a^3*b^6*(4*A*b + 7*a*B)*x^16)/8 + (15*a^2*b^7*(3*A*b + 8*a*B)*x^17)/17 + (5*a*b^8*(2*A*b + 9*a*B)*x^18)/18 + (b^9*(A*b + 10*a*B)*x^19)/19 + (b^10*B*x^20)/20","A",1
140,1,227,215,0.0460047,"\int x^7 (a+b x)^{10} (A+B x) \, dx","Integrate[x^7*(a + b*x)^10*(A + B*x),x]","\frac{1}{8} a^{10} A x^8+\frac{1}{9} a^9 x^9 (a B+10 A b)+\frac{1}{2} a^8 b x^{10} (2 a B+9 A b)+\frac{15}{11} a^7 b^2 x^{11} (3 a B+8 A b)+\frac{5}{2} a^6 b^3 x^{12} (4 a B+7 A b)+\frac{42}{13} a^5 b^4 x^{13} (5 a B+6 A b)+3 a^4 b^5 x^{14} (6 a B+5 A b)+2 a^3 b^6 x^{15} (7 a B+4 A b)+\frac{15}{16} a^2 b^7 x^{16} (8 a B+3 A b)+\frac{1}{18} b^9 x^{18} (10 a B+A b)+\frac{5}{17} a b^8 x^{17} (9 a B+2 A b)+\frac{1}{19} b^{10} B x^{19}","-\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,"(a^10*A*x^8)/8 + (a^9*(10*A*b + a*B)*x^9)/9 + (a^8*b*(9*A*b + 2*a*B)*x^10)/2 + (15*a^7*b^2*(8*A*b + 3*a*B)*x^11)/11 + (5*a^6*b^3*(7*A*b + 4*a*B)*x^12)/2 + (42*a^5*b^4*(6*A*b + 5*a*B)*x^13)/13 + 3*a^4*b^5*(5*A*b + 6*a*B)*x^14 + 2*a^3*b^6*(4*A*b + 7*a*B)*x^15 + (15*a^2*b^7*(3*A*b + 8*a*B)*x^16)/16 + (5*a*b^8*(2*A*b + 9*a*B)*x^17)/17 + (b^9*(A*b + 10*a*B)*x^18)/18 + (b^10*B*x^19)/19","A",1
141,1,228,191,0.0416816,"\int x^6 (a+b x)^{10} (A+B x) \, dx","Integrate[x^6*(a + b*x)^10*(A + B*x),x]","\frac{1}{7} a^{10} A x^7+\frac{1}{8} a^9 x^8 (a B+10 A b)+\frac{5}{9} a^8 b x^9 (2 a B+9 A b)+\frac{3}{2} a^7 b^2 x^{10} (3 a B+8 A b)+\frac{30}{11} a^6 b^3 x^{11} (4 a B+7 A b)+\frac{7}{2} a^5 b^4 x^{12} (5 a B+6 A b)+\frac{42}{13} a^4 b^5 x^{13} (6 a B+5 A b)+\frac{15}{7} a^3 b^6 x^{14} (7 a B+4 A b)+a^2 b^7 x^{15} (8 a B+3 A b)+\frac{1}{17} b^9 x^{17} (10 a B+A b)+\frac{5}{16} a b^8 x^{16} (9 a B+2 A b)+\frac{1}{18} b^{10} B x^{18}","\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,"(a^10*A*x^7)/7 + (a^9*(10*A*b + a*B)*x^8)/8 + (5*a^8*b*(9*A*b + 2*a*B)*x^9)/9 + (3*a^7*b^2*(8*A*b + 3*a*B)*x^10)/2 + (30*a^6*b^3*(7*A*b + 4*a*B)*x^11)/11 + (7*a^5*b^4*(6*A*b + 5*a*B)*x^12)/2 + (42*a^4*b^5*(5*A*b + 6*a*B)*x^13)/13 + (15*a^3*b^6*(4*A*b + 7*a*B)*x^14)/7 + a^2*b^7*(3*A*b + 8*a*B)*x^15 + (5*a*b^8*(2*A*b + 9*a*B)*x^16)/16 + (b^9*(A*b + 10*a*B)*x^17)/17 + (b^10*B*x^18)/18","A",1
142,1,229,163,0.0386122,"\int x^5 (a+b x)^{10} (A+B x) \, dx","Integrate[x^5*(a + b*x)^10*(A + B*x),x]","\frac{1}{6} a^{10} A x^6+\frac{1}{7} a^9 x^7 (a B+10 A b)+\frac{5}{8} a^8 b x^8 (2 a B+9 A b)+\frac{5}{3} a^7 b^2 x^9 (3 a B+8 A b)+3 a^6 b^3 x^{10} (4 a B+7 A b)+\frac{42}{11} a^5 b^4 x^{11} (5 a B+6 A b)+\frac{7}{2} a^4 b^5 x^{12} (6 a B+5 A b)+\frac{30}{13} a^3 b^6 x^{13} (7 a B+4 A b)+\frac{15}{14} a^2 b^7 x^{14} (8 a B+3 A b)+\frac{1}{16} b^9 x^{16} (10 a B+A b)+\frac{1}{3} a b^8 x^{15} (9 a B+2 A b)+\frac{1}{17} b^{10} B x^{17}","-\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,"(a^10*A*x^6)/6 + (a^9*(10*A*b + a*B)*x^7)/7 + (5*a^8*b*(9*A*b + 2*a*B)*x^8)/8 + (5*a^7*b^2*(8*A*b + 3*a*B)*x^9)/3 + 3*a^6*b^3*(7*A*b + 4*a*B)*x^10 + (42*a^5*b^4*(6*A*b + 5*a*B)*x^11)/11 + (7*a^4*b^5*(5*A*b + 6*a*B)*x^12)/2 + (30*a^3*b^6*(4*A*b + 7*a*B)*x^13)/13 + (15*a^2*b^7*(3*A*b + 8*a*B)*x^14)/14 + (a*b^8*(2*A*b + 9*a*B)*x^15)/3 + (b^9*(A*b + 10*a*B)*x^16)/16 + (b^10*B*x^17)/17","A",1
143,1,231,139,0.0421158,"\int x^4 (a+b x)^{10} (A+B x) \, dx","Integrate[x^4*(a + b*x)^10*(A + B*x),x]","\frac{1}{5} a^{10} A x^5+\frac{1}{6} a^9 x^6 (a B+10 A b)+\frac{5}{7} a^8 b x^7 (2 a B+9 A b)+\frac{15}{8} a^7 b^2 x^8 (3 a B+8 A b)+\frac{10}{3} a^6 b^3 x^9 (4 a B+7 A b)+\frac{21}{5} a^5 b^4 x^{10} (5 a B+6 A b)+\frac{42}{11} a^4 b^5 x^{11} (6 a B+5 A b)+\frac{5}{2} a^3 b^6 x^{12} (7 a B+4 A b)+\frac{15}{13} a^2 b^7 x^{13} (8 a B+3 A b)+\frac{1}{15} b^9 x^{15} (10 a B+A b)+\frac{5}{14} a b^8 x^{14} (9 a B+2 A b)+\frac{1}{16} b^{10} B x^{16}","\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,"(a^10*A*x^5)/5 + (a^9*(10*A*b + a*B)*x^6)/6 + (5*a^8*b*(9*A*b + 2*a*B)*x^7)/7 + (15*a^7*b^2*(8*A*b + 3*a*B)*x^8)/8 + (10*a^6*b^3*(7*A*b + 4*a*B)*x^9)/3 + (21*a^5*b^4*(6*A*b + 5*a*B)*x^10)/5 + (42*a^4*b^5*(5*A*b + 6*a*B)*x^11)/11 + (5*a^3*b^6*(4*A*b + 7*a*B)*x^12)/2 + (15*a^2*b^7*(3*A*b + 8*a*B)*x^13)/13 + (5*a*b^8*(2*A*b + 9*a*B)*x^14)/14 + (b^9*(A*b + 10*a*B)*x^15)/15 + (b^10*B*x^16)/16","A",1
144,1,231,112,0.0358328,"\int x^3 (a+b x)^{10} (A+B x) \, dx","Integrate[x^3*(a + b*x)^10*(A + B*x),x]","\frac{1}{4} a^{10} A x^4+\frac{1}{5} a^9 x^5 (a B+10 A b)+\frac{5}{6} a^8 b x^6 (2 a B+9 A b)+\frac{15}{7} a^7 b^2 x^7 (3 a B+8 A b)+\frac{15}{4} a^6 b^3 x^8 (4 a B+7 A b)+\frac{14}{3} a^5 b^4 x^9 (5 a B+6 A b)+\frac{21}{5} a^4 b^5 x^{10} (6 a B+5 A b)+\frac{30}{11} a^3 b^6 x^{11} (7 a B+4 A b)+\frac{5}{4} a^2 b^7 x^{12} (8 a B+3 A b)+\frac{1}{14} b^9 x^{14} (10 a B+A b)+\frac{5}{13} a b^8 x^{13} (9 a B+2 A b)+\frac{1}{15} b^{10} B x^{15}","-\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,"(a^10*A*x^4)/4 + (a^9*(10*A*b + a*B)*x^5)/5 + (5*a^8*b*(9*A*b + 2*a*B)*x^6)/6 + (15*a^7*b^2*(8*A*b + 3*a*B)*x^7)/7 + (15*a^6*b^3*(7*A*b + 4*a*B)*x^8)/4 + (14*a^5*b^4*(6*A*b + 5*a*B)*x^9)/3 + (21*a^4*b^5*(5*A*b + 6*a*B)*x^10)/5 + (30*a^3*b^6*(4*A*b + 7*a*B)*x^11)/11 + (5*a^2*b^7*(3*A*b + 8*a*B)*x^12)/4 + (5*a*b^8*(2*A*b + 9*a*B)*x^13)/13 + (b^9*(A*b + 10*a*B)*x^14)/14 + (b^10*B*x^15)/15","B",1
145,1,226,87,0.039878,"\int x^2 (a+b x)^{10} (A+B x) \, dx","Integrate[x^2*(a + b*x)^10*(A + B*x),x]","\frac{1}{3} a^{10} A x^3+\frac{1}{4} a^9 x^4 (a B+10 A b)+a^8 b x^5 (2 a B+9 A b)+\frac{5}{2} a^7 b^2 x^6 (3 a B+8 A b)+\frac{30}{7} a^6 b^3 x^7 (4 a B+7 A b)+\frac{21}{4} a^5 b^4 x^8 (5 a B+6 A b)+\frac{14}{3} a^4 b^5 x^9 (6 a B+5 A b)+3 a^3 b^6 x^{10} (7 a B+4 A b)+\frac{15}{11} a^2 b^7 x^{11} (8 a B+3 A b)+\frac{1}{13} b^9 x^{13} (10 a B+A b)+\frac{5}{12} a b^8 x^{12} (9 a B+2 A b)+\frac{1}{14} b^{10} B x^{14}","\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,"(a^10*A*x^3)/3 + (a^9*(10*A*b + a*B)*x^4)/4 + a^8*b*(9*A*b + 2*a*B)*x^5 + (5*a^7*b^2*(8*A*b + 3*a*B)*x^6)/2 + (30*a^6*b^3*(7*A*b + 4*a*B)*x^7)/7 + (21*a^5*b^4*(6*A*b + 5*a*B)*x^8)/4 + (14*a^4*b^5*(5*A*b + 6*a*B)*x^9)/3 + 3*a^3*b^6*(4*A*b + 7*a*B)*x^10 + (15*a^2*b^7*(3*A*b + 8*a*B)*x^11)/11 + (5*a*b^8*(2*A*b + 9*a*B)*x^12)/12 + (b^9*(A*b + 10*a*B)*x^13)/13 + (b^10*B*x^14)/14","B",1
146,1,218,61,0.0476091,"\int x (a+b x)^{10} (A+B x) \, dx","Integrate[x*(a + b*x)^10*(A + B*x),x]","\frac{1}{6} a^{10} x^2 (3 A+2 B x)+\frac{5}{6} a^9 b x^3 (4 A+3 B x)+\frac{9}{4} a^8 b^2 x^4 (5 A+4 B x)+4 a^7 b^3 x^5 (6 A+5 B x)+5 a^6 b^4 x^6 (7 A+6 B x)+\frac{9}{2} a^5 b^5 x^7 (8 A+7 B x)+\frac{35}{12} a^4 b^6 x^8 (9 A+8 B x)+\frac{4}{3} a^3 b^7 x^9 (10 A+9 B x)+\frac{9}{22} a^2 b^8 x^{10} (11 A+10 B x)+\frac{5}{66} a b^9 x^{11} (12 A+11 B x)+\frac{1}{156} b^{10} x^{12} (13 A+12 B x)","\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,"(a^10*x^2*(3*A + 2*B*x))/6 + (5*a^9*b*x^3*(4*A + 3*B*x))/6 + (9*a^8*b^2*x^4*(5*A + 4*B*x))/4 + 4*a^7*b^3*x^5*(6*A + 5*B*x) + 5*a^6*b^4*x^6*(7*A + 6*B*x) + (9*a^5*b^5*x^7*(8*A + 7*B*x))/2 + (35*a^4*b^6*x^8*(9*A + 8*B*x))/12 + (4*a^3*b^7*x^9*(10*A + 9*B*x))/3 + (9*a^2*b^8*x^10*(11*A + 10*B*x))/22 + (5*a*b^9*x^11*(12*A + 11*B*x))/66 + (b^10*x^12*(13*A + 12*B*x))/156","B",1
147,1,198,38,0.0753271,"\int (a+b x)^{10} (A+B x) \, dx","Integrate[(a + b*x)^10*(A + B*x),x]","\frac{1}{132} x \left(66 a^{10} (2 A+B x)+220 a^9 b x (3 A+2 B x)+495 a^8 b^2 x^2 (4 A+3 B x)+792 a^7 b^3 x^3 (5 A+4 B x)+924 a^6 b^4 x^4 (6 A+5 B x)+792 a^5 b^5 x^5 (7 A+6 B x)+495 a^4 b^6 x^6 (8 A+7 B x)+220 a^3 b^7 x^7 (9 A+8 B x)+66 a^2 b^8 x^8 (10 A+9 B x)+12 a b^9 x^9 (11 A+10 B x)+b^{10} x^{10} (12 A+11 B x)\right)","\frac{(a+b x)^{11} (A b-a B)}{11 b^2}+\frac{B (a+b x)^{12}}{12 b^2}",1,"(x*(66*a^10*(2*A + B*x) + 220*a^9*b*x*(3*A + 2*B*x) + 495*a^8*b^2*x^2*(4*A + 3*B*x) + 792*a^7*b^3*x^3*(5*A + 4*B*x) + 924*a^6*b^4*x^4*(6*A + 5*B*x) + 792*a^5*b^5*x^5*(7*A + 6*B*x) + 495*a^4*b^6*x^6*(8*A + 7*B*x) + 220*a^3*b^7*x^7*(9*A + 8*B*x) + 66*a^2*b^8*x^8*(10*A + 9*B*x) + 12*a*b^9*x^9*(11*A + 10*B*x) + b^10*x^10*(12*A + 11*B*x)))/132","B",1
148,1,208,148,0.0697721,"\int \frac{(a+b x)^{10} (A+B x)}{x} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x,x]","a^{10} A \log (x)+a^{10} B x+5 a^9 b x (2 A+B x)+\frac{15}{2} a^8 b^2 x^2 (3 A+2 B x)+10 a^7 b^3 x^3 (4 A+3 B x)+\frac{21}{2} a^6 b^4 x^4 (5 A+4 B x)+\frac{42}{5} a^5 b^5 x^5 (6 A+5 B x)+5 a^4 b^6 x^6 (7 A+6 B x)+\frac{15}{7} a^3 b^7 x^7 (8 A+7 B x)+\frac{5}{8} a^2 b^8 x^8 (9 A+8 B x)+\frac{1}{9} a b^9 x^9 (10 A+9 B x)+\frac{1}{110} b^{10} x^{10} (11 A+10 B x)","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,"a^10*B*x + 5*a^9*b*x*(2*A + B*x) + (15*a^8*b^2*x^2*(3*A + 2*B*x))/2 + 10*a^7*b^3*x^3*(4*A + 3*B*x) + (21*a^6*b^4*x^4*(5*A + 4*B*x))/2 + (42*a^5*b^5*x^5*(6*A + 5*B*x))/5 + 5*a^4*b^6*x^6*(7*A + 6*B*x) + (15*a^3*b^7*x^7*(8*A + 7*B*x))/7 + (5*a^2*b^8*x^8*(9*A + 8*B*x))/8 + (a*b^9*x^9*(10*A + 9*B*x))/9 + (b^10*x^10*(11*A + 10*B*x))/110 + a^10*A*Log[x]","A",1
149,1,209,217,0.102543,"\int \frac{(a+b x)^{10} (A+B x)}{x^2} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^2,x]","-\frac{a^{10} A}{x}+a^9 \log (x) (a B+10 A b)+10 a^9 b B x+\frac{45}{2} a^8 b^2 x (2 A+B x)+20 a^7 b^3 x^2 (3 A+2 B x)+\frac{35}{2} a^6 b^4 x^3 (4 A+3 B x)+\frac{63}{5} a^5 b^5 x^4 (5 A+4 B x)+7 a^4 b^6 x^5 (6 A+5 B x)+\frac{20}{7} a^3 b^7 x^6 (7 A+6 B x)+\frac{45}{56} a^2 b^8 x^7 (8 A+7 B x)+\frac{5}{36} a b^9 x^8 (9 A+8 B x)+\frac{1}{90} b^{10} x^9 (10 A+9 B 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,"-((a^10*A)/x) + 10*a^9*b*B*x + (45*a^8*b^2*x*(2*A + B*x))/2 + 20*a^7*b^3*x^2*(3*A + 2*B*x) + (35*a^6*b^4*x^3*(4*A + 3*B*x))/2 + (63*a^5*b^5*x^4*(5*A + 4*B*x))/5 + 7*a^4*b^6*x^5*(6*A + 5*B*x) + (20*a^3*b^7*x^6*(7*A + 6*B*x))/7 + (45*a^2*b^8*x^7*(8*A + 7*B*x))/56 + (5*a*b^9*x^8*(9*A + 8*B*x))/36 + (b^10*x^9*(10*A + 9*B*x))/90 + a^9*(10*A*b + a*B)*Log[x]","A",1
150,1,206,216,0.1106476,"\int \frac{(a+b x)^{10} (A+B x)}{x^3} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^3,x]","-\frac{a^{10} (A+2 B x)}{2 x^2}-\frac{10 a^9 A b}{x}+5 a^8 b \log (x) (2 a B+9 A b)+45 a^8 b^2 B x+60 a^7 b^3 x (2 A+B x)+35 a^6 b^4 x^2 (3 A+2 B x)+21 a^5 b^5 x^3 (4 A+3 B x)+\frac{21}{2} a^4 b^6 x^4 (5 A+4 B x)+4 a^3 b^7 x^5 (6 A+5 B x)+\frac{15}{14} a^2 b^8 x^6 (7 A+6 B x)+\frac{5}{28} a b^9 x^7 (8 A+7 B x)+\frac{1}{72} b^{10} x^8 (9 A+8 B x)","-\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,"(-10*a^9*A*b)/x + 45*a^8*b^2*B*x + 60*a^7*b^3*x*(2*A + B*x) - (a^10*(A + 2*B*x))/(2*x^2) + 35*a^6*b^4*x^2*(3*A + 2*B*x) + 21*a^5*b^5*x^3*(4*A + 3*B*x) + (21*a^4*b^6*x^4*(5*A + 4*B*x))/2 + 4*a^3*b^7*x^5*(6*A + 5*B*x) + (15*a^2*b^8*x^6*(7*A + 6*B*x))/14 + (5*a*b^9*x^7*(8*A + 7*B*x))/28 + (b^10*x^8*(9*A + 8*B*x))/72 + 5*a^8*b*(9*A*b + 2*a*B)*Log[x]","A",1
151,1,208,216,0.1190026,"\int \frac{(a+b x)^{10} (A+B x)}{x^4} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^4,x]","-\frac{a^{10} (2 A+3 B x)}{6 x^3}-\frac{5 a^9 b (A+2 B x)}{x^2}-\frac{45 a^8 A b^2}{x}+15 a^7 b^2 \log (x) (3 a B+8 A b)+120 a^7 b^3 B x+105 a^6 b^4 x (2 A+B x)+42 a^5 b^5 x^2 (3 A+2 B x)+\frac{35}{2} a^4 b^6 x^3 (4 A+3 B x)+6 a^3 b^7 x^4 (5 A+4 B x)+\frac{3}{2} a^2 b^8 x^5 (6 A+5 B x)+\frac{5}{21} a b^9 x^6 (7 A+6 B x)+\frac{1}{56} b^{10} x^7 (8 A+7 B x)","-\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,"(-45*a^8*A*b^2)/x + 120*a^7*b^3*B*x + 105*a^6*b^4*x*(2*A + B*x) - (5*a^9*b*(A + 2*B*x))/x^2 + 42*a^5*b^5*x^2*(3*A + 2*B*x) - (a^10*(2*A + 3*B*x))/(6*x^3) + (35*a^4*b^6*x^3*(4*A + 3*B*x))/2 + 6*a^3*b^7*x^4*(5*A + 4*B*x) + (3*a^2*b^8*x^5*(6*A + 5*B*x))/2 + (5*a*b^9*x^6*(7*A + 6*B*x))/21 + (b^10*x^7*(8*A + 7*B*x))/56 + 15*a^7*b^2*(8*A*b + 3*a*B)*Log[x]","A",1
152,1,210,215,0.1081403,"\int \frac{(a+b x)^{10} (A+B x)}{x^5} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^5,x]","-\frac{a^{10} (3 A+4 B x)}{12 x^4}-\frac{5 a^9 b (2 A+3 B x)}{3 x^3}-\frac{45 a^8 b^2 (A+2 B x)}{2 x^2}-\frac{120 a^7 A b^3}{x}+30 a^6 b^3 \log (x) (4 a B+7 A b)+210 a^6 b^4 B x+126 a^5 b^5 x (2 A+B x)+35 a^4 b^6 x^2 (3 A+2 B x)+10 a^3 b^7 x^3 (4 A+3 B x)+\frac{9}{4} a^2 b^8 x^4 (5 A+4 B x)+\frac{1}{3} a b^9 x^5 (6 A+5 B x)+\frac{1}{42} b^{10} x^6 (7 A+6 B x)","-\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,"(-120*a^7*A*b^3)/x + 210*a^6*b^4*B*x + 126*a^5*b^5*x*(2*A + B*x) - (45*a^8*b^2*(A + 2*B*x))/(2*x^2) + 35*a^4*b^6*x^2*(3*A + 2*B*x) - (5*a^9*b*(2*A + 3*B*x))/(3*x^3) + 10*a^3*b^7*x^3*(4*A + 3*B*x) - (a^10*(3*A + 4*B*x))/(12*x^4) + (9*a^2*b^8*x^4*(5*A + 4*B*x))/4 + (a*b^9*x^5*(6*A + 5*B*x))/3 + (b^10*x^6*(7*A + 6*B*x))/42 + 30*a^6*b^3*(7*A*b + 4*a*B)*Log[x]","A",1
153,1,210,218,0.1060683,"\int \frac{(a+b x)^{10} (A+B x)}{x^6} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^6,x]","-\frac{a^{10} (4 A+5 B x)}{20 x^5}-\frac{5 a^9 b (3 A+4 B x)}{6 x^4}-\frac{15 a^8 b^2 (2 A+3 B x)}{2 x^3}-\frac{60 a^7 b^3 (A+2 B x)}{x^2}-\frac{210 a^6 A b^4}{x}+42 a^5 b^4 \log (x) (5 a B+6 A b)+252 a^5 b^5 B x+105 a^4 b^6 x (2 A+B x)+20 a^3 b^7 x^2 (3 A+2 B x)+\frac{15}{4} a^2 b^8 x^3 (4 A+3 B x)+\frac{1}{2} a b^9 x^4 (5 A+4 B x)+\frac{1}{30} b^{10} x^5 (6 A+5 B x)","-\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,"(-210*a^6*A*b^4)/x + 252*a^5*b^5*B*x + 105*a^4*b^6*x*(2*A + B*x) - (60*a^7*b^3*(A + 2*B*x))/x^2 + 20*a^3*b^7*x^2*(3*A + 2*B*x) - (15*a^8*b^2*(2*A + 3*B*x))/(2*x^3) + (15*a^2*b^8*x^3*(4*A + 3*B*x))/4 - (5*a^9*b*(3*A + 4*B*x))/(6*x^4) + (a*b^9*x^4*(5*A + 4*B*x))/2 - (a^10*(4*A + 5*B*x))/(20*x^5) + (b^10*x^5*(6*A + 5*B*x))/30 + 42*a^5*b^4*(6*A*b + 5*a*B)*Log[x]","A",1
154,1,210,218,0.1243834,"\int \frac{(a+b x)^{10} (A+B x)}{x^7} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^7,x]","-\frac{a^{10} (5 A+6 B x)}{30 x^6}-\frac{a^9 b (4 A+5 B x)}{2 x^5}-\frac{15 a^8 b^2 (3 A+4 B x)}{4 x^4}-\frac{20 a^7 b^3 (2 A+3 B x)}{x^3}-\frac{105 a^6 b^4 (A+2 B x)}{x^2}-\frac{252 a^5 A b^5}{x}+42 a^4 b^5 \log (x) (6 a B+5 A b)+210 a^4 b^6 B x+60 a^3 b^7 x (2 A+B x)+\frac{15}{2} a^2 b^8 x^2 (3 A+2 B x)+\frac{5}{6} a b^9 x^3 (4 A+3 B x)+\frac{1}{20} b^{10} x^4 (5 A+4 B x)","-\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,"(-252*a^5*A*b^5)/x + 210*a^4*b^6*B*x + 60*a^3*b^7*x*(2*A + B*x) - (105*a^6*b^4*(A + 2*B*x))/x^2 + (15*a^2*b^8*x^2*(3*A + 2*B*x))/2 - (20*a^7*b^3*(2*A + 3*B*x))/x^3 + (5*a*b^9*x^3*(4*A + 3*B*x))/6 - (15*a^8*b^2*(3*A + 4*B*x))/(4*x^4) + (b^10*x^4*(5*A + 4*B*x))/20 - (a^9*b*(4*A + 5*B*x))/(2*x^5) - (a^10*(5*A + 6*B*x))/(30*x^6) + 42*a^4*b^5*(5*A*b + 6*a*B)*Log[x]","A",1
155,1,210,216,0.1193767,"\int \frac{(a+b x)^{10} (A+B x)}{x^8} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^8,x]","-\frac{a^{10} (6 A+7 B x)}{42 x^7}-\frac{a^9 b (5 A+6 B x)}{3 x^6}-\frac{9 a^8 b^2 (4 A+5 B x)}{4 x^5}-\frac{10 a^7 b^3 (3 A+4 B x)}{x^4}-\frac{35 a^6 b^4 (2 A+3 B x)}{x^3}-\frac{126 a^5 b^5 (A+2 B x)}{x^2}-\frac{210 a^4 A b^6}{x}+30 a^3 b^6 \log (x) (7 a B+4 A b)+120 a^3 b^7 B x+\frac{45}{2} a^2 b^8 x (2 A+B x)+\frac{5}{3} a b^9 x^2 (3 A+2 B x)+\frac{1}{12} b^{10} x^3 (4 A+3 B x)","-\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,"(-210*a^4*A*b^6)/x + 120*a^3*b^7*B*x + (45*a^2*b^8*x*(2*A + B*x))/2 - (126*a^5*b^5*(A + 2*B*x))/x^2 + (5*a*b^9*x^2*(3*A + 2*B*x))/3 - (35*a^6*b^4*(2*A + 3*B*x))/x^3 + (b^10*x^3*(4*A + 3*B*x))/12 - (10*a^7*b^3*(3*A + 4*B*x))/x^4 - (9*a^8*b^2*(4*A + 5*B*x))/(4*x^5) - (a^9*b*(5*A + 6*B*x))/(3*x^6) - (a^10*(6*A + 7*B*x))/(42*x^7) + 30*a^3*b^6*(4*A*b + 7*a*B)*Log[x]","A",1
156,1,208,216,0.1157355,"\int \frac{(a+b x)^{10} (A+B x)}{x^9} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^9,x]","-\frac{a^{10} (7 A+8 B x)}{56 x^8}-\frac{5 a^9 b (6 A+7 B x)}{21 x^7}-\frac{3 a^8 b^2 (5 A+6 B x)}{2 x^6}-\frac{6 a^7 b^3 (4 A+5 B x)}{x^5}-\frac{35 a^6 b^4 (3 A+4 B x)}{2 x^4}-\frac{42 a^5 b^5 (2 A+3 B x)}{x^3}-\frac{105 a^4 b^6 (A+2 B x)}{x^2}-\frac{120 a^3 A b^7}{x}+15 a^2 b^7 \log (x) (8 a B+3 A b)+45 a^2 b^8 B x+5 a b^9 x (2 A+B x)+\frac{1}{6} b^{10} x^2 (3 A+2 B x)","-\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,"(-120*a^3*A*b^7)/x + 45*a^2*b^8*B*x + 5*a*b^9*x*(2*A + B*x) - (105*a^4*b^6*(A + 2*B*x))/x^2 + (b^10*x^2*(3*A + 2*B*x))/6 - (42*a^5*b^5*(2*A + 3*B*x))/x^3 - (35*a^6*b^4*(3*A + 4*B*x))/(2*x^4) - (6*a^7*b^3*(4*A + 5*B*x))/x^5 - (3*a^8*b^2*(5*A + 6*B*x))/(2*x^6) - (5*a^9*b*(6*A + 7*B*x))/(21*x^7) - (a^10*(7*A + 8*B*x))/(56*x^8) + 15*a^2*b^7*(3*A*b + 8*a*B)*Log[x]","A",1
157,1,206,215,0.1200668,"\int \frac{(a+b x)^{10} (A+B x)}{x^{10}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^10,x]","-\frac{a^{10} (8 A+9 B x)}{72 x^9}-\frac{5 a^9 b (7 A+8 B x)}{28 x^8}-\frac{15 a^8 b^2 (6 A+7 B x)}{14 x^7}-\frac{4 a^7 b^3 (5 A+6 B x)}{x^6}-\frac{21 a^6 b^4 (4 A+5 B x)}{2 x^5}-\frac{21 a^5 b^5 (3 A+4 B x)}{x^4}-\frac{35 a^4 b^6 (2 A+3 B x)}{x^3}-\frac{60 a^3 b^7 (A+2 B x)}{x^2}-\frac{45 a^2 A b^8}{x}+5 a b^8 \log (x) (9 a B+2 A b)+10 a b^9 B x+\frac{1}{2} b^{10} x (2 A+B x)","-\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,"(-45*a^2*A*b^8)/x + 10*a*b^9*B*x + (b^10*x*(2*A + B*x))/2 - (60*a^3*b^7*(A + 2*B*x))/x^2 - (35*a^4*b^6*(2*A + 3*B*x))/x^3 - (21*a^5*b^5*(3*A + 4*B*x))/x^4 - (21*a^6*b^4*(4*A + 5*B*x))/(2*x^5) - (4*a^7*b^3*(5*A + 6*B*x))/x^6 - (15*a^8*b^2*(6*A + 7*B*x))/(14*x^7) - (5*a^9*b*(7*A + 8*B*x))/(28*x^8) - (a^10*(8*A + 9*B*x))/(72*x^9) + 5*a*b^8*(2*A*b + 9*a*B)*Log[x]","A",1
158,1,209,216,0.1332593,"\int \frac{(a+b x)^{10} (A+B x)}{x^{11}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^11,x]","-\frac{a^{10} (9 A+10 B x)}{90 x^{10}}-\frac{5 a^9 b (8 A+9 B x)}{36 x^9}-\frac{45 a^8 b^2 (7 A+8 B x)}{56 x^8}-\frac{20 a^7 b^3 (6 A+7 B x)}{7 x^7}-\frac{7 a^6 b^4 (5 A+6 B x)}{x^6}-\frac{63 a^5 b^5 (4 A+5 B x)}{5 x^5}-\frac{35 a^4 b^6 (3 A+4 B x)}{2 x^4}-\frac{20 a^3 b^7 (2 A+3 B x)}{x^3}-\frac{45 a^2 b^8 (A+2 B x)}{2 x^2}+b^9 \log (x) (10 a B+A b)-\frac{10 a A b^9}{x}+b^{10} B x","-\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,"(-10*a*A*b^9)/x + b^10*B*x - (45*a^2*b^8*(A + 2*B*x))/(2*x^2) - (20*a^3*b^7*(2*A + 3*B*x))/x^3 - (35*a^4*b^6*(3*A + 4*B*x))/(2*x^4) - (63*a^5*b^5*(4*A + 5*B*x))/(5*x^5) - (7*a^6*b^4*(5*A + 6*B*x))/x^6 - (20*a^7*b^3*(6*A + 7*B*x))/(7*x^7) - (45*a^8*b^2*(7*A + 8*B*x))/(56*x^8) - (5*a^9*b*(8*A + 9*B*x))/(36*x^9) - (a^10*(9*A + 10*B*x))/(90*x^10) + b^9*(A*b + 10*a*B)*Log[x]","A",1
159,1,212,153,0.1243299,"\int \frac{(a+b x)^{10} (A+B x)}{x^{12}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^12,x]","-\frac{a^{10} (10 A+11 B x)}{110 x^{11}}-\frac{a^9 b (9 A+10 B x)}{9 x^{10}}-\frac{5 a^8 b^2 (8 A+9 B x)}{8 x^9}-\frac{15 a^7 b^3 (7 A+8 B x)}{7 x^8}-\frac{5 a^6 b^4 (6 A+7 B x)}{x^7}-\frac{42 a^5 b^5 (5 A+6 B x)}{5 x^6}-\frac{21 a^4 b^6 (4 A+5 B x)}{2 x^5}-\frac{10 a^3 b^7 (3 A+4 B x)}{x^4}-\frac{15 a^2 b^8 (2 A+3 B x)}{2 x^3}-\frac{5 a b^9 (A+2 B x)}{x^2}-\frac{A b^{10}}{x}+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,"-((A*b^10)/x) - (5*a*b^9*(A + 2*B*x))/x^2 - (15*a^2*b^8*(2*A + 3*B*x))/(2*x^3) - (10*a^3*b^7*(3*A + 4*B*x))/x^4 - (21*a^4*b^6*(4*A + 5*B*x))/(2*x^5) - (42*a^5*b^5*(5*A + 6*B*x))/(5*x^6) - (5*a^6*b^4*(6*A + 7*B*x))/x^7 - (15*a^7*b^3*(7*A + 8*B*x))/(7*x^8) - (5*a^8*b^2*(8*A + 9*B*x))/(8*x^9) - (a^9*b*(9*A + 10*B*x))/(9*x^10) - (a^10*(10*A + 11*B*x))/(110*x^11) + b^10*B*Log[x]","A",1
160,1,199,44,0.0747627,"\int \frac{(a+b x)^{10} (A+B x)}{x^{13}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^13,x]","-\frac{a^{10} (11 A+12 B x)+12 a^9 b x (10 A+11 B x)+66 a^8 b^2 x^2 (9 A+10 B x)+220 a^7 b^3 x^3 (8 A+9 B x)+495 a^6 b^4 x^4 (7 A+8 B x)+792 a^5 b^5 x^5 (6 A+7 B x)+924 a^4 b^6 x^6 (5 A+6 B x)+792 a^3 b^7 x^7 (4 A+5 B x)+495 a^2 b^8 x^8 (3 A+4 B x)+220 a b^9 x^9 (2 A+3 B x)+66 b^{10} x^{10} (A+2 B x)}{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,"-1/132*(66*b^10*x^10*(A + 2*B*x) + 220*a*b^9*x^9*(2*A + 3*B*x) + 495*a^2*b^8*x^8*(3*A + 4*B*x) + 792*a^3*b^7*x^7*(4*A + 5*B*x) + 924*a^4*b^6*x^6*(5*A + 6*B*x) + 792*a^5*b^5*x^5*(6*A + 7*B*x) + 495*a^6*b^4*x^4*(7*A + 8*B*x) + 220*a^7*b^3*x^3*(8*A + 9*B*x) + 66*a^8*b^2*x^2*(9*A + 10*B*x) + 12*a^9*b*x*(10*A + 11*B*x) + a^10*(11*A + 12*B*x))/x^12","B",1
161,1,202,72,0.0780931,"\int \frac{(a+b x)^{10} (A+B x)}{x^{14}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^14,x]","-\frac{11 a^{10} (12 A+13 B x)+130 a^9 b x (11 A+12 B x)+702 a^8 b^2 x^2 (10 A+11 B x)+2288 a^7 b^3 x^3 (9 A+10 B x)+5005 a^6 b^4 x^4 (8 A+9 B x)+7722 a^5 b^5 x^5 (7 A+8 B x)+8580 a^4 b^6 x^6 (6 A+7 B x)+6864 a^3 b^7 x^7 (5 A+6 B x)+3861 a^2 b^8 x^8 (4 A+5 B x)+1430 a b^9 x^9 (3 A+4 B x)+286 b^{10} x^{10} (2 A+3 B x)}{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,"-1/1716*(286*b^10*x^10*(2*A + 3*B*x) + 1430*a*b^9*x^9*(3*A + 4*B*x) + 3861*a^2*b^8*x^8*(4*A + 5*B*x) + 6864*a^3*b^7*x^7*(5*A + 6*B*x) + 8580*a^4*b^6*x^6*(6*A + 7*B*x) + 7722*a^5*b^5*x^5*(7*A + 8*B*x) + 5005*a^6*b^4*x^4*(8*A + 9*B*x) + 2288*a^7*b^3*x^3*(9*A + 10*B*x) + 702*a^8*b^2*x^2*(10*A + 11*B*x) + 130*a^9*b*x*(11*A + 12*B*x) + 11*a^10*(12*A + 13*B*x))/x^13","B",1
162,1,202,101,0.0743338,"\int \frac{(a+b x)^{10} (A+B x)}{x^{15}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^15,x]","-\frac{66 a^{10} (13 A+14 B x)+770 a^9 b x (12 A+13 B x)+4095 a^8 b^2 x^2 (11 A+12 B x)+13104 a^7 b^3 x^3 (10 A+11 B x)+28028 a^6 b^4 x^4 (9 A+10 B x)+42042 a^5 b^5 x^5 (8 A+9 B x)+45045 a^4 b^6 x^6 (7 A+8 B x)+34320 a^3 b^7 x^7 (6 A+7 B x)+18018 a^2 b^8 x^8 (5 A+6 B x)+6006 a b^9 x^9 (4 A+5 B x)+1001 b^{10} x^{10} (3 A+4 B x)}{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,"-1/12012*(1001*b^10*x^10*(3*A + 4*B*x) + 6006*a*b^9*x^9*(4*A + 5*B*x) + 18018*a^2*b^8*x^8*(5*A + 6*B*x) + 34320*a^3*b^7*x^7*(6*A + 7*B*x) + 45045*a^4*b^6*x^6*(7*A + 8*B*x) + 42042*a^5*b^5*x^5*(8*A + 9*B*x) + 28028*a^6*b^4*x^4*(9*A + 10*B*x) + 13104*a^7*b^3*x^3*(10*A + 11*B*x) + 4095*a^8*b^2*x^2*(11*A + 12*B*x) + 770*a^9*b*x*(12*A + 13*B*x) + 66*a^10*(13*A + 14*B*x))/x^14","A",1
163,1,202,130,0.0693882,"\int \frac{(a+b x)^{10} (A+B x)}{x^{16}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^16,x]","-\frac{286 a^{10} (14 A+15 B x)+3300 a^9 b x (13 A+14 B x)+17325 a^8 b^2 x^2 (12 A+13 B x)+54600 a^7 b^3 x^3 (11 A+12 B x)+114660 a^6 b^4 x^4 (10 A+11 B x)+168168 a^5 b^5 x^5 (9 A+10 B x)+175175 a^4 b^6 x^6 (8 A+9 B x)+128700 a^3 b^7 x^7 (7 A+8 B x)+64350 a^2 b^8 x^8 (6 A+7 B x)+20020 a b^9 x^9 (5 A+6 B x)+3003 b^{10} x^{10} (4 A+5 B x)}{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,"-1/60060*(3003*b^10*x^10*(4*A + 5*B*x) + 20020*a*b^9*x^9*(5*A + 6*B*x) + 64350*a^2*b^8*x^8*(6*A + 7*B*x) + 128700*a^3*b^7*x^7*(7*A + 8*B*x) + 175175*a^4*b^6*x^6*(8*A + 9*B*x) + 168168*a^5*b^5*x^5*(9*A + 10*B*x) + 114660*a^6*b^4*x^4*(10*A + 11*B*x) + 54600*a^7*b^3*x^3*(11*A + 12*B*x) + 17325*a^8*b^2*x^2*(12*A + 13*B*x) + 3300*a^9*b*x*(13*A + 14*B*x) + 286*a^10*(14*A + 15*B*x))/x^15","A",1
164,1,222,159,0.0899765,"\int \frac{(a+b x)^{10} (A+B x)}{x^{17}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^17,x]","-\frac{a^{10} (15 A+16 B x)}{240 x^{16}}-\frac{a^9 b (14 A+15 B x)}{21 x^{15}}-\frac{45 a^8 b^2 (13 A+14 B x)}{182 x^{14}}-\frac{10 a^7 b^3 (12 A+13 B x)}{13 x^{13}}-\frac{35 a^6 b^4 (11 A+12 B x)}{22 x^{12}}-\frac{126 a^5 b^5 (10 A+11 B x)}{55 x^{11}}-\frac{7 a^4 b^6 (9 A+10 B x)}{3 x^{10}}-\frac{5 a^3 b^7 (8 A+9 B x)}{3 x^9}-\frac{45 a^2 b^8 (7 A+8 B x)}{56 x^8}-\frac{5 a b^9 (6 A+7 B x)}{21 x^7}-\frac{b^{10} (5 A+6 B x)}{30 x^6}","\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,"-1/30*(b^10*(5*A + 6*B*x))/x^6 - (5*a*b^9*(6*A + 7*B*x))/(21*x^7) - (45*a^2*b^8*(7*A + 8*B*x))/(56*x^8) - (5*a^3*b^7*(8*A + 9*B*x))/(3*x^9) - (7*a^4*b^6*(9*A + 10*B*x))/(3*x^10) - (126*a^5*b^5*(10*A + 11*B*x))/(55*x^11) - (35*a^6*b^4*(11*A + 12*B*x))/(22*x^12) - (10*a^7*b^3*(12*A + 13*B*x))/(13*x^13) - (45*a^8*b^2*(13*A + 14*B*x))/(182*x^14) - (a^9*b*(14*A + 15*B*x))/(21*x^15) - (a^10*(15*A + 16*B*x))/(240*x^16)","A",1
165,1,222,188,0.0895323,"\int \frac{(a+b x)^{10} (A+B x)}{x^{18}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^18,x]","-\frac{a^{10} (16 A+17 B x)}{272 x^{17}}-\frac{a^9 b (15 A+16 B x)}{24 x^{16}}-\frac{3 a^8 b^2 (14 A+15 B x)}{14 x^{15}}-\frac{60 a^7 b^3 (13 A+14 B x)}{91 x^{14}}-\frac{35 a^6 b^4 (12 A+13 B x)}{26 x^{13}}-\frac{21 a^5 b^5 (11 A+12 B x)}{11 x^{12}}-\frac{21 a^4 b^6 (10 A+11 B x)}{11 x^{11}}-\frac{4 a^3 b^7 (9 A+10 B x)}{3 x^{10}}-\frac{5 a^2 b^8 (8 A+9 B x)}{8 x^9}-\frac{5 a b^9 (7 A+8 B x)}{28 x^8}-\frac{b^{10} (6 A+7 B x)}{42 x^7}","-\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,"-1/42*(b^10*(6*A + 7*B*x))/x^7 - (5*a*b^9*(7*A + 8*B*x))/(28*x^8) - (5*a^2*b^8*(8*A + 9*B*x))/(8*x^9) - (4*a^3*b^7*(9*A + 10*B*x))/(3*x^10) - (21*a^4*b^6*(10*A + 11*B*x))/(11*x^11) - (21*a^5*b^5*(11*A + 12*B*x))/(11*x^12) - (35*a^6*b^4*(12*A + 13*B*x))/(26*x^13) - (60*a^7*b^3*(13*A + 14*B*x))/(91*x^14) - (3*a^8*b^2*(14*A + 15*B*x))/(14*x^15) - (a^9*b*(15*A + 16*B*x))/(24*x^16) - (a^10*(16*A + 17*B*x))/(272*x^17)","A",1
166,1,222,229,0.0966269,"\int \frac{(a+b x)^{10} (A+B x)}{x^{19}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^19,x]","-\frac{a^{10} (17 A+18 B x)}{306 x^{18}}-\frac{5 a^9 b (16 A+17 B x)}{136 x^{17}}-\frac{3 a^8 b^2 (15 A+16 B x)}{16 x^{16}}-\frac{4 a^7 b^3 (14 A+15 B x)}{7 x^{15}}-\frac{15 a^6 b^4 (13 A+14 B x)}{13 x^{14}}-\frac{21 a^5 b^5 (12 A+13 B x)}{13 x^{13}}-\frac{35 a^4 b^6 (11 A+12 B x)}{22 x^{12}}-\frac{12 a^3 b^7 (10 A+11 B x)}{11 x^{11}}-\frac{a^2 b^8 (9 A+10 B x)}{2 x^{10}}-\frac{5 a b^9 (8 A+9 B x)}{36 x^9}-\frac{b^{10} (7 A+8 B x)}{56 x^8}","-\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,"-1/56*(b^10*(7*A + 8*B*x))/x^8 - (5*a*b^9*(8*A + 9*B*x))/(36*x^9) - (a^2*b^8*(9*A + 10*B*x))/(2*x^10) - (12*a^3*b^7*(10*A + 11*B*x))/(11*x^11) - (35*a^4*b^6*(11*A + 12*B*x))/(22*x^12) - (21*a^5*b^5*(12*A + 13*B*x))/(13*x^13) - (15*a^6*b^4*(13*A + 14*B*x))/(13*x^14) - (4*a^7*b^3*(14*A + 15*B*x))/(7*x^15) - (3*a^8*b^2*(15*A + 16*B*x))/(16*x^16) - (5*a^9*b*(16*A + 17*B*x))/(136*x^17) - (a^10*(17*A + 18*B*x))/(306*x^18)","A",1
167,1,220,227,0.0940912,"\int \frac{(a+b x)^{10} (A+B x)}{x^{20}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^20,x]","-\frac{a^{10} (18 A+19 B x)}{342 x^{19}}-\frac{5 a^9 b (17 A+18 B x)}{153 x^{18}}-\frac{45 a^8 b^2 (16 A+17 B x)}{272 x^{17}}-\frac{a^7 b^3 (15 A+16 B x)}{2 x^{16}}-\frac{a^6 b^4 (14 A+15 B x)}{x^{15}}-\frac{18 a^5 b^5 (13 A+14 B x)}{13 x^{14}}-\frac{35 a^4 b^6 (12 A+13 B x)}{26 x^{13}}-\frac{10 a^3 b^7 (11 A+12 B x)}{11 x^{12}}-\frac{9 a^2 b^8 (10 A+11 B x)}{22 x^{11}}-\frac{a b^9 (9 A+10 B x)}{9 x^{10}}-\frac{b^{10} (8 A+9 B x)}{72 x^9}","-\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,"-1/72*(b^10*(8*A + 9*B*x))/x^9 - (a*b^9*(9*A + 10*B*x))/(9*x^10) - (9*a^2*b^8*(10*A + 11*B*x))/(22*x^11) - (10*a^3*b^7*(11*A + 12*B*x))/(11*x^12) - (35*a^4*b^6*(12*A + 13*B*x))/(26*x^13) - (18*a^5*b^5*(13*A + 14*B*x))/(13*x^14) - (a^6*b^4*(14*A + 15*B*x))/x^15 - (a^7*b^3*(15*A + 16*B*x))/(2*x^16) - (45*a^8*b^2*(16*A + 17*B*x))/(272*x^17) - (5*a^9*b*(17*A + 18*B*x))/(153*x^18) - (a^10*(18*A + 19*B*x))/(342*x^19)","A",1
168,1,222,229,0.1038128,"\int \frac{(a+b x)^{10} (A+B x)}{x^{21}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/x^21,x]","-\frac{a^{10} (19 A+20 B x)}{380 x^{20}}-\frac{5 a^9 b (18 A+19 B x)}{171 x^{19}}-\frac{5 a^8 b^2 (17 A+18 B x)}{34 x^{18}}-\frac{15 a^7 b^3 (16 A+17 B x)}{34 x^{17}}-\frac{7 a^6 b^4 (15 A+16 B x)}{8 x^{16}}-\frac{6 a^5 b^5 (14 A+15 B x)}{5 x^{15}}-\frac{15 a^4 b^6 (13 A+14 B x)}{13 x^{14}}-\frac{10 a^3 b^7 (12 A+13 B x)}{13 x^{13}}-\frac{15 a^2 b^8 (11 A+12 B x)}{44 x^{12}}-\frac{a b^9 (10 A+11 B x)}{11 x^{11}}-\frac{b^{10} (9 A+10 B x)}{90 x^{10}}","-\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,"-1/90*(b^10*(9*A + 10*B*x))/x^10 - (a*b^9*(10*A + 11*B*x))/(11*x^11) - (15*a^2*b^8*(11*A + 12*B*x))/(44*x^12) - (10*a^3*b^7*(12*A + 13*B*x))/(13*x^13) - (15*a^4*b^6*(13*A + 14*B*x))/(13*x^14) - (6*a^5*b^5*(14*A + 15*B*x))/(5*x^15) - (7*a^6*b^4*(15*A + 16*B*x))/(8*x^16) - (15*a^7*b^3*(16*A + 17*B*x))/(34*x^17) - (5*a^8*b^2*(17*A + 18*B*x))/(34*x^18) - (5*a^9*b*(18*A + 19*B*x))/(171*x^19) - (a^10*(19*A + 20*B*x))/(380*x^20)","A",1
169,1,359,114,0.0991641,"\int x^3 (a+b x) (c+d x)^{16} \, dx","Integrate[x^3*(a + b*x)*(c + d*x)^16,x]","\frac{1}{5} c^{15} x^5 (16 a d+b c)+\frac{4}{3} c^{14} d x^6 (15 a d+2 b c)+\frac{40}{7} c^{13} d^2 x^7 (14 a d+3 b c)+\frac{35}{2} c^{12} d^3 x^8 (13 a d+4 b c)+\frac{364}{9} c^{11} d^4 x^9 (12 a d+5 b c)+\frac{364}{5} c^{10} d^5 x^{10} (11 a d+6 b c)+104 c^9 d^6 x^{11} (10 a d+7 b c)+\frac{715}{6} c^8 d^7 x^{12} (9 a d+8 b c)+110 c^7 d^8 x^{13} (8 a d+9 b c)+\frac{572}{7} c^6 d^9 x^{14} (7 a d+10 b c)+\frac{728}{15} c^5 d^{10} x^{15} (6 a d+11 b c)+\frac{91}{4} c^4 d^{11} x^{16} (5 a d+12 b c)+\frac{140}{17} c^3 d^{12} x^{17} (4 a d+13 b c)+\frac{20}{9} c^2 d^{13} x^{18} (3 a d+14 b c)+\frac{1}{20} d^{15} x^{20} (a d+16 b c)+\frac{8}{19} c d^{14} x^{19} (2 a d+15 b c)+\frac{1}{4} a c^{16} x^4+\frac{1}{21} b d^{16} x^{21}","\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,"(a*c^16*x^4)/4 + (c^15*(b*c + 16*a*d)*x^5)/5 + (4*c^14*d*(2*b*c + 15*a*d)*x^6)/3 + (40*c^13*d^2*(3*b*c + 14*a*d)*x^7)/7 + (35*c^12*d^3*(4*b*c + 13*a*d)*x^8)/2 + (364*c^11*d^4*(5*b*c + 12*a*d)*x^9)/9 + (364*c^10*d^5*(6*b*c + 11*a*d)*x^10)/5 + 104*c^9*d^6*(7*b*c + 10*a*d)*x^11 + (715*c^8*d^7*(8*b*c + 9*a*d)*x^12)/6 + 110*c^7*d^8*(9*b*c + 8*a*d)*x^13 + (572*c^6*d^9*(10*b*c + 7*a*d)*x^14)/7 + (728*c^5*d^10*(11*b*c + 6*a*d)*x^15)/15 + (91*c^4*d^11*(12*b*c + 5*a*d)*x^16)/4 + (140*c^3*d^12*(13*b*c + 4*a*d)*x^17)/17 + (20*c^2*d^13*(14*b*c + 3*a*d)*x^18)/9 + (8*c*d^14*(15*b*c + 2*a*d)*x^19)/19 + (d^15*(16*b*c + a*d)*x^20)/20 + (b*d^16*x^21)/21","B",1
170,1,355,88,0.0793607,"\int x^2 (a+b x) (c+d x)^{16} \, dx","Integrate[x^2*(a + b*x)*(c + d*x)^16,x]","\frac{1}{4} c^{15} x^4 (16 a d+b c)+\frac{8}{5} c^{14} d x^5 (15 a d+2 b c)+\frac{20}{3} c^{13} d^2 x^6 (14 a d+3 b c)+20 c^{12} d^3 x^7 (13 a d+4 b c)+\frac{91}{2} c^{11} d^4 x^8 (12 a d+5 b c)+\frac{728}{9} c^{10} d^5 x^9 (11 a d+6 b c)+\frac{572}{5} c^9 d^6 x^{10} (10 a d+7 b c)+130 c^8 d^7 x^{11} (9 a d+8 b c)+\frac{715}{6} c^7 d^8 x^{12} (8 a d+9 b c)+88 c^6 d^9 x^{13} (7 a d+10 b c)+52 c^5 d^{10} x^{14} (6 a d+11 b c)+\frac{364}{15} c^4 d^{11} x^{15} (5 a d+12 b c)+\frac{35}{4} c^3 d^{12} x^{16} (4 a d+13 b c)+\frac{40}{17} c^2 d^{13} x^{17} (3 a d+14 b c)+\frac{1}{19} d^{15} x^{19} (a d+16 b c)+\frac{4}{9} c d^{14} x^{18} (2 a d+15 b c)+\frac{1}{3} a c^{16} x^3+\frac{1}{20} b d^{16} x^{20}","-\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,"(a*c^16*x^3)/3 + (c^15*(b*c + 16*a*d)*x^4)/4 + (8*c^14*d*(2*b*c + 15*a*d)*x^5)/5 + (20*c^13*d^2*(3*b*c + 14*a*d)*x^6)/3 + 20*c^12*d^3*(4*b*c + 13*a*d)*x^7 + (91*c^11*d^4*(5*b*c + 12*a*d)*x^8)/2 + (728*c^10*d^5*(6*b*c + 11*a*d)*x^9)/9 + (572*c^9*d^6*(7*b*c + 10*a*d)*x^10)/5 + 130*c^8*d^7*(8*b*c + 9*a*d)*x^11 + (715*c^7*d^8*(9*b*c + 8*a*d)*x^12)/6 + 88*c^6*d^9*(10*b*c + 7*a*d)*x^13 + 52*c^5*d^10*(11*b*c + 6*a*d)*x^14 + (364*c^4*d^11*(12*b*c + 5*a*d)*x^15)/15 + (35*c^3*d^12*(13*b*c + 4*a*d)*x^16)/4 + (40*c^2*d^13*(14*b*c + 3*a*d)*x^17)/17 + (4*c*d^14*(15*b*c + 2*a*d)*x^18)/9 + (d^15*(16*b*c + a*d)*x^19)/19 + (b*d^16*x^20)/20","B",1
171,1,347,62,0.0707898,"\int x (a+b x) (c+d x)^{16} \, dx","Integrate[x*(a + b*x)*(c + d*x)^16,x]","\frac{1}{3} c^{15} x^3 (16 a d+b c)+2 c^{14} d x^4 (15 a d+2 b c)+8 c^{13} d^2 x^5 (14 a d+3 b c)+\frac{70}{3} c^{12} d^3 x^6 (13 a d+4 b c)+52 c^{11} d^4 x^7 (12 a d+5 b c)+91 c^{10} d^5 x^8 (11 a d+6 b c)+\frac{1144}{9} c^9 d^6 x^9 (10 a d+7 b c)+143 c^8 d^7 x^{10} (9 a d+8 b c)+130 c^7 d^8 x^{11} (8 a d+9 b c)+\frac{286}{3} c^6 d^9 x^{12} (7 a d+10 b c)+56 c^5 d^{10} x^{13} (6 a d+11 b c)+26 c^4 d^{11} x^{14} (5 a d+12 b c)+\frac{28}{3} c^3 d^{12} x^{15} (4 a d+13 b c)+\frac{5}{2} c^2 d^{13} x^{16} (3 a d+14 b c)+\frac{1}{18} d^{15} x^{18} (a d+16 b c)+\frac{8}{17} c d^{14} x^{17} (2 a d+15 b c)+\frac{1}{2} a c^{16} x^2+\frac{1}{19} b d^{16} x^{19}","-\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,"(a*c^16*x^2)/2 + (c^15*(b*c + 16*a*d)*x^3)/3 + 2*c^14*d*(2*b*c + 15*a*d)*x^4 + 8*c^13*d^2*(3*b*c + 14*a*d)*x^5 + (70*c^12*d^3*(4*b*c + 13*a*d)*x^6)/3 + 52*c^11*d^4*(5*b*c + 12*a*d)*x^7 + 91*c^10*d^5*(6*b*c + 11*a*d)*x^8 + (1144*c^9*d^6*(7*b*c + 10*a*d)*x^9)/9 + 143*c^8*d^7*(8*b*c + 9*a*d)*x^10 + 130*c^7*d^8*(9*b*c + 8*a*d)*x^11 + (286*c^6*d^9*(10*b*c + 7*a*d)*x^12)/3 + 56*c^5*d^10*(11*b*c + 6*a*d)*x^13 + 26*c^4*d^11*(12*b*c + 5*a*d)*x^14 + (28*c^3*d^12*(13*b*c + 4*a*d)*x^15)/3 + (5*c^2*d^13*(14*b*c + 3*a*d)*x^16)/2 + (8*c*d^14*(15*b*c + 2*a*d)*x^17)/17 + (d^15*(16*b*c + a*d)*x^18)/18 + (b*d^16*x^19)/19","B",1
172,1,342,38,0.0611668,"\int (a+b x) (c+d x)^{16} \, dx","Integrate[(a + b*x)*(c + d*x)^16,x]","\frac{1}{2} c^{15} x^2 (16 a d+b c)+\frac{8}{3} c^{14} d x^3 (15 a d+2 b c)+10 c^{13} d^2 x^4 (14 a d+3 b c)+28 c^{12} d^3 x^5 (13 a d+4 b c)+\frac{182}{3} c^{11} d^4 x^6 (12 a d+5 b c)+104 c^{10} d^5 x^7 (11 a d+6 b c)+143 c^9 d^6 x^8 (10 a d+7 b c)+\frac{1430}{9} c^8 d^7 x^9 (9 a d+8 b c)+143 c^7 d^8 x^{10} (8 a d+9 b c)+104 c^6 d^9 x^{11} (7 a d+10 b c)+\frac{182}{3} c^5 d^{10} x^{12} (6 a d+11 b c)+28 c^4 d^{11} x^{13} (5 a d+12 b c)+10 c^3 d^{12} x^{14} (4 a d+13 b c)+\frac{8}{3} c^2 d^{13} x^{15} (3 a d+14 b c)+\frac{1}{17} d^{15} x^{17} (a d+16 b c)+\frac{1}{2} c d^{14} x^{16} (2 a d+15 b c)+a c^{16} x+\frac{1}{18} b d^{16} x^{18}","\frac{b (c+d x)^{18}}{18 d^2}-\frac{(c+d x)^{17} (b c-a d)}{17 d^2}",1,"a*c^16*x + (c^15*(b*c + 16*a*d)*x^2)/2 + (8*c^14*d*(2*b*c + 15*a*d)*x^3)/3 + 10*c^13*d^2*(3*b*c + 14*a*d)*x^4 + 28*c^12*d^3*(4*b*c + 13*a*d)*x^5 + (182*c^11*d^4*(5*b*c + 12*a*d)*x^6)/3 + 104*c^10*d^5*(6*b*c + 11*a*d)*x^7 + 143*c^9*d^6*(7*b*c + 10*a*d)*x^8 + (1430*c^8*d^7*(8*b*c + 9*a*d)*x^9)/9 + 143*c^7*d^8*(9*b*c + 8*a*d)*x^10 + 104*c^6*d^9*(10*b*c + 7*a*d)*x^11 + (182*c^5*d^10*(11*b*c + 6*a*d)*x^12)/3 + 28*c^4*d^11*(12*b*c + 5*a*d)*x^13 + 10*c^3*d^12*(13*b*c + 4*a*d)*x^14 + (8*c^2*d^13*(14*b*c + 3*a*d)*x^15)/3 + (c*d^14*(15*b*c + 2*a*d)*x^16)/2 + (d^15*(16*b*c + a*d)*x^17)/17 + (b*d^16*x^18)/18","B",1
173,1,42,12,0.0025768,"\int x^2 (2+x)^5 (2+3 x) \, dx","Integrate[x^2*(2 + x)^5*(2 + 3*x),x]","\frac{x^9}{3}+4 x^8+20 x^7+\frac{160 x^6}{3}+80 x^5+64 x^4+\frac{64 x^3}{3}","\frac{1}{3} x^3 (x+2)^6",1,"(64*x^3)/3 + 64*x^4 + 80*x^5 + (160*x^6)/3 + 20*x^7 + 4*x^8 + x^9/3","B",1
174,1,100,108,0.0479077,"\int \frac{x^4 (A+B x)}{a+b x} \, dx","Integrate[(x^4*(A + B*x))/(a + b*x),x]","\frac{b x \left(60 a^4 B-30 a^3 b (2 A+B x)+10 a^2 b^2 x (3 A+2 B x)-5 a b^3 x^2 (4 A+3 B x)+3 b^4 x^3 (5 A+4 B x)\right)-60 a^4 (a B-A b) \log (a+b x)}{60 b^6}","\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,"(b*x*(60*a^4*B - 30*a^3*b*(2*A + B*x) + 10*a^2*b^2*x*(3*A + 2*B*x) - 5*a*b^3*x^2*(4*A + 3*B*x) + 3*b^4*x^3*(5*A + 4*B*x)) - 60*a^4*(-(A*b) + a*B)*Log[a + b*x])/(60*b^6)","A",1
175,1,80,87,0.0307947,"\int \frac{x^3 (A+B x)}{a+b x} \, dx","Integrate[(x^3*(A + B*x))/(a + b*x),x]","\frac{12 a^3 (a B-A b) \log (a+b x)+b x \left(-12 a^3 B+6 a^2 b (2 A+B x)-2 a b^2 x (3 A+2 B x)+b^3 x^2 (4 A+3 B x)\right)}{12 b^5}","-\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,"(b*x*(-12*a^3*B + 6*a^2*b*(2*A + B*x) - 2*a*b^2*x*(3*A + 2*B*x) + b^3*x^2*(4*A + 3*B*x)) + 12*a^3*(-(A*b) + a*B)*Log[a + b*x])/(12*b^5)","A",1
176,1,61,66,0.0235256,"\int \frac{x^2 (A+B x)}{a+b x} \, dx","Integrate[(x^2*(A + B*x))/(a + b*x),x]","\frac{b x \left(6 a^2 B-3 a b (2 A+B x)+b^2 x (3 A+2 B x)\right)+6 a^2 (A b-a B) \log (a+b x)}{6 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,"(b*x*(6*a^2*B - 3*a*b*(2*A + B*x) + b^2*x*(3*A + 2*B*x)) + 6*a^2*(A*b - a*B)*Log[a + b*x])/(6*b^4)","A",1
177,1,41,45,0.0193275,"\int \frac{x (A+B x)}{a+b x} \, dx","Integrate[(x*(A + B*x))/(a + b*x),x]","\frac{b x (-2 a B+2 A b+b B x)+2 a (a B-A b) \log (a+b x)}{2 b^3}","-\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,"(b*x*(2*A*b - 2*a*B + b*B*x) + 2*a*(-(A*b) + a*B)*Log[a + b*x])/(2*b^3)","A",1
178,1,25,25,0.0144301,"\int \frac{A+B x}{a+b x} \, dx","Integrate[(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
179,1,29,30,0.0106263,"\int \frac{A+B x}{x (a+b x)} \, dx","Integrate[(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
180,1,42,43,0.0305396,"\int \frac{A+B x}{x^2 (a+b x)} \, dx","Integrate[(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
181,1,58,62,0.0396328,"\int \frac{A+B x}{x^3 (a+b x)} \, dx","Integrate[(A + B*x)/(x^3*(a + b*x)),x]","\frac{-\frac{a (a A+2 a B x-2 A b x)}{x^2}+2 b \log (x) (A b-a B)+2 b (a B-A b) \log (a+b x)}{2 a^3}","\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*A - 2*A*b*x + 2*a*B*x))/x^2) + 2*b*(A*b - a*B)*Log[x] + 2*b*(-(A*b) + a*B)*Log[a + b*x])/(2*a^3)","A",1
182,1,81,86,0.069375,"\int \frac{A+B x}{x^4 (a+b x)} \, dx","Integrate[(A + B*x)/(x^4*(a + b*x)),x]","\frac{\frac{a \left(-\left(a^2 (2 A+3 B x)\right)+3 a b x (A+2 B x)-6 A b^2 x^2\right)}{x^3}+6 b^2 \log (x) (a B-A b)+6 b^2 (A b-a B) \log (a+b x)}{6 a^4}","-\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,"((a*(-6*A*b^2*x^2 + 3*a*b*x*(A + 2*B*x) - a^2*(2*A + 3*B*x)))/x^3 + 6*b^2*(-(A*b) + a*B)*Log[x] + 6*b^2*(A*b - a*B)*Log[a + b*x])/(6*a^4)","A",1
183,1,100,106,0.0767559,"\int \frac{A+B x}{x^5 (a+b x)} \, dx","Integrate[(A + B*x)/(x^5*(a + b*x)),x]","\frac{\frac{a \left(-\left(a^3 (3 A+4 B x)\right)+2 a^2 b x (2 A+3 B x)-6 a b^2 x^2 (A+2 B x)+12 A b^3 x^3\right)}{x^4}+12 b^3 \log (x) (A b-a B)-12 b^3 (A b-a B) \log (a+b x)}{12 a^5}","\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,"((a*(12*A*b^3*x^3 - 6*a*b^2*x^2*(A + 2*B*x) + 2*a^2*b*x*(2*A + 3*B*x) - a^3*(3*A + 4*B*x)))/x^4 + 12*b^3*(A*b - a*B)*Log[x] - 12*b^3*(A*b - a*B)*Log[a + b*x])/(12*a^5)","A",1
184,1,107,113,0.0696138,"\int \frac{x^4 (A+B x)}{(a+b x)^2} \, dx","Integrate[(x^4*(A + B*x))/(a + b*x)^2,x]","\frac{\frac{12 a^4 (a B-A b)}{a+b x}+12 a^3 (5 a B-4 A b) \log (a+b x)-12 a^2 b x (4 a B-3 A b)+4 b^3 x^3 (A b-2 a B)+6 a b^2 x^2 (3 a B-2 A b)+3 b^4 B x^4}{12 b^6}","-\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^2*b*(-3*A*b + 4*a*B)*x + 6*a*b^2*(-2*A*b + 3*a*B)*x^2 + 4*b^3*(A*b - 2*a*B)*x^3 + 3*b^4*B*x^4 + (12*a^4*(-(A*b) + a*B))/(a + b*x) + 12*a^3*(-4*A*b + 5*a*B)*Log[a + b*x])/(12*b^6)","A",1
185,1,87,90,0.0747578,"\int \frac{x^3 (A+B x)}{(a+b x)^2} \, dx","Integrate[(x^3*(A + B*x))/(a + b*x)^2,x]","\frac{\frac{6 a^3 (A b-a B)}{a+b x}+6 a^2 (3 A b-4 a B) \log (a+b x)+3 b^2 x^2 (A b-2 a B)+6 a b x (3 a B-2 A b)+2 b^3 B x^3}{6 b^5}","\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*b*(-2*A*b + 3*a*B)*x + 3*b^2*(A*b - 2*a*B)*x^2 + 2*b^3*B*x^3 + (6*a^3*(A*b - a*B))/(a + b*x) + 6*a^2*(3*A*b - 4*a*B)*Log[a + b*x])/(6*b^5)","A",1
186,1,66,69,0.0760395,"\int \frac{x^2 (A+B x)}{(a+b x)^2} \, dx","Integrate[(x^2*(A + B*x))/(a + b*x)^2,x]","\frac{\frac{2 a^2 (a B-A b)}{a+b x}+2 b x (A b-2 a B)+2 a (3 a B-2 A b) \log (a+b x)+b^2 B x^2}{2 b^4}","-\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*b*(A*b - 2*a*B)*x + b^2*B*x^2 + (2*a^2*(-(A*b) + a*B))/(a + b*x) + 2*a*(-2*A*b + 3*a*B)*Log[a + b*x])/(2*b^4)","A",1
187,1,41,45,0.0312264,"\int \frac{x (A+B x)}{(a+b x)^2} \, dx","Integrate[(x*(A + B*x))/(a + b*x)^2,x]","\frac{\frac{a (A b-a B)}{a+b x}+(A b-2 a B) \log (a+b x)+b 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,"(b*B*x + (a*(A*b - a*B))/(a + b*x) + (A*b - 2*a*B)*Log[a + b*x])/b^3","A",1
188,1,31,32,0.0129924,"\int \frac{A+B x}{(a+b x)^2} \, dx","Integrate[(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
189,1,38,42,0.0322996,"\int \frac{A+B x}{x (a+b x)^2} \, dx","Integrate[(A + B*x)/(x*(a + b*x)^2),x]","\frac{\frac{a (A b-a B)}{b (a+b x)}-A \log (a+b x)+A \log (x)}{a^2}","-\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*(A*b - a*B))/(b*(a + b*x)) + A*Log[x] - A*Log[a + b*x])/a^2","A",1
190,1,56,65,0.055109,"\int \frac{A+B x}{x^2 (a+b x)^2} \, dx","Integrate[(A + B*x)/(x^2*(a + b*x)^2),x]","\frac{\frac{a (a B-A b)}{a+b x}+\log (x) (a B-2 A b)+(2 A b-a B) \log (a+b x)-\frac{a A}{x}}{a^3}","-\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)/x) + (a*(-(A*b) + a*B))/(a + b*x) + (-2*A*b + a*B)*Log[x] + (2*A*b - a*B)*Log[a + b*x])/a^3","A",1
191,1,85,85,0.092353,"\int \frac{A+B x}{x^3 (a+b x)^2} \, dx","Integrate[(A + B*x)/(x^3*(a + b*x)^2),x]","\frac{-\frac{a \left(a^2 (A+2 B x)+a b x (4 B x-3 A)-6 A b^2 x^2\right)}{x^2 (a+b x)}+2 b \log (x) (3 A b-2 a B)+2 b (2 a B-3 A b) \log (a+b x)}{2 a^4}","\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*(-6*A*b^2*x^2 + a^2*(A + 2*B*x) + a*b*x*(-3*A + 4*B*x)))/(x^2*(a + b*x))) + 2*b*(3*A*b - 2*a*B)*Log[x] + 2*b*(-3*A*b + 2*a*B)*Log[a + b*x])/(2*a^4)","A",1
192,1,106,113,0.1116242,"\int \frac{A+B x}{x^4 (a+b x)^2} \, dx","Integrate[(A + B*x)/(x^4*(a + b*x)^2),x]","\frac{-\frac{2 a^3 A}{x^3}-\frac{3 a^2 (a B-2 A b)}{x^2}+\frac{6 a b^2 (a B-A b)}{a+b x}+6 b^2 \log (x) (3 a B-4 A b)+6 b^2 (4 A b-3 a B) \log (a+b x)+\frac{6 a b (2 a B-3 A b)}{x}}{6 a^5}","-\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)/x^3 - (3*a^2*(-2*A*b + a*B))/x^2 + (6*a*b*(-3*A*b + 2*a*B))/x + (6*a*b^2*(-(A*b) + a*B))/(a + b*x) + 6*b^2*(-4*A*b + 3*a*B)*Log[x] + 6*b^2*(4*A*b - 3*a*B)*Log[a + b*x])/(6*a^5)","A",1
193,1,108,116,0.0878475,"\int \frac{x^4 (A+B x)}{(a+b x)^3} \, dx","Integrate[(x^4*(A + B*x))/(a + b*x)^3,x]","\frac{\frac{3 a^4 (a B-A b)}{(a+b x)^2}+\frac{6 a^3 (4 A b-5 a B)}{a+b x}-12 a^2 (5 a B-3 A b) \log (a+b x)+3 b^2 x^2 (A b-3 a B)+18 a b x (2 a B-A b)+2 b^3 B x^3}{6 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,"(18*a*b*(-(A*b) + 2*a*B)*x + 3*b^2*(A*b - 3*a*B)*x^2 + 2*b^3*B*x^3 + (3*a^4*(-(A*b) + a*B))/(a + b*x)^2 + (6*a^3*(4*A*b - 5*a*B))/(a + b*x) - 12*a^2*(-3*A*b + 5*a*B)*Log[a + b*x])/(6*b^6)","A",1
194,1,86,94,0.0768677,"\int \frac{x^3 (A+B x)}{(a+b x)^3} \, dx","Integrate[(x^3*(A + B*x))/(a + b*x)^3,x]","\frac{\frac{a^3 (A b-a B)}{(a+b x)^2}+\frac{2 a^2 (4 a B-3 A b)}{a+b x}+2 b x (A b-3 a B)+6 a (2 a B-A b) \log (a+b x)+b^2 B x^2}{2 b^5}","\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,"(2*b*(A*b - 3*a*B)*x + b^2*B*x^2 + (a^3*(A*b - a*B))/(a + b*x)^2 + (2*a^2*(-3*A*b + 4*a*B))/(a + b*x) + 6*a*(-(A*b) + 2*a*B)*Log[a + b*x])/(2*b^5)","A",1
195,1,75,71,0.0323529,"\int \frac{x^2 (A+B x)}{(a+b x)^3} \, dx","Integrate[(x^2*(A + B*x))/(a + b*x)^3,x]","\frac{2 a A b-3 a^2 B}{b^4 (a+b x)}+\frac{a^3 B-a^2 A b}{2 b^4 (a+b x)^2}+\frac{(A b-3 a B) \log (a+b x)}{b^4}+\frac{B x}{b^3}","-\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,"(B*x)/b^3 + (-(a^2*A*b) + a^3*B)/(2*b^4*(a + b*x)^2) + (2*a*A*b - 3*a^2*B)/(b^4*(a + b*x)) + ((A*b - 3*a*B)*Log[a + b*x])/b^4","A",1
196,1,54,55,0.0226253,"\int \frac{x (A+B x)}{(a+b x)^3} \, dx","Integrate[(x*(A + B*x))/(a + b*x)^3,x]","\frac{3 a^2 B-a b (A-4 B x)+2 B (a+b x)^2 \log (a+b x)-2 A b^2 x}{2 b^3 (a+b x)^2}","-\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,"(3*a^2*B - 2*A*b^2*x - a*b*(A - 4*B*x) + 2*B*(a + b*x)^2*Log[a + b*x])/(2*b^3*(a + b*x)^2)","A",1
197,1,26,28,0.0133185,"\int \frac{A+B x}{(a+b x)^3} \, dx","Integrate[(A + B*x)/(a + b*x)^3,x]","-\frac{B (a+2 b x)+A b}{2 b^2 (a+b x)^2}","-\frac{(A+B x)^2}{2 (a+b x)^2 (A b-a B)}",1,"-1/2*(A*b + B*(a + 2*b*x))/(b^2*(a + b*x)^2)","A",1
198,1,53,57,0.0524523,"\int \frac{A+B x}{x (a+b x)^3} \, dx","Integrate[(A + B*x)/(x*(a + b*x)^3),x]","\frac{\frac{a \left(a^2 (-B)+3 a A b+2 A b^2 x\right)}{b (a+b x)^2}-2 A \log (a+b x)+2 A \log (x)}{2 a^3}","-\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,"((a*(3*a*A*b - a^2*B + 2*A*b^2*x))/(b*(a + b*x)^2) + 2*A*Log[x] - 2*A*Log[a + b*x])/(2*a^3)","A",1
199,1,81,88,0.0670064,"\int \frac{A+B x}{x^2 (a+b x)^3} \, dx","Integrate[(A + B*x)/(x^2*(a + b*x)^3),x]","\frac{\frac{a^2 (a B-A b)}{(a+b x)^2}+\frac{2 a (a B-2 A b)}{a+b x}+2 \log (x) (a B-3 A b)+2 (3 A b-a B) \log (a+b x)-\frac{2 a A}{x}}{2 a^4}","-\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*A)/x + (a^2*(-(A*b) + a*B))/(a + b*x)^2 + (2*a*(-2*A*b + a*B))/(a + b*x) + 2*(-3*A*b + a*B)*Log[x] + 2*(3*A*b - a*B)*Log[a + b*x])/(2*a^4)","A",1
200,1,102,110,0.1112605,"\int \frac{A+B x}{x^3 (a+b x)^3} \, dx","Integrate[(A + B*x)/(x^3*(a + b*x)^3),x]","\frac{-\frac{a \left(a^3 (A+2 B x)+a^2 b x (9 B x-4 A)+6 a b^2 x^2 (B x-3 A)-12 A b^3 x^3\right)}{x^2 (a+b x)^2}+6 b \log (x) (2 A b-a B)+6 b (a B-2 A b) \log (a+b x)}{2 a^5}","\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*(-12*A*b^3*x^3 + 6*a*b^2*x^2*(-3*A + B*x) + a^3*(A + 2*B*x) + a^2*b*x*(-4*A + 9*B*x)))/(x^2*(a + b*x)^2)) + 6*b*(2*A*b - a*B)*Log[x] + 6*b*(-2*A*b + a*B)*Log[a + b*x])/(2*a^5)","A",1
201,1,129,140,0.1675759,"\int \frac{A+B x}{x^4 (a+b x)^3} \, dx","Integrate[(A + B*x)/(x^4*(a + b*x)^3),x]","\frac{\frac{a \left(-\left(a^4 (2 A+3 B x)\right)+a^3 b x (5 A+12 B x)+2 a^2 b^2 x^2 (27 B x-10 A)+18 a b^3 x^3 (2 B x-5 A)-60 A b^4 x^4\right)}{x^3 (a+b x)^2}+12 b^2 \log (x) (3 a B-5 A b)+12 b^2 (5 A b-3 a B) \log (a+b x)}{6 a^6}","-\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,"((a*(-60*A*b^4*x^4 + 18*a*b^3*x^3*(-5*A + 2*B*x) - a^4*(2*A + 3*B*x) + a^3*b*x*(5*A + 12*B*x) + 2*a^2*b^2*x^2*(-10*A + 27*B*x)))/(x^3*(a + b*x)^2) + 12*b^2*(-5*A*b + 3*a*B)*Log[x] + 12*b^2*(5*A*b - 3*a*B)*Log[a + b*x])/(6*a^6)","A",1
202,1,589,177,0.1546424,"\int x^3 (a+b x)^2 (c+d x)^{16} \, dx","Integrate[x^3*(a + b*x)^2*(c + d*x)^16,x]","\frac{1}{20} d^{14} x^{20} \left(a^2 d^2+32 a b c d+120 b^2 c^2\right)+\frac{16}{19} c d^{13} x^{19} \left(a^2 d^2+15 a b c d+35 b^2 c^2\right)+\frac{10}{9} c^2 d^{12} x^{18} \left(6 a^2 d^2+56 a b c d+91 b^2 c^2\right)+\frac{1}{6} c^{14} x^6 \left(120 a^2 d^2+32 a b c d+b^2 c^2\right)+\frac{16}{7} c^{13} d x^7 \left(35 a^2 d^2+15 a b c d+b^2 c^2\right)+\frac{5}{2} c^{12} d^2 x^8 \left(91 a^2 d^2+56 a b c d+6 b^2 c^2\right)+\frac{56}{9} c^{11} d^3 x^9 \left(78 a^2 d^2+65 a b c d+10 b^2 c^2\right)+\frac{182}{5} c^{10} d^4 x^{10} \left(22 a^2 d^2+24 a b c d+5 b^2 c^2\right)+\frac{208}{11} c^9 d^5 x^{11} \left(55 a^2 d^2+77 a b c d+21 b^2 c^2\right)+\frac{143}{6} c^8 d^6 x^{12} \left(45 a^2 d^2+80 a b c d+28 b^2 c^2\right)+220 c^7 d^7 x^{13} \left(4 a^2 d^2+9 a b c d+4 b^2 c^2\right)+\frac{143}{7} c^6 d^8 x^{14} \left(28 a^2 d^2+80 a b c d+45 b^2 c^2\right)+\frac{208}{15} c^5 d^9 x^{15} \left(21 a^2 d^2+77 a b c d+55 b^2 c^2\right)+\frac{91}{4} c^4 d^{10} x^{16} \left(5 a^2 d^2+24 a b c d+22 b^2 c^2\right)+\frac{56}{17} c^3 d^{11} x^{17} \left(10 a^2 d^2+65 a b c d+78 b^2 c^2\right)+\frac{1}{4} a^2 c^{16} x^4+\frac{2}{5} a c^{15} x^5 (8 a d+b c)+\frac{2}{21} b d^{15} x^{21} (a d+8 b c)+\frac{1}{22} b^2 d^{16} x^{22}","\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,"(a^2*c^16*x^4)/4 + (2*a*c^15*(b*c + 8*a*d)*x^5)/5 + (c^14*(b^2*c^2 + 32*a*b*c*d + 120*a^2*d^2)*x^6)/6 + (16*c^13*d*(b^2*c^2 + 15*a*b*c*d + 35*a^2*d^2)*x^7)/7 + (5*c^12*d^2*(6*b^2*c^2 + 56*a*b*c*d + 91*a^2*d^2)*x^8)/2 + (56*c^11*d^3*(10*b^2*c^2 + 65*a*b*c*d + 78*a^2*d^2)*x^9)/9 + (182*c^10*d^4*(5*b^2*c^2 + 24*a*b*c*d + 22*a^2*d^2)*x^10)/5 + (208*c^9*d^5*(21*b^2*c^2 + 77*a*b*c*d + 55*a^2*d^2)*x^11)/11 + (143*c^8*d^6*(28*b^2*c^2 + 80*a*b*c*d + 45*a^2*d^2)*x^12)/6 + 220*c^7*d^7*(4*b^2*c^2 + 9*a*b*c*d + 4*a^2*d^2)*x^13 + (143*c^6*d^8*(45*b^2*c^2 + 80*a*b*c*d + 28*a^2*d^2)*x^14)/7 + (208*c^5*d^9*(55*b^2*c^2 + 77*a*b*c*d + 21*a^2*d^2)*x^15)/15 + (91*c^4*d^10*(22*b^2*c^2 + 24*a*b*c*d + 5*a^2*d^2)*x^16)/4 + (56*c^3*d^11*(78*b^2*c^2 + 65*a*b*c*d + 10*a^2*d^2)*x^17)/17 + (10*c^2*d^12*(91*b^2*c^2 + 56*a*b*c*d + 6*a^2*d^2)*x^18)/9 + (16*c*d^13*(35*b^2*c^2 + 15*a*b*c*d + a^2*d^2)*x^19)/19 + (d^14*(120*b^2*c^2 + 32*a*b*c*d + a^2*d^2)*x^20)/20 + (2*b*d^15*(8*b*c + a*d)*x^21)/21 + (b^2*d^16*x^22)/22","B",1
203,1,585,137,0.1066143,"\int x^2 (a+b x)^2 (c+d x)^{16} \, dx","Integrate[x^2*(a + b*x)^2*(c + d*x)^16,x]","\frac{1}{19} d^{14} x^{19} \left(a^2 d^2+32 a b c d+120 b^2 c^2\right)+\frac{8}{9} c d^{13} x^{18} \left(a^2 d^2+15 a b c d+35 b^2 c^2\right)+\frac{20}{17} c^2 d^{12} x^{17} \left(6 a^2 d^2+56 a b c d+91 b^2 c^2\right)+\frac{1}{5} c^{14} x^5 \left(120 a^2 d^2+32 a b c d+b^2 c^2\right)+\frac{8}{3} c^{13} d x^6 \left(35 a^2 d^2+15 a b c d+b^2 c^2\right)+\frac{20}{7} c^{12} d^2 x^7 \left(91 a^2 d^2+56 a b c d+6 b^2 c^2\right)+7 c^{11} d^3 x^8 \left(78 a^2 d^2+65 a b c d+10 b^2 c^2\right)+\frac{364}{9} c^{10} d^4 x^9 \left(22 a^2 d^2+24 a b c d+5 b^2 c^2\right)+\frac{104}{5} c^9 d^5 x^{10} \left(55 a^2 d^2+77 a b c d+21 b^2 c^2\right)+26 c^8 d^6 x^{11} \left(45 a^2 d^2+80 a b c d+28 b^2 c^2\right)+\frac{715}{3} c^7 d^7 x^{12} \left(4 a^2 d^2+9 a b c d+4 b^2 c^2\right)+22 c^6 d^8 x^{13} \left(28 a^2 d^2+80 a b c d+45 b^2 c^2\right)+\frac{104}{7} c^5 d^9 x^{14} \left(21 a^2 d^2+77 a b c d+55 b^2 c^2\right)+\frac{364}{15} c^4 d^{10} x^{15} \left(5 a^2 d^2+24 a b c d+22 b^2 c^2\right)+\frac{7}{2} c^3 d^{11} x^{16} \left(10 a^2 d^2+65 a b c d+78 b^2 c^2\right)+\frac{1}{3} a^2 c^{16} x^3+\frac{1}{2} a c^{15} x^4 (8 a d+b c)+\frac{1}{10} b d^{15} x^{20} (a d+8 b c)+\frac{1}{21} b^2 d^{16} x^{21}","\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,"(a^2*c^16*x^3)/3 + (a*c^15*(b*c + 8*a*d)*x^4)/2 + (c^14*(b^2*c^2 + 32*a*b*c*d + 120*a^2*d^2)*x^5)/5 + (8*c^13*d*(b^2*c^2 + 15*a*b*c*d + 35*a^2*d^2)*x^6)/3 + (20*c^12*d^2*(6*b^2*c^2 + 56*a*b*c*d + 91*a^2*d^2)*x^7)/7 + 7*c^11*d^3*(10*b^2*c^2 + 65*a*b*c*d + 78*a^2*d^2)*x^8 + (364*c^10*d^4*(5*b^2*c^2 + 24*a*b*c*d + 22*a^2*d^2)*x^9)/9 + (104*c^9*d^5*(21*b^2*c^2 + 77*a*b*c*d + 55*a^2*d^2)*x^10)/5 + 26*c^8*d^6*(28*b^2*c^2 + 80*a*b*c*d + 45*a^2*d^2)*x^11 + (715*c^7*d^7*(4*b^2*c^2 + 9*a*b*c*d + 4*a^2*d^2)*x^12)/3 + 22*c^6*d^8*(45*b^2*c^2 + 80*a*b*c*d + 28*a^2*d^2)*x^13 + (104*c^5*d^9*(55*b^2*c^2 + 77*a*b*c*d + 21*a^2*d^2)*x^14)/7 + (364*c^4*d^10*(22*b^2*c^2 + 24*a*b*c*d + 5*a^2*d^2)*x^15)/15 + (7*c^3*d^11*(78*b^2*c^2 + 65*a*b*c*d + 10*a^2*d^2)*x^16)/2 + (20*c^2*d^12*(91*b^2*c^2 + 56*a*b*c*d + 6*a^2*d^2)*x^17)/17 + (8*c*d^13*(35*b^2*c^2 + 15*a*b*c*d + a^2*d^2)*x^18)/9 + (d^14*(120*b^2*c^2 + 32*a*b*c*d + a^2*d^2)*x^19)/19 + (b*d^15*(8*b*c + a*d)*x^20)/10 + (b^2*d^16*x^21)/21","B",1
204,1,583,98,0.1174436,"\int x (a+b x)^2 (c+d x)^{16} \, dx","Integrate[x*(a + b*x)^2*(c + d*x)^16,x]","\frac{1}{18} d^{14} x^{18} \left(a^2 d^2+32 a b c d+120 b^2 c^2\right)+\frac{16}{17} c d^{13} x^{17} \left(a^2 d^2+15 a b c d+35 b^2 c^2\right)+\frac{5}{4} c^2 d^{12} x^{16} \left(6 a^2 d^2+56 a b c d+91 b^2 c^2\right)+\frac{1}{4} c^{14} x^4 \left(120 a^2 d^2+32 a b c d+b^2 c^2\right)+\frac{16}{5} c^{13} d x^5 \left(35 a^2 d^2+15 a b c d+b^2 c^2\right)+\frac{10}{3} c^{12} d^2 x^6 \left(91 a^2 d^2+56 a b c d+6 b^2 c^2\right)+8 c^{11} d^3 x^7 \left(78 a^2 d^2+65 a b c d+10 b^2 c^2\right)+\frac{91}{2} c^{10} d^4 x^8 \left(22 a^2 d^2+24 a b c d+5 b^2 c^2\right)+\frac{208}{9} c^9 d^5 x^9 \left(55 a^2 d^2+77 a b c d+21 b^2 c^2\right)+\frac{143}{5} c^8 d^6 x^{10} \left(45 a^2 d^2+80 a b c d+28 b^2 c^2\right)+260 c^7 d^7 x^{11} \left(4 a^2 d^2+9 a b c d+4 b^2 c^2\right)+\frac{143}{6} c^6 d^8 x^{12} \left(28 a^2 d^2+80 a b c d+45 b^2 c^2\right)+16 c^5 d^9 x^{13} \left(21 a^2 d^2+77 a b c d+55 b^2 c^2\right)+26 c^4 d^{10} x^{14} \left(5 a^2 d^2+24 a b c d+22 b^2 c^2\right)+\frac{56}{15} c^3 d^{11} x^{15} \left(10 a^2 d^2+65 a b c d+78 b^2 c^2\right)+\frac{1}{2} a^2 c^{16} x^2+\frac{2}{3} a c^{15} x^3 (8 a d+b c)+\frac{2}{19} b d^{15} x^{19} (a d+8 b c)+\frac{1}{20} b^2 d^{16} x^{20}","-\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,"(a^2*c^16*x^2)/2 + (2*a*c^15*(b*c + 8*a*d)*x^3)/3 + (c^14*(b^2*c^2 + 32*a*b*c*d + 120*a^2*d^2)*x^4)/4 + (16*c^13*d*(b^2*c^2 + 15*a*b*c*d + 35*a^2*d^2)*x^5)/5 + (10*c^12*d^2*(6*b^2*c^2 + 56*a*b*c*d + 91*a^2*d^2)*x^6)/3 + 8*c^11*d^3*(10*b^2*c^2 + 65*a*b*c*d + 78*a^2*d^2)*x^7 + (91*c^10*d^4*(5*b^2*c^2 + 24*a*b*c*d + 22*a^2*d^2)*x^8)/2 + (208*c^9*d^5*(21*b^2*c^2 + 77*a*b*c*d + 55*a^2*d^2)*x^9)/9 + (143*c^8*d^6*(28*b^2*c^2 + 80*a*b*c*d + 45*a^2*d^2)*x^10)/5 + 260*c^7*d^7*(4*b^2*c^2 + 9*a*b*c*d + 4*a^2*d^2)*x^11 + (143*c^6*d^8*(45*b^2*c^2 + 80*a*b*c*d + 28*a^2*d^2)*x^12)/6 + 16*c^5*d^9*(55*b^2*c^2 + 77*a*b*c*d + 21*a^2*d^2)*x^13 + 26*c^4*d^10*(22*b^2*c^2 + 24*a*b*c*d + 5*a^2*d^2)*x^14 + (56*c^3*d^11*(78*b^2*c^2 + 65*a*b*c*d + 10*a^2*d^2)*x^15)/15 + (5*c^2*d^12*(91*b^2*c^2 + 56*a*b*c*d + 6*a^2*d^2)*x^16)/4 + (16*c*d^13*(35*b^2*c^2 + 15*a*b*c*d + a^2*d^2)*x^17)/17 + (d^14*(120*b^2*c^2 + 32*a*b*c*d + a^2*d^2)*x^18)/18 + (2*b*d^15*(8*b*c + a*d)*x^19)/19 + (b^2*d^16*x^20)/20","B",1
205,1,80,87,0.0388806,"\int \frac{x^3 (c+d x)}{a+b x} \, dx","Integrate[(x^3*(c + d*x))/(a + b*x),x]","\frac{12 a^3 (a d-b c) \log (a+b x)+b x \left(-12 a^3 d+6 a^2 b (2 c+d x)-2 a b^2 x (3 c+2 d x)+b^3 x^2 (4 c+3 d x)\right)}{12 b^5}","-\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,"(b*x*(-12*a^3*d + 6*a^2*b*(2*c + d*x) - 2*a*b^2*x*(3*c + 2*d*x) + b^3*x^2*(4*c + 3*d*x)) + 12*a^3*(-(b*c) + a*d)*Log[a + b*x])/(12*b^5)","A",1
206,1,61,66,0.0285088,"\int \frac{x^2 (c+d x)}{a+b x} \, dx","Integrate[(x^2*(c + d*x))/(a + b*x),x]","\frac{b x \left(6 a^2 d-3 a b (2 c+d x)+b^2 x (3 c+2 d x)\right)+6 a^2 (b c-a d) \log (a+b x)}{6 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,"(b*x*(6*a^2*d - 3*a*b*(2*c + d*x) + b^2*x*(3*c + 2*d*x)) + 6*a^2*(b*c - a*d)*Log[a + b*x])/(6*b^4)","A",1
207,1,41,45,0.0196283,"\int \frac{x (c+d x)}{a+b x} \, dx","Integrate[(x*(c + d*x))/(a + b*x),x]","\frac{b x (-2 a d+2 b c+b d x)+2 a (a d-b c) \log (a+b x)}{2 b^3}","-\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,"(b*x*(2*b*c - 2*a*d + b*d*x) + 2*a*(-(b*c) + a*d)*Log[a + b*x])/(2*b^3)","A",1
208,1,25,25,0.0077688,"\int \frac{c+d x}{a+b x} \, dx","Integrate[(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
209,1,29,30,0.0192106,"\int \frac{c+d x}{x (a+b x)} \, dx","Integrate[(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
210,1,42,43,0.0235991,"\int \frac{c+d x}{x^2 (a+b x)} \, dx","Integrate[(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
211,1,58,62,0.0492288,"\int \frac{c+d x}{x^3 (a+b x)} \, dx","Integrate[(c + d*x)/(x^3*(a + b*x)),x]","\frac{-\frac{a (a c+2 a d x-2 b c x)}{x^2}+2 b \log (x) (b c-a d)+2 b (a d-b c) \log (a+b x)}{2 a^3}","\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*(a*c - 2*b*c*x + 2*a*d*x))/x^2) + 2*b*(b*c - a*d)*Log[x] + 2*b*(-(b*c) + a*d)*Log[a + b*x])/(2*a^3)","A",1
212,1,81,86,0.0627899,"\int \frac{c+d x}{x^4 (a+b x)} \, dx","Integrate[(c + d*x)/(x^4*(a + b*x)),x]","\frac{\frac{a \left(-\left(a^2 (2 c+3 d x)\right)+3 a b x (c+2 d x)-6 b^2 c x^2\right)}{x^3}+6 b^2 \log (x) (a d-b c)+6 b^2 (b c-a d) \log (a+b x)}{6 a^4}","-\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,"((a*(-6*b^2*c*x^2 + 3*a*b*x*(c + 2*d*x) - a^2*(2*c + 3*d*x)))/x^3 + 6*b^2*(-(b*c) + a*d)*Log[x] + 6*b^2*(b*c - a*d)*Log[a + b*x])/(6*a^4)","A",1
213,1,112,117,0.0825323,"\int \frac{x^3 (c+d x)^2}{a+b x} \, dx","Integrate[(x^3*(c + d*x)^2)/(a + b*x),x]","\frac{-60 a^3 (b c-a d)^2 \log (a+b x)+60 a^2 b x (b c-a d)^2+15 b^4 d x^4 (2 b c-a d)+20 b^3 x^3 (b c-a d)^2-30 a b^2 x^2 (b c-a d)^2+12 b^5 d^2 x^5}{60 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,"(60*a^2*b*(b*c - a*d)^2*x - 30*a*b^2*(b*c - a*d)^2*x^2 + 20*b^3*(b*c - a*d)^2*x^3 + 15*b^4*d*(2*b*c - a*d)*x^4 + 12*b^5*d^2*x^5 - 60*a^3*(b*c - a*d)^2*Log[a + b*x])/(60*b^6)","A",1
214,1,103,94,0.0507221,"\int \frac{x^2 (c+d x)^2}{a+b x} \, dx","Integrate[(x^2*(c + d*x)^2)/(a + b*x),x]","\frac{12 a^2 (b c-a d)^2 \log (a+b x)+b x \left(-12 a^3 d^2+6 a^2 b d (4 c+d x)-4 a b^2 \left(3 c^2+3 c d x+d^2 x^2\right)+b^3 x \left(6 c^2+8 c d x+3 d^2 x^2\right)\right)}{12 b^5}","\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,"(b*x*(-12*a^3*d^2 + 6*a^2*b*d*(4*c + d*x) - 4*a*b^2*(3*c^2 + 3*c*d*x + d^2*x^2) + b^3*x*(6*c^2 + 8*c*d*x + 3*d^2*x^2)) + 12*a^2*(b*c - a*d)^2*Log[a + b*x])/(12*b^5)","A",1
215,1,74,71,0.0332855,"\int \frac{x (c+d x)^2}{a+b x} \, dx","Integrate[(x*(c + d*x)^2)/(a + b*x),x]","\frac{b x \left(6 a^2 d^2-3 a b d (4 c+d x)+2 b^2 \left(3 c^2+3 c d x+d^2 x^2\right)\right)-6 a (b c-a d)^2 \log (a+b x)}{6 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,"(b*x*(6*a^2*d^2 - 3*a*b*d*(4*c + d*x) + 2*b^2*(3*c^2 + 3*c*d*x + d^2*x^2)) - 6*a*(b*c - a*d)^2*Log[a + b*x])/(6*b^4)","A",1
216,1,43,49,0.0175418,"\int \frac{(c+d x)^2}{a+b x} \, dx","Integrate[(c + d*x)^2/(a + b*x),x]","\frac{b d x (-2 a d+4 b c+b d x)+2 (b c-a d)^2 \log (a+b x)}{2 b^3}","\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,"(b*d*x*(4*b*c - 2*a*d + b*d*x) + 2*(b*c - a*d)^2*Log[a + b*x])/(2*b^3)","A",1
217,1,42,42,0.0293799,"\int \frac{(c+d x)^2}{x (a+b x)} \, dx","Integrate[(c + d*x)^2/(x*(a + b*x)),x]","\frac{-(b c-a d)^2 \log (a+b x)+a b d^2 x+b^2 c^2 \log (x)}{a b^2}","-\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,"(a*b*d^2*x + b^2*c^2*Log[x] - (b*c - a*d)^2*Log[a + b*x])/(a*b^2)","A",1
218,1,51,51,0.0345122,"\int \frac{(c+d x)^2}{x^2 (a+b x)} \, dx","Integrate[(c + d*x)^2/(x^2*(a + b*x)),x]","\frac{-a b c^2+b c x \log (x) (2 a d-b c)+x (b c-a d)^2 \log (a+b x)}{a^2 b 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,"(-(a*b*c^2) + b*c*(-(b*c) + 2*a*d)*x*Log[x] + (b*c - a*d)^2*x*Log[a + b*x])/(a^2*b*x)","A",1
219,1,60,67,0.0750511,"\int \frac{(c+d x)^2}{x^3 (a+b x)} \, dx","Integrate[(c + d*x)^2/(x^3*(a + b*x)),x]","-\frac{\frac{a c (a c+4 a d x-2 b c x)}{x^2}-2 \log (x) (b c-a d)^2+2 (b c-a d)^2 \log (a+b x)}{2 a^3}","\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*((a*c*(a*c - 2*b*c*x + 4*a*d*x))/x^2 - 2*(b*c - a*d)^2*Log[x] + 2*(b*c - a*d)^2*Log[a + b*x])/a^3","A",1
220,1,99,90,0.0553143,"\int \frac{(c+d x)^2}{x^4 (a+b x)} \, dx","Integrate[(c + d*x)^2/(x^4*(a + b*x)),x]","\frac{-2 a^3 \left(c^2+3 c d x+3 d^2 x^2\right)+3 a^2 b c x (c+4 d x)-6 a b^2 c^2 x^2-6 b x^3 \log (x) (b c-a d)^2+6 b x^3 (b c-a d)^2 \log (a+b x)}{6 a^4 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,"(-6*a*b^2*c^2*x^2 + 3*a^2*b*c*x*(c + 4*d*x) - 2*a^3*(c^2 + 3*c*d*x + 3*d^2*x^2) - 6*b*(b*c - a*d)^2*x^3*Log[x] + 6*b*(b*c - a*d)^2*x^3*Log[a + b*x])/(6*a^4*x^3)","A",1
221,1,127,114,0.1223538,"\int \frac{(c+d x)^2}{x^5 (a+b x)} \, dx","Integrate[(c + d*x)^2/(x^5*(a + b*x)),x]","\frac{\frac{a \left(-\left(a^3 \left(3 c^2+8 c d x+6 d^2 x^2\right)\right)+4 a^2 b x \left(c^2+3 c d x+3 d^2 x^2\right)-6 a b^2 c x^2 (c+4 d x)+12 b^3 c^2 x^3\right)}{x^4}+12 b^2 \log (x) (b c-a d)^2-12 b^2 (b c-a d)^2 \log (a+b x)}{12 a^5}","\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,"((a*(12*b^3*c^2*x^3 - 6*a*b^2*c*x^2*(c + 4*d*x) + 4*a^2*b*x*(c^2 + 3*c*d*x + 3*d^2*x^2) - a^3*(3*c^2 + 8*c*d*x + 6*d^2*x^2)))/x^4 + 12*b^2*(b*c - a*d)^2*Log[x] - 12*b^2*(b*c - a*d)^2*Log[a + b*x])/(12*a^5)","A",1
222,1,145,152,0.1137052,"\int \frac{x^3 (c+d x)^3}{a+b x} \, dx","Integrate[(x^3*(c + d*x)^3)/(a + b*x),x]","\frac{60 a^3 (a d-b c)^3 \log (a+b x)+15 b^4 d x^4 \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)-60 a^2 b x (a d-b c)^3+12 b^5 d^2 x^5 (3 b c-a d)+20 b^3 x^3 (b c-a d)^3+30 a b^2 x^2 (a d-b c)^3+10 b^6 d^3 x^6}{60 b^7}","-\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,"(-60*a^2*b*(-(b*c) + a*d)^3*x + 30*a*b^2*(-(b*c) + a*d)^3*x^2 + 20*b^3*(b*c - a*d)^3*x^3 + 15*b^4*d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x^4 + 12*b^5*d^2*(3*b*c - a*d)*x^5 + 10*b^6*d^3*x^6 + 60*a^3*(-(b*c) + a*d)^3*Log[a + b*x])/(60*b^7)","A",1
223,1,124,129,0.0864516,"\int \frac{x^2 (c+d x)^3}{a+b x} \, dx","Integrate[(x^2*(c + d*x)^3)/(a + b*x),x]","\frac{20 b^3 d x^3 \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)+60 a^2 (b c-a d)^3 \log (a+b x)+15 b^4 d^2 x^4 (3 b c-a d)+30 b^2 x^2 (b c-a d)^3+60 a b x (a d-b c)^3+12 b^5 d^3 x^5}{60 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,"(60*a*b*(-(b*c) + a*d)^3*x + 30*b^2*(b*c - a*d)^3*x^2 + 20*b^3*d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x^3 + 15*b^4*d^2*(3*b*c - a*d)*x^4 + 12*b^5*d^3*x^5 + 60*a^2*(b*c - a*d)^3*Log[a + b*x])/(60*b^6)","A",1
224,1,115,106,0.0625854,"\int \frac{x (c+d x)^3}{a+b x} \, dx","Integrate[(x*(c + d*x)^3)/(a + b*x),x]","\frac{b x \left(-12 a^3 d^3+6 a^2 b d^2 (6 c+d x)-2 a b^2 d \left(18 c^2+9 c d x+2 d^2 x^2\right)+3 b^3 \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)\right)+12 a (a d-b c)^3 \log (a+b x)}{12 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,"(b*x*(-12*a^3*d^3 + 6*a^2*b*d^2*(6*c + d*x) - 2*a*b^2*d*(18*c^2 + 9*c*d*x + 2*d^2*x^2) + 3*b^3*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)) + 12*a*(-(b*c) + a*d)^3*Log[a + b*x])/(12*b^5)","A",1
225,1,74,73,0.0353348,"\int \frac{(c+d x)^3}{a+b x} \, dx","Integrate[(c + d*x)^3/(a + b*x),x]","\frac{b d x \left(6 a^2 d^2-3 a b d (6 c+d x)+b^2 \left(18 c^2+9 c d x+2 d^2 x^2\right)\right)+6 (b c-a d)^3 \log (a+b x)}{6 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,"(b*d*x*(6*a^2*d^2 - 3*a*b*d*(6*c + d*x) + b^2*(18*c^2 + 9*c*d*x + 2*d^2*x^2)) + 6*(b*c - a*d)^3*Log[a + b*x])/(6*b^4)","A",1
226,1,59,64,0.0361384,"\int \frac{(c+d x)^3}{x (a+b x)} \, dx","Integrate[(c + d*x)^3/(x*(a + b*x)),x]","\frac{a b d^2 x (-2 a d+6 b c+b d x)-2 (b c-a d)^3 \log (a+b x)+2 b^3 c^3 \log (x)}{2 a b^3}","-\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,"(a*b*d^2*x*(6*b*c - 2*a*d + b*d*x) + 2*b^3*c^3*Log[x] - 2*(b*c - a*d)^3*Log[a + b*x])/(2*a*b^3)","A",1
227,1,66,61,0.0361995,"\int \frac{(c+d x)^3}{x^2 (a+b x)} \, dx","Integrate[(c + d*x)^3/(x^2*(a + b*x)),x]","\frac{b^2 c^2 x \log (x) (3 a d-b c)+a b \left(a d^3 x^2-b c^3\right)+x (b c-a d)^3 \log (a+b x)}{a^2 b^2 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,"(a*b*(-(b*c^3) + a*d^3*x^2) + b^2*c^2*(-(b*c) + 3*a*d)*x*Log[x] + (b*c - a*d)^3*x*Log[a + b*x])/(a^2*b^2*x)","A",1
228,1,78,85,0.1118778,"\int \frac{(c+d x)^3}{x^3 (a+b x)} \, dx","Integrate[(c + d*x)^3/(x^3*(a + b*x)),x]","-\frac{-2 c \log (x) \left(3 a^2 d^2-3 a b c d+b^2 c^2\right)+\frac{a c^2 (a (c+6 d x)-2 b c x)}{x^2}+\frac{2 (b c-a d)^3 \log (a+b x)}{b}}{2 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*((a*c^2*(-2*b*c*x + a*(c + 6*d*x)))/x^2 - 2*c*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2)*Log[x] + (2*(b*c - a*d)^3*Log[a + b*x])/b)/a^3","A",1
229,1,93,103,0.0822221,"\int \frac{(c+d x)^3}{x^4 (a+b x)} \, dx","Integrate[(c + d*x)^3/(x^4*(a + b*x)),x]","-\frac{\frac{a c \left(a^2 \left(2 c^2+9 c d x+18 d^2 x^2\right)-3 a b c x (c+6 d x)+6 b^2 c^2 x^2\right)}{x^3}+6 \log (x) (b c-a d)^3-6 (b c-a d)^3 \log (a+b x)}{6 a^4}","-\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*((a*c*(6*b^2*c^2*x^2 - 3*a*b*c*x*(c + 6*d*x) + a^2*(2*c^2 + 9*c*d*x + 18*d^2*x^2)))/x^3 + 6*(b*c - a*d)^3*Log[x] - 6*(b*c - a*d)^3*Log[a + b*x])/a^4","A",1
230,1,137,124,0.1372178,"\int \frac{(c+d x)^3}{x^5 (a+b x)} \, dx","Integrate[(c + d*x)^3/(x^5*(a + b*x)),x]","\frac{\frac{a \left(-3 a^3 \left(c^3+4 c^2 d x+6 c d^2 x^2+4 d^3 x^3\right)+2 a^2 b c x \left(2 c^2+9 c d x+18 d^2 x^2\right)-6 a b^2 c^2 x^2 (c+6 d x)+12 b^3 c^3 x^3\right)}{x^4}+12 b \log (x) (b c-a d)^3-12 b (b c-a d)^3 \log (a+b x)}{12 a^5}","\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,"((a*(12*b^3*c^3*x^3 - 6*a*b^2*c^2*x^2*(c + 6*d*x) + 2*a^2*b*c*x*(2*c^2 + 9*c*d*x + 18*d^2*x^2) - 3*a^3*(c^3 + 4*c^2*d*x + 6*c*d^2*x^2 + 4*d^3*x^3)))/x^4 + 12*b*(b*c - a*d)^3*Log[x] - 12*b*(b*c - a*d)^3*Log[a + b*x])/(12*a^5)","A",1
231,1,188,150,0.0994691,"\int \frac{(c+d x)^3}{x^6 (a+b x)} \, dx","Integrate[(c + d*x)^3/(x^6*(a + b*x)),x]","\frac{-3 a^5 \left(4 c^3+15 c^2 d x+20 c d^2 x^2+10 d^3 x^3\right)+15 a^4 b x \left(c^3+4 c^2 d x+6 c d^2 x^2+4 d^3 x^3\right)-10 a^3 b^2 c x^2 \left(2 c^2+9 c d x+18 d^2 x^2\right)+30 a^2 b^3 c^2 x^3 (c+6 d x)-60 a b^4 c^3 x^4-60 b^2 x^5 \log (x) (b c-a d)^3+60 b^2 x^5 (b c-a d)^3 \log (a+b x)}{60 a^6 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,"(-60*a*b^4*c^3*x^4 + 30*a^2*b^3*c^2*x^3*(c + 6*d*x) - 10*a^3*b^2*c*x^2*(2*c^2 + 9*c*d*x + 18*d^2*x^2) + 15*a^4*b*x*(c^3 + 4*c^2*d*x + 6*c*d^2*x^2 + 4*d^3*x^3) - 3*a^5*(4*c^3 + 15*c^2*d*x + 20*c*d^2*x^2 + 10*d^3*x^3) - 60*b^2*(b*c - a*d)^3*x^5*Log[x] + 60*b^2*(b*c - a*d)^3*x^5*Log[a + b*x])/(60*a^6*x^5)","A",1
232,1,133,145,0.0806277,"\int \frac{x^5}{(a+b x) (c+d x)} \, dx","Integrate[x^5/((a + b*x)*(c + d*x)),x]","\frac{-12 a^5 d^5 \log (a+b x)+b d x \left(12 a^4 d^4-6 a^3 b d^4 x+4 a^2 b^2 d^4 x^2-3 a b^3 d^4 x^3+b^4 c \left(-12 c^3+6 c^2 d x-4 c d^2 x^2+3 d^3 x^3\right)\right)+12 b^5 c^5 \log (c+d x)}{12 b^5 d^5 (b c-a d)}","-\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,"(b*d*x*(12*a^4*d^4 - 6*a^3*b*d^4*x + 4*a^2*b^2*d^4*x^2 - 3*a*b^3*d^4*x^3 + b^4*c*(-12*c^3 + 6*c^2*d*x - 4*c*d^2*x^2 + 3*d^3*x^3)) - 12*a^5*d^5*Log[a + b*x] + 12*b^5*c^5*Log[c + d*x])/(12*b^5*d^5*(b*c - a*d))","A",1
233,1,105,109,0.0678536,"\int \frac{x^4}{(a+b x) (c+d x)} \, dx","Integrate[x^4/((a + b*x)*(c + d*x)),x]","\frac{6 a^4 d^4 \log (a+b x)+b d x (b c-a d) \left(6 a^2 d^2-3 a b d (d x-2 c)+b^2 \left(6 c^2-3 c d x+2 d^2 x^2\right)\right)-6 b^4 c^4 \log (c+d x)}{6 b^4 d^4 (b c-a d)}","\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,"(b*d*(b*c - a*d)*x*(6*a^2*d^2 - 3*a*b*d*(-2*c + d*x) + b^2*(6*c^2 - 3*c*d*x + 2*d^2*x^2)) + 6*a^4*d^4*Log[a + b*x] - 6*b^4*c^4*Log[c + d*x])/(6*b^4*d^4*(b*c - a*d))","A",1
234,1,74,77,0.0467181,"\int \frac{x^3}{(a+b x) (c+d x)} \, dx","Integrate[x^3/((a + b*x)*(c + d*x)),x]","\frac{-2 a^3 d^3 \log (a+b x)+b d x (b c-a d) (-2 a d-2 b c+b d x)+2 b^3 c^3 \log (c+d x)}{2 b^3 d^3 (b c-a d)}","-\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,"(b*d*(b*c - a*d)*x*(-2*b*c - 2*a*d + b*d*x) - 2*a^3*d^3*Log[a + b*x] + 2*b^3*c^3*Log[c + d*x])/(2*b^3*d^3*(b*c - a*d))","A",1
235,1,56,56,0.0352459,"\int \frac{x^2}{(a+b x) (c+d x)} \, dx","Integrate[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 (b c-a d)}+\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
236,1,38,44,0.0175521,"\int \frac{x}{(a+b x) (c+d x)} \, dx","Integrate[x/((a + b*x)*(c + d*x)),x]","-\frac{a d \log (a+b x)-b c \log (c+d x)}{b^2 c d-a b d^2}","\frac{c \log (c+d x)}{d (b c-a d)}-\frac{a \log (a+b x)}{b (b c-a d)}",1,"-((a*d*Log[a + b*x] - b*c*Log[c + d*x])/(b^2*c*d - a*b*d^2))","A",1
237,1,26,36,0.0138121,"\int \frac{1}{(a+b x) (c+d x)} \, dx","Integrate[1/((a + b*x)*(c + d*x)),x]","\frac{\log (a+b x)-\log (c+d x)}{b c-a d}","\frac{\log (a+b x)}{b c-a d}-\frac{\log (c+d x)}{b c-a d}",1,"(Log[a + b*x] - Log[c + d*x])/(b*c - a*d)","A",1
238,1,48,53,0.0315993,"\int \frac{1}{x (a+b x) (c+d x)} \, dx","Integrate[1/(x*(a + b*x)*(c + d*x)),x]","\frac{-b c \log (a+b x)+a d \log (c+d x)-a d \log (x)+b c \log (x)}{a b c^2-a^2 c d}","-\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,"(b*c*Log[x] - a*d*Log[x] - b*c*Log[a + b*x] + a*d*Log[c + d*x])/(a*b*c^2 - a^2*c*d)","A",1
239,1,78,76,0.0396226,"\int \frac{1}{x^2 (a+b x) (c+d x)} \, dx","Integrate[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
240,1,106,107,0.0632086,"\int \frac{1}{x^3 (a+b x) (c+d x)} \, dx","Integrate[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 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}","-\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,"-1/2*1/(a*c*x^2) + (b*c + a*d)/(a^2*c^2*x) + ((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
241,1,139,144,0.0785064,"\int \frac{1}{x^4 (a+b x) (c+d x)} \, dx","Integrate[1/(x^4*(a + b*x)*(c + d*x)),x]","\frac{6 x^3 \log (x) \left(b^4 c^4-a^4 d^4\right)+a \left(a^3 c d \left(-2 c^2+3 c d x-6 d^2 x^2\right)+6 a^3 d^4 x^3 \log (c+d x)+2 a^2 b c^4-3 a b^2 c^4 x+6 b^3 c^4 x^2\right)-6 b^4 c^4 x^3 \log (a+b x)}{6 a^4 c^4 x^3 (a d-b c)}","\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,"(6*(b^4*c^4 - a^4*d^4)*x^3*Log[x] - 6*b^4*c^4*x^3*Log[a + b*x] + a*(2*a^2*b*c^4 - 3*a*b^2*c^4*x + 6*b^3*c^4*x^2 + a^3*c*d*(-2*c^2 + 3*c*d*x - 6*d^2*x^2) + 6*a^3*d^4*x^3*Log[c + d*x]))/(6*a^4*c^4*(-(b*c) + a*d)*x^3)","A",1
242,1,147,147,0.1887165,"\int \frac{x^5}{(a+b x) (c+d x)^2} \, dx","Integrate[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{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) (a d-b c)}+\frac{\left(5 a c^4 d-4 b c^5\right) \log (c+d x)}{d^5 (b c-a d)^2}+\frac{x^3}{3 b d^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,"((3*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*x)/(b^3*d^4) - ((2*b*c + a*d)*x^2)/(2*b^2*d^3) + x^3/(3*b*d^2) + c^5/(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
243,1,107,110,0.2292617,"\int \frac{x^4}{(a+b x) (c+d x)^2} \, dx","Integrate[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{-\frac{2 a d^2 x}{b^2}+\frac{2 c^4}{(c+d x) (b c-a d)}+\frac{2 c^3 (3 b c-4 a d) \log (c+d x)}{(b c-a d)^2}+\frac{d x (d x-4 c)}{b}}{2 d^4}","\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,"(a^4*Log[a + b*x])/(b^3*(b*c - a*d)^2) + ((-2*a*d^2*x)/b^2 + (d*x*(-4*c + d*x))/b + (2*c^4)/((b*c - a*d)*(c + d*x)) + (2*c^3*(3*b*c - 4*a*d)*Log[c + d*x])/(b*c - a*d)^2)/(2*d^4)","A",1
244,1,87,91,0.1418067,"\int \frac{x^3}{(a+b x) (c+d x)^2} \, dx","Integrate[x^3/((a + b*x)*(c + d*x)^2),x]","\frac{\frac{c^3}{(c+d x) (a d-b c)}-\frac{c^2 (2 b c-3 a d) \log (c+d x)}{(b c-a d)^2}+\frac{d x}{b}}{d^3}-\frac{a^3 \log (a+b x)}{b^2 (b c-a d)^2}","-\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,"-((a^3*Log[a + b*x])/(b^2*(b*c - a*d)^2)) + ((d*x)/b + c^3/((-(b*c) + a*d)*(c + d*x)) - (c^2*(2*b*c - 3*a*d)*Log[c + d*x])/(b*c - a*d)^2)/d^3","A",1
245,1,77,77,0.0501552,"\int \frac{x^2}{(a+b x) (c+d x)^2} \, dx","Integrate[x^2/((a + b*x)*(c + d*x)^2),x]","\frac{a^2 d^2 (c+d x) \log (a+b x)+b c ((c+d x) (b c-2 a d) \log (c+d x)+c (b c-a d))}{b d^2 (c+d x) (b c-a d)^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,"(a^2*d^2*(c + d*x)*Log[a + b*x] + b*c*(c*(b*c - a*d) + (b*c - 2*a*d)*(c + d*x)*Log[c + d*x]))/(b*d^2*(b*c - a*d)^2*(c + d*x))","A",1
246,1,60,61,0.0384024,"\int \frac{x}{(a+b x) (c+d x)^2} \, dx","Integrate[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
247,1,53,56,0.0345202,"\int \frac{1}{(a+b x) (c+d x)^2} \, dx","Integrate[1/((a + b*x)*(c + d*x)^2),x]","\frac{b (c+d x) \log (a+b x)-a d-b (c+d x) \log (c+d x)+b c}{(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,"(b*c - a*d + b*(c + d*x)*Log[a + b*x] - b*(c + d*x)*Log[c + d*x])/((b*c - a*d)^2*(c + d*x))","A",1
248,1,83,87,0.1344066,"\int \frac{1}{x (a+b x) (c+d x)^2} \, dx","Integrate[1/(x*(a + b*x)*(c + d*x)^2),x]","\frac{\frac{a d ((c+d x) (2 b c-a d) \log (c+d x)+c (a d-b c))-b^2 c^2 (c+d x) \log (a+b x)}{(c+d x) (b c-a d)^2}+\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,"(Log[x] + (-(b^2*c^2*(c + d*x)*Log[a + b*x]) + a*d*(c*(-(b*c) + a*d) + (2*b*c - a*d)*(c + d*x)*Log[c + d*x]))/((b*c - a*d)^2*(c + d*x)))/(a*c^2)","A",1
249,1,111,110,0.1294218,"\int \frac{1}{x^2 (a+b x) (c+d x)^2} \, dx","Integrate[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{d^2}{c^2 (c+d x) (b c-a d)}-\frac{1}{a c^2 x}","\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,"-(1/(a*c^2*x)) + d^2/(c^2*(b*c - a*d)*(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
250,1,143,144,0.5293799,"\int \frac{1}{x^3 (a+b x) (c+d x)^2} \, dx","Integrate[1/(x^3*(a + b*x)*(c + d*x)^2),x]","-\frac{b^4 \log (a+b x)}{a^3 (b c-a d)^2}+\frac{c \left(\frac{2 b c}{a^2 x}+\frac{2 d^3}{(c+d x) (a d-b c)}-\frac{c-4 d x}{a x^2}\right)+\frac{2 d^3 (4 b c-3 a d) \log (c+d x)}{(b c-a d)^2}}{2 c^4}+\frac{\log (x) \left(3 a^2 d^2+2 a b c d+b^2 c^2\right)}{a^3 c^4}","-\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,"((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) + (c*((2*b*c)/(a^2*x) - (c - 4*d*x)/(a*x^2) + (2*d^3)/((-(b*c) + a*d)*(c + d*x))) + (2*d^3*(4*b*c - 3*a*d)*Log[c + d*x])/(b*c - a*d)^2)/(2*c^4)","A",1
251,1,161,161,0.2510428,"\int \frac{x^5}{(a+b x) (c+d x)^3} \, dx","Integrate[x^5/((a + b*x)*(c + d*x)^3),x]","\frac{1}{2} \left(-\frac{2 a^5 \log (a+b x)}{b^3 (b c-a d)^3}-\frac{2 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 (a d-b c)^3}-\frac{2 x (a d+3 b c)}{b^2 d^4}+\frac{c^5}{d^5 (c+d x)^2 (a d-b c)}+\frac{2 c^4 (4 b c-5 a d)}{d^5 (c+d x) (b c-a d)^2}+\frac{x^2}{b d^3}\right)","-\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,"((-2*(3*b*c + a*d)*x)/(b^2*d^4) + x^2/(b*d^3) + c^5/(d^5*(-(b*c) + a*d)*(c + d*x)^2) + (2*c^4*(4*b*c - 5*a*d))/(d^5*(b*c - a*d)^2*(c + d*x)) - (2*a^5*Log[a + b*x])/(b^3*(b*c - a*d)^3) - (2*c^3*(6*b^2*c^2 - 15*a*b*c*d + 10*a^2*d^2)*Log[c + d*x])/(d^5*(-(b*c) + a*d)^3))/2","A",1
252,1,138,140,0.1856166,"\int \frac{x^4}{(a+b x) (c+d x)^3} \, dx","Integrate[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{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 (a d-b c)^3}-\frac{c^4}{2 d^4 (c+d x)^2 (a d-b c)}+\frac{c^3 (4 a d-3 b c)}{d^4 (c+d x) (b c-a d)^2}+\frac{x}{b d^3}","\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,"x/(b*d^3) - c^4/(2*d^4*(-(b*c) + a*d)*(c + d*x)^2) + (c^3*(-3*b*c + 4*a*d))/(d^4*(b*c - a*d)^2*(c + d*x)) + (a^4*Log[a + b*x])/(b^2*(b*c - a*d)^3) + (c^2*(3*b^2*c^2 - 8*a*b*c*d + 6*a^2*d^2)*Log[c + d*x])/(d^4*(-(b*c) + a*d)^3)","A",1
253,1,134,128,0.0700449,"\int \frac{x^3}{(a+b x) (c+d x)^3} \, dx","Integrate[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 (b c-a d)^3}+\frac{c^3}{2 d^3 (c+d x)^2 (a d-b c)}+\frac{2 b c^3-3 a c^2 d}{d^3 (c+d x) (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^3/(2*d^3*(-(b*c) + a*d)*(c + d*x)^2) + (2*b*c^3 - 3*a*c^2*d)/(d^3*(-(b*c) + a*d)^2*(c + d*x)) - (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
254,1,99,100,0.0851768,"\int \frac{x^2}{(a+b x) (c+d x)^3} \, dx","Integrate[x^2/((a + b*x)*(c + d*x)^3),x]","\frac{-2 a^2 d^2 (c+d x)^2 \log (a+b x)+2 a^2 d^2 (c+d x)^2 \log (c+d x)+c (b c-a d) (b c (c+2 d x)-a d (3 c+4 d x))}{2 d^2 (c+d x)^2 (a d-b c)^3}","\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,"(c*(b*c - a*d)*(b*c*(c + 2*d*x) - a*d*(3*c + 4*d*x)) - 2*a^2*d^2*(c + d*x)^2*Log[a + b*x] + 2*a^2*d^2*(c + d*x)^2*Log[c + d*x])/(2*d^2*(-(b*c) + a*d)^3*(c + d*x)^2)","A",1
255,1,85,85,0.0593344,"\int \frac{x}{(a+b x) (c+d x)^3} \, dx","Integrate[x/((a + b*x)*(c + d*x)^3),x]","-\frac{a}{(c+d x) (b c-a d)^2}+\frac{c}{2 d (c+d x)^2 (a d-b c)}-\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,"c/(2*d*(-(b*c) + a*d)*(c + d*x)^2) - a/((b*c - a*d)^2*(c + d*x)) - (a*b*Log[a + b*x])/(b*c - a*d)^3 + (a*b*Log[c + d*x])/(b*c - a*d)^3","A",1
256,1,67,82,0.0705118,"\int \frac{1}{(a+b x) (c+d x)^3} \, dx","Integrate[1/((a + b*x)*(c + d*x)^3),x]","\frac{2 b^2 \log (a+b x)+\frac{(b c-a d) (-a d+3 b c+2 b d x)}{(c+d x)^2}-2 b^2 \log (c+d x)}{2 (b c-a d)^3}","\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,"(((b*c - a*d)*(3*b*c - a*d + 2*b*d*x))/(c + d*x)^2 + 2*b^2*Log[a + b*x] - 2*b^2*Log[c + d*x])/(2*(b*c - a*d)^3)","A",1
257,1,116,134,0.3010396,"\int \frac{1}{x (a+b x) (c+d x)^3} \, dx","Integrate[1/(x*(a + b*x)*(c + d*x)^3),x]","\frac{\frac{d \left(\frac{c (b c-a d) (b c (5 c+4 d x)-a d (3 c+2 d x))}{(c+d x)^2}-2 \left(a^2 d^2-3 a b c d+3 b^2 c^2\right) \log (c+d x)\right)}{c^3}+\frac{2 b^3 \log (a+b x)}{a}}{2 (a d-b c)^3}+\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,"Log[x]/(a*c^3) + ((2*b^3*Log[a + b*x])/a + (d*((c*(b*c - a*d)*(-(a*d*(3*c + 2*d*x)) + b*c*(5*c + 4*d*x)))/(c + d*x)^2 - 2*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*Log[c + d*x]))/c^3)/(2*(-(b*c) + a*d)^3)","A",1
258,1,163,160,0.1871475,"\int \frac{1}{x^2 (a+b x) (c+d x)^3} \, dx","Integrate[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{\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}","\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,"-(1/(a*c^3*x)) + d^2/(2*c^2*(b*c - a*d)*(c + d*x)^2) + (d^2*(3*b*c - 2*a*d))/(c^3*(b*c - a*d)^2*(c + d*x)) + ((-(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
259,1,183,165,0.131019,"\int \frac{x^4 (c+d x)^2}{(a+b x)^2} \, dx","Integrate[(x^4*(c + d*x)^2)/(a + b*x)^2,x]","\frac{-\frac{30 a^4 (b c-a d)^2}{a+b x}-30 a b^2 x^2 \left(2 a^2 d^2-3 a b c d+b^2 c^2\right)+30 a^2 b x \left(5 a^2 d^2-8 a b c d+3 b^2 c^2\right)+10 b^3 x^3 \left(3 a^2 d^2-4 a b c d+b^2 c^2\right)-60 a^3 \left(3 a^2 d^2-5 a b c d+2 b^2 c^2\right) \log (a+b x)+15 b^4 d x^4 (b c-a d)+6 b^5 d^2 x^5}{30 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^2*b*(3*b^2*c^2 - 8*a*b*c*d + 5*a^2*d^2)*x - 30*a*b^2*(b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^2 + 10*b^3*(b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*x^3 + 15*b^4*d*(b*c - a*d)*x^4 + 6*b^5*d^2*x^5 - (30*a^4*(b*c - a*d)^2)/(a + b*x) - 60*a^3*(2*b^2*c^2 - 5*a*b*c*d + 3*a^2*d^2)*Log[a + b*x])/(30*b^7)","A",1
260,1,149,136,0.1021652,"\int \frac{x^3 (c+d x)^2}{(a+b x)^2} \, dx","Integrate[(x^3*(c + d*x)^2)/(a + b*x)^2,x]","\frac{\frac{12 a^3 (b c-a d)^2}{a+b x}+6 b^2 x^2 \left(3 a^2 d^2-4 a b c d+b^2 c^2\right)-24 a b x \left(2 a^2 d^2-3 a b c d+b^2 c^2\right)+12 a^2 \left(5 a^2 d^2-8 a b c d+3 b^2 c^2\right) \log (a+b x)+8 b^3 d x^3 (b c-a d)+3 b^4 d^2 x^4}{12 b^6}","\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,"(-24*a*b*(b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x + 6*b^2*(b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*x^2 + 8*b^3*d*(b*c - a*d)*x^3 + 3*b^4*d^2*x^4 + (12*a^3*(b*c - a*d)^2)/(a + b*x) + 12*a^2*(3*b^2*c^2 - 8*a*b*c*d + 5*a^2*d^2)*Log[a + b*x])/(12*b^6)","A",1
261,1,114,104,0.0976073,"\int \frac{x^2 (c+d x)^2}{(a+b x)^2} \, dx","Integrate[(x^2*(c + d*x)^2)/(a + b*x)^2,x]","\frac{3 b x \left(3 a^2 d^2-4 a b c d+b^2 c^2\right)-6 a \left(2 a^2 d^2-3 a b c d+b^2 c^2\right) \log (a+b x)-\frac{3 a^2 (b c-a d)^2}{a+b x}+3 b^2 d x^2 (b c-a d)+b^3 d^2 x^3}{3 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*b*(b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*x + 3*b^2*d*(b*c - a*d)*x^2 + b^3*d^2*x^3 - (3*a^2*(b*c - a*d)^2)/(a + b*x) - 6*a*(b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*Log[a + b*x])/(3*b^5)","A",1
262,1,81,77,0.0562118,"\int \frac{x (c+d x)^2}{(a+b x)^2} \, dx","Integrate[(x*(c + d*x)^2)/(a + b*x)^2,x]","\frac{2 \left(3 a^2 d^2-4 a b c d+b^2 c^2\right) \log (a+b x)+\frac{2 a (b c-a d)^2}{a+b x}+4 b d x (b c-a d)+b^2 d^2 x^2}{2 b^4}","\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,"(4*b*d*(b*c - a*d)*x + b^2*d^2*x^2 + (2*a*(b*c - a*d)^2)/(a + b*x) + 2*(b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*Log[a + b*x])/(2*b^4)","A",1
263,1,47,51,0.0562588,"\int \frac{(c+d x)^2}{(a+b x)^2} \, dx","Integrate[(c + d*x)^2/(a + b*x)^2,x]","\frac{-\frac{(b c-a d)^2}{a+b x}+2 d (b c-a d) \log (a+b x)+b d^2 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*d^2*x - (b*c - a*d)^2/(a + b*x) + 2*d*(b*c - a*d)*Log[a + b*x])/b^3","A",1
264,1,60,58,0.0616338,"\int \frac{(c+d x)^2}{x (a+b x)^2} \, dx","Integrate[(c + d*x)^2/(x*(a + b*x)^2),x]","\frac{\frac{(a d-b c) ((a+b x) (a d+b c) \log (a+b x)+a (a d-b c))}{b^2 (a+b x)}+c^2 \log (x)}{a^2}","-\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,"(c^2*Log[x] + ((-(b*c) + a*d)*(a*(-(b*c) + a*d) + (b*c + a*d)*(a + b*x)*Log[a + b*x]))/(b^2*(a + b*x)))/a^2","A",1
265,1,67,73,0.0940474,"\int \frac{(c+d x)^2}{x^2 (a+b x)^2} \, dx","Integrate[(c + d*x)^2/(x^2*(a + b*x)^2),x]","\frac{-\frac{a (b c-a d)^2}{b (a+b x)}+2 c \log (x) (a d-b c)+2 c (b c-a d) \log (a+b x)-\frac{a c^2}{x}}{a^3}","-\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*c^2)/x) - (a*(b*c - a*d)^2)/(b*(a + b*x)) + 2*c*(-(b*c) + a*d)*Log[x] + 2*c*(b*c - a*d)*Log[a + b*x])/a^3","A",1
266,1,109,103,0.1293347,"\int \frac{(c+d x)^2}{x^3 (a+b x)^2} \, dx","Integrate[(c + d*x)^2/(x^3*(a + b*x)^2),x]","-\frac{-2 \log (x) \left(a^2 d^2-4 a b c d+3 b^2 c^2\right)+2 \left(a^2 d^2-4 a b c d+3 b^2 c^2\right) \log (a+b x)+\frac{a^2 c^2}{x^2}+\frac{4 a c (a d-b c)}{x}-\frac{2 a (b c-a d)^2}{a+b x}}{2 a^4}","\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,"-1/2*((a^2*c^2)/x^2 + (4*a*c*(-(b*c) + a*d))/x - (2*a*(b*c - a*d)^2)/(a + b*x) - 2*(3*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*Log[x] + 2*(3*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*Log[a + b*x])/a^4","A",1
267,1,142,132,0.1711438,"\int \frac{(c+d x)^2}{x^4 (a+b x)^2} \, dx","Integrate[(c + d*x)^2/(x^4*(a + b*x)^2),x]","-\frac{\frac{a^3 c^2}{x^3}+\frac{3 a \left(a^2 d^2-4 a b c d+3 b^2 c^2\right)}{x}+6 b \log (x) \left(a^2 d^2-3 a b c d+2 b^2 c^2\right)-6 b \left(a^2 d^2-3 a b c d+2 b^2 c^2\right) \log (a+b x)+\frac{3 a^2 c (a d-b c)}{x^2}+\frac{3 a b (b c-a d)^2}{a+b x}}{3 a^5}","-\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,"-1/3*((a^3*c^2)/x^3 + (3*a^2*c*(-(b*c) + a*d))/x^2 + (3*a*(3*b^2*c^2 - 4*a*b*c*d + a^2*d^2))/x + (3*a*b*(b*c - a*d)^2)/(a + b*x) + 6*b*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*Log[x] - 6*b*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*Log[a + b*x])/a^5","A",1
268,1,182,167,0.1721761,"\int \frac{(c+d x)^2}{x^5 (a+b x)^2} \, dx","Integrate[(c + d*x)^2/(x^5*(a + b*x)^2),x]","\frac{-\frac{3 a^4 c^2}{x^4}-\frac{8 a^3 c (a d-b c)}{x^3}-\frac{6 a^2 \left(a^2 d^2-4 a b c d+3 b^2 c^2\right)}{x^2}+\frac{24 a b \left(a^2 d^2-3 a b c d+2 b^2 c^2\right)}{x}+12 b^2 \log (x) \left(3 a^2 d^2-8 a b c d+5 b^2 c^2\right)-12 b^2 \left(3 a^2 d^2-8 a b c d+5 b^2 c^2\right) \log (a+b x)+\frac{12 a b^2 (b c-a d)^2}{a+b x}}{12 a^6}","\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)/x^4 - (8*a^3*c*(-(b*c) + a*d))/x^3 - (6*a^2*(3*b^2*c^2 - 4*a*b*c*d + a^2*d^2))/x^2 + (24*a*b*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2))/x + (12*a*b^2*(b*c - a*d)^2)/(a + b*x) + 12*b^2*(5*b^2*c^2 - 8*a*b*c*d + 3*a^2*d^2)*Log[x] - 12*b^2*(5*b^2*c^2 - 8*a*b*c*d + 3*a^2*d^2)*Log[a + b*x])/(12*a^6)","A",1
269,1,190,200,0.0950593,"\int \frac{x^4 (c+d x)^3}{(a+b x)^2} \, dx","Integrate[(x^4*(c + d*x)^3)/(a + b*x)^2,x]","\frac{\frac{60 a^4 (a d-b c)^3}{a+b x}+60 a^3 (b c-a d)^2 (7 a d-4 b c) \log (a+b x)-180 a^2 b x (b c-a d)^2 (2 a d-b c)+12 b^5 d^2 x^5 (3 b c-2 a d)+45 b^4 d x^4 (b c-a d)^2+20 b^3 x^3 (b c-4 a d) (b c-a d)^2+30 a b^2 x^2 (b c-a d)^2 (5 a d-2 b c)+10 b^6 d^3 x^6}{60 b^8}","-\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,"(-180*a^2*b*(b*c - a*d)^2*(-(b*c) + 2*a*d)*x + 30*a*b^2*(b*c - a*d)^2*(-2*b*c + 5*a*d)*x^2 + 20*b^3*(b*c - 4*a*d)*(b*c - a*d)^2*x^3 + 45*b^4*d*(b*c - a*d)^2*x^4 + 12*b^5*d^2*(3*b*c - 2*a*d)*x^5 + 10*b^6*d^3*x^6 + (60*a^4*(-(b*c) + a*d)^3)/(a + b*x) + 60*a^3*(b*c - a*d)^2*(-4*b*c + 7*a*d)*Log[a + b*x])/(60*b^8)","A",1
270,1,160,164,0.0729765,"\int \frac{x^3 (c+d x)^3}{(a+b x)^2} \, dx","Integrate[(x^3*(c + d*x)^3)/(a + b*x)^2,x]","\frac{-\frac{20 a^3 (a d-b c)^3}{a+b x}-60 a^2 (b c-a d)^2 (2 a d-b c) \log (a+b x)+5 b^4 d^2 x^4 (3 b c-2 a d)+20 b^3 d x^3 (b c-a d)^2+10 b^2 x^2 (b c-4 a d) (b c-a d)^2+20 a b x (b c-a d)^2 (5 a d-2 b c)+4 b^5 d^3 x^5}{20 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*b*(b*c - a*d)^2*(-2*b*c + 5*a*d)*x + 10*b^2*(b*c - 4*a*d)*(b*c - a*d)^2*x^2 + 20*b^3*d*(b*c - a*d)^2*x^3 + 5*b^4*d^2*(3*b*c - 2*a*d)*x^4 + 4*b^5*d^3*x^5 - (20*a^3*(-(b*c) + a*d)^3)/(a + b*x) - 60*a^2*(b*c - a*d)^2*(-(b*c) + 2*a*d)*Log[a + b*x])/(20*b^7)","A",1
271,1,130,136,0.0713412,"\int \frac{x^2 (c+d x)^3}{(a+b x)^2} \, dx","Integrate[(x^2*(c + d*x)^3)/(a + b*x)^2,x]","\frac{\frac{12 a^2 (a d-b c)^3}{a+b x}+4 b^3 d^2 x^3 (3 b c-2 a d)+18 b^2 d x^2 (b c-a d)^2+12 b x (b c-4 a d) (b c-a d)^2+12 a (b c-a d)^2 (5 a d-2 b c) \log (a+b x)+3 b^4 d^3 x^4}{12 b^6}","-\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*b*(b*c - 4*a*d)*(b*c - a*d)^2*x + 18*b^2*d*(b*c - a*d)^2*x^2 + 4*b^3*d^2*(3*b*c - 2*a*d)*x^3 + 3*b^4*d^3*x^4 + (12*a^2*(-(b*c) + a*d)^3)/(a + b*x) + 12*a*(b*c - a*d)^2*(-2*b*c + 5*a*d)*Log[a + b*x])/(12*b^6)","A",1
272,1,100,103,0.0889022,"\int \frac{x (c+d x)^3}{(a+b x)^2} \, dx","Integrate[(x*(c + d*x)^3)/(a + b*x)^2,x]","\frac{3 b^2 d^2 x^2 (3 b c-2 a d)-\frac{6 a (a d-b c)^3}{a+b x}+18 b d x (b c-a d)^2+6 (b c-4 a d) (b c-a d)^2 \log (a+b x)+2 b^3 d^3 x^3}{6 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,"(18*b*d*(b*c - a*d)^2*x + 3*b^2*d^2*(3*b*c - 2*a*d)*x^2 + 2*b^3*d^3*x^3 - (6*a*(-(b*c) + a*d)^3)/(a + b*x) + 6*(b*c - 4*a*d)*(b*c - a*d)^2*Log[a + b*x])/(6*b^5)","A",1
273,1,72,75,0.0688758,"\int \frac{(c+d x)^3}{(a+b x)^2} \, dx","Integrate[(c + d*x)^3/(a + b*x)^2,x]","\frac{2 b d^2 x (3 b c-2 a d)-\frac{2 (b c-a d)^3}{a+b x}+6 d (b c-a d)^2 \log (a+b x)+b^2 d^3 x^2}{2 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*d^2*(3*b*c - 2*a*d)*x + b^2*d^3*x^2 - (2*(b*c - a*d)^3)/(a + b*x) + 6*d*(b*c - a*d)^2*Log[a + b*x])/(2*b^4)","A",1
274,1,74,74,0.0719671,"\int \frac{(c+d x)^3}{x (a+b x)^2} \, dx","Integrate[(c + d*x)^3/(x*(a + b*x)^2),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}","-\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,"(d^3*x)/b^2 + (b*c - a*d)^3/(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
275,1,79,87,0.0945694,"\int \frac{(c+d x)^3}{x^2 (a+b x)^2} \, dx","Integrate[(c + d*x)^3/(x^2*(a + b*x)^2),x]","\frac{\frac{a (a d-b c)^3}{b^2 (a+b x)}+\frac{(b c-a d)^2 (a d+2 b c) \log (a+b x)}{b^2}+c^2 \log (x) (3 a d-2 b c)-\frac{a c^3}{x}}{a^3}","\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*c^3)/x) + (a*(-(b*c) + a*d)^3)/(b^2*(a + b*x)) + c^2*(-2*b*c + 3*a*d)*Log[x] + ((b*c - a*d)^2*(2*b*c + a*d)*Log[a + b*x])/b^2)/a^3","A",1
276,1,93,97,0.1364067,"\int \frac{(c+d x)^3}{x^3 (a+b x)^2} \, dx","Integrate[(c + d*x)^3/(x^3*(a + b*x)^2),x]","-\frac{\frac{a^2 c^3}{x^2}+\frac{2 a c^2 (3 a d-2 b c)}{x}+\frac{2 a (a d-b c)^3}{b (a+b x)}-6 c \log (x) (b c-a d)^2+6 c (b c-a d)^2 \log (a+b x)}{2 a^4}","\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,"-1/2*((a^2*c^3)/x^2 + (2*a*c^2*(-2*b*c + 3*a*d))/x + (2*a*(-(b*c) + a*d)^3)/(b*(a + b*x)) - 6*c*(b*c - a*d)^2*Log[x] + 6*c*(b*c - a*d)^2*Log[a + b*x])/a^4","A",1
277,1,126,132,0.084234,"\int \frac{(c+d x)^3}{x^4 (a+b x)^2} \, dx","Integrate[(c + d*x)^3/(x^4*(a + b*x)^2),x]","-\frac{\frac{2 a^3 c^3}{x^3}+\frac{3 a^2 c^2 (3 a d-2 b c)}{x^2}+\frac{18 a c (b c-a d)^2}{x}-\frac{6 a (a d-b c)^3}{a+b x}+6 \log (x) (b c-a d)^2 (4 b c-a d)-6 (b c-a d)^2 (4 b c-a d) \log (a+b x)}{6 a^5}","-\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,"-1/6*((2*a^3*c^3)/x^3 + (3*a^2*c^2*(-2*b*c + 3*a*d))/x^2 + (18*a*c*(b*c - a*d)^2)/x - (6*a*(-(b*c) + a*d)^3)/(a + b*x) + 6*(b*c - a*d)^2*(4*b*c - a*d)*Log[x] - 6*(b*c - a*d)^2*(4*b*c - a*d)*Log[a + b*x])/a^5","A",1
278,1,155,162,0.1113655,"\int \frac{(c+d x)^3}{x^5 (a+b x)^2} \, dx","Integrate[(c + d*x)^3/(x^5*(a + b*x)^2),x]","-\frac{\frac{3 a^4 c^3}{x^4}+\frac{4 a^3 c^2 (3 a d-2 b c)}{x^3}+\frac{18 a^2 c (b c-a d)^2}{x^2}+\frac{12 a (b c-a d)^2 (a d-4 b c)}{x}+\frac{12 a b (a d-b c)^3}{a+b x}-12 b \log (x) (5 b c-2 a d) (b c-a d)^2+12 b (5 b c-2 a d) (b c-a d)^2 \log (a+b x)}{12 a^6}","\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,"-1/12*((3*a^4*c^3)/x^4 + (4*a^3*c^2*(-2*b*c + 3*a*d))/x^3 + (18*a^2*c*(b*c - a*d)^2)/x^2 + (12*a*(b*c - a*d)^2*(-4*b*c + a*d))/x + (12*a*b*(-(b*c) + a*d)^3)/(a + b*x) - 12*b*(5*b*c - 2*a*d)*(b*c - a*d)^2*Log[x] + 12*b*(5*b*c - 2*a*d)*(b*c - a*d)^2*Log[a + b*x])/a^6","A",1
279,1,189,199,0.1272935,"\int \frac{(c+d x)^3}{x^6 (a+b x)^2} \, dx","Integrate[(c + d*x)^3/(x^6*(a + b*x)^2),x]","-\frac{\frac{4 a^5 c^3}{x^5}+\frac{5 a^4 c^2 (3 a d-2 b c)}{x^4}+\frac{20 a^3 c (b c-a d)^2}{x^3}+\frac{10 a^2 (b c-a d)^2 (a d-4 b c)}{x^2}-\frac{20 a b^2 (a d-b c)^3}{a+b x}+60 b^2 \log (x) (b c-a d)^2 (2 b c-a d)-60 b^2 (b c-a d)^2 (2 b c-a d) \log (a+b x)-\frac{20 a b (b c-a d)^2 (2 a d-5 b c)}{x}}{20 a^7}","-\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,"-1/20*((4*a^5*c^3)/x^5 + (5*a^4*c^2*(-2*b*c + 3*a*d))/x^4 + (20*a^3*c*(b*c - a*d)^2)/x^3 + (10*a^2*(b*c - a*d)^2*(-4*b*c + a*d))/x^2 - (20*a*b*(b*c - a*d)^2*(-5*b*c + 2*a*d))/x - (20*a*b^2*(-(b*c) + a*d)^3)/(a + b*x) + 60*b^2*(b*c - a*d)^2*(2*b*c - a*d)*Log[x] - 60*b^2*(b*c - a*d)^2*(2*b*c - a*d)*Log[a + b*x])/a^7","A",1
280,1,179,179,0.2565454,"\int \frac{x^6}{(a+b x)^2 (c+d x)^2} \, dx","Integrate[x^6/((a + b*x)^2*(c + d*x)^2),x]","-\frac{a^6}{b^5 (a+b x) (b c-a d)^2}+\frac{2 a^5 (2 a d-3 b c) \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 (a d-b c)^3}+\frac{x^3}{3 b^2 d^2}","-\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*b^2*c^2 + 4*a*b*c*d + 3*a^2*d^2)*x)/(b^4*d^4) - ((b*c + a*d)*x^2)/(b^3*d^3) + x^3/(3*b^2*d^2) - a^6/(b^5*(b*c - a*d)^2*(a + b*x)) - c^6/(d^5*(b*c - a*d)^2*(c + d*x)) + (2*a^5*(-3*b*c + 2*a*d)*Log[a + b*x])/(b^5*(b*c - a*d)^3) + (2*c^5*(2*b*c - 3*a*d)*Log[c + d*x])/(d^5*(-(b*c) + a*d)^3)","A",1
281,1,142,142,0.2040645,"\int \frac{x^5}{(a+b x)^2 (c+d x)^2} \, dx","Integrate[x^5/((a + b*x)^2*(c + d*x)^2),x]","\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 (5 a d-3 b c) \log (c+d x)}{d^4 (a d-b c)^3}+\frac{x^2}{2 b^2 d^2}","\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*(b*c + a*d)*x)/(b^3*d^3) + x^2/(2*b^2*d^2) + a^5/(b^4*(b*c - a*d)^2*(a + b*x)) + c^5/(d^4*(b*c - a*d)^2*(c + d*x)) + (a^4*(5*b*c - 3*a*d)*Log[a + b*x])/(b^4*(b*c - a*d)^3) + (c^4*(-3*b*c + 5*a*d)*Log[c + d*x])/(d^4*(-(b*c) + a*d)^3)","A",1
282,1,123,124,0.1726544,"\int \frac{x^4}{(a+b x)^2 (c+d x)^2} \, dx","Integrate[x^4/((a + b*x)^2*(c + d*x)^2),x]","-\frac{a^4}{b^3 (a+b x) (b c-a d)^2}+\frac{2 a^3 (a d-2 b c) \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 (a d-b c)^3}+\frac{x}{b^2 d^2}","-\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,"x/(b^2*d^2) - a^4/(b^3*(b*c - a*d)^2*(a + b*x)) - c^4/(d^3*(b*c - a*d)^2*(c + d*x)) + (2*a^3*(-2*b*c + a*d)*Log[a + b*x])/(b^3*(b*c - a*d)^3) + (2*c^3*(b*c - 2*a*d)*Log[c + d*x])/(d^3*(-(b*c) + a*d)^3)","A",1
283,1,105,112,0.2126766,"\int \frac{x^3}{(a+b x)^2 (c+d x)^2} \, dx","Integrate[x^3/((a + b*x)^2*(c + d*x)^2),x]","\frac{\frac{a^3}{b^2 (a+b x)}+\frac{c^3}{d^2 (c+d 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^2 (3 a d-b c) \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^3/(b^2*(a + b*x)) + c^3/(d^2*(c + d*x)))/(b*c - a*d)^2 + (a^2*(3*b*c - a*d)*Log[a + b*x])/(b^2*(b*c - a*d)^3) + (c^2*(-(b*c) + 3*a*d)*Log[c + d*x])/(d^2*(-(b*c) + a*d)^3)","A",1
284,1,71,91,0.1822195,"\int \frac{x^2}{(a+b x)^2 (c+d x)^2} \, dx","Integrate[x^2/((a + b*x)^2*(c + d*x)^2),x]","\frac{-\left((b c-a d) \left(\frac{a^2}{b (a+b x)}+\frac{c^2}{d (c+d x)}\right)\right)-2 a c \log (a+b x)+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,"(-((b*c - a*d)*(a^2/(b*(a + b*x)) + c^2/(d*(c + d*x)))) - 2*a*c*Log[a + b*x] + 2*a*c*Log[c + d*x])/(b*c - a*d)^3","A",1
285,1,75,88,0.0960577,"\int \frac{x}{(a+b x)^2 (c+d x)^2} \, dx","Integrate[x/((a + b*x)^2*(c + d*x)^2),x]","\frac{\frac{a (b c-a d)}{a+b x}+\frac{c (b c-a d)}{c+d x}+(a d+b c) \log (a+b x)-(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,"((a*(b*c - a*d))/(a + b*x) + (c*(b*c - a*d))/(c + d*x) + (b*c + a*d)*Log[a + b*x] - (b*c + a*d)*Log[c + d*x])/(b*c - a*d)^3","A",1
286,1,66,81,0.0900718,"\int \frac{1}{(a+b x)^2 (c+d x)^2} \, dx","Integrate[1/((a + b*x)^2*(c + d*x)^2),x]","\frac{\frac{b (a d-b c)}{a+b x}+\frac{d (a d-b c)}{c+d x}-2 b d \log (a+b x)+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*(-(b*c) + a*d))/(a + b*x) + (d*(-(b*c) + a*d))/(c + d*x) - 2*b*d*Log[a + b*x] + 2*b*d*Log[c + d*x])/(b*c - a*d)^3","A",1
287,1,120,123,0.2311411,"\int \frac{1}{x (a+b x)^2 (c+d x)^2} \, dx","Integrate[1/(x*(a + b*x)^2*(c + d*x)^2),x]","\frac{b^2 (b c-3 a d) \log (a+b x)}{a^2 (a d-b c)^3}+\frac{\log (x)}{a^2 c^2}+\frac{b^2}{a (a+b x) (b c-a d)^2}+\frac{d^2 (a d-3 b c) \log (c+d x)}{c^2 (b c-a d)^3}+\frac{d^2}{c (c+d x) (b c-a d)^2}","-\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/(a*(b*c - a*d)^2*(a + b*x)) + d^2/(c*(b*c - a*d)^2*(c + d*x)) + Log[x]/(a^2*c^2) + (b^2*(b*c - 3*a*d)*Log[a + b*x])/(a^2*(-(b*c) + a*d)^3) + (d^2*(-3*b*c + a*d)*Log[c + d*x])/(c^2*(b*c - a*d)^3)","A",1
288,1,145,144,0.2124193,"\int \frac{1}{x^2 (a+b x)^2 (c+d x)^2} \, dx","Integrate[1/(x^2*(a + b*x)^2*(c + d*x)^2),x]","\frac{2 b^3 (2 a d-b c) \log (a+b x)}{a^3 (a d-b c)^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}","\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,"-(1/(a^2*c^2*x)) - b^3/(a^2*(b*c - a*d)^2*(a + b*x)) - d^3/(c^2*(b*c - a*d)^2*(c + d*x)) - (2*(b*c + a*d)*Log[x])/(a^3*c^3) + (2*b^3*(-(b*c) + 2*a*d)*Log[a + b*x])/(a^3*(-(b*c) + a*d)^3) + (2*d^3*(2*b*c - a*d)*Log[c + d*x])/(c^3*(b*c - a*d)^3)","A",1
289,1,176,178,0.2179803,"\int \frac{1}{x^3 (a+b x)^2 (c+d x)^2} \, dx","Integrate[1/(x^3*(a + b*x)^2*(c + d*x)^2),x]","\frac{b^4 (3 b c-5 a d) \log (a+b x)}{a^4 (a d-b c)^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 (3 a d-5 b c) \log (c+d x)}{c^4 (b c-a d)^3}+\frac{d^4}{c^3 (c+d x) (b c-a d)^2}","-\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,"-1/2*1/(a^2*c^2*x^2) + (2*(b*c + a*d))/(a^3*c^3*x) + b^4/(a^3*(b*c - a*d)^2*(a + b*x)) + d^4/(c^3*(b*c - a*d)^2*(c + d*x)) + ((3*b^2*c^2 + 4*a*b*c*d + 3*a^2*d^2)*Log[x])/(a^4*c^4) + (b^4*(3*b*c - 5*a*d)*Log[a + b*x])/(a^4*(-(b*c) + a*d)^3) + (d^4*(-5*b*c + 3*a*d)*Log[c + d*x])/(c^4*(b*c - a*d)^3)","A",1
290,1,230,231,0.3749359,"\int \frac{x^7}{(a+b x)^2 (c+d x)^3} \, dx","Integrate[x^7/((a + b*x)^2*(c + d*x)^3),x]","\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) (a d-b c)^3}+\frac{x^3}{3 b^2 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,"(3*(2*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*x)/(b^4*d^5) - ((3*b*c + 2*a*d)*x^2)/(2*b^3*d^4) + x^3/(3*b^2*d^3) + a^7/(b^5*(b*c - a*d)^3*(a + b*x)) + c^7/(2*d^6*(b*c - a*d)^2*(c + d*x)^2) + (c^6*(5*b*c - 7*a*d))/(d^6*(-(b*c) + a*d)^3*(c + d*x)) + (a^6*(7*b*c - 4*a*d)*Log[a + b*x])/(b^5*(b*c - a*d)^4) - (c^5*(10*b^2*c^2 - 28*a*b*c*d + 21*a^2*d^2)*Log[c + d*x])/(d^6*(b*c - a*d)^4)","A",1
291,1,198,198,0.3098883,"\int \frac{x^6}{(a+b x)^2 (c+d x)^3} \, dx","Integrate[x^6/((a + b*x)^2*(c + d*x)^3),x]","-\frac{a^6}{b^4 (a+b x) (b c-a d)^3}+\frac{3 a^5 (a d-2 b c) \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{6 a c^5 d-4 b c^6}{d^5 (c+d x) (a d-b c)^3}+\frac{x^2}{2 b^2 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,"-(((3*b*c + 2*a*d)*x)/(b^3*d^4)) + x^2/(2*b^2*d^3) - a^6/(b^4*(b*c - a*d)^3*(a + b*x)) - c^6/(2*d^5*(b*c - a*d)^2*(c + d*x)^2) + (-4*b*c^6 + 6*a*c^5*d)/(d^5*(-(b*c) + a*d)^3*(c + d*x)) + (3*a^5*(-2*b*c + a*d)*Log[a + b*x])/(b^4*(b*c - a*d)^4) + (3*c^4*(2*b^2*c^2 - 6*a*b*c*d + 5*a^2*d^2)*Log[c + d*x])/(d^5*(b*c - a*d)^4)","A",1
292,1,172,173,0.2740772,"\int \frac{x^5}{(a+b x)^2 (c+d x)^3} \, dx","Integrate[x^5/((a + b*x)^2*(c + d*x)^3),x]","\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) (a d-b c)^3}+\frac{x}{b^2 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,"x/(b^2*d^3) + a^5/(b^3*(b*c - a*d)^3*(a + b*x)) + c^5/(2*d^4*(b*c - a*d)^2*(c + d*x)^2) + (c^4*(3*b*c - 5*a*d))/(d^4*(-(b*c) + a*d)^3*(c + d*x)) + (a^4*(5*b*c - 2*a*d)*Log[a + b*x])/(b^3*(b*c - a*d)^4) - (c^3*(3*b^2*c^2 - 10*a*b*c*d + 10*a^2*d^2)*Log[c + d*x])/(d^4*(b*c - a*d)^4)","A",1
293,1,162,164,0.2772672,"\int \frac{x^4}{(a+b x)^2 (c+d x)^3} \, dx","Integrate[x^4/((a + b*x)^2*(c + d*x)^3),x]","-\frac{a^4}{b^2 (a+b x) (b c-a d)^3}+\frac{a^3 (a d-4 b c) \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) (a d-b c)^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,"-(a^4/(b^2*(b*c - a*d)^3*(a + b*x))) - c^4/(2*d^3*(b*c - a*d)^2*(c + d*x)^2) - (2*c^3*(b*c - 2*a*d))/(d^3*(-(b*c) + a*d)^3*(c + d*x)) + (a^3*(-4*b*c + a*d)*Log[a + b*x])/(b^2*(b*c - a*d)^4) + (c^2*(b^2*c^2 - 4*a*b*c*d + 6*a^2*d^2)*Log[c + d*x])/(d^3*(b*c - a*d)^4)","A",1
294,1,130,129,0.1965695,"\int \frac{x^3}{(a+b x)^2 (c+d x)^3} \, dx","Integrate[x^3/((a + b*x)^2*(c + d*x)^3),x]","\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 (a d-b c)^2}+\frac{b c^3-3 a c^2 d}{d^2 (c+d x) (a d-b c)^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^3/(b*(b*c - a*d)^3*(a + b*x)) + c^3/(2*d^2*(-(b*c) + a*d)^2*(c + d*x)^2) + (b*c^3 - 3*a*c^2*d)/(d^2*(-(b*c) + a*d)^3*(c + d*x)) + (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
295,1,123,124,0.1728312,"\int \frac{x^2}{(a+b x)^2 (c+d x)^3} \, dx","Integrate[x^2/((a + b*x)^2*(c + d*x)^3),x]","\frac{a^2}{(a+b x) (a d-b c)^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}","-\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^2/((-(b*c) + a*d)^3*(a + b*x)) - c^2/(2*d*(b*c - a*d)^2*(c + d*x)^2) - (2*a*c)/((b*c - a*d)^3*(c + d*x)) - (a*(2*b*c + a*d)*Log[a + b*x])/(b*c - a*d)^4 + (a*(2*b*c + a*d)*Log[c + d*x])/(b*c - a*d)^4","A",1
296,1,111,121,0.1543649,"\int \frac{x}{(a+b x)^2 (c+d x)^3} \, dx","Integrate[x/((a + b*x)^2*(c + d*x)^3),x]","\frac{\frac{c (b c-a d)^2}{(c+d x)^2}+\frac{2 a b (b c-a d)}{a+b x}+\frac{2 (a d+b c) (b c-a d)}{c+d x}+2 b (2 a d+b c) \log (a+b x)-2 b (2 a d+b c) \log (c+d x)}{2 (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,"((2*a*b*(b*c - a*d))/(a + b*x) + (c*(b*c - a*d)^2)/(c + d*x)^2 + (2*(b*c - a*d)*(b*c + a*d))/(c + d*x) + 2*b*(b*c + 2*a*d)*Log[a + b*x] - 2*b*(b*c + 2*a*d)*Log[c + d*x])/(2*(b*c - a*d)^4)","A",1
297,1,97,110,0.1290178,"\int \frac{1}{(a+b x)^2 (c+d x)^3} \, dx","Integrate[1/((a + b*x)^2*(c + d*x)^3),x]","-\frac{\frac{2 b^2 (b c-a d)}{a+b x}+6 b^2 d \log (a+b x)+\frac{4 b d (b c-a d)}{c+d x}+\frac{d (b c-a d)^2}{(c+d x)^2}-6 b^2 d \log (c+d x)}{2 (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,"-1/2*((2*b^2*(b*c - a*d))/(a + b*x) + (d*(b*c - a*d)^2)/(c + d*x)^2 + (4*b*d*(b*c - a*d))/(c + d*x) + 6*b^2*d*Log[a + b*x] - 6*b^2*d*Log[c + d*x])/(b*c - a*d)^4","A",1
298,1,173,172,0.2753021,"\int \frac{1}{x (a+b x)^2 (c+d x)^3} \, dx","Integrate[1/(x*(a + b*x)^2*(c + d*x)^3),x]","\frac{b^3 (4 a d-b c) \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) (a d-b c)^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}","-\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,"-(b^3/(a*(-(b*c) + a*d)^3*(a + b*x))) + d^2/(2*c*(b*c - a*d)^2*(c + d*x)^2) + (d^2*(3*b*c - a*d))/(c^2*(b*c - a*d)^3*(c + d*x)) + Log[x]/(a^2*c^3) + (b^3*(-(b*c) + 4*a*d)*Log[a + b*x])/(a^2*(b*c - a*d)^4) - (d^2*(6*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*Log[c + d*x])/(c^3*(b*c - a*d)^4)","A",1
299,1,193,195,0.3178978,"\int \frac{1}{x^2 (a+b x)^2 (c+d x)^3} \, dx","Integrate[1/(x^2*(a + b*x)^2*(c + d*x)^3),x]","\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) (a d-b c)^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 (a d-2 b c)}{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}","\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,"-(1/(a^2*c^3*x)) + b^4/(a^2*(-(b*c) + a*d)^3*(a + b*x)) - d^3/(2*c^2*(b*c - a*d)^2*(c + d*x)^2) + (2*d^3*(-2*b*c + a*d))/(c^3*(b*c - a*d)^3*(c + d*x)) - ((2*b*c + 3*a*d)*Log[x])/(a^3*c^4) + (b^4*(2*b*c - 5*a*d)*Log[a + b*x])/(a^3*(b*c - a*d)^4) + (d^3*(10*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*Log[c + d*x])/(c^4*(b*c - a*d)^4)","A",1
300,1,230,228,0.341264,"\int \frac{1}{x^3 (a+b x)^2 (c+d x)^3} \, dx","Integrate[1/(x^3*(a + b*x)^2*(c + d*x)^3),x]","\frac{3 b^5 (2 a d-b c) \log (a+b x)}{a^4 (b c-a d)^4}-\frac{b^5}{a^3 (a+b x) (a d-b c)^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}","-\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,"-1/2*1/(a^2*c^3*x^2) + (2*b*c + 3*a*d)/(a^3*c^4*x) - b^5/(a^3*(-(b*c) + a*d)^3*(a + b*x)) + d^4/(2*c^3*(b*c - a*d)^2*(c + d*x)^2) + (d^4*(5*b*c - 3*a*d))/(c^4*(b*c - a*d)^3*(c + d*x)) + (3*(b^2*c^2 + 2*a*b*c*d + 2*a^2*d^2)*Log[x])/(a^4*c^5) + (3*b^5*(-(b*c) + 2*a*d)*Log[a + b*x])/(a^4*(b*c - a*d)^4) - (3*d^4*(5*b^2*c^2 - 6*a*b*c*d + 2*a^2*d^2)*Log[c + d*x])/(c^5*(b*c - a*d)^4)","A",1
301,1,207,196,0.1982543,"\int \frac{x^3 (c+d x)^3}{(a+b x)^3} \, dx","Integrate[(x^3*(c + d*x)^3)/(a + b*x)^3,x]","\frac{\frac{2 a^3 (b c-a d)^3}{(a+b x)^2}+6 b^2 d x^2 \left(2 a^2 d^2-3 a b c d+b^2 c^2\right)+\frac{12 a^2 (b c-a d)^2 (2 a d-b c)}{a+b x}+4 b x \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)+12 a \left(5 a^3 d^3-10 a^2 b c d^2+6 a b^2 c^2 d-b^3 c^3\right) \log (a+b x)+4 b^3 d^2 x^3 (b c-a d)+b^4 d^3 x^4}{4 b^7}","\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,"(4*b*(b^3*c^3 - 9*a*b^2*c^2*d + 18*a^2*b*c*d^2 - 10*a^3*d^3)*x + 6*b^2*d*(b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^2 + 4*b^3*d^2*(b*c - a*d)*x^3 + b^4*d^3*x^4 + (2*a^3*(b*c - a*d)^3)/(a + b*x)^2 + (12*a^2*(b*c - a*d)^2*(-(b*c) + 2*a*d))/(a + b*x) + 12*a*(-(b^3*c^3) + 6*a*b^2*c^2*d - 10*a^2*b*c*d^2 + 5*a^3*d^3)*Log[a + b*x])/(4*b^7)","A",1
302,1,160,156,0.1162243,"\int \frac{x^2 (c+d x)^3}{(a+b x)^3} \, dx","Integrate[(x^2*(c + d*x)^3)/(a + b*x)^3,x]","\frac{18 b d x \left(2 a^2 d^2-3 a b c d+b^2 c^2\right)+\frac{3 a^2 (a d-b c)^3}{(a+b x)^2}+6 \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)+9 b^2 d^2 x^2 (b c-a d)-\frac{6 a (b c-a d)^2 (5 a d-2 b c)}{a+b x}+2 b^3 d^3 x^3}{6 b^6}","-\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,"(18*b*d*(b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x + 9*b^2*d^2*(b*c - a*d)*x^2 + 2*b^3*d^3*x^3 + (3*a^2*(-(b*c) + a*d)^3)/(a + b*x)^2 - (6*a*(b*c - a*d)^2*(-2*b*c + 5*a*d))/(a + b*x) + 6*(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])/(6*b^6)","A",1
303,1,165,114,0.0747254,"\int \frac{x (c+d x)^3}{(a+b x)^3} \, dx","Integrate[(x*(c + d*x)^3)/(a + b*x)^3,x]","\frac{7 a^4 d^3+a^3 b d^2 (2 d x-15 c)+a^2 b^2 d \left(9 c^2-12 c d x-11 d^2 x^2\right)+6 d (a+b x)^2 \left(2 a^2 d^2-3 a b c d+b^2 c^2\right) \log (a+b x)-a b^3 \left(c^3-12 c^2 d x-12 c d^2 x^2+4 d^3 x^3\right)+b^4 x \left(-2 c^3+6 c d^2 x^2+d^3 x^3\right)}{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,"(7*a^4*d^3 + a^3*b*d^2*(-15*c + 2*d*x) + a^2*b^2*d*(9*c^2 - 12*c*d*x - 11*d^2*x^2) + b^4*x*(-2*c^3 + 6*c*d^2*x^2 + d^3*x^3) - a*b^3*(c^3 - 12*c^2*d*x - 12*c*d^2*x^2 + 4*d^3*x^3) + 6*d*(b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*(a + b*x)^2*Log[a + b*x])/(2*b^5*(a + b*x)^2)","A",1
304,1,114,78,0.0575816,"\int \frac{(c+d x)^3}{(a+b x)^3} \, dx","Integrate[(c + d*x)^3/(a + b*x)^3,x]","\frac{-5 a^3 d^3+a^2 b d^2 (9 c-4 d x)+a b^2 d \left(-3 c^2+12 c d x+4 d^2 x^2\right)-6 d^2 (a+b x)^2 (a d-b c) \log (a+b x)-\left(b^3 \left(c^3+6 c^2 d x-2 d^3 x^3\right)\right)}{2 b^4 (a+b x)^2}","\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,"(-5*a^3*d^3 + a^2*b*d^2*(9*c - 4*d*x) + a*b^2*d*(-3*c^2 + 12*c*d*x + 4*d^2*x^2) - b^3*(c^3 + 6*c^2*d*x - 2*d^3*x^3) - 6*d^2*(-(b*c) + a*d)*(a + b*x)^2*Log[a + b*x])/(2*b^4*(a + b*x)^2)","A",1
305,1,88,93,0.1063175,"\int \frac{(c+d x)^3}{x (a+b x)^3} \, dx","Integrate[(c + d*x)^3/(x*(a + b*x)^3),x]","\frac{\frac{2 \left(a^3 d^3-b^3 c^3\right) \log (a+b x)+\frac{a (b c-a d)^2 \left(3 a^2 d+a b (3 c+4 d x)+2 b^2 c x\right)}{(a+b x)^2}}{b^3}+2 c^3 \log (x)}{2 a^3}","-\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,"(2*c^3*Log[x] + ((a*(b*c - a*d)^2*(3*a^2*d + 2*b^2*c*x + a*b*(3*c + 4*d*x)))/(a + b*x)^2 + 2*(-(b^3*c^3) + a^3*d^3)*Log[a + b*x])/b^3)/(2*a^3)","A",1
306,1,106,112,0.1213715,"\int \frac{(c+d x)^3}{x^2 (a+b x)^3} \, dx","Integrate[(c + d*x)^3/(x^2*(a + b*x)^3),x]","\frac{\frac{a^2 (a d-b c)^3}{b^2 (a+b x)^2}-\frac{2 a (b c-a d)^2 (a d+2 b c)}{b^2 (a+b x)}+6 c^2 \log (x) (a d-b c)+6 c^2 (b c-a d) \log (a+b x)-\frac{2 a c^3}{x}}{2 a^4}","-\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*c^3)/x + (a^2*(-(b*c) + a*d)^3)/(b^2*(a + b*x)^2) - (2*a*(b*c - a*d)^2*(2*b*c + a*d))/(b^2*(a + b*x)) + 6*c^2*(-(b*c) + a*d)*Log[x] + 6*c^2*(b*c - a*d)*Log[a + b*x])/(2*a^4)","A",1
307,1,138,137,0.2014035,"\int \frac{(c+d x)^3}{x^3 (a+b x)^3} \, dx","Integrate[(c + d*x)^3/(x^3*(a + b*x)^3),x]","-\frac{-6 c \log (x) \left(a^2 d^2-3 a b c d+2 b^2 c^2\right)+6 c \left(a^2 d^2-3 a b c d+2 b^2 c^2\right) \log (a+b x)+\frac{a^2 (a d-b c)^3}{b (a+b x)^2}+\frac{a^2 c^3}{x^2}+\frac{6 a c^2 (a d-b c)}{x}-\frac{6 a c (b c-a d)^2}{a+b x}}{2 a^5}","\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,"-1/2*((a^2*c^3)/x^2 + (6*a*c^2*(-(b*c) + a*d))/x + (a^2*(-(b*c) + a*d)^3)/(b*(a + b*x)^2) - (6*a*c*(b*c - a*d)^2)/(a + b*x) - 6*c*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*Log[x] + 6*c*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*Log[a + b*x])/a^5","A",1
308,1,202,193,0.1896588,"\int \frac{(c+d x)^3}{x^4 (a+b x)^3} \, dx","Integrate[(c + d*x)^3/(x^4*(a + b*x)^3),x]","\frac{-\frac{2 a^3 c^3}{x^3}-\frac{18 a c \left(a^2 d^2-3 a b c d+2 b^2 c^2\right)}{x}-\frac{9 a^2 c^2 (a d-b c)}{x^2}+\frac{3 a^2 (a d-b c)^3}{(a+b x)^2}+6 \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)+6 \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)+\frac{6 a (b c-a d)^2 (a d-4 b c)}{a+b x}}{6 a^6}","-\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^3*c^3)/x^3 - (9*a^2*c^2*(-(b*c) + a*d))/x^2 - (18*a*c*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2))/x + (3*a^2*(-(b*c) + a*d)^3)/(a + b*x)^2 + (6*a*(b*c - a*d)^2*(-4*b*c + a*d))/(a + b*x) + 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[x] + 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])/(6*a^6)","A",1
309,1,241,245,0.5432454,"\int \frac{x^7}{(a+b x)^3 (c+d x)^3} \, dx","Integrate[x^7/((a + b*x)^3*(c + d*x)^3),x]","\frac{1}{2} \left(\frac{a^7}{b^5 (a+b x)^2 (b c-a d)^3}+\frac{2 a^6 (4 a d-7 b c)}{b^5 (a+b x) (b c-a d)^4}-\frac{6 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 (a d-b c)^5}-\frac{6 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{6 x (a d+b c)}{b^4 d^4}+\frac{c^7}{d^5 (c+d x)^2 (a d-b c)^3}+\frac{2 c^6 (4 b c-7 a d)}{d^5 (c+d x) (b c-a d)^4}+\frac{x^2}{b^3 d^3}\right)","\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,"((-6*(b*c + a*d)*x)/(b^4*d^4) + x^2/(b^3*d^3) + a^7/(b^5*(b*c - a*d)^3*(a + b*x)^2) + (2*a^6*(-7*b*c + 4*a*d))/(b^5*(b*c - a*d)^4*(a + b*x)) + c^7/(d^5*(-(b*c) + a*d)^3*(c + d*x)^2) + (2*c^6*(4*b*c - 7*a*d))/(d^5*(b*c - a*d)^4*(c + d*x)) - (6*a^5*(7*b^2*c^2 - 7*a*b*c*d + 2*a^2*d^2)*Log[a + b*x])/(b^5*(b*c - a*d)^5) - (6*c^5*(2*b^2*c^2 - 7*a*b*c*d + 7*a^2*d^2)*Log[c + d*x])/(d^5*(-(b*c) + a*d)^5))/2","A",1
310,1,221,222,0.3827367,"\int \frac{x^6}{(a+b x)^3 (c+d x)^3} \, dx","Integrate[x^6/((a + b*x)^3*(c + d*x)^3),x]","-\frac{a^6}{2 b^4 (a+b x)^2 (b c-a d)^3}-\frac{3 a^5 (a d-2 b c)}{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 (a d-b c)^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 (a d-b c)^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}","-\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,"x/(b^3*d^3) - a^6/(2*b^4*(b*c - a*d)^3*(a + b*x)^2) - (3*a^5*(-2*b*c + a*d))/(b^4*(b*c - a*d)^4*(a + b*x)) - c^6/(2*d^4*(-(b*c) + a*d)^3*(c + d*x)^2) - (3*c^5*(b*c - 2*a*d))/(d^4*(b*c - a*d)^4*(c + d*x)) + (3*a^4*(5*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*Log[a + b*x])/(b^4*(b*c - a*d)^5) + (3*c^4*(b^2*c^2 - 4*a*b*c*d + 5*a^2*d^2)*Log[c + d*x])/(d^4*(-(b*c) + a*d)^5)","A",1
311,1,213,213,0.4378987,"\int \frac{x^5}{(a+b x)^3 (c+d x)^3} \, dx","Integrate[x^5/((a + b*x)^3*(c + d*x)^3),x]","\frac{a^5}{2 b^3 (a+b x)^2 (b c-a d)^3}+\frac{a^4 (2 a d-5 b c)}{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 (a d-b c)^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 (a d-b c)^3}+\frac{c^4 (2 b c-5 a d)}{d^3 (c+d x) (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,"a^5/(2*b^3*(b*c - a*d)^3*(a + b*x)^2) + (a^4*(-5*b*c + 2*a*d))/(b^3*(b*c - a*d)^4*(a + b*x)) + c^5/(2*d^3*(-(b*c) + a*d)^3*(c + d*x)^2) + (c^4*(2*b*c - 5*a*d))/(d^3*(b*c - a*d)^4*(c + d*x)) - (a^3*(10*b^2*c^2 - 5*a*b*c*d + a^2*d^2)*Log[a + b*x])/(b^3*(b*c - a*d)^5) - (c^3*(b^2*c^2 - 5*a*b*c*d + 10*a^2*d^2)*Log[c + d*x])/(d^3*(-(b*c) + a*d)^5)","A",1
312,1,171,169,0.312999,"\int \frac{x^4}{(a+b x)^3 (c+d x)^3} \, dx","Integrate[x^4/((a + b*x)^3*(c + d*x)^3),x]","-\frac{a^4}{2 b^2 (a+b x)^2 (b c-a d)^3}+\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{4 a^3 b c-a^4 d}{b^2 (a+b x) (b c-a d)^4}-\frac{c^4}{2 d^2 (c+d x)^2 (a d-b c)^3}-\frac{c^3 (b c-4 a d)}{d^2 (c+d x) (a d-b c)^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,"-1/2*a^4/(b^2*(b*c - a*d)^3*(a + b*x)^2) + (4*a^3*b*c - a^4*d)/(b^2*(b*c - a*d)^4*(a + b*x)) - c^4/(2*d^2*(-(b*c) + a*d)^3*(c + d*x)^2) - (c^3*(b*c - 4*a*d))/(d^2*(-(b*c) + a*d)^4*(c + d*x)) + (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
313,1,153,155,0.2829788,"\int \frac{x^3}{(a+b x)^3 (c+d x)^3} \, dx","Integrate[x^3/((a + b*x)^3*(c + d*x)^3),x]","\frac{1}{2} \left(\frac{a^3}{b (a+b x)^2 (b c-a d)^3}-\frac{6 a^2 c}{(a+b x) (b c-a d)^4}+\frac{c^3}{d (c+d x)^2 (a d-b c)^3}-\frac{6 a c^2}{(c+d x) (b c-a d)^4}-\frac{6 a c (a d+b c) \log (a+b x)}{(b c-a d)^5}+\frac{6 a c (a d+b c) \log (c+d x)}{(b c-a d)^5}\right)","\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^3/(b*(b*c - a*d)^3*(a + b*x)^2) - (6*a^2*c)/((b*c - a*d)^4*(a + b*x)) + c^3/(d*(-(b*c) + a*d)^3*(c + d*x)^2) - (6*a*c^2)/((b*c - a*d)^4*(c + d*x)) - (6*a*c*(b*c + a*d)*Log[a + b*x])/(b*c - a*d)^5 + (6*a*c*(b*c + a*d)*Log[c + d*x])/(b*c - a*d)^5)/2","A",1
314,1,168,180,0.2367903,"\int \frac{x^2}{(a+b x)^3 (c+d x)^3} \, dx","Integrate[x^2/((a + b*x)^3*(c + d*x)^3),x]","\frac{2 \left(a^2 d^2+4 a b c d+b^2 c^2\right) \log (a+b x)-2 \left(a^2 d^2+4 a b c d+b^2 c^2\right) \log (c+d x)-\frac{a^2 (b c-a d)^2}{(a+b x)^2}+\frac{c^2 (b c-a d)^2}{(c+d x)^2}+\frac{2 a (a d+2 b c) (b c-a d)}{a+b x}+\frac{2 c (2 a d+b c) (b c-a d)}{c+d x}}{2 (b c-a d)^5}","\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,"(-((a^2*(b*c - a*d)^2)/(a + b*x)^2) + (2*a*(b*c - a*d)*(2*b*c + a*d))/(a + b*x) + (c^2*(b*c - a*d)^2)/(c + d*x)^2 + (2*c*(b*c - a*d)*(b*c + 2*a*d))/(c + d*x) + 2*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*Log[a + b*x] - 2*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*Log[c + d*x])/(2*(b*c - a*d)^5)","A",1
315,1,142,157,0.2107208,"\int \frac{x}{(a+b x)^3 (c+d x)^3} \, dx","Integrate[x/((a + b*x)^3*(c + d*x)^3),x]","\frac{\frac{a b (b c-a d)^2}{(a+b x)^2}-\frac{c d (b c-a d)^2}{(c+d x)^2}-\frac{2 b (2 a d+b c) (b c-a d)}{a+b x}+\frac{2 d (a d-b c) (a d+2 b c)}{c+d x}-6 b d (a d+b c) \log (a+b x)+6 b d (a d+b c) \log (c+d x)}{2 (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*(b*c - a*d)^2)/(a + b*x)^2 - (2*b*(b*c - a*d)*(b*c + 2*a*d))/(a + b*x) - (c*d*(b*c - a*d)^2)/(c + d*x)^2 + (2*d*(-(b*c) + a*d)*(2*b*c + a*d))/(c + d*x) - 6*b*d*(b*c + a*d)*Log[a + b*x] + 6*b*d*(b*c + a*d)*Log[c + d*x])/(2*(b*c - a*d)^5)","A",1
316,1,128,143,0.1351102,"\int \frac{1}{(a+b x)^3 (c+d x)^3} \, dx","Integrate[1/((a + b*x)^3*(c + d*x)^3),x]","\frac{\frac{6 b^2 d (b c-a d)}{a+b x}-\frac{b^2 (b c-a d)^2}{(a+b x)^2}+12 b^2 d^2 \log (a+b x)+\frac{6 b d^2 (b c-a d)}{c+d x}+\frac{d^2 (b c-a d)^2}{(c+d x)^2}-12 b^2 d^2 \log (c+d x)}{2 (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^2*(b*c - a*d)^2)/(a + b*x)^2) + (6*b^2*d*(b*c - a*d))/(a + b*x) + (d^2*(b*c - a*d)^2)/(c + d*x)^2 + (6*b*d^2*(b*c - a*d))/(c + d*x) + 12*b^2*d^2*Log[a + b*x] - 12*b^2*d^2*Log[c + d*x])/(2*(b*c - a*d)^5)","A",1
317,1,218,221,0.4367056,"\int \frac{1}{x (a+b x)^3 (c+d x)^3} \, dx","Integrate[1/(x*(a + b*x)^3*(c + d*x)^3),x]","\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 (a d-b c)^5}-\frac{b^3}{2 a (a+b x)^2 (a d-b c)^3}+\frac{d^3 (a d-4 b c)}{c^2 (c+d x) (b c-a d)^4}-\frac{d^3}{2 c (c+d x)^2 (b c-a d)^3}","\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,"-1/2*b^3/(a*(-(b*c) + a*d)^3*(a + b*x)^2) + (b^3*(b*c - 4*a*d))/(a^2*(b*c - a*d)^4*(a + b*x)) - d^3/(2*c*(b*c - a*d)^3*(c + d*x)^2) + (d^3*(-4*b*c + a*d))/(c^2*(b*c - a*d)^4*(c + d*x)) + Log[x]/(a^3*c^3) + (b^3*(b^2*c^2 - 5*a*b*c*d + 10*a^2*d^2)*Log[a + b*x])/(a^3*(-(b*c) + a*d)^5) + (d^3*(10*b^2*c^2 - 5*a*b*c*d + a^2*d^2)*Log[c + d*x])/(c^3*(b*c - a*d)^5)","A",1
318,1,241,242,0.4399798,"\int \frac{1}{x^2 (a+b x)^3 (c+d x)^3} \, dx","Integrate[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{b^4 (5 a d-2 b c)}{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 (a d-b c)^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 (a d-b c)^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}","-\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,"-(1/(a^3*c^3*x)) + b^4/(2*a^2*(-(b*c) + a*d)^3*(a + b*x)^2) + (b^4*(-2*b*c + 5*a*d))/(a^3*(b*c - a*d)^4*(a + b*x)) + d^4/(2*c^2*(b*c - a*d)^3*(c + d*x)^2) + (d^4*(5*b*c - 2*a*d))/(c^3*(b*c - a*d)^4*(c + d*x)) - (3*(b*c + a*d)*Log[x])/(a^4*c^4) - (3*b^4*(b^2*c^2 - 4*a*b*c*d + 5*a^2*d^2)*Log[a + b*x])/(a^4*(-(b*c) + a*d)^5) - (3*d^4*(5*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*Log[c + d*x])/(c^4*(b*c - a*d)^5)","A",1
319,1,33,39,0.0206627,"\int x^{7/2} (a+b x) (A+B x) \, dx","Integrate[x^(7/2)*(a + b*x)*(A + B*x),x]","\frac{2 x^{9/2} (13 a (11 A+9 B x)+9 b x (13 A+11 B x))}{1287}","\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*x^(9/2)*(13*a*(11*A + 9*B*x) + 9*b*x*(13*A + 11*B*x)))/1287","A",1
320,1,33,39,0.0118829,"\int x^{5/2} (a+b x) (A+B x) \, dx","Integrate[x^(5/2)*(a + b*x)*(A + B*x),x]","\frac{2}{693} x^{7/2} (11 a (9 A+7 B x)+7 b x (11 A+9 B 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}",1,"(2*x^(7/2)*(11*a*(9*A + 7*B*x) + 7*b*x*(11*A + 9*B*x)))/693","A",1
321,1,33,39,0.0188027,"\int x^{3/2} (a+b x) (A+B x) \, dx","Integrate[x^(3/2)*(a + b*x)*(A + B*x),x]","\frac{2}{315} x^{5/2} (9 a (7 A+5 B x)+5 b x (9 A+7 B 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}",1,"(2*x^(5/2)*(9*a*(7*A + 5*B*x) + 5*b*x*(9*A + 7*B*x)))/315","A",1
322,1,33,39,0.015714,"\int \sqrt{x} (a+b x) (A+B x) \, dx","Integrate[Sqrt[x]*(a + b*x)*(A + B*x),x]","\frac{2}{105} x^{3/2} (7 a (5 A+3 B x)+3 b x (7 A+5 B 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}",1,"(2*x^(3/2)*(7*a*(5*A + 3*B*x) + 3*b*x*(7*A + 5*B*x)))/105","A",1
323,1,31,37,0.0192104,"\int \frac{(a+b x) (A+B x)}{\sqrt{x}} \, dx","Integrate[((a + b*x)*(A + B*x))/Sqrt[x],x]","\frac{2}{15} \sqrt{x} (5 a (3 A+B x)+b x (5 A+3 B x))","\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*Sqrt[x]*(5*a*(3*A + B*x) + b*x*(5*A + 3*B*x)))/15","A",1
324,1,29,35,0.014651,"\int \frac{(a+b x) (A+B x)}{x^{3/2}} \, dx","Integrate[((a + b*x)*(A + B*x))/x^(3/2),x]","\frac{2 (b x (3 A+B x)-3 a (A-B x))}{3 \sqrt{x}}","2 \sqrt{x} (a B+A b)-\frac{2 a A}{\sqrt{x}}+\frac{2}{3} b B x^{3/2}",1,"(2*(-3*a*(A - B*x) + b*x*(3*A + B*x)))/(3*Sqrt[x])","A",1
325,1,28,35,0.0113767,"\int \frac{(a+b x) (A+B x)}{x^{5/2}} \, dx","Integrate[((a + b*x)*(A + B*x))/x^(5/2),x]","-\frac{2 (a (A+3 B x)+3 b x (A-B x))}{3 x^{3/2}}","-\frac{2 (a B+A b)}{\sqrt{x}}-\frac{2 a A}{3 x^{3/2}}+2 b B \sqrt{x}",1,"(-2*(3*b*x*(A - B*x) + a*(A + 3*B*x)))/(3*x^(3/2))","A",1
326,1,30,37,0.0132905,"\int \frac{(a+b x) (A+B x)}{x^{7/2}} \, dx","Integrate[((a + b*x)*(A + B*x))/x^(7/2),x]","-\frac{2 (a (3 A+5 B x)+5 b x (A+3 B x))}{15 x^{5/2}}","-\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*(5*b*x*(A + 3*B*x) + a*(3*A + 5*B*x)))/(15*x^(5/2))","A",1
327,1,52,63,0.0210736,"\int x^{7/2} (a+b x)^2 (A+B x) \, dx","Integrate[x^(7/2)*(a + b*x)^2*(A + B*x),x]","\frac{2 x^{9/2} \left(65 a^2 (11 A+9 B x)+90 a b x (13 A+11 B x)+33 b^2 x^2 (15 A+13 B x)\right)}{6435}","\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*x^(9/2)*(65*a^2*(11*A + 9*B*x) + 90*a*b*x*(13*A + 11*B*x) + 33*b^2*x^2*(15*A + 13*B*x)))/6435","A",1
328,1,52,63,0.0237265,"\int x^{5/2} (a+b x)^2 (A+B x) \, dx","Integrate[x^(5/2)*(a + b*x)^2*(A + B*x),x]","\frac{2 x^{7/2} \left(143 a^2 (9 A+7 B x)+182 a b x (11 A+9 B x)+63 b^2 x^2 (13 A+11 B x)\right)}{9009}","\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*x^(7/2)*(143*a^2*(9*A + 7*B*x) + 182*a*b*x*(11*A + 9*B*x) + 63*b^2*x^2*(13*A + 11*B*x)))/9009","A",1
329,1,52,63,0.0273504,"\int x^{3/2} (a+b x)^2 (A+B x) \, dx","Integrate[x^(3/2)*(a + b*x)^2*(A + B*x),x]","\frac{2 x^{5/2} \left(99 a^2 (7 A+5 B x)+110 a b x (9 A+7 B x)+35 b^2 x^2 (11 A+9 B x)\right)}{3465}","\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*x^(5/2)*(99*a^2*(7*A + 5*B*x) + 110*a*b*x*(9*A + 7*B*x) + 35*b^2*x^2*(11*A + 9*B*x)))/3465","A",1
330,1,52,63,0.02237,"\int \sqrt{x} (a+b x)^2 (A+B x) \, dx","Integrate[Sqrt[x]*(a + b*x)^2*(A + B*x),x]","\frac{2}{315} x^{3/2} \left(21 a^2 (5 A+3 B x)+18 a b x (7 A+5 B x)+5 b^2 x^2 (9 A+7 B x)\right)","\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*x^(3/2)*(21*a^2*(5*A + 3*B*x) + 18*a*b*x*(7*A + 5*B*x) + 5*b^2*x^2*(9*A + 7*B*x)))/315","A",1
331,1,51,61,0.0244236,"\int \frac{(a+b x)^2 (A+B x)}{\sqrt{x}} \, dx","Integrate[((a + b*x)^2*(A + B*x))/Sqrt[x],x]","\frac{2}{105} \sqrt{x} \left(35 a^2 (3 A+B x)+14 a b x (5 A+3 B x)+3 b^2 x^2 (7 A+5 B x)\right)","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*Sqrt[x]*(35*a^2*(3*A + B*x) + 14*a*b*x*(5*A + 3*B*x) + 3*b^2*x^2*(7*A + 5*B*x)))/105","A",1
332,1,49,59,0.0233701,"\int \frac{(a+b x)^2 (A+B x)}{x^{3/2}} \, dx","Integrate[((a + b*x)^2*(A + B*x))/x^(3/2),x]","\frac{-30 a^2 (A-B x)+20 a b x (3 A+B x)+2 b^2 x^2 (5 A+3 B x)}{15 \sqrt{x}}","-\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,"(-30*a^2*(A - B*x) + 20*a*b*x*(3*A + B*x) + 2*b^2*x^2*(5*A + 3*B*x))/(15*Sqrt[x])","A",1
333,1,47,59,0.0190526,"\int \frac{(a+b x)^2 (A+B x)}{x^{5/2}} \, dx","Integrate[((a + b*x)^2*(A + B*x))/x^(5/2),x]","\frac{2 \left(-\left(a^2 (A+3 B x)\right)+6 a b x (B x-A)+b^2 x^2 (3 A+B x)\right)}{3 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*(6*a*b*x*(-A + B*x) + b^2*x^2*(3*A + B*x) - a^2*(A + 3*B*x)))/(3*x^(3/2))","A",1
334,1,47,59,0.0329312,"\int \frac{(a+b x)^2 (A+B x)}{x^{7/2}} \, dx","Integrate[((a + b*x)^2*(A + B*x))/x^(7/2),x]","-\frac{2 \left(a^2 (3 A+5 B x)+10 a b x (A+3 B x)+15 b^2 x^2 (A-B x)\right)}{15 x^{5/2}}","-\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*(15*b^2*x^2*(A - B*x) + 10*a*b*x*(A + 3*B*x) + a^2*(3*A + 5*B*x)))/(15*x^(5/2))","A",1
335,1,71,85,0.0412678,"\int x^{7/2} (a+b x)^3 (A+B x) \, dx","Integrate[x^(7/2)*(a + b*x)^3*(A + B*x),x]","\frac{2 x^{9/2} \left(1105 a^3 (11 A+9 B x)+2295 a^2 b x (13 A+11 B x)+1683 a b^2 x^2 (15 A+13 B x)+429 b^3 x^3 (17 A+15 B x)\right)}{109395}","\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*x^(9/2)*(1105*a^3*(11*A + 9*B*x) + 2295*a^2*b*x*(13*A + 11*B*x) + 1683*a*b^2*x^2*(15*A + 13*B*x) + 429*b^3*x^3*(17*A + 15*B*x)))/109395","A",1
336,1,71,85,0.0358454,"\int x^{5/2} (a+b x)^3 (A+B x) \, dx","Integrate[x^(5/2)*(a + b*x)^3*(A + B*x),x]","\frac{2 x^{7/2} \left(715 a^3 (9 A+7 B x)+1365 a^2 b x (11 A+9 B x)+945 a b^2 x^2 (13 A+11 B x)+231 b^3 x^3 (15 A+13 B x)\right)}{45045}","\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*x^(7/2)*(715*a^3*(9*A + 7*B*x) + 1365*a^2*b*x*(11*A + 9*B*x) + 945*a*b^2*x^2*(13*A + 11*B*x) + 231*b^3*x^3*(15*A + 13*B*x)))/45045","A",1
337,1,71,85,0.0331281,"\int x^{3/2} (a+b x)^3 (A+B x) \, dx","Integrate[x^(3/2)*(a + b*x)^3*(A + B*x),x]","\frac{2 x^{5/2} \left(429 a^3 (7 A+5 B x)+715 a^2 b x (9 A+7 B x)+455 a b^2 x^2 (11 A+9 B x)+105 b^3 x^3 (13 A+11 B x)\right)}{15015}","\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*x^(5/2)*(429*a^3*(7*A + 5*B*x) + 715*a^2*b*x*(9*A + 7*B*x) + 455*a*b^2*x^2*(11*A + 9*B*x) + 105*b^3*x^3*(13*A + 11*B*x)))/15015","A",1
338,1,71,85,0.0296202,"\int \sqrt{x} (a+b x)^3 (A+B x) \, dx","Integrate[Sqrt[x]*(a + b*x)^3*(A + B*x),x]","\frac{2 x^{3/2} \left(231 a^3 (5 A+3 B x)+297 a^2 b x (7 A+5 B x)+165 a b^2 x^2 (9 A+7 B x)+35 b^3 x^3 (11 A+9 B x)\right)}{3465}","\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*x^(3/2)*(231*a^3*(5*A + 3*B*x) + 297*a^2*b*x*(7*A + 5*B*x) + 165*a*b^2*x^2*(9*A + 7*B*x) + 35*b^3*x^3*(11*A + 9*B*x)))/3465","A",1
339,1,70,83,0.0350789,"\int \frac{(a+b x)^3 (A+B x)}{\sqrt{x}} \, dx","Integrate[((a + b*x)^3*(A + B*x))/Sqrt[x],x]","\frac{2}{315} \sqrt{x} \left(105 a^3 (3 A+B x)+63 a^2 b x (5 A+3 B x)+27 a b^2 x^2 (7 A+5 B x)+5 b^3 x^3 (9 A+7 B x)\right)","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*Sqrt[x]*(105*a^3*(3*A + B*x) + 63*a^2*b*x*(5*A + 3*B*x) + 27*a*b^2*x^2*(7*A + 5*B*x) + 5*b^3*x^3*(9*A + 7*B*x)))/315","A",1
340,1,67,79,0.028084,"\int \frac{(a+b x)^3 (A+B x)}{x^{3/2}} \, dx","Integrate[((a + b*x)^3*(A + B*x))/x^(3/2),x]","\frac{2 \left(-35 a^3 (A-B x)+35 a^2 b x (3 A+B x)+7 a b^2 x^2 (5 A+3 B x)+b^3 x^3 (7 A+5 B x)\right)}{35 \sqrt{x}}","-\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*(-35*a^3*(A - B*x) + 35*a^2*b*x*(3*A + B*x) + 7*a*b^2*x^2*(5*A + 3*B*x) + b^3*x^3*(7*A + 5*B*x)))/(35*Sqrt[x])","A",1
341,1,66,81,0.0372139,"\int \frac{(a+b x)^3 (A+B x)}{x^{5/2}} \, dx","Integrate[((a + b*x)^3*(A + B*x))/x^(5/2),x]","\frac{2 \left(-5 a^3 (A+3 B x)+45 a^2 b x (B x-A)+15 a b^2 x^2 (3 A+B x)+b^3 x^3 (5 A+3 B x)\right)}{15 x^{3/2}}","-\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*(45*a^2*b*x*(-A + B*x) + 15*a*b^2*x^2*(3*A + B*x) - 5*a^3*(A + 3*B*x) + b^3*x^3*(5*A + 3*B*x)))/(15*x^(3/2))","A",1
342,1,65,81,0.0336734,"\int \frac{(a+b x)^3 (A+B x)}{x^{7/2}} \, dx","Integrate[((a + b*x)^3*(A + B*x))/x^(7/2),x]","-\frac{2 \left(a^3 (3 A+5 B x)+15 a^2 b x (A+3 B x)+45 a b^2 x^2 (A-B x)-5 b^3 x^3 (3 A+B x)\right)}{15 x^{5/2}}","-\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*(45*a*b^2*x^2*(A - B*x) - 5*b^3*x^3*(3*A + B*x) + 15*a^2*b*x*(A + 3*B*x) + a^3*(3*A + 5*B*x)))/(15*x^(5/2))","A",1
343,1,38,44,0.0195333,"\int \frac{(2-3 x)^3 \sqrt{x}}{(1+x)^2} \, dx","Integrate[((2 - 3*x)^3*Sqrt[x])/(1 + x)^2,x]","575 \tan ^{-1}\left(\sqrt{x}\right)-\frac{\sqrt{x} \left(54 x^3-306 x^2+1890 x+2875\right)}{5 (x+1)}","-\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,"-1/5*(Sqrt[x]*(2875 + 1890*x - 306*x^2 + 54*x^3))/(1 + x) + 575*ArcTan[Sqrt[x]]","A",1
344,1,120,136,0.1252039,"\int \frac{x^{7/2} (A+B x)}{a+b x} \, dx","Integrate[(x^(7/2)*(A + B*x))/(a + b*x),x]","\frac{2 \sqrt{x} \left(315 a^4 B-105 a^3 b (3 A+B x)+21 a^2 b^2 x (5 A+3 B x)-9 a b^3 x^2 (7 A+5 B x)+5 b^4 x^3 (9 A+7 B x)\right)}{315 b^5}-\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^{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*Sqrt[x]*(315*a^4*B - 105*a^3*b*(3*A + B*x) + 21*a^2*b^2*x*(5*A + 3*B*x) - 9*a*b^3*x^2*(7*A + 5*B*x) + 5*b^4*x^3*(9*A + 7*B*x)))/(315*b^5) - (2*a^(7/2)*(-(A*b) + a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(11/2)","A",1
345,1,101,113,0.0796414,"\int \frac{x^{5/2} (A+B x)}{a+b x} \, dx","Integrate[(x^(5/2)*(A + B*x))/(a + b*x),x]","\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 \sqrt{x} \left(-105 a^3 B+35 a^2 b (3 A+B x)-7 a b^2 x (5 A+3 B x)+3 b^3 x^2 (7 A+5 B x)\right)}{105 b^4}","-\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*Sqrt[x]*(-105*a^3*B + 35*a^2*b*(3*A + B*x) - 7*a*b^2*x*(5*A + 3*B*x) + 3*b^3*x^2*(7*A + 5*B*x)))/(105*b^4) + (2*a^(5/2)*(-(A*b) + a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(9/2)","A",1
346,1,81,90,0.0816432,"\int \frac{x^{3/2} (A+B x)}{a+b x} \, dx","Integrate[(x^(3/2)*(A + B*x))/(a + b*x),x]","\frac{2 \sqrt{x} \left(15 a^2 B-5 a b (3 A+B x)+b^2 x (5 A+3 B x)\right)}{15 b^3}-\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^{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*Sqrt[x]*(15*a^2*B - 5*a*b*(3*A + B*x) + b^2*x*(5*A + 3*B*x)))/(15*b^3) - (2*a^(3/2)*(-(A*b) + a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(7/2)","A",1
347,1,63,69,0.0408584,"\int \frac{\sqrt{x} (A+B x)}{a+b x} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(a + b*x),x]","\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} (-3 a B+3 A b+b B x)}{3 b^2}","-\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*Sqrt[x]*(3*A*b - 3*a*B + b*B*x))/(3*b^2) + (2*Sqrt[a]*(-(A*b) + a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(5/2)","A",1
348,1,49,49,0.038285,"\int \frac{A+B x}{\sqrt{x} (a+b x)} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(a + b*x)),x]","\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}","\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
349,1,49,49,0.0443187,"\int \frac{A+B x}{x^{3/2} (a+b x)} \, dx","Integrate[(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
350,1,43,69,0.0141806,"\int \frac{A+B x}{x^{5/2} (a+b x)} \, dx","Integrate[(A + B*x)/(x^(5/2)*(a + b*x)),x]","\frac{6 x (A b-a B) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{b x}{a}\right)-2 a A}{3 a^2 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*A + 6*(A*b - a*B)*x*Hypergeometric2F1[-1/2, 1, 1/2, -((b*x)/a)])/(3*a^2*x^(3/2))","C",1
351,1,44,90,0.0204522,"\int \frac{A+B x}{x^{7/2} (a+b x)} \, dx","Integrate[(A + B*x)/(x^(7/2)*(a + b*x)),x]","-\frac{2 \left(\, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{b x}{a}\right) (5 a B x-5 A b x)+3 a A\right)}{15 a^2 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*(3*a*A + (-5*A*b*x + 5*a*B*x)*Hypergeometric2F1[-3/2, 1, -1/2, -((b*x)/a)]))/(15*a^2*x^(5/2))","C",1
352,1,44,113,0.0227846,"\int \frac{A+B x}{x^{9/2} (a+b x)} \, dx","Integrate[(A + B*x)/(x^(9/2)*(a + b*x)),x]","-\frac{2 \left(\, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};-\frac{b x}{a}\right) (7 a B x-7 A b x)+5 a A\right)}{35 a^2 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*(5*a*A + (-7*A*b*x + 7*a*B*x)*Hypergeometric2F1[-5/2, 1, -3/2, -((b*x)/a)]))/(35*a^2*x^(7/2))","C",1
353,1,44,136,0.0189044,"\int \frac{A+B x}{x^{11/2} (a+b x)} \, dx","Integrate[(A + B*x)/(x^(11/2)*(a + b*x)),x]","-\frac{2 \left(\, _2F_1\left(-\frac{7}{2},1;-\frac{5}{2};-\frac{b x}{a}\right) (9 a B x-9 A b x)+7 a A\right)}{63 a^2 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*(7*a*A + (-9*A*b*x + 9*a*B*x)*Hypergeometric2F1[-7/2, 1, -5/2, -((b*x)/a)]))/(63*a^2*x^(9/2))","C",1
354,1,128,154,0.1141276,"\int \frac{x^{7/2} (A+B x)}{(a+b x)^2} \, dx","Integrate[(x^(7/2)*(A + B*x))/(a + b*x)^2,x]","\frac{a^{5/2} (9 a B-7 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{11/2}}+\frac{\sqrt{x} \left(-945 a^4 B+105 a^3 b (7 A-6 B x)+14 a^2 b^2 x (35 A+9 B x)-2 a b^3 x^2 (49 A+27 B x)+6 b^4 x^3 (7 A+5 B x)\right)}{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,"(Sqrt[x]*(-945*a^4*B + 105*a^3*b*(7*A - 6*B*x) + 6*b^4*x^3*(7*A + 5*B*x) + 14*a^2*b^2*x*(35*A + 9*B*x) - 2*a*b^3*x^2*(49*A + 27*B*x)))/(105*b^5*(a + b*x)) + (a^(5/2)*(-7*A*b + 9*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(11/2)","A",1
355,1,110,130,0.0972187,"\int \frac{x^{5/2} (A+B x)}{(a+b x)^2} \, dx","Integrate[(x^(5/2)*(A + B*x))/(a + b*x)^2,x]","\frac{\sqrt{x} \left(105 a^3 B+a^2 (70 b B x-75 A b)-2 a b^2 x (25 A+7 B x)+2 b^3 x^2 (5 A+3 B x)\right)}{15 b^4 (a+b x)}-\frac{a^{3/2} (7 a B-5 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{9/2}}","\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,"(Sqrt[x]*(105*a^3*B + 2*b^3*x^2*(5*A + 3*B*x) - 2*a*b^2*x*(25*A + 7*B*x) + a^2*(-75*A*b + 70*b*B*x)))/(15*b^4*(a + b*x)) - (a^(3/2)*(-5*A*b + 7*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(9/2)","A",1
356,1,88,108,0.0835027,"\int \frac{x^{3/2} (A+B x)}{(a+b x)^2} \, dx","Integrate[(x^(3/2)*(A + B*x))/(a + b*x)^2,x]","\frac{\sqrt{x} \left(-15 a^2 B+a b (9 A-10 B x)+2 b^2 x (3 A+B x)\right)}{3 b^3 (a+b x)}+\frac{\sqrt{a} (5 a B-3 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}","-\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,"(Sqrt[x]*(-15*a^2*B + a*b*(9*A - 10*B*x) + 2*b^2*x*(3*A + B*x)))/(3*b^3*(a + b*x)) + (Sqrt[a]*(-3*A*b + 5*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(7/2)","A",1
357,1,67,85,0.0592904,"\int \frac{\sqrt{x} (A+B x)}{(a+b x)^2} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(a + b*x)^2,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} (3 a B-A b+2 b B x)}{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,"(Sqrt[x]*(-(A*b) + 3*a*B + 2*b*B*x))/(b^2*(a + b*x)) + ((A*b - 3*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[a]*b^(5/2))","A",1
358,1,63,63,0.044832,"\int \frac{A+B x}{\sqrt{x} (a+b x)^2} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(a + b*x)^2),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)}","\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*b - a*B)*Sqrt[x])/(a*b*(a + b*x)) + ((A*b + a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(a^(3/2)*b^(3/2))","A",1
359,1,59,88,0.0227544,"\int \frac{A+B x}{x^{3/2} (a+b x)^2} \, dx","Integrate[(A + B*x)/(x^(3/2)*(a + b*x)^2),x]","\frac{(a+b x) (a B-3 A b) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{b x}{a}\right)+a (A b-a B)}{a^2 b \sqrt{x} (a+b x)}","-\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,"(a*(A*b - a*B) + (-3*A*b + a*B)*(a + b*x)*Hypergeometric2F1[-1/2, 1, 1/2, -((b*x)/a)])/(a^2*b*Sqrt[x]*(a + b*x))","C",1
360,1,64,107,0.0239715,"\int \frac{A+B x}{x^{5/2} (a+b x)^2} \, dx","Integrate[(A + B*x)/(x^(5/2)*(a + b*x)^2),x]","\frac{(a+b x) (3 a B-5 A b) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{b x}{a}\right)+3 a (A b-a B)}{3 a^2 b x^{3/2} (a+b x)}","\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,"(3*a*(A*b - a*B) + (-5*A*b + 3*a*B)*(a + b*x)*Hypergeometric2F1[-3/2, 1, -1/2, -((b*x)/a)])/(3*a^2*b*x^(3/2)*(a + b*x))","C",1
361,1,64,131,0.028744,"\int \frac{A+B x}{x^{7/2} (a+b x)^2} \, dx","Integrate[(A + B*x)/(x^(7/2)*(a + b*x)^2),x]","\frac{(a+b x) (5 a B-7 A b) \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};-\frac{b x}{a}\right)+5 a (A b-a B)}{5 a^2 b x^{5/2} (a+b x)}","-\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,"(5*a*(A*b - a*B) + (-7*A*b + 5*a*B)*(a + b*x)*Hypergeometric2F1[-5/2, 1, -3/2, -((b*x)/a)])/(5*a^2*b*x^(5/2)*(a + b*x))","C",1
362,1,64,153,0.0234769,"\int \frac{A+B x}{x^{9/2} (a+b x)^2} \, dx","Integrate[(A + B*x)/(x^(9/2)*(a + b*x)^2),x]","\frac{(a+b x) (7 a B-9 A b) \, _2F_1\left(-\frac{7}{2},1;-\frac{5}{2};-\frac{b x}{a}\right)+7 a (A b-a B)}{7 a^2 b x^{7/2} (a+b x)}","\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,"(7*a*(A*b - a*B) + (-9*A*b + 7*a*B)*(a + b*x)*Hypergeometric2F1[-7/2, 1, -5/2, -((b*x)/a)])/(7*a^2*b*x^(7/2)*(a + b*x))","C",1
363,1,61,169,0.0331542,"\int \frac{x^{7/2} (A+B x)}{(a+b x)^3} \, dx","Integrate[(x^(7/2)*(A + B*x))/(a + b*x)^3,x]","\frac{x^{9/2} \left(\frac{9 a^2 (A b-a B)}{(a+b x)^2}+(9 a B-5 A b) \, _2F_1\left(2,\frac{9}{2};\frac{11}{2};-\frac{b x}{a}\right)\right)}{18 a^3 b}","\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,"(x^(9/2)*((9*a^2*(A*b - a*B))/(a + b*x)^2 + (-5*A*b + 9*a*B)*Hypergeometric2F1[2, 9/2, 11/2, -((b*x)/a)]))/(18*a^3*b)","C",1
364,1,61,147,0.0290838,"\int \frac{x^{5/2} (A+B x)}{(a+b x)^3} \, dx","Integrate[(x^(5/2)*(A + B*x))/(a + b*x)^3,x]","\frac{x^{7/2} \left(\frac{7 a^2 (A b-a B)}{(a+b x)^2}+(7 a B-3 A b) \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};-\frac{b x}{a}\right)\right)}{14 a^3 b}","-\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,"(x^(7/2)*((7*a^2*(A*b - a*B))/(a + b*x)^2 + (-3*A*b + 7*a*B)*Hypergeometric2F1[2, 7/2, 9/2, -((b*x)/a)]))/(14*a^3*b)","C",1
365,1,61,123,0.0301448,"\int \frac{x^{3/2} (A+B x)}{(a+b x)^3} \, dx","Integrate[(x^(3/2)*(A + B*x))/(a + b*x)^3,x]","\frac{x^{5/2} \left(\frac{5 a^2 (A b-a B)}{(a+b x)^2}+(5 a B-A b) \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};-\frac{b x}{a}\right)\right)}{10 a^3 b}","\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,"(x^(5/2)*((5*a^2*(A*b - a*B))/(a + b*x)^2 + (-(A*b) + 5*a*B)*Hypergeometric2F1[2, 5/2, 7/2, -((b*x)/a)]))/(10*a^3*b)","C",1
366,1,85,100,0.0981655,"\int \frac{\sqrt{x} (A+B x)}{(a+b x)^3} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(a + b*x)^3,x]","\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} \left(-3 a^2 B-a b (A+5 B x)+A b^2 x\right)}{4 a b^2 (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]*(-3*a^2*B + A*b^2*x - a*b*(A + 5*B*x)))/(4*a*b^2*(a + b*x)^2) + ((A*b + 3*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(3/2)*b^(5/2))","A",1
367,1,91,100,0.1394525,"\int \frac{A+B x}{\sqrt{x} (a+b x)^3} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(a + b*x)^3),x]","\frac{\sqrt{x} \left(\frac{a^2 (A b-a B)}{(a+b x)^2}-\frac{1}{2} (-a B-3 A b) \left(\frac{a}{a+b x}+\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{b} \sqrt{x}}\right)\right)}{2 a^3 b}","\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]*((a^2*(A*b - a*B))/(a + b*x)^2 - ((-3*A*b - a*B)*(a/(a + b*x) + (Sqrt[a]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[b]*Sqrt[x])))/2))/(2*a^3*b)","A",1
368,1,59,126,0.0293619,"\int \frac{A+B x}{x^{3/2} (a+b x)^3} \, dx","Integrate[(A + B*x)/(x^(3/2)*(a + b*x)^3),x]","\frac{\frac{a^2 (A b-a B)}{(a+b x)^2}+(a B-5 A b) \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};-\frac{b x}{a}\right)}{2 a^3 b \sqrt{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,"((a^2*(A*b - a*B))/(a + b*x)^2 + (-5*A*b + a*B)*Hypergeometric2F1[-1/2, 2, 1/2, -((b*x)/a)])/(2*a^3*b*Sqrt[x])","C",1
369,1,61,147,0.0321715,"\int \frac{A+B x}{x^{5/2} (a+b x)^3} \, dx","Integrate[(A + B*x)/(x^(5/2)*(a + b*x)^3),x]","\frac{\frac{3 a^2 (A b-a B)}{(a+b x)^2}+(3 a B-7 A b) \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};-\frac{b x}{a}\right)}{6 a^3 b x^{3/2}}","\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,"((3*a^2*(A*b - a*B))/(a + b*x)^2 + (-7*A*b + 3*a*B)*Hypergeometric2F1[-3/2, 2, -1/2, -((b*x)/a)])/(6*a^3*b*x^(3/2))","C",1
370,1,61,169,0.034511,"\int \frac{A+B x}{x^{7/2} (a+b x)^3} \, dx","Integrate[(A + B*x)/(x^(7/2)*(a + b*x)^3),x]","\frac{\frac{5 a^2 (A b-a B)}{(a+b x)^2}+(5 a B-9 A b) \, _2F_1\left(-\frac{5}{2},2;-\frac{3}{2};-\frac{b x}{a}\right)}{10 a^3 b x^{5/2}}","-\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,"((5*a^2*(A*b - a*B))/(a + b*x)^2 + (-9*A*b + 5*a*B)*Hypergeometric2F1[-5/2, 2, -3/2, -((b*x)/a)])/(10*a^3*b*x^(5/2))","C",1
371,1,103,125,0.2007631,"\int x^m (a+b x)^4 (A+B x) \, dx","Integrate[x^m*(a + b*x)^4*(A + B*x),x]","\frac{x^{m+1} \left(\left(\frac{a^4}{m+1}+\frac{4 a^3 b x}{m+2}+\frac{6 a^2 b^2 x^2}{m+3}+\frac{4 a b^3 x^3}{m+4}+\frac{b^4 x^4}{m+5}\right) (A b (m+6)-a B (m+1))+B (a+b x)^5\right)}{b (m+6)}","\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,"(x^(1 + m)*(B*(a + b*x)^5 + (-(a*B*(1 + m)) + A*b*(6 + m))*(a^4/(1 + m) + (4*a^3*b*x)/(2 + m) + (6*a^2*b^2*x^2)/(3 + m) + (4*a*b^3*x^3)/(4 + m) + (b^4*x^4)/(5 + m))))/(b*(6 + m))","A",1
372,1,87,96,0.1401451,"\int x^m (a+b x)^3 (A+B x) \, dx","Integrate[x^m*(a + b*x)^3*(A + B*x),x]","\frac{x^{m+1} \left(\left(\frac{a^3}{m+1}+\frac{3 a^2 b x}{m+2}+\frac{3 a b^2 x^2}{m+3}+\frac{b^3 x^3}{m+4}\right) (A b (m+5)-a B (m+1))+B (a+b x)^4\right)}{b (m+5)}","\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,"(x^(1 + m)*(B*(a + b*x)^4 + (-(a*B*(1 + m)) + A*b*(5 + m))*(a^3/(1 + m) + (3*a^2*b*x)/(2 + m) + (3*a*b^2*x^2)/(3 + m) + (b^3*x^3)/(4 + m))))/(b*(5 + m))","A",1
373,1,71,71,0.1238904,"\int x^m (a+b x)^2 (A+B x) \, dx","Integrate[x^m*(a + b*x)^2*(A + B*x),x]","\frac{x^{m+1} \left(\left(\frac{a^2}{m+1}+\frac{2 a b x}{m+2}+\frac{b^2 x^2}{m+3}\right) (A b (m+4)-a B (m+1))+B (a+b x)^3\right)}{b (m+4)}","\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,"(x^(1 + m)*(B*(a + b*x)^3 + (-(a*B*(1 + m)) + A*b*(4 + m))*(a^2/(1 + m) + (2*a*b*x)/(2 + m) + (b^2*x^2)/(3 + m))))/(b*(4 + m))","A",1
374,1,57,45,0.0629103,"\int x^m (a+b x) (A+B x) \, dx","Integrate[x^m*(a + b*x)*(A + B*x),x]","\frac{x^{m+1} (a (m+3) (A (m+2)+B (m+1) x)+b (m+1) x (A (m+3)+B (m+2) x))}{(m+1) (m+2) (m+3)}","\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,"(x^(1 + m)*(a*(3 + m)*(A*(2 + m) + B*(1 + m)*x) + b*(1 + m)*x*(A*(3 + m) + B*(2 + m)*x)))/((1 + m)*(2 + m)*(3 + m))","A",1
375,1,45,56,0.0244291,"\int \frac{x^m (A+B x)}{a+b x} \, dx","Integrate[(x^m*(A + B*x))/(a + b*x),x]","\frac{x^{m+1} \left((A b-a B) \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)+a B\right)}{a b (m+1)}","\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,"(x^(1 + m)*(a*B + (A*b - a*B)*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*x)/a)]))/(a*b*(1 + m))","A",1
376,1,63,73,0.0549572,"\int \frac{x^m (A+B x)}{(a+b x)^2} \, dx","Integrate[(x^m*(A + B*x))/(a + b*x)^2,x]","\frac{x^{m+1} \left(\frac{(a B (m+1)-A b m) \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{m+1}+\frac{a (A b-a B)}{a+b x}\right)}{a^2 b}","\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,"(x^(1 + m)*((a*(A*b - a*B))/(a + b*x) + ((-(A*b*m) + a*B*(1 + m))*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*x)/a)])/(1 + m)))/(a^2*b)","A",1
377,1,71,81,0.0352467,"\int \frac{x^m (A+B x)}{(a+b x)^3} \, dx","Integrate[(x^m*(A + B*x))/(a + b*x)^3,x]","\frac{x^{m+1} \left(\frac{a^2 (A b-a B)}{(a+b x)^2}-\frac{(A b (m-1)-a B (m+1)) \, _2F_1\left(2,m+1;m+2;-\frac{b x}{a}\right)}{m+1}\right)}{2 a^3 b}","\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,"(x^(1 + m)*((a^2*(A*b - a*B))/(a + b*x)^2 - ((A*b*(-1 + m) - a*B*(1 + m))*Hypergeometric2F1[2, 1 + m, 2 + m, -((b*x)/a)])/(1 + m)))/(2*a^3*b)","A",1
378,1,216,231,0.285331,"\int x^m (a+b x)^2 (c+d x)^5 \, dx","Integrate[x^m*(a + b*x)^2*(c + d*x)^5,x]","x^{m+1} \left(\frac{5 c d^2 x^4 \left(a^2 d^2+4 a b c d+2 b^2 c^2\right)}{m+5}+\frac{5 c^2 d x^3 \left(2 a^2 d^2+4 a b c d+b^2 c^2\right)}{m+4}+\frac{d^3 x^5 \left(a^2 d^2+10 a b c d+10 b^2 c^2\right)}{m+6}+\frac{c^3 x^2 \left(10 a^2 d^2+10 a b c d+b^2 c^2\right)}{m+3}+\frac{a^2 c^5}{m+1}+\frac{a c^4 x (5 a d+2 b c)}{m+2}+\frac{b d^4 x^6 (2 a d+5 b c)}{m+7}+\frac{b^2 d^5 x^7}{m+8}\right)","\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,"x^(1 + m)*((a^2*c^5)/(1 + m) + (a*c^4*(2*b*c + 5*a*d)*x)/(2 + m) + (c^3*(b^2*c^2 + 10*a*b*c*d + 10*a^2*d^2)*x^2)/(3 + m) + (5*c^2*d*(b^2*c^2 + 4*a*b*c*d + 2*a^2*d^2)*x^3)/(4 + m) + (5*c*d^2*(2*b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^4)/(5 + m) + (d^3*(10*b^2*c^2 + 10*a*b*c*d + a^2*d^2)*x^5)/(6 + m) + (b*d^4*(5*b*c + 2*a*d)*x^6)/(7 + m) + (b^2*d^5*x^7)/(8 + m))","A",1
379,1,118,127,0.2452522,"\int \frac{x^m (c+d x)^3}{a+b x} \, dx","Integrate[(x^m*(c + d*x)^3)/(a + b*x),x]","\frac{x^{m+1} \left(d \left(\frac{a^2 d^2}{m+1}+a b d \left(-\frac{3 c}{m+1}-\frac{d x}{m+2}\right)+b^2 \left(\frac{3 c^2}{m+1}+\frac{3 c d x}{m+2}+\frac{d^2 x^2}{m+3}\right)\right)+\frac{(b c-a d)^3 \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{a (m+1)}\right)}{b^3}","\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,"(x^(1 + m)*(d*((a^2*d^2)/(1 + m) + a*b*d*((-3*c)/(1 + m) - (d*x)/(2 + m)) + b^2*((3*c^2)/(1 + m) + (3*c*d*x)/(2 + m) + (d^2*x^2)/(3 + m))) + ((b*c - a*d)^3*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*x)/a)])/(a*(1 + m))))/b^3","A",1
380,1,77,99,0.0923136,"\int \frac{x^m (c+d x)^2}{a+b x} \, dx","Integrate[(x^m*(c + d*x)^2)/(a + b*x),x]","\frac{x^{m+1} \left((m+2) (b c-a d)^2 \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)+a d (-a d (m+2)+2 b c (m+2)+b d (m+1) x)\right)}{a b^2 (m+1) (m+2)}","\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,"(x^(1 + m)*(a*d*(2*b*c*(2 + m) - a*d*(2 + m) + b*d*(1 + m)*x) + (b*c - a*d)^2*(2 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*x)/a)]))/(a*b^2*(1 + m)*(2 + m))","A",1
381,1,45,56,0.0283239,"\int \frac{x^m (c+d x)}{a+b x} \, dx","Integrate[(x^m*(c + d*x))/(a + b*x),x]","\frac{x^{m+1} \left((b c-a d) \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)+a d\right)}{a b (m+1)}","\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,"(x^(1 + m)*(a*d + (b*c - a*d)*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*x)/a)]))/(a*b*(1 + m))","A",1
382,1,65,82,0.0196847,"\int \frac{x^m}{(a+b x) (c+d x)} \, dx","Integrate[x^m/((a + b*x)*(c + d*x)),x]","\frac{x^{m+1} \left(a d \, _2F_1\left(1,m+1;m+2;-\frac{d x}{c}\right)-b c \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)\right)}{a c (m+1) (a d-b c)}","\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,"(x^(1 + m)*(-(b*c*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*x)/a)]) + a*d*Hypergeometric2F1[1, 1 + m, 2 + m, -((d*x)/c)]))/(a*c*(-(b*c) + a*d)*(1 + m))","A",1
383,1,113,125,0.1023605,"\int \frac{x^m}{(a+b x) (c+d x)^2} \, dx","Integrate[x^m/((a + b*x)*(c + d*x)^2),x]","\frac{x^{m+1} \left(b^2 c^2 (c+d x) \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)+a d \left((c+d x) (b c (m-1)-a d m) \, _2F_1\left(1,m+1;m+2;-\frac{d x}{c}\right)-c (m+1) (b c-a d)\right)\right)}{a c^2 (m+1) (c+d x) (b c-a d)^2}","\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,"(x^(1 + m)*(b^2*c^2*(c + d*x)*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*x)/a)] + a*d*(-(c*(b*c - a*d)*(1 + m)) + (b*c*(-1 + m) - a*d*m)*(c + d*x)*Hypergeometric2F1[1, 1 + m, 2 + m, -((d*x)/c)])))/(a*c^2*(b*c - a*d)^2*(1 + m)*(c + d*x))","A",1
384,1,169,206,0.2742432,"\int \frac{x^m}{(a+b x) (c+d x)^3} \, dx","Integrate[x^m/((a + b*x)*(c + d*x)^3),x]","\frac{x^{m+1} \left(\frac{a d \left(a^2 d^2 (m-1) m-2 a b c d (m-2) 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 b^3 c^3 \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{a c^2 (m+1) (b c-a d)^2}+\frac{d (a d (m-1)-b c (m-3))}{c (c+d x) (b c-a d)}+\frac{d}{(c+d x)^2}\right)}{2 c (a d-b c)}","\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,"(x^(1 + m)*(d/(c + d*x)^2 + (d*(-(b*c*(-3 + m)) + a*d*(-1 + m)))/(c*(b*c - a*d)*(c + d*x)) + (-2*b^3*c^3*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*x)/a)] + a*d*(-2*a*b*c*d*(-2 + m)*m + a^2*d^2*(-1 + m)*m + b^2*c^2*(2 - 3*m + m^2))*Hypergeometric2F1[1, 1 + m, 2 + m, -((d*x)/c)])/(a*c^2*(b*c - a*d)^2*(1 + m))))/(2*c*(-(b*c) + a*d))","A",1
385,1,38,36,0.0183885,"\int \frac{b^2 x^m}{\left(b+a x^2\right)^2} \, dx","Integrate[(b^2*x^m)/(b + a*x^2)^2,x]","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+1}{2}+1;-\frac{a x^2}{b}\right)}{m+1}","\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,"(x^(1 + m)*Hypergeometric2F1[2, (1 + m)/2, 1 + (1 + m)/2, -((a*x^2)/b)])/(1 + m)","A",1
386,1,38,36,0.0101334,"\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","Integrate[x^m/((1 - (Sqrt[a]*x)/Sqrt[-b])^2*(1 + (Sqrt[a]*x)/Sqrt[-b])^2),x]","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+1}{2}+1;-\frac{a x^2}{b}\right)}{m+1}","\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,"(x^(1 + m)*Hypergeometric2F1[2, (1 + m)/2, 1 + (1 + m)/2, -((a*x^2)/b)])/(1 + m)","A",1
387,1,106,151,0.1237194,"\int x^4 \sqrt{a+b x} (A+B x) \, dx","Integrate[x^4*Sqrt[a + b*x]*(A + B*x),x]","\frac{2 (a+b x)^{3/2} \left(-1280 a^5 B+128 a^4 b (13 A+15 B x)-96 a^3 b^2 x (26 A+25 B x)+80 a^2 b^3 x^2 (39 A+35 B x)-70 a b^4 x^3 (52 A+45 B x)+315 b^5 x^4 (13 A+11 B x)\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*(a + b*x)^(3/2)*(-1280*a^5*B + 315*b^5*x^4*(13*A + 11*B*x) + 128*a^4*b*(13*A + 15*B*x) - 96*a^3*b^2*x*(26*A + 25*B*x) + 80*a^2*b^3*x^2*(39*A + 35*B*x) - 70*a*b^4*x^3*(52*A + 45*B*x)))/(45045*b^6)","A",1
388,1,87,122,0.0905849,"\int x^3 \sqrt{a+b x} (A+B x) \, dx","Integrate[x^3*Sqrt[a + b*x]*(A + B*x),x]","\frac{2 (a+b x)^{3/2} \left(128 a^4 B-16 a^3 b (11 A+12 B x)+24 a^2 b^2 x (11 A+10 B x)-10 a b^3 x^2 (33 A+28 B x)+35 b^4 x^3 (11 A+9 B x)\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*(a + b*x)^(3/2)*(128*a^4*B + 35*b^4*x^3*(11*A + 9*B*x) + 24*a^2*b^2*x*(11*A + 10*B*x) - 16*a^3*b*(11*A + 12*B*x) - 10*a*b^3*x^2*(33*A + 28*B*x)))/(3465*b^5)","A",1
389,1,65,95,0.0718251,"\int x^2 \sqrt{a+b x} (A+B x) \, dx","Integrate[x^2*Sqrt[a + b*x]*(A + B*x),x]","\frac{2 (a+b x)^{3/2} \left(-16 a^3 B+24 a^2 b (A+B x)-6 a b^2 x (6 A+5 B x)+5 b^3 x^2 (9 A+7 B x)\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*(a + b*x)^(3/2)*(-16*a^3*B + 24*a^2*b*(A + B*x) - 6*a*b^2*x*(6*A + 5*B*x) + 5*b^3*x^2*(9*A + 7*B*x)))/(315*b^4)","A",1
390,1,49,67,0.0517977,"\int x \sqrt{a+b x} (A+B x) \, dx","Integrate[x*Sqrt[a + b*x]*(A + B*x),x]","\frac{2 (a+b x)^{3/2} \left(8 a^2 B-2 a b (7 A+6 B x)+3 b^2 x (7 A+5 B x)\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*(a + b*x)^(3/2)*(8*a^2*B + 3*b^2*x*(7*A + 5*B*x) - 2*a*b*(7*A + 6*B*x)))/(105*b^3)","A",1
391,1,30,42,0.0288907,"\int \sqrt{a+b x} (A+B x) \, dx","Integrate[Sqrt[a + b*x]*(A + B*x),x]","\frac{2 (a+b x)^{3/2} (-2 a B+5 A b+3 b B x)}{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*(a + b*x)^(3/2)*(5*A*b - 2*a*B + 3*b*B*x))/(15*b^2)","A",1
392,1,55,54,0.069432,"\int \frac{\sqrt{a+b x} (A+B x)}{x} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/x,x]","A \left(2 \sqrt{a+b x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)\right)+\frac{2 B (a+b x)^{3/2}}{3 b}","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*B*(a + b*x)^(3/2))/(3*b) + A*(2*Sqrt[a + b*x] - 2*Sqrt[a]*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])","A",1
393,1,53,71,0.0432231,"\int \frac{\sqrt{a+b x} (A+B x)}{x^2} \, dx","Integrate[(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
394,1,81,82,0.0829792,"\int \frac{\sqrt{a+b x} (A+B x)}{x^3} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/x^3,x]","\frac{-b x^2 \sqrt{\frac{b x}{a}+1} (4 a B-A b) \tanh ^{-1}\left(\sqrt{\frac{b x}{a}+1}\right)-(a+b x) (2 a (A+2 B x)+A b x)}{4 a x^2 \sqrt{a+b x}}","\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,"(-((a + b*x)*(A*b*x + 2*a*(A + 2*B*x))) - b*(-(A*b) + 4*a*B)*x^2*Sqrt[1 + (b*x)/a]*ArcTanh[Sqrt[1 + (b*x)/a]])/(4*a*x^2*Sqrt[a + b*x])","A",1
395,1,57,112,0.0296546,"\int \frac{\sqrt{a+b x} (A+B x)}{x^4} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/x^4,x]","-\frac{(a+b x)^{3/2} \left(a^3 A+b^2 x^3 (2 a B-A b) \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{b x}{a}+1\right)\right)}{3 a^4 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,"-1/3*((a + b*x)^(3/2)*(a^3*A + b^2*(-(A*b) + 2*a*B)*x^3*Hypergeometric2F1[3/2, 3, 5/2, 1 + (b*x)/a]))/(a^4*x^3)","C",1
396,1,58,146,0.0261566,"\int \frac{\sqrt{a+b x} (A+B x)}{x^5} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/x^5,x]","-\frac{(a+b x)^{3/2} \left(3 a^4 A+b^3 x^4 (5 A b-8 a B) \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};\frac{b x}{a}+1\right)\right)}{12 a^5 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,"-1/12*((a + b*x)^(3/2)*(3*a^4*A + b^3*(5*A*b - 8*a*B)*x^4*Hypergeometric2F1[3/2, 4, 5/2, 1 + (b*x)/a]))/(a^5*x^4)","C",1
397,1,58,177,0.0250186,"\int \frac{\sqrt{a+b x} (A+B x)}{x^6} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/x^6,x]","-\frac{(a+b x)^{3/2} \left(3 a^5 A+b^4 x^5 (10 a B-7 A b) \, _2F_1\left(\frac{3}{2},5;\frac{5}{2};\frac{b x}{a}+1\right)\right)}{15 a^6 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,"-1/15*((a + b*x)^(3/2)*(3*a^5*A + b^4*(-7*A*b + 10*a*B)*x^5*Hypergeometric2F1[3/2, 5, 5/2, 1 + (b*x)/a]))/(a^6*x^5)","C",1
398,1,103,151,0.1084262,"\int x^4 (a+b x)^{3/2} (A+B x) \, dx","Integrate[x^4*(a + b*x)^(3/2)*(A + B*x),x]","\frac{2 (a+b x)^{5/2} \left(-256 a^5 B+128 a^4 b (3 A+5 B x)-160 a^3 b^2 x (6 A+7 B x)+1680 a^2 b^3 x^2 (A+B x)-210 a b^4 x^3 (12 A+11 B x)+231 b^5 x^4 (15 A+13 B x)\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*(a + b*x)^(5/2)*(-256*a^5*B + 1680*a^2*b^3*x^2*(A + B*x) + 128*a^4*b*(3*A + 5*B*x) - 160*a^3*b^2*x*(6*A + 7*B*x) - 210*a*b^4*x^3*(12*A + 11*B*x) + 231*b^5*x^4*(15*A + 13*B*x)))/(45045*b^6)","A",1
399,1,87,122,0.0859694,"\int x^3 (a+b x)^{3/2} (A+B x) \, dx","Integrate[x^3*(a + b*x)^(3/2)*(A + B*x),x]","\frac{2 (a+b x)^{5/2} \left(128 a^4 B-16 a^3 b (13 A+20 B x)+40 a^2 b^2 x (13 A+14 B x)-70 a b^3 x^2 (13 A+12 B x)+105 b^4 x^3 (13 A+11 B x)\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*(a + b*x)^(5/2)*(128*a^4*B + 105*b^4*x^3*(13*A + 11*B*x) - 70*a*b^3*x^2*(13*A + 12*B*x) + 40*a^2*b^2*x*(13*A + 14*B*x) - 16*a^3*b*(13*A + 20*B*x)))/(15015*b^5)","A",1
400,1,68,95,0.0727997,"\int x^2 (a+b x)^{3/2} (A+B x) \, dx","Integrate[x^2*(a + b*x)^(3/2)*(A + B*x),x]","\frac{2 (a+b x)^{5/2} \left(-48 a^3 B+8 a^2 b (11 A+15 B x)-10 a b^2 x (22 A+21 B x)+35 b^3 x^2 (11 A+9 B x)\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*(a + b*x)^(5/2)*(-48*a^3*B + 35*b^3*x^2*(11*A + 9*B*x) + 8*a^2*b*(11*A + 15*B*x) - 10*a*b^2*x*(22*A + 21*B*x)))/(3465*b^4)","A",1
401,1,49,67,0.0524521,"\int x (a+b x)^{3/2} (A+B x) \, dx","Integrate[x*(a + b*x)^(3/2)*(A + B*x),x]","\frac{2 (a+b x)^{5/2} \left(8 a^2 B-2 a b (9 A+10 B x)+5 b^2 x (9 A+7 B x)\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*(a + b*x)^(5/2)*(8*a^2*B + 5*b^2*x*(9*A + 7*B*x) - 2*a*b*(9*A + 10*B*x)))/(315*b^3)","A",1
402,1,30,42,0.032544,"\int (a+b x)^{3/2} (A+B x) \, dx","Integrate[(a + b*x)^(3/2)*(A + B*x),x]","\frac{2 (a+b x)^{5/2} (-2 a B+7 A b+5 b B x)}{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*(a + b*x)^(5/2)*(7*A*b - 2*a*B + 5*b*B*x))/(35*b^2)","A",1
403,1,71,69,0.0963905,"\int \frac{(a+b x)^{3/2} (A+B x)}{x} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/x,x]","A \left(\frac{2}{3} (a+b x)^{3/2}+a \left(2 \sqrt{a+b x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)\right)\right)+\frac{2 B (a+b x)^{5/2}}{5 b}","-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*B*(a + b*x)^(5/2))/(5*b) + A*((2*(a + b*x)^(3/2))/3 + a*(2*Sqrt[a + b*x] - 2*Sqrt[a]*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]))","A",1
404,1,71,95,0.0551303,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^2} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/x^2,x]","\frac{\sqrt{a+b x} (a (8 B x-3 A)+2 b x (3 A+B x))}{3 x}-\sqrt{a} (2 a B+3 A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","\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]*(2*b*x*(3*A + B*x) + a*(-3*A + 8*B*x)))/(3*x) - Sqrt[a]*(3*A*b + 2*a*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
405,1,55,107,0.031332,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^3} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/x^3,x]","\frac{(a+b x)^{5/2} \left(b x^2 (4 a B+A b) \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{b x}{a}+1\right)-5 a^2 A\right)}{10 a^3 x^2}","-\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,"((a + b*x)^(5/2)*(-5*a^2*A + b*(A*b + 4*a*B)*x^2*Hypergeometric2F1[2, 5/2, 7/2, 1 + (b*x)/a]))/(10*a^3*x^2)","C",1
406,1,105,112,0.1162158,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^4} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/x^4,x]","\frac{-(a+b x) \left(4 a^2 (2 A+3 B x)+2 a b x (7 A+15 B x)+3 A b^2 x^2\right)-3 b^2 x^3 \sqrt{\frac{b x}{a}+1} (6 a B-A b) \tanh ^{-1}\left(\sqrt{\frac{b x}{a}+1}\right)}{24 a x^3 \sqrt{a+b x}}","\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,"(-((a + b*x)*(3*A*b^2*x^2 + 4*a^2*(2*A + 3*B*x) + 2*a*b*x*(7*A + 15*B*x))) - 3*b^2*(-(A*b) + 6*a*B)*x^3*Sqrt[1 + (b*x)/a]*ArcTanh[Sqrt[1 + (b*x)/a]])/(24*a*x^3*Sqrt[a + b*x])","A",1
407,1,58,146,0.0253766,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^5} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/x^5,x]","-\frac{(a+b x)^{5/2} \left(5 a^4 A+b^3 x^4 (3 A b-8 a B) \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};\frac{b x}{a}+1\right)\right)}{20 a^5 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,"-1/20*((a + b*x)^(5/2)*(5*a^4*A + b^3*(3*A*b - 8*a*B)*x^4*Hypergeometric2F1[5/2, 4, 7/2, 1 + (b*x)/a]))/(a^5*x^4)","C",1
408,1,57,172,0.0265538,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^6} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/x^6,x]","-\frac{(a+b x)^{5/2} \left(a^5 A+b^4 x^5 (2 a B-A b) \, _2F_1\left(\frac{5}{2},5;\frac{7}{2};\frac{b x}{a}+1\right)\right)}{5 a^6 x^5}","\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,"-1/5*((a + b*x)^(5/2)*(a^5*A + b^4*(-(A*b) + 2*a*B)*x^5*Hypergeometric2F1[5/2, 5, 7/2, 1 + (b*x)/a]))/(a^6*x^5)","C",1
409,1,58,208,0.032981,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^7} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/x^7,x]","-\frac{(a+b x)^{5/2} \left(5 a^6 A+b^5 x^6 (7 A b-12 a B) \, _2F_1\left(\frac{5}{2},6;\frac{7}{2};\frac{b x}{a}+1\right)\right)}{30 a^7 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,"-1/30*((a + b*x)^(5/2)*(5*a^6*A + b^5*(7*A*b - 12*a*B)*x^6*Hypergeometric2F1[5/2, 6, 7/2, 1 + (b*x)/a]))/(a^7*x^6)","C",1
410,1,106,151,0.1387547,"\int x^4 (a+b x)^{5/2} (A+B x) \, dx","Integrate[x^4*(a + b*x)^(5/2)*(A + B*x),x]","\frac{2 (a+b x)^{7/2} \left(-1280 a^5 B+128 a^4 b (17 A+35 B x)-224 a^3 b^2 x (34 A+45 B x)+336 a^2 b^3 x^2 (51 A+55 B x)-462 a b^4 x^3 (68 A+65 B x)+3003 b^5 x^4 (17 A+15 B x)\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*(a + b*x)^(7/2)*(-1280*a^5*B + 3003*b^5*x^4*(17*A + 15*B*x) + 128*a^4*b*(17*A + 35*B*x) - 224*a^3*b^2*x*(34*A + 45*B*x) + 336*a^2*b^3*x^2*(51*A + 55*B*x) - 462*a*b^4*x^3*(68*A + 65*B*x)))/(765765*b^6)","A",1
411,1,87,122,0.0857647,"\int x^3 (a+b x)^{5/2} (A+B x) \, dx","Integrate[x^3*(a + b*x)^(5/2)*(A + B*x),x]","\frac{2 (a+b x)^{7/2} \left(128 a^4 B-16 a^3 b (15 A+28 B x)+168 a^2 b^2 x (5 A+6 B x)-42 a b^3 x^2 (45 A+44 B x)+231 b^4 x^3 (15 A+13 B x)\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*(a + b*x)^(7/2)*(128*a^4*B + 168*a^2*b^2*x*(5*A + 6*B*x) + 231*b^4*x^3*(15*A + 13*B*x) - 16*a^3*b*(15*A + 28*B*x) - 42*a*b^3*x^2*(45*A + 44*B*x)))/(45045*b^5)","A",1
412,1,68,95,0.0730809,"\int x^2 (a+b x)^{5/2} (A+B x) \, dx","Integrate[x^2*(a + b*x)^(5/2)*(A + B*x),x]","\frac{2 (a+b x)^{7/2} \left(-48 a^3 B+8 a^2 b (13 A+21 B x)-14 a b^2 x (26 A+27 B x)+63 b^3 x^2 (13 A+11 B x)\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*(a + b*x)^(7/2)*(-48*a^3*B + 63*b^3*x^2*(13*A + 11*B*x) + 8*a^2*b*(13*A + 21*B*x) - 14*a*b^2*x*(26*A + 27*B*x)))/(9009*b^4)","A",1
413,1,49,67,0.0501866,"\int x (a+b x)^{5/2} (A+B x) \, dx","Integrate[x*(a + b*x)^(5/2)*(A + B*x),x]","\frac{2 (a+b x)^{7/2} \left(8 a^2 B-2 a b (11 A+14 B x)+7 b^2 x (11 A+9 B x)\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*(a + b*x)^(7/2)*(8*a^2*B + 7*b^2*x*(11*A + 9*B*x) - 2*a*b*(11*A + 14*B*x)))/(693*b^3)","A",1
414,1,30,42,0.0326861,"\int (a+b x)^{5/2} (A+B x) \, dx","Integrate[(a + b*x)^(5/2)*(A + B*x),x]","\frac{2 (a+b x)^{7/2} (-2 a B+9 A b+7 b B x)}{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*(a + b*x)^(7/2)*(9*A*b - 2*a*B + 7*b*B*x))/(63*b^2)","A",1
415,1,78,86,0.1447538,"\int \frac{(a+b x)^{5/2} (A+B x)}{x} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/x,x]","-2 a^{5/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{2}{5} A (a+b x)^{5/2}+\frac{2}{3} a A (4 a+b x) \sqrt{a+b x}+\frac{2 B (a+b x)^{7/2}}{7 b}","-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*A*(a + b*x)^(5/2))/5 + (2*B*(a + b*x)^(7/2))/(7*b) + (2*a*A*Sqrt[a + b*x]*(4*a + b*x))/3 - 2*a^(5/2)*A*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
416,1,91,118,0.0826864,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^2} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/x^2,x]","\frac{\sqrt{a+b x} \left(a^2 (46 B x-15 A)+2 a b x (35 A+11 B x)+2 b^2 x^2 (5 A+3 B x)\right)}{15 x}-a^{3/2} (2 a B+5 A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","-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]*(2*b^2*x^2*(5*A + 3*B*x) + 2*a*b*x*(35*A + 11*B*x) + a^2*(-15*A + 46*B*x)))/(15*x) - a^(3/2)*(5*A*b + 2*a*B)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
417,1,56,133,0.0330352,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^3} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/x^3,x]","\frac{(a+b x)^{7/2} \left(b x^2 (4 a B+3 A b) \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};\frac{b x}{a}+1\right)-7 a^2 A\right)}{14 a^3 x^2}","-\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,"((a + b*x)^(7/2)*(-7*a^2*A + b*(3*A*b + 4*a*B)*x^2*Hypergeometric2F1[2, 7/2, 9/2, 1 + (b*x)/a]))/(14*a^3*x^2)","C",1
418,1,57,139,0.0338395,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^4} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/x^4,x]","-\frac{(a+b x)^{7/2} \left(7 a^3 A+b^2 x^3 (6 a B+A b) \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};\frac{b x}{a}+1\right)\right)}{21 a^4 x^3}","\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,"-1/21*((a + b*x)^(7/2)*(7*a^3*A + b^2*(A*b + 6*a*B)*x^3*Hypergeometric2F1[3, 7/2, 9/2, 1 + (b*x)/a]))/(a^4*x^3)","C",1
419,1,124,142,0.1292969,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^5} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/x^5,x]","\frac{-(a+b x) \left(16 a^3 (3 A+4 B x)+8 a^2 b x (17 A+26 B x)+2 a b^2 x^2 (59 A+132 B x)+15 A b^3 x^3\right)-15 b^3 x^4 \sqrt{\frac{b x}{a}+1} (8 a B-A b) \tanh ^{-1}\left(\sqrt{\frac{b x}{a}+1}\right)}{192 a x^4 \sqrt{a+b x}}","\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,"(-((a + b*x)*(15*A*b^3*x^3 + 16*a^3*(3*A + 4*B*x) + 8*a^2*b*x*(17*A + 26*B*x) + 2*a*b^2*x^2*(59*A + 132*B*x))) - 15*b^3*(-(A*b) + 8*a*B)*x^4*Sqrt[1 + (b*x)/a]*ArcTanh[Sqrt[1 + (b*x)/a]])/(192*a*x^4*Sqrt[a + b*x])","A",1
420,1,58,177,0.0353191,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^6} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/x^6,x]","-\frac{(a+b x)^{7/2} \left(7 a^5 A+b^4 x^5 (10 a B-3 A b) \, _2F_1\left(\frac{7}{2},5;\frac{9}{2};\frac{b x}{a}+1\right)\right)}{35 a^6 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,"-1/35*((a + b*x)^(7/2)*(7*a^5*A + b^4*(-3*A*b + 10*a*B)*x^5*Hypergeometric2F1[7/2, 5, 9/2, 1 + (b*x)/a]))/(a^6*x^5)","C",1
421,1,58,208,0.0289456,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^7} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/x^7,x]","-\frac{(a+b x)^{7/2} \left(7 a^6 A+b^5 x^6 (5 A b-12 a B) \, _2F_1\left(\frac{7}{2},6;\frac{9}{2};\frac{b x}{a}+1\right)\right)}{42 a^7 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,"-1/42*((a + b*x)^(7/2)*(7*a^6*A + b^5*(5*A*b - 12*a*B)*x^6*Hypergeometric2F1[7/2, 6, 9/2, 1 + (b*x)/a]))/(a^7*x^6)","C",1
422,1,57,232,0.0324772,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^8} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/x^8,x]","-\frac{(a+b x)^{7/2} \left(a^7 A+b^6 x^7 (2 a B-A b) \, _2F_1\left(\frac{7}{2},7;\frac{9}{2};\frac{b x}{a}+1\right)\right)}{7 a^8 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,"-1/7*((a + b*x)^(7/2)*(a^7*A + b^6*(-(A*b) + 2*a*B)*x^7*Hypergeometric2F1[7/2, 7, 9/2, 1 + (b*x)/a]))/(a^8*x^7)","C",1
423,1,106,149,0.1118787,"\int \frac{x^4 (A+B x)}{\sqrt{a+b x}} \, dx","Integrate[(x^4*(A + B*x))/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \left(-1280 a^5 B+128 a^4 b (11 A+5 B x)-32 a^3 b^2 x (22 A+15 B x)+16 a^2 b^3 x^2 (33 A+25 B x)-10 a b^4 x^3 (44 A+35 B x)+35 b^5 x^4 (11 A+9 B x)\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]*(-1280*a^5*B + 128*a^4*b*(11*A + 5*B*x) + 35*b^5*x^4*(11*A + 9*B*x) - 32*a^3*b^2*x*(22*A + 15*B*x) + 16*a^2*b^3*x^2*(33*A + 25*B*x) - 10*a*b^4*x^3*(44*A + 35*B*x)))/(3465*b^6)","A",1
424,1,87,120,0.0982082,"\int \frac{x^3 (A+B x)}{\sqrt{a+b x}} \, dx","Integrate[(x^3*(A + B*x))/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \left(128 a^4 B-16 a^3 b (9 A+4 B x)+24 a^2 b^2 x (3 A+2 B x)-2 a b^3 x^2 (27 A+20 B x)+5 b^4 x^3 (9 A+7 B x)\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]*(128*a^4*B + 24*a^2*b^2*x*(3*A + 2*B*x) - 16*a^3*b*(9*A + 4*B*x) + 5*b^4*x^3*(9*A + 7*B*x) - 2*a*b^3*x^2*(27*A + 20*B*x)))/(315*b^5)","A",1
425,1,68,93,0.0665682,"\int \frac{x^2 (A+B x)}{\sqrt{a+b x}} \, dx","Integrate[(x^2*(A + B*x))/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \left(-48 a^3 B+8 a^2 b (7 A+3 B x)-2 a b^2 x (14 A+9 B x)+3 b^3 x^2 (7 A+5 B x)\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]*(-48*a^3*B + 8*a^2*b*(7*A + 3*B*x) + 3*b^3*x^2*(7*A + 5*B*x) - 2*a*b^2*x*(14*A + 9*B*x)))/(105*b^4)","A",1
426,1,48,65,0.0502255,"\int \frac{x (A+B x)}{\sqrt{a+b x}} \, dx","Integrate[(x*(A + B*x))/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \left(8 a^2 B-2 a b (5 A+2 B x)+b^2 x (5 A+3 B x)\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]*(8*a^2*B - 2*a*b*(5*A + 2*B*x) + b^2*x*(5*A + 3*B*x)))/(15*b^3)","A",1
427,1,29,40,0.0245258,"\int \frac{A+B x}{\sqrt{a+b x}} \, dx","Integrate[(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
428,1,40,40,0.019115,"\int \frac{A+B x}{x \sqrt{a+b x}} \, dx","Integrate[(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
429,1,49,49,0.0328905,"\int \frac{A+B x}{x^2 \sqrt{a+b x}} \, dx","Integrate[(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
430,1,73,84,0.2069717,"\int \frac{A+B x}{x^3 \sqrt{a+b x}} \, dx","Integrate[(A + B*x)/(x^3*Sqrt[a + b*x]),x]","\frac{\sqrt{a+b x} \left(\frac{a (3 A b x-2 a (A+2 B x))}{x^2}+\frac{b (4 a B-3 A b) \tanh ^{-1}\left(\sqrt{\frac{b x}{a}+1}\right)}{\sqrt{\frac{b x}{a}+1}}\right)}{4 a^3}","-\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]*((a*(3*A*b*x - 2*a*(A + 2*B*x)))/x^2 + (b*(-3*A*b + 4*a*B)*ArcTanh[Sqrt[1 + (b*x)/a]])/Sqrt[1 + (b*x)/a]))/(4*a^3)","A",1
431,1,57,115,0.0274001,"\int \frac{A+B x}{x^4 \sqrt{a+b x}} \, dx","Integrate[(A + B*x)/(x^4*Sqrt[a + b*x]),x]","-\frac{\sqrt{a+b x} \left(a^3 A+b^2 x^3 (6 a B-5 A b) \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{b x}{a}+1\right)\right)}{3 a^4 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,"-1/3*(Sqrt[a + b*x]*(a^3*A + b^2*(-5*A*b + 6*a*B)*x^3*Hypergeometric2F1[1/2, 3, 3/2, 1 + (b*x)/a]))/(a^4*x^3)","C",1
432,1,57,146,0.0184521,"\int \frac{A+B x}{x^5 \sqrt{a+b x}} \, dx","Integrate[(A + B*x)/(x^5*Sqrt[a + b*x]),x]","-\frac{\sqrt{a+b x} \left(a^4 A+b^3 x^4 (7 A b-8 a B) \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};\frac{b x}{a}+1\right)\right)}{4 a^5 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,"-1/4*(Sqrt[a + b*x]*(a^4*A + b^3*(7*A*b - 8*a*B)*x^4*Hypergeometric2F1[1/2, 4, 3/2, 1 + (b*x)/a]))/(a^5*x^4)","C",1
433,1,57,177,0.0279659,"\int \frac{A+B x}{x^6 \sqrt{a+b x}} \, dx","Integrate[(A + B*x)/(x^6*Sqrt[a + b*x]),x]","-\frac{\sqrt{a+b x} \left(a^5 A+b^4 x^5 (10 a B-9 A b) \, _2F_1\left(\frac{1}{2},5;\frac{3}{2};\frac{b x}{a}+1\right)\right)}{5 a^6 x^5}","\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,"-1/5*(Sqrt[a + b*x]*(a^5*A + b^4*(-9*A*b + 10*a*B)*x^5*Hypergeometric2F1[1/2, 5, 3/2, 1 + (b*x)/a]))/(a^6*x^5)","C",1
434,1,106,147,0.1038722,"\int \frac{x^4 (A+B x)}{(a+b x)^{3/2}} \, dx","Integrate[(x^4*(A + B*x))/(a + b*x)^(3/2),x]","\frac{2560 a^5 B-256 a^4 b (9 A-5 B x)-64 a^3 b^2 x (18 A+5 B x)+32 a^2 b^3 x^2 (9 A+5 B x)-4 a b^4 x^3 (36 A+25 B x)+10 b^5 x^4 (9 A+7 B x)}{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,"(2560*a^5*B - 256*a^4*b*(9*A - 5*B*x) + 32*a^2*b^3*x^2*(9*A + 5*B*x) - 64*a^3*b^2*x*(18*A + 5*B*x) + 10*b^5*x^4*(9*A + 7*B*x) - 4*a*b^4*x^3*(36*A + 25*B*x))/(315*b^6*Sqrt[a + b*x])","A",1
435,1,86,116,0.0850522,"\int \frac{x^3 (A+B x)}{(a+b x)^{3/2}} \, dx","Integrate[(x^3*(A + B*x))/(a + b*x)^(3/2),x]","\frac{2 \left(-128 a^4 B+16 a^3 b (7 A-4 B x)+8 a^2 b^2 x (7 A+2 B x)-2 a b^3 x^2 (7 A+4 B x)+b^4 x^3 (7 A+5 B x)\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*(-128*a^4*B + 16*a^3*b*(7*A - 4*B*x) + 8*a^2*b^2*x*(7*A + 2*B*x) - 2*a*b^3*x^2*(7*A + 4*B*x) + b^4*x^3*(7*A + 5*B*x)))/(35*b^5*Sqrt[a + b*x])","A",1
436,1,67,91,0.0661301,"\int \frac{x^2 (A+B x)}{(a+b x)^{3/2}} \, dx","Integrate[(x^2*(A + B*x))/(a + b*x)^(3/2),x]","\frac{2 \left(48 a^3 B-8 a^2 b (5 A-3 B x)-2 a b^2 x (10 A+3 B x)+b^3 x^2 (5 A+3 B x)\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*(48*a^3*B - 8*a^2*b*(5*A - 3*B*x) + b^3*x^2*(5*A + 3*B*x) - 2*a*b^2*x*(10*A + 3*B*x)))/(15*b^4*Sqrt[a + b*x])","A",1
437,1,47,63,0.0398811,"\int \frac{x (A+B x)}{(a+b x)^{3/2}} \, dx","Integrate[(x*(A + B*x))/(a + b*x)^(3/2),x]","\frac{2 \left(-8 a^2 B+a (6 A b-4 b B x)+b^2 x (3 A+B x)\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*(-8*a^2*B + b^2*x*(3*A + B*x) + a*(6*A*b - 4*b*B*x)))/(3*b^3*Sqrt[a + b*x])","A",1
438,1,27,38,0.0233689,"\int \frac{A+B x}{(a+b x)^{3/2}} \, dx","Integrate[(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
439,1,50,50,0.0502091,"\int \frac{A+B x}{x (a+b x)^{3/2}} \, dx","Integrate[(A + B*x)/(x*(a + b*x)^(3/2)),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}}","\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
440,1,49,73,0.0156834,"\int \frac{A+B x}{x^2 (a+b x)^{3/2}} \, dx","Integrate[(A + B*x)/(x^2*(a + b*x)^(3/2)),x]","\frac{\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b x}{a}+1\right) (2 a B x-3 A b x)-a A}{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)*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (b*x)/a])/(a^2*x*Sqrt[a + b*x])","C",1
441,1,56,110,0.0241171,"\int \frac{A+B x}{x^3 (a+b x)^{3/2}} \, dx","Integrate[(A + B*x)/(x^3*(a + b*x)^(3/2)),x]","\frac{b x^2 (5 A b-4 a B) \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};\frac{b x}{a}+1\right)-a^2 A}{2 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,"(-(a^2*A) + b*(5*A*b - 4*a*B)*x^2*Hypergeometric2F1[-1/2, 2, 1/2, 1 + (b*x)/a])/(2*a^3*x^2*Sqrt[a + b*x])","C",1
442,1,58,143,0.0205211,"\int \frac{A+B x}{x^4 (a+b x)^{3/2}} \, dx","Integrate[(A + B*x)/(x^4*(a + b*x)^(3/2)),x]","\frac{b^2 x^3 (6 a B-7 A b) \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};\frac{b x}{a}+1\right)-a^3 A}{3 a^4 x^3 \sqrt{a+b x}}","\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,"(-(a^3*A) + b^2*(-7*A*b + 6*a*B)*x^3*Hypergeometric2F1[-1/2, 3, 1/2, 1 + (b*x)/a])/(3*a^4*x^3*Sqrt[a + b*x])","C",1
443,1,58,174,0.0240542,"\int \frac{A+B x}{x^5 (a+b x)^{3/2}} \, dx","Integrate[(A + B*x)/(x^5*(a + b*x)^(3/2)),x]","\frac{b^3 x^4 (9 A b-8 a B) \, _2F_1\left(-\frac{1}{2},4;\frac{1}{2};\frac{b x}{a}+1\right)-a^4 A}{4 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,"(-(a^4*A) + b^3*(9*A*b - 8*a*B)*x^4*Hypergeometric2F1[-1/2, 4, 1/2, 1 + (b*x)/a])/(4*a^5*x^4*Sqrt[a + b*x])","C",1
444,1,106,147,0.1153103,"\int \frac{x^4 (A+B x)}{(a+b x)^{5/2}} \, dx","Integrate[(x^4*(A + B*x))/(a + b*x)^(5/2),x]","\frac{-2560 a^5 B+256 a^4 b (7 A-15 B x)+192 a^3 b^2 x (14 A-5 B x)+32 a^2 b^3 x^2 (21 A+5 B x)-4 a b^4 x^3 (28 A+15 B x)+6 b^5 x^4 (7 A+5 B x)}{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,"(-2560*a^5*B + 256*a^4*b*(7*A - 15*B*x) + 192*a^3*b^2*x*(14*A - 5*B*x) + 6*b^5*x^4*(7*A + 5*B*x) + 32*a^2*b^3*x^2*(21*A + 5*B*x) - 4*a*b^4*x^3*(28*A + 15*B*x))/(105*b^6*(a + b*x)^(3/2))","A",1
445,1,86,118,0.0786562,"\int \frac{x^3 (A+B x)}{(a+b x)^{5/2}} \, dx","Integrate[(x^3*(A + B*x))/(a + b*x)^(5/2),x]","\frac{2 \left(128 a^4 B+a^3 (192 b B x-80 A b)+24 a^2 b^2 x (2 B x-5 A)-2 a b^3 x^2 (15 A+4 B x)+b^4 x^3 (5 A+3 B x)\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*(128*a^4*B + 24*a^2*b^2*x*(-5*A + 2*B*x) + b^4*x^3*(5*A + 3*B*x) - 2*a*b^3*x^2*(15*A + 4*B*x) + a^3*(-80*A*b + 192*b*B*x)))/(15*b^5*(a + b*x)^(3/2))","A",1
446,1,63,91,0.0627752,"\int \frac{x^2 (A+B x)}{(a+b x)^{5/2}} \, dx","Integrate[(x^2*(A + B*x))/(a + b*x)^(5/2),x]","\frac{2 \left(-16 a^3 B+8 a^2 b (A-3 B x)-6 a b^2 x (B x-2 A)+b^3 x^2 (3 A+B x)\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*(-16*a^3*B + 8*a^2*b*(A - 3*B*x) - 6*a*b^2*x*(-2*A + B*x) + b^3*x^2*(3*A + B*x)))/(3*b^4*(a + b*x)^(3/2))","A",1
447,1,46,63,0.047698,"\int \frac{x (A+B x)}{(a+b x)^{5/2}} \, dx","Integrate[(x*(A + B*x))/(a + b*x)^(5/2),x]","\frac{16 a^2 B-4 a b (A-6 B x)+6 b^2 x (B x-A)}{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,"(16*a^2*B - 4*a*b*(A - 6*B*x) + 6*b^2*x*(-A + B*x))/(3*b^3*(a + b*x)^(3/2))","A",1
448,1,29,40,0.02365,"\int \frac{A+B x}{(a+b x)^{5/2}} \, dx","Integrate[(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
449,1,56,67,0.0248442,"\int \frac{A+B x}{x (a+b x)^{5/2}} \, dx","Integrate[(A + B*x)/(x*(a + b*x)^(5/2)),x]","\frac{2 a (A b-a B)+6 A b (a+b x) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b x}{a}+1\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*a*(A*b - a*B) + 6*A*b*(a + b*x)*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (b*x)/a])/(3*a^2*b*(a + b*x)^(3/2))","C",1
450,1,52,98,0.0274849,"\int \frac{A+B x}{x^2 (a+b x)^{5/2}} \, dx","Integrate[(A + B*x)/(x^2*(a + b*x)^(5/2)),x]","\frac{\, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{b x}{a}+1\right) (2 a B x-5 A b x)-3 a A}{3 a^2 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*A + (-5*A*b*x + 2*a*B*x)*Hypergeometric2F1[-3/2, 1, -1/2, 1 + (b*x)/a])/(3*a^2*x*(a + b*x)^(3/2))","C",1
451,1,56,136,0.0298321,"\int \frac{A+B x}{x^3 (a+b x)^{5/2}} \, dx","Integrate[(A + B*x)/(x^3*(a + b*x)^(5/2)),x]","\frac{b x^2 (7 A b-4 a B) \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};\frac{b x}{a}+1\right)-3 a^2 A}{6 a^3 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,"(-3*a^2*A + b*(7*A*b - 4*a*B)*x^2*Hypergeometric2F1[-3/2, 2, -1/2, 1 + (b*x)/a])/(6*a^3*x^2*(a + b*x)^(3/2))","C",1
452,1,58,171,0.0353424,"\int \frac{A+B x}{x^4 (a+b x)^{5/2}} \, dx","Integrate[(A + B*x)/(x^4*(a + b*x)^(5/2)),x]","\frac{b^2 x^3 (2 a B-3 A b) \, _2F_1\left(-\frac{3}{2},3;-\frac{1}{2};\frac{b x}{a}+1\right)-a^3 A}{3 a^4 x^3 (a+b x)^{3/2}}","\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,"(-(a^3*A) + b^2*(-3*A*b + 2*a*B)*x^3*Hypergeometric2F1[-3/2, 3, -1/2, 1 + (b*x)/a])/(3*a^4*x^3*(a + b*x)^(3/2))","C",1
453,1,58,202,0.0266762,"\int \frac{A+B x}{x^5 (a+b x)^{5/2}} \, dx","Integrate[(A + B*x)/(x^5*(a + b*x)^(5/2)),x]","\frac{b^3 x^4 (11 A b-8 a B) \, _2F_1\left(-\frac{3}{2},4;-\frac{1}{2};\frac{b x}{a}+1\right)-3 a^4 A}{12 a^5 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,"(-3*a^4*A + b^3*(11*A*b - 8*a*B)*x^4*Hypergeometric2F1[-3/2, 4, -1/2, 1 + (b*x)/a])/(12*a^5*x^4*(a + b*x)^(3/2))","C",1
454,1,65,71,0.0653342,"\int \frac{(a+b x)^2}{x^2 \sqrt{c+d x}} \, dx","Integrate[(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{a (a d-4 b c) \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) + (a*(-4*b*c + a*d)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/c^(3/2)","A",1
455,1,197,209,0.4533619,"\int \frac{x^3 (c+d x)^{5/2}}{a+b x} \, dx","Integrate[(x^3*(c + d*x)^(5/2))/(a + b*x),x]","-\frac{2 a^3 (a d-b c) \left(3 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)-\sqrt{b} \sqrt{c+d x} (-3 a d+4 b c+b d x)\right)}{3 b^{13/2}}-\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}","\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*a^3*(c + d*x)^(5/2))/(5*b^4) + (2*(b^2*c^2 + a*b*c*d + a^2*d^2)*(c + d*x)^(7/2))/(7*b^3*d^3) - (2*(2*b*c + a*d)*(c + d*x)^(9/2))/(9*b^2*d^3) + (2*(c + d*x)^(11/2))/(11*b*d^3) - (2*a^3*(-(b*c) + a*d)*(-(Sqrt[b]*Sqrt[c + d*x]*(4*b*c - 3*a*d + b*d*x)) + 3*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]]))/(3*b^(13/2))","A",1
456,1,151,169,0.2950769,"\int \frac{x^2 (c+d x)^{5/2}}{a+b x} \, dx","Integrate[(x^2*(c + d*x)^(5/2))/(a + b*x),x]","\frac{2 \left(\frac{105 a^2 (a d-b c) \left(3 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)-\sqrt{b} \sqrt{c+d x} (-3 a d+4 b c+b d x)\right)}{b^{5/2}}+63 a^2 (c+d x)^{5/2}-\frac{45 b (c+d x)^{7/2} (a d+b c)}{d^2}+\frac{35 b^2 (c+d x)^{9/2}}{d^2}\right)}{315 b^3}","-\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*(63*a^2*(c + d*x)^(5/2) - (45*b*(b*c + a*d)*(c + d*x)^(7/2))/d^2 + (35*b^2*(c + d*x)^(9/2))/d^2 + (105*a^2*(-(b*c) + a*d)*(-(Sqrt[b]*Sqrt[c + d*x]*(4*b*c - 3*a*d + b*d*x)) + 3*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]]))/b^(5/2)))/(315*b^3)","A",1
457,1,126,135,0.3122189,"\int \frac{x (c+d x)^{5/2}}{a+b x} \, dx","Integrate[(x*(c + d*x)^(5/2))/(a + b*x),x]","-\frac{2 a (b c-a d) \left(\sqrt{b} \sqrt{c+d x} (-3 a d+4 b c+b d x)-3 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)\right)}{3 b^{9/2}}-\frac{2 a (c+d x)^{5/2}}{5 b^2}+\frac{2 (c+d x)^{7/2}}{7 b d}","\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*a*(c + d*x)^(5/2))/(5*b^2) + (2*(c + d*x)^(7/2))/(7*b*d) - (2*a*(b*c - a*d)*(Sqrt[b]*Sqrt[c + d*x]*(4*b*c - 3*a*d + b*d*x) - 3*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]]))/(3*b^(9/2))","A",1
458,1,105,112,0.1679909,"\int \frac{(c+d x)^{5/2}}{a+b x} \, dx","Integrate[(c + d*x)^(5/2)/(a + b*x),x]","\frac{2 (b c-a d) \left(\sqrt{b} \sqrt{c+d x} (-3 a d+4 b c+b d x)-3 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)\right)}{3 b^{7/2}}+\frac{2 (c+d x)^{5/2}}{5 b}","-\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*(c + d*x)^(5/2))/(5*b) + (2*(b*c - a*d)*(Sqrt[b]*Sqrt[c + d*x]*(4*b*c - 3*a*d + b*d*x) - 3*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]]))/(3*b^(7/2))","A",1
459,1,107,118,0.1642231,"\int \frac{(c+d x)^{5/2}}{x (a+b x)} \, dx","Integrate[(c + d*x)^(5/2)/(x*(a + b*x)),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 b^{5/2}}+\frac{2 d \sqrt{c+d x} (-3 a d+7 b c+b d x)}{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*d*Sqrt[c + d*x]*(7*b*c - 3*a*d + b*d*x))/(3*b^2) - (2*c^(5/2)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/a + (2*(b*c - a*d)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(a*b^(5/2))","A",1
460,1,114,128,0.1725229,"\int \frac{(c+d x)^{5/2}}{x^2 (a+b x)} \, dx","Integrate[(c + d*x)^(5/2)/(x^2*(a + b*x)),x]","\frac{-\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^{3/2}}+c^{3/2} (2 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)+\frac{a \sqrt{c+d x} \left(2 a d^2 x-b c^2\right)}{b x}}{a^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)}{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,"((a*Sqrt[c + d*x]*(-(b*c^2) + 2*a*d^2*x))/(b*x) + c^(3/2)*(2*b*c - 5*a*d)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]] - (2*(b*c - a*d)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/b^(3/2))/a^2","A",1
461,1,131,151,0.1991574,"\int \frac{(c+d x)^{5/2}}{x^3 (a+b x)} \, dx","Integrate[(c + d*x)^(5/2)/(x^3*(a + b*x)),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)+\frac{a c \sqrt{c+d x} (-2 a c-9 a d x+4 b c x)}{x^2}+\frac{8 (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{\sqrt{b}}}{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,"((a*c*Sqrt[c + d*x]*(-2*a*c + 4*b*c*x - 9*a*d*x))/x^2 - Sqrt[c]*(8*b^2*c^2 - 20*a*b*c*d + 15*a^2*d^2)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]] + (8*(b*c - a*d)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/Sqrt[b])/(4*a^3)","A",1
462,1,178,207,0.4595126,"\int \frac{(c+d x)^{5/2}}{x^4 (a+b x)} \, dx","Integrate[(c + d*x)^(5/2)/(x^4*(a + b*x)),x]","-\frac{\frac{a \sqrt{c+d x} \left(a^2 \left(8 c^2+26 c d x+33 d^2 x^2\right)-6 a b c x (2 c+9 d x)+24 b^2 c^2 x^2\right)}{x^3}-\frac{3 \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)}{\sqrt{c}}+48 \sqrt{b} (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{24 a^4}","-\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,"-1/24*((a*Sqrt[c + d*x]*(24*b^2*c^2*x^2 - 6*a*b*c*x*(2*c + 9*d*x) + a^2*(8*c^2 + 26*c*d*x + 33*d^2*x^2)))/x^3 - (3*(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]])/Sqrt[c] + 48*Sqrt[b]*(b*c - a*d)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/a^4","A",1
463,1,61,199,0.0518162,"\int \frac{1}{\sqrt[3]{x} \sqrt{c+d x} (4 c+d x)} \, dx","Integrate[1/(x^(1/3)*Sqrt[c + d*x]*(4*c + d*x)),x]","\frac{3 x^{2/3} \sqrt{\frac{c+d x}{c}} F_1\left(\frac{2}{3};\frac{1}{2},1;\frac{5}{3};-\frac{d x}{c},-\frac{d x}{4 c}\right)}{8 c \sqrt{c+d x}}","-\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,"(3*x^(2/3)*Sqrt[(c + d*x)/c]*AppellF1[2/3, 1/2, 1, 5/3, -((d*x)/c), -1/4*(d*x)/c])/(8*c*Sqrt[c + d*x])","C",0
464,1,61,143,0.0567548,"\int \frac{1}{\sqrt[3]{x} (8 c-d x) \sqrt{c+d x}} \, dx","Integrate[1/(x^(1/3)*(8*c - d*x)*Sqrt[c + d*x]),x]","\frac{3 x^{2/3} \sqrt{\frac{c+d x}{c}} F_1\left(\frac{2}{3};\frac{1}{2},1;\frac{5}{3};-\frac{d x}{c},\frac{d x}{8 c}\right)}{16 c \sqrt{c+d x}}","-\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,"(3*x^(2/3)*Sqrt[(c + d*x)/c]*AppellF1[2/3, 1/2, 1, 5/3, -((d*x)/c), (d*x)/(8*c)])/(16*c*Sqrt[c + d*x])","C",0
465,1,169,140,0.3297501,"\int \frac{\sqrt{c+d x}}{x^2 (a+b x)^2} \, dx","Integrate[Sqrt[c + d*x]/(x^2*(a + b*x)^2),x]","\frac{\sqrt{c} \left(a (a+2 b x) \sqrt{c+d x} (b c-a d)+\sqrt{b} x (a+b x) (4 b c-3 a d) \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)\right)-x (a+b x) \left(a^2 d^2-5 a b c d+4 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3 \sqrt{c} x (a+b x) (a d-b c)}","-\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,"(-((4*b^2*c^2 - 5*a*b*c*d + a^2*d^2)*x*(a + b*x)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]]) + Sqrt[c]*(a*(b*c - a*d)*(a + 2*b*x)*Sqrt[c + d*x] + Sqrt[b]*(4*b*c - 3*a*d)*Sqrt[b*c - a*d]*x*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]]))/(a^3*Sqrt[c]*(-(b*c) + a*d)*x*(a + b*x))","A",1
466,1,111,115,0.2033418,"\int \frac{(c+d x)^{3/2}}{x (a+b x)^2} \, dx","Integrate[(c + d*x)^(3/2)/(x*(a + b*x)^2),x]","\frac{\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)}{b^{3/2}}+\frac{a \sqrt{c+d x} (b c-a d)}{b (a+b x)}-2 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^2}","\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,"((a*(b*c - a*d)*Sqrt[c + d*x])/(b*(a + b*x)) - 2*c^(3/2)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]] + (Sqrt[b*c - a*d]*(2*b*c + a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/b^(3/2))/a^2","A",1
467,1,127,149,0.2656278,"\int \frac{(c+d x)^{3/2}}{x^2 (a+b x)^2} \, dx","Integrate[(c + d*x)^(3/2)/(x^2*(a + b*x)^2),x]","\frac{\frac{a \sqrt{c+d x} (-a c+a d x-2 b c x)}{x (a+b x)}+\sqrt{c} (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)-\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)}{\sqrt{b}}}{a^3}","\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,"((a*Sqrt[c + d*x]*(-(a*c) - 2*b*c*x + a*d*x))/(x*(a + b*x)) + Sqrt[c]*(4*b*c - 3*a*d)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]] - (Sqrt[b*c - a*d]*(4*b*c - a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/Sqrt[b])/a^3","A",1
468,1,246,220,0.8180337,"\int \frac{x^3 (c+d x)^{5/2}}{(a+b x)^2} \, dx","Integrate[(x^3*(c + d*x)^(5/2))/(a + b*x)^2,x]","\frac{21 a^2 d^2 (a+b x) (6 b c-11 a d) \left(\sqrt{b} \sqrt{c+d x} \left(15 a^2 d^2-5 a b d (7 c+d x)+b^2 \left(23 c^2+11 c d x+3 d^2 x^2\right)\right)-15 (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)\right)+5 b^{7/2} (c+d x)^{7/2} \left(99 a^3 d^2+2 a^2 b d (11 d x-16 c)-2 a b^2 c (2 c+9 d x)-4 b^3 c^2 x\right)+70 b^{11/2} d x^2 (c+d x)^{7/2} (b c-a d)}{315 b^{13/2} d^2 (a+b x) (b c-a d)}","-\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,"(70*b^(11/2)*d*(b*c - a*d)*x^2*(c + d*x)^(7/2) + 5*b^(7/2)*(c + d*x)^(7/2)*(99*a^3*d^2 - 4*b^3*c^2*x - 2*a*b^2*c*(2*c + 9*d*x) + 2*a^2*b*d*(-16*c + 11*d*x)) + 21*a^2*d^2*(6*b*c - 11*a*d)*(a + b*x)*(Sqrt[b]*Sqrt[c + d*x]*(15*a^2*d^2 - 5*a*b*d*(7*c + d*x) + b^2*(23*c^2 + 11*c*d*x + 3*d^2*x^2)) - 15*(b*c - a*d)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]]))/(315*b^(13/2)*d^2*(b*c - a*d)*(a + b*x))","A",1
469,1,181,204,0.3684349,"\int \frac{x^2 (c+d x)^{5/2}}{(a+b x)^2} \, dx","Integrate[(x^2*(c + d*x)^(5/2))/(a + b*x)^2,x]","\frac{\frac{a (9 a d-4 b c) \left(\sqrt{b} \sqrt{c+d x} \left(15 a^2 d^2-5 a b d (7 c+d x)+b^2 \left(23 c^2+11 c d x+3 d^2 x^2\right)\right)-15 (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)\right)}{15 b^{7/2}}-\frac{a^2 (c+d x)^{7/2}}{a+b x}+\frac{2 (c+d x)^{7/2} (b c-a d)}{7 d}}{b^2 (b c-a d)}","-\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,"((2*(b*c - a*d)*(c + d*x)^(7/2))/(7*d) - (a^2*(c + d*x)^(7/2))/(a + b*x) + (a*(-4*b*c + 9*a*d)*(Sqrt[b]*Sqrt[c + d*x]*(15*a^2*d^2 - 5*a*b*d*(7*c + d*x) + b^2*(23*c^2 + 11*c*d*x + 3*d^2*x^2)) - 15*(b*c - a*d)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]]))/(15*b^(7/2)))/(b^2*(b*c - a*d))","A",1
470,1,150,178,0.348591,"\int \frac{x (c+d x)^{5/2}}{(a+b x)^2} \, dx","Integrate[(x*(c + d*x)^(5/2))/(a + b*x)^2,x]","\frac{\frac{2 \left(b c-\frac{7 a d}{2}\right) \left(5 (b c-a d) \left(\sqrt{b} \sqrt{c+d x} (-3 a d+4 b c+b d x)-3 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)\right)+3 b^{5/2} (c+d x)^{5/2}\right)}{15 b^{7/2}}+\frac{a (c+d x)^{7/2}}{a+b x}}{b (b c-a d)}","-\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,"((a*(c + d*x)^(7/2))/(a + b*x) + (2*(b*c - (7*a*d)/2)*(3*b^(5/2)*(c + d*x)^(5/2) + 5*(b*c - a*d)*(Sqrt[b]*Sqrt[c + d*x]*(4*b*c - 3*a*d + b*d*x) - 3*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])))/(15*b^(7/2)))/(b*(b*c - a*d))","A",1
471,1,50,110,0.0159301,"\int \frac{(c+d x)^{5/2}}{(a+b x)^2} \, dx","Integrate[(c + d*x)^(5/2)/(a + b*x)^2,x]","\frac{2 d (c+d x)^{7/2} \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};-\frac{b (c+d x)}{a d-b c}\right)}{7 (a d-b c)^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,"(2*d*(c + d*x)^(7/2)*Hypergeometric2F1[2, 7/2, 9/2, -((b*(c + d*x))/(-(b*c) + a*d))])/(7*(-(b*c) + a*d)^2)","C",1
472,1,145,142,0.3055756,"\int \frac{(c+d x)^{5/2}}{x (a+b x)^2} \, dx","Integrate[(c + d*x)^(5/2)/(x*(a + b*x)^2),x]","\frac{\frac{a \sqrt{c+d x} \left(3 a^2 d^2+2 a b d (d x-c)+b^2 c^2\right)}{b^2 (a+b x)}+\frac{\sqrt{b c-a d} \left(-3 a^2 d^2+a b c d+2 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{5/2}}-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,"((a*Sqrt[c + d*x]*(b^2*c^2 + 3*a^2*d^2 + 2*a*b*d*(-c + d*x)))/(b^2*(a + b*x)) - 2*c^(5/2)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]] + (Sqrt[b*c - a*d]*(2*b^2*c^2 + a*b*c*d - 3*a^2*d^2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/b^(5/2))/a^2","A",1
473,1,159,147,0.3516477,"\int \frac{(c+d x)^{5/2}}{x^2 (a+b x)^2} \, dx","Integrate[(c + d*x)^(5/2)/(x^2*(a + b*x)^2),x]","\frac{-\frac{a \sqrt{c+d x} \left(a^2 d^2 x+a b c (c-2 d x)+2 b^2 c^2 x\right)}{b x (a+b x)}-\frac{\sqrt{b c-a d} \left(-a^2 d^2-3 a b c d+4 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{3/2}}+c^{3/2} (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3}","-\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,"(-((a*Sqrt[c + d*x]*(2*b^2*c^2*x + a^2*d^2*x + a*b*c*(c - 2*d*x)))/(b*x*(a + b*x))) + c^(3/2)*(4*b*c - 5*a*d)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]] - (Sqrt[b*c - a*d]*(4*b^2*c^2 - 3*a*b*c*d - a^2*d^2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/b^(3/2))/a^3","A",1
474,1,192,219,0.3694847,"\int \frac{(c+d x)^{5/2}}{x^3 (a+b x)^2} \, dx","Integrate[(c + d*x)^(5/2)/(x^3*(a + b*x)^2),x]","\frac{\frac{a \sqrt{c+d x} \left(a^2 \left(-2 c^2-9 c d x+4 d^2 x^2\right)+a b c x (6 c-17 d x)+12 b^2 c^2 x^2\right)}{x^2 (a+b x)}-\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)+\frac{4 \sqrt{b c-a d} \left(a^2 d^2-7 a b c d+6 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{\sqrt{b}}}{4 a^4}","\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,"((a*Sqrt[c + d*x]*(12*b^2*c^2*x^2 + a*b*c*x*(6*c - 17*d*x) + a^2*(-2*c^2 - 9*c*d*x + 4*d^2*x^2)))/(x^2*(a + b*x)) - Sqrt[c]*(24*b^2*c^2 - 40*a*b*c*d + 15*a^2*d^2)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]] + (4*Sqrt[b*c - a*d]*(6*b^2*c^2 - 7*a*b*c*d + a^2*d^2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/Sqrt[b])/(4*a^4)","A",1
475,1,237,284,0.6799137,"\int \frac{(c+d x)^{5/2}}{x^4 (a+b x)^2} \, dx","Integrate[(c + d*x)^(5/2)/(x^4*(a + b*x)^2),x]","-\frac{24 \sqrt{b} \sqrt{b c-a d} \left(3 a^2 d^2-11 a b c d+8 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)+\frac{a \sqrt{c+d x} \left(a^3 \left(8 c^2+26 c d x+33 d^2 x^2\right)+a^2 b x \left(-16 c^2-82 c d x+57 d^2 x^2\right)+12 a b^2 c x^2 (4 c-13 d x)+96 b^3 c^2 x^3\right)}{x^3 (a+b x)}-\frac{3 \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)}{\sqrt{c}}}{24 a^5}","-\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,"-1/24*((a*Sqrt[c + d*x]*(96*b^3*c^2*x^3 + 12*a*b^2*c*x^2*(4*c - 13*d*x) + a^3*(8*c^2 + 26*c*d*x + 33*d^2*x^2) + a^2*b*x*(-16*c^2 - 82*c*d*x + 57*d^2*x^2)))/(x^3*(a + b*x)) - (3*(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]])/Sqrt[c] + 24*Sqrt[b]*Sqrt[b*c - a*d]*(8*b^2*c^2 - 11*a*b*c*d + 3*a^2*d^2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/a^5","A",1
476,1,148,164,0.5900868,"\int \frac{1}{x^2 (a+b x)^2 \sqrt{c+d x}} \, dx","Integrate[1/(x^2*(a + b*x)^2*Sqrt[c + d*x]),x]","\frac{\frac{a \sqrt{c+d x} \left(a^2 d+a b (d x-c)-2 b^2 c x\right)}{x (a+b x) (b c-a d)}+\frac{b^{3/2} c (5 a d-4 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{3/2}}+\frac{(a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{\sqrt{c}}}{a^3 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,"((a*Sqrt[c + d*x]*(a^2*d - 2*b^2*c*x + a*b*(-c + d*x)))/((b*c - a*d)*x*(a + b*x)) + ((4*b*c + a*d)*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/Sqrt[c] + (b^(3/2)*c*(-4*b*c + 5*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(b*c - a*d)^(3/2))/(a^3*c)","A",1
477,1,166,216,0.1502836,"\int \frac{1}{x^2 (a+b x)^2 (c+d x)^{3/2}} \, dx","Integrate[1/(x^2*(a + b*x)^2*(c + d*x)^(3/2)),x]","\frac{b^2 c^2 x (a+b x) (4 b c-7 a d) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b (c+d x)}{b c-a d}\right)-(a d-b c) \left(x (a+b x) \left(3 a^2 d^2+a b c d-4 b^2 c^2\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{d x}{c}+1\right)+a c \left(a^2 d+a b (d x-c)-2 b^2 c x\right)\right)}{a^3 c^2 x (a+b x) \sqrt{c+d x} (b c-a d)^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,"(b^2*c^2*(4*b*c - 7*a*d)*x*(a + b*x)*Hypergeometric2F1[-1/2, 1, 1/2, (b*(c + d*x))/(b*c - a*d)] - (-(b*c) + a*d)*(a*c*(a^2*d - 2*b^2*c*x + a*b*(-c + d*x)) + (-4*b^2*c^2 + a*b*c*d + 3*a^2*d^2)*x*(a + b*x)*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (d*x)/c]))/(a^3*c^2*(b*c - a*d)^2*x*(a + b*x)*Sqrt[c + d*x])","C",1
478,1,170,277,0.154759,"\int \frac{1}{x^2 (a+b x)^2 (c+d x)^{5/2}} \, dx","Integrate[1/(x^2*(a + b*x)^2*(c + d*x)^(5/2)),x]","\frac{b^2 c^2 x (a+b x) (4 b c-9 a d) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{b (c+d x)}{b c-a d}\right)-(b c-a d) \left(x (a+b x) \left(-5 a^2 d^2+a b c d+4 b^2 c^2\right) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{d x}{c}+1\right)-3 a c \left(a^2 d+a b (d x-c)-2 b^2 c x\right)\right)}{3 a^3 c^2 x (a+b x) (c+d x)^{3/2} (b c-a d)^2}","-\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,"(b^2*c^2*(4*b*c - 9*a*d)*x*(a + b*x)*Hypergeometric2F1[-3/2, 1, -1/2, (b*(c + d*x))/(b*c - a*d)] - (b*c - a*d)*(-3*a*c*(a^2*d - 2*b^2*c*x + a*b*(-c + d*x)) + (4*b^2*c^2 + a*b*c*d - 5*a^2*d^2)*x*(a + b*x)*Hypergeometric2F1[-3/2, 1, -1/2, 1 + (d*x)/c]))/(3*a^3*c^2*(b*c - a*d)^2*x*(a + b*x)*(c + d*x)^(3/2))","C",1
479,1,146,192,0.3205989,"\int x^{5/2} \sqrt{a+b x} (A+B x) \, dx","Integrate[x^(5/2)*Sqrt[a + b*x]*(A + B*x),x]","\frac{\sqrt{a+b x} \left(\frac{15 a^{7/2} (7 a B-10 A b) \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}+\sqrt{b} \sqrt{x} \left(-105 a^4 B+10 a^3 b (15 A+7 B x)-4 a^2 b^2 x (25 A+14 B x)+16 a b^3 x^2 (5 A+3 B x)+96 b^4 x^3 (5 A+4 B x)\right)\right)}{1920 b^{9/2}}","-\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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(-105*a^4*B + 16*a*b^3*x^2*(5*A + 3*B*x) + 96*b^4*x^3*(5*A + 4*B*x) + 10*a^3*b*(15*A + 7*B*x) - 4*a^2*b^2*x*(25*A + 14*B*x)) + (15*a^(7/2)*(-10*A*b + 7*a*B)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(1920*b^(9/2))","A",1
480,1,126,159,0.3106078,"\int x^{3/2} \sqrt{a+b x} (A+B x) \, dx","Integrate[x^(3/2)*Sqrt[a + b*x]*(A + B*x),x]","\frac{\sqrt{a+b x} \left(\sqrt{b} \sqrt{x} \left(15 a^3 B-2 a^2 b (12 A+5 B x)+8 a b^2 x (2 A+B x)+16 b^3 x^2 (4 A+3 B x)\right)-\frac{3 a^{5/2} (5 a B-8 A b) \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}\right)}{192 b^{7/2}}","\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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(15*a^3*B + 8*a*b^2*x*(2*A + B*x) + 16*b^3*x^2*(4*A + 3*B*x) - 2*a^2*b*(12*A + 5*B*x)) - (3*a^(5/2)*(-8*A*b + 5*a*B)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(192*b^(7/2))","A",1
481,1,106,126,0.2485248,"\int \sqrt{x} \sqrt{a+b x} (A+B x) \, dx","Integrate[Sqrt[x]*Sqrt[a + b*x]*(A + B*x),x]","\frac{\sqrt{a+b x} \left(\frac{3 a^{3/2} (a B-2 A b) \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}+\sqrt{b} \sqrt{x} \left(-3 a^2 B+2 a b (3 A+B x)+4 b^2 x (3 A+2 B x)\right)\right)}{24 b^{5/2}}","-\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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(-3*a^2*B + 2*a*b*(3*A + B*x) + 4*b^2*x*(3*A + 2*B*x)) + (3*a^(3/2)*(-2*A*b + a*B)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(24*b^(5/2))","A",1
482,1,87,93,0.2195619,"\int \frac{\sqrt{a+b x} (A+B x)}{\sqrt{x}} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/Sqrt[x],x]","\frac{\sqrt{a+b x} \left(\sqrt{b} \sqrt{x} (B (a+2 b x)+4 A b)-\frac{\sqrt{a} (a B-4 A b) \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}\right)}{4 b^{3/2}}","\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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(4*A*b + B*(a + 2*b*x)) - (Sqrt[a]*(-4*A*b + a*B)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(4*b^(3/2))","A",1
483,1,72,82,0.1922272,"\int \frac{\sqrt{a+b x} (A+B x)}{x^{3/2}} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/x^(3/2),x]","\sqrt{a+b x} \left(\frac{(a B+2 A b) \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \sqrt{\frac{b x}{a}+1}}+\frac{B x-2 A}{\sqrt{x}}\right)","\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,"Sqrt[a + b*x]*((-2*A + B*x)/Sqrt[x] + ((2*A*b + a*B)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Sqrt[1 + (b*x)/a]))","A",1
484,1,85,69,0.104197,"\int \frac{\sqrt{a+b x} (A+B x)}{x^{5/2}} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/x^(5/2),x]","-\frac{2 (a+b x)^{3/2} (A b-a B)}{3 a b x^{3/2}}-\frac{2 a B \sqrt{a+b x} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};-\frac{b x}{a}\right)}{3 b x^{3/2} \sqrt{\frac{b x}{a}+1}}","-\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*(A*b - a*B)*(a + b*x)^(3/2))/(3*a*b*x^(3/2)) - (2*a*B*Sqrt[a + b*x]*Hypergeometric2F1[-3/2, -3/2, -1/2, -((b*x)/a)])/(3*b*x^(3/2)*Sqrt[1 + (b*x)/a])","C",1
485,1,36,53,0.0154842,"\int \frac{\sqrt{a+b x} (A+B x)}{x^{7/2}} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/x^(7/2),x]","-\frac{2 (a+b x)^{3/2} (3 a A+5 a B x-2 A b x)}{15 a^2 x^{5/2}}","\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,"(-2*(a + b*x)^(3/2)*(3*a*A - 2*A*b*x + 5*a*B*x))/(15*a^2*x^(5/2))","A",1
486,1,57,84,0.0352675,"\int \frac{\sqrt{a+b x} (A+B x)}{x^{9/2}} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/x^(9/2),x]","-\frac{2 (a+b x)^{3/2} \left(3 a^2 (5 A+7 B x)-2 a b x (6 A+7 B x)+8 A b^2 x^2\right)}{105 a^3 x^{7/2}}","-\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,"(-2*(a + b*x)^(3/2)*(8*A*b^2*x^2 + 3*a^2*(5*A + 7*B*x) - 2*a*b*x*(6*A + 7*B*x)))/(105*a^3*x^(7/2))","A",1
487,1,73,117,0.0414873,"\int \frac{\sqrt{a+b x} (A+B x)}{x^{11/2}} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/x^(11/2),x]","-\frac{2 (a+b x)^{3/2} \left(5 a^3 (7 A+9 B x)-6 a^2 b x (5 A+6 B x)+24 a b^2 x^2 (A+B x)-16 A b^3 x^3\right)}{315 a^4 x^{9/2}}","\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,"(-2*(a + b*x)^(3/2)*(-16*A*b^3*x^3 + 24*a*b^2*x^2*(A + B*x) - 6*a^2*b*x*(5*A + 6*B*x) + 5*a^3*(7*A + 9*B*x)))/(315*a^4*x^(9/2))","A",1
488,1,95,150,0.0470691,"\int \frac{\sqrt{a+b x} (A+B x)}{x^{13/2}} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/x^(13/2),x]","-\frac{2 (a+b x)^{3/2} \left(35 a^4 (9 A+11 B x)-10 a^3 b x (28 A+33 B x)+24 a^2 b^2 x^2 (10 A+11 B x)-16 a b^3 x^3 (12 A+11 B x)+128 A b^4 x^4\right)}{3465 a^5 x^{11/2}}","-\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,"(-2*(a + b*x)^(3/2)*(128*A*b^4*x^4 + 35*a^4*(9*A + 11*B*x) + 24*a^2*b^2*x^2*(10*A + 11*B*x) - 16*a*b^3*x^3*(12*A + 11*B*x) - 10*a^3*b*x*(28*A + 33*B*x)))/(3465*a^5*x^(11/2))","A",1
489,1,114,183,0.0497847,"\int \frac{\sqrt{a+b x} (A+B x)}{x^{15/2}} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/x^(15/2),x]","-\frac{2 (a+b x)^{3/2} \left(315 a^5 (11 A+13 B x)-70 a^4 b x (45 A+52 B x)+80 a^3 b^2 x^2 (35 A+39 B x)-96 a^2 b^3 x^3 (25 A+26 B x)+128 a b^4 x^4 (15 A+13 B x)-1280 A b^5 x^5\right)}{45045 a^6 x^{13/2}}","\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,"(-2*(a + b*x)^(3/2)*(-1280*A*b^5*x^5 + 315*a^5*(11*A + 13*B*x) + 128*a*b^4*x^4*(15*A + 13*B*x) - 96*a^2*b^3*x^3*(25*A + 26*B*x) + 80*a^3*b^2*x^2*(35*A + 39*B*x) - 70*a^4*b*x*(45*A + 52*B*x)))/(45045*a^6*x^(13/2))","A",1
490,1,151,225,0.4012389,"\int x^{5/2} (a+b x)^{3/2} (A+B x) \, dx","Integrate[x^(5/2)*(a + b*x)^(3/2)*(A + B*x),x]","\frac{\sqrt{a+b x} (12 A b-7 a B) \left(\sqrt{b} \sqrt{x} \sqrt{\frac{b x}{a}+1} \left(15 a^4-10 a^3 b x+8 a^2 b^2 x^2+176 a b^3 x^3+128 b^4 x^4\right)-15 a^{9/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)\right)}{7680 b^{9/2} \sqrt{\frac{b x}{a}+1}}+\frac{B x^{7/2} (a+b x)^{5/2}}{6 b}","-\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,"(B*x^(7/2)*(a + b*x)^(5/2))/(6*b) + ((12*A*b - 7*a*B)*Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*Sqrt[1 + (b*x)/a]*(15*a^4 - 10*a^3*b*x + 8*a^2*b^2*x^2 + 176*a*b^3*x^3 + 128*b^4*x^4) - 15*a^(9/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(7680*b^(9/2)*Sqrt[1 + (b*x)/a])","A",1
491,1,144,192,0.3173892,"\int x^{3/2} (a+b x)^{3/2} (A+B x) \, dx","Integrate[x^(3/2)*(a + b*x)^(3/2)*(A + B*x),x]","\frac{\sqrt{a+b x} \left(\sqrt{b} \sqrt{x} \left(15 a^4 B-10 a^3 b (3 A+B x)+4 a^2 b^2 x (5 A+2 B x)+16 a b^3 x^2 (15 A+11 B x)+32 b^4 x^3 (5 A+4 B x)\right)-\frac{15 a^{7/2} (a B-2 A b) \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}\right)}{640 b^{7/2}}","\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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(15*a^4*B - 10*a^3*b*(3*A + B*x) + 4*a^2*b^2*x*(5*A + 2*B*x) + 32*b^4*x^3*(5*A + 4*B*x) + 16*a*b^3*x^2*(15*A + 11*B*x)) - (15*a^(7/2)*(-2*A*b + a*B)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(640*b^(7/2))","A",1
492,1,126,159,0.2731145,"\int \sqrt{x} (a+b x)^{3/2} (A+B x) \, dx","Integrate[Sqrt[x]*(a + b*x)^(3/2)*(A + B*x),x]","\frac{\sqrt{a+b x} \left(\frac{3 a^{5/2} (3 a B-8 A b) \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}+\sqrt{b} \sqrt{x} \left(-9 a^3 B+6 a^2 b (4 A+B x)+8 a b^2 x (14 A+9 B x)+16 b^3 x^2 (4 A+3 B x)\right)\right)}{192 b^{5/2}}","-\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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(-9*a^3*B + 6*a^2*b*(4*A + B*x) + 16*b^3*x^2*(4*A + 3*B*x) + 8*a*b^2*x*(14*A + 9*B*x)) + (3*a^(5/2)*(-8*A*b + 3*a*B)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(192*b^(5/2))","A",1
493,1,107,126,0.2853189,"\int \frac{(a+b x)^{3/2} (A+B x)}{\sqrt{x}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/Sqrt[x],x]","\frac{\sqrt{a+b x} \left(\sqrt{b} \sqrt{x} \left(3 a^2 B+2 a b (15 A+7 B x)+4 b^2 x (3 A+2 B x)\right)-\frac{3 a^{3/2} (a B-6 A b) \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}\right)}{24 b^{3/2}}","\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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(3*a^2*B + 4*b^2*x*(3*A + 2*B*x) + 2*a*b*(15*A + 7*B*x)) - (3*a^(3/2)*(-6*A*b + a*B)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(24*b^(3/2))","A",1
494,1,91,115,0.2262295,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^{3/2}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/x^(3/2),x]","\frac{1}{4} \sqrt{a+b x} \left(\frac{a (5 B x-8 A)+2 b x (2 A+B x)}{\sqrt{x}}+\frac{3 \sqrt{a} (a B+4 A b) \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{b} \sqrt{\frac{b x}{a}+1}}\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,"(Sqrt[a + b*x]*((2*b*x*(2*A + B*x) + a*(-8*A + 5*B*x))/Sqrt[x] + (3*Sqrt[a]*(4*A*b + a*B)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[b]*Sqrt[1 + (b*x)/a])))/4","A",1
495,1,73,117,0.0923832,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^{5/2}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/x^(5/2),x]","\frac{2 \sqrt{a+b x} \left(-\frac{x (3 a B+2 A b) \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-\frac{b x}{a}\right)}{\sqrt{\frac{b x}{a}+1}}-\frac{A (a+b x)^2}{a}\right)}{3 x^{3/2}}","-\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,"(2*Sqrt[a + b*x]*(-((A*(a + b*x)^2)/a) - ((2*A*b + 3*a*B)*x*Hypergeometric2F1[-3/2, -1/2, 1/2, -((b*x)/a)])/Sqrt[1 + (b*x)/a]))/(3*x^(3/2))","C",1
496,1,77,89,0.083732,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^{7/2}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/x^(7/2),x]","\frac{2 \sqrt{a+b x} \left(-\frac{a^3 B \, _2F_1\left(-\frac{5}{2},-\frac{5}{2};-\frac{3}{2};-\frac{b x}{a}\right)}{\sqrt{\frac{b x}{a}+1}}-(a+b x)^2 (A b-a B)\right)}{5 a b x^{5/2}}","-\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,"(2*Sqrt[a + b*x]*(-((A*b - a*B)*(a + b*x)^2) - (a^3*B*Hypergeometric2F1[-5/2, -5/2, -3/2, -((b*x)/a)])/Sqrt[1 + (b*x)/a]))/(5*a*b*x^(5/2))","C",1
497,1,36,53,0.0203696,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^{9/2}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/x^(9/2),x]","-\frac{2 (a+b x)^{5/2} (5 a A+7 a B x-2 A b x)}{35 a^2 x^{7/2}}","\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,"(-2*(a + b*x)^(5/2)*(5*a*A - 2*A*b*x + 7*a*B*x))/(35*a^2*x^(7/2))","A",1
498,1,57,84,0.0373922,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^{11/2}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/x^(11/2),x]","-\frac{2 (a+b x)^{5/2} \left(5 a^2 (7 A+9 B x)-2 a b x (10 A+9 B x)+8 A b^2 x^2\right)}{315 a^3 x^{9/2}}","-\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,"(-2*(a + b*x)^(5/2)*(8*A*b^2*x^2 + 5*a^2*(7*A + 9*B*x) - 2*a*b*x*(10*A + 9*B*x)))/(315*a^3*x^(9/2))","A",1
499,1,76,117,0.0364196,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^{13/2}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/x^(13/2),x]","-\frac{2 (a+b x)^{5/2} \left(35 a^3 (9 A+11 B x)-10 a^2 b x (21 A+22 B x)+8 a b^2 x^2 (15 A+11 B x)-48 A b^3 x^3\right)}{3465 a^4 x^{11/2}}","\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,"(-2*(a + b*x)^(5/2)*(-48*A*b^3*x^3 + 35*a^3*(9*A + 11*B*x) + 8*a*b^2*x^2*(15*A + 11*B*x) - 10*a^2*b*x*(21*A + 22*B*x)))/(3465*a^4*x^(11/2))","A",1
500,1,95,150,0.0508675,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^{15/2}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/x^(15/2),x]","-\frac{2 (a+b x)^{5/2} \left(105 a^4 (11 A+13 B x)-70 a^3 b x (12 A+13 B x)+40 a^2 b^2 x^2 (14 A+13 B x)-16 a b^3 x^3 (20 A+13 B x)+128 A b^4 x^4\right)}{15015 a^5 x^{13/2}}","-\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,"(-2*(a + b*x)^(5/2)*(128*A*b^4*x^4 + 105*a^4*(11*A + 13*B*x) - 70*a^3*b*x*(12*A + 13*B*x) + 40*a^2*b^2*x^2*(14*A + 13*B*x) - 16*a*b^3*x^3*(20*A + 13*B*x)))/(15015*a^5*x^(13/2))","A",1
501,1,111,183,0.0635696,"\int \frac{(a+b x)^{3/2} (A+B x)}{x^{17/2}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/x^(17/2),x]","-\frac{2 (a+b x)^{5/2} \left(231 a^5 (13 A+15 B x)-210 a^4 b x (11 A+12 B x)+1680 a^3 b^2 x^2 (A+B x)-160 a^2 b^3 x^3 (7 A+6 B x)+128 a b^4 x^4 (5 A+3 B x)-256 A b^5 x^5\right)}{45045 a^6 x^{15/2}}","\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,"(-2*(a + b*x)^(5/2)*(-256*A*b^5*x^5 + 1680*a^3*b^2*x^2*(A + B*x) + 128*a*b^4*x^4*(5*A + 3*B*x) - 160*a^2*b^3*x^3*(7*A + 6*B*x) - 210*a^4*b*x*(11*A + 12*B*x) + 231*a^5*(13*A + 15*B*x)))/(45045*a^6*x^(15/2))","A",1
502,1,151,225,0.4130426,"\int x^{3/2} (a+b x)^{5/2} (A+B x) \, dx","Integrate[x^(3/2)*(a + b*x)^(5/2)*(A + B*x),x]","\frac{\sqrt{a+b x} (12 A b-5 a B) \left(15 a^{9/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\sqrt{b} \sqrt{x} \sqrt{\frac{b x}{a}+1} \left(-15 a^4+10 a^3 b x+248 a^2 b^2 x^2+336 a b^3 x^3+128 b^4 x^4\right)\right)}{7680 b^{7/2} \sqrt{\frac{b x}{a}+1}}+\frac{B x^{5/2} (a+b x)^{7/2}}{6 b}","\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,"(B*x^(5/2)*(a + b*x)^(7/2))/(6*b) + ((12*A*b - 5*a*B)*Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*Sqrt[1 + (b*x)/a]*(-15*a^4 + 10*a^3*b*x + 248*a^2*b^2*x^2 + 336*a*b^3*x^3 + 128*b^4*x^4) + 15*a^(9/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(7680*b^(7/2)*Sqrt[1 + (b*x)/a])","A",1
503,1,145,192,0.3276116,"\int \sqrt{x} (a+b x)^{5/2} (A+B x) \, dx","Integrate[Sqrt[x]*(a + b*x)^(5/2)*(A + B*x),x]","\frac{\sqrt{a+b x} \left(\frac{15 a^{7/2} (3 a B-10 A b) \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}+\sqrt{b} \sqrt{x} \left(-45 a^4 B+30 a^3 b (5 A+B x)+4 a^2 b^2 x (295 A+186 B x)+16 a b^3 x^2 (85 A+63 B x)+96 b^4 x^3 (5 A+4 B x)\right)\right)}{1920 b^{5/2}}","-\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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(-45*a^4*B + 30*a^3*b*(5*A + B*x) + 96*b^4*x^3*(5*A + 4*B*x) + 16*a*b^3*x^2*(85*A + 63*B*x) + 4*a^2*b^2*x*(295*A + 186*B*x)) + (15*a^(7/2)*(-10*A*b + 3*a*B)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(1920*b^(5/2))","A",1
504,1,126,159,0.2932473,"\int \frac{(a+b x)^{5/2} (A+B x)}{\sqrt{x}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/Sqrt[x],x]","\frac{\sqrt{a+b x} \left(\sqrt{b} \sqrt{x} \left(15 a^3 B+2 a^2 b (132 A+59 B x)+8 a b^2 x (26 A+17 B x)+16 b^3 x^2 (4 A+3 B x)\right)-\frac{15 a^{5/2} (a B-8 A b) \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}\right)}{192 b^{3/2}}","\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,"(Sqrt[a + b*x]*(Sqrt[b]*Sqrt[x]*(15*a^3*B + 16*b^3*x^2*(4*A + 3*B*x) + 8*a*b^2*x*(26*A + 17*B*x) + 2*a^2*b*(132*A + 59*B*x)) - (15*a^(5/2)*(-8*A*b + a*B)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(192*b^(3/2))","A",1
505,1,111,144,0.3181251,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{3/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/x^(3/2),x]","\frac{1}{24} \sqrt{a+b x} \left(\frac{15 a^{3/2} (a B+6 A b) \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{b} \sqrt{\frac{b x}{a}+1}}+\frac{a^2 (33 B x-48 A)+2 a b x (27 A+13 B x)+4 b^2 x^2 (3 A+2 B x)}{\sqrt{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*x]*((4*b^2*x^2*(3*A + 2*B*x) + 2*a*b*x*(27*A + 13*B*x) + a^2*(-48*A + 33*B*x))/Sqrt[x] + (15*a^(3/2)*(6*A*b + a*B)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[b]*Sqrt[1 + (b*x)/a])))/24","A",1
506,1,76,152,0.0537156,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{5/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/x^(5/2),x]","\frac{2 \sqrt{a+b x} \left(-\frac{a^2 x (3 a B+4 A b) \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};-\frac{b x}{a}\right)}{\sqrt{\frac{b x}{a}+1}}-A (a+b x)^3\right)}{3 a x^{3/2}}","-\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,"(2*Sqrt[a + b*x]*(-(A*(a + b*x)^3) - (a^2*(4*A*b + 3*a*B)*x*Hypergeometric2F1[-5/2, -1/2, 1/2, -((b*x)/a)])/Sqrt[1 + (b*x)/a]))/(3*a*x^(3/2))","C",1
507,1,76,150,0.0514491,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{7/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/x^(7/2),x]","\frac{2 \sqrt{a+b x} \left(-\frac{a^2 x (5 a B+2 A b) \, _2F_1\left(-\frac{5}{2},-\frac{3}{2};-\frac{1}{2};-\frac{b x}{a}\right)}{\sqrt{\frac{b x}{a}+1}}-3 A (a+b x)^3\right)}{15 a x^{5/2}}","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,"(2*Sqrt[a + b*x]*(-3*A*(a + b*x)^3 - (a^2*(2*A*b + 5*a*B)*x*Hypergeometric2F1[-5/2, -3/2, -1/2, -((b*x)/a)])/Sqrt[1 + (b*x)/a]))/(15*a*x^(5/2))","C",1
508,1,77,111,0.0831794,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{9/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/x^(9/2),x]","\frac{2 \sqrt{a+b x} \left(-\frac{a^4 B \, _2F_1\left(-\frac{7}{2},-\frac{7}{2};-\frac{5}{2};-\frac{b x}{a}\right)}{\sqrt{\frac{b x}{a}+1}}-(a+b x)^3 (A b-a B)\right)}{7 a b x^{7/2}}","-\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,"(2*Sqrt[a + b*x]*(-((A*b - a*B)*(a + b*x)^3) - (a^4*B*Hypergeometric2F1[-7/2, -7/2, -5/2, -((b*x)/a)])/Sqrt[1 + (b*x)/a]))/(7*a*b*x^(7/2))","C",1
509,1,36,53,0.0239473,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{11/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/x^(11/2),x]","-\frac{2 (a+b x)^{7/2} (7 a A+9 a B x-2 A b x)}{63 a^2 x^{9/2}}","\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,"(-2*(a + b*x)^(7/2)*(7*a*A - 2*A*b*x + 9*a*B*x))/(63*a^2*x^(9/2))","A",1
510,1,57,84,0.0383439,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{13/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/x^(13/2),x]","-\frac{2 (a+b x)^{7/2} \left(7 a^2 (9 A+11 B x)-2 a b x (14 A+11 B x)+8 A b^2 x^2\right)}{693 a^3 x^{11/2}}","-\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,"(-2*(a + b*x)^(7/2)*(8*A*b^2*x^2 + 7*a^2*(9*A + 11*B*x) - 2*a*b*x*(14*A + 11*B*x)))/(693*a^3*x^(11/2))","A",1
511,1,76,117,0.0442577,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{15/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/x^(15/2),x]","-\frac{2 (a+b x)^{7/2} \left(63 a^3 (11 A+13 B x)-14 a^2 b x (27 A+26 B x)+8 a b^2 x^2 (21 A+13 B x)-48 A b^3 x^3\right)}{9009 a^4 x^{13/2}}","\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,"(-2*(a + b*x)^(7/2)*(-48*A*b^3*x^3 + 63*a^3*(11*A + 13*B*x) + 8*a*b^2*x^2*(21*A + 13*B*x) - 14*a^2*b*x*(27*A + 26*B*x)))/(9009*a^4*x^(13/2))","A",1
512,1,95,150,0.0642841,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{17/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/x^(17/2),x]","-\frac{2 (a+b x)^{7/2} \left(231 a^4 (13 A+15 B x)-42 a^3 b x (44 A+45 B x)+168 a^2 b^2 x^2 (6 A+5 B x)-16 a b^3 x^3 (28 A+15 B x)+128 A b^4 x^4\right)}{45045 a^5 x^{15/2}}","-\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,"(-2*(a + b*x)^(7/2)*(128*A*b^4*x^4 + 168*a^2*b^2*x^2*(6*A + 5*B*x) + 231*a^4*(13*A + 15*B*x) - 16*a*b^3*x^3*(28*A + 15*B*x) - 42*a^3*b*x*(44*A + 45*B*x)))/(45045*a^5*x^(15/2))","A",1
513,1,114,183,0.0603853,"\int \frac{(a+b x)^{5/2} (A+B x)}{x^{19/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/x^(19/2),x]","-\frac{2 (a+b x)^{7/2} \left(3003 a^5 (15 A+17 B x)-462 a^4 b x (65 A+68 B x)+336 a^3 b^2 x^2 (55 A+51 B x)-224 a^2 b^3 x^3 (45 A+34 B x)+128 a b^4 x^4 (35 A+17 B x)-1280 A b^5 x^5\right)}{765765 a^6 x^{17/2}}","\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,"(-2*(a + b*x)^(7/2)*(-1280*A*b^5*x^5 + 3003*a^5*(15*A + 17*B*x) + 128*a*b^4*x^4*(35*A + 17*B*x) - 224*a^2*b^3*x^3*(45*A + 34*B*x) + 336*a^3*b^2*x^2*(55*A + 51*B*x) - 462*a^4*b*x*(65*A + 68*B*x)))/(765765*a^6*x^(17/2))","A",1
514,1,133,192,0.3944156,"\int \frac{x^{7/2} (A+B x)}{\sqrt{a+b x}} \, dx","Integrate[(x^(7/2)*(A + B*x))/Sqrt[a + b*x],x]","\frac{\sqrt{a+b x} \left(\frac{(10 A b-9 a B) \left(105 a^{7/2} \sqrt{b} \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+b x \sqrt{\frac{b x}{a}+1} \left(-105 a^3+70 a^2 b x-56 a b^2 x^2+48 b^3 x^3\right)\right)}{\sqrt{\frac{b x}{a}+1}}+384 b^5 B x^5\right)}{1920 b^6 \sqrt{x}}","\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,"(Sqrt[a + b*x]*(384*b^5*B*x^5 + ((10*A*b - 9*a*B)*(b*x*Sqrt[1 + (b*x)/a]*(-105*a^3 + 70*a^2*b*x - 56*a*b^2*x^2 + 48*b^3*x^3) + 105*a^(7/2)*Sqrt[b]*Sqrt[x]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/Sqrt[1 + (b*x)/a]))/(1920*b^6*Sqrt[x])","A",1
515,1,122,159,0.3317751,"\int \frac{x^{5/2} (A+B x)}{\sqrt{a+b x}} \, dx","Integrate[(x^(5/2)*(A + B*x))/Sqrt[a + b*x],x]","\frac{\sqrt{a+b x} \left(\frac{(8 A b-7 a B) \left(b x \sqrt{\frac{b x}{a}+1} \left(15 a^2-10 a b x+8 b^2 x^2\right)-15 a^{5/2} \sqrt{b} \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)\right)}{\sqrt{\frac{b x}{a}+1}}+48 b^4 B x^4\right)}{192 b^5 \sqrt{x}}","-\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,"(Sqrt[a + b*x]*(48*b^4*B*x^4 + ((8*A*b - 7*a*B)*(b*x*Sqrt[1 + (b*x)/a]*(15*a^2 - 10*a*b*x + 8*b^2*x^2) - 15*a^(5/2)*Sqrt[b]*Sqrt[x]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/Sqrt[1 + (b*x)/a]))/(192*b^5*Sqrt[x])","A",1
516,1,113,126,0.116853,"\int \frac{x^{3/2} (A+B x)}{\sqrt{a+b x}} \, dx","Integrate[(x^(3/2)*(A + B*x))/Sqrt[a + b*x],x]","\frac{\sqrt{b} \sqrt{x} (a+b x) \left(15 a^2 B-2 a b (9 A+5 B x)+4 b^2 x (3 A+2 B x)\right)-3 a^{5/2} \sqrt{\frac{b x}{a}+1} (5 a B-6 A b) \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{24 b^{7/2} \sqrt{a+b x}}","\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,"(Sqrt[b]*Sqrt[x]*(a + b*x)*(15*a^2*B + 4*b^2*x*(3*A + 2*B*x) - 2*a*b*(9*A + 5*B*x)) - 3*a^(5/2)*(-6*A*b + 5*a*B)*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(24*b^(7/2)*Sqrt[a + b*x])","A",1
517,1,93,93,0.1161745,"\int \frac{\sqrt{x} (A+B x)}{\sqrt{a+b x}} \, dx","Integrate[(Sqrt[x]*(A + B*x))/Sqrt[a + b*x],x]","\frac{a^{3/2} \sqrt{\frac{b x}{a}+1} (3 a B-4 A b) \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\sqrt{b} \sqrt{x} (a+b x) (-3 a B+4 A b+2 b B x)}{4 b^{5/2} \sqrt{a+b x}}","-\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,"(Sqrt[b]*Sqrt[x]*(a + b*x)*(4*A*b - 3*a*B + 2*b*B*x) + a^(3/2)*(-4*A*b + 3*a*B)*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*b^(5/2)*Sqrt[a + b*x])","A",1
518,1,77,56,0.0755899,"\int \frac{A+B x}{\sqrt{x} \sqrt{a+b x}} \, dx","Integrate[(A + B*x)/(Sqrt[x]*Sqrt[a + b*x]),x]","\frac{\sqrt{b} B \sqrt{x} (a+b x)-\sqrt{a} \sqrt{\frac{b x}{a}+1} (a B-2 A b) \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{3/2} \sqrt{a+b x}}","\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,"(Sqrt[b]*B*Sqrt[x]*(a + b*x) - Sqrt[a]*(-2*A*b + a*B)*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(b^(3/2)*Sqrt[a + b*x])","A",1
519,1,69,50,0.187598,"\int \frac{A+B x}{x^{3/2} \sqrt{a+b x}} \, dx","Integrate[(A + B*x)/(x^(3/2)*Sqrt[a + b*x]),x]","\frac{2 \left(\frac{a^{3/2} B \sqrt{\frac{b x}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{b}}-\frac{A (a+b x)}{\sqrt{x}}\right)}{a \sqrt{a+b x}}","\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*(a + b*x))/Sqrt[x]) + (a^(3/2)*B*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[b]))/(a*Sqrt[a + b*x])","A",1
520,1,35,53,0.0208135,"\int \frac{A+B x}{x^{5/2} \sqrt{a+b x}} \, dx","Integrate[(A + B*x)/(x^(5/2)*Sqrt[a + b*x]),x]","-\frac{2 \sqrt{a+b x} (a (A+3 B x)-2 A b x)}{3 a^2 x^{3/2}}","\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,"(-2*Sqrt[a + b*x]*(-2*A*b*x + a*(A + 3*B*x)))/(3*a^2*x^(3/2))","A",1
521,1,56,84,0.0221552,"\int \frac{A+B x}{x^{7/2} \sqrt{a+b x}} \, dx","Integrate[(A + B*x)/(x^(7/2)*Sqrt[a + b*x]),x]","-\frac{2 \sqrt{a+b x} \left(a^2 (3 A+5 B x)-2 a b x (2 A+5 B x)+8 A b^2 x^2\right)}{15 a^3 x^{5/2}}","-\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,"(-2*Sqrt[a + b*x]*(8*A*b^2*x^2 - 2*a*b*x*(2*A + 5*B*x) + a^2*(3*A + 5*B*x)))/(15*a^3*x^(5/2))","A",1
522,1,76,117,0.0332592,"\int \frac{A+B x}{x^{9/2} \sqrt{a+b x}} \, dx","Integrate[(A + B*x)/(x^(9/2)*Sqrt[a + b*x]),x]","-\frac{2 \sqrt{a+b x} \left(3 a^3 (5 A+7 B x)-2 a^2 b x (9 A+14 B x)+8 a b^2 x^2 (3 A+7 B x)-48 A b^3 x^3\right)}{105 a^4 x^{7/2}}","\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,"(-2*Sqrt[a + b*x]*(-48*A*b^3*x^3 + 8*a*b^2*x^2*(3*A + 7*B*x) + 3*a^3*(5*A + 7*B*x) - 2*a^2*b*x*(9*A + 14*B*x)))/(105*a^4*x^(7/2))","A",1
523,1,95,150,0.040521,"\int \frac{A+B x}{x^{11/2} \sqrt{a+b x}} \, dx","Integrate[(A + B*x)/(x^(11/2)*Sqrt[a + b*x]),x]","-\frac{2 \sqrt{a+b x} \left(5 a^4 (7 A+9 B x)-2 a^3 b x (20 A+27 B x)+24 a^2 b^2 x^2 (2 A+3 B x)-16 a b^3 x^3 (4 A+9 B x)+128 A b^4 x^4\right)}{315 a^5 x^{9/2}}","-\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,"(-2*Sqrt[a + b*x]*(128*A*b^4*x^4 + 24*a^2*b^2*x^2*(2*A + 3*B*x) - 16*a*b^3*x^3*(4*A + 9*B*x) + 5*a^4*(7*A + 9*B*x) - 2*a^3*b*x*(20*A + 27*B*x)))/(315*a^5*x^(9/2))","A",1
524,1,114,183,0.0434735,"\int \frac{A+B x}{x^{13/2} \sqrt{a+b x}} \, dx","Integrate[(A + B*x)/(x^(13/2)*Sqrt[a + b*x]),x]","-\frac{2 \sqrt{a+b x} \left(35 a^5 (9 A+11 B x)-10 a^4 b x (35 A+44 B x)+16 a^3 b^2 x^2 (25 A+33 B x)-32 a^2 b^3 x^3 (15 A+22 B x)+128 a b^4 x^4 (5 A+11 B x)-1280 A b^5 x^5\right)}{3465 a^6 x^{11/2}}","\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,"(-2*Sqrt[a + b*x]*(-1280*A*b^5*x^5 + 128*a*b^4*x^4*(5*A + 11*B*x) + 35*a^5*(9*A + 11*B*x) - 32*a^2*b^3*x^3*(15*A + 22*B*x) + 16*a^3*b^2*x^2*(25*A + 33*B*x) - 10*a^4*b*x*(35*A + 44*B*x)))/(3465*a^6*x^(11/2))","A",1
525,1,133,216,0.0567718,"\int \frac{A+B x}{x^{15/2} \sqrt{a+b x}} \, dx","Integrate[(A + B*x)/(x^(15/2)*Sqrt[a + b*x]),x]","-\frac{2 \sqrt{a+b x} \left(63 a^6 (11 A+13 B x)-14 a^5 b x (54 A+65 B x)+40 a^4 b^2 x^2 (21 A+26 B x)-96 a^3 b^3 x^3 (10 A+13 B x)+128 a^2 b^4 x^4 (9 A+13 B x)-256 a b^5 x^5 (6 A+13 B x)+3072 A b^6 x^6\right)}{9009 a^7 x^{13/2}}","-\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,"(-2*Sqrt[a + b*x]*(3072*A*b^6*x^6 - 256*a*b^5*x^5*(6*A + 13*B*x) + 128*a^2*b^4*x^4*(9*A + 13*B*x) - 96*a^3*b^3*x^3*(10*A + 13*B*x) + 63*a^6*(11*A + 13*B*x) + 40*a^4*b^2*x^2*(21*A + 26*B*x) - 14*a^5*b*x*(54*A + 65*B*x)))/(9009*a^7*x^(13/2))","A",1
526,1,151,200,0.2593,"\int \frac{x^{7/2} (A+B x)}{(a+b x)^{3/2}} \, dx","Integrate[(x^(7/2)*(A + B*x))/(a + b*x)^(3/2),x]","\frac{\frac{(a+b x) (9 a B-8 A b) \left(105 a^{7/2} \sqrt{b} \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+b x \sqrt{\frac{b x}{a}+1} \left(-105 a^3+70 a^2 b x-56 a b^2 x^2+48 b^3 x^3\right)\right)}{3 \sqrt{\frac{b x}{a}+1}}+128 b^5 x^5 (A b-a B)}{64 a b^6 \sqrt{x} \sqrt{a+b x}}","-\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,"(128*b^5*(A*b - a*B)*x^5 + ((-8*A*b + 9*a*B)*(a + b*x)*(b*x*Sqrt[1 + (b*x)/a]*(-105*a^3 + 70*a^2*b*x - 56*a*b^2*x^2 + 48*b^3*x^3) + 105*a^(7/2)*Sqrt[b]*Sqrt[x]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(3*Sqrt[1 + (b*x)/a]))/(64*a*b^6*Sqrt[x]*Sqrt[a + b*x])","A",1
527,1,140,167,0.2042289,"\int \frac{x^{5/2} (A+B x)}{(a+b x)^{3/2}} \, dx","Integrate[(x^(5/2)*(A + B*x))/(a + b*x)^(3/2),x]","\frac{\frac{(a+b x) (7 a B-6 A b) \left(b x \sqrt{\frac{b x}{a}+1} \left(15 a^2-10 a b x+8 b^2 x^2\right)-15 a^{5/2} \sqrt{b} \sqrt{x} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)\right)}{3 \sqrt{\frac{b x}{a}+1}}+16 b^4 x^4 (A b-a B)}{8 a b^5 \sqrt{x} \sqrt{a+b x}}","\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,"(16*b^4*(A*b - a*B)*x^4 + ((-6*A*b + 7*a*B)*(a + b*x)*(b*x*Sqrt[1 + (b*x)/a]*(15*a^2 - 10*a*b*x + 8*b^2*x^2) - 15*a^(5/2)*Sqrt[b]*Sqrt[x]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(3*Sqrt[1 + (b*x)/a]))/(8*a*b^5*Sqrt[x]*Sqrt[a + b*x])","A",1
528,1,106,134,0.1119133,"\int \frac{x^{3/2} (A+B x)}{(a+b x)^{3/2}} \, dx","Integrate[(x^(3/2)*(A + B*x))/(a + b*x)^(3/2),x]","\frac{3 a^{3/2} \sqrt{\frac{b x}{a}+1} (5 a B-4 A b) \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\sqrt{b} \sqrt{x} \left(-15 a^2 B+a b (12 A-5 B x)+2 b^2 x (2 A+B x)\right)}{4 b^{7/2} \sqrt{a+b x}}","-\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[b]*Sqrt[x]*(-15*a^2*B + a*b*(12*A - 5*B*x) + 2*b^2*x*(2*A + B*x)) + 3*a^(3/2)*(-4*A*b + 5*a*B)*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*b^(7/2)*Sqrt[a + b*x])","A",1
529,1,85,98,0.087634,"\int \frac{\sqrt{x} (A+B x)}{(a+b x)^{3/2}} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(a + b*x)^(3/2),x]","\frac{\sqrt{b} \sqrt{x} (3 a B-2 A b+b B x)-\sqrt{a} \sqrt{\frac{b x}{a}+1} (3 a B-2 A b) \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{5/2} \sqrt{a+b 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,"(Sqrt[b]*Sqrt[x]*(-2*A*b + 3*a*B + b*B*x) - Sqrt[a]*(-2*A*b + 3*a*B)*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(b^(5/2)*Sqrt[a + b*x])","A",1
530,1,76,60,0.0757427,"\int \frac{A+B x}{\sqrt{x} (a+b x)^{3/2}} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(a + b*x)^(3/2)),x]","\frac{2 a^{3/2} B \sqrt{\frac{b x}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+2 \sqrt{b} \sqrt{x} (A b-a B)}{a b^{3/2} \sqrt{a+b 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,"(2*Sqrt[b]*(A*b - a*B)*Sqrt[x] + 2*a^(3/2)*B*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(a*b^(3/2)*Sqrt[a + b*x])","A",1
531,1,33,49,0.0162385,"\int \frac{A+B x}{x^{3/2} (a+b x)^{3/2}} \, dx","Integrate[(A + B*x)/(x^(3/2)*(a + b*x)^(3/2)),x]","\frac{2 (-a A+a B x-2 A b x)}{a^2 \sqrt{x} \sqrt{a+b x}}","-\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,"(2*(-(a*A) - 2*A*b*x + a*B*x))/(a^2*Sqrt[x]*Sqrt[a + b*x])","A",1
532,1,54,83,0.0228617,"\int \frac{A+B x}{x^{5/2} (a+b x)^{3/2}} \, dx","Integrate[(A + B*x)/(x^(5/2)*(a + b*x)^(3/2)),x]","-\frac{2 \left(a^2 (A+3 B x)+2 a b x (3 B x-2 A)-8 A b^2 x^2\right)}{3 a^3 x^{3/2} \sqrt{a+b x}}","\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,"(-2*(-8*A*b^2*x^2 + 2*a*b*x*(-2*A + 3*B*x) + a^2*(A + 3*B*x)))/(3*a^3*x^(3/2)*Sqrt[a + b*x])","A",1
533,1,75,114,0.0395242,"\int \frac{A+B x}{x^{7/2} (a+b x)^{3/2}} \, dx","Integrate[(A + B*x)/(x^(7/2)*(a + b*x)^(3/2)),x]","-\frac{2 \left(a^3 (3 A+5 B x)-2 a^2 b x (3 A+10 B x)+8 a b^2 x^2 (3 A-5 B x)+48 A b^3 x^3\right)}{15 a^4 x^{5/2} \sqrt{a+b x}}","-\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,"(-2*(48*A*b^3*x^3 + 8*a*b^2*x^2*(3*A - 5*B*x) + a^3*(3*A + 5*B*x) - 2*a^2*b*x*(3*A + 10*B*x)))/(15*a^4*x^(5/2)*Sqrt[a + b*x])","A",1
534,1,94,147,0.0342642,"\int \frac{A+B x}{x^{9/2} (a+b x)^{3/2}} \, dx","Integrate[(A + B*x)/(x^(9/2)*(a + b*x)^(3/2)),x]","-\frac{2 \left(a^4 (5 A+7 B x)-2 a^3 b x (4 A+7 B x)+8 a^2 b^2 x^2 (2 A+7 B x)+16 a b^3 x^3 (7 B x-4 A)-128 A b^4 x^4\right)}{35 a^5 x^{7/2} \sqrt{a+b x}}","\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,"(-2*(-128*A*b^4*x^4 + 16*a*b^3*x^3*(-4*A + 7*B*x) + 8*a^2*b^2*x^2*(2*A + 7*B*x) - 2*a^3*b*x*(4*A + 7*B*x) + a^4*(5*A + 7*B*x)))/(35*a^5*x^(7/2)*Sqrt[a + b*x])","A",1
535,1,114,180,0.0482785,"\int \frac{A+B x}{x^{11/2} (a+b x)^{3/2}} \, dx","Integrate[(A + B*x)/(x^(11/2)*(a + b*x)^(3/2)),x]","-\frac{2 \left(5 a^5 (7 A+9 B x)-2 a^4 b x (25 A+36 B x)+16 a^3 b^2 x^2 (5 A+9 B x)-32 a^2 b^3 x^3 (5 A+18 B x)+128 a b^4 x^4 (5 A-9 B x)+1280 A b^5 x^5\right)}{315 a^6 x^{9/2} \sqrt{a+b x}}","-\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,"(-2*(1280*A*b^5*x^5 + 128*a*b^4*x^4*(5*A - 9*B*x) + 16*a^3*b^2*x^2*(5*A + 9*B*x) + 5*a^5*(7*A + 9*B*x) - 32*a^2*b^3*x^3*(5*A + 18*B*x) - 2*a^4*b*x*(25*A + 36*B*x)))/(315*a^6*x^(9/2)*Sqrt[a + b*x])","A",1
536,1,133,213,0.0560187,"\int \frac{A+B x}{x^{13/2} (a+b x)^{3/2}} \, dx","Integrate[(A + B*x)/(x^(13/2)*(a + b*x)^(3/2)),x]","-\frac{2 \left(7 a^6 (9 A+11 B x)-2 a^5 b x (42 A+55 B x)+8 a^4 b^2 x^2 (15 A+22 B x)-32 a^3 b^3 x^3 (6 A+11 B x)+128 a^2 b^4 x^4 (3 A+11 B x)+256 a b^5 x^5 (11 B x-6 A)-3072 A b^6 x^6\right)}{693 a^7 x^{11/2} \sqrt{a+b x}}","\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,"(-2*(-3072*A*b^6*x^6 + 256*a*b^5*x^5*(-6*A + 11*B*x) + 128*a^2*b^4*x^4*(3*A + 11*B*x) - 32*a^3*b^3*x^3*(6*A + 11*B*x) + 7*a^6*(9*A + 11*B*x) + 8*a^4*b^2*x^2*(15*A + 22*B*x) - 2*a^5*b*x*(42*A + 55*B*x)))/(693*a^7*x^(11/2)*Sqrt[a + b*x])","A",1
537,1,80,200,0.069705,"\int \frac{x^{7/2} (A+B x)}{(a+b x)^{5/2}} \, dx","Integrate[(x^(7/2)*(A + B*x))/(a + b*x)^(5/2),x]","\frac{2 x^{9/2} \left((a+b x) \sqrt{\frac{b x}{a}+1} (3 a B-2 A b) \, _2F_1\left(\frac{3}{2},\frac{9}{2};\frac{11}{2};-\frac{b x}{a}\right)+3 a (A b-a B)\right)}{9 a^2 b (a+b x)^{3/2}}","\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,"(2*x^(9/2)*(3*a*(A*b - a*B) + (-2*A*b + 3*a*B)*(a + b*x)*Sqrt[1 + (b*x)/a]*Hypergeometric2F1[3/2, 9/2, 11/2, -((b*x)/a)]))/(9*a^2*b*(a + b*x)^(3/2))","C",1
538,1,80,169,0.0755669,"\int \frac{x^{5/2} (A+B x)}{(a+b x)^{5/2}} \, dx","Integrate[(x^(5/2)*(A + B*x))/(a + b*x)^(5/2),x]","\frac{2 x^{7/2} \left((a+b x) \sqrt{\frac{b x}{a}+1} (7 a B-4 A b) \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};-\frac{b x}{a}\right)+7 a (A b-a B)\right)}{21 a^2 b (a+b x)^{3/2}}","-\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,"(2*x^(7/2)*(7*a*(A*b - a*B) + (-4*A*b + 7*a*B)*(a + b*x)*Sqrt[1 + (b*x)/a]*Hypergeometric2F1[3/2, 7/2, 9/2, -((b*x)/a)]))/(21*a^2*b*(a + b*x)^(3/2))","C",1
539,1,80,133,0.0782778,"\int \frac{x^{3/2} (A+B x)}{(a+b x)^{5/2}} \, dx","Integrate[(x^(3/2)*(A + B*x))/(a + b*x)^(5/2),x]","\frac{2 x^{5/2} \left((a+b x) \sqrt{\frac{b x}{a}+1} (5 a B-2 A b) \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};-\frac{b x}{a}\right)+5 a (A b-a B)\right)}{15 a^2 b (a+b x)^{3/2}}","\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,"(2*x^(5/2)*(5*a*(A*b - a*B) + (-2*A*b + 5*a*B)*(a + b*x)*Sqrt[1 + (b*x)/a]*Hypergeometric2F1[3/2, 5/2, 7/2, -((b*x)/a)]))/(15*a^2*b*(a + b*x)^(3/2))","C",1
540,1,95,82,0.1190521,"\int \frac{\sqrt{x} (A+B x)}{(a+b x)^{5/2}} \, dx","Integrate[(Sqrt[x]*(A + B*x))/(a + b*x)^(5/2),x]","\frac{6 a^{3/2} B (a+b x) \sqrt{\frac{b x}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+2 \sqrt{b} \sqrt{x} \left(-3 a^2 B-4 a b B x+A b^2 x\right)}{3 a b^{5/2} (a+b x)^{3/2}}","\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*Sqrt[b]*Sqrt[x]*(-3*a^2*B + A*b^2*x - 4*a*b*B*x) + 6*a^(3/2)*B*(a + b*x)*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(3*a*b^(5/2)*(a + b*x)^(3/2))","A",1
541,1,35,65,0.0174599,"\int \frac{A+B x}{\sqrt{x} (a+b x)^{5/2}} \, dx","Integrate[(A + B*x)/(Sqrt[x]*(a + b*x)^(5/2)),x]","\frac{2 \sqrt{x} (3 a A+a B x+2 A b x)}{3 a^2 (a+b x)^{3/2}}","\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,"(2*Sqrt[x]*(3*a*A + 2*A*b*x + a*B*x))/(3*a^2*(a + b*x)^(3/2))","A",1
542,1,54,81,0.0296539,"\int \frac{A+B x}{x^{3/2} (a+b x)^{5/2}} \, dx","Integrate[(A + B*x)/(x^(3/2)*(a + b*x)^(5/2)),x]","\frac{-6 a^2 (A-B x)+4 a b x (B x-6 A)-16 A b^2 x^2}{3 a^3 \sqrt{x} (a+b x)^{3/2}}","-\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,"(-16*A*b^2*x^2 - 6*a^2*(A - B*x) + 4*a*b*x*(-6*A + B*x))/(3*a^3*Sqrt[x]*(a + b*x)^(3/2))","A",1
543,1,70,113,0.0374969,"\int \frac{A+B x}{x^{5/2} (a+b x)^{5/2}} \, dx","Integrate[(A + B*x)/(x^(5/2)*(a + b*x)^(5/2)),x]","-\frac{2 \left(a^3 (A+3 B x)-6 a^2 b x (A-2 B x)+8 a b^2 x^2 (B x-3 A)-16 A b^3 x^3\right)}{3 a^4 x^{3/2} (a+b x)^{3/2}}","\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,"(-2*(-16*A*b^3*x^3 - 6*a^2*b*x*(A - 2*B*x) + 8*a*b^2*x^2*(-3*A + B*x) + a^3*(A + 3*B*x)))/(3*a^4*x^(3/2)*(a + b*x)^(3/2))","A",1
544,1,94,144,0.0423931,"\int \frac{A+B x}{x^{7/2} (a+b x)^{5/2}} \, dx","Integrate[(A + B*x)/(x^(7/2)*(a + b*x)^(5/2)),x]","-\frac{2 \left(a^4 (3 A+5 B x)-2 a^3 b x (4 A+15 B x)+24 a^2 b^2 x^2 (2 A-5 B x)+16 a b^3 x^3 (12 A-5 B x)+128 A b^4 x^4\right)}{15 a^5 x^{5/2} (a+b x)^{3/2}}","-\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,"(-2*(128*A*b^4*x^4 + 24*a^2*b^2*x^2*(2*A - 5*B*x) + 16*a*b^3*x^3*(12*A - 5*B*x) + a^4*(3*A + 5*B*x) - 2*a^3*b*x*(4*A + 15*B*x)))/(15*a^5*x^(5/2)*(a + b*x)^(3/2))","A",1
545,1,114,177,0.0459674,"\int \frac{A+B x}{x^{9/2} (a+b x)^{5/2}} \, dx","Integrate[(A + B*x)/(x^(9/2)*(a + b*x)^(5/2)),x]","-\frac{2 \left(3 a^5 (5 A+7 B x)-2 a^4 b x (15 A+28 B x)+16 a^3 b^2 x^2 (5 A+21 B x)+96 a^2 b^3 x^3 (14 B x-5 A)+128 a b^4 x^4 (7 B x-15 A)-1280 A b^5 x^5\right)}{105 a^6 x^{7/2} (a+b x)^{3/2}}","\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,"(-2*(-1280*A*b^5*x^5 + 128*a*b^4*x^4*(-15*A + 7*B*x) + 3*a^5*(5*A + 7*B*x) + 96*a^2*b^3*x^3*(-5*A + 14*B*x) + 16*a^3*b^2*x^2*(5*A + 21*B*x) - 2*a^4*b*x*(15*A + 28*B*x)))/(105*a^6*x^(7/2)*(a + b*x)^(3/2))","A",1
546,1,127,210,0.0614052,"\int \frac{A+B x}{x^{11/2} (a+b x)^{5/2}} \, dx","Integrate[(A + B*x)/(x^(11/2)*(a + b*x)^(5/2)),x]","-\frac{2 \left(a^6 (7 A+9 B x)-6 a^5 b x (2 A+3 B x)+24 a^4 b^2 x^2 (A+2 B x)-32 a^3 b^3 x^3 (2 A+9 B x)+384 a^2 b^4 x^4 (A-3 B x)-768 a b^5 x^5 (B x-2 A)+1024 A b^6 x^6\right)}{63 a^7 x^{9/2} (a+b x)^{3/2}}","-\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,"(-2*(1024*A*b^6*x^6 + 384*a^2*b^4*x^4*(A - 3*B*x) - 768*a*b^5*x^5*(-2*A + B*x) + 24*a^4*b^2*x^2*(A + 2*B*x) - 6*a^5*b*x*(2*A + 3*B*x) - 32*a^3*b^3*x^3*(2*A + 9*B*x) + a^6*(7*A + 9*B*x)))/(63*a^7*x^(9/2)*(a + b*x)^(3/2))","A",1
547,1,282,302,1.1480331,"\int x^3 \sqrt{a+b x} \sqrt{c+d x} \, dx","Integrate[x^3*Sqrt[a + b*x]*Sqrt[c + d*x],x]","\frac{15 (b c-a d)^{5/2} \left(7 a^3 d^3+9 a^2 b c d^2+9 a b^2 c^2 d+7 b^3 c^3\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)-b \sqrt{d} \sqrt{a+b x} (c+d x) \left(105 a^4 d^4-10 a^3 b d^3 (4 c+7 d x)+2 a^2 b^2 d^2 \left(-17 c^2+11 c d x+28 d^2 x^2\right)-2 a b^3 d \left(20 c^3-11 c^2 d x+8 c d^2 x^2+24 d^3 x^3\right)+b^4 \left(105 c^4-70 c^3 d x+56 c^2 d^2 x^2-48 c d^3 x^3-384 d^4 x^4\right)\right)}{1920 b^5 d^{9/2} \sqrt{c+d x}}","\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,"(-(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(105*a^4*d^4 - 10*a^3*b*d^3*(4*c + 7*d*x) + 2*a^2*b^2*d^2*(-17*c^2 + 11*c*d*x + 28*d^2*x^2) - 2*a*b^3*d*(20*c^3 - 11*c^2*d*x + 8*c*d^2*x^2 + 24*d^3*x^3) + b^4*(105*c^4 - 70*c^3*d*x + 56*c^2*d^2*x^2 - 48*c*d^3*x^3 - 384*d^4*x^4))) + 15*(b*c - a*d)^(5/2)*(7*b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + 7*a^3*d^3)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(1920*b^5*d^(9/2)*Sqrt[c + d*x])","A",1
548,1,214,237,0.5708572,"\int x^2 \sqrt{a+b x} \sqrt{c+d x} \, dx","Integrate[x^2*Sqrt[a + b*x]*Sqrt[c + d*x],x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) \left(15 a^3 d^3-a^2 b d^2 (7 c+10 d x)+a b^2 d \left(-7 c^2+4 c d x+8 d^2 x^2\right)+b^3 \left(15 c^3-10 c^2 d x+8 c d^2 x^2+48 d^3 x^3\right)\right)-3 (b c-a d)^{5/2} \left(5 a^2 d^2+6 a b c d+5 b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{192 b^4 d^{7/2} \sqrt{c+d x}}","\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,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(15*a^3*d^3 - a^2*b*d^2*(7*c + 10*d*x) + a*b^2*d*(-7*c^2 + 4*c*d*x + 8*d^2*x^2) + b^3*(15*c^3 - 10*c^2*d*x + 8*c*d^2*x^2 + 48*d^3*x^3)) - 3*(b*c - a*d)^(5/2)*(5*b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(192*b^4*d^(7/2)*Sqrt[c + d*x])","A",1
549,1,156,163,0.5739479,"\int x \sqrt{a+b x} \sqrt{c+d x} \, dx","Integrate[x*Sqrt[a + b*x]*Sqrt[c + d*x],x]","\frac{3 (b c-a d)^{5/2} (a d+b c) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)-b \sqrt{d} \sqrt{a+b x} (c+d x) \left(3 a^2 d^2-2 a b d (c+d x)+b^2 \left(3 c^2-2 c d x-8 d^2 x^2\right)\right)}{24 b^3 d^{5/2} \sqrt{c+d x}}","\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,"(-(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(3*a^2*d^2 - 2*a*b*d*(c + d*x) + b^2*(3*c^2 - 2*c*d*x - 8*d^2*x^2))) + 3*(b*c - a*d)^(5/2)*(b*c + a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(24*b^3*d^(5/2)*Sqrt[c + d*x])","A",1
550,1,118,116,0.3310676,"\int \sqrt{a+b x} \sqrt{c+d x} \, dx","Integrate[Sqrt[a + b*x]*Sqrt[c + d*x],x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) (a d+b (c+2 d x))-(b c-a d)^{5/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{4 b^2 d^{3/2} \sqrt{c+d x}}","-\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,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(a*d + b*(c + 2*d*x)) - (b*c - a*d)^(5/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(4*b^2*d^(3/2)*Sqrt[c + d*x])","A",1
551,1,162,110,0.6110655,"\int \frac{\sqrt{a+b x} \sqrt{c+d x}}{x} \, dx","Integrate[(Sqrt[a + b*x]*Sqrt[c + d*x])/x,x]","\frac{\sqrt{b c-a d} (a d+b c) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)+b \sqrt{d} \left(\sqrt{a+b x} (c+d x)-2 \sqrt{a} \sqrt{c} \sqrt{c+d x} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)}{b \sqrt{d} \sqrt{c+d x}}","\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[b*c - a*d]*(b*c + a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] + b*Sqrt[d]*(Sqrt[a + b*x]*(c + d*x) - 2*Sqrt[a]*Sqrt[c]*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(b*Sqrt[d]*Sqrt[c + d*x])","A",1
552,1,150,115,0.9990941,"\int \frac{\sqrt{a+b x} \sqrt{c+d x}}{x^2} \, dx","Integrate[(Sqrt[a + b*x]*Sqrt[c + d*x])/x^2,x]","-\frac{\sqrt{a+b x} \sqrt{c+d x}}{x}+\frac{2 \sqrt{d} \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{c+d 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}}","-\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,"-((Sqrt[a + b*x]*Sqrt[c + d*x])/x) + (2*Sqrt[d]*Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[c + d*x] - ((b*c + a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(Sqrt[a]*Sqrt[c])","A",1
553,1,99,122,0.0921756,"\int \frac{\sqrt{a+b x} \sqrt{c+d x}}{x^3} \, dx","Integrate[(Sqrt[a + b*x]*Sqrt[c + d*x])/x^3,x]","\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} \sqrt{c+d x} (2 a c+a d x+b c x)}{4 a c x^2}","\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,"-1/4*(Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c + b*c*x + a*d*x))/(a*c*x^2) + ((b*c - a*d)^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*a^(3/2)*c^(3/2))","A",1
554,1,142,172,0.2480029,"\int \frac{\sqrt{a+b x} \sqrt{c+d x}}{x^4} \, dx","Integrate[(Sqrt[a + b*x]*Sqrt[c + d*x])/x^4,x]","-\frac{\frac{3 x (a d+b c) \left(x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)-\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+a d x+b c x)\right)}{a^{3/2} c^{3/2}}+8 (a+b x)^{3/2} (c+d x)^{3/2}}{24 a c x^3}","-\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,"-1/24*(8*(a + b*x)^(3/2)*(c + d*x)^(3/2) + (3*(b*c + a*d)*x*(-(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c + b*c*x + a*d*x)) + (b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(3/2)*c^(3/2)))/(a*c*x^3)","A",1
555,1,194,256,0.2829011,"\int \frac{\sqrt{a+b x} \sqrt{c+d x}}{x^5} \, dx","Integrate[(Sqrt[a + b*x]*Sqrt[c + d*x])/x^5,x]","\frac{\frac{3 x^2 \left(5 a^2 d^2+6 a b c d+5 b^2 c^2\right) \left(x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)-\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+a d x+b c x)\right)}{a^{5/2} c^{5/2}}+\frac{40 x (a+b x)^{3/2} (c+d x)^{3/2} (a d+b c)}{a c}-48 (a+b x)^{3/2} (c+d x)^{3/2}}{192 a c x^4}","\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,"(-48*(a + b*x)^(3/2)*(c + d*x)^(3/2) + (40*(b*c + a*d)*x*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(a*c) + (3*(5*b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*x^2*(-(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c + b*c*x + a*d*x)) + (b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(5/2)*c^(5/2)))/(192*a*c*x^4)","A",1
556,1,253,345,0.6133091,"\int \frac{\sqrt{a+b x} \sqrt{c+d x}}{x^6} \, dx","Integrate[(Sqrt[a + b*x]*Sqrt[c + d*x])/x^6,x]","-\frac{\frac{8 x^2 (a+b x)^{3/2} (c+d x)^{3/2} \left(35 a^2 d^2+38 a b c d+35 b^2 c^2\right)}{a^2 c^2}+\frac{15 x^3 (a d+b c) \left(7 a^2 d^2+2 a b c d+7 b^2 c^2\right) \left(x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)-\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+a d x+b c x)\right)}{a^{7/2} c^{7/2}}-\frac{336 x (a+b x)^{3/2} (c+d x)^{3/2} (a d+b c)}{a c}+384 (a+b x)^{3/2} (c+d x)^{3/2}}{1920 a c x^5}","\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,"-1/1920*(384*(a + b*x)^(3/2)*(c + d*x)^(3/2) - (336*(b*c + a*d)*x*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(a*c) + (8*(35*b^2*c^2 + 38*a*b*c*d + 35*a^2*d^2)*x^2*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(a^2*c^2) + (15*(b*c + a*d)*(7*b^2*c^2 + 2*a*b*c*d + 7*a^2*d^2)*x^3*(-(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c + b*c*x + a*d*x)) + (b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(7/2)*c^(7/2)))/(a*c*x^5)","A",1
557,1,268,315,0.7666724,"\int x^2 \sqrt{a+b x} (c+d x)^{3/2} \, dx","Integrate[x^2*Sqrt[a + b*x]*(c + d*x)^(3/2),x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) \left(-105 a^4 d^4+10 a^3 b d^3 (19 c+7 d x)-2 a^2 b^2 d^2 \left(18 c^2+61 c d x+28 d^2 x^2\right)+6 a b^3 d \left(-5 c^3+3 c^2 d x+16 c d^2 x^2+8 d^3 x^3\right)+3 b^4 \left(15 c^4-10 c^3 d x+8 c^2 d^2 x^2+176 c d^3 x^3+128 d^4 x^4\right)\right)-15 (b c-a d)^{7/2} \left(7 a^2 d^2+6 a b c d+3 b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{1920 b^5 d^{7/2} \sqrt{c+d x}}","-\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,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(-105*a^4*d^4 + 10*a^3*b*d^3*(19*c + 7*d*x) - 2*a^2*b^2*d^2*(18*c^2 + 61*c*d*x + 28*d^2*x^2) + 6*a*b^3*d*(-5*c^3 + 3*c^2*d*x + 16*c*d^2*x^2 + 8*d^3*x^3) + 3*b^4*(15*c^4 - 10*c^3*d*x + 8*c^2*d^2*x^2 + 176*c*d^3*x^3 + 128*d^4*x^4)) - 15*(b*c - a*d)^(7/2)*(3*b^2*c^2 + 6*a*b*c*d + 7*a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(1920*b^5*d^(7/2)*Sqrt[c + d*x])","A",1
558,1,200,221,0.6509239,"\int x \sqrt{a+b x} (c+d x)^{3/2} \, dx","Integrate[x*Sqrt[a + b*x]*(c + d*x)^(3/2),x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) \left(15 a^3 d^3-a^2 b d^2 (31 c+10 d x)+a b^2 d \left(9 c^2+20 c d x+8 d^2 x^2\right)+b^3 \left(-9 c^3+6 c^2 d x+72 c d^2 x^2+48 d^3 x^3\right)\right)+3 (5 a d+3 b c) (b c-a d)^{7/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{192 b^4 d^{5/2} \sqrt{c+d x}}","\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,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(15*a^3*d^3 - a^2*b*d^2*(31*c + 10*d*x) + a*b^2*d*(9*c^2 + 20*c*d*x + 8*d^2*x^2) + b^3*(-9*c^3 + 6*c^2*d*x + 72*c*d^2*x^2 + 48*d^3*x^3)) + 3*(b*c - a*d)^(7/2)*(3*b*c + 5*a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(192*b^4*d^(5/2)*Sqrt[c + d*x])","A",1
559,1,152,151,0.5387606,"\int \sqrt{a+b x} (c+d x)^{3/2} \, dx","Integrate[Sqrt[a + b*x]*(c + d*x)^(3/2),x]","\frac{-b \sqrt{d} \sqrt{a+b x} (c+d x) \left(3 a^2 d^2-2 a b d (4 c+d x)-\left(b^2 \left(3 c^2+14 c d x+8 d^2 x^2\right)\right)\right)-3 (b c-a d)^{7/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{24 b^3 d^{3/2} \sqrt{c+d x}}","-\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,"(-(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(3*a^2*d^2 - 2*a*b*d*(4*c + d*x) - b^2*(3*c^2 + 14*c*d*x + 8*d^2*x^2))) - 3*(b*c - a*d)^(7/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(24*b^3*d^(3/2)*Sqrt[c + d*x])","A",1
560,1,195,165,0.8432222,"\int \frac{\sqrt{a+b x} (c+d x)^{3/2}}{x} \, dx","Integrate[(Sqrt[a + b*x]*(c + d*x)^(3/2))/x,x]","\frac{\sqrt{b c-a d} \left(-a^2 d^2+6 a b c d+3 b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)+b \sqrt{d} \left(\sqrt{a+b x} (c+d x) (a d+5 b c+2 b d x)-8 \sqrt{a} b c^{3/2} \sqrt{c+d x} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)}{4 b^2 \sqrt{d} \sqrt{c+d x}}","\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,"(Sqrt[b*c - a*d]*(3*b^2*c^2 + 6*a*b*c*d - a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] + b*Sqrt[d]*(Sqrt[a + b*x]*(c + d*x)*(5*b*c + a*d + 2*b*d*x) - 8*Sqrt[a]*b*c^(3/2)*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(4*b^2*Sqrt[d]*Sqrt[c + d*x])","A",1
561,1,174,144,1.044575,"\int \frac{\sqrt{a+b x} (c+d x)^{3/2}}{x^2} \, dx","Integrate[(Sqrt[a + b*x]*(c + d*x)^(3/2))/x^2,x]","\frac{\frac{\sqrt{a+b x} \left(d^2 x^2-c^2\right)}{x}+\frac{\sqrt{d} \sqrt{b c-a d} (a d+3 b c) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b}-\frac{\sqrt{c} \sqrt{c+d x} (3 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+d 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[a + b*x]*(-c^2 + d^2*x^2))/x + (Sqrt[d]*Sqrt[b*c - a*d]*(3*b*c + a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/b - (Sqrt[c]*(b*c + 3*a*d)*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/Sqrt[a])/Sqrt[c + d*x]","A",1
562,1,186,170,1.3843965,"\int \frac{\sqrt{a+b x} (c+d x)^{3/2}}{x^3} \, dx","Integrate[(Sqrt[a + b*x]*(c + d*x)^(3/2))/x^3,x]","\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}}+\frac{2 d^{3/2} \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{c+d x}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x+b c x)}{4 a x^2}","\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,"-1/4*(Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c + b*c*x + 5*a*d*x))/(a*x^2) + (2*d^(3/2)*Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[c + d*x] + ((b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*a^(3/2)*Sqrt[c])","A",1
563,1,141,163,0.2647547,"\int \frac{\sqrt{a+b x} (c+d x)^{3/2}}{x^4} \, dx","Integrate[(Sqrt[a + b*x]*(c + d*x)^(3/2))/x^4,x]","-\frac{\frac{x (b c-a d) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)\right)}{a^{5/2} \sqrt{c}}+8 \sqrt{a+b x} (c+d x)^{5/2}}{24 c x^3}","-\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,"-1/24*(8*Sqrt[a + b*x]*(c + d*x)^(5/2) + ((b*c - a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(5/2)*Sqrt[c]))/(c*x^3)","A",1
564,1,179,233,0.2518468,"\int \frac{\sqrt{a+b x} (c+d x)^{3/2}}{x^5} \, dx","Integrate[(Sqrt[a + b*x]*(c + d*x)^(3/2))/x^5,x]","\frac{\frac{x (3 a d+5 b c) \left(\frac{x (b c-a d) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)\right)}{a^{5/2} \sqrt{c}}+8 \sqrt{a+b x} (c+d x)^{5/2}\right)}{c}-48 (a+b x)^{3/2} (c+d x)^{5/2}}{192 a c x^4}","\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,"(-48*(a + b*x)^(3/2)*(c + d*x)^(5/2) + ((5*b*c + 3*a*d)*x*(8*Sqrt[a + b*x]*(c + d*x)^(5/2) + ((b*c - a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(5/2)*Sqrt[c])))/c)/(192*a*c*x^4)","A",1
565,1,232,340,0.359538,"\int \frac{\sqrt{a+b x} (c+d x)^{3/2}}{x^6} \, dx","Integrate[(Sqrt[a + b*x]*(c + d*x)^(3/2))/x^6,x]","\frac{-\frac{5 \left(3 a^2 d^2+6 a b c d+7 b^2 c^2\right) \left(\frac{x (b c-a d) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)\right)}{a^{5/2} \sqrt{c}}+8 \sqrt{a+b x} (c+d x)^{5/2}\right)}{24 c x^3}-\frac{16 a c (a+b x)^{3/2} (c+d x)^{5/2}}{x^5}+\frac{2 (a+b x)^{3/2} (c+d x)^{5/2} (5 a d+7 b c)}{x^4}}{80 a^2 c^2}","-\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,"((-16*a*c*(a + b*x)^(3/2)*(c + d*x)^(5/2))/x^5 + (2*(7*b*c + 5*a*d)*(a + b*x)^(3/2)*(c + d*x)^(5/2))/x^4 - (5*(7*b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*(8*Sqrt[a + b*x]*(c + d*x)^(5/2) + ((b*c - a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(5/2)*Sqrt[c])))/(24*c*x^3))/(80*a^2*c^2)","A",1
566,1,320,376,2.0108816,"\int x^2 \sqrt{a+b x} (c+d x)^{5/2} \, dx","Integrate[x^2*Sqrt[a + b*x]*(c + d*x)^(5/2),x]","\frac{(a+b x)^{3/2} (c+d x)^{7/2} \left(\frac{3 \left(21 a^2 d^2+14 a b c d+5 b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \left(2 b^5 d^2 (a+b x)^2 (b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(15 a^2 d^2-10 a b d (5 c+2 d x)+b^2 \left(59 c^2+68 c d x+24 d^2 x^2\right)\right)+15 b^5 d (a+b x) (b c-a d)^{9/2} \sqrt{\frac{b (c+d x)}{b c-a d}}-15 b^5 \sqrt{d} \sqrt{a+b x} (b c-a d)^5 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)}{128 b^9 d^2 (a+b x)^2 (c+d x)^4 \sqrt{b c-a d}}-3 (9 a d+5 b c)+30 b d x\right)}{180 b^2 d^2}","-\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,"((a + b*x)^(3/2)*(c + d*x)^(7/2)*(-3*(5*b*c + 9*a*d) + 30*b*d*x + (3*(5*b^2*c^2 + 14*a*b*c*d + 21*a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*(15*b^5*d*(b*c - a*d)^(9/2)*(a + b*x)*Sqrt[(b*(c + d*x))/(b*c - a*d)] + 2*b^5*d^2*(b*c - a*d)^(3/2)*(a + b*x)^2*Sqrt[(b*(c + d*x))/(b*c - a*d)]*(15*a^2*d^2 - 10*a*b*d*(5*c + 2*d*x) + b^2*(59*c^2 + 68*c*d*x + 24*d^2*x^2)) - 15*b^5*Sqrt[d]*(b*c - a*d)^5*Sqrt[a + b*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]]))/(128*b^9*d^2*Sqrt[b*c - a*d]*(a + b*x)^2*(c + d*x)^4)))/(180*b^2*d^2)","A",1
567,1,291,268,1.6320441,"\int x \sqrt{a+b x} (c+d x)^{5/2} \, dx","Integrate[x*Sqrt[a + b*x]*(c + d*x)^(5/2),x]","\frac{(a+b x)^{3/2} (c+d x)^{7/2} \left(3-\frac{(7 a d+3 b c) \sqrt{\frac{b (c+d x)}{b c-a d}} \left(2 b^5 d^2 (a+b x)^2 (b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(15 a^2 d^2-10 a b d (5 c+2 d x)+b^2 \left(59 c^2+68 c d x+24 d^2 x^2\right)\right)+15 b^5 d (a+b x) (b c-a d)^{9/2} \sqrt{\frac{b (c+d x)}{b c-a d}}-15 b^5 \sqrt{d} \sqrt{a+b x} (b c-a d)^5 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)}{128 b^9 d^2 (a+b x)^2 (c+d x)^4 \sqrt{b c-a d}}\right)}{15 b d}","\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,"((a + b*x)^(3/2)*(c + d*x)^(7/2)*(3 - ((3*b*c + 7*a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*(15*b^5*d*(b*c - a*d)^(9/2)*(a + b*x)*Sqrt[(b*(c + d*x))/(b*c - a*d)] + 2*b^5*d^2*(b*c - a*d)^(3/2)*(a + b*x)^2*Sqrt[(b*(c + d*x))/(b*c - a*d)]*(15*a^2*d^2 - 10*a*b*d*(5*c + 2*d*x) + b^2*(59*c^2 + 68*c*d*x + 24*d^2*x^2)) - 15*b^5*Sqrt[d]*(b*c - a*d)^5*Sqrt[a + b*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]]))/(128*b^9*d^2*Sqrt[b*c - a*d]*(a + b*x)^2*(c + d*x)^4)))/(15*b*d)","A",1
568,1,191,186,0.7181023,"\int \sqrt{a+b x} (c+d x)^{5/2} \, dx","Integrate[Sqrt[a + b*x]*(c + d*x)^(5/2),x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) \left(15 a^3 d^3-5 a^2 b d^2 (11 c+2 d x)+a b^2 d \left(73 c^2+36 c d x+8 d^2 x^2\right)+b^3 \left(15 c^3+118 c^2 d x+136 c d^2 x^2+48 d^3 x^3\right)\right)-15 (b c-a d)^{9/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{192 b^4 d^{3/2} \sqrt{c+d x}}","-\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,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(15*a^3*d^3 - 5*a^2*b*d^2*(11*c + 2*d*x) + a*b^2*d*(73*c^2 + 36*c*d*x + 8*d^2*x^2) + b^3*(15*c^3 + 118*c^2*d*x + 136*c*d^2*x^2 + 48*d^3*x^3)) - 15*(b*c - a*d)^(9/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(192*b^4*d^(3/2)*Sqrt[c + d*x])","A",1
569,1,274,219,1.0136805,"\int \frac{\sqrt{a+b x} (c+d x)^{5/2}}{x} \, dx","Integrate[(Sqrt[a + b*x]*(c + d*x)^(5/2))/x,x]","\frac{\sqrt{c+d x} \left(-\frac{b \sqrt{d} \left(\sqrt{a+b x} (c+d x) \left(-3 a^2 d^2+2 a b d (7 c+d x)+b^2 \left(33 c^2+26 c d x+8 d^2 x^2\right)\right)-48 \sqrt{a} b^2 c^{5/2} \sqrt{c+d x} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)}{\sqrt{\frac{b (c+d x)}{b c-a d}}}-3 \sqrt{b c-a d} \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) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)}{24 b^2 \sqrt{d} (a d-b c) \sqrt{\frac{b (c+d x)}{b c-a d}}}","\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,"(Sqrt[c + d*x]*(-3*Sqrt[b*c - a*d]*(5*b^3*c^3 + 15*a*b^2*c^2*d - 5*a^2*b*c*d^2 + a^3*d^3)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] - (b*Sqrt[d]*(Sqrt[a + b*x]*(c + d*x)*(-3*a^2*d^2 + 2*a*b*d*(7*c + d*x) + b^2*(33*c^2 + 26*c*d*x + 8*d^2*x^2)) - 48*Sqrt[a]*b^2*c^(5/2)*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/Sqrt[(b*(c + d*x))/(b*c - a*d)]))/(24*b^2*Sqrt[d]*(-(b*c) + a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)])","A",1
570,1,208,198,1.3107986,"\int \frac{\sqrt{a+b x} (c+d x)^{5/2}}{x^2} \, dx","Integrate[(Sqrt[a + b*x]*(c + d*x)^(5/2))/x^2,x]","\frac{\frac{\sqrt{d} \sqrt{c+d x} \left(-a^2 d^2+10 a b c d+15 b^2 c^2\right) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}}-\frac{4 b 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} \sqrt{c+d x} \left(a d^2 x+b \left(-4 c^2+9 c d x+2 d^2 x^2\right)\right)}{x}}{4 b}","\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,"((Sqrt[a + b*x]*Sqrt[c + d*x]*(a*d^2*x + b*(-4*c^2 + 9*c*d*x + 2*d^2*x^2)))/x + (Sqrt[d]*(15*b^2*c^2 + 10*a*b*c*d - a^2*d^2)*Sqrt[c + d*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]) - (4*b*c^(3/2)*(b*c + 5*a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/Sqrt[a])/(4*b)","A",1
571,1,207,211,1.4019167,"\int \frac{\sqrt{a+b x} (c+d x)^{5/2}}{x^3} \, dx","Integrate[(Sqrt[a + b*x]*(c + d*x)^(5/2))/x^3,x]","\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{\sqrt{a+b x} \sqrt{c+d x} \left(a \left(2 c^2+9 c d x-4 d^2 x^2\right)+b c^2 x\right)}{4 a x^2}+\frac{d^{3/2} \sqrt{c+d x} (a d+5 b c) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}}","\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,"-1/4*(Sqrt[a + b*x]*Sqrt[c + d*x]*(b*c^2*x + a*(2*c^2 + 9*c*d*x - 4*d^2*x^2)))/(a*x^2) + (d^(3/2)*(5*b*c + a*d)*Sqrt[c + d*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]) + (Sqrt[c]*(b^2*c^2 - 10*a*b*c*d - 15*a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*a^(3/2))","A",1
572,1,233,227,2.2553982,"\int \frac{\sqrt{a+b x} (c+d x)^{5/2}}{x^4} \, dx","Integrate[(Sqrt[a + b*x]*(c + d*x)^(5/2))/x^4,x]","-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(a^2 \left(8 c^2+26 c d x+33 d^2 x^2\right)+2 a b c x (c+7 d x)-3 b^2 c^2 x^2\right)}{24 a^2 x^3}-\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}}+\frac{2 d^{5/2} \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{c+d x}}","\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,"-1/24*(Sqrt[a + b*x]*Sqrt[c + d*x]*(-3*b^2*c^2*x^2 + 2*a*b*c*x*(c + 7*d*x) + a^2*(8*c^2 + 26*c*d*x + 33*d^2*x^2)))/(a^2*x^3) + (2*d^(5/2)*Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[c + d*x] - ((b^3*c^3 - 5*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 5*a^3*d^3)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(8*a^(5/2)*Sqrt[c])","A",1
573,1,176,204,0.4271759,"\int \frac{\sqrt{a+b x} (c+d x)^{5/2}}{x^5} \, dx","Integrate[(Sqrt[a + b*x]*(c + d*x)^(5/2))/x^5,x]","\frac{\frac{x (b c-a d) \left(\frac{5 x (b c-a d) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)\right)}{a^{5/2} \sqrt{c}}-8 \sqrt{a+b x} (c+d x)^{5/2}\right)}{a}-48 \sqrt{a+b x} (c+d x)^{7/2}}{192 c x^4}","\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,"(-48*Sqrt[a + b*x]*(c + d*x)^(7/2) + ((b*c - a*d)*x*(-8*Sqrt[a + b*x]*(c + d*x)^(5/2) + (5*(b*c - a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(5/2)*Sqrt[c])))/a)/(192*c*x^4)","A",1
574,1,218,283,0.4678102,"\int \frac{\sqrt{a+b x} (c+d x)^{5/2}}{x^6} \, dx","Integrate[(Sqrt[a + b*x]*(c + d*x)^(5/2))/x^6,x]","-\frac{\frac{(3 a d+7 b c) \left(\frac{x (b c-a d) \left(\frac{5 x (b c-a d) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)\right)}{a^{5/2} \sqrt{c}}-8 \sqrt{a+b x} (c+d x)^{5/2}\right)}{a}-48 \sqrt{a+b x} (c+d x)^{7/2}\right)}{384 c x^4}+\frac{(a+b x)^{3/2} (c+d x)^{7/2}}{x^5}}{5 a c}","-\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,"-1/5*(((a + b*x)^(3/2)*(c + d*x)^(7/2))/x^5 + ((7*b*c + 3*a*d)*(-48*Sqrt[a + b*x]*(c + d*x)^(7/2) + ((b*c - a*d)*x*(-8*Sqrt[a + b*x]*(c + d*x)^(5/2) + (5*(b*c - a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(5/2)*Sqrt[c])))/a))/(384*c*x^4))/(a*c)","A",1
575,1,267,436,0.4929822,"\int \frac{\sqrt{a+b x} (c+d x)^{5/2}}{x^7} \, dx","Integrate[(Sqrt[a + b*x]*(c + d*x)^(5/2))/x^7,x]","\frac{\frac{\left(5 a^2 d^2+14 a b c d+21 b^2 c^2\right) \left(\frac{x (b c-a d) \left(\frac{5 x (b c-a d) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)\right)}{a^{5/2} \sqrt{c}}-8 \sqrt{a+b x} (c+d x)^{5/2}\right)}{a}-48 \sqrt{a+b x} (c+d x)^{7/2}\right)}{64 c x^4}-\frac{20 a c (a+b x)^{3/2} (c+d x)^{7/2}}{x^6}+\frac{2 (a+b x)^{3/2} (c+d x)^{7/2} (5 a d+9 b c)}{x^5}}{120 a^2 c^2}","\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,"((-20*a*c*(a + b*x)^(3/2)*(c + d*x)^(7/2))/x^6 + (2*(9*b*c + 5*a*d)*(a + b*x)^(3/2)*(c + d*x)^(7/2))/x^5 + ((21*b^2*c^2 + 14*a*b*c*d + 5*a^2*d^2)*(-48*Sqrt[a + b*x]*(c + d*x)^(7/2) + ((b*c - a*d)*x*(-8*Sqrt[a + b*x]*(c + d*x)^(5/2) + (5*(b*c - a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(5/2)*Sqrt[c])))/a))/(64*c*x^4))/(120*a^2*c^2)","A",1
576,1,227,251,0.9031504,"\int \frac{x^3 \sqrt{a+b x}}{\sqrt{c+d x}} \, dx","Integrate[(x^3*Sqrt[a + b*x])/Sqrt[c + d*x],x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) \left(15 a^3 d^3+a^2 b d^2 (17 c-10 d x)+a b^2 d \left(25 c^2-12 c d x+8 d^2 x^2\right)+b^3 \left(-105 c^3+70 c^2 d x-56 c d^2 x^2+48 d^3 x^3\right)\right)+3 \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) (b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{192 b^4 d^{9/2} \sqrt{c+d x}}","\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,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(15*a^3*d^3 + a^2*b*d^2*(17*c - 10*d*x) + a*b^2*d*(25*c^2 - 12*c*d*x + 8*d^2*x^2) + b^3*(-105*c^3 + 70*c^2*d*x - 56*c*d^2*x^2 + 48*d^3*x^3)) + 3*(b*c - a*d)^(3/2)*(35*b^3*c^3 + 15*a*b^2*c^2*d + 9*a^2*b*c*d^2 + 5*a^3*d^3)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(192*b^4*d^(9/2)*Sqrt[c + d*x])","A",1
577,1,173,191,0.4643203,"\int \frac{x^2 \sqrt{a+b x}}{\sqrt{c+d x}} \, dx","Integrate[(x^2*Sqrt[a + b*x])/Sqrt[c + d*x],x]","\frac{-b \sqrt{d} \sqrt{a+b x} (c+d x) \left(3 a^2 d^2-2 a b d (d x-2 c)+b^2 \left(-15 c^2+10 c d x-8 d^2 x^2\right)\right)-3 \left(a^2 d^2+2 a b c d+5 b^2 c^2\right) (b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{24 b^3 d^{7/2} \sqrt{c+d x}}","\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,"(-(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(3*a^2*d^2 - 2*a*b*d*(-2*c + d*x) + b^2*(-15*c^2 + 10*c*d*x - 8*d^2*x^2))) - 3*(b*c - a*d)^(3/2)*(5*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(24*b^3*d^(7/2)*Sqrt[c + d*x])","A",1
578,1,126,125,0.3418033,"\int \frac{x \sqrt{a+b x}}{\sqrt{c+d x}} \, dx","Integrate[(x*Sqrt[a + b*x])/Sqrt[c + d*x],x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) (a d-3 b c+2 b d x)+(a d+3 b c) (b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{4 b^2 d^{5/2} \sqrt{c+d x}}","\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,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(-3*b*c + a*d + 2*b*d*x) + (b*c - a*d)^(3/2)*(3*b*c + a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(4*b^2*d^(5/2)*Sqrt[c + d*x])","A",1
579,1,103,73,0.3085111,"\int \frac{\sqrt{a+b x}}{\sqrt{c+d x}} \, dx","Integrate[Sqrt[a + b*x]/Sqrt[c + d*x],x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x)-(b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b d^{3/2} \sqrt{c+d x}}","\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,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x) - (b*c - a*d)^(3/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(b*d^(3/2)*Sqrt[c + d*x])","A",1
580,1,120,85,0.1781209,"\int \frac{\sqrt{a+b x}}{x \sqrt{c+d x}} \, dx","Integrate[Sqrt[a + b*x]/(x*Sqrt[c + d*x]),x]","\frac{2 \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{d} \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)}{\sqrt{c}}","\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,"(2*Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[d]*Sqrt[c + d*x]) - (2*Sqrt[a]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/Sqrt[c]","A",1
581,1,77,77,0.0564939,"\int \frac{\sqrt{a+b x}}{x^2 \sqrt{c+d x}} \, dx","Integrate[Sqrt[a + b*x]/(x^2*Sqrt[c + d*x]),x]","-\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}","-\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*x]*Sqrt[c + d*x])/(c*x)) - ((b*c - a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(Sqrt[a]*c^(3/2))","A",1
582,1,113,131,0.0929147,"\int \frac{\sqrt{a+b x}}{x^3 \sqrt{c+d x}} \, dx","Integrate[Sqrt[a + b*x]/(x^3*Sqrt[c + d*x]),x]","\frac{\left(-3 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^{3/2} c^{5/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (-2 a c+3 a d x-b c x)}{4 a c^2 x^2}","\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*x]*Sqrt[c + d*x]*(-2*a*c - b*c*x + 3*a*d*x))/(4*a*c^2*x^2) + ((b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*a^(3/2)*c^(5/2))","A",1
583,1,158,190,0.1576052,"\int \frac{\sqrt{a+b x}}{x^4 \sqrt{c+d x}} \, dx","Integrate[Sqrt[a + b*x]/(x^4*Sqrt[c + d*x]),x]","\frac{\sqrt{a+b x} \sqrt{c+d x} \left(a^2 \left(-8 c^2+10 c d x-15 d^2 x^2\right)-2 a b c x (c-2 d x)+3 b^2 c^2 x^2\right)}{24 a^2 c^3 x^3}-\frac{\left(-5 a^3 d^3+3 a^2 b c d^2+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} c^{7/2}}","\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,"(Sqrt[a + b*x]*Sqrt[c + d*x]*(3*b^2*c^2*x^2 - 2*a*b*c*x*(c - 2*d*x) + a^2*(-8*c^2 + 10*c*d*x - 15*d^2*x^2)))/(24*a^2*c^3*x^3) - ((b^3*c^3 + a*b^2*c^2*d + 3*a^2*b*c*d^2 - 5*a^3*d^3)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(8*a^(5/2)*c^(7/2))","A",1
584,1,244,279,0.32534,"\int \frac{\sqrt{a+b x}}{x^5 \sqrt{c+d x}} \, dx","Integrate[Sqrt[a + b*x]/(x^5*Sqrt[c + d*x]),x]","\frac{-\frac{2 x^2 (a+b x)^{3/2} \sqrt{c+d x} \left(35 a^2 d^2+22 a b c d+15 b^2 c^2\right)}{a^2 c^2}+\frac{3 x^3 \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) \left(\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x}+x (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)}{a^{5/2} c^{7/2}}+\frac{8 x (a+b x)^{3/2} \sqrt{c+d x} (7 a d+5 b c)}{a c}-48 (a+b x)^{3/2} \sqrt{c+d x}}{192 a c x^4}","\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,"(-48*(a + b*x)^(3/2)*Sqrt[c + d*x] + (8*(5*b*c + 7*a*d)*x*(a + b*x)^(3/2)*Sqrt[c + d*x])/(a*c) - (2*(15*b^2*c^2 + 22*a*b*c*d + 35*a^2*d^2)*x^2*(a + b*x)^(3/2)*Sqrt[c + d*x])/(a^2*c^2) + (3*(5*b^3*c^3 + 9*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 35*a^3*d^3)*x^3*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x] + (b*c - a*d)*x*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(5/2)*c^(7/2)))/(192*a*c*x^4)","A",1
585,1,193,189,0.4169931,"\int \frac{x^2 \sqrt{a+b x}}{(c+d x)^{3/2}} \, dx","Integrate[(x^2*Sqrt[a + b*x])/(c + d*x)^(3/2),x]","\frac{\frac{b \sqrt{d} \left(a^2 d (c+d x)+a b \left(-15 c^2-4 c d x+3 d^2 x^2\right)+b^2 x \left(-15 c^2-5 c d x+2 d^2 x^2\right)\right)}{\sqrt{a+b x}}+\frac{\left(a^3 d^3+5 a^2 b c d^2-21 a b^2 c^2 d+15 b^3 c^3\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{b c-a d}}}{4 b^2 d^{7/2} \sqrt{c+d x}}","\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,"((b*Sqrt[d]*(a^2*d*(c + d*x) + b^2*x*(-15*c^2 - 5*c*d*x + 2*d^2*x^2) + a*b*(-15*c^2 - 4*c*d*x + 3*d^2*x^2)))/Sqrt[a + b*x] + ((15*b^3*c^3 - 21*a*b^2*c^2*d + 5*a^2*b*c*d^2 + a^3*d^3)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[b*c - a*d])/(4*b^2*d^(7/2)*Sqrt[c + d*x])","A",1
586,1,126,127,0.4166148,"\int \frac{x \sqrt{a+b x}}{(c+d x)^{3/2}} \, dx","Integrate[(x*Sqrt[a + b*x])/(c + d*x)^(3/2),x]","\frac{\sqrt{d} \sqrt{a+b x} (3 c+d x)-\frac{\left(a^2 d^2-4 a b c d+3 b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b \sqrt{b c-a d}}}{d^{5/2} \sqrt{c+d x}}","-\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[d]*Sqrt[a + b*x]*(3*c + d*x) - ((3*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(b*Sqrt[b*c - a*d]))/(d^(5/2)*Sqrt[c + d*x])","A",1
587,1,95,66,0.3867552,"\int \frac{\sqrt{a+b x}}{(c+d x)^{3/2}} \, dx","Integrate[Sqrt[a + b*x]/(c + d*x)^(3/2),x]","\frac{2 \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)-2 \sqrt{d} \sqrt{a+b x}}{d^{3/2} \sqrt{c+d x}}","\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[d]*Sqrt[a + b*x] + 2*Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(d^(3/2)*Sqrt[c + d*x])","A",1
588,1,66,66,0.0429098,"\int \frac{\sqrt{a+b x}}{x (c+d x)^{3/2}} \, dx","Integrate[Sqrt[a + b*x]/(x*(c + d*x)^(3/2)),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}}","\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*Sqrt[a + b*x])/(c*Sqrt[c + d*x]) - (2*Sqrt[a]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/c^(3/2)","A",1
589,1,83,113,0.0864953,"\int \frac{\sqrt{a+b x}}{x^2 (c+d x)^{3/2}} \, dx","Integrate[Sqrt[a + b*x]/(x^2*(c + d*x)^(3/2)),x]","\frac{(3 a d-b c) \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} (c+3 d x)}{c^2 x \sqrt{c+d x}}","-\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,"-((Sqrt[a + b*x]*(c + 3*d*x))/(c^2*x*Sqrt[c + d*x])) + ((-(b*c) + 3*a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(Sqrt[a]*c^(5/2))","A",1
590,1,130,171,0.1196869,"\int \frac{\sqrt{a+b x}}{x^3 (c+d x)^{3/2}} \, dx","Integrate[Sqrt[a + b*x]/(x^3*(c + d*x)^(3/2)),x]","\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{\sqrt{a+b x} \left(a \left(-2 c^2+5 c d x+15 d^2 x^2\right)-b c x (c+d x)\right)}{4 a c^3 x^2 \sqrt{c+d x}}","\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,"(Sqrt[a + b*x]*(-(b*c*x*(c + d*x)) + a*(-2*c^2 + 5*c*d*x + 15*d^2*x^2)))/(4*a*c^3*x^2*Sqrt[c + d*x]) + ((b^2*c^2 + 6*a*b*c*d - 15*a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*a^(3/2)*c^(7/2))","A",1
591,1,249,218,1.2992215,"\int \frac{x^3 \sqrt{a+b x}}{(c+d x)^{5/2}} \, dx","Integrate[(x^3*Sqrt[a + b*x])/(c + d*x)^(5/2),x]","\frac{\frac{3 (c+d x)^2 \left(-a^2 d^2-10 a b c d+35 b^2 c^2\right) \left(\sqrt{a+b x} (b c-a d) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)-\sqrt{d} (a+b x) \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}\right)}{d^{7/2} (b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}}}+\frac{2 c (a+b x)^2 (3 a d (c+2 d x)-7 b c (5 c+6 d x))}{d^2 (a d-b c)}+6 x^2 (a+b x)^2}{12 b d \sqrt{a+b x} (c+d x)^{3/2}}","-\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,"(6*x^2*(a + b*x)^2 + (2*c*(a + b*x)^2*(3*a*d*(c + 2*d*x) - 7*b*c*(5*c + 6*d*x)))/(d^2*(-(b*c) + a*d)) + (3*(35*b^2*c^2 - 10*a*b*c*d - a^2*d^2)*(c + d*x)^2*(-(Sqrt[d]*Sqrt[b*c - a*d]*(a + b*x)*Sqrt[(b*(c + d*x))/(b*c - a*d)]) + (b*c - a*d)*Sqrt[a + b*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]]))/(d^(7/2)*(b*c - a*d)^(3/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]))/(12*b*d*Sqrt[a + b*x]*(c + d*x)^(3/2))","A",1
592,1,203,165,0.7879693,"\int \frac{x^2 \sqrt{a+b x}}{(c+d x)^{5/2}} \, dx","Integrate[(x^2*Sqrt[a + b*x])/(c + d*x)^(5/2),x]","\frac{\frac{\sqrt{d} \left(a^2 (-d) \left(13 c^2+18 c d x+3 d^2 x^2\right)+a b \left(15 c^3+7 c^2 d x-15 c d^2 x^2-3 d^3 x^3\right)+b^2 c x \left(15 c^2+20 c d x+3 d^2 x^2\right)\right)}{\sqrt{a+b x} (b c-a d)}-\frac{3 (b c-a d)^{3/2} (5 b c-a d) \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b^2}}{3 d^{7/2} (c+d x)^{3/2}}","\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,"((Sqrt[d]*(-(a^2*d*(13*c^2 + 18*c*d*x + 3*d^2*x^2)) + b^2*c*x*(15*c^2 + 20*c*d*x + 3*d^2*x^2) + a*b*(15*c^3 + 7*c^2*d*x - 15*c*d^2*x^2 - 3*d^3*x^3)))/((b*c - a*d)*Sqrt[a + b*x]) - (3*(b*c - a*d)^(3/2)*(5*b*c - a*d)*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/b^2)/(3*d^(7/2)*(c + d*x)^(3/2))","A",1
593,1,164,102,0.667303,"\int \frac{x \sqrt{a+b x}}{(c+d x)^{5/2}} \, dx","Integrate[(x*Sqrt[a + b*x])/(c + d*x)^(5/2),x]","\frac{2 \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{d^{5/2} \sqrt{c+d x}}-\frac{2 \left(a^2 (-d) (2 c+3 d x)+a b \left(3 c^2+2 c d x-3 d^2 x^2\right)+b^2 c x (3 c+4 d x)\right)}{3 d^2 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)}","\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,"(-2*(-(a^2*d*(2*c + 3*d*x)) + b^2*c*x*(3*c + 4*d*x) + a*b*(3*c^2 + 2*c*d*x - 3*d^2*x^2)))/(3*d^2*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(3/2)) + (2*Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(d^(5/2)*Sqrt[c + d*x])","A",1
594,1,32,32,0.0123127,"\int \frac{\sqrt{a+b x}}{(c+d x)^{5/2}} \, dx","Integrate[Sqrt[a + b*x]/(c + d*x)^(5/2),x]","\frac{2 (a+b x)^{3/2}}{3 (c+d x)^{3/2} (b c-a d)}","\frac{2 (a+b x)^{3/2}}{3 (c+d x)^{3/2} (b c-a d)}",1,"(2*(a + b*x)^(3/2))/(3*(b*c - a*d)*(c + d*x)^(3/2))","A",1
595,1,102,102,0.2560044,"\int \frac{\sqrt{a+b x}}{x (c+d x)^{5/2}} \, dx","Integrate[Sqrt[a + b*x]/(x*(c + d*x)^(5/2)),x]","\frac{2 \sqrt{a+b x} (b c (3 c+2 d x)-a d (4 c+3 d x))}{3 c^2 (c+d x)^{3/2} (b c-a d)}-\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} \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,"(2*Sqrt[a + b*x]*(b*c*(3*c + 2*d*x) - a*d*(4*c + 3*d*x)))/(3*c^2*(b*c - a*d)*(c + d*x)^(3/2)) - (2*Sqrt[a]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/c^(5/2)","A",1
596,1,150,148,0.2728545,"\int \frac{\sqrt{a+b x}}{x^2 (c+d x)^{5/2}} \, dx","Integrate[Sqrt[a + b*x]/(x^2*(c + d*x)^(5/2)),x]","\frac{\frac{3 (c+d x) (b c-5 a d) \left(\sqrt{c} \sqrt{a+b x}-\sqrt{a} \sqrt{c+d x} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)}{c^{5/2}}-\frac{d (a+b x)^{3/2} (3 b c-5 a d)}{c (b c-a d)}-\frac{3 (a+b x)^{3/2}}{x}}{3 a c (c+d x)^{3/2}}","-\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,"(-((d*(3*b*c - 5*a*d)*(a + b*x)^(3/2))/(c*(b*c - a*d))) - (3*(a + b*x)^(3/2))/x + (3*(b*c - 5*a*d)*(c + d*x)*(Sqrt[c]*Sqrt[a + b*x] - Sqrt[a]*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/c^(5/2))/(3*a*c*(c + d*x)^(3/2))","A",1
597,1,236,234,0.454385,"\int \frac{\sqrt{a+b x}}{x^3 (c+d x)^{5/2}} \, dx","Integrate[Sqrt[a + b*x]/(x^3*(c + d*x)^(5/2)),x]","\frac{x^2 \left(c^{3/2} d (a+b x)^{3/2} \left(-35 a^2 d^2+24 a b c d+3 b^2 c^2\right)-3 (c+d x) (b c-a d) \left(-35 a^2 d^2+10 a b c d+b^2 c^2\right) \left(\sqrt{c} \sqrt{a+b x}-\sqrt{a} \sqrt{c+d x} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)\right)+6 a c^{7/2} (a+b x)^{3/2} (a d-b c)+3 c^{5/2} x (a+b x)^{3/2} (b c-a d) (7 a d+b c)}{12 a^2 c^{9/2} x^2 (c+d x)^{3/2} (b c-a d)}","-\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,"(6*a*c^(7/2)*(-(b*c) + a*d)*(a + b*x)^(3/2) + 3*c^(5/2)*(b*c - a*d)*(b*c + 7*a*d)*x*(a + b*x)^(3/2) + x^2*(c^(3/2)*d*(3*b^2*c^2 + 24*a*b*c*d - 35*a^2*d^2)*(a + b*x)^(3/2) - 3*(b*c - a*d)*(b^2*c^2 + 10*a*b*c*d - 35*a^2*d^2)*(c + d*x)*(Sqrt[c]*Sqrt[a + b*x] - Sqrt[a]*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])))/(12*a^2*c^(9/2)*(b*c - a*d)*x^2*(c + d*x)^(3/2))","A",1
598,1,265,315,0.7421987,"\int x^2 (a+b x)^{3/2} \sqrt{c+d x} \, dx","Integrate[x^2*(a + b*x)^(3/2)*Sqrt[c + d*x],x]","\frac{15 (b c-a d)^{7/2} \left(3 a^2 d^2+6 a b c d+7 b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)-b \sqrt{d} \sqrt{a+b x} (c+d x) \left(-45 a^4 d^4+30 a^3 b d^3 (c+d x)-6 a^2 b^2 d^2 \left(-6 c^2+3 c d x+4 d^2 x^2\right)-2 a b^3 d \left(95 c^3-61 c^2 d x+48 c d^2 x^2+264 d^3 x^3\right)+b^4 \left(105 c^4-70 c^3 d x+56 c^2 d^2 x^2-48 c d^3 x^3-384 d^4 x^4\right)\right)}{1920 b^4 d^{9/2} \sqrt{c+d x}}","\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,"(-(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(-45*a^4*d^4 + 30*a^3*b*d^3*(c + d*x) - 6*a^2*b^2*d^2*(-6*c^2 + 3*c*d*x + 4*d^2*x^2) - 2*a*b^3*d*(95*c^3 - 61*c^2*d*x + 48*c*d^2*x^2 + 264*d^3*x^3) + b^4*(105*c^4 - 70*c^3*d*x + 56*c^2*d^2*x^2 - 48*c*d^3*x^3 - 384*d^4*x^4))) + 15*(b*c - a*d)^(7/2)*(7*b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(1920*b^4*d^(9/2)*Sqrt[c + d*x])","A",1
599,1,299,221,1.5662653,"\int x (a+b x)^{3/2} \sqrt{c+d x} \, dx","Integrate[x*(a + b*x)^(3/2)*Sqrt[c + d*x],x]","\frac{(a+b x)^{5/2} (c+d x)^{3/2} \left(5-\frac{5 (3 a d+5 b c) \left(8 b^3 d^3 (a+b x)^3 \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}-b (b c-a d) \left(-2 b^2 d^2 (a+b x)^2 \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}+3 b^2 d (a+b x) (b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}}-3 b^2 \sqrt{d} \sqrt{a+b x} (b c-a d)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)\right)}{48 b^3 d^3 (a+b x)^3 (b c-a d)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2}}\right)}{20 b d}","-\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,"((a + b*x)^(5/2)*(c + d*x)^(3/2)*(5 - (5*(5*b*c + 3*a*d)*(8*b^3*d^3*Sqrt[b*c - a*d]*(a + b*x)^3*Sqrt[(b*(c + d*x))/(b*c - a*d)] - b*(b*c - a*d)*(3*b^2*d*(b*c - a*d)^(3/2)*(a + b*x)*Sqrt[(b*(c + d*x))/(b*c - a*d)] - 2*b^2*d^2*Sqrt[b*c - a*d]*(a + b*x)^2*Sqrt[(b*(c + d*x))/(b*c - a*d)] - 3*b^2*Sqrt[d]*(b*c - a*d)^2*Sqrt[a + b*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])))/(48*b^3*d^3*(b*c - a*d)^(3/2)*(a + b*x)^3*((b*(c + d*x))/(b*c - a*d))^(3/2))))/(20*b*d)","A",1
600,1,151,154,0.5130522,"\int (a+b x)^{3/2} \sqrt{c+d x} \, dx","Integrate[(a + b*x)^(3/2)*Sqrt[c + d*x],x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) \left(3 a^2 d^2+2 a b d (4 c+7 d x)+b^2 \left(-3 c^2+2 c d x+8 d^2 x^2\right)\right)+3 (b c-a d)^{7/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{24 b^2 d^{5/2} \sqrt{c+d x}}","\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,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(3*a^2*d^2 + 2*a*b*d*(4*c + 7*d*x) + b^2*(-3*c^2 + 2*c*d*x + 8*d^2*x^2)) + 3*(b*c - a*d)^(7/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(24*b^2*d^(5/2)*Sqrt[c + d*x])","A",1
601,1,194,164,0.8755023,"\int \frac{(a+b x)^{3/2} \sqrt{c+d x}}{x} \, dx","Integrate[((a + b*x)^(3/2)*Sqrt[c + d*x])/x,x]","\frac{\sqrt{d} \left(\sqrt{a+b x} (c+d x) (5 a d+b c+2 b d x)-8 a^{3/2} \sqrt{c} d \sqrt{c+d x} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)-\frac{\sqrt{b c-a d} \left(-3 a^2 d^2-6 a b c d+b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b}}{4 d^{3/2} \sqrt{c+d x}}","-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,"(-((Sqrt[b*c - a*d]*(b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/b) + Sqrt[d]*(Sqrt[a + b*x]*(c + d*x)*(b*c + 5*a*d + 2*b*d*x) - 8*a^(3/2)*Sqrt[c]*d*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(4*d^(3/2)*Sqrt[c + d*x])","A",1
602,1,164,144,0.9570344,"\int \frac{(a+b x)^{3/2} \sqrt{c+d x}}{x^2} \, dx","Integrate[((a + b*x)^(3/2)*Sqrt[c + d*x])/x^2,x]","\frac{\sqrt{a+b x} (b x-a) \sqrt{c+d x}}{x}+\frac{\sqrt{b c-a d} (3 a d+b c) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{d} \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{(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,"((-a + b*x)*Sqrt[a + b*x]*Sqrt[c + d*x])/x + (Sqrt[b*c - a*d]*(b*c + 3*a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[d]*Sqrt[c + d*x]) - (Sqrt[a]*(3*b*c + a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/Sqrt[c]","A",1
603,1,185,171,1.4003824,"\int \frac{(a+b x)^{3/2} \sqrt{c+d x}}{x^3} \, dx","Integrate[((a + b*x)^(3/2)*Sqrt[c + d*x])/x^3,x]","\frac{1}{4} \left(\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)}{\sqrt{a} c^{3/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (2 a c+a d x+5 b c x)}{c x^2}+\frac{8 \sqrt{d} (b c-a d)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{(c+d x)^{3/2}}\right)","-\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,"(-((Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c + 5*b*c*x + a*d*x))/(c*x^2)) + (8*Sqrt[d]*(b*c - a*d)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(c + d*x)^(3/2) + ((-3*b^2*c^2 - 6*a*b*c*d + a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(Sqrt[a]*c^(3/2)))/4","A",1
604,1,140,160,0.2143421,"\int \frac{(a+b x)^{3/2} \sqrt{c+d x}}{x^4} \, dx","Integrate[((a + b*x)^(3/2)*Sqrt[c + d*x])/x^4,x]","\frac{\frac{3 x (b c-a d) \left(x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)-\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+a d x+b c x)\right)}{a^{3/2} c^{3/2}}-8 (a+b x)^{3/2} (c+d x)^{3/2}}{24 c x^3}","\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,"(-8*(a + b*x)^(3/2)*(c + d*x)^(3/2) + (3*(b*c - a*d)*x*(-(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c + b*c*x + a*d*x)) + (b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(3/2)*c^(3/2)))/(24*c*x^3)","A",1
605,1,182,233,0.3237529,"\int \frac{(a+b x)^{3/2} \sqrt{c+d x}}{x^5} \, dx","Integrate[((a + b*x)^(3/2)*Sqrt[c + d*x])/x^5,x]","-\frac{\frac{(5 a d+3 b c) \left(\frac{3 x (b c-a d) \left(x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)-\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+a d x+b c x)\right)}{a^{3/2} c^{3/2}}-8 (a+b x)^{3/2} (c+d x)^{3/2}\right)}{48 c x^3}+\frac{(a+b x)^{5/2} (c+d x)^{3/2}}{x^4}}{4 a c}","-\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,"-1/4*(((a + b*x)^(5/2)*(c + d*x)^(3/2))/x^4 + ((3*b*c + 5*a*d)*(-8*(a + b*x)^(3/2)*(c + d*x)^(3/2) + (3*(b*c - a*d)*x*(-(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c + b*c*x + a*d*x)) + (b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(3/2)*c^(3/2))))/(48*c*x^3))/(a*c)","A",1
606,1,231,340,0.3564881,"\int \frac{(a+b x)^{3/2} \sqrt{c+d x}}{x^6} \, dx","Integrate[((a + b*x)^(3/2)*Sqrt[c + d*x])/x^6,x]","\frac{\frac{5 \left(7 a^2 d^2+6 a b c d+3 b^2 c^2\right) \left(\frac{3 x (b c-a d) \left(x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)-\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+a d x+b c x)\right)}{a^{3/2} c^{3/2}}-8 (a+b x)^{3/2} (c+d x)^{3/2}\right)}{24 c x^3}-\frac{16 a c (a+b x)^{5/2} (c+d x)^{3/2}}{x^5}+\frac{2 (a+b x)^{5/2} (c+d x)^{3/2} (7 a d+5 b c)}{x^4}}{80 a^2 c^2}","\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,"((-16*a*c*(a + b*x)^(5/2)*(c + d*x)^(3/2))/x^5 + (2*(5*b*c + 7*a*d)*(a + b*x)^(5/2)*(c + d*x)^(3/2))/x^4 + (5*(3*b^2*c^2 + 6*a*b*c*d + 7*a^2*d^2)*(-8*(a + b*x)^(3/2)*(c + d*x)^(3/2) + (3*(b*c - a*d)*x*(-(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c + b*c*x + a*d*x)) + (b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(3/2)*c^(3/2))))/(24*c*x^3))/(80*a^2*c^2)","A",1
607,1,218,349,1.8553835,"\int x^2 (a+b x)^{3/2} (c+d x)^{3/2} \, dx","Integrate[x^2*(a + b*x)^(3/2)*(c + d*x)^(3/2),x]","\frac{(a+b x)^{5/2} (c+d x)^{5/2} \left(\frac{25 \left(7 a^2 d^2+10 a b c d+7 b^2 c^2\right) \left(\frac{3 (b c-a d)^{7/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{d^{5/2} (a+b x)^{5/2} \sqrt{\frac{b (c+d x)}{b c-a d}}}+\frac{3 (a d-b c)^3}{d^2 (a+b x)^2}+\frac{2 (b c-a d)^2}{d (a+b x)}-8 a d+16 b (c+d x)+8 b c\right)}{128 b^2 (c+d x)^2}-35 (a d+b c)+50 b d x\right)}{300 b^2 d^2}","-\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,"((a + b*x)^(5/2)*(c + d*x)^(5/2)*(-35*(b*c + a*d) + 50*b*d*x + (25*(7*b^2*c^2 + 10*a*b*c*d + 7*a^2*d^2)*(8*b*c - 8*a*d + (3*(-(b*c) + a*d)^3)/(d^2*(a + b*x)^2) + (2*(b*c - a*d)^2)/(d*(a + b*x)) + 16*b*(c + d*x) + (3*(b*c - a*d)^(7/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(d^(5/2)*(a + b*x)^(5/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(128*b^2*(c + d*x)^2)))/(300*b^2*d^2)","A",1
608,1,250,258,0.7670312,"\int x (a+b x)^{3/2} (c+d x)^{3/2} \, dx","Integrate[x*(a + b*x)^(3/2)*(c + d*x)^(3/2),x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) \left(15 a^4 d^4-10 a^3 b d^3 (4 c+d x)+2 a^2 b^2 d^2 \left(9 c^2+13 c d x+4 d^2 x^2\right)+2 a b^3 d \left(-20 c^3+13 c^2 d x+136 c d^2 x^2+88 d^3 x^3\right)+b^4 \left(15 c^4-10 c^3 d x+8 c^2 d^2 x^2+176 c d^3 x^3+128 d^4 x^4\right)\right)-15 (b c-a d)^{9/2} (a d+b c) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{640 b^4 d^{7/2} \sqrt{c+d x}}","-\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,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(15*a^4*d^4 - 10*a^3*b*d^3*(4*c + d*x) + 2*a^2*b^2*d^2*(9*c^2 + 13*c*d*x + 4*d^2*x^2) + 2*a*b^3*d*(-20*c^3 + 13*c^2*d*x + 136*c*d^2*x^2 + 88*d^3*x^3) + b^4*(15*c^4 - 10*c^3*d*x + 8*c^2*d^2*x^2 + 176*c*d^3*x^3 + 128*d^4*x^4)) - 15*(b*c - a*d)^(9/2)*(b*c + a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(640*b^4*d^(7/2)*Sqrt[c + d*x])","A",1
609,1,193,189,0.5854608,"\int (a+b x)^{3/2} (c+d x)^{3/2} \, dx","Integrate[(a + b*x)^(3/2)*(c + d*x)^(3/2),x]","\frac{3 (b c-a d)^{9/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)-b \sqrt{d} \sqrt{a+b x} (c+d x) \left(3 a^3 d^3-a^2 b d^2 (11 c+2 d x)-a b^2 d \left(11 c^2+44 c d x+24 d^2 x^2\right)+b^3 \left(3 c^3-2 c^2 d x-24 c d^2 x^2-16 d^3 x^3\right)\right)}{64 b^3 d^{5/2} \sqrt{c+d x}}","\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,"(-(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(3*a^3*d^3 - a^2*b*d^2*(11*c + 2*d*x) - a*b^2*d*(11*c^2 + 44*c*d*x + 24*d^2*x^2) + b^3*(3*c^3 - 2*c^2*d*x - 24*c*d^2*x^2 - 16*d^3*x^3))) + 3*(b*c - a*d)^(9/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(64*b^3*d^(5/2)*Sqrt[c + d*x])","A",1
610,1,243,213,0.9036954,"\int \frac{(a+b x)^{3/2} (c+d x)^{3/2}}{x} \, dx","Integrate[((a + b*x)^(3/2)*(c + d*x)^(3/2))/x,x]","\frac{\sqrt{d} \left(\sqrt{a+b x} (c+d x) \left(3 a^2 d^2+2 a b d (19 c+7 d x)+b^2 \left(3 c^2+14 c d x+8 d^2 x^2\right)\right)-48 a^{3/2} b c^{3/2} d \sqrt{c+d x} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)-\frac{3 \sqrt{b c-a d} \left(a^3 d^3-9 a^2 b c d^2-9 a b^2 c^2 d+b^3 c^3\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b}}{24 b d^{3/2} \sqrt{c+d x}}","-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,"((-3*Sqrt[b*c - a*d]*(b^3*c^3 - 9*a*b^2*c^2*d - 9*a^2*b*c*d^2 + a^3*d^3)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/b + Sqrt[d]*(Sqrt[a + b*x]*(c + d*x)*(3*a^2*d^2 + 2*a*b*d*(19*c + 7*d*x) + b^2*(3*c^2 + 14*c*d*x + 8*d^2*x^2)) - 48*a^(3/2)*b*c^(3/2)*d*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(24*b*d^(3/2)*Sqrt[c + d*x])","A",1
611,1,197,191,1.2487084,"\int \frac{(a+b x)^{3/2} (c+d x)^{3/2}}{x^2} \, dx","Integrate[((a + b*x)^(3/2)*(c + d*x)^(3/2))/x^2,x]","\frac{3 \sqrt{c+d x} \left(a^2 d^2+6 a b c d+b^2 c^2\right) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{4 \sqrt{d} \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}}+\frac{\sqrt{a+b x} \sqrt{c+d x} (a (5 d x-4 c)+b x (5 c+2 d x))}{4 x}-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)","\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,"(Sqrt[a + b*x]*Sqrt[c + d*x]*(b*x*(5*c + 2*d*x) + a*(-4*c + 5*d*x)))/(4*x) + (3*(b^2*c^2 + 6*a*b*c*d + a^2*d^2)*Sqrt[c + d*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(4*Sqrt[d]*Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]) - 3*Sqrt[a]*Sqrt[c]*(b*c + a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]","A",1
612,1,197,209,1.3629101,"\int \frac{(a+b x)^{3/2} (c+d x)^{3/2}}{x^3} \, dx","Integrate[((a + b*x)^(3/2)*(c + d*x)^(3/2))/x^3,x]","-\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{\sqrt{a+b x} \sqrt{c+d x} (a (2 c+5 d x)+b x (5 c-4 d x))}{4 x^2}+\frac{3 \sqrt{d} \sqrt{b c-a d} (a d+b c) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{c+d x}}","-\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,"-1/4*(Sqrt[a + b*x]*Sqrt[c + d*x]*(b*x*(5*c - 4*d*x) + a*(2*c + 5*d*x)))/x^2 + (3*Sqrt[d]*Sqrt[b*c - a*d]*(b*c + a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[c + d*x] - (3*(b^2*c^2 + 6*a*b*c*d + a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*Sqrt[a]*Sqrt[c])","A",1
613,1,237,222,2.4961204,"\int \frac{(a+b x)^{3/2} (c+d x)^{3/2}}{x^4} \, dx","Integrate[((a + b*x)^(3/2)*(c + d*x)^(3/2))/x^4,x]","-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(a^2 \left(8 c^2+14 c d x+3 d^2 x^2\right)+2 a b c x (7 c+19 d x)+3 b^2 c^2 x^2\right)}{24 a c x^3}+\frac{\left(a^3 d^3-9 a^2 b c d^2-9 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} c^{3/2}}+\frac{2 d^{3/2} (b c-a d)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{(c+d x)^{3/2}}","\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,"-1/24*(Sqrt[a + b*x]*Sqrt[c + d*x]*(3*b^2*c^2*x^2 + 2*a*b*c*x*(7*c + 19*d*x) + a^2*(8*c^2 + 14*c*d*x + 3*d^2*x^2)))/(a*c*x^3) + (2*d^(3/2)*(b*c - a*d)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(c + d*x)^(3/2) + ((b^3*c^3 - 9*a*b^2*c^2*d - 9*a^2*b*c*d^2 + a^3*d^3)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(8*a^(3/2)*c^(3/2))","A",1
614,1,173,201,0.4536843,"\int \frac{(a+b x)^{3/2} (c+d x)^{3/2}}{x^5} \, dx","Integrate[((a + b*x)^(3/2)*(c + d*x)^(3/2))/x^5,x]","-\frac{x (b c-a d) \left(\frac{x (b c-a d) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)\right)}{a^{5/2} \sqrt{c}}+8 \sqrt{a+b x} (c+d x)^{5/2}\right)+16 c (a+b x)^{3/2} (c+d x)^{5/2}}{64 c^2 x^4}","-\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,"-1/64*(16*c*(a + b*x)^(3/2)*(c + d*x)^(5/2) + (b*c - a*d)*x*(8*Sqrt[a + b*x]*(c + d*x)^(5/2) + ((b*c - a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(5/2)*Sqrt[c])))/(c^2*x^4)","A",1
615,1,228,273,0.7363435,"\int \frac{(a+b x)^{3/2} (c+d x)^{3/2}}{x^6} \, dx","Integrate[((a + b*x)^(3/2)*(c + d*x)^(3/2))/x^6,x]","\frac{(a d+b c) \left(16 a^{5/2} c^{3/2} (a+b x)^{3/2} (c+d x)^{5/2}+x (b c-a d) \left(8 a^{5/2} \sqrt{c} \sqrt{a+b x} (c+d x)^{5/2}+x (b c-a d) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)\right)\right)\right)}{128 a^{7/2} c^{7/2} x^4}-\frac{(a+b x)^{5/2} (c+d x)^{5/2}}{5 a c x^5}","\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,"-1/5*((a + b*x)^(5/2)*(c + d*x)^(5/2))/(a*c*x^5) + ((b*c + a*d)*(16*a^(5/2)*c^(3/2)*(a + b*x)^(3/2)*(c + d*x)^(5/2) + (b*c - a*d)*x*(8*a^(5/2)*Sqrt[c]*Sqrt[a + b*x]*(c + d*x)^(5/2) + (b*c - a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))))/(128*a^(7/2)*c^(7/2)*x^4)","A",1
616,1,369,437,3.5896194,"\int x^2 (a+b x)^{3/2} (c+d x)^{5/2} \, dx","Integrate[x^2*(a + b*x)^(3/2)*(c + d*x)^(5/2),x]","\frac{(a+b x)^{5/2} (c+d x)^{7/2} \left(\frac{7 \left(9 a^2 d^2+10 a b c d+5 b^2 c^2\right) \left(8 b^6 d^3 (a+b x)^3 (b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(5 a^2 d^2-10 a b d (2 c+d x)+b^2 \left(31 c^2+42 c d x+16 d^2 x^2\right)\right)+5 b^6 \sqrt{d} \left(2 d^{3/2} (a+b x)^2 (b c-a d)^{9/2} \sqrt{\frac{b (c+d x)}{b c-a d}}-3 \sqrt{d} (a+b x) (b c-a d)^{11/2} \sqrt{\frac{b (c+d x)}{b c-a d}}+3 \sqrt{a+b x} (b c-a d)^6 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)\right)}{256 b^9 d^4 (a+b x)^3 (c+d x)^2 (b c-a d)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2}}-\frac{45 a}{b}-\frac{35 c}{d}+60 x\right)}{420 b d}","\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,"((a + b*x)^(5/2)*(c + d*x)^(7/2)*((-45*a)/b - (35*c)/d + 60*x + (7*(5*b^2*c^2 + 10*a*b*c*d + 9*a^2*d^2)*(8*b^6*d^3*(b*c - a*d)^(3/2)*(a + b*x)^3*Sqrt[(b*(c + d*x))/(b*c - a*d)]*(5*a^2*d^2 - 10*a*b*d*(2*c + d*x) + b^2*(31*c^2 + 42*c*d*x + 16*d^2*x^2)) + 5*b^6*Sqrt[d]*(-3*Sqrt[d]*(b*c - a*d)^(11/2)*(a + b*x)*Sqrt[(b*(c + d*x))/(b*c - a*d)] + 2*d^(3/2)*(b*c - a*d)^(9/2)*(a + b*x)^2*Sqrt[(b*(c + d*x))/(b*c - a*d)] + 3*(b*c - a*d)^6*Sqrt[a + b*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])))/(256*b^9*d^4*(b*c - a*d)^(5/2)*(a + b*x)^3*(c + d*x)^2*((b*(c + d*x))/(b*c - a*d))^(3/2))))/(420*b*d)","A",1
617,1,345,315,2.0779089,"\int x (a+b x)^{3/2} (c+d x)^{5/2} \, dx","Integrate[x*(a + b*x)^(3/2)*(c + d*x)^(5/2),x]","\frac{(a+b x)^{5/2} \sqrt{c+d x} \left(5 b^3 (c+d x)^3-\frac{(7 a d+5 b c) \left(8 b^6 d^3 (a+b x)^3 (b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(5 a^2 d^2-10 a b d (2 c+d x)+b^2 \left(31 c^2+42 c d x+16 d^2 x^2\right)\right)+5 b^6 \sqrt{d} \left(2 d^{3/2} (a+b x)^2 (b c-a d)^{9/2} \sqrt{\frac{b (c+d x)}{b c-a d}}-3 \sqrt{d} (a+b x) (b c-a d)^{11/2} \sqrt{\frac{b (c+d x)}{b c-a d}}+3 \sqrt{a+b x} (b c-a d)^6 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)\right)}{256 b^6 d^3 (a+b x)^3 (b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{30 b^4 d}","-\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,"((a + b*x)^(5/2)*Sqrt[c + d*x]*(5*b^3*(c + d*x)^3 - ((5*b*c + 7*a*d)*(8*b^6*d^3*(b*c - a*d)^(3/2)*(a + b*x)^3*Sqrt[(b*(c + d*x))/(b*c - a*d)]*(5*a^2*d^2 - 10*a*b*d*(2*c + d*x) + b^2*(31*c^2 + 42*c*d*x + 16*d^2*x^2)) + 5*b^6*Sqrt[d]*(-3*Sqrt[d]*(b*c - a*d)^(11/2)*(a + b*x)*Sqrt[(b*(c + d*x))/(b*c - a*d)] + 2*d^(3/2)*(b*c - a*d)^(9/2)*(a + b*x)^2*Sqrt[(b*(c + d*x))/(b*c - a*d)] + 3*(b*c - a*d)^6*Sqrt[a + b*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])))/(256*b^6*d^3*(b*c - a*d)^(3/2)*(a + b*x)^3*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(30*b^4*d)","A",1
618,1,187,224,0.0928206,"\int (a+b x)^{3/2} (c+d x)^{5/2} \, dx","Integrate[(a + b*x)^(3/2)*(c + d*x)^(5/2),x]","\frac{(a+b x)^{5/2} \sqrt{c+d x} \left(\frac{15 (b c-a d)^{9/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{d^{5/2} (a+b x)^{5/2} \sqrt{\frac{b (c+d x)}{b c-a d}}}-\frac{15 (b c-a d)^4}{d^2 (a+b x)^2}+\frac{10 (b c-a d)^3}{d (a+b x)}+80 b (c+d x) (b c-a d)+40 (b c-a d)^2+128 b^2 (c+d x)^2\right)}{640 b^3}","\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,"((a + b*x)^(5/2)*Sqrt[c + d*x]*(40*(b*c - a*d)^2 - (15*(b*c - a*d)^4)/(d^2*(a + b*x)^2) + (10*(b*c - a*d)^3)/(d*(a + b*x)) + 80*b*(b*c - a*d)*(c + d*x) + 128*b^2*(c + d*x)^2 + (15*(b*c - a*d)^(9/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(d^(5/2)*(a + b*x)^(5/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(640*b^3)","A",1
619,1,910,304,2.9273967,"\int \frac{(a+b x)^{3/2} (c+d x)^{5/2}}{x} \, dx","Integrate[((a + b*x)^(3/2)*(c + d*x)^(5/2))/x,x]","\frac{\sqrt{c+d x} \left(-15 b^4 (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right) c^4+15 b \sqrt{d} (b c-a d)^{5/2} \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c^3+180 a b^3 d (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right) c^3-384 a^{3/2} b d^{3/2} (b c-a d)^{3/2} \sqrt{c+d x} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right) c^{5/2}+337 a d^{3/2} (b c-a d)^{5/2} \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c^2+118 b d^{3/2} (b c-a d)^{5/2} x \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c^2+270 a^2 b^2 d^2 (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right) c^2+\frac{57 a^2 d^{5/2} (b c-a d)^{5/2} \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c}{b}+136 b d^{5/2} (b c-a d)^{5/2} x^2 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c+244 a d^{5/2} (b c-a d)^{5/2} x \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c-60 a^3 b d^3 (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right) c+48 b d^{7/2} (b c-a d)^{5/2} x^3 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}+72 a d^{7/2} (b c-a d)^{5/2} x^2 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}+\frac{6 a^2 d^{7/2} (b c-a d)^{5/2} x \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}}{b}+9 a^4 d^4 (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)-9 a^3 d^{7/2} \sqrt{b c-a d} \sqrt{a+b x} (c+d x)^2 \sqrt{\frac{b (c+d x)}{b c-a d}}\right)}{192 d^{3/2} (b c-a d)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}}","-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,"(Sqrt[c + d*x]*(-9*a^3*d^(7/2)*Sqrt[b*c - a*d]*Sqrt[a + b*x]*(c + d*x)^2*Sqrt[(b*(c + d*x))/(b*c - a*d)] + 15*b*c^3*Sqrt[d]*(b*c - a*d)^(5/2)*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 337*a*c^2*d^(3/2)*(b*c - a*d)^(5/2)*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + (57*a^2*c*d^(5/2)*(b*c - a*d)^(5/2)*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2))/b + 118*b*c^2*d^(3/2)*(b*c - a*d)^(5/2)*x*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 244*a*c*d^(5/2)*(b*c - a*d)^(5/2)*x*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + (6*a^2*d^(7/2)*(b*c - a*d)^(5/2)*x*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2))/b + 136*b*c*d^(5/2)*(b*c - a*d)^(5/2)*x^2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 72*a*d^(7/2)*(b*c - a*d)^(5/2)*x^2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 48*b*d^(7/2)*(b*c - a*d)^(5/2)*x^3*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) - 15*b^4*c^4*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] + 180*a*b^3*c^3*d*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] + 270*a^2*b^2*c^2*d^2*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] - 60*a^3*b*c*d^3*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] + 9*a^4*d^4*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] - 384*a^(3/2)*b*c^(5/2)*d^(3/2)*(b*c - a*d)^(3/2)*Sqrt[c + d*x]*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(192*d^(3/2)*(b*c - a*d)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(5/2))","B",1
620,1,253,257,2.5003746,"\int \frac{(a+b x)^{3/2} (c+d x)^{5/2}}{x^2} \, dx","Integrate[((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^2,x]","\frac{\frac{\sqrt{a+b x} \sqrt{c+d x} \left(3 a^2 d^2 x+2 a b \left(-12 c^2+34 c d x+7 d^2 x^2\right)+b^2 x \left(33 c^2+26 c d x+8 d^2 x^2\right)\right)}{x}+\frac{3 \sqrt{c+d x} \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) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{d} \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}}-24 \sqrt{a} b 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)}{24 b}","\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,"((Sqrt[a + b*x]*Sqrt[c + d*x]*(3*a^2*d^2*x + 2*a*b*(-12*c^2 + 34*c*d*x + 7*d^2*x^2) + b^2*x*(33*c^2 + 26*c*d*x + 8*d^2*x^2)))/x + (3*(5*b^3*c^3 + 45*a*b^2*c^2*d + 15*a^2*b*c*d^2 - a^3*d^3)*Sqrt[c + d*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[d]*Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]) - 24*Sqrt[a]*b*c^(3/2)*(3*b*c + 5*a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(24*b)","A",1
621,1,234,258,2.0506245,"\int \frac{(a+b x)^{3/2} (c+d x)^{5/2}}{x^3} \, dx","Integrate[((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^3,x]","\frac{1}{4} \left(\frac{3 \sqrt{d} \sqrt{c+d x} \left(a^2 d^2+10 a b c d+5 b^2 c^2\right) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}}-\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)}{\sqrt{a}}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(a \left(-2 c^2-9 c d x+5 d^2 x^2\right)+b x \left(-5 c^2+9 c d x+2 d^2 x^2\right)\right)}{x^2}\right)","-\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,"((Sqrt[a + b*x]*Sqrt[c + d*x]*(b*x*(-5*c^2 + 9*c*d*x + 2*d^2*x^2) + a*(-2*c^2 - 9*c*d*x + 5*d^2*x^2)))/x^2 + (3*Sqrt[d]*(5*b^2*c^2 + 10*a*b*c*d + a^2*d^2)*Sqrt[c + d*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]) - (3*Sqrt[c]*(b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/Sqrt[a])/4","A",1
622,1,254,292,2.9685866,"\int \frac{(a+b x)^{3/2} (c+d x)^{5/2}}{x^4} \, dx","Integrate[((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^4,x]","-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(a^2 \left(8 c^2+26 c d x+33 d^2 x^2\right)+2 a b x \left(7 c^2+34 c d x-12 d^2 x^2\right)+3 b^2 c^2 x^2\right)}{24 a x^3}-\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{d^{3/2} \sqrt{b c-a d} (3 a d+5 b c) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{c+d x}}","\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,"-1/24*(Sqrt[a + b*x]*Sqrt[c + d*x]*(3*b^2*c^2*x^2 + 2*a*b*x*(7*c^2 + 34*c*d*x - 12*d^2*x^2) + a^2*(8*c^2 + 26*c*d*x + 33*d^2*x^2)))/(a*x^3) + (d^(3/2)*Sqrt[b*c - a*d]*(5*b*c + 3*a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[c + d*x] - ((-(b^3*c^3) + 15*a*b^2*c^2*d + 45*a^2*b*c*d^2 + 5*a^3*d^3)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(8*a^(3/2)*Sqrt[c])","A",1
623,1,296,316,3.4388506,"\int \frac{(a+b x)^{3/2} (c+d x)^{5/2}}{x^5} \, dx","Integrate[((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^5,x]","-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(a^3 \left(48 c^3+136 c^2 d x+118 c d^2 x^2+15 d^3 x^3\right)+a^2 b c x \left(72 c^2+244 c d x+337 d^2 x^2\right)+3 a b^2 c^2 x^2 (2 c+19 d x)-9 b^3 c^3 x^3\right)}{192 a^2 c x^4}+\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}}+\frac{2 d^{5/2} (b c-a d)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{(c+d x)^{3/2}}","\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,"-1/192*(Sqrt[a + b*x]*Sqrt[c + d*x]*(-9*b^3*c^3*x^3 + 3*a*b^2*c^2*x^2*(2*c + 19*d*x) + a^2*b*c*x*(72*c^2 + 244*c*d*x + 337*d^2*x^2) + a^3*(48*c^3 + 136*c^2*d*x + 118*c*d^2*x^2 + 15*d^3*x^3)))/(a^2*c*x^4) + (2*d^(5/2)*(b*c - a*d)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(c + d*x)^(3/2) + ((-3*b^4*c^4 + 20*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 - 60*a^3*b*c*d^3 + 5*a^4*d^4)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(64*a^(5/2)*c^(3/2))","A",1
624,1,208,242,0.5474118,"\int \frac{(a+b x)^{3/2} (c+d x)^{5/2}}{x^6} \, dx","Integrate[((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^6,x]","\frac{x (b c-a d) \left(\frac{x (b c-a d) \left(\frac{5 x (b c-a d) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)\right)}{a^{5/2} \sqrt{c}}-8 \sqrt{a+b x} (c+d x)^{5/2}\right)}{a}-48 \sqrt{a+b x} (c+d x)^{7/2}\right)-128 c (a+b x)^{3/2} (c+d x)^{7/2}}{640 c^2 x^5}","\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,"(-128*c*(a + b*x)^(3/2)*(c + d*x)^(7/2) + (b*c - a*d)*x*(-48*Sqrt[a + b*x]*(c + d*x)^(7/2) + ((b*c - a*d)*x*(-8*Sqrt[a + b*x]*(c + d*x)^(5/2) + (5*(b*c - a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(5/2)*Sqrt[c])))/a))/(640*c^2*x^5)","A",1
625,1,272,333,0.9368459,"\int \frac{(a+b x)^{3/2} (c+d x)^{5/2}}{x^7} \, dx","Integrate[((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^7,x]","\frac{(5 a d+7 b c) \left(128 a^{7/2} c^{3/2} (a+b x)^{3/2} (c+d x)^{7/2}+x (b c-a d) \left(x (b c-a d) \left(8 a^{5/2} \sqrt{c} \sqrt{a+b x} (c+d x)^{5/2}-5 x (b c-a d) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)\right)\right)+48 a^{7/2} \sqrt{c} \sqrt{a+b x} (c+d x)^{7/2}\right)\right)}{7680 a^{9/2} c^{7/2} x^5}-\frac{(a+b x)^{5/2} (c+d x)^{7/2}}{6 a c x^6}","-\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,"-1/6*((a + b*x)^(5/2)*(c + d*x)^(7/2))/(a*c*x^6) + ((7*b*c + 5*a*d)*(128*a^(7/2)*c^(3/2)*(a + b*x)^(3/2)*(c + d*x)^(7/2) + (b*c - a*d)*x*(48*a^(7/2)*Sqrt[c]*Sqrt[a + b*x]*(c + d*x)^(7/2) + (b*c - a*d)*x*(8*a^(5/2)*Sqrt[c]*Sqrt[a + b*x]*(c + d*x)^(5/2) - 5*(b*c - a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])))))/(7680*a^(9/2)*c^(7/2)*x^5)","A",1
626,1,215,254,0.6405279,"\int \frac{x^2 (a+b x)^{3/2}}{\sqrt{c+d x}} \, dx","Integrate[(x^2*(a + b*x)^(3/2))/Sqrt[c + d*x],x]","\frac{3 (b c-a d)^{5/2} \left(3 a^2 d^2+10 a b c d+35 b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)-b \sqrt{d} \sqrt{a+b x} (c+d x) \left(9 a^3 d^3+3 a^2 b d^2 (5 c-2 d x)+a b^2 d \left(-145 c^2+92 c d x-72 d^2 x^2\right)+b^3 \left(105 c^3-70 c^2 d x+56 c d^2 x^2-48 d^3 x^3\right)\right)}{192 b^3 d^{9/2} \sqrt{c+d x}}","-\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,"(-(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(9*a^3*d^3 + 3*a^2*b*d^2*(5*c - 2*d*x) + a*b^2*d*(-145*c^2 + 92*c*d*x - 72*d^2*x^2) + b^3*(105*c^3 - 70*c^2*d*x + 56*c*d^2*x^2 - 48*d^3*x^3))) + 3*(b*c - a*d)^(5/2)*(35*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(192*b^3*d^(9/2)*Sqrt[c + d*x])","A",1
627,1,159,171,0.4875259,"\int \frac{x (a+b x)^{3/2}}{\sqrt{c+d x}} \, dx","Integrate[(x*(a + b*x)^(3/2))/Sqrt[c + d*x],x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) \left(3 a^2 d^2+2 a b d (7 d x-11 c)+b^2 \left(15 c^2-10 c d x+8 d^2 x^2\right)\right)-3 (b c-a d)^{5/2} (a d+5 b c) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{24 b^2 d^{7/2} \sqrt{c+d x}}","-\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,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(3*a^2*d^2 + 2*a*b*d*(-11*c + 7*d*x) + b^2*(15*c^2 - 10*c*d*x + 8*d^2*x^2)) - 3*(b*c - a*d)^(5/2)*(5*b*c + a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(24*b^2*d^(7/2)*Sqrt[c + d*x])","A",1
628,1,119,113,0.4245903,"\int \frac{(a+b x)^{3/2}}{\sqrt{c+d x}} \, dx","Integrate[(a + b*x)^(3/2)/Sqrt[c + d*x],x]","\frac{\sqrt{d} \sqrt{a+b x} (c+d x) (5 a d-3 b c+2 b d x)+\frac{3 (b c-a d)^{5/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b}}{4 d^{5/2} \sqrt{c+d x}}","\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,"(Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(-3*b*c + 5*a*d + 2*b*d*x) + (3*(b*c - a*d)^(5/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/b)/(4*d^(5/2)*Sqrt[c + d*x])","A",1
629,1,176,116,0.7518764,"\int \frac{(a+b x)^{3/2}}{x \sqrt{c+d x}} \, dx","Integrate[(a + b*x)^(3/2)/(x*Sqrt[c + d*x]),x]","\frac{\sqrt{d} \left(b \sqrt{a+b x} (c+d x)-\frac{2 a^{3/2} d \sqrt{c+d x} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{c}}\right)-\frac{\left(3 a^2 d^2-4 a b c d+b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{b c-a d}}}{d^{3/2} \sqrt{c+d x}}","-\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^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[b*c - a*d]) + Sqrt[d]*(b*Sqrt[a + b*x]*(c + d*x) - (2*a^(3/2)*d*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/Sqrt[c]))/(d^(3/2)*Sqrt[c + d*x])","A",1
630,1,154,121,0.8936485,"\int \frac{(a+b x)^{3/2}}{x^2 \sqrt{c+d x}} \, dx","Integrate[(a + b*x)^(3/2)/(x^2*Sqrt[c + d*x]),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)}{c^{3/2}}-\frac{a \sqrt{a+b x} \sqrt{c+d x}}{c x}+\frac{2 (b c-a d)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{d} (c+d x)^{3/2}}","\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,"-((a*Sqrt[a + b*x]*Sqrt[c + d*x])/(c*x)) + (2*(b*c - a*d)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[d]*(c + d*x)^(3/2)) + (Sqrt[a]*(-3*b*c + a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/c^(3/2)","A",1
631,1,98,119,0.0687623,"\int \frac{(a+b x)^{3/2}}{x^3 \sqrt{c+d x}} \, dx","Integrate[(a + b*x)^(3/2)/(x^3*Sqrt[c + d*x]),x]","\frac{\sqrt{a+b x} \sqrt{c+d x} (-2 a c+3 a d x-5 b c x)}{4 c^2 x^2}-\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 (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*x]*Sqrt[c + d*x]*(-2*a*c - 5*b*c*x + 3*a*d*x))/(4*c^2*x^2) - (3*(b*c - a*d)^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*Sqrt[a]*c^(5/2))","A",1
632,1,144,180,0.1772184,"\int \frac{(a+b x)^{3/2}}{x^4 \sqrt{c+d x}} \, dx","Integrate[(a + b*x)^(3/2)/(x^4*Sqrt[c + d*x]),x]","\frac{\frac{x (5 a d+b c) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c-3 a d x+5 b c x)\right)}{\sqrt{a} c^{5/2}}-8 (a+b x)^{5/2} \sqrt{c+d x}}{24 a c x^3}","\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,"(-8*(a + b*x)^(5/2)*Sqrt[c + d*x] + ((b*c + 5*a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c + 5*b*c*x - 3*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(Sqrt[a]*c^(5/2)))/(24*a*c*x^3)","A",1
633,1,193,266,0.3130672,"\int \frac{(a+b x)^{3/2}}{x^5 \sqrt{c+d x}} \, dx","Integrate[(a + b*x)^(3/2)/(x^5*Sqrt[c + d*x]),x]","-\frac{\frac{x^2 \left(35 a^2 d^2+10 a b c d+3 b^2 c^2\right) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c-3 a d x+5 b c x)\right)}{\sqrt{a} c^{5/2}}+48 a c (a+b x)^{5/2} \sqrt{c+d x}-8 x (a+b x)^{5/2} \sqrt{c+d x} (7 a d+3 b c)}{192 a^2 c^2 x^4}","-\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,"-1/192*(48*a*c*(a + b*x)^(5/2)*Sqrt[c + d*x] - 8*(3*b*c + 7*a*d)*x*(a + b*x)^(5/2)*Sqrt[c + d*x] + ((3*b^2*c^2 + 10*a*b*c*d + 35*a^2*d^2)*x^2*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c + 5*b*c*x - 3*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(Sqrt[a]*c^(5/2)))/(a^2*c^2*x^4)","A",1
634,1,233,248,0.4880352,"\int \frac{x^2 (a+b x)^{3/2}}{(c+d x)^{3/2}} \, dx","Integrate[(x^2*(a + b*x)^(3/2))/(c + d*x)^(3/2),x]","\frac{\frac{b \sqrt{d} \left(3 a^3 d^2 (c+d x)+a^2 b d \left(-100 c^2-35 c d x+17 d^2 x^2\right)+a b^2 \left(105 c^3-65 c^2 d x-52 c d^2 x^2+22 d^3 x^3\right)+b^3 x \left(105 c^3+35 c^2 d x-14 c d^2 x^2+8 d^3 x^3\right)\right)}{\sqrt{a+b x}}-3 (b c-a d)^{3/2} \left(-a^2 d^2-10 a b c d+35 b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{24 b^2 d^{9/2} \sqrt{c+d x}}","\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,"((b*Sqrt[d]*(3*a^3*d^2*(c + d*x) + a^2*b*d*(-100*c^2 - 35*c*d*x + 17*d^2*x^2) + b^3*x*(105*c^3 + 35*c^2*d*x - 14*c*d^2*x^2 + 8*d^3*x^3) + a*b^2*(105*c^3 - 65*c^2*d*x - 52*c*d^2*x^2 + 22*d^3*x^3)))/Sqrt[a + b*x] - 3*(b*c - a*d)^(3/2)*(35*b^2*c^2 - 10*a*b*c*d - a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(24*b^2*d^(9/2)*Sqrt[c + d*x])","A",1
635,1,169,174,0.4164599,"\int \frac{x (a+b x)^{3/2}}{(c+d x)^{3/2}} \, dx","Integrate[(x*(a + b*x)^(3/2))/(c + d*x)^(3/2),x]","\frac{\frac{\sqrt{d} \left(a^2 d (13 c+5 d x)+a b \left(-15 c^2+8 c d x+7 d^2 x^2\right)+b^2 x \left(-15 c^2-5 c d x+2 d^2 x^2\right)\right)}{\sqrt{a+b x}}+\frac{3 (5 b c-a d) (b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b}}{4 d^{7/2} \sqrt{c+d x}}","\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,"((Sqrt[d]*(a^2*d*(13*c + 5*d*x) + b^2*x*(-15*c^2 - 5*c*d*x + 2*d^2*x^2) + a*b*(-15*c^2 + 8*c*d*x + 7*d^2*x^2)))/Sqrt[a + b*x] + (3*(b*c - a*d)^(3/2)*(5*b*c - a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/b)/(4*d^(7/2)*Sqrt[c + d*x])","A",1
636,1,73,98,0.0533409,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^(3/2)/(c + d*x)^(3/2),x]","\frac{2 (a+b x)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{5 b (c+d x)^{3/2}}","-\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,"(2*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(3/2)*Hypergeometric2F1[3/2, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(3/2))","C",1
637,1,162,119,0.8273352,"\int \frac{(a+b x)^{3/2}}{x (c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^(3/2)/(x*(c + d*x)^(3/2)),x]","\frac{2 \left(\frac{\sqrt{d} \left(\sqrt{c} \sqrt{a+b x} (a d-b c)-a^{3/2} d \sqrt{c+d x} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)}{c^{3/2}}+b \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)}{d^{3/2} \sqrt{c+d 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*(b*Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] + (Sqrt[d]*(Sqrt[c]*(-(b*c) + a*d)*Sqrt[a + b*x] - a^(3/2)*d*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/c^(3/2)))/(d^(3/2)*Sqrt[c + d*x])","A",1
638,1,91,108,0.0838148,"\int \frac{(a+b x)^{3/2}}{x^2 (c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^(3/2)/(x^2*(c + d*x)^(3/2)),x]","\frac{3 \sqrt{a} (a d-b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{c^{5/2}}+\frac{\sqrt{a+b x} (2 b c x-a (c+3 d x))}{c^2 x \sqrt{c+d x}}","-\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,"(Sqrt[a + b*x]*(2*b*c*x - a*(c + 3*d*x)))/(c^2*x*Sqrt[c + d*x]) + (3*Sqrt[a]*(-(b*c) + a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/c^(5/2)","A",1
639,1,130,175,0.0984738,"\int \frac{(a+b x)^{3/2}}{x^3 (c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^(3/2)/(x^3*(c + d*x)^(3/2)),x]","\frac{\sqrt{a+b x} \left(a \left(-2 c^2+5 c d x+15 d^2 x^2\right)-b c x (5 c+13 d x)\right)}{4 c^3 x^2 \sqrt{c+d x}}-\frac{3 \left(5 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} c^{7/2}}","-\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,"(Sqrt[a + b*x]*(-(b*c*x*(5*c + 13*d*x)) + a*(-2*c^2 + 5*c*d*x + 15*d^2*x^2)))/(4*c^3*x^2*Sqrt[c + d*x]) - (3*(b^2*c^2 - 6*a*b*c*d + 5*a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*Sqrt[a]*c^(7/2))","A",1
640,1,188,240,0.1532221,"\int \frac{(a+b x)^{3/2}}{x^4 (c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^(3/2)/(x^4*(c + d*x)^(3/2)),x]","\frac{\left(35 a^3 d^3-45 a^2 b c d^2+9 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} c^{9/2}}-\frac{\sqrt{a+b x} \left(a^2 \left(8 c^3-14 c^2 d x+35 c d^2 x^2+105 d^3 x^3\right)+2 a b c x \left(7 c^2-19 c d x-50 d^2 x^2\right)+3 b^2 c^2 x^2 (c+d x)\right)}{24 a c^4 x^3 \sqrt{c+d x}}","-\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,"-1/24*(Sqrt[a + b*x]*(3*b^2*c^2*x^2*(c + d*x) + 2*a*b*c*x*(7*c^2 - 19*c*d*x - 50*d^2*x^2) + a^2*(8*c^3 - 14*c^2*d*x + 35*c*d^2*x^2 + 105*d^3*x^3)))/(a*c^4*x^3*Sqrt[c + d*x]) + ((b^3*c^3 + 9*a*b^2*c^2*d - 45*a^2*b*c*d^2 + 35*a^3*d^3)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(8*a^(3/2)*c^(9/2))","A",1
641,1,220,267,0.7532908,"\int \frac{x^2 (a+b x)^{3/2}}{(c+d x)^{5/2}} \, dx","Integrate[(x^2*(a + b*x)^(3/2))/(c + d*x)^(5/2),x]","\frac{\frac{3 (c+d x)^2 \left(3 a^2 d^2-30 a b c d+35 b^2 c^2\right) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}}+\frac{\sqrt{d} \left(a^2 d \left(55 c^2+78 c d x+15 d^2 x^2\right)+a b \left(-105 c^3-85 c^2 d x+57 c d^2 x^2+21 d^3 x^3\right)+b^2 x \left(-105 c^3-140 c^2 d x-21 c d^2 x^2+6 d^3 x^3\right)\right)}{\sqrt{a+b x}}}{12 d^{9/2} (c+d x)^{3/2}}","\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,"((Sqrt[d]*(a^2*d*(55*c^2 + 78*c*d*x + 15*d^2*x^2) + b^2*x*(-105*c^3 - 140*c^2*d*x - 21*c*d^2*x^2 + 6*d^3*x^3) + a*b*(-105*c^3 - 85*c^2*d*x + 57*c*d^2*x^2 + 21*d^3*x^3)))/Sqrt[a + b*x] + (3*(35*b^2*c^2 - 30*a*b*c*d + 3*a^2*d^2)*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]))/(12*d^(9/2)*(c + d*x)^(3/2))","A",1
642,1,110,174,0.1389938,"\int \frac{x (a+b x)^{3/2}}{(c+d x)^{5/2}} \, dx","Integrate[(x*(a + b*x)^(3/2))/(c + d*x)^(5/2),x]","\frac{2 (a+b x)^{5/2} \left((c+d x) (5 b c-3 a d) \sqrt{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)+5 c (a d-b c)\right)}{15 d (c+d x)^{3/2} (b c-a d)^2}","-\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,"(2*(a + b*x)^(5/2)*(5*c*(-(b*c) + a*d) + (5*b*c - 3*a*d)*(c + d*x)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Hypergeometric2F1[3/2, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)]))/(15*d*(b*c - a*d)^2*(c + d*x)^(3/2))","C",1
643,1,111,92,0.538258,"\int \frac{(a+b x)^{3/2}}{(c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^(3/2)/(c + d*x)^(5/2),x]","\frac{6 (b c-a d)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)-2 \sqrt{d} \sqrt{a+b x} (a d+3 b c+4 b d x)}{3 d^{5/2} (c+d x)^{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^{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,"(-2*Sqrt[d]*Sqrt[a + b*x]*(3*b*c + a*d + 4*b*d*x) + 6*(b*c - a*d)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(3*d^(5/2)*(c + d*x)^(3/2))","A",1
644,1,82,92,0.0817366,"\int \frac{(a+b x)^{3/2}}{x (c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^(3/2)/(x*(c + d*x)^(5/2)),x]","\frac{2 \sqrt{a+b x} (4 a c+3 a d x+b c x)}{3 c^2 (c+d x)^{3/2}}-\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^{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,"(2*Sqrt[a + b*x]*(4*a*c + b*c*x + 3*a*d*x))/(3*c^2*(c + d*x)^(3/2)) - (2*a^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/c^(5/2)","A",1
645,1,128,149,0.1709349,"\int \frac{(a+b x)^{3/2}}{x^2 (c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^(3/2)/(x^2*(c + d*x)^(5/2)),x]","\frac{x (3 b c-5 a d) \left(\sqrt{c} \sqrt{a+b x} (4 a c+3 a d x+b c x)-3 a^{3/2} (c+d x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)-3 c^{5/2} (a+b x)^{5/2}}{3 a c^{7/2} x (c+d x)^{3/2}}","-\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,"(-3*c^(5/2)*(a + b*x)^(5/2) + (3*b*c - 5*a*d)*x*(Sqrt[c]*Sqrt[a + b*x]*(4*a*c + b*c*x + 3*a*d*x) - 3*a^(3/2)*(c + d*x)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(3*a*c^(7/2)*x*(c + d*x)^(3/2))","A",1
646,1,171,204,0.2174418,"\int \frac{(a+b x)^{3/2}}{x^3 (c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^(3/2)/(x^3*(c + d*x)^(5/2)),x]","-\frac{-x^2 \left(35 a^2 d^2-30 a b c d+3 b^2 c^2\right) \left(\sqrt{c} \sqrt{a+b x} (4 a c+3 a d x+b c x)-3 a^{3/2} (c+d x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)+3 c^{5/2} x (a+b x)^{5/2} (b c-7 a d)+6 a c^{7/2} (a+b x)^{5/2}}{12 a^2 c^{9/2} x^2 (c+d x)^{3/2}}","-\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,"-1/12*(6*a*c^(7/2)*(a + b*x)^(5/2) + 3*c^(5/2)*(b*c - 7*a*d)*x*(a + b*x)^(5/2) - (3*b^2*c^2 - 30*a*b*c*d + 35*a^2*d^2)*x^2*(Sqrt[c]*Sqrt[a + b*x]*(4*a*c + b*c*x + 3*a*d*x) - 3*a^(3/2)*(c + d*x)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^2*c^(9/2)*x^2*(c + d*x)^(3/2))","A",1
647,1,227,376,2.0342029,"\int x^2 (a+b x)^{5/2} \sqrt{c+d x} \, dx","Integrate[x^2*(a + b*x)^(5/2)*Sqrt[c + d*x],x]","\frac{(a+b x)^{7/2} (c+d x)^{3/2} \left(\frac{7 \left(5 a^2 d^2+14 a b c d+21 b^2 c^2\right) \left(-\frac{15 (b c-a d)^{7/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{d^{7/2} (a+b x)^{7/2} \sqrt{\frac{b (c+d x)}{b c-a d}}}+\frac{15 (b c-a d)^3}{d^3 (a+b x)^3}-\frac{10 (b c-a d)^2}{d^2 (a+b x)^2}+\frac{8 b c-8 a d}{a d+b d x}+48\right)}{128 b^2 d (c+d x)}-\frac{35 a}{b}-\frac{63 c}{d}+70 x\right)}{420 b d}","-\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,"((a + b*x)^(7/2)*(c + d*x)^(3/2)*((-35*a)/b - (63*c)/d + 70*x + (7*(21*b^2*c^2 + 14*a*b*c*d + 5*a^2*d^2)*(48 + (15*(b*c - a*d)^3)/(d^3*(a + b*x)^3) - (10*(b*c - a*d)^2)/(d^2*(a + b*x)^2) + (8*b*c - 8*a*d)/(a*d + b*d*x) - (15*(b*c - a*d)^(7/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(d^(7/2)*(a + b*x)^(7/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(128*b^2*d*(c + d*x))))/(420*b*d)","A",1
648,1,346,268,2.0738948,"\int x (a+b x)^{5/2} \sqrt{c+d x} \, dx","Integrate[x*(a + b*x)^(5/2)*Sqrt[c + d*x],x]","\frac{(a+b x)^{7/2} (c+d x)^{3/2} \left(7-\frac{7 (3 a d+7 b c) \left(48 b^4 d^4 (a+b x)^4 \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}+b (b c-a d) \left(8 b^3 d^3 (a+b x)^3 \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}-10 b^3 d^2 (a+b x)^2 (b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}}+15 b^3 d (a+b x) (b c-a d)^{5/2} \sqrt{\frac{b (c+d x)}{b c-a d}}-15 b^3 \sqrt{d} \sqrt{a+b x} (b c-a d)^3 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)\right)}{384 b^4 d^4 (a+b x)^4 (b c-a d)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2}}\right)}{35 b d}","\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,"((a + b*x)^(7/2)*(c + d*x)^(3/2)*(7 - (7*(7*b*c + 3*a*d)*(48*b^4*d^4*Sqrt[b*c - a*d]*(a + b*x)^4*Sqrt[(b*(c + d*x))/(b*c - a*d)] + b*(b*c - a*d)*(15*b^3*d*(b*c - a*d)^(5/2)*(a + b*x)*Sqrt[(b*(c + d*x))/(b*c - a*d)] - 10*b^3*d^2*(b*c - a*d)^(3/2)*(a + b*x)^2*Sqrt[(b*(c + d*x))/(b*c - a*d)] + 8*b^3*d^3*Sqrt[b*c - a*d]*(a + b*x)^3*Sqrt[(b*(c + d*x))/(b*c - a*d)] - 15*b^3*Sqrt[d]*(b*c - a*d)^3*Sqrt[a + b*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])))/(384*b^4*d^4*(b*c - a*d)^(3/2)*(a + b*x)^4*((b*(c + d*x))/(b*c - a*d))^(3/2))))/(35*b*d)","A",1
649,1,190,192,0.5973024,"\int (a+b x)^{5/2} \sqrt{c+d x} \, dx","Integrate[(a + b*x)^(5/2)*Sqrt[c + d*x],x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) \left(15 a^3 d^3+a^2 b d^2 (73 c+118 d x)+a b^2 d \left(-55 c^2+36 c d x+136 d^2 x^2\right)+b^3 \left(15 c^3-10 c^2 d x+8 c d^2 x^2+48 d^3 x^3\right)\right)-15 (b c-a d)^{9/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{192 b^2 d^{7/2} \sqrt{c+d x}}","-\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,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(15*a^3*d^3 + a^2*b*d^2*(73*c + 118*d*x) + a*b^2*d*(-55*c^2 + 36*c*d*x + 136*d^2*x^2) + b^3*(15*c^3 - 10*c^2*d*x + 8*c*d^2*x^2 + 48*d^3*x^3)) - 15*(b*c - a*d)^(9/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(192*b^2*d^(7/2)*Sqrt[c + d*x])","A",1
650,1,242,218,0.8201623,"\int \frac{(a+b x)^{5/2} \sqrt{c+d x}}{x} \, dx","Integrate[((a + b*x)^(5/2)*Sqrt[c + d*x])/x,x]","\frac{\sqrt{d} \left(\sqrt{a+b x} (c+d x) \left(33 a^2 d^2+2 a b d (7 c+13 d x)+b^2 \left(-3 c^2+2 c d x+8 d^2 x^2\right)\right)-48 a^{5/2} \sqrt{c} d^2 \sqrt{c+d x} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)+\frac{3 \sqrt{b c-a d} \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) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b}}{24 d^{5/2} \sqrt{c+d x}}","-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,"((3*Sqrt[b*c - a*d]*(b^3*c^3 - 5*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 5*a^3*d^3)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/b + Sqrt[d]*(Sqrt[a + b*x]*(c + d*x)*(33*a^2*d^2 + 2*a*b*d*(7*c + 13*d*x) + b^2*(-3*c^2 + 2*c*d*x + 8*d^2*x^2)) - 48*a^(5/2)*Sqrt[c]*d^2*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(24*d^(5/2)*Sqrt[c + d*x])","A",1
651,1,204,197,1.0065858,"\int \frac{(a+b x)^{5/2} \sqrt{c+d x}}{x^2} \, dx","Integrate[((a + b*x)^(5/2)*Sqrt[c + d*x])/x^2,x]","-\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 c-a d} \left(-15 a^2 d^2-10 a b c d+b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{4 d^{3/2} \sqrt{c+d x}}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-4 a^2 d+9 a b d x+b^2 x (c+2 d x)\right)}{4 d x}","-\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,"(Sqrt[a + b*x]*Sqrt[c + d*x]*(-4*a^2*d + 9*a*b*d*x + b^2*x*(c + 2*d*x)))/(4*d*x) - (Sqrt[b*c - a*d]*(b^2*c^2 - 10*a*b*c*d - 15*a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(4*d^(3/2)*Sqrt[c + d*x]) - (a^(3/2)*(5*b*c + a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/Sqrt[c]","A",1
652,1,206,212,1.8631913,"\int \frac{(a+b x)^{5/2} \sqrt{c+d x}}{x^3} \, dx","Integrate[((a + b*x)^(5/2)*Sqrt[c + d*x])/x^3,x]","\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{\sqrt{a+b x} \sqrt{c+d x} \left(a^2 (2 c+d x)+9 a b c x-4 b^2 c x^2\right)}{4 c x^2}+\frac{(b c-a d)^{3/2} (5 a d+b c) \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{d} (c+d x)^{3/2}}","-\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,"-1/4*(Sqrt[a + b*x]*Sqrt[c + d*x]*(9*a*b*c*x - 4*b^2*c*x^2 + a^2*(2*c + d*x)))/(c*x^2) + ((b*c - a*d)^(3/2)*(b*c + 5*a*d)*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[d]*(c + d*x)^(3/2)) + (Sqrt[a]*(-15*b^2*c^2 - 10*a*b*c*d + a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*c^(3/2))","A",1
653,1,235,228,2.1123367,"\int \frac{(a+b x)^{5/2} \sqrt{c+d x}}{x^4} \, dx","Integrate[((a + b*x)^(5/2)*Sqrt[c + d*x])/x^4,x]","-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(a^2 \left(8 c^2+2 c d x-3 d^2 x^2\right)+2 a b c x (13 c+7 d x)+33 b^2 c^2 x^2\right)}{24 c^2 x^3}-\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}}+\frac{2 \sqrt{d} (b c-a d)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{(c+d x)^{5/2}}","-\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,"-1/24*(Sqrt[a + b*x]*Sqrt[c + d*x]*(33*b^2*c^2*x^2 + 2*a*b*c*x*(13*c + 7*d*x) + a^2*(8*c^2 + 2*c*d*x - 3*d^2*x^2)))/(c^2*x^3) + (2*Sqrt[d]*(b*c - a*d)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(5/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(c + d*x)^(5/2) - ((5*b^3*c^3 + 15*a*b^2*c^2*d - 5*a^2*b*c*d^2 + a^3*d^3)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(8*Sqrt[a]*c^(5/2))","A",1
654,1,173,198,0.4159935,"\int \frac{(a+b x)^{5/2} \sqrt{c+d x}}{x^5} \, dx","Integrate[((a + b*x)^(5/2)*Sqrt[c + d*x])/x^5,x]","\frac{5 x (b c-a d) \left(\frac{3 x (b c-a d) \left(x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)-\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+a d x+b c x)\right)}{a^{3/2} c^{3/2}}-8 (a+b x)^{3/2} (c+d x)^{3/2}\right)-48 c (a+b x)^{5/2} (c+d x)^{3/2}}{192 c^2 x^4}","\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,"(-48*c*(a + b*x)^(5/2)*(c + d*x)^(3/2) + 5*(b*c - a*d)*x*(-8*(a + b*x)^(3/2)*(c + d*x)^(3/2) + (3*(b*c - a*d)*x*(-(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c + b*c*x + a*d*x)) + (b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(3/2)*c^(3/2))))/(192*c^2*x^4)","A",1
655,1,215,283,0.4465268,"\int \frac{(a+b x)^{5/2} \sqrt{c+d x}}{x^6} \, dx","Integrate[((a + b*x)^(5/2)*Sqrt[c + d*x])/x^6,x]","-\frac{\frac{(7 a d+3 b c) \left(5 x (b c-a d) \left(\frac{3 x (b c-a d) \left(x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)-\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+a d x+b c x)\right)}{a^{3/2} c^{3/2}}-8 (a+b x)^{3/2} (c+d x)^{3/2}\right)-48 c (a+b x)^{5/2} (c+d x)^{3/2}\right)}{384 c^2 x^4}+\frac{(a+b x)^{7/2} (c+d x)^{3/2}}{x^5}}{5 a c}","-\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,"-1/5*(((a + b*x)^(7/2)*(c + d*x)^(3/2))/x^5 + ((3*b*c + 7*a*d)*(-48*c*(a + b*x)^(5/2)*(c + d*x)^(3/2) + 5*(b*c - a*d)*x*(-8*(a + b*x)^(3/2)*(c + d*x)^(3/2) + (3*(b*c - a*d)*x*(-(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c + b*c*x + a*d*x)) + (b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(3/2)*c^(3/2)))))/(384*c^2*x^4))/(a*c)","A",1
656,1,376,437,3.2499094,"\int x^2 (a+b x)^{5/2} (c+d x)^{3/2} \, dx","Integrate[x^2*(a + b*x)^(5/2)*(c + d*x)^(3/2),x]","\frac{(a+b x)^{7/2} (c+d x)^{5/2} \left(\frac{49 \sqrt{b c-a d} \left(5 a^2 d^2+10 a b c d+9 b^2 c^2\right) \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \left(-10 d^{3/2} (a+b x)^2 (b c-a d)^{9/2} \sqrt{\frac{b (c+d x)}{b c-a d}}+8 d^{5/2} (a+b x)^3 (b c-a d)^{7/2} \sqrt{\frac{b (c+d x)}{b c-a d}}+16 d^{7/2} (a+b x)^4 (b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}} (-3 a d+11 b c+8 b d x)+15 \sqrt{d} (a+b x) (b c-a d)^{11/2} \sqrt{\frac{b (c+d x)}{b c-a d}}-15 \sqrt{a+b x} (b c-a d)^6 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)}{1280 b^5 d^{9/2} (a+b x)^4 (c+d x)^4}-\frac{49 a}{b}-\frac{63 c}{d}+84 x\right)}{588 b d}","-\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,"((a + b*x)^(7/2)*(c + d*x)^(5/2)*((-49*a)/b - (63*c)/d + 84*x + (49*Sqrt[b*c - a*d]*(9*b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*((b*(c + d*x))/(b*c - a*d))^(3/2)*(15*Sqrt[d]*(b*c - a*d)^(11/2)*(a + b*x)*Sqrt[(b*(c + d*x))/(b*c - a*d)] - 10*d^(3/2)*(b*c - a*d)^(9/2)*(a + b*x)^2*Sqrt[(b*(c + d*x))/(b*c - a*d)] + 8*d^(5/2)*(b*c - a*d)^(7/2)*(a + b*x)^3*Sqrt[(b*(c + d*x))/(b*c - a*d)] + 16*d^(7/2)*(b*c - a*d)^(3/2)*(a + b*x)^4*Sqrt[(b*(c + d*x))/(b*c - a*d)]*(11*b*c - 3*a*d + 8*b*d*x) - 15*(b*c - a*d)^6*Sqrt[a + b*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]]))/(1280*b^5*d^(9/2)*(a + b*x)^4*(c + d*x)^4)))/(588*b*d)","A",1
657,1,348,315,2.1458688,"\int x (a+b x)^{5/2} (c+d x)^{3/2} \, dx","Integrate[x*(a + b*x)^(5/2)*(c + d*x)^(3/2),x]","\frac{(a+b x)^{7/2} (c+d x)^{5/2} \left(7-\frac{7 \sqrt{b c-a d} (5 a d+7 b c) \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \left(-10 d^{3/2} (a+b x)^2 (b c-a d)^{9/2} \sqrt{\frac{b (c+d x)}{b c-a d}}+8 d^{5/2} (a+b x)^3 (b c-a d)^{7/2} \sqrt{\frac{b (c+d x)}{b c-a d}}+16 d^{7/2} (a+b x)^4 (b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}} (-3 a d+11 b c+8 b d x)+15 \sqrt{d} (a+b x) (b c-a d)^{11/2} \sqrt{\frac{b (c+d x)}{b c-a d}}-15 \sqrt{a+b x} (b c-a d)^6 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)}{1280 b^4 d^{7/2} (a+b x)^4 (c+d x)^4}\right)}{42 b d}","\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,"((a + b*x)^(7/2)*(c + d*x)^(5/2)*(7 - (7*Sqrt[b*c - a*d]*(7*b*c + 5*a*d)*((b*(c + d*x))/(b*c - a*d))^(3/2)*(15*Sqrt[d]*(b*c - a*d)^(11/2)*(a + b*x)*Sqrt[(b*(c + d*x))/(b*c - a*d)] - 10*d^(3/2)*(b*c - a*d)^(9/2)*(a + b*x)^2*Sqrt[(b*(c + d*x))/(b*c - a*d)] + 8*d^(5/2)*(b*c - a*d)^(7/2)*(a + b*x)^3*Sqrt[(b*(c + d*x))/(b*c - a*d)] + 16*d^(7/2)*(b*c - a*d)^(3/2)*(a + b*x)^4*Sqrt[(b*(c + d*x))/(b*c - a*d)]*(11*b*c - 3*a*d + 8*b*d*x) - 15*(b*c - a*d)^6*Sqrt[a + b*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]]))/(1280*b^4*d^(7/2)*(a + b*x)^4*(c + d*x)^4)))/(42*b*d)","A",1
658,1,187,227,1.7922662,"\int (a+b x)^{5/2} (c+d x)^{3/2} \, dx","Integrate[(a + b*x)^(5/2)*(c + d*x)^(3/2),x]","\frac{(a+b x)^{7/2} \sqrt{c+d x} \left(-\frac{15 (b c-a d)^{9/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{d^{7/2} (a+b x)^{7/2} \sqrt{\frac{b (c+d x)}{b c-a d}}}+\frac{15 (b c-a d)^4}{d^3 (a+b x)^3}+\frac{10 (a d-b c)^3}{d^2 (a+b x)^2}+\frac{8 (b c-a d)^2}{d (a+b x)}+48 (b c-a d)+128 b (c+d x)\right)}{640 b^2}","-\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,"((a + b*x)^(7/2)*Sqrt[c + d*x]*(48*(b*c - a*d) + (15*(b*c - a*d)^4)/(d^3*(a + b*x)^3) + (10*(-(b*c) + a*d)^3)/(d^2*(a + b*x)^2) + (8*(b*c - a*d)^2)/(d*(a + b*x)) + 128*b*(c + d*x) - (15*(b*c - a*d)^(9/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(d^(7/2)*(a + b*x)^(7/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(640*b^2)","A",1
659,1,300,299,1.0979704,"\int \frac{(a+b x)^{5/2} (c+d x)^{3/2}}{x} \, dx","Integrate[((a + b*x)^(5/2)*(c + d*x)^(3/2))/x,x]","\frac{\sqrt{d} \left(\sqrt{a+b x} (c+d x) \left(15 a^3 d^3+a^2 b d^2 (337 c+118 d x)+a b^2 d \left(57 c^2+244 c d x+136 d^2 x^2\right)+b^3 \left(-9 c^3+6 c^2 d x+72 c d^2 x^2+48 d^3 x^3\right)\right)-384 a^{5/2} b c^{3/2} d^2 \sqrt{c+d x} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)+\frac{3 \sqrt{b c-a d} \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) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b}}{192 b d^{5/2} \sqrt{c+d x}}","-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,"((3*Sqrt[b*c - a*d]*(3*b^4*c^4 - 20*a*b^3*c^3*d + 90*a^2*b^2*c^2*d^2 + 60*a^3*b*c*d^3 - 5*a^4*d^4)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/b + Sqrt[d]*(Sqrt[a + b*x]*(c + d*x)*(15*a^3*d^3 + a^2*b*d^2*(337*c + 118*d*x) + a*b^2*d*(57*c^2 + 244*c*d*x + 136*d^2*x^2) + b^3*(-9*c^3 + 6*c^2*d*x + 72*c*d^2*x^2 + 48*d^3*x^3)) - 384*a^(5/2)*b*c^(3/2)*d^2*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(192*b*d^(5/2)*Sqrt[c + d*x])","A",1
660,1,261,259,1.4117524,"\int \frac{(a+b x)^{5/2} (c+d x)^{3/2}}{x^2} \, dx","Integrate[((a + b*x)^(5/2)*(c + d*x)^(3/2))/x^2,x]","\frac{\frac{\sqrt{d} \left(\sqrt{a+b x} (c+d x) \left(3 a^2 d (11 d x-8 c)+2 a b d x (34 c+13 d x)+b^2 x \left(3 c^2+14 c d x+8 d^2 x^2\right)\right)-24 a^{3/2} \sqrt{c} d x \sqrt{c+d x} (3 a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)}{x}-\frac{3 \sqrt{b c-a d} \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) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b}}{24 d^{3/2} \sqrt{c+d x}}","-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,"((-3*Sqrt[b*c - a*d]*(b^3*c^3 - 15*a*b^2*c^2*d - 45*a^2*b*c*d^2 - 5*a^3*d^3)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/b + (Sqrt[d]*(Sqrt[a + b*x]*(c + d*x)*(3*a^2*d*(-8*c + 11*d*x) + 2*a*b*d*x*(34*c + 13*d*x) + b^2*x*(3*c^2 + 14*c*d*x + 8*d^2*x^2)) - 24*a^(3/2)*Sqrt[c]*d*(5*b*c + 3*a*d)*x*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/x)/(24*d^(3/2)*Sqrt[c + d*x])","A",1
661,1,233,275,2.090605,"\int \frac{(a+b x)^{5/2} (c+d x)^{3/2}}{x^3} \, dx","Integrate[((a + b*x)^(5/2)*(c + d*x)^(3/2))/x^3,x]","\frac{3 \sqrt{b c-a d} \left(5 a^2 d^2+10 a b c d+b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{4 \sqrt{d} \sqrt{c+d x}}-\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{\sqrt{a+b x} \sqrt{c+d x} \left(a^2 (2 c+5 d x)+9 a b x (c-d x)-b^2 x^2 (5 c+2 d x)\right)}{4 x^2}","\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,"-1/4*(Sqrt[a + b*x]*Sqrt[c + d*x]*(9*a*b*x*(c - d*x) - b^2*x^2*(5*c + 2*d*x) + a^2*(2*c + 5*d*x)))/x^2 + (3*Sqrt[b*c - a*d]*(b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(4*Sqrt[d]*Sqrt[c + d*x]) - (3*Sqrt[a]*(5*b^2*c^2 + 10*a*b*c*d + a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*Sqrt[c])","A",1
662,1,249,294,2.3417433,"\int \frac{(a+b x)^{5/2} (c+d x)^{3/2}}{x^4} \, dx","Integrate[((a + b*x)^(5/2)*(c + d*x)^(3/2))/x^4,x]","-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(a^2 \left(8 c^2+14 c d x+3 d^2 x^2\right)+2 a b c x (13 c+34 d x)+3 b^2 c x^2 (11 c-8 d x)\right)}{24 c x^3}+\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}}+\frac{\sqrt{d} (b c-a d)^{3/2} (5 a d+3 b c) \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{(c+d x)^{3/2}}","-\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,"-1/24*(Sqrt[a + b*x]*Sqrt[c + d*x]*(3*b^2*c*x^2*(11*c - 8*d*x) + 2*a*b*c*x*(13*c + 34*d*x) + a^2*(8*c^2 + 14*c*d*x + 3*d^2*x^2)))/(c*x^3) + (Sqrt[d]*(b*c - a*d)^(3/2)*(3*b*c + 5*a*d)*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(c + d*x)^(3/2) + ((-5*b^3*c^3 - 45*a*b^2*c^2*d - 15*a^2*b*c*d^2 + a^3*d^3)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(8*Sqrt[a]*c^(3/2))","A",1
663,1,295,313,3.3947608,"\int \frac{(a+b x)^{5/2} (c+d x)^{3/2}}{x^5} \, dx","Integrate[((a + b*x)^(5/2)*(c + d*x)^(3/2))/x^5,x]","-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(a^3 \left(48 c^3+72 c^2 d x+6 c d^2 x^2-9 d^3 x^3\right)+a^2 b c x \left(136 c^2+244 c d x+57 d^2 x^2\right)+a b^2 c^2 x^2 (118 c+337 d x)+15 b^3 c^3 x^3\right)}{192 a c^2 x^4}-\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}}+\frac{2 d^{3/2} (b c-a d)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{(c+d x)^{5/2}}","-\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,"-1/192*(Sqrt[a + b*x]*Sqrt[c + d*x]*(15*b^3*c^3*x^3 + a*b^2*c^2*x^2*(118*c + 337*d*x) + a^2*b*c*x*(136*c^2 + 244*c*d*x + 57*d^2*x^2) + a^3*(48*c^3 + 72*c^2*d*x + 6*c*d^2*x^2 - 9*d^3*x^3)))/(a*c^2*x^4) + (2*d^(3/2)*(b*c - a*d)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(5/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(c + d*x)^(5/2) - ((-5*b^4*c^4 + 60*a*b^3*c^3*d + 90*a^2*b^2*c^2*d^2 - 20*a^3*b*c*d^3 + 3*a^4*d^4)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(64*a^(3/2)*c^(5/2))","A",1
664,1,208,239,0.684281,"\int \frac{(a+b x)^{5/2} (c+d x)^{3/2}}{x^6} \, dx","Integrate[((a + b*x)^(5/2)*(c + d*x)^(3/2))/x^6,x]","-\frac{5 x (b c-a d) \left(x (b c-a d) \left(\frac{x (b c-a d) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)\right)}{a^{5/2} \sqrt{c}}+8 \sqrt{a+b x} (c+d x)^{5/2}\right)+16 c (a+b x)^{3/2} (c+d x)^{5/2}\right)+128 c^2 (a+b x)^{5/2} (c+d x)^{5/2}}{640 c^3 x^5}","-\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,"-1/640*(128*c^2*(a + b*x)^(5/2)*(c + d*x)^(5/2) + 5*(b*c - a*d)*x*(16*c*(a + b*x)^(3/2)*(c + d*x)^(5/2) + (b*c - a*d)*x*(8*Sqrt[a + b*x]*(c + d*x)^(5/2) + ((b*c - a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(5/2)*Sqrt[c]))))/(c^3*x^5)","A",1
665,1,377,348,3.1133208,"\int x (a+b x)^{5/2} (c+d x)^{5/2} \, dx","Integrate[x*(a + b*x)^(5/2)*(c + d*x)^(5/2),x]","\frac{(a+b x)^{7/2} (c+d x)^{7/2} \left(7-\frac{49 \sqrt{b c-a d} (a d+b c) \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \left(16 d^{7/2} (a+b x)^4 (b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(3 a^2 d^2-2 a b d (7 c+4 d x)+b^2 \left(27 c^2+40 c d x+16 d^2 x^2\right)\right)-10 d^{3/2} (a+b x)^2 (b c-a d)^{11/2} \sqrt{\frac{b (c+d x)}{b c-a d}}+8 d^{5/2} (a+b x)^3 (b c-a d)^{9/2} \sqrt{\frac{b (c+d x)}{b c-a d}}+15 \sqrt{d} (a+b x) (b c-a d)^{13/2} \sqrt{\frac{b (c+d x)}{b c-a d}}-15 \sqrt{a+b x} (b c-a d)^7 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)}{3072 b^5 d^{7/2} (a+b x)^4 (c+d x)^5}\right)}{49 b d}","\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,"((a + b*x)^(7/2)*(c + d*x)^(7/2)*(7 - (49*Sqrt[b*c - a*d]*(b*c + a*d)*((b*(c + d*x))/(b*c - a*d))^(3/2)*(15*Sqrt[d]*(b*c - a*d)^(13/2)*(a + b*x)*Sqrt[(b*(c + d*x))/(b*c - a*d)] - 10*d^(3/2)*(b*c - a*d)^(11/2)*(a + b*x)^2*Sqrt[(b*(c + d*x))/(b*c - a*d)] + 8*d^(5/2)*(b*c - a*d)^(9/2)*(a + b*x)^3*Sqrt[(b*(c + d*x))/(b*c - a*d)] + 16*d^(7/2)*(b*c - a*d)^(3/2)*(a + b*x)^4*Sqrt[(b*(c + d*x))/(b*c - a*d)]*(3*a^2*d^2 - 2*a*b*d*(7*c + 4*d*x) + b^2*(27*c^2 + 40*c*d*x + 16*d^2*x^2)) - 15*(b*c - a*d)^7*Sqrt[a + b*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]]))/(3072*b^5*d^(7/2)*(a + b*x)^4*(c + d*x)^5)))/(49*b*d)","A",1
666,1,209,262,1.9016685,"\int (a+b x)^{5/2} (c+d x)^{5/2} \, dx","Integrate[(a + b*x)^(5/2)*(c + d*x)^(5/2),x]","\frac{(a+b x)^{7/2} \sqrt{c+d x} \left(-\frac{15 (b c-a d)^{11/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{d^{7/2} (a+b x)^{7/2} \sqrt{\frac{b (c+d x)}{b c-a d}}}+\frac{15 (b c-a d)^5}{d^3 (a+b x)^3}-\frac{10 (b c-a d)^4}{d^2 (a+b x)^2}+\frac{8 (b c-a d)^3}{d (a+b x)}+128 b (c+d x) (b c-a d)+48 (b c-a d)^2+256 b^2 (c+d x)^2\right)}{1536 b^3}","-\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,"((a + b*x)^(7/2)*Sqrt[c + d*x]*(48*(b*c - a*d)^2 + (15*(b*c - a*d)^5)/(d^3*(a + b*x)^3) - (10*(b*c - a*d)^4)/(d^2*(a + b*x)^2) + (8*(b*c - a*d)^3)/(d*(a + b*x)) + 128*b*(b*c - a*d)*(c + d*x) + 256*b^2*(c + d*x)^2 - (15*(b*c - a*d)^(11/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(d^(7/2)*(a + b*x)^(7/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(1536*b^3)","A",1
667,1,1249,391,3.6186268,"\int \frac{(a+b x)^{5/2} (c+d x)^{5/2}}{x} \, dx","Integrate[((a + b*x)^(5/2)*(c + d*x)^(5/2))/x,x]","\frac{\sqrt{c+d x} \left(45 b^5 (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right) c^5-45 b^2 \sqrt{d} (b c-a d)^{5/2} \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c^4-375 a b^4 d (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right) c^4+360 a b d^{3/2} (b c-a d)^{5/2} \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c^3+30 b^2 d^{3/2} (b c-a d)^{5/2} x \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c^3+2250 a^2 b^3 d^2 (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right) c^3-3840 a^{5/2} b d^{5/2} (b c-a d)^{3/2} \sqrt{c+d x} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right) c^{5/2}+3754 a^2 d^{5/2} (b c-a d)^{5/2} \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c^2+744 b^2 d^{5/2} (b c-a d)^{5/2} x^2 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c^2+2578 a b d^{5/2} (b c-a d)^{5/2} x \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c^2+2250 a^3 b^2 d^3 (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right) c^2+1008 b^2 d^{7/2} (b c-a d)^{5/2} x^3 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c+\frac{360 a^3 d^{7/2} (b c-a d)^{5/2} \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c}{b}+2896 a b d^{7/2} (b c-a d)^{5/2} x^2 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c+2578 a^2 d^{7/2} (b c-a d)^{5/2} x \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c-375 a^4 b d^4 (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right) c+384 b^2 d^{9/2} (b c-a d)^{5/2} x^4 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}+1008 a b d^{9/2} (b c-a d)^{5/2} x^3 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}+744 a^2 d^{9/2} (b c-a d)^{5/2} x^2 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}+\frac{30 a^3 d^{9/2} (b c-a d)^{5/2} x \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}}{b}+45 a^5 d^5 (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)-45 a^4 d^{9/2} \sqrt{b c-a d} \sqrt{a+b x} (c+d x)^2 \sqrt{\frac{b (c+d x)}{b c-a d}}\right)}{1920 d^{5/2} (b c-a d)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}}","-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,"(Sqrt[c + d*x]*(-45*a^4*d^(9/2)*Sqrt[b*c - a*d]*Sqrt[a + b*x]*(c + d*x)^2*Sqrt[(b*(c + d*x))/(b*c - a*d)] - 45*b^2*c^4*Sqrt[d]*(b*c - a*d)^(5/2)*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 360*a*b*c^3*d^(3/2)*(b*c - a*d)^(5/2)*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 3754*a^2*c^2*d^(5/2)*(b*c - a*d)^(5/2)*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + (360*a^3*c*d^(7/2)*(b*c - a*d)^(5/2)*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2))/b + 30*b^2*c^3*d^(3/2)*(b*c - a*d)^(5/2)*x*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 2578*a*b*c^2*d^(5/2)*(b*c - a*d)^(5/2)*x*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 2578*a^2*c*d^(7/2)*(b*c - a*d)^(5/2)*x*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + (30*a^3*d^(9/2)*(b*c - a*d)^(5/2)*x*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2))/b + 744*b^2*c^2*d^(5/2)*(b*c - a*d)^(5/2)*x^2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 2896*a*b*c*d^(7/2)*(b*c - a*d)^(5/2)*x^2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 744*a^2*d^(9/2)*(b*c - a*d)^(5/2)*x^2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 1008*b^2*c*d^(7/2)*(b*c - a*d)^(5/2)*x^3*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 1008*a*b*d^(9/2)*(b*c - a*d)^(5/2)*x^3*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 384*b^2*d^(9/2)*(b*c - a*d)^(5/2)*x^4*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 45*b^5*c^5*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] - 375*a*b^4*c^4*d*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] + 2250*a^2*b^3*c^3*d^2*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] + 2250*a^3*b^2*c^2*d^3*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] - 375*a^4*b*c*d^4*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] + 45*a^5*d^5*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] - 3840*a^(5/2)*b*c^(5/2)*d^(5/2)*(b*c - a*d)^(3/2)*Sqrt[c + d*x]*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(1920*d^(5/2)*(b*c - a*d)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(5/2))","B",1
668,1,1077,334,4.8795185,"\int \frac{(a+b x)^{5/2} (c+d x)^{5/2}}{x^2} \, dx","Integrate[((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^2,x]","\frac{-15 b^4 x (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right) c^4+15 b \sqrt{d} (b c-a d)^{5/2} x \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c^3+300 a b^3 d x (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right) c^3-960 a^{3/2} b d^{3/2} (b c-a d)^{3/2} x \sqrt{c+d x} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right) c^{5/2}-\frac{192 a^2 d^{3/2} (b c-a d)^{5/2} \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c^2}{b}+118 b d^{3/2} (b c-a d)^{5/2} x^2 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c^2+601 a d^{3/2} (b c-a d)^{5/2} x \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c^2+1350 a^2 b^2 d^2 x (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right) c^2-960 a^{5/2} d^{5/2} (b c-a d)^{3/2} x \sqrt{c+d x} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right) c^{3/2}+136 b d^{5/2} (b c-a d)^{5/2} x^3 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c+452 a d^{5/2} (b c-a d)^{5/2} x^2 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c+\frac{601 a^2 d^{5/2} (b c-a d)^{5/2} x \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} c}{b}+300 a^3 b d^3 x (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right) c+48 b d^{7/2} (b c-a d)^{5/2} x^4 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}+136 a d^{7/2} (b c-a d)^{5/2} x^3 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}+\frac{118 a^2 d^{7/2} (b c-a d)^{5/2} x^2 \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}}{b}-15 a^4 d^4 x (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)+15 a^3 d^{7/2} \sqrt{b c-a d} x \sqrt{a+b x} (c+d x)^2 \sqrt{\frac{b (c+d x)}{b c-a d}}}{192 d^{3/2} (b c-a d)^{3/2} x \sqrt{c+d x} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2}}","-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,"(15*a^3*d^(7/2)*Sqrt[b*c - a*d]*x*Sqrt[a + b*x]*(c + d*x)^2*Sqrt[(b*(c + d*x))/(b*c - a*d)] - (192*a^2*c^2*d^(3/2)*(b*c - a*d)^(5/2)*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2))/b + 15*b*c^3*Sqrt[d]*(b*c - a*d)^(5/2)*x*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 601*a*c^2*d^(3/2)*(b*c - a*d)^(5/2)*x*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + (601*a^2*c*d^(5/2)*(b*c - a*d)^(5/2)*x*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2))/b + 118*b*c^2*d^(3/2)*(b*c - a*d)^(5/2)*x^2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 452*a*c*d^(5/2)*(b*c - a*d)^(5/2)*x^2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + (118*a^2*d^(7/2)*(b*c - a*d)^(5/2)*x^2*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2))/b + 136*b*c*d^(5/2)*(b*c - a*d)^(5/2)*x^3*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 136*a*d^(7/2)*(b*c - a*d)^(5/2)*x^3*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) + 48*b*d^(7/2)*(b*c - a*d)^(5/2)*x^4*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2) - 15*b^4*c^4*x*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] + 300*a*b^3*c^3*d*x*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] + 1350*a^2*b^2*c^2*d^2*x*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] + 300*a^3*b*c*d^3*x*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] - 15*a^4*d^4*x*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] - 960*a^(3/2)*b*c^(5/2)*d^(3/2)*(b*c - a*d)^(3/2)*x*Sqrt[c + d*x]*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])] - 960*a^(5/2)*c^(3/2)*d^(5/2)*(b*c - a*d)^(3/2)*x*Sqrt[c + d*x]*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(192*d^(3/2)*(b*c - a*d)^(3/2)*x*Sqrt[c + d*x]*((b*(c + d*x))/(b*c - a*d))^(3/2))","B",1
669,1,282,319,2.7872818,"\int \frac{(a+b x)^{5/2} (c+d x)^{5/2}}{x^3} \, dx","Integrate[((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^3,x]","\frac{\sqrt{a+b x} \sqrt{c+d x} \left(-3 a^2 \left(4 c^2+18 c d x-11 d^2 x^2\right)+2 a b x \left(-27 c^2+61 c d x+13 d^2 x^2\right)+b^2 x^2 \left(33 c^2+26 c d x+8 d^2 x^2\right)\right)}{24 x^2}-\frac{5}{4} \sqrt{a} \sqrt{c} \left(3 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)+\frac{5 \sqrt{c+d x} \left(a^3 d^3+15 a^2 b c d^2+15 a b^2 c^2 d+b^3 c^3\right) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{8 \sqrt{d} \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}}","\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,"(Sqrt[a + b*x]*Sqrt[c + d*x]*(-3*a^2*(4*c^2 + 18*c*d*x - 11*d^2*x^2) + b^2*x^2*(33*c^2 + 26*c*d*x + 8*d^2*x^2) + 2*a*b*x*(-27*c^2 + 61*c*d*x + 13*d^2*x^2)))/(24*x^2) + (5*(b^3*c^3 + 15*a*b^2*c^2*d + 15*a^2*b*c*d^2 + a^3*d^3)*Sqrt[c + d*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(8*Sqrt[d]*Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]) - (5*Sqrt[a]*Sqrt[c]*(3*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/4","A",1
670,1,282,339,3.2553774,"\int \frac{(a+b x)^{5/2} (c+d x)^{5/2}}{x^4} \, dx","Integrate[((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^4,x]","-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(a^2 \left(8 c^2+26 c d x+33 d^2 x^2\right)+2 a b x \left(13 c^2+61 c d x-27 d^2 x^2\right)-3 b^2 x^2 \left(-11 c^2+18 c d x+4 d^2 x^2\right)\right)}{24 x^3}+\frac{5 \sqrt{d} \sqrt{b c-a d} \left(3 a^2 d^2+10 a b c d+3 b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{4 \sqrt{c+d x}}-\frac{5 \left(a^3 d^3+15 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 \sqrt{a} \sqrt{c}}","-\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,"-1/24*(Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*b*x*(13*c^2 + 61*c*d*x - 27*d^2*x^2) - 3*b^2*x^2*(-11*c^2 + 18*c*d*x + 4*d^2*x^2) + a^2*(8*c^2 + 26*c*d*x + 33*d^2*x^2)))/x^3 + (5*Sqrt[d]*Sqrt[b*c - a*d]*(3*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(4*Sqrt[c + d*x]) - (5*(b^3*c^3 + 15*a*b^2*c^2*d + 15*a^2*b*c*d^2 + a^3*d^3)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(8*Sqrt[a]*Sqrt[c])","A",1
671,1,309,380,4.1893434,"\int \frac{(a+b x)^{5/2} (c+d x)^{5/2}}{x^5} \, dx","Integrate[((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^5,x]","-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(a^3 \left(48 c^3+136 c^2 d x+118 c d^2 x^2+15 d^3 x^3\right)+a^2 b c x \left(136 c^2+452 c d x+601 d^2 x^2\right)+a b^2 c x^2 \left(118 c^2+601 c d x-192 d^2 x^2\right)+15 b^3 c^3 x^3\right)}{192 a c x^4}+\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}}+\frac{5 d^{3/2} (b c-a d)^{3/2} (a d+b c) \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{(c+d x)^{3/2}}","-\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,"-1/192*(Sqrt[a + b*x]*Sqrt[c + d*x]*(15*b^3*c^3*x^3 + a*b^2*c*x^2*(118*c^2 + 601*c*d*x - 192*d^2*x^2) + a^2*b*c*x*(136*c^2 + 452*c*d*x + 601*d^2*x^2) + a^3*(48*c^3 + 136*c^2*d*x + 118*c*d^2*x^2 + 15*d^3*x^3)))/(a*c*x^4) + (5*d^(3/2)*(b*c - a*d)^(3/2)*(b*c + a*d)*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(c + d*x)^(3/2) + (5*(b^4*c^4 - 20*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 - 20*a^3*b*c*d^3 + a^4*d^4)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(64*a^(3/2)*c^(3/2))","A",1
672,1,365,406,4.4852441,"\int \frac{(a+b x)^{5/2} (c+d x)^{5/2}}{x^6} \, dx","Integrate[((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^6,x]","-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(3 a^4 \left(128 c^4+336 c^3 d x+248 c^2 d^2 x^2+10 c d^3 x^3-15 d^4 x^4\right)+2 a^3 b c x \left(504 c^3+1448 c^2 d x+1289 c d^2 x^2+180 d^3 x^3\right)+2 a^2 b^2 c^2 x^2 \left(372 c^2+1289 c d x+1877 d^2 x^2\right)+30 a b^3 c^3 x^3 (c+12 d x)-45 b^4 c^4 x^4\right)}{1920 a^2 c^2 x^5}-\frac{\left(3 a^5 d^5-25 a^4 b c d^4+150 a^3 b^2 c^2 d^3+150 a^2 b^3 c^3 d^2-25 a b^4 c^4 d+3 b^5 c^5\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}}+\frac{2 d^{5/2} (b c-a d)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{(c+d x)^{5/2}}","-\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,"-1/1920*(Sqrt[a + b*x]*Sqrt[c + d*x]*(-45*b^4*c^4*x^4 + 30*a*b^3*c^3*x^3*(c + 12*d*x) + 2*a^2*b^2*c^2*x^2*(372*c^2 + 1289*c*d*x + 1877*d^2*x^2) + 2*a^3*b*c*x*(504*c^3 + 1448*c^2*d*x + 1289*c*d^2*x^2 + 180*d^3*x^3) + 3*a^4*(128*c^4 + 336*c^3*d*x + 248*c^2*d^2*x^2 + 10*c*d^3*x^3 - 15*d^4*x^4)))/(a^2*c^2*x^5) + (2*d^(5/2)*(b*c - a*d)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(5/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(c + d*x)^(5/2) - ((3*b^5*c^5 - 25*a*b^4*c^4*d + 150*a^2*b^3*c^3*d^2 + 150*a^3*b^2*c^2*d^3 - 25*a^4*b*c*d^4 + 3*a^5*d^5)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(128*a^(5/2)*c^(5/2))","A",1
673,1,268,280,0.8324262,"\int \frac{(a+b x)^{5/2} (c+d x)^{5/2}}{x^7} \, dx","Integrate[((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^7,x]","-\frac{(b c-a d) \left(128 a^{7/2} c^{3/2} (a+b x)^{3/2} (c+d x)^{7/2}+x (b c-a d) \left(x (b c-a d) \left(8 a^{5/2} \sqrt{c} \sqrt{a+b x} (c+d x)^{5/2}-5 x (b c-a d) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)\right)\right)+48 a^{7/2} \sqrt{c} \sqrt{a+b x} (c+d x)^{7/2}\right)\right)}{1536 a^{7/2} c^{7/2} x^5}-\frac{(a+b x)^{5/2} (c+d x)^{7/2}}{6 c x^6}","\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,"-1/6*((a + b*x)^(5/2)*(c + d*x)^(7/2))/(c*x^6) - ((b*c - a*d)*(128*a^(7/2)*c^(3/2)*(a + b*x)^(3/2)*(c + d*x)^(7/2) + (b*c - a*d)*x*(48*a^(7/2)*Sqrt[c]*Sqrt[a + b*x]*(c + d*x)^(7/2) + (b*c - a*d)*x*(8*a^(5/2)*Sqrt[c]*Sqrt[a + b*x]*(c + d*x)^(5/2) - 5*(b*c - a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])))))/(1536*a^(7/2)*c^(7/2)*x^5)","A",1
674,1,249,314,1.1036578,"\int \frac{x^2 (a+b x)^{5/2}}{\sqrt{c+d x}} \, dx","Integrate[(x^2*(a + b*x)^(5/2))/Sqrt[c + d*x],x]","\frac{\sqrt{c+d x} \left(\frac{5 (b c-a d)^3 \left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right) \left(\frac{16 d^3 (a+b x)^3}{15 (b c-a d)^3}-\frac{4 d^2 (a+b x)^2}{3 (b c-a d)^2}+\frac{2 d (a+b x)}{b c-a d}-\frac{2 \sqrt{d} \sqrt{a+b x} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{4 b d^5}-\frac{24 (a+b x)^4 (a d+3 b c)}{b d}+64 x (a+b x)^4\right)}{320 b d \sqrt{a+b x}}","\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,"(Sqrt[c + d*x]*((-24*(3*b*c + a*d)*(a + b*x)^4)/(b*d) + 64*x*(a + b*x)^4 + (5*(b*c - a*d)^3*(63*b^2*c^2 + 14*a*b*c*d + 3*a^2*d^2)*((2*d*(a + b*x))/(b*c - a*d) - (4*d^2*(a + b*x)^2)/(3*(b*c - a*d)^2) + (16*d^3*(a + b*x)^3)/(15*(b*c - a*d)^3) - (2*Sqrt[d]*Sqrt[a + b*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(4*b*d^5)))/(320*b*d*Sqrt[a + b*x])","A",1
675,1,198,217,0.579146,"\int \frac{x (a+b x)^{5/2}}{\sqrt{c+d x}} \, dx","Integrate[(x*(a + b*x)^(5/2))/Sqrt[c + d*x],x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) \left(15 a^3 d^3+a^2 b d^2 (118 d x-191 c)+a b^2 d \left(265 c^2-172 c d x+136 d^2 x^2\right)+b^3 \left(-105 c^3+70 c^2 d x-56 c d^2 x^2+48 d^3 x^3\right)\right)+15 (a d+7 b c) (b c-a d)^{7/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{192 b^2 d^{9/2} \sqrt{c+d x}}","\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,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(15*a^3*d^3 + a^2*b*d^2*(-191*c + 118*d*x) + a*b^2*d*(265*c^2 - 172*c*d*x + 136*d^2*x^2) + b^3*(-105*c^3 + 70*c^2*d*x - 56*c*d^2*x^2 + 48*d^3*x^3)) + 15*(b*c - a*d)^(7/2)*(7*b*c + a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(192*b^2*d^(9/2)*Sqrt[c + d*x])","A",1
676,1,150,148,0.521999,"\int \frac{(a+b x)^{5/2}}{\sqrt{c+d x}} \, dx","Integrate[(a + b*x)^(5/2)/Sqrt[c + d*x],x]","\frac{\sqrt{d} \sqrt{a+b x} (c+d x) \left(33 a^2 d^2+2 a b d (13 d x-20 c)+b^2 \left(15 c^2-10 c d x+8 d^2 x^2\right)\right)-\frac{15 (b c-a d)^{7/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b}}{24 d^{7/2} \sqrt{c+d x}}","-\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,"(Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(33*a^2*d^2 + 2*a*b*d*(-20*c + 13*d*x) + b^2*(15*c^2 - 10*c*d*x + 8*d^2*x^2)) - (15*(b*c - a*d)^(7/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/b)/(24*d^(7/2)*Sqrt[c + d*x])","A",1
677,1,197,171,0.6289233,"\int \frac{(a+b x)^{5/2}}{x \sqrt{c+d x}} \, dx","Integrate[(a + b*x)^(5/2)/(x*Sqrt[c + d*x]),x]","\frac{1}{4} \left(-\frac{8 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{c}}+\frac{\left(-15 a^3 d^3+25 a^2 b c d^2-13 a b^2 c^2 d+3 b^3 c^3\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{d^{5/2} \sqrt{c+d x} \sqrt{b c-a d}}+\frac{b \sqrt{a+b x} \sqrt{c+d x} (9 a d-3 b c+2 b d x)}{d^2}\right)","-\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,"((b*Sqrt[a + b*x]*Sqrt[c + d*x]*(-3*b*c + 9*a*d + 2*b*d*x))/d^2 + ((3*b^3*c^3 - 13*a*b^2*c^2*d + 25*a^2*b*c*d^2 - 15*a^3*d^3)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(d^(5/2)*Sqrt[b*c - a*d]*Sqrt[c + d*x]) - (8*a^(5/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/Sqrt[c])/4","A",1
678,1,176,162,0.8706329,"\int \frac{(a+b x)^{5/2}}{x^2 \sqrt{c+d x}} \, dx","Integrate[(a + b*x)^(5/2)/(x^2*Sqrt[c + d*x]),x]","\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)}{c^{3/2}}+\frac{\sqrt{a+b x} \sqrt{c+d x} \left(b^2 c x-a^2 d\right)}{c d x}-\frac{(b c-5 a d) (b c-a d)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{d^{3/2} (c+d x)^{3/2}}","-\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,"(Sqrt[a + b*x]*(-(a^2*d) + b^2*c*x)*Sqrt[c + d*x])/(c*d*x) - ((b*c - 5*a*d)*(b*c - a*d)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(d^(3/2)*(c + d*x)^(3/2)) + (a^(3/2)*(-5*b*c + a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/c^(3/2)","A",1
679,1,189,177,1.1685401,"\int \frac{(a+b x)^{5/2}}{x^3 \sqrt{c+d x}} \, dx","Integrate[(a + b*x)^(5/2)/(x^3*Sqrt[c + d*x]),x]","-\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{a \sqrt{a+b x} \sqrt{c+d x} (-2 a c+3 a d x-9 b c x)}{4 c^2 x^2}+\frac{2 (b c-a d)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{d} (c+d x)^{5/2}}","-\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,"(a*Sqrt[a + b*x]*Sqrt[c + d*x]*(-2*a*c - 9*b*c*x + 3*a*d*x))/(4*c^2*x^2) + (2*(b*c - a*d)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(5/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[d]*(c + d*x)^(5/2)) - (Sqrt[a]*(15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*c^(5/2))","A",1
680,1,142,157,0.2243436,"\int \frac{(a+b x)^{5/2}}{x^4 \sqrt{c+d x}} \, dx","Integrate[(a + b*x)^(5/2)/(x^4*Sqrt[c + d*x]),x]","-\frac{\frac{5 x (b c-a d) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c-3 a d x+5 b c x)\right)}{\sqrt{a} c^{5/2}}+8 (a+b x)^{5/2} \sqrt{c+d x}}{24 c x^3}","-\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,"-1/24*(8*(a + b*x)^(5/2)*Sqrt[c + d*x] + (5*(b*c - a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c + 5*b*c*x - 3*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(Sqrt[a]*c^(5/2)))/(c*x^3)","A",1
681,1,179,229,0.2107419,"\int \frac{(a+b x)^{5/2}}{x^5 \sqrt{c+d x}} \, dx","Integrate[(a + b*x)^(5/2)/(x^5*Sqrt[c + d*x]),x]","\frac{\frac{x (7 a d+b c) \left(\frac{5 x (b c-a d) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c-3 a d x+5 b c x)\right)}{\sqrt{a} c^{5/2}}+8 (a+b x)^{5/2} \sqrt{c+d x}\right)}{c}-48 (a+b x)^{7/2} \sqrt{c+d x}}{192 a c x^4}","\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,"(-48*(a + b*x)^(7/2)*Sqrt[c + d*x] + ((b*c + 7*a*d)*x*(8*(a + b*x)^(5/2)*Sqrt[c + d*x] + (5*(b*c - a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c + 5*b*c*x - 3*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(Sqrt[a]*c^(5/2))))/c)/(192*a*c*x^4)","A",1
682,1,296,309,0.6580744,"\int \frac{x^2 (a+b x)^{5/2}}{(c+d x)^{3/2}} \, dx","Integrate[(x^2*(a + b*x)^(5/2))/(c + d*x)^(3/2),x]","\frac{15 \left(-a^2 d^2-14 a b c d+63 b^2 c^2\right) (b c-a d)^{5/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)+\frac{b \sqrt{d} \left(15 a^4 d^3 (c+d x)+a^3 b d^2 \left(-839 c^2-322 c d x+133 d^2 x^2\right)+a^2 b^2 d \left(1785 c^3-202 c^2 d x-581 c d^2 x^2+254 d^3 x^3\right)+a b^3 \left(-945 c^4+1470 c^3 d x+763 c^2 d^2 x^2-316 c d^3 x^3+184 d^4 x^4\right)+3 b^4 x \left(-315 c^4-105 c^3 d x+42 c^2 d^2 x^2-24 c d^3 x^3+16 d^4 x^4\right)\right)}{\sqrt{a+b x}}}{192 b^2 d^{11/2} \sqrt{c+d x}}","-\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,"((b*Sqrt[d]*(15*a^4*d^3*(c + d*x) + a^3*b*d^2*(-839*c^2 - 322*c*d*x + 133*d^2*x^2) + a^2*b^2*d*(1785*c^3 - 202*c^2*d*x - 581*c*d^2*x^2 + 254*d^3*x^3) + 3*b^4*x*(-315*c^4 - 105*c^3*d*x + 42*c^2*d^2*x^2 - 24*c*d^3*x^3 + 16*d^4*x^4) + a*b^3*(-945*c^4 + 1470*c^3*d*x + 763*c^2*d^2*x^2 - 316*c*d^3*x^3 + 184*d^4*x^4)))/Sqrt[a + b*x] + 15*(b*c - a*d)^(5/2)*(63*b^2*c^2 - 14*a*b*c*d - a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(192*b^2*d^(11/2)*Sqrt[c + d*x])","A",1
683,1,221,218,0.5888636,"\int \frac{x (a+b x)^{5/2}}{(c+d x)^{3/2}} \, dx","Integrate[(x*(a + b*x)^(5/2))/(c + d*x)^(3/2),x]","\frac{\frac{\sqrt{d} \left(3 a^3 d^2 (27 c+11 d x)+a^2 b d \left(-190 c^2+13 c d x+59 d^2 x^2\right)+a b^2 \left(105 c^3-155 c^2 d x-82 c d^2 x^2+34 d^3 x^3\right)+b^3 x \left(105 c^3+35 c^2 d x-14 c d^2 x^2+8 d^3 x^3\right)\right)}{\sqrt{a+b x}}-\frac{15 (b c-a d)^{5/2} (7 b c-a d) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b}}{24 d^{9/2} \sqrt{c+d x}}","-\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,"((Sqrt[d]*(3*a^3*d^2*(27*c + 11*d*x) + a^2*b*d*(-190*c^2 + 13*c*d*x + 59*d^2*x^2) + b^3*x*(105*c^3 + 35*c^2*d*x - 14*c*d^2*x^2 + 8*d^3*x^3) + a*b^2*(105*c^3 - 155*c^2*d*x - 82*c*d^2*x^2 + 34*d^3*x^3)))/Sqrt[a + b*x] - (15*(b*c - a*d)^(5/2)*(7*b*c - a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/b)/(24*d^(9/2)*Sqrt[c + d*x])","A",1
684,1,73,138,0.0601898,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^(5/2)/(c + d*x)^(3/2),x]","\frac{2 (a+b x)^{7/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};\frac{d (a+b x)}{a d-b c}\right)}{7 b (c+d x)^{3/2}}","\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,"(2*(a + b*x)^(7/2)*((b*(c + d*x))/(b*c - a*d))^(3/2)*Hypergeometric2F1[3/2, 7/2, 9/2, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(3/2))","C",1
685,1,226,163,1.6561368,"\int \frac{(a+b x)^{5/2}}{x (c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^(5/2)/(x*(c + d*x)^(3/2)),x]","\frac{2 \left(5 a \left(-\frac{a^{3/2} \sqrt{c+d x} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{c^{3/2}}+\frac{b \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{d^{3/2}}+\frac{\sqrt{a+b x} (a d-b c)}{c d}\right)+\frac{(a+b x)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{c+d x}\right)}{5 \sqrt{c+d x}}","-\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,"(2*(5*a*(((-(b*c) + a*d)*Sqrt[a + b*x])/(c*d) + (b*Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/d^(3/2) - (a^(3/2)*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/c^(3/2)) + ((a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(3/2)*Hypergeometric2F1[3/2, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(c + d*x)))/(5*Sqrt[c + d*x])","C",1
686,1,333,164,4.9215718,"\int \frac{(a+b x)^{5/2}}{x^2 (c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^(5/2)/(x^2*(c + d*x)^(3/2)),x]","\frac{10 a^{5/2} \sqrt{c+d x} (3 a d-5 b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\frac{5 b c^{3/2} \sqrt{b c-a d} \left(9 a^2 d^2-8 a b c d+3 b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{d^{5/2}}-\frac{5 \sqrt{c} \sqrt{a+b x} \left(2 a^3 d^2 (c+3 d x)-2 a^2 b c d^2 x-a b^2 c d x (7 c+3 d x)+b^3 c^2 x (3 c+d x)\right)}{d^2 x}+\frac{2 c^{3/2} (a+b x)^{5/2} (b c-3 a d) \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};\frac{d (a+b x)}{a d-b c}\right)}{c+d x}}{10 a c^{5/2} \sqrt{c+d x}}","-\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,"((-5*Sqrt[c]*Sqrt[a + b*x]*(-2*a^2*b*c*d^2*x + b^3*c^2*x*(3*c + d*x) + 2*a^3*d^2*(c + 3*d*x) - a*b^2*c*d*x*(7*c + 3*d*x)))/(d^2*x) + (5*b*c^(3/2)*Sqrt[b*c - a*d]*(3*b^2*c^2 - 8*a*b*c*d + 9*a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/d^(5/2) + 10*a^(5/2)*(-5*b*c + 3*a*d)*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])] + (2*c^(3/2)*(b*c - 3*a*d)*(a + b*x)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(3/2)*Hypergeometric2F1[3/2, 5/2, 7/2, (d*(a + b*x))/(-(b*c) + a*d)])/(c + d*x))/(10*a*c^(5/2)*Sqrt[c + d*x])","C",1
687,1,132,154,0.1070853,"\int \frac{(a+b x)^{5/2}}{x^3 (c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^(5/2)/(x^3*(c + d*x)^(3/2)),x]","\frac{\sqrt{a+b x} \left(a^2 \left(-2 c^2+5 c d x+15 d^2 x^2\right)-a b c x (9 c+25 d x)+8 b^2 c^2 x^2\right)}{4 c^3 x^2 \sqrt{c+d x}}-\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 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,"(Sqrt[a + b*x]*(8*b^2*c^2*x^2 - a*b*c*x*(9*c + 25*d*x) + a^2*(-2*c^2 + 5*c*d*x + 15*d^2*x^2)))/(4*c^3*x^2*Sqrt[c + d*x]) - (15*Sqrt[a]*(b*c - a*d)^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*c^(7/2))","A",1
688,1,167,226,0.2960858,"\int \frac{(a+b x)^{5/2}}{x^4 (c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^(5/2)/(x^4*(c + d*x)^(3/2)),x]","\frac{-\frac{1}{2} x (b c-7 a d) \left(2 c^{5/2} (a+b x)^{5/2}+5 x (b c-a d) \left(\sqrt{c} \sqrt{a+b x} (a (c+3 d x)-2 b c x)+3 \sqrt{a} x \sqrt{c+d x} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)\right)-4 c^{7/2} (a+b x)^{7/2}}{12 a c^{9/2} x^3 \sqrt{c+d x}}","-\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,"(-4*c^(7/2)*(a + b*x)^(7/2) - ((b*c - 7*a*d)*x*(2*c^(5/2)*(a + b*x)^(5/2) + 5*(b*c - a*d)*x*(Sqrt[c]*Sqrt[a + b*x]*(-2*b*c*x + a*(c + 3*d*x)) + 3*Sqrt[a]*(b*c - a*d)*x*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])))/2)/(12*a*c^(9/2)*x^3*Sqrt[c + d*x])","A",1
689,1,206,317,0.2956919,"\int \frac{(a+b x)^{5/2}}{x^5 (c+d x)^{3/2}} \, dx","Integrate[(a + b*x)^(5/2)/(x^5*(c + d*x)^(3/2)),x]","\frac{x^2 \left(-63 a^2 d^2+14 a b c d+b^2 c^2\right) \left(2 c^{5/2} (a+b x)^{5/2}+5 x (b c-a d) \left(\sqrt{c} \sqrt{a+b x} (a (c+3 d x)-2 b c x)+3 \sqrt{a} x \sqrt{c+d x} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)\right)+8 c^{7/2} x (a+b x)^{7/2} (9 a d+b c)-48 a c^{9/2} (a+b x)^{7/2}}{192 a^2 c^{11/2} x^4 \sqrt{c+d x}}","-\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,"(-48*a*c^(9/2)*(a + b*x)^(7/2) + 8*c^(7/2)*(b*c + 9*a*d)*x*(a + b*x)^(7/2) + (b^2*c^2 + 14*a*b*c*d - 63*a^2*d^2)*x^2*(2*c^(5/2)*(a + b*x)^(5/2) + 5*(b*c - a*d)*x*(Sqrt[c]*Sqrt[a + b*x]*(-2*b*c*x + a*(c + 3*d*x)) + 3*Sqrt[a]*(b*c - a*d)*x*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])))/(192*a^2*c^(11/2)*x^4*Sqrt[c + d*x])","A",1
690,1,331,377,2.5942852,"\int \frac{x^3 (a+b x)^{5/2}}{(c+d x)^{5/2}} \, dx","Integrate[(x^3*(a + b*x)^(5/2))/(c + d*x)^(5/2),x]","\frac{\frac{16 c (a+b x)^4 \left(3 a^2 d^2 (c+2 d x)-14 a b c d (5 c+6 d x)+11 b^2 c^2 (9 c+10 d x)\right)}{d^2 (b c-a d)^2}-\frac{(c+d x)^2 \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) \left(\sqrt{d} (a+b x) \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(33 a^2 d^2+2 a b d (13 d x-20 c)+b^2 \left(15 c^2-10 c d x+8 d^2 x^2\right)\right)-15 \sqrt{a+b x} (b c-a d)^3 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)}{d^{11/2} (b c-a d)^{5/2} \sqrt{\frac{b (c+d x)}{b c-a d}}}+48 x^2 (a+b x)^4}{192 b d \sqrt{a+b x} (c+d x)^{3/2}}","-\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,"(48*x^2*(a + b*x)^4 + (16*c*(a + b*x)^4*(3*a^2*d^2*(c + 2*d*x) - 14*a*b*c*d*(5*c + 6*d*x) + 11*b^2*c^2*(9*c + 10*d*x)))/(d^2*(b*c - a*d)^2) - ((231*b^3*c^3 - 189*a*b^2*c^2*d + 21*a^2*b*c*d^2 + a^3*d^3)*(c + d*x)^2*(Sqrt[d]*Sqrt[b*c - a*d]*(a + b*x)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*(33*a^2*d^2 + 2*a*b*d*(-20*c + 13*d*x) + b^2*(15*c^2 - 10*c*d*x + 8*d^2*x^2)) - 15*(b*c - a*d)^3*Sqrt[a + b*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]]))/(d^(11/2)*(b*c - a*d)^(5/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]))/(192*b*d*Sqrt[a + b*x]*(c + d*x)^(3/2))","A",1
691,1,282,319,1.4652824,"\int \frac{x^2 (a+b x)^{5/2}}{(c+d x)^{5/2}} \, dx","Integrate[(x^2*(a + b*x)^(5/2))/(c + d*x)^(5/2),x]","\frac{\frac{15 (c+d x)^2 (b c-a d)^3 \left(a^2 d^2-14 a b c d+21 b^2 c^2\right) \left(\frac{16 d^3 (a+b x)^3}{15 (b c-a d)^3}-\frac{4 d^2 (a+b x)^2}{3 (b c-a d)^2}+\frac{2 d (a+b x)}{b c-a d}-\frac{2 \sqrt{d} \sqrt{a+b x} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{4 d^4 (a d-b c)}-8 c^2 (a+b x)^4+\frac{16 c (a+b x)^4 (c+d x) (5 b c-3 a d)}{b c-a d}}{12 d^2 \sqrt{a+b x} (c+d x)^{3/2} (a d-b c)}","-\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,"(-8*c^2*(a + b*x)^4 + (16*c*(5*b*c - 3*a*d)*(a + b*x)^4*(c + d*x))/(b*c - a*d) + (15*(b*c - a*d)^3*(21*b^2*c^2 - 14*a*b*c*d + a^2*d^2)*(c + d*x)^2*((2*d*(a + b*x))/(b*c - a*d) - (4*d^2*(a + b*x)^2)/(3*(b*c - a*d)^2) + (16*d^3*(a + b*x)^3)/(15*(b*c - a*d)^3) - (2*Sqrt[d]*Sqrt[a + b*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(4*d^4*(-(b*c) + a*d)))/(12*d^2*(-(b*c) + a*d)*Sqrt[a + b*x]*(c + d*x)^(3/2))","A",1
692,1,110,222,0.1557029,"\int \frac{x (a+b x)^{5/2}}{(c+d x)^{5/2}} \, dx","Integrate[(x*(a + b*x)^(5/2))/(c + d*x)^(5/2),x]","\frac{2 (a+b x)^{7/2} \left((c+d x) (7 b c-3 a d) \sqrt{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};\frac{d (a+b x)}{a d-b c}\right)+7 c (a d-b c)\right)}{21 d (c+d x)^{3/2} (b c-a d)^2}","\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,"(2*(a + b*x)^(7/2)*(7*c*(-(b*c) + a*d) + (7*b*c - 3*a*d)*(c + d*x)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Hypergeometric2F1[3/2, 7/2, 9/2, (d*(a + b*x))/(-(b*c) + a*d)]))/(21*d*(b*c - a*d)^2*(c + d*x)^(3/2))","C",1
693,1,73,128,0.078403,"\int \frac{(a+b x)^{5/2}}{(c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^(5/2)/(c + d*x)^(5/2),x]","\frac{2 (a+b x)^{7/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} \, _2F_1\left(\frac{5}{2},\frac{7}{2};\frac{9}{2};\frac{d (a+b x)}{a d-b c}\right)}{7 b (c+d x)^{5/2}}","-\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,"(2*(a + b*x)^(7/2)*((b*(c + d*x))/(b*c - a*d))^(5/2)*Hypergeometric2F1[5/2, 7/2, 9/2, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(5/2))","C",1
694,1,206,157,1.0427335,"\int \frac{(a+b x)^{5/2}}{x (c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^(5/2)/(x*(c + d*x)^(5/2)),x]","-\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 (b c-a d) \left(a^2 d (4 c+3 d x)+a b \left(3 c^2+8 c d x+3 d^2 x^2\right)+b^2 c x (3 c+4 d x)\right)}{3 c^2 d^2 \sqrt{a+b x} (c+d x)^{3/2}}+\frac{2 (b c-a d)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{d^{5/2} (c+d x)^{5/2}}","-\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,"(-2*(b*c - a*d)*(a^2*d*(4*c + 3*d*x) + b^2*c*x*(3*c + 4*d*x) + a*b*(3*c^2 + 8*c*d*x + 3*d^2*x^2)))/(3*c^2*d^2*Sqrt[a + b*x]*(c + d*x)^(3/2)) + (2*(b*c - a*d)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(5/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(d^(5/2)*(c + d*x)^(5/2)) - (2*a^(5/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/c^(5/2)","A",1
695,1,125,142,0.1810844,"\int \frac{(a+b x)^{5/2}}{x^2 (c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^(5/2)/(x^2*(c + d*x)^(5/2)),x]","\frac{5 x (b c-a d) \left(\sqrt{c} \sqrt{a+b x} (4 a c+3 a d x+b c x)-3 a^{3/2} (c+d x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)-3 c^{5/2} (a+b x)^{5/2}}{3 c^{7/2} x (c+d x)^{3/2}}","-\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,"(-3*c^(5/2)*(a + b*x)^(5/2) + 5*(b*c - a*d)*x*(Sqrt[c]*Sqrt[a + b*x]*(4*a*c + b*c*x + 3*a*d*x) - 3*a^(3/2)*(c + d*x)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(3*c^(7/2)*x*(c + d*x)^(3/2))","A",1
696,1,159,220,0.2741661,"\int \frac{(a+b x)^{5/2}}{x^3 (c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^(5/2)/(x^3*(c + d*x)^(5/2)),x]","\frac{-\frac{1}{2} x (3 b c-7 a d) \left(3 c^{5/2} (a+b x)^{5/2}-5 x (b c-a d) \left(\sqrt{c} \sqrt{a+b x} (4 a c+3 a d x+b c x)-3 a^{3/2} (c+d x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)\right)-3 c^{7/2} (a+b x)^{7/2}}{6 a c^{9/2} x^2 (c+d x)^{3/2}}","-\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,"(-3*c^(7/2)*(a + b*x)^(7/2) - ((3*b*c - 7*a*d)*x*(3*c^(5/2)*(a + b*x)^(5/2) - 5*(b*c - a*d)*x*(Sqrt[c]*Sqrt[a + b*x]*(4*a*c + b*c*x + 3*a*d*x) - 3*a^(3/2)*(c + d*x)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])))/2)/(6*a*c^(9/2)*x^2*(c + d*x)^(3/2))","A",1
697,1,198,278,0.3337505,"\int \frac{(a+b x)^{5/2}}{x^4 (c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^(5/2)/(x^4*(c + d*x)^(5/2)),x]","\frac{-x^2 \left(21 a^2 d^2-14 a b c d+b^2 c^2\right) \left(3 c^{5/2} (a+b x)^{5/2}-5 x (b c-a d) \left(\sqrt{c} \sqrt{a+b x} (4 a c+3 a d x+b c x)-3 a^{3/2} (c+d x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)\right)-2 c^{7/2} x (a+b x)^{7/2} (b c-9 a d)-8 a c^{9/2} (a+b x)^{7/2}}{24 a^2 c^{11/2} x^3 (c+d x)^{3/2}}","-\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,"(-8*a*c^(9/2)*(a + b*x)^(7/2) - 2*c^(7/2)*(b*c - 9*a*d)*x*(a + b*x)^(7/2) - (b^2*c^2 - 14*a*b*c*d + 21*a^2*d^2)*x^2*(3*c^(5/2)*(a + b*x)^(5/2) - 5*(b*c - a*d)*x*(Sqrt[c]*Sqrt[a + b*x]*(4*a*c + b*c*x + 3*a*d*x) - 3*a^(3/2)*(c + d*x)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])))/(24*a^2*c^(11/2)*x^3*(c + d*x)^(3/2))","A",1
698,1,255,388,0.7051957,"\int \frac{(a+b x)^{5/2}}{x^5 (c+d x)^{5/2}} \, dx","Integrate[(a + b*x)^(5/2)/(x^5*(c + d*x)^(5/2)),x]","\frac{-48 a^2 c^{11/2} (a+b x)^{7/2}+x^2 \left(2 c^{7/2} (a+b x)^{7/2} \left(-99 a^2 d^2+26 a b c d+b^2 c^2\right)+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) \left(3 c^{5/2} (a+b x)^{5/2}-5 x (b c-a d) \left(\sqrt{c} \sqrt{a+b x} (4 a c+3 a d x+b c x)-3 a^{3/2} (c+d x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)\right)\right)+8 a c^{9/2} x (a+b x)^{7/2} (11 a d+b c)}{192 a^3 c^{13/2} x^4 (c+d x)^{3/2}}","-\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,"(-48*a^2*c^(11/2)*(a + b*x)^(7/2) + 8*a*c^(9/2)*(b*c + 11*a*d)*x*(a + b*x)^(7/2) + x^2*(2*c^(7/2)*(b^2*c^2 + 26*a*b*c*d - 99*a^2*d^2)*(a + b*x)^(7/2) + (b^3*c^3 + 21*a*b^2*c^2*d - 189*a^2*b*c*d^2 + 231*a^3*d^3)*x*(3*c^(5/2)*(a + b*x)^(5/2) - 5*(b*c - a*d)*x*(Sqrt[c]*Sqrt[a + b*x]*(4*a*c + b*c*x + 3*a*d*x) - 3*a^(3/2)*(c + d*x)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))))/(192*a^3*c^(13/2)*x^4*(c + d*x)^(3/2))","A",1
699,1,167,191,0.3804364,"\int \frac{x^2 \sqrt{c+d x}}{\sqrt{a+b x}} \, dx","Integrate[(x^2*Sqrt[c + d*x])/Sqrt[a + b*x],x]","\frac{\sqrt{c+d x} \left(\sqrt{d} \sqrt{a+b x} \left(15 a^2 d^2-2 a b d (2 c+5 d x)+b^2 \left(-3 c^2+2 c d x+8 d^2 x^2\right)\right)+\frac{3 \sqrt{b c-a d} \left(5 a^2 d^2+2 a b c d+b^2 c^2\right) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{24 b^3 d^{5/2}}","\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,"(Sqrt[c + d*x]*(Sqrt[d]*Sqrt[a + b*x]*(15*a^2*d^2 - 2*a*b*d*(2*c + 5*d*x) + b^2*(-3*c^2 + 2*c*d*x + 8*d^2*x^2)) + (3*Sqrt[b*c - a*d]*(b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[(b*(c + d*x))/(b*c - a*d)]))/(24*b^3*d^(5/2))","A",1
700,1,121,125,0.2898879,"\int \frac{x \sqrt{c+d x}}{\sqrt{a+b x}} \, dx","Integrate[(x*Sqrt[c + d*x])/Sqrt[a + b*x],x]","\frac{\sqrt{c+d x} \left(\sqrt{d} \sqrt{a+b x} (b (c+2 d x)-3 a d)-\frac{\sqrt{b c-a d} (3 a d+b c) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{4 b^2 d^{3/2}}","-\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[c + d*x]*(Sqrt[d]*Sqrt[a + b*x]*(-3*a*d + b*(c + 2*d*x)) - (Sqrt[b*c - a*d]*(b*c + 3*a*d)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[(b*(c + d*x))/(b*c - a*d)]))/(4*b^2*d^(3/2))","A",1
701,1,117,72,0.1020935,"\int \frac{\sqrt{c+d x}}{\sqrt{a+b x}} \, dx","Integrate[Sqrt[c + d*x]/Sqrt[a + b*x],x]","\frac{\sqrt{c+d x} \left(\sqrt{d} \sqrt{a+b x} \sqrt{\frac{b (c+d x)}{b c-a d}}+\sqrt{b c-a d} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)}{b \sqrt{d} \sqrt{\frac{b (c+d x)}{b c-a d}}}","\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[c + d*x]*(Sqrt[d]*Sqrt[a + b*x]*Sqrt[(b*(c + d*x))/(b*c - a*d)] + Sqrt[b*c - a*d]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]]))/(b*Sqrt[d]*Sqrt[(b*(c + d*x))/(b*c - a*d)])","A",1
702,1,120,85,0.3140282,"\int \frac{\sqrt{c+d x}}{x \sqrt{a+b x}} \, dx","Integrate[Sqrt[c + d*x]/(x*Sqrt[a + b*x]),x]","\frac{2 \sqrt{d} \sqrt{c+d x} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}}-\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{a}}","\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,"(2*Sqrt[d]*Sqrt[c + d*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]) - (2*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/Sqrt[a]","A",1
703,1,77,76,0.046093,"\int \frac{\sqrt{c+d x}}{x^2 \sqrt{a+b x}} \, dx","Integrate[Sqrt[c + d*x]/(x^2*Sqrt[a + b*x]),x]","-\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} \sqrt{c}}-\frac{\sqrt{a+b x} \sqrt{c+d x}}{a x}","\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[a + b*x]*Sqrt[c + d*x])/(a*x)) - ((-(b*c) + a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(a^(3/2)*Sqrt[c])","A",1
704,1,112,131,0.0873287,"\int \frac{\sqrt{c+d x}}{x^3 \sqrt{a+b x}} \, dx","Integrate[Sqrt[c + d*x]/(x^3*Sqrt[a + b*x]),x]","\frac{\left(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^{3/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} (2 a c+a d x-3 b c x)}{4 a^2 c x^2}","-\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,"-1/4*(Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + a*d*x))/(a^2*c*x^2) + ((-3*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*a^(5/2)*c^(3/2))","A",1
705,1,160,191,0.1432766,"\int \frac{\sqrt{c+d x}}{x^4 \sqrt{a+b x}} \, dx","Integrate[Sqrt[c + d*x]/(x^4*Sqrt[a + b*x]),x]","\frac{\sqrt{a+b x} \sqrt{c+d x} \left(a^2 \left(-8 c^2-2 c d x+3 d^2 x^2\right)+2 a b c x (5 c+2 d x)-15 b^2 c^2 x^2\right)}{24 a^3 c^2 x^3}-\frac{\left(a^3 d^3+a^2 b c d^2+3 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 a^{7/2} c^{5/2}}","-\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,"(Sqrt[a + b*x]*Sqrt[c + d*x]*(-15*b^2*c^2*x^2 + 2*a*b*c*x*(5*c + 2*d*x) + a^2*(-8*c^2 - 2*c*d*x + 3*d^2*x^2)))/(24*a^3*c^2*x^3) - ((-5*b^3*c^3 + 3*a*b^2*c^2*d + a^2*b*c*d^2 + a^3*d^3)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(8*a^(7/2)*c^(5/2))","A",1
706,1,209,254,0.6946667,"\int \frac{x^2 (c+d x)^{3/2}}{\sqrt{a+b x}} \, dx","Integrate[(x^2*(c + d*x)^(3/2))/Sqrt[a + b*x],x]","\frac{\sqrt{c+d x} \left(\frac{3 \left(35 a^2 d^2+10 a b c d+3 b^2 c^2\right) (b c-a d)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{\frac{b (c+d x)}{b c-a d}}}+\sqrt{d} \sqrt{a+b x} \left(-105 a^3 d^3+5 a^2 b d^2 (29 c+14 d x)-a b^2 d \left(15 c^2+92 c d x+56 d^2 x^2\right)+b^3 \left(-9 c^3+6 c^2 d x+72 c d^2 x^2+48 d^3 x^3\right)\right)\right)}{192 b^4 d^{5/2}}","\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,"(Sqrt[c + d*x]*(Sqrt[d]*Sqrt[a + b*x]*(-105*a^3*d^3 + 5*a^2*b*d^2*(29*c + 14*d*x) - a*b^2*d*(15*c^2 + 92*c*d*x + 56*d^2*x^2) + b^3*(-9*c^3 + 6*c^2*d*x + 72*c*d^2*x^2 + 48*d^3*x^3)) + (3*(b*c - a*d)^(3/2)*(3*b^2*c^2 + 10*a*b*c*d + 35*a^2*d^2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[(b*(c + d*x))/(b*c - a*d)]))/(192*b^4*d^(5/2))","A",1
707,1,153,171,0.4629191,"\int \frac{x (c+d x)^{3/2}}{\sqrt{a+b x}} \, dx","Integrate[(x*(c + d*x)^(3/2))/Sqrt[a + b*x],x]","\frac{\sqrt{c+d x} \left(\sqrt{d} \sqrt{a+b x} \left(15 a^2 d^2-2 a b d (11 c+5 d x)+b^2 \left(3 c^2+14 c d x+8 d^2 x^2\right)\right)-\frac{3 (b c-a d)^{3/2} (5 a d+b c) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{24 b^3 d^{3/2}}","-\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,"(Sqrt[c + d*x]*(Sqrt[d]*Sqrt[a + b*x]*(15*a^2*d^2 - 2*a*b*d*(11*c + 5*d*x) + b^2*(3*c^2 + 14*c*d*x + 8*d^2*x^2)) - (3*(b*c - a*d)^(3/2)*(b*c + 5*a*d)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[(b*(c + d*x))/(b*c - a*d)]))/(24*b^3*d^(3/2))","A",1
708,1,109,113,0.2917125,"\int \frac{(c+d x)^{3/2}}{\sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(3/2)/Sqrt[a + b*x],x]","\frac{\sqrt{c+d x} \left(\sqrt{a+b x} (-3 a d+5 b c+2 b d x)+\frac{3 (b c-a d)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{d} \sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{4 b^2}","\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[c + d*x]*(Sqrt[a + b*x]*(5*b*c - 3*a*d + 2*b*d*x) + (3*(b*c - a*d)^(3/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[d]*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(4*b^2)","A",1
709,1,171,116,0.9682974,"\int \frac{(c+d x)^{3/2}}{x \sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(3/2)/(x*Sqrt[a + b*x]),x]","\frac{b \left(\sqrt{a} d \sqrt{a+b x} (c+d x)-2 b c^{3/2} \sqrt{c+d x} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)+\sqrt{a} \sqrt{d} \sqrt{b c-a d} (3 b c-a d) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{a} b^2 \sqrt{c+d x}}","\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]*Sqrt[d]*Sqrt[b*c - a*d]*(3*b*c - a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] + b*(Sqrt[a]*d*Sqrt[a + b*x]*(c + d*x) - 2*b*c^(3/2)*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(Sqrt[a]*b^2*Sqrt[c + d*x])","A",1
710,1,154,119,1.074816,"\int \frac{(c+d x)^{3/2}}{x^2 \sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(3/2)/(x^2*Sqrt[a + b*x]),x]","\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} \sqrt{c+d x} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}}-\frac{c \sqrt{a+b x} \sqrt{c+d x}}{a x}","\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[a + b*x]*Sqrt[c + d*x])/(a*x)) + (2*d^(3/2)*Sqrt[c + d*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]) + (Sqrt[c]*(b*c - 3*a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/a^(3/2)","A",1
711,1,98,119,0.0853295,"\int \frac{(c+d x)^{3/2}}{x^3 \sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(3/2)/(x^3*Sqrt[a + b*x]),x]","-\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{\sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)}{4 a^2 x^2}","-\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,"-1/4*(Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x))/(a^2*x^2) - (3*(b*c - a*d)^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*a^(5/2)*Sqrt[c])","A",1
712,1,144,180,0.1887924,"\int \frac{(c+d x)^{3/2}}{x^4 \sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(3/2)/(x^4*Sqrt[a + b*x]),x]","\frac{\frac{x (a d+5 b c) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)\right)}{a^{5/2} \sqrt{c}}-8 \sqrt{a+b x} (c+d x)^{5/2}}{24 a c x^3}","\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,"(-8*Sqrt[a + b*x]*(c + d*x)^(5/2) + ((5*b*c + a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(5/2)*Sqrt[c]))/(24*a*c*x^3)","A",1
713,1,193,266,0.3272866,"\int \frac{(c+d x)^{3/2}}{x^5 \sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(3/2)/(x^5*Sqrt[a + b*x]),x]","-\frac{\frac{x^2 \left(3 a^2 d^2+10 a b c d+35 b^2 c^2\right) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)\right)}{a^{5/2} \sqrt{c}}+48 a c \sqrt{a+b x} (c+d x)^{5/2}-8 x \sqrt{a+b x} (c+d x)^{5/2} (3 a d+7 b c)}{192 a^2 c^2 x^4}","\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,"-1/192*(48*a*c*Sqrt[a + b*x]*(c + d*x)^(5/2) - 8*(7*b*c + 3*a*d)*x*Sqrt[a + b*x]*(c + d*x)^(5/2) + ((35*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*x^2*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(5/2)*Sqrt[c]))/(a^2*c^2*x^4)","A",1
714,1,239,314,1.1091804,"\int \frac{x^2 (c+d x)^{5/2}}{\sqrt{a+b x}} \, dx","Integrate[(x^2*(c + d*x)^(5/2))/Sqrt[a + b*x],x]","\frac{\sqrt{a+b x} (c+d x)^{7/2} \left(\frac{\left(63 a^2 d^2+14 a b c d+3 b^2 c^2\right) \left(\sqrt{d} \sqrt{a+b x} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(15 a^2 d^2-10 a b d (4 c+d x)+b^2 \left(33 c^2+26 c d x+8 d^2 x^2\right)\right)+15 (b c-a d)^{5/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)}{48 b^4 d^{3/2} \sqrt{a+b x} (c+d x)^3 \sqrt{\frac{b (c+d x)}{b c-a d}}}-\frac{9 a}{b}-\frac{3 c}{d}+8 x\right)}{40 b d}","\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,"(Sqrt[a + b*x]*(c + d*x)^(7/2)*((-9*a)/b - (3*c)/d + 8*x + ((3*b^2*c^2 + 14*a*b*c*d + 63*a^2*d^2)*(Sqrt[d]*Sqrt[a + b*x]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*(15*a^2*d^2 - 10*a*b*d*(4*c + d*x) + b^2*(33*c^2 + 26*c*d*x + 8*d^2*x^2)) + 15*(b*c - a*d)^(5/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]]))/(48*b^4*d^(3/2)*Sqrt[a + b*x]*(c + d*x)^3*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(40*b*d)","A",1
715,1,194,217,0.5642565,"\int \frac{x (c+d x)^{5/2}}{\sqrt{a+b x}} \, dx","Integrate[(x*(c + d*x)^(5/2))/Sqrt[a + b*x],x]","\frac{\sqrt{c+d x} \left(\sqrt{d} \sqrt{a+b x} \left(-105 a^3 d^3+5 a^2 b d^2 (53 c+14 d x)-a b^2 d \left(191 c^2+172 c d x+56 d^2 x^2\right)+b^3 \left(15 c^3+118 c^2 d x+136 c d^2 x^2+48 d^3 x^3\right)\right)-\frac{15 (b c-a d)^{5/2} (7 a d+b c) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{192 b^4 d^{3/2}}","-\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,"(Sqrt[c + d*x]*(Sqrt[d]*Sqrt[a + b*x]*(-105*a^3*d^3 + 5*a^2*b*d^2*(53*c + 14*d*x) - a*b^2*d*(191*c^2 + 172*c*d*x + 56*d^2*x^2) + b^3*(15*c^3 + 118*c^2*d*x + 136*c*d^2*x^2 + 48*d^3*x^3)) - (15*(b*c - a*d)^(5/2)*(b*c + 7*a*d)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[(b*(c + d*x))/(b*c - a*d)]))/(192*b^4*d^(3/2))","A",1
716,1,139,148,0.2430218,"\int \frac{(c+d x)^{5/2}}{\sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(5/2)/Sqrt[a + b*x],x]","\frac{\sqrt{c+d x} \left(\sqrt{a+b x} \left(15 a^2 d^2-10 a b d (4 c+d x)+b^2 \left(33 c^2+26 c d x+8 d^2 x^2\right)\right)+\frac{15 (b c-a d)^{5/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{d} \sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{24 b^3}","\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,"(Sqrt[c + d*x]*(Sqrt[a + b*x]*(15*a^2*d^2 - 10*a*b*d*(4*c + d*x) + b^2*(33*c^2 + 26*c*d*x + 8*d^2*x^2)) + (15*(b*c - a*d)^(5/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[d]*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(24*b^3)","A",1
717,1,186,171,1.1302953,"\int \frac{(c+d x)^{5/2}}{x \sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(5/2)/(x*Sqrt[a + b*x]),x]","\frac{1}{4} \left(\frac{\sqrt{d} \sqrt{b c-a d} \left(3 a^2 d^2-10 a b c d+15 b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b^3 \sqrt{c+d x}}+\frac{d \sqrt{a+b x} \sqrt{c+d x} (-3 a d+9 b c+2 b d x)}{b^2}-\frac{8 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{a}}\right)","\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,"((d*Sqrt[a + b*x]*Sqrt[c + d*x]*(9*b*c - 3*a*d + 2*b*d*x))/b^2 + (Sqrt[d]*Sqrt[b*c - a*d]*(15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(b^3*Sqrt[c + d*x]) - (8*c^(5/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/Sqrt[a])/4","A",1
718,1,195,160,1.0085681,"\int \frac{(c+d x)^{5/2}}{x^2 \sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(5/2)/(x^2*Sqrt[a + b*x]),x]","\frac{a^{3/2} d^{3/2} x \sqrt{b c-a d} (5 b c-a d) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)+b \left(b c^{3/2} x \sqrt{c+d x} (b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{a+b x} (c+d x) \left(a d^2 x-b c^2\right)\right)}{a^{3/2} b^2 x \sqrt{c+d x}}","\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,"(a^(3/2)*d^(3/2)*Sqrt[b*c - a*d]*(5*b*c - a*d)*x*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] + b*(Sqrt[a]*Sqrt[a + b*x]*(c + d*x)*(-(b*c^2) + a*d^2*x) + b*c^(3/2)*(b*c - 5*a*d)*x*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(3/2)*b^2*x*Sqrt[c + d*x])","A",1
719,1,189,177,1.1367922,"\int \frac{(c+d x)^{5/2}}{x^3 \sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(5/2)/(x^3*Sqrt[a + b*x]),x]","-\frac{c \sqrt{a+b x} \sqrt{c+d x} (2 a c+9 a d x-3 b c x)}{4 a^2 x^2}-\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} \sqrt{c+d x} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}}","\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,"-1/4*(c*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 9*a*d*x))/(a^2*x^2) + (2*d^(5/2)*Sqrt[c + d*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]) - (Sqrt[c]*(3*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*a^(5/2))","A",1
720,1,142,157,0.1919396,"\int \frac{(c+d x)^{5/2}}{x^4 \sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(5/2)/(x^4*Sqrt[a + b*x]),x]","\frac{\frac{5 x (b c-a d) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)\right)}{a^{5/2} \sqrt{c}}-8 \sqrt{a+b x} (c+d x)^{5/2}}{24 a x^3}","\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,"(-8*Sqrt[a + b*x]*(c + d*x)^(5/2) + (5*(b*c - a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(5/2)*Sqrt[c]))/(24*a*x^3)","A",1
721,1,183,229,0.2819246,"\int \frac{(c+d x)^{5/2}}{x^5 \sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(5/2)/(x^5*Sqrt[a + b*x]),x]","-\frac{\frac{(a d+7 b c) \left(\frac{5 x (b c-a d) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)\right)}{a^{5/2} \sqrt{c}}-8 \sqrt{a+b x} (c+d x)^{5/2}\right)}{48 a x^3}+\frac{\sqrt{a+b x} (c+d x)^{7/2}}{x^4}}{4 a c}","-\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,"-1/4*((Sqrt[a + b*x]*(c + d*x)^(7/2))/x^4 + ((7*b*c + a*d)*(-8*Sqrt[a + b*x]*(c + d*x)^(5/2) + (5*(b*c - a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(5/2)*Sqrt[c])))/(48*a*x^3))/(a*c)","A",1
722,1,232,346,0.3053019,"\int \frac{(c+d x)^{5/2}}{x^6 \sqrt{a+b x}} \, dx","Integrate[(c + d*x)^(5/2)/(x^6*Sqrt[a + b*x]),x]","\frac{\frac{\left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right) \left(\frac{5 x (b c-a d) \left(3 x^2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} \sqrt{a+b x} \sqrt{c+d x} (2 a c+5 a d x-3 b c x)\right)}{a^{5/2} \sqrt{c}}-8 \sqrt{a+b x} (c+d x)^{5/2}\right)}{24 a x^3}-\frac{16 a c \sqrt{a+b x} (c+d x)^{7/2}}{x^5}+\frac{6 \sqrt{a+b x} (c+d x)^{7/2} (a d+3 b c)}{x^4}}{80 a^2 c^2}","\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,"((-16*a*c*Sqrt[a + b*x]*(c + d*x)^(7/2))/x^5 + (6*(3*b*c + a*d)*Sqrt[a + b*x]*(c + d*x)^(7/2))/x^4 + ((63*b^2*c^2 + 14*a*b*c*d + 3*a^2*d^2)*(-8*Sqrt[a + b*x]*(c + d*x)^(5/2) + (5*(b*c - a*d)*x*(Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*Sqrt[c + d*x]*(2*a*c - 3*b*c*x + 5*a*d*x) + 3*(b*c - a*d)^2*x^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(5/2)*Sqrt[c])))/(24*a*x^3))/(80*a^2*c^2)","A",1
723,1,71,118,0.0445278,"\int \frac{x^4 (1+x)^{3/2}}{\sqrt{1-x}} \, dx","Integrate[(x^4*(1 + x)^(3/2))/Sqrt[1 - x],x]","\frac{\sqrt{x+1} \left(40 x^6+56 x^5+14 x^4+18 x^3+37 x^2+91 x-256\right)}{240 \sqrt{1-x}}-\frac{11}{8} \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\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,"(Sqrt[1 + x]*(-256 + 91*x + 37*x^2 + 18*x^3 + 14*x^4 + 56*x^5 + 40*x^6))/(240*Sqrt[1 - x]) - (11*ArcSin[Sqrt[1 - x]/Sqrt[2]])/8","A",1
724,1,56,110,0.0628834,"\int \frac{x^3 (1+x)^{3/2}}{\sqrt{1-x}} \, dx","Integrate[(x^3*(1 + x)^(3/2))/Sqrt[1 - x],x]","-\frac{1}{20} \sqrt{1-x^2} \left(4 x^4+10 x^3+12 x^2+15 x+24\right)-\frac{3}{2} \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\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,"-1/20*(Sqrt[1 - x^2]*(24 + 15*x + 12*x^2 + 10*x^3 + 4*x^4)) - (3*ArcSin[Sqrt[1 - x]/Sqrt[2]])/2","A",1
725,1,51,88,0.0332715,"\int \frac{x^2 (1+x)^{3/2}}{\sqrt{1-x}} \, dx","Integrate[(x^2*(1 + x)^(3/2))/Sqrt[1 - x],x]","-\frac{1}{24} \sqrt{1-x^2} \left(6 x^3+16 x^2+21 x+32\right)-\frac{7}{4} \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\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,"-1/24*(Sqrt[1 - x^2]*(32 + 21*x + 16*x^2 + 6*x^3)) - (7*ArcSin[Sqrt[1 - x]/Sqrt[2]])/4","A",1
726,1,42,61,0.0273979,"\int \frac{x (1+x)^{3/2}}{\sqrt{1-x}} \, dx","Integrate[(x*(1 + x)^(3/2))/Sqrt[1 - x],x]","-\frac{1}{3} \sqrt{1-x^2} \left(x^2+3 x+5\right)-2 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\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,"-1/3*(Sqrt[1 - x^2]*(5 + 3*x + x^2)) - 2*ArcSin[Sqrt[1 - x]/Sqrt[2]]","A",1
727,1,37,47,0.0125218,"\int \frac{(1+x)^{3/2}}{\sqrt{1-x}} \, dx","Integrate[(1 + x)^(3/2)/Sqrt[1 - x],x]","-\frac{1}{2} \sqrt{1-x^2} (x+4)-3 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\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,"-1/2*((4 + x)*Sqrt[1 - x^2]) - 3*ArcSin[Sqrt[1 - x]/Sqrt[2]]","A",1
728,1,64,43,0.045843,"\int \frac{(1+x)^{3/2}}{\sqrt{1-x} x} \, dx","Integrate[(1 + x)^(3/2)/(Sqrt[1 - x]*x),x]","\frac{x^2+\sqrt{1-x^2} \sin ^{-1}(x)-1}{\sqrt{1-x^2}}-\tanh ^{-1}\left(\sqrt{1-x^2}\right)-2 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)","-\sqrt{1-x} \sqrt{x+1}+2 \sin ^{-1}(x)-\tanh ^{-1}\left(\sqrt{1-x} \sqrt{x+1}\right)",1,"-2*ArcSin[Sqrt[1 - x]/Sqrt[2]] + (-1 + x^2 + Sqrt[1 - x^2]*ArcSin[x])/Sqrt[1 - x^2] - ArcTanh[Sqrt[1 - x^2]]","A",1
729,1,66,44,0.0505049,"\int \frac{(1+x)^{3/2}}{\sqrt{1-x} x^2} \, dx","Integrate[(1 + x)^(3/2)/(Sqrt[1 - x]*x^2),x]","\frac{x}{\sqrt{1-x^2}}-\frac{1}{\sqrt{1-x^2} x}-2 \tanh ^{-1}\left(\sqrt{1-x^2}\right)+2 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)+2 \sin ^{-1}(x)","-\frac{\sqrt{1-x} \sqrt{x+1}}{x}+\sin ^{-1}(x)-2 \tanh ^{-1}\left(\sqrt{1-x} \sqrt{x+1}\right)",1,"-(1/(x*Sqrt[1 - x^2])) + x/Sqrt[1 - x^2] + 2*ArcSin[Sqrt[1 - x]/Sqrt[2]] + 2*ArcSin[x] - 2*ArcTanh[Sqrt[1 - x^2]]","A",1
730,1,59,69,0.0151738,"\int \frac{(1+x)^{3/2}}{\sqrt{1-x} x^3} \, dx","Integrate[(1 + x)^(3/2)/(Sqrt[1 - x]*x^3),x]","\frac{4 x^3+x^2-3 \sqrt{1-x^2} x^2 \tanh ^{-1}\left(\sqrt{1-x^2}\right)-4 x-1}{2 x^2 \sqrt{1-x^2}}","-\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,"(-1 - 4*x + x^2 + 4*x^3 - 3*x^2*Sqrt[1 - x^2]*ArcTanh[Sqrt[1 - x^2]])/(2*x^2*Sqrt[1 - x^2])","A",1
731,1,66,88,0.0232299,"\int \frac{(1+x)^{3/2}}{\sqrt{1-x} x^4} \, dx","Integrate[(1 + x)^(3/2)/(Sqrt[1 - x]*x^4),x]","-\frac{-5 x^4-3 x^3+4 x^2+3 \sqrt{1-x^2} x^3 \tanh ^{-1}\left(\sqrt{1-x^2}\right)+3 x+1}{3 x^3 \sqrt{1-x^2}}","-\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,"-1/3*(1 + 3*x + 4*x^2 - 3*x^3 - 5*x^4 + 3*x^3*Sqrt[1 - x^2]*ArcTanh[Sqrt[1 - x^2]])/(x^3*Sqrt[1 - x^2])","A",1
732,1,71,115,0.024071,"\int \frac{(1+x)^{3/2}}{\sqrt{1-x} x^5} \, dx","Integrate[(1 + x)^(3/2)/(Sqrt[1 - x]*x^5),x]","-\frac{-32 x^5-21 x^4+16 x^3+15 x^2+21 \sqrt{1-x^2} x^4 \tanh ^{-1}\left(\sqrt{1-x^2}\right)+16 x+6}{24 x^4 \sqrt{1-x^2}}","-\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,"-1/24*(6 + 16*x + 15*x^2 + 16*x^3 - 21*x^4 - 32*x^5 + 21*x^4*Sqrt[1 - x^2]*ArcTanh[Sqrt[1 - x^2]])/(x^4*Sqrt[1 - x^2])","A",1
733,1,188,169,0.7599149,"\int \frac{x^3}{\sqrt{a+b x} \sqrt{c+d x}} \, dx","Integrate[x^3/(Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x) \left(15 a^2 d^2+2 a b d (7 c-5 d x)+b^2 \left(15 c^2-10 c d x+8 d^2 x^2\right)\right)-3 \sqrt{b c-a d} \left(5 a^3 d^3+3 a^2 b c d^2+3 a b^2 c^2 d+5 b^3 c^3\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{24 b^4 d^{7/2} \sqrt{c+d x}}","-\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,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(15*a^2*d^2 + 2*a*b*d*(7*c - 5*d*x) + b^2*(15*c^2 - 10*c*d*x + 8*d^2*x^2)) - 3*Sqrt[b*c - a*d]*(5*b^3*c^3 + 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 + 5*a^3*d^3)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(24*b^4*d^(7/2)*Sqrt[c + d*x])","A",1
734,1,142,127,0.2494192,"\int \frac{x^2}{\sqrt{a+b x} \sqrt{c+d x}} \, dx","Integrate[x^2/(Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\frac{\sqrt{b c-a d} \left(3 a^2 d^2+2 a b c d+3 b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)+b \sqrt{d} \sqrt{a+b x} (c+d x) (-3 a d-3 b c+2 b d x)}{4 b^3 d^{5/2} \sqrt{c+d x}}","-\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,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x)*(-3*b*c - 3*a*d + 2*b*d*x) + Sqrt[b*c - a*d]*(3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(4*b^3*d^(5/2)*Sqrt[c + d*x])","A",1
735,1,110,75,0.1723936,"\int \frac{x}{\sqrt{a+b x} \sqrt{c+d x}} \, dx","Integrate[x/(Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\frac{b \sqrt{d} \sqrt{a+b x} (c+d x)-\sqrt{b c-a d} (a d+b c) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b^2 d^{3/2} \sqrt{c+d x}}","\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,"(b*Sqrt[d]*Sqrt[a + b*x]*(c + d*x) - Sqrt[b*c - a*d]*(b*c + a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(b^2*d^(3/2)*Sqrt[c + d*x])","A",1
736,1,77,42,0.06123,"\int \frac{1}{\sqrt{a+b x} \sqrt{c+d x}} \, dx","Integrate[1/(Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\frac{2 \sqrt{c+d x} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{d} \sqrt{b c-a d} \sqrt{\frac{b (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)}{\sqrt{b} \sqrt{d}}",1,"(2*Sqrt[c + d*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[d]*Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)])","A",1
737,1,42,42,0.0093182,"\int \frac{1}{x \sqrt{a+b x} \sqrt{c+d x}} \, dx","Integrate[1/(x*Sqrt[a + b*x]*Sqrt[c + d*x]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{a} \sqrt{c}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{\sqrt{a} \sqrt{c}}",1,"(-2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(Sqrt[a]*Sqrt[c])","A",1
738,1,78,78,0.0450073,"\int \frac{1}{x^2 \sqrt{a+b x} \sqrt{c+d x}} \, dx","Integrate[1/(x^2*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)}{a^{3/2} c^{3/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x}}{a c x}","\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,"-((Sqrt[a + b*x]*Sqrt[c + d*x])/(a*c*x)) + ((b*c + a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(a^(3/2)*c^(3/2))","A",1
739,1,114,137,0.081285,"\int \frac{1}{x^3 \sqrt{a+b x} \sqrt{c+d x}} \, dx","Integrate[1/(x^3*Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\frac{\sqrt{a+b x} \sqrt{c+d x} (-2 a c+3 a d x+3 b c x)}{4 a^2 c^2 x^2}-\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{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,"(Sqrt[a + b*x]*Sqrt[c + d*x]*(-2*a*c + 3*b*c*x + 3*a*d*x))/(4*a^2*c^2*x^2) - ((3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*a^(5/2)*c^(5/2))","A",1
740,1,162,198,0.1350367,"\int \frac{1}{x^4 \sqrt{a+b x} \sqrt{c+d x}} \, dx","Integrate[1/(x^4*Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\frac{\left(5 a^3 d^3+3 a^2 b c d^2+3 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 a^{7/2} c^{7/2}}-\frac{\sqrt{a+b x} \sqrt{c+d x} \left(a^2 \left(8 c^2-10 c d x+15 d^2 x^2\right)+2 a b c x (7 d x-5 c)+15 b^2 c^2 x^2\right)}{24 a^3 c^3 x^3}","\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,"-1/24*(Sqrt[a + b*x]*Sqrt[c + d*x]*(15*b^2*c^2*x^2 + 2*a*b*c*x*(-5*c + 7*d*x) + a^2*(8*c^2 - 10*c*d*x + 15*d^2*x^2)))/(a^3*c^3*x^3) + ((5*b^3*c^3 + 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 + 5*a^3*d^3)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(8*a^(7/2)*c^(7/2))","A",1
741,1,210,175,0.3501748,"\int \frac{x^3}{\sqrt{a+b x} (c+d x)^{3/2}} \, dx","Integrate[x^3/(Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\frac{-b \sqrt{d} \sqrt{a+b x} \left(3 a^2 d^2 (c+d x)+2 a b d \left(2 c^2+c d x-d^2 x^2\right)+b^2 c \left(-15 c^2-5 c d x+2 d^2 x^2\right)\right)-3 \sqrt{b c-a d} \left(-a^3 d^3-a^2 b c d^2-3 a b^2 c^2 d+5 b^3 c^3\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{4 b^3 d^{7/2} \sqrt{c+d x} (a d-b c)}","\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,"(-(b*Sqrt[d]*Sqrt[a + b*x]*(3*a^2*d^2*(c + d*x) + 2*a*b*d*(2*c^2 + c*d*x - d^2*x^2) + b^2*c*(-15*c^2 - 5*c*d*x + 2*d^2*x^2))) - 3*Sqrt[b*c - a*d]*(5*b^3*c^3 - 3*a*b^2*c^2*d - a^2*b*c*d^2 - a^3*d^3)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(4*b^3*d^(7/2)*(-(b*c) + a*d)*Sqrt[c + d*x])","A",1
742,1,151,112,0.2222593,"\int \frac{x^2}{\sqrt{a+b x} (c+d x)^{3/2}} \, dx","Integrate[x^2/(Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\frac{b \sqrt{d} \sqrt{a+b x} (b c (3 c+d x)-a d (c+d x))-\sqrt{b c-a d} \left(-a^2 d^2-2 a b c d+3 b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b^2 d^{5/2} \sqrt{c+d x} (b c-a d)}","-\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,"(b*Sqrt[d]*Sqrt[a + b*x]*(-(a*d*(c + d*x)) + b*c*(3*c + d*x)) - Sqrt[b*c - a*d]*(3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(b^2*d^(5/2)*(b*c - a*d)*Sqrt[c + d*x])","A",1
743,1,110,77,0.1826317,"\int \frac{x}{\sqrt{a+b x} (c+d x)^{3/2}} \, dx","Integrate[x/(Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\frac{2 \left(b c \sqrt{d} \sqrt{a+b x}-(b c-a d)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)}{b d^{3/2} \sqrt{c+d x} (a d-b c)}","\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*(b*c*Sqrt[d]*Sqrt[a + b*x] - (b*c - a*d)^(3/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]]))/(b*d^(3/2)*(-(b*c) + a*d)*Sqrt[c + d*x])","A",1
744,1,30,30,0.0071444,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{3/2}} \, dx","Integrate[1/(Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\frac{2 \sqrt{a+b x}}{\sqrt{c+d x} (b c-a d)}","\frac{2 \sqrt{a+b x}}{\sqrt{c+d x} (b c-a d)}",1,"(2*Sqrt[a + b*x])/((b*c - a*d)*Sqrt[c + d*x])","A",1
745,1,77,77,0.0768509,"\int \frac{1}{x \sqrt{a+b x} (c+d x)^{3/2}} \, dx","Integrate[1/(x*Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\frac{2 d \sqrt{a+b x}}{c \sqrt{c+d x} (a d-b c)}-\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 \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[a + b*x])/(c*(-(b*c) + a*d)*Sqrt[c + d*x]) - (2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(Sqrt[a]*c^(3/2))","A",1
746,1,126,124,0.1231159,"\int \frac{1}{x^2 \sqrt{a+b x} (c+d x)^{3/2}} \, dx","Integrate[1/(x^2*Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\frac{\left(-3 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)+\frac{\sqrt{a} \sqrt{c} \sqrt{a+b x} (a d (c+3 d x)-b c (c+d x))}{x \sqrt{c+d x}}}{a^{3/2} c^{5/2} (b c-a d)}","\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,"((Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*(-(b*c*(c + d*x)) + a*d*(c + 3*d*x)))/(x*Sqrt[c + d*x]) + (b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(a^(3/2)*c^(5/2)*(b*c - a*d))","A",1
747,1,186,194,0.1850735,"\int \frac{1}{x^3 \sqrt{a+b x} (c+d x)^{3/2}} \, dx","Integrate[1/(x^3*Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","\frac{\frac{\sqrt{a} \sqrt{c} \sqrt{a+b x} \left(a^2 d \left(2 c^2-5 c d x-15 d^2 x^2\right)+2 a b c \left(-c^2+c d x+2 d^2 x^2\right)+3 b^2 c^2 x (c+d x)\right)}{x^2 \sqrt{c+d x}}-3 \left(-5 a^3 d^3+3 a^2 b c d^2+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)}{4 a^{5/2} c^{7/2} (b c-a d)}","\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,"((Sqrt[a]*Sqrt[c]*Sqrt[a + b*x]*(3*b^2*c^2*x*(c + d*x) + a^2*d*(2*c^2 - 5*c*d*x - 15*d^2*x^2) + 2*a*b*c*(-c^2 + c*d*x + 2*d^2*x^2)))/(x^2*Sqrt[c + d*x]) - 3*(b^3*c^3 + a*b^2*c^2*d + 3*a^2*b*c*d^2 - 5*a^3*d^3)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*a^(5/2)*c^(7/2)*(b*c - a*d))","A",1
748,1,367,258,0.9792296,"\int \frac{x^4}{\sqrt{a+b x} (c+d x)^{5/2}} \, dx","Integrate[x^4/(Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\frac{-3 (c+d x) (b c-a d) (3 a d+7 b c) \left(-d \sqrt{b c-a d} \left(-a^2 d^2-2 a b c d+3 b^2 c^2\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)+2 b^2 c^2 d^{3/2} \sqrt{a+b x}+b d^{3/2} \sqrt{a+b x} (c+d x) (b c-a d)\right)+6 b^2 d^{9/2} x^3 \sqrt{a+b x} (b c-a d)^2-2 b c d (3 a d-7 b c) \left(b c^2 \sqrt{d} \sqrt{a+b x} (b c-a d)-(c+d x) \left(2 b c \sqrt{d} \sqrt{a+b x} (2 b c-3 a d)-3 (b c-a d)^{5/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)\right)}{12 b^3 d^{11/2} (c+d x)^{3/2} (b c-a d)^2}","\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,"(6*b^2*d^(9/2)*(b*c - a*d)^2*x^3*Sqrt[a + b*x] - 3*(b*c - a*d)*(7*b*c + 3*a*d)*(c + d*x)*(2*b^2*c^2*d^(3/2)*Sqrt[a + b*x] + b*d^(3/2)*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x) - d*Sqrt[b*c - a*d]*(3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]]) - 2*b*c*d*(-7*b*c + 3*a*d)*(b*c^2*Sqrt[d]*(b*c - a*d)*Sqrt[a + b*x] - (c + d*x)*(2*b*c*Sqrt[d]*(2*b*c - 3*a*d)*Sqrt[a + b*x] - 3*(b*c - a*d)^(5/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])))/(12*b^3*d^(11/2)*(b*c - a*d)^2*(c + d*x)^(3/2))","A",1
749,1,182,174,0.3979254,"\int \frac{x^3}{\sqrt{a+b x} (c+d x)^{5/2}} \, dx","Integrate[x^3/(Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\frac{\frac{c \sqrt{a+b x} \left(3 a^2 d^2 (c+2 d x)-2 a b c d (11 c+15 d x)+5 b^2 c^2 (3 c+4 d x)\right)}{d^2 (b c-a d)^2}-\frac{3 (b c-a d)^{3/2} (a d+5 b c) \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b^2 d^{5/2}}+3 x^2 \sqrt{a+b x}}{3 b d (c+d x)^{3/2}}","\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,"(3*x^2*Sqrt[a + b*x] + (c*Sqrt[a + b*x]*(3*a^2*d^2*(c + 2*d*x) + 5*b^2*c^2*(3*c + 4*d*x) - 2*a*b*c*d*(11*c + 15*d*x)))/(d^2*(b*c - a*d)^2) - (3*(b*c - a*d)^(3/2)*(5*b*c + a*d)*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(b^2*d^(5/2)))/(3*b*d*(c + d*x)^(3/2))","A",1
750,1,148,126,0.3211357,"\int \frac{x^2}{\sqrt{a+b x} (c+d x)^{5/2}} \, dx","Integrate[x^2/(Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\frac{2 \left(-\frac{3 (b c-a d)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b^2 \sqrt{d}}-c^2 \sqrt{a+b x}+\frac{2 c \sqrt{a+b x} (c+d x) (2 b c-3 a d)}{b c-a d}\right)}{3 d^2 (c+d x)^{3/2} (a d-b c)}","\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,"(2*(-(c^2*Sqrt[a + b*x]) + (2*c*(2*b*c - 3*a*d)*Sqrt[a + b*x]*(c + d*x))/(b*c - a*d) - (3*(b*c - a*d)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(b^2*Sqrt[d])))/(3*d^2*(-(b*c) + a*d)*(c + d*x)^(3/2))","A",1
751,1,46,80,0.0173795,"\int \frac{x}{\sqrt{a+b x} (c+d x)^{5/2}} \, dx","Integrate[x/(Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\frac{2 \sqrt{a+b x} (-2 a c-3 a d x+b c x)}{3 (c+d x)^{3/2} (b c-a d)^2}","\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,"(2*Sqrt[a + b*x]*(-2*a*c + b*c*x - 3*a*d*x))/(3*(b*c - a*d)^2*(c + d*x)^(3/2))","A",1
752,1,46,66,0.0125593,"\int \frac{1}{\sqrt{a+b x} (c+d x)^{5/2}} \, dx","Integrate[1/(Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\frac{2 \sqrt{a+b x} (-a d+3 b c+2 b d x)}{3 (c+d x)^{3/2} (b c-a d)^2}","\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,"(2*Sqrt[a + b*x]*(3*b*c - a*d + 2*b*d*x))/(3*(b*c - a*d)^2*(c + d*x)^(3/2))","A",1
753,1,125,124,0.1769064,"\int \frac{1}{x \sqrt{a+b x} (c+d x)^{5/2}} \, dx","Integrate[1/(x*Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\frac{2 \left(\frac{3 (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{d \sqrt{a+b x} (b c (6 c+5 d x)-a d (4 c+3 d x))}{c (c+d x)^{3/2} (b c-a d)}\right)}{3 c (a d-b c)}","-\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,"(2*((d*Sqrt[a + b*x]*(-(a*d*(4*c + 3*d*x)) + b*c*(6*c + 5*d*x)))/(c*(b*c - a*d)*(c + d*x)^(3/2)) + (3*(b*c - a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(Sqrt[a]*c^(3/2))))/(3*c*(-(b*c) + a*d))","A",1
754,1,198,189,0.3627639,"\int \frac{1}{x^2 \sqrt{a+b x} (c+d x)^{5/2}} \, dx","Integrate[1/(x^2*Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\frac{\frac{(c+d x) \left(\sqrt{a} \sqrt{c} d \sqrt{a+b x} \left(-15 a^2 d^2+22 a b c d-3 b^2 c^2\right)+3 \sqrt{c+d x} (5 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)\right)}{\sqrt{a} c^{5/2} (b c-a d)^2}-\frac{d \sqrt{a+b x} (3 b c-5 a d)}{c (b c-a d)}-\frac{3 \sqrt{a+b x}}{x}}{3 a c (c+d x)^{3/2}}","\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,"(-((d*(3*b*c - 5*a*d)*Sqrt[a + b*x])/(c*(b*c - a*d))) - (3*Sqrt[a + b*x])/x + ((c + d*x)*(Sqrt[a]*Sqrt[c]*d*(-3*b^2*c^2 + 22*a*b*c*d - 15*a^2*d^2)*Sqrt[a + b*x] + 3*(b*c - a*d)^2*(b*c + 5*a*d)*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(Sqrt[a]*c^(5/2)*(b*c - a*d)^2))/(3*a*c*(c + d*x)^(3/2))","A",1
755,1,274,277,0.5366054,"\int \frac{1}{x^3 \sqrt{a+b x} (c+d x)^{5/2}} \, dx","Integrate[1/(x^3*Sqrt[a + b*x]*(c + d*x)^(5/2)),x]","\frac{\frac{d \sqrt{a+b x} \left(35 a^2 d^2-18 a b c d-9 b^2 c^2\right)}{a c^2 (a d-b c)}-\frac{(c+d x) \left(3 \sqrt{c+d x} (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{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)-\sqrt{a} \sqrt{c} 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)\right)}{a^{3/2} c^{7/2} (b c-a d)^2}+\frac{3 \sqrt{a+b x} (7 a d+3 b c)}{a c x}-\frac{6 \sqrt{a+b x}}{x^2}}{12 a c (c+d x)^{3/2}}","\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,"((d*(-9*b^2*c^2 - 18*a*b*c*d + 35*a^2*d^2)*Sqrt[a + b*x])/(a*c^2*(-(b*c) + a*d)) - (6*Sqrt[a + b*x])/x^2 + (3*(3*b*c + 7*a*d)*Sqrt[a + b*x])/(a*c*x) - ((c + d*x)*(-(Sqrt[a]*Sqrt[c]*d*(9*b^3*c^3 + 15*a*b^2*c^2*d - 145*a^2*b*c*d^2 + 105*a^3*d^3)*Sqrt[a + b*x]) + 3*(b*c - a*d)^2*(3*b^2*c^2 + 10*a*b*c*d + 35*a^2*d^2)*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(3/2)*c^(7/2)*(b*c - a*d)^2))/(12*a*c*(c + d*x)^(3/2))","A",1
756,1,23,21,0.0100044,"\int \frac{1}{x \sqrt{c x} \sqrt{a+b x}} \, dx","Integrate[1/(x*Sqrt[c*x]*Sqrt[a + b*x]),x]","-\frac{2 c x \sqrt{a+b x}}{a (c x)^{3/2}}","-\frac{2 \sqrt{a+b x}}{a \sqrt{c x}}",1,"(-2*c*x*Sqrt[a + b*x])/(a*(c*x)^(3/2))","A",1
757,1,63,42,0.0265447,"\int \frac{1}{x \sqrt{a+b x} \sqrt{a c-b c x}} \, dx","Integrate[1/(x*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]),x]","-\frac{\sqrt{a^2-b^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{a^2-b^2 x^2}}{a}\right)}{a \sqrt{a+b x} \sqrt{c (a-b x)}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x} \sqrt{a c-b c x}}{a \sqrt{c}}\right)}{a \sqrt{c}}",1,"-((Sqrt[a^2 - b^2*x^2]*ArcTanh[Sqrt[a^2 - b^2*x^2]/a])/(a*Sqrt[c*(a - b*x)]*Sqrt[a + b*x]))","A",1
758,1,92,54,0.0477818,"\int \frac{1}{x \sqrt{1-a-b x} \sqrt{1+a+b x}} \, dx","Integrate[1/(x*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x]),x]","\frac{2 \sqrt{a+b x-1} \sqrt{a+b x+1} \tanh ^{-1}\left(\sqrt{\frac{a+1}{a-1}} \sqrt{\frac{a+b x-1}{a+b x+1}}\right)}{\sqrt{-a-1} \sqrt{1-a} \sqrt{-((a+b x-1) (a+b x+1))}}","-\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,"(2*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]*ArcTanh[Sqrt[(1 + a)/(-1 + a)]*Sqrt[(-1 + a + b*x)/(1 + a + b*x)]])/(Sqrt[-1 - a]*Sqrt[1 - a]*Sqrt[-((-1 + a + b*x)*(1 + a + b*x))])","A",1
759,1,260,271,0.8232568,"\int \frac{x^3 (c+d x)^{3/2}}{(a+b x)^{3/2}} \, dx","Integrate[(x^3*(c + d*x)^(3/2))/(a + b*x)^(3/2),x]","\frac{\sqrt{c+d x} \left(\frac{3 \sqrt{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) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{\frac{b (c+d x)}{b c-a d}}}-\frac{\sqrt{d} \left(315 a^4 d^3+105 a^3 b d^2 (d x-3 c)+a^2 b^2 d \left(13 c^2-119 c d x-42 d^2 x^2\right)+a b^3 \left(3 c^3+11 c^2 d x+44 c d^2 x^2+24 d^3 x^3\right)-b^4 x \left(-3 c^3+2 c^2 d x+24 c d^2 x^2+16 d^3 x^3\right)\right)}{\sqrt{a+b x}}\right)}{64 b^5 d^{5/2}}","-\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,"(Sqrt[c + d*x]*(-((Sqrt[d]*(315*a^4*d^3 + 105*a^3*b*d^2*(-3*c + d*x) + a^2*b^2*d*(13*c^2 - 119*c*d*x - 42*d^2*x^2) - b^4*x*(-3*c^3 + 2*c^2*d*x + 24*c*d^2*x^2 + 16*d^3*x^3) + a*b^3*(3*c^3 + 11*c^2*d*x + 44*c*d^2*x^2 + 24*d^3*x^3)))/Sqrt[a + b*x]) + (3*Sqrt[b*c - a*d]*(b^3*c^3 + 5*a*b^2*c^2*d + 35*a^2*b*c*d^2 - 105*a^3*d^3)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[(b*(c + d*x))/(b*c - a*d)]))/(64*b^5*d^(5/2))","A",1
760,1,194,246,0.5212753,"\int \frac{x^2 (c+d x)^{3/2}}{(a+b x)^{3/2}} \, dx","Integrate[(x^2*(c + d*x)^(3/2))/(a + b*x)^(3/2),x]","\frac{\sqrt{c+d x} \left(\frac{\sqrt{d} \left(105 a^3 d^2+5 a^2 b d (7 d x-20 c)+a b^2 \left(3 c^2-38 c d x-14 d^2 x^2\right)+b^3 x \left(3 c^2+14 c d x+8 d^2 x^2\right)\right)}{\sqrt{a+b x}}-\frac{3 \sqrt{b c-a d} \left(-35 a^2 d^2+10 a b c d+b^2 c^2\right) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{24 b^4 d^{3/2}}","-\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,"(Sqrt[c + d*x]*((Sqrt[d]*(105*a^3*d^2 + 5*a^2*b*d*(-20*c + 7*d*x) + a*b^2*(3*c^2 - 38*c*d*x - 14*d^2*x^2) + b^3*x*(3*c^2 + 14*c*d*x + 8*d^2*x^2)))/Sqrt[a + b*x] - (3*Sqrt[b*c - a*d]*(b^2*c^2 + 10*a*b*c*d - 35*a^2*d^2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[(b*(c + d*x))/(b*c - a*d)]))/(24*b^4*d^(3/2))","A",1
761,1,134,171,0.4288942,"\int \frac{x (c+d x)^{3/2}}{(a+b x)^{3/2}} \, dx","Integrate[(x*(c + d*x)^(3/2))/(a + b*x)^(3/2),x]","\frac{\sqrt{c+d x} \left(\frac{-15 a^2 d+a b (13 c-5 d x)+b^2 x (5 c+2 d x)}{\sqrt{a+b x}}+\frac{3 (b c-5 a d) \sqrt{b c-a d} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{d} \sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{4 b^3}","\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,"(Sqrt[c + d*x]*((-15*a^2*d + a*b*(13*c - 5*d*x) + b^2*x*(5*c + 2*d*x))/Sqrt[a + b*x] + (3*(b*c - 5*a*d)*Sqrt[b*c - a*d]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[d]*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(4*b^3)","A",1
762,1,71,98,0.0442548,"\int \frac{(c+d x)^{3/2}}{(a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(3/2)/(a + b*x)^(3/2),x]","-\frac{2 (c+d x)^{3/2} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2}}","\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,"(-2*(c + d*x)^(3/2)*Hypergeometric2F1[-3/2, -1/2, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(3/2))","C",1
763,1,158,119,1.1410738,"\int \frac{(c+d x)^{3/2}}{x (a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(3/2)/(x*(a + b*x)^(3/2)),x]","\frac{2 \left(-\frac{b^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{d^{3/2} \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{c+d x}}+\frac{b \sqrt{c+d x} (b c-a d)}{a \sqrt{a+b x}}\right)}{b^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*((b*(b*c - a*d)*Sqrt[c + d*x])/(a*Sqrt[a + b*x]) + (d^(3/2)*Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[c + d*x] - (b^2*c^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/a^(3/2)))/b^2","A",1
764,1,91,108,0.0883536,"\int \frac{(c+d x)^{3/2}}{x^2 (a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(3/2)/(x^2*(a + b*x)^(3/2)),x]","\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{\sqrt{c+d x} (-a c+2 a d x-3 b c x)}{a^2 x \sqrt{a+b x}}","\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,"(Sqrt[c + d*x]*(-(a*c) - 3*b*c*x + 2*a*d*x))/(a^2*x*Sqrt[a + b*x]) + (3*Sqrt[c]*(b*c - a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/a^(5/2)","A",1
765,1,130,178,0.1045215,"\int \frac{(c+d x)^{3/2}}{x^3 (a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(3/2)/(x^3*(a + b*x)^(3/2)),x]","\frac{\sqrt{c+d x} \left(-\left(a^2 (2 c+5 d x)\right)+a b x (5 c-13 d x)+15 b^2 c x^2\right)}{4 a^3 x^2 \sqrt{a+b x}}-\frac{3 \left(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} \sqrt{c}}","-\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,"(Sqrt[c + d*x]*(15*b^2*c*x^2 + a*b*x*(5*c - 13*d*x) - a^2*(2*c + 5*d*x)))/(4*a^3*x^2*Sqrt[a + b*x]) - (3*(5*b^2*c^2 - 6*a*b*c*d + a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*a^(7/2)*Sqrt[c])","A",1
766,1,190,241,0.1605189,"\int \frac{(c+d x)^{3/2}}{x^4 (a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(3/2)/(x^4*(a + b*x)^(3/2)),x]","\frac{\left(a^3 d^3+9 a^2 b c d^2-45 a b^2 c^2 d+35 b^3 c^3\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{\sqrt{c+d x} \left(a^3 \left(8 c^2+14 c d x+3 d^2 x^2\right)+a^2 b x \left(-14 c^2-38 c d x+3 d^2 x^2\right)+5 a b^2 c x^2 (7 c-20 d x)+105 b^3 c^2 x^3\right)}{24 a^4 c x^3 \sqrt{a+b x}}","-\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,"-1/24*(Sqrt[c + d*x]*(105*b^3*c^2*x^3 + 5*a*b^2*c*x^2*(7*c - 20*d*x) + a^2*b*x*(-14*c^2 - 38*c*d*x + 3*d^2*x^2) + a^3*(8*c^2 + 14*c*d*x + 3*d^2*x^2)))/(a^4*c*x^3*Sqrt[a + b*x]) + ((35*b^3*c^3 - 45*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(8*a^(9/2)*c^(3/2))","A",1
767,1,324,346,1.4501258,"\int \frac{x^3 (c+d x)^{5/2}}{(a+b x)^{3/2}} \, dx","Integrate[(x^3*(c + d*x)^(5/2))/(a + b*x)^(3/2),x]","\frac{\sqrt{c+d x} \left(\frac{15 \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) (b c-a d)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{\frac{b (c+d x)}{b c-a d}}}+\frac{\sqrt{d} \left(3465 a^5 d^4+105 a^4 b d^3 (11 d x-64 c)-42 a^3 b^2 d^2 \left(-79 c^2+57 c d x+11 d^2 x^2\right)+2 a^2 b^3 d \left(-40 c^3+662 c^2 d x+459 c d^2 x^2+132 d^3 x^3\right)-a b^4 \left(15 c^4+70 c^3 d x+466 c^2 d^2 x^2+512 c d^3 x^3+176 d^4 x^4\right)+b^5 x \left(-15 c^4+10 c^3 d x+248 c^2 d^2 x^2+336 c d^3 x^3+128 d^4 x^4\right)\right)}{\sqrt{a+b x}}\right)}{640 b^6 d^{5/2}}","-\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,"(Sqrt[c + d*x]*((Sqrt[d]*(3465*a^5*d^4 + 105*a^4*b*d^3*(-64*c + 11*d*x) - 42*a^3*b^2*d^2*(-79*c^2 + 57*c*d*x + 11*d^2*x^2) + 2*a^2*b^3*d*(-40*c^3 + 662*c^2*d*x + 459*c*d^2*x^2 + 132*d^3*x^3) + b^5*x*(-15*c^4 + 10*c^3*d*x + 248*c^2*d^2*x^2 + 336*c*d^3*x^3 + 128*d^4*x^4) - a*b^4*(15*c^4 + 70*c^3*d*x + 466*c^2*d^2*x^2 + 512*c*d^3*x^3 + 176*d^4*x^4)))/Sqrt[a + b*x] + (15*(b*c - a*d)^(3/2)*(b^3*c^3 + 7*a*b^2*c^2*d + 63*a^2*b*c*d^2 - 231*a^3*d^3)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[(b*(c + d*x))/(b*c - a*d)]))/(640*b^6*d^(5/2))","A",1
768,1,245,306,0.9139607,"\int \frac{x^2 (c+d x)^{5/2}}{(a+b x)^{3/2}} \, dx","Integrate[(x^2*(c + d*x)^(5/2))/(a + b*x)^(3/2),x]","\frac{\sqrt{c+d x} \left(\frac{\sqrt{d} \left(-945 a^4 d^3+105 a^3 b d^2 (17 c-3 d x)+a^2 b^2 d \left(-839 c^2+637 c d x+126 d^2 x^2\right)+a b^3 \left(15 c^3-337 c^2 d x-244 c d^2 x^2-72 d^3 x^3\right)+b^4 x \left(15 c^3+118 c^2 d x+136 c d^2 x^2+48 d^3 x^3\right)\right)}{\sqrt{a+b x}}-\frac{15 (b c-a d)^{3/2} \left(-63 a^2 d^2+14 a b c d+b^2 c^2\right) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{192 b^5 d^{3/2}}","-\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,"(Sqrt[c + d*x]*((Sqrt[d]*(-945*a^4*d^3 + 105*a^3*b*d^2*(17*c - 3*d*x) + a^2*b^2*d*(-839*c^2 + 637*c*d*x + 126*d^2*x^2) + a*b^3*(15*c^3 - 337*c^2*d*x - 244*c*d^2*x^2 - 72*d^3*x^3) + b^4*x*(15*c^3 + 118*c^2*d*x + 136*c*d^2*x^2 + 48*d^3*x^3)))/Sqrt[a + b*x] - (15*(b*c - a*d)^(3/2)*(b^2*c^2 + 14*a*b*c*d - 63*a^2*d^2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[(b*(c + d*x))/(b*c - a*d)]))/(192*b^5*d^(3/2))","A",1
769,1,175,214,0.6507304,"\int \frac{x (c+d x)^{5/2}}{(a+b x)^{3/2}} \, dx","Integrate[(x*(c + d*x)^(5/2))/(a + b*x)^(3/2),x]","\frac{\sqrt{c+d x} \left(\frac{105 a^3 d^2+5 a^2 b d (7 d x-38 c)+a b^2 \left(81 c^2-68 c d x-14 d^2 x^2\right)+b^3 x \left(33 c^2+26 c d x+8 d^2 x^2\right)}{\sqrt{a+b x}}+\frac{15 (b c-7 a d) (b c-a d)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{d} \sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{24 b^4}","\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,"(Sqrt[c + d*x]*((105*a^3*d^2 + 5*a^2*b*d*(-38*c + 7*d*x) + a*b^2*(81*c^2 - 68*c*d*x - 14*d^2*x^2) + b^3*x*(33*c^2 + 26*c*d*x + 8*d^2*x^2))/Sqrt[a + b*x] + (15*(b*c - 7*a*d)*(b*c - a*d)^(3/2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[d]*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(24*b^4)","A",1
770,1,71,138,0.0633621,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(5/2)/(a + b*x)^(3/2),x]","-\frac{2 (c+d x)^{5/2} \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}}","\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,"(-2*(c + d*x)^(5/2)*Hypergeometric2F1[-5/2, -1/2, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2))","C",1
771,1,274,163,1.4663946,"\int \frac{(c+d x)^{5/2}}{x (a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(5/2)/(x*(a + b*x)^(3/2)),x]","-\frac{2 \left(b c \left(\sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(b c^{3/2} \sqrt{a+b x} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c+d x} (a d-b c)\right)-a^{3/2} d^{3/2} \sqrt{a+b x} \sqrt{c+d x} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)+a^{3/2} d \sqrt{c+d x} (b c-a d)^{3/2} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)\right)}{a^{3/2} b^2 \sqrt{a+b x} \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}}","-\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,"(-2*(b*c*(-(a^(3/2)*d^(3/2)*Sqrt[a + b*x]*Sqrt[c + d*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]]) + Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*(Sqrt[a]*(-(b*c) + a*d)*Sqrt[c + d*x] + b*c^(3/2)*Sqrt[a + b*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])) + a^(3/2)*d*(b*c - a*d)^(3/2)*Sqrt[c + d*x]*Hypergeometric2F1[-3/2, -1/2, 1/2, (d*(a + b*x))/(-(b*c) + a*d)]))/(a^(3/2)*b^2*Sqrt[b*c - a*d]*Sqrt[a + b*x]*Sqrt[(b*(c + d*x))/(b*c - a*d)])","C",1
772,1,934,163,3.4241802,"\int \frac{(c+d x)^{5/2}}{x^2 (a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(5/2)/(x^2*(a + b*x)^(3/2)),x]","-\frac{\sqrt{c+d x} \left(-3 d^{7/2} x \sqrt{a+b x} (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right) a^{7/2}-2 d^3 \sqrt{b c-a d} x (c+d x)^2 \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right) a^{7/2}+3 d^3 \sqrt{b c-a d} x (c+d x)^2 \sqrt{\frac{b (c+d x)}{b c-a d}} a^{7/2}+\frac{d^3 (b c-a d)^{5/2} x^2 \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} a^{5/2}}{b}-\frac{7 c d^2 (b c-a d)^{5/2} x \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} a^{5/2}}{b}+8 b c d^{5/2} x \sqrt{a+b x} (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right) a^{5/2}+8 b c d^2 \sqrt{b c-a d} x (c+d x)^2 \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right) a^{5/2}+2 c^3 (b c-a d)^{5/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} a^{3/2}-3 c d^2 (b c-a d)^{5/2} x^2 \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} a^{3/2}-2 c^2 d (b c-a d)^{5/2} x \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} a^{3/2}-9 b^2 c^2 d^{3/2} x \sqrt{a+b x} (c+d x)^2 \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right) a^{3/2}-6 b^2 c^2 d \sqrt{b c-a d} x (c+d x)^2 \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right) a^{3/2}+10 b c^{5/2} d (b c-a d)^{3/2} x \sqrt{a+b x} \sqrt{c+d x} \left(\frac{b (c+d x)}{b c-a d}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right) a+6 b c^3 (b c-a d)^{5/2} x \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2} \sqrt{a}-6 b^3 c^{7/2} \sqrt{b c-a d} x \sqrt{a+b x} (c+d x)^{3/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)}{2 a^{5/2} c (b c-a d)^{5/2} x \sqrt{a+b x} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}}","\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,"-1/2*(Sqrt[c + d*x]*(3*a^(7/2)*d^3*Sqrt[b*c - a*d]*x*(c + d*x)^2*Sqrt[(b*(c + d*x))/(b*c - a*d)] + 2*a^(3/2)*c^3*(b*c - a*d)^(5/2)*((b*(c + d*x))/(b*c - a*d))^(5/2) + 6*Sqrt[a]*b*c^3*(b*c - a*d)^(5/2)*x*((b*(c + d*x))/(b*c - a*d))^(5/2) - 2*a^(3/2)*c^2*d*(b*c - a*d)^(5/2)*x*((b*(c + d*x))/(b*c - a*d))^(5/2) - (7*a^(5/2)*c*d^2*(b*c - a*d)^(5/2)*x*((b*(c + d*x))/(b*c - a*d))^(5/2))/b - 3*a^(3/2)*c*d^2*(b*c - a*d)^(5/2)*x^2*((b*(c + d*x))/(b*c - a*d))^(5/2) + (a^(5/2)*d^3*(b*c - a*d)^(5/2)*x^2*((b*(c + d*x))/(b*c - a*d))^(5/2))/b - 9*a^(3/2)*b^2*c^2*d^(3/2)*x*Sqrt[a + b*x]*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] + 8*a^(5/2)*b*c*d^(5/2)*x*Sqrt[a + b*x]*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] - 3*a^(7/2)*d^(7/2)*x*Sqrt[a + b*x]*(c + d*x)^2*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]] - 6*b^3*c^(7/2)*Sqrt[b*c - a*d]*x*Sqrt[a + b*x]*(c + d*x)^(3/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])] + 10*a*b*c^(5/2)*d*(b*c - a*d)^(3/2)*x*Sqrt[a + b*x]*Sqrt[c + d*x]*((b*(c + d*x))/(b*c - a*d))^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])] - 6*a^(3/2)*b^2*c^2*d*Sqrt[b*c - a*d]*x*(c + d*x)^2*Hypergeometric2F1[-3/2, -1/2, 1/2, (d*(a + b*x))/(-(b*c) + a*d)] + 8*a^(5/2)*b*c*d^2*Sqrt[b*c - a*d]*x*(c + d*x)^2*Hypergeometric2F1[-3/2, -1/2, 1/2, (d*(a + b*x))/(-(b*c) + a*d)] - 2*a^(7/2)*d^3*Sqrt[b*c - a*d]*x*(c + d*x)^2*Hypergeometric2F1[-3/2, -1/2, 1/2, (d*(a + b*x))/(-(b*c) + a*d)]))/(a^(5/2)*c*(b*c - a*d)^(5/2)*x*Sqrt[a + b*x]*((b*(c + d*x))/(b*c - a*d))^(5/2))","C",1
773,1,130,154,0.1091777,"\int \frac{(c+d x)^{5/2}}{x^3 (a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(5/2)/(x^3*(a + b*x)^(3/2)),x]","\frac{\sqrt{c+d x} \left(a^2 \left(-2 c^2-9 c d x+8 d^2 x^2\right)+5 a b c x (c-5 d x)+15 b^2 c^2 x^2\right)}{4 a^3 x^2 \sqrt{a+b x}}-\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} (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,"(Sqrt[c + d*x]*(15*b^2*c^2*x^2 + 5*a*b*c*x*(c - 5*d*x) + a^2*(-2*c^2 - 9*c*d*x + 8*d^2*x^2)))/(4*a^3*x^2*Sqrt[a + b*x]) - (15*Sqrt[c]*(b*c - a*d)^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*a^(7/2))","A",1
774,1,168,230,0.2995234,"\int \frac{(c+d x)^{5/2}}{x^4 (a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(5/2)/(x^4*(a + b*x)^(3/2)),x]","\frac{\frac{1}{2} x (7 b c-a d) \left(2 a^{5/2} (c+d x)^{5/2}-5 x (b c-a d) \left(\sqrt{a} \sqrt{c+d x} (a (c-2 d x)+3 b c x)-3 \sqrt{c} x \sqrt{a+b x} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)\right)-4 a^{7/2} (c+d x)^{7/2}}{12 a^{9/2} c x^3 \sqrt{a+b x}}","\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,"(-4*a^(7/2)*(c + d*x)^(7/2) + ((7*b*c - a*d)*x*(2*a^(5/2)*(c + d*x)^(5/2) - 5*(b*c - a*d)*x*(Sqrt[a]*Sqrt[c + d*x]*(3*b*c*x + a*(c - 2*d*x)) - 3*Sqrt[c]*(b*c - a*d)*x*Sqrt[a + b*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])))/2)/(12*a^(9/2)*c*x^3*Sqrt[a + b*x])","A",1
775,1,208,318,0.2995225,"\int \frac{(c+d x)^{5/2}}{x^5 (a+b x)^{3/2}} \, dx","Integrate[(c + d*x)^(5/2)/(x^5*(a + b*x)^(3/2)),x]","\frac{8 a^{7/2} x (c+d x)^{7/2} (a d+9 b c)-48 a^{9/2} c (c+d x)^{7/2}-x^2 \left(-a^2 d^2-14 a b c d+63 b^2 c^2\right) \left(2 a^{5/2} (c+d x)^{5/2}-5 x (b c-a d) \left(\sqrt{a} \sqrt{c+d x} (a (c-2 d x)+3 b c x)-3 \sqrt{c} x \sqrt{a+b x} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)\right)}{192 a^{11/2} c^2 x^4 \sqrt{a+b x}}","-\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,"(-48*a^(9/2)*c*(c + d*x)^(7/2) + 8*a^(7/2)*(9*b*c + a*d)*x*(c + d*x)^(7/2) - (63*b^2*c^2 - 14*a*b*c*d - a^2*d^2)*x^2*(2*a^(5/2)*(c + d*x)^(5/2) - 5*(b*c - a*d)*x*(Sqrt[a]*Sqrt[c + d*x]*(3*b*c*x + a*(c - 2*d*x)) - 3*Sqrt[c]*(b*c - a*d)*x*Sqrt[a + b*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])))/(192*a^(11/2)*c^2*x^4*Sqrt[a + b*x])","A",1
776,1,285,250,0.9853755,"\int \frac{x^4}{(a+b x)^{3/2} (c+d x)^{3/2}} \, dx","Integrate[x^4/((a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","\frac{3 \sqrt{a+b x} \left(5 a^2 d^2+6 a b c d+5 b^2 c^2\right) (b c-a d)^{5/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)+b \sqrt{d} \left(-15 a^4 d^3 (c+d x)+a^3 b d^2 \left(7 c^2+2 c d x-5 d^2 x^2\right)+a^2 b^2 d \left(7 c^3+10 c^2 d x+5 c d^2 x^2+2 d^3 x^3\right)+a b^3 c \left(-15 c^3+2 c^2 d x+5 c d^2 x^2-4 d^3 x^3\right)+b^4 c^2 x \left(-15 c^2-5 c d x+2 d^2 x^2\right)\right)}{4 b^4 d^{7/2} \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}","\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,"(b*Sqrt[d]*(-15*a^4*d^3*(c + d*x) + a^3*b*d^2*(7*c^2 + 2*c*d*x - 5*d^2*x^2) + b^4*c^2*x*(-15*c^2 - 5*c*d*x + 2*d^2*x^2) + a*b^3*c*(-15*c^3 + 2*c^2*d*x + 5*c*d^2*x^2 - 4*d^3*x^3) + a^2*b^2*d*(7*c^3 + 10*c^2*d*x + 5*c*d^2*x^2 + 2*d^3*x^3)) + 3*(b*c - a*d)^(5/2)*(5*b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*Sqrt[a + b*x]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(4*b^4*d^(7/2)*(b*c - a*d)^2*Sqrt[a + b*x]*Sqrt[c + d*x])","A",1
777,1,195,167,0.7460646,"\int \frac{x^3}{(a+b x)^{3/2} (c+d x)^{3/2}} \, dx","Integrate[x^3/((a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","\frac{\frac{\sqrt{d} \left(3 a^3 d^2 (c+d x)+a^2 b d \left(-2 c^2-c d x+d^2 x^2\right)+a b^2 c \left(3 c^2-c d x-2 d^2 x^2\right)+b^3 c^2 x (3 c+d x)\right)}{\sqrt{a+b x} (b c-a d)^2}-\frac{3 \sqrt{b c-a d} (a d+b c) \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{b}}{b^2 d^{5/2} \sqrt{c+d x}}","\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,"((Sqrt[d]*(3*a^3*d^2*(c + d*x) + b^3*c^2*x*(3*c + d*x) + a*b^2*c*(3*c^2 - c*d*x - 2*d^2*x^2) + a^2*b*d*(-2*c^2 - c*d*x + d^2*x^2)))/((b*c - a*d)^2*Sqrt[a + b*x]) - (3*Sqrt[b*c - a*d]*(b*c + a*d)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/b)/(b^2*d^(5/2)*Sqrt[c + d*x])","A",1
778,1,143,130,0.3252732,"\int \frac{x^2}{(a+b x)^{3/2} (c+d x)^{3/2}} \, dx","Integrate[x^2/((a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","\frac{2 \sqrt{a+b x} (b c-a d)^{5/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)-2 b \sqrt{d} \left(a^2 d (c+d x)+a b c^2+b^2 c^2 x\right)}{b^2 d^{3/2} \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}","-\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*b*Sqrt[d]*(a*b*c^2 + b^2*c^2*x + a^2*d*(c + d*x)) + 2*(b*c - a*d)^(5/2)*Sqrt[a + b*x]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(b^2*d^(3/2)*(b*c - a*d)^2*Sqrt[a + b*x]*Sqrt[c + d*x])","A",1
779,1,43,75,0.0178235,"\int \frac{x}{(a+b x)^{3/2} (c+d x)^{3/2}} \, dx","Integrate[x/((a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","\frac{2 (2 a c+a d x+b c x)}{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}","\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,"(2*(2*a*c + b*c*x + a*d*x))/((b*c - a*d)^2*Sqrt[a + b*x]*Sqrt[c + d*x])","A",1
780,1,42,62,0.0166496,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{3/2}} \, dx","Integrate[1/((a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","-\frac{2 (a d+b (c+2 d x))}{\sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}","-\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,"(-2*(a*d + b*(c + 2*d*x)))/((b*c - a*d)^2*Sqrt[a + b*x]*Sqrt[c + d*x])","A",1
781,1,104,121,0.1361566,"\int \frac{1}{x (a+b x)^{3/2} (c+d x)^{3/2}} \, dx","Integrate[1/(x*(a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","\frac{2 \left(a^2 d^2+a b d^2 x+b^2 c (c+d x)\right)}{a c \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}-\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 \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,"(2*(a^2*d^2 + a*b*d^2*x + b^2*c*(c + d*x)))/(a*c*(b*c - a*d)^2*Sqrt[a + b*x]*Sqrt[c + d*x]) - (2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(a^(3/2)*c^(3/2))","A",1
782,1,165,185,0.2127543,"\int \frac{1}{x^2 (a+b x)^{3/2} (c+d x)^{3/2}} \, dx","Integrate[1/(x^2*(a + b*x)^(3/2)*(c + d*x)^(3/2)),x]","\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{a^3 \left(-d^2\right) (c+3 d x)+a^2 b d \left(2 c^2+c d x-3 d^2 x^2\right)+a b^2 c \left(-c^2+c d x+2 d^2 x^2\right)-3 b^3 c^2 x (c+d x)}{a^2 c^2 x \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}","\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,"(-3*b^3*c^2*x*(c + d*x) - a^3*d^2*(c + 3*d*x) + a^2*b*d*(2*c^2 + c*d*x - 3*d^2*x^2) + a*b^2*c*(-c^2 + c*d*x + 2*d^2*x^2))/(a^2*c^2*(b*c - a*d)^2*x*Sqrt[a + b*x]*Sqrt[c + d*x]) + (3*(b*c + a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(a^(5/2)*c^(5/2))","A",1
783,1,254,268,0.2920565,"\int \frac{1}{x^3 (a+b x)^{3/2} (c+d x)^{3/2}} \, dx","Integrate[1/(x^3*(a + b*x)^(3/2)*(c + d*x)^(3/2)),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{a^4 d^2 \left(2 c^2-5 c d x-15 d^2 x^2\right)+a^3 b d \left(-4 c^3+5 c^2 d x+2 c d^2 x^2-15 d^3 x^3\right)+a^2 b^2 c \left(2 c^3+5 c^2 d x+10 c d^2 x^2+7 d^3 x^3\right)+a b^3 c^2 x \left(-5 c^2+2 c d x+7 d^2 x^2\right)-15 b^4 c^3 x^2 (c+d x)}{4 a^3 c^3 x^2 \sqrt{a+b x} \sqrt{c+d x} (b c-a d)^2}","\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,"-1/4*(-15*b^4*c^3*x^2*(c + d*x) + a^4*d^2*(2*c^2 - 5*c*d*x - 15*d^2*x^2) + a*b^3*c^2*x*(-5*c^2 + 2*c*d*x + 7*d^2*x^2) + a^3*b*d*(-4*c^3 + 5*c^2*d*x + 2*c*d^2*x^2 - 15*d^3*x^3) + a^2*b^2*c*(2*c^3 + 5*c^2*d*x + 10*c*d^2*x^2 + 7*d^3*x^3))/(a^3*c^3*(b*c - a*d)^2*x^2*Sqrt[a + b*x]*Sqrt[c + d*x]) - (3*(5*b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(4*a^(7/2)*c^(7/2))","A",1
784,1,214,351,5.5328002,"\int \frac{x^5}{(a+b x)^{3/2} (c+d x)^{5/2}} \, dx","Integrate[x^5/((a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\frac{1}{12} \sqrt{a+b x} \sqrt{c+d x} \left(\frac{24 a^5}{b^3 (a+b x) (b c-a d)^3}-\frac{3 (7 a d+11 b c)}{b^3 d^4}+\frac{8 c^5}{d^4 (c+d x)^2 (b c-a d)^2}+\frac{40 c^4 (2 b c-3 a d)}{d^4 (c+d x) (a d-b c)^3}+\frac{6 x}{b^2 d^3}\right)+\frac{5 \left(3 a^2 d^2+6 a b c d+7 b^2 c^2\right) \log \left(2 \sqrt{b} \sqrt{d} \sqrt{a+b x} \sqrt{c+d x}+a d+b c+2 b d x\right)}{8 b^{7/2} d^{9/2}}","-\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,"(Sqrt[a + b*x]*Sqrt[c + d*x]*((-3*(11*b*c + 7*a*d))/(b^3*d^4) + (6*x)/(b^2*d^3) + (24*a^5)/(b^3*(b*c - a*d)^3*(a + b*x)) + (8*c^5)/(d^4*(b*c - a*d)^2*(c + d*x)^2) + (40*c^4*(2*b*c - 3*a*d))/(d^4*(-(b*c) + a*d)^3*(c + d*x))))/12 + (5*(7*b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*Log[b*c + a*d + 2*b*d*x + 2*Sqrt[b]*Sqrt[d]*Sqrt[a + b*x]*Sqrt[c + d*x]])/(8*b^(7/2)*d^(9/2))","A",1
785,1,285,251,0.7111932,"\int \frac{x^4}{(a+b x)^{3/2} (c+d x)^{5/2}} \, dx","Integrate[x^4/((a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\frac{-a b d^{5/2} (3 a d-b c) \left(a^2 \left(8 c^2+12 c d x+3 d^2 x^2\right)+2 a b c x (2 c+3 d x)-b^2 c^2 x^2\right)+3 b^2 d^{5/2} x^3 (b c-a d)^3-\sqrt{a+b x} (b c-a d) (3 a d+5 b c) \left(b c^2 \sqrt{d} \sqrt{a+b x} (b c-a d)-(c+d x) \left(2 b c \sqrt{d} \sqrt{a+b x} (2 b c-3 a d)-3 (b c-a d)^{5/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)\right)}{3 b^3 d^{7/2} \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^3}","\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,"(3*b^2*d^(5/2)*(b*c - a*d)^3*x^3 - a*b*d^(5/2)*(-(b*c) + 3*a*d)*(-(b^2*c^2*x^2) + 2*a*b*c*x*(2*c + 3*d*x) + a^2*(8*c^2 + 12*c*d*x + 3*d^2*x^2)) - (b*c - a*d)*(5*b*c + 3*a*d)*Sqrt[a + b*x]*(b*c^2*Sqrt[d]*(b*c - a*d)*Sqrt[a + b*x] - (c + d*x)*(2*b*c*Sqrt[d]*(2*b*c - 3*a*d)*Sqrt[a + b*x] - 3*(b*c - a*d)^(5/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])))/(3*b^3*d^(7/2)*(b*c - a*d)^3*Sqrt[a + b*x]*(c + d*x)^(3/2))","A",1
786,1,160,165,5.3122195,"\int \frac{x^3}{(a+b x)^{3/2} (c+d x)^{5/2}} \, dx","Integrate[x^3/((a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\frac{2}{3} \sqrt{a+b x} \sqrt{c+d x} \left(\frac{3 a^3}{b (a+b x) (b c-a d)^3}+\frac{c^3}{d^2 (c+d x)^2 (b c-a d)^2}+\frac{c^2 (4 b c-9 a d)}{d^2 (c+d x) (a d-b c)^3}\right)+\frac{\log \left(2 \sqrt{b} \sqrt{d} \sqrt{a+b x} \sqrt{c+d x}+a d+b c+2 b d x\right)}{b^{3/2} d^{5/2}}","-\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,"(2*Sqrt[a + b*x]*Sqrt[c + d*x]*((3*a^3)/(b*(b*c - a*d)^3*(a + b*x)) + c^3/(d^2*(b*c - a*d)^2*(c + d*x)^2) + (c^2*(4*b*c - 9*a*d))/(d^2*(-(b*c) + a*d)^3*(c + d*x))))/3 + Log[b*c + a*d + 2*b*d*x + 2*Sqrt[b]*Sqrt[d]*Sqrt[a + b*x]*Sqrt[c + d*x]]/(b^(3/2)*d^(5/2))","A",1
787,1,82,151,0.044784,"\int \frac{x^2}{(a+b x)^{3/2} (c+d x)^{5/2}} \, dx","Integrate[x^2/((a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\frac{-2 a^2 \left(8 c^2+12 c d x+3 d^2 x^2\right)-4 a b c x (2 c+3 d x)+2 b^2 c^2 x^2}{3 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^3}","\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,"(2*b^2*c^2*x^2 - 4*a*b*c*x*(2*c + 3*d*x) - 2*a^2*(8*c^2 + 12*c*d*x + 3*d^2*x^2))/(3*(b*c - a*d)^3*Sqrt[a + b*x]*(c + d*x)^(3/2))","A",1
788,1,83,118,0.0290177,"\int \frac{x}{(a+b x)^{3/2} (c+d x)^{5/2}} \, dx","Integrate[x/((a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\frac{2 \left(a^2 d (2 c+3 d x)+2 a b \left(3 c^2+5 c d x+3 d^2 x^2\right)+b^2 c x (3 c+2 d x)\right)}{3 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^3}","\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,"(2*(b^2*c*x*(3*c + 2*d*x) + a^2*d*(2*c + 3*d*x) + 2*a*b*(3*c^2 + 5*c*d*x + 3*d^2*x^2)))/(3*(b*c - a*d)^3*Sqrt[a + b*x]*(c + d*x)^(3/2))","A",1
789,1,78,98,0.024808,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{5/2}} \, dx","Integrate[1/((a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\frac{2 a^2 d^2-4 a b d (3 c+2 d x)-2 b^2 \left(3 c^2+12 c d x+8 d^2 x^2\right)}{3 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^3}","-\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,"(2*a^2*d^2 - 4*a*b*d*(3*c + 2*d*x) - 2*b^2*(3*c^2 + 12*c*d*x + 8*d^2*x^2))/(3*(b*c - a*d)^3*Sqrt[a + b*x]*(c + d*x)^(3/2))","A",1
790,1,158,180,0.4139614,"\int \frac{1}{x (a+b x)^{3/2} (c+d x)^{5/2}} \, dx","Integrate[1/(x*(a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\frac{2 \left(-a^3 d^3 (4 c+3 d x)+a^2 b d^2 \left(9 c^2+4 c d x-3 d^2 x^2\right)+a b^2 c d^2 x (9 c+8 d x)+3 b^3 c^2 (c+d x)^2\right)}{3 a c^2 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^3}-\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 \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,"(2*(3*b^3*c^2*(c + d*x)^2 - a^3*d^3*(4*c + 3*d*x) + a*b^2*c*d^2*x*(9*c + 8*d*x) + a^2*b*d^2*(9*c^2 + 4*c*d*x - 3*d^2*x^2)))/(3*a*c^2*(b*c - a*d)^3*Sqrt[a + b*x]*(c + d*x)^(3/2)) - (2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/(a^(3/2)*c^(5/2))","A",1
791,1,263,264,0.5812142,"\int \frac{1}{x^2 (a+b x)^{3/2} (c+d x)^{5/2}} \, dx","Integrate[1/(x^2*(a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\frac{-\frac{d \sqrt{a+b x} \left(5 a^2 d^2-6 a b c d+9 b^2 c^2\right)}{a c (b c-a d)^2}+\frac{(c+d x) \left(\sqrt{a} \sqrt{c} 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 \sqrt{c+d x} (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)\right)}{a^{3/2} c^{5/2} (b c-a d)^3}-\frac{3 b (a d-3 b c)}{a \sqrt{a+b x} (a d-b c)}-\frac{3}{x \sqrt{a+b x}}}{3 a c (c+d x)^{3/2}}","\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,"((-3*b*(-3*b*c + a*d))/(a*(-(b*c) + a*d)*Sqrt[a + b*x]) - 3/(x*Sqrt[a + b*x]) - (d*(9*b^2*c^2 - 6*a*b*c*d + 5*a^2*d^2)*Sqrt[a + b*x])/(a*c*(b*c - a*d)^2) + ((c + d*x)*(Sqrt[a]*Sqrt[c]*d*(-9*b^3*c^3 + 9*a*b^2*c^2*d - 31*a^2*b*c*d^2 + 15*a^3*d^3)*Sqrt[a + b*x] + 3*(b*c - a*d)^3*(3*b*c + 5*a*d)*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(3/2)*c^(5/2)*(b*c - a*d)^3))/(3*a*c*(c + d*x)^(3/2))","A",1
792,1,374,361,0.7386201,"\int \frac{1}{x^3 (a+b x)^{3/2} (c+d x)^{5/2}} \, dx","Integrate[1/(x^3*(a + b*x)^(3/2)*(c + d*x)^(5/2)),x]","\frac{3 a^{3/2} c^{5/2} x (b c-a d)^3 (7 a d+5 b c)+6 a^{5/2} c^{7/2} (a d-b c)^3-3 \sqrt{a} c^{5/2} x^2 (b c-a d)^2 \left(7 a^2 b d^2-15 b^3 c^2\right)+x^2 \left(-\sqrt{a} c^{3/2} d (a+b x) (a d-b c) \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)-\sqrt{a+b x} (c+d x) \left(15 \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)^3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)+\sqrt{a} \sqrt{c} 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)\right)\right)}{12 a^{7/2} c^{9/2} x^2 \sqrt{a+b x} (c+d x)^{3/2} (b c-a d)^3}","\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,"(6*a^(5/2)*c^(7/2)*(-(b*c) + a*d)^3 + 3*a^(3/2)*c^(5/2)*(b*c - a*d)^3*(5*b*c + 7*a*d)*x - 3*Sqrt[a]*c^(5/2)*(b*c - a*d)^2*(-15*b^3*c^2 + 7*a^2*b*d^2)*x^2 + x^2*(-(Sqrt[a]*c^(3/2)*d*(-(b*c) + a*d)*(45*b^3*c^3 - 15*a*b^2*c^2*d - 33*a^2*b*c*d^2 + 35*a^3*d^3)*(a + b*x)) - Sqrt[a + b*x]*(c + d*x)*(Sqrt[a]*Sqrt[c]*d*(-45*b^4*c^4 + 30*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 - 190*a^3*b*c*d^3 + 105*a^4*d^4)*Sqrt[a + b*x] + 15*(b*c - a*d)^3*(3*b^2*c^2 + 6*a*b*c*d + 7*a^2*d^2)*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])))/(12*a^(7/2)*c^(9/2)*(b*c - a*d)^3*x^2*Sqrt[a + b*x]*(c + d*x)^(3/2))","A",1
793,1,391,497,1.8575861,"\int \frac{x^4 (c+d x)^{5/2}}{(a+b x)^{5/2}} \, dx","Integrate[(x^4*(c + d*x)^(5/2))/(a + b*x)^(5/2),x]","\frac{\sqrt{c+d x} \left(\frac{15 \sqrt{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) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{\frac{b (c+d x)}{b c-a d}}}+\frac{\sqrt{d} \left(45045 a^6 d^4+2310 a^5 b d^3 (26 d x-31 c)+21 a^4 b^2 d^2 \left(1304 c^2-4642 c d x+429 d^2 x^2\right)-6 a^3 b^3 d \left(65 c^3-6441 c^2 d x+2673 c d^2 x^2+429 d^3 x^3\right)+a^2 b^4 \left(-45 c^4-750 c^3 d x+7404 c^2 d^2 x^2+4378 c d^3 x^3+1144 d^4 x^4\right)-2 a b^5 x \left(45 c^4+165 c^3 d x+917 c^2 d^2 x^2+944 c d^3 x^3+312 d^4 x^4\right)+3 b^6 x^2 \left(-15 c^4+10 c^3 d x+248 c^2 d^2 x^2+336 c d^3 x^3+128 d^4 x^4\right)\right)}{(a+b x)^{3/2}}\right)}{1920 b^7 d^{5/2}}","-\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,"(Sqrt[c + d*x]*((Sqrt[d]*(45045*a^6*d^4 + 2310*a^5*b*d^3*(-31*c + 26*d*x) + 21*a^4*b^2*d^2*(1304*c^2 - 4642*c*d*x + 429*d^2*x^2) - 6*a^3*b^3*d*(65*c^3 - 6441*c^2*d*x + 2673*c*d^2*x^2 + 429*d^3*x^3) + 3*b^6*x^2*(-15*c^4 + 10*c^3*d*x + 248*c^2*d^2*x^2 + 336*c*d^3*x^3 + 128*d^4*x^4) - 2*a*b^5*x*(45*c^4 + 165*c^3*d*x + 917*c^2*d^2*x^2 + 944*c*d^3*x^3 + 312*d^4*x^4) + a^2*b^4*(-45*c^4 - 750*c^3*d*x + 7404*c^2*d^2*x^2 + 4378*c*d^3*x^3 + 1144*d^4*x^4)))/(a + b*x)^(3/2) + (15*Sqrt[b*c - a*d]*(3*b^4*c^4 + 28*a*b^3*c^3*d + 378*a^2*b^2*c^2*d^2 - 2772*a^3*b*c*d^3 + 3003*a^4*d^4)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[(b*(c + d*x))/(b*c - a*d)]))/(1920*b^7*d^(5/2))","A",1
794,1,302,377,1.1319233,"\int \frac{x^3 (c+d x)^{5/2}}{(a+b x)^{5/2}} \, dx","Integrate[(x^3*(c + d*x)^(5/2))/(a + b*x)^(5/2),x]","\frac{\sqrt{c+d x} \left(\frac{\sqrt{d} \left(-3465 a^5 d^3+105 a^4 b d^2 (49 c-44 d x)-21 a^3 b^2 d \left(83 c^2-334 c d x+33 d^2 x^2\right)+3 a^2 b^3 \left(5 c^3-824 c^2 d x+387 c d^2 x^2+66 d^3 x^3\right)-a b^4 x \left(-30 c^3+483 c^2 d x+316 c d^2 x^2+88 d^3 x^3\right)+b^5 x^2 \left(15 c^3+118 c^2 d x+136 c d^2 x^2+48 d^3 x^3\right)\right)}{(a+b x)^{3/2}}-\frac{15 \sqrt{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) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{192 b^6 d^{3/2}}","\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,"(Sqrt[c + d*x]*((Sqrt[d]*(-3465*a^5*d^3 + 105*a^4*b*d^2*(49*c - 44*d*x) - 21*a^3*b^2*d*(83*c^2 - 334*c*d*x + 33*d^2*x^2) + b^5*x^2*(15*c^3 + 118*c^2*d*x + 136*c*d^2*x^2 + 48*d^3*x^3) + 3*a^2*b^3*(5*c^3 - 824*c^2*d*x + 387*c*d^2*x^2 + 66*d^3*x^3) - a*b^4*x*(-30*c^3 + 483*c^2*d*x + 316*c*d^2*x^2 + 88*d^3*x^3)))/(a + b*x)^(3/2) - (15*Sqrt[b*c - a*d]*(b^3*c^3 + 21*a*b^2*c^2*d - 189*a^2*b*c*d^2 + 231*a^3*d^3)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/Sqrt[(b*(c + d*x))/(b*c - a*d)]))/(192*b^6*d^(3/2))","A",1
795,1,218,319,0.8015395,"\int \frac{x^2 (c+d x)^{5/2}}{(a+b x)^{5/2}} \, dx","Integrate[(x^2*(c + d*x)^(5/2))/(a + b*x)^(5/2),x]","\frac{\sqrt{c+d x} \left(\frac{15 \sqrt{b c-a d} \left(21 a^2 d^2-14 a b c d+b^2 c^2\right) \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{d} \sqrt{\frac{b (c+d x)}{b c-a d}}}+\frac{315 a^4 d^2+420 a^3 b d (d x-c)+a^2 b^2 \left(113 c^2-574 c d x+63 d^2 x^2\right)-6 a b^3 x \left(-27 c^2+16 c d x+3 d^2 x^2\right)+b^4 x^2 \left(33 c^2+26 c d x+8 d^2 x^2\right)}{(a+b x)^{3/2}}\right)}{24 b^5}","-\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,"(Sqrt[c + d*x]*((315*a^4*d^2 + 420*a^3*b*d*(-c + d*x) - 6*a*b^3*x*(-27*c^2 + 16*c*d*x + 3*d^2*x^2) + b^4*x^2*(33*c^2 + 26*c*d*x + 8*d^2*x^2) + a^2*b^2*(113*c^2 - 574*c*d*x + 63*d^2*x^2))/(a + b*x)^(3/2) + (15*Sqrt[b*c - a*d]*(b^2*c^2 - 14*a*b*c*d + 21*a^2*d^2)*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[d]*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(24*b^5)","A",1
796,1,122,222,0.1205698,"\int \frac{x (c+d x)^{5/2}}{(a+b x)^{5/2}} \, dx","Integrate[(x*(c + d*x)^(5/2))/(a + b*x)^(5/2),x]","\frac{2 \sqrt{c+d x} \left(a b^3 (c+d x)^3-\frac{(a+b x) (3 b c-7 a d) (b c-a d)^2 \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{\sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{3 b^4 (a+b x)^{3/2} (b c-a d)}","\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,"(2*Sqrt[c + d*x]*(a*b^3*(c + d*x)^3 - ((3*b*c - 7*a*d)*(b*c - a*d)^2*(a + b*x)*Hypergeometric2F1[-5/2, -1/2, 1/2, (d*(a + b*x))/(-(b*c) + a*d)])/Sqrt[(b*(c + d*x))/(b*c - a*d)]))/(3*b^4*(b*c - a*d)*(a + b*x)^(3/2))","C",1
797,1,73,128,0.0678417,"\int \frac{(c+d x)^{5/2}}{(a+b x)^{5/2}} \, dx","Integrate[(c + d*x)^(5/2)/(a + b*x)^(5/2),x]","-\frac{2 (c+d x)^{5/2} \, _2F_1\left(-\frac{5}{2},-\frac{3}{2};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{3 b (a+b x)^{3/2} \left(\frac{b (c+d x)}{b c-a d}\right)^{5/2}}","\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,"(-2*(c + d*x)^(5/2)*Hypergeometric2F1[-5/2, -3/2, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(3*b*(a + b*x)^(3/2)*((b*(c + d*x))/(b*c - a*d))^(5/2))","C",1
798,1,163,157,0.4030444,"\int \frac{(c+d x)^{5/2}}{x (a+b x)^{5/2}} \, dx","Integrate[(c + d*x)^(5/2)/(x*(a + b*x)^(5/2)),x]","\frac{2 \left(-\frac{3 c^{5/2} (a+b x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)}{a^{5/2}}+\frac{c \sqrt{c+d x} (4 a c+a d x+3 b c x)}{a^2}+\frac{d \sqrt{c+d x} (a d-b c) \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};\frac{d (a+b x)}{a d-b c}\right)}{b^2 \sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{3 (a+b x)^{3/2}}","-\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,"(2*((c*Sqrt[c + d*x]*(4*a*c + 3*b*c*x + a*d*x))/a^2 - (3*c^(5/2)*(a + b*x)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])/a^(5/2) + (d*(-(b*c) + a*d)*Sqrt[c + d*x]*Hypergeometric2F1[-3/2, -3/2, -1/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b^2*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(3*(a + b*x)^(3/2))","C",1
799,1,125,142,0.1648405,"\int \frac{(c+d x)^{5/2}}{x^2 (a+b x)^{5/2}} \, dx","Integrate[(c + d*x)^(5/2)/(x^2*(a + b*x)^(5/2)),x]","-\frac{3 a^{5/2} (c+d x)^{5/2}+5 x (b c-a d) \left(\sqrt{a} \sqrt{c+d x} (4 a c+a d x+3 b c x)-3 c^{3/2} (a+b x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)}{3 a^{7/2} x (a+b x)^{3/2}}","\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,"-1/3*(3*a^(5/2)*(c + d*x)^(5/2) + 5*(b*c - a*d)*x*(Sqrt[a]*Sqrt[c + d*x]*(4*a*c + 3*b*c*x + a*d*x) - 3*c^(3/2)*(a + b*x)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(7/2)*x*(a + b*x)^(3/2))","A",1
800,1,159,220,0.2218845,"\int \frac{(c+d x)^{5/2}}{x^3 (a+b x)^{5/2}} \, dx","Integrate[(c + d*x)^(5/2)/(x^3*(a + b*x)^(5/2)),x]","\frac{\frac{1}{2} x (7 b c-3 a d) \left(3 a^{5/2} (c+d x)^{5/2}+5 x (b c-a d) \left(\sqrt{a} \sqrt{c+d x} (4 a c+a d x+3 b c x)-3 c^{3/2} (a+b x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)\right)-3 a^{7/2} (c+d x)^{7/2}}{6 a^{9/2} c x^2 (a+b x)^{3/2}}","-\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,"(-3*a^(7/2)*(c + d*x)^(7/2) + ((7*b*c - 3*a*d)*x*(3*a^(5/2)*(c + d*x)^(5/2) + 5*(b*c - a*d)*x*(Sqrt[a]*Sqrt[c + d*x]*(4*a*c + 3*b*c*x + a*d*x) - 3*c^(3/2)*(a + b*x)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])))/2)/(6*a^(9/2)*c*x^2*(a + b*x)^(3/2))","A",1
801,1,199,278,0.324148,"\int \frac{(c+d x)^{5/2}}{x^4 (a+b x)^{5/2}} \, dx","Integrate[(c + d*x)^(5/2)/(x^4*(a + b*x)^(5/2)),x]","\frac{2 a^{7/2} x (c+d x)^{7/2} (9 b c-a d)-8 a^{9/2} c (c+d x)^{7/2}-x^2 \left(a^2 d^2-14 a b c d+21 b^2 c^2\right) \left(3 a^{5/2} (c+d x)^{5/2}+5 x (b c-a d) \left(\sqrt{a} \sqrt{c+d x} (4 a c+a d x+3 b c x)-3 c^{3/2} (a+b x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)\right)}{24 a^{11/2} c^2 x^3 (a+b x)^{3/2}}","-\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,"(-8*a^(9/2)*c*(c + d*x)^(7/2) + 2*a^(7/2)*(9*b*c - a*d)*x*(c + d*x)^(7/2) - (21*b^2*c^2 - 14*a*b*c*d + a^2*d^2)*x^2*(3*a^(5/2)*(c + d*x)^(5/2) + 5*(b*c - a*d)*x*(Sqrt[a]*Sqrt[c + d*x]*(4*a*c + 3*b*c*x + a*d*x) - 3*c^(3/2)*(a + b*x)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])))/(24*a^(11/2)*c^2*x^3*(a + b*x)^(3/2))","A",1
802,1,256,388,0.5236009,"\int \frac{(c+d x)^{5/2}}{x^5 (a+b x)^{5/2}} \, dx","Integrate[(c + d*x)^(5/2)/(x^5*(a + b*x)^(5/2)),x]","\frac{8 a^{9/2} c x (c+d x)^{7/2} (a d+11 b c)-48 a^{11/2} c^2 (c+d x)^{7/2}-2 a^{7/2} x^2 (c+d x)^{7/2} \left(-a^2 d^2-26 a b c d+99 b^2 c^2\right)+x^3 \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) \left(3 a^{5/2} (c+d x)^{5/2}+5 x (b c-a d) \left(\sqrt{a} \sqrt{c+d x} (4 a c+a d x+3 b c x)-3 c^{3/2} (a+b x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)\right)\right)}{192 a^{13/2} c^3 x^4 (a+b x)^{3/2}}","-\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,"(-48*a^(11/2)*c^2*(c + d*x)^(7/2) + 8*a^(9/2)*c*(11*b*c + a*d)*x*(c + d*x)^(7/2) - 2*a^(7/2)*(99*b^2*c^2 - 26*a*b*c*d - a^2*d^2)*x^2*(c + d*x)^(7/2) + (231*b^3*c^3 - 189*a*b^2*c^2*d + 21*a^2*b*c*d^2 + a^3*d^3)*x^3*(3*a^(5/2)*(c + d*x)^(5/2) + 5*(b*c - a*d)*x*(Sqrt[a]*Sqrt[c + d*x]*(4*a*c + 3*b*c*x + a*d*x) - 3*c^(3/2)*(a + b*x)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])))/(192*a^(13/2)*c^3*x^4*(a + b*x)^(3/2))","A",1
803,1,198,126,0.4634465,"\int \frac{x^2}{(a+b x)^{5/2} \sqrt{c+d x}} \, dx","Integrate[x^2/((a + b*x)^(5/2)*Sqrt[c + d*x]),x]","\frac{2 \sqrt{c+d x} \left(\frac{(a+b x) \left(3 b^2 c^2-a^2 d^2\right)}{d (b c-a d)^2}+\frac{a^2}{a d-b c}-\frac{3 (a+b x) \left(\sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}-\sqrt{d} \sqrt{a+b x} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)}{d \sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}}\right)}{3 b^2 (a+b x)^{3/2}}","-\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,"(2*Sqrt[c + d*x]*(a^2/(-(b*c) + a*d) + ((3*b^2*c^2 - a^2*d^2)*(a + b*x))/(d*(b*c - a*d)^2) - (3*(a + b*x)*(Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)] - Sqrt[d]*Sqrt[a + b*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]]))/(d*Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)])))/(3*b^2*(a + b*x)^(3/2))","A",1
804,1,246,445,5.8158817,"\int \frac{x^6}{(a+b x)^{5/2} (c+d x)^{5/2}} \, dx","Integrate[x^6/((a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\frac{5 \left(7 a^2 d^2+10 a b c d+7 b^2 c^2\right) \log \left(2 \sqrt{b} \sqrt{d} \sqrt{a+b x} \sqrt{c+d x}+a d+b c+2 b d x\right)}{8 b^{9/2} d^{9/2}}+\frac{1}{12} \sqrt{a+b x} \sqrt{c+d x} \left(-\frac{8 a^6}{b^4 (a+b x)^2 (b c-a d)^3}-\frac{16 a^5 (5 a d-9 b c)}{b^4 (a+b x) (b c-a d)^4}-\frac{33 (a d+b c)}{b^4 d^4}-\frac{8 c^6}{d^4 (c+d x)^2 (a d-b c)^3}-\frac{16 c^5 (5 b c-9 a d)}{d^4 (c+d x) (b c-a d)^4}+\frac{6 x}{b^3 d^3}\right)","-\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,"(Sqrt[a + b*x]*Sqrt[c + d*x]*((-33*(b*c + a*d))/(b^4*d^4) + (6*x)/(b^3*d^3) - (8*a^6)/(b^4*(b*c - a*d)^3*(a + b*x)^2) - (16*a^5*(-9*b*c + 5*a*d))/(b^4*(b*c - a*d)^4*(a + b*x)) - (8*c^6)/(d^4*(-(b*c) + a*d)^3*(c + d*x)^2) - (16*c^5*(5*b*c - 9*a*d))/(d^4*(b*c - a*d)^4*(c + d*x))))/12 + (5*(7*b^2*c^2 + 10*a*b*c*d + 7*a^2*d^2)*Log[b*c + a*d + 2*b*d*x + 2*Sqrt[b]*Sqrt[d]*Sqrt[a + b*x]*Sqrt[c + d*x]])/(8*b^(9/2)*d^(9/2))","A",1
805,1,1498,341,8.3749644,"\int \frac{x^5}{(a+b x)^{5/2} (c+d x)^{5/2}} \, dx","Integrate[x^5/((a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\frac{x^4}{b d (a+b x)^{3/2} (c+d x)^{3/2}}+\frac{\frac{\left(\frac{5}{2} a (b c+a d)-4 a b c\right) \left(\frac{2 c \left(\frac{2 \left(\frac{4 \left(\frac{1}{2} a b d (b c+3 a d)-\frac{1}{2} b \left(\frac{b c}{2}-\frac{3 a d}{2}\right) (b c-a d)\right) \sqrt{a+b x}}{3 d (b c-a d) (a d-b c) \sqrt{c+d x}}-\frac{2 \left(-\frac{1}{2} b c (b c-a d)-\frac{1}{2} a d (b c+3 a d)\right) \sqrt{a+b x}}{3 d (a d-b c) (c+d x)^{3/2}}\right)}{b^2 (b c-a d)}-\frac{2 a^2}{b^2 (b c-a d) \sqrt{a+b x} (c+d x)^{3/2}}\right)}{b c-a d}-\frac{2 x^3}{3 (b c-a d) (a+b x)^{3/2} (c+d x)^{3/2}}\right)}{b}-\frac{5 a^3 (b c+a d) \left(\frac{b}{\frac{b^2 c}{b c-a d}-\frac{a b d}{b c-a d}}\right)^{5/2} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(\frac{56 d^2 \, _2F_1\left(\frac{3}{2},\frac{9}{2};\frac{11}{2};\frac{d (a+b x)}{a d-b c}\right) (a+b x)^5}{a^3 (b c-a d)^2}-\frac{280 d^2 \, _2F_1\left(\frac{3}{2},\frac{9}{2};\frac{11}{2};\frac{d (a+b x)}{a d-b c}\right) (a+b x)^4}{a^2 (b c-a d)^2}+\frac{96 d \, _4F_3\left(\frac{1}{2},2,2,\frac{7}{2};1,1,\frac{9}{2};\frac{d (a+b x)}{a d-b c}\right) (a+b x)^4}{a^3 (a d-b c)}+\frac{294 \sin ^{-1}\left(\sqrt{\frac{d (a+b x)}{a d-b c}}\right) (a+b x)^3}{a^3 \left(\frac{d (a+b x)}{a d-b c}\right)^{5/2}}+\frac{392 d^2 \, _2F_1\left(\frac{3}{2},\frac{9}{2};\frac{11}{2};\frac{d (a+b x)}{a d-b c}\right) (a+b x)^3}{a (b c-a d)^2}-\frac{288 d \, _4F_3\left(\frac{1}{2},2,2,\frac{7}{2};1,1,\frac{9}{2};\frac{d (a+b x)}{a d-b c}\right) (a+b x)^3}{a^2 (a d-b c)}-\frac{1575 \sin ^{-1}\left(\sqrt{\frac{d (a+b x)}{a d-b c}}\right) (a+b x)^2}{a^2 \left(\frac{d (a+b x)}{a d-b c}\right)^{5/2}}-\frac{168 d^2 \, _2F_1\left(\frac{3}{2},\frac{9}{2};\frac{11}{2};\frac{d (a+b x)}{a d-b c}\right) (a+b x)^2}{(b c-a d)^2}+\frac{288 d \, _4F_3\left(\frac{1}{2},2,2,\frac{7}{2};1,1,\frac{9}{2};\frac{d (a+b x)}{a d-b c}\right) (a+b x)^2}{a (a d-b c)}+\frac{196 b (c+d x) (a+b x)^2}{a^3 d \sqrt{\frac{b (c+d x)}{b c-a d}}}+\frac{3780 \sin ^{-1}\left(\sqrt{\frac{d (a+b x)}{a d-b c}}\right) (a+b x)}{a \left(\frac{d (a+b x)}{a d-b c}\right)^{5/2}}-\frac{96 d \, _4F_3\left(\frac{1}{2},2,2,\frac{7}{2};1,1,\frac{9}{2};\frac{d (a+b x)}{a d-b c}\right) (a+b x)}{a d-b c}-\frac{294 (b c-a d)^2 \sqrt{\frac{b (c+d x)}{b c-a d}} (a+b x)}{a^3 d^2}-\frac{1050 b (c+d x) (a+b x)}{a^2 d \sqrt{\frac{b (c+d x)}{b c-a d}}}-\frac{1995 \sin ^{-1}\left(\sqrt{\frac{d (a+b x)}{a d-b c}}\right)}{\left(\frac{d (a+b x)}{a d-b c}\right)^{5/2}}-56 \left(\frac{b x}{a}+1\right)^3 \sqrt{\frac{b (c+d x)}{b c-a d}}+\frac{1575 (b c-a d)^2 \sqrt{\frac{b (c+d x)}{b c-a d}}}{a^2 d^2}+336 \left(\frac{b x}{a}+1\right)^2 \sqrt{\frac{b (c+d x)}{b c-a d}}-504 \left(\frac{b x}{a}+1\right) \sqrt{\frac{b (c+d x)}{b c-a d}}+1568 \sqrt{\frac{b (c+d x)}{b c-a d}}+\frac{2520 b (c+d x)}{a d \sqrt{\frac{b (c+d x)}{b c-a d}}}-\frac{3780 (b c-a d)^2 \sqrt{\frac{b (c+d x)}{b c-a d}}}{a d^2 (a+b x)}-\frac{1330 b (c+d x)}{d \sqrt{\frac{b (c+d x)}{b c-a d}} (a+b x)}+\frac{1995 (b c-a d)^2 \sqrt{\frac{b (c+d x)}{b c-a d}}}{d^2 (a+b x)^2}\right)}{504 b^3 (b c-a d)^2 \sqrt{a+b x} \sqrt{c+d x}}}{b d}","-\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,"x^4/(b*d*(a + b*x)^(3/2)*(c + d*x)^(3/2)) + (((-4*a*b*c + (5*a*(b*c + a*d))/2)*((-2*x^3)/(3*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2)) + (2*c*((-2*a^2)/(b^2*(b*c - a*d)*Sqrt[a + b*x]*(c + d*x)^(3/2)) + (2*((-2*(-1/2*(b*c*(b*c - a*d)) - (a*d*(b*c + 3*a*d))/2)*Sqrt[a + b*x])/(3*d*(-(b*c) + a*d)*(c + d*x)^(3/2)) + (4*(-1/2*(b*((b*c)/2 - (3*a*d)/2)*(b*c - a*d)) + (a*b*d*(b*c + 3*a*d))/2)*Sqrt[a + b*x])/(3*d*(b*c - a*d)*(-(b*c) + a*d)*Sqrt[c + d*x])))/(b^2*(b*c - a*d))))/(b*c - a*d)))/b - (5*a^3*(b*c + a*d)*(b/((b^2*c)/(b*c - a*d) - (a*b*d)/(b*c - a*d)))^(5/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*((2520*b*(c + d*x))/(a*d*Sqrt[(b*(c + d*x))/(b*c - a*d)]) - (1330*b*(c + d*x))/(d*(a + b*x)*Sqrt[(b*(c + d*x))/(b*c - a*d)]) - (1050*b*(a + b*x)*(c + d*x))/(a^2*d*Sqrt[(b*(c + d*x))/(b*c - a*d)]) + (196*b*(a + b*x)^2*(c + d*x))/(a^3*d*Sqrt[(b*(c + d*x))/(b*c - a*d)]) + 1568*Sqrt[(b*(c + d*x))/(b*c - a*d)] + (1575*(b*c - a*d)^2*Sqrt[(b*(c + d*x))/(b*c - a*d)])/(a^2*d^2) + (1995*(b*c - a*d)^2*Sqrt[(b*(c + d*x))/(b*c - a*d)])/(d^2*(a + b*x)^2) - (3780*(b*c - a*d)^2*Sqrt[(b*(c + d*x))/(b*c - a*d)])/(a*d^2*(a + b*x)) - (294*(b*c - a*d)^2*(a + b*x)*Sqrt[(b*(c + d*x))/(b*c - a*d)])/(a^3*d^2) - 504*(1 + (b*x)/a)*Sqrt[(b*(c + d*x))/(b*c - a*d)] + 336*(1 + (b*x)/a)^2*Sqrt[(b*(c + d*x))/(b*c - a*d)] - 56*(1 + (b*x)/a)^3*Sqrt[(b*(c + d*x))/(b*c - a*d)] - (1995*ArcSin[Sqrt[(d*(a + b*x))/(-(b*c) + a*d)]])/((d*(a + b*x))/(-(b*c) + a*d))^(5/2) + (3780*(a + b*x)*ArcSin[Sqrt[(d*(a + b*x))/(-(b*c) + a*d)]])/(a*((d*(a + b*x))/(-(b*c) + a*d))^(5/2)) - (1575*(a + b*x)^2*ArcSin[Sqrt[(d*(a + b*x))/(-(b*c) + a*d)]])/(a^2*((d*(a + b*x))/(-(b*c) + a*d))^(5/2)) + (294*(a + b*x)^3*ArcSin[Sqrt[(d*(a + b*x))/(-(b*c) + a*d)]])/(a^3*((d*(a + b*x))/(-(b*c) + a*d))^(5/2)) - (168*d^2*(a + b*x)^2*Hypergeometric2F1[3/2, 9/2, 11/2, (d*(a + b*x))/(-(b*c) + a*d)])/(b*c - a*d)^2 + (392*d^2*(a + b*x)^3*Hypergeometric2F1[3/2, 9/2, 11/2, (d*(a + b*x))/(-(b*c) + a*d)])/(a*(b*c - a*d)^2) - (280*d^2*(a + b*x)^4*Hypergeometric2F1[3/2, 9/2, 11/2, (d*(a + b*x))/(-(b*c) + a*d)])/(a^2*(b*c - a*d)^2) + (56*d^2*(a + b*x)^5*Hypergeometric2F1[3/2, 9/2, 11/2, (d*(a + b*x))/(-(b*c) + a*d)])/(a^3*(b*c - a*d)^2) - (96*d*(a + b*x)*HypergeometricPFQ[{1/2, 2, 2, 7/2}, {1, 1, 9/2}, (d*(a + b*x))/(-(b*c) + a*d)])/(-(b*c) + a*d) + (288*d*(a + b*x)^2*HypergeometricPFQ[{1/2, 2, 2, 7/2}, {1, 1, 9/2}, (d*(a + b*x))/(-(b*c) + a*d)])/(a*(-(b*c) + a*d)) - (288*d*(a + b*x)^3*HypergeometricPFQ[{1/2, 2, 2, 7/2}, {1, 1, 9/2}, (d*(a + b*x))/(-(b*c) + a*d)])/(a^2*(-(b*c) + a*d)) + (96*d*(a + b*x)^4*HypergeometricPFQ[{1/2, 2, 2, 7/2}, {1, 1, 9/2}, (d*(a + b*x))/(-(b*c) + a*d)])/(a^3*(-(b*c) + a*d))))/(504*b^3*(b*c - a*d)^2*Sqrt[a + b*x]*Sqrt[c + d*x]))/(b*d)","C",0
806,1,194,241,5.4573745,"\int \frac{x^4}{(a+b x)^{5/2} (c+d x)^{5/2}} \, dx","Integrate[x^4/((a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\frac{2}{3} \sqrt{a+b x} \sqrt{c+d x} \left(-\frac{a^4}{b^2 (a+b x)^2 (b c-a d)^3}-\frac{4 a^3 (a d-3 b c)}{b^2 (a+b x) (b c-a d)^4}-\frac{c^4}{d^2 (c+d x)^2 (a d-b c)^3}-\frac{4 c^3 (b c-3 a d)}{d^2 (c+d x) (b c-a d)^4}\right)+\frac{\log \left(2 \sqrt{b} \sqrt{d} \sqrt{a+b x} \sqrt{c+d x}+a d+b c+2 b d x\right)}{b^{5/2} d^{5/2}}","-\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,"(2*Sqrt[a + b*x]*Sqrt[c + d*x]*(-(a^4/(b^2*(b*c - a*d)^3*(a + b*x)^2)) - (4*a^3*(-3*b*c + a*d))/(b^2*(b*c - a*d)^4*(a + b*x)) - c^4/(d^2*(-(b*c) + a*d)^3*(c + d*x)^2) - (4*c^3*(b*c - 3*a*d))/(d^2*(b*c - a*d)^4*(c + d*x))))/3 + Log[b*c + a*d + 2*b*d*x + 2*Sqrt[b]*Sqrt[d]*Sqrt[a + b*x]*Sqrt[c + d*x]]/(b^(5/2)*d^(5/2))","A",1
807,1,125,189,0.0576007,"\int \frac{x^3}{(a+b x)^{5/2} (c+d x)^{5/2}} \, dx","Integrate[x^3/((a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","-\frac{2 \left(a^3 \left(16 c^3+24 c^2 d x+6 c d^2 x^2-d^3 x^3\right)+3 a^2 b c x \left(8 c^2+12 c d x+3 d^2 x^2\right)+3 a b^2 c^2 x^2 (2 c+3 d x)-b^3 c^3 x^3\right)}{3 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)^4}","\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,"(-2*(-(b^3*c^3*x^3) + 3*a*b^2*c^2*x^2*(2*c + 3*d*x) + 3*a^2*b*c*x*(8*c^2 + 12*c*d*x + 3*d^2*x^2) + a^3*(16*c^3 + 24*c^2*d*x + 6*c*d^2*x^2 - d^3*x^3)))/(3*(b*c - a*d)^4*(a + b*x)^(3/2)*(c + d*x)^(3/2))","A",1
808,1,137,186,0.0537422,"\int \frac{x^2}{(a+b x)^{5/2} (c+d x)^{5/2}} \, dx","Integrate[x^2/((a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\frac{2 \left(a^3 d \left(8 c^2+12 c d x+3 d^2 x^2\right)+a^2 b \left(8 c^3+24 c^2 d x+21 c d^2 x^2+2 d^3 x^3\right)+3 a b^2 c x \left(4 c^2+7 c d x+4 d^2 x^2\right)+b^3 c^2 x^2 (3 c+2 d x)\right)}{3 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)^4}","\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,"(2*(b^3*c^2*x^2*(3*c + 2*d*x) + a^3*d*(8*c^2 + 12*c*d*x + 3*d^2*x^2) + 3*a*b^2*c*x*(4*c^2 + 7*c*d*x + 4*d^2*x^2) + a^2*b*(8*c^3 + 24*c^2*d*x + 21*c*d^2*x^2 + 2*d^3*x^3)))/(3*(b*c - a*d)^4*(a + b*x)^(3/2)*(c + d*x)^(3/2))","A",1
809,1,134,158,0.0444463,"\int \frac{x}{(a+b x)^{5/2} (c+d x)^{5/2}} \, dx","Integrate[x/((a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","-\frac{2 \left(a^3 d^2 (2 c+3 d x)+3 a^2 b d \left(4 c^2+7 c d x+4 d^2 x^2\right)+a b^2 \left(2 c^3+21 c^2 d x+24 c d^2 x^2+8 d^3 x^3\right)+b^3 c x \left(3 c^2+12 c d x+8 d^2 x^2\right)\right)}{3 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)^4}","-\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,"(-2*(a^3*d^2*(2*c + 3*d*x) + 3*a^2*b*d*(4*c^2 + 7*c*d*x + 4*d^2*x^2) + b^3*c*x*(3*c^2 + 12*c*d*x + 8*d^2*x^2) + a*b^2*(2*c^3 + 21*c^2*d*x + 24*c*d^2*x^2 + 8*d^3*x^3)))/(3*(b*c - a*d)^4*(a + b*x)^(3/2)*(c + d*x)^(3/2))","A",1
810,1,118,135,0.04129,"\int \frac{1}{(a+b x)^{5/2} (c+d x)^{5/2}} \, dx","Integrate[1/((a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\frac{-2 a^3 d^3+6 a^2 b d^2 (3 c+2 d x)+6 a b^2 d \left(3 c^2+12 c d x+8 d^2 x^2\right)+b^3 \left(-2 c^3+12 c^2 d x+48 c d^2 x^2+32 d^3 x^3\right)}{3 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)^4}","\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,"(-2*a^3*d^3 + 6*a^2*b*d^2*(3*c + 2*d*x) + 6*a*b^2*d*(3*c^2 + 12*c*d*x + 8*d^2*x^2) + b^3*(-2*c^3 + 12*c^2*d*x + 48*c*d^2*x^2 + 32*d^3*x^3))/(3*(b*c - a*d)^4*(a + b*x)^(3/2)*(c + d*x)^(3/2))","A",1
811,1,265,252,0.576234,"\int \frac{1}{x (a+b x)^{5/2} (c+d x)^{5/2}} \, dx","Integrate[1/(x*(a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\frac{2 \left(-\frac{3 d \sqrt{a+b x} \left(a^2 d^2+10 a b c d-3 b^2 c^2\right)}{a c (b c-a d)^2}-\frac{(c+d x) \left(9 \sqrt{c+d x} (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)-3 \sqrt{a} \sqrt{c} d \sqrt{a+b x} \left(3 a^3 d^3-11 a^2 b c d^2-11 a b^2 c^2 d+3 b^3 c^3\right)\right)}{a^{3/2} c^{5/2} (b c-a d)^3}-\frac{18 b d}{\sqrt{a+b x} (b c-a d)}+\frac{9 b}{a \sqrt{a+b x}}+\frac{3 b}{(a+b x)^{3/2}}\right)}{9 a (c+d x)^{3/2} (b c-a d)}","-\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,"(2*((3*b)/(a + b*x)^(3/2) + (9*b)/(a*Sqrt[a + b*x]) - (18*b*d)/((b*c - a*d)*Sqrt[a + b*x]) - (3*d*(-3*b^2*c^2 + 10*a*b*c*d + a^2*d^2)*Sqrt[a + b*x])/(a*c*(b*c - a*d)^2) - ((c + d*x)*(-3*Sqrt[a]*Sqrt[c]*d*(3*b^3*c^3 - 11*a*b^2*c^2*d - 11*a^2*b*c*d^2 + 3*a^3*d^3)*Sqrt[a + b*x] + 9*(b*c - a*d)^4*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))/(a^(3/2)*c^(5/2)*(b*c - a*d)^3)))/(9*a*(b*c - a*d)*(c + d*x)^(3/2))","A",1
812,1,382,352,0.9090076,"\int \frac{1}{x^2 (a+b x)^{5/2} (c+d x)^{5/2}} \, dx","Integrate[1/(x^2*(a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\frac{-3 a^{3/2} b c^{5/2} x (a d-b c)^3 (3 a d-5 b c)-9 a^{5/2} c^{5/2} (b c-a d)^4+x (a+b x) \left(18 a^{3/2} b c^{5/2} d (5 b c-3 a d) (b c-a d)^2-3 \sqrt{a} c^{3/2} d (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) (a d-b c)+\sqrt{a+b x} (c+d x) \left(45 \sqrt{c+d x} (b c-a d)^4 (a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{c+d x}}\right)-3 \sqrt{a} \sqrt{c} 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)\right)+45 \sqrt{a} b c^{5/2} (a d+b c) (a d-b c)^3\right)}{9 a^{7/2} c^{7/2} x (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)^4}","\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,"(-9*a^(5/2)*c^(5/2)*(b*c - a*d)^4 - 3*a^(3/2)*b*c^(5/2)*(-(b*c) + a*d)^3*(-5*b*c + 3*a*d)*x + x*(a + b*x)*(18*a^(3/2)*b*c^(5/2)*d*(5*b*c - 3*a*d)*(b*c - a*d)^2 + 45*Sqrt[a]*b*c^(5/2)*(-(b*c) + a*d)^3*(b*c + a*d) - 3*Sqrt[a]*c^(3/2)*d*(-(b*c) + a*d)*(-15*b^3*c^3 + 35*a*b^2*c^2*d - 9*a^2*b*c*d^2 + 5*a^3*d^3)*(a + b*x) + Sqrt[a + b*x]*(c + d*x)*(-3*Sqrt[a]*Sqrt[c]*d*(15*b^4*c^4 - 40*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 - 40*a^3*b*c*d^3 + 15*a^4*d^4)*Sqrt[a + b*x] + 45*(b*c - a*d)^4*(b*c + a*d)*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])])))/(9*a^(7/2)*c^(7/2)*(b*c - a*d)^4*x*(a + b*x)^(3/2)*(c + d*x)^(3/2))","A",1
813,1,504,462,1.3933111,"\int \frac{1}{x^3 (a+b x)^{5/2} (c+d x)^{5/2}} \, dx","Integrate[1/(x^3*(a + b*x)^(5/2)*(c + d*x)^(5/2)),x]","\frac{63 a^{5/2} c^{5/2} x (a d+b c) (b c-a d)^4-18 a^{7/2} c^{7/2} (b c-a d)^4-x^2 \left((a+b x) \left(45 \sqrt{a} b c^{5/2} \left(7 a^2 d^2+10 a b c d+7 b^2 c^2\right) (a d-b c)^3-18 a^{3/2} b c^{5/2} d (b c-a d)^2 \left(21 a^2 d^2+6 a b c d-35 b^2 c^2\right)-3 \sqrt{a} c^{3/2} d (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) (a d-b c)+\sqrt{a+b x} (c+d x) \left(45 \sqrt{c+d x} (b c-a d)^4 \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)-3 \sqrt{a} \sqrt{c} d \sqrt{a+b x} \left(105 a^5 d^5-235 a^4 b c d^4+66 a^3 b^2 c^2 d^3+66 a^2 b^3 c^3 d^2-235 a b^4 c^4 d+105 b^5 c^5\right)\right)\right)-3 a^{3/2} b c^{5/2} (a d-b c)^3 \left(21 a^2 d^2+6 a b c d-35 b^2 c^2\right)\right)}{36 a^{9/2} c^{9/2} x^2 (a+b x)^{3/2} (c+d x)^{3/2} (b c-a d)^4}","\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,"(-18*a^(7/2)*c^(7/2)*(b*c - a*d)^4 + 63*a^(5/2)*c^(5/2)*(b*c - a*d)^4*(b*c + a*d)*x - x^2*(-3*a^(3/2)*b*c^(5/2)*(-(b*c) + a*d)^3*(-35*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2) + (a + b*x)*(45*Sqrt[a]*b*c^(5/2)*(-(b*c) + a*d)^3*(7*b^2*c^2 + 10*a*b*c*d + 7*a^2*d^2) - 18*a^(3/2)*b*c^(5/2)*d*(b*c - a*d)^2*(-35*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2) - 3*Sqrt[a]*c^(3/2)*d*(-(b*c) + a*d)*(-105*b^4*c^4 + 200*a*b^3*c^3*d - 18*a^2*b^2*c^2*d^2 - 48*a^3*b*c*d^3 + 35*a^4*d^4)*(a + b*x) + Sqrt[a + b*x]*(c + d*x)*(-3*Sqrt[a]*Sqrt[c]*d*(105*b^5*c^5 - 235*a*b^4*c^4*d + 66*a^2*b^3*c^3*d^2 + 66*a^3*b^2*c^2*d^3 - 235*a^4*b*c*d^4 + 105*a^5*d^5)*Sqrt[a + b*x] + 45*(b*c - a*d)^4*(7*b^2*c^2 + 10*a*b*c*d + 7*a^2*d^2)*Sqrt[c + d*x]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + d*x])]))))/(36*a^(9/2)*c^(9/2)*(b*c - a*d)^4*x^2*(a + b*x)^(3/2)*(c + d*x)^(3/2))","A",1
814,1,28,28,0.0084307,"\int \frac{x^2 \sqrt{a+b x}}{\sqrt{-a-b x}} \, dx","Integrate[(x^2*Sqrt[a + b*x])/Sqrt[-a - b*x],x]","\frac{x^3 \sqrt{a+b x}}{3 \sqrt{-a-b x}}","\frac{x^3 \sqrt{a+b x}}{3 \sqrt{-a-b x}}",1,"(x^3*Sqrt[a + b*x])/(3*Sqrt[-a - b*x])","A",1
815,1,28,28,0.0054145,"\int \frac{x \sqrt{a+b x}}{\sqrt{-a-b x}} \, dx","Integrate[(x*Sqrt[a + b*x])/Sqrt[-a - b*x],x]","\frac{x^2 \sqrt{a+b x}}{2 \sqrt{-a-b x}}","\frac{x^2 \sqrt{a+b x}}{2 \sqrt{-a-b x}}",1,"(x^2*Sqrt[a + b*x])/(2*Sqrt[-a - b*x])","A",1
816,1,23,23,0.0038011,"\int \frac{\sqrt{a+b x}}{\sqrt{-a-b x}} \, dx","Integrate[Sqrt[a + b*x]/Sqrt[-a - b*x],x]","\frac{x \sqrt{a+b x}}{\sqrt{-a-b x}}","\frac{x \sqrt{a+b x}}{\sqrt{-a-b x}}",1,"(x*Sqrt[a + b*x])/Sqrt[-a - b*x]","A",1
817,1,24,24,0.0049686,"\int \frac{\sqrt{a+b x}}{x \sqrt{-a-b x}} \, dx","Integrate[Sqrt[a + b*x]/(x*Sqrt[-a - b*x]),x]","\frac{\log (x) \sqrt{a+b x}}{\sqrt{-a-b x}}","\frac{\log (x) \sqrt{a+b x}}{\sqrt{-a-b x}}",1,"(Sqrt[a + b*x]*Log[x])/Sqrt[-a - b*x]","A",1
818,1,26,26,0.0048178,"\int \frac{\sqrt{a+b x}}{x^2 \sqrt{-a-b x}} \, dx","Integrate[Sqrt[a + b*x]/(x^2*Sqrt[-a - b*x]),x]","-\frac{\sqrt{a+b x}}{x \sqrt{-a-b x}}","-\frac{\sqrt{a+b x}}{x \sqrt{-a-b x}}",1,"-(Sqrt[a + b*x]/(x*Sqrt[-a - b*x]))","A",1
819,1,28,28,0.0045086,"\int \frac{\sqrt{a+b x}}{x^3 \sqrt{-a-b x}} \, dx","Integrate[Sqrt[a + b*x]/(x^3*Sqrt[-a - b*x]),x]","-\frac{\sqrt{a+b x}}{2 x^2 \sqrt{-a-b x}}","-\frac{\sqrt{a+b x}}{2 x^2 \sqrt{-a-b x}}",1,"-1/2*Sqrt[a + b*x]/(x^2*Sqrt[-a - b*x])","A",1
820,1,36,36,0.0121267,"\int \frac{x^{-m} \sqrt{a+b x}}{\sqrt{-a-b x}} \, dx","Integrate[Sqrt[a + b*x]/(x^m*Sqrt[-a - b*x]),x]","\frac{x^{1-m} \sqrt{a+b x}}{(1-m) \sqrt{-a-b x}}","\frac{x^{1-m} \sqrt{a+b x}}{(1-m) \sqrt{-a-b x}}",1,"(x^(1 - m)*Sqrt[a + b*x])/((1 - m)*Sqrt[-a - b*x])","A",1
821,1,26,26,0.0051267,"\int x^2 (-a-b x)^{-n} (a+b x)^n \, dx","Integrate[(x^2*(a + b*x)^n)/(-a - b*x)^n,x]","\frac{1}{3} x^3 (-a-b x)^{-n} (a+b x)^n","\frac{1}{3} x^3 (-a-b x)^{-n} (a+b x)^n",1,"(x^3*(a + b*x)^n)/(3*(-a - b*x)^n)","A",1
822,1,26,26,0.0031997,"\int x (-a-b x)^{-n} (a+b x)^n \, dx","Integrate[(x*(a + b*x)^n)/(-a - b*x)^n,x]","\frac{1}{2} x^2 (-a-b x)^{-n} (a+b x)^n","\frac{1}{2} x^2 (-a-b x)^{-n} (a+b x)^n",1,"(x^2*(a + b*x)^n)/(2*(-a - b*x)^n)","A",1
823,1,21,21,0.0022463,"\int (-a-b x)^{-n} (a+b x)^n \, dx","Integrate[(a + b*x)^n/(-a - b*x)^n,x]","x (-a-b x)^{-n} (a+b x)^n","x (-a-b x)^{-n} (a+b x)^n",1,"(x*(a + b*x)^n)/(-a - b*x)^n","A",1
824,1,22,22,0.002849,"\int \frac{(-a-b x)^{-n} (a+b x)^n}{x} \, dx","Integrate[(a + b*x)^n/(x*(-a - b*x)^n),x]","\log (x) (-a-b x)^{-n} (a+b x)^n","\log (x) (-a-b x)^{-n} (a+b x)^n",1,"((a + b*x)^n*Log[x])/(-a - b*x)^n","A",1
825,1,24,24,0.0030991,"\int \frac{(-a-b x)^{-n} (a+b x)^n}{x^2} \, dx","Integrate[(a + b*x)^n/(x^2*(-a - b*x)^n),x]","-\frac{(-a-b x)^{-n} (a+b x)^n}{x}","-\frac{(-a-b x)^{-n} (a+b x)^n}{x}",1,"-((a + b*x)^n/(x*(-a - b*x)^n))","A",1
826,1,26,26,0.0028961,"\int \frac{(-a-b x)^{-n} (a+b x)^n}{x^3} \, dx","Integrate[(a + b*x)^n/(x^3*(-a - b*x)^n),x]","-\frac{(-a-b x)^{-n} (a+b x)^n}{2 x^2}","-\frac{(-a-b x)^{-n} (a+b x)^n}{2 x^2}",1,"-1/2*(a + b*x)^n/(x^2*(-a - b*x)^n)","A",1
827,1,34,34,0.0072132,"\int x^{-m} (-a-b x)^{-n} (a+b x)^n \, dx","Integrate[(a + b*x)^n/(x^m*(-a - b*x)^n),x]","\frac{x^{1-m} (-a-b x)^{-n} (a+b x)^n}{1-m}","\frac{x^{1-m} (-a-b x)^{-n} (a+b x)^n}{1-m}",1,"(x^(1 - m)*(a + b*x)^n)/((1 - m)*(-a - b*x)^n)","A",1
828,1,54,78,0.037251,"\int \frac{x^3 \sqrt{1+x}}{(1-x)^{5/2}} \, dx","Integrate[(x^3*Sqrt[1 + x])/(1 - x)^(5/2),x]","-\frac{\sqrt{x+1} \left(3 x^3+12 x^2-71 x+52\right)}{6 (1-x)^{3/2}}-11 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\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,"-1/6*(Sqrt[1 + x]*(52 - 71*x + 12*x^2 + 3*x^3))/(1 - x)^(3/2) - 11*ArcSin[Sqrt[1 - x]/Sqrt[2]]","A",1
829,1,49,61,0.0314075,"\int \frac{x^2 \sqrt{1+x}}{(1-x)^{5/2}} \, dx","Integrate[(x^2*Sqrt[1 + x])/(1 - x)^(5/2),x]","-\frac{\sqrt{x+1} \left(3 x^2-19 x+14\right)}{3 (1-x)^{3/2}}-6 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\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,"-1/3*(Sqrt[1 + x]*(14 - 19*x + 3*x^2))/(1 - x)^(3/2) - 6*ArcSin[Sqrt[1 - x]/Sqrt[2]]","A",1
830,1,47,41,0.0367245,"\int \frac{x \sqrt{1+x}}{(1-x)^{5/2}} \, dx","Integrate[(x*Sqrt[1 + x])/(1 - x)^(5/2),x]","-\frac{(x+1)^{3/2}-4 \sqrt{2} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};\frac{1-x}{2}\right)}{3 (1-x)^{3/2}}","\frac{(x+1)^{3/2}}{3 (1-x)^{3/2}}-\frac{2 \sqrt{x+1}}{\sqrt{1-x}}+\sin ^{-1}(x)",1,"-1/3*((1 + x)^(3/2) - 4*Sqrt[2]*Hypergeometric2F1[-3/2, -3/2, -1/2, (1 - x)/2])/(1 - x)^(3/2)","C",1
831,1,20,20,0.0044403,"\int \frac{\sqrt{1+x}}{(1-x)^{5/2}} \, dx","Integrate[Sqrt[1 + x]/(1 - x)^(5/2),x]","\frac{(x+1)^{3/2}}{3 (1-x)^{3/2}}","\frac{(x+1)^{3/2}}{3 (1-x)^{3/2}}",1,"(1 + x)^(3/2)/(3*(1 - x)^(3/2))","A",1
832,1,18,18,0.0081809,"\int \frac{\sqrt{1+x}}{(-1+x)^{5/2}} \, dx","Integrate[Sqrt[1 + x]/(-1 + x)^(5/2),x]","-\frac{(x+1)^{3/2}}{3 (x-1)^{3/2}}","-\frac{(x+1)^{3/2}}{3 (x-1)^{3/2}}",1,"-1/3*(1 + x)^(3/2)/(-1 + x)^(3/2)","A",1
833,1,58,59,0.0234754,"\int \frac{\sqrt{1+x}}{(1-x)^{5/2} x} \, dx","Integrate[Sqrt[1 + x]/((1 - x)^(5/2)*x),x]","\frac{5 x^2-3 (x-1) \sqrt{1-x^2} \tanh ^{-1}\left(\sqrt{1-x^2}\right)-2 x-7}{3 (x-1) \sqrt{1-x^2}}","\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,"(-7 - 2*x + 5*x^2 - 3*(-1 + x)*Sqrt[1 - x^2]*ArcTanh[Sqrt[1 - x^2]])/(3*(-1 + x)*Sqrt[1 - x^2])","A",0
834,1,67,87,0.0265635,"\int \frac{\sqrt{1+x}}{(1-x)^{5/2} x^2} \, dx","Integrate[Sqrt[1 + x]/((1 - x)^(5/2)*x^2),x]","\frac{14 x^3-5 x^2-9 (x-1) \sqrt{1-x^2} x \tanh ^{-1}\left(\sqrt{1-x^2}\right)-16 x+3}{3 (x-1) x \sqrt{1-x^2}}","\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,"(3 - 16*x - 5*x^2 + 14*x^3 - 9*(-1 + x)*x*Sqrt[1 - x^2]*ArcTanh[Sqrt[1 - x^2]])/(3*(-1 + x)*x*Sqrt[1 - x^2])","A",0
835,1,74,112,0.0293811,"\int \frac{\sqrt{1+x}}{(1-x)^{5/2} x^3} \, dx","Integrate[Sqrt[1 + x]/((1 - x)^(5/2)*x^3),x]","\frac{52 x^4-19 x^3-59 x^2-33 (x-1) \sqrt{1-x^2} x^2 \tanh ^{-1}\left(\sqrt{1-x^2}\right)+15 x+3}{6 (x-1) x^2 \sqrt{1-x^2}}","-\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 + 15*x - 59*x^2 - 19*x^3 + 52*x^4 - 33*(-1 + x)*x^2*Sqrt[1 - x^2]*ArcTanh[Sqrt[1 - x^2]])/(6*(-1 + x)*x^2*Sqrt[1 - x^2])","A",0
836,1,36,26,0.010886,"\int \frac{x^2}{\sqrt{-1+x} \sqrt{1+x}} \, dx","Integrate[x^2/(Sqrt[-1 + x]*Sqrt[1 + x]),x]","\frac{1}{2} \sqrt{x-1} \sqrt{x+1} x+\tanh ^{-1}\left(\frac{\sqrt{x-1}}{\sqrt{x+1}}\right)","\frac{1}{2} \sqrt{x-1} \sqrt{x+1} x+\frac{1}{2} \cosh ^{-1}(x)",1,"(Sqrt[-1 + x]*x*Sqrt[1 + x])/2 + ArcTanh[Sqrt[-1 + x]/Sqrt[1 + x]]","A",1
837,1,15,15,0.0038797,"\int \frac{x}{\sqrt{-1+x} \sqrt{1+x}} \, dx","Integrate[x/(Sqrt[-1 + x]*Sqrt[1 + x]),x]","\sqrt{x-1} \sqrt{x+1}","\sqrt{x-1} \sqrt{x+1}",1,"Sqrt[-1 + x]*Sqrt[1 + x]","A",1
838,1,18,2,0.0025248,"\int \frac{1}{\sqrt{-1+x} \sqrt{1+x}} \, dx","Integrate[1/(Sqrt[-1 + x]*Sqrt[1 + x]),x]","2 \tanh ^{-1}\left(\frac{\sqrt{x-1}}{\sqrt{x+1}}\right)","\cosh ^{-1}(x)",1,"2*ArcTanh[Sqrt[-1 + x]/Sqrt[1 + x]]","B",1
839,1,34,16,0.0078637,"\int \frac{1}{\sqrt{-1+x} x \sqrt{1+x}} \, dx","Integrate[1/(Sqrt[-1 + x]*x*Sqrt[1 + x]),x]","\frac{\sqrt{x^2-1} \tan ^{-1}\left(\sqrt{x^2-1}\right)}{\sqrt{x-1} \sqrt{x+1}}","\tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)",1,"(Sqrt[-1 + x^2]*ArcTan[Sqrt[-1 + x^2]])/(Sqrt[-1 + x]*Sqrt[1 + x])","B",1
840,1,18,18,0.0065371,"\int \frac{1}{\sqrt{-1+x} x^2 \sqrt{1+x}} \, dx","Integrate[1/(Sqrt[-1 + x]*x^2*Sqrt[1 + x]),x]","\frac{\sqrt{x-1} \sqrt{x+1}}{x}","\frac{\sqrt{x-1} \sqrt{x+1}}{x}",1,"(Sqrt[-1 + x]*Sqrt[1 + x])/x","A",1
841,1,63,45,0.0219781,"\int \sqrt{-1+x} x^2 \sqrt{1+x} \, dx","Integrate[Sqrt[-1 + x]*x^2*Sqrt[1 + x],x]","\frac{x \sqrt{x+1} \left(2 x^3-2 x^2-x+1\right)+2 \sqrt{1-x} \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)}{8 \sqrt{x-1}}","\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,"(x*Sqrt[1 + x]*(1 - x - 2*x^2 + 2*x^3) + 2*Sqrt[1 - x]*ArcSin[Sqrt[1 - x]/Sqrt[2]])/(8*Sqrt[-1 + x])","A",1
842,1,18,18,0.003933,"\int \sqrt{-1+x} x \sqrt{1+x} \, dx","Integrate[Sqrt[-1 + x]*x*Sqrt[1 + x],x]","\frac{1}{3} (x-1)^{3/2} (x+1)^{3/2}","\frac{1}{3} (x-1)^{3/2} (x+1)^{3/2}",1,"((-1 + x)^(3/2)*(1 + x)^(3/2))/3","A",1
843,1,51,26,0.0142877,"\int \sqrt{-1+x} \sqrt{1+x} \, dx","Integrate[Sqrt[-1 + x]*Sqrt[1 + x],x]","\frac{(x-1) \sqrt{x+1} x+2 \sqrt{1-x} \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)}{2 \sqrt{x-1}}","\frac{1}{2} \sqrt{x-1} x \sqrt{x+1}-\frac{1}{2} \cosh ^{-1}(x)",1,"((-1 + x)*x*Sqrt[1 + x] + 2*Sqrt[1 - x]*ArcSin[Sqrt[1 - x]/Sqrt[2]])/(2*Sqrt[-1 + x])","A",1
844,1,101,34,0.1252261,"\int \frac{\sqrt{-1+x} \sqrt{1+x}}{x} \, dx","Integrate[(Sqrt[-1 + x]*Sqrt[1 + x])/x,x]","\frac{\sqrt{1-x} \left(x^2-\sqrt{x^2-1} \tan ^{-1}\left(\sqrt{x^2-1}\right)-1\right)+2 (x-1) \sqrt{x+1} \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)}{\sqrt{-(x-1)^2} \sqrt{x+1}}-2 \tanh ^{-1}\left(\sqrt{\frac{x-1}{x+1}}\right)","\sqrt{x-1} \sqrt{x+1}-\tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)",1,"(2*(-1 + x)*Sqrt[1 + x]*ArcSin[Sqrt[1 - x]/Sqrt[2]] + Sqrt[1 - x]*(-1 + x^2 - Sqrt[-1 + x^2]*ArcTan[Sqrt[-1 + x^2]]))/(Sqrt[-(-1 + x)^2]*Sqrt[1 + x]) - 2*ArcTanh[Sqrt[(-1 + x)/(1 + x)]]","B",0
845,1,52,22,0.0193121,"\int \frac{\sqrt{-1+x} \sqrt{1+x}}{x^2} \, dx","Integrate[(Sqrt[-1 + x]*Sqrt[1 + x])/x^2,x]","\frac{-\sqrt{x+1} (x-1)-2 \sqrt{1-x} x \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)}{\sqrt{x-1} x}","\cosh ^{-1}(x)-\frac{\sqrt{x-1} \sqrt{x+1}}{x}",1,"(-((-1 + x)*Sqrt[1 + x]) - 2*Sqrt[1 - x]*x*ArcSin[Sqrt[1 - x]/Sqrt[2]])/(Sqrt[-1 + x]*x)","B",1
846,1,31,16,0.0105792,"\int \frac{1}{\sqrt{1+2 x} \sqrt{3+2 x}} \, dx","Integrate[1/(Sqrt[1 + 2*x]*Sqrt[3 + 2*x]),x]","\frac{\sqrt{2 x+1} \sin ^{-1}\left(\sqrt{-x-\frac{1}{2}}\right)}{\sqrt{-2 x-1}}","\sinh ^{-1}\left(\frac{\sqrt{2 x+1}}{\sqrt{2}}\right)",1,"(Sqrt[1 + 2*x]*ArcSin[Sqrt[-1/2 - x]])/Sqrt[-1 - 2*x]","A",1
847,1,30,35,0.0150986,"\int \frac{1}{x \sqrt{-2+3 x} \sqrt{3+5 x}} \, dx","Integrate[1/(x*Sqrt[-2 + 3*x]*Sqrt[3 + 5*x]),x]","\sqrt{\frac{2}{3}} \tan ^{-1}\left(\frac{\sqrt{\frac{9 x}{2}-3}}{\sqrt{5 x+3}}\right)","\sqrt{\frac{2}{3}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} \sqrt{3 x-2}}{\sqrt{5 x+3}}\right)",1,"Sqrt[2/3]*ArcTan[Sqrt[-3 + (9*x)/2]/Sqrt[3 + 5*x]]","A",1
848,1,31,35,0.0101804,"\int \frac{1}{(-1+x)^{3/2} x (1+x)^{3/2}} \, dx","Integrate[1/((-1 + x)^(3/2)*x*(1 + x)^(3/2)),x]","-\frac{\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};1-x^2\right)}{\sqrt{x-1} \sqrt{x+1}}","-\frac{1}{\sqrt{x-1} \sqrt{x+1}}-\tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)",1,"-(Hypergeometric2F1[-1/2, 1, 1/2, 1 - x^2]/(Sqrt[-1 + x]*Sqrt[1 + x]))","C",1
849,1,15,20,0.0027887,"\int \sqrt{1-x} x \sqrt{1+x} \, dx","Integrate[Sqrt[1 - x]*x*Sqrt[1 + x],x]","-\frac{1}{3} \left(1-x^2\right)^{3/2}","-\frac{1}{3} (1-x)^{3/2} (x+1)^{3/2}",1,"-1/3*(1 - x^2)^(3/2)","A",1
850,1,75,146,0.1583642,"\int x^3 (2+3 x)^{3/2} \sqrt{1+4 x} \, dx","Integrate[x^3*(2 + 3*x)^(3/2)*Sqrt[1 + 4*x],x]","\frac{6 \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)+5339375 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{4 x+1}\right)}{1274019840}","\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,"(6*Sqrt[2 + 3*x]*Sqrt[1 + 4*x]*(-881613 + 1089592*x - 1849728*x^2 + 4119552*x^3 + 94666752*x^4 + 106168320*x^5) + 5339375*Sqrt[3]*ArcSinh[Sqrt[3/5]*Sqrt[1 + 4*x]])/1274019840","A",1
851,1,22,22,0.0113717,"\int \frac{1}{\sqrt{-1+a+b x} \sqrt{1+a+b x}} \, dx","Integrate[1/(Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]),x]","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{a+b x-1}}{\sqrt{2}}\right)}{b}","\frac{2 \sinh ^{-1}\left(\frac{\sqrt{a+b x-1}}{\sqrt{2}}\right)}{b}",1,"(2*ArcSinh[Sqrt[-1 + a + b*x]/Sqrt[2]])/b","A",1
852,1,63,75,0.0261144,"\int \frac{1}{\sqrt{x} \sqrt{a-b x} \sqrt{a+b x}} \, dx","Integrate[1/(Sqrt[x]*Sqrt[a - b*x]*Sqrt[a + b*x]),x]","\frac{2 \sqrt{x} \sqrt{1-\frac{b^2 x^2}{a^2}} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\frac{b^2 x^2}{a^2}\right)}{\sqrt{a-b x} \sqrt{a+b x}}","\frac{2 \sqrt{a} \sqrt{1-\frac{b x}{a}} \sqrt{\frac{b x}{a}+1} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right),-1\right)}{\sqrt{b} \sqrt{a-b x} \sqrt{a+b x}}",1,"(2*Sqrt[x]*Sqrt[1 - (b^2*x^2)/a^2]*Hypergeometric2F1[1/4, 1/2, 5/4, (b^2*x^2)/a^2])/(Sqrt[a - b*x]*Sqrt[a + b*x])","C",1
853,1,66,77,0.027301,"\int \frac{1}{\sqrt{-x} \sqrt{a-b x} \sqrt{a+b x}} \, dx","Integrate[1/(Sqrt[-x]*Sqrt[a - b*x]*Sqrt[a + b*x]),x]","\frac{2 x \sqrt{1-\frac{b^2 x^2}{a^2}} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\frac{b^2 x^2}{a^2}\right)}{\sqrt{-x} \sqrt{a-b x} \sqrt{a+b x}}","-\frac{2 \sqrt{a} \sqrt{1-\frac{b x}{a}} \sqrt{\frac{b x}{a}+1} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{-x}}{\sqrt{a}}\right),-1\right)}{\sqrt{b} \sqrt{a-b x} \sqrt{a+b x}}",1,"(2*x*Sqrt[1 - (b^2*x^2)/a^2]*Hypergeometric2F1[1/4, 1/2, 5/4, (b^2*x^2)/a^2])/(Sqrt[-x]*Sqrt[a - b*x]*Sqrt[a + b*x])","C",1
854,1,66,87,0.0236096,"\int \frac{1}{\sqrt{e x} \sqrt{a-b x} \sqrt{a+b x}} \, dx","Integrate[1/(Sqrt[e*x]*Sqrt[a - b*x]*Sqrt[a + b*x]),x]","\frac{2 x \sqrt{1-\frac{b^2 x^2}{a^2}} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\frac{b^2 x^2}{a^2}\right)}{\sqrt{e x} \sqrt{a-b x} \sqrt{a+b x}}","\frac{2 \sqrt{a} \sqrt{1-\frac{b x}{a}} \sqrt{\frac{b x}{a}+1} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{a} \sqrt{e}}\right),-1\right)}{\sqrt{b} \sqrt{e} \sqrt{a-b x} \sqrt{a+b x}}",1,"(2*x*Sqrt[1 - (b^2*x^2)/a^2]*Hypergeometric2F1[1/4, 1/2, 5/4, (b^2*x^2)/a^2])/(Sqrt[e*x]*Sqrt[a - b*x]*Sqrt[a + b*x])","C",1
855,1,26,30,0.0098863,"\int \frac{1}{\sqrt{x} \sqrt{2-b x} \sqrt{2+b x}} \, dx","Integrate[1/(Sqrt[x]*Sqrt[2 - b*x]*Sqrt[2 + b*x]),x]","\sqrt{x} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\frac{b^2 x^2}{4}\right)","\frac{\sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right),-1\right)}{\sqrt{b}}",1,"Sqrt[x]*Hypergeometric2F1[1/4, 1/2, 5/4, (b^2*x^2)/4]","C",1
856,1,29,33,0.0091477,"\int \frac{1}{\sqrt{-x} \sqrt{2-b x} \sqrt{2+b x}} \, dx","Integrate[1/(Sqrt[-x]*Sqrt[2 - b*x]*Sqrt[2 + b*x]),x]","\frac{x \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\frac{b^2 x^2}{4}\right)}{\sqrt{-x}}","-\frac{\sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{-x}}{\sqrt{2}}\right),-1\right)}{\sqrt{b}}",1,"(x*Hypergeometric2F1[1/4, 1/2, 5/4, (b^2*x^2)/4])/Sqrt[-x]","C",1
857,1,29,42,0.0096367,"\int \frac{1}{\sqrt{e x} \sqrt{2-b x} \sqrt{2+b x}} \, dx","Integrate[1/(Sqrt[e*x]*Sqrt[2 - b*x]*Sqrt[2 + b*x]),x]","\frac{x \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\frac{b^2 x^2}{4}\right)}{\sqrt{e x}}","\frac{\sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{b} \sqrt{e x}}{\sqrt{2} \sqrt{e}}\right),-1\right)}{\sqrt{b} \sqrt{e}}",1,"(x*Hypergeometric2F1[1/4, 1/2, 5/4, (b^2*x^2)/4])/Sqrt[e*x]","C",1
858,1,23,24,0.0077128,"\int \frac{1}{\sqrt{2-3 x} \sqrt{x} \sqrt{2+3 x}} \, dx","Integrate[1/(Sqrt[2 - 3*x]*Sqrt[x]*Sqrt[2 + 3*x]),x]","\sqrt{x} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\frac{9 x^2}{4}\right)","\sqrt{\frac{2}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} \sqrt{x}\right),-1\right)",1,"Sqrt[x]*Hypergeometric2F1[1/4, 1/2, 5/4, (9*x^2)/4]","C",1
859,1,26,27,0.0080403,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-x} \sqrt{2+3 x}} \, dx","Integrate[1/(Sqrt[2 - 3*x]*Sqrt[-x]*Sqrt[2 + 3*x]),x]","\frac{x \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\frac{9 x^2}{4}\right)}{\sqrt{-x}}","-\sqrt{\frac{2}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} \sqrt{-x}\right),-1\right)",1,"(x*Hypergeometric2F1[1/4, 1/2, 5/4, (9*x^2)/4])/Sqrt[-x]","C",1
860,1,26,36,0.0093907,"\int \frac{1}{\sqrt{2-3 x} \sqrt{e x} \sqrt{2+3 x}} \, dx","Integrate[1/(Sqrt[2 - 3*x]*Sqrt[e*x]*Sqrt[2 + 3*x]),x]","\frac{x \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\frac{9 x^2}{4}\right)}{\sqrt{e x}}","\frac{\sqrt{\frac{2}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{\frac{3}{2}} \sqrt{e x}}{\sqrt{e}}\right),-1\right)}{\sqrt{e}}",1,"(x*Hypergeometric2F1[1/4, 1/2, 5/4, (9*x^2)/4])/Sqrt[e*x]","C",1
861,1,44,10,0.0150445,"\int \frac{1}{\sqrt{1-x} \sqrt{x} \sqrt{1+x}} \, dx","Integrate[1/(Sqrt[1 - x]*Sqrt[x]*Sqrt[1 + x]),x]","\frac{2 x \sqrt{1-x^2} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};x^2\right)}{\sqrt{-((x-1) x)} \sqrt{x+1}}","2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{x}\right),-1\right)",1,"(2*x*Sqrt[1 - x^2]*Hypergeometric2F1[1/4, 1/2, 5/4, x^2])/(Sqrt[-((-1 + x)*x)]*Sqrt[1 + x])","C",1
862,1,44,10,0.0102342,"\int \frac{1}{\sqrt{1+x} \sqrt{x-x^2}} \, dx","Integrate[1/(Sqrt[1 + x]*Sqrt[x - x^2]),x]","\frac{2 x \sqrt{1-x^2} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};x^2\right)}{\sqrt{-((x-1) x)} \sqrt{x+1}}","2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{x}\right),-1\right)",1,"(2*x*Sqrt[1 - x^2]*Hypergeometric2F1[1/4, 1/2, 5/4, x^2])/(Sqrt[-((-1 + x)*x)]*Sqrt[1 + x])","C",1
863,1,27,33,0.0119821,"\int \frac{1}{\sqrt{b x} \sqrt{1-c x} \sqrt{1+c x}} \, dx","Integrate[1/(Sqrt[b*x]*Sqrt[1 - c*x]*Sqrt[1 + c*x]),x]","\frac{2 x \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};c^2 x^2\right)}{\sqrt{b x}}","\frac{2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{b x}}{\sqrt{b}}\right),-1\right)}{\sqrt{b} \sqrt{c}}",1,"(2*x*Hypergeometric2F1[1/4, 1/2, 5/4, c^2*x^2])/Sqrt[b*x]","C",1
864,1,89,38,0.1341256,"\int \frac{1}{\sqrt{b x} \sqrt{1-c x} \sqrt{1+d x}} \, dx","Integrate[1/(Sqrt[b*x]*Sqrt[1 - c*x]*Sqrt[1 + d*x]),x]","-\frac{2 x^{3/2} \sqrt{\frac{c-\frac{1}{x}}{c}} \sqrt{\frac{d+\frac{1}{x}}{d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{\frac{1}{c}}}{\sqrt{x}}\right),-\frac{c}{d}\right)}{\sqrt{\frac{1}{c}} \sqrt{b x} \sqrt{1-c x} \sqrt{d x+1}}","\frac{2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{b x}}{\sqrt{b}}\right),-\frac{d}{c}\right)}{\sqrt{b} \sqrt{c}}",1,"(-2*Sqrt[(c - x^(-1))/c]*Sqrt[(d + x^(-1))/d]*x^(3/2)*EllipticF[ArcSin[Sqrt[c^(-1)]/Sqrt[x]], -(c/d)])/(Sqrt[c^(-1)]*Sqrt[b*x]*Sqrt[1 - c*x]*Sqrt[1 + d*x])","B",1
865,1,64,10,0.0257919,"\int \frac{\sqrt{1+x}}{\sqrt{1-x} \sqrt{x}} \, dx","Integrate[Sqrt[1 + x]/(Sqrt[1 - x]*Sqrt[x]),x]","\frac{2 x \sqrt{1-x^2} \left(3 \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};x^2\right)+x \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};x^2\right)\right)}{3 \sqrt{-((x-1) x)} \sqrt{x+1}}","2 E\left(\left.\sin ^{-1}\left(\sqrt{x}\right)\right|-1\right)",1,"(2*x*Sqrt[1 - x^2]*(3*Hypergeometric2F1[1/4, 1/2, 5/4, x^2] + x*Hypergeometric2F1[1/2, 3/4, 7/4, x^2]))/(3*Sqrt[-((-1 + x)*x)]*Sqrt[1 + x])","C",1
866,1,64,10,0.023397,"\int \frac{\sqrt{1+x}}{\sqrt{x-x^2}} \, dx","Integrate[Sqrt[1 + x]/Sqrt[x - x^2],x]","\frac{2 x \sqrt{1-x^2} \left(3 \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};x^2\right)+x \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};x^2\right)\right)}{3 \sqrt{-((x-1) x)} \sqrt{x+1}}","2 E\left(\left.\sin ^{-1}\left(\sqrt{x}\right)\right|-1\right)",1,"(2*x*Sqrt[1 - x^2]*(3*Hypergeometric2F1[1/4, 1/2, 5/4, x^2] + x*Hypergeometric2F1[1/2, 3/4, 7/4, x^2]))/(3*Sqrt[-((-1 + x)*x)]*Sqrt[1 + x])","C",1
867,1,52,33,0.0353366,"\int \frac{\sqrt{1+c x}}{\sqrt{b x} \sqrt{1-c x}} \, dx","Integrate[Sqrt[1 + c*x]/(Sqrt[b*x]*Sqrt[1 - c*x]),x]","\frac{2 x \left(3 \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};c^2 x^2\right)+c x \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};c^2 x^2\right)\right)}{3 \sqrt{b x}}","\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,"(2*x*(3*Hypergeometric2F1[1/4, 1/2, 5/4, c^2*x^2] + c*x*Hypergeometric2F1[1/2, 3/4, 7/4, c^2*x^2]))/(3*Sqrt[b*x])","C",0
868,1,102,38,0.3895014,"\int \frac{\sqrt{1+c x}}{\sqrt{b x} \sqrt{1-d x}} \, dx","Integrate[Sqrt[1 + c*x]/(Sqrt[b*x]*Sqrt[1 - d*x]),x]","\frac{2 \sqrt{1-d x} \left(\frac{\sqrt{x} \sqrt{\frac{1}{c x}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{-\frac{1}{c}}}{\sqrt{x}}\right)|-\frac{c}{d}\right)}{\sqrt{-\frac{1}{c}} \sqrt{1-\frac{1}{d x}}}-c x-1\right)}{d \sqrt{b x} \sqrt{c x+1}}","\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,"(2*Sqrt[1 - d*x]*(-1 - c*x + (Sqrt[1 + 1/(c*x)]*Sqrt[x]*EllipticE[ArcSin[Sqrt[-c^(-1)]/Sqrt[x]], -(c/d)])/(Sqrt[-c^(-1)]*Sqrt[1 - 1/(d*x)])))/(d*Sqrt[b*x]*Sqrt[1 + c*x])","B",1
869,1,40,24,0.0231841,"\int \frac{\sqrt{1-x}}{\sqrt{x} \sqrt{1+x}} \, dx","Integrate[Sqrt[1 - x]/(Sqrt[x]*Sqrt[1 + x]),x]","-\frac{2}{3} \sqrt{x} \left(x \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};x^2\right)-3 \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};x^2\right)\right)","-\frac{2 \sqrt{-x} E\left(\left.\sin ^{-1}\left(\sqrt{-x}\right)\right|-1\right)}{\sqrt{x}}",1,"(-2*Sqrt[x]*(-3*Hypergeometric2F1[1/4, 1/2, 5/4, x^2] + x*Hypergeometric2F1[1/2, 3/4, 7/4, x^2]))/3","C",0
870,1,66,24,0.0457227,"\int \frac{\sqrt{-1+\frac{1}{x}} \sqrt{\frac{1}{x}} \sqrt{x}}{\sqrt{1+x}} \, dx","Integrate[(Sqrt[-1 + x^(-1)]*Sqrt[x^(-1)]*Sqrt[x])/Sqrt[1 + x],x]","-\frac{2 \sqrt{\frac{x}{x+1}} \sqrt{1-x^2} \left(x \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};x^2\right)-3 \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};x^2\right)\right)}{3 \sqrt{1-x}}","-\frac{2 \sqrt{-x} E\left(\left.\sin ^{-1}\left(\sqrt{-x}\right)\right|-1\right)}{\sqrt{x}}",1,"(-2*Sqrt[x/(1 + x)]*Sqrt[1 - x^2]*(-3*Hypergeometric2F1[1/4, 1/2, 5/4, x^2] + x*Hypergeometric2F1[1/2, 3/4, 7/4, x^2]))/(3*Sqrt[1 - x])","C",0
871,1,52,37,0.0347596,"\int \frac{\sqrt{1-c x}}{\sqrt{b x} \sqrt{1+c x}} \, dx","Integrate[Sqrt[1 - c*x]/(Sqrt[b*x]*Sqrt[1 + c*x]),x]","-\frac{2 x \left(c x \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};c^2 x^2\right)-3 \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};c^2 x^2\right)\right)}{3 \sqrt{b x}}","-\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,"(-2*x*(-3*Hypergeometric2F1[1/4, 1/2, 5/4, c^2*x^2] + c*x*Hypergeometric2F1[1/2, 3/4, 7/4, c^2*x^2]))/(3*Sqrt[b*x])","C",0
872,1,112,42,0.4456815,"\int \frac{\sqrt{1-c x}}{\sqrt{b x} \sqrt{1+d x}} \, dx","Integrate[Sqrt[1 - c*x]/(Sqrt[b*x]*Sqrt[1 + d*x]),x]","\frac{-2 x^{3/2} \sqrt{1-\frac{1}{c x}} \sqrt{\frac{1}{d x}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{1}{c}}}{\sqrt{x}}\right)|-\frac{c}{d}\right)-\frac{2 \sqrt{\frac{1}{c}} (c x-1) (d x+1)}{d}}{\sqrt{\frac{1}{c}} \sqrt{b x} \sqrt{1-c x} \sqrt{d x+1}}","-\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,"((-2*Sqrt[c^(-1)]*(-1 + c*x)*(1 + d*x))/d - 2*Sqrt[1 - 1/(c*x)]*Sqrt[1 + 1/(d*x)]*x^(3/2)*EllipticE[ArcSin[Sqrt[c^(-1)]/Sqrt[x]], -(c/d)])/(Sqrt[c^(-1)]*Sqrt[b*x]*Sqrt[1 - c*x]*Sqrt[1 + d*x])","B",1
873,1,72,51,0.209583,"\int \frac{1}{\sqrt{2-3 x} \sqrt{x} \sqrt{d+e x}} \, dx","Integrate[1/(Sqrt[2 - 3*x]*Sqrt[x]*Sqrt[d + e*x]),x]","-\frac{\sqrt{x} \sqrt{\frac{d+e x}{e (3 x-2)}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{1}{\sqrt{1-\frac{3 x}{2}}}\right),\frac{3 d}{2 e}+1\right)}{\sqrt{\frac{x}{6 x-4}} \sqrt{d+e x}}","\frac{2 \sqrt{\frac{e x}{d}+1} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} \sqrt{x}\right),-\frac{2 e}{3 d}\right)}{\sqrt{3} \sqrt{d+e x}}",1,"-((Sqrt[x]*Sqrt[(d + e*x)/(e*(-2 + 3*x))]*EllipticF[ArcSin[1/Sqrt[1 - (3*x)/2]], 1 + (3*d)/(2*e)])/(Sqrt[x/(-4 + 6*x)]*Sqrt[d + e*x]))","A",1
874,1,125,51,0.8406367,"\int \frac{\sqrt{d+e x}}{\sqrt{2-3 x} \sqrt{x}} \, dx","Integrate[Sqrt[d + e*x]/(Sqrt[2 - 3*x]*Sqrt[x]),x]","\frac{2 \sqrt{x} \left(\frac{3 (d+e x)}{\sqrt{2-3 x}}-\frac{(3 d+2 e) \sqrt{\frac{d+e x}{e (3 x-2)}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{3 d}{e}+2}}{\sqrt{2-3 x}}\right)|\frac{2 e}{3 d+2 e}\right)}{\sqrt{\frac{x}{3 x-2}} \sqrt{\frac{3 d}{e}+2}}\right)}{3 \sqrt{d+e x}}","\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,"(2*Sqrt[x]*((3*(d + e*x))/Sqrt[2 - 3*x] - ((3*d + 2*e)*Sqrt[(d + e*x)/(e*(-2 + 3*x))]*EllipticE[ArcSin[Sqrt[2 + (3*d)/e]/Sqrt[2 - 3*x]], (2*e)/(3*d + 2*e)])/(Sqrt[2 + (3*d)/e]*Sqrt[x/(-2 + 3*x)])))/(3*Sqrt[d + e*x])","B",1
875,1,72,752,0.0495767,"\int \frac{x^4}{\sqrt[3]{1-x} \sqrt[3]{2-x}} \, dx","Integrate[x^4/((1 - x)^(1/3)*(2 - x)^(1/3)),x]","\frac{3 (1-x)^{2/3} \left(-2475 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x-1\right)-2772 (x-1) \, _2F_1\left(\frac{1}{3},\frac{5}{3};\frac{8}{3};x-1\right)+(2-x)^{2/3} \left(140 x^3+462 x^2+1224 x-261\right)\right)}{1820}","-\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}} \operatorname{EllipticF}\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{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{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,"(3*(1 - x)^(2/3)*((2 - x)^(2/3)*(-261 + 1224*x + 462*x^2 + 140*x^3) - 2475*Hypergeometric2F1[1/3, 2/3, 5/3, -1 + x] - 2772*(-1 + x)*Hypergeometric2F1[1/3, 5/3, 8/3, -1 + x]))/1820","C",1
876,1,72,727,0.0650587,"\int \frac{x^3}{\sqrt[3]{1-x} \sqrt[3]{2-x}} \, dx","Integrate[x^3/((1 - x)^(1/3)*(2 - x)^(1/3)),x]","\frac{3}{10} (1-x)^{2/3} \left(-12 \, _2F_1\left(-\frac{5}{3},\frac{2}{3};\frac{5}{3};x-1\right)+42 \, _2F_1\left(-\frac{2}{3},\frac{2}{3};\frac{5}{3};x-1\right)-36 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x-1\right)+(2-x)^{2/3} x^2\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}} \operatorname{EllipticF}\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{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{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,"(3*(1 - x)^(2/3)*((2 - x)^(2/3)*x^2 - 12*Hypergeometric2F1[-5/3, 2/3, 5/3, -1 + x] + 42*Hypergeometric2F1[-2/3, 2/3, 5/3, -1 + x] - 36*Hypergeometric2F1[1/3, 2/3, 5/3, -1 + x]))/10","C",1
877,1,44,720,0.0205506,"\int \frac{x^2}{\sqrt[3]{1-x} \sqrt[3]{2-x}} \, dx","Integrate[x^2/((1 - x)^(1/3)*(2 - x)^(1/3)),x]","\frac{3}{28} (1-x)^{2/3} \left((2-x)^{2/3} (4 x+15)-33 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x-1\right)\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}} \operatorname{EllipticF}\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{(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{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,"(3*(1 - x)^(2/3)*((2 - x)^(2/3)*(15 + 4*x) - 33*Hypergeometric2F1[1/3, 2/3, 5/3, -1 + x]))/28","C",1
878,1,38,695,0.0106033,"\int \frac{x}{\sqrt[3]{1-x} \sqrt[3]{2-x}} \, dx","Integrate[x/((1 - x)^(1/3)*(2 - x)^(1/3)),x]","\frac{3}{4} (1-x)^{2/3} \left((2-x)^{2/3}-3 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x-1\right)\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}} \operatorname{EllipticF}\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{(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{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,"(3*(1 - x)^(2/3)*((2 - x)^(2/3) - 3*Hypergeometric2F1[1/3, 2/3, 5/3, -1 + x]))/4","C",1
879,1,26,671,0.0050959,"\int \frac{1}{\sqrt[3]{1-x} \sqrt[3]{2-x}} \, dx","Integrate[1/((1 - x)^(1/3)*(2 - x)^(1/3)),x]","-\frac{3}{2} (1-x)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x-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}} \operatorname{EllipticF}\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{(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{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,"(-3*(1 - x)^(2/3)*Hypergeometric2F1[1/3, 2/3, 5/3, -1 + x])/2","C",1
880,1,32,99,0.0257536,"\int \frac{1}{\sqrt[3]{1-x} \sqrt[3]{2-x} x} \, dx","Integrate[1/((1 - x)^(1/3)*(2 - x)^(1/3)*x),x]","-\frac{3}{2} (1-x)^{2/3} F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};x-1,1-x\right)","\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,"(-3*(1 - x)^(2/3)*AppellF1[2/3, 1/3, 1, 5/3, -1 + x, 1 - x])/2","C",0
881,1,74,796,0.0617231,"\int \frac{1}{\sqrt[3]{1-x} \sqrt[3]{2-x} x^2} \, dx","Integrate[1/((1 - x)^(1/3)*(2 - x)^(1/3)*x^2),x]","-\frac{(1-x)^{2/3} \left(10 x F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};x-1,1-x\right)+(x-1) x F_1\left(\frac{5}{3};\frac{1}{3},1;\frac{8}{3};x-1,1-x\right)+5 (2-x)^{2/3}\right)}{10 x}","-\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}} \operatorname{EllipticF}\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,"-1/10*((1 - x)^(2/3)*(5*(2 - x)^(2/3) + 10*x*AppellF1[2/3, 1/3, 1, 5/3, -1 + x, 1 - x] + (-1 + x)*x*AppellF1[5/3, 1/3, 1, 8/3, -1 + x, 1 - x]))/x","C",0
882,1,84,821,0.0602149,"\int \frac{1}{\sqrt[3]{1-x} \sqrt[3]{2-x} x^3} \, dx","Integrate[1/((1 - x)^(1/3)*(2 - x)^(1/3)*x^3),x]","-\frac{(1-x)^{2/3} \left(15 x^2 F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};x-1,1-x\right)+2 (x-1) x^2 F_1\left(\frac{5}{3};\frac{1}{3},1;\frac{8}{3};x-1,1-x\right)+5 (2-x)^{2/3} (2 x+1)\right)}{20 x^2}","-\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}} \operatorname{EllipticF}\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,"-1/20*((1 - x)^(2/3)*(5*(2 - x)^(2/3)*(1 + 2*x) + 15*x^2*AppellF1[2/3, 1/3, 1, 5/3, -1 + x, 1 - x] + 2*(-1 + x)*x^2*AppellF1[5/3, 1/3, 1, 8/3, -1 + x, 1 - x]))/x^2","C",0
883,1,233,340,0.677217,"\int \frac{x^3 \sqrt[4]{a+b x}}{\sqrt[4]{c+d x}} \, dx","Integrate[(x^3*(a + b*x)^(1/4))/(c + d*x)^(1/4),x]","\frac{(a+b x)^{5/4} \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \left(b \left(2 c \left(-7 a^2 d^2-6 a b c d+13 b^2 c^2\right) \, _2F_1\left(-\frac{3}{4},\frac{5}{4};\frac{9}{4};\frac{d (a+b x)}{a d-b c}\right)+b \left(\frac{5 b d^2 x^2 (c+d x)}{\sqrt[4]{\frac{b (c+d x)}{b c-a d}}}-c^2 (3 a d+13 b c) \, _2F_1\left(\frac{1}{4},\frac{5}{4};\frac{9}{4};\frac{d (a+b x)}{a d-b c}\right)\right)\right)-(b c-a d)^2 (11 a d+13 b c) \, _2F_1\left(-\frac{7}{4},\frac{5}{4};\frac{9}{4};\frac{d (a+b x)}{a d-b c}\right)\right)}{20 b^4 d^3 \sqrt[4]{c+d x}}","\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,"((a + b*x)^(5/4)*((b*(c + d*x))/(b*c - a*d))^(1/4)*(-((b*c - a*d)^2*(13*b*c + 11*a*d)*Hypergeometric2F1[-7/4, 5/4, 9/4, (d*(a + b*x))/(-(b*c) + a*d)]) + b*(2*c*(13*b^2*c^2 - 6*a*b*c*d - 7*a^2*d^2)*Hypergeometric2F1[-3/4, 5/4, 9/4, (d*(a + b*x))/(-(b*c) + a*d)] + b*((5*b*d^2*x^2*(c + d*x))/((b*(c + d*x))/(b*c - a*d))^(1/4) - c^2*(13*b*c + 3*a*d)*Hypergeometric2F1[1/4, 5/4, 9/4, (d*(a + b*x))/(-(b*c) + a*d)]))))/(20*b^4*d^3*(c + d*x)^(1/4))","C",1
884,1,124,268,0.1453714,"\int \frac{x^2 \sqrt[4]{a+b x}}{\sqrt[4]{c+d x}} \, dx","Integrate[(x^2*(a + b*x)^(1/4))/(c + d*x)^(1/4),x]","\frac{(a+b x)^{5/4} \left(3 \left(7 a^2 d^2+10 a b c d+15 b^2 c^2\right) \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{4},\frac{5}{4};\frac{9}{4};\frac{d (a+b x)}{a d-b c}\right)-5 b (c+d x) (7 a d+9 b c-8 b d x)\right)}{120 b^3 d^2 \sqrt[4]{c+d x}}","\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,"((a + b*x)^(5/4)*(-5*b*(c + d*x)*(9*b*c + 7*a*d - 8*b*d*x) + 3*(15*b^2*c^2 + 10*a*b*c*d + 7*a^2*d^2)*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[1/4, 5/4, 9/4, (d*(a + b*x))/(-(b*c) + a*d)]))/(120*b^3*d^2*(c + d*x)^(1/4))","C",1
885,1,96,188,0.0897913,"\int \frac{x \sqrt[4]{a+b x}}{\sqrt[4]{c+d x}} \, dx","Integrate[(x*(a + b*x)^(1/4))/(c + d*x)^(1/4),x]","\frac{(a+b x)^{5/4} \left(5 b (c+d x)-(3 a d+5 b c) \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{4},\frac{5}{4};\frac{9}{4};\frac{d (a+b x)}{a d-b c}\right)\right)}{10 b^2 d \sqrt[4]{c+d x}}","\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,"((a + b*x)^(5/4)*(5*b*(c + d*x) - (5*b*c + 3*a*d)*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[1/4, 5/4, 9/4, (d*(a + b*x))/(-(b*c) + a*d)]))/(10*b^2*d*(c + d*x)^(1/4))","C",1
886,1,73,127,0.027322,"\int \frac{\sqrt[4]{a+b x}}{\sqrt[4]{c+d x}} \, dx","Integrate[(a + b*x)^(1/4)/(c + d*x)^(1/4),x]","\frac{4 (a+b x)^{5/4} \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{4},\frac{5}{4};\frac{9}{4};\frac{d (a+b x)}{a d-b c}\right)}{5 b \sqrt[4]{c+d x}}","-\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,"(4*(a + b*x)^(5/4)*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[1/4, 5/4, 9/4, (d*(a + b*x))/(-(b*c) + a*d)])/(5*b*(c + d*x)^(1/4))","C",1
887,1,97,169,0.0554358,"\int \frac{\sqrt[4]{a+b x}}{x \sqrt[4]{c+d x}} \, dx","Integrate[(a + b*x)^(1/4)/(x*(c + d*x)^(1/4)),x]","\frac{4 \sqrt[4]{a+b x} \left(\sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{d (a+b x)}{a d-b c}\right)-\, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{c (a+b x)}{a (c+d x)}\right)\right)}{\sqrt[4]{c+d x}}","-\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,"(4*(a + b*x)^(1/4)*(((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (d*(a + b*x))/(-(b*c) + a*d)] - Hypergeometric2F1[1/4, 1, 5/4, (c*(a + b*x))/(a*(c + d*x))]))/(c + d*x)^(1/4)","C",1
888,1,73,131,0.0223786,"\int \frac{\sqrt[4]{a+b x}}{x^2 \sqrt[4]{c+d x}} \, dx","Integrate[(a + b*x)^(1/4)/(x^2*(c + d*x)^(1/4)),x]","\frac{\sqrt[4]{a+b x} \left((a d x-b c x) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{c (a+b x)}{a (c+d x)}\right)-a (c+d x)\right)}{a c x \sqrt[4]{c+d 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,"((a + b*x)^(1/4)*(-(a*(c + d*x)) + (-(b*c*x) + a*d*x)*Hypergeometric2F1[1/4, 1, 5/4, (c*(a + b*x))/(a*(c + d*x))]))/(a*c*x*(c + d*x)^(1/4))","C",1
889,1,106,194,0.0570958,"\int \frac{\sqrt[4]{a+b x}}{x^3 \sqrt[4]{c+d x}} \, dx","Integrate[(a + b*x)^(1/4)/(x^3*(c + d*x)^(1/4)),x]","\frac{\sqrt[4]{a+b x} \left(x^2 \left(-5 a^2 d^2+2 a b c d+3 b^2 c^2\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{c (a+b x)}{a (c+d x)}\right)-a (c+d x) (4 a c-5 a d x+b c x)\right)}{8 a^2 c^2 x^2 \sqrt[4]{c+d x}}","\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,"((a + b*x)^(1/4)*(-(a*(c + d*x)*(4*a*c + b*c*x - 5*a*d*x)) + (3*b^2*c^2 + 2*a*b*c*d - 5*a^2*d^2)*x^2*Hypergeometric2F1[1/4, 1, 5/4, (c*(a + b*x))/(a*(c + d*x))]))/(8*a^2*c^2*x^2*(c + d*x)^(1/4))","C",1
890,1,155,266,0.0793752,"\int \frac{\sqrt[4]{a+b x}}{x^4 \sqrt[4]{c+d x}} \, dx","Integrate[(a + b*x)^(1/4)/(x^4*(c + d*x)^(1/4)),x]","\frac{\sqrt[4]{a+b x} \left(a (c+d x) \left(a^2 \left(-32 c^2+36 c d x-45 d^2 x^2\right)+2 a b c x (3 d x-2 c)+7 b^2 c^2 x^2\right)-3 x^3 \left(-15 a^3 d^3+5 a^2 b c d^2+3 a b^2 c^2 d+7 b^3 c^3\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{c (a+b x)}{a (c+d x)}\right)\right)}{96 a^3 c^3 x^3 \sqrt[4]{c+d x}}","\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,"((a + b*x)^(1/4)*(a*(c + d*x)*(7*b^2*c^2*x^2 + 2*a*b*c*x*(-2*c + 3*d*x) + a^2*(-32*c^2 + 36*c*d*x - 45*d^2*x^2)) - 3*(7*b^3*c^3 + 3*a*b^2*c^2*d + 5*a^2*b*c*d^2 - 15*a^3*d^3)*x^3*Hypergeometric2F1[1/4, 1, 5/4, (c*(a + b*x))/(a*(c + d*x))]))/(96*a^3*c^3*x^3*(c + d*x)^(1/4))","C",1
891,1,212,368,0.1420009,"\int \frac{\sqrt[4]{a+b x}}{x^5 \sqrt[4]{c+d x}} \, dx","Integrate[(a + b*x)^(1/4)/(x^5*(c + d*x)^(1/4)),x]","\frac{\sqrt[4]{a+b x} \left(3 x^4 \left(-195 a^4 d^4+60 a^3 b c d^3+30 a^2 b^2 c^2 d^2+28 a b^3 c^3 d+77 b^4 c^4\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{c (a+b x)}{a (c+d x)}\right)-a (c+d x) \left(a^3 \left(384 c^3-416 c^2 d x+468 c d^2 x^2-585 d^3 x^3\right)+a^2 b c x \left(32 c^2-40 c d x+63 d^2 x^2\right)+a b^2 c^2 x^2 (61 d x-44 c)+77 b^3 c^3 x^3\right)\right)}{1536 a^4 c^4 x^4 \sqrt[4]{c+d x}}","\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,"((a + b*x)^(1/4)*(-(a*(c + d*x)*(77*b^3*c^3*x^3 + a*b^2*c^2*x^2*(-44*c + 61*d*x) + a^2*b*c*x*(32*c^2 - 40*c*d*x + 63*d^2*x^2) + a^3*(384*c^3 - 416*c^2*d*x + 468*c*d^2*x^2 - 585*d^3*x^3))) + 3*(77*b^4*c^4 + 28*a*b^3*c^3*d + 30*a^2*b^2*c^2*d^2 + 60*a^3*b*c*d^3 - 195*a^4*d^4)*x^4*Hypergeometric2F1[1/4, 1, 5/4, (c*(a + b*x))/(a*(c + d*x))]))/(1536*a^4*c^4*x^4*(c + d*x)^(1/4))","C",1
892,1,58,234,0.0280453,"\int \frac{x^2 \sqrt[4]{1+x}}{\sqrt[4]{1-x}} \, dx","Integrate[(x^2*(1 + x)^(1/4))/(1 - x)^(1/4),x]","-\frac{1}{12} (1-x)^{3/4} \left(6 \sqrt[4]{2} \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{1-x}{2}\right)+\sqrt[4]{x+1} \left(4 x^2+5 x+1\right)\right)","-\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,"-1/12*((1 - x)^(3/4)*((1 + x)^(1/4)*(1 + 5*x + 4*x^2) + 6*2^(1/4)*Hypergeometric2F1[-1/4, 3/4, 7/4, (1 - x)/2]))","C",1
893,1,49,213,0.0190621,"\int \frac{x \sqrt[4]{1+x}}{\sqrt[4]{1-x}} \, dx","Integrate[(x*(1 + x)^(1/4))/(1 - x)^(1/4),x]","-\frac{1}{6} (1-x)^{3/4} \left(2 \sqrt[4]{2} \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{1-x}{2}\right)+3 (x+1)^{5/4}\right)","-\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,"-1/6*((1 - x)^(3/4)*(3*(1 + x)^(5/4) + 2*2^(1/4)*Hypergeometric2F1[-1/4, 3/4, 7/4, (1 - x)/2]))","C",1
894,1,37,186,0.0056434,"\int \frac{\sqrt[4]{1+x}}{\sqrt[4]{1-x}} \, dx","Integrate[(1 + x)^(1/4)/(1 - x)^(1/4),x]","-\frac{4}{3} \sqrt[4]{2} (1-x)^{3/4} \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{1-x}{2}\right)","-(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,"(-4*2^(1/4)*(1 - x)^(3/4)*Hypergeometric2F1[-1/4, 3/4, 7/4, (1 - x)/2])/3","C",1
895,1,74,203,0.0251171,"\int \frac{\sqrt[4]{1+x}}{\sqrt[4]{1-x} x} \, dx","Integrate[(1 + x)^(1/4)/((1 - x)^(1/4)*x),x]","-\frac{2 (1-x)^{3/4} \left(\sqrt[4]{2} (x+1)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{1-x}{2}\right)+2 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-x}{x+1}\right)\right)}{3 (x+1)^{3/4}}","-\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*(1 - x)^(3/4)*(2^(1/4)*(1 + x)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (1 - x)/2] + 2*Hypergeometric2F1[3/4, 1, 7/4, (1 - x)/(1 + x)]))/(3*(1 + x)^(3/4))","C",1
896,1,50,62,0.0138541,"\int \frac{\sqrt[4]{1+x}}{\sqrt[4]{1-x} x^2} \, dx","Integrate[(1 + x)^(1/4)/((1 - x)^(1/4)*x^2),x]","-\frac{(1-x)^{3/4} \left(2 x \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-x}{x+1}\right)+3 x+3\right)}{3 x (x+1)^{3/4}}","-\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,"-1/3*((1 - x)^(3/4)*(3 + 3*x + 2*x*Hypergeometric2F1[3/4, 1, 7/4, (1 - x)/(1 + x)]))/(x*(1 + x)^(3/4))","C",1
897,1,57,91,0.0156094,"\int \frac{\sqrt[4]{1+x}}{\sqrt[4]{1-x} x^3} \, dx","Integrate[(1 + x)^(1/4)/((1 - x)^(1/4)*x^3),x]","-\frac{(1-x)^{3/4} \left(2 x^2 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-x}{x+1}\right)+9 x^2+15 x+6\right)}{12 x^2 (x+1)^{3/4}}","-\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,"-1/12*((1 - x)^(3/4)*(6 + 15*x + 9*x^2 + 2*x^2*Hypergeometric2F1[3/4, 1, 7/4, (1 - x)/(1 + x)]))/(x^2*(1 + x)^(3/4))","C",1
898,1,62,114,0.0174925,"\int \frac{\sqrt[4]{1+x}}{\sqrt[4]{1-x} x^4} \, dx","Integrate[(1 + x)^(1/4)/((1 - x)^(1/4)*x^4),x]","-\frac{(1-x)^{3/4} \left(6 x^3 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-x}{x+1}\right)+11 x^3+21 x^2+18 x+8\right)}{24 x^3 (x+1)^{3/4}}","-\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,"-1/24*((1 - x)^(3/4)*(8 + 18*x + 21*x^2 + 11*x^3 + 6*x^3*Hypergeometric2F1[3/4, 1, 7/4, (1 - x)/(1 + x)]))/(x^3*(1 + x)^(3/4))","C",1
899,1,67,137,0.0213592,"\int \frac{\sqrt[4]{1+x}}{\sqrt[4]{1-x} x^5} \, dx","Integrate[(1 + x)^(1/4)/((1 - x)^(1/4)*x^5),x]","-\frac{(1-x)^{3/4} \left(22 x^4 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-x}{x+1}\right)+83 x^4+141 x^3+114 x^2+104 x+48\right)}{192 x^4 (x+1)^{3/4}}","-\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,"-1/192*((1 - x)^(3/4)*(48 + 104*x + 114*x^2 + 141*x^3 + 83*x^4 + 22*x^4*Hypergeometric2F1[3/4, 1, 7/4, (1 - x)/(1 + x)]))/(x^4*(1 + x)^(3/4))","C",1
900,1,231,259,0.6396911,"\int \frac{x^3}{(a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","Integrate[x^3/((a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","\frac{\sqrt[4]{a+b x} \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \left(b \left(2 c \left(-7 a^2 d^2-2 a b c d+9 b^2 c^2\right) \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};\frac{d (a+b x)}{a d-b c}\right)+b \left(\frac{b d^2 x^2 (c+d x)}{\sqrt[4]{\frac{b (c+d x)}{b c-a d}}}-3 c^2 (a d+3 b c) \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{d (a+b x)}{a d-b c}\right)\right)\right)-(b c-a d)^2 (11 a d+9 b c) \, _2F_1\left(-\frac{7}{4},\frac{1}{4};\frac{5}{4};\frac{d (a+b x)}{a d-b c}\right)\right)}{3 b^4 d^3 \sqrt[4]{c+d x}}","\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,"((a + b*x)^(1/4)*((b*(c + d*x))/(b*c - a*d))^(1/4)*(-((b*c - a*d)^2*(9*b*c + 11*a*d)*Hypergeometric2F1[-7/4, 1/4, 5/4, (d*(a + b*x))/(-(b*c) + a*d)]) + b*(2*c*(9*b^2*c^2 - 2*a*b*c*d - 7*a^2*d^2)*Hypergeometric2F1[-3/4, 1/4, 5/4, (d*(a + b*x))/(-(b*c) + a*d)] + b*((b*d^2*x^2*(c + d*x))/((b*(c + d*x))/(b*c - a*d))^(1/4) - 3*c^2*(3*b*c + a*d)*Hypergeometric2F1[1/4, 1/4, 5/4, (d*(a + b*x))/(-(b*c) + a*d)]))))/(3*b^4*d^3*(c + d*x)^(1/4))","C",1
901,1,123,201,0.134928,"\int \frac{x^2}{(a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","Integrate[x^2/((a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","\frac{\sqrt[4]{a+b x} \left(\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{d (a+b x)}{a d-b c}\right)-b (c+d x) (7 a d+5 b c-4 b d x)\right)}{8 b^3 d^2 \sqrt[4]{c+d x}}","\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,"((a + b*x)^(1/4)*(-(b*(c + d*x)*(5*b*c + 7*a*d - 4*b*d*x)) + (5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (d*(a + b*x))/(-(b*c) + a*d)]))/(8*b^3*d^2*(c + d*x)^(1/4))","C",1
902,1,91,130,0.1011223,"\int \frac{x}{(a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","Integrate[x/((a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","\frac{\sqrt[4]{a+b x} \left(b (c+d x)-(3 a d+b c) \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{d (a+b x)}{a d-b c}\right)\right)}{b^2 d \sqrt[4]{c+d x}}","-\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,"((a + b*x)^(1/4)*(b*(c + d*x) - (b*c + 3*a*d)*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (d*(a + b*x))/(-(b*c) + a*d)]))/(b^2*d*(c + d*x)^(1/4))","C",1
903,1,71,85,0.0292264,"\int \frac{1}{(a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","Integrate[1/((a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","\frac{4 \sqrt[4]{a+b x} \sqrt[4]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{d (a+b x)}{a d-b c}\right)}{b \sqrt[4]{c+d x}}","\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,"(4*(a + b*x)^(1/4)*((b*(c + d*x))/(b*c - a*d))^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(c + d*x)^(1/4))","C",1
904,1,48,85,0.0115588,"\int \frac{1}{x (a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","Integrate[1/(x*(a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","-\frac{4 \sqrt[4]{a+b x} \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{c (a+b x)}{a (c+d x)}\right)}{a \sqrt[4]{c+d x}}","-\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,"(-4*(a + b*x)^(1/4)*Hypergeometric2F1[1/4, 1, 5/4, (c*(a + b*x))/(a*(c + d*x))])/(a*(c + d*x)^(1/4))","C",1
905,1,72,134,0.0229106,"\int \frac{1}{x^2 (a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","Integrate[1/(x^2*(a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","\frac{\sqrt[4]{a+b x} \left(x (a d+3 b c) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{c (a+b x)}{a (c+d x)}\right)-a (c+d x)\right)}{a^2 c x \sqrt[4]{c+d 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)*(-(a*(c + d*x)) + (3*b*c + a*d)*x*Hypergeometric2F1[1/4, 1, 5/4, (c*(a + b*x))/(a*(c + d*x))]))/(a^2*c*x*(c + d*x)^(1/4))","C",1
906,1,106,206,0.0451341,"\int \frac{1}{x^3 (a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","Integrate[1/(x^3*(a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","-\frac{\sqrt[4]{a+b x} \left(x^2 \left(5 a^2 d^2+6 a b c d+21 b^2 c^2\right) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{c (a+b x)}{a (c+d x)}\right)+a (c+d x) (4 a c-5 a d x-7 b c x)\right)}{8 a^3 c^2 x^2 \sqrt[4]{c+d x}}","\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,"-1/8*((a + b*x)^(1/4)*(a*(c + d*x)*(4*a*c - 7*b*c*x - 5*a*d*x) + (21*b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*x^2*Hypergeometric2F1[1/4, 1, 5/4, (c*(a + b*x))/(a*(c + d*x))]))/(a^3*c^2*x^2*(c + d*x)^(1/4))","C",1
907,1,156,288,0.0821676,"\int \frac{1}{x^4 (a+b x)^{3/4} \sqrt[4]{c+d x}} \, dx","Integrate[1/(x^4*(a + b*x)^(3/4)*(c + d*x)^(1/4)),x]","\frac{\sqrt[4]{a+b x} \left(3 x^3 \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) \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{c (a+b x)}{a (c+d x)}\right)-a (c+d x) \left(a^2 \left(32 c^2-36 c d x+45 d^2 x^2\right)+2 a b c x (27 d x-22 c)+77 b^2 c^2 x^2\right)\right)}{96 a^4 c^3 x^3 \sqrt[4]{c+d x}}","\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,"((a + b*x)^(1/4)*(-(a*(c + d*x)*(77*b^2*c^2*x^2 + 2*a*b*c*x*(-22*c + 27*d*x) + a^2*(32*c^2 - 36*c*d*x + 45*d^2*x^2))) + 3*(77*b^3*c^3 + 21*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 15*a^3*d^3)*x^3*Hypergeometric2F1[1/4, 1, 5/4, (c*(a + b*x))/(a*(c + d*x))]))/(96*a^4*c^3*x^3*(c + d*x)^(1/4))","C",1
908,1,190,244,0.097891,"\int \frac{(e x)^{3/2}}{\sqrt[4]{1-x} \sqrt[4]{1+x}} \, dx","Integrate[(e*x)^(3/2)/((1 - x)^(1/4)*(1 + x)^(1/4)),x]","-\frac{(e x)^{3/2} \left(8 \sqrt{x} \left(1-x^2\right)^{3/4}+\sqrt{2} \log \left(\frac{x}{\sqrt{1-x^2}}-\frac{\sqrt{2} \sqrt{x}}{\sqrt[4]{1-x^2}}+1\right)-\sqrt{2} \log \left(\frac{x}{\sqrt{1-x^2}}+\frac{\sqrt{2} \sqrt{x}}{\sqrt[4]{1-x^2}}+1\right)+2 \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{x}}{\sqrt[4]{1-x^2}}\right)-2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt[4]{1-x^2}}+1\right)\right)}{16 x^{3/2}}","-\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} \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,"-1/16*((e*x)^(3/2)*(8*Sqrt[x]*(1 - x^2)^(3/4) + 2*Sqrt[2]*ArcTan[1 - (Sqrt[2]*Sqrt[x])/(1 - x^2)^(1/4)] - 2*Sqrt[2]*ArcTan[1 + (Sqrt[2]*Sqrt[x])/(1 - x^2)^(1/4)] + Sqrt[2]*Log[1 + x/Sqrt[1 - x^2] - (Sqrt[2]*Sqrt[x])/(1 - x^2)^(1/4)] - Sqrt[2]*Log[1 + x/Sqrt[1 - x^2] + (Sqrt[2]*Sqrt[x])/(1 - x^2)^(1/4)]))/x^(3/2)","A",1
909,1,156,216,0.0389531,"\int \frac{1}{\sqrt[4]{1-x} \sqrt{e x} \sqrt[4]{1+x}} \, dx","Integrate[1/((1 - x)^(1/4)*Sqrt[e*x]*(1 + x)^(1/4)),x]","\frac{\sqrt{x} \left(-\log \left(\frac{x}{\sqrt{1-x^2}}-\frac{\sqrt{2} \sqrt{x}}{\sqrt[4]{1-x^2}}+1\right)+\log \left(\frac{x}{\sqrt{1-x^2}}+\frac{\sqrt{2} \sqrt{x}}{\sqrt[4]{1-x^2}}+1\right)-2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{x}}{\sqrt[4]{1-x^2}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt[4]{1-x^2}}+1\right)\right)}{2 \sqrt{2} \sqrt{e x}}","-\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,"(Sqrt[x]*(-2*ArcTan[1 - (Sqrt[2]*Sqrt[x])/(1 - x^2)^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*Sqrt[x])/(1 - x^2)^(1/4)] - Log[1 + x/Sqrt[1 - x^2] - (Sqrt[2]*Sqrt[x])/(1 - x^2)^(1/4)] + Log[1 + x/Sqrt[1 - x^2] + (Sqrt[2]*Sqrt[x])/(1 - x^2)^(1/4)]))/(2*Sqrt[2]*Sqrt[e*x])","A",1
910,1,23,30,0.0075896,"\int \frac{1}{\sqrt[4]{1-x} (e x)^{5/2} \sqrt[4]{1+x}} \, dx","Integrate[1/((1 - x)^(1/4)*(e*x)^(5/2)*(1 + x)^(1/4)),x]","-\frac{2 x \left(1-x^2\right)^{3/4}}{3 (e x)^{5/2}}","-\frac{2 (1-x)^{3/4} (x+1)^{3/4}}{3 e (e x)^{3/2}}",1,"(-2*x*(1 - x^2)^(3/4))/(3*(e*x)^(5/2))","A",1
911,1,35,51,0.0148017,"\int \frac{1}{\sqrt[4]{1-x} (e x)^{9/2} \sqrt[4]{1+x}} \, dx","Integrate[1/((1 - x)^(1/4)*(e*x)^(9/2)*(1 + x)^(1/4)),x]","-\frac{2 \left(1-x^2\right)^{3/4} \left(4 x^2+3\right) \sqrt{e x}}{21 e^5 x^4}","\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,"(-2*Sqrt[e*x]*(1 - x^2)^(3/4)*(3 + 4*x^2))/(21*e^5*x^4)","A",1
912,1,40,76,0.0189007,"\int \frac{1}{\sqrt[4]{1-x} (e x)^{13/2} \sqrt[4]{1+x}} \, dx","Integrate[1/((1 - x)^(1/4)*(e*x)^(13/2)*(1 + x)^(1/4)),x]","-\frac{2 \left(1-x^2\right)^{3/4} \left(32 x^4+24 x^2+21\right) \sqrt{e x}}{231 e^7 x^6}","-\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,"(-2*Sqrt[e*x]*(1 - x^2)^(3/4)*(21 + 24*x^2 + 32*x^4))/(231*e^7*x^6)","A",1
913,1,39,93,0.0152942,"\int \frac{(e x)^{5/2}}{\sqrt[4]{1-x} \sqrt[4]{1+x}} \, dx","Integrate[(e*x)^(5/2)/((1 - x)^(1/4)*(1 + x)^(1/4)),x]","-\frac{1}{3} e (e x)^{3/2} \left(\left(1-x^2\right)^{3/4}-\, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{7}{4};x^2\right)\right)","-\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,"-1/3*(e*(e*x)^(3/2)*((1 - x^2)^(3/4) - Hypergeometric2F1[1/4, 3/4, 7/4, x^2]))","C",1
914,1,25,60,0.0054736,"\int \frac{\sqrt{e x}}{\sqrt[4]{1-x} \sqrt[4]{1+x}} \, dx","Integrate[Sqrt[e*x]/((1 - x)^(1/4)*(1 + x)^(1/4)),x]","\frac{2}{3} x \sqrt{e x} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{7}{4};x^2\right)","\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,"(2*x*Sqrt[e*x]*Hypergeometric2F1[1/4, 3/4, 7/4, x^2])/3","C",1
915,1,23,42,0.008282,"\int \frac{1}{\sqrt[4]{1-x} (e x)^{3/2} \sqrt[4]{1+x}} \, dx","Integrate[1/((1 - x)^(1/4)*(e*x)^(3/2)*(1 + x)^(1/4)),x]","-\frac{2 x \, _2F_1\left(-\frac{1}{4},\frac{1}{4};\frac{3}{4};x^2\right)}{(e x)^{3/2}}","-\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,"(-2*x*Hypergeometric2F1[-1/4, 1/4, 3/4, x^2])/(e*x)^(3/2)","C",1
916,1,25,70,0.009017,"\int \frac{1}{\sqrt[4]{1-x} (e x)^{7/2} \sqrt[4]{1+x}} \, dx","Integrate[1/((1 - x)^(1/4)*(e*x)^(7/2)*(1 + x)^(1/4)),x]","-\frac{2 x \, _2F_1\left(-\frac{5}{4},\frac{1}{4};-\frac{1}{4};x^2\right)}{5 (e x)^{7/2}}","-\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,"(-2*x*Hypergeometric2F1[-5/4, 1/4, -1/4, x^2])/(5*(e*x)^(7/2))","C",1
917,1,25,95,0.0091166,"\int \frac{1}{\sqrt[4]{1-x} (e x)^{11/2} \sqrt[4]{1+x}} \, dx","Integrate[1/((1 - x)^(1/4)*(e*x)^(11/2)*(1 + x)^(1/4)),x]","-\frac{2 x \, _2F_1\left(-\frac{9}{4},\frac{1}{4};-\frac{5}{4};x^2\right)}{9 (e x)^{11/2}}","-\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,"(-2*x*Hypergeometric2F1[-9/4, 1/4, -5/4, x^2])/(9*(e*x)^(11/2))","C",1
918,1,87,104,0.0753836,"\int x^2 (a+b x)^n (c+d x) \, dx","Integrate[x^2*(a + b*x)^n*(c + d*x),x]","\frac{(a+b x)^{n+1} \left(\frac{a^2 (b c-a d)}{n+1}+\frac{(a+b x)^2 (b c-3 a d)}{n+3}+\frac{a (a+b x) (3 a d-2 b c)}{n+2}+\frac{d (a+b x)^3}{n+4}\right)}{b^4}","\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,"((a + b*x)^(1 + n)*((a^2*(b*c - a*d))/(1 + n) + (a*(-2*b*c + 3*a*d)*(a + b*x))/(2 + n) + ((b*c - 3*a*d)*(a + b*x)^2)/(3 + n) + (d*(a + b*x)^3)/(4 + n)))/b^4","A",1
919,1,74,74,0.054359,"\int x (a+b x)^n (c+d x) \, dx","Integrate[x*(a + b*x)^n*(c + d*x),x]","-\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)}","-\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,"-((a*(b*c - a*d)*(a + b*x)^(1 + n))/(b^3*(1 + n))) + ((b*c - 2*a*d)*(a + b*x)^(2 + n))/(b^3*(2 + n)) + (d*(a + b*x)^(3 + n))/(b^3*(3 + n))","A",1
920,1,41,46,0.0296968,"\int (a+b x)^n (c+d x) \, dx","Integrate[(a + b*x)^n*(c + d*x),x]","\frac{(a+b x)^{n+1} (-a d+b c (n+2)+b d (n+1) x)}{b^2 (n+1) (n+2)}","\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,"((a + b*x)^(1 + n)*(-(a*d) + b*c*(2 + n) + b*d*(1 + n)*x))/(b^2*(1 + n)*(2 + n))","A",1
921,1,45,56,0.0145795,"\int \frac{(a+b x)^n (c+d x)}{x} \, dx","Integrate[((a + b*x)^n*(c + d*x))/x,x]","\frac{(a+b x)^{n+1} \left(a d-b c \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)\right)}{a b (n+1)}","\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,"((a + b*x)^(1 + n)*(a*d - b*c*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a]))/(a*b*(1 + n))","A",1
922,1,55,62,0.0212131,"\int \frac{(a+b x)^n (c+d x)}{x^2} \, dx","Integrate[((a + b*x)^n*(c + d*x))/x^2,x]","-\frac{(a+b x)^{n+1} \left(x (a d+b c n) \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)+a c (n+1)\right)}{a^2 (n+1) x}","-\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,"-(((a + b*x)^(1 + n)*(a*c*(1 + n) + (a*d + b*c*n)*x*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a]))/(a^2*(1 + n)*x))","A",1
923,1,136,157,0.1083325,"\int x^2 (a+b x)^n (c+d x)^2 \, dx","Integrate[x^2*(a + b*x)^n*(c + d*x)^2,x]","\frac{(a+b x)^{n+1} \left(\frac{(a+b x)^2 \left(6 a^2 d^2-6 a b c d+b^2 c^2\right)}{n+3}+\frac{a^2 (b c-a d)^2}{n+1}+\frac{2 d (a+b x)^3 (b c-2 a d)}{n+4}-\frac{2 a (a+b x) (b c-2 a d) (b c-a d)}{n+2}+\frac{d^2 (a+b x)^4}{n+5}\right)}{b^5}","\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,"((a + b*x)^(1 + n)*((a^2*(b*c - a*d)^2)/(1 + n) - (2*a*(b*c - 2*a*d)*(b*c - a*d)*(a + b*x))/(2 + n) + ((b^2*c^2 - 6*a*b*c*d + 6*a^2*d^2)*(a + b*x)^2)/(3 + n) + (2*d*(b*c - 2*a*d)*(a + b*x)^3)/(4 + n) + (d^2*(a + b*x)^4)/(5 + n)))/b^5","A",1
924,1,98,114,0.0715733,"\int x (a+b x)^n (c+d x)^2 \, dx","Integrate[x*(a + b*x)^n*(c + d*x)^2,x]","\frac{(a+b x)^{n+1} \left(\frac{d (a+b x)^2 (2 b c-3 a d)}{n+3}+\frac{(a+b x) (b c-3 a d) (b c-a d)}{n+2}-\frac{a (b c-a d)^2}{n+1}+\frac{d^2 (a+b x)^3}{n+4}\right)}{b^4}","-\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,"((a + b*x)^(1 + n)*(-((a*(b*c - a*d)^2)/(1 + n)) + ((b*c - 3*a*d)*(b*c - a*d)*(a + b*x))/(2 + n) + (d*(2*b*c - 3*a*d)*(a + b*x)^2)/(3 + n) + (d^2*(a + b*x)^3)/(4 + n)))/b^4","A",1
925,1,67,78,0.0787817,"\int (a+b x)^n (c+d x)^2 \, dx","Integrate[(a + b*x)^n*(c + d*x)^2,x]","\frac{(a+b x)^{n+1} \left(\frac{2 d (a+b x) (b c-a d)}{n+2}+\frac{(b c-a d)^2}{n+1}+\frac{d^2 (a+b x)^2}{n+3}\right)}{b^3}","\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,"((a + b*x)^(1 + n)*((b*c - a*d)^2/(1 + n) + (2*d*(b*c - a*d)*(a + b*x))/(2 + n) + (d^2*(a + b*x)^2)/(3 + n)))/b^3","A",1
926,1,77,88,0.0641925,"\int \frac{(a+b x)^n (c+d x)^2}{x} \, dx","Integrate[((a + b*x)^n*(c + d*x)^2)/x,x]","-\frac{(a+b x)^{n+1} \left(b^2 c^2 (n+2) \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)+a d (a d-b (2 c (n+2)+d (n+1) x))\right)}{a b^2 (n+1) (n+2)}","\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,"-(((a + b*x)^(1 + n)*(a*d*(a*d - b*(2*c*(2 + n) + d*(1 + n)*x)) + b^2*c^2*(2 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a]))/(a*b^2*(1 + n)*(2 + n)))","A",1
927,1,73,87,0.0336312,"\int \frac{(a+b x)^n (c+d x)^2}{x^2} \, dx","Integrate[((a + b*x)^n*(c + d*x)^2)/x^2,x]","\frac{(a+b x)^{n+1} \left(a \left(a d^2 x-b c^2 (n+1)\right)-b c x (2 a d+b c n) \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)\right)}{a^2 b (n+1) x}","-\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,"((a + b*x)^(1 + n)*(a*(-(b*c^2*(1 + n)) + a*d^2*x) - b*c*(2*a*d + b*c*n)*x*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a]))/(a^2*b*(1 + n)*x)","A",1
928,1,94,124,0.0530401,"\int \frac{(a+b x)^n (c+d x)^2}{x^3} \, dx","Integrate[((a + b*x)^n*(c + d*x)^2)/x^3,x]","-\frac{(a+b x)^{n+1} \left(x^2 \left(2 a^2 d^2+4 a b c d n+b^2 c^2 (n-1) n\right) \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)+a c (n+1) (a (c+4 d x)+b c (n-1) x)\right)}{2 a^3 (n+1) x^2}","-\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,"-1/2*((a + b*x)^(1 + n)*(a*c*(1 + n)*(b*c*(-1 + n)*x + a*(c + 4*d*x)) + (2*a^2*d^2 + 4*a*b*c*d*n + b^2*c^2*(-1 + n)*n)*x^2*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a]))/(a^3*(1 + n)*x^2)","A",1
929,1,105,130,0.0577925,"\int \frac{(a+b x)^n (c+d x)^2}{x^4} \, dx","Integrate[((a + b*x)^n*(c + d*x)^2)/x^4,x]","\frac{(a+b x)^{n+1} \left(b x^3 \left(6 a^2 d^2+6 a b c d (n-1)+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)-a^2 c (n+1) (2 a (c+3 d x)+b c (n-2) x)\right)}{6 a^4 (n+1) x^3}","-\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,"((a + b*x)^(1 + n)*(-(a^2*c*(1 + n)*(b*c*(-2 + n)*x + 2*a*(c + 3*d*x))) + b*(6*a^2*d^2 + 6*a*b*c*d*(-1 + n) + b^2*c^2*(2 - 3*n + n^2))*x^3*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (b*x)/a]))/(6*a^4*(1 + n)*x^3)","A",1
930,1,185,212,0.2017749,"\int x^2 (a+b x)^n (c+d x)^3 \, dx","Integrate[x^2*(a + b*x)^n*(c + d*x)^3,x]","\frac{(a+b x)^{n+1} \left(\frac{d (a+b x)^3 \left(10 a^2 d^2-12 a b c d+3 b^2 c^2\right)}{n+4}+\frac{(a+b x)^2 (b c-a d) \left(10 a^2 d^2-8 a b c d+b^2 c^2\right)}{n+3}+\frac{a^2 (b c-a d)^3}{n+1}+\frac{d^2 (a+b x)^4 (3 b c-5 a d)}{n+5}+\frac{a (a+b x) (b c-a d)^2 (5 a d-2 b c)}{n+2}+\frac{d^3 (a+b x)^5}{n+6}\right)}{b^6}","\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,"((a + b*x)^(1 + n)*((a^2*(b*c - a*d)^3)/(1 + n) + (a*(b*c - a*d)^2*(-2*b*c + 5*a*d)*(a + b*x))/(2 + n) + ((b*c - a*d)*(b^2*c^2 - 8*a*b*c*d + 10*a^2*d^2)*(a + b*x)^2)/(3 + n) + (d*(3*b^2*c^2 - 12*a*b*c*d + 10*a^2*d^2)*(a + b*x)^3)/(4 + n) + (d^2*(3*b*c - 5*a*d)*(a + b*x)^4)/(5 + n) + (d^3*(a + b*x)^5)/(6 + n)))/b^6","A",1
931,1,132,154,0.1338342,"\int x (a+b x)^n (c+d x)^3 \, dx","Integrate[x*(a + b*x)^n*(c + d*x)^3,x]","\frac{(a+b x)^{n+1} \left(\frac{d^2 (a+b x)^3 (3 b c-4 a d)}{n+4}+\frac{3 d (a+b x)^2 (b c-2 a d) (b c-a d)}{n+3}+\frac{(a+b x) (b c-4 a d) (b c-a d)^2}{n+2}+\frac{a (a d-b c)^3}{n+1}+\frac{d^3 (a+b x)^4}{n+5}\right)}{b^5}","\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,"((a + b*x)^(1 + n)*((a*(-(b*c) + a*d)^3)/(1 + n) + ((b*c - 4*a*d)*(b*c - a*d)^2*(a + b*x))/(2 + n) + (3*d*(b*c - 2*a*d)*(b*c - a*d)*(a + b*x)^2)/(3 + n) + (d^2*(3*b*c - 4*a*d)*(a + b*x)^3)/(4 + n) + (d^3*(a + b*x)^4)/(5 + n)))/b^5","A",1
932,1,94,110,0.0788744,"\int (a+b x)^n (c+d x)^3 \, dx","Integrate[(a + b*x)^n*(c + d*x)^3,x]","\frac{(a+b x)^{n+1} \left(\frac{3 d^2 (a+b x)^2 (b c-a d)}{n+3}+\frac{3 d (a+b x) (b c-a d)^2}{n+2}+\frac{(b c-a d)^3}{n+1}+\frac{d^3 (a+b x)^3}{n+4}\right)}{b^4}","\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,"((a + b*x)^(1 + n)*((b*c - a*d)^3/(1 + n) + (3*d*(b*c - a*d)^2*(a + b*x))/(2 + n) + (3*d^2*(b*c - a*d)*(a + b*x)^2)/(3 + n) + (d^3*(a + b*x)^3)/(4 + n)))/b^4","A",1
933,1,117,131,0.1311158,"\int \frac{(a+b x)^n (c+d x)^3}{x} \, dx","Integrate[((a + b*x)^n*(c + d*x)^3)/x,x]","(a+b x)^{n+1} \left(\frac{d \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{b^3 (n+1)}+\frac{d^2 (a+b x) (3 b c-2 a d)}{b^3 (n+2)}+\frac{d^3 (a+b x)^2}{b^3 (n+3)}-\frac{c^3 \, _2F_1\left(1,n+1;n+2;\frac{a+b x}{a}\right)}{a n+a}\right)","\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,"(a + b*x)^(1 + n)*((d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2))/(b^3*(1 + n)) + (d^2*(3*b*c - 2*a*d)*(a + b*x))/(b^3*(2 + n)) + (d^3*(a + b*x)^2)/(b^3*(3 + n)) - (c^3*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*x)/a])/(a + a*n))","A",1
934,1,114,143,0.0778818,"\int \frac{(a+b x)^n (c+d x)^3}{x^2} \, dx","Integrate[((a + b*x)^n*(c + d*x)^3)/x^2,x]","-\frac{(a+b x)^{n+1} \left(a \left(a^2 d^3 x-a b d^2 x (3 c (n+2)+d (n+1) x)+b^2 c^3 \left(n^2+3 n+2\right)\right)+b^2 c^2 (n+2) x (3 a d+b c n) \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)\right)}{a^2 b^2 (n+1) (n+2) x}","-\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,"-(((a + b*x)^(1 + n)*(a*(b^2*c^3*(2 + 3*n + n^2) + a^2*d^3*x - a*b*d^2*x*(3*c*(2 + n) + d*(1 + n)*x)) + b^2*c^2*(2 + n)*(3*a*d + b*c*n)*x*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a]))/(a^2*b^2*(1 + n)*(2 + n)*x))","A",1
935,1,122,176,0.0700955,"\int \frac{(a+b x)^n (c+d x)^3}{x^3} \, dx","Integrate[((a + b*x)^n*(c + d*x)^3)/x^3,x]","\frac{(a+b x)^{n+1} \left(a \left(2 a^2 d^3 x^2-a b c^2 (n+1) (c+6 d x)-b^2 c^3 \left(n^2-1\right) x\right)-b c x^2 \left(6 a^2 d^2+6 a b c d n+b^2 c^2 (n-1) n\right) \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)\right)}{2 a^3 b (n+1) x^2}","-\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,"((a + b*x)^(1 + n)*(a*(-(b^2*c^3*(-1 + n^2)*x) + 2*a^2*d^3*x^2 - a*b*c^2*(1 + n)*(c + 6*d*x)) - b*c*(6*a^2*d^2 + 6*a*b*c*d*n + b^2*c^2*(-1 + n)*n)*x^2*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a]))/(2*a^3*b*(1 + n)*x^2)","A",1
936,1,22,22,0.0106937,"\int x^{1+2 n} (a+b x)^n (2 a+3 b x) \, dx","Integrate[x^(1 + 2*n)*(a + b*x)^n*(2*a + 3*b*x),x]","\frac{x^{2 n+2} (a+b x)^{n+1}}{n+1}","\frac{x^{2 (n+1)} (a+b x)^{n+1}}{n+1}",1,"(x^(2 + 2*n)*(a + b*x)^(1 + n))/(1 + n)","A",1
937,1,100,108,0.1005138,"\int \frac{x^2 (a+b x)^n}{c+d x} \, dx","Integrate[(x^2*(a + b*x)^n)/(c + d*x),x]","\frac{(a+b x)^{n+1} \left(b^2 c^2 (n+2) \, _2F_1\left(1,n+1;n+2;\frac{d (a+b x)}{a d-b c}\right)-(b c-a d) (a d+b c (n+2)-b d (n+1) x)\right)}{b^2 d^2 (n+1) (n+2) (b c-a d)}","-\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,"((a + b*x)^(1 + n)*(-((b*c - a*d)*(a*d + b*c*(2 + n) - b*d*(1 + n)*x)) + b^2*c^2*(2 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)]))/(b^2*d^2*(b*c - a*d)*(1 + n)*(2 + n))","A",1
938,1,68,78,0.0173455,"\int \frac{x (a+b x)^n}{c+d x} \, dx","Integrate[(x*(a + b*x)^n)/(c + d*x),x]","-\frac{(a+b x)^{n+1} \left(b c \, _2F_1\left(1,n+1;n+2;\frac{d (a+b x)}{a d-b c}\right)+a d-b c\right)}{b d (n+1) (b c-a d)}","\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,"-(((a + b*x)^(1 + n)*(-(b*c) + a*d + b*c*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)]))/(b*d*(b*c - a*d)*(1 + n)))","A",1
939,1,51,51,0.0096424,"\int \frac{(a+b x)^n}{c+d x} \, dx","Integrate[(a + b*x)^n/(c + d*x),x]","-\frac{(a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{d (a+b x)}{a d-b c}\right)}{(n+1) (a d-b c)}","\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,"-(((a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)])/((-(b*c) + a*d)*(1 + n)))","A",1
940,1,85,95,0.0300537,"\int \frac{(a+b x)^n}{x (c+d x)} \, dx","Integrate[(a + b*x)^n/(x*(c + d*x)),x]","\frac{(a+b x)^{n+1} \left(a d \, _2F_1\left(1,n+1;n+2;\frac{d (a+b x)}{a d-b c}\right)+(b c-a d) \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)\right)}{a c (n+1) (a d-b c)}","-\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,"((a + b*x)^(1 + n)*(a*d*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)] + (b*c - a*d)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a]))/(a*c*(-(b*c) + a*d)*(1 + n))","A",1
941,1,113,124,0.0546038,"\int \frac{(a+b x)^n}{x^2 (c+d x)} \, dx","Integrate[(a + b*x)^n/(x^2*(c + d*x)),x]","-\frac{(a+b x)^{n+1} \left(a^2 d^2 x \, _2F_1\left(1,n+1;n+2;\frac{d (a+b x)}{a d-b c}\right)+(a d-b c) \left(\, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right) (b c n x-a d x)+a c (n+1)\right)\right)}{a^2 c^2 (n+1) x (a d-b c)}","\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,"-(((a + b*x)^(1 + n)*(a^2*d^2*x*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)] + (-(b*c) + a*d)*(a*c*(1 + n) + (-(a*d*x) + b*c*n*x)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])))/(a^2*c^2*(-(b*c) + a*d)*(1 + n)*x))","A",1
942,1,176,203,0.2183143,"\int \frac{x^3 (a+b x)^n}{(c+d x)^2} \, dx","Integrate[(x^3*(a + b*x)^n)/(c + d*x)^2,x]","\frac{(a+b x)^{n+1} \left(\frac{a^2 d^2 (c+d x)+a b c d (c (2 n+3)+d (n+2) x)-b^2 c^2 (n+3) (c (n+2)+d x)}{b d^2 (n+1) (c+d x) (b c-a d)}+\frac{b c^2 (n+2) (b c (n+3)-3 a d) \, _2F_1\left(1,n+1;n+2;\frac{d (a+b x)}{a d-b c}\right)}{d^2 (n+1) (b c-a d)^2}+\frac{x^2}{c+d x}\right)}{b d (n+2)}","-\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,"((a + b*x)^(1 + n)*(x^2/(c + d*x) + (a^2*d^2*(c + d*x) - b^2*c^2*(3 + n)*(c*(2 + n) + d*x) + a*b*c*d*(c*(3 + 2*n) + d*(2 + n)*x))/(b*d^2*(b*c - a*d)*(1 + n)*(c + d*x)) + (b*c^2*(2 + n)*(-3*a*d + b*c*(3 + n))*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)])/(d^2*(b*c - a*d)^2*(1 + n))))/(b*d*(2 + n))","A",1
943,1,115,122,0.0891193,"\int \frac{x^2 (a+b x)^n}{(c+d x)^2} \, dx","Integrate[(x^2*(a + b*x)^n)/(c + d*x)^2,x]","\frac{(a+b x)^{n+1} \left((b c-a d) (b c (c (n+2)+d x)-a d (c+d x))-b c (c+d x) (b c (n+2)-2 a d) \, _2F_1\left(1,n+1;n+2;\frac{d (a+b x)}{a d-b c}\right)\right)}{b d^2 (n+1) (c+d x) (b c-a d)^2}","\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,"((a + b*x)^(1 + n)*((b*c - a*d)*(-(a*d*(c + d*x)) + b*c*(c*(2 + n) + d*x)) - b*c*(-2*a*d + b*c*(2 + n))*(c + d*x)*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)]))/(b*d^2*(b*c - a*d)^2*(1 + n)*(c + d*x))","A",1
944,1,83,99,0.0418958,"\int \frac{x (a+b x)^n}{(c+d x)^2} \, dx","Integrate[(x*(a + b*x)^n)/(c + d*x)^2,x]","\frac{(a+b x)^{n+1} \left(\frac{(b c (n+1)-a d) \, _2F_1\left(1,n+1;n+2;\frac{d (a+b x)}{a d-b c}\right)}{n+1}+\frac{c (a d-b c)}{c+d x}\right)}{d (b c-a d)^2}","-\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,"((a + b*x)^(1 + n)*((c*(-(b*c) + a*d))/(c + d*x) + ((-(a*d) + b*c*(1 + n))*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)])/(1 + n)))/(d*(b*c - a*d)^2)","A",1
945,1,52,52,0.014665,"\int \frac{(a+b x)^n}{(c+d x)^2} \, dx","Integrate[(a + b*x)^n/(c + d*x)^2,x]","\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}","\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,"(b*(a + b*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))])/((b*c - a*d)^2*(1 + n))","A",1
946,1,111,139,0.1392324,"\int \frac{(a+b x)^n}{x (c+d x)^2} \, dx","Integrate[(a + b*x)^n/(x*(c + d*x)^2),x]","\frac{(a+b x)^{n+1} \left(\frac{d \left(\frac{(a d+b c (n-1)) \, _2F_1\left(1,n+1;n+2;\frac{d (a+b x)}{a d-b c}\right)}{n+1}+\frac{c (a d-b c)}{c+d x}\right)}{(b c-a d)^2}-\frac{\, _2F_1\left(1,n+1;n+2;\frac{a+b x}{a}\right)}{a n+a}\right)}{c^2}","\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,"((a + b*x)^(1 + n)*(-(Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*x)/a]/(a + a*n)) + (d*((c*(-(b*c) + a*d))/(c + d*x) + ((a*d + b*c*(-1 + n))*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)])/(1 + n)))/(b*c - a*d)^2))/c^2","A",1
947,1,176,190,0.1676211,"\int \frac{(a+b x)^n}{x^2 (c+d x)^2} \, dx","Integrate[(a + b*x)^n/(x^2*(c + d*x)^2),x]","-\frac{(a+b x)^{n+1} \left(-x (c+d x) \left((b c-a d)^2 (2 a d-b c n) \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)-a^2 d^2 (2 a d+b c (n-2)) \, _2F_1\left(1,n+1;n+2;\frac{d (a+b x)}{a d-b c}\right)\right)+a c^2 (n+1) (b c-a d)^2+a c d (n+1) x (a d-b c) (2 a d-b c)\right)}{a^2 c^3 (n+1) x (c+d x) (b c-a d)^2}","\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,"-(((a + b*x)^(1 + n)*(a*c^2*(b*c - a*d)^2*(1 + n) + a*c*d*(-(b*c) + a*d)*(-(b*c) + 2*a*d)*(1 + n)*x - x*(c + d*x)*(-(a^2*d^2*(2*a*d + b*c*(-2 + n))*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)]) + (b*c - a*d)^2*(2*a*d - b*c*n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])))/(a^2*c^3*(b*c - a*d)^2*(1 + n)*x*(c + d*x)))","A",1
948,1,146,195,0.154072,"\int (b x)^{5/2} (c+d x)^n (e+f x)^2 \, dx","Integrate[(b*x)^(5/2)*(c + d*x)^n*(e + f*x)^2,x]","\frac{2 x (b x)^{5/2} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} \left(\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 f (c+d x) \left(\frac{d x}{c}+1\right)^n (9 c f-d (e (4 n+22)+f (2 n+9) x))\right)}{7 d^2 (2 n+9) (2 n+11)}","\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,"(2*x*(b*x)^(5/2)*(c + d*x)^n*(-7*f*(c + d*x)*(1 + (d*x)/c)^n*(9*c*f - d*(e*(22 + 4*n) + f*(9 + 2*n)*x)) + (63*c^2*f^2 - 14*c*d*e*f*(11 + 2*n) + d^2*e^2*(99 + 40*n + 4*n^2))*Hypergeometric2F1[7/2, -n, 9/2, -((d*x)/c)]))/(7*d^2*(9 + 2*n)*(11 + 2*n)*(1 + (d*x)/c)^n)","A",1
949,1,91,107,0.0548019,"\int (b x)^{5/2} (c+d x)^n (e+f x) \, dx","Integrate[(b*x)^(5/2)*(c + d*x)^n*(e + f*x),x]","\frac{2 x (b x)^{5/2} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} \left((d e (2 n+9)-7 c f) \, _2F_1\left(\frac{7}{2},-n;\frac{9}{2};-\frac{d x}{c}\right)+7 f (c+d x) \left(\frac{d x}{c}+1\right)^n\right)}{7 d (2 n+9)}","\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,"(2*x*(b*x)^(5/2)*(c + d*x)^n*(7*f*(c + d*x)*(1 + (d*x)/c)^n + (-7*c*f + d*e*(9 + 2*n))*Hypergeometric2F1[7/2, -n, 9/2, -((d*x)/c)]))/(7*d*(9 + 2*n)*(1 + (d*x)/c)^n)","A",1
950,1,134,61,0.1350353,"\int \frac{(b x)^{5/2} (c+d x)^n}{e+f x} \, dx","Integrate[((b*x)^(5/2)*(c + d*x)^n)/(e + f*x),x]","\frac{2 b^2 \sqrt{b x} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} \left(-15 e^2 F_1\left(\frac{1}{2};-n,1;\frac{3}{2};-\frac{d x}{c},-\frac{f x}{e}\right)+15 e^2 \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};-\frac{d x}{c}\right)+f x \left(3 f x \, _2F_1\left(\frac{5}{2},-n;\frac{7}{2};-\frac{d x}{c}\right)-5 e \, _2F_1\left(\frac{3}{2},-n;\frac{5}{2};-\frac{d x}{c}\right)\right)\right)}{15 f^3}","\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,"(2*b^2*Sqrt[b*x]*(c + d*x)^n*(-15*e^2*AppellF1[1/2, -n, 1, 3/2, -((d*x)/c), -((f*x)/e)] + 15*e^2*Hypergeometric2F1[1/2, -n, 3/2, -((d*x)/c)] + f*x*(-5*e*Hypergeometric2F1[3/2, -n, 5/2, -((d*x)/c)] + 3*f*x*Hypergeometric2F1[5/2, -n, 7/2, -((d*x)/c)])))/(15*f^3*(1 + (d*x)/c)^n)","B",0
951,1,133,61,0.1384456,"\int \frac{(b x)^{5/2} (c+d x)^n}{(e+f x)^2} \, dx","Integrate[((b*x)^(5/2)*(c + d*x)^n)/(e + f*x)^2,x]","\frac{2 b^2 \sqrt{b x} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} \left(9 e F_1\left(\frac{1}{2};-n,1;\frac{3}{2};-\frac{d x}{c},-\frac{f x}{e}\right)-3 e F_1\left(\frac{1}{2};-n,2;\frac{3}{2};-\frac{d x}{c},-\frac{f x}{e}\right)-6 e \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};-\frac{d x}{c}\right)+f x \, _2F_1\left(\frac{3}{2},-n;\frac{5}{2};-\frac{d x}{c}\right)\right)}{3 f^3}","\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,"(2*b^2*Sqrt[b*x]*(c + d*x)^n*(9*e*AppellF1[1/2, -n, 1, 3/2, -((d*x)/c), -((f*x)/e)] - 3*e*AppellF1[1/2, -n, 2, 3/2, -((d*x)/c), -((f*x)/e)] - 6*e*Hypergeometric2F1[1/2, -n, 3/2, -((d*x)/c)] + f*x*Hypergeometric2F1[3/2, -n, 5/2, -((d*x)/c)]))/(3*f^3*(1 + (d*x)/c)^n)","B",0
952,1,153,209,0.282137,"\int (b x)^m (c+d x)^n (e+f x)^2 \, dx","Integrate[(b*x)^m*(c + d*x)^n*(e + f*x)^2,x]","\frac{x (b x)^m (c+d x)^n \left(f (c+d x) (e+f x)-\frac{\left(\frac{d x}{c}+1\right)^{-n} (d e (m+n+2) (c f (m+1)-d e (m+n+3))-c f (m+1) (c f (m+2)-d e (m+n+4))) \, _2F_1\left(m+1,-n;m+2;-\frac{d x}{c}\right)+f (m+1) (c+d x) (c f (m+2)-d e (m+n+4))}{d (m+1) (m+n+2)}\right)}{d (m+n+3)}","\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,"(x*(b*x)^m*(c + d*x)^n*(f*(c + d*x)*(e + f*x) - (f*(1 + m)*(c*f*(2 + m) - d*e*(4 + m + n))*(c + d*x) + ((d*e*(2 + m + n)*(c*f*(1 + m) - d*e*(3 + m + n)) - c*f*(1 + m)*(c*f*(2 + m) - d*e*(4 + m + n)))*Hypergeometric2F1[1 + m, -n, 2 + m, -((d*x)/c)])/(1 + (d*x)/c)^n)/(d*(1 + m)*(2 + m + n))))/(d*(3 + m + n))","A",1
953,1,81,108,0.0386101,"\int (b x)^m (c+d x)^n (e+f x) \, dx","Integrate[(b*x)^m*(c + d*x)^n*(e + f*x),x]","\frac{x (b x)^m (c+d x)^n \left(\frac{\left(\frac{d x}{c}+1\right)^{-n} (d e (m+n+2)-c f (m+1)) \, _2F_1\left(m+1,-n;m+2;-\frac{d x}{c}\right)}{m+1}+f (c+d x)\right)}{d (m+n+2)}","\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,"(x*(b*x)^m*(c + d*x)^n*(f*(c + d*x) + ((-(c*f*(1 + m)) + d*e*(2 + m + n))*Hypergeometric2F1[1 + m, -n, 2 + m, -((d*x)/c)])/((1 + m)*(1 + (d*x)/c)^n)))/(d*(2 + m + n))","A",1
954,1,60,63,0.0637389,"\int \frac{(b x)^m (c+d x)^n}{e+f x} \, dx","Integrate[((b*x)^m*(c + d*x)^n)/(e + f*x),x]","\frac{x (b x)^m (c+d x)^n \left(\frac{c+d x}{c}\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{d x}{c},-\frac{f x}{e}\right)}{e (m+1)}","\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,"(x*(b*x)^m*(c + d*x)^n*AppellF1[1 + m, -n, 1, 2 + m, -((d*x)/c), -((f*x)/e)])/(e*(1 + m)*((c + d*x)/c)^n)","A",1
955,1,60,63,0.0611325,"\int \frac{(b x)^m (c+d x)^n}{(e+f x)^2} \, dx","Integrate[((b*x)^m*(c + d*x)^n)/(e + f*x)^2,x]","\frac{x (b x)^m (c+d x)^n \left(\frac{c+d x}{c}\right)^{-n} F_1\left(m+1;-n,2;m+2;-\frac{d x}{c},-\frac{f x}{e}\right)}{e^2 (m+1)}","\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,"(x*(b*x)^m*(c + d*x)^n*AppellF1[1 + m, -n, 2, 2 + m, -((d*x)/c), -((f*x)/e)])/(e^2*(1 + m)*((c + d*x)/c)^n)","A",1
956,1,79,81,0.1119044,"\int (b x)^m (c+d x)^n (e+f x)^p \, dx","Integrate[(b*x)^m*(c + d*x)^n*(e + f*x)^p,x]","\frac{x (b x)^m (c+d x)^n \left(\frac{c+d x}{c}\right)^{-n} (e+f x)^p \left(\frac{e+f x}{e}\right)^{-p} F_1\left(m+1;-n,-p;m+2;-\frac{d x}{c},-\frac{f x}{e}\right)}{m+1}","\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,"(x*(b*x)^m*(c + d*x)^n*(e + f*x)^p*AppellF1[1 + m, -n, -p, 2 + m, -((d*x)/c), -((f*x)/e)])/((1 + m)*((c + d*x)/c)^n*((e + f*x)/e)^p)","A",1
957,1,172,211,0.1222362,"\int (e x)^m (a-b x)^{2+n} (a+b x)^n \, dx","Integrate[(e*x)^m*(a - b*x)^(2 + n)*(a + b*x)^n,x]","\frac{x (e x)^m (a-b x)^n (a+b x)^n \left(1-\frac{b^2 x^2}{a^2}\right)^{-n} \left(a^2 \left(m^2+5 m+6\right) \, _2F_1\left(\frac{m+1}{2},-n;\frac{m+3}{2};\frac{b^2 x^2}{a^2}\right)-b (m+1) x \left(2 a (m+3) \, _2F_1\left(\frac{m+2}{2},-n;\frac{m+4}{2};\frac{b^2 x^2}{a^2}\right)-b (m+2) x \, _2F_1\left(\frac{m+3}{2},-n;\frac{m+5}{2};\frac{b^2 x^2}{a^2}\right)\right)\right)}{(m+1) (m+2) (m+3)}","-\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,"(x*(e*x)^m*(a - b*x)^n*(a + b*x)^n*(a^2*(6 + 5*m + m^2)*Hypergeometric2F1[(1 + m)/2, -n, (3 + m)/2, (b^2*x^2)/a^2] - b*(1 + m)*x*(2*a*(3 + m)*Hypergeometric2F1[(2 + m)/2, -n, (4 + m)/2, (b^2*x^2)/a^2] - b*(2 + m)*x*Hypergeometric2F1[(3 + m)/2, -n, (5 + m)/2, (b^2*x^2)/a^2])))/((1 + m)*(2 + m)*(3 + m)*(1 - (b^2*x^2)/a^2)^n)","A",1
958,1,178,206,0.2406551,"\int x^2 (a+b x)^n (c+d x)^p \, dx","Integrate[x^2*(a + b*x)^n*(c + d*x)^p,x]","\frac{(a+b x)^{n+1} (c+d x)^p \left(\frac{\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) \left(\frac{b (c+d x)}{b c-a d}\right)^{-p} \, _2F_1\left(n+1,-p;n+2;\frac{d (a+b x)}{a d-b c}\right)}{b^2 d (n+1) (n+p+2)}-\frac{(c+d x) (a d (p+2)+b c (n+2))}{b d (n+p+2)}+x (c+d x)\right)}{b d (n+p+3)}","-\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,"((a + b*x)^(1 + n)*(c + d*x)^p*(-(((b*c*(2 + n) + a*d*(2 + p))*(c + d*x))/(b*d*(2 + n + p))) + x*(c + d*x) + ((b^2*c^2*(2 + 3*n + n^2) + 2*a*b*c*d*(1 + n)*(1 + p) + a^2*d^2*(2 + 3*p + p^2))*Hypergeometric2F1[1 + n, -p, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)])/(b^2*d*(1 + n)*(2 + n + p)*((b*(c + d*x))/(b*c - a*d))^p)))/(b*d*(3 + n + p))","A",1
959,1,105,117,0.072724,"\int x (a+b x)^n (c+d x)^p \, dx","Integrate[x*(a + b*x)^n*(c + d*x)^p,x]","\frac{(a+b x)^{n+1} (c+d x)^p \left(b (c+d x)-\frac{(a d (p+1)+b c (n+1)) \left(\frac{b (c+d x)}{b c-a d}\right)^{-p} \, _2F_1\left(n+1,-p;n+2;\frac{d (a+b x)}{a d-b c}\right)}{n+1}\right)}{b^2 d (n+p+2)}","\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,"((a + b*x)^(1 + n)*(c + d*x)^p*(b*(c + d*x) - ((b*c*(1 + n) + a*d*(1 + p))*Hypergeometric2F1[1 + n, -p, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)])/((1 + n)*((b*(c + d*x))/(b*c - a*d))^p)))/(b^2*d*(2 + n + p))","A",1
960,1,73,61,0.0222928,"\int (a+b x)^n (c+d x)^p \, dx","Integrate[(a + b*x)^n*(c + d*x)^p,x]","\frac{(a+b x)^{n+1} (c+d x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-p} \, _2F_1\left(n+1,-p;n+2;\frac{d (a+b x)}{a d-b c}\right)}{b (n+1)}","-\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,"((a + b*x)^(1 + n)*(c + d*x)^p*Hypergeometric2F1[1 + n, -p, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(1 + n)*((b*(c + d*x))/(b*c - a*d))^p)","A",1
961,1,88,85,0.063829,"\int \frac{(a+b x)^n (c+d x)^p}{x} \, dx","Integrate[((a + b*x)^n*(c + d*x)^p)/x,x]","\frac{\left(\frac{a}{b x}+1\right)^{-n} (a+b x)^n \left(\frac{c}{d x}+1\right)^{-p} (c+d x)^p F_1\left(-n-p;-n,-p;-n-p+1;-\frac{a}{b x},-\frac{c}{d x}\right)}{n+p}","-\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,"((a + b*x)^n*(c + d*x)^p*AppellF1[-n - p, -n, -p, 1 - n - p, -(a/(b*x)), -(c/(d*x))])/((n + p)*(1 + a/(b*x))^n*(1 + c/(d*x))^p)","A",0
962,1,93,85,0.057858,"\int \frac{(a+b x)^n (c+d x)^p}{x^2} \, dx","Integrate[((a + b*x)^n*(c + d*x)^p)/x^2,x]","\frac{\left(\frac{a}{b x}+1\right)^{-n} (a+b x)^n \left(\frac{c}{d x}+1\right)^{-p} (c+d x)^p F_1\left(-n-p+1;-n,-p;-n-p+2;-\frac{a}{b x},-\frac{c}{d x}\right)}{x (n+p-1)}","\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,"((a + b*x)^n*(c + d*x)^p*AppellF1[1 - n - p, -n, -p, 2 - n - p, -(a/(b*x)), -(c/(d*x))])/((-1 + n + p)*(1 + a/(b*x))^n*(1 + c/(d*x))^p*x)","A",0
963,1,79,79,0.0799068,"\int (b x)^{3/2} (c+d x)^n (e+f x)^p \, dx","Integrate[(b*x)^(3/2)*(c + d*x)^n*(e + f*x)^p,x]","\frac{2}{5} x (b x)^{3/2} (c+d x)^n \left(\frac{c+d x}{c}\right)^{-n} (e+f x)^p \left(\frac{e+f x}{e}\right)^{-p} F_1\left(\frac{5}{2};-n,-p;\frac{7}{2};-\frac{d x}{c},-\frac{f x}{e}\right)","\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,"(2*x*(b*x)^(3/2)*(c + d*x)^n*(e + f*x)^p*AppellF1[5/2, -n, -p, 7/2, -((d*x)/c), -((f*x)/e)])/(5*((c + d*x)/c)^n*((e + f*x)/e)^p)","A",1
964,1,79,79,0.0568185,"\int \sqrt{b x} (c+d x)^n (e+f x)^p \, dx","Integrate[Sqrt[b*x]*(c + d*x)^n*(e + f*x)^p,x]","\frac{2}{3} x \sqrt{b x} (c+d x)^n \left(\frac{c+d x}{c}\right)^{-n} (e+f x)^p \left(\frac{e+f x}{e}\right)^{-p} F_1\left(\frac{3}{2};-n,-p;\frac{5}{2};-\frac{d x}{c},-\frac{f x}{e}\right)","\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,"(2*x*Sqrt[b*x]*(c + d*x)^n*(e + f*x)^p*AppellF1[3/2, -n, -p, 5/2, -((d*x)/c), -((f*x)/e)])/(3*((c + d*x)/c)^n*((e + f*x)/e)^p)","A",1
965,1,77,77,0.0530266,"\int \frac{(c+d x)^n (e+f x)^p}{\sqrt{b x}} \, dx","Integrate[((c + d*x)^n*(e + f*x)^p)/Sqrt[b*x],x]","\frac{2 x (c+d x)^n \left(\frac{c+d x}{c}\right)^{-n} (e+f x)^p \left(\frac{e+f x}{e}\right)^{-p} F_1\left(\frac{1}{2};-n,-p;\frac{3}{2};-\frac{d x}{c},-\frac{f x}{e}\right)}{\sqrt{b x}}","\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,"(2*x*(c + d*x)^n*(e + f*x)^p*AppellF1[1/2, -n, -p, 3/2, -((d*x)/c), -((f*x)/e)])/(Sqrt[b*x]*((c + d*x)/c)^n*((e + f*x)/e)^p)","A",1
966,1,45,49,0.0983559,"\int (b x)^m (\pi +d x)^n (e+f x)^p \, dx","Integrate[(b*x)^m*(Pi + d*x)^n*(E + f*x)^p,x]","\frac{\pi ^n e^p x (b x)^m F_1\left(m+1;-n,-p;m+2;-\frac{d x}{\pi },-\frac{f x}{e}\right)}{m+1}","\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,"(E^p*Pi^n*x*(b*x)^m*AppellF1[1 + m, -n, -p, 2 + m, -((d*x)/Pi), -((f*x)/E)])/(1 + m)","A",1
967,1,62,65,0.0988753,"\int (b x)^m (\pi +d x)^n (e+f x)^p \, dx","Integrate[(b*x)^m*(Pi + d*x)^n*(e + f*x)^p,x]","\frac{\pi ^n x (b x)^m (e+f x)^p \left(\frac{e+f x}{e}\right)^{-p} F_1\left(m+1;-n,-p;m+2;-\frac{d x}{\pi },-\frac{f x}{e}\right)}{m+1}","\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,"(Pi^n*x*(b*x)^m*(e + f*x)^p*AppellF1[1 + m, -n, -p, 2 + m, -((d*x)/Pi), -((f*x)/e)])/((1 + m)*((e + f*x)/e)^p)","A",1
968,1,45,47,0.0698545,"\int (b x)^{5/2} (\pi +d x)^n (e+f x)^p \, dx","Integrate[(b*x)^(5/2)*(Pi + d*x)^n*(E + f*x)^p,x]","\frac{2}{7} \pi ^n e^p x (b x)^{5/2} F_1\left(\frac{7}{2};-n,-p;\frac{9}{2};-\frac{d x}{\pi },-\frac{f x}{e}\right)","\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,"(2*E^p*Pi^n*x*(b*x)^(5/2)*AppellF1[7/2, -n, -p, 9/2, -((d*x)/Pi), -((f*x)/E)])/7","A",1
969,1,62,63,0.07354,"\int (b x)^{5/2} (\pi +d x)^n (e+f x)^p \, dx","Integrate[(b*x)^(5/2)*(Pi + d*x)^n*(e + f*x)^p,x]","\frac{2}{7} \pi ^n x (b x)^{5/2} (e+f x)^p \left(\frac{e+f x}{e}\right)^{-p} F_1\left(\frac{7}{2};-n,-p;\frac{9}{2};-\frac{d x}{\pi },-\frac{f x}{e}\right)","\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,"(2*Pi^n*x*(b*x)^(5/2)*(e + f*x)^p*AppellF1[7/2, -n, -p, 9/2, -((d*x)/Pi), -((f*x)/e)])/(7*((e + f*x)/e)^p)","A",1
970,1,262,295,0.3952103,"\int x^3 (a+b x)^n (c+d x)^{-n} \, dx","Integrate[(x^3*(a + b*x)^n)/(c + d*x)^n,x]","\frac{(a+b x)^{n+1} (c+d x)^{-n} \left(-b^2 c^2 (b c (n+3)-a d (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)}{a d-b c}\right)-(b c-a d)^2 (b c (n+3)-a d (n-3)) \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n-2,n+1;n+2;\frac{d (a+b x)}{a d-b c}\right)+2 b c (b c-a d) (b c (n+3)-a d (n-2)) \left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n-1,n+1;n+2;\frac{d (a+b x)}{a d-b c}\right)+b^3 d^2 (n+1) x^2 (c+d x)\right)}{4 b^4 d^3 (n+1)}","\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,"((a + b*x)^(1 + n)*(b^3*d^2*(1 + n)*x^2*(c + d*x) - (b*c - a*d)^2*(-(a*d*(-3 + n)) + b*c*(3 + n))*((b*(c + d*x))/(b*c - a*d))^n*Hypergeometric2F1[-2 + n, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)] + 2*b*c*(b*c - a*d)*(-(a*d*(-2 + n)) + b*c*(3 + n))*((b*(c + d*x))/(b*c - a*d))^n*Hypergeometric2F1[-1 + n, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)] - b^2*c^2*(-(a*d*(-1 + n)) + b*c*(3 + n))*((b*(c + d*x))/(b*c - a*d))^n*Hypergeometric2F1[n, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)]))/(4*b^4*d^3*(1 + n)*(c + d*x)^n)","A",1
971,1,154,199,0.1402122,"\int x^2 (a+b x)^n (c+d x)^{-n} \, dx","Integrate[(x^2*(a + b*x)^n)/(c + d*x)^n,x]","\frac{(a+b x)^{n+1} (c+d x)^{-n} \left(\frac{\left(a^2 d^2 \left(n^2-3 n+2\right)-2 a b c d \left(n^2-1\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)}{a d-b c}\right)}{n+1}+b (c+d x) (a d (n-2)-b c (n+2))+2 b^2 d x (c+d x)\right)}{6 b^3 d^2}","\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,"((a + b*x)^(1 + n)*(b*(a*d*(-2 + n) - b*c*(2 + n))*(c + d*x) + 2*b^2*d*x*(c + d*x) + ((-2*a*b*c*d*(-1 + n^2) + a^2*d^2*(2 - 3*n + n^2) + b^2*c^2*(2 + 3*n + n^2))*((b*(c + d*x))/(b*c - a*d))^n*Hypergeometric2F1[n, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)])/(1 + n)))/(6*b^3*d^2*(c + d*x)^n)","A",1
972,1,101,124,0.0767705,"\int x (a+b x)^n (c+d x)^{-n} \, dx","Integrate[(x*(a + b*x)^n)/(c + d*x)^n,x]","\frac{(a+b x)^{n+1} (c+d x)^{-n} \left(b (c+d x)-\frac{(b c (n+1)-a d (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)}{a d-b c}\right)}{n+1}\right)}{2 b^2 d}","\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,"((a + b*x)^(1 + n)*(b*(c + d*x) - ((-(a*d*(-1 + n)) + b*c*(1 + n))*((b*(c + d*x))/(b*c - a*d))^n*Hypergeometric2F1[n, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)])/(1 + n)))/(2*b^2*d*(c + d*x)^n)","A",1
973,1,71,72,0.0196223,"\int (a+b x)^n (c+d x)^{-n} \, dx","Integrate[(a + b*x)^n/(c + d*x)^n,x]","\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)}{a d-b c}\right)}{b (n+1)}","\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,"((a + b*x)^(1 + n)*((b*(c + d*x))/(b*c - a*d))^n*Hypergeometric2F1[n, 1 + n, 2 + n, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(1 + n)*(c + d*x)^n)","A",1
974,1,89,108,0.0314845,"\int \frac{(a+b x)^n (c+d x)^{-n}}{x} \, dx","Integrate[(a + b*x)^n/(x*(c + d*x)^n),x]","\frac{(a+b x)^n (c+d x)^{-n} \left(\left(\frac{b (c+d x)}{b c-a d}\right)^n \, _2F_1\left(n,n;n+1;\frac{d (a+b x)}{a d-b c}\right)-\, _2F_1\left(1,n;n+1;\frac{c (a+b x)}{a (c+d x)}\right)\right)}{n}","\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,"((a + b*x)^n*(-Hypergeometric2F1[1, n, 1 + n, (c*(a + b*x))/(a*(c + d*x))] + ((b*(c + d*x))/(b*c - a*d))^n*Hypergeometric2F1[n, n, 1 + n, (d*(a + b*x))/(-(b*c) + a*d)]))/(n*(c + d*x)^n)","A",1
975,1,62,62,0.0167609,"\int \frac{(a+b x)^n (c+d x)^{-n}}{x^2} \, dx","Integrate[(a + b*x)^n/(x^2*(c + d*x)^n),x]","\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)}","\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,"((b*c - a*d)*(a + b*x)^(1 + n)*(c + d*x)^(-1 - n)*Hypergeometric2F1[2, 1 + n, 2 + n, (c*(a + b*x))/(a*(c + d*x))])/(a^2*(1 + n))","A",1
976,1,99,117,0.0576461,"\int \frac{(a+b x)^n (c+d x)^{-n}}{x^3} \, dx","Integrate[(a + b*x)^n/(x^3*(c + d*x)^n),x]","\frac{(a+b x)^{n+1} (c+d x)^{-n-1} \left(\frac{(b c-a d) (b c (n-1)-a d (n+1)) \, _2F_1\left(2,n+1;n+2;\frac{c (a+b x)}{a (c+d x)}\right)}{n+1}-\frac{a^2 (c+d x)^2}{x^2}\right)}{2 a^3 c}","-\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,"((a + b*x)^(1 + n)*(c + d*x)^(-1 - n)*(-((a^2*(c + d*x)^2)/x^2) + ((b*c - a*d)*(b*c*(-1 + n) - a*d*(1 + n))*Hypergeometric2F1[2, 1 + n, 2 + n, (c*(a + b*x))/(a*(c + d*x))])/(1 + n)))/(2*a^3*c)","A",1
977,1,156,194,0.1751963,"\int \frac{(a+b x)^n (c+d x)^{-n}}{x^4} \, dx","Integrate[(a + b*x)^n/(x^4*(c + d*x)^n),x]","\frac{(a+b x)^{n+1} (c+d x)^{-n-1} \left(-\frac{2 a^3 c (c+d x)^2}{x^3}+\frac{(b c-a d) \left(a^2 d^2 \left(n^2+3 n+2\right)-2 a b c d \left(n^2-1\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)}{n+1}+\frac{a^2 (c+d x)^2 (a d (n+2)-b c (n-2))}{x^2}\right)}{6 a^4 c^2}","\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,"((a + b*x)^(1 + n)*(c + d*x)^(-1 - n)*((-2*a^3*c*(c + d*x)^2)/x^3 + (a^2*(-(b*c*(-2 + n)) + a*d*(2 + n))*(c + d*x)^2)/x^2 + ((b*c - a*d)*(-2*a*b*c*d*(-1 + n^2) + b^2*c^2*(2 - 3*n + n^2) + a^2*d^2*(2 + 3*n + n^2))*Hypergeometric2F1[2, 1 + n, 2 + n, (c*(a + b*x))/(a*(c + d*x))])/(1 + n)))/(6*a^4*c^2)","A",1
978,1,128,105,0.1267251,"\int (1-x)^n x^3 (1+x)^{-n} \, dx","Integrate[((1 - x)^n*x^3)/(1 + x)^n,x]","\frac{2^{-n-2} (x-1) (1-x)^n (x+1)^{-n} \left((n+1) \left(2^n x^2 (x+1)-2 (x+1)^n \, _2F_1\left(n,n+1;n+2;\frac{1-x}{2}\right)\right)-8 n (x+1)^n \, _2F_1\left(n-2,n+1;n+2;\frac{1-x}{2}\right)+4 (2 n+1) (x+1)^n \, _2F_1\left(n-1,n+1;n+2;\frac{1-x}{2}\right)\right)}{n+1}","\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,"(2^(-2 - n)*(1 - x)^n*(-1 + x)*(-8*n*(1 + x)^n*Hypergeometric2F1[-2 + n, 1 + n, 2 + n, (1 - x)/2] + 4*(1 + 2*n)*(1 + x)^n*Hypergeometric2F1[-1 + n, 1 + n, 2 + n, (1 - x)/2] + (1 + n)*(2^n*x^2*(1 + x) - 2*(1 + x)^n*Hypergeometric2F1[n, 1 + n, 2 + n, (1 - x)/2])))/((1 + n)*(1 + x)^n)","A",1
979,1,76,94,0.0352631,"\int (1-x)^n x^2 (1+x)^{-n} \, dx","Integrate[((1 - x)^n*x^2)/(1 + x)^n,x]","-\frac{2^{-n} (1-x)^{n+1} (x+1)^{-n} \left(\left(2 n^2+1\right) (x+1)^n \, _2F_1\left(n,n+1;n+2;\frac{1-x}{2}\right)+2^n (n+1) (x+1) (x-n)\right)}{3 (n+1)}","-\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,"-1/3*((1 - x)^(1 + n)*(2^n*(1 + n)*(1 + x)*(-n + x) + (1 + 2*n^2)*(1 + x)^n*Hypergeometric2F1[n, 1 + n, 2 + n, (1 - x)/2]))/(2^n*(1 + n)*(1 + x)^n)","A",1
980,1,56,61,0.033203,"\int (1-x)^n x (1+x)^{-n} \, dx","Integrate[((1 - x)^n*x)/(1 + x)^n,x]","\frac{1}{2} (1-x)^{n+1} \left(\frac{2^{1-n} n \, _2F_1\left(n,n+1;n+2;\frac{1-x}{2}\right)}{n+1}-(x+1)^{1-n}\right)","\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,"((1 - x)^(1 + n)*(-(1 + x)^(1 - n) + (2^(1 - n)*n*Hypergeometric2F1[n, 1 + n, 2 + n, (1 - x)/2])/(1 + n)))/2","A",1
981,1,38,38,0.0064801,"\int (1-x)^n (1+x)^{-n} \, dx","Integrate[(1 - x)^n/(1 + x)^n,x]","-\frac{2^{-n} (1-x)^{n+1} \, _2F_1\left(n,n+1;n+2;\frac{1-x}{2}\right)}{n+1}","-\frac{2^{-n} (1-x)^{n+1} \, _2F_1\left(n,n+1;n+2;\frac{1-x}{2}\right)}{n+1}",1,"-(((1 - x)^(1 + n)*Hypergeometric2F1[n, 1 + n, 2 + n, (1 - x)/2])/(2^n*(1 + n)))","A",1
982,1,67,68,0.0205108,"\int \frac{(1-x)^n (1+x)^{-n}}{x} \, dx","Integrate[(1 - x)^n/(x*(1 + x)^n),x]","\frac{2^{-n} (1-x)^n (x+1)^{-n} \left((x+1)^n \, _2F_1\left(n,n;n+1;\frac{1-x}{2}\right)-2^n \, _2F_1\left(1,n;n+1;\frac{1-x}{x+1}\right)\right)}{n}","\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,"((1 - x)^n*(-(2^n*Hypergeometric2F1[1, n, 1 + n, (1 - x)/(1 + x)]) + (1 + x)^n*Hypergeometric2F1[n, n, 1 + n, (1 - x)/2]))/(2^n*n*(1 + x)^n)","A",1
983,1,44,44,0.0113582,"\int \frac{(1-x)^n (1+x)^{-n}}{x^2} \, dx","Integrate[(1 - x)^n/(x^2*(1 + x)^n),x]","-\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}","-\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,"(-2*(1 - x)^(1 + n)*(1 + x)^(-1 - n)*Hypergeometric2F1[2, 1 + n, 2 + n, (1 - x)/(1 + x)])/(1 + n)","A",1
984,1,66,71,0.0247706,"\int \frac{(1-x)^n (1+x)^{-n}}{x^3} \, dx","Integrate[(1 - x)^n/(x^3*(1 + x)^n),x]","\frac{(1-x)^{n+1} (x+1)^{-n-1} \left(4 n x^2 \, _2F_1\left(2,n+1;n+2;\frac{1-x}{x+1}\right)-(n+1) (x+1)^2\right)}{2 (n+1) x^2}","\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,"((1 - x)^(1 + n)*(1 + x)^(-1 - n)*(-((1 + n)*(1 + x)^2) + 4*n*x^2*Hypergeometric2F1[2, 1 + n, 2 + n, (1 - x)/(1 + x)]))/(2*(1 + n)*x^2)","A",1
985,1,77,105,0.0403793,"\int \frac{(1-x)^n (1+x)^{-n}}{x^4} \, dx","Integrate[(1 - x)^n/(x^4*(1 + x)^n),x]","-\frac{(1-x)^{n+1} (x+1)^{-n-1} \left(2 \left(2 n^2+1\right) x^3 \, _2F_1\left(2,n+1;n+2;\frac{1-x}{x+1}\right)-(n+1) (x+1)^2 (n x-1)\right)}{3 (n+1) x^3}","-\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,"-1/3*((1 - x)^(1 + n)*(1 + x)^(-1 - n)*(-((1 + n)*(1 + x)^2*(-1 + n*x)) + 2*(1 + 2*n^2)*x^3*Hypergeometric2F1[2, 1 + n, 2 + n, (1 - x)/(1 + x)]))/((1 + n)*x^3)","A",1
986,1,38,36,0.0091122,"\int x^m (1-a x)^n (1+a x)^n \, dx","Integrate[x^m*(1 - a*x)^n*(1 + a*x)^n,x]","\frac{x^{m+1} \, _2F_1\left(\frac{m+1}{2},-n;\frac{m+1}{2}+1;a^2 x^2\right)}{m+1}","\frac{x^{m+1} \, _2F_1\left(\frac{m+1}{2},-n;\frac{m+3}{2};a^2 x^2\right)}{m+1}",1,"(x^(1 + m)*Hypergeometric2F1[(1 + m)/2, -n, 1 + (1 + m)/2, a^2*x^2])/(1 + m)","A",1
987,1,39,39,0.0229984,"\int x^m (1-a x)^n (2+2 a x)^n \, dx","Integrate[x^m*(1 - a*x)^n*(2 + 2*a*x)^n,x]","\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}","\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,"(2^n*x^(1 + m)*Hypergeometric2F1[(1 + m)/2, -n, (3 + m)/2, a^2*x^2])/(1 + m)","A",1
988,1,44,42,0.008207,"\int x^m (2-a x)^n (2+a x)^n \, dx","Integrate[x^m*(2 - a*x)^n*(2 + a*x)^n,x]","\frac{4^n x^{m+1} \, _2F_1\left(\frac{m+1}{2},-n;\frac{m+1}{2}+1;\frac{a^2 x^2}{4}\right)}{m+1}","\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,"(4^n*x^(1 + m)*Hypergeometric2F1[(1 + m)/2, -n, 1 + (1 + m)/2, (a^2*x^2)/4])/(1 + m)","A",1
989,1,42,42,0.0213351,"\int x^m \left(1-\frac{a x}{2}\right)^n (2+a x)^n \, dx","Integrate[x^m*(1 - (a*x)/2)^n*(2 + a*x)^n,x]","\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}","\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,"(2^n*x^(1 + m)*Hypergeometric2F1[(1 + m)/2, -n, (3 + m)/2, (a^2*x^2)/4])/(1 + m)","A",1
990,1,166,151,0.1406009,"\int x^m (3-2 a x)^{2+n} (6+4 a x)^n \, dx","Integrate[x^m*(3 - 2*a*x)^(2 + n)*(6 + 4*a*x)^n,x]","\frac{x^{m+1} \left(9-4 a^2 x^2\right)^n \left(\frac{1}{2}-\frac{2 a^2 x^2}{9}\right)^{-n} \left(9 \left(m^2+5 m+6\right) \, _2F_1\left(\frac{m+1}{2},-n;\frac{m+3}{2};\frac{4 a^2 x^2}{9}\right)-4 a (m+1) x \left(3 (m+3) \, _2F_1\left(\frac{m+2}{2},-n;\frac{m+4}{2};\frac{4 a^2 x^2}{9}\right)-a (m+2) x \, _2F_1\left(\frac{m+3}{2},-n;\frac{m+5}{2};\frac{4 a^2 x^2}{9}\right)\right)\right)}{(m+1) (m+2) (m+3)}","\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,"(x^(1 + m)*(9 - 4*a^2*x^2)^n*(9*(6 + 5*m + m^2)*Hypergeometric2F1[(1 + m)/2, -n, (3 + m)/2, (4*a^2*x^2)/9] - 4*a*(1 + m)*x*(3*(3 + m)*Hypergeometric2F1[(2 + m)/2, -n, (4 + m)/2, (4*a^2*x^2)/9] - a*(2 + m)*x*Hypergeometric2F1[(3 + m)/2, -n, (5 + m)/2, (4*a^2*x^2)/9])))/((1 + m)*(2 + m)*(3 + m)*(1/2 - (2*a^2*x^2)/9)^n)","A",1
991,1,115,99,0.0613026,"\int x^m (3-2 a x)^{1+n} (6+4 a x)^n \, dx","Integrate[x^m*(3 - 2*a*x)^(1 + n)*(6 + 4*a*x)^n,x]","\frac{x^{m+1} \left(9-4 a^2 x^2\right)^n \left(\frac{1}{2}-\frac{2 a^2 x^2}{9}\right)^{-n} \left(3 (m+2) \, _2F_1\left(\frac{m+1}{2},-n;\frac{m+3}{2};\frac{4 a^2 x^2}{9}\right)-2 a (m+1) x \, _2F_1\left(\frac{m}{2}+1,-n;\frac{m}{2}+2;\frac{4 a^2 x^2}{9}\right)\right)}{(m+1) (m+2)}","\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,"(x^(1 + m)*(9 - 4*a^2*x^2)^n*(-2*a*(1 + m)*x*Hypergeometric2F1[1 + m/2, -n, 2 + m/2, (4*a^2*x^2)/9] + 3*(2 + m)*Hypergeometric2F1[(1 + m)/2, -n, (3 + m)/2, (4*a^2*x^2)/9]))/((1 + m)*(2 + m)*(1/2 - (2*a^2*x^2)/9)^n)","A",1
992,1,69,42,0.0169828,"\int x^m (3-2 a x)^n (6+4 a x)^n \, dx","Integrate[x^m*(3 - 2*a*x)^n*(6 + 4*a*x)^n,x]","\frac{x^{m+1} (54-36 a x)^n (4 a x+6)^n \left(18-8 a^2 x^2\right)^{-n} \, _2F_1\left(\frac{m+1}{2},-n;\frac{m+3}{2};\frac{4 a^2 x^2}{9}\right)}{m+1}","\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,"(x^(1 + m)*(54 - 36*a*x)^n*(6 + 4*a*x)^n*Hypergeometric2F1[(1 + m)/2, -n, (3 + m)/2, (4*a^2*x^2)/9])/((1 + m)*(18 - 8*a^2*x^2)^n)","A",1
993,1,120,104,0.050724,"\int x^m (3-2 a x)^{-1+n} (6+4 a x)^n \, dx","Integrate[x^m*(3 - 2*a*x)^(-1 + n)*(6 + 4*a*x)^n,x]","\frac{9^{n-1} x^{m+1} \left(36-16 a^2 x^2\right)^n \left(18-8 a^2 x^2\right)^{-n} \left(2 a (m+1) x \, _2F_1\left(\frac{m}{2}+1,1-n;\frac{m}{2}+2;\frac{4 a^2 x^2}{9}\right)+3 (m+2) \, _2F_1\left(\frac{m+1}{2},1-n;\frac{m+3}{2};\frac{4 a^2 x^2}{9}\right)\right)}{(m+1) (m+2)}","\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,"(9^(-1 + n)*x^(1 + m)*(36 - 16*a^2*x^2)^n*(2*a*(1 + m)*x*Hypergeometric2F1[1 + m/2, 1 - n, 2 + m/2, (4*a^2*x^2)/9] + 3*(2 + m)*Hypergeometric2F1[(1 + m)/2, 1 - n, (3 + m)/2, (4*a^2*x^2)/9]))/((1 + m)*(2 + m)*(18 - 8*a^2*x^2)^n)","A",1
994,1,172,158,0.126977,"\int x^m (3-2 a x)^{-2+n} (6+4 a x)^n \, dx","Integrate[x^m*(3 - 2*a*x)^(-2 + n)*(6 + 4*a*x)^n,x]","\frac{9^{n-2} x^{m+1} \left(36-16 a^2 x^2\right)^n \left(18-8 a^2 x^2\right)^{-n} \left(9 \left(m^2+5 m+6\right) \, _2F_1\left(\frac{m+1}{2},2-n;\frac{m+3}{2};\frac{4 a^2 x^2}{9}\right)+4 a (m+1) x \left(3 (m+3) \, _2F_1\left(\frac{m+2}{2},2-n;\frac{m+4}{2};\frac{4 a^2 x^2}{9}\right)+a (m+2) x \, _2F_1\left(\frac{m+3}{2},2-n;\frac{m+5}{2};\frac{4 a^2 x^2}{9}\right)\right)\right)}{(m+1) (m+2) (m+3)}","\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,"(9^(-2 + n)*x^(1 + m)*(36 - 16*a^2*x^2)^n*(9*(6 + 5*m + m^2)*Hypergeometric2F1[(1 + m)/2, 2 - n, (3 + m)/2, (4*a^2*x^2)/9] + 4*a*(1 + m)*x*(3*(3 + m)*Hypergeometric2F1[(2 + m)/2, 2 - n, (4 + m)/2, (4*a^2*x^2)/9] + a*(2 + m)*x*Hypergeometric2F1[(3 + m)/2, 2 - n, (5 + m)/2, (4*a^2*x^2)/9])))/((1 + m)*(2 + m)*(3 + m)*(18 - 8*a^2*x^2)^n)","A",1
995,1,120,79,0.2050686,"\int x^m (a+b x)^{1+n} (c+d x)^n \, dx","Integrate[x^m*(a + b*x)^(1 + n)*(c + d*x)^n,x]","\frac{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} \left(a (m+2) F_1\left(m+1;-n,-n;m+2;-\frac{b x}{a},-\frac{d x}{c}\right)+b (m+1) x F_1\left(m+2;-n,-n;m+3;-\frac{b x}{a},-\frac{d x}{c}\right)\right)}{(m+1) (m+2)}","\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,"(x^(1 + m)*(a + b*x)^n*(c + d*x)^n*(a*(2 + m)*AppellF1[1 + m, -n, -n, 2 + m, -((b*x)/a), -((d*x)/c)] + b*(1 + m)*x*AppellF1[2 + m, -n, -n, 3 + m, -((b*x)/a), -((d*x)/c)]))/((1 + m)*(2 + m)*(1 + (b*x)/a)^n*(1 + (d*x)/c)^n)","A",0
996,1,77,79,0.1045379,"\int (a-x)^m (f x)^p (c+d x)^n \, dx","Integrate[(a - x)^m*(f*x)^p*(c + d*x)^n,x]","\frac{x (a-x)^m \left(\frac{a-x}{a}\right)^{-m} (f x)^p (c+d x)^n \left(\frac{c+d x}{c}\right)^{-n} F_1\left(p+1;-m,-n;p+2;\frac{x}{a},-\frac{d x}{c}\right)}{p+1}","\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,"((a - x)^m*x*(f*x)^p*(c + d*x)^n*AppellF1[1 + p, -m, -n, 2 + p, x/a, -((d*x)/c)])/((1 + p)*((a - x)/a)^m*((c + d*x)/c)^n)","A",1
997,1,82,83,0.0430188,"\int (1-x)^{-\frac{1}{2}+p} (c x)^{-2 (1+p)} (1+x)^{\frac{1}{2}+p} \, dx","Integrate[((1 - x)^(-1/2 + p)*(1 + x)^(1/2 + p))/(c*x)^(2*(1 + p)),x]","-\frac{4^{p+1} (1-x)^{p+\frac{1}{2}} \left(\frac{x}{x+1}\right)^{2 p} (x+1)^{p-\frac{1}{2}} (c x)^{-2 p} \, _2F_1\left(p+\frac{1}{2},2 p+2;p+\frac{3}{2};\frac{1-x}{x+1}\right)}{c^2 (2 p+1)}","-\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,"-((4^(1 + p)*(1 - x)^(1/2 + p)*(x/(1 + x))^(2*p)*(1 + x)^(-1/2 + p)*Hypergeometric2F1[1/2 + p, 2 + 2*p, 3/2 + p, (1 - x)/(1 + x)])/(c^2*(1 + 2*p)*(c*x)^(2*p)))","A",1
998,1,70,70,0.0337422,"\int \frac{\left(1-\frac{x}{a}\right)^{-n/2} \left(1+\frac{x}{a}\right)^{n/2}}{x^2} \, dx","Integrate[(1 + x/a)^(n/2)/(x^2*(1 - x/a)^(n/2)),x]","-\frac{4 \left(\frac{a+x}{a}\right)^{\frac{n+2}{2}} \left(1-\frac{x}{a}\right)^{-n/2} \, _2F_1\left(2,\frac{n}{2}+1;\frac{n}{2}+2;\frac{a+x}{a-x}\right)}{(n+2) (x-a)}","-\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,"(-4*((a + x)/a)^((2 + n)/2)*Hypergeometric2F1[2, 1 + n/2, 2 + n/2, (a + x)/(a - x)])/((2 + n)*(-a + x)*(1 - x/a)^(n/2))","A",1
999,1,44,50,0.0174198,"\int (b x)^{-2-2 m} (1-a x)^m (1+a x)^m \, dx","Integrate[(b*x)^(-2 - 2*m)*(1 - a*x)^m*(1 + a*x)^m,x]","-\frac{(b x)^{-2 m-1} \, _2F_1\left(-m-\frac{1}{2},-m;\frac{1}{2}-m;a^2 x^2\right)}{2 b m+b}","-\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,"-(((b*x)^(-1 - 2*m)*Hypergeometric2F1[-1/2 - m, -m, 1/2 - m, a^2*x^2])/(b + 2*b*m))","A",1
1000,1,74,86,0.0258743,"\int \frac{(1-a x)^{-n} (1+a x)^n}{x} \, dx","Integrate[(1 + a*x)^n/(x*(1 - a*x)^n),x]","\frac{(1-a x)^{-n} \left((a x+1)^n \, _2F_1\left(1,-n;1-n;\frac{1-a x}{a x+1}\right)-2^n \, _2F_1\left(-n,-n;1-n;\frac{1}{2} (1-a x)\right)\right)}{n}","\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,"((1 + a*x)^n*Hypergeometric2F1[1, -n, 1 - n, (1 - a*x)/(1 + a*x)] - 2^n*Hypergeometric2F1[-n, -n, 1 - n, (1 - a*x)/2])/(n*(1 - a*x)^n)","A",1
1001,1,128,106,0.1083427,"\int \frac{(1-a x)^{1-n} (1+a x)^{1+n}}{x^2} \, dx","Integrate[((1 - a*x)^(1 - n)*(1 + a*x)^(1 + n))/x^2,x]","-\frac{\left(1-\frac{1}{a x}\right)^n \left(\frac{1}{a x}+1\right)^{-n} (a x+1)^n (1-a x)^{-n} F_1\left(1;n,-n;2;\frac{1}{a x},-\frac{1}{a x}\right)}{x}-\frac{a (a x+1)^{n+1} \left(\frac{1}{2} (-a x-1)+1\right)^n (1-a x)^{-n} \, _2F_1\left(n,n+1;n+2;\frac{1}{2} (a x+1)\right)}{n+1}","\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,"-(((1 - 1/(a*x))^n*(1 + a*x)^n*AppellF1[1, n, -n, 2, 1/(a*x), -(1/(a*x))])/((1 + 1/(a*x))^n*x*(1 - a*x)^n)) - (a*(1 + a*x)^(1 + n)*(1 + (-1 - a*x)/2)^n*Hypergeometric2F1[n, 1 + n, 2 + n, (1 + a*x)/2])/((1 + n)*(1 - a*x)^n)","C",0
1002,1,27,28,0.0179288,"\int \frac{x^2}{(1-a x)^7 (1+a x)^4} \, dx","Integrate[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
1003,1,27,28,0.0247005,"\int \frac{x^2}{(1-a x)^{11} (1+a x)^7} \, dx","Integrate[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
1004,1,27,28,0.0479379,"\int \frac{x^2}{(1-a x)^{16} (1+a x)^{11}} \, dx","Integrate[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
1005,1,49,54,0.073568,"\int x^2 (1-a x)^{-1-\frac{1}{2} n (1+n)} (1+a x)^{-1-\frac{1}{2} (-1+n) n} \, dx","Integrate[x^2*(1 - a*x)^(-1 - (n*(1 + n))/2)*(1 + a*x)^(-1 - ((-1 + n)*n)/2),x]","\frac{(1-a x)^{-\frac{1}{2} n (n+1)} (a x+1)^{-\frac{1}{2} (n-1) n} (a n x-1)}{a^3 n \left(n^2-1\right)}","\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,"(-1 + a*n*x)/(a^3*n*(-1 + n^2)*(1 - a*x)^((n*(1 + n))/2)*(1 + a*x)^(((-1 + n)*n)/2))","A",1
1006,1,160,142,0.1369439,"\int \frac{(a-b x)^{-n} (a+b x)^{1+n}}{x} \, dx","Integrate[(a + b*x)^(1 + n)/(x*(a - b*x)^n),x]","\frac{2^{-n} (a-b x)^{-n} (a+b x)^n \left(\frac{b x}{a}+1\right)^{-n} \left(n (a+b x) \left(1-\frac{b^2 x^2}{a^2}\right)^n \, _2F_1\left(n,n+1;n+2;\frac{a+b x}{2 a}\right)+a (n+1) \left(\frac{2 b x}{a}+2\right)^n \, _2F_1\left(1,-n;1-n;\frac{a-b x}{a+b x}\right)-a 4^n (n+1) \, _2F_1\left(-n,-n;1-n;\frac{a-b x}{2 a}\right)\right)}{n (n+1)}","-\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,"((a + b*x)^n*(a*(1 + n)*(2 + (2*b*x)/a)^n*Hypergeometric2F1[1, -n, 1 - n, (a - b*x)/(a + b*x)] - 4^n*a*(1 + n)*Hypergeometric2F1[-n, -n, 1 - n, (a - b*x)/(2*a)] + n*(a + b*x)*(1 - (b^2*x^2)/a^2)^n*Hypergeometric2F1[n, 1 + n, 2 + n, (a + b*x)/(2*a)]))/(2^n*n*(1 + n)*(a - b*x)^n*(1 + (b*x)/a)^n)","A",1
1007,1,146,140,0.2650108,"\int \frac{(a-b x)^{-n} (a+b x)^{1+n}}{x^2} \, dx","Integrate[(a + b*x)^(1 + n)/(x^2*(a - b*x)^n),x]","\frac{(a-b x)^{-n} (a+b x)^n \left(\frac{b 2^n (a-b x) \left(\frac{b x}{a}+1\right)^{-n} F_1\left(1-n;-n,1;2-n;\frac{a-b x}{2 a},1-\frac{b x}{a}\right)}{n-1}-\frac{a^2 \left(1-\frac{a}{b x}\right)^n \left(\frac{a}{b x}+1\right)^{-n} F_1\left(1;n,-n;2;\frac{a}{b x},-\frac{a}{b x}\right)}{x}\right)}{a}","\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,"((a + b*x)^n*(-((a^2*(1 - a/(b*x))^n*AppellF1[1, n, -n, 2, a/(b*x), -(a/(b*x))])/((1 + a/(b*x))^n*x)) + (2^n*b*(a - b*x)*AppellF1[1 - n, -n, 1, 2 - n, (a - b*x)/(2*a), 1 - (b*x)/a])/((-1 + n)*(1 + (b*x)/a)^n)))/(a*(a - b*x)^n)","C",0
1008,1,62,62,0.0281562,"\int \frac{(a-b x)^{-n} (a+b x)^{1+n}}{x^3} \, dx","Integrate[(a + b*x)^(1 + n)/(x^3*(a - b*x)^n),x]","-\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)}","-\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,"(-4*b^2*(a - b*x)^(1 - n)*(a + b*x)^(-1 + n)*Hypergeometric2F1[3, 1 - n, 2 - n, (a - b*x)/(a + b*x)])/(a*(1 - n))","A",1
1009,1,88,101,0.0433922,"\int \frac{(a-b x)^{-n} (a+b x)^{1+n}}{x^4} \, dx","Integrate[(a + b*x)^(1 + n)/(x^4*(a - b*x)^n),x]","\frac{(a-b x)^{1-n} (a+b x)^{n-1} \left(4 b^3 (2 n+1) x^3 \, _2F_1\left(3,1-n;2-n;\frac{a-b x}{a+b x}\right)-(n-1) (a+b x)^3\right)}{3 a^2 (n-1) x^3}","-\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,"((a - b*x)^(1 - n)*(a + b*x)^(-1 + n)*(-((-1 + n)*(a + b*x)^3) + 4*b^3*(1 + 2*n)*x^3*Hypergeometric2F1[3, 1 - n, 2 - n, (a - b*x)/(a + b*x)]))/(3*a^2*(-1 + n)*x^3)","A",1
1010,1,101,139,0.0607327,"\int \frac{(a-b x)^{-n} (a+b x)^{1+n}}{x^5} \, dx","Integrate[(a + b*x)^(1 + n)/(x^5*(a - b*x)^n),x]","\frac{(a-b x)^{1-n} (a+b x)^{n-1} \left(16 b^4 \left(n^2+n+1\right) x^4 \, _2F_1\left(3,1-n;2-n;\frac{a-b x}{a+b x}\right)-(n-1) (a+b x)^3 (3 a+b (2 n+1) x)\right)}{12 a^3 (n-1) x^4}","-\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,"((a - b*x)^(1 - n)*(a + b*x)^(-1 + n)*(-((-1 + n)*(a + b*x)^3*(3*a + b*(1 + 2*n)*x)) + 16*b^4*(1 + n + n^2)*x^4*Hypergeometric2F1[3, 1 - n, 2 - n, (a - b*x)/(a + b*x)]))/(12*a^3*(-1 + n)*x^4)","A",1
1011,1,172,77,0.0649866,"\int (a+b x) (A+B x) (d+e x)^4 \, dx","Integrate[(a + b*x)*(A + B*x)*(d + e*x)^4,x]","\frac{1}{2} d^3 x^2 (4 a A e+a B d+A b d)+\frac{1}{3} d^2 x^3 (2 a e (3 A e+2 B d)+b d (4 A e+B d))+\frac{1}{6} e^3 x^6 (a B e+A b e+4 b B d)+\frac{1}{5} e^2 x^5 (a e (A e+4 B d)+2 b d (2 A e+3 B d))+\frac{1}{2} d e x^4 (a e (2 A e+3 B d)+b d (3 A e+2 B d))+a A d^4 x+\frac{1}{7} b B e^4 x^7","-\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,"a*A*d^4*x + (d^3*(A*b*d + a*B*d + 4*a*A*e)*x^2)/2 + (d^2*(2*a*e*(2*B*d + 3*A*e) + b*d*(B*d + 4*A*e))*x^3)/3 + (d*e*(a*e*(3*B*d + 2*A*e) + b*d*(2*B*d + 3*A*e))*x^4)/2 + (e^2*(a*e*(4*B*d + A*e) + 2*b*d*(3*B*d + 2*A*e))*x^5)/5 + (e^3*(4*b*B*d + A*b*e + a*B*e)*x^6)/6 + (b*B*e^4*x^7)/7","B",1
1012,1,130,77,0.0471966,"\int (a+b x) (A+B x) (d+e x)^3 \, dx","Integrate[(a + b*x)*(A + B*x)*(d + e*x)^3,x]","\frac{1}{2} d^2 x^2 (3 a A e+a B d+A b d)+\frac{1}{5} e^2 x^5 (a B e+A b e+3 b B d)+\frac{1}{4} e x^4 (a e (A e+3 B d)+3 b d (A e+B d))+\frac{1}{3} d x^3 (3 a e (A e+B d)+b d (3 A e+B d))+a A d^3 x+\frac{1}{6} b B e^3 x^6","-\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,"a*A*d^3*x + (d^2*(A*b*d + a*B*d + 3*a*A*e)*x^2)/2 + (d*(3*a*e*(B*d + A*e) + b*d*(B*d + 3*A*e))*x^3)/3 + (e*(3*b*d*(B*d + A*e) + a*e*(3*B*d + A*e))*x^4)/4 + (e^2*(3*b*B*d + A*b*e + a*B*e)*x^5)/5 + (b*B*e^3*x^6)/6","A",1
1013,1,96,77,0.0346462,"\int (a+b x) (A+B x) (d+e x)^2 \, dx","Integrate[(a + b*x)*(A + B*x)*(d + e*x)^2,x]","\frac{1}{3} x^3 \left(a A e^2+2 a B d e+2 A b d e+b B d^2\right)+\frac{1}{4} e x^4 (a B e+A b e+2 b B d)+\frac{1}{2} d x^2 (2 a A e+a B d+A b d)+a A d^2 x+\frac{1}{5} b B e^2 x^5","-\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,"a*A*d^2*x + (d*(A*b*d + a*B*d + 2*a*A*e)*x^2)/2 + ((b*B*d^2 + 2*A*b*d*e + 2*a*B*d*e + a*A*e^2)*x^3)/3 + (e*(2*b*B*d + A*b*e + a*B*e)*x^4)/4 + (b*B*e^2*x^5)/5","A",1
1014,1,53,56,0.0228932,"\int (a+b x) (A+B x) (d+e x) \, dx","Integrate[(a + b*x)*(A + B*x)*(d + e*x),x]","\frac{1}{12} x \left(4 x^2 (a B e+A b e+b B d)+6 x (a A e+a B d+A b d)+12 a A d+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 + a*B*d + a*A*e)*x + 4*(b*B*d + A*b*e + a*B*e)*x^2 + 3*b*B*e*x^3))/12","A",1
1015,1,28,28,0.0048123,"\int (a+b x) (A+B x) \, dx","Integrate[(a + b*x)*(A + B*x),x]","\frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} b B x^3","\frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} b B x^3",1,"a*A*x + ((A*b + a*B)*x^2)/2 + (b*B*x^3)/3","A",1
1016,1,56,60,0.0274627,"\int \frac{(a+b x) (A+B x)}{d+e x} \, dx","Integrate[((a + b*x)*(A + B*x))/(d + e*x),x]","\frac{e x (2 a B e+b (2 A e-2 B d+B e x))+2 (b d-a e) (B d-A e) \log (d+e x)}{2 e^3}","\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,"(e*x*(2*a*B*e + b*(-2*B*d + 2*A*e + B*e*x)) + 2*(b*d - a*e)*(B*d - A*e)*Log[d + e*x])/(2*e^3)","A",1
1017,1,56,63,0.0484551,"\int \frac{(a+b x) (A+B x)}{(d+e x)^2} \, dx","Integrate[((a + b*x)*(A + B*x))/(d + e*x)^2,x]","\frac{-\frac{(b d-a e) (B d-A e)}{d+e x}+\log (d+e x) (a B e+A b e-2 b B d)+b B e x}{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*e*x - ((b*d - a*e)*(B*d - A*e))/(d + e*x) + (-2*b*B*d + A*b*e + a*B*e)*Log[d + e*x])/e^3","A",1
1018,1,72,70,0.0362102,"\int \frac{(a+b x) (A+B x)}{(d+e x)^3} \, dx","Integrate[((a + b*x)*(A + B*x))/(d + e*x)^3,x]","\frac{-a e (A e+B (d+2 e x))+b (B d (3 d+4 e x)-A e (d+2 e x))+2 b B (d+e x)^2 \log (d+e x)}{2 e^3 (d+e x)^2}","-\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,"(-(a*e*(A*e + B*(d + 2*e*x))) + b*(-(A*e*(d + 2*e*x)) + B*d*(3*d + 4*e*x)) + 2*b*B*(d + e*x)^2*Log[d + e*x])/(2*e^3*(d + e*x)^2)","A",1
1019,1,63,75,0.0318565,"\int \frac{(a+b x) (A+B x)}{(d+e x)^4} \, dx","Integrate[((a + b*x)*(A + B*x))/(d + e*x)^4,x]","-\frac{a e (2 A e+B (d+3 e x))+b \left(A e (d+3 e x)+2 B \left(d^2+3 d e x+3 e^2 x^2\right)\right)}{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,"-1/6*(a*e*(2*A*e + B*(d + 3*e*x)) + b*(A*e*(d + 3*e*x) + 2*B*(d^2 + 3*d*e*x + 3*e^2*x^2)))/(e^3*(d + e*x)^3)","A",1
1020,1,62,77,0.0315807,"\int \frac{(a+b x) (A+B x)}{(d+e x)^5} \, dx","Integrate[((a + b*x)*(A + B*x))/(d + e*x)^5,x]","-\frac{a e (3 A e+B (d+4 e x))+b \left(A e (d+4 e x)+B \left(d^2+4 d e x+6 e^2 x^2\right)\right)}{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,"-1/12*(a*e*(3*A*e + B*(d + 4*e*x)) + b*(A*e*(d + 4*e*x) + B*(d^2 + 4*d*e*x + 6*e^2*x^2)))/(e^3*(d + e*x)^4)","A",1
1021,1,65,77,0.0332323,"\int \frac{(a+b x) (A+B x)}{(d+e x)^6} \, dx","Integrate[((a + b*x)*(A + B*x))/(d + e*x)^6,x]","-\frac{3 a e (4 A e+B (d+5 e x))+b \left(3 A e (d+5 e x)+2 B \left(d^2+5 d e x+10 e^2 x^2\right)\right)}{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,"-1/60*(3*a*e*(4*A*e + B*(d + 5*e*x)) + b*(3*A*e*(d + 5*e*x) + 2*B*(d^2 + 5*d*e*x + 10*e^2*x^2)))/(e^3*(d + e*x)^5)","A",1
1022,1,283,120,0.10024,"\int (a+b x)^2 (A+B x) (d+e x)^4 \, dx","Integrate[(a + b*x)^2*(A + B*x)*(d + e*x)^4,x]","\frac{1}{5} e x^5 \left(a^2 e^2 (A e+4 B d)+4 a b d e (2 A e+3 B d)+2 b^2 d^2 (3 A e+2 B d)\right)+\frac{1}{4} d x^4 \left(2 a^2 e^2 (2 A e+3 B d)+4 a b d e (3 A e+2 B d)+b^2 d^2 (4 A e+B d)\right)+\frac{1}{3} d^2 x^3 \left(A \left(6 a^2 e^2+8 a b d e+b^2 d^2\right)+2 a B d (2 a e+b d)\right)+\frac{1}{6} e^2 x^6 \left(a^2 B e^2+2 a b e (A e+4 B d)+2 b^2 d (2 A e+3 B d)\right)+a^2 A d^4 x+\frac{1}{2} a d^3 x^2 (4 a A e+a B d+2 A b d)+\frac{1}{7} b e^3 x^7 (2 a B e+A b e+4 b B d)+\frac{1}{8} b^2 B e^4 x^8","-\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,"a^2*A*d^4*x + (a*d^3*(2*A*b*d + a*B*d + 4*a*A*e)*x^2)/2 + (d^2*(2*a*B*d*(b*d + 2*a*e) + A*(b^2*d^2 + 8*a*b*d*e + 6*a^2*e^2))*x^3)/3 + (d*(2*a^2*e^2*(3*B*d + 2*A*e) + 4*a*b*d*e*(2*B*d + 3*A*e) + b^2*d^2*(B*d + 4*A*e))*x^4)/4 + (e*(a^2*e^2*(4*B*d + A*e) + 4*a*b*d*e*(3*B*d + 2*A*e) + 2*b^2*d^2*(2*B*d + 3*A*e))*x^5)/5 + (e^2*(a^2*B*e^2 + 2*a*b*e*(4*B*d + A*e) + 2*b^2*d*(3*B*d + 2*A*e))*x^6)/6 + (b*e^3*(4*b*B*d + A*b*e + 2*a*B*e)*x^7)/7 + (b^2*B*e^4*x^8)/8","B",1
1023,1,216,120,0.0753903,"\int (a+b x)^2 (A+B x) (d+e x)^3 \, dx","Integrate[(a + b*x)^2*(A + B*x)*(d + e*x)^3,x]","\frac{1}{4} x^4 \left(a^2 e^2 (A e+3 B d)+6 a b d e (A e+B d)+b^2 d^2 (3 A e+B d)\right)+\frac{1}{3} d x^3 \left(A \left(3 a^2 e^2+6 a b d e+b^2 d^2\right)+a B d (3 a e+2 b d)\right)+\frac{1}{5} e x^5 \left(a^2 B e^2+2 a b e (A e+3 B d)+3 b^2 d (A e+B d)\right)+a^2 A d^3 x+\frac{1}{2} a d^2 x^2 (3 a A e+a B d+2 A b d)+\frac{1}{6} b e^2 x^6 (2 a B e+A b e+3 b B d)+\frac{1}{7} b^2 B e^3 x^7","-\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,"a^2*A*d^3*x + (a*d^2*(2*A*b*d + a*B*d + 3*a*A*e)*x^2)/2 + (d*(a*B*d*(2*b*d + 3*a*e) + A*(b^2*d^2 + 6*a*b*d*e + 3*a^2*e^2))*x^3)/3 + ((6*a*b*d*e*(B*d + A*e) + a^2*e^2*(3*B*d + A*e) + b^2*d^2*(B*d + 3*A*e))*x^4)/4 + (e*(a^2*B*e^2 + 3*b^2*d*(B*d + A*e) + 2*a*b*e*(3*B*d + A*e))*x^5)/5 + (b*e^2*(3*b*B*d + A*b*e + 2*a*B*e)*x^6)/6 + (b^2*B*e^3*x^7)/7","A",1
1024,1,157,118,0.0544908,"\int (a+b x)^2 (A+B x) (d+e x)^2 \, dx","Integrate[(a + b*x)^2*(A + B*x)*(d + e*x)^2,x]","\frac{1}{3} x^3 \left(A \left(a^2 e^2+4 a b d e+b^2 d^2\right)+2 a B d (a e+b d)\right)+\frac{1}{4} x^4 \left(a^2 B e^2+2 a b e (A e+2 B d)+b^2 d (2 A e+B d)\right)+a^2 A d^2 x+\frac{1}{5} b e x^5 (2 a B e+A b e+2 b B d)+\frac{1}{2} a d x^2 (2 A (a e+b d)+a B d)+\frac{1}{6} b^2 B e^2 x^6","\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,"a^2*A*d^2*x + (a*d*(a*B*d + 2*A*(b*d + a*e))*x^2)/2 + ((2*a*B*d*(b*d + a*e) + A*(b^2*d^2 + 4*a*b*d*e + a^2*e^2))*x^3)/3 + ((a^2*B*e^2 + 2*a*b*e*(2*B*d + A*e) + b^2*d*(B*d + 2*A*e))*x^4)/4 + (b*e*(2*b*B*d + A*b*e + 2*a*B*e)*x^5)/5 + (b^2*B*e^2*x^6)/6","A",1
1025,1,96,75,0.02812,"\int (a+b x)^2 (A+B x) (d+e x) \, dx","Integrate[(a + b*x)^2*(A + B*x)*(d + e*x),x]","\frac{1}{3} x^3 \left(a^2 B e+2 a A b e+2 a b B d+A b^2 d\right)+a^2 A d x+\frac{1}{4} b x^4 (2 a B e+A b e+b B d)+\frac{1}{2} a x^2 (a A e+a B d+2 A b d)+\frac{1}{5} b^2 B e x^5","\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,"a^2*A*d*x + (a*(2*A*b*d + a*B*d + a*A*e)*x^2)/2 + ((A*b^2*d + 2*a*b*B*d + 2*a*A*b*e + a^2*B*e)*x^3)/3 + (b*(b*B*d + A*b*e + 2*a*B*e)*x^4)/4 + (b^2*B*e*x^5)/5","A",1
1026,1,46,38,0.009935,"\int (a+b x)^2 (A+B x) \, dx","Integrate[(a + b*x)^2*(A + B*x),x]","\frac{1}{12} x \left(6 a^2 (2 A+B x)+4 a b x (3 A+2 B x)+b^2 x^2 (4 A+3 B x)\right)","\frac{(a+b x)^3 (A b-a B)}{3 b^2}+\frac{B (a+b x)^4}{4 b^2}",1,"(x*(6*a^2*(2*A + B*x) + 4*a*b*x*(3*A + 2*B*x) + b^2*x^2*(4*A + 3*B*x)))/12","A",1
1027,1,102,92,0.060221,"\int \frac{(a+b x)^2 (A+B x)}{d+e x} \, dx","Integrate[((a + b*x)^2*(A + B*x))/(d + e*x),x]","\frac{e x \left(6 a^2 B e^2+6 a b e (2 A e-2 B d+B e x)+b^2 \left(3 A e (e x-2 d)+B \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)\right)-6 (b d-a e)^2 (B d-A e) \log (d+e x)}{6 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,"(e*x*(6*a^2*B*e^2 + 6*a*b*e*(-2*B*d + 2*A*e + B*e*x) + b^2*(3*A*e*(-2*d + e*x) + B*(6*d^2 - 3*d*e*x + 2*e^2*x^2))) - 6*(b*d - a*e)^2*(B*d - A*e)*Log[d + e*x])/(6*e^4)","A",1
1028,1,98,101,0.0866403,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^2} \, dx","Integrate[((a + b*x)^2*(A + B*x))/(d + e*x)^2,x]","\frac{\frac{2 (b d-a e)^2 (B d-A e)}{d+e x}+2 b e x (2 a B e+A b e-2 b B d)+2 (b d-a e) \log (d+e x) (-a B e-2 A b e+3 b B d)+b^2 B e^2 x^2}{2 e^4}","\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*e*(-2*b*B*d + A*b*e + 2*a*B*e)*x + b^2*B*e^2*x^2 + (2*(b*d - a*e)^2*(B*d - A*e))/(d + e*x) + 2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*Log[d + e*x])/(2*e^4)","A",1
1029,1,143,106,0.0836669,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^3} \, dx","Integrate[((a + b*x)^2*(A + B*x))/(d + e*x)^3,x]","-\frac{a^2 e^2 (A e+B (d+2 e x))+2 a b e (A e (d+2 e x)-B d (3 d+4 e x))+2 b (d+e x)^2 \log (d+e x) (-2 a B e-A b e+3 b B d)-\left(b^2 \left(A d e (3 d+4 e x)+B \left(-5 d^3-4 d^2 e x+4 d e^2 x^2+2 e^3 x^3\right)\right)\right)}{2 e^4 (d+e x)^2}","-\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,"-1/2*(a^2*e^2*(A*e + B*(d + 2*e*x)) + 2*a*b*e*(A*e*(d + 2*e*x) - B*d*(3*d + 4*e*x)) - b^2*(A*d*e*(3*d + 4*e*x) + B*(-5*d^3 - 4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3)) + 2*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2*Log[d + e*x])/(e^4*(d + e*x)^2)","A",1
1030,1,138,101,0.0676726,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^4} \, dx","Integrate[((a + b*x)^2*(A + B*x))/(d + e*x)^4,x]","\frac{-a^2 e^2 (2 A e+B (d+3 e x))-2 a b e \left(A e (d+3 e x)+2 B \left(d^2+3 d e x+3 e^2 x^2\right)\right)+b^2 \left(B d \left(11 d^2+27 d e x+18 e^2 x^2\right)-2 A e \left(d^2+3 d e x+3 e^2 x^2\right)\right)+6 b^2 B (d+e x)^3 \log (d+e x)}{6 e^4 (d+e x)^3}","-\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,"(-(a^2*e^2*(2*A*e + B*(d + 3*e*x))) - 2*a*b*e*(A*e*(d + 3*e*x) + 2*B*(d^2 + 3*d*e*x + 3*e^2*x^2)) + b^2*(-2*A*e*(d^2 + 3*d*e*x + 3*e^2*x^2) + B*d*(11*d^2 + 27*d*e*x + 18*e^2*x^2)) + 6*b^2*B*(d + e*x)^3*Log[d + e*x])/(6*e^4*(d + e*x)^3)","A",1
1031,1,125,86,0.0593194,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^5} \, dx","Integrate[((a + b*x)^2*(A + B*x))/(d + e*x)^5,x]","-\frac{a^2 e^2 (3 A e+B (d+4 e x))+2 a b e \left(A e (d+4 e x)+B \left(d^2+4 d e x+6 e^2 x^2\right)\right)+b^2 \left(A e \left(d^2+4 d e x+6 e^2 x^2\right)+3 B \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)\right)}{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,"-1/12*(a^2*e^2*(3*A*e + B*(d + 4*e*x)) + 2*a*b*e*(A*e*(d + 4*e*x) + B*(d^2 + 4*d*e*x + 6*e^2*x^2)) + b^2*(A*e*(d^2 + 4*d*e*x + 6*e^2*x^2) + 3*B*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3)))/(e^4*(d + e*x)^4)","A",1
1032,1,129,120,0.0580381,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^6} \, dx","Integrate[((a + b*x)^2*(A + B*x))/(d + e*x)^6,x]","-\frac{3 a^2 e^2 (4 A e+B (d+5 e x))+2 a b e \left(3 A e (d+5 e x)+2 B \left(d^2+5 d e x+10 e^2 x^2\right)\right)+b^2 \left(2 A e \left(d^2+5 d e x+10 e^2 x^2\right)+3 B \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)\right)}{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,"-1/60*(3*a^2*e^2*(4*A*e + B*(d + 5*e*x)) + 2*a*b*e*(3*A*e*(d + 5*e*x) + 2*B*(d^2 + 5*d*e*x + 10*e^2*x^2)) + b^2*(2*A*e*(d^2 + 5*d*e*x + 10*e^2*x^2) + 3*B*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3)))/(e^4*(d + e*x)^5)","A",1
1033,1,126,120,0.0598622,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^7} \, dx","Integrate[((a + b*x)^2*(A + B*x))/(d + e*x)^7,x]","-\frac{2 a^2 e^2 (5 A e+B (d+6 e x))+2 a b e \left(2 A e (d+6 e x)+B \left(d^2+6 d e x+15 e^2 x^2\right)\right)+b^2 \left(A e \left(d^2+6 d e x+15 e^2 x^2\right)+B \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)\right)}{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,"-1/60*(2*a^2*e^2*(5*A*e + B*(d + 6*e*x)) + 2*a*b*e*(2*A*e*(d + 6*e*x) + B*(d^2 + 6*d*e*x + 15*e^2*x^2)) + b^2*(A*e*(d^2 + 6*d*e*x + 15*e^2*x^2) + B*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3)))/(e^4*(d + e*x)^6)","A",1
1034,1,129,120,0.0601891,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^8} \, dx","Integrate[((a + b*x)^2*(A + B*x))/(d + e*x)^8,x]","-\frac{10 a^2 e^2 (6 A e+B (d+7 e x))+4 a b e \left(5 A e (d+7 e x)+2 B \left(d^2+7 d e x+21 e^2 x^2\right)\right)+b^2 \left(4 A e \left(d^2+7 d e x+21 e^2 x^2\right)+3 B \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)\right)}{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,"-1/420*(10*a^2*e^2*(6*A*e + B*(d + 7*e*x)) + 4*a*b*e*(5*A*e*(d + 7*e*x) + 2*B*(d^2 + 7*d*e*x + 21*e^2*x^2)) + b^2*(4*A*e*(d^2 + 7*d*e*x + 21*e^2*x^2) + 3*B*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3)))/(e^4*(d + e*x)^7)","A",1
1035,1,471,163,0.1720974,"\int (a+b x)^3 (A+B x) (d+e x)^5 \, dx","Integrate[(a + b*x)^3*(A + B*x)*(d + e*x)^5,x]","a^3 A d^5 x+\frac{1}{3} a d^3 x^3 \left(A \left(10 a^2 e^2+15 a b d e+3 b^2 d^2\right)+a B d (5 a e+3 b d)\right)+\frac{1}{8} b e^3 x^8 \left(3 a^2 B e^2+3 a b e (A e+5 B d)+5 b^2 d (A e+2 B d)\right)+\frac{1}{2} a^2 d^4 x^2 (5 a A e+a B d+3 A b d)+\frac{1}{7} e^2 x^7 \left(a^3 B e^3+3 a^2 b e^2 (A e+5 B d)+15 a b^2 d e (A e+2 B d)+10 b^3 d^2 (A e+B d)\right)+\frac{1}{6} e x^6 \left(a^3 e^3 (A e+5 B d)+15 a^2 b d e^2 (A e+2 B d)+30 a b^2 d^2 e (A e+B d)+5 b^3 d^3 (2 A e+B d)\right)+\frac{1}{5} d x^5 \left(5 a^3 e^3 (A e+2 B d)+30 a^2 b d e^2 (A e+B d)+15 a b^2 d^2 e (2 A e+B d)+b^3 d^3 (5 A e+B d)\right)+\frac{1}{4} d^2 x^4 \left(a B d \left(10 a^2 e^2+15 a b d e+3 b^2 d^2\right)+A \left(10 a^3 e^3+30 a^2 b d e^2+15 a b^2 d^2 e+b^3 d^3\right)\right)+\frac{1}{9} b^2 e^4 x^9 (3 a B e+A b e+5 b B d)+\frac{1}{10} b^3 B e^5 x^{10}","-\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,"a^3*A*d^5*x + (a^2*d^4*(3*A*b*d + a*B*d + 5*a*A*e)*x^2)/2 + (a*d^3*(a*B*d*(3*b*d + 5*a*e) + A*(3*b^2*d^2 + 15*a*b*d*e + 10*a^2*e^2))*x^3)/3 + (d^2*(a*B*d*(3*b^2*d^2 + 15*a*b*d*e + 10*a^2*e^2) + A*(b^3*d^3 + 15*a*b^2*d^2*e + 30*a^2*b*d*e^2 + 10*a^3*e^3))*x^4)/4 + (d*(30*a^2*b*d*e^2*(B*d + A*e) + 5*a^3*e^3*(2*B*d + A*e) + 15*a*b^2*d^2*e*(B*d + 2*A*e) + b^3*d^3*(B*d + 5*A*e))*x^5)/5 + (e*(30*a*b^2*d^2*e*(B*d + A*e) + 15*a^2*b*d*e^2*(2*B*d + A*e) + a^3*e^3*(5*B*d + A*e) + 5*b^3*d^3*(B*d + 2*A*e))*x^6)/6 + (e^2*(a^3*B*e^3 + 10*b^3*d^2*(B*d + A*e) + 15*a*b^2*d*e*(2*B*d + A*e) + 3*a^2*b*e^2*(5*B*d + A*e))*x^7)/7 + (b*e^3*(3*a^2*B*e^2 + 5*b^2*d*(2*B*d + A*e) + 3*a*b*e*(5*B*d + A*e))*x^8)/8 + (b^2*e^4*(5*b*B*d + A*b*e + 3*a*B*e)*x^9)/9 + (b^3*B*e^5*x^10)/10","B",1
1036,1,397,163,0.1405748,"\int (a+b x)^3 (A+B x) (d+e x)^4 \, dx","Integrate[(a + b*x)^3*(A + B*x)*(d + e*x)^4,x]","a^3 A d^4 x+\frac{1}{3} a d^2 x^3 \left(3 A \left(2 a^2 e^2+4 a b d e+b^2 d^2\right)+a B d (4 a e+3 b d)\right)+\frac{1}{7} b e^2 x^7 \left(3 a^2 B e^2+3 a b e (A e+4 B d)+2 b^2 d (2 A e+3 B d)\right)+\frac{1}{2} a^2 d^3 x^2 (4 a A e+a B d+3 A b d)+\frac{1}{6} e x^6 \left(a^3 B e^3+3 a^2 b e^2 (A e+4 B d)+6 a b^2 d e (2 A e+3 B d)+2 b^3 d^2 (3 A e+2 B d)\right)+\frac{1}{5} x^5 \left(a^3 e^3 (A e+4 B d)+6 a^2 b d e^2 (2 A e+3 B d)+6 a b^2 d^2 e (3 A e+2 B d)+b^3 d^3 (4 A e+B d)\right)+\frac{1}{4} d x^4 \left(3 a B d \left(2 a^2 e^2+4 a b d e+b^2 d^2\right)+A \left(4 a^3 e^3+18 a^2 b d e^2+12 a b^2 d^2 e+b^3 d^3\right)\right)+\frac{1}{8} b^2 e^3 x^8 (3 a B e+A b e+4 b B d)+\frac{1}{9} b^3 B e^4 x^9","-\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,"a^3*A*d^4*x + (a^2*d^3*(3*A*b*d + a*B*d + 4*a*A*e)*x^2)/2 + (a*d^2*(a*B*d*(3*b*d + 4*a*e) + 3*A*(b^2*d^2 + 4*a*b*d*e + 2*a^2*e^2))*x^3)/3 + (d*(3*a*B*d*(b^2*d^2 + 4*a*b*d*e + 2*a^2*e^2) + A*(b^3*d^3 + 12*a*b^2*d^2*e + 18*a^2*b*d*e^2 + 4*a^3*e^3))*x^4)/4 + ((a^3*e^3*(4*B*d + A*e) + 6*a^2*b*d*e^2*(3*B*d + 2*A*e) + 6*a*b^2*d^2*e*(2*B*d + 3*A*e) + b^3*d^3*(B*d + 4*A*e))*x^5)/5 + (e*(a^3*B*e^3 + 3*a^2*b*e^2*(4*B*d + A*e) + 6*a*b^2*d*e*(3*B*d + 2*A*e) + 2*b^3*d^2*(2*B*d + 3*A*e))*x^6)/6 + (b*e^2*(3*a^2*B*e^2 + 3*a*b*e*(4*B*d + A*e) + 2*b^2*d*(3*B*d + 2*A*e))*x^7)/7 + (b^2*e^3*(4*b*B*d + A*b*e + 3*a*B*e)*x^8)/8 + (b^3*B*e^4*x^9)/9","B",1
1037,1,297,159,0.1094775,"\int (a+b x)^3 (A+B x) (d+e x)^3 \, dx","Integrate[(a + b*x)^3*(A + B*x)*(d + e*x)^3,x]","a^3 A d^3 x+a d x^3 \left(A \left(a^2 e^2+3 a b d e+b^2 d^2\right)+a B d (a e+b d)\right)+\frac{1}{2} b e x^6 \left(a^2 B e^2+a b e (A e+3 B d)+b^2 d (A e+B d)\right)+\frac{1}{2} a^2 d^2 x^2 (3 A (a e+b d)+a B d)+\frac{1}{5} x^5 \left(a^3 B e^3+3 a^2 b e^2 (A e+3 B d)+9 a b^2 d e (A e+B d)+b^3 d^2 (3 A e+B d)\right)+\frac{1}{4} x^4 \left(3 a B d \left(a^2 e^2+3 a b d e+b^2 d^2\right)+A \left(a^3 e^3+9 a^2 b d e^2+9 a b^2 d^2 e+b^3 d^3\right)\right)+\frac{1}{7} b^2 e^2 x^7 (3 a B e+A b e+3 b B d)+\frac{1}{8} b^3 B e^3 x^8","\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,"a^3*A*d^3*x + (a^2*d^2*(a*B*d + 3*A*(b*d + a*e))*x^2)/2 + a*d*(a*B*d*(b*d + a*e) + A*(b^2*d^2 + 3*a*b*d*e + a^2*e^2))*x^3 + ((3*a*B*d*(b^2*d^2 + 3*a*b*d*e + a^2*e^2) + A*(b^3*d^3 + 9*a*b^2*d^2*e + 9*a^2*b*d*e^2 + a^3*e^3))*x^4)/4 + ((a^3*B*e^3 + 9*a*b^2*d*e*(B*d + A*e) + 3*a^2*b*e^2*(3*B*d + A*e) + b^3*d^2*(B*d + 3*A*e))*x^5)/5 + (b*e*(a^2*B*e^2 + b^2*d*(B*d + A*e) + a*b*e*(3*B*d + A*e))*x^6)/2 + (b^2*e^2*(3*b*B*d + A*b*e + 3*a*B*e)*x^7)/7 + (b^3*B*e^3*x^8)/8","A",1
1038,1,224,118,0.081355,"\int (a+b x)^3 (A+B x) (d+e x)^2 \, dx","Integrate[(a + b*x)^3*(A + B*x)*(d + e*x)^2,x]","a^3 A d^2 x+\frac{1}{4} x^4 \left(A b \left(3 a^2 e^2+6 a b d e+b^2 d^2\right)+a B \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)\right)+\frac{1}{3} a x^3 \left(A \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)+a B d (2 a e+3 b d)\right)+\frac{1}{5} b x^5 \left(3 a^2 B e^2+3 a b e (A e+2 B d)+b^2 d (2 A e+B d)\right)+\frac{1}{2} a^2 d x^2 (2 a A e+a B d+3 A b d)+\frac{1}{6} b^2 e x^6 (3 a B e+A b e+2 b B d)+\frac{1}{7} b^3 B e^2 x^7","\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,"a^3*A*d^2*x + (a^2*d*(3*A*b*d + a*B*d + 2*a*A*e)*x^2)/2 + (a*(a*B*d*(3*b*d + 2*a*e) + A*(3*b^2*d^2 + 6*a*b*d*e + a^2*e^2))*x^3)/3 + ((a*B*(3*b^2*d^2 + 6*a*b*d*e + a^2*e^2) + A*b*(b^2*d^2 + 6*a*b*d*e + 3*a^2*e^2))*x^4)/4 + (b*(3*a^2*B*e^2 + 3*a*b*e*(2*B*d + A*e) + b^2*d*(B*d + 2*A*e))*x^5)/5 + (b^2*e*(2*b*B*d + A*b*e + 3*a*B*e)*x^6)/6 + (b^3*B*e^2*x^7)/7","A",1
1039,1,130,75,0.0435866,"\int (a+b x)^3 (A+B x) (d+e x) \, dx","Integrate[(a + b*x)^3*(A + B*x)*(d + e*x),x]","a^3 A d x+\frac{1}{2} a^2 x^2 (a A e+a B d+3 A b d)+\frac{1}{5} b^2 x^5 (3 a B e+A b e+b B d)+\frac{1}{4} b x^4 (A b (3 a e+b d)+3 a B (a e+b d))+\frac{1}{3} a x^3 (3 A b (a e+b d)+a B (a e+3 b d))+\frac{1}{6} b^3 B e x^6","\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,"a^3*A*d*x + (a^2*(3*A*b*d + a*B*d + a*A*e)*x^2)/2 + (a*(3*A*b*(b*d + a*e) + a*B*(3*b*d + a*e))*x^3)/3 + (b*(3*a*B*(b*d + a*e) + A*b*(b*d + 3*a*e))*x^4)/4 + (b^2*(b*B*d + A*b*e + 3*a*B*e)*x^5)/5 + (b^3*B*e*x^6)/6","A",1
1040,1,67,38,0.0119958,"\int (a+b x)^3 (A+B x) \, dx","Integrate[(a + b*x)^3*(A + B*x),x]","a^3 A x+\frac{1}{2} a^2 x^2 (a B+3 A b)+\frac{1}{4} b^2 x^4 (3 a B+A b)+a b x^3 (a B+A b)+\frac{1}{5} b^3 B x^5","\frac{(a+b x)^4 (A b-a B)}{4 b^2}+\frac{B (a+b x)^5}{5 b^2}",1,"a^3*A*x + (a^2*(3*A*b + a*B)*x^2)/2 + a*b*(A*b + a*B)*x^3 + (b^2*(A*b + 3*a*B)*x^4)/4 + (b^3*B*x^5)/5","A",1
1041,1,169,124,0.0961752,"\int \frac{(a+b x)^3 (A+B x)}{d+e x} \, dx","Integrate[((a + b*x)^3*(A + B*x))/(d + e*x),x]","\frac{e x \left(12 a^3 B e^3+18 a^2 b e^2 (2 A e-2 B d+B e x)+6 a b^2 e \left(3 A e (e x-2 d)+B \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)+b^3 \left(2 A e \left(6 d^2-3 d e x+2 e^2 x^2\right)+B \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)\right)\right)+12 (b d-a e)^3 (B d-A e) \log (d+e x)}{12 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,"(e*x*(12*a^3*B*e^3 + 18*a^2*b*e^2*(-2*B*d + 2*A*e + B*e*x) + 6*a*b^2*e*(3*A*e*(-2*d + e*x) + B*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) + b^3*(2*A*e*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + B*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3))) + 12*(b*d - a*e)^3*(B*d - A*e)*Log[d + e*x])/(12*e^5)","A",1
1042,1,244,150,0.1121441,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^2} \, dx","Integrate[((a + b*x)^3*(A + B*x))/(d + e*x)^2,x]","\frac{6 a^3 e^3 (B d-A e)+18 a^2 b e^2 \left(A d e+B \left(-d^2+d e x+e^2 x^2\right)\right)+9 a b^2 e \left(2 A e \left(-d^2+d e x+e^2 x^2\right)+B \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)\right)-6 (d+e x) (b d-a e)^2 \log (d+e x) (-a B e-3 A b e+4 b B d)+b^3 \left(3 A e \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)+2 B \left(-3 d^4+9 d^3 e x+6 d^2 e^2 x^2-2 d e^3 x^3+e^4 x^4\right)\right)}{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*a^3*e^3*(B*d - A*e) + 18*a^2*b*e^2*(A*d*e + B*(-d^2 + d*e*x + e^2*x^2)) + 9*a*b^2*e*(2*A*e*(-d^2 + d*e*x + e^2*x^2) + B*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3)) + b^3*(3*A*e*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3) + 2*B*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4)) - 6*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)*Log[d + e*x])/(6*e^5*(d + e*x))","A",1
1043,1,238,145,0.1224444,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^3} \, dx","Integrate[((a + b*x)^3*(A + B*x))/(d + e*x)^3,x]","\frac{-a^3 e^3 (A e+B (d+2 e x))-3 a^2 b e^2 (A e (d+2 e x)-B d (3 d+4 e x))+3 a b^2 e \left(A d e (3 d+4 e x)+B \left(-5 d^3-4 d^2 e x+4 d e^2 x^2+2 e^3 x^3\right)\right)+6 b (d+e x)^2 (b d-a e) \log (d+e x) (-a B e-A b e+2 b B d)+b^3 \left(A e \left(-5 d^3-4 d^2 e x+4 d e^2 x^2+2 e^3 x^3\right)+B \left(7 d^4+2 d^3 e x-11 d^2 e^2 x^2-4 d e^3 x^3+e^4 x^4\right)\right)}{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,"(-(a^3*e^3*(A*e + B*(d + 2*e*x))) - 3*a^2*b*e^2*(A*e*(d + 2*e*x) - B*d*(3*d + 4*e*x)) + 3*a*b^2*e*(A*d*e*(3*d + 4*e*x) + B*(-5*d^3 - 4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3)) + b^3*(A*e*(-5*d^3 - 4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3) + B*(7*d^4 + 2*d^3*e*x - 11*d^2*e^2*x^2 - 4*d*e^3*x^3 + e^4*x^4)) + 6*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2*Log[d + e*x])/(2*e^5*(d + e*x)^2)","A",1
1044,1,232,149,0.1148217,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^4} \, dx","Integrate[((a + b*x)^3*(A + B*x))/(d + e*x)^4,x]","\frac{-a^3 e^3 (2 A e+B (d+3 e x))-3 a^2 b e^2 \left(A e (d+3 e x)+2 B \left(d^2+3 d e x+3 e^2 x^2\right)\right)+3 a b^2 e \left(B d \left(11 d^2+27 d e x+18 e^2 x^2\right)-2 A e \left(d^2+3 d e x+3 e^2 x^2\right)\right)-6 b^2 (d+e x)^3 \log (d+e x) (-3 a B e-A b e+4 b B d)+b^3 \left(A d e \left(11 d^2+27 d e x+18 e^2 x^2\right)-2 B \left(13 d^4+27 d^3 e x+9 d^2 e^2 x^2-9 d e^3 x^3-3 e^4 x^4\right)\right)}{6 e^5 (d+e x)^3}","-\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,"(-(a^3*e^3*(2*A*e + B*(d + 3*e*x))) - 3*a^2*b*e^2*(A*e*(d + 3*e*x) + 2*B*(d^2 + 3*d*e*x + 3*e^2*x^2)) + 3*a*b^2*e*(-2*A*e*(d^2 + 3*d*e*x + 3*e^2*x^2) + B*d*(11*d^2 + 27*d*e*x + 18*e^2*x^2)) + b^3*(A*d*e*(11*d^2 + 27*d*e*x + 18*e^2*x^2) - 2*B*(13*d^4 + 27*d^3*e*x + 9*d^2*e^2*x^2 - 9*d*e^3*x^3 - 3*e^4*x^4)) - 6*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^3*Log[d + e*x])/(6*e^5*(d + e*x)^3)","A",1
1045,1,222,129,0.1148961,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^5} \, dx","Integrate[((a + b*x)^3*(A + B*x))/(d + e*x)^5,x]","\frac{-a^3 e^3 (3 A e+B (d+4 e x))-3 a^2 b e^2 \left(A e (d+4 e x)+B \left(d^2+4 d e x+6 e^2 x^2\right)\right)-3 a b^2 e \left(A e \left(d^2+4 d e x+6 e^2 x^2\right)+3 B \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)\right)+b^3 \left(B d \left(25 d^3+88 d^2 e x+108 d e^2 x^2+48 e^3 x^3\right)-3 A e \left(d^3+4 d^2 e x+6 d e^2 x^2+4 e^3 x^3\right)\right)+12 b^3 B (d+e x)^4 \log (d+e x)}{12 e^5 (d+e x)^4}","-\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,"(-(a^3*e^3*(3*A*e + B*(d + 4*e*x))) - 3*a^2*b*e^2*(A*e*(d + 4*e*x) + B*(d^2 + 4*d*e*x + 6*e^2*x^2)) - 3*a*b^2*e*(A*e*(d^2 + 4*d*e*x + 6*e^2*x^2) + 3*B*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3)) + b^3*(-3*A*e*(d^3 + 4*d^2*e*x + 6*d*e^2*x^2 + 4*e^3*x^3) + B*d*(25*d^3 + 88*d^2*e*x + 108*d*e^2*x^2 + 48*e^3*x^3)) + 12*b^3*B*(d + e*x)^4*Log[d + e*x])/(12*e^5*(d + e*x)^4)","A",1
1046,1,211,86,0.1009212,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^6} \, dx","Integrate[((a + b*x)^3*(A + B*x))/(d + e*x)^6,x]","-\frac{a^3 e^3 (4 A e+B (d+5 e x))+a^2 b e^2 \left(3 A e (d+5 e x)+2 B \left(d^2+5 d e x+10 e^2 x^2\right)\right)+a b^2 e \left(2 A e \left(d^2+5 d e x+10 e^2 x^2\right)+3 B \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)\right)+b^3 \left(A e \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)+4 B \left(d^4+5 d^3 e x+10 d^2 e^2 x^2+10 d e^3 x^3+5 e^4 x^4\right)\right)}{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,"-1/20*(a^3*e^3*(4*A*e + B*(d + 5*e*x)) + a^2*b*e^2*(3*A*e*(d + 5*e*x) + 2*B*(d^2 + 5*d*e*x + 10*e^2*x^2)) + a*b^2*e*(2*A*e*(d^2 + 5*d*e*x + 10*e^2*x^2) + 3*B*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3)) + b^3*(A*e*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3) + 4*B*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4)))/(e^5*(d + e*x)^5)","B",1
1047,1,211,133,0.1004754,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^7} \, dx","Integrate[((a + b*x)^3*(A + B*x))/(d + e*x)^7,x]","-\frac{2 a^3 e^3 (5 A e+B (d+6 e x))+3 a^2 b e^2 \left(2 A e (d+6 e x)+B \left(d^2+6 d e x+15 e^2 x^2\right)\right)+3 a b^2 e \left(A e \left(d^2+6 d e x+15 e^2 x^2\right)+B \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)\right)+b^3 \left(A e \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)+2 B \left(d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right)\right)}{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,"-1/60*(2*a^3*e^3*(5*A*e + B*(d + 6*e*x)) + 3*a^2*b*e^2*(2*A*e*(d + 6*e*x) + B*(d^2 + 6*d*e*x + 15*e^2*x^2)) + 3*a*b^2*e*(A*e*(d^2 + 6*d*e*x + 15*e^2*x^2) + B*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3)) + b^3*(A*e*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3) + 2*B*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4)))/(e^5*(d + e*x)^6)","A",1
1048,1,215,163,0.0966803,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^8} \, dx","Integrate[((a + b*x)^3*(A + B*x))/(d + e*x)^8,x]","-\frac{10 a^3 e^3 (6 A e+B (d+7 e x))+6 a^2 b e^2 \left(5 A e (d+7 e x)+2 B \left(d^2+7 d e x+21 e^2 x^2\right)\right)+3 a b^2 e \left(4 A e \left(d^2+7 d e x+21 e^2 x^2\right)+3 B \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)\right)+b^3 \left(3 A e \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)+4 B \left(d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right)\right)}{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,"-1/420*(10*a^3*e^3*(6*A*e + B*(d + 7*e*x)) + 6*a^2*b*e^2*(5*A*e*(d + 7*e*x) + 2*B*(d^2 + 7*d*e*x + 21*e^2*x^2)) + 3*a*b^2*e*(4*A*e*(d^2 + 7*d*e*x + 21*e^2*x^2) + 3*B*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3)) + b^3*(3*A*e*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3) + 4*B*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4)))/(e^5*(d + e*x)^7)","A",1
1049,1,211,163,0.0954641,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^9} \, dx","Integrate[((a + b*x)^3*(A + B*x))/(d + e*x)^9,x]","-\frac{5 a^3 e^3 (7 A e+B (d+8 e x))+5 a^2 b e^2 \left(3 A e (d+8 e x)+B \left(d^2+8 d e x+28 e^2 x^2\right)\right)+a b^2 e \left(5 A e \left(d^2+8 d e x+28 e^2 x^2\right)+3 B \left(d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right)\right)+b^3 \left(A e \left(d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right)+B \left(d^4+8 d^3 e x+28 d^2 e^2 x^2+56 d e^3 x^3+70 e^4 x^4\right)\right)}{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,"-1/280*(5*a^3*e^3*(7*A*e + B*(d + 8*e*x)) + 5*a^2*b*e^2*(3*A*e*(d + 8*e*x) + B*(d^2 + 8*d*e*x + 28*e^2*x^2)) + a*b^2*e*(5*A*e*(d^2 + 8*d*e*x + 28*e^2*x^2) + 3*B*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3)) + b^3*(A*e*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3) + B*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4)))/(e^5*(d + e*x)^8)","A",1
1050,1,214,163,0.1067061,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^{10}} \, dx","Integrate[((a + b*x)^3*(A + B*x))/(d + e*x)^10,x]","-\frac{35 a^3 e^3 (8 A e+B (d+9 e x))+15 a^2 b e^2 \left(7 A e (d+9 e x)+2 B \left(d^2+9 d e x+36 e^2 x^2\right)\right)+15 a b^2 e \left(2 A e \left(d^2+9 d e x+36 e^2 x^2\right)+B \left(d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right)\right)+b^3 \left(5 A e \left(d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right)+4 B \left(d^4+9 d^3 e x+36 d^2 e^2 x^2+84 d e^3 x^3+126 e^4 x^4\right)\right)}{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,"-1/2520*(35*a^3*e^3*(8*A*e + B*(d + 9*e*x)) + 15*a^2*b*e^2*(7*A*e*(d + 9*e*x) + 2*B*(d^2 + 9*d*e*x + 36*e^2*x^2)) + 15*a*b^2*e*(2*A*e*(d^2 + 9*d*e*x + 36*e^2*x^2) + B*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3)) + b^3*(5*A*e*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3) + 4*B*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4)))/(e^5*(d + e*x)^9)","A",1
1051,1,1385,292,0.5225195,"\int (a+b x)^6 (A+B x) (d+e x)^8 \, dx","Integrate[(a + b*x)^6*(A + B*x)*(d + e*x)^8,x]","\frac{1}{16} b^6 B e^8 x^{16}+\frac{1}{15} b^5 e^7 (8 b B d+A b e+6 a B e) x^{15}+\frac{1}{14} b^4 e^6 \left(4 d (7 B d+2 A e) b^2+6 a e (8 B d+A e) b+15 a^2 B e^2\right) x^{14}+\frac{1}{13} b^3 e^5 \left(28 d^2 (2 B d+A e) b^3+24 a d e (7 B d+2 A e) b^2+15 a^2 e^2 (8 B d+A e) b+20 a^3 B e^3\right) x^{13}+\frac{1}{12} b^2 e^4 \left(14 d^3 (5 B d+4 A e) b^4+168 a d^2 e (2 B d+A e) b^3+60 a^2 d e^2 (7 B d+2 A e) b^2+20 a^3 e^3 (8 B d+A e) b+15 a^4 B e^4\right) x^{12}+\frac{1}{11} b e^3 \left(14 d^4 (4 B d+5 A e) b^5+84 a d^3 e (5 B d+4 A e) b^4+420 a^2 d^2 e^2 (2 B d+A e) b^3+80 a^3 d e^3 (7 B d+2 A e) b^2+15 a^4 e^4 (8 B d+A e) b+6 a^5 B e^5\right) x^{11}+\frac{1}{10} e^2 \left(28 d^5 (B d+2 A e) b^6+84 a d^4 e (4 B d+5 A e) b^5+210 a^2 d^3 e^2 (5 B d+4 A e) b^4+560 a^3 d^2 e^3 (2 B d+A e) b^3+60 a^4 d e^4 (7 B d+2 A e) b^2+6 a^5 e^5 (8 B d+A e) b+a^6 B e^6\right) x^{10}+\frac{1}{9} e \left(4 b^6 (2 B d+7 A e) d^6+168 a b^5 e (B d+2 A e) d^5+210 a^2 b^4 e^2 (4 B d+5 A e) d^4+280 a^3 b^3 e^3 (5 B d+4 A e) d^3+420 a^4 b^2 e^4 (2 B d+A e) d^2+24 a^5 b e^5 (7 B d+2 A e) d+a^6 e^6 (8 B d+A e)\right) x^9+\frac{1}{8} d \left(b^6 (B d+8 A e) d^6+24 a b^5 e (2 B d+7 A e) d^5+420 a^2 b^4 e^2 (B d+2 A e) d^4+280 a^3 b^3 e^3 (4 B d+5 A e) d^3+210 a^4 b^2 e^4 (5 B d+4 A e) d^2+168 a^5 b e^5 (2 B d+A e) d+4 a^6 e^6 (7 B d+2 A e)\right) x^8+\frac{1}{7} d^2 \left(2 a B d \left(3 b^5 d^5+60 a b^4 e d^4+280 a^2 b^3 e^2 d^3+420 a^3 b^2 e^3 d^2+210 a^4 b e^4 d+28 a^5 e^5\right)+A \left(b^6 d^6+48 a b^5 e d^5+420 a^2 b^4 e^2 d^4+1120 a^3 b^3 e^3 d^3+1050 a^4 b^2 e^4 d^2+336 a^5 b e^5 d+28 a^6 e^6\right)\right) x^7+\frac{1}{6} a d^3 \left(a B d \left(15 b^4 d^4+160 a b^3 e d^3+420 a^2 b^2 e^2 d^2+336 a^3 b e^3 d+70 a^4 e^4\right)+2 A \left(3 b^5 d^5+60 a b^4 e d^4+280 a^2 b^3 e^2 d^3+420 a^3 b^2 e^3 d^2+210 a^4 b e^4 d+28 a^5 e^5\right)\right) x^6+\frac{1}{5} a^2 d^4 \left(4 a B d \left(5 b^3 d^3+30 a b^2 e d^2+42 a^2 b e^2 d+14 a^3 e^3\right)+A \left(15 b^4 d^4+160 a b^3 e d^3+420 a^2 b^2 e^2 d^2+336 a^3 b e^3 d+70 a^4 e^4\right)\right) x^5+\frac{1}{4} a^3 d^5 \left(a B d \left(15 b^2 d^2+48 a b e d+28 a^2 e^2\right)+4 A \left(5 b^3 d^3+30 a b^2 e d^2+42 a^2 b e^2 d+14 a^3 e^3\right)\right) x^4+\frac{1}{3} a^4 d^6 \left(2 a B d (3 b d+4 a e)+A \left(15 b^2 d^2+48 a b e d+28 a^2 e^2\right)\right) x^3+\frac{1}{2} a^5 d^7 (6 A b d+a B d+8 a A e) x^2+a^6 A d^8 x","-\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,"a^6*A*d^8*x + (a^5*d^7*(6*A*b*d + a*B*d + 8*a*A*e)*x^2)/2 + (a^4*d^6*(2*a*B*d*(3*b*d + 4*a*e) + A*(15*b^2*d^2 + 48*a*b*d*e + 28*a^2*e^2))*x^3)/3 + (a^3*d^5*(a*B*d*(15*b^2*d^2 + 48*a*b*d*e + 28*a^2*e^2) + 4*A*(5*b^3*d^3 + 30*a*b^2*d^2*e + 42*a^2*b*d*e^2 + 14*a^3*e^3))*x^4)/4 + (a^2*d^4*(4*a*B*d*(5*b^3*d^3 + 30*a*b^2*d^2*e + 42*a^2*b*d*e^2 + 14*a^3*e^3) + A*(15*b^4*d^4 + 160*a*b^3*d^3*e + 420*a^2*b^2*d^2*e^2 + 336*a^3*b*d*e^3 + 70*a^4*e^4))*x^5)/5 + (a*d^3*(a*B*d*(15*b^4*d^4 + 160*a*b^3*d^3*e + 420*a^2*b^2*d^2*e^2 + 336*a^3*b*d*e^3 + 70*a^4*e^4) + 2*A*(3*b^5*d^5 + 60*a*b^4*d^4*e + 280*a^2*b^3*d^3*e^2 + 420*a^3*b^2*d^2*e^3 + 210*a^4*b*d*e^4 + 28*a^5*e^5))*x^6)/6 + (d^2*(2*a*B*d*(3*b^5*d^5 + 60*a*b^4*d^4*e + 280*a^2*b^3*d^3*e^2 + 420*a^3*b^2*d^2*e^3 + 210*a^4*b*d*e^4 + 28*a^5*e^5) + A*(b^6*d^6 + 48*a*b^5*d^5*e + 420*a^2*b^4*d^4*e^2 + 1120*a^3*b^3*d^3*e^3 + 1050*a^4*b^2*d^2*e^4 + 336*a^5*b*d*e^5 + 28*a^6*e^6))*x^7)/7 + (d*(168*a^5*b*d*e^5*(2*B*d + A*e) + 420*a^2*b^4*d^4*e^2*(B*d + 2*A*e) + 4*a^6*e^6*(7*B*d + 2*A*e) + 210*a^4*b^2*d^2*e^4*(5*B*d + 4*A*e) + 280*a^3*b^3*d^3*e^3*(4*B*d + 5*A*e) + 24*a*b^5*d^5*e*(2*B*d + 7*A*e) + b^6*d^6*(B*d + 8*A*e))*x^8)/8 + (e*(420*a^4*b^2*d^2*e^4*(2*B*d + A*e) + a^6*e^6*(8*B*d + A*e) + 168*a*b^5*d^5*e*(B*d + 2*A*e) + 24*a^5*b*d*e^5*(7*B*d + 2*A*e) + 280*a^3*b^3*d^3*e^3*(5*B*d + 4*A*e) + 210*a^2*b^4*d^4*e^2*(4*B*d + 5*A*e) + 4*b^6*d^6*(2*B*d + 7*A*e))*x^9)/9 + (e^2*(a^6*B*e^6 + 560*a^3*b^3*d^2*e^3*(2*B*d + A*e) + 6*a^5*b*e^5*(8*B*d + A*e) + 28*b^6*d^5*(B*d + 2*A*e) + 60*a^4*b^2*d*e^4*(7*B*d + 2*A*e) + 210*a^2*b^4*d^3*e^2*(5*B*d + 4*A*e) + 84*a*b^5*d^4*e*(4*B*d + 5*A*e))*x^10)/10 + (b*e^3*(6*a^5*B*e^5 + 420*a^2*b^3*d^2*e^2*(2*B*d + A*e) + 15*a^4*b*e^4*(8*B*d + A*e) + 80*a^3*b^2*d*e^3*(7*B*d + 2*A*e) + 84*a*b^4*d^3*e*(5*B*d + 4*A*e) + 14*b^5*d^4*(4*B*d + 5*A*e))*x^11)/11 + (b^2*e^4*(15*a^4*B*e^4 + 168*a*b^3*d^2*e*(2*B*d + A*e) + 20*a^3*b*e^3*(8*B*d + A*e) + 60*a^2*b^2*d*e^2*(7*B*d + 2*A*e) + 14*b^4*d^3*(5*B*d + 4*A*e))*x^12)/12 + (b^3*e^5*(20*a^3*B*e^3 + 28*b^3*d^2*(2*B*d + A*e) + 15*a^2*b*e^2*(8*B*d + A*e) + 24*a*b^2*d*e*(7*B*d + 2*A*e))*x^13)/13 + (b^4*e^6*(15*a^2*B*e^2 + 6*a*b*e*(8*B*d + A*e) + 4*b^2*d*(7*B*d + 2*A*e))*x^14)/14 + (b^5*e^7*(8*b*B*d + A*b*e + 6*a*B*e)*x^15)/15 + (b^6*B*e^8*x^16)/16","B",1
1052,1,1224,292,0.461313,"\int (a+b x)^6 (A+B x) (d+e x)^7 \, dx","Integrate[(a + b*x)^6*(A + B*x)*(d + e*x)^7,x]","\frac{1}{15} b^6 B e^7 x^{15}+\frac{1}{14} b^5 e^6 (7 b B d+A b e+6 a B e) x^{14}+\frac{1}{13} b^4 e^5 \left(7 d (3 B d+A e) b^2+6 a e (7 B d+A e) b+15 a^2 B e^2\right) x^{13}+\frac{1}{12} b^3 e^4 \left(7 d^2 (5 B d+3 A e) b^3+42 a d e (3 B d+A e) b^2+15 a^2 e^2 (7 B d+A e) b+20 a^3 B e^3\right) x^{12}+\frac{1}{11} b^2 e^3 \left(35 d^3 (B d+A e) b^4+42 a d^2 e (5 B d+3 A e) b^3+105 a^2 d e^2 (3 B d+A e) b^2+20 a^3 e^3 (7 B d+A e) b+15 a^4 B e^4\right) x^{11}+\frac{1}{10} b e^2 \left(7 d^4 (3 B d+5 A e) b^5+210 a d^3 e (B d+A e) b^4+105 a^2 d^2 e^2 (5 B d+3 A e) b^3+140 a^3 d e^3 (3 B d+A e) b^2+15 a^4 e^4 (7 B d+A e) b+6 a^5 B e^5\right) x^{10}+\frac{1}{9} e \left(7 d^5 (B d+3 A e) b^6+42 a d^4 e (3 B d+5 A e) b^5+525 a^2 d^3 e^2 (B d+A e) b^4+140 a^3 d^2 e^3 (5 B d+3 A e) b^3+105 a^4 d e^4 (3 B d+A e) b^2+6 a^5 e^5 (7 B d+A e) b+a^6 B e^6\right) x^9+\frac{1}{8} \left(b^6 (B d+7 A e) d^6+42 a b^5 e (B d+3 A e) d^5+105 a^2 b^4 e^2 (3 B d+5 A e) d^4+700 a^3 b^3 e^3 (B d+A e) d^3+105 a^4 b^2 e^4 (5 B d+3 A e) d^2+42 a^5 b e^5 (3 B d+A e) d+a^6 e^6 (7 B d+A e)\right) x^8+\frac{1}{7} d \left(3 a B d \left(2 b^5 d^5+35 a b^4 e d^4+140 a^2 b^3 e^2 d^3+175 a^3 b^2 e^3 d^2+70 a^4 b e^4 d+7 a^5 e^5\right)+A \left(b^6 d^6+42 a b^5 e d^5+315 a^2 b^4 e^2 d^4+700 a^3 b^3 e^3 d^3+525 a^4 b^2 e^4 d^2+126 a^5 b e^5 d+7 a^6 e^6\right)\right) x^7+\frac{1}{6} a d^2 \left(5 a B d \left(3 b^4 d^4+28 a b^3 e d^3+63 a^2 b^2 e^2 d^2+42 a^3 b e^3 d+7 a^4 e^4\right)+3 A \left(2 b^5 d^5+35 a b^4 e d^4+140 a^2 b^3 e^2 d^3+175 a^3 b^2 e^3 d^2+70 a^4 b e^4 d+7 a^5 e^5\right)\right) x^6+\frac{1}{5} a^2 d^3 \left(a B d \left(20 b^3 d^3+105 a b^2 e d^2+126 a^2 b e^2 d+35 a^3 e^3\right)+5 A \left(3 b^4 d^4+28 a b^3 e d^3+63 a^2 b^2 e^2 d^2+42 a^3 b e^3 d+7 a^4 e^4\right)\right) x^5+\frac{1}{4} a^3 d^4 \left(3 a B d \left(5 b^2 d^2+14 a b e d+7 a^2 e^2\right)+A \left(20 b^3 d^3+105 a b^2 e d^2+126 a^2 b e^2 d+35 a^3 e^3\right)\right) x^4+\frac{1}{3} a^4 d^5 \left(a B d (6 b d+7 a e)+3 A \left(5 b^2 d^2+14 a b e d+7 a^2 e^2\right)\right) x^3+\frac{1}{2} a^5 d^6 (6 A b d+a B d+7 a A e) x^2+a^6 A d^7 x","-\frac{b^5 (d+e x)^{14} (-6 a B e-A b e+7 b B d)}{14 e^8}+\frac{3 b^4 (d+e x)^{13} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{13 e^8}-\frac{5 b^3 (d+e x)^{12} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{12 e^8}+\frac{5 b^2 (d+e x)^{11} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{11 e^8}-\frac{3 b (d+e x)^{10} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{10 e^8}+\frac{(d+e x)^9 (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{9 e^8}-\frac{(d+e x)^8 (b d-a e)^6 (B d-A e)}{8 e^8}+\frac{b^6 B (d+e x)^{15}}{15 e^8}",1,"a^6*A*d^7*x + (a^5*d^6*(6*A*b*d + a*B*d + 7*a*A*e)*x^2)/2 + (a^4*d^5*(a*B*d*(6*b*d + 7*a*e) + 3*A*(5*b^2*d^2 + 14*a*b*d*e + 7*a^2*e^2))*x^3)/3 + (a^3*d^4*(3*a*B*d*(5*b^2*d^2 + 14*a*b*d*e + 7*a^2*e^2) + A*(20*b^3*d^3 + 105*a*b^2*d^2*e + 126*a^2*b*d*e^2 + 35*a^3*e^3))*x^4)/4 + (a^2*d^3*(a*B*d*(20*b^3*d^3 + 105*a*b^2*d^2*e + 126*a^2*b*d*e^2 + 35*a^3*e^3) + 5*A*(3*b^4*d^4 + 28*a*b^3*d^3*e + 63*a^2*b^2*d^2*e^2 + 42*a^3*b*d*e^3 + 7*a^4*e^4))*x^5)/5 + (a*d^2*(5*a*B*d*(3*b^4*d^4 + 28*a*b^3*d^3*e + 63*a^2*b^2*d^2*e^2 + 42*a^3*b*d*e^3 + 7*a^4*e^4) + 3*A*(2*b^5*d^5 + 35*a*b^4*d^4*e + 140*a^2*b^3*d^3*e^2 + 175*a^3*b^2*d^2*e^3 + 70*a^4*b*d*e^4 + 7*a^5*e^5))*x^6)/6 + (d*(3*a*B*d*(2*b^5*d^5 + 35*a*b^4*d^4*e + 140*a^2*b^3*d^3*e^2 + 175*a^3*b^2*d^2*e^3 + 70*a^4*b*d*e^4 + 7*a^5*e^5) + A*(b^6*d^6 + 42*a*b^5*d^5*e + 315*a^2*b^4*d^4*e^2 + 700*a^3*b^3*d^3*e^3 + 525*a^4*b^2*d^2*e^4 + 126*a^5*b*d*e^5 + 7*a^6*e^6))*x^7)/7 + ((700*a^3*b^3*d^3*e^3*(B*d + A*e) + 42*a^5*b*d*e^5*(3*B*d + A*e) + a^6*e^6*(7*B*d + A*e) + 42*a*b^5*d^5*e*(B*d + 3*A*e) + 105*a^4*b^2*d^2*e^4*(5*B*d + 3*A*e) + 105*a^2*b^4*d^4*e^2*(3*B*d + 5*A*e) + b^6*d^6*(B*d + 7*A*e))*x^8)/8 + (e*(a^6*B*e^6 + 525*a^2*b^4*d^3*e^2*(B*d + A*e) + 105*a^4*b^2*d*e^4*(3*B*d + A*e) + 6*a^5*b*e^5*(7*B*d + A*e) + 7*b^6*d^5*(B*d + 3*A*e) + 140*a^3*b^3*d^2*e^3*(5*B*d + 3*A*e) + 42*a*b^5*d^4*e*(3*B*d + 5*A*e))*x^9)/9 + (b*e^2*(6*a^5*B*e^5 + 210*a*b^4*d^3*e*(B*d + A*e) + 140*a^3*b^2*d*e^3*(3*B*d + A*e) + 15*a^4*b*e^4*(7*B*d + A*e) + 105*a^2*b^3*d^2*e^2*(5*B*d + 3*A*e) + 7*b^5*d^4*(3*B*d + 5*A*e))*x^10)/10 + (b^2*e^3*(15*a^4*B*e^4 + 35*b^4*d^3*(B*d + A*e) + 105*a^2*b^2*d*e^2*(3*B*d + A*e) + 20*a^3*b*e^3*(7*B*d + A*e) + 42*a*b^3*d^2*e*(5*B*d + 3*A*e))*x^11)/11 + (b^3*e^4*(20*a^3*B*e^3 + 42*a*b^2*d*e*(3*B*d + A*e) + 15*a^2*b*e^2*(7*B*d + A*e) + 7*b^3*d^2*(5*B*d + 3*A*e))*x^12)/12 + (b^4*e^5*(15*a^2*B*e^2 + 7*b^2*d*(3*B*d + A*e) + 6*a*b*e*(7*B*d + A*e))*x^13)/13 + (b^5*e^6*(7*b*B*d + A*b*e + 6*a*B*e)*x^14)/14 + (b^6*B*e^7*x^15)/15","B",1
1053,1,1069,290,0.3949465,"\int (a+b x)^6 (A+B x) (d+e x)^6 \, dx","Integrate[(a + b*x)^6*(A + B*x)*(d + e*x)^6,x]","\frac{1}{14} b^6 B e^6 x^{14}+\frac{1}{13} b^5 e^5 (6 b B d+A b e+6 a B e) x^{13}+\frac{1}{4} b^4 e^4 \left(d (5 B d+2 A e) b^2+2 a e (6 B d+A e) b+5 a^2 B e^2\right) x^{12}+\frac{1}{11} b^3 e^3 \left(5 d^2 (4 B d+3 A e) b^3+18 a d e (5 B d+2 A e) b^2+15 a^2 e^2 (6 B d+A e) b+20 a^3 B e^3\right) x^{11}+\frac{1}{2} b^2 e^2 \left(d^3 (3 B d+4 A e) b^4+6 a d^2 e (4 B d+3 A e) b^3+9 a^2 d e^2 (5 B d+2 A e) b^2+4 a^3 e^3 (6 B d+A e) b+3 a^4 B e^4\right) x^{10}+\frac{1}{3} b e \left(d^4 (2 B d+5 A e) b^5+10 a d^3 e (3 B d+4 A e) b^4+25 a^2 d^2 e^2 (4 B d+3 A e) b^3+20 a^3 d e^3 (5 B d+2 A e) b^2+5 a^4 e^4 (6 B d+A e) b+2 a^5 B e^5\right) x^9+\frac{1}{8} \left(d^5 (B d+6 A e) b^6+18 a d^4 e (2 B d+5 A e) b^5+75 a^2 d^3 e^2 (3 B d+4 A e) b^4+100 a^3 d^2 e^3 (4 B d+3 A e) b^3+45 a^4 d e^4 (5 B d+2 A e) b^2+6 a^5 e^5 (6 B d+A e) b+a^6 B e^6\right) x^8+\frac{1}{7} \left(6 a B d \left(b^5 d^5+15 a b^4 e d^4+50 a^2 b^3 e^2 d^3+50 a^3 b^2 e^3 d^2+15 a^4 b e^4 d+a^5 e^5\right)+A \left(b^6 d^6+36 a b^5 e d^5+225 a^2 b^4 e^2 d^4+400 a^3 b^3 e^3 d^3+225 a^4 b^2 e^4 d^2+36 a^5 b e^5 d+a^6 e^6\right)\right) x^7+\frac{1}{2} a d \left(5 a B d \left(b^4 d^4+8 a b^3 e d^3+15 a^2 b^2 e^2 d^2+8 a^3 b e^3 d+a^4 e^4\right)+2 A \left(b^5 d^5+15 a b^4 e d^4+50 a^2 b^3 e^2 d^3+50 a^3 b^2 e^3 d^2+15 a^4 b e^4 d+a^5 e^5\right)\right) x^6+a^2 d^2 \left(2 a B d \left(2 b^3 d^3+9 a b^2 e d^2+9 a^2 b e^2 d+2 a^3 e^3\right)+3 A \left(b^4 d^4+8 a b^3 e d^3+15 a^2 b^2 e^2 d^2+8 a^3 b e^3 d+a^4 e^4\right)\right) x^5+\frac{1}{4} a^3 d^3 \left(3 a B d \left(5 b^2 d^2+12 a b e d+5 a^2 e^2\right)+10 A \left(2 b^3 d^3+9 a b^2 e d^2+9 a^2 b e^2 d+2 a^3 e^3\right)\right) x^4+a^4 d^4 \left(2 a B d (b d+a e)+A \left(5 b^2 d^2+12 a b e d+5 a^2 e^2\right)\right) x^3+\frac{1}{2} a^5 d^5 (a B d+6 A (b d+a e)) x^2+a^6 A d^6 x","\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,"a^6*A*d^6*x + (a^5*d^5*(a*B*d + 6*A*(b*d + a*e))*x^2)/2 + a^4*d^4*(2*a*B*d*(b*d + a*e) + A*(5*b^2*d^2 + 12*a*b*d*e + 5*a^2*e^2))*x^3 + (a^3*d^3*(3*a*B*d*(5*b^2*d^2 + 12*a*b*d*e + 5*a^2*e^2) + 10*A*(2*b^3*d^3 + 9*a*b^2*d^2*e + 9*a^2*b*d*e^2 + 2*a^3*e^3))*x^4)/4 + a^2*d^2*(2*a*B*d*(2*b^3*d^3 + 9*a*b^2*d^2*e + 9*a^2*b*d*e^2 + 2*a^3*e^3) + 3*A*(b^4*d^4 + 8*a*b^3*d^3*e + 15*a^2*b^2*d^2*e^2 + 8*a^3*b*d*e^3 + a^4*e^4))*x^5 + (a*d*(5*a*B*d*(b^4*d^4 + 8*a*b^3*d^3*e + 15*a^2*b^2*d^2*e^2 + 8*a^3*b*d*e^3 + a^4*e^4) + 2*A*(b^5*d^5 + 15*a*b^4*d^4*e + 50*a^2*b^3*d^3*e^2 + 50*a^3*b^2*d^2*e^3 + 15*a^4*b*d*e^4 + a^5*e^5))*x^6)/2 + ((6*a*B*d*(b^5*d^5 + 15*a*b^4*d^4*e + 50*a^2*b^3*d^3*e^2 + 50*a^3*b^2*d^2*e^3 + 15*a^4*b*d*e^4 + a^5*e^5) + A*(b^6*d^6 + 36*a*b^5*d^5*e + 225*a^2*b^4*d^4*e^2 + 400*a^3*b^3*d^3*e^3 + 225*a^4*b^2*d^2*e^4 + 36*a^5*b*d*e^5 + a^6*e^6))*x^7)/7 + ((a^6*B*e^6 + 6*a^5*b*e^5*(6*B*d + A*e) + 45*a^4*b^2*d*e^4*(5*B*d + 2*A*e) + 100*a^3*b^3*d^2*e^3*(4*B*d + 3*A*e) + 75*a^2*b^4*d^3*e^2*(3*B*d + 4*A*e) + 18*a*b^5*d^4*e*(2*B*d + 5*A*e) + b^6*d^5*(B*d + 6*A*e))*x^8)/8 + (b*e*(2*a^5*B*e^5 + 5*a^4*b*e^4*(6*B*d + A*e) + 20*a^3*b^2*d*e^3*(5*B*d + 2*A*e) + 25*a^2*b^3*d^2*e^2*(4*B*d + 3*A*e) + 10*a*b^4*d^3*e*(3*B*d + 4*A*e) + b^5*d^4*(2*B*d + 5*A*e))*x^9)/3 + (b^2*e^2*(3*a^4*B*e^4 + 4*a^3*b*e^3*(6*B*d + A*e) + 9*a^2*b^2*d*e^2*(5*B*d + 2*A*e) + 6*a*b^3*d^2*e*(4*B*d + 3*A*e) + b^4*d^3*(3*B*d + 4*A*e))*x^10)/2 + (b^3*e^3*(20*a^3*B*e^3 + 15*a^2*b*e^2*(6*B*d + A*e) + 18*a*b^2*d*e*(5*B*d + 2*A*e) + 5*b^3*d^2*(4*B*d + 3*A*e))*x^11)/11 + (b^4*e^4*(5*a^2*B*e^2 + 2*a*b*e*(6*B*d + A*e) + b^2*d*(5*B*d + 2*A*e))*x^12)/4 + (b^5*e^5*(6*b*B*d + A*b*e + 6*a*B*e)*x^13)/13 + (b^6*B*e^6*x^14)/14","B",1
1054,1,907,240,0.3258598,"\int (a+b x)^6 (A+B x) (d+e x)^5 \, dx","Integrate[(a + b*x)^6*(A + B*x)*(d + e*x)^5,x]","\frac{1}{13} b^6 B e^5 x^{13}+\frac{1}{12} b^5 e^4 (5 b B d+A b e+6 a B e) x^{12}+\frac{1}{11} b^4 e^3 \left(5 d (2 B d+A e) b^2+6 a e (5 B d+A e) b+15 a^2 B e^2\right) x^{11}+\frac{1}{2} b^3 e^2 \left(2 d^2 (B d+A e) b^3+6 a d e (2 B d+A e) b^2+3 a^2 e^2 (5 B d+A e) b+4 a^3 B e^3\right) x^{10}+\frac{5}{9} b^2 e \left(d^3 (B d+2 A e) b^4+12 a d^2 e (B d+A e) b^3+15 a^2 d e^2 (2 B d+A e) b^2+4 a^3 e^3 (5 B d+A e) b+3 a^4 B e^4\right) x^9+\frac{1}{8} b \left(d^4 (B d+5 A e) b^5+30 a d^3 e (B d+2 A e) b^4+150 a^2 d^2 e^2 (B d+A e) b^3+100 a^3 d e^3 (2 B d+A e) b^2+15 a^4 e^4 (5 B d+A e) b+6 a^5 B e^5\right) x^8+\frac{1}{7} \left(a B \left(6 b^5 d^5+75 a b^4 e d^4+200 a^2 b^3 e^2 d^3+150 a^3 b^2 e^3 d^2+30 a^4 b e^4 d+a^5 e^5\right)+A b \left(b^5 d^5+30 a b^4 e d^4+150 a^2 b^3 e^2 d^3+200 a^3 b^2 e^3 d^2+75 a^4 b e^4 d+6 a^5 e^5\right)\right) x^7+\frac{1}{6} a \left(5 a B d \left(3 b^4 d^4+20 a b^3 e d^3+30 a^2 b^2 e^2 d^2+12 a^3 b e^3 d+a^4 e^4\right)+A \left(6 b^5 d^5+75 a b^4 e d^4+200 a^2 b^3 e^2 d^3+150 a^3 b^2 e^3 d^2+30 a^4 b e^4 d+a^5 e^5\right)\right) x^6+a^2 d \left(a B d \left(4 b^3 d^3+15 a b^2 e d^2+12 a^2 b e^2 d+2 a^3 e^3\right)+A \left(3 b^4 d^4+20 a b^3 e d^3+30 a^2 b^2 e^2 d^2+12 a^3 b e^3 d+a^4 e^4\right)\right) x^5+\frac{5}{4} a^3 d^2 \left(a B d \left(3 b^2 d^2+6 a b e d+2 a^2 e^2\right)+A \left(4 b^3 d^3+15 a b^2 e d^2+12 a^2 b e^2 d+2 a^3 e^3\right)\right) x^4+\frac{1}{3} a^4 d^3 \left(a B d (6 b d+5 a e)+5 A \left(3 b^2 d^2+6 a b e d+2 a^2 e^2\right)\right) x^3+\frac{1}{2} a^5 d^4 (6 A b d+a B d+5 a A e) x^2+a^6 A d^5 x","\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,"a^6*A*d^5*x + (a^5*d^4*(6*A*b*d + a*B*d + 5*a*A*e)*x^2)/2 + (a^4*d^3*(a*B*d*(6*b*d + 5*a*e) + 5*A*(3*b^2*d^2 + 6*a*b*d*e + 2*a^2*e^2))*x^3)/3 + (5*a^3*d^2*(a*B*d*(3*b^2*d^2 + 6*a*b*d*e + 2*a^2*e^2) + A*(4*b^3*d^3 + 15*a*b^2*d^2*e + 12*a^2*b*d*e^2 + 2*a^3*e^3))*x^4)/4 + a^2*d*(a*B*d*(4*b^3*d^3 + 15*a*b^2*d^2*e + 12*a^2*b*d*e^2 + 2*a^3*e^3) + A*(3*b^4*d^4 + 20*a*b^3*d^3*e + 30*a^2*b^2*d^2*e^2 + 12*a^3*b*d*e^3 + a^4*e^4))*x^5 + (a*(5*a*B*d*(3*b^4*d^4 + 20*a*b^3*d^3*e + 30*a^2*b^2*d^2*e^2 + 12*a^3*b*d*e^3 + a^4*e^4) + A*(6*b^5*d^5 + 75*a*b^4*d^4*e + 200*a^2*b^3*d^3*e^2 + 150*a^3*b^2*d^2*e^3 + 30*a^4*b*d*e^4 + a^5*e^5))*x^6)/6 + ((a*B*(6*b^5*d^5 + 75*a*b^4*d^4*e + 200*a^2*b^3*d^3*e^2 + 150*a^3*b^2*d^2*e^3 + 30*a^4*b*d*e^4 + a^5*e^5) + A*b*(b^5*d^5 + 30*a*b^4*d^4*e + 150*a^2*b^3*d^3*e^2 + 200*a^3*b^2*d^2*e^3 + 75*a^4*b*d*e^4 + 6*a^5*e^5))*x^7)/7 + (b*(6*a^5*B*e^5 + 150*a^2*b^3*d^2*e^2*(B*d + A*e) + 100*a^3*b^2*d*e^3*(2*B*d + A*e) + 15*a^4*b*e^4*(5*B*d + A*e) + 30*a*b^4*d^3*e*(B*d + 2*A*e) + b^5*d^4*(B*d + 5*A*e))*x^8)/8 + (5*b^2*e*(3*a^4*B*e^4 + 12*a*b^3*d^2*e*(B*d + A*e) + 15*a^2*b^2*d*e^2*(2*B*d + A*e) + 4*a^3*b*e^3*(5*B*d + A*e) + b^4*d^3*(B*d + 2*A*e))*x^9)/9 + (b^3*e^2*(4*a^3*B*e^3 + 2*b^3*d^2*(B*d + A*e) + 6*a*b^2*d*e*(2*B*d + A*e) + 3*a^2*b*e^2*(5*B*d + A*e))*x^10)/2 + (b^4*e^3*(15*a^2*B*e^2 + 5*b^2*d*(2*B*d + A*e) + 6*a*b*e*(5*B*d + A*e))*x^11)/11 + (b^5*e^4*(5*b*B*d + A*b*e + 6*a*B*e)*x^12)/12 + (b^6*B*e^5*x^13)/13","B",1
1055,1,762,204,0.2710886,"\int (a+b x)^6 (A+B x) (d+e x)^4 \, dx","Integrate[(a + b*x)^6*(A + B*x)*(d + e*x)^4,x]","a^6 A d^4 x+\frac{1}{2} a^5 d^3 x^2 (4 a A e+a B d+6 A b d)+\frac{1}{10} b^4 e^2 x^{10} \left(15 a^2 B e^2+6 a b e (A e+4 B d)+2 b^2 d (2 A e+3 B d)\right)+\frac{1}{3} a^4 d^2 x^3 \left(3 A \left(2 a^2 e^2+8 a b d e+5 b^2 d^2\right)+2 a B d (2 a e+3 b d)\right)+\frac{1}{9} b^3 e x^9 \left(20 a^3 B e^3+15 a^2 b e^2 (A e+4 B d)+12 a b^2 d e (2 A e+3 B d)+2 b^3 d^2 (3 A e+2 B d)\right)+\frac{1}{4} a^3 d x^4 \left(3 a B d \left(2 a^2 e^2+8 a b d e+5 b^2 d^2\right)+4 A \left(a^3 e^3+9 a^2 b d e^2+15 a b^2 d^2 e+5 b^3 d^3\right)\right)+\frac{1}{8} b^2 x^8 \left(15 a^4 B e^4+20 a^3 b e^3 (A e+4 B d)+30 a^2 b^2 d e^2 (2 A e+3 B d)+12 a b^3 d^2 e (3 A e+2 B d)+b^4 d^3 (4 A e+B d)\right)+\frac{1}{7} b x^7 \left(A b \left(15 a^4 e^4+80 a^3 b d e^3+90 a^2 b^2 d^2 e^2+24 a b^3 d^3 e+b^4 d^4\right)+6 a B \left(a^4 e^4+10 a^3 b d e^3+20 a^2 b^2 d^2 e^2+10 a b^3 d^3 e+b^4 d^4\right)\right)+\frac{1}{6} a x^6 \left(6 A b \left(a^4 e^4+10 a^3 b d e^3+20 a^2 b^2 d^2 e^2+10 a b^3 d^3 e+b^4 d^4\right)+a B \left(a^4 e^4+24 a^3 b d e^3+90 a^2 b^2 d^2 e^2+80 a b^3 d^3 e+15 b^4 d^4\right)\right)+\frac{1}{5} a^2 x^5 \left(4 a B d \left(a^3 e^3+9 a^2 b d e^2+15 a b^2 d^2 e+5 b^3 d^3\right)+A \left(a^4 e^4+24 a^3 b d e^3+90 a^2 b^2 d^2 e^2+80 a b^3 d^3 e+15 b^4 d^4\right)\right)+\frac{1}{11} b^5 e^3 x^{11} (6 a B e+A b e+4 b B d)+\frac{1}{12} b^6 B e^4 x^{12}","\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,"a^6*A*d^4*x + (a^5*d^3*(6*A*b*d + a*B*d + 4*a*A*e)*x^2)/2 + (a^4*d^2*(2*a*B*d*(3*b*d + 2*a*e) + 3*A*(5*b^2*d^2 + 8*a*b*d*e + 2*a^2*e^2))*x^3)/3 + (a^3*d*(3*a*B*d*(5*b^2*d^2 + 8*a*b*d*e + 2*a^2*e^2) + 4*A*(5*b^3*d^3 + 15*a*b^2*d^2*e + 9*a^2*b*d*e^2 + a^3*e^3))*x^4)/4 + (a^2*(4*a*B*d*(5*b^3*d^3 + 15*a*b^2*d^2*e + 9*a^2*b*d*e^2 + a^3*e^3) + A*(15*b^4*d^4 + 80*a*b^3*d^3*e + 90*a^2*b^2*d^2*e^2 + 24*a^3*b*d*e^3 + a^4*e^4))*x^5)/5 + (a*(6*A*b*(b^4*d^4 + 10*a*b^3*d^3*e + 20*a^2*b^2*d^2*e^2 + 10*a^3*b*d*e^3 + a^4*e^4) + a*B*(15*b^4*d^4 + 80*a*b^3*d^3*e + 90*a^2*b^2*d^2*e^2 + 24*a^3*b*d*e^3 + a^4*e^4))*x^6)/6 + (b*(6*a*B*(b^4*d^4 + 10*a*b^3*d^3*e + 20*a^2*b^2*d^2*e^2 + 10*a^3*b*d*e^3 + a^4*e^4) + A*b*(b^4*d^4 + 24*a*b^3*d^3*e + 90*a^2*b^2*d^2*e^2 + 80*a^3*b*d*e^3 + 15*a^4*e^4))*x^7)/7 + (b^2*(15*a^4*B*e^4 + 20*a^3*b*e^3*(4*B*d + A*e) + 30*a^2*b^2*d*e^2*(3*B*d + 2*A*e) + 12*a*b^3*d^2*e*(2*B*d + 3*A*e) + b^4*d^3*(B*d + 4*A*e))*x^8)/8 + (b^3*e*(20*a^3*B*e^3 + 15*a^2*b*e^2*(4*B*d + A*e) + 12*a*b^2*d*e*(3*B*d + 2*A*e) + 2*b^3*d^2*(2*B*d + 3*A*e))*x^9)/9 + (b^4*e^2*(15*a^2*B*e^2 + 6*a*b*e*(4*B*d + A*e) + 2*b^2*d*(3*B*d + 2*A*e))*x^10)/10 + (b^5*e^3*(4*b*B*d + A*b*e + 6*a*B*e)*x^11)/11 + (b^6*B*e^4*x^12)/12","B",1
1056,1,586,159,0.2114605,"\int (a+b x)^6 (A+B x) (d+e x)^3 \, dx","Integrate[(a + b*x)^6*(A + B*x)*(d + e*x)^3,x]","a^6 A d^3 x+\frac{1}{2} a^5 d^2 x^2 (3 a A e+a B d+6 A b d)+\frac{1}{3} b^4 e x^9 \left(5 a^2 B e^2+2 a b e (A e+3 B d)+b^2 d (A e+B d)\right)+a^4 d x^3 \left(A \left(a^2 e^2+6 a b d e+5 b^2 d^2\right)+a B d (a e+2 b d)\right)+\frac{1}{8} b^3 x^8 \left(20 a^3 B e^3+15 a^2 b e^2 (A e+3 B d)+18 a b^2 d e (A e+B d)+b^3 d^2 (3 A e+B d)\right)+\frac{1}{7} b^2 x^7 \left(A b \left(20 a^3 e^3+45 a^2 b d e^2+18 a b^2 d^2 e+b^3 d^3\right)+3 a B \left(5 a^3 e^3+20 a^2 b d e^2+15 a b^2 d^2 e+2 b^3 d^3\right)\right)+\frac{1}{2} a b x^6 \left(A b \left(5 a^3 e^3+20 a^2 b d e^2+15 a b^2 d^2 e+2 b^3 d^3\right)+a B \left(2 a^3 e^3+15 a^2 b d e^2+20 a b^2 d^2 e+5 b^3 d^3\right)\right)+\frac{1}{5} a^2 x^5 \left(3 A b \left(2 a^3 e^3+15 a^2 b d e^2+20 a b^2 d^2 e+5 b^3 d^3\right)+a B \left(a^3 e^3+18 a^2 b d e^2+45 a b^2 d^2 e+20 b^3 d^3\right)\right)+\frac{1}{4} a^3 x^4 \left(3 a B d \left(a^2 e^2+6 a b d e+5 b^2 d^2\right)+A \left(a^3 e^3+18 a^2 b d e^2+45 a b^2 d^2 e+20 b^3 d^3\right)\right)+\frac{1}{10} b^5 e^2 x^{10} (6 a B e+A b e+3 b B d)+\frac{1}{11} b^6 B e^3 x^{11}","\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,"a^6*A*d^3*x + (a^5*d^2*(6*A*b*d + a*B*d + 3*a*A*e)*x^2)/2 + a^4*d*(a*B*d*(2*b*d + a*e) + A*(5*b^2*d^2 + 6*a*b*d*e + a^2*e^2))*x^3 + (a^3*(3*a*B*d*(5*b^2*d^2 + 6*a*b*d*e + a^2*e^2) + A*(20*b^3*d^3 + 45*a*b^2*d^2*e + 18*a^2*b*d*e^2 + a^3*e^3))*x^4)/4 + (a^2*(a*B*(20*b^3*d^3 + 45*a*b^2*d^2*e + 18*a^2*b*d*e^2 + a^3*e^3) + 3*A*b*(5*b^3*d^3 + 20*a*b^2*d^2*e + 15*a^2*b*d*e^2 + 2*a^3*e^3))*x^5)/5 + (a*b*(a*B*(5*b^3*d^3 + 20*a*b^2*d^2*e + 15*a^2*b*d*e^2 + 2*a^3*e^3) + A*b*(2*b^3*d^3 + 15*a*b^2*d^2*e + 20*a^2*b*d*e^2 + 5*a^3*e^3))*x^6)/2 + (b^2*(3*a*B*(2*b^3*d^3 + 15*a*b^2*d^2*e + 20*a^2*b*d*e^2 + 5*a^3*e^3) + A*b*(b^3*d^3 + 18*a*b^2*d^2*e + 45*a^2*b*d*e^2 + 20*a^3*e^3))*x^7)/7 + (b^3*(20*a^3*B*e^3 + 18*a*b^2*d*e*(B*d + A*e) + 15*a^2*b*e^2*(3*B*d + A*e) + b^3*d^2*(B*d + 3*A*e))*x^8)/8 + (b^4*e*(5*a^2*B*e^2 + b^2*d*(B*d + A*e) + 2*a*b*e*(3*B*d + A*e))*x^9)/3 + (b^5*e^2*(3*b*B*d + A*b*e + 6*a*B*e)*x^10)/10 + (b^6*B*e^3*x^11)/11","B",1
1057,1,386,118,0.2297956,"\int (a+b x)^6 (A+B x) (d+e x)^2 \, dx","Integrate[(a + b*x)^6*(A + B*x)*(d + e*x)^2,x]","\frac{x \left(210 a^6 \left(4 A \left(3 d^2+3 d e x+e^2 x^2\right)+B x \left(6 d^2+8 d e x+3 e^2 x^2\right)\right)+252 a^5 b x \left(5 A \left(6 d^2+8 d e x+3 e^2 x^2\right)+2 B x \left(10 d^2+15 d e x+6 e^2 x^2\right)\right)+630 a^4 b^2 x^2 \left(2 A \left(10 d^2+15 d e x+6 e^2 x^2\right)+B x \left(15 d^2+24 d e x+10 e^2 x^2\right)\right)+120 a^3 b^3 x^3 \left(7 A \left(15 d^2+24 d e x+10 e^2 x^2\right)+4 B x \left(21 d^2+35 d e x+15 e^2 x^2\right)\right)+45 a^2 b^4 x^4 \left(8 A \left(21 d^2+35 d e x+15 e^2 x^2\right)+5 B x \left(28 d^2+48 d e x+21 e^2 x^2\right)\right)+30 a b^5 x^5 \left(3 A \left(28 d^2+48 d e x+21 e^2 x^2\right)+2 B x \left(36 d^2+63 d e x+28 e^2 x^2\right)\right)+b^6 x^6 \left(10 A \left(36 d^2+63 d e x+28 e^2 x^2\right)+7 B x \left(45 d^2+80 d e x+36 e^2 x^2\right)\right)\right)}{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,"(x*(210*a^6*(4*A*(3*d^2 + 3*d*e*x + e^2*x^2) + B*x*(6*d^2 + 8*d*e*x + 3*e^2*x^2)) + 252*a^5*b*x*(5*A*(6*d^2 + 8*d*e*x + 3*e^2*x^2) + 2*B*x*(10*d^2 + 15*d*e*x + 6*e^2*x^2)) + 630*a^4*b^2*x^2*(2*A*(10*d^2 + 15*d*e*x + 6*e^2*x^2) + B*x*(15*d^2 + 24*d*e*x + 10*e^2*x^2)) + 120*a^3*b^3*x^3*(7*A*(15*d^2 + 24*d*e*x + 10*e^2*x^2) + 4*B*x*(21*d^2 + 35*d*e*x + 15*e^2*x^2)) + 45*a^2*b^4*x^4*(8*A*(21*d^2 + 35*d*e*x + 15*e^2*x^2) + 5*B*x*(28*d^2 + 48*d*e*x + 21*e^2*x^2)) + 30*a*b^5*x^5*(3*A*(28*d^2 + 48*d*e*x + 21*e^2*x^2) + 2*B*x*(36*d^2 + 63*d*e*x + 28*e^2*x^2)) + b^6*x^6*(10*A*(36*d^2 + 63*d*e*x + 28*e^2*x^2) + 7*B*x*(45*d^2 + 80*d*e*x + 36*e^2*x^2))))/2520","B",1
1058,1,231,75,0.1414936,"\int (a+b x)^6 (A+B x) (d+e x) \, dx","Integrate[(a + b*x)^6*(A + B*x)*(d + e*x),x]","\frac{1}{504} x \left(84 a^6 (3 A (2 d+e x)+B x (3 d+2 e x))+252 a^5 b x (A (6 d+4 e x)+B x (4 d+3 e x))+126 a^4 b^2 x^2 (5 A (4 d+3 e x)+3 B x (5 d+4 e x))+168 a^3 b^3 x^3 (3 A (5 d+4 e x)+2 B x (6 d+5 e x))+36 a^2 b^4 x^4 (7 A (6 d+5 e x)+5 B x (7 d+6 e x))+18 a b^5 x^5 (4 A (7 d+6 e x)+3 B x (8 d+7 e x))+b^6 x^6 (9 A (8 d+7 e x)+7 B x (9 d+8 e x))\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,"(x*(84*a^6*(3*A*(2*d + e*x) + B*x*(3*d + 2*e*x)) + 126*a^4*b^2*x^2*(5*A*(4*d + 3*e*x) + 3*B*x*(5*d + 4*e*x)) + 252*a^5*b*x*(B*x*(4*d + 3*e*x) + A*(6*d + 4*e*x)) + 168*a^3*b^3*x^3*(3*A*(5*d + 4*e*x) + 2*B*x*(6*d + 5*e*x)) + 36*a^2*b^4*x^4*(7*A*(6*d + 5*e*x) + 5*B*x*(7*d + 6*e*x)) + 18*a*b^5*x^5*(4*A*(7*d + 6*e*x) + 3*B*x*(8*d + 7*e*x)) + b^6*x^6*(9*A*(8*d + 7*e*x) + 7*B*x*(9*d + 8*e*x))))/504","B",1
1059,1,122,38,0.0398635,"\int (a+b x)^6 (A+B x) \, dx","Integrate[(a + b*x)^6*(A + B*x),x]","\frac{1}{56} x \left(28 a^6 (2 A+B x)+56 a^5 b x (3 A+2 B x)+70 a^4 b^2 x^2 (4 A+3 B x)+56 a^3 b^3 x^3 (5 A+4 B x)+28 a^2 b^4 x^4 (6 A+5 B x)+8 a b^5 x^5 (7 A+6 B x)+b^6 x^6 (8 A+7 B x)\right)","\frac{(a+b x)^7 (A b-a B)}{7 b^2}+\frac{B (a+b x)^8}{8 b^2}",1,"(x*(28*a^6*(2*A + B*x) + 56*a^5*b*x*(3*A + 2*B*x) + 70*a^4*b^2*x^2*(4*A + 3*B*x) + 56*a^3*b^3*x^3*(5*A + 4*B*x) + 28*a^2*b^4*x^4*(6*A + 5*B*x) + 8*a*b^5*x^5*(7*A + 6*B*x) + b^6*x^6*(8*A + 7*B*x)))/56","B",1
1060,1,501,220,0.2833329,"\int \frac{(a+b x)^6 (A+B x)}{d+e x} \, dx","Integrate[((a + b*x)^6*(A + B*x))/(d + e*x),x]","\frac{e x \left(420 a^6 B e^6+1260 a^5 b e^5 (2 A e-2 B d+B e x)+1050 a^4 b^2 e^4 \left(3 A e (e x-2 d)+B \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)+700 a^3 b^3 e^3 \left(2 A e \left(6 d^2-3 d e x+2 e^2 x^2\right)+B \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)\right)+105 a^2 b^4 e^2 \left(5 A e \left(-12 d^3+6 d^2 e x-4 d e^2 x^2+3 e^3 x^3\right)+B \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)\right)+42 a b^5 e \left(A e \left(60 d^4-30 d^3 e x+20 d^2 e^2 x^2-15 d e^3 x^3+12 e^4 x^4\right)+B \left(-60 d^5+30 d^4 e x-20 d^3 e^2 x^2+15 d^2 e^3 x^3-12 d e^4 x^4+10 e^5 x^5\right)\right)+b^6 \left(7 A e \left(-60 d^5+30 d^4 e x-20 d^3 e^2 x^2+15 d^2 e^3 x^3-12 d e^4 x^4+10 e^5 x^5\right)+B \left(420 d^6-210 d^5 e x+140 d^4 e^2 x^2-105 d^3 e^3 x^3+84 d^2 e^4 x^4-70 d e^5 x^5+60 e^6 x^6\right)\right)\right)-420 (b d-a e)^6 (B d-A e) \log (d+e x)}{420 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,"(e*x*(420*a^6*B*e^6 + 1260*a^5*b*e^5*(-2*B*d + 2*A*e + B*e*x) + 1050*a^4*b^2*e^4*(3*A*e*(-2*d + e*x) + B*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) + 700*a^3*b^3*e^3*(2*A*e*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + B*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3)) + 105*a^2*b^4*e^2*(5*A*e*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3) + B*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4)) + 42*a*b^5*e*(A*e*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4) + B*(-60*d^5 + 30*d^4*e*x - 20*d^3*e^2*x^2 + 15*d^2*e^3*x^3 - 12*d*e^4*x^4 + 10*e^5*x^5)) + b^6*(7*A*e*(-60*d^5 + 30*d^4*e*x - 20*d^3*e^2*x^2 + 15*d^2*e^3*x^3 - 12*d*e^4*x^4 + 10*e^5*x^5) + B*(420*d^6 - 210*d^5*e*x + 140*d^4*e^2*x^2 - 105*d^3*e^3*x^3 + 84*d^2*e^4*x^4 - 70*d*e^5*x^5 + 60*e^6*x^6))) - 420*(b*d - a*e)^6*(B*d - A*e)*Log[d + e*x])/(420*e^8)","B",1
1061,1,643,277,0.286846,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^2} \, dx","Integrate[((a + b*x)^6*(A + B*x))/(d + e*x)^2,x]","\frac{60 a^6 e^6 (B d-A e)+360 a^5 b e^5 \left(A d e+B \left(-d^2+d e x+e^2 x^2\right)\right)+450 a^4 b^2 e^4 \left(2 A e \left(-d^2+d e x+e^2 x^2\right)+B \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)\right)+200 a^3 b^3 e^3 \left(3 A e \left(2 d^3-4 d^2 e x-3 d e^2 x^2+e^3 x^3\right)+2 B \left(-3 d^4+9 d^3 e x+6 d^2 e^2 x^2-2 d e^3 x^3+e^4 x^4\right)\right)+75 a^2 b^4 e^2 \left(4 A e \left(-3 d^4+9 d^3 e x+6 d^2 e^2 x^2-2 d e^3 x^3+e^4 x^4\right)+B \left(12 d^5-48 d^4 e x-30 d^3 e^2 x^2+10 d^2 e^3 x^3-5 d e^4 x^4+3 e^5 x^5\right)\right)+6 a b^5 e \left(5 A e \left(12 d^5-48 d^4 e x-30 d^3 e^2 x^2+10 d^2 e^3 x^3-5 d e^4 x^4+3 e^5 x^5\right)-6 B \left(10 d^6-50 d^5 e x-30 d^4 e^2 x^2+10 d^3 e^3 x^3-5 d^2 e^4 x^4+3 d e^5 x^5-2 e^6 x^6\right)\right)+60 (d+e x) (b d-a e)^5 \log (d+e x) (-a B e-6 A b e+7 b B d)+b^6 \left(6 A e \left(-10 d^6+50 d^5 e x+30 d^4 e^2 x^2-10 d^3 e^3 x^3+5 d^2 e^4 x^4-3 d e^5 x^5+2 e^6 x^6\right)+B \left(60 d^7-360 d^6 e x-210 d^5 e^2 x^2+70 d^4 e^3 x^3-35 d^3 e^4 x^4+21 d^2 e^5 x^5-14 d e^6 x^6+10 e^7 x^7\right)\right)}{60 e^8 (d+e x)}","-\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*a^6*e^6*(B*d - A*e) + 360*a^5*b*e^5*(A*d*e + B*(-d^2 + d*e*x + e^2*x^2)) + 450*a^4*b^2*e^4*(2*A*e*(-d^2 + d*e*x + e^2*x^2) + B*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3)) + 200*a^3*b^3*e^3*(3*A*e*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3) + 2*B*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4)) + 75*a^2*b^4*e^2*(4*A*e*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4) + B*(12*d^5 - 48*d^4*e*x - 30*d^3*e^2*x^2 + 10*d^2*e^3*x^3 - 5*d*e^4*x^4 + 3*e^5*x^5)) + 6*a*b^5*e*(5*A*e*(12*d^5 - 48*d^4*e*x - 30*d^3*e^2*x^2 + 10*d^2*e^3*x^3 - 5*d*e^4*x^4 + 3*e^5*x^5) - 6*B*(10*d^6 - 50*d^5*e*x - 30*d^4*e^2*x^2 + 10*d^3*e^3*x^3 - 5*d^2*e^4*x^4 + 3*d*e^5*x^5 - 2*e^6*x^6)) + b^6*(6*A*e*(-10*d^6 + 50*d^5*e*x + 30*d^4*e^2*x^2 - 10*d^3*e^3*x^3 + 5*d^2*e^4*x^4 - 3*d*e^5*x^5 + 2*e^6*x^6) + B*(60*d^7 - 360*d^6*e*x - 210*d^5*e^2*x^2 + 70*d^4*e^3*x^3 - 35*d^3*e^4*x^4 + 21*d^2*e^5*x^5 - 14*d*e^6*x^6 + 10*e^7*x^7)) + 60*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x)*Log[d + e*x])/(60*e^8*(d + e*x))","B",1
1062,1,352,276,0.1893261,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^3} \, dx","Integrate[((a + b*x)^6*(A + B*x))/(d + e*x)^3,x]","\frac{-20 b^4 e^3 x^3 \left(-5 a^2 B e^2-2 a b e (A e-3 B d)+b^2 d (A e-2 B d)\right)+10 b^3 e^2 x^2 \left(20 a^3 B e^3+15 a^2 b e^2 (A e-3 B d)+18 a b^2 d e (2 B d-A e)+2 b^3 d^2 (3 A e-5 B d)\right)-20 b^2 e x \left(-15 a^4 B e^4-20 a^3 b e^3 (A e-3 B d)+45 a^2 b^2 d e^2 (A e-2 B d)+12 a b^3 d^2 e (5 B d-3 A e)-5 b^4 d^3 (3 B d-2 A e)\right)+5 b^5 e^4 x^4 (6 a B e+A b e-3 b B d)-\frac{20 (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{d+e x}+\frac{10 (b d-a e)^6 (B d-A e)}{(d+e x)^2}-60 b (b d-a e)^4 \log (d+e x) (-2 a B e-5 A b e+7 b B d)+4 b^6 B e^5 x^5}{20 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,"(-20*b^2*e*(-15*a^4*B*e^4 + 12*a*b^3*d^2*e*(5*B*d - 3*A*e) - 5*b^4*d^3*(3*B*d - 2*A*e) - 20*a^3*b*e^3*(-3*B*d + A*e) + 45*a^2*b^2*d*e^2*(-2*B*d + A*e))*x + 10*b^3*e^2*(20*a^3*B*e^3 + 18*a*b^2*d*e*(2*B*d - A*e) + 15*a^2*b*e^2*(-3*B*d + A*e) + 2*b^3*d^2*(-5*B*d + 3*A*e))*x^2 - 20*b^4*e^3*(-5*a^2*B*e^2 - 2*a*b*e*(-3*B*d + A*e) + b^2*d*(-2*B*d + A*e))*x^3 + 5*b^5*e^4*(-3*b*B*d + A*b*e + 6*a*B*e)*x^4 + 4*b^6*B*e^5*x^5 + (10*(b*d - a*e)^6*(B*d - A*e))/(d + e*x)^2 - (20*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e))/(d + e*x) - 60*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*Log[d + e*x])/(20*e^8)","A",1
1063,1,297,279,0.1851296,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^4} \, dx","Integrate[((a + b*x)^6*(A + B*x))/(d + e*x)^4,x]","\frac{-6 b^4 e^2 x^2 \left(-15 a^2 B e^2-6 a b e (A e-4 B d)+2 b^2 d (2 A e-5 B d)\right)+12 b^3 e x \left(20 a^3 B e^3+15 a^2 b e^2 (A e-4 B d)+12 a b^2 d e (5 B d-2 A e)+10 b^3 d^2 (A e-2 B d)\right)+4 b^5 e^3 x^3 (6 a B e+A b e-4 b B d)+60 b^2 (b d-a e)^3 \log (d+e x) (-3 a B e-4 A b e+7 b B d)+\frac{36 b (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{d+e x}-\frac{6 (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{(d+e x)^2}+\frac{4 (b d-a e)^6 (B d-A e)}{(d+e x)^3}+3 b^6 B e^4 x^4}{12 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,"(12*b^3*e*(20*a^3*B*e^3 + 12*a*b^2*d*e*(5*B*d - 2*A*e) + 15*a^2*b*e^2*(-4*B*d + A*e) + 10*b^3*d^2*(-2*B*d + A*e))*x - 6*b^4*e^2*(-15*a^2*B*e^2 - 6*a*b*e*(-4*B*d + A*e) + 2*b^2*d*(-5*B*d + 2*A*e))*x^2 + 4*b^5*e^3*(-4*b*B*d + A*b*e + 6*a*B*e)*x^3 + 3*b^6*B*e^4*x^4 + (4*(b*d - a*e)^6*(B*d - A*e))/(d + e*x)^3 - (6*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e))/(d + e*x)^2 + (36*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e))/(d + e*x) + 60*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*Log[d + e*x])/(12*e^8)","A",1
1064,1,263,279,0.1955552,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^5} \, dx","Integrate[((a + b*x)^6*(A + B*x))/(d + e*x)^5,x]","\frac{-12 b^4 e x \left(-15 a^2 B e^2-6 a b e (A e-5 B d)+5 b^2 d (A e-3 B d)\right)+6 b^5 e^2 x^2 (6 a B e+A b e-5 b B d)-60 b^3 (b d-a e)^2 \log (d+e x) (-4 a B e-3 A b e+7 b B d)-\frac{60 b^2 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{d+e x}+\frac{18 b (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{(d+e x)^2}-\frac{4 (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{(d+e x)^3}+\frac{3 (b d-a e)^6 (B d-A e)}{(d+e x)^4}+4 b^6 B e^3 x^3}{12 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,"(-12*b^4*e*(-15*a^2*B*e^2 - 6*a*b*e*(-5*B*d + A*e) + 5*b^2*d*(-3*B*d + A*e))*x + 6*b^5*e^2*(-5*b*B*d + A*b*e + 6*a*B*e)*x^2 + 4*b^6*B*e^3*x^3 + (3*(b*d - a*e)^6*(B*d - A*e))/(d + e*x)^4 - (4*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e))/(d + e*x)^3 + (18*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e))/(d + e*x)^2 - (60*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e))/(d + e*x) - 60*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*Log[d + e*x])/(12*e^8)","A",1
1065,1,633,272,0.3315276,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^6} \, dx","Integrate[((a + b*x)^6*(A + B*x))/(d + e*x)^6,x]","\frac{-a^6 e^6 (4 A e+B (d+5 e x))-2 a^5 b e^5 \left(3 A e (d+5 e x)+2 B \left(d^2+5 d e x+10 e^2 x^2\right)\right)-5 a^4 b^2 e^4 \left(2 A e \left(d^2+5 d e x+10 e^2 x^2\right)+3 B \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)\right)-20 a^3 b^3 e^3 \left(A e \left(d^3+5 d^2 e x+10 d e^2 x^2+10 e^3 x^3\right)+4 B \left(d^4+5 d^3 e x+10 d^2 e^2 x^2+10 d e^3 x^3+5 e^4 x^4\right)\right)+5 a^2 b^4 e^2 \left(B d \left(137 d^4+625 d^3 e x+1100 d^2 e^2 x^2+900 d e^3 x^3+300 e^4 x^4\right)-12 A e \left(d^4+5 d^3 e x+10 d^2 e^2 x^2+10 d e^3 x^3+5 e^4 x^4\right)\right)+2 a b^5 e \left(A d e \left(137 d^4+625 d^3 e x+1100 d^2 e^2 x^2+900 d e^3 x^3+300 e^4 x^4\right)-6 B \left(87 d^6+375 d^5 e x+600 d^4 e^2 x^2+400 d^3 e^3 x^3+50 d^2 e^4 x^4-50 d e^5 x^5-10 e^6 x^6\right)\right)+60 b^4 (d+e x)^5 (b d-a e) \log (d+e x) (-5 a B e-2 A b e+7 b B d)+b^6 \left(B \left(459 d^7+1875 d^6 e x+2700 d^5 e^2 x^2+1300 d^4 e^3 x^3-400 d^3 e^4 x^4-500 d^2 e^5 x^5-70 d e^6 x^6+10 e^7 x^7\right)-2 A e \left(87 d^6+375 d^5 e x+600 d^4 e^2 x^2+400 d^3 e^3 x^3+50 d^2 e^4 x^4-50 d e^5 x^5-10 e^6 x^6\right)\right)}{20 e^8 (d+e x)^5}","-\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,"(-(a^6*e^6*(4*A*e + B*(d + 5*e*x))) - 2*a^5*b*e^5*(3*A*e*(d + 5*e*x) + 2*B*(d^2 + 5*d*e*x + 10*e^2*x^2)) - 5*a^4*b^2*e^4*(2*A*e*(d^2 + 5*d*e*x + 10*e^2*x^2) + 3*B*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3)) - 20*a^3*b^3*e^3*(A*e*(d^3 + 5*d^2*e*x + 10*d*e^2*x^2 + 10*e^3*x^3) + 4*B*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4)) + 5*a^2*b^4*e^2*(-12*A*e*(d^4 + 5*d^3*e*x + 10*d^2*e^2*x^2 + 10*d*e^3*x^3 + 5*e^4*x^4) + B*d*(137*d^4 + 625*d^3*e*x + 1100*d^2*e^2*x^2 + 900*d*e^3*x^3 + 300*e^4*x^4)) + 2*a*b^5*e*(A*d*e*(137*d^4 + 625*d^3*e*x + 1100*d^2*e^2*x^2 + 900*d*e^3*x^3 + 300*e^4*x^4) - 6*B*(87*d^6 + 375*d^5*e*x + 600*d^4*e^2*x^2 + 400*d^3*e^3*x^3 + 50*d^2*e^4*x^4 - 50*d*e^5*x^5 - 10*e^6*x^6)) + b^6*(-2*A*e*(87*d^6 + 375*d^5*e*x + 600*d^4*e^2*x^2 + 400*d^3*e^3*x^3 + 50*d^2*e^4*x^4 - 50*d*e^5*x^5 - 10*e^6*x^6) + B*(459*d^7 + 1875*d^6*e*x + 2700*d^5*e^2*x^2 + 1300*d^4*e^3*x^3 - 400*d^3*e^4*x^4 - 500*d^2*e^5*x^5 - 70*d*e^6*x^6 + 10*e^7*x^7)) + 60*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^5*Log[d + e*x])/(20*e^8*(d + e*x)^5)","B",1
1066,1,619,278,0.3516962,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^7} \, dx","Integrate[((a + b*x)^6*(A + B*x))/(d + e*x)^7,x]","-\frac{2 a^6 e^6 (5 A e+B (d+6 e x))+6 a^5 b e^5 \left(2 A e (d+6 e x)+B \left(d^2+6 d e x+15 e^2 x^2\right)\right)+15 a^4 b^2 e^4 \left(A e \left(d^2+6 d e x+15 e^2 x^2\right)+B \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)\right)+20 a^3 b^3 e^3 \left(A e \left(d^3+6 d^2 e x+15 d e^2 x^2+20 e^3 x^3\right)+2 B \left(d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right)\right)+30 a^2 b^4 e^2 \left(A e \left(d^4+6 d^3 e x+15 d^2 e^2 x^2+20 d e^3 x^3+15 e^4 x^4\right)+5 B \left(d^5+6 d^4 e x+15 d^3 e^2 x^2+20 d^2 e^3 x^3+15 d e^4 x^4+6 e^5 x^5\right)\right)-6 a b^5 e \left(B d \left(147 d^5+822 d^4 e x+1875 d^3 e^2 x^2+2200 d^2 e^3 x^3+1350 d e^4 x^4+360 e^5 x^5\right)-10 A e \left(d^5+6 d^4 e x+15 d^3 e^2 x^2+20 d^2 e^3 x^3+15 d e^4 x^4+6 e^5 x^5\right)\right)+60 b^5 (d+e x)^6 \log (d+e x) (-6 a B e-A b e+7 b B d)-\left(b^6 \left(A d e \left(147 d^5+822 d^4 e x+1875 d^3 e^2 x^2+2200 d^2 e^3 x^3+1350 d e^4 x^4+360 e^5 x^5\right)-B \left(669 d^7+3594 d^6 e x+7725 d^5 e^2 x^2+8200 d^4 e^3 x^3+4050 d^3 e^4 x^4+360 d^2 e^5 x^5-360 d e^6 x^6-60 e^7 x^7\right)\right)\right)}{60 e^8 (d+e x)^6}","-\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,"-1/60*(2*a^6*e^6*(5*A*e + B*(d + 6*e*x)) + 6*a^5*b*e^5*(2*A*e*(d + 6*e*x) + B*(d^2 + 6*d*e*x + 15*e^2*x^2)) + 15*a^4*b^2*e^4*(A*e*(d^2 + 6*d*e*x + 15*e^2*x^2) + B*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3)) + 20*a^3*b^3*e^3*(A*e*(d^3 + 6*d^2*e*x + 15*d*e^2*x^2 + 20*e^3*x^3) + 2*B*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4)) + 30*a^2*b^4*e^2*(A*e*(d^4 + 6*d^3*e*x + 15*d^2*e^2*x^2 + 20*d*e^3*x^3 + 15*e^4*x^4) + 5*B*(d^5 + 6*d^4*e*x + 15*d^3*e^2*x^2 + 20*d^2*e^3*x^3 + 15*d*e^4*x^4 + 6*e^5*x^5)) - 6*a*b^5*e*(-10*A*e*(d^5 + 6*d^4*e*x + 15*d^3*e^2*x^2 + 20*d^2*e^3*x^3 + 15*d*e^4*x^4 + 6*e^5*x^5) + B*d*(147*d^5 + 822*d^4*e*x + 1875*d^3*e^2*x^2 + 2200*d^2*e^3*x^3 + 1350*d*e^4*x^4 + 360*e^5*x^5)) - b^6*(A*d*e*(147*d^5 + 822*d^4*e*x + 1875*d^3*e^2*x^2 + 2200*d^2*e^3*x^3 + 1350*d*e^4*x^4 + 360*e^5*x^5) - B*(669*d^7 + 3594*d^6*e*x + 7725*d^5*e^2*x^2 + 8200*d^4*e^3*x^3 + 4050*d^3*e^4*x^4 + 360*d^2*e^5*x^5 - 360*d*e^6*x^6 - 60*e^7*x^7)) + 60*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^6*Log[d + e*x])/(e^8*(d + e*x)^6)","B",1
1067,1,615,213,0.479487,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^8} \, dx","Integrate[((a + b*x)^6*(A + B*x))/(d + e*x)^8,x]","-\frac{10 a^6 e^6 (6 A e+B (d+7 e x))+12 a^5 b e^5 \left(5 A e (d+7 e x)+2 B \left(d^2+7 d e x+21 e^2 x^2\right)\right)+15 a^4 b^2 e^4 \left(4 A e \left(d^2+7 d e x+21 e^2 x^2\right)+3 B \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)\right)+20 a^3 b^3 e^3 \left(3 A e \left(d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right)+4 B \left(d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right)\right)+30 a^2 b^4 e^2 \left(2 A e \left(d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right)+5 B \left(d^5+7 d^4 e x+21 d^3 e^2 x^2+35 d^2 e^3 x^3+35 d e^4 x^4+21 e^5 x^5\right)\right)+60 a b^5 e \left(A e \left(d^5+7 d^4 e x+21 d^3 e^2 x^2+35 d^2 e^3 x^3+35 d e^4 x^4+21 e^5 x^5\right)+6 B \left(d^6+7 d^5 e x+21 d^4 e^2 x^2+35 d^3 e^3 x^3+35 d^2 e^4 x^4+21 d e^5 x^5+7 e^6 x^6\right)\right)+b^6 \left(60 A e \left(d^6+7 d^5 e x+21 d^4 e^2 x^2+35 d^3 e^3 x^3+35 d^2 e^4 x^4+21 d e^5 x^5+7 e^6 x^6\right)-B d \left(1089 d^6+7203 d^5 e x+20139 d^4 e^2 x^2+30625 d^3 e^3 x^3+26950 d^2 e^4 x^4+13230 d e^5 x^5+2940 e^6 x^6\right)\right)-420 b^6 B (d+e x)^7 \log (d+e 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,"-1/420*(10*a^6*e^6*(6*A*e + B*(d + 7*e*x)) + 12*a^5*b*e^5*(5*A*e*(d + 7*e*x) + 2*B*(d^2 + 7*d*e*x + 21*e^2*x^2)) + 15*a^4*b^2*e^4*(4*A*e*(d^2 + 7*d*e*x + 21*e^2*x^2) + 3*B*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3)) + 20*a^3*b^3*e^3*(3*A*e*(d^3 + 7*d^2*e*x + 21*d*e^2*x^2 + 35*e^3*x^3) + 4*B*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4)) + 30*a^2*b^4*e^2*(2*A*e*(d^4 + 7*d^3*e*x + 21*d^2*e^2*x^2 + 35*d*e^3*x^3 + 35*e^4*x^4) + 5*B*(d^5 + 7*d^4*e*x + 21*d^3*e^2*x^2 + 35*d^2*e^3*x^3 + 35*d*e^4*x^4 + 21*e^5*x^5)) + 60*a*b^5*e*(A*e*(d^5 + 7*d^4*e*x + 21*d^3*e^2*x^2 + 35*d^2*e^3*x^3 + 35*d*e^4*x^4 + 21*e^5*x^5) + 6*B*(d^6 + 7*d^5*e*x + 21*d^4*e^2*x^2 + 35*d^3*e^3*x^3 + 35*d^2*e^4*x^4 + 21*d*e^5*x^5 + 7*e^6*x^6)) + b^6*(60*A*e*(d^6 + 7*d^5*e*x + 21*d^4*e^2*x^2 + 35*d^3*e^3*x^3 + 35*d^2*e^4*x^4 + 21*d*e^5*x^5 + 7*e^6*x^6) - B*d*(1089*d^6 + 7203*d^5*e*x + 20139*d^4*e^2*x^2 + 30625*d^3*e^3*x^3 + 26950*d^2*e^4*x^4 + 13230*d*e^5*x^5 + 2940*e^6*x^6)) - 420*b^6*B*(d + e*x)^7*Log[d + e*x])/(e^8*(d + e*x)^7)","B",1
1068,1,597,86,0.2891315,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^9} \, dx","Integrate[((a + b*x)^6*(A + B*x))/(d + e*x)^9,x]","-\frac{a^6 e^6 (7 A e+B (d+8 e x))+2 a^5 b e^5 \left(3 A e (d+8 e x)+B \left(d^2+8 d e x+28 e^2 x^2\right)\right)+a^4 b^2 e^4 \left(5 A e \left(d^2+8 d e x+28 e^2 x^2\right)+3 B \left(d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right)\right)+4 a^3 b^3 e^3 \left(A e \left(d^3+8 d^2 e x+28 d e^2 x^2+56 e^3 x^3\right)+B \left(d^4+8 d^3 e x+28 d^2 e^2 x^2+56 d e^3 x^3+70 e^4 x^4\right)\right)+a^2 b^4 e^2 \left(3 A e \left(d^4+8 d^3 e x+28 d^2 e^2 x^2+56 d e^3 x^3+70 e^4 x^4\right)+5 B \left(d^5+8 d^4 e x+28 d^3 e^2 x^2+56 d^2 e^3 x^3+70 d e^4 x^4+56 e^5 x^5\right)\right)+2 a b^5 e \left(A e \left(d^5+8 d^4 e x+28 d^3 e^2 x^2+56 d^2 e^3 x^3+70 d e^4 x^4+56 e^5 x^5\right)+3 B \left(d^6+8 d^5 e x+28 d^4 e^2 x^2+56 d^3 e^3 x^3+70 d^2 e^4 x^4+56 d e^5 x^5+28 e^6 x^6\right)\right)+b^6 \left(A e \left(d^6+8 d^5 e x+28 d^4 e^2 x^2+56 d^3 e^3 x^3+70 d^2 e^4 x^4+56 d e^5 x^5+28 e^6 x^6\right)+7 B \left(d^7+8 d^6 e x+28 d^5 e^2 x^2+56 d^4 e^3 x^3+70 d^3 e^4 x^4+56 d^2 e^5 x^5+28 d e^6 x^6+8 e^7 x^7\right)\right)}{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,"-1/56*(a^6*e^6*(7*A*e + B*(d + 8*e*x)) + 2*a^5*b*e^5*(3*A*e*(d + 8*e*x) + B*(d^2 + 8*d*e*x + 28*e^2*x^2)) + a^4*b^2*e^4*(5*A*e*(d^2 + 8*d*e*x + 28*e^2*x^2) + 3*B*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3)) + 4*a^3*b^3*e^3*(A*e*(d^3 + 8*d^2*e*x + 28*d*e^2*x^2 + 56*e^3*x^3) + B*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4)) + a^2*b^4*e^2*(3*A*e*(d^4 + 8*d^3*e*x + 28*d^2*e^2*x^2 + 56*d*e^3*x^3 + 70*e^4*x^4) + 5*B*(d^5 + 8*d^4*e*x + 28*d^3*e^2*x^2 + 56*d^2*e^3*x^3 + 70*d*e^4*x^4 + 56*e^5*x^5)) + 2*a*b^5*e*(A*e*(d^5 + 8*d^4*e*x + 28*d^3*e^2*x^2 + 56*d^2*e^3*x^3 + 70*d*e^4*x^4 + 56*e^5*x^5) + 3*B*(d^6 + 8*d^5*e*x + 28*d^4*e^2*x^2 + 56*d^3*e^3*x^3 + 70*d^2*e^4*x^4 + 56*d*e^5*x^5 + 28*e^6*x^6)) + b^6*(A*e*(d^6 + 8*d^5*e*x + 28*d^4*e^2*x^2 + 56*d^3*e^3*x^3 + 70*d^2*e^4*x^4 + 56*d*e^5*x^5 + 28*e^6*x^6) + 7*B*(d^7 + 8*d^6*e*x + 28*d^5*e^2*x^2 + 56*d^4*e^3*x^3 + 70*d^3*e^4*x^4 + 56*d^2*e^5*x^5 + 28*d*e^6*x^6 + 8*e^7*x^7)))/(e^8*(d + e*x)^8)","B",1
1069,1,603,135,0.2812458,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^{10}} \, dx","Integrate[((a + b*x)^6*(A + B*x))/(d + e*x)^10,x]","-\frac{7 a^6 e^6 (8 A e+B (d+9 e x))+6 a^5 b e^5 \left(7 A e (d+9 e x)+2 B \left(d^2+9 d e x+36 e^2 x^2\right)\right)+15 a^4 b^2 e^4 \left(2 A e \left(d^2+9 d e x+36 e^2 x^2\right)+B \left(d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right)\right)+4 a^3 b^3 e^3 \left(5 A e \left(d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right)+4 B \left(d^4+9 d^3 e x+36 d^2 e^2 x^2+84 d e^3 x^3+126 e^4 x^4\right)\right)+3 a^2 b^4 e^2 \left(4 A e \left(d^4+9 d^3 e x+36 d^2 e^2 x^2+84 d e^3 x^3+126 e^4 x^4\right)+5 B \left(d^5+9 d^4 e x+36 d^3 e^2 x^2+84 d^2 e^3 x^3+126 d e^4 x^4+126 e^5 x^5\right)\right)+6 a b^5 e \left(A e \left(d^5+9 d^4 e x+36 d^3 e^2 x^2+84 d^2 e^3 x^3+126 d e^4 x^4+126 e^5 x^5\right)+2 B \left(d^6+9 d^5 e x+36 d^4 e^2 x^2+84 d^3 e^3 x^3+126 d^2 e^4 x^4+126 d e^5 x^5+84 e^6 x^6\right)\right)+b^6 \left(2 A e \left(d^6+9 d^5 e x+36 d^4 e^2 x^2+84 d^3 e^3 x^3+126 d^2 e^4 x^4+126 d e^5 x^5+84 e^6 x^6\right)+7 B \left(d^7+9 d^6 e x+36 d^5 e^2 x^2+84 d^4 e^3 x^3+126 d^3 e^4 x^4+126 d^2 e^5 x^5+84 d e^6 x^6+36 e^7 x^7\right)\right)}{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,"-1/504*(7*a^6*e^6*(8*A*e + B*(d + 9*e*x)) + 6*a^5*b*e^5*(7*A*e*(d + 9*e*x) + 2*B*(d^2 + 9*d*e*x + 36*e^2*x^2)) + 15*a^4*b^2*e^4*(2*A*e*(d^2 + 9*d*e*x + 36*e^2*x^2) + B*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3)) + 4*a^3*b^3*e^3*(5*A*e*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3) + 4*B*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4)) + 3*a^2*b^4*e^2*(4*A*e*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4) + 5*B*(d^5 + 9*d^4*e*x + 36*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 126*d*e^4*x^4 + 126*e^5*x^5)) + 6*a*b^5*e*(A*e*(d^5 + 9*d^4*e*x + 36*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 126*d*e^4*x^4 + 126*e^5*x^5) + 2*B*(d^6 + 9*d^5*e*x + 36*d^4*e^2*x^2 + 84*d^3*e^3*x^3 + 126*d^2*e^4*x^4 + 126*d*e^5*x^5 + 84*e^6*x^6)) + b^6*(2*A*e*(d^6 + 9*d^5*e*x + 36*d^4*e^2*x^2 + 84*d^3*e^3*x^3 + 126*d^2*e^4*x^4 + 126*d*e^5*x^5 + 84*e^6*x^6) + 7*B*(d^7 + 9*d^6*e*x + 36*d^5*e^2*x^2 + 84*d^4*e^3*x^3 + 126*d^3*e^4*x^4 + 126*d^2*e^5*x^5 + 84*d*e^6*x^6 + 36*e^7*x^7)))/(e^8*(d + e*x)^9)","B",1
1070,1,602,185,0.2742004,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^{11}} \, dx","Integrate[((a + b*x)^6*(A + B*x))/(d + e*x)^11,x]","-\frac{28 a^6 e^6 (9 A e+B (d+10 e x))+42 a^5 b e^5 \left(4 A e (d+10 e x)+B \left(d^2+10 d e x+45 e^2 x^2\right)\right)+15 a^4 b^2 e^4 \left(7 A e \left(d^2+10 d e x+45 e^2 x^2\right)+3 B \left(d^3+10 d^2 e x+45 d e^2 x^2+120 e^3 x^3\right)\right)+20 a^3 b^3 e^3 \left(3 A e \left(d^3+10 d^2 e x+45 d e^2 x^2+120 e^3 x^3\right)+2 B \left(d^4+10 d^3 e x+45 d^2 e^2 x^2+120 d e^3 x^3+210 e^4 x^4\right)\right)+30 a^2 b^4 e^2 \left(A e \left(d^4+10 d^3 e x+45 d^2 e^2 x^2+120 d e^3 x^3+210 e^4 x^4\right)+B \left(d^5+10 d^4 e x+45 d^3 e^2 x^2+120 d^2 e^3 x^3+210 d e^4 x^4+252 e^5 x^5\right)\right)+6 a b^5 e \left(2 A e \left(d^5+10 d^4 e x+45 d^3 e^2 x^2+120 d^2 e^3 x^3+210 d e^4 x^4+252 e^5 x^5\right)+3 B \left(d^6+10 d^5 e x+45 d^4 e^2 x^2+120 d^3 e^3 x^3+210 d^2 e^4 x^4+252 d e^5 x^5+210 e^6 x^6\right)\right)+b^6 \left(3 A e \left(d^6+10 d^5 e x+45 d^4 e^2 x^2+120 d^3 e^3 x^3+210 d^2 e^4 x^4+252 d e^5 x^5+210 e^6 x^6\right)+7 B \left(d^7+10 d^6 e x+45 d^5 e^2 x^2+120 d^4 e^3 x^3+210 d^3 e^4 x^4+252 d^2 e^5 x^5+210 d e^6 x^6+120 e^7 x^7\right)\right)}{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,"-1/2520*(28*a^6*e^6*(9*A*e + B*(d + 10*e*x)) + 42*a^5*b*e^5*(4*A*e*(d + 10*e*x) + B*(d^2 + 10*d*e*x + 45*e^2*x^2)) + 15*a^4*b^2*e^4*(7*A*e*(d^2 + 10*d*e*x + 45*e^2*x^2) + 3*B*(d^3 + 10*d^2*e*x + 45*d*e^2*x^2 + 120*e^3*x^3)) + 20*a^3*b^3*e^3*(3*A*e*(d^3 + 10*d^2*e*x + 45*d*e^2*x^2 + 120*e^3*x^3) + 2*B*(d^4 + 10*d^3*e*x + 45*d^2*e^2*x^2 + 120*d*e^3*x^3 + 210*e^4*x^4)) + 30*a^2*b^4*e^2*(A*e*(d^4 + 10*d^3*e*x + 45*d^2*e^2*x^2 + 120*d*e^3*x^3 + 210*e^4*x^4) + B*(d^5 + 10*d^4*e*x + 45*d^3*e^2*x^2 + 120*d^2*e^3*x^3 + 210*d*e^4*x^4 + 252*e^5*x^5)) + 6*a*b^5*e*(2*A*e*(d^5 + 10*d^4*e*x + 45*d^3*e^2*x^2 + 120*d^2*e^3*x^3 + 210*d*e^4*x^4 + 252*e^5*x^5) + 3*B*(d^6 + 10*d^5*e*x + 45*d^4*e^2*x^2 + 120*d^3*e^3*x^3 + 210*d^2*e^4*x^4 + 252*d*e^5*x^5 + 210*e^6*x^6)) + b^6*(3*A*e*(d^6 + 10*d^5*e*x + 45*d^4*e^2*x^2 + 120*d^3*e^3*x^3 + 210*d^2*e^4*x^4 + 252*d*e^5*x^5 + 210*e^6*x^6) + 7*B*(d^7 + 10*d^6*e*x + 45*d^5*e^2*x^2 + 120*d^4*e^3*x^3 + 210*d^3*e^4*x^4 + 252*d^2*e^5*x^5 + 210*d*e^6*x^6 + 120*e^7*x^7)))/(e^8*(d + e*x)^10)","B",1
1071,1,605,235,0.2775474,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^{12}} \, dx","Integrate[((a + b*x)^6*(A + B*x))/(d + e*x)^12,x]","-\frac{84 a^6 e^6 (10 A e+B (d+11 e x))+56 a^5 b e^5 \left(9 A e (d+11 e x)+2 B \left(d^2+11 d e x+55 e^2 x^2\right)\right)+35 a^4 b^2 e^4 \left(8 A e \left(d^2+11 d e x+55 e^2 x^2\right)+3 B \left(d^3+11 d^2 e x+55 d e^2 x^2+165 e^3 x^3\right)\right)+20 a^3 b^3 e^3 \left(7 A e \left(d^3+11 d^2 e x+55 d e^2 x^2+165 e^3 x^3\right)+4 B \left(d^4+11 d^3 e x+55 d^2 e^2 x^2+165 d e^3 x^3+330 e^4 x^4\right)\right)+10 a^2 b^4 e^2 \left(6 A e \left(d^4+11 d^3 e x+55 d^2 e^2 x^2+165 d e^3 x^3+330 e^4 x^4\right)+5 B \left(d^5+11 d^4 e x+55 d^3 e^2 x^2+165 d^2 e^3 x^3+330 d e^4 x^4+462 e^5 x^5\right)\right)+4 a b^5 e \left(5 A e \left(d^5+11 d^4 e x+55 d^3 e^2 x^2+165 d^2 e^3 x^3+330 d e^4 x^4+462 e^5 x^5\right)+6 B \left(d^6+11 d^5 e x+55 d^4 e^2 x^2+165 d^3 e^3 x^3+330 d^2 e^4 x^4+462 d e^5 x^5+462 e^6 x^6\right)\right)+b^6 \left(4 A e \left(d^6+11 d^5 e x+55 d^4 e^2 x^2+165 d^3 e^3 x^3+330 d^2 e^4 x^4+462 d e^5 x^5+462 e^6 x^6\right)+7 B \left(d^7+11 d^6 e x+55 d^5 e^2 x^2+165 d^4 e^3 x^3+330 d^3 e^4 x^4+462 d^2 e^5 x^5+462 d e^6 x^6+330 e^7 x^7\right)\right)}{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,"-1/9240*(84*a^6*e^6*(10*A*e + B*(d + 11*e*x)) + 56*a^5*b*e^5*(9*A*e*(d + 11*e*x) + 2*B*(d^2 + 11*d*e*x + 55*e^2*x^2)) + 35*a^4*b^2*e^4*(8*A*e*(d^2 + 11*d*e*x + 55*e^2*x^2) + 3*B*(d^3 + 11*d^2*e*x + 55*d*e^2*x^2 + 165*e^3*x^3)) + 20*a^3*b^3*e^3*(7*A*e*(d^3 + 11*d^2*e*x + 55*d*e^2*x^2 + 165*e^3*x^3) + 4*B*(d^4 + 11*d^3*e*x + 55*d^2*e^2*x^2 + 165*d*e^3*x^3 + 330*e^4*x^4)) + 10*a^2*b^4*e^2*(6*A*e*(d^4 + 11*d^3*e*x + 55*d^2*e^2*x^2 + 165*d*e^3*x^3 + 330*e^4*x^4) + 5*B*(d^5 + 11*d^4*e*x + 55*d^3*e^2*x^2 + 165*d^2*e^3*x^3 + 330*d*e^4*x^4 + 462*e^5*x^5)) + 4*a*b^5*e*(5*A*e*(d^5 + 11*d^4*e*x + 55*d^3*e^2*x^2 + 165*d^2*e^3*x^3 + 330*d*e^4*x^4 + 462*e^5*x^5) + 6*B*(d^6 + 11*d^5*e*x + 55*d^4*e^2*x^2 + 165*d^3*e^3*x^3 + 330*d^2*e^4*x^4 + 462*d*e^5*x^5 + 462*e^6*x^6)) + b^6*(4*A*e*(d^6 + 11*d^5*e*x + 55*d^4*e^2*x^2 + 165*d^3*e^3*x^3 + 330*d^2*e^4*x^4 + 462*d*e^5*x^5 + 462*e^6*x^6) + 7*B*(d^7 + 11*d^6*e*x + 55*d^5*e^2*x^2 + 165*d^4*e^3*x^3 + 330*d^3*e^4*x^4 + 462*d^2*e^5*x^5 + 462*d*e^6*x^6 + 330*e^7*x^7)))/(e^8*(d + e*x)^11)","B",1
1072,1,600,292,0.2829097,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^{13}} \, dx","Integrate[((a + b*x)^6*(A + B*x))/(d + e*x)^13,x]","-\frac{210 a^6 e^6 (11 A e+B (d+12 e x))+252 a^5 b e^5 \left(5 A e (d+12 e x)+B \left(d^2+12 d e x+66 e^2 x^2\right)\right)+210 a^4 b^2 e^4 \left(3 A e \left(d^2+12 d e x+66 e^2 x^2\right)+B \left(d^3+12 d^2 e x+66 d e^2 x^2+220 e^3 x^3\right)\right)+140 a^3 b^3 e^3 \left(2 A e \left(d^3+12 d^2 e x+66 d e^2 x^2+220 e^3 x^3\right)+B \left(d^4+12 d^3 e x+66 d^2 e^2 x^2+220 d e^3 x^3+495 e^4 x^4\right)\right)+15 a^2 b^4 e^2 \left(7 A e \left(d^4+12 d^3 e x+66 d^2 e^2 x^2+220 d e^3 x^3+495 e^4 x^4\right)+5 B \left(d^5+12 d^4 e x+66 d^3 e^2 x^2+220 d^2 e^3 x^3+495 d e^4 x^4+792 e^5 x^5\right)\right)+30 a b^5 e \left(A e \left(d^5+12 d^4 e x+66 d^3 e^2 x^2+220 d^2 e^3 x^3+495 d e^4 x^4+792 e^5 x^5\right)+B \left(d^6+12 d^5 e x+66 d^4 e^2 x^2+220 d^3 e^3 x^3+495 d^2 e^4 x^4+792 d e^5 x^5+924 e^6 x^6\right)\right)+b^6 \left(5 A e \left(d^6+12 d^5 e x+66 d^4 e^2 x^2+220 d^3 e^3 x^3+495 d^2 e^4 x^4+792 d e^5 x^5+924 e^6 x^6\right)+7 B \left(d^7+12 d^6 e x+66 d^5 e^2 x^2+220 d^4 e^3 x^3+495 d^3 e^4 x^4+792 d^2 e^5 x^5+924 d e^6 x^6+792 e^7 x^7\right)\right)}{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,"-1/27720*(210*a^6*e^6*(11*A*e + B*(d + 12*e*x)) + 252*a^5*b*e^5*(5*A*e*(d + 12*e*x) + B*(d^2 + 12*d*e*x + 66*e^2*x^2)) + 210*a^4*b^2*e^4*(3*A*e*(d^2 + 12*d*e*x + 66*e^2*x^2) + B*(d^3 + 12*d^2*e*x + 66*d*e^2*x^2 + 220*e^3*x^3)) + 140*a^3*b^3*e^3*(2*A*e*(d^3 + 12*d^2*e*x + 66*d*e^2*x^2 + 220*e^3*x^3) + B*(d^4 + 12*d^3*e*x + 66*d^2*e^2*x^2 + 220*d*e^3*x^3 + 495*e^4*x^4)) + 15*a^2*b^4*e^2*(7*A*e*(d^4 + 12*d^3*e*x + 66*d^2*e^2*x^2 + 220*d*e^3*x^3 + 495*e^4*x^4) + 5*B*(d^5 + 12*d^4*e*x + 66*d^3*e^2*x^2 + 220*d^2*e^3*x^3 + 495*d*e^4*x^4 + 792*e^5*x^5)) + 30*a*b^5*e*(A*e*(d^5 + 12*d^4*e*x + 66*d^3*e^2*x^2 + 220*d^2*e^3*x^3 + 495*d*e^4*x^4 + 792*e^5*x^5) + B*(d^6 + 12*d^5*e*x + 66*d^4*e^2*x^2 + 220*d^3*e^3*x^3 + 495*d^2*e^4*x^4 + 792*d*e^5*x^5 + 924*e^6*x^6)) + b^6*(5*A*e*(d^6 + 12*d^5*e*x + 66*d^4*e^2*x^2 + 220*d^3*e^3*x^3 + 495*d^2*e^4*x^4 + 792*d*e^5*x^5 + 924*e^6*x^6) + 7*B*(d^7 + 12*d^6*e*x + 66*d^5*e^2*x^2 + 220*d^4*e^3*x^3 + 495*d^3*e^4*x^4 + 792*d^2*e^5*x^5 + 924*d*e^6*x^6 + 792*e^7*x^7)))/(e^8*(d + e*x)^12)","B",1
1073,1,605,292,0.2897533,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^{14}} \, dx","Integrate[((a + b*x)^6*(A + B*x))/(d + e*x)^14,x]","-\frac{462 a^6 e^6 (12 A e+B (d+13 e x))+252 a^5 b e^5 \left(11 A e (d+13 e x)+2 B \left(d^2+13 d e x+78 e^2 x^2\right)\right)+126 a^4 b^2 e^4 \left(10 A e \left(d^2+13 d e x+78 e^2 x^2\right)+3 B \left(d^3+13 d^2 e x+78 d e^2 x^2+286 e^3 x^3\right)\right)+56 a^3 b^3 e^3 \left(9 A e \left(d^3+13 d^2 e x+78 d e^2 x^2+286 e^3 x^3\right)+4 B \left(d^4+13 d^3 e x+78 d^2 e^2 x^2+286 d e^3 x^3+715 e^4 x^4\right)\right)+21 a^2 b^4 e^2 \left(8 A e \left(d^4+13 d^3 e x+78 d^2 e^2 x^2+286 d e^3 x^3+715 e^4 x^4\right)+5 B \left(d^5+13 d^4 e x+78 d^3 e^2 x^2+286 d^2 e^3 x^3+715 d e^4 x^4+1287 e^5 x^5\right)\right)+6 a b^5 e \left(7 A e \left(d^5+13 d^4 e x+78 d^3 e^2 x^2+286 d^2 e^3 x^3+715 d e^4 x^4+1287 e^5 x^5\right)+6 B \left(d^6+13 d^5 e x+78 d^4 e^2 x^2+286 d^3 e^3 x^3+715 d^2 e^4 x^4+1287 d e^5 x^5+1716 e^6 x^6\right)\right)+b^6 \left(6 A e \left(d^6+13 d^5 e x+78 d^4 e^2 x^2+286 d^3 e^3 x^3+715 d^2 e^4 x^4+1287 d e^5 x^5+1716 e^6 x^6\right)+7 B \left(d^7+13 d^6 e x+78 d^5 e^2 x^2+286 d^4 e^3 x^3+715 d^3 e^4 x^4+1287 d^2 e^5 x^5+1716 d e^6 x^6+1716 e^7 x^7\right)\right)}{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,"-1/72072*(462*a^6*e^6*(12*A*e + B*(d + 13*e*x)) + 252*a^5*b*e^5*(11*A*e*(d + 13*e*x) + 2*B*(d^2 + 13*d*e*x + 78*e^2*x^2)) + 126*a^4*b^2*e^4*(10*A*e*(d^2 + 13*d*e*x + 78*e^2*x^2) + 3*B*(d^3 + 13*d^2*e*x + 78*d*e^2*x^2 + 286*e^3*x^3)) + 56*a^3*b^3*e^3*(9*A*e*(d^3 + 13*d^2*e*x + 78*d*e^2*x^2 + 286*e^3*x^3) + 4*B*(d^4 + 13*d^3*e*x + 78*d^2*e^2*x^2 + 286*d*e^3*x^3 + 715*e^4*x^4)) + 21*a^2*b^4*e^2*(8*A*e*(d^4 + 13*d^3*e*x + 78*d^2*e^2*x^2 + 286*d*e^3*x^3 + 715*e^4*x^4) + 5*B*(d^5 + 13*d^4*e*x + 78*d^3*e^2*x^2 + 286*d^2*e^3*x^3 + 715*d*e^4*x^4 + 1287*e^5*x^5)) + 6*a*b^5*e*(7*A*e*(d^5 + 13*d^4*e*x + 78*d^3*e^2*x^2 + 286*d^2*e^3*x^3 + 715*d*e^4*x^4 + 1287*e^5*x^5) + 6*B*(d^6 + 13*d^5*e*x + 78*d^4*e^2*x^2 + 286*d^3*e^3*x^3 + 715*d^2*e^4*x^4 + 1287*d*e^5*x^5 + 1716*e^6*x^6)) + b^6*(6*A*e*(d^6 + 13*d^5*e*x + 78*d^4*e^2*x^2 + 286*d^3*e^3*x^3 + 715*d^2*e^4*x^4 + 1287*d*e^5*x^5 + 1716*e^6*x^6) + 7*B*(d^7 + 13*d^6*e*x + 78*d^5*e^2*x^2 + 286*d^4*e^3*x^3 + 715*d^3*e^4*x^4 + 1287*d^2*e^5*x^5 + 1716*d*e^6*x^6 + 1716*e^7*x^7)))/(e^8*(d + e*x)^13)","B",1
1074,1,602,292,0.2927384,"\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^{15}} \, dx","Integrate[((a + b*x)^6*(A + B*x))/(d + e*x)^15,x]","-\frac{132 a^6 e^6 (13 A e+B (d+14 e x))+132 a^5 b e^5 \left(6 A e (d+14 e x)+B \left(d^2+14 d e x+91 e^2 x^2\right)\right)+30 a^4 b^2 e^4 \left(11 A e \left(d^2+14 d e x+91 e^2 x^2\right)+3 B \left(d^3+14 d^2 e x+91 d e^2 x^2+364 e^3 x^3\right)\right)+24 a^3 b^3 e^3 \left(5 A e \left(d^3+14 d^2 e x+91 d e^2 x^2+364 e^3 x^3\right)+2 B \left(d^4+14 d^3 e x+91 d^2 e^2 x^2+364 d e^3 x^3+1001 e^4 x^4\right)\right)+4 a^2 b^4 e^2 \left(9 A e \left(d^4+14 d^3 e x+91 d^2 e^2 x^2+364 d e^3 x^3+1001 e^4 x^4\right)+5 B \left(d^5+14 d^4 e x+91 d^3 e^2 x^2+364 d^2 e^3 x^3+1001 d e^4 x^4+2002 e^5 x^5\right)\right)+2 a b^5 e \left(4 A e \left(d^5+14 d^4 e x+91 d^3 e^2 x^2+364 d^2 e^3 x^3+1001 d e^4 x^4+2002 e^5 x^5\right)+3 B \left(d^6+14 d^5 e x+91 d^4 e^2 x^2+364 d^3 e^3 x^3+1001 d^2 e^4 x^4+2002 d e^5 x^5+3003 e^6 x^6\right)\right)+b^6 \left(A e \left(d^6+14 d^5 e x+91 d^4 e^2 x^2+364 d^3 e^3 x^3+1001 d^2 e^4 x^4+2002 d e^5 x^5+3003 e^6 x^6\right)+B \left(d^7+14 d^6 e x+91 d^5 e^2 x^2+364 d^4 e^3 x^3+1001 d^3 e^4 x^4+2002 d^2 e^5 x^5+3003 d e^6 x^6+3432 e^7 x^7\right)\right)}{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,"-1/24024*(132*a^6*e^6*(13*A*e + B*(d + 14*e*x)) + 132*a^5*b*e^5*(6*A*e*(d + 14*e*x) + B*(d^2 + 14*d*e*x + 91*e^2*x^2)) + 30*a^4*b^2*e^4*(11*A*e*(d^2 + 14*d*e*x + 91*e^2*x^2) + 3*B*(d^3 + 14*d^2*e*x + 91*d*e^2*x^2 + 364*e^3*x^3)) + 24*a^3*b^3*e^3*(5*A*e*(d^3 + 14*d^2*e*x + 91*d*e^2*x^2 + 364*e^3*x^3) + 2*B*(d^4 + 14*d^3*e*x + 91*d^2*e^2*x^2 + 364*d*e^3*x^3 + 1001*e^4*x^4)) + 4*a^2*b^4*e^2*(9*A*e*(d^4 + 14*d^3*e*x + 91*d^2*e^2*x^2 + 364*d*e^3*x^3 + 1001*e^4*x^4) + 5*B*(d^5 + 14*d^4*e*x + 91*d^3*e^2*x^2 + 364*d^2*e^3*x^3 + 1001*d*e^4*x^4 + 2002*e^5*x^5)) + 2*a*b^5*e*(4*A*e*(d^5 + 14*d^4*e*x + 91*d^3*e^2*x^2 + 364*d^2*e^3*x^3 + 1001*d*e^4*x^4 + 2002*e^5*x^5) + 3*B*(d^6 + 14*d^5*e*x + 91*d^4*e^2*x^2 + 364*d^3*e^3*x^3 + 1001*d^2*e^4*x^4 + 2002*d*e^5*x^5 + 3003*e^6*x^6)) + b^6*(A*e*(d^6 + 14*d^5*e*x + 91*d^4*e^2*x^2 + 364*d^3*e^3*x^3 + 1001*d^2*e^4*x^4 + 2002*d*e^5*x^5 + 3003*e^6*x^6) + B*(d^7 + 14*d^6*e*x + 91*d^5*e^2*x^2 + 364*d^4*e^3*x^3 + 1001*d^3*e^4*x^4 + 2002*d^2*e^5*x^5 + 3003*d*e^6*x^6 + 3432*e^7*x^7)))/(e^8*(d + e*x)^14)","B",1
1075,1,3532,464,1.6172618,"\int (a+b x)^{10} (A+B x) (d+e x)^{13} \, dx","Integrate[(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,"a^10*A*d^13*x + (a^9*d^12*(10*A*b*d + a*B*d + 13*a*A*e)*x^2)/2 + (a^8*d^11*(a*B*d*(10*b*d + 13*a*e) + A*(45*b^2*d^2 + 130*a*b*d*e + 78*a^2*e^2))*x^3)/3 + (a^7*d^10*(a*B*d*(45*b^2*d^2 + 130*a*b*d*e + 78*a^2*e^2) + A*(120*b^3*d^3 + 585*a*b^2*d^2*e + 780*a^2*b*d*e^2 + 286*a^3*e^3))*x^4)/4 + (a^6*d^9*(a*B*d*(120*b^3*d^3 + 585*a*b^2*d^2*e + 780*a^2*b*d*e^2 + 286*a^3*e^3) + 5*A*(42*b^4*d^4 + 312*a*b^3*d^3*e + 702*a^2*b^2*d^2*e^2 + 572*a^3*b*d*e^3 + 143*a^4*e^4))*x^5)/5 + (a^5*d^8*(5*a*B*d*(42*b^4*d^4 + 312*a*b^3*d^3*e + 702*a^2*b^2*d^2*e^2 + 572*a^3*b*d*e^3 + 143*a^4*e^4) + A*(252*b^5*d^5 + 2730*a*b^4*d^4*e + 9360*a^2*b^3*d^3*e^2 + 12870*a^3*b^2*d^2*e^3 + 7150*a^4*b*d*e^4 + 1287*a^5*e^5))*x^6)/6 + (a^4*d^7*(a*B*d*(252*b^5*d^5 + 2730*a*b^4*d^4*e + 9360*a^2*b^3*d^3*e^2 + 12870*a^3*b^2*d^2*e^3 + 7150*a^4*b*d*e^4 + 1287*a^5*e^5) + 3*A*(70*b^6*d^6 + 1092*a*b^5*d^5*e + 5460*a^2*b^4*d^4*e^2 + 11440*a^3*b^3*d^3*e^3 + 10725*a^4*b^2*d^2*e^4 + 4290*a^5*b*d*e^5 + 572*a^6*e^6))*x^7)/7 + (3*a^3*d^6*(a*B*d*(70*b^6*d^6 + 1092*a*b^5*d^5*e + 5460*a^2*b^4*d^4*e^2 + 11440*a^3*b^3*d^3*e^3 + 10725*a^4*b^2*d^2*e^4 + 4290*a^5*b*d*e^5 + 572*a^6*e^6) + A*(40*b^7*d^7 + 910*a*b^6*d^6*e + 6552*a^2*b^5*d^5*e^2 + 20020*a^3*b^4*d^4*e^3 + 28600*a^4*b^3*d^3*e^4 + 19305*a^5*b^2*d^2*e^5 + 5720*a^6*b*d*e^6 + 572*a^7*e^7))*x^8)/8 + (a^2*d^5*(a*B*d*(40*b^7*d^7 + 910*a*b^6*d^6*e + 6552*a^2*b^5*d^5*e^2 + 20020*a^3*b^4*d^4*e^3 + 28600*a^4*b^3*d^3*e^4 + 19305*a^5*b^2*d^2*e^5 + 5720*a^6*b*d*e^6 + 572*a^7*e^7) + A*(15*b^8*d^8 + 520*a*b^7*d^7*e + 5460*a^2*b^6*d^6*e^2 + 24024*a^3*b^5*d^5*e^3 + 50050*a^4*b^4*d^4*e^4 + 51480*a^5*b^3*d^3*e^5 + 25740*a^6*b^2*d^2*e^6 + 5720*a^7*b*d*e^7 + 429*a^8*e^8))*x^9)/3 + (a*d^4*(3*a*B*d*(15*b^8*d^8 + 520*a*b^7*d^7*e + 5460*a^2*b^6*d^6*e^2 + 24024*a^3*b^5*d^5*e^3 + 50050*a^4*b^4*d^4*e^4 + 51480*a^5*b^3*d^3*e^5 + 25740*a^6*b^2*d^2*e^6 + 5720*a^7*b*d*e^7 + 429*a^8*e^8) + 5*A*(2*b^9*d^9 + 117*a*b^8*d^8*e + 1872*a^2*b^7*d^7*e^2 + 12012*a^3*b^6*d^6*e^3 + 36036*a^4*b^5*d^5*e^4 + 54054*a^5*b^4*d^4*e^5 + 41184*a^6*b^3*d^3*e^6 + 15444*a^7*b^2*d^2*e^7 + 2574*a^8*b*d*e^8 + 143*a^9*e^9))*x^10)/10 + (d^3*(5*a*B*d*(2*b^9*d^9 + 117*a*b^8*d^8*e + 1872*a^2*b^7*d^7*e^2 + 12012*a^3*b^6*d^6*e^3 + 36036*a^4*b^5*d^5*e^4 + 54054*a^5*b^4*d^4*e^5 + 41184*a^6*b^3*d^3*e^6 + 15444*a^7*b^2*d^2*e^7 + 2574*a^8*b*d*e^8 + 143*a^9*e^9) + A*(b^10*d^10 + 130*a*b^9*d^9*e + 3510*a^2*b^8*d^8*e^2 + 34320*a^3*b^7*d^7*e^3 + 150150*a^4*b^6*d^6*e^4 + 324324*a^5*b^5*d^5*e^5 + 360360*a^6*b^4*d^4*e^6 + 205920*a^7*b^3*d^3*e^7 + 57915*a^8*b^2*d^2*e^8 + 7150*a^9*b*d*e^9 + 286*a^10*e^10))*x^11)/11 + (d^2*(360360*a^6*b^4*d^4*e^6*(B*d + A*e) + 1430*a^9*b*d*e^9*(5*B*d + 2*A*e) + 51480*a^7*b^3*d^3*e^7*(4*B*d + 3*A*e) + 26*a^10*e^10*(11*B*d + 3*A*e) + 108108*a^5*b^5*d^5*e^5*(3*B*d + 4*A*e) + 17160*a^3*b^7*d^7*e^3*(2*B*d + 5*A*e) + 6435*a^8*b^2*d^2*e^8*(9*B*d + 5*A*e) + 130*a*b^9*d^9*e*(B*d + 6*A*e) + 30030*a^4*b^6*d^6*e^4*(5*B*d + 9*A*e) + 1170*a^2*b^8*d^8*e^2*(3*B*d + 11*A*e) + b^10*d^10*(B*d + 13*A*e))*x^12)/12 + d*e*(33264*a^5*b^5*d^5*e^5*(B*d + A*e) + a^10*e^10*(6*B*d + A*e) + 495*a^8*b^2*d^2*e^8*(5*B*d + 2*A*e) + 6930*a^6*b^4*d^4*e^6*(4*B*d + 3*A*e) + 20*a^9*b*d*e^9*(11*B*d + 3*A*e) + 6930*a^4*b^6*d^6*e^4*(3*B*d + 4*A*e) + 495*a^2*b^8*d^8*e^2*(2*B*d + 5*A*e) + 1320*a^7*b^3*d^3*e^7*(9*B*d + 5*A*e) + b^10*d^10*(B*d + 6*A*e) + 1320*a^3*b^7*d^7*e^3*(5*B*d + 9*A*e) + 20*a*b^9*d^9*e*(3*B*d + 11*A*e))*x^13 + (e^2*(360360*a^4*b^6*d^6*e^4*(B*d + A*e) + 130*a^9*b*d*e^9*(6*B*d + A*e) + a^10*e^10*(13*B*d + A*e) + 17160*a^7*b^3*d^3*e^7*(5*B*d + 2*A*e) + 108108*a^5*b^5*d^5*e^5*(4*B*d + 3*A*e) + 1170*a^8*b^2*d^2*e^8*(11*B*d + 3*A*e) + 51480*a^3*b^7*d^7*e^3*(3*B*d + 4*A*e) + 1430*a*b^9*d^9*e*(2*B*d + 5*A*e) + 30030*a^6*b^4*d^4*e^6*(9*B*d + 5*A*e) + 6435*a^2*b^8*d^8*e^2*(5*B*d + 9*A*e) + 26*b^10*d^10*(3*B*d + 11*A*e))*x^14)/14 + (e^3*(a^10*B*e^10 + 205920*a^3*b^7*d^6*e^3*(B*d + A*e) + 585*a^8*b^2*d*e^8*(6*B*d + A*e) + 10*a^9*b*e^9*(13*B*d + A*e) + 30030*a^6*b^4*d^3*e^6*(5*B*d + 2*A*e) + 90090*a^4*b^6*d^5*e^4*(4*B*d + 3*A*e) + 3120*a^7*b^3*d^2*e^7*(11*B*d + 3*A*e) + 19305*a^2*b^8*d^7*e^2*(3*B*d + 4*A*e) + 143*b^10*d^9*(2*B*d + 5*A*e) + 36036*a^5*b^5*d^4*e^5*(9*B*d + 5*A*e) + 1430*a*b^9*d^8*e*(5*B*d + 9*A*e))*x^15)/15 + (b*e^4*(10*a^9*B*e^9 + 77220*a^2*b^7*d^6*e^2*(B*d + A*e) + 1560*a^7*b^2*d*e^7*(6*B*d + A*e) + 45*a^8*b*e^8*(13*B*d + A*e) + 36036*a^5*b^4*d^3*e^5*(5*B*d + 2*A*e) + 51480*a^3*b^6*d^5*e^3*(4*B*d + 3*A*e) + 5460*a^6*b^3*d^2*e^6*(11*B*d + 3*A*e) + 4290*a*b^8*d^7*e*(3*B*d + 4*A*e) + 30030*a^4*b^5*d^4*e^4*(9*B*d + 5*A*e) + 143*b^9*d^8*(5*B*d + 9*A*e))*x^16)/16 + (3*b^2*e^5*(15*a^8*B*e^8 + 5720*a*b^7*d^6*e*(B*d + A*e) + 910*a^6*b^2*d*e^6*(6*B*d + A*e) + 40*a^7*b*e^7*(13*B*d + A*e) + 10010*a^4*b^4*d^3*e^4*(5*B*d + 2*A*e) + 6435*a^2*b^6*d^5*e^2*(4*B*d + 3*A*e) + 2184*a^5*b^3*d^2*e^5*(11*B*d + 3*A*e) + 143*b^8*d^7*(3*B*d + 4*A*e) + 5720*a^3*b^5*d^4*e^3*(9*B*d + 5*A*e))*x^17)/17 + (b^3*e^6*(40*a^7*B*e^7 + 572*b^7*d^6*(B*d + A*e) + 1092*a^5*b^2*d*e^5*(6*B*d + A*e) + 70*a^6*b*e^6*(13*B*d + A*e) + 5720*a^3*b^4*d^3*e^3*(5*B*d + 2*A*e) + 1430*a*b^6*d^5*e*(4*B*d + 3*A*e) + 1820*a^4*b^3*d^2*e^4*(11*B*d + 3*A*e) + 2145*a^2*b^5*d^4*e^2*(9*B*d + 5*A*e))*x^18)/6 + (b^4*e^7*(210*a^6*B*e^6 + 2730*a^4*b^2*d*e^4*(6*B*d + A*e) + 252*a^5*b*e^5*(13*B*d + A*e) + 6435*a^2*b^4*d^3*e^2*(5*B*d + 2*A*e) + 429*b^6*d^5*(4*B*d + 3*A*e) + 3120*a^3*b^3*d^2*e^3*(11*B*d + 3*A*e) + 1430*a*b^5*d^4*e*(9*B*d + 5*A*e))*x^19)/19 + (b^5*e^8*(252*a^5*B*e^5 + 1560*a^3*b^2*d*e^3*(6*B*d + A*e) + 210*a^4*b*e^4*(13*B*d + A*e) + 1430*a*b^4*d^3*e*(5*B*d + 2*A*e) + 1170*a^2*b^3*d^2*e^2*(11*B*d + 3*A*e) + 143*b^5*d^4*(9*B*d + 5*A*e))*x^20)/20 + (b^6*e^9*(210*a^4*B*e^4 + 585*a^2*b^2*d*e^2*(6*B*d + A*e) + 120*a^3*b*e^3*(13*B*d + A*e) + 143*b^4*d^3*(5*B*d + 2*A*e) + 260*a*b^3*d^2*e*(11*B*d + 3*A*e))*x^21)/21 + (b^7*e^10*(120*a^3*B*e^3 + 130*a*b^2*d*e*(6*B*d + A*e) + 45*a^2*b*e^2*(13*B*d + A*e) + 26*b^3*d^2*(11*B*d + 3*A*e))*x^22)/22 + (b^8*e^11*(45*a^2*B*e^2 + 13*b^2*d*(6*B*d + A*e) + 10*a*b*e*(13*B*d + A*e))*x^23)/23 + (b^9*e^12*(13*b*B*d + A*b*e + 10*a*B*e)*x^24)/24 + (b^10*B*e^13*x^25)/25","B",1
1076,1,3320,464,1.520603,"\int (a+b x)^{10} (A+B x) (d+e x)^{12} \, dx","Integrate[(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,"a^10*A*d^12*x + (a^9*d^11*(a*B*d + 2*A*(5*b*d + 6*a*e))*x^2)/2 + (a^8*d^10*(2*a*B*d*(5*b*d + 6*a*e) + 3*A*(15*b^2*d^2 + 40*a*b*d*e + 22*a^2*e^2))*x^3)/3 + (a^7*d^9*(3*a*B*d*(15*b^2*d^2 + 40*a*b*d*e + 22*a^2*e^2) + 20*A*(6*b^3*d^3 + 27*a*b^2*d^2*e + 33*a^2*b*d*e^2 + 11*a^3*e^3))*x^4)/4 + a^6*d^8*(4*a*B*d*(6*b^3*d^3 + 27*a*b^2*d^2*e + 33*a^2*b*d*e^2 + 11*a^3*e^3) + A*(42*b^4*d^4 + 288*a*b^3*d^3*e + 594*a^2*b^2*d^2*e^2 + 440*a^3*b*d*e^3 + 99*a^4*e^4))*x^5 + (a^5*d^7*(5*a*B*d*(42*b^4*d^4 + 288*a*b^3*d^3*e + 594*a^2*b^2*d^2*e^2 + 440*a^3*b*d*e^3 + 99*a^4*e^4) + 18*A*(14*b^5*d^5 + 140*a*b^4*d^4*e + 440*a^2*b^3*d^3*e^2 + 550*a^3*b^2*d^2*e^3 + 275*a^4*b*d*e^4 + 44*a^5*e^5))*x^6)/6 + (3*a^4*d^6*(6*a*B*d*(14*b^5*d^5 + 140*a*b^4*d^4*e + 440*a^2*b^3*d^3*e^2 + 550*a^3*b^2*d^2*e^3 + 275*a^4*b*d*e^4 + 44*a^5*e^5) + A*(70*b^6*d^6 + 1008*a*b^5*d^5*e + 4620*a^2*b^4*d^4*e^2 + 8800*a^3*b^3*d^3*e^3 + 7425*a^4*b^2*d^2*e^4 + 2640*a^5*b*d*e^5 + 308*a^6*e^6))*x^7)/7 + (3*a^3*d^5*(a*B*d*(70*b^6*d^6 + 1008*a*b^5*d^5*e + 4620*a^2*b^4*d^4*e^2 + 8800*a^3*b^3*d^3*e^3 + 7425*a^4*b^2*d^2*e^4 + 2640*a^5*b*d*e^5 + 308*a^6*e^6) + 8*A*(5*b^7*d^7 + 105*a*b^6*d^6*e + 693*a^2*b^5*d^5*e^2 + 1925*a^3*b^4*d^4*e^3 + 2475*a^4*b^3*d^3*e^4 + 1485*a^5*b^2*d^2*e^5 + 385*a^6*b*d*e^6 + 33*a^7*e^7))*x^8)/8 + (a^2*d^4*(8*a*B*d*(5*b^7*d^7 + 105*a*b^6*d^6*e + 693*a^2*b^5*d^5*e^2 + 1925*a^3*b^4*d^4*e^3 + 2475*a^4*b^3*d^3*e^4 + 1485*a^5*b^2*d^2*e^5 + 385*a^6*b*d*e^6 + 33*a^7*e^7) + 15*A*(b^8*d^8 + 32*a*b^7*d^7*e + 308*a^2*b^6*d^6*e^2 + 1232*a^3*b^5*d^5*e^3 + 2310*a^4*b^4*d^4*e^4 + 2112*a^5*b^3*d^3*e^5 + 924*a^6*b^2*d^2*e^6 + 176*a^7*b*d*e^7 + 11*a^8*e^8))*x^9)/3 + (a*d^3*(9*a*B*d*(b^8*d^8 + 32*a*b^7*d^7*e + 308*a^2*b^6*d^6*e^2 + 1232*a^3*b^5*d^5*e^3 + 2310*a^4*b^4*d^4*e^4 + 2112*a^5*b^3*d^3*e^5 + 924*a^6*b^2*d^2*e^6 + 176*a^7*b*d*e^7 + 11*a^8*e^8) + 2*A*(b^9*d^9 + 54*a*b^8*d^8*e + 792*a^2*b^7*d^7*e^2 + 4620*a^3*b^6*d^6*e^3 + 12474*a^4*b^5*d^5*e^4 + 16632*a^5*b^4*d^4*e^5 + 11088*a^6*b^3*d^3*e^6 + 3564*a^7*b^2*d^2*e^7 + 495*a^8*b*d*e^8 + 22*a^9*e^9))*x^10)/2 + (d^2*(10*a*B*d*(b^9*d^9 + 54*a*b^8*d^8*e + 792*a^2*b^7*d^7*e^2 + 4620*a^3*b^6*d^6*e^3 + 12474*a^4*b^5*d^5*e^4 + 16632*a^5*b^4*d^4*e^5 + 11088*a^6*b^3*d^3*e^6 + 3564*a^7*b^2*d^2*e^7 + 495*a^8*b*d*e^8 + 22*a^9*e^9) + A*(b^10*d^10 + 120*a*b^9*d^9*e + 2970*a^2*b^8*d^8*e^2 + 26400*a^3*b^7*d^7*e^3 + 103950*a^4*b^6*d^6*e^4 + 199584*a^5*b^5*d^5*e^5 + 194040*a^6*b^4*d^4*e^6 + 95040*a^7*b^3*d^3*e^7 + 22275*a^8*b^2*d^2*e^8 + 2200*a^9*b*d*e^9 + 66*a^10*e^10))*x^11)/11 + (d*(6*a^10*e^10*(11*B*d + 2*A*e) + 220*a^9*b*d*e^9*(10*B*d + 3*A*e) + 2475*a^8*b^2*d^2*e^8*(9*B*d + 4*A*e) + 11880*a^7*b^3*d^3*e^7*(8*B*d + 5*A*e) + 27720*a^6*b^4*d^4*e^6*(7*B*d + 6*A*e) + 33264*a^5*b^5*d^5*e^5*(6*B*d + 7*A*e) + 20790*a^4*b^6*d^6*e^4*(5*B*d + 8*A*e) + 6600*a^3*b^7*d^7*e^3*(4*B*d + 9*A*e) + 990*a^2*b^8*d^8*e^2*(3*B*d + 10*A*e) + 60*a*b^9*d^9*e*(2*B*d + 11*A*e) + b^10*d^10*(B*d + 12*A*e))*x^12)/12 + (e*(a^10*e^10*(12*B*d + A*e) + 60*a^9*b*d*e^9*(11*B*d + 2*A*e) + 990*a^8*b^2*d^2*e^8*(10*B*d + 3*A*e) + 6600*a^7*b^3*d^3*e^7*(9*B*d + 4*A*e) + 20790*a^6*b^4*d^4*e^6*(8*B*d + 5*A*e) + 33264*a^5*b^5*d^5*e^5*(7*B*d + 6*A*e) + 27720*a^4*b^6*d^6*e^4*(6*B*d + 7*A*e) + 11880*a^3*b^7*d^7*e^3*(5*B*d + 8*A*e) + 2475*a^2*b^8*d^8*e^2*(4*B*d + 9*A*e) + 220*a*b^9*d^9*e*(3*B*d + 10*A*e) + 6*b^10*d^10*(2*B*d + 11*A*e))*x^13)/13 + (e^2*(a^10*B*e^10 + 10*a^9*b*e^9*(12*B*d + A*e) + 270*a^8*b^2*d*e^8*(11*B*d + 2*A*e) + 2640*a^7*b^3*d^2*e^7*(10*B*d + 3*A*e) + 11550*a^6*b^4*d^3*e^6*(9*B*d + 4*A*e) + 24948*a^5*b^5*d^4*e^5*(8*B*d + 5*A*e) + 27720*a^4*b^6*d^5*e^4*(7*B*d + 6*A*e) + 15840*a^3*b^7*d^6*e^3*(6*B*d + 7*A*e) + 4455*a^2*b^8*d^7*e^2*(5*B*d + 8*A*e) + 550*a*b^9*d^8*e*(4*B*d + 9*A*e) + 22*b^10*d^9*(3*B*d + 10*A*e))*x^14)/14 + (b*e^3*(2*a^9*B*e^9 + 9*a^8*b*e^8*(12*B*d + A*e) + 144*a^7*b^2*d*e^7*(11*B*d + 2*A*e) + 924*a^6*b^3*d^2*e^6*(10*B*d + 3*A*e) + 2772*a^5*b^4*d^3*e^5*(9*B*d + 4*A*e) + 4158*a^4*b^5*d^4*e^4*(8*B*d + 5*A*e) + 3168*a^3*b^6*d^5*e^3*(7*B*d + 6*A*e) + 1188*a^2*b^7*d^6*e^2*(6*B*d + 7*A*e) + 198*a*b^8*d^7*e*(5*B*d + 8*A*e) + 11*b^9*d^8*(4*B*d + 9*A*e))*x^15)/3 + (3*b^2*e^4*(15*a^8*B*e^8 + 40*a^7*b*e^7*(12*B*d + A*e) + 420*a^6*b^2*d*e^6*(11*B*d + 2*A*e) + 1848*a^5*b^3*d^2*e^5*(10*B*d + 3*A*e) + 3850*a^4*b^4*d^3*e^4*(9*B*d + 4*A*e) + 3960*a^3*b^5*d^4*e^3*(8*B*d + 5*A*e) + 1980*a^2*b^6*d^5*e^2*(7*B*d + 6*A*e) + 440*a*b^7*d^6*e*(6*B*d + 7*A*e) + 33*b^8*d^7*(5*B*d + 8*A*e))*x^16)/16 + (3*b^3*e^5*(40*a^7*B*e^7 + 70*a^6*b*e^6*(12*B*d + A*e) + 504*a^5*b^2*d*e^5*(11*B*d + 2*A*e) + 1540*a^4*b^3*d^2*e^4*(10*B*d + 3*A*e) + 2200*a^3*b^4*d^3*e^3*(9*B*d + 4*A*e) + 1485*a^2*b^5*d^4*e^2*(8*B*d + 5*A*e) + 440*a*b^6*d^5*e*(7*B*d + 6*A*e) + 44*b^7*d^6*(6*B*d + 7*A*e))*x^17)/17 + (b^4*e^6*(70*a^6*B*e^6 + 84*a^5*b*e^5*(12*B*d + A*e) + 420*a^4*b^2*d*e^4*(11*B*d + 2*A*e) + 880*a^3*b^3*d^2*e^3*(10*B*d + 3*A*e) + 825*a^2*b^4*d^3*e^2*(9*B*d + 4*A*e) + 330*a*b^5*d^4*e*(8*B*d + 5*A*e) + 44*b^6*d^5*(7*B*d + 6*A*e))*x^18)/6 + (b^5*e^7*(252*a^5*B*e^5 + 210*a^4*b*e^4*(12*B*d + A*e) + 720*a^3*b^2*d*e^3*(11*B*d + 2*A*e) + 990*a^2*b^3*d^2*e^2*(10*B*d + 3*A*e) + 550*a*b^4*d^3*e*(9*B*d + 4*A*e) + 99*b^5*d^4*(8*B*d + 5*A*e))*x^19)/19 + (b^6*e^8*(42*a^4*B*e^4 + 24*a^3*b*e^3*(12*B*d + A*e) + 54*a^2*b^2*d*e^2*(11*B*d + 2*A*e) + 44*a*b^3*d^2*e*(10*B*d + 3*A*e) + 11*b^4*d^3*(9*B*d + 4*A*e))*x^20)/4 + (b^7*e^9*(120*a^3*B*e^3 + 45*a^2*b*e^2*(12*B*d + A*e) + 60*a*b^2*d*e*(11*B*d + 2*A*e) + 22*b^3*d^2*(10*B*d + 3*A*e))*x^21)/21 + (b^8*e^10*(45*a^2*B*e^2 + 10*a*b*e*(12*B*d + A*e) + 6*b^2*d*(11*B*d + 2*A*e))*x^22)/22 + (b^9*e^11*(12*b*B*d + A*b*e + 10*a*B*e)*x^23)/23 + (b^10*B*e^12*x^24)/24","B",1
1077,1,3018,461,1.3249523,"\int (a+b x)^{10} (A+B x) (d+e x)^{11} \, dx","Integrate[(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 e^{12}}",1,"a^10*A*d^11*x + (a^9*d^10*(10*A*b*d + a*B*d + 11*a*A*e)*x^2)/2 + (a^8*d^9*(a*B*d*(10*b*d + 11*a*e) + 5*A*(9*b^2*d^2 + 22*a*b*d*e + 11*a^2*e^2))*x^3)/3 + (5*a^7*d^8*(a*B*d*(9*b^2*d^2 + 22*a*b*d*e + 11*a^2*e^2) + A*(24*b^3*d^3 + 99*a*b^2*d^2*e + 110*a^2*b*d*e^2 + 33*a^3*e^3))*x^4)/4 + a^6*d^7*(a*B*d*(24*b^3*d^3 + 99*a*b^2*d^2*e + 110*a^2*b*d*e^2 + 33*a^3*e^3) + 3*A*(14*b^4*d^4 + 88*a*b^3*d^3*e + 165*a^2*b^2*d^2*e^2 + 110*a^3*b*d*e^3 + 22*a^4*e^4))*x^5 + (a^5*d^6*(5*a*B*d*(14*b^4*d^4 + 88*a*b^3*d^3*e + 165*a^2*b^2*d^2*e^2 + 110*a^3*b*d*e^3 + 22*a^4*e^4) + A*(84*b^5*d^5 + 770*a*b^4*d^4*e + 2200*a^2*b^3*d^3*e^2 + 2475*a^3*b^2*d^2*e^3 + 1100*a^4*b*d*e^4 + 154*a^5*e^5))*x^6)/2 + (3*a^4*d^5*(a*B*d*(84*b^5*d^5 + 770*a*b^4*d^4*e + 2200*a^2*b^3*d^3*e^2 + 2475*a^3*b^2*d^2*e^3 + 1100*a^4*b*d*e^4 + 154*a^5*e^5) + 2*A*(35*b^6*d^6 + 462*a*b^5*d^5*e + 1925*a^2*b^4*d^4*e^2 + 3300*a^3*b^3*d^3*e^3 + 2475*a^4*b^2*d^2*e^4 + 770*a^5*b*d*e^5 + 77*a^6*e^6))*x^7)/7 + (3*a^3*d^4*(a*B*d*(35*b^6*d^6 + 462*a*b^5*d^5*e + 1925*a^2*b^4*d^4*e^2 + 3300*a^3*b^3*d^3*e^3 + 2475*a^4*b^2*d^2*e^4 + 770*a^5*b*d*e^5 + 77*a^6*e^6) + 5*A*(4*b^7*d^7 + 77*a*b^6*d^6*e + 462*a^2*b^5*d^5*e^2 + 1155*a^3*b^4*d^4*e^3 + 1320*a^4*b^3*d^3*e^4 + 693*a^5*b^2*d^2*e^5 + 154*a^6*b*d*e^6 + 11*a^7*e^7))*x^8)/4 + (5*a^2*d^3*(2*a*B*d*(4*b^7*d^7 + 77*a*b^6*d^6*e + 462*a^2*b^5*d^5*e^2 + 1155*a^3*b^4*d^4*e^3 + 1320*a^4*b^3*d^3*e^4 + 693*a^5*b^2*d^2*e^5 + 154*a^6*b*d*e^6 + 11*a^7*e^7) + A*(3*b^8*d^8 + 88*a*b^7*d^7*e + 770*a^2*b^6*d^6*e^2 + 2772*a^3*b^5*d^5*e^3 + 4620*a^4*b^4*d^4*e^4 + 3696*a^5*b^3*d^3*e^5 + 1386*a^6*b^2*d^2*e^6 + 220*a^7*b*d*e^7 + 11*a^8*e^8))*x^9)/3 + (a*d^2*(3*a*B*d*(3*b^8*d^8 + 88*a*b^7*d^7*e + 770*a^2*b^6*d^6*e^2 + 2772*a^3*b^5*d^5*e^3 + 4620*a^4*b^4*d^4*e^4 + 3696*a^5*b^3*d^3*e^5 + 1386*a^6*b^2*d^2*e^6 + 220*a^7*b*d*e^7 + 11*a^8*e^8) + A*(2*b^9*d^9 + 99*a*b^8*d^8*e + 1320*a^2*b^7*d^7*e^2 + 6930*a^3*b^6*d^6*e^3 + 16632*a^4*b^5*d^5*e^4 + 19404*a^5*b^4*d^4*e^5 + 11088*a^6*b^3*d^3*e^6 + 2970*a^7*b^2*d^2*e^7 + 330*a^8*b*d*e^8 + 11*a^9*e^9))*x^10)/2 + (d*(5*a*B*d*(2*b^9*d^9 + 99*a*b^8*d^8*e + 1320*a^2*b^7*d^7*e^2 + 6930*a^3*b^6*d^6*e^3 + 16632*a^4*b^5*d^5*e^4 + 19404*a^5*b^4*d^4*e^5 + 11088*a^6*b^3*d^3*e^6 + 2970*a^7*b^2*d^2*e^7 + 330*a^8*b*d*e^8 + 11*a^9*e^9) + A*(b^10*d^10 + 110*a*b^9*d^9*e + 2475*a^2*b^8*d^8*e^2 + 19800*a^3*b^7*d^7*e^3 + 69300*a^4*b^6*d^6*e^4 + 116424*a^5*b^5*d^5*e^5 + 97020*a^6*b^4*d^4*e^6 + 39600*a^7*b^3*d^3*e^7 + 7425*a^8*b^2*d^2*e^8 + 550*a^9*b*d*e^9 + 11*a^10*e^10))*x^11)/11 + ((116424*a^5*b^5*d^5*e^5*(B*d + A*e) + 19800*a^7*b^3*d^3*e^7*(2*B*d + A*e) + 2475*a^8*b^2*d^2*e^8*(3*B*d + A*e) + 110*a^9*b*d*e^9*(5*B*d + A*e) + a^10*e^10*(11*B*d + A*e) + 19800*a^3*b^7*d^7*e^3*(B*d + 2*A*e) + 2475*a^2*b^8*d^8*e^2*(B*d + 3*A*e) + 110*a*b^9*d^9*e*(B*d + 5*A*e) + 13860*a^6*b^4*d^4*e^6*(7*B*d + 5*A*e) + 13860*a^4*b^6*d^6*e^4*(5*B*d + 7*A*e) + b^10*d^10*(B*d + 11*A*e))*x^12)/12 + (e*(a^10*B*e^10 + 97020*a^4*b^6*d^5*e^4*(B*d + A*e) + 34650*a^6*b^4*d^3*e^6*(2*B*d + A*e) + 6600*a^7*b^3*d^2*e^7*(3*B*d + A*e) + 495*a^8*b^2*d*e^8*(5*B*d + A*e) + 10*a^9*b*e^9*(11*B*d + A*e) + 7425*a^2*b^8*d^7*e^2*(B*d + 2*A*e) + 550*a*b^9*d^8*e*(B*d + 3*A*e) + 11*b^10*d^9*(B*d + 5*A*e) + 16632*a^5*b^5*d^4*e^5*(7*B*d + 5*A*e) + 7920*a^3*b^7*d^6*e^3*(5*B*d + 7*A*e))*x^13)/13 + (5*b*e^2*(2*a^9*B*e^9 + 11088*a^3*b^6*d^5*e^3*(B*d + A*e) + 8316*a^5*b^4*d^3*e^5*(2*B*d + A*e) + 2310*a^6*b^3*d^2*e^6*(3*B*d + A*e) + 264*a^7*b^2*d*e^7*(5*B*d + A*e) + 9*a^8*b*e^8*(11*B*d + A*e) + 330*a*b^8*d^7*e*(B*d + 2*A*e) + 11*b^9*d^8*(B*d + 3*A*e) + 2772*a^4*b^5*d^4*e^4*(7*B*d + 5*A*e) + 594*a^2*b^7*d^6*e^2*(5*B*d + 7*A*e))*x^14)/14 + b^2*e^3*(3*a^8*B*e^8 + 1386*a^2*b^6*d^5*e^2*(B*d + A*e) + 2310*a^4*b^4*d^3*e^4*(2*B*d + A*e) + 924*a^5*b^3*d^2*e^5*(3*B*d + A*e) + 154*a^6*b^2*d*e^6*(5*B*d + A*e) + 8*a^7*b*e^7*(11*B*d + A*e) + 11*b^8*d^7*(B*d + 2*A*e) + 528*a^3*b^5*d^4*e^3*(7*B*d + 5*A*e) + 44*a*b^7*d^6*e*(5*B*d + 7*A*e))*x^15 + (3*b^3*e^4*(20*a^7*B*e^7 + 770*a*b^6*d^5*e*(B*d + A*e) + 3300*a^3*b^4*d^3*e^3*(2*B*d + A*e) + 1925*a^4*b^3*d^2*e^4*(3*B*d + A*e) + 462*a^5*b^2*d*e^5*(5*B*d + A*e) + 35*a^6*b*e^6*(11*B*d + A*e) + 495*a^2*b^5*d^4*e^2*(7*B*d + 5*A*e) + 11*b^7*d^6*(5*B*d + 7*A*e))*x^16)/8 + (3*b^4*e^5*(70*a^6*B*e^6 + 154*b^6*d^5*(B*d + A*e) + 2475*a^2*b^4*d^3*e^2*(2*B*d + A*e) + 2200*a^3*b^3*d^2*e^3*(3*B*d + A*e) + 770*a^4*b^2*d*e^4*(5*B*d + A*e) + 84*a^5*b*e^5*(11*B*d + A*e) + 220*a*b^5*d^4*e*(7*B*d + 5*A*e))*x^17)/17 + (b^5*e^6*(84*a^5*B*e^5 + 550*a*b^4*d^3*e*(2*B*d + A*e) + 825*a^2*b^3*d^2*e^2*(3*B*d + A*e) + 440*a^3*b^2*d*e^3*(5*B*d + A*e) + 70*a^4*b*e^4*(11*B*d + A*e) + 22*b^5*d^4*(7*B*d + 5*A*e))*x^18)/6 + (5*b^6*e^7*(42*a^4*B*e^4 + 33*b^4*d^3*(2*B*d + A*e) + 110*a*b^3*d^2*e*(3*B*d + A*e) + 99*a^2*b^2*d*e^2*(5*B*d + A*e) + 24*a^3*b*e^3*(11*B*d + A*e))*x^19)/19 + (b^7*e^8*(24*a^3*B*e^3 + 11*b^3*d^2*(3*B*d + A*e) + 22*a*b^2*d*e*(5*B*d + A*e) + 9*a^2*b*e^2*(11*B*d + A*e))*x^20)/4 + (b^8*e^9*(45*a^2*B*e^2 + 11*b^2*d*(5*B*d + A*e) + 10*a*b*e*(11*B*d + A*e))*x^21)/21 + (b^9*e^10*(11*b*B*d + A*b*e + 10*a*B*e)*x^22)/22 + (b^10*B*e^11*x^23)/23","B",1
1078,1,2815,460,1.211486,"\int (a+b x)^{10} (A+B x) (d+e x)^{10} \, dx","Integrate[(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,"a^10*A*d^10*x + (a^9*d^9*(a*B*d + 10*A*(b*d + a*e))*x^2)/2 + (5*a^8*d^8*(2*a*B*d*(b*d + a*e) + A*(9*b^2*d^2 + 20*a*b*d*e + 9*a^2*e^2))*x^3)/3 + (5*a^7*d^7*(a*B*d*(9*b^2*d^2 + 20*a*b*d*e + 9*a^2*e^2) + 6*A*(4*b^3*d^3 + 15*a*b^2*d^2*e + 15*a^2*b*d*e^2 + 4*a^3*e^3))*x^4)/4 + 3*a^6*d^6*(2*a*B*d*(4*b^3*d^3 + 15*a*b^2*d^2*e + 15*a^2*b*d*e^2 + 4*a^3*e^3) + A*(14*b^4*d^4 + 80*a*b^3*d^3*e + 135*a^2*b^2*d^2*e^2 + 80*a^3*b*d*e^3 + 14*a^4*e^4))*x^5 + (a^5*d^5*(5*a*B*d*(14*b^4*d^4 + 80*a*b^3*d^3*e + 135*a^2*b^2*d^2*e^2 + 80*a^3*b*d*e^3 + 14*a^4*e^4) + 4*A*(21*b^5*d^5 + 175*a*b^4*d^4*e + 450*a^2*b^3*d^3*e^2 + 450*a^3*b^2*d^2*e^3 + 175*a^4*b*d*e^4 + 21*a^5*e^5))*x^6)/2 + (6*a^4*d^4*(2*a*B*d*(21*b^5*d^5 + 175*a*b^4*d^4*e + 450*a^2*b^3*d^3*e^2 + 450*a^3*b^2*d^2*e^3 + 175*a^4*b*d*e^4 + 21*a^5*e^5) + 5*A*(7*b^6*d^6 + 84*a*b^5*d^5*e + 315*a^2*b^4*d^4*e^2 + 480*a^3*b^3*d^3*e^3 + 315*a^4*b^2*d^2*e^4 + 84*a^5*b*d*e^5 + 7*a^6*e^6))*x^7)/7 + (15*a^3*d^3*(a*B*d*(7*b^6*d^6 + 84*a*b^5*d^5*e + 315*a^2*b^4*d^4*e^2 + 480*a^3*b^3*d^3*e^3 + 315*a^4*b^2*d^2*e^4 + 84*a^5*b*d*e^5 + 7*a^6*e^6) + A*(4*b^7*d^7 + 70*a*b^6*d^6*e + 378*a^2*b^5*d^5*e^2 + 840*a^3*b^4*d^4*e^3 + 840*a^4*b^3*d^3*e^4 + 378*a^5*b^2*d^2*e^5 + 70*a^6*b*d*e^6 + 4*a^7*e^7))*x^8)/4 + (5*a^2*d^2*(4*a*B*d*(2*b^7*d^7 + 35*a*b^6*d^6*e + 189*a^2*b^5*d^5*e^2 + 420*a^3*b^4*d^4*e^3 + 420*a^4*b^3*d^3*e^4 + 189*a^5*b^2*d^2*e^5 + 35*a^6*b*d*e^6 + 2*a^7*e^7) + A*(3*b^8*d^8 + 80*a*b^7*d^7*e + 630*a^2*b^6*d^6*e^2 + 2016*a^3*b^5*d^5*e^3 + 2940*a^4*b^4*d^4*e^4 + 2016*a^5*b^3*d^3*e^5 + 630*a^6*b^2*d^2*e^6 + 80*a^7*b*d*e^7 + 3*a^8*e^8))*x^9)/3 + (a*d*(3*a*B*d*(3*b^8*d^8 + 80*a*b^7*d^7*e + 630*a^2*b^6*d^6*e^2 + 2016*a^3*b^5*d^5*e^3 + 2940*a^4*b^4*d^4*e^4 + 2016*a^5*b^3*d^3*e^5 + 630*a^6*b^2*d^2*e^6 + 80*a^7*b*d*e^7 + 3*a^8*e^8) + 2*A*(b^9*d^9 + 45*a*b^8*d^8*e + 540*a^2*b^7*d^7*e^2 + 2520*a^3*b^6*d^6*e^3 + 5292*a^4*b^5*d^5*e^4 + 5292*a^5*b^4*d^4*e^5 + 2520*a^6*b^3*d^3*e^6 + 540*a^7*b^2*d^2*e^7 + 45*a^8*b*d*e^8 + a^9*e^9))*x^10)/2 + ((10*a*B*d*(b^9*d^9 + 45*a*b^8*d^8*e + 540*a^2*b^7*d^7*e^2 + 2520*a^3*b^6*d^6*e^3 + 5292*a^4*b^5*d^5*e^4 + 5292*a^5*b^4*d^4*e^5 + 2520*a^6*b^3*d^3*e^6 + 540*a^7*b^2*d^2*e^7 + 45*a^8*b*d*e^8 + a^9*e^9) + A*(b^10*d^10 + 100*a*b^9*d^9*e + 2025*a^2*b^8*d^8*e^2 + 14400*a^3*b^7*d^7*e^3 + 44100*a^4*b^6*d^6*e^4 + 63504*a^5*b^5*d^5*e^5 + 44100*a^6*b^4*d^4*e^6 + 14400*a^7*b^3*d^3*e^7 + 2025*a^8*b^2*d^2*e^8 + 100*a^9*b*d*e^9 + a^10*e^10))*x^11)/11 + ((a^10*B*e^10 + 10*a^9*b*e^9*(10*B*d + A*e) + 225*a^8*b^2*d*e^8*(9*B*d + 2*A*e) + 1800*a^7*b^3*d^2*e^7*(8*B*d + 3*A*e) + 6300*a^6*b^4*d^3*e^6*(7*B*d + 4*A*e) + 10584*a^5*b^5*d^4*e^5*(6*B*d + 5*A*e) + 8820*a^4*b^6*d^5*e^4*(5*B*d + 6*A*e) + 3600*a^3*b^7*d^6*e^3*(4*B*d + 7*A*e) + 675*a^2*b^8*d^7*e^2*(3*B*d + 8*A*e) + 50*a*b^9*d^8*e*(2*B*d + 9*A*e) + b^10*d^9*(B*d + 10*A*e))*x^12)/12 + (5*b*e*(2*a^9*B*e^9 + 9*a^8*b*e^8*(10*B*d + A*e) + 120*a^7*b^2*d*e^7*(9*B*d + 2*A*e) + 630*a^6*b^3*d^2*e^6*(8*B*d + 3*A*e) + 1512*a^5*b^4*d^3*e^5*(7*B*d + 4*A*e) + 1764*a^4*b^5*d^4*e^4*(6*B*d + 5*A*e) + 1008*a^3*b^6*d^5*e^3*(5*B*d + 6*A*e) + 270*a^2*b^7*d^6*e^2*(4*B*d + 7*A*e) + 30*a*b^8*d^7*e*(3*B*d + 8*A*e) + b^9*d^8*(2*B*d + 9*A*e))*x^13)/13 + (15*b^2*e^2*(3*a^8*B*e^8 + 8*a^7*b*e^7*(10*B*d + A*e) + 70*a^6*b^2*d*e^6*(9*B*d + 2*A*e) + 252*a^5*b^3*d^2*e^5*(8*B*d + 3*A*e) + 420*a^4*b^4*d^3*e^4*(7*B*d + 4*A*e) + 336*a^3*b^5*d^4*e^3*(6*B*d + 5*A*e) + 126*a^2*b^6*d^5*e^2*(5*B*d + 6*A*e) + 20*a*b^7*d^6*e*(4*B*d + 7*A*e) + b^8*d^7*(3*B*d + 8*A*e))*x^14)/14 + 2*b^3*e^3*(4*a^7*B*e^7 + 7*a^6*b*e^6*(10*B*d + A*e) + 42*a^5*b^2*d*e^5*(9*B*d + 2*A*e) + 105*a^4*b^3*d^2*e^4*(8*B*d + 3*A*e) + 120*a^3*b^4*d^3*e^3*(7*B*d + 4*A*e) + 63*a^2*b^5*d^4*e^2*(6*B*d + 5*A*e) + 14*a*b^6*d^5*e*(5*B*d + 6*A*e) + b^7*d^6*(4*B*d + 7*A*e))*x^15 + (3*b^4*e^4*(35*a^6*B*e^6 + 42*a^5*b*e^5*(10*B*d + A*e) + 175*a^4*b^2*d*e^4*(9*B*d + 2*A*e) + 300*a^3*b^3*d^2*e^3*(8*B*d + 3*A*e) + 225*a^2*b^4*d^3*e^2*(7*B*d + 4*A*e) + 70*a*b^5*d^4*e*(6*B*d + 5*A*e) + 7*b^6*d^5*(5*B*d + 6*A*e))*x^16)/8 + (3*b^5*e^5*(84*a^5*B*e^5 + 70*a^4*b*e^4*(10*B*d + A*e) + 200*a^3*b^2*d*e^3*(9*B*d + 2*A*e) + 225*a^2*b^3*d^2*e^2*(8*B*d + 3*A*e) + 100*a*b^4*d^3*e*(7*B*d + 4*A*e) + 14*b^5*d^4*(6*B*d + 5*A*e))*x^17)/17 + (5*b^6*e^6*(14*a^4*B*e^4 + 8*a^3*b*e^3*(10*B*d + A*e) + 15*a^2*b^2*d*e^2*(9*B*d + 2*A*e) + 10*a*b^3*d^2*e*(8*B*d + 3*A*e) + 2*b^4*d^3*(7*B*d + 4*A*e))*x^18)/6 + (5*b^7*e^7*(24*a^3*B*e^3 + 9*a^2*b*e^2*(10*B*d + A*e) + 10*a*b^2*d*e*(9*B*d + 2*A*e) + 3*b^3*d^2*(8*B*d + 3*A*e))*x^19)/19 + (b^8*e^8*(9*a^2*B*e^2 + 2*a*b*e*(10*B*d + A*e) + b^2*d*(9*B*d + 2*A*e))*x^20)/4 + (b^9*e^9*(10*b*B*d + A*b*e + 10*a*B*e)*x^21)/21 + (b^10*B*e^10*x^22)/22","B",1
1079,1,2553,415,1.0890101,"\int (a+b x)^{10} (A+B x) (d+e x)^9 \, dx","Integrate[(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,"a^10*A*d^9*x + (a^9*d^8*(10*A*b*d + a*B*d + 9*a*A*e)*x^2)/2 + (a^8*d^7*(a*B*d*(10*b*d + 9*a*e) + 9*A*(5*b^2*d^2 + 10*a*b*d*e + 4*a^2*e^2))*x^3)/3 + (3*a^7*d^6*(3*a*B*d*(5*b^2*d^2 + 10*a*b*d*e + 4*a^2*e^2) + A*(40*b^3*d^3 + 135*a*b^2*d^2*e + 120*a^2*b*d*e^2 + 28*a^3*e^3))*x^4)/4 + (3*a^6*d^5*(a*B*d*(40*b^3*d^3 + 135*a*b^2*d^2*e + 120*a^2*b*d*e^2 + 28*a^3*e^3) + A*(70*b^4*d^4 + 360*a*b^3*d^3*e + 540*a^2*b^2*d^2*e^2 + 280*a^3*b*d*e^3 + 42*a^4*e^4))*x^5)/5 + a^5*d^4*(a*B*d*(35*b^4*d^4 + 180*a*b^3*d^3*e + 270*a^2*b^2*d^2*e^2 + 140*a^3*b*d*e^3 + 21*a^4*e^4) + 3*A*(14*b^5*d^5 + 105*a*b^4*d^4*e + 240*a^2*b^3*d^3*e^2 + 210*a^3*b^2*d^2*e^3 + 70*a^4*b*d*e^4 + 7*a^5*e^5))*x^6 + (6*a^4*d^3*(3*a*B*d*(14*b^5*d^5 + 105*a*b^4*d^4*e + 240*a^2*b^3*d^3*e^2 + 210*a^3*b^2*d^2*e^3 + 70*a^4*b*d*e^4 + 7*a^5*e^5) + 7*A*(5*b^6*d^6 + 54*a*b^5*d^5*e + 180*a^2*b^4*d^4*e^2 + 240*a^3*b^3*d^3*e^3 + 135*a^4*b^2*d^2*e^4 + 30*a^5*b*d*e^5 + 2*a^6*e^6))*x^7)/7 + (3*a^3*d^2*(7*a*B*d*(5*b^6*d^6 + 54*a*b^5*d^5*e + 180*a^2*b^4*d^4*e^2 + 240*a^3*b^3*d^3*e^3 + 135*a^4*b^2*d^2*e^4 + 30*a^5*b*d*e^5 + 2*a^6*e^6) + A*(20*b^7*d^7 + 315*a*b^6*d^6*e + 1512*a^2*b^5*d^5*e^2 + 2940*a^3*b^4*d^4*e^3 + 2520*a^4*b^3*d^3*e^4 + 945*a^5*b^2*d^2*e^5 + 140*a^6*b*d*e^6 + 6*a^7*e^7))*x^8)/4 + (a^2*d*(2*a*B*d*(20*b^7*d^7 + 315*a*b^6*d^6*e + 1512*a^2*b^5*d^5*e^2 + 2940*a^3*b^4*d^4*e^3 + 2520*a^4*b^3*d^3*e^4 + 945*a^5*b^2*d^2*e^5 + 140*a^6*b*d*e^6 + 6*a^7*e^7) + 3*A*(5*b^8*d^8 + 120*a*b^7*d^7*e + 840*a^2*b^6*d^6*e^2 + 2352*a^3*b^5*d^5*e^3 + 2940*a^4*b^4*d^4*e^4 + 1680*a^5*b^3*d^3*e^5 + 420*a^6*b^2*d^2*e^6 + 40*a^7*b*d*e^7 + a^8*e^8))*x^9)/3 + (a*(9*a*B*d*(5*b^8*d^8 + 120*a*b^7*d^7*e + 840*a^2*b^6*d^6*e^2 + 2352*a^3*b^5*d^5*e^3 + 2940*a^4*b^4*d^4*e^4 + 1680*a^5*b^3*d^3*e^5 + 420*a^6*b^2*d^2*e^6 + 40*a^7*b*d*e^7 + a^8*e^8) + A*(10*b^9*d^9 + 405*a*b^8*d^8*e + 4320*a^2*b^7*d^7*e^2 + 17640*a^3*b^6*d^6*e^3 + 31752*a^4*b^5*d^5*e^4 + 26460*a^5*b^4*d^4*e^5 + 10080*a^6*b^3*d^3*e^6 + 1620*a^7*b^2*d^2*e^7 + 90*a^8*b*d*e^8 + a^9*e^9))*x^10)/10 + ((a*B*(10*b^9*d^9 + 405*a*b^8*d^8*e + 4320*a^2*b^7*d^7*e^2 + 17640*a^3*b^6*d^6*e^3 + 31752*a^4*b^5*d^5*e^4 + 26460*a^5*b^4*d^4*e^5 + 10080*a^6*b^3*d^3*e^6 + 1620*a^7*b^2*d^2*e^7 + 90*a^8*b*d*e^8 + a^9*e^9) + A*b*(b^9*d^9 + 90*a*b^8*d^8*e + 1620*a^2*b^7*d^7*e^2 + 10080*a^3*b^6*d^6*e^3 + 26460*a^4*b^5*d^5*e^4 + 31752*a^5*b^4*d^4*e^5 + 17640*a^6*b^3*d^3*e^6 + 4320*a^7*b^2*d^2*e^7 + 405*a^8*b*d*e^8 + 10*a^9*e^9))*x^11)/11 + (b*(10*a^9*B*e^9 + 26460*a^4*b^5*d^4*e^4*(B*d + A*e) + 1080*a^7*b^2*d*e^7*(4*B*d + A*e) + 45*a^8*b*e^8*(9*B*d + A*e) + 10584*a^5*b^4*d^3*e^5*(3*B*d + 2*A*e) + 5040*a^3*b^6*d^5*e^3*(2*B*d + 3*A*e) + 2520*a^6*b^3*d^2*e^6*(7*B*d + 3*A*e) + 90*a*b^8*d^7*e*(B*d + 4*A*e) + 540*a^2*b^7*d^6*e^2*(3*B*d + 7*A*e) + b^9*d^8*(B*d + 9*A*e))*x^12)/12 + (3*b^2*e*(15*a^8*B*e^8 + 5040*a^3*b^5*d^4*e^3*(B*d + A*e) + 630*a^6*b^2*d*e^6*(4*B*d + A*e) + 40*a^7*b*e^7*(9*B*d + A*e) + 2940*a^4*b^4*d^3*e^4*(3*B*d + 2*A*e) + 630*a^2*b^6*d^5*e^2*(2*B*d + 3*A*e) + 1008*a^5*b^3*d^2*e^5*(7*B*d + 3*A*e) + 3*b^8*d^7*(B*d + 4*A*e) + 40*a*b^7*d^6*e*(3*B*d + 7*A*e))*x^13)/13 + (3*b^3*e^2*(20*a^7*B*e^7 + 945*a^2*b^5*d^4*e^2*(B*d + A*e) + 378*a^5*b^2*d*e^5*(4*B*d + A*e) + 35*a^6*b*e^6*(9*B*d + A*e) + 840*a^3*b^4*d^3*e^3*(3*B*d + 2*A*e) + 70*a*b^6*d^5*e*(2*B*d + 3*A*e) + 420*a^4*b^3*d^2*e^4*(7*B*d + 3*A*e) + 2*b^7*d^6*(3*B*d + 7*A*e))*x^14)/7 + (2*b^4*e^3*(35*a^6*B*e^6 + 210*a*b^5*d^4*e*(B*d + A*e) + 315*a^4*b^2*d*e^4*(4*B*d + A*e) + 42*a^5*b*e^5*(9*B*d + A*e) + 315*a^2*b^4*d^3*e^2*(3*B*d + 2*A*e) + 7*b^6*d^5*(2*B*d + 3*A*e) + 240*a^3*b^3*d^2*e^3*(7*B*d + 3*A*e))*x^15)/5 + (3*b^5*e^4*(42*a^5*B*e^5 + 21*b^5*d^4*(B*d + A*e) + 180*a^3*b^2*d*e^3*(4*B*d + A*e) + 35*a^4*b*e^4*(9*B*d + A*e) + 70*a*b^4*d^3*e*(3*B*d + 2*A*e) + 90*a^2*b^3*d^2*e^2*(7*B*d + 3*A*e))*x^16)/8 + (3*b^6*e^5*(70*a^4*B*e^4 + 135*a^2*b^2*d*e^2*(4*B*d + A*e) + 40*a^3*b*e^3*(9*B*d + A*e) + 14*b^4*d^3*(3*B*d + 2*A*e) + 40*a*b^3*d^2*e*(7*B*d + 3*A*e))*x^17)/17 + (b^7*e^6*(40*a^3*B*e^3 + 30*a*b^2*d*e*(4*B*d + A*e) + 15*a^2*b*e^2*(9*B*d + A*e) + 4*b^3*d^2*(7*B*d + 3*A*e))*x^18)/6 + (b^8*e^7*(45*a^2*B*e^2 + 9*b^2*d*(4*B*d + A*e) + 10*a*b*e*(9*B*d + A*e))*x^19)/19 + (b^9*e^8*(9*b*B*d + A*b*e + 10*a*B*e)*x^20)/20 + (b^10*B*e^9*x^21)/21","B",1
1080,1,2307,372,0.9092665,"\int (a+b x)^{10} (A+B x) (d+e x)^8 \, dx","Integrate[(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,"a^10*A*d^8*x + (a^9*d^7*(10*A*b*d + a*B*d + 8*a*A*e)*x^2)/2 + (a^8*d^6*(2*a*B*d*(5*b*d + 4*a*e) + A*(45*b^2*d^2 + 80*a*b*d*e + 28*a^2*e^2))*x^3)/3 + (a^7*d^5*(a*B*d*(45*b^2*d^2 + 80*a*b*d*e + 28*a^2*e^2) + 8*A*(15*b^3*d^3 + 45*a*b^2*d^2*e + 35*a^2*b*d*e^2 + 7*a^3*e^3))*x^4)/4 + (2*a^6*d^4*(4*a*B*d*(15*b^3*d^3 + 45*a*b^2*d^2*e + 35*a^2*b*d*e^2 + 7*a^3*e^3) + 5*A*(21*b^4*d^4 + 96*a*b^3*d^3*e + 126*a^2*b^2*d^2*e^2 + 56*a^3*b*d*e^3 + 7*a^4*e^4))*x^5)/5 + (a^5*d^3*(5*a*B*d*(21*b^4*d^4 + 96*a*b^3*d^3*e + 126*a^2*b^2*d^2*e^2 + 56*a^3*b*d*e^3 + 7*a^4*e^4) + 14*A*(9*b^5*d^5 + 60*a*b^4*d^4*e + 120*a^2*b^3*d^3*e^2 + 90*a^3*b^2*d^2*e^3 + 25*a^4*b*d*e^4 + 2*a^5*e^5))*x^6)/3 + 2*a^4*d^2*(2*a*B*d*(9*b^5*d^5 + 60*a*b^4*d^4*e + 120*a^2*b^3*d^3*e^2 + 90*a^3*b^2*d^2*e^3 + 25*a^4*b*d*e^4 + 2*a^5*e^5) + A*(15*b^6*d^6 + 144*a*b^5*d^5*e + 420*a^2*b^4*d^4*e^2 + 480*a^3*b^3*d^3*e^3 + 225*a^4*b^2*d^2*e^4 + 40*a^5*b*d*e^5 + 2*a^6*e^6))*x^7 + (a^3*d*(7*a*B*d*(15*b^6*d^6 + 144*a*b^5*d^5*e + 420*a^2*b^4*d^4*e^2 + 480*a^3*b^3*d^3*e^3 + 225*a^4*b^2*d^2*e^4 + 40*a^5*b*d*e^5 + 2*a^6*e^6) + 4*A*(15*b^7*d^7 + 210*a*b^6*d^6*e + 882*a^2*b^5*d^5*e^2 + 1470*a^3*b^4*d^4*e^3 + 1050*a^4*b^3*d^3*e^4 + 315*a^5*b^2*d^2*e^5 + 35*a^6*b*d*e^6 + a^7*e^7))*x^8)/4 + (a^2*(8*a*B*d*(15*b^7*d^7 + 210*a*b^6*d^6*e + 882*a^2*b^5*d^5*e^2 + 1470*a^3*b^4*d^4*e^3 + 1050*a^4*b^3*d^3*e^4 + 315*a^5*b^2*d^2*e^5 + 35*a^6*b*d*e^6 + a^7*e^7) + A*(45*b^8*d^8 + 960*a*b^7*d^7*e + 5880*a^2*b^6*d^6*e^2 + 14112*a^3*b^5*d^5*e^3 + 14700*a^4*b^4*d^4*e^4 + 6720*a^5*b^3*d^3*e^5 + 1260*a^6*b^2*d^2*e^6 + 80*a^7*b*d*e^7 + a^8*e^8))*x^9)/9 + (a*(10*A*b*(b^8*d^8 + 36*a*b^7*d^7*e + 336*a^2*b^6*d^6*e^2 + 1176*a^3*b^5*d^5*e^3 + 1764*a^4*b^4*d^4*e^4 + 1176*a^5*b^3*d^3*e^5 + 336*a^6*b^2*d^2*e^6 + 36*a^7*b*d*e^7 + a^8*e^8) + a*B*(45*b^8*d^8 + 960*a*b^7*d^7*e + 5880*a^2*b^6*d^6*e^2 + 14112*a^3*b^5*d^5*e^3 + 14700*a^4*b^4*d^4*e^4 + 6720*a^5*b^3*d^3*e^5 + 1260*a^6*b^2*d^2*e^6 + 80*a^7*b*d*e^7 + a^8*e^8))*x^10)/10 + (b*(10*a*B*(b^8*d^8 + 36*a*b^7*d^7*e + 336*a^2*b^6*d^6*e^2 + 1176*a^3*b^5*d^5*e^3 + 1764*a^4*b^4*d^4*e^4 + 1176*a^5*b^3*d^3*e^5 + 336*a^6*b^2*d^2*e^6 + 36*a^7*b*d*e^7 + a^8*e^8) + A*b*(b^8*d^8 + 80*a*b^7*d^7*e + 1260*a^2*b^6*d^6*e^2 + 6720*a^3*b^5*d^5*e^3 + 14700*a^4*b^4*d^4*e^4 + 14112*a^5*b^3*d^3*e^5 + 5880*a^6*b^2*d^2*e^6 + 960*a^7*b*d*e^7 + 45*a^8*e^8))*x^11)/11 + (b^2*(45*a^8*B*e^8 + 7056*a^5*b^3*d^2*e^5*(2*B*d + A*e) + 120*a^7*b*e^7*(8*B*d + A*e) + 1260*a^2*b^6*d^5*e^2*(B*d + 2*A*e) + 840*a^6*b^2*d*e^6*(7*B*d + 2*A*e) + 2940*a^4*b^4*d^3*e^4*(5*B*d + 4*A*e) + 1680*a^3*b^5*d^4*e^3*(4*B*d + 5*A*e) + 40*a*b^7*d^6*e*(2*B*d + 7*A*e) + b^8*d^7*(B*d + 8*A*e))*x^12)/12 + (2*b^3*e*(60*a^7*B*e^7 + 2940*a^4*b^3*d^2*e^4*(2*B*d + A*e) + 105*a^6*b*e^6*(8*B*d + A*e) + 140*a*b^6*d^5*e*(B*d + 2*A*e) + 504*a^5*b^2*d*e^5*(7*B*d + 2*A*e) + 840*a^3*b^4*d^3*e^3*(5*B*d + 4*A*e) + 315*a^2*b^5*d^4*e^2*(4*B*d + 5*A*e) + 2*b^7*d^6*(2*B*d + 7*A*e))*x^13)/13 + b^4*e^2*(15*a^6*B*e^6 + 240*a^3*b^3*d^2*e^3*(2*B*d + A*e) + 18*a^5*b*e^5*(8*B*d + A*e) + 2*b^6*d^5*(B*d + 2*A*e) + 60*a^4*b^2*d*e^4*(7*B*d + 2*A*e) + 45*a^2*b^4*d^3*e^2*(5*B*d + 4*A*e) + 10*a*b^5*d^4*e*(4*B*d + 5*A*e))*x^14 + (2*b^5*e^3*(126*a^5*B*e^5 + 630*a^2*b^3*d^2*e^2*(2*B*d + A*e) + 105*a^4*b*e^4*(8*B*d + A*e) + 240*a^3*b^2*d*e^3*(7*B*d + 2*A*e) + 70*a*b^4*d^3*e*(5*B*d + 4*A*e) + 7*b^5*d^4*(4*B*d + 5*A*e))*x^15)/15 + (b^6*e^4*(105*a^4*B*e^4 + 140*a*b^3*d^2*e*(2*B*d + A*e) + 60*a^3*b*e^3*(8*B*d + A*e) + 90*a^2*b^2*d*e^2*(7*B*d + 2*A*e) + 7*b^4*d^3*(5*B*d + 4*A*e))*x^16)/8 + (b^7*e^5*(120*a^3*B*e^3 + 28*b^3*d^2*(2*B*d + A*e) + 45*a^2*b*e^2*(8*B*d + A*e) + 40*a*b^2*d*e*(7*B*d + 2*A*e))*x^17)/17 + (b^8*e^6*(45*a^2*B*e^2 + 10*a*b*e*(8*B*d + A*e) + 4*b^2*d*(7*B*d + 2*A*e))*x^18)/18 + (b^9*e^7*(8*b*B*d + A*b*e + 10*a*B*e)*x^19)/19 + (b^10*B*e^8*x^20)/20","B",1
1081,1,2034,329,0.8039187,"\int (a+b x)^{10} (A+B x) (d+e x)^7 \, dx","Integrate[(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,"a^10*A*d^7*x + (a^9*d^6*(10*A*b*d + a*B*d + 7*a*A*e)*x^2)/2 + (a^8*d^5*(a*B*d*(10*b*d + 7*a*e) + A*(45*b^2*d^2 + 70*a*b*d*e + 21*a^2*e^2))*x^3)/3 + (a^7*d^4*(a*B*d*(45*b^2*d^2 + 70*a*b*d*e + 21*a^2*e^2) + 5*A*(24*b^3*d^3 + 63*a*b^2*d^2*e + 42*a^2*b*d*e^2 + 7*a^3*e^3))*x^4)/4 + a^6*d^3*(a*B*d*(24*b^3*d^3 + 63*a*b^2*d^2*e + 42*a^2*b*d*e^2 + 7*a^3*e^3) + 7*A*(6*b^4*d^4 + 24*a*b^3*d^3*e + 27*a^2*b^2*d^2*e^2 + 10*a^3*b*d*e^3 + a^4*e^4))*x^5 + (7*a^5*d^2*(5*a*B*d*(6*b^4*d^4 + 24*a*b^3*d^3*e + 27*a^2*b^2*d^2*e^2 + 10*a^3*b*d*e^3 + a^4*e^4) + A*(36*b^5*d^5 + 210*a*b^4*d^4*e + 360*a^2*b^3*d^3*e^2 + 225*a^3*b^2*d^2*e^3 + 50*a^4*b*d*e^4 + 3*a^5*e^5))*x^6)/6 + a^4*d*(a*B*d*(36*b^5*d^5 + 210*a*b^4*d^4*e + 360*a^2*b^3*d^3*e^2 + 225*a^3*b^2*d^2*e^3 + 50*a^4*b*d*e^4 + 3*a^5*e^5) + A*(30*b^6*d^6 + 252*a*b^5*d^5*e + 630*a^2*b^4*d^4*e^2 + 600*a^3*b^3*d^3*e^3 + 225*a^4*b^2*d^2*e^4 + 30*a^5*b*d*e^5 + a^6*e^6))*x^7 + (a^3*(7*a*B*d*(30*b^6*d^6 + 252*a*b^5*d^5*e + 630*a^2*b^4*d^4*e^2 + 600*a^3*b^3*d^3*e^3 + 225*a^4*b^2*d^2*e^4 + 30*a^5*b*d*e^5 + a^6*e^6) + A*(120*b^7*d^7 + 1470*a*b^6*d^6*e + 5292*a^2*b^5*d^5*e^2 + 7350*a^3*b^4*d^4*e^3 + 4200*a^4*b^3*d^3*e^4 + 945*a^5*b^2*d^2*e^5 + 70*a^6*b*d*e^6 + a^7*e^7))*x^8)/8 + (a^2*(a*B*(120*b^7*d^7 + 1470*a*b^6*d^6*e + 5292*a^2*b^5*d^5*e^2 + 7350*a^3*b^4*d^4*e^3 + 4200*a^4*b^3*d^3*e^4 + 945*a^5*b^2*d^2*e^5 + 70*a^6*b*d*e^6 + a^7*e^7) + 5*A*b*(9*b^7*d^7 + 168*a*b^6*d^6*e + 882*a^2*b^5*d^5*e^2 + 1764*a^3*b^4*d^4*e^3 + 1470*a^4*b^3*d^3*e^4 + 504*a^5*b^2*d^2*e^5 + 63*a^6*b*d*e^6 + 2*a^7*e^7))*x^9)/9 + (a*b*(a*B*(9*b^7*d^7 + 168*a*b^6*d^6*e + 882*a^2*b^5*d^5*e^2 + 1764*a^3*b^4*d^4*e^3 + 1470*a^4*b^3*d^3*e^4 + 504*a^5*b^2*d^2*e^5 + 63*a^6*b*d*e^6 + 2*a^7*e^7) + A*b*(2*b^7*d^7 + 63*a*b^6*d^6*e + 504*a^2*b^5*d^5*e^2 + 1470*a^3*b^4*d^4*e^3 + 1764*a^4*b^3*d^3*e^4 + 882*a^5*b^2*d^2*e^5 + 168*a^6*b*d*e^6 + 9*a^7*e^7))*x^10)/2 + (b^2*(5*a*B*(2*b^7*d^7 + 63*a*b^6*d^6*e + 504*a^2*b^5*d^5*e^2 + 1470*a^3*b^4*d^4*e^3 + 1764*a^4*b^3*d^3*e^4 + 882*a^5*b^2*d^2*e^5 + 168*a^6*b*d*e^6 + 9*a^7*e^7) + A*b*(b^7*d^7 + 70*a*b^6*d^6*e + 945*a^2*b^5*d^5*e^2 + 4200*a^3*b^4*d^4*e^3 + 7350*a^4*b^3*d^3*e^4 + 5292*a^5*b^2*d^2*e^5 + 1470*a^6*b*d*e^6 + 120*a^7*e^7))*x^11)/11 + (b^3*(120*a^7*B*e^7 + 4200*a^3*b^4*d^3*e^3*(B*d + A*e) + 1764*a^5*b^2*d*e^5*(3*B*d + A*e) + 210*a^6*b*e^6*(7*B*d + A*e) + 70*a*b^6*d^5*e*(B*d + 3*A*e) + 1470*a^4*b^3*d^2*e^4*(5*B*d + 3*A*e) + 315*a^2*b^5*d^4*e^2*(3*B*d + 5*A*e) + b^7*d^6*(B*d + 7*A*e))*x^12)/12 + (7*b^4*e*(30*a^6*B*e^6 + 225*a^2*b^4*d^3*e^2*(B*d + A*e) + 210*a^4*b^2*d*e^4*(3*B*d + A*e) + 36*a^5*b*e^5*(7*B*d + A*e) + b^6*d^5*(B*d + 3*A*e) + 120*a^3*b^3*d^2*e^3*(5*B*d + 3*A*e) + 10*a*b^5*d^4*e*(3*B*d + 5*A*e))*x^13)/13 + (b^5*e^2*(36*a^5*B*e^5 + 50*a*b^4*d^3*e*(B*d + A*e) + 120*a^3*b^2*d*e^3*(3*B*d + A*e) + 30*a^4*b*e^4*(7*B*d + A*e) + 45*a^2*b^3*d^2*e^2*(5*B*d + 3*A*e) + b^5*d^4*(3*B*d + 5*A*e))*x^14)/2 + (b^6*e^3*(42*a^4*B*e^4 + 7*b^4*d^3*(B*d + A*e) + 63*a^2*b^2*d*e^2*(3*B*d + A*e) + 24*a^3*b*e^3*(7*B*d + A*e) + 14*a*b^3*d^2*e*(5*B*d + 3*A*e))*x^15)/3 + (b^7*e^4*(120*a^3*B*e^3 + 70*a*b^2*d*e*(3*B*d + A*e) + 45*a^2*b*e^2*(7*B*d + A*e) + 7*b^3*d^2*(5*B*d + 3*A*e))*x^16)/16 + (b^8*e^5*(45*a^2*B*e^2 + 7*b^2*d*(3*B*d + A*e) + 10*a*b*e*(7*B*d + A*e))*x^17)/17 + (b^9*e^6*(7*b*B*d + A*b*e + 10*a*B*e)*x^18)/18 + (b^10*B*e^7*x^19)/19","B",1
1082,1,1788,290,0.6678179,"\int (a+b x)^{10} (A+B x) (d+e x)^6 \, dx","Integrate[(a + b*x)^10*(A + B*x)*(d + e*x)^6,x]","\frac{1}{18} b^{10} B e^6 x^{18}+\frac{1}{17} b^9 e^5 (6 b B d+A b e+10 a B e) x^{17}+\frac{1}{16} b^8 e^4 \left(3 d (5 B d+2 A e) b^2+10 a e (6 B d+A e) b+45 a^2 B e^2\right) x^{16}+\frac{1}{3} b^7 e^3 \left(d^2 (4 B d+3 A e) b^3+6 a d e (5 B d+2 A e) b^2+9 a^2 e^2 (6 B d+A e) b+24 a^3 B e^3\right) x^{15}+\frac{5}{14} b^6 e^2 \left(d^3 (3 B d+4 A e) b^4+10 a d^2 e (4 B d+3 A e) b^3+27 a^2 d e^2 (5 B d+2 A e) b^2+24 a^3 e^3 (6 B d+A e) b+42 a^4 B e^4\right) x^{14}+\frac{1}{13} b^5 e \left(3 d^4 (2 B d+5 A e) b^5+50 a d^3 e (3 B d+4 A e) b^4+225 a^2 d^2 e^2 (4 B d+3 A e) b^3+360 a^3 d e^3 (5 B d+2 A e) b^2+210 a^4 e^4 (6 B d+A e) b+252 a^5 B e^5\right) x^{13}+\frac{1}{12} b^4 \left(d^5 (B d+6 A e) b^6+30 a d^4 e (2 B d+5 A e) b^5+225 a^2 d^3 e^2 (3 B d+4 A e) b^4+600 a^3 d^2 e^3 (4 B d+3 A e) b^3+630 a^4 d e^4 (5 B d+2 A e) b^2+252 a^5 e^5 (6 B d+A e) b+210 a^6 B e^6\right) x^{12}+\frac{1}{11} b^3 \left(10 a B \left(b^6 d^6+27 a b^5 e d^5+180 a^2 b^4 e^2 d^4+420 a^3 b^3 e^3 d^3+378 a^4 b^2 e^4 d^2+126 a^5 b e^5 d+12 a^6 e^6\right)+A b \left(b^6 d^6+60 a b^5 e d^5+675 a^2 b^4 e^2 d^4+2400 a^3 b^3 e^3 d^3+3150 a^4 b^2 e^4 d^2+1512 a^5 b e^5 d+210 a^6 e^6\right)\right) x^{11}+\frac{1}{2} a b^2 \left(9 a B \left(b^6 d^6+16 a b^5 e d^5+70 a^2 b^4 e^2 d^4+112 a^3 b^3 e^3 d^3+70 a^4 b^2 e^4 d^2+16 a^5 b e^5 d+a^6 e^6\right)+2 A b \left(b^6 d^6+27 a b^5 e d^5+180 a^2 b^4 e^2 d^4+420 a^3 b^3 e^3 d^3+378 a^4 b^2 e^4 d^2+126 a^5 b e^5 d+12 a^6 e^6\right)\right) x^{10}+\frac{5}{9} a^2 b \left(9 A b \left(b^6 d^6+16 a b^5 e d^5+70 a^2 b^4 e^2 d^4+112 a^3 b^3 e^3 d^3+70 a^4 b^2 e^4 d^2+16 a^5 b e^5 d+a^6 e^6\right)+2 a B \left(12 b^6 d^6+126 a b^5 e d^5+378 a^2 b^4 e^2 d^4+420 a^3 b^3 e^3 d^3+180 a^4 b^2 e^4 d^2+27 a^5 b e^5 d+a^6 e^6\right)\right) x^9+\frac{1}{8} a^3 \left(10 A b \left(12 b^6 d^6+126 a b^5 e d^5+378 a^2 b^4 e^2 d^4+420 a^3 b^3 e^3 d^3+180 a^4 b^2 e^4 d^2+27 a^5 b e^5 d+a^6 e^6\right)+a B \left(210 b^6 d^6+1512 a b^5 e d^5+3150 a^2 b^4 e^2 d^4+2400 a^3 b^3 e^3 d^3+675 a^4 b^2 e^4 d^2+60 a^5 b e^5 d+a^6 e^6\right)\right) x^8+\frac{1}{7} a^4 \left(6 a B d \left(42 b^5 d^5+210 a b^4 e d^4+300 a^2 b^3 e^2 d^3+150 a^3 b^2 e^3 d^2+25 a^4 b e^4 d+a^5 e^5\right)+A \left(210 b^6 d^6+1512 a b^5 e d^5+3150 a^2 b^4 e^2 d^4+2400 a^3 b^3 e^3 d^3+675 a^4 b^2 e^4 d^2+60 a^5 b e^5 d+a^6 e^6\right)\right) x^7+\frac{1}{6} a^5 d \left(5 a B d \left(42 b^4 d^4+144 a b^3 e d^3+135 a^2 b^2 e^2 d^2+40 a^3 b e^3 d+3 a^4 e^4\right)+6 A \left(42 b^5 d^5+210 a b^4 e d^4+300 a^2 b^3 e^2 d^3+150 a^3 b^2 e^3 d^2+25 a^4 b e^4 d+a^5 e^5\right)\right) x^6+a^6 d^2 \left(2 a B d \left(12 b^3 d^3+27 a b^2 e d^2+15 a^2 b e^2 d+2 a^3 e^3\right)+A \left(42 b^4 d^4+144 a b^3 e d^3+135 a^2 b^2 e^2 d^2+40 a^3 b e^3 d+3 a^4 e^4\right)\right) x^5+\frac{5}{4} a^7 d^3 \left(3 a B d \left(3 b^2 d^2+4 a b e d+a^2 e^2\right)+A \left(24 b^3 d^3+54 a b^2 e d^2+30 a^2 b e^2 d+4 a^3 e^3\right)\right) x^4+\frac{1}{3} a^8 d^4 \left(2 a B d (5 b d+3 a e)+15 A \left(3 b^2 d^2+4 a b e d+a^2 e^2\right)\right) x^3+\frac{1}{2} a^9 d^5 (10 A b d+a B d+6 a A e) x^2+a^{10} A d^6 x","\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,"a^10*A*d^6*x + (a^9*d^5*(10*A*b*d + a*B*d + 6*a*A*e)*x^2)/2 + (a^8*d^4*(2*a*B*d*(5*b*d + 3*a*e) + 15*A*(3*b^2*d^2 + 4*a*b*d*e + a^2*e^2))*x^3)/3 + (5*a^7*d^3*(3*a*B*d*(3*b^2*d^2 + 4*a*b*d*e + a^2*e^2) + A*(24*b^3*d^3 + 54*a*b^2*d^2*e + 30*a^2*b*d*e^2 + 4*a^3*e^3))*x^4)/4 + a^6*d^2*(2*a*B*d*(12*b^3*d^3 + 27*a*b^2*d^2*e + 15*a^2*b*d*e^2 + 2*a^3*e^3) + A*(42*b^4*d^4 + 144*a*b^3*d^3*e + 135*a^2*b^2*d^2*e^2 + 40*a^3*b*d*e^3 + 3*a^4*e^4))*x^5 + (a^5*d*(5*a*B*d*(42*b^4*d^4 + 144*a*b^3*d^3*e + 135*a^2*b^2*d^2*e^2 + 40*a^3*b*d*e^3 + 3*a^4*e^4) + 6*A*(42*b^5*d^5 + 210*a*b^4*d^4*e + 300*a^2*b^3*d^3*e^2 + 150*a^3*b^2*d^2*e^3 + 25*a^4*b*d*e^4 + a^5*e^5))*x^6)/6 + (a^4*(6*a*B*d*(42*b^5*d^5 + 210*a*b^4*d^4*e + 300*a^2*b^3*d^3*e^2 + 150*a^3*b^2*d^2*e^3 + 25*a^4*b*d*e^4 + a^5*e^5) + A*(210*b^6*d^6 + 1512*a*b^5*d^5*e + 3150*a^2*b^4*d^4*e^2 + 2400*a^3*b^3*d^3*e^3 + 675*a^4*b^2*d^2*e^4 + 60*a^5*b*d*e^5 + a^6*e^6))*x^7)/7 + (a^3*(10*A*b*(12*b^6*d^6 + 126*a*b^5*d^5*e + 378*a^2*b^4*d^4*e^2 + 420*a^3*b^3*d^3*e^3 + 180*a^4*b^2*d^2*e^4 + 27*a^5*b*d*e^5 + a^6*e^6) + a*B*(210*b^6*d^6 + 1512*a*b^5*d^5*e + 3150*a^2*b^4*d^4*e^2 + 2400*a^3*b^3*d^3*e^3 + 675*a^4*b^2*d^2*e^4 + 60*a^5*b*d*e^5 + a^6*e^6))*x^8)/8 + (5*a^2*b*(9*A*b*(b^6*d^6 + 16*a*b^5*d^5*e + 70*a^2*b^4*d^4*e^2 + 112*a^3*b^3*d^3*e^3 + 70*a^4*b^2*d^2*e^4 + 16*a^5*b*d*e^5 + a^6*e^6) + 2*a*B*(12*b^6*d^6 + 126*a*b^5*d^5*e + 378*a^2*b^4*d^4*e^2 + 420*a^3*b^3*d^3*e^3 + 180*a^4*b^2*d^2*e^4 + 27*a^5*b*d*e^5 + a^6*e^6))*x^9)/9 + (a*b^2*(9*a*B*(b^6*d^6 + 16*a*b^5*d^5*e + 70*a^2*b^4*d^4*e^2 + 112*a^3*b^3*d^3*e^3 + 70*a^4*b^2*d^2*e^4 + 16*a^5*b*d*e^5 + a^6*e^6) + 2*A*b*(b^6*d^6 + 27*a*b^5*d^5*e + 180*a^2*b^4*d^4*e^2 + 420*a^3*b^3*d^3*e^3 + 378*a^4*b^2*d^2*e^4 + 126*a^5*b*d*e^5 + 12*a^6*e^6))*x^10)/2 + (b^3*(10*a*B*(b^6*d^6 + 27*a*b^5*d^5*e + 180*a^2*b^4*d^4*e^2 + 420*a^3*b^3*d^3*e^3 + 378*a^4*b^2*d^2*e^4 + 126*a^5*b*d*e^5 + 12*a^6*e^6) + A*b*(b^6*d^6 + 60*a*b^5*d^5*e + 675*a^2*b^4*d^4*e^2 + 2400*a^3*b^3*d^3*e^3 + 3150*a^4*b^2*d^2*e^4 + 1512*a^5*b*d*e^5 + 210*a^6*e^6))*x^11)/11 + (b^4*(210*a^6*B*e^6 + 252*a^5*b*e^5*(6*B*d + A*e) + 630*a^4*b^2*d*e^4*(5*B*d + 2*A*e) + 600*a^3*b^3*d^2*e^3*(4*B*d + 3*A*e) + 225*a^2*b^4*d^3*e^2*(3*B*d + 4*A*e) + 30*a*b^5*d^4*e*(2*B*d + 5*A*e) + b^6*d^5*(B*d + 6*A*e))*x^12)/12 + (b^5*e*(252*a^5*B*e^5 + 210*a^4*b*e^4*(6*B*d + A*e) + 360*a^3*b^2*d*e^3*(5*B*d + 2*A*e) + 225*a^2*b^3*d^2*e^2*(4*B*d + 3*A*e) + 50*a*b^4*d^3*e*(3*B*d + 4*A*e) + 3*b^5*d^4*(2*B*d + 5*A*e))*x^13)/13 + (5*b^6*e^2*(42*a^4*B*e^4 + 24*a^3*b*e^3*(6*B*d + A*e) + 27*a^2*b^2*d*e^2*(5*B*d + 2*A*e) + 10*a*b^3*d^2*e*(4*B*d + 3*A*e) + b^4*d^3*(3*B*d + 4*A*e))*x^14)/14 + (b^7*e^3*(24*a^3*B*e^3 + 9*a^2*b*e^2*(6*B*d + A*e) + 6*a*b^2*d*e*(5*B*d + 2*A*e) + b^3*d^2*(4*B*d + 3*A*e))*x^15)/3 + (b^8*e^4*(45*a^2*B*e^2 + 10*a*b*e*(6*B*d + A*e) + 3*b^2*d*(5*B*d + 2*A*e))*x^16)/16 + (b^9*e^5*(6*b*B*d + A*b*e + 10*a*B*e)*x^17)/17 + (b^10*B*e^6*x^18)/18","B",1
1083,1,1509,243,0.5190798,"\int (a+b x)^{10} (A+B x) (d+e x)^5 \, dx","Integrate[(a + b*x)^10*(A + B*x)*(d + e*x)^5,x]","\frac{1}{17} b^{10} B e^5 x^{17}+\frac{1}{16} b^9 e^4 (5 b B d+A b e+10 a B e) x^{16}+\frac{1}{3} b^8 e^3 \left(d (2 B d+A e) b^2+2 a e (5 B d+A e) b+9 a^2 B e^2\right) x^{15}+\frac{5}{14} b^7 e^2 \left(2 d^2 (B d+A e) b^3+10 a d e (2 B d+A e) b^2+9 a^2 e^2 (5 B d+A e) b+24 a^3 B e^3\right) x^{14}+\frac{5}{13} b^6 e \left(d^3 (B d+2 A e) b^4+20 a d^2 e (B d+A e) b^3+45 a^2 d e^2 (2 B d+A e) b^2+24 a^3 e^3 (5 B d+A e) b+42 a^4 B e^4\right) x^{13}+\frac{1}{12} b^5 \left(d^4 (B d+5 A e) b^5+50 a d^3 e (B d+2 A e) b^4+450 a^2 d^2 e^2 (B d+A e) b^3+600 a^3 d e^3 (2 B d+A e) b^2+210 a^4 e^4 (5 B d+A e) b+252 a^5 B e^5\right) x^{12}+\frac{1}{11} b^4 \left(5 a B \left(2 b^5 d^5+45 a b^4 e d^4+240 a^2 b^3 e^2 d^3+420 a^3 b^2 e^3 d^2+252 a^4 b e^4 d+42 a^5 e^5\right)+A b \left(b^5 d^5+50 a b^4 e d^4+450 a^2 b^3 e^2 d^3+1200 a^3 b^2 e^3 d^2+1050 a^4 b e^4 d+252 a^5 e^5\right)\right) x^{11}+\frac{1}{2} a b^3 \left(3 a B \left(3 b^5 d^5+40 a b^4 e d^4+140 a^2 b^3 e^2 d^3+168 a^3 b^2 e^3 d^2+70 a^4 b e^4 d+8 a^5 e^5\right)+A b \left(2 b^5 d^5+45 a b^4 e d^4+240 a^2 b^3 e^2 d^3+420 a^3 b^2 e^3 d^2+252 a^4 b e^4 d+42 a^5 e^5\right)\right) x^{10}+\frac{5}{3} a^2 b^2 \left(a B \left(8 b^5 d^5+70 a b^4 e d^4+168 a^2 b^3 e^2 d^3+140 a^3 b^2 e^3 d^2+40 a^4 b e^4 d+3 a^5 e^5\right)+A b \left(3 b^5 d^5+40 a b^4 e d^4+140 a^2 b^3 e^2 d^3+168 a^3 b^2 e^3 d^2+70 a^4 b e^4 d+8 a^5 e^5\right)\right) x^9+\frac{5}{8} a^3 b \left(a B \left(42 b^5 d^5+252 a b^4 e d^4+420 a^2 b^3 e^2 d^3+240 a^3 b^2 e^3 d^2+45 a^4 b e^4 d+2 a^5 e^5\right)+3 A b \left(8 b^5 d^5+70 a b^4 e d^4+168 a^2 b^3 e^2 d^3+140 a^3 b^2 e^3 d^2+40 a^4 b e^4 d+3 a^5 e^5\right)\right) x^8+\frac{1}{7} a^4 \left(a B \left(252 b^5 d^5+1050 a b^4 e d^4+1200 a^2 b^3 e^2 d^3+450 a^3 b^2 e^3 d^2+50 a^4 b e^4 d+a^5 e^5\right)+5 A b \left(42 b^5 d^5+252 a b^4 e d^4+420 a^2 b^3 e^2 d^3+240 a^3 b^2 e^3 d^2+45 a^4 b e^4 d+2 a^5 e^5\right)\right) x^7+\frac{1}{6} a^5 \left(5 a B d \left(42 b^4 d^4+120 a b^3 e d^3+90 a^2 b^2 e^2 d^2+20 a^3 b e^3 d+a^4 e^4\right)+A \left(252 b^5 d^5+1050 a b^4 e d^4+1200 a^2 b^3 e^2 d^3+450 a^3 b^2 e^3 d^2+50 a^4 b e^4 d+a^5 e^5\right)\right) x^6+a^6 d \left(a B d \left(24 b^3 d^3+45 a b^2 e d^2+20 a^2 b e^2 d+2 a^3 e^3\right)+A \left(42 b^4 d^4+120 a b^3 e d^3+90 a^2 b^2 e^2 d^2+20 a^3 b e^3 d+a^4 e^4\right)\right) x^5+\frac{5}{4} a^7 d^2 \left(a B d \left(9 b^2 d^2+10 a b e d+2 a^2 e^2\right)+A \left(24 b^3 d^3+45 a b^2 e d^2+20 a^2 b e^2 d+2 a^3 e^3\right)\right) x^4+\frac{5}{3} a^8 d^3 \left(a B d (2 b d+a e)+A \left(9 b^2 d^2+10 a b e d+2 a^2 e^2\right)\right) x^3+\frac{1}{2} a^9 d^4 (a B d+5 A (2 b d+a e)) x^2+a^{10} A d^5 x","\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,"a^10*A*d^5*x + (a^9*d^4*(a*B*d + 5*A*(2*b*d + a*e))*x^2)/2 + (5*a^8*d^3*(a*B*d*(2*b*d + a*e) + A*(9*b^2*d^2 + 10*a*b*d*e + 2*a^2*e^2))*x^3)/3 + (5*a^7*d^2*(a*B*d*(9*b^2*d^2 + 10*a*b*d*e + 2*a^2*e^2) + A*(24*b^3*d^3 + 45*a*b^2*d^2*e + 20*a^2*b*d*e^2 + 2*a^3*e^3))*x^4)/4 + a^6*d*(a*B*d*(24*b^3*d^3 + 45*a*b^2*d^2*e + 20*a^2*b*d*e^2 + 2*a^3*e^3) + A*(42*b^4*d^4 + 120*a*b^3*d^3*e + 90*a^2*b^2*d^2*e^2 + 20*a^3*b*d*e^3 + a^4*e^4))*x^5 + (a^5*(5*a*B*d*(42*b^4*d^4 + 120*a*b^3*d^3*e + 90*a^2*b^2*d^2*e^2 + 20*a^3*b*d*e^3 + a^4*e^4) + A*(252*b^5*d^5 + 1050*a*b^4*d^4*e + 1200*a^2*b^3*d^3*e^2 + 450*a^3*b^2*d^2*e^3 + 50*a^4*b*d*e^4 + a^5*e^5))*x^6)/6 + (a^4*(a*B*(252*b^5*d^5 + 1050*a*b^4*d^4*e + 1200*a^2*b^3*d^3*e^2 + 450*a^3*b^2*d^2*e^3 + 50*a^4*b*d*e^4 + a^5*e^5) + 5*A*b*(42*b^5*d^5 + 252*a*b^4*d^4*e + 420*a^2*b^3*d^3*e^2 + 240*a^3*b^2*d^2*e^3 + 45*a^4*b*d*e^4 + 2*a^5*e^5))*x^7)/7 + (5*a^3*b*(a*B*(42*b^5*d^5 + 252*a*b^4*d^4*e + 420*a^2*b^3*d^3*e^2 + 240*a^3*b^2*d^2*e^3 + 45*a^4*b*d*e^4 + 2*a^5*e^5) + 3*A*b*(8*b^5*d^5 + 70*a*b^4*d^4*e + 168*a^2*b^3*d^3*e^2 + 140*a^3*b^2*d^2*e^3 + 40*a^4*b*d*e^4 + 3*a^5*e^5))*x^8)/8 + (5*a^2*b^2*(a*B*(8*b^5*d^5 + 70*a*b^4*d^4*e + 168*a^2*b^3*d^3*e^2 + 140*a^3*b^2*d^2*e^3 + 40*a^4*b*d*e^4 + 3*a^5*e^5) + A*b*(3*b^5*d^5 + 40*a*b^4*d^4*e + 140*a^2*b^3*d^3*e^2 + 168*a^3*b^2*d^2*e^3 + 70*a^4*b*d*e^4 + 8*a^5*e^5))*x^9)/3 + (a*b^3*(3*a*B*(3*b^5*d^5 + 40*a*b^4*d^4*e + 140*a^2*b^3*d^3*e^2 + 168*a^3*b^2*d^2*e^3 + 70*a^4*b*d*e^4 + 8*a^5*e^5) + A*b*(2*b^5*d^5 + 45*a*b^4*d^4*e + 240*a^2*b^3*d^3*e^2 + 420*a^3*b^2*d^2*e^3 + 252*a^4*b*d*e^4 + 42*a^5*e^5))*x^10)/2 + (b^4*(5*a*B*(2*b^5*d^5 + 45*a*b^4*d^4*e + 240*a^2*b^3*d^3*e^2 + 420*a^3*b^2*d^2*e^3 + 252*a^4*b*d*e^4 + 42*a^5*e^5) + A*b*(b^5*d^5 + 50*a*b^4*d^4*e + 450*a^2*b^3*d^3*e^2 + 1200*a^3*b^2*d^2*e^3 + 1050*a^4*b*d*e^4 + 252*a^5*e^5))*x^11)/11 + (b^5*(252*a^5*B*e^5 + 450*a^2*b^3*d^2*e^2*(B*d + A*e) + 600*a^3*b^2*d*e^3*(2*B*d + A*e) + 210*a^4*b*e^4*(5*B*d + A*e) + 50*a*b^4*d^3*e*(B*d + 2*A*e) + b^5*d^4*(B*d + 5*A*e))*x^12)/12 + (5*b^6*e*(42*a^4*B*e^4 + 20*a*b^3*d^2*e*(B*d + A*e) + 45*a^2*b^2*d*e^2*(2*B*d + A*e) + 24*a^3*b*e^3*(5*B*d + A*e) + b^4*d^3*(B*d + 2*A*e))*x^13)/13 + (5*b^7*e^2*(24*a^3*B*e^3 + 2*b^3*d^2*(B*d + A*e) + 10*a*b^2*d*e*(2*B*d + A*e) + 9*a^2*b*e^2*(5*B*d + A*e))*x^14)/14 + (b^8*e^3*(9*a^2*B*e^2 + b^2*d*(2*B*d + A*e) + 2*a*b*e*(5*B*d + A*e))*x^15)/3 + (b^9*e^4*(5*b*B*d + A*b*e + 10*a*B*e)*x^16)/16 + (b^10*B*e^5*x^17)/17","B",1
1084,1,1098,204,0.7002926,"\int (a+b x)^{10} (A+B x) (d+e x)^4 \, dx","Integrate[(a + b*x)^10*(A + B*x)*(d + e*x)^4,x]","\frac{x \left(8008 \left(6 A \left(5 d^4+10 e x d^3+10 e^2 x^2 d^2+5 e^3 x^3 d+e^4 x^4\right)+B x \left(15 d^4+40 e x d^3+45 e^2 x^2 d^2+24 e^3 x^3 d+5 e^4 x^4\right)\right) a^{10}+11440 b x \left(7 A \left(15 d^4+40 e x d^3+45 e^2 x^2 d^2+24 e^3 x^3 d+5 e^4 x^4\right)+2 B x \left(35 d^4+105 e x d^3+126 e^2 x^2 d^2+70 e^3 x^3 d+15 e^4 x^4\right)\right) a^9+12870 b^2 x^2 \left(8 A \left(35 d^4+105 e x d^3+126 e^2 x^2 d^2+70 e^3 x^3 d+15 e^4 x^4\right)+3 B x \left(70 d^4+224 e x d^3+280 e^2 x^2 d^2+160 e^3 x^3 d+35 e^4 x^4\right)\right) a^8+11440 b^3 x^3 \left(9 A \left(70 d^4+224 e x d^3+280 e^2 x^2 d^2+160 e^3 x^3 d+35 e^4 x^4\right)+4 B x \left(126 d^4+420 e x d^3+540 e^2 x^2 d^2+315 e^3 x^3 d+70 e^4 x^4\right)\right) a^7+40040 b^4 x^4 \left(2 A \left(126 d^4+420 e x d^3+540 e^2 x^2 d^2+315 e^3 x^3 d+70 e^4 x^4\right)+B x \left(210 d^4+720 e x d^3+945 e^2 x^2 d^2+560 e^3 x^3 d+126 e^4 x^4\right)\right) a^6+4368 b^5 x^5 \left(11 A \left(210 d^4+720 e x d^3+945 e^2 x^2 d^2+560 e^3 x^3 d+126 e^4 x^4\right)+6 B x \left(330 d^4+1155 e x d^3+1540 e^2 x^2 d^2+924 e^3 x^3 d+210 e^4 x^4\right)\right) a^5+1820 b^6 x^6 \left(12 A \left(330 d^4+1155 e x d^3+1540 e^2 x^2 d^2+924 e^3 x^3 d+210 e^4 x^4\right)+7 B x \left(495 d^4+1760 e x d^3+2376 e^2 x^2 d^2+1440 e^3 x^3 d+330 e^4 x^4\right)\right) a^4+560 b^7 x^7 \left(13 A \left(495 d^4+1760 e x d^3+2376 e^2 x^2 d^2+1440 e^3 x^3 d+330 e^4 x^4\right)+8 B x \left(715 d^4+2574 e x d^3+3510 e^2 x^2 d^2+2145 e^3 x^3 d+495 e^4 x^4\right)\right) a^3+120 b^8 x^8 \left(14 A \left(715 d^4+2574 e x d^3+3510 e^2 x^2 d^2+2145 e^3 x^3 d+495 e^4 x^4\right)+9 B x \left(1001 d^4+3640 e x d^3+5005 e^2 x^2 d^2+3080 e^3 x^3 d+715 e^4 x^4\right)\right) a^2+80 b^9 x^9 \left(3 A \left(1001 d^4+3640 e x d^3+5005 e^2 x^2 d^2+3080 e^3 x^3 d+715 e^4 x^4\right)+2 B x \left(1365 d^4+5005 e x d^3+6930 e^2 x^2 d^2+4290 e^3 x^3 d+1001 e^4 x^4\right)\right) a+b^{10} x^{10} \left(16 A \left(1365 d^4+5005 e x d^3+6930 e^2 x^2 d^2+4290 e^3 x^3 d+1001 e^4 x^4\right)+11 B x \left(1820 d^4+6720 e x d^3+9360 e^2 x^2 d^2+5824 e^3 x^3 d+1365 e^4 x^4\right)\right)\right)}{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,"(x*(8008*a^10*(6*A*(5*d^4 + 10*d^3*e*x + 10*d^2*e^2*x^2 + 5*d*e^3*x^3 + e^4*x^4) + B*x*(15*d^4 + 40*d^3*e*x + 45*d^2*e^2*x^2 + 24*d*e^3*x^3 + 5*e^4*x^4)) + 11440*a^9*b*x*(7*A*(15*d^4 + 40*d^3*e*x + 45*d^2*e^2*x^2 + 24*d*e^3*x^3 + 5*e^4*x^4) + 2*B*x*(35*d^4 + 105*d^3*e*x + 126*d^2*e^2*x^2 + 70*d*e^3*x^3 + 15*e^4*x^4)) + 12870*a^8*b^2*x^2*(8*A*(35*d^4 + 105*d^3*e*x + 126*d^2*e^2*x^2 + 70*d*e^3*x^3 + 15*e^4*x^4) + 3*B*x*(70*d^4 + 224*d^3*e*x + 280*d^2*e^2*x^2 + 160*d*e^3*x^3 + 35*e^4*x^4)) + 11440*a^7*b^3*x^3*(9*A*(70*d^4 + 224*d^3*e*x + 280*d^2*e^2*x^2 + 160*d*e^3*x^3 + 35*e^4*x^4) + 4*B*x*(126*d^4 + 420*d^3*e*x + 540*d^2*e^2*x^2 + 315*d*e^3*x^3 + 70*e^4*x^4)) + 40040*a^6*b^4*x^4*(2*A*(126*d^4 + 420*d^3*e*x + 540*d^2*e^2*x^2 + 315*d*e^3*x^3 + 70*e^4*x^4) + B*x*(210*d^4 + 720*d^3*e*x + 945*d^2*e^2*x^2 + 560*d*e^3*x^3 + 126*e^4*x^4)) + 4368*a^5*b^5*x^5*(11*A*(210*d^4 + 720*d^3*e*x + 945*d^2*e^2*x^2 + 560*d*e^3*x^3 + 126*e^4*x^4) + 6*B*x*(330*d^4 + 1155*d^3*e*x + 1540*d^2*e^2*x^2 + 924*d*e^3*x^3 + 210*e^4*x^4)) + 1820*a^4*b^6*x^6*(12*A*(330*d^4 + 1155*d^3*e*x + 1540*d^2*e^2*x^2 + 924*d*e^3*x^3 + 210*e^4*x^4) + 7*B*x*(495*d^4 + 1760*d^3*e*x + 2376*d^2*e^2*x^2 + 1440*d*e^3*x^3 + 330*e^4*x^4)) + 560*a^3*b^7*x^7*(13*A*(495*d^4 + 1760*d^3*e*x + 2376*d^2*e^2*x^2 + 1440*d*e^3*x^3 + 330*e^4*x^4) + 8*B*x*(715*d^4 + 2574*d^3*e*x + 3510*d^2*e^2*x^2 + 2145*d*e^3*x^3 + 495*e^4*x^4)) + 120*a^2*b^8*x^8*(14*A*(715*d^4 + 2574*d^3*e*x + 3510*d^2*e^2*x^2 + 2145*d*e^3*x^3 + 495*e^4*x^4) + 9*B*x*(1001*d^4 + 3640*d^3*e*x + 5005*d^2*e^2*x^2 + 3080*d*e^3*x^3 + 715*e^4*x^4)) + 80*a*b^9*x^9*(3*A*(1001*d^4 + 3640*d^3*e*x + 5005*d^2*e^2*x^2 + 3080*d*e^3*x^3 + 715*e^4*x^4) + 2*B*x*(1365*d^4 + 5005*d^3*e*x + 6930*d^2*e^2*x^2 + 4290*d*e^3*x^3 + 1001*e^4*x^4)) + b^10*x^10*(16*A*(1365*d^4 + 5005*d^3*e*x + 6930*d^2*e^2*x^2 + 4290*d*e^3*x^3 + 1001*e^4*x^4) + 11*B*x*(1820*d^4 + 6720*d^3*e*x + 9360*d^2*e^2*x^2 + 5824*d*e^3*x^3 + 1365*e^4*x^4))))/240240","B",1
1085,1,855,159,0.5395581,"\int (a+b x)^{10} (A+B x) (d+e x)^3 \, dx","Integrate[(a + b*x)^10*(A + B*x)*(d + e*x)^3,x]","\frac{x \left(3003 \left(5 A \left(4 d^3+6 e x d^2+4 e^2 x^2 d+e^3 x^3\right)+B x \left(10 d^3+20 e x d^2+15 e^2 x^2 d+4 e^3 x^3\right)\right) a^{10}+10010 b x \left(3 A \left(10 d^3+20 e x d^2+15 e^2 x^2 d+4 e^3 x^3\right)+B x \left(20 d^3+45 e x d^2+36 e^2 x^2 d+10 e^3 x^3\right)\right) a^9+6435 b^2 x^2 \left(7 A \left(20 d^3+45 e x d^2+36 e^2 x^2 d+10 e^3 x^3\right)+3 B x \left(35 d^3+84 e x d^2+70 e^2 x^2 d+20 e^3 x^3\right)\right) a^8+25740 b^3 x^3 \left(2 A \left(35 d^3+84 e x d^2+70 e^2 x^2 d+20 e^3 x^3\right)+B x \left(56 d^3+140 e x d^2+120 e^2 x^2 d+35 e^3 x^3\right)\right) a^7+5005 b^4 x^4 \left(9 A \left(56 d^3+140 e x d^2+120 e^2 x^2 d+35 e^3 x^3\right)+5 B x \left(84 d^3+216 e x d^2+189 e^2 x^2 d+56 e^3 x^3\right)\right) a^6+6006 b^5 x^5 \left(5 A \left(84 d^3+216 e x d^2+189 e^2 x^2 d+56 e^3 x^3\right)+3 B x \left(120 d^3+315 e x d^2+280 e^2 x^2 d+84 e^3 x^3\right)\right) a^5+1365 b^6 x^6 \left(11 A \left(120 d^3+315 e x d^2+280 e^2 x^2 d+84 e^3 x^3\right)+7 B x \left(165 d^3+440 e x d^2+396 e^2 x^2 d+120 e^3 x^3\right)\right) a^4+1820 b^7 x^7 \left(3 A \left(165 d^3+440 e x d^2+396 e^2 x^2 d+120 e^3 x^3\right)+2 B x \left(220 d^3+594 e x d^2+540 e^2 x^2 d+165 e^3 x^3\right)\right) a^3+105 b^8 x^8 \left(13 A \left(220 d^3+594 e x d^2+540 e^2 x^2 d+165 e^3 x^3\right)+9 B x \left(286 d^3+780 e x d^2+715 e^2 x^2 d+220 e^3 x^3\right)\right) a^2+30 b^9 x^9 \left(7 A \left(286 d^3+780 e x d^2+715 e^2 x^2 d+220 e^3 x^3\right)+5 B x \left(364 d^3+1001 e x d^2+924 e^2 x^2 d+286 e^3 x^3\right)\right) a+b^{10} x^{10} \left(15 A \left(364 d^3+1001 e x d^2+924 e^2 x^2 d+286 e^3 x^3\right)+11 B x \left(455 d^3+1260 e x d^2+1170 e^2 x^2 d+364 e^3 x^3\right)\right)\right)}{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,"(x*(3003*a^10*(5*A*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3) + B*x*(10*d^3 + 20*d^2*e*x + 15*d*e^2*x^2 + 4*e^3*x^3)) + 10010*a^9*b*x*(3*A*(10*d^3 + 20*d^2*e*x + 15*d*e^2*x^2 + 4*e^3*x^3) + B*x*(20*d^3 + 45*d^2*e*x + 36*d*e^2*x^2 + 10*e^3*x^3)) + 6435*a^8*b^2*x^2*(7*A*(20*d^3 + 45*d^2*e*x + 36*d*e^2*x^2 + 10*e^3*x^3) + 3*B*x*(35*d^3 + 84*d^2*e*x + 70*d*e^2*x^2 + 20*e^3*x^3)) + 25740*a^7*b^3*x^3*(2*A*(35*d^3 + 84*d^2*e*x + 70*d*e^2*x^2 + 20*e^3*x^3) + B*x*(56*d^3 + 140*d^2*e*x + 120*d*e^2*x^2 + 35*e^3*x^3)) + 5005*a^6*b^4*x^4*(9*A*(56*d^3 + 140*d^2*e*x + 120*d*e^2*x^2 + 35*e^3*x^3) + 5*B*x*(84*d^3 + 216*d^2*e*x + 189*d*e^2*x^2 + 56*e^3*x^3)) + 6006*a^5*b^5*x^5*(5*A*(84*d^3 + 216*d^2*e*x + 189*d*e^2*x^2 + 56*e^3*x^3) + 3*B*x*(120*d^3 + 315*d^2*e*x + 280*d*e^2*x^2 + 84*e^3*x^3)) + 1365*a^4*b^6*x^6*(11*A*(120*d^3 + 315*d^2*e*x + 280*d*e^2*x^2 + 84*e^3*x^3) + 7*B*x*(165*d^3 + 440*d^2*e*x + 396*d*e^2*x^2 + 120*e^3*x^3)) + 1820*a^3*b^7*x^7*(3*A*(165*d^3 + 440*d^2*e*x + 396*d*e^2*x^2 + 120*e^3*x^3) + 2*B*x*(220*d^3 + 594*d^2*e*x + 540*d*e^2*x^2 + 165*e^3*x^3)) + 105*a^2*b^8*x^8*(13*A*(220*d^3 + 594*d^2*e*x + 540*d*e^2*x^2 + 165*e^3*x^3) + 9*B*x*(286*d^3 + 780*d^2*e*x + 715*d*e^2*x^2 + 220*e^3*x^3)) + 30*a*b^9*x^9*(7*A*(286*d^3 + 780*d^2*e*x + 715*d*e^2*x^2 + 220*e^3*x^3) + 5*B*x*(364*d^3 + 1001*d^2*e*x + 924*d*e^2*x^2 + 286*e^3*x^3)) + b^10*x^10*(15*A*(364*d^3 + 1001*d^2*e*x + 924*d*e^2*x^2 + 286*e^3*x^3) + 11*B*x*(455*d^3 + 1260*d^2*e*x + 1170*d*e^2*x^2 + 364*e^3*x^3))))/60060","B",1
1086,1,614,118,0.4240386,"\int (a+b x)^{10} (A+B x) (d+e x)^2 \, dx","Integrate[(a + b*x)^10*(A + B*x)*(d + e*x)^2,x]","\frac{x \left(1001 a^{10} \left(4 A \left(3 d^2+3 d e x+e^2 x^2\right)+B x \left(6 d^2+8 d e x+3 e^2 x^2\right)\right)+2002 a^9 b x \left(5 A \left(6 d^2+8 d e x+3 e^2 x^2\right)+2 B x \left(10 d^2+15 d e x+6 e^2 x^2\right)\right)+9009 a^8 b^2 x^2 \left(2 A \left(10 d^2+15 d e x+6 e^2 x^2\right)+B x \left(15 d^2+24 d e x+10 e^2 x^2\right)\right)+3432 a^7 b^3 x^3 \left(7 A \left(15 d^2+24 d e x+10 e^2 x^2\right)+4 B x \left(21 d^2+35 d e x+15 e^2 x^2\right)\right)+3003 a^6 b^4 x^4 \left(8 A \left(21 d^2+35 d e x+15 e^2 x^2\right)+5 B x \left(28 d^2+48 d e x+21 e^2 x^2\right)\right)+6006 a^5 b^5 x^5 \left(3 A \left(28 d^2+48 d e x+21 e^2 x^2\right)+2 B x \left(36 d^2+63 d e x+28 e^2 x^2\right)\right)+1001 a^4 b^6 x^6 \left(10 A \left(36 d^2+63 d e x+28 e^2 x^2\right)+7 B x \left(45 d^2+80 d e x+36 e^2 x^2\right)\right)+364 a^3 b^7 x^7 \left(11 A \left(45 d^2+80 d e x+36 e^2 x^2\right)+8 B x \left(55 d^2+99 d e x+45 e^2 x^2\right)\right)+273 a^2 b^8 x^8 \left(4 A \left(55 d^2+99 d e x+45 e^2 x^2\right)+3 B x \left(66 d^2+120 d e x+55 e^2 x^2\right)\right)+14 a b^9 x^9 \left(13 A \left(66 d^2+120 d e x+55 e^2 x^2\right)+10 B x \left(78 d^2+143 d e x+66 e^2 x^2\right)\right)+b^{10} x^{10} \left(14 A \left(78 d^2+143 d e x+66 e^2 x^2\right)+11 B x \left(91 d^2+168 d e x+78 e^2 x^2\right)\right)\right)}{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,"(x*(1001*a^10*(4*A*(3*d^2 + 3*d*e*x + e^2*x^2) + B*x*(6*d^2 + 8*d*e*x + 3*e^2*x^2)) + 2002*a^9*b*x*(5*A*(6*d^2 + 8*d*e*x + 3*e^2*x^2) + 2*B*x*(10*d^2 + 15*d*e*x + 6*e^2*x^2)) + 9009*a^8*b^2*x^2*(2*A*(10*d^2 + 15*d*e*x + 6*e^2*x^2) + B*x*(15*d^2 + 24*d*e*x + 10*e^2*x^2)) + 3432*a^7*b^3*x^3*(7*A*(15*d^2 + 24*d*e*x + 10*e^2*x^2) + 4*B*x*(21*d^2 + 35*d*e*x + 15*e^2*x^2)) + 3003*a^6*b^4*x^4*(8*A*(21*d^2 + 35*d*e*x + 15*e^2*x^2) + 5*B*x*(28*d^2 + 48*d*e*x + 21*e^2*x^2)) + 6006*a^5*b^5*x^5*(3*A*(28*d^2 + 48*d*e*x + 21*e^2*x^2) + 2*B*x*(36*d^2 + 63*d*e*x + 28*e^2*x^2)) + 1001*a^4*b^6*x^6*(10*A*(36*d^2 + 63*d*e*x + 28*e^2*x^2) + 7*B*x*(45*d^2 + 80*d*e*x + 36*e^2*x^2)) + 364*a^3*b^7*x^7*(11*A*(45*d^2 + 80*d*e*x + 36*e^2*x^2) + 8*B*x*(55*d^2 + 99*d*e*x + 45*e^2*x^2)) + 273*a^2*b^8*x^8*(4*A*(55*d^2 + 99*d*e*x + 45*e^2*x^2) + 3*B*x*(66*d^2 + 120*d*e*x + 55*e^2*x^2)) + 14*a*b^9*x^9*(13*A*(66*d^2 + 120*d*e*x + 55*e^2*x^2) + 10*B*x*(78*d^2 + 143*d*e*x + 66*e^2*x^2)) + b^10*x^10*(14*A*(78*d^2 + 143*d*e*x + 66*e^2*x^2) + 11*B*x*(91*d^2 + 168*d*e*x + 78*e^2*x^2))))/12012","B",1
1087,1,383,75,0.21342,"\int (a+b x)^{10} (A+B x) (d+e x) \, dx","Integrate[(a + b*x)^10*(A + B*x)*(d + e*x),x]","\frac{1}{6} a^{10} x (3 A (2 d+e x)+B x (3 d+2 e x))+\frac{5}{6} a^9 b x^2 (A (6 d+4 e x)+B x (4 d+3 e x))+\frac{3}{4} a^8 b^2 x^3 (5 A (4 d+3 e x)+3 B x (5 d+4 e x))+2 a^7 b^3 x^4 (3 A (5 d+4 e x)+2 B x (6 d+5 e x))+a^6 b^4 x^5 (7 A (6 d+5 e x)+5 B x (7 d+6 e x))+\frac{3}{2} a^5 b^5 x^6 (4 A (7 d+6 e x)+3 B x (8 d+7 e x))+\frac{5}{12} a^4 b^6 x^7 (9 A (8 d+7 e x)+7 B x (9 d+8 e x))+\frac{1}{3} a^3 b^7 x^8 (5 A (9 d+8 e x)+4 B x (10 d+9 e x))+\frac{1}{22} a^2 b^8 x^9 \left(110 A d+99 A e x+99 B d x+90 B e x^2\right)+\frac{1}{66} a b^9 x^{10} \left(66 A d+60 A e x+60 B d x+55 B e x^2\right)+\frac{b^{10} x^{11} (13 A (12 d+11 e x)+11 B x (13 d+12 e x))}{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,"(a*b^9*x^10*(66*A*d + 60*B*d*x + 60*A*e*x + 55*B*e*x^2))/66 + (a^2*b^8*x^9*(110*A*d + 99*B*d*x + 99*A*e*x + 90*B*e*x^2))/22 + (a^10*x*(3*A*(2*d + e*x) + B*x*(3*d + 2*e*x)))/6 + (3*a^8*b^2*x^3*(5*A*(4*d + 3*e*x) + 3*B*x*(5*d + 4*e*x)))/4 + (5*a^9*b*x^2*(B*x*(4*d + 3*e*x) + A*(6*d + 4*e*x)))/6 + 2*a^7*b^3*x^4*(3*A*(5*d + 4*e*x) + 2*B*x*(6*d + 5*e*x)) + a^6*b^4*x^5*(7*A*(6*d + 5*e*x) + 5*B*x*(7*d + 6*e*x)) + (3*a^5*b^5*x^6*(4*A*(7*d + 6*e*x) + 3*B*x*(8*d + 7*e*x)))/2 + (5*a^4*b^6*x^7*(9*A*(8*d + 7*e*x) + 7*B*x*(9*d + 8*e*x)))/12 + (a^3*b^7*x^8*(5*A*(9*d + 8*e*x) + 4*B*x*(10*d + 9*e*x)))/3 + (b^10*x^11*(13*A*(12*d + 11*e*x) + 11*B*x*(13*d + 12*e*x)))/1716","B",1
1088,1,198,38,0.0655402,"\int (a+b x)^{10} (A+B x) \, dx","Integrate[(a + b*x)^10*(A + B*x),x]","\frac{1}{132} x \left(66 a^{10} (2 A+B x)+220 a^9 b x (3 A+2 B x)+495 a^8 b^2 x^2 (4 A+3 B x)+792 a^7 b^3 x^3 (5 A+4 B x)+924 a^6 b^4 x^4 (6 A+5 B x)+792 a^5 b^5 x^5 (7 A+6 B x)+495 a^4 b^6 x^6 (8 A+7 B x)+220 a^3 b^7 x^7 (9 A+8 B x)+66 a^2 b^8 x^8 (10 A+9 B x)+12 a b^9 x^9 (11 A+10 B x)+b^{10} x^{10} (12 A+11 B x)\right)","\frac{(a+b x)^{11} (A b-a B)}{11 b^2}+\frac{B (a+b x)^{12}}{12 b^2}",1,"(x*(66*a^10*(2*A + B*x) + 220*a^9*b*x*(3*A + 2*B*x) + 495*a^8*b^2*x^2*(4*A + 3*B*x) + 792*a^7*b^3*x^3*(5*A + 4*B*x) + 924*a^6*b^4*x^4*(6*A + 5*B*x) + 792*a^5*b^5*x^5*(7*A + 6*B*x) + 495*a^4*b^6*x^6*(8*A + 7*B*x) + 220*a^3*b^7*x^7*(9*A + 8*B*x) + 66*a^2*b^8*x^8*(10*A + 9*B*x) + 12*a*b^9*x^9*(11*A + 10*B*x) + b^10*x^10*(12*A + 11*B*x)))/132","B",1
1089,1,1252,348,1.2443622,"\int \frac{(a+b x)^{10} (A+B x)}{d+e x} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x),x]","\frac{(A e-B d) \log (d+e x) (b d-a e)^{10}}{e^{12}}+\frac{x \left(\left(11 A e \left(-2520 d^9+1260 e x d^8-840 e^2 x^2 d^7+630 e^3 x^3 d^6-504 e^4 x^4 d^5+420 e^5 x^5 d^4-360 e^6 x^6 d^3+315 e^7 x^7 d^2-280 e^8 x^8 d+252 e^9 x^9\right)+B \left(27720 d^{10}-13860 e x d^9+9240 e^2 x^2 d^8-6930 e^3 x^3 d^7+5544 e^4 x^4 d^6-4620 e^5 x^5 d^5+3960 e^6 x^6 d^4-3465 e^7 x^7 d^3+3080 e^8 x^8 d^2-2772 e^9 x^9 d+2520 e^{10} x^{10}\right)\right) b^{10}+110 a e \left(A e \left(2520 d^8-1260 e x d^7+840 e^2 x^2 d^6-630 e^3 x^3 d^5+504 e^4 x^4 d^4-420 e^5 x^5 d^3+360 e^6 x^6 d^2-315 e^7 x^7 d+280 e^8 x^8\right)+B \left(-2520 d^9+1260 e x d^8-840 e^2 x^2 d^7+630 e^3 x^3 d^6-504 e^4 x^4 d^5+420 e^5 x^5 d^4-360 e^6 x^6 d^3+315 e^7 x^7 d^2-280 e^8 x^8 d+252 e^9 x^9\right)\right) b^9+495 a^2 e^2 \left(3 A e \left(-840 d^7+420 e x d^6-280 e^2 x^2 d^5+210 e^3 x^3 d^4-168 e^4 x^4 d^3+140 e^5 x^5 d^2-120 e^6 x^6 d+105 e^7 x^7\right)+B \left(2520 d^8-1260 e x d^7+840 e^2 x^2 d^6-630 e^3 x^3 d^5+504 e^4 x^4 d^4-420 e^5 x^5 d^3+360 e^6 x^6 d^2-315 e^7 x^7 d+280 e^8 x^8\right)\right) b^8+3960 a^3 e^3 \left(2 A e \left(420 d^6-210 e x d^5+140 e^2 x^2 d^4-105 e^3 x^3 d^3+84 e^4 x^4 d^2-70 e^5 x^5 d+60 e^6 x^6\right)+B \left(-840 d^7+420 e x d^6-280 e^2 x^2 d^5+210 e^3 x^3 d^4-168 e^4 x^4 d^3+140 e^5 x^5 d^2-120 e^6 x^6 d+105 e^7 x^7\right)\right) b^7+13860 a^4 e^4 \left(7 A e \left(-60 d^5+30 e x d^4-20 e^2 x^2 d^3+15 e^3 x^3 d^2-12 e^4 x^4 d+10 e^5 x^5\right)+B \left(420 d^6-210 e x d^5+140 e^2 x^2 d^4-105 e^3 x^3 d^3+84 e^4 x^4 d^2-70 e^5 x^5 d+60 e^6 x^6\right)\right) b^6+116424 a^5 e^5 \left(A e \left(60 d^4-30 e x d^3+20 e^2 x^2 d^2-15 e^3 x^3 d+12 e^4 x^4\right)+B \left(-60 d^5+30 e x d^4-20 e^2 x^2 d^3+15 e^3 x^3 d^2-12 e^4 x^4 d+10 e^5 x^5\right)\right) b^5+97020 a^6 e^6 \left(5 A e \left(-12 d^3+6 e x d^2-4 e^2 x^2 d+3 e^3 x^3\right)+B \left(60 d^4-30 e x d^3+20 e^2 x^2 d^2-15 e^3 x^3 d+12 e^4 x^4\right)\right) b^4+277200 a^7 e^7 \left(2 A e \left(6 d^2-3 e x d+2 e^2 x^2\right)+B \left(-12 d^3+6 e x d^2-4 e^2 x^2 d+3 e^3 x^3\right)\right) b^3+207900 a^8 e^8 \left(3 A e (e x-2 d)+B \left(6 d^2-3 e x d+2 e^2 x^2\right)\right) b^2+138600 a^9 e^9 (-2 B d+2 A e+B e x) b+27720 a^{10} B e^{10}\right)}{27720 e^{11}}","-\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,"(x*(27720*a^10*B*e^10 + 138600*a^9*b*e^9*(-2*B*d + 2*A*e + B*e*x) + 207900*a^8*b^2*e^8*(3*A*e*(-2*d + e*x) + B*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) + 277200*a^7*b^3*e^7*(2*A*e*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + B*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3)) + 97020*a^6*b^4*e^6*(5*A*e*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3) + B*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4)) + 116424*a^5*b^5*e^5*(A*e*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4) + B*(-60*d^5 + 30*d^4*e*x - 20*d^3*e^2*x^2 + 15*d^2*e^3*x^3 - 12*d*e^4*x^4 + 10*e^5*x^5)) + 13860*a^4*b^6*e^4*(7*A*e*(-60*d^5 + 30*d^4*e*x - 20*d^3*e^2*x^2 + 15*d^2*e^3*x^3 - 12*d*e^4*x^4 + 10*e^5*x^5) + B*(420*d^6 - 210*d^5*e*x + 140*d^4*e^2*x^2 - 105*d^3*e^3*x^3 + 84*d^2*e^4*x^4 - 70*d*e^5*x^5 + 60*e^6*x^6)) + 3960*a^3*b^7*e^3*(2*A*e*(420*d^6 - 210*d^5*e*x + 140*d^4*e^2*x^2 - 105*d^3*e^3*x^3 + 84*d^2*e^4*x^4 - 70*d*e^5*x^5 + 60*e^6*x^6) + B*(-840*d^7 + 420*d^6*e*x - 280*d^5*e^2*x^2 + 210*d^4*e^3*x^3 - 168*d^3*e^4*x^4 + 140*d^2*e^5*x^5 - 120*d*e^6*x^6 + 105*e^7*x^7)) + 495*a^2*b^8*e^2*(3*A*e*(-840*d^7 + 420*d^6*e*x - 280*d^5*e^2*x^2 + 210*d^4*e^3*x^3 - 168*d^3*e^4*x^4 + 140*d^2*e^5*x^5 - 120*d*e^6*x^6 + 105*e^7*x^7) + B*(2520*d^8 - 1260*d^7*e*x + 840*d^6*e^2*x^2 - 630*d^5*e^3*x^3 + 504*d^4*e^4*x^4 - 420*d^3*e^5*x^5 + 360*d^2*e^6*x^6 - 315*d*e^7*x^7 + 280*e^8*x^8)) + 110*a*b^9*e*(A*e*(2520*d^8 - 1260*d^7*e*x + 840*d^6*e^2*x^2 - 630*d^5*e^3*x^3 + 504*d^4*e^4*x^4 - 420*d^3*e^5*x^5 + 360*d^2*e^6*x^6 - 315*d*e^7*x^7 + 280*e^8*x^8) + B*(-2520*d^9 + 1260*d^8*e*x - 840*d^7*e^2*x^2 + 630*d^6*e^3*x^3 - 504*d^5*e^4*x^4 + 420*d^4*e^5*x^5 - 360*d^3*e^6*x^6 + 315*d^2*e^7*x^7 - 280*d*e^8*x^8 + 252*e^9*x^9)) + b^10*(11*A*e*(-2520*d^9 + 1260*d^8*e*x - 840*d^7*e^2*x^2 + 630*d^6*e^3*x^3 - 504*d^5*e^4*x^4 + 420*d^4*e^5*x^5 - 360*d^3*e^6*x^6 + 315*d^2*e^7*x^7 - 280*d*e^8*x^8 + 252*e^9*x^9) + B*(27720*d^10 - 13860*d^9*e*x + 9240*d^8*e^2*x^2 - 6930*d^7*e^3*x^3 + 5544*d^6*e^4*x^4 - 4620*d^5*e^5*x^5 + 3960*d^4*e^6*x^6 - 3465*d^3*e^7*x^7 + 3080*d^2*e^8*x^8 - 2772*d*e^9*x^9 + 2520*e^10*x^10))))/(27720*e^11) + ((b*d - a*e)^10*(-(B*d) + A*e)*Log[d + e*x])/e^12","B",1
1090,1,1486,445,0.8621291,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^2} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^2,x]","\frac{\left(10 A e \left(-252 d^{10}+2268 e x d^9+1260 e^2 x^2 d^8-420 e^3 x^3 d^7+210 e^4 x^4 d^6-126 e^5 x^5 d^5+84 e^6 x^6 d^4-60 e^7 x^7 d^3+45 e^8 x^8 d^2-35 e^9 x^9 d+28 e^{10} x^{10}\right)+B \left(2520 d^{11}-25200 e x d^{10}-13860 e^2 x^2 d^9+4620 e^3 x^3 d^8-2310 e^4 x^4 d^7+1386 e^5 x^5 d^6-924 e^6 x^6 d^5+660 e^7 x^7 d^4-495 e^8 x^8 d^3+385 e^9 x^9 d^2-308 e^{10} x^{10} d+252 e^{11} x^{11}\right)\right) b^{10}+10 a e \left(9 A e \left(280 d^9-2240 e x d^8-1260 e^2 x^2 d^7+420 e^3 x^3 d^6-210 e^4 x^4 d^5+126 e^5 x^5 d^4-84 e^6 x^6 d^3+60 e^7 x^7 d^2-45 e^8 x^8 d+35 e^9 x^9\right)-10 B \left(252 d^{10}-2268 e x d^9-1260 e^2 x^2 d^8+420 e^3 x^3 d^7-210 e^4 x^4 d^6+126 e^5 x^5 d^5-84 e^6 x^6 d^4+60 e^7 x^7 d^3-45 e^8 x^8 d^2+35 e^9 x^9 d-28 e^{10} x^{10}\right)\right) b^9+135 a^2 e^2 \left(8 A e \left(-105 d^8+735 e x d^7+420 e^2 x^2 d^6-140 e^3 x^3 d^5+70 e^4 x^4 d^4-42 e^5 x^5 d^3+28 e^6 x^6 d^2-20 e^7 x^7 d+15 e^8 x^8\right)+3 B \left(280 d^9-2240 e x d^8-1260 e^2 x^2 d^7+420 e^3 x^3 d^6-210 e^4 x^4 d^5+126 e^5 x^5 d^4-84 e^6 x^6 d^3+60 e^7 x^7 d^2-45 e^8 x^8 d+35 e^9 x^9\right)\right) b^8+720 a^3 e^3 \left(7 A e \left(60 d^7-360 e x d^6-210 e^2 x^2 d^5+70 e^3 x^3 d^4-35 e^4 x^4 d^3+21 e^5 x^5 d^2-14 e^6 x^6 d+10 e^7 x^7\right)-4 B \left(105 d^8-735 e x d^7-420 e^2 x^2 d^6+140 e^3 x^3 d^5-70 e^4 x^4 d^4+42 e^5 x^5 d^3-28 e^6 x^6 d^2+20 e^7 x^7 d-15 e^8 x^8\right)\right) b^7+8820 a^4 e^4 \left(6 A e \left(-10 d^6+50 e x d^5+30 e^2 x^2 d^4-10 e^3 x^3 d^3+5 e^4 x^4 d^2-3 e^5 x^5 d+2 e^6 x^6\right)+B \left(60 d^7-360 e x d^6-210 e^2 x^2 d^5+70 e^3 x^3 d^4-35 e^4 x^4 d^3+21 e^5 x^5 d^2-14 e^6 x^6 d+10 e^7 x^7\right)\right) b^6+10584 a^5 e^5 \left(5 A e \left(12 d^5-48 e x d^4-30 e^2 x^2 d^3+10 e^3 x^3 d^2-5 e^4 x^4 d+3 e^5 x^5\right)-6 B \left(10 d^6-50 e x d^5-30 e^2 x^2 d^4+10 e^3 x^3 d^3-5 e^4 x^4 d^2+3 e^5 x^5 d-2 e^6 x^6\right)\right) b^5+44100 a^6 e^6 \left(4 A e \left(-3 d^4+9 e x d^3+6 e^2 x^2 d^2-2 e^3 x^3 d+e^4 x^4\right)+B \left(12 d^5-48 e x d^4-30 e^2 x^2 d^3+10 e^3 x^3 d^2-5 e^4 x^4 d+3 e^5 x^5\right)\right) b^4+50400 a^7 e^7 \left(3 A e \left(2 d^3-4 e x d^2-3 e^2 x^2 d+e^3 x^3\right)+2 B \left(-3 d^4+9 e x d^3+6 e^2 x^2 d^2-2 e^3 x^3 d+e^4 x^4\right)\right) b^3+56700 a^8 e^8 \left(2 A e \left(-d^2+e x d+e^2 x^2\right)+B \left(2 d^3-4 e x d^2-3 e^2 x^2 d+e^3 x^3\right)\right) b^2+25200 a^9 e^9 \left(A d e+B \left(-d^2+e x d+e^2 x^2\right)\right) b-2520 a^{10} e^{10} (A e-B d)+2520 (b d-a e)^9 (11 b B d-10 A b e-a B e) (d+e x) \log (d+e x)}{2520 e^{12} (d+e x)}","-\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*a^10*e^10*(-(B*d) + A*e) + 25200*a^9*b*e^9*(A*d*e + B*(-d^2 + d*e*x + e^2*x^2)) + 56700*a^8*b^2*e^8*(2*A*e*(-d^2 + d*e*x + e^2*x^2) + B*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3)) + 50400*a^7*b^3*e^7*(3*A*e*(2*d^3 - 4*d^2*e*x - 3*d*e^2*x^2 + e^3*x^3) + 2*B*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4)) + 44100*a^6*b^4*e^6*(4*A*e*(-3*d^4 + 9*d^3*e*x + 6*d^2*e^2*x^2 - 2*d*e^3*x^3 + e^4*x^4) + B*(12*d^5 - 48*d^4*e*x - 30*d^3*e^2*x^2 + 10*d^2*e^3*x^3 - 5*d*e^4*x^4 + 3*e^5*x^5)) + 10584*a^5*b^5*e^5*(5*A*e*(12*d^5 - 48*d^4*e*x - 30*d^3*e^2*x^2 + 10*d^2*e^3*x^3 - 5*d*e^4*x^4 + 3*e^5*x^5) - 6*B*(10*d^6 - 50*d^5*e*x - 30*d^4*e^2*x^2 + 10*d^3*e^3*x^3 - 5*d^2*e^4*x^4 + 3*d*e^5*x^5 - 2*e^6*x^6)) + 8820*a^4*b^6*e^4*(6*A*e*(-10*d^6 + 50*d^5*e*x + 30*d^4*e^2*x^2 - 10*d^3*e^3*x^3 + 5*d^2*e^4*x^4 - 3*d*e^5*x^5 + 2*e^6*x^6) + B*(60*d^7 - 360*d^6*e*x - 210*d^5*e^2*x^2 + 70*d^4*e^3*x^3 - 35*d^3*e^4*x^4 + 21*d^2*e^5*x^5 - 14*d*e^6*x^6 + 10*e^7*x^7)) + 720*a^3*b^7*e^3*(7*A*e*(60*d^7 - 360*d^6*e*x - 210*d^5*e^2*x^2 + 70*d^4*e^3*x^3 - 35*d^3*e^4*x^4 + 21*d^2*e^5*x^5 - 14*d*e^6*x^6 + 10*e^7*x^7) - 4*B*(105*d^8 - 735*d^7*e*x - 420*d^6*e^2*x^2 + 140*d^5*e^3*x^3 - 70*d^4*e^4*x^4 + 42*d^3*e^5*x^5 - 28*d^2*e^6*x^6 + 20*d*e^7*x^7 - 15*e^8*x^8)) + 135*a^2*b^8*e^2*(8*A*e*(-105*d^8 + 735*d^7*e*x + 420*d^6*e^2*x^2 - 140*d^5*e^3*x^3 + 70*d^4*e^4*x^4 - 42*d^3*e^5*x^5 + 28*d^2*e^6*x^6 - 20*d*e^7*x^7 + 15*e^8*x^8) + 3*B*(280*d^9 - 2240*d^8*e*x - 1260*d^7*e^2*x^2 + 420*d^6*e^3*x^3 - 210*d^5*e^4*x^4 + 126*d^4*e^5*x^5 - 84*d^3*e^6*x^6 + 60*d^2*e^7*x^7 - 45*d*e^8*x^8 + 35*e^9*x^9)) + 10*a*b^9*e*(9*A*e*(280*d^9 - 2240*d^8*e*x - 1260*d^7*e^2*x^2 + 420*d^6*e^3*x^3 - 210*d^5*e^4*x^4 + 126*d^4*e^5*x^5 - 84*d^3*e^6*x^6 + 60*d^2*e^7*x^7 - 45*d*e^8*x^8 + 35*e^9*x^9) - 10*B*(252*d^10 - 2268*d^9*e*x - 1260*d^8*e^2*x^2 + 420*d^7*e^3*x^3 - 210*d^6*e^4*x^4 + 126*d^5*e^5*x^5 - 84*d^4*e^6*x^6 + 60*d^3*e^7*x^7 - 45*d^2*e^8*x^8 + 35*d*e^9*x^9 - 28*e^10*x^10)) + b^10*(10*A*e*(-252*d^10 + 2268*d^9*e*x + 1260*d^8*e^2*x^2 - 420*d^7*e^3*x^3 + 210*d^6*e^4*x^4 - 126*d^5*e^5*x^5 + 84*d^4*e^6*x^6 - 60*d^3*e^7*x^7 + 45*d^2*e^8*x^8 - 35*d*e^9*x^9 + 28*e^10*x^10) + B*(2520*d^11 - 25200*d^10*e*x - 13860*d^9*e^2*x^2 + 4620*d^8*e^3*x^3 - 2310*d^7*e^4*x^4 + 1386*d^6*e^5*x^5 - 924*d^5*e^6*x^6 + 660*d^4*e^7*x^7 - 495*d^3*e^8*x^8 + 385*d^2*e^9*x^9 - 308*d*e^10*x^10 + 252*e^11*x^11)) + 2520*(b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e)*(d + e*x)*Log[d + e*x])/(2520*e^12*(d + e*x))","B",1
1091,1,1480,445,0.9277901,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^3} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^3,x]","\frac{\left(9 A e \left(532 d^{10}-1456 e x d^9-3248 e^2 x^2 d^8-840 e^3 x^3 d^7+210 e^4 x^4 d^6-84 e^5 x^5 d^5+42 e^6 x^6 d^4-24 e^7 x^7 d^3+15 e^8 x^8 d^2-10 e^9 x^9 d+7 e^{10} x^{10}\right)+B \left(-5292 d^{11}+17136 e x d^{10}+36288 e^2 x^2 d^9+9240 e^3 x^3 d^8-2310 e^4 x^4 d^7+924 e^5 x^5 d^6-462 e^6 x^6 d^5+264 e^7 x^7 d^4-165 e^8 x^8 d^3+110 e^9 x^9 d^2-77 e^{10} x^{10} d+56 e^{11} x^{11}\right)\right) b^{10}+18 a e \left(4 A e \left(-595 d^9+1330 e x d^8+3185 e^2 x^2 d^7+840 e^3 x^3 d^6-210 e^4 x^4 d^5+84 e^5 x^5 d^4-42 e^6 x^6 d^3+24 e^7 x^7 d^2-15 e^8 x^8 d+10 e^9 x^9\right)+5 B \left(532 d^{10}-1456 e x d^9-3248 e^2 x^2 d^8-840 e^3 x^3 d^7+210 e^4 x^4 d^6-84 e^5 x^5 d^5+42 e^6 x^6 d^4-24 e^7 x^7 d^3+15 e^8 x^8 d^2-10 e^9 x^9 d+7 e^{10} x^{10}\right)\right) b^9+108 a^2 e^2 \left(7 A e \left(225 d^8-390 e x d^7-1035 e^2 x^2 d^6-280 e^3 x^3 d^5+70 e^4 x^4 d^4-28 e^5 x^5 d^3+14 e^6 x^6 d^2-8 e^7 x^7 d+5 e^8 x^8\right)-3 B \left(595 d^9-1330 e x d^8-3185 e^2 x^2 d^7-840 e^3 x^3 d^6+210 e^4 x^4 d^5-84 e^5 x^5 d^4+42 e^6 x^6 d^3-24 e^7 x^7 d^2+15 e^8 x^8 d-10 e^9 x^9\right)\right) b^8+1008 a^3 e^3 \left(3 A e \left(-130 d^7+160 e x d^6+500 e^2 x^2 d^5+140 e^3 x^3 d^4-35 e^4 x^4 d^3+14 e^5 x^5 d^2-7 e^6 x^6 d+4 e^7 x^7\right)+2 B \left(225 d^8-390 e x d^7-1035 e^2 x^2 d^6-280 e^3 x^3 d^5+70 e^4 x^4 d^4-28 e^5 x^5 d^3+14 e^6 x^6 d^2-8 e^7 x^7 d+5 e^8 x^8\right)\right) b^7+5292 a^4 e^4 \left(5 A e \left(22 d^6-16 e x d^5-68 e^2 x^2 d^4-20 e^3 x^3 d^3+5 e^4 x^4 d^2-2 e^5 x^5 d+e^6 x^6\right)+B \left(-130 d^7+160 e x d^6+500 e^2 x^2 d^5+140 e^3 x^3 d^4-35 e^4 x^4 d^3+14 e^5 x^5 d^2-7 e^6 x^6 d+4 e^7 x^7\right)\right) b^6+10584 a^5 e^5 \left(2 A e \left(-27 d^5+6 e x d^4+63 e^2 x^2 d^3+20 e^3 x^3 d^2-5 e^4 x^4 d+2 e^5 x^5\right)+3 B \left(22 d^6-16 e x d^5-68 e^2 x^2 d^4-20 e^3 x^3 d^3+5 e^4 x^4 d^2-2 e^5 x^5 d+e^6 x^6\right)\right) b^5+17640 a^6 e^6 \left(3 A e \left(7 d^4+2 e x d^3-11 e^2 x^2 d^2-4 e^3 x^3 d+e^4 x^4\right)+B \left(-27 d^5+6 e x d^4+63 e^2 x^2 d^3+20 e^3 x^3 d^2-5 e^4 x^4 d+2 e^5 x^5\right)\right) b^4+30240 a^7 e^7 \left(A e \left(-5 d^3-4 e x d^2+4 e^2 x^2 d+2 e^3 x^3\right)+B \left(7 d^4+2 e x d^3-11 e^2 x^2 d^2-4 e^3 x^3 d+e^4 x^4\right)\right) b^3+11340 a^8 e^8 \left(A d e (3 d+4 e x)+B \left(-5 d^3-4 e x d^2+4 e^2 x^2 d+2 e^3 x^3\right)\right) b^2-2520 a^9 e^9 (A e (d+2 e x)-B d (3 d+4 e x)) b-2520 (b d-a e)^8 (11 b B d-9 A b e-2 a B e) (d+e x)^2 \log (d+e x) b-252 a^{10} e^{10} (A e+B (d+2 e x))}{504 e^{12} (d+e x)^2}","-\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,"(-252*a^10*e^10*(A*e + B*(d + 2*e*x)) - 2520*a^9*b*e^9*(A*e*(d + 2*e*x) - B*d*(3*d + 4*e*x)) + 11340*a^8*b^2*e^8*(A*d*e*(3*d + 4*e*x) + B*(-5*d^3 - 4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3)) + 30240*a^7*b^3*e^7*(A*e*(-5*d^3 - 4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3) + B*(7*d^4 + 2*d^3*e*x - 11*d^2*e^2*x^2 - 4*d*e^3*x^3 + e^4*x^4)) + 17640*a^6*b^4*e^6*(3*A*e*(7*d^4 + 2*d^3*e*x - 11*d^2*e^2*x^2 - 4*d*e^3*x^3 + e^4*x^4) + B*(-27*d^5 + 6*d^4*e*x + 63*d^3*e^2*x^2 + 20*d^2*e^3*x^3 - 5*d*e^4*x^4 + 2*e^5*x^5)) + 10584*a^5*b^5*e^5*(2*A*e*(-27*d^5 + 6*d^4*e*x + 63*d^3*e^2*x^2 + 20*d^2*e^3*x^3 - 5*d*e^4*x^4 + 2*e^5*x^5) + 3*B*(22*d^6 - 16*d^5*e*x - 68*d^4*e^2*x^2 - 20*d^3*e^3*x^3 + 5*d^2*e^4*x^4 - 2*d*e^5*x^5 + e^6*x^6)) + 5292*a^4*b^6*e^4*(5*A*e*(22*d^6 - 16*d^5*e*x - 68*d^4*e^2*x^2 - 20*d^3*e^3*x^3 + 5*d^2*e^4*x^4 - 2*d*e^5*x^5 + e^6*x^6) + B*(-130*d^7 + 160*d^6*e*x + 500*d^5*e^2*x^2 + 140*d^4*e^3*x^3 - 35*d^3*e^4*x^4 + 14*d^2*e^5*x^5 - 7*d*e^6*x^6 + 4*e^7*x^7)) + 1008*a^3*b^7*e^3*(3*A*e*(-130*d^7 + 160*d^6*e*x + 500*d^5*e^2*x^2 + 140*d^4*e^3*x^3 - 35*d^3*e^4*x^4 + 14*d^2*e^5*x^5 - 7*d*e^6*x^6 + 4*e^7*x^7) + 2*B*(225*d^8 - 390*d^7*e*x - 1035*d^6*e^2*x^2 - 280*d^5*e^3*x^3 + 70*d^4*e^4*x^4 - 28*d^3*e^5*x^5 + 14*d^2*e^6*x^6 - 8*d*e^7*x^7 + 5*e^8*x^8)) + 108*a^2*b^8*e^2*(7*A*e*(225*d^8 - 390*d^7*e*x - 1035*d^6*e^2*x^2 - 280*d^5*e^3*x^3 + 70*d^4*e^4*x^4 - 28*d^3*e^5*x^5 + 14*d^2*e^6*x^6 - 8*d*e^7*x^7 + 5*e^8*x^8) - 3*B*(595*d^9 - 1330*d^8*e*x - 3185*d^7*e^2*x^2 - 840*d^6*e^3*x^3 + 210*d^5*e^4*x^4 - 84*d^4*e^5*x^5 + 42*d^3*e^6*x^6 - 24*d^2*e^7*x^7 + 15*d*e^8*x^8 - 10*e^9*x^9)) + 18*a*b^9*e*(4*A*e*(-595*d^9 + 1330*d^8*e*x + 3185*d^7*e^2*x^2 + 840*d^6*e^3*x^3 - 210*d^5*e^4*x^4 + 84*d^4*e^5*x^5 - 42*d^3*e^6*x^6 + 24*d^2*e^7*x^7 - 15*d*e^8*x^8 + 10*e^9*x^9) + 5*B*(532*d^10 - 1456*d^9*e*x - 3248*d^8*e^2*x^2 - 840*d^7*e^3*x^3 + 210*d^6*e^4*x^4 - 84*d^5*e^5*x^5 + 42*d^4*e^6*x^6 - 24*d^3*e^7*x^7 + 15*d^2*e^8*x^8 - 10*d*e^9*x^9 + 7*e^10*x^10)) + b^10*(9*A*e*(532*d^10 - 1456*d^9*e*x - 3248*d^8*e^2*x^2 - 840*d^7*e^3*x^3 + 210*d^6*e^4*x^4 - 84*d^5*e^5*x^5 + 42*d^4*e^6*x^6 - 24*d^3*e^7*x^7 + 15*d^2*e^8*x^8 - 10*d*e^9*x^9 + 7*e^10*x^10) + B*(-5292*d^11 + 17136*d^10*e*x + 36288*d^9*e^2*x^2 + 9240*d^8*e^3*x^3 - 2310*d^7*e^4*x^4 + 924*d^6*e^5*x^5 - 462*d^5*e^6*x^6 + 264*d^4*e^7*x^7 - 165*d^3*e^8*x^8 + 110*d^2*e^9*x^9 - 77*d*e^10*x^10 + 56*e^11*x^11)) - 2520*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e)*(d + e*x)^2*Log[d + e*x])/(504*e^12*(d + e*x)^2)","B",1
1092,1,814,445,0.5656005,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^4} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^4,x]","\frac{21 B e^8 x^8 b^{10}+24 e^7 (-4 b B d+A b e+10 a B e) x^7 b^9-28 e^6 \left(2 d (2 A e-5 B d) b^2-10 a e (A e-4 B d) b-45 a^2 B e^2\right) x^6 b^8+168 e^5 \left(2 d^2 (A e-2 B d) b^3+4 a d e (5 B d-2 A e) b^2+9 a^2 e^2 (A e-4 B d) b+24 a^3 B e^3\right) x^5 b^7-210 e^4 \left(d^3 (4 A e-7 B d) b^4+20 a d^2 e (2 B d-A e) b^3+18 a^2 d e^2 (2 A e-5 B d) b^2-24 a^3 e^3 (A e-4 B d) b-42 a^4 B e^4\right) x^4 b^6+56 e^3 \left(-7 d^4 (8 B d-5 A e) b^5+50 a d^3 e (7 B d-4 A e) b^4-450 a^2 d^2 e^2 (2 B d-A e) b^3+240 a^3 d e^3 (5 B d-2 A e) b^2+210 a^4 e^4 (A e-4 B d) b+252 a^5 B e^5\right) x^3 b^5-84 e^2 \left(28 d^5 (2 A e-3 B d) b^6+70 a d^4 e (8 B d-5 A e) b^5-225 a^2 d^3 e^2 (7 B d-4 A e) b^4+1200 a^3 d^2 e^3 (2 B d-A e) b^3-420 a^4 d e^4 (5 B d-2 A e) b^2-252 a^5 e^5 (A e-4 B d) b-210 a^6 B e^6\right) x^2 b^4+168 e \left(12 d^6 (7 A e-10 B d) b^7+280 a d^5 e (3 B d-2 A e) b^6-315 a^2 d^4 e^2 (8 B d-5 A e) b^5+600 a^3 d^3 e^3 (7 B d-4 A e) b^4-2100 a^4 d^2 e^4 (2 B d-A e) b^3+504 a^5 d e^5 (5 B d-2 A e) b^2+210 a^6 e^6 (A e-4 B d) b+120 a^7 B e^7\right) x b^3+2520 (b d-a e)^7 (11 b B d-8 A b e-3 a B e) \log (d+e x) b^2+\frac{840 (b d-a e)^8 (11 b B d-9 A b e-2 a B e) b}{d+e x}-\frac{84 (b d-a e)^9 (11 b B d-10 A b e-a B e)}{(d+e x)^2}+\frac{56 (b d-a e)^{10} (B d-A e)}{(d+e x)^3}}{168 e^{12}}","-\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,"(168*b^3*e*(120*a^7*B*e^7 - 315*a^2*b^5*d^4*e^2*(8*B*d - 5*A*e) + 600*a^3*b^4*d^3*e^3*(7*B*d - 4*A*e) + 280*a*b^6*d^5*e*(3*B*d - 2*A*e) + 504*a^5*b^2*d*e^5*(5*B*d - 2*A*e) - 2100*a^4*b^3*d^2*e^4*(2*B*d - A*e) + 210*a^6*b*e^6*(-4*B*d + A*e) + 12*b^7*d^6*(-10*B*d + 7*A*e))*x - 84*b^4*e^2*(-210*a^6*B*e^6 + 70*a*b^5*d^4*e*(8*B*d - 5*A*e) - 225*a^2*b^4*d^3*e^2*(7*B*d - 4*A*e) - 420*a^4*b^2*d*e^4*(5*B*d - 2*A*e) + 1200*a^3*b^3*d^2*e^3*(2*B*d - A*e) - 252*a^5*b*e^5*(-4*B*d + A*e) + 28*b^6*d^5*(-3*B*d + 2*A*e))*x^2 + 56*b^5*e^3*(252*a^5*B*e^5 - 7*b^5*d^4*(8*B*d - 5*A*e) + 50*a*b^4*d^3*e*(7*B*d - 4*A*e) + 240*a^3*b^2*d*e^3*(5*B*d - 2*A*e) - 450*a^2*b^3*d^2*e^2*(2*B*d - A*e) + 210*a^4*b*e^4*(-4*B*d + A*e))*x^3 - 210*b^6*e^4*(-42*a^4*B*e^4 + 20*a*b^3*d^2*e*(2*B*d - A*e) - 24*a^3*b*e^3*(-4*B*d + A*e) + 18*a^2*b^2*d*e^2*(-5*B*d + 2*A*e) + b^4*d^3*(-7*B*d + 4*A*e))*x^4 + 168*b^7*e^5*(24*a^3*B*e^3 + 4*a*b^2*d*e*(5*B*d - 2*A*e) + 9*a^2*b*e^2*(-4*B*d + A*e) + 2*b^3*d^2*(-2*B*d + A*e))*x^5 - 28*b^8*e^6*(-45*a^2*B*e^2 - 10*a*b*e*(-4*B*d + A*e) + 2*b^2*d*(-5*B*d + 2*A*e))*x^6 + 24*b^9*e^7*(-4*b*B*d + A*b*e + 10*a*B*e)*x^7 + 21*b^10*B*e^8*x^8 + (56*(b*d - a*e)^10*(B*d - A*e))/(d + e*x)^3 - (84*(b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(d + e*x)^2 + (840*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(d + e*x) + 2520*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e)*Log[d + e*x])/(168*e^12)","A",1
1093,1,686,444,0.5311623,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^5} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^5,x]","\frac{-84 b^8 e^5 x^5 \left(-9 a^2 B e^2-2 a b e (A e-5 B d)+b^2 d (A e-3 B d)\right)+105 b^7 e^4 x^4 \left(24 a^3 B e^3+9 a^2 b e^2 (A e-5 B d)+10 a b^2 d e (3 B d-A e)+b^3 d^2 (3 A e-7 B d)\right)-140 b^6 e^3 x^3 \left(-42 a^4 B e^4-24 a^3 b e^3 (A e-5 B d)-45 a^2 b^2 d e^2 (3 B d-A e)+10 a b^3 d^2 e (7 B d-3 A e)+7 b^4 d^3 (A e-2 B d)\right)+42 b^5 e^2 x^2 \left(252 a^5 B e^5+210 a^4 b e^4 (A e-5 B d)+600 a^3 b^2 d e^3 (3 B d-A e)-225 a^2 b^3 d^2 e^2 (7 B d-3 A e)+350 a b^4 d^3 e (2 B d-A e)-14 b^5 d^4 (9 B d-5 A e)\right)-84 b^4 e x \left(-210 a^6 B e^6-252 a^5 b e^5 (A e-5 B d)-1050 a^4 b^2 d e^4 (3 B d-A e)+600 a^3 b^3 d^2 e^3 (7 B d-3 A e)-1575 a^2 b^4 d^3 e^2 (2 B d-A e)+140 a b^5 d^4 e (9 B d-5 A e)-42 b^6 d^5 (5 B d-3 A e)\right)+14 b^9 e^6 x^6 (10 a B e+A b e-5 b B d)-2520 b^3 (b d-a e)^6 \log (d+e x) (-4 a B e-7 A b e+11 b B d)-\frac{1260 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{d+e x}+\frac{210 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{(d+e x)^2}-\frac{28 (b d-a e)^9 (-a B e-10 A b e+11 b B d)}{(d+e x)^3}+\frac{21 (b d-a e)^{10} (B d-A e)}{(d+e x)^4}+12 b^{10} B e^7 x^7}{84 e^{12}}","-\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,"(-84*b^4*e*(-210*a^6*B*e^6 + 140*a*b^5*d^4*e*(9*B*d - 5*A*e) - 42*b^6*d^5*(5*B*d - 3*A*e) + 600*a^3*b^3*d^2*e^3*(7*B*d - 3*A*e) - 1575*a^2*b^4*d^3*e^2*(2*B*d - A*e) - 1050*a^4*b^2*d*e^4*(3*B*d - A*e) - 252*a^5*b*e^5*(-5*B*d + A*e))*x + 42*b^5*e^2*(252*a^5*B*e^5 - 14*b^5*d^4*(9*B*d - 5*A*e) - 225*a^2*b^3*d^2*e^2*(7*B*d - 3*A*e) + 350*a*b^4*d^3*e*(2*B*d - A*e) + 600*a^3*b^2*d*e^3*(3*B*d - A*e) + 210*a^4*b*e^4*(-5*B*d + A*e))*x^2 - 140*b^6*e^3*(-42*a^4*B*e^4 + 10*a*b^3*d^2*e*(7*B*d - 3*A*e) - 45*a^2*b^2*d*e^2*(3*B*d - A*e) - 24*a^3*b*e^3*(-5*B*d + A*e) + 7*b^4*d^3*(-2*B*d + A*e))*x^3 + 105*b^7*e^4*(24*a^3*B*e^3 + 10*a*b^2*d*e*(3*B*d - A*e) + 9*a^2*b*e^2*(-5*B*d + A*e) + b^3*d^2*(-7*B*d + 3*A*e))*x^4 - 84*b^8*e^5*(-9*a^2*B*e^2 - 2*a*b*e*(-5*B*d + A*e) + b^2*d*(-3*B*d + A*e))*x^5 + 14*b^9*e^6*(-5*b*B*d + A*b*e + 10*a*B*e)*x^6 + 12*b^10*B*e^7*x^7 + (21*(b*d - a*e)^10*(B*d - A*e))/(d + e*x)^4 - (28*(b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(d + e*x)^3 + (210*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(d + e*x)^2 - (1260*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(d + e*x) - 2520*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e)*Log[d + e*x])/(84*e^12)","A",1
1094,1,587,447,0.5836655,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^6} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^6,x]","\frac{-15 b^8 e^4 x^4 \left(-45 a^2 B e^2-10 a b e (A e-6 B d)+3 b^2 d (2 A e-7 B d)\right)+20 b^7 e^3 x^3 \left(120 a^3 B e^3+45 a^2 b e^2 (A e-6 B d)+30 a b^2 d e (7 B d-2 A e)-7 b^3 d^2 (8 B d-3 A e)\right)-30 b^6 e^2 x^2 \left(-210 a^4 B e^4-120 a^3 b e^3 (A e-6 B d)-135 a^2 b^2 d e^2 (7 B d-2 A e)+70 a b^3 d^2 e (8 B d-3 A e)-14 b^4 d^3 (9 B d-4 A e)\right)+60 b^5 e x \left(252 a^5 B e^5+210 a^4 b e^4 (A e-6 B d)+360 a^3 b^2 d e^3 (7 B d-2 A e)-315 a^2 b^3 d^2 e^2 (8 B d-3 A e)+140 a b^4 d^3 e (9 B d-4 A e)-126 b^5 d^4 (2 B d-A e)\right)+12 b^9 e^5 x^5 (10 a B e+A b e-6 b B d)+2520 b^4 (b d-a e)^5 \log (d+e x) (-5 a B e-6 A b e+11 b B d)+\frac{1800 b^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{d+e x}-\frac{450 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{(d+e x)^2}+\frac{100 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{(d+e x)^3}-\frac{15 (b d-a e)^9 (-a B e-10 A b e+11 b B d)}{(d+e x)^4}+\frac{12 (b d-a e)^{10} (B d-A e)}{(d+e x)^5}+10 b^{10} B e^6 x^6}{60 e^{12}}","-\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,"(60*b^5*e*(252*a^5*B*e^5 + 140*a*b^4*d^3*e*(9*B*d - 4*A*e) - 315*a^2*b^3*d^2*e^2*(8*B*d - 3*A*e) + 360*a^3*b^2*d*e^3*(7*B*d - 2*A*e) - 126*b^5*d^4*(2*B*d - A*e) + 210*a^4*b*e^4*(-6*B*d + A*e))*x - 30*b^6*e^2*(-210*a^4*B*e^4 - 14*b^4*d^3*(9*B*d - 4*A*e) + 70*a*b^3*d^2*e*(8*B*d - 3*A*e) - 135*a^2*b^2*d*e^2*(7*B*d - 2*A*e) - 120*a^3*b*e^3*(-6*B*d + A*e))*x^2 + 20*b^7*e^3*(120*a^3*B*e^3 - 7*b^3*d^2*(8*B*d - 3*A*e) + 30*a*b^2*d*e*(7*B*d - 2*A*e) + 45*a^2*b*e^2*(-6*B*d + A*e))*x^3 - 15*b^8*e^4*(-45*a^2*B*e^2 - 10*a*b*e*(-6*B*d + A*e) + 3*b^2*d*(-7*B*d + 2*A*e))*x^4 + 12*b^9*e^5*(-6*b*B*d + A*b*e + 10*a*B*e)*x^5 + 10*b^10*B*e^6*x^6 + (12*(b*d - a*e)^10*(B*d - A*e))/(d + e*x)^5 - (15*(b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(d + e*x)^4 + (100*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(d + e*x)^3 - (450*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(d + e*x)^2 + (1800*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(d + e*x) + 2520*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e)*Log[d + e*x])/(60*e^12)","A",1
1095,1,505,447,0.6021803,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^7} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^7,x]","\frac{-20 b^8 e^3 x^3 \left(-45 a^2 B e^2-10 a b e (A e-7 B d)+7 b^2 d (A e-4 B d)\right)+30 b^7 e^2 x^2 \left(120 a^3 B e^3+45 a^2 b e^2 (A e-7 B d)+70 a b^2 d e (4 B d-A e)+28 b^3 d^2 (A e-3 B d)\right)-60 b^6 e x \left(-210 a^4 B e^4-120 a^3 b e^3 (A e-7 B d)-315 a^2 b^2 d e^2 (4 B d-A e)+280 a b^3 d^2 e (3 B d-A e)-42 b^4 d^3 (5 B d-2 A e)\right)+15 b^9 e^4 x^4 (10 a B e+A b e-7 b B d)-2520 b^5 (b d-a e)^4 \log (d+e x) (-6 a B e-5 A b e+11 b B d)-\frac{2520 b^4 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{d+e x}+\frac{900 b^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{(d+e x)^2}-\frac{300 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{(d+e x)^3}+\frac{75 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{(d+e x)^4}-\frac{12 (b d-a e)^9 (-a B e-10 A b e+11 b B d)}{(d+e x)^5}+\frac{10 (b d-a e)^{10} (B d-A e)}{(d+e x)^6}+12 b^{10} B e^5 x^5}{60 e^{12}}","-\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,"(-60*b^6*e*(-210*a^4*B*e^4 - 42*b^4*d^3*(5*B*d - 2*A*e) + 280*a*b^3*d^2*e*(3*B*d - A*e) - 315*a^2*b^2*d*e^2*(4*B*d - A*e) - 120*a^3*b*e^3*(-7*B*d + A*e))*x + 30*b^7*e^2*(120*a^3*B*e^3 + 70*a*b^2*d*e*(4*B*d - A*e) + 45*a^2*b*e^2*(-7*B*d + A*e) + 28*b^3*d^2*(-3*B*d + A*e))*x^2 - 20*b^8*e^3*(-45*a^2*B*e^2 - 10*a*b*e*(-7*B*d + A*e) + 7*b^2*d*(-4*B*d + A*e))*x^3 + 15*b^9*e^4*(-7*b*B*d + A*b*e + 10*a*B*e)*x^4 + 12*b^10*B*e^5*x^5 + (10*(b*d - a*e)^10*(B*d - A*e))/(d + e*x)^6 - (12*(b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(d + e*x)^5 + (75*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(d + e*x)^4 - (300*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(d + e*x)^3 + (900*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(d + e*x)^2 - (2520*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e))/(d + e*x) - 2520*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e)*Log[d + e*x])/(60*e^12)","A",1
1096,1,450,444,0.6278364,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^8} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^8,x]","\frac{-42 b^8 e^2 x^2 \left(-45 a^2 B e^2-10 a b e (A e-8 B d)+4 b^2 d (2 A e-9 B d)\right)+84 b^7 e x \left(120 a^3 B e^3+45 a^2 b e^2 (A e-8 B d)+40 a b^2 d e (9 B d-2 A e)+12 b^3 d^2 (3 A e-10 B d)\right)+28 b^9 e^3 x^3 (10 a B e+A b e-8 b B d)+2520 b^6 (b d-a e)^3 \log (d+e x) (-7 a B e-4 A b e+11 b B d)+\frac{3528 b^5 (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{d+e x}-\frac{1764 b^4 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{(d+e x)^2}+\frac{840 b^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{(d+e x)^3}-\frac{315 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{(d+e x)^4}+\frac{84 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{(d+e x)^5}-\frac{14 (b d-a e)^9 (-a B e-10 A b e+11 b B d)}{(d+e x)^6}+\frac{12 (b d-a e)^{10} (B d-A e)}{(d+e x)^7}+21 b^{10} B e^4 x^4}{84 e^{12}}","-\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,"(84*b^7*e*(120*a^3*B*e^3 + 40*a*b^2*d*e*(9*B*d - 2*A*e) + 45*a^2*b*e^2*(-8*B*d + A*e) + 12*b^3*d^2*(-10*B*d + 3*A*e))*x - 42*b^8*e^2*(-45*a^2*B*e^2 - 10*a*b*e*(-8*B*d + A*e) + 4*b^2*d*(-9*B*d + 2*A*e))*x^2 + 28*b^9*e^3*(-8*b*B*d + A*b*e + 10*a*B*e)*x^3 + 21*b^10*B*e^4*x^4 + (12*(b*d - a*e)^10*(B*d - A*e))/(d + e*x)^7 - (14*(b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(d + e*x)^6 + (84*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(d + e*x)^5 - (315*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(d + e*x)^4 + (840*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(d + e*x)^3 - (1764*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e))/(d + e*x)^2 + (3528*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e))/(d + e*x) + 2520*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e)*Log[d + e*x])/(84*e^12)","A",1
1097,1,415,445,0.692287,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^9} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^9,x]","\frac{-168 b^8 e x \left(-45 a^2 B e^2-10 a b e (A e-9 B d)+9 b^2 d (A e-5 B d)\right)+84 b^9 e^2 x^2 (10 a B e+A b e-9 b B d)-2520 b^7 (b d-a e)^2 \log (d+e x) (-8 a B e-3 A b e+11 b B d)-\frac{5040 b^6 (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{d+e x}+\frac{3528 b^5 (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{(d+e x)^2}-\frac{2352 b^4 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{(d+e x)^3}+\frac{1260 b^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{(d+e x)^4}-\frac{504 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{(d+e x)^5}+\frac{140 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{(d+e x)^6}-\frac{24 (b d-a e)^9 (-a B e-10 A b e+11 b B d)}{(d+e x)^7}+\frac{21 (b d-a e)^{10} (B d-A e)}{(d+e x)^8}+56 b^{10} B e^3 x^3}{168 e^{12}}","-\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,"(-168*b^8*e*(-45*a^2*B*e^2 - 10*a*b*e*(-9*B*d + A*e) + 9*b^2*d*(-5*B*d + A*e))*x + 84*b^9*e^2*(-9*b*B*d + A*b*e + 10*a*B*e)*x^2 + 56*b^10*B*e^3*x^3 + (21*(b*d - a*e)^10*(B*d - A*e))/(d + e*x)^8 - (24*(b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(d + e*x)^7 + (140*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(d + e*x)^6 - (504*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(d + e*x)^5 + (1260*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(d + e*x)^4 - (2352*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e))/(d + e*x)^3 + (3528*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e))/(d + e*x)^2 - (5040*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e))/(d + e*x) - 2520*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e)*Log[d + e*x])/(168*e^12)","A",1
1098,1,1460,441,1.1052324,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{10}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^10,x]","-\frac{-\left(\left(B \left(42131 d^{11}+351459 e x d^{10}+1281096 e^2 x^2 d^9+2656584 e^3 x^3 d^8+3402756 e^4 x^4 d^7+2704212 e^5 x^5 d^6+1220688 e^6 x^6 d^5+190512 e^7 x^7 d^4-77112 e^8 x^8 d^3-36288 e^9 x^9 d^2-2772 e^{10} x^{10} d+252 e^{11} x^{11}\right)-2 A e \left(4861 d^{10}+41229 e x d^9+153576 e^2 x^2 d^8+328104 e^3 x^3 d^7+439236 e^4 x^4 d^6+375732 e^5 x^5 d^5+197568 e^6 x^6 d^4+54432 e^7 x^7 d^3+2268 e^8 x^8 d^2-2268 e^9 x^9 d-252 e^{10} x^{10}\right)\right) b^{10}\right)-2 a e \left(A d e \left(7129 d^8+61641 e x d^7+235224 e^2 x^2 d^6+518616 e^3 x^3 d^5+725004 e^4 x^4 d^4+661500 e^5 x^5 d^3+388080 e^6 x^6 d^2+136080 e^7 x^7 d+22680 e^8 x^8\right)-10 B \left(4861 d^{10}+41229 e x d^9+153576 e^2 x^2 d^8+328104 e^3 x^3 d^7+439236 e^4 x^4 d^6+375732 e^5 x^5 d^5+197568 e^6 x^6 d^4+54432 e^7 x^7 d^3+2268 e^8 x^8 d^2-2268 e^9 x^9 d-252 e^{10} x^{10}\right)\right) b^9-9 a^2 e^2 \left(B d \left(7129 d^8+61641 e x d^7+235224 e^2 x^2 d^6+518616 e^3 x^3 d^5+725004 e^4 x^4 d^4+661500 e^5 x^5 d^3+388080 e^6 x^6 d^2+136080 e^7 x^7 d+22680 e^8 x^8\right)-280 A e \left(d^8+9 e x d^7+36 e^2 x^2 d^6+84 e^3 x^3 d^5+126 e^4 x^4 d^4+126 e^5 x^5 d^3+84 e^6 x^6 d^2+36 e^7 x^7 d+9 e^8 x^8\right)\right) b^8-2520 (b d-a e) (11 b B d-2 A b e-9 a B e) (d+e x)^9 \log (d+e x) b^8+840 a^3 e^3 \left(A e \left(d^7+9 e x d^6+36 e^2 x^2 d^5+84 e^3 x^3 d^4+126 e^4 x^4 d^3+126 e^5 x^5 d^2+84 e^6 x^6 d+36 e^7 x^7\right)+8 B \left(d^8+9 e x d^7+36 e^2 x^2 d^6+84 e^3 x^3 d^5+126 e^4 x^4 d^4+126 e^5 x^5 d^3+84 e^6 x^6 d^2+36 e^7 x^7 d+9 e^8 x^8\right)\right) b^7+210 a^4 e^4 \left(2 A e \left(d^6+9 e x d^5+36 e^2 x^2 d^4+84 e^3 x^3 d^3+126 e^4 x^4 d^2+126 e^5 x^5 d+84 e^6 x^6\right)+7 B \left(d^7+9 e x d^6+36 e^2 x^2 d^5+84 e^3 x^3 d^4+126 e^4 x^4 d^3+126 e^5 x^5 d^2+84 e^6 x^6 d+36 e^7 x^7\right)\right) b^6+252 a^5 e^5 \left(A e \left(d^5+9 e x d^4+36 e^2 x^2 d^3+84 e^3 x^3 d^2+126 e^4 x^4 d+126 e^5 x^5\right)+2 B \left(d^6+9 e x d^5+36 e^2 x^2 d^4+84 e^3 x^3 d^3+126 e^4 x^4 d^2+126 e^5 x^5 d+84 e^6 x^6\right)\right) b^5+42 a^6 e^6 \left(4 A e \left(d^4+9 e x d^3+36 e^2 x^2 d^2+84 e^3 x^3 d+126 e^4 x^4\right)+5 B \left(d^5+9 e x d^4+36 e^2 x^2 d^3+84 e^3 x^3 d^2+126 e^4 x^4 d+126 e^5 x^5\right)\right) b^4+24 a^7 e^7 \left(5 A e \left(d^3+9 e x d^2+36 e^2 x^2 d+84 e^3 x^3\right)+4 B \left(d^4+9 e x d^3+36 e^2 x^2 d^2+84 e^3 x^3 d+126 e^4 x^4\right)\right) b^3+45 a^8 e^8 \left(2 A e \left(d^2+9 e x d+36 e^2 x^2\right)+B \left(d^3+9 e x d^2+36 e^2 x^2 d+84 e^3 x^3\right)\right) b^2+10 a^9 e^9 \left(7 A e (d+9 e x)+2 B \left(d^2+9 e x d+36 e^2 x^2\right)\right) b+7 a^{10} e^{10} (8 A e+B (d+9 e x))}{504 e^{12} (d+e x)^9}","-\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,"-1/504*(7*a^10*e^10*(8*A*e + B*(d + 9*e*x)) + 10*a^9*b*e^9*(7*A*e*(d + 9*e*x) + 2*B*(d^2 + 9*d*e*x + 36*e^2*x^2)) + 45*a^8*b^2*e^8*(2*A*e*(d^2 + 9*d*e*x + 36*e^2*x^2) + B*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3)) + 24*a^7*b^3*e^7*(5*A*e*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3) + 4*B*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4)) + 42*a^6*b^4*e^6*(4*A*e*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4) + 5*B*(d^5 + 9*d^4*e*x + 36*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 126*d*e^4*x^4 + 126*e^5*x^5)) + 252*a^5*b^5*e^5*(A*e*(d^5 + 9*d^4*e*x + 36*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 126*d*e^4*x^4 + 126*e^5*x^5) + 2*B*(d^6 + 9*d^5*e*x + 36*d^4*e^2*x^2 + 84*d^3*e^3*x^3 + 126*d^2*e^4*x^4 + 126*d*e^5*x^5 + 84*e^6*x^6)) + 210*a^4*b^6*e^4*(2*A*e*(d^6 + 9*d^5*e*x + 36*d^4*e^2*x^2 + 84*d^3*e^3*x^3 + 126*d^2*e^4*x^4 + 126*d*e^5*x^5 + 84*e^6*x^6) + 7*B*(d^7 + 9*d^6*e*x + 36*d^5*e^2*x^2 + 84*d^4*e^3*x^3 + 126*d^3*e^4*x^4 + 126*d^2*e^5*x^5 + 84*d*e^6*x^6 + 36*e^7*x^7)) + 840*a^3*b^7*e^3*(A*e*(d^7 + 9*d^6*e*x + 36*d^5*e^2*x^2 + 84*d^4*e^3*x^3 + 126*d^3*e^4*x^4 + 126*d^2*e^5*x^5 + 84*d*e^6*x^6 + 36*e^7*x^7) + 8*B*(d^8 + 9*d^7*e*x + 36*d^6*e^2*x^2 + 84*d^5*e^3*x^3 + 126*d^4*e^4*x^4 + 126*d^3*e^5*x^5 + 84*d^2*e^6*x^6 + 36*d*e^7*x^7 + 9*e^8*x^8)) - 9*a^2*b^8*e^2*(-280*A*e*(d^8 + 9*d^7*e*x + 36*d^6*e^2*x^2 + 84*d^5*e^3*x^3 + 126*d^4*e^4*x^4 + 126*d^3*e^5*x^5 + 84*d^2*e^6*x^6 + 36*d*e^7*x^7 + 9*e^8*x^8) + B*d*(7129*d^8 + 61641*d^7*e*x + 235224*d^6*e^2*x^2 + 518616*d^5*e^3*x^3 + 725004*d^4*e^4*x^4 + 661500*d^3*e^5*x^5 + 388080*d^2*e^6*x^6 + 136080*d*e^7*x^7 + 22680*e^8*x^8)) - 2*a*b^9*e*(A*d*e*(7129*d^8 + 61641*d^7*e*x + 235224*d^6*e^2*x^2 + 518616*d^5*e^3*x^3 + 725004*d^4*e^4*x^4 + 661500*d^3*e^5*x^5 + 388080*d^2*e^6*x^6 + 136080*d*e^7*x^7 + 22680*e^8*x^8) - 10*B*(4861*d^10 + 41229*d^9*e*x + 153576*d^8*e^2*x^2 + 328104*d^7*e^3*x^3 + 439236*d^6*e^4*x^4 + 375732*d^5*e^5*x^5 + 197568*d^4*e^6*x^6 + 54432*d^3*e^7*x^7 + 2268*d^2*e^8*x^8 - 2268*d*e^9*x^9 - 252*e^10*x^10)) - b^10*(-2*A*e*(4861*d^10 + 41229*d^9*e*x + 153576*d^8*e^2*x^2 + 328104*d^7*e^3*x^3 + 439236*d^6*e^4*x^4 + 375732*d^5*e^5*x^5 + 197568*d^4*e^6*x^6 + 54432*d^3*e^7*x^7 + 2268*d^2*e^8*x^8 - 2268*d*e^9*x^9 - 252*e^10*x^10) + B*(42131*d^11 + 351459*d^10*e*x + 1281096*d^9*e^2*x^2 + 2656584*d^8*e^3*x^3 + 3402756*d^7*e^4*x^4 + 2704212*d^6*e^5*x^5 + 1220688*d^5*e^6*x^6 + 190512*d^4*e^7*x^7 - 77112*d^3*e^8*x^8 - 36288*d^2*e^9*x^9 - 2772*d*e^10*x^10 + 252*e^11*x^11)) - 2520*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*(d + e*x)^9*Log[d + e*x])/(e^12*(d + e*x)^9)","B",1
1099,1,1447,446,1.075128,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{11}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^11,x]","-\frac{-\left(\left(A d e \left(7381 d^9+71290 e x d^8+308205 e^2 x^2 d^7+784080 e^3 x^3 d^6+1296540 e^4 x^4 d^5+1450008 e^5 x^5 d^4+1102500 e^6 x^6 d^3+554400 e^7 x^7 d^2+170100 e^8 x^8 d+25200 e^9 x^9\right)-B \left(55991 d^{11}+532190 e x d^{10}+2256255 e^2 x^2 d^9+5600880 e^3 x^3 d^8+8969940 e^4 x^4 d^7+9599688 e^5 x^5 d^6+6835500 e^6 x^6 d^5+3074400 e^7 x^7 d^4+737100 e^8 x^8 d^3+25200 e^9 x^9 d^2-25200 e^{10} x^{10} d-2520 e^{11} x^{11}\right)\right) b^{10}\right)-10 a e \left(B d \left(7381 d^9+71290 e x d^8+308205 e^2 x^2 d^7+784080 e^3 x^3 d^6+1296540 e^4 x^4 d^5+1450008 e^5 x^5 d^4+1102500 e^6 x^6 d^3+554400 e^7 x^7 d^2+170100 e^8 x^8 d+25200 e^9 x^9\right)-252 A e \left(d^9+10 e x d^8+45 e^2 x^2 d^7+120 e^3 x^3 d^6+210 e^4 x^4 d^5+252 e^5 x^5 d^4+210 e^6 x^6 d^3+120 e^7 x^7 d^2+45 e^8 x^8 d+10 e^9 x^9\right)\right) b^9+2520 (11 b B d-A b e-10 a B e) (d+e x)^{10} \log (d+e x) b^9+1260 a^2 e^2 \left(A e \left(d^8+10 e x d^7+45 e^2 x^2 d^6+120 e^3 x^3 d^5+210 e^4 x^4 d^4+252 e^5 x^5 d^3+210 e^6 x^6 d^2+120 e^7 x^7 d+45 e^8 x^8\right)+9 B \left(d^9+10 e x d^8+45 e^2 x^2 d^7+120 e^3 x^3 d^6+210 e^4 x^4 d^5+252 e^5 x^5 d^4+210 e^6 x^6 d^3+120 e^7 x^7 d^2+45 e^8 x^8 d+10 e^9 x^9\right)\right) b^8+840 a^3 e^3 \left(A e \left(d^7+10 e x d^6+45 e^2 x^2 d^5+120 e^3 x^3 d^4+210 e^4 x^4 d^3+252 e^5 x^5 d^2+210 e^6 x^6 d+120 e^7 x^7\right)+4 B \left(d^8+10 e x d^7+45 e^2 x^2 d^6+120 e^3 x^3 d^5+210 e^4 x^4 d^4+252 e^5 x^5 d^3+210 e^6 x^6 d^2+120 e^7 x^7 d+45 e^8 x^8\right)\right) b^7+210 a^4 e^4 \left(3 A e \left(d^6+10 e x d^5+45 e^2 x^2 d^4+120 e^3 x^3 d^3+210 e^4 x^4 d^2+252 e^5 x^5 d+210 e^6 x^6\right)+7 B \left(d^7+10 e x d^6+45 e^2 x^2 d^5+120 e^3 x^3 d^4+210 e^4 x^4 d^3+252 e^5 x^5 d^2+210 e^6 x^6 d+120 e^7 x^7\right)\right) b^6+252 a^5 e^5 \left(2 A e \left(d^5+10 e x d^4+45 e^2 x^2 d^3+120 e^3 x^3 d^2+210 e^4 x^4 d+252 e^5 x^5\right)+3 B \left(d^6+10 e x d^5+45 e^2 x^2 d^4+120 e^3 x^3 d^3+210 e^4 x^4 d^2+252 e^5 x^5 d+210 e^6 x^6\right)\right) b^5+420 a^6 e^6 \left(A e \left(d^4+10 e x d^3+45 e^2 x^2 d^2+120 e^3 x^3 d+210 e^4 x^4\right)+B \left(d^5+10 e x d^4+45 e^2 x^2 d^3+120 e^3 x^3 d^2+210 e^4 x^4 d+252 e^5 x^5\right)\right) b^4+120 a^7 e^7 \left(3 A e \left(d^3+10 e x d^2+45 e^2 x^2 d+120 e^3 x^3\right)+2 B \left(d^4+10 e x d^3+45 e^2 x^2 d^2+120 e^3 x^3 d+210 e^4 x^4\right)\right) b^3+45 a^8 e^8 \left(7 A e \left(d^2+10 e x d+45 e^2 x^2\right)+3 B \left(d^3+10 e x d^2+45 e^2 x^2 d+120 e^3 x^3\right)\right) b^2+70 a^9 e^9 \left(4 A e (d+10 e x)+B \left(d^2+10 e x d+45 e^2 x^2\right)\right) b+28 a^{10} e^{10} (9 A e+B (d+10 e x))}{2520 e^{12} (d+e x)^{10}}","-\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,"-1/2520*(28*a^10*e^10*(9*A*e + B*(d + 10*e*x)) + 70*a^9*b*e^9*(4*A*e*(d + 10*e*x) + B*(d^2 + 10*d*e*x + 45*e^2*x^2)) + 45*a^8*b^2*e^8*(7*A*e*(d^2 + 10*d*e*x + 45*e^2*x^2) + 3*B*(d^3 + 10*d^2*e*x + 45*d*e^2*x^2 + 120*e^3*x^3)) + 120*a^7*b^3*e^7*(3*A*e*(d^3 + 10*d^2*e*x + 45*d*e^2*x^2 + 120*e^3*x^3) + 2*B*(d^4 + 10*d^3*e*x + 45*d^2*e^2*x^2 + 120*d*e^3*x^3 + 210*e^4*x^4)) + 420*a^6*b^4*e^6*(A*e*(d^4 + 10*d^3*e*x + 45*d^2*e^2*x^2 + 120*d*e^3*x^3 + 210*e^4*x^4) + B*(d^5 + 10*d^4*e*x + 45*d^3*e^2*x^2 + 120*d^2*e^3*x^3 + 210*d*e^4*x^4 + 252*e^5*x^5)) + 252*a^5*b^5*e^5*(2*A*e*(d^5 + 10*d^4*e*x + 45*d^3*e^2*x^2 + 120*d^2*e^3*x^3 + 210*d*e^4*x^4 + 252*e^5*x^5) + 3*B*(d^6 + 10*d^5*e*x + 45*d^4*e^2*x^2 + 120*d^3*e^3*x^3 + 210*d^2*e^4*x^4 + 252*d*e^5*x^5 + 210*e^6*x^6)) + 210*a^4*b^6*e^4*(3*A*e*(d^6 + 10*d^5*e*x + 45*d^4*e^2*x^2 + 120*d^3*e^3*x^3 + 210*d^2*e^4*x^4 + 252*d*e^5*x^5 + 210*e^6*x^6) + 7*B*(d^7 + 10*d^6*e*x + 45*d^5*e^2*x^2 + 120*d^4*e^3*x^3 + 210*d^3*e^4*x^4 + 252*d^2*e^5*x^5 + 210*d*e^6*x^6 + 120*e^7*x^7)) + 840*a^3*b^7*e^3*(A*e*(d^7 + 10*d^6*e*x + 45*d^5*e^2*x^2 + 120*d^4*e^3*x^3 + 210*d^3*e^4*x^4 + 252*d^2*e^5*x^5 + 210*d*e^6*x^6 + 120*e^7*x^7) + 4*B*(d^8 + 10*d^7*e*x + 45*d^6*e^2*x^2 + 120*d^5*e^3*x^3 + 210*d^4*e^4*x^4 + 252*d^3*e^5*x^5 + 210*d^2*e^6*x^6 + 120*d*e^7*x^7 + 45*e^8*x^8)) + 1260*a^2*b^8*e^2*(A*e*(d^8 + 10*d^7*e*x + 45*d^6*e^2*x^2 + 120*d^5*e^3*x^3 + 210*d^4*e^4*x^4 + 252*d^3*e^5*x^5 + 210*d^2*e^6*x^6 + 120*d*e^7*x^7 + 45*e^8*x^8) + 9*B*(d^9 + 10*d^8*e*x + 45*d^7*e^2*x^2 + 120*d^6*e^3*x^3 + 210*d^5*e^4*x^4 + 252*d^4*e^5*x^5 + 210*d^3*e^6*x^6 + 120*d^2*e^7*x^7 + 45*d*e^8*x^8 + 10*e^9*x^9)) - 10*a*b^9*e*(-252*A*e*(d^9 + 10*d^8*e*x + 45*d^7*e^2*x^2 + 120*d^6*e^3*x^3 + 210*d^5*e^4*x^4 + 252*d^4*e^5*x^5 + 210*d^3*e^6*x^6 + 120*d^2*e^7*x^7 + 45*d*e^8*x^8 + 10*e^9*x^9) + B*d*(7381*d^9 + 71290*d^8*e*x + 308205*d^7*e^2*x^2 + 784080*d^6*e^3*x^3 + 1296540*d^5*e^4*x^4 + 1450008*d^4*e^5*x^5 + 1102500*d^3*e^6*x^6 + 554400*d^2*e^7*x^7 + 170100*d*e^8*x^8 + 25200*e^9*x^9)) - b^10*(A*d*e*(7381*d^9 + 71290*d^8*e*x + 308205*d^7*e^2*x^2 + 784080*d^6*e^3*x^3 + 1296540*d^5*e^4*x^4 + 1450008*d^4*e^5*x^5 + 1102500*d^3*e^6*x^6 + 554400*d^2*e^7*x^7 + 170100*d*e^8*x^8 + 25200*e^9*x^9) - B*(55991*d^11 + 532190*d^10*e*x + 2256255*d^9*e^2*x^2 + 5600880*d^8*e^3*x^3 + 8969940*d^7*e^4*x^4 + 9599688*d^6*e^5*x^5 + 6835500*d^5*e^6*x^6 + 3074400*d^4*e^7*x^7 + 737100*d^3*e^8*x^8 + 25200*d^2*e^9*x^9 - 25200*d*e^10*x^10 - 2520*e^11*x^11)) + 2520*b^9*(11*b*B*d - A*b*e - 10*a*B*e)*(d + e*x)^10*Log[d + e*x])/(e^12*(d + e*x)^10)","B",1
1100,1,1443,321,2.0863644,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{12}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^12,x]","-\frac{-27720 b^{10} B \log (d+e x) (d+e x)^{11}+252 a^{10} e^{10} (10 A e+B (d+11 e x))+280 a^9 b e^9 \left(9 A e (d+11 e x)+2 B \left(d^2+11 e x d+55 e^2 x^2\right)\right)+315 a^8 b^2 e^8 \left(8 A e \left(d^2+11 e x d+55 e^2 x^2\right)+3 B \left(d^3+11 e x d^2+55 e^2 x^2 d+165 e^3 x^3\right)\right)+360 a^7 b^3 e^7 \left(7 A e \left(d^3+11 e x d^2+55 e^2 x^2 d+165 e^3 x^3\right)+4 B \left(d^4+11 e x d^3+55 e^2 x^2 d^2+165 e^3 x^3 d+330 e^4 x^4\right)\right)+420 a^6 b^4 e^6 \left(6 A e \left(d^4+11 e x d^3+55 e^2 x^2 d^2+165 e^3 x^3 d+330 e^4 x^4\right)+5 B \left(d^5+11 e x d^4+55 e^2 x^2 d^3+165 e^3 x^3 d^2+330 e^4 x^4 d+462 e^5 x^5\right)\right)+504 a^5 b^5 e^5 \left(5 A e \left(d^5+11 e x d^4+55 e^2 x^2 d^3+165 e^3 x^3 d^2+330 e^4 x^4 d+462 e^5 x^5\right)+6 B \left(d^6+11 e x d^5+55 e^2 x^2 d^4+165 e^3 x^3 d^3+330 e^4 x^4 d^2+462 e^5 x^5 d+462 e^6 x^6\right)\right)+630 a^4 b^6 e^4 \left(4 A e \left(d^6+11 e x d^5+55 e^2 x^2 d^4+165 e^3 x^3 d^3+330 e^4 x^4 d^2+462 e^5 x^5 d+462 e^6 x^6\right)+7 B \left(d^7+11 e x d^6+55 e^2 x^2 d^5+165 e^3 x^3 d^4+330 e^4 x^4 d^3+462 e^5 x^5 d^2+462 e^6 x^6 d+330 e^7 x^7\right)\right)+840 a^3 b^7 e^3 \left(3 A e \left(d^7+11 e x d^6+55 e^2 x^2 d^5+165 e^3 x^3 d^4+330 e^4 x^4 d^3+462 e^5 x^5 d^2+462 e^6 x^6 d+330 e^7 x^7\right)+8 B \left(d^8+11 e x d^7+55 e^2 x^2 d^6+165 e^3 x^3 d^5+330 e^4 x^4 d^4+462 e^5 x^5 d^3+462 e^6 x^6 d^2+330 e^7 x^7 d+165 e^8 x^8\right)\right)+1260 a^2 b^8 e^2 \left(2 A e \left(d^8+11 e x d^7+55 e^2 x^2 d^6+165 e^3 x^3 d^5+330 e^4 x^4 d^4+462 e^5 x^5 d^3+462 e^6 x^6 d^2+330 e^7 x^7 d+165 e^8 x^8\right)+9 B \left(d^9+11 e x d^8+55 e^2 x^2 d^7+165 e^3 x^3 d^6+330 e^4 x^4 d^5+462 e^5 x^5 d^4+462 e^6 x^6 d^3+330 e^7 x^7 d^2+165 e^8 x^8 d+55 e^9 x^9\right)\right)+2520 a b^9 e \left(A e \left(d^9+11 e x d^8+55 e^2 x^2 d^7+165 e^3 x^3 d^6+330 e^4 x^4 d^5+462 e^5 x^5 d^4+462 e^6 x^6 d^3+330 e^7 x^7 d^2+165 e^8 x^8 d+55 e^9 x^9\right)+10 B \left(d^{10}+11 e x d^9+55 e^2 x^2 d^8+165 e^3 x^3 d^7+330 e^4 x^4 d^6+462 e^5 x^5 d^5+462 e^6 x^6 d^4+330 e^7 x^7 d^3+165 e^8 x^8 d^2+55 e^9 x^9 d+11 e^{10} x^{10}\right)\right)+b^{10} \left(2520 A e \left(d^{10}+11 e x d^9+55 e^2 x^2 d^8+165 e^3 x^3 d^7+330 e^4 x^4 d^6+462 e^5 x^5 d^5+462 e^6 x^6 d^4+330 e^7 x^7 d^3+165 e^8 x^8 d^2+55 e^9 x^9 d+11 e^{10} x^{10}\right)-B d \left(83711 d^{10}+893101 e x d^9+4313045 e^2 x^2 d^8+12430935 e^3 x^3 d^7+23718420 e^4 x^4 d^6+31376268 e^5 x^5 d^5+29241828 e^6 x^6 d^4+19057500 e^7 x^7 d^3+8385300 e^8 x^8 d^2+2286900 e^9 x^9 d+304920 e^{10} x^{10}\right)\right)}{27720 e^{12} (d+e x)^{11}}","-\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,"-1/27720*(252*a^10*e^10*(10*A*e + B*(d + 11*e*x)) + 280*a^9*b*e^9*(9*A*e*(d + 11*e*x) + 2*B*(d^2 + 11*d*e*x + 55*e^2*x^2)) + 315*a^8*b^2*e^8*(8*A*e*(d^2 + 11*d*e*x + 55*e^2*x^2) + 3*B*(d^3 + 11*d^2*e*x + 55*d*e^2*x^2 + 165*e^3*x^3)) + 360*a^7*b^3*e^7*(7*A*e*(d^3 + 11*d^2*e*x + 55*d*e^2*x^2 + 165*e^3*x^3) + 4*B*(d^4 + 11*d^3*e*x + 55*d^2*e^2*x^2 + 165*d*e^3*x^3 + 330*e^4*x^4)) + 420*a^6*b^4*e^6*(6*A*e*(d^4 + 11*d^3*e*x + 55*d^2*e^2*x^2 + 165*d*e^3*x^3 + 330*e^4*x^4) + 5*B*(d^5 + 11*d^4*e*x + 55*d^3*e^2*x^2 + 165*d^2*e^3*x^3 + 330*d*e^4*x^4 + 462*e^5*x^5)) + 504*a^5*b^5*e^5*(5*A*e*(d^5 + 11*d^4*e*x + 55*d^3*e^2*x^2 + 165*d^2*e^3*x^3 + 330*d*e^4*x^4 + 462*e^5*x^5) + 6*B*(d^6 + 11*d^5*e*x + 55*d^4*e^2*x^2 + 165*d^3*e^3*x^3 + 330*d^2*e^4*x^4 + 462*d*e^5*x^5 + 462*e^6*x^6)) + 630*a^4*b^6*e^4*(4*A*e*(d^6 + 11*d^5*e*x + 55*d^4*e^2*x^2 + 165*d^3*e^3*x^3 + 330*d^2*e^4*x^4 + 462*d*e^5*x^5 + 462*e^6*x^6) + 7*B*(d^7 + 11*d^6*e*x + 55*d^5*e^2*x^2 + 165*d^4*e^3*x^3 + 330*d^3*e^4*x^4 + 462*d^2*e^5*x^5 + 462*d*e^6*x^6 + 330*e^7*x^7)) + 840*a^3*b^7*e^3*(3*A*e*(d^7 + 11*d^6*e*x + 55*d^5*e^2*x^2 + 165*d^4*e^3*x^3 + 330*d^3*e^4*x^4 + 462*d^2*e^5*x^5 + 462*d*e^6*x^6 + 330*e^7*x^7) + 8*B*(d^8 + 11*d^7*e*x + 55*d^6*e^2*x^2 + 165*d^5*e^3*x^3 + 330*d^4*e^4*x^4 + 462*d^3*e^5*x^5 + 462*d^2*e^6*x^6 + 330*d*e^7*x^7 + 165*e^8*x^8)) + 1260*a^2*b^8*e^2*(2*A*e*(d^8 + 11*d^7*e*x + 55*d^6*e^2*x^2 + 165*d^5*e^3*x^3 + 330*d^4*e^4*x^4 + 462*d^3*e^5*x^5 + 462*d^2*e^6*x^6 + 330*d*e^7*x^7 + 165*e^8*x^8) + 9*B*(d^9 + 11*d^8*e*x + 55*d^7*e^2*x^2 + 165*d^6*e^3*x^3 + 330*d^5*e^4*x^4 + 462*d^4*e^5*x^5 + 462*d^3*e^6*x^6 + 330*d^2*e^7*x^7 + 165*d*e^8*x^8 + 55*e^9*x^9)) + 2520*a*b^9*e*(A*e*(d^9 + 11*d^8*e*x + 55*d^7*e^2*x^2 + 165*d^6*e^3*x^3 + 330*d^5*e^4*x^4 + 462*d^4*e^5*x^5 + 462*d^3*e^6*x^6 + 330*d^2*e^7*x^7 + 165*d*e^8*x^8 + 55*e^9*x^9) + 10*B*(d^10 + 11*d^9*e*x + 55*d^8*e^2*x^2 + 165*d^7*e^3*x^3 + 330*d^6*e^4*x^4 + 462*d^5*e^5*x^5 + 462*d^4*e^6*x^6 + 330*d^3*e^7*x^7 + 165*d^2*e^8*x^8 + 55*d*e^9*x^9 + 11*e^10*x^10)) + b^10*(2520*A*e*(d^10 + 11*d^9*e*x + 55*d^8*e^2*x^2 + 165*d^7*e^3*x^3 + 330*d^6*e^4*x^4 + 462*d^5*e^5*x^5 + 462*d^4*e^6*x^6 + 330*d^3*e^7*x^7 + 165*d^2*e^8*x^8 + 55*d*e^9*x^9 + 11*e^10*x^10) - B*d*(83711*d^10 + 893101*d^9*e*x + 4313045*d^8*e^2*x^2 + 12430935*d^7*e^3*x^3 + 23718420*d^6*e^4*x^4 + 31376268*d^5*e^5*x^5 + 29241828*d^4*e^6*x^6 + 19057500*d^3*e^7*x^7 + 8385300*d^2*e^8*x^8 + 2286900*d*e^9*x^9 + 304920*e^10*x^10)) - 27720*b^10*B*(d + e*x)^11*Log[d + e*x])/(e^12*(d + e*x)^11)","B",1
1101,1,1421,86,0.9104199,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{13}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^13,x]","-\frac{\left(A e \left(d^{10}+12 e x d^9+66 e^2 x^2 d^8+220 e^3 x^3 d^7+495 e^4 x^4 d^6+792 e^5 x^5 d^5+924 e^6 x^6 d^4+792 e^7 x^7 d^3+495 e^8 x^8 d^2+220 e^9 x^9 d+66 e^{10} x^{10}\right)+11 B \left(d^{11}+12 e x d^{10}+66 e^2 x^2 d^9+220 e^3 x^3 d^8+495 e^4 x^4 d^7+792 e^5 x^5 d^6+924 e^6 x^6 d^5+792 e^7 x^7 d^4+495 e^8 x^8 d^3+220 e^9 x^9 d^2+66 e^{10} x^{10} d+12 e^{11} x^{11}\right)\right) b^{10}+2 a e \left(A e \left(d^9+12 e x d^8+66 e^2 x^2 d^7+220 e^3 x^3 d^6+495 e^4 x^4 d^5+792 e^5 x^5 d^4+924 e^6 x^6 d^3+792 e^7 x^7 d^2+495 e^8 x^8 d+220 e^9 x^9\right)+5 B \left(d^{10}+12 e x d^9+66 e^2 x^2 d^8+220 e^3 x^3 d^7+495 e^4 x^4 d^6+792 e^5 x^5 d^5+924 e^6 x^6 d^4+792 e^7 x^7 d^3+495 e^8 x^8 d^2+220 e^9 x^9 d+66 e^{10} x^{10}\right)\right) b^9+3 a^2 e^2 \left(A e \left(d^8+12 e x d^7+66 e^2 x^2 d^6+220 e^3 x^3 d^5+495 e^4 x^4 d^4+792 e^5 x^5 d^3+924 e^6 x^6 d^2+792 e^7 x^7 d+495 e^8 x^8\right)+3 B \left(d^9+12 e x d^8+66 e^2 x^2 d^7+220 e^3 x^3 d^6+495 e^4 x^4 d^5+792 e^5 x^5 d^4+924 e^6 x^6 d^3+792 e^7 x^7 d^2+495 e^8 x^8 d+220 e^9 x^9\right)\right) b^8+4 a^3 e^3 \left(A e \left(d^7+12 e x d^6+66 e^2 x^2 d^5+220 e^3 x^3 d^4+495 e^4 x^4 d^3+792 e^5 x^5 d^2+924 e^6 x^6 d+792 e^7 x^7\right)+2 B \left(d^8+12 e x d^7+66 e^2 x^2 d^6+220 e^3 x^3 d^5+495 e^4 x^4 d^4+792 e^5 x^5 d^3+924 e^6 x^6 d^2+792 e^7 x^7 d+495 e^8 x^8\right)\right) b^7+a^4 e^4 \left(5 A e \left(d^6+12 e x d^5+66 e^2 x^2 d^4+220 e^3 x^3 d^3+495 e^4 x^4 d^2+792 e^5 x^5 d+924 e^6 x^6\right)+7 B \left(d^7+12 e x d^6+66 e^2 x^2 d^5+220 e^3 x^3 d^4+495 e^4 x^4 d^3+792 e^5 x^5 d^2+924 e^6 x^6 d+792 e^7 x^7\right)\right) b^6+6 a^5 e^5 \left(A e \left(d^5+12 e x d^4+66 e^2 x^2 d^3+220 e^3 x^3 d^2+495 e^4 x^4 d+792 e^5 x^5\right)+B \left(d^6+12 e x d^5+66 e^2 x^2 d^4+220 e^3 x^3 d^3+495 e^4 x^4 d^2+792 e^5 x^5 d+924 e^6 x^6\right)\right) b^5+a^6 e^6 \left(7 A e \left(d^4+12 e x d^3+66 e^2 x^2 d^2+220 e^3 x^3 d+495 e^4 x^4\right)+5 B \left(d^5+12 e x d^4+66 e^2 x^2 d^3+220 e^3 x^3 d^2+495 e^4 x^4 d+792 e^5 x^5\right)\right) b^4+4 a^7 e^7 \left(2 A e \left(d^3+12 e x d^2+66 e^2 x^2 d+220 e^3 x^3\right)+B \left(d^4+12 e x d^3+66 e^2 x^2 d^2+220 e^3 x^3 d+495 e^4 x^4\right)\right) b^3+3 a^8 e^8 \left(3 A e \left(d^2+12 e x d+66 e^2 x^2\right)+B \left(d^3+12 e x d^2+66 e^2 x^2 d+220 e^3 x^3\right)\right) b^2+2 a^9 e^9 \left(5 A e (d+12 e x)+B \left(d^2+12 e x d+66 e^2 x^2\right)\right) b+a^{10} e^{10} (11 A e+B (d+12 e x))}{132 e^{12} (d+e x)^{12}}","\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,"-1/132*(a^10*e^10*(11*A*e + B*(d + 12*e*x)) + 2*a^9*b*e^9*(5*A*e*(d + 12*e*x) + B*(d^2 + 12*d*e*x + 66*e^2*x^2)) + 3*a^8*b^2*e^8*(3*A*e*(d^2 + 12*d*e*x + 66*e^2*x^2) + B*(d^3 + 12*d^2*e*x + 66*d*e^2*x^2 + 220*e^3*x^3)) + 4*a^7*b^3*e^7*(2*A*e*(d^3 + 12*d^2*e*x + 66*d*e^2*x^2 + 220*e^3*x^3) + B*(d^4 + 12*d^3*e*x + 66*d^2*e^2*x^2 + 220*d*e^3*x^3 + 495*e^4*x^4)) + a^6*b^4*e^6*(7*A*e*(d^4 + 12*d^3*e*x + 66*d^2*e^2*x^2 + 220*d*e^3*x^3 + 495*e^4*x^4) + 5*B*(d^5 + 12*d^4*e*x + 66*d^3*e^2*x^2 + 220*d^2*e^3*x^3 + 495*d*e^4*x^4 + 792*e^5*x^5)) + 6*a^5*b^5*e^5*(A*e*(d^5 + 12*d^4*e*x + 66*d^3*e^2*x^2 + 220*d^2*e^3*x^3 + 495*d*e^4*x^4 + 792*e^5*x^5) + B*(d^6 + 12*d^5*e*x + 66*d^4*e^2*x^2 + 220*d^3*e^3*x^3 + 495*d^2*e^4*x^4 + 792*d*e^5*x^5 + 924*e^6*x^6)) + a^4*b^6*e^4*(5*A*e*(d^6 + 12*d^5*e*x + 66*d^4*e^2*x^2 + 220*d^3*e^3*x^3 + 495*d^2*e^4*x^4 + 792*d*e^5*x^5 + 924*e^6*x^6) + 7*B*(d^7 + 12*d^6*e*x + 66*d^5*e^2*x^2 + 220*d^4*e^3*x^3 + 495*d^3*e^4*x^4 + 792*d^2*e^5*x^5 + 924*d*e^6*x^6 + 792*e^7*x^7)) + 4*a^3*b^7*e^3*(A*e*(d^7 + 12*d^6*e*x + 66*d^5*e^2*x^2 + 220*d^4*e^3*x^3 + 495*d^3*e^4*x^4 + 792*d^2*e^5*x^5 + 924*d*e^6*x^6 + 792*e^7*x^7) + 2*B*(d^8 + 12*d^7*e*x + 66*d^6*e^2*x^2 + 220*d^5*e^3*x^3 + 495*d^4*e^4*x^4 + 792*d^3*e^5*x^5 + 924*d^2*e^6*x^6 + 792*d*e^7*x^7 + 495*e^8*x^8)) + 3*a^2*b^8*e^2*(A*e*(d^8 + 12*d^7*e*x + 66*d^6*e^2*x^2 + 220*d^5*e^3*x^3 + 495*d^4*e^4*x^4 + 792*d^3*e^5*x^5 + 924*d^2*e^6*x^6 + 792*d*e^7*x^7 + 495*e^8*x^8) + 3*B*(d^9 + 12*d^8*e*x + 66*d^7*e^2*x^2 + 220*d^6*e^3*x^3 + 495*d^5*e^4*x^4 + 792*d^4*e^5*x^5 + 924*d^3*e^6*x^6 + 792*d^2*e^7*x^7 + 495*d*e^8*x^8 + 220*e^9*x^9)) + 2*a*b^9*e*(A*e*(d^9 + 12*d^8*e*x + 66*d^7*e^2*x^2 + 220*d^6*e^3*x^3 + 495*d^5*e^4*x^4 + 792*d^4*e^5*x^5 + 924*d^3*e^6*x^6 + 792*d^2*e^7*x^7 + 495*d*e^8*x^8 + 220*e^9*x^9) + 5*B*(d^10 + 12*d^9*e*x + 66*d^8*e^2*x^2 + 220*d^7*e^3*x^3 + 495*d^6*e^4*x^4 + 792*d^5*e^5*x^5 + 924*d^4*e^6*x^6 + 792*d^3*e^7*x^7 + 495*d^2*e^8*x^8 + 220*d*e^9*x^9 + 66*e^10*x^10)) + b^10*(A*e*(d^10 + 12*d^9*e*x + 66*d^8*e^2*x^2 + 220*d^7*e^3*x^3 + 495*d^6*e^4*x^4 + 792*d^5*e^5*x^5 + 924*d^4*e^6*x^6 + 792*d^3*e^7*x^7 + 495*d^2*e^8*x^8 + 220*d*e^9*x^9 + 66*e^10*x^10) + 11*B*(d^11 + 12*d^10*e*x + 66*d^9*e^2*x^2 + 220*d^8*e^3*x^3 + 495*d^7*e^4*x^4 + 792*d^6*e^5*x^5 + 924*d^5*e^6*x^6 + 792*d^4*e^7*x^7 + 495*d^3*e^8*x^8 + 220*d^2*e^9*x^9 + 66*d*e^10*x^10 + 12*e^11*x^11)))/(e^12*(d + e*x)^12)","B",1
1102,1,1433,135,1.0072128,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{14}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^14,x]","-\frac{\left(2 A e \left(d^{10}+13 e x d^9+78 e^2 x^2 d^8+286 e^3 x^3 d^7+715 e^4 x^4 d^6+1287 e^5 x^5 d^5+1716 e^6 x^6 d^4+1716 e^7 x^7 d^3+1287 e^8 x^8 d^2+715 e^9 x^9 d+286 e^{10} x^{10}\right)+11 B \left(d^{11}+13 e x d^{10}+78 e^2 x^2 d^9+286 e^3 x^3 d^8+715 e^4 x^4 d^7+1287 e^5 x^5 d^6+1716 e^6 x^6 d^5+1716 e^7 x^7 d^4+1287 e^8 x^8 d^3+715 e^9 x^9 d^2+286 e^{10} x^{10} d+78 e^{11} x^{11}\right)\right) b^{10}+2 a e \left(3 A e \left(d^9+13 e x d^8+78 e^2 x^2 d^7+286 e^3 x^3 d^6+715 e^4 x^4 d^5+1287 e^5 x^5 d^4+1716 e^6 x^6 d^3+1716 e^7 x^7 d^2+1287 e^8 x^8 d+715 e^9 x^9\right)+10 B \left(d^{10}+13 e x d^9+78 e^2 x^2 d^8+286 e^3 x^3 d^7+715 e^4 x^4 d^6+1287 e^5 x^5 d^5+1716 e^6 x^6 d^4+1716 e^7 x^7 d^3+1287 e^8 x^8 d^2+715 e^9 x^9 d+286 e^{10} x^{10}\right)\right) b^9+3 a^2 e^2 \left(4 A e \left(d^8+13 e x d^7+78 e^2 x^2 d^6+286 e^3 x^3 d^5+715 e^4 x^4 d^4+1287 e^5 x^5 d^3+1716 e^6 x^6 d^2+1716 e^7 x^7 d+1287 e^8 x^8\right)+9 B \left(d^9+13 e x d^8+78 e^2 x^2 d^7+286 e^3 x^3 d^6+715 e^4 x^4 d^5+1287 e^5 x^5 d^4+1716 e^6 x^6 d^3+1716 e^7 x^7 d^2+1287 e^8 x^8 d+715 e^9 x^9\right)\right) b^8+4 a^3 e^3 \left(5 A e \left(d^7+13 e x d^6+78 e^2 x^2 d^5+286 e^3 x^3 d^4+715 e^4 x^4 d^3+1287 e^5 x^5 d^2+1716 e^6 x^6 d+1716 e^7 x^7\right)+8 B \left(d^8+13 e x d^7+78 e^2 x^2 d^6+286 e^3 x^3 d^5+715 e^4 x^4 d^4+1287 e^5 x^5 d^3+1716 e^6 x^6 d^2+1716 e^7 x^7 d+1287 e^8 x^8\right)\right) b^7+5 a^4 e^4 \left(6 A e \left(d^6+13 e x d^5+78 e^2 x^2 d^4+286 e^3 x^3 d^3+715 e^4 x^4 d^2+1287 e^5 x^5 d+1716 e^6 x^6\right)+7 B \left(d^7+13 e x d^6+78 e^2 x^2 d^5+286 e^3 x^3 d^4+715 e^4 x^4 d^3+1287 e^5 x^5 d^2+1716 e^6 x^6 d+1716 e^7 x^7\right)\right) b^6+6 a^5 e^5 \left(7 A e \left(d^5+13 e x d^4+78 e^2 x^2 d^3+286 e^3 x^3 d^2+715 e^4 x^4 d+1287 e^5 x^5\right)+6 B \left(d^6+13 e x d^5+78 e^2 x^2 d^4+286 e^3 x^3 d^3+715 e^4 x^4 d^2+1287 e^5 x^5 d+1716 e^6 x^6\right)\right) b^5+7 a^6 e^6 \left(8 A e \left(d^4+13 e x d^3+78 e^2 x^2 d^2+286 e^3 x^3 d+715 e^4 x^4\right)+5 B \left(d^5+13 e x d^4+78 e^2 x^2 d^3+286 e^3 x^3 d^2+715 e^4 x^4 d+1287 e^5 x^5\right)\right) b^4+8 a^7 e^7 \left(9 A e \left(d^3+13 e x d^2+78 e^2 x^2 d+286 e^3 x^3\right)+4 B \left(d^4+13 e x d^3+78 e^2 x^2 d^2+286 e^3 x^3 d+715 e^4 x^4\right)\right) b^3+9 a^8 e^8 \left(10 A e \left(d^2+13 e x d+78 e^2 x^2\right)+3 B \left(d^3+13 e x d^2+78 e^2 x^2 d+286 e^3 x^3\right)\right) b^2+10 a^9 e^9 \left(11 A e (d+13 e x)+2 B \left(d^2+13 e x d+78 e^2 x^2\right)\right) b+11 a^{10} e^{10} (12 A e+B (d+13 e x))}{1716 e^{12} (d+e x)^{13}}","\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,"-1/1716*(11*a^10*e^10*(12*A*e + B*(d + 13*e*x)) + 10*a^9*b*e^9*(11*A*e*(d + 13*e*x) + 2*B*(d^2 + 13*d*e*x + 78*e^2*x^2)) + 9*a^8*b^2*e^8*(10*A*e*(d^2 + 13*d*e*x + 78*e^2*x^2) + 3*B*(d^3 + 13*d^2*e*x + 78*d*e^2*x^2 + 286*e^3*x^3)) + 8*a^7*b^3*e^7*(9*A*e*(d^3 + 13*d^2*e*x + 78*d*e^2*x^2 + 286*e^3*x^3) + 4*B*(d^4 + 13*d^3*e*x + 78*d^2*e^2*x^2 + 286*d*e^3*x^3 + 715*e^4*x^4)) + 7*a^6*b^4*e^6*(8*A*e*(d^4 + 13*d^3*e*x + 78*d^2*e^2*x^2 + 286*d*e^3*x^3 + 715*e^4*x^4) + 5*B*(d^5 + 13*d^4*e*x + 78*d^3*e^2*x^2 + 286*d^2*e^3*x^3 + 715*d*e^4*x^4 + 1287*e^5*x^5)) + 6*a^5*b^5*e^5*(7*A*e*(d^5 + 13*d^4*e*x + 78*d^3*e^2*x^2 + 286*d^2*e^3*x^3 + 715*d*e^4*x^4 + 1287*e^5*x^5) + 6*B*(d^6 + 13*d^5*e*x + 78*d^4*e^2*x^2 + 286*d^3*e^3*x^3 + 715*d^2*e^4*x^4 + 1287*d*e^5*x^5 + 1716*e^6*x^6)) + 5*a^4*b^6*e^4*(6*A*e*(d^6 + 13*d^5*e*x + 78*d^4*e^2*x^2 + 286*d^3*e^3*x^3 + 715*d^2*e^4*x^4 + 1287*d*e^5*x^5 + 1716*e^6*x^6) + 7*B*(d^7 + 13*d^6*e*x + 78*d^5*e^2*x^2 + 286*d^4*e^3*x^3 + 715*d^3*e^4*x^4 + 1287*d^2*e^5*x^5 + 1716*d*e^6*x^6 + 1716*e^7*x^7)) + 4*a^3*b^7*e^3*(5*A*e*(d^7 + 13*d^6*e*x + 78*d^5*e^2*x^2 + 286*d^4*e^3*x^3 + 715*d^3*e^4*x^4 + 1287*d^2*e^5*x^5 + 1716*d*e^6*x^6 + 1716*e^7*x^7) + 8*B*(d^8 + 13*d^7*e*x + 78*d^6*e^2*x^2 + 286*d^5*e^3*x^3 + 715*d^4*e^4*x^4 + 1287*d^3*e^5*x^5 + 1716*d^2*e^6*x^6 + 1716*d*e^7*x^7 + 1287*e^8*x^8)) + 3*a^2*b^8*e^2*(4*A*e*(d^8 + 13*d^7*e*x + 78*d^6*e^2*x^2 + 286*d^5*e^3*x^3 + 715*d^4*e^4*x^4 + 1287*d^3*e^5*x^5 + 1716*d^2*e^6*x^6 + 1716*d*e^7*x^7 + 1287*e^8*x^8) + 9*B*(d^9 + 13*d^8*e*x + 78*d^7*e^2*x^2 + 286*d^6*e^3*x^3 + 715*d^5*e^4*x^4 + 1287*d^4*e^5*x^5 + 1716*d^3*e^6*x^6 + 1716*d^2*e^7*x^7 + 1287*d*e^8*x^8 + 715*e^9*x^9)) + 2*a*b^9*e*(3*A*e*(d^9 + 13*d^8*e*x + 78*d^7*e^2*x^2 + 286*d^6*e^3*x^3 + 715*d^5*e^4*x^4 + 1287*d^4*e^5*x^5 + 1716*d^3*e^6*x^6 + 1716*d^2*e^7*x^7 + 1287*d*e^8*x^8 + 715*e^9*x^9) + 10*B*(d^10 + 13*d^9*e*x + 78*d^8*e^2*x^2 + 286*d^7*e^3*x^3 + 715*d^6*e^4*x^4 + 1287*d^5*e^5*x^5 + 1716*d^4*e^6*x^6 + 1716*d^3*e^7*x^7 + 1287*d^2*e^8*x^8 + 715*d*e^9*x^9 + 286*e^10*x^10)) + b^10*(2*A*e*(d^10 + 13*d^9*e*x + 78*d^8*e^2*x^2 + 286*d^7*e^3*x^3 + 715*d^6*e^4*x^4 + 1287*d^5*e^5*x^5 + 1716*d^4*e^6*x^6 + 1716*d^3*e^7*x^7 + 1287*d^2*e^8*x^8 + 715*d*e^9*x^9 + 286*e^10*x^10) + 11*B*(d^11 + 13*d^10*e*x + 78*d^9*e^2*x^2 + 286*d^8*e^3*x^3 + 715*d^7*e^4*x^4 + 1287*d^6*e^5*x^5 + 1716*d^5*e^6*x^6 + 1716*d^4*e^7*x^7 + 1287*d^3*e^8*x^8 + 715*d^2*e^9*x^9 + 286*d*e^10*x^10 + 78*e^11*x^11)))/(e^12*(d + e*x)^13)","B",1
1103,1,1430,185,0.9387174,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{15}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^15,x]","-\frac{\left(3 A e \left(d^{10}+14 e x d^9+91 e^2 x^2 d^8+364 e^3 x^3 d^7+1001 e^4 x^4 d^6+2002 e^5 x^5 d^5+3003 e^6 x^6 d^4+3432 e^7 x^7 d^3+3003 e^8 x^8 d^2+2002 e^9 x^9 d+1001 e^{10} x^{10}\right)+11 B \left(d^{11}+14 e x d^{10}+91 e^2 x^2 d^9+364 e^3 x^3 d^8+1001 e^4 x^4 d^7+2002 e^5 x^5 d^6+3003 e^6 x^6 d^5+3432 e^7 x^7 d^4+3003 e^8 x^8 d^3+2002 e^9 x^9 d^2+1001 e^{10} x^{10} d+364 e^{11} x^{11}\right)\right) b^{10}+6 a e \left(2 A e \left(d^9+14 e x d^8+91 e^2 x^2 d^7+364 e^3 x^3 d^6+1001 e^4 x^4 d^5+2002 e^5 x^5 d^4+3003 e^6 x^6 d^3+3432 e^7 x^7 d^2+3003 e^8 x^8 d+2002 e^9 x^9\right)+5 B \left(d^{10}+14 e x d^9+91 e^2 x^2 d^8+364 e^3 x^3 d^7+1001 e^4 x^4 d^6+2002 e^5 x^5 d^5+3003 e^6 x^6 d^4+3432 e^7 x^7 d^3+3003 e^8 x^8 d^2+2002 e^9 x^9 d+1001 e^{10} x^{10}\right)\right) b^9+6 a^2 e^2 \left(5 A e \left(d^8+14 e x d^7+91 e^2 x^2 d^6+364 e^3 x^3 d^5+1001 e^4 x^4 d^4+2002 e^5 x^5 d^3+3003 e^6 x^6 d^2+3432 e^7 x^7 d+3003 e^8 x^8\right)+9 B \left(d^9+14 e x d^8+91 e^2 x^2 d^7+364 e^3 x^3 d^6+1001 e^4 x^4 d^5+2002 e^5 x^5 d^4+3003 e^6 x^6 d^3+3432 e^7 x^7 d^2+3003 e^8 x^8 d+2002 e^9 x^9\right)\right) b^8+20 a^3 e^3 \left(3 A e \left(d^7+14 e x d^6+91 e^2 x^2 d^5+364 e^3 x^3 d^4+1001 e^4 x^4 d^3+2002 e^5 x^5 d^2+3003 e^6 x^6 d+3432 e^7 x^7\right)+4 B \left(d^8+14 e x d^7+91 e^2 x^2 d^6+364 e^3 x^3 d^5+1001 e^4 x^4 d^4+2002 e^5 x^5 d^3+3003 e^6 x^6 d^2+3432 e^7 x^7 d+3003 e^8 x^8\right)\right) b^7+105 a^4 e^4 \left(A e \left(d^6+14 e x d^5+91 e^2 x^2 d^4+364 e^3 x^3 d^3+1001 e^4 x^4 d^2+2002 e^5 x^5 d+3003 e^6 x^6\right)+B \left(d^7+14 e x d^6+91 e^2 x^2 d^5+364 e^3 x^3 d^4+1001 e^4 x^4 d^3+2002 e^5 x^5 d^2+3003 e^6 x^6 d+3432 e^7 x^7\right)\right) b^6+42 a^5 e^5 \left(4 A e \left(d^5+14 e x d^4+91 e^2 x^2 d^3+364 e^3 x^3 d^2+1001 e^4 x^4 d+2002 e^5 x^5\right)+3 B \left(d^6+14 e x d^5+91 e^2 x^2 d^4+364 e^3 x^3 d^3+1001 e^4 x^4 d^2+2002 e^5 x^5 d+3003 e^6 x^6\right)\right) b^5+28 a^6 e^6 \left(9 A e \left(d^4+14 e x d^3+91 e^2 x^2 d^2+364 e^3 x^3 d+1001 e^4 x^4\right)+5 B \left(d^5+14 e x d^4+91 e^2 x^2 d^3+364 e^3 x^3 d^2+1001 e^4 x^4 d+2002 e^5 x^5\right)\right) b^4+72 a^7 e^7 \left(5 A e \left(d^3+14 e x d^2+91 e^2 x^2 d+364 e^3 x^3\right)+2 B \left(d^4+14 e x d^3+91 e^2 x^2 d^2+364 e^3 x^3 d+1001 e^4 x^4\right)\right) b^3+45 a^8 e^8 \left(11 A e \left(d^2+14 e x d+91 e^2 x^2\right)+3 B \left(d^3+14 e x d^2+91 e^2 x^2 d+364 e^3 x^3\right)\right) b^2+110 a^9 e^9 \left(6 A e (d+14 e x)+B \left(d^2+14 e x d+91 e^2 x^2\right)\right) b+66 a^{10} e^{10} (13 A e+B (d+14 e x))}{12012 e^{12} (d+e x)^{14}}","\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,"-1/12012*(66*a^10*e^10*(13*A*e + B*(d + 14*e*x)) + 110*a^9*b*e^9*(6*A*e*(d + 14*e*x) + B*(d^2 + 14*d*e*x + 91*e^2*x^2)) + 45*a^8*b^2*e^8*(11*A*e*(d^2 + 14*d*e*x + 91*e^2*x^2) + 3*B*(d^3 + 14*d^2*e*x + 91*d*e^2*x^2 + 364*e^3*x^3)) + 72*a^7*b^3*e^7*(5*A*e*(d^3 + 14*d^2*e*x + 91*d*e^2*x^2 + 364*e^3*x^3) + 2*B*(d^4 + 14*d^3*e*x + 91*d^2*e^2*x^2 + 364*d*e^3*x^3 + 1001*e^4*x^4)) + 28*a^6*b^4*e^6*(9*A*e*(d^4 + 14*d^3*e*x + 91*d^2*e^2*x^2 + 364*d*e^3*x^3 + 1001*e^4*x^4) + 5*B*(d^5 + 14*d^4*e*x + 91*d^3*e^2*x^2 + 364*d^2*e^3*x^3 + 1001*d*e^4*x^4 + 2002*e^5*x^5)) + 42*a^5*b^5*e^5*(4*A*e*(d^5 + 14*d^4*e*x + 91*d^3*e^2*x^2 + 364*d^2*e^3*x^3 + 1001*d*e^4*x^4 + 2002*e^5*x^5) + 3*B*(d^6 + 14*d^5*e*x + 91*d^4*e^2*x^2 + 364*d^3*e^3*x^3 + 1001*d^2*e^4*x^4 + 2002*d*e^5*x^5 + 3003*e^6*x^6)) + 105*a^4*b^6*e^4*(A*e*(d^6 + 14*d^5*e*x + 91*d^4*e^2*x^2 + 364*d^3*e^3*x^3 + 1001*d^2*e^4*x^4 + 2002*d*e^5*x^5 + 3003*e^6*x^6) + B*(d^7 + 14*d^6*e*x + 91*d^5*e^2*x^2 + 364*d^4*e^3*x^3 + 1001*d^3*e^4*x^4 + 2002*d^2*e^5*x^5 + 3003*d*e^6*x^6 + 3432*e^7*x^7)) + 20*a^3*b^7*e^3*(3*A*e*(d^7 + 14*d^6*e*x + 91*d^5*e^2*x^2 + 364*d^4*e^3*x^3 + 1001*d^3*e^4*x^4 + 2002*d^2*e^5*x^5 + 3003*d*e^6*x^6 + 3432*e^7*x^7) + 4*B*(d^8 + 14*d^7*e*x + 91*d^6*e^2*x^2 + 364*d^5*e^3*x^3 + 1001*d^4*e^4*x^4 + 2002*d^3*e^5*x^5 + 3003*d^2*e^6*x^6 + 3432*d*e^7*x^7 + 3003*e^8*x^8)) + 6*a^2*b^8*e^2*(5*A*e*(d^8 + 14*d^7*e*x + 91*d^6*e^2*x^2 + 364*d^5*e^3*x^3 + 1001*d^4*e^4*x^4 + 2002*d^3*e^5*x^5 + 3003*d^2*e^6*x^6 + 3432*d*e^7*x^7 + 3003*e^8*x^8) + 9*B*(d^9 + 14*d^8*e*x + 91*d^7*e^2*x^2 + 364*d^6*e^3*x^3 + 1001*d^5*e^4*x^4 + 2002*d^4*e^5*x^5 + 3003*d^3*e^6*x^6 + 3432*d^2*e^7*x^7 + 3003*d*e^8*x^8 + 2002*e^9*x^9)) + 6*a*b^9*e*(2*A*e*(d^9 + 14*d^8*e*x + 91*d^7*e^2*x^2 + 364*d^6*e^3*x^3 + 1001*d^5*e^4*x^4 + 2002*d^4*e^5*x^5 + 3003*d^3*e^6*x^6 + 3432*d^2*e^7*x^7 + 3003*d*e^8*x^8 + 2002*e^9*x^9) + 5*B*(d^10 + 14*d^9*e*x + 91*d^8*e^2*x^2 + 364*d^7*e^3*x^3 + 1001*d^6*e^4*x^4 + 2002*d^5*e^5*x^5 + 3003*d^4*e^6*x^6 + 3432*d^3*e^7*x^7 + 3003*d^2*e^8*x^8 + 2002*d*e^9*x^9 + 1001*e^10*x^10)) + b^10*(3*A*e*(d^10 + 14*d^9*e*x + 91*d^8*e^2*x^2 + 364*d^7*e^3*x^3 + 1001*d^6*e^4*x^4 + 2002*d^5*e^5*x^5 + 3003*d^4*e^6*x^6 + 3432*d^3*e^7*x^7 + 3003*d^2*e^8*x^8 + 2002*d*e^9*x^9 + 1001*e^10*x^10) + 11*B*(d^11 + 14*d^10*e*x + 91*d^9*e^2*x^2 + 364*d^8*e^3*x^3 + 1001*d^7*e^4*x^4 + 2002*d^6*e^5*x^5 + 3003*d^5*e^6*x^6 + 3432*d^4*e^7*x^7 + 3003*d^3*e^8*x^8 + 2002*d^2*e^9*x^9 + 1001*d*e^10*x^10 + 364*e^11*x^11)))/(e^12*(d + e*x)^14)","B",1
1104,1,1430,235,1.005017,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{16}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^16,x]","-\frac{\left(4 A e \left(d^{10}+15 e x d^9+105 e^2 x^2 d^8+455 e^3 x^3 d^7+1365 e^4 x^4 d^6+3003 e^5 x^5 d^5+5005 e^6 x^6 d^4+6435 e^7 x^7 d^3+6435 e^8 x^8 d^2+5005 e^9 x^9 d+3003 e^{10} x^{10}\right)+11 B \left(d^{11}+15 e x d^{10}+105 e^2 x^2 d^9+455 e^3 x^3 d^8+1365 e^4 x^4 d^7+3003 e^5 x^5 d^6+5005 e^6 x^6 d^5+6435 e^7 x^7 d^4+6435 e^8 x^8 d^3+5005 e^9 x^9 d^2+3003 e^{10} x^{10} d+1365 e^{11} x^{11}\right)\right) b^{10}+20 a e \left(A e \left(d^9+15 e x d^8+105 e^2 x^2 d^7+455 e^3 x^3 d^6+1365 e^4 x^4 d^5+3003 e^5 x^5 d^4+5005 e^6 x^6 d^3+6435 e^7 x^7 d^2+6435 e^8 x^8 d+5005 e^9 x^9\right)+2 B \left(d^{10}+15 e x d^9+105 e^2 x^2 d^8+455 e^3 x^3 d^7+1365 e^4 x^4 d^6+3003 e^5 x^5 d^5+5005 e^6 x^6 d^4+6435 e^7 x^7 d^3+6435 e^8 x^8 d^2+5005 e^9 x^9 d+3003 e^{10} x^{10}\right)\right) b^9+30 a^2 e^2 \left(2 A e \left(d^8+15 e x d^7+105 e^2 x^2 d^6+455 e^3 x^3 d^5+1365 e^4 x^4 d^4+3003 e^5 x^5 d^3+5005 e^6 x^6 d^2+6435 e^7 x^7 d+6435 e^8 x^8\right)+3 B \left(d^9+15 e x d^8+105 e^2 x^2 d^7+455 e^3 x^3 d^6+1365 e^4 x^4 d^5+3003 e^5 x^5 d^4+5005 e^6 x^6 d^3+6435 e^7 x^7 d^2+6435 e^8 x^8 d+5005 e^9 x^9\right)\right) b^8+20 a^3 e^3 \left(7 A e \left(d^7+15 e x d^6+105 e^2 x^2 d^5+455 e^3 x^3 d^4+1365 e^4 x^4 d^3+3003 e^5 x^5 d^2+5005 e^6 x^6 d+6435 e^7 x^7\right)+8 B \left(d^8+15 e x d^7+105 e^2 x^2 d^6+455 e^3 x^3 d^5+1365 e^4 x^4 d^4+3003 e^5 x^5 d^3+5005 e^6 x^6 d^2+6435 e^7 x^7 d+6435 e^8 x^8\right)\right) b^7+35 a^4 e^4 \left(8 A e \left(d^6+15 e x d^5+105 e^2 x^2 d^4+455 e^3 x^3 d^3+1365 e^4 x^4 d^2+3003 e^5 x^5 d+5005 e^6 x^6\right)+7 B \left(d^7+15 e x d^6+105 e^2 x^2 d^5+455 e^3 x^3 d^4+1365 e^4 x^4 d^3+3003 e^5 x^5 d^2+5005 e^6 x^6 d+6435 e^7 x^7\right)\right) b^6+168 a^5 e^5 \left(3 A e \left(d^5+15 e x d^4+105 e^2 x^2 d^3+455 e^3 x^3 d^2+1365 e^4 x^4 d+3003 e^5 x^5\right)+2 B \left(d^6+15 e x d^5+105 e^2 x^2 d^4+455 e^3 x^3 d^3+1365 e^4 x^4 d^2+3003 e^5 x^5 d+5005 e^6 x^6\right)\right) b^5+420 a^6 e^6 \left(2 A e \left(d^4+15 e x d^3+105 e^2 x^2 d^2+455 e^3 x^3 d+1365 e^4 x^4\right)+B \left(d^5+15 e x d^4+105 e^2 x^2 d^3+455 e^3 x^3 d^2+1365 e^4 x^4 d+3003 e^5 x^5\right)\right) b^4+120 a^7 e^7 \left(11 A e \left(d^3+15 e x d^2+105 e^2 x^2 d+455 e^3 x^3\right)+4 B \left(d^4+15 e x d^3+105 e^2 x^2 d^2+455 e^3 x^3 d+1365 e^4 x^4\right)\right) b^3+495 a^8 e^8 \left(4 A e \left(d^2+15 e x d+105 e^2 x^2\right)+B \left(d^3+15 e x d^2+105 e^2 x^2 d+455 e^3 x^3\right)\right) b^2+220 a^9 e^9 \left(13 A e (d+15 e x)+2 B \left(d^2+15 e x d+105 e^2 x^2\right)\right) b+286 a^{10} e^{10} (14 A e+B (d+15 e x))}{60060 e^{12} (d+e x)^{15}}","\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,"-1/60060*(286*a^10*e^10*(14*A*e + B*(d + 15*e*x)) + 220*a^9*b*e^9*(13*A*e*(d + 15*e*x) + 2*B*(d^2 + 15*d*e*x + 105*e^2*x^2)) + 495*a^8*b^2*e^8*(4*A*e*(d^2 + 15*d*e*x + 105*e^2*x^2) + B*(d^3 + 15*d^2*e*x + 105*d*e^2*x^2 + 455*e^3*x^3)) + 120*a^7*b^3*e^7*(11*A*e*(d^3 + 15*d^2*e*x + 105*d*e^2*x^2 + 455*e^3*x^3) + 4*B*(d^4 + 15*d^3*e*x + 105*d^2*e^2*x^2 + 455*d*e^3*x^3 + 1365*e^4*x^4)) + 420*a^6*b^4*e^6*(2*A*e*(d^4 + 15*d^3*e*x + 105*d^2*e^2*x^2 + 455*d*e^3*x^3 + 1365*e^4*x^4) + B*(d^5 + 15*d^4*e*x + 105*d^3*e^2*x^2 + 455*d^2*e^3*x^3 + 1365*d*e^4*x^4 + 3003*e^5*x^5)) + 168*a^5*b^5*e^5*(3*A*e*(d^5 + 15*d^4*e*x + 105*d^3*e^2*x^2 + 455*d^2*e^3*x^3 + 1365*d*e^4*x^4 + 3003*e^5*x^5) + 2*B*(d^6 + 15*d^5*e*x + 105*d^4*e^2*x^2 + 455*d^3*e^3*x^3 + 1365*d^2*e^4*x^4 + 3003*d*e^5*x^5 + 5005*e^6*x^6)) + 35*a^4*b^6*e^4*(8*A*e*(d^6 + 15*d^5*e*x + 105*d^4*e^2*x^2 + 455*d^3*e^3*x^3 + 1365*d^2*e^4*x^4 + 3003*d*e^5*x^5 + 5005*e^6*x^6) + 7*B*(d^7 + 15*d^6*e*x + 105*d^5*e^2*x^2 + 455*d^4*e^3*x^3 + 1365*d^3*e^4*x^4 + 3003*d^2*e^5*x^5 + 5005*d*e^6*x^6 + 6435*e^7*x^7)) + 20*a^3*b^7*e^3*(7*A*e*(d^7 + 15*d^6*e*x + 105*d^5*e^2*x^2 + 455*d^4*e^3*x^3 + 1365*d^3*e^4*x^4 + 3003*d^2*e^5*x^5 + 5005*d*e^6*x^6 + 6435*e^7*x^7) + 8*B*(d^8 + 15*d^7*e*x + 105*d^6*e^2*x^2 + 455*d^5*e^3*x^3 + 1365*d^4*e^4*x^4 + 3003*d^3*e^5*x^5 + 5005*d^2*e^6*x^6 + 6435*d*e^7*x^7 + 6435*e^8*x^8)) + 30*a^2*b^8*e^2*(2*A*e*(d^8 + 15*d^7*e*x + 105*d^6*e^2*x^2 + 455*d^5*e^3*x^3 + 1365*d^4*e^4*x^4 + 3003*d^3*e^5*x^5 + 5005*d^2*e^6*x^6 + 6435*d*e^7*x^7 + 6435*e^8*x^8) + 3*B*(d^9 + 15*d^8*e*x + 105*d^7*e^2*x^2 + 455*d^6*e^3*x^3 + 1365*d^5*e^4*x^4 + 3003*d^4*e^5*x^5 + 5005*d^3*e^6*x^6 + 6435*d^2*e^7*x^7 + 6435*d*e^8*x^8 + 5005*e^9*x^9)) + 20*a*b^9*e*(A*e*(d^9 + 15*d^8*e*x + 105*d^7*e^2*x^2 + 455*d^6*e^3*x^3 + 1365*d^5*e^4*x^4 + 3003*d^4*e^5*x^5 + 5005*d^3*e^6*x^6 + 6435*d^2*e^7*x^7 + 6435*d*e^8*x^8 + 5005*e^9*x^9) + 2*B*(d^10 + 15*d^9*e*x + 105*d^8*e^2*x^2 + 455*d^7*e^3*x^3 + 1365*d^6*e^4*x^4 + 3003*d^5*e^5*x^5 + 5005*d^4*e^6*x^6 + 6435*d^3*e^7*x^7 + 6435*d^2*e^8*x^8 + 5005*d*e^9*x^9 + 3003*e^10*x^10)) + b^10*(4*A*e*(d^10 + 15*d^9*e*x + 105*d^8*e^2*x^2 + 455*d^7*e^3*x^3 + 1365*d^6*e^4*x^4 + 3003*d^5*e^5*x^5 + 5005*d^4*e^6*x^6 + 6435*d^3*e^7*x^7 + 6435*d^2*e^8*x^8 + 5005*d*e^9*x^9 + 3003*e^10*x^10) + 11*B*(d^11 + 15*d^10*e*x + 105*d^9*e^2*x^2 + 455*d^8*e^3*x^3 + 1365*d^7*e^4*x^4 + 3003*d^6*e^5*x^5 + 5005*d^5*e^6*x^6 + 6435*d^4*e^7*x^7 + 6435*d^3*e^8*x^8 + 5005*d^2*e^9*x^9 + 3003*d*e^10*x^10 + 1365*e^11*x^11)))/(e^12*(d + e*x)^15)","B",1
1105,1,1429,285,0.9736307,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{17}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^17,x]","-\frac{\left(5 A e \left(d^{10}+16 e x d^9+120 e^2 x^2 d^8+560 e^3 x^3 d^7+1820 e^4 x^4 d^6+4368 e^5 x^5 d^5+8008 e^6 x^6 d^4+11440 e^7 x^7 d^3+12870 e^8 x^8 d^2+11440 e^9 x^9 d+8008 e^{10} x^{10}\right)+11 B \left(d^{11}+16 e x d^{10}+120 e^2 x^2 d^9+560 e^3 x^3 d^8+1820 e^4 x^4 d^7+4368 e^5 x^5 d^6+8008 e^6 x^6 d^5+11440 e^7 x^7 d^4+12870 e^8 x^8 d^3+11440 e^9 x^9 d^2+8008 e^{10} x^{10} d+4368 e^{11} x^{11}\right)\right) b^{10}+10 a e \left(3 A e \left(d^9+16 e x d^8+120 e^2 x^2 d^7+560 e^3 x^3 d^6+1820 e^4 x^4 d^5+4368 e^5 x^5 d^4+8008 e^6 x^6 d^3+11440 e^7 x^7 d^2+12870 e^8 x^8 d+11440 e^9 x^9\right)+5 B \left(d^{10}+16 e x d^9+120 e^2 x^2 d^8+560 e^3 x^3 d^7+1820 e^4 x^4 d^6+4368 e^5 x^5 d^5+8008 e^6 x^6 d^4+11440 e^7 x^7 d^3+12870 e^8 x^8 d^2+11440 e^9 x^9 d+8008 e^{10} x^{10}\right)\right) b^9+15 a^2 e^2 \left(7 A e \left(d^8+16 e x d^7+120 e^2 x^2 d^6+560 e^3 x^3 d^5+1820 e^4 x^4 d^4+4368 e^5 x^5 d^3+8008 e^6 x^6 d^2+11440 e^7 x^7 d+12870 e^8 x^8\right)+9 B \left(d^9+16 e x d^8+120 e^2 x^2 d^7+560 e^3 x^3 d^6+1820 e^4 x^4 d^5+4368 e^5 x^5 d^4+8008 e^6 x^6 d^3+11440 e^7 x^7 d^2+12870 e^8 x^8 d+11440 e^9 x^9\right)\right) b^8+280 a^3 e^3 \left(A e \left(d^7+16 e x d^6+120 e^2 x^2 d^5+560 e^3 x^3 d^4+1820 e^4 x^4 d^3+4368 e^5 x^5 d^2+8008 e^6 x^6 d+11440 e^7 x^7\right)+B \left(d^8+16 e x d^7+120 e^2 x^2 d^6+560 e^3 x^3 d^5+1820 e^4 x^4 d^4+4368 e^5 x^5 d^3+8008 e^6 x^6 d^2+11440 e^7 x^7 d+12870 e^8 x^8\right)\right) b^7+70 a^4 e^4 \left(9 A e \left(d^6+16 e x d^5+120 e^2 x^2 d^4+560 e^3 x^3 d^3+1820 e^4 x^4 d^2+4368 e^5 x^5 d+8008 e^6 x^6\right)+7 B \left(d^7+16 e x d^6+120 e^2 x^2 d^5+560 e^3 x^3 d^4+1820 e^4 x^4 d^3+4368 e^5 x^5 d^2+8008 e^6 x^6 d+11440 e^7 x^7\right)\right) b^6+252 a^5 e^5 \left(5 A e \left(d^5+16 e x d^4+120 e^2 x^2 d^3+560 e^3 x^3 d^2+1820 e^4 x^4 d+4368 e^5 x^5\right)+3 B \left(d^6+16 e x d^5+120 e^2 x^2 d^4+560 e^3 x^3 d^3+1820 e^4 x^4 d^2+4368 e^5 x^5 d+8008 e^6 x^6\right)\right) b^5+210 a^6 e^6 \left(11 A e \left(d^4+16 e x d^3+120 e^2 x^2 d^2+560 e^3 x^3 d+1820 e^4 x^4\right)+5 B \left(d^5+16 e x d^4+120 e^2 x^2 d^3+560 e^3 x^3 d^2+1820 e^4 x^4 d+4368 e^5 x^5\right)\right) b^4+1320 a^7 e^7 \left(3 A e \left(d^3+16 e x d^2+120 e^2 x^2 d+560 e^3 x^3\right)+B \left(d^4+16 e x d^3+120 e^2 x^2 d^2+560 e^3 x^3 d+1820 e^4 x^4\right)\right) b^3+495 a^8 e^8 \left(13 A e \left(d^2+16 e x d+120 e^2 x^2\right)+3 B \left(d^3+16 e x d^2+120 e^2 x^2 d+560 e^3 x^3\right)\right) b^2+1430 a^9 e^9 \left(7 A e (d+16 e x)+B \left(d^2+16 e x d+120 e^2 x^2\right)\right) b+1001 a^{10} e^{10} (15 A e+B (d+16 e x))}{240240 e^{12} (d+e x)^{16}}","\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,"-1/240240*(1001*a^10*e^10*(15*A*e + B*(d + 16*e*x)) + 1430*a^9*b*e^9*(7*A*e*(d + 16*e*x) + B*(d^2 + 16*d*e*x + 120*e^2*x^2)) + 495*a^8*b^2*e^8*(13*A*e*(d^2 + 16*d*e*x + 120*e^2*x^2) + 3*B*(d^3 + 16*d^2*e*x + 120*d*e^2*x^2 + 560*e^3*x^3)) + 1320*a^7*b^3*e^7*(3*A*e*(d^3 + 16*d^2*e*x + 120*d*e^2*x^2 + 560*e^3*x^3) + B*(d^4 + 16*d^3*e*x + 120*d^2*e^2*x^2 + 560*d*e^3*x^3 + 1820*e^4*x^4)) + 210*a^6*b^4*e^6*(11*A*e*(d^4 + 16*d^3*e*x + 120*d^2*e^2*x^2 + 560*d*e^3*x^3 + 1820*e^4*x^4) + 5*B*(d^5 + 16*d^4*e*x + 120*d^3*e^2*x^2 + 560*d^2*e^3*x^3 + 1820*d*e^4*x^4 + 4368*e^5*x^5)) + 252*a^5*b^5*e^5*(5*A*e*(d^5 + 16*d^4*e*x + 120*d^3*e^2*x^2 + 560*d^2*e^3*x^3 + 1820*d*e^4*x^4 + 4368*e^5*x^5) + 3*B*(d^6 + 16*d^5*e*x + 120*d^4*e^2*x^2 + 560*d^3*e^3*x^3 + 1820*d^2*e^4*x^4 + 4368*d*e^5*x^5 + 8008*e^6*x^6)) + 70*a^4*b^6*e^4*(9*A*e*(d^6 + 16*d^5*e*x + 120*d^4*e^2*x^2 + 560*d^3*e^3*x^3 + 1820*d^2*e^4*x^4 + 4368*d*e^5*x^5 + 8008*e^6*x^6) + 7*B*(d^7 + 16*d^6*e*x + 120*d^5*e^2*x^2 + 560*d^4*e^3*x^3 + 1820*d^3*e^4*x^4 + 4368*d^2*e^5*x^5 + 8008*d*e^6*x^6 + 11440*e^7*x^7)) + 280*a^3*b^7*e^3*(A*e*(d^7 + 16*d^6*e*x + 120*d^5*e^2*x^2 + 560*d^4*e^3*x^3 + 1820*d^3*e^4*x^4 + 4368*d^2*e^5*x^5 + 8008*d*e^6*x^6 + 11440*e^7*x^7) + B*(d^8 + 16*d^7*e*x + 120*d^6*e^2*x^2 + 560*d^5*e^3*x^3 + 1820*d^4*e^4*x^4 + 4368*d^3*e^5*x^5 + 8008*d^2*e^6*x^6 + 11440*d*e^7*x^7 + 12870*e^8*x^8)) + 15*a^2*b^8*e^2*(7*A*e*(d^8 + 16*d^7*e*x + 120*d^6*e^2*x^2 + 560*d^5*e^3*x^3 + 1820*d^4*e^4*x^4 + 4368*d^3*e^5*x^5 + 8008*d^2*e^6*x^6 + 11440*d*e^7*x^7 + 12870*e^8*x^8) + 9*B*(d^9 + 16*d^8*e*x + 120*d^7*e^2*x^2 + 560*d^6*e^3*x^3 + 1820*d^5*e^4*x^4 + 4368*d^4*e^5*x^5 + 8008*d^3*e^6*x^6 + 11440*d^2*e^7*x^7 + 12870*d*e^8*x^8 + 11440*e^9*x^9)) + 10*a*b^9*e*(3*A*e*(d^9 + 16*d^8*e*x + 120*d^7*e^2*x^2 + 560*d^6*e^3*x^3 + 1820*d^5*e^4*x^4 + 4368*d^4*e^5*x^5 + 8008*d^3*e^6*x^6 + 11440*d^2*e^7*x^7 + 12870*d*e^8*x^8 + 11440*e^9*x^9) + 5*B*(d^10 + 16*d^9*e*x + 120*d^8*e^2*x^2 + 560*d^7*e^3*x^3 + 1820*d^6*e^4*x^4 + 4368*d^5*e^5*x^5 + 8008*d^4*e^6*x^6 + 11440*d^3*e^7*x^7 + 12870*d^2*e^8*x^8 + 11440*d*e^9*x^9 + 8008*e^10*x^10)) + b^10*(5*A*e*(d^10 + 16*d^9*e*x + 120*d^8*e^2*x^2 + 560*d^7*e^3*x^3 + 1820*d^6*e^4*x^4 + 4368*d^5*e^5*x^5 + 8008*d^4*e^6*x^6 + 11440*d^3*e^7*x^7 + 12870*d^2*e^8*x^8 + 11440*d*e^9*x^9 + 8008*e^10*x^10) + 11*B*(d^11 + 16*d^10*e*x + 120*d^9*e^2*x^2 + 560*d^8*e^3*x^3 + 1820*d^7*e^4*x^4 + 4368*d^6*e^5*x^5 + 8008*d^5*e^6*x^6 + 11440*d^4*e^7*x^7 + 12870*d^3*e^8*x^8 + 11440*d^2*e^9*x^9 + 8008*d*e^10*x^10 + 4368*e^11*x^11)))/(e^12*(d + e*x)^16)","B",1
1106,1,1433,335,1.0442354,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{18}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^18,x]","-\frac{\left(6 A e \left(d^{10}+17 e x d^9+136 e^2 x^2 d^8+680 e^3 x^3 d^7+2380 e^4 x^4 d^6+6188 e^5 x^5 d^5+12376 e^6 x^6 d^4+19448 e^7 x^7 d^3+24310 e^8 x^8 d^2+24310 e^9 x^9 d+19448 e^{10} x^{10}\right)+11 B \left(d^{11}+17 e x d^{10}+136 e^2 x^2 d^9+680 e^3 x^3 d^8+2380 e^4 x^4 d^7+6188 e^5 x^5 d^6+12376 e^6 x^6 d^5+19448 e^7 x^7 d^4+24310 e^8 x^8 d^3+24310 e^9 x^9 d^2+19448 e^{10} x^{10} d+12376 e^{11} x^{11}\right)\right) b^{10}+6 a e \left(7 A e \left(d^9+17 e x d^8+136 e^2 x^2 d^7+680 e^3 x^3 d^6+2380 e^4 x^4 d^5+6188 e^5 x^5 d^4+12376 e^6 x^6 d^3+19448 e^7 x^7 d^2+24310 e^8 x^8 d+24310 e^9 x^9\right)+10 B \left(d^{10}+17 e x d^9+136 e^2 x^2 d^8+680 e^3 x^3 d^7+2380 e^4 x^4 d^6+6188 e^5 x^5 d^5+12376 e^6 x^6 d^4+19448 e^7 x^7 d^3+24310 e^8 x^8 d^2+24310 e^9 x^9 d+19448 e^{10} x^{10}\right)\right) b^9+21 a^2 e^2 \left(8 A e \left(d^8+17 e x d^7+136 e^2 x^2 d^6+680 e^3 x^3 d^5+2380 e^4 x^4 d^4+6188 e^5 x^5 d^3+12376 e^6 x^6 d^2+19448 e^7 x^7 d+24310 e^8 x^8\right)+9 B \left(d^9+17 e x d^8+136 e^2 x^2 d^7+680 e^3 x^3 d^6+2380 e^4 x^4 d^5+6188 e^5 x^5 d^4+12376 e^6 x^6 d^3+19448 e^7 x^7 d^2+24310 e^8 x^8 d+24310 e^9 x^9\right)\right) b^8+56 a^3 e^3 \left(9 A e \left(d^7+17 e x d^6+136 e^2 x^2 d^5+680 e^3 x^3 d^4+2380 e^4 x^4 d^3+6188 e^5 x^5 d^2+12376 e^6 x^6 d+19448 e^7 x^7\right)+8 B \left(d^8+17 e x d^7+136 e^2 x^2 d^6+680 e^3 x^3 d^5+2380 e^4 x^4 d^4+6188 e^5 x^5 d^3+12376 e^6 x^6 d^2+19448 e^7 x^7 d+24310 e^8 x^8\right)\right) b^7+126 a^4 e^4 \left(10 A e \left(d^6+17 e x d^5+136 e^2 x^2 d^4+680 e^3 x^3 d^3+2380 e^4 x^4 d^2+6188 e^5 x^5 d+12376 e^6 x^6\right)+7 B \left(d^7+17 e x d^6+136 e^2 x^2 d^5+680 e^3 x^3 d^4+2380 e^4 x^4 d^3+6188 e^5 x^5 d^2+12376 e^6 x^6 d+19448 e^7 x^7\right)\right) b^6+252 a^5 e^5 \left(11 A e \left(d^5+17 e x d^4+136 e^2 x^2 d^3+680 e^3 x^3 d^2+2380 e^4 x^4 d+6188 e^5 x^5\right)+6 B \left(d^6+17 e x d^5+136 e^2 x^2 d^4+680 e^3 x^3 d^3+2380 e^4 x^4 d^2+6188 e^5 x^5 d+12376 e^6 x^6\right)\right) b^5+462 a^6 e^6 \left(12 A e \left(d^4+17 e x d^3+136 e^2 x^2 d^2+680 e^3 x^3 d+2380 e^4 x^4\right)+5 B \left(d^5+17 e x d^4+136 e^2 x^2 d^3+680 e^3 x^3 d^2+2380 e^4 x^4 d+6188 e^5 x^5\right)\right) b^4+792 a^7 e^7 \left(13 A e \left(d^3+17 e x d^2+136 e^2 x^2 d+680 e^3 x^3\right)+4 B \left(d^4+17 e x d^3+136 e^2 x^2 d^2+680 e^3 x^3 d+2380 e^4 x^4\right)\right) b^3+1287 a^8 e^8 \left(14 A e \left(d^2+17 e x d+136 e^2 x^2\right)+3 B \left(d^3+17 e x d^2+136 e^2 x^2 d+680 e^3 x^3\right)\right) b^2+2002 a^9 e^9 \left(15 A e (d+17 e x)+2 B \left(d^2+17 e x d+136 e^2 x^2\right)\right) b+3003 a^{10} e^{10} (16 A e+B (d+17 e x))}{816816 e^{12} (d+e x)^{17}}","\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,"-1/816816*(3003*a^10*e^10*(16*A*e + B*(d + 17*e*x)) + 2002*a^9*b*e^9*(15*A*e*(d + 17*e*x) + 2*B*(d^2 + 17*d*e*x + 136*e^2*x^2)) + 1287*a^8*b^2*e^8*(14*A*e*(d^2 + 17*d*e*x + 136*e^2*x^2) + 3*B*(d^3 + 17*d^2*e*x + 136*d*e^2*x^2 + 680*e^3*x^3)) + 792*a^7*b^3*e^7*(13*A*e*(d^3 + 17*d^2*e*x + 136*d*e^2*x^2 + 680*e^3*x^3) + 4*B*(d^4 + 17*d^3*e*x + 136*d^2*e^2*x^2 + 680*d*e^3*x^3 + 2380*e^4*x^4)) + 462*a^6*b^4*e^6*(12*A*e*(d^4 + 17*d^3*e*x + 136*d^2*e^2*x^2 + 680*d*e^3*x^3 + 2380*e^4*x^4) + 5*B*(d^5 + 17*d^4*e*x + 136*d^3*e^2*x^2 + 680*d^2*e^3*x^3 + 2380*d*e^4*x^4 + 6188*e^5*x^5)) + 252*a^5*b^5*e^5*(11*A*e*(d^5 + 17*d^4*e*x + 136*d^3*e^2*x^2 + 680*d^2*e^3*x^3 + 2380*d*e^4*x^4 + 6188*e^5*x^5) + 6*B*(d^6 + 17*d^5*e*x + 136*d^4*e^2*x^2 + 680*d^3*e^3*x^3 + 2380*d^2*e^4*x^4 + 6188*d*e^5*x^5 + 12376*e^6*x^6)) + 126*a^4*b^6*e^4*(10*A*e*(d^6 + 17*d^5*e*x + 136*d^4*e^2*x^2 + 680*d^3*e^3*x^3 + 2380*d^2*e^4*x^4 + 6188*d*e^5*x^5 + 12376*e^6*x^6) + 7*B*(d^7 + 17*d^6*e*x + 136*d^5*e^2*x^2 + 680*d^4*e^3*x^3 + 2380*d^3*e^4*x^4 + 6188*d^2*e^5*x^5 + 12376*d*e^6*x^6 + 19448*e^7*x^7)) + 56*a^3*b^7*e^3*(9*A*e*(d^7 + 17*d^6*e*x + 136*d^5*e^2*x^2 + 680*d^4*e^3*x^3 + 2380*d^3*e^4*x^4 + 6188*d^2*e^5*x^5 + 12376*d*e^6*x^6 + 19448*e^7*x^7) + 8*B*(d^8 + 17*d^7*e*x + 136*d^6*e^2*x^2 + 680*d^5*e^3*x^3 + 2380*d^4*e^4*x^4 + 6188*d^3*e^5*x^5 + 12376*d^2*e^6*x^6 + 19448*d*e^7*x^7 + 24310*e^8*x^8)) + 21*a^2*b^8*e^2*(8*A*e*(d^8 + 17*d^7*e*x + 136*d^6*e^2*x^2 + 680*d^5*e^3*x^3 + 2380*d^4*e^4*x^4 + 6188*d^3*e^5*x^5 + 12376*d^2*e^6*x^6 + 19448*d*e^7*x^7 + 24310*e^8*x^8) + 9*B*(d^9 + 17*d^8*e*x + 136*d^7*e^2*x^2 + 680*d^6*e^3*x^3 + 2380*d^5*e^4*x^4 + 6188*d^4*e^5*x^5 + 12376*d^3*e^6*x^6 + 19448*d^2*e^7*x^7 + 24310*d*e^8*x^8 + 24310*e^9*x^9)) + 6*a*b^9*e*(7*A*e*(d^9 + 17*d^8*e*x + 136*d^7*e^2*x^2 + 680*d^6*e^3*x^3 + 2380*d^5*e^4*x^4 + 6188*d^4*e^5*x^5 + 12376*d^3*e^6*x^6 + 19448*d^2*e^7*x^7 + 24310*d*e^8*x^8 + 24310*e^9*x^9) + 10*B*(d^10 + 17*d^9*e*x + 136*d^8*e^2*x^2 + 680*d^7*e^3*x^3 + 2380*d^6*e^4*x^4 + 6188*d^5*e^5*x^5 + 12376*d^4*e^6*x^6 + 19448*d^3*e^7*x^7 + 24310*d^2*e^8*x^8 + 24310*d*e^9*x^9 + 19448*e^10*x^10)) + b^10*(6*A*e*(d^10 + 17*d^9*e*x + 136*d^8*e^2*x^2 + 680*d^7*e^3*x^3 + 2380*d^6*e^4*x^4 + 6188*d^5*e^5*x^5 + 12376*d^4*e^6*x^6 + 19448*d^3*e^7*x^7 + 24310*d^2*e^8*x^8 + 24310*d*e^9*x^9 + 19448*e^10*x^10) + 11*B*(d^11 + 17*d^10*e*x + 136*d^9*e^2*x^2 + 680*d^8*e^3*x^3 + 2380*d^7*e^4*x^4 + 6188*d^6*e^5*x^5 + 12376*d^5*e^6*x^6 + 19448*d^4*e^7*x^7 + 24310*d^3*e^8*x^8 + 24310*d^2*e^9*x^9 + 19448*d*e^10*x^10 + 12376*e^11*x^11)))/(e^12*(d + e*x)^17)","B",1
1107,1,1428,385,1.0036916,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{19}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^19,x]","-\frac{\left(7 A e \left(d^{10}+18 e x d^9+153 e^2 x^2 d^8+816 e^3 x^3 d^7+3060 e^4 x^4 d^6+8568 e^5 x^5 d^5+18564 e^6 x^6 d^4+31824 e^7 x^7 d^3+43758 e^8 x^8 d^2+48620 e^9 x^9 d+43758 e^{10} x^{10}\right)+11 B \left(d^{11}+18 e x d^{10}+153 e^2 x^2 d^9+816 e^3 x^3 d^8+3060 e^4 x^4 d^7+8568 e^5 x^5 d^6+18564 e^6 x^6 d^5+31824 e^7 x^7 d^4+43758 e^8 x^8 d^3+48620 e^9 x^9 d^2+43758 e^{10} x^{10} d+31824 e^{11} x^{11}\right)\right) b^{10}+14 a e \left(4 A e \left(d^9+18 e x d^8+153 e^2 x^2 d^7+816 e^3 x^3 d^6+3060 e^4 x^4 d^5+8568 e^5 x^5 d^4+18564 e^6 x^6 d^3+31824 e^7 x^7 d^2+43758 e^8 x^8 d+48620 e^9 x^9\right)+5 B \left(d^{10}+18 e x d^9+153 e^2 x^2 d^8+816 e^3 x^3 d^7+3060 e^4 x^4 d^6+8568 e^5 x^5 d^5+18564 e^6 x^6 d^4+31824 e^7 x^7 d^3+43758 e^8 x^8 d^2+48620 e^9 x^9 d+43758 e^{10} x^{10}\right)\right) b^9+252 a^2 e^2 \left(A e \left(d^8+18 e x d^7+153 e^2 x^2 d^6+816 e^3 x^3 d^5+3060 e^4 x^4 d^4+8568 e^5 x^5 d^3+18564 e^6 x^6 d^2+31824 e^7 x^7 d+43758 e^8 x^8\right)+B \left(d^9+18 e x d^8+153 e^2 x^2 d^7+816 e^3 x^3 d^6+3060 e^4 x^4 d^5+8568 e^5 x^5 d^4+18564 e^6 x^6 d^3+31824 e^7 x^7 d^2+43758 e^8 x^8 d+48620 e^9 x^9\right)\right) b^8+168 a^3 e^3 \left(5 A e \left(d^7+18 e x d^6+153 e^2 x^2 d^5+816 e^3 x^3 d^4+3060 e^4 x^4 d^3+8568 e^5 x^5 d^2+18564 e^6 x^6 d+31824 e^7 x^7\right)+4 B \left(d^8+18 e x d^7+153 e^2 x^2 d^6+816 e^3 x^3 d^5+3060 e^4 x^4 d^4+8568 e^5 x^5 d^3+18564 e^6 x^6 d^2+31824 e^7 x^7 d+43758 e^8 x^8\right)\right) b^7+210 a^4 e^4 \left(11 A e \left(d^6+18 e x d^5+153 e^2 x^2 d^4+816 e^3 x^3 d^3+3060 e^4 x^4 d^2+8568 e^5 x^5 d+18564 e^6 x^6\right)+7 B \left(d^7+18 e x d^6+153 e^2 x^2 d^5+816 e^3 x^3 d^4+3060 e^4 x^4 d^3+8568 e^5 x^5 d^2+18564 e^6 x^6 d+31824 e^7 x^7\right)\right) b^6+2772 a^5 e^5 \left(2 A e \left(d^5+18 e x d^4+153 e^2 x^2 d^3+816 e^3 x^3 d^2+3060 e^4 x^4 d+8568 e^5 x^5\right)+B \left(d^6+18 e x d^5+153 e^2 x^2 d^4+816 e^3 x^3 d^3+3060 e^4 x^4 d^2+8568 e^5 x^5 d+18564 e^6 x^6\right)\right) b^5+924 a^6 e^6 \left(13 A e \left(d^4+18 e x d^3+153 e^2 x^2 d^2+816 e^3 x^3 d+3060 e^4 x^4\right)+5 B \left(d^5+18 e x d^4+153 e^2 x^2 d^3+816 e^3 x^3 d^2+3060 e^4 x^4 d+8568 e^5 x^5\right)\right) b^4+3432 a^7 e^7 \left(7 A e \left(d^3+18 e x d^2+153 e^2 x^2 d+816 e^3 x^3\right)+2 B \left(d^4+18 e x d^3+153 e^2 x^2 d^2+816 e^3 x^3 d+3060 e^4 x^4\right)\right) b^3+9009 a^8 e^8 \left(5 A e \left(d^2+18 e x d+153 e^2 x^2\right)+B \left(d^3+18 e x d^2+153 e^2 x^2 d+816 e^3 x^3\right)\right) b^2+10010 a^9 e^9 \left(8 A e (d+18 e x)+B \left(d^2+18 e x d+153 e^2 x^2\right)\right) b+8008 a^{10} e^{10} (17 A e+B (d+18 e x))}{2450448 e^{12} (d+e x)^{18}}","\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,"-1/2450448*(8008*a^10*e^10*(17*A*e + B*(d + 18*e*x)) + 10010*a^9*b*e^9*(8*A*e*(d + 18*e*x) + B*(d^2 + 18*d*e*x + 153*e^2*x^2)) + 9009*a^8*b^2*e^8*(5*A*e*(d^2 + 18*d*e*x + 153*e^2*x^2) + B*(d^3 + 18*d^2*e*x + 153*d*e^2*x^2 + 816*e^3*x^3)) + 3432*a^7*b^3*e^7*(7*A*e*(d^3 + 18*d^2*e*x + 153*d*e^2*x^2 + 816*e^3*x^3) + 2*B*(d^4 + 18*d^3*e*x + 153*d^2*e^2*x^2 + 816*d*e^3*x^3 + 3060*e^4*x^4)) + 924*a^6*b^4*e^6*(13*A*e*(d^4 + 18*d^3*e*x + 153*d^2*e^2*x^2 + 816*d*e^3*x^3 + 3060*e^4*x^4) + 5*B*(d^5 + 18*d^4*e*x + 153*d^3*e^2*x^2 + 816*d^2*e^3*x^3 + 3060*d*e^4*x^4 + 8568*e^5*x^5)) + 2772*a^5*b^5*e^5*(2*A*e*(d^5 + 18*d^4*e*x + 153*d^3*e^2*x^2 + 816*d^2*e^3*x^3 + 3060*d*e^4*x^4 + 8568*e^5*x^5) + B*(d^6 + 18*d^5*e*x + 153*d^4*e^2*x^2 + 816*d^3*e^3*x^3 + 3060*d^2*e^4*x^4 + 8568*d*e^5*x^5 + 18564*e^6*x^6)) + 210*a^4*b^6*e^4*(11*A*e*(d^6 + 18*d^5*e*x + 153*d^4*e^2*x^2 + 816*d^3*e^3*x^3 + 3060*d^2*e^4*x^4 + 8568*d*e^5*x^5 + 18564*e^6*x^6) + 7*B*(d^7 + 18*d^6*e*x + 153*d^5*e^2*x^2 + 816*d^4*e^3*x^3 + 3060*d^3*e^4*x^4 + 8568*d^2*e^5*x^5 + 18564*d*e^6*x^6 + 31824*e^7*x^7)) + 168*a^3*b^7*e^3*(5*A*e*(d^7 + 18*d^6*e*x + 153*d^5*e^2*x^2 + 816*d^4*e^3*x^3 + 3060*d^3*e^4*x^4 + 8568*d^2*e^5*x^5 + 18564*d*e^6*x^6 + 31824*e^7*x^7) + 4*B*(d^8 + 18*d^7*e*x + 153*d^6*e^2*x^2 + 816*d^5*e^3*x^3 + 3060*d^4*e^4*x^4 + 8568*d^3*e^5*x^5 + 18564*d^2*e^6*x^6 + 31824*d*e^7*x^7 + 43758*e^8*x^8)) + 252*a^2*b^8*e^2*(A*e*(d^8 + 18*d^7*e*x + 153*d^6*e^2*x^2 + 816*d^5*e^3*x^3 + 3060*d^4*e^4*x^4 + 8568*d^3*e^5*x^5 + 18564*d^2*e^6*x^6 + 31824*d*e^7*x^7 + 43758*e^8*x^8) + B*(d^9 + 18*d^8*e*x + 153*d^7*e^2*x^2 + 816*d^6*e^3*x^3 + 3060*d^5*e^4*x^4 + 8568*d^4*e^5*x^5 + 18564*d^3*e^6*x^6 + 31824*d^2*e^7*x^7 + 43758*d*e^8*x^8 + 48620*e^9*x^9)) + 14*a*b^9*e*(4*A*e*(d^9 + 18*d^8*e*x + 153*d^7*e^2*x^2 + 816*d^6*e^3*x^3 + 3060*d^5*e^4*x^4 + 8568*d^4*e^5*x^5 + 18564*d^3*e^6*x^6 + 31824*d^2*e^7*x^7 + 43758*d*e^8*x^8 + 48620*e^9*x^9) + 5*B*(d^10 + 18*d^9*e*x + 153*d^8*e^2*x^2 + 816*d^7*e^3*x^3 + 3060*d^6*e^4*x^4 + 8568*d^5*e^5*x^5 + 18564*d^4*e^6*x^6 + 31824*d^3*e^7*x^7 + 43758*d^2*e^8*x^8 + 48620*d*e^9*x^9 + 43758*e^10*x^10)) + b^10*(7*A*e*(d^10 + 18*d^9*e*x + 153*d^8*e^2*x^2 + 816*d^7*e^3*x^3 + 3060*d^6*e^4*x^4 + 8568*d^5*e^5*x^5 + 18564*d^4*e^6*x^6 + 31824*d^3*e^7*x^7 + 43758*d^2*e^8*x^8 + 48620*d*e^9*x^9 + 43758*e^10*x^10) + 11*B*(d^11 + 18*d^10*e*x + 153*d^9*e^2*x^2 + 816*d^8*e^3*x^3 + 3060*d^7*e^4*x^4 + 8568*d^6*e^5*x^5 + 18564*d^5*e^6*x^6 + 31824*d^4*e^7*x^7 + 43758*d^3*e^8*x^8 + 48620*d^2*e^9*x^9 + 43758*d*e^10*x^10 + 31824*e^11*x^11)))/(e^12*(d + e*x)^18)","B",1
1108,1,1433,460,1.1330446,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{20}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^20,x]","-\frac{\left(8 A e \left(d^{10}+19 e x d^9+171 e^2 x^2 d^8+969 e^3 x^3 d^7+3876 e^4 x^4 d^6+11628 e^5 x^5 d^5+27132 e^6 x^6 d^4+50388 e^7 x^7 d^3+75582 e^8 x^8 d^2+92378 e^9 x^9 d+92378 e^{10} x^{10}\right)+11 B \left(d^{11}+19 e x d^{10}+171 e^2 x^2 d^9+969 e^3 x^3 d^8+3876 e^4 x^4 d^7+11628 e^5 x^5 d^6+27132 e^6 x^6 d^5+50388 e^7 x^7 d^4+75582 e^8 x^8 d^3+92378 e^9 x^9 d^2+92378 e^{10} x^{10} d+75582 e^{11} x^{11}\right)\right) b^{10}+8 a e \left(9 A e \left(d^9+19 e x d^8+171 e^2 x^2 d^7+969 e^3 x^3 d^6+3876 e^4 x^4 d^5+11628 e^5 x^5 d^4+27132 e^6 x^6 d^3+50388 e^7 x^7 d^2+75582 e^8 x^8 d+92378 e^9 x^9\right)+10 B \left(d^{10}+19 e x d^9+171 e^2 x^2 d^8+969 e^3 x^3 d^7+3876 e^4 x^4 d^6+11628 e^5 x^5 d^5+27132 e^6 x^6 d^4+50388 e^7 x^7 d^3+75582 e^8 x^8 d^2+92378 e^9 x^9 d+92378 e^{10} x^{10}\right)\right) b^9+36 a^2 e^2 \left(10 A e \left(d^8+19 e x d^7+171 e^2 x^2 d^6+969 e^3 x^3 d^5+3876 e^4 x^4 d^4+11628 e^5 x^5 d^3+27132 e^6 x^6 d^2+50388 e^7 x^7 d+75582 e^8 x^8\right)+9 B \left(d^9+19 e x d^8+171 e^2 x^2 d^7+969 e^3 x^3 d^6+3876 e^4 x^4 d^5+11628 e^5 x^5 d^4+27132 e^6 x^6 d^3+50388 e^7 x^7 d^2+75582 e^8 x^8 d+92378 e^9 x^9\right)\right) b^8+120 a^3 e^3 \left(11 A e \left(d^7+19 e x d^6+171 e^2 x^2 d^5+969 e^3 x^3 d^4+3876 e^4 x^4 d^3+11628 e^5 x^5 d^2+27132 e^6 x^6 d+50388 e^7 x^7\right)+8 B \left(d^8+19 e x d^7+171 e^2 x^2 d^6+969 e^3 x^3 d^5+3876 e^4 x^4 d^4+11628 e^5 x^5 d^3+27132 e^6 x^6 d^2+50388 e^7 x^7 d+75582 e^8 x^8\right)\right) b^7+330 a^4 e^4 \left(12 A e \left(d^6+19 e x d^5+171 e^2 x^2 d^4+969 e^3 x^3 d^3+3876 e^4 x^4 d^2+11628 e^5 x^5 d+27132 e^6 x^6\right)+7 B \left(d^7+19 e x d^6+171 e^2 x^2 d^5+969 e^3 x^3 d^4+3876 e^4 x^4 d^3+11628 e^5 x^5 d^2+27132 e^6 x^6 d+50388 e^7 x^7\right)\right) b^6+792 a^5 e^5 \left(13 A e \left(d^5+19 e x d^4+171 e^2 x^2 d^3+969 e^3 x^3 d^2+3876 e^4 x^4 d+11628 e^5 x^5\right)+6 B \left(d^6+19 e x d^5+171 e^2 x^2 d^4+969 e^3 x^3 d^3+3876 e^4 x^4 d^2+11628 e^5 x^5 d+27132 e^6 x^6\right)\right) b^5+1716 a^6 e^6 \left(14 A e \left(d^4+19 e x d^3+171 e^2 x^2 d^2+969 e^3 x^3 d+3876 e^4 x^4\right)+5 B \left(d^5+19 e x d^4+171 e^2 x^2 d^3+969 e^3 x^3 d^2+3876 e^4 x^4 d+11628 e^5 x^5\right)\right) b^4+3432 a^7 e^7 \left(15 A e \left(d^3+19 e x d^2+171 e^2 x^2 d+969 e^3 x^3\right)+4 B \left(d^4+19 e x d^3+171 e^2 x^2 d^2+969 e^3 x^3 d+3876 e^4 x^4\right)\right) b^3+6435 a^8 e^8 \left(16 A e \left(d^2+19 e x d+171 e^2 x^2\right)+3 B \left(d^3+19 e x d^2+171 e^2 x^2 d+969 e^3 x^3\right)\right) b^2+11440 a^9 e^9 \left(17 A e (d+19 e x)+2 B \left(d^2+19 e x d+171 e^2 x^2\right)\right) b+19448 a^{10} e^{10} (18 A e+B (d+19 e x))}{6651216 e^{12} (d+e x)^{19}}","\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,"-1/6651216*(19448*a^10*e^10*(18*A*e + B*(d + 19*e*x)) + 11440*a^9*b*e^9*(17*A*e*(d + 19*e*x) + 2*B*(d^2 + 19*d*e*x + 171*e^2*x^2)) + 6435*a^8*b^2*e^8*(16*A*e*(d^2 + 19*d*e*x + 171*e^2*x^2) + 3*B*(d^3 + 19*d^2*e*x + 171*d*e^2*x^2 + 969*e^3*x^3)) + 3432*a^7*b^3*e^7*(15*A*e*(d^3 + 19*d^2*e*x + 171*d*e^2*x^2 + 969*e^3*x^3) + 4*B*(d^4 + 19*d^3*e*x + 171*d^2*e^2*x^2 + 969*d*e^3*x^3 + 3876*e^4*x^4)) + 1716*a^6*b^4*e^6*(14*A*e*(d^4 + 19*d^3*e*x + 171*d^2*e^2*x^2 + 969*d*e^3*x^3 + 3876*e^4*x^4) + 5*B*(d^5 + 19*d^4*e*x + 171*d^3*e^2*x^2 + 969*d^2*e^3*x^3 + 3876*d*e^4*x^4 + 11628*e^5*x^5)) + 792*a^5*b^5*e^5*(13*A*e*(d^5 + 19*d^4*e*x + 171*d^3*e^2*x^2 + 969*d^2*e^3*x^3 + 3876*d*e^4*x^4 + 11628*e^5*x^5) + 6*B*(d^6 + 19*d^5*e*x + 171*d^4*e^2*x^2 + 969*d^3*e^3*x^3 + 3876*d^2*e^4*x^4 + 11628*d*e^5*x^5 + 27132*e^6*x^6)) + 330*a^4*b^6*e^4*(12*A*e*(d^6 + 19*d^5*e*x + 171*d^4*e^2*x^2 + 969*d^3*e^3*x^3 + 3876*d^2*e^4*x^4 + 11628*d*e^5*x^5 + 27132*e^6*x^6) + 7*B*(d^7 + 19*d^6*e*x + 171*d^5*e^2*x^2 + 969*d^4*e^3*x^3 + 3876*d^3*e^4*x^4 + 11628*d^2*e^5*x^5 + 27132*d*e^6*x^6 + 50388*e^7*x^7)) + 120*a^3*b^7*e^3*(11*A*e*(d^7 + 19*d^6*e*x + 171*d^5*e^2*x^2 + 969*d^4*e^3*x^3 + 3876*d^3*e^4*x^4 + 11628*d^2*e^5*x^5 + 27132*d*e^6*x^6 + 50388*e^7*x^7) + 8*B*(d^8 + 19*d^7*e*x + 171*d^6*e^2*x^2 + 969*d^5*e^3*x^3 + 3876*d^4*e^4*x^4 + 11628*d^3*e^5*x^5 + 27132*d^2*e^6*x^6 + 50388*d*e^7*x^7 + 75582*e^8*x^8)) + 36*a^2*b^8*e^2*(10*A*e*(d^8 + 19*d^7*e*x + 171*d^6*e^2*x^2 + 969*d^5*e^3*x^3 + 3876*d^4*e^4*x^4 + 11628*d^3*e^5*x^5 + 27132*d^2*e^6*x^6 + 50388*d*e^7*x^7 + 75582*e^8*x^8) + 9*B*(d^9 + 19*d^8*e*x + 171*d^7*e^2*x^2 + 969*d^6*e^3*x^3 + 3876*d^5*e^4*x^4 + 11628*d^4*e^5*x^5 + 27132*d^3*e^6*x^6 + 50388*d^2*e^7*x^7 + 75582*d*e^8*x^8 + 92378*e^9*x^9)) + 8*a*b^9*e*(9*A*e*(d^9 + 19*d^8*e*x + 171*d^7*e^2*x^2 + 969*d^6*e^3*x^3 + 3876*d^5*e^4*x^4 + 11628*d^4*e^5*x^5 + 27132*d^3*e^6*x^6 + 50388*d^2*e^7*x^7 + 75582*d*e^8*x^8 + 92378*e^9*x^9) + 10*B*(d^10 + 19*d^9*e*x + 171*d^8*e^2*x^2 + 969*d^7*e^3*x^3 + 3876*d^6*e^4*x^4 + 11628*d^5*e^5*x^5 + 27132*d^4*e^6*x^6 + 50388*d^3*e^7*x^7 + 75582*d^2*e^8*x^8 + 92378*d*e^9*x^9 + 92378*e^10*x^10)) + b^10*(8*A*e*(d^10 + 19*d^9*e*x + 171*d^8*e^2*x^2 + 969*d^7*e^3*x^3 + 3876*d^6*e^4*x^4 + 11628*d^5*e^5*x^5 + 27132*d^4*e^6*x^6 + 50388*d^3*e^7*x^7 + 75582*d^2*e^8*x^8 + 92378*d*e^9*x^9 + 92378*e^10*x^10) + 11*B*(d^11 + 19*d^10*e*x + 171*d^9*e^2*x^2 + 969*d^8*e^3*x^3 + 3876*d^7*e^4*x^4 + 11628*d^6*e^5*x^5 + 27132*d^5*e^6*x^6 + 50388*d^4*e^7*x^7 + 75582*d^3*e^8*x^8 + 92378*d^2*e^9*x^9 + 92378*d*e^10*x^10 + 75582*e^11*x^11)))/(e^12*(d + e*x)^19)","B",1
1109,1,1428,462,1.0125139,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{21}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^21,x]","-\frac{\left(9 A e \left(d^{10}+20 e x d^9+190 e^2 x^2 d^8+1140 e^3 x^3 d^7+4845 e^4 x^4 d^6+15504 e^5 x^5 d^5+38760 e^6 x^6 d^4+77520 e^7 x^7 d^3+125970 e^8 x^8 d^2+167960 e^9 x^9 d+184756 e^{10} x^{10}\right)+11 B \left(d^{11}+20 e x d^{10}+190 e^2 x^2 d^9+1140 e^3 x^3 d^8+4845 e^4 x^4 d^7+15504 e^5 x^5 d^6+38760 e^6 x^6 d^5+77520 e^7 x^7 d^4+125970 e^8 x^8 d^3+167960 e^9 x^9 d^2+184756 e^{10} x^{10} d+167960 e^{11} x^{11}\right)\right) b^{10}+90 a e \left(A e \left(d^9+20 e x d^8+190 e^2 x^2 d^7+1140 e^3 x^3 d^6+4845 e^4 x^4 d^5+15504 e^5 x^5 d^4+38760 e^6 x^6 d^3+77520 e^7 x^7 d^2+125970 e^8 x^8 d+167960 e^9 x^9\right)+B \left(d^{10}+20 e x d^9+190 e^2 x^2 d^8+1140 e^3 x^3 d^7+4845 e^4 x^4 d^6+15504 e^5 x^5 d^5+38760 e^6 x^6 d^4+77520 e^7 x^7 d^3+125970 e^8 x^8 d^2+167960 e^9 x^9 d+184756 e^{10} x^{10}\right)\right) b^9+45 a^2 e^2 \left(11 A e \left(d^8+20 e x d^7+190 e^2 x^2 d^6+1140 e^3 x^3 d^5+4845 e^4 x^4 d^4+15504 e^5 x^5 d^3+38760 e^6 x^6 d^2+77520 e^7 x^7 d+125970 e^8 x^8\right)+9 B \left(d^9+20 e x d^8+190 e^2 x^2 d^7+1140 e^3 x^3 d^6+4845 e^4 x^4 d^5+15504 e^5 x^5 d^4+38760 e^6 x^6 d^3+77520 e^7 x^7 d^2+125970 e^8 x^8 d+167960 e^9 x^9\right)\right) b^8+660 a^3 e^3 \left(3 A e \left(d^7+20 e x d^6+190 e^2 x^2 d^5+1140 e^3 x^3 d^4+4845 e^4 x^4 d^3+15504 e^5 x^5 d^2+38760 e^6 x^6 d+77520 e^7 x^7\right)+2 B \left(d^8+20 e x d^7+190 e^2 x^2 d^6+1140 e^3 x^3 d^5+4845 e^4 x^4 d^4+15504 e^5 x^5 d^3+38760 e^6 x^6 d^2+77520 e^7 x^7 d+125970 e^8 x^8\right)\right) b^7+495 a^4 e^4 \left(13 A e \left(d^6+20 e x d^5+190 e^2 x^2 d^4+1140 e^3 x^3 d^3+4845 e^4 x^4 d^2+15504 e^5 x^5 d+38760 e^6 x^6\right)+7 B \left(d^7+20 e x d^6+190 e^2 x^2 d^5+1140 e^3 x^3 d^4+4845 e^4 x^4 d^3+15504 e^5 x^5 d^2+38760 e^6 x^6 d+77520 e^7 x^7\right)\right) b^6+2574 a^5 e^5 \left(7 A e \left(d^5+20 e x d^4+190 e^2 x^2 d^3+1140 e^3 x^3 d^2+4845 e^4 x^4 d+15504 e^5 x^5\right)+3 B \left(d^6+20 e x d^5+190 e^2 x^2 d^4+1140 e^3 x^3 d^3+4845 e^4 x^4 d^2+15504 e^5 x^5 d+38760 e^6 x^6\right)\right) b^5+15015 a^6 e^6 \left(3 A e \left(d^4+20 e x d^3+190 e^2 x^2 d^2+1140 e^3 x^3 d+4845 e^4 x^4\right)+B \left(d^5+20 e x d^4+190 e^2 x^2 d^3+1140 e^3 x^3 d^2+4845 e^4 x^4 d+15504 e^5 x^5\right)\right) b^4+25740 a^7 e^7 \left(4 A e \left(d^3+20 e x d^2+190 e^2 x^2 d+1140 e^3 x^3\right)+B \left(d^4+20 e x d^3+190 e^2 x^2 d^2+1140 e^3 x^3 d+4845 e^4 x^4\right)\right) b^3+12870 a^8 e^8 \left(17 A e \left(d^2+20 e x d+190 e^2 x^2\right)+3 B \left(d^3+20 e x d^2+190 e^2 x^2 d+1140 e^3 x^3\right)\right) b^2+48620 a^9 e^9 \left(9 A e (d+20 e x)+B \left(d^2+20 e x d+190 e^2 x^2\right)\right) b+43758 a^{10} e^{10} (19 A e+B (d+20 e x))}{16628040 e^{12} (d+e x)^{20}}","\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,"-1/16628040*(43758*a^10*e^10*(19*A*e + B*(d + 20*e*x)) + 48620*a^9*b*e^9*(9*A*e*(d + 20*e*x) + B*(d^2 + 20*d*e*x + 190*e^2*x^2)) + 12870*a^8*b^2*e^8*(17*A*e*(d^2 + 20*d*e*x + 190*e^2*x^2) + 3*B*(d^3 + 20*d^2*e*x + 190*d*e^2*x^2 + 1140*e^3*x^3)) + 25740*a^7*b^3*e^7*(4*A*e*(d^3 + 20*d^2*e*x + 190*d*e^2*x^2 + 1140*e^3*x^3) + B*(d^4 + 20*d^3*e*x + 190*d^2*e^2*x^2 + 1140*d*e^3*x^3 + 4845*e^4*x^4)) + 15015*a^6*b^4*e^6*(3*A*e*(d^4 + 20*d^3*e*x + 190*d^2*e^2*x^2 + 1140*d*e^3*x^3 + 4845*e^4*x^4) + B*(d^5 + 20*d^4*e*x + 190*d^3*e^2*x^2 + 1140*d^2*e^3*x^3 + 4845*d*e^4*x^4 + 15504*e^5*x^5)) + 2574*a^5*b^5*e^5*(7*A*e*(d^5 + 20*d^4*e*x + 190*d^3*e^2*x^2 + 1140*d^2*e^3*x^3 + 4845*d*e^4*x^4 + 15504*e^5*x^5) + 3*B*(d^6 + 20*d^5*e*x + 190*d^4*e^2*x^2 + 1140*d^3*e^3*x^3 + 4845*d^2*e^4*x^4 + 15504*d*e^5*x^5 + 38760*e^6*x^6)) + 495*a^4*b^6*e^4*(13*A*e*(d^6 + 20*d^5*e*x + 190*d^4*e^2*x^2 + 1140*d^3*e^3*x^3 + 4845*d^2*e^4*x^4 + 15504*d*e^5*x^5 + 38760*e^6*x^6) + 7*B*(d^7 + 20*d^6*e*x + 190*d^5*e^2*x^2 + 1140*d^4*e^3*x^3 + 4845*d^3*e^4*x^4 + 15504*d^2*e^5*x^5 + 38760*d*e^6*x^6 + 77520*e^7*x^7)) + 660*a^3*b^7*e^3*(3*A*e*(d^7 + 20*d^6*e*x + 190*d^5*e^2*x^2 + 1140*d^4*e^3*x^3 + 4845*d^3*e^4*x^4 + 15504*d^2*e^5*x^5 + 38760*d*e^6*x^6 + 77520*e^7*x^7) + 2*B*(d^8 + 20*d^7*e*x + 190*d^6*e^2*x^2 + 1140*d^5*e^3*x^3 + 4845*d^4*e^4*x^4 + 15504*d^3*e^5*x^5 + 38760*d^2*e^6*x^6 + 77520*d*e^7*x^7 + 125970*e^8*x^8)) + 45*a^2*b^8*e^2*(11*A*e*(d^8 + 20*d^7*e*x + 190*d^6*e^2*x^2 + 1140*d^5*e^3*x^3 + 4845*d^4*e^4*x^4 + 15504*d^3*e^5*x^5 + 38760*d^2*e^6*x^6 + 77520*d*e^7*x^7 + 125970*e^8*x^8) + 9*B*(d^9 + 20*d^8*e*x + 190*d^7*e^2*x^2 + 1140*d^6*e^3*x^3 + 4845*d^5*e^4*x^4 + 15504*d^4*e^5*x^5 + 38760*d^3*e^6*x^6 + 77520*d^2*e^7*x^7 + 125970*d*e^8*x^8 + 167960*e^9*x^9)) + 90*a*b^9*e*(A*e*(d^9 + 20*d^8*e*x + 190*d^7*e^2*x^2 + 1140*d^6*e^3*x^3 + 4845*d^5*e^4*x^4 + 15504*d^4*e^5*x^5 + 38760*d^3*e^6*x^6 + 77520*d^2*e^7*x^7 + 125970*d*e^8*x^8 + 167960*e^9*x^9) + B*(d^10 + 20*d^9*e*x + 190*d^8*e^2*x^2 + 1140*d^7*e^3*x^3 + 4845*d^6*e^4*x^4 + 15504*d^5*e^5*x^5 + 38760*d^4*e^6*x^6 + 77520*d^3*e^7*x^7 + 125970*d^2*e^8*x^8 + 167960*d*e^9*x^9 + 184756*e^10*x^10)) + b^10*(9*A*e*(d^10 + 20*d^9*e*x + 190*d^8*e^2*x^2 + 1140*d^7*e^3*x^3 + 4845*d^6*e^4*x^4 + 15504*d^5*e^5*x^5 + 38760*d^4*e^6*x^6 + 77520*d^3*e^7*x^7 + 125970*d^2*e^8*x^8 + 167960*d*e^9*x^9 + 184756*e^10*x^10) + 11*B*(d^11 + 20*d^10*e*x + 190*d^9*e^2*x^2 + 1140*d^8*e^3*x^3 + 4845*d^7*e^4*x^4 + 15504*d^6*e^5*x^5 + 38760*d^5*e^6*x^6 + 77520*d^4*e^7*x^7 + 125970*d^3*e^8*x^8 + 167960*d^2*e^9*x^9 + 184756*d*e^10*x^10 + 167960*e^11*x^11)))/(e^12*(d + e*x)^20)","B",1
1110,1,1431,464,1.0214441,"\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{22}} \, dx","Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^22,x]","-\frac{\left(10 A e \left(d^{10}+21 e x d^9+210 e^2 x^2 d^8+1330 e^3 x^3 d^7+5985 e^4 x^4 d^6+20349 e^5 x^5 d^5+54264 e^6 x^6 d^4+116280 e^7 x^7 d^3+203490 e^8 x^8 d^2+293930 e^9 x^9 d+352716 e^{10} x^{10}\right)+11 B \left(d^{11}+21 e x d^{10}+210 e^2 x^2 d^9+1330 e^3 x^3 d^8+5985 e^4 x^4 d^7+20349 e^5 x^5 d^6+54264 e^6 x^6 d^5+116280 e^7 x^7 d^4+203490 e^8 x^8 d^3+293930 e^9 x^9 d^2+352716 e^{10} x^{10} d+352716 e^{11} x^{11}\right)\right) b^{10}+10 a e \left(11 A e \left(d^9+21 e x d^8+210 e^2 x^2 d^7+1330 e^3 x^3 d^6+5985 e^4 x^4 d^5+20349 e^5 x^5 d^4+54264 e^6 x^6 d^3+116280 e^7 x^7 d^2+203490 e^8 x^8 d+293930 e^9 x^9\right)+10 B \left(d^{10}+21 e x d^9+210 e^2 x^2 d^8+1330 e^3 x^3 d^7+5985 e^4 x^4 d^6+20349 e^5 x^5 d^5+54264 e^6 x^6 d^4+116280 e^7 x^7 d^3+203490 e^8 x^8 d^2+293930 e^9 x^9 d+352716 e^{10} x^{10}\right)\right) b^9+165 a^2 e^2 \left(4 A e \left(d^8+21 e x d^7+210 e^2 x^2 d^6+1330 e^3 x^3 d^5+5985 e^4 x^4 d^4+20349 e^5 x^5 d^3+54264 e^6 x^6 d^2+116280 e^7 x^7 d+203490 e^8 x^8\right)+3 B \left(d^9+21 e x d^8+210 e^2 x^2 d^7+1330 e^3 x^3 d^6+5985 e^4 x^4 d^5+20349 e^5 x^5 d^4+54264 e^6 x^6 d^3+116280 e^7 x^7 d^2+203490 e^8 x^8 d+293930 e^9 x^9\right)\right) b^8+220 a^3 e^3 \left(13 A e \left(d^7+21 e x d^6+210 e^2 x^2 d^5+1330 e^3 x^3 d^4+5985 e^4 x^4 d^3+20349 e^5 x^5 d^2+54264 e^6 x^6 d+116280 e^7 x^7\right)+8 B \left(d^8+21 e x d^7+210 e^2 x^2 d^6+1330 e^3 x^3 d^5+5985 e^4 x^4 d^4+20349 e^5 x^5 d^3+54264 e^6 x^6 d^2+116280 e^7 x^7 d+203490 e^8 x^8\right)\right) b^7+5005 a^4 e^4 \left(2 A e \left(d^6+21 e x d^5+210 e^2 x^2 d^4+1330 e^3 x^3 d^3+5985 e^4 x^4 d^2+20349 e^5 x^5 d+54264 e^6 x^6\right)+B \left(d^7+21 e x d^6+210 e^2 x^2 d^5+1330 e^3 x^3 d^4+5985 e^4 x^4 d^3+20349 e^5 x^5 d^2+54264 e^6 x^6 d+116280 e^7 x^7\right)\right) b^6+6006 a^5 e^5 \left(5 A e \left(d^5+21 e x d^4+210 e^2 x^2 d^3+1330 e^3 x^3 d^2+5985 e^4 x^4 d+20349 e^5 x^5\right)+2 B \left(d^6+21 e x d^5+210 e^2 x^2 d^4+1330 e^3 x^3 d^3+5985 e^4 x^4 d^2+20349 e^5 x^5 d+54264 e^6 x^6\right)\right) b^5+5005 a^6 e^6 \left(16 A e \left(d^4+21 e x d^3+210 e^2 x^2 d^2+1330 e^3 x^3 d+5985 e^4 x^4\right)+5 B \left(d^5+21 e x d^4+210 e^2 x^2 d^3+1330 e^3 x^3 d^2+5985 e^4 x^4 d+20349 e^5 x^5\right)\right) b^4+11440 a^7 e^7 \left(17 A e \left(d^3+21 e x d^2+210 e^2 x^2 d+1330 e^3 x^3\right)+4 B \left(d^4+21 e x d^3+210 e^2 x^2 d^2+1330 e^3 x^3 d+5985 e^4 x^4\right)\right) b^3+72930 a^8 e^8 \left(6 A e \left(d^2+21 e x d+210 e^2 x^2\right)+B \left(d^3+21 e x d^2+210 e^2 x^2 d+1330 e^3 x^3\right)\right) b^2+48620 a^9 e^9 \left(19 A e (d+21 e x)+2 B \left(d^2+21 e x d+210 e^2 x^2\right)\right) b+92378 a^{10} e^{10} (20 A e+B (d+21 e x))}{38798760 e^{12} (d+e x)^{21}}","\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,"-1/38798760*(92378*a^10*e^10*(20*A*e + B*(d + 21*e*x)) + 48620*a^9*b*e^9*(19*A*e*(d + 21*e*x) + 2*B*(d^2 + 21*d*e*x + 210*e^2*x^2)) + 72930*a^8*b^2*e^8*(6*A*e*(d^2 + 21*d*e*x + 210*e^2*x^2) + B*(d^3 + 21*d^2*e*x + 210*d*e^2*x^2 + 1330*e^3*x^3)) + 11440*a^7*b^3*e^7*(17*A*e*(d^3 + 21*d^2*e*x + 210*d*e^2*x^2 + 1330*e^3*x^3) + 4*B*(d^4 + 21*d^3*e*x + 210*d^2*e^2*x^2 + 1330*d*e^3*x^3 + 5985*e^4*x^4)) + 5005*a^6*b^4*e^6*(16*A*e*(d^4 + 21*d^3*e*x + 210*d^2*e^2*x^2 + 1330*d*e^3*x^3 + 5985*e^4*x^4) + 5*B*(d^5 + 21*d^4*e*x + 210*d^3*e^2*x^2 + 1330*d^2*e^3*x^3 + 5985*d*e^4*x^4 + 20349*e^5*x^5)) + 6006*a^5*b^5*e^5*(5*A*e*(d^5 + 21*d^4*e*x + 210*d^3*e^2*x^2 + 1330*d^2*e^3*x^3 + 5985*d*e^4*x^4 + 20349*e^5*x^5) + 2*B*(d^6 + 21*d^5*e*x + 210*d^4*e^2*x^2 + 1330*d^3*e^3*x^3 + 5985*d^2*e^4*x^4 + 20349*d*e^5*x^5 + 54264*e^6*x^6)) + 5005*a^4*b^6*e^4*(2*A*e*(d^6 + 21*d^5*e*x + 210*d^4*e^2*x^2 + 1330*d^3*e^3*x^3 + 5985*d^2*e^4*x^4 + 20349*d*e^5*x^5 + 54264*e^6*x^6) + B*(d^7 + 21*d^6*e*x + 210*d^5*e^2*x^2 + 1330*d^4*e^3*x^3 + 5985*d^3*e^4*x^4 + 20349*d^2*e^5*x^5 + 54264*d*e^6*x^6 + 116280*e^7*x^7)) + 220*a^3*b^7*e^3*(13*A*e*(d^7 + 21*d^6*e*x + 210*d^5*e^2*x^2 + 1330*d^4*e^3*x^3 + 5985*d^3*e^4*x^4 + 20349*d^2*e^5*x^5 + 54264*d*e^6*x^6 + 116280*e^7*x^7) + 8*B*(d^8 + 21*d^7*e*x + 210*d^6*e^2*x^2 + 1330*d^5*e^3*x^3 + 5985*d^4*e^4*x^4 + 20349*d^3*e^5*x^5 + 54264*d^2*e^6*x^6 + 116280*d*e^7*x^7 + 203490*e^8*x^8)) + 165*a^2*b^8*e^2*(4*A*e*(d^8 + 21*d^7*e*x + 210*d^6*e^2*x^2 + 1330*d^5*e^3*x^3 + 5985*d^4*e^4*x^4 + 20349*d^3*e^5*x^5 + 54264*d^2*e^6*x^6 + 116280*d*e^7*x^7 + 203490*e^8*x^8) + 3*B*(d^9 + 21*d^8*e*x + 210*d^7*e^2*x^2 + 1330*d^6*e^3*x^3 + 5985*d^5*e^4*x^4 + 20349*d^4*e^5*x^5 + 54264*d^3*e^6*x^6 + 116280*d^2*e^7*x^7 + 203490*d*e^8*x^8 + 293930*e^9*x^9)) + 10*a*b^9*e*(11*A*e*(d^9 + 21*d^8*e*x + 210*d^7*e^2*x^2 + 1330*d^6*e^3*x^3 + 5985*d^5*e^4*x^4 + 20349*d^4*e^5*x^5 + 54264*d^3*e^6*x^6 + 116280*d^2*e^7*x^7 + 203490*d*e^8*x^8 + 293930*e^9*x^9) + 10*B*(d^10 + 21*d^9*e*x + 210*d^8*e^2*x^2 + 1330*d^7*e^3*x^3 + 5985*d^6*e^4*x^4 + 20349*d^5*e^5*x^5 + 54264*d^4*e^6*x^6 + 116280*d^3*e^7*x^7 + 203490*d^2*e^8*x^8 + 293930*d*e^9*x^9 + 352716*e^10*x^10)) + b^10*(10*A*e*(d^10 + 21*d^9*e*x + 210*d^8*e^2*x^2 + 1330*d^7*e^3*x^3 + 5985*d^6*e^4*x^4 + 20349*d^5*e^5*x^5 + 54264*d^4*e^6*x^6 + 116280*d^3*e^7*x^7 + 203490*d^2*e^8*x^8 + 293930*d*e^9*x^9 + 352716*e^10*x^10) + 11*B*(d^11 + 21*d^10*e*x + 210*d^9*e^2*x^2 + 1330*d^8*e^3*x^3 + 5985*d^7*e^4*x^4 + 20349*d^6*e^5*x^5 + 54264*d^5*e^6*x^6 + 116280*d^4*e^7*x^7 + 203490*d^3*e^8*x^8 + 293930*d^2*e^9*x^9 + 352716*d*e^10*x^10 + 352716*e^11*x^11)))/(e^12*(d + e*x)^21)","B",1
1111,1,368,187,0.2517109,"\int \frac{(A+B x) (d+e x)^5}{a+b x} \, dx","Integrate[((A + B*x)*(d + e*x)^5)/(a + b*x),x]","\frac{b x \left(-60 a^5 B e^5+30 a^4 b e^4 (2 A e+10 B d+B e x)-10 a^3 b^2 e^3 \left(3 A e (10 d+e x)+B \left(60 d^2+15 d e x+2 e^2 x^2\right)\right)+5 a^2 b^3 e^2 \left(2 A e \left(60 d^2+15 d e x+2 e^2 x^2\right)+B \left(120 d^3+60 d^2 e x+20 d e^2 x^2+3 e^3 x^3\right)\right)-a b^4 e \left(5 A e \left(120 d^3+60 d^2 e x+20 d e^2 x^2+3 e^3 x^3\right)+B \left(300 d^4+300 d^3 e x+200 d^2 e^2 x^2+75 d e^3 x^3+12 e^4 x^4\right)\right)+b^5 \left(A e \left(300 d^4+300 d^3 e x+200 d^2 e^2 x^2+75 d e^3 x^3+12 e^4 x^4\right)+10 B \left(6 d^5+15 d^4 e x+20 d^3 e^2 x^2+15 d^2 e^3 x^3+6 d e^4 x^4+e^5 x^5\right)\right)\right)+60 (A b-a B) (b d-a e)^5 \log (a+b x)}{60 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,"(b*x*(-60*a^5*B*e^5 + 30*a^4*b*e^4*(10*B*d + 2*A*e + B*e*x) - 10*a^3*b^2*e^3*(3*A*e*(10*d + e*x) + B*(60*d^2 + 15*d*e*x + 2*e^2*x^2)) + 5*a^2*b^3*e^2*(2*A*e*(60*d^2 + 15*d*e*x + 2*e^2*x^2) + B*(120*d^3 + 60*d^2*e*x + 20*d*e^2*x^2 + 3*e^3*x^3)) - a*b^4*e*(5*A*e*(120*d^3 + 60*d^2*e*x + 20*d*e^2*x^2 + 3*e^3*x^3) + B*(300*d^4 + 300*d^3*e*x + 200*d^2*e^2*x^2 + 75*d*e^3*x^3 + 12*e^4*x^4)) + b^5*(A*e*(300*d^4 + 300*d^3*e*x + 200*d^2*e^2*x^2 + 75*d*e^3*x^3 + 12*e^4*x^4) + 10*B*(6*d^5 + 15*d^4*e*x + 20*d^3*e^2*x^2 + 15*d^2*e^3*x^3 + 6*d*e^4*x^4 + e^5*x^5))) + 60*(A*b - a*B)*(b*d - a*e)^5*Log[a + b*x])/(60*b^7)","A",1
1112,1,257,155,0.1827242,"\int \frac{(A+B x) (d+e x)^4}{a+b x} \, dx","Integrate[((A + B*x)*(d + e*x)^4)/(a + b*x),x]","\frac{b x \left(60 a^4 B e^4-30 a^3 b e^3 (2 A e+8 B d+B e x)+10 a^2 b^2 e^2 \left(3 A e (8 d+e x)+2 B \left(18 d^2+6 d e x+e^2 x^2\right)\right)-5 a b^3 e \left(4 A e \left(18 d^2+6 d e x+e^2 x^2\right)+B \left(48 d^3+36 d^2 e x+16 d e^2 x^2+3 e^3 x^3\right)\right)+b^4 \left(5 A e \left(48 d^3+36 d^2 e x+16 d e^2 x^2+3 e^3 x^3\right)+12 B \left(5 d^4+10 d^3 e x+10 d^2 e^2 x^2+5 d e^3 x^3+e^4 x^4\right)\right)\right)+60 (A b-a B) (b d-a e)^4 \log (a+b x)}{60 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,"(b*x*(60*a^4*B*e^4 - 30*a^3*b*e^3*(8*B*d + 2*A*e + B*e*x) + 10*a^2*b^2*e^2*(3*A*e*(8*d + e*x) + 2*B*(18*d^2 + 6*d*e*x + e^2*x^2)) - 5*a*b^3*e*(4*A*e*(18*d^2 + 6*d*e*x + e^2*x^2) + B*(48*d^3 + 36*d^2*e*x + 16*d*e^2*x^2 + 3*e^3*x^3)) + b^4*(5*A*e*(48*d^3 + 36*d^2*e*x + 16*d*e^2*x^2 + 3*e^3*x^3) + 12*B*(5*d^4 + 10*d^3*e*x + 10*d^2*e^2*x^2 + 5*d*e^3*x^3 + e^4*x^4))) + 60*(A*b - a*B)*(b*d - a*e)^4*Log[a + b*x])/(60*b^6)","A",1
1113,1,169,123,0.1167111,"\int \frac{(A+B x) (d+e x)^3}{a+b x} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(a + b*x),x]","\frac{b x \left(-12 a^3 B e^3+6 a^2 b e^2 (2 A e+6 B d+B e x)-2 a b^2 e \left(3 A e (6 d+e x)+B \left(18 d^2+9 d e x+2 e^2 x^2\right)\right)+b^3 \left(2 A e \left(18 d^2+9 d e x+2 e^2 x^2\right)+3 B \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)\right)\right)+12 (A b-a B) (b d-a e)^3 \log (a+b x)}{12 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,"(b*x*(-12*a^3*B*e^3 + 6*a^2*b*e^2*(6*B*d + 2*A*e + B*e*x) - 2*a*b^2*e*(3*A*e*(6*d + e*x) + B*(18*d^2 + 9*d*e*x + 2*e^2*x^2)) + b^3*(2*A*e*(18*d^2 + 9*d*e*x + 2*e^2*x^2) + 3*B*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3))) + 12*(A*b - a*B)*(b*d - a*e)^3*Log[a + b*x])/(12*b^5)","A",1
1114,1,102,91,0.0759745,"\int \frac{(A+B x) (d+e x)^2}{a+b x} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/(a + b*x),x]","\frac{b x \left(6 a^2 B e^2-3 a b e (2 A e+4 B d+B e x)+b^2 \left(3 A e (4 d+e x)+2 B \left(3 d^2+3 d e x+e^2 x^2\right)\right)\right)+6 (A b-a B) (b d-a e)^2 \log (a+b x)}{6 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,"(b*x*(6*a^2*B*e^2 - 3*a*b*e*(4*B*d + 2*A*e + B*e*x) + b^2*(3*A*e*(4*d + e*x) + 2*B*(3*d^2 + 3*d*e*x + e^2*x^2))) + 6*(A*b - a*B)*(b*d - a*e)^2*Log[a + b*x])/(6*b^4)","A",1
1115,1,56,59,0.0361092,"\int \frac{(A+B x) (d+e x)}{a+b x} \, dx","Integrate[((A + B*x)*(d + e*x))/(a + b*x),x]","\frac{b x (b (2 A e+2 B d+B e x)-2 a B e)+2 (A b-a B) (b d-a e) \log (a+b x)}{2 b^3}","\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,"(b*x*(-2*a*B*e + b*(2*B*d + 2*A*e + B*e*x)) + 2*(A*b - a*B)*(b*d - a*e)*Log[a + b*x])/(2*b^3)","A",1
1116,1,25,25,0.0081144,"\int \frac{A+B x}{a+b x} \, dx","Integrate[(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
1117,1,50,57,0.03463,"\int \frac{A+B x}{(a+b x) (d+e x)} \, dx","Integrate[(A + B*x)/((a + b*x)*(d + e*x)),x]","\frac{e (A b-a B) \log (a+b x)+b (B d-A e) \log (d+e x)}{b e (b d-a e)}","\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)*e*Log[a + b*x] + b*(B*d - A*e)*Log[d + e*x])/(b*e*(b*d - a*e))","A",1
1118,1,80,82,0.1060721,"\int \frac{A+B x}{(a+b x) (d+e x)^2} \, dx","Integrate[(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
1119,1,112,112,0.1346036,"\int \frac{A+B x}{(a+b x) (d+e x)^3} \, dx","Integrate[(A + B*x)/((a + b*x)*(d + e*x)^3),x]","\frac{A b-a B}{(d+e x) (b d-a e)^2}+\frac{B d-A e}{2 e (d+e x)^2 (a e-b d)}+\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}","\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*d - A*e)/(2*e*(-(b*d) + a*e)*(d + e*x)^2) + (A*b - a*B)/((b*d - a*e)^2*(d + e*x)) + (b*(A*b - a*B)*Log[a + b*x])/(b*d - a*e)^3 - (b*(A*b - a*B)*Log[d + e*x])/(b*d - a*e)^3","A",1
1120,1,145,146,0.2481468,"\int \frac{A+B x}{(a+b x) (d+e x)^4} \, dx","Integrate[(A + B*x)/((a + b*x)*(d + e*x)^4),x]","\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{B d-A e}{3 e (d+e x)^3 (a e-b d)}","\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,"(B*d - A*e)/(3*e*(-(b*d) + a*e)*(d + e*x)^3) + (A*b - a*B)/(2*(b*d - a*e)^2*(d + e*x)^2) + (b*(A*b - a*B))/((b*d - a*e)^3*(d + e*x)) + (b^2*(A*b - a*B)*Log[a + b*x])/(b*d - a*e)^4 + (b^2*(-(A*b) + a*B)*Log[d + e*x])/(b*d - a*e)^4","A",1
1121,1,183,178,0.1333408,"\int \frac{A+B x}{(a+b x) (d+e x)^5} \, dx","Integrate[(A + B*x)/((a + b*x)*(d + e*x)^5),x]","\frac{12 b^3 e (d+e x)^4 (A b-a B) \log (a+b x)-12 b^3 e (d+e x)^4 (A b-a B) \log (d+e x)+12 b^2 e (d+e x)^3 (A b-a B) (b d-a e)+4 e (d+e x) (A b-a B) (b d-a e)^3+6 b e (d+e x)^2 (A b-a B) (b d-a e)^2-3 (b d-a e)^4 (B d-A e)}{12 e (d+e x)^4 (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*d - a*e)^4*(B*d - A*e) + 4*(A*b - a*B)*e*(b*d - a*e)^3*(d + e*x) + 6*b*(A*b - a*B)*e*(b*d - a*e)^2*(d + e*x)^2 + 12*b^2*(A*b - a*B)*e*(b*d - a*e)*(d + e*x)^3 + 12*b^3*(A*b - a*B)*e*(d + e*x)^4*Log[a + b*x] - 12*b^3*(A*b - a*B)*e*(d + e*x)^4*Log[d + e*x])/(12*e*(b*d - a*e)^5*(d + e*x)^4)","A",1
1122,1,500,227,0.3048423,"\int \frac{(A+B x) (d+e x)^5}{(a+b x)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^5)/(a + b*x)^2,x]","\frac{-5 A b \left(-12 a^5 e^5+12 a^4 b e^4 (5 d+4 e x)+30 a^3 b^2 e^3 \left(-4 d^2-6 d e x+e^2 x^2\right)-10 a^2 b^3 e^2 \left(-12 d^3-24 d^2 e x+12 d e^2 x^2+e^3 x^3\right)+5 a b^4 e \left(-12 d^4-24 d^3 e x+36 d^2 e^2 x^2+8 d e^3 x^3+e^4 x^4\right)+b^5 \left(12 d^5-120 d^3 e^2 x^2-60 d^2 e^3 x^3-20 d e^4 x^4-3 e^5 x^5\right)\right)+B \left(-60 a^6 e^5+300 a^5 b e^4 (d+e x)+60 a^4 b^2 e^3 \left(-10 d^2-20 d e x+3 e^2 x^2\right)+30 a^3 b^3 e^2 \left(20 d^3+60 d^2 e x-25 d e^2 x^2-2 e^3 x^3\right)+10 a^2 b^4 e \left(-30 d^4-120 d^3 e x+120 d^2 e^2 x^2+25 d e^3 x^3+3 e^4 x^4\right)+a b^5 \left(60 d^5+300 d^4 e x-900 d^3 e^2 x^2-400 d^2 e^3 x^3-125 d e^4 x^4-18 e^5 x^5\right)+b^6 e x^2 \left(300 d^4+300 d^3 e x+200 d^2 e^2 x^2+75 d e^3 x^3+12 e^4 x^4\right)\right)+60 (a+b x) (b d-a e)^4 \log (a+b x) (-6 a B e+5 A b e+b B d)}{60 b^7 (a+b x)}","\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,"(B*(-60*a^6*e^5 + 300*a^5*b*e^4*(d + e*x) + 60*a^4*b^2*e^3*(-10*d^2 - 20*d*e*x + 3*e^2*x^2) + 30*a^3*b^3*e^2*(20*d^3 + 60*d^2*e*x - 25*d*e^2*x^2 - 2*e^3*x^3) + 10*a^2*b^4*e*(-30*d^4 - 120*d^3*e*x + 120*d^2*e^2*x^2 + 25*d*e^3*x^3 + 3*e^4*x^4) + b^6*e*x^2*(300*d^4 + 300*d^3*e*x + 200*d^2*e^2*x^2 + 75*d*e^3*x^3 + 12*e^4*x^4) + a*b^5*(60*d^5 + 300*d^4*e*x - 900*d^3*e^2*x^2 - 400*d^2*e^3*x^3 - 125*d*e^4*x^4 - 18*e^5*x^5)) - 5*A*b*(-12*a^5*e^5 + 12*a^4*b*e^4*(5*d + 4*e*x) + 30*a^3*b^2*e^3*(-4*d^2 - 6*d*e*x + e^2*x^2) - 10*a^2*b^3*e^2*(-12*d^3 - 24*d^2*e*x + 12*d*e^2*x^2 + e^3*x^3) + 5*a*b^4*e*(-12*d^4 - 24*d^3*e*x + 36*d^2*e^2*x^2 + 8*d*e^3*x^3 + e^4*x^4) + b^5*(12*d^5 - 120*d^3*e^2*x^2 - 60*d^2*e^3*x^3 - 20*d*e^4*x^4 - 3*e^5*x^5)) + 60*(b*d - a*e)^4*(b*B*d + 5*A*b*e - 6*a*B*e)*(a + b*x)*Log[a + b*x])/(60*b^7*(a + b*x))","B",1
1123,1,365,187,0.2170378,"\int \frac{(A+B x) (d+e x)^4}{(a+b x)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^4)/(a + b*x)^2,x]","\frac{-4 A b \left(3 a^4 e^4-3 a^3 b e^3 (4 d+3 e x)+6 a^2 b^2 e^2 \left(3 d^2+4 d e x-e^2 x^2\right)+2 a b^3 e \left(-6 d^3-9 d^2 e x+9 d e^2 x^2+e^3 x^3\right)+b^4 \left(3 d^4-18 d^2 e^2 x^2-6 d e^3 x^3-e^4 x^4\right)\right)+B \left(12 a^5 e^4-48 a^4 b e^3 (d+e x)+6 a^3 b^2 e^2 \left(12 d^2+24 d e x-5 e^2 x^2\right)+2 a^2 b^3 e \left(-24 d^3-72 d^2 e x+48 d e^2 x^2+5 e^3 x^3\right)+a b^4 \left(12 d^4+48 d^3 e x-108 d^2 e^2 x^2-32 d e^3 x^3-5 e^4 x^4\right)+b^5 e x^2 \left(48 d^3+36 d^2 e x+16 d e^2 x^2+3 e^3 x^3\right)\right)+12 (a+b x) (b d-a e)^3 \log (a+b x) (-5 a B e+4 A b e+b B d)}{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,"(B*(12*a^5*e^4 - 48*a^4*b*e^3*(d + e*x) + 6*a^3*b^2*e^2*(12*d^2 + 24*d*e*x - 5*e^2*x^2) + b^5*e*x^2*(48*d^3 + 36*d^2*e*x + 16*d*e^2*x^2 + 3*e^3*x^3) + 2*a^2*b^3*e*(-24*d^3 - 72*d^2*e*x + 48*d*e^2*x^2 + 5*e^3*x^3) + a*b^4*(12*d^4 + 48*d^3*e*x - 108*d^2*e^2*x^2 - 32*d*e^3*x^3 - 5*e^4*x^4)) - 4*A*b*(3*a^4*e^4 - 3*a^3*b*e^3*(4*d + 3*e*x) + 6*a^2*b^2*e^2*(3*d^2 + 4*d*e*x - e^2*x^2) + 2*a*b^3*e*(-6*d^3 - 9*d^2*e*x + 9*d*e^2*x^2 + e^3*x^3) + b^4*(3*d^4 - 18*d^2*e^2*x^2 - 6*d*e^3*x^3 - e^4*x^4)) + 12*(b*d - a*e)^3*(b*B*d + 4*A*b*e - 5*a*B*e)*(a + b*x)*Log[a + b*x])/(12*b^6*(a + b*x))","A",1
1124,1,250,145,0.1630385,"\int \frac{(A+B x) (d+e x)^3}{(a+b x)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(a + b*x)^2,x]","\frac{-3 A b \left(-2 a^3 e^3+2 a^2 b e^2 (3 d+2 e x)+3 a b^2 e \left(-2 d^2-2 d e x+e^2 x^2\right)+b^3 \left(2 d^3-6 d e^2 x^2-e^3 x^3\right)\right)+B \left(-6 a^4 e^3+18 a^3 b e^2 (d+e x)+6 a^2 b^2 e \left(-3 d^2-6 d e x+2 e^2 x^2\right)+a b^3 \left(6 d^3+18 d^2 e x-27 d e^2 x^2-4 e^3 x^3\right)+b^4 e x^2 \left(18 d^2+9 d e x+2 e^2 x^2\right)\right)+6 (a+b x) (b d-a e)^2 \log (a+b x) (-4 a B e+3 A b e+b B d)}{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,"(B*(-6*a^4*e^3 + 18*a^3*b*e^2*(d + e*x) + 6*a^2*b^2*e*(-3*d^2 - 6*d*e*x + 2*e^2*x^2) + b^4*e*x^2*(18*d^2 + 9*d*e*x + 2*e^2*x^2) + a*b^3*(6*d^3 + 18*d^2*e*x - 27*d*e^2*x^2 - 4*e^3*x^3)) - 3*A*b*(-2*a^3*e^3 + 2*a^2*b*e^2*(3*d + 2*e*x) + 3*a*b^2*e*(-2*d^2 - 2*d*e*x + e^2*x^2) + b^3*(2*d^3 - 6*d*e^2*x^2 - e^3*x^3)) + 6*(b*d - a*e)^2*(b*B*d + 3*A*b*e - 4*a*B*e)*(a + b*x)*Log[a + b*x])/(6*b^5*(a + b*x))","A",1
1125,1,153,99,0.0990924,"\int \frac{(A+B x) (d+e x)^2}{(a+b x)^2} \, dx","Integrate[((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{a^3 B e^2-a^2 A b e^2-2 a^2 b B d e+2 a A b^2 d e+a b^2 B d^2-A b^3 d^2}{b^4 (a+b x)}+\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}","-\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,"(e*(2*b*B*d + A*b*e - 2*a*B*e)*x)/b^3 + (B*e^2*x^2)/(2*b^2) + (-(A*b^3*d^2) + a*b^2*B*d^2 + 2*a*A*b^2*d*e - 2*a^2*b*B*d*e - a^2*A*b*e^2 + a^3*B*e^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","A",1
1126,1,56,60,0.0586741,"\int \frac{(A+B x) (d+e x)}{(a+b x)^2} \, dx","Integrate[((A + B*x)*(d + e*x))/(a + b*x)^2,x]","\frac{-\frac{(A b-a B) (b d-a e)}{a+b x}+\log (a+b x) (-2 a B e+A b e+b B d)+b B e x}{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,"(b*B*e*x - ((A*b - a*B)*(b*d - a*e))/(a + b*x) + (b*B*d + A*b*e - 2*a*B*e)*Log[a + b*x])/b^3","A",1
1127,1,31,32,0.0113866,"\int \frac{A+B x}{(a+b x)^2} \, dx","Integrate[(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
1128,1,69,82,0.0822362,"\int \frac{A+B x}{(a+b x)^2 (d+e x)} \, dx","Integrate[(A + B*x)/((a + b*x)^2*(d + e*x)),x]","\frac{\frac{(a B-A b) (b d-a e)}{b (a+b x)}+\log (a+b x) (B d-A e)+(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*d - a*e))/(b*(a + b*x)) + (B*d - A*e)*Log[a + b*x] + (-(B*d) + A*e)*Log[d + e*x])/(b*d - a*e)^2","A",1
1129,1,103,117,0.1461566,"\int \frac{A+B x}{(a+b x)^2 (d+e x)^2} \, dx","Integrate[(A + B*x)/((a + b*x)^2*(d + e*x)^2),x]","\frac{\frac{(a B-A b) (b d-a e)}{a+b x}+\frac{(b d-a e) (B d-A e)}{d+e x}+\log (a+b x) (a B e-2 A b e+b B d)-\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) + a*B)*(b*d - a*e))/(a + b*x) + ((b*d - a*e)*(B*d - A*e))/(d + e*x) + (b*B*d - 2*A*b*e + a*B*e)*Log[a + b*x] - (b*B*d - 2*A*b*e + a*B*e)*Log[d + e*x])/(b*d - a*e)^3","A",1
1130,1,146,157,0.1556875,"\int \frac{A+B x}{(a+b x)^2 (d+e x)^3} \, dx","Integrate[(A + B*x)/((a + b*x)^2*(d + e*x)^3),x]","\frac{\frac{(b d-a e)^2 (B d-A e)}{(d+e x)^2}-\frac{2 b (A b-a B) (b d-a e)}{a+b x}+\frac{2 (b d-a e) (a B e-2 A b e+b B d)}{d+e x}+2 b \log (a+b x) (2 a B e-3 A b e+b B d)-2 b \log (d+e x) (2 a B e-3 A b e+b B d)}{2 (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*b*(A*b - a*B)*(b*d - a*e))/(a + b*x) + ((b*d - a*e)^2*(B*d - A*e))/(d + e*x)^2 + (2*(b*d - a*e)*(b*B*d - 2*A*b*e + a*B*e))/(d + e*x) + 2*b*(b*B*d - 3*A*b*e + 2*a*B*e)*Log[a + b*x] - 2*b*(b*B*d - 3*A*b*e + 2*a*B*e)*Log[d + e*x])/(2*(b*d - a*e)^4)","A",1
1131,1,188,200,0.2156976,"\int \frac{A+B x}{(a+b x)^2 (d+e x)^4} \, dx","Integrate[(A + B*x)/((a + b*x)^2*(d + e*x)^4),x]","\frac{-\frac{6 b^2 (A b-a B) (b d-a e)}{a+b x}+6 b^2 \log (a+b x) (3 a B e-4 A b e+b B d)-6 b^2 \log (d+e x) (3 a B e-4 A b e+b B d)+\frac{2 (b d-a e)^3 (B d-A e)}{(d+e x)^3}+\frac{3 (b d-a e)^2 (a B e-2 A b e+b B d)}{(d+e x)^2}+\frac{6 b (b d-a e) (2 a B e-3 A b e+b B d)}{d+e x}}{6 (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*b^2*(A*b - a*B)*(b*d - a*e))/(a + b*x) + (2*(b*d - a*e)^3*(B*d - A*e))/(d + e*x)^3 + (3*(b*d - a*e)^2*(b*B*d - 2*A*b*e + a*B*e))/(d + e*x)^2 + (6*b*(b*d - a*e)*(b*B*d - 3*A*b*e + 2*a*B*e))/(d + e*x) + 6*b^2*(b*B*d - 4*A*b*e + 3*a*B*e)*Log[a + b*x] - 6*b^2*(b*B*d - 4*A*b*e + 3*a*B*e)*Log[d + e*x])/(6*(b*d - a*e)^5)","A",1
1132,1,225,239,0.2768003,"\int \frac{A+B x}{(a+b x)^2 (d+e x)^5} \, dx","Integrate[(A + B*x)/((a + b*x)^2*(d + e*x)^5),x]","\frac{-\frac{12 b^3 (A b-a B) (b d-a e)}{a+b x}+12 b^3 \log (a+b x) (4 a B e-5 A b e+b B d)-12 b^3 \log (d+e x) (4 a B e-5 A b e+b B d)+\frac{12 b^2 (b d-a e) (3 a B e-4 A b e+b B d)}{d+e x}+\frac{3 (b d-a e)^4 (B d-A e)}{(d+e x)^4}+\frac{4 (b d-a e)^3 (a B e-2 A b e+b B d)}{(d+e x)^3}+\frac{6 b (b d-a e)^2 (2 a B e-3 A b e+b B d)}{(d+e x)^2}}{12 (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*b^3*(A*b - a*B)*(b*d - a*e))/(a + b*x) + (3*(b*d - a*e)^4*(B*d - A*e))/(d + e*x)^4 + (4*(b*d - a*e)^3*(b*B*d - 2*A*b*e + a*B*e))/(d + e*x)^3 + (6*b*(b*d - a*e)^2*(b*B*d - 3*A*b*e + 2*a*B*e))/(d + e*x)^2 + (12*b^2*(b*d - a*e)*(b*B*d - 4*A*b*e + 3*a*B*e))/(d + e*x) + 12*b^3*(b*B*d - 5*A*b*e + 4*a*B*e)*Log[a + b*x] - 12*b^3*(b*B*d - 5*A*b*e + 4*a*B*e)*Log[d + e*x])/(12*(b*d - a*e)^6)","A",1
1133,1,254,230,0.1762281,"\int \frac{(A+B x) (d+e x)^5}{(a+b x)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^5)/(a + b*x)^3,x]","\frac{6 b^2 e^3 x^2 \left(6 a^2 B e^2-3 a b e (A e+5 B d)+5 b^2 d (A e+2 B d)\right)+12 b e^2 x \left(-10 a^3 B e^3+6 a^2 b e^2 (A e+5 B d)-15 a b^2 d e (A e+2 B d)+10 b^3 d^2 (A e+B d)\right)+4 b^3 e^4 x^3 (-3 a B e+A b e+5 b B d)-\frac{12 (b d-a e)^4 (-6 a B e+5 A b e+b B d)}{a+b x}-\frac{6 (A b-a B) (b d-a e)^5}{(a+b x)^2}+60 e (b d-a e)^3 \log (a+b x) (-3 a B e+2 A b e+b B d)+3 b^4 B e^5 x^4}{12 b^7}","\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,"(12*b*e^2*(-10*a^3*B*e^3 + 10*b^3*d^2*(B*d + A*e) - 15*a*b^2*d*e*(2*B*d + A*e) + 6*a^2*b*e^2*(5*B*d + A*e))*x + 6*b^2*e^3*(6*a^2*B*e^2 + 5*b^2*d*(2*B*d + A*e) - 3*a*b*e*(5*B*d + A*e))*x^2 + 4*b^3*e^4*(5*b*B*d + A*b*e - 3*a*B*e)*x^3 + 3*b^4*B*e^5*x^4 - (6*(A*b - a*B)*(b*d - a*e)^5)/(a + b*x)^2 - (12*(b*d - a*e)^4*(b*B*d + 5*A*b*e - 6*a*B*e))/(a + b*x) + 60*e*(b*d - a*e)^3*(b*B*d + 2*A*b*e - 3*a*B*e)*Log[a + b*x])/(12*b^7)","A",1
1134,1,187,191,0.1362241,"\int \frac{(A+B x) (d+e x)^4}{(a+b x)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^4)/(a + b*x)^3,x]","\frac{6 b e^2 x \left(6 a^2 B e^2-3 a b e (A e+4 B d)+2 b^2 d (2 A e+3 B d)\right)+3 b^2 e^3 x^2 (-3 a B e+A b e+4 b B d)-\frac{6 (b d-a e)^3 (-5 a B e+4 A b e+b B d)}{a+b x}-\frac{3 (A b-a B) (b d-a e)^4}{(a+b x)^2}+12 e (b d-a e)^2 \log (a+b x) (-5 a B e+3 A b e+2 b B d)+2 b^3 B e^4 x^3}{6 b^6}","\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,"(6*b*e^2*(6*a^2*B*e^2 - 3*a*b*e*(4*B*d + A*e) + 2*b^2*d*(3*B*d + 2*A*e))*x + 3*b^2*e^3*(4*b*B*d + A*b*e - 3*a*B*e)*x^2 + 2*b^3*B*e^4*x^3 - (3*(A*b - a*B)*(b*d - a*e)^4)/(a + b*x)^2 - (6*(b*d - a*e)^3*(b*B*d + 4*A*b*e - 5*a*B*e))/(a + b*x) + 12*e*(b*d - a*e)^2*(2*b*B*d + 3*A*b*e - 5*a*B*e)*Log[a + b*x])/(6*b^6)","A",1
1135,1,245,141,0.1638238,"\int \frac{(A+B x) (d+e x)^3}{(a+b x)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^3)/(a + b*x)^3,x]","\frac{-A b \left(5 a^3 e^3+a^2 b e^2 (4 e x-9 d)+a b^2 e \left(3 d^2-12 d e x-4 e^2 x^2\right)+b^3 \left(d^3+6 d^2 e x-2 e^3 x^3\right)\right)+B \left(7 a^4 e^3+a^3 b e^2 (2 e x-15 d)+a^2 b^2 e \left(9 d^2-12 d e x-11 e^2 x^2\right)-a b^3 \left(d^3-12 d^2 e x-12 d e^2 x^2+4 e^3 x^3\right)+b^4 x \left(-2 d^3+6 d e^2 x^2+e^3 x^3\right)\right)+6 e (a+b x)^2 (b d-a e) \log (a+b x) (-2 a B e+A b e+b B d)}{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*(5*a^3*e^3 + a^2*b*e^2*(-9*d + 4*e*x) + a*b^2*e*(3*d^2 - 12*d*e*x - 4*e^2*x^2) + b^3*(d^3 + 6*d^2*e*x - 2*e^3*x^3))) + B*(7*a^4*e^3 + a^3*b*e^2*(-15*d + 2*e*x) + a^2*b^2*e*(9*d^2 - 12*d*e*x - 11*e^2*x^2) + b^4*x*(-2*d^3 + 6*d*e^2*x^2 + e^3*x^3) - a*b^3*(d^3 - 12*d^2*e*x - 12*d*e^2*x^2 + 4*e^3*x^3)) + 6*e*(b*d - a*e)*(b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^2*Log[a + b*x])/(2*b^5*(a + b*x)^2)","A",1
1136,1,140,103,0.0948174,"\int \frac{(A+B x) (d+e x)^2}{(a+b x)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^2)/(a + b*x)^3,x]","\frac{B \left(-5 a^3 e^2+2 a^2 b e (3 d-2 e x)+a b^2 \left(-d^2+8 d e x+4 e^2 x^2\right)+2 b^3 x \left(e^2 x^2-d^2\right)\right)+2 e (a+b x)^2 \log (a+b x) (-3 a B e+A b e+2 b B d)-A b (b d-a e) (3 a e+b (d+4 e x))}{2 b^4 (a+b x)^2}","-\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*(b*d - a*e)*(3*a*e + b*(d + 4*e*x))) + B*(-5*a^3*e^2 + 2*a^2*b*e*(3*d - 2*e*x) + 2*b^3*x*(-d^2 + e^2*x^2) + a*b^2*(-d^2 + 8*d*e*x + 4*e^2*x^2)) + 2*e*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^2*Log[a + b*x])/(2*b^4*(a + b*x)^2)","A",1
1137,1,75,69,0.0444998,"\int \frac{(A+B x) (d+e x)}{(a+b x)^3} \, dx","Integrate[((A + B*x)*(d + e*x))/(a + b*x)^3,x]","\frac{B \left(3 a^2 e-a b d+4 a b e x-2 b^2 d x\right)-A b (a e+b d+2 b e x)+2 B e (a+b x)^2 \log (a+b x)}{2 b^3 (a+b x)^2}","-\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*(b*d + a*e + 2*b*e*x)) + B*(-(a*b*d) + 3*a^2*e - 2*b^2*d*x + 4*a*b*e*x) + 2*B*e*(a + b*x)^2*Log[a + b*x])/(2*b^3*(a + b*x)^2)","A",1
1138,1,26,28,0.0127185,"\int \frac{A+B x}{(a+b x)^3} \, dx","Integrate[(A + B*x)/(a + b*x)^3,x]","-\frac{B (a+2 b x)+A b}{2 b^2 (a+b x)^2}","-\frac{(A+B x)^2}{2 (a+b x)^2 (A b-a B)}",1,"-1/2*(A*b + B*(a + 2*b*x))/(b^2*(a + b*x)^2)","A",1
1139,1,103,113,0.0842524,"\int \frac{A+B x}{(a+b x)^3 (d+e x)} \, dx","Integrate[(A + B*x)/((a + b*x)^3*(d + e*x)),x]","\frac{\frac{(a B-A b) (b d-a e)^2}{b (a+b x)^2}+\frac{2 (b d-a e) (A e-B d)}{a+b x}+2 e \log (a+b x) (A e-B d)+2 e (B d-A e) \log (d+e x)}{2 (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) + a*B)*(b*d - a*e)^2)/(b*(a + b*x)^2) + (2*(b*d - a*e)*(-(B*d) + A*e))/(a + b*x) + 2*e*(-(B*d) + A*e)*Log[a + b*x] + 2*e*(B*d - A*e)*Log[d + e*x])/(2*(b*d - a*e)^3)","A",1
1140,1,146,158,0.1375499,"\int \frac{A+B x}{(a+b x)^3 (d+e x)^2} \, dx","Integrate[(A + B*x)/((a + b*x)^3*(d + e*x)^2),x]","\frac{\frac{(a B-A b) (b d-a e)^2}{(a+b x)^2}-\frac{2 (b d-a e) (a B e-2 A b e+b B d)}{a+b x}+\frac{2 e (b d-a e) (A e-B d)}{d+e x}-2 e \log (a+b x) (a B e-3 A b e+2 b B d)+2 e \log (d+e x) (a B e-3 A b e+2 b B d)}{2 (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) + a*B)*(b*d - a*e)^2)/(a + b*x)^2 - (2*(b*d - a*e)*(b*B*d - 2*A*b*e + a*B*e))/(a + b*x) + (2*e*(b*d - a*e)*(-(B*d) + A*e))/(d + e*x) - 2*e*(2*b*B*d - 3*A*b*e + a*B*e)*Log[a + b*x] + 2*e*(2*b*B*d - 3*A*b*e + a*B*e)*Log[d + e*x])/(2*(b*d - a*e)^4)","A",1
1141,1,185,199,0.2174594,"\int \frac{A+B x}{(a+b x)^3 (d+e x)^3} \, dx","Integrate[(A + B*x)/((a + b*x)^3*(d + e*x)^3),x]","\frac{-\frac{b (A b-a B) (b d-a e)^2}{(a+b x)^2}+\frac{e (b d-a e)^2 (A e-B d)}{(d+e x)^2}-\frac{2 b (b d-a e) (2 a B e-3 A b e+b B d)}{a+b x}+\frac{2 e (b d-a e) (-a B e+3 A b e-2 b B d)}{d+e x}-6 b e \log (a+b x) (a B e-2 A b e+b B d)+6 b e \log (d+e x) (a B e-2 A b e+b B d)}{2 (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,"(-((b*(A*b - a*B)*(b*d - a*e)^2)/(a + b*x)^2) - (2*b*(b*d - a*e)*(b*B*d - 3*A*b*e + 2*a*B*e))/(a + b*x) + (e*(b*d - a*e)^2*(-(B*d) + A*e))/(d + e*x)^2 + (2*e*(b*d - a*e)*(-2*b*B*d + 3*A*b*e - a*B*e))/(d + e*x) - 6*b*e*(b*B*d - 2*A*b*e + a*B*e)*Log[a + b*x] + 6*b*e*(b*B*d - 2*A*b*e + a*B*e)*Log[d + e*x])/(2*(b*d - a*e)^5)","A",1
1142,1,233,248,0.2812727,"\int \frac{A+B x}{(a+b x)^3 (d+e x)^4} \, dx","Integrate[(A + B*x)/((a + b*x)^3*(d + e*x)^4),x]","\frac{-\frac{3 b^2 (A b-a B) (b d-a e)^2}{(a+b x)^2}-\frac{6 b^2 (b d-a e) (3 a B e-4 A b e+b B d)}{a+b x}+12 b^2 e \log (a+b x) (-3 a B e+5 A b e-2 b B d)+12 b^2 e \log (d+e x) (3 a B e-5 A b e+2 b B d)+\frac{2 e (b d-a e)^3 (A e-B d)}{(d+e x)^3}+\frac{3 e (b d-a e)^2 (-a B e+3 A b e-2 b B d)}{(d+e x)^2}+\frac{18 b e (a e-b d) (a B e-2 A b e+b B d)}{d+e x}}{6 (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*b^2*(A*b - a*B)*(b*d - a*e)^2)/(a + b*x)^2 - (6*b^2*(b*d - a*e)*(b*B*d - 4*A*b*e + 3*a*B*e))/(a + b*x) + (2*e*(b*d - a*e)^3*(-(B*d) + A*e))/(d + e*x)^3 + (3*e*(b*d - a*e)^2*(-2*b*B*d + 3*A*b*e - a*B*e))/(d + e*x)^2 + (18*b*e*(-(b*d) + a*e)*(b*B*d - 2*A*b*e + a*B*e))/(d + e*x) + 12*b^2*e*(-2*b*B*d + 5*A*b*e - 3*a*B*e)*Log[a + b*x] + 12*b^2*e*(2*b*B*d - 5*A*b*e + 3*a*B*e)*Log[d + e*x])/(6*(b*d - a*e)^6)","A",1
1143,1,62,34,0.0043514,"\int (1-2 x) (2+3 x)^8 (3+5 x) \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x),x]","-\frac{65610 x^{11}}{11}-\frac{356481 x^{10}}{10}-92421 x^9-133164 x^8-110160 x^7-41328 x^6+\frac{62496 x^5}{5}+24576 x^4+\frac{42752 x^3}{3}+4480 x^2+768 x","-\frac{10}{297} (3 x+2)^{11}+\frac{37}{270} (3 x+2)^{10}-\frac{7}{243} (3 x+2)^9",1,"768*x + 4480*x^2 + (42752*x^3)/3 + 24576*x^4 + (62496*x^5)/5 - 41328*x^6 - 110160*x^7 - 133164*x^8 - 92421*x^9 - (356481*x^10)/10 - (65610*x^11)/11","A",1
1144,1,53,34,0.0030257,"\int (1-2 x) (2+3 x)^7 (3+5 x) \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^7*(3 + 5*x),x]","-2187 x^{10}-11583 x^9-\frac{207765 x^8}{8}-30942 x^7-18774 x^6-1512 x^5+6468 x^4+\frac{15520 x^3}{3}+1952 x^2+384 x","-\frac{1}{27} (3 x+2)^{10}+\frac{37}{243} (3 x+2)^9-\frac{7}{216} (3 x+2)^8",1,"384*x + 1952*x^2 + (15520*x^3)/3 + 6468*x^4 - 1512*x^5 - 18774*x^6 - 30942*x^7 - (207765*x^8)/8 - 11583*x^9 - 2187*x^10","A",1
1145,1,48,34,0.0024283,"\int (1-2 x) (2+3 x)^6 (3+5 x) \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^6*(3 + 5*x),x]","-810 x^9-\frac{29889 x^8}{8}-7047 x^7-6552 x^6-2268 x^5+1260 x^4+\frac{5264 x^3}{3}+832 x^2+192 x","-\frac{10}{243} (3 x+2)^9+\frac{37}{216} (3 x+2)^8-\frac{1}{27} (3 x+2)^7",1,"192*x + 832*x^2 + (5264*x^3)/3 + 1260*x^4 - 2268*x^5 - 6552*x^6 - 7047*x^7 - (29889*x^8)/8 - 810*x^9","A",1
1146,1,47,34,0.002142,"\int (1-2 x) (2+3 x)^5 (3+5 x) \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^5*(3 + 5*x),x]","-\frac{1215 x^8}{4}-\frac{8343 x^7}{7}-\frac{3627 x^6}{2}-1170 x^5+30 x^4+\frac{1600 x^3}{3}+344 x^2+96 x","-\frac{5}{108} (3 x+2)^8+\frac{37}{189} (3 x+2)^7-\frac{7}{162} (3 x+2)^6",1,"96*x + 344*x^2 + (1600*x^3)/3 + 30*x^4 - 1170*x^5 - (3627*x^6)/2 - (8343*x^7)/7 - (1215*x^8)/4","A",1
1147,1,42,34,0.0018078,"\int (1-2 x) (2+3 x)^4 (3+5 x) \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x),x]","-\frac{810 x^7}{7}-\frac{747 x^6}{2}-\frac{2133 x^5}{5}-132 x^4+\frac{392 x^3}{3}+136 x^2+48 x","-\frac{10}{189} (3 x+2)^7+\frac{37}{162} (3 x+2)^6-\frac{7}{135} (3 x+2)^5",1,"48*x + 136*x^2 + (392*x^3)/3 - 132*x^4 - (2133*x^5)/5 - (747*x^6)/2 - (810*x^7)/7","A",1
1148,1,35,34,0.0015469,"\int (1-2 x) (2+3 x)^3 (3+5 x) \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x),x]","-45 x^6-\frac{567 x^5}{5}-\frac{333 x^4}{4}+\frac{46 x^3}{3}+50 x^2+24 x","-\frac{5}{81} (3 x+2)^6+\frac{37}{135} (3 x+2)^5-\frac{7}{108} (3 x+2)^4",1,"24*x + 50*x^2 + (46*x^3)/3 - (333*x^4)/4 - (567*x^5)/5 - 45*x^6","A",1
1149,1,28,28,0.0012995,"\int (1-2 x) (2+3 x)^2 (3+5 x) \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x),x]","-18 x^5-\frac{129 x^4}{4}-\frac{25 x^3}{3}+16 x^2+12 x","-18 x^5-\frac{129 x^4}{4}-\frac{25 x^3}{3}+16 x^2+12 x",1,"12*x + 16*x^2 - (25*x^3)/3 - (129*x^4)/4 - 18*x^5","A",1
1150,1,25,25,0.0013004,"\int (1-2 x) (2+3 x) (3+5 x) \, dx","Integrate[(1 - 2*x)*(2 + 3*x)*(3 + 5*x),x]","-\frac{15 x^4}{2}-\frac{23 x^3}{3}+\frac{7 x^2}{2}+6 x","-\frac{15 x^4}{2}-\frac{23 x^3}{3}+\frac{7 x^2}{2}+6 x",1,"6*x + (7*x^2)/2 - (23*x^3)/3 - (15*x^4)/2","A",1
1151,1,18,18,0.0010877,"\int (1-2 x) (3+5 x) \, dx","Integrate[(1 - 2*x)*(3 + 5*x),x]","-\frac{10 x^3}{3}-\frac{x^2}{2}+3 x","-\frac{10 x^3}{3}-\frac{x^2}{2}+3 x",1,"3*x - x^2/2 - (10*x^3)/3","A",1
1152,1,22,23,0.007081,"\int \frac{(1-2 x) (3+5 x)}{2+3 x} \, dx","Integrate[((1 - 2*x)*(3 + 5*x))/(2 + 3*x),x]","\frac{1}{27} \left(-45 x^2+51 x-7 \log (3 x+2)+54\right)","-\frac{5 x^2}{3}+\frac{17 x}{9}-\frac{7}{27} \log (3 x+2)",1,"(54 + 51*x - 45*x^2 - 7*Log[2 + 3*x])/27","A",1
1153,1,26,27,0.0160019,"\int \frac{(1-2 x) (3+5 x)}{(2+3 x)^2} \, dx","Integrate[((1 - 2*x)*(3 + 5*x))/(2 + 3*x)^2,x]","\frac{1}{27} \left(-30 x+\frac{7}{3 x+2}+37 \log (3 x+2)-20\right)","-\frac{10 x}{9}+\frac{7}{27 (3 x+2)}+\frac{37}{27} \log (3 x+2)",1,"(-20 - 30*x + 7/(2 + 3*x) + 37*Log[2 + 3*x])/27","A",1
1154,1,27,33,0.012535,"\int \frac{(1-2 x) (3+5 x)}{(2+3 x)^3} \, dx","Integrate[((1 - 2*x)*(3 + 5*x))/(2 + 3*x)^3,x]","\frac{1}{54} \left(-\frac{3 (74 x+47)}{(3 x+2)^2}-20 \log (3 x+2)\right)","-\frac{37}{27 (3 x+2)}+\frac{7}{54 (3 x+2)^2}-\frac{10}{27} \log (3 x+2)",1,"((-3*(47 + 74*x))/(2 + 3*x)^2 - 20*Log[2 + 3*x])/54","A",1
1155,1,21,34,0.0071008,"\int \frac{(1-2 x) (3+5 x)}{(2+3 x)^4} \, dx","Integrate[((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
1156,1,21,34,0.0088359,"\int \frac{(1-2 x) (3+5 x)}{(2+3 x)^5} \, dx","Integrate[((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
1157,1,21,34,0.0090897,"\int \frac{(1-2 x) (3+5 x)}{(2+3 x)^6} \, dx","Integrate[((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
1158,1,69,45,0.0030002,"\int (1-2 x) (2+3 x)^8 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x)^2,x]","-\frac{54675 x^{12}}{2}-\frac{1979235 x^{11}}{11}-\frac{2614194 x^{10}}{5}-869103 x^9-881442 x^8-507600 x^7-71904 x^6+\frac{679008 x^5}{5}+127168 x^4+\frac{173056 x^3}{3}+15360 x^2+2304 x","-\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,"2304*x + 15360*x^2 + (173056*x^3)/3 + 127168*x^4 + (679008*x^5)/5 - 71904*x^6 - 507600*x^7 - 881442*x^8 - 869103*x^9 - (2614194*x^10)/5 - (1979235*x^11)/11 - (54675*x^12)/2","A",1
1159,1,62,45,0.0033961,"\int (1-2 x) (2+3 x)^7 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^7*(3 + 5*x)^2,x]","-\frac{109350 x^{11}}{11}-\frac{117369 x^{10}}{2}-150174 x^9-\frac{1706265 x^8}{8}-173286 x^7-62622 x^6+21336 x^5+38804 x^4+\frac{66080 x^3}{3}+6816 x^2+1152 x","-\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,"1152*x + 6816*x^2 + (66080*x^3)/3 + 38804*x^4 + 21336*x^5 - 62622*x^6 - 173286*x^7 - (1706265*x^8)/8 - 150174*x^9 - (117369*x^10)/2 - (109350*x^11)/11","A",1
1160,1,51,45,0.0024726,"\int (1-2 x) (2+3 x)^6 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)^2,x]","-3645 x^{10}-19035 x^9-42039 x^8-49221 x^7-29106 x^6-1764 x^5+10360 x^4+\frac{24112 x^3}{3}+2976 x^2+576 x","-\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,"576*x + 2976*x^2 + (24112*x^3)/3 + 10360*x^4 - 1764*x^5 - 29106*x^6 - 49221*x^7 - 42039*x^8 - 19035*x^9 - 3645*x^10","A",1
1161,1,52,45,0.0025457,"\int (1-2 x) (2+3 x)^5 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)^2,x]","-1350 x^9-\frac{49005 x^8}{8}-\frac{79434 x^7}{7}-\frac{20631 x^6}{2}-3390 x^5+2090 x^4+\frac{8240 x^3}{3}+1272 x^2+288 x","-\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,"288*x + 1272*x^2 + (8240*x^3)/3 + 2090*x^4 - 3390*x^5 - (20631*x^6)/2 - (79434*x^7)/7 - (49005*x^8)/8 - 1350*x^9","A",1
1162,1,47,45,0.0012708,"\int (1-2 x) (2+3 x)^4 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^2,x]","-\frac{2025 x^8}{4}-\frac{13635 x^7}{7}-2898 x^6-\frac{9039 x^5}{5}+94 x^4+\frac{2536 x^3}{3}+528 x^2+144 x","-\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,"144*x + 528*x^2 + (2536*x^3)/3 + 94*x^4 - (9039*x^5)/5 - 2898*x^6 - (13635*x^7)/7 - (2025*x^8)/4","A",1
1163,1,44,44,0.0012349,"\int (1-2 x) (2+3 x)^3 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^2,x]","-\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","-\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,"72*x + 210*x^2 + (638*x^3)/3 - (769*x^4)/4 - (3366*x^5)/5 - (1215*x^6)/2 - (1350*x^7)/7","A",1
1164,1,31,31,0.0013477,"\int (1-2 x) (2+3 x)^2 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^2,x]","-75 x^6-183 x^5-128 x^4+\frac{85 x^3}{3}+78 x^2+36 x","-75 x^6-183 x^5-128 x^4+\frac{85 x^3}{3}+78 x^2+36 x",1,"36*x + 78*x^2 + (85*x^3)/3 - 128*x^4 - 183*x^5 - 75*x^6","A",1
1165,1,30,30,0.0010433,"\int (1-2 x) (2+3 x) (3+5 x)^2 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^2,x]","-30 x^5-\frac{205 x^4}{4}-\frac{34 x^3}{3}+\frac{51 x^2}{2}+18 x","-30 x^5-\frac{205 x^4}{4}-\frac{34 x^3}{3}+\frac{51 x^2}{2}+18 x",1,"18*x + (51*x^2)/2 - (34*x^3)/3 - (205*x^4)/4 - 30*x^5","A",1
1166,1,23,23,0.0008211,"\int (1-2 x) (3+5 x)^2 \, dx","Integrate[(1 - 2*x)*(3 + 5*x)^2,x]","-\frac{25 x^4}{2}-\frac{35 x^3}{3}+6 x^2+9 x","-\frac{25 x^4}{2}-\frac{35 x^3}{3}+6 x^2+9 x",1,"9*x + 6*x^2 - (35*x^3)/3 - (25*x^4)/2","A",1
1167,1,27,30,0.0108671,"\int \frac{(1-2 x) (3+5 x)^2}{2+3 x} \, dx","Integrate[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x),x]","\frac{1}{486} \left(-2700 x^3-135 x^2+2124 x+42 \log (3 x+2)+676\right)","-\frac{50 x^3}{9}-\frac{5 x^2}{18}+\frac{118 x}{27}+\frac{7}{81} \log (3 x+2)",1,"(676 + 2124*x - 135*x^2 - 2700*x^3 + 42*Log[2 + 3*x])/486","A",1
1168,1,36,34,0.0226933,"\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^2} \, dx","Integrate[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^2,x]","\frac{-225 x^3+135 x^2+480 x-24 (3 x+2) \log (3 x+2)+191}{81 x+54}","-\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 - 24*(2 + 3*x)*Log[2 + 3*x])/(54 + 81*x)","A",1
1169,1,35,38,0.0309681,"\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^3} \, dx","Integrate[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^3,x]","\frac{1}{162} \left(-\frac{3 \left(600 x^2+656 x+173\right)}{(3 x+2)^2}-300 x+390 \log (3 x+2)\right)","-\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,"(-300*x - (3*(173 + 656*x + 600*x^2))/(2 + 3*x)^2 + 390*Log[2 + 3*x])/162","A",1
1170,1,36,44,0.0224763,"\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^4} \, dx","Integrate[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^4,x]","-\frac{5265 x^2+6696 x+150 (3 x+2)^3 \log (3 x+2)+2131}{243 (3 x+2)^3}","-\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,"-1/243*(2131 + 6696*x + 5265*x^2 + 150*(2 + 3*x)^3*Log[2 + 3*x])/(2 + 3*x)^3","A",1
1171,1,26,37,0.0100236,"\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^5} \, dx","Integrate[((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
1172,1,26,45,0.0207863,"\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^6} \, dx","Integrate[((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
1173,1,26,45,0.0132425,"\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^7} \, dx","Integrate[((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
1174,1,26,45,0.0093957,"\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^8} \, dx","Integrate[((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
1175,1,74,56,0.003703,"\int (1-2 x) (2+3 x)^8 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x)^3,x]","-\frac{1640250 x^{13}}{13}-\frac{3626775 x^{12}}{4}-\frac{32079645 x^{11}}{11}-\frac{54794799 x^{10}}{10}-6524829 x^9-4865076 x^8-1830960 x^7+350128 x^6+\frac{4580384 x^5}{5}+597824 x^4+224256 x^3+51840 x^2+6912 x","-\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,"6912*x + 51840*x^2 + 224256*x^3 + 597824*x^4 + (4580384*x^5)/5 + 350128*x^6 - 1830960*x^7 - 4865076*x^8 - 6524829*x^9 - (54794799*x^10)/10 - (32079645*x^11)/11 - (3626775*x^12)/4 - (1640250*x^13)/13","A",1
1176,1,67,56,0.0033262,"\int (1-2 x) (2+3 x)^7 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^7*(3 + 5*x)^3,x]","-\frac{91125 x^{12}}{2}-\frac{3262275 x^{11}}{11}-\frac{1703673 x^{10}}{2}-1398447 x^9-\frac{11183805 x^8}{8}-788238 x^7-98966 x^6+219224 x^5+199012 x^4+88800 x^3+23328 x^2+3456 x","-\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,"3456*x + 23328*x^2 + 88800*x^3 + 199012*x^4 + 219224*x^5 - 98966*x^6 - 788238*x^7 - (11183805*x^8)/8 - 1398447*x^9 - (1703673*x^10)/2 - (3262275*x^11)/11 - (91125*x^12)/2","A",1
1177,1,60,56,0.0025816,"\int (1-2 x) (2+3 x)^6 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)^3,x]","-\frac{182250 x^{11}}{11}-\frac{193185 x^{10}}{2}-243945 x^9-\frac{2731671 x^8}{8}-272403 x^7-94668 x^6+36148 x^5+61220 x^4+34032 x^3+10368 x^2+1728 x","-\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,"1728*x + 10368*x^2 + 34032*x^3 + 61220*x^4 + 36148*x^5 - 94668*x^6 - 272403*x^7 - (2731671*x^8)/8 - 243945*x^9 - (193185*x^10)/2 - (182250*x^11)/11","A",1
1178,1,55,56,0.0024176,"\int (1-2 x) (2+3 x)^5 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)^3,x]","-6075 x^{10}-31275 x^9-\frac{544185 x^8}{8}-\frac{547767 x^7}{7}-\frac{90143 x^6}{2}-1810 x^5+16570 x^4+12480 x^3+4536 x^2+864 x","-\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,"864*x + 4536*x^2 + 12480*x^3 + 16570*x^4 - 1810*x^5 - (90143*x^6)/2 - (547767*x^7)/7 - (544185*x^8)/8 - 31275*x^9 - 6075*x^10","A",1
1179,1,52,56,0.00246,"\int (1-2 x) (2+3 x)^4 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^3,x]","-2250 x^9-\frac{80325 x^8}{8}-\frac{127845 x^7}{7}-\frac{32453 x^6}{2}-\frac{25237 x^5}{5}+3452 x^4+4296 x^3+1944 x^2+432 x","-\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,"432*x + 1944*x^2 + 4296*x^3 + 3452*x^4 - (25237*x^5)/5 - (32453*x^6)/2 - (127845*x^7)/7 - (80325*x^8)/8 - 2250*x^9","A",1
1180,1,49,49,0.0014678,"\int (1-2 x) (2+3 x)^3 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^3,x]","-\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","-\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,"216*x + 810*x^2 + 1338*x^3 + (883*x^4)/4 - (13943*x^5)/5 - (9255*x^6)/2 - (22275*x^7)/7 - (3375*x^8)/4","A",1
1181,1,40,40,0.0011158,"\int (1-2 x) (2+3 x)^2 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^3,x]","-\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","-\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,"108*x + 324*x^2 + 345*x^3 - (1111*x^4)/4 - 1061*x^5 - (1975*x^6)/2 - (2250*x^7)/7","A",1
1182,1,33,34,0.001574,"\int (1-2 x) (2+3 x) (3+5 x)^3 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^3,x]","-125 x^6-295 x^5-\frac{785 x^4}{4}+51 x^3+\frac{243 x^2}{2}+54 x","-\frac{1}{125} (5 x+3)^6+\frac{31}{625} (5 x+3)^5+\frac{11}{500} (5 x+3)^4",1,"54*x + (243*x^2)/2 + 51*x^3 - (785*x^4)/4 - 295*x^5 - 125*x^6","A",1
1183,1,28,23,0.0010226,"\int (1-2 x) (3+5 x)^3 \, dx","Integrate[(1 - 2*x)*(3 + 5*x)^3,x]","-50 x^5-\frac{325 x^4}{4}-15 x^3+\frac{81 x^2}{2}+27 x","\frac{11}{100} (5 x+3)^4-\frac{2}{125} (5 x+3)^5",1,"27*x + (81*x^2)/2 - 15*x^3 - (325*x^4)/4 - 50*x^5","A",1
1184,1,32,37,0.0157832,"\int \frac{(1-2 x) (3+5 x)^3}{2+3 x} \, dx","Integrate[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x),x]","\frac{-30375 x^4-25650 x^3+14715 x^2+19746 x-42 \log (3 x+2)+5024}{1458}","-\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,"(5024 + 19746*x + 14715*x^2 - 25650*x^3 - 30375*x^4 - 42*Log[2 + 3*x])/1458","A",1
1185,1,44,41,0.0173565,"\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^2} \, dx","Integrate[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^2,x]","\frac{-40500 x^4-24975 x^3+28080 x^2+22740 x+642 (3 x+2) \log (3 x+2)+3322}{1458 (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 + 642*(2 + 3*x)*Log[2 + 3*x])/(1458*(2 + 3*x))","A",1
1186,1,46,45,0.0172003,"\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^3} \, dx","Integrate[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^3,x]","\frac{-6750 x^4+450 x^3+18900 x^2+16386 x-370 (3 x+2)^2 \log (3 x+2)+3993}{162 (3 x+2)^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,"(3993 + 16386*x + 18900*x^2 + 450*x^3 - 6750*x^4 - 370*(2 + 3*x)^2*Log[2 + 3*x])/(162*(2 + 3*x)^2)","A",1
1187,1,47,49,0.0273052,"\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^4} \, dx","Integrate[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^4,x]","\frac{-1500 (3 x+2)+\frac{3330}{3 x+2}-\frac{321}{(3 x+2)^2}+\frac{14}{(3 x+2)^3}+6150 \log (3 x+2)}{1458}","-\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,"(14/(2 + 3*x)^3 - 321/(2 + 3*x)^2 + 3330/(2 + 3*x) - 1500*(2 + 3*x) + 6150*Log[2 + 3*x])/1458","A",1
1188,1,41,55,0.0179671,"\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^5} \, dx","Integrate[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^5,x]","-\frac{332100 x^3+634230 x^2+404124 x+3000 (3 x+2)^4 \log (3 x+2)+85915}{2916 (3 x+2)^4}","-\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,"-1/2916*(85915 + 404124*x + 634230*x^2 + 332100*x^3 + 3000*(2 + 3*x)^4*Log[2 + 3*x])/(2 + 3*x)^4","A",1
1189,1,31,37,0.0135349,"\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^6} \, dx","Integrate[((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
1190,1,31,55,0.012215,"\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^7} \, dx","Integrate[((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
1191,1,31,56,0.0117738,"\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^8} \, dx","Integrate[((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
1192,1,56,18,0.0031135,"\int (5-2 x)^6 (2+3 x)^3 (-16+33 x) \, dx","Integrate[(5 - 2*x)^6*(2 + 3*x)^3*(-16 + 33*x),x]","5184 x^{11}-76896 x^{10}+452304 x^9-1256376 x^8+1235404 x^7+1497230 x^6-3816225 x^5-\frac{98125 x^4}{2}+3987500 x^3-37500 x^2-2000000 x","-\frac{1}{2} (5-2 x)^7 (3 x+2)^4",1,"-2000000*x - 37500*x^2 + 3987500*x^3 - (98125*x^4)/2 - 3816225*x^5 + 1497230*x^6 + 1235404*x^7 - 1256376*x^8 + 452304*x^9 - 76896*x^10 + 5184*x^11","B",1
1193,1,47,58,0.0203728,"\int \frac{(1-2 x) (2+3 x)^6}{3+5 x} \, dx","Integrate[((1 - 2*x)*(2 + 3*x)^6)/(3 + 5*x),x]","\frac{-2278125000 x^7-7707656250 x^6-9334237500 x^5-3335259375 x^4+2668207500 x^3+3111113250 x^2+1166664100 x+1540 \log (5 x+3)+158585307}{54687500}","-\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,"(158585307 + 1166664100*x + 3111113250*x^2 + 2668207500*x^3 - 3335259375*x^4 - 9334237500*x^5 - 7707656250*x^6 - 2278125000*x^7 + 1540*Log[3 + 5*x])/54687500","A",1
1194,1,42,51,0.0155514,"\int \frac{(1-2 x) (2+3 x)^5}{3+5 x} \, dx","Integrate[((1 - 2*x)*(2 + 3*x)^5)/(3 + 5*x),x]","\frac{-25312500 x^6-67837500 x^5-54590625 x^4+6172500 x^3+31944750 x^2+16666300 x+220 \log (5 x+3)+2813811}{1562500}","-\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,"(2813811 + 16666300*x + 31944750*x^2 + 6172500*x^3 - 54590625*x^4 - 67837500*x^5 - 25312500*x^6 + 220*Log[3 + 5*x])/1562500","A",1
1195,1,37,44,0.0207584,"\int \frac{(1-2 x) (2+3 x)^4}{3+5 x} \, dx","Integrate[((1 - 2*x)*(2 + 3*x)^4)/(3 + 5*x),x]","\frac{-2025000 x^5-3965625 x^4-1327500 x^3+1944750 x^2+1666300 x+220 \log (5 x+3)+369411}{312500}","-\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,"(369411 + 1666300*x + 1944750*x^2 - 1327500*x^3 - 3965625*x^4 - 2025000*x^5 + 220*Log[3 + 5*x])/312500","A",1
1196,1,35,37,0.0136758,"\int \frac{(1-2 x) (2+3 x)^3}{3+5 x} \, dx","Integrate[((1 - 2*x)*(2 + 3*x)^3)/(3 + 5*x),x]","\frac{5 \left(-3375 x^4-4050 x^3+1395 x^2+3326 x+1056\right)+22 \log (5 x+3)}{6250}","-\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,"(5*(1056 + 3326*x + 1395*x^2 - 4050*x^3 - 3375*x^4) + 22*Log[3 + 5*x])/6250","A",1
1197,1,27,30,0.0162833,"\int \frac{(1-2 x) (2+3 x)^2}{3+5 x} \, dx","Integrate[((1 - 2*x)*(2 + 3*x)^2)/(3 + 5*x),x]","\frac{-1500 x^3-525 x^2+1630 x+22 \log (5 x+3)+843}{1250}","-\frac{6 x^3}{5}-\frac{21 x^2}{50}+\frac{163 x}{125}+\frac{11}{625} \log (5 x+3)",1,"(843 + 1630*x - 525*x^2 - 1500*x^3 + 22*Log[3 + 5*x])/1250","A",1
1198,1,22,23,0.0073413,"\int \frac{(1-2 x) (2+3 x)}{3+5 x} \, dx","Integrate[((1 - 2*x)*(2 + 3*x))/(3 + 5*x),x]","\frac{1}{125} \left(-75 x^2+65 x+11 \log (5 x+3)+66\right)","-\frac{3 x^2}{5}+\frac{13 x}{25}+\frac{11}{125} \log (5 x+3)",1,"(66 + 65*x - 75*x^2 + 11*Log[3 + 5*x])/125","A",1
1199,1,17,16,0.0028528,"\int \frac{1-2 x}{3+5 x} \, dx","Integrate[(1 - 2*x)/(3 + 5*x),x]","\frac{1}{25} (-10 x+11 \log (5 x+3)-6)","\frac{11}{25} \log (5 x+3)-\frac{2 x}{5}",1,"(-6 - 10*x + 11*Log[3 + 5*x])/25","A",1
1200,1,21,21,0.0054611,"\int \frac{1-2 x}{(2+3 x) (3+5 x)} \, dx","Integrate[(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
1201,1,38,28,0.0189555,"\int \frac{1-2 x}{(2+3 x)^2 (3+5 x)} \, dx","Integrate[(1 - 2*x)/((2 + 3*x)^2*(3 + 5*x)),x]","\frac{-33 (3 x+2) \log (3 x+2)+33 (3 x+2) \log (-3 (5 x+3))+7}{9 x+6}","\frac{7}{3 (3 x+2)}-11 \log (3 x+2)+11 \log (5 x+3)",1,"(7 - 33*(2 + 3*x)*Log[2 + 3*x] + 33*(2 + 3*x)*Log[-3*(3 + 5*x)])/(6 + 9*x)","A",1
1202,1,35,37,0.0264748,"\int \frac{1-2 x}{(2+3 x)^3 (3+5 x)} \, dx","Integrate[(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 (-3 (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*(3 + 5*x)]","A",1
1203,1,40,48,0.036749,"\int \frac{1-2 x}{(2+3 x)^4 (3+5 x)} \, dx","Integrate[(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 (-3 (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*(3 + 5*x)]","A",1
1204,1,45,59,0.0408329,"\int \frac{1-2 x}{(2+3 x)^5 (3+5 x)} \, dx","Integrate[(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 (-3 (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*(3 + 5*x)]","A",1
1205,1,50,70,0.0456433,"\int \frac{1-2 x}{(2+3 x)^6 (3+5 x)} \, dx","Integrate[(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 (-3 (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*(3 + 5*x)]","A",1
1206,1,75,81,0.0761571,"\int \frac{1-2 x}{(2+3 x)^7 (3+5 x)} \, dx","Integrate[(1 - 2*x)/((2 + 3*x)^7*(3 + 5*x)),x]","\frac{1237500 (3 x+2)^5+123750 (3 x+2)^4+16500 (3 x+2)^3+2475 (3 x+2)^2+396 (3 x+2)+70}{180 (3 x+2)^6}-34375 \log (3 x+2)+34375 \log (-3 (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,"(70 + 396*(2 + 3*x) + 2475*(2 + 3*x)^2 + 16500*(2 + 3*x)^3 + 123750*(2 + 3*x)^4 + 1237500*(2 + 3*x)^5)/(180*(2 + 3*x)^6) - 34375*Log[2 + 3*x] + 34375*Log[-3*(3 + 5*x)]","A",1
1207,1,85,69,0.03975,"\int \frac{(1-2 x) (2+3 x)^7}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)*(2 + 3*x)^7)/(3 + 5*x)^2,x]","\frac{-1875000 (3 x+2)^7+6781250 (3 x+2)^6+3360000 (3 x+2)^5+1273125 (3 x+2)^4+455000 (3 x+2)^3+171150 (3 x+2)^2+82320 (3 x+2)-\frac{924}{5 x+3}+19236 \log (-3 (5 x+3))}{164062500}","-\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,"(82320*(2 + 3*x) + 171150*(2 + 3*x)^2 + 455000*(2 + 3*x)^3 + 1273125*(2 + 3*x)^4 + 3360000*(2 + 3*x)^5 + 6781250*(2 + 3*x)^6 - 1875000*(2 + 3*x)^7 - 924/(3 + 5*x) + 19236*Log[-3*(3 + 5*x)])/164062500","A",1
1208,1,59,62,0.0202198,"\int \frac{(1-2 x) (2+3 x)^6}{(3+5 x)^2} \, dx","Integrate[((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+980 (5 x+3) \log (5 x+3)+7302662}{1953125 (5 x+3)}","-\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 + 980*(3 + 5*x)*Log[3 + 5*x])/(1953125*(3 + 5*x))","A",1
1209,1,48,55,0.0294326,"\int \frac{(1-2 x) (2+3 x)^5}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)*(2 + 3*x)^5)/(3 + 5*x)^2,x]","\frac{-3645000 x^5-7441875 x^4-2781000 x^3+3613950 x^2+3330000 x-\frac{132}{5 x+3}+1956 \log (-3 (5 x+3))+779800}{937500}","-\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,"(779800 + 3330000*x + 3613950*x^2 - 2781000*x^3 - 7441875*x^4 - 3645000*x^5 - 132/(3 + 5*x) + 1956*Log[-3*(3 + 5*x)])/937500","A",1
1210,1,49,48,0.0216666,"\int \frac{(1-2 x) (2+3 x)^4}{(3+5 x)^2} \, dx","Integrate[((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+52 (5 x+3) \log (5 x+3)+11233}{6250 (5 x+3)}","-\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 + 52*(3 + 5*x)*Log[3 + 5*x])/(6250*(3 + 5*x))","A",1
1211,1,46,41,0.0176099,"\int \frac{(1-2 x) (2+3 x)^3}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)*(2 + 3*x)^3)/(3 + 5*x)^2,x]","\frac{-67500 x^4-70875 x^3+60075 x^2+92680 x+582 (5 x+3) \log (-3 (5 x+3))+27354}{18750 (5 x+3)}","-\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 + 582*(3 + 5*x)*Log[-3*(3 + 5*x)])/(18750*(3 + 5*x))","A",1
1212,1,41,34,0.0218561,"\int \frac{(1-2 x) (2+3 x)^2}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)*(2 + 3*x)^2)/(3 + 5*x)^2,x]","\frac{-1125 x^3+150 x^2+1545 x+64 (5 x+3) \log (-3 (5 x+3))+619}{625 (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 + 64*(3 + 5*x)*Log[-3*(3 + 5*x)])/(625*(3 + 5*x))","A",1
1213,1,26,27,0.0129484,"\int \frac{(1-2 x) (2+3 x)}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)*(2 + 3*x))/(3 + 5*x)^2,x]","\frac{1}{125} \left(-30 x-\frac{11}{5 x+3}+31 \log (5 x+3)-18\right)","-\frac{6 x}{25}-\frac{11}{125 (5 x+3)}+\frac{31}{125} \log (5 x+3)",1,"(-18 - 30*x - 11/(3 + 5*x) + 31*Log[3 + 5*x])/125","A",1
1214,1,22,22,0.0046696,"\int \frac{1-2 x}{(3+5 x)^2} \, dx","Integrate[(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
1215,1,30,28,0.0234028,"\int \frac{1-2 x}{(2+3 x) (3+5 x)^2} \, dx","Integrate[(1 - 2*x)/((2 + 3*x)*(3 + 5*x)^2),x]","-\frac{11}{5 (5 x+3)}+7 \log (5 (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[5*(2 + 3*x)] - 7*Log[3 + 5*x]","A",1
1216,1,37,35,0.024918,"\int \frac{1-2 x}{(2+3 x)^2 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)/((2 + 3*x)^2*(3 + 5*x)^2),x]","-\frac{7}{3 x+2}-\frac{11}{5 x+3}+68 \log (3 x+2)-68 \log (-3 (5 x+3))","-\frac{7}{3 x+2}-\frac{11}{5 x+3}+68 \log (3 x+2)-68 \log (5 x+3)",1,"-7/(2 + 3*x) - 11/(3 + 5*x) + 68*Log[2 + 3*x] - 68*Log[-3*(3 + 5*x)]","A",1
1217,1,48,46,0.0302307,"\int \frac{1-2 x}{(2+3 x)^3 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)/((2 + 3*x)^3*(3 + 5*x)^2),x]","-\frac{68}{3 x+2}-\frac{55}{5 x+3}-\frac{7}{2 (3 x+2)^2}+505 \log (3 x+2)-505 \log (-3 (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,"-7/(2*(2 + 3*x)^2) - 68/(2 + 3*x) - 55/(3 + 5*x) + 505*Log[2 + 3*x] - 505*Log[-3*(3 + 5*x)]","A",1
1218,1,57,55,0.036797,"\int \frac{1-2 x}{(2+3 x)^4 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)/((2 + 3*x)^4*(3 + 5*x)^2),x]","-\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 (-3 (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,"-7/(3*(2 + 3*x)^3) - 34/(2 + 3*x)^2 - 505/(2 + 3*x) - 275/(3 + 5*x) + 3350*Log[2 + 3*x] - 3350*Log[-3*(3 + 5*x)]","A",1
1219,1,70,68,0.0435733,"\int \frac{1-2 x}{(2+3 x)^5 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)/((2 + 3*x)^5*(3 + 5*x)^2),x]","-\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 (-3 (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,"-7/(4*(2 + 3*x)^4) - 68/(3*(2 + 3*x)^3) - 505/(2*(2 + 3*x)^2) - 3350/(2 + 3*x) - 1375/(3 + 5*x) + 20875*Log[2 + 3*x] - 20875*Log[-3*(3 + 5*x)]","A",1
1220,1,77,75,0.0506123,"\int \frac{1-2 x}{(2+3 x)^6 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)/((2 + 3*x)^6*(3 + 5*x)^2),x]","-\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 (-3 (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,"-7/(5*(2 + 3*x)^5) - 17/(2 + 3*x)^4 - 505/(3*(2 + 3*x)^3) - 1675/(2 + 3*x)^2 - 20875/(2 + 3*x) - 6875/(3 + 5*x) + 125000*Log[2 + 3*x] - 125000*Log[-3*(3 + 5*x)]","A",1
1221,1,92,90,0.0616196,"\int \frac{1-2 x}{(2+3 x)^7 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)/((2 + 3*x)^7*(3 + 5*x)^2),x]","-\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 (-3 (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,"-7/(6*(2 + 3*x)^6) - 68/(5*(2 + 3*x)^5) - 505/(4*(2 + 3*x)^4) - 3350/(3*(2 + 3*x)^3) - 20875/(2*(2 + 3*x)^2) - 125000/(2 + 3*x) - 34375/(3 + 5*x) + 728125*Log[2 + 3*x] - 728125*Log[-3*(3 + 5*x)]","A",1
1222,1,64,73,0.0294981,"\int \frac{(1-2 x) (2+3 x)^7}{(3+5 x)^3} \, dx","Integrate[((1 - 2*x)*(2 + 3*x)^7)/(3 + 5*x)^3,x]","\frac{8148 \log (-3 (5 x+3))-\frac{5 \left(227812500 x^8+920362500 x^7+1425650625 x^6+887969250 x^5-150703875 x^4-583310700 x^3-372626040 x^2-107200136 x-12167374\right)}{(5 x+3)^2}}{7812500}","-\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,"((-5*(-12167374 - 107200136*x - 372626040*x^2 - 583310700*x^3 - 150703875*x^4 + 887969250*x^5 + 1425650625*x^6 + 920362500*x^7 + 227812500*x^8))/(3 + 5*x)^2 + 8148*Log[-3*(3 + 5*x)])/7812500","A",1
1223,1,61,66,0.0222476,"\int \frac{(1-2 x) (2+3 x)^6}{(3+5 x)^3} \, dx","Integrate[((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+28980 (5 x+3)^2 \log (5 x+3)+40891591}{7812500 (5 x+3)^2}","-\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 + 28980*(3 + 5*x)^2*Log[3 + 5*x])/(7812500*(3 + 5*x)^2)","A",1
1224,1,58,59,0.0233404,"\int \frac{(1-2 x) (2+3 x)^5}{(3+5 x)^3} \, dx","Integrate[((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+1920 (5 x+3)^2 \log (-3 (5 x+3))+604711}{156250 (5 x+3)^2}","-\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 + 1920*(3 + 5*x)^2*Log[-3*(3 + 5*x)])/(156250*(3 + 5*x)^2)","A",1
1225,1,51,52,0.0237938,"\int \frac{(1-2 x) (2+3 x)^4}{(3+5 x)^3} \, dx","Integrate[((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+228 (5 x+3)^2 \log (5 x+3)+17192}{6250 (5 x+3)^2}","-\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 + 228*(3 + 5*x)^2*Log[3 + 5*x])/(6250*(3 + 5*x)^2)","A",1
1226,1,48,45,0.0152516,"\int \frac{(1-2 x) (2+3 x)^3}{(3+5 x)^3} \, dx","Integrate[((1 - 2*x)*(2 + 3*x)^3)/(3 + 5*x)^3,x]","\frac{-33750 x^4-20250 x^3+40650 x^2+40520 x+558 (5 x+3)^2 \log (-3 (5 x+3))+9667}{6250 (5 x+3)^2}","-\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 + 558*(3 + 5*x)^2*Log[-3*(3 + 5*x)])/(6250*(3 + 5*x)^2)","A",1
1227,1,39,38,0.0245798,"\int \frac{(1-2 x) (2+3 x)^2}{(3+5 x)^3} \, dx","Integrate[((1 - 2*x)*(2 + 3*x)^2)/(3 + 5*x)^3,x]","\frac{87}{625} \log (-3 (5 x+3))-\frac{900 x^3+1680 x^2+1172 x+295}{250 (5 x+3)^2}","-\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,"-1/250*(295 + 1172*x + 1680*x^2 + 900*x^3)/(3 + 5*x)^2 + (87*Log[-3*(3 + 5*x)])/625","A",1
1228,1,33,33,0.0082051,"\int \frac{(1-2 x) (2+3 x)}{(3+5 x)^3} \, dx","Integrate[((1 - 2*x)*(2 + 3*x))/(3 + 5*x)^3,x]","-\frac{31}{125 (5 x+3)}-\frac{11}{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,"-11/(250*(3 + 5*x)^2) - 31/(125*(3 + 5*x)) - (6*Log[3 + 5*x])/125","A",1
1229,1,16,18,0.0039007,"\int \frac{1-2 x}{(3+5 x)^3} \, dx","Integrate[(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
1230,1,48,37,0.0218013,"\int \frac{1-2 x}{(2+3 x) (3+5 x)^3} \, dx","Integrate[(1 - 2*x)/((2 + 3*x)*(3 + 5*x)^3),x]","\frac{350 x-210 (5 x+3)^2 \log (5 (3 x+2))+210 (5 x+3)^2 \log (5 x+3)+199}{10 (5 x+3)^2}","\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 - 210*(3 + 5*x)^2*Log[5*(2 + 3*x)] + 210*(3 + 5*x)^2*Log[3 + 5*x])/(10*(3 + 5*x)^2)","A",1
1231,1,48,46,0.0305983,"\int \frac{1-2 x}{(2+3 x)^2 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)/((2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{21}{3 x+2}+\frac{68}{5 x+3}-\frac{11}{2 (5 x+3)^2}-309 \log (3 x+2)+309 \log (-3 (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,"21/(2 + 3*x) - 11/(2*(3 + 5*x)^2) + 68/(3 + 5*x) - 309*Log[2 + 3*x] + 309*Log[-3*(3 + 5*x)]","A",1
1232,1,59,57,0.0417422,"\int \frac{1-2 x}{(2+3 x)^3 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)/((2 + 3*x)^3*(3 + 5*x)^3),x]","\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 (-3 (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,"21/(2*(2 + 3*x)^2) + 309/(2 + 3*x) - 55/(2*(3 + 5*x)^2) + 505/(3 + 5*x) - 3060*Log[2 + 3*x] + 3060*Log[-3*(3 + 5*x)]","A",1
1233,1,68,66,0.0450275,"\int \frac{1-2 x}{(2+3 x)^4 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)/((2 + 3*x)^4*(3 + 5*x)^3),x]","\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 (-3 (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,"7/(2 + 3*x)^3 + 309/(2*(2 + 3*x)^2) + 3060/(2 + 3*x) - 275/(2*(3 + 5*x)^2) + 3350/(3 + 5*x) - 25350*Log[2 + 3*x] + 25350*Log[-3*(3 + 5*x)]","A",1
1234,1,77,75,0.0532599,"\int \frac{1-2 x}{(2+3 x)^5 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)/((2 + 3*x)^5*(3 + 5*x)^3),x]","\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 (-3 (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,"21/(4*(2 + 3*x)^4) + 103/(2 + 3*x)^3 + 1530/(2 + 3*x)^2 + 25350/(2 + 3*x) - 1375/(2*(3 + 5*x)^2) + 20875/(3 + 5*x) - 189375*Log[2 + 3*x] + 189375*Log[-3*(3 + 5*x)]","A",1
1235,1,88,86,0.050282,"\int \frac{1-2 x}{(2+3 x)^6 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)/((2 + 3*x)^6*(3 + 5*x)^3),x]","\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 (-3 (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,"21/(5*(2 + 3*x)^5) + 309/(4*(2 + 3*x)^4) + 1020/(2 + 3*x)^3 + 12675/(2 + 3*x)^2 + 189375/(2 + 3*x) - 6875/(2*(3 + 5*x)^2) + 125000/(3 + 5*x) - 1321875*Log[2 + 3*x] + 1321875*Log[-3*(3 + 5*x)]","A",1
1236,1,67,45,0.0030044,"\int (1-2 x)^2 (2+3 x)^8 (3+5 x) \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x),x]","10935 x^{12}+\frac{647352 x^{11}}{11}+\frac{1307097 x^{10}}{10}+144315 x^9+59616 x^8-39312 x^7-62160 x^6-\frac{134112 x^5}{5}+3200 x^4+\frac{24832 x^3}{3}+3712 x^2+768 x","\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,"768*x + 3712*x^2 + (24832*x^3)/3 + 3200*x^4 - (134112*x^5)/5 - 62160*x^6 - 39312*x^7 + 59616*x^8 + 144315*x^9 + (1307097*x^10)/10 + (647352*x^11)/11 + 10935*x^12","A",1
1237,1,64,45,0.0033545,"\int (1-2 x)^2 (2+3 x)^7 (3+5 x) \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x),x]","\frac{43740 x^{11}}{11}+\frac{93312 x^{10}}{5}+34587 x^9+\frac{225423 x^8}{8}+1242 x^7-16254 x^6-\frac{59304 x^5}{5}-1292 x^4+\frac{7712 x^3}{3}+1568 x^2+384 x","\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,"384*x + 1568*x^2 + (7712*x^3)/3 - 1292*x^4 - (59304*x^5)/5 - 16254*x^6 + 1242*x^7 + (225423*x^8)/8 + 34587*x^9 + (93312*x^10)/5 + (43740*x^11)/11","A",1
1238,1,53,45,0.002968,"\int (1-2 x)^2 (2+3 x)^6 (3+5 x) \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x),x]","1458 x^{10}+5832 x^9+\frac{68769 x^8}{8}+4185 x^7-2772 x^6-4284 x^5-1372 x^4+\frac{1936 x^3}{3}+640 x^2+192 x","\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,"192*x + 640*x^2 + (1936*x^3)/3 - 1372*x^4 - 4284*x^5 - 2772*x^6 + 4185*x^7 + (68769*x^8)/8 + 5832*x^9 + 1458*x^10","A",1
1239,1,48,45,0.0024556,"\int (1-2 x)^2 (2+3 x)^5 (3+5 x) \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x),x]","540 x^9+1782 x^8+1917 x^7+\frac{273 x^6}{2}-1218 x^5-770 x^4+\frac{224 x^3}{3}+248 x^2+96 x","\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,"96*x + 248*x^2 + (224*x^3)/3 - 770*x^4 - 1218*x^5 + (273*x^6)/2 + 1917*x^7 + 1782*x^8 + 540*x^9","A",1
1240,1,49,45,0.0011965,"\int (1-2 x)^2 (2+3 x)^4 (3+5 x) \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x),x]","\frac{405 x^8}{2}+\frac{3672 x^7}{7}+\frac{675 x^6}{2}-\frac{1077 x^5}{5}-328 x^4-\frac{152 x^3}{3}+88 x^2+48 x","\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,"48*x + 88*x^2 - (152*x^3)/3 - 328*x^4 - (1077*x^5)/5 + (675*x^6)/2 + (3672*x^7)/7 + (405*x^8)/2","A",1
1241,1,42,42,0.0014208,"\int (1-2 x)^2 (2+3 x)^3 (3+5 x) \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x),x]","\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","\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,"24*x + 26*x^2 - (154*x^3)/3 - (425*x^4)/4 + (99*x^5)/5 + 144*x^6 + (540*x^7)/7","A",1
1242,1,35,35,0.0018384,"\int (1-2 x)^2 (2+3 x)^2 (3+5 x) \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x),x]","30 x^6+\frac{168 x^5}{5}-\frac{79 x^4}{4}-\frac{89 x^3}{3}+4 x^2+12 x","30 x^6+\frac{168 x^5}{5}-\frac{79 x^4}{4}-\frac{89 x^3}{3}+4 x^2+12 x",1,"12*x + 4*x^2 - (89*x^3)/3 - (79*x^4)/4 + (168*x^5)/5 + 30*x^6","A",1
1243,1,28,28,0.0012898,"\int (1-2 x)^2 (2+3 x) (3+5 x) \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)*(3 + 5*x),x]","12 x^5+4 x^4-\frac{37 x^3}{3}-\frac{5 x^2}{2}+6 x","12 x^5+4 x^4-\frac{37 x^3}{3}-\frac{5 x^2}{2}+6 x",1,"6*x - (5*x^2)/2 - (37*x^3)/3 + 4*x^4 + 12*x^5","A",1
1244,1,23,23,0.0008269,"\int (1-2 x)^2 (3+5 x) \, dx","Integrate[(1 - 2*x)^2*(3 + 5*x),x]","5 x^4-\frac{8 x^3}{3}-\frac{7 x^2}{2}+3 x","5 x^4-\frac{8 x^3}{3}-\frac{7 x^2}{2}+3 x",1,"3*x - (7*x^2)/2 - (8*x^3)/3 + 5*x^4","A",1
1245,1,27,30,0.0134215,"\int \frac{(1-2 x)^2 (3+5 x)}{2+3 x} \, dx","Integrate[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x),x]","\frac{1}{243} \left(540 x^3-864 x^2+585 x-147 \log (3 x+2)+934\right)","\frac{20 x^3}{9}-\frac{32 x^2}{9}+\frac{65 x}{27}-\frac{49}{81} \log (3 x+2)",1,"(934 + 585*x - 864*x^2 + 540*x^3 - 147*Log[2 + 3*x])/243","A",1
1246,1,39,34,0.0180361,"\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^2} \, dx","Integrate[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^2,x]","\frac{540 x^3-1512 x^2-447 x+546 (3 x+2) \log (6 x+4)+632}{162 (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 + 546*(2 + 3*x)*Log[4 + 6*x])/(162*(2 + 3*x))","A",1
1247,1,41,38,0.0155274,"\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^3} \, dx","Integrate[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^3,x]","\frac{1080 x^3+900 x^2-1878 x-288 (3 x+2)^2 \log (6 x+4)-1283}{162 (3 x+2)^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 - 288*(2 + 3*x)^2*Log[4 + 6*x])/(162*(2 + 3*x)^2)","A",1
1248,1,36,44,0.0154327,"\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^4} \, dx","Integrate[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^4,x]","\frac{7776 x^2+7911 x+120 (3 x+2)^3 \log (3 x+2)+1916}{486 (3 x+2)^3}","\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 + 120*(2 + 3*x)^3*Log[2 + 3*x])/(486*(2 + 3*x)^3)","A",1
1249,1,26,37,0.0136465,"\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^5} \, dx","Integrate[((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,"-1/324*(167 + 516*x + 1728*x^2 + 2160*x^3)/(2 + 3*x)^4","A",1
1250,1,26,45,0.0179174,"\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^6} \, dx","Integrate[((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,"-1/540*(98 - 75*x + 720*x^2 + 1800*x^3)/(2 + 3*x)^5","A",1
1251,1,26,45,0.0158585,"\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^7} \, dx","Integrate[((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,"-1/2430*(311 - 846*x + 1080*x^2 + 5400*x^3)/(2 + 3*x)^6","A",1
1252,1,26,45,0.0201831,"\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^8} \, dx","Integrate[((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,"-1/810*(88 - 291*x + 108*x^2 + 1350*x^3)/(2 + 3*x)^7","A",1
1253,1,74,56,0.0041271,"\int (1-2 x)^2 (2+3 x)^8 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x)^2,x]","\frac{656100 x^{13}}{13}+302535 x^{12}+\frac{8477541 x^{11}}{11}+\frac{5207733 x^{10}}{5}+697905 x^9+6858 x^8-384336 x^7-298240 x^6-\frac{338336 x^5}{5}+40640 x^4+\frac{111616 x^3}{3}+13056 x^2+2304 x","\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,"2304*x + 13056*x^2 + (111616*x^3)/3 + 40640*x^4 - (338336*x^5)/5 - 298240*x^6 - 384336*x^7 + 6858*x^8 + 697905*x^9 + (5207733*x^10)/5 + (8477541*x^11)/11 + 302535*x^12 + (656100*x^13)/13","A",1
1254,1,69,56,0.0025129,"\int (1-2 x)^2 (2+3 x)^7 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x)^2,x]","18225 x^{12}+\frac{1064340 x^{11}}{11}+\frac{2116287 x^{10}}{10}+228996 x^9+\frac{719739 x^8}{8}-65934 x^7-98182 x^6-\frac{203752 x^5}{5}+5764 x^4+\frac{38816 x^3}{3}+5664 x^2+1152 x","\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,"1152*x + 5664*x^2 + (38816*x^3)/3 + 5764*x^4 - (203752*x^5)/5 - 98182*x^6 - 65934*x^7 + (719739*x^8)/8 + 228996*x^9 + (2116287*x^10)/10 + (1064340*x^11)/11 + 18225*x^12","A",1
1255,1,60,56,0.0026342,"\int (1-2 x)^2 (2+3 x)^6 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x)^2,x]","\frac{72900 x^{11}}{11}+30618 x^{10}+55701 x^9+\frac{176391 x^8}{4}+675 x^7-26166 x^6-18340 x^5-1696 x^4+\frac{12208 x^3}{3}+2400 x^2+576 x","\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,"576*x + 2400*x^2 + (12208*x^3)/3 - 1696*x^4 - 18340*x^5 - 26166*x^6 + 675*x^7 + (176391*x^8)/4 + 55701*x^9 + 30618*x^10 + (72900*x^11)/11","A",1
1256,1,55,56,0.0023418,"\int (1-2 x)^2 (2+3 x)^5 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x)^2,x]","2430 x^{10}+9540 x^9+\frac{109863 x^8}{8}+6336 x^7-\frac{9331 x^6}{2}-6734 x^5-2030 x^4+\frac{3152 x^3}{3}+984 x^2+288 x","\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,"288*x + 984*x^2 + (3152*x^3)/3 - 2030*x^4 - 6734*x^5 - (9331*x^6)/2 + 6336*x^7 + (109863*x^8)/8 + 9540*x^9 + 2430*x^10","A",1
1257,1,52,56,0.0023892,"\int (1-2 x)^2 (2+3 x)^4 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^2,x]","900 x^9+\frac{5805 x^8}{2}+\frac{21141 x^7}{7}+115 x^6-\frac{9791 x^5}{5}-1174 x^4+\frac{424 x^3}{3}+384 x^2+144 x","\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,"144*x + 384*x^2 + (424*x^3)/3 - 1174*x^4 - (9791*x^5)/5 + 115*x^6 + (21141*x^7)/7 + (5805*x^8)/2 + 900*x^9","A",1
1258,1,51,51,0.0025439,"\int (1-2 x)^2 (2+3 x)^3 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x)^2,x]","\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","\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,"72*x + 138*x^2 - (202*x^3)/3 - (2045*x^4)/4 - (1828*x^5)/5 + (1029*x^6)/2 + (5940*x^7)/7 + (675*x^8)/2","A",1
1259,1,42,42,0.00133,"\int (1-2 x)^2 (2+3 x)^2 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x)^2,x]","\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","\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,"36*x + 42*x^2 - (227*x^3)/3 - (341*x^4)/2 + (109*x^5)/5 + 230*x^6 + (900*x^7)/7","A",1
1260,1,35,35,0.0012304,"\int (1-2 x)^2 (2+3 x) (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)*(3 + 5*x)^2,x]","50 x^6+52 x^5-\frac{137 x^4}{4}-\frac{136 x^3}{3}+\frac{15 x^2}{2}+18 x","50 x^6+52 x^5-\frac{137 x^4}{4}-\frac{136 x^3}{3}+\frac{15 x^2}{2}+18 x",1,"18*x + (15*x^2)/2 - (136*x^3)/3 - (137*x^4)/4 + 52*x^5 + 50*x^6","A",1
1261,1,26,26,0.0012107,"\int (1-2 x)^2 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^2*(3 + 5*x)^2,x]","20 x^5+5 x^4-\frac{59 x^3}{3}-3 x^2+9 x","20 x^5+5 x^4-\frac{59 x^3}{3}-3 x^2+9 x",1,"9*x - 3*x^2 - (59*x^3)/3 + 5*x^4 + 20*x^5","A",1
1262,1,32,37,0.0157397,"\int \frac{(1-2 x)^2 (3+5 x)^2}{2+3 x} \, dx","Integrate[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x),x]","\frac{12150 x^4-7560 x^3-6777 x^2+6120 x+294 \log (3 x+2)+2452}{1458}","\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,"(2452 + 6120*x - 6777*x^2 - 7560*x^3 + 12150*x^4 + 294*Log[2 + 3*x])/1458","A",1
1263,1,44,41,0.014844,"\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^2} \, dx","Integrate[((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-1554 (3 x+2) \log (3 x+2)+10681}{729 (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 - 1554*(2 + 3*x)*Log[2 + 3*x])/(729*(2 + 3*x))","A",1
1264,1,42,45,0.0229324,"\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^3} \, dx","Integrate[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^3,x]","\frac{503}{81} \log (3 x+2)-\frac{-900 x^4+2040 x^3+6480 x^2+4508 x+913}{54 (3 x+2)^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,"-1/54*(913 + 4508*x + 6480*x^2 + 2040*x^3 - 900*x^4)/(2 + 3*x)^2 + (503*Log[2 + 3*x])/81","A",1
1265,1,46,49,0.0192738,"\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^4} \, dx","Integrate[((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-2220 (3 x+2)^3 \log (3 x+2)-11803}{729 (3 x+2)^3}","\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 - 2220*(2 + 3*x)^3*Log[2 + 3*x])/(729*(2 + 3*x)^3)","A",1
1266,1,41,55,0.0167952,"\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^5} \, dx","Integrate[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^5,x]","\frac{239760 x^3+398034 x^2+217248 x+1200 (3 x+2)^4 \log (3 x+2)+38821}{2916 (3 x+2)^4}","\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 + 1200*(2 + 3*x)^4*Log[2 + 3*x])/(2916*(2 + 3*x)^4)","A",1
1267,1,31,56,0.0143611,"\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^6} \, dx","Integrate[((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,"-1/2430*(4028 + 19275*x + 61470*x^2 + 116100*x^3 + 81000*x^4)/(2 + 3*x)^5","A",1
1268,1,31,56,0.0137647,"\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^7} \, dx","Integrate[((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,"-1/14580*(8198 + 8172*x + 52515*x^2 + 248400*x^3 + 243000*x^4)/(2 + 3*x)^6","A",1
1269,1,31,56,0.0135794,"\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^8} \, dx","Integrate[((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
1270,1,93,67,0.0036937,"\int (1-2 x)^2 (2+3 x)^{10} (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^10*(3 + 5*x)^3,x]","\frac{7381125 x^{16}}{4}+14696640 x^{15}+\frac{734077485 x^{14}}{14}+\frac{1417418757 x^{13}}{13}+\frac{569034801 x^{12}}{4}+\frac{1233925083 x^{11}}{11}+36043704 x^{10}-26237700 x^9-40113468 x^8-\frac{154612896 x^7}{7}-\frac{10627328 x^6}{3}+3185792 x^5+2644160 x^4+1000704 x^3+221184 x^2+27648 x","\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,"27648*x + 221184*x^2 + 1000704*x^3 + 2644160*x^4 + 3185792*x^5 - (10627328*x^6)/3 - (154612896*x^7)/7 - 40113468*x^8 - 26237700*x^9 + 36043704*x^10 + (1233925083*x^11)/11 + (569034801*x^12)/4 + (1417418757*x^13)/13 + (734077485*x^14)/14 + 14696640*x^15 + (7381125*x^16)/4","A",1
1271,1,90,67,0.003459,"\int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^9*(3 + 5*x)^3,x]","656100 x^{15}+\frac{33461100 x^{14}}{7}+\frac{200077695 x^{13}}{13}+\frac{113029263 x^{12}}{4}+\frac{342976275 x^{11}}{11}+\frac{182657511 x^{10}}{10}-180666 x^9-9703638 x^8-\frac{55216512 x^7}{7}-\frac{7363312 x^6}{3}+\frac{2732864 x^5}{5}+871936 x^4+400128 x^3+100224 x^2+13824 x","\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,"13824*x + 100224*x^2 + 400128*x^3 + 871936*x^4 + (2732864*x^5)/5 - (7363312*x^6)/3 - (55216512*x^7)/7 - 9703638*x^8 - 180666*x^9 + (182657511*x^10)/10 + (342976275*x^11)/11 + (113029263*x^12)/4 + (200077695*x^13)/13 + (33461100*x^14)/7 + 656100*x^15","A",1
1272,1,85,67,0.0030316,"\int (1-2 x)^2 (2+3 x)^8 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x)^3,x]","\frac{1640250 x^{14}}{7}+\frac{20120400 x^{13}}{13}+\frac{17759655 x^{12}}{4}+\frac{77509953 x^{11}}{11}+\frac{62652123 x^{10}}{10}+2124195 x^9-1660896 x^8-\frac{17018256 x^7}{7}-\frac{3530000 x^6}{3}-\frac{202208 x^5}{5}+261440 x^4+155136 x^3+44928 x^2+6912 x","\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,"6912*x + 44928*x^2 + 155136*x^3 + 261440*x^4 - (202208*x^5)/5 - (3530000*x^6)/3 - (17018256*x^7)/7 - 1660896*x^8 + 2124195*x^9 + (62652123*x^10)/10 + (77509953*x^11)/11 + (17759655*x^12)/4 + (20120400*x^13)/13 + (1640250*x^14)/7","A",1
1273,1,76,67,0.0031678,"\int (1-2 x)^2 (2+3 x)^7 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x)^3,x]","\frac{1093500 x^{13}}{13}+498150 x^{12}+\frac{13774455 x^{11}}{11}+\frac{16653681 x^{10}}{10}+1086843 x^9-\frac{148473 x^8}{8}-618582 x^7-\frac{1393018 x^6}{3}-\frac{495976 x^5}{5}+65812 x^4+57696 x^3+19872 x^2+3456 x","\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,"3456*x + 19872*x^2 + 57696*x^3 + 65812*x^4 - (495976*x^5)/5 - (1393018*x^6)/3 - 618582*x^7 - (148473*x^8)/8 + 1086843*x^9 + (16653681*x^10)/10 + (13774455*x^11)/11 + 498150*x^12 + (1093500*x^13)/13","A",1
1274,1,67,67,0.0031652,"\int (1-2 x)^2 (2+3 x)^6 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x)^3,x]","30375 x^{12}+\frac{1749600 x^{11}}{11}+\frac{685017 x^{10}}{2}+363093 x^9+\frac{1081971 x^8}{8}-110115 x^7-\frac{464744 x^6}{3}-61804 x^5+10172 x^4+20208 x^3+8640 x^2+1728 x","\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,"1728*x + 8640*x^2 + 20208*x^3 + 10172*x^4 - 61804*x^5 - (464744*x^6)/3 - 110115*x^7 + (1081971*x^8)/8 + 363093*x^9 + (685017*x^10)/2 + (1749600*x^11)/11 + 30375*x^12","A",1
1275,1,60,67,0.0026405,"\int (1-2 x)^2 (2+3 x)^5 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x)^3,x]","\frac{121500 x^{11}}{11}+50220 x^{10}+89655 x^9+\frac{551349 x^8}{8}-987 x^7-\frac{252329 x^6}{6}-28322 x^5-2150 x^4+6432 x^3+3672 x^2+864 x","\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,"864*x + 3672*x^2 + 6432*x^3 - 2150*x^4 - 28322*x^5 - (252329*x^6)/6 - 987*x^7 + (551349*x^8)/8 + 89655*x^9 + 50220*x^10 + (121500*x^11)/11","A",1
1276,1,57,67,0.00351,"\int (1-2 x)^2 (2+3 x)^4 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^3,x]","4050 x^{10}+15600 x^9+\frac{175365 x^8}{8}+\frac{66873 x^7}{7}-\frac{46885 x^6}{6}-\frac{52853 x^5}{5}-2992 x^4+1704 x^3+1512 x^2+432 x","\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,"432*x + 1512*x^2 + 1704*x^3 - 2992*x^4 - (52853*x^5)/5 - (46885*x^6)/6 + (66873*x^7)/7 + (175365*x^8)/8 + 15600*x^9 + 4050*x^10","A",1
1277,1,52,52,0.0029163,"\int (1-2 x)^2 (2+3 x)^3 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x)^3,x]","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","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,"216*x + 594*x^2 + 258*x^3 - (7145*x^4)/4 - (15709*x^5)/5 + (121*x^6)/6 + (33255*x^7)/7 + 4725*x^8 + 1500*x^9","A",1
1278,1,49,49,0.0031737,"\int (1-2 x)^2 (2+3 x)^2 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x)^3,x]","\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","\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,"108*x + 216*x^2 - 87*x^3 - (3181*x^4)/4 - (3083*x^5)/5 + (4685*x^6)/6 + (9600*x^7)/7 + (1125*x^8)/2","A",1
1279,1,42,42,0.00099,"\int (1-2 x)^2 (2+3 x) (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^2*(2 + 3*x)*(3 + 5*x)^3,x]","\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","\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,"54*x + (135*x^2)/2 - 111*x^3 - (1091*x^4)/4 + 19*x^5 + (1100*x^6)/3 + (1500*x^7)/7","A",1
1280,1,35,34,0.0013756,"\int (1-2 x)^2 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^2*(3 + 5*x)^3,x]","\frac{250 x^6}{3}+80 x^5-\frac{235 x^4}{4}-69 x^3+\frac{27 x^2}{2}+27 x","\frac{2}{375} (5 x+3)^6-\frac{44}{625} (5 x+3)^5+\frac{121}{500} (5 x+3)^4",1,"27*x + (27*x^2)/2 - 69*x^3 - (235*x^4)/4 + 80*x^5 + (250*x^6)/3","A",1
1281,1,37,44,0.0151222,"\int \frac{(1-2 x)^2 (3+5 x)^3}{2+3 x} \, dx","Integrate[((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x),x]","\frac{145800 x^5+24300 x^4-135810 x^3-15093 x^2+59490 x-294 \log (3 x+2)+20528}{4374}","\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,"(20528 + 59490*x - 15093*x^2 - 135810*x^3 + 24300*x^4 + 145800*x^5 - 294*Log[2 + 3*x])/4374","A",1
1282,1,49,48,0.0404243,"\int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^2} \, dx","Integrate[((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+4578 (3 x+2) \log (30 x+20)+3158}{4374 (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 + 4578*(2 + 3*x)*Log[20 + 30*x])/(4374*(2 + 3*x))","A",1
1283,1,51,52,0.0331033,"\int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^3} \, dx","Integrate[((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-24594 (3 x+2)^2 \log (30 x+20)+238271}{4374 (3 x+2)^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 - 24594*(2 + 3*x)^2*Log[20 + 30*x])/(4374*(2 + 3*x)^2)","A",1
1284,1,51,56,0.0453997,"\int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^4} \, dx","Integrate[((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-49710 (3 x+2)^3 \log (30 x+20)+222904}{4374 (3 x+2)^3}","\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,"-1/4374*(222904 + 1540539*x + 3623454*x^2 + 3304800*x^3 + 631800*x^4 - 364500*x^5 - 49710*(2 + 3*x)^3*Log[20 + 30*x])/(2 + 3*x)^3","A",1
1285,1,51,60,0.0395151,"\int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^5} \, dx","Integrate[((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-45600 (3 x+2)^4 \log (30 x+20)-510941}{8748 (3 x+2)^4}","\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 - 45600*(2 + 3*x)^4*Log[20 + 30*x])/(8748*(2 + 3*x)^4)","A",1
1286,1,46,66,0.0418195,"\int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^6} \, dx","Integrate[((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+30000 (3 x+2)^5 \log (30 x+20)+1965218}{43740 (3 x+2)^5}","\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 + 30000*(2 + 3*x)^5*Log[20 + 30*x])/(43740*(2 + 3*x)^5)","A",1
1287,1,36,67,0.0287563,"\int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^7} \, dx","Integrate[((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,"-1/43740*(233482 + 1510848*x + 5370435*x^2 + 12249900*x^3 + 15066000*x^4 + 7290000*x^5)/(2 + 3*x)^6","A",1
1288,1,36,67,0.0340428,"\int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^8} \, dx","Integrate[((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,"-1/43740*(76288 + 210534*x + 652158*x^2 + 3139425*x^3 + 5994000*x^4 + 3645000*x^5)/(2 + 3*x)^7","A",1
1289,1,57,72,0.0163825,"\int \frac{(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx","Integrate[((1 - 2*x)^2*(2 + 3*x)^7)/(3 + 5*x),x]","\frac{265781250000 x^9+916945312500 x^8+1051354687500 x^7+142606406250 x^6-640145362500 x^5-450125353125 x^4+23225282500 x^3+140972245750 x^2+58333305100 x+16940 \log (5 x+3)+7880238537}{1367187500}","\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,"(7880238537 + 58333305100*x + 140972245750*x^2 + 23225282500*x^3 - 450125353125*x^4 - 640145362500*x^5 + 142606406250*x^6 + 1051354687500*x^7 + 916945312500*x^8 + 265781250000*x^9 + 16940*Log[3 + 5*x])/1367187500","A",1
1290,1,52,65,0.0151608,"\int \frac{(1-2 x)^2 (2+3 x)^6}{3+5 x} \, dx","Integrate[((1 - 2*x)^2*(2 + 3*x)^6)/(3 + 5*x),x]","\frac{19933593750 x^8+54675000000 x^7+39247031250 x^6-19989112500 x^5-36687853125 x^4-7399717500 x^3+9722245750 x^2+5833305100 x+16940 \log (5 x+3)+966660747}{273437500}","\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,"(966660747 + 5833305100*x + 9722245750*x^2 - 7399717500*x^3 - 36687853125*x^4 - 19989112500*x^5 + 39247031250*x^6 + 54675000000*x^7 + 19933593750*x^8 + 16940*Log[3 + 5*x])/273437500","A",1
1291,1,47,58,0.0130361,"\int \frac{(1-2 x)^2 (2+3 x)^5}{3+5 x} \, dx","Integrate[((1 - 2*x)^2*(2 + 3*x)^5)/(3 + 5*x),x]","\frac{1518750000 x^7+3071250000 x^6+682762500 x^5-2234728125 x^4-1274717500 x^3+534745750 x^2+583305100 x+16940 \log (5 x+3)+124071027}{54687500}","\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,"(124071027 + 583305100*x + 534745750*x^2 - 1274717500*x^3 - 2234728125*x^4 + 682762500*x^5 + 3071250000*x^6 + 1518750000*x^7 + 16940*Log[3 + 5*x])/54687500","A",1
1292,1,42,51,0.0148213,"\int \frac{(1-2 x)^2 (2+3 x)^4}{3+5 x} \, dx","Integrate[((1 - 2*x)^2*(2 + 3*x)^4)/(3 + 5*x),x]","\frac{16875000 x^6+21600000 x^5-9871875 x^4-19602500 x^3+1392250 x^2+8329300 x+2420 \log (5 x+3)+2433921}{1562500}","\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,"(2433921 + 8329300*x + 1392250*x^2 - 19602500*x^3 - 9871875*x^4 + 21600000*x^5 + 16875000*x^6 + 2420*Log[3 + 5*x])/1562500","A",1
1293,1,37,44,0.0115905,"\int \frac{(1-2 x)^2 (2+3 x)^3}{3+5 x} \, dx","Integrate[((1 - 2*x)^2*(2 + 3*x)^3)/(3 + 5*x),x]","\frac{675000 x^5+337500 x^4-738750 x^3-241375 x^2+414650 x+1210 \log (5 x+3)+184863}{156250}","\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,"(184863 + 414650*x - 241375*x^2 - 738750*x^3 + 337500*x^4 + 675000*x^5 + 1210*Log[3 + 5*x])/156250","A",1
1294,1,35,37,0.0145732,"\int \frac{(1-2 x)^2 (2+3 x)^2}{3+5 x} \, dx","Integrate[((1 - 2*x)^2*(2 + 3*x)^2)/(3 + 5*x),x]","\frac{5 \left(2250 x^4-800 x^3-2155 x^2+1586 x+1263\right)+242 \log (5 x+3)}{6250}","\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,"(5*(1263 + 1586*x - 2155*x^2 - 800*x^3 + 2250*x^4) + 242*Log[3 + 5*x])/6250","A",1
1295,1,27,30,0.0125775,"\int \frac{(1-2 x)^2 (2+3 x)}{3+5 x} \, dx","Integrate[((1 - 2*x)^2*(2 + 3*x))/(3 + 5*x),x]","\frac{1}{625} \left(500 x^3-700 x^2+215 x+121 \log (5 x+3)+489\right)","\frac{4 x^3}{5}-\frac{28 x^2}{25}+\frac{43 x}{125}+\frac{121}{625} \log (5 x+3)",1,"(489 + 215*x - 700*x^2 + 500*x^3 + 121*Log[3 + 5*x])/625","A",1
1296,1,22,23,0.0058693,"\int \frac{(1-2 x)^2}{3+5 x} \, dx","Integrate[(1 - 2*x)^2/(3 + 5*x),x]","\frac{1}{125} \left(50 x^2-160 x+121 \log (5 x+3)-114\right)","\frac{2 x^2}{5}-\frac{32 x}{25}+\frac{121}{125} \log (5 x+3)",1,"(-114 - 160*x + 50*x^2 + 121*Log[3 + 5*x])/125","A",1
1297,1,27,26,0.0138087,"\int \frac{(1-2 x)^2}{(2+3 x) (3+5 x)} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)*(3 + 5*x)),x]","\frac{1}{225} (60 x-1225 \log (3 x+2)+1089 \log (-3 (5 x+3))+40)","\frac{4 x}{15}-\frac{49}{9} \log (3 x+2)+\frac{121}{25} \log (5 x+3)",1,"(40 + 60*x - 1225*Log[2 + 3*x] + 1089*Log[-3*(3 + 5*x)])/225","A",1
1298,1,32,32,0.0225852,"\int \frac{(1-2 x)^2}{(2+3 x)^2 (3+5 x)} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)^2*(3 + 5*x)),x]","\frac{49}{27 x+18}-\frac{217}{9} \log (5 (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/(18 + 27*x) - (217*Log[5*(2 + 3*x)])/9 + (121*Log[3 + 5*x])/5","A",1
1299,1,48,39,0.0236634,"\int \frac{(1-2 x)^2}{(2+3 x)^3 (3+5 x)} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)^3*(3 + 5*x)),x]","\frac{1302 x-2178 (3 x+2)^2 \log (5 (3 x+2))+2178 (3 x+2)^2 \log (5 x+3)+917}{18 (3 x+2)^2}","\frac{217}{9 (3 x+2)}+\frac{49}{18 (3 x+2)^2}-121 \log (3 x+2)+121 \log (5 x+3)",1,"(917 + 1302*x - 2178*(2 + 3*x)^2*Log[5*(2 + 3*x)] + 2178*(2 + 3*x)^2*Log[3 + 5*x])/(18*(2 + 3*x)^2)","A",1
1300,1,40,48,0.0411244,"\int \frac{(1-2 x)^2}{(2+3 x)^4 (3+5 x)} \, dx","Integrate[(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 (5 (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[5*(2 + 3*x)] + 605*Log[3 + 5*x]","A",1
1301,1,45,59,0.0526477,"\int \frac{(1-2 x)^2}{(2+3 x)^5 (3+5 x)} \, dx","Integrate[(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 (5 (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[5*(2 + 3*x)] + 3025*Log[3 + 5*x]","A",1
1302,1,57,70,0.0543229,"\int \frac{(1-2 x)^2}{(2+3 x)^6 (3+5 x)} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)^6*(3 + 5*x)),x]","\frac{44104500 x^4+119082150 x^3+120617640 x^2+54322575 x+2722500 (3 x+2)^5 \log (5 x+3)+9179006}{180 (3 x+2)^5}-15125 \log (5 (3 x+2))","\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,"-15125*Log[5*(2 + 3*x)] + (9179006 + 54322575*x + 120617640*x^2 + 119082150*x^3 + 44104500*x^4 + 2722500*(2 + 3*x)^5*Log[3 + 5*x])/(180*(2 + 3*x)^5)","A",1
1303,1,55,81,0.099053,"\int \frac{(1-2 x)^2}{(2+3 x)^7 (3+5 x)} \, dx","Integrate[(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 (5 (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[5*(2 + 3*x)] + 75625*Log[3 + 5*x]","A",1
1304,1,84,92,0.1377796,"\int \frac{(1-2 x)^2}{(2+3 x)^8 (3+5 x)} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)^8*(3 + 5*x)),x]","\frac{40837500 (3 x+2)^6+4083750 (3 x+2)^5+544500 (3 x+2)^4+81675 (3 x+2)^3+13068 (3 x+2)^2+2170 (3 x+2)+420}{540 (3 x+2)^7}-378125 \log (5 (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,"(420 + 2170*(2 + 3*x) + 13068*(2 + 3*x)^2 + 81675*(2 + 3*x)^3 + 544500*(2 + 3*x)^4 + 4083750*(2 + 3*x)^5 + 40837500*(2 + 3*x)^6)/(540*(2 + 3*x)^7) - 378125*Log[5*(2 + 3*x)] + 378125*Log[3 + 5*x]","A",1
1305,1,69,76,0.0323914,"\int \frac{(1-2 x)^2 (2+3 x)^7}{(3+5 x)^2} \, dx","Integrate[((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+349580 (5 x+3) \log (5 x+3)+9997654777}{1367187500 (5 x+3)}","\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 + 349580*(3 + 5*x)*Log[3 + 5*x])/(1367187500*(3 + 5*x))","A",1
1306,1,66,69,0.0403276,"\int \frac{(1-2 x)^2 (2+3 x)^6}{(3+5 x)^2} \, dx","Integrate[((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+149380 (5 x+3) \log (6 (5 x+3))+648854027}{136718750 (5 x+3)}","\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 + 149380*(3 + 5*x)*Log[6*(3 + 5*x)])/(136718750*(3 + 5*x))","A",1
1307,1,61,62,0.0412412,"\int \frac{(1-2 x)^2 (2+3 x)^5}{(3+5 x)^2} \, dx","Integrate[((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+35420 (5 x+3) \log (6 (5 x+3))+25866973}{7812500 (5 x+3)}","\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 + 35420*(3 + 5*x)*Log[6*(3 + 5*x)])/(7812500*(3 + 5*x))","A",1
1308,1,56,55,0.052939,"\int \frac{(1-2 x)^2 (2+3 x)^4}{(3+5 x)^2} \, dx","Integrate[((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+7040 (5 x+3) \log (6 (5 x+3))+990421}{390625 (5 x+3)}","\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 + 7040*(3 + 5*x)*Log[6*(3 + 5*x)])/(390625*(3 + 5*x))","A",1
1309,1,51,48,0.0483936,"\int \frac{(1-2 x)^2 (2+3 x)^3}{(3+5 x)^2} \, dx","Integrate[((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+418 (5 x+3) \log (6 (5 x+3))+12683}{6250 (5 x+3)}","\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 + 418*(3 + 5*x)*Log[6*(3 + 5*x)])/(6250*(3 + 5*x))","A",1
1310,1,42,41,0.0238805,"\int \frac{(1-2 x)^2 (2+3 x)^2}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)^2*(2 + 3*x)^2)/(3 + 5*x)^2,x]","\frac{\frac{5 \left(1500 x^4-1050 x^3-985 x^2+1248 x+658\right)}{5 x+3}+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,"((5*(658 + 1248*x - 985*x^2 - 1050*x^3 + 1500*x^4))/(3 + 5*x) + 682*Log[3 + 5*x])/3125","A",1
1311,1,39,34,0.0166796,"\int \frac{(1-2 x)^2 (2+3 x)}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)^2*(2 + 3*x))/(3 + 5*x)^2,x]","\frac{1500 x^3-3700 x^2-835 x+638 (5 x+3) \log (10 x+6)+913}{1250 (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 + 638*(3 + 5*x)*Log[6 + 10*x])/(1250*(3 + 5*x))","A",1
1312,1,34,27,0.0116881,"\int \frac{(1-2 x)^2}{(3+5 x)^2} \, dx","Integrate[(1 - 2*x)^2/(3 + 5*x)^2,x]","\frac{100 x^2+10 x-44 (5 x+3) \log (10 x+6)-151}{125 (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 - 44*(3 + 5*x)*Log[6 + 10*x])/(125*(3 + 5*x))","A",1
1313,1,32,32,0.0275665,"\int \frac{(1-2 x)^2}{(2+3 x) (3+5 x)^2} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)*(3 + 5*x)^2),x]","-\frac{121}{125 x+75}+\frac{49}{3} \log (3 x+2)-\frac{407}{25} \log (-3 (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/(75 + 125*x) + (49*Log[2 + 3*x])/3 - (407*Log[-3*(3 + 5*x)])/25","A",1
1314,1,61,39,0.0544259,"\int \frac{(1-2 x)^2}{(2+3 x)^2 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)^2*(3 + 5*x)^2),x]","-\frac{-2310 \left(15 x^2+19 x+6\right) \log (5 (3 x+2))+2310 \left(15 x^2+19 x+6\right) \log (5 x+3)+2314 x+1461}{15 (3 x+2) (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,"-1/15*(1461 + 2314*x - 2310*(6 + 19*x + 15*x^2)*Log[5*(2 + 3*x)] + 2310*(6 + 19*x + 15*x^2)*Log[3 + 5*x])/((2 + 3*x)*(3 + 5*x))","A",1
1315,1,48,46,0.0408742,"\int \frac{(1-2 x)^2}{(2+3 x)^3 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)^3*(3 + 5*x)^2),x]","-\frac{154}{3 x+2}-\frac{121}{5 x+3}-\frac{49}{6 (3 x+2)^2}+1133 \log (5 (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,"-49/(6*(2 + 3*x)^2) - 154/(2 + 3*x) - 121/(3 + 5*x) + 1133*Log[5*(2 + 3*x)] - 1133*Log[3 + 5*x]","A",1
1316,1,57,55,0.0503923,"\int \frac{(1-2 x)^2}{(2+3 x)^4 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)^4*(3 + 5*x)^2),x]","-\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 (5 (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,"-49/(9*(2 + 3*x)^3) - 77/(2 + 3*x)^2 - 1133/(2 + 3*x) - 605/(3 + 5*x) + 7480*Log[5*(2 + 3*x)] - 7480*Log[3 + 5*x]","A",1
1317,1,57,68,0.116608,"\int \frac{(1-2 x)^2}{(2+3 x)^5 (3+5 x)^2} \, dx","Integrate[(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 (5 (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,"-1/4*(940153 + 5720639*x + 13046462*x^2 + 13217490*x^3 + 5019300*x^4)/((2 + 3*x)^4*(3 + 5*x)) + 46475*Log[5*(2 + 3*x)] - 46475*Log[3 + 5*x]","A",1
1318,1,62,77,0.0957445,"\int \frac{(1-2 x)^2}{(2+3 x)^6 (3+5 x)^2} \, dx","Integrate[(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 (5 (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,"-1/30*(84279984 + 639246515*x + 1938789435*x^2 + 2939206050*x^3 + 2227277250*x^4 + 674932500*x^5)/((2 + 3*x)^5*(3 + 5*x)) + 277750*Log[5*(2 + 3*x)] - 277750*Log[3 + 5*x]","A",1
1319,1,92,90,0.1653134,"\int \frac{(1-2 x)^2}{(2+3 x)^7 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)^7*(3 + 5*x)^2),x]","-\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 (5 (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,"-49/(18*(2 + 3*x)^6) - 154/(5*(2 + 3*x)^5) - 1133/(4*(2 + 3*x)^4) - 7480/(3*(2 + 3*x)^3) - 46475/(2*(2 + 3*x)^2) - 277750/(2 + 3*x) - 75625/(3 + 5*x) + 1615625*Log[5*(2 + 3*x)] - 1615625*Log[3 + 5*x]","A",1
1320,1,99,97,0.1499269,"\int \frac{(1-2 x)^2}{(2+3 x)^8 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)^8*(3 + 5*x)^2),x]","-\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 (5 (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,"-7/(3*(2 + 3*x)^7) - 77/(3*(2 + 3*x)^6) - 1133/(5*(2 + 3*x)^5) - 1870/(2 + 3*x)^4 - 46475/(3*(2 + 3*x)^3) - 138875/(2 + 3*x)^2 - 1615625/(2 + 3*x) - 378125/(3 + 5*x) + 9212500*Log[5*(2 + 3*x)] - 9212500*Log[3 + 5*x]","A",1
1321,1,76,87,0.0385285,"\int \frac{(1-2 x)^2 (2+3 x)^8}{(3+5 x)^3} \, dx","Integrate[((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+412160 (5 x+3)^2 \log (5 x+3)+10358007077}{683593750 (5 x+3)^2}","\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 + 412160*(3 + 5*x)^2*Log[3 + 5*x])/(683593750*(3 + 5*x)^2)","A",1
1322,1,71,80,0.0359525,"\int \frac{(1-2 x)^2 (2+3 x)^7}{(3+5 x)^3} \, dx","Integrate[((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+3072860 (5 x+3)^2 \log (5 x+3)+13601177777}{1367187500 (5 x+3)^2}","\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 + 3072860*(3 + 5*x)^2*Log[3 + 5*x])/(1367187500*(3 + 5*x)^2)","A",1
1323,1,68,73,0.0450583,"\int \frac{(1-2 x)^2 (2+3 x)^6}{(3+5 x)^3} \, dx","Integrate[((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+310940 (5 x+3)^2 \log (6 (5 x+3))+274543613}{39062500 (5 x+3)^2}","\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 + 310940*(3 + 5*x)^2*Log[6*(3 + 5*x)])/(39062500*(3 + 5*x)^2)","A",1
1324,1,63,66,0.0616359,"\int \frac{(1-2 x)^2 (2+3 x)^5}{(3+5 x)^3} \, dx","Integrate[((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+102340 (5 x+3)^2 \log (6 (5 x+3))+20870428}{3906250 (5 x+3)^2}","\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 + 102340*(3 + 5*x)^2*Log[6*(3 + 5*x)])/(3906250*(3 + 5*x)^2)","A",1
1325,1,58,59,0.0579477,"\int \frac{(1-2 x)^2 (2+3 x)^4}{(3+5 x)^3} \, dx","Integrate[((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+2404 (5 x+3)^2 \log (6 (5 x+3))+121714}{31250 (5 x+3)^2}","\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 + 2404*(3 + 5*x)^2*Log[6*(3 + 5*x)])/(31250*(3 + 5*x)^2)","A",1
1326,1,48,52,0.0482819,"\int \frac{(1-2 x)^2 (2+3 x)^3}{(3+5 x)^3} \, dx","Integrate[((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+1150 (5 x+3)^2 \log (6 (5 x+3))+7567}{6250 (5 x+3)^2}","\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 + 1150*(3 + 5*x)^2*Log[6*(3 + 5*x)])/(6250*(3 + 5*x)^2)","A",1
1327,1,42,45,0.0217804,"\int \frac{(1-2 x)^2 (2+3 x)^2}{(3+5 x)^3} \, dx","Integrate[((1 - 2*x)^2*(2 + 3*x)^2)/(3 + 5*x)^3,x]","\frac{\frac{5 \left(4500 x^4-7800 x^3-23760 x^2-17564 x-4277\right)}{(5 x+3)^2}+1658 \log (5 x+3)}{6250}","\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,"((5*(-4277 - 17564*x - 23760*x^2 - 7800*x^3 + 4500*x^4))/(3 + 5*x)^2 + 1658*Log[3 + 5*x])/6250","A",1
1328,1,37,38,0.0243655,"\int \frac{(1-2 x)^2 (2+3 x)}{(3+5 x)^3} \, dx","Integrate[((1 - 2*x)^2*(2 + 3*x))/(3 + 5*x)^3,x]","\frac{\frac{5 \left(600 x^3+420 x^2-782 x-515\right)}{(5 x+3)^2}-256 \log (10 x+6)}{1250}","\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,"((5*(-515 - 782*x + 420*x^2 + 600*x^3))/(3 + 5*x)^2 - 256*Log[6 + 10*x])/1250","A",1
1329,1,31,33,0.0213702,"\int \frac{(1-2 x)^2}{(3+5 x)^3} \, dx","Integrate[(1 - 2*x)^2/(3 + 5*x)^3,x]","\frac{440 x+8 (5 x+3)^2 \log (10 x+6)+143}{250 (5 x+3)^2}","\frac{44}{125 (5 x+3)}-\frac{121}{250 (5 x+3)^2}+\frac{4}{125} \log (5 x+3)",1,"(143 + 440*x + 8*(3 + 5*x)^2*Log[6 + 10*x])/(250*(3 + 5*x)^2)","A",1
1330,1,48,39,0.023075,"\int \frac{(1-2 x)^2}{(2+3 x) (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)*(3 + 5*x)^3),x]","\frac{4070 x-2450 (5 x+3)^2 \log (3 x+2)+2450 (5 x+3)^2 \log (-3 (5 x+3))+2321}{50 (5 x+3)^2}","\frac{407}{25 (5 x+3)}-\frac{121}{50 (5 x+3)^2}-49 \log (3 x+2)+49 \log (5 x+3)",1,"(2321 + 4070*x - 2450*(3 + 5*x)^2*Log[2 + 3*x] + 2450*(3 + 5*x)^2*Log[-3*(3 + 5*x)])/(50*(3 + 5*x)^2)","A",1
1331,1,48,46,0.0319489,"\int \frac{(1-2 x)^2}{(2+3 x)^2 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{49}{3 x+2}+\frac{154}{5 x+3}-\frac{121}{10 (5 x+3)^2}-707 \log (5 (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,"49/(2 + 3*x) - 121/(10*(3 + 5*x)^2) + 154/(3 + 5*x) - 707*Log[5*(2 + 3*x)] + 707*Log[3 + 5*x]","A",1
1332,1,59,57,0.0396612,"\int \frac{(1-2 x)^2}{(2+3 x)^3 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)^3*(3 + 5*x)^3),x]","\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 (5 (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,"49/(2*(2 + 3*x)^2) + 707/(2 + 3*x) - 121/(2*(3 + 5*x)^2) + 1133/(3 + 5*x) - 6934*Log[5*(2 + 3*x)] + 6934*Log[3 + 5*x]","A",1
1333,1,70,68,0.0695898,"\int \frac{(1-2 x)^2}{(2+3 x)^4 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)^4*(3 + 5*x)^3),x]","\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 (5 (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,"49/(3*(2 + 3*x)^3) + 707/(2*(2 + 3*x)^2) + 6934/(2 + 3*x) - 605/(2*(3 + 5*x)^2) + 7480/(3 + 5*x) - 57110*Log[5*(2 + 3*x)] + 57110*Log[3 + 5*x]","A",1
1334,1,79,77,0.0783895,"\int \frac{(1-2 x)^2}{(2+3 x)^5 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)^5*(3 + 5*x)^3),x]","\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 (5 (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,"49/(4*(2 + 3*x)^4) + 707/(3*(2 + 3*x)^3) + 3467/(2 + 3*x)^2 + 57110/(2 + 3*x) - 3025/(2*(3 + 5*x)^2) + 46475/(3 + 5*x) - 424975*Log[5*(2 + 3*x)] + 424975*Log[3 + 5*x]","A",1
1335,1,90,88,0.1004498,"\int \frac{(1-2 x)^2}{(2+3 x)^6 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)^6*(3 + 5*x)^3),x]","\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 (5 (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,"49/(5*(2 + 3*x)^5) + 707/(4*(2 + 3*x)^4) + 6934/(3*(2 + 3*x)^3) + 28555/(2 + 3*x)^2 + 424975/(2 + 3*x) - 15125/(2*(3 + 5*x)^2) + 277750/(3 + 5*x) - 2958125*Log[5*(2 + 3*x)] + 2958125*Log[3 + 5*x]","A",1
1336,1,103,101,0.132862,"\int \frac{(1-2 x)^2}{(2+3 x)^7 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)^7*(3 + 5*x)^3),x]","\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 (5 (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,"49/(6*(2 + 3*x)^6) + 707/(5*(2 + 3*x)^5) + 3467/(2*(2 + 3*x)^4) + 57110/(3*(2 + 3*x)^3) + 424975/(2*(2 + 3*x)^2) + 2958125/(2 + 3*x) - 75625/(2*(3 + 5*x)^2) + 1615625/(3 + 5*x) - 19637500*Log[5*(2 + 3*x)] + 19637500*Log[3 + 5*x]","A",1
1337,1,112,110,0.1410552,"\int \frac{(1-2 x)^2}{(2+3 x)^8 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^2/((2 + 3*x)^8*(3 + 5*x)^3),x]","\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 (5 (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,"7/(2 + 3*x)^7 + 707/(6*(2 + 3*x)^6) + 6934/(5*(2 + 3*x)^5) + 28555/(2*(2 + 3*x)^4) + 424975/(3*(2 + 3*x)^3) + 2958125/(2*(2 + 3*x)^2) + 19637500/(2 + 3*x) - 378125/(2*(3 + 5*x)^2) + 9212500/(3 + 5*x) - 125825000*Log[5*(2 + 3*x)] + 125825000*Log[3 + 5*x]","A",1
1338,1,72,56,0.0033833,"\int (1-2 x)^3 (2+3 x)^8 (3+5 x) \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^8*(3 + 5*x),x]","-\frac{262440 x^{13}}{13}-96957 x^{12}-\frac{1966842 x^{11}}{11}-\frac{1290573 x^{10}}{10}+38331 x^9+128412 x^8+67248 x^7-17456 x^6-\frac{159712 x^5}{5}-9216 x^4+3328 x^3+2944 x^2+768 x","-\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,"768*x + 2944*x^2 + 3328*x^3 - 9216*x^4 - (159712*x^5)/5 - 17456*x^6 + 67248*x^7 + 128412*x^8 + 38331*x^9 - (1290573*x^10)/10 - (1966842*x^11)/11 - 96957*x^12 - (262440*x^13)/13","A",1
1339,1,67,56,0.0027722,"\int (1-2 x)^3 (2+3 x)^7 (3+5 x) \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^7*(3 + 5*x),x]","-7290 x^{12}-\frac{329508 x^{11}}{11}-\frac{217971 x^{10}}{5}-15507 x^9+\frac{208035 x^8}{8}+29106 x^7+3514 x^6-\frac{48968 x^5}{5}-5148 x^4+480 x^3+1184 x^2+384 x","-\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,"384*x + 1184*x^2 + 480*x^3 - 5148*x^4 - (48968*x^5)/5 + 3514*x^6 + 29106*x^7 + (208035*x^8)/8 - 15507*x^9 - (217971*x^10)/5 - (329508*x^11)/11 - 7290*x^12","A",1
1340,1,62,56,0.0029428,"\int (1-2 x)^3 (2+3 x)^6 (3+5 x) \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x),x]","-\frac{29160 x^{11}}{11}-\frac{45198 x^{10}}{5}-9450 x^9+\frac{10179 x^8}{8}+8937 x^7+4368 x^6-\frac{10444 x^5}{5}-2340 x^4-208 x^3+448 x^2+192 x","-\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,"192*x + 448*x^2 - 208*x^3 - 2340*x^4 - (10444*x^5)/5 + 4368*x^6 + 8937*x^7 + (10179*x^8)/8 - 9450*x^9 - (45198*x^10)/5 - (29160*x^11)/11","A",1
1341,1,53,56,0.0030538,"\int (1-2 x)^3 (2+3 x)^5 (3+5 x) \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^5*(3 + 5*x),x]","-972 x^{10}-2628 x^9-\frac{6291 x^8}{4}+1683 x^7+\frac{4333 x^6}{2}+14 x^5-882 x^4-256 x^3+152 x^2+96 x","-\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,"96*x + 152*x^2 - 256*x^3 - 882*x^4 + 14*x^5 + (4333*x^6)/2 + 1683*x^7 - (6291*x^8)/4 - 2628*x^9 - 972*x^10","A",1
1342,1,50,56,0.0022756,"\int (1-2 x)^3 (2+3 x)^4 (3+5 x) \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x),x]","-360 x^9-\frac{1431 x^8}{2}-54 x^7+\frac{1393 x^6}{2}+\frac{1547 x^5}{5}-252 x^4-168 x^3+40 x^2+48 x","-\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,"48*x + 40*x^2 - 168*x^3 - 252*x^4 + (1547*x^5)/5 + (1393*x^6)/2 - 54*x^7 - (1431*x^8)/2 - 360*x^9","A",1
1343,1,45,45,0.0020627,"\int (1-2 x)^3 (2+3 x)^3 (3+5 x) \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x),x]","-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","-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,"24*x + 2*x^2 - 86*x^3 - (117*x^4)/4 + (949*x^5)/5 + 111*x^6 - (1188*x^7)/7 - 135*x^8","A",1
1344,1,40,40,0.0012357,"\int (1-2 x)^3 (2+3 x)^2 (3+5 x) \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x),x]","-\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","-\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,"12*x - 8*x^2 - 35*x^3 + (99*x^4)/4 + (326*x^5)/5 - 26*x^6 - (360*x^7)/7","A",1
1345,1,35,34,0.0014645,"\int (1-2 x)^3 (2+3 x) (3+5 x) \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)*(3 + 5*x),x]","-20 x^6+\frac{28 x^5}{5}+\frac{45 x^4}{2}-9 x^3-\frac{17 x^2}{2}+6 x","-\frac{5}{16} (1-2 x)^6+\frac{17}{10} (1-2 x)^5-\frac{77}{32} (1-2 x)^4",1,"6*x - (17*x^2)/2 - 9*x^3 + (45*x^4)/2 + (28*x^5)/5 - 20*x^6","A",1
1346,1,26,23,0.0012857,"\int (1-2 x)^3 (3+5 x) \, dx","Integrate[(1 - 2*x)^3*(3 + 5*x),x]","-8 x^5+9 x^4+2 x^3-\frac{13 x^2}{2}+3 x","\frac{1}{4} (1-2 x)^5-\frac{11}{16} (1-2 x)^4",1,"3*x - (13*x^2)/2 + 2*x^3 + 9*x^4 - 8*x^5","A",1
1347,1,32,37,0.0163156,"\int \frac{(1-2 x)^3 (3+5 x)}{2+3 x} \, dx","Integrate[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x),x]","\frac{1}{729} \left(-2430 x^4+5076 x^3-4347 x^2+2637 x-1029 \log (3 x+2)+5674\right)","-\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,"(5674 + 2637*x - 4347*x^2 + 5076*x^3 - 2430*x^4 - 1029*Log[2 + 3*x])/729","A",1
1348,1,44,41,0.0219903,"\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^2} \, dx","Integrate[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^2,x]","\frac{-2160 x^4+5796 x^3-10620 x^2-4113 x+4018 (3 x+2) \log (6 x+4)+4808}{486 (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 + 4018*(2 + 3*x)*Log[4 + 6*x])/(486*(2 + 3*x))","A",1
1349,1,46,45,0.0207087,"\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^3} \, dx","Integrate[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^3,x]","-\frac{3240 x^4-14472 x^3-15030 x^2+15150 x+3108 (3 x+2)^2 \log (6 x+4)+11509}{486 (3 x+2)^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,"-1/486*(11509 + 15150*x - 15030*x^2 - 14472*x^3 + 3240*x^4 + 3108*(2 + 3*x)^2*Log[4 + 6*x])/(2 + 3*x)^2","A",1
1350,1,46,49,0.0170784,"\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^4} \, dx","Integrate[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^4,x]","\frac{-19440 x^4-51840 x^3+32076 x^2+70767 x+2568 (3 x+2)^3 \log (3 x+2)+22088}{1458 (3 x+2)^3}","-\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 + 2568*(2 + 3*x)^3*Log[2 + 3*x])/(1458*(2 + 3*x)^3)","A",1
1351,1,41,55,0.0206725,"\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^5} \, dx","Integrate[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^5,x]","-\frac{138672 x^3+193428 x^2+97116 x+480 (3 x+2)^4 \log (6 x+4)+18835}{2916 (3 x+2)^4}","-\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,"-1/2916*(18835 + 97116*x + 193428*x^2 + 138672*x^3 + 480*(2 + 3*x)^4*Log[4 + 6*x])/(2 + 3*x)^4","A",1
1352,1,31,37,0.0264204,"\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^6} \, dx","Integrate[((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
1353,1,31,55,0.0189049,"\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^7} \, dx","Integrate[((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
1354,1,31,56,0.0140856,"\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^8} \, dx","Integrate[((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
1355,1,87,67,0.0050885,"\int (1-2 x)^3 (2+3 x)^8 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^8*(3 + 5*x)^2,x]","-\frac{656100 x^{14}}{7}-\frac{6604740 x^{13}}{13}-\frac{2220777 x^{12}}{2}-\frac{12353391 x^{11}}{11}-\frac{1073412 x^{10}}{5}+685713 x^9+679446 x^8+\frac{888528 x^7}{7}-\frac{556384 x^6}{3}-\frac{663456 x^5}{5}-15168 x^4+\frac{59392 x^3}{3}+10752 x^2+2304 x","-\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,"2304*x + 10752*x^2 + (59392*x^3)/3 - 15168*x^4 - (663456*x^5)/5 - (556384*x^6)/3 + (888528*x^7)/7 + 679446*x^8 + 685713*x^9 - (1073412*x^10)/5 - (12353391*x^11)/11 - (2220777*x^12)/2 - (6604740*x^13)/13 - (656100*x^14)/7","A",1
1356,1,78,67,0.0029509,"\int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^7*(3 + 5*x)^2,x]","-\frac{437400 x^{13}}{13}-159165 x^{12}-\frac{3168234 x^{11}}{11}-\frac{2005641 x^{10}}{10}+69054 x^9+\frac{1642815 x^8}{8}+102378 x^7-\frac{90794 x^6}{3}-\frac{249864 x^5}{5}-13644 x^4+\frac{16160 x^3}{3}+4512 x^2+1152 x","-\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,"1152*x + 4512*x^2 + (16160*x^3)/3 - 13644*x^4 - (249864*x^5)/5 - (90794*x^6)/3 + 102378*x^7 + (1642815*x^8)/8 + 69054*x^9 - (2005641*x^10)/10 - (3168234*x^11)/11 - 159165*x^12 - (437400*x^13)/13","A",1
1357,1,71,67,0.0032694,"\int (1-2 x)^3 (2+3 x)^6 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^2,x]","-12150 x^{12}-\frac{539460 x^{11}}{11}-\frac{348219 x^{10}}{5}-22695 x^9+\frac{85833 x^8}{2}+45531 x^7+\frac{13202 x^6}{3}-\frac{78132 x^5}{5}-7800 x^4+\frac{2608 x^3}{3}+1824 x^2+576 x","-\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,"576*x + 1824*x^2 + (2608*x^3)/3 - 7800*x^4 - (78132*x^5)/5 + (13202*x^6)/3 + 45531*x^7 + (85833*x^8)/2 - 22695*x^9 - (348219*x^10)/5 - (539460*x^11)/11 - 12150*x^12","A",1
1358,1,62,67,0.0034911,"\int (1-2 x)^3 (2+3 x)^5 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^5*(3 + 5*x)^2,x]","-\frac{48600 x^{11}}{11}-14742 x^{10}-14874 x^9+\frac{21159 x^8}{8}+14334 x^7+\frac{39347 x^6}{6}-3486 x^5-3606 x^4-\frac{784 x^3}{3}+696 x^2+288 x","-\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,"288*x + 696*x^2 - (784*x^3)/3 - 3606*x^4 - 3486*x^5 + (39347*x^6)/6 + 14334*x^7 + (21159*x^8)/8 - 14874*x^9 - 14742*x^10 - (48600*x^11)/11","A",1
1359,1,57,67,0.0033621,"\int (1-2 x)^3 (2+3 x)^4 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^2,x]","-1620 x^{10}-4260 x^9-\frac{9531 x^8}{4}+2823 x^7+\frac{10136 x^6}{3}-\frac{399 x^5}{5}-1386 x^4-\frac{1112 x^3}{3}+240 x^2+144 x","-\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,"144*x + 240*x^2 - (1112*x^3)/3 - 1386*x^4 - (399*x^5)/5 + (10136*x^6)/3 + 2823*x^7 - (9531*x^8)/4 - 4260*x^9 - 1620*x^10","A",1
1360,1,56,56,0.0030097,"\int (1-2 x)^3 (2+3 x)^3 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^2,x]","-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","-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,"72*x + 66*x^2 - (754*x^3)/3 - (1641*x^4)/4 + (2262*x^5)/5 + (6743*x^6)/6 - (234*x^7)/7 - (2295*x^8)/2 - 600*x^9","A",1
1361,1,47,47,0.0014303,"\int (1-2 x)^3 (2+3 x)^2 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)^2,x]","-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","-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,"36*x + 6*x^2 - (395*x^3)/3 - 57*x^4 + (1473*x^5)/5 + (581*x^6)/3 - (1860*x^7)/7 - 225*x^8","A",1
1362,1,46,46,0.0009769,"\int (1-2 x)^3 (2+3 x) (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)*(3 + 5*x)^2,x]","-\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","-\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,"18*x - (21*x^2)/2 - (166*x^3)/3 + (135*x^4)/4 + (534*x^5)/5 - (110*x^6)/3 - (600*x^7)/7","A",1
1363,1,35,34,0.0011541,"\int (1-2 x)^3 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^3*(3 + 5*x)^2,x]","-\frac{100 x^6}{3}+12 x^5+\frac{69 x^4}{2}-\frac{47 x^3}{3}-12 x^2+9 x","-\frac{25}{48} (1-2 x)^6+\frac{11}{4} (1-2 x)^5-\frac{121}{32} (1-2 x)^4",1,"9*x - 12*x^2 - (47*x^3)/3 + (69*x^4)/2 + 12*x^5 - (100*x^6)/3","A",1
1364,1,37,44,0.0136819,"\int \frac{(1-2 x)^3 (3+5 x)^2}{2+3 x} \, dx","Integrate[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x),x]","\frac{-58320 x^5+70470 x^4+4428 x^3-38691 x^2+16596 x+2058 \log (3 x+2)+7972}{4374}","-\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,"(7972 + 16596*x - 38691*x^2 + 4428*x^3 + 70470*x^4 - 58320*x^5 + 2058*Log[2 + 3*x])/4374","A",1
1365,1,49,48,0.0508249,"\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^2} \, dx","Integrate[((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-11172 (3 x+2) \log (30 x+20)+69863}{2187 (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 - 11172*(2 + 3*x)*Log[20 + 30*x])/(2187*(2 + 3*x))","A",1
1366,1,51,52,0.0503987,"\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^3} \, dx","Integrate[((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-69594 (3 x+2)^2 \log (30 x+20)+258005}{4374 (3 x+2)^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,"-1/4374*(258005 + 1171896*x + 1531512*x^2 + 347436*x^3 - 205740*x^4 + 97200*x^5 - 69594*(2 + 3*x)^2*Log[20 + 30*x])/(2 + 3*x)^2","A",1
1367,1,51,56,0.0530545,"\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^4} \, dx","Integrate[((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-24594 (3 x+2)^3 \log (30 x+20)-33319}{2187 (3 x+2)^3}","-\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 - 24594*(2 + 3*x)^3*Log[20 + 30*x])/(2187*(2 + 3*x)^3)","A",1
1368,1,51,60,0.044486,"\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^5} \, dx","Integrate[((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+26160 (3 x+2)^4 \log (30 x+20)+460595}{8748 (3 x+2)^4}","-\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 + 26160*(2 + 3*x)^4*Log[20 + 30*x])/(8748*(2 + 3*x)^4)","A",1
1369,1,46,66,0.0483535,"\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^6} \, dx","Integrate[((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+3000 (3 x+2)^5 \log (30 x+20)+236399}{10935 (3 x+2)^5}","-\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,"-1/10935*(236399 + 1579785*x + 4264965*x^2 + 5403105*x^3 + 2648700*x^4 + 3000*(2 + 3*x)^5*Log[20 + 30*x])/(2 + 3*x)^5","A",1
1370,1,36,67,0.0427602,"\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^7} \, dx","Integrate[((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
1371,1,36,67,0.0304372,"\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^8} \, dx","Integrate[((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
1372,1,85,78,0.0042923,"\int (1-2 x)^3 (2+3 x)^7 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^7*(3 + 5*x)^3,x]","-\frac{1093500 x^{14}}{7}-\frac{10862100 x^{13}}{13}-\frac{3595185 x^{12}}{2}-\frac{19532907 x^{11}}{11}-\frac{2909493 x^{10}}{10}+1119837 x^9+\frac{8511675 x^8}{8}+\frac{1241998 x^7}{7}-299014 x^6-\frac{1022472 x^5}{5}-20732 x^4+31200 x^3+16416 x^2+3456 x","-\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,"3456*x + 16416*x^2 + 31200*x^3 - 20732*x^4 - (1022472*x^5)/5 - 299014*x^6 + (1241998*x^7)/7 + (8511675*x^8)/8 + 1119837*x^9 - (2909493*x^10)/10 - (19532907*x^11)/11 - (3595185*x^12)/2 - (10862100*x^13)/13 - (1093500*x^14)/7","A",1
1373,1,74,78,0.0029583,"\int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^3,x]","-\frac{729000 x^{13}}{13}-261225 x^{12}-\frac{5100570 x^{11}}{11}-\frac{3110589 x^{10}}{10}+122655 x^9+\frac{2623581 x^8}{8}+155453 x^7-51908 x^6-\frac{390396 x^5}{5}-20140 x^4+8688 x^3+6912 x^2+1728 x","-\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,"1728*x + 6912*x^2 + 8688*x^3 - 20140*x^4 - (390396*x^5)/5 - 51908*x^6 + 155453*x^7 + (2623581*x^8)/8 + 122655*x^9 - (3110589*x^10)/10 - (5100570*x^11)/11 - 261225*x^12 - (729000*x^13)/13","A",1
1374,1,65,78,0.0032578,"\int (1-2 x)^3 (2+3 x)^5 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^5*(3 + 5*x)^3,x]","-20250 x^{12}-\frac{882900 x^{11}}{11}-111159 x^{10}-32867 x^9+\frac{565167 x^8}{8}+71107 x^7+\frac{10297 x^6}{2}-24882 x^5-11798 x^4+1536 x^3+2808 x^2+864 x","-\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,"864*x + 2808*x^2 + 1536*x^3 - 11798*x^4 - 24882*x^5 + (10297*x^6)/2 + 71107*x^7 + (565167*x^8)/8 - 32867*x^9 - 111159*x^10 - (882900*x^11)/11 - 20250*x^12","A",1
1375,1,62,62,0.003143,"\int (1-2 x)^3 (2+3 x)^4 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^3,x]","-\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","-\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,"432*x + 1080*x^2 - 312*x^3 - 5548*x^4 - (28917*x^5)/5 + (19607*x^6)/2 + 22949*x^7 + (41619*x^8)/8 - 23370*x^9 - 24030*x^10 - (81000*x^11)/11","A",1
1376,1,59,59,0.0032195,"\int (1-2 x)^3 (2+3 x)^3 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^3,x]","-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","-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,"216*x + 378*x^2 - 534*x^3 - (8693*x^4)/4 - (1419*x^5)/5 + (10513*x^6)/2 + (33013*x^7)/7 - (14355*x^8)/4 - 6900*x^9 - 2700*x^10","A",1
1377,1,54,54,0.0025205,"\int (1-2 x)^3 (2+3 x)^2 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)^3,x]","-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","-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,"108*x + 108*x^2 - 375*x^3 - (2659*x^4)/4 + (3279*x^5)/5 + (3617*x^6)/2 + (230*x^7)/7 - (3675*x^8)/2 - 1000*x^9","A",1
1378,1,47,47,0.0015181,"\int (1-2 x)^3 (2+3 x) (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^3*(2 + 3*x)*(3 + 5*x)^3,x]","-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","-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,"54*x + (27*x^2)/2 - 201*x^3 - (425*x^4)/4 + (2277*x^5)/5 + 335*x^6 - (2900*x^7)/7 - 375*x^8","A",1
1379,1,40,40,0.0017802,"\int (1-2 x)^3 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^3*(3 + 5*x)^3,x]","-\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","-\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,"27*x - (27*x^2)/2 - 87*x^3 + (179*x^4)/4 + 174*x^5 - 50*x^6 - (1000*x^7)/7","A",1
1380,1,42,51,0.0138931,"\int \frac{(1-2 x)^3 (3+5 x)^3}{2+3 x} \, dx","Integrate[((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x),x]","\frac{-243000 x^6+106920 x^5+228015 x^4-115686 x^3-74583 x^2+60078 x-686 \log (3 x+2)+29296}{4374}","-\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,"(29296 + 60078*x - 74583*x^2 - 115686*x^3 + 228015*x^4 + 106920*x^5 - 243000*x^6 - 686*Log[2 + 3*x])/4374","A",1
1381,1,54,55,0.0208401,"\int \frac{(1-2 x)^3 (3+5 x)^3}{(2+3 x)^2} \, dx","Integrate[((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-10878 (3 x+2) \log (3 x+2)+20002}{4374 (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,"-1/4374*(20002 + 3588*x + 54000*x^2 + 163269*x^3 - 220320*x^4 - 182250*x^5 + 291600*x^6 - 10878*(2 + 3*x)*Log[2 + 3*x])/(2 + 3*x)","A",1
1382,1,56,59,0.0225615,"\int \frac{(1-2 x)^3 (3+5 x)^3}{(2+3 x)^3} \, dx","Integrate[((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-60438 (3 x+2)^2 \log (3 x+2)+551755}{4374 (3 x+2)^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 - 60438*(2 + 3*x)^2*Log[2 + 3*x])/(4374*(2 + 3*x)^2)","A",1
1383,1,52,63,0.0255128,"\int \frac{(1-2 x)^3 (3+5 x)^3}{(2+3 x)^4} \, dx","Integrate[((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^4,x]","\frac{132386 \log (3 x+2)-\frac{3 \left(162000 x^6-251100 x^5+414180 x^4+3180480 x^3+3851166 x^2+1766567 x+279268\right)}{(3 x+2)^3}}{4374}","-\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,"((-3*(279268 + 1766567*x + 3851166*x^2 + 3180480*x^3 + 414180*x^4 - 251100*x^5 + 162000*x^6))/(2 + 3*x)^3 + 132386*Log[2 + 3*x])/4374","A",1
1384,1,56,67,0.0201485,"\int \frac{(1-2 x)^3 (3+5 x)^3}{(2+3 x)^5} \, dx","Integrate[((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-172680 (3 x+2)^4 \log (3 x+2)-597785}{8748 (3 x+2)^4}","-\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 - 172680*(2 + 3*x)^4*Log[2 + 3*x])/(8748*(2 + 3*x)^4)","A",1
1385,1,56,71,0.0307859,"\int \frac{(1-2 x)^3 (3+5 x)^3}{(2+3 x)^6} \, dx","Integrate[((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+222000 (3 x+2)^5 \log (3 x+2)+7991782}{43740 (3 x+2)^5}","-\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 + 222000*(2 + 3*x)^5*Log[2 + 3*x])/(43740*(2 + 3*x)^5)","A",1
1386,1,51,77,0.0251397,"\int \frac{(1-2 x)^3 (3+5 x)^3}{(2+3 x)^7} \, dx","Integrate[((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+20000 (3 x+2)^6 \log (3 x+2)+3165082}{43740 (3 x+2)^6}","-\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,"-1/43740*(3165082 + 25975248*x + 89062425*x^2 + 158427540*x^3 + 144852300*x^4 + 53946000*x^5 + 20000*(2 + 3*x)^6*Log[2 + 3*x])/(2 + 3*x)^6","A",1
1387,1,41,78,0.0140187,"\int \frac{(1-2 x)^3 (3+5 x)^3}{(2+3 x)^8} \, dx","Integrate[((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
1388,1,57,72,0.0177105,"\int \frac{(1-2 x)^3 (2+3 x)^6}{3+5 x} \, dx","Integrate[((1 - 2*x)^3*(2 + 3*x)^6)/(3 + 5*x),x]","\frac{-531562500000 x^9-1136214843750 x^8-189084375000 x^7+1088433281250 x^6+580671787500 x^5-383824153125 x^4-305440677500 x^3+58334109750 x^2+87499068300 x+559020 \log (5 x+3)+18072649071}{4101562500}","-\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,"(18072649071 + 87499068300*x + 58334109750*x^2 - 305440677500*x^3 - 383824153125*x^4 + 580671787500*x^5 + 1088433281250*x^6 - 189084375000*x^7 - 1136214843750*x^8 - 531562500000*x^9 + 559020*Log[3 + 5*x])/4101562500","A",1
1389,1,52,65,0.0139451,"\int \frac{(1-2 x)^3 (2+3 x)^5}{3+5 x} \, dx","Integrate[((1 - 2*x)^3*(2 + 3*x)^5)/(3 + 5*x),x]","\frac{-39867187500 x^8-56193750000 x^7+28999687500 x^6+63874912500 x^5-4839778125 x^4-29815677500 x^3-728390250 x^2+8749068300 x+559020 \log (5 x+3)+2409164451}{820312500}","-\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,"(2409164451 + 8749068300*x - 728390250*x^2 - 29815677500*x^3 - 4839778125*x^4 + 63874912500*x^5 + 28999687500*x^6 - 56193750000*x^7 - 39867187500*x^8 + 559020*Log[3 + 5*x])/820312500","A",1
1390,1,47,58,0.0142132,"\int \frac{(1-2 x)^3 (2+3 x)^4}{3+5 x} \, dx","Integrate[((1 - 2*x)^3*(2 + 3*x)^4)/(3 + 5*x),x]","\frac{-3037500000 x^7-2008125000 x^6+3926475000 x^5+2050846875 x^4-2253177500 x^3-728390250 x^2+874068300 x+559020 \log (5 x+3)+348168591}{164062500}","-\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,"(348168591 + 874068300*x - 728390250*x^2 - 2253177500*x^3 + 2050846875*x^4 + 3926475000*x^5 - 2008125000*x^6 - 3037500000*x^7 + 559020*Log[3 + 5*x])/164062500","A",1
1391,1,42,51,0.0135632,"\int \frac{(1-2 x)^3 (2+3 x)^3}{3+5 x} \, dx","Integrate[((1 - 2*x)^3*(2 + 3*x)^3)/(3 + 5*x),x]","\frac{-16875000 x^6+2025000 x^5+21684375 x^4-6253750 x^3-9840375 x^2+6183450 x+39930 \log (5 x+3)+4036284}{2343750}","-\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,"(4036284 + 6183450*x - 9840375*x^2 - 6253750*x^3 + 21684375*x^4 + 2025000*x^5 - 16875000*x^6 + 39930*Log[3 + 5*x])/2343750","A",1
1392,1,37,44,0.01268,"\int \frac{(1-2 x)^3 (2+3 x)^2}{3+5 x} \, dx","Integrate[((1 - 2*x)^3*(2 + 3*x)^2)/(3 + 5*x),x]","\frac{-1350000 x^5+1293750 x^4+777500 x^3-1402875 x^2+558450 x+39930 \log (5 x+3)+735399}{468750}","-\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,"(735399 + 558450*x - 1402875*x^2 + 777500*x^3 + 1293750*x^4 - 1350000*x^5 + 39930*Log[3 + 5*x])/468750","A",1
1393,1,35,37,0.0252014,"\int \frac{(1-2 x)^3 (2+3 x)}{3+5 x} \, dx","Integrate[((1 - 2*x)^3*(2 + 3*x))/(3 + 5*x),x]","\frac{3993 \log (5 x+3)-5 \left(2250 x^4-4300 x^3+2745 x^2+81 x-2160\right)}{9375}","-\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,"(-5*(-2160 + 81*x + 2745*x^2 - 4300*x^3 + 2250*x^4) + 3993*Log[3 + 5*x])/9375","A",1
1394,1,27,30,0.0099331,"\int \frac{(1-2 x)^3}{3+5 x} \, dx","Integrate[(1 - 2*x)^3/(3 + 5*x),x]","\frac{-1000 x^3+3150 x^2-6030 x+3993 \log (5 x+3)-4968}{1875}","-\frac{8 x^3}{15}+\frac{42 x^2}{25}-\frac{402 x}{125}+\frac{1331}{625} \log (5 x+3)",1,"(-4968 - 6030*x + 3150*x^2 - 1000*x^3 + 3993*Log[3 + 5*x])/1875","A",1
1395,1,35,33,0.0133109,"\int \frac{(1-2 x)^3}{(2+3 x) (3+5 x)} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)*(3 + 5*x)),x]","\frac{60 \left(-15 x^2+83 x+62\right)-42875 \log (3 x+2)+35937 \log (-3 (5 x+3))}{3375}","-\frac{4 x^2}{15}+\frac{332 x}{225}-\frac{343}{27} \log (3 x+2)+\frac{1331}{125} \log (5 x+3)",1,"(60*(62 + 83*x - 15*x^2) - 42875*Log[2 + 3*x] + 35937*Log[-3*(3 + 5*x)])/3375","A",1
1396,1,36,37,0.0271926,"\int \frac{(1-2 x)^3}{(2+3 x)^2 (3+5 x)} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)^2*(3 + 5*x)),x]","\frac{1}{675} \left(-120 x+\frac{8575}{3 x+2}-35525 \log (5 (3 x+2))+35937 \log (5 x+3)-72\right)","-\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,"(-72 - 120*x + 8575/(2 + 3*x) - 35525*Log[5*(2 + 3*x)] + 35937*Log[3 + 5*x])/675","A",1
1397,1,39,43,0.04249,"\int \frac{(1-2 x)^3}{(2+3 x)^3 (3+5 x)} \, dx","Integrate[(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 (5 (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[5*(2 + 3*x)])/27 + (1331*Log[3 + 5*x])/5","A",1
1398,1,40,50,0.0452355,"\int \frac{(1-2 x)^3}{(2+3 x)^4 (3+5 x)} \, dx","Integrate[(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 (5 (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[5*(2 + 3*x)] + 1331*Log[3 + 5*x]","A",1
1399,1,45,59,0.0512793,"\int \frac{(1-2 x)^3}{(2+3 x)^5 (3+5 x)} \, dx","Integrate[(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 (5 (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[5*(2 + 3*x)] + 6655*Log[3 + 5*x]","A",1
1400,1,50,70,0.0779844,"\int \frac{(1-2 x)^3}{(2+3 x)^6 (3+5 x)} \, dx","Integrate[(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 (5 (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[5*(2 + 3*x)] + 33275*Log[3 + 5*x]","A",1
1401,1,75,81,0.1015216,"\int \frac{(1-2 x)^3}{(2+3 x)^7 (3+5 x)} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)^7*(3 + 5*x)),x]","\frac{53905500 (3 x+2)^5+5390550 (3 x+2)^4+718740 (3 x+2)^3+107835 (3 x+2)^2+17052 (3 x+2)+3430}{1620 (3 x+2)^6}-166375 \log (5 (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,"(3430 + 17052*(2 + 3*x) + 107835*(2 + 3*x)^2 + 718740*(2 + 3*x)^3 + 5390550*(2 + 3*x)^4 + 53905500*(2 + 3*x)^5)/(1620*(2 + 3*x)^6) - 166375*Log[5*(2 + 3*x)] + 166375*Log[3 + 5*x]","A",1
1402,1,84,92,0.1145876,"\int \frac{(1-2 x)^3}{(2+3 x)^8 (3+5 x)} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)^8*(3 + 5*x)),x]","\frac{269527500 (3 x+2)^6+26952750 (3 x+2)^5+3593700 (3 x+2)^4+539055 (3 x+2)^3+86268 (3 x+2)^2+14210 (3 x+2)+2940}{1620 (3 x+2)^7}-831875 \log (5 (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,"(2940 + 14210*(2 + 3*x) + 86268*(2 + 3*x)^2 + 539055*(2 + 3*x)^3 + 3593700*(2 + 3*x)^4 + 26952750*(2 + 3*x)^5 + 269527500*(2 + 3*x)^6)/(1620*(2 + 3*x)^7) - 831875*Log[5*(2 + 3*x)] + 831875*Log[3 + 5*x]","A",1
1403,1,71,76,0.0495325,"\int \frac{(1-2 x)^3 (2+3 x)^6}{(3+5 x)^2} \, dx","Integrate[((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+813120 (5 x+3) \log (6 (5 x+3))+2118706028}{341796875 (5 x+3)}","-\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 + 813120*(3 + 5*x)*Log[6*(3 + 5*x)])/(341796875*(3 + 5*x))","A",1
1404,1,66,69,0.0445533,"\int \frac{(1-2 x)^3 (2+3 x)^5}{(3+5 x)^2} \, dx","Integrate[((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+2693460 (5 x+3) \log (6 (5 x+3))+1247330759}{273437500 (5 x+3)}","-\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 + 2693460*(3 + 5*x)*Log[6*(3 + 5*x)])/(273437500*(3 + 5*x))","A",1
1405,1,61,62,0.0409768,"\int \frac{(1-2 x)^3 (2+3 x)^4}{(3+5 x)^2} \, dx","Integrate[((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+152460 (5 x+3) \log (6 (5 x+3))+14487499}{3906250 (5 x+3)}","-\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 + 152460*(3 + 5*x)*Log[6*(3 + 5*x)])/(3906250*(3 + 5*x))","A",1
1406,1,54,55,0.0178177,"\int \frac{(1-2 x)^3 (2+3 x)^3}{(3+5 x)^2} \, dx","Integrate[((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+112530 (5 x+3) \log (5 x+3)+2378647}{781250 (5 x+3)}","-\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 + 112530*(3 + 5*x)*Log[3 + 5*x])/(781250*(3 + 5*x))","A",1
1407,1,51,48,0.0407528,"\int \frac{(1-2 x)^3 (2+3 x)^2}{(3+5 x)^2} \, dx","Integrate[((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+1452 (5 x+3) \log (6 (5 x+3))+3449}{3125 (5 x+3)}","-\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 + 1452*(3 + 5*x)*Log[6*(3 + 5*x)])/(3125*(3 + 5*x))","A",1
1408,1,44,41,0.0260355,"\int \frac{(1-2 x)^3 (2+3 x)}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)^3*(2 + 3*x))/(3 + 5*x)^2,x]","\frac{-10000 x^4+24500 x^3-36600 x^2-11865 x+6534 (5 x+3) \log (10 x+6)+9983}{6250 (5 x+3)}","-\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 + 6534*(3 + 5*x)*Log[6 + 10*x])/(6250*(3 + 5*x))","A",1
1409,1,39,34,0.012037,"\int \frac{(1-2 x)^3}{(3+5 x)^2} \, dx","Integrate[(1 - 2*x)^3/(3 + 5*x)^2,x]","\frac{-500 x^3+2400 x^2+395 x-726 (5 x+3) \log (10 x+6)-2066}{625 (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 - 726*(3 + 5*x)*Log[6 + 10*x])/(625*(3 + 5*x))","A",1
1410,1,36,37,0.030727,"\int \frac{(1-2 x)^3}{(2+3 x) (3+5 x)^2} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)*(3 + 5*x)^2),x]","\frac{-120 x-\frac{11979}{5 x+3}+42875 \log (3 x+2)-42471 \log (-3 (5 x+3))-80}{1125}","-\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,"(-80 - 120*x - 11979/(3 + 5*x) + 42875*Log[2 + 3*x] - 42471*Log[-3*(3 + 5*x)])/1125","A",1
1411,1,61,43,0.0475561,"\int \frac{(1-2 x)^3}{(2+3 x)^2 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)^2*(3 + 5*x)^2),x]","-\frac{-78400 \left(15 x^2+19 x+6\right) \log (5 (3 x+2))+78408 \left(15 x^2+19 x+6\right) \log (5 x+3)+78812 x+49683}{225 (3 x+2) (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,"-1/225*(49683 + 78812*x - 78400*(6 + 19*x + 15*x^2)*Log[5*(2 + 3*x)] + 78408*(6 + 19*x + 15*x^2)*Log[3 + 5*x])/((2 + 3*x)*(3 + 5*x))","A",1
1412,1,47,50,0.0417497,"\int \frac{(1-2 x)^3}{(2+3 x)^3 (3+5 x)^2} \, dx","Integrate[(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 (5 (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,"-1/90*(289137 + 891911*x + 686022*x^2)/((2 + 3*x)^2*(3 + 5*x)) + 2541*Log[5*(2 + 3*x)] - 2541*Log[3 + 5*x]","A",1
1413,1,59,57,0.04023,"\int \frac{(1-2 x)^3}{(2+3 x)^4 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)^4*(3 + 5*x)^2),x]","-\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 (5 (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,"-343/(27*(2 + 3*x)^3) - 1568/(9*(2 + 3*x)^2) - 2541/(2 + 3*x) - 1331/(3 + 5*x) + 16698*Log[5*(2 + 3*x)] - 16698*Log[3 + 5*x]","A",1
1414,1,70,68,0.0496942,"\int \frac{(1-2 x)^3}{(2+3 x)^5 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)^5*(3 + 5*x)^2),x]","-\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 (5 (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,"-343/(36*(2 + 3*x)^4) - 3136/(27*(2 + 3*x)^3) - 2541/(2*(2 + 3*x)^2) - 16698/(2 + 3*x) - 6655/(3 + 5*x) + 103455*Log[5*(2 + 3*x)] - 103455*Log[3 + 5*x]","A",1
1415,1,62,75,0.0977813,"\int \frac{(1-2 x)^3}{(2+3 x)^6 (3+5 x)^2} \, dx","Integrate[(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 (5 (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,"-1/45*(280877649 + 2130399775*x + 6461351715*x^2 + 9795413430*x^3 + 7422787350*x^4 + 2249329500*x^5)/((2 + 3*x)^5*(3 + 5*x)) + 617100*Log[5*(2 + 3*x)] - 617100*Log[3 + 5*x]","A",1
1416,1,90,88,0.1195933,"\int \frac{(1-2 x)^3}{(2+3 x)^7 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)^7*(3 + 5*x)^2),x]","-\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 (5 (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,"-343/(54*(2 + 3*x)^6) - 3136/(45*(2 + 3*x)^5) - 2541/(4*(2 + 3*x)^4) - 5566/(2 + 3*x)^3 - 103455/(2*(2 + 3*x)^2) - 617100/(2 + 3*x) - 166375/(3 + 5*x) + 3584625*Log[5*(2 + 3*x)] - 3584625*Log[3 + 5*x]","A",1
1417,1,99,97,0.1792928,"\int \frac{(1-2 x)^3}{(2+3 x)^8 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)^8*(3 + 5*x)^2),x]","-\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 (5 (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,"-49/(9*(2 + 3*x)^7) - 1568/(27*(2 + 3*x)^6) - 2541/(5*(2 + 3*x)^5) - 8349/(2*(2 + 3*x)^4) - 34485/(2 + 3*x)^3 - 308550/(2 + 3*x)^2 - 3584625/(2 + 3*x) - 831875/(3 + 5*x) + 20418750*Log[5*(2 + 3*x)] - 20418750*Log[3 + 5*x]","A",1
1418,1,76,87,0.0355146,"\int \frac{(1-2 x)^3 (2+3 x)^7}{(3+5 x)^3} \, dx","Integrate[((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+6620460 (5 x+3)^2 \log (5 x+3)+17925405377}{1367187500 (5 x+3)^2}","-\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 + 6620460*(3 + 5*x)^2*Log[3 + 5*x])/(1367187500*(3 + 5*x)^2)","A",1
1419,1,73,80,0.0420921,"\int \frac{(1-2 x)^3 (2+3 x)^6}{(3+5 x)^3} \, dx","Integrate[((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+23344860 (5 x+3)^2 \log (6 (5 x+3))+13353609877}{1367187500 (5 x+3)^2}","-\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 + 23344860*(3 + 5*x)^2*Log[6*(3 + 5*x)])/(1367187500*(3 + 5*x)^2)","A",1
1420,1,68,73,0.0391735,"\int \frac{(1-2 x)^3 (2+3 x)^5}{(3+5 x)^3} \, dx","Integrate[((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+1090320 (5 x+3)^2 \log (6 (5 x+3))+151973789}{19531250 (5 x+3)^2}","-\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 + 1090320*(3 + 5*x)^2*Log[6*(3 + 5*x)])/(19531250*(3 + 5*x)^2)","A",1
1421,1,63,66,0.0410549,"\int \frac{(1-2 x)^3 (2+3 x)^4}{(3+5 x)^3} \, dx","Integrate[((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+632940 (5 x+3)^2 \log (6 (5 x+3))+21586298}{3906250 (5 x+3)^2}","-\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 + 632940*(3 + 5*x)^2*Log[6*(3 + 5*x)])/(3906250*(3 + 5*x)^2)","A",1
1422,1,56,59,0.018183,"\int \frac{(1-2 x)^3 (2+3 x)^3}{(3+5 x)^3} \, dx","Integrate[((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-11814 (5 x+3)^2 \log (5 x+3)-7139}{31250 (5 x+3)^2}","-\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,"-1/31250*(-7139 + 70080*x + 416250*x^2 + 393250*x^3 - 348750*x^4 - 180000*x^5 + 337500*x^6 - 11814*(3 + 5*x)^2*Log[3 + 5*x])/(3 + 5*x)^2","A",1
1423,1,53,52,0.0469148,"\int \frac{(1-2 x)^3 (2+3 x)^2}{(3+5 x)^3} \, dx","Integrate[((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-3102 (5 x+3)^2 \log (6 (5 x+3))+54943}{6250 (5 x+3)^2}","-\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,"-1/6250*(54943 + 221340*x + 274500*x^2 + 53500*x^3 - 52500*x^4 + 30000*x^5 - 3102*(3 + 5*x)^2*Log[6*(3 + 5*x)])/(3 + 5*x)^2","A",1
1424,1,46,45,0.0286725,"\int \frac{(1-2 x)^3 (2+3 x)}{(3+5 x)^3} \, dx","Integrate[((1 - 2*x)^3*(2 + 3*x))/(3 + 5*x)^3,x]","-\frac{15000 x^4-61000 x^3-53650 x^2+47130 x+4092 (5 x+3)^2 \log (10 x+6)+33803}{6250 (5 x+3)^2}","-\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,"-1/6250*(33803 + 47130*x - 53650*x^2 - 61000*x^3 + 15000*x^4 + 4092*(3 + 5*x)^2*Log[6 + 10*x])/(3 + 5*x)^2","A",1
1425,1,37,38,0.025963,"\int \frac{(1-2 x)^3}{(3+5 x)^3} \, dx","Integrate[(1 - 2*x)^3/(3 + 5*x)^3,x]","\frac{\frac{5 \left(-400 x^3-280 x^2+1548 x+677\right)}{(5 x+3)^2}+264 \log (10 x+6)}{1250}","-\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,"((5*(677 + 1548*x - 280*x^2 - 400*x^3))/(3 + 5*x)^2 + 264*Log[6 + 10*x])/1250","A",1
1426,1,44,43,0.030136,"\int \frac{(1-2 x)^3}{(2+3 x) (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)*(3 + 5*x)^3),x]","\frac{11 \left(4290 x+2598 (5 x+3)^2 \log (-3 (5 x+3))+2453\right)}{250 (5 x+3)^2}-\frac{343}{3} \log (3 x+2)","\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,"(-343*Log[2 + 3*x])/3 + (11*(2453 + 4290*x + 2598*(3 + 5*x)^2*Log[-3*(3 + 5*x)]))/(250*(3 + 5*x)^2)","A",1
1427,1,48,50,0.035781,"\int \frac{(1-2 x)^3}{(2+3 x)^2 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{343}{9 x+6}+\frac{8712}{125 x+75}-\frac{1331}{50 (5 x+3)^2}-1617 \log (5 (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,"-1331/(50*(3 + 5*x)^2) + 343/(6 + 9*x) + 8712/(75 + 125*x) - 1617*Log[5*(2 + 3*x)] + 1617*Log[3 + 5*x]","A",1
1428,1,59,57,0.0496453,"\int \frac{(1-2 x)^3}{(2+3 x)^3 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)^3*(3 + 5*x)^3),x]","\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 (5 (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,"343/(6*(2 + 3*x)^2) + 1617/(2 + 3*x) - 1331/(10*(3 + 5*x)^2) + 2541/(3 + 5*x) - 15708*Log[5*(2 + 3*x)] + 15708*Log[3 + 5*x]","A",1
1429,1,70,68,0.040806,"\int \frac{(1-2 x)^3}{(2+3 x)^4 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)^4*(3 + 5*x)^3),x]","\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 (5 (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,"343/(9*(2 + 3*x)^3) + 1617/(2*(2 + 3*x)^2) + 15708/(2 + 3*x) - 1331/(2*(3 + 5*x)^2) + 16698/(3 + 5*x) - 128634*Log[5*(2 + 3*x)] + 128634*Log[3 + 5*x]","A",1
1430,1,77,75,0.0487072,"\int \frac{(1-2 x)^3}{(2+3 x)^5 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)^5*(3 + 5*x)^3),x]","\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 (5 (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,"343/(12*(2 + 3*x)^4) + 539/(2 + 3*x)^3 + 7854/(2 + 3*x)^2 + 128634/(2 + 3*x) - 6655/(2*(3 + 5*x)^2) + 103455/(3 + 5*x) - 953535*Log[5*(2 + 3*x)] + 953535*Log[3 + 5*x]","A",1
1431,1,88,86,0.1011266,"\int \frac{(1-2 x)^3}{(2+3 x)^6 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)^6*(3 + 5*x)^3),x]","\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 (5 (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,"343/(15*(2 + 3*x)^5) + 1617/(4*(2 + 3*x)^4) + 5236/(2 + 3*x)^3 + 64317/(2 + 3*x)^2 + 953535/(2 + 3*x) - 33275/(2*(3 + 5*x)^2) + 617100/(3 + 5*x) - 6618975*Log[5*(2 + 3*x)] + 6618975*Log[3 + 5*x]","A",1
1432,1,99,97,0.1595555,"\int \frac{(1-2 x)^3}{(2+3 x)^7 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)^7*(3 + 5*x)^3),x]","\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 (5 (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,"343/(18*(2 + 3*x)^6) + 1617/(5*(2 + 3*x)^5) + 3927/(2 + 3*x)^4 + 42878/(2 + 3*x)^3 + 953535/(2*(2 + 3*x)^2) + 6618975/(2 + 3*x) - 166375/(2*(3 + 5*x)^2) + 3584625/(3 + 5*x) - 43848750*Log[5*(2 + 3*x)] + 43848750*Log[3 + 5*x]","A",1
1433,1,112,110,0.1606626,"\int \frac{(1-2 x)^3}{(2+3 x)^8 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^3/((2 + 3*x)^8*(3 + 5*x)^3),x]","\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 (5 (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,"49/(3*(2 + 3*x)^7) + 539/(2*(2 + 3*x)^6) + 15708/(5*(2 + 3*x)^5) + 64317/(2*(2 + 3*x)^4) + 317845/(2 + 3*x)^3 + 6618975/(2*(2 + 3*x)^2) + 43848750/(2 + 3*x) - 831875/(2*(3 + 5*x)^2) + 20418750/(3 + 5*x) - 280500000*Log[5*(2 + 3*x)] + 280500000*Log[3 + 5*x]","A",1
1434,1,57,72,0.0194616,"\int \frac{(2+3 x)^8 (3+5 x)}{1-2 x} \, dx","Integrate[((2 + 3*x)^8*(3 + 5*x))/(1 - 2*x),x]","\frac{-74649600 x^9-540276480 x^8-1810252800 x^7-3750001920 x^6-5445667584 x^5-6035631840 x^4-5565161280 x^3-4826609520 x^2-5041567600 x-2536512440 \log (1-2 x)+5045478077}{40960}","-\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,"(5045478077 - 5041567600*x - 4826609520*x^2 - 5565161280*x^3 - 6035631840*x^4 - 5445667584*x^5 - 3750001920*x^6 - 1810252800*x^7 - 540276480*x^8 - 74649600*x^9 - 2536512440*Log[1 - 2*x])/40960","A",1
1435,1,52,65,0.0179866,"\int \frac{(2+3 x)^7 (3+5 x)}{1-2 x} \, dx","Integrate[((2 + 3*x)^7*(3 + 5*x))/(1 - 2*x),x]","\frac{-97977600 x^8-645719040 x^7-1961729280 x^6-3680619264 x^5-4874415840 x^4-5055946560 x^3-4683085680 x^2-5017974640 x-2536512440 \log (1-2 x)+4767501827}{143360}","-\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,"(4767501827 - 5017974640*x - 4683085680*x^2 - 5055946560*x^3 - 4874415840*x^4 - 3680619264*x^5 - 1961729280*x^6 - 645719040*x^7 - 97977600*x^8 - 2536512440*Log[1 - 2*x])/143360","A",1
1436,1,47,58,0.0164892,"\int \frac{(2+3 x)^6 (3+5 x)}{1-2 x} \, dx","Integrate[((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x),x]","\frac{-9331200 x^7-55520640 x^6-151756416 x^5-256934160 x^4-313215840 x^3-318777480 x^2-355477640 x-181179460 \log (1-2 x)+318326353}{35840}","-\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,"(318326353 - 355477640*x - 318777480*x^2 - 313215840*x^3 - 256934160*x^4 - 151756416*x^5 - 55520640*x^6 - 9331200*x^7 - 181179460*Log[1 - 2*x])/35840","A",1
1437,1,42,51,0.0212019,"\int \frac{(2+3 x)^5 (3+5 x)}{1-2 x} \, dx","Integrate[((2 + 3*x)^5*(3 + 5*x))/(1 - 2*x),x]","\frac{-259200 x^6-1378944 x^5-3367440 x^4-5163360 x^3-6022920 x^2-7149320 x-3697540 \log (1-2 x)+5983417}{2560}","-\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,"(5983417 - 7149320*x - 6022920*x^2 - 5163360*x^3 - 3367440*x^4 - 1378944*x^5 - 259200*x^6 - 3697540*Log[1 - 2*x])/2560","A",1
1438,1,37,44,0.0167858,"\int \frac{(2+3 x)^4 (3+5 x)}{1-2 x} \, dx","Integrate[((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x),x]","\frac{1}{256} \left(-10368 x^5-48816 x^4-106272 x^3-151896 x^2-199000 x-105644 \log (1-2 x)+154133\right)","-\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,"(154133 - 199000*x - 151896*x^2 - 106272*x^3 - 48816*x^4 - 10368*x^5 - 105644*Log[1 - 2*x])/256","A",1
1439,1,32,37,0.0176472,"\int \frac{(2+3 x)^3 (3+5 x)}{1-2 x} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x),x]","\frac{1}{128} \left(-2160 x^4-8928 x^3-17640 x^2-27112 x-15092 \log (1-2 x)+19217\right)","-\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,"(19217 - 27112*x - 17640*x^2 - 8928*x^3 - 2160*x^4 - 15092*Log[1 - 2*x])/128","A",1
1440,1,27,30,0.0108989,"\int \frac{(2+3 x)^2 (3+5 x)}{1-2 x} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x))/(1 - 2*x),x]","\frac{1}{32} \left(-240 x^3-876 x^2-1772 x-1078 \log (1-2 x)+1135\right)","-\frac{15 x^3}{2}-\frac{219 x^2}{8}-\frac{443 x}{8}-\frac{539}{16} \log (1-2 x)",1,"(1135 - 1772*x - 876*x^2 - 240*x^3 - 1078*Log[1 - 2*x])/32","A",1
1441,1,22,23,0.0059173,"\int \frac{(2+3 x) (3+5 x)}{1-2 x} \, dx","Integrate[((2 + 3*x)*(3 + 5*x))/(1 - 2*x),x]","\frac{1}{16} \left(-60 x^2-212 x-154 \log (1-2 x)+121\right)","-\frac{15 x^2}{4}-\frac{53 x}{4}-\frac{77}{8} \log (1-2 x)",1,"(121 - 212*x - 60*x^2 - 154*Log[1 - 2*x])/16","A",1
1442,1,17,16,0.0033237,"\int \frac{3+5 x}{1-2 x} \, dx","Integrate[(3 + 5*x)/(1 - 2*x),x]","\frac{1}{4} (-10 x-11 \log (1-2 x)+5)","-\frac{5 x}{2}-\frac{11}{4} \log (1-2 x)",1,"(5 - 10*x - 11*Log[1 - 2*x])/4","A",1
1443,1,21,21,0.0077033,"\int \frac{3+5 x}{(1-2 x) (2+3 x)} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)),x]","-\frac{11}{14} \log (1-2 x)-\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
1444,1,30,32,0.0207022,"\int \frac{3+5 x}{(1-2 x) (2+3 x)^2} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^2),x]","\frac{1}{147} \left(\frac{7}{3 x+2}-33 \log (3-6 x)+33 \log (3 x+2)\right)","\frac{1}{21 (3 x+2)}-\frac{11}{49} \log (1-2 x)+\frac{11}{49} \log (3 x+2)",1,"(7/(2 + 3*x) - 33*Log[3 - 6*x] + 33*Log[2 + 3*x])/147","A",1
1445,1,35,43,0.0342618,"\int \frac{3+5 x}{(1-2 x) (2+3 x)^3} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^3),x]","\frac{-\frac{7 (198 x+125)}{(3 x+2)^2}-132 \log (3-6 x)+132 \log (3 x+2)}{2058}","-\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,"((-7*(125 + 198*x))/(2 + 3*x)^2 - 132*Log[3 - 6*x] + 132*Log[2 + 3*x])/2058","A",1
1446,1,40,54,0.0362089,"\int \frac{3+5 x}{(1-2 x) (2+3 x)^4} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^4),x]","\frac{-\frac{7 \left(3564 x^2+6831 x+2872\right)}{(3 x+2)^3}-792 \log (3-6 x)+792 \log (3 x+2)}{43218}","-\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,"((-7*(2872 + 6831*x + 3564*x^2))/(2 + 3*x)^3 - 792*Log[3 - 6*x] + 792*Log[2 + 3*x])/43218","A",1
1447,1,45,65,0.0465323,"\int \frac{3+5 x}{(1-2 x) (2+3 x)^5} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^5),x]","\frac{-\frac{7 \left(4752 x^3+12276 x^2+12188 x+3963\right)}{(3 x+2)^4}-352 \log (3-6 x)+352 \log (3 x+2)}{67228}","-\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,"((-7*(3963 + 12188*x + 12276*x^2 + 4752*x^3))/(2 + 3*x)^4 - 352*Log[3 - 6*x] + 352*Log[2 + 3*x])/67228","A",1
1448,1,50,76,0.0505965,"\int \frac{3+5 x}{(1-2 x) (2+3 x)^6} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^6),x]","\frac{-\frac{7 \left(427680 x^4+1389960 x^3+1833480 x^2+1268025 x+348226\right)}{(3 x+2)^5}-10560 \log (3-6 x)+10560 \log (3 x+2)}{7058940}","-\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,"((-7*(348226 + 1268025*x + 1833480*x^2 + 1389960*x^3 + 427680*x^4))/(2 + 3*x)^5 - 10560*Log[3 - 6*x] + 10560*Log[2 + 3*x])/7058940","A",1
1449,1,55,87,0.0990787,"\int \frac{3+5 x}{(1-2 x) (2+3 x)^7} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^7),x]","\frac{-\frac{7 \left(3849120 x^5+15075720 x^4+24841080 x^3+22413105 x^2+12254814 x+3013741\right)}{(3 x+2)^6}-31680 \log (3-6 x)+31680 \log (3 x+2)}{74118870}","-\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,"((-7*(3013741 + 12254814*x + 22413105*x^2 + 24841080*x^3 + 15075720*x^4 + 3849120*x^5))/(2 + 3*x)^6 - 31680*Log[3 - 6*x] + 31680*Log[2 + 3*x])/74118870","A",1
1450,1,60,98,0.0663786,"\int \frac{3+5 x}{(1-2 x) (2+3 x)^8} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^8),x]","\frac{-\frac{7 \left(7698240 x^6+35283600 x^5+69783120 x^4+77947650 x^3+54393768 x^2+25308459 x+5811068\right)}{(3 x+2)^7}-21120 \log (3-6 x)+21120 \log (3 x+2)}{172944030}","-\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,"((-7*(5811068 + 25308459*x + 54393768*x^2 + 77947650*x^3 + 69783120*x^4 + 35283600*x^5 + 7698240*x^6))/(2 + 3*x)^7 - 21120*Log[3 - 6*x] + 21120*Log[2 + 3*x])/172944030","A",1
1451,1,62,79,0.0170938,"\int \frac{(2+3 x)^8 (3+5 x)^2}{1-2 x} \, dx","Integrate[((2 + 3*x)^8*(3 + 5*x)^2)/(1 - 2*x),x]","\frac{-671846400 x^{10}-5250355200 x^9-19081370880 x^8-43004390400 x^7-67880574720 x^6-80959060224 x^5-77952500640 x^4-65568364480 x^3-54167495120 x^2-55614530000 x-27901636840 \log (1-2 x)+58429239347}{81920}","-\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,"(58429239347 - 55614530000*x - 54167495120*x^2 - 65568364480*x^3 - 77952500640*x^4 - 80959060224*x^5 - 67880574720*x^6 - 43004390400*x^7 - 19081370880*x^8 - 5250355200*x^9 - 671846400*x^10 - 27901636840*Log[1 - 2*x])/81920","A",1
1452,1,75,72,0.0183842,"\int \frac{(2+3 x)^7 (3+5 x)^2}{1-2 x} \, dx","Integrate[((2 + 3*x)^7*(3 + 5*x)^2)/(1 - 2*x),x]","-\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}+\frac{55685576347}{286720}","-\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,"55685576347/286720 - (99058879*x)/512 - (94979263*x^2)/512 - (27480469*x^3)/128 - (59969727*x^4)/256 - (34084287*x^5)/160 - (4736853*x^6)/32 - (4040847*x^7)/56 - (696195*x^8)/32 - (6075*x^9)/2 - (99648703*Log[1 - 2*x])/1024","A",1
1453,1,52,65,0.0170794,"\int \frac{(2+3 x)^6 (3+5 x)^2}{1-2 x} \, dx","Integrate[((2 + 3*x)^6*(3 + 5*x)^2)/(1 - 2*x),x]","\frac{-163296000 x^8-1063756800 x^7-3195521280 x^6-5932023552 x^5-7781447520 x^4-8008956480 x^3-7380106160 x^2-7889320880 x-3985948120 \log (1-2 x)+7521401241}{143360}","-\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,"(7521401241 - 7889320880*x - 7380106160*x^2 - 8008956480*x^3 - 7781447520*x^4 - 5932023552*x^5 - 3195521280*x^6 - 1063756800*x^7 - 163296000*x^8 - 3985948120*Log[1 - 2*x])/143360","A",1
1454,1,47,58,0.0211436,"\int \frac{(2+3 x)^5 (3+5 x)^2}{1-2 x} \, dx","Integrate[((2 + 3*x)^5*(3 + 5*x)^2)/(1 - 2*x),x]","\frac{-15552000 x^7-91324800 x^6-246492288 x^5-412508880 x^4-497930720 x^3-503188840 x^2-559099240 x-284710580 \log (1-2 x)+502621309}{35840}","-\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,"(502621309 - 559099240*x - 503188840*x^2 - 497930720*x^3 - 412508880*x^4 - 246492288*x^5 - 91324800*x^6 - 15552000*x^7 - 284710580*Log[1 - 2*x])/35840","A",1
1455,1,42,51,0.0152147,"\int \frac{(2+3 x)^4 (3+5 x)^2}{1-2 x} \, dx","Integrate[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x),x]","\frac{1}{512} \left(-86400 x^6-452736 x^5-1089936 x^4-1650272 x^3-1906376 x^2-2250440 x-1162084 \log (1-2 x)+1891717\right)","-\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,"(1891717 - 2250440*x - 1906376*x^2 - 1650272*x^3 - 1089936*x^4 - 452736*x^5 - 86400*x^6 - 1162084*Log[1 - 2*x])/512","A",1
1456,1,37,44,0.0197744,"\int \frac{(2+3 x)^3 (3+5 x)^2}{1-2 x} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x)^2)/(1 - 2*x),x]","\frac{1}{256} \left(-17280 x^5-79920 x^4-171168 x^3-241400 x^2-313592 x-166012 \log (1-2 x)+244077\right)","-\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,"(244077 - 313592*x - 241400*x^2 - 171168*x^3 - 79920*x^4 - 17280*x^5 - 166012*Log[1 - 2*x])/256","A",1
1457,1,32,37,0.012239,"\int \frac{(2+3 x)^2 (3+5 x)^2}{1-2 x} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x),x]","\frac{1}{128} \left(-3600 x^4-14560 x^3-28232 x^2-42824 x-23716 \log (1-2 x)+30515\right)","-\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,"(30515 - 42824*x - 28232*x^2 - 14560*x^3 - 3600*x^4 - 23716*Log[1 - 2*x])/128","A",1
1458,1,27,30,0.010686,"\int \frac{(2+3 x) (3+5 x)^2}{1-2 x} \, dx","Integrate[((2 + 3*x)*(3 + 5*x)^2)/(1 - 2*x),x]","\frac{1}{32} \left(-400 x^3-1420 x^2-2812 x-1694 \log (1-2 x)+1811\right)","-\frac{25 x^3}{2}-\frac{355 x^2}{8}-\frac{703 x}{8}-\frac{847}{16} \log (1-2 x)",1,"(1811 - 2812*x - 1420*x^2 - 400*x^3 - 1694*Log[1 - 2*x])/32","A",1
1459,1,25,23,0.0082209,"\int \frac{(3+5 x)^2}{1-2 x} \, dx","Integrate[(3 + 5*x)^2/(1 - 2*x),x]","\frac{1}{16} \left(-5 \left(20 x^2+68 x-39\right)-242 \log (1-2 x)\right)","-\frac{25 x^2}{4}-\frac{85 x}{4}-\frac{121}{8} \log (1-2 x)",1,"(-5*(-39 + 68*x + 20*x^2) - 242*Log[1 - 2*x])/16","A",1
1460,1,32,26,0.0149165,"\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)),x]","-\frac{5}{6} (5 x+3)-\frac{121}{28} \log (5-10 x)+\frac{1}{63} \log (5 (3 x+2))","-\frac{25 x}{6}-\frac{121}{28} \log (1-2 x)+\frac{1}{63} \log (3 x+2)",1,"(-5*(3 + 5*x))/6 - (121*Log[5 - 10*x])/28 + Log[5*(2 + 3*x)]/63","A",1
1461,1,30,32,0.0319377,"\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^2),x]","\frac{1}{882} \left(-\frac{14}{3 x+2}-1089 \log (1-2 x)-136 \log (6 x+4)\right)","-\frac{1}{63 (3 x+2)}-\frac{121}{98} \log (1-2 x)-\frac{68}{441} \log (3 x+2)",1,"(-14/(2 + 3*x) - 1089*Log[1 - 2*x] - 136*Log[4 + 6*x])/882","A",1
1462,1,35,43,0.025066,"\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^3),x]","\frac{\frac{7 (408 x+265)}{(3 x+2)^2}-2178 \log (1-2 x)+2178 \log (6 x+4)}{6174}","\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,"((7*(265 + 408*x))/(2 + 3*x)^2 - 2178*Log[1 - 2*x] + 2178*Log[4 + 6*x])/6174","A",1
1463,1,40,54,0.0503143,"\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^4),x]","\frac{-\frac{7 \left(29403 x^2+37062 x+11689\right)}{(3 x+2)^3}-6534 \log (1-2 x)+6534 \log (6 x+4)}{64827}","-\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,"((-7*(11689 + 37062*x + 29403*x^2))/(2 + 3*x)^3 - 6534*Log[1 - 2*x] + 6534*Log[4 + 6*x])/64827","A",1
1464,1,47,65,0.051234,"\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^5} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^5),x]","\frac{2 \left(-\frac{7 \left(705672 x^3+1822986 x^2+1449768 x+366413\right)}{8 (3 x+2)^4}-6534 \log (1-2 x)+6534 \log (6 x+4)\right)}{453789}","-\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,"(2*((-7*(366413 + 1449768*x + 1822986*x^2 + 705672*x^3))/(8*(2 + 3*x)^4) - 6534*Log[1 - 2*x] + 6534*Log[4 + 6*x]))/453789","A",1
1465,1,52,76,0.0838815,"\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^6} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^6),x]","\frac{4 \left(-\frac{7 \left(1764180 x^4+5733585 x^3+7563105 x^2+4442775 x+953231\right)}{4 (3 x+2)^5}-10890 \log (1-2 x)+10890 \log (6 x+4)\right)}{5294205}","-\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,"(4*((-7*(953231 + 4442775*x + 7563105*x^2 + 5733585*x^3 + 1764180*x^4))/(4*(2 + 3*x)^5) - 10890*Log[1 - 2*x] + 10890*Log[4 + 6*x]))/5294205","A",1
1466,1,57,87,0.1042177,"\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^7} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^7),x]","\frac{4 \left(-\frac{7 \left(127020960 x^5+497498760 x^4+819755640 x^3+739632465 x^2+351466812 x+67099978\right)}{16 (3 x+2)^6}-65340 \log (1-2 x)+65340 \log (6 x+4)\right)}{111178305}","-\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,"(4*((-7*(67099978 + 351466812*x + 739632465*x^2 + 819755640*x^3 + 497498760*x^4 + 127020960*x^5))/(16*(2 + 3*x)^6) - 65340*Log[1 - 2*x] + 65340*Log[4 + 6*x]))/111178305","A",1
1467,1,62,98,0.1104145,"\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^8} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^8),x]","\frac{8 \left(-\frac{7 \left(381062880 x^6+1746538200 x^5+3454264440 x^4+3858408675 x^3+2692491516 x^2+1098354408 x+193528666\right)}{16 (3 x+2)^7}-65340 \log (1-2 x)+65340 \log (6 x+4)\right)}{778248135}","-\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,"(8*((-7*(193528666 + 1098354408*x + 2692491516*x^2 + 3858408675*x^3 + 3454264440*x^4 + 1746538200*x^5 + 381062880*x^6))/(16*(2 + 3*x)^7) - 65340*Log[1 - 2*x] + 65340*Log[4 + 6*x]))/778248135","A",1
1468,1,82,79,0.0214353,"\int \frac{(2+3 x)^7 (3+5 x)^3}{1-2 x} \, dx","Integrate[((2 + 3*x)^7*(3 + 5*x)^3)/(1 - 2*x),x]","-\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}+\frac{1933652224451}{1720320}","-\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,"1933652224451/1720320 - (1092596789*x)/1024 - (1065169973*x^2)/1024 - (969544757*x^3)/768 - (772025397*x^4)/512 - (504354357*x^5)/320 - (85228263*x^6)/64 - (95297877*x^7)/112 - (24381405*x^8)/64 - (423225*x^9)/4 - (54675*x^10)/4 - (1096135733*Log[1 - 2*x])/2048","A",1
1469,1,75,72,0.0167028,"\int \frac{(2+3 x)^6 (3+5 x)^3}{1-2 x} \, dx","Integrate[((2 + 3*x)^6*(3 + 5*x)^3)/(1 - 2*x),x]","-\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}+\frac{263385079253}{860160}","-\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,"263385079253/860160 - (155706083*x)/512 - (149512931*x^2)/512 - (130251491*x^3)/384 - (95317731*x^4)/256 - (54600291*x^5)/160 - (7656993*x^6)/32 - (6596235*x^7)/56 - (1148175*x^8)/32 - (10125*x^9)/2 - (156590819*Log[1 - 2*x])/1024","A",1
1470,1,68,65,0.0157799,"\int \frac{(2+3 x)^5 (3+5 x)^3}{1-2 x} \, dx","Integrate[((2 + 3*x)^5*(3 + 5*x)^3)/(1 - 2*x),x]","-\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)+\frac{35596520969}{430080}","-\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,"35596520969/430080 - (22148933*x)/256 - (20766533*x^2)/256 - (16987973*x^3)/192 - (11088453*x^4)/128 - (5333733*x^5)/80 - (580815*x^6)/16 - (342225*x^7)/28 - (30375*x^8)/16 - (22370117*Log[1 - 2*x])/512","A",1
1471,1,47,58,0.0160866,"\int \frac{(2+3 x)^4 (3+5 x)^3}{1-2 x} \, dx","Integrate[((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x),x]","\frac{-15552000 x^7-90115200 x^6-240153984 x^5-397249776 x^4-474826912 x^3-476499576 x^2-527593080 x-268441404 \log (1-2 x)+476137271}{21504}","-\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,"(476137271 - 527593080*x - 476499576*x^2 - 474826912*x^3 - 397249776*x^4 - 240153984*x^5 - 90115200*x^6 - 15552000*x^7 - 268441404*Log[1 - 2*x])/21504","A",1
1472,1,42,51,0.0124682,"\int \frac{(2+3 x)^3 (3+5 x)^3}{1-2 x} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x)^3)/(1 - 2*x),x]","\frac{-432000 x^6-2229120 x^5-5289840 x^4-7909024 x^3-9049080 x^2-10625016 x-5478396 \log (1-2 x)+8970431}{1536}","-\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,"(8970431 - 10625016*x - 9049080*x^2 - 7909024*x^3 - 5289840*x^4 - 2229120*x^5 - 432000*x^6 - 5478396*Log[1 - 2*x])/1536","A",1
1473,1,37,44,0.01343,"\int \frac{(2+3 x)^2 (3+5 x)^3}{1-2 x} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x)^3)/(1 - 2*x),x]","\frac{1}{768} \left(-86400 x^5-392400 x^4-826720 x^3-1150536 x^2-1482312 x-782628 \log (1-2 x)+1159355\right)","-\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,"(1159355 - 1482312*x - 1150536*x^2 - 826720*x^3 - 392400*x^4 - 86400*x^5 - 782628*Log[1 - 2*x])/768","A",1
1474,1,32,37,0.0160072,"\int \frac{(2+3 x) (3+5 x)^3}{1-2 x} \, dx","Integrate[((2 + 3*x)*(3 + 5*x)^3)/(1 - 2*x),x]","\frac{1}{384} \left(-18000 x^4-71200 x^3-135480 x^2-202872 x-111804 \log (1-2 x)+145331\right)","-\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,"(145331 - 202872*x - 135480*x^2 - 71200*x^3 - 18000*x^4 - 111804*Log[1 - 2*x])/384","A",1
1475,1,30,30,0.012786,"\int \frac{(3+5 x)^3}{1-2 x} \, dx","Integrate[(3 + 5*x)^3/(1 - 2*x),x]","\frac{1}{96} \left(-5 \left(400 x^3+1380 x^2+2676 x-1733\right)-7986 \log (1-2 x)\right)","-\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) - 7986*Log[1 - 2*x])/96","A",1
1476,1,35,33,0.0182576,"\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)),x]","\frac{-1050 \left(15 x^2+49 x+24\right)-35937 \log (5-10 x)-8 \log (5 (3 x+2))}{1512}","-\frac{125 x^2}{12}-\frac{1225 x}{36}-\frac{1331}{56} \log (1-2 x)-\frac{1}{189} \log (3 x+2)",1,"(-1050*(24 + 49*x + 15*x^2) - 35937*Log[5 - 10*x] - 8*Log[5*(2 + 3*x)])/1512","A",1
1477,1,37,37,0.0341021,"\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^2),x]","\frac{18375 (1-2 x)+\frac{28}{3 x+2}-35937 \log (1-2 x)+412 \log (6 x+4)}{5292}","-\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,"(18375*(1 - 2*x) + 28/(2 + 3*x) - 35937*Log[1 - 2*x] + 412*Log[4 + 6*x])/5292","A",1
1478,1,35,43,0.0353836,"\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^3),x]","\frac{-\frac{21 (206 x+135)}{(3 x+2)^2}-35937 \log (1-2 x)-6938 \log (6 x+4)}{18522}","-\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,"((-21*(135 + 206*x))/(2 + 3*x)^2 - 35937*Log[1 - 2*x] - 6938*Log[4 + 6*x])/18522","A",1
1479,1,40,54,0.0369128,"\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^4),x]","\frac{\frac{7 \left(187326 x^2+243279 x+79028\right)}{(3 x+2)^3}-215622 \log (1-2 x)+215622 \log (6 x+4)}{388962}","\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,"((7*(79028 + 243279*x + 187326*x^2))/(2 + 3*x)^3 - 215622*Log[1 - 2*x] + 215622*Log[4 + 6*x])/388962","A",1
1480,1,47,65,0.0581762,"\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^5} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^5),x]","\frac{2 \left(-\frac{7 \left(11643588 x^3+21975894 x^2+13836972 x+2906507\right)}{8 (3 x+2)^4}-107811 \log (1-2 x)+107811 \log (6 x+4)\right)}{1361367}","-\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,"(2*((-7*(2906507 + 13836972*x + 21975894*x^2 + 11643588*x^3))/(8*(2 + 3*x)^4) - 107811*Log[1 - 2*x] + 107811*Log[4 + 6*x]))/1361367","A",1
1481,1,52,76,0.0821257,"\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^6} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^6),x]","\frac{2 \left(-\frac{7 \left(349307640 x^4+1135249830 x^3+1308416040 x^2+646472325 x+116805778\right)}{8 (3 x+2)^5}-1078110 \log (1-2 x)+1078110 \log (6 x+4)\right)}{47647845}","-\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,"(2*((-7*(116805778 + 646472325*x + 1308416040*x^2 + 1135249830*x^3 + 349307640*x^4))/(8*(2 + 3*x)^5) - 1078110*Log[1 - 2*x] + 1078110*Log[4 + 6*x]))/47647845","A",1
1482,1,57,87,0.0833737,"\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^7} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^7),x]","\frac{4 \left(-\frac{7 \left(2095845840 x^5+8208729540 x^4+13525968060 x^3+11211272235 x^2+4581535248 x+733614062\right)}{16 (3 x+2)^6}-1078110 \log (1-2 x)+1078110 \log (6 x+4)\right)}{333534915}","-\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,"(4*((-7*(733614062 + 4581535248*x + 11211272235*x^2 + 13525968060*x^3 + 8208729540*x^4 + 2095845840*x^5))/(16*(2 + 3*x)^6) - 1078110*Log[1 - 2*x] + 1078110*Log[4 + 6*x]))/333534915","A",1
1483,1,62,98,0.1110926,"\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^8} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^8),x]","\frac{4 \left(-\frac{7 \left(12575075040 x^6+57635760600 x^5+113990726520 x^4+127327486275 x^3+83293304778 x^2+29451465714 x+4309941128\right)}{16 (3 x+2)^7}-2156220 \log (1-2 x)+2156220 \log (6 x+4)\right)}{2334744405}","-\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,"(4*((-7*(4309941128 + 29451465714*x + 83293304778*x^2 + 127327486275*x^3 + 113990726520*x^4 + 57635760600*x^5 + 12575075040*x^6))/(16*(2 + 3*x)^7) - 2156220*Log[1 - 2*x] + 2156220*Log[4 + 6*x]))/2334744405","A",1
1484,1,99,104,0.0996733,"\int \frac{(a+b x)^3}{(c+d x) (e+f x)} \, dx","Integrate[(a + b*x)^3/((c + d*x)*(e + f*x)),x]","\frac{b^2 d f x (d e-c f) (6 a d f+b (-2 c f-2 d e+d f x))-2 f^3 (b c-a d)^3 \log (c+d x)+2 d^3 (b e-a f)^3 \log (e+f x)}{2 d^3 f^3 (d e-c f)}","-\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*d*f*(d*e - c*f)*x*(6*a*d*f + b*(-2*d*e - 2*c*f + d*f*x)) - 2*(b*c - a*d)^3*f^3*Log[c + d*x] + 2*d^3*(b*e - a*f)^3*Log[e + f*x])/(2*d^3*f^3*(d*e - c*f))","A",1
1485,1,62,68,0.0411662,"\int \frac{(2+3 x)^8}{(1-2 x) (3+5 x)} \, dx","Integrate[(2 + 3*x)^8/((1 - 2*x)*(3 + 5*x)),x]","-\frac{3 \left(2187000000 x^7+13352850000 x^6+37418598000 x^5+64835457750 x^4+80624571300 x^3+83255588955 x^2+93542996379 x+40324556806\right)}{70000000}-\frac{5764801 \log (3-6 x)}{2816}+\frac{\log (-3 (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,"(-3*(40324556806 + 93542996379*x + 83255588955*x^2 + 80624571300*x^3 + 64835457750*x^4 + 37418598000*x^5 + 13352850000*x^6 + 2187000000*x^7))/70000000 - (5764801*Log[3 - 6*x])/2816 + Log[-3*(3 + 5*x)]/4296875","A",1
1486,1,58,61,0.0325107,"\int \frac{(2+3 x)^7}{(1-2 x) (3+5 x)} \, dx","Integrate[(2 + 3*x)^7/((1 - 2*x)*(3 + 5*x)),x]","\frac{64 \log (-3 (5 x+3))-165 \left(12150000 x^6+66582000 x^5+167244750 x^4+262991700 x^3+312898095 x^2+375712911 x+163998254\right)}{55000000}-\frac{823543 \log (3-6 x)}{1408}","-\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,"(-823543*Log[3 - 6*x])/1408 + (-165*(163998254 + 375712911*x + 312898095*x^2 + 262991700*x^3 + 167244750*x^4 + 66582000*x^5 + 12150000*x^6) + 64*Log[-3*(3 + 5*x)])/55000000","A",1
1487,1,50,54,0.0306692,"\int \frac{(2+3 x)^6}{(1-2 x) (3+5 x)} \, dx","Integrate[(2 + 3*x)^6/((1 - 2*x)*(3 + 5*x)),x]","\frac{-2970 \left(54000 x^5+263250 x^4+591900 x^3+869165 x^2+1158877 x+516778\right)-1838265625 \log (3-6 x)+64 \log (-3 (5 x+3))}{11000000}","-\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,"(-2970*(516778 + 1158877*x + 869165*x^2 + 591900*x^3 + 263250*x^4 + 54000*x^5) - 1838265625*Log[3 - 6*x] + 64*Log[-3*(3 + 5*x)])/11000000","A",1
1488,1,45,47,0.0265588,"\int \frac{(2+3 x)^5}{(1-2 x) (3+5 x)} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)*(3 + 5*x)),x]","\frac{-110 \left(60750 x^4+261900 x^3+537165 x^2+848277 x+392378\right)-52521875 \log (3-6 x)+32 \log (-3 (5 x+3))}{1100000}","-\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,"(-110*(392378 + 848277*x + 537165*x^2 + 261900*x^3 + 60750*x^4) - 52521875*Log[3 - 6*x] + 32*Log[-3*(3 + 5*x)])/1100000","A",1
1489,1,43,40,0.0242499,"\int \frac{(2+3 x)^4}{(1-2 x) (3+5 x)} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)*(3 + 5*x)),x]","\frac{8 \log (-3 (5 x+3))-55 \left(2700 x^3+10395 x^2+21951 x+10814\right)}{55000}-\frac{2401}{176} \log (3-6 x)","-\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,"(-2401*Log[3 - 6*x])/176 + (-55*(10814 + 21951*x + 10395*x^2 + 2700*x^3) + 8*Log[-3*(3 + 5*x)])/55000","A",1
1490,1,35,33,0.0156576,"\int \frac{(2+3 x)^3}{(1-2 x) (3+5 x)} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)*(3 + 5*x)),x]","\frac{-330 \left(45 x^2+171 x+94\right)-42875 \log (3-6 x)+8 \log (-3 (5 x+3))}{11000}","-\frac{27 x^2}{20}-\frac{513 x}{100}-\frac{343}{88} \log (1-2 x)+\frac{\log (5 x+3)}{1375}",1,"(-330*(94 + 171*x + 45*x^2) - 42875*Log[3 - 6*x] + 8*Log[-3*(3 + 5*x)])/11000","A",1
1491,1,31,26,0.0206443,"\int \frac{(2+3 x)^2}{(1-2 x) (3+5 x)} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)*(3 + 5*x)),x]","-\frac{9 x}{10}-\frac{49}{44} \log (3-6 x)+\frac{1}{275} \log (-3 (5 x+3))-\frac{3}{5}","-\frac{9 x}{10}-\frac{49}{44} \log (1-2 x)+\frac{1}{275} \log (5 x+3)",1,"-3/5 - (9*x)/10 - (49*Log[3 - 6*x])/44 + Log[-3*(3 + 5*x)]/275","A",1
1492,1,21,21,0.0059242,"\int \frac{2+3 x}{(1-2 x) (3+5 x)} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)*(3 + 5*x)),x]","\frac{1}{55} \log (5 x+3)-\frac{7}{22} \log (1-2 x)","\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
1493,1,21,21,0.003865,"\int \frac{1}{(1-2 x) (3+5 x)} \, dx","Integrate[1/((1 - 2*x)*(3 + 5*x)),x]","\frac{1}{11} \log (5 x+3)-\frac{1}{11} \log (1-2 x)","\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
1494,1,31,31,0.0076513,"\int \frac{1}{(1-2 x) (2+3 x) (3+5 x)} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)*(3 + 5*x)),x]","-\frac{2}{77} \log (1-2 x)-\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
1495,1,38,42,0.0301806,"\int \frac{1}{(1-2 x) (2+3 x)^2 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)),x]","\frac{1}{539} \left(\frac{231}{3 x+2}-4 \log (1-2 x)-1221 \log (6 x+4)+1225 \log (10 x+6)\right)","\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,"(231/(2 + 3*x) - 4*Log[1 - 2*x] - 1221*Log[4 + 6*x] + 1225*Log[6 + 10*x])/539","A",1
1496,1,49,53,0.0331048,"\int \frac{1}{(1-2 x) (2+3 x)^3 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)),x]","\frac{\frac{8547}{3 x+2}+\frac{1617}{2 (3 x+2)^2}-8 \log (1-2 x)-42867 \log (6 x+4)+42875 \log (10 x+6)}{3773}","\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,"(1617/(2*(2 + 3*x)^2) + 8547/(2 + 3*x) - 8*Log[1 - 2*x] - 42867*Log[4 + 6*x] + 42875*Log[6 + 10*x])/3773","A",1
1497,1,50,64,0.0770447,"\int \frac{1}{(1-2 x) (2+3 x)^4 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)),x]","\frac{\frac{77 \left(70146 x^2+95859 x+32828\right)}{2 (3 x+2)^3}-16 \log (1-2 x)-1500609 \log (6 x+4)+1500625 \log (10 x+6)}{26411}","\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,"((77*(32828 + 95859*x + 70146*x^2))/(2*(2 + 3*x)^3) - 16*Log[1 - 2*x] - 1500609*Log[4 + 6*x] + 1500625*Log[6 + 10*x])/26411","A",1
1498,1,55,75,0.1002376,"\int \frac{1}{(1-2 x) (2+3 x)^5 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)),x]","\frac{\frac{77 \left(14733252 x^3+29957526 x^2+20320788 x+4599173\right)}{4 (3 x+2)^4}-32 \log (1-2 x)-52521843 \log (6 x+4)+52521875 \log (10 x+6)}{184877}","\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,"((77*(4599173 + 20320788*x + 29957526*x^2 + 14733252*x^3))/(4*(2 + 3*x)^4) - 32*Log[1 - 2*x] - 52521843*Log[4 + 6*x] + 52521875*Log[6 + 10*x])/184877","A",1
1499,1,60,86,0.1093803,"\int \frac{1}{(1-2 x) (2+3 x)^6 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)),x]","\frac{\frac{2079 \left(286482780 x^4+773503410 x^3+783477080 x^2+352854525 x+59622386\right)}{4 (3 x+2)^5}-320 \log (1-2 x)-9191327805 \log (6 x+4)+9191328125 \log (10 x+6)}{6470695}","\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,"((2079*(59622386 + 352854525*x + 783477080*x^2 + 773503410*x^3 + 286482780*x^4))/(4*(2 + 3*x)^5) - 320*Log[1 - 2*x] - 9191327805*Log[4 + 6*x] + 9191328125*Log[6 + 10*x])/6470695","A",1
1500,1,97,97,0.0619669,"\int \frac{1}{(1-2 x) (2+3 x)^7 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)^7*(3 + 5*x)),x]","\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 (6 x+4)}{823543}+\frac{78125}{11} \log (10 x+6)","\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,"1/(14*(2 + 3*x)^6) + 111/(245*(2 + 3*x)^5) + 3897/(1372*(2 + 3*x)^4) + 45473/(2401*(2 + 3*x)^3) + 4774713/(33614*(2 + 3*x)^2) + 167115051/(117649*(2 + 3*x)) - (128*Log[1 - 2*x])/9058973 - (5849026977*Log[4 + 6*x])/823543 + (78125*Log[6 + 10*x])/11","A",1
1501,1,64,72,0.0726523,"\int \frac{(2+3 x)^8}{(1-2 x) (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^8/((1 - 2*x)*(3 + 5*x)^2),x]","\frac{22 \left(-6014250000 x^6-33439230000 x^5-85171803750 x^4-135631138500 x^3-162997423875 x^2-196893724995 x-\frac{64}{5 x+3}-86057647830\right)-2251875390625 \log (3-6 x)+34048 \log (-3 (5 x+3))}{6050000000}","-\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,"(22*(-86057647830 - 196893724995*x - 162997423875*x^2 - 135631138500*x^3 - 85171803750*x^4 - 33439230000*x^5 - 6014250000*x^6 - 64/(3 + 5*x)) - 2251875390625*Log[3 - 6*x] + 34048*Log[-3*(3 + 5*x)])/6050000000","A",1
1502,1,60,65,0.0366475,"\int \frac{(2+3 x)^7}{(1-2 x) (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^7/((1 - 2*x)*(3 + 5*x)^2),x]","\frac{-\frac{11 \left(9622800000 x^6+53486730000 x^5+137632770000 x^4+227660301000 x^3+315671083200 x^2-35641061775 x-99978641969\right)}{5 x+3}-257357187500 \log (1-2 x)+59648 \log (10 x+6)}{2420000000}","-\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,"((-11*(-99978641969 - 35641061775*x + 315671083200*x^2 + 227660301000*x^3 + 137632770000*x^4 + 53486730000*x^5 + 9622800000*x^6))/(3 + 5*x) - 257357187500*Log[1 - 2*x] + 59648*Log[6 + 10*x])/2420000000","A",1
1503,1,54,58,0.0451517,"\int \frac{(2+3 x)^6}{(1-2 x) (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^6/((1 - 2*x)*(3 + 5*x)^2),x]","\frac{-80190000 x^4-352836000 x^3-737213400 x^2-1180479960 x-\frac{128}{5 x+3}+823659705}{22000000}-\frac{117649 \log (1-2 x)}{3872}+\frac{8 \log (10 x+6)}{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,"(823659705 - 1180479960*x - 737213400*x^2 - 352836000*x^3 - 80190000*x^4 - 128/(3 + 5*x))/22000000 - (117649*Log[1 - 2*x])/3872 + (8*Log[6 + 10*x])/75625","A",1
1504,1,50,51,0.0353597,"\int \frac{(2+3 x)^5}{(1-2 x) (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)*(3 + 5*x)^2),x]","\frac{-\frac{11 \left(8910000 x^4+40540500 x^3+97059600 x^2-2318085 x-28730263\right)}{5 x+3}-105043750 \log (1-2 x)+5344 \log (10 x+6)}{12100000}","-\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,"((-11*(-28730263 - 2318085*x + 97059600*x^2 + 40540500*x^3 + 8910000*x^4))/(3 + 5*x) - 105043750*Log[1 - 2*x] + 5344*Log[6 + 10*x])/12100000","A",1
1505,1,52,44,0.0403854,"\int \frac{(2+3 x)^4}{(1-2 x) (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)*(3 + 5*x)^2),x]","-\frac{81}{400} (1-2 x)^2+\frac{999}{500} (1-2 x)-\frac{1}{6875 (5 x+3)}-\frac{2401}{968} \log (1-2 x)+\frac{134 \log (10 x+6)}{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,"(999*(1 - 2*x))/500 - (81*(1 - 2*x)^2)/400 - 1/(6875*(3 + 5*x)) - (2401*Log[1 - 2*x])/968 + (134*Log[6 + 10*x])/75625","A",1
1506,1,37,37,0.0343059,"\int \frac{(2+3 x)^3}{(1-2 x) (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)*(3 + 5*x)^2),x]","\frac{16335 (1-2 x)-\frac{44}{5 x+3}-42875 \log (1-2 x)+404 \log (10 x+6)}{60500}","-\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,"(16335*(1 - 2*x) - 44/(3 + 5*x) - 42875*Log[1 - 2*x] + 404*Log[6 + 10*x])/60500","A",1
1507,1,30,32,0.0200462,"\int \frac{(2+3 x)^2}{(1-2 x) (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)*(3 + 5*x)^2),x]","\frac{-\frac{22}{5 x+3}-1225 \log (1-2 x)+136 \log (10 x+6)}{6050}","-\frac{1}{275 (5 x+3)}-\frac{49}{242} \log (1-2 x)+\frac{68 \log (5 x+3)}{3025}",1,"(-22/(3 + 5*x) - 1225*Log[1 - 2*x] + 136*Log[6 + 10*x])/6050","A",1
1508,1,30,32,0.0239051,"\int \frac{2+3 x}{(1-2 x) (3+5 x)^2} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)*(3 + 5*x)^2),x]","\frac{1}{605} \left(-\frac{11}{5 x+3}-35 \log (5-10 x)+35 \log (5 x+3)\right)","-\frac{1}{55 (5 x+3)}-\frac{7}{121} \log (1-2 x)+\frac{7}{121} \log (5 x+3)",1,"(-11/(3 + 5*x) - 35*Log[5 - 10*x] + 35*Log[3 + 5*x])/605","A",1
1509,1,30,32,0.0136554,"\int \frac{1}{(1-2 x) (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)*(3 + 5*x)^2),x]","\frac{1}{121} \left(-\frac{11}{5 x+3}-2 \log (5-10 x)+2 \log (5 x+3)\right)","-\frac{1}{11 (5 x+3)}-\frac{2}{121} \log (1-2 x)+\frac{2}{121} \log (5 x+3)",1,"(-11/(3 + 5*x) - 2*Log[5 - 10*x] + 2*Log[3 + 5*x])/121","A",1
1510,1,38,42,0.0306294,"\int \frac{1}{(1-2 x) (2+3 x) (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)*(3 + 5*x)^2),x]","\frac{1}{847} \left(-\frac{385}{5 x+3}-4 \log (1-2 x)+1089 \log (6 x+4)-1085 \log (10 x+6)\right)","-\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,"(-385/(3 + 5*x) - 4*Log[1 - 2*x] + 1089*Log[4 + 6*x] - 1085*Log[6 + 10*x])/847","A",1
1511,1,47,53,0.0381669,"\int \frac{1}{(1-2 x) (2+3 x)^2 (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{2 \left(-\frac{7623}{6 x+4}-\frac{13475}{10 x+6}-4 \log (1-2 x)+39204 \log (6 x+4)-39200 \log (10 x+6)\right)}{5929}","-\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,"(2*(-7623/(4 + 6*x) - 13475/(6 + 10*x) - 4*Log[1 - 2*x] + 39204*Log[4 + 6*x] - 39200*Log[6 + 10*x]))/5929","A",1
1512,1,60,64,0.0411227,"\int \frac{1}{(1-2 x) (2+3 x)^3 (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^2),x]","-\frac{125}{55 x+33}-\frac{648}{147 x+98}-\frac{9}{14 (3 x+2)^2}-\frac{16 \log (1-2 x)}{41503}+\frac{34371}{343} \log (6 x+4)-\frac{12125}{121} \log (10 x+6)","-\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,"-9/(14*(2 + 3*x)^2) - 125/(33 + 55*x) - 648/(98 + 147*x) - (16*Log[1 - 2*x])/41503 + (34371*Log[4 + 6*x])/343 - (12125*Log[6 + 10*x])/121","A",1
1513,1,62,75,0.1159204,"\int \frac{1}{(1-2 x) (2+3 x)^4 (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^2),x]","\frac{2 \left(-\frac{77 \left(22801770 x^3+44843517 x^2+29372133 x+6406511\right)}{2 (3 x+2)^3 (5 x+3)}-16 \log (1-2 x)+97540641 \log (6 x+4)-97540625 \log (10 x+6)\right)}{290521}","-\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,"(2*((-77*(6406511 + 29372133*x + 44843517*x^2 + 22801770*x^3))/(2*(2 + 3*x)^3*(3 + 5*x)) - 16*Log[1 - 2*x] + 97540641*Log[4 + 6*x] - 97540625*Log[6 + 10*x]))/290521","A",1
1514,1,84,86,0.0554549,"\int \frac{1}{(1-2 x) (2+3 x)^5 (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)^2),x]","-\frac{1612242}{2401 (3 x+2)}-\frac{3125}{55 x+33}-\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 (6 x+4)}{16807}-\frac{509375}{121} \log (10 x+6)","-\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,"-9/(28*(2 + 3*x)^4) - 216/(49*(2 + 3*x)^3) - 34371/(686*(2 + 3*x)^2) - 1612242/(2401*(2 + 3*x)) - 3125/(33 + 55*x) - (64*Log[1 - 2*x])/2033647 + (70752609*Log[4 + 6*x])/16807 - (509375*Log[6 + 10*x])/121","A",1
1515,1,95,97,0.0661878,"\int \frac{1}{(1-2 x) (2+3 x)^6 (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)^2),x]","-\frac{70752609}{16807 (3 x+2)}-\frac{15625}{55 x+33}-\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 (6 x+4)}{117649}-\frac{3062500}{121} \log (10 x+6)","-\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,"-9/(35*(2 + 3*x)^5) - 162/(49*(2 + 3*x)^4) - 11457/(343*(2 + 3*x)^3) - 806121/(2401*(2 + 3*x)^2) - 70752609/(16807*(2 + 3*x)) - 15625/(33 + 55*x) - (128*Log[1 - 2*x])/14235529 + (2977686468*Log[4 + 6*x])/117649 - (3062500*Log[6 + 10*x])/121","A",1
1516,1,68,76,0.0951389,"\int \frac{(2+3 x)^8}{(1-2 x) (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^8/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{22 \left(-7938810000 x^5-40024833750 x^4-92898778500 x^3-140182477875 x^2-190375359075 x-\frac{8512}{5 x+3}-\frac{176}{(5 x+3)^2}-85278446550\right)-2251875390625 \log (3-6 x)+1985536 \log (-3 (5 x+3))}{33275000000}","-\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,"(22*(-85278446550 - 190375359075*x - 140182477875*x^2 - 92898778500*x^3 - 40024833750*x^4 - 7938810000*x^5 - 176/(3 + 5*x)^2 - 8512/(3 + 5*x)) - 2251875390625*Log[3 - 6*x] + 1985536*Log[-3*(3 + 5*x)])/33275000000","A",1
1517,1,60,69,0.0486688,"\int \frac{(2+3 x)^7}{(1-2 x) (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^7/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{-\frac{11 \left(66156750000 x^6+376358400000 x^5+1012198275000 x^4+1891740015000 x^3+746752646475 x^2-485450731630 x-256487424349\right)}{(5 x+3)^2}-257357187500 \log (1-2 x)+2986880 \log (10 x+6)}{13310000000}","-\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,"((-11*(-256487424349 - 485450731630*x + 746752646475*x^2 + 1891740015000*x^3 + 1012198275000*x^4 + 376358400000*x^5 + 66156750000*x^6))/(3 + 5*x)^2 - 257357187500*Log[1 - 2*x] + 2986880*Log[6 + 10*x])/13310000000","A",1
1518,1,56,62,0.0570279,"\int \frac{(2+3 x)^6}{(1-2 x) (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^6/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{11 \left(-58806000 x^3-238164300 x^2-525137580 x-\frac{6400}{5 x+3}-\frac{176}{(5 x+3)^2}+329460615\right)-3676531250 \log (1-2 x)+535520 \log (10 x+6)}{665500000}","-\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,"(11*(329460615 - 525137580*x - 238164300*x^2 - 58806000*x^3 - 176/(3 + 5*x)^2 - 6400/(3 + 5*x)) - 3676531250*Log[1 - 2*x] + 535520*Log[6 + 10*x])/665500000","A",1
1519,1,50,55,0.0328934,"\int \frac{(2+3 x)^5}{(1-2 x) (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{-\frac{11 \left(73507500 x^4+387139500 x^3+217337175 x^2-93782210 x-60415061\right)}{(5 x+3)^2}-105043750 \log (1-2 x)+179584 \log (10 x+6)}{66550000}","-\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,"((-11*(-60415061 - 93782210*x + 217337175*x^2 + 387139500*x^3 + 73507500*x^4))/(3 + 5*x)^2 - 105043750*Log[1 - 2*x] + 179584*Log[6 + 10*x])/66550000","A",1
1520,1,45,48,0.042376,"\int \frac{(2+3 x)^4}{(1-2 x) (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{-\frac{55 \left(490050 x^3+343035 x^2-117076 x-87883\right)}{(5 x+3)^2}-1500625 \log (1-2 x)+27208 \log (10 x+6)}{3327500}","-\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,"((-55*(-87883 - 117076*x + 343035*x^2 + 490050*x^3))/(3 + 5*x)^2 - 1500625*Log[1 - 2*x] + 27208*Log[6 + 10*x])/3327500","A",1
1521,1,35,43,0.0318455,"\int \frac{(2+3 x)^3}{(1-2 x) (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{-\frac{11 (1010 x+617)}{(5 x+3)^2}-42875 \log (1-2 x)+6938 \log (10 x+6)}{332750}","-\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,"((-11*(617 + 1010*x))/(3 + 5*x)^2 - 42875*Log[1 - 2*x] + 6938*Log[6 + 10*x])/332750","A",1
1522,1,35,43,0.0265477,"\int \frac{(2+3 x)^2}{(1-2 x) (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{-\frac{11 (680 x+419)}{(5 x+3)^2}-2450 \log (1-2 x)+2450 \log (10 x+6)}{66550}","-\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,"((-11*(419 + 680*x))/(3 + 5*x)^2 - 2450*Log[1 - 2*x] + 2450*Log[6 + 10*x])/66550","A",1
1523,1,35,43,0.0263087,"\int \frac{2+3 x}{(1-2 x) (3+5 x)^3} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{-\frac{11 (350 x+221)}{(5 x+3)^2}-140 \log (5-10 x)+140 \log (5 x+3)}{13310}","-\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,"((-11*(221 + 350*x))/(3 + 5*x)^2 - 140*Log[5 - 10*x] + 140*Log[3 + 5*x])/13310","A",1
1524,1,35,43,0.0288535,"\int \frac{1}{(1-2 x) (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{-\frac{11 (20 x+23)}{(5 x+3)^2}-8 \log (5-10 x)+8 \log (5 x+3)}{2662}","-\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,"((-11*(23 + 20*x))/(3 + 5*x)^2 - 8*Log[5 - 10*x] + 8*Log[3 + 5*x])/2662","A",1
1525,1,43,53,0.0484185,"\int \frac{1}{(1-2 x) (2+3 x) (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)*(3 + 5*x)^3),x]","\frac{\frac{1925 (62 x+35)}{(5 x+3)^2}-16 \log (1-2 x)-71874 \log (6 x+4)+71890 \log (10 x+6)}{18634}","\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,"((1925*(35 + 62*x))/(3 + 5*x)^2 - 16*Log[1 - 2*x] - 71874*Log[4 + 6*x] + 71890*Log[6 + 10*x])/18634","A",1
1526,1,60,64,0.033311,"\int \frac{1}{(1-2 x) (2+3 x)^2 (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{27}{21 x+14}+\frac{1600}{605 x+363}-\frac{25}{22 (5 x+3)^2}-\frac{16 \log (1-2 x)}{65219}-\frac{2889}{49} \log (6 x+4)+\frac{78475 \log (10 x+6)}{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,"-25/(22*(3 + 5*x)^2) + 27/(14 + 21*x) + 1600/(363 + 605*x) - (16*Log[1 - 2*x])/65219 - (2889*Log[4 + 6*x])/49 + (78475*Log[6 + 10*x])/1331","A",1
1527,1,71,75,0.0437976,"\int \frac{1}{(1-2 x) (2+3 x)^3 (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{2889}{147 x+98}+\frac{12125}{605 x+363}+\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 (6 x+4)+\frac{792500 \log (10 x+6)}{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,"27/(14*(2 + 3*x)^2) - 125/(22*(3 + 5*x)^2) + 2889/(98 + 147*x) + 12125/(363 + 605*x) - (32*Log[1 - 2*x])/456533 - (204228*Log[4 + 6*x])/343 + (792500*Log[6 + 10*x])/1331","A",1
1528,1,84,86,0.0593632,"\int \frac{1}{(1-2 x) (2+3 x)^4 (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^3),x]","\frac{204228}{343 (3 x+2)}+\frac{81250}{605 x+363}+\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 (6 x+4)}{2401}+\frac{6643750 \log (10 x+6)}{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,"9/(7*(2 + 3*x)^3) + 2889/(98*(2 + 3*x)^2) + 204228/(343*(2 + 3*x)) - 625/(22*(3 + 5*x)^2) + 81250/(363 + 605*x) - (64*Log[1 - 2*x])/3195731 - (11984706*Log[4 + 6*x])/2401 + (6643750*Log[6 + 10*x])/1331","A",1
1529,1,95,97,0.0693349,"\int \frac{1}{(1-2 x) (2+3 x)^5 (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)^3),x]","\frac{11984706}{2401 (3 x+2)}+\frac{509375}{605 x+363}+\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 (6 x+4)}{16807}+\frac{50028125 \log (10 x+6)}{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,"27/(28*(2 + 3*x)^4) + 963/(49*(2 + 3*x)^3) + 102114/(343*(2 + 3*x)^2) + 11984706/(2401*(2 + 3*x)) - 3125/(22*(3 + 5*x)^2) + 509375/(363 + 605*x) - (128*Log[1 - 2*x])/22370117 - (631722537*Log[4 + 6*x])/16807 + (50028125*Log[6 + 10*x])/1331","A",1
1530,1,86,103,0.0727149,"\int \frac{(c+d x)^4}{(a-b x) (a+b x)} \, dx","Integrate[(c + d*x)^4/((a - b*x)*(a + b*x)),x]","\frac{-2 a b d^2 x \left(3 a^2 d^2+b^2 \left(18 c^2+6 c d x+d^2 x^2\right)\right)+3 (b c-a d)^4 \log (a+b x)-3 (a d+b c)^4 \log (a-b x)}{6 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,"(-2*a*b*d^2*x*(3*a^2*d^2 + b^2*(18*c^2 + 6*c*d*x + d^2*x^2)) - 3*(b*c + a*d)^4*Log[a - b*x] + 3*(b*c - a*d)^4*Log[a + b*x])/(6*a*b^5)","A",1
1531,1,62,76,0.046013,"\int \frac{(c+d x)^3}{(a-b x) (a+b x)} \, dx","Integrate[(c + d*x)^3/((a - b*x)*(a + b*x)),x]","-\frac{a b^2 d^2 x (6 c+d x)+(b c-a d)^3 (-\log (a+b x))+(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{(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*(a*b^2*d^2*x*(6*c + d*x) + (b*c + a*d)^3*Log[a - b*x] - (b*c - a*d)^3*Log[a + b*x])/(a*b^4)","A",1
1532,1,54,62,0.0313963,"\int \frac{(c+d x)^2}{(a-b x) (a+b x)} \, dx","Integrate[(c + d*x)^2/((a - b*x)*(a + b*x)),x]","\frac{-(a d+b c)^2 \log (a-b x)+(b c-a d)^2 \log (a+b x)-2 a b d^2 x}{2 a b^3}","-\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,"(-2*a*b*d^2*x - (b*c + a*d)^2*Log[a - b*x] + (b*c - a*d)^2*Log[a + b*x])/(2*a*b^3)","A",1
1533,1,37,49,0.0114022,"\int \frac{c+d x}{(a-b x) (a+b x)} \, dx","Integrate[(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
1534,1,14,14,0.0038447,"\int \frac{1}{(a-b x) (a+b x)} \, dx","Integrate[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
1535,1,68,74,0.0470764,"\int \frac{1}{(a-b x) (a+b x) (c+d x)} \, dx","Integrate[1/((a - b*x)*(a + b*x)*(c + d*x)),x]","\frac{(b c-a d) \log (a-b x)-(a d+b c) \log (a+b x)+2 a d \log (c+d x)}{2 a (a d-b c) (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,"((b*c - a*d)*Log[a - b*x] - (b*c + a*d)*Log[a + b*x] + 2*a*d*Log[c + d*x])/(2*a*(-(b*c) + a*d)*(b*c + a*d))","A",1
1536,1,102,107,0.261969,"\int \frac{1}{(a-b x) (a+b x) (c+d x)^2} \, dx","Integrate[1/((a - b*x)*(a + b*x)*(c + d*x)^2),x]","\frac{1}{2} \left(\frac{\frac{b \log (a+b x)}{a}-\frac{2 d \left(a^2 d^2+b^2 \left(-c^2\right)+2 b^2 c (c+d x) \log (c+d x)\right)}{(c+d x) (a d+b c)^2}}{(b c-a d)^2}-\frac{b \log (a-b x)}{a (a d+b c)^2}\right)","\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,"(-((b*Log[a - b*x])/(a*(b*c + a*d)^2)) + ((b*Log[a + b*x])/a - (2*d*(-(b^2*c^2) + a^2*d^2 + 2*b^2*c*(c + d*x)*Log[c + d*x]))/((b*c + a*d)^2*(c + d*x)))/(b*c - a*d)^2)/2","A",1
1537,1,147,161,0.3832243,"\int \frac{1}{(a-b x) (a+b x) (c+d x)^3} \, dx","Integrate[1/((a - b*x)*(a + b*x)*(c + d*x)^3),x]","\frac{1}{2} \left(\frac{d \left(\frac{\left(b^2 c^2-a^2 d^2\right) \left(b^2 c (5 c+4 d x)-a^2 d^2\right)}{(c+d x)^2}-2 \left(a^2 b^2 d^2+3 b^4 c^2\right) \log (c+d x)\right)}{\left(b^2 c^2-a^2 d^2\right)^3}-\frac{b^2 \log (a-b x)}{a (a d+b c)^3}-\frac{b^2 \log (a+b x)}{a (a d-b c)^3}\right)","\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,"(-((b^2*Log[a - b*x])/(a*(b*c + a*d)^3)) - (b^2*Log[a + b*x])/(a*(-(b*c) + a*d)^3) + (d*(((b^2*c^2 - a^2*d^2)*(-(a^2*d^2) + b^2*c*(5*c + 4*d*x)))/(c + d*x)^2 - 2*(3*b^4*c^2 + a^2*b^2*d^2)*Log[c + d*x]))/(b^2*c^2 - a^2*d^2)^3)/2","A",1
1538,1,69,76,0.0165156,"\int \frac{(2+3 x)^8 (3+5 x)}{(1-2 x)^2} \, dx","Integrate[((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+68947019960 (2 x-1) \log (1-2 x)+60471800653}{286720 (2 x-1)}","\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 + 68947019960*(-1 + 2*x)*Log[1 - 2*x])/(286720*(-1 + 2*x))","A",1
1539,1,64,69,0.0159793,"\int \frac{(2+3 x)^7 (3+5 x)}{(1-2 x)^2} \, dx","Integrate[((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+2190624380 (2 x-1) \log (1-2 x)+1648903399}{35840 (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 + 2190624380*(-1 + 2*x)*Log[1 - 2*x])/(35840*(-1 + 2*x))","A",1
1540,1,59,62,0.0145352,"\int \frac{(2+3 x)^6 (3+5 x)}{(1-2 x)^2} \, dx","Integrate[((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+78320620 (2 x-1) \log (1-2 x)+47812811}{5120 (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 + 78320620*(-1 + 2*x)*Log[1 - 2*x])/(5120*(-1 + 2*x))","A",1
1541,1,51,55,0.0197517,"\int \frac{(2+3 x)^5 (3+5 x)}{(1-2 x)^2} \, dx","Integrate[((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+60025 (2 x-1) \log (1-2 x)+26663}{32 x-16}","\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 + 60025*(-1 + 2*x)*Log[1 - 2*x])/(-16 + 32*x)","A",1
1542,1,49,46,0.012513,"\int \frac{(2+3 x)^4 (3+5 x)}{(1-2 x)^2} \, dx","Integrate[((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+229124 (2 x-1) \log (1-2 x)+55831}{256 (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 + 229124*(-1 + 2*x)*Log[1 - 2*x])/(256*(-1 + 2*x))","A",1
1543,1,41,41,0.0174419,"\int \frac{(2+3 x)^3 (3+5 x)}{(1-2 x)^2} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x)^2,x]","\frac{720 x^4+3528 x^3+10764 x^2-13770 x+6566 (2 x-1) \log (1-2 x)-65}{64 x-32}","\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 + 6566*(-1 + 2*x)*Log[1 - 2*x])/(-32 + 64*x)","A",1
1544,1,36,32,0.0110923,"\int \frac{(2+3 x)^2 (3+5 x)}{(1-2 x)^2} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x))/(1 - 2*x)^2,x]","\frac{360 x^3+1932 x^2-2202 x+1414 (2 x-1) \log (1-2 x)-505}{64 x-32}","\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 + 1414*(-1 + 2*x)*Log[1 - 2*x])/(-32 + 64*x)","A",1
1545,1,26,27,0.0176991,"\int \frac{(2+3 x) (3+5 x)}{(1-2 x)^2} \, dx","Integrate[((2 + 3*x)*(3 + 5*x))/(1 - 2*x)^2,x]","\frac{1}{8} \left(30 x+\frac{77}{1-2 x}+68 \log (1-2 x)-15\right)","\frac{15 x}{4}+\frac{77}{8 (1-2 x)}+\frac{17}{2} \log (1-2 x)",1,"(-15 + 77/(1 - 2*x) + 30*x + 68*Log[1 - 2*x])/8","A",1
1546,1,22,22,0.0082983,"\int \frac{3+5 x}{(1-2 x)^2} \, dx","Integrate[(3 + 5*x)/(1 - 2*x)^2,x]","\frac{11}{4 (1-2 x)}+\frac{5}{4} \log (1-2 x)","\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
1547,1,37,32,0.0155819,"\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)),x]","\frac{(4 x-2) \log (1-2 x)+(2-4 x) \log (6 x+4)-77}{98 (2 x-1)}","\frac{11}{14 (1-2 x)}+\frac{1}{49} \log (1-2 x)-\frac{1}{49} \log (3 x+2)",1,"(-77 + (-2 + 4*x)*Log[1 - 2*x] + (2 - 4*x)*Log[4 + 6*x])/(98*(-1 + 2*x))","A",1
1548,1,40,43,0.0233994,"\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^2} \, dx","Integrate[(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{31}{343} \log (1-2 x)+\frac{31}{343} \log (3 x+2)","\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)) - (31*Log[1 - 2*x])/343 + (31*Log[2 + 3*x])/343","A",1
1549,1,47,54,0.0460013,"\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^3} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^3),x]","\frac{-\frac{7 \left(768 x^2+576 x+59\right)}{(2 x-1) (3 x+2)^2}-256 \log (1-2 x)+256 \log (6 x+4)}{4802}","\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,"((-7*(59 + 576*x + 768*x^2))/((-1 + 2*x)*(2 + 3*x)^2) - 256*Log[1 - 2*x] + 256*Log[4 + 6*x])/4802","A",1
1550,1,52,65,0.0486885,"\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^4} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^4),x]","\frac{-\frac{7 \left(20952 x^3+29682 x^2+6887 x-2164\right)}{(2 x-1) (3 x+2)^3}-2328 \log (3-6 x)+2328 \log (3 x+2)}{100842}","\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,"((-7*(-2164 + 6887*x + 29682*x^2 + 20952*x^3))/((-1 + 2*x)*(2 + 3*x)^3) - 2328*Log[3 - 6*x] + 2328*Log[2 + 3*x])/100842","A",1
1551,1,59,76,0.0747104,"\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^5} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^5),x]","\frac{4 \left(-\frac{7 \left(336960 x^4+702000 x^3+429000 x^2-9230 x-52979\right)}{16 (2 x-1) (3 x+2)^4}-780 \log (1-2 x)+780 \log (6 x+4)\right)}{352947}","\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,"(4*((-7*(-52979 - 9230*x + 429000*x^2 + 702000*x^3 + 336960*x^4))/(16*(-1 + 2*x)*(2 + 3*x)^4) - 780*Log[1 - 2*x] + 780*Log[4 + 6*x]))/352947","A",1
1552,1,62,87,0.0661177,"\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^6} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^6),x]","\frac{-\frac{7 \left(12674880 x^5+34855920 x^4+33741000 x^3+10410810 x^2-3488689 x-2104258\right)}{(2 x-1) (3 x+2)^5}-156480 \log (3-6 x)+156480 \log (3 x+2)}{49412580}","\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,"((-7*(-2104258 - 3488689*x + 10410810*x^2 + 33741000*x^3 + 34855920*x^4 + 12674880*x^5))/((-1 + 2*x)*(2 + 3*x)^5) - 156480*Log[3 - 6*x] + 156480*Log[2 + 3*x])/49412580","A",1
1553,1,67,98,0.0653449,"\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^7} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^7),x]","\frac{-\frac{7 \left(311040 x^6+1062720 x^5+1398240 x^4+807480 x^3+84708 x^2-132772 x-49131\right)}{(2 x-1) (3 x+2)^6}-1280 \log (1-2 x)+1280 \log (6 x+4)}{1176490}","\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,"((-7*(-49131 - 132772*x + 84708*x^2 + 807480*x^3 + 1398240*x^4 + 1062720*x^5 + 311040*x^6))/((-1 + 2*x)*(2 + 3*x)^6) - 1280*Log[1 - 2*x] + 1280*Log[4 + 6*x])/1176490","A",1
1554,1,74,81,0.0272742,"\int \frac{(2+3 x)^8 (3+5 x)^2}{(1-2 x)^2} \, dx","Integrate[((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+423597577480 (2 x-1) \log (1-2 x)+420890769939}{286720 (2 x-1)}","\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 + 423597577480*(-1 + 2*x)*Log[1 - 2*x])/(286720*(-1 + 2*x))","A",1
1555,1,69,76,0.0287168,"\int \frac{(2+3 x)^7 (3+5 x)^2}{(1-2 x)^2} \, dx","Integrate[((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+109070034920 (2 x-1) \log (1-2 x)+96389258691}{286720 (2 x-1)}","\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 + 109070034920*(-1 + 2*x)*Log[1 - 2*x])/(286720*(-1 + 2*x))","A",1
1556,1,64,69,0.0262406,"\int \frac{(2+3 x)^6 (3+5 x)^2}{(1-2 x)^2} \, dx","Integrate[((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+1734146260 (2 x-1) \log (1-2 x)+1318304553}{17920 (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 + 1734146260*(-1 + 2*x)*Log[1 - 2*x])/(17920*(-1 + 2*x))","A",1
1557,1,59,62,0.0211733,"\int \frac{(2+3 x)^5 (3+5 x)^2}{(1-2 x)^2} \, dx","Integrate[((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+24826340 (2 x-1) \log (1-2 x)+15368793}{1024 (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 + 24826340*(-1 + 2*x)*Log[1 - 2*x])/(1024*(-1 + 2*x))","A",1
1558,1,54,55,0.0195381,"\int \frac{(2+3 x)^4 (3+5 x)^2}{(1-2 x)^2} \, dx","Integrate[((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+1524292 (2 x-1) \log (1-2 x)+692403}{256 (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 + 1524292*(-1 + 2*x)*Log[1 - 2*x])/(256*(-1 + 2*x))","A",1
1559,1,49,48,0.0184967,"\int \frac{(2+3 x)^3 (3+5 x)^2}{(1-2 x)^2} \, dx","Integrate[((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+364364 (2 x-1) \log (1-2 x)+93225}{256 (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 + 364364*(-1 + 2*x)*Log[1 - 2*x])/(256*(-1 + 2*x))","A",1
1560,1,41,41,0.0166182,"\int \frac{(2+3 x)^2 (3+5 x)^2}{(1-2 x)^2} \, dx","Integrate[((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+2618 (2 x-1) \log (1-2 x)+15}{16 x-8}","\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 + 2618*(-1 + 2*x)*Log[1 - 2*x])/(-8 + 16*x)","A",1
1561,1,36,34,0.0167129,"\int \frac{(2+3 x) (3+5 x)^2}{(1-2 x)^2} \, dx","Integrate[((2 + 3*x)*(3 + 5*x)^2)/(1 - 2*x)^2,x]","\frac{600 x^3+3140 x^2-3590 x+2266 (2 x-1) \log (1-2 x)-759}{64 x-32}","\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 + 2266*(-1 + 2*x)*Log[1 - 2*x])/(-32 + 64*x)","A",1
1562,1,26,27,0.0136704,"\int \frac{(3+5 x)^2}{(1-2 x)^2} \, dx","Integrate[(3 + 5*x)^2/(1 - 2*x)^2,x]","\frac{1}{8} \left(50 x+\frac{121}{1-2 x}+110 \log (1-2 x)-25\right)","\frac{25 x}{4}+\frac{121}{8 (1-2 x)}+\frac{55}{4} \log (1-2 x)",1,"(-25 + 121/(1 - 2*x) + 50*x + 110*Log[1 - 2*x])/8","A",1
1563,1,40,32,0.0263497,"\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)),x]","-\frac{363}{28 (2 (3 x+2)-7)}+\frac{1}{147} \log (3 x+2)+\frac{407}{196} \log (7-2 (3 x+2))","\frac{121}{28 (1-2 x)}+\frac{407}{196} \log (1-2 x)+\frac{1}{147} \log (3 x+2)",1,"-363/(28*(-7 + 2*(2 + 3*x))) + Log[2 + 3*x]/147 + (407*Log[7 - 2*(2 + 3*x)])/196","A",1
1564,1,38,43,0.0372812,"\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^2),x]","\frac{-\frac{7 (1093 x+724)}{6 x^2+x-2}+132 \log (1-2 x)-132 \log (3 x+2)}{2058}","\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,"((-7*(724 + 1093*x))/(-2 + x + 6*x^2) + 132*Log[1 - 2*x] - 132*Log[2 + 3*x])/2058","A",1
1565,1,47,54,0.0374536,"\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^3),x]","\frac{-\frac{7 \left(5742 x^2+8594 x+3161\right)}{(2 x-1) (3 x+2)^2}-1914 \log (1-2 x)+1914 \log (6 x+4)}{14406}","\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,"((-7*(3161 + 8594*x + 5742*x^2))/((-1 + 2*x)*(2 + 3*x)^2) - 1914*Log[1 - 2*x] + 1914*Log[4 + 6*x])/14406","A",1
1566,1,54,65,0.0617881,"\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^4),x]","\frac{2 \left(-\frac{7 \left(110484 x^3+156519 x^2+66329 x+7277\right)}{2 (2 x-1) (3 x+2)^3}-6138 \log (1-2 x)+6138 \log (6 x+4)\right)}{151263}","\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,"(2*((-7*(7277 + 66329*x + 156519*x^2 + 110484*x^3))/(2*(-1 + 2*x)*(2 + 3*x)^3) - 6138*Log[1 - 2*x] + 6138*Log[4 + 6*x]))/151263","A",1
1567,1,59,76,0.0638775,"\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^5} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^5),x]","\frac{2 \left(-\frac{7 \left(1354320 x^4+2821500 x^3+1724250 x^2+172990 x-83327\right)}{8 (2 x-1) (3 x+2)^4}-6270 \log (1-2 x)+6270 \log (6 x+4)\right)}{352947}","\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,"(2*((-7*(-83327 + 172990*x + 1724250*x^2 + 2821500*x^3 + 1354320*x^4))/(8*(-1 + 2*x)*(2 + 3*x)^4) - 6270*Log[1 - 2*x] + 6270*Log[4 + 6*x]))/352947","A",1
1568,1,64,87,0.1023911,"\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^6} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^6),x]","\frac{8 \left(-\frac{21 \left(9123840 x^5+25090560 x^4+24288000 x^3+7494080 x^2-1530877 x-913244\right)}{16 (2 x-1) (3 x+2)^5}-21120 \log (1-2 x)+21120 \log (6 x+4)\right)}{12353145}","\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,"(8*((-21*(-913244 - 1530877*x + 7494080*x^2 + 24288000*x^3 + 25090560*x^4 + 9123840*x^5))/(16*(-1 + 2*x)*(2 + 3*x)^5) - 21120*Log[1 - 2*x] + 21120*Log[4 + 6*x]))/12353145","A",1
1569,1,69,98,0.0864738,"\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^7} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^7),x]","\frac{4 \left(-\frac{7 \left(177059520 x^6+604953360 x^5+795948120 x^4+459657990 x^3+48220029 x^2-60874336 x-18979078\right)}{16 (2 x-1) (3 x+2)^6}-45540 \log (1-2 x)+45540 \log (6 x+4)\right)}{37059435}","\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,"(4*((-7*(-18979078 - 60874336*x + 48220029*x^2 + 459657990*x^3 + 795948120*x^4 + 604953360*x^5 + 177059520*x^6))/(16*(-1 + 2*x)*(2 + 3*x)^6) - 45540*Log[1 - 2*x] + 45540*Log[4 + 6*x]))/37059435","A",1
1570,1,74,109,0.1407926,"\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^8} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^8),x]","\frac{16 \left(-\frac{7 \left(746729280 x^7+3049144560 x^6+5057708040 x^5+4176440730 x^4+1495734471 x^3-183177225 x^2-327016403 x-76539293\right)}{16 (2 x-1) (3 x+2)^7}-64020 \log (1-2 x)+64020 \log (6 x+4)\right)}{605304105}","\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,"(16*((-7*(-76539293 - 327016403*x - 183177225*x^2 + 1495734471*x^3 + 4176440730*x^4 + 5057708040*x^5 + 3049144560*x^6 + 746729280*x^7))/(16*(-1 + 2*x)*(2 + 3*x)^7) - 64020*Log[1 - 2*x] + 64020*Log[4 + 6*x]))/605304105","A",1
1571,1,79,90,0.0275753,"\int \frac{(2+3 x)^8 (3+5 x)^3}{(1-2 x)^2} \, dx","Integrate[((2 + 3*x)^8*(3 + 5*x)^3)/(1 - 2*x)^2,x]","\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+10295703993960 (2 x-1) \log (1-2 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 + 10295703993960*(-1 + 2*x)*Log[1 - 2*x])/(1146880*(-1 + 2*x))","A",1
1572,1,74,83,0.0217003,"\int \frac{(2+3 x)^7 (3+5 x)^3}{(1-2 x)^2} \, dx","Integrate[((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+167409821040 (2 x-1) \log (1-2 x)+167338715917}{71680 (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 + 167409821040*(-1 + 2*x)*Log[1 - 2*x])/(71680*(-1 + 2*x))","A",1
1573,1,69,76,0.0188685,"\int \frac{(2+3 x)^6 (3+5 x)^3}{(1-2 x)^2} \, dx","Integrate[((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+172534611480 (2 x-1) \log (1-2 x)+153617806869}{286720 (2 x-1)}","\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 + 172534611480*(-1 + 2*x)*Log[1 - 2*x])/(286720*(-1 + 2*x))","A",1
1574,1,64,69,0.0258292,"\int \frac{(2+3 x)^5 (3+5 x)^3}{(1-2 x)^2} \, dx","Integrate[((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+1098169380 (2 x-1) \log (1-2 x)+843009185}{7168 (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 + 1098169380*(-1 + 2*x)*Log[1 - 2*x])/(7168*(-1 + 2*x))","A",1
1575,1,59,62,0.0166524,"\int \frac{(2+3 x)^4 (3+5 x)^3}{(1-2 x)^2} \, dx","Integrate[((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+39344844 (2 x-1) \log (1-2 x)+24691451}{1024 (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 + 39344844*(-1 + 2*x)*Log[1 - 2*x])/(1024*(-1 + 2*x))","A",1
1576,1,54,55,0.0245382,"\int \frac{(2+3 x)^3 (3+5 x)^3}{(1-2 x)^2} \, dx","Integrate[((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+1209516 (2 x-1) \log (1-2 x)+561465}{128 (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 + 1209516*(-1 + 2*x)*Log[1 - 2*x])/(128*(-1 + 2*x))","A",1
1577,1,49,48,0.0150718,"\int \frac{(2+3 x)^2 (3+5 x)^3}{(1-2 x)^2} \, dx","Integrate[((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+579348 (2 x-1) \log (1-2 x)+155215}{256 (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 + 579348*(-1 + 2*x)*Log[1 - 2*x])/(256*(-1 + 2*x))","A",1
1578,1,41,41,0.0151962,"\int \frac{(2+3 x) (3+5 x)^3}{(1-2 x)^2} \, dx","Integrate[((2 + 3*x)*(3 + 5*x)^3)/(1 - 2*x)^2,x]","\frac{2000 x^4+9400 x^3+27780 x^2-35830 x+16698 (2 x-1) \log (1-2 x)+353}{64 x-32}","\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 + 16698*(-1 + 2*x)*Log[1 - 2*x])/(-32 + 64*x)","A",1
1579,1,36,34,0.0091954,"\int \frac{(3+5 x)^3}{(1-2 x)^2} \, dx","Integrate[(3 + 5*x)^3/(1 - 2*x)^2,x]","\frac{1000 x^3+5100 x^2-5850 x+3630 (2 x-1) \log (1-2 x)-1137}{64 x-32}","\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 + 3630*(-1 + 2*x)*Log[1 - 2*x])/(-32 + 64*x)","A",1
1580,1,37,37,0.0341804,"\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)),x]","\frac{12250 (3 x+2)+\frac{83853}{1-2 x}+78408 \log (3-6 x)-8 \log (3 x+2)}{3528}","\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,"(83853/(1 - 2*x) + 12250*(2 + 3*x) + 78408*Log[3 - 6*x] - 8*Log[2 + 3*x])/3528","A",1
1581,1,40,43,0.0376638,"\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^2),x]","\frac{-\frac{7 (35929 x+23962)}{6 x^2+x-2}+42471 \log (5-10 x)+404 \log (5 (3 x+2))}{12348}","\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,"((-7*(23962 + 35929*x))/(-2 + x + 6*x^2) + 42471*Log[5 - 10*x] + 404*Log[5*(2 + 3*x)])/12348","A",1
1582,1,48,54,0.0501149,"\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^3),x]","\frac{\frac{83853}{1-2 x}-\frac{1414}{3 x+2}+\frac{49}{(3 x+2)^2}+6534 \log (1-2 x)-6534 \log (6 x+4)}{43218}","\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,"(83853/(1 - 2*x) + 49/(2 + 3*x)^2 - 1414/(2 + 3*x) + 6534*Log[1 - 2*x] - 6534*Log[4 + 6*x])/43218","A",1
1583,1,62,65,0.0684979,"\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^4),x]","\frac{\frac{7}{2} \left(\frac{19602}{3 x+2}-\frac{2121}{(3 x+2)^2}+\frac{98}{(3 x+2)^3}+\frac{71874}{1-2 x}\right)-88209 \log (1-2 x)+88209 \log (6 x+4)}{453789}","\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,"((7*(71874/(1 - 2*x) + 98/(2 + 3*x)^3 - 2121/(2 + 3*x)^2 + 19602/(2 + 3*x)))/2 - 88209*Log[1 - 2*x] + 88209*Log[4 + 6*x])/453789","A",1
1584,1,59,76,0.0790035,"\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^5} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^5),x]","\frac{2 \left(-\frac{7 \left(42340320 x^4+88209000 x^3+66510750 x^2+21109490 x+2287541\right)}{8 (2 x-1) (3 x+2)^4}-196020 \log (1-2 x)+196020 \log (6 x+4)\right)}{3176523}","\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,"(2*((-7*(2287541 + 21109490*x + 66510750*x^2 + 88209000*x^3 + 42340320*x^4))/(8*(-1 + 2*x)*(2 + 3*x)^4) - 196020*Log[1 - 2*x] + 196020*Log[4 + 6*x]))/3176523","A",1
1585,1,64,87,0.1059214,"\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^6} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^6),x]","\frac{2 \left(-\frac{7 \left(656274960 x^5+1804756140 x^4+1747028250 x^3+649342770 x^2+25985087 x-23684986\right)}{8 (2 x-1) (3 x+2)^5}-1012770 \log (1-2 x)+1012770 \log (6 x+4)\right)}{37059435}","\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,"(2*((-7*(-23684986 + 25985087*x + 649342770*x^2 + 1747028250*x^3 + 1804756140*x^4 + 656274960*x^5))/(8*(-1 + 2*x)*(2 + 3*x)^5) - 1012770*Log[1 - 2*x] + 1012770*Log[4 + 6*x]))/37059435","A",1
1586,1,69,98,0.0979353,"\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^7} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^7),x]","\frac{4 \left(-\frac{7 \left(2286377280 x^6+7811789040 x^5+10278112680 x^4+5935583610 x^3+887377581 x^2-461259404 x-145404842\right)}{16 (2 x-1) (3 x+2)^6}-588060 \log (1-2 x)+588060 \log (6 x+4)\right)}{111178305}","\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,"(4*((-7*(-145404842 - 461259404*x + 887377581*x^2 + 5935583610*x^3 + 10278112680*x^4 + 7811789040*x^5 + 2286377280*x^6))/(16*(-1 + 2*x)*(2 + 3*x)^6) - 588060*Log[1 - 2*x] + 588060*Log[4 + 6*x]))/111178305","A",1
1587,1,74,109,0.1240256,"\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^8} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^8),x]","\frac{4 \left(-\frac{7 \left(121177995840 x^7+494810149680 x^6+820756518120 x^5+677745912690 x^4+242725322763 x^3-18916696050 x^2-39853850134 x-8381276704\right)}{16 (2 x-1) (3 x+2)^7}-10389060 \log (1-2 x)+10389060 \log (6 x+4)\right)}{5447736945}","\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,"(4*((-7*(-8381276704 - 39853850134*x - 18916696050*x^2 + 242725322763*x^3 + 677745912690*x^4 + 820756518120*x^5 + 494810149680*x^6 + 121177995840*x^7))/(16*(-1 + 2*x)*(2 + 3*x)^7) - 10389060*Log[1 - 2*x] + 10389060*Log[4 + 6*x]))/5447736945","A",1
1588,1,66,72,0.0690907,"\int \frac{(2+3 x)^8}{(1-2 x)^2 (3+5 x)} \, dx","Integrate[(2 + 3*x)^8/((1 - 2*x)^2*(3 + 5*x)),x]","\frac{109350000 x^6+752328000 x^5+2474772750 x^4+5354731800 x^3+9199057005 x^2+16335250344 x+\frac{90075015625}{22-44 x}+7988912316}{2000000}+\frac{188591347 \log (3-6 x)}{30976}+\frac{\log (-3 (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,"(7988912316 + 90075015625/(22 - 44*x) + 16335250344*x + 9199057005*x^2 + 5354731800*x^3 + 2474772750*x^4 + 752328000*x^5 + 109350000*x^6)/2000000 + (188591347*Log[3 - 6*x])/30976 + Log[-3*(3 + 5*x)]/9453125","A",1
1589,1,60,65,0.0592483,"\int \frac{(2+3 x)^7}{(1-2 x)^2 (3+5 x)} \, dx","Integrate[(2 + 3*x)^7/((1 - 2*x)^2*(3 + 5*x)),x]","\frac{\frac{11 \left(4811400000 x^6+28066500000 x^5+78666390000 x^4+153656514000 x^3+306816622200 x^2-14798867886 x-158719988357\right)}{2 x-1}+1801500312500 \log (5-10 x)+640 \log (5 x+3)}{1210000000}","\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,"((11*(-158719988357 - 14798867886*x + 306816622200*x^2 + 153656514000*x^3 + 78666390000*x^4 + 28066500000*x^5 + 4811400000*x^6))/(-1 + 2*x) + 1801500312500*Log[5 - 10*x] + 640*Log[3 + 5*x])/1210000000","A",1
1590,1,55,58,0.0375585,"\int \frac{(2+3 x)^6}{(1-2 x)^2 (3+5 x)} \, dx","Integrate[(2 + 3*x)^6/((1 - 2*x)^2*(3 + 5*x)),x]","\frac{\frac{55 \left(8019000 x^5+43035300 x^4+117237780 x^3+276893694 x^2-6823872 x-156937135\right)}{2 x-1}+8561065625 \log (5-10 x)+64 \log (5 x+3)}{24200000}","\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,"((55*(-156937135 - 6823872*x + 276893694*x^2 + 117237780*x^3 + 43035300*x^4 + 8019000*x^5))/(-1 + 2*x) + 8561065625*Log[5 - 10*x] + 64*Log[3 + 5*x])/24200000","A",1
1591,1,52,51,0.0355556,"\int \frac{(2+3 x)^5}{(1-2 x)^2 (3+5 x)} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^2*(3 + 5*x)),x]","\frac{81 x^3}{20}+\frac{567 x^2}{25}+\frac{152793 x}{2000}+\frac{16807}{352-704 x}+\frac{156065 \log (5-10 x)}{1936}+\frac{\log (5 x+3)}{75625}+\frac{385479}{10000}","\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,"385479/10000 + 16807/(352 - 704*x) + (152793*x)/2000 + (567*x^2)/25 + (81*x^3)/20 + (156065*Log[5 - 10*x])/1936 + Log[3 + 5*x]/75625","A",1
1592,1,45,44,0.0251271,"\int \frac{(2+3 x)^4}{(1-2 x)^2 (3+5 x)} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^2*(3 + 5*x)),x]","\frac{81 x^2}{40}+\frac{621 x}{50}+\frac{2401}{176-352 x}+\frac{33271 \log (5-10 x)}{1936}+\frac{\log (5 x+3)}{15125}+\frac{6723}{1000}","\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,"6723/1000 + 2401/(176 - 352*x) + (621*x)/50 + (81*x^2)/40 + (33271*Log[5 - 10*x])/1936 + Log[3 + 5*x]/15125","A",1
1593,1,37,37,0.0279953,"\int \frac{(2+3 x)^3}{(1-2 x)^2 (3+5 x)} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^2*(3 + 5*x)),x]","\frac{6534 (5 x+3)+\frac{94325}{1-2 x}+78400 \log (5-10 x)+8 \log (5 x+3)}{24200}","\frac{27 x}{20}+\frac{343}{88 (1-2 x)}+\frac{392}{121} \log (1-2 x)+\frac{\log (5 x+3)}{3025}",1,"(94325/(1 - 2*x) + 6534*(3 + 5*x) + 78400*Log[5 - 10*x] + 8*Log[3 + 5*x])/24200","A",1
1594,1,40,32,0.0169197,"\int \frac{(2+3 x)^2}{(1-2 x)^2 (3+5 x)} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^2*(3 + 5*x)),x]","-\frac{245}{44 (2 (5 x+3)-11)}+\frac{1}{605} \log (5 x+3)+\frac{217}{484} \log (11-2 (5 x+3))","\frac{49}{44 (1-2 x)}+\frac{217}{484} \log (1-2 x)+\frac{1}{605} \log (5 x+3)",1,"-245/(44*(-11 + 2*(3 + 5*x))) + Log[3 + 5*x]/605 + (217*Log[11 - 2*(3 + 5*x)])/484","A",1
1595,1,37,32,0.0178497,"\int \frac{2+3 x}{(1-2 x)^2 (3+5 x)} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)^2*(3 + 5*x)),x]","\frac{(2-4 x) \log (1-2 x)+(4 x-2) \log (10 x+6)-77}{242 (2 x-1)}","\frac{7}{22 (1-2 x)}-\frac{1}{121} \log (1-2 x)+\frac{1}{121} \log (5 x+3)",1,"(-77 + (2 - 4*x)*Log[1 - 2*x] + (-2 + 4*x)*Log[6 + 10*x])/(242*(-1 + 2*x))","A",1
1596,1,38,32,0.0189302,"\int \frac{1}{(1-2 x)^2 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^2*(3 + 5*x)),x]","\frac{(5-10 x) \log (1-2 x)+5 (2 x-1) \log (10 x+6)-11}{121 (2 x-1)}","\frac{1}{11 (1-2 x)}-\frac{5}{121} \log (1-2 x)+\frac{5}{121} \log (5 x+3)",1,"(-11 + (5 - 10*x)*Log[1 - 2*x] + 5*(-1 + 2*x)*Log[6 + 10*x])/(121*(-1 + 2*x))","A",1
1597,1,40,42,0.0262808,"\int \frac{1}{(1-2 x)^2 (2+3 x) (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^2*(2 + 3*x)*(3 + 5*x)),x]","\frac{\frac{154}{1-2 x}-136 \log (3-6 x)-1089 \log (3 x+2)+1225 \log (-3 (5 x+3))}{5929}","\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,"(154/(1 - 2*x) - 136*Log[3 - 6*x] - 1089*Log[2 + 3*x] + 1225*Log[-3*(3 + 5*x)])/5929","A",1
1598,1,56,53,0.0383843,"\int \frac{1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x)),x]","\frac{\frac{14322 x}{6 x^2+x-2}-\frac{8239}{6 x^2+x-2}-404 \log (5-10 x)-42471 \log (5 (3 x+2))+42875 \log (5 x+3)}{41503}","\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,"(-8239/(-2 + x + 6*x^2) + (14322*x)/(-2 + x + 6*x^2) - 404*Log[5 - 10*x] - 42471*Log[5*(2 + 3*x)] + 42875*Log[3 + 5*x])/41503","A",1
1599,1,61,64,0.0660302,"\int \frac{1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x)),x]","\frac{-2144 \log (5-10 x)-2999106 \log (5 (3 x+2))+7 \left(\frac{176}{1-2 x}+\frac{84942}{3 x+2}+\frac{7623}{(3 x+2)^2}+428750 \log (5 x+3)\right)}{581042}","\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,"(-2144*Log[5 - 10*x] - 2999106*Log[5*(2 + 3*x)] + 7*(176/(1 - 2*x) + 7623/(2 + 3*x)^2 + 84942/(2 + 3*x) + 428750*Log[3 + 5*x]))/581042","A",1
1600,1,70,75,0.080293,"\int \frac{1}{(1-2 x)^2 (2+3 x)^4 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)),x]","\frac{77 \left(\frac{272646}{3 x+2}+\frac{27027}{(3 x+2)^2}+\frac{3234}{(3 x+2)^3}+\frac{32}{1-2 x}\right)-5344 \log (5-10 x)-105038406 \log (5 (3 x+2))+105043750 \log (5 x+3)}{4067294}","\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,"(77*(32/(1 - 2*x) + 3234/(2 + 3*x)^3 + 27027/(2 + 3*x)^2 + 272646/(2 + 3*x)) - 5344*Log[5 - 10*x] - 105038406*Log[5*(2 + 3*x)] + 105043750*Log[3 + 5*x])/4067294","A",1
1601,1,81,86,0.1235863,"\int \frac{1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x)),x]","\frac{5 \left(\frac{77}{5} \left(\frac{19097892}{3 x+2}+\frac{1908522}{(3 x+2)^2}+\frac{252252}{(3 x+2)^3}+\frac{33957}{(3 x+2)^4}+\frac{128}{1-2 x}\right)-5120 \log (5-10 x)-1470607380 \log (5 (3 x+2))+1470612500 \log (5 x+3)\right)}{56942116}","\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,"(5*((77*(128/(1 - 2*x) + 33957/(2 + 3*x)^4 + 252252/(2 + 3*x)^3 + 1908522/(2 + 3*x)^2 + 19097892/(2 + 3*x)))/5 - 5120*Log[5 - 10*x] - 1470607380*Log[5*(2 + 3*x)] + 1470612500*Log[3 + 5*x]))/56942116","A",1
1602,1,87,97,0.0681305,"\int \frac{1}{(1-2 x)^2 (2+3 x)^6 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x)),x]","\frac{\frac{19712}{1-2 x}+\frac{51471258300}{3 x+2}+\frac{5146881894}{(3 x+2)^2}+\frac{685795572}{(3 x+2)^3}+\frac{101972871}{(3 x+2)^4}+\frac{73211292}{5 (3 x+2)^5}-59648 \log (5-10 x)-257357127852 \log (5 (3 x+2))+257357187500 \log (5 x+3)}{398594812}","\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,"(19712/(1 - 2*x) + 73211292/(5*(2 + 3*x)^5) + 101972871/(2 + 3*x)^4 + 685795572/(2 + 3*x)^3 + 5146881894/(2 + 3*x)^2 + 51471258300/(2 + 3*x) - 59648*Log[5 - 10*x] - 257357127852*Log[5*(2 + 3*x)] + 257357187500*Log[3 + 5*x])/398594812","A",1
1603,1,95,76,0.0486709,"\int \frac{(2+3 x)^8}{(1-2 x)^2 (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^8/((1 - 2*x)^2*(3 + 5*x)^2),x]","-\frac{2251875390881 x+1351125234247}{1210000000 \left(10 x^2+x-3\right)}+\frac{27}{500} (3 x+2)^5+\frac{999 (3 x+2)^4}{2000}+\frac{35703 (3 x+2)^3}{10000}+\frac{78921 (3 x+2)^2}{3125}+\frac{44471943 (3 x+2)}{200000}+\frac{79883671 \log (3-6 x)}{85184}+\frac{268 \log (-3 (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,"(44471943*(2 + 3*x))/200000 + (78921*(2 + 3*x)^2)/3125 + (35703*(2 + 3*x)^3)/10000 + (999*(2 + 3*x)^4)/2000 + (27*(2 + 3*x)^5)/500 - (1351125234247 + 2251875390881*x)/(1210000000*(-3 + x + 10*x^2)) + (79883671*Log[3 - 6*x])/85184 + (268*Log[-3*(3 + 5*x)])/103984375","A",1
1604,1,74,69,0.0516194,"\int \frac{(2+3 x)^7}{(1-2 x)^2 (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^7/((1 - 2*x)^2*(3 + 5*x)^2),x]","\frac{-\frac{11 (64339297003 x+38603578061)}{10 x^2+x-3}+89842500 (3 x+2)^4+886446000 (3 x+2)^3+7128103950 (3 x+2)^2+67228064640 (3 x+2)+295960765625 \log (3-6 x)+15040 \log (-3 (5 x+3))}{1331000000}","\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,"(67228064640*(2 + 3*x) + 7128103950*(2 + 3*x)^2 + 886446000*(2 + 3*x)^3 + 89842500*(2 + 3*x)^4 - (11*(38603578061 + 64339297003*x))/(-3 + x + 10*x^2) + 295960765625*Log[3 - 6*x] + 15040*Log[-3*(3 + 5*x)])/1331000000","A",1
1605,1,65,62,0.0378727,"\int \frac{(2+3 x)^6}{(1-2 x)^2 (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^6/((1 - 2*x)^2*(3 + 5*x)^2),x]","\frac{-\frac{11 (1838265689 x+1102959343)}{10 x^2+x-3}+11979000 (3 x+2)^3+132966900 (3 x+2)^2+1425620790 (3 x+2)+6722800000 \log (3-6 x)+6464 \log (-3 (5 x+3))}{133100000}","\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,"(1425620790*(2 + 3*x) + 132966900*(2 + 3*x)^2 + 11979000*(2 + 3*x)^3 - (11*(1102959343 + 1838265689*x))/(-3 + x + 10*x^2) + 6722800000*Log[3 - 6*x] + 6464*Log[-3*(3 + 5*x)])/133100000","A",1
1606,1,56,55,0.0406296,"\int \frac{(2+3 x)^5}{(1-2 x)^2 (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^2*(3 + 5*x)^2),x]","\frac{-\frac{11 (52521907 x+31513109)}{10 x^2+x-3}+1796850 (3 x+2)^2+26593380 (3 x+2)+142559375 \log (3-6 x)+2704 \log (-3 (5 x+3))}{13310000}","\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,"(26593380*(2 + 3*x) + 1796850*(2 + 3*x)^2 - (11*(31513109 + 52521907*x))/(-3 + x + 10*x^2) + 142559375*Log[3 - 6*x] + 2704*Log[-3*(3 + 5*x)])/13310000","A",1
1607,1,47,48,0.0403727,"\int \frac{(2+3 x)^4}{(1-2 x)^2 (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^2*(3 + 5*x)^2),x]","\frac{-\frac{11 (1500641 x+900367)}{10 x^2+x-3}+359370 (3 x+2)+2658250 \log (3-6 x)+1088 \log (-3 (5 x+3))}{1331000}","\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,"(359370*(2 + 3*x) - (11*(900367 + 1500641*x))/(-3 + x + 10*x^2) + 2658250*Log[3 - 6*x] + 1088*Log[-3*(3 + 5*x)])/1331000","A",1
1608,1,40,43,0.0276128,"\int \frac{(2+3 x)^3}{(1-2 x)^2 (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^2*(3 + 5*x)^2),x]","\frac{-\frac{11 (42883 x+25721)}{10 x^2+x-3}+35525 \log (3-6 x)+412 \log (-3 (5 x+3))}{133100}","\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,"((-11*(25721 + 42883*x))/(-3 + x + 10*x^2) + 35525*Log[3 - 6*x] + 412*Log[-3*(3 + 5*x)])/133100","A",1
1609,1,38,43,0.0392906,"\int \frac{(2+3 x)^2}{(1-2 x)^2 (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^2*(3 + 5*x)^2),x]","\frac{-\frac{11 (1229 x+733)}{10 x^2+x-3}+140 \log (-5 x-3)-140 \log (1-2 x)}{13310}","\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,"((-11*(733 + 1229*x))/(-3 + x + 10*x^2) + 140*Log[-3 - 5*x] - 140*Log[1 - 2*x])/13310","A",1
1610,1,40,43,0.0196808,"\int \frac{2+3 x}{(1-2 x)^2 (3+5 x)^2} \, dx","Integrate[(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 (1-2 x)}{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
1611,1,40,43,0.0228856,"\int \frac{1}{(1-2 x)^2 (3+5 x)^2} \, dx","Integrate[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 (1-2 x)}{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
1612,1,48,53,0.0392765,"\int \frac{1}{(1-2 x)^2 (2+3 x) (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^2*(2 + 3*x)*(3 + 5*x)^2),x]","\frac{-\frac{77 (370 x-163)}{10 x^2+x-3}-412 \log (3-6 x)+35937 \log (3 x+2)-35525 \log (-3 (5 x+3))}{65219}","\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,"((-77*(-163 + 370*x))/(-3 + x + 10*x^2) - 412*Log[3 - 6*x] + 35937*Log[2 + 3*x] - 35525*Log[-3*(3 + 5*x)])/65219","A",1
1613,1,59,64,0.0755059,"\int \frac{1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{2 \left(-544 \log (1-2 x)+1329669 \log (6 x+4)+7 \left(\frac{44}{1-2 x}-\frac{35937}{6 x+4}-\frac{67375}{10 x+6}-189875 \log (10 x+6)\right)\right)}{456533}","\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,"(2*(-544*Log[1 - 2*x] + 1329669*Log[4 + 6*x] + 7*(44/(1 - 2*x) - 35937/(4 + 6*x) - 67375/(6 + 10*x) - 189875*Log[6 + 10*x])))/456533","A",1
1614,1,65,75,0.0968646,"\int \frac{1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x)^2),x]","\frac{-\frac{77 \left(22224420 x^3+17783592 x^2-5074951 x-4684319\right)}{(3 x+2)^2 \left(10 x^2+x-3\right)}-5408 \log (3-6 x)+285124158 \log (3 x+2)-285118750 \log (-3 (5 x+3))}{6391462}","\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,"((-77*(-4684319 - 5074951*x + 17783592*x^2 + 22224420*x^3))/((2 + 3*x)^2*(-3 + x + 10*x^2)) - 5408*Log[3 - 6*x] + 285124158*Log[2 + 3*x] - 285118750*Log[-3*(3 + 5*x)])/6391462","A",1
1615,1,70,86,0.1227013,"\int \frac{1}{(1-2 x)^2 (2+3 x)^4 (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^2),x]","\frac{-\frac{77 \left(1571590080 x^4+2305013328 x^3+479067048 x^2-570653522 x-220783501\right)}{(3 x+2)^3 \left(10 x^2+x-3\right)}-6464 \log (3-6 x)+6722806464 \log (3 x+2)-6722800000 \log (-3 (5 x+3))}{22370117}","\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,"((-77*(-220783501 - 570653522*x + 479067048*x^2 + 2305013328*x^3 + 1571590080*x^4))/((2 + 3*x)^3*(-3 + x + 10*x^2)) - 6464*Log[3 - 6*x] + 6722806464*Log[2 + 3*x] - 6722800000*Log[-3*(3 + 5*x)])/22370117","A",1
1616,1,75,97,0.1356263,"\int \frac{1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x)^2),x]","\frac{-\frac{77 \left(830228340600 x^5+1771154199360 x^4+1064845635750 x^3-132753874800 x^2-317609203475 x-77754195847\right)}{(3 x+2)^4 \left(10 x^2+x-3\right)}-60160 \log (3-6 x)+1183843122660 \log (3 x+2)-1183843062500 \log (-3 (5 x+3))}{626363276}","\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,"((-77*(-77754195847 - 317609203475*x - 132753874800*x^2 + 1064845635750*x^3 + 1771154199360*x^4 + 830228340600*x^5))/((2 + 3*x)^4*(-3 + x + 10*x^2)) - 60160*Log[3 - 6*x] + 1183843122660*Log[2 + 3*x] - 1183843062500*Log[-3*(3 + 5*x)])/626363276","A",1
1617,1,74,80,0.0959629,"\int \frac{(2+3 x)^8}{(1-2 x)^2 (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^8/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{3 \left(\frac{11}{3} \left(21831727500 x^4+131960664000 x^3+405536467050 x^2+1022339369700 x+\frac{450375078125}{1-2 x}-\frac{17152}{5 x+3}-\frac{352}{(5 x+3)^2}+536108166000\right)+3409982734375 \log (3-6 x)+673280 \log (-3 (5 x+3))\right)}{73205000000}","\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,"(3*((11*(536108166000 + 450375078125/(1 - 2*x) + 1022339369700*x + 405536467050*x^2 + 131960664000*x^3 + 21831727500*x^4 - 352/(3 + 5*x)^2 - 17152/(3 + 5*x)))/3 + 3409982734375*Log[3 - 6*x] + 673280*Log[-3*(3 + 5*x)]))/73205000000","A",1
1618,1,67,73,0.0592401,"\int \frac{(2+3 x)^7}{(1-2 x)^2 (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^7/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{\frac{11 \left(48514950000 x^6+315347175000 x^5+1161933052500 x^4+42644641050 x^3-1002031406415 x^2-426293494632 x-14162188399\right)}{(2 x-1) (5 x+3)^2}+231621468750 \log (1-2 x)+761760 \log (10 x+6)}{7320500000}","\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,"((11*(-14162188399 - 426293494632*x - 1002031406415*x^2 + 42644641050*x^3 + 1161933052500*x^4 + 315347175000*x^5 + 48514950000*x^6))/((-1 + 2*x)*(3 + 5*x)^2) + 231621468750*Log[1 - 2*x] + 761760*Log[6 + 10*x])/7320500000","A",1
1619,1,60,66,0.0616146,"\int \frac{(2+3 x)^6}{(1-2 x)^2 (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^6/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{11 \left(97029900 x^2+620991360 x+\frac{735306250}{1-2 x}-\frac{6464}{5 x+3}-\frac{176}{(5 x+3)^2}-334753155\right)+9769068750 \log (1-2 x)+548448 \log (10 x+6)}{1464100000}","\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,"(11*(-334753155 + 735306250/(1 - 2*x) + 620991360*x + 97029900*x^2 - 176/(3 + 5*x)^2 - 6464/(3 + 5*x)) + 9769068750*Log[1 - 2*x] + 548448*Log[6 + 10*x])/1464100000","A",1
1620,1,55,59,0.0593591,"\int \frac{(2+3 x)^5}{(1-2 x)^2 (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{17788815 (2 x-1)+\frac{115548125}{1-2 x}-\frac{14872}{5 x+3}-\frac{484}{(5 x+3)^2}+90037500 \log (1-2 x)+92496 \log (10 x+6)}{73205000}","\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,"(115548125/(1 - 2*x) + 17788815*(-1 + 2*x) - 484/(3 + 5*x)^2 - 14872/(3 + 5*x) + 90037500*Log[1 - 2*x] + 92496*Log[6 + 10*x])/73205000","A",1
1621,1,48,54,0.049683,"\int \frac{(2+3 x)^4}{(1-2 x)^2 (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{\frac{3301375}{1-2 x}-\frac{5984}{5 x+3}-\frac{242}{(5 x+3)^2}+1157625 \log (1-2 x)+28296 \log (10 x+6)}{7320500}","\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,"(3301375/(1 - 2*x) - 242/(3 + 5*x)^2 - 5984/(3 + 5*x) + 1157625*Log[1 - 2*x] + 28296*Log[6 + 10*x])/7320500","A",1
1622,1,47,54,0.0418465,"\int \frac{(2+3 x)^3}{(1-2 x)^2 (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{-\frac{11 \left(216435 x^2+257478 x+76546\right)}{(2 x-1) (5 x+3)^2}-7350 \log (1-2 x)+7350 \log (10 x+6)}{732050}","\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,"((-11*(76546 + 257478*x + 216435*x^2))/((-1 + 2*x)*(3 + 5*x)^2) - 7350*Log[1 - 2*x] + 7350*Log[6 + 10*x])/732050","A",1
1623,1,47,54,0.0450587,"\int \frac{(2+3 x)^2}{(1-2 x)^2 (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{-\frac{11 \left(13650 x^2+14862 x+3979\right)}{(2 x-1) (5 x+3)^2}-2730 \log (1-2 x)+2730 \log (10 x+6)}{146410}","\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,"((-11*(3979 + 14862*x + 13650*x^2))/((-1 + 2*x)*(3 + 5*x)^2) - 2730*Log[1 - 2*x] + 2730*Log[6 + 10*x])/146410","A",1
1624,1,47,54,0.042849,"\int \frac{2+3 x}{(1-2 x)^2 (3+5 x)^3} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{-\frac{11 \left(1440 x^2+936 x+19\right)}{(2 x-1) (5 x+3)^2}-288 \log (1-2 x)+288 \log (10 x+6)}{29282}","\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,"((-11*(19 + 936*x + 1440*x^2))/((-1 + 2*x)*(3 + 5*x)^2) - 288*Log[1 - 2*x] + 288*Log[6 + 10*x])/29282","A",1
1625,1,47,54,0.0309368,"\int \frac{1}{(1-2 x)^2 (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^2*(3 + 5*x)^3),x]","\frac{-\frac{11 \left(600 x^2+390 x-103\right)}{(2 x-1) (5 x+3)^2}-120 \log (1-2 x)+120 \log (10 x+6)}{29282}","\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,"((-11*(-103 + 390*x + 600*x^2))/((-1 + 2*x)*(3 + 5*x)^2) - 120*Log[1 - 2*x] + 120*Log[6 + 10*x])/29282","A",1
1626,1,60,64,0.0391409,"\int \frac{1}{(1-2 x)^2 (2+3 x) (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^2*(2 + 3*x)*(3 + 5*x)^3),x]","\frac{3 \left(\frac{1232}{3-6 x}+\frac{781550}{15 x+9}-\frac{148225}{3 (5 x+3)^2}-736 \log (3-6 x)-790614 \log (3 x+2)+791350 \log (-3 (5 x+3))\right)}{1434818}","\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,"(3*(1232/(3 - 6*x) - 148225/(3*(3 + 5*x)^2) + 781550/(9 + 15*x) - 736*Log[3 - 6*x] - 790614*Log[2 + 3*x] + 791350*Log[-3*(3 + 5*x)]))/1434818","A",1
1627,1,65,75,0.1020383,"\int \frac{1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{\frac{77 \left(33563700 x^3+24606540 x^2-7974123 x-6363424\right)}{(5 x+3)^2 \left(6 x^2+x-2\right)}-5472 \log (5-10 x)-258530778 \log (5 (3 x+2))+258536250 \log (5 x+3)}{10043726}","\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,"((77*(-6363424 - 7974123*x + 24606540*x^2 + 33563700*x^3))/((3 + 5*x)^2*(-2 + x + 6*x^2)) - 5472*Log[5 - 10*x] - 258530778*Log[5*(2 + 3*x)] + 258536250*Log[3 + 5*x])/10043726","A",1
1628,1,79,86,0.1611867,"\int \frac{1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{2 \left(\frac{77}{4} \left(\frac{23502798}{3 x+2}+\frac{40731250}{5 x+3}+\frac{754677}{(3 x+2)^2}-\frac{2358125}{(5 x+3)^2}+\frac{64}{1-2 x}\right)-3264 \log (1-2 x)-4614418611 \log (6 x+4)+4614421875 \log (10 x+6)\right)}{35153041}","\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,"(2*((77*(64/(1 - 2*x) + 754677/(2 + 3*x)^2 + 23502798/(2 + 3*x) - 2358125/(3 + 5*x)^2 + 40731250/(3 + 5*x)))/4 - 3264*Log[1 - 2*x] - 4614418611*Log[4 + 6*x] + 4614421875*Log[6 + 10*x]))/35153041","A",1
1629,1,88,97,0.1401482,"\int \frac{1}{(1-2 x)^2 (2+3 x)^4 (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^3),x]","\frac{2 \left(\frac{77}{4} \left(\frac{1677970404}{3 x+2}+\frac{1920800000}{5 x+3}+\frac{82259793}{(3 x+2)^2}-\frac{82534375}{(5 x+3)^2}+\frac{3521826}{(3 x+2)^3}+\frac{128}{1-2 x}\right)-7584 \log (1-2 x)-272430958041 \log (6 x+4)+272430965625 \log (10 x+6)\right)}{246071287}","\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,"(2*((77*(128/(1 - 2*x) + 3521826/(2 + 3*x)^3 + 82259793/(2 + 3*x)^2 + 1677970404/(2 + 3*x) - 82534375/(3 + 5*x)^2 + 1920800000/(3 + 5*x)))/4 - 7584*Log[1 - 2*x] - 272430958041*Log[4 + 6*x] + 272430965625*Log[6 + 10*x]))/246071287","A",1
1630,1,71,80,0.0335097,"\int \frac{(2+3 x)^8 (3+5 x)}{(1-2 x)^3} \, dx","Integrate[((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+14873186580 (1-2 x)^2 \log (1-2 x)-3752427799}{35840 (1-2 x)^2}","-\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,"-1/35840*(-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 + 14873186580*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2","A",1
1631,1,66,73,0.0199621,"\int \frac{(2+3 x)^7 (3+5 x)}{(1-2 x)^3} \, dx","Integrate[((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+472948980 (1-2 x)^2 \log (1-2 x)-52207049}{5120 (1-2 x)^2}","-\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,"-1/5120*(-52207049 + 1152760076*x - 3056516316*x^2 + 1218762720*x^3 + 512613360*x^4 + 263003328*x^5 + 113980608*x^6 + 33219072*x^7 + 4665600*x^8 + 472948980*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2","A",1
1632,1,61,66,0.0225006,"\int \frac{(2+3 x)^6 (3+5 x)}{(1-2 x)^3} \, dx","Integrate[((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+20312460 (1-2 x)^2 \log (1-2 x)+1114981}{1024 (1-2 x)^2}","-\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,"-1/1024*(1114981 + 35968388*x - 118266804*x^2 + 50971680*x^3 + 19403280*x^4 + 8112960*x^5 + 2472768*x^6 + 373248*x^7 + 20312460*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2","A",1
1633,1,56,59,0.0275362,"\int \frac{(2+3 x)^5 (3+5 x)}{(1-2 x)^3} \, dx","Integrate[((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+2078580 (1-2 x)^2 \log (1-2 x)+524947}{512 (1-2 x)^2}","-\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,"-1/512*(524947 + 2008220*x - 10547820*x^2 + 4969440*x^3 + 1609200*x^4 + 485568*x^5 + 77760*x^6 + 2078580*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2","A",1
1634,1,51,50,0.0197396,"\int \frac{(2+3 x)^4 (3+5 x)}{(1-2 x)^3} \, dx","Integrate[((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+24843 (1-2 x)^2 \log (1-2 x)+12365}{32 (1-2 x)^2}","-\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,"-1/32*(12365 - 1310*x - 103950*x^2 + 54216*x^3 + 13284*x^4 + 2160*x^5 + 24843*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2","A",1
1635,1,46,45,0.019976,"\int \frac{(2+3 x)^3 (3+5 x)}{(1-2 x)^3} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x)^3,x]","-\frac{1080 x^4+7776 x^3-13284 x^2-6220 x+4284 (1-2 x)^2 \log (1-2 x)+3505}{32 (1-2 x)^2}","-\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,"-1/32*(3505 - 6220*x - 13284*x^2 + 7776*x^3 + 1080*x^4 + 4284*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2","A",1
1636,1,34,38,0.0266475,"\int \frac{(2+3 x)^2 (3+5 x)}{(1-2 x)^3} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x))/(1 - 2*x)^3,x]","\frac{1}{32} \left(\frac{360 x^2+2468 x-785}{(1-2 x)^2}-180 x-618 \log (1-2 x)\right)","-\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,"(-180*x + (-785 + 2468*x + 360*x^2)/(1 - 2*x)^2 - 618*Log[1 - 2*x])/32","A",1
1637,1,33,33,0.0106677,"\int \frac{(2+3 x) (3+5 x)}{(1-2 x)^3} \, dx","Integrate[((2 + 3*x)*(3 + 5*x))/(1 - 2*x)^3,x]","-\frac{17}{2 (1-2 x)}+\frac{77}{16 (1-2 x)^2}-\frac{15}{8} \log (1-2 x)","-\frac{17}{2 (1-2 x)}+\frac{77}{16 (1-2 x)^2}-\frac{15}{8} \log (1-2 x)",1,"77/(16*(1 - 2*x)^2) - 17/(2*(1 - 2*x)) - (15*Log[1 - 2*x])/8","A",1
1638,1,16,18,0.0049593,"\int \frac{3+5 x}{(1-2 x)^3} \, dx","Integrate[(3 + 5*x)/(1 - 2*x)^3,x]","\frac{20 x+1}{8 (1-2 x)^2}","\frac{(5 x+3)^2}{22 (1-2 x)^2}",1,"(1 + 20*x)/(8*(1 - 2*x)^2)","A",1
1639,1,35,43,0.0219707,"\int \frac{3+5 x}{(1-2 x)^3 (2+3 x)} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)),x]","\frac{\frac{7 (8 x+73)}{(1-2 x)^2}+12 \log (1-2 x)-12 \log (6 x+4)}{1372}","-\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,"((7*(73 + 8*x))/(1 - 2*x)^2 + 12*Log[1 - 2*x] - 12*Log[4 + 6*x])/1372","A",1
1640,1,47,54,0.0585216,"\int \frac{3+5 x}{(1-2 x)^3 (2+3 x)^2} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)^2),x]","\frac{\frac{7 \left(-348 x^2+145 x+284\right)}{(1-2 x)^2 (3 x+2)}-174 \log (1-2 x)+174 \log (6 x+4)}{4802}","\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,"((7*(284 + 145*x - 348*x^2))/((1 - 2*x)^2*(2 + 3*x)) - 174*Log[1 - 2*x] + 174*Log[4 + 6*x])/4802","A",1
1641,1,48,65,0.0332753,"\int \frac{3+5 x}{(1-2 x)^3 (2+3 x)^3} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)^3),x]","\frac{\frac{7 \left(-6696 x^3-1674 x^2+3658 x+1313\right)}{\left(6 x^2+x-2\right)^2}-1116 \log (1-2 x)+1116 \log (3 x+2)}{33614}","\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,"((7*(1313 + 3658*x - 1674*x^2 - 6696*x^3))/(-2 + x + 6*x^2)^2 - 1116*Log[1 - 2*x] + 1116*Log[2 + 3*x])/33614","A",1
1642,1,57,76,0.0475763,"\int \frac{3+5 x}{(1-2 x)^3 (2+3 x)^4} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)^4),x]","\frac{-\frac{7 \left(82080 x^4+75240 x^3-31160 x^2-33725 x-3088\right)}{(1-2 x)^2 (3 x+2)^3}-4560 \log (3-6 x)+4560 \log (3 x+2)}{235298}","\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,"((-7*(-3088 - 33725*x - 31160*x^2 + 75240*x^3 + 82080*x^4))/((1 - 2*x)^2*(2 + 3*x)^3) - 4560*Log[3 - 6*x] + 4560*Log[2 + 3*x])/235298","A",1
1643,1,64,87,0.083965,"\int \frac{3+5 x}{(1-2 x)^3 (2+3 x)^5} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)^5),x]","\frac{4 \left(-\frac{7 \left(1658880 x^5+2626560 x^4+384000 x^3-1101440 x^2-403584 x+28275\right)}{16 (1-2 x)^2 (3 x+2)^4}-1920 \log (1-2 x)+1920 \log (6 x+4)\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,"(4*((-7*(28275 - 403584*x - 1101440*x^2 + 384000*x^3 + 2626560*x^4 + 1658880*x^5))/(16*(1 - 2*x)^2*(2 + 3*x)^4) - 1920*Log[1 - 2*x] + 1920*Log[4 + 6*x]))/823543","A",1
1644,1,69,98,0.082646,"\int \frac{3+5 x}{(1-2 x)^3 (2+3 x)^6} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)^6),x]","\frac{3 \left(-\frac{7 \left(10730880 x^6+24144480 x^5+13811040 x^4-5468940 x^3-7360644 x^2-1134751 x+381394\right)}{3 (1-2 x)^2 (3 x+2)^5}-22080 \log (3-6 x)+22080 \log (3 x+2)\right)}{16470860}","\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,"(3*((-7*(381394 - 1134751*x - 7360644*x^2 - 5468940*x^3 + 13811040*x^4 + 24144480*x^5 + 10730880*x^6))/(3*(1 - 2*x)^2*(2 + 3*x)^5) - 22080*Log[3 - 6*x] + 22080*Log[2 + 3*x]))/16470860","A",1
1645,1,71,80,0.0244443,"\int \frac{(2+3 x)^7 (3+5 x)^2}{(1-2 x)^3} \, dx","Integrate[((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+5921274170 (1-2 x)^2 \log (1-2 x)-1533057471}{8960 (1-2 x)^2}","-\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,"-1/8960*(-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 + 5921274170*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2","A",1
1646,1,66,73,0.0261972,"\int \frac{(2+3 x)^6 (3+5 x)^2}{(1-2 x)^3} \, dx","Integrate[((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+75439420 (1-2 x)^2 \log (1-2 x)-8887005}{512 (1-2 x)^2}","-\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,"-1/512*(-8887005 + 186131948*x - 489708252*x^2 + 194631840*x^3 + 82201680*x^4 + 42481728*x^5 + 18584640*x^6 + 5474304*x^7 + 777600*x^8 + 75439420*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2","A",1
1647,1,61,66,0.0215962,"\int \frac{(2+3 x)^5 (3+5 x)^2}{(1-2 x)^3} \, dx","Integrate[((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+32468380 (1-2 x)^2 \log (1-2 x)+1508337}{1024 (1-2 x)^2}","-\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,"-1/1024*(1508337 + 58608500*x - 190079460*x^2 + 81639840*x^3 + 31266000*x^4 + 13197888*x^5 + 4069440*x^6 + 622080*x^7 + 32468380*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2","A",1
1648,1,56,59,0.0267444,"\int \frac{(2+3 x)^4 (3+5 x)^2}{(1-2 x)^3} \, dx","Integrate[((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+3331804 (1-2 x)^2 \log (1-2 x)+808965}{512 (1-2 x)^2}","-\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,"-1/512*(808965 + 3354020*x - 17025300*x^2 + 7993248*x^3 + 2611152*x^4 + 797760*x^5 + 129600*x^6 + 3331804*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2","A",1
1649,1,47,52,0.0348776,"\int \frac{(2+3 x)^3 (3+5 x)^2}{(1-2 x)^3} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x)^2)/(1 - 2*x)^3,x]","\frac{1}{32} \left(-\frac{2 \left(1800 x^5+10890 x^4+43884 x^3-84411 x^2-55 x+9720\right)}{(1-2 x)^2}-39977 \log (1-2 x)\right)","-\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,"((-2*(9720 - 55*x - 84411*x^2 + 43884*x^3 + 10890*x^4 + 1800*x^5))/(1 - 2*x)^2 - 39977*Log[1 - 2*x])/32","A",1
1650,1,46,45,0.0180889,"\int \frac{(2+3 x)^2 (3+5 x)^2}{(1-2 x)^3} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x)^3,x]","-\frac{900 x^4+6360 x^3-10890 x^2-4802 x+3467 (1-2 x)^2 \log (1-2 x)+2790}{16 (1-2 x)^2}","-\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,"-1/16*(2790 - 4802*x - 10890*x^2 + 6360*x^3 + 900*x^4 + 3467*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2","A",1
1651,1,34,38,0.0326617,"\int \frac{(2+3 x) (3+5 x)^2}{(1-2 x)^3} \, dx","Integrate[((2 + 3*x)*(3 + 5*x)^2)/(1 - 2*x)^3,x]","\frac{1}{32} \left(\frac{600 x^2+3932 x-1269}{(1-2 x)^2}-300 x-1010 \log (1-2 x)\right)","-\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,"(-300*x + (-1269 + 3932*x + 600*x^2)/(1 - 2*x)^2 - 1010*Log[1 - 2*x])/32","A",1
1652,1,33,33,0.0086913,"\int \frac{(3+5 x)^2}{(1-2 x)^3} \, dx","Integrate[(3 + 5*x)^2/(1 - 2*x)^3,x]","-\frac{55}{4 (1-2 x)}+\frac{121}{16 (1-2 x)^2}-\frac{25}{8} \log (1-2 x)","-\frac{55}{4 (1-2 x)}+\frac{121}{16 (1-2 x)^2}-\frac{25}{8} \log (1-2 x)",1,"121/(16*(1 - 2*x)^2) - 55/(4*(1 - 2*x)) - (25*Log[1 - 2*x])/8","A",1
1653,1,35,43,0.0359776,"\int \frac{(3+5 x)^2}{(1-2 x)^3 (2+3 x)} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)),x]","\frac{\frac{77 (148 x+3)}{(1-2 x)^2}-8 \log (3-6 x)+8 \log (3 x+2)}{2744}","-\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,"((77*(3 + 148*x))/(1 - 2*x)^2 - 8*Log[3 - 6*x] + 8*Log[2 + 3*x])/2744","A",1
1654,1,47,54,0.0605878,"\int \frac{(3+5 x)^2}{(1-2 x)^3 (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^2),x]","\frac{\frac{7 \left(512 x^2+2645 x+1514\right)}{(1-2 x)^2 (3 x+2)}+256 \log (1-2 x)-256 \log (6 x+4)}{9604}","-\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,"((7*(1514 + 2645*x + 512*x^2))/((1 - 2*x)^2*(2 + 3*x)) + 256*Log[1 - 2*x] - 256*Log[4 + 6*x])/9604","A",1
1655,1,48,65,0.0383231,"\int \frac{(3+5 x)^2}{(1-2 x)^3 (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^3),x]","\frac{-\frac{7 \left(9948 x^3+2487 x^2-12104 x-6189\right)}{\left(6 x^2+x-2\right)^2}-1658 \log (1-2 x)+1658 \log (3 x+2)}{33614}","\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,"((-7*(-6189 - 12104*x + 2487*x^2 + 9948*x^3))/(-2 + x + 6*x^2)^2 - 1658*Log[1 - 2*x] + 1658*Log[2 + 3*x])/33614","A",1
1656,1,57,76,0.0766384,"\int \frac{(3+5 x)^2}{(1-2 x)^3 (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^4),x]","\frac{\frac{7 \left(-310500 x^4-284625 x^3+117875 x^2+180100 x+44411\right)}{(1-2 x)^2 (3 x+2)^3}-17250 \log (1-2 x)+17250 \log (6 x+4)}{352947}","\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,"((7*(44411 + 180100*x + 117875*x^2 - 284625*x^3 - 310500*x^4))/((1 - 2*x)^2*(2 + 3*x)^3) - 17250*Log[1 - 2*x] + 17250*Log[4 + 6*x])/352947","A",1
1657,1,64,87,0.0849607,"\int \frac{(3+5 x)^2}{(1-2 x)^3 (2+3 x)^5} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^5),x]","\frac{2 \left(-\frac{7 \left(15577920 x^5+24665040 x^4+3606000 x^3-10343210 x^2-4966396 x-460595\right)}{8 (1-2 x)^2 (3 x+2)^4}-36060 \log (1-2 x)+36060 \log (6 x+4)\right)}{2470629}","\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,"(2*((-7*(-460595 - 4966396*x - 10343210*x^2 + 3606000*x^3 + 24665040*x^4 + 15577920*x^5))/(8*(1 - 2*x)^2*(2 + 3*x)^4) - 36060*Log[1 - 2*x] + 36060*Log[4 + 6*x]))/2470629","A",1
1658,1,69,98,0.1004318,"\int \frac{(3+5 x)^2}{(1-2 x)^3 (2+3 x)^6} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^6),x]","\frac{4 \left(-\frac{7 \left(28421280 x^6+63947880 x^5+36579240 x^4-14484765 x^3-19495039 x^2-4230956 x+258089\right)}{4 (1-2 x)^2 (3 x+2)^5}-43860 \log (1-2 x)+43860 \log (6 x+4)\right)}{12353145}","\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,"(4*((-7*(258089 - 4230956*x - 19495039*x^2 - 14484765*x^3 + 36579240*x^4 + 63947880*x^5 + 28421280*x^6))/(4*(1 - 2*x)^2*(2 + 3*x)^5) - 43860*Log[1 - 2*x] + 43860*Log[4 + 6*x]))/12353145","A",1
1659,1,71,80,0.0286505,"\int \frac{(2+3 x)^6 (3+5 x)^3}{(1-2 x)^3} \, dx","Integrate[((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+3771490800 (1-2 x)^2 \log (1-2 x)-1001301969}{3584 (1-2 x)^2}","-\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,"-1/3584*(-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 + 3771490800*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2","A",1
1660,1,66,73,0.0303467,"\int \frac{(2+3 x)^5 (3+5 x)^3}{(1-2 x)^3} \, dx","Integrate[((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+240641940 (1-2 x)^2 \log (1-2 x)-30126129}{1024 (1-2 x)^2}","-\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,"-1/1024*(-30126129 + 600903660*x - 1569001020*x^2 + 621559520*x^3 + 263583600*x^4 + 137206464*x^5 + 60592320*x^6 + 18040320*x^7 + 2592000*x^8 + 240641940*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2","A",1
1661,1,61,64,0.0262038,"\int \frac{(2+3 x)^4 (3+5 x)^3}{(1-2 x)^3} \, dx","Integrate[((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+51892764 (1-2 x)^2 \log (1-2 x)+1974585}{1024 (1-2 x)^2}","-\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,"-1/1024*(1974585 + 95444820*x - 305448900*x^2 + 130737568*x^3 + 50369232*x^4 + 21464640*x^5 + 6696000*x^6 + 1036800*x^7 + 51892764*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2","A",1
1662,1,56,59,0.0275801,"\int \frac{(2+3 x)^3 (3+5 x)^3}{(1-2 x)^3} \, dx","Integrate[((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+5339796 (1-2 x)^2 \log (1-2 x)+1244595}{512 (1-2 x)^2}","-\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,"-1/512*(1244595 + 5590620*x - 27475116*x^2 + 12853984*x^3 + 4235760*x^4 + 1310400*x^5 + 216000*x^6 + 5339796*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2","A",1
1663,1,47,52,0.0244313,"\int \frac{(2+3 x)^2 (3+5 x)^3}{(1-2 x)^3} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x)^3)/(1 - 2*x)^3,x]","\frac{1}{32} \left(-\frac{2 \left(3000 x^5+17850 x^4+71020 x^3-137055 x^2+1509 x+15270\right)}{(1-2 x)^2}-64317 \log (1-2 x)\right)","-\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,"((-2*(15270 + 1509*x - 137055*x^2 + 71020*x^3 + 17850*x^4 + 3000*x^5))/(1 - 2*x)^2 - 64317*Log[1 - 2*x])/32","A",1
1664,1,46,45,0.0307048,"\int \frac{(2+3 x) (3+5 x)^3}{(1-2 x)^3} \, dx","Integrate[((2 + 3*x)*(3 + 5*x)^3)/(1 - 2*x)^3,x]","-\frac{3000 x^4+20800 x^3-35700 x^2-14796 x+11220 (1-2 x)^2 \log (1-2 x)+8877}{32 (1-2 x)^2}","-\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,"-1/32*(8877 - 14796*x - 35700*x^2 + 20800*x^3 + 3000*x^4 + 11220*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2","A",1
1665,1,34,38,0.0233659,"\int \frac{(3+5 x)^3}{(1-2 x)^3} \, dx","Integrate[(3 + 5*x)^3/(1 - 2*x)^3,x]","\frac{1}{32} \left(\frac{1000 x^2+6260 x-2049}{(1-2 x)^2}-500 x-1650 \log (1-2 x)\right)","-\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,"(-500*x + (-2049 + 6260*x + 1000*x^2)/(1 - 2*x)^2 - 1650*Log[1 - 2*x])/32","A",1
1666,1,35,43,0.0337084,"\int \frac{(3+5 x)^3}{(1-2 x)^3 (2+3 x)} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^3*(2 + 3*x)),x]","\frac{\frac{2541 (288 x-67)}{(1-2 x)^2}-85734 \log (3-6 x)-16 \log (3 x+2)}{16464}","-\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,"((2541*(-67 + 288*x))/(1 - 2*x)^2 - 85734*Log[3 - 6*x] - 16*Log[2 + 3*x])/16464","A",1
1667,1,47,54,0.0563965,"\int \frac{(3+5 x)^3}{(1-2 x)^3 (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^3*(2 + 3*x)^2),x]","\frac{\frac{7 \left(169916 x^2+112135 x-718\right)}{(1-2 x)^2 (3 x+2)}-792 \log (1-2 x)+792 \log (6 x+4)}{57624}","-\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,"((7*(-718 + 112135*x + 169916*x^2))/((1 - 2*x)^2*(2 + 3*x)) - 792*Log[1 - 2*x] + 792*Log[4 + 6*x])/57624","A",1
1668,1,48,65,0.0472389,"\int \frac{(3+5 x)^3}{(1-2 x)^3 (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^3*(2 + 3*x)^3),x]","\frac{\frac{7 \left(73656 x^3+318539 x^2+319912 x+93602\right)}{\left(6 x^2+x-2\right)^2}+12276 \log (1-2 x)-12276 \log (3 x+2)}{201684}","-\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,"((7*(93602 + 319912*x + 318539*x^2 + 73656*x^3))/(-2 + x + 6*x^2)^2 + 12276*Log[1 - 2*x] - 12276*Log[2 + 3*x])/201684","A",1
1669,1,57,76,0.0945639,"\int \frac{(3+5 x)^3}{(1-2 x)^3 (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^3*(2 + 3*x)^4),x]","\frac{\frac{7 \left(-2512620 x^4-2303235 x^3+3054740 x^2+4131175 x+1210868\right)}{(1-2 x)^2 (3 x+2)^3}-139590 \log (1-2 x)+139590 \log (6 x+4)}{2117682}","\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,"((7*(1210868 + 4131175*x + 3054740*x^2 - 2303235*x^3 - 2512620*x^4))/((1 - 2*x)^2*(2 + 3*x)^3) - 139590*Log[1 - 2*x] + 139590*Log[4 + 6*x])/2117682","A",1
1670,1,64,87,0.0862549,"\int \frac{(3+5 x)^3}{(1-2 x)^3 (2+3 x)^5} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^3*(2 + 3*x)^5),x]","\frac{-\frac{7 \left(38277360 x^5+60605820 x^4+8860500 x^3-32767930 x^2-21371408 x-3991495\right)}{4 (1-2 x)^2 (3 x+2)^4}-177210 \log (1-2 x)+177210 \log (6 x+4)}{2470629}","\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,"((-7*(-3991495 - 21371408*x - 32767930*x^2 + 8860500*x^3 + 60605820*x^4 + 38277360*x^5))/(4*(1 - 2*x)^2*(2 + 3*x)^4) - 177210*Log[1 - 2*x] + 177210*Log[4 + 6*x])/2470629","A",1
1671,1,98,76,0.0601729,"\int \frac{(2+3 x)^8}{(1-2 x)^3 (3+5 x)} \, dx","Integrate[(2 + 3*x)^8/((1 - 2*x)^3*(3 + 5*x)),x]","-\frac{27}{200} (3 x+2)^5-\frac{2889 (3 x+2)^4}{1600}-\frac{17019 (3 x+2)^3}{1000}-\frac{5992353 (3 x+2)^2}{40000}-\frac{631722537 (3 x+2)}{400000}+\frac{188591347}{30976 (2 x-1)}+\frac{5764801}{5632 (1-2 x)^2}-\frac{2644396573 \log (3-6 x)}{340736}+\frac{\log (-3 (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,"5764801/(5632*(1 - 2*x)^2) + 188591347/(30976*(-1 + 2*x)) - (631722537*(2 + 3*x))/400000 - (5992353*(2 + 3*x)^2)/40000 - (17019*(2 + 3*x)^3)/1000 - (2889*(2 + 3*x)^4)/1600 - (27*(2 + 3*x)^5)/200 - (2644396573*Log[3 - 6*x])/340736 + Log[-3*(3 + 5*x)]/20796875","A",1
1672,1,60,69,0.0475187,"\int \frac{(2+3 x)^7}{(1-2 x)^3 (3+5 x)} \, dx","Integrate[(2 + 3*x)^7/((1 - 2*x)^3*(3 + 5*x)),x]","\frac{-\frac{55 \left(1058508000 x^6+6797973600 x^5+23090763960 x^4+72578051568 x^3-42333890544 x^2-83615877112 x+35985148011\right)}{(1-2 x)^2}-1681645393750 \log (5-10 x)+256 \log (5 x+3)}{1064800000}","-\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,"((-55*(35985148011 - 83615877112*x - 42333890544*x^2 + 72578051568*x^3 + 23090763960*x^4 + 6797973600*x^5 + 1058508000*x^6))/(1 - 2*x)^2 - 1681645393750*Log[5 - 10*x] + 256*Log[3 + 5*x])/1064800000","A",1
1673,1,55,62,0.0356845,"\int \frac{(2+3 x)^6}{(1-2 x)^3 (3+5 x)} \, dx","Integrate[(2 + 3*x)^6/((1 - 2*x)^3*(3 + 5*x)),x]","\frac{-\frac{11 \left(235224000 x^5+1493672400 x^4+6252253920 x^3-3308307948 x^2-9050078692 x+3661042443\right)}{(1-2 x)^2}-31903287500 \log (5-10 x)+128 \log (5 x+3)}{106480000}","-\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,"((-11*(3661042443 - 9050078692*x - 3308307948*x^2 + 6252253920*x^3 + 1493672400*x^4 + 235224000*x^5))/(1 - 2*x)^2 - 31903287500*Log[5 - 10*x] + 128*Log[3 + 5*x])/106480000","A",1
1674,1,55,55,0.0404793,"\int \frac{(2+3 x)^5}{(1-2 x)^3 (3+5 x)} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^3*(3 + 5*x)),x]","\frac{-1293732 (5 x+3)^2-47005596 (5 x+3)+\frac{858357500}{2 x-1}+\frac{254205875}{(1-2 x)^2}-543655000 \log (5-10 x)+64 \log (5 x+3)}{10648000}","-\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,"(254205875/(1 - 2*x)^2 + 858357500/(-1 + 2*x) - 47005596*(3 + 5*x) - 1293732*(3 + 5*x)^2 - 543655000*Log[5 - 10*x] + 64*Log[3 + 5*x])/10648000","A",1
1675,1,46,48,0.0400266,"\int \frac{(2+3 x)^4}{(1-2 x)^3 (3+5 x)} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^3*(3 + 5*x)),x]","\frac{-431244 (5 x+3)+\frac{18299050}{2 x-1}+\frac{7263025}{(1-2 x)^2}-7690550 \log (5-10 x)+32 \log (5 x+3)}{1064800}","-\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,"(7263025/(1 - 2*x)^2 + 18299050/(-1 + 2*x) - 431244*(3 + 5*x) - 7690550*Log[5 - 10*x] + 32*Log[3 + 5*x])/1064800","A",1
1676,1,35,43,0.0329772,"\int \frac{(2+3 x)^3}{(1-2 x)^3 (3+5 x)} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^3*(3 + 5*x)),x]","\frac{\frac{2695 (256 x-51)}{(1-2 x)^2}-71890 \log (5-10 x)+16 \log (5 x+3)}{106480}","-\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,"((2695*(-51 + 256*x))/(1 - 2*x)^2 - 71890*Log[5 - 10*x] + 16*Log[3 + 5*x])/106480","A",1
1677,1,35,43,0.0334446,"\int \frac{(2+3 x)^2}{(1-2 x)^3 (3+5 x)} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^3*(3 + 5*x)),x]","\frac{\frac{77 (124 x+15)}{(1-2 x)^2}-8 \log (5-10 x)+8 \log (5 x+3)}{10648}","-\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,"((77*(15 + 124*x))/(1 - 2*x)^2 - 8*Log[5 - 10*x] + 8*Log[3 + 5*x])/10648","A",1
1678,1,46,43,0.0262826,"\int \frac{2+3 x}{(1-2 x)^3 (3+5 x)} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)^3*(3 + 5*x)),x]","\frac{-88 x-20 (1-2 x)^2 \log (1-2 x)+20 (1-2 x)^2 \log (10 x+6)+891}{5324 (1-2 x)^2}","\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,"(891 - 88*x - 20*(1 - 2*x)^2*Log[1 - 2*x] + 20*(1 - 2*x)^2*Log[6 + 10*x])/(5324*(1 - 2*x)^2)","A",1
1679,1,46,43,0.0152738,"\int \frac{1}{(1-2 x)^3 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^3*(3 + 5*x)),x]","\frac{-220 x-50 (1-2 x)^2 \log (1-2 x)+50 (1-2 x)^2 \log (10 x+6)+231}{2662 (1-2 x)^2}","\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,"(231 - 220*x - 50*(1 - 2*x)^2*Log[1 - 2*x] + 50*(1 - 2*x)^2*Log[6 + 10*x])/(2662*(1 - 2*x)^2)","A",1
1680,1,52,53,0.0344795,"\int \frac{1}{(1-2 x)^3 (2+3 x) (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^3*(2 + 3*x)*(3 + 5*x)),x]","\frac{-6938 \log (3-6 x)-35937 \log (3 x+2)+\frac{7 \left(-2992 x+6125 (1-2 x)^2 \log (-3 (5 x+3))+2343\right)}{(1-2 x)^2}}{456533}","\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,"(-6938*Log[3 - 6*x] - 35937*Log[2 + 3*x] + (7*(2343 - 2992*x + 6125*(1 - 2*x)^2*Log[-3*(3 + 5*x)]))/(1 - 2*x)^2)/456533","A",1
1681,1,57,64,0.082744,"\int \frac{1}{(1-2 x)^3 (2+3 x)^2 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)),x]","\frac{\frac{77 \left(10644 x^2-13010 x+4383\right)}{(1-2 x)^2 (3 x+2)}-27208 \log (5-10 x)-1473417 \log (5 (3 x+2))+1500625 \log (5 x+3)}{3195731}","\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,"((77*(4383 - 13010*x + 10644*x^2))/((1 - 2*x)^2*(2 + 3*x)) - 27208*Log[5 - 10*x] - 1473417*Log[5*(2 + 3*x)] + 1500625*Log[3 + 5*x])/3195731","A",1
1682,1,58,75,0.0771679,"\int \frac{1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)),x]","\frac{\frac{77 \left(3176136 x^3-1006716 x^2-1414978 x+569697\right)}{\left(6 x^2+x-2\right)^2}-179584 \log (5-10 x)-104864166 \log (5 (3 x+2))+105043750 \log (5 x+3)}{44740234}","\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,"((77*(569697 - 1414978*x - 1006716*x^2 + 3176136*x^3))/(-2 + x + 6*x^2)^2 - 179584*Log[5 - 10*x] - 104864166*Log[5*(2 + 3*x)] + 105043750*Log[3 + 5*x])/44740234","A",1
1683,1,69,86,0.1118715,"\int \frac{1}{(1-2 x)^3 (2+3 x)^4 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)),x]","\frac{5 \left(\frac{77 \left(342903240 x^4+125249220 x^3-222614730 x^2-43096225 x+40167012\right)}{5 (1-2 x)^2 (3 x+2)^3}-107104 \log (5-10 x)-735199146 \log (5 (3 x+2))+735306250 \log (5 x+3)\right)}{313181638}","\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,"(5*((77*(40167012 - 43096225*x - 222614730*x^2 + 125249220*x^3 + 342903240*x^4))/(5*(1 - 2*x)^2*(2 + 3*x)^3) - 107104*Log[5 - 10*x] - 735199146*Log[5*(2 + 3*x)] + 735306250*Log[3 + 5*x]))/313181638","A",1
1684,1,98,80,0.0586048,"\int \frac{(2+3 x)^8}{(1-2 x)^3 (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^8/((1 - 2*x)^3*(3 + 5*x)^2),x]","-\frac{81}{800} (3 x+2)^4-\frac{2943 (3 x+2)^3}{2000}-\frac{315171 (3 x+2)^2}{20000}-\frac{18607401 (3 x+2)}{100000}+\frac{79883671}{85184 (2 x-1)}-\frac{1}{20796875 (5 x+3)}+\frac{5764801}{30976 (1-2 x)^2}-\frac{1845559863 \log (3-6 x)}{1874048}+\frac{54 \log (-3 (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,"5764801/(30976*(1 - 2*x)^2) + 79883671/(85184*(-1 + 2*x)) - (18607401*(2 + 3*x))/100000 - (315171*(2 + 3*x)^2)/20000 - (2943*(2 + 3*x)^3)/2000 - (81*(2 + 3*x)^4)/800 - 1/(20796875*(3 + 5*x)) - (1845559863*Log[3 - 6*x])/1874048 + (54*Log[-3*(3 + 5*x)])/45753125","A",1
1685,1,67,73,0.0603948,"\int \frac{(2+3 x)^7}{(1-2 x)^3 (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^7/((1 - 2*x)^3*(3 + 5*x)^2),x]","\frac{-\frac{22 \left(4851495000 x^6+34203039750 x^5+151415158950 x^4-172378468845 x^3-163837494156 x^2+25343933346 x+19763981131\right)}{(1-2 x)^2 (5 x+3)}-272430965625 \log (1-2 x)+7584 \log (10 x+6)}{1464100000}","-\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,"((-22*(19763981131 + 25343933346*x - 163837494156*x^2 - 172378468845*x^3 + 151415158950*x^4 + 34203039750*x^5 + 4851495000*x^6))/((1 - 2*x)^2*(3 + 5*x)) - 272430965625*Log[1 - 2*x] + 7584*Log[6 + 10*x])/1464100000","A",1
1686,1,74,66,0.0543528,"\int \frac{(2+3 x)^6}{(1-2 x)^3 (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^6/((1 - 2*x)^3*(3 + 5*x)^2),x]","-\frac{729 (1-2 x)^2}{1600}+\frac{2187}{250} (1-2 x)+\frac{67228}{1331 (2 x-1)}-\frac{1}{831875 (5 x+3)}+\frac{117649}{7744 (1-2 x)^2}-\frac{7383075 \log (1-2 x)}{234256}+\frac{204 \log (10 x+6)}{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,"117649/(7744*(1 - 2*x)^2) + (2187*(1 - 2*x))/250 - (729*(1 - 2*x)^2)/1600 + 67228/(1331*(-1 + 2*x)) - 1/(831875*(3 + 5*x)) - (7383075*Log[1 - 2*x])/234256 + (204*Log[6 + 10*x])/9150625","A",1
1687,1,55,59,0.0478159,"\int \frac{(2+3 x)^5}{(1-2 x)^3 (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^3*(3 + 5*x)^2),x]","\frac{35577630 (1-2 x)+\frac{627261250}{2 x-1}-\frac{352}{5 x+3}+\frac{254205875}{(1-2 x)^2}-258536250 \log (1-2 x)+5472 \log (10 x+6)}{58564000}","-\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,"(254205875/(1 - 2*x)^2 + 35577630*(1 - 2*x) + 627261250/(-1 + 2*x) - 352/(3 + 5*x) - 258536250*Log[1 - 2*x] + 5472*Log[6 + 10*x])/58564000","A",1
1688,1,48,54,0.0416969,"\int \frac{(2+3 x)^4}{(1-2 x)^3 (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^3*(3 + 5*x)^2),x]","\frac{\frac{11696300}{2 x-1}-\frac{176}{5 x+3}+\frac{7263025}{(1-2 x)^2}-2374050 \log (1-2 x)+2208 \log (10 x+6)}{5856400}","-\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,"(7263025/(1 - 2*x)^2 + 11696300/(-1 + 2*x) - 176/(3 + 5*x) - 2374050*Log[1 - 2*x] + 2208*Log[6 + 10*x])/5856400","A",1
1689,1,47,54,0.0437854,"\int \frac{(2+3 x)^3}{(1-2 x)^3 (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^3*(3 + 5*x)^2),x]","\frac{\frac{11 \left(142068 x^2+108567 x+13957\right)}{(1-2 x)^2 (5 x+3)}-840 \log (1-2 x)+840 \log (10 x+6)}{585640}","-\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,"((11*(13957 + 108567*x + 142068*x^2))/((1 - 2*x)^2*(3 + 5*x)) - 840*Log[1 - 2*x] + 840*Log[6 + 10*x])/585640","A",1
1690,1,48,54,0.0464088,"\int \frac{(2+3 x)^2}{(1-2 x)^3 (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^3*(3 + 5*x)^2),x]","\frac{\frac{616}{1-2 x}-\frac{44}{5 x+3}+\frac{5929}{(1-2 x)^2}-288 \log (1-2 x)+288 \log (10 x+6)}{58564}","\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,"(5929/(1 - 2*x)^2 + 616/(1 - 2*x) - 44/(3 + 5*x) - 288*Log[1 - 2*x] + 288*Log[6 + 10*x])/58564","A",1
1691,1,62,54,0.0244607,"\int \frac{2+3 x}{(1-2 x)^3 (3+5 x)^2} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)^3*(3 + 5*x)^2),x]","\frac{10}{1331 (5 (1-2 x)-11)}+\frac{37}{1331 (1-2 x)}+\frac{7}{242 (1-2 x)^2}+\frac{195 \log (11-5 (1-2 x))}{14641}-\frac{195 \log (1-2 x)}{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,"10/(1331*(-11 + 5*(1 - 2*x))) + 7/(242*(1 - 2*x)^2) + 37/(1331*(1 - 2*x)) + (195*Log[11 - 5*(1 - 2*x)])/14641 - (195*Log[1 - 2*x])/14641","A",1
1692,1,62,54,0.0262045,"\int \frac{1}{(1-2 x)^3 (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^3*(3 + 5*x)^2),x]","\frac{50}{1331 (5 (1-2 x)-11)}+\frac{20}{1331 (1-2 x)}+\frac{1}{121 (1-2 x)^2}+\frac{150 \log (11-5 (1-2 x))}{14641}-\frac{150 \log (1-2 x)}{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,"50/(1331*(-11 + 5*(1 - 2*x))) + 1/(121*(1 - 2*x)^2) + 20/(1331*(1 - 2*x)) + (150*Log[11 - 5*(1 - 2*x)])/14641 - (150*Log[1 - 2*x])/14641","A",1
1693,1,60,64,0.040926,"\int \frac{1}{(1-2 x)^3 (2+3 x) (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^3*(2 + 3*x)*(3 + 5*x)^2),x]","\frac{3 \left(\frac{31724}{3-6 x}-\frac{471625}{15 x+9}+\frac{11858}{3 (1-2 x)^2}-9432 \log (3-6 x)+395307 \log (3 x+2)-385875 \log (-3 (5 x+3))\right)}{5021863}","\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,"(3*(31724/(3 - 6*x) + 11858/(3*(1 - 2*x)^2) - 471625/(9 + 15*x) - 9432*Log[3 - 6*x] + 395307*Log[2 + 3*x] - 385875*Log[-3*(3 + 5*x)]))/5021863","A",1
1694,1,68,75,0.0997779,"\int \frac{1}{(1-2 x)^3 (2+3 x)^2 (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{2 \left(77 \left(-\frac{107811}{6 x+4}-\frac{214375}{10 x+6}+\frac{544}{1-2 x}+\frac{154}{(1-2 x)^2}\right)-46248 \log (1-2 x)+45064998 \log (6 x+4)-45018750 \log (10 x+6)\right)}{35153041}","\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,"(2*(77*(154/(1 - 2*x)^2 + 544/(1 - 2*x) - 107811/(4 + 6*x) - 214375/(6 + 10*x)) - 46248*Log[1 - 2*x] + 45064998*Log[4 + 6*x] - 45018750*Log[6 + 10*x]))/35153041","A",1
1695,1,74,86,0.0797082,"\int \frac{1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^2),x]","\frac{\frac{41503 (6558 x-3251)}{\left(6 x^2+x-2\right)^2}-\frac{154 (16395384 x-7937593)}{6 x^2+x-2}-\frac{1155481250}{5 x+3}-548448 \log (5-10 x)+9769617198 \log (5 (3 x+2))-9769068750 \log (5 x+3)}{492142574}","\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,"(-1155481250/(3 + 5*x) + (41503*(-3251 + 6558*x))/(-2 + x + 6*x^2)^2 - (154*(-7937593 + 16395384*x))/(-2 + x + 6*x^2) - 548448*Log[5 - 10*x] + 9769617198*Log[5*(2 + 3*x)] - 9769068750*Log[3 + 5*x])/492142574","A",1
1696,1,88,97,0.1838957,"\int \frac{1}{(1-2 x)^3 (2+3 x)^4 (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^2),x]","\frac{2 \left(\frac{77}{2} \left(-\frac{444073509}{3 x+2}-\frac{262609375}{5 x+3}-\frac{28677726}{(3 x+2)^2}-\frac{1760913}{(3 x+2)^3}+\frac{6464}{1-2 x}+\frac{1232}{(1-2 x)^2}\right)-380880 \log (1-2 x)+115811115255 \log (6 x+4)-115810734375 \log (10 x+6)\right)}{1722499009}","\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,"(2*((77*(1232/(1 - 2*x)^2 + 6464/(1 - 2*x) - 1760913/(2 + 3*x)^3 - 28677726/(2 + 3*x)^2 - 444073509/(2 + 3*x) - 262609375/(3 + 5*x)))/2 - 380880*Log[1 - 2*x] + 115811115255*Log[4 + 6*x] - 115810734375*Log[6 + 10*x]))/1722499009","A",1
1697,1,75,91,0.0513509,"\int \frac{(2+3 x)^9}{(1-2 x)^3 (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^9/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{-\frac{11 \left(144089401500000 x^8+1123897331700000 x^7+4502793796875000 x^6+14903967293820000 x^5+8450955823285800 x^4-15846035365304040 x^3-12213049363361937 x^2+1867950230356442 x+1977372328510687\right)}{\left(10 x^2+x-3\right)^2}-1977661307343750 \log (3-6 x)+10498560 \log (-3 (5 x+3))}{3221020000000}","-\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,"((-11*(1977372328510687 + 1867950230356442*x - 12213049363361937*x^2 - 15846035365304040*x^3 + 8450955823285800*x^4 + 14903967293820000*x^5 + 4502793796875000*x^6 + 1123897331700000*x^7 + 144089401500000*x^8))/(-3 + x + 10*x^2)^2 - 1977661307343750*Log[3 - 6*x] + 10498560*Log[-3*(3 + 5*x)])/3221020000000","A",1
1698,1,70,84,0.0451224,"\int \frac{(2+3 x)^8}{(1-2 x)^3 (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^8/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{-\frac{11 \left(6403973400000 x^7+49630793850000 x^6+232677700200000 x^5+148045752548100 x^4-314407515766380 x^3-254889143270829 x^2+31893783102814 x+39754322426279\right)}{\left(10 x^2+x-3\right)^2}-37213849312500 \log (3-6 x)+4108800 \log (-3 (5 x+3))}{322102000000}","-\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,"((-11*(39754322426279 + 31893783102814*x - 254889143270829*x^2 - 314407515766380*x^3 + 148045752548100*x^4 + 232677700200000*x^5 + 49630793850000*x^6 + 6403973400000*x^7))/(-3 + x + 10*x^2)^2 - 37213849312500*Log[3 - 6*x] + 4108800*Log[-3*(3 + 5*x)])/322102000000","A",1
1699,1,65,77,0.0460261,"\int \frac{(2+3 x)^7}{(1-2 x)^3 (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^7/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{-\frac{11 \left(320198670000 x^6+2860441452000 x^5+2092320420300 x^4-5957126547060 x^3-5105353973121 x^2+410862940766 x+734029874011\right)}{\left(10 x^2+x-3\right)^2}-626480925000 \log (3-6 x)+1553856 \log (-3 (5 x+3))}{32210200000}","-\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,"((-11*(734029874011 + 410862940766*x - 5105353973121*x^2 - 5957126547060*x^3 + 2092320420300*x^4 + 2860441452000*x^5 + 320198670000*x^6))/(-3 + x + 10*x^2)^2 - 626480925000*Log[3 - 6*x] + 1553856*Log[-3*(3 + 5*x)])/32210200000","A",1
1700,1,60,70,0.0512051,"\int \frac{(2+3 x)^6}{(1-2 x)^3 (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^6/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{-\frac{55 \left(4269315600 x^5+3700073520 x^4-21487765512 x^3-19656314001 x^2+49588250 x+2317121263\right)}{\left(10 x^2+x-3\right)^2}-8688618750 \log (3-6 x)+561504 \log (-3 (5 x+3))}{3221020000}","-\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,"((-55*(2317121263 + 49588250*x - 19656314001*x^2 - 21487765512*x^3 + 3700073520*x^4 + 4269315600*x^5))/(-3 + x + 10*x^2)^2 - 8688618750*Log[3 - 6*x] + 561504*Log[-3*(3 + 5*x)])/3221020000","A",1
1701,1,50,65,0.0406873,"\int \frac{(2+3 x)^5}{(1-2 x)^3 (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{\frac{11 \left(1800695280 x^3+1838287161 x^2+261128254 x-116156671\right)}{\left(10 x^2+x-3\right)^2}-78461250 \log (3-6 x)+190464 \log (-3 (5 x+3))}{322102000}","-\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,"((11*(-116156671 + 261128254*x + 1838287161*x^2 + 1800695280*x^3))/(-3 + x + 10*x^2)^2 - 78461250*Log[3 - 6*x] + 190464*Log[-3*(3 + 5*x)])/322102000","A",1
1702,1,48,65,0.0405168,"\int \frac{(2+3 x)^4}{(1-2 x)^3 (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{\frac{11 \left(23130420 x^3+32722281 x^2+14259554 x+1771669\right)}{\left(10 x^2+x-3\right)^2}+58800 \log (-5 x-3)-58800 \log (1-2 x)}{32210200}","-\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,"((11*(1771669 + 14259554*x + 32722281*x^2 + 23130420*x^3))/(-3 + x + 10*x^2)^2 + 58800*Log[-3 - 5*x] - 58800*Log[1 - 2*x])/32210200","A",1
1703,1,48,65,0.0346623,"\int \frac{(2+3 x)^3}{(1-2 x)^3 (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{-\frac{11 \left(155400 x^3-371997 x^2-604258 x-194963\right)}{\left(10 x^2+x-3\right)^2}+15540 \log (-5 x-3)-15540 \log (1-2 x)}{3221020}","\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,"((-11*(-194963 - 604258*x - 371997*x^2 + 155400*x^3))/(-3 + x + 10*x^2)^2 + 15540*Log[-3 - 5*x] - 15540*Log[1 - 2*x])/3221020","A",1
1704,1,48,65,0.0358094,"\int \frac{(2+3 x)^2}{(1-2 x)^3 (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{-\frac{11 \left(30180 x^3+4527 x^2-23774 x-9322\right)}{\left(10 x^2+x-3\right)^2}+3018 \log (-5 x-3)-3018 \log (1-2 x)}{322102}","\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,"((-11*(-9322 - 23774*x + 4527*x^2 + 30180*x^3))/(-3 + x + 10*x^2)^2 + 3018*Log[-3 - 5*x] - 3018*Log[1 - 2*x])/322102","A",1
1705,1,48,65,0.0291705,"\int \frac{2+3 x}{(1-2 x)^3 (3+5 x)^3} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{\frac{11 \left(-22200 x^3-3330 x^2+11026 x+2753\right)}{\left(10 x^2+x-3\right)^2}-2220 \log (1-2 x)+2220 \log (5 x+3)}{322102}","\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,"((11*(2753 + 11026*x - 3330*x^2 - 22200*x^3))/(-3 + x + 10*x^2)^2 - 2220*Log[1 - 2*x] + 2220*Log[3 + 5*x])/322102","A",1
1706,1,48,65,0.030125,"\int \frac{1}{(1-2 x)^3 (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^3*(3 + 5*x)^3),x]","\frac{-\frac{11 \left(12000 x^3+1800 x^2-5960 x-301\right)}{\left(10 x^2+x-3\right)^2}-1200 \log (1-2 x)+1200 \log (5 x+3)}{322102}","\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,"((-11*(-301 - 5960*x + 1800*x^2 + 12000*x^3))/(-3 + x + 10*x^2)^2 - 1200*Log[1 - 2*x] + 1200*Log[3 + 5*x])/322102","A",1
1707,1,60,75,0.089817,"\int \frac{1}{(1-2 x)^3 (2+3 x) (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^3*(2 + 3*x)*(3 + 5*x)^3),x]","-\frac{3 \left(-\frac{77 \left(6504600 x^3-2977380 x^2-2000774 x+950291\right)}{3 \left(10 x^2+x-3\right)^2}+63488 \log (3-6 x)+26090262 \log (3 x+2)-26153750 \log (-3 (5 x+3))\right)}{110480986}","\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,"(-3*((-77*(950291 - 2000774*x - 2977380*x^2 + 6504600*x^3))/(3*(-3 + x + 10*x^2)^2) + 63488*Log[3 - 6*x] + 26090262*Log[2 + 3*x] - 26153750*Log[-3*(3 + 5*x)]))/110480986","A",1
1708,1,76,86,0.0850542,"\int \frac{1}{(1-2 x)^3 (2+3 x)^2 (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)^3),x]","-\frac{3 \left(-\frac{65219 (12290 x-6101)}{3 \left(10 x^2+x-3\right)^2}-\frac{154 (8570440 x-4446931)}{10 x^2+x-3}-\frac{182631834}{3 x+2}+187168 \log (3-6 x)+2896019082 \log (3 x+2)-2896206250 \log (-3 (5 x+3))\right)}{773366902}","\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,"(-3*(-182631834/(2 + 3*x) - (65219*(-6101 + 12290*x))/(3*(-3 + x + 10*x^2)^2) - (154*(-4446931 + 8570440*x))/(-3 + x + 10*x^2) + 187168*Log[3 - 6*x] + 2896019082*Log[2 + 3*x] - 2896206250*Log[-3*(3 + 5*x)]))/773366902","A",1
1709,1,88,97,0.2063246,"\int \frac{1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{2 \left(\frac{77}{4} \left(\frac{789823386}{3 x+2}+\frac{1395581250}{5 x+3}+\frac{24904341}{(3 x+2)^2}-\frac{82534375}{(5 x+3)^2}+\frac{13056}{1-2 x}+\frac{2464}{(1-2 x)^2}\right)-388464 \log (1-2 x)-156619842786 \log (6 x+4)+156620231250 \log (10 x+6)\right)}{2706784157}","\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,"(2*((77*(2464/(1 - 2*x)^2 + 13056/(1 - 2*x) + 24904341/(2 + 3*x)^2 + 789823386/(2 + 3*x) - 82534375/(3 + 5*x)^2 + 1395581250/(3 + 5*x)))/4 - 388464*Log[1 - 2*x] - 156619842786*Log[4 + 6*x] + 156620231250*Log[6 + 10*x]))/2706784157","A",1
1710,1,82,108,0.145686,"\int \frac{1}{(1-2 x)^3 (2+3 x)^4 (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^3),x]","-\frac{3 \left(-\frac{77 \left(86993245890000 x^6+136289326113000 x^5+13177709631900 x^4-67213599053550 x^3-23334840827100 x^2+8254486652965 x+3666255393392\right)}{3 (3 x+2)^3 \left(10 x^2+x-3\right)^2}+1369600 \log (3-6 x)+12404615067900 \log (3 x+2)-12404616437500 \log (-3 (5 x+3))\right)}{37894978198}","\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,"(-3*((-77*(3666255393392 + 8254486652965*x - 23334840827100*x^2 - 67213599053550*x^3 + 13177709631900*x^4 + 136289326113000*x^5 + 86993245890000*x^6))/(3*(2 + 3*x)^3*(-3 + x + 10*x^2)^2) + 1369600*Log[3 - 6*x] + 12404615067900*Log[2 + 3*x] - 12404616437500*Log[-3*(3 + 5*x)]))/37894978198","A",1
1711,1,653,361,0.3228222,"\int (a+b x)^3 (c+d x)^3 (e+f x)^3 \, dx","Integrate[(a + b*x)^3*(c + d*x)^3*(e + f*x)^3,x]","a^3 c^3 e^3 x+\frac{3}{8} b d f x^8 \left(a^2 d^2 f^2+3 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)+a c e x^3 \left(a^2 \left(c^2 f^2+3 c d e f+d^2 e^2\right)+3 a b c e (c f+d e)+b^2 c^2 e^2\right)+\frac{3}{2} a^2 c^2 e^2 x^2 (a c f+a d e+b c e)+\frac{1}{7} x^7 \left(a^3 d^3 f^3+9 a^2 b d^2 f^2 (c f+d e)+9 a b^2 d f \left(c^2 f^2+3 c d e f+d^2 e^2\right)+b^3 \left(c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+d^3 e^3\right)\right)+\frac{1}{2} x^6 \left(a^3 d^2 f^2 (c f+d e)+3 a^2 b d f \left(c^2 f^2+3 c d e f+d^2 e^2\right)+a b^2 \left(c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+d^3 e^3\right)+b^3 c e \left(c^2 f^2+3 c d e f+d^2 e^2\right)\right)+\frac{3}{5} x^5 \left(a^3 d f \left(c^2 f^2+3 c d e f+d^2 e^2\right)+a^2 b \left(c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+d^3 e^3\right)+3 a b^2 c e \left(c^2 f^2+3 c d e f+d^2 e^2\right)+b^3 c^2 e^2 (c f+d e)\right)+\frac{1}{4} x^4 \left(a^3 \left(c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+d^3 e^3\right)+9 a^2 b c e \left(c^2 f^2+3 c d e f+d^2 e^2\right)+9 a b^2 c^2 e^2 (c f+d e)+b^3 c^3 e^3\right)+\frac{1}{3} b^2 d^2 f^2 x^9 (a d f+b c f+b d e)+\frac{1}{10} b^3 d^3 f^3 x^{10}","\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,"a^3*c^3*e^3*x + (3*a^2*c^2*e^2*(b*c*e + a*d*e + a*c*f)*x^2)/2 + a*c*e*(b^2*c^2*e^2 + 3*a*b*c*e*(d*e + c*f) + a^2*(d^2*e^2 + 3*c*d*e*f + c^2*f^2))*x^3 + ((b^3*c^3*e^3 + 9*a*b^2*c^2*e^2*(d*e + c*f) + 9*a^2*b*c*e*(d^2*e^2 + 3*c*d*e*f + c^2*f^2) + a^3*(d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + c^3*f^3))*x^4)/4 + (3*(b^3*c^2*e^2*(d*e + c*f) + 3*a*b^2*c*e*(d^2*e^2 + 3*c*d*e*f + c^2*f^2) + a^3*d*f*(d^2*e^2 + 3*c*d*e*f + c^2*f^2) + a^2*b*(d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + c^3*f^3))*x^5)/5 + ((a^3*d^2*f^2*(d*e + c*f) + b^3*c*e*(d^2*e^2 + 3*c*d*e*f + c^2*f^2) + 3*a^2*b*d*f*(d^2*e^2 + 3*c*d*e*f + c^2*f^2) + a*b^2*(d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + c^3*f^3))*x^6)/2 + ((a^3*d^3*f^3 + 9*a^2*b*d^2*f^2*(d*e + c*f) + 9*a*b^2*d*f*(d^2*e^2 + 3*c*d*e*f + c^2*f^2) + b^3*(d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + c^3*f^3))*x^7)/7 + (3*b*d*f*(a^2*d^2*f^2 + 3*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + 3*c*d*e*f + c^2*f^2))*x^8)/8 + (b^2*d^2*f^2*(b*d*e + b*c*f + a*d*f)*x^9)/3 + (b^3*d^3*f^3*x^10)/10","A",1
1712,1,241,193,0.1293769,"\int (a+b x)^2 (c+d x)^2 (e+f x)^2 \, dx","Integrate[(a + b*x)^2*(c + d*x)^2*(e + f*x)^2,x]","\frac{1}{5} x^5 \left(a^2 d^2 f^2+4 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)+\frac{1}{2} x^4 \left(a^2 d f (c f+d e)+a b \left(c^2 f^2+4 c d e f+d^2 e^2\right)+b^2 c e (c f+d e)\right)+\frac{1}{3} x^3 \left(a^2 \left(c^2 f^2+4 c d e f+d^2 e^2\right)+4 a b c e (c f+d e)+b^2 c^2 e^2\right)+a^2 c^2 e^2 x+\frac{1}{3} b d f x^6 (a d f+b c f+b d e)+a c e x^2 (a c f+a d e+b c e)+\frac{1}{7} b^2 d^2 f^2 x^7","\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,"a^2*c^2*e^2*x + a*c*e*(b*c*e + a*d*e + a*c*f)*x^2 + ((b^2*c^2*e^2 + 4*a*b*c*e*(d*e + c*f) + a^2*(d^2*e^2 + 4*c*d*e*f + c^2*f^2))*x^3)/3 + ((b^2*c*e*(d*e + c*f) + a^2*d*f*(d*e + c*f) + a*b*(d^2*e^2 + 4*c*d*e*f + c^2*f^2))*x^4)/2 + ((a^2*d^2*f^2 + 4*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + 4*c*d*e*f + c^2*f^2))*x^5)/5 + (b*d*f*(b*d*e + b*c*f + a*d*f)*x^6)/3 + (b^2*d^2*f^2*x^7)/7","A",1
1713,1,53,56,0.0277897,"\int (a+b x) (c+d x) (e+f x) \, dx","Integrate[(a + b*x)*(c + d*x)*(e + f*x),x]","\frac{1}{12} x \left(4 x^2 (a d f+b c f+b d e)+6 x (a c f+a d e+b c e)+12 a c e+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 + a*d*e + a*c*f)*x + 4*(b*d*e + b*c*f + a*d*f)*x^2 + 3*b*d*f*x^3))/12","A",1
1714,1,80,86,0.070788,"\int \frac{1}{(a+b x) (c+d x) (e+f x)} \, dx","Integrate[1/((a + b*x)*(c + d*x)*(e + f*x)),x]","\frac{b \log (a+b x) (c f-d e)+d (b e-a f) \log (c+d x)+f (a d-b c) \log (e+f x)}{(b c-a d) (b e-a f) (c f-d e)}","\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*(-(d*e) + c*f)*Log[a + b*x] + d*(b*e - a*f)*Log[c + d*x] + (-(b*c) + a*d)*f*Log[e + f*x])/((b*c - a*d)*(b*e - a*f)*(-(d*e) + c*f))","A",1
1715,1,232,234,0.7369902,"\int \frac{1}{(a+b x)^2 (c+d x)^2 (e+f x)^2} \, dx","Integrate[1/((a + b*x)^2*(c + d*x)^2*(e + f*x)^2),x]","-\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 (c f-d e)^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}","-\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/((b*c - a*d)^2*(b*e - a*f)^2*(a + b*x))) - d^3/((b*c - a*d)^2*(d*e - c*f)^2*(c + d*x)) - f^3/((b*e - a*f)^2*(d*e - c*f)^2*(e + f*x)) - (2*b^3*(b*d*e + b*c*f - 2*a*d*f)*Log[a + b*x])/((b*c - a*d)^3*(b*e - a*f)^3) - (2*d^3*(b*d*e - 2*b*c*f + a*d*f)*Log[c + d*x])/((b*c - a*d)^3*(-(d*e) + c*f)^3) - (2*f^3*(-2*b*d*e + b*c*f + a*d*f)*Log[e + f*x])/((b*e - a*f)^3*(d*e - c*f)^3)","A",1
1716,1,490,495,1.7082314,"\int \frac{1}{(a+b x)^3 (c+d x)^3 (e+f x)^3} \, dx","Integrate[1/((a + b*x)^3*(c + d*x)^3*(e + f*x)^3),x]","\frac{1}{2} \left(\frac{6 f^5 \log (e+f x) \left(2 a^2 d^2 f^2+a b d f (3 c f-7 d e)+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{6 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 (c f-d e)^5}+\frac{6 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{6 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}{(a+b x)^2 (b c-a d)^3 (b e-a f)^3}+\frac{6 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}{(c+d x)^2 (b c-a d)^3 (c f-d e)^3}+\frac{6 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}{(e+f x)^2 (b e-a f)^3 (d e-c f)^3}\right)","\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^5/((b*c - a*d)^3*(b*e - a*f)^3*(a + b*x)^2)) + (6*b^5*(b*d*e + b*c*f - 2*a*d*f))/((b*c - a*d)^4*(b*e - a*f)^4*(a + b*x)) - d^5/((b*c - a*d)^3*(-(d*e) + c*f)^3*(c + d*x)^2) + (6*d^5*(b*d*e - 2*b*c*f + a*d*f))/((b*c - a*d)^4*(d*e - c*f)^4*(c + d*x)) - f^5/((b*e - a*f)^3*(d*e - c*f)^3*(e + f*x)^2) + (6*f^5*(-2*b*d*e + b*c*f + a*d*f))/((b*e - a*f)^4*(d*e - c*f)^4*(e + f*x)) + (6*b^5*(7*a^2*d^2*f^2 - 7*a*b*d*f*(d*e + c*f) + b^2*(2*d^2*e^2 + 3*c*d*e*f + 2*c^2*f^2))*Log[a + b*x])/((b*c - a*d)^5*(b*e - a*f)^5) + (6*d^5*(2*a^2*d^2*f^2 + a*b*d*f*(3*d*e - 7*c*f) + b^2*(2*d^2*e^2 - 7*c*d*e*f + 7*c^2*f^2))*Log[c + d*x])/((b*c - a*d)^5*(-(d*e) + c*f)^5) + (6*f^5*(2*a^2*d^2*f^2 + a*b*d*f*(-7*d*e + 3*c*f) + b^2*(7*d^2*e^2 - 7*c*d*e*f + 2*c^2*f^2))*Log[e + f*x])/((b*e - a*f)^5*(d*e - c*f)^5))/2","A",1
1717,1,265,170,0.6974873,"\int \frac{(c+d x)^{3/2}}{(a+b x)^2 (e+f x)} \, dx","Integrate[(c + d*x)^(3/2)/((a + b*x)^2*(e + f*x)),x]","\frac{\frac{(-a d f-2 b c f+3 b d e) \left(\sqrt{b} \sqrt{c+d x} (-3 a d+4 b c+b d x)-3 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)\right)}{b^{3/2} (b e-a f)}+\frac{2 (b c-a d) \left(\sqrt{f} \sqrt{c+d x} \sqrt{d e-c f} (4 c f-3 d e+d f x)+3 (d e-c f)^2 \tan ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d e-c f}}\right)\right)}{\sqrt{f} (b e-a f) \sqrt{d e-c f}}-\frac{3 b (c+d x)^{5/2}}{a+b x}}{3 (b c-a d) (b e-a f)}","-\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,"((-3*b*(c + d*x)^(5/2))/(a + b*x) + (2*(b*c - a*d)*(Sqrt[f]*Sqrt[d*e - c*f]*Sqrt[c + d*x]*(-3*d*e + 4*c*f + d*f*x) + 3*(d*e - c*f)^2*ArcTan[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[d*e - c*f]]))/(Sqrt[f]*(b*e - a*f)*Sqrt[d*e - c*f]) + ((3*b*d*e - 2*b*c*f - a*d*f)*(Sqrt[b]*Sqrt[c + d*x]*(4*b*c - 3*a*d + b*d*x) - 3*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]]))/(b^(3/2)*(b*e - a*f)))/(3*(b*c - a*d)*(b*e - a*f))","A",1
1718,1,70,83,0.1121762,"\int (a+b x) (A+B x) (d+e x)^{7/2} \, dx","Integrate[(a + b*x)*(A + B*x)*(d + e*x)^(7/2),x]","\frac{2 (d+e x)^{9/2} \left(13 a e (11 A e-2 B d+9 B e x)+13 A b e (9 e x-2 d)+b B \left(8 d^2-36 d e x+99 e^2 x^2\right)\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*(d + e*x)^(9/2)*(13*A*b*e*(-2*d + 9*e*x) + 13*a*e*(-2*B*d + 11*A*e + 9*B*e*x) + b*B*(8*d^2 - 36*d*e*x + 99*e^2*x^2)))/(1287*e^3)","A",1
1719,1,70,83,0.0838429,"\int (a+b x) (A+B x) (d+e x)^{5/2} \, dx","Integrate[(a + b*x)*(A + B*x)*(d + e*x)^(5/2),x]","\frac{2 (d+e x)^{7/2} \left(11 a e (9 A e-2 B d+7 B e x)+11 A b e (7 e x-2 d)+b B \left(8 d^2-28 d e x+63 e^2 x^2\right)\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*(d + e*x)^(7/2)*(11*A*b*e*(-2*d + 7*e*x) + 11*a*e*(-2*B*d + 9*A*e + 7*B*e*x) + b*B*(8*d^2 - 28*d*e*x + 63*e^2*x^2)))/(693*e^3)","A",1
1720,1,70,83,0.0834566,"\int (a+b x) (A+B x) (d+e x)^{3/2} \, dx","Integrate[(a + b*x)*(A + B*x)*(d + e*x)^(3/2),x]","\frac{2 (d+e x)^{5/2} \left(9 a e (7 A e-2 B d+5 B e x)+9 A b e (5 e x-2 d)+b B \left(8 d^2-20 d e x+35 e^2 x^2\right)\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*(d + e*x)^(5/2)*(9*A*b*e*(-2*d + 5*e*x) + 9*a*e*(-2*B*d + 7*A*e + 5*B*e*x) + b*B*(8*d^2 - 20*d*e*x + 35*e^2*x^2)))/(315*e^3)","A",1
1721,1,70,83,0.076861,"\int (a+b x) (A+B x) \sqrt{d+e x} \, dx","Integrate[(a + b*x)*(A + B*x)*Sqrt[d + e*x],x]","\frac{2 (d+e x)^{3/2} \left(7 a e (5 A e-2 B d+3 B e x)+7 A b e (3 e x-2 d)+b B \left(8 d^2-12 d e x+15 e^2 x^2\right)\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*(d + e*x)^(3/2)*(7*A*b*e*(-2*d + 3*e*x) + 7*a*e*(-2*B*d + 5*A*e + 3*B*e*x) + b*B*(8*d^2 - 12*d*e*x + 15*e^2*x^2)))/(105*e^3)","A",1
1722,1,68,81,0.0759428,"\int \frac{(a+b x) (A+B x)}{\sqrt{d+e x}} \, dx","Integrate[((a + b*x)*(A + B*x))/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(5 a e (3 A e-2 B d+B e x)+5 A b e (e x-2 d)+b B \left(8 d^2-4 d e x+3 e^2 x^2\right)\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]*(5*A*b*e*(-2*d + e*x) + 5*a*e*(-2*B*d + 3*A*e + B*e*x) + b*B*(8*d^2 - 4*d*e*x + 3*e^2*x^2)))/(15*e^3)","A",1
1723,1,68,79,0.0698601,"\int \frac{(a+b x) (A+B x)}{(d+e x)^{3/2}} \, dx","Integrate[((a + b*x)*(A + B*x))/(d + e*x)^(3/2),x]","\frac{6 a e (-A e+2 B d+B e x)+6 A b e (2 d+e x)+2 b B \left(-8 d^2-4 d e x+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,"(6*A*b*e*(2*d + e*x) + 6*a*e*(2*B*d - A*e + B*e*x) + 2*b*B*(-8*d^2 - 4*d*e*x + e^2*x^2))/(3*e^3*Sqrt[d + e*x])","A",1
1724,1,68,79,0.0899804,"\int \frac{(a+b x) (A+B x)}{(d+e x)^{5/2}} \, dx","Integrate[((a + b*x)*(A + B*x))/(d + e*x)^(5/2),x]","-\frac{2 \left(a e (A e+2 B d+3 B e x)+A b e (2 d+3 e x)-b B \left(8 d^2+12 d e x+3 e^2 x^2\right)\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*(A*b*e*(2*d + 3*e*x) + a*e*(2*B*d + A*e + 3*B*e*x) - b*B*(8*d^2 + 12*d*e*x + 3*e^2*x^2)))/(3*e^3*(d + e*x)^(3/2))","A",1
1725,1,68,81,0.0660188,"\int \frac{(a+b x) (A+B x)}{(d+e x)^{7/2}} \, dx","Integrate[((a + b*x)*(A + B*x))/(d + e*x)^(7/2),x]","-\frac{2 \left(a e (3 A e+2 B d+5 B e x)+A b e (2 d+5 e x)+b B \left(8 d^2+20 d e x+15 e^2 x^2\right)\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*(A*b*e*(2*d + 5*e*x) + a*e*(2*B*d + 3*A*e + 5*B*e*x) + b*B*(8*d^2 + 20*d*e*x + 15*e^2*x^2)))/(15*e^3*(d + e*x)^(5/2))","A",1
1726,1,107,128,0.1971587,"\int (a+b x)^2 (A+B x) (d+e x)^{7/2} \, dx","Integrate[(a + b*x)^2*(A + B*x)*(d + e*x)^(7/2),x]","\frac{2 (d+e x)^{9/2} \left(-495 b (d+e x)^2 (-2 a B e-A b e+3 b B d)+585 (d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)-715 (b d-a e)^2 (B d-A e)+429 b^2 B (d+e x)^3\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*(d + e*x)^(9/2)*(-715*(b*d - a*e)^2*(B*d - A*e) + 585*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x) - 495*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2 + 429*b^2*B*(d + e*x)^3))/(6435*e^4)","A",1
1727,1,107,128,0.154857,"\int (a+b x)^2 (A+B x) (d+e x)^{5/2} \, dx","Integrate[(a + b*x)^2*(A + B*x)*(d + e*x)^(5/2),x]","\frac{2 (d+e x)^{7/2} \left(-819 b (d+e x)^2 (-2 a B e-A b e+3 b B d)+1001 (d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)-1287 (b d-a e)^2 (B d-A e)+693 b^2 B (d+e x)^3\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*(d + e*x)^(7/2)*(-1287*(b*d - a*e)^2*(B*d - A*e) + 1001*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x) - 819*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2 + 693*b^2*B*(d + e*x)^3))/(9009*e^4)","A",1
1728,1,107,128,0.1377446,"\int (a+b x)^2 (A+B x) (d+e x)^{3/2} \, dx","Integrate[(a + b*x)^2*(A + B*x)*(d + e*x)^(3/2),x]","\frac{2 (d+e x)^{5/2} \left(-385 b (d+e x)^2 (-2 a B e-A b e+3 b B d)+495 (d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)-693 (b d-a e)^2 (B d-A e)+315 b^2 B (d+e x)^3\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*(d + e*x)^(5/2)*(-693*(b*d - a*e)^2*(B*d - A*e) + 495*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x) - 385*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2 + 315*b^2*B*(d + e*x)^3))/(3465*e^4)","A",1
1729,1,107,128,0.1276763,"\int (a+b x)^2 (A+B x) \sqrt{d+e x} \, dx","Integrate[(a + b*x)^2*(A + B*x)*Sqrt[d + e*x],x]","\frac{2 (d+e x)^{3/2} \left(-45 b (d+e x)^2 (-2 a B e-A b e+3 b B d)+63 (d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)-105 (b d-a e)^2 (B d-A e)+35 b^2 B (d+e x)^3\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*(d + e*x)^(3/2)*(-105*(b*d - a*e)^2*(B*d - A*e) + 63*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x) - 45*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2 + 35*b^2*B*(d + e*x)^3))/(315*e^4)","A",1
1730,1,107,126,0.1206503,"\int \frac{(a+b x)^2 (A+B x)}{\sqrt{d+e x}} \, dx","Integrate[((a + b*x)^2*(A + B*x))/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(-21 b (d+e x)^2 (-2 a B e-A b e+3 b B d)+35 (d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)-105 (b d-a e)^2 (B d-A e)+15 b^2 B (d+e 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]*(-105*(b*d - a*e)^2*(B*d - A*e) + 35*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x) - 21*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2 + 15*b^2*B*(d + e*x)^3))/(105*e^4)","A",1
1731,1,107,124,0.1262736,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^{3/2}} \, dx","Integrate[((a + b*x)^2*(A + B*x))/(d + e*x)^(3/2),x]","\frac{2 \left(-5 b (d+e x)^2 (-2 a B e-A b e+3 b B d)+15 (d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)+15 (b d-a e)^2 (B d-A e)+3 b^2 B (d+e 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*(15*(b*d - a*e)^2*(B*d - A*e) + 15*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x) - 5*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2 + 3*b^2*B*(d + e*x)^3))/(15*e^4*Sqrt[d + e*x])","A",1
1732,1,105,124,0.1362902,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^{5/2}} \, dx","Integrate[((a + b*x)^2*(A + B*x))/(d + e*x)^(5/2),x]","\frac{2 \left(-3 b (d+e x)^2 (-2 a B e-A b e+3 b B d)-3 (d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)+(b d-a e)^2 (B d-A e)+b^2 B (d+e 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*((b*d - a*e)^2*(B*d - A*e) - 3*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x) - 3*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2 + b^2*B*(d + e*x)^3))/(3*e^4*(d + e*x)^(3/2))","A",1
1733,1,107,124,0.1258411,"\int \frac{(a+b x)^2 (A+B x)}{(d+e x)^{7/2}} \, dx","Integrate[((a + b*x)^2*(A + B*x))/(d + e*x)^(7/2),x]","\frac{2 \left(15 b (d+e x)^2 (-2 a B e-A b e+3 b B d)-5 (d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)+3 (b d-a e)^2 (B d-A e)+15 b^2 B (d+e 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*(3*(b*d - a*e)^2*(B*d - A*e) - 5*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x) + 15*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2 + 15*b^2*B*(d + e*x)^3))/(15*e^4*(d + e*x)^(5/2))","A",1
1734,1,145,173,0.2769678,"\int (a+b x)^3 (A+B x) (d+e x)^{7/2} \, dx","Integrate[(a + b*x)^3*(A + B*x)*(d + e*x)^(7/2),x]","\frac{2 (d+e x)^{9/2} \left(-7293 b^2 (d+e x)^3 (-3 a B e-A b e+4 b B d)+25245 b (d+e x)^2 (b d-a e) (-a B e-A b e+2 b B d)-9945 (d+e x) (b d-a e)^2 (-a B e-3 A b e+4 b B d)+12155 (b d-a e)^3 (B d-A e)+6435 b^3 B (d+e 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*(d + e*x)^(9/2)*(12155*(b*d - a*e)^3*(B*d - A*e) - 9945*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x) + 25245*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2 - 7293*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^3 + 6435*b^3*B*(d + e*x)^4))/(109395*e^5)","A",1
1735,1,145,173,0.2247228,"\int (a+b x)^3 (A+B x) (d+e x)^{5/2} \, dx","Integrate[(a + b*x)^3*(A + B*x)*(d + e*x)^(5/2),x]","\frac{2 (d+e x)^{7/2} \left(-3465 b^2 (d+e x)^3 (-3 a B e-A b e+4 b B d)+12285 b (d+e x)^2 (b d-a e) (-a B e-A b e+2 b B d)-5005 (d+e x) (b d-a e)^2 (-a B e-3 A b e+4 b B d)+6435 (b d-a e)^3 (B d-A e)+3003 b^3 B (d+e x)^4\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*(d + e*x)^(7/2)*(6435*(b*d - a*e)^3*(B*d - A*e) - 5005*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x) + 12285*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2 - 3465*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^3 + 3003*b^3*B*(d + e*x)^4))/(45045*e^5)","A",1
1736,1,145,173,0.1957279,"\int (a+b x)^3 (A+B x) (d+e x)^{3/2} \, dx","Integrate[(a + b*x)^3*(A + B*x)*(d + e*x)^(3/2),x]","\frac{2 (d+e x)^{5/2} \left(-1365 b^2 (d+e x)^3 (-3 a B e-A b e+4 b B d)+5005 b (d+e x)^2 (b d-a e) (-a B e-A b e+2 b B d)-2145 (d+e x) (b d-a e)^2 (-a B e-3 A b e+4 b B d)+3003 (b d-a e)^3 (B d-A e)+1155 b^3 B (d+e x)^4\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*(d + e*x)^(5/2)*(3003*(b*d - a*e)^3*(B*d - A*e) - 2145*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x) + 5005*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2 - 1365*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^3 + 1155*b^3*B*(d + e*x)^4))/(15015*e^5)","A",1
1737,1,145,173,0.2071647,"\int (a+b x)^3 (A+B x) \sqrt{d+e x} \, dx","Integrate[(a + b*x)^3*(A + B*x)*Sqrt[d + e*x],x]","\frac{2 (d+e x)^{3/2} \left(-385 b^2 (d+e x)^3 (-3 a B e-A b e+4 b B d)+1485 b (d+e x)^2 (b d-a e) (-a B e-A b e+2 b B d)-693 (d+e x) (b d-a e)^2 (-a B e-3 A b e+4 b B d)+1155 (b d-a e)^3 (B d-A e)+315 b^3 B (d+e x)^4\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*(d + e*x)^(3/2)*(1155*(b*d - a*e)^3*(B*d - A*e) - 693*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x) + 1485*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2 - 385*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^3 + 315*b^3*B*(d + e*x)^4))/(3465*e^5)","A",1
1738,1,145,171,0.111599,"\int \frac{(a+b x)^3 (A+B x)}{\sqrt{d+e x}} \, dx","Integrate[((a + b*x)^3*(A + B*x))/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(-45 b^2 (d+e x)^3 (-3 a B e-A b e+4 b B d)+189 b (d+e x)^2 (b d-a e) (-a B e-A b e+2 b B d)-105 (d+e x) (b d-a e)^2 (-a B e-3 A b e+4 b B d)+315 (b d-a e)^3 (B d-A e)+35 b^3 B (d+e 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]*(315*(b*d - a*e)^3*(B*d - A*e) - 105*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x) + 189*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2 - 45*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^3 + 35*b^3*B*(d + e*x)^4))/(315*e^5)","A",1
1739,1,145,167,0.1640241,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^{3/2}} \, dx","Integrate[((a + b*x)^3*(A + B*x))/(d + e*x)^(3/2),x]","\frac{2 \left(-7 b^2 (d+e x)^3 (-3 a B e-A b e+4 b B d)+35 b (d+e x)^2 (b d-a e) (-a B e-A b e+2 b B d)-35 (d+e x) (b d-a e)^2 (-a B e-3 A b e+4 b B d)-35 (b d-a e)^3 (B d-A e)+5 b^3 B (d+e 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*(-35*(b*d - a*e)^3*(B*d - A*e) - 35*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x) + 35*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2 - 7*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^3 + 5*b^3*B*(d + e*x)^4))/(35*e^5*Sqrt[d + e*x])","A",1
1740,1,145,169,0.1734543,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^{5/2}} \, dx","Integrate[((a + b*x)^3*(A + B*x))/(d + e*x)^(5/2),x]","\frac{2 \left(-5 b^2 (d+e x)^3 (-3 a B e-A b e+4 b B d)+45 b (d+e x)^2 (b d-a e) (-a B e-A b e+2 b B d)+15 (d+e x) (b d-a e)^2 (-a B e-3 A b e+4 b B d)-5 (b d-a e)^3 (B d-A e)+3 b^3 B (d+e 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*(-5*(b*d - a*e)^3*(B*d - A*e) + 15*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x) + 45*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2 - 5*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^3 + 3*b^3*B*(d + e*x)^4))/(15*e^5*(d + e*x)^(3/2))","A",1
1741,1,145,169,0.1815061,"\int \frac{(a+b x)^3 (A+B x)}{(d+e x)^{7/2}} \, dx","Integrate[((a + b*x)^3*(A + B*x))/(d + e*x)^(7/2),x]","\frac{2 \left(-15 b^2 (d+e x)^3 (-3 a B e-A b e+4 b B d)-45 b (d+e x)^2 (b d-a e) (-a B e-A b e+2 b B d)+5 (d+e x) (b d-a e)^2 (-a B e-3 A b e+4 b B d)-3 (b d-a e)^3 (B d-A e)+5 b^3 B (d+e 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*(-3*(b*d - a*e)^3*(B*d - A*e) + 5*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x) - 45*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2 - 15*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^3 + 5*b^3*B*(d + e*x)^4))/(15*e^5*(d + e*x)^(5/2))","A",1
1742,1,165,198,0.5520959,"\int \frac{(A+B x) (d+e x)^{7/2}}{a+b x} \, dx","Integrate[((A + B*x)*(d + e*x)^(7/2))/(a + b*x),x]","\frac{2 \left(\frac{3 e (A b-a B) \left(7 (b d-a e) \left(5 (b d-a e) \left(\sqrt{b} \sqrt{d+e x} (-3 a e+4 b d+b e x)-3 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)\right)+3 b^{5/2} (d+e x)^{5/2}\right)+15 b^{7/2} (d+e x)^{7/2}\right)}{35 b^{9/2}}+B (d+e x)^{9/2}\right)}{9 b e}","-\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*(B*(d + e*x)^(9/2) + (3*(A*b - a*B)*e*(15*b^(7/2)*(d + e*x)^(7/2) + 7*(b*d - a*e)*(3*b^(5/2)*(d + e*x)^(5/2) + 5*(b*d - a*e)*(Sqrt[b]*Sqrt[d + e*x]*(4*b*d - 3*a*e + b*e*x) - 3*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]))))/(35*b^(9/2))))/(9*b*e)","A",1
1743,1,136,164,0.2650943,"\int \frac{(A+B x) (d+e x)^{5/2}}{a+b x} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/(a + b*x),x]","\frac{2 (A b-a B) \left(5 (b d-a e) \left(\sqrt{b} \sqrt{d+e x} (-3 a e+4 b d+b e x)-3 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)\right)+3 b^{5/2} (d+e x)^{5/2}\right)}{15 b^{9/2}}+\frac{2 B (d+e x)^{7/2}}{7 b e}","-\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*B*(d + e*x)^(7/2))/(7*b*e) + (2*(A*b - a*B)*(3*b^(5/2)*(d + e*x)^(5/2) + 5*(b*d - a*e)*(Sqrt[b]*Sqrt[d + e*x]*(4*b*d - 3*a*e + b*e*x) - 3*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])))/(15*b^(9/2))","A",1
1744,1,109,130,0.2260068,"\int \frac{(A+B x) (d+e x)^{3/2}}{a+b x} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(a + b*x),x]","\frac{2 (A b-a B) \left(\sqrt{b} \sqrt{d+e x} (-3 a e+4 b d+b e x)-3 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)\right)}{3 b^{7/2}}+\frac{2 B (d+e x)^{5/2}}{5 b e}","-\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*B*(d + e*x)^(5/2))/(5*b*e) + (2*(A*b - a*B)*(Sqrt[b]*Sqrt[d + e*x]*(4*b*d - 3*a*e + b*e*x) - 3*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]))/(3*b^(7/2))","A",1
1745,1,94,98,0.1472669,"\int \frac{(A+B x) \sqrt{d+e x}}{a+b x} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(a + b*x),x]","\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} (-3 a B e+3 A b e+b B (d+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]*(3*A*b*e - 3*a*B*e + b*B*(d + e*x)))/(3*b^2*e) + (2*(-(A*b) + a*B)*Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/b^(5/2)","A",1
1746,1,74,74,0.1696933,"\int \frac{A+B x}{(a+b x) \sqrt{d+e x}} \, dx","Integrate[(A + B*x)/((a + b*x)*Sqrt[d + e*x]),x]","\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}}+\frac{2 B \sqrt{d+e x}}{b e}","\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)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b^(3/2)*Sqrt[b*d - a*e])","A",1
1747,1,88,88,0.315136,"\int \frac{A+B x}{(a+b x) (d+e x)^{3/2}} \, dx","Integrate[(A + B*x)/((a + b*x)*(d + e*x)^(3/2)),x]","\frac{2 B d-2 A e}{e \sqrt{d+e x} (a e-b d)}+\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}}","-\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 - 2*A*e)/(e*(-(b*d) + a*e)*Sqrt[d + e*x]) + (2*(-(A*b) + a*B)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(Sqrt[b]*(b*d - a*e)^(3/2))","A",1
1748,1,86,119,0.0491691,"\int \frac{A+B x}{(a+b x) (d+e x)^{5/2}} \, dx","Integrate[(A + B*x)/((a + b*x)*(d + e*x)^(5/2)),x]","\frac{6 e (d+e x) (A b-a B) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)-2 (b d-a e) (B d-A e)}{3 e (d+e x)^{3/2} (b d-a e)^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*d - a*e)*(B*d - A*e) + 6*(A*b - a*B)*e*(d + e*x)*Hypergeometric2F1[-1/2, 1, 1/2, (b*(d + e*x))/(b*d - a*e)])/(3*e*(b*d - a*e)^2*(d + e*x)^(3/2))","C",1
1749,1,86,151,0.0645376,"\int \frac{A+B x}{(a+b x) (d+e x)^{7/2}} \, dx","Integrate[(A + B*x)/((a + b*x)*(d + e*x)^(7/2)),x]","\frac{10 e (d+e x) (A b-a B) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)-6 (b d-a e) (B d-A e)}{15 e (d+e x)^{5/2} (b d-a e)^2}","-\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,"(-6*(b*d - a*e)*(B*d - A*e) + 10*(A*b - a*B)*e*(d + e*x)*Hypergeometric2F1[-3/2, 1, -1/2, (b*(d + e*x))/(b*d - a*e)])/(15*e*(b*d - a*e)^2*(d + e*x)^(5/2))","C",1
1750,1,193,256,0.6464597,"\int \frac{(A+B x) (d+e x)^{7/2}}{(a+b x)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(7/2))/(a + b*x)^2,x]","\frac{\frac{2 \left(-\frac{9 a B e}{2}+\frac{7 A b e}{2}+b B d\right) \left(7 (b d-a e) \left(5 (b d-a e) \left(\sqrt{b} \sqrt{d+e x} (-3 a e+4 b d+b e x)-3 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)\right)+3 b^{5/2} (d+e x)^{5/2}\right)+15 b^{7/2} (d+e x)^{7/2}\right)}{105 b^{9/2}}+\frac{(d+e x)^{9/2} (a B-A b)}{a+b x}}{b (b d-a e)}","-\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,"(((-(A*b) + a*B)*(d + e*x)^(9/2))/(a + b*x) + (2*(b*B*d + (7*A*b*e)/2 - (9*a*B*e)/2)*(15*b^(7/2)*(d + e*x)^(7/2) + 7*(b*d - a*e)*(3*b^(5/2)*(d + e*x)^(5/2) + 5*(b*d - a*e)*(Sqrt[b]*Sqrt[d + e*x]*(4*b*d - 3*a*e + b*e*x) - 3*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]))))/(105*b^(9/2)))/(b*(b*d - a*e))","A",1
1751,1,166,214,0.4980103,"\int \frac{(A+B x) (d+e x)^{5/2}}{(a+b x)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/(a + b*x)^2,x]","\frac{\frac{2 \left(-\frac{7 a B e}{2}+\frac{5 A b e}{2}+b B d\right) \left(5 (b d-a e) \left(\sqrt{b} \sqrt{d+e x} (-3 a e+4 b d+b e x)-3 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)\right)+3 b^{5/2} (d+e x)^{5/2}\right)}{15 b^{7/2}}+\frac{(d+e x)^{7/2} (a B-A b)}{a+b x}}{b (b d-a e)}","-\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,"(((-(A*b) + a*B)*(d + e*x)^(7/2))/(a + b*x) + (2*(b*B*d + (5*A*b*e)/2 - (7*a*B*e)/2)*(3*b^(5/2)*(d + e*x)^(5/2) + 5*(b*d - a*e)*(Sqrt[b]*Sqrt[d + e*x]*(4*b*d - 3*a*e + b*e*x) - 3*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])))/(15*b^(7/2)))/(b*(b*d - a*e))","A",1
1752,1,136,174,0.2966946,"\int \frac{(A+B x) (d+e x)^{3/2}}{(a+b x)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(a + b*x)^2,x]","\frac{\frac{(-5 a B e+3 A b e+2 b B d) \left(\sqrt{b} \sqrt{d+e x} (-3 a e+4 b d+b e x)-3 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)\right)}{3 b^{5/2}}+\frac{(d+e x)^{5/2} (a B-A b)}{a+b x}}{b (b d-a e)}","-\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,"(((-(A*b) + a*B)*(d + e*x)^(5/2))/(a + b*x) + ((2*b*B*d + 3*A*b*e - 5*a*B*e)*(Sqrt[b]*Sqrt[d + e*x]*(4*b*d - 3*a*e + b*e*x) - 3*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]))/(3*b^(5/2)))/(b*(b*d - a*e))","A",1
1753,1,119,140,0.1829264,"\int \frac{(A+B x) \sqrt{d+e x}}{(a+b x)^2} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(a + b*x)^2,x]","\frac{\frac{(-3 a B e+A b e+2 b B d) \left(\sqrt{b} \sqrt{d+e x}-\sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)\right)}{b^{3/2}}+\frac{(d+e x)^{3/2} (a B-A b)}{a+b x}}{b (b d-a e)}","-\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) + a*B)*(d + e*x)^(3/2))/(a + b*x) + ((2*b*B*d + A*b*e - 3*a*B*e)*(Sqrt[b]*Sqrt[d + e*x] - Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]]))/b^(3/2))/(b*(b*d - a*e))","A",1
1754,1,102,103,0.1042424,"\int \frac{A+B x}{(a+b x)^2 \sqrt{d+e x}} \, dx","Integrate[(A + B*x)/((a + b*x)^2*Sqrt[d + e*x]),x]","\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{(-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)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b^(3/2)*(b*d - a*e)^(3/2))","A",1
1755,1,95,140,0.0551008,"\int \frac{A+B x}{(a+b x)^2 (d+e x)^{3/2}} \, dx","Integrate[(A + B*x)/((a + b*x)^2*(d + e*x)^(3/2)),x]","\frac{(a+b x) (a B e-3 A b e+2 b B d) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)-(A b-a B) (b d-a e)}{b (a+b x) \sqrt{d+e x} (b d-a e)^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 - a*B)*(b*d - a*e)) + (2*b*B*d - 3*A*b*e + a*B*e)*(a + b*x)*Hypergeometric2F1[-1/2, 1, 1/2, (b*(d + e*x))/(b*d - a*e)])/(b*(b*d - a*e)^2*(a + b*x)*Sqrt[d + e*x])","C",1
1756,1,94,181,0.0590955,"\int \frac{A+B x}{(a+b x)^2 (d+e x)^{5/2}} \, dx","Integrate[(A + B*x)/((a + b*x)^2*(d + e*x)^(5/2)),x]","\frac{(3 a B e-5 A b e+2 b B d) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)-\frac{3 (A b-a B) (b d-a e)}{a+b x}}{3 b (d+e x)^{3/2} (b d-a e)^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 - a*B)*(b*d - a*e))/(a + b*x) + (2*b*B*d - 5*A*b*e + 3*a*B*e)*Hypergeometric2F1[-3/2, 1, -1/2, (b*(d + e*x))/(b*d - a*e)])/(3*b*(b*d - a*e)^2*(d + e*x)^(3/2))","C",1
1757,1,94,221,0.0582663,"\int \frac{A+B x}{(a+b x)^2 (d+e x)^{7/2}} \, dx","Integrate[(A + B*x)/((a + b*x)^2*(d + e*x)^(7/2)),x]","\frac{(5 a B e-7 A b e+2 b B d) \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\frac{b (d+e x)}{b d-a e}\right)-\frac{5 (A b-a B) (b d-a e)}{a+b x}}{5 b (d+e x)^{5/2} (b d-a e)^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,"((-5*(A*b - a*B)*(b*d - a*e))/(a + b*x) + (2*b*B*d - 7*A*b*e + 5*a*B*e)*Hypergeometric2F1[-5/2, 1, -3/2, (b*(d + e*x))/(b*d - a*e)])/(5*b*(b*d - a*e)^2*(d + e*x)^(5/2))","C",1
1758,1,97,274,0.1236543,"\int \frac{(A+B x) (d+e x)^{7/2}}{(a+b x)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^(7/2))/(a + b*x)^3,x]","\frac{(d+e x)^{9/2} \left(\frac{e (-9 a B e+5 A b e+4 b B d) \, _2F_1\left(2,\frac{9}{2};\frac{11}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^2}+\frac{9 a B-9 A b}{(a+b x)^2}\right)}{18 b (b d-a e)}","-\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,"((d + e*x)^(9/2)*((-9*A*b + 9*a*B)/(a + b*x)^2 + (e*(4*b*B*d + 5*A*b*e - 9*a*B*e)*Hypergeometric2F1[2, 9/2, 11/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^2))/(18*b*(b*d - a*e))","C",1
1759,1,97,233,0.0988373,"\int \frac{(A+B x) (d+e x)^{5/2}}{(a+b x)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/(a + b*x)^3,x]","\frac{(d+e x)^{7/2} \left(\frac{e (-7 a B e+3 A b e+4 b B d) \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^2}+\frac{7 a B-7 A b}{(a+b x)^2}\right)}{14 b (b d-a e)}","-\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,"((d + e*x)^(7/2)*((-7*A*b + 7*a*B)/(a + b*x)^2 + (e*(4*b*B*d + 3*A*b*e - 7*a*B*e)*Hypergeometric2F1[2, 7/2, 9/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^2))/(14*b*(b*d - a*e))","C",1
1760,1,96,197,0.0884163,"\int \frac{(A+B x) (d+e x)^{3/2}}{(a+b x)^3} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(a + b*x)^3,x]","\frac{(d+e x)^{5/2} \left(\frac{e (-5 a B e+A b e+4 b B d) \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^2}+\frac{5 a B-5 A b}{(a+b x)^2}\right)}{10 b (b d-a e)}","-\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,"((d + e*x)^(5/2)*((-5*A*b + 5*a*B)/(a + b*x)^2 + (e*(4*b*B*d + A*b*e - 5*a*B*e)*Hypergeometric2F1[2, 5/2, 7/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^2))/(10*b*(b*d - a*e))","C",1
1761,1,158,157,0.3744078,"\int \frac{(A+B x) \sqrt{d+e x}}{(a+b x)^3} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(a + b*x)^3,x]","\frac{\frac{(a+b x) (-3 a B e-A b e+4 b B d) \left(\sqrt{b} e (a+b x) \sqrt{d+e x} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{a e-b d}}\right)-b (d+e x) \sqrt{a e-b d}\right)}{\sqrt{a e-b d}}-2 b^2 (d+e x)^2 (A b-a B)}{4 b^3 (a+b x)^2 \sqrt{d+e x} (b d-a e)}","-\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,"(-2*b^2*(A*b - a*B)*(d + e*x)^2 + ((4*b*B*d - A*b*e - 3*a*B*e)*(a + b*x)*(-(b*Sqrt[-(b*d) + a*e]*(d + e*x)) + Sqrt[b]*e*(a + b*x)*Sqrt[d + e*x]*ArcTan[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[-(b*d) + a*e]]))/Sqrt[-(b*d) + a*e])/(4*b^3*(b*d - a*e)*(a + b*x)^2*Sqrt[d + e*x])","A",1
1762,1,149,157,0.3451041,"\int \frac{A+B x}{(a+b x)^3 \sqrt{d+e x}} \, dx","Integrate[(A + B*x)/((a + b*x)^3*Sqrt[d + e*x]),x]","\frac{\sqrt{d+e x} \left(\frac{e (-a B e-3 A b e+4 b B d) \left(\frac{a e-b d}{e (a+b x)}+\frac{\sqrt{a e-b d} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{a e-b d}}\right)}{\sqrt{b} \sqrt{d+e x}}\right)}{2 (b d-a e)^2}+\frac{a B-A b}{(a+b x)^2}\right)}{2 b (b d-a e)}","\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]*((-(A*b) + a*B)/(a + b*x)^2 + (e*(4*b*B*d - 3*A*b*e - a*B*e)*((-(b*d) + a*e)/(e*(a + b*x)) + (Sqrt[-(b*d) + a*e]*ArcTan[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[-(b*d) + a*e]])/(Sqrt[b]*Sqrt[d + e*x])))/(2*(b*d - a*e)^2)))/(2*b*(b*d - a*e))","A",1
1763,1,96,197,0.0753563,"\int \frac{A+B x}{(a+b x)^3 (d+e x)^{3/2}} \, dx","Integrate[(A + B*x)/((a + b*x)^3*(d + e*x)^(3/2)),x]","\frac{\frac{e (-a B e+5 A b e-4 b B d) \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^2}+\frac{a B-A b}{(a+b x)^2}}{2 b \sqrt{d+e x} (b d-a e)}","-\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,"((-(A*b) + a*B)/(a + b*x)^2 + (e*(-4*b*B*d + 5*A*b*e - a*B*e)*Hypergeometric2F1[-1/2, 2, 1/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^2)/(2*b*(b*d - a*e)*Sqrt[d + e*x])","C",1
1764,1,97,240,0.0726909,"\int \frac{A+B x}{(a+b x)^3 (d+e x)^{5/2}} \, dx","Integrate[(A + B*x)/((a + b*x)^3*(d + e*x)^(5/2)),x]","\frac{\frac{e (-3 a B e+7 A b e-4 b B d) \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^2}+\frac{3 a B-3 A b}{(a+b x)^2}}{6 b (d+e x)^{3/2} (b d-a e)}","-\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,"((-3*A*b + 3*a*B)/(a + b*x)^2 + (e*(-4*b*B*d + 7*A*b*e - 3*a*B*e)*Hypergeometric2F1[-3/2, 2, -1/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^2)/(6*b*(b*d - a*e)*(d + e*x)^(3/2))","C",1
1765,1,97,281,0.0805751,"\int \frac{A+B x}{(a+b x)^3 (d+e x)^{7/2}} \, dx","Integrate[(A + B*x)/((a + b*x)^3*(d + e*x)^(7/2)),x]","\frac{\frac{e (-5 a B e+9 A b e-4 b B d) \, _2F_1\left(-\frac{5}{2},2;-\frac{3}{2};\frac{b (d+e x)}{b d-a e}\right)}{(b d-a e)^2}+\frac{5 a B-5 A b}{(a+b x)^2}}{10 b (d+e x)^{5/2} (b d-a e)}","\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,"((-5*A*b + 5*a*B)/(a + b*x)^2 + (e*(-4*b*B*d + 9*A*b*e - 5*a*B*e)*Hypergeometric2F1[-5/2, 2, -3/2, (b*(d + e*x))/(b*d - a*e)])/(b*d - a*e)^2)/(10*b*(b*d - a*e)*(d + e*x)^(5/2))","C",1
1766,1,136,164,0.3658388,"\int \frac{(a+b x) (e+f x)^{5/2}}{c+d x} \, dx","Integrate[((a + b*x)*(e + f*x)^(5/2))/(c + d*x),x]","\frac{2 b (e+f x)^{7/2}}{7 d f}-\frac{2 (b c-a d) \left(5 (d e-c f) \left(\sqrt{d} \sqrt{e+f x} (-3 c f+4 d e+d f x)-3 (d e-c f)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)\right)+3 d^{5/2} (e+f x)^{5/2}\right)}{15 d^{9/2}}","\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*b*(e + f*x)^(7/2))/(7*d*f) - (2*(b*c - a*d)*(3*d^(5/2)*(e + f*x)^(5/2) + 5*(d*e - c*f)*(Sqrt[d]*Sqrt[e + f*x]*(4*d*e - 3*c*f + d*f*x) - 3*(d*e - c*f)^(3/2)*ArcTanh[(Sqrt[d]*Sqrt[e + f*x])/Sqrt[d*e - c*f]])))/(15*d^(9/2))","A",1
1767,1,112,130,0.2103551,"\int \frac{(a+b x) (e+f x)^{3/2}}{c+d x} \, dx","Integrate[((a + b*x)*(e + f*x)^(3/2))/(c + d*x),x]","\frac{2 \left(\frac{5 (a d f-b c f) \left(\sqrt{d} \sqrt{e+f x} (-3 c f+4 d e+d f x)-3 (d e-c f)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)\right)}{3 d^{5/2}}+b (e+f x)^{5/2}\right)}{5 d f}","\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*(b*(e + f*x)^(5/2) + (5*(-(b*c*f) + a*d*f)*(Sqrt[d]*Sqrt[e + f*x]*(4*d*e - 3*c*f + d*f*x) - 3*(d*e - c*f)^(3/2)*ArcTanh[(Sqrt[d]*Sqrt[e + f*x])/Sqrt[d*e - c*f]]))/(3*d^(5/2))))/(5*d*f)","A",1
1768,1,94,98,0.1495121,"\int \frac{(a+b x) \sqrt{e+f x}}{c+d x} \, dx","Integrate[((a + b*x)*Sqrt[e + f*x])/(c + d*x),x]","\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} (3 a d f-3 b c f+b d (e+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]*(-3*b*c*f + 3*a*d*f + b*d*(e + f*x)))/(3*d^2*f) + (2*(b*c - a*d)*Sqrt[d*e - c*f]*ArcTanh[(Sqrt[d]*Sqrt[e + f*x])/Sqrt[d*e - c*f]])/d^(5/2)","A",1
1769,1,74,74,0.1918418,"\int \frac{a+b x}{(c+d x) \sqrt{e+f x}} \, dx","Integrate[(a + b*x)/((c + d*x)*Sqrt[e + f*x]),x]","\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}","\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)*ArcTanh[(Sqrt[d]*Sqrt[e + f*x])/Sqrt[d*e - c*f]])/(d^(3/2)*Sqrt[d*e - c*f])","A",1
1770,1,88,88,0.3361522,"\int \frac{a+b x}{(c+d x) (e+f x)^{3/2}} \, dx","Integrate[(a + b*x)/((c + d*x)*(e + f*x)^(3/2)),x]","\frac{2 b e-2 a f}{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 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 - 2*a*f)/(f*(-(d*e) + c*f)*Sqrt[e + f*x]) + (2*(b*c - a*d)*ArcTanh[(Sqrt[d]*Sqrt[e + f*x])/Sqrt[d*e - c*f]])/(Sqrt[d]*(d*e - c*f)^(3/2))","A",1
1771,1,86,119,0.0535272,"\int \frac{a+b x}{(c+d x) (e+f x)^{5/2}} \, dx","Integrate[(a + b*x)/((c + d*x)*(e + f*x)^(5/2)),x]","\frac{-6 f (e+f x) (b c-a d) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{d (e+f x)}{d e-c f}\right)-2 (b e-a f) (d e-c f)}{3 f (e+f x)^{3/2} (d e-c f)^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*e - a*f)*(d*e - c*f) - 6*(b*c - a*d)*f*(e + f*x)*Hypergeometric2F1[-1/2, 1, 1/2, (d*(e + f*x))/(d*e - c*f)])/(3*f*(d*e - c*f)^2*(e + f*x)^(3/2))","C",1
1772,1,86,151,0.0577014,"\int \frac{a+b x}{(c+d x) (e+f x)^{7/2}} \, dx","Integrate[(a + b*x)/((c + d*x)*(e + f*x)^(7/2)),x]","-\frac{2 \left(5 f (e+f x) (b c-a d) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{d (e+f x)}{d e-c f}\right)+3 (b e-a f) (d e-c f)\right)}{15 f (e+f x)^{5/2} (d e-c f)^2}","\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*e - a*f)*(d*e - c*f) + 5*(b*c - a*d)*f*(e + f*x)*Hypergeometric2F1[-3/2, 1, -1/2, (d*(e + f*x))/(d*e - c*f)]))/(15*f*(d*e - c*f)^2*(e + f*x)^(5/2))","C",1
1773,1,86,185,0.0564817,"\int \frac{a+b x}{(c+d x) (e+f x)^{9/2}} \, dx","Integrate[(a + b*x)/((c + d*x)*(e + f*x)^(9/2)),x]","-\frac{2 \left(7 f (e+f x) (b c-a d) \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\frac{d (e+f x)}{d e-c f}\right)+5 (b e-a f) (d e-c f)\right)}{35 f (e+f x)^{7/2} (d e-c f)^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*(5*(b*e - a*f)*(d*e - c*f) + 7*(b*c - a*d)*f*(e + f*x)*Hypergeometric2F1[-5/2, 1, -3/2, (d*(e + f*x))/(d*e - c*f)]))/(35*f*(d*e - c*f)^2*(e + f*x)^(7/2))","C",1
1774,1,175,208,0.6024466,"\int \frac{(a+b x)^2 (e+f x)^{5/2}}{c+d x} \, dx","Integrate[((a + b*x)^2*(e + f*x)^(5/2))/(c + d*x),x]","\frac{2 \left(\frac{105 (b c-a d)^2 (d e-c f) \left(\sqrt{d} \sqrt{e+f x} (-3 c f+4 d e+d f x)-3 (d e-c f)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)\right)}{d^{5/2}}-\frac{45 b d (e+f x)^{7/2} (-2 a d f+b c f+b d e)}{f^2}+63 (e+f x)^{5/2} (b c-a d)^2+\frac{35 b^2 d^2 (e+f x)^{9/2}}{f^2}\right)}{315 d^3}","-\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*(63*(b*c - a*d)^2*(e + f*x)^(5/2) - (45*b*d*(b*d*e + b*c*f - 2*a*d*f)*(e + f*x)^(7/2))/f^2 + (35*b^2*d^2*(e + f*x)^(9/2))/f^2 + (105*(b*c - a*d)^2*(d*e - c*f)*(Sqrt[d]*Sqrt[e + f*x]*(4*d*e - 3*c*f + d*f*x) - 3*(d*e - c*f)^(3/2)*ArcTanh[(Sqrt[d]*Sqrt[e + f*x])/Sqrt[d*e - c*f]]))/d^(5/2)))/(315*d^3)","A",1
1775,1,160,172,0.2261277,"\int \frac{(a+b x)^2 (e+f x)^{3/2}}{c+d x} \, dx","Integrate[((a + b*x)^2*(e + f*x)^(3/2))/(c + d*x),x]","\frac{2 \left(105 (b c-a d)^2 (d e-c f) \left(\frac{\sqrt{e+f x}}{d}-\frac{\sqrt{d e-c f} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)}{d^{3/2}}\right)-\frac{21 b d (e+f x)^{5/2} (-2 a d f+b c f+b d e)}{f^2}+35 (e+f x)^{3/2} (b c-a d)^2+\frac{15 b^2 d^2 (e+f x)^{7/2}}{f^2}\right)}{105 d^3}","-\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*(35*(b*c - a*d)^2*(e + f*x)^(3/2) - (21*b*d*(b*d*e + b*c*f - 2*a*d*f)*(e + f*x)^(5/2))/f^2 + (15*b^2*d^2*(e + f*x)^(7/2))/f^2 + 105*(b*c - a*d)^2*(d*e - c*f)*(Sqrt[e + f*x]/d - (Sqrt[d*e - c*f]*ArcTanh[(Sqrt[d]*Sqrt[e + f*x])/Sqrt[d*e - c*f]])/d^(3/2))))/(105*d^3)","A",1
1776,1,138,138,0.1511613,"\int \frac{(a+b x)^2 \sqrt{e+f x}}{c+d x} \, dx","Integrate[((a + b*x)^2*Sqrt[e + f*x])/(c + d*x),x]","-\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}","-\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*(b*c - a*d)^2*Sqrt[e + f*x])/d^3 - (2*b*(b*d*e + b*c*f - 2*a*d*f)*(e + f*x)^(3/2))/(3*d^2*f^2) + (2*b^2*(e + f*x)^(5/2))/(5*d*f^2) - (2*(b*c - a*d)^2*Sqrt[d*e - c*f]*ArcTanh[(Sqrt[d]*Sqrt[e + f*x])/Sqrt[d*e - c*f]])/d^(7/2)","A",1
1777,1,112,112,0.1377508,"\int \frac{(a+b x)^2}{(c+d x) \sqrt{e+f x}} \, dx","Integrate[(a + b*x)^2/((c + d*x)*Sqrt[e + f*x]),x]","-\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}","-\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*b*(b*d*e + b*c*f - 2*a*d*f)*Sqrt[e + f*x])/(d^2*f^2) + (2*b^2*(e + f*x)^(3/2))/(3*d*f^2) - (2*(b*c - a*d)^2*ArcTanh[(Sqrt[d]*Sqrt[e + f*x])/Sqrt[d*e - c*f]])/(d^(5/2)*Sqrt[d*e - c*f])","A",1
1778,1,98,112,0.1140305,"\int \frac{(a+b x)^2}{(c+d x) (e+f x)^{3/2}} \, dx","Integrate[(a + b*x)^2/((c + d*x)*(e + f*x)^(3/2)),x]","\frac{-2 f^2 (b c-a d)^2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{d (e+f x)}{d e-c f}\right)-2 b (d e-c f) (b (c f+2 d e+d f x)-2 a d f)}{d^2 f^2 \sqrt{e+f x} (c f-d e)}","-\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*b*(d*e - c*f)*(-2*a*d*f + b*(2*d*e + c*f + d*f*x)) - 2*(b*c - a*d)^2*f^2*Hypergeometric2F1[-1/2, 1, 1/2, (d*(e + f*x))/(d*e - c*f)])/(d^2*f^2*(-(d*e) + c*f)*Sqrt[e + f*x])","C",1
1779,1,103,140,0.1120294,"\int \frac{(a+b x)^2}{(c+d x) (e+f x)^{5/2}} \, dx","Integrate[(a + b*x)^2/((c + d*x)*(e + f*x)^(5/2)),x]","\frac{2 b (d e-c f) (2 a d f+b (-c f+2 d e+3 d f x))-2 f^2 (b c-a d)^2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{d (e+f x)}{d e-c f}\right)}{3 d^2 f^2 (e+f x)^{3/2} (c f-d e)}","-\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*b*(d*e - c*f)*(2*a*d*f + b*(2*d*e - c*f + 3*d*f*x)) - 2*(b*c - a*d)^2*f^2*Hypergeometric2F1[-3/2, 1, -1/2, (d*(e + f*x))/(d*e - c*f)])/(3*d^2*f^2*(-(d*e) + c*f)*(e + f*x)^(3/2))","C",1
1780,1,103,173,0.1315847,"\int \frac{(a+b x)^2}{(c+d x) (e+f x)^{7/2}} \, dx","Integrate[(a + b*x)^2/((c + d*x)*(e + f*x)^(7/2)),x]","\frac{2 b (d e-c f) (6 a d f+b (-3 c f+2 d e+5 d f x))-6 f^2 (b c-a d)^2 \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\frac{d (e+f x)}{d e-c f}\right)}{15 d^2 f^2 (e+f x)^{5/2} (c f-d e)}","-\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*b*(d*e - c*f)*(6*a*d*f + b*(2*d*e - 3*c*f + 5*d*f*x)) - 6*(b*c - a*d)^2*f^2*Hypergeometric2F1[-5/2, 1, -3/2, (d*(e + f*x))/(d*e - c*f)])/(15*d^2*f^2*(-(d*e) + c*f)*(e + f*x)^(5/2))","C",1
1781,1,102,207,0.1348965,"\int \frac{(a+b x)^2}{(c+d x) (e+f x)^{9/2}} \, dx","Integrate[(a + b*x)^2/((c + d*x)*(e + f*x)^(9/2)),x]","\frac{2 \left(b (d e-c f) (10 a d f+b (-5 c f+2 d e+7 d f x))-5 f^2 (b c-a d)^2 \, _2F_1\left(-\frac{7}{2},1;-\frac{5}{2};\frac{d (e+f x)}{d e-c f}\right)\right)}{35 d^2 f^2 (e+f x)^{7/2} (c f-d e)}","-\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*(b*(d*e - c*f)*(10*a*d*f + b*(2*d*e - 5*c*f + 7*d*f*x)) - 5*(b*c - a*d)^2*f^2*Hypergeometric2F1[-7/2, 1, -5/2, (d*(e + f*x))/(d*e - c*f)]))/(35*d^2*f^2*(-(d*e) + c*f)*(e + f*x)^(7/2))","C",1
1782,1,253,280,0.9135488,"\int \frac{(a+b x)^3 (e+f x)^{5/2}}{c+d x} \, dx","Integrate[((a + b*x)^3*(e + f*x)^(5/2))/(c + d*x),x]","\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 (a d-b c)^3 (d e-c f) \left(\sqrt{d} \sqrt{e+f x} (-3 c f+4 d e+d f x)-3 (d e-c f)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)\right)}{3 d^{13/2}}+\frac{2 (e+f x)^{5/2} (a d-b c)^3}{5 d^4}+\frac{2 b^3 (e+f x)^{11/2}}{11 d 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*(-(b*c) + a*d)^3*(e + f*x)^(5/2))/(5*d^4) + (2*b*(3*a^2*d^2*f^2 - 3*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + c*d*e*f + c^2*f^2))*(e + f*x)^(7/2))/(7*d^3*f^3) - (2*b^2*(2*b*d*e + b*c*f - 3*a*d*f)*(e + f*x)^(9/2))/(9*d^2*f^3) + (2*b^3*(e + f*x)^(11/2))/(11*d*f^3) + (2*(-(b*c) + a*d)^3*(d*e - c*f)*(Sqrt[d]*Sqrt[e + f*x]*(4*d*e - 3*c*f + d*f*x) - 3*(d*e - c*f)^(3/2)*ArcTanh[(Sqrt[d]*Sqrt[e + f*x])/Sqrt[d*e - c*f]]))/(3*d^(13/2))","A",1
1783,1,232,244,0.4794711,"\int \frac{(a+b x)^3 (e+f x)^{3/2}}{c+d x} \, dx","Integrate[((a + b*x)^3*(e + f*x)^(3/2))/(c + d*x),x]","\frac{2 \left(\frac{63 b d (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)}{f^3}-\frac{45 b^2 d^2 (e+f x)^{7/2} (-3 a d f+b c f+2 b d e)}{f^3}+\frac{315 (a d-b c)^3 (d e-c f) \left(\sqrt{d} \sqrt{e+f x}-\sqrt{d e-c f} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{e+f x}}{\sqrt{d e-c f}}\right)\right)}{d^{3/2}}-105 (e+f x)^{3/2} (b c-a d)^3+\frac{35 b^3 d^3 (e+f x)^{9/2}}{f^3}\right)}{315 d^4}","\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*(-105*(b*c - a*d)^3*(e + f*x)^(3/2) + (63*b*d*(3*a^2*d^2*f^2 - 3*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + c*d*e*f + c^2*f^2))*(e + f*x)^(5/2))/f^3 - (45*b^2*d^2*(2*b*d*e + b*c*f - 3*a*d*f)*(e + f*x)^(7/2))/f^3 + (35*b^3*d^3*(e + f*x)^(9/2))/f^3 + (315*(-(b*c) + a*d)^3*(d*e - c*f)*(Sqrt[d]*Sqrt[e + f*x] - Sqrt[d*e - c*f]*ArcTanh[(Sqrt[d]*Sqrt[e + f*x])/Sqrt[d*e - c*f]]))/d^(3/2)))/(315*d^4)","A",1
1784,1,210,210,0.2786759,"\int \frac{(a+b x)^3 \sqrt{e+f x}}{c+d x} \, dx","Integrate[((a + b*x)^3*Sqrt[e + f*x])/(c + d*x),x]","\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}","\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*(b*c - a*d)^3*Sqrt[e + f*x])/d^4 + (2*b*(3*a^2*d^2*f^2 - 3*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + c*d*e*f + c^2*f^2))*(e + f*x)^(3/2))/(3*d^3*f^3) - (2*b^2*(2*b*d*e + b*c*f - 3*a*d*f)*(e + f*x)^(5/2))/(5*d^2*f^3) + (2*b^3*(e + f*x)^(7/2))/(7*d*f^3) + (2*(b*c - a*d)^3*Sqrt[d*e - c*f]*ArcTanh[(Sqrt[d]*Sqrt[e + f*x])/Sqrt[d*e - c*f]])/d^(9/2)","A",1
1785,1,184,184,0.1993929,"\int \frac{(a+b x)^3}{(c+d x) \sqrt{e+f x}} \, dx","Integrate[(a + b*x)^3/((c + d*x)*Sqrt[e + f*x]),x]","\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}","\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*b*(3*a^2*d^2*f^2 - 3*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + c*d*e*f + c^2*f^2))*Sqrt[e + f*x])/(d^3*f^3) - (2*b^2*(2*b*d*e + b*c*f - 3*a*d*f)*(e + f*x)^(3/2))/(3*d^2*f^3) + (2*b^3*(e + f*x)^(5/2))/(5*d*f^3) + (2*(b*c - a*d)^3*ArcTanh[(Sqrt[d]*Sqrt[e + f*x])/Sqrt[d*e - c*f]])/(d^(7/2)*Sqrt[d*e - c*f])","A",1
1786,1,165,149,0.1835916,"\int \frac{(a+b x)^3}{(c+d x) (e+f x)^{3/2}} \, dx","Integrate[(a + b*x)^3/((c + d*x)*(e + f*x)^(3/2)),x]","\frac{2 \left(-\frac{3 b \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)}{f^3}-\frac{3 b^2 d (e+f x) (-3 a d f+b c f+2 b d e)}{f^3}+\frac{3 (b c-a d)^3 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{d (e+f x)}{d e-c f}\right)}{c f-d e}+\frac{b^3 d^2 (e+f x)^2}{f^3}\right)}{3 d^3 \sqrt{e+f x}}","-\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*((-3*b*(3*a^2*d^2*f^2 - 3*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + c*d*e*f + c^2*f^2)))/f^3 - (3*b^2*d*(2*b*d*e + b*c*f - 3*a*d*f)*(e + f*x))/f^3 + (b^3*d^2*(e + f*x)^2)/f^3 + (3*(b*c - a*d)^3*Hypergeometric2F1[-1/2, 1, 1/2, (d*(e + f*x))/(d*e - c*f)])/(-(d*e) + c*f)))/(3*d^3*Sqrt[e + f*x])","C",1
1787,1,165,163,0.1764388,"\int \frac{(a+b x)^3}{(c+d x) (e+f x)^{5/2}} \, dx","Integrate[(a + b*x)^3/((c + d*x)*(e + f*x)^(5/2)),x]","\frac{2 \left(-\frac{b \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)}{f^3}+\frac{3 b^2 d (e+f x) (-3 a d f+b c f+2 b d e)}{f^3}+\frac{(b c-a d)^3 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{d (e+f x)}{d e-c f}\right)}{c f-d e}+\frac{3 b^3 d^2 (e+f x)^2}{f^3}\right)}{3 d^3 (e+f x)^{3/2}}","\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*(-((b*(3*a^2*d^2*f^2 - 3*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + c*d*e*f + c^2*f^2)))/f^3) + (3*b^2*d*(2*b*d*e + b*c*f - 3*a*d*f)*(e + f*x))/f^3 + (3*b^3*d^2*(e + f*x)^2)/f^3 + ((b*c - a*d)^3*Hypergeometric2F1[-3/2, 1, -1/2, (d*(e + f*x))/(d*e - c*f)])/(-(d*e) + c*f)))/(3*d^3*(e + f*x)^(3/2))","C",1
1788,1,166,227,0.1835692,"\int \frac{(a+b x)^3}{(c+d x) (e+f x)^{7/2}} \, dx","Integrate[(a + b*x)^3/((c + d*x)*(e + f*x)^(7/2)),x]","\frac{2 \left(-\frac{3 b \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)}{f^3}+\frac{5 b^2 d (e+f x) (-3 a d f+b c f+2 b d e)}{f^3}+\frac{3 (b c-a d)^3 \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\frac{d (e+f x)}{d e-c f}\right)}{c f-d e}-\frac{15 b^3 d^2 (e+f x)^2}{f^3}\right)}{15 d^3 (e+f x)^{5/2}}","-\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*((-3*b*(3*a^2*d^2*f^2 - 3*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + c*d*e*f + c^2*f^2)))/f^3 + (5*b^2*d*(2*b*d*e + b*c*f - 3*a*d*f)*(e + f*x))/f^3 - (15*b^3*d^2*(e + f*x)^2)/f^3 + (3*(b*c - a*d)^3*Hypergeometric2F1[-5/2, 1, -3/2, (d*(e + f*x))/(d*e - c*f)])/(-(d*e) + c*f)))/(15*d^3*(e + f*x)^(5/2))","C",1
1789,1,166,260,0.1908674,"\int \frac{(a+b x)^3}{(c+d x) (e+f x)^{9/2}} \, dx","Integrate[(a + b*x)^3/((c + d*x)*(e + f*x)^(9/2)),x]","\frac{2 \left(-\frac{15 b \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)}{f^3}+\frac{21 b^2 d (e+f x) (-3 a d f+b c f+2 b d e)}{f^3}+\frac{15 (b c-a d)^3 \, _2F_1\left(-\frac{7}{2},1;-\frac{5}{2};\frac{d (e+f x)}{d e-c f}\right)}{c f-d e}-\frac{35 b^3 d^2 (e+f x)^2}{f^3}\right)}{105 d^3 (e+f x)^{7/2}}","-\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*((-15*b*(3*a^2*d^2*f^2 - 3*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + c*d*e*f + c^2*f^2)))/f^3 + (21*b^2*d*(2*b*d*e + b*c*f - 3*a*d*f)*(e + f*x))/f^3 - (35*b^3*d^2*(e + f*x)^2)/f^3 + (15*(b*c - a*d)^3*Hypergeometric2F1[-7/2, 1, -5/2, (d*(e + f*x))/(d*e - c*f)])/(-(d*e) + c*f)))/(105*d^3*(e + f*x)^(7/2))","C",1
1790,1,48,105,0.0345681,"\int \sqrt{1-2 x} (2+3 x)^6 (3+5 x) \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^6*(3 + 5*x),x]","-\frac{(1-2 x)^{3/2} \left(7818525 x^7+44409222 x^6+113196204 x^5+171389520 x^4+172440720 x^3+122662080 x^2+64000896 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,"-1/36465*((1 - 2*x)^(3/2)*(23667392 + 64000896*x + 122662080*x^2 + 172440720*x^3 + 171389520*x^4 + 113196204*x^5 + 44409222*x^6 + 7818525*x^7))","A",1
1791,1,43,92,0.0240097,"\int \sqrt{1-2 x} (2+3 x)^5 (3+5 x) \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^5*(3 + 5*x),x]","-\frac{1}{33} (1-2 x)^{3/2} \left(2673 x^6+13365 x^5+29565 x^4+38220 x^3+32220 x^2+18696 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,"-1/33*((1 - 2*x)^(3/2)*(7288 + 18696*x + 32220*x^2 + 38220*x^3 + 29565*x^4 + 13365*x^5 + 2673*x^6))","A",1
1792,1,38,79,0.0236219,"\int \sqrt{1-2 x} (2+3 x)^4 (3+5 x) \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x),x]","-\frac{(1-2 x)^{3/2} \left(66825 x^5+288360 x^4+540000 x^3+577080 x^2+388704 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,"-1/2145*((1 - 2*x)^(3/2)*(163888 + 388704*x + 577080*x^2 + 540000*x^3 + 288360*x^4 + 66825*x^5))","A",1
1793,1,33,66,0.0224021,"\int \sqrt{1-2 x} (2+3 x)^3 (3+5 x) \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x),x]","-\frac{1}{165} (1-2 x)^{3/2} \left(2025 x^4+7335 x^3+11205 x^2+9366 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,"-1/165*((1 - 2*x)^(3/2)*(4442 + 9366*x + 11205*x^2 + 7335*x^3 + 2025*x^4))","A",1
1794,1,28,53,0.0151696,"\int \sqrt{1-2 x} (2+3 x)^2 (3+5 x) \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x),x]","-\frac{1}{105} (1-2 x)^{3/2} \left(525 x^3+1530 x^2+1788 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,"-1/105*((1 - 2*x)^(3/2)*(1016 + 1788*x + 1530*x^2 + 525*x^3))","A",1
1795,1,23,40,0.018098,"\int \sqrt{1-2 x} (2+3 x) (3+5 x) \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x),x]","-\frac{1}{105} (1-2 x)^{3/2} \left(225 x^2+489 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,"-1/105*((1 - 2*x)^(3/2)*(373 + 489*x + 225*x^2))","A",1
1796,1,18,27,0.0117361,"\int \sqrt{1-2 x} (3+5 x) \, dx","Integrate[Sqrt[1 - 2*x]*(3 + 5*x),x]","-\frac{1}{3} (1-2 x)^{3/2} (3 x+4)","\frac{1}{2} (1-2 x)^{5/2}-\frac{11}{6} (1-2 x)^{3/2}",1,"-1/3*((1 - 2*x)^(3/2)*(4 + 3*x))","A",1
1797,1,46,56,0.0416789,"\int \frac{\sqrt{1-2 x} (3+5 x)}{2+3 x} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x))/(2 + 3*x),x]","\frac{1}{27} \left(3 \sqrt{1-2 x} (10 x-7)+2 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)\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,"(3*Sqrt[1 - 2*x]*(-7 + 10*x) + 2*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/27","A",1
1798,1,55,59,0.0233738,"\int \frac{\sqrt{1-2 x} (3+5 x)}{(2+3 x)^2} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x))/(2 + 3*x)^2,x]","\frac{7 \sqrt{1-2 x} (10 x+7)-8 \sqrt{21} (3 x+2) \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{63 x+42}","\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,"(7*Sqrt[1 - 2*x]*(7 + 10*x) - 8*Sqrt[21]*(2 + 3*x)*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(42 + 63*x)","A",1
1799,1,69,68,0.1038151,"\int \frac{\sqrt{1-2 x} (3+5 x)}{(2+3 x)^3} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x))/(2 + 3*x)^3,x]","\frac{21 \left(142 x^2+19 x-45\right)-46 (3 x+2)^2 \sqrt{42 x-21} \tan ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{2 x-1}\right)}{882 \sqrt{1-2 x} (3 x+2)^2}","\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,"(21*(-45 + 19*x + 142*x^2) - 46*(2 + 3*x)^2*Sqrt[-21 + 42*x]*ArcTan[Sqrt[3/7]*Sqrt[-1 + 2*x]])/(882*Sqrt[1 - 2*x]*(2 + 3*x)^2)","A",1
1800,1,42,88,0.0245196,"\int \frac{\sqrt{1-2 x} (3+5 x)}{(2+3 x)^4} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x))/(2 + 3*x)^4,x]","\frac{(1-2 x)^{3/2} \left(\frac{343}{(3 x+2)^3}-272 \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{21609}","\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,"((1 - 2*x)^(3/2)*(343/(2 + 3*x)^3 - 272*Hypergeometric2F1[3/2, 3, 5/2, 3/7 - (6*x)/7]))/21609","C",1
1801,1,42,110,0.0186487,"\int \frac{\sqrt{1-2 x} (3+5 x)}{(2+3 x)^5} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x))/(2 + 3*x)^5,x]","\frac{(1-2 x)^{3/2} \left(\frac{2401}{(3 x+2)^4}-720 \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{201684}","\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,"((1 - 2*x)^(3/2)*(2401/(2 + 3*x)^4 - 720*Hypergeometric2F1[3/2, 4, 5/2, 3/7 - (6*x)/7]))/201684","C",1
1802,1,42,128,0.0230149,"\int \frac{\sqrt{1-2 x} (3+5 x)}{(2+3 x)^6} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x))/(2 + 3*x)^6,x]","\frac{(1-2 x)^{3/2} \left(\frac{2401}{(3 x+2)^5}-256 \, _2F_1\left(\frac{3}{2},5;\frac{5}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{252105}","\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,"((1 - 2*x)^(3/2)*(2401/(2 + 3*x)^5 - 256*Hypergeometric2F1[3/2, 5, 5/2, 3/7 - (6*x)/7]))/252105","C",1
1803,1,43,92,0.0273295,"\int \sqrt{1-2 x} (2+3 x)^4 (3+5 x)^2 \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^2,x]","-\frac{(1-2 x)^{3/2} \left(289575 x^6+1425600 x^5+3106755 x^4+3960500 x^3+3298140 x^2+1895832 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,"-1/2145*((1 - 2*x)^(3/2)*(734904 + 1895832*x + 3298140*x^2 + 3960500*x^3 + 3106755*x^4 + 1425600*x^5 + 289575*x^6))","A",1
1804,1,38,79,0.0242025,"\int \sqrt{1-2 x} (2+3 x)^3 (3+5 x)^2 \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^2,x]","-\frac{(1-2 x)^{3/2} \left(111375 x^5+471825 x^4+868215 x^3+913245 x^2+607254 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,"-1/2145*((1 - 2*x)^(3/2)*(253898 + 607254*x + 913245*x^2 + 868215*x^3 + 471825*x^4 + 111375*x^5))","A",1
1805,1,33,66,0.0162785,"\int \sqrt{1-2 x} (2+3 x)^2 (3+5 x)^2 \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^2,x]","-\frac{(1-2 x)^{3/2} \left(23625 x^4+83650 x^3+125115 x^2+102714 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,"-1/1155*((1 - 2*x)^(3/2)*(48098 + 102714*x + 125115*x^2 + 83650*x^3 + 23625*x^4))","A",1
1806,1,28,53,0.0164714,"\int \sqrt{1-2 x} (2+3 x) (3+5 x)^2 \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^2,x]","-\frac{1}{105} (1-2 x)^{3/2} \left(875 x^3+2475 x^2+2817 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,"-1/105*((1 - 2*x)^(3/2)*(1569 + 2817*x + 2475*x^2 + 875*x^3))","A",1
1807,1,23,40,0.0113848,"\int \sqrt{1-2 x} (3+5 x)^2 \, dx","Integrate[Sqrt[1 - 2*x]*(3 + 5*x)^2,x]","-\frac{1}{21} (1-2 x)^{3/2} \left(75 x^2+156 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,"-1/21*((1 - 2*x)^(3/2)*(115 + 156*x + 75*x^2))","A",1
1808,1,51,69,0.052521,"\int \frac{\sqrt{1-2 x} (3+5 x)^2}{2+3 x} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^2)/(2 + 3*x),x]","\frac{1}{81} \left(3 \sqrt{1-2 x} \left(90 x^2+65 x-53\right)-2 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)\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,"(3*Sqrt[1 - 2*x]*(-53 + 65*x + 90*x^2) - 2*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/81","A",1
1809,1,55,74,0.0647974,"\int \frac{\sqrt{1-2 x} (3+5 x)^2}{(2+3 x)^2} \, dx","Integrate[(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)}{81 x+54}+\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))/(54 + 81*x) + (142*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(27*Sqrt[21])","A",1
1810,1,58,81,0.0549954,"\int \frac{\sqrt{1-2 x} (3+5 x)^2}{(2+3 x)^3} \, dx","Integrate[(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
1811,1,74,88,0.0919023,"\int \frac{\sqrt{1-2 x} (3+5 x)^2}{(2+3 x)^4} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^2)/(2 + 3*x)^4,x]","-\frac{4762 (3 x+2)^3 \sqrt{42 x-21} \tan ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{2 x-1}\right)-21 \left(45342 x^3+34831 x^2-10503 x-9124\right)}{55566 \sqrt{1-2 x} (3 x+2)^3}","\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,"-1/55566*(-21*(-9124 - 10503*x + 34831*x^2 + 45342*x^3) + 4762*(2 + 3*x)^3*Sqrt[-21 + 42*x]*ArcTan[Sqrt[3/7]*Sqrt[-1 + 2*x]])/(Sqrt[1 - 2*x]*(2 + 3*x)^3)","A",1
1812,1,54,108,0.0331518,"\int \frac{\sqrt{1-2 x} (3+5 x)^2}{(2+3 x)^5} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^2)/(2 + 3*x)^5,x]","\frac{(1-2 x)^{3/2} \left(343 (825 x+529)-37000 (3 x+2)^4 \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{1815156 (3 x+2)^4}","\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,"((1 - 2*x)^(3/2)*(343*(529 + 825*x) - 37000*(2 + 3*x)^4*Hypergeometric2F1[3/2, 3, 5/2, 3/7 - (6*x)/7]))/(1815156*(2 + 3*x)^4)","C",1
1813,1,47,128,0.0300746,"\int \frac{\sqrt{1-2 x} (3+5 x)^2}{(2+3 x)^6} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^2)/(2 + 3*x)^6,x]","\frac{(1-2 x)^{3/2} \left(\frac{343 (147 x+94)}{(3 x+2)^5}-2480 \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{432180}","\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,"((1 - 2*x)^(3/2)*((343*(94 + 147*x))/(2 + 3*x)^5 - 2480*Hypergeometric2F1[3/2, 4, 5/2, 3/7 - (6*x)/7]))/432180","C",1
1814,1,47,148,0.0455139,"\int \frac{\sqrt{1-2 x} (3+5 x)^2}{(2+3 x)^7} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^2)/(2 + 3*x)^7,x]","\frac{(1-2 x)^{3/2} \left(\frac{2401 (1233 x+787)}{(3 x+2)^6}-51616 \, _2F_1\left(\frac{3}{2},5;\frac{5}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{31765230}","\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,"((1 - 2*x)^(3/2)*((2401*(787 + 1233*x))/(2 + 3*x)^6 - 51616*Hypergeometric2F1[3/2, 5, 5/2, 3/7 - (6*x)/7]))/31765230","C",1
1815,1,48,105,0.0281,"\int \sqrt{1-2 x} (2+3 x)^4 (3+5 x)^3 \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^3,x]","-\frac{(1-2 x)^{3/2} \left(65154375 x^7+360231300 x^6+894452625 x^5+1320982290 x^4+1299289000 x^3+906777120 x^2+466679856 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,"-1/109395*((1 - 2*x)^(3/2)*(171312832 + 466679856*x + 906777120*x^2 + 1299289000*x^3 + 1320982290*x^4 + 894452625*x^5 + 360231300*x^6 + 65154375*x^7))","A",1
1816,1,43,92,0.0301324,"\int \sqrt{1-2 x} (2+3 x)^3 (3+5 x)^3 \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^3,x]","-\frac{(1-2 x)^{3/2} \left(1447875 x^6+7016625 x^5+15061950 x^4+18934285 x^3+15577455 x^2+8871906 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,"-1/6435*((1 - 2*x)^(3/2)*(3420622 + 8871906*x + 15577455*x^2 + 18934285*x^3 + 15061950*x^4 + 7016625*x^5 + 1447875*x^6))","A",1
1817,1,38,79,0.0201385,"\int \sqrt{1-2 x} (2+3 x)^2 (3+5 x)^3 \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^3,x]","-\frac{(1-2 x)^{3/2} \left(3898125 x^5+16206750 x^4+29300075 x^3+30337080 x^2+19918608 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,"-1/45045*((1 - 2*x)^(3/2)*(8261156 + 19918608*x + 30337080*x^2 + 29300075*x^3 + 16206750*x^4 + 3898125*x^5))","A",1
1818,1,33,66,0.0192254,"\int \sqrt{1-2 x} (2+3 x) (3+5 x)^3 \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^3,x]","-\frac{(1-2 x)^{3/2} \left(118125 x^4+408625 x^3+598350 x^2+482583 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,"-1/3465*((1 - 2*x)^(3/2)*(223231 + 482583*x + 598350*x^2 + 408625*x^3 + 118125*x^4))","A",1
1819,1,28,53,0.0144244,"\int \sqrt{1-2 x} (3+5 x)^3 \, dx","Integrate[Sqrt[1 - 2*x]*(3 + 5*x)^3,x]","-\frac{1}{63} (1-2 x)^{3/2} \left(875 x^3+2400 x^2+2661 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,"-1/63*((1 - 2*x)^(3/2)*(1454 + 2661*x + 2400*x^2 + 875*x^3))","A",1
1820,1,58,82,0.0446194,"\int \frac{\sqrt{1-2 x} (3+5 x)^3}{2+3 x} \, dx","Integrate[(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
1821,1,63,93,0.0596575,"\int \frac{\sqrt{1-2 x} (3+5 x)^3}{(2+3 x)^2} \, dx","Integrate[(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
1822,1,63,100,0.0654577,"\int \frac{\sqrt{1-2 x} (3+5 x)^3}{(2+3 x)^3} \, dx","Integrate[(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
1823,1,79,107,0.0957285,"\int \frac{\sqrt{1-2 x} (3+5 x)^3}{(2+3 x)^4} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^3)/(2 + 3*x)^4,x]","-\frac{21 \left(661500 x^4+1059336 x^3+274193 x^2-260244 x-112187\right)-92996 (3 x+2)^3 \sqrt{42 x-21} \tan ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{2 x-1}\right)}{83349 \sqrt{1-2 x} (3 x+2)^3}","-\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,"-1/83349*(21*(-112187 - 260244*x + 274193*x^2 + 1059336*x^3 + 661500*x^4) - 92996*(2 + 3*x)^3*Sqrt[-21 + 42*x]*ArcTan[Sqrt[3/7]*Sqrt[-1 + 2*x]])/(Sqrt[1 - 2*x]*(2 + 3*x)^3)","A",1
1824,1,59,107,0.0371934,"\int \frac{\sqrt{1-2 x} (3+5 x)^3}{(2+3 x)^5} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^3)/(2 + 3*x)^5,x]","\frac{(1-2 x)^{3/2} \left(343 \left(661500 x^2+880755 x+293191\right)-2629720 (3 x+2)^4 \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{5445468 (3 x+2)^4}","-\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,"((1 - 2*x)^(3/2)*(343*(293191 + 880755*x + 661500*x^2) - 2629720*(2 + 3*x)^4*Hypergeometric2F1[3/2, 3, 5/2, 3/7 - (6*x)/7]))/(5445468*(2 + 3*x)^4)","C",1
1825,1,52,127,0.0390903,"\int \frac{\sqrt{1-2 x} (3+5 x)^3}{(2+3 x)^6} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^3)/(2 + 3*x)^6,x]","\frac{(1-2 x)^{3/2} \left(\frac{4802 \left(78750 x^2+104667 x+34784\right)}{(3 x+2)^5}-1797920 \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{27227340}","-\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,"((1 - 2*x)^(3/2)*((4802*(34784 + 104667*x + 78750*x^2))/(2 + 3*x)^5 - 1797920*Hypergeometric2F1[3/2, 4, 5/2, 3/7 - (6*x)/7]))/27227340","C",1
1826,1,52,147,0.0371634,"\int \frac{\sqrt{1-2 x} (3+5 x)^3}{(2+3 x)^7} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^3)/(2 + 3*x)^7,x]","\frac{(1-2 x)^{3/2} \left(\frac{12005 \left(330750 x^2+439137 x+145793\right)}{(3 x+2)^6}-7033120 \, _2F_1\left(\frac{3}{2},5;\frac{5}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{476478450}","-\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,"((1 - 2*x)^(3/2)*((12005*(145793 + 439137*x + 330750*x^2))/(2 + 3*x)^6 - 7033120*Hypergeometric2F1[3/2, 5, 5/2, 3/7 - (6*x)/7]))/476478450","C",1
1827,1,52,167,0.0390499,"\int \frac{\sqrt{1-2 x} (3+5 x)^3}{(2+3 x)^8} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^3)/(2 + 3*x)^8,x]","\frac{(1-2 x)^{3/2} \left(\frac{235298 \left(165375 x^2+219414 x+72797\right)}{(3 x+2)^7}-24286208 \, _2F_1\left(\frac{3}{2},6;\frac{5}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{6537284334}","-\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,"((1 - 2*x)^(3/2)*((235298*(72797 + 219414*x + 165375*x^2))/(2 + 3*x)^7 - 24286208*Hypergeometric2F1[3/2, 6, 5/2, 3/7 - (6*x)/7]))/6537284334","C",1
1828,1,61,95,0.0616982,"\int \frac{\sqrt{1-2 x} (2+3 x)^4}{3+5 x} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^4)/(3 + 5*x),x]","\frac{5 \sqrt{1-2 x} \left(78750 x^4+203625 x^3+177930 x^2+27865 x-88776\right)-14 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{109375}","\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,"(5*Sqrt[1 - 2*x]*(-88776 + 27865*x + 177930*x^2 + 203625*x^3 + 78750*x^4) - 14*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/109375","A",1
1829,1,56,82,0.0371029,"\int \frac{\sqrt{1-2 x} (2+3 x)^3}{3+5 x} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^3)/(3 + 5*x),x]","\frac{5 \sqrt{1-2 x} \left(6750 x^3+12555 x^2+5115 x-6526\right)-14 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{21875}","-\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,"(5*Sqrt[1 - 2*x]*(-6526 + 5115*x + 12555*x^2 + 6750*x^3) - 14*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/21875","A",1
1830,1,51,69,0.0390597,"\int \frac{\sqrt{1-2 x} (2+3 x)^2}{3+5 x} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^2)/(3 + 5*x),x]","\frac{1}{625} \left(5 \sqrt{1-2 x} \left(90 x^2+95 x-68\right)-2 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)\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,"(5*Sqrt[1 - 2*x]*(-68 + 95*x + 90*x^2) - 2*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/625","A",1
1831,1,46,56,0.0217948,"\int \frac{\sqrt{1-2 x} (2+3 x)}{3+5 x} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x))/(3 + 5*x),x]","\frac{1}{125} \left(5 \sqrt{1-2 x} (10 x-3)-2 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)\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,"(5*Sqrt[1 - 2*x]*(-3 + 10*x) - 2*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/125","A",1
1832,1,43,43,0.0087546,"\int \frac{\sqrt{1-2 x}}{3+5 x} \, dx","Integrate[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
1833,1,55,55,0.0806799,"\int \frac{\sqrt{1-2 x}}{(2+3 x) (3+5 x)} \, dx","Integrate[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
1834,1,81,68,0.0604592,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^2 (3+5 x)} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^2*(3 + 5*x)),x]","\frac{68 \sqrt{21} (3 x+2) \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+21 \left(\sqrt{1-2 x}-2 \sqrt{55} (3 x+2) \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)\right)}{63 x+42}","\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,"(68*Sqrt[21]*(2 + 3*x)*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] + 21*(Sqrt[1 - 2*x] - 2*Sqrt[55]*(2 + 3*x)*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]))/(42 + 63*x)","A",1
1835,1,80,95,0.0948286,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^3 (3+5 x)} \, dx","Integrate[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
1836,1,83,113,0.1223873,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^4 (3+5 x)} \, dx","Integrate[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
1837,1,88,133,0.2512368,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^5 (3+5 x)} \, dx","Integrate[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
1838,1,73,133,0.0943024,"\int \frac{\sqrt{1-2 x} (2+3 x)^5}{(3+5 x)^2} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^5)/(3 + 5*x)^2,x]","\frac{\frac{55 \sqrt{1-2 x} \left(1181250 x^5+3864375 x^4+4760100 x^3+2225760 x^2-1133340 x-862072\right)}{5 x+3}-2296 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{6015625}","-\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,"((55*Sqrt[1 - 2*x]*(-862072 - 1133340*x + 2225760*x^2 + 4760100*x^3 + 3864375*x^4 + 1181250*x^5))/(3 + 5*x) - 2296*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/6015625","A",1
1839,1,68,113,0.0926278,"\int \frac{\sqrt{1-2 x} (2+3 x)^4}{(3+5 x)^2} \, dx","Integrate[(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
1840,1,63,88,0.0460038,"\int \frac{\sqrt{1-2 x} (2+3 x)^3}{(3+5 x)^2} \, dx","Integrate[(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
1841,1,58,74,0.0435473,"\int \frac{\sqrt{1-2 x} (2+3 x)^2}{(3+5 x)^2} \, dx","Integrate[(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
1842,1,53,61,0.0280938,"\int \frac{\sqrt{1-2 x} (2+3 x)}{(3+5 x)^2} \, dx","Integrate[(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
1843,1,67,48,0.039449,"\int \frac{\sqrt{1-2 x}}{(3+5 x)^2} \, dx","Integrate[Sqrt[1 - 2*x]/(3 + 5*x)^2,x]","\frac{\sqrt{1-2 x} \left(-110 x+2 \sqrt{55} \sqrt{2 x-1} (5 x+3) \tan ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)+55\right)}{275 \left(10 x^2+x-3\right)}","\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,"(Sqrt[1 - 2*x]*(55 - 110*x + 2*Sqrt[55]*Sqrt[-1 + 2*x]*(3 + 5*x)*ArcTan[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/(275*(-3 + x + 10*x^2))","A",1
1844,1,69,69,0.057383,"\int \frac{\sqrt{1-2 x}}{(2+3 x) (3+5 x)^2} \, dx","Integrate[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
1845,1,105,97,0.0871174,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^2 (3+5 x)^2} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{-1518 \sqrt{21} \left(15 x^2+19 x+6\right) \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+938 \sqrt{55} \left(15 x^2+19 x+6\right) \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)-77 \sqrt{1-2 x} (30 x+19)}{77 (3 x+2) (5 x+3)}","-\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,"(-77*Sqrt[1 - 2*x]*(19 + 30*x) - 1518*Sqrt[21]*(6 + 19*x + 15*x^2)*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] + 938*Sqrt[55]*(6 + 19*x + 15*x^2)*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(77*(2 + 3*x)*(3 + 5*x))","A",1
1846,1,94,131,0.1335097,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^3 (3+5 x)^2} \, dx","Integrate[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,"-1/14*(Sqrt[1 - 2*x]*(3965 + 12228*x + 9405*x^2))/((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
1847,1,99,158,0.160998,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^4 (3+5 x)^2} \, dx","Integrate[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,"-1/98*(Sqrt[1 - 2*x]*(369116 + 1692159*x + 2583264*x^2 + 1313415*x^3))/((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
1848,1,68,120,0.1028368,"\int \frac{\sqrt{1-2 x} (2+3 x)^4}{(3+5 x)^3} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^4)/(3 + 5*x)^3,x]","\frac{\frac{55 \sqrt{1-2 x} \left(445500 x^4+1103850 x^3+506880 x^2-200305 x-121976\right)}{(5 x+3)^2}-25606 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3781250}","-\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,"((55*Sqrt[1 - 2*x]*(-121976 - 200305*x + 506880*x^2 + 1103850*x^3 + 445500*x^4))/(3 + 5*x)^2 - 25606*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/3781250","A",1
1849,1,63,100,0.0554758,"\int \frac{\sqrt{1-2 x} (2+3 x)^3}{(3+5 x)^3} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^3)/(3 + 5*x)^3,x]","\frac{\frac{55 \sqrt{1-2 x} \left(9900 x^3+12870 x^2+4555 x+236\right)}{(5 x+3)^2}-2534 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{151250}","-\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,"((55*Sqrt[1 - 2*x]*(236 + 4555*x + 12870*x^2 + 9900*x^3))/(3 + 5*x)^2 - 2534*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/151250","A",1
1850,1,58,81,0.0497087,"\int \frac{\sqrt{1-2 x} (2+3 x)^2}{(3+5 x)^3} \, dx","Integrate[(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
1851,1,74,68,0.0881369,"\int \frac{\sqrt{1-2 x} (2+3 x)}{(3+5 x)^3} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x))/(3 + 5*x)^3,x]","\frac{55 \left(650 x^2+87 x-206\right)-134 \sqrt{55} \sqrt{2 x-1} (5 x+3)^2 \tan ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{30250 \sqrt{1-2 x} (5 x+3)^2}","-\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,"(55*(-206 + 87*x + 650*x^2) - 134*Sqrt[55]*Sqrt[-1 + 2*x]*(3 + 5*x)^2*ArcTan[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(30250*Sqrt[1 - 2*x]*(3 + 5*x)^2)","A",1
1852,1,30,68,0.007943,"\int \frac{\sqrt{1-2 x}}{(3+5 x)^3} \, dx","Integrate[Sqrt[1 - 2*x]/(3 + 5*x)^3,x]","-\frac{8 (1-2 x)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};-\frac{5}{11} (2 x-1)\right)}{3993}","\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,"(-8*(1 - 2*x)^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, (-5*(-1 + 2*x))/11])/3993","C",1
1853,1,78,93,0.0959985,"\int \frac{\sqrt{1-2 x}}{(2+3 x) (3+5 x)^3} \, dx","Integrate[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
1854,1,94,121,0.1216163,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^2 (3+5 x)^3} \, dx","Integrate[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
1855,1,119,153,0.1268708,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^3 (3+5 x)^3} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{10519014 \sqrt{21} \left(15 x^2+19 x+6\right)^2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-6499850 \sqrt{55} \left(15 x^2+19 x+6\right)^2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)+77 \sqrt{1-2 x} \left(3118950 x^3+5926515 x^2+3748007 x+788875\right)}{11858 (3 x+2)^2 (5 x+3)^2}","\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,"(77*Sqrt[1 - 2*x]*(788875 + 3748007*x + 5926515*x^2 + 3118950*x^3) + 10519014*Sqrt[21]*(6 + 19*x + 15*x^2)^2*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - 6499850*Sqrt[55]*(6 + 19*x + 15*x^2)^2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(11858*(2 + 3*x)^2*(3 + 5*x)^2)","A",1
1856,1,167,180,0.2529938,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^4 (3+5 x)^3} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^4*(3 + 5*x)^3),x]","\frac{-22497365 (1-2 x)^{3/2} (3 x+2)^3+2977568 (1-2 x)^{3/2} (3 x+2)^2+150766 (1-2 x)^{3/2} (3 x+2)+11858 (1-2 x)^{3/2}+(5 x+3) (3 x+2)^3 \left(301398449 \sqrt{1-2 x}+611795844 \sqrt{21} (5 x+3) \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-378037450 \sqrt{55} (5 x+3) \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)\right)}{83006 (3 x+2)^3 (5 x+3)^2}","\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,"(11858*(1 - 2*x)^(3/2) + 150766*(1 - 2*x)^(3/2)*(2 + 3*x) + 2977568*(1 - 2*x)^(3/2)*(2 + 3*x)^2 - 22497365*(1 - 2*x)^(3/2)*(2 + 3*x)^3 + (2 + 3*x)^3*(3 + 5*x)*(301398449*Sqrt[1 - 2*x] + 611795844*Sqrt[21]*(3 + 5*x)*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - 378037450*Sqrt[55]*(3 + 5*x)*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]))/(83006*(2 + 3*x)^3*(3 + 5*x)^2)","A",1
1857,1,48,105,0.0306551,"\int (1-2 x)^{3/2} (2+3 x)^6 (3+5 x) \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^6*(3 + 5*x),x]","-\frac{(1-2 x)^{5/2} \left(44304975 x^7+246022920 x^6+607227192 x^5+876286620 x^4+817490880 x^3+512679760 x^2+214047840 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,"-1/230945*((1 - 2*x)^(5/2)*(51677856 + 214047840*x + 512679760*x^2 + 817490880*x^3 + 876286620*x^4 + 607227192*x^5 + 246022920*x^6 + 44304975*x^7))","A",1
1858,1,43,92,0.0315776,"\int (1-2 x)^{3/2} (2+3 x)^5 (3+5 x) \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^5*(3 + 5*x),x]","-\frac{(1-2 x)^{5/2} \left(2606175 x^6+12660219 x^5+26832465 x^4+32431860 x^3+24424220 x^2+11562520 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,"-1/36465*((1 - 2*x)^(5/2)*(3012632 + 11562520*x + 24424220*x^2 + 32431860*x^3 + 26832465*x^4 + 12660219*x^5 + 2606175*x^6))","A",1
1859,1,38,79,0.026363,"\int (1-2 x)^{3/2} (2+3 x)^4 (3+5 x) \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x),x]","-\frac{(1-2 x)^{5/2} \left(57915 x^5+240570 x^4+424440 x^3+410320 x^2+230000 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,"-1/2145*((1 - 2*x)^(5/2)*(66592 + 230000*x + 410320*x^2 + 424440*x^3 + 240570*x^4 + 57915*x^5))","A",1
1860,1,33,66,0.0225391,"\int (1-2 x)^{3/2} (2+3 x)^3 (3+5 x) \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x),x]","-\frac{1}{715} (1-2 x)^{5/2} \left(7425 x^4+25515 x^3+35675 x^2+25310 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,"-1/715*((1 - 2*x)^(5/2)*(8494 + 25310*x + 35675*x^2 + 25515*x^3 + 7425*x^4))","A",1
1861,1,28,53,0.0206446,"\int (1-2 x)^{3/2} (2+3 x)^2 (3+5 x) \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x),x]","-\frac{1}{165} (1-2 x)^{5/2} \left(675 x^3+1820 x^2+1840 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,"-1/165*((1 - 2*x)^(5/2)*(764 + 1840*x + 1820*x^2 + 675*x^3))","A",1
1862,1,23,40,0.0128697,"\int (1-2 x)^{3/2} (2+3 x) (3+5 x) \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x),x]","-\frac{1}{105} (1-2 x)^{5/2} \left(175 x^2+335 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,"-1/105*((1 - 2*x)^(5/2)*(193 + 335*x + 175*x^2))","A",1
1863,1,18,27,0.0165051,"\int (1-2 x)^{3/2} (3+5 x) \, dx","Integrate[(1 - 2*x)^(3/2)*(3 + 5*x),x]","-\frac{1}{35} (1-2 x)^{5/2} (25 x+26)","\frac{5}{14} (1-2 x)^{7/2}-\frac{11}{10} (1-2 x)^{5/2}",1,"-1/35*((1 - 2*x)^(5/2)*(26 + 25*x))","A",1
1864,1,51,69,0.0281549,"\int \frac{(1-2 x)^{3/2} (3+5 x)}{2+3 x} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x),x]","\frac{1}{81} \left(14 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-3 \sqrt{1-2 x} \left(36 x^2-40 x+25\right)\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,"(-3*Sqrt[1 - 2*x]*(25 - 40*x + 36*x^2) + 14*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/81","A",1
1865,1,58,76,0.048032,"\int \frac{(1-2 x)^{3/2} (3+5 x)}{(2+3 x)^2} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x)^2,x]","\frac{1}{81} \left(\frac{3 \sqrt{1-2 x} \left(-60 x^2+212 x+175\right)}{3 x+2}-76 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)\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,"((3*Sqrt[1 - 2*x]*(175 + 212*x - 60*x^2))/(2 + 3*x) - 76*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/81","A",1
1866,1,48,81,0.0226374,"\int \frac{(1-2 x)^{3/2} (3+5 x)}{(2+3 x)^3} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x)^3,x]","\frac{(1-2 x)^{5/2} \left(245-284 (3 x+2)^2 \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{10290 (3 x+2)^2}","\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,"((1 - 2*x)^(5/2)*(245 - 284*(2 + 3*x)^2*Hypergeometric2F1[2, 5/2, 7/2, 3/7 - (6*x)/7]))/(10290*(2 + 3*x)^2)","C",1
1867,1,74,88,0.1191696,"\int \frac{(1-2 x)^{3/2} (3+5 x)}{(2+3 x)^4} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x)^4,x]","-\frac{21 \left(1584 x^3+536 x^2-450 x-107\right)-104 (3 x+2)^3 \sqrt{42 x-21} \tan ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{2 x-1}\right)}{3969 \sqrt{1-2 x} (3 x+2)^3}","\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,"-1/3969*(21*(-107 - 450*x + 536*x^2 + 1584*x^3) - 104*(2 + 3*x)^3*Sqrt[-21 + 42*x]*ArcTan[Sqrt[3/7]*Sqrt[-1 + 2*x]])/(Sqrt[1 - 2*x]*(2 + 3*x)^3)","A",1
1868,1,42,108,0.0194174,"\int \frac{(1-2 x)^{3/2} (3+5 x)}{(2+3 x)^5} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x)^5,x]","\frac{(1-2 x)^{5/2} \left(\frac{12005}{(3 x+2)^4}-2192 \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{1008420}","\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,"((1 - 2*x)^(5/2)*(12005/(2 + 3*x)^4 - 2192*Hypergeometric2F1[5/2, 4, 7/2, 3/7 - (6*x)/7]))/1008420","C",1
1869,1,42,128,0.0210178,"\int \frac{(1-2 x)^{3/2} (3+5 x)}{(2+3 x)^6} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x)^6,x]","\frac{(1-2 x)^{5/2} \left(\frac{16807}{(3 x+2)^5}-1088 \, _2F_1\left(\frac{5}{2},5;\frac{7}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{1764735}","\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,"((1 - 2*x)^(5/2)*(16807/(2 + 3*x)^5 - 1088*Hypergeometric2F1[5/2, 5, 7/2, 3/7 - (6*x)/7]))/1764735","C",1
1870,1,43,92,0.0242407,"\int (1-2 x)^{3/2} (2+3 x)^4 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x)^2,x]","-\frac{(1-2 x)^{5/2} \left(13030875 x^6+62316540 x^5+130072635 x^4+154943820 x^3+115145660 x^2+53902600 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,"-1/109395*((1 - 2*x)^(5/2)*(13931096 + 53902600*x + 115145660*x^2 + 154943820*x^3 + 130072635*x^4 + 62316540*x^5 + 13030875*x^6))","A",1
1871,1,38,79,0.0208444,"\int (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^2,x]","-\frac{(1-2 x)^{5/2} \left(289575 x^5+1180575 x^4+2045655 x^3+1944575 x^2+1074070 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,"-1/6435*((1 - 2*x)^(5/2)*(307478 + 1074070*x + 1944575*x^2 + 2045655*x^3 + 1180575*x^4 + 289575*x^5))","A",1
1872,1,33,66,0.0251888,"\int (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^2,x]","-\frac{(1-2 x)^{5/2} \left(111375 x^4+373950 x^3+511465 x^2+355730 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,"-1/6435*((1 - 2*x)^(5/2)*(117478 + 355730*x + 511465*x^2 + 373950*x^3 + 111375*x^4))","A",1
1873,1,28,53,0.017094,"\int (1-2 x)^{3/2} (2+3 x) (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^2,x]","-\frac{(1-2 x)^{5/2} \left(23625 x^3+61775 x^2+60715 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,"-1/3465*((1 - 2*x)^(5/2)*(24617 + 60715*x + 61775*x^2 + 23625*x^3))","A",1
1874,1,23,40,0.0190481,"\int (1-2 x)^{3/2} (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^(3/2)*(3 + 5*x)^2,x]","-\frac{1}{315} (1-2 x)^{5/2} \left(875 x^2+1600 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,"-1/315*((1 - 2*x)^(5/2)*(887 + 1600*x + 875*x^2))","A",1
1875,1,56,82,0.044973,"\int \frac{(1-2 x)^{3/2} (3+5 x)^2}{2+3 x} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x),x]","\frac{3 \sqrt{1-2 x} \left(-2700 x^3+144 x^2+1853 x-527\right)-98 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{1701}","\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,"(3*Sqrt[1 - 2*x]*(-527 + 1853*x + 144*x^2 - 2700*x^3) - 98*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/1701","A",1
1876,1,63,89,0.046385,"\int \frac{(1-2 x)^{3/2} (3+5 x)^2}{(2+3 x)^2} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^2,x]","\frac{1}{243} \left(146 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-\frac{3 \sqrt{1-2 x} \left(540 x^3-300 x^2+187 x+425\right)}{3 x+2}\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,"((-3*Sqrt[1 - 2*x]*(425 + 187*x - 300*x^2 + 540*x^3))/(2 + 3*x) + 146*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/243","A",1
1877,1,63,94,0.0529679,"\int \frac{(1-2 x)^{3/2} (3+5 x)^2}{(2+3 x)^3} \, dx","Integrate[((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
1878,1,54,101,0.0256648,"\int \frac{(1-2 x)^{3/2} (3+5 x)^2}{(2+3 x)^4} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^4,x]","\frac{(1-2 x)^{5/2} \left(245 (627 x+404)-30236 (3 x+2)^3 \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{648270 (3 x+2)^3}","\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,"((1 - 2*x)^(5/2)*(245*(404 + 627*x) - 30236*(2 + 3*x)^3*Hypergeometric2F1[2, 5/2, 7/2, 3/7 - (6*x)/7]))/(648270*(2 + 3*x)^3)","C",1
1879,1,79,108,0.1170344,"\int \frac{(1-2 x)^{3/2} (3+5 x)^2}{(2+3 x)^5} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^5,x]","-\frac{21 \left(1337958 x^4+1307091 x^3-80575 x^2-331950 x-60890\right)-28846 (3 x+2)^4 \sqrt{42 x-21} \tan ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{2 x-1}\right)}{666792 \sqrt{1-2 x} (3 x+2)^4}","\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,"-1/666792*(21*(-60890 - 331950*x - 80575*x^2 + 1307091*x^3 + 1337958*x^4) - 28846*(2 + 3*x)^4*Sqrt[-21 + 42*x]*ArcTan[Sqrt[3/7]*Sqrt[-1 + 2*x]])/(Sqrt[1 - 2*x]*(2 + 3*x)^4)","A",1
1880,1,47,128,0.0301587,"\int \frac{(1-2 x)^{3/2} (3+5 x)^2}{(2+3 x)^6} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^6,x]","\frac{(1-2 x)^{5/2} \left(\frac{2401 (1035 x+662)}{(3 x+2)^5}-75088 \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{21176820}","\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,"((1 - 2*x)^(5/2)*((2401*(662 + 1035*x))/(2 + 3*x)^5 - 75088*Hypergeometric2F1[5/2, 4, 7/2, 3/7 - (6*x)/7]))/21176820","C",1
1881,1,47,148,0.0396939,"\int \frac{(1-2 x)^{3/2} (3+5 x)^2}{(2+3 x)^7} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^7,x]","\frac{(1-2 x)^{5/2} \left(\frac{16807 (177 x+113)}{(3 x+2)^6}-31712 \, _2F_1\left(\frac{5}{2},5;\frac{7}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{31765230}","\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,"((1 - 2*x)^(5/2)*((16807*(113 + 177*x))/(2 + 3*x)^6 - 31712*Hypergeometric2F1[5/2, 5, 7/2, 3/7 - (6*x)/7]))/31765230","C",1
1882,1,48,105,0.0337084,"\int (1-2 x)^{3/2} (2+3 x)^4 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x)^3,x]","-\frac{(1-2 x)^{5/2} \left(369208125 x^7+1995171750 x^6+4795033815 x^5+6744559140 x^4+6142984080 x^3+3771434840 x^2+1547888800 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,"-1/692835*((1 - 2*x)^(5/2)*(369438704 + 1547888800*x + 3771434840*x^2 + 6142984080*x^3 + 6744559140*x^4 + 4795033815*x^5 + 1995171750*x^6 + 369208125*x^7))","A",1
1883,1,43,92,0.0258063,"\int (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^3,x]","-\frac{(1-2 x)^{5/2} \left(7239375 x^6+34073325 x^5+70032600 x^4+82215885 x^3+60296725 x^2+27917090 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,"-1/36465*((1 - 2*x)^(5/2)*(7158706 + 27917090*x + 60296725*x^2 + 82215885*x^3 + 70032600*x^4 + 34073325*x^5 + 7239375*x^6))","A",1
1884,1,38,79,0.0238986,"\int (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^3,x]","-\frac{1}{165} (1-2 x)^{5/2} \left(12375 x^5+49500 x^4+84225 x^3+78730 x^2+42860 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,"-1/165*((1 - 2*x)^(5/2)*(12136 + 42860*x + 78730*x^2 + 84225*x^3 + 49500*x^4 + 12375*x^5))","A",1
1885,1,33,66,0.0234169,"\int (1-2 x)^{3/2} (2+3 x) (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^3,x]","-\frac{(1-2 x)^{5/2} \left(433125 x^4+1420125 x^3+1899800 x^2+1295695 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,"-1/15015*((1 - 2*x)^(5/2)*(421301 + 1295695*x + 1899800*x^2 + 1420125*x^3 + 433125*x^4))","A",1
1886,1,28,53,0.0148289,"\int (1-2 x)^{3/2} (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^(3/2)*(3 + 5*x)^3,x]","-\frac{(1-2 x)^{5/2} \left(13125 x^3+33250 x^2+31775 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,"-1/1155*((1 - 2*x)^(5/2)*(12592 + 31775*x + 33250*x^2 + 13125*x^3))","A",1
1887,1,61,95,0.0516228,"\int \frac{(1-2 x)^{3/2} (3+5 x)^3}{2+3 x} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x),x]","\frac{98 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-3 \sqrt{1-2 x} \left(31500 x^4+23400 x^3-17649 x^2-15679 x+7456\right)}{5103}","-\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,"(-3*Sqrt[1 - 2*x]*(7456 - 15679*x - 17649*x^2 + 23400*x^3 + 31500*x^4) + 98*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/5103","A",1
1888,1,70,108,0.0560481,"\int \frac{(1-2 x)^{3/2} (3+5 x)^3}{(2+3 x)^2} \, dx","Integrate[((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,"-1/63*(Sqrt[1 - 2*x]*(85 - 442*x - 1005*x^2 + 780*x^3 + 1500*x^4))/(2 + 3*x) - (8*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/9","A",1
1889,1,63,118,0.0685598,"\int \frac{(1-2 x)^{3/2} (3+5 x)^3}{(2+3 x)^3} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^3,x]","\frac{887 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{27 \sqrt{21}}-\frac{\sqrt{1-2 x} \left(1800 x^4+570 x^2+2965 x+1367\right)}{54 (3 x+2)^2}","\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,"-1/54*(Sqrt[1 - 2*x]*(1367 + 2965*x + 570*x^2 + 1800*x^4))/(2 + 3*x)^2 + (887*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(27*Sqrt[21])","A",1
1890,1,59,125,0.0224434,"\int \frac{(1-2 x)^{3/2} (3+5 x)^3}{(2+3 x)^4} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^4,x]","\frac{(1-2 x)^{5/2} \left(72076 (3 x+2)^3 \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{3}{7}-\frac{6 x}{7}\right)-245 \left(18375 x^2+24657 x+8269\right)\right)}{324135 (3 x+2)^3}","\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,"((1 - 2*x)^(5/2)*(-245*(8269 + 24657*x + 18375*x^2) + 72076*(2 + 3*x)^3*Hypergeometric2F1[2, 5/2, 7/2, 3/7 - (6*x)/7]))/(324135*(2 + 3*x)^3)","C",1
1891,1,84,131,0.1212507,"\int \frac{(1-2 x)^{3/2} (3+5 x)^3}{(2+3 x)^5} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^5,x]","-\frac{26486 (3 x+2)^4 \sqrt{42 x-21} \tan ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{2 x-1}\right)-21 \left(392000 x^5+1127278 x^4+915191 x^3+15285 x^2-252230 x-74810\right)}{24696 \sqrt{1-2 x} (3 x+2)^4}","\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,"-1/24696*(-21*(-74810 - 252230*x + 15285*x^2 + 915191*x^3 + 1127278*x^4 + 392000*x^5) + 26486*(2 + 3*x)^4*Sqrt[-21 + 42*x]*ArcTan[Sqrt[3/7]*Sqrt[-1 + 2*x]])/(Sqrt[1 - 2*x]*(2 + 3*x)^4)","A",1
1892,1,52,134,0.041939,"\int \frac{(1-2 x)^{3/2} (3+5 x)^3}{(2+3 x)^6} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^6,x]","\frac{(1-2 x)^{5/2} \left(\frac{86436 \left(30625 x^2+40790 x+13583\right)}{(3 x+2)^5}-8001792 \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{63530460}","\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,"((1 - 2*x)^(5/2)*((86436*(13583 + 40790*x + 30625*x^2))/(2 + 3*x)^5 - 8001792*Hypergeometric2F1[5/2, 4, 7/2, 3/7 - (6*x)/7]))/63530460","C",1
1893,1,52,154,0.0406093,"\int \frac{(1-2 x)^{3/2} (3+5 x)^3}{(2+3 x)^7} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^7,x]","\frac{(1-2 x)^{5/2} \left(\frac{16807 \left(26250 x^2+34911 x+11609\right)}{(3 x+2)^6}-490016 \, _2F_1\left(\frac{5}{2},5;\frac{7}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{31765230}","\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,"((1 - 2*x)^(5/2)*((16807*(11609 + 34911*x + 26250*x^2))/(2 + 3*x)^6 - 490016*Hypergeometric2F1[5/2, 5, 7/2, 3/7 - (6*x)/7]))/31765230","C",1
1894,1,52,174,0.0469324,"\int \frac{(1-2 x)^{3/2} (3+5 x)^3}{(2+3 x)^8} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^8,x]","\frac{(1-2 x)^{5/2} \left(\frac{84035 \left(8575 x^2+11393 x+3785\right)}{(3 x+2)^7}-279616 \, _2F_1\left(\frac{5}{2},6;\frac{7}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{86472015}","\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,"((1 - 2*x)^(5/2)*((84035*(3785 + 11393*x + 8575*x^2))/(2 + 3*x)^7 - 279616*Hypergeometric2F1[5/2, 6, 7/2, 3/7 - (6*x)/7]))/86472015","C",1
1895,1,76,134,0.1200752,"\int \frac{(1-2 x)^{3/2} (2+3 x)^6}{3+5 x} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^6)/(3 + 5*x),x]","\frac{-5 \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)-66066 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{5865234375}","\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,"(-5*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) - 66066*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/5865234375","A",1
1896,1,71,121,0.0840902,"\int \frac{(1-2 x)^{3/2} (2+3 x)^5}{3+5 x} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^5)/(3 + 5*x),x]","\frac{-5 \sqrt{1-2 x} \left(3508312500 x^6+9100350000 x^5+6683000625 x^4-1659418875 x^3-4276774170 x^2-1321809935 x+1180568944\right)-66066 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1173046875}","-\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,"(-5*Sqrt[1 - 2*x]*(1180568944 - 1321809935*x - 4276774170*x^2 - 1659418875*x^3 + 6683000625*x^4 + 9100350000*x^5 + 3508312500*x^6) - 66066*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1173046875","A",1
1897,1,66,108,0.0832337,"\int \frac{(1-2 x)^{3/2} (2+3 x)^4}{3+5 x} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^4)/(3 + 5*x),x]","\frac{-5 \sqrt{1-2 x} \left(21262500 x^5+39532500 x^4+9559125 x^3-21433590 x^2-12144995 x+7095688\right)-5082 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{18046875}","\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,"(-5*Sqrt[1 - 2*x]*(7095688 - 12144995*x - 21433590*x^2 + 9559125*x^3 + 39532500*x^4 + 21262500*x^5) - 5082*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/18046875","A",1
1898,1,61,95,0.0663101,"\int \frac{(1-2 x)^{3/2} (2+3 x)^3}{3+5 x} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^3)/(3 + 5*x),x]","\frac{-5 \sqrt{1-2 x} \left(157500 x^4+171000 x^3-83565 x^2-123295 x+50858\right)-462 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{328125}","-\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,"(-5*Sqrt[1 - 2*x]*(50858 - 123295*x - 83565*x^2 + 171000*x^3 + 157500*x^4) - 462*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/328125","A",1
1899,1,56,82,0.0617565,"\int \frac{(1-2 x)^{3/2} (2+3 x)^2}{3+5 x} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^2)/(3 + 5*x),x]","\frac{-5 \sqrt{1-2 x} \left(13500 x^3+3060 x^2-13045 x+3608\right)-462 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{65625}","\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,"(-5*Sqrt[1 - 2*x]*(3608 - 13045*x + 3060*x^2 + 13500*x^3) - 462*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/65625","A",1
1900,1,51,69,0.0264351,"\int \frac{(1-2 x)^{3/2} (2+3 x)}{3+5 x} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x))/(3 + 5*x),x]","\frac{5 \sqrt{1-2 x} \left(-180 x^2+160 x+31\right)-66 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1875}","-\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,"(5*Sqrt[1 - 2*x]*(31 + 160*x - 180*x^2) - 66*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1875","A",1
1901,1,46,56,0.0325135,"\int \frac{(1-2 x)^{3/2}}{3+5 x} \, dx","Integrate[(1 - 2*x)^(3/2)/(3 + 5*x),x]","-\frac{2}{375} \left(10 \sqrt{1-2 x} (5 x-19)+33 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)\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,"(-2*(10*Sqrt[1 - 2*x]*(-19 + 5*x) + 33*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]))/375","A",1
1902,1,66,72,0.0252068,"\int \frac{(1-2 x)^{3/2}}{(2+3 x) (3+5 x)} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)*(3 + 5*x)),x]","-\frac{2}{225} \left(30 \sqrt{1-2 x}-175 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+99 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)\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,"(-2*(30*Sqrt[1 - 2*x] - 175*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] + 99*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]))/225","A",1
1903,1,75,77,0.0817881,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^2 (3+5 x)} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^2*(3 + 5*x)),x]","\frac{7 \sqrt{1-2 x}}{9 x+6}+\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])/(6 + 9*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
1904,1,78,93,0.0897335,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^3 (3+5 x)} \, dx","Integrate[(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
1905,1,83,113,0.1159256,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^4 (3+5 x)} \, dx","Integrate[(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
1906,1,90,133,0.1784919,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^5 (3+5 x)} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^5*(3 + 5*x)),x]","\frac{21 \left(\frac{\sqrt{1-2 x} \left(8603361 x^3+17494905 x^2+11868230 x+2686470\right)}{(3 x+2)^4}-646800 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)\right)+21981686 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{24696}","\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,"(21981686*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] + 21*((Sqrt[1 - 2*x]*(2686470 + 11868230*x + 17494905*x^2 + 8603361*x^3))/(2 + 3*x)^4 - 646800*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]))/24696","A",1
1907,1,93,153,0.1622736,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^6 (3+5 x)} \, dx","Integrate[(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
1908,1,78,148,0.1057766,"\int \frac{(1-2 x)^{3/2} (2+3 x)^5}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^5)/(3 + 5*x)^2,x]","\frac{-\frac{5 \sqrt{1-2 x} \left(106312500 x^6+270112500 x^5+181738125 x^4-76760550 x^3-135193430 x^2-2532130 x+23061496\right)}{5 x+3}-24948 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{30078125}","-\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,"((-5*Sqrt[1 - 2*x]*(23061496 - 2532130*x - 135193430*x^2 - 76760550*x^3 + 181738125*x^4 + 270112500*x^5 + 106312500*x^6))/(3 + 5*x) - 24948*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/30078125","A",1
1909,1,78,128,0.1084376,"\int \frac{(1-2 x)^{3/2} (2+3 x)^4}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^4)/(3 + 5*x)^2,x]","-\frac{5 \sqrt{1-2 x} \left(787500 x^5+1395000 x^4+157275 x^3-924335 x^2-143235 x+161312\right)+1806 \sqrt{55} (5 x+3) \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{546875 (5 x+3)}","-\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,"-1/546875*(5*Sqrt[1 - 2*x]*(161312 - 143235*x - 924335*x^2 + 157275*x^3 + 1395000*x^4 + 787500*x^5) + 1806*Sqrt[55]*(3 + 5*x)*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(3 + 5*x)","A",1
1910,1,68,108,0.0538018,"\int \frac{(1-2 x)^{3/2} (2+3 x)^3}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^3)/(3 + 5*x)^2,x]","\frac{-\frac{5 \sqrt{1-2 x} \left(67500 x^4+62100 x^3-57165 x^2-27640 x+8738\right)}{5 x+3}-1344 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{109375}","-\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,"((-5*Sqrt[1 - 2*x]*(8738 - 27640*x - 57165*x^2 + 62100*x^3 + 67500*x^4))/(3 + 5*x) - 1344*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/109375","A",1
1911,1,63,89,0.0488898,"\int \frac{(1-2 x)^{3/2} (2+3 x)^2}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^2)/(3 + 5*x)^2,x]","\frac{\frac{5 \sqrt{1-2 x} \left(-900 x^3+160 x^2+935 x+298\right)}{5 x+3}-126 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{3125}","-\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,"((5*Sqrt[1 - 2*x]*(298 + 935*x + 160*x^2 - 900*x^3))/(3 + 5*x) - 126*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/3125","A",1
1912,1,58,76,0.0423562,"\int \frac{(1-2 x)^{3/2} (2+3 x)}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x))/(3 + 5*x)^2,x]","\frac{1}{125} \left(\frac{5 \sqrt{1-2 x} \left(-20 x^2+60 x+41\right)}{5 x+3}-12 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)\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,"((5*Sqrt[1 - 2*x]*(41 + 60*x - 20*x^2))/(3 + 5*x) - 12*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/125","A",1
1913,1,30,63,0.0080287,"\int \frac{(1-2 x)^{3/2}}{(3+5 x)^2} \, dx","Integrate[(1 - 2*x)^(3/2)/(3 + 5*x)^2,x]","-\frac{4}{605} (1-2 x)^{5/2} \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};-\frac{5}{11} (2 x-1)\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,"(-4*(1 - 2*x)^(5/2)*Hypergeometric2F1[2, 5/2, 7/2, (-5*(-1 + 2*x))/11])/605","C",1
1914,1,76,77,0.1194916,"\int \frac{(1-2 x)^{3/2}}{(2+3 x) (3+5 x)^2} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)*(3 + 5*x)^2),x]","\frac{1}{25} \left(72 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)-\frac{55 \sqrt{1-2 x}}{5 x+3}\right)-14 \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \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,"-14*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] + ((-55*Sqrt[1 - 2*x])/(3 + 5*x) + 72*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/25","A",1
1915,1,105,102,0.0719406,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^2 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{-670 \sqrt{21} \left(15 x^2+19 x+6\right) \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+414 \sqrt{55} \left(15 x^2+19 x+6\right) \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)-15 \sqrt{1-2 x} (68 x+43)}{15 (3 x+2) (5 x+3)}","-\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,"(-15*Sqrt[1 - 2*x]*(43 + 68*x) - 670*Sqrt[21]*(6 + 19*x + 15*x^2)*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] + 414*Sqrt[55]*(6 + 19*x + 15*x^2)*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(15*(2 + 3*x)*(3 + 5*x))","A",1
1916,1,90,127,0.1417511,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^3 (3+5 x)^2} \, dx","Integrate[(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,"-1/2*(Sqrt[1 - 2*x]*(1271 + 3920*x + 3015*x^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
1917,1,95,154,0.1660915,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^4 (3+5 x)^2} \, dx","Integrate[(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,"-1/14*(Sqrt[1 - 2*x]*(117752 + 539819*x + 824092*x^2 + 418995*x^3))/((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
1918,1,100,181,0.1899802,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^5 (3+5 x)^2} \, dx","Integrate[(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,"-1/392*(Sqrt[1 - 2*x]*(41029970 + 249642200*x + 569295605*x^2 + 576721848*x^3 + 218994705*x^4))/((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
1919,1,73,140,0.1148824,"\int \frac{(1-2 x)^{3/2} (2+3 x)^4}{(3+5 x)^3} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^4)/(3 + 5*x)^3,x]","\frac{-\frac{55 \sqrt{1-2 x} \left(2025000 x^5+3267000 x^4-496350 x^3-2120880 x^2-489445 x+96776\right)}{(5 x+3)^2}-171906 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{12031250}","-\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,"((-55*Sqrt[1 - 2*x]*(96776 - 489445*x - 2120880*x^2 - 496350*x^3 + 3267000*x^4 + 2025000*x^5))/(3 + 5*x)^2 - 171906*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/12031250","A",1
1920,1,68,120,0.0791343,"\int \frac{(1-2 x)^{3/2} (2+3 x)^3}{(3+5 x)^3} \, dx","Integrate[((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
1921,1,63,94,0.0622813,"\int \frac{(1-2 x)^{3/2} (2+3 x)^2}{(3+5 x)^3} \, dx","Integrate[((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
1922,1,48,81,0.0228201,"\int \frac{(1-2 x)^{3/2} (2+3 x)}{(3+5 x)^3} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x))/(3 + 5*x)^3,x]","-\frac{(1-2 x)^{5/2} \left(52 (5 x+3)^2 \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};-\frac{5}{11} (2 x-1)\right)+121\right)}{13310 (5 x+3)^2}","-\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,"-1/13310*((1 - 2*x)^(5/2)*(121 + 52*(3 + 5*x)^2*Hypergeometric2F1[2, 5/2, 7/2, (-5*(-1 + 2*x))/11]))/(3 + 5*x)^2","C",1
1923,1,74,68,0.0635909,"\int \frac{(1-2 x)^{3/2}}{(3+5 x)^3} \, dx","Integrate[(1 - 2*x)^(3/2)/(3 + 5*x)^3,x]","\frac{55 \left(-50 x^2+17 x+4\right)+6 \sqrt{55} \sqrt{2 x-1} (5 x+3)^2 \tan ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{2750 \sqrt{1-2 x} (5 x+3)^2}","-\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,"(55*(4 + 17*x - 50*x^2) + 6*Sqrt[55]*Sqrt[-1 + 2*x]*(3 + 5*x)^2*ArcTan[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(2750*Sqrt[1 - 2*x]*(3 + 5*x)^2)","A",1
1924,1,78,93,0.0958053,"\int \frac{(1-2 x)^{3/2}}{(2+3 x) (3+5 x)^3} \, dx","Integrate[(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
1925,1,88,118,0.1112461,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^2 (3+5 x)^3} \, dx","Integrate[(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
1926,1,119,147,0.1181785,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^3 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{309606 \sqrt{21} \left(15 x^2+19 x+6\right)^2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-191310 \sqrt{55} \left(15 x^2+19 x+6\right)^2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)+77 \sqrt{1-2 x} \left(91800 x^3+174435 x^2+110315 x+23219\right)}{154 (3 x+2)^2 (5 x+3)^2}","\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,"(77*Sqrt[1 - 2*x]*(23219 + 110315*x + 174435*x^2 + 91800*x^3) + 309606*Sqrt[21]*(6 + 19*x + 15*x^2)^2*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - 191310*Sqrt[55]*(6 + 19*x + 15*x^2)^2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(154*(2 + 3*x)^2*(3 + 5*x)^2)","A",1
1927,1,104,178,0.1697157,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^4 (3+5 x)^3} \, dx","Integrate[(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
1928,1,48,105,0.0366288,"\int (1-2 x)^{5/2} (2+3 x)^6 (3+5 x) \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^6*(3 + 5*x),x]","-\frac{(1-2 x)^{7/2} \left(505076715 x^7+2753997246 x^6+6628858236 x^5+9228315096 x^4+8157896208 x^3+4700947104 x^2+1706820416 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,"-1/2909907*((1 - 2*x)^(7/2)*(323646080 + 1706820416*x + 4700947104*x^2 + 8157896208*x^3 + 9228315096*x^4 + 6628858236*x^5 + 2753997246*x^6 + 505076715*x^7))","A",1
1929,1,43,92,0.0311684,"\int (1-2 x)^{5/2} (2+3 x)^5 (3+5 x) \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^5*(3 + 5*x),x]","-\frac{(1-2 x)^{7/2} \left(26582985 x^6+126243117 x^5+259076961 x^4+298438668 x^3+208370124 x^2+86950792 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,"-1/415701*((1 - 2*x)^(7/2)*(18122584 + 86950792*x + 208370124*x^2 + 298438668*x^3 + 259076961*x^4 + 126243117*x^5 + 26582985*x^6))","A",1
1930,1,38,79,0.0315177,"\int (1-2 x)^{5/2} (2+3 x)^4 (3+5 x) \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^4*(3 + 5*x),x]","-\frac{(1-2 x)^{7/2} \left(2606175 x^5+10517364 x^4+17777232 x^3+16066296 x^2+8043328 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,"-1/109395*((1 - 2*x)^(7/2)*(1899184 + 8043328*x + 16066296*x^2 + 17777232*x^3 + 10517364*x^4 + 2606175*x^5))","A",1
1931,1,33,66,0.0242137,"\int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x) \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x),x]","-\frac{(1-2 x)^{7/2} \left(11583 x^4+38313 x^3+50463 x^2+32378 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,"-1/1287*((1 - 2*x)^(7/2)*(9038 + 32378*x + 50463*x^2 + 38313*x^3 + 11583*x^4))","A",1
1932,1,28,53,0.0268821,"\int (1-2 x)^{5/2} (2+3 x)^2 (3+5 x) \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x),x]","-\frac{(1-2 x)^{7/2} \left(4455 x^3+11394 x^2+10540 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,"-1/1287*((1 - 2*x)^(7/2)*(3712 + 10540*x + 11394*x^2 + 4455*x^3))","A",1
1933,1,23,40,0.016818,"\int (1-2 x)^{5/2} (2+3 x) (3+5 x) \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x),x]","-\frac{1}{99} (1-2 x)^{7/2} \left(135 x^2+239 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,"-1/99*((1 - 2*x)^(7/2)*(119 + 239*x + 135*x^2))","A",1
1934,1,18,27,0.0193818,"\int (1-2 x)^{5/2} (3+5 x) \, dx","Integrate[(1 - 2*x)^(5/2)*(3 + 5*x),x]","-\frac{1}{63} (1-2 x)^{7/2} (35 x+32)","\frac{5}{18} (1-2 x)^{9/2}-\frac{11}{14} (1-2 x)^{7/2}",1,"-1/63*((1 - 2*x)^(7/2)*(32 + 35*x))","A",1
1935,1,56,82,0.0380361,"\int \frac{(1-2 x)^{5/2} (3+5 x)}{2+3 x} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x),x]","\frac{3 \sqrt{1-2 x} \left(5400 x^3-8604 x^2+5534 x-4721\right)+3430 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{8505}","-\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,"(3*Sqrt[1 - 2*x]*(-4721 + 5534*x - 8604*x^2 + 5400*x^3) + 3430*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/8505","A",1
1936,1,63,89,0.0440152,"\int \frac{(1-2 x)^{5/2} (3+5 x)}{(2+3 x)^2} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^2,x]","\frac{1}{243} \left(\frac{3 \sqrt{1-2 x} \left(216 x^3-516 x^2+1474 x+1325\right)}{3 x+2}-560 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)\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,"((3*Sqrt[1 - 2*x]*(1325 + 1474*x - 516*x^2 + 216*x^3))/(2 + 3*x) - 560*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/243","A",1
1937,1,48,96,0.0330879,"\int \frac{(1-2 x)^{5/2} (3+5 x)}{(2+3 x)^3} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^3,x]","\frac{(1-2 x)^{7/2} \left(343-292 (3 x+2)^2 \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{14406 (3 x+2)^2}","\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,"((1 - 2*x)^(7/2)*(343 - 292*(2 + 3*x)^2*Hypergeometric2F1[2, 7/2, 9/2, 3/7 - (6*x)/7]))/(14406*(2 + 3*x)^2)","C",1
1938,1,42,101,0.0204909,"\int \frac{(1-2 x)^{5/2} (3+5 x)}{(2+3 x)^4} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^4,x]","\frac{(1-2 x)^{7/2} \left(\frac{2401}{(3 x+2)^3}-848 \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{151263}","\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,"((1 - 2*x)^(7/2)*(2401/(2 + 3*x)^3 - 848*Hypergeometric2F1[3, 7/2, 9/2, 3/7 - (6*x)/7]))/151263","C",1
1939,1,79,108,0.1209438,"\int \frac{(1-2 x)^{5/2} (3+5 x)}{(2+3 x)^5} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^5,x]","-\frac{1390 (3 x+2)^4 \sqrt{42 x-21} \tan ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{2 x-1}\right)-21 \left(83430 x^4+46227 x^3-7183 x^2-9606 x-4394\right)}{95256 \sqrt{1-2 x} (3 x+2)^4}","\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,"-1/95256*(-21*(-4394 - 9606*x - 7183*x^2 + 46227*x^3 + 83430*x^4) + 1390*(2 + 3*x)^4*Sqrt[-21 + 42*x]*ArcTan[Sqrt[3/7]*Sqrt[-1 + 2*x]])/(Sqrt[1 - 2*x]*(2 + 3*x)^4)","A",1
1940,1,42,128,0.0218964,"\int \frac{(1-2 x)^{5/2} (3+5 x)}{(2+3 x)^6} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^6,x]","\frac{(1-2 x)^{7/2} \left(\frac{117649}{(3 x+2)^5}-5504 \, _2F_1\left(\frac{7}{2},5;\frac{9}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{12353145}","\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,"((1 - 2*x)^(7/2)*(117649/(2 + 3*x)^5 - 5504*Hypergeometric2F1[7/2, 5, 9/2, 3/7 - (6*x)/7]))/12353145","C",1
1941,1,42,148,0.0186841,"\int \frac{(1-2 x)^{5/2} (3+5 x)}{(2+3 x)^7} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^7,x]","\frac{(1-2 x)^{7/2} \left(\frac{823543}{(3 x+2)^6}-13120 \, _2F_1\left(\frac{7}{2},6;\frac{9}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{103766418}","\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,"((1 - 2*x)^(7/2)*(823543/(2 + 3*x)^6 - 13120*Hypergeometric2F1[7/2, 6, 9/2, 3/7 - (6*x)/7]))/103766418","C",1
1942,1,43,92,0.0316517,"\int (1-2 x)^{5/2} (2+3 x)^4 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^4*(3 + 5*x)^2,x]","-\frac{(1-2 x)^{7/2} \left(221524875 x^6+1035520200 x^5+2092364703 x^4+2374399764 x^3+1634664492 x^2+673648856 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,"-1/2078505*((1 - 2*x)^(7/2)*(138993368 + 673648856*x + 1634664492*x^2 + 2374399764*x^3 + 2092364703*x^4 + 1035520200*x^5 + 221524875*x^6))","A",1
1943,1,38,79,0.030943,"\int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^2,x]","-\frac{(1-2 x)^{7/2} \left(868725 x^5+3440151 x^4+5708637 x^3+5069475 x^2+2497634 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,"-1/21879*((1 - 2*x)^(7/2)*(581846 + 2497634*x + 5069475*x^2 + 5708637*x^3 + 3440151*x^4 + 868725*x^5))","A",1
1944,1,33,66,0.0205757,"\int (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^2,x]","-\frac{(1-2 x)^{7/2} \left(19305 x^4+62370 x^3+80307 x^2+50450 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,"-1/1287*((1 - 2*x)^(7/2)*(13826 + 50450*x + 80307*x^2 + 62370*x^3 + 19305*x^4))","A",1
1945,1,28,53,0.0243338,"\int (1-2 x)^{5/2} (2+3 x) (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^2,x]","-\frac{(1-2 x)^{7/2} \left(7425 x^3+18405 x^2+16531 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,"-1/1287*((1 - 2*x)^(7/2)*(5671 + 16531*x + 18405*x^2 + 7425*x^3))","A",1
1946,1,23,40,0.0127552,"\int (1-2 x)^{5/2} (3+5 x)^2 \, dx","Integrate[(1 - 2*x)^(5/2)*(3 + 5*x)^2,x]","-\frac{1}{693} (1-2 x)^{7/2} \left(1575 x^2+2660 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,"-1/693*((1 - 2*x)^(7/2)*(1271 + 2660*x + 1575*x^2))","A",1
1947,1,63,95,0.0898986,"\int \frac{(1-2 x)^{5/2} (3+5 x)^2}{2+3 x} \, dx","Integrate[((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
1948,1,70,102,0.0571196,"\int \frac{(1-2 x)^{5/2} (3+5 x)^2}{(2+3 x)^2} \, dx","Integrate[((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
1949,1,68,109,0.0543377,"\int \frac{(1-2 x)^{5/2} (3+5 x)^2}{(2+3 x)^3} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^3,x]","\frac{1}{486} \left(\frac{3 \sqrt{1-2 x} \left(2160 x^4-3960 x^3+12828 x^2+25987 x+10007\right)}{(3 x+2)^2}-2110 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)\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,"((3*Sqrt[1 - 2*x]*(10007 + 25987*x + 12828*x^2 - 3960*x^3 + 2160*x^4))/(2 + 3*x)^2 - 2110*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/486","A",1
1950,1,54,114,0.0300828,"\int \frac{(1-2 x)^{5/2} (3+5 x)^2}{(2+3 x)^4} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^4,x]","\frac{(1-2 x)^{7/2} \left(343 (211 x+136)-10644 (3 x+2)^3 \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{302526 (3 x+2)^3}","\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,"((1 - 2*x)^(7/2)*(343*(136 + 211*x) - 10644*(2 + 3*x)^3*Hypergeometric2F1[2, 7/2, 9/2, 3/7 - (6*x)/7]))/(302526*(2 + 3*x)^3)","C",1
1951,1,47,121,0.0358091,"\int \frac{(1-2 x)^{5/2} (3+5 x)^2}{(2+3 x)^5} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^5,x]","\frac{(1-2 x)^{7/2} \left(\frac{2401 (279 x+179)}{(3 x+2)^4}-39944 \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{4235364}","\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,"((1 - 2*x)^(7/2)*((2401*(179 + 279*x))/(2 + 3*x)^4 - 39944*Hypergeometric2F1[3, 7/2, 9/2, 3/7 - (6*x)/7]))/4235364","C",1
1952,1,84,128,0.1281581,"\int \frac{(1-2 x)^{5/2} (3+5 x)^2}{(2+3 x)^6} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^6,x]","-\frac{80510 (3 x+2)^5 \sqrt{42 x-21} \tan ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{2 x-1}\right)-21 \left(14646690 x^5+17489565 x^4+4147953 x^3-2438512 x^2-1912794 x-503276\right)}{3333960 \sqrt{1-2 x} (3 x+2)^5}","\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,"-1/3333960*(-21*(-503276 - 1912794*x - 2438512*x^2 + 4147953*x^3 + 17489565*x^4 + 14646690*x^5) + 80510*(2 + 3*x)^5*Sqrt[-21 + 42*x]*ArcTan[Sqrt[3/7]*Sqrt[-1 + 2*x]])/(Sqrt[1 - 2*x]*(2 + 3*x)^5)","A",1
1953,1,47,148,0.0450769,"\int \frac{(1-2 x)^{5/2} (3+5 x)^2}{(2+3 x)^7} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^7,x]","\frac{(1-2 x)^{7/2} \left(\frac{352947 (83 x+53)}{(3 x+2)^6}-227232 \, _2F_1\left(\frac{7}{2},5;\frac{9}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{311299254}","\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,"((1 - 2*x)^(7/2)*((352947*(53 + 83*x))/(2 + 3*x)^6 - 227232*Hypergeometric2F1[7/2, 5, 9/2, 3/7 - (6*x)/7]))/311299254","C",1
1954,1,47,168,0.0386616,"\int \frac{(1-2 x)^{5/2} (3+5 x)^2}{(2+3 x)^8} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^8,x]","\frac{(1-2 x)^{7/2} \left(\frac{823543 (69 x+44)}{(3 x+2)^7}-149440 \, _2F_1\left(\frac{7}{2},6;\frac{9}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{726364926}","\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,"((1 - 2*x)^(7/2)*((823543*(44 + 69*x))/(2 + 3*x)^7 - 149440*Hypergeometric2F1[7/2, 6, 9/2, 3/7 - (6*x)/7]))/726364926","C",1
1955,1,48,105,0.0330168,"\int (1-2 x)^{5/2} (2+3 x)^4 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^4*(3 + 5*x)^3,x]","-\frac{(1-2 x)^{7/2} \left(212574375 x^7+1127763000 x^6+2642319225 x^5+3583371246 x^4+3089723448 x^3+1740153744 x^2+619493392 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,"-1/440895*((1 - 2*x)^(7/2)*(115708576 + 619493392*x + 1740153744*x^2 + 3089723448*x^3 + 3583371246*x^4 + 2642319225*x^5 + 1127763000*x^6 + 212574375*x^7))","A",1
1956,1,43,92,0.0350047,"\int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^3,x]","-\frac{1}{741} (1-2 x)^{7/2} \left(131625 x^6+605475 x^5+1204398 x^4+1346367 x^3+914049 x^2+372070 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,"-1/741*((1 - 2*x)^(7/2)*(76018 + 372070*x + 914049*x^2 + 1346367*x^3 + 1204398*x^4 + 605475*x^5 + 131625*x^6))","A",1
1957,1,38,79,0.0317305,"\int (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^3,x]","-\frac{1}{221} (1-2 x)^{7/2} \left(14625 x^5+56810 x^4+92535 x^3+80748 x^2+39160 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,"-1/221*((1 - 2*x)^(7/2)*(9004 + 39160*x + 80748*x^2 + 92535*x^3 + 56810*x^4 + 14625*x^5))","A",1
1958,1,33,66,0.0220293,"\int (1-2 x)^{5/2} (2+3 x) (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^3,x]","-\frac{1}{39} (1-2 x)^{7/2} \left(975 x^4+3075 x^3+3870 x^2+2381 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,"-1/39*((1 - 2*x)^(7/2)*(641 + 2381*x + 3870*x^2 + 3075*x^3 + 975*x^4))","A",1
1959,1,28,53,0.0188177,"\int (1-2 x)^{5/2} (3+5 x)^3 \, dx","Integrate[(1 - 2*x)^(5/2)*(3 + 5*x)^3,x]","-\frac{1}{273} (1-2 x)^{7/2} \left(2625 x^3+6300 x^2+5495 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,"-1/273*((1 - 2*x)^(7/2)*(1838 + 5495*x + 6300*x^2 + 2625*x^3))","A",1
1960,1,68,108,0.0934914,"\int \frac{(1-2 x)^{5/2} (3+5 x)^3}{2+3 x} \, dx","Integrate[((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
1961,1,73,121,0.0557908,"\int \frac{(1-2 x)^{5/2} (3+5 x)^3}{(2+3 x)^2} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^2,x]","\frac{\frac{3 \sqrt{1-2 x} \left(189000 x^5-17100 x^4-159714 x^3+25275 x^2+65558 x+13759\right)}{3 x+2}-10780 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{15309}","-\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,"((3*Sqrt[1 - 2*x]*(13759 + 65558*x + 25275*x^2 - 159714*x^3 - 17100*x^4 + 189000*x^5))/(2 + 3*x) - 10780*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/15309","A",1
1962,1,75,135,0.0574263,"\int \frac{(1-2 x)^{5/2} (3+5 x)^3}{(2+3 x)^3} \, dx","Integrate[((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
1963,1,59,147,0.0318287,"\int \frac{(1-2 x)^{5/2} (3+5 x)^3}{(2+3 x)^4} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^4,x]","\frac{(1-2 x)^{7/2} \left(49632 (3 x+2)^3 \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};\frac{3}{7}-\frac{6 x}{7}\right)-343 \left(11025 x^2+14858 x+5003\right)\right)}{453789 (3 x+2)^3}","-\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,"((1 - 2*x)^(7/2)*(-343*(5003 + 14858*x + 11025*x^2) + 49632*(2 + 3*x)^3*Hypergeometric2F1[2, 7/2, 9/2, 3/7 - (6*x)/7]))/(453789*(2 + 3*x)^3)","C",1
1964,1,59,154,0.0331278,"\int \frac{(1-2 x)^{5/2} (3+5 x)^3}{(2+3 x)^5} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^5,x]","\frac{(1-2 x)^{7/2} \left(1033384 (3 x+2)^4 \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};\frac{3}{7}-\frac{6 x}{7}\right)-2401 \left(73500 x^2+98419 x+32939\right)\right)}{12706092 (3 x+2)^4}","-\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,"((1 - 2*x)^(7/2)*(-2401*(32939 + 98419*x + 73500*x^2) + 1033384*(2 + 3*x)^4*Hypergeometric2F1[3, 7/2, 9/2, 3/7 - (6*x)/7]))/(12706092*(2 + 3*x)^4)","C",1
1965,1,89,161,0.1283374,"\int \frac{(1-2 x)^{5/2} (3+5 x)^3}{(2+3 x)^6} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^6,x]","-\frac{21 \left(52920000 x^6+226697490 x^5+288394965 x^4+106869513 x^3-43687652 x^2-40879074 x-7933096\right)-1469710 (3 x+2)^5 \sqrt{42 x-21} \tan ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{2 x-1}\right)}{1666980 \sqrt{1-2 x} (3 x+2)^5}","\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,"-1/1666980*(21*(-7933096 - 40879074*x - 43687652*x^2 + 106869513*x^3 + 288394965*x^4 + 226697490*x^5 + 52920000*x^6) - 1469710*(2 + 3*x)^5*Sqrt[-21 + 42*x]*ArcTan[Sqrt[3/7]*Sqrt[-1 + 2*x]])/(Sqrt[1 - 2*x]*(2 + 3*x)^5)","A",1
1966,1,52,162,0.0374732,"\int \frac{(1-2 x)^{5/2} (3+5 x)^3}{(2+3 x)^7} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^7,x]","\frac{(1-2 x)^{7/2} \left(\frac{1764735 \left(110250 x^2+146875 x+48919\right)}{(3 x+2)^6}-161172000 \, _2F_1\left(\frac{7}{2},5;\frac{9}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{4669488810}","\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,"((1 - 2*x)^(7/2)*((1764735*(48919 + 146875*x + 110250*x^2))/(2 + 3*x)^6 - 161172000*Hypergeometric2F1[7/2, 5, 9/2, 3/7 - (6*x)/7]))/4669488810","C",1
1967,1,52,181,0.0425696,"\int \frac{(1-2 x)^{5/2} (3+5 x)^3}{(2+3 x)^8} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^8,x]","\frac{(1-2 x)^{7/2} \left(\frac{823543 \left(18375 x^2+24448 x+8133\right)}{(3 x+2)^7}-4343680 \, _2F_1\left(\frac{7}{2},6;\frac{9}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{1089547389}","\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,"((1 - 2*x)^(7/2)*((823543*(8133 + 24448*x + 18375*x^2))/(2 + 3*x)^7 - 4343680*Hypergeometric2F1[7/2, 6, 9/2, 3/7 - (6*x)/7]))/1089547389","C",1
1968,1,71,121,0.120632,"\int \frac{(1-2 x)^{5/2} (2+3 x)^4}{3+5 x} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^4)/(3 + 5*x),x]","\frac{5 \sqrt{1-2 x} \left(2338875000 x^6+2842087500 x^5-1540428750 x^4-2556079875 x^3+399578370 x^2+960784285 x-289133384\right)-726726 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1173046875}","\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,"(5*Sqrt[1 - 2*x]*(-289133384 + 960784285*x + 399578370*x^2 - 2556079875*x^3 - 1540428750*x^4 + 2842087500*x^5 + 2338875000*x^6) - 726726*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1173046875","A",1
1969,1,66,108,0.0935218,"\int \frac{(1-2 x)^{5/2} (2+3 x)^3}{3+5 x} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(3 + 5*x),x]","\frac{5 \sqrt{1-2 x} \left(14175000 x^5+6142500 x^4-15572250 x^3-3564885 x^2+7726195 x-1796318\right)-55902 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{18046875}","-\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,"(5*Sqrt[1 - 2*x]*(-1796318 + 7726195*x - 3564885*x^2 - 15572250*x^3 + 6142500*x^4 + 14175000*x^5) - 55902*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/18046875","A",1
1970,1,61,95,0.0799035,"\int \frac{(1-2 x)^{5/2} (2+3 x)^2}{3+5 x} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^2)/(3 + 5*x),x]","\frac{5 \sqrt{1-2 x} \left(105000 x^4-43500 x^3-91410 x^2+69995 x-8188\right)-5082 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{328125}","\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,"(5*Sqrt[1 - 2*x]*(-8188 + 69995*x - 91410*x^2 - 43500*x^3 + 105000*x^4) - 5082*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/328125","A",1
1971,1,56,82,0.0366339,"\int \frac{(1-2 x)^{5/2} (2+3 x)}{3+5 x} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x))/(3 + 5*x),x]","\frac{5 \sqrt{1-2 x} \left(9000 x^3-12660 x^2+4370 x+4937\right)-5082 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{65625}","-\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,"(5*Sqrt[1 - 2*x]*(4937 + 4370*x - 12660*x^2 + 9000*x^3) - 5082*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/65625","A",1
1972,1,51,69,0.0426981,"\int \frac{(1-2 x)^{5/2}}{3+5 x} \, dx","Integrate[(1 - 2*x)^(5/2)/(3 + 5*x),x]","\frac{2 \left(5 \sqrt{1-2 x} \left(60 x^2-170 x+433\right)-363 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)\right)}{1875}","\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*(5*Sqrt[1 - 2*x]*(433 - 170*x + 60*x^2) - 363*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]))/1875","A",1
1973,1,71,85,0.0628161,"\int \frac{(1-2 x)^{5/2}}{(2+3 x) (3+5 x)} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)*(3 + 5*x)),x]","\frac{2 \left(30 \sqrt{1-2 x} (10 x-73)+6125 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-3267 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)\right)}{3375}","-\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,"(2*(30*Sqrt[1 - 2*x]*(-73 + 10*x) + 6125*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - 3267*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]))/3375","A",1
1974,1,78,92,0.0898873,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^2 (3+5 x)} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^2*(3 + 5*x)),x]","\frac{1}{225} \left(\frac{15 \sqrt{1-2 x} (8 x+87)}{3 x+2}+3500 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-2178 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)\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,"((15*Sqrt[1 - 2*x]*(87 + 8*x))/(2 + 3*x) + 3500*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - 2178*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/225","A",1
1975,1,80,95,0.0938649,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^3 (3+5 x)} \, dx","Integrate[(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
1976,1,83,113,0.1314934,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^4 (3+5 x)} \, dx","Integrate[(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
1977,1,88,133,0.135973,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^5 (3+5 x)} \, dx","Integrate[(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
1978,1,93,153,0.1692868,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^6 (3+5 x)} \, dx","Integrate[(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
1979,1,98,173,0.1888154,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^7 (3+5 x)} \, dx","Integrate[(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
1980,1,78,141,0.1186383,"\int \frac{(1-2 x)^{5/2} (2+3 x)^4}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^4)/(3 + 5*x)^2,x]","\frac{\frac{5 \sqrt{1-2 x} \left(212625000 x^6+237037500 x^5-173598750 x^4-214071975 x^3+85482115 x^2+50081215 x-15982128\right)}{5 x+3}-645414 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{90234375}","-\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,"((5*Sqrt[1 - 2*x]*(-15982128 + 50081215*x + 85482115*x^2 - 214071975*x^3 - 173598750*x^4 + 237037500*x^5 + 212625000*x^6))/(3 + 5*x) - 645414*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/90234375","A",1
1981,1,73,121,0.0626856,"\int \frac{(1-2 x)^{5/2} (2+3 x)^3}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(3 + 5*x)^2,x]","\frac{\frac{5 \sqrt{1-2 x} \left(1575000 x^5+427500 x^4-1858950 x^3+152105 x^2+680930 x+16794\right)}{5 x+3}-43428 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1640625}","-\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,"((5*Sqrt[1 - 2*x]*(16794 + 680930*x + 152105*x^2 - 1858950*x^3 + 427500*x^4 + 1575000*x^5))/(3 + 5*x) - 43428*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1640625","A",1
1982,1,68,102,0.0533112,"\int \frac{(1-2 x)^{5/2} (2+3 x)^2}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^2)/(3 + 5*x)^2,x]","\frac{\frac{5 \sqrt{1-2 x} \left(135000 x^4-96300 x^3-75130 x^2+173795 x+90486\right)}{5 x+3}-28182 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{328125}","-\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,"((5*Sqrt[1 - 2*x]*(90486 + 173795*x - 75130*x^2 - 96300*x^3 + 135000*x^4))/(3 + 5*x) - 28182*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/328125","A",1
1983,1,63,89,0.0538986,"\int \frac{(1-2 x)^{5/2} (2+3 x)}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x))/(3 + 5*x)^2,x]","\frac{\frac{5 \sqrt{1-2 x} \left(1800 x^3-3820 x^2+8630 x+6579\right)}{5 x+3}-1848 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{9375}","-\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,"((5*Sqrt[1 - 2*x]*(6579 + 8630*x - 3820*x^2 + 1800*x^3))/(3 + 5*x) - 1848*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/9375","A",1
1984,1,30,76,0.0067857,"\int \frac{(1-2 x)^{5/2}}{(3+5 x)^2} \, dx","Integrate[(1 - 2*x)^(5/2)/(3 + 5*x)^2,x]","-\frac{4}{847} (1-2 x)^{7/2} \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};-\frac{5}{11} (2 x-1)\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,"(-4*(1 - 2*x)^(7/2)*Hypergeometric2F1[2, 7/2, 9/2, (-5*(-1 + 2*x))/11])/847","C",1
1985,1,83,92,0.1423329,"\int \frac{(1-2 x)^{5/2}}{(2+3 x) (3+5 x)^2} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)*(3 + 5*x)^2),x]","\frac{1}{375} \left(\frac{5 \sqrt{1-2 x} (40 x-339)}{5 x+3}+2508 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)\right)-\frac{98}{3} \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \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,"(-98*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/3 + ((5*Sqrt[1 - 2*x]*(-339 + 40*x))/(3 + 5*x) + 2508*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/375","A",1
1986,1,105,106,0.084408,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^2 (3+5 x)^2} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{-22750 \sqrt{21} \left(15 x^2+19 x+6\right) \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+14058 \sqrt{55} \left(15 x^2+19 x+6\right) \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)-15 \sqrt{1-2 x} (2314 x+1461)}{225 (3 x+2) (5 x+3)}","\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,"(-15*Sqrt[1 - 2*x]*(1461 + 2314*x) - 22750*Sqrt[21]*(6 + 19*x + 15*x^2)*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] + 14058*Sqrt[55]*(6 + 19*x + 15*x^2)*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(225*(2 + 3*x)*(3 + 5*x))","A",1
1987,1,94,131,0.1319818,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^3 (3+5 x)^2} \, dx","Integrate[(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,"-1/6*(Sqrt[1 - 2*x]*(8553 + 26380*x + 20289*x^2))/((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
1988,1,95,154,0.1702077,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^4 (3+5 x)^2} \, dx","Integrate[(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,"-1/6*(Sqrt[1 - 2*x]*(112668 + 516513*x + 788512*x^2 + 400905*x^3))/((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
1989,1,100,181,0.192329,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^5 (3+5 x)^2} \, dx","Integrate[(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,"-1/168*(Sqrt[1 - 2*x]*(39145938 + 238179048*x + 543154477*x^2 + 550239720*x^3 + 208938825*x^4))/((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
1990,1,105,208,0.2095953,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^6 (3+5 x)^2} \, dx","Integrate[(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,"-1/5880*(Sqrt[1 - 2*x]*(16360698684 + 124085884254*x + 376323861626*x^2 + 570477768855*x^3 + 432275892930*x^4 + 130986207675*x^5))/((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
1991,1,78,155,0.1356609,"\int \frac{(1-2 x)^{5/2} (2+3 x)^4}{(3+5 x)^3} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^4)/(3 + 5*x)^3,x]","\frac{\frac{5 \sqrt{1-2 x} \left(15750000 x^6+15075000 x^5-16051500 x^4-11139550 x^3+9372960 x^2+6891315 x+871208\right)}{(5 x+3)^2}-164682 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{5468750}","-\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,"((5*Sqrt[1 - 2*x]*(871208 + 6891315*x + 9372960*x^2 - 11139550*x^3 - 16051500*x^4 + 15075000*x^5 + 15750000*x^6))/(3 + 5*x)^2 - 164682*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/5468750","A",1
1992,1,73,135,0.0684753,"\int \frac{(1-2 x)^{5/2} (2+3 x)^3}{(3+5 x)^3} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(3 + 5*x)^3,x]","\frac{\frac{5 \sqrt{1-2 x} \left(1350000 x^5-27000 x^4-1506900 x^3+1651030 x^2+2637795 x+770444\right)}{(5 x+3)^2}-77826 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1093750}","-\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,"((5*Sqrt[1 - 2*x]*(770444 + 2637795*x + 1651030*x^2 - 1506900*x^3 - 27000*x^4 + 1350000*x^5))/(3 + 5*x)^2 - 77826*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1093750","A",1
1993,1,68,109,0.0632234,"\int \frac{(1-2 x)^{5/2} (2+3 x)^2}{(3+5 x)^3} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^2)/(3 + 5*x)^3,x]","\frac{\frac{5 \sqrt{1-2 x} \left(18000 x^4-25400 x^3+51980 x^2+98595 x+32504\right)}{(5 x+3)^2}-3066 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{31250}","-\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,"((5*Sqrt[1 - 2*x]*(32504 + 98595*x + 51980*x^2 - 25400*x^3 + 18000*x^4))/(3 + 5*x)^2 - 3066*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/31250","A",1
1994,1,48,96,0.0257323,"\int \frac{(1-2 x)^{5/2} (2+3 x)}{(3+5 x)^3} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x))/(3 + 5*x)^3,x]","-\frac{(1-2 x)^{7/2} \left(36 (5 x+3)^2 \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};-\frac{5}{11} (2 x-1)\right)+121\right)}{13310 (5 x+3)^2}","-\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,"-1/13310*((1 - 2*x)^(7/2)*(121 + 36*(3 + 5*x)^2*Hypergeometric2F1[2, 7/2, 9/2, (-5*(-1 + 2*x))/11]))/(3 + 5*x)^2","C",1
1995,1,30,83,0.0076832,"\int \frac{(1-2 x)^{5/2}}{(3+5 x)^3} \, dx","Integrate[(1 - 2*x)^(5/2)/(3 + 5*x)^3,x]","-\frac{8 (1-2 x)^{7/2} \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};-\frac{5}{11} (2 x-1)\right)}{9317}","-\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,"(-8*(1 - 2*x)^(7/2)*Hypergeometric2F1[3, 7/2, 9/2, (-5*(-1 + 2*x))/11])/9317","C",1
1996,1,81,97,0.1478559,"\int \frac{(1-2 x)^{5/2}}{(2+3 x) (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)*(3 + 5*x)^3),x]","98 \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{1}{250} \left(\frac{55 \sqrt{1-2 x} (375 x+214)}{(5 x+3)^2}-5046 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)\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,"98*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] + ((55*Sqrt[1 - 2*x]*(214 + 375*x))/(3 + 5*x)^2 - 5046*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/250","A",1
1997,1,93,124,0.1615853,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^2 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{1}{50} \left(\frac{5 \sqrt{1-2 x} \left(35515 x^2+43806 x+13474\right)}{(3 x+2) (5 x+3)^2}-14418 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)\right)+1400 \sqrt{\frac{7}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \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,"1400*Sqrt[7/3]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] + ((5*Sqrt[1 - 2*x]*(13474 + 43806*x + 35515*x^2))/((2 + 3*x)*(3 + 5*x)^2) - 14418*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/50","A",1
1998,1,119,145,0.1139168,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^3 (3+5 x)^3} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{45550 \sqrt{21} \left(15 x^2+19 x+6\right)^2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)-28146 \sqrt{55} \left(15 x^2+19 x+6\right)^2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)+5 \sqrt{1-2 x} \left(207990 x^3+395215 x^2+249939 x+52607\right)}{10 (3 x+2)^2 (5 x+3)^2}","\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,"(5*Sqrt[1 - 2*x]*(52607 + 249939*x + 395215*x^2 + 207990*x^3) + 45550*Sqrt[21]*(6 + 19*x + 15*x^2)^2*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] - 28146*Sqrt[55]*(6 + 19*x + 15*x^2)^2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(10*(2 + 3*x)^2*(3 + 5*x)^2)","A",1
1999,1,98,172,0.1655755,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^4 (3+5 x)^3} \, dx","Integrate[(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
2000,1,105,201,0.2059623,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^5 (3+5 x)^3} \, dx","Integrate[(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
2001,1,43,92,0.0215935,"\int \frac{(2+3 x)^5 (3+5 x)}{\sqrt{1-2 x}} \, dx","Integrate[((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,"-1/429*(Sqrt[1 - 2*x]*(638648 + 597464*x + 707436*x^2 + 698580*x^3 + 488925*x^4 + 208251*x^5 + 40095*x^6))","A",1
2002,1,38,79,0.0212586,"\int \frac{(2+3 x)^4 (3+5 x)}{\sqrt{1-2 x}} \, dx","Integrate[((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,"-1/165*(Sqrt[1 - 2*x]*(75584 + 67664*x + 71136*x^2 + 56520*x^3 + 27630*x^4 + 6075*x^5))","A",1
2003,1,33,66,0.0190728,"\int \frac{(2+3 x)^3 (3+5 x)}{\sqrt{1-2 x}} \, dx","Integrate[((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,"-1/105*(Sqrt[1 - 2*x]*(14954 + 12434*x + 10881*x^2 + 6165*x^3 + 1575*x^4))","A",1
2004,1,28,53,0.0214544,"\int \frac{(2+3 x)^2 (3+5 x)}{\sqrt{1-2 x}} \, dx","Integrate[((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,"-1/105*(Sqrt[1 - 2*x]*(4708 + 3448*x + 2232*x^2 + 675*x^3))","A",1
2005,1,23,40,0.010822,"\int \frac{(2+3 x) (3+5 x)}{\sqrt{1-2 x}} \, dx","Integrate[((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,"-1/3*(Sqrt[1 - 2*x]*(43 + 25*x + 9*x^2))","A",1
2006,1,18,27,0.00615,"\int \frac{3+5 x}{\sqrt{1-2 x}} \, dx","Integrate[(3 + 5*x)/Sqrt[1 - 2*x],x]","-\frac{1}{3} \sqrt{1-2 x} (5 x+14)","\frac{5}{6} (1-2 x)^{3/2}-\frac{11}{2} \sqrt{1-2 x}",1,"-1/3*(Sqrt[1 - 2*x]*(14 + 5*x))","A",1
2007,1,41,41,0.0206644,"\int \frac{3+5 x}{\sqrt{1-2 x} (2+3 x)} \, dx","Integrate[(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
2008,1,45,48,0.0331171,"\int \frac{3+5 x}{\sqrt{1-2 x} (2+3 x)^2} \, dx","Integrate[(3 + 5*x)/(Sqrt[1 - 2*x]*(2 + 3*x)^2),x]","\frac{\sqrt{1-2 x}}{63 x+42}-\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]/(42 + 63*x) - (68*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(21*Sqrt[21])","A",1
2009,1,62,68,0.063288,"\int \frac{3+5 x}{\sqrt{1-2 x} (2+3 x)^3} \, dx","Integrate[(3 + 5*x)/(Sqrt[1 - 2*x]*(2 + 3*x)^3),x]","\frac{\sqrt{1-2 x} \left(-\frac{21 (201 x+127)}{(3 x+2)^2}-\frac{134 \sqrt{21} \tan ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{2 x-1}\right)}{\sqrt{2 x-1}}\right)}{6174}","-\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,"(Sqrt[1 - 2*x]*((-21*(127 + 201*x))/(2 + 3*x)^2 - (134*Sqrt[21]*ArcTan[Sqrt[3/7]*Sqrt[-1 + 2*x]])/Sqrt[-1 + 2*x]))/6174","A",1
2010,1,42,88,0.0168009,"\int \frac{3+5 x}{\sqrt{1-2 x} (2+3 x)^4} \, dx","Integrate[(3 + 5*x)/(Sqrt[1 - 2*x]*(2 + 3*x)^4),x]","\frac{\sqrt{1-2 x} \left(\frac{343}{(3 x+2)^3}-800 \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{21609}","-\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]*(343/(2 + 3*x)^3 - 800*Hypergeometric2F1[1/2, 3, 3/2, 3/7 - (6*x)/7]))/21609","C",1
2011,1,42,108,0.0175187,"\int \frac{3+5 x}{\sqrt{1-2 x} (2+3 x)^5} \, dx","Integrate[(3 + 5*x)/(Sqrt[1 - 2*x]*(2 + 3*x)^5),x]","\frac{\sqrt{1-2 x} \left(\frac{343}{(3 x+2)^4}-304 \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{28812}","-\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]*(343/(2 + 3*x)^4 - 304*Hypergeometric2F1[1/2, 4, 3/2, 3/7 - (6*x)/7]))/28812","C",1
2012,1,48,105,0.0240405,"\int \frac{(2+3 x)^5 (3+5 x)^2}{\sqrt{1-2 x}} \, dx","Integrate[((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,"-1/429*(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))","A",1
2013,1,43,92,0.0227808,"\int \frac{(2+3 x)^4 (3+5 x)^2}{\sqrt{1-2 x}} \, dx","Integrate[((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,"-1/2145*(Sqrt[1 - 2*x]*(4994536 + 4685656*x + 5587044*x^2 + 5576580*x^3 + 3954645*x^4 + 1709100*x^5 + 334125*x^6))","A",1
2014,1,38,79,0.0232778,"\int \frac{(2+3 x)^3 (3+5 x)^2}{\sqrt{1-2 x}} \, dx","Integrate[((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,"-1/1155*(Sqrt[1 - 2*x]*(826982 + 743822*x + 790023*x^2 + 636795*x^3 + 316575*x^4 + 70875*x^5))","A",1
2015,1,33,66,0.0152016,"\int \frac{(2+3 x)^2 (3+5 x)^2}{\sqrt{1-2 x}} \, dx","Integrate[((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,"-1/105*(Sqrt[1 - 2*x]*(23354 + 19574*x + 17391*x^2 + 10050*x^3 + 2625*x^4))","A",1
2016,1,28,53,0.0147588,"\int \frac{(2+3 x) (3+5 x)^2}{\sqrt{1-2 x}} \, dx","Integrate[((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,"-1/21*(Sqrt[1 - 2*x]*(1469 + 1091*x + 723*x^2 + 225*x^3))","A",1
2017,1,23,40,0.0093961,"\int \frac{(3+5 x)^2}{\sqrt{1-2 x}} \, dx","Integrate[(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,"-1/3*(Sqrt[1 - 2*x]*(67 + 40*x + 15*x^2))","A",1
2018,1,46,54,0.0509577,"\int \frac{(3+5 x)^2}{\sqrt{1-2 x} (2+3 x)} \, dx","Integrate[(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
2019,1,51,61,0.0476042,"\int \frac{(3+5 x)^2}{\sqrt{1-2 x} (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^2/(Sqrt[1 - 2*x]*(2 + 3*x)^2),x]","\frac{46 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{21 \sqrt{21}}-\frac{\sqrt{1-2 x} (175 x+117)}{63 x+42}","-\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,"-((Sqrt[1 - 2*x]*(117 + 175*x))/(42 + 63*x)) + (46*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(21*Sqrt[21])","A",1
2020,1,53,68,0.0349485,"\int \frac{(3+5 x)^2}{\sqrt{1-2 x} (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^2/(Sqrt[1 - 2*x]*(2 + 3*x)^3),x]","\frac{\frac{7 \sqrt{1-2 x} (137 x+89)}{(3 x+2)^2}-514 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{2058}","\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,"((7*Sqrt[1 - 2*x]*(89 + 137*x))/(2 + 3*x)^2 - 514*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/2058","A",1
2021,1,67,88,0.0783571,"\int \frac{(3+5 x)^2}{\sqrt{1-2 x} (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^2/(Sqrt[1 - 2*x]*(2 + 3*x)^4),x]","\frac{\sqrt{1-2 x} \left(-\frac{21 \left(20205 x^2+25505 x+8056\right)}{(3 x+2)^3}-\frac{4490 \sqrt{21} \tan ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{2 x-1}\right)}{\sqrt{2 x-1}}\right)}{129654}","-\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]*((-21*(8056 + 25505*x + 20205*x^2))/(2 + 3*x)^3 - (4490*Sqrt[21]*ArcTan[Sqrt[3/7]*Sqrt[-1 + 2*x]])/Sqrt[-1 + 2*x]))/129654","A",1
2022,1,47,108,0.0268357,"\int \frac{(3+5 x)^2}{\sqrt{1-2 x} (2+3 x)^5} \, dx","Integrate[(3 + 5*x)^2/(Sqrt[1 - 2*x]*(2 + 3*x)^5),x]","\frac{\sqrt{1-2 x} \left(\frac{343 (39 x+25)}{(3 x+2)^4}-5080 \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{86436}","-\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]*((343*(25 + 39*x))/(2 + 3*x)^4 - 5080*Hypergeometric2F1[1/2, 3, 3/2, 3/7 - (6*x)/7]))/86436","C",1
2023,1,47,130,0.0285846,"\int \frac{(3+5 x)^2}{\sqrt{1-2 x} (2+3 x)^6} \, dx","Integrate[(3 + 5*x)^2/(Sqrt[1 - 2*x]*(2 + 3*x)^6),x]","\frac{\sqrt{1-2 x} \left(\frac{1029 (341 x+218)}{(3 x+2)^5}-50544 \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{3025260}","-\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]*((1029*(218 + 341*x))/(2 + 3*x)^5 - 50544*Hypergeometric2F1[1/2, 4, 3/2, 3/7 - (6*x)/7]))/3025260","C",1
2024,1,48,105,0.0218168,"\int \frac{(2+3 x)^4 (3+5 x)^3}{\sqrt{1-2 x}} \, dx","Integrate[((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,"-1/2145*(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))","A",1
2025,1,43,92,0.0223545,"\int \frac{(2+3 x)^3 (3+5 x)^3}{\sqrt{1-2 x}} \, dx","Integrate[((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,"-1/5005*(Sqrt[1 - 2*x]*(18228666 + 17147586*x + 20586249*x^2 + 20766885*x^3 + 14921900*x^4 + 6544125*x^5 + 1299375*x^6))","A",1
2026,1,38,79,0.0216503,"\int \frac{(2+3 x)^2 (3+5 x)^3}{\sqrt{1-2 x}} \, dx","Integrate[((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,"-1/1155*(Sqrt[1 - 2*x]*(1292672 + 1167932*x + 1252938*x^2 + 1024475*x^3 + 518000*x^4 + 118125*x^5))","A",1
2027,1,33,66,0.015221,"\int \frac{(2+3 x) (3+5 x)^3}{\sqrt{1-2 x}} \, dx","Integrate[((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,"-1/21*(Sqrt[1 - 2*x]*(7295 + 6161*x + 5556*x^2 + 3275*x^3 + 875*x^4))","A",1
2028,1,28,53,0.012927,"\int \frac{(3+5 x)^3}{\sqrt{1-2 x}} \, dx","Integrate[(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,"-1/7*(Sqrt[1 - 2*x]*(764 + 575*x + 390*x^2 + 125*x^3))","A",1
2029,1,51,67,0.0490027,"\int \frac{(3+5 x)^3}{\sqrt{1-2 x} (2+3 x)} \, dx","Integrate[(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
2030,1,58,73,0.0392818,"\int \frac{(3+5 x)^3}{\sqrt{1-2 x} (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^3/(Sqrt[1 - 2*x]*(2 + 3*x)^2),x]","\frac{-\frac{21 \sqrt{1-2 x} \left(2625 x^2+8050 x+4199\right)}{3 x+2}-208 \sqrt{21} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{3969}","\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,"((-21*Sqrt[1 - 2*x]*(4199 + 8050*x + 2625*x^2))/(2 + 3*x) - 208*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/3969","A",1
2031,1,58,80,0.0503844,"\int \frac{(3+5 x)^3}{\sqrt{1-2 x} (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^3/(Sqrt[1 - 2*x]*(2 + 3*x)^3),x]","\frac{2381 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{441 \sqrt{21}}-\frac{\sqrt{1-2 x} \left(36750 x^2+49207 x+16469\right)}{882 (3 x+2)^2}","\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,"-1/882*(Sqrt[1 - 2*x]*(16469 + 49207*x + 36750*x^2))/(2 + 3*x)^2 + (2381*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(441*Sqrt[21])","A",1
2032,1,67,80,0.1015419,"\int \frac{(3+5 x)^3}{\sqrt{1-2 x} (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^3/(Sqrt[1 - 2*x]*(2 + 3*x)^4),x]","\frac{\sqrt{1-2 x} \left(\frac{21 \left(31680 x^2+41155 x+13373\right)}{(3 x+2)^3}-\frac{78710 \sqrt{21} \tan ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{2 x-1}\right)}{\sqrt{2 x-1}}\right)}{194481}","\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]*((21*(13373 + 41155*x + 31680*x^2))/(2 + 3*x)^3 - (78710*Sqrt[21]*ArcTan[Sqrt[3/7]*Sqrt[-1 + 2*x]])/Sqrt[-1 + 2*x]))/194481","A",1
2033,1,52,100,0.0451522,"\int \frac{(3+5 x)^3}{\sqrt{1-2 x} (2+3 x)^5} \, dx","Integrate[(3 + 5*x)^3/(Sqrt[1 - 2*x]*(2 + 3*x)^5),x]","\frac{\sqrt{1-2 x} \left(\frac{343 \left(31500 x^2+41823 x+13885\right)}{(3 x+2)^4}-343960 \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{777924}","\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]*((343*(13885 + 41823*x + 31500*x^2))/(2 + 3*x)^4 - 343960*Hypergeometric2F1[1/2, 3, 3/2, 3/7 - (6*x)/7]))/777924","C",1
2034,1,52,120,0.0365656,"\int \frac{(3+5 x)^3}{\sqrt{1-2 x} (2+3 x)^6} \, dx","Integrate[(3 + 5*x)^3/(Sqrt[1 - 2*x]*(2 + 3*x)^6),x]","\frac{\sqrt{1-2 x} \left(\frac{343 \left(18375 x^2+24371 x+8083\right)}{(3 x+2)^5}-84688 \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};\frac{3}{7}-\frac{6 x}{7}\right)\right)}{756315}","\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]*((343*(8083 + 24371*x + 18375*x^2))/(2 + 3*x)^5 - 84688*Hypergeometric2F1[1/2, 4, 3/2, 3/7 - (6*x)/7]))/756315","C",1
2035,1,132,132,0.1974613,"\int \frac{(a+b x)^2}{(c+d x)^2 \sqrt{e+f x}} \, dx","Integrate[(a + b*x)^2/((c + d*x)^2*Sqrt[e + f*x]),x]","-\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}","\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,"(2*b^2*Sqrt[e + f*x])/(d^2*f) - ((b*c - a*d)^2*Sqrt[e + f*x])/(d^2*(d*e - c*f)*(c + d*x)) - ((b*c - a*d)*(-4*b*d*e + 3*b*c*f + a*d*f)*ArcTanh[(Sqrt[d]*Sqrt[e + f*x])/Sqrt[d*e - c*f]])/(d^(5/2)*(d*e - c*f)^(3/2))","A",1
2036,1,61,93,0.0687065,"\int \frac{(2+3 x)^5}{\sqrt{1-2 x} (3+5 x)} \, dx","Integrate[(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
2037,1,56,80,0.0692616,"\int \frac{(2+3 x)^4}{\sqrt{1-2 x} (3+5 x)} \, dx","Integrate[(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
2038,1,51,67,0.0469051,"\int \frac{(2+3 x)^3}{\sqrt{1-2 x} (3+5 x)} \, dx","Integrate[(2 + 3*x)^3/(Sqrt[1 - 2*x]*(3 + 5*x)),x]","\frac{-495 \sqrt{1-2 x} \left(15 x^2+45 x+82\right)-2 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{6875}","-\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,"(-495*Sqrt[1 - 2*x]*(82 + 45*x + 15*x^2) - 2*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/6875","A",1
2039,1,46,54,0.0451578,"\int \frac{(2+3 x)^2}{\sqrt{1-2 x} (3+5 x)} \, dx","Integrate[(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
2040,1,41,41,0.0117489,"\int \frac{2+3 x}{\sqrt{1-2 x} (3+5 x)} \, dx","Integrate[(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
2041,1,25,25,0.0059318,"\int \frac{1}{\sqrt{1-2 x} (3+5 x)} \, dx","Integrate[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
2042,1,55,55,0.0530576,"\int \frac{1}{\sqrt{1-2 x} (2+3 x) (3+5 x)} \, dx","Integrate[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
2043,1,77,77,0.074464,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^2 (3+5 x)} \, dx","Integrate[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
2044,1,82,97,0.0714706,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^3 (3+5 x)} \, dx","Integrate[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
2045,1,87,117,0.0918688,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^4 (3+5 x)} \, dx","Integrate[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
2046,1,92,137,0.1308472,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^5 (3+5 x)} \, dx","Integrate[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
2047,1,73,133,0.1125521,"\int \frac{(2+3 x)^6}{\sqrt{1-2 x} (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^6/(Sqrt[1 - 2*x]*(3 + 5*x)^2),x]","\frac{-\frac{55 \sqrt{1-2 x} \left(19490625 x^5+92998125 x^4+200942775 x^3+273540465 x^2+334366065 x+135011752\right)}{5 x+3}-2786 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{66171875}","-\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,"((-55*Sqrt[1 - 2*x]*(135011752 + 334366065*x + 273540465*x^2 + 200942775*x^3 + 92998125*x^4 + 19490625*x^5))/(3 + 5*x) - 2786*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/66171875","A",1
2048,1,68,113,0.0871782,"\int \frac{(2+3 x)^5}{\sqrt{1-2 x} (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^5/(Sqrt[1 - 2*x]*(3 + 5*x)^2),x]","\frac{-\frac{55 \sqrt{1-2 x} \left(1670625 x^4+6994350 x^3+13532310 x^2+20175210 x+8527768\right)}{5 x+3}-2324 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{13234375}","-\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,"((-55*Sqrt[1 - 2*x]*(8527768 + 20175210*x + 13532310*x^2 + 6994350*x^3 + 1670625*x^4))/(3 + 5*x) - 2324*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/13234375","A",1
2049,1,63,93,0.0797973,"\int \frac{(2+3 x)^4}{\sqrt{1-2 x} (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^4/(Sqrt[1 - 2*x]*(3 + 5*x)^2),x]","\frac{-\frac{55 \sqrt{1-2 x} \left(22275 x^3+82665 x^2+171765 x+78112\right)}{5 x+3}-266 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{378125}","-\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,"((-55*Sqrt[1 - 2*x]*(78112 + 171765*x + 82665*x^2 + 22275*x^3))/(3 + 5*x) - 266*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/378125","A",1
2050,1,58,73,0.0456335,"\int \frac{(2+3 x)^3}{\sqrt{1-2 x} (3+5 x)^2} \, dx","Integrate[(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,"-1/55*(Sqrt[1 - 2*x]*(202 + 396*x + 99*x^2))/(3 + 5*x) - (8*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(55*Sqrt[55])","A",1
2051,1,53,61,0.0420749,"\int \frac{(2+3 x)^2}{\sqrt{1-2 x} (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^2/(Sqrt[1 - 2*x]*(3 + 5*x)^2),x]","-\frac{\sqrt{1-2 x} (495 x+298)}{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,"-1/275*(Sqrt[1 - 2*x]*(298 + 495*x))/(3 + 5*x) - (134*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(275*Sqrt[55])","A",1
2052,1,48,48,0.0366515,"\int \frac{2+3 x}{\sqrt{1-2 x} (3+5 x)^2} \, dx","Integrate[(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
2053,1,56,48,0.0566411,"\int \frac{1}{\sqrt{1-2 x} (3+5 x)^2} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(3 + 5*x)^2),x]","-\frac{2}{605} \sqrt{1-2 x} \left(\frac{55}{10 x+6}+\frac{\sqrt{55} \tan ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{\sqrt{2 x-1}}\right)","-\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,"(-2*Sqrt[1 - 2*x]*(55/(6 + 10*x) + (Sqrt[55]*ArcTan[Sqrt[5/11]*Sqrt[-1 + 2*x]])/Sqrt[-1 + 2*x]))/605","A",1
2054,1,77,77,0.0854707,"\int \frac{1}{\sqrt{1-2 x} (2+3 x) (3+5 x)^2} \, dx","Integrate[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
2055,1,100,106,0.09019,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^2 (3+5 x)^2} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{4550 \sqrt{55} \left(15 x^2+19 x+6\right) \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)-11 \sqrt{1-2 x} (1020 x+647)}{847 (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{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,"(-426*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/7 + (-11*Sqrt[1 - 2*x]*(647 + 1020*x) + 4550*Sqrt[55]*(6 + 19*x + 15*x^2)*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(847*(2 + 3*x)*(3 + 5*x))","A",1
2056,1,96,133,0.1184292,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^3 (3+5 x)^2} \, dx","Integrate[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,"-1/1078*(Sqrt[1 - 2*x]*(136021 + 419448*x + 322605*x^2))/((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
2057,1,101,160,0.1328366,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^4 (3+5 x)^2} \, dx","Integrate[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,"-1/7546*(Sqrt[1 - 2*x]*(12724912 + 58335165*x + 89054820*x^2 + 45278325*x^3))/((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
2058,1,73,140,0.1086839,"\int \frac{(2+3 x)^6}{\sqrt{1-2 x} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^6/(Sqrt[1 - 2*x]*(3 + 5*x)^3),x]","\frac{-\frac{55 \sqrt{1-2 x} \left(551306250 x^5+2690374500 x^4+6078090150 x^3+9876010320 x^2+7254126105 x+1804176536\right)}{(5 x+3)^2}-462966 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1455781250}","-\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,"((-55*Sqrt[1 - 2*x]*(1804176536 + 7254126105*x + 9876010320*x^2 + 6078090150*x^3 + 2690374500*x^4 + 551306250*x^5))/(3 + 5*x)^2 - 462966*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1455781250","A",1
2059,1,68,120,0.0982413,"\int \frac{(2+3 x)^5}{\sqrt{1-2 x} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^5/(Sqrt[1 - 2*x]*(3 + 5*x)^3),x]","\frac{-\frac{55 \sqrt{1-2 x} \left(7350750 x^4+32506650 x^3+76970520 x^2+63610155 x+16525496\right)}{(5 x+3)^2}-44226 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{41593750}","-\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,"((-55*Sqrt[1 - 2*x]*(16525496 + 63610155*x + 76970520*x^2 + 32506650*x^3 + 7350750*x^4))/(3 + 5*x)^2 - 44226*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/41593750","A",1
2060,1,63,100,0.0876917,"\int \frac{(2+3 x)^4}{\sqrt{1-2 x} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^4/(Sqrt[1 - 2*x]*(3 + 5*x)^3),x]","\frac{-\frac{55 \sqrt{1-2 x} \left(163350 x^3+784080 x^2+764745 x+211864\right)}{(5 x+3)^2}-5334 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1663750}","-\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,"((-55*Sqrt[1 - 2*x]*(211864 + 764745*x + 784080*x^2 + 163350*x^3))/(3 + 5*x)^2 - 5334*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1663750","A",1
2061,1,58,80,0.0472348,"\int \frac{(2+3 x)^3}{\sqrt{1-2 x} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^3/(Sqrt[1 - 2*x]*(3 + 5*x)^3),x]","\frac{-\frac{55 \sqrt{1-2 x} \left(32670 x^2+39405 x+11884\right)}{(5 x+3)^2}-2694 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{332750}","-\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,"((-55*Sqrt[1 - 2*x]*(11884 + 39405*x + 32670*x^2))/(3 + 5*x)^2 - 2694*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/332750","A",1
2062,1,53,68,0.04918,"\int \frac{(2+3 x)^2}{\sqrt{1-2 x} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^2/(Sqrt[1 - 2*x]*(3 + 5*x)^3),x]","\frac{-\frac{55 \sqrt{1-2 x} (675 x+416)}{(5 x+3)^2}-4626 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{332750}","-\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,"((-55*Sqrt[1 - 2*x]*(416 + 675*x))/(3 + 5*x)^2 - 4626*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/332750","A",1
2063,1,62,68,0.0629161,"\int \frac{2+3 x}{\sqrt{1-2 x} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)/(Sqrt[1 - 2*x]*(3 + 5*x)^3),x]","\frac{\sqrt{1-2 x} \left(-\frac{55 (345 x+218)}{(5 x+3)^2}-\frac{138 \sqrt{55} \tan ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{\sqrt{2 x-1}}\right)}{66550}","-\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,"(Sqrt[1 - 2*x]*((-55*(218 + 345*x))/(3 + 5*x)^2 - (138*Sqrt[55]*ArcTan[Sqrt[5/11]*Sqrt[-1 + 2*x]])/Sqrt[-1 + 2*x]))/66550","A",1
2064,1,30,68,0.0053997,"\int \frac{1}{\sqrt{1-2 x} (3+5 x)^3} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(3 + 5*x)^3),x]","-\frac{8 \sqrt{1-2 x} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};-\frac{5}{11} (2 x-1)\right)}{1331}","-\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,"(-8*Sqrt[1 - 2*x]*Hypergeometric2F1[1/2, 3, 3/2, (-5*(-1 + 2*x))/11])/1331","C",1
2065,1,81,97,0.1084724,"\int \frac{1}{\sqrt{1-2 x} (2+3 x) (3+5 x)^3} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^3),x]","18 \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)+\frac{5 \left(\frac{11 \sqrt{1-2 x} (315 x+178)}{(5 x+3)^2}-846 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)\right)}{2662}","\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,"18*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]] + (5*((11*Sqrt[1 - 2*x]*(178 + 315*x))/(3 + 5*x)^2 - 846*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]))/2662","A",1
2066,1,95,126,0.1124084,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^2 (3+5 x)^3} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{\frac{11 \sqrt{1-2 x} \left(501975 x^2+619170 x+190406\right)}{(3 x+2) (5 x+3)^2}-448350 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{18634}+\frac{1908}{7} \sqrt{\frac{3}{7}} \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \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,"(1908*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/7 + ((11*Sqrt[1 - 2*x]*(190406 + 619170*x + 501975*x^2))/((2 + 3*x)*(3 + 5*x)^2) - 448350*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/18634","A",1
2067,1,112,153,0.1193778,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^3 (3+5 x)^3} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{11 \sqrt{1-2 x} \left(105937200 x^3+201297915 x^2+127303347 x+26794499\right)-31538850 \sqrt{55} \left(15 x^2+19 x+6\right)^2 \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{130438 (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{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,"(134217*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/49 + (11*Sqrt[1 - 2*x]*(26794499 + 127303347*x + 201297915*x^2 + 105937200*x^3) - 31538850*Sqrt[55]*(6 + 19*x + 15*x^2)^2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(130438*(2 + 3*x)^2*(3 + 5*x)^2)","A",1
2068,1,106,180,0.1356585,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^4 (3+5 x)^3} \, dx","Integrate[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
2069,1,53,118,0.0273443,"\int \frac{(2+3 x)^7 (3+5 x)}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^7*(3 + 5*x))/(1 - 2*x)^(3/2),x]","\frac{-104247 x^8-697653 x^7-2168775 x^6-4220622 x^5-5949090 x^4-6921432 x^3-8106616 x^2-16881328 x+16936240}{143 \sqrt{1-2 x}}","-\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,"(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*Sqrt[1 - 2*x])","A",1
2070,1,48,105,0.0245966,"\int \frac{(2+3 x)^6 (3+5 x)}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x)^(3/2),x]","\frac{-40095 x^7-243486 x^6-687420 x^5-1230120 x^4-1663632 x^3-2109792 x^2-4512448 x+4539904}{143 \sqrt{1-2 x}}","\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,"(4539904 - 4512448*x - 2109792*x^2 - 1663632*x^3 - 1230120*x^4 - 687420*x^5 - 243486*x^6 - 40095*x^7)/(143*Sqrt[1 - 2*x])","A",1
2071,1,43,92,0.0246586,"\int \frac{(2+3 x)^5 (3+5 x)}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^5*(3 + 5*x))/(1 - 2*x)^(3/2),x]","\frac{-1215 x^6-6651 x^5-17055 x^4-28692 x^3-41012 x^2-91704 x+92760}{11 \sqrt{1-2 x}}","-\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,"(92760 - 91704*x - 41012*x^2 - 28692*x^3 - 17055*x^4 - 6651*x^5 - 1215*x^6)/(11*Sqrt[1 - 2*x])","A",1
2072,1,38,79,0.0189997,"\int \frac{(2+3 x)^4 (3+5 x)}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x)^(3/2),x]","\frac{-1575 x^5-7740 x^4-18288 x^3-31448 x^2-75776 x+77456}{35 \sqrt{1-2 x}}","\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,"(77456 - 75776*x - 31448*x^2 - 18288*x^3 - 7740*x^4 - 1575*x^5)/(35*Sqrt[1 - 2*x])","A",1
2073,1,33,66,0.0213475,"\int \frac{(2+3 x)^3 (3+5 x)}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x)^(3/2),x]","\frac{-675 x^4-2997 x^3-6987 x^2-19154 x+19994}{35 \sqrt{1-2 x}}","-\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,"(19994 - 19154*x - 6987*x^2 - 2997*x^3 - 675*x^4)/(35*Sqrt[1 - 2*x])","A",1
2074,1,25,53,0.0123235,"\int \frac{(2+3 x)^2 (3+5 x)}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x))/(1 - 2*x)^(3/2),x]","\frac{-9 x^3-38 x^2-132 x+144}{\sqrt{1-2 x}}","\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,"(144 - 132*x - 38*x^2 - 9*x^3)/Sqrt[1 - 2*x]","A",1
2075,1,20,38,0.0170122,"\int \frac{(2+3 x) (3+5 x)}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)*(3 + 5*x))/(1 - 2*x)^(3/2),x]","\frac{-5 x^2-29 x+35}{\sqrt{1-2 x}}","-\frac{5}{4} (1-2 x)^{3/2}+17 \sqrt{1-2 x}+\frac{77}{4 \sqrt{1-2 x}}",1,"(35 - 29*x - 5*x^2)/Sqrt[1 - 2*x]","A",1
2076,1,15,27,0.0088353,"\int \frac{3+5 x}{(1-2 x)^{3/2}} \, dx","Integrate[(3 + 5*x)/(1 - 2*x)^(3/2),x]","\frac{8-5 x}{\sqrt{1-2 x}}","\frac{5}{2} \sqrt{1-2 x}+\frac{11}{2 \sqrt{1-2 x}}",1,"(8 - 5*x)/Sqrt[1 - 2*x]","A",1
2077,1,41,41,0.0309578,"\int \frac{3+5 x}{(1-2 x)^{3/2} (2+3 x)} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)),x]","\frac{11}{7 \sqrt{1-2 x}}+\frac{2 \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{7 \sqrt{21}}","\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/(7*Sqrt[1 - 2*x]) + (2*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(7*Sqrt[21])","A",1
2078,1,46,61,0.0202482,"\int \frac{3+5 x}{(1-2 x)^{3/2} (2+3 x)^2} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^2),x]","\frac{64 (3 x+2) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+7}{147 \sqrt{1-2 x} (3 x+2)}","\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,"(7 + 64*(2 + 3*x)*Hypergeometric2F1[-1/2, 1, 1/2, 3/7 - (6*x)/7])/(147*Sqrt[1 - 2*x]*(2 + 3*x))","C",1
2079,1,48,83,0.0172971,"\int \frac{3+5 x}{(1-2 x)^{3/2} (2+3 x)^3} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^3),x]","\frac{260 (3 x+2)^2 \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+49}{2058 \sqrt{1-2 x} (3 x+2)^2}","\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,"(49 + 260*(2 + 3*x)^2*Hypergeometric2F1[-1/2, 2, 1/2, 3/7 - (6*x)/7])/(2058*Sqrt[1 - 2*x]*(2 + 3*x)^2)","C",1
2080,1,42,101,0.0155129,"\int \frac{3+5 x}{(1-2 x)^{3/2} (2+3 x)^4} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^4),x]","\frac{16 \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+\frac{7}{(3 x+2)^3}}{441 \sqrt{1-2 x}}","\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,"(7/(2 + 3*x)^3 + 16*Hypergeometric2F1[-1/2, 3, 1/2, 3/7 - (6*x)/7])/(441*Sqrt[1 - 2*x])","C",1
2081,1,42,121,0.0210373,"\int \frac{3+5 x}{(1-2 x)^{3/2} (2+3 x)^5} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^5),x]","\frac{2096 \, _2F_1\left(-\frac{1}{2},4;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+\frac{2401}{(3 x+2)^4}}{201684 \sqrt{1-2 x}}","\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,"(2401/(2 + 3*x)^4 + 2096*Hypergeometric2F1[-1/2, 4, 1/2, 3/7 - (6*x)/7])/(201684*Sqrt[1 - 2*x])","C",1
2082,1,42,143,0.0241974,"\int \frac{3+5 x}{(1-2 x)^{3/2} (2+3 x)^6} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^6),x]","\frac{5248 \, _2F_1\left(-\frac{1}{2},5;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+\frac{16807}{(3 x+2)^5}}{1764735 \sqrt{1-2 x}}","\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,"(16807/(2 + 3*x)^5 + 5248*Hypergeometric2F1[-1/2, 5, 1/2, 3/7 - (6*x)/7])/(1764735*Sqrt[1 - 2*x])","C",1
2083,1,48,105,0.0310967,"\int \frac{(2+3 x)^5 (3+5 x)^2}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^5*(3 + 5*x)^2)/(1 - 2*x)^(3/2),x]","\frac{-200475 x^7-1201635 x^6-3350637 x^5-5928885 x^4-7945164 x^3-10015804 x^2-21370088 x+21493640}{429 \sqrt{1-2 x}}","\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,"(21493640 - 21370088*x - 10015804*x^2 - 7945164*x^3 - 5928885*x^4 - 3350637*x^5 - 1201635*x^6 - 200475*x^7)/(429*Sqrt[1 - 2*x])","A",1
2084,1,43,92,0.0263614,"\int \frac{(2+3 x)^4 (3+5 x)^2}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^(3/2),x]","\frac{-212625 x^6-1146600 x^5-2899485 x^4-4819932 x^3-6831172 x^2-15214664 x+15380984}{1155 \sqrt{1-2 x}}","-\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,"(15380984 - 15214664*x - 6831172*x^2 - 4819932*x^3 - 2899485*x^4 - 1146600*x^5 - 212625*x^6)/(1155*Sqrt[1 - 2*x])","A",1
2085,1,38,79,0.0205296,"\int \frac{(2+3 x)^3 (3+5 x)^2}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x)^2)/(1 - 2*x)^(3/2),x]","\frac{-7875 x^5-38025 x^4-88443 x^3-150253 x^2-359726 x+367286}{105 \sqrt{1-2 x}}","\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,"(367286 - 359726*x - 150253*x^2 - 88443*x^3 - 38025*x^4 - 7875*x^5)/(105*Sqrt[1 - 2*x])","A",1
2086,1,33,66,0.0202068,"\int \frac{(2+3 x)^2 (3+5 x)^2}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x)^(3/2),x]","\frac{-675 x^4-2934 x^3-6721 x^2-18230 x+18986}{21 \sqrt{1-2 x}}","-\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,"(18986 - 18230*x - 6721*x^2 - 2934*x^3 - 675*x^4)/(21*Sqrt[1 - 2*x])","A",1
2087,1,28,53,0.014289,"\int \frac{(2+3 x) (3+5 x)^2}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)*(3 + 5*x)^2)/(1 - 2*x)^(3/2),x]","\frac{-45 x^3-185 x^2-631 x+685}{3 \sqrt{1-2 x}}","\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,"(685 - 631*x - 185*x^2 - 45*x^3)/(3*Sqrt[1 - 2*x])","A",1
2088,1,23,40,0.0150264,"\int \frac{(3+5 x)^2}{(1-2 x)^{3/2}} \, dx","Integrate[(3 + 5*x)^2/(1 - 2*x)^(3/2),x]","\frac{-25 x^2-140 x+167}{3 \sqrt{1-2 x}}","-\frac{25}{12} (1-2 x)^{3/2}+\frac{55}{2} \sqrt{1-2 x}+\frac{121}{4 \sqrt{1-2 x}}",1,"(167 - 140*x - 25*x^2)/(3*Sqrt[1 - 2*x])","A",1
2089,1,37,54,0.0254912,"\int \frac{(3+5 x)^2}{(1-2 x)^{3/2} (2+3 x)} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^(3/2)*(2 + 3*x)),x]","\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)-525 x+805}{63 \sqrt{1-2 x}}","\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,"(805 - 525*x + 2*Hypergeometric2F1[-1/2, 1, 1/2, 3/7 - (6*x)/7])/(63*Sqrt[1 - 2*x])","C",1
2090,1,62,68,0.0513951,"\int \frac{(3+5 x)^2}{(1-2 x)^{3/2} (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^(3/2)*(2 + 3*x)^2),x]","\frac{21 (1091 x+725)+134 \sqrt{21-42 x} (3 x+2) \tanh ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)}{3087 \sqrt{1-2 x} (3 x+2)}","-\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,"(21*(725 + 1091*x) + 134*Sqrt[21 - 42*x]*(2 + 3*x)*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/(3087*Sqrt[1 - 2*x]*(2 + 3*x))","A",1
2091,1,83,88,0.0647534,"\int \frac{(3+5 x)^2}{(1-2 x)^{3/2} (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^(3/2)*(2 + 3*x)^3),x]","\frac{21 \sqrt{2 x-1} \left(12270 x^2+17305 x+6067\right)+4090 \sqrt{21} (2 x-1) (3 x+2)^2 \tan ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{2 x-1}\right)}{43218 \sqrt{-(1-2 x)^2} (3 x+2)^2}","-\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,"(21*Sqrt[-1 + 2*x]*(6067 + 17305*x + 12270*x^2) + 4090*Sqrt[21]*(-1 + 2*x)*(2 + 3*x)^2*ArcTan[Sqrt[3/7]*Sqrt[-1 + 2*x]])/(43218*Sqrt[-(1 - 2*x)^2]*(2 + 3*x)^2)","A",0
2092,1,59,108,0.0243103,"\int \frac{(3+5 x)^2}{(1-2 x)^{3/2} (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^(3/2)*(2 + 3*x)^4),x]","\frac{7240 (2 x-1) (3 x+2)^3 \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{3}{7}-\frac{6 x}{7}\right)+343 (467 x+311)}{21609 \sqrt{1-2 x} (3 x+2)^3}","-\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,"(343*(311 + 467*x) + 7240*(-1 + 2*x)*(2 + 3*x)^3*Hypergeometric2F1[1/2, 3, 3/2, 3/7 - (6*x)/7])/(21609*Sqrt[1 - 2*x]*(2 + 3*x)^3)","C",1
2093,1,60,128,0.0304913,"\int \frac{(3+5 x)^2}{(1-2 x)^{3/2} (2+3 x)^5} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^(3/2)*(2 + 3*x)^5),x]","\frac{29264 (2 x-1) (3 x+2)^4 \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};\frac{3}{7}-\frac{6 x}{7}\right)+747397 (2 x-1)+1743126}{201684 \sqrt{1-2 x} (3 x+2)^4}","-\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,"(1743126 + 747397*(-1 + 2*x) + 29264*(-1 + 2*x)*(2 + 3*x)^4*Hypergeometric2F1[1/2, 4, 3/2, 3/7 - (6*x)/7])/(201684*Sqrt[1 - 2*x]*(2 + 3*x)^4)","C",1
2094,1,48,105,0.0288751,"\int \frac{(2+3 x)^4 (3+5 x)^3}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x)^(3/2),x]","\frac{-3898125 x^7-23058000 x^6-63495075 x^5-111095730 x^4-147527176 x^3-184884496 x^2-393552752 x+395714912}{5005 \sqrt{1-2 x}}","\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,"(395714912 - 393552752*x - 184884496*x^2 - 147527176*x^3 - 111095730*x^4 - 63495075*x^5 - 23058000*x^6 - 3898125*x^7)/(5005*Sqrt[1 - 2*x])","A",1
2095,1,43,92,0.0209625,"\int \frac{(2+3 x)^3 (3+5 x)^3}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x)^3)/(1 - 2*x)^(3/2),x]","\frac{-118125 x^6-627375 x^5-1564350 x^4-2569643 x^3-3611453 x^2-8012926 x+8096086}{385 \sqrt{1-2 x}}","-\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,"(8096086 - 8012926*x - 3611453*x^2 - 2569643*x^3 - 1564350*x^4 - 627375*x^5 - 118125*x^6)/(385*Sqrt[1 - 2*x])","A",1
2096,1,38,79,0.0253699,"\int \frac{(2+3 x)^2 (3+5 x)^3}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x)^3)/(1 - 2*x)^(3/2),x]","\frac{-875 x^5-4150 x^4-9501 x^3-15948 x^2-37944 x+38700}{7 \sqrt{1-2 x}}","\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,"(38700 - 37944*x - 15948*x^2 - 9501*x^3 - 4150*x^4 - 875*x^5)/(7*Sqrt[1 - 2*x])","A",1
2097,1,33,66,0.0134802,"\int \frac{(2+3 x) (3+5 x)^3}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)*(3 + 5*x)^3)/(1 - 2*x)^(3/2),x]","\frac{-375 x^4-1595 x^3-3590 x^2-9637 x+10015}{7 \sqrt{1-2 x}}","-\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,"(10015 - 9637*x - 3590*x^2 - 1595*x^3 - 375*x^4)/(7*Sqrt[1 - 2*x])","A",1
2098,1,25,53,0.0137171,"\int \frac{(3+5 x)^3}{(1-2 x)^{3/2}} \, dx","Integrate[(3 + 5*x)^3/(1 - 2*x)^(3/2),x]","\frac{-25 x^3-100 x^2-335 x+362}{\sqrt{1-2 x}}","\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,"(362 - 335*x - 100*x^2 - 25*x^3)/Sqrt[1 - 2*x]","A",1
2099,1,45,67,0.0282414,"\int \frac{(3+5 x)^3}{(1-2 x)^{3/2} (2+3 x)} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^(3/2)*(2 + 3*x)),x]","\frac{-2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)-35 \left(75 x^2+405 x-478\right)}{189 \sqrt{1-2 x}}","-\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,"(-35*(-478 + 405*x + 75*x^2) - 2*Hypergeometric2F1[-1/2, 1, 1/2, 3/7 - (6*x)/7])/(189*Sqrt[1 - 2*x])","C",1
2100,1,79,80,0.0571128,"\int \frac{(3+5 x)^3}{(1-2 x)^{3/2} (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^(3/2)*(2 + 3*x)^2),x]","\frac{68 \sqrt{21} \left(6 x^2+x-2\right) \tan ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{2 x-1}\right)-21 \sqrt{2 x-1} \left(6125 x^2-4968 x-6035\right)}{3087 \sqrt{-(1-2 x)^2} (3 x+2)}","\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,"(-21*Sqrt[-1 + 2*x]*(-6035 - 4968*x + 6125*x^2) + 68*Sqrt[21]*(-2 + x + 6*x^2)*ArcTan[Sqrt[3/7]*Sqrt[-1 + 2*x]])/(3087*Sqrt[-(1 - 2*x)^2]*(2 + 3*x))","A",0
2101,1,59,80,0.0404199,"\int \frac{(3+5 x)^3}{(1-2 x)^{3/2} (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^(3/2)*(2 + 3*x)^3),x]","\frac{7 \left(36750 x^2+48795 x+16199\right)-4490 (3 x+2)^2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)}{6174 \sqrt{1-2 x} (3 x+2)^2}","\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,"(7*(16199 + 48795*x + 36750*x^2) - 4490*(2 + 3*x)^2*Hypergeometric2F1[-1/2, 1, 1/2, 3/7 - (6*x)/7])/(6174*Sqrt[1 - 2*x]*(2 + 3*x)^2)","C",1
2102,1,59,100,0.028046,"\int \frac{(3+5 x)^3}{(1-2 x)^{3/2} (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^(3/2)*(2 + 3*x)^4),x]","\frac{18640 (3 x+2)^3 \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+49 \left(7875 x^2+10434 x+3457\right)}{27783 \sqrt{1-2 x} (3 x+2)^3}","\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,"(49*(3457 + 10434*x + 7875*x^2) + 18640*(2 + 3*x)^3*Hypergeometric2F1[-1/2, 2, 1/2, 3/7 - (6*x)/7])/(27783*Sqrt[1 - 2*x]*(2 + 3*x)^3)","C",1
2103,1,59,120,0.0298041,"\int \frac{(3+5 x)^3}{(1-2 x)^{3/2} (2+3 x)^5} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^(3/2)*(2 + 3*x)^5),x]","\frac{62696 (3 x+2)^4 \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+49 \left(44100 x^2+58389 x+19333\right)}{259308 \sqrt{1-2 x} (3 x+2)^4}","\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,"(49*(19333 + 58389*x + 44100*x^2) + 62696*(2 + 3*x)^4*Hypergeometric2F1[-1/2, 3, 1/2, 3/7 - (6*x)/7])/(259308*Sqrt[1 - 2*x]*(2 + 3*x)^4)","C",1
2104,1,60,106,0.051642,"\int \frac{(2+3 x)^6}{(1-2 x)^{3/2} (3+5 x)} \, dx","Integrate[(2 + 3*x)^6/((1 - 2*x)^(3/2)*(3 + 5*x)),x]","\frac{14 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{5}{11} (1-2 x)\right)-99 \left(196875 x^5+1001250 x^4+2440575 x^3+4301000 x^2+10503235 x-10762494\right)}{1203125 \sqrt{1-2 x}}","\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,"(-99*(-10762494 + 10503235*x + 4301000*x^2 + 2440575*x^3 + 1001250*x^4 + 196875*x^5) + 14*Hypergeometric2F1[-1/2, 1, 1/2, (5*(1 - 2*x))/11])/(1203125*Sqrt[1 - 2*x])","C",1
2105,1,55,93,0.0413183,"\int \frac{(2+3 x)^5}{(1-2 x)^{3/2} (3+5 x)} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^(3/2)*(3 + 5*x)),x]","\frac{14 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{5}{11} (1-2 x)\right)-33 \left(50625 x^4+234225 x^3+565500 x^2+1584705 x-1662482\right)}{240625 \sqrt{1-2 x}}","-\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,"(-33*(-1662482 + 1584705*x + 565500*x^2 + 234225*x^3 + 50625*x^4) + 14*Hypergeometric2F1[-1/2, 1, 1/2, (5*(1 - 2*x))/11])/(240625*Sqrt[1 - 2*x])","C",1
2106,1,50,80,0.0388105,"\int \frac{(2+3 x)^4}{(1-2 x)^{3/2} (3+5 x)} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^(3/2)*(3 + 5*x)),x]","\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{5}{11} (1-2 x)\right)-33 \left(675 x^3+3000 x^2+10815 x-11926\right)}{6875 \sqrt{1-2 x}}","\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,"(-33*(-11926 + 10815*x + 3000*x^2 + 675*x^3) + 2*Hypergeometric2F1[-1/2, 1, 1/2, (5*(1 - 2*x))/11])/(6875*Sqrt[1 - 2*x])","C",1
2107,1,45,67,0.0327364,"\int \frac{(2+3 x)^3}{(1-2 x)^{3/2} (3+5 x)} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)),x]","\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{5}{11} (1-2 x)\right)-99 \left(25 x^2+155 x-192\right)}{1375 \sqrt{1-2 x}}","-\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,"(-99*(-192 + 155*x + 25*x^2) + 2*Hypergeometric2F1[-1/2, 1, 1/2, (5*(1 - 2*x))/11])/(1375*Sqrt[1 - 2*x])","C",1
2108,1,37,54,0.0295264,"\int \frac{(2+3 x)^2}{(1-2 x)^{3/2} (3+5 x)} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^(3/2)*(3 + 5*x)),x]","\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{5}{11} (1-2 x)\right)-495 x+858}{275 \sqrt{1-2 x}}","\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,"(858 - 495*x + 2*Hypergeometric2F1[-1/2, 1, 1/2, (5*(1 - 2*x))/11])/(275*Sqrt[1 - 2*x])","C",1
2109,1,41,41,0.0253507,"\int \frac{2+3 x}{(1-2 x)^{3/2} (3+5 x)} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)^(3/2)*(3 + 5*x)),x]","\frac{7}{11 \sqrt{1-2 x}}-\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/(11*Sqrt[1 - 2*x]) - (2*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(11*Sqrt[55])","A",1
2110,1,30,43,0.0071533,"\int \frac{1}{(1-2 x)^{3/2} (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(3 + 5*x)),x]","\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)}{11 \sqrt{1-2 x}}","\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*Hypergeometric2F1[-1/2, 1, 1/2, (-5*(-1 + 2*x))/11])/(11*Sqrt[1 - 2*x])","C",1
2111,1,72,72,0.0886865,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x) (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)),x]","\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)","\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/(77*Sqrt[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
2112,1,70,92,0.0439014,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^2 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)),x]","\frac{-2508 (3 x+2) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+2450 (3 x+2) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+231}{539 \sqrt{1-2 x} (3 x+2)}","-\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,"(231 - 2508*(2 + 3*x)*Hypergeometric2F1[-1/2, 1, 1/2, 3/7 - (6*x)/7] + 2450*(2 + 3*x)*Hypergeometric2F1[-1/2, 1, 1/2, (-5*(-1 + 2*x))/11])/(539*Sqrt[1 - 2*x]*(2 + 3*x))","C",1
2113,1,80,112,0.048294,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^3 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)),x]","\frac{7 \left(24500 (3 x+2)^2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+7425 x+5181\right)-176550 (3 x+2)^2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)}{7546 \sqrt{1-2 x} (3 x+2)^2}","-\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,"(-176550*(2 + 3*x)^2*Hypergeometric2F1[-1/2, 1, 1/2, 3/7 - (6*x)/7] + 7*(5181 + 7425*x + 24500*(2 + 3*x)^2*Hypergeometric2F1[-1/2, 1, 1/2, (-5*(-1 + 2*x))/11]))/(7546*Sqrt[1 - 2*x]*(2 + 3*x)^2)","C",1
2114,1,85,132,0.0636521,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^4 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x)),x]","\frac{-441540 (3 x+2)^3 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+428750 (3 x+2)^3 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+231 \left(1695 x^2+2316 x+793\right)}{3773 \sqrt{1-2 x} (3 x+2)^3}","-\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,"(231*(793 + 2316*x + 1695*x^2) - 441540*(2 + 3*x)^3*Hypergeometric2F1[-1/2, 1, 1/2, 3/7 - (6*x)/7] + 428750*(2 + 3*x)^3*Hypergeometric2F1[-1/2, 1, 1/2, (-5*(-1 + 2*x))/11])/(3773*Sqrt[1 - 2*x]*(2 + 3*x)^3)","C",1
2115,1,101,140,0.1314147,"\int \frac{(2+3 x)^6}{(1-2 x)^{3/2} (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^6/((1 - 2*x)^(3/2)*(3 + 5*x)^2),x]","\frac{\frac{8820 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{5}{11} (1-2 x)\right)}{\sqrt{1-2 x}}-\frac{55 \left(5011875 x^5+26663175 x^4+72309105 x^3+199582515 x^2-74439831 x-103960660\right)}{\sqrt{1-2 x} (5 x+3)}+546 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{13234375}","\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,"((-55*(-103960660 - 74439831*x + 199582515*x^2 + 72309105*x^3 + 26663175*x^4 + 5011875*x^5))/(Sqrt[1 - 2*x]*(3 + 5*x)) + 546*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]] + (8820*Hypergeometric2F1[-1/2, 1, 1/2, (5*(1 - 2*x))/11])/Sqrt[1 - 2*x])/13234375","C",1
2116,1,96,120,0.1110627,"\int \frac{(2+3 x)^5}{(1-2 x)^{3/2} (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^(3/2)*(3 + 5*x)^2),x]","\frac{\frac{1260 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{5}{11} (1-2 x)\right)}{\sqrt{1-2 x}}-\frac{55 \left(66825 x^4+344520 x^3+1300860 x^2-569364 x-744172\right)}{\sqrt{1-2 x} (5 x+3)}+84 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{378125}","\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,"((-55*(-744172 - 569364*x + 1300860*x^2 + 344520*x^3 + 66825*x^4))/(Sqrt[1 - 2*x]*(3 + 5*x)) + 84*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]] + (1260*Hypergeometric2F1[-1/2, 1, 1/2, (5*(1 - 2*x))/11])/Sqrt[1 - 2*x])/378125","C",1
2117,1,91,100,0.1340484,"\int \frac{(2+3 x)^4}{(1-2 x)^{3/2} (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^(3/2)*(3 + 5*x)^2),x]","\frac{\frac{252 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{5}{11} (1-2 x)\right)}{\sqrt{1-2 x}}+\frac{11 \left(-7425 x^3-51975 x^2+31095 x+35764\right)}{\sqrt{1-2 x} (5 x+3)}+18 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{15125}","\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,"((11*(35764 + 31095*x - 51975*x^2 - 7425*x^3))/(Sqrt[1 - 2*x]*(3 + 5*x)) + 18*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]] + (252*Hypergeometric2F1[-1/2, 1, 1/2, (5*(1 - 2*x))/11])/Sqrt[1 - 2*x])/15125","C",1
2118,1,79,80,0.051803,"\int \frac{(2+3 x)^3}{(1-2 x)^{3/2} (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)^2),x]","\frac{55 \sqrt{2 x-1} \left(-16335 x^2+19806 x+17762\right)+204 \sqrt{55} \left(10 x^2+x-3\right) \tan ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{166375 \sqrt{-(1-2 x)^2} (5 x+3)}","\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,"(55*Sqrt[-1 + 2*x]*(17762 + 19806*x - 16335*x^2) + 204*Sqrt[55]*(-3 + x + 10*x^2)*ArcTan[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(166375*Sqrt[-(1 - 2*x)^2]*(3 + 5*x))","A",0
2119,1,53,68,0.0456986,"\int \frac{(2+3 x)^2}{(1-2 x)^{3/2} (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^(3/2)*(3 + 5*x)^2),x]","\frac{1227 x+734}{605 \sqrt{1-2 x} (5 x+3)}-\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)/(605*Sqrt[1 - 2*x]*(3 + 5*x)) - (138*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(605*Sqrt[55])","A",1
2120,1,46,61,0.0137764,"\int \frac{2+3 x}{(1-2 x)^{3/2} (3+5 x)^2} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)^(3/2)*(3 + 5*x)^2),x]","\frac{72 (5 x+3) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)-11}{605 \sqrt{1-2 x} (5 x+3)}","\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,"(-11 + 72*(3 + 5*x)*Hypergeometric2F1[-1/2, 1, 1/2, (-5*(-1 + 2*x))/11])/(605*Sqrt[1 - 2*x]*(3 + 5*x))","C",1
2121,1,30,63,0.0087823,"\int \frac{1}{(1-2 x)^{3/2} (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(3 + 5*x)^2),x]","\frac{4 \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)}{121 \sqrt{1-2 x}}","\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,"(4*Hypergeometric2F1[-1/2, 2, 1/2, (-5*(-1 + 2*x))/11])/(121*Sqrt[1 - 2*x])","C",1
2122,1,73,92,0.0332998,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x) (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^2),x]","\frac{2178 (5 x+3) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)-35 \left(60 (5 x+3) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+11\right)}{847 \sqrt{1-2 x} (5 x+3)}","\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,"(2178*(3 + 5*x)*Hypergeometric2F1[-1/2, 1, 1/2, 3/7 - (6*x)/7] - 35*(11 + 60*(3 + 5*x)*Hypergeometric2F1[-1/2, 1, 1/2, (-5*(-1 + 2*x))/11]))/(847*Sqrt[1 - 2*x]*(3 + 5*x))","C",1
2123,1,93,119,0.0457386,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^2),x]","\frac{158994 \left(15 x^2+19 x+6\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)-7 \left(22050 \left(15 x^2+19 x+6\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+11220 x+7117\right)}{5929 \sqrt{1-2 x} (3 x+2) (5 x+3)}","\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,"(158994*(6 + 19*x + 15*x^2)*Hypergeometric2F1[-1/2, 1, 1/2, 3/7 - (6*x)/7] - 7*(7117 + 11220*x + 22050*(6 + 19*x + 15*x^2)*Hypergeometric2F1[-1/2, 1, 1/2, (-5*(-1 + 2*x))/11]))/(5929*Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x))","C",1
2124,1,78,146,0.0583925,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^2),x]","\frac{16955730 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)-16464000 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)-\frac{77 \left(325575 x^2+423210 x+137209\right)}{(3 x+2)^2 (5 x+3)}}{83006 \sqrt{1-2 x}}","\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,"((-77*(137209 + 423210*x + 325575*x^2))/((2 + 3*x)^2*(3 + 5*x)) + 16955730*Hypergeometric2F1[-1/2, 1, 1/2, 3/7 - (6*x)/7] - 16464000*Hypergeometric2F1[-1/2, 1, 1/2, (-5*(-1 + 2*x))/11])/(83006*Sqrt[1 - 2*x])","C",1
2125,1,101,147,0.1501462,"\int \frac{(2+3 x)^6}{(1-2 x)^{3/2} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^6/((1 - 2*x)^(3/2)*(3 + 5*x)^3),x]","\frac{\frac{13230 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{5}{11} (1-2 x)\right)}{\sqrt{1-2 x}}-\frac{55 \left(22052250 x^5+129373200 x^4+516610710 x^3+69300960 x^2-377289427 x-154786070\right)}{\sqrt{1-2 x} (5 x+3)^2}-4956 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{41593750}","\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,"((-55*(-154786070 - 377289427*x + 69300960*x^2 + 516610710*x^3 + 129373200*x^4 + 22052250*x^5))/(Sqrt[1 - 2*x]*(3 + 5*x)^2) - 4956*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]] + (13230*Hypergeometric2F1[-1/2, 1, 1/2, (5*(1 - 2*x))/11])/Sqrt[1 - 2*x])/41593750","C",1
2126,1,96,127,0.1386932,"\int \frac{(2+3 x)^5}{(1-2 x)^{3/2} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^(3/2)*(3 + 5*x)^3),x]","\frac{\frac{2415 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{5}{11} (1-2 x)\right)}{\sqrt{1-2 x}}-\frac{55 \left(490050 x^4+3822390 x^3-68385 x^2-3786773 x-1485319\right)}{\sqrt{1-2 x} (5 x+3)^2}-609 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{1663750}","\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,"((-55*(-1485319 - 3786773*x - 68385*x^2 + 3822390*x^3 + 490050*x^4))/(Sqrt[1 - 2*x]*(3 + 5*x)^2) - 609*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]] + (2415*Hypergeometric2F1[-1/2, 1, 1/2, (5*(1 - 2*x))/11])/Sqrt[1 - 2*x])/1663750","C",1
2127,1,91,107,0.1277208,"\int \frac{(2+3 x)^4}{(1-2 x)^{3/2} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^(3/2)*(3 + 5*x)^3),x]","\frac{\frac{2184 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{5}{11} (1-2 x)\right)}{\sqrt{1-2 x}}+\frac{11 \left(-490050 x^3+334350 x^2+930205 x+331904\right)}{\sqrt{1-2 x} (5 x+3)^2}-306 \sqrt{55} \tanh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{332750}","\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,"((11*(331904 + 930205*x + 334350*x^2 - 490050*x^3))/(Sqrt[1 - 2*x]*(3 + 5*x)^2) - 306*Sqrt[55]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]] + (2184*Hypergeometric2F1[-1/2, 1, 1/2, (5*(1 - 2*x))/11])/Sqrt[1 - 2*x])/332750","C",1
2128,1,59,80,0.0222377,"\int \frac{(2+3 x)^3}{(1-2 x)^{3/2} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)^3),x]","\frac{14286 (5 x+3)^2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+11 \left(163350 x^2+195005 x+58186\right)}{332750 \sqrt{1-2 x} (5 x+3)^2}","\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,"(11*(58186 + 195005*x + 163350*x^2) + 14286*(3 + 5*x)^2*Hypergeometric2F1[-1/2, 1, 1/2, (-5*(-1 + 2*x))/11])/(332750*Sqrt[1 - 2*x]*(3 + 5*x)^2)","C",1
2129,1,83,88,0.0519528,"\int \frac{(2+3 x)^2}{(1-2 x)^{3/2} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^(3/2)*(3 + 5*x)^3),x]","\frac{55 \sqrt{2 x-1} \left(25890 x^2+29561 x+8392\right)+5178 \sqrt{55} (2 x-1) (5 x+3)^2 \tan ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{732050 \sqrt{-(1-2 x)^2} (5 x+3)^2}","-\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,"(55*Sqrt[-1 + 2*x]*(8392 + 29561*x + 25890*x^2) + 5178*Sqrt[55]*(-1 + 2*x)*(3 + 5*x)^2*ArcTan[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(732050*Sqrt[-(1 - 2*x)^2]*(3 + 5*x)^2)","A",0
2130,1,48,81,0.0143622,"\int \frac{2+3 x}{(1-2 x)^{3/2} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)^(3/2)*(3 + 5*x)^3),x]","\frac{284 (5 x+3)^2 \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)-121}{13310 \sqrt{1-2 x} (5 x+3)^2}","\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,"(-121 + 284*(3 + 5*x)^2*Hypergeometric2F1[-1/2, 2, 1/2, (-5*(-1 + 2*x))/11])/(13310*Sqrt[1 - 2*x]*(3 + 5*x)^2)","C",1
2131,1,30,83,0.0062695,"\int \frac{1}{(1-2 x)^{3/2} (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(3 + 5*x)^3),x]","\frac{8 \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)}{1331 \sqrt{1-2 x}}","\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,"(8*Hypergeometric2F1[-1/2, 3, 1/2, (-5*(-1 + 2*x))/11])/(1331*Sqrt[1 - 2*x])","C",1
2132,1,73,112,0.0618882,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x) (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^3),x]","\frac{\frac{35 \left(3990 (5 x+3)^2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+3355 x+1892\right)}{(5 x+3)^2}-143748 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)}{18634 \sqrt{1-2 x}}","-\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,"(-143748*Hypergeometric2F1[-1/2, 1, 1/2, 3/7 - (6*x)/7] + (35*(1892 + 3355*x + 3990*(3 + 5*x)^2*Hypergeometric2F1[-1/2, 1, 1/2, (-5*(-1 + 2*x))/11]))/(3 + 5*x)^2)/(18634*Sqrt[1 - 2*x])","C",1
2133,1,78,139,0.0643806,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{-15524784 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+15074850 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+\frac{77 \left(496725 x^2+612520 x+188306\right)}{(3 x+2) (5 x+3)^2}}{130438 \sqrt{1-2 x}}","-\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,"((77*(188306 + 612520*x + 496725*x^2))/((2 + 3*x)*(3 + 5*x)^2) - 15524784*Hypergeometric2F1[-1/2, 1, 1/2, 3/7 - (6*x)/7] + 15074850*Hypergeometric2F1[-1/2, 1, 1/2, (-5*(-1 + 2*x))/11])/(130438*Sqrt[1 - 2*x])","C",1
2134,1,83,166,0.0988915,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{-1102906530 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+1070931750 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+\frac{77 \left(105876000 x^3+201146925 x^2+127185805 x+26765111\right)}{(3 x+2)^2 (5 x+3)^2}}{913066 \sqrt{1-2 x}}","-\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,"((77*(26765111 + 127185805*x + 201146925*x^2 + 105876000*x^3))/((2 + 3*x)^2*(3 + 5*x)^2) - 1102906530*Hypergeometric2F1[-1/2, 1, 1/2, 3/7 - (6*x)/7] + 1070931750*Hypergeometric2F1[-1/2, 1, 1/2, (-5*(-1 + 2*x))/11])/(913066*Sqrt[1 - 2*x])","C",1
2135,1,43,92,0.0251007,"\int \frac{(2+3 x)^5 (3+5 x)}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^5*(3 + 5*x))/(1 - 2*x)^(5/2),x]","-\frac{2835 x^6+16767 x^5+49653 x^4+114084 x^3+412812 x^2-844104 x+280696}{21 (1-2 x)^{3/2}}","-\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,"-1/21*(280696 - 844104*x + 412812*x^2 + 114084*x^3 + 49653*x^4 + 16767*x^5 + 2835*x^6)/(1 - 2*x)^(3/2)","A",1
2136,1,38,79,0.021266,"\int \frac{(2+3 x)^4 (3+5 x)}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x)^(5/2),x]","-\frac{6075 x^5+33858 x^4+105624 x^3+435312 x^2-909264 x+301408}{105 (1-2 x)^{3/2}}","\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,"-1/105*(301408 - 909264*x + 435312*x^2 + 105624*x^3 + 33858*x^4 + 6075*x^5)/(1 - 2*x)^(3/2)","A",1
2137,1,33,66,0.0237423,"\int \frac{(2+3 x)^3 (3+5 x)}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x)^(5/2),x]","-\frac{81 x^4+459 x^3+2403 x^2-5250 x+1726}{3 (1-2 x)^{3/2}}","-\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,"-1/3*(1726 - 5250*x + 2403*x^2 + 459*x^3 + 81*x^4)/(1 - 2*x)^(3/2)","A",1
2138,1,28,53,0.0144943,"\int \frac{(2+3 x)^2 (3+5 x)}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x))/(1 - 2*x)^(5/2),x]","-\frac{45 x^3+396 x^2-960 x+308}{3 (1-2 x)^{3/2}}","\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,"-1/3*(308 - 960*x + 396*x^2 + 45*x^3)/(1 - 2*x)^(3/2)","A",1
2139,1,23,38,0.0137485,"\int \frac{(2+3 x) (3+5 x)}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)*(3 + 5*x))/(1 - 2*x)^(5/2),x]","-\frac{45 x^2-147 x+43}{3 (1-2 x)^{3/2}}","-\frac{15}{4} \sqrt{1-2 x}-\frac{17}{\sqrt{1-2 x}}+\frac{77}{12 (1-2 x)^{3/2}}",1,"-1/3*(43 - 147*x + 45*x^2)/(1 - 2*x)^(3/2)","A",1
2140,1,18,27,0.0096896,"\int \frac{3+5 x}{(1-2 x)^{5/2}} \, dx","Integrate[(3 + 5*x)/(1 - 2*x)^(5/2),x]","\frac{15 x-2}{3 (1-2 x)^{3/2}}","\frac{11}{6 (1-2 x)^{3/2}}-\frac{5}{2 \sqrt{1-2 x}}",1,"(-2 + 15*x)/(3*(1 - 2*x)^(3/2))","A",1
2141,1,38,56,0.0179022,"\int \frac{3+5 x}{(1-2 x)^{5/2} (2+3 x)} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)),x]","-\frac{(6-12 x) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)-77}{147 (1-2 x)^{3/2}}","-\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,"-1/147*(-77 + (6 - 12*x)*Hypergeometric2F1[-1/2, 1, 1/2, 3/7 - (6*x)/7])/(1 - 2*x)^(3/2)","C",1
2142,1,46,76,0.022106,"\int \frac{3+5 x}{(1-2 x)^{5/2} (2+3 x)^2} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^2),x]","-\frac{-20 (3 x+2) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)-7}{147 (1-2 x)^{3/2} (3 x+2)}","\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,"-1/147*(-7 - 20*(2 + 3*x)*Hypergeometric2F1[-3/2, 1, -1/2, 3/7 - (6*x)/7])/((1 - 2*x)^(3/2)*(2 + 3*x))","C",1
2143,1,48,96,0.0238915,"\int \frac{3+5 x}{(1-2 x)^{5/2} (2+3 x)^3} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^3),x]","-\frac{-12 (3 x+2)^2 \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)-7}{294 (1-2 x)^{3/2} (3 x+2)^2}","\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,"-1/294*(-7 - 12*(2 + 3*x)^2*Hypergeometric2F1[-3/2, 2, -1/2, 3/7 - (6*x)/7])/((1 - 2*x)^(3/2)*(2 + 3*x)^2)","C",1
2144,1,42,116,0.0192591,"\int \frac{3+5 x}{(1-2 x)^{5/2} (2+3 x)^4} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]","\frac{256 \, _2F_1\left(-\frac{3}{2},3;-\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+\frac{343}{(3 x+2)^3}}{21609 (1-2 x)^{3/2}}","\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,"(343/(2 + 3*x)^3 + 256*Hypergeometric2F1[-3/2, 3, -1/2, 3/7 - (6*x)/7])/(21609*(1 - 2*x)^(3/2))","C",1
2145,1,42,136,0.022213,"\int \frac{3+5 x}{(1-2 x)^{5/2} (2+3 x)^5} \, dx","Integrate[(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^5),x]","\frac{688 \, _2F_1\left(-\frac{3}{2},4;-\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+\frac{2401}{(3 x+2)^4}}{201684 (1-2 x)^{3/2}}","\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,"(2401/(2 + 3*x)^4 + 688*Hypergeometric2F1[-3/2, 4, -1/2, 3/7 - (6*x)/7])/(201684*(1 - 2*x)^(3/2))","C",1
2146,1,48,105,0.0283269,"\int \frac{(2+3 x)^5 (3+5 x)^2}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^5*(3 + 5*x)^2)/(1 - 2*x)^(5/2),x]","-\frac{127575 x^7+806085 x^6+2456001 x^5+5121279 x^4+9702012 x^3+32450916 x^2-65622552 x+21852008}{231 (1-2 x)^{3/2}}","\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,"-1/231*(21852008 - 65622552*x + 32450916*x^2 + 9702012*x^3 + 5121279*x^4 + 2456001*x^5 + 806085*x^6 + 127575*x^7)/(1 - 2*x)^(3/2)","A",1
2147,1,43,92,0.0259966,"\int \frac{(2+3 x)^4 (3+5 x)^2}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^(5/2),x]","-\frac{23625 x^6+137700 x^5+402489 x^4+915492 x^3+3294996 x^2-6731112 x+2238664}{105 (1-2 x)^{3/2}}","-\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,"-1/105*(2238664 - 6731112*x + 3294996*x^2 + 915492*x^3 + 402489*x^4 + 137700*x^5 + 23625*x^6)/(1 - 2*x)^(3/2)","A",1
2148,1,38,79,0.0234699,"\int \frac{(2+3 x)^3 (3+5 x)^2}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x)^2)/(1 - 2*x)^(5/2),x]","-\frac{2025 x^5+11097 x^4+34137 x^3+139497 x^2-290838 x+96442}{21 (1-2 x)^{3/2}}","\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,"-1/21*(96442 - 290838*x + 139497*x^2 + 34137*x^3 + 11097*x^4 + 2025*x^5)/(1 - 2*x)^(3/2)","A",1
2149,1,33,66,0.0189033,"\int \frac{(2+3 x)^2 (3+5 x)^2}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x)^(5/2),x]","-\frac{135 x^4+750 x^3+3873 x^2-8430 x+2774}{3 (1-2 x)^{3/2}}","-\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,"-1/3*(2774 - 8430*x + 3873*x^2 + 750*x^3 + 135*x^4)/(1 - 2*x)^(3/2)","A",1
2150,1,28,53,0.0195437,"\int \frac{(2+3 x) (3+5 x)^2}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)*(3 + 5*x)^2)/(1 - 2*x)^(5/2),x]","-\frac{75 x^3+645 x^2-1551 x+499}{3 (1-2 x)^{3/2}}","\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,"-1/3*(499 - 1551*x + 645*x^2 + 75*x^3)/(1 - 2*x)^(3/2)","A",1
2151,1,23,40,0.0158988,"\int \frac{(3+5 x)^2}{(1-2 x)^{5/2}} \, dx","Integrate[(3 + 5*x)^2/(1 - 2*x)^(5/2),x]","-\frac{75 x^2-240 x+71}{3 (1-2 x)^{3/2}}","-\frac{25}{4} \sqrt{1-2 x}-\frac{55}{2 \sqrt{1-2 x}}+\frac{121}{12 (1-2 x)^{3/2}}",1,"-1/3*(71 - 240*x + 75*x^2)/(1 - 2*x)^(3/2)","A",1
2152,1,40,54,0.0364914,"\int \frac{(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)),x]","\frac{2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+35 (45 x-7)}{189 (1-2 x)^{3/2}}","-\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,"(35*(-7 + 45*x) + 2*Hypergeometric2F1[-3/2, 1, -1/2, 3/7 - (6*x)/7])/(189*(1 - 2*x)^(3/2))","C",1
2153,1,55,81,0.0244105,"\int \frac{(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)^2),x]","-\frac{-130 \left(6 x^2+x-2\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)-7 (365 x+241)}{1029 (1-2 x)^{3/2} (3 x+2)}","-\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,"-1/1029*(-7*(241 + 365*x) - 130*(-2 + x + 6*x^2)*Hypergeometric2F1[-1/2, 1, 1/2, 3/7 - (6*x)/7])/((1 - 2*x)^(3/2)*(2 + 3*x))","C",1
2154,1,59,103,0.0310315,"\int \frac{(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)^3),x]","-\frac{340 (2 x-1) (3 x+2)^2 \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)-49 (104 x+69)}{2058 (1-2 x)^{3/2} (3 x+2)^2}","\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,"-1/2058*(-49*(69 + 104*x) + 340*(-1 + 2*x)*(2 + 3*x)^2*Hypergeometric2F1[-1/2, 2, 1/2, 3/7 - (6*x)/7])/((1 - 2*x)^(3/2)*(2 + 3*x)^2)","C",1
2155,1,59,121,0.0280252,"\int \frac{(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]","-\frac{2264 (2 x-1) (3 x+2)^3 \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)-49 (1091 x+725)}{21609 (1-2 x)^{3/2} (3 x+2)^3}","\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,"-1/21609*(-49*(725 + 1091*x) + 2264*(-1 + 2*x)*(2 + 3*x)^3*Hypergeometric2F1[-1/2, 3, 1/2, 3/7 - (6*x)/7])/((1 - 2*x)^(3/2)*(2 + 3*x)^3)","C",1
2156,1,60,141,0.0222134,"\int \frac{(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)^5} \, dx","Integrate[(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)^5),x]","\frac{65488 (1-2 x) (3 x+2)^4 \, _2F_1\left(-\frac{1}{2},4;\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+1745527 (2 x-1)+4067294}{1411788 (1-2 x)^{3/2} (3 x+2)^4}","\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,"(4067294 + 1745527*(-1 + 2*x) + 65488*(1 - 2*x)*(2 + 3*x)^4*Hypergeometric2F1[-1/2, 4, 1/2, 3/7 - (6*x)/7])/(1411788*(1 - 2*x)^(3/2)*(2 + 3*x)^4)","C",1
2157,1,53,118,0.028225,"\int \frac{(2+3 x)^5 (3+5 x)^3}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^5*(3 + 5*x)^3)/(1 - 2*x)^(5/2),x]","-\frac{7016625 x^8+47670525 x^7+153878760 x^6+324478899 x^5+540496701 x^4+905206628 x^3+2892917004 x^2-5818266408 x+1938557272}{3003 (1-2 x)^{3/2}}","-\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,"-1/3003*(1938557272 - 5818266408*x + 2892917004*x^2 + 905206628*x^3 + 540496701*x^4 + 324478899*x^5 + 153878760*x^6 + 47670525*x^7 + 7016625*x^8)/(1 - 2*x)^(3/2)","A",1
2158,1,48,105,0.0280239,"\int \frac{(2+3 x)^4 (3+5 x)^3}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x)^(5/2),x]","-\frac{1063125 x^7+6630750 x^6+19961775 x^5+41201532 x^4+77493296 x^3+258342648 x^2-522173856 x+173891632}{1155 (1-2 x)^{3/2}}","\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,"-1/1155*(173891632 - 522173856*x + 258342648*x^2 + 77493296*x^3 + 41201532*x^4 + 19961775*x^5 + 6630750*x^6 + 1063125*x^7)/(1 - 2*x)^(3/2)","A",1
2159,1,43,92,0.0291506,"\int \frac{(2+3 x)^3 (3+5 x)^3}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x)^3)/(1 - 2*x)^(5/2),x]","-\frac{7875 x^6+45225 x^5+130464 x^4+293785 x^3+1051833 x^2-2146758 x+714074}{21 (1-2 x)^{3/2}}","-\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,"-1/21*(714074 - 2146758*x + 1051833*x^2 + 293785*x^3 + 130464*x^4 + 45225*x^5 + 7875*x^6)/(1 - 2*x)^(3/2)","A",1
2160,1,38,79,0.0236269,"\int \frac{(2+3 x)^2 (3+5 x)^3}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x)^3)/(1 - 2*x)^(5/2),x]","-\frac{3375 x^5+18180 x^4+55145 x^3+223458 x^2-465060 x+154264}{21 (1-2 x)^{3/2}}","\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,"-1/21*(154264 - 465060*x + 223458*x^2 + 55145*x^3 + 18180*x^4 + 3375*x^5)/(1 - 2*x)^(3/2)","A",1
2161,1,33,66,0.0219819,"\int \frac{(2+3 x) (3+5 x)^3}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)*(3 + 5*x)^3)/(1 - 2*x)^(5/2),x]","-\frac{225 x^4+1225 x^3+6240 x^2-13533 x+4457}{3 (1-2 x)^{3/2}}","-\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,"-1/3*(4457 - 13533*x + 6240*x^2 + 1225*x^3 + 225*x^4)/(1 - 2*x)^(3/2)","A",1
2162,1,28,53,0.0139267,"\int \frac{(3+5 x)^3}{(1-2 x)^{5/2}} \, dx","Integrate[(3 + 5*x)^3/(1 - 2*x)^(5/2),x]","-\frac{125 x^3+1050 x^2-2505 x+808}{3 (1-2 x)^{3/2}}","\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,"-1/3*(808 - 2505*x + 1050*x^2 + 125*x^3)/(1 - 2*x)^(3/2)","A",1
2163,1,45,67,0.026956,"\int \frac{(3+5 x)^3}{(1-2 x)^{5/2} (2+3 x)} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)),x]","-\frac{2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+35 \left(675 x^2-2115 x+632\right)}{567 (1-2 x)^{3/2}}","-\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,"-1/567*(35*(632 - 2115*x + 675*x^2) + 2*Hypergeometric2F1[-3/2, 1, -1/2, 3/7 - (6*x)/7])/(1 - 2*x)^(3/2)","C",1
2164,1,65,80,0.1505935,"\int \frac{(3+5 x)^3}{(1-2 x)^{5/2} (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)^2),x]","\frac{200 \sqrt{42 x-21} \tan ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{2 x-1}\right)-\frac{21 \left(42475 x^2+21050 x-4839\right)}{6 x^2+x-2}}{21609 \sqrt{1-2 x}}","\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,"((-21*(-4839 + 21050*x + 42475*x^2))/(-2 + x + 6*x^2) + 200*Sqrt[-21 + 42*x]*ArcTan[Sqrt[3/7]*Sqrt[-1 + 2*x]])/(21609*Sqrt[1 - 2*x])","A",1
2165,1,62,100,0.026592,"\int \frac{(3+5 x)^3}{(1-2 x)^{5/2} (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)^3),x]","-\frac{-7240 \left(6 x^2+x-2\right)^2 \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{3}{7}-\frac{6 x}{7}\right)-343 \left(875 x^2+1303 x+128\right)}{21609 (1-2 x)^{3/2} (3 x+2)^2}","\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,"-1/21609*(-343*(128 + 1303*x + 875*x^2) - 7240*(-2 + x + 6*x^2)^2*Hypergeometric2F1[1/2, 3, 3/2, 3/7 - (6*x)/7])/((1 - 2*x)^(3/2)*(2 + 3*x)^2)","C",1
2166,1,59,120,0.043553,"\int \frac{(3+5 x)^3}{(1-2 x)^{5/2} (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]","\frac{\frac{343 \left(1225 x^2-136 x+2091\right)}{(3 x+2)^3}-24032 (1-2 x)^2 \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};\frac{3}{7}-\frac{6 x}{7}\right)}{50421 (1-2 x)^{3/2}}","\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,"((343*(2091 - 136*x + 1225*x^2))/(2 + 3*x)^3 - 24032*(1 - 2*x)^2*Hypergeometric2F1[1/2, 4, 3/2, 3/7 - (6*x)/7])/(50421*(1 - 2*x)^(3/2))","C",1
2167,1,61,140,0.069868,"\int \frac{(3+5 x)^3}{(1-2 x)^{5/2} (2+3 x)^5} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)^5),x]","\frac{875 x^2-3779 x+4000}{147 (1-2 x)^{3/2} (3 x+2)^4}-\frac{1136864 \sqrt{1-2 x} \, _2F_1\left(\frac{1}{2},5;\frac{3}{2};\frac{3}{7}-\frac{6 x}{7}\right)}{2470629}","\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,"(4000 - 3779*x + 875*x^2)/(147*(1 - 2*x)^(3/2)*(2 + 3*x)^4) - (1136864*Sqrt[1 - 2*x]*Hypergeometric2F1[1/2, 5, 3/2, 3/7 - (6*x)/7])/2470629","C",1
2168,1,61,160,0.0797472,"\int \frac{(3+5 x)^3}{(1-2 x)^{5/2} (2+3 x)^6} \, dx","Integrate[(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)^6),x]","\frac{6125 x^2-68198 x+53531}{1323 (1-2 x)^{3/2} (3 x+2)^5}-\frac{41849344 \sqrt{1-2 x} \, _2F_1\left(\frac{1}{2},6;\frac{3}{2};\frac{3}{7}-\frac{6 x}{7}\right)}{155649627}","\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,"(53531 - 68198*x + 6125*x^2)/(1323*(1 - 2*x)^(3/2)*(2 + 3*x)^5) - (41849344*Sqrt[1 - 2*x]*Hypergeometric2F1[1/2, 6, 3/2, 3/7 - (6*x)/7])/155649627","C",1
2169,1,60,106,0.0560665,"\int \frac{(2+3 x)^6}{(1-2 x)^{5/2} (3+5 x)} \, dx","Integrate[(2 + 3*x)^6/((1 - 2*x)^(5/2)*(3 + 5*x)),x]","\frac{14 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{5}{11} (1-2 x)\right)-99 \left(759375 x^5+4374000 x^4+14029875 x^3+58833450 x^2-123370605 x+40864276\right)}{3609375 (1-2 x)^{3/2}}","\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,"(-99*(40864276 - 123370605*x + 58833450*x^2 + 14029875*x^3 + 4374000*x^4 + 759375*x^5) + 14*Hypergeometric2F1[-3/2, 1, -1/2, (5*(1 - 2*x))/11])/(3609375*(1 - 2*x)^(3/2))","C",1
2170,1,55,93,0.0437017,"\int \frac{(2+3 x)^5}{(1-2 x)^{5/2} (3+5 x)} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)),x]","\frac{2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{5}{11} (1-2 x)\right)-33 \left(30375 x^4+178875 x^3+962550 x^2-2119545 x+695404\right)}{103125 (1-2 x)^{3/2}}","-\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,"(-33*(695404 - 2119545*x + 962550*x^2 + 178875*x^3 + 30375*x^4) + 2*Hypergeometric2F1[-3/2, 1, -1/2, (5*(1 - 2*x))/11])/(103125*(1 - 2*x)^(3/2))","C",1
2171,1,50,80,0.0397434,"\int \frac{(2+3 x)^4}{(1-2 x)^{5/2} (3+5 x)} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^(5/2)*(3 + 5*x)),x]","\frac{2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{5}{11} (1-2 x)\right)-33 \left(3375 x^3+31050 x^2-76545 x+24404\right)}{20625 (1-2 x)^{3/2}}","\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,"(-33*(24404 - 76545*x + 31050*x^2 + 3375*x^3) + 2*Hypergeometric2F1[-3/2, 1, -1/2, (5*(1 - 2*x))/11])/(20625*(1 - 2*x)^(3/2))","C",1
2172,1,45,67,0.0412731,"\int \frac{(2+3 x)^3}{(1-2 x)^{5/2} (3+5 x)} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^(5/2)*(3 + 5*x)),x]","\frac{2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{5}{11} (1-2 x)\right)-99 \left(225 x^2-765 x+218\right)}{4125 (1-2 x)^{3/2}}","-\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,"(-99*(218 - 765*x + 225*x^2) + 2*Hypergeometric2F1[-3/2, 1, -1/2, (5*(1 - 2*x))/11])/(4125*(1 - 2*x)^(3/2))","C",1
2173,1,40,54,0.0258551,"\int \frac{(2+3 x)^2}{(1-2 x)^{5/2} (3+5 x)} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^(5/2)*(3 + 5*x)),x]","\frac{2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{5}{11} (1-2 x)\right)+33 (45 x-4)}{825 (1-2 x)^{3/2}}","-\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,"(33*(-4 + 45*x) + 2*Hypergeometric2F1[-3/2, 1, -1/2, (5*(1 - 2*x))/11])/(825*(1 - 2*x)^(3/2))","C",1
2174,1,38,56,0.0166813,"\int \frac{2+3 x}{(1-2 x)^{5/2} (3+5 x)} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)^(5/2)*(3 + 5*x)),x]","\frac{(6-12 x) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+77}{363 (1-2 x)^{3/2}}","\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,"(77 + (6 - 12*x)*Hypergeometric2F1[-1/2, 1, 1/2, (-5*(-1 + 2*x))/11])/(363*(1 - 2*x)^(3/2))","C",1
2175,1,30,56,0.0065367,"\int \frac{1}{(1-2 x)^{5/2} (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(3 + 5*x)),x]","\frac{2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{5}{11} (2 x-1)\right)}{33 (1-2 x)^{3/2}}","\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,"(2*Hypergeometric2F1[-3/2, 1, -1/2, (-5*(-1 + 2*x))/11])/(33*(1 - 2*x)^(3/2))","C",1
2176,1,85,85,0.0915681,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x) (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)),x]","\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)","\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/(231*(1 - 2*x)^(3/2)) + 272/(5929*Sqrt[1 - 2*x]) + (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
2177,1,73,105,0.0330158,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^2 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)),x]","-\frac{2640 (3 x+2) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)-7 \left(350 (3 x+2) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+99\right)}{1617 (1-2 x)^{3/2} (3 x+2)}","-\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,"-1/1617*(2640*(2 + 3*x)*Hypergeometric2F1[-3/2, 1, -1/2, 3/7 - (6*x)/7] - 7*(99 + 350*(2 + 3*x)*Hypergeometric2F1[-3/2, 1, -1/2, (-5*(-1 + 2*x))/11]))/((1 - 2*x)^(3/2)*(2 + 3*x))","C",1
2178,1,83,125,0.0542042,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^3 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)),x]","-\frac{26730 (3 x+2)^2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)-7 \left(3500 (3 x+2)^2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+99 (33 x+23)\right)}{3234 (1-2 x)^{3/2} (3 x+2)^2}","-\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,"-1/3234*(26730*(2 + 3*x)^2*Hypergeometric2F1[-3/2, 1, -1/2, 3/7 - (6*x)/7] - 7*(99*(23 + 33*x) + 3500*(2 + 3*x)^2*Hypergeometric2F1[-3/2, 1, -1/2, (-5*(-1 + 2*x))/11]))/((1 - 2*x)^(3/2)*(2 + 3*x)^2)","C",1
2179,1,71,145,0.0824135,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^4 (3+5 x)} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^4*(3 + 5*x)),x]","\frac{-468270 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+428750 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+\frac{231 \left(5238 x^2+7155 x+2449\right)}{(3 x+2)^3}}{11319 (1-2 x)^{3/2}}","-\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,"((231*(2449 + 7155*x + 5238*x^2))/(2 + 3*x)^3 - 468270*Hypergeometric2F1[-3/2, 1, -1/2, 3/7 - (6*x)/7] + 428750*Hypergeometric2F1[-3/2, 1, -1/2, (-5*(-1 + 2*x))/11])/(11319*(1 - 2*x)^(3/2))","C",1
2180,1,99,140,0.0927336,"\int \frac{(2+3 x)^6}{(1-2 x)^{5/2} (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^6/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]","-\frac{-252 \left(10 x^2+x-3\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{5}{11} (1-2 x)\right)-266 (5 x+3) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{5}{11} (1-2 x)\right)+33 \left(1002375 x^5+6615675 x^4+36419625 x^3-52861545 x^2-19753541 x+14265224\right)}{1134375 (1-2 x)^{3/2} (5 x+3)}","\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,"-1/1134375*(33*(14265224 - 19753541*x - 52861545*x^2 + 36419625*x^3 + 6615675*x^4 + 1002375*x^5) - 266*(3 + 5*x)*Hypergeometric2F1[-3/2, 1, -1/2, (5*(1 - 2*x))/11] - 252*(-3 + x + 10*x^2)*Hypergeometric2F1[-1/2, 1, 1/2, (5*(1 - 2*x))/11])/((1 - 2*x)^(3/2)*(3 + 5*x))","C",1
2181,1,94,120,0.07994,"\int \frac{(2+3 x)^5}{(1-2 x)^{5/2} (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]","-\frac{-270 \left(10 x^2+x-3\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{5}{11} (1-2 x)\right)-266 (5 x+3) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{5}{11} (1-2 x)\right)+33 \left(111375 x^4+1113750 x^3-1975050 x^2-734880 x+496226\right)}{226875 (1-2 x)^{3/2} (5 x+3)}","\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,"-1/226875*(33*(496226 - 734880*x - 1975050*x^2 + 1113750*x^3 + 111375*x^4) - 266*(3 + 5*x)*Hypergeometric2F1[-3/2, 1, -1/2, (5*(1 - 2*x))/11] - 270*(-3 + x + 10*x^2)*Hypergeometric2F1[-1/2, 1, 1/2, (5*(1 - 2*x))/11])/((1 - 2*x)^(3/2)*(3 + 5*x))","C",1
2182,1,89,100,0.0764647,"\int \frac{(2+3 x)^4}{(1-2 x)^{5/2} (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]","-\frac{-288 \left(10 x^2+x-3\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{5}{11} (1-2 x)\right)-266 (5 x+3) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{5}{11} (1-2 x)\right)+33 \left(22275 x^3-63855 x^2-24619 x+13028\right)}{45375 (1-2 x)^{3/2} (5 x+3)}","\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,"-1/45375*(33*(13028 - 24619*x - 63855*x^2 + 22275*x^3) - 266*(3 + 5*x)*Hypergeometric2F1[-3/2, 1, -1/2, (5*(1 - 2*x))/11] - 288*(-3 + x + 10*x^2)*Hypergeometric2F1[-1/2, 1, 1/2, (5*(1 - 2*x))/11])/((1 - 2*x)^(3/2)*(3 + 5*x))","C",1
2183,1,70,80,0.1167403,"\int \frac{(2+3 x)^3}{(1-2 x)^{5/2} (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]","\frac{624 \sqrt{55} \sqrt{2 x-1} \tan ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-\frac{55 \left(106563 x^2+57832 x-3678\right)}{10 x^2+x-3}}{1098075 \sqrt{1-2 x}}","\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,"((-55*(-3678 + 57832*x + 106563*x^2))/(-3 + x + 10*x^2) + 624*Sqrt[55]*Sqrt[-1 + 2*x]*ArcTan[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(1098075*Sqrt[1 - 2*x])","A",1
2184,1,55,81,0.0190906,"\int \frac{(2+3 x)^2}{(1-2 x)^{5/2} (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]","-\frac{426 \left(10 x^2+x-3\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)-11 (1231 x+732)}{19965 (1-2 x)^{3/2} (5 x+3)}","\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,"-1/19965*(-11*(732 + 1231*x) + 426*(-3 + x + 10*x^2)*Hypergeometric2F1[-1/2, 1, 1/2, (-5*(-1 + 2*x))/11])/((1 - 2*x)^(3/2)*(3 + 5*x))","C",1
2185,1,46,76,0.0168983,"\int \frac{2+3 x}{(1-2 x)^{5/2} (3+5 x)^2} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]","-\frac{33-76 (5 x+3) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{5}{11} (2 x-1)\right)}{1815 (1-2 x)^{3/2} (5 x+3)}","\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,"-1/1815*(33 - 76*(3 + 5*x)*Hypergeometric2F1[-3/2, 1, -1/2, (-5*(-1 + 2*x))/11])/((1 - 2*x)^(3/2)*(3 + 5*x))","C",1
2186,1,30,76,0.0083041,"\int \frac{1}{(1-2 x)^{5/2} (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]","\frac{4 \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};-\frac{5}{11} (2 x-1)\right)}{363 (1-2 x)^{3/2}}","\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,"(4*Hypergeometric2F1[-3/2, 2, -1/2, (-5*(-1 + 2*x))/11])/(363*(1 - 2*x)^(3/2))","C",1
2187,1,73,105,0.0424077,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x) (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^2),x]","-\frac{35 \left(56 (5 x+3) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+33\right)-2178 (5 x+3) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)}{2541 (1-2 x)^{3/2} (5 x+3)}","\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,"-1/2541*(-2178*(3 + 5*x)*Hypergeometric2F1[-3/2, 1, -1/2, 3/7 - (6*x)/7] + 35*(33 + 56*(3 + 5*x)*Hypergeometric2F1[-3/2, 1, -1/2, (-5*(-1 + 2*x))/11]))/((1 - 2*x)^(3/2)*(3 + 5*x))","C",1
2188,1,93,132,0.0554353,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^2),x]","-\frac{-163350 \left(15 x^2+19 x+6\right) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+149450 \left(15 x^2+19 x+6\right) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+231 (1020 x+647)}{17787 (1-2 x)^{3/2} (3 x+2) (5 x+3)}","\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,"-1/17787*(231*(647 + 1020*x) - 163350*(6 + 19*x + 15*x^2)*Hypergeometric2F1[-3/2, 1, -1/2, 3/7 - (6*x)/7] + 149450*(6 + 19*x + 15*x^2)*Hypergeometric2F1[-3/2, 1, -1/2, (-5*(-1 + 2*x))/11])/((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x))","C",1
2189,1,78,159,0.0796272,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^2} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^2),x]","\frac{359370 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)-329000 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{5}{11} (2 x-1)\right)-\frac{33 \left(46935 x^2+60996 x+19771\right)}{(3 x+2)^2 (5 x+3)}}{5082 (1-2 x)^{3/2}}","\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,"((-33*(19771 + 60996*x + 46935*x^2))/((2 + 3*x)^2*(3 + 5*x)) + 359370*Hypergeometric2F1[-3/2, 1, -1/2, 3/7 - (6*x)/7] - 329000*Hypergeometric2F1[-3/2, 1, -1/2, (-5*(-1 + 2*x))/11])/(5082*(1 - 2*x)^(3/2))","C",1
2190,1,105,147,0.1054881,"\int \frac{(2+3 x)^6}{(1-2 x)^{5/2} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^6/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]","-\frac{-1204 (5 x+3)^2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{5}{11} (1-2 x)\right)+2142 (2 x-1) (5 x+3)^2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{5}{11} (1-2 x)\right)+33 \left(7350750 x^5+79388100 x^4-89679150 x^3-130986110 x^2+3498263 x+20166158\right)}{4991250 (1-2 x)^{3/2} (5 x+3)^2}","\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,"-1/4991250*(33*(20166158 + 3498263*x - 130986110*x^2 - 89679150*x^3 + 79388100*x^4 + 7350750*x^5) - 1204*(3 + 5*x)^2*Hypergeometric2F1[-3/2, 1, -1/2, (5*(1 - 2*x))/11] + 2142*(-1 + 2*x)*(3 + 5*x)^2*Hypergeometric2F1[-1/2, 1, 1/2, (5*(1 - 2*x))/11])/((1 - 2*x)^(3/2)*(3 + 5*x)^2)","C",1
2191,1,100,127,0.0865366,"\int \frac{(2+3 x)^5}{(1-2 x)^{5/2} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]","-\frac{-5327 (5 x+3)^2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{5}{11} (1-2 x)\right)+5535 (2 x-1) (5 x+3)^2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{5}{11} (1-2 x)\right)+33 \left(7350750 x^4-17151750 x^3-21347475 x^2-741695 x+2582641\right)}{4991250 (1-2 x)^{3/2} (5 x+3)^2}","\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,"-1/4991250*(33*(2582641 - 741695*x - 21347475*x^2 - 17151750*x^3 + 7350750*x^4) - 5327*(3 + 5*x)^2*Hypergeometric2F1[-3/2, 1, -1/2, (5*(1 - 2*x))/11] + 5535*(-1 + 2*x)*(3 + 5*x)^2*Hypergeometric2F1[-1/2, 1, 1/2, (5*(1 - 2*x))/11])/((1 - 2*x)^(3/2)*(3 + 5*x)^2)","C",1
2192,1,95,107,0.0758816,"\int \frac{(2+3 x)^4}{(1-2 x)^{5/2} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]","-\frac{-4634 (5 x+3)^2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{5}{11} (1-2 x)\right)+1548 (2 x-1) (5 x+3)^2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{5}{11} (1-2 x)\right)-33 \left(490050 x^3+567140 x^2+151043 x-7696\right)}{998250 (1-2 x)^{3/2} (5 x+3)^2}","\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,"-1/998250*(-33*(-7696 + 151043*x + 567140*x^2 + 490050*x^3) - 4634*(3 + 5*x)^2*Hypergeometric2F1[-3/2, 1, -1/2, (5*(1 - 2*x))/11] + 1548*(-1 + 2*x)*(3 + 5*x)^2*Hypergeometric2F1[-1/2, 1, 1/2, (5*(1 - 2*x))/11])/((1 - 2*x)^(3/2)*(3 + 5*x)^2)","C",1
2193,1,62,100,0.0321919,"\int \frac{(2+3 x)^3}{(1-2 x)^{5/2} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]","-\frac{60472 \left(10 x^2+x-3\right)^2 \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};-\frac{5}{11} (2 x-1)\right)-1331 \left(3267 x^2+3103 x+2348\right)}{2415765 (1-2 x)^{3/2} (5 x+3)^2}","\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,"-1/2415765*(-1331*(2348 + 3103*x + 3267*x^2) + 60472*(-3 + x + 10*x^2)^2*Hypergeometric2F1[1/2, 3, 3/2, (-5*(-1 + 2*x))/11])/((1 - 2*x)^(3/2)*(3 + 5*x)^2)","C",1
2194,1,59,101,0.0220404,"\int \frac{(2+3 x)^2}{(1-2 x)^{5/2} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]","-\frac{11492 (2 x-1) (5 x+3)^2 \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};-\frac{5}{11} (2 x-1)\right)-121 (2456 x+1467)}{439230 (1-2 x)^{3/2} (5 x+3)^2}","\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,"-1/439230*(-121*(1467 + 2456*x) + 11492*(-1 + 2*x)*(3 + 5*x)^2*Hypergeometric2F1[-1/2, 2, 1/2, (-5*(-1 + 2*x))/11])/((1 - 2*x)^(3/2)*(3 + 5*x)^2)","C",1
2195,1,48,96,0.0168162,"\int \frac{2+3 x}{(1-2 x)^{5/2} (3+5 x)^3} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]","-\frac{363-292 (5 x+3)^2 \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};-\frac{5}{11} (2 x-1)\right)}{39930 (1-2 x)^{3/2} (5 x+3)^2}","\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,"-1/39930*(363 - 292*(3 + 5*x)^2*Hypergeometric2F1[-3/2, 2, -1/2, (-5*(-1 + 2*x))/11])/((1 - 2*x)^(3/2)*(3 + 5*x)^2)","C",1
2196,1,30,96,0.0067467,"\int \frac{1}{(1-2 x)^{5/2} (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]","\frac{8 \, _2F_1\left(-\frac{3}{2},3;-\frac{1}{2};-\frac{5}{11} (2 x-1)\right)}{3993 (1-2 x)^{3/2}}","\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,"(8*Hypergeometric2F1[-3/2, 3, -1/2, (-5*(-1 + 2*x))/11])/(3993*(1 - 2*x)^(3/2))","C",1
2197,1,73,125,0.065485,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x) (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^3),x]","\frac{\frac{35 \left(3766 (5 x+3)^2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+9735 x+5478\right)}{(5 x+3)^2}-143748 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)}{55902 (1-2 x)^{3/2}}","-\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,"(-143748*Hypergeometric2F1[-3/2, 1, -1/2, 3/7 - (6*x)/7] + (35*(5478 + 9735*x + 3766*(3 + 5*x)^2*Hypergeometric2F1[-3/2, 1, -1/2, (-5*(-1 + 2*x))/11]))/(3 + 5*x)^2)/(55902*(1 - 2*x)^(3/2))","C",1
2198,1,78,152,0.0942206,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^3),x]","\frac{-15812280 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+14477050 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+\frac{231 \left(491475 x^2+605870 x+186206\right)}{(3 x+2) (5 x+3)^2}}{391314 (1-2 x)^{3/2}}","-\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,"((231*(186206 + 605870*x + 491475*x^2))/((2 + 3*x)*(3 + 5*x)^2) - 15812280*Hypergeometric2F1[-3/2, 1, -1/2, 3/7 - (6*x)/7] + 14477050*Hypergeometric2F1[-3/2, 1, -1/2, (-5*(-1 + 2*x))/11])/(391314*(1 - 2*x)^(3/2))","C",1
2199,1,83,179,0.1142153,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^3} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^3),x]","\frac{-162075870 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right)+148384250 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+\frac{231 \left(15116400 x^3+28713705 x^2+18152609 x+3819389\right)}{(3 x+2)^2 (5 x+3)^2}}{391314 (1-2 x)^{3/2}}","-\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,"((231*(3819389 + 18152609*x + 28713705*x^2 + 15116400*x^3))/((2 + 3*x)^2*(3 + 5*x)^2) - 162075870*Hypergeometric2F1[-3/2, 1, -1/2, 3/7 - (6*x)/7] + 148384250*Hypergeometric2F1[-3/2, 1, -1/2, (-5*(-1 + 2*x))/11])/(391314*(1 - 2*x)^(3/2))","C",1
2200,1,301,304,3.3673123,"\int \sqrt{a+b x} (A+B x) (d+e x)^{5/2} \, dx","Integrate[Sqrt[a + b*x]*(A + B*x)*(d + e*x)^(5/2),x]","\frac{\sqrt{d+e x} \left(\frac{\left(-\frac{7 a B e}{2}+5 A b e-\frac{3}{2} b B d\right) \left(2 b^5 e^2 (a+b x)^2 (b d-a e)^{3/2} \sqrt{\frac{b (d+e x)}{b d-a e}} \left(15 a^2 e^2-10 a b e (5 d+2 e x)+b^2 \left(59 d^2+68 d e x+24 e^2 x^2\right)\right)+15 b^5 e (a+b x) (b d-a e)^{9/2} \sqrt{\frac{b (d+e x)}{b d-a e}}-15 b^5 \sqrt{e} \sqrt{a+b x} (b d-a e)^5 \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)\right)}{(b d-a e)^{3/2} \sqrt{\frac{b (d+e x)}{b d-a e}}}+192 b^8 B e^2 (a+b x)^2 (d+e x)^3\right)}{960 b^9 e^3 \sqrt{a+b x}}","\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,"(Sqrt[d + e*x]*(192*b^8*B*e^2*(a + b*x)^2*(d + e*x)^3 + (((-3*b*B*d)/2 + 5*A*b*e - (7*a*B*e)/2)*(15*b^5*e*(b*d - a*e)^(9/2)*(a + b*x)*Sqrt[(b*(d + e*x))/(b*d - a*e)] + 2*b^5*e^2*(b*d - a*e)^(3/2)*(a + b*x)^2*Sqrt[(b*(d + e*x))/(b*d - a*e)]*(15*a^2*e^2 - 10*a*b*e*(5*d + 2*e*x) + b^2*(59*d^2 + 68*d*e*x + 24*e^2*x^2)) - 15*b^5*Sqrt[e]*(b*d - a*e)^5*Sqrt[a + b*x]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]]))/((b*d - a*e)^(3/2)*Sqrt[(b*(d + e*x))/(b*d - a*e)])))/(960*b^9*e^3*Sqrt[a + b*x])","A",1
2201,1,266,250,2.2211323,"\int \sqrt{a+b x} (A+B x) (d+e x)^{3/2} \, dx","Integrate[Sqrt[a + b*x]*(A + B*x)*(d + e*x)^(3/2),x]","\frac{\sqrt{b d-a e} \left(\frac{b (d+e x)}{b d-a e}\right)^{3/2} (-5 a B e+8 A b e-3 b B d) \left(2 b^4 e^2 (a+b x)^2 (b d-a e)^{3/2} \sqrt{\frac{b (d+e x)}{b d-a e}} (-3 a e+7 b d+4 b e x)+3 b^4 e (a+b x) (b d-a e)^{7/2} \sqrt{\frac{b (d+e x)}{b d-a e}}-3 b^4 \sqrt{e} \sqrt{a+b x} (b d-a e)^4 \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)\right)+48 b^8 B e^2 (a+b x)^2 (d+e x)^4}{192 b^9 e^3 \sqrt{a+b x} (d+e x)^{3/2}}","\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,"(48*b^8*B*e^2*(a + b*x)^2*(d + e*x)^4 + Sqrt[b*d - a*e]*(-3*b*B*d + 8*A*b*e - 5*a*B*e)*((b*(d + e*x))/(b*d - a*e))^(3/2)*(3*b^4*e*(b*d - a*e)^(7/2)*(a + b*x)*Sqrt[(b*(d + e*x))/(b*d - a*e)] + 2*b^4*e^2*(b*d - a*e)^(3/2)*(a + b*x)^2*Sqrt[(b*(d + e*x))/(b*d - a*e)]*(7*b*d - 3*a*e + 4*b*e*x) - 3*b^4*Sqrt[e]*(b*d - a*e)^4*Sqrt[a + b*x]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]]))/(192*b^9*e^3*Sqrt[a + b*x]*(d + e*x)^(3/2))","A",1
2202,1,201,196,1.2955134,"\int \sqrt{a+b x} (A+B x) \sqrt{d+e x} \, dx","Integrate[Sqrt[a + b*x]*(A + B*x)*Sqrt[d + e*x],x]","\frac{(a+b x)^{3/2} (d+e x)^{3/2} \left(3 B-\frac{9 (a B e-2 A b e+b B d) \left(\sqrt{e} (a+b x) \sqrt{b d-a e} \sqrt{\frac{b (d+e x)}{b d-a e}} (a e+b (d+2 e x))-\sqrt{a+b x} (b d-a e)^2 \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)\right)}{8 e^{3/2} (a+b x)^2 (b d-a e)^{3/2} \left(\frac{b (d+e x)}{b d-a e}\right)^{3/2}}\right)}{9 b e}","-\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,"((a + b*x)^(3/2)*(d + e*x)^(3/2)*(3*B - (9*(b*B*d - 2*A*b*e + a*B*e)*(Sqrt[e]*Sqrt[b*d - a*e]*(a + b*x)*Sqrt[(b*(d + e*x))/(b*d - a*e)]*(a*e + b*(d + 2*e*x)) - (b*d - a*e)^2*Sqrt[a + b*x]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]]))/(8*e^(3/2)*(b*d - a*e)^(3/2)*(a + b*x)^2*((b*(d + e*x))/(b*d - a*e))^(3/2))))/(9*b*e)","A",1
2203,1,185,140,0.7643866,"\int \frac{\sqrt{a+b x} (A+B x)}{\sqrt{d+e x}} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/Sqrt[d + e*x],x]","\frac{\sqrt{d+e x} \left(2 B e^2 (a+b x)^2-\frac{(a B e-4 A b e+3 b B d) \left(e (a+b x) \sqrt{b d-a e} \sqrt{\frac{b (d+e x)}{b d-a e}}-\sqrt{e} \sqrt{a+b x} (b d-a e) \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)\right)}{\sqrt{b d-a e} \sqrt{\frac{b (d+e x)}{b d-a e}}}\right)}{4 b e^3 \sqrt{a+b x}}","\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*x]*(2*B*e^2*(a + b*x)^2 - ((3*b*B*d - 4*A*b*e + a*B*e)*(e*Sqrt[b*d - a*e]*(a + b*x)*Sqrt[(b*(d + e*x))/(b*d - a*e)] - Sqrt[e]*(b*d - a*e)*Sqrt[a + b*x]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]]))/(Sqrt[b*d - a*e]*Sqrt[(b*(d + e*x))/(b*d - a*e)])))/(4*b*e^3*Sqrt[a + b*x])","A",1
2204,1,129,148,0.425554,"\int \frac{\sqrt{a+b x} (A+B x)}{(d+e x)^{3/2}} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/(d + e*x)^(3/2),x]","\frac{\sqrt{a+b x} (-2 A e+3 B d+B e x)}{e^2 \sqrt{d+e x}}-\frac{\sqrt{d+e x} (-a B e-2 A b e+3 b B d) \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)}{e^{5/2} \sqrt{b d-a e} \sqrt{\frac{b (d+e x)}{b d-a e}}}","-\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,"(Sqrt[a + b*x]*(3*B*d - 2*A*e + B*e*x))/(e^2*Sqrt[d + e*x]) - ((3*b*B*d - 2*A*b*e - a*B*e)*Sqrt[d + e*x]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]])/(e^(5/2)*Sqrt[b*d - a*e]*Sqrt[(b*(d + e*x))/(b*d - a*e)])","A",1
2205,1,148,111,1.0309918,"\int \frac{\sqrt{a+b x} (A+B x)}{(d+e x)^{5/2}} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/(d + e*x)^(5/2),x]","\frac{2 \left(\frac{\sqrt{e} \sqrt{a+b x} \left(a e (A e+2 B d+3 B e x)+A b e^2 x-b B d (3 d+4 e x)\right)}{b d-a e}+\frac{3 B (b d-a e)^{3/2} \left(\frac{b (d+e x)}{b d-a e}\right)^{3/2} \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)}{b}\right)}{3 e^{5/2} (d+e x)^{3/2}}","-\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,"(2*((Sqrt[e]*Sqrt[a + b*x]*(A*b*e^2*x - b*B*d*(3*d + 4*e*x) + a*e*(2*B*d + A*e + 3*B*e*x)))/(b*d - a*e) + (3*B*(b*d - a*e)^(3/2)*((b*(d + e*x))/(b*d - a*e))^(3/2)*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]])/b))/(3*e^(5/2)*(d + e*x)^(3/2))","A",1
2206,1,66,95,0.0595114,"\int \frac{\sqrt{a+b x} (A+B x)}{(d+e x)^{7/2}} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/(d + e*x)^(7/2),x]","\frac{2 (a+b x)^{3/2} (A (-3 a e+5 b d+2 b e x)+B (-2 a d-5 a e x+3 b d x))}{15 (d+e x)^{5/2} (b d-a e)^2}","\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,"(2*(a + b*x)^(3/2)*(B*(-2*a*d + 3*b*d*x - 5*a*e*x) + A*(5*b*d - 3*a*e + 2*b*e*x)))/(15*(b*d - a*e)^2*(d + e*x)^(5/2))","A",1
2207,1,135,147,0.1156649,"\int \frac{\sqrt{a+b x} (A+B x)}{(d+e x)^{9/2}} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/(d + e*x)^(9/2),x]","\frac{2 (a+b x)^{3/2} \left(A \left(15 a^2 e^2-6 a b e (7 d+2 e x)+b^2 \left(35 d^2+28 d e x+8 e^2 x^2\right)\right)+B \left(3 a^2 e (2 d+7 e x)-2 a b \left(7 d^2+29 d e x+7 e^2 x^2\right)+3 b^2 d x (7 d+2 e x)\right)\right)}{105 (d+e x)^{7/2} (b d-a e)^3}","\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,"(2*(a + b*x)^(3/2)*(B*(3*b^2*d*x*(7*d + 2*e*x) + 3*a^2*e*(2*d + 7*e*x) - 2*a*b*(7*d^2 + 29*d*e*x + 7*e^2*x^2)) + A*(15*a^2*e^2 - 6*a*b*e*(7*d + 2*e*x) + b^2*(35*d^2 + 28*d*e*x + 8*e^2*x^2))))/(105*(b*d - a*e)^3*(d + e*x)^(7/2))","A",1
2208,1,113,198,0.3520158,"\int \frac{\sqrt{a+b x} (A+B x)}{(d+e x)^{11/2}} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/(d + e*x)^(11/2),x]","\frac{2 (a+b x)^{3/2} \left(105 (B d-A e)-\frac{3 (d+e x) \left(4 b (d+e x) (-3 a e+5 b d+2 b e x)+15 (b d-a e)^2\right) (-3 a B e+2 A b e+b B d)}{(b d-a e)^3}\right)}{945 e (d+e x)^{9/2} (a e-b d)}","\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,"(2*(a + b*x)^(3/2)*(105*(B*d - A*e) - (3*(b*B*d + 2*A*b*e - 3*a*B*e)*(d + e*x)*(15*(b*d - a*e)^2 + 4*b*(d + e*x)*(5*b*d - 3*a*e + 2*b*e*x)))/(b*d - a*e)^3))/(945*e*(-(b*d) + a*e)*(d + e*x)^(9/2))","A",1
2209,1,135,255,0.4282911,"\int \frac{\sqrt{a+b x} (A+B x)}{(d+e x)^{13/2}} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/(d + e*x)^(13/2),x]","\frac{2 (a+b x)^{3/2} \left(315 (B d-A e)-\frac{(d+e x) \left(2 b (d+e x) \left(4 b (d+e x) (-3 a e+5 b d+2 b e x)+15 (b d-a e)^2\right)+35 (b d-a e)^3\right) (-11 a B e+8 A b e+3 b B d)}{(b d-a e)^4}\right)}{3465 e (d+e x)^{11/2} (a e-b d)}","\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,"(2*(a + b*x)^(3/2)*(315*(B*d - A*e) - ((3*b*B*d + 8*A*b*e - 11*a*B*e)*(d + e*x)*(35*(b*d - a*e)^3 + 2*b*(d + e*x)*(15*(b*d - a*e)^2 + 4*b*(d + e*x)*(5*b*d - 3*a*e + 2*b*e*x))))/(b*d - a*e)^4))/(3465*e*(-(b*d) + a*e)*(d + e*x)^(11/2))","A",1
2210,1,160,309,0.3561772,"\int \frac{\sqrt{a+b x} (A+B x)}{(d+e x)^{15/2}} \, dx","Integrate[(Sqrt[a + b*x]*(A + B*x))/(d + e*x)^(15/2),x]","\frac{2 (a+b x)^{3/2} \left(3465 (B d-A e)-\frac{2 (d+e x) \left(8 b (d+e x) \left(2 b (d+e x) \left(4 b (d+e x) (-3 a e+5 b d+2 b e x)+15 (b d-a e)^2\right)+35 (b d-a e)^3\right)+315 (b d-a e)^4\right) \left(-\frac{13 a B e}{2}+5 A b e+\frac{3 b B d}{2}\right)}{(b d-a e)^5}\right)}{45045 e (d+e x)^{13/2} (a e-b d)}","\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,"(2*(a + b*x)^(3/2)*(3465*(B*d - A*e) - (2*((3*b*B*d)/2 + 5*A*b*e - (13*a*B*e)/2)*(d + e*x)*(315*(b*d - a*e)^4 + 8*b*(d + e*x)*(35*(b*d - a*e)^3 + 2*b*(d + e*x)*(15*(b*d - a*e)^2 + 4*b*(d + e*x)*(5*b*d - 3*a*e + 2*b*e*x)))))/(b*d - a*e)^5))/(45045*e*(-(b*d) + a*e)*(d + e*x)^(13/2))","A",1
2211,1,357,358,4.2852598,"\int (a+b x)^{3/2} (A+B x) (d+e x)^{5/2} \, dx","Integrate[(a + b*x)^(3/2)*(A + B*x)*(d + e*x)^(5/2),x]","\frac{(a+b x)^{5/2} \sqrt{d+e x} \left(\frac{\left(-\frac{7 a B e}{2}+6 A b e-\frac{5}{2} b B d\right) \left(8 b^6 e^3 (a+b x)^3 (b d-a e)^{3/2} \sqrt{\frac{b (d+e x)}{b d-a e}} \left(5 a^2 e^2-10 a b e (2 d+e x)+b^2 \left(31 d^2+42 d e x+16 e^2 x^2\right)\right)+5 b^6 \sqrt{e} \left(2 e^{3/2} (a+b x)^2 (b d-a e)^{9/2} \sqrt{\frac{b (d+e x)}{b d-a e}}-3 \sqrt{e} (a+b x) (b d-a e)^{11/2} \sqrt{\frac{b (d+e x)}{b d-a e}}+3 \sqrt{a+b x} (b d-a e)^6 \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)\right)\right)}{128 b^6 e^3 (a+b x)^3 (b d-a e)^{3/2} \sqrt{\frac{b (d+e x)}{b d-a e}}}+5 b^3 B (d+e x)^3\right)}{30 b^4 e}","-\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,"((a + b*x)^(5/2)*Sqrt[d + e*x]*(5*b^3*B*(d + e*x)^3 + (((-5*b*B*d)/2 + 6*A*b*e - (7*a*B*e)/2)*(8*b^6*e^3*(b*d - a*e)^(3/2)*(a + b*x)^3*Sqrt[(b*(d + e*x))/(b*d - a*e)]*(5*a^2*e^2 - 10*a*b*e*(2*d + e*x) + b^2*(31*d^2 + 42*d*e*x + 16*e^2*x^2)) + 5*b^6*Sqrt[e]*(-3*Sqrt[e]*(b*d - a*e)^(11/2)*(a + b*x)*Sqrt[(b*(d + e*x))/(b*d - a*e)] + 2*e^(3/2)*(b*d - a*e)^(9/2)*(a + b*x)^2*Sqrt[(b*(d + e*x))/(b*d - a*e)] + 3*(b*d - a*e)^6*Sqrt[a + b*x]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]])))/(128*b^6*e^3*(b*d - a*e)^(3/2)*(a + b*x)^3*Sqrt[(b*(d + e*x))/(b*d - a*e)])))/(30*b^4*e)","A",1
2212,1,313,304,3.207219,"\int (a+b x)^{3/2} (A+B x) (d+e x)^{3/2} \, dx","Integrate[(a + b*x)^(3/2)*(A + B*x)*(d + e*x)^(3/2),x]","\frac{128 b^9 B e^3 (a+b x)^3 (d+e x)^4-5 \sqrt{b d-a e} \left(\frac{b (d+e x)}{b d-a e}\right)^{3/2} (a B e-2 A b e+b B d) \left(8 b^5 e^3 (a+b x)^3 (b d-a e)^{3/2} \sqrt{\frac{b (d+e x)}{b d-a e}} (-a e+3 b d+2 b e x)+2 b^5 e^2 (a+b x)^2 (b d-a e)^{7/2} \sqrt{\frac{b (d+e x)}{b d-a e}}-3 b^5 e (a+b x) (b d-a e)^{9/2} \sqrt{\frac{b (d+e x)}{b d-a e}}+3 b^5 \sqrt{e} \sqrt{a+b x} (b d-a e)^5 \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)\right)}{640 b^{10} e^4 \sqrt{a+b x} (d+e x)^{3/2}}","\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,"(128*b^9*B*e^3*(a + b*x)^3*(d + e*x)^4 - 5*Sqrt[b*d - a*e]*(b*B*d - 2*A*b*e + a*B*e)*((b*(d + e*x))/(b*d - a*e))^(3/2)*(-3*b^5*e*(b*d - a*e)^(9/2)*(a + b*x)*Sqrt[(b*(d + e*x))/(b*d - a*e)] + 2*b^5*e^2*(b*d - a*e)^(7/2)*(a + b*x)^2*Sqrt[(b*(d + e*x))/(b*d - a*e)] + 8*b^5*e^3*(b*d - a*e)^(3/2)*(a + b*x)^3*Sqrt[(b*(d + e*x))/(b*d - a*e)]*(3*b*d - a*e + 2*b*e*x) + 3*b^5*Sqrt[e]*(b*d - a*e)^5*Sqrt[a + b*x]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]]))/(640*b^10*e^4*Sqrt[a + b*x]*(d + e*x)^(3/2))","A",1
2213,1,308,250,2.2398678,"\int (a+b x)^{3/2} (A+B x) \sqrt{d+e x} \, dx","Integrate[(a + b*x)^(3/2)*(A + B*x)*Sqrt[d + e*x],x]","\frac{(a+b x)^{5/2} (d+e x)^{3/2} \left(\frac{5 (-3 a B e+8 A b e-5 b B d) \left(8 b^3 e^3 (a+b x)^3 \sqrt{b d-a e} \sqrt{\frac{b (d+e x)}{b d-a e}}-b (b d-a e) \left(-2 b^2 e^2 (a+b x)^2 \sqrt{b d-a e} \sqrt{\frac{b (d+e x)}{b d-a e}}+3 b^2 e (a+b x) (b d-a e)^{3/2} \sqrt{\frac{b (d+e x)}{b d-a e}}-3 b^2 \sqrt{e} \sqrt{a+b x} (b d-a e)^2 \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)\right)\right)}{48 b^3 e^3 (a+b x)^3 (b d-a e)^{3/2} \left(\frac{b (d+e x)}{b d-a e}\right)^{3/2}}+5 B\right)}{20 b e}","-\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,"((a + b*x)^(5/2)*(d + e*x)^(3/2)*(5*B + (5*(-5*b*B*d + 8*A*b*e - 3*a*B*e)*(8*b^3*e^3*Sqrt[b*d - a*e]*(a + b*x)^3*Sqrt[(b*(d + e*x))/(b*d - a*e)] - b*(b*d - a*e)*(3*b^2*e*(b*d - a*e)^(3/2)*(a + b*x)*Sqrt[(b*(d + e*x))/(b*d - a*e)] - 2*b^2*e^2*Sqrt[b*d - a*e]*(a + b*x)^2*Sqrt[(b*(d + e*x))/(b*d - a*e)] - 3*b^2*Sqrt[e]*(b*d - a*e)^2*Sqrt[a + b*x]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]])))/(48*b^3*e^3*(b*d - a*e)^(3/2)*(a + b*x)^3*((b*(d + e*x))/(b*d - a*e))^(3/2))))/(20*b*e)","A",1
2214,1,201,193,1.1396504,"\int \frac{(a+b x)^{3/2} (A+B x)}{\sqrt{d+e x}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/Sqrt[d + e*x],x]","\frac{\sqrt{d+e x} \left(8 B e^3 (a+b x)^3-\frac{(a B e-6 A b e+5 b B d) \left(e (a+b x) \sqrt{b d-a e} \sqrt{\frac{b (d+e x)}{b d-a e}} (5 a e-3 b d+2 b e x)+3 \sqrt{e} \sqrt{a+b x} (b d-a e)^2 \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)\right)}{\sqrt{b d-a e} \sqrt{\frac{b (d+e x)}{b d-a e}}}\right)}{24 b e^4 \sqrt{a+b x}}","-\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,"(Sqrt[d + e*x]*(8*B*e^3*(a + b*x)^3 - ((5*b*B*d - 6*A*b*e + a*B*e)*(e*Sqrt[b*d - a*e]*(a + b*x)*Sqrt[(b*(d + e*x))/(b*d - a*e)]*(-3*b*d + 5*a*e + 2*b*e*x) + 3*Sqrt[e]*(b*d - a*e)^2*Sqrt[a + b*x]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]]))/(Sqrt[b*d - a*e]*Sqrt[(b*(d + e*x))/(b*d - a*e)])))/(24*b*e^4*Sqrt[a + b*x])","A",1
2215,1,168,202,0.7448815,"\int \frac{(a+b x)^{3/2} (A+B x)}{(d+e x)^{3/2}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(3/2),x]","\frac{\sqrt{e} \sqrt{a+b x} \left(a e (-8 A e+13 B d+5 B e x)+4 A b e (3 d+e x)+b B \left(-15 d^2-5 d e x+2 e^2 x^2\right)\right)+\frac{3 (b d-a e)^{3/2} \sqrt{\frac{b (d+e x)}{b d-a e}} (-a B e-4 A b e+5 b B d) \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)}{b}}{4 e^{7/2} \sqrt{d+e x}}","\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,"(Sqrt[e]*Sqrt[a + b*x]*(4*A*b*e*(3*d + e*x) + a*e*(13*B*d - 8*A*e + 5*B*e*x) + b*B*(-15*d^2 - 5*d*e*x + 2*e^2*x^2)) + (3*(b*d - a*e)^(3/2)*(5*b*B*d - 4*A*b*e - a*B*e)*Sqrt[(b*(d + e*x))/(b*d - a*e)]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]])/b)/(4*e^(7/2)*Sqrt[d + e*x])","A",1
2216,1,113,202,0.1793026,"\int \frac{(a+b x)^{3/2} (A+B x)}{(d+e x)^{5/2}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(5/2),x]","\frac{2 (a+b x)^{5/2} \left(-\frac{\left(\frac{b (d+e x)}{b d-a e}\right)^{3/2} (-3 a B e-2 A b e+5 b B d) \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};\frac{e (a+b x)}{a e-b d}\right)}{b}-5 A e+5 B d\right)}{15 e (d+e x)^{3/2} (a e-b d)}","-\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,"(2*(a + b*x)^(5/2)*(5*B*d - 5*A*e - ((5*b*B*d - 2*A*b*e - 3*a*B*e)*((b*(d + e*x))/(b*d - a*e))^(3/2)*Hypergeometric2F1[3/2, 5/2, 7/2, (e*(a + b*x))/(-(b*d) + a*e)])/b))/(15*e*(-(b*d) + a*e)*(d + e*x)^(3/2))","C",1
2217,1,173,138,1.4856259,"\int \frac{(a+b x)^{3/2} (A+B x)}{(d+e x)^{7/2}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(7/2),x]","\frac{2 \left(e^3 (a+b x)^3 (A e-B d)+\frac{5}{3} B e (a+b x) (d+e x) (a e-b d) (a e+3 b d+4 b e x)+\frac{5 B \sqrt{e} \sqrt{a+b x} (b d-a e)^{7/2} \left(\frac{b (d+e x)}{b d-a e}\right)^{5/2} \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)}{b}\right)}{5 e^4 \sqrt{a+b x} (d+e x)^{5/2} (b d-a e)}","-\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,"(2*(e^3*(-(B*d) + A*e)*(a + b*x)^3 + (5*B*e*(-(b*d) + a*e)*(a + b*x)*(d + e*x)*(3*b*d + a*e + 4*b*e*x))/3 + (5*B*Sqrt[e]*(b*d - a*e)^(7/2)*Sqrt[a + b*x]*((b*(d + e*x))/(b*d - a*e))^(5/2)*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]])/b))/(5*e^4*(b*d - a*e)*Sqrt[a + b*x]*(d + e*x)^(5/2))","A",1
2218,1,66,95,0.0749591,"\int \frac{(a+b x)^{3/2} (A+B x)}{(d+e x)^{9/2}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(9/2),x]","\frac{2 (a+b x)^{5/2} (A (-5 a e+7 b d+2 b e x)+B (-2 a d-7 a e x+5 b d x))}{35 (d+e x)^{7/2} (b d-a e)^2}","\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,"(2*(a + b*x)^(5/2)*(B*(-2*a*d + 5*b*d*x - 7*a*e*x) + A*(7*b*d - 5*a*e + 2*b*e*x)))/(35*(b*d - a*e)^2*(d + e*x)^(7/2))","A",1
2219,1,135,147,0.1275587,"\int \frac{(a+b x)^{3/2} (A+B x)}{(d+e x)^{11/2}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(11/2),x]","\frac{2 (a+b x)^{5/2} \left(A \left(35 a^2 e^2-10 a b e (9 d+2 e x)+b^2 \left(63 d^2+36 d e x+8 e^2 x^2\right)\right)+B \left(5 a^2 e (2 d+9 e x)-2 a b \left(9 d^2+53 d e x+9 e^2 x^2\right)+5 b^2 d x (9 d+2 e x)\right)\right)}{315 (d+e x)^{9/2} (b d-a e)^3}","\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,"(2*(a + b*x)^(5/2)*(A*(35*a^2*e^2 - 10*a*b*e*(9*d + 2*e*x) + b^2*(63*d^2 + 36*d*e*x + 8*e^2*x^2)) + B*(5*b^2*d*x*(9*d + 2*e*x) + 5*a^2*e*(2*d + 9*e*x) - 2*a*b*(9*d^2 + 53*d*e*x + 9*e^2*x^2))))/(315*(b*d - a*e)^3*(d + e*x)^(9/2))","A",1
2220,1,114,201,0.3910869,"\int \frac{(a+b x)^{3/2} (A+B x)}{(d+e x)^{13/2}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(13/2),x]","\frac{2 (a+b x)^{5/2} \left(315 (B d-A e)-\frac{(d+e x) \left(4 b (d+e x) (-5 a e+7 b d+2 b e x)+35 (b d-a e)^2\right) (-11 a B e+6 A b e+5 b B d)}{(b d-a e)^3}\right)}{3465 e (d+e x)^{11/2} (a e-b d)}","\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,"(2*(a + b*x)^(5/2)*(315*(B*d - A*e) - ((5*b*B*d + 6*A*b*e - 11*a*B*e)*(d + e*x)*(35*(b*d - a*e)^2 + 4*b*(d + e*x)*(7*b*d - 5*a*e + 2*b*e*x)))/(b*d - a*e)^3))/(3465*e*(-(b*d) + a*e)*(d + e*x)^(11/2))","A",1
2221,1,135,255,0.4847975,"\int \frac{(a+b x)^{3/2} (A+B x)}{(d+e x)^{15/2}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(15/2),x]","\frac{2 (a+b x)^{5/2} \left(1155 (B d-A e)-\frac{(d+e x) \left(2 b (d+e x) \left(4 b (d+e x) (-5 a e+7 b d+2 b e x)+35 (b d-a e)^2\right)+105 (b d-a e)^3\right) (-13 a B e+8 A b e+5 b B d)}{(b d-a e)^4}\right)}{15015 e (d+e x)^{13/2} (a e-b d)}","\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,"(2*(a + b*x)^(5/2)*(1155*(B*d - A*e) - ((5*b*B*d + 8*A*b*e - 13*a*B*e)*(d + e*x)*(105*(b*d - a*e)^3 + 2*b*(d + e*x)*(35*(b*d - a*e)^2 + 4*b*(d + e*x)*(7*b*d - 5*a*e + 2*b*e*x))))/(b*d - a*e)^4))/(15015*e*(-(b*d) + a*e)*(d + e*x)^(13/2))","A",1
2222,1,155,304,0.4076475,"\int \frac{(a+b x)^{3/2} (A+B x)}{(d+e x)^{17/2}} \, dx","Integrate[((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(17/2),x]","\frac{2 (a+b x)^{5/2} \left(15015 (B d-A e)-\frac{5 (d+e x) \left(8 b (d+e x) \left(2 b (d+e x) \left(4 b (d+e x) (-5 a e+7 b d+2 b e x)+35 (b d-a e)^2\right)+105 (b d-a e)^3\right)+1155 (b d-a e)^4\right) (-3 a B e+2 A b e+b B d)}{(b d-a e)^5}\right)}{225225 e (d+e x)^{15/2} (a e-b d)}","\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,"(2*(a + b*x)^(5/2)*(15015*(B*d - A*e) - (5*(b*B*d + 2*A*b*e - 3*a*B*e)*(d + e*x)*(1155*(b*d - a*e)^4 + 8*b*(d + e*x)*(105*(b*d - a*e)^3 + 2*b*(d + e*x)*(35*(b*d - a*e)^2 + 4*b*(d + e*x)*(7*b*d - 5*a*e + 2*b*e*x)))))/(b*d - a*e)^5))/(225225*e*(-(b*d) + a*e)*(d + e*x)^(15/2))","A",1
2223,1,388,412,5.7273595,"\int (a+b x)^{5/2} (A+B x) (d+e x)^{5/2} \, dx","Integrate[(a + b*x)^(5/2)*(A + B*x)*(d + e*x)^(5/2),x]","\frac{B (a+b x)^{7/2} (d+e x)^{7/2}}{7 b e}-\frac{\sqrt{b d-a e} \left(\frac{b (d+e x)}{b d-a e}\right)^{3/2} (a B e-2 A b e+b B d) \left(16 e^{7/2} (a+b x)^4 (b d-a e)^{3/2} \sqrt{\frac{b (d+e x)}{b d-a e}} \left(3 a^2 e^2-2 a b e (7 d+4 e x)+b^2 \left(27 d^2+40 d e x+16 e^2 x^2\right)\right)-10 e^{3/2} (a+b x)^2 (b d-a e)^{11/2} \sqrt{\frac{b (d+e x)}{b d-a e}}+8 e^{5/2} (a+b x)^3 (b d-a e)^{9/2} \sqrt{\frac{b (d+e x)}{b d-a e}}+15 \sqrt{e} (a+b x) (b d-a e)^{13/2} \sqrt{\frac{b (d+e x)}{b d-a e}}-15 \sqrt{a+b x} (b d-a e)^7 \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)\right)}{3072 b^6 e^{9/2} \sqrt{a+b x} (d+e x)^{3/2}}","-\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,"(B*(a + b*x)^(7/2)*(d + e*x)^(7/2))/(7*b*e) - (Sqrt[b*d - a*e]*(b*B*d - 2*A*b*e + a*B*e)*((b*(d + e*x))/(b*d - a*e))^(3/2)*(15*Sqrt[e]*(b*d - a*e)^(13/2)*(a + b*x)*Sqrt[(b*(d + e*x))/(b*d - a*e)] - 10*e^(3/2)*(b*d - a*e)^(11/2)*(a + b*x)^2*Sqrt[(b*(d + e*x))/(b*d - a*e)] + 8*e^(5/2)*(b*d - a*e)^(9/2)*(a + b*x)^3*Sqrt[(b*(d + e*x))/(b*d - a*e)] + 16*e^(7/2)*(b*d - a*e)^(3/2)*(a + b*x)^4*Sqrt[(b*(d + e*x))/(b*d - a*e)]*(3*a^2*e^2 - 2*a*b*e*(7*d + 4*e*x) + b^2*(27*d^2 + 40*d*e*x + 16*e^2*x^2)) - 15*(b*d - a*e)^7*Sqrt[a + b*x]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]]))/(3072*b^6*e^(9/2)*Sqrt[a + b*x]*(d + e*x)^(3/2))","A",1
2224,1,360,358,4.6135502,"\int (a+b x)^{5/2} (A+B x) (d+e x)^{3/2} \, dx","Integrate[(a + b*x)^(5/2)*(A + B*x)*(d + e*x)^(3/2),x]","\frac{\sqrt{b d-a e} \left(\frac{b (d+e x)}{b d-a e}\right)^{3/2} \left(-\frac{5 a B e}{2}+6 A b e-\frac{7}{2} b B d\right) \left(-10 e^{3/2} (a+b x)^2 (b d-a e)^{9/2} \sqrt{\frac{b (d+e x)}{b d-a e}}+8 e^{5/2} (a+b x)^3 (b d-a e)^{7/2} \sqrt{\frac{b (d+e x)}{b d-a e}}+16 e^{7/2} (a+b x)^4 (b d-a e)^{3/2} \sqrt{\frac{b (d+e x)}{b d-a e}} (-3 a e+11 b d+8 b e x)+15 \sqrt{e} (a+b x) (b d-a e)^{11/2} \sqrt{\frac{b (d+e x)}{b d-a e}}-15 \sqrt{a+b x} (b d-a e)^6 \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)\right)+640 b^4 B e^{7/2} (a+b x)^4 (d+e x)^4}{3840 b^5 e^{9/2} \sqrt{a+b x} (d+e x)^{3/2}}","\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,"(640*b^4*B*e^(7/2)*(a + b*x)^4*(d + e*x)^4 + Sqrt[b*d - a*e]*((-7*b*B*d)/2 + 6*A*b*e - (5*a*B*e)/2)*((b*(d + e*x))/(b*d - a*e))^(3/2)*(15*Sqrt[e]*(b*d - a*e)^(11/2)*(a + b*x)*Sqrt[(b*(d + e*x))/(b*d - a*e)] - 10*e^(3/2)*(b*d - a*e)^(9/2)*(a + b*x)^2*Sqrt[(b*(d + e*x))/(b*d - a*e)] + 8*e^(5/2)*(b*d - a*e)^(7/2)*(a + b*x)^3*Sqrt[(b*(d + e*x))/(b*d - a*e)] + 16*e^(7/2)*(b*d - a*e)^(3/2)*(a + b*x)^4*Sqrt[(b*(d + e*x))/(b*d - a*e)]*(11*b*d - 3*a*e + 8*b*e*x) - 15*(b*d - a*e)^6*Sqrt[a + b*x]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]]))/(3840*b^5*e^(9/2)*Sqrt[a + b*x]*(d + e*x)^(3/2))","A",1
2225,1,359,304,3.4618025,"\int (a+b x)^{5/2} (A+B x) \sqrt{d+e x} \, dx","Integrate[(a + b*x)^(5/2)*(A + B*x)*Sqrt[d + e*x],x]","\frac{(a+b x)^{7/2} (d+e x)^{3/2} \left(\frac{7 \left(-\frac{3 a B e}{2}+5 A b e-\frac{7}{2} b B d\right) \left(48 b^4 e^4 (a+b x)^4 \sqrt{b d-a e} \sqrt{\frac{b (d+e x)}{b d-a e}}+b (b d-a e) \left(8 b^3 e^3 (a+b x)^3 \sqrt{b d-a e} \sqrt{\frac{b (d+e x)}{b d-a e}}-10 b^3 e^2 (a+b x)^2 (b d-a e)^{3/2} \sqrt{\frac{b (d+e x)}{b d-a e}}+15 b^3 e (a+b x) (b d-a e)^{5/2} \sqrt{\frac{b (d+e x)}{b d-a e}}-15 b^3 \sqrt{e} \sqrt{a+b x} (b d-a e)^3 \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)\right)\right)}{192 b^4 e^4 (a+b x)^4 (b d-a e)^{3/2} \left(\frac{b (d+e x)}{b d-a e}\right)^{3/2}}+7 B\right)}{35 b e}","\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,"((a + b*x)^(7/2)*(d + e*x)^(3/2)*(7*B + (7*((-7*b*B*d)/2 + 5*A*b*e - (3*a*B*e)/2)*(48*b^4*e^4*Sqrt[b*d - a*e]*(a + b*x)^4*Sqrt[(b*(d + e*x))/(b*d - a*e)] + b*(b*d - a*e)*(15*b^3*e*(b*d - a*e)^(5/2)*(a + b*x)*Sqrt[(b*(d + e*x))/(b*d - a*e)] - 10*b^3*e^2*(b*d - a*e)^(3/2)*(a + b*x)^2*Sqrt[(b*(d + e*x))/(b*d - a*e)] + 8*b^3*e^3*Sqrt[b*d - a*e]*(a + b*x)^3*Sqrt[(b*(d + e*x))/(b*d - a*e)] - 15*b^3*Sqrt[e]*(b*d - a*e)^3*Sqrt[a + b*x]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]])))/(192*b^4*e^4*(b*d - a*e)^(3/2)*(a + b*x)^4*((b*(d + e*x))/(b*d - a*e))^(3/2))))/(35*b*e)","A",1
2226,1,297,246,1.4727092,"\int \frac{(a+b x)^{5/2} (A+B x)}{\sqrt{d+e x}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/Sqrt[d + e*x],x]","\frac{\sqrt{d+e x} \left(\frac{b (-a B e+8 A b e-7 b B d) \left(8 b^3 e^3 (a+b x)^3 \sqrt{b d-a e} \sqrt{\frac{b (d+e x)}{b d-a e}}-10 b^3 e^2 (a+b x)^2 (b d-a e)^{3/2} \sqrt{\frac{b (d+e x)}{b d-a e}}+15 b^3 e (a+b x) (b d-a e)^{5/2} \sqrt{\frac{b (d+e x)}{b d-a e}}-15 b^3 \sqrt{e} \sqrt{a+b x} (b d-a e)^3 \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)\right)}{3 \sqrt{b d-a e} \sqrt{\frac{b (d+e x)}{b d-a e}}}+16 b^4 B e^4 (a+b x)^4\right)}{64 b^5 e^5 \sqrt{a+b x}}","\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,"(Sqrt[d + e*x]*(16*b^4*B*e^4*(a + b*x)^4 + (b*(-7*b*B*d + 8*A*b*e - a*B*e)*(15*b^3*e*(b*d - a*e)^(5/2)*(a + b*x)*Sqrt[(b*(d + e*x))/(b*d - a*e)] - 10*b^3*e^2*(b*d - a*e)^(3/2)*(a + b*x)^2*Sqrt[(b*(d + e*x))/(b*d - a*e)] + 8*b^3*e^3*Sqrt[b*d - a*e]*(a + b*x)^3*Sqrt[(b*(d + e*x))/(b*d - a*e)] - 15*b^3*Sqrt[e]*(b*d - a*e)^3*Sqrt[a + b*x]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]]))/(3*Sqrt[b*d - a*e]*Sqrt[(b*(d + e*x))/(b*d - a*e)])))/(64*b^5*e^5*Sqrt[a + b*x])","A",1
2227,1,309,253,1.5857277,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{3/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(3/2),x]","\frac{\frac{\sqrt{b d-a e} \sqrt{\frac{b (d+e x)}{b d-a e}} (a B e+6 A b e-7 b B d) \left(8 b^3 e^3 (a+b x)^3 \sqrt{b d-a e} \sqrt{\frac{b (d+e x)}{b d-a e}}-10 b^3 e^2 (a+b x)^2 (b d-a e)^{3/2} \sqrt{\frac{b (d+e x)}{b d-a e}}+15 b^3 e (a+b x) (b d-a e)^{5/2} \sqrt{\frac{b (d+e x)}{b d-a e}}-15 b^3 \sqrt{e} \sqrt{a+b x} (b d-a e)^3 \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)\right)}{3 b^4}+16 e^4 (a+b x)^4 (B d-A e)}{8 e^5 \sqrt{a+b x} \sqrt{d+e x} (a e-b d)}","-\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,"(16*e^4*(B*d - A*e)*(a + b*x)^4 + (Sqrt[b*d - a*e]*(-7*b*B*d + 6*A*b*e + a*B*e)*Sqrt[(b*(d + e*x))/(b*d - a*e)]*(15*b^3*e*(b*d - a*e)^(5/2)*(a + b*x)*Sqrt[(b*(d + e*x))/(b*d - a*e)] - 10*b^3*e^2*(b*d - a*e)^(3/2)*(a + b*x)^2*Sqrt[(b*(d + e*x))/(b*d - a*e)] + 8*b^3*e^3*Sqrt[b*d - a*e]*(a + b*x)^3*Sqrt[(b*(d + e*x))/(b*d - a*e)] - 15*b^3*Sqrt[e]*(b*d - a*e)^3*Sqrt[a + b*x]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]]))/(3*b^4))/(8*e^5*(-(b*d) + a*e)*Sqrt[a + b*x]*Sqrt[d + e*x])","A",1
2228,1,113,257,0.2032678,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{5/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(5/2),x]","\frac{2 (a+b x)^{7/2} \left(-\frac{\left(\frac{b (d+e x)}{b d-a e}\right)^{3/2} (-3 a B e-4 A b e+7 b B d) \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};\frac{e (a+b x)}{a e-b d}\right)}{b}-7 A e+7 B d\right)}{21 e (d+e x)^{3/2} (a e-b d)}","\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,"(2*(a + b*x)^(7/2)*(7*B*d - 7*A*e - ((7*b*B*d - 4*A*b*e - 3*a*B*e)*((b*(d + e*x))/(b*d - a*e))^(3/2)*Hypergeometric2F1[3/2, 7/2, 9/2, (e*(a + b*x))/(-(b*d) + a*e)])/b))/(21*e*(-(b*d) + a*e)*(d + e*x)^(3/2))","C",1
2229,1,113,256,0.2383089,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{7/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(7/2),x]","\frac{2 (a+b x)^{7/2} \left(-\frac{\left(\frac{b (d+e x)}{b d-a e}\right)^{5/2} (-5 a B e-2 A b e+7 b B d) \, _2F_1\left(\frac{5}{2},\frac{7}{2};\frac{9}{2};\frac{e (a+b x)}{a e-b d}\right)}{b}-7 A e+7 B d\right)}{35 e (d+e x)^{5/2} (a e-b d)}","-\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,"(2*(a + b*x)^(7/2)*(7*B*d - 7*A*e - ((7*b*B*d - 2*A*b*e - 5*a*B*e)*((b*(d + e*x))/(b*d - a*e))^(5/2)*Hypergeometric2F1[5/2, 7/2, 9/2, (e*(a + b*x))/(-(b*d) + a*e)])/b))/(35*e*(-(b*d) + a*e)*(d + e*x)^(5/2))","C",1
2230,1,222,167,2.7856849,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{9/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(9/2),x]","\frac{2 \left(e^4 (a+b x)^4 (A e-B d)-7 b^2 B e (a+b x) (d+e x)^3 (b d-a e)+\frac{7}{5} B e^3 (a+b x)^3 (d+e x) (a e-b d)-\frac{7}{3} b B e^2 (a+b x)^2 (d+e x)^2 (b d-a e)+\frac{7 B \sqrt{e} \sqrt{a+b x} (b d-a e)^{9/2} \left(\frac{b (d+e x)}{b d-a e}\right)^{7/2} \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)}{b}\right)}{7 e^5 \sqrt{a+b x} (d+e x)^{7/2} (b d-a e)}","-\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,"(2*(e^4*(-(B*d) + A*e)*(a + b*x)^4 + (7*B*e^3*(-(b*d) + a*e)*(a + b*x)^3*(d + e*x))/5 - (7*b*B*e^2*(b*d - a*e)*(a + b*x)^2*(d + e*x)^2)/3 - 7*b^2*B*e*(b*d - a*e)*(a + b*x)*(d + e*x)^3 + (7*B*Sqrt[e]*(b*d - a*e)^(9/2)*Sqrt[a + b*x]*((b*(d + e*x))/(b*d - a*e))^(7/2)*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]])/b))/(7*e^5*(b*d - a*e)*Sqrt[a + b*x]*(d + e*x)^(7/2))","A",1
2231,1,66,95,0.0822227,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{11/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(11/2),x]","\frac{2 (a+b x)^{7/2} (A (-7 a e+9 b d+2 b e x)+B (-2 a d-9 a e x+7 b d x))}{63 (d+e x)^{9/2} (b d-a e)^2}","\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,"(2*(a + b*x)^(7/2)*(B*(-2*a*d + 7*b*d*x - 9*a*e*x) + A*(9*b*d - 7*a*e + 2*b*e*x)))/(63*(b*d - a*e)^2*(d + e*x)^(9/2))","A",1
2232,1,135,147,0.1446056,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{13/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(13/2),x]","\frac{2 (a+b x)^{7/2} \left(A \left(63 a^2 e^2-14 a b e (11 d+2 e x)+b^2 \left(99 d^2+44 d e x+8 e^2 x^2\right)\right)+B \left(7 a^2 e (2 d+11 e x)-2 a b \left(11 d^2+85 d e x+11 e^2 x^2\right)+7 b^2 d x (11 d+2 e x)\right)\right)}{693 (d+e x)^{11/2} (b d-a e)^3}","\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,"(2*(a + b*x)^(7/2)*(A*(63*a^2*e^2 - 14*a*b*e*(11*d + 2*e*x) + b^2*(99*d^2 + 44*d*e*x + 8*e^2*x^2)) + B*(7*b^2*d*x*(11*d + 2*e*x) + 7*a^2*e*(2*d + 11*e*x) - 2*a*b*(11*d^2 + 85*d*e*x + 11*e^2*x^2))))/(693*(b*d - a*e)^3*(d + e*x)^(11/2))","A",1
2233,1,114,201,0.4094922,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{15/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(15/2),x]","\frac{2 (a+b x)^{7/2} \left(693 (B d-A e)-\frac{(d+e x) \left(4 b (d+e x) (-7 a e+9 b d+2 b e x)+63 (b d-a e)^2\right) (-13 a B e+6 A b e+7 b B d)}{(b d-a e)^3}\right)}{9009 e (d+e x)^{13/2} (a e-b d)}","\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,"(2*(a + b*x)^(7/2)*(693*(B*d - A*e) - ((7*b*B*d + 6*A*b*e - 13*a*B*e)*(d + e*x)*(63*(b*d - a*e)^2 + 4*b*(d + e*x)*(9*b*d - 7*a*e + 2*b*e*x)))/(b*d - a*e)^3))/(9009*e*(-(b*d) + a*e)*(d + e*x)^(13/2))","A",1
2234,1,135,255,0.5249319,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{17/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(17/2),x]","\frac{2 (a+b x)^{7/2} \left(3003 (B d-A e)-\frac{(d+e x) \left(2 b (d+e x) \left(4 b (d+e x) (-7 a e+9 b d+2 b e x)+63 (b d-a e)^2\right)+231 (b d-a e)^3\right) (-15 a B e+8 A b e+7 b B d)}{(b d-a e)^4}\right)}{45045 e (d+e x)^{15/2} (a e-b d)}","\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,"(2*(a + b*x)^(7/2)*(3003*(B*d - A*e) - ((7*b*B*d + 8*A*b*e - 15*a*B*e)*(d + e*x)*(231*(b*d - a*e)^3 + 2*b*(d + e*x)*(63*(b*d - a*e)^2 + 4*b*(d + e*x)*(9*b*d - 7*a*e + 2*b*e*x))))/(b*d - a*e)^4))/(45045*e*(-(b*d) + a*e)*(d + e*x)^(15/2))","A",1
2235,1,160,309,0.4216317,"\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{19/2}} \, dx","Integrate[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(19/2),x]","\frac{2 (a+b x)^{7/2} \left(45045 (B d-A e)-\frac{2 (d+e x) \left(8 b (d+e x) \left(2 b (d+e x) \left(4 b (d+e x) (-7 a e+9 b d+2 b e x)+63 (b d-a e)^2\right)+231 (b d-a e)^3\right)+3003 (b d-a e)^4\right) \left(-\frac{17 a B e}{2}+5 A b e+\frac{7 b B d}{2}\right)}{(b d-a e)^5}\right)}{765765 e (d+e x)^{17/2} (a e-b d)}","\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,"(2*(a + b*x)^(7/2)*(45045*(B*d - A*e) - (2*((7*b*B*d)/2 + 5*A*b*e - (17*a*B*e)/2)*(d + e*x)*(3003*(b*d - a*e)^4 + 8*b*(d + e*x)*(231*(b*d - a*e)^3 + 2*b*(d + e*x)*(63*(b*d - a*e)^2 + 4*b*(d + e*x)*(9*b*d - 7*a*e + 2*b*e*x)))))/(b*d - a*e)^5))/(765765*e*(-(b*d) + a*e)*(d + e*x)^(17/2))","A",1
2236,1,210,246,1.5830339,"\int \frac{(A+B x) (d+e x)^{5/2}}{\sqrt{a+b x}} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/Sqrt[a + b*x],x]","\frac{\sqrt{d+e x} \left(48 b^3 B \sqrt{e} \sqrt{a+b x} (d+e x)^3-\frac{(7 a B e-8 A b e+b B d) \left(\sqrt{e} \sqrt{a+b x} \sqrt{\frac{b (d+e x)}{b d-a e}} \left(15 a^2 e^2-10 a b e (4 d+e x)+b^2 \left(33 d^2+26 d e x+8 e^2 x^2\right)\right)+15 (b d-a e)^{5/2} \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)\right)}{\sqrt{\frac{b (d+e x)}{b d-a e}}}\right)}{192 b^4 e^{3/2}}","-\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,"(Sqrt[d + e*x]*(48*b^3*B*Sqrt[e]*Sqrt[a + b*x]*(d + e*x)^3 - ((b*B*d - 8*A*b*e + 7*a*B*e)*(Sqrt[e]*Sqrt[a + b*x]*Sqrt[(b*(d + e*x))/(b*d - a*e)]*(15*a^2*e^2 - 10*a*b*e*(4*d + e*x) + b^2*(33*d^2 + 26*d*e*x + 8*e^2*x^2)) + 15*(b*d - a*e)^(5/2)*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]]))/Sqrt[(b*(d + e*x))/(b*d - a*e)]))/(192*b^4*e^(3/2))","A",1
2237,1,182,193,0.6994448,"\int \frac{(A+B x) (d+e x)^{3/2}}{\sqrt{a+b x}} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/Sqrt[a + b*x],x]","\frac{\sqrt{d+e x} \left(\sqrt{e} \sqrt{a+b x} \left(15 a^2 B e^2-2 a b e (9 A e+11 B d+5 B e x)+b^2 \left(6 A e (5 d+2 e x)+B \left(3 d^2+14 d e x+8 e^2 x^2\right)\right)\right)-\frac{3 (b d-a e)^{3/2} (5 a B e-6 A b e+b B d) \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)}{\sqrt{\frac{b (d+e x)}{b d-a e}}}\right)}{24 b^3 e^{3/2}}","-\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,"(Sqrt[d + e*x]*(Sqrt[e]*Sqrt[a + b*x]*(15*a^2*B*e^2 - 2*a*b*e*(11*B*d + 9*A*e + 5*B*e*x) + b^2*(6*A*e*(5*d + 2*e*x) + B*(3*d^2 + 14*d*e*x + 8*e^2*x^2))) - (3*(b*d - a*e)^(3/2)*(b*B*d - 6*A*b*e + 5*a*B*e)*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]])/Sqrt[(b*(d + e*x))/(b*d - a*e)]))/(24*b^3*e^(3/2))","A",1
2238,1,135,140,0.3921108,"\int \frac{(A+B x) \sqrt{d+e x}}{\sqrt{a+b x}} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/Sqrt[a + b*x],x]","\frac{\sqrt{d+e x} \left(\sqrt{e} \sqrt{a+b x} (-3 a B e+4 A b e+b B (d+2 e x))-\frac{\sqrt{b d-a e} (3 a B e-4 A b e+b B d) \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)}{\sqrt{\frac{b (d+e x)}{b d-a e}}}\right)}{4 b^2 e^{3/2}}","-\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*x]*(Sqrt[e]*Sqrt[a + b*x]*(4*A*b*e - 3*a*B*e + b*B*(d + 2*e*x)) - (Sqrt[b*d - a*e]*(b*B*d - 4*A*b*e + 3*a*B*e)*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]])/Sqrt[(b*(d + e*x))/(b*d - a*e)]))/(4*b^2*e^(3/2))","A",1
2239,1,118,84,0.2511881,"\int \frac{A+B x}{\sqrt{a+b x} \sqrt{d+e x}} \, dx","Integrate[(A + B*x)/(Sqrt[a + b*x]*Sqrt[d + e*x]),x]","\frac{b B \sqrt{e} \sqrt{a+b x} (d+e x)-\sqrt{b d-a e} \sqrt{\frac{b (d+e x)}{b d-a e}} (a B e-2 A b e+b B d) \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)}{b^2 e^{3/2} \sqrt{d+e x}}","\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,"(b*B*Sqrt[e]*Sqrt[a + b*x]*(d + e*x) - Sqrt[b*d - a*e]*(b*B*d - 2*A*b*e + a*B*e)*Sqrt[(b*(d + e*x))/(b*d - a*e)]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]])/(b^2*e^(3/2)*Sqrt[d + e*x])","A",1
2240,1,118,85,0.3058058,"\int \frac{A+B x}{\sqrt{a+b x} (d+e x)^{3/2}} \, dx","Integrate[(A + B*x)/(Sqrt[a + b*x]*(d + e*x)^(3/2)),x]","\frac{2 b \sqrt{e} \sqrt{a+b x} (B d-A e)-2 B (b d-a e)^{3/2} \sqrt{\frac{b (d+e x)}{b d-a e}} \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)}{b e^{3/2} \sqrt{d+e x} (a e-b d)}","\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*b*Sqrt[e]*(B*d - A*e)*Sqrt[a + b*x] - 2*B*(b*d - a*e)^(3/2)*Sqrt[(b*(d + e*x))/(b*d - a*e)]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]])/(b*e^(3/2)*(-(b*d) + a*e)*Sqrt[d + e*x])","A",1
2241,1,65,94,0.0430184,"\int \frac{A+B x}{\sqrt{a+b x} (d+e x)^{5/2}} \, dx","Integrate[(A + B*x)/(Sqrt[a + b*x]*(d + e*x)^(5/2)),x]","\frac{2 \sqrt{a+b x} (A (-a e+3 b d+2 b e x)+B (-2 a d-3 a e x+b d x))}{3 (d+e x)^{3/2} (b d-a e)^2}","\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,"(2*Sqrt[a + b*x]*(B*(-2*a*d + b*d*x - 3*a*e*x) + A*(3*b*d - a*e + 2*b*e*x)))/(3*(b*d - a*e)^2*(d + e*x)^(3/2))","A",1
2242,1,133,145,0.1057241,"\int \frac{A+B x}{\sqrt{a+b x} (d+e x)^{7/2}} \, dx","Integrate[(A + B*x)/(Sqrt[a + b*x]*(d + e*x)^(7/2)),x]","\frac{2 \sqrt{a+b x} \left(A \left(3 a^2 e^2-2 a b e (5 d+2 e x)+b^2 \left(15 d^2+20 d e x+8 e^2 x^2\right)\right)+B \left(a^2 e (2 d+5 e x)-2 a b \left(5 d^2+13 d e x+5 e^2 x^2\right)+b^2 d x (5 d+2 e x)\right)\right)}{15 (d+e x)^{5/2} (b d-a e)^3}","-\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,"(2*Sqrt[a + b*x]*(B*(b^2*d*x*(5*d + 2*e*x) + a^2*e*(2*d + 5*e*x) - 2*a*b*(5*d^2 + 13*d*e*x + 5*e^2*x^2)) + A*(3*a^2*e^2 - 2*a*b*e*(5*d + 2*e*x) + b^2*(15*d^2 + 20*d*e*x + 8*e^2*x^2))))/(15*(b*d - a*e)^3*(d + e*x)^(5/2))","A",1
2243,1,113,198,0.2957077,"\int \frac{A+B x}{\sqrt{a+b x} (d+e x)^{9/2}} \, dx","Integrate[(A + B*x)/(Sqrt[a + b*x]*(d + e*x)^(9/2)),x]","\frac{2 \sqrt{a+b x} \left(15 (B d-A e)-\frac{(d+e x) \left(4 b (d+e x) (-a e+3 b d+2 b e x)+3 (b d-a e)^2\right) (-7 a B e+6 A b e+b B d)}{(b d-a e)^3}\right)}{105 e (d+e x)^{7/2} (a e-b d)}","\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,"(2*Sqrt[a + b*x]*(15*(B*d - A*e) - ((b*B*d + 6*A*b*e - 7*a*B*e)*(d + e*x)*(3*(b*d - a*e)^2 + 4*b*(d + e*x)*(3*b*d - a*e + 2*b*e*x)))/(b*d - a*e)^3))/(105*e*(-(b*d) + a*e)*(d + e*x)^(7/2))","A",1
2244,1,134,251,0.3752651,"\int \frac{A+B x}{\sqrt{a+b x} (d+e x)^{11/2}} \, dx","Integrate[(A + B*x)/(Sqrt[a + b*x]*(d + e*x)^(11/2)),x]","\frac{2 \sqrt{a+b x} \left(35 (B d-A e)-\frac{(d+e x) \left(2 b (d+e x) \left(4 b (d+e x) (-a e+3 b d+2 b e x)+3 (b d-a e)^2\right)+5 (b d-a e)^3\right) (-9 a B e+8 A b e+b B d)}{(b d-a e)^4}\right)}{315 e (d+e x)^{9/2} (a e-b d)}","\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,"(2*Sqrt[a + b*x]*(35*(B*d - A*e) - ((b*B*d + 8*A*b*e - 9*a*B*e)*(d + e*x)*(5*(b*d - a*e)^3 + 2*b*(d + e*x)*(3*(b*d - a*e)^2 + 4*b*(d + e*x)*(3*b*d - a*e + 2*b*e*x))))/(b*d - a*e)^4))/(315*e*(-(b*d) + a*e)*(d + e*x)^(9/2))","A",1
2245,1,229,249,1.6567211,"\int \frac{(A+B x) (d+e x)^{5/2}}{(a+b x)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/(a + b*x)^(3/2),x]","\frac{(d+e x)^{3/2} \left(\frac{(-7 a B e+6 A b e+b B d) \left(\sqrt{e} \sqrt{a+b x} \sqrt{\frac{b (d+e x)}{b d-a e}} \left(15 a^2 e^2-10 a b e (4 d+e x)+b^2 \left(33 d^2+26 d e x+8 e^2 x^2\right)\right)+15 (b d-a e)^{5/2} \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)\right)}{\sqrt{e} \left(\frac{b (d+e x)}{b d-a e}\right)^{3/2}}-\frac{48 b^2 (d+e x)^2 (A b-a B) (b d-a e)}{\sqrt{a+b x}}\right)}{24 b^3 (b d-a e)^2}","\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,"((d + e*x)^(3/2)*((-48*b^2*(A*b - a*B)*(b*d - a*e)*(d + e*x)^2)/Sqrt[a + b*x] + ((b*B*d + 6*A*b*e - 7*a*B*e)*(Sqrt[e]*Sqrt[a + b*x]*Sqrt[(b*(d + e*x))/(b*d - a*e)]*(15*a^2*e^2 - 10*a*b*e*(4*d + e*x) + b^2*(33*d^2 + 26*d*e*x + 8*e^2*x^2)) + 15*(b*d - a*e)^(5/2)*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]]))/(Sqrt[e]*((b*(d + e*x))/(b*d - a*e))^(3/2))))/(24*b^3*(b*d - a*e)^2)","A",1
2246,1,161,199,0.5950002,"\int \frac{(A+B x) (d+e x)^{3/2}}{(a+b x)^{3/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(a + b*x)^(3/2),x]","\frac{\sqrt{d+e x} \left(\frac{B \left(-15 a^2 e+a b (13 d-5 e x)+b^2 x (5 d+2 e x)\right)+4 A b (3 a e-2 b d+b e x)}{\sqrt{a+b x}}+\frac{3 \sqrt{b d-a e} (-5 a B e+4 A b e+b B d) \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)}{\sqrt{e} \sqrt{\frac{b (d+e x)}{b d-a e}}}\right)}{4 b^3}","\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,"(Sqrt[d + e*x]*((4*A*b*(-2*b*d + 3*a*e + b*e*x) + B*(-15*a^2*e + a*b*(13*d - 5*e*x) + b^2*x*(5*d + 2*e*x)))/Sqrt[a + b*x] + (3*Sqrt[b*d - a*e]*(b*B*d + 4*A*b*e - 5*a*B*e)*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]])/(Sqrt[e]*Sqrt[(b*(d + e*x))/(b*d - a*e)])))/(4*b^3)","A",1
2247,1,125,145,0.4880906,"\int \frac{(A+B x) \sqrt{d+e x}}{(a+b x)^{3/2}} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(a + b*x)^(3/2),x]","\frac{\frac{b (d+e x) (3 a B-2 A b+b B x)}{\sqrt{a+b x}}+\frac{\sqrt{b d-a e} \sqrt{\frac{b (d+e x)}{b d-a e}} (-3 a B e+2 A b e+b B d) \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)}{\sqrt{e}}}{b^3 \sqrt{d+e x}}","\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,"((b*(-2*A*b + 3*a*B + b*B*x)*(d + e*x))/Sqrt[a + b*x] + (Sqrt[b*d - a*e]*(b*B*d + 2*A*b*e - 3*a*B*e)*Sqrt[(b*(d + e*x))/(b*d - a*e)]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]])/Sqrt[e])/(b^3*Sqrt[d + e*x])","A",1
2248,1,117,85,0.5858071,"\int \frac{A+B x}{(a+b x)^{3/2} \sqrt{d+e x}} \, dx","Integrate[(A + B*x)/((a + b*x)^(3/2)*Sqrt[d + e*x]),x]","\frac{2 \left(\frac{b (d+e x) (a B-A b)}{\sqrt{a+b x} (b d-a e)}+\frac{B \sqrt{b d-a e} \sqrt{\frac{b (d+e x)}{b d-a e}} \sinh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b d-a e}}\right)}{\sqrt{e}}\right)}{b^2 \sqrt{d+e x}}","\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*((b*(-(A*b) + a*B)*(d + e*x))/((b*d - a*e)*Sqrt[a + b*x]) + (B*Sqrt[b*d - a*e]*Sqrt[(b*(d + e*x))/(b*d - a*e)]*ArcSinh[(Sqrt[e]*Sqrt[a + b*x])/Sqrt[b*d - a*e]])/Sqrt[e]))/(b^2*Sqrt[d + e*x])","A",1
2249,1,61,89,0.0344457,"\int \frac{A+B x}{(a+b x)^{3/2} (d+e x)^{3/2}} \, dx","Integrate[(A + B*x)/((a + b*x)^(3/2)*(d + e*x)^(3/2)),x]","\frac{2 B (2 a d+a e x+b d x)-2 A (a e+b (d+2 e x))}{\sqrt{a+b x} \sqrt{d+e x} (b d-a e)^2}","\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,"(2*B*(2*a*d + b*d*x + a*e*x) - 2*A*(a*e + b*(d + 2*e*x)))/((b*d - a*e)^2*Sqrt[a + b*x]*Sqrt[d + e*x])","A",1
2250,1,133,139,0.0669407,"\int \frac{A+B x}{(a+b x)^{3/2} (d+e x)^{5/2}} \, dx","Integrate[(A + B*x)/((a + b*x)^(3/2)*(d + e*x)^(5/2)),x]","\frac{2 \left(a^2 A e^2+a^2 B e (2 d+3 e x)-2 a A b e (3 d+2 e x)+2 a b B \left(3 d^2+5 d e x+3 e^2 x^2\right)-A b^2 \left(3 d^2+12 d e x+8 e^2 x^2\right)+b^2 B d x (3 d+2 e x)\right)}{3 \sqrt{a+b x} (d+e x)^{3/2} (b d-a e)^3}","-\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,"(2*(a^2*A*e^2 - 2*a*A*b*e*(3*d + 2*e*x) + b^2*B*d*x*(3*d + 2*e*x) + a^2*B*e*(2*d + 3*e*x) + 2*a*b*B*(3*d^2 + 5*d*e*x + 3*e^2*x^2) - A*b^2*(3*d^2 + 12*d*e*x + 8*e^2*x^2)))/(3*(b*d - a*e)^3*Sqrt[a + b*x]*(d + e*x)^(3/2))","A",1
2251,1,114,187,0.1941907,"\int \frac{A+B x}{(a+b x)^{3/2} (d+e x)^{7/2}} \, dx","Integrate[(A + B*x)/((a + b*x)^(3/2)*(d + e*x)^(7/2)),x]","\frac{2 \left(-(a+b x) \left(4 b (d+e x) (-a e+3 b d+2 b e x)+3 (b d-a e)^2\right) (-5 a B e+6 A b e-b B d)-15 (A b-a B) (b d-a e)^3\right)}{15 b \sqrt{a+b x} (d+e x)^{5/2} (b d-a e)^4}","-\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,"(2*(-15*(A*b - a*B)*(b*d - a*e)^3 - (-(b*B*d) + 6*A*b*e - 5*a*B*e)*(a + b*x)*(3*(b*d - a*e)^2 + 4*b*(d + e*x)*(3*b*d - a*e + 2*b*e*x))))/(15*b*(b*d - a*e)^4*Sqrt[a + b*x]*(d + e*x)^(5/2))","A",1
2252,1,135,237,0.2639981,"\int \frac{A+B x}{(a+b x)^{3/2} (d+e x)^{9/2}} \, dx","Integrate[(A + B*x)/((a + b*x)^(3/2)*(d + e*x)^(9/2)),x]","\frac{2 \left(-(a+b x) \left(2 b (d+e x) \left(4 b (d+e x) (-a e+3 b d+2 b e x)+3 (b d-a e)^2\right)+5 (b d-a e)^3\right) (-7 a B e+8 A b e-b B d)-35 (A b-a B) (b d-a e)^4\right)}{35 b \sqrt{a+b x} (d+e x)^{7/2} (b d-a e)^5}","\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,"(2*(-35*(A*b - a*B)*(b*d - a*e)^4 - (-(b*B*d) + 8*A*b*e - 7*a*B*e)*(a + b*x)*(5*(b*d - a*e)^3 + 2*b*(d + e*x)*(3*(b*d - a*e)^2 + 4*b*(d + e*x)*(3*b*d - a*e + 2*b*e*x)))))/(35*b*(b*d - a*e)^5*Sqrt[a + b*x]*(d + e*x)^(7/2))","A",1
2253,1,136,302,0.1394279,"\int \frac{(A+B x) (d+e x)^{7/2}}{(a+b x)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(7/2))/(a + b*x)^(5/2),x]","\frac{2 \sqrt{d+e x} \left(-b^4 (d+e x)^4 (A b-a B)-\frac{3 (a+b x) (b d-a e)^3 (-3 a B e+2 A b e+b B d) \, _2F_1\left(-\frac{7}{2},-\frac{1}{2};\frac{1}{2};\frac{e (a+b x)}{a e-b d}\right)}{\sqrt{\frac{b (d+e x)}{b d-a e}}}\right)}{3 b^5 (a+b x)^{3/2} (b d-a e)}","\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,"(2*Sqrt[d + e*x]*(-(b^4*(A*b - a*B)*(d + e*x)^4) - (3*(b*d - a*e)^3*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)*Hypergeometric2F1[-7/2, -1/2, 1/2, (e*(a + b*x))/(-(b*d) + a*e)])/Sqrt[(b*(d + e*x))/(b*d - a*e)]))/(3*b^5*(b*d - a*e)*(a + b*x)^(3/2))","C",1
2254,1,137,257,0.1588365,"\int \frac{(A+B x) (d+e x)^{5/2}}{(a+b x)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(5/2))/(a + b*x)^(5/2),x]","\frac{2 \sqrt{d+e x} \left(-b^3 (d+e x)^3 (A b-a B)-\frac{(a+b x) (b d-a e)^2 (-7 a B e+4 A b e+3 b B d) \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};\frac{e (a+b x)}{a e-b d}\right)}{\sqrt{\frac{b (d+e x)}{b d-a e}}}\right)}{3 b^4 (a+b x)^{3/2} (b d-a e)}","\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,"(2*Sqrt[d + e*x]*(-(b^3*(A*b - a*B)*(d + e*x)^3) - ((b*d - a*e)^2*(3*b*B*d + 4*A*b*e - 7*a*B*e)*(a + b*x)*Hypergeometric2F1[-5/2, -1/2, 1/2, (e*(a + b*x))/(-(b*d) + a*e)])/Sqrt[(b*(d + e*x))/(b*d - a*e)]))/(3*b^4*(b*d - a*e)*(a + b*x)^(3/2))","C",1
2255,1,127,201,0.1366097,"\int \frac{(A+B x) (d+e x)^{3/2}}{(a+b x)^{5/2}} \, dx","Integrate[((A + B*x)*(d + e*x)^(3/2))/(a + b*x)^(5/2),x]","\frac{2 \sqrt{d+e x} \left(-\frac{b^2 (d+e x)^2 (A b-a B)}{b d-a e}-\frac{(a+b x) (-5 a B e+2 A b e+3 b B d) \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};\frac{e (a+b x)}{a e-b d}\right)}{\sqrt{\frac{b (d+e x)}{b d-a e}}}\right)}{3 b^3 (a+b x)^{3/2}}","\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,"(2*Sqrt[d + e*x]*(-((b^2*(A*b - a*B)*(d + e*x)^2)/(b*d - a*e)) - ((3*b*B*d + 2*A*b*e - 5*a*B*e)*(a + b*x)*Hypergeometric2F1[-3/2, -1/2, 1/2, (e*(a + b*x))/(-(b*d) + a*e)])/Sqrt[(b*(d + e*x))/(b*d - a*e)]))/(3*b^3*(a + b*x)^(3/2))","C",1
2256,1,114,111,0.1669006,"\int \frac{(A+B x) \sqrt{d+e x}}{(a+b x)^{5/2}} \, dx","Integrate[((A + B*x)*Sqrt[d + e*x])/(a + b*x)^(5/2),x]","\frac{2 \sqrt{d+e x} \left((d+e x) (B d-A e)-\frac{B (b d-a e)^2 \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};\frac{e (a+b x)}{a e-b d}\right)}{b^2 \sqrt{\frac{b (d+e x)}{b d-a e}}}\right)}{3 e (a+b x)^{3/2} (b d-a e)}","-\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,"(2*Sqrt[d + e*x]*((B*d - A*e)*(d + e*x) - (B*(b*d - a*e)^2*Hypergeometric2F1[-3/2, -3/2, -1/2, (e*(a + b*x))/(-(b*d) + a*e)])/(b^2*Sqrt[(b*(d + e*x))/(b*d - a*e)])))/(3*e*(b*d - a*e)*(a + b*x)^(3/2))","C",1
2257,1,64,95,0.0329734,"\int \frac{A+B x}{(a+b x)^{5/2} \sqrt{d+e x}} \, dx","Integrate[(A + B*x)/((a + b*x)^(5/2)*Sqrt[d + e*x]),x]","-\frac{2 \sqrt{d+e x} (-3 a A e+B (2 a d-a e x+3 b d x)+A b (d-2 e x))}{3 (a+b x)^{3/2} (b d-a e)^2}","-\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,"(-2*Sqrt[d + e*x]*(-3*a*A*e + A*b*(d - 2*e*x) + B*(2*a*d + 3*b*d*x - a*e*x)))/(3*(b*d - a*e)^2*(a + b*x)^(3/2))","A",1
2258,1,125,139,0.0701195,"\int \frac{A+B x}{(a+b x)^{5/2} (d+e x)^{3/2}} \, dx","Integrate[(A + B*x)/((a + b*x)^(5/2)*(d + e*x)^(3/2)),x]","-\frac{2 \left(A \left(-3 a^2 e^2-6 a b e (d+2 e x)+b^2 \left(d^2-4 d e x-8 e^2 x^2\right)\right)+B \left(3 a^2 e (2 d+e x)+2 a b \left(d^2+5 d e x+e^2 x^2\right)+3 b^2 d x (d+2 e x)\right)\right)}{3 (a+b x)^{3/2} \sqrt{d+e x} (b d-a e)^3}","-\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,"(-2*(A*(-3*a^2*e^2 - 6*a*b*e*(d + 2*e*x) + b^2*(d^2 - 4*d*e*x - 8*e^2*x^2)) + B*(3*a^2*e*(2*d + e*x) + 3*b^2*d*x*(d + 2*e*x) + 2*a*b*(d^2 + 5*d*e*x + e^2*x^2))))/(3*(b*d - a*e)^3*(a + b*x)^(3/2)*Sqrt[d + e*x])","A",1
2259,1,107,186,0.2519145,"\int \frac{A+B x}{(a+b x)^{5/2} (d+e x)^{5/2}} \, dx","Integrate[(A + B*x)/((a + b*x)^(5/2)*(d + e*x)^(5/2)),x]","\frac{2 \left(\frac{(-d-e x) \left((b d-a e)^2-4 e (a+b x) (a e+b (d+2 e x))\right) (a B e-2 A b e+b B d)}{(b d-a e)^3}-A e+B d\right)}{3 e (a+b x)^{3/2} (d+e x)^{3/2} (a e-b d)}","-\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,"(2*(B*d - A*e + ((b*B*d - 2*A*b*e + a*B*e)*(-d - e*x)*((b*d - a*e)^2 - 4*e*(a + b*x)*(a*e + b*(d + 2*e*x))))/(b*d - a*e)^3))/(3*e*(-(b*d) + a*e)*(a + b*x)^(3/2)*(d + e*x)^(3/2))","A",1
2260,1,134,246,0.2692962,"\int \frac{A+B x}{(a+b x)^{5/2} (d+e x)^{7/2}} \, dx","Integrate[(A + B*x)/((a + b*x)^(5/2)*(d + e*x)^(7/2)),x]","\frac{2 \left((a+b x) \left(2 e (a+b x) \left(4 b (d+e x) (-a e+3 b d+2 b e x)+3 (b d-a e)^2\right)+5 (b d-a e)^3\right) (-5 a B e+8 A b e-3 b B d)-5 (A b-a B) (b d-a e)^4\right)}{15 b (a+b x)^{3/2} (d+e x)^{5/2} (b d-a e)^5}","-\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,"(2*(-5*(A*b - a*B)*(b*d - a*e)^4 + (-3*b*B*d + 8*A*b*e - 5*a*B*e)*(a + b*x)*(5*(b*d - a*e)^3 + 2*e*(a + b*x)*(3*(b*d - a*e)^2 + 4*b*(d + e*x)*(3*b*d - a*e + 2*b*e*x)))))/(15*b*(b*d - a*e)^5*(a + b*x)^(3/2)*(d + e*x)^(5/2))","A",1
2261,1,160,298,0.2213146,"\int \frac{A+B x}{(a+b x)^{5/2} (d+e x)^{9/2}} \, dx","Integrate[(A + B*x)/((a + b*x)^(5/2)*(d + e*x)^(9/2)),x]","\frac{2 \left(2 (a+b x) \left(8 e (a+b x) \left(2 b (d+e x) \left(4 b (d+e x) (-a e+3 b d+2 b e x)+3 (b d-a e)^2\right)+5 (b d-a e)^3\right)+35 (b d-a e)^4\right) \left(-\frac{7 a B e}{2}+5 A b e-\frac{3}{2} b B d\right)-35 (A b-a B) (b d-a e)^5\right)}{105 b (a+b x)^{3/2} (d+e x)^{7/2} (b d-a e)^6}","-\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,"(2*(-35*(A*b - a*B)*(b*d - a*e)^5 + 2*((-3*b*B*d)/2 + 5*A*b*e - (7*a*B*e)/2)*(a + b*x)*(35*(b*d - a*e)^4 + 8*e*(a + b*x)*(5*(b*d - a*e)^3 + 2*b*(d + e*x)*(3*(b*d - a*e)^2 + 4*b*(d + e*x)*(3*b*d - a*e + 2*b*e*x))))))/(105*b*(b*d - a*e)^6*(a + b*x)^(3/2)*(d + e*x)^(7/2))","A",1
2262,1,84,157,0.1134985,"\int \sqrt{1-2 x} (2+3 x)^4 \sqrt{3+5 x} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^4*Sqrt[3 + 5*x],x]","\frac{4122385421 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(1382400000 x^6+3746304000 x^5+3260908800 x^4+198117440 x^3-1377410040 x^2-1082027818 x+518122939\right)}{512000000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(518122939 - 1082027818*x - 1377410040*x^2 + 198117440*x^3 + 3260908800*x^4 + 3746304000*x^5 + 1382400000*x^6) + 4122385421*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(512000000*Sqrt[1 - 2*x])","A",1
2263,1,79,128,0.1763439,"\int \sqrt{1-2 x} (2+3 x)^3 \sqrt{3+5 x} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^3*Sqrt[3 + 5*x],x]","\frac{39142411 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(13824000 x^5+27820800 x^4+12527040 x^3-8941640 x^2-11567238 x+4282349\right)}{12800000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(4282349 - 11567238*x - 8941640*x^2 + 12527040*x^3 + 27820800*x^4 + 13824000*x^5) + 39142411*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(12800000*Sqrt[1 - 2*x])","A",1
2264,1,74,121,0.0760209,"\int \sqrt{1-2 x} (2+3 x)^2 \sqrt{3+5 x} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^2*Sqrt[3 + 5*x],x]","\frac{158873 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(57600 x^4+74560 x^3-6680 x^2-49154 x+13327\right)}{128000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(13327 - 49154*x - 6680*x^2 + 74560*x^3 + 57600*x^4) + 158873*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(128000*Sqrt[1 - 2*x])","A",1
2265,1,69,94,0.0636574,"\int \sqrt{1-2 x} (2+3 x) \sqrt{3+5 x} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)*Sqrt[3 + 5*x],x]","\frac{4477 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(1600 x^3+840 x^2-1226 x+203\right)}{8000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(203 - 1226*x + 840*x^2 + 1600*x^3) + 4477*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(8000*Sqrt[1 - 2*x])","A",1
2266,1,64,72,0.0526186,"\int \sqrt{1-2 x} \sqrt{3+5 x} \, dx","Integrate[Sqrt[1 - 2*x]*Sqrt[3 + 5*x],x]","\frac{10 \sqrt{5 x+3} \left(-40 x^2+18 x+1\right)+121 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{400 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(1 + 18*x - 40*x^2) + 121*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(400*Sqrt[1 - 2*x])","A",1
2267,1,103,84,0.0768972,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{2+3 x} \, dx","Integrate[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x),x]","\frac{30 \sqrt{-(2 x-1)^2} \sqrt{5 x+3}+20 \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-37 \sqrt{10-20 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{90 \sqrt{2 x-1}}","\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,"(30*Sqrt[-(-1 + 2*x)^2]*Sqrt[3 + 5*x] - 37*Sqrt[10 - 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 20*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(90*Sqrt[-1 + 2*x])","A",0
2268,1,120,91,0.1243123,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^2} \, dx","Integrate[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^2,x]","\frac{-21 \sqrt{-(2 x-1)^2} \sqrt{5 x+3}-37 (3 x+2) \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+14 \sqrt{10-20 x} (3 x+2) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{63 \sqrt{2 x-1} (3 x+2)}","-\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,"(-21*Sqrt[-(-1 + 2*x)^2]*Sqrt[3 + 5*x] + 14*Sqrt[10 - 20*x]*(2 + 3*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 37*(2 + 3*x)*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(63*Sqrt[-1 + 2*x]*(2 + 3*x))","A",0
2269,1,69,93,0.0407066,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^3} \, dx","Integrate[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^3,x]","\frac{1}{196} \left(\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} (37 x+20)}{(3 x+2)^2}-121 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(20 + 37*x))/(2 + 3*x)^2 - 121*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/196","A",1
2270,1,74,122,0.0514694,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^4} \, dx","Integrate[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^4,x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(3547 x^2+4902 x+1648\right)}{(3 x+2)^3}-4477 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2744}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1648 + 4902*x + 3547*x^2))/(2 + 3*x)^3 - 4477*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/2744","A",1
2271,1,79,151,0.0605598,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^5} \, dx","Integrate[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^5,x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(1875345 x^3+3834760 x^2+2617388 x+594416\right)}{(3 x+2)^4}-794365 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{153664}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(594416 + 2617388*x + 3834760*x^2 + 1875345*x^3))/(2 + 3*x)^4 - 794365*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/153664","A",1
2272,1,135,180,0.1443784,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^6} \, dx","Integrate[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^6,x]","\frac{1}{35} \left(\frac{5 \left(\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(4398843 x^2+6119462 x+2067760\right)}{(3 x+2)^3}-5591773 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{43904}+\frac{111 (1-2 x)^{3/2} (5 x+3)^{3/2}}{8 (3 x+2)^4}+\frac{3 (1-2 x)^{3/2} (5 x+3)^{3/2}}{(3 x+2)^5}\right)","\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,"((3*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^5 + (111*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(8*(2 + 3*x)^4) + (5*((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(2067760 + 6119462*x + 4398843*x^2))/(2 + 3*x)^3 - 5591773*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/43904)/35","A",1
2273,1,193,209,0.2212758,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^7} \, dx","Integrate[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^7,x]","\frac{1}{42} \left(\frac{999 (1-2 x)^{3/2} (5 x+3)^{3/2}}{70 (3 x+2)^5}+\frac{3 (1-2 x)^{3/2} (5 x+3)^{3/2}}{(3 x+2)^6}+\frac{3 \left(64324848 (1-2 x)^{3/2} (5 x+3)^{3/2}+5 (3 x+2) \left(53882360 (1-2 x)^{3/2} (5 x+3)^{3/2}+4867043 (3 x+2) \left(7 \sqrt{1-2 x} \sqrt{5 x+3} (37 x+20)-121 \sqrt{7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)\right)\right)}{3073280 (3 x+2)^4}\right)","\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,"((3*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^6 + (999*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(70*(2 + 3*x)^5) + (3*(64324848*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2) + 5*(2 + 3*x)*(53882360*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2) + 4867043*(2 + 3*x)*(7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(20 + 37*x) - 121*Sqrt[7]*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))))/(3073280*(2 + 3*x)^4))/42","A",1
2274,1,89,179,0.12274,"\int \sqrt{1-2 x} (2+3 x)^4 (3+5 x)^{3/2} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^(3/2),x]","\frac{1474705073919 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(497664000000 x^7+1651968000000 x^6+2010963456000 x^5+842711443200 x^4-356020459840 x^3-548703531560 x^2-330110729902 x+201521732121\right)}{43008000000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(201521732121 - 330110729902*x - 548703531560*x^2 - 356020459840*x^3 + 842711443200*x^4 + 2010963456000*x^5 + 1651968000000*x^6 + 497664000000*x^7) + 1474705073919*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(43008000000*Sqrt[1 - 2*x])","A",1
2275,1,84,150,0.1902734,"\int \sqrt{1-2 x} (2+3 x)^3 (3+5 x)^{3/2} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^(3/2),x]","\frac{3809246133 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(1382400000 x^6+3635712000 x^5+3038342400 x^4+97901120 x^3-1305876920 x^2-989489914 x+483864147\right)}{307200000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(483864147 - 989489914*x - 1305876920*x^2 + 97901120*x^3 + 3038342400*x^4 + 3635712000*x^5 + 1382400000*x^6) + 3809246133*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(307200000*Sqrt[1 - 2*x])","A",1
2276,1,79,143,0.0792563,"\int \sqrt{1-2 x} (2+3 x)^2 (3+5 x)^{3/2} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^(3/2),x]","\frac{35964951 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(13824000 x^5+26668800 x^4+11035840 x^3-8808040 x^2-10584158 x+4015809\right)}{7680000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(4015809 - 10584158*x - 8808040*x^2 + 11035840*x^3 + 26668800*x^4 + 13824000*x^5) + 35964951*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(7680000*Sqrt[1 - 2*x])","A",1
2277,1,74,116,0.0697159,"\int \sqrt{1-2 x} (2+3 x) (3+5 x)^{3/2} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^(3/2),x]","\frac{722733 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(288000 x^4+347200 x^3-46840 x^2-226154 x+63387\right)}{384000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(63387 - 226154*x - 46840*x^2 + 347200*x^3 + 288000*x^4) + 722733*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(384000*Sqrt[1 - 2*x])","A",1
2278,1,69,94,0.0632651,"\int \sqrt{1-2 x} (3+5 x)^{3/2} \, dx","Integrate[Sqrt[1 - 2*x]*(3 + 5*x)^(3/2),x]","\frac{3993 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(1600 x^3+680 x^2-1154 x+207\right)}{4800 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(207 - 1154*x + 680*x^2 + 1600*x^3) + 3993*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(4800*Sqrt[1 - 2*x])","A",1
2279,1,108,106,0.1092565,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{2+3 x} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x),x]","\frac{150 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} (12 x-1)-160 \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-793 \sqrt{10-20 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{2160 \sqrt{2 x-1}}","\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,"(150*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(-1 + 12*x) - 793*Sqrt[10 - 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 160*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(2160*Sqrt[-1 + 2*x])","A",0
2280,1,125,115,0.1782086,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^2} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^2,x]","\frac{42 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} (15 x+11)+214 (3 x+2) \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-287 \sqrt{10-20 x} (3 x+2) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{378 \sqrt{2 x-1} (3 x+2)}","-\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,"(42*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(11 + 15*x) - 287*Sqrt[10 - 20*x]*(2 + 3*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 214*(2 + 3*x)*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(378*Sqrt[-1 + 2*x]*(2 + 3*x))","A",0
2281,1,129,120,0.1752405,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^3} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^3,x]","\frac{-21 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} (531 x+340)-4091 \sqrt{14 x-7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+1960 \sqrt{10-20 x} (3 x+2)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{5292 \sqrt{2 x-1} (3 x+2)^2}","-\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,"(-21*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(340 + 531*x) + 1960*Sqrt[10 - 20*x]*(2 + 3*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 4091*(2 + 3*x)^2*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(5292*Sqrt[-1 + 2*x]*(2 + 3*x)^2)","A",0
2282,1,74,122,0.0504785,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^4} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^4,x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(4223 x^2+4478 x+1152\right)}{(3 x+2)^3}-3993 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{8232}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1152 + 4478*x + 4223*x^2))/(2 + 3*x)^3 - 3993*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/8232","A",1
2283,1,79,151,0.0604558,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^5} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^5,x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(1104135 x^3+2269240 x^2+1512052 x+328464\right)}{(3 x+2)^4}-459195 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{460992}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(328464 + 1512052*x + 2269240*x^2 + 1104135*x^3))/(2 + 3*x)^4 - 459195*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/460992","A",1
2284,1,133,180,0.1168991,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^6} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^6,x]","\frac{589 \left(\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(4223 x^2+4478 x+1152\right)}{(3 x+2)^3}-3993 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{921984}+\frac{81 (1-2 x)^{3/2} (5 x+3)^{5/2}}{280 (3 x+2)^4}+\frac{3 (1-2 x)^{3/2} (5 x+3)^{5/2}}{35 (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,"(3*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(35*(2 + 3*x)^5) + (81*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(280*(2 + 3*x)^4) + (589*((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1152 + 4478*x + 4223*x^2))/(2 + 3*x)^3 - 3993*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/921984","A",1
2285,1,171,209,0.1457588,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^7} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^7,x]","\frac{1}{42} \left(\frac{48569 \left(7 \sqrt{1-2 x} \sqrt{5 x+3} \left(4223 x^2+4478 x+1152\right)-3993 \sqrt{7} (3 x+2)^3 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{614656 (3 x+2)^3}+\frac{20103 (1-2 x)^{3/2} (5 x+3)^{5/2}}{560 (3 x+2)^4}+\frac{789 (1-2 x)^{3/2} (5 x+3)^{5/2}}{70 (3 x+2)^5}+\frac{3 (1-2 x)^{3/2} (5 x+3)^{5/2}}{(3 x+2)^6}\right)","-\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,"((3*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^6 + (789*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(70*(2 + 3*x)^5) + (20103*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(560*(2 + 3*x)^4) + (48569*(7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1152 + 4478*x + 4223*x^2) - 3993*Sqrt[7]*(2 + 3*x)^3*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/(614656*(2 + 3*x)^3))/42","A",1
2286,1,94,201,0.1300013,"\int \sqrt{1-2 x} (2+3 x)^4 (3+5 x)^{5/2} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^(5/2),x]","\frac{41758617880749 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(13934592000000 x^8+54709862400000 x^7+84655134720000 x^6+58945337856000 x^5+6568746067200 x^4-18691732680640 x^3-14866250752760 x^2-7954905832042 x+5973304472091\right)}{275251200000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(5973304472091 - 7954905832042*x - 14866250752760*x^2 - 18691732680640*x^3 + 6568746067200*x^4 + 58945337856000*x^5 + 84655134720000*x^6 + 54709862400000*x^7 + 13934592000000*x^8) + 41758617880749*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(275251200000*Sqrt[1 - 2*x])","A",1
2287,1,89,172,0.211525,"\int \sqrt{1-2 x} (2+3 x)^3 (3+5 x)^{5/2} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^(5/2),x]","\frac{91203078813 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(33177600000 x^7+107550720000 x^6+127277568000 x^5+50509190400 x^4-23917446080 x^3-34142598520 x^2-20160334154 x+12531569067\right)}{1720320000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(12531569067 - 20160334154*x - 34142598520*x^2 - 23917446080*x^3 + 50509190400*x^4 + 127277568000*x^5 + 107550720000*x^6 + 33177600000*x^7) + 91203078813*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(1720320000*Sqrt[1 - 2*x])","A",1
2288,1,84,165,0.0907478,"\int \sqrt{1-2 x} (2+3 x)^2 (3+5 x)^{5/2} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^(5/2),x]","\frac{46953687 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(18432000 x^6+47001600 x^5+37666560 x^4+128192 x^3-16472168 x^2-12064222 x+6023169\right)}{2457600 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(6023169 - 12064222*x - 16472168*x^2 + 128192*x^3 + 37666560*x^4 + 47001600*x^5 + 18432000*x^6) + 46953687*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(2457600*Sqrt[1 - 2*x])","A",1
2289,1,79,138,0.0860277,"\int \sqrt{1-2 x} (2+3 x) (3+5 x)^{5/2} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^(5/2),x]","\frac{11024673 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(4608000 x^5+8505600 x^4+3215680 x^3-2873560 x^2-3226514 x+1254087\right)}{1536000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(1254087 - 3226514*x - 2873560*x^2 + 3215680*x^3 + 8505600*x^4 + 4608000*x^5) + 11024673*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(1536000*Sqrt[1 - 2*x])","A",1
2290,1,74,116,0.066836,"\int \sqrt{1-2 x} (3+5 x)^{5/2} \, dx","Integrate[Sqrt[1 - 2*x]*(3 + 5*x)^(5/2),x]","\frac{43923 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(19200 x^4+21440 x^3-3848 x^2-13846 x+4005\right)}{15360 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(4005 - 13846*x - 3848*x^2 + 21440*x^3 + 19200*x^4) + 43923*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(15360*Sqrt[1 - 2*x])","A",1
2291,1,113,130,0.1338233,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{2+3 x} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x),x]","\frac{6 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(2400 x^2+1980 x-601\right)+128 \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-6553 \sqrt{10-20 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{5184 \sqrt{2 x-1}}","\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,"(6*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(-601 + 1980*x + 2400*x^2) - 6553*Sqrt[10 - 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 128*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(5184*Sqrt[-1 + 2*x])","A",0
2292,1,130,137,0.1871207,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^2} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^2,x]","\frac{42 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(300 x^2+135 x-46\right)-944 (3 x+2) \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-1085 \sqrt{10-20 x} (3 x+2) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{3024 \sqrt{2 x-1} (3 x+2)}","-\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,"(42*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(-46 + 135*x + 300*x^2) - 1085*Sqrt[10 - 20*x]*(2 + 3*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 944*(2 + 3*x)*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(3024*Sqrt[-1 + 2*x]*(2 + 3*x))","A",0
2293,1,134,144,0.1860697,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^3} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^3,x]","\frac{21 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(700 x^2+1039 x+380\right)+2119 \sqrt{14 x-7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-2450 \sqrt{10-20 x} (3 x+2)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{1764 \sqrt{2 x-1} (3 x+2)^2}","-\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,"(21*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(380 + 1039*x + 700*x^2) - 2450*Sqrt[10 - 20*x]*(2 + 3*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 2119*(2 + 3*x)^2*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(1764*Sqrt[-1 + 2*x]*(2 + 3*x)^2)","A",0
2294,1,134,149,0.2113858,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^4} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^4,x]","\frac{-21 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(124179 x^2+159174 x+51056\right)-250433 \sqrt{14 x-7} (3 x+2)^3 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+137200 \sqrt{10-20 x} (3 x+2)^3 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{222264 \sqrt{2 x-1} (3 x+2)^3}","-\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,"(-21*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(51056 + 159174*x + 124179*x^2) + 137200*Sqrt[10 - 20*x]*(2 + 3*x)^3*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 250433*(2 + 3*x)^3*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(222264*Sqrt[-1 + 2*x]*(2 + 3*x)^3)","A",0
2295,1,79,151,0.0630395,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^5} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^5,x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(814395 x^3+1285720 x^2+654436 x+105552\right)}{(3 x+2)^4}-219615 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{460992}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(105552 + 654436*x + 1285720*x^2 + 814395*x^3))/(2 + 3*x)^4 - 219615*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/460992","A",1
2296,1,84,180,0.0694373,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^6} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^6,x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(27422145 x^4+74915550 x^3+74550556 x^2+32206264 x+5112864\right)}{(3 x+2)^5}-3733455 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{4609920}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(5112864 + 32206264*x + 74550556*x^2 + 74915550*x^3 + 27422145*x^4))/(2 + 3*x)^5 - 3733455*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/4609920","A",1
2297,1,140,209,0.1521349,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^7} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^7,x]","\frac{1}{42} \left(\frac{1027 \left(\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(814395 x^3+1285720 x^2+654436 x+105552\right)}{(3 x+2)^4}-219615 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{3073280}+\frac{579 (1-2 x)^{3/2} (5 x+3)^{7/2}}{70 (3 x+2)^5}+\frac{3 (1-2 x)^{3/2} (5 x+3)^{7/2}}{(3 x+2)^6}\right)","-\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,"((3*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2))/(2 + 3*x)^6 + (579*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2))/(70*(2 + 3*x)^5) + (1027*((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(105552 + 654436*x + 1285720*x^2 + 814395*x^3))/(2 + 3*x)^4 - 219615*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/3073280)/42","A",1
2298,1,221,238,0.3056654,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^8} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^8,x]","\frac{1}{49} \left(\frac{267 (1-2 x)^{3/2} (5 x+3)^{7/2}}{28 (3 x+2)^6}+\frac{3 (1-2 x)^{3/2} (5 x+3)^{7/2}}{(3 x+2)^7}+\frac{6344698752 (1-2 x)^{3/2} (5 x+3)^{7/2}+255169 (3 x+2) \left(115248 \sqrt{1-2 x} (5 x+3)^{7/2}-11 (3 x+2) \left(2744 \sqrt{1-2 x} (5 x+3)^{5/2}+55 (3 x+2) \left(7 \sqrt{1-2 x} \sqrt{5 x+3} (169 x+108)+363 \sqrt{7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)\right)\right)}{258155520 (3 x+2)^5}\right)","-\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,"((3*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2))/(2 + 3*x)^7 + (267*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2))/(28*(2 + 3*x)^6) + (6344698752*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2) + 255169*(2 + 3*x)*(115248*Sqrt[1 - 2*x]*(3 + 5*x)^(7/2) - 11*(2 + 3*x)*(2744*Sqrt[1 - 2*x]*(3 + 5*x)^(5/2) + 55*(2 + 3*x)*(7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(108 + 169*x) + 363*Sqrt[7]*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))))/(258155520*(2 + 3*x)^5))/49","A",1
2299,1,152,119,0.2824388,"\int \frac{\sqrt{a+b x}}{\sqrt{c+d x} (e+f x)} \, dx","Integrate[Sqrt[a + b*x]/(Sqrt[c + d*x]*(e + f*x)),x]","\frac{2 \left(\frac{\sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{d} \sqrt{c+d x}}-\frac{\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)}{\sqrt{d e-c f}}\right)}{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,"(2*((Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[d]*Sqrt[c + d*x]) - (Sqrt[b*e - a*f]*ArcTanh[(Sqrt[d*e - c*f]*Sqrt[a + b*x])/(Sqrt[b*e - a*f]*Sqrt[c + d*x])])/Sqrt[d*e - c*f]))/f","A",1
2300,1,152,119,0.4539565,"\int \frac{\sqrt{c+d x}}{\sqrt{a+b x} (e+f x)} \, dx","Integrate[Sqrt[c + d*x]/(Sqrt[a + b*x]*(e + f*x)),x]","\frac{2 \left(\frac{\sqrt{d} \sqrt{c+d x} \sinh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{\sqrt{b c-a d} \sqrt{\frac{b (c+d x)}{b c-a d}}}-\frac{\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)}{\sqrt{b e-a f}}\right)}{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,"(2*((Sqrt[d]*Sqrt[c + d*x]*ArcSinh[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(Sqrt[b*c - a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]) - (Sqrt[d*e - c*f]*ArcTanh[(Sqrt[d*e - c*f]*Sqrt[a + b*x])/(Sqrt[b*e - a*f]*Sqrt[c + d*x])])/Sqrt[b*e - a*f]))/f","A",1
2301,1,74,106,0.1229534,"\int \frac{\sqrt{1-2 x} (2+3 x)^3}{\sqrt{3+5 x}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^3)/Sqrt[3 + 5*x],x]","\frac{525371 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(172800 x^4+239040 x^3-10440 x^2-159718 x+41789\right)}{640000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(41789 - 159718*x - 10440*x^2 + 239040*x^3 + 172800*x^4) + 525371*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(640000*Sqrt[1 - 2*x])","A",1
2302,1,69,99,0.0646463,"\int \frac{\sqrt{1-2 x} (2+3 x)^2}{\sqrt{3+5 x}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^2)/Sqrt[3 + 5*x],x]","\frac{3047 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(960 x^3+600 x^2-766 x+113\right)}{8000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(113 - 766*x + 600*x^2 + 960*x^3) + 3047*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(8000*Sqrt[1 - 2*x])","A",1
2303,1,64,72,0.0579032,"\int \frac{\sqrt{1-2 x} (2+3 x)}{\sqrt{3+5 x}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x))/Sqrt[3 + 5*x],x]","\frac{10 \sqrt{5 x+3} \left(-120 x^2+38 x+11\right)+451 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{2000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(11 + 38*x - 120*x^2) + 451*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(2000*Sqrt[1 - 2*x])","A",1
2304,1,59,50,0.0433613,"\int \frac{\sqrt{1-2 x}}{\sqrt{3+5 x}} \, dx","Integrate[Sqrt[1 - 2*x]/Sqrt[3 + 5*x],x]","\frac{10 \sqrt{5 x+3} (1-2 x)+11 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{50 \sqrt{1-2 x}}","\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,"(10*(1 - 2*x)*Sqrt[3 + 5*x] + 11*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(50*Sqrt[1 - 2*x])","A",1
2305,1,74,64,0.0479413,"\int \frac{\sqrt{1-2 x}}{(2+3 x) \sqrt{3+5 x}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)*Sqrt[3 + 5*x]),x]","\frac{2}{15} \left(\frac{\sqrt{10-20 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{\sqrt{2 x-1}}-5 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\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,"(2*((Sqrt[10 - 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/Sqrt[-1 + 2*x] - 5*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/15","A",1
2306,1,59,59,0.0237727,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^2 \sqrt{3+5 x}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^2*Sqrt[3 + 5*x]),x]","\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}}","\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[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x) - (11*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/Sqrt[7]","A",1
2307,1,69,93,0.0408687,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^3 \sqrt{3+5 x}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^3*Sqrt[3 + 5*x]),x]","\frac{1}{196} \left(\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} (309 x+220)}{(3 x+2)^2}-1177 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(220 + 309*x))/(2 + 3*x)^2 - 1177*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/196","A",1
2308,1,74,122,0.0499282,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^4 \sqrt{3+5 x}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^4*Sqrt[3 + 5*x]),x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(54249 x^2+74754 x+25856\right)}{(3 x+2)^3}-68959 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2744}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(25856 + 74754*x + 54249*x^2))/(2 + 3*x)^3 - 68959*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/2744","A",1
2309,1,79,151,0.060907,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^5 \sqrt{3+5 x}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^5*Sqrt[3 + 5*x]),x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(39943125 x^3+81668520 x^2+55729116 x+12696112\right)}{(3 x+2)^4}-16925425 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{153664}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(12696112 + 55729116*x + 81668520*x^2 + 39943125*x^3))/(2 + 3*x)^4 - 16925425*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/153664","A",1
2310,1,83,113,0.0681888,"\int \frac{\sqrt{1-2 x} (2+3 x)^3}{(3+5 x)^{3/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^3)/(3 + 5*x)^(3/2),x]","\frac{10409 \sqrt{5 x+3} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \left(14400 x^4+19080 x^3-5490 x^2-5611 x+893\right)}{40000 \sqrt{1-2 x} \sqrt{5 x+3}}","-\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,"(-10*(893 - 5611*x - 5490*x^2 + 19080*x^3 + 14400*x^4) + 10409*Sqrt[3 + 5*x]*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(40000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])","A",1
2311,1,78,94,0.0572687,"\int \frac{\sqrt{1-2 x} (2+3 x)^2}{(3+5 x)^{3/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^2)/(3 + 5*x)^(3/2),x]","\frac{10 \left(-360 x^3-150 x^2+103 x+31\right)+317 \sqrt{5 x+3} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{2000 \sqrt{1-2 x} \sqrt{5 x+3}}","-\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,"(10*(31 + 103*x - 150*x^2 - 360*x^3) + 317*Sqrt[3 + 5*x]*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(2000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])","A",1
2312,1,71,72,0.0504792,"\int \frac{\sqrt{1-2 x} (2+3 x)}{(3+5 x)^{3/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x))/(3 + 5*x)^(3/2),x]","\frac{10 \left(-30 x^2+x+7\right)+29 \sqrt{5 x+3} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{250 \sqrt{1-2 x} \sqrt{5 x+3}}","-\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,"(10*(7 + x - 30*x^2) + 29*Sqrt[3 + 5*x]*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(250*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])","A",1
2313,1,58,52,0.0843791,"\int \frac{\sqrt{1-2 x}}{(3+5 x)^{3/2}} \, dx","Integrate[Sqrt[1 - 2*x]/(3 + 5*x)^(3/2),x]","\frac{2}{25} \sqrt{1-2 x} \left(\frac{\sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{\sqrt{2 x-1}}-\frac{5}{\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,"(2*Sqrt[1 - 2*x]*(-5/Sqrt[3 + 5*x] + (Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/Sqrt[-1 + 2*x]))/25","A",1
2314,1,53,53,0.0164147,"\int \frac{\sqrt{1-2 x}}{(2+3 x) (3+5 x)^{3/2}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)*(3 + 5*x)^(3/2)),x]","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}}","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,"(-2*Sqrt[1 - 2*x])/Sqrt[3 + 5*x] + 2*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]","A",1
2315,1,65,84,0.0394197,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^2 (3+5 x)^{3/2}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^2*(3 + 5*x)^(3/2)),x]","\frac{103 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{\sqrt{7}}-\frac{\sqrt{1-2 x} (45 x+29)}{(3 x+2) \sqrt{5 x+3}}","\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]*(29 + 45*x))/((2 + 3*x)*Sqrt[3 + 5*x])) + (103*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/Sqrt[7]","A",1
2316,1,74,115,0.0521544,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^3 (3+5 x)^{3/2}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^3*(3 + 5*x)^(3/2)),x]","\frac{1}{196} \left(17951 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-\frac{7 \sqrt{1-2 x} \left(23535 x^2+30861 x+10100\right)}{(3 x+2)^2 \sqrt{5 x+3}}\right)","-\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,"((-7*Sqrt[1 - 2*x]*(10100 + 30861*x + 23535*x^2))/((2 + 3*x)^2*Sqrt[3 + 5*x]) + 17951*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/196","A",1
2317,1,79,144,0.0646086,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^4 (3+5 x)^{3/2}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^4*(3 + 5*x)^(3/2)),x]","\frac{1463447 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-\frac{7 \sqrt{1-2 x} \left(5756085 x^3+11385261 x^2+7502166 x+1646704\right)}{(3 x+2)^3 \sqrt{5 x+3}}}{2744}","-\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,"((-7*Sqrt[1 - 2*x]*(1646704 + 7502166*x + 11385261*x^2 + 5756085*x^3))/((2 + 3*x)^3*Sqrt[3 + 5*x]) + 1463447*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/2744","A",1
2318,1,88,142,0.1089936,"\int \frac{\sqrt{1-2 x} (2+3 x)^4}{(3+5 x)^{5/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^4)/(3 + 5*x)^(5/2),x]","\frac{1171863 (5 x+3)^{3/2} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \left(7128000 x^5+14434200 x^4+3768930 x^3-4392275 x^2-1433776 x+218953\right)}{6600000 \sqrt{1-2 x} (5 x+3)^{3/2}}","-\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,"(-10*(218953 - 1433776*x - 4392275*x^2 + 3768930*x^3 + 14434200*x^4 + 7128000*x^5) + 1171863*(3 + 5*x)^(3/2)*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(6600000*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))","A",1
2319,1,83,113,0.0947255,"\int \frac{\sqrt{1-2 x} (2+3 x)^3}{(3+5 x)^{5/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^3)/(3 + 5*x)^(5/2),x]","\frac{35343 (5 x+3)^{3/2} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \left(178200 x^4+204930 x^3+3925 x^2-52336 x-11567\right)}{330000 \sqrt{1-2 x} (5 x+3)^{3/2}}","-\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,"(-10*(-11567 - 52336*x + 3925*x^2 + 204930*x^3 + 178200*x^4) + 35343*(3 + 5*x)^(3/2)*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(330000*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))","A",1
2320,1,78,94,0.0921014,"\int \frac{\sqrt{1-2 x} (2+3 x)^2}{(3+5 x)^{5/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^2)/(3 + 5*x)^(5/2),x]","\frac{10 \left(-594 x^3-259 x^2+160 x+59\right)+99 \sqrt{20 x-10} (5 x+3)^{3/2} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{1650 \sqrt{1-2 x} (5 x+3)^{3/2}}","-\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,"(10*(59 + 160*x - 259*x^2 - 594*x^3) + 99*(3 + 5*x)^(3/2)*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(1650*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))","A",1
2321,1,73,74,0.0873228,"\int \frac{\sqrt{1-2 x} (2+3 x)}{(3+5 x)^{5/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x))/(3 + 5*x)^(5/2),x]","\frac{10 \left(970 x^2+119 x-302\right)-198 (5 x+3)^{3/2} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{4125 \sqrt{1-2 x} (5 x+3)^{3/2}}","-\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,"(10*(-302 + 119*x + 970*x^2) - 198*(3 + 5*x)^(3/2)*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(4125*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))","A",1
2322,1,22,22,0.0060672,"\int \frac{\sqrt{1-2 x}}{(3+5 x)^{5/2}} \, dx","Integrate[Sqrt[1 - 2*x]/(3 + 5*x)^(5/2),x]","-\frac{2 (1-2 x)^{3/2}}{33 (5 x+3)^{3/2}}","-\frac{2 (1-2 x)^{3/2}}{33 (5 x+3)^{3/2}}",1,"(-2*(1 - 2*x)^(3/2))/(33*(3 + 5*x)^(3/2))","A",1
2323,1,60,75,0.0410035,"\int \frac{\sqrt{1-2 x}}{(2+3 x) (3+5 x)^{5/2}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)*(3 + 5*x)^(5/2)),x]","\frac{2 \sqrt{1-2 x} (505 x+292)}{33 (5 x+3)^{3/2}}-6 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+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[1 - 2*x]*(292 + 505*x))/(33*(3 + 5*x)^(3/2)) - 6*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]","A",1
2324,1,93,103,0.0441968,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^2 (3+5 x)^{5/2}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^2*(3 + 5*x)^(5/2)),x]","\frac{7 \sqrt{1-2 x} \left(37425 x^2+46580 x+14453\right)-17127 \sqrt{7} \sqrt{5 x+3} \left(15 x^2+19 x+6\right) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{231 (3 x+2) (5 x+3)^{3/2}}","\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,"(7*Sqrt[1 - 2*x]*(14453 + 46580*x + 37425*x^2) - 17127*Sqrt[7]*Sqrt[3 + 5*x]*(6 + 19*x + 15*x^2)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(231*(2 + 3*x)*(3 + 5*x)^(3/2))","A",1
2325,1,79,137,0.0702549,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^3 (3+5 x)^{5/2}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^3*(3 + 5*x)^(5/2)),x]","\frac{\sqrt{1-2 x} \left(27368325 x^3+52308690 x^2+33277877 x+7046540\right)}{924 (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}}","\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,"(Sqrt[1 - 2*x]*(7046540 + 33277877*x + 52308690*x^2 + 27368325*x^3))/(924*(2 + 3*x)^2*(3 + 5*x)^(3/2)) - (126513*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(28*Sqrt[7])","A",1
2326,1,84,166,0.0848756,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^4 (3+5 x)^{5/2}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^4*(3 + 5*x)^(5/2)),x]","\frac{\frac{7 \sqrt{1-2 x} \left(8596610325 x^4+22161651840 x^3+21406565457 x^2+9181937962 x+1475586688\right)}{(3 x+2)^3 (5 x+3)^{3/2}}-437126283 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{90552}","\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,"((7*Sqrt[1 - 2*x]*(1475586688 + 9181937962*x + 21406565457*x^2 + 22161651840*x^3 + 8596610325*x^4))/((2 + 3*x)^3*(3 + 5*x)^(3/2)) - 437126283*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/90552","A",1
2327,1,84,150,0.1716983,"\int (1-2 x)^{3/2} (2+3 x)^3 \sqrt{3+5 x} \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^3*Sqrt[3 + 5*x],x]","\frac{10 \sqrt{5 x+3} \left(1382400000 x^6+1810944000 x^5-634003200 x^4-1555668160 x^3-125580440 x^2+537385502 x-81405921\right)+1357552119 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{768000000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(-81405921 + 537385502*x - 125580440*x^2 - 1555668160*x^3 - 634003200*x^4 + 1810944000*x^5 + 1382400000*x^6) + 1357552119*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(768000000*Sqrt[1 - 2*x])","A",1
2328,1,79,143,0.0608944,"\int (1-2 x)^{3/2} (2+3 x)^2 \sqrt{3+5 x} \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^2*Sqrt[3 + 5*x],x]","\frac{10 \sqrt{5 x+3} \left(13824000 x^5+7660800 x^4-13568960 x^3-6603640 x^2+5636662 x-382101\right)+16463139 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{19200000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(-382101 + 5636662*x - 6603640*x^2 - 13568960*x^3 + 7660800*x^4 + 13824000*x^5) + 16463139*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(19200000*Sqrt[1 - 2*x])","A",1
2329,1,74,116,0.0523793,"\int (1-2 x)^{3/2} (2+3 x) \sqrt{3+5 x} \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)*Sqrt[3 + 5*x],x]","\frac{10 \sqrt{5 x+3} \left(57600 x^4-15040 x^3-53720 x^2+19502 x+1959\right)+91839 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{192000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(1959 + 19502*x - 53720*x^2 - 15040*x^3 + 57600*x^4) + 91839*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(192000*Sqrt[1 - 2*x])","A",1
2330,1,69,94,0.0418281,"\int (1-2 x)^{3/2} \sqrt{3+5 x} \, dx","Integrate[(1 - 2*x)^(3/2)*Sqrt[3 + 5*x],x]","\frac{10 \sqrt{5 x+3} \left(1600 x^3-1960 x^2+34 x+273\right)+3993 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{12000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(273 + 34*x - 1960*x^2 + 1600*x^3) + 3993*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(12000*Sqrt[1 - 2*x])","A",1
2331,1,108,106,0.1222724,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{2+3 x} \, dx","Integrate[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x),x]","\frac{30 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} (137-60 x)+2800 \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-4091 \sqrt{10-20 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{5400 \sqrt{2 x-1}}","\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,"(30*(137 - 60*x)*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x] - 4091*Sqrt[10 - 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 2800*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(5400*Sqrt[-1 + 2*x])","A",0
2332,1,128,115,0.1929267,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^2} \, dx","Integrate[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^2,x]","\frac{107 \sqrt{10-20 x} (3 x+2) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-5 \left(3 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} (6 x+11)+41 (3 x+2) \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{135 \sqrt{2 x-1} (3 x+2)}","-\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,"(107*Sqrt[10 - 20*x]*(2 + 3*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 5*(3*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(11 + 6*x) + 41*(2 + 3*x)*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/(135*Sqrt[-1 + 2*x]*(2 + 3*x))","A",0
2333,1,129,120,0.1772115,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^3} \, dx","Integrate[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^3,x]","\frac{21 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} (135 x+76)-793 \sqrt{14 x-7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-112 \sqrt{10-20 x} (3 x+2)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{756 \sqrt{2 x-1} (3 x+2)^2}","-\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,"(21*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(76 + 135*x) - 112*Sqrt[10 - 20*x]*(2 + 3*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 793*(2 + 3*x)^2*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(756*Sqrt[-1 + 2*x]*(2 + 3*x)^2)","A",0
2334,1,74,122,0.0527468,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^4} \, dx","Integrate[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^4,x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(3103 x^2+4366 x+1488\right)}{(3 x+2)^3}-3993 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1176}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1488 + 4366*x + 3103*x^2))/(2 + 3*x)^3 - 3993*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/1176","A",1
2335,1,79,151,0.0578293,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^5} \, dx","Integrate[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^5,x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(1705089 x^3+3485960 x^2+2381420 x+541680\right)}{(3 x+2)^4}-722733 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{65856}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(541680 + 2381420*x + 3485960*x^2 + 1705089*x^3))/(2 + 3*x)^4 - 722733*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/65856","A",1
2336,1,140,180,0.0843785,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^6} \, dx","Integrate[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^6,x]","\frac{9007 \left(7 \sqrt{1-2 x} \sqrt{5 x+3} \left(3103 x^2+4366 x+1488\right)-3993 \sqrt{7} (3 x+2)^3 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{921984 (3 x+2)^3}+\frac{153 (5 x+3)^{3/2} (1-2 x)^{5/2}}{392 (3 x+2)^4}+\frac{3 (5 x+3)^{3/2} (1-2 x)^{5/2}}{35 (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,"(3*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(35*(2 + 3*x)^5) + (153*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(392*(2 + 3*x)^4) + (9007*(7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1488 + 4366*x + 3103*x^2) - 3993*Sqrt[7]*(2 + 3*x)^3*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/(921984*(2 + 3*x)^3)","A",1
2337,1,89,172,0.1826776,"\int (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{3/2} \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(3/2),x]","\frac{10 \sqrt{5 x+3} \left(55296000000 x^7+108288000000 x^6+25496064000 x^5-71786259200 x^4-44888000960 x^3+10130684360 x^2+17193258662 x-3952411101\right)+43536170139 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{7168000000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(-3952411101 + 17193258662*x + 10130684360*x^2 - 44888000960*x^3 - 71786259200*x^4 + 25496064000*x^5 + 108288000000*x^6 + 55296000000*x^7) + 43536170139*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(7168000000*Sqrt[1 - 2*x])","A",1
2338,1,84,165,0.068595,"\int (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^{3/2} \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2),x]","\frac{10 \sqrt{5 x+3} \left(153600000 x^6+188928000 x^5-77254400 x^4-160790720 x^3-8083480 x^2+54699134 x-8705457\right)+136205223 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{51200000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(-8705457 + 54699134*x - 8083480*x^2 - 160790720*x^3 - 77254400*x^4 + 188928000*x^5 + 153600000*x^6) + 136205223*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(51200000*Sqrt[1 - 2*x])","A",1
2339,1,79,138,0.0583194,"\int (1-2 x)^{3/2} (2+3 x) (3+5 x)^{3/2} \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(3/2),x]","\frac{10 \sqrt{5 x+3} \left(1536000 x^5+723200 x^4-1474240 x^3-614360 x^2+582958 x-46809\right)+1625151 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{1280000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(-46809 + 582958*x - 614360*x^2 - 1474240*x^3 + 723200*x^4 + 1536000*x^5) + 1625151*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(1280000*Sqrt[1 - 2*x])","A",1
2340,1,74,116,0.0506179,"\int (1-2 x)^{3/2} (3+5 x)^{3/2} \, dx","Integrate[(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2),x]","\frac{10 \sqrt{5 x+3} \left(32000 x^4-11200 x^3-26360 x^2+10774 x+603\right)+43923 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{64000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(603 + 10774*x - 26360*x^2 - 11200*x^3 + 32000*x^4) + 43923*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(64000*Sqrt[1 - 2*x])","A",1
2341,1,113,128,0.136101,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{2+3 x} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x),x]","\frac{-30 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(2400 x^2-1980 x-271\right)-11200 \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-19573 \sqrt{10-20 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{64800 \sqrt{2 x-1}}","\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,"(-30*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(-271 - 1980*x + 2400*x^2) - 19573*Sqrt[10 - 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 11200*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(64800*Sqrt[-1 + 2*x])","A",0
2342,1,130,135,0.204887,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^2} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^2,x]","\frac{-30 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(60 x^2-105 x-106\right)+1480 (3 x+2) \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-1649 \sqrt{10-20 x} (3 x+2) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{1080 \sqrt{2 x-1} (3 x+2)}","-\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,"(-30*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(-106 - 105*x + 60*x^2) - 1649*Sqrt[10 - 20*x]*(2 + 3*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 1480*(2 + 3*x)*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(1080*Sqrt[-1 + 2*x]*(2 + 3*x))","A",0
2343,1,134,142,0.195142,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^3} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^3,x]","\frac{-21 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(120 x^2+345 x+172\right)-1649 \sqrt{14 x-7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+1036 \sqrt{10-20 x} (3 x+2)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{756 \sqrt{2 x-1} (3 x+2)^2}","\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,"(-21*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(172 + 345*x + 120*x^2) + 1036*Sqrt[10 - 20*x]*(2 + 3*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 1649*(2 + 3*x)^2*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(756*Sqrt[-1 + 2*x]*(2 + 3*x)^2)","A",0
2344,1,134,149,0.2396616,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^4} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^4,x]","\frac{21 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(19041 x^2+21762 x+6176\right)-19573 \sqrt{14 x-7} (3 x+2)^3 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-7840 \sqrt{10-20 x} (3 x+2)^3 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{31752 \sqrt{2 x-1} (3 x+2)^3}","\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,"(21*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(6176 + 21762*x + 19041*x^2) - 7840*Sqrt[10 - 20*x]*(2 + 3*x)^3*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 19573*(2 + 3*x)^3*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(31752*Sqrt[-1 + 2*x]*(2 + 3*x)^3)","A",0
2345,1,79,151,0.0614001,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^5} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^5,x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(100159 x^3+213240 x^2+145940 x+32400\right)}{(3 x+2)^4}-43923 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{21952}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(32400 + 145940*x + 213240*x^2 + 100159*x^3))/(2 + 3*x)^4 - 43923*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/21952","A",1
2346,1,109,180,0.0917418,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^6} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^6,x]","\frac{37 \left(\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(100159 x^3+213240 x^2+145940 x+32400\right)}{(3 x+2)^4}-43923 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{307328}+\frac{3 (1-2 x)^{5/2} (5 x+3)^{5/2}}{35 (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,"(3*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(35*(2 + 3*x)^5) + (37*((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(32400 + 145940*x + 213240*x^2 + 100159*x^3))/(2 + 3*x)^4 - 43923*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/307328","A",1
2347,1,138,209,0.1507821,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^7} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^7,x]","\frac{1}{280} \left(\frac{2215 \left(\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(100159 x^3+213240 x^2+145940 x+32400\right)}{(3 x+2)^4}-43923 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{21952}+\frac{74 (1-2 x)^{5/2} (5 x+3)^{5/2}}{(3 x+2)^5}+\frac{20 (1-2 x)^{5/2} (5 x+3)^{5/2}}{(3 x+2)^6}\right)","\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,"((20*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^6 + (74*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^5 + (2215*((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(32400 + 145940*x + 213240*x^2 + 100159*x^3))/(2 + 3*x)^4 - 43923*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/21952)/280","A",1
2348,1,176,238,0.1670847,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^8} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^8,x]","\frac{1}{49} \left(\frac{141599 \left(7 \sqrt{1-2 x} \sqrt{5 x+3} \left(100159 x^3+213240 x^2+145940 x+32400\right)-43923 \sqrt{7} (3 x+2)^4 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{2458624 (3 x+2)^4}+\frac{11841 (1-2 x)^{5/2} (5 x+3)^{5/2}}{280 (3 x+2)^5}+\frac{333 (1-2 x)^{5/2} (5 x+3)^{5/2}}{28 (3 x+2)^6}+\frac{3 (1-2 x)^{5/2} (5 x+3)^{5/2}}{(3 x+2)^7}\right)","\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,"((3*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^7 + (333*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(28*(2 + 3*x)^6) + (11841*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(280*(2 + 3*x)^5) + (141599*(7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(32400 + 145940*x + 213240*x^2 + 100159*x^3) - 43923*Sqrt[7]*(2 + 3*x)^4*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/(2458624*(2 + 3*x)^4))/49","A",1
2349,1,94,194,0.2041842,"\int (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{5/2} \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(5/2),x]","\frac{10 \sqrt{5 x+3} \left(1548288000000 x^8+4014489600000 x^7+2714081280000 x^6-1370011136000 x^5-2412933395200 x^4-588662541760 x^3+472622713160 x^2+370542366022 x-116041578381\right)+1035011806059 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{45875200000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(-116041578381 + 370542366022*x + 472622713160*x^2 - 588662541760*x^3 - 2412933395200*x^4 - 1370011136000*x^5 + 2714081280000*x^6 + 4014489600000*x^7 + 1548288000000*x^8) + 1035011806059*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(45875200000*Sqrt[1 - 2*x])","A",1
2350,1,89,187,0.0721456,"\int (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^{5/2} \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2),x]","\frac{10 \sqrt{5 x+3} \left(3686400000 x^7+6932480000 x^6+1347072000 x^5-4641542400 x^4-2692390720 x^3+690468120 x^2+1044112194 x-247243887\right)+2648161593 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{286720000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(-247243887 + 1044112194*x + 690468120*x^2 - 2692390720*x^3 - 4641542400*x^4 + 1347072000*x^5 + 6932480000*x^6 + 3686400000*x^7) + 2648161593*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(286720000*Sqrt[1 - 2*x])","A",1
2351,1,84,160,0.0655028,"\int (1-2 x)^{3/2} (2+3 x) (3+5 x)^{5/2} \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(5/2),x]","\frac{10 \sqrt{5 x+3} \left(10240000 x^6+11776000 x^5-5536000 x^4-9933120 x^3-211240 x^2+3335698 x-555399\right)+8213601 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{2048000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(-555399 + 3335698*x - 211240*x^2 - 9933120*x^3 - 5536000*x^4 + 11776000*x^5 + 10240000*x^6) + 8213601*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(2048000*Sqrt[1 - 2*x])","A",1
2352,1,79,138,0.058049,"\int (1-2 x)^{3/2} (3+5 x)^{5/2} \, dx","Integrate[(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2),x]","\frac{10 \sqrt{5 x+3} \left(512000 x^5+198400 x^4-476480 x^3-169640 x^2+179954 x-16407\right)+483153 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{256000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(-16407 + 179954*x - 169640*x^2 - 476480*x^3 + 198400*x^4 + 512000*x^5) + 483153*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(256000*Sqrt[1 - 2*x])","A",1
2353,1,118,150,0.16604,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{2+3 x} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x),x]","\frac{-30 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(86400 x^3+5280 x^2-58356 x-2389\right)+35840 \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-648919 \sqrt{10-20 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{622080 \sqrt{2 x-1}}","\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,"(-30*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(-2389 - 58356*x + 5280*x^2 + 86400*x^3) - 648919*Sqrt[10 - 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 35840*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(622080*Sqrt[-1 + 2*x])","A",0
2354,1,135,159,0.2301794,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^2} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^2,x]","\frac{-6 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(7200 x^3-1860 x^2-3513 x+730\right)-5792 (3 x+2) \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+43 \sqrt{10-20 x} (3 x+2) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{7776 \sqrt{2 x-1} (3 x+2)}","-\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,"(-6*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(730 - 3513*x - 1860*x^2 + 7200*x^3) + 43*Sqrt[10 - 20*x]*(2 + 3*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 5792*(2 + 3*x)*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(7776*Sqrt[-1 + 2*x]*(2 + 3*x))","A",0
2355,1,139,166,0.2399791,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^3} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^3,x]","\frac{-42 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(900 x^3-1095 x^2-2985 x-1232\right)+13658 \sqrt{14 x-7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-13615 \sqrt{10-20 x} (3 x+2)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{4536 \sqrt{2 x-1} (3 x+2)^2}","\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,"(-42*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(-1232 - 2985*x - 1095*x^2 + 900*x^3) - 13615*Sqrt[10 - 20*x]*(2 + 3*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 13658*(2 + 3*x)^2*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(4536*Sqrt[-1 + 2*x]*(2 + 3*x)^2)","A",0
2356,1,139,171,0.2456436,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^4} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^4,x]","\frac{-21 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(75600 x^3+286791 x^2+275022 x+78416\right)-326717 \sqrt{14 x-7} (3 x+2)^3 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+225400 \sqrt{10-20 x} (3 x+2)^3 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{95256 \sqrt{2 x-1} (3 x+2)^3}","\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,"(-21*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(78416 + 275022*x + 286791*x^2 + 75600*x^3) + 225400*Sqrt[10 - 20*x]*(2 + 3*x)^3*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 326717*(2 + 3*x)^3*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(95256*Sqrt[-1 + 2*x]*(2 + 3*x)^3)","A",0
2357,1,139,178,0.2699745,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^5} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^5,x]","\frac{21 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(13290147 x^3+23185560 x^2+13434180 x+2583760\right)-1922677 \sqrt{14 x-7} (3 x+2)^4 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-2195200 \sqrt{10-20 x} (3 x+2)^4 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{5334336 \sqrt{2 x-1} (3 x+2)^4}","\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,"(21*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(2583760 + 13434180*x + 23185560*x^2 + 13290147*x^3) - 2195200*Sqrt[10 - 20*x]*(2 + 3*x)^4*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 1922677*(2 + 3*x)^4*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(5334336*Sqrt[-1 + 2*x]*(2 + 3*x)^4)","A",0
2358,1,84,180,0.0702334,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^6} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^6,x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(15899035 x^4+46076650 x^3+47906548 x^2+21437032 x+3507552\right)}{(3 x+2)^5}-2415765 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1536640}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(3507552 + 21437032*x + 47906548*x^2 + 46076650*x^3 + 15899035*x^4))/(2 + 3*x)^5 - 2415765*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/1536640","A",1
2359,1,138,209,0.1407966,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^7} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^7,x]","\frac{99 \left(\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(814395 x^3+1285720 x^2+654436 x+105552\right)}{(3 x+2)^4}-219615 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{6146560}+\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{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,"((1 - 2*x)^(5/2)*(3 + 5*x)^(7/2))/(14*(2 + 3*x)^6) + (9*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2))/(20*(2 + 3*x)^5) + (99*((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(105552 + 654436*x + 1285720*x^2 + 814395*x^3))/(2 + 3*x)^4 - 219615*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/6146560","A",1
2360,1,221,238,0.2571335,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^8} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^8,x]","\frac{1}{49} \left(\frac{263 (1-2 x)^{5/2} (5 x+3)^{7/2}}{28 (3 x+2)^6}+\frac{3 (1-2 x)^{5/2} (5 x+3)^{7/2}}{(3 x+2)^7}+\frac{2287 \left(307328 (1-2 x)^{3/2} (5 x+3)^{7/2}+11 (3 x+2) \left(115248 \sqrt{1-2 x} (5 x+3)^{7/2}-11 (3 x+2) \left(2744 \sqrt{1-2 x} (5 x+3)^{5/2}+55 (3 x+2) \left(7 \sqrt{1-2 x} \sqrt{5 x+3} (169 x+108)+363 \sqrt{7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)\right)\right)\right)}{12293120 (3 x+2)^5}\right)","\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,"((3*(1 - 2*x)^(5/2)*(3 + 5*x)^(7/2))/(2 + 3*x)^7 + (263*(1 - 2*x)^(5/2)*(3 + 5*x)^(7/2))/(28*(2 + 3*x)^6) + (2287*(307328*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2) + 11*(2 + 3*x)*(115248*Sqrt[1 - 2*x]*(3 + 5*x)^(7/2) - 11*(2 + 3*x)*(2744*Sqrt[1 - 2*x]*(3 + 5*x)^(5/2) + 55*(2 + 3*x)*(7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(108 + 169*x) + 363*Sqrt[7]*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])))))/(12293120*(2 + 3*x)^5))/49","A",1
2361,1,79,128,0.144212,"\int \frac{(1-2 x)^{3/2} (2+3 x)^3}{\sqrt{3+5 x}} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^3)/Sqrt[3 + 5*x],x]","\frac{10 \sqrt{5 x+3} \left(13824000 x^5+8812800 x^4-13767360 x^3-7793240 x^2+6001742 x-314441\right)+18648399 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{32000000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(-314441 + 6001742*x - 7793240*x^2 - 13767360*x^3 + 8812800*x^4 + 13824000*x^5) + 18648399*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(32000000*Sqrt[1 - 2*x])","A",1
2362,1,74,121,0.0601242,"\int \frac{(1-2 x)^{3/2} (2+3 x)^2}{\sqrt{3+5 x}} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^2)/Sqrt[3 + 5*x],x]","\frac{10 \sqrt{5 x+3} \left(57600 x^4-9920 x^3-59480 x^2+18254 x+3383\right)+109263 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{320000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(3383 + 18254*x - 59480*x^2 - 9920*x^3 + 57600*x^4) + 109263*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(320000*Sqrt[1 - 2*x])","A",1
2363,1,69,94,0.0463933,"\int \frac{(1-2 x)^{3/2} (2+3 x)}{\sqrt{3+5 x}} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x))/Sqrt[3 + 5*x],x]","\frac{10 \sqrt{5 x+3} \left(320 x^3-360 x^2-78 x+89\right)+1089 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{4000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(89 - 78*x - 360*x^2 + 320*x^3) + 1089*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(4000*Sqrt[1 - 2*x])","A",1
2364,1,64,72,0.0376986,"\int \frac{(1-2 x)^{3/2}}{\sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(3/2)/Sqrt[3 + 5*x],x]","\frac{10 \sqrt{5 x+3} \left(40 x^2-106 x+43\right)+363 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{1000 \sqrt{1-2 x}}","\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,"(10*Sqrt[3 + 5*x]*(43 - 106*x + 40*x^2) + 363*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(1000*Sqrt[1 - 2*x])","A",1
2365,1,103,86,0.0687902,"\int \frac{(1-2 x)^{3/2}}{(2+3 x) \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)*Sqrt[3 + 5*x]),x]","\frac{-30 \sqrt{-(2 x-1)^2} \sqrt{5 x+3}-350 \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+103 \sqrt{10-20 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{225 \sqrt{2 x-1}}","-\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,"(-30*Sqrt[-(-1 + 2*x)^2]*Sqrt[3 + 5*x] + 103*Sqrt[10 - 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 350*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(225*Sqrt[-1 + 2*x])","A",0
2366,1,120,93,0.1389078,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^2 \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^2*Sqrt[3 + 5*x]),x]","\frac{105 \sqrt{-(2 x-1)^2} \sqrt{5 x+3}-145 (3 x+2) \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-4 \sqrt{10-20 x} (3 x+2) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{45 \sqrt{2 x-1} (3 x+2)}","\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,"(105*Sqrt[-(-1 + 2*x)^2]*Sqrt[3 + 5*x] - 4*Sqrt[10 - 20*x]*(2 + 3*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 145*(2 + 3*x)*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(45*Sqrt[-1 + 2*x]*(2 + 3*x))","A",0
2367,1,69,93,0.04112,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^3 \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^3*Sqrt[3 + 5*x]),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} (95 x+68)}{4 (3 x+2)^2}-\frac{363 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{4 \sqrt{7}}","\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[1 - 2*x]*Sqrt[3 + 5*x]*(68 + 95*x))/(4*(2 + 3*x)^2) - (363*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(4*Sqrt[7])","A",1
2368,1,74,122,0.0511316,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^4 \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^4*Sqrt[3 + 5*x]),x]","\frac{1}{392} \left(\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(16847 x^2+23214 x+8032\right)}{(3 x+2)^3}-21417 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(8032 + 23214*x + 16847*x^2))/(2 + 3*x)^3 - 21417*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/392","A",1
2369,1,79,151,0.0630933,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^5 \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^5*Sqrt[3 + 5*x]),x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(12446391 x^3+25448120 x^2+17365300 x+3956240\right)}{(3 x+2)^4}-5274027 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{21952}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(3956240 + 17365300*x + 25448120*x^2 + 12446391*x^3))/(2 + 3*x)^4 - 5274027*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/21952","A",1
2370,1,135,180,0.1404909,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^6 \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^6*Sqrt[3 + 5*x]),x]","\frac{1}{35} \left(\frac{5 \left(\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(262124349 x^2+361165738 x+124968544\right)}{(3 x+2)^3}-333216939 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{43904}+\frac{975 \sqrt{5 x+3} (1-2 x)^{5/2}}{56 (3 x+2)^4}+\frac{3 \sqrt{5 x+3} (1-2 x)^{5/2}}{(3 x+2)^5}\right)","\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,"((3*(1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^5 + (975*(1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(56*(2 + 3*x)^4) + (5*((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(124968544 + 361165738*x + 262124349*x^2))/(2 + 3*x)^3 - 333216939*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/43904)/35","A",1
2371,1,88,135,0.0565941,"\int \frac{(1-2 x)^{3/2} (2+3 x)^3}{(3+5 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^3)/(3 + 5*x)^(3/2),x]","\frac{10 \left(864000 x^5+446400 x^4-1014120 x^3-346790 x^2+223559 x+46783\right)+390621 \sqrt{5 x+3} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{1600000 \sqrt{1-2 x} \sqrt{5 x+3}}","-\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,"(10*(46783 + 223559*x - 346790*x^2 - 1014120*x^3 + 446400*x^4 + 864000*x^5) + 390621*Sqrt[3 + 5*x]*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(1600000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])","A",1
2372,1,83,116,0.0507523,"\int \frac{(1-2 x)^{3/2} (2+3 x)^2}{(3+5 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^2)/(3 + 5*x)^(3/2),x]","\frac{10 \left(4800 x^4-2040 x^3-5330 x^2+533 x+1021\right)+3927 \sqrt{5 x+3} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{20000 \sqrt{1-2 x} \sqrt{5 x+3}}","-\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,"(10*(1021 + 533*x - 5330*x^2 - 2040*x^3 + 4800*x^4) + 3927*Sqrt[3 + 5*x]*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(20000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])","A",1
2373,1,78,94,0.0399511,"\int \frac{(1-2 x)^{3/2} (2+3 x)}{(3+5 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x))/(3 + 5*x)^(3/2),x]","\frac{10 \left(24 x^3-46 x^2-5 x+11\right)+33 \sqrt{5 x+3} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{200 \sqrt{1-2 x} \sqrt{5 x+3}}","-\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,"(10*(11 - 5*x - 46*x^2 + 24*x^3) + 33*Sqrt[3 + 5*x]*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(200*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])","A",1
2374,1,39,74,0.0099479,"\int \frac{(1-2 x)^{3/2}}{(3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/(3 + 5*x)^(3/2),x]","-\frac{2}{55} \sqrt{\frac{2}{11}} (1-2 x)^{5/2} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};-\frac{5}{11} (2 x-1)\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[2/11]*(1 - 2*x)^(5/2)*Hypergeometric2F1[3/2, 5/2, 7/2, (-5*(-1 + 2*x))/11])/55","C",1
2375,1,100,86,0.3245506,"\int \frac{(1-2 x)^{3/2}}{(2+3 x) (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)*(3 + 5*x)^(3/2)),x]","\frac{2}{75} \left(-\frac{165 \sqrt{1-2 x}}{\sqrt{5 x+3}}+175 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+\frac{2 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{\sqrt{-(1-2 x)^2}}\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,"(2*((-165*Sqrt[1 - 2*x])/Sqrt[3 + 5*x] + (2*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/Sqrt[-(1 - 2*x)^2] + 175*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/75","A",1
2376,1,65,79,0.0349721,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^2 (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^2*(3 + 5*x)^(3/2)),x]","33 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-\frac{\sqrt{1-2 x} (101 x+65)}{(3 x+2) \sqrt{5 x+3}}","\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]*(65 + 101*x))/((2 + 3*x)*Sqrt[3 + 5*x])) + 33*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]","A",1
2377,1,74,115,0.0534303,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^3 (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^3*(3 + 5*x)^(3/2)),x]","\frac{5709 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{4 \sqrt{7}}-\frac{\sqrt{1-2 x} \left(7485 x^2+9815 x+3212\right)}{4 (3 x+2)^2 \sqrt{5 x+3}}","\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,"-1/4*(Sqrt[1 - 2*x]*(3212 + 9815*x + 7485*x^2))/((2 + 3*x)^2*Sqrt[3 + 5*x]) + (5709*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(4*Sqrt[7])","A",1
2378,1,79,144,0.0616812,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^4 (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^4*(3 + 5*x)^(3/2)),x]","\frac{1}{392} \left(463881 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-\frac{7 \sqrt{1-2 x} \left(1824555 x^3+3608883 x^2+2378026 x+521968\right)}{(3 x+2)^3 \sqrt{5 x+3}}\right)","-\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,"((-7*Sqrt[1 - 2*x]*(521968 + 2378026*x + 3608883*x^2 + 1824555*x^3))/((2 + 3*x)^3*Sqrt[3 + 5*x]) + 463881*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/392","A",1
2379,1,84,173,0.0756444,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^5 (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^5*(3 + 5*x)^(3/2)),x]","\frac{145708761 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-\frac{7 \sqrt{1-2 x} \left(1719322065 x^4+4546951839 x^3+4508028900 x^2+1985778980 x+327908240\right)}{(3 x+2)^4 \sqrt{5 x+3}}}{21952}","-\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,"((-7*Sqrt[1 - 2*x]*(327908240 + 1985778980*x + 4508028900*x^2 + 4546951839*x^3 + 1719322065*x^4))/((2 + 3*x)^4*Sqrt[3 + 5*x]) + 145708761*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/21952","A",1
2380,1,88,142,0.0714776,"\int \frac{(1-2 x)^{3/2} (2+3 x)^3}{(3+5 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^3)/(3 + 5*x)^(5/2),x]","\frac{10 \left(216000 x^5+59400 x^4-320490 x^3-141425 x^2+67568 x+31171\right)+39459 \sqrt{20 x-10} (5 x+3)^{3/2} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{300000 \sqrt{1-2 x} (5 x+3)^{3/2}}","-\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,"(10*(31171 + 67568*x - 141425*x^2 - 320490*x^3 + 59400*x^4 + 216000*x^5) + 39459*(3 + 5*x)^(3/2)*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(300000*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))","A",1
2381,1,83,116,0.0683307,"\int \frac{(1-2 x)^{3/2} (2+3 x)^2}{(3+5 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^2)/(3 + 5*x)^(5/2),x]","\frac{10 \left(5400 x^4-6390 x^3-5375 x^2+1808 x+901\right)+1029 \sqrt{20 x-10} (5 x+3)^{3/2} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{15000 \sqrt{1-2 x} (5 x+3)^{3/2}}","-\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,"(10*(901 + 1808*x - 5375*x^2 - 6390*x^3 + 5400*x^4) + 1029*(3 + 5*x)^(3/2)*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(15000*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))","A",1
2382,1,59,96,0.0332999,"\int \frac{(1-2 x)^{3/2} (2+3 x)}{(3+5 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x))/(3 + 5*x)^(5/2),x]","-\frac{2 (1-2 x)^{5/2} \left(19 \sqrt{22} (5 x+3)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};-\frac{5}{11} (2 x-1)\right)+121\right)}{19965 (5 x+3)^{3/2}}","-\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*(1 - 2*x)^(5/2)*(121 + 19*Sqrt[22]*(3 + 5*x)^(3/2)*Hypergeometric2F1[3/2, 5/2, 7/2, (-5*(-1 + 2*x))/11]))/(19965*(3 + 5*x)^(3/2))","C",1
2383,1,70,74,0.0988325,"\int \frac{(1-2 x)^{3/2}}{(3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/(3 + 5*x)^(5/2),x]","\frac{-800 x^2+140 x+12 (5 x+3)^{3/2} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)+130}{375 \sqrt{1-2 x} (5 x+3)^{3/2}}","-\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,"(130 + 140*x - 800*x^2 + 12*(3 + 5*x)^(3/2)*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(375*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))","A",1
2384,1,60,75,0.0484073,"\int \frac{(1-2 x)^{3/2}}{(2+3 x) (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)*(3 + 5*x)^(5/2)),x]","\frac{2 \sqrt{1-2 x} (107 x+62)}{3 (5 x+3)^{3/2}}-14 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+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,"(2*Sqrt[1 - 2*x]*(62 + 107*x))/(3*(3 + 5*x)^(3/2)) - 14*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]","A",1
2385,1,92,104,0.0410948,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^2 (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^2*(3 + 5*x)^(5/2)),x]","\frac{\sqrt{1-2 x} \left(7755 x^2+9652 x+2995\right)-507 \sqrt{7} \sqrt{5 x+3} \left(15 x^2+19 x+6\right) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{3 (3 x+2) (5 x+3)^{3/2}}","\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,"(Sqrt[1 - 2*x]*(2995 + 9652*x + 7755*x^2) - 507*Sqrt[7]*Sqrt[3 + 5*x]*(6 + 19*x + 15*x^2)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(3*(2 + 3*x)*(3 + 5*x)^(3/2))","A",1
2386,1,79,137,0.0665945,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^3 (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^3*(3 + 5*x)^(5/2)),x]","\frac{\sqrt{1-2 x} \left(802125 x^3+1533090 x^2+975325 x+206524\right)}{12 (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}}","\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,"(Sqrt[1 - 2*x]*(206524 + 975325*x + 1533090*x^2 + 802125*x^3))/(12*(2 + 3*x)^2*(3 + 5*x)^(3/2)) - (40787*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(4*Sqrt[7])","A",1
2387,1,84,166,0.0777949,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^4 (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^4*(3 + 5*x)^(5/2)),x]","\frac{\sqrt{1-2 x} \left(250551225 x^4+645909120 x^3+623901861 x^2+267610802 x+43006496\right)}{168 (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}}","\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,"(Sqrt[1 - 2*x]*(43006496 + 267610802*x + 623901861*x^2 + 645909120*x^3 + 250551225*x^4))/(168*(2 + 3*x)^3*(3 + 5*x)^(3/2)) - (4246733*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(56*Sqrt[7])","A",1
2388,1,89,172,0.1978231,"\int (1-2 x)^{5/2} (2+3 x)^3 \sqrt{3+5 x} \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^3*Sqrt[3 + 5*x],x]","\frac{78454515909 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(165888000000 x^7+111974400000 x^6-202397184000 x^5-117722284800 x^4+104908893760 x^3+49731440840 x^2-31177591322 x+679278531\right)}{53760000000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(679278531 - 31177591322*x + 49731440840*x^2 + 104908893760*x^3 - 117722284800*x^4 - 202397184000*x^5 + 111974400000*x^6 + 165888000000*x^7) + 78454515909*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(53760000000*Sqrt[1 - 2*x])","A",1
2389,1,84,165,0.0905255,"\int (1-2 x)^{5/2} (2+3 x)^2 \sqrt{3+5 x} \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^2*Sqrt[3 + 5*x],x]","\frac{315762447 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(460800000 x^6-41472000 x^5-568838400 x^4+114662080 x^3+266309720 x^2-83915726 x-9303927\right)}{384000000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(-9303927 - 83915726*x + 266309720*x^2 + 114662080*x^3 - 568838400*x^4 - 41472000*x^5 + 460800000*x^6) + 315762447*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(384000000*Sqrt[1 - 2*x])","A",1
2390,1,79,138,0.0831108,"\int (1-2 x)^{5/2} (2+3 x) \sqrt{3+5 x} \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)*Sqrt[3 + 5*x],x]","\frac{10 \sqrt{5 x+3} \left(-4608000 x^5+4166400 x^4+2768320 x^3-4066120 x^2+396346 x+355917\right)+5226837 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{9600000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(355917 + 396346*x - 4066120*x^2 + 2768320*x^3 + 4166400*x^4 - 4608000*x^5) + 5226837*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(9600000*Sqrt[1 - 2*x])","A",1
2391,1,74,116,0.0714386,"\int (1-2 x)^{5/2} \sqrt{3+5 x} \, dx","Integrate[(1 - 2*x)^(5/2)*Sqrt[3 + 5*x],x]","\frac{43923 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(19200 x^4-34880 x^3+18680 x^2+5866 x-4443\right)}{96000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(-4443 + 5866*x + 18680*x^2 - 34880*x^3 + 19200*x^4) + 43923*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(96000*Sqrt[1 - 2*x])","A",1
2392,1,113,128,0.151921,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{2+3 x} \, dx","Integrate[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x),x]","\frac{30 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(2400 x^2-5940 x+8771\right)+196000 \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-250433 \sqrt{10-20 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{162000 \sqrt{2 x-1}}","\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,"(30*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(8771 - 5940*x + 2400*x^2) - 250433*Sqrt[10 - 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 196000*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(162000*Sqrt[-1 + 2*x])","A",0
2393,1,130,135,0.2351454,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^2} \, dx","Integrate[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^2,x]","\frac{30 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(20 x^2-79 x-116\right)-3500 (3 x+2) \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+2119 \sqrt{10-20 x} (3 x+2) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{900 \sqrt{2 x-1} (3 x+2)}","-\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,"(30*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(-116 - 79*x + 20*x^2) + 2119*Sqrt[10 - 20*x]*(2 + 3*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 3500*(2 + 3*x)*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(900*Sqrt[-1 + 2*x]*(2 + 3*x))","A",0
2394,1,134,144,0.2325041,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^3} \, dx","Integrate[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^3,x]","\frac{15 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(48 x^2+435 x+236\right)-775 \sqrt{14 x-7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-472 \sqrt{10-20 x} (3 x+2)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{540 \sqrt{2 x-1} (3 x+2)^2}","-\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,"(15*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(236 + 435*x + 48*x^2) - 472*Sqrt[10 - 20*x]*(2 + 3*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 775*(2 + 3*x)^2*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(540*Sqrt[-1 + 2*x]*(2 + 3*x)^2)","A",0
2395,1,134,149,0.2405949,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^4} \, dx","Integrate[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^4,x]","\frac{21 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(7689 x^2+11106 x+3856\right)-32765 \sqrt{14 x-7} (3 x+2)^3 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+448 \sqrt{10-20 x} (3 x+2)^3 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{4536 \sqrt{2 x-1} (3 x+2)^3}","-\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,"(21*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(3856 + 11106*x + 7689*x^2) + 448*Sqrt[10 - 20*x]*(2 + 3*x)^3*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 32765*(2 + 3*x)^3*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(4536*Sqrt[-1 + 2*x]*(2 + 3*x)^3)","A",0
2396,1,79,151,0.0626561,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^5} \, dx","Integrate[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^5,x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(518715 x^3+1059032 x^2+723428 x+164688\right)}{(3 x+2)^4}-219615 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{9408}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(164688 + 723428*x + 1059032*x^2 + 518715*x^3))/(2 + 3*x)^4 - 219615*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/9408","A",1
2397,1,164,180,0.2044958,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^6} \, dx","Integrate[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^6,x]","\frac{1}{70} \left(\frac{6 (5 x+3)^{3/2} (1-2 x)^{7/2}}{(3 x+2)^5}+\frac{251 \left(2352 (5 x+3)^{3/2} (1-2 x)^{5/2}+55 (3 x+2) \left(392 (1-2 x)^{3/2} (5 x+3)^{3/2}+33 (3 x+2) \left(7 \sqrt{1-2 x} \sqrt{5 x+3} (37 x+20)-121 \sqrt{7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)\right)\right)}{9408 (3 x+2)^4}\right)","\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,"((6*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^5 + (251*(2352*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2) + 55*(2 + 3*x)*(392*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2) + 33*(2 + 3*x)*(7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(20 + 37*x) - 121*Sqrt[7]*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))))/(9408*(2 + 3*x)^4))/70","A",1
2398,1,191,209,0.1528735,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^7} \, dx","Integrate[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^7,x]","\frac{1}{392} \left(\frac{130 (5 x+3)^{3/2} (1-2 x)^{7/2}}{(3 x+2)^5}+\frac{28 (5 x+3)^{3/2} (1-2 x)^{7/2}}{(3 x+2)^6}+\frac{5345 \left(2352 (5 x+3)^{3/2} (1-2 x)^{5/2}+55 (3 x+2) \left(392 (1-2 x)^{3/2} (5 x+3)^{3/2}+33 (3 x+2) \left(7 \sqrt{1-2 x} \sqrt{5 x+3} (37 x+20)-121 \sqrt{7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)\right)\right)}{9408 (3 x+2)^4}\right)","-\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,"((28*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^6 + (130*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^5 + (5345*(2352*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2) + 55*(2 + 3*x)*(392*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2) + 33*(2 + 3*x)*(7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(20 + 37*x) - 121*Sqrt[7]*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))))/(9408*(2 + 3*x)^4))/392","A",1
2399,1,94,194,0.2220094,"\int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^{3/2} \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^(3/2),x]","\frac{2487306914169 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(7741440000000 x^8+10340352000000 x^7-5488281600000 x^6-11337362944000 x^5+569714643200 x^4+4956975460160 x^3+580113118440 x^2-1173301694402 x+115416461871\right)}{573440000000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(115416461871 - 1173301694402*x + 580113118440*x^2 + 4956975460160*x^3 + 569714643200*x^4 - 11337362944000*x^5 - 5488281600000*x^6 + 10340352000000*x^7 + 7741440000000*x^8) + 2487306914169*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(573440000000*Sqrt[1 - 2*x])","A",1
2400,1,89,187,0.0972569,"\int (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{3/2} \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2),x]","\frac{7734796377 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(18432000000 x^7+11008000000 x^6-22359552000 x^5-11310534400 x^4+11299817280 x^3+4697196520 x^2-3203105666 x+104420943\right)}{3584000000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(104420943 - 3203105666*x + 4697196520*x^2 + 11299817280*x^3 - 11310534400*x^4 - 22359552000*x^5 + 11008000000*x^6 + 18432000000*x^7) + 7734796377*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(3584000000*Sqrt[1 - 2*x])","A",1
2401,1,84,160,0.0888653,"\int (1-2 x)^{5/2} (2+3 x) (3+5 x)^{3/2} \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^(3/2),x]","\frac{30438639 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(51200000 x^6-8704000 x^5-59500800 x^4+15200960 x^3+25975640 x^2-8971662 x-717399\right)}{25600000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(-717399 - 8971662*x + 25975640*x^2 + 15200960*x^3 - 59500800*x^4 - 8704000*x^5 + 51200000*x^6) + 30438639*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(25600000*Sqrt[1 - 2*x])","A",1
2402,1,79,138,0.0787006,"\int (1-2 x)^{5/2} (3+5 x)^{3/2} \, dx","Integrate[(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2),x]","\frac{10 \sqrt{5 x+3} \left(-512000 x^5+505600 x^4+230080 x^3-410280 x^2+57074 x+29673\right)+483153 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{640000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(29673 + 57074*x - 410280*x^2 + 230080*x^3 + 505600*x^4 - 512000*x^5) + 483153*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(640000*Sqrt[1 - 2*x])","A",1
2403,1,118,150,0.1814761,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{2+3 x} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x),x]","\frac{30 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(432000 x^3-607200 x^2+230940 x+59599\right)-3136000 \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-1922677 \sqrt{10-20 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{7776000 \sqrt{2 x-1}}","\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,"(30*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(59599 + 230940*x - 607200*x^2 + 432000*x^3) - 1922677*Sqrt[10 - 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 3136000*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(7776000*Sqrt[-1 + 2*x])","A",0
2404,1,135,157,0.2503263,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^2} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^2,x]","\frac{30 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(7200 x^3-13740 x^2+17277 x+21718\right)+322000 (3 x+2) \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-326717 \sqrt{10-20 x} (3 x+2) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{97200 \sqrt{2 x-1} (3 x+2)}","-\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,"(30*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(21718 + 17277*x - 13740*x^2 + 7200*x^3) - 326717*Sqrt[10 - 20*x]*(2 + 3*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 322000*(2 + 3*x)*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(97200*Sqrt[-1 + 2*x]*(2 + 3*x))","A",0
2405,1,139,164,0.2684127,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^3} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^3,x]","\frac{15 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(360 x^3-1230 x^2-3471 x-1628\right)-9725 \sqrt{14 x-7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+6829 \sqrt{10-20 x} (3 x+2)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{1620 \sqrt{2 x-1} (3 x+2)^2}","-\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,"(15*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(-1628 - 3471*x - 1230*x^2 + 360*x^3) + 6829*Sqrt[10 - 20*x]*(2 + 3*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 9725*(2 + 3*x)^2*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(1620*Sqrt[-1 + 2*x]*(2 + 3*x)^2)","A",0
2406,1,139,171,0.2766627,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^4} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^4,x]","\frac{21 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(4320 x^3+34341 x^2+36234 x+10304\right)+215 \sqrt{14 x-7} (3 x+2)^3 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-20272 \sqrt{10-20 x} (3 x+2)^3 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{13608 \sqrt{2 x-1} (3 x+2)^3}","-\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,"(21*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(10304 + 36234*x + 34341*x^2 + 4320*x^3) - 20272*Sqrt[10 - 20*x]*(2 + 3*x)^3*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 215*(2 + 3*x)^3*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(13608*Sqrt[-1 + 2*x]*(2 + 3*x)^3)","A",0
2407,1,139,178,0.3110513,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^5} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^5,x]","\frac{21 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(1790325 x^3+4103592 x^2+2947548 x+677168\right)-3244595 \sqrt{14 x-7} (3 x+2)^4 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+125440 \sqrt{10-20 x} (3 x+2)^4 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{762048 \sqrt{2 x-1} (3 x+2)^4}","-\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,"(21*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(677168 + 2947548*x + 4103592*x^2 + 1790325*x^3) + 125440*Sqrt[10 - 20*x]*(2 + 3*x)^4*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 3244595*(2 + 3*x)^4*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(762048*Sqrt[-1 + 2*x]*(2 + 3*x)^4)","A",0
2408,1,109,180,0.120121,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^6} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^6,x]","\frac{11 \left(\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(100159 x^3+213240 x^2+145940 x+32400\right)}{(3 x+2)^4}-43923 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{43904}+\frac{(1-2 x)^{5/2} (5 x+3)^{5/2}}{5 (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,"((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(5*(2 + 3*x)^5) + (11*((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(32400 + 145940*x + 213240*x^2 + 100159*x^3))/(2 + 3*x)^4 - 43923*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/43904","A",1
2409,1,138,209,0.1427542,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^7} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^7,x]","\frac{1}{28} \left(\frac{935 \left(\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(100159 x^3+213240 x^2+145940 x+32400\right)}{(3 x+2)^4}-43923 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{43904}+\frac{2 (5 x+3)^{5/2} (1-2 x)^{7/2}}{(3 x+2)^6}+\frac{17 (5 x+3)^{5/2} (1-2 x)^{5/2}}{(3 x+2)^5}\right)","\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,"((2*(1 - 2*x)^(7/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^6 + (17*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^5 + (935*((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(32400 + 145940*x + 213240*x^2 + 100159*x^3))/(2 + 3*x)^4 - 43923*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/43904)/28","A",1
2410,1,221,238,0.3182913,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^8} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^8,x]","\frac{1}{49} \left(\frac{47 (5 x+3)^{5/2} (1-2 x)^{7/2}}{4 (3 x+2)^6}+\frac{3 (5 x+3)^{5/2} (1-2 x)^{7/2}}{(3 x+2)^7}+\frac{783 \left(43904 (1-2 x)^{5/2} (5 x+3)^{5/2}+55 (3 x+2) \left(5488 (1-2 x)^{3/2} (5 x+3)^{5/2}+11 (3 x+2) \left(2744 \sqrt{1-2 x} (5 x+3)^{5/2}-11 (3 x+2) \left(7 \sqrt{1-2 x} \sqrt{5 x+3} (169 x+108)+363 \sqrt{7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)\right)\right)\right)}{351232 (3 x+2)^5}\right)","-\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,"((3*(1 - 2*x)^(7/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^7 + (47*(1 - 2*x)^(7/2)*(3 + 5*x)^(5/2))/(4*(2 + 3*x)^6) + (783*(43904*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2) + 55*(2 + 3*x)*(5488*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2) + 11*(2 + 3*x)*(2744*Sqrt[1 - 2*x]*(3 + 5*x)^(5/2) - 11*(2 + 3*x)*(7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(108 + 169*x) + 363*Sqrt[7]*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])))))/(351232*(2 + 3*x)^5))/49","A",1
2411,1,99,216,0.2432712,"\int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^{5/2} \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^(5/2),x]","\frac{19572494692443 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(82575360000000 x^9+163602432000000 x^8+16806297600000 x^7-152280832000000 x^6-74172819968000 x^5+48825346630400 x^4+38603789187520 x^3-3650664293320 x^2-9390934073894 x+1496712721437\right)}{1376256000000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(1496712721437 - 9390934073894*x - 3650664293320*x^2 + 38603789187520*x^3 + 48825346630400*x^4 - 74172819968000*x^5 - 152280832000000*x^6 + 16806297600000*x^7 + 163602432000000*x^8 + 82575360000000*x^9) + 19572494692443*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(1376256000000*Sqrt[1 - 2*x])","A",1
2412,1,94,209,0.1053722,"\int (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{5/2} \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2),x]","\frac{447958686021 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(1548288000000 x^8+1950105600000 x^7-1168107520000 x^6-2124371456000 x^5+186330348800 x^4+919076261440 x^3+85960565960 x^2-214160462618 x+22414998339\right)}{68812800000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(22414998339 - 214160462618*x + 85960565960*x^2 + 919076261440*x^3 + 186330348800*x^4 - 2124371456000*x^5 - 1168107520000*x^6 + 1950105600000*x^7 + 1548288000000*x^8) + 447958686021*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(68812800000*Sqrt[1 - 2*x])","A",1
2413,1,89,182,0.0976288,"\int (1-2 x)^{5/2} (2+3 x) (3+5 x)^{5/2} \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^(5/2),x]","\frac{1376502897 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(3686400000 x^7+1914880000 x^6-4423168000 x^5-1928902400 x^4+2174838080 x^3+793975720 x^2-590379826 x+24901623\right)}{430080000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(24901623 - 590379826*x + 793975720*x^2 + 2174838080*x^3 - 1928902400*x^4 - 4423168000*x^5 + 1914880000*x^6 + 3686400000*x^7) + 1376502897*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(430080000*Sqrt[1 - 2*x])","A",1
2414,1,84,160,0.0870777,"\int (1-2 x)^{5/2} (3+5 x)^{5/2} \, dx","Integrate[(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2),x]","\frac{5314683 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(10240000 x^6-2560000 x^5-11091200 x^4+3408320 x^3+4538680 x^2-1703014 x-96003\right)}{3072000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(-96003 - 1703014*x + 4538680*x^2 + 3408320*x^3 - 11091200*x^4 - 2560000*x^5 + 10240000*x^6) + 5314683*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(3072000*Sqrt[1 - 2*x])","A",1
2415,1,123,172,0.2105106,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{2+3 x} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x),x]","\frac{30 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(20736000 x^4-11836800 x^3-11943840 x^2+8506260 x+2165117\right)+12544000 \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-109715471 \sqrt{10-20 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{93312000 \sqrt{2 x-1}}","\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,"(30*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(2165117 + 8506260*x - 11943840*x^2 - 11836800*x^3 + 20736000*x^4) - 109715471*Sqrt[10 - 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 12544000*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(93312000*Sqrt[-1 + 2*x])","A",0
2416,1,140,179,0.2777233,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^2} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^2,x]","\frac{30 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(259200 x^4-214560 x^3-60348 x^2+72849 x-45658\right)-1657600 (3 x+2) \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+660959 \sqrt{10-20 x} (3 x+2) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{933120 \sqrt{2 x-1} (3 x+2)}","-\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,"(30*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(-45658 + 72849*x - 60348*x^2 - 214560*x^3 + 259200*x^4) + 660959*Sqrt[10 - 20*x]*(2 + 3*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 1657600*(2 + 3*x)*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(933120*Sqrt[-1 + 2*x]*(2 + 3*x))","A",0
2417,1,144,188,0.2777534,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^3} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^3,x]","\frac{6 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(21600 x^4-28980 x^3+31731 x^2+120534 x+53204\right)+87740 \sqrt{14 x-7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-81733 \sqrt{10-20 x} (3 x+2)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{11664 \sqrt{2 x-1} (3 x+2)^2}","\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,"(6*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(53204 + 120534*x + 31731*x^2 - 28980*x^3 + 21600*x^4) - 81733*Sqrt[10 - 20*x]*(2 + 3*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 87740*(2 + 3*x)^2*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(11664*Sqrt[-1 + 2*x]*(2 + 3*x)^2)","A",0
2418,1,144,195,0.3224514,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^4} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^4,x]","\frac{21 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(32400 x^4-93420 x^3-420531 x^2-391014 x-107984\right)-408665 \sqrt{14 x-7} (3 x+2)^3 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+307090 \sqrt{10-20 x} (3 x+2)^3 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{40824 \sqrt{2 x-1} (3 x+2)^3}","-\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,"(21*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(-107984 - 391014*x - 420531*x^2 - 93420*x^3 + 32400*x^4) + 307090*Sqrt[10 - 20*x]*(2 + 3*x)^3*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 408665*(2 + 3*x)^3*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(40824*Sqrt[-1 + 2*x]*(2 + 3*x)^3)","A",0
2419,1,144,200,0.3547607,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^5} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^5,x]","\frac{21 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(3628800 x^4+29475315 x^3+45563928 x^2+25998852 x+5093072\right)+3304795 \sqrt{14 x-7} (3 x+2)^4 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-5801600 \sqrt{10-20 x} (3 x+2)^4 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{2286144 \sqrt{2 x-1} (3 x+2)^4}","\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,"(21*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(5093072 + 25998852*x + 45563928*x^2 + 29475315*x^3 + 3628800*x^4) - 5801600*Sqrt[10 - 20*x]*(2 + 3*x)^4*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 3304795*(2 + 3*x)^4*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(2286144*Sqrt[-1 + 2*x]*(2 + 3*x)^4)","A",0
2420,1,144,207,0.3788406,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^6} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^6,x]","\frac{21 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} \left(490413015 x^4+1809469170 x^3+2146957188 x^2+1044006792 x+180761312\right)-548577355 \sqrt{14 x-7} (3 x+2)^5 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+43904000 \sqrt{10-20 x} (3 x+2)^5 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{160030080 \sqrt{2 x-1} (3 x+2)^5}","\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,"(21*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(180761312 + 1044006792*x + 2146957188*x^2 + 1809469170*x^3 + 490413015*x^4) + 43904000*Sqrt[10 - 20*x]*(2 + 3*x)^5*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 548577355*(2 + 3*x)^5*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(160030080*Sqrt[-1 + 2*x]*(2 + 3*x)^5)","A",0
2421,1,138,209,0.142892,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^7} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^7,x]","\frac{121 \left(\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(814395 x^3+1285720 x^2+654436 x+105552\right)}{(3 x+2)^4}-219615 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{3687936}+\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{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,"((1 - 2*x)^(5/2)*(3 + 5*x)^(7/2))/(6*(2 + 3*x)^6) + (11*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2))/(12*(2 + 3*x)^5) + (121*((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(105552 + 654436*x + 1285720*x^2 + 814395*x^3))/(2 + 3*x)^4 - 219615*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/3687936","A",1
2422,1,219,238,0.2180017,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^8} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^8,x]","\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{407 \left(307328 (1-2 x)^{3/2} (5 x+3)^{7/2}+11 (3 x+2) \left(115248 \sqrt{1-2 x} (5 x+3)^{7/2}-11 (3 x+2) \left(2744 \sqrt{1-2 x} (5 x+3)^{5/2}+55 (3 x+2) \left(7 \sqrt{1-2 x} \sqrt{5 x+3} (169 x+108)+363 \sqrt{7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)\right)\right)\right)}{51631104 (3 x+2)^5}","\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,"(3*(1 - 2*x)^(7/2)*(3 + 5*x)^(7/2))/(49*(2 + 3*x)^7) + (37*(1 - 2*x)^(5/2)*(3 + 5*x)^(7/2))/(84*(2 + 3*x)^6) + (407*(307328*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2) + 11*(2 + 3*x)*(115248*Sqrt[1 - 2*x]*(3 + 5*x)^(7/2) - 11*(2 + 3*x)*(2744*Sqrt[1 - 2*x]*(3 + 5*x)^(5/2) + 55*(2 + 3*x)*(7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(108 + 169*x) + 363*Sqrt[7]*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])))))/(51631104*(2 + 3*x)^5)","A",1
2423,1,249,267,0.3033126,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^9} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^9,x]","\frac{1}{56} \left(\frac{999 (1-2 x)^{7/2} (5 x+3)^{7/2}}{98 (3 x+2)^7}+\frac{3 (1-2 x)^{7/2} (5 x+3)^{7/2}}{(3 x+2)^8}+\frac{12041 \left(614656 (1-2 x)^{5/2} (5 x+3)^{7/2}+11 (3 x+2) \left(307328 (1-2 x)^{3/2} (5 x+3)^{7/2}+11 (3 x+2) \left(115248 \sqrt{1-2 x} (5 x+3)^{7/2}-11 (3 x+2) \left(2744 \sqrt{1-2 x} (5 x+3)^{5/2}+55 (3 x+2) \left(7 \sqrt{1-2 x} \sqrt{5 x+3} (169 x+108)+363 \sqrt{7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)\right)\right)\right)\right)}{103262208 (3 x+2)^6}\right)","\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,"((3*(1 - 2*x)^(7/2)*(3 + 5*x)^(7/2))/(2 + 3*x)^8 + (999*(1 - 2*x)^(7/2)*(3 + 5*x)^(7/2))/(98*(2 + 3*x)^7) + (12041*(614656*(1 - 2*x)^(5/2)*(3 + 5*x)^(7/2) + 11*(2 + 3*x)*(307328*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2) + 11*(2 + 3*x)*(115248*Sqrt[1 - 2*x]*(3 + 5*x)^(7/2) - 11*(2 + 3*x)*(2744*Sqrt[1 - 2*x]*(3 + 5*x)^(5/2) + 55*(2 + 3*x)*(7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(108 + 169*x) + 363*Sqrt[7]*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))))))/(103262208*(2 + 3*x)^6))/56","A",1
2424,1,89,179,0.1156594,"\int \frac{(1-2 x)^{5/2} (2+3 x)^4}{\sqrt{3+5 x}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^4)/Sqrt[3 + 5*x],x]","\frac{266276571099 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(497664000000 x^7+374630400000 x^6-607578624000 x^5-403491052800 x^4+322052135360 x^3+174481885240 x^2-100668418342 x+920643741\right)}{268800000000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(920643741 - 100668418342*x + 174481885240*x^2 + 322052135360*x^3 - 403491052800*x^4 - 607578624000*x^5 + 374630400000*x^6 + 497664000000*x^7) + 266276571099*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(268800000000*Sqrt[1 - 2*x])","A",1
2425,1,84,150,0.150072,"\int \frac{(1-2 x)^{5/2} (2+3 x)^3}{\sqrt{3+5 x}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^3)/Sqrt[3 + 5*x],x]","\frac{1104036549 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(1382400000 x^6-13824000 x^5-1797292800 x^4+261623360 x^3+903127240 x^2-254844442 x-39899709\right)}{1920000000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(-39899709 - 254844442*x + 903127240*x^2 + 261623360*x^3 - 1797292800*x^4 - 13824000*x^5 + 1382400000*x^6) + 1104036549*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(1920000000*Sqrt[1 - 2*x])","A",1
2426,1,79,143,0.0826602,"\int \frac{(1-2 x)^{5/2} (2+3 x)^2}{\sqrt{3+5 x}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^2)/Sqrt[3 + 5*x],x]","\frac{10 \sqrt{5 x+3} \left(-13824000 x^5+11347200 x^4+10295360 x^3-13024760 x^2+387158 x+1498491\right)+19593651 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{48000000 \sqrt{1-2 x}}","-\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,"(10*Sqrt[3 + 5*x]*(1498491 + 387158*x - 13024760*x^2 + 10295360*x^3 + 11347200*x^4 - 13824000*x^5) + 19593651*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(48000000*Sqrt[1 - 2*x])","A",1
2427,1,74,116,0.0726546,"\int \frac{(1-2 x)^{5/2} (2+3 x)}{\sqrt{3+5 x}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x))/Sqrt[3 + 5*x],x]","\frac{195657 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{5 x+3} \left(57600 x^4-99520 x^3+41320 x^2+40094 x-21537\right)}{480000 \sqrt{1-2 x}}","-\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,"(-10*Sqrt[3 + 5*x]*(-21537 + 40094*x + 41320*x^2 - 99520*x^3 + 57600*x^4) + 195657*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(480000*Sqrt[1 - 2*x])","A",1
2428,1,69,94,0.065262,"\int \frac{(1-2 x)^{5/2}}{\sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(5/2)/Sqrt[3 + 5*x],x]","\frac{10 \sqrt{5 x+3} \left(-320 x^3+920 x^2-1406 x+513\right)+3993 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{6000 \sqrt{1-2 x}}","\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,"(10*Sqrt[3 + 5*x]*(513 - 1406*x + 920*x^2 - 320*x^3) + 3993*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(6000*Sqrt[1 - 2*x])","A",1
2429,1,108,106,0.1198419,"\int \frac{(1-2 x)^{5/2}}{(2+3 x) \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)*Sqrt[3 + 5*x]),x]","\frac{30 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} (60 x-269)-49000 \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+17687 \sqrt{10-20 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{13500 \sqrt{2 x-1}}","-\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,"(30*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(-269 + 60*x) + 17687*Sqrt[10 - 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 49000*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(13500*Sqrt[-1 + 2*x])","A",0
2430,1,125,115,0.1833786,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^2 \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^2*Sqrt[3 + 5*x]),x]","\frac{15 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} (12 x+253)-4375 (3 x+2) \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-346 \sqrt{10-20 x} (3 x+2) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{675 \sqrt{2 x-1} (3 x+2)}","\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,"(15*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(253 + 12*x) - 346*Sqrt[10 - 20*x]*(2 + 3*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 4375*(2 + 3*x)*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(675*Sqrt[-1 + 2*x]*(2 + 3*x))","A",0
2431,1,129,122,0.1970384,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^3 \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^3*Sqrt[3 + 5*x]),x]","\frac{105 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} (261 x+188)-15175 \sqrt{14 x-7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+32 \sqrt{10-20 x} (3 x+2)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{540 \sqrt{2 x-1} (3 x+2)^2}","\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,"(105*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(188 + 261*x) + 32*Sqrt[10 - 20*x]*(2 + 3*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 15175*(2 + 3*x)^2*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(540*Sqrt[-1 + 2*x]*(2 + 3*x)^2)","A",0
2432,1,74,122,0.0507144,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^4 \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^4*Sqrt[3 + 5*x]),x]","\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(15707 x^2+21638 x+7488\right)}{24 (3 x+2)^3}-\frac{6655 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{8 \sqrt{7}}","\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[1 - 2*x]*Sqrt[3 + 5*x]*(7488 + 21638*x + 15707*x^2))/(24*(2 + 3*x)^3) - (6655*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(8*Sqrt[7])","A",1
2433,1,104,151,0.1045268,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^5 \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^5*Sqrt[3 + 5*x]),x]","\frac{247 \left(\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(15707 x^2+21638 x+7488\right)}{(3 x+2)^3}-19965 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{9408}+\frac{3 \sqrt{5 x+3} (1-2 x)^{7/2}}{28 (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,"(3*(1 - 2*x)^(7/2)*Sqrt[3 + 5*x])/(28*(2 + 3*x)^4) + (247*((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(7488 + 21638*x + 15707*x^2))/(2 + 3*x)^3 - 19965*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/9408","A",1
2434,1,135,180,0.1108778,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^6 \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^6*Sqrt[3 + 5*x]),x]","\frac{1}{35} \left(\frac{78167 \left(\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(15707 x^2+21638 x+7488\right)}{(3 x+2)^3}-19965 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{18816}+\frac{963 \sqrt{5 x+3} (1-2 x)^{7/2}}{56 (3 x+2)^4}+\frac{3 \sqrt{5 x+3} (1-2 x)^{7/2}}{(3 x+2)^5}\right)","\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,"((3*(1 - 2*x)^(7/2)*Sqrt[3 + 5*x])/(2 + 3*x)^5 + (963*(1 - 2*x)^(7/2)*Sqrt[3 + 5*x])/(56*(2 + 3*x)^4) + (78167*((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(7488 + 21638*x + 15707*x^2))/(2 + 3*x)^3 - 19965*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/18816)/35","A",1
2435,1,193,209,0.217947,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^7 \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^7*Sqrt[3 + 5*x]),x]","\frac{1}{42} \left(\frac{237 \sqrt{5 x+3} (1-2 x)^{7/2}}{14 (3 x+2)^5}+\frac{3 \sqrt{5 x+3} (1-2 x)^{7/2}}{(3 x+2)^6}+\frac{8332464 \sqrt{5 x+3} (1-2 x)^{7/2}+2012291 (3 x+2) \left(56 \sqrt{5 x+3} (1-2 x)^{5/2}+55 (3 x+2) \left(7 \sqrt{1-2 x} \sqrt{5 x+3} (95 x+68)-363 \sqrt{7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)\right)}{87808 (3 x+2)^4}\right)","\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,"((3*(1 - 2*x)^(7/2)*Sqrt[3 + 5*x])/(2 + 3*x)^6 + (237*(1 - 2*x)^(7/2)*Sqrt[3 + 5*x])/(14*(2 + 3*x)^5) + (8332464*(1 - 2*x)^(7/2)*Sqrt[3 + 5*x] + 2012291*(2 + 3*x)*(56*(1 - 2*x)^(5/2)*Sqrt[3 + 5*x] + 55*(2 + 3*x)*(7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(68 + 95*x) - 363*Sqrt[7]*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])))/(87808*(2 + 3*x)^4))/42","A",1
2436,1,98,186,0.0965512,"\int \frac{(1-2 x)^{5/2} (2+3 x)^4}{(3+5 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^4)/(3 + 5*x)^(3/2),x]","\frac{1298595837 \sqrt{5 x+3} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \left(6912000000 x^7+4631040000 x^6-9103968000 x^5-4815780800 x^4+5550785640 x^3+1793366630 x^2-1029299623 x-168414751\right)}{3200000000 \sqrt{1-2 x} \sqrt{5 x+3}}","-\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,"(-10*(-168414751 - 1029299623*x + 1793366630*x^2 + 5550785640*x^3 - 4815780800*x^4 - 9103968000*x^5 + 4631040000*x^6 + 6912000000*x^7) + 1298595837*Sqrt[3 + 5*x]*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(3200000000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])","A",1
2437,1,93,157,0.0743476,"\int \frac{(1-2 x)^{5/2} (2+3 x)^3}{(3+5 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(3 + 5*x)^(3/2),x]","\frac{24319911 \sqrt{5 x+3} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \left(69120000 x^6-9504000 x^5-91502400 x^4+31284920 x^3+44775890 x^2-8158469 x-6089453\right)}{80000000 \sqrt{1-2 x} \sqrt{5 x+3}}","-\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,"(-10*(-6089453 - 8158469*x + 44775890*x^2 + 31284920*x^3 - 91502400*x^4 - 9504000*x^5 + 69120000*x^6) + 24319911*Sqrt[3 + 5*x]*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(80000000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])","A",1
2438,1,88,138,0.0756895,"\int \frac{(1-2 x)^{5/2} (2+3 x)^2}{(3+5 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^2)/(3 + 5*x)^(3/2),x]","\frac{236313 \sqrt{5 x+3} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \left(288000 x^5-299200 x^4-147640 x^3+381870 x^2+24773 x-79699\right)}{800000 \sqrt{1-2 x} \sqrt{5 x+3}}","-\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,"(-10*(-79699 + 24773*x + 381870*x^2 - 147640*x^3 - 299200*x^4 + 288000*x^5) + 236313*Sqrt[3 + 5*x]*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(800000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])","A",1
2439,1,83,116,0.0634879,"\int \frac{(1-2 x)^{5/2} (2+3 x)}{(3+5 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x))/(3 + 5*x)^(3/2),x]","\frac{2541 \sqrt{5 x+3} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \left(1600 x^4-3480 x^3+3590 x^2+761 x-943\right)}{10000 \sqrt{1-2 x} \sqrt{5 x+3}}","-\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,"(-10*(-943 + 761*x + 3590*x^2 - 3480*x^3 + 1600*x^4) + 2541*Sqrt[3 + 5*x]*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(10000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])","A",1
2440,1,39,94,0.0118526,"\int \frac{(1-2 x)^{5/2}}{(3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/(3 + 5*x)^(3/2),x]","-\frac{2}{77} \sqrt{\frac{2}{11}} (1-2 x)^{7/2} \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};-\frac{5}{11} (2 x-1)\right)","-\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,"(-2*Sqrt[2/11]*(1 - 2*x)^(7/2)*Hypergeometric2F1[3/2, 7/2, 9/2, (-5*(-1 + 2*x))/11])/77","C",1
2441,1,140,108,0.8211706,"\int \frac{(1-2 x)^{5/2}}{(2+3 x) (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)*(3 + 5*x)^(3/2)),x]","\frac{2 \left(6 \sqrt{22} (1-2 x)^{5/2} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};-\frac{5}{11} (2 x-1)\right)+847 \left(-\frac{33 \sqrt{1-2 x}}{\sqrt{5 x+3}}+35 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+\frac{2 \sqrt{\frac{2}{5}} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{\sqrt{-(1-2 x)^2}}\right)\right)}{5445}","-\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*(847*((-33*Sqrt[1 - 2*x])/Sqrt[3 + 5*x] + (2*Sqrt[2/5]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/Sqrt[-(1 - 2*x)^2] + 35*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]) + 6*Sqrt[22]*(1 - 2*x)^(5/2)*Hypergeometric2F1[3/2, 5/2, 7/2, (-5*(-1 + 2*x))/11]))/5445","C",1
2442,1,196,115,0.3735177,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^2 (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^2*(3 + 5*x)^(3/2)),x]","\frac{-15450 \sqrt{22} \left(15 x^2+19 x+6\right) \left(-(1-2 x)^2\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};-\frac{5}{11} (2 x-1)\right)-1815 \sqrt{5 x+3} \left(3090 x^2+129817 x+82313\right) \sqrt{-(1-2 x)^2}+70406875 \sqrt{14 x-7} \left(15 x^2+19 x+6\right) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+1267717 \sqrt{10-20 x} \left(15 x^2+19 x+6\right) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{952875 \sqrt{2 x-1} (3 x+2) (5 x+3)}","\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,"(-1815*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(82313 + 129817*x + 3090*x^2) + 1267717*Sqrt[10 - 20*x]*(6 + 19*x + 15*x^2)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 70406875*Sqrt[-7 + 14*x]*(6 + 19*x + 15*x^2)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])] - 15450*Sqrt[22]*(-(1 - 2*x)^2)^(3/2)*(6 + 19*x + 15*x^2)*Hypergeometric2F1[3/2, 5/2, 7/2, (-5*(-1 + 2*x))/11])/(952875*Sqrt[-1 + 2*x]*(2 + 3*x)*(3 + 5*x))","C",0
2443,1,74,115,0.0459312,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^3 (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^3*(3 + 5*x)^(3/2)),x]","\frac{1815}{4} \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-\frac{\sqrt{1-2 x} \left(16657 x^2+21843 x+7148\right)}{4 (3 x+2)^2 \sqrt{5 x+3}}","\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,"-1/4*(Sqrt[1 - 2*x]*(7148 + 21843*x + 16657*x^2))/((2 + 3*x)^2*Sqrt[3 + 5*x]) + (1815*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/4","A",1
2444,1,79,144,0.0718991,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^4 (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^4*(3 + 5*x)^(3/2)),x]","\frac{147015 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{8 \sqrt{7}}-\frac{\sqrt{1-2 x} \left(578245 x^3+1143741 x^2+753654 x+165424\right)}{8 (3 x+2)^3 \sqrt{5 x+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,"-1/8*(Sqrt[1 - 2*x]*(165424 + 753654*x + 1143741*x^2 + 578245*x^3))/((2 + 3*x)^3*Sqrt[3 + 5*x]) + (147015*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(8*Sqrt[7])","A",1
2445,1,84,173,0.0786495,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^5 (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^5*(3 + 5*x)^(3/2)),x]","\frac{46095555 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-\frac{7 \sqrt{1-2 x} \left(543914475 x^4+1438446565 x^3+1426133132 x^2+628209228 x+103735088\right)}{(3 x+2)^4 \sqrt{5 x+3}}}{3136}","\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,"((-7*Sqrt[1 - 2*x]*(103735088 + 628209228*x + 1426133132*x^2 + 1438446565*x^3 + 543914475*x^4))/((2 + 3*x)^4*Sqrt[3 + 5*x]) + 46095555*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/3136","A",1
2446,1,157,202,0.2019961,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^6 (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^6*(3 + 5*x)^(3/2)),x]","\frac{131376 (3 x+2) (1-2 x)^{7/2}+18816 (1-2 x)^{7/2}+(3 x+2)^2 \left(973656 (1-2 x)^{7/2}+9748787 (3 x+2) \left(2 (1-2 x)^{5/2}+55 (3 x+2) \left(33 \sqrt{7} (3 x+2) \sqrt{5 x+3} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-\sqrt{1-2 x} (101 x+65)\right)\right)\right)}{219520 (3 x+2)^5 \sqrt{5 x+3}}","\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,"(18816*(1 - 2*x)^(7/2) + 131376*(1 - 2*x)^(7/2)*(2 + 3*x) + (2 + 3*x)^2*(973656*(1 - 2*x)^(7/2) + 9748787*(2 + 3*x)*(2*(1 - 2*x)^(5/2) + 55*(2 + 3*x)*(-(Sqrt[1 - 2*x]*(65 + 101*x)) + 33*Sqrt[7]*(2 + 3*x)*Sqrt[3 + 5*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))))/(219520*(2 + 3*x)^5*Sqrt[3 + 5*x])","A",1
2447,1,98,193,0.1353438,"\int \frac{(1-2 x)^{5/2} (2+3 x)^4}{(3+5 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^4)/(3 + 5*x)^(5/2),x]","\frac{264889779 (5 x+3)^{3/2} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \left(3110400000 x^7+1697760000 x^6-4464936000 x^5-1391171400 x^4+3137091690 x^3+1095371425 x^2-558948208 x-210855251\right)}{1200000000 \sqrt{1-2 x} (5 x+3)^{3/2}}","-\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,"(-10*(-210855251 - 558948208*x + 1095371425*x^2 + 3137091690*x^3 - 1391171400*x^4 - 4464936000*x^5 + 1697760000*x^6 + 3110400000*x^7) + 264889779*(3 + 5*x)^(3/2)*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(1200000000*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))","A",1
2448,1,93,164,0.1072678,"\int \frac{(1-2 x)^{5/2} (2+3 x)^3}{(3+5 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(3 + 5*x)^(5/2),x]","\frac{2300529 (5 x+3)^{3/2} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \left(12960000 x^6-4536000 x^5-16421400 x^4+13874190 x^3+12677675 x^2-3232208 x-2322001\right)}{12000000 \sqrt{1-2 x} (5 x+3)^{3/2}}","-\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,"(-10*(-2322001 - 3232208*x + 12677675*x^2 + 13874190*x^3 - 16421400*x^4 - 4536000*x^5 + 12960000*x^6) + 2300529*(3 + 5*x)^(3/2)*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(12000000*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))","A",1
2449,1,88,138,0.101404,"\int \frac{(1-2 x)^{5/2} (2+3 x)^2}{(3+5 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^2)/(3 + 5*x)^(5/2),x]","\frac{10857 (5 x+3)^{3/2} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \left(72000 x^5-106200 x^4+42270 x^3+78275 x^2-19664 x-10633\right)}{150000 \sqrt{1-2 x} (5 x+3)^{3/2}}","-\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,"(-10*(-10633 - 19664*x + 78275*x^2 + 42270*x^3 - 106200*x^4 + 72000*x^5) + 10857*(3 + 5*x)^(3/2)*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(150000*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))","A",1
2450,1,59,116,0.040255,"\int \frac{(1-2 x)^{5/2} (2+3 x)}{(3+5 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x))/(3 + 5*x)^(5/2),x]","-\frac{2 (1-2 x)^{7/2} \left(13 \sqrt{22} (5 x+3)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};-\frac{5}{11} (2 x-1)\right)+121\right)}{19965 (5 x+3)^{3/2}}","-\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,"(-2*(1 - 2*x)^(7/2)*(121 + 13*Sqrt[22]*(3 + 5*x)^(3/2)*Hypergeometric2F1[3/2, 7/2, 9/2, (-5*(-1 + 2*x))/11]))/(19965*(3 + 5*x)^(3/2))","C",1
2451,1,39,96,0.0108529,"\int \frac{(1-2 x)^{5/2}}{(3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/(3 + 5*x)^(5/2),x]","-\frac{4}{847} \sqrt{\frac{2}{11}} (1-2 x)^{7/2} \, _2F_1\left(\frac{5}{2},\frac{7}{2};\frac{9}{2};-\frac{5}{11} (2 x-1)\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,"(-4*Sqrt[2/11]*(1 - 2*x)^(7/2)*Hypergeometric2F1[5/2, 7/2, 9/2, (-5*(-1 + 2*x))/11])/847","C",1
2452,1,107,108,0.2403169,"\int \frac{(1-2 x)^{5/2}}{(2+3 x) (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)*(3 + 5*x)^(5/2)),x]","\frac{2}{375} \left(\frac{55 \sqrt{1-2 x} (565 x+328)}{(5 x+3)^{3/2}}-6125 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+\frac{4 \sqrt{10} \sqrt{-(1-2 x)^2} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{2 x-1}\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,"(2*((55*Sqrt[1 - 2*x]*(328 + 565*x))/(3 + 5*x)^(3/2) + (4*Sqrt[10]*Sqrt[-(1 - 2*x)^2]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(-1 + 2*x) - 6125*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/375","A",0
2453,1,92,101,0.0430224,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^2 (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^2*(3 + 5*x)^(5/2)),x]","\frac{\sqrt{1-2 x} \left(17667 x^2+21988 x+6823\right)-1155 \sqrt{7} \sqrt{5 x+3} \left(15 x^2+19 x+6\right) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{3 (3 x+2) (5 x+3)^{3/2}}","\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,"(Sqrt[1 - 2*x]*(6823 + 21988*x + 17667*x^2) - 1155*Sqrt[7]*Sqrt[3 + 5*x]*(6 + 19*x + 15*x^2)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(3*(2 + 3*x)*(3 + 5*x)^(3/2))","A",1
2454,1,78,137,0.0659152,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^3 (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^3*(3 + 5*x)^(5/2)),x]","\frac{1}{12} \left(\frac{\sqrt{1-2 x} \left(1809585 x^3+3458634 x^2+2200321 x+465916\right)}{(3 x+2)^2 (5 x+3)^{3/2}}-39435 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\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,"((Sqrt[1 - 2*x]*(465916 + 2200321*x + 3458634*x^2 + 1809585*x^3))/((2 + 3*x)^2*(3 + 5*x)^(3/2)) - 39435*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/12","A",1
2455,1,84,166,0.0746538,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^4 (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^4*(3 + 5*x)^(5/2)),x]","\frac{\sqrt{1-2 x} \left(80308575 x^4+207031680 x^3+199977747 x^2+85776638 x+13784768\right)}{24 (3 x+2)^3 (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}}","\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,"(Sqrt[1 - 2*x]*(13784768 + 85776638*x + 199977747*x^2 + 207031680*x^3 + 80308575*x^4))/(24*(2 + 3*x)^3*(3 + 5*x)^(3/2)) - (1361195*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(8*Sqrt[7])","A",1
2456,1,152,195,0.2159195,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^5 (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^5*(3 + 5*x)^(5/2)),x]","\frac{65016 (3 x+2) (1-2 x)^{7/2}+7056 (1-2 x)^{7/2}+(3 x+2)^2 \left(716706 (1-2 x)^{7/2}+9444023 (3 x+2) \left(3 (1-2 x)^{5/2}-55 (3 x+2) \left(21 \sqrt{7} (5 x+3)^{3/2} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-\sqrt{1-2 x} (107 x+62)\right)\right)\right)}{65856 (3 x+2)^4 (5 x+3)^{3/2}}","\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,"(7056*(1 - 2*x)^(7/2) + 65016*(1 - 2*x)^(7/2)*(2 + 3*x) + (2 + 3*x)^2*(716706*(1 - 2*x)^(7/2) + 9444023*(2 + 3*x)*(3*(1 - 2*x)^(5/2) - 55*(2 + 3*x)*(-(Sqrt[1 - 2*x]*(62 + 107*x)) + 21*Sqrt[7]*(3 + 5*x)^(3/2)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))))/(65856*(2 + 3*x)^4*(3 + 5*x)^(3/2))","A",1
2457,1,170,224,0.2419119,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^6 (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^6*(3 + 5*x)^(5/2)),x]","\frac{3252816 (3 x+2) (1-2 x)^{7/2}+395136 (1-2 x)^{7/2}+(3 x+2)^2 \left(29407896 (1-2 x)^{7/2}+(3 x+2) \left(324091386 (1-2 x)^{7/2}+4270537963 (3 x+2) \left(3 (1-2 x)^{5/2}-55 (3 x+2) \left(21 \sqrt{7} (5 x+3)^{3/2} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-\sqrt{1-2 x} (107 x+62)\right)\right)\right)\right)}{4609920 (3 x+2)^5 (5 x+3)^{3/2}}","\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,"(395136*(1 - 2*x)^(7/2) + 3252816*(1 - 2*x)^(7/2)*(2 + 3*x) + (2 + 3*x)^2*(29407896*(1 - 2*x)^(7/2) + (2 + 3*x)*(324091386*(1 - 2*x)^(7/2) + 4270537963*(2 + 3*x)*(3*(1 - 2*x)^(5/2) - 55*(2 + 3*x)*(-(Sqrt[1 - 2*x]*(62 + 107*x)) + 21*Sqrt[7]*(3 + 5*x)^(3/2)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])))))/(4609920*(2 + 3*x)^5*(3 + 5*x)^(3/2))","A",1
2458,1,88,135,0.0827253,"\int \frac{(2+3 x)^4 \sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","Integrate[((2 + 3*x)^4*Sqrt[3 + 5*x])/Sqrt[1 - 2*x],x]","-\frac{\sqrt{1-2 x} \left(10 \sqrt{2 x-1} \sqrt{5 x+3} \left(20736000 x^4+82339200 x^3+146144160 x^2+163168620 x+157419203\right)+1067352517 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{25600000 \sqrt{2 x-1}}","-\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,"-1/25600000*(Sqrt[1 - 2*x]*(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(157419203 + 163168620*x + 146144160*x^2 + 82339200*x^3 + 20736000*x^4) + 1067352517*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/Sqrt[-1 + 2*x]","A",1
2459,1,83,106,0.1237818,"\int \frac{(2+3 x)^3 \sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","Integrate[((2 + 3*x)^3*Sqrt[3 + 5*x])/Sqrt[1 - 2*x],x]","-\frac{\sqrt{1-2 x} \left(10 \sqrt{2 x-1} \sqrt{5 x+3} \left(17280 x^3+57888 x^2+88092 x+97295\right)+677017 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{51200 \sqrt{2 x-1}}","-\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,"-1/51200*(Sqrt[1 - 2*x]*(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(97295 + 88092*x + 57888*x^2 + 17280*x^3) + 677017*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/Sqrt[-1 + 2*x]","A",1
2460,1,78,99,0.0431335,"\int \frac{(2+3 x)^2 \sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","Integrate[((2 + 3*x)^2*Sqrt[3 + 5*x])/Sqrt[1 - 2*x],x]","-\frac{\sqrt{1-2 x} \left(10 \sqrt{2 x-1} \sqrt{5 x+3} \left(2400 x^2+6660 x+9401\right)+68959 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{16000 \sqrt{2 x-1}}","-\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,"-1/16000*(Sqrt[1 - 2*x]*(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(9401 + 6660*x + 2400*x^2) + 68959*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/Sqrt[-1 + 2*x]","A",1
2461,1,73,72,0.0356234,"\int \frac{(2+3 x) \sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","Integrate[((2 + 3*x)*Sqrt[3 + 5*x])/Sqrt[1 - 2*x],x]","-\frac{\sqrt{1-2 x} \left(10 \sqrt{2 x-1} \sqrt{5 x+3} (60 x+143)+1177 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{800 \sqrt{2 x-1}}","-\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,"-1/800*(Sqrt[1 - 2*x]*(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(143 + 60*x) + 1177*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/Sqrt[-1 + 2*x]","A",1
2462,1,68,50,0.0177575,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","Integrate[Sqrt[3 + 5*x]/Sqrt[1 - 2*x],x]","-\frac{\sqrt{1-2 x} \left(10 \sqrt{2 x-1} \sqrt{5 x+3}+11 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{20 \sqrt{2 x-1}}","\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,"-1/20*(Sqrt[1 - 2*x]*(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x] + 11*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/Sqrt[-1 + 2*x]","A",1
2463,1,75,62,0.0432866,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)} \, dx","Integrate[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*(2 + 3*x)),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{3 \sqrt{7}}-\frac{\sqrt{10-20 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{3 \sqrt{2 x-1}}","\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,"-1/3*(Sqrt[10 - 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/Sqrt[-1 + 2*x] + (2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(3*Sqrt[7])","A",1
2464,1,64,64,0.0276291,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^2} \, dx","Integrate[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*(2 + 3*x)^2),x]","-\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}}","-\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,"-1/7*(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x) - (11*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(7*Sqrt[7])","A",1
2465,1,69,93,0.0377815,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^3} \, dx","Integrate[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*(2 + 3*x)^3),x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} (87 x+44)}{(3 x+2)^2}-451 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1372}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(44 + 87*x))/(2 + 3*x)^2 - 451*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/1372","A",1
2466,1,74,122,0.049193,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^4} \, dx","Integrate[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*(2 + 3*x)^4),x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(11685 x^2+15930 x+5296\right)}{(3 x+2)^3}-15235 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{19208}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(5296 + 15930*x + 11685*x^2))/(2 + 3*x)^3 - 15235*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/19208","A",1
2467,1,79,151,0.059007,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^5} \, dx","Integrate[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*(2 + 3*x)^5),x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(883845 x^3+1806120 x^2+1230876 x+278960\right)}{(3 x+2)^4}-375265 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{153664}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(278960 + 1230876*x + 1806120*x^2 + 883845*x^3))/(2 + 3*x)^4 - 375265*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/153664","A",1
2468,1,88,128,0.1435542,"\int \frac{(2+3 x)^3 (3+5 x)^{3/2}}{\sqrt{1-2 x}} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x)^(3/2))/Sqrt[1 - 2*x],x]","-\frac{\sqrt{1-2 x} \left(10 \sqrt{2 x-1} \sqrt{5 x+3} \left(6912000 x^4+26870400 x^3+46785120 x^2+51453140 x+49229901\right)+333216939 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{5120000 \sqrt{2 x-1}}","-\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,"-1/5120000*(Sqrt[1 - 2*x]*(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(49229901 + 51453140*x + 46785120*x^2 + 26870400*x^3 + 6912000*x^4) + 333216939*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/Sqrt[-1 + 2*x]","A",1
2469,1,83,121,0.0562726,"\int \frac{(2+3 x)^2 (3+5 x)^{3/2}}{\sqrt{1-2 x}} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x)^(3/2))/Sqrt[1 - 2*x],x]","-\frac{\sqrt{1-2 x} \left(10 \sqrt{2 x-1} \sqrt{5 x+3} \left(144000 x^3+469600 x^2+698580 x+760653\right)+5274027 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{256000 \sqrt{2 x-1}}","-\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,"-1/256000*(Sqrt[1 - 2*x]*(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(760653 + 698580*x + 469600*x^2 + 144000*x^3) + 5274027*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/Sqrt[-1 + 2*x]","A",1
2470,1,78,94,0.0438144,"\int \frac{(2+3 x) (3+5 x)^{3/2}}{\sqrt{1-2 x}} \, dx","Integrate[((2 + 3*x)*(3 + 5*x)^(3/2))/Sqrt[1 - 2*x],x]","-\frac{\sqrt{1-2 x} \left(10 \sqrt{2 x-1} \sqrt{5 x+3} \left(800 x^2+2140 x+2943\right)+21417 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{3200 \sqrt{2 x-1}}","-\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,"-1/3200*(Sqrt[1 - 2*x]*(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(2943 + 2140*x + 800*x^2) + 21417*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/Sqrt[-1 + 2*x]","A",1
2471,1,73,72,0.0347463,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x}} \, dx","Integrate[(3 + 5*x)^(3/2)/Sqrt[1 - 2*x],x]","-\frac{\sqrt{1-2 x} \left(50 \sqrt{2 x-1} \sqrt{5 x+3} (4 x+9)+363 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{160 \sqrt{2 x-1}}","-\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,"-1/160*(Sqrt[1 - 2*x]*(50*Sqrt[-1 + 2*x]*(9 + 4*x)*Sqrt[3 + 5*x] + 363*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/Sqrt[-1 + 2*x]","A",1
2472,1,103,86,0.0644666,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)} \, dx","Integrate[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)),x]","\frac{-210 \sqrt{-(2 x-1)^2} \sqrt{5 x+3}-8 \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-203 \sqrt{10-20 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{252 \sqrt{2 x-1}}","-\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,"(-210*Sqrt[-(-1 + 2*x)^2]*Sqrt[3 + 5*x] - 203*Sqrt[10 - 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 8*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(252*Sqrt[-1 + 2*x])","A",1
2473,1,120,91,0.1122576,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^2),x]","\frac{21 \sqrt{-(2 x-1)^2} \sqrt{5 x+3}+103 (3 x+2) \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-245 \sqrt{10-20 x} (3 x+2) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{441 \sqrt{2 x-1} (3 x+2)}","\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,"(21*Sqrt[-(-1 + 2*x)^2]*Sqrt[3 + 5*x] - 245*Sqrt[10 - 20*x]*(2 + 3*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 103*(2 + 3*x)*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(441*Sqrt[-1 + 2*x]*(2 + 3*x))","A",1
2474,1,69,93,0.0404914,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^3),x]","\frac{-\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} (169 x+108)}{(3 x+2)^2}-363 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1372}","-\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,"((-7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(108 + 169*x))/(2 + 3*x)^2 - 363*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/1372","A",1
2475,1,74,122,0.0503659,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^4),x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(2195 x^2+1830 x+288\right)}{(3 x+2)^3}-5445 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{19208}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(288 + 1830*x + 2195*x^2))/(2 + 3*x)^3 - 5445*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/19208","A",1
2476,1,79,151,0.0586631,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^5} \, dx","Integrate[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^5),x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(172785 x^3+346760 x^2+226348 x+48240\right)}{(3 x+2)^4}-78045 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{153664}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(48240 + 226348*x + 346760*x^2 + 172785*x^3))/(2 + 3*x)^4 - 78045*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/153664","A",1
2477,1,84,180,0.0698712,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^6} \, dx","Integrate[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^6),x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(93720915 x^4+253769850 x^3+257531412 x^2+115804328 x+19437408\right)}{(3 x+2)^5}-13320285 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{10756480}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(19437408 + 115804328*x + 257531412*x^2 + 253769850*x^3 + 93720915*x^4))/(2 + 3*x)^5 - 13320285*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/10756480","A",1
2478,1,93,150,0.16277,"\int \frac{(2+3 x)^3 (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x)^(5/2))/Sqrt[1 - 2*x],x]","-\frac{\sqrt{1-2 x} \left(10 \sqrt{2 x-1} \sqrt{5 x+3} \left(138240000 x^5+615168000 x^4+1229558400 x^3+1505007200 x^2+1362715220 x+1202896557\right)+8035077963 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{24576000 \sqrt{2 x-1}}","-\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,"-1/24576000*(Sqrt[1 - 2*x]*(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(1202896557 + 1362715220*x + 1505007200*x^2 + 1229558400*x^3 + 615168000*x^4 + 138240000*x^5) + 8035077963*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/Sqrt[-1 + 2*x]","A",1
2479,1,88,143,0.0750918,"\int \frac{(2+3 x)^2 (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x)^(5/2))/Sqrt[1 - 2*x],x]","-\frac{\sqrt{1-2 x} \left(10 \sqrt{2 x-1} \sqrt{5 x+3} \left(6912000 x^4+26294400 x^3+44906720 x^2+48658820 x+46187289\right)+312120831 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{3072000 \sqrt{2 x-1}}","-\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,"-1/3072000*(Sqrt[1 - 2*x]*(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(46187289 + 48658820*x + 44906720*x^2 + 26294400*x^3 + 6912000*x^4) + 312120831*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/Sqrt[-1 + 2*x]","A",1
2480,1,83,116,0.0644545,"\int \frac{(2+3 x) (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","Integrate[((2 + 3*x)*(3 + 5*x)^(5/2))/Sqrt[1 - 2*x],x]","-\frac{\sqrt{1-2 x} \left(10 \sqrt{2 x-1} \sqrt{5 x+3} \left(28800 x^3+91360 x^2+132868 x+142713\right)+986271 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{30720 \sqrt{2 x-1}}","-\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,"-1/30720*(Sqrt[1 - 2*x]*(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(142713 + 132868*x + 91360*x^2 + 28800*x^3) + 986271*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/Sqrt[-1 + 2*x]","A",1
2481,1,78,96,0.0406836,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","Integrate[(3 + 5*x)^(5/2)/Sqrt[1 - 2*x],x]","-\frac{\sqrt{1-2 x} \left(2 \sqrt{2 x-1} \sqrt{5 x+3} \left(800 x^2+2060 x+2763\right)+3993 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{384 \sqrt{2 x-1}}","-\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,"-1/384*(Sqrt[1 - 2*x]*(2*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(2763 + 2060*x + 800*x^2) + 3993*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/Sqrt[-1 + 2*x]","A",1
2482,1,108,108,0.110094,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)} \, dx","Integrate[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)),x]","\frac{-210 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} (60 x+127)+64 \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-21245 \sqrt{10-20 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{6048 \sqrt{2 x-1}}","-\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,"(-210*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(127 + 60*x) - 21245*Sqrt[10 - 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 64*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(6048*Sqrt[-1 + 2*x])","A",1
2483,1,125,115,0.1895467,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^2),x]","\frac{-42 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} (525 x+352)-692 (3 x+2) \sqrt{14 x-7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-6125 \sqrt{10-20 x} (3 x+2) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{5292 \sqrt{2 x-1} (3 x+2)}","\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,"(-42*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(352 + 525*x) - 6125*Sqrt[10 - 20*x]*(2 + 3*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 692*(2 + 3*x)*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(5292*Sqrt[-1 + 2*x]*(2 + 3*x))","A",1
2484,1,129,120,0.1491683,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^3),x]","\frac{21 \sqrt{-(1-2 x)^2} \sqrt{5 x+3} (927 x+604)+17687 \sqrt{14 x-7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-34300 \sqrt{10-20 x} (3 x+2)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{37044 \sqrt{2 x-1} (3 x+2)^2}","\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,"(21*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x]*(604 + 927*x) - 34300*Sqrt[10 - 20*x]*(2 + 3*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 17687*(2 + 3*x)^2*Sqrt[-7 + 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(37044*Sqrt[-1 + 2*x]*(2 + 3*x)^2)","A",1
2485,1,74,122,0.0543643,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^4),x]","\frac{-\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(37685 x^2+48170 x+15408\right)}{(3 x+2)^3}-19965 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{57624}","-\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,"((-7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(15408 + 48170*x + 37685*x^2))/(2 + 3*x)^3 - 19965*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/57624","A",1
2486,1,79,151,0.0596875,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^5} \, dx","Integrate[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^5),x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(12945 x^3+6920 x^2-6484 x-3600\right)}{(3 x+2)^4}-19965 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{65856}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-3600 - 6484*x + 6920*x^2 + 12945*x^3))/(2 + 3*x)^4 - 19965*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/65856","A",1
2487,1,84,180,0.0713362,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^6} \, dx","Integrate[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^6),x]","\frac{\frac{7 \sqrt{1-2 x} \sqrt{5 x+3} \left(87703335 x^4+231277650 x^3+222865988 x^2+93291272 x+14330592\right)}{(3 x+2)^5}-13995465 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{32269440}","\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,"((7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(14330592 + 93291272*x + 222865988*x^2 + 231277650*x^3 + 87703335*x^4))/(2 + 3*x)^5 - 13995465*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/32269440","A",1
2488,1,193,209,0.2164811,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^7} \, dx","Integrate[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^7),x]","\frac{1}{42} \left(\frac{591 \sqrt{1-2 x} (5 x+3)^{7/2}}{70 (3 x+2)^5}+\frac{3 \sqrt{1-2 x} (5 x+3)^{7/2}}{(3 x+2)^6}+\frac{352839984 \sqrt{1-2 x} (5 x+3)^{7/2}-39499 (3 x+2) \left(2744 \sqrt{1-2 x} (5 x+3)^{5/2}+55 (3 x+2) \left(7 \sqrt{1-2 x} \sqrt{5 x+3} (169 x+108)+363 \sqrt{7} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)\right)}{21512960 (3 x+2)^4}\right)","\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,"((3*Sqrt[1 - 2*x]*(3 + 5*x)^(7/2))/(2 + 3*x)^6 + (591*Sqrt[1 - 2*x]*(3 + 5*x)^(7/2))/(70*(2 + 3*x)^5) + (352839984*Sqrt[1 - 2*x]*(3 + 5*x)^(7/2) - 39499*(2 + 3*x)*(2744*Sqrt[1 - 2*x]*(3 + 5*x)^(5/2) + 55*(2 + 3*x)*(7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(108 + 169*x) + 363*Sqrt[7]*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])))/(21512960*(2 + 3*x)^4))/42","A",1
2489,1,83,113,0.069882,"\int \frac{(2+3 x)^4}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^4/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","-\frac{\sqrt{1-2 x} \left(30 \sqrt{2 x-1} \sqrt{5 x+3} \left(86400 x^3+297120 x^2+462540 x+518491\right)+10866247 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{1280000 \sqrt{2 x-1}}","-\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,"-1/1280000*(Sqrt[1 - 2*x]*(30*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(518491 + 462540*x + 297120*x^2 + 86400*x^3) + 10866247*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/Sqrt[-1 + 2*x]","A",1
2490,1,78,84,0.1096612,"\int \frac{(2+3 x)^3}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^3/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","-\frac{\sqrt{1-2 x} \left(90 \sqrt{2 x-1} \sqrt{5 x+3} \left(160 x^2+460 x+667\right)+44437 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{16000 \sqrt{2 x-1}}","-\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,"-1/16000*(Sqrt[1 - 2*x]*(90*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(667 + 460*x + 160*x^2) + 44437*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/Sqrt[-1 + 2*x]","A",1
2491,1,73,77,0.0364097,"\int \frac{(2+3 x)^2}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^2/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","-\frac{\sqrt{1-2 x} \left(30 \sqrt{2 x-1} \sqrt{5 x+3} (60 x+151)+3827 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{4000 \sqrt{2 x-1}}","-\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,"-1/4000*(Sqrt[1 - 2*x]*(30*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(151 + 60*x) + 3827*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/Sqrt[-1 + 2*x]","A",1
2492,1,68,50,0.0185819,"\int \frac{2+3 x}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","-\frac{3}{10} \sqrt{1-2 x} \sqrt{5 x+3}-\frac{37 \sqrt{1-2 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{10 \sqrt{10} \sqrt{2 x-1}}","\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*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/10 - (37*Sqrt[1 - 2*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(10*Sqrt[10]*Sqrt[-1 + 2*x])","A",1
2493,1,45,26,0.0097919,"\int \frac{1}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","-\frac{\sqrt{\frac{2}{5}} \sqrt{1-2 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{\sqrt{2 x-1}}","\sqrt{\frac{2}{5}} \sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)",1,"-((Sqrt[2/5]*Sqrt[1 - 2*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/Sqrt[-1 + 2*x])","A",1
2494,1,32,32,0.0100414,"\int \frac{1}{\sqrt{1-2 x} (2+3 x) \sqrt{3+5 x}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)*Sqrt[3 + 5*x]),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{\sqrt{7}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{\sqrt{7}}",1,"(-2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/Sqrt[7]","A",1
2495,1,64,64,0.0293781,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^2 \sqrt{3+5 x}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^2*Sqrt[3 + 5*x]),x]","\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}}","\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*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(7*(2 + 3*x)) - (37*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(7*Sqrt[7])","A",1
2496,1,69,93,0.0397837,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^3 \sqrt{3+5 x}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^3*Sqrt[3 + 5*x]),x]","\frac{\frac{21 \sqrt{1-2 x} \sqrt{5 x+3} (333 x+236)}{(3 x+2)^2}-3827 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1372}","\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,"((21*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(236 + 333*x))/(2 + 3*x)^2 - 3827*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/1372","A",1
2497,1,74,122,0.0535849,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^4 \sqrt{3+5 x}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^4*Sqrt[3 + 5*x]),x]","\frac{\frac{63 \sqrt{1-2 x} \sqrt{5 x+3} \left(19415 x^2+26750 x+9248\right)}{(3 x+2)^3}-222185 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{19208}","\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,"((63*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(9248 + 26750*x + 19415*x^2))/(2 + 3*x)^3 - 222185*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/19208","A",1
2498,1,87,113,0.0620361,"\int \frac{(2+3 x)^4}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^4/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","-\frac{\sqrt{1-2 x} \left(10 \sqrt{2 x-1} \left(237600 x^3+849420 x^2+1477575 x+632101\right)+1576113 \sqrt{50 x+30} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{880000 \sqrt{2 x-1} \sqrt{5 x+3}}","-\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,"-1/880000*(Sqrt[1 - 2*x]*(10*Sqrt[-1 + 2*x]*(632101 + 1477575*x + 849420*x^2 + 237600*x^3) + 1576113*Sqrt[30 + 50*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/(Sqrt[-1 + 2*x]*Sqrt[3 + 5*x])","A",1
2499,1,82,84,0.0382442,"\int \frac{(2+3 x)^3}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^3/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","-\frac{\sqrt{1-2 x} \left(10 \sqrt{2 x-1} \left(5940 x^2+19305 x+9451\right)+27423 \sqrt{50 x+30} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{44000 \sqrt{2 x-1} \sqrt{5 x+3}}","-\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,"-1/44000*(Sqrt[1 - 2*x]*(10*Sqrt[-1 + 2*x]*(9451 + 19305*x + 5940*x^2) + 27423*Sqrt[30 + 50*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/(Sqrt[-1 + 2*x]*Sqrt[3 + 5*x])","A",1
2500,1,77,72,0.0378945,"\int \frac{(2+3 x)^2}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^2/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","-\frac{\sqrt{1-2 x} \left(10 \sqrt{2 x-1} (495 x+301)+1353 \sqrt{50 x+30} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)\right)}{5500 \sqrt{2 x-1} \sqrt{5 x+3}}","-\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,"-1/5500*(Sqrt[1 - 2*x]*(10*Sqrt[-1 + 2*x]*(301 + 495*x) + 1353*Sqrt[30 + 50*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/(Sqrt[-1 + 2*x]*Sqrt[3 + 5*x])","A",1
2501,1,59,52,0.0743889,"\int \frac{2+3 x}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","\frac{1}{275} \sqrt{1-2 x} \left(-\frac{10}{\sqrt{5 x+3}}-\frac{33 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{\sqrt{2 x-1}}\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[1 - 2*x]*(-10/Sqrt[3 + 5*x] - (33*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/Sqrt[-1 + 2*x]))/275","A",1
2502,1,22,22,0.0040759,"\int \frac{1}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","-\frac{2 \sqrt{1-2 x}}{11 \sqrt{5 x+3}}","-\frac{2 \sqrt{1-2 x}}{11 \sqrt{5 x+3}}",1,"(-2*Sqrt[1 - 2*x])/(11*Sqrt[3 + 5*x])","A",1
2503,1,55,55,0.0228302,"\int \frac{1}{\sqrt{1-2 x} (2+3 x) (3+5 x)^{3/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^(3/2)),x]","\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}}","\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*Sqrt[1 - 2*x])/(11*Sqrt[3 + 5*x]) + (6*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/Sqrt[7]","A",1
2504,1,69,86,0.0436733,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^2 (3+5 x)^{3/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^(3/2)),x]","\frac{321 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{7 \sqrt{7}}-\frac{\sqrt{1-2 x} (1545 x+997)}{77 (3 x+2) \sqrt{5 x+3}}","-\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,"-1/77*(Sqrt[1 - 2*x]*(997 + 1545*x))/((2 + 3*x)*Sqrt[3 + 5*x]) + (321*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(7*Sqrt[7])","A",1
2505,1,74,115,0.0537731,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^3 (3+5 x)^{3/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^(3/2)),x]","\frac{620631 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-\frac{7 \sqrt{1-2 x} \left(813735 x^2+1067061 x+349252\right)}{(3 x+2)^2 \sqrt{5 x+3}}}{15092}","-\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,"((-7*Sqrt[1 - 2*x]*(349252 + 1067061*x + 813735*x^2))/((2 + 3*x)^2*Sqrt[3 + 5*x]) + 620631*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/15092","A",1
2506,1,79,144,0.0657871,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^4 (3+5 x)^{3/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^(3/2)),x]","\frac{50776275 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-\frac{7 \sqrt{1-2 x} \left(199715625 x^3+395028225 x^2+260298990 x+57135248\right)}{(3 x+2)^3 \sqrt{5 x+3}}}{211288}","-\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,"((-7*Sqrt[1 - 2*x]*(57135248 + 260298990*x + 395028225*x^2 + 199715625*x^3))/((2 + 3*x)^3*Sqrt[3 + 5*x]) + 50776275*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/211288","A",1
2507,1,79,142,0.1164407,"\int \frac{(2+3 x)^5}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^5/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\frac{\sqrt{1-2 x} \left(-\frac{10 \left(117612000 x^4+502791300 x^3+1030526145 x^2+795297410 x+199549721\right)}{(5 x+3)^{3/2}}-\frac{167835591 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{\sqrt{2 x-1}}\right)}{145200000}","-\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,"(Sqrt[1 - 2*x]*((-10*(199549721 + 795297410*x + 1030526145*x^2 + 502791300*x^3 + 117612000*x^4))/(3 + 5*x)^(3/2) - (167835591*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/Sqrt[-1 + 2*x]))/145200000","A",1
2508,1,74,113,0.147422,"\int \frac{(2+3 x)^4}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^4/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\frac{\sqrt{1-2 x} \left(-\frac{10 \left(2940300 x^3+11712195 x^2+10891910 x+2953931\right)}{(5 x+3)^{3/2}}-\frac{2950101 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{\sqrt{2 x-1}}\right)}{7260000}","-\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,"(Sqrt[1 - 2*x]*((-10*(2953931 + 10891910*x + 11712195*x^2 + 2940300*x^3))/(3 + 5*x)^(3/2) - (2950101*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/Sqrt[-1 + 2*x]))/7260000","A",1
2509,1,69,84,0.0703448,"\int \frac{(2+3 x)^3}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^3/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\frac{\sqrt{1-2 x} \left(-\frac{10 \left(49005 x^2+60010 x+18373\right)}{(5 x+3)^{3/2}}-\frac{29403 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{\sqrt{2 x-1}}\right)}{181500}","-\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,"(Sqrt[1 - 2*x]*((-10*(18373 + 60010*x + 49005*x^2))/(3 + 5*x)^(3/2) - (29403*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/Sqrt[-1 + 2*x]))/181500","A",1
2510,1,64,74,0.0772359,"\int \frac{(2+3 x)^2}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^2/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\frac{\sqrt{1-2 x} \left(-\frac{10 (1010 x+617)}{(5 x+3)^{3/2}}-\frac{3267 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{\sqrt{2 x-1}}\right)}{45375}","-\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,"(Sqrt[1 - 2*x]*((-10*(617 + 1010*x))/(3 + 5*x)^(3/2) - (3267*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/Sqrt[-1 + 2*x]))/45375","A",1
2511,1,27,45,0.0090165,"\int \frac{2+3 x}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","-\frac{2 \sqrt{1-2 x} (103 x+64)}{363 (5 x+3)^{3/2}}","-\frac{206 \sqrt{1-2 x}}{1815 \sqrt{5 x+3}}-\frac{2 \sqrt{1-2 x}}{165 (5 x+3)^{3/2}}",1,"(-2*Sqrt[1 - 2*x]*(64 + 103*x))/(363*(3 + 5*x)^(3/2))","A",1
2512,1,27,45,0.0068038,"\int \frac{1}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","-\frac{2 \sqrt{1-2 x} (20 x+23)}{363 (5 x+3)^{3/2}}","-\frac{8 \sqrt{1-2 x}}{363 \sqrt{5 x+3}}-\frac{2 \sqrt{1-2 x}}{33 (5 x+3)^{3/2}}",1,"(-2*Sqrt[1 - 2*x]*(23 + 20*x))/(363*(3 + 5*x)^(3/2))","A",1
2513,1,60,77,0.0538583,"\int \frac{1}{\sqrt{1-2 x} (2+3 x) (3+5 x)^{5/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^(5/2)),x]","\frac{10 \sqrt{1-2 x} (475 x+274)}{363 (5 x+3)^{3/2}}-\frac{18 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{\sqrt{7}}","\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,"(10*Sqrt[1 - 2*x]*(274 + 475*x))/(363*(3 + 5*x)^(3/2)) - (18*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/Sqrt[7]","A",1
2514,1,93,108,0.0437873,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^2 (3+5 x)^{5/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^(5/2)),x]","\frac{7 \sqrt{1-2 x} \left(1263525 x^2+1572580 x+487909\right)-578259 \sqrt{7} \sqrt{5 x+3} \left(15 x^2+19 x+6\right) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{17787 (3 x+2) (5 x+3)^{3/2}}","\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,"(7*Sqrt[1 - 2*x]*(487909 + 1572580*x + 1263525*x^2) - 578259*Sqrt[7]*Sqrt[3 + 5*x]*(6 + 19*x + 15*x^2)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(17787*(2 + 3*x)*(3 + 5*x)^(3/2))","A",1
2515,1,79,137,0.0702588,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^3 (3+5 x)^{5/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^(5/2)),x]","\frac{\sqrt{1-2 x} \left(933479325 x^3+1784145090 x^2+1135041037 x+240342364\right)}{71148 (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}}","\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,"(Sqrt[1 - 2*x]*(240342364 + 1135041037*x + 1784145090*x^2 + 933479325*x^3))/(71148*(2 + 3*x)^2*(3 + 5*x)^(3/2)) - (392283*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(196*Sqrt[7])","A",1
2516,1,84,166,0.0833803,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^4 (3+5 x)^{5/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^(5/2)),x]","\frac{\sqrt{1-2 x} \left(294889892625 x^4+760212086400 x^3+734310313245 x^2+314968389410 x+50617099616\right)}{996072 (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}}","\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,"(Sqrt[1 - 2*x]*(50617099616 + 314968389410*x + 734310313245*x^2 + 760212086400*x^3 + 294889892625*x^4))/(996072*(2 + 3*x)^3*(3 + 5*x)^(3/2)) - (41307885*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(2744*Sqrt[7])","A",1
2517,1,82,59,0.0594124,"\int \frac{1}{\sqrt{a+b x} (e+f x) \sqrt{2 b e-a f+b f x}} \, dx","Integrate[1/(Sqrt[a + b*x]*(e + f*x)*Sqrt[2*b*e - a*f + b*f*x]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x} \sqrt{f (a f-b e)}}{\sqrt{b e-a f} \sqrt{-a f+2 b e+b f x}}\right)}{\sqrt{b e-a f} \sqrt{f (a f-b e)}}","\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,"(2*ArcTanh[(Sqrt[f*(-(b*e) + a*f)]*Sqrt[a + b*x])/(Sqrt[b*e - a*f]*Sqrt[2*b*e - a*f + b*f*x])])/(Sqrt[b*e - a*f]*Sqrt[f*(-(b*e) + a*f)])","A",1
2518,1,93,168,0.1517631,"\int \frac{(2+3 x)^5 \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^5*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\frac{-10 \sqrt{2 x-1} \sqrt{5 x+3} \left(124416000 x^5+613267200 x^4+1429191360 x^3+2297649240 x^2+3810769458 x-5389783159\right)-35439958001 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{51200000 \sqrt{-(1-2 x)^2}}","\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,"(-10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(-5389783159 + 3810769458*x + 2297649240*x^2 + 1429191360*x^3 + 613267200*x^4 + 124416000*x^5) - 35439958001*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(51200000*Sqrt[-(1 - 2*x)^2])","A",0
2519,1,88,139,0.0719764,"\int \frac{(2+3 x)^4 \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^4*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\frac{-10 \sqrt{2 x-1} \sqrt{5 x+3} \left(518400 x^4+2283840 x^3+5020200 x^2+9587886 x-14050073\right)-92108287 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{512000 \sqrt{-(1-2 x)^2}}","\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,"(-10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(-14050073 + 9587886*x + 5020200*x^2 + 2283840*x^3 + 518400*x^4) - 92108287*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(512000*Sqrt[-(1 - 2*x)^2])","A",0
2520,1,83,110,0.0565333,"\int \frac{(2+3 x)^3 \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^3*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\frac{-10 \sqrt{2 x-1} \sqrt{5 x+3} \left(14400 x^3+57960 x^2+142686 x-224833\right)-1463447 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{32000 \sqrt{-(1-2 x)^2}}","\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,"(-10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(-224833 + 142686*x + 57960*x^2 + 14400*x^3) - 1463447*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(32000*Sqrt[-(1 - 2*x)^2])","A",0
2521,1,78,94,0.0476855,"\int \frac{(2+3 x)^2 \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^2*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\frac{-10 \sqrt{2 x-1} \sqrt{5 x+3} \left(360 x^2+1518 x-2809\right)-17951 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{1600 \sqrt{-(1-2 x)^2}}","\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,"(-10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(-2809 + 1518*x + 360*x^2) - 17951*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(1600*Sqrt[-(1 - 2*x)^2])","A",0
2522,1,73,72,0.0377878,"\int \frac{(2+3 x) \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\frac{10 (17-6 x) \sqrt{2 x-1} \sqrt{5 x+3}-103 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{40 \sqrt{-(1-2 x)^2}}","\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,"(10*(17 - 6*x)*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x] - 103*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(40*Sqrt[-(1 - 2*x)^2])","A",0
2523,1,54,47,0.0183964,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","Integrate[Sqrt[3 + 5*x]/(1 - 2*x)^(3/2),x]","\frac{2 \sqrt{5 x+3}-\sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{2 \sqrt{1-2 x}}","\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,"(2*Sqrt[3 + 5*x] - Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(2*Sqrt[1 - 2*x])","A",1
2524,1,57,57,0.0269795,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)} \, dx","Integrate[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*(2 + 3*x)),x]","\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}}","\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,"(2*Sqrt[3 + 5*x])/(7*Sqrt[1 - 2*x]) + (2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(7*Sqrt[7])","A",1
2525,1,78,93,0.0372682,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)^2} \, dx","Integrate[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*(2 + 3*x)^2),x]","\frac{7 \sqrt{5 x+3} (18 x+5)-29 \sqrt{7-14 x} (3 x+2) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{343 \sqrt{1-2 x} (3 x+2)}","\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,"(7*Sqrt[3 + 5*x]*(5 + 18*x) - 29*Sqrt[7 - 14*x]*(2 + 3*x)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(343*Sqrt[1 - 2*x]*(2 + 3*x))","A",1
2526,1,85,122,0.0506125,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)^3} \, dx","Integrate[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*(2 + 3*x)^3),x]","\frac{7 \sqrt{5 x+3} \left(-90 x^2+405 x+212\right)-1585 \sqrt{7-14 x} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{9604 \sqrt{1-2 x} (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,"(7*Sqrt[3 + 5*x]*(212 + 405*x - 90*x^2) - 1585*Sqrt[7 - 14*x]*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(9604*Sqrt[1 - 2*x]*(2 + 3*x)^2)","A",1
2527,1,90,151,0.0621464,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)^4} \, dx","Integrate[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*(2 + 3*x)^4),x]","\frac{7 \sqrt{5 x+3} \left(-10170 x^3-8055 x^2+3114 x+2512\right)-7435 \sqrt{7-14 x} (3 x+2)^3 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{19208 \sqrt{1-2 x} (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,"(7*Sqrt[3 + 5*x]*(2512 + 3114*x - 8055*x^2 - 10170*x^3) - 7435*Sqrt[7 - 14*x]*(2 + 3*x)^3*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(19208*Sqrt[1 - 2*x]*(2 + 3*x)^3)","A",1
2528,1,95,180,0.0777312,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)^5} \, dx","Integrate[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*(2 + 3*x)^5),x]","\frac{-7 \sqrt{5 x+3} \left(5791230 x^4+8897265 x^3+2075184 x^2-2239092 x-917264\right)-1244755 \sqrt{7-14 x} (3 x+2)^4 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1075648 \sqrt{1-2 x} (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,"(-7*Sqrt[3 + 5*x]*(-917264 - 2239092*x + 2075184*x^2 + 8897265*x^3 + 5791230*x^4) - 1244755*Sqrt[7 - 14*x]*(2 + 3*x)^4*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(1075648*Sqrt[1 - 2*x]*(2 + 3*x)^4)","A",1
2529,1,93,161,0.0782002,"\int \frac{(2+3 x)^4 (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^4*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]","\frac{-10 \sqrt{2 x-1} \sqrt{5 x+3} \left(41472000 x^5+200966400 x^4+461171520 x^3+732415080 x^2+1206337246 x-1702927233\right)-11199264087 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{10240000 \sqrt{-(1-2 x)^2}}","\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,"(-10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(-1702927233 + 1206337246*x + 732415080*x^2 + 461171520*x^3 + 200966400*x^4 + 41472000*x^5) - 11199264087*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(10240000*Sqrt[-(1 - 2*x)^2])","A",0
2530,1,88,132,0.0639034,"\int \frac{(2+3 x)^3 (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]","\frac{-10 \sqrt{2 x-1} \sqrt{5 x+3} \left(864000 x^4+3729600 x^3+8057880 x^2+15218818 x-22217679\right)-145708761 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{512000 \sqrt{-(1-2 x)^2}}","\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,"(-10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(-22217679 + 15218818*x + 8057880*x^2 + 3729600*x^3 + 864000*x^4) - 145708761*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(512000*Sqrt[-(1 - 2*x)^2])","A",0
2531,1,83,116,0.0583841,"\int \frac{(2+3 x)^2 (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]","\frac{-10 \sqrt{2 x-1} \sqrt{5 x+3} \left(4800 x^3+18840 x^2+45538 x-71199\right)-463881 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{6400 \sqrt{-(1-2 x)^2}}","\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,"(-10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(-71199 + 45538*x + 18840*x^2 + 4800*x^3) - 463881*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(6400*Sqrt[-(1 - 2*x)^2])","A",0
2532,1,78,94,0.0466157,"\int \frac{(2+3 x) (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]","\frac{-10 \sqrt{2 x-1} \sqrt{5 x+3} \left(120 x^2+490 x-891\right)-5709 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{320 \sqrt{-(1-2 x)^2}}","\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,"(-10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(-891 + 490*x + 120*x^2) - 5709*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(320*Sqrt[-(1 - 2*x)^2])","A",0
2533,1,39,71,0.0102528,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","Integrate[(3 + 5*x)^(3/2)/(1 - 2*x)^(3/2),x]","\frac{11 \sqrt{\frac{11}{2}} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-\frac{5}{11} (2 x-1)\right)}{2 \sqrt{1-2 x}}","\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,"(11*Sqrt[11/2]*Hypergeometric2F1[-3/2, -1/2, 1/2, (-5*(-1 + 2*x))/11])/(2*Sqrt[1 - 2*x])","C",1
2534,1,90,86,0.0412264,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)),x]","\frac{462 \sqrt{5 x+3}-4 \sqrt{7-14 x} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-245 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{294 \sqrt{1-2 x}}","\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,"(462*Sqrt[3 + 5*x] - 245*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 4*Sqrt[7 - 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(294*Sqrt[1 - 2*x])","A",1
2535,1,78,93,0.0378341,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^2),x]","\frac{7 \sqrt{5 x+3} (64 x+45)+33 \sqrt{7-14 x} (3 x+2) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{343 \sqrt{1-2 x} (3 x+2)}","\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,"(7*Sqrt[3 + 5*x]*(45 + 64*x) + 33*Sqrt[7 - 14*x]*(2 + 3*x)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(343*Sqrt[1 - 2*x]*(2 + 3*x))","A",1
2536,1,85,122,0.0513616,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^3),x]","\frac{7 \sqrt{5 x+3} \left(2550 x^2+2245 x+396\right)-825 \sqrt{7-14 x} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{9604 \sqrt{1-2 x} (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,"(7*Sqrt[3 + 5*x]*(396 + 2245*x + 2550*x^2) - 825*Sqrt[7 - 14*x]*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(9604*Sqrt[1 - 2*x]*(2 + 3*x)^2)","A",1
2537,1,90,151,0.0642617,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^4),x]","\frac{7 \sqrt{5 x+3} \left(2490 x^3+6135 x^2+3782 x+576\right)-2805 \sqrt{7-14 x} (3 x+2)^3 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{19208 \sqrt{1-2 x} (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,"(7*Sqrt[3 + 5*x]*(576 + 3782*x + 6135*x^2 + 2490*x^3) - 2805*Sqrt[7 - 14*x]*(2 + 3*x)^3*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(19208*Sqrt[1 - 2*x]*(2 + 3*x)^3)","A",1
2538,1,95,180,0.075363,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^5} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^5),x]","\frac{7 \sqrt{5 x+3} \left(-917190 x^4-1188045 x^3+60048 x^2+538276 x+163152\right)-279015 \sqrt{7-14 x} (3 x+2)^4 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1075648 \sqrt{1-2 x} (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,"(7*Sqrt[3 + 5*x]*(163152 + 538276*x + 60048*x^2 - 1188045*x^3 - 917190*x^4) - 279015*Sqrt[7 - 14*x]*(2 + 3*x)^4*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(1075648*Sqrt[1 - 2*x]*(2 + 3*x)^4)","A",1
2539,1,98,183,0.0946047,"\int \frac{(2+3 x)^4 (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^4*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]","\frac{-10 \sqrt{2 x-1} \sqrt{5 x+3} \left(276480000 x^6+1479168000 x^5+3687379200 x^4+5945485120 x^3+7755469800 x^2+11734056318 x-16267424049\right)-107121749031 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{16384000 \sqrt{-(1-2 x)^2}}","\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,"(-10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(-16267424049 + 11734056318*x + 7755469800*x^2 + 5945485120*x^3 + 3687379200*x^4 + 1479168000*x^5 + 276480000*x^6) - 107121749031*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(16384000*Sqrt[-(1 - 2*x)^2])","A",0
2540,1,93,154,0.0730335,"\int \frac{(2+3 x)^3 (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]","\frac{-10 \sqrt{2 x-1} \sqrt{5 x+3} \left(13824000 x^5+65836800 x^4+148751040 x^3+233394520 x^2+381820658 x-538018839\right)-3538809681 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{2048000 \sqrt{-(1-2 x)^2}}","\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,"(-10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(-538018839 + 381820658*x + 233394520*x^2 + 148751040*x^3 + 65836800*x^4 + 13824000*x^5) - 3538809681*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(2048000*Sqrt[-(1 - 2*x)^2])","A",0
2541,1,88,138,0.0662081,"\int \frac{(2+3 x)^2 (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]","\frac{-10 \sqrt{2 x-1} \sqrt{5 x+3} \left(57600 x^4+243520 x^3+517096 x^2+966014 x-1405233\right)-9219111 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{20480 \sqrt{-(1-2 x)^2}}","\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,"(-10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(-1405233 + 966014*x + 517096*x^2 + 243520*x^3 + 57600*x^4) - 9219111*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(20480*Sqrt[-(1 - 2*x)^2])","A",0
2542,1,83,118,0.0538566,"\int \frac{(2+3 x) (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]","\frac{-2 \sqrt{2 x-1} \sqrt{5 x+3} \left(1600 x^3+6120 x^2+14526 x-22545\right)-29403 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{256 \sqrt{-(1-2 x)^2}}","\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,"(-2*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(-22545 + 14526*x + 6120*x^2 + 1600*x^3) - 29403*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(256*Sqrt[-(1 - 2*x)^2])","A",0
2543,1,39,93,0.0111982,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","Integrate[(3 + 5*x)^(5/2)/(1 - 2*x)^(3/2),x]","\frac{121 \sqrt{\frac{11}{2}} \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};-\frac{5}{11} (2 x-1)\right)}{4 \sqrt{1-2 x}}","\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,"(121*Sqrt[11/2]*Hypergeometric2F1[-5/2, -1/2, 1/2, (-5*(-1 + 2*x))/11])/(4*Sqrt[1 - 2*x])","C",1
2544,1,116,108,0.0694854,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)),x]","\frac{8085 \sqrt{22} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-\frac{5}{11} (2 x-1)\right)-924 \sqrt{5 x+3}+8 \sqrt{7-14 x} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+490 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{1764 \sqrt{1-2 x}}","\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,"(-924*Sqrt[3 + 5*x] + 490*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] + 8*Sqrt[7 - 14*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])] + 8085*Sqrt[22]*Hypergeometric2F1[-3/2, -1/2, 1/2, (-5*(-1 + 2*x))/11])/(1764*Sqrt[1 - 2*x])","C",1
2545,1,173,122,0.2447215,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^2),x]","\frac{-468930 (3 x+2) \sqrt{44 x-22} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-\frac{5}{11} (2 x-1)\right)-42 \sqrt{2 x-1} \sqrt{5 x+3} \left(30450 x^2-70643 x-60610\right)-771995 \sqrt{10} \left(6 x^2+x-2\right) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-2704 \sqrt{7} \sqrt{-(1-2 x)^2} (3 x+2) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{49392 \sqrt{-(1-2 x)^2} (3 x+2)}","\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,"(-42*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(-60610 - 70643*x + 30450*x^2) - 771995*Sqrt[10]*(-2 + x + 6*x^2)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]] - 2704*Sqrt[7]*Sqrt[-(1 - 2*x)^2]*(2 + 3*x)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])] - 468930*(2 + 3*x)*Sqrt[-22 + 44*x]*Hypergeometric2F1[-3/2, -1/2, 1/2, (-5*(-1 + 2*x))/11])/(49392*Sqrt[-(1 - 2*x)^2]*(2 + 3*x))","C",1
2546,1,85,122,0.0485736,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^3),x]","\frac{7 \sqrt{5 x+3} \left(8110 x^2+11525 x+4068\right)+1815 \sqrt{7-14 x} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{9604 \sqrt{1-2 x} (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,"(7*Sqrt[3 + 5*x]*(4068 + 11525*x + 8110*x^2) + 1815*Sqrt[7 - 14*x]*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(9604*Sqrt[1 - 2*x]*(2 + 3*x)^2)","A",1
2547,1,90,151,0.0617907,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^4),x]","\frac{7 \sqrt{5 x+3} \left(24670 x^3+37405 x^2+17666 x+2448\right)-1815 \sqrt{7-14 x} (3 x+2)^3 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{19208 \sqrt{1-2 x} (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,"(7*Sqrt[3 + 5*x]*(2448 + 17666*x + 37405*x^2 + 24670*x^3) - 1815*Sqrt[7 - 14*x]*(2 + 3*x)^3*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(19208*Sqrt[1 - 2*x]*(2 + 3*x)^3)","A",1
2548,1,95,180,0.0742897,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^5} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^5),x]","\frac{7 \sqrt{5 x+3} \left(1002930 x^4+2578615 x^3+2184144 x^2+687828 x+53136\right)-168795 \sqrt{7-14 x} (3 x+2)^4 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1075648 \sqrt{1-2 x} (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,"(7*Sqrt[3 + 5*x]*(53136 + 687828*x + 2184144*x^2 + 2578615*x^3 + 1002930*x^4) - 168795*Sqrt[7 - 14*x]*(2 + 3*x)^4*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(1075648*Sqrt[1 - 2*x]*(2 + 3*x)^4)","A",1
2549,1,100,209,0.0887225,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^6} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^6),x]","\frac{7 \sqrt{5 x+3} \left(-115230870 x^5-180017865 x^4+19738914 x^3+164918884 x^2+95331368 x+16456032\right)-17371365 \sqrt{7-14 x} (3 x+2)^5 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{75295360 \sqrt{1-2 x} (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,"(7*Sqrt[3 + 5*x]*(16456032 + 95331368*x + 164918884*x^2 + 19738914*x^3 - 180017865*x^4 - 115230870*x^5) - 17371365*Sqrt[7 - 14*x]*(2 + 3*x)^5*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(75295360*Sqrt[1 - 2*x]*(2 + 3*x)^5)","A",1
2550,1,88,142,0.141133,"\int \frac{(2+3 x)^5}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{-10 \sqrt{2 x-1} \sqrt{5 x+3} \left(17107200 x^4+76887360 x^3+171939240 x^2+332129358 x-488641609\right)-3202057551 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{28160000 \sqrt{-(1-2 x)^2}}","\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,"(-10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(-488641609 + 332129358*x + 171939240*x^2 + 76887360*x^3 + 17107200*x^4) - 3202057551*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(28160000*Sqrt[-(1 - 2*x)^2])","A",0
2551,1,83,113,0.0583771,"\int \frac{(2+3 x)^4}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{-10 \sqrt{2 x-1} \sqrt{5 x+3} \left(19008 x^3+78408 x^2+196614 x-312365\right)-2031051 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{70400 \sqrt{-(1-2 x)^2}}","\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,"(-10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(-312365 + 196614*x + 78408*x^2 + 19008*x^3) - 2031051*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(70400*Sqrt[-(1 - 2*x)^2])","A",0
2552,1,78,84,0.0519912,"\int \frac{(2+3 x)^3}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{-10 \sqrt{2 x-1} \sqrt{5 x+3} \left(11880 x^2+51678 x-97409\right)-620631 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{88000 \sqrt{-(1-2 x)^2}}","\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,"(-10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(-97409 + 51678*x + 11880*x^2) - 620631*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(88000*Sqrt[-(1 - 2*x)^2])","A",0
2553,1,73,72,0.038639,"\int \frac{(2+3 x)^2}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{10 (589-198 x) \sqrt{2 x-1} \sqrt{5 x+3}-3531 \sqrt{10} (2 x-1) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{2200 \sqrt{-(1-2 x)^2}}","\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,"(10*(589 - 198*x)*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x] - 3531*Sqrt[10]*(-1 + 2*x)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(2200*Sqrt[-(1 - 2*x)^2])","A",0
2554,1,54,48,0.0617893,"\int \frac{2+3 x}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{70 \sqrt{5 x+3}-33 \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{110 \sqrt{1-2 x}}","\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,"(70*Sqrt[3 + 5*x] - 33*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(110*Sqrt[1 - 2*x])","A",1
2555,1,22,22,0.004219,"\int \frac{1}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{2 \sqrt{5 x+3}}{11 \sqrt{1-2 x}}","\frac{2 \sqrt{5 x+3}}{11 \sqrt{1-2 x}}",1,"(2*Sqrt[3 + 5*x])/(11*Sqrt[1 - 2*x])","A",1
2556,1,57,57,0.0282777,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x) \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)*Sqrt[3 + 5*x]),x]","\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}}","\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*Sqrt[3 + 5*x])/(77*Sqrt[1 - 2*x]) - (6*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(7*Sqrt[7])","A",1
2557,1,78,86,0.0384289,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^2 \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*Sqrt[3 + 5*x]),x]","\frac{7 (115-174 x) \sqrt{5 x+3}-1353 \sqrt{7-14 x} (3 x+2) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{3773 \sqrt{1-2 x} (3 x+2)}","-\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,"(7*(115 - 174*x)*Sqrt[3 + 5*x] - 1353*Sqrt[7 - 14*x]*(2 + 3*x)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(3773*Sqrt[1 - 2*x]*(2 + 3*x))","A",1
2558,1,85,115,0.0502419,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^3 \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*Sqrt[3 + 5*x]),x]","\frac{-7 \sqrt{5 x+3} \left(70110 x^2+13785 x-25204\right)-137115 \sqrt{7-14 x} (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{105644 \sqrt{1-2 x} (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,"(-7*Sqrt[3 + 5*x]*(-25204 + 13785*x + 70110*x^2) - 137115*Sqrt[7 - 14*x]*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(105644*Sqrt[1 - 2*x]*(2 + 3*x)^2)","A",1
2559,1,90,144,0.0653443,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^4 \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^4*Sqrt[3 + 5*x]),x]","\frac{-7 \sqrt{5 x+3} \left(1767690 x^3+1549935 x^2-377658 x-421184\right)-1125795 \sqrt{7-14 x} (3 x+2)^3 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{211288 \sqrt{1-2 x} (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,"(-7*Sqrt[3 + 5*x]*(-421184 - 377658*x + 1549935*x^2 + 1767690*x^3) - 1125795*Sqrt[7 - 14*x]*(2 + 3*x)^3*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(211288*Sqrt[1 - 2*x]*(2 + 3*x)^3)","A",1
2560,1,95,173,0.0770368,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^5 \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^5*Sqrt[3 + 5*x]),x]","\frac{-7 \sqrt{5 x+3} \left(1293749010 x^4+1998242055 x^3+482249808 x^2-491393004 x-205593328\right)-274145685 \sqrt{7-14 x} (3 x+2)^4 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{11832128 \sqrt{1-2 x} (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,"(-7*Sqrt[3 + 5*x]*(-205593328 - 491393004*x + 482249808*x^2 + 1998242055*x^3 + 1293749010*x^4) - 274145685*Sqrt[7 - 14*x]*(2 + 3*x)^4*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(11832128*Sqrt[1 - 2*x]*(2 + 3*x)^4)","A",1
2561,1,98,142,0.0807018,"\int \frac{(2+3 x)^5}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{-352281699 \sqrt{10} \left(10 x^2+x-3\right) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-10 \sqrt{2 x-1} \sqrt{5 x+3} \left(15681600 x^4+75663720 x^3+208989990 x^2-169670279 x-162727423\right)}{19360000 \sqrt{-(1-2 x)^2} (5 x+3)}","\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,"(-10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(-162727423 - 169670279*x + 208989990*x^2 + 75663720*x^3 + 15681600*x^4) - 352281699*Sqrt[10]*(-3 + x + 10*x^2)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(19360000*Sqrt[-(1 - 2*x)^2]*(3 + 5*x))","A",0
2562,1,87,113,0.1057096,"\int \frac{(2+3 x)^4}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{10 \sqrt{2 x-1} \left(-392040 x^3-1992870 x^2+2323271 x+2026687\right)-4289571 (2 x-1) \sqrt{50 x+30} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{968000 \sqrt{-(1-2 x)^2} \sqrt{5 x+3}}","\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,"(10*Sqrt[-1 + 2*x]*(2026687 + 2323271*x - 1992870*x^2 - 392040*x^3) - 4289571*(-1 + 2*x)*Sqrt[30 + 50*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(968000*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x])","A",0
2563,1,70,84,0.0622502,"\int \frac{(2+3 x)^3}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{-326700 x^2+824990 x-120879 \sqrt{5 x+3} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)+612430}{121000 \sqrt{1-2 x} \sqrt{5 x+3}}","\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,"(612430 + 824990*x - 326700*x^2 - 120879*Sqrt[3 + 5*x]*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(121000*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])","A",1
2564,1,77,72,0.0651271,"\int \frac{(2+3 x)^2}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{10 \sqrt{2 x-1} (1229 x+733)-1089 (2 x-1) \sqrt{50 x+30} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{6050 \sqrt{-(1-2 x)^2} \sqrt{5 x+3}}","-\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,"(10*Sqrt[-1 + 2*x]*(733 + 1229*x) - 1089*(-1 + 2*x)*Sqrt[30 + 50*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(6050*Sqrt[-(1 - 2*x)^2]*Sqrt[3 + 5*x])","A",0
2565,1,27,45,0.0088929,"\int \frac{2+3 x}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{2 (37 x+20)}{121 \sqrt{1-2 x} \sqrt{5 x+3}}","\frac{74 \sqrt{5 x+3}}{605 \sqrt{1-2 x}}-\frac{2}{55 \sqrt{1-2 x} \sqrt{5 x+3}}",1,"(2*(20 + 37*x))/(121*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])","A",1
2566,1,27,45,0.0062448,"\int \frac{1}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{2 (20 x+1)}{121 \sqrt{1-2 x} \sqrt{5 x+3}}","\frac{2}{11 \sqrt{1-2 x} \sqrt{5 x+3}}-\frac{20 \sqrt{1-2 x}}{121 \sqrt{5 x+3}}",1,"(2*(1 + 20*x))/(121*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])","A",1
2567,1,72,79,0.0299644,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x) (3+5 x)^{3/2}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(3/2)),x]","\frac{5180 x+2178 \sqrt{7-14 x} \sqrt{5 x+3} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-2282}{5929 \sqrt{1-2 x} \sqrt{5 x+3}}","-\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,"(-2282 + 5180*x + 2178*Sqrt[7 - 14*x]*Sqrt[3 + 5*x]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(5929*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])","A",1
2568,1,74,108,0.0669009,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^{3/2}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2)),x]","\frac{106410 x^2+15821 x-34205}{5929 \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}}","-\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,"(-34205 + 15821*x + 106410*x^2)/(5929*Sqrt[1 - 2*x]*(2 + 3*x)*Sqrt[3 + 5*x]) + (999*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(49*Sqrt[7])","A",1
2569,1,79,137,0.079044,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{3/2}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(3/2)),x]","\frac{\frac{7 \left(56260350 x^3+45655035 x^2-12730165 x-12072596\right)}{\sqrt{1-2 x} (3 x+2)^2 \sqrt{5 x+3}}+21447855 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1162084}","-\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,"((7*(-12072596 - 12730165*x + 45655035*x^2 + 56260350*x^3))/(Sqrt[1 - 2*x]*(2 + 3*x)^2*Sqrt[3 + 5*x]) + 21447855*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/1162084","A",1
2570,1,84,166,0.0929582,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^4 (3+5 x)^{3/2}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x)^(3/2)),x]","\frac{\frac{7 \left(1979479350 x^4+2925598635 x^3+622325745 x^2-723664682 x-283149136\right)}{\sqrt{1-2 x} (3 x+2)^3 \sqrt{5 x+3}}+251629785 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{2324168}","-\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,"((7*(-283149136 - 723664682*x + 622325745*x^2 + 2925598635*x^3 + 1979479350*x^4))/(Sqrt[1 - 2*x]*(2 + 3*x)^3*Sqrt[3 + 5*x]) + 251629785*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/2324168","A",1
2571,1,275,142,1.7055304,"\int \frac{(2+3 x)^5}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{\frac{173 \left(1320000 \sqrt{22} (2 x-1) (3 x+2)^3 \, _4F_3\left(\frac{1}{2},2,2,\frac{7}{2};1,1,\frac{9}{2};-\frac{5}{11} (2 x-1)\right)-1050000 \sqrt{22} (x+3) \left(6 x^2+x-2\right)^2 \, _2F_1\left(\frac{3}{2},\frac{9}{2};\frac{11}{2};-\frac{5}{11} (2 x-1)\right)-\frac{23674497 \sqrt{10} \left(108 x^3+513 x^2+1296 x+374\right) \sin ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{(1-2 x)^{5/2}}+\frac{8470 \sqrt{5 x+3} \left(43200 x^5+28080 x^4-400032 x^3+1229303 x^2+2053496 x+1669914\right)}{(1-2 x)^2}\right)}{1089}+2079 (1-2 x) \left(\frac{10 \left(49005 x^2+60010 x+18373\right)}{(5 x+3)^{3/2}}+\frac{29403 \sqrt{10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{\sqrt{2 x-1}}\right)-\frac{7986000 (3 x+2)^4}{(5 x+3)^{3/2}}}{53240000 \sqrt{1-2 x}}","\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,"((-7986000*(2 + 3*x)^4)/(3 + 5*x)^(3/2) + 2079*(1 - 2*x)*((10*(18373 + 60010*x + 49005*x^2))/(3 + 5*x)^(3/2) + (29403*Sqrt[10]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/Sqrt[-1 + 2*x]) + (173*((8470*Sqrt[3 + 5*x]*(1669914 + 2053496*x + 1229303*x^2 - 400032*x^3 + 28080*x^4 + 43200*x^5))/(1 - 2*x)^2 - (23674497*Sqrt[10]*(374 + 1296*x + 513*x^2 + 108*x^3)*ArcSin[Sqrt[5/11]*Sqrt[1 - 2*x]])/(1 - 2*x)^(5/2) - 1050000*Sqrt[22]*(3 + x)*(-2 + x + 6*x^2)^2*Hypergeometric2F1[3/2, 9/2, 11/2, (-5*(-1 + 2*x))/11] + 1320000*Sqrt[22]*(-1 + 2*x)*(2 + 3*x)^3*HypergeometricPFQ[{1/2, 2, 2, 7/2}, {1, 1, 9/2}, (-5*(-1 + 2*x))/11]))/1089)/(53240000*Sqrt[1 - 2*x])","C",0
2572,1,90,113,0.1100033,"\int \frac{(2+3 x)^4}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{10 \sqrt{2 x-1} \left(-3234330 x^3+6746215 x^2+11581424 x+3821563\right)-2479653 \sqrt{50 x+30} \left(10 x^2+x-3\right) \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{3993000 \sqrt{-(1-2 x)^2} (5 x+3)^{3/2}}","\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,"(10*Sqrt[-1 + 2*x]*(3821563 + 11581424*x + 6746215*x^2 - 3234330*x^3) - 2479653*Sqrt[30 + 50*x]*(-3 + x + 10*x^2)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(3993000*Sqrt[-(1 - 2*x)^2]*(3 + 5*x)^(3/2))","A",0
2573,1,189,84,0.9051217,"\int \frac{(2+3 x)^3}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{343 \left(\frac{160 (2 x-1) (3 x+2)^3 \, _4F_3\left(\frac{1}{2},2,2,\frac{7}{2};1,1,\frac{9}{2};-\frac{5}{11} (2 x-1)\right)}{79233}-\frac{200 (x+3) \left(6 x^2+x-2\right)^2 \, _2F_1\left(\frac{3}{2},\frac{9}{2};\frac{11}{2};-\frac{5}{11} (2 x-1)\right)}{124509}+\frac{\sqrt{10-20 x} \sqrt{5 x+3} \left(43200 x^5+28080 x^4-400032 x^3+1229303 x^2+2053496 x+1669914\right)-27951 \left(108 x^3+513 x^2+1296 x+374\right) \sin ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{154350 \sqrt{55} (1-2 x)^{5/2}}\right)}{121 \sqrt{22-44 x}}","\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,"(343*((Sqrt[10 - 20*x]*Sqrt[3 + 5*x]*(1669914 + 2053496*x + 1229303*x^2 - 400032*x^3 + 28080*x^4 + 43200*x^5) - 27951*(374 + 1296*x + 513*x^2 + 108*x^3)*ArcSin[Sqrt[5/11]*Sqrt[1 - 2*x]])/(154350*Sqrt[55]*(1 - 2*x)^(5/2)) - (200*(3 + x)*(-2 + x + 6*x^2)^2*Hypergeometric2F1[3/2, 9/2, 11/2, (-5*(-1 + 2*x))/11])/124509 + (160*(-1 + 2*x)*(2 + 3*x)^3*HypergeometricPFQ[{1/2, 2, 2, 7/2}, {1, 1, 9/2}, (-5*(-1 + 2*x))/11])/79233))/(121*Sqrt[22 - 44*x])","C",0
2574,1,32,67,0.0142616,"\int \frac{(2+3 x)^2}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{2 \left(4091 x^2+4456 x+1196\right)}{3993 \sqrt{1-2 x} (5 x+3)^{3/2}}","-\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,"(2*(1196 + 4456*x + 4091*x^2))/(3993*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))","A",1
2575,1,32,67,0.00962,"\int \frac{2+3 x}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{2 \left(2140 x^2+1391 x+40\right)}{3993 \sqrt{1-2 x} (5 x+3)^{3/2}}","-\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,"(2*(40 + 1391*x + 2140*x^2))/(3993*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))","A",1
2576,1,32,67,0.0070551,"\int \frac{1}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{2 \left(800 x^2+520 x-97\right)}{3993 \sqrt{1-2 x} (5 x+3)^{3/2}}","-\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,"(2*(-97 + 520*x + 800*x^2))/(3993*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))","A",1
2577,1,67,101,0.0685293,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x) (3+5 x)^{5/2}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(5/2)),x]","-\frac{2 \left(155150 x^2+11005 x-45016\right)}{27951 \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}}","\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,"(-2*(-45016 + 11005*x + 155150*x^2))/(27951*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)) - (54*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(7*Sqrt[7])","A",1
2578,1,102,130,0.066517,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^{5/2}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2)),x]","\frac{-19513791 \sqrt{7-14 x} \sqrt{5 x+3} \left(15 x^2+19 x+6\right) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-7 \left(85254450 x^3+63467215 x^2-20145298 x-16461125\right)}{1369599 \sqrt{1-2 x} (3 x+2) (5 x+3)^{3/2}}","\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,"(-7*(-16461125 - 20145298*x + 63467215*x^2 + 85254450*x^3) - 19513791*Sqrt[7 - 14*x]*Sqrt[3 + 5*x]*(6 + 19*x + 15*x^2)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(1369599*Sqrt[1 - 2*x]*(2 + 3*x)*(3 + 5*x)^(3/2))","A",1
2579,1,84,159,0.1002605,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{5/2}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(5/2)),x]","\frac{-\frac{7 \left(63655742250 x^4+89836042575 x^3+16567908760 x^2-22311149965 x-8194676012\right)}{\sqrt{1-2 x} (3 x+2)^2 (5 x+3)^{3/2}}-4855268385 \sqrt{7} \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{38348772}","\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,"((-7*(-8194676012 - 22311149965*x + 16567908760*x^2 + 89836042575*x^3 + 63655742250*x^4))/(Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x)^(3/2)) - 4855268385*Sqrt[7]*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/38348772","A",1
2580,1,95,142,0.0665994,"\int \frac{(2+3 x)^4 \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^4*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","\frac{10 \sqrt{2 x-1} \sqrt{5 x+3} \left(2851200 x^4+15040080 x^3+52700868 x^2-183672928 x+66038637\right)+437126283 \sqrt{10} (1-2 x)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{2112000 \sqrt{1-2 x} (2 x-1)^{3/2}}","\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,"(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(66038637 - 183672928*x + 52700868*x^2 + 15040080*x^3 + 2851200*x^4) + 437126283*Sqrt[10]*(1 - 2*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(2112000*Sqrt[1 - 2*x]*(-1 + 2*x)^(3/2))","A",1
2581,1,90,113,0.0511646,"\int \frac{(2+3 x)^3 \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^3*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","\frac{10 \sqrt{2 x-1} \sqrt{5 x+3} \left(71280 x^3+431244 x^2-1786144 x+625431\right)+4174929 \sqrt{10} (1-2 x)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{105600 \sqrt{1-2 x} (2 x-1)^{3/2}}","\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,"(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(625431 - 1786144*x + 431244*x^2 + 71280*x^3) + 4174929*Sqrt[10]*(1 - 2*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(105600*Sqrt[1 - 2*x]*(-1 + 2*x)^(3/2))","A",1
2582,1,73,94,0.0934023,"\int \frac{(2+3 x)^2 \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^2*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","-\frac{\sqrt{5 x+3} \left(1188 x^2-7712 x+2481\right)}{264 (1-2 x)^{3/2}}-\frac{519 \sqrt{1-2 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{8 \sqrt{20 x-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,"-1/264*(Sqrt[3 + 5*x]*(2481 - 7712*x + 1188*x^2))/(1 - 2*x)^(3/2) - (519*Sqrt[1 - 2*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(8*Sqrt[-10 + 20*x])","A",1
2583,1,51,74,0.0590709,"\int \frac{(2+3 x) \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","\frac{363 \sqrt{22} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};\frac{5}{11} (1-2 x)\right)+8 (5 x+3)^{3/2}}{660 (1-2 x)^{3/2}}","\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,"(8*(3 + 5*x)^(3/2) + 363*Sqrt[22]*Hypergeometric2F1[-3/2, -3/2, -1/2, (5*(1 - 2*x))/11])/(660*(1 - 2*x)^(3/2))","C",1
2584,1,22,22,0.0056059,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","Integrate[Sqrt[3 + 5*x]/(1 - 2*x)^(5/2),x]","\frac{2 (5 x+3)^{3/2}}{33 (1-2 x)^{3/2}}","\frac{2 (5 x+3)^{3/2}}{33 (1-2 x)^{3/2}}",1,"(2*(3 + 5*x)^(3/2))/(33*(1 - 2*x)^(3/2))","A",1
2585,1,71,79,0.0407848,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} (2+3 x)} \, dx","Integrate[Sqrt[3 + 5*x]/((1 - 2*x)^(5/2)*(2 + 3*x)),x]","-\frac{2 \left(7 \sqrt{5 x+3} (128 x-141)+99 \sqrt{7-14 x} (2 x-1) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{11319 (1-2 x)^{3/2}}","\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*(7*Sqrt[3 + 5*x]*(-141 + 128*x) + 99*Sqrt[7 - 14*x]*(-1 + 2*x)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/(11319*(1 - 2*x)^(3/2))","A",1
2586,1,86,115,0.0508904,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} (2+3 x)^2} \, dx","Integrate[Sqrt[3 + 5*x]/((1 - 2*x)^(5/2)*(2 + 3*x)^2),x]","-\frac{7 \sqrt{5 x+3} \left(5100 x^2-1460 x-1623\right)-2475 \sqrt{7-14 x} \left(6 x^2+x-2\right) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{79233 (1-2 x)^{3/2} (3 x+2)}","\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,"-1/79233*(7*Sqrt[3 + 5*x]*(-1623 - 1460*x + 5100*x^2) - 2475*Sqrt[7 - 14*x]*(-2 + x + 6*x^2)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/((1 - 2*x)^(3/2)*(2 + 3*x))","A",1
2587,1,95,144,0.0639054,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} (2+3 x)^3} \, dx","Integrate[Sqrt[3 + 5*x]/((1 - 2*x)^(5/2)*(2 + 3*x)^3),x]","-\frac{7 \sqrt{5 x+3} \left(14940 x^3+19380 x^2-8633 x-6708\right)-25245 \sqrt{7-14 x} (2 x-1) (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{316932 (1-2 x)^{3/2} (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,"-1/316932*(7*Sqrt[3 + 5*x]*(-6708 - 8633*x + 19380*x^2 + 14940*x^3) - 25245*Sqrt[7 - 14*x]*(-1 + 2*x)*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/((1 - 2*x)^(3/2)*(2 + 3*x)^2)","A",1
2588,1,100,173,0.0768597,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} (2+3 x)^4} \, dx","Integrate[Sqrt[3 + 5*x]/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]","-\frac{-7 \sqrt{5 x+3} \left(1834380 x^4+235980 x^3-1465461 x^2-39530 x+302352\right)-837045 \sqrt{7-14 x} (2 x-1) (3 x+2)^3 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{4437048 (1-2 x)^{3/2} (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,"-1/4437048*(-7*Sqrt[3 + 5*x]*(302352 - 39530*x - 1465461*x^2 + 235980*x^3 + 1834380*x^4) - 837045*Sqrt[7 - 14*x]*(-1 + 2*x)*(2 + 3*x)^3*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/((1 - 2*x)^(3/2)*(2 + 3*x)^3)","A",1
2589,1,100,164,0.0794683,"\int \frac{(2+3 x)^4 (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^4*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2),x]","\frac{10 \sqrt{2 x-1} \sqrt{5 x+3} \left(15552000 x^5+83548800 x^4+236669040 x^3+633940524 x^2-2034703904 x+739060191\right)+4878634569 \sqrt{10} (1-2 x)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{3072000 \sqrt{1-2 x} (2 x-1)^{3/2}}","\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,"(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(739060191 - 2034703904*x + 633940524*x^2 + 236669040*x^3 + 83548800*x^4 + 15552000*x^5) + 4878634569*Sqrt[10]*(1 - 2*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(3072000*Sqrt[1 - 2*x]*(-1 + 2*x)^(3/2))","A",1
2590,1,95,135,0.0608443,"\int \frac{(2+3 x)^3 (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2),x]","\frac{10 \sqrt{2 x-1} \sqrt{5 x+3} \left(86400 x^4+447120 x^3+1544724 x^2-5349344 x+1925361\right)+12740199 \sqrt{10} (1-2 x)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{38400 \sqrt{1-2 x} (2 x-1)^{3/2}}","\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,"(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(1925361 - 5349344*x + 1544724*x^2 + 447120*x^3 + 86400*x^4) + 12740199*Sqrt[10]*(1 - 2*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(38400*Sqrt[1 - 2*x]*(-1 + 2*x)^(3/2))","A",1
2591,1,90,116,0.0540157,"\int \frac{(2+3 x)^2 (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2),x]","\frac{10 \sqrt{2 x-1} \sqrt{5 x+3} \left(2160 x^3+12780 x^2-52256 x+18351\right)+122361 \sqrt{10} (1-2 x)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{1920 \sqrt{1-2 x} (2 x-1)^{3/2}}","-\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,"(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(18351 - 52256*x + 12780*x^2 + 2160*x^3) + 122361*Sqrt[10]*(1 - 2*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(1920*Sqrt[1 - 2*x]*(-1 + 2*x)^(3/2))","A",1
2592,1,56,96,0.0329872,"\int \frac{(2+3 x) (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2),x]","\frac{1859 \sqrt{22} (2 x-1) \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+56 (5 x+3)^{5/2}}{264 (1-2 x)^{3/2}}","\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,"(56*(3 + 5*x)^(5/2) + 1859*Sqrt[22]*(-1 + 2*x)*Hypergeometric2F1[-3/2, -1/2, 1/2, (-5*(-1 + 2*x))/11])/(264*(1 - 2*x)^(3/2))","C",1
2593,1,39,74,0.0089583,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","Integrate[(3 + 5*x)^(3/2)/(1 - 2*x)^(5/2),x]","\frac{11 \sqrt{\frac{11}{2}} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};-\frac{5}{11} (2 x-1)\right)}{6 (1-2 x)^{3/2}}","\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[11/2]*Hypergeometric2F1[-3/2, -3/2, -1/2, (-5*(-1 + 2*x))/11])/(6*(1 - 2*x)^(3/2))","C",1
2594,1,71,79,0.0437539,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} (2+3 x)} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)),x]","\frac{2 \left(7 \sqrt{5 x+3} (41 x+18)+3 \sqrt{7-14 x} (2 x-1) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)\right)}{1029 (1-2 x)^{3/2}}","\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,"(2*(7*Sqrt[3 + 5*x]*(18 + 41*x) + 3*Sqrt[7 - 14*x]*(-1 + 2*x)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))/(1029*(1 - 2*x)^(3/2))","A",1
2595,1,86,122,0.0496516,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^2),x]","-\frac{7 \sqrt{5 x+3} \left(660 x^2-310 x-549\right)+285 \sqrt{7-14 x} \left(6 x^2+x-2\right) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{7203 (1-2 x)^{3/2} (3 x+2)}","\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,"-1/7203*(7*Sqrt[3 + 5*x]*(-549 - 310*x + 660*x^2) + 285*Sqrt[7 - 14*x]*(-2 + x + 6*x^2)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/((1 - 2*x)^(3/2)*(2 + 3*x))","A",1
2596,1,95,144,0.0620651,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^3),x]","-\frac{7 \sqrt{5 x+3} \left(180 x^3+60 x^2-91 x-36\right)-15 \sqrt{7-14 x} (2 x-1) (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{588 (1-2 x)^{3/2} (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,"-1/588*(7*Sqrt[3 + 5*x]*(-36 - 91*x + 60*x^2 + 180*x^3) - 15*Sqrt[7 - 14*x]*(-1 + 2*x)*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/((1 - 2*x)^(3/2)*(2 + 3*x)^2)","A",1
2597,1,100,173,0.0742785,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]","-\frac{7 \sqrt{5 x+3} \left(150660 x^4+193860 x^3-17127 x^2-80510 x-19296\right)-28185 \sqrt{7-14 x} (2 x-1) (3 x+2)^3 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{403368 (1-2 x)^{3/2} (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,"-1/403368*(7*Sqrt[3 + 5*x]*(-19296 - 80510*x - 17127*x^2 + 193860*x^3 + 150660*x^4) - 28185*Sqrt[7 - 14*x]*(-1 + 2*x)*(2 + 3*x)^3*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/((1 - 2*x)^(3/2)*(2 + 3*x)^3)","A",1
2598,1,105,186,0.0870376,"\int \frac{(2+3 x)^4 (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^4*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2),x]","\frac{10 \sqrt{2 x-1} \sqrt{5 x+3} \left(248832000 x^6+1423526400 x^5+4002203520 x^4+8217694800 x^3+18987469764 x^2-58600061024 x+21368105901\right)+140927752779 \sqrt{10} (1-2 x)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{12288000 \sqrt{1-2 x} (2 x-1)^{3/2}}","\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,"(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(21368105901 - 58600061024*x + 18987469764*x^2 + 8217694800*x^3 + 4002203520*x^4 + 1423526400*x^5 + 248832000*x^6) + 140927752779*Sqrt[10]*(1 - 2*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(12288000*Sqrt[1 - 2*x]*(-1 + 2*x)^(3/2))","A",1
2599,1,100,157,0.0682598,"\int \frac{(2+3 x)^3 (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^3*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2),x]","\frac{10 \sqrt{2 x-1} \sqrt{5 x+3} \left(1036800 x^5+5477760 x^4+15301008 x^3+40614996 x^2-129940960 x+47216961\right)+311652759 \sqrt{10} (1-2 x)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{122880 \sqrt{1-2 x} (2 x-1)^{3/2}}","\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,"(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(47216961 - 129940960*x + 40614996*x^2 + 15301008*x^3 + 5477760*x^4 + 1036800*x^5) + 311652759*Sqrt[10]*(1 - 2*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(122880*Sqrt[1 - 2*x]*(-1 + 2*x)^(3/2))","A",1
2600,1,95,140,0.0589912,"\int \frac{(2+3 x)^2 (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^2*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2),x]","\frac{2 \sqrt{2 x-1} \sqrt{5 x+3} \left(28800 x^4+146160 x^3+497868 x^2-1713440 x+617319\right)+816717 \sqrt{10} (1-2 x)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{1536 \sqrt{1-2 x} (2 x-1)^{3/2}}","-\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,"(2*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(617319 - 1713440*x + 497868*x^2 + 146160*x^3 + 28800*x^4) + 816717*Sqrt[10]*(1 - 2*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(1536*Sqrt[1 - 2*x]*(-1 + 2*x)^(3/2))","A",1
2601,1,56,118,0.0255432,"\int \frac{(2+3 x) (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2),x]","\frac{28919 \sqrt{22} (2 x-1) \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+112 (5 x+3)^{7/2}}{528 (1-2 x)^{3/2}}","\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,"(112*(3 + 5*x)^(7/2) + 28919*Sqrt[22]*(-1 + 2*x)*Hypergeometric2F1[-5/2, -1/2, 1/2, (-5*(-1 + 2*x))/11])/(528*(1 - 2*x)^(3/2))","C",1
2602,1,39,96,0.0086566,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","Integrate[(3 + 5*x)^(5/2)/(1 - 2*x)^(5/2),x]","\frac{121 \sqrt{\frac{11}{2}} \, _2F_1\left(-\frac{5}{2},-\frac{3}{2};-\frac{1}{2};-\frac{5}{11} (2 x-1)\right)}{12 (1-2 x)^{3/2}}","\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,"(121*Sqrt[11/2]*Hypergeometric2F1[-5/2, -3/2, -1/2, (-5*(-1 + 2*x))/11])/(12*(1 - 2*x)^(3/2))","C",1
2603,1,97,108,0.0727423,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)),x]","-\frac{-18865 \sqrt{22} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};-\frac{5}{11} (2 x-1)\right)+56 \sqrt{5 x+3} (41 x+18)+24 \sqrt{7-14 x} (2 x-1) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{12348 (1-2 x)^{3/2}}","\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,"-1/12348*(56*Sqrt[3 + 5*x]*(18 + 41*x) + 24*Sqrt[7 - 14*x]*(-1 + 2*x)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])] - 18865*Sqrt[22]*Hypergeometric2F1[-3/2, -3/2, -1/2, (-5*(-1 + 2*x))/11])/(1 - 2*x)^(3/2)","C",1
2604,1,86,122,0.0477699,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^2} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^2),x]","-\frac{-7 \sqrt{5 x+3} \left(3090 x^2+3070 x+657\right)-165 \sqrt{7-14 x} \left(6 x^2+x-2\right) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{7203 (1-2 x)^{3/2} (3 x+2)}","\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,"-1/7203*(-7*Sqrt[3 + 5*x]*(657 + 3070*x + 3090*x^2) - 165*Sqrt[7 - 14*x]*(-2 + x + 6*x^2)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/((1 - 2*x)^(3/2)*(2 + 3*x))","A",1
2605,1,95,151,0.0594836,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^3} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^3),x]","-\frac{7 \sqrt{5 x+3} \left(10260 x^3+1620 x^2-13627 x-6732\right)+2145 \sqrt{7-14 x} (2 x-1) (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{28812 (1-2 x)^{3/2} (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,"-1/28812*(7*Sqrt[3 + 5*x]*(-6732 - 13627*x + 1620*x^2 + 10260*x^3) + 2145*Sqrt[7 - 14*x]*(-1 + 2*x)*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/((1 - 2*x)^(3/2)*(2 + 3*x)^2)","A",1
2606,1,100,173,0.0737676,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^4} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]","-\frac{7 \sqrt{5 x+3} \left(567180 x^4+552780 x^3-169221 x^2-304730 x-75888\right)-7755 \sqrt{7-14 x} (2 x-1) (3 x+2)^3 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{403368 (1-2 x)^{3/2} (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,"-1/403368*(7*Sqrt[3 + 5*x]*(-75888 - 304730*x - 169221*x^2 + 552780*x^3 + 567180*x^4) - 7755*Sqrt[7 - 14*x]*(-1 + 2*x)*(2 + 3*x)^3*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/((1 - 2*x)^(3/2)*(2 + 3*x)^3)","A",1
2607,1,105,202,0.0872961,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^5} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^5),x]","-\frac{7 \sqrt{5 x+3} \left(45277380 x^5+82071900 x^4+25673409 x^3-27318504 x^2-18627988 x-2906640\right)-1643235 \sqrt{7-14 x} (2 x-1) (3 x+2)^4 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{22588608 (1-2 x)^{3/2} (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,"-1/22588608*(7*Sqrt[3 + 5*x]*(-2906640 - 18627988*x - 27318504*x^2 + 25673409*x^3 + 82071900*x^4 + 45277380*x^5) - 1643235*Sqrt[7 - 14*x]*(-1 + 2*x)*(2 + 3*x)^4*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/((1 - 2*x)^(3/2)*(2 + 3*x)^4)","A",1
2608,1,95,142,0.0665703,"\int \frac{(2+3 x)^5}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","\frac{10 \sqrt{2 x-1} \sqrt{5 x+3} \left(18817920 x^4+101146320 x^3+359461476 x^2-1261070176 x+452899509\right)+2998952451 \sqrt{10} (1-2 x)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{23232000 \sqrt{1-2 x} (2 x-1)^{3/2}}","\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,"(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(452899509 - 1261070176*x + 359461476*x^2 + 101146320*x^3 + 18817920*x^4) + 2998952451*Sqrt[10]*(1 - 2*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(23232000*Sqrt[1 - 2*x]*(-1 + 2*x)^(3/2))","A",1
2609,1,90,113,0.1088917,"\int \frac{(2+3 x)^4}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","\frac{10 \sqrt{2 x-1} \sqrt{5 x+3} \left(2352240 x^3+14544684 x^2-61036064 x+21305631\right)+142398729 \sqrt{10} (1-2 x)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{5808000 \sqrt{1-2 x} (2 x-1)^{3/2}}","\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,"(10*Sqrt[-1 + 2*x]*Sqrt[3 + 5*x]*(21305631 - 61036064*x + 14544684*x^2 + 2352240*x^3) + 142398729*Sqrt[10]*(1 - 2*x)^2*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(5808000*Sqrt[1 - 2*x]*(-1 + 2*x)^(3/2))","A",1
2610,1,73,84,0.0902727,"\int \frac{(2+3 x)^3}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","-\frac{\sqrt{5 x+3} \left(39204 x^2-261664 x+83301\right)}{14520 (1-2 x)^{3/2}}-\frac{1593 \sqrt{1-2 x} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{40 \sqrt{20 x-10}}","\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,"-1/14520*(Sqrt[3 + 5*x]*(83301 - 261664*x + 39204*x^2))/(1 - 2*x)^(3/2) - (1593*Sqrt[1 - 2*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(40*Sqrt[-10 + 20*x])","A",1
2611,1,64,72,0.0616278,"\int \frac{(2+3 x)^2}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","-\frac{70 (51-256 x) \sqrt{5 x+3}+3267 \sqrt{10} (2 x-1)^{3/2} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{7260 (1-2 x)^{3/2}}","-\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,"-1/7260*(70*(51 - 256*x)*Sqrt[3 + 5*x] + 3267*Sqrt[10]*(-1 + 2*x)^(3/2)*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(1 - 2*x)^(3/2)","A",1
2612,1,27,45,0.0102845,"\int \frac{2+3 x}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","\frac{2 \sqrt{5 x+3} (29 x+24)}{363 (1-2 x)^{3/2}}","\frac{7 \sqrt{5 x+3}}{33 (1-2 x)^{3/2}}-\frac{29 \sqrt{5 x+3}}{363 \sqrt{1-2 x}}",1,"(2*Sqrt[3 + 5*x]*(24 + 29*x))/(363*(1 - 2*x)^(3/2))","A",1
2613,1,27,45,0.0062851,"\int \frac{1}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","-\frac{2 \sqrt{5 x+3} (20 x-21)}{363 (1-2 x)^{3/2}}","\frac{20 \sqrt{5 x+3}}{363 \sqrt{1-2 x}}+\frac{2 \sqrt{5 x+3}}{33 (1-2 x)^{3/2}}",1,"(-2*Sqrt[3 + 5*x]*(-21 + 20*x))/(363*(1 - 2*x)^(3/2))","A",1
2614,1,71,79,0.0581085,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x) \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)*Sqrt[3 + 5*x]),x]","\frac{56 \sqrt{5 x+3} (123-169 x)+6534 \sqrt{7-14 x} (2 x-1) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{124509 (1-2 x)^{3/2}}","\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,"(56*(123 - 169*x)*Sqrt[3 + 5*x] + 6534*Sqrt[7 - 14*x]*(-1 + 2*x)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(124509*(1 - 2*x)^(3/2))","A",1
2615,1,86,108,0.0538983,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^2 \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*Sqrt[3 + 5*x]),x]","-\frac{-7 \sqrt{5 x+3} \left(26340 x^2-39500 x+15321\right)-147015 \sqrt{7-14 x} \left(6 x^2+x-2\right) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{871563 (1-2 x)^{3/2} (3 x+2)}","-\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,"-1/871563*(-7*Sqrt[3 + 5*x]*(15321 - 39500*x + 26340*x^2) - 147015*Sqrt[7 - 14*x]*(-2 + x + 6*x^2)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/((1 - 2*x)^(3/2)*(2 + 3*x))","A",1
2616,1,95,137,0.064618,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^3 \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*Sqrt[3 + 5*x]),x]","-\frac{-7 \sqrt{5 x+3} \left(2073420 x^3-676860 x^2-945629 x+391476\right)-2107215 \sqrt{7-14 x} (2 x-1) (3 x+2)^2 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{3486252 (1-2 x)^{3/2} (3 x+2)^2}","-\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,"-1/3486252*(-7*Sqrt[3 + 5*x]*(391476 - 945629*x - 676860*x^2 + 2073420*x^3) - 2107215*Sqrt[7 - 14*x]*(-1 + 2*x)*(2 + 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/((1 - 2*x)^(3/2)*(2 + 3*x)^2)","A",1
2617,1,100,166,0.0777067,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^4 \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^4*Sqrt[3 + 5*x]),x]","-\frac{-7 \sqrt{5 x+3} \left(374883660 x^4+140350860 x^3-244982277 x^2-48873610 x+44829024\right)-119882565 \sqrt{7-14 x} (2 x-1) (3 x+2)^3 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{48807528 (1-2 x)^{3/2} (3 x+2)^3}","-\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,"-1/48807528*(-7*Sqrt[3 + 5*x]*(44829024 - 48873610*x - 244982277*x^2 + 140350860*x^3 + 374883660*x^4) - 119882565*Sqrt[7 - 14*x]*(-1 + 2*x)*(2 + 3*x)^3*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/((1 - 2*x)^(3/2)*(2 + 3*x)^3)","A",1
2618,1,246,142,3.9917121,"\int \frac{(2+3 x)^5}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{1}{20} \left(\frac{1673 \left(50000 (1-2 x)^{3/2} \left(6 x^2+x-2\right)^3 \, _2F_1\left(\frac{3}{2},\frac{9}{2};\frac{11}{2};-\frac{5}{11} (2 x-1)\right)+33 \sqrt{55} \left(\sqrt{10-20 x} \sqrt{5 x+3} \left(21600 x^5-43740 x^4+79209 x^3+272474 x^2+678368 x+129582\right)-3993 \left(513 x^3+2538 x^2+936 x+334\right) \sin ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)\right)\right)}{52707600 \sqrt{22} (1-2 x)^3}+\frac{153 \left(326700 x^2-824990 x+120879 \sqrt{5 x+3} \sqrt{20 x-10} \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)-612430\right)}{96800 \sqrt{1-2 x} \sqrt{5 x+3}}-\frac{3 (3 x+2)^4}{(1-2 x)^{3/2} \sqrt{5 x+3}}\right)","\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,"((-3*(2 + 3*x)^4)/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]) + (153*(-612430 - 824990*x + 326700*x^2 + 120879*Sqrt[3 + 5*x]*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]]))/(96800*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]) + (1673*(33*Sqrt[55]*(Sqrt[10 - 20*x]*Sqrt[3 + 5*x]*(129582 + 678368*x + 272474*x^2 + 79209*x^3 - 43740*x^4 + 21600*x^5) - 3993*(334 + 936*x + 2538*x^2 + 513*x^3)*ArcSin[Sqrt[5/11]*Sqrt[1 - 2*x]]) + 50000*(1 - 2*x)^(3/2)*(-2 + x + 6*x^2)^3*Hypergeometric2F1[3/2, 9/2, 11/2, (-5*(-1 + 2*x))/11]))/(52707600*Sqrt[22]*(1 - 2*x)^3))/20","C",0
2619,1,94,113,0.1022575,"\int \frac{(2+3 x)^4}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{10 \sqrt{2 x-1} \left(6468660 x^3-40488772 x^2-12657123 x+8379147\right)+19513791 \sqrt{50 x+30} (1-2 x)^2 \sinh ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{2 x-1}\right)}{7986000 \sqrt{1-2 x} (2 x-1)^{3/2} \sqrt{5 x+3}}","\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,"(10*Sqrt[-1 + 2*x]*(8379147 - 12657123*x - 40488772*x^2 + 6468660*x^3) + 19513791*(1 - 2*x)^2*Sqrt[30 + 50*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(7986000*Sqrt[1 - 2*x]*(-1 + 2*x)^(3/2)*Sqrt[3 + 5*x])","A",1
2620,1,143,84,0.2513982,"\int \frac{(2+3 x)^3}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{\sqrt{10-20 x} \sqrt{5 x+3} \left(21600 x^5-43740 x^4+79209 x^3+272474 x^2+678368 x+129582\right)-3993 \left(513 x^3+2538 x^2+936 x+334\right) \sin ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{79860 \sqrt{10} (1-2 x)^3}-\frac{250 \sqrt{\frac{2}{11}} (1-2 x)^{3/2} (3 x+2)^3 \, _2F_1\left(\frac{3}{2},\frac{9}{2};\frac{11}{2};-\frac{5}{11} (2 x-1)\right)}{131769}","\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,"(Sqrt[10 - 20*x]*Sqrt[3 + 5*x]*(129582 + 678368*x + 272474*x^2 + 79209*x^3 - 43740*x^4 + 21600*x^5) - 3993*(334 + 936*x + 2538*x^2 + 513*x^3)*ArcSin[Sqrt[5/11]*Sqrt[1 - 2*x]])/(79860*Sqrt[10]*(1 - 2*x)^3) - (250*Sqrt[2/11]*(1 - 2*x)^(3/2)*(2 + 3*x)^3*Hypergeometric2F1[3/2, 9/2, 11/2, (-5*(-1 + 2*x))/11])/131769","C",0
2621,1,32,67,0.0139794,"\int \frac{(2+3 x)^2}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{2 \left(793 x^2+1440 x+564\right)}{3993 (1-2 x)^{3/2} \sqrt{5 x+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,"(2*(564 + 1440*x + 793*x^2))/(3993*(1 - 2*x)^(3/2)*Sqrt[3 + 5*x])","A",1
2622,1,32,67,0.0106436,"\int \frac{2+3 x}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{-1640 x^2+738 x+888}{3993 (1-2 x)^{3/2} \sqrt{5 x+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,"(888 + 738*x - 1640*x^2)/(3993*(1 - 2*x)^(3/2)*Sqrt[3 + 5*x])","A",1
2623,1,32,67,0.0091818,"\int \frac{1}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{-1600 x^2+720 x+282}{3993 (1-2 x)^{3/2} \sqrt{5 x+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,"(282 + 720*x - 1600*x^2)/(3993*(1 - 2*x)^(3/2)*Sqrt[3 + 5*x])","A",1
2624,1,67,101,0.0806757,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x) (3+5 x)^{3/2}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^(3/2)),x]","\frac{54 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{49 \sqrt{7}}-\frac{2 \left(84460 x^2-73944 x+14163\right)}{195657 (1-2 x)^{3/2} \sqrt{5 x+3}}","-\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,"(-2*(14163 - 73944*x + 84460*x^2))/(195657*(1 - 2*x)^(3/2)*Sqrt[3 + 5*x]) + (54*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(49*Sqrt[7])","A",1
2625,1,100,130,0.0635755,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{3/2}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2)),x]","-\frac{12398265 \sqrt{7-14 x} \sqrt{5 x+3} \left(6 x^2+x-2\right) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+7 \left(22082700 x^3-7613680 x^2-8760465 x+3499599\right)}{9587193 (1-2 x)^{3/2} (3 x+2) \sqrt{5 x+3}}","-\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,"-1/9587193*(7*(3499599 - 8760465*x - 7613680*x^2 + 22082700*x^3) + 12398265*Sqrt[7 - 14*x]*Sqrt[3 + 5*x]*(-2 + x + 6*x^2)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/((1 - 2*x)^(3/2)*(2 + 3*x)*Sqrt[3 + 5*x])","A",1
2626,1,84,159,0.1453721,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^{3/2}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^(3/2)),x]","\frac{79515 \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)}{1372 \sqrt{7}}-\frac{1667076300 x^4+520073880 x^3-1053213025 x^2-169466391 x+178740084}{5478396 (1-2 x)^{3/2} (3 x+2)^2 \sqrt{5 x+3}}","-\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,"-1/5478396*(178740084 - 169466391*x - 1053213025*x^2 + 520073880*x^3 + 1667076300*x^4)/((1 - 2*x)^(3/2)*(2 + 3*x)^2*Sqrt[3 + 5*x]) + (79515*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(1372*Sqrt[7])","A",1
2627,1,75,171,15.2026322,"\int \frac{(2+3 x)^6}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^6/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","-\frac{12807946800 x^5+97980793020 x^4-252342435560 x^3-274128335769 x^2+19932058554 x+44437106459}{351384000 (1-2 x)^{3/2} (5 x+3)^{3/2}}-\frac{753543 \sin ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{8000 \sqrt{10}}","\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,"-1/351384000*(44437106459 + 19932058554*x - 274128335769*x^2 - 252342435560*x^3 + 97980793020*x^4 + 12807946800*x^5)/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) - (753543*ArcSin[Sqrt[5/11]*Sqrt[1 - 2*x]])/(8000*Sqrt[10])","A",1
2628,1,257,142,1.3708566,"\int \frac{(2+3 x)^5}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","-\frac{37 \left(-1320000 (3 x+2)^3 (1-2 x)^{7/2} \, _4F_3\left(\frac{1}{2},2,2,\frac{7}{2};1,1,\frac{9}{2};-\frac{5}{11} (2 x-1)\right)-1050000 (x+3) \left(6 x^2+x-2\right)^2 (1-2 x)^{5/2} \, _2F_1\left(\frac{3}{2},\frac{9}{2};\frac{11}{2};-\frac{5}{11} (2 x-1)\right)+77 \sqrt{55} \left(\sqrt{10-20 x} \sqrt{5 x+3} \left(43200 x^5+28080 x^4-400032 x^3+1229303 x^2+2053496 x+1669914\right)-27951 \left(108 x^3+513 x^2+1296 x+374\right) \sin ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)\right)\right)}{614922000 \sqrt{22} (1-2 x)^3}+\frac{1183 \left(19573 x^3+62232 x^2+52044 x+13040\right)}{878460 (1-2 x)^{3/2} (5 x+3)^{3/2}}-\frac{3 (3 x+2)^4}{10 (1-2 x)^{3/2} (5 x+3)^{3/2}}","\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,"(-3*(2 + 3*x)^4)/(10*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + (1183*(13040 + 52044*x + 62232*x^2 + 19573*x^3))/(878460*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) - (37*(77*Sqrt[55]*(Sqrt[10 - 20*x]*Sqrt[3 + 5*x]*(1669914 + 2053496*x + 1229303*x^2 - 400032*x^3 + 28080*x^4 + 43200*x^5) - 27951*(374 + 1296*x + 513*x^2 + 108*x^3)*ArcSin[Sqrt[5/11]*Sqrt[1 - 2*x]]) - 1050000*(1 - 2*x)^(5/2)*(3 + x)*(-2 + x + 6*x^2)^2*Hypergeometric2F1[3/2, 9/2, 11/2, (-5*(-1 + 2*x))/11] - 1320000*(1 - 2*x)^(7/2)*(2 + 3*x)^3*HypergeometricPFQ[{1/2, 2, 2, 7/2}, {1, 1, 9/2}, (-5*(-1 + 2*x))/11]))/(614922000*Sqrt[22]*(1 - 2*x)^3)","C",0
2629,1,65,113,15.2250986,"\int \frac{(2+3 x)^4}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^4/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{49702040 x^3+51334383 x^2+7883562 x-3014813}{2196150 (1-2 x)^{3/2} (5 x+3)^{3/2}}-\frac{81 \sin ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)}{50 \sqrt{10}}","\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,"(-3014813 + 7883562*x + 51334383*x^2 + 49702040*x^3)/(2196150*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) - (81*ArcSin[Sqrt[5/11]*Sqrt[1 - 2*x]])/(50*Sqrt[10])","A",1
2630,1,37,96,0.0351906,"\int \frac{(2+3 x)^3}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^3/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{2 \left(19573 x^3+62232 x^2+52044 x+13040\right)}{43923 (1-2 x)^{3/2} (5 x+3)^{3/2}}","\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,"(2*(13040 + 52044*x + 62232*x^2 + 19573*x^3))/(43923*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))","A",1
2631,1,37,89,0.0222417,"\int \frac{(2+3 x)^2}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^2/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{-65960 x^3-9894 x^2+49200 x+18728}{43923 (1-2 x)^{3/2} (5 x+3)^{3/2}}","-\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,"(18728 + 49200*x - 9894*x^2 - 65960*x^3)/(43923*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))","A",1
2632,1,37,89,0.0211094,"\int \frac{2+3 x}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{-59200 x^3-8880 x^2+26418 x+5728}{43923 (1-2 x)^{3/2} (5 x+3)^{3/2}}","-\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,"(5728 + 26418*x - 8880*x^2 - 59200*x^3)/(43923*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))","A",1
2633,1,37,89,0.0146034,"\int \frac{1}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{-32000 x^3-4800 x^2+14280 x+722}{43923 (1-2 x)^{3/2} (5 x+3)^{3/2}}","-\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,"(722 + 14280*x - 4800*x^2 - 32000*x^3)/(43923*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))","A",1
2634,1,93,123,0.125963,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x) (3+5 x)^{5/2}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^(5/2)),x]","\frac{7115526 \sqrt{7-14 x} \sqrt{5 x+3} \left(10 x^2+x-3\right) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)+14 \left(10015900 x^3-4427220 x^2-3234261 x+1490582\right)}{15065589 (1-2 x)^{3/2} (5 x+3)^{3/2}}","\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,"(14*(1490582 - 3234261*x - 4427220*x^2 + 10015900*x^3) + 7115526*Sqrt[7 - 14*x]*Sqrt[3 + 5*x]*(-3 + x + 10*x^2)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(15065589*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))","A",1
2635,1,112,152,0.1206286,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{5/2}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2)),x]","-\frac{-658186155 \sqrt{7-14 x} \sqrt{5 x+3} \left(30 x^3+23 x^2-7 x-6\right) \tan ^{-1}\left(\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right)-7 \left(5746984500 x^4+1402439900 x^3-3498236655 x^2-429626520 x+555141781\right)}{105459123 (1-2 x)^{3/2} (3 x+2) (5 x+3)^{3/2}}","\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,"-1/105459123*(-7*(555141781 - 429626520*x - 3498236655*x^2 + 1402439900*x^3 + 5746984500*x^4) - 658186155*Sqrt[7 - 14*x]*Sqrt[3 + 5*x]*(-6 - 7*x + 23*x^2 + 30*x^3)*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(3/2))","A",1
2636,1,89,181,0.1472614,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^{5/2}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^(5/2)),x]","\frac{619886659500 x^5+564878517900 x^4-276089438305 x^3-297937101390 x^2+28838387211 x+39900939556}{60262356 (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}}","\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,"(39900939556 + 28838387211*x - 297937101390*x^2 - 276089438305*x^3 + 564878517900*x^4 + 619886659500*x^5)/(60262356*(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2)) - (538245*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(1372*Sqrt[7])","A",1
2637,1,129,58,0.3887874,"\int \frac{1}{\sqrt{a+b x} \sqrt{c+\frac{b (-1+c) x}{a}} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","Integrate[1/(Sqrt[a + b*x]*Sqrt[c + (b*(-1 + c)*x)/a]*Sqrt[e + (b*(-1 + e)*x)/a]),x]","-\frac{2 (a+b x) \sqrt{\frac{\frac{a}{a+b x}+c-1}{c-1}} \sqrt{\frac{\frac{a}{a+b x}+e-1}{e-1}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{-\frac{a}{c-1}}}{\sqrt{a+b x}}\right),\frac{c-1}{e-1}\right)}{b \sqrt{-\frac{a}{c-1}} \sqrt{\frac{b (c-1) x}{a}+c} \sqrt{\frac{b (e-1) x}{a}+e}}","\frac{2 \sqrt{a} \operatorname{EllipticF}\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,"(-2*(a + b*x)*Sqrt[(-1 + c + a/(a + b*x))/(-1 + c)]*Sqrt[(-1 + e + a/(a + b*x))/(-1 + e)]*EllipticF[ArcSin[Sqrt[-(a/(-1 + c))]/Sqrt[a + b*x]], (-1 + c)/(-1 + e)])/(b*Sqrt[-(a/(-1 + c))]*Sqrt[c + (b*(-1 + c)*x)/a]*Sqrt[e + (b*(-1 + e)*x)/a])","B",1
2638,1,126,96,0.5268589,"\int \frac{1}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","Integrate[1/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + (b*(-1 + e)*x)/a]),x]","-\frac{2 \sqrt{c+d x} \sqrt{\frac{\frac{a}{a+b x}+e-1}{e-1}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{-\frac{a}{e-1}}}{\sqrt{a+b x}}\right),\frac{(e-1) (b c-a d)}{a d}\right)}{d \sqrt{-\frac{a}{e-1}} \sqrt{\frac{b (e-1) x}{a}+e} \sqrt{\frac{b (c+d x)}{d (a+b x)}}}","\frac{2 \sqrt{a} \sqrt{\frac{b (c+d x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{1-e} \sqrt{a+b x}}{\sqrt{a}}\right),-\frac{a d}{(1-e) (b c-a d)}\right)}{b \sqrt{1-e} \sqrt{c+d x}}",1,"(-2*Sqrt[c + d*x]*Sqrt[(-1 + e + a/(a + b*x))/(-1 + e)]*EllipticF[ArcSin[Sqrt[-(a/(-1 + e))]/Sqrt[a + b*x]], ((b*c - a*d)*(-1 + e))/(a*d)])/(d*Sqrt[-(a/(-1 + e))]*Sqrt[(b*(c + d*x))/(d*(a + b*x))]*Sqrt[e + (b*(-1 + e)*x)/a])","A",1
2639,1,126,134,0.5687542,"\int \frac{1}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x}} \, dx","Integrate[1/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","-\frac{2 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{f (a+b x)}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{a-\frac{b c}{d}}}{\sqrt{a+b x}}\right),\frac{b d e-a d f}{b c f-a d f}\right)}{d \sqrt{e+f x} \sqrt{a-\frac{b c}{d}} \sqrt{\frac{b (c+d x)}{d (a+b x)}}}","\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right),\frac{f (b c-a d)}{d (b e-a f)}\right)}{b \sqrt{d} \sqrt{c+d x} \sqrt{e+f x}}",1,"(-2*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(f*(a + b*x))]*EllipticF[ArcSin[Sqrt[a - (b*c)/d]/Sqrt[a + b*x]], (b*d*e - a*d*f)/(b*c*f - a*d*f)])/(Sqrt[a - (b*c)/d]*d*Sqrt[(b*(c + d*x))/(d*(a + b*x))]*Sqrt[e + f*x])","A",1
2640,1,191,58,0.856261,"\int \frac{\sqrt{e+\frac{b (-1+e) x}{a}}}{\sqrt{a+b x} \sqrt{c+\frac{b (-1+c) x}{a}}} \, dx","Integrate[Sqrt[e + (b*(-1 + e)*x)/a]/(Sqrt[a + b*x]*Sqrt[c + (b*(-1 + c)*x)/a]),x]","-\frac{2 (a+b x)^{3/2} \left(\frac{a \sqrt{\frac{\frac{a}{a+b x}+c-1}{c-1}} \sqrt{\frac{\frac{a}{a+b x}+e-1}{e-1}} E\left(\sin ^{-1}\left(\frac{\sqrt{-\frac{a}{e-1}}}{\sqrt{a+b x}}\right)|\frac{e-1}{c-1}\right)}{\sqrt{a+b x}}-\frac{\sqrt{-\frac{a}{e-1}} \left(\frac{a}{a+b x}+c-1\right) \left(\frac{a}{a+b x}+e-1\right)}{c-1}\right)}{a b \sqrt{-\frac{a}{e-1}} \sqrt{\frac{b (c-1) x}{a}+c} \sqrt{\frac{b (e-1) x}{a}+e}}","\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,"(-2*(a + b*x)^(3/2)*(-((Sqrt[-(a/(-1 + e))]*(-1 + c + a/(a + b*x))*(-1 + e + a/(a + b*x)))/(-1 + c)) + (a*Sqrt[(-1 + c + a/(a + b*x))/(-1 + c)]*Sqrt[(-1 + e + a/(a + b*x))/(-1 + e)]*EllipticE[ArcSin[Sqrt[-(a/(-1 + e))]/Sqrt[a + b*x]], (-1 + e)/(-1 + c)])/Sqrt[a + b*x]))/(a*b*Sqrt[-(a/(-1 + e))]*Sqrt[c + (b*(-1 + c)*x)/a]*Sqrt[e + (b*(-1 + e)*x)/a])","B",1
2641,1,200,96,1.3811589,"\int \frac{\sqrt{c+d x}}{\sqrt{a+b x} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","Integrate[Sqrt[c + d*x]/(Sqrt[a + b*x]*Sqrt[e + (b*(-1 + e)*x)/a]),x]","\frac{2 \sqrt{\frac{\frac{a}{a+b x}+e-1}{e-1}} \left(b \sqrt{a+b x} (c+d x) \sqrt{a-\frac{b c}{d}} \sqrt{\frac{a e+b (e-1) x}{(e-1) (a+b x)}}-(a+b x) (b c-a d) \sqrt{\frac{b (c+d x)}{d (a+b x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{a-\frac{b c}{d}}}{\sqrt{a+b x}}\right)|\frac{a d}{(b c-a d) (e-1)}\right)\right)}{b^2 \sqrt{c+d x} \sqrt{a-\frac{b c}{d}} \sqrt{\frac{b (e-1) x}{a}+e}}","\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,"(2*Sqrt[(-1 + e + a/(a + b*x))/(-1 + e)]*(b*Sqrt[a - (b*c)/d]*Sqrt[a + b*x]*(c + d*x)*Sqrt[(a*e + b*(-1 + e)*x)/((-1 + e)*(a + b*x))] - (b*c - a*d)*(a + b*x)*Sqrt[(b*(c + d*x))/(d*(a + b*x))]*EllipticE[ArcSin[Sqrt[a - (b*c)/d]/Sqrt[a + b*x]], (a*d)/((b*c - a*d)*(-1 + e))]))/(b^2*Sqrt[a - (b*c)/d]*Sqrt[c + d*x]*Sqrt[e + (b*(-1 + e)*x)/a])","B",1
2642,1,103,162,0.255617,"\int \frac{\sqrt{a+b x}}{\sqrt{c+\frac{b (-1+c) x}{a}} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","Integrate[Sqrt[a + b*x]/(Sqrt[c + (b*(-1 + c)*x)/a]*Sqrt[e + (b*(-1 + e)*x)/a]),x]","-\frac{2 i a \sqrt{a+b x} \left(E\left(i \sinh ^{-1}\left(\sqrt{\frac{(c-1) (a+b x)}{a}}\right)|\frac{e-1}{c-1}\right)-\operatorname{EllipticF}\left(i \sinh ^{-1}\left(\sqrt{\frac{(c-1) (a+b x)}{a}}\right),\frac{e-1}{c-1}\right)\right)}{b (e-1) \sqrt{\frac{(c-1) (a+b x)}{a}}}","-\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,"((-2*I)*a*Sqrt[a + b*x]*(EllipticE[I*ArcSinh[Sqrt[((-1 + c)*(a + b*x))/a]], (-1 + e)/(-1 + c)] - EllipticF[I*ArcSinh[Sqrt[((-1 + c)*(a + b*x))/a]], (-1 + e)/(-1 + c)]))/(b*(-1 + e)*Sqrt[((-1 + c)*(a + b*x))/a])","C",1
2643,1,154,134,1.7155705,"\int \frac{\sqrt{e+f x}}{\sqrt{a+b x} \sqrt{c+d x}} \, dx","Integrate[Sqrt[e + f*x]/(Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\frac{2 \sqrt{c+d x} \left(\frac{(a f-b e) \sqrt{\frac{b (e+f x)}{f (a+b x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{a-\frac{b e}{f}}}{\sqrt{a+b x}}\right)|\frac{b c f-a d f}{b d e-a d f}\right)}{b \sqrt{a-\frac{b e}{f}} \sqrt{\frac{b (c+d x)}{d (a+b x)}}}+\frac{e+f x}{\sqrt{a+b x}}\right)}{d \sqrt{e+f x}}","\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,"(2*Sqrt[c + d*x]*((e + f*x)/Sqrt[a + b*x] + ((-(b*e) + a*f)*Sqrt[(b*(e + f*x))/(f*(a + b*x))]*EllipticE[ArcSin[Sqrt[a - (b*e)/f]/Sqrt[a + b*x]], (b*c*f - a*d*f)/(b*d*e - a*d*f)])/(b*Sqrt[a - (b*e)/f]*Sqrt[(b*(c + d*x))/(d*(a + b*x))])))/(d*Sqrt[e + f*x])","A",1
2644,1,123,101,0.3724014,"\int \frac{1}{\sqrt{-c+d x} \sqrt{c+d x} \sqrt{e+f x}} \, dx","Integrate[1/(Sqrt[-c + d*x]*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\frac{\sqrt{2} (c-d x) \sqrt{\frac{c+d x}{d x-c}} \sqrt{\frac{d (e+f x)}{f (d x-c)}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{-c}}{\sqrt{d x-c}}\right),\frac{1}{2} \left(\frac{d e}{c f}+1\right)\right)}{\sqrt{-c} d \sqrt{c+d x} \sqrt{e+f x}}","\frac{2 \sqrt{c} \sqrt{\frac{c-d x}{c}} \sqrt{\frac{d (e+f x)}{d e-c f}} \operatorname{EllipticF}\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,"(Sqrt[2]*(c - d*x)*Sqrt[(c + d*x)/(-c + d*x)]*Sqrt[(d*(e + f*x))/(f*(-c + d*x))]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[-c])/Sqrt[-c + d*x]], (1 + (d*e)/(c*f))/2])/(Sqrt[-c]*d*Sqrt[c + d*x]*Sqrt[e + f*x])","A",1
2645,1,102,191,0.361372,"\int \sqrt{1-2 x} (2+3 x)^{5/2} \sqrt{3+5 x} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x],x]","\frac{-5867645 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(472500 x^3+861750 x^2+410490 x-136987\right)+11646308 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{3543750 \sqrt{2}}","-\frac{175111 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1181250}+\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{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,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-136987 + 410490*x + 861750*x^2 + 472500*x^3) + 11646308*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5867645*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(3543750*Sqrt[2])","A",1
2646,1,97,160,0.2758004,"\int \sqrt{1-2 x} (2+3 x)^{3/2} \sqrt{3+5 x} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x],x]","\frac{-27860 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(2250 x^2+2445 x-166\right)+55019 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{39375 \sqrt{2}}","-\frac{823 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{13125}+\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{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,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-166 + 2445*x + 2250*x^2) + 55019*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 27860*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(39375*Sqrt[2])","A",1
2647,1,97,129,0.2276405,"\int \sqrt{1-2 x} \sqrt{2+3 x} \sqrt{3+5 x} \, dx","Integrate[Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x],x]","\frac{-1295 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+30 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3} (90 x+23)+2318 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{6750}","-\frac{31 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1125}+\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{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,"(30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(23 + 90*x) + 2318*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 1295*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/6750","A",1
2648,1,92,98,0.2150248,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{\sqrt{2+3 x}} \, dx","Integrate[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/Sqrt[2 + 3*x],x]","\frac{1}{135} \left(-70 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+30 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+37 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","\frac{2}{45} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\frac{2}{9} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\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,"(30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] + 37*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 70*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/135","A",1
2649,1,92,98,0.2470806,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^{3/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^(3/2),x]","\frac{1}{9} \left(37 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{6 \sqrt{1-2 x} \sqrt{5 x+3}}{\sqrt{3 x+2}}-4 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{2}{3} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{3 \sqrt{3 x+2}}+\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,"((-6*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/Sqrt[2 + 3*x] - 4*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 37*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/9","A",1
2650,1,97,129,0.1807739,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^{5/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^(5/2),x]","\frac{2}{189} \left(-70 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} (111 x+67)}{(3 x+2)^{3/2}}+37 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","\frac{4}{63} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(67 + 111*x))/(2 + 3*x)^(3/2) + 37*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 70*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/189","A",1
2651,1,99,160,0.3451939,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^{7/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^(7/2),x]","\frac{2 \left(\sqrt{2} \left(2318 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-1295 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(20862 x^2+28593 x+9643\right)}{(3 x+2)^{5/2}}\right)}{6615}","-\frac{124 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{2205}+\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(9643 + 28593*x + 20862*x^2))/(2 + 3*x)^(5/2) + Sqrt[2]*(2318*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 1295*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/6615","A",1
2652,1,106,191,0.3171964,"\int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^{9/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2 + 3*x)^(9/2),x]","\frac{4 \left(\sqrt{2} \left(55019 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-27860 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(2971026 x^3+6042348 x^2+4100535 x+926791\right)}{2 (3 x+2)^{7/2}}\right)}{108045}","-\frac{6584 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{36015}+\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{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,"(4*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(926791 + 4100535*x + 6042348*x^2 + 2971026*x^3))/(2*(2 + 3*x)^(7/2)) + Sqrt[2]*(55019*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 27860*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/108045","A",1
2653,1,107,218,0.3342577,"\int \sqrt{1-2 x} (2+3 x)^{5/2} (3+5 x)^{3/2} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2),x]","\frac{-759987865 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(63787500 x^4+156161250 x^3+132234750 x^2+29706255 x-27010769\right)+1508889271 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{116943750 \sqrt{2}}","-\frac{11346991 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1771875 \sqrt{33}}+\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{1508889271 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{7087500 \sqrt{33}}",1,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-27010769 + 29706255*x + 132234750*x^2 + 156161250*x^3 + 63787500*x^4) + 1508889271*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 759987865*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(116943750*Sqrt[2])","A",1
2654,1,102,191,0.3241307,"\int \sqrt{1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2),x]","\frac{-5366165 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(472500 x^3+821250 x^2+366480 x-133999\right)+10655966 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{2126250 \sqrt{2}}","-\frac{160297 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{708750}+\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{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,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-133999 + 366480*x + 821250*x^2 + 472500*x^3) + 10655966*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5366165*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(2126250*Sqrt[2])","A",1
2655,1,97,160,0.2962439,"\int \sqrt{1-2 x} \sqrt{2+3 x} (3+5 x)^{3/2} \, dx","Integrate[Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2),x]","\frac{-74515 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(6750 x^2+6705 x-659\right)+148831 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{70875 \sqrt{2}}","-\frac{2252 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{23625}+\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{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,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-659 + 6705*x + 6750*x^2) + 148831*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 74515*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(70875*Sqrt[2])","A",1
2656,1,92,129,0.2564042,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{\sqrt{2+3 x}} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/Sqrt[2 + 3*x],x]","\frac{-595 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} (90 x+13)+1948 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{2025 \sqrt{2}}","-\frac{41}{675} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(13 + 90*x) + 1948*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 595*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(2025*Sqrt[2])","A",1
2657,1,97,129,0.2707116,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{3/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^(3/2),x]","\frac{1}{81} \left(-181 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{6 \sqrt{1-2 x} \sqrt{5 x+3} (15 x+13)}{\sqrt{3 x+2}}+49 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","\frac{8}{27} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"((6*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(13 + 15*x))/Sqrt[2 + 3*x] + 49*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 181*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/81","A",1
2658,1,97,129,0.2906449,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{5/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^(5/2),x]","\frac{1}{567} \left(4025 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{6 \sqrt{1-2 x} \sqrt{5 x+3} (426 x+277)}{(3 x+2)^{3/2}}-494 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{214}{189} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"((-6*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(277 + 426*x))/(2 + 3*x)^(3/2) - 494*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 4025*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/567","A",1
2659,1,99,160,0.2845183,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{7/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^(7/2),x]","\frac{2 \left(\sqrt{2} \left(4157 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-10955 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(37413 x^2+45432 x+13807\right)}{(3 x+2)^{5/2}}\right)}{19845}","\frac{824 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{6615}-\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(13807 + 45432*x + 37413*x^2))/(2 + 3*x)^(5/2) + Sqrt[2]*(4157*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 10955*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/19845","A",1
2660,1,104,191,0.3370806,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{9/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^(9/2),x]","\frac{2 \left(\sqrt{2} \left(237796 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-150115 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(6420492 x^3+13111191 x^2+8796570 x+1944697\right)}{(3 x+2)^{7/2}}\right)}{972405}","-\frac{10628 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{324135}-\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1944697 + 8796570*x + 13111191*x^2 + 6420492*x^3))/(2 + 3*x)^(7/2) + Sqrt[2]*(237796*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 150115*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/972405","A",1
2661,1,107,222,0.3910917,"\int \frac{\sqrt{1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{11/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^(11/2),x]","\frac{-93064160 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{24 \sqrt{2-4 x} \sqrt{5 x+3} \left(920917674 x^4+2487189618 x^3+2520548433 x^2+1134125364 x+190959271\right)}{(3 x+2)^{9/2}}+181909664 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{81682020 \sqrt{2}}","-\frac{673072 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{6806835}-\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{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,"((24*Sqrt[2 - 4*x]*Sqrt[3 + 5*x]*(190959271 + 1134125364*x + 2520548433*x^2 + 2487189618*x^3 + 920917674*x^4))/(2 + 3*x)^(9/2) + 181909664*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 93064160*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(81682020*Sqrt[2])","A",1
2662,1,112,249,0.3710495,"\int \sqrt{1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2),x]","\frac{-16537733765 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(1403325000 x^5+4299277500 x^4+5075689500 x^3+2626854750 x^2+139824180 x-707313559\right)+32833974506 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{608107500 \sqrt{2}}","-\frac{493825477 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{18427500 \sqrt{33}}+\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{16416987253 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{18427500 \sqrt{33}}",1,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-707313559 + 139824180*x + 2626854750*x^2 + 5075689500*x^3 + 4299277500*x^4 + 1403325000*x^5) + 32833974506*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 16537733765*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(608107500*Sqrt[2])","A",1
2663,1,107,218,0.3412325,"\int \sqrt{1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2} \, dx","Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2),x]","\frac{-15576890 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(1417500 x^4+3354750 x^3+2737800 x^2+570555 x-567484\right)+30926081 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{1559250 \sqrt{2}}","-\frac{465127 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{47250 \sqrt{33}}+\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{30926081 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{94500 \sqrt{33}}",1,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-567484 + 570555*x + 2737800*x^2 + 3354750*x^3 + 1417500*x^4) + 30926081*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 15576890*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1559250*Sqrt[2])","A",1
2664,1,102,191,0.3394863,"\int \sqrt{1-2 x} \sqrt{2+3 x} (3+5 x)^{5/2} \, dx","Integrate[Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3 + 5*x)^(5/2),x]","\frac{-983815 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(94500 x^3+156150 x^2+65250 x-26009\right)+1952596 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{255150 \sqrt{2}}","-\frac{29357 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{85050}+\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{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,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-26009 + 65250*x + 156150*x^2 + 94500*x^3) + 1952596*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 983815*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(255150*Sqrt[2])","A",1
2665,1,97,160,0.2708389,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{\sqrt{2+3 x}} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/Sqrt[2 + 3*x],x]","\frac{-4690 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+75 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(90 x^2+81 x-10\right)+9013 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{2835 \sqrt{2}}","-\frac{131}{945} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(75*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-10 + 81*x + 90*x^2) + 9013*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 4690*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(2835*Sqrt[2])","A",1
2666,1,112,156,0.247072,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{3/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^(3/2),x]","\frac{15 \sqrt{2} (3 x+2) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{1-2 x} x \sqrt{3 x+2} \sqrt{5 x+3} (10 x+7)+18 \sqrt{2} (3 x+2) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{90 x+60}","-\frac{1}{5} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{3}{5} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"(10*Sqrt[1 - 2*x]*x*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(7 + 10*x) + 18*Sqrt[2]*(2 + 3*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 15*Sqrt[2]*(2 + 3*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(60 + 90*x)","A",1
2667,1,102,160,0.3309038,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{5/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^(5/2),x]","\frac{-10360 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{6 \sqrt{1-2 x} \sqrt{5 x+3} \left(1575 x^2+2841 x+1187\right)}{(3 x+2)^{3/2}}+2209 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{1701}","\frac{494}{567} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"((6*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1187 + 2841*x + 1575*x^2))/(2 + 3*x)^(3/2) + 2209*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 10360*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/1701","A",1
2668,1,99,160,0.3015589,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{7/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^(7/2),x]","\frac{\sqrt{2} \left(242095 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-31588 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)-\frac{6 \sqrt{1-2 x} \sqrt{5 x+3} \left(87021 x^2+113319 x+36919\right)}{(3 x+2)^{5/2}}}{19845}","-\frac{12758 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{6615}-\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{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,"((-6*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(36919 + 113319*x + 87021*x^2))/(2 + 3*x)^(5/2) + Sqrt[2]*(-31588*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 242095*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/19845","A",1
2669,1,104,191,0.3093681,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{9/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^(9/2),x]","\frac{2 \left(\sqrt{2} \left(86741 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-281540 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(2342007 x^3+4290411 x^2+2623695 x+535637\right)}{(3 x+2)^{7/2}}\right)}{324135}","\frac{23612 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{108045}-\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(535637 + 2623695*x + 4290411*x^2 + 2342007*x^3))/(2 + 3*x)^(7/2) + Sqrt[2]*(86741*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 281540*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/324135","A",1
2670,1,110,222,0.3710285,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{11/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^(11/2),x]","\frac{8 \sqrt{2} \left(13599226 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-9945565 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{24 \sqrt{1-2 x} \sqrt{5 x+3} \left(1101537306 x^4+2991138867 x^3+3003721227 x^2+1325733891 x+217427099\right)}{(3 x+2)^{9/2}}}{245046060}","-\frac{442868 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{20420505}-\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{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,"((24*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(217427099 + 1325733891*x + 3003721227*x^2 + 2991138867*x^3 + 1101537306*x^4))/(2 + 3*x)^(9/2) + 8*Sqrt[2]*(13599226*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 9945565*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/245046060","A",1
2671,1,112,249,0.4296996,"\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{13/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2))/(2 + 3*x)^(13/2),x]","\frac{-10873573760 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{48 \sqrt{2-4 x} \sqrt{5 x+3} \left(158560640046 x^5+534040213536 x^4+719808574005 x^3+484598540169 x^2+162787885893 x+21813966691\right)}{(3 x+2)^{11/2}}+20880413504 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{12579031080 \sqrt{2}}","-\frac{37904696 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{47647845 \sqrt{33}}-\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{1305025844 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{47647845 \sqrt{33}}",1,"((48*Sqrt[2 - 4*x]*Sqrt[3 + 5*x]*(21813966691 + 162787885893*x + 484598540169*x^2 + 719808574005*x^3 + 534040213536*x^4 + 158560640046*x^5))/(2 + 3*x)^(11/2) + 20880413504*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 10873573760*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(12579031080*Sqrt[2])","A",1
2672,1,154,134,0.8590513,"\int \frac{\sqrt{e+f x}}{\sqrt{a+b x} \sqrt{c+d x}} \, dx","Integrate[Sqrt[e + f*x]/(Sqrt[a + b*x]*Sqrt[c + d*x]),x]","\frac{2 \sqrt{c+d x} \left(\frac{(a f-b e) \sqrt{\frac{b (e+f x)}{f (a+b x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{a-\frac{b e}{f}}}{\sqrt{a+b x}}\right)|\frac{b c f-a d f}{b d e-a d f}\right)}{b \sqrt{a-\frac{b e}{f}} \sqrt{\frac{b (c+d x)}{d (a+b x)}}}+\frac{e+f x}{\sqrt{a+b x}}\right)}{d \sqrt{e+f x}}","\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,"(2*Sqrt[c + d*x]*((e + f*x)/Sqrt[a + b*x] + ((-(b*e) + a*f)*Sqrt[(b*(e + f*x))/(f*(a + b*x))]*EllipticE[ArcSin[Sqrt[a - (b*e)/f]/Sqrt[a + b*x]], (b*c*f - a*d*f)/(b*d*e - a*d*f)])/(b*Sqrt[a - (b*e)/f]*Sqrt[(b*(c + d*x))/(d*(a + b*x))])))/(d*Sqrt[e + f*x])","A",1
2673,1,126,184,0.9364768,"\int \frac{\sqrt{e+f x}}{(a+b x)^{3/2} \sqrt{c+d x}} \, dx","Integrate[Sqrt[e + f*x]/((a + b*x)^(3/2)*Sqrt[c + d*x]),x]","-\frac{2 \sqrt{e+f x} \sqrt{\frac{b (c+d x)}{d (a+b x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{a-\frac{b c}{d}}}{\sqrt{a+b x}}\right)|\frac{b d e-a d f}{b c f-a d f}\right)}{b \sqrt{c+d x} \sqrt{a-\frac{b c}{d}} \sqrt{\frac{b (e+f x)}{f (a+b x)}}}","\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,"(-2*Sqrt[(b*(c + d*x))/(d*(a + b*x))]*Sqrt[e + f*x]*EllipticE[ArcSin[Sqrt[a - (b*c)/d]/Sqrt[a + b*x]], (b*d*e - a*d*f)/(b*c*f - a*d*f)])/(b*Sqrt[a - (b*c)/d]*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(f*(a + b*x))])","A",1
2674,1,109,31,0.4596569,"\int \frac{\sqrt{1-2 x}}{\sqrt{-3-5 x} \sqrt{2+3 x}} \, dx","Integrate[Sqrt[1 - 2*x]/(Sqrt[-3 - 5*x]*Sqrt[2 + 3*x]),x]","-\frac{2 \left(\frac{3 \left(10 x^2+x-3\right)}{\sqrt{3 x+2}}+\sqrt{35} \sqrt{\frac{2 x-1}{3 x+2}} (3 x+2) \sqrt{\frac{5 x+3}{3 x+2}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{7}{2}}}{\sqrt{3 x+2}}\right)|\frac{2}{35}\right)\right)}{15 \sqrt{-5 x-3} \sqrt{1-2 x}}","\frac{2}{3} \sqrt{\frac{7}{5}} E\left(\sin ^{-1}\left(\sqrt{5} \sqrt{3 x+2}\right)|\frac{2}{35}\right)",1,"(-2*((3*(-3 + x + 10*x^2))/Sqrt[2 + 3*x] + Sqrt[35]*Sqrt[(-1 + 2*x)/(2 + 3*x)]*(2 + 3*x)*Sqrt[(3 + 5*x)/(2 + 3*x)]*EllipticE[ArcSin[Sqrt[7/2]/Sqrt[2 + 3*x]], 2/35]))/(15*Sqrt[-3 - 5*x]*Sqrt[1 - 2*x])","B",1
2675,1,97,158,0.3526367,"\int \frac{\sqrt{1-2 x} (2+3 x)^{5/2}}{\sqrt{3+5 x}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2))/Sqrt[3 + 5*x],x]","\frac{-30065 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(2250 x^2+2655 x-89\right)+61151 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{65625 \sqrt{2}}","-\frac{314 \sqrt{33} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{21875}+\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{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,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-89 + 2655*x + 2250*x^2) + 61151*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 30065*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(65625*Sqrt[2])","A",1
2676,1,97,127,0.3683479,"\int \frac{\sqrt{1-2 x} (2+3 x)^{3/2}}{\sqrt{3+5 x}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2))/Sqrt[3 + 5*x],x]","\frac{-105 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3} (30 x+11)+292 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{1250}","-\frac{17}{625} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{146}{625} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"(10*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(11 + 30*x) + 292*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 105*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/1250","A",1
2677,1,92,98,0.2710871,"\int \frac{\sqrt{1-2 x} \sqrt{2+3 x}}{\sqrt{3+5 x}} \, dx","Integrate[(Sqrt[1 - 2*x]*Sqrt[2 + 3*x])/Sqrt[3 + 5*x],x]","\frac{1}{225} \left(35 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+30 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+31 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{4}{75} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\frac{2}{15} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\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,"(30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] + 31*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 35*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/225","A",1
2678,1,121,49,0.3415404,"\int \frac{\sqrt{1-2 x}}{\sqrt{2+3 x} \sqrt{3+5 x}} \, dx","Integrate[Sqrt[1 - 2*x]/(Sqrt[2 + 3*x]*Sqrt[3 + 5*x]),x]","\frac{2 \sqrt{1-2 x} \left(5 \left(6 x^2+x-2\right) \sqrt{5 x+3}+\sqrt{33} \sqrt{\frac{2 x-1}{5 x+3}} \sqrt{\frac{3 x+2}{5 x+3}} (5 x+3)^2 E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{11}{2}}}{\sqrt{5 x+3}}\right)|-\frac{2}{33}\right)\right)}{15 \sqrt{3 x+2} \left(10 x^2+x-3\right)}","\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,"(2*Sqrt[1 - 2*x]*(5*Sqrt[3 + 5*x]*(-2 + x + 6*x^2) + Sqrt[33]*Sqrt[(-1 + 2*x)/(3 + 5*x)]*Sqrt[(2 + 3*x)/(3 + 5*x)]*(3 + 5*x)^2*EllipticE[ArcSin[Sqrt[11/2]/Sqrt[3 + 5*x]], -2/33]))/(15*Sqrt[2 + 3*x]*(-3 + x + 10*x^2))","B",1
2679,1,106,61,0.1546107,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{-2 \sqrt{2} (3 x+2) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+6 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+2 \sqrt{2} (3 x+2) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{9 x+6}","\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,"(6*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] + 2*Sqrt[2]*(2 + 3*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 2*Sqrt[2]*(2 + 3*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(6 + 9*x)","A",1
2680,1,97,129,0.3634328,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^(5/2)*Sqrt[3 + 5*x]),x]","\frac{2}{63} \left(-35 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} (204 x+143)}{(3 x+2)^{3/2}}+68 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{4}{21} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(143 + 204*x))/(2 + 3*x)^(3/2) + 68*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 35*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/63","A",1
2681,1,101,158,0.3261921,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^(7/2)*Sqrt[3 + 5*x]),x]","\frac{4}{735} \left(\sqrt{2} \left(1597 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-805 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(28746 x^2+39294 x+13469\right)}{2 (3 x+2)^{5/2}}\right)","-\frac{64}{245} \sqrt{33} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(4*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(13469 + 39294*x + 28746*x^2))/(2*(2 + 3*x)^(5/2)) + Sqrt[2]*(1597*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 805*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/735","A",1
2682,1,107,189,0.4075989,"\int \frac{\sqrt{1-2 x} (2+3 x)^{7/2}}{(3+5 x)^{3/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2))/(3 + 5*x)^(3/2),x]","\frac{-87010 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{30 \sqrt{1-2 x} \sqrt{3 x+2} \left(33750 x^3+63225 x^2+25955 x+32\right)}{\sqrt{5 x+3}}+203179 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{656250}","-\frac{38723 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{109375 \sqrt{33}}-\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{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,"((30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(32 + 25955*x + 63225*x^2 + 33750*x^3))/Sqrt[3 + 5*x] + 203179*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 87010*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/656250","A",1
2683,1,102,158,0.3555771,"\int \frac{\sqrt{1-2 x} (2+3 x)^{5/2}}{(3+5 x)^{3/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2))/(3 + 5*x)^(3/2),x]","\frac{455 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{30 \sqrt{1-2 x} \sqrt{3 x+2} \left(450 x^2+485 x+119\right)}{\sqrt{5 x+3}}+2818 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{18750}","-\frac{1091 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3125 \sqrt{33}}-\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{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,"((30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(119 + 485*x + 450*x^2))/Sqrt[3 + 5*x] + 2818*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 455*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/18750","A",1
2684,1,97,127,0.3188399,"\int \frac{\sqrt{1-2 x} (2+3 x)^{3/2}}{(3+5 x)^{3/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2))/(3 + 5*x)^(3/2),x]","\frac{1}{375} \left(140 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{30 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+2)}{\sqrt{5 x+3}}+19 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{106 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{125 \sqrt{33}}-\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{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,"((30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(2 + 5*x))/Sqrt[3 + 5*x] + 19*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 140*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/375","A",1
2685,1,92,94,0.289545,"\int \frac{\sqrt{1-2 x} \sqrt{2+3 x}}{(3+5 x)^{3/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*Sqrt[2 + 3*x])/(3 + 5*x)^(3/2),x]","\frac{1}{25} \left(35 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{10 \sqrt{1-2 x} \sqrt{3 x+2}}{\sqrt{5 x+3}}-4 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{62 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{25 \sqrt{33}}-\frac{2 \sqrt{1-2 x} \sqrt{3 x+2}}{5 \sqrt{5 x+3}}+\frac{4}{25} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"((-10*Sqrt[1 - 2*x]*Sqrt[2 + 3*x])/Sqrt[3 + 5*x] - 4*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 35*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/25","A",1
2686,1,61,61,0.1069646,"\int \frac{\sqrt{1-2 x}}{\sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","Integrate[Sqrt[1 - 2*x]/(Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)),x]","-\frac{2 \sqrt{1-2 x} \sqrt{3 x+2}}{\sqrt{5 x+3}}-\frac{2}{5} \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)","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,"(-2*Sqrt[1 - 2*x]*Sqrt[2 + 3*x])/Sqrt[3 + 5*x] - (2*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/5","A",1
2687,1,128,117,0.2618934,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{2 \sqrt{2} \left(15 x^2+19 x+6\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-4 \sqrt{2} \left(15 x^2+19 x+6\right) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-2 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3} (30 x+19)}{(3 x+2) (5 x+3)}","\frac{4 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{\sqrt{33}}-\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}}+4 \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"(-2*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(19 + 30*x) - 4*Sqrt[2]*(6 + 19*x + 15*x^2)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 2*Sqrt[2]*(6 + 19*x + 15*x^2)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/((2 + 3*x)*(3 + 5*x))","A",1
2688,1,100,158,0.2897715,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)),x]","-\frac{4}{21} \sqrt{2} \left(139 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-70 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)-\frac{2 \sqrt{1-2 x} \left(4170 x^2+5422 x+1759\right)}{7 (3 x+2)^{3/2} \sqrt{5 x+3}}","\frac{184 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{7 \sqrt{33}}-\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{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,"(-2*Sqrt[1 - 2*x]*(1759 + 5422*x + 4170*x^2))/(7*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x]) - (4*Sqrt[2]*(139*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 70*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/21","A",1
2689,1,105,189,0.3137956,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)),x]","\frac{2}{735} \left(-2 \sqrt{2} \left(29116 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-14665 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)-\frac{3 \sqrt{1-2 x} \left(2620440 x^3+5154174 x^2+3376856 x+736871\right)}{(3 x+2)^{5/2} \sqrt{5 x+3}}\right)","\frac{38536 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{245 \sqrt{33}}-\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{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,"(2*((-3*Sqrt[1 - 2*x]*(736871 + 3376856*x + 5154174*x^2 + 2620440*x^3))/((2 + 3*x)^(5/2)*Sqrt[3 + 5*x]) - 2*Sqrt[2]*(29116*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 14665*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/735","A",1
2690,1,112,218,0.3999302,"\int \frac{\sqrt{1-2 x} (2+3 x)^{9/2}}{(3+5 x)^{5/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^(9/2))/(3 + 5*x)^(5/2),x]","\frac{-441035 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{10 \sqrt{1-2 x} \sqrt{3 x+2} \left(3341250 x^4+8575875 x^3+6882975 x^2+1854575 x+54083\right)}{(5 x+3)^{3/2}}+1473539 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{7218750}","-\frac{31288 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{109375 \sqrt{33}}-\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{1473539 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{218750 \sqrt{33}}",1,"((10*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(54083 + 1854575*x + 6882975*x^2 + 8575875*x^3 + 3341250*x^4))/(3 + 5*x)^(3/2) + 1473539*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 441035*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/7218750","A",1
2691,1,107,189,0.3513675,"\int \frac{\sqrt{1-2 x} (2+3 x)^{7/2}}{(3+5 x)^{5/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2))/(3 + 5*x)^(5/2),x]","\frac{95165 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{10 \sqrt{1-2 x} \sqrt{3 x+2} \left(222750 x^3+398475 x^2+221200 x+37273\right)}{(5 x+3)^{3/2}}+94684 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{1031250}","-\frac{523 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{15625}-\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{47342 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{15625 \sqrt{33}}",1,"((10*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(37273 + 221200*x + 398475*x^2 + 222750*x^3))/(3 + 5*x)^(3/2) + 94684*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 95165*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/1031250","A",1
2692,1,102,156,0.3334061,"\int \frac{\sqrt{1-2 x} (2+3 x)^{5/2}}{(3+5 x)^{5/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2))/(3 + 5*x)^(5/2),x]","\frac{8015 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{10 \sqrt{1-2 x} \sqrt{3 x+2} \left(2475 x^2+1825 x+193\right)}{(5 x+3)^{3/2}}+169 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{20625}","-\frac{496 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{625 \sqrt{33}}-\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{169 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{625 \sqrt{33}}",1,"((10*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(193 + 1825*x + 2475*x^2))/(3 + 5*x)^(3/2) + 169*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 8015*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/20625","A",1
2693,1,97,125,0.3642251,"\int \frac{\sqrt{1-2 x} (2+3 x)^{3/2}}{(3+5 x)^{5/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2))/(3 + 5*x)^(5/2),x]","\frac{3395 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{10 \sqrt{1-2 x} \sqrt{3 x+2} (650 x+401)}{(5 x+3)^{3/2}}-458 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{4125}","-\frac{178 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{125 \sqrt{33}}-\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{458 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{125 \sqrt{33}}",1,"((-10*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(401 + 650*x))/(3 + 5*x)^(3/2) - 458*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 3395*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/4125","A",1
2694,1,97,125,0.2703263,"\int \frac{\sqrt{1-2 x} \sqrt{2+3 x}}{(3+5 x)^{5/2}} \, dx","Integrate[(Sqrt[1 - 2*x]*Sqrt[2 + 3*x])/(3 + 5*x)^(5/2),x]","\frac{2}{825} \left(-35 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{5 \sqrt{1-2 x} \sqrt{3 x+2} (155 x+104)}{(5 x+3)^{3/2}}-31 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","\frac{8 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{25 \sqrt{33}}-\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{62 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{25 \sqrt{33}}",1,"(2*((-5*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(104 + 155*x))/(3 + 5*x)^(3/2) - 31*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 35*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/825","A",1
2695,1,97,125,0.2232223,"\int \frac{\sqrt{1-2 x}}{\sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","Integrate[Sqrt[1 - 2*x]/(Sqrt[2 + 3*x]*(3 + 5*x)^(5/2)),x]","\frac{2}{165} \left(-35 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{5 \sqrt{1-2 x} \sqrt{3 x+2} (340 x+193)}{(5 x+3)^{3/2}}+68 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{4 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{5 \sqrt{33}}+\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{136 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5 \sqrt{33}}",1,"(2*((5*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(193 + 340*x))/(3 + 5*x)^(3/2) + 68*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 35*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/165","A",1
2696,1,99,150,0.2463693,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{2}{33} \left(2 \sqrt{2} \left(133 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-67 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{\sqrt{1-2 x} \left(19950 x^2+24610 x+7573\right)}{\sqrt{3 x+2} (5 x+3)^{3/2}}\right)","-\frac{16 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{\sqrt{33}}+\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{532 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{\sqrt{33}}",1,"(2*((Sqrt[1 - 2*x]*(7573 + 24610*x + 19950*x^2))/(Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)) + 2*Sqrt[2]*(133*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 67*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/33","A",1
2697,1,104,187,0.3244358,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{2}{231} \left(2 \sqrt{2} \left(9242 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-4655 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{\sqrt{1-2 x} \left(4158900 x^3+7902930 x^2+4998904 x+1052533\right)}{(3 x+2)^{3/2} (5 x+3)^{3/2}}\right)","-\frac{1112 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{7 \sqrt{33}}+\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{36968 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{7 \sqrt{33}}",1,"(2*((Sqrt[1 - 2*x]*(1052533 + 4998904*x + 7902930*x^2 + 4158900*x^3))/((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + 2*Sqrt[2]*(9242*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 4655*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/231","A",1
2698,1,109,218,0.3313742,"\int \frac{\sqrt{1-2 x}}{(2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)),x]","\frac{2 \left(4 \sqrt{2} \left(1289089 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-649285 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{\sqrt{1-2 x} \left(3480540300 x^4+8934240060 x^3+8592783498 x^2+3669873602 x+587237237\right)}{(3 x+2)^{5/2} (5 x+3)^{3/2}}\right)}{8085}","-\frac{310208 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{245 \sqrt{33}}+\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{10312712 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{245 \sqrt{33}}",1,"(2*((Sqrt[1 - 2*x]*(587237237 + 3669873602*x + 8592783498*x^2 + 8934240060*x^3 + 3480540300*x^4))/((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + 4*Sqrt[2]*(1289089*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 649285*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/8085","A",1
2699,1,107,218,0.3360552,"\int (1-2 x)^{3/2} (2+3 x)^{5/2} \sqrt{3+5 x} \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x],x]","\frac{-609979405 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(-127575000 x^4-140805000 x^3+48345750 x^2+89595360 x+4295257\right)+1209831262 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{584718750 \sqrt{2}}","-\frac{18177329 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{17718750 \sqrt{33}}+\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{604915631 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{17718750 \sqrt{33}}",1,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(4295257 + 89595360*x + 48345750*x^2 - 140805000*x^3 - 127575000*x^4) + 1209831262*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 609979405*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(584718750*Sqrt[2])","A",1
2700,1,105,191,0.3148873,"\int (1-2 x)^{3/2} (2+3 x)^{3/2} \sqrt{3+5 x} \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x],x]","\frac{5684677 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5 \left(581651 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+3 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(472500 x^3+153000 x^2-359685 x-84697\right)\right)}{5315625 \sqrt{2}}","-\frac{84134 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1771875}+\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{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,"(5684677*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5*(3*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-84697 - 359685*x + 153000*x^2 + 472500*x^3) + 581651*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(5315625*Sqrt[2])","A",1
2701,1,97,160,0.2893822,"\int (1-2 x)^{3/2} \sqrt{2+3 x} \sqrt{3+5 x} \, dx","Integrate[(1 - 2*x)^(3/2)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x],x]","\frac{-150115 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(-13500 x^2+7380 x+6631\right)+237796 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{354375 \sqrt{2}}","-\frac{2657 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{118125}+\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{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,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(6631 + 7380*x - 13500*x^2) + 237796*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 150115*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(354375*Sqrt[2])","A",1
2702,1,97,129,0.1340072,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{\sqrt{2+3 x}} \, dx","Integrate[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/Sqrt[2 + 3*x],x]","\frac{-10955 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-60 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3} (45 x-76)+4157 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{10125}","\frac{412 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3375}+\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{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,"(-60*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-76 + 45*x) + 4157*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 10955*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/10125","A",1
2703,1,97,129,0.2034598,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(3/2),x]","\frac{1}{405} \left(4025 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{30 \sqrt{1-2 x} \sqrt{5 x+3} (6 x+25)}{\sqrt{3 x+2}}-494 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{214}{135} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"((-30*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(25 + 6*x))/Sqrt[2 + 3*x] - 494*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 4025*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/405","A",1
2704,1,97,129,0.1937575,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(5/2),x]","\frac{2}{81} \left(-181 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} (129 x+79)}{(3 x+2)^{3/2}}+49 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","\frac{16}{27} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(79 + 129*x))/(2 + 3*x)^(3/2) + 49*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 181*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/81","A",1
2705,1,99,160,0.1795141,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^{7/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(7/2),x]","\frac{2 \left(\sqrt{2} \left(1948 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-595 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(17532 x^2+24363 x+8303\right)}{(3 x+2)^{5/2}}\right)}{2835}","-\frac{164}{945} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(8303 + 24363*x + 17532*x^2))/(2 + 3*x)^(5/2) + Sqrt[2]*(1948*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 595*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/2835","A",1
2706,1,106,191,0.3169712,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^{9/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(9/2),x]","\frac{4 \left(\sqrt{2} \left(148831 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-74515 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(8036874 x^3+16342002 x^2+11095995 x+2510369\right)}{2 (3 x+2)^{7/2}}\right)}{138915}","-\frac{18016 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{46305}-\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{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,"(4*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(2510369 + 11095995*x + 16342002*x^2 + 8036874*x^3))/(2*(2 + 3*x)^(7/2)) + Sqrt[2]*(148831*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 74515*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/138915","A",1
2707,1,111,222,0.3391721,"\int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^{11/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(11/2),x]","\frac{4 \left(\sqrt{2} \left(10655966 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5366165 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(1726266492 x^4+4661331894 x^3+4722182964 x^2+2127363207 x+359554583\right)}{2 (3 x+2)^{9/2}}\right)}{2917215}","-\frac{1282376 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{972405}-\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{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,"(4*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(359554583 + 2127363207*x + 4722182964*x^2 + 4661331894*x^3 + 1726266492*x^4))/(2*(2 + 3*x)^(9/2)) + Sqrt[2]*(10655966*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5366165*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/2917215","A",1
2708,1,115,249,0.4063362,"\int (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{3/2} \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2),x]","\frac{51601293223 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5 \left(5197919174 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+3 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(7016625000 x^5+12374775000 x^4+3047388750 x^3-5775295500 x^2-3548873565 x+325972172\right)\right)}{7601343750 \sqrt{2}}","-\frac{776112041 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{230343750 \sqrt{33}}+\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{51601293223 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{460687500 \sqrt{33}}",1,"(51601293223*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5*(3*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(325972172 - 3548873565*x - 5775295500*x^2 + 3047388750*x^3 + 12374775000*x^4 + 7016625000*x^5) + 5197919174*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(7601343750*Sqrt[2])","A",1
2709,1,110,218,0.3483362,"\int (1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2} \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2),x]","\frac{361589456 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5 \left(36399853 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+3 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(42525000 x^4+43470000 x^3-17237250 x^2-27227430 x-810641\right)\right)}{116943750 \sqrt{2}}","-\frac{5442127 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3543750 \sqrt{33}}+\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{90397364 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1771875 \sqrt{33}}",1,"(361589456*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5*(3*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-810641 - 27227430*x - 17237250*x^2 + 43470000*x^3 + 42525000*x^4) + 36399853*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(116943750*Sqrt[2])","A",1
2710,1,105,191,0.3136338,"\int (1-2 x)^{3/2} \sqrt{2+3 x} (3+5 x)^{3/2} \, dx","Integrate[(1 - 2*x)^(3/2)*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2),x]","\frac{4971289 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5 \left(491582 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+3 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(472500 x^3+112500 x^2-337545 x-64804\right)\right)}{3189375 \sqrt{2}}","-\frac{76163 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1063125}+\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{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,"(4971289*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5*(3*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-64804 - 337545*x + 112500*x^2 + 472500*x^3) + 491582*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(3189375*Sqrt[2])","A",1
2711,1,97,160,0.3004582,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{\sqrt{2+3 x}} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/Sqrt[2 + 3*x],x]","\frac{1085 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(-4500 x^2+2880 x+1501\right)+59866 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{70875 \sqrt{2}}","-\frac{1847 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{23625}+\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{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,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(1501 + 2880*x - 4500*x^2) + 59866*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 1085*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(70875*Sqrt[2])","A",1
2712,1,102,160,0.2636643,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(3/2),x]","\frac{-10360 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{30 \sqrt{1-2 x} \sqrt{5 x+3} \left(90 x^2-102 x-143\right)}{\sqrt{3 x+2}}+2209 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{2025}","\frac{494}{675} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"((-30*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-143 - 102*x + 90*x^2))/Sqrt[2 + 3*x] + 2209*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 10360*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/2025","A",1
2713,1,102,160,0.3152209,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(5/2),x]","\frac{1}{243} \left(4387 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{6 \sqrt{1-2 x} \sqrt{5 x+3} \left(90 x^2+564 x+329\right)}{(3 x+2)^{3/2}}-592 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{230}{81} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"((-6*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(329 + 564*x + 90*x^2))/(2 + 3*x)^(3/2) - 592*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 4387*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/243","A",1
2714,1,99,160,0.2023358,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{7/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(7/2),x]","\frac{2 \left(\sqrt{2} \left(2209 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-10360 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(16731 x^2+20754 x+6449\right)}{(3 x+2)^{5/2}}\right)}{2835}","\frac{988}{945} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(6449 + 20754*x + 16731*x^2))/(2 + 3*x)^(5/2) + Sqrt[2]*(2209*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 10360*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/2835","A",1
2715,1,104,191,0.2148978,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{9/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(9/2),x]","\frac{2 \left(\sqrt{2} \left(1085 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+59866 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(1616382 x^3+3385161 x^2+2314860 x+519367\right)}{(3 x+2)^{7/2}}\right)}{138915}","-\frac{7388 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{46305}+\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(519367 + 2314860*x + 3385161*x^2 + 1616382*x^3))/(2 + 3*x)^(7/2) + Sqrt[2]*(59866*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 1085*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/138915","A",1
2716,1,111,222,0.3233463,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{11/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(11/2),x]","\frac{4 \left(\sqrt{2} \left(4971289 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-2457910 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(805348818 x^4+2174142276 x^3+2204875881 x^2+993561978 x+167622907\right)}{2 (3 x+2)^{9/2}}\right)}{8751645}","-\frac{609304 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{2917215}+\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{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,"(4*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(167622907 + 993561978*x + 2204875881*x^2 + 2174142276*x^3 + 805348818*x^4))/(2*(2 + 3*x)^(9/2)) + Sqrt[2]*(4971289*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 2457910*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/8751645","A",1
2717,1,112,249,0.4029663,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^{13/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(13/2),x]","\frac{-5823976480 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{24 \sqrt{2-4 x} \sqrt{5 x+3} \left(175732475616 x^5+591671694906 x^4+797050394730 x^3+537061687749 x^2+180988667568 x+24398176891\right)}{(3 x+2)^{11/2}}+11570862592 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{898502220 \sqrt{2}}","-\frac{43537016 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{6806835 \sqrt{33}}+\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{1446357824 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6806835 \sqrt{33}}",1,"((24*Sqrt[2 - 4*x]*Sqrt[3 + 5*x]*(24398176891 + 180988667568*x + 537061687749*x^2 + 797050394730*x^3 + 591671694906*x^4 + 175732475616*x^5))/(2 + 3*x)^(11/2) + 11570862592*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5823976480*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(898502220*Sqrt[2])","A",1
2718,1,119,280,0.3473221,"\int (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2} \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2),x]","\frac{\sqrt{2} \left(3344364736684 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-1684482853585 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)-30 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(547296750000 x^6+1316318850000 x^5+888419542500 x^4-227285730000 x^3-522917547750 x^2-177853891770 x+44426819351\right)}{273648375000}","-\frac{50299451003 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{4146187500 \sqrt{33}}+\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{836091184171 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2073093750 \sqrt{33}}",1,"(-30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(44426819351 - 177853891770*x - 522917547750*x^2 - 227285730000*x^3 + 888419542500*x^4 + 1316318850000*x^5 + 547296750000*x^6) + Sqrt[2]*(3344364736684*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 1684482853585*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/273648375000","A",1
2719,1,115,249,0.3787418,"\int (1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{5/2} \, dx","Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2),x]","\frac{9380126059 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5 \left(944944217 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+3 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(1403325000 x^5+2364390000 x^4+496455750 x^3-1110242250 x^2-638983395 x+67302101\right)\right)}{912161250 \sqrt{2}}","-\frac{70536439 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{13820625 \sqrt{33}}+\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{9380126059 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{55282500 \sqrt{33}}",1,"(9380126059*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5*(3*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(67302101 - 638983395*x - 1110242250*x^2 + 496455750*x^3 + 2364390000*x^4 + 1403325000*x^5) + 944944217*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(912161250*Sqrt[2])","A",1
2720,1,107,218,0.3352584,"\int (1-2 x)^{3/2} \sqrt{2+3 x} (3+5 x)^{5/2} \, dx","Integrate[(1 - 2*x)^(3/2)*Sqrt[2 + 3*x]*(3 + 5*x)^(5/2),x]","\frac{-98384755 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(25515000 x^4+24003000 x^3-10837350 x^2-14851260 x-201247\right)+195080002 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{42099750 \sqrt{2}}","-\frac{2930159 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1275750 \sqrt{33}}+\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{97540001 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1275750 \sqrt{33}}",1,"(-15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-201247 - 14851260*x - 10837350*x^2 + 24003000*x^3 + 25515000*x^4) + 195080002*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 98384755*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(42099750*Sqrt[2])","A",1
2721,1,105,191,0.3287737,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{\sqrt{2+3 x}} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/Sqrt[2 + 3*x],x]","\frac{886499 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5 \left(98707 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+3 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(94500 x^3+14400 x^2-62325 x-10259\right)\right)}{382725 \sqrt{2}}","-\frac{11908 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{127575}+\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{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,"(886499*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5*(3*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-10259 - 62325*x + 14400*x^2 + 94500*x^3) + 98707*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(382725*Sqrt[2])","A",1
2722,1,107,191,0.3524829,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(3/2),x]","\frac{29225 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{30 \sqrt{1-2 x} \sqrt{5 x+3} \left(-2700 x^3+180 x^2+1767 x+200\right)}{\sqrt{3 x+2}}+5788 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{17010}","-\frac{1061 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{2835}-\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{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,"((30*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(200 + 1767*x + 180*x^2 - 2700*x^3))/Sqrt[2 + 3*x] + 5788*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 29225*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/17010","A",1
2723,1,107,191,0.3820586,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(5/2),x]","\frac{-53015 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{30 \sqrt{1-2 x} \sqrt{5 x+3} \left(810 x^3-468 x^2-2463 x-1187\right)}{(3 x+2)^{3/2}}+9587 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{3645}","\frac{2632 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1215}+\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{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,"((-30*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-1187 - 2463*x - 468*x^2 + 810*x^3))/(2 + 3*x)^(3/2) + 9587*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 53015*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/3645","A",1
2724,1,104,191,0.3286917,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{7/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(7/2),x]","\frac{\sqrt{2} \left(829885 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-116854 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)-\frac{6 \sqrt{1-2 x} \sqrt{5 x+3} \left(47250 x^3+377793 x^2+432387 x+134497\right)}{(3 x+2)^{5/2}}}{25515}","-\frac{43214 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{8505}+\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{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,"((-6*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(134497 + 432387*x + 377793*x^2 + 47250*x^3))/(2 + 3*x)^(5/2) + Sqrt[2]*(-116854*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 829885*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/25515","A",1
2725,1,104,191,0.3158013,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{9/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(9/2),x]","\frac{2 \left(\sqrt{2} \left(481339 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-2539285 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(10680903 x^3+20067219 x^2+12594615 x+2640643\right)}{(3 x+2)^{7/2}}\right)}{416745}","\frac{249448 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{138915}+\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(2640643 + 12594615*x + 20067219*x^2 + 10680903*x^3))/(2 + 3*x)^(7/2) + Sqrt[2]*(481339*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 2539285*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/416745","A",1
2726,1,110,222,0.3731818,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{11/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(11/2),x]","\frac{8 \sqrt{2} \left(5257595 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+8915212 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{24 \sqrt{1-2 x} \sqrt{5 x+3} \left(722132172 x^4+2043155529 x^3+2115318249 x^2+955601637 x+159578303\right)}{(3 x+2)^{9/2}}}{105019740}","-\frac{1717916 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{8751645}+\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{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,"((24*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(159578303 + 955601637*x + 2115318249*x^2 + 2043155529*x^3 + 722132172*x^4))/(2 + 3*x)^(9/2) + 8*Sqrt[2]*(8915212*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 5257595*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/105019740","A",1
2727,1,112,249,0.3999211,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{13/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(13/2),x]","\frac{-25619043520 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{48 \sqrt{2-4 x} \sqrt{5 x+3} \left(402980457942 x^5+1356237833922 x^4+1829570010885 x^3+1234133449713 x^2+415681177941 x+55875107717\right)}{(3 x+2)^{11/2}}+53067385408 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{16173039960 \sqrt{2}}","-\frac{103970992 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{61261515 \sqrt{33}}+\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{3316711588 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{61261515 \sqrt{33}}",1,"((48*Sqrt[2 - 4*x]*Sqrt[3 + 5*x]*(55875107717 + 415681177941*x + 1234133449713*x^2 + 1829570010885*x^3 + 1356237833922*x^4 + 402980457942*x^5))/(2 + 3*x)^(11/2) + 53067385408*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 25619043520*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(16173039960*Sqrt[2])","A",1
2728,1,117,280,0.4302488,"\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^{15/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(15/2),x]","\frac{-1973150325440 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{48 \sqrt{2-4 x} \sqrt{5 x+3} \left(89405458177572 x^6+360618554767050 x^5+606171513555828 x^4+543590753927373 x^3+274263621177573 x^2+73802680969881 x+8272877174903\right)}{(3 x+2)^{13/2}}+3924519426176 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{490582212120 \sqrt{2}}","-\frac{7391549624 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1858265955 \sqrt{33}}+\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{245282464136 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1858265955 \sqrt{33}}",1,"((48*Sqrt[2 - 4*x]*Sqrt[3 + 5*x]*(8272877174903 + 73802680969881*x + 274263621177573*x^2 + 543590753927373*x^3 + 606171513555828*x^4 + 360618554767050*x^5 + 89405458177572*x^6))/(2 + 3*x)^(13/2) + 3924519426176*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 1973150325440*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(490582212120*Sqrt[2])","A",1
2729,1,105,191,0.3357985,"\int \frac{(1-2 x)^{3/2} (2+3 x)^{5/2}}{\sqrt{3+5 x}} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2))/Sqrt[3 + 5*x],x]","\frac{6515539 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5 \left(612332 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+3 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(472500 x^3+193500 x^2-378045 x-110554\right)\right)}{8859375 \sqrt{2}}","-\frac{104663 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{2953125}+\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{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,"(6515539*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5*(3*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-110554 - 378045*x + 193500*x^2 + 472500*x^3) + 612332*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(8859375*Sqrt[2])","A",1
2730,1,97,160,0.2857267,"\int \frac{(1-2 x)^{3/2} (2+3 x)^{3/2}}{\sqrt{3+5 x}} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2))/Sqrt[3 + 5*x],x]","\frac{-17045 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(-4500 x^2+2040 x+2873\right)+92318 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{196875 \sqrt{2}}","-\frac{2281 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{65625}+\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{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,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(2873 + 2040*x - 4500*x^2) + 92318*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 17045*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(196875*Sqrt[2])","A",1
2731,1,97,129,0.2450909,"\int \frac{(1-2 x)^{3/2} \sqrt{2+3 x}}{\sqrt{3+5 x}} \, dx","Integrate[((1 - 2*x)^(3/2)*Sqrt[2 + 3*x])/Sqrt[3 + 5*x],x]","\frac{7070 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+60 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3} (71-45 x)+2797 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{16875}","-\frac{598 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{5625}+\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{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,"(60*(71 - 45*x)*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] + 2797*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 7070*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/16875","A",1
2732,1,92,98,0.2001832,"\int \frac{(1-2 x)^{3/2}}{\sqrt{2+3 x} \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(3/2)/(Sqrt[2 + 3*x]*Sqrt[3 + 5*x]),x]","\frac{1}{675} \left(3605 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-60 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-272 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{202}{225} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\frac{4}{45} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+\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,"(-60*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] - 272*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 3605*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/675","A",1
2733,1,92,98,0.1961643,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{2}{45} \left(-70 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{105 \sqrt{1-2 x} \sqrt{5 x+3}}{\sqrt{3 x+2}}+37 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","\frac{4}{15} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\frac{14 \sqrt{1-2 x} \sqrt{5 x+3}}{3 \sqrt{3 x+2}}-\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,"(2*((105*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/Sqrt[2 + 3*x] + 37*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 70*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/45","A",1
2734,1,97,129,0.2956836,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^(5/2)*Sqrt[3 + 5*x]),x]","\frac{2}{27} \left(-29 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} (186 x+131)}{(3 x+2)^{3/2}}+62 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{4}{9} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(131 + 186*x))/(2 + 3*x)^(3/2) + 62*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 29*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/27","A",1
2735,1,101,160,0.3168097,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^(7/2)*Sqrt[3 + 5*x]),x]","\frac{4}{945} \left(\sqrt{2} \left(4451 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-2240 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(80118 x^2+109512 x+37547\right)}{2 (3 x+2)^{5/2}}\right)","-\frac{536}{315} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(4*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(37547 + 109512*x + 80118*x^2))/(2*(2 + 3*x)^(5/2)) + Sqrt[2]*(4451*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 2240*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/945","A",1
2736,1,106,191,0.3369824,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{9/2} \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^(9/2)*Sqrt[3 + 5*x]),x]","\frac{4 \left(\sqrt{2} \left(313888 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-158095 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(16949952 x^3+34469046 x^2+23387310 x+5295887\right)}{2 (3 x+2)^{7/2}}\right)}{15435}","-\frac{37768 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{5145}+\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{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,"(4*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(5295887 + 23387310*x + 34469046*x^2 + 16949952*x^3))/(2*(2 + 3*x)^(7/2)) + Sqrt[2]*(313888*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 158095*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/15435","A",1
2737,1,132,222,0.204155,"\int \frac{(1-2 x)^{3/2} (2+3 x)^{7/2}}{(3+5 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2))/(3 + 5*x)^(3/2),x]","\frac{1473539 \sqrt{2} (5 x+3) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5 \left(88207 \sqrt{2} (5 x+3) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+6 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(472500 x^4+517500 x^3-252225 x^2-377530 x-83787\right)\right)}{5906250 (5 x+3)}","-\frac{31288 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{984375}-\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{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,"(1473539*Sqrt[2]*(3 + 5*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5*(6*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-83787 - 377530*x - 252225*x^2 + 517500*x^3 + 472500*x^4) + 88207*Sqrt[2]*(3 + 5*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(5906250*(3 + 5*x))","A",1
2738,1,107,191,0.3039569,"\int \frac{(1-2 x)^{3/2} (2+3 x)^{5/2}}{(3+5 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2))/(3 + 5*x)^(3/2),x]","\frac{95165 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{30 \sqrt{1-2 x} \sqrt{3 x+2} \left(22500 x^3+5400 x^2-22305 x-9697\right)}{\sqrt{5 x+3}}+94684 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{656250}","-\frac{5753 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{109375}-\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{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,"((-30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(-9697 - 22305*x + 5400*x^2 + 22500*x^3))/Sqrt[3 + 5*x] + 94684*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 95165*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/656250","A",1
2739,1,102,160,0.2392363,"\int \frac{(1-2 x)^{3/2} (2+3 x)^{3/2}}{(3+5 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2))/(3 + 5*x)^(3/2),x]","\frac{8015 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{30 \sqrt{1-2 x} \sqrt{3 x+2} \left(-150 x^2+130 x+77\right)}{\sqrt{5 x+3}}+169 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{9375}","-\frac{496 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3125}-\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{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,"((30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(77 + 130*x - 150*x^2))/Sqrt[3 + 5*x] + 169*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 8015*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/9375","A",1
2740,1,97,129,0.2091547,"\int \frac{(1-2 x)^{3/2} \sqrt{2+3 x}}{(3+5 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*Sqrt[2 + 3*x])/(3 + 5*x)^(3/2),x]","\frac{3395 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{30 \sqrt{1-2 x} \sqrt{3 x+2} (10 x+39)}{\sqrt{5 x+3}}-458 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{1125}","-\frac{178}{375} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"((-30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(39 + 10*x))/Sqrt[3 + 5*x] - 458*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 3395*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/1125","A",1
2741,1,92,98,0.223307,"\int \frac{(1-2 x)^{3/2}}{\sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/(Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)),x]","\frac{1}{75} \left(-70 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{330 \sqrt{1-2 x} \sqrt{3 x+2}}{\sqrt{5 x+3}}-62 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","\frac{8}{25} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\frac{22 \sqrt{1-2 x} \sqrt{3 x+2}}{5 \sqrt{5 x+3}}+\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,"((-330*Sqrt[1 - 2*x]*Sqrt[2 + 3*x])/Sqrt[3 + 5*x] - 62*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 70*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/75","A",1
2742,1,131,129,0.1793637,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{70 \sqrt{2} \left(15 x^2+19 x+6\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-136 \sqrt{2} \left(15 x^2+19 x+6\right) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-30 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3} (68 x+43)}{15 (3 x+2) (5 x+3)}","\frac{4}{5} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"(-30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(43 + 68*x) - 136*Sqrt[2]*(6 + 19*x + 15*x^2)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 70*Sqrt[2]*(6 + 19*x + 15*x^2)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(15*(2 + 3*x)*(3 + 5*x))","A",1
2743,1,100,160,0.169545,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)),x]","-\frac{4}{9} \sqrt{2} \left(133 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-67 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)-\frac{2 \sqrt{1-2 x} \left(3990 x^2+5188 x+1683\right)}{3 (3 x+2)^{3/2} \sqrt{5 x+3}}","\frac{16}{3} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"(-2*Sqrt[1 - 2*x]*(1683 + 5188*x + 3990*x^2))/(3*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x]) - (4*Sqrt[2]*(133*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 67*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/9","A",1
2744,1,105,191,0.1880635,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)),x]","\frac{2}{105} \left(-2 \sqrt{2} \left(9242 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-4655 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)-\frac{3 \sqrt{1-2 x} \left(831780 x^3+1636038 x^2+1071882 x+233897\right)}{(3 x+2)^{5/2} \sqrt{5 x+3}}\right)","\frac{1112}{35} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"(2*((-3*Sqrt[1 - 2*x]*(233897 + 1071882*x + 1636038*x^2 + 831780*x^3))/((2 + 3*x)^(5/2)*Sqrt[3 + 5*x]) - 2*Sqrt[2]*(9242*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 4655*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/105","A",1
2745,1,110,222,0.2317301,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{9/2} (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^(9/2)*(3 + 5*x)^(3/2)),x]","\frac{2 \left(-4 \sqrt{2} \left(1289089 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-649285 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)-\frac{3 \sqrt{1-2 x} \left(696108060 x^4+1833255216 x^3+1809835578 x^2+793777840 x+130497191\right)}{(3 x+2)^{7/2} \sqrt{5 x+3}}\right)}{5145}","\frac{310208 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1715}-\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{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,"(2*((-3*Sqrt[1 - 2*x]*(130497191 + 793777840*x + 1809835578*x^2 + 1833255216*x^3 + 696108060*x^4))/((2 + 3*x)^(7/2)*Sqrt[3 + 5*x]) - 4*Sqrt[2]*(1289089*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 649285*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/5145","A",1
2746,1,112,220,0.4108646,"\int \frac{(1-2 x)^{3/2} (2+3 x)^{7/2}}{(3+5 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2))/(3 + 5*x)^(5/2),x]","\frac{168035 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{10 \sqrt{1-2 x} \sqrt{3 x+2} \left(-202500 x^4-189000 x^3+174525 x^2+216050 x+52067\right)}{(5 x+3)^{3/2}}+51286 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{656250}","-\frac{24369 \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{109375}-\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{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,"((10*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(52067 + 216050*x + 174525*x^2 - 189000*x^3 - 202500*x^4))/(3 + 5*x)^(3/2) + 51286*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 168035*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/656250","A",1
2747,1,107,191,0.4185816,"\int \frac{(1-2 x)^{3/2} (2+3 x)^{5/2}}{(3+5 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2))/(3 + 5*x)^(5/2),x]","\frac{39620 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{10 \sqrt{1-2 x} \sqrt{3 x+2} \left(-6750 x^3+1050 x^2+2975 x-106\right)}{(5 x+3)^{3/2}}-1973 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{46875}","-\frac{8366 \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{15625}-\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{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,"((10*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(-106 + 2975*x + 1050*x^2 - 6750*x^3))/(3 + 5*x)^(3/2) - 1973*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 39620*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/46875","A",1
2748,1,102,160,0.3640149,"\int \frac{(1-2 x)^{3/2} (2+3 x)^{3/2}}{(3+5 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2))/(3 + 5*x)^(5/2),x]","\frac{3115 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{10 \sqrt{1-2 x} \sqrt{3 x+2} \left(150 x^2+800 x+437\right)}{(5 x+3)^{3/2}}-496 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{1875}","-\frac{582}{625} \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"((-10*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(437 + 800*x + 150*x^2))/(3 + 5*x)^(3/2) - 496*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 3115*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/1875","A",1
2749,1,97,127,0.2662571,"\int \frac{(1-2 x)^{3/2} \sqrt{2+3 x}}{(3+5 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(3/2)*Sqrt[2 + 3*x])/(3 + 5*x)^(5/2),x]","\frac{2}{375} \left(-140 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{5 \sqrt{1-2 x} \sqrt{3 x+2} (125 x+86)}{(5 x+3)^{3/2}}-19 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","\frac{212 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{125 \sqrt{33}}-\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{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,"(2*((-5*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(86 + 125*x))/(3 + 5*x)^(3/2) - 19*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 140*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/375","A",1
2750,1,97,127,0.3367251,"\int \frac{(1-2 x)^{3/2}}{\sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/(Sqrt[2 + 3*x]*(3 + 5*x)^(5/2)),x]","\frac{2}{75} \left(-35 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{5 \sqrt{1-2 x} \sqrt{3 x+2} (370 x+211)}{(5 x+3)^{3/2}}+74 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{52 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{25 \sqrt{33}}+\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{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,"(2*((5*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(211 + 370*x))/(3 + 5*x)^(3/2) + 74*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 35*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/75","A",1
2751,1,100,158,0.1867183,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{4}{15} \sqrt{2} \left(139 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-70 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{2 \sqrt{1-2 x} \left(4170 x^2+5144 x+1583\right)}{3 \sqrt{3 x+2} (5 x+3)^{3/2}}","-\frac{184 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{5 \sqrt{33}}+\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{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,"(2*Sqrt[1 - 2*x]*(1583 + 5144*x + 4170*x^2))/(3*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)) + (4*Sqrt[2]*(139*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 70*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/15","A",1
2752,1,104,185,0.307986,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{2}{3} \left(2 \sqrt{2} \left(272 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-137 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{\sqrt{1-2 x} \left(122400 x^3+232590 x^2+147122 x+30977\right)}{(3 x+2)^{3/2} (5 x+3)^{3/2}}\right)","-120 \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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}}-1088 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"(2*((Sqrt[1 - 2*x]*(30977 + 147122*x + 232590*x^2 + 122400*x^3))/((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + 2*Sqrt[2]*(272*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 137*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/3","A",1
2753,1,109,222,0.3504582,"\int \frac{(1-2 x)^{3/2}}{(2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)),x]","\frac{2}{105} \left(4 \sqrt{2} \left(37663 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-18970 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{\sqrt{1-2 x} \left(101690100 x^4+261029520 x^3+251053266 x^2+107221804 x+17157169\right)}{(3 x+2)^{5/2} (5 x+3)^{3/2}}\right)","-\frac{33232}{35} \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(2*((Sqrt[1 - 2*x]*(17157169 + 107221804*x + 251053266*x^2 + 261029520*x^3 + 101690100*x^4))/((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + 4*Sqrt[2]*(37663*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 18970*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/105","A",1
2754,1,112,249,0.37773,"\int (1-2 x)^{5/2} (2+3 x)^{5/2} \sqrt{3+5 x} \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x],x]","\frac{-2349857545 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(935550000 x^5+433755000 x^4-936022500 x^3-309143250 x^2+380959290 x+84411073\right)+4653552268 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{2533781250 \sqrt{2}}","-\frac{69808931 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{76781250 \sqrt{33}}+\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{1163388067 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{38390625 \sqrt{33}}",1,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(84411073 + 380959290*x - 309143250*x^2 - 936022500*x^3 + 433755000*x^4 + 935550000*x^5) + 4653552268*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 2349857545*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(2533781250*Sqrt[2])","A",1
2755,1,107,218,0.3395237,"\int (1-2 x)^{5/2} (2+3 x)^{3/2} \sqrt{3+5 x} \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x],x]","\frac{-169899590 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(42525000 x^4-13702500 x^3-35750250 x^2+16294455 x+9437696\right)+326256461 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{292359375 \sqrt{2}}","-\frac{4738087 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{8859375 \sqrt{33}}+\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{326256461 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{17718750 \sqrt{33}}",1,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(9437696 + 16294455*x - 35750250*x^2 - 13702500*x^3 + 42525000*x^4) + 326256461*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 169899590*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(292359375*Sqrt[2])","A",1
2756,1,102,191,0.3123809,"\int (1-2 x)^{5/2} \sqrt{2+3 x} \sqrt{3+5 x} \, dx","Integrate[(1 - 2*x)^(5/2)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x],x]","\frac{-9945565 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(945000 x^3-1111500 x^2+55530 x+526861\right)+13599226 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{15946875 \sqrt{2}}","-\frac{110717 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{5315625}+\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{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,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(526861 + 55530*x - 1111500*x^2 + 945000*x^3) + 13599226*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 9945565*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(15946875*Sqrt[2])","A",1
2757,1,102,160,0.1394727,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{\sqrt{2+3 x}} \, dx","Integrate[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/Sqrt[2 + 3*x],x]","\frac{-281540 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+30 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(1500 x^2-3270 x+3401\right)+86741 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{118125}","\frac{11806 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{39375}+\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{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,"(30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(3401 - 3270*x + 1500*x^2) + 86741*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 281540*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/118125","A",1
2758,1,102,160,0.2236898,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(3/2),x]","\frac{242095 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{30 \sqrt{1-2 x} \sqrt{5 x+3} \left(180 x^2-534 x-1661\right)}{\sqrt{3 x+2}}-31588 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{10125}","-\frac{12758 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3375}-\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{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,"((30*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-1661 - 534*x + 180*x^2))/Sqrt[2 + 3*x] - 31588*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 242095*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/10125","A",1
2759,1,102,160,0.3031993,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(5/2),x]","\frac{2 \left(-10360 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{15 \sqrt{1-2 x} \sqrt{5 x+3} \left(36 x^2+1077 x+653\right)}{(3 x+2)^{3/2}}+2209 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)}{1215}","\frac{988}{405} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"(2*((15*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(653 + 1077*x + 36*x^2))/(2 + 3*x)^(3/2) + 2209*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 10360*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/1215","A",1
2760,1,99,156,0.2201084,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{7/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(7/2),x]","\frac{2}{15} \left(3 \sqrt{2} \left(5 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+6 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(506 x^2+719 x+249\right)}{(3 x+2)^{5/2}}\right)","-\frac{4}{5} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{12}{5} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"(2*((Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(249 + 719*x + 506*x^2))/(2 + 3*x)^(5/2) + 3*Sqrt[2]*(6*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 5*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/15","A",1
2761,1,106,191,0.3394156,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{9/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(9/2),x]","\frac{4 \left(\sqrt{2} \left(9013 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-4690 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(486702 x^3+988524 x^2+671007 x+151859\right)}{2 (3 x+2)^{7/2}}\right)}{3969}","-\frac{1048 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1323}-\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{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,"(4*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(151859 + 671007*x + 988524*x^2 + 486702*x^3))/(2*(2 + 3*x)^(7/2)) + Sqrt[2]*(9013*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 4690*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/3969","A",1
2762,1,111,222,0.3464162,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{11/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(11/2),x]","\frac{4 \left(\sqrt{2} \left(1952596 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-983815 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(316320552 x^4+854146674 x^3+865270206 x^2+389804925 x+65886031\right)}{2 (3 x+2)^{9/2}}\right)}{250047}","-\frac{234856 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{83349}-\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{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,"(4*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(65886031 + 389804925*x + 865270206*x^2 + 854146674*x^3 + 316320552*x^4))/(2*(2 + 3*x)^(9/2)) + Sqrt[2]*(1952596*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 983815*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/250047","A",1
2763,1,115,249,0.4047955,"\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^{13/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^(13/2),x]","\frac{32 \sqrt{2} \left(30926081 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-15576890 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{24 \sqrt{1-2 x} \sqrt{5 x+3} \left(30060150732 x^5+101209884912 x^4+136342955970 x^3+91862628912 x^2+30956769477 x+4174268813\right)}{(3 x+2)^{11/2}}}{8557164}","-\frac{7442032 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{64827 \sqrt{33}}-\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{247408648 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{64827 \sqrt{33}}",1,"((24*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(4174268813 + 30956769477*x + 91862628912*x^2 + 136342955970*x^3 + 101209884912*x^4 + 30060150732*x^5))/(2 + 3*x)^(11/2) + 32*Sqrt[2]*(30926081*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 15576890*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/8557164","A",1
2764,1,119,280,0.3630131,"\int (1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{3/2} \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2),x]","\frac{\sqrt{2} \left(1764163292393 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-888487137545 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+30 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(547296750000 x^6+621672975000 x^5-336683182500 x^4-528977216250 x^3+48836706750 x^2+173484591165 x+12155574323\right)}{684120937500}","-\frac{13267820528 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{5182734375 \sqrt{33}}+\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{1764163292393 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{20730937500 \sqrt{33}}",1,"(30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(12155574323 + 173484591165*x + 48836706750*x^2 - 528977216250*x^3 - 336683182500*x^4 + 621672975000*x^5 + 547296750000*x^6) + Sqrt[2]*(1764163292393*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 888487137545*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/684120937500","A",1
2765,1,112,249,0.3732352,"\int (1-2 x)^{5/2} (2+3 x)^{3/2} (3+5 x)^{3/2} \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2),x]","\frac{-30830473835 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(14033250000 x^5+5400675000 x^4-13684072500 x^3-3707642250 x^2+5290733520 x+1020785999\right)+61320616034 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{22804031250 \sqrt{2}}","-\frac{923943703 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{691031250 \sqrt{33}}+\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{30660308017 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{691031250 \sqrt{33}}",1,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(1020785999 + 5290733520*x - 3707642250*x^2 - 13684072500*x^3 + 5400675000*x^4 + 14033250000*x^5) + 61320616034*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 30830473835*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(22804031250*Sqrt[2])","A",1
2766,1,107,218,0.3341376,"\int (1-2 x)^{5/2} \sqrt{2+3 x} (3+5 x)^{3/2} \, dx","Integrate[(1 - 2*x)^(5/2)*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2),x]","\frac{-400297555 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(127575000 x^4-51502500 x^3-95024250 x^2+48272535 x+22517617\right)+829177897 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{526246875 \sqrt{2}}","-\frac{12996374 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{15946875 \sqrt{33}}+\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{829177897 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{31893750 \sqrt{33}}",1,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(22517617 + 48272535*x - 95024250*x^2 - 51502500*x^3 + 127575000*x^4) + 829177897*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 400297555*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(526246875*Sqrt[2])","A",1
2767,1,102,191,0.1926855,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{\sqrt{2+3 x}} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/Sqrt[2 + 3*x],x]","\frac{5257595 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(945000 x^3-1192500 x^2+232110 x+343207\right)+8915212 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{9568125 \sqrt{2}}","-\frac{429479 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3189375}+\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{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,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(343207 + 232110*x - 1192500*x^2 + 945000*x^3) + 8915212*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 5257595*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(9568125*Sqrt[2])","A",1
2768,1,107,191,0.2599147,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(3/2),x]","\frac{-2539285 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{30 \sqrt{1-2 x} \sqrt{5 x+3} \left(13500 x^3-21690 x^2+14727 x+32033\right)}{\sqrt{3 x+2}}+481339 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{212625}","\frac{124724 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{70875}-\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{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,"((30*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(32033 + 14727*x - 21690*x^2 + 13500*x^3))/Sqrt[2 + 3*x] + 481339*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 2539285*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/212625","A",1
2769,1,107,191,0.2579763,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(5/2),x]","\frac{829885 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{30 \sqrt{1-2 x} \sqrt{5 x+3} \left(1620 x^3-3906 x^2-23538 x-13231\right)}{(3 x+2)^{3/2}}-116854 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{18225}","-\frac{43214 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{6075}-\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{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,"((30*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-13231 - 23538*x - 3906*x^2 + 1620*x^3))/(2 + 3*x)^(3/2) - 116854*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 829885*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/18225","A",1
2770,1,104,191,0.2129903,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{7/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(7/2),x]","\frac{2 \left(\sqrt{2} \left(9587 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-53015 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(2700 x^3+68913 x^2+83412 x+25927\right)}{(3 x+2)^{5/2}}\right)}{3645}","\frac{5264 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1215}-\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(25927 + 83412*x + 68913*x^2 + 2700*x^3))/(2 + 3*x)^(5/2) + Sqrt[2]*(9587*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 53015*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/3645","A",1
2771,1,104,191,0.2235273,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{9/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(9/2),x]","\frac{2 \left(\sqrt{2} \left(29225 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+5788 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(182736 x^3+409005 x^2+292578 x+67759\right)}{(3 x+2)^{7/2}}\right)}{11907}","-\frac{4244 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3969}-\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(67759 + 292578*x + 409005*x^2 + 182736*x^3))/(2 + 3*x)^(7/2) + Sqrt[2]*(5788*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 29225*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/11907","A",1
2772,1,111,222,0.3530932,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{11/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(11/2),x]","\frac{4 \left(\sqrt{2} \left(886499 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-493535 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(143612838 x^4+386630766 x^3+391601529 x^2+176436240 x+29785139\right)}{2 (3 x+2)^{9/2}}\right)}{750141}","-\frac{95264 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{250047}-\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{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,"(4*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(29785139 + 176436240*x + 391601529*x^2 + 386630766*x^3 + 143612838*x^4))/(2*(2 + 3*x)^(9/2)) + Sqrt[2]*(886499*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 493535*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/750141","A",1
2773,1,115,249,0.3955972,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{13/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(13/2),x]","\frac{16 \sqrt{2} \left(195080002 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-98384755 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{24 \sqrt{1-2 x} \sqrt{5 x+3} \left(94808880972 x^5+319217269302 x^4+429993423180 x^3+289719086787 x^2+97637232762 x+13163824553\right)}{(3 x+2)^{11/2}}}{231043428}","-\frac{23441272 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1750329 \sqrt{33}}-\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{780320008 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1750329 \sqrt{33}}",1,"((24*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(13163824553 + 97637232762*x + 289719086787*x^2 + 429993423180*x^3 + 319217269302*x^4 + 94808880972*x^5))/(2 + 3*x)^(11/2) + 16*Sqrt[2]*(195080002*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 98384755*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/231043428","A",1
2774,1,117,280,0.4063117,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^{15/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(15/2),x]","\frac{-604764298880 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{48 \sqrt{2-4 x} \sqrt{5 x+3} \left(27352447588044 x^6+110328276131100 x^5+185457331738206 x^4+166295375376786 x^3+83893544414217 x^2+22577209892436 x+2532151719515\right)}{(3 x+2)^{13/2}}+1200656135552 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{14016634632 \sqrt{2}}","-\frac{2257166048 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{53093313 \sqrt{33}}-\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{75041008472 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{53093313 \sqrt{33}}",1,"((48*Sqrt[2 - 4*x]*Sqrt[3 + 5*x]*(2532151719515 + 22577209892436*x + 83893544414217*x^2 + 166295375376786*x^3 + 185457331738206*x^4 + 110328276131100*x^5 + 27352447588044*x^6))/(2 + 3*x)^(13/2) + 1200656135552*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 604764298880*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(14016634632*Sqrt[2])","A",1
2775,1,119,280,0.3178059,"\int (1-2 x)^{5/2} (2+3 x)^{3/2} (3+5 x)^{5/2} \, dx","Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2),x]","\frac{\sqrt{2} \left(1580201444291 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-795995716040 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+30 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(547296750000 x^6+579573225000 x^5-352885207500 x^4-487924998750 x^3+59959633500 x^2+157612390605 x+9093216326\right)}{410472562500}","-\frac{23763809947 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{6219281250 \sqrt{33}}+\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{1580201444291 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{12438562500 \sqrt{33}}",1,"(30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(9093216326 + 157612390605*x + 59959633500*x^2 - 487924998750*x^3 - 352885207500*x^4 + 579573225000*x^5 + 547296750000*x^6) + Sqrt[2]*(1580201444291*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 795995716040*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/410472562500","A",1
2776,1,112,249,0.3755139,"\int (1-2 x)^{5/2} \sqrt{2+3 x} (3+5 x)^{5/2} \, dx","Integrate[(1 - 2*x)^(5/2)*Sqrt[2 + 3*x]*(3 + 5*x)^(5/2),x]","\frac{-16416737015 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(8419950000 x^5+2577015000 x^4-7942630500 x^3-1730459250 x^2+2923422930 x+495379991\right)+32480644556 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{8209451250 \sqrt{2}}","-\frac{486785077 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{248771250 \sqrt{33}}+\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{8120161139 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{124385625 \sqrt{33}}",1,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(495379991 + 2923422930*x - 1730459250*x^2 - 7942630500*x^3 + 2577015000*x^4 + 8419950000*x^5) + 32480644556*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 16416737015*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(8209451250*Sqrt[2])","A",1
2777,1,107,218,0.3381567,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{\sqrt{2+3 x}} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/Sqrt[2 + 3*x],x]","\frac{-91626220 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(25515000 x^4-12379500 x^3-16381350 x^2+9143865 x+3748468\right)+146222113 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{63149625 \sqrt{2}}","-\frac{1654421 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1913625 \sqrt{33}}+\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{146222113 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3827250 \sqrt{33}}",1,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(3748468 + 9143865*x - 16381350*x^2 - 12379500*x^3 + 25515000*x^4) + 146222113*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 91626220*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(63149625*Sqrt[2])","A",1
2778,1,112,222,0.3892549,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(3/2),x]","\frac{10192945 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{30 \sqrt{1-2 x} \sqrt{5 x+3} \left(567000 x^4-386100 x^3-259650 x^2+245751 x+21964\right)}{\sqrt{3 x+2}}+50222 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{2296350}","-\frac{310399 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{382725}-\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{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,"((30*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(21964 + 245751*x - 259650*x^2 - 386100*x^3 + 567000*x^4))/Sqrt[2 + 3*x] + 50222*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 10192945*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/2296350","A",1
2779,1,112,222,0.3730413,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(5/2),x]","\frac{-2685410 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{30 \sqrt{1-2 x} \sqrt{5 x+3} \left(24300 x^4-25110 x^3+5949 x^2+108285 x+56963\right)}{(3 x+2)^{3/2}}+452399 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{76545}","\frac{135334 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{25515}+\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{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,"((30*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(56963 + 108285*x + 5949*x^2 - 25110*x^3 + 24300*x^4))/(2 + 3*x)^(3/2) + 452399*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 2685410*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/76545","A",1
2780,1,109,222,0.3187389,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{7/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(7/2),x]","\frac{\sqrt{2} \left(935915 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-136028 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{6 \sqrt{1-2 x} \sqrt{5 x+3} \left(24300 x^4-45090 x^3-461043 x^2-517257 x-158237\right)}{(3 x+2)^{5/2}}}{10935}","-\frac{48478 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3645}-\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{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,"((6*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(-158237 - 517257*x - 461043*x^2 - 45090*x^3 + 24300*x^4))/(2 + 3*x)^(5/2) + Sqrt[2]*(-136028*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 935915*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/10935","A",1
2781,1,109,222,0.2340998,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{9/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(9/2),x]","\frac{2 \left(\sqrt{2} \left(452399 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-2685410 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(396900 x^4+9846603 x^3+17788023 x^2+11107911 x+2337569\right)}{(3 x+2)^{7/2}}\right)}{107163}","\frac{270668 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{35721}-\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(2337569 + 11107911*x + 17788023*x^2 + 9846603*x^3 + 396900*x^4))/(2 + 3*x)^(7/2) + Sqrt[2]*(452399*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 2685410*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/107163","A",1
2782,1,109,222,0.2643795,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{11/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(11/2),x]","\frac{2 \left(\sqrt{2} \left(10192945 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+50222 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(29072682 x^4+115002639 x^3+142557831 x^2+71920155 x+12903031\right)}{(3 x+2)^{9/2}}\right)}{2250423}","-\frac{1241596 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{750141}+\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(12903031 + 71920155*x + 142557831*x^2 + 115002639*x^3 + 29072682*x^4))/(2 + 3*x)^(9/2) + Sqrt[2]*(50222*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 10192945*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/2250423","A",1
2783,1,112,249,0.4252533,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{13/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(13/2),x]","\frac{-5864078080 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{48 \sqrt{2-4 x} \sqrt{5 x+3} \left(71063946918 x^5+237923150688 x^4+320012032635 x^3+215597947743 x^2+72620507583 x+9770732477\right)}{(3 x+2)^{11/2}}+9358215232 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{1386260568 \sqrt{2}}","-\frac{13235368 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{5250987 \sqrt{33}}+\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{584888452 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5250987 \sqrt{33}}",1,"((48*Sqrt[2 - 4*x]*Sqrt[3 + 5*x]*(9770732477 + 72620507583*x + 215597947743*x^2 + 320012032635*x^3 + 237923150688*x^4 + 71063946918*x^5))/(2 + 3*x)^(11/2) + 9358215232*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5864078080*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1386260568*Sqrt[2])","A",1
2784,1,117,280,0.4128,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{15/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(15/2),x]","\frac{-1050671168960 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{48 \sqrt{2-4 x} \sqrt{5 x+3} \left(47356779762648 x^6+191022825888450 x^5+321056742490902 x^4+287874442427697 x^3+145238558453649 x^2+39086872650957 x+4382625184685\right)}{(3 x+2)^{13/2}}+2078761251584 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{126149711688 \sqrt{2}}","-\frac{3894280616 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{477839817 \sqrt{33}}+\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{129922578224 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{477839817 \sqrt{33}}",1,"((48*Sqrt[2 - 4*x]*Sqrt[3 + 5*x]*(4382625184685 + 39086872650957*x + 145238558453649*x^2 + 287874442427697*x^3 + 321056742490902*x^4 + 191022825888450*x^5 + 47356779762648*x^6))/(2 + 3*x)^(13/2) + 2078761251584*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 1050671168960*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(126149711688*Sqrt[2])","A",1
2785,1,122,311,0.4424702,"\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^{17/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(17/2),x]","\frac{-203774903306240 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{96 \sqrt{2-4 x} \sqrt{5 x+3} \left(13823602234657668 x^7+64974368463330312 x^6+130900492508039982 x^5+146528498784887100 x^4+98427465692862075 x^3+39676146370896231 x^2+8886579657279639 x+853124799464729\right)}{(3 x+2)^{15/2}}+404531569738496 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{8830479818160 \sqrt{2}}","-\frac{380220959152 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{16724393595 \sqrt{33}}+\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{12641611554328 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{16724393595 \sqrt{33}}",1,"((96*Sqrt[2 - 4*x]*Sqrt[3 + 5*x]*(853124799464729 + 8886579657279639*x + 39676146370896231*x^2 + 98427465692862075*x^3 + 146528498784887100*x^4 + 130900492508039982*x^5 + 64974368463330312*x^6 + 13823602234657668*x^7))/(2 + 3*x)^(15/2) + 404531569738496*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 203774903306240*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(8830479818160*Sqrt[2])","A",1
2786,1,107,218,0.3561211,"\int \frac{(1-2 x)^{5/2} (2+3 x)^{5/2}}{\sqrt{3+5 x}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2))/Sqrt[3 + 5*x],x]","\frac{-100280635 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(25515000 x^4-6142500 x^3-23717250 x^2+9526995 x+7167169\right)+231061879 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{292359375 \sqrt{2}}","-\frac{3963068 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{8859375 \sqrt{33}}+\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{231061879 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{17718750 \sqrt{33}}",1,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(7167169 + 9526995*x - 23717250*x^2 - 6142500*x^3 + 25515000*x^4) + 231061879*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 100280635*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(292359375*Sqrt[2])","A",1
2787,1,102,191,0.3317603,"\int \frac{(1-2 x)^{5/2} (2+3 x)^{3/2}}{\sqrt{3+5 x}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2))/Sqrt[3 + 5*x],x]","\frac{754145 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(945000 x^3-1030500 x^2-113490 x+683887\right)+16049092 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{26578125 \sqrt{2}}","-\frac{509189 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{8859375}+\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{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,"(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(683887 - 113490*x - 1030500*x^2 + 945000*x^3) + 16049092*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 754145*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(26578125*Sqrt[2])","A",1
2788,1,102,160,0.2462526,"\int \frac{(1-2 x)^{5/2} \sqrt{2+3 x}}{\sqrt{3+5 x}} \, dx","Integrate[((1 - 2*x)^(5/2)*Sqrt[2 + 3*x])/Sqrt[3 + 5*x],x]","\frac{1783285 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+30 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(13500 x^2-28170 x+26171\right)+408311 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{1771875}","-\frac{132824 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{590625}+\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{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,"(30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(26171 - 28170*x + 13500*x^2) + 408311*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 1783285*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/1771875","A",1
2789,1,97,129,0.2142748,"\int \frac{(1-2 x)^{5/2}}{\sqrt{2+3 x} \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(5/2)/(Sqrt[2 + 3*x]*Sqrt[3 + 5*x]),x]","\frac{616735 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+60 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3} (90 x-317)-53194 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{50625}","-\frac{34154 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{16875}-\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{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,"(60*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-317 + 90*x) - 53194*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 616735*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/50625","A",1
2790,1,97,129,0.2377721,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{2 \left(-10955 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{15 \sqrt{1-2 x} \sqrt{5 x+3} (12 x+743)}{\sqrt{3 x+2}}+4157 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)}{2025}","\frac{824}{675} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(2*((15*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(743 + 12*x))/Sqrt[2 + 3*x] + 4157*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 10955*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/2025","A",1
2791,1,97,129,0.2223308,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^(5/2)*Sqrt[3 + 5*x]),x]","\frac{2}{405} \left(-595 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{735 \sqrt{1-2 x} \sqrt{5 x+3} (24 x+17)}{(3 x+2)^{3/2}}+1948 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{164}{135} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(2*((735*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(17 + 24*x))/(2 + 3*x)^(3/2) + 1948*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 595*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/405","A",1
2792,1,101,160,0.2915379,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^(7/2)*Sqrt[3 + 5*x]),x]","\frac{4}{405} \left(\sqrt{2} \left(4141 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-2095 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(74538 x^2+101862 x+34927\right)}{2 (3 x+2)^{5/2}}\right)","-\frac{496}{135} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(4*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(34927 + 101862*x + 74538*x^2))/(2*(2 + 3*x)^(5/2)) + Sqrt[2]*(4141*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 2095*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/405","A",1
2793,1,107,191,0.3228194,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{9/2} \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^(9/2)*Sqrt[3 + 5*x]),x]","\frac{4 \left(5 \sqrt{2} \left(35174 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-17717 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(9496980 x^3+19312866 x^2+13103724 x+2967269\right)}{2 (3 x+2)^{7/2}}\right)}{3969}","-\frac{21160 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1323}+\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{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,"(4*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(2967269 + 13103724*x + 19312866*x^2 + 9496980*x^3))/(2*(2 + 3*x)^(7/2)) + 5*Sqrt[2]*(35174*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 17717*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/3969","A",1
2794,1,111,222,0.3543655,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{11/2} \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^(11/2)*Sqrt[3 + 5*x]),x]","\frac{8 \left(\sqrt{2} \left(8256877 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-4158805 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(2675228148 x^4+7223771916 x^3+7318104714 x^2+3296666850 x+557240459\right)}{4 (3 x+2)^{9/2}}\right)}{83349}","-\frac{1986944 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{27783}+\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{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,"(8*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(557240459 + 3296666850*x + 7318104714*x^2 + 7223771916*x^3 + 2675228148*x^4))/(4*(2 + 3*x)^(9/2)) + Sqrt[2]*(8256877*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 4158805*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/83349","A",1
2795,1,115,249,0.4249337,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{13/2} \sqrt{3+5 x}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^(13/2)*Sqrt[3 + 5*x]),x]","\frac{16 \sqrt{2} \left(2900562916 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-1460947915 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{12 \sqrt{1-2 x} \sqrt{5 x+3} \left(2819347154352 x^5+9492493272732 x^4+12787628716260 x^3+8615827181322 x^2+2903435279352 x+391506734113\right)}{(3 x+2)^{11/2}}}{12835746}","-\frac{697995152 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{194481 \sqrt{33}}+\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{23204503328 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{194481 \sqrt{33}}",1,"((12*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(391506734113 + 2903435279352*x + 8615827181322*x^2 + 12787628716260*x^3 + 9492493272732*x^4 + 2819347154352*x^5))/(2 + 3*x)^(11/2) + 16*Sqrt[2]*(2900562916*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 1460947915*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/12835746","A",1
2796,1,125,249,0.4132597,"\int \frac{(1-2 x)^{5/2} (2+3 x)^{7/2}}{(3+5 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2))/(3 + 5*x)^(3/2),x]","\frac{-24628520 \sqrt{10 x+6} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+30 \sqrt{1-2 x} \sqrt{3 x+2} \left(127575000 x^5+56227500 x^4-141221250 x^3-32807925 x^2+71568535 x+26378214\right)+264260033 \sqrt{10 x+6} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{974531250 \sqrt{5 x+3}}","-\frac{7261561 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{14765625 \sqrt{33}}-\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{264260033 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{29531250 \sqrt{33}}",1,"(30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(26378214 + 71568535*x - 32807925*x^2 - 141221250*x^3 + 56227500*x^4 + 127575000*x^5) + 264260033*Sqrt[6 + 10*x]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 24628520*Sqrt[6 + 10*x]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(974531250*Sqrt[3 + 5*x])","A",1
2797,1,112,222,0.4170823,"\int \frac{(1-2 x)^{5/2} (2+3 x)^{5/2}}{(3+5 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2))/(3 + 5*x)^(3/2),x]","\frac{6877465 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{30 \sqrt{1-2 x} \sqrt{3 x+2} \left(945000 x^4-382500 x^3-844650 x^2+650155 x+443337\right)}{\sqrt{5 x+3}}+3018014 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{17718750}","-\frac{299863 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{2953125}-\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{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,"((30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(443337 + 650155*x - 844650*x^2 - 382500*x^3 + 945000*x^4))/Sqrt[3 + 5*x] + 3018014*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 6877465*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/17718750","A",1
2798,1,107,191,0.3949883,"\int \frac{(1-2 x)^{5/2} (2+3 x)^{3/2}}{(3+5 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2))/(3 + 5*x)^(3/2),x]","\frac{1868510 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{30 \sqrt{1-2 x} \sqrt{3 x+2} \left(22500 x^3-31350 x^2+9545 x+9168\right)}{\sqrt{5 x+3}}-53279 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{984375}","-\frac{110014 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{328125}-\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{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,"((30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(9168 + 9545*x - 31350*x^2 + 22500*x^3))/Sqrt[3 + 5*x] - 53279*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 1868510*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/984375","A",1
2799,1,102,160,0.375791,"\int \frac{(1-2 x)^{5/2} \sqrt{2+3 x}}{(3+5 x)^{3/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*Sqrt[2 + 3*x])/(3 + 5*x)^(3/2),x]","\frac{546035 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{30 \sqrt{1-2 x} \sqrt{3 x+2} \left(900 x^2-2530 x-7287\right)}{\sqrt{5 x+3}}-81164 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{84375}","-\frac{28174 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{28125}-\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{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,"((30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(-7287 - 2530*x + 900*x^2))/Sqrt[3 + 5*x] - 81164*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 546035*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/84375","A",1
2800,1,97,129,0.3447804,"\int \frac{(1-2 x)^{5/2}}{\sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/(Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)),x]","\frac{2 \left(-7070 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{15 \sqrt{1-2 x} \sqrt{3 x+2} (20 x-1077)}{\sqrt{5 x+3}}-2797 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)}{3375}","\frac{1196 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1125}-\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{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,"(2*((15*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(-1077 + 20*x))/Sqrt[3 + 5*x] - 2797*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 7070*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/3375","A",1
2801,1,131,129,0.1872517,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{2590 \sqrt{2} \left(15 x^2+19 x+6\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-4636 \sqrt{2} \left(15 x^2+19 x+6\right) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-30 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3} (2314 x+1461)}{225 (3 x+2) (5 x+3)}","\frac{124}{75} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(-30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(1461 + 2314*x) - 4636*Sqrt[2]*(6 + 19*x + 15*x^2)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 2590*Sqrt[2]*(6 + 19*x + 15*x^2)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(225*(2 + 3*x)*(3 + 5*x))","A",1
2802,1,100,160,0.1976455,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)),x]","-\frac{4}{135} \sqrt{2} \left(4451 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-2240 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)-\frac{2 \sqrt{1-2 x} \left(26706 x^2+34726 x+11265\right)}{9 (3 x+2)^{3/2} \sqrt{5 x+3}}","\frac{536}{45} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(-2*Sqrt[1 - 2*x]*(11265 + 34726*x + 26706*x^2))/(9*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x]) - (4*Sqrt[2]*(4451*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 2240*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/135","A",1
2803,1,105,191,0.3209362,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)),x]","\frac{2}{135} \left(-2 \sqrt{2} \left(26396 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-13295 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)-\frac{3 \sqrt{1-2 x} \left(2375640 x^3+4672674 x^2+3061396 x+668031\right)}{(3 x+2)^{5/2} \sqrt{5 x+3}}\right)","\frac{3176}{45} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(2*((-3*Sqrt[1 - 2*x]*(668031 + 3061396*x + 4672674*x^2 + 2375640*x^3))/((2 + 3*x)^(5/2)*Sqrt[3 + 5*x]) - 2*Sqrt[2]*(26396*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 13295*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/135","A",1
2804,1,110,222,0.3488097,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{9/2} (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^(9/2)*(3 + 5*x)^(3/2)),x]","\frac{2}{441} \left(-4 \sqrt{2} \left(244879 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-123340 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)-\frac{3 \sqrt{1-2 x} \left(132234660 x^4+348250356 x^3+343801494 x^2+150788294 x+24789615\right)}{(3 x+2)^{7/2} \sqrt{5 x+3}}\right)","\frac{58928}{147} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(2*((-3*Sqrt[1 - 2*x]*(24789615 + 150788294*x + 343801494*x^2 + 348250356*x^3 + 132234660*x^4))/((2 + 3*x)^(7/2)*Sqrt[3 + 5*x]) - 4*Sqrt[2]*(244879*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 123340*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/441","A",1
2805,1,115,253,0.3707196,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{11/2} (3+5 x)^{3/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^(11/2)*(3 + 5*x)^(3/2)),x]","\frac{2 \left(-4 \sqrt{2} \left(85393762 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-43010905 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)-\frac{3 \sqrt{1-2 x} \left(138337894440 x^5+456548966244 x^4+602551975428 x^3+397527527442 x^2+131099014240 x+17289178827\right)}{(3 x+2)^{9/2} \sqrt{5 x+3}}\right)}{27783}","\frac{20549264 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{9261}+\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{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,"(2*((-3*Sqrt[1 - 2*x]*(17289178827 + 131099014240*x + 397527527442*x^2 + 602551975428*x^3 + 456548966244*x^4 + 138337894440*x^5))/((2 + 3*x)^(9/2)*Sqrt[3 + 5*x]) - 4*Sqrt[2]*(85393762*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 43010905*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/27783","A",1
2806,1,117,253,0.4310089,"\int \frac{(1-2 x)^{5/2} (2+3 x)^{7/2}}{(3+5 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2))/(3 + 5*x)^(5/2),x]","\frac{17517535 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{30 \sqrt{1-2 x} \sqrt{3 x+2} \left(4725000 x^5+1327500 x^4-5654250 x^3+470675 x^2+4026600 x+1215489\right)}{(5 x+3)^{3/2}}+2130236 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{29531250}","-\frac{595387 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{4921875}-\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{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,"((30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(1215489 + 4026600*x + 470675*x^2 - 5654250*x^3 + 1327500*x^4 + 4725000*x^5))/(3 + 5*x)^(3/2) + 2130236*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 17517535*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/29531250","A",1
2807,1,112,222,0.3741809,"\int \frac{(1-2 x)^{5/2} (2+3 x)^{5/2}}{(3+5 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2))/(3 + 5*x)^(5/2),x]","\frac{591115 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{10 \sqrt{1-2 x} \sqrt{3 x+2} \left(67500 x^4-47250 x^3-41025 x^2-23425 x-19087\right)}{(5 x+3)^{3/2}}-49321 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{328125}","-\frac{32836 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{109375}-\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{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,"((10*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(-19087 - 23425*x - 41025*x^2 - 47250*x^3 + 67500*x^4))/(3 + 5*x)^(3/2) - 49321*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 591115*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/328125","A",1
2808,1,107,189,0.375113,"\int \frac{(1-2 x)^{5/2} (2+3 x)^{3/2}}{(3+5 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2))/(3 + 5*x)^(5/2),x]","\frac{155295 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{10 \sqrt{1-2 x} \sqrt{3 x+2} \left(4500 x^3-9450 x^2-48650 x-25421\right)}{(5 x+3)^{3/2}}-27618 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{46875}","-\frac{7738 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{15625}-\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{9206 \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{15625}",1,"((10*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(-25421 - 48650*x - 9450*x^2 + 4500*x^3))/(3 + 5*x)^(3/2) - 27618*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 155295*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/46875","A",1
2809,1,102,160,0.3125034,"\int \frac{(1-2 x)^{5/2} \sqrt{2+3 x}}{(3+5 x)^{5/2}} \, dx","Integrate[((1 - 2*x)^(5/2)*Sqrt[2 + 3*x])/(3 + 5*x)^(5/2),x]","\frac{2 \left(-8015 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{15 \sqrt{1-2 x} \sqrt{3 x+2} \left(100 x^2-925 x-712\right)}{(5 x+3)^{3/2}}-169 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)}{5625}","\frac{992 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1875}-\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{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,"(2*((15*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(-712 - 925*x + 100*x^2))/(3 + 5*x)^(3/2) - 169*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 8015*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/5625","A",1
2810,1,97,127,0.2278199,"\int \frac{(1-2 x)^{5/2}}{\sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/(Sqrt[2 + 3*x]*(3 + 5*x)^(5/2)),x]","\frac{2}{375} \left(-315 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{55 \sqrt{1-2 x} \sqrt{3 x+2} (400 x+229)}{(5 x+3)^{3/2}}+876 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{68}{125} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{584}{125} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"(2*((55*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(229 + 400*x))/(3 + 5*x)^(3/2) + 876*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 315*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/375","A",1
2811,1,100,158,0.2071918,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{2}{75} \left(2 \sqrt{2} \left(1597 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-805 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{5 \sqrt{1-2 x} \left(47910 x^2+59098 x+18187\right)}{\sqrt{3 x+2} (5 x+3)^{3/2}}\right)","-\frac{64}{25} \sqrt{33} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(2*((5*Sqrt[1 - 2*x]*(18187 + 59098*x + 47910*x^2))/(Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)) + 2*Sqrt[2]*(1597*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 805*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/75","A",1
2812,1,105,191,0.2211605,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{4}{45} \sqrt{2} \left(9242 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-4655 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{2 \sqrt{1-2 x} \left(277260 x^3+526862 x^2+333260 x+70169\right)}{3 (3 x+2)^{3/2} (5 x+3)^{3/2}}","-\frac{1112}{15} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(2*Sqrt[1 - 2*x]*(70169 + 333260*x + 526862*x^2 + 277260*x^3))/(3*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (4*Sqrt[2]*(9242*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 4655*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/45","A",1
2813,1,109,222,0.3913929,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)),x]","\frac{2}{15} \left(4 \sqrt{2} \left(12101 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-6095 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{\sqrt{1-2 x} \left(32672700 x^4+83867940 x^3+80662602 x^2+34450018 x+5512543\right)}{(3 x+2)^{5/2} (5 x+3)^{3/2}}\right)","-\frac{2912}{5} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(2*((Sqrt[1 - 2*x]*(5512543 + 34450018*x + 80662602*x^2 + 83867940*x^3 + 32672700*x^4))/((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + 4*Sqrt[2]*(12101*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 6095*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/15","A",1
2814,1,114,251,0.4105117,"\int \frac{(1-2 x)^{5/2}}{(2+3 x)^{9/2} (3+5 x)^{5/2}} \, dx","Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^(9/2)*(3 + 5*x)^(5/2)),x]","\frac{2}{147} \left(12 \sqrt{2} \left(279276 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-140665 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{\sqrt{1-2 x} \left(6786406800 x^5+21944379060 x^4+28367736228 x^3+18325125498 x^2+5915384456 x+763335749\right)}{(3 x+2)^{7/2} (5 x+3)^{3/2}}\right)","-\frac{201616}{49} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{2234208}{49} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"(2*((Sqrt[1 - 2*x]*(763335749 + 5915384456*x + 18325125498*x^2 + 28367736228*x^3 + 21944379060*x^4 + 6786406800*x^5))/((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)) + 12*Sqrt[2]*(279276*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 140665*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/147","A",1
2815,1,97,158,0.2855561,"\int \frac{(2+3 x)^{5/2} \sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","Integrate[((2 + 3*x)^(5/2)*Sqrt[3 + 5*x])/Sqrt[1 - 2*x],x]","\frac{-56455 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-5 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(2250 x^2+6120 x+7919\right)+112082 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{8750 \sqrt{2}}","-\frac{5057 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{8750}-\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{56041 \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{8750}",1,"(-5*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(7919 + 6120*x + 2250*x^2) + 112082*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 56455*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(8750*Sqrt[2])","A",1
2816,1,92,127,0.2330637,"\int \frac{(2+3 x)^{3/2} \sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","Integrate[((2 + 3*x)^(3/2)*Sqrt[3 + 5*x])/Sqrt[1 - 2*x],x]","\frac{-805 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-45 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} (5 x+11)+1597 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{375 \sqrt{2}}","-\frac{8}{125} \sqrt{33} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"(-45*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(11 + 5*x) + 1597*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 805*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(375*Sqrt[2])","A",1
2817,1,92,98,0.1866445,"\int \frac{\sqrt{2+3 x} \sqrt{3+5 x}}{\sqrt{1-2 x}} \, dx","Integrate[(Sqrt[2 + 3*x]*Sqrt[3 + 5*x])/Sqrt[1 - 2*x],x]","\frac{1}{90} \left(-35 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-30 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+68 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{1}{15} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\frac{1}{3} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\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,"(-30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] + 68*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 35*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/90","A",1
2818,1,56,31,0.0864233,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} \sqrt{2+3 x}} \, dx","Integrate[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*Sqrt[2 + 3*x]),x]","\frac{1}{3} \sqrt{2} \left(E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-\operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)","-\sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"(Sqrt[2]*(EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/3","A",1
2819,1,70,81,0.1077955,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^{3/2}} \, dx","Integrate[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)),x]","\frac{-6 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-2 i \sqrt{33} (3 x+2) E\left(i \sinh ^{-1}\left(\sqrt{15 x+9}\right)|-\frac{2}{33}\right)}{63 x+42}","\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,"(-6*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] - (2*I)*Sqrt[33]*(2 + 3*x)*EllipticE[I*ArcSinh[Sqrt[9 + 15*x]], -2/33])/(42 + 63*x)","C",1
2820,1,97,129,0.1784535,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^{5/2}} \, dx","Integrate[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)),x]","\frac{2}{441} \left(35 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} (93 x+55)}{(3 x+2)^{3/2}}+31 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{8}{147} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(55 + 93*x))/(2 + 3*x)^(3/2) + 31*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 35*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/441","A",1
2821,1,98,158,0.1726423,"\int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^{7/2}} \, dx","Integrate[Sqrt[3 + 5*x]/(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2)),x]","\frac{2 \left(\sqrt{2} \left(292 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-105 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{\sqrt{1-2 x} \sqrt{5 x+3} \left(7884 x^2+10701 x+3581\right)}{(3 x+2)^{5/2}}\right)}{1715}","-\frac{68 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1715}+\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{584 \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1715}",1,"(2*((Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(3581 + 10701*x + 7884*x^2))/(2 + 3*x)^(5/2) + Sqrt[2]*(292*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 105*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/1715","A",1
2822,1,105,191,0.3054305,"\int \frac{(2+3 x)^{5/2} (3+5 x)^{3/2}}{\sqrt{1-2 x}} \, dx","Integrate[((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/Sqrt[1 - 2*x],x]","\frac{44109377 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5 \left(4443376 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+3 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(236250 x^3+765000 x^2+1114065 x+1107478\right)\right)}{708750 \sqrt{2}}","-\frac{663409 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{236250}-\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{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,"(44109377*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5*(3*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(1107478 + 1114065*x + 765000*x^2 + 236250*x^3) + 4443376*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(708750*Sqrt[2])","A",1
2823,1,100,160,0.2672279,"\int \frac{(2+3 x)^{3/2} (3+5 x)^{3/2}}{\sqrt{1-2 x}} \, dx","Integrate[((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/Sqrt[1 - 2*x],x]","\frac{313888 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5 \left(31619 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+3 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(2250 x^2+5910 x+7457\right)\right)}{15750 \sqrt{2}}","-\frac{4721 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{5250}-\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{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,"(313888*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5*(3*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(7457 + 5910*x + 2250*x^2) + 31619*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(15750*Sqrt[2])","A",1
2824,1,95,129,0.2388653,"\int \frac{\sqrt{2+3 x} (3+5 x)^{3/2}}{\sqrt{1-2 x}} \, dx","Integrate[(Sqrt[2 + 3*x]*(3 + 5*x)^(3/2))/Sqrt[1 - 2*x],x]","\frac{4451 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5 \left(448 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+3 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} (45 x+94)\right)}{675 \sqrt{2}}","-\frac{67}{225} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"(4451*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5*(3*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(94 + 45*x) + 448*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(675*Sqrt[2])","A",1
2825,1,92,98,0.0793697,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} \sqrt{2+3 x}} \, dx","Integrate[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*Sqrt[2 + 3*x]),x]","\frac{1}{54} \left(-29 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-30 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+62 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{1}{9} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\frac{5}{9} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\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,"(-30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] + 62*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 29*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/54","A",1
2826,1,92,98,0.1414246,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^{3/2}} \, dx","Integrate[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)),x]","\frac{1}{63} \left(-70 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{6 \sqrt{1-2 x} \sqrt{5 x+3}}{\sqrt{3 x+2}}+37 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","\frac{2}{21} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{21 \sqrt{3 x+2}}-\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,"((6*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/Sqrt[2 + 3*x] + 37*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 70*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/63","A",1
2827,1,97,129,0.2111402,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^{5/2}} \, dx","Integrate[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)),x]","\frac{3605 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{6 \sqrt{1-2 x} \sqrt{5 x+3} (408 x+265)}{(3 x+2)^{3/2}}-272 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{1323}","-\frac{202}{441} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"((-6*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(265 + 408*x))/(2 + 3*x)^(3/2) - 272*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 3605*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/1323","A",1
2828,1,99,160,0.180577,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^{7/2}} \, dx","Integrate[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2)),x]","\frac{2 \left(\sqrt{2} \left(7070 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+2797 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(25173 x^2+29322 x+8507\right)}{(3 x+2)^{5/2}}\right)}{46305}","-\frac{1196 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{15435}+\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(8507 + 29322*x + 25173*x^2))/(2 + 3*x)^(5/2) + Sqrt[2]*(2797*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 7070*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/46305","A",1
2829,1,104,191,0.2147436,"\int \frac{(3+5 x)^{3/2}}{\sqrt{1-2 x} (2+3 x)^{9/2}} \, dx","Integrate[(3 + 5*x)^(3/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(9/2)),x]","\frac{2 \left(\sqrt{2} \left(92318 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-17045 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(2492586 x^3+5015853 x^2+3324960 x+727631\right)}{(3 x+2)^{7/2}}\right)}{756315}","-\frac{9124 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{252105}+\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(727631 + 3324960*x + 5015853*x^2 + 2492586*x^3))/(2 + 3*x)^(7/2) + Sqrt[2]*(92318*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 17045*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/756315","A",1
2830,1,115,249,0.3606498,"\int \frac{(2+3 x)^{7/2} (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","Integrate[((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2))/Sqrt[1 - 2*x],x]","\frac{610627101631 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5 \left(61511810003 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+3 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(2104987500 x^5+9351247500 x^4+18620894250 x^3+22592085750 x^2+19961825445 x+16001700059\right)\right)}{608107500 \sqrt{2}}","-\frac{2295970088 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{4606875 \sqrt{33}}-\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{610627101631 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{36855000 \sqrt{33}}",1,"(610627101631*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5*(3*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(16001700059 + 19961825445*x + 22592085750*x^2 + 18620894250*x^3 + 9351247500*x^4 + 2104987500*x^5) + 61511810003*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(608107500*Sqrt[2])","A",1
2831,1,110,218,0.339539,"\int \frac{(2+3 x)^{5/2} (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","Integrate[((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/Sqrt[1 - 2*x],x]","\frac{2900562916 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5 \left(292189583 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+3 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(12757500 x^4+48384000 x^3+81985950 x^2+86822370 x+75000749\right)\right)}{9355500 \sqrt{2}}","-\frac{43624697 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{283500 \sqrt{33}}-\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{725140729 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{141750 \sqrt{33}}",1,"(2900562916*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5*(3*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(75000749 + 86822370*x + 81985950*x^2 + 48384000*x^3 + 12757500*x^4) + 292189583*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(9355500*Sqrt[2])","A",1
2832,1,105,191,0.293794,"\int \frac{(2+3 x)^{3/2} (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","Integrate[((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/Sqrt[1 - 2*x],x]","\frac{8256877 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5 \left(831761 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+3 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(47250 x^3+148950 x^2+212175 x+208073\right)\right)}{85050 \sqrt{2}}","-\frac{62092 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{14175}-\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{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,"(8256877*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5*(3*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(208073 + 212175*x + 148950*x^2 + 47250*x^3) + 831761*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(85050*Sqrt[2])","A",1
2833,1,97,160,0.2482267,"\int \frac{\sqrt{2+3 x} (3+5 x)^{5/2}}{\sqrt{1-2 x}} \, dx","Integrate[(Sqrt[2 + 3*x]*(3 + 5*x)^(5/2))/Sqrt[1 - 2*x],x]","\frac{-17717 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-3 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(1350 x^2+3420 x+4211\right)+35174 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{1134 \sqrt{2}}","-\frac{529}{378} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"(-3*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(4211 + 3420*x + 1350*x^2) + 35174*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 17717*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1134*Sqrt[2])","A",1
2834,1,95,129,0.2629823,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} \sqrt{2+3 x}} \, dx","Integrate[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*Sqrt[2 + 3*x]),x]","\frac{4141 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5 \left(419 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+3 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} (45 x+89)\right)}{405 \sqrt{2}}","-\frac{62}{135} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"(4141*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5*(3*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(89 + 45*x) + 419*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(405*Sqrt[2])","A",1
2835,1,97,129,0.1917816,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{3/2}} \, dx","Integrate[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)),x]","\frac{-595 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{6 \sqrt{1-2 x} \sqrt{5 x+3} (525 x+356)}{\sqrt{3 x+2}}+1948 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{1134}","-\frac{41}{189} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"((-6*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(356 + 525*x))/Sqrt[2 + 3*x] + 1948*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 595*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/1134","A",1
2836,1,97,129,0.2014771,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{5/2}} \, dx","Integrate[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)),x]","\frac{-10955 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{6 \sqrt{1-2 x} \sqrt{5 x+3} (723 x+475)}{(3 x+2)^{3/2}}+4157 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{3969}","\frac{412 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1323}+\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{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,"((6*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(475 + 723*x))/(2 + 3*x)^(3/2) + 4157*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 10955*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/3969","A",1
2837,1,99,160,0.1847659,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{7/2}} \, dx","Integrate[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2)),x]","\frac{\sqrt{2} \left(616735 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-53194 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)-\frac{6 \sqrt{1-2 x} \sqrt{5 x+3} \left(239373 x^2+311247 x+101257\right)}{(3 x+2)^{5/2}}}{138915}","-\frac{34154 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{46305}+\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{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,"((-6*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(101257 + 311247*x + 239373*x^2))/(2 + 3*x)^(5/2) + Sqrt[2]*(-53194*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 616735*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/138915","A",1
2838,1,104,191,0.2083968,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{9/2}} \, dx","Integrate[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(9/2)),x]","\frac{2 \left(\sqrt{2} \left(1783285 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+408311 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(11024397 x^3+18838881 x^2+10645545 x+1985537\right)}{(3 x+2)^{7/2}}\right)}{6806835}","-\frac{265648 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{2268945}+\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(1985537 + 10645545*x + 18838881*x^2 + 11024397*x^3))/(2 + 3*x)^(7/2) + Sqrt[2]*(408311*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 1783285*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/6806835","A",1
2839,1,107,222,0.2556143,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{11/2}} \, dx","Integrate[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(11/2)),x]","\frac{12066320 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{24 \sqrt{2-4 x} \sqrt{5 x+3} \left(1299976452 x^4+3462531489 x^3+3421407609 x^2+1489220097 x+241253543\right)}{(3 x+2)^{9/2}}+256785472 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{571774140 \sqrt{2}}","-\frac{2036756 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{47647845}+\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{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,"((24*Sqrt[2 - 4*x]*Sqrt[3 + 5*x]*(241253543 + 1489220097*x + 3421407609*x^2 + 3462531489*x^3 + 1299976452*x^4))/(2 + 3*x)^(9/2) + 256785472*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 12066320*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(571774140*Sqrt[2])","A",1
2840,1,112,249,0.4048591,"\int \frac{(3+5 x)^{5/2}}{\sqrt{1-2 x} (2+3 x)^{13/2}} \, dx","Integrate[(3 + 5*x)^(5/2)/(Sqrt[1 - 2*x]*(2 + 3*x)^(13/2)),x]","\frac{-6417960640 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{48 \sqrt{2-4 x} \sqrt{5 x+3} \left(112296073194 x^5+377569336554 x^4+507518001945 x^3+340525216341 x^2+113962415157 x+15211411193\right)}{(3 x+2)^{11/2}}+14787960256 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{17610643512 \sqrt{2}}","-\frac{31704544 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{66706983 \sqrt{33}}+\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{924247516 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{66706983 \sqrt{33}}",1,"((48*Sqrt[2 - 4*x]*Sqrt[3 + 5*x]*(15211411193 + 113962415157*x + 340525216341*x^2 + 507518001945*x^3 + 377569336554*x^4 + 112296073194*x^5))/(2 + 3*x)^(11/2) + 14787960256*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 6417960640*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(17610643512*Sqrt[2])","A",1
2841,1,55,12,0.1207459,"\int \frac{1}{\sqrt{1+x} \sqrt{2+x} \sqrt{3+x}} \, dx","Integrate[1/(Sqrt[1 + x]*Sqrt[2 + x]*Sqrt[3 + x]),x]","\frac{2 i \sqrt{\frac{1}{x+1}+1} \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x+1}}\right),2\right)}{\sqrt{\frac{x+2}{x+3}} \sqrt{\frac{x+3}{x+1}}}","-2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{1}{\sqrt{x+3}}\right),2\right)",1,"((2*I)*Sqrt[1 + (1 + x)^(-1)]*EllipticF[I*ArcSinh[1/Sqrt[1 + x]], 2])/(Sqrt[(2 + x)/(3 + x)]*Sqrt[(3 + x)/(1 + x)])","C",1
2842,1,74,16,0.1142164,"\int \frac{1}{\sqrt{3-x} \sqrt{1+x} \sqrt{2+x}} \, dx","Integrate[1/(Sqrt[3 - x]*Sqrt[1 + x]*Sqrt[2 + x]),x]","\frac{i \sqrt{\frac{4}{x-3}+1} \sqrt{\frac{5}{x-3}+1} (x-3)^{3/2} \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{2}{\sqrt{x-3}}\right),\frac{5}{4}\right)}{\sqrt{-((x-3) (x+1))} \sqrt{x+2}}","2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{x+1}}{2}\right),-4\right)",1,"(I*Sqrt[1 + 4/(-3 + x)]*Sqrt[1 + 5/(-3 + x)]*(-3 + x)^(3/2)*EllipticF[I*ArcSinh[2/Sqrt[-3 + x]], 5/4])/(Sqrt[-((-3 + x)*(1 + x))]*Sqrt[2 + x])","C",1
2843,1,67,24,0.1193965,"\int \frac{1}{\sqrt{2-x} \sqrt{1+x} \sqrt{3+x}} \, dx","Integrate[1/(Sqrt[2 - x]*Sqrt[1 + x]*Sqrt[3 + x]),x]","-\frac{2 (x+3) \sqrt{1-\frac{5}{x+3}} \sqrt{1-\frac{2}{x+3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{5}}{\sqrt{x+3}}\right),\frac{2}{5}\right)}{\sqrt{-5 (x+3)^2+35 (x+3)-50}}","\sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{3}}\right),-\frac{3}{2}\right)",1,"(-2*(3 + x)*Sqrt[1 - 5/(3 + x)]*Sqrt[1 - 2/(3 + x)]*EllipticF[ArcSin[Sqrt[5]/Sqrt[3 + x]], 2/5])/Sqrt[-50 + 35*(3 + x) - 5*(3 + x)^2]","B",1
2844,1,65,18,0.1122205,"\int \frac{1}{\sqrt{2-x} \sqrt{3-x} \sqrt{1+x}} \, dx","Integrate[1/(Sqrt[2 - x]*Sqrt[3 - x]*Sqrt[1 + x]),x]","-\frac{2 i \sqrt{1-\frac{3}{2-x}} \sqrt{\frac{1}{2-x}+1} (2-x) \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{2-x}}\right),-3\right)}{\sqrt{-((x-3) (x+1))}}","\operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{3}}\right),\frac{3}{4}\right)",1,"((-2*I)*Sqrt[1 - 3/(2 - x)]*Sqrt[1 + (2 - x)^(-1)]*(2 - x)*EllipticF[I*ArcSinh[1/Sqrt[2 - x]], -3])/Sqrt[-((-3 + x)*(1 + x))]","C",1
2845,1,78,18,0.1416123,"\int \frac{1}{\sqrt{1-x} \sqrt{2+x} \sqrt{3+x}} \, dx","Integrate[1/(Sqrt[1 - x]*Sqrt[2 + x]*Sqrt[3 + x]),x]","-\frac{2 i \sqrt{-((x-1) (x+2))} \sqrt{x+3} \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{3}}{\sqrt{x-1}}\right),\frac{4}{3}\right)}{\sqrt{\frac{9}{x-1}+3} (x-1)^{3/2} \sqrt{\frac{x+3}{x-1}}}","2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{x+2}}{\sqrt{3}}\right),-3\right)",1,"((-2*I)*Sqrt[-((-1 + x)*(2 + x))]*Sqrt[3 + x]*EllipticF[I*ArcSinh[Sqrt[3]/Sqrt[-1 + x]], 4/3])/(Sqrt[3 + 9/(-1 + x)]*(-1 + x)^(3/2)*Sqrt[(3 + x)/(-1 + x)])","C",1
2846,1,68,25,0.0880189,"\int \frac{1}{\sqrt{1-x} \sqrt{3-x} \sqrt{2+x}} \, dx","Integrate[1/(Sqrt[1 - x]*Sqrt[3 - x]*Sqrt[2 + x]),x]","-\frac{2 \sqrt{\frac{x-3}{x-1}} (x-1) \sqrt{\frac{x+2}{x-1}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{3}}{\sqrt{1-x}}\right),-\frac{2}{3}\right)}{\sqrt{3} \sqrt{-x^2+x+6}}","\frac{2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{x+2}}{\sqrt{3}}\right),\frac{3}{5}\right)}{\sqrt{5}}",1,"(-2*Sqrt[(-3 + x)/(-1 + x)]*(-1 + x)*Sqrt[(2 + x)/(-1 + x)]*EllipticF[ArcSin[Sqrt[3]/Sqrt[1 - x]], -2/3])/(Sqrt[3]*Sqrt[6 + x - x^2])","B",1
2847,1,65,23,0.1089272,"\int \frac{1}{\sqrt{1-x} \sqrt{2-x} \sqrt{3+x}} \, dx","Integrate[1/(Sqrt[1 - x]*Sqrt[2 - x]*Sqrt[3 + x]),x]","-\frac{2 i \sqrt{1-\frac{4}{1-x}} \sqrt{\frac{1}{1-x}+1} (1-x) \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{1-x}}\right),-4\right)}{\sqrt{-((x-2) (x+3))}}","\frac{2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{x+3}}{2}\right),\frac{4}{5}\right)}{\sqrt{5}}",1,"((-2*I)*Sqrt[1 - 4/(1 - x)]*Sqrt[1 + (1 - x)^(-1)]*(1 - x)*EllipticF[I*ArcSinh[1/Sqrt[1 - x]], -4])/Sqrt[-((-2 + x)*(3 + x))]","C",1
2848,1,67,14,0.0510731,"\int \frac{1}{\sqrt{1-x} \sqrt{2-x} \sqrt{3-x}} \, dx","Integrate[1/(Sqrt[1 - x]*Sqrt[2 - x]*Sqrt[3 - x]),x]","\frac{2 i \sqrt{\frac{x-3}{x-1}} \sqrt{\frac{x-2}{x-1}} (x-1) \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{1-x}}\right),2\right)}{\sqrt{2-x} \sqrt{3-x}}","2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{1}{\sqrt{3-x}}\right),2\right)",1,"((2*I)*Sqrt[(-3 + x)/(-1 + x)]*Sqrt[(-2 + x)/(-1 + x)]*(-1 + x)*EllipticF[I*ArcSinh[1/Sqrt[1 - x]], 2])/(Sqrt[2 - x]*Sqrt[3 - x])","C",1
2849,1,59,12,0.0548319,"\int \frac{1}{\sqrt{-3+x} \sqrt{-2+x} \sqrt{-1+x}} \, dx","Integrate[1/(Sqrt[-3 + x]*Sqrt[-2 + x]*Sqrt[-1 + x]),x]","\frac{2 i \sqrt{\frac{1}{x-3}+1} \sqrt{\frac{2}{x-3}+1} (x-3) \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{x-3}}\right),2\right)}{\sqrt{x-2} \sqrt{x-1}}","-2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{1}{\sqrt{x-1}}\right),2\right)",1,"((2*I)*Sqrt[1 + (-3 + x)^(-1)]*Sqrt[1 + 2/(-3 + x)]*(-3 + x)*EllipticF[I*ArcSinh[1/Sqrt[-3 + x]], 2])/(Sqrt[-2 + x]*Sqrt[-1 + x])","C",1
2850,1,63,57,0.1437802,"\int \frac{1}{\sqrt{-3-x} \sqrt{-2+x} \sqrt{-1+x}} \, dx","Integrate[1/(Sqrt[-3 - x]*Sqrt[-2 + x]*Sqrt[-1 + x]),x]","\frac{i \sqrt{\frac{x-2}{x-1}} \sqrt{\frac{x-1}{x+3}} \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{2}{\sqrt{-x-3}}\right),\frac{5}{4}\right)}{\sqrt{\frac{x-2}{x+3}}}","-\frac{\sqrt{x+3} \operatorname{EllipticF}\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,"(I*Sqrt[(-2 + x)/(-1 + x)]*Sqrt[(-1 + x)/(3 + x)]*EllipticF[I*ArcSinh[2/Sqrt[-3 - x]], 5/4])/Sqrt[(-2 + x)/(3 + x)]","A",1
2851,1,72,41,0.1288694,"\int \frac{1}{\sqrt{-2-x} \sqrt{-3+x} \sqrt{-1+x}} \, dx","Integrate[1/(Sqrt[-2 - x]*Sqrt[-3 + x]*Sqrt[-1 + x]),x]","\frac{2 i \sqrt{\frac{x-3}{x-1}} \sqrt{\frac{x-1}{x+2}} \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{3}}{\sqrt{-x-2}}\right),\frac{5}{3}\right)}{\sqrt{3} \sqrt{\frac{x-3}{x+2}}}","-\frac{2 \sqrt{x+2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{1}{\sqrt{\frac{x}{3}+\frac{2}{3}}}\right),\frac{5}{3}\right)}{\sqrt{3} \sqrt{-x-2}}",1,"((2*I)*Sqrt[(-3 + x)/(-1 + x)]*Sqrt[(-1 + x)/(2 + x)]*EllipticF[I*ArcSinh[Sqrt[3]/Sqrt[-2 - x]], 5/3])/(Sqrt[3]*Sqrt[(-3 + x)/(2 + x)])","C",0
2852,1,75,92,0.1703389,"\int \frac{1}{\sqrt{-3-x} \sqrt{-2-x} \sqrt{-1+x}} \, dx","Integrate[1/(Sqrt[-3 - x]*Sqrt[-2 - x]*Sqrt[-1 + x]),x]","\frac{2 i \sqrt{\frac{3}{x-1}+1} \sqrt{\frac{4}{x-1}+1} (x-1) \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{3}}{\sqrt{x-1}}\right),\frac{4}{3}\right)}{\sqrt{-3 (x-1)-12} \sqrt{-x-2}}","-\frac{\sqrt{x+2} \sqrt{x+3} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{2}{\sqrt{x+3}}\right),\frac{1}{4}\right)}{\sqrt{-x-3} \sqrt{-x-2}}-\frac{2 i K(4) \sqrt{x+2}}{\sqrt{-x-2}}+\frac{K\left(\frac{3}{4}\right) \sqrt{x+3}}{\sqrt{-x-3}}",1,"((2*I)*Sqrt[1 + 3/(-1 + x)]*Sqrt[1 + 4/(-1 + x)]*(-1 + x)*EllipticF[I*ArcSinh[Sqrt[3]/Sqrt[-1 + x]], 4/3])/(Sqrt[-12 - 3*(-1 + x)]*Sqrt[-2 - x])","A",1
2853,1,72,41,0.0885947,"\int \frac{1}{\sqrt{-1-x} \sqrt{-3+x} \sqrt{-2+x}} \, dx","Integrate[1/(Sqrt[-1 - x]*Sqrt[-3 + x]*Sqrt[-2 + x]),x]","\frac{2 i \sqrt{\frac{x-3}{x-2}} \sqrt{\frac{x-2}{x+1}} \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{3}}{\sqrt{-x-1}}\right),\frac{4}{3}\right)}{\sqrt{3} \sqrt{\frac{x-3}{x+1}}}","-\frac{2 \sqrt{x+1} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{1}{\sqrt{\frac{x}{3}+\frac{1}{3}}}\right),\frac{4}{3}\right)}{\sqrt{3} \sqrt{-x-1}}",1,"((2*I)*Sqrt[(-3 + x)/(-2 + x)]*Sqrt[(-2 + x)/(1 + x)]*EllipticF[I*ArcSinh[Sqrt[3]/Sqrt[-1 - x]], 4/3])/(Sqrt[3]*Sqrt[(-3 + x)/(1 + x)])","C",1
2854,1,75,57,0.0784146,"\int \frac{1}{\sqrt{-3-x} \sqrt{-1-x} \sqrt{-2+x}} \, dx","Integrate[1/(Sqrt[-3 - x]*Sqrt[-1 - x]*Sqrt[-2 + x]),x]","\frac{2 i \sqrt{\frac{3}{x-2}+1} \sqrt{\frac{5}{x-2}+1} (x-2) \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{3}}{\sqrt{x-2}}\right),\frac{5}{3}\right)}{\sqrt{-3 (x-2)-15} \sqrt{-x-1}}","-\frac{2 \sqrt{x+1} \sqrt{x+3} \operatorname{EllipticF}\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,"((2*I)*Sqrt[1 + 3/(-2 + x)]*Sqrt[1 + 5/(-2 + x)]*(-2 + x)*EllipticF[I*ArcSinh[Sqrt[3]/Sqrt[-2 + x]], 5/3])/(Sqrt[-15 - 3*(-2 + x)]*Sqrt[-1 - x])","C",1
2855,1,69,57,0.0816984,"\int \frac{1}{\sqrt{-2-x} \sqrt{-1-x} \sqrt{-3+x}} \, dx","Integrate[1/(Sqrt[-2 - x]*Sqrt[-1 - x]*Sqrt[-3 + x]),x]","\frac{i \sqrt{\frac{4}{x-3}+1} \sqrt{\frac{5}{x-3}+1} (x-3) \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{2}{\sqrt{x-3}}\right),\frac{5}{4}\right)}{\sqrt{-x-2} \sqrt{-x-1}}","-\frac{2 \sqrt{x+1} \sqrt{x+2} \operatorname{EllipticF}\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,"(I*Sqrt[1 + 4/(-3 + x)]*Sqrt[1 + 5/(-3 + x)]*(-3 + x)*EllipticF[I*ArcSinh[2/Sqrt[-3 + x]], 5/4])/(Sqrt[-2 - x]*Sqrt[-1 - x])","C",1
2856,1,67,14,0.0689552,"\int \frac{1}{\sqrt{-3-x} \sqrt{-2-x} \sqrt{-1-x}} \, dx","Integrate[1/(Sqrt[-3 - x]*Sqrt[-2 - x]*Sqrt[-1 - x]),x]","\frac{2 i \sqrt{\frac{x+1}{x+3}} \sqrt{\frac{x+2}{x+3}} (x+3) \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{-x-3}}\right),2\right)}{\sqrt{-x-2} \sqrt{-x-1}}","2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{1}{\sqrt{-x-1}}\right),2\right)",1,"((2*I)*Sqrt[(1 + x)/(3 + x)]*Sqrt[(2 + x)/(3 + x)]*(3 + x)*EllipticF[I*ArcSinh[1/Sqrt[-3 - x]], 2])/(Sqrt[-2 - x]*Sqrt[-1 - x])","C",1
2857,1,201,204,1.3457078,"\int \frac{1}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx","Integrate[1/((a + b*x)^(3/2)*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\frac{2 b \sqrt{c+d x} \sqrt{e+f x} \left(-1-\frac{i \sqrt{\frac{d (a+b x)}{b (c+d x)}} \left(E\left(i \sinh ^{-1}\left(\sqrt{\frac{d (a+b x)}{b c-a d}}\right)|\frac{b c f-a d f}{b d e-a d f}\right)-\operatorname{EllipticF}\left(i \sinh ^{-1}\left(\sqrt{\frac{d (a+b x)}{b c-a d}}\right),\frac{b c f-a d f}{b d e-a d f}\right)\right)}{\sqrt{\frac{b (e+f x)}{b e-a f}}}\right)}{\sqrt{a+b x} (b c-a d) (b e-a f)}","\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,"(2*b*Sqrt[c + d*x]*Sqrt[e + f*x]*(-1 - (I*Sqrt[(d*(a + b*x))/(b*(c + d*x))]*(EllipticE[I*ArcSinh[Sqrt[(d*(a + b*x))/(b*c - a*d)]], (b*c*f - a*d*f)/(b*d*e - a*d*f)] - EllipticF[I*ArcSinh[Sqrt[(d*(a + b*x))/(b*c - a*d)]], (b*c*f - a*d*f)/(b*d*e - a*d*f)]))/Sqrt[(b*(e + f*x))/(b*e - a*f)]))/((b*c - a*d)*(b*e - a*f)*Sqrt[a + b*x])","C",1
2858,1,449,437,4.5145779,"\int \frac{1}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx","Integrate[1/((a + b*x)^(5/2)*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","-\frac{2 \left(b^2 (c+d x) (e+f x) \sqrt{\frac{b c}{d}-a} ((b c-a d) (b e-a f)-2 (a+b x) (-2 a d f+b c f+b d e))+(a+b x) \left(-i f (a+b x)^{3/2} (b c-a d) \sqrt{\frac{b (c+d x)}{d (a+b x)}} \sqrt{\frac{b (e+f x)}{f (a+b x)}} (-3 a d f+2 b c f+b d e) \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b c}{d}-a}}{\sqrt{a+b x}}\right),\frac{b d e-a d f}{b c f-a d f}\right)+2 b^2 (c+d x) (e+f x) \sqrt{\frac{b c}{d}-a} (-2 a d f+b c f+b d e)+2 i f (a+b x)^{3/2} (b c-a d) \sqrt{\frac{b (c+d x)}{d (a+b x)}} \sqrt{\frac{b (e+f x)}{f (a+b x)}} (-2 a d f+b c f+b d e) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{b c}{d}-a}}{\sqrt{a+b x}}\right)|\frac{b d e-a d f}{b c f-a d f}\right)\right)\right)}{3 b (a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{\frac{b c}{d}-a} (b c-a d)^2 (b e-a f)^2}","\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) \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right),\frac{f (b c-a d)}{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 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{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,"(-2*(b^2*Sqrt[-a + (b*c)/d]*(c + d*x)*(e + f*x)*((b*c - a*d)*(b*e - a*f) - 2*(b*d*e + b*c*f - 2*a*d*f)*(a + b*x)) + (a + b*x)*(2*b^2*Sqrt[-a + (b*c)/d]*(b*d*e + b*c*f - 2*a*d*f)*(c + d*x)*(e + f*x) + (2*I)*(b*c - a*d)*f*(b*d*e + b*c*f - 2*a*d*f)*(a + b*x)^(3/2)*Sqrt[(b*(c + d*x))/(d*(a + b*x))]*Sqrt[(b*(e + f*x))/(f*(a + b*x))]*EllipticE[I*ArcSinh[Sqrt[-a + (b*c)/d]/Sqrt[a + b*x]], (b*d*e - a*d*f)/(b*c*f - a*d*f)] - I*(b*c - a*d)*f*(b*d*e + 2*b*c*f - 3*a*d*f)*(a + b*x)^(3/2)*Sqrt[(b*(c + d*x))/(d*(a + b*x))]*Sqrt[(b*(e + f*x))/(f*(a + b*x))]*EllipticF[I*ArcSinh[Sqrt[-a + (b*c)/d]/Sqrt[a + b*x]], (b*d*e - a*d*f)/(b*c*f - a*d*f)])))/(3*b*Sqrt[-a + (b*c)/d]*(b*c - a*d)^2*(b*e - a*f)^2*(a + b*x)^(3/2)*Sqrt[c + d*x]*Sqrt[e + f*x])","C",1
2859,1,97,158,0.293114,"\int \frac{(2+3 x)^{7/2}}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^(7/2)/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","\frac{-544355 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(6750 x^2+18990 x+25213\right)+1080992 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{131250 \sqrt{2}}","-\frac{178879 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{43750 \sqrt{33}}-\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{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,"(-15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(25213 + 18990*x + 6750*x^2) + 1080992*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 544355*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(131250*Sqrt[2])","A",1
2860,1,95,127,0.2477085,"\int \frac{(2+3 x)^{5/2}}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^(5/2)/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","\frac{5161 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5 \left(518 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+3 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} (45 x+104)\right)}{1875 \sqrt{2}}","-\frac{857 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{625 \sqrt{33}}-\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{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,"(5161*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5*(3*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(104 + 45*x) + 518*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(1875*Sqrt[2])","A",1
2861,1,92,96,0.0795105,"\int \frac{(2+3 x)^{3/2}}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^(3/2)/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","\frac{1}{150} \left(-35 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-30 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+74 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{13 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{25 \sqrt{33}}-\frac{1}{5} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\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,"(-30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] + 74*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 35*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/150","A",1
2862,1,129,31,0.2113138,"\int \frac{\sqrt{2+3 x}}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx","Integrate[Sqrt[2 + 3*x]/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]","\frac{\sqrt{3 x+2} \sqrt{\frac{2 x-1}{5 x+3}} \left(5 \sqrt{\frac{2 x-1}{5 x+3}} \sqrt{\frac{3 x+2}{5 x+3}} \sqrt{5 x+3}+i \sqrt{2} E\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{15 x+9}}\right)|-\frac{33}{2}\right)\right)}{5 \sqrt{1-2 x} \sqrt{\frac{3 x+2}{5 x+3}}}","-\sqrt{\frac{7}{5}} E\left(\sin ^{-1}\left(\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right)|\frac{33}{35}\right)",1,"(Sqrt[2 + 3*x]*Sqrt[(-1 + 2*x)/(3 + 5*x)]*(5*Sqrt[(-1 + 2*x)/(3 + 5*x)]*Sqrt[(2 + 3*x)/(3 + 5*x)]*Sqrt[3 + 5*x] + I*Sqrt[2]*EllipticE[I*ArcSinh[1/Sqrt[9 + 15*x]], -33/2]))/(5*Sqrt[1 - 2*x]*Sqrt[(2 + 3*x)/(3 + 5*x)])","C",1
2863,1,74,29,0.1496409,"\int \frac{1}{\sqrt{1-2 x} \sqrt{2+3 x} \sqrt{3+5 x}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]),x]","\frac{i \sqrt{3 x+2} \sqrt{\frac{4 x-2}{5 x+3}} \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{1}{\sqrt{15 x+9}}\right),-\frac{33}{2}\right)}{\sqrt{1-2 x} \sqrt{\frac{3 x+2}{5 x+3}}}","-\frac{2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{\sqrt{33}}",1,"(I*Sqrt[2 + 3*x]*Sqrt[(-2 + 4*x)/(3 + 5*x)]*EllipticF[I*ArcSinh[1/Sqrt[9 + 15*x]], -33/2])/(Sqrt[1 - 2*x]*Sqrt[(2 + 3*x)/(3 + 5*x)])","C",1
2864,1,62,63,0.1361186,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{2}{7} \left(\frac{3 \sqrt{1-2 x} \sqrt{5 x+3}}{\sqrt{3 x+2}}+\sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","\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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/Sqrt[2 + 3*x] + Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/7","A",1
2865,1,97,127,0.1916265,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x]),x]","\frac{2}{147} \left(-35 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} (222 x+155)}{(3 x+2)^{3/2}}+74 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{52 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{49 \sqrt{33}}+\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{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,"(2*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(155 + 222*x))/(2 + 3*x)^(3/2) + 74*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 35*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/147","A",1
2866,1,101,158,0.3084176,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2)*Sqrt[3 + 5*x]),x]","\frac{4 \left(\sqrt{2} \left(5161 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-2590 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} \left(92898 x^2+126972 x+43507\right)}{2 (3 x+2)^{5/2}}\right)}{5145}","-\frac{6856 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1715 \sqrt{33}}+\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{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,"(4*((3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(43507 + 126972*x + 92898*x^2))/(2*(2 + 3*x)^(5/2)) + Sqrt[2]*(5161*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 2590*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/5145","A",1
2867,1,122,160,0.2796246,"\int \frac{(2+3 x)^{7/2}}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^(7/2)/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","\frac{61151 \sqrt{2} (5 x+3) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5 \left(6013 \sqrt{2} (5 x+3) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+2 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3} \left(7425 x^2+22440 x+10801\right)\right)}{68750 (5 x+3)}","-\frac{942 \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3125}-\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{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,"(61151*Sqrt[2]*(3 + 5*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5*(2*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(10801 + 22440*x + 7425*x^2) + 6013*Sqrt[2]*(3 + 5*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(68750*(3 + 5*x))","A",1
2868,1,97,129,0.2450863,"\int \frac{(2+3 x)^{5/2}}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^(5/2)/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","\frac{-315 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{10 \sqrt{1-2 x} \sqrt{3 x+2} (165 x+101)}{\sqrt{5 x+3}}+876 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{2750}","-\frac{17}{125} \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"((-10*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(101 + 165*x))/Sqrt[3 + 5*x] + 876*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 315*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/2750","A",1
2869,1,92,98,0.1441075,"\int \frac{(2+3 x)^{3/2}}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^(3/2)/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","\frac{1}{275} \left(35 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{10 \sqrt{1-2 x} \sqrt{3 x+2}}{\sqrt{5 x+3}}+31 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{4}{25} \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\frac{2 \sqrt{1-2 x} \sqrt{3 x+2}}{55 \sqrt{5 x+3}}-\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,"((-10*Sqrt[1 - 2*x]*Sqrt[2 + 3*x])/Sqrt[3 + 5*x] + 31*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 35*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/275","A",1
2870,1,61,81,0.1130273,"\int \frac{\sqrt{2+3 x}}{\sqrt{1-2 x} (3+5 x)^{3/2}} \, dx","Integrate[Sqrt[2 + 3*x]/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)),x]","\frac{2}{55} \left(-\frac{5 \sqrt{1-2 x} \sqrt{3 x+2}}{\sqrt{5 x+3}}-i \sqrt{33} E\left(i \sinh ^{-1}\left(\sqrt{15 x+9}\right)|-\frac{2}{33}\right)\right)","\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,"(2*((-5*Sqrt[1 - 2*x]*Sqrt[2 + 3*x])/Sqrt[3 + 5*x] - I*Sqrt[33]*EllipticE[I*ArcSinh[Sqrt[9 + 15*x]], -2/33]))/55","C",1
2871,1,106,63,0.1030087,"\int \frac{1}{\sqrt{1-2 x} \sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)),x]","-\frac{2 \left(-\sqrt{2} (5 x+3) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+5 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}+\sqrt{2} (5 x+3) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)}{55 x+33}","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,"(-2*(5*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] + Sqrt[2]*(3 + 5*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - Sqrt[2]*(3 + 5*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(33 + 55*x)","A",1
2872,1,130,129,0.147109,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)),x]","-\frac{2 \left(-35 \sqrt{2} \left(15 x^2+19 x+6\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+68 \sqrt{2} \left(15 x^2+19 x+6\right) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)+\sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3} (1020 x+647)\right)}{77 (3 x+2) (5 x+3)}","\frac{4}{7} \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"(-2*(Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(647 + 1020*x) + 68*Sqrt[2]*(6 + 19*x + 15*x^2)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 35*Sqrt[2]*(6 + 19*x + 15*x^2)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/(77*(2 + 3*x)*(3 + 5*x))","A",1
2873,1,100,160,0.1633866,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{2}{539} \left(-2 \sqrt{2} \left(1597 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-805 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)-\frac{\sqrt{1-2 x} \left(143730 x^2+186888 x+60635\right)}{(3 x+2)^{3/2} \sqrt{5 x+3}}\right)","\frac{192}{49} \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"(2*(-((Sqrt[1 - 2*x]*(60635 + 186888*x + 143730*x^2))/((2 + 3*x)^(3/2)*Sqrt[3 + 5*x])) - 2*Sqrt[2]*(1597*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 805*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/539","A",1
2874,1,105,191,0.2943921,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)),x]","\frac{2 \left(-6 \sqrt{2} \left(112082 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-56455 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)-\frac{\sqrt{1-2 x} \left(90786420 x^3+178568982 x^2+116993058 x+25529443\right)}{(3 x+2)^{5/2} \sqrt{5 x+3}}\right)}{18865}","\frac{40456 \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1715}-\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{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,"(2*(-((Sqrt[1 - 2*x]*(25529443 + 116993058*x + 178568982*x^2 + 90786420*x^3))/((2 + 3*x)^(5/2)*Sqrt[3 + 5*x])) - 6*Sqrt[2]*(112082*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 56455*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/18865","A",1
2875,1,107,187,0.3134015,"\int \frac{(2+3 x)^{9/2}}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^(9/2)/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\frac{-3061660 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{10 \sqrt{1-2 x} \sqrt{3 x+2} \left(3675375 x^3+13721400 x^2+12517925 x+3365042\right)}{(5 x+3)^{3/2}}+6515539 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{11343750}","-\frac{104663 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{171875 \sqrt{33}}-\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{6515539 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{343750 \sqrt{33}}",1,"((-10*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3365042 + 12517925*x + 13721400*x^2 + 3675375*x^3))/(3 + 5*x)^(3/2) + 6515539*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 3061660*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/11343750","A",1
2876,1,102,156,0.3679995,"\int \frac{(2+3 x)^{7/2}}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^(7/2)/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\frac{-17045 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{10 \sqrt{1-2 x} \sqrt{3 x+2} \left(81675 x^2+101350 x+31429\right)}{(5 x+3)^{3/2}}+92318 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{453750}","-\frac{2281 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{6875 \sqrt{33}}-\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{46159 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6875 \sqrt{33}}",1,"((-10*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(31429 + 101350*x + 81675*x^2))/(3 + 5*x)^(3/2) + 92318*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 17045*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/453750","A",1
2877,1,97,125,0.3248372,"\int \frac{(2+3 x)^{5/2}}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^(5/2)/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\frac{7070 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{10 \sqrt{1-2 x} \sqrt{3 x+2} (1175 x+716)}{(5 x+3)^{3/2}}+2797 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{45375}","-\frac{598 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1375 \sqrt{33}}-\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{2797 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1375 \sqrt{33}}",1,"((-10*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(716 + 1175*x))/(3 + 5*x)^(3/2) + 2797*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 7070*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/45375","A",1
2878,1,97,125,0.3278814,"\int \frac{(2+3 x)^{3/2}}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^(3/2)/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\frac{3605 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{10 \sqrt{1-2 x} \sqrt{3 x+2} (680 x+419)}{(5 x+3)^{3/2}}-272 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{9075}","-\frac{202 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{275 \sqrt{33}}-\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{272 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{275 \sqrt{33}}",1,"((-10*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(419 + 680*x))/(3 + 5*x)^(3/2) - 272*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 3605*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/9075","A",1
2879,1,97,125,0.3712516,"\int \frac{\sqrt{2+3 x}}{\sqrt{1-2 x} (3+5 x)^{5/2}} \, dx","Integrate[Sqrt[2 + 3*x]/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]","\frac{2 \left(70 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{5 \sqrt{1-2 x} \sqrt{3 x+2} (185 x+122)}{(5 x+3)^{3/2}}-37 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)}{1815}","-\frac{4 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{55 \sqrt{33}}-\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{74 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{55 \sqrt{33}}",1,"(2*((-5*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(122 + 185*x))/(3 + 5*x)^(3/2) - 37*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 70*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/1815","A",1
2880,1,97,125,0.2889596,"\int \frac{1}{\sqrt{1-2 x} \sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3 + 5*x)^(5/2)),x]","\frac{2}{363} \left(-29 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{25 \sqrt{1-2 x} \sqrt{3 x+2} (62 x+35)}{(5 x+3)^{3/2}}+62 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","-\frac{4 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{11 \sqrt{33}}+\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{124 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{11 \sqrt{33}}",1,"(2*((25*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(35 + 62*x))/(3 + 5*x)^(3/2) + 62*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 29*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/363","A",1
2881,1,99,156,0.1990579,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{2 \left(2 \sqrt{2} \left(4451 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-2240 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{\sqrt{1-2 x} \left(667650 x^2+823580 x+253409\right)}{\sqrt{3 x+2} (5 x+3)^{3/2}}\right)}{2541}","-\frac{536 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{77 \sqrt{33}}+\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{17804 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{77 \sqrt{33}}",1,"(2*((Sqrt[1 - 2*x]*(253409 + 823580*x + 667650*x^2))/(Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)) + 2*Sqrt[2]*(4451*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 2240*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/2541","A",1
2882,1,104,187,0.2243897,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{2 \left(2 \sqrt{2} \left(313888 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-158095 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{\sqrt{1-2 x} \left(141249600 x^3+268408770 x^2+169778606 x+35747225\right)}{(3 x+2)^{3/2} (5 x+3)^{3/2}}\right)}{17787}","-\frac{37768 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{539 \sqrt{33}}+\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{1255552 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{539 \sqrt{33}}",1,"(2*((Sqrt[1 - 2*x]*(35747225 + 169778606*x + 268408770*x^2 + 141249600*x^3))/((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + 2*Sqrt[2]*(313888*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 158095*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/17787","A",1
2883,1,109,218,0.3858923,"\int \frac{1}{\sqrt{1-2 x} (2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)),x]","\frac{2 \left(4 \sqrt{2} \left(44109377 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-22216880 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{\sqrt{1-2 x} \left(119095317900 x^4+305707177080 x^3+294023389014 x^2+125573817736 x+20093773321\right)}{(3 x+2)^{5/2} (5 x+3)^{3/2}}\right)}{622545}","-\frac{10614544 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{18865 \sqrt{33}}+\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{352875016 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{18865 \sqrt{33}}",1,"(2*((Sqrt[1 - 2*x]*(20093773321 + 125573817736*x + 294023389014*x^2 + 305707177080*x^3 + 119095317900*x^4))/((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + 4*Sqrt[2]*(44109377*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 22216880*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/622545","A",1
2884,1,120,86,0.1746581,"\int \frac{\sqrt{x}}{\sqrt{a+2 x} \sqrt{c+2 x}} \, dx","Integrate[Sqrt[x]/(Sqrt[a + 2*x]*Sqrt[c + 2*x]),x]","-\frac{i c \sqrt{\frac{2 x}{a}+1} \sqrt{\frac{2 x}{c}+1} \left(E\left(i \sinh ^{-1}\left(\sqrt{2} \sqrt{\frac{1}{a}} \sqrt{x}\right)|\frac{a}{c}\right)-\operatorname{EllipticF}\left(i \sinh ^{-1}\left(\sqrt{2} \sqrt{\frac{1}{a}} \sqrt{x}\right),\frac{a}{c}\right)\right)}{\sqrt{2} \sqrt{\frac{1}{a}} \sqrt{a+2 x} \sqrt{c+2 x}}","\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,"((-I)*c*Sqrt[1 + (2*x)/a]*Sqrt[1 + (2*x)/c]*(EllipticE[I*ArcSinh[Sqrt[2]*Sqrt[a^(-1)]*Sqrt[x]], a/c] - EllipticF[I*ArcSinh[Sqrt[2]*Sqrt[a^(-1)]*Sqrt[x]], a/c]))/(Sqrt[2]*Sqrt[a^(-1)]*Sqrt[a + 2*x]*Sqrt[c + 2*x])","C",1
2885,1,28,18,0.0207336,"\int \frac{1}{\sqrt{4-x} \sqrt{5-x} \sqrt{-3+x}} \, dx","Integrate[1/(Sqrt[4 - x]*Sqrt[5 - x]*Sqrt[-3 + x]),x]","-2 \sqrt{4-x} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};(x-4)^2\right)","\sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{x-3}\right),\frac{1}{2}\right)",1,"-2*Sqrt[4 - x]*HypergeometricPFQ[{1/4, 1/2}, {5/4}, (-4 + x)^2]","C",1
2886,1,28,14,0.0186635,"\int \frac{1}{\sqrt{4-x} \sqrt{(5-x) (-3+x)}} \, dx","Integrate[1/(Sqrt[4 - x]*Sqrt[(5 - x)*(-3 + x)]),x]","-2 \sqrt{4-x} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};(x-4)^2\right)","-2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{4-x}\right),-1\right)",1,"-2*Sqrt[4 - x]*HypergeometricPFQ[{1/4, 1/2}, {5/4}, (-4 + x)^2]","C",1
2887,1,28,14,0.0244413,"\int \frac{1}{\sqrt{4-x} \sqrt{-15+8 x-x^2}} \, dx","Integrate[1/(Sqrt[4 - x]*Sqrt[-15 + 8*x - x^2]),x]","-2 \sqrt{4-x} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};(4-x)^2\right)","-2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{4-x}\right),-1\right)",1,"-2*Sqrt[4 - x]*Hypergeometric2F1[1/4, 1/2, 5/4, (4 - x)^2]","C",1
2888,1,74,16,0.0799765,"\int \frac{1}{\sqrt{6-x} \sqrt{-2+x} \sqrt{-1+x}} \, dx","Integrate[1/(Sqrt[6 - x]*Sqrt[-2 + x]*Sqrt[-1 + x]),x]","\frac{i \sqrt{\frac{4}{x-6}+1} \sqrt{\frac{5}{x-6}+1} (x-6)^{3/2} \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{2}{\sqrt{x-6}}\right),\frac{5}{4}\right)}{\sqrt{-((x-6) (x-2))} \sqrt{x-1}}","2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{x-2}}{2}\right),-4\right)",1,"(I*Sqrt[1 + 4/(-6 + x)]*Sqrt[1 + 5/(-6 + x)]*(-6 + x)^(3/2)*EllipticF[I*ArcSinh[2/Sqrt[-6 + x]], 5/4])/(Sqrt[-((-6 + x)*(-2 + x))]*Sqrt[-1 + x])","C",1
2889,1,74,25,0.0440146,"\int \frac{1}{\sqrt{(6-x) (-2+x)} \sqrt{-1+x}} \, dx","Integrate[1/(Sqrt[(6 - x)*(-2 + x)]*Sqrt[-1 + x]),x]","\frac{i \sqrt{\frac{4}{x-6}+1} \sqrt{\frac{5}{x-6}+1} (x-6)^{3/2} \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{2}{\sqrt{x-6}}\right),\frac{5}{4}\right)}{\sqrt{-((x-6) (x-2))} \sqrt{x-1}}","-\frac{2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{6-x}}{2}\right),\frac{4}{5}\right)}{\sqrt{5}}",1,"(I*Sqrt[1 + 4/(-6 + x)]*Sqrt[1 + 5/(-6 + x)]*(-6 + x)^(3/2)*EllipticF[I*ArcSinh[2/Sqrt[-6 + x]], 5/4])/(Sqrt[-((-6 + x)*(-2 + x))]*Sqrt[-1 + x])","C",1
2890,1,68,25,0.0957889,"\int \frac{1}{\sqrt{-1+x} \sqrt{-12+8 x-x^2}} \, dx","Integrate[1/(Sqrt[-1 + x]*Sqrt[-12 + 8*x - x^2]),x]","-\frac{2 \sqrt{\frac{x-6}{x-1}} \sqrt{\frac{x-2}{x-1}} (x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{5}}{\sqrt{x-1}}\right),\frac{1}{5}\right)}{\sqrt{5} \sqrt{-x^2+8 x-12}}","-\frac{2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{6-x}}{2}\right),\frac{4}{5}\right)}{\sqrt{5}}",1,"(-2*Sqrt[(-6 + x)/(-1 + x)]*Sqrt[(-2 + x)/(-1 + x)]*(-1 + x)*EllipticF[ArcSin[Sqrt[5]/Sqrt[-1 + x]], 1/5])/(Sqrt[5]*Sqrt[-12 + 8*x - x^2])","B",1
2891,1,115,186,0.2998656,"\int \frac{(2+3 x)^{7/2} \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^(7/2)*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\frac{2050510 \sqrt{2-4 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-30 \sqrt{3 x+2} \sqrt{5 x+3} \left(6750 x^3+26010 x^2+54757 x-109756\right)-4071079 \sqrt{2-4 x} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{52500 \sqrt{1-2 x}}","\frac{673523 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{8750 \sqrt{33}}+\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{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,"(-30*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-109756 + 54757*x + 26010*x^2 + 6750*x^3) - 4071079*Sqrt[2 - 4*x]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 2050510*Sqrt[2 - 4*x]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(52500*Sqrt[1 - 2*x])","A",1
2892,1,110,155,0.264208,"\int \frac{(2+3 x)^{5/2} \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^(5/2)*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\frac{14665 \sqrt{2-4 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-30 \sqrt{3 x+2} \sqrt{5 x+3} \left(90 x^2+328 x-799\right)-29116 \sqrt{2-4 x} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{1500 \sqrt{1-2 x}}","\frac{4817 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{250 \sqrt{33}}+\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{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,"(-30*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-799 + 328*x + 90*x^2) - 29116*Sqrt[2 - 4*x]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 14665*Sqrt[2 - 4*x]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1500*Sqrt[1 - 2*x])","A",1
2893,1,103,122,0.2256842,"\int \frac{(2+3 x)^{3/2} \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^(3/2)*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\frac{70 \sqrt{2-4 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-30 \sqrt{3 x+2} \sqrt{5 x+3} (x-4)-139 \sqrt{2-4 x} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{30 \sqrt{1-2 x}}","\frac{23 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{5 \sqrt{33}}+\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{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,"(-30*(-4 + x)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] - 139*Sqrt[2 - 4*x]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 70*Sqrt[2 - 4*x]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(30*Sqrt[1 - 2*x])","A",1
2894,1,86,85,0.1939401,"\int \frac{\sqrt{2+3 x} \sqrt{3+5 x}}{(1-2 x)^{3/2}} \, dx","Integrate[(Sqrt[2 + 3*x]*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]","\frac{\operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)}{\sqrt{2}}+\frac{\sqrt{3 x+2} \sqrt{5 x+3}}{\sqrt{1-2 x}}-\sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)","\frac{\operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{\sqrt{33}}+\frac{\sqrt{3 x+2} \sqrt{5 x+3}}{\sqrt{1-2 x}}+\sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"(Sqrt[2 + 3*x]*Sqrt[3 + 5*x])/Sqrt[1 - 2*x] - Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]/Sqrt[2]","A",1
2895,1,63,62,0.0690343,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} \sqrt{2+3 x}} \, dx","Integrate[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]),x]","\frac{1}{7} \left(\frac{2 \sqrt{3 x+2} \sqrt{5 x+3}}{\sqrt{1-2 x}}-\sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","\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,"((2*Sqrt[2 + 3*x]*Sqrt[3 + 5*x])/Sqrt[1 - 2*x] - Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/7","A",1
2896,1,122,125,0.1530934,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)^{3/2}} \, dx","Integrate[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)),x]","\frac{35 \sqrt{2-4 x} (3 x+2) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+2 \sqrt{3 x+2} \sqrt{5 x+3} (12 x+1)-4 \sqrt{2-4 x} (3 x+2) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{49 \sqrt{1-2 x} (3 x+2)}","-\frac{62 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{49 \sqrt{33}}-\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{4}{49} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"(2*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(1 + 12*x) - 4*Sqrt[2 - 4*x]*(2 + 3*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 35*Sqrt[2 - 4*x]*(2 + 3*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(49*Sqrt[1 - 2*x]*(2 + 3*x))","A",1
2897,1,99,158,0.1653985,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)^{5/2}} \, dx","Integrate[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)),x]","\frac{2 \left(\sqrt{2} \left(140 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+19 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)-\frac{3 \sqrt{5 x+3} \left(114 x^2-37 x-59\right)}{\sqrt{1-2 x} (3 x+2)^{3/2}}\right)}{1029}","-\frac{212 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{343 \sqrt{33}}+\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{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,"(2*((-3*Sqrt[3 + 5*x]*(-59 - 37*x + 114*x^2))/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)) + Sqrt[2]*(19*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 140*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/1029","A",1
2898,1,104,189,0.2130344,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{3/2} (2+3 x)^{7/2}} \, dx","Integrate[Sqrt[3 + 5*x]/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)),x]","\frac{2 \left(\sqrt{2} \left(455 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+2818 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)-\frac{3 \sqrt{5 x+3} \left(50724 x^3+41724 x^2-13127 x-11923\right)}{\sqrt{1-2 x} (3 x+2)^{5/2}}\right)}{36015}","-\frac{4364 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{12005 \sqrt{33}}+\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{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,"(2*((-3*Sqrt[3 + 5*x]*(-11923 - 13127*x + 41724*x^2 + 50724*x^3))/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)) + Sqrt[2]*(2818*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 455*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/36015","A",1
2899,1,120,219,0.291806,"\int \frac{(2+3 x)^{7/2} (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]","\frac{226741655 \sqrt{2-4 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-30 \sqrt{3 x+2} \sqrt{5 x+3} \left(472500 x^4+2002500 x^3+4128030 x^2+6609296 x-12044593\right)-450172412 \sqrt{2-4 x} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{945000 \sqrt{1-2 x}}","\frac{6770629 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{157500}+\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{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,"(-30*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-12044593 + 6609296*x + 4128030*x^2 + 2002500*x^3 + 472500*x^4) - 450172412*Sqrt[2 - 4*x]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 226741655*Sqrt[2 - 4*x]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(945000*Sqrt[1 - 2*x])","A",1
2900,1,115,188,0.2923815,"\int \frac{(2+3 x)^{5/2} (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]","\frac{649285 \sqrt{2-4 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-30 \sqrt{3 x+2} \sqrt{5 x+3} \left(2250 x^3+8460 x^2+17487 x-34721\right)-1289089 \sqrt{2-4 x} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{10500 \sqrt{1-2 x}}","\frac{9694}{875} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(-30*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-34721 + 17487*x + 8460*x^2 + 2250*x^3) - 1289089*Sqrt[2 - 4*x]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 649285*Sqrt[2 - 4*x]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(10500*Sqrt[1 - 2*x])","A",1
2901,1,110,157,0.2429783,"\int \frac{(2+3 x)^{3/2} (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]","\frac{4655 \sqrt{2-4 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-30 \sqrt{3 x+2} \sqrt{5 x+3} \left(30 x^2+106 x-253\right)-9242 \sqrt{2-4 x} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{300 \sqrt{1-2 x}}","\frac{139}{50} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(-30*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-253 + 106*x + 30*x^2) - 9242*Sqrt[2 - 4*x]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 4655*Sqrt[2 - 4*x]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(300*Sqrt[1 - 2*x])","A",1
2902,1,105,126,0.2063022,"\int \frac{\sqrt{2+3 x} (3+5 x)^{3/2}}{(1-2 x)^{3/2}} \, dx","Integrate[(Sqrt[2 + 3*x]*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]","\frac{67 \sqrt{2-4 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+6 \sqrt{3 x+2} \sqrt{5 x+3} (19-5 x)-133 \sqrt{2-4 x} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{18 \sqrt{1-2 x}}","\frac{2}{3} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(6*(19 - 5*x)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] - 133*Sqrt[2 - 4*x]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 67*Sqrt[2 - 4*x]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(18*Sqrt[1 - 2*x])","A",1
2903,1,92,98,0.1170399,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} \sqrt{2+3 x}} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]),x]","\frac{1}{42} \left(35 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{66 \sqrt{3 x+2} \sqrt{5 x+3}}{\sqrt{1-2 x}}-68 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","\frac{1}{7} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\frac{11 \sqrt{3 x+2} \sqrt{5 x+3}}{7 \sqrt{1-2 x}}+\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,"((66*Sqrt[2 + 3*x]*Sqrt[3 + 5*x])/Sqrt[1 - 2*x] - 68*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 35*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/42","A",1
2904,1,122,129,0.1564526,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^{3/2}} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)),x]","\frac{-35 \sqrt{2-4 x} (3 x+2) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+6 \sqrt{3 x+2} \sqrt{5 x+3} (31 x+23)-31 \sqrt{2-4 x} (3 x+2) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{147 \sqrt{1-2 x} (3 x+2)}","\frac{4}{49} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"(6*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(23 + 31*x) - 31*Sqrt[2 - 4*x]*(2 + 3*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 35*Sqrt[2 - 4*x]*(2 + 3*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(147*Sqrt[1 - 2*x]*(2 + 3*x))","A",1
2905,1,97,160,0.2649863,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^{5/2}} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)),x]","\frac{\sqrt{2} \left(3395 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{3 \sqrt{10 x+6} \left(1374 x^2+908 x+11\right)}{\sqrt{1-2 x} (3 x+2)^{3/2}}-458 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)}{3087}","-\frac{178 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1029}-\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{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,"(Sqrt[2]*((3*Sqrt[6 + 10*x]*(11 + 908*x + 1374*x^2))/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)) - 458*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 3395*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/3087","A",1
2906,1,104,191,0.1888248,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^{7/2}} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)),x]","\frac{2 \left(\sqrt{2} \left(8015 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+169 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)-\frac{3 \sqrt{5 x+3} \left(3042 x^3-7083 x^2-10266 x-2909\right)}{\sqrt{1-2 x} (3 x+2)^{5/2}}\right)}{36015}","-\frac{992 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{12005}+\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{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,"(2*((-3*Sqrt[3 + 5*x]*(-2909 - 10266*x - 7083*x^2 + 3042*x^3))/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)) + Sqrt[2]*(169*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 8015*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/36015","A",1
2907,1,109,222,0.2458653,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^{9/2}} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(9/2)),x]","\frac{2 \left(\sqrt{2} \left(95165 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+94684 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)-\frac{3 \sqrt{5 x+3} \left(5112936 x^4+7326810 x^3+1004571 x^2-2279324 x-809083\right)}{\sqrt{1-2 x} (3 x+2)^{7/2}}\right)}{1764735}","-\frac{23012 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{588245}+\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{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,"(2*((-3*Sqrt[3 + 5*x]*(-809083 - 2279324*x + 1004571*x^2 + 7326810*x^3 + 5112936*x^4))/(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2)) + Sqrt[2]*(94684*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 95165*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/1764735","A",1
2908,1,125,246,0.3071904,"\int \frac{(2+3 x)^{7/2} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]","\frac{9010073170 \sqrt{2-4 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-30 \sqrt{3 x+2} \sqrt{5 x+3} \left(12757500 x^5+60196500 x^4+133330950 x^3+198895770 x^2+273928969 x-477155552\right)-17888580643 \sqrt{2-4 x} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{6237000 \sqrt{1-2 x}}","\frac{269045681 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{94500 \sqrt{33}}+\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{17888580643 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{189000 \sqrt{33}}",1,"(-30*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-477155552 + 273928969*x + 198895770*x^2 + 133330950*x^3 + 60196500*x^4 + 12757500*x^5) - 17888580643*Sqrt[2 - 4*x]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 9010073170*Sqrt[2 - 4*x]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(6237000*Sqrt[1 - 2*x])","A",1
2909,1,120,219,0.2993079,"\int \frac{(2+3 x)^{5/2} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]","\frac{43010905 \sqrt{2-4 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-30 \sqrt{3 x+2} \sqrt{5 x+3} \left(94500 x^4+392400 x^3+795150 x^2+1258906 x-2283923\right)-85393762 \sqrt{2-4 x} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{113400 \sqrt{1-2 x}}","\frac{1284329 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{18900}+\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{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,"(-30*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-2283923 + 1258906*x + 795150*x^2 + 392400*x^3 + 94500*x^4) - 85393762*Sqrt[2 - 4*x]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 43010905*Sqrt[2 - 4*x]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(113400*Sqrt[1 - 2*x])","A",1
2910,1,115,188,0.2712015,"\int \frac{(2+3 x)^{3/2} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","Integrate[((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]","\frac{123340 \sqrt{2-4 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-30 \sqrt{3 x+2} \sqrt{5 x+3} \left(450 x^3+1650 x^2+3349 x-6590\right)-244879 \sqrt{2-4 x} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{1260 \sqrt{1-2 x}}","\frac{3683}{210} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(-30*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-6590 + 3349*x + 1650*x^2 + 450*x^3) - 244879*Sqrt[2 - 4*x]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 123340*Sqrt[2 - 4*x]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1260*Sqrt[1 - 2*x])","A",1
2911,1,110,155,0.2825312,"\int \frac{\sqrt{2+3 x} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx","Integrate[(Sqrt[2 + 3*x]*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]","\frac{13295 \sqrt{2-4 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-30 \sqrt{3 x+2} \sqrt{5 x+3} \left(90 x^2+308 x-721\right)-26396 \sqrt{2-4 x} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{540 \sqrt{1-2 x}}","\frac{397}{90} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(-30*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-721 + 308*x + 90*x^2) - 26396*Sqrt[2 - 4*x]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 13295*Sqrt[2 - 4*x]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(540*Sqrt[1 - 2*x])","A",1
2912,1,105,129,0.1279486,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} \sqrt{2+3 x}} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]),x]","\frac{2240 \sqrt{2-4 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+6 \sqrt{3 x+2} \sqrt{5 x+3} (632-175 x)-4451 \sqrt{2-4 x} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{378 \sqrt{1-2 x}}","\frac{67}{63} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(6*(632 - 175*x)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] - 4451*Sqrt[2 - 4*x]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 2240*Sqrt[2 - 4*x]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(378*Sqrt[1 - 2*x])","A",1
2913,1,122,129,0.1730878,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^{3/2}} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)),x]","\frac{1295 \sqrt{2-4 x} (3 x+2) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+6 \sqrt{3 x+2} \sqrt{5 x+3} (1093 x+724)-2318 \sqrt{2-4 x} (3 x+2) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{882 \sqrt{1-2 x} (3 x+2)}","\frac{31}{147} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(6*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(724 + 1093*x) - 2318*Sqrt[2 - 4*x]*(2 + 3*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 1295*Sqrt[2 - 4*x]*(2 + 3*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(882*Sqrt[1 - 2*x]*(2 + 3*x))","A",1
2914,1,100,160,0.183347,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^{5/2}} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)),x]","\frac{\frac{6 \sqrt{5 x+3} \left(8391 x^2+12847 x+4819\right)}{\sqrt{1-2 x} (3 x+2)^{3/2}}-\sqrt{2} \left(7070 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+2797 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)}{9261}","\frac{598 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3087}+\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{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,"((6*Sqrt[3 + 5*x]*(4819 + 12847*x + 8391*x^2))/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)) - Sqrt[2]*(2797*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 7070*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/9261","A",1
2915,1,104,191,0.2016857,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^{7/2}} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)),x]","\frac{\sqrt{2} \left(546035 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-81164 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{6 \sqrt{5 x+3} \left(730476 x^3+936351 x^2+292777 x-4877\right)}{\sqrt{1-2 x} (3 x+2)^{5/2}}}{324135}","-\frac{28174 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{108045}+\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{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,"((6*Sqrt[3 + 5*x]*(-4877 + 292777*x + 936351*x^2 + 730476*x^3))/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)) + Sqrt[2]*(-81164*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 546035*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/324135","A",1
2916,1,109,222,0.2418034,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^{9/2}} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(9/2)),x]","\frac{2 \left(\sqrt{2} \left(1868510 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-53279 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{3 \sqrt{5 x+3} \left(2877066 x^4+11042235 x^3+12020751 x^2+4889131 x+616327\right)}{\sqrt{1-2 x} (3 x+2)^{7/2}}\right)}{5294205}","-\frac{220028 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1764735}+\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{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,"(2*((3*Sqrt[3 + 5*x]*(616327 + 4889131*x + 12020751*x^2 + 11042235*x^3 + 2877066*x^4))/(Sqrt[1 - 2*x]*(2 + 3*x)^(7/2)) + Sqrt[2]*(-53279*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 1868510*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/5294205","A",1
2917,1,115,253,0.2984387,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{3/2} (2+3 x)^{11/2}} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(11/2)),x]","\frac{8 \sqrt{2} \left(6877465 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+3018014 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)-\frac{24 \sqrt{5 x+3} \left(488918268 x^5+985046292 x^4+466728543 x^3-227945505 x^2-243200677 x-52688263\right)}{\sqrt{1-2 x} (3 x+2)^{9/2}}}{266827932}","-\frac{1199452 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{22235661}+\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{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,"((-24*Sqrt[3 + 5*x]*(-52688263 - 243200677*x - 227945505*x^2 + 466728543*x^3 + 985046292*x^4 + 488918268*x^5))/(Sqrt[1 - 2*x]*(2 + 3*x)^(9/2)) + 8*Sqrt[2]*(3018014*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 6877465*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/266827932","A",1
2918,1,110,160,0.1432891,"\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^(7/2)/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{169365 \sqrt{2-4 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-10 \sqrt{3 x+2} \sqrt{5 x+3} \left(2970 x^2+11154 x-27757\right)-336246 \sqrt{2-4 x} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{27500 \sqrt{1-2 x}}","\frac{5057 \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1250}+\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{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,"(-10*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-27757 + 11154*x + 2970*x^2) - 336246*Sqrt[2 - 4*x]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 169365*Sqrt[2 - 4*x]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(27500*Sqrt[1 - 2*x])","A",1
2919,1,105,129,0.1148591,"\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^(5/2)/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{805 \sqrt{2-4 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{3 x+2} \sqrt{5 x+3} (139-33 x)-1597 \sqrt{2-4 x} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{550 \sqrt{1-2 x}}","\frac{24}{25} \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(10*(139 - 33*x)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] - 1597*Sqrt[2 - 4*x]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 805*Sqrt[2 - 4*x]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(550*Sqrt[1 - 2*x])","A",1
2920,1,92,98,0.1158031,"\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^(3/2)/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{1}{110} \left(35 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{70 \sqrt{3 x+2} \sqrt{5 x+3}}{\sqrt{1-2 x}}-68 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","\frac{1}{5} \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\frac{7 \sqrt{3 x+2} \sqrt{5 x+3}}{11 \sqrt{1-2 x}}+\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,"((70*Sqrt[2 + 3*x]*Sqrt[3 + 5*x])/Sqrt[1 - 2*x] - 68*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 35*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/110","A",1
2921,1,91,62,0.0900825,"\int \frac{\sqrt{2+3 x}}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx","Integrate[Sqrt[2 + 3*x]/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{1}{11} \left(\sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{2 \sqrt{3 x+2} \sqrt{5 x+3}}{\sqrt{1-2 x}}-\sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)","\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,"((2*Sqrt[2 + 3*x]*Sqrt[3 + 5*x])/Sqrt[1 - 2*x] - Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/11","A",1
2922,1,61,81,0.0891159,"\int \frac{1}{(1-2 x)^{3/2} \sqrt{2+3 x} \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]),x]","\frac{2}{77} \left(\frac{2 \sqrt{3 x+2} \sqrt{5 x+3}}{\sqrt{1-2 x}}-i \sqrt{33} E\left(i \sinh ^{-1}\left(\sqrt{15 x+9}\right)|-\frac{2}{33}\right)\right)","\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,"(2*((2*Sqrt[2 + 3*x]*Sqrt[3 + 5*x])/Sqrt[1 - 2*x] - I*Sqrt[33]*EllipticE[I*ArcSinh[Sqrt[9 + 15*x]], -2/33]))/77","C",1
2923,1,122,129,0.2219672,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{70 \sqrt{2-4 x} (3 x+2) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+2 \sqrt{3 x+2} \sqrt{5 x+3} (107-186 x)+62 \sqrt{2-4 x} (3 x+2) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{539 \sqrt{1-2 x} (3 x+2)}","-\frac{8}{49} \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(2*(107 - 186*x)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] + 62*Sqrt[2 - 4*x]*(2 + 3*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 70*Sqrt[2 - 4*x]*(2 + 3*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(539*Sqrt[1 - 2*x]*(2 + 3*x))","A",1
2924,1,99,160,0.183198,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x]),x]","\frac{2 \left(3 \sqrt{2} \left(292 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-105 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{\sqrt{5 x+3} \left(-15768 x^2-3006 x+5543\right)}{\sqrt{1-2 x} (3 x+2)^{3/2}}\right)}{3773}","-\frac{68}{343} \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(2*((Sqrt[3 + 5*x]*(5543 - 3006*x - 15768*x^2))/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)) + 3*Sqrt[2]*(292*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 105*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/3773","A",1
2925,1,106,191,0.2067723,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)*Sqrt[3 + 5*x]),x]","\frac{4 \left(\sqrt{2} \left(61151 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-30065 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{\sqrt{5 x+3} \left(-6604308 x^3-5720058 x^2+1424784 x+1546591\right)}{2 \sqrt{1-2 x} (3 x+2)^{5/2}}\right)}{132055}","-\frac{7536 \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{12005}+\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{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,"(4*((Sqrt[3 + 5*x]*(1546591 + 1424784*x - 5720058*x^2 - 6604308*x^3))/(2*Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)) + Sqrt[2]*(61151*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 30065*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/132055","A",1
2926,1,132,191,0.3182245,"\int \frac{(2+3 x)^{9/2}}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^(9/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{5867645 \sqrt{2-4 x} (5 x+3) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{3 x+2} \sqrt{5 x+3} \left(-490050 x^3-2188890 x^2+3684629 x+2892883\right)-11646308 \sqrt{2-4 x} (5 x+3) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{1512500 \sqrt{1-2 x} (5 x+3)}","\frac{175111 \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{68750}+\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{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,"(10*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(2892883 + 3684629*x - 2188890*x^2 - 490050*x^3) - 11646308*Sqrt[2 - 4*x]*(3 + 5*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 5867645*Sqrt[2 - 4*x]*(3 + 5*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1512500*Sqrt[1 - 2*x]*(3 + 5*x))","A",1
2927,1,127,160,0.1945703,"\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^(7/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{27860 \sqrt{2-4 x} (5 x+3) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{3 x+2} \sqrt{5 x+3} \left(-5445 x^2+20897 x+14494\right)-55019 \sqrt{2-4 x} (5 x+3) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{30250 \sqrt{1-2 x} (5 x+3)}","\frac{823 \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1375}+\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{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,"(10*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(14494 + 20897*x - 5445*x^2) - 55019*Sqrt[2 - 4*x]*(3 + 5*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 27860*Sqrt[2 - 4*x]*(3 + 5*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(30250*Sqrt[1 - 2*x]*(3 + 5*x))","A",1
2928,1,122,129,0.1730157,"\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^(5/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{1295 \sqrt{2-4 x} (5 x+3) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{3 x+2} \sqrt{5 x+3} (1229 x+733)-2318 \sqrt{2-4 x} (5 x+3) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{6050 \sqrt{1-2 x} (5 x+3)}","\frac{31}{275} \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"(10*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(733 + 1229*x) - 2318*Sqrt[2 - 4*x]*(3 + 5*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 1295*Sqrt[2 - 4*x]*(3 + 5*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(6050*Sqrt[1 - 2*x]*(3 + 5*x))","A",1
2929,1,122,129,0.1792331,"\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^(3/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{70 \sqrt{2-4 x} (5 x+3) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{3 x+2} \sqrt{5 x+3} (37 x+20)-37 \sqrt{2-4 x} (5 x+3) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{605 \sqrt{1-2 x} (5 x+3)}","-\frac{2}{55} \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"(10*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(20 + 37*x) - 37*Sqrt[2 - 4*x]*(3 + 5*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 70*Sqrt[2 - 4*x]*(3 + 5*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(605*Sqrt[1 - 2*x]*(3 + 5*x))","A",1
2930,1,122,129,0.1751898,"\int \frac{\sqrt{2+3 x}}{(1-2 x)^{3/2} (3+5 x)^{3/2}} \, dx","Integrate[Sqrt[2 + 3*x]/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{37 \sqrt{2-4 x} (5 x+3) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+2 \sqrt{3 x+2} \sqrt{5 x+3} (20 x+1)-4 \sqrt{2-4 x} (5 x+3) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{121 \sqrt{1-2 x} (5 x+3)}","-\frac{2}{11} \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"(2*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(1 + 20*x) - 4*Sqrt[2 - 4*x]*(3 + 5*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 37*Sqrt[2 - 4*x]*(3 + 5*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(121*Sqrt[1 - 2*x]*(3 + 5*x))","A",1
2931,1,122,129,0.1834303,"\int \frac{1}{(1-2 x)^{3/2} \sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)),x]","\frac{140 \sqrt{2-4 x} (5 x+3) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+2 \sqrt{3 x+2} \sqrt{5 x+3} (370 x-163)-74 \sqrt{2-4 x} (5 x+3) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{847 \sqrt{1-2 x} (5 x+3)}","-\frac{4}{77} \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"(2*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-163 + 370*x) - 74*Sqrt[2 - 4*x]*(3 + 5*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 140*Sqrt[2 - 4*x]*(3 + 5*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(847*Sqrt[1 - 2*x]*(3 + 5*x))","A",1
2932,1,98,160,0.2036387,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{2 \left(\sqrt{2} \left(1295 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-2318 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{69540 x^2+9544 x-22003}{\sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}\right)}{5929}","\frac{124}{539} \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)-\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{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,"(2*((-22003 + 9544*x + 69540*x^2)/(Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]) + Sqrt[2]*(-2318*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 1295*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/5929","A",1
2933,1,104,191,0.1894971,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{2 \left(\frac{9903420 x^3+7926942 x^2-2259236 x-2088967}{\sqrt{1-2 x} (3 x+2)^{3/2} \sqrt{5 x+3}}-2 \sqrt{2} \left(55019 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-27860 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)\right)}{41503}","\frac{6584 \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3773}-\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{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,"(2*((-2088967 - 2259236*x + 7926942*x^2 + 9903420*x^3)/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x]) - 2*Sqrt[2]*(55019*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 27860*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/41503","A",1
2934,1,109,222,0.2232035,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)),x]","\frac{2 \left(\frac{6289006320 x^4+9225477612 x^3+1919527182 x^2-2283681406 x-884250959}{\sqrt{1-2 x} (3 x+2)^{5/2} \sqrt{5 x+3}}-2 \sqrt{2} \left(11646308 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5867645 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)\right)}{1452605}","\frac{1400888 \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{132055}-\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{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,"(2*((-884250959 - 2283681406*x + 1919527182*x^2 + 9225477612*x^3 + 6289006320*x^4)/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x]) - 2*Sqrt[2]*(11646308*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5867645*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/1452605","A",1
2935,1,141,218,0.3151537,"\int \frac{(2+3 x)^{11/2}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^(11/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{609979405 \sqrt{2-4 x} (5 x+3)^2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{3 x+2} \left(-242574750 x^4-1255998150 x^3+1267558775 x^2+2667846028 x+904528061\right) \sqrt{5 x+3}-1209831262 \sqrt{2-4 x} (5 x+3)^2 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{249562500 \sqrt{1-2 x} (5 x+3)^2}","\frac{18177329 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3781250 \sqrt{33}}+\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{604915631 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3781250 \sqrt{33}}",1,"(10*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(904528061 + 2667846028*x + 1267558775*x^2 - 1255998150*x^3 - 242574750*x^4) - 1209831262*Sqrt[2 - 4*x]*(3 + 5*x)^2*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 609979405*Sqrt[2 - 4*x]*(3 + 5*x)^2*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(249562500*Sqrt[1 - 2*x]*(3 + 5*x)^2)","A",1
2936,1,136,187,0.2084018,"\int \frac{(2+3 x)^{9/2}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^(9/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{2908255 \sqrt{2-4 x} (5 x+3)^2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{3 x+2} \left(-2695275 x^3+9376775 x^2+14153413 x+4534181\right) \sqrt{5 x+3}-5684677 \sqrt{2-4 x} (5 x+3)^2 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{4991250 \sqrt{1-2 x} (5 x+3)^2}","\frac{84134 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{75625 \sqrt{33}}+\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{5684677 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{151250 \sqrt{33}}",1,"(10*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(4534181 + 14153413*x + 9376775*x^2 - 2695275*x^3) - 5684677*Sqrt[2 - 4*x]*(3 + 5*x)^2*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 2908255*Sqrt[2 - 4*x]*(3 + 5*x)^2*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(4991250*Sqrt[1 - 2*x]*(3 + 5*x)^2)","A",1
2937,1,102,156,0.1685896,"\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^(7/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{150115 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{10 \sqrt{3 x+2} \left(649925 x^2+772474 x+229463\right)}{\sqrt{1-2 x} (5 x+3)^{3/2}}-237796 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{998250}","\frac{2657 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{15125 \sqrt{33}}+\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{118898 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{15125 \sqrt{33}}",1,"((10*Sqrt[2 + 3*x]*(229463 + 772474*x + 649925*x^2))/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)) - 237796*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 150115*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/998250","A",1
2938,1,97,156,0.2913285,"\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^(5/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{\sqrt{2} \left(10955 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{5 \sqrt{6 x+4} \left(20785 x^2+22313 x+5881\right)}{\sqrt{1-2 x} (5 x+3)^{3/2}}-4157 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)}{99825}","-\frac{412 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3025 \sqrt{33}}+\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{4157 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3025 \sqrt{33}}",1,"(Sqrt[2]*((5*Sqrt[4 + 6*x]*(5881 + 22313*x + 20785*x^2))/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)) - 4157*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 10955*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/99825","A",1
2939,1,97,156,0.2916931,"\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^(3/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{\sqrt{2} \left(4025 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{5 \sqrt{6 x+4} \left(2470 x^2+1424 x-59\right)}{\sqrt{1-2 x} (5 x+3)^{3/2}}-494 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)}{19965}","-\frac{214 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{605 \sqrt{33}}-\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{494 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{605 \sqrt{33}}",1,"(Sqrt[2]*((5*Sqrt[4 + 6*x]*(-59 + 1424*x + 2470*x^2))/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)) - 494*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 4025*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/19965","A",1
2940,1,96,156,0.2641801,"\int \frac{\sqrt{2+3 x}}{(1-2 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[Sqrt[2 + 3*x]/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{\sqrt{2} \left(362 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{\sqrt{6 x+4} \left(2450 x^2+685 x-592\right)}{\sqrt{1-2 x} (5 x+3)^{3/2}}-98 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)}{3993}","-\frac{16 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{121 \sqrt{33}}-\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{98 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{121 \sqrt{33}}",1,"(Sqrt[2]*((Sqrt[4 + 6*x]*(-592 + 685*x + 2450*x^2))/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)) - 98*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 362*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/3993","A",1
2941,1,98,156,0.1789767,"\int \frac{1}{(1-2 x)^{3/2} \sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]*(3 + 5*x)^(5/2)),x]","\frac{2 \left(\sqrt{2} \left(1948 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-595 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{\sqrt{3 x+2} \left(-97400 x^2-5230 x+27691\right)}{\sqrt{1-2 x} (5 x+3)^{3/2}}\right)}{27951}","-\frac{164 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{847 \sqrt{33}}+\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{3896 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{847 \sqrt{33}}",1,"(2*((Sqrt[2 + 3*x]*(27691 - 5230*x - 97400*x^2))/(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)) + Sqrt[2]*(1948*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 595*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/27951","A",1
2942,1,104,187,0.2226772,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{2 \left(2 \sqrt{2} \left(148831 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-74515 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{-44649300 x^3-32744810 x^2+10598372 x+8473261}{\sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}\right)}{195657}","-\frac{18016 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{5929 \sqrt{33}}+\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{595324 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5929 \sqrt{33}}",1,"(2*((8473261 + 10598372*x - 32744810*x^2 - 44649300*x^3)/(Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)) + 2*Sqrt[2]*(148831*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 74515*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/195657","A",1
2943,1,109,218,0.2645931,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{2 \left(2 \sqrt{2} \left(10655966 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-5366165 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{-9590369400 x^4-13428808080 x^3-2415287594 x^2+3336610202 x+1213551469}{\sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{3/2}}\right)}{1369599}","-\frac{1282376 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{41503 \sqrt{33}}+\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{42623864 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{41503 \sqrt{33}}",1,"(2*((1213551469 + 3336610202*x - 2415287594*x^2 - 13428808080*x^3 - 9590369400*x^4)/(Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + 2*Sqrt[2]*(10655966*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5366165*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/1369599","A",1
2944,1,114,249,0.3925987,"\int \frac{1}{(1-2 x)^{3/2} (2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)),x]","\frac{2 \left(4 \sqrt{2} \left(1508889271 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-759987865 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{-8148002063400 x^5-16841199826980 x^4-9658241620704 x^3+1466692421066 x^2+2920885694212 x+687365548973}{\sqrt{1-2 x} (3 x+2)^{5/2} (5 x+3)^{3/2}}\right)}{47935965}","-\frac{363103712 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1452605 \sqrt{33}}+\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{12071114168 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1452605 \sqrt{33}}",1,"(2*((687365548973 + 2920885694212*x + 1466692421066*x^2 - 9658241620704*x^3 - 16841199826980*x^4 - 8148002063400*x^5)/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + 4*Sqrt[2]*(1508889271*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 759987865*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/47935965","A",1
2945,1,130,218,0.3391314,"\int \frac{(2+3 x)^{9/2} \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^(9/2)*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","-\frac{-226741655 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{3 x+2} \sqrt{5 x+3} \left(1336500 x^4+6664680 x^3+19375686 x^2-94671446 x+35797779\right)+450172412 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{1155000 (1-2 x)^{3/2}}","-\frac{6770629 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{17500 \sqrt{33}}+\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{112543103 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{8750 \sqrt{33}}",1,"-1/1155000*(10*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(35797779 - 94671446*x + 19375686*x^2 + 6664680*x^3 + 1336500*x^4) + 450172412*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 226741655*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)","A",1
2946,1,125,187,0.3034661,"\int \frac{(2+3 x)^{7/2} \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^(7/2)*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","-\frac{-649285 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{3 x+2} \sqrt{5 x+3} \left(8910 x^3+45342 x^2-275587 x+101763\right)+1289089 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{16500 (1-2 x)^{3/2}}","-\frac{9694 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{125 \sqrt{33}}+\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{1289089 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{500 \sqrt{33}}",1,"-1/16500*(10*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(101763 - 275587*x + 45342*x^2 + 8910*x^3) + 1289089*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 649285*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)","A",1
2947,1,120,156,0.2837842,"\int \frac{(2+3 x)^{5/2} \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^(5/2)*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","-\frac{-4655 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{3 x+2} \sqrt{5 x+3} \left(198 x^2-2060 x+711\right)+9242 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{660 (1-2 x)^{3/2}}","-\frac{139 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{10 \sqrt{33}}+\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{4621 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{10 \sqrt{33}}",1,"-1/660*(10*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(711 - 2060*x + 198*x^2) + 9242*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 4655*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)","A",1
2948,1,115,123,0.249878,"\int \frac{(2+3 x)^{3/2} \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^(3/2)*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","-\frac{-67 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+2 \sqrt{3 x+2} \sqrt{5 x+3} (45-167 x)+133 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{66 (1-2 x)^{3/2}}","-\frac{2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{\sqrt{33}}+\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{133 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2 \sqrt{33}}",1,"-1/66*(2*(45 - 167*x)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] + 133*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 67*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)","A",1
2949,1,115,125,0.1872054,"\int \frac{\sqrt{2+3 x} \sqrt{3+5 x}}{(1-2 x)^{5/2}} \, dx","Integrate[(Sqrt[2 + 3*x]*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]","\frac{35 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+2 \sqrt{3 x+2} \sqrt{5 x+3} (136 x+9)-68 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{462 (1-2 x)^{3/2}}","-\frac{\operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{7 \sqrt{33}}-\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{34 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{7 \sqrt{33}}",1,"(2*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(9 + 136*x) - 68*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 35*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(462*(1 - 2*x)^(3/2))","A",1
2950,1,115,125,0.2103565,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} \sqrt{2+3 x}} \, dx","Integrate[Sqrt[3 + 5*x]/((1 - 2*x)^(5/2)*Sqrt[2 + 3*x]),x]","\frac{35 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+4 \sqrt{3 x+2} \sqrt{5 x+3} (54-31 x)+31 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{1617 (1-2 x)^{3/2}}","\frac{4 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{49 \sqrt{33}}+\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{31 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{49 \sqrt{33}}",1,"(4*(54 - 31*x)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] + 31*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 35*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1617*(1 - 2*x)^(3/2))","A",1
2951,1,99,156,0.1787164,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} (2+3 x)^{3/2}} \, dx","Integrate[Sqrt[3 + 5*x]/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)),x]","\frac{\sqrt{2} \left(3395 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-458 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)-\frac{2 \sqrt{5 x+3} \left(2748 x^2-1390 x-531\right)}{(1-2 x)^{3/2} \sqrt{3 x+2}}}{11319}","-\frac{178 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{343 \sqrt{33}}-\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{458 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{343 \sqrt{33}}",1,"((-2*Sqrt[3 + 5*x]*(-531 - 1390*x + 2748*x^2))/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]) + Sqrt[2]*(-458*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 3395*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/11319","A",1
2952,1,103,187,0.2282384,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} (2+3 x)^{5/2}} \, dx","Integrate[Sqrt[3 + 5*x]/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)),x]","\frac{2 \left(\sqrt{2} \left(8015 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+169 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{\sqrt{5 x+3} \left(6084 x^3-21264 x^2+727 x+7965\right)}{(1-2 x)^{3/2} (3 x+2)^{3/2}}\right)}{79233}","-\frac{992 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{2401 \sqrt{33}}+\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{338 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{2401 \sqrt{33}}",1,"(2*((Sqrt[3 + 5*x]*(7965 + 727*x - 21264*x^2 + 6084*x^3))/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)) + Sqrt[2]*(169*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 8015*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/79233","A",1
2953,1,108,220,0.2365966,"\int \frac{\sqrt{3+5 x}}{(1-2 x)^{5/2} (2+3 x)^{7/2}} \, dx","Integrate[Sqrt[3 + 5*x]/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)),x]","\frac{2 \left(\sqrt{2} \left(95165 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+94684 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{\sqrt{5 x+3} \left(10225872 x^4+2723436 x^3-7133292 x^2-807691 x+1339677\right)}{(1-2 x)^{3/2} (3 x+2)^{5/2}}\right)}{2773155}","-\frac{2092 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{84035}+\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{189368 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{84035 \sqrt{33}}",1,"(2*((Sqrt[3 + 5*x]*(1339677 - 807691*x - 7133292*x^2 + 2723436*x^3 + 10225872*x^4))/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)) + Sqrt[2]*(94684*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 95165*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/2773155","A",1
2954,1,130,222,0.3358692,"\int \frac{(2+3 x)^{7/2} (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2),x]","-\frac{-6595505 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{3 x+2} \sqrt{5 x+3} \left(40500 x^4+198180 x^3+567906 x^2-2751916 x+1041609\right)+13094702 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{21000 (1-2 x)^{3/2}}","-\frac{722133 \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3500}+\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{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,"-1/21000*(10*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(1041609 - 2751916*x + 567906*x^2 + 198180*x^3 + 40500*x^4) + 13094702*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 6595505*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)","A",1
2955,1,125,191,0.3157213,"\int \frac{(2+3 x)^{5/2} (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2),x]","-\frac{-18970 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{3 x+2} \sqrt{5 x+3} \left(270 x^3+1344 x^2-8039 x+2976\right)+37663 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{300 (1-2 x)^{3/2}}","-\frac{2077}{50} \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"-1/300*(10*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(2976 - 8039*x + 1344*x^2 + 270*x^3) + 37663*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 18970*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)","A",1
2956,1,120,158,0.257841,"\int \frac{(2+3 x)^{3/2} (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2),x]","-\frac{-137 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+2 \sqrt{3 x+2} \sqrt{5 x+3} \left(30 x^2-302 x+105\right)+272 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{12 (1-2 x)^{3/2}}","-\frac{15}{2} \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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}-68 \sqrt{\frac{11}{3}} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"-1/12*(2*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(105 - 302*x + 30*x^2) + 272*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 137*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)","A",1
2957,1,115,127,0.1641193,"\int \frac{\sqrt{2+3 x} (3+5 x)^{3/2}}{(1-2 x)^{5/2}} \, dx","Integrate[(Sqrt[2 + 3*x]*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2),x]","-\frac{-70 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+2 \sqrt{3 x+2} \sqrt{5 x+3} (48-173 x)+139 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{42 (1-2 x)^{3/2}}","-\frac{23 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{7 \sqrt{33}}+\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{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,"-1/42*(2*(48 - 173*x)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] + 139*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 70*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)","A",1
2958,1,115,127,0.1999206,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} \sqrt{2+3 x}} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*Sqrt[2 + 3*x]),x]","\frac{35 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+2 \sqrt{3 x+2} \sqrt{5 x+3} (148 x+3)-74 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{294 (1-2 x)^{3/2}}","-\frac{13 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{49 \sqrt{33}}-\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{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,"(2*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(3 + 148*x) - 74*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 35*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(294*(1 - 2*x)^(3/2))","A",1
2959,1,100,158,0.1876512,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} (2+3 x)^{3/2}} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)),x]","\frac{-\sqrt{2} \left(140 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+19 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)-\frac{2 \sqrt{5 x+3} \left(114 x^2-170 x-213\right)}{(1-2 x)^{3/2} \sqrt{3 x+2}}}{1029}","\frac{106 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{343 \sqrt{33}}-\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{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,"((-2*Sqrt[3 + 5*x]*(-213 - 170*x + 114*x^2))/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]) - Sqrt[2]*(19*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 140*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/1029","A",1
2960,1,104,191,0.2188009,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} (2+3 x)^{5/2}} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)),x]","\frac{\sqrt{2} \left(3115 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-496 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)-\frac{2 \sqrt{5 x+3} \left(8928 x^3+762 x^2-4616 x-885\right)}{(1-2 x)^{3/2} (3 x+2)^{3/2}}}{7203}","-\frac{582 \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{2401}-\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{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,"((-2*Sqrt[3 + 5*x]*(-885 - 4616*x + 762*x^2 + 8928*x^3))/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)) + Sqrt[2]*(-496*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 3115*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/7203","A",1
2961,1,108,222,0.2699032,"\int \frac{(3+5 x)^{3/2}}{(1-2 x)^{5/2} (2+3 x)^{7/2}} \, dx","Integrate[(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)),x]","\frac{2 \left(\sqrt{2} \left(39620 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-1973 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{\sqrt{5 x+3} \left(-213084 x^4-356292 x^3+2199 x^2+158902 x+43881\right)}{(1-2 x)^{3/2} (3 x+2)^{5/2}}\right)}{252105}","-\frac{16732 \sqrt{\frac{3}{11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{84035}-\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{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,"(2*((Sqrt[3 + 5*x]*(43881 + 158902*x + 2199*x^2 - 356292*x^3 - 213084*x^4))/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)) + Sqrt[2]*(-1973*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 39620*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/252105","A",1
2962,1,135,253,0.3060003,"\int \frac{(2+3 x)^{7/2} (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2),x]","-\frac{-87969665 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+30 \sqrt{3 x+2} \sqrt{5 x+3} \left(94500 x^5+486900 x^4+1279350 x^3+2783146 x^2-12151171 x+4641769\right)+174654791 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{37800 (1-2 x)^{3/2}}","-\frac{1313411 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3150}+\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{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,"-1/37800*(30*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(4641769 - 12151171*x + 2783146*x^2 + 1279350*x^3 + 486900*x^4 + 94500*x^5) + 174654791*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 87969665*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)","A",1
2963,1,130,220,0.3019789,"\int \frac{(2+3 x)^{5/2} (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2),x]","-\frac{-421995 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{3 x+2} \sqrt{5 x+3} \left(2700 x^4+12960 x^3+36606 x^2-175958 x+66663\right)+837828 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{840 (1-2 x)^{3/2}}","-\frac{12601}{140} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{69819}{70} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"-1/840*(10*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(66663 - 175958*x + 36606*x^2 + 12960*x^3 + 2700*x^4) + 837828*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 421995*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)","A",1
2964,1,125,189,0.2910171,"\int \frac{(2+3 x)^{3/2} (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","Integrate[((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2),x]","-\frac{-6095 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{3 x+2} \sqrt{5 x+3} \left(90 x^3+438 x^2-2579 x+957\right)+12101 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{60 (1-2 x)^{3/2}}","-\frac{91}{5} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"-1/60*(10*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(957 - 2579*x + 438*x^2 + 90*x^3) + 12101*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 6095*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)","A",1
2965,1,120,160,0.1620357,"\int \frac{\sqrt{2+3 x} (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx","Integrate[(Sqrt[2 + 3*x]*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2),x]","-\frac{-4655 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+6 \sqrt{3 x+2} \sqrt{5 x+3} \left(350 x^2-3408 x+1193\right)+9242 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{252 (1-2 x)^{3/2}}","-\frac{139}{42} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"-1/252*(6*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(1193 - 3408*x + 350*x^2) + 9242*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 4655*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)","A",1
2966,1,115,127,0.164638,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} \sqrt{2+3 x}} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*Sqrt[2 + 3*x]),x]","-\frac{-805 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+22 \sqrt{3 x+2} \sqrt{5 x+3} (51-179 x)+1597 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{294 (1-2 x)^{3/2}}","-\frac{8}{49} \sqrt{33} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{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,"-1/294*(22*(51 - 179*x)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x] + 1597*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 805*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)","A",1
2967,1,102,158,0.1957387,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^{3/2}} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)),x]","\frac{-315 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{2 \sqrt{5 x+3} \left(5256 x^2+3445 x-72\right)}{(1-2 x)^{3/2} \sqrt{3 x+2}}+876 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{2058}","-\frac{17}{343} \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)+\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{146}{343} \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)",1,"((2*Sqrt[3 + 5*x]*(-72 + 3445*x + 5256*x^2))/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]) + 876*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 315*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/2058","A",1
2968,1,105,191,0.2233679,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^{5/2}} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)),x]","\frac{-\sqrt{2} \left(8015 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+169 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)-\frac{6 \sqrt{5 x+3} \left(1014 x^3-3544 x^2-9883 x-4675\right)}{(1-2 x)^{3/2} (3 x+2)^{3/2}}}{21609}","\frac{496 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{7203}+\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{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,"((-6*Sqrt[3 + 5*x]*(-4675 - 9883*x - 3544*x^2 + 1014*x^3))/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)) - Sqrt[2]*(169*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 8015*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/21609","A",1
2969,1,110,220,0.2530893,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^{7/2}} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)),x]","\frac{3 \sqrt{2} \left(51765 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-9206 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)-\frac{2 \sqrt{5 x+3} \left(1491372 x^4+1056186 x^3-718167 x^2-640441 x-88623\right)}{(1-2 x)^{3/2} (3 x+2)^{5/2}}}{252105}","-\frac{7738 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{84035}+\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{9206 \sqrt{33} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{84035}",1,"((-2*Sqrt[3 + 5*x]*(-88623 - 640441*x - 718167*x^2 + 1056186*x^3 + 1491372*x^4))/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)) + 3*Sqrt[2]*(-9206*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 51765*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/252105","A",1
2970,1,113,253,0.3236605,"\int \frac{(3+5 x)^{5/2}}{(1-2 x)^{5/2} (2+3 x)^{9/2}} \, dx","Integrate[(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(9/2)),x]","\frac{2 \left(\sqrt{2} \left(591115 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-49321 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{\sqrt{5 x+3} \left(-15980004 x^5-28748088 x^4-7681599 x^3+10746933 x^2+6524789 x+866085\right)}{(1-2 x)^{3/2} (3 x+2)^{7/2}}\right)}{2470629}","-\frac{65672 \sqrt{\frac{11}{3}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{823543}+\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{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,"(2*((Sqrt[3 + 5*x]*(866085 + 6524789*x + 10746933*x^2 - 7681599*x^3 - 28748088*x^4 - 15980004*x^5))/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)) + Sqrt[2]*(-49321*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 591115*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/2470629","A",1
2971,1,125,187,0.3380209,"\int \frac{(2+3 x)^{9/2}}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^(9/2)/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","-\frac{-22216880 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{3 x+2} \sqrt{5 x+3} \left(294030 x^3+1528956 x^2-9445541 x+3478434\right)+44109377 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{907500 (1-2 x)^{3/2}}","-\frac{663409 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{13750 \sqrt{33}}+\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{44109377 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{27500 \sqrt{33}}",1,"-1/907500*(10*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(3478434 - 9445541*x + 1528956*x^2 + 294030*x^3) + 44109377*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 22216880*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)","A",1
2972,1,120,156,0.2932944,"\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^(7/2)/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","-\frac{-158095 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+10 \sqrt{3 x+2} \sqrt{5 x+3} \left(6534 x^2-70234 x+24051\right)+313888 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{36300 (1-2 x)^{3/2}}","-\frac{4721 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{550 \sqrt{33}}+\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{78472 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{275 \sqrt{33}}",1,"-1/36300*(10*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(24051 - 70234*x + 6534*x^2) + 313888*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 158095*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)","A",1
2973,1,120,125,0.3258178,"\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^(5/2)/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","-\frac{2240 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{11-5 (1-2 x)}}{\sqrt{11}}\right),-\frac{33}{2}\right)-4451 E\left(\sin ^{-1}\left(\frac{\sqrt{11-5 (1-2 x)}}{\sqrt{11}}\right)|-\frac{33}{2}\right)}{1815 \sqrt{2}}-\frac{1}{2} \sqrt{11-5 (1-2 x)} \sqrt{7-3 (1-2 x)} \left(\frac{1127}{726 \sqrt{1-2 x}}-\frac{49}{66 (1-2 x)^{3/2}}\right)","-\frac{67 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{55 \sqrt{33}}+\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{4451 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{110 \sqrt{33}}",1,"-1/2*((-49/(66*(1 - 2*x)^(3/2)) + 1127/(726*Sqrt[1 - 2*x]))*Sqrt[11 - 5*(1 - 2*x)]*Sqrt[7 - 3*(1 - 2*x)]) - (-4451*EllipticE[ArcSin[Sqrt[11 - 5*(1 - 2*x)]/Sqrt[11]], -33/2] + 2240*EllipticF[ArcSin[Sqrt[11 - 5*(1 - 2*x)]/Sqrt[11]], -33/2])/(1815*Sqrt[2])","A",1
2974,1,115,125,0.2022964,"\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","Integrate[(2 + 3*x)^(3/2)/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","\frac{29 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+2 \sqrt{3 x+2} \sqrt{5 x+3} (124 x+15)-62 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{726 (1-2 x)^{3/2}}","-\frac{\operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{11 \sqrt{33}}-\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{31 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{11 \sqrt{33}}",1,"(2*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(15 + 124*x) - 62*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 29*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(726*(1 - 2*x)^(3/2))","A",1
2975,1,115,125,0.1758633,"\int \frac{\sqrt{2+3 x}}{(1-2 x)^{5/2} \sqrt{3+5 x}} \, dx","Integrate[Sqrt[2 + 3*x]/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]","-\frac{70 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+4 \sqrt{3 x+2} \sqrt{5 x+3} (37 x-57)-37 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{2541 (1-2 x)^{3/2}}","-\frac{2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{77 \sqrt{33}}+\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{37 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{77 \sqrt{33}}",1,"-1/2541*(4*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-57 + 37*x) - 37*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 70*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)","A",1
2976,1,115,125,0.2137728,"\int \frac{1}{(1-2 x)^{5/2} \sqrt{2+3 x} \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]),x]","-\frac{3605 \sqrt{2-4 x} (2 x-1) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+4 \sqrt{3 x+2} \sqrt{5 x+3} (272 x-213)-272 \sqrt{2-4 x} (2 x-1) E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{17787 (1-2 x)^{3/2}}","-\frac{202 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{539 \sqrt{33}}+\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{272 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{539 \sqrt{33}}",1,"-1/17787*(4*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-213 + 272*x) - 272*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 3605*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)","A",1
2977,1,98,156,0.1772273,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{3/2} \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x]),x]","\frac{2 \left(\sqrt{2} \left(7070 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+2797 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{\sqrt{5 x+3} \left(33564 x^2-39220 x+12297\right)}{(1-2 x)^{3/2} \sqrt{3 x+2}}\right)}{124509}","-\frac{1196 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3773 \sqrt{33}}+\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{5594 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3773 \sqrt{33}}",1,"(2*((Sqrt[3 + 5*x]*(12297 - 39220*x + 33564*x^2))/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]) + Sqrt[2]*(2797*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 7070*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/124509","A",1
2978,1,103,187,0.2362577,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{5/2} \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x]),x]","\frac{2 \left(\sqrt{2} \left(92318 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-17045 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{\sqrt{5 x+3} \left(3323448 x^3-1066908 x^2-1478206 x+597945\right)}{(1-2 x)^{3/2} (3 x+2)^{3/2}}\right)}{871563}","-\frac{9124 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{26411 \sqrt{33}}+\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{184636 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{26411 \sqrt{33}}",1,"(2*((Sqrt[3 + 5*x]*(597945 - 1478206*x - 1066908*x^2 + 3323448*x^3))/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)) + Sqrt[2]*(92318*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 17045*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/871563","A",1
2979,1,107,218,0.3824457,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{7/2} \sqrt{3+5 x}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)*Sqrt[3 + 5*x]),x]","\frac{-24493280 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{2 \sqrt{10 x+6} \left(1407356424 x^4+513206712 x^3-914077314 x^2-176797172 x+165071409\right)}{(1-2 x)^{3/2} (3 x+2)^{5/2}}+52124312 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{30504705 \sqrt{2}}","-\frac{837304 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{924385 \sqrt{33}}+\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{26062156 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{924385 \sqrt{33}}",1,"((2*Sqrt[6 + 10*x]*(165071409 - 176797172*x - 914077314*x^2 + 513206712*x^3 + 1407356424*x^4))/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)) + 52124312*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 24493280*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(30504705*Sqrt[2])","A",1
2980,1,107,218,0.3606717,"\int \frac{(2+3 x)^{11/2}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^(11/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{-759987865 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{5 \sqrt{6 x+4} \left(48514950 x^4+286777260 x^3-1463754851 x^2-376752444 x+356556921\right)}{(1-2 x)^{3/2} \sqrt{5 x+3}}+1508889271 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{24956250 \sqrt{2}}","-\frac{11346991 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{378125 \sqrt{33}}+\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{1508889271 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1512500 \sqrt{33}}",1,"((-5*Sqrt[4 + 6*x]*(356556921 - 376752444*x - 1463754851*x^2 + 286777260*x^3 + 48514950*x^4))/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]) + 1508889271*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 759987865*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(24956250*Sqrt[2])","A",1
2981,1,102,187,0.3283092,"\int \frac{(2+3 x)^{9/2}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^(9/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{-5366165 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{5 \sqrt{6 x+4} \left(1078110 x^3-11321446 x^2-3117099 x+2438391\right)}{(1-2 x)^{3/2} \sqrt{5 x+3}}+10655966 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{998250 \sqrt{2}}","-\frac{160297 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{30250 \sqrt{33}}+\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{5327983 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{30250 \sqrt{33}}",1,"((-5*Sqrt[4 + 6*x]*(2438391 - 3117099*x - 11321446*x^2 + 1078110*x^3))/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]) + 10655966*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 5366165*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(998250*Sqrt[2])","A",1
2982,1,97,156,0.3083937,"\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^(7/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{-74515 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{5 \sqrt{6 x+4} \left(189851 x^2+66174 x-28671\right)}{(1-2 x)^{3/2} \sqrt{5 x+3}}+148831 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{99825 \sqrt{2}}","-\frac{2252 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3025 \sqrt{33}}+\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{148831 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6050 \sqrt{33}}",1,"((5*Sqrt[4 + 6*x]*(-28671 + 66174*x + 189851*x^2))/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]) + 148831*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 74515*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(99825*Sqrt[2])","A",1
2983,1,102,156,0.1771495,"\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^(5/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{-595 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{10 \sqrt{3 x+2} \left(3896 x^2+3111 x+435\right)}{(1-2 x)^{3/2} \sqrt{5 x+3}}+1948 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{39930}","-\frac{41 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{605 \sqrt{33}}+\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{974 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{605 \sqrt{33}}",1,"((10*Sqrt[2 + 3*x]*(435 + 3111*x + 3896*x^2))/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]) + 1948*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 595*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/39930","A",1
2984,1,99,156,0.1684886,"\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[(2 + 3*x)^(3/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{\sqrt{2} \left(181 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-49 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)-\frac{2 \sqrt{3 x+2} \left(490 x^2-402 x-345\right)}{(1-2 x)^{3/2} \sqrt{5 x+3}}}{3993}","-\frac{8 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{121 \sqrt{33}}-\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{49 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{121 \sqrt{33}}",1,"((-2*Sqrt[2 + 3*x]*(-345 - 402*x + 490*x^2))/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]) + Sqrt[2]*(-49*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 181*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/3993","A",1
2985,1,99,156,0.1574532,"\int \frac{\sqrt{2+3 x}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[Sqrt[2 + 3*x]/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{\sqrt{2} \left(4025 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-494 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)-\frac{2 \sqrt{3 x+2} \left(4940 x^2-2586 x-789\right)}{(1-2 x)^{3/2} \sqrt{5 x+3}}}{27951}","-\frac{214 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{847 \sqrt{33}}-\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{494 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{847 \sqrt{33}}",1,"((-2*Sqrt[2 + 3*x]*(-789 - 2586*x + 4940*x^2))/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]) + Sqrt[2]*(-494*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 4025*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/27951","A",1
2986,1,98,156,0.1995564,"\int \frac{1}{(1-2 x)^{5/2} \sqrt{2+3 x} (3+5 x)^{3/2}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)),x]","\frac{2 \left(\sqrt{2} \left(10955 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-4157 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{\sqrt{3 x+2} \left(-83140 x^2+74076 x-14559\right)}{(1-2 x)^{3/2} \sqrt{5 x+3}}\right)}{195657}","-\frac{824 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{5929 \sqrt{33}}-\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{8314 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{5929 \sqrt{33}}",1,"(2*((Sqrt[2 + 3*x]*(-14559 + 74076*x - 83140*x^2))/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]) + Sqrt[2]*(-4157*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 10955*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/195657","A",1
2987,1,103,187,0.2557953,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)),x]","\frac{2 \left(\sqrt{2} \left(150115 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-237796 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{-14267760 x^3+5106644 x^2+5510400 x-2236533}{(1-2 x)^{3/2} \sqrt{3 x+2} \sqrt{5 x+3}}\right)}{1369599}","\frac{10628 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{41503 \sqrt{33}}-\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{475592 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{41503 \sqrt{33}}",1,"(2*((-2236533 + 5510400*x + 5106644*x^2 - 14267760*x^3)/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]) + Sqrt[2]*(-237796*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 150115*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/1369599","A",1
2988,1,109,218,0.2683718,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)),x]","\frac{2 \left(\frac{-2046483720 x^4-615527112 x^3+1285584962 x^2+198573504 x-215753865}{(1-2 x)^{3/2} (3 x+2)^{3/2} \sqrt{5 x+3}}-2 \sqrt{2} \left(5684677 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-2908255 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)\right)}{9587193}","\frac{673072 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{290521 \sqrt{33}}-\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{22738708 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{290521 \sqrt{33}}",1,"(2*((-215753865 + 198573504*x + 1285584962*x^2 - 615527112*x^3 - 2046483720*x^4)/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x]) - 2*Sqrt[2]*(5684677*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 2908255*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/9587193","A",1
2989,1,115,249,0.2586921,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)),x]","\frac{2 \left(-2 \sqrt{2} \left(1209831262 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-609979405 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)-\frac{1306617762960 x^5+1263428429256 x^4-559512908172 x^3-673871013766 x^2+53503915182 x+91855922241}{(1-2 x)^{3/2} (3 x+2)^{5/2} \sqrt{5 x+3}}\right)}{335551755}","\frac{145418632 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{10168235 \sqrt{33}}-\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{4839325048 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{10168235 \sqrt{33}}",1,"(2*(-((91855922241 + 53503915182*x - 673871013766*x^2 - 559512908172*x^3 + 1263428429256*x^4 + 1306617762960*x^5)/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x])) - 2*Sqrt[2]*(1209831262*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 609979405*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/335551755","A",1
2990,1,117,249,0.3840276,"\int \frac{(2+3 x)^{13/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^(13/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{-25989595870 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{10 \sqrt{3 x+2} \left(8004966750 x^5+53010668700 x^4-222254370925 x^3-215557803774 x^2+21979664649 x+36533948644\right)}{(1-2 x)^{3/2} (5 x+3)^{3/2}}+51601293223 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{2745187500}","-\frac{776112041 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{41593750 \sqrt{33}}+\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{51601293223 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{83187500 \sqrt{33}}",1,"((-10*Sqrt[2 + 3*x]*(36533948644 + 21979664649*x - 215557803774*x^2 - 222254370925*x^3 + 53010668700*x^4 + 8004966750*x^5))/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + 51601293223*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 25989595870*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/2745187500","A",1
2991,1,112,218,0.3474016,"\int \frac{(2+3 x)^{11/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^(11/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{-181999265 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-\frac{10 \sqrt{3 x+2} \left(177888150 x^4-1825153850 x^3-1696384053 x^2+89252928 x+246962693\right)}{(1-2 x)^{3/2} (5 x+3)^{3/2}}+361589456 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{109807500}","-\frac{5442127 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1663750 \sqrt{33}}+\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{90397364 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{831875 \sqrt{33}}",1,"((-10*Sqrt[2 + 3*x]*(246962693 + 89252928*x - 1696384053*x^2 - 1825153850*x^3 + 177888150*x^4))/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + 361589456*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 181999265*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/109807500","A",1
2992,1,107,187,0.3358424,"\int \frac{(2+3 x)^{9/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^(9/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{-2457910 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{10 \sqrt{3 x+2} \left(31924075 x^3+30619782 x^2+2244393 x-2780992\right)}{(1-2 x)^{3/2} (5 x+3)^{3/2}}+4971289 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{10980750}","-\frac{76163 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{166375 \sqrt{33}}+\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{4971289 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{332750 \sqrt{33}}",1,"((10*Sqrt[2 + 3*x]*(-2780992 + 2244393*x + 30619782*x^2 + 31924075*x^3))/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + 4971289*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 2457910*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/10980750","A",1
2993,1,107,187,0.2342871,"\int \frac{(2+3 x)^{7/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^(7/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{1085 \sqrt{2} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+\frac{10 \sqrt{3 x+2} \left(598660 x^3+905823 x^2+423882 x+57437\right)}{(1-2 x)^{3/2} (5 x+3)^{3/2}}+59866 \sqrt{2} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)}{2196150}","-\frac{1847 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{33275 \sqrt{33}}+\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{29933 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{33275 \sqrt{33}}",1,"((10*Sqrt[2 + 3*x]*(57437 + 423882*x + 905823*x^2 + 598660*x^3))/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + 59866*Sqrt[2]*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 1085*Sqrt[2]*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/2196150","A",1
2994,1,104,187,0.2167093,"\int \frac{(2+3 x)^{5/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^(5/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{\sqrt{2} \left(10360 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-2209 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)-\frac{10 \sqrt{3 x+2} \left(22090 x^3-3402 x^2-22059 x-7186\right)}{(1-2 x)^{3/2} (5 x+3)^{3/2}}}{219615}","-\frac{494 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{6655 \sqrt{33}}+\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{2209 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{6655 \sqrt{33}}",1,"((-10*Sqrt[2 + 3*x]*(-7186 - 22059*x - 3402*x^2 + 22090*x^3))/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + Sqrt[2]*(-2209*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 10360*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/219615","A",1
2995,1,104,187,0.1960924,"\int \frac{(2+3 x)^{3/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[(2 + 3*x)^(3/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{\sqrt{2} \left(4387 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-592 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)-\frac{2 \sqrt{3 x+2} \left(29600 x^3+810 x^2-13572 x-1775\right)}{(1-2 x)^{3/2} (5 x+3)^{3/2}}}{43923}","-\frac{230 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{1331 \sqrt{33}}-\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{592 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{1331 \sqrt{33}}",1,"((-2*Sqrt[2 + 3*x]*(-1775 - 13572*x + 810*x^2 + 29600*x^3))/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + Sqrt[2]*(-592*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 4387*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/43923","A",1
2996,1,103,187,0.2170699,"\int \frac{\sqrt{2+3 x}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[Sqrt[2 + 3*x]/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{2 \left(\sqrt{2} \left(10360 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)-2209 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{\sqrt{3 x+2} \left(-220900 x^3+34020 x^2+88821 x-15986\right)}{(1-2 x)^{3/2} (5 x+3)^{3/2}}\right)}{307461}","-\frac{988 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{9317 \sqrt{33}}-\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{4418 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{9317 \sqrt{33}}",1,"(2*((Sqrt[2 + 3*x]*(-15986 + 88821*x + 34020*x^2 - 220900*x^3))/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + Sqrt[2]*(-2209*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 10360*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/307461","A",1
2997,1,103,187,0.1949824,"\int \frac{1}{(1-2 x)^{5/2} \sqrt{2+3 x} (3+5 x)^{5/2}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*Sqrt[2 + 3*x]*(3 + 5*x)^(5/2)),x]","\frac{2 \left(\sqrt{2} \left(1085 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)+59866 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)\right)+\frac{\sqrt{3 x+2} \left(5986600 x^3-2800980 x^2-1822554 x+881831\right)}{(1-2 x)^{3/2} (5 x+3)^{3/2}}\right)}{2152227}","-\frac{7388 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{65219 \sqrt{33}}+\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{119732 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{65219 \sqrt{33}}",1,"(2*((Sqrt[2 + 3*x]*(881831 - 1822554*x - 2800980*x^2 + 5986600*x^3))/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + Sqrt[2]*(59866*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 1085*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/2152227","A",1
2998,1,109,218,0.2697291,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)),x]","\frac{2 \left(2 \sqrt{2} \left(4971289 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-2457910 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{2982773400 x^4+694871080 x^3-1802210526 x^2-211488180 x+283144937}{(1-2 x)^{3/2} \sqrt{3 x+2} (5 x+3)^{3/2}}\right)}{15065589}","-\frac{609304 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{456533 \sqrt{33}}+\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{19885156 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{456533 \sqrt{33}}",1,"(2*((283144937 - 211488180*x - 1802210526*x^2 + 694871080*x^3 + 2982773400*x^4)/((1 - 2*x)^(3/2)*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)) + 2*Sqrt[2]*(4971289*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 2457910*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/15065589","A",1
2999,1,114,249,0.2974899,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)),x]","\frac{2 \left(2 \sqrt{2} \left(361589456 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-181999265 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{650861020800 x^5+585919463160 x^4-291775464272 x^3-308398535118 x^2+30866656614 x+41179778225}{(1-2 x)^{3/2} (3 x+2)^{3/2} (5 x+3)^{3/2}}\right)}{105459123}","-\frac{43537016 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{3195731 \sqrt{33}}+\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{1446357824 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{3195731 \sqrt{33}}",1,"(2*((41179778225 + 30866656614*x - 308398535118*x^2 - 291775464272*x^3 + 585919463160*x^4 + 650861020800*x^5)/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + 2*Sqrt[2]*(361589456*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 181999265*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/105459123","A",1
3000,1,119,280,0.4391628,"\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx","Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)),x]","\frac{2 \left(4 \sqrt{2} \left(51601293223 E\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right)|-\frac{33}{2}\right)-25989595870 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right),-\frac{33}{2}\right)\right)+\frac{557293966808400 x^6+873229924799280 x^5+84649478011164 x^4-430611138612568 x^3-149619576926754 x^2+52875828155808 x+23506658680609}{(1-2 x)^{3/2} (3 x+2)^{5/2} (5 x+3)^{3/2}}\right)}{3691069305}","-\frac{12417792656 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right),\frac{35}{33}\right)}{111850585 \sqrt{33}}+\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{412810345784 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right)|\frac{35}{33}\right)}{111850585 \sqrt{33}}",1,"(2*((23506658680609 + 52875828155808*x - 149619576926754*x^2 - 430611138612568*x^3 + 84649478011164*x^4 + 873229924799280*x^5 + 557293966808400*x^6)/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + 4*Sqrt[2]*(51601293223*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 25989595870*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/3691069305","A",1
3001,1,179,571,0.3424362,"\int \sqrt[3]{a+b x} (c+d x)^{2/3} (e+f x)^2 \, dx","Integrate[(a + b*x)^(1/3)*(c + d*x)^(2/3)*(e + f*x)^2,x]","\frac{(a+b x)^{4/3} (c+d x)^{2/3} \left(\frac{\left(10 a^2 d^2 f^2+10 a b d f (c f-3 d e)+b^2 \left(7 c^2 f^2-24 c d e f+27 d^2 e^2\right)\right) \, _2F_1\left(-\frac{2}{3},\frac{4}{3};\frac{7}{3};\frac{d (a+b x)}{a d-b c}\right)}{b^2 d \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3}}+\frac{f (c+d x) (-8 a d f-7 b c f+15 b d e)}{b d}+9 f (c+d x) (e+f x)\right)}{36 b d}","\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,"((a + b*x)^(4/3)*(c + d*x)^(2/3)*((f*(15*b*d*e - 7*b*c*f - 8*a*d*f)*(c + d*x))/(b*d) + 9*f*(c + d*x)*(e + f*x) + ((10*a^2*d^2*f^2 + 10*a*b*d*f*(-3*d*e + c*f) + b^2*(27*d^2*e^2 - 24*c*d*e*f + 7*c^2*f^2))*Hypergeometric2F1[-2/3, 4/3, 7/3, (d*(a + b*x))/(-(b*c) + a*d)])/(b^2*d*((b*(c + d*x))/(b*c - a*d))^(2/3))))/(36*b*d)","C",1
3002,1,103,331,0.2120913,"\int \sqrt[3]{a+b x} (c+d x)^{2/3} (e+f x) \, dx","Integrate[(a + b*x)^(1/3)*(c + d*x)^(2/3)*(e + f*x),x]","\frac{(a+b x)^{4/3} (c+d x)^{2/3} \left(\frac{(-5 a d f-4 b c f+9 b d e) \, _2F_1\left(-\frac{2}{3},\frac{4}{3};\frac{7}{3};\frac{d (a+b x)}{a d-b c}\right)}{\left(\frac{b (c+d x)}{b c-a d}\right)^{2/3}}+4 b f (c+d x)\right)}{12 b^2 d}","\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,"((a + b*x)^(4/3)*(c + d*x)^(2/3)*(4*b*f*(c + d*x) + ((9*b*d*e - 4*b*c*f - 5*a*d*f)*Hypergeometric2F1[-2/3, 4/3, 7/3, (d*(a + b*x))/(-(b*c) + a*d)])/((b*(c + d*x))/(b*c - a*d))^(2/3)))/(12*b^2*d)","C",1
3003,1,73,219,0.0394533,"\int \sqrt[3]{a+b x} (c+d x)^{2/3} \, dx","Integrate[(a + b*x)^(1/3)*(c + d*x)^(2/3),x]","\frac{3 (a+b x)^{4/3} (c+d x)^{2/3} \, _2F_1\left(-\frac{2}{3},\frac{4}{3};\frac{7}{3};\frac{d (a+b x)}{a d-b c}\right)}{4 b \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3}}","\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,"(3*(a + b*x)^(4/3)*(c + d*x)^(2/3)*Hypergeometric2F1[-2/3, 4/3, 7/3, (d*(a + b*x))/(-(b*c) + a*d)])/(4*b*((b*(c + d*x))/(b*c - a*d))^(2/3))","C",1
3004,1,194,409,0.2075842,"\int \frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{e+f x} \, dx","Integrate[((a + b*x)^(1/3)*(c + d*x)^(2/3))/(e + f*x),x]","\frac{3 \sqrt[3]{a+b x} \left(-\frac{d (b e-a f) \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{d (a+b x)}{a d-b c}\right)}{b f}+\frac{(d e-c f) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{f}+\frac{(c+d x) \, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};\frac{d (a+b x)}{a d-b c}\right)}{\left(\frac{b (c+d x)}{b c-a d}\right)^{2/3}}\right)}{f \sqrt[3]{c+d x}}","\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,"(3*(a + b*x)^(1/3)*(((c + d*x)*Hypergeometric2F1[-2/3, 1/3, 4/3, (d*(a + b*x))/(-(b*c) + a*d)])/((b*(c + d*x))/(b*c - a*d))^(2/3) - (d*(b*e - a*f)*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, (d*(a + b*x))/(-(b*c) + a*d)])/(b*f) + ((d*e - c*f)*Hypergeometric2F1[1/3, 1, 4/3, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/f))/(f*(c + d*x)^(1/3))","C",1
3005,1,504,417,2.7842542,"\int \frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{(e+f x)^2} \, dx","Integrate[((a + b*x)^(1/3)*(c + d*x)^(2/3))/(e + f*x)^2,x]","\frac{(c+d x)^{2/3} \left(\left(\frac{d (a+b x)}{c+d x}\right)^{2/3} \left(3 \sqrt[3]{b} \left(\log \left(\sqrt[3]{b} \sqrt[3]{\frac{d (a+b x)}{c+d x}}+\left(\frac{d (a+b x)}{c+d x}\right)^{2/3}+b^{2/3}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{\frac{d (a+b x)}{c+d x}}}{\sqrt[3]{b}}+1}{\sqrt{3}}\right)\right)+\frac{2 (-2 a d f-b c f+3 b d e) \log \left(\sqrt[3]{d} \sqrt[3]{b e-a f}-\sqrt[3]{d e-c f} \sqrt[3]{\frac{d (a+b x)}{c+d x}}\right)}{d^{2/3} (b e-a f)^{2/3} \sqrt[3]{d e-c f}}-\frac{(-2 a d f-b c f+3 b d e) \left(\log \left(\sqrt[3]{d} \sqrt[3]{b e-a f} \sqrt[3]{d e-c f} \sqrt[3]{\frac{d (a+b x)}{c+d x}}+(d e-c f)^{2/3} \left(\frac{d (a+b x)}{c+d x}\right)^{2/3}+d^{2/3} (b e-a f)^{2/3}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{d e-c f} \sqrt[3]{\frac{d (a+b x)}{c+d x}}}{\sqrt[3]{d} \sqrt[3]{b e-a f}}+1}{\sqrt{3}}\right)\right)}{d^{2/3} (b e-a f)^{2/3} \sqrt[3]{d e-c f}}-6 \sqrt[3]{b} \log \left(\sqrt[3]{b}-\sqrt[3]{\frac{d (a+b x)}{c+d x}}\right)\right)-\frac{6 f (a+b x)}{e+f x}\right)}{6 f^2 (a+b x)^{2/3}}","-\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,"((c + d*x)^(2/3)*((-6*f*(a + b*x))/(e + f*x) + ((d*(a + b*x))/(c + d*x))^(2/3)*(-6*b^(1/3)*Log[b^(1/3) - ((d*(a + b*x))/(c + d*x))^(1/3)] + (2*(3*b*d*e - b*c*f - 2*a*d*f)*Log[d^(1/3)*(b*e - a*f)^(1/3) - (d*e - c*f)^(1/3)*((d*(a + b*x))/(c + d*x))^(1/3)])/(d^(2/3)*(b*e - a*f)^(2/3)*(d*e - c*f)^(1/3)) + 3*b^(1/3)*(2*Sqrt[3]*ArcTan[(1 + (2*((d*(a + b*x))/(c + d*x))^(1/3))/b^(1/3))/Sqrt[3]] + Log[b^(2/3) + b^(1/3)*((d*(a + b*x))/(c + d*x))^(1/3) + ((d*(a + b*x))/(c + d*x))^(2/3)]) - ((3*b*d*e - b*c*f - 2*a*d*f)*(2*Sqrt[3]*ArcTan[(1 + (2*(d*e - c*f)^(1/3)*((d*(a + b*x))/(c + d*x))^(1/3))/(d^(1/3)*(b*e - a*f)^(1/3)))/Sqrt[3]] + Log[d^(2/3)*(b*e - a*f)^(2/3) + d^(1/3)*(b*e - a*f)^(1/3)*(d*e - c*f)^(1/3)*((d*(a + b*x))/(c + d*x))^(1/3) + (d*e - c*f)^(2/3)*((d*(a + b*x))/(c + d*x))^(2/3)]))/(d^(2/3)*(b*e - a*f)^(2/3)*(d*e - c*f)^(1/3)))))/(6*f^2*(a + b*x)^(2/3))","A",1
3006,1,142,325,0.1538304,"\int \frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{(e+f x)^3} \, dx","Integrate[((a + b*x)^(1/3)*(c + d*x)^(2/3))/(e + f*x)^3,x]","\frac{\sqrt[3]{a+b x} \left(\frac{(e+f x) (b c-a d) \left(2 (e+f x) (b c-a d) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)+(c+d x) (b e-a f)\right)}{(b e-a f)^2}-3 (c+d x)^2\right)}{6 \sqrt[3]{c+d x} (e+f x)^2 (c f-d e)}","-\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,"((a + b*x)^(1/3)*(-3*(c + d*x)^2 + ((b*c - a*d)*(e + f*x)*((b*e - a*f)*(c + d*x) + 2*(b*c - a*d)*(e + f*x)*Hypergeometric2F1[1/3, 1, 4/3, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]))/(b*e - a*f)^2))/(6*(-(d*e) + c*f)*(c + d*x)^(1/3)*(e + f*x)^2)","C",1
3007,1,214,465,0.4671983,"\int \frac{\sqrt[3]{a+b x} (c+d x)^{2/3}}{(e+f x)^4} \, dx","Integrate[((a + b*x)^(1/3)*(c + d*x)^(2/3))/(e + f*x)^4,x]","\frac{\sqrt[3]{a+b x} \left(\frac{(e+f x) (-4 a d f-5 b c f+9 b d e) \left(3 (c+d x)^2 (b e-a f)^2-(e+f x) (b c-a d) \left(2 (e+f x) (b c-a d) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)+(c+d x) (b e-a f)\right)\right)}{3 (b e-a f)^2 (d e-c f)}-6 f (a+b x) (c+d x)^2\right)}{18 \sqrt[3]{c+d x} (e+f x)^3 (b e-a f) (d e-c f)}","-\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,"((a + b*x)^(1/3)*(-6*f*(a + b*x)*(c + d*x)^2 + ((9*b*d*e - 5*b*c*f - 4*a*d*f)*(e + f*x)*(3*(b*e - a*f)^2*(c + d*x)^2 - (b*c - a*d)*(e + f*x)*((b*e - a*f)*(c + d*x) + 2*(b*c - a*d)*(e + f*x)*Hypergeometric2F1[1/3, 1, 4/3, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])))/(3*(b*e - a*f)^2*(d*e - c*f))))/(18*(b*e - a*f)*(d*e - c*f)*(c + d*x)^(1/3)*(e + f*x)^3)","C",1
3008,1,175,475,0.2750294,"\int \frac{\sqrt[3]{a+b x} (e+f x)^2}{\sqrt[3]{c+d x}} \, dx","Integrate[((a + b*x)^(1/3)*(e + f*x)^2)/(c + d*x)^(1/3),x]","\frac{(a+b x)^{4/3} \left(2 \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \left(5 a^2 d^2 f^2+2 a b d f (4 c f-9 d e)+b^2 \left(14 c^2 f^2-36 c d e f+27 d^2 e^2\right)\right) \, _2F_1\left(\frac{1}{3},\frac{4}{3};\frac{7}{3};\frac{d (a+b x)}{a d-b c}\right)-4 b f (c+d x) (5 a d f+7 b c f-12 b d e)+24 b^2 d f (c+d x) (e+f x)\right)}{72 b^3 d^2 \sqrt[3]{c+d x}}","\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,"((a + b*x)^(4/3)*(-4*b*f*(-12*b*d*e + 7*b*c*f + 5*a*d*f)*(c + d*x) + 24*b^2*d*f*(c + d*x)*(e + f*x) + 2*(5*a^2*d^2*f^2 + 2*a*b*d*f*(-9*d*e + 4*c*f) + b^2*(27*d^2*e^2 - 36*c*d*e*f + 14*c^2*f^2))*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[1/3, 4/3, 7/3, (d*(a + b*x))/(-(b*c) + a*d)]))/(72*b^3*d^2*(c + d*x)^(1/3))","C",1
3009,1,103,273,0.169248,"\int \frac{\sqrt[3]{a+b x} (e+f x)}{\sqrt[3]{c+d x}} \, dx","Integrate[((a + b*x)^(1/3)*(e + f*x))/(c + d*x)^(1/3),x]","\frac{(a+b x)^{4/3} \left(\sqrt[3]{\frac{b (c+d x)}{b c-a d}} (-a d f-2 b c f+3 b d e) \, _2F_1\left(\frac{1}{3},\frac{4}{3};\frac{7}{3};\frac{d (a+b x)}{a d-b c}\right)+2 b f (c+d x)\right)}{4 b^2 d \sqrt[3]{c+d x}}","\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,"((a + b*x)^(4/3)*(2*b*f*(c + d*x) + (3*b*d*e - 2*b*c*f - a*d*f)*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[1/3, 4/3, 7/3, (d*(a + b*x))/(-(b*c) + a*d)]))/(4*b^2*d*(c + d*x)^(1/3))","C",1
3010,1,73,171,0.0319906,"\int \frac{\sqrt[3]{a+b x}}{\sqrt[3]{c+d x}} \, dx","Integrate[(a + b*x)^(1/3)/(c + d*x)^(1/3),x]","\frac{3 (a+b x)^{4/3} \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{3},\frac{4}{3};\frac{7}{3};\frac{d (a+b x)}{a d-b c}\right)}{4 b \sqrt[3]{c+d x}}","\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,"(3*(a + b*x)^(4/3)*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[1/3, 4/3, 7/3, (d*(a + b*x))/(-(b*c) + a*d)])/(4*b*(c + d*x)^(1/3))","C",1
3011,1,114,339,0.0948295,"\int \frac{\sqrt[3]{a+b x}}{\sqrt[3]{c+d x} (e+f x)} \, dx","Integrate[(a + b*x)^(1/3)/((c + d*x)^(1/3)*(e + f*x)),x]","\frac{3 \sqrt[3]{a+b x} \left(\sqrt[3]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};\frac{d (a+b x)}{a d-b c}\right)-\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)\right)}{f \sqrt[3]{c+d x}}","-\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,"(3*(a + b*x)^(1/3)*(((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, (d*(a + b*x))/(-(b*c) + a*d)] - Hypergeometric2F1[1/3, 1, 4/3, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]))/(f*(c + d*x)^(1/3))","C",1
3012,1,115,256,0.0618187,"\int \frac{\sqrt[3]{a+b x}}{\sqrt[3]{c+d x} (e+f x)^2} \, dx","Integrate[(a + b*x)^(1/3)/((c + d*x)^(1/3)*(e + f*x)^2),x]","\frac{\sqrt[3]{a+b x} \left((c+d x) (b e-a f)-(e+f x) (b c-a d) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)\right)}{\sqrt[3]{c+d x} (e+f x) (b e-a f) (d e-c f)}","\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,"((a + b*x)^(1/3)*((b*e - a*f)*(c + d*x) - (b*c - a*d)*(e + f*x)*Hypergeometric2F1[1/3, 1, 4/3, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]))/((b*e - a*f)*(d*e - c*f)*(c + d*x)^(1/3)*(e + f*x))","C",1
3013,1,175,386,0.2641136,"\int \frac{\sqrt[3]{a+b x}}{\sqrt[3]{c+d x} (e+f x)^3} \, dx","Integrate[(a + b*x)^(1/3)/((c + d*x)^(1/3)*(e + f*x)^3),x]","\frac{\sqrt[3]{a+b x} \left(\frac{2 (e+f x) (-2 a d f-b c f+3 b d e) \left((c+d x) (b e-a f)-(e+f x) (b c-a d) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)\right)}{(b e-a f) (d e-c f)}-3 f (a+b x) (c+d x)\right)}{6 \sqrt[3]{c+d x} (e+f x)^2 (b e-a f) (d e-c f)}","-\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,"((a + b*x)^(1/3)*(-3*f*(a + b*x)*(c + d*x) + (2*(3*b*d*e - b*c*f - 2*a*d*f)*(e + f*x)*((b*e - a*f)*(c + d*x) - (b*c - a*d)*(e + f*x)*Hypergeometric2F1[1/3, 1, 4/3, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]))/((b*e - a*f)*(d*e - c*f))))/(6*(b*e - a*f)*(d*e - c*f)*(c + d*x)^(1/3)*(e + f*x)^2)","C",1
3014,1,265,591,0.6743753,"\int \frac{\sqrt[3]{a+b x}}{\sqrt[3]{c+d x} (e+f x)^4} \, dx","Integrate[(a + b*x)^(1/3)/((c + d*x)^(1/3)*(e + f*x)^4),x]","\frac{\sqrt[3]{a+b x} \left(\frac{2 (e+f x)^2 \left(14 a^2 d^2 f^2+4 a b d f (2 c f-9 d e)+b^2 \left(5 c^2 f^2-18 c d e f+27 d^2 e^2\right)\right) \left((c+d x) (b e-a f)-(e+f x) (b c-a d) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)\right)}{(b e-a f) (d e-c f)}+3 f (a+b x) (c+d x) (e+f x) (7 a d f+5 b c f-12 b d e)-18 f (a+b x) (c+d x) (a f-b e) (c f-d e)\right)}{54 \sqrt[3]{c+d x} (e+f x)^3 (b e-a f)^2 (d e-c f)^2}","\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,"((a + b*x)^(1/3)*(-18*f*(-(b*e) + a*f)*(-(d*e) + c*f)*(a + b*x)*(c + d*x) + 3*f*(-12*b*d*e + 5*b*c*f + 7*a*d*f)*(a + b*x)*(c + d*x)*(e + f*x) + (2*(14*a^2*d^2*f^2 + 4*a*b*d*f*(-9*d*e + 2*c*f) + b^2*(27*d^2*e^2 - 18*c*d*e*f + 5*c^2*f^2))*(e + f*x)^2*((b*e - a*f)*(c + d*x) - (b*c - a*d)*(e + f*x)*Hypergeometric2F1[1/3, 1, 4/3, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]))/((b*e - a*f)*(d*e - c*f))))/(54*(b*e - a*f)^2*(d*e - c*f)^2*(c + d*x)^(1/3)*(e + f*x)^3)","C",1
3015,1,291,587,0.790504,"\int \frac{(e+f x)^3}{\sqrt[3]{a+b x} (c+d x)^{2/3}} \, dx","Integrate[(e + f*x)^3/((a + b*x)^(1/3)*(c + d*x)^(2/3)),x]","\frac{(a+b x)^{2/3} \left(\frac{f^2 (c+d x)^2 (-7 a d f-8 b c f+15 b d e) \, _2F_1\left(-\frac{4}{3},\frac{2}{3};\frac{5}{3};\frac{d (a+b x)}{a d-b c}\right)}{b d^2 \left(\frac{b (c+d x)}{b c-a d}\right)^{4/3}}+\frac{(d e-c f)^2 \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} (-a d f-8 b c f+9 b d e) \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{d (a+b x)}{a d-b c}\right)}{b d^2}+\frac{8 f (c+d x) (c f-d e) (a d f+2 b c f-3 b d e) \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};\frac{d (a+b x)}{a d-b c}\right)}{b d^2 \sqrt[3]{\frac{b (c+d x)}{b c-a d}}}+2 f (c+d x) (e+f x)^2\right)}{6 b d (c+d x)^{2/3}}","\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,"((a + b*x)^(2/3)*(2*f*(c + d*x)*(e + f*x)^2 + (f^2*(15*b*d*e - 8*b*c*f - 7*a*d*f)*(c + d*x)^2*Hypergeometric2F1[-4/3, 2/3, 5/3, (d*(a + b*x))/(-(b*c) + a*d)])/(b*d^2*((b*(c + d*x))/(b*c - a*d))^(4/3)) + (8*f*(-(d*e) + c*f)*(-3*b*d*e + 2*b*c*f + a*d*f)*(c + d*x)*Hypergeometric2F1[-1/3, 2/3, 5/3, (d*(a + b*x))/(-(b*c) + a*d)])/(b*d^2*((b*(c + d*x))/(b*c - a*d))^(1/3)) + ((d*e - c*f)^2*(9*b*d*e - 8*b*c*f - a*d*f)*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, (d*(a + b*x))/(-(b*c) + a*d)])/(b*d^2)))/(6*b*d*(c + d*x)^(2/3))","C",1
3016,1,174,369,0.152466,"\int \frac{(e+f x)^2}{\sqrt[3]{a+b x} (c+d x)^{2/3}} \, dx","Integrate[(e + f*x)^2/((a + b*x)^(1/3)*(c + d*x)^(2/3)),x]","\frac{(a+b x)^{2/3} \left(2 \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} \left(2 a^2 d^2 f^2+2 a b d f (c f-3 d e)+b^2 \left(5 c^2 f^2-12 c d e f+9 d^2 e^2\right)\right) \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{d (a+b x)}{a d-b c}\right)-2 b f (c+d x) (4 a d f+5 b c f-9 b d e)+6 b^2 d f (c+d x) (e+f x)\right)}{12 b^3 d^2 (c+d x)^{2/3}}","-\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,"((a + b*x)^(2/3)*(-2*b*f*(-9*b*d*e + 5*b*c*f + 4*a*d*f)*(c + d*x) + 6*b^2*d*f*(c + d*x)*(e + f*x) + 2*(2*a^2*d^2*f^2 + 2*a*b*d*f*(-3*d*e + c*f) + b^2*(9*d^2*e^2 - 12*c*d*e*f + 5*c^2*f^2))*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, (d*(a + b*x))/(-(b*c) + a*d)]))/(12*b^3*d^2*(c + d*x)^(2/3))","C",1
3017,1,103,200,0.1196081,"\int \frac{e+f x}{\sqrt[3]{a+b x} (c+d x)^{2/3}} \, dx","Integrate[(e + f*x)/((a + b*x)^(1/3)*(c + d*x)^(2/3)),x]","\frac{(a+b x)^{2/3} \left(\left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} (-a d f-2 b c f+3 b d e) \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{d (a+b x)}{a d-b c}\right)+2 b f (c+d x)\right)}{2 b^2 d (c+d x)^{2/3}}","-\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,"((a + b*x)^(2/3)*(2*b*f*(c + d*x) + (3*b*d*e - 2*b*c*f - a*d*f)*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, (d*(a + b*x))/(-(b*c) + a*d)]))/(2*b^2*d*(c + d*x)^(2/3))","C",1
3018,1,73,126,0.0287436,"\int \frac{1}{\sqrt[3]{a+b x} (c+d x)^{2/3}} \, dx","Integrate[1/((a + b*x)^(1/3)*(c + d*x)^(2/3)),x]","\frac{3 (a+b x)^{2/3} \left(\frac{b (c+d x)}{b c-a d}\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{d (a+b x)}{a d-b c}\right)}{2 b (c+d x)^{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,"(3*(a + b*x)^(2/3)*((b*(c + d*x))/(b*c - a*d))^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, (d*(a + b*x))/(-(b*c) + a*d)])/(2*b*(c + d*x)^(2/3))","C",1
3019,1,71,197,0.0188588,"\int \frac{1}{\sqrt[3]{a+b x} (c+d x)^{2/3} (e+f x)} \, dx","Integrate[1/((a + b*x)^(1/3)*(c + d*x)^(2/3)*(e + f*x)),x]","\frac{3 (a+b x)^{2/3} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{2 (c+d x)^{2/3} (b e-a f)}","\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,"(3*(a + b*x)^(2/3)*Hypergeometric2F1[2/3, 1, 5/3, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/(2*(b*e - a*f)*(c + d*x)^(2/3))","C",1
3020,1,124,293,0.0515858,"\int \frac{1}{\sqrt[3]{a+b x} (c+d x)^{2/3} (e+f x)^2} \, dx","Integrate[1/((a + b*x)^(1/3)*(c + d*x)^(2/3)*(e + f*x)^2),x]","\frac{(a+b x)^{2/3} \left(\frac{(-2 a d f-b c f+3 b d e) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{b e-a f}-\frac{2 f (c+d x)}{e+f x}\right)}{2 (c+d x)^{2/3} (b e-a f) (d e-c f)}","-\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,"((a + b*x)^(2/3)*((-2*f*(c + d*x))/(e + f*x) + ((3*b*d*e - b*c*f - 2*a*d*f)*Hypergeometric2F1[2/3, 1, 5/3, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/(b*e - a*f)))/(2*(b*e - a*f)*(d*e - c*f)*(c + d*x)^(2/3))","C",1
3021,1,221,477,0.2475133,"\int \frac{1}{\sqrt[3]{a+b x} (c+d x)^{2/3} (e+f x)^3} \, dx","Integrate[1/((a + b*x)^(1/3)*(c + d*x)^(2/3)*(e + f*x)^3),x]","\frac{(a+b x)^{2/3} \left(\frac{\left(5 a^2 d^2 f^2+2 a b d f (c f-6 d e)+b^2 \left(2 c^2 f^2-6 c d e f+9 d^2 e^2\right)\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{(b e-a f)^2 (d e-c f)}+\frac{f (c+d x) (5 a d f+4 b c f-9 b d e)}{(e+f x) (b e-a f) (d e-c f)}-\frac{3 f (c+d x)}{(e+f x)^2}\right)}{6 (c+d x)^{2/3} (b e-a f) (d e-c f)}","\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,"((a + b*x)^(2/3)*((-3*f*(c + d*x))/(e + f*x)^2 + (f*(-9*b*d*e + 4*b*c*f + 5*a*d*f)*(c + d*x))/((b*e - a*f)*(d*e - c*f)*(e + f*x)) + ((5*a^2*d^2*f^2 + 2*a*b*d*f*(-6*d*e + c*f) + b^2*(9*d^2*e^2 - 6*c*d*e*f + 2*c^2*f^2))*Hypergeometric2F1[2/3, 1, 5/3, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/((b*e - a*f)^2*(d*e - c*f))))/(6*(b*e - a*f)*(d*e - c*f)*(c + d*x)^(2/3))","C",1
3022,1,173,1389,0.6815871,"\int \frac{(a+b x)^3}{\sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","Integrate[(a + b*x)^3/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)),x]","\frac{3 (c+d x)^{2/3} (a d+b (c+2 d x))^{2/3} \left(\frac{3 (b c-a d)^2 \left(2 \, _2F_1\left(-\frac{5}{3},\frac{2}{3};\frac{5}{3};\frac{2 b (c+d x)}{b c-a d}\right)+3 \, _2F_1\left(-\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{2 b (c+d x)}{b c-a d}\right)+\, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};\frac{2 b (c+d x)}{b c-a d}\right)\right)}{d^2 \left(\frac{a d+b (c+2 d x)}{a d-b c}\right)^{2/3}}+2 (a+b x)^2\right)}{40 d^2}","\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}} \operatorname{EllipticF}\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,"(3*(c + d*x)^(2/3)*(a*d + b*(c + 2*d*x))^(2/3)*(2*(a + b*x)^2 + (3*(b*c - a*d)^2*(2*Hypergeometric2F1[-5/3, 2/3, 5/3, (2*b*(c + d*x))/(b*c - a*d)] + 3*Hypergeometric2F1[-2/3, 2/3, 5/3, (2*b*(c + d*x))/(b*c - a*d)] + Hypergeometric2F1[1/3, 2/3, 5/3, (2*b*(c + d*x))/(b*c - a*d)]))/(d^2*((a*d + b*(c + 2*d*x))/(-(b*c) + a*d))^(2/3))))/(40*d^2)","C",1
3023,1,144,1373,0.2262942,"\int \frac{(a+b x)^2}{\sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","Integrate[(a + b*x)^2/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)),x]","\frac{3 (c+d x)^{2/3} \left(23 a^2 d^2+33 (b c-a d)^2 \sqrt[3]{\frac{a d+b (c+2 d x)}{a d-b c}} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};\frac{2 b (c+d x)}{b c-a d}\right)+2 a b d (4 c+27 d x)+b^2 \left(-15 c^2-22 c d x+16 d^2 x^2\right)\right)}{112 d^3 \sqrt[3]{a d+b (c+2 d x)}}","-\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}} \operatorname{EllipticF}\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,"(3*(c + d*x)^(2/3)*(23*a^2*d^2 + 2*a*b*d*(4*c + 27*d*x) + b^2*(-15*c^2 - 22*c*d*x + 16*d^2*x^2) + 33*(b*c - a*d)^2*((a*d + b*(c + 2*d*x))/(-(b*c) + a*d))^(1/3)*Hypergeometric2F1[1/3, 2/3, 5/3, (2*b*(c + d*x))/(b*c - a*d)]))/(112*d^3*(a*d + b*(c + 2*d*x))^(1/3))","C",1
3024,1,109,1326,0.1284829,"\int \frac{a+b x}{\sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","Integrate[(a + b*x)/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)),x]","\frac{3 (c+d x)^{2/3} \left(3 (a d-b c) \sqrt[3]{\frac{a d+b (c+2 d x)}{a d-b c}} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};\frac{2 b (c+d x)}{b c-a d}\right)+a d+b (c+2 d x)\right)}{8 d^2 \sqrt[3]{a d+b (c+2 d x)}}","\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}} \operatorname{EllipticF}\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,"(3*(c + d*x)^(2/3)*(a*d + b*(c + 2*d*x) + 3*(-(b*c) + a*d)*((a*d + b*(c + 2*d*x))/(-(b*c) + a*d))^(1/3)*Hypergeometric2F1[1/3, 2/3, 5/3, (2*b*(c + d*x))/(b*c - a*d)]))/(8*d^2*(a*d + b*(c + 2*d*x))^(1/3))","C",1
3025,1,87,1283,0.0370456,"\int \frac{1}{\sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","Integrate[1/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)),x]","\frac{3 (c+d x)^{2/3} \sqrt[3]{\frac{a d+b (c+2 d x)}{a d-b c}} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};\frac{2 b (c+d x)}{b c-a d}\right)}{2 d \sqrt[3]{a d+b (c+2 d x)}}","-\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}} \operatorname{EllipticF}\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,"(3*(c + d*x)^(2/3)*((a*d + b*(c + 2*d*x))/(-(b*c) + a*d))^(1/3)*Hypergeometric2F1[1/3, 2/3, 5/3, (2*b*(c + d*x))/(b*c - a*d)])/(2*d*(a*d + b*(c + 2*d*x))^(1/3))","C",1
3026,1,140,178,0.1574278,"\int \frac{1}{(a+b x) \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","Integrate[1/((a + b*x)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)),x]","-\frac{3 \sqrt[3]{\frac{b c-a d}{2 d (a+b x)}+1} \sqrt[3]{\frac{b c-a d}{d (a+b x)}+1} F_1\left(\frac{2}{3};\frac{1}{3},\frac{1}{3};\frac{5}{3};-\frac{b c-a d}{d (a+b x)},\frac{a d-b c}{2 d (a+b x)}\right)}{2 b \sqrt[3]{c+d x} \sqrt[3]{a d+b (c+2 d x)}}","-\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,"(-3*(1 + (b*c - a*d)/(2*d*(a + b*x)))^(1/3)*(1 + (b*c - a*d)/(d*(a + b*x)))^(1/3)*AppellF1[2/3, 1/3, 1/3, 5/3, -((b*c - a*d)/(d*(a + b*x))), (-(b*c) + a*d)/(2*d*(a + b*x))])/(2*b*(c + d*x)^(1/3)*(a*d + b*(c + 2*d*x))^(1/3))","C",0
3027,1,288,1510,1.1711424,"\int \frac{1}{(a+b x)^2 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","Integrate[1/((a + b*x)^2*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)),x]","\frac{(c+d x)^{2/3} \left(\frac{d \left(-2^{2/3} (b c-a d)^2 \sqrt[3]{\frac{a d+b c+2 b d x}{b c+b d x}} F_1\left(\frac{5}{3};\frac{1}{3},1;\frac{8}{3};\frac{b c-a d}{2 b c+2 b d x},\frac{b c-a d}{b c+b d x}\right)+10\ 2^{2/3} b (c+d x) (b c-a d) \sqrt[3]{\frac{a d+b c+2 b d x}{b c+b d x}} F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};\frac{b c-a d}{2 b c+2 b d x},\frac{b c-a d}{b c+b d x}\right)+10 b (c+d x) (a d+b (c+2 d x))\right)}{b^2 (c+d x)^2}-\frac{10 (a d+b (c+2 d x))}{a+b x}\right)}{10 (b c-a d)^2 \sqrt[3]{a d+b (c+2 d x)}}","\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}} \operatorname{EllipticF}\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,"((c + d*x)^(2/3)*((-10*(a*d + b*(c + 2*d*x)))/(a + b*x) + (d*(10*b*(c + d*x)*(a*d + b*(c + 2*d*x)) + 10*2^(2/3)*b*(b*c - a*d)*(c + d*x)*((b*c + a*d + 2*b*d*x)/(b*c + b*d*x))^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, (b*c - a*d)/(2*b*c + 2*b*d*x), (b*c - a*d)/(b*c + b*d*x)] - 2^(2/3)*(b*c - a*d)^2*((b*c + a*d + 2*b*d*x)/(b*c + b*d*x))^(1/3)*AppellF1[5/3, 1/3, 1, 8/3, (b*c - a*d)/(2*b*c + 2*b*d*x), (b*c - a*d)/(b*c + b*d*x)]))/(b^2*(c + d*x)^2)))/(10*(b*c - a*d)^2*(a*d + b*(c + 2*d*x))^(1/3))","C",0
3028,1,305,1558,1.1431656,"\int \frac{1}{(a+b x)^3 \sqrt[3]{c+d x} \sqrt[3]{b c+a d+2 b d x}} \, dx","Integrate[1/((a + b*x)^3*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)),x]","\frac{(c+d x)^{2/3} \left(\frac{5 (5 a d-b c+4 b d x) (a d+b (c+2 d x))}{(a+b x)^2}-\frac{d^2 \left(-2\ 2^{2/3} (b c-a d)^2 \sqrt[3]{\frac{a d+b c+2 b d x}{b c+b d x}} F_1\left(\frac{5}{3};\frac{1}{3},1;\frac{8}{3};\frac{b c-a d}{2 b c+2 b d x},\frac{b c-a d}{b c+b d x}\right)+15\ 2^{2/3} b (c+d x) (b c-a d) \sqrt[3]{\frac{a d+b c+2 b d x}{b c+b d x}} F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};\frac{b c-a d}{2 b c+2 b d x},\frac{b c-a d}{b c+b d x}\right)+20 b (c+d x) (a d+b (c+2 d x))\right)}{b^2 (c+d x)^2}\right)}{10 (b c-a d)^3 \sqrt[3]{a d+b (c+2 d x)}}","-\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}} \operatorname{EllipticF}\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,"((c + d*x)^(2/3)*((5*(-(b*c) + 5*a*d + 4*b*d*x)*(a*d + b*(c + 2*d*x)))/(a + b*x)^2 - (d^2*(20*b*(c + d*x)*(a*d + b*(c + 2*d*x)) + 15*2^(2/3)*b*(b*c - a*d)*(c + d*x)*((b*c + a*d + 2*b*d*x)/(b*c + b*d*x))^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, (b*c - a*d)/(2*b*c + 2*b*d*x), (b*c - a*d)/(b*c + b*d*x)] - 2*2^(2/3)*(b*c - a*d)^2*((b*c + a*d + 2*b*d*x)/(b*c + b*d*x))^(1/3)*AppellF1[5/3, 1/3, 1, 8/3, (b*c - a*d)/(2*b*c + 2*b*d*x), (b*c - a*d)/(b*c + b*d*x)]))/(b^2*(c + d*x)^2)))/(10*(b*c - a*d)^3*(a*d + b*(c + 2*d*x))^(1/3))","C",0
3029,1,144,1388,0.2523239,"\int \frac{(a+b x)^3}{\sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","Integrate[(a + b*x)^3/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)),x]","\frac{3 (c+d x)^{2/3} \left(29 a^2 d^2+27 (b c-a d)^2 \sqrt[3]{\frac{a d+b (c+2 d x)}{a d-b c}} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};\frac{2 b (c+d x)}{b c-a d}\right)+2 a b d (17 d x-12 c)+b^2 \left(3 c^2-18 c d x+8 d^2 x^2\right)\right)}{112 d^4 \sqrt[3]{a d+b (c+2 d x)}}","-\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}} \operatorname{EllipticF}\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,"(3*(c + d*x)^(2/3)*(29*a^2*d^2 + 2*a*b*d*(-12*c + 17*d*x) + b^2*(3*c^2 - 18*c*d*x + 8*d^2*x^2) + 27*(b*c - a*d)^2*((a*d + b*(c + 2*d*x))/(-(b*c) + a*d))^(1/3)*Hypergeometric2F1[1/3, 2/3, 5/3, (2*b*(c + d*x))/(b*c - a*d)]))/(112*d^4*(a*d + b*(c + 2*d*x))^(1/3))","C",1
3030,1,111,1366,0.1572313,"\int \frac{(a+b x)^2}{\sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","Integrate[(a + b*x)^2/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)),x]","\frac{3 (c+d x)^{2/3} \left(3 (a d-b c) \sqrt[3]{\frac{a d+b (c+2 d x)}{a d-b c}} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};\frac{2 b (c+d x)}{b c-a d}\right)+5 a d-3 b c+2 b d x\right)}{16 d^3 \sqrt[3]{a d+b (c+2 d x)}}","\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}} \operatorname{EllipticF}\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,"(3*(c + d*x)^(2/3)*(-3*b*c + 5*a*d + 2*b*d*x + 3*(-(b*c) + a*d)*((a*d + b*(c + 2*d*x))/(-(b*c) + a*d))^(1/3)*Hypergeometric2F1[1/3, 2/3, 5/3, (2*b*(c + d*x))/(b*c - a*d)]))/(16*d^3*(a*d + b*(c + 2*d*x))^(1/3))","C",1
3031,1,32,32,0.0265704,"\int \frac{a+b x}{\sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","Integrate[(a + b*x)/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)),x]","\frac{3 (c+d x)^{2/3}}{2 d^2 \sqrt[3]{a d+b (c+2 d x)}}","\frac{3 (c+d x)^{2/3}}{2 d^2 \sqrt[3]{a d+b c+2 b d x}}",1,"(3*(c + d*x)^(2/3))/(2*d^2*(a*d + b*(c + 2*d*x))^(1/3))","A",1
3032,1,87,1333,0.0733817,"\int \frac{1}{\sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","Integrate[1/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)),x]","\frac{3 (c+d x)^{2/3} \left(\frac{a d+b (c+2 d x)}{a d-b c}\right)^{4/3} \, _2F_1\left(\frac{2}{3},\frac{4}{3};\frac{5}{3};\frac{2 b (c+d x)}{b c-a d}\right)}{2 d (a d+b (c+2 d x))^{4/3}}","-\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}} \operatorname{EllipticF}\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,"(3*(c + d*x)^(2/3)*((a*d + b*(c + 2*d*x))/(-(b*c) + a*d))^(4/3)*Hypergeometric2F1[2/3, 4/3, 5/3, (2*b*(c + d*x))/(b*c - a*d)])/(2*d*(a*d + b*(c + 2*d*x))^(4/3))","C",1
3033,1,145,113,0.8479825,"\int \frac{1}{(a+b x) \sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","Integrate[1/((a + b*x)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)),x]","\frac{3 \left(2 b (c+d x)-\frac{(a d+b (c+2 d x)) F_1\left(\frac{2}{3};-\frac{2}{3},1;\frac{5}{3};\frac{b c-a d}{2 b c+2 b d x},\frac{b c-a d}{b c+b d x}\right)}{\left(\frac{a d+b c+2 b d x}{2 b c+2 b d x}\right)^{2/3}}\right)}{2 b^2 (c+d x)^{4/3} (b c-a d) \sqrt[3]{a d+b (c+2 d x)}}","\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,"(3*(2*b*(c + d*x) - ((a*d + b*(c + 2*d*x))*AppellF1[2/3, -2/3, 1, 5/3, (b*c - a*d)/(2*b*c + 2*b*d*x), (b*c - a*d)/(b*c + b*d*x)])/((b*c + a*d + 2*b*d*x)/(2*b*c + 2*b*d*x))^(2/3)))/(2*b^2*(b*c - a*d)*(c + d*x)^(4/3)*(a*d + b*(c + 2*d*x))^(1/3))","A",0
3034,1,289,114,1.1248281,"\int \frac{1}{(a+b x)^2 \sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","Integrate[1/((a + b*x)^2*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)),x]","\frac{(c+d x)^{2/3} \left(\frac{d \left(-7\ 2^{2/3} (b c-a d)^2 \sqrt[3]{\frac{a d+b c+2 b d x}{b c+b d x}} F_1\left(\frac{5}{3};\frac{1}{3},1;\frac{8}{3};\frac{b c-a d}{2 b c+2 b d x},\frac{b c-a d}{b c+b d x}\right)+40\ 2^{2/3} b (c+d x) (b c-a d) \sqrt[3]{\frac{a d+b c+2 b d x}{b c+b d x}} F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};\frac{b c-a d}{2 b c+2 b d x},\frac{b c-a d}{b c+b d x}\right)+70 b (c+d x) (a d+b (c+2 d x))\right)}{b^2 (c+d x)^2}-\frac{10 (13 a d+b (c+14 d x))}{a+b x}\right)}{10 (b c-a d)^3 \sqrt[3]{a d+b (c+2 d x)}}","-\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,"((c + d*x)^(2/3)*((-10*(13*a*d + b*(c + 14*d*x)))/(a + b*x) + (d*(70*b*(c + d*x)*(a*d + b*(c + 2*d*x)) + 40*2^(2/3)*b*(b*c - a*d)*(c + d*x)*((b*c + a*d + 2*b*d*x)/(b*c + b*d*x))^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, (b*c - a*d)/(2*b*c + 2*b*d*x), (b*c - a*d)/(b*c + b*d*x)] - 7*2^(2/3)*(b*c - a*d)^2*((b*c + a*d + 2*b*d*x)/(b*c + b*d*x))^(1/3)*AppellF1[5/3, 1/3, 1, 8/3, (b*c - a*d)/(2*b*c + 2*b*d*x), (b*c - a*d)/(b*c + b*d*x)]))/(b^2*(c + d*x)^2)))/(10*(b*c - a*d)^3*(a*d + b*(c + 2*d*x))^(1/3))","B",0
3035,1,324,116,1.2605201,"\int \frac{1}{(a+b x)^3 \sqrt[3]{c+d x} (b c+a d+2 b d x)^{4/3}} \, dx","Integrate[1/((a + b*x)^3*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)),x]","\frac{(c+d x)^{2/3} \left(\frac{5 \left(57 a^2 d^2+2 a b d (4 c+61 d x)+b^2 \left(-c^2+6 c d x+64 d^2 x^2\right)\right)}{(a+b x)^2}-\frac{d^2 \left(-16\ 2^{2/3} (b c-a d)^2 \sqrt[3]{\frac{a d+b c+2 b d x}{b c+b d x}} F_1\left(\frac{5}{3};\frac{1}{3},1;\frac{8}{3};\frac{b c-a d}{2 b c+2 b d x},\frac{b c-a d}{b c+b d x}\right)+95\ 2^{2/3} b (c+d x) (b c-a d) \sqrt[3]{\frac{a d+b c+2 b d x}{b c+b d x}} F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};\frac{b c-a d}{2 b c+2 b d x},\frac{b c-a d}{b c+b d x}\right)+160 b (c+d x) (a d+b (c+2 d x))\right)}{b^2 (c+d x)^2}\right)}{10 (b c-a d)^4 \sqrt[3]{a d+b (c+2 d x)}}","\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,"((c + d*x)^(2/3)*((5*(57*a^2*d^2 + 2*a*b*d*(4*c + 61*d*x) + b^2*(-c^2 + 6*c*d*x + 64*d^2*x^2)))/(a + b*x)^2 - (d^2*(160*b*(c + d*x)*(a*d + b*(c + 2*d*x)) + 95*2^(2/3)*b*(b*c - a*d)*(c + d*x)*((b*c + a*d + 2*b*d*x)/(b*c + b*d*x))^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, (b*c - a*d)/(2*b*c + 2*b*d*x), (b*c - a*d)/(b*c + b*d*x)] - 16*2^(2/3)*(b*c - a*d)^2*((b*c + a*d + 2*b*d*x)/(b*c + b*d*x))^(1/3)*AppellF1[5/3, 1/3, 1, 8/3, (b*c - a*d)/(2*b*c + 2*b*d*x), (b*c - a*d)/(b*c + b*d*x)]))/(b^2*(c + d*x)^2)))/(10*(b*c - a*d)^4*(a*d + b*(c + 2*d*x))^(1/3))","B",0
3036,1,100,120,0.0826351,"\int \frac{1}{\sqrt[3]{d-3 e x} (d+e x) \sqrt[3]{d+3 e x}} \, dx","Integrate[1/((d - 3*e*x)^(1/3)*(d + e*x)*(d + 3*e*x)^(1/3)),x]","-\frac{3 \sqrt[3]{1-\frac{4 d}{3 (d+e x)}} \sqrt[3]{1-\frac{2 d}{3 (d+e x)}} F_1\left(\frac{2}{3};\frac{1}{3},\frac{1}{3};\frac{5}{3};\frac{4 d}{3 (d+e x)},\frac{2 d}{3 (d+e x)}\right)}{2 e \sqrt[3]{d-3 e x} \sqrt[3]{d+3 e x}}","\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,"(-3*(1 - (4*d)/(3*(d + e*x)))^(1/3)*(1 - (2*d)/(3*(d + e*x)))^(1/3)*AppellF1[2/3, 1/3, 1/3, 5/3, (4*d)/(3*(d + e*x)), (2*d)/(3*(d + e*x))])/(2*e*(d - 3*e*x)^(1/3)*(d + 3*e*x)^(1/3))","C",0
3037,1,175,562,0.2293937,"\int \frac{(a+b x)^{4/3} (e+f x)^2}{(c+d x)^{4/3}} \, dx","Integrate[((a + b*x)^(4/3)*(e + f*x)^2)/(c + d*x)^(4/3),x]","\frac{(a+b x)^{7/3} \left(\frac{2 \sqrt[3]{\frac{b (c+d x)}{b c-a d}} \left(-a^2 d^2 f^2+a b d f (9 d e-7 c f)+b^2 \left(35 c^2 f^2-63 c d e f+27 d^2 e^2\right)\right) \, _2F_1\left(\frac{1}{3},\frac{7}{3};\frac{10}{3};\frac{d (a+b x)}{a d-b c}\right)}{b^2}-\frac{7 f^2 (c+d x) (b c-a d)}{b}-63 (d e-c f)^2\right)}{21 d^2 \sqrt[3]{c+d x} (a d-b c)}","-\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,"((a + b*x)^(7/3)*(-63*(d*e - c*f)^2 - (7*(b*c - a*d)*f^2*(c + d*x))/b + (2*(-(a^2*d^2*f^2) + a*b*d*f*(9*d*e - 7*c*f) + b^2*(27*d^2*e^2 - 63*c*d*e*f + 35*c^2*f^2))*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[1/3, 7/3, 10/3, (d*(a + b*x))/(-(b*c) + a*d)])/b^2))/(21*d^2*(-(b*c) + a*d)*(c + d*x)^(1/3))","C",1
3038,1,114,328,0.1475855,"\int \frac{(a+b x)^{4/3} (e+f x)}{(c+d x)^{4/3}} \, dx","Integrate[((a + b*x)^(4/3)*(e + f*x))/(c + d*x)^(4/3),x]","\frac{3 (a+b x)^{7/3} \left(\sqrt[3]{\frac{b (c+d x)}{b c-a d}} (a d f-7 b c f+6 b d e) \, _2F_1\left(\frac{1}{3},\frac{7}{3};\frac{10}{3};\frac{d (a+b x)}{a d-b c}\right)+b (7 c f-7 d e)\right)}{7 b d \sqrt[3]{c+d x} (a d-b c)}","\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,"(3*(a + b*x)^(7/3)*(b*(-7*d*e + 7*c*f) + (6*b*d*e - 7*b*c*f + a*d*f)*((b*(c + d*x))/(b*c - a*d))^(1/3)*Hypergeometric2F1[1/3, 7/3, 10/3, (d*(a + b*x))/(-(b*c) + a*d)]))/(7*b*d*(-(b*c) + a*d)*(c + d*x)^(1/3))","C",1
3039,1,73,195,0.0528391,"\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3}} \, dx","Integrate[(a + b*x)^(4/3)/(c + d*x)^(4/3),x]","\frac{3 (a+b x)^{7/3} \left(\frac{b (c+d x)}{b c-a d}\right)^{4/3} \, _2F_1\left(\frac{4}{3},\frac{7}{3};\frac{10}{3};\frac{d (a+b x)}{a d-b c}\right)}{7 b (c+d x)^{4/3}}","\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,"(3*(a + b*x)^(7/3)*((b*(c + d*x))/(b*c - a*d))^(4/3)*Hypergeometric2F1[4/3, 7/3, 10/3, (d*(a + b*x))/(-(b*c) + a*d)])/(7*b*(c + d*x)^(4/3))","C",1
3040,1,148,380,0.1946919,"\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3} (e+f x)} \, dx","Integrate[(a + b*x)^(4/3)/((c + d*x)^(4/3)*(e + f*x)),x]","\frac{3 \sqrt[3]{a+b x} \left(\frac{(a+b x) \left(\frac{b (c+d x)}{b c-a d}\right)^{4/3} \, _2F_1\left(\frac{4}{3},\frac{4}{3};\frac{7}{3};\frac{d (a+b x)}{a d-b c}\right)}{c+d x}-\frac{4 (b e-a f) \left(\, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)-1\right)}{d e-c f}\right)}{4 f \sqrt[3]{c+d x}}","-\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,"(3*(a + b*x)^(1/3)*((-4*(b*e - a*f)*(-1 + Hypergeometric2F1[1/3, 1, 4/3, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]))/(d*e - c*f) + ((a + b*x)*((b*(c + d*x))/(b*c - a*d))^(4/3)*Hypergeometric2F1[4/3, 4/3, 7/3, (d*(a + b*x))/(-(b*c) + a*d)])/(c + d*x)))/(4*f*(c + d*x)^(1/3))","C",1
3041,1,123,301,0.0604522,"\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3} (e+f x)^2} \, dx","Integrate[(a + b*x)^(4/3)/((c + d*x)^(4/3)*(e + f*x)^2),x]","\frac{\sqrt[3]{a+b x} \left(-4 (e+f x) (b c-a d) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)-a (c f+3 d e+4 d f x)+b (4 c e+3 c f x+d e x)\right)}{\sqrt[3]{c+d x} (e+f x) (d e-c f)^2}","-\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,"((a + b*x)^(1/3)*(b*(4*c*e + d*e*x + 3*c*f*x) - a*(3*d*e + c*f + 4*d*f*x) - 4*(b*c - a*d)*(e + f*x)*Hypergeometric2F1[1/3, 1, 4/3, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]))/((d*e - c*f)^2*(c + d*x)^(1/3)*(e + f*x))","C",1
3042,1,214,434,0.430465,"\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3} (e+f x)^3} \, dx","Integrate[(a + b*x)^(4/3)/((c + d*x)^(4/3)*(e + f*x)^3),x]","\frac{\frac{\sqrt[3]{a+b x} (-7 a d f+b c f+6 b d e) \left(3 (a+b x) (c+d x) (b e-a f) (d e-c f)-4 (e+f x) (b c-a d) \left((c+d x) (b e-a f)-(e+f x) (b c-a d) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)\right)\right)}{3 (b e-a f) (d e-c f)^2}-6 d (a+b x)^{7/3}}{2 \sqrt[3]{c+d x} (e+f x)^2 (b c-a d) (c f-d e)}","\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,"(-6*d*(a + b*x)^(7/3) + ((6*b*d*e + b*c*f - 7*a*d*f)*(a + b*x)^(1/3)*(3*(b*e - a*f)*(d*e - c*f)*(a + b*x)*(c + d*x) - 4*(b*c - a*d)*(e + f*x)*((b*e - a*f)*(c + d*x) - (b*c - a*d)*(e + f*x)*Hypergeometric2F1[1/3, 1, 4/3, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])))/(3*(b*e - a*f)*(d*e - c*f)^2))/(2*(b*c - a*d)*(-(d*e) + c*f)*(c + d*x)^(1/3)*(e + f*x)^2)","C",1
3043,1,320,645,0.8055649,"\int \frac{(a+b x)^{4/3}}{(c+d x)^{4/3} (e+f x)^4} \, dx","Integrate[(a + b*x)^(4/3)/((c + d*x)^(4/3)*(e + f*x)^4),x]","\frac{\sqrt[3]{a+b x} \left((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) \left(3 (a+b x) (c+d x) (b e-a f) (d e-c f)-4 (e+f x) (b c-a d) \left((c+d x) (b e-a f)-(e+f x) (b c-a d) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)\right)\right)-81 d (a+b x)^2 (b e-a f)^2 (d e-c f)^3+9 f (a+b x)^2 (c+d x) (a f-b e) (d e-c f)^2 (-10 a d f+b c f+9 b d e)\right)}{27 \sqrt[3]{c+d x} (e+f x)^3 (b c-a d) (b e-a f)^2 (d e-c f)^3 (c f-d e)}","\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,"((a + b*x)^(1/3)*(-81*d*(b*e - a*f)^2*(d*e - c*f)^3*(a + b*x)^2 + 9*f*(-(b*e) + a*f)*(d*e - c*f)^2*(9*b*d*e + b*c*f - 10*a*d*f)*(a + b*x)^2*(c + d*x) + (35*a^2*d^2*f^2 - 7*a*b*d*f*(9*d*e + c*f) + b^2*(27*d^2*e^2 + 9*c*d*e*f - c^2*f^2))*(e + f*x)*(3*(b*e - a*f)*(d*e - c*f)*(a + b*x)*(c + d*x) - 4*(b*c - a*d)*(e + f*x)*((b*e - a*f)*(c + d*x) - (b*c - a*d)*(e + f*x)*Hypergeometric2F1[1/3, 1, 4/3, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]))))/(27*(b*c - a*d)*(b*e - a*f)^2*(d*e - c*f)^3*(-(d*e) + c*f)*(c + d*x)^(1/3)*(e + f*x)^3)","C",1
3044,1,118,266,0.113163,"\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt[4]{e+f x}} \, dx","Integrate[1/((a + b*x)*Sqrt[c + d*x]*(e + f*x)^(1/4)),x]","-\frac{4 \sqrt{\frac{b (c+d x)}{d (a+b x)}} \sqrt[4]{\frac{b (e+f x)}{f (a+b x)}} F_1\left(\frac{3}{4};\frac{1}{2},\frac{1}{4};\frac{7}{4};\frac{a d-b c}{d (a+b x)},\frac{a f-b e}{f (a+b x)}\right)}{3 b \sqrt{c+d x} \sqrt[4]{e+f x}}","\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,"(-4*Sqrt[(b*(c + d*x))/(d*(a + b*x))]*((b*(e + f*x))/(f*(a + b*x)))^(1/4)*AppellF1[3/4, 1/2, 1/4, 7/4, (-(b*c) + a*d)/(d*(a + b*x)), (-(b*e) + a*f)/(f*(a + b*x))])/(3*b*Sqrt[c + d*x]*(e + f*x)^(1/4))","C",0
3045,1,118,252,0.1026211,"\int \frac{1}{(a+b x) \sqrt{c+d x} (e+f x)^{3/4}} \, dx","Integrate[1/((a + b*x)*Sqrt[c + d*x]*(e + f*x)^(3/4)),x]","-\frac{4 \sqrt{\frac{b (c+d x)}{d (a+b x)}} \left(\frac{b (e+f x)}{f (a+b x)}\right)^{3/4} F_1\left(\frac{5}{4};\frac{1}{2},\frac{3}{4};\frac{9}{4};\frac{a d-b c}{d (a+b x)},\frac{a f-b e}{f (a+b x)}\right)}{5 b \sqrt{c+d x} (e+f x)^{3/4}}","-\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,"(-4*Sqrt[(b*(c + d*x))/(d*(a + b*x))]*((b*(e + f*x))/(f*(a + b*x)))^(3/4)*AppellF1[5/4, 1/2, 3/4, 9/4, (-(b*c) + a*d)/(d*(a + b*x)), (-(b*e) + a*f)/(f*(a + b*x))])/(5*b*Sqrt[c + d*x]*(e + f*x)^(3/4))","C",0
3046,1,114,125,0.1958936,"\int (a+b x)^p (A+B x) (d+e x)^{-2-p} \, dx","Integrate[(a + b*x)^p*(A + B*x)*(d + e*x)^(-2 - p),x]","\frac{(a+b x)^p (d+e x)^{-p} \left(\frac{e (a+b x) (A e-B d)}{(p+1) (d+e x) (b d-a e)}-\frac{B \left(\frac{e (a+b x)}{a e-b d}\right)^{-p} \, _2F_1\left(-p,-p;1-p;\frac{b (d+e x)}{b d-a e}\right)}{p}\right)}{e^2}","-\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,"((a + b*x)^p*((e*(-(B*d) + A*e)*(a + b*x))/((b*d - a*e)*(1 + p)*(d + e*x)) - (B*Hypergeometric2F1[-p, -p, 1 - p, (b*(d + e*x))/(b*d - a*e)])/(p*((e*(a + b*x))/(-(b*d) + a*e))^p)))/(e^2*(d + e*x)^p)","A",1
3047,1,109,134,0.0996122,"\int (a+b x) (c+d x)^n (e+f x)^{-n} \, dx","Integrate[((a + b*x)*(c + d*x)^n)/(e + f*x)^n,x]","\frac{(c+d x)^{n+1} (e+f x)^{-n} \left(b d (e+f x)-\frac{\left(\frac{d (e+f x)}{d e-c f}\right)^n (-2 a d f-b c f (n-1)+b d e (n+1)) \, _2F_1\left(n,n+1;n+2;\frac{f (c+d x)}{c f-d e}\right)}{n+1}\right)}{2 d^2 f}","\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,"((c + d*x)^(1 + n)*(b*d*(e + f*x) - ((-2*a*d*f - b*c*f*(-1 + n) + b*d*e*(1 + n))*((d*(e + f*x))/(d*e - c*f))^n*Hypergeometric2F1[n, 1 + n, 2 + n, (f*(c + d*x))/(-(d*e) + c*f)])/(1 + n)))/(2*d^2*f*(e + f*x)^n)","A",1
3048,1,124,152,0.0958965,"\int (a+b x) (c+d x)^{-1+n} (e+f x)^{-n} \, dx","Integrate[((a + b*x)*(c + d*x)^(-1 + n))/(e + f*x)^n,x]","\frac{(c+d x)^n (e+f x)^{-n} \left(\frac{(c+d x) \left(\frac{d (e+f x)}{d e-c f}\right)^n (-a d f+b c (f-f n)+b d e n) \, _2F_1\left(n,n+1;n+2;\frac{f (c+d x)}{c f-d e}\right)}{n+1}+d (e+f x) (a d-b c)\right)}{d^2 n (d e-c f)}","-\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,"((c + d*x)^n*(d*(-(b*c) + a*d)*(e + f*x) + ((-(a*d*f) + b*d*e*n + b*c*(f - f*n))*(c + d*x)*((d*(e + f*x))/(d*e - c*f))^n*Hypergeometric2F1[n, 1 + n, 2 + n, (f*(c + d*x))/(-(d*e) + c*f)])/(1 + n)))/(d^2*(d*e - c*f)*n*(e + f*x)^n)","A",1
3049,1,115,117,0.1652488,"\int (a+b x) (c+d x)^{-2+n} (e+f x)^{-n} \, dx","Integrate[((a + b*x)*(c + d*x)^(-2 + n))/(e + f*x)^n,x]","\frac{(c+d x)^{n-1} (e+f x)^{-n} \left(d^2 (e+f x) (b e-a f)-b (d e-c f)^2 \left(\frac{d (e+f x)}{d e-c f}\right)^n \, _2F_1\left(n-1,n-1;n;\frac{f (c+d x)}{c f-d e}\right)\right)}{d^2 f (n-1) (c f-d e)}","\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,"((c + d*x)^(-1 + n)*(d^2*(b*e - a*f)*(e + f*x) - b*(d*e - c*f)^2*((d*(e + f*x))/(d*e - c*f))^n*Hypergeometric2F1[-1 + n, -1 + n, n, (f*(c + d*x))/(-(d*e) + c*f)]))/(d^2*f*(-(d*e) + c*f)*(-1 + n)*(e + f*x)^n)","A",1
3050,1,82,123,0.0683353,"\int (a+b x) (c+d x)^{-3+n} (e+f x)^{-n} \, dx","Integrate[((a + b*x)*(c + d*x)^(-3 + n))/(e + f*x)^n,x]","\frac{(c+d x)^{n-2} (e+f x)^{1-n} (-a c f (n-2)+a d e (n-1)+a d f x-b c (e+f (n-1) x)+b d e (n-2) x)}{(n-2) (n-1) (d e-c f)^2}","\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,"((c + d*x)^(-2 + n)*(e + f*x)^(1 - n)*(-(a*c*f*(-2 + n)) + a*d*e*(-1 + n) + a*d*f*x + b*d*e*(-2 + n)*x - b*c*(e + f*(-1 + n)*x)))/((d*e - c*f)^2*(-2 + n)*(-1 + n))","A",1
3051,1,112,207,0.3306006,"\int (a+b x) (c+d x)^{-4+n} (e+f x)^{-n} \, dx","Integrate[((a + b*x)*(c + d*x)^(-4 + n))/(e + f*x)^n,x]","\frac{(c+d x)^{n-3} (e+f x)^{1-n} \left(\frac{(c+d x) (-c f (n-2)+d e (n-1)+d f x) (2 a d f-b c f (n-1)+b d e (n-3))}{(n-2) (n-1) (d e-c f)^2}+a d-b c\right)}{d (n-3) (d e-c f)}","\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,"((c + d*x)^(-3 + n)*(e + f*x)^(1 - n)*(-(b*c) + a*d + ((2*a*d*f + b*d*e*(-3 + n) - b*c*f*(-1 + n))*(c + d*x)*(-(c*f*(-2 + n)) + d*e*(-1 + n) + d*f*x))/((d*e - c*f)^2*(-2 + n)*(-1 + n))))/(d*(d*e - c*f)*(-3 + n))","A",1
3052,1,165,299,0.2871957,"\int (a+b x) (c+d x)^{-5+n} (e+f x)^{-n} \, dx","Integrate[((a + b*x)*(c + d*x)^(-5 + n))/(e + f*x)^n,x]","\frac{(c+d x)^{n-4} (e+f x)^{1-n} \left(\frac{(c+d x) \left(c^2 f^2 \left(n^2-5 n+6\right)-2 c d f (n-3) (e (n-1)+f x)+d^2 \left(e^2 \left(n^2-3 n+2\right)+2 e f (n-1) x+2 f^2 x^2\right)\right) (3 a d f-b c f (n-1)+b d e (n-4))}{(n-3) (n-2) (n-1) (d e-c f)^3}+a d-b c\right)}{d (n-4) (d e-c f)}","\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,"((c + d*x)^(-4 + n)*(e + f*x)^(1 - n)*(-(b*c) + a*d + ((3*a*d*f + b*d*e*(-4 + n) - b*c*f*(-1 + n))*(c + d*x)*(c^2*f^2*(6 - 5*n + n^2) - 2*c*d*f*(-3 + n)*(e*(-1 + n) + f*x) + d^2*(e^2*(2 - 3*n + n^2) + 2*e*f*(-1 + n)*x + 2*f^2*x^2)))/((d*e - c*f)^3*(-3 + n)*(-2 + n)*(-1 + n))))/(d*(d*e - c*f)*(-4 + n))","A",1
3053,1,108,135,0.1245136,"\int (a+b x)^{-n} (c+d x) (e+f x)^n \, dx","Integrate[((c + d*x)*(e + f*x)^n)/(a + b*x)^n,x]","\frac{(a+b x)^{-n} (e+f x)^{n+1} \left(\frac{\left(\frac{f (a+b x)}{a f-b e}\right)^n (-a d f (n+1)+2 b c f+b d e (n-1)) \, _2F_1\left(n,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)}{n+1}+d f (a+b x)\right)}{2 b f^2}","\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,"((e + f*x)^(1 + n)*(d*f*(a + b*x) + ((2*b*c*f + b*d*e*(-1 + n) - a*d*f*(1 + n))*((f*(a + b*x))/(-(b*e) + a*f))^n*Hypergeometric2F1[n, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)])/(1 + n)))/(2*b*f^2*(a + b*x)^n)","A",1
3054,1,123,151,0.1350375,"\int (a+b x)^{-n} (c+d x) (e+f x)^{-1+n} \, dx","Integrate[((c + d*x)*(e + f*x)^(-1 + n))/(a + b*x)^n,x]","\frac{(a+b x)^{-n} (e+f x)^n \left(\frac{(e+f x) \left(\frac{f (a+b x)}{a f-b e}\right)^n (a d f n-b (c f+d e (n-1))) \, _2F_1\left(n,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)}{n+1}+f (a+b x) (c f-d e)\right)}{f^2 n (a f-b e)}","\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,"((e + f*x)^n*(f*(-(d*e) + c*f)*(a + b*x) + ((-(b*(c*f + d*e*(-1 + n))) + a*d*f*n)*((f*(a + b*x))/(-(b*e) + a*f))^n*(e + f*x)*Hypergeometric2F1[n, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)])/(1 + n)))/(f^2*(-(b*e) + a*f)*n*(a + b*x)^n)","A",1
3055,1,105,118,0.2040553,"\int (a+b x)^{-n} (c+d x) (e+f x)^{-2+n} \, dx","Integrate[((c + d*x)*(e + f*x)^(-2 + n))/(a + b*x)^n,x]","\frac{(a+b x)^{-n} (e+f x)^n \left(\frac{f (a+b x) (d e-c f)}{(n-1) (e+f x) (b e-a f)}+\frac{d \left(\frac{f (a+b x)}{a f-b e}\right)^n \, _2F_1\left(n,n;n+1;\frac{b (e+f x)}{b e-a f}\right)}{n}\right)}{f^2}","\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,"((e + f*x)^n*((f*(d*e - c*f)*(a + b*x))/((b*e - a*f)*(-1 + n)*(e + f*x)) + (d*((f*(a + b*x))/(-(b*e) + a*f))^n*Hypergeometric2F1[n, n, 1 + n, (b*(e + f*x))/(b*e - a*f)])/n))/(f^2*(a + b*x)^n)","A",1
3056,1,84,125,0.0972265,"\int (a+b x)^{-n} (c+d x) (e+f x)^{-3+n} \, dx","Integrate[((c + d*x)*(e + f*x)^(-3 + n))/(a + b*x)^n,x]","\frac{(a+b x)^{1-n} (e+f x)^{n-2} (a c f (n-1)-a d e+a d f (n-2) x+b c (f x-e (n-2))-b d e (n-1) x)}{(n-2) (n-1) (b e-a f)^2}","-\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,"((a + b*x)^(1 - n)*(e + f*x)^(-2 + n)*(-(a*d*e) + a*c*f*(-1 + n) + a*d*f*(-2 + n)*x - b*d*e*(-1 + n)*x + b*c*(-(e*(-2 + n)) + f*x)))/((b*e - a*f)^2*(-2 + n)*(-1 + n))","A",1
3057,1,180,207,0.2031246,"\int (a+b x)^{-n} (c+d x) (e+f x)^{-4+n} \, dx","Integrate[((c + d*x)*(e + f*x)^(-4 + n))/(a + b*x)^n,x]","\frac{(a+b x)^{1-n} (e+f x)^{n-3} \left(a^2 f (n-1) (c f (n-2)-d e+d f (n-3) x)+a b \left(2 c f (n-1) (f x-e (n-3))+d \left(e^2 (n-3)-2 e f \left(n^2-4 n+5\right) x+f^2 (n-3) x^2\right)\right)+b^2 \left(c \left(e^2 \left(n^2-5 n+6\right)-2 e f (n-3) x+2 f^2 x^2\right)+d e (n-1) x (e (n-3)-f x)\right)\right)}{(n-3) (n-2) (n-1) (a f-b e)^3}","-\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,"((a + b*x)^(1 - n)*(e + f*x)^(-3 + n)*(a^2*f*(-1 + n)*(-(d*e) + c*f*(-2 + n) + d*f*(-3 + n)*x) + b^2*(d*e*(-1 + n)*x*(e*(-3 + n) - f*x) + c*(e^2*(6 - 5*n + n^2) - 2*e*f*(-3 + n)*x + 2*f^2*x^2)) + a*b*(2*c*f*(-1 + n)*(-(e*(-3 + n)) + f*x) + d*(e^2*(-3 + n) - 2*e*f*(5 - 4*n + n^2)*x + f^2*(-3 + n)*x^2))))/((-(b*e) + a*f)^3*(-3 + n)*(-2 + n)*(-1 + n))","A",1
3058,1,145,300,0.4966571,"\int (a+b x)^{-n} (c+d x) (e+f x)^{-5+n} \, dx","Integrate[((c + d*x)*(e + f*x)^(-5 + n))/(a + b*x)^n,x]","\frac{(a+b x)^{1-n} (e+f x)^{n-4} \left(-\frac{(e+f x) \left((n-2) (n-1) (b e-a f)^2-2 b (e+f x) (-a f (n-1)+b e (n-2)-b f x)\right) (a d f (n-4)+3 b c f-b d e (n-1))}{(n-3) (n-2) (n-1) (b e-a f)^3}+c f-d e\right)}{f (n-4) (a f-b e)}","\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,"((a + b*x)^(1 - n)*(e + f*x)^(-4 + n)*(-(d*e) + c*f - ((3*b*c*f + a*d*f*(-4 + n) - b*d*e*(-1 + n))*(e + f*x)*((b*e - a*f)^2*(-2 + n)*(-1 + n) - 2*b*(e + f*x)*(b*e*(-2 + n) - a*f*(-1 + n) - b*f*x)))/((b*e - a*f)^3*(-3 + n)*(-2 + n)*(-1 + n))))/(f*(-(b*e) + a*f)*(-4 + n))","A",1
3059,1,119,121,0.1988611,"\int (a+b x)^m (c+d x)^{-m} (e+f x)^p \, dx","Integrate[((a + b*x)^m*(e + f*x)^p)/(c + d*x)^m,x]","\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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{b (m+1)}","\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,"((a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*(e + f*x)^p*AppellF1[1 + m, m, -p, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/(b*(1 + m)*(c + d*x)^m*((b*(e + f*x))/(b*e - a*f))^p)","A",1
3060,1,227,188,0.4108502,"\int (5-4 x)^4 (1+2 x)^{-m} (2+3 x)^m \, dx","Integrate[((5 - 4*x)^4*(2 + 3*x)^m)/(1 + 2*x)^m,x]","\frac{(2 x+1)^{1-m} \left(483 \left(2^{-m} \left(-2 m^2+132 m-1453\right) \, _2F_1(1-m,-m;2-m;-6 x-3)+4 (m-1) (m+12 x-59) (3 x+2)^{m+1}\right)-(88-m) \left(2^{2-m} (m-66) \, _2F_1(-m-2,1-m;2-m;-6 x-3)+23\ 2^{1-m} (111-2 m) \, _2F_1(-m-1,1-m;2-m;-6 x-3)+529\ 2^{-m} (m-45) \, _2F_1(1-m,-m;2-m;-6 x-3)-18 (m-1) (5-4 x)^2 (3 x+2)^{m+1}\right)-108 (m-1) (4 x-5)^3 (3 x+2)^{m+1}\right)}{810 (1-m)}","\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,"((1 + 2*x)^(1 - m)*(-108*(-1 + m)*(2 + 3*x)^(1 + m)*(-5 + 4*x)^3 - (88 - m)*(-18*(-1 + m)*(5 - 4*x)^2*(2 + 3*x)^(1 + m) + 2^(2 - m)*(-66 + m)*Hypergeometric2F1[-2 - m, 1 - m, 2 - m, -3 - 6*x] + 23*2^(1 - m)*(111 - 2*m)*Hypergeometric2F1[-1 - m, 1 - m, 2 - m, -3 - 6*x] + (529*(-45 + m)*Hypergeometric2F1[1 - m, -m, 2 - m, -3 - 6*x])/2^m) + 483*(4*(-1 + m)*(2 + 3*x)^(1 + m)*(-59 + m + 12*x) + ((-1453 + 132*m - 2*m^2)*Hypergeometric2F1[1 - m, -m, 2 - m, -3 - 6*x])/2^m)))/(810*(1 - m))","A",1
3061,1,304,432,0.7379746,"\int (a+b x)^m (c+d x)^{-m} (e+f x)^3 \, dx","Integrate[((a + b*x)^m*(e + f*x)^3)/(c + d*x)^m,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(b^2 (d e-c f)^2 \left(\frac{b (c+d x)}{b c-a d}\right)^m (a d f (m-1)-b c f (m+3)+4 b d e) \, _2F_1\left(m,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)+f^2 (b c-a d)^2 \left(\frac{b (c+d x)}{b c-a d}\right)^m (a d f (m-3)-b c f (m+3)+6 b d e) \, _2F_1\left(m-2,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)+2 b f (b c-a d) (d e-c f) \left(\frac{b (c+d x)}{b c-a d}\right)^m (a d f (m-2)-b c f (m+3)+5 b d e) \, _2F_1\left(m-1,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)+b^3 d^2 f (m+1) (c+d x) (e+f x)^2\right)}{4 b^4 d^3 (m+1)}","\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,"((a + b*x)^(1 + m)*(b^3*d^2*f*(1 + m)*(c + d*x)*(e + f*x)^2 + (b*c - a*d)^2*f^2*(6*b*d*e + a*d*f*(-3 + m) - b*c*f*(3 + m))*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[-2 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)] + 2*b*(b*c - a*d)*f*(d*e - c*f)*(5*b*d*e + a*d*f*(-2 + m) - b*c*f*(3 + m))*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[-1 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)] + b^2*(d*e - c*f)^2*(4*b*d*e + a*d*f*(-1 + m) - b*c*f*(3 + m))*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)]))/(4*b^4*d^3*(1 + m)*(c + d*x)^m)","A",1
3062,1,201,250,0.2475602,"\int (a+b x)^m (c+d x)^{-m} (e+f x)^2 \, dx","Integrate[((a + b*x)^m*(e + f*x)^2)/(c + d*x)^m,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(\frac{\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 (m-1) (c f (m+1)-3 d e)+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)}{a d-b c}\right)}{m+1}+b f (c+d x) (a d f (m-2)-b c f (m+2)+4 b d e)+2 b^2 d f (c+d x) (e+f x)\right)}{6 b^3 d^2}","\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,"((a + b*x)^(1 + m)*(b*f*(4*b*d*e + a*d*f*(-2 + m) - b*c*f*(2 + m))*(c + d*x) + 2*b^2*d*f*(c + d*x)*(e + f*x) + ((a^2*d^2*f^2*(2 - 3*m + m^2) - 2*a*b*d*f*(-1 + m)*(-3*d*e + c*f*(1 + m)) + b^2*(6*d^2*e^2 - 6*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)))*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])/(1 + m)))/(6*b^3*d^2*(c + d*x)^m)","A",1
3063,1,109,135,0.0820885,"\int (a+b x)^m (c+d x)^{-m} (e+f x) \, dx","Integrate[((a + b*x)^m*(e + f*x))/(c + d*x)^m,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(b f (c+d x)-\frac{\left(\frac{b (c+d x)}{b c-a d}\right)^m (-a d f (m-1)+b c f (m+1)-2 b d e) \, _2F_1\left(m,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)}{m+1}\right)}{2 b^2 d}","\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,"((a + b*x)^(1 + m)*(b*f*(c + d*x) - ((-2*b*d*e - a*d*f*(-1 + m) + b*c*f*(1 + m))*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])/(1 + m)))/(2*b^2*d*(c + d*x)^m)","A",1
3064,1,71,72,0.0186711,"\int (a+b x)^m (c+d x)^{-m} \, dx","Integrate[(a + b*x)^m/(c + d*x)^m,x]","\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)}{a d-b c}\right)}{b (m+1)}","\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,"((a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(1 + m)*(c + d*x)^m)","A",1
3065,1,106,128,0.0375016,"\int \frac{(a+b x)^m (c+d x)^{-m}}{e+f x} \, dx","Integrate[(a + b*x)^m/((c + d*x)^m*(e + f*x)),x]","\frac{(a+b x)^m (c+d x)^{-m} \left(\left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m,m;m+1;\frac{d (a+b x)}{a d-b c}\right)-\, _2F_1\left(1,m;m+1;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)\right)}{f m}","\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,"((a + b*x)^m*(-Hypergeometric2F1[1, m, 1 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))] + ((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, m, 1 + m, (d*(a + b*x))/(-(b*c) + a*d)]))/(f*m*(c + d*x)^m)","A",1
3066,1,83,83,0.0246696,"\int \frac{(a+b x)^m (c+d x)^{-m}}{(e+f x)^2} \, dx","Integrate[(a + b*x)^m/((c + d*x)^m*(e + f*x)^2),x]","\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}","\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,"((b*c - a*d)*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*Hypergeometric2F1[2, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/((b*e - a*f)^2*(1 + m))","A",1
3067,1,146,174,0.113969,"\int \frac{(a+b x)^m (c+d x)^{-m}}{(e+f x)^3} \, dx","Integrate[(a + b*x)^m/((c + d*x)^m*(e + f*x)^3),x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-1} \left(\frac{(b c-a d) (-a d f (m+1)+b c f (m-1)+2 b 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+1) (b e-a f)^2}-\frac{f (c+d x)^2}{(e+f x)^2}\right)}{2 (b e-a f) (d e-c f)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*(-((f*(c + d*x)^2)/(e + f*x)^2) + ((b*c - a*d)*(2*b*d*e + b*c*f*(-1 + m) - a*d*f*(1 + m))*Hypergeometric2F1[2, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/((b*e - a*f)^2*(1 + m))))/(2*(b*e - a*f)*(d*e - c*f))","A",1
3068,1,255,309,0.5315813,"\int \frac{(a+b x)^m (c+d x)^{-m}}{(e+f x)^4} \, dx","Integrate[(a + b*x)^m/((c + d*x)^m*(e + f*x)^4),x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-1} \left(\frac{(b c-a d) \left(a^2 d^2 f^2 \left(m^2+3 m+2\right)-2 a b d f (m+1) (c f (m-1)+3 d e)+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(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}-\frac{f (c+d x)^2 (-a d f (m+2)+b c f (m-2)+4 b d e)}{(e+f x)^2}-\frac{2 f (c+d x)^2 (a f-b e) (c f-d e)}{(e+f x)^3}\right)}{6 (b e-a f)^2 (d e-c f)^2}","-\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,"((a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*((-2*f*(-(b*e) + a*f)*(-(d*e) + c*f)*(c + d*x)^2)/(e + f*x)^3 - (f*(4*b*d*e + b*c*f*(-2 + m) - a*d*f*(2 + m))*(c + d*x)^2)/(e + f*x)^2 + ((b*c - a*d)*(-2*a*b*d*f*(3*d*e + c*f*(-1 + m))*(1 + m) + a^2*d^2*f^2*(2 + 3*m + m^2) + b^2*(6*d^2*e^2 + 6*c*d*e*f*(-1 + m) + c^2*f^2*(2 - 3*m + m^2)))*Hypergeometric2F1[2, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/((b*e - a*f)^2*(1 + m))))/(6*(b*e - a*f)^2*(d*e - c*f)^2)","A",1
3069,1,131,179,0.1437164,"\int \frac{(1+2 x)^{-m} (2+3 x)^m}{(5-4 x)^5} \, dx","Integrate[(2 + 3*x)^m/((5 - 4*x)^5*(1 + 2*x)^m),x]","\frac{(2 x+1)^{1-m} (3 x+2)^{m-1} \left(-\frac{\left(m^3+132 m^2+4358 m+32010\right) \, _2F_1\left(2,1-m;2-m;\frac{46 x+23}{42 x+28}\right)}{m-1}+\frac{98 \left(2 m^2+220 m+4359\right) (3 x+2)^2}{(5-4 x)^2}-\frac{31556 (m+66) (3 x+2)^2}{(4 x-5)^3}+\frac{7620774 (3 x+2)^2}{(5-4 x)^4}\right)}{2453889228}","\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,"((1 + 2*x)^(1 - m)*(2 + 3*x)^(-1 + m)*((7620774*(2 + 3*x)^2)/(5 - 4*x)^4 + (98*(4359 + 220*m + 2*m^2)*(2 + 3*x)^2)/(5 - 4*x)^2 - (31556*(66 + m)*(2 + 3*x)^2)/(-5 + 4*x)^3 - ((32010 + 4358*m + 132*m^2 + m^3)*Hypergeometric2F1[2, 1 - m, 2 - m, (23 + 46*x)/(28 + 42*x)])/(-1 + m)))/2453889228","A",1
3070,1,125,130,0.1833071,"\int (a+b x)^m (c+d x)^{-1-m} (e+f x)^p \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-1 - m)*(e + f*x)^p,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-1} (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{m+1} \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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{b (m+1)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*((b*(c + d*x))/(b*c - a*d))^(1 + m)*(e + f*x)^p*AppellF1[1 + m, 1 + m, -p, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/(b*(1 + m)*((b*(e + f*x))/(b*e - a*f))^p)","A",1
3071,1,106,142,0.0979464,"\int (5-4 x)^3 (1+2 x)^{-1-m} (2+3 x)^m \, dx","Integrate[(5 - 4*x)^3*(1 + 2*x)^(-1 - m)*(2 + 3*x)^m,x]","\frac{2^{-m-1} (2 x+1)^{-m} \left(\left(4 m^3-390 m^2+8324 m-27783\right) (2 x+1) \, _2F_1(1-m,-m;2-m;-6 x-3)-(m-1) (6 x+4)^{m+1} \left(m^2 (8 x+4)+m \left(96 x^2-676 x-362\right)+9261\right)\right)}{27 (m-1) m}","\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,"(2^(-1 - m)*(-((-1 + m)*(4 + 6*x)^(1 + m)*(9261 + m^2*(4 + 8*x) + m*(-362 - 676*x + 96*x^2))) + (-27783 + 8324*m - 390*m^2 + 4*m^3)*(1 + 2*x)*Hypergeometric2F1[1 - m, -m, 2 - m, -3 - 6*x]))/(27*(-1 + m)*m*(1 + 2*x)^m)","A",1
3072,1,96,121,0.0989826,"\int (5-4 x)^2 (1+2 x)^{-1-m} (2+3 x)^m \, dx","Integrate[(5 - 4*x)^2*(1 + 2*x)^(-1 - m)*(2 + 3*x)^m,x]","\frac{1}{6} (2 x+1)^{-m} \left(-\frac{2^{-m} \left(2 m^2-86 m+441\right) (2 x+1) \, _2F_1(1-m,-m;2-m;-6 x-3)}{(m-1) m}+2 (4 x-5) (3 x+2)^{m+1}+\frac{14 (m-21) (3 x+2)^{m+1}}{m}\right)","\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,"((14*(-21 + m)*(2 + 3*x)^(1 + m))/m + 2*(2 + 3*x)^(1 + m)*(-5 + 4*x) - ((441 - 86*m + 2*m^2)*(1 + 2*x)*Hypergeometric2F1[1 - m, -m, 2 - m, -3 - 6*x])/(2^m*(-1 + m)*m))/(6*(1 + 2*x)^m)","A",1
3073,1,114,152,0.0874945,"\int (a+b x)^m (c+d x)^{-1-m} (e+f x) \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-1 - m)*(e + f*x),x]","\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(\frac{\left(\frac{b (c+d x)}{b c-a d}\right)^m (a d f m-b c f (m+1)+b d e) \, _2F_1\left(m,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)}{b (m+1)}+c f-d e\right)}{d m (a d-b c)}","\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,"((a + b*x)^(1 + m)*(-(d*e) + c*f + ((b*d*e + a*d*f*m - b*c*f*(1 + m))*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(1 + m))))/(d*(-(b*c) + a*d)*m*(c + d*x)^m)","A",1
3074,1,74,75,0.0282277,"\int (a+b x)^m (c+d x)^{-1-m} \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-1 - m),x]","-\frac{(a+b x)^m (c+d x)^{-m} \left(\frac{d (a+b x)}{a d-b c}\right)^{-m} \, _2F_1\left(-m,-m;1-m;\frac{b (c+d x)}{b c-a d}\right)}{d m}","-\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,"-(((a + b*x)^m*Hypergeometric2F1[-m, -m, 1 - m, (b*(c + d*x))/(b*c - a*d)])/(d*m*((d*(a + b*x))/(-(b*c) + a*d))^m*(c + d*x)^m))","A",1
3075,1,75,72,0.0214851,"\int \frac{(a+b x)^m (c+d x)^{-1-m}}{e+f x} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(-1 - m))/(e + f*x),x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-1} \, _2F_1\left(1,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)}","-\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,"((a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*Hypergeometric2F1[1, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/((b*e - a*f)*(1 + m))","A",1
3076,1,142,158,0.1653452,"\int \frac{(a+b x)^m (c+d x)^{-1-m}}{(e+f x)^2} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(-1 - m))/(e + f*x)^2,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(\frac{(b c-a d) (b (c f m+d e)-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)}{(m+1) (c+d x) (b e-a f)^2}-\frac{d}{e+f x}\right)}{m (b c-a d) (c f-d e)}","\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,"((a + b*x)^(1 + m)*(-(d/(e + f*x)) + ((b*c - a*d)*(-(a*d*f*(1 + m)) + b*(d*e + c*f*m))*Hypergeometric2F1[2, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/((b*e - a*f)^2*(1 + m)*(c + d*x))))/((b*c - a*d)*(-(d*e) + c*f)*m*(c + d*x)^m)","A",1
3077,1,260,283,0.526943,"\int \frac{(a+b x)^m (c+d x)^{-1-m}}{(e+f x)^3} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(-1 - m))/(e + f*x)^3,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(-\frac{(b c-a d) \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)+b^2 \left(c^2 f^2 (m-1) m+4 c d e f m+2 d^2 e^2\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)}{(m+1) (c+d x) (b e-a f)^3 (c f-d e)}-\frac{f (c+d x) (b (c f m+2 d e)-a d f (m+2))}{(e+f x)^2 (b e-a f) (d e-c f)}-\frac{2 d}{(e+f x)^2}\right)}{2 m (b c-a d) (c f-d e)}","\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,"((a + b*x)^(1 + m)*((-2*d)/(e + f*x)^2 - (f*(-(a*d*f*(2 + m)) + b*(2*d*e + c*f*m))*(c + d*x))/((b*e - a*f)*(d*e - c*f)*(e + f*x)^2) - ((b*c - a*d)*(-2*a*b*d*f*(1 + m)*(2*d*e + c*f*m) + b^2*(2*d^2*e^2 + 4*c*d*e*f*m + c^2*f^2*(-1 + m)*m) + a^2*d^2*f^2*(2 + 3*m + m^2))*Hypergeometric2F1[2, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/((b*e - a*f)^3*(-(d*e) + c*f)*(1 + m)*(c + d*x))))/(2*(b*c - a*d)*(-(d*e) + c*f)*m*(c + d*x)^m)","A",1
3078,1,466,498,1.8035871,"\int \frac{(a+b x)^m (c+d x)^{-1-m}}{(e+f x)^4} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(-1 - m))/(e + f*x)^4,x]","-\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(-\frac{(e+f x) \left(f (m+1) (c+d x)^2 (b e-a f)^2 \left(-a^2 d^2 f^2 \left(m^2+5 m+6\right)+a b d f (c f m (2 m+3)+d e (7 m+12))-\left(b^2 \left(c^2 f^2 (m-2) m+7 c d e f m+6 d^2 e^2\right)\right)\right)+(e+f x)^2 (b c-a d) \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 (m-1) m+6 c d e f m+6 d^2 e^2\right)+b^3 \left(c^3 f^3 m \left(m^2-3 m+2\right)+9 c^2 d e f^2 (m-1) m+18 c d^2 e^2 f m+6 d^3 e^3\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)\right)}{c+d x}+2 f (m+1) (c+d x) (a f-b e)^3 (c f-d e) (b (c f m+3 d e)-a d f (m+3))+6 d (m+1) (b e-a f)^4 (d e-c f)^2\right)}{6 m (m+1) (e+f x)^3 (b c-a d) (b e-a f)^4 (d e-c f)^2 (c f-d e)}","-\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,"-1/6*((a + b*x)^(1 + m)*(6*d*(b*e - a*f)^4*(d*e - c*f)^2*(1 + m) + 2*f*(-(b*e) + a*f)^3*(-(d*e) + c*f)*(1 + m)*(-(a*d*f*(3 + m)) + b*(3*d*e + c*f*m))*(c + d*x) - ((e + f*x)*(f*(b*e - a*f)^2*(1 + m)*(-(b^2*(6*d^2*e^2 + 7*c*d*e*f*m + c^2*f^2*(-2 + m)*m)) - a^2*d^2*f^2*(6 + 5*m + m^2) + a*b*d*f*(c*f*m*(3 + 2*m) + d*e*(12 + 7*m)))*(c + d*x)^2 + (b*c - a*d)*(-3*a*b^2*d*f*(1 + m)*(6*d^2*e^2 + 6*c*d*e*f*m + c^2*f^2*(-1 + m)*m) + 3*a^2*b*d^2*f^2*(3*d*e + c*f*m)*(2 + 3*m + m^2) - a^3*d^3*f^3*(6 + 11*m + 6*m^2 + m^3) + b^3*(6*d^3*e^3 + 18*c*d^2*e^2*f*m + 9*c^2*d*e*f^2*(-1 + m)*m + c^3*f^3*m*(2 - 3*m + m^2)))*(e + f*x)^2*Hypergeometric2F1[2, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]))/(c + d*x)))/((b*c - a*d)*(b*e - a*f)^4*(d*e - c*f)^2*(-(d*e) + c*f)*m*(1 + m)*(c + d*x)^m*(e + f*x)^3)","A",1
3079,1,129,131,0.2026288,"\int (a+b x)^m (c+d x)^{-2-m} (e+f x)^p \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-2 - m)*(e + f*x)^p,x]","\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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{(m+1) (b c-a d)^2}","\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,"(b*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*(e + f*x)^p*AppellF1[1 + m, 2 + m, -p, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/((b*c - a*d)^2*(1 + m)*(c + d*x)^m*((b*(e + f*x))/(b*e - a*f))^p)","A",1
3080,1,114,132,0.1030703,"\int (5-4 x)^3 (1+2 x)^{-2-m} (2+3 x)^m \, dx","Integrate[(5 - 4*x)^3*(1 + 2*x)^(-2 - m)*(2 + 3*x)^m,x]","\frac{2^{-m} (2 x+1)^{-m-1} \left(\left(2 m^3-126 m^2+1195 m+1323\right) (2 x+1) \, _2F_1(-m,-m;1-m;-6 x-3)-2^m m (3 x+2)^{m+1} \left(m^2 (8 x+4)+24 m \left(2 x^2-19 x-10\right)+48 x^2-464 x+2843\right)\right)}{9 m (m+1)}","\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,"((1 + 2*x)^(-1 - m)*(-(2^m*m*(2 + 3*x)^(1 + m)*(2843 - 464*x + 48*x^2 + m^2*(4 + 8*x) + 24*m*(-10 - 19*x + 2*x^2))) + (1323 + 1195*m - 126*m^2 + 2*m^3)*(1 + 2*x)*Hypergeometric2F1[-m, -m, 1 - m, -3 - 6*x]))/(9*2^m*m*(1 + m))","A",1
3081,1,179,204,0.416006,"\int (a+b x)^m (c+d x)^{-2-m} (e+f x)^2 \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-2 - m)*(e + f*x)^2,x]","\frac{(a+b x)^m (c+d x)^{-m} \left(\frac{f \left(\frac{d (a+b x)}{a d-b c}\right)^{-m} (-a d f m+b c f (m+2)-2 b d e) \, _2F_1\left(-m,-m;1-m;\frac{b (c+d x)}{b c-a d}\right)}{d^2 m}+\frac{(a+b x) (d e-c f) (a d f (m+1)-b c f (m+2)+b d e)}{d (m+1) (c+d x) (b c-a d)}+\frac{f (a+b x) (e+f x)}{c+d x}\right)}{b d}","-\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,"((a + b*x)^m*(((d*e - c*f)*(b*d*e + a*d*f*(1 + m) - b*c*f*(2 + m))*(a + b*x))/(d*(b*c - a*d)*(1 + m)*(c + d*x)) + (f*(a + b*x)*(e + f*x))/(c + d*x) + (f*(-2*b*d*e - a*d*f*m + b*c*f*(2 + m))*Hypergeometric2F1[-m, -m, 1 - m, (b*(c + d*x))/(b*c - a*d)])/(d^2*m*((d*(a + b*x))/(-(b*c) + a*d))^m)))/(b*d*(c + d*x)^m)","A",1
3082,1,114,124,0.1509818,"\int (a+b x)^m (c+d x)^{-2-m} (e+f x) \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-2 - m)*(e + f*x),x]","\frac{(a+b x)^m (c+d x)^{-m} \left(\frac{d (a+b x) (d e-c f)}{(m+1) (c+d x) (b c-a d)}-\frac{f \left(\frac{d (a+b x)}{a d-b c}\right)^{-m} \, _2F_1\left(-m,-m;1-m;\frac{b (c+d x)}{b c-a d}\right)}{m}\right)}{d^2}","\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,"((a + b*x)^m*((d*(d*e - c*f)*(a + b*x))/((b*c - a*d)*(1 + m)*(c + d*x)) - (f*Hypergeometric2F1[-m, -m, 1 - m, (b*(c + d*x))/(b*c - a*d)])/(m*((d*(a + b*x))/(-(b*c) + a*d))^m)))/(d^2*(c + d*x)^m)","A",1
3083,1,36,36,0.0116444,"\int (a+b x)^m (c+d x)^{-2-m} \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-2 - m),x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-1}}{(m+1) (b c-a d)}","\frac{(a+b x)^{m+1} (c+d x)^{-m-1}}{(m+1) (b c-a d)}",1,"((a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/((b*c - a*d)*(1 + m))","A",1
3084,1,115,120,0.0617221,"\int \frac{(a+b x)^m (c+d x)^{-2-m}}{e+f x} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(-2 - m))/(e + f*x),x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-1} \left(f (b c-a d) \, _2F_1\left(1,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)+a d f-b d e\right)}{(m+1) (b c-a d) (b e-a f) (c f-d e)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*(-(b*d*e) + a*d*f + (b*c - a*d)*f*Hypergeometric2F1[1, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]))/((b*c - a*d)*(b*e - a*f)*(-(d*e) + c*f)*(1 + m))","A",1
3085,1,193,233,0.2871821,"\int \frac{(a+b x)^m (c+d x)^{-2-m}}{(e+f x)^2} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(-2 - m))/(e + f*x)^2,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-1} \left(f (e+f x) (b c-a d) (a d f (m+2)-b (c f m+2 d e)) \, _2F_1\left(1,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)+f (c+d x) (b e-a f) (-a d f (m+2)+b c f (m+1)+b d e)+d (b e-a f)^2 (d e-c f)\right)}{(m+1) (e+f x) (b c-a d) (b e-a f)^2 (d e-c f)^2}","-\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,"((a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*(d*(b*e - a*f)^2*(d*e - c*f) + f*(b*e - a*f)*(b*d*e + b*c*f*(1 + m) - a*d*f*(2 + m))*(c + d*x) + (b*c - a*d)*f*(a*d*f*(2 + m) - b*(2*d*e + c*f*m))*(e + f*x)*Hypergeometric2F1[1, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]))/((b*c - a*d)*(b*e - a*f)^2*(d*e - c*f)^2*(1 + m)*(e + f*x))","A",1
3086,1,374,432,1.0450832,"\int \frac{(a+b x)^m (c+d x)^{-2-m}}{(e+f x)^3} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(-2 - m))/(e + f*x)^3,x]","-\frac{(a+b x)^{m+1} (c+d x)^{-m} \left((e+f x) \left(f (b e-a f) \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(m^2-1\right)+5 c d e f (m+1)+2 d^2 e^2\right)\right)-\frac{f (e+f x) (b c-a d) \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)+b^2 \left(c^2 f^2 (m-1) m+6 c d e f m+6 d^2 e^2\right)\right) \, _2F_1\left(1,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{c+d x}\right)+f (b e-a f)^2 (d e-c f) (-a d f (m+3)+b c f (m+1)+2 b d e)+\frac{2 d (b e-a f)^3 (d e-c f)^2}{c+d x}\right)}{2 (m+1) (e+f x)^2 (b c-a d) (b e-a f)^3 (d e-c f)^2 (c f-d e)}","-\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,"-1/2*((a + b*x)^(1 + m)*(f*(b*e - a*f)^2*(d*e - c*f)*(2*b*d*e + b*c*f*(1 + m) - a*d*f*(3 + m)) + (2*d*(b*e - a*f)^3*(d*e - c*f)^2)/(c + d*x) + (e + f*x)*(f*(b*e - a*f)*(a^2*d^2*f^2*(6 + 5*m + m^2) + b^2*(2*d^2*e^2 + 5*c*d*e*f*(1 + m) + c^2*f^2*(-1 + m^2)) - a*b*d*f*(d*e*(9 + 5*m) + c*f*(3 + 5*m + 2*m^2))) - ((b*c - a*d)*f*(-2*a*b*d*f*(2 + m)*(3*d*e + c*f*m) + b^2*(6*d^2*e^2 + 6*c*d*e*f*m + c^2*f^2*(-1 + m)*m) + a^2*d^2*f^2*(6 + 5*m + m^2))*(e + f*x)*Hypergeometric2F1[1, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/(c + d*x))))/((b*c - a*d)*(b*e - a*f)^3*(d*e - c*f)^2*(-(d*e) + c*f)*(1 + m)*(c + d*x)^m*(e + f*x)^2)","A",1
3087,1,131,133,0.4331306,"\int (a+b x)^m (c+d x)^{-3-m} (e+f x)^p \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-3 - m)*(e + f*x)^p,x]","\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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{(m+1) (b c-a d)^3}","\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,"(b^2*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*(e + f*x)^p*AppellF1[1 + m, 3 + m, -p, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/((b*c - a*d)^3*(1 + m)*(c + d*x)^m*((b*(e + f*x))/(b*e - a*f))^p)","A",1
3088,1,153,188,0.2465664,"\int (5-4 x)^4 (1+2 x)^{-3-m} (2+3 x)^m \, dx","Integrate[(5 - 4*x)^4*(1 + 2*x)^(-3 - m)*(2 + 3*x)^m,x]","\frac{2^{-m} (2 x+1)^{-m-2} \left(2^m (3 x+2)^{m+1} \left(16 m^3 \left(6 x^2+7 x+2\right)+32 m^2 \left(18 x^3-219 x^2-274 x-80\right)+m \left(1728 x^3-21696 x^2+143632 x+12629\right)+6 \left(192 x^3-2432 x^2+118699 x+49177\right)\right)-4 \left(m^3-83 m^2+1153 m+2646\right) (2 x+1) \, _2F_1(-m-1,-m-1;-m;-6 x-3)\right)}{27 (m+1) (m+2)}","-\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,"((1 + 2*x)^(-2 - m)*(2^m*(2 + 3*x)^(1 + m)*(16*m^3*(2 + 7*x + 6*x^2) + 32*m^2*(-80 - 274*x - 219*x^2 + 18*x^3) + 6*(49177 + 118699*x - 2432*x^2 + 192*x^3) + m*(12629 + 143632*x - 21696*x^2 + 1728*x^3)) - 4*(2646 + 1153*m - 83*m^2 + m^3)*(1 + 2*x)*Hypergeometric2F1[-1 - m, -1 - m, -m, -3 - 6*x]))/(27*2^m*(1 + m)*(2 + m))","A",1
3089,1,123,139,0.1063008,"\int (5-4 x)^3 (1+2 x)^{-3-m} (2+3 x)^m \, dx","Integrate[(5 - 4*x)^3*(1 + 2*x)^(-3 - m)*(2 + 3*x)^m,x]","\frac{2^{-m} (2 x+1)^{-m-2} \left(2 \left(2 m^3-57 m^2-185 m-126\right) (2 x+1)^2 \, _2F_1(-m,-m;1-m;-6 x-3)-2^m m (3 x+2)^{m+1} \left(3 m \left(32 x^2-556 x+57\right)+8 (2 m x+m)^2+64 x^2-9638 x-3806\right)\right)}{3 m (m+1) (m+2)}","-\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,"((1 + 2*x)^(-2 - m)*(-(2^m*m*(2 + 3*x)^(1 + m)*(-3806 - 9638*x + 64*x^2 + 8*(m + 2*m*x)^2 + 3*m*(57 - 556*x + 32*x^2))) + 2*(-126 - 185*m - 57*m^2 + 2*m^3)*(1 + 2*x)^2*Hypergeometric2F1[-m, -m, 1 - m, -3 - 6*x]))/(3*2^m*m*(1 + m)*(2 + m))","A",1
3090,1,184,205,0.4734984,"\int (a+b x)^m (c+d x)^{-3-m} (e+f x)^2 \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-3 - m)*(e + f*x)^2,x]","\frac{(a+b x)^m (c+d x)^{-m} \left(\frac{(a+b x) (d e-c f) (-2 a d f (m+2)+b c f (2 m+3)+b d e)}{(m+1) (c+d x) (b c-a d)}+\frac{(a+b x) (d e-c f)^2}{(c+d x)^2}+\frac{f^2 (m+2) (a+b x) \left(\frac{d (a+b x)}{a d-b c}\right)^{-m-1} \, _2F_1\left(-m,-m;1-m;\frac{b (c+d x)}{b c-a d}\right)}{m}\right)}{d^2 (m+2) (b c-a d)}","-\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,"((a + b*x)^m*(((d*e - c*f)^2*(a + b*x))/(c + d*x)^2 + ((d*e - c*f)*(b*d*e - 2*a*d*f*(2 + m) + b*c*f*(3 + 2*m))*(a + b*x))/((b*c - a*d)*(1 + m)*(c + d*x)) + (f^2*(2 + m)*(a + b*x)*((d*(a + b*x))/(-(b*c) + a*d))^(-1 - m)*Hypergeometric2F1[-m, -m, 1 - m, (b*(c + d*x))/(b*c - a*d)])/m))/(d^2*(b*c - a*d)*(2 + m)*(c + d*x)^m)","A",1
3091,1,82,114,0.0601022,"\int (a+b x)^m (c+d x)^{-3-m} (e+f x) \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-3 - m)*(e + f*x),x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-2} (b (c e (m+2)+c f (m+1) x+d e x)-a (c f+d e (m+1)+d f (m+2) x))}{(m+1) (m+2) (b c-a d)^2}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-2 - m)*(b*(c*e*(2 + m) + d*e*x + c*f*(1 + m)*x) - a*(c*f + d*e*(1 + m) + d*f*(2 + m)*x)))/((b*c - a*d)^2*(1 + m)*(2 + m))","A",1
3092,1,59,79,0.0247427,"\int (a+b x)^m (c+d x)^{-3-m} \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-3 - m),x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-2} (-a d (m+1)+b c (m+2)+b d x)}{(m+1) (m+2) (b c-a d)^2}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-2 - m)*(-(a*d*(1 + m)) + b*c*(2 + m) + b*d*x))/((b*c - a*d)^2*(1 + m)*(2 + m))","A",1
3093,1,186,196,0.248618,"\int \frac{(a+b x)^m (c+d x)^{-3-m}}{e+f x} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(-3 - m))/(e + f*x),x]","-\frac{(a+b x)^{m+1} (c+d x)^{-m-2} \left(\frac{f^2 (m+2) (c+d x) (b c-a d) \, _2F_1\left(1,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) (d e-c f)}-\frac{d (c+d x) (a d f (m+2)-b c f (m+3)+b d e)}{(m+1) (b c-a d) (c f-d e)}+d\right)}{(m+2) (b c-a d) (c f-d e)}","-\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,"-(((a + b*x)^(1 + m)*(c + d*x)^(-2 - m)*(d - (d*(b*d*e + a*d*f*(2 + m) - b*c*f*(3 + m))*(c + d*x))/((b*c - a*d)*(-(d*e) + c*f)*(1 + m)) + ((b*c - a*d)*f^2*(2 + m)*(c + d*x)*Hypergeometric2F1[1, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/((b*e - a*f)*(d*e - c*f)*(1 + m))))/((b*c - a*d)*(-(d*e) + c*f)*(2 + m)))","A",1
3094,1,333,384,1.0740007,"\int \frac{(a+b x)^m (c+d x)^{-3-m}}{(e+f x)^2} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(-3 - m))/(e + f*x)^2,x]","-\frac{(a+b x)^{m+1} (c+d x)^{-m-2} \left(\frac{(c+d x) \left(d (m+1) (b e-a f) \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)+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)+f^2 \left(m^2+3 m+2\right) (b c-a d)^2 (b (c f m+3 d e)-a d f (m+3)) \, _2F_1\left(1,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)\right)}{(m+1)^2 (b c-a d) (b e-a f)^2 (d e-c f)^2}+\frac{f (c+d x) (-a d f (m+3)+b c f (m+2)+b d e)}{(e+f x) (b e-a f) (d e-c f)}+\frac{d}{e+f x}\right)}{(m+2) (b c-a d) (c f-d e)}","-\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,"-(((a + b*x)^(1 + m)*(c + d*x)^(-2 - m)*(d/(e + f*x) + (f*(b*d*e + b*c*f*(2 + m) - a*d*f*(3 + m))*(c + d*x))/((b*e - a*f)*(d*e - c*f)*(e + f*x)) + ((c + d*x)*(d*(b*e - a*f)*(1 + m)*(-(a^2*d^2*f^2*(6 + 5*m + m^2)) + b^2*(d^2*e^2 - c*d*e*f*(5 + 2*m) - c^2*f^2*(2 + 3*m + m^2)) + a*b*d*f*(d*e*(3 + 2*m) + c*f*(9 + 8*m + 2*m^2))) + (b*c - a*d)^2*f^2*(2 + 3*m + m^2)*(-(a*d*f*(3 + m)) + b*(3*d*e + c*f*m))*Hypergeometric2F1[1, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]))/((b*c - a*d)*(b*e - a*f)^2*(d*e - c*f)^2*(1 + m)^2)))/((b*c - a*d)*(-(d*e) + c*f)*(2 + m)))","A",1
3095,1,131,133,1.1013394,"\int (a+b x)^m (c+d x)^{-4-m} (e+f x)^p \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-4 - m)*(e + f*x)^p,x]","\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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{(m+1) (b c-a d)^4}","\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,"(b^3*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*(e + f*x)^p*AppellF1[1 + m, 4 + m, -p, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/((b*c - a*d)^4*(1 + m)*(c + d*x)^m*((b*(e + f*x))/(b*e - a*f))^p)","A",1
3096,1,161,333,0.1915635,"\int (5-4 x)^4 (1+2 x)^{-4-m} (2+3 x)^m \, dx","Integrate[(5 - 4*x)^4*(1 + 2*x)^(-4 - m)*(2 + 3*x)^m,x]","\frac{2^{-m} (2 x+1)^{-m-3} \left(2^m (3 x+2)^{m+1} \left(32 m^3 (2 x+1)^2 (3 x+2)+m^2 \left(2304 x^3-41248 x^2+6416 x-7801\right)+m \left(4224 x^3-514752 x^2-61044 x+33867\right)+18 \left(128 x^3-150644 x^2-128102 x-28775\right)\right)-8 \left(m^3-37 m^2-204 m-252\right) (2 x+1)^2 \, _2F_1(-m-1,-m-1;-m;-6 x-3)\right)}{9 (m+1) (m+2) (m+3)}","\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,"((1 + 2*x)^(-3 - m)*(2^m*(2 + 3*x)^(1 + m)*(32*m^3*(1 + 2*x)^2*(2 + 3*x) + 18*(-28775 - 128102*x - 150644*x^2 + 128*x^3) + m^2*(-7801 + 6416*x - 41248*x^2 + 2304*x^3) + m*(33867 - 61044*x - 514752*x^2 + 4224*x^3)) - 8*(-252 - 204*m - 37*m^2 + m^3)*(1 + 2*x)^2*Hypergeometric2F1[-1 - m, -1 - m, -m, -3 - 6*x]))/(9*2^m*(1 + m)*(2 + m)*(3 + m))","A",1
3097,1,1150,406,35.0941213,"\int (a+b x)^m (c+d x)^{-4-m} (e+f x)^3 \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-4 - m)*(e + f*x)^3,x]","\frac{1}{4} (a+b x)^m (c+d x)^{-m} \left(-\frac{4 e^3 \, _2F_1\left(-m-3,-m;-m-2;\frac{b (c+d x)}{b c-a d}\right) \left(\frac{d (a+b x)}{a d-b c}\right)^{-m}}{d (m+3) (c+d x)^3}+\frac{12 e f^2 \left(\frac{b x}{a}+1\right)^{-m} \left(\frac{d x}{c}+1\right)^m \left(b^3 c^3 \left(m^2+3 m+2\right) x^3 \left(\frac{c (a+b x)}{a (c+d x)}\right)^m-a b^2 c^2 (m+1) x^2 (2 d (m+3) x-c m) \left(\frac{c (a+b x)}{a (c+d x)}\right)^m+a^2 b c x \left(-2 m c^2-2 d m (m+3) x c+d^2 \left(m^2+5 m+6\right) x^2\right) \left(\frac{c (a+b x)}{a (c+d x)}\right)^m+a^3 \left(2 \left(\left(\frac{c (a+b x)}{a (c+d x)}\right)^m-1\right) c^3+2 d x \left(m \left(\frac{c (a+b x)}{a (c+d x)}\right)^m+3 \left(\frac{c (a+b x)}{a (c+d x)}\right)^m-3\right) c^2+d^2 x^2 \left(m^2 \left(\frac{c (a+b x)}{a (c+d x)}\right)^m+5 m \left(\frac{c (a+b x)}{a (c+d x)}\right)^m+6 \left(\frac{c (a+b x)}{a (c+d x)}\right)^m-6\right) c-2 d^3 x^3\right)\right)}{c (b c-a d)^3 (m+1) (m+2) (m+3) (c+d x)^3}+\frac{f^3 x^4 \left(\frac{b x}{a}+1\right)^{-m} \left(\frac{d x}{c}+1\right)^m F_1\left(4;-m,m+4;5;-\frac{b x}{a},-\frac{d x}{c}\right)}{c^4}+\frac{6 e^2 f \left((c+d x) \left(\left(2 d^3 m x^3 \left(\frac{a (c+d x)}{c (a+b x)}\right)^m-6 c^3 \left(\left(\frac{a (c+d x)}{c (a+b x)}\right)^m-1\right)+2 c^2 d x \left(-6 \left(\frac{a (c+d x)}{c (a+b x)}\right)^m+m \left(\left(\frac{a (c+d x)}{c (a+b x)}\right)^m+2\right)+6\right)+c d^2 x^2 \left(-6 \left(\frac{a (c+d x)}{c (a+b x)}\right)^m+m^2+m \left(4 \left(\frac{a (c+d x)}{c (a+b x)}\right)^m+5\right)+6\right)\right) a^3-b c x \left(2 \left(m \left(\frac{a (c+d x)}{c (a+b x)}\right)^m+3 \left(\frac{a (c+d x)}{c (a+b x)}\right)^m+2 m-3\right) c^2+2 d (m+3) x \left(2 \left(\frac{a (c+d x)}{c (a+b x)}\right)^m+m-2\right) c+d^2 (m+3) x^2 \left(2 \left(\frac{a (c+d x)}{c (a+b x)}\right)^m-m-2\right)\right) a^2+b^2 c^2 m x^2 (c (m-3)-2 d (m+3) x) a+b^3 c^3 m (m+1) x^3\right) \operatorname{Gamma}(1-m)+m (3 c+d x) \left(\left(-2 d^3 x^3 \left(\frac{a (c+d x)}{c (a+b x)}\right)^m-2 c^3 \left(\left(\frac{a (c+d x)}{c (a+b x)}\right)^m-1\right)-2 c^2 d x \left(3 \left(\frac{a (c+d x)}{c (a+b x)}\right)^m-m-3\right)-c d^2 x^2 \left(6 \left(\frac{a (c+d x)}{c (a+b x)}\right)^m-m^2-5 m-6\right)\right) a^3+b c x \left(-2 m c^2-2 d m (m+3) x c+d^2 \left(m^2+5 m+6\right) x^2\right) a^2+b^2 c^2 (m+1) x^2 (c m-2 d (m+3) x) a+b^3 c^3 \left(m^2+3 m+2\right) x^3\right) \operatorname{Gamma}(-m)\right)}{c^2 (b c-a d)^3 m (m+1) (m+2) (m+3) x (c+d x)^3 \operatorname{Gamma}(-m)}\right)","\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,"((a + b*x)^m*((12*e*f^2*(1 + (d*x)/c)^m*(b^3*c^3*(2 + 3*m + m^2)*x^3*((c*(a + b*x))/(a*(c + d*x)))^m - a*b^2*c^2*(1 + m)*x^2*((c*(a + b*x))/(a*(c + d*x)))^m*(-(c*m) + 2*d*(3 + m)*x) + a^2*b*c*x*((c*(a + b*x))/(a*(c + d*x)))^m*(-2*c^2*m - 2*c*d*m*(3 + m)*x + d^2*(6 + 5*m + m^2)*x^2) + a^3*(-2*d^3*x^3 + 2*c^3*(-1 + ((c*(a + b*x))/(a*(c + d*x)))^m) + 2*c^2*d*x*(-3 + 3*((c*(a + b*x))/(a*(c + d*x)))^m + m*((c*(a + b*x))/(a*(c + d*x)))^m) + c*d^2*x^2*(-6 + 6*((c*(a + b*x))/(a*(c + d*x)))^m + 5*m*((c*(a + b*x))/(a*(c + d*x)))^m + m^2*((c*(a + b*x))/(a*(c + d*x)))^m))))/(c*(b*c - a*d)^3*(1 + m)*(2 + m)*(3 + m)*(1 + (b*x)/a)^m*(c + d*x)^3) + (f^3*x^4*(1 + (d*x)/c)^m*AppellF1[4, -m, 4 + m, 5, -((b*x)/a), -((d*x)/c)])/(c^4*(1 + (b*x)/a)^m) + (6*e^2*f*((c + d*x)*(b^3*c^3*m*(1 + m)*x^3 + a*b^2*c^2*m*x^2*(c*(-3 + m) - 2*d*(3 + m)*x) - a^2*b*c*x*(d^2*(3 + m)*x^2*(-2 - m + 2*((a*(c + d*x))/(c*(a + b*x)))^m) + 2*c*d*(3 + m)*x*(-2 + m + 2*((a*(c + d*x))/(c*(a + b*x)))^m) + 2*c^2*(-3 + 2*m + 3*((a*(c + d*x))/(c*(a + b*x)))^m + m*((a*(c + d*x))/(c*(a + b*x)))^m)) + a^3*(2*d^3*m*x^3*((a*(c + d*x))/(c*(a + b*x)))^m - 6*c^3*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m) + 2*c^2*d*x*(6 - 6*((a*(c + d*x))/(c*(a + b*x)))^m + m*(2 + ((a*(c + d*x))/(c*(a + b*x)))^m)) + c*d^2*x^2*(6 + m^2 - 6*((a*(c + d*x))/(c*(a + b*x)))^m + m*(5 + 4*((a*(c + d*x))/(c*(a + b*x)))^m))))*Gamma[1 - m] + m*(3*c + d*x)*(b^3*c^3*(2 + 3*m + m^2)*x^3 + a*b^2*c^2*(1 + m)*x^2*(c*m - 2*d*(3 + m)*x) + a^2*b*c*x*(-2*c^2*m - 2*c*d*m*(3 + m)*x + d^2*(6 + 5*m + m^2)*x^2) + a^3*(-2*d^3*x^3*((a*(c + d*x))/(c*(a + b*x)))^m - 2*c^3*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m) - 2*c^2*d*x*(-3 - m + 3*((a*(c + d*x))/(c*(a + b*x)))^m) - c*d^2*x^2*(-6 - 5*m - m^2 + 6*((a*(c + d*x))/(c*(a + b*x)))^m)))*Gamma[-m]))/(c^2*(b*c - a*d)^3*m*(1 + m)*(2 + m)*(3 + m)*x*(c + d*x)^3*Gamma[-m]) - (4*e^3*Hypergeometric2F1[-3 - m, -m, -2 - m, (b*(c + d*x))/(b*c - a*d)])/(d*(3 + m)*((d*(a + b*x))/(-(b*c) + a*d))^m*(c + d*x)^3)))/(4*(c + d*x)^m)","C",0
3098,1,286,353,0.2869192,"\int (a+b x)^m (c+d x)^{-4-m} (e+f x)^2 \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-4 - m)*(e + f*x)^2,x]","-\frac{(a+b x)^{m+1} (c+d x)^{-m-3} \left(a^2 \left(2 c^2 f^2+2 c d f (e (m+1)+f (m+3) x)+d^2 \left(e^2 \left(m^2+3 m+2\right)+2 e f \left(m^2+4 m+3\right) x+f^2 \left(m^2+5 m+6\right) x^2\right)\right)-2 a b \left(c^2 f (e (m+3)+f (m+1) x)+c d \left(e^2 \left(m^2+4 m+3\right)+2 e f \left(m^2+4 m+5\right) x+f^2 \left(m^2+4 m+3\right) x^2\right)+d^2 e x (e (m+1)+f (m+3) x)\right)+b^2 \left(c^2 \left(e^2 \left(m^2+5 m+6\right)+2 e f \left(m^2+4 m+3\right) x+f^2 \left(m^2+3 m+2\right) x^2\right)+2 c d e x (e (m+3)+f (m+1) x)+2 d^2 e^2 x^2\right)\right)}{(m+1) (m+2) (m+3) (a d-b c)^3}","\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,"-(((a + b*x)^(1 + m)*(c + d*x)^(-3 - m)*(b^2*(2*d^2*e^2*x^2 + 2*c*d*e*x*(e*(3 + m) + f*(1 + m)*x) + c^2*(e^2*(6 + 5*m + m^2) + 2*e*f*(3 + 4*m + m^2)*x + f^2*(2 + 3*m + m^2)*x^2)) - 2*a*b*(c^2*f*(e*(3 + m) + f*(1 + m)*x) + d^2*e*x*(e*(1 + m) + f*(3 + m)*x) + c*d*(e^2*(3 + 4*m + m^2) + 2*e*f*(5 + 4*m + m^2)*x + f^2*(3 + 4*m + m^2)*x^2)) + a^2*(2*c^2*f^2 + 2*c*d*f*(e*(1 + m) + f*(3 + m)*x) + d^2*(e^2*(2 + 3*m + m^2) + 2*e*f*(3 + 4*m + m^2)*x + f^2*(6 + 5*m + m^2)*x^2))))/((-(b*c) + a*d)^3*(1 + m)*(2 + m)*(3 + m)))","A",1
3099,1,179,188,0.1405046,"\int (a+b x)^m (c+d x)^{-4-m} (e+f x) \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-4 - m)*(e + f*x),x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-3} \left(a^2 d (m+1) (c f+d e (m+2)+d f (m+3) x)-a b \left(c^2 f (m+3)+2 c d \left(e \left(m^2+4 m+3\right)+f \left(m^2+4 m+5\right) x\right)+d^2 x (2 e (m+1)+f (m+3) x)\right)+b^2 \left(c^2 (m+3) (e (m+2)+f (m+1) x)+c d x (2 e (m+3)+f (m+1) x)+2 d^2 e x^2\right)\right)}{(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}}{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,"((a + b*x)^(1 + m)*(c + d*x)^(-3 - m)*(a^2*d*(1 + m)*(c*f + d*e*(2 + m) + d*f*(3 + m)*x) + b^2*(2*d^2*e*x^2 + c^2*(3 + m)*(e*(2 + m) + f*(1 + m)*x) + c*d*x*(2*e*(3 + m) + f*(1 + m)*x)) - a*b*(c^2*f*(3 + m) + d^2*x*(2*e*(1 + m) + f*(3 + m)*x) + 2*c*d*(e*(3 + 4*m + m^2) + f*(5 + 4*m + m^2)*x))))/((b*c - a*d)^3*(1 + m)*(2 + m)*(3 + m))","A",1
3100,1,112,130,0.0608378,"\int (a+b x)^m (c+d x)^{-4-m} \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-4 - m),x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-3} \left(a^2 d^2 \left(m^2+3 m+2\right)-2 a b d (m+1) (c (m+3)+d x)+b^2 \left(c^2 \left(m^2+5 m+6\right)+2 c d (m+3) x+2 d^2 x^2\right)\right)}{(m+1) (m+2) (m+3) (b c-a d)^3}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-3 - m)*(a^2*d^2*(2 + 3*m + m^2) - 2*a*b*d*(1 + m)*(c*(3 + m) + d*x) + b^2*(c^2*(6 + 5*m + m^2) + 2*c*d*(3 + m)*x + 2*d^2*x^2)))/((b*c - a*d)^3*(1 + m)*(2 + m)*(3 + m))","A",1
3101,1,301,330,0.8288631,"\int \frac{(a+b x)^m (c+d x)^{-4-m}}{e+f x} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(-4 - m))/(e + f*x),x]","-\frac{(a+b x)^{m+1} (c+d x)^{-m-3} \left(-\frac{(c+d x)^2 \left(f^3 \left(m^2+5 m+6\right) (b c-a d)^3 \, _2F_1\left(1,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)-d (b e-a f) \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)\right)}{(m+1) (m+2) (b c-a d)^2 (b e-a f) (d e-c f)^2}+\frac{d (c+d x) (-a d f (m+3)+b c f (m+5)-2 b d e)}{(m+2) (b c-a d) (c f-d e)}+d\right)}{(m+3) (b c-a d) (c f-d e)}","\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,"-(((a + b*x)^(1 + m)*(c + d*x)^(-3 - m)*(d + (d*(-2*b*d*e - a*d*f*(3 + m) + b*c*f*(5 + m))*(c + d*x))/((b*c - a*d)*(-(d*e) + c*f)*(2 + m)) - ((c + d*x)^2*(-(d*(b*e - a*f)*(a^2*d^2*f^2*(6 + 5*m + m^2) + a*b*d*f*(3 + m)*(d*e - c*f*(5 + 2*m)) + b^2*(2*d^2*e^2 - c*d*e*f*(7 + m) + c^2*f^2*(11 + 6*m + m^2)))) + (b*c - a*d)^3*f^3*(6 + 5*m + m^2)*Hypergeometric2F1[1, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]))/((b*c - a*d)^2*(b*e - a*f)*(d*e - c*f)^2*(1 + m)*(2 + m))))/((b*c - a*d)*(-(d*e) + c*f)*(3 + m)))","A",1
3102,1,562,634,2.8836179,"\int \frac{(a+b x)^m (c+d x)^{-4-m}}{(e+f x)^2} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(-4 - m))/(e + f*x)^2,x]","-\frac{(a+b x)^{m+1} (c+d x)^{-m-3} \left(\frac{(c+d x) \left(d (m+1)^2 (b c-a d) (b e-a f) (d e-c f) \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)+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)+(c+d x) \left(d (m+1) (b e-a f) \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)+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)-f^3 \left(m^3+6 m^2+11 m+6\right) (b c-a d)^3 (b (c f m+4 d e)-a d f (m+4)) \, _2F_1\left(1,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)\right)\right)}{(m+1)^2 (m+2) (b c-a d)^2 (b e-a f)^2 (d e-c f)^3}+\frac{f (c+d x) (-a d f (m+4)+b c f (m+3)+b d e)}{(e+f x) (b e-a f) (d e-c f)}+\frac{d}{e+f x}\right)}{(m+3) (b c-a d) (c f-d e)}","-\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,"-(((a + b*x)^(1 + m)*(c + d*x)^(-3 - m)*(d/(e + f*x) + (f*(b*d*e + b*c*f*(3 + m) - a*d*f*(4 + m))*(c + d*x))/((b*e - a*f)*(d*e - c*f)*(e + f*x)) + ((c + d*x)*(d*(b*c - a*d)*(b*e - a*f)*(d*e - c*f)*(1 + m)^2*(-(a^2*d^2*f^2*(12 + 7*m + m^2)) + b^2*(2*d^2*e^2 - 2*c*d*e*f*(4 + m) - c^2*f^2*(6 + 5*m + m^2)) + 2*a*b*d*f*(d*e*(2 + m) + c*f*(10 + 6*m + m^2))) + (c + d*x)*(d*(b*e - a*f)*(1 + m)*(-(a^3*d^3*f^3*(24 + 26*m + 9*m^2 + m^3)) + a^2*b*d^2*f^2*(3 + m)*(d*e*(4 + 3*m) + c*f*(20 + 15*m + 3*m^2)) + b^3*(2*d^3*e^3 - 2*c*d^2*e^2*f*(5 + m) + c^2*d*e*f^2*(26 + 17*m + 3*m^2) + c^3*f^3*(6 + 11*m + 6*m^2 + m^3)) + a*b^2*d*f*(2*d^2*e^2*(2 + m) - 2*c*d*e*f*(16 + 15*m + 3*m^2) - c^2*f^2*(44 + 50*m + 21*m^2 + 3*m^3))) - (b*c - a*d)^3*f^3*(6 + 11*m + 6*m^2 + m^3)*(-(a*d*f*(4 + m)) + b*(4*d*e + c*f*m))*Hypergeometric2F1[1, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])))/((b*c - a*d)^2*(b*e - a*f)^2*(d*e - c*f)^3*(1 + m)^2*(2 + m))))/((b*c - a*d)*(-(d*e) + c*f)*(3 + m)))","A",1
3103,1,131,133,2.8719439,"\int (a+b x)^m (c+d x)^{-5-m} (e+f x)^p \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-5 - m)*(e + f*x)^p,x]","\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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{(m+1) (b c-a d)^5}","\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,"(b^4*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*(e + f*x)^p*AppellF1[1 + m, 5 + m, -p, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/((b*c - a*d)^5*(1 + m)*(c + d*x)^m*((b*(e + f*x))/(b*e - a*f))^p)","A",1
3104,1,274,546,10.4914598,"\int (5-4 x)^5 (1+2 x)^{-5-m} (2+3 x)^m \, dx","Integrate[(5 - 4*x)^5*(1 + 2*x)^(-5 - m)*(2 + 3*x)^m,x]","\frac{2^{4-m} (2 x+1)^{1-m} \, _2F_1(1-m,-m;2-m;-6 x-3)}{m-1}-\frac{560 (-6 x-3)^m (3 x+2)^{m+1} (2 x+1)^{-m} \, _2F_1(m+1,m+1;m+2;6 x+4)}{m+1}-\frac{13720\ 3^{m+2} (-2 x-1)^m (3 x+2)^{m+1} (2 x+1)^{-m} \, _2F_1(m+1,m+3;m+2;6 x+4)}{m+1}-\frac{16807\ 3^{m+4} (-2 x-1)^m (3 x+2)^{m+1} (2 x+1)^{-m} \, _2F_1(m+1,m+5;m+2;6 x+4)}{m+1}-\frac{12005\ 3^{m+3} (-2 x-1)^m (4 x+2)^{-m} (6 x+4)^{m+1} \, _2F_1(m+1,m+4;m+2;6 x+4)}{m+1}+\frac{3920 (3 x+2)^{m+1} (2 x+1)^{-m-1}}{m+1}","-\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,"(3920*(1 + 2*x)^(-1 - m)*(2 + 3*x)^(1 + m))/(1 + m) + (2^(4 - m)*(1 + 2*x)^(1 - m)*Hypergeometric2F1[1 - m, -m, 2 - m, -3 - 6*x])/(-1 + m) - (560*(-3 - 6*x)^m*(2 + 3*x)^(1 + m)*Hypergeometric2F1[1 + m, 1 + m, 2 + m, 4 + 6*x])/((1 + m)*(1 + 2*x)^m) - (13720*3^(2 + m)*(-1 - 2*x)^m*(2 + 3*x)^(1 + m)*Hypergeometric2F1[1 + m, 3 + m, 2 + m, 4 + 6*x])/((1 + m)*(1 + 2*x)^m) - (12005*3^(3 + m)*(-1 - 2*x)^m*(4 + 6*x)^(1 + m)*Hypergeometric2F1[1 + m, 4 + m, 2 + m, 4 + 6*x])/((1 + m)*(2 + 4*x)^m) - (16807*3^(4 + m)*(-1 - 2*x)^m*(2 + 3*x)^(1 + m)*Hypergeometric2F1[1 + m, 5 + m, 2 + m, 4 + 6*x])/((1 + m)*(1 + 2*x)^m)","A",0
3105,1,4261,650,39.8080276,"\int (a+b x)^m (c+d x)^{-5-m} (e+f x)^4 \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-5 - m)*(e + f*x)^4,x]","\text{Result too large to show}","\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,"(-4*e*f^3*(a + b*x)^m*(c + d*x)^(-5 - m)*((c + d*x)/c)^(5 + m)*(-6*a^4*c^4 - 24*a^4*c^3*d*x - 36*a^4*c^2*d^2*x^2 - 24*a^4*c*d^3*x^3 - 6*a^4*d^4*x^4 + 6*a^4*c^4*((a*c + b*c*x)/(a*(c + d*x)))^m + 24*a^4*c^3*d*x*((a*c + b*c*x)/(a*(c + d*x)))^m - 6*a^3*b*c^4*m*x*((a*c + b*c*x)/(a*(c + d*x)))^m + 6*a^4*c^3*d*m*x*((a*c + b*c*x)/(a*(c + d*x)))^m + 36*a^4*c^2*d^2*x^2*((a*c + b*c*x)/(a*(c + d*x)))^m + 3*a^2*b^2*c^4*m*x^2*((a*c + b*c*x)/(a*(c + d*x)))^m - 24*a^3*b*c^3*d*m*x^2*((a*c + b*c*x)/(a*(c + d*x)))^m + 21*a^4*c^2*d^2*m*x^2*((a*c + b*c*x)/(a*(c + d*x)))^m + 3*a^2*b^2*c^4*m^2*x^2*((a*c + b*c*x)/(a*(c + d*x)))^m - 6*a^3*b*c^3*d*m^2*x^2*((a*c + b*c*x)/(a*(c + d*x)))^m + 3*a^4*c^2*d^2*m^2*x^2*((a*c + b*c*x)/(a*(c + d*x)))^m + 24*a^4*c*d^3*x^3*((a*c + b*c*x)/(a*(c + d*x)))^m - 2*a*b^3*c^4*m*x^3*((a*c + b*c*x)/(a*(c + d*x)))^m + 12*a^2*b^2*c^3*d*m*x^3*((a*c + b*c*x)/(a*(c + d*x)))^m - 36*a^3*b*c^2*d^2*m*x^3*((a*c + b*c*x)/(a*(c + d*x)))^m + 26*a^4*c*d^3*m*x^3*((a*c + b*c*x)/(a*(c + d*x)))^m - 3*a*b^3*c^4*m^2*x^3*((a*c + b*c*x)/(a*(c + d*x)))^m + 15*a^2*b^2*c^3*d*m^2*x^3*((a*c + b*c*x)/(a*(c + d*x)))^m - 21*a^3*b*c^2*d^2*m^2*x^3*((a*c + b*c*x)/(a*(c + d*x)))^m + 9*a^4*c*d^3*m^2*x^3*((a*c + b*c*x)/(a*(c + d*x)))^m - a*b^3*c^4*m^3*x^3*((a*c + b*c*x)/(a*(c + d*x)))^m + 3*a^2*b^2*c^3*d*m^3*x^3*((a*c + b*c*x)/(a*(c + d*x)))^m - 3*a^3*b*c^2*d^2*m^3*x^3*((a*c + b*c*x)/(a*(c + d*x)))^m + a^4*c*d^3*m^3*x^3*((a*c + b*c*x)/(a*(c + d*x)))^m - 6*b^4*c^4*x^4*((a*c + b*c*x)/(a*(c + d*x)))^m + 24*a*b^3*c^3*d*x^4*((a*c + b*c*x)/(a*(c + d*x)))^m - 36*a^2*b^2*c^2*d^2*x^4*((a*c + b*c*x)/(a*(c + d*x)))^m + 24*a^3*b*c*d^3*x^4*((a*c + b*c*x)/(a*(c + d*x)))^m - 11*b^4*c^4*m*x^4*((a*c + b*c*x)/(a*(c + d*x)))^m + 42*a*b^3*c^3*d*m*x^4*((a*c + b*c*x)/(a*(c + d*x)))^m - 57*a^2*b^2*c^2*d^2*m*x^4*((a*c + b*c*x)/(a*(c + d*x)))^m + 26*a^3*b*c*d^3*m*x^4*((a*c + b*c*x)/(a*(c + d*x)))^m - 6*b^4*c^4*m^2*x^4*((a*c + b*c*x)/(a*(c + d*x)))^m + 21*a*b^3*c^3*d*m^2*x^4*((a*c + b*c*x)/(a*(c + d*x)))^m - 24*a^2*b^2*c^2*d^2*m^2*x^4*((a*c + b*c*x)/(a*(c + d*x)))^m + 9*a^3*b*c*d^3*m^2*x^4*((a*c + b*c*x)/(a*(c + d*x)))^m - b^4*c^4*m^3*x^4*((a*c + b*c*x)/(a*(c + d*x)))^m + 3*a*b^3*c^3*d*m^3*x^4*((a*c + b*c*x)/(a*(c + d*x)))^m - 3*a^2*b^2*c^2*d^2*m^3*x^4*((a*c + b*c*x)/(a*(c + d*x)))^m + a^3*b*c*d^3*m^3*x^4*((a*c + b*c*x)/(a*(c + d*x)))^m))/((b*c - a*d)^4*(1 + m)*(2 + m)*(3 + m)*(4 + m)*((a + b*x)/a)^m*(1 + (d*x)/c)^4) + (f^4*x^5*(a + b*x)^m*(c + d*x)^(-5 - m)*((c + d*x)/c)^(5 + m)*AppellF1[5, -m, 5 + m, 6, -((b*x)/a), -((d*x)/c)])/(5*((a + b*x)/a)^m) + (2*e^2*f^2*(a + b*x)^m*(1 + (b*x)/a)^m*(c + d*x)^(-5 - m)*((c + d*x)/c)^(5 + m)*(1 + (d*x)/c)^(-4 - m)*((c + d*x)*(b^4*c^4*m*(2 + 3*m + m^2)*x^4 + a*b^3*c^3*m*(1 + m)*x^3*(c*(-4 + m) - 3*d*(4 + m)*x) + 3*a^2*b^2*c^2*m*x^2*(-2*c^2*(-2 + m) - c*d*(-12 + m + m^2)*x + d^2*(12 + 7*m + m^2)*x^2) + a^4*(-6*d^4*m*x^4*((a*(c + d*x))/(c*(a + b*x)))^m + 24*c^4*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m) - 6*c^2*d^2*x^2*(12 + 7*m + m^2 - 12*((a*(c + d*x))/(c*(a + b*x)))^m + 3*m*((a*(c + d*x))/(c*(a + b*x)))^m) - c*d^3*x^3*(24 + 26*m + 9*m^2 + m^3 - 24*((a*(c + d*x))/(c*(a + b*x)))^m + 18*m*((a*(c + d*x))/(c*(a + b*x)))^m) - 6*c^3*d*x*(-12*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m) + m*(3 + ((a*(c + d*x))/(c*(a + b*x)))^m))) + a^3*b*c*x*(-(d^3*(4 + m)*x^3*(6 + 5*m + m^2 - 6*((a*(c + d*x))/(c*(a + b*x)))^m)) + 6*c^2*d*(4 + m)*x*(-3 + 2*m + 3*((a*(c + d*x))/(c*(a + b*x)))^m) + 3*c*d^2*(4 + m)*x^2*(-6 + m + m^2 + 6*((a*(c + d*x))/(c*(a + b*x)))^m) + 6*c^3*(4*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m) + m*(3 + ((a*(c + d*x))/(c*(a + b*x)))^m))))*Gamma[1 - m] + m*(4*c + d*x)*(b^4*c^4*(6 + 11*m + 6*m^2 + m^3)*x^4 + a*b^3*c^3*(2 + 3*m + m^2)*x^3*(c*m - 3*d*(4 + m)*x) - 3*a^2*b^2*c^2*(1 + m)*x^2*(c^2*m + c*d*m*(4 + m)*x - d^2*(12 + 7*m + m^2)*x^2) + a^3*b*c*x*(6*c^3*m + 6*c^2*d*m*(4 + m)*x + 3*c*d^2*m*(12 + 7*m + m^2)*x^2 - d^3*(24 + 26*m + 9*m^2 + m^3)*x^3) + a^4*(6*d^4*x^4*((a*(c + d*x))/(c*(a + b*x)))^m + 6*c^4*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m) + 6*c^3*d*x*(-4 - m + 4*((a*(c + d*x))/(c*(a + b*x)))^m) + 3*c^2*d^2*x^2*(-7*m - m^2 + 12*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m)) + c*d^3*x^3*(-26*m - 9*m^2 - m^3 + 24*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m))))*Gamma[-m]))/(c*(b*c - a*d)^4*m*(1 + m)*(2 + m)*(3 + m)*(4 + m)*x*((a + b*x)/a)^m*Gamma[-m]) + (2*e^3*f*(a + b*x)^m*(1 + (b*x)/a)^m*(c + d*x)^(-5 - m)*((c + d*x)/c)^(5 + m)*(1 + (d*x)/c)^(-4 - m)*(2*(c + d*x)*(b^4*c^4*m*(1 + m)*x^4*(3*c*(3 + m) + d*(5 + m)*x) - a*b^3*c^3*m*x^3*(-3*c^2*(-8 - m + m^2) + 4*c*d*(19 + 12*m + 2*m^2)*x + 3*d^2*(12 + 7*m + m^2)*x^2) + a^3*b*c*x*(36*c^4*m + 6*c*d^3*(4 + m)*x^3*(-3 - m + 3*((a*(c + d*x))/(c*(a + b*x)))^m + 3*m*((a*(c + d*x))/(c*(a + b*x)))^m) + 3*c^2*d^2*(4 + m)*x^2*(-6 + 7*m + 3*m^2 + 6*((a*(c + d*x))/(c*(a + b*x)))^m + 6*m*((a*(c + d*x))/(c*(a + b*x)))^m) - d^4*(4 + m)*x^4*(6 + m^2 - 6*((a*(c + d*x))/(c*(a + b*x)))^m + m*(5 - 6*((a*(c + d*x))/(c*(a + b*x)))^m)) + 6*c^3*d*x*(4*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m) + m^2*(5 + ((a*(c + d*x))/(c*(a + b*x)))^m) + m*(17 + 5*((a*(c + d*x))/(c*(a + b*x)))^m))) - 3*a^2*b^2*c^2*x^2*(d^3*(12 + 7*m + m^2)*x^3*(-1 - m + ((a*(c + d*x))/(c*(a + b*x)))^m) + c*d^2*(12 + 7*m + m^2)*x^2*(-3 - 2*m + 3*((a*(c + d*x))/(c*(a + b*x)))^m) + c^3*(12*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m) + m^2*(5 + ((a*(c + d*x))/(c*(a + b*x)))^m) + m*(-1 + 7*((a*(c + d*x))/(c*(a + b*x)))^m)) + c^2*d*x*(3*m^3 + 36*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m) + m^2*(8 + 3*((a*(c + d*x))/(c*(a + b*x)))^m) + m*(-19 + 21*((a*(c + d*x))/(c*(a + b*x)))^m))) + a^4*(-3*d^5*m*(3 + m)*x^5*((a*(c + d*x))/(c*(a + b*x)))^m + 36*c^5*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m) + 12*c^4*d*x*(-3*m + 11*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m)) - 3*c^3*d^2*x^2*(-60*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m) + m^2*(5 + ((a*(c + d*x))/(c*(a + b*x)))^m) + m*(35 + 3*((a*(c + d*x))/(c*(a + b*x)))^m)) - 3*c^2*d^3*x^3*(m^3 - 36*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m) + m^2*(10 + 3*((a*(c + d*x))/(c*(a + b*x)))^m) + m*(33 + 9*((a*(c + d*x))/(c*(a + b*x)))^m)) - c*d^4*x^4*(m^3 - 24*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m) + 9*m^2*(1 + ((a*(c + d*x))/(c*(a + b*x)))^m) + m*(26 + 27*((a*(c + d*x))/(c*(a + b*x)))^m))))*Gamma[1 - m] + 2*m*(6*c^2 + 4*c*d*x + d^2*x^2)*(b^4*c^4*(6 + 11*m + 6*m^2 + m^3)*x^4 + a*b^3*c^3*(2 + 3*m + m^2)*x^3*(c*m - 3*d*(4 + m)*x) - 3*a^2*b^2*c^2*(1 + m)*x^2*(c^2*m + c*d*m*(4 + m)*x - d^2*(12 + 7*m + m^2)*x^2) + a^3*b*c*x*(6*c^3*m + 6*c^2*d*m*(4 + m)*x + 3*c*d^2*m*(12 + 7*m + m^2)*x^2 - d^3*(24 + 26*m + 9*m^2 + m^3)*x^3) + a^4*(6*d^4*x^4*((a*(c + d*x))/(c*(a + b*x)))^m + 6*c^4*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m) + 6*c^3*d*x*(-4 - m + 4*((a*(c + d*x))/(c*(a + b*x)))^m) + 3*c^2*d^2*x^2*(-7*m - m^2 + 12*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m)) + c*d^3*x^3*(-26*m - 9*m^2 - m^3 + 24*(-1 + ((a*(c + d*x))/(c*(a + b*x)))^m))))*Gamma[-m]))/(3*c^2*(b*c - a*d)^4*m*(1 + m)*(2 + m)*(3 + m)*(4 + m)*x^2*((a + b*x)/a)^m*Gamma[-m]) - (e^4*(c + d*x)^(-4 - m)*(a - (b*c)/d + (b*(c + d*x))/d)^m*Hypergeometric2F1[-4 - m, -m, -3 - m, -((b*(c + d*x))/((a - (b*c)/d)*d))])/(d*(4 + m)*(1 + (b*(c + d*x))/((a - (b*c)/d)*d))^m)","C",0
3106,1,263,460,0.8736651,"\int (a+b x)^m (c+d x)^{-5-m} (e+f x)^3 \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-5 - m)*(e + f*x)^3,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-4} \left((e+f x)^3-\frac{3 (c+d x) (b e-a f) \left(-(c+d x) (-a d (m+1)+b c (m+2)+b d x) \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 f (m+1) (m+2) (m+3) (e+f x) (b c-a d)^3+(m+1) (m+2) (b c-a d)^2 (c f-d e) (-a d f (m+3)+b c f (m+2)+b d e)\right)}{b d^2 (m+1) (m+2) (m+3) (b c-a d)^3}\right)}{(m+4) (b c-a d)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-4 - m)*((e + f*x)^3 - (3*(b*e - a*f)*(c + d*x)*((b*c - a*d)^2*(-(d*e) + c*f)*(1 + m)*(2 + m)*(b*d*e + b*c*f*(2 + m) - a*d*f*(3 + m)) - (a^2*d^2*f^2*(6 + 5*m + m^2) - 2*a*b*d*f*(3 + m)*(d*e + c*f*(1 + m)) + b^2*(2*d^2*e^2 + 2*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)))*(c + d*x)*(-(a*d*(1 + m)) + b*c*(2 + m) + b*d*x) + d*(b*c - a*d)^3*f*(1 + m)*(2 + m)*(3 + m)*(e + f*x)))/(b*d^2*(b*c - a*d)^3*(1 + m)*(2 + m)*(3 + m))))/((b*c - a*d)*(4 + m))","A",1
3107,1,269,494,0.6813812,"\int (a+b x)^m (c+d x)^{-5-m} (e+f x)^2 \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-5 - m)*(e + f*x)^2,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-4} \left(\frac{(c+d x) \left(a^2 d^2 \left(m^2+3 m+2\right)-2 a b d (m+1) (c (m+3)+d x)+b^2 \left(c^2 \left(m^2+5 m+6\right)+2 c d (m+3) x+2 d^2 x^2\right)\right) \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 (m+1) (m+2) (m+3) (m+4) (b c-a d)^4}-\frac{(d e-c f) (-a d f (m+4)+b c f (m+2)+2 b d e)}{d (m+4) (a d-b c)}-f (e+f x)\right)}{2 b d}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-4 - m)*(-(((d*e - c*f)*(2*b*d*e + b*c*f*(2 + m) - a*d*f*(4 + m)))/(d*(-(b*c) + a*d)*(4 + m))) - f*(e + f*x) + ((a^2*d^2*f^2*(12 + 7*m + m^2) - 2*a*b*d*f*(4 + m)*(2*d*e + c*f*(1 + m)) + b^2*(6*d^2*e^2 + 4*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)))*(c + d*x)*(a^2*d^2*(2 + 3*m + m^2) - 2*a*b*d*(1 + m)*(c*(3 + m) + d*x) + b^2*(c^2*(6 + 5*m + m^2) + 2*c*d*(3 + m)*x + 2*d^2*x^2)))/(d*(b*c - a*d)^4*(1 + m)*(2 + m)*(3 + m)*(4 + m))))/(2*b*d)","A",1
3108,1,144,268,0.3926437,"\int (a+b x)^m (c+d x)^{-5-m} (e+f x) \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-5 - m)*(e + f*x),x]","-\frac{(a+b x)^{m+1} (c+d x)^{-m-4} \left(\frac{(c+d x) \left(2 b (c+d x) (-a d (m+1)+b c (m+2)+b d x)+(m+1) (m+2) (b c-a d)^2\right) (-a d f (m+4)+b c f (m+1)+3 b d e)}{(m+1) (m+2) (m+3) (b c-a d)^3}-c f+d e\right)}{d (m+4) (a d-b c)}","-\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,"-(((a + b*x)^(1 + m)*(c + d*x)^(-4 - m)*(d*e - c*f + ((3*b*d*e + b*c*f*(1 + m) - a*d*f*(4 + m))*(c + d*x)*((b*c - a*d)^2*(1 + m)*(2 + m) + 2*b*(c + d*x)*(-(a*d*(1 + m)) + b*c*(2 + m) + b*d*x)))/((b*c - a*d)^3*(1 + m)*(2 + m)*(3 + m))))/(d*(-(b*c) + a*d)*(4 + m)))","A",1
3109,1,195,185,0.0970133,"\int (a+b x)^m (c+d x)^{-5-m} \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-5 - m),x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-4} \left(-a^3 d^3 \left(m^3+6 m^2+11 m+6\right)+3 a^2 b d^2 \left(m^2+3 m+2\right) (c (m+4)+d x)-3 a b^2 d (m+1) \left(c^2 \left(m^2+7 m+12\right)+2 c d (m+4) x+2 d^2 x^2\right)+b^3 \left(c^3 \left(m^3+9 m^2+26 m+24\right)+3 c^2 d \left(m^2+7 m+12\right) x+6 c d^2 (m+4) x^2+6 d^3 x^3\right)\right)}{(m+1) (m+2) (m+3) (m+4) (b c-a d)^4}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-4 - m)*(-(a^3*d^3*(6 + 11*m + 6*m^2 + m^3)) + 3*a^2*b*d^2*(2 + 3*m + m^2)*(c*(4 + m) + d*x) - 3*a*b^2*d*(1 + m)*(c^2*(12 + 7*m + m^2) + 2*c*d*(4 + m)*x + 2*d^2*x^2) + b^3*(c^3*(24 + 26*m + 9*m^2 + m^3) + 3*c^2*d*(12 + 7*m + m^2)*x + 6*c*d^2*(4 + m)*x^2 + 6*d^3*x^3)))/((b*c - a*d)^4*(1 + m)*(2 + m)*(3 + m)*(4 + m))","A",1
3110,1,525,557,2.1555145,"\int \frac{(a+b x)^m (c+d x)^{-5-m}}{e+f x} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(-5 - m))/(e + f*x),x]","-\frac{(a+b x)^{m+1} (c+d x)^{-m-4} \left(-\frac{(c+d x)^2 \left(d (m+1)^2 (b c-a d) (b e-a f) (d e-c f) \left(-a^2 d^2 f^2 \left(m^2+7 m+12\right)+2 a b d f (m+4) (c f (m+4)-d e)-\left(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)\right)+(c+d x) \left(f^4 \left(m^4+10 m^3+35 m^2+50 m+24\right) \left(-(b c-a d)^4\right) \, _2F_1\left(1,m+1;m+2;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)-d (m+1) (b e-a f) \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)\right)\right)}{(m+1)^2 (m+2) (m+3) (b c-a d)^3 (b e-a f) (d e-c f)^3}-\frac{d (c+d x) (a d f (m+4)-b c f (m+7)+3 b d e)}{(m+3) (b c-a d) (c f-d e)}+d\right)}{(m+4) (b c-a d) (c f-d e)}","\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,"-(((a + b*x)^(1 + m)*(c + d*x)^(-4 - m)*(d - (d*(3*b*d*e + a*d*f*(4 + m) - b*c*f*(7 + m))*(c + d*x))/((b*c - a*d)*(-(d*e) + c*f)*(3 + m)) - ((c + d*x)^2*(d*(b*c - a*d)*(b*e - a*f)*(d*e - c*f)*(1 + m)^2*(-(a^2*d^2*f^2*(12 + 7*m + m^2)) + 2*a*b*d*f*(4 + m)*(-(d*e) + c*f*(4 + m)) - b^2*(6*d^2*e^2 - 2*c*d*e*f*(10 + m) + c^2*f^2*(26 + 9*m + m^2))) + (c + d*x)*(-(d*(b*e - a*f)*(1 + m)*(a^3*d^3*f^3*(24 + 26*m + 9*m^2 + m^3) + a^2*b*d^2*f^2*(12 + 7*m + m^2)*(d*e - c*f*(7 + 3*m)) + a*b^2*d*f*(4 + m)*(2*d^2*e^2 - 2*c*d*e*f*(5 + m) + c^2*f^2*(26 + 17*m + 3*m^2)) + b^3*(6*d^3*e^3 - 2*c*d^2*e^2*f*(13 + m) + c^2*d*e*f^2*(46 + 11*m + m^2) - c^3*f^3*(50 + 35*m + 10*m^2 + m^3)))) - (b*c - a*d)^4*f^4*(24 + 50*m + 35*m^2 + 10*m^3 + m^4)*Hypergeometric2F1[1, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])))/((b*c - a*d)^3*(b*e - a*f)*(d*e - c*f)^3*(1 + m)^2*(2 + m)*(3 + m))))/((b*c - a*d)*(-(d*e) + c*f)*(4 + m)))","A",1
3111,1,125,131,0.3037589,"\int (a+b x)^m (c+d x)^{1-m} (e+f x)^p \, dx","Integrate[(a + b*x)^m*(c + d*x)^(1 - m)*(e + f*x)^p,x]","\frac{(a+b x)^{m+1} (c+d x)^{1-m} (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{m-1} \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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{b (m+1)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(1 - m)*((b*(c + d*x))/(b*c - a*d))^(-1 + m)*(e + f*x)^p*AppellF1[1 + m, -1 + m, -p, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/(b*(1 + m)*((b*(e + f*x))/(b*e - a*f))^p)","A",1
3112,1,317,445,0.7622327,"\int (a+b x)^m (c+d x)^{1-m} (e+f x)^3 \, dx","Integrate[(a + b*x)^m*(c + d*x)^(1 - m)*(e + f*x)^3,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(b^3 (c+d x) (d e-c f)^2 \left(\frac{b (c+d x)}{b c-a d}\right)^{m-1} (a d f (m-2)-b c f (m+3)+5 b d e) \, _2F_1\left(m-1,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)+f^2 (b c-a d)^3 \left(\frac{b (c+d x)}{b c-a d}\right)^m (a d f (m-4)-b c f (m+3)+7 b d e) \, _2F_1\left(m-3,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)+2 b f (b c-a d)^2 (d e-c f) \left(\frac{b (c+d x)}{b c-a d}\right)^m (a d f (m-3)-b c f (m+3)+6 b d e) \, _2F_1\left(m-2,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)+b^4 d^2 f (m+1) (c+d x)^2 (e+f x)^2\right)}{5 b^5 d^3 (m+1)}","\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,"((a + b*x)^(1 + m)*(b^4*d^2*f*(1 + m)*(c + d*x)^2*(e + f*x)^2 + (b*c - a*d)^3*f^2*(7*b*d*e + a*d*f*(-4 + m) - b*c*f*(3 + m))*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[-3 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)] + 2*b*(b*c - a*d)^2*f*(d*e - c*f)*(6*b*d*e + a*d*f*(-3 + m) - b*c*f*(3 + m))*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[-2 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)] + b^3*(d*e - c*f)^2*(5*b*d*e + a*d*f*(-2 + m) - b*c*f*(3 + m))*(c + d*x)*((b*(c + d*x))/(b*c - a*d))^(-1 + m)*Hypergeometric2F1[-1 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)]))/(5*b^5*d^3*(1 + m)*(c + d*x)^m)","A",1
3113,1,223,260,0.3335274,"\int (a+b x)^m (c+d x)^{1-m} (e+f x)^2 \, dx","Integrate[(a + b*x)^m*(c + d*x)^(1 - m)*(e + f*x)^2,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m} \left((b c-a d) \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 (m-2) (c f (m+1)-4 d e)+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)}{a d-b c}\right)+b^2 f (m+1) (c+d x)^2 (a d f (m-3)-b c f (m+2)+5 b d e)+3 b^3 d f (m+1) (c+d x)^2 (e+f x)\right)}{12 b^4 d^2 (m+1)}","\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,"((a + b*x)^(1 + m)*(b^2*f*(1 + m)*(5*b*d*e + a*d*f*(-3 + m) - b*c*f*(2 + m))*(c + d*x)^2 + 3*b^3*d*f*(1 + m)*(c + d*x)^2*(e + f*x) + (b*c - a*d)*(a^2*d^2*f^2*(6 - 5*m + m^2) - 2*a*b*d*f*(-2 + m)*(-4*d*e + c*f*(1 + m)) + b^2*(12*d^2*e^2 - 8*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)))*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[-1 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)]))/(12*b^4*d^2*(1 + m)*(c + d*x)^m)","A",1
3114,1,126,145,0.13102,"\int (a+b x)^m (c+d x)^{1-m} (e+f x) \, dx","Integrate[(a + b*x)^m*(c + d*x)^(1 - m)*(e + f*x),x]","\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(b^2 f (m+1) (c+d x)^2-(b c-a d) \left(\frac{b (c+d x)}{b c-a d}\right)^m (-a d f (m-2)+b c f (m+1)-3 b d e) \, _2F_1\left(m-1,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)\right)}{3 b^3 d (m+1)}","\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,"((a + b*x)^(1 + m)*(b^2*f*(1 + m)*(c + d*x)^2 - (b*c - a*d)*(-3*b*d*e - a*d*f*(-2 + m) + b*c*f*(1 + m))*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[-1 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)]))/(3*b^3*d*(1 + m)*(c + d*x)^m)","A",1
3115,1,77,82,0.0348744,"\int (a+b x)^m (c+d x)^{1-m} \, dx","Integrate[(a + b*x)^m*(c + d*x)^(1 - m),x]","\frac{(a+b x)^{m+1} (c+d x)^{1-m} \left(\frac{b (c+d x)}{b c-a d}\right)^{m-1} \, _2F_1\left(m-1,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)}{b (m+1)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(1 - m)*((b*(c + d*x))/(b*c - a*d))^(-1 + m)*Hypergeometric2F1[-1 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(1 + m))","A",1
3116,1,177,230,0.1813072,"\int \frac{(a+b x)^m (c+d x)^{1-m}}{e+f x} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(1 - m))/(e + f*x),x]","\frac{(a+b x)^m (c+d x)^{-m} \left(\frac{(d e-c f) \left(\, _2F_1\left(1,m;m+1;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)-\left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m,m;m+1;\frac{d (a+b x)}{a d-b c}\right)\right)}{f m}+\frac{d (a+b x) \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)}{a d-b c}\right)}{b (m+1)}\right)}{f}","-\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,"((a + b*x)^m*(((d*e - c*f)*(Hypergeometric2F1[1, m, 1 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))] - ((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, m, 1 + m, (d*(a + b*x))/(-(b*c) + a*d)]))/(f*m) + (d*(a + b*x)*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(1 + m))))/(f*(c + d*x)^m)","A",1
3117,1,203,190,0.2459397,"\int \frac{(a+b x)^m (c+d x)^{1-m}}{(e+f x)^2} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(1 - m))/(e + f*x)^2,x]","-\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \left(\frac{b (e+f x)}{b e-a f}\right)^{-m} \left(d (e+f x) \left(\frac{b (e+f x)}{b e-a f}\right)^m F_1\left(m+1;m,1;m+2;\frac{d (a+b x)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)+(c f-d e) \, _2F_1\left(m,m+1;m+2;\frac{(c f-d e) (a+b x)}{(b c-a d) (e+f x)}\right)\right)}{f (m+1) (e+f x) (a f-b e)}","\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,"-(((a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*(d*(e + f*x)*((b*(e + f*x))/(b*e - a*f))^m*AppellF1[1 + m, m, 1, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)] + (-(d*e) + c*f)*Hypergeometric2F1[m, 1 + m, 2 + m, ((-(d*e) + c*f)*(a + b*x))/((b*c - a*d)*(e + f*x))]))/(f*(-(b*e) + a*f)*(1 + m)*(c + d*x)^m*(e + f*x)*((b*(e + f*x))/(b*e - a*f))^m))","C",0
3118,1,85,85,0.0281071,"\int \frac{(a+b x)^m (c+d x)^{1-m}}{(e+f x)^3} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(1 - m))/(e + f*x)^3,x]","\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}","\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,"((b*c - a*d)^2*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*Hypergeometric2F1[3, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/((b*e - a*f)^3*(1 + m))","A",1
3119,1,148,176,0.1456757,"\int \frac{(a+b x)^m (c+d x)^{1-m}}{(e+f x)^4} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(1 - m))/(e + f*x)^4,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-1} \left(\frac{(b c-a d)^2 (-a d f (m+1)+b c f (m-2)+3 b d e) \, _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}-\frac{f (c+d x)^3}{(e+f x)^3}\right)}{3 (b e-a f) (d e-c f)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*(-((f*(c + d*x)^3)/(e + f*x)^3) + ((b*c - a*d)^2*(3*b*d*e + b*c*f*(-2 + m) - a*d*f*(1 + m))*Hypergeometric2F1[3, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/((b*e - a*f)^3*(1 + m))))/(3*(b*e - a*f)*(d*e - c*f))","A",1
3120,1,271,311,0.8978242,"\int \frac{(a+b x)^m (c+d x)^{1-m}}{(e+f x)^5} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(1 - m))/(e + f*x)^5,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-1} \left(\frac{(b c-a d)^2 \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)+4 d e)+b^2 \left(c^2 f^2 \left(m^2-5 m+6\right)+8 c d e f (m-2)+12 d^2 e^2\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)}{(m+1) (b e-a f)^4 (d e-c f)}-\frac{f (c+d x)^3 (-a d f (m+2)+b c f (m-3)+5 b d e)}{(e+f x)^3 (b e-a f) (d e-c f)}-\frac{3 f (c+d x)^3}{(e+f x)^4}\right)}{12 (b e-a f) (d e-c f)}","-\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,"((a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*((-3*f*(c + d*x)^3)/(e + f*x)^4 - (f*(5*b*d*e + b*c*f*(-3 + m) - a*d*f*(2 + m))*(c + d*x)^3)/((b*e - a*f)*(d*e - c*f)*(e + f*x)^3) + ((b*c - a*d)^2*(-2*a*b*d*f*(4*d*e + c*f*(-2 + m))*(1 + m) + a^2*d^2*f^2*(2 + 3*m + m^2) + b^2*(12*d^2*e^2 + 8*c*d*e*f*(-2 + m) + c^2*f^2*(6 - 5*m + m^2)))*Hypergeometric2F1[3, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/((b*e - a*f)^4*(d*e - c*f)*(1 + m))))/(12*(b*e - a*f)*(d*e - c*f))","A",1
3121,1,484,542,3.4465813,"\int \frac{(a+b x)^m (c+d x)^{1-m}}{(e+f x)^6} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(1 - m))/(e + f*x)^6,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-1} \left(-\frac{(e+f x)^2 \left(f (m+1) (c+d x)^3 (b e-a f)^3 \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+2 m+9\right)-3 d e (4 m+7)\right)+b^2 \left(c^2 f^2 \left(m^2-7 m+12\right)+3 c d e f (4 m-11)+27 d^2 e^2\right)\right)-(e+f x)^3 (b c-a d)^2 \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-2)+5 d e)-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 (m-2)+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 (m-2)+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)\right)}{(m+1) (b e-a f)^5 (d e-c f)^2}+\frac{3 f (c+d x)^3 (e+f x) (a d f (m+3)-b (c f (m-4)+7 d e))}{(b e-a f) (d e-c f)}-12 f (c+d x)^3\right)}{60 (e+f x)^5 (b e-a f) (d e-c f)}","-\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,"((a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*(-12*f*(c + d*x)^3 + (3*f*(-(b*(7*d*e + c*f*(-4 + m))) + a*d*f*(3 + m))*(c + d*x)^3*(e + f*x))/((b*e - a*f)*(d*e - c*f)) - ((e + f*x)^2*(f*(b*e - a*f)^3*(1 + m)*(a^2*d^2*f^2*(6 + 5*m + m^2) + a*b*d*f*(-3*d*e*(7 + 4*m) + c*f*(9 + 2*m - 2*m^2)) + b^2*(27*d^2*e^2 + 3*c*d*e*f*(-11 + 4*m) + c^2*f^2*(12 - 7*m + m^2)))*(c + d*x)^3 - (b*c - a*d)^2*(3*a^2*b*d^2*f^2*(5*d*e + c*f*(-2 + m))*(2 + 3*m + m^2) - a^3*d^3*f^3*(6 + 11*m + 6*m^2 + m^3) - 3*a*b^2*d*f*(1 + m)*(20*d^2*e^2 + 10*c*d*e*f*(-2 + m) + c^2*f^2*(6 - 5*m + m^2)) + b^3*(60*d^3*e^3 + 60*c*d^2*e^2*f*(-2 + m) + 15*c^2*d*e*f^2*(6 - 5*m + m^2) + c^3*f^3*(-24 + 26*m - 9*m^2 + m^3)))*(e + f*x)^3*Hypergeometric2F1[3, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]))/((b*e - a*f)^5*(d*e - c*f)^2*(1 + m))))/(60*(b*e - a*f)*(d*e - c*f)*(e + f*x)^5)","A",1
3122,1,131,133,0.4231933,"\int (a+b x)^m (c+d x)^{2-m} (e+f x)^p \, dx","Integrate[(a + b*x)^m*(c + d*x)^(2 - m)*(e + f*x)^p,x]","\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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{b^3 (m+1)}","\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,"((b*c - a*d)^2*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*(e + f*x)^p*AppellF1[1 + m, -2 + m, -p, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/(b^3*(1 + m)*(c + d*x)^m*((b*(e + f*x))/(b*e - a*f))^p)","A",1
3123,1,320,447,0.8392648,"\int (a+b x)^m (c+d x)^{2-m} (e+f x)^3 \, dx","Integrate[(a + b*x)^m*(c + d*x)^(2 - m)*(e + f*x)^3,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(b^2 (b c-a d)^2 (d e-c f)^2 \left(\frac{b (c+d x)}{b c-a d}\right)^m (a d f (m-3)-b c f (m+3)+6 b d e) \, _2F_1\left(m-2,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)+f^2 (b c-a d)^4 \left(\frac{b (c+d x)}{b c-a d}\right)^m (a d f (m-5)-b c f (m+3)+8 b d e) \, _2F_1\left(m-4,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)+2 b f (b c-a d)^3 (d e-c f) \left(\frac{b (c+d x)}{b c-a d}\right)^m (a d f (m-4)-b c f (m+3)+7 b d e) \, _2F_1\left(m-3,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)+b^5 d^2 f (m+1) (c+d x)^3 (e+f x)^2\right)}{6 b^6 d^3 (m+1)}","\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,"((a + b*x)^(1 + m)*(b^5*d^2*f*(1 + m)*(c + d*x)^3*(e + f*x)^2 + (b*c - a*d)^4*f^2*(8*b*d*e + a*d*f*(-5 + m) - b*c*f*(3 + m))*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[-4 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)] + 2*b*(b*c - a*d)^3*f*(d*e - c*f)*(7*b*d*e + a*d*f*(-4 + m) - b*c*f*(3 + m))*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[-3 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)] + b^2*(b*c - a*d)^2*(d*e - c*f)^2*(6*b*d*e + a*d*f*(-3 + m) - b*c*f*(3 + m))*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[-2 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)]))/(6*b^6*d^3*(1 + m)*(c + d*x)^m)","A",1
3124,1,225,262,0.3689471,"\int (a+b x)^m (c+d x)^{2-m} (e+f x)^2 \, dx","Integrate[(a + b*x)^m*(c + d*x)^(2 - m)*(e + f*x)^2,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m} \left((b c-a d)^2 \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 (m-3) (c f (m+1)-5 d e)+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)}{a d-b c}\right)+b^3 f (m+1) (c+d x)^3 (a d f (m-4)-b c f (m+2)+6 b d e)+4 b^4 d f (m+1) (c+d x)^3 (e+f x)\right)}{20 b^5 d^2 (m+1)}","\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,"((a + b*x)^(1 + m)*(b^3*f*(1 + m)*(6*b*d*e + a*d*f*(-4 + m) - b*c*f*(2 + m))*(c + d*x)^3 + 4*b^4*d*f*(1 + m)*(c + d*x)^3*(e + f*x) + (b*c - a*d)^2*(a^2*d^2*f^2*(12 - 7*m + m^2) - 2*a*b*d*f*(-3 + m)*(-5*d*e + c*f*(1 + m)) + b^2*(20*d^2*e^2 - 10*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)))*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[-2 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)]))/(20*b^5*d^2*(1 + m)*(c + d*x)^m)","A",1
3125,1,128,147,0.1409907,"\int (a+b x)^m (c+d x)^{2-m} (e+f x) \, dx","Integrate[(a + b*x)^m*(c + d*x)^(2 - m)*(e + f*x),x]","\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(b^3 f (m+1) (c+d x)^3-(b c-a d)^2 \left(\frac{b (c+d x)}{b c-a d}\right)^m (-a d f (m-3)+b c f (m+1)-4 b d e) \, _2F_1\left(m-2,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)\right)}{4 b^4 d (m+1)}","\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,"((a + b*x)^(1 + m)*(b^3*f*(1 + m)*(c + d*x)^3 - (b*c - a*d)^2*(-4*b*d*e - a*d*f*(-3 + m) + b*c*f*(1 + m))*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[-2 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)]))/(4*b^4*d*(1 + m)*(c + d*x)^m)","A",1
3126,1,83,84,0.0328735,"\int (a+b x)^m (c+d x)^{2-m} \, dx","Integrate[(a + b*x)^m*(c + d*x)^(2 - m),x]","\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)}{a d-b c}\right)}{b^3 (m+1)}","\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,"((b*c - a*d)^2*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[-2 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])/(b^3*(1 + m)*(c + d*x)^m)","A",1
3127,1,258,370,0.24739,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{e+f x} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(2 - m))/(e + f*x),x]","\frac{(a+b x)^m (c+d x)^{-m} \left(-b (d e-c f) \left(b (m+1) (d e-c f) \left(\, _2F_1\left(1,m;m+1;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)-\left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m,m;m+1;\frac{d (a+b x)}{a d-b c}\right)\right)+d f m (a+b x) \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)}{a d-b c}\right)\right)-d f^2 m (a+b x) (a d-b c) \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)}{a d-b c}\right)\right)}{b^2 f^3 m (m+1)}","\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,"((a + b*x)^m*(-(d*(-(b*c) + a*d)*f^2*m*(a + b*x)*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[-1 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)]) - b*(d*e - c*f)*(b*(d*e - c*f)*(1 + m)*(Hypergeometric2F1[1, m, 1 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))] - ((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, m, 1 + m, (d*(a + b*x))/(-(b*c) + a*d)]) + d*f*m*(a + b*x)*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])))/(b^2*f^3*m*(1 + m)*(c + d*x)^m)","A",1
3128,1,103,316,0.187704,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^2} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(2 - m))/(e + f*x)^2,x]","\frac{b (a+b x)^{m+1} (c+d x)^{2-m} \left(\frac{b (c+d x)}{b c-a d}\right)^{m-2} F_1\left(m+1;m-2,2;m+2;\frac{d (a+b x)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{(m+1) (b e-a f)^2}","\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,"(b*(a + b*x)^(1 + m)*(c + d*x)^(2 - m)*((b*(c + d*x))/(b*c - a*d))^(-2 + m)*AppellF1[1 + m, -2 + m, 2, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/((b*e - a*f)^2*(1 + m))","C",0
3129,1,108,362,0.3073551,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^3} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(2 - m))/(e + f*x)^3,x]","\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 F_1\left(m+1;m-2,3;m+2;\frac{d (a+b x)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{(m+1) (b e-a f)^3}","-\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,"((b*c - a*d)^2*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*AppellF1[1 + m, -2 + m, 3, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/((b*e - a*f)^3*(1 + m)*(c + d*x)^m)","C",0
3130,1,85,85,0.0303052,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^4} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(2 - m))/(e + f*x)^4,x]","\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}","\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,"((b*c - a*d)^3*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*Hypergeometric2F1[4, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/((b*e - a*f)^4*(1 + m))","A",1
3131,1,148,176,0.1827358,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^5} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(2 - m))/(e + f*x)^5,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-1} \left(\frac{(b c-a d)^3 (-a d f (m+1)+b c f (m-3)+4 b d e) \, _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}-\frac{f (c+d x)^4}{(e+f x)^4}\right)}{4 (b e-a f) (d e-c f)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*(-((f*(c + d*x)^4)/(e + f*x)^4) + ((b*c - a*d)^3*(4*b*d*e + b*c*f*(-3 + m) - a*d*f*(1 + m))*Hypergeometric2F1[4, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/((b*e - a*f)^4*(1 + m))))/(4*(b*e - a*f)*(d*e - c*f))","A",1
3132,1,271,311,0.8887526,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^6} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(2 - m))/(e + f*x)^6,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-1} \left(\frac{(b c-a d)^3 \left(a^2 d^2 f^2 \left(m^2+3 m+2\right)-2 a b d f (m+1) (c f (m-3)+5 d e)+b^2 \left(c^2 f^2 \left(m^2-7 m+12\right)+10 c d e f (m-3)+20 d^2 e^2\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)}{(m+1) (b e-a f)^5 (d e-c f)}-\frac{f (c+d x)^4 (-a d f (m+2)+b c f (m-4)+6 b d e)}{(e+f x)^4 (b e-a f) (d e-c f)}-\frac{4 f (c+d x)^4}{(e+f x)^5}\right)}{20 (b e-a f) (d e-c f)}","-\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,"((a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*((-4*f*(c + d*x)^4)/(e + f*x)^5 - (f*(6*b*d*e + b*c*f*(-4 + m) - a*d*f*(2 + m))*(c + d*x)^4)/((b*e - a*f)*(d*e - c*f)*(e + f*x)^4) + ((b*c - a*d)^3*(-2*a*b*d*f*(5*d*e + c*f*(-3 + m))*(1 + m) + a^2*d^2*f^2*(2 + 3*m + m^2) + b^2*(20*d^2*e^2 + 10*c*d*e*f*(-3 + m) + c^2*f^2*(12 - 7*m + m^2)))*Hypergeometric2F1[4, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/((b*e - a*f)^5*(d*e - c*f)*(1 + m))))/(20*(b*e - a*f)*(d*e - c*f))","A",1
3133,1,482,541,6.1045464,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(e+f x)^7} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(2 - m))/(e + f*x)^7,x]","\frac{(a+b x)^{m+1} (c+d x)^{-m-1} \left(-\frac{(e+f x)^2 \left(f (m+1) (c+d x)^4 (b e-a f)^4 \left(a^2 d^2 f^2 \left(m^2+5 m+6\right)-2 a b d f \left(c f \left(m^2-2 m-6\right)+d e (7 m+12)\right)+b^2 \left(c^2 f^2 \left(m^2-9 m+20\right)+2 c d e f (7 m-26)+38 d^2 e^2\right)\right)-(e+f x)^4 (b c-a d)^3 \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)+6 d e)-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 (m-3)+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 (m-3)+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)\right)}{(m+1) (b e-a f)^6 (d e-c f)^2}+\frac{4 f (c+d x)^4 (e+f x) (a d f (m+3)-b (c f (m-5)+8 d e))}{(b e-a f) (d e-c f)}-20 f (c+d x)^4\right)}{120 (e+f x)^6 (b e-a f) (d e-c f)}","-\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,"((a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*(-20*f*(c + d*x)^4 + (4*f*(-(b*(8*d*e + c*f*(-5 + m))) + a*d*f*(3 + m))*(c + d*x)^4*(e + f*x))/((b*e - a*f)*(d*e - c*f)) - ((e + f*x)^2*(f*(b*e - a*f)^4*(1 + m)*(a^2*d^2*f^2*(6 + 5*m + m^2) + b^2*(38*d^2*e^2 + 2*c*d*e*f*(-26 + 7*m) + c^2*f^2*(20 - 9*m + m^2)) - 2*a*b*d*f*(d*e*(12 + 7*m) + c*f*(-6 - 2*m + m^2)))*(c + d*x)^4 - (b*c - a*d)^3*(3*a^2*b*d^2*f^2*(6*d*e + c*f*(-3 + m))*(2 + 3*m + m^2) - a^3*d^3*f^3*(6 + 11*m + 6*m^2 + m^3) - 3*a*b^2*d*f*(1 + m)*(30*d^2*e^2 + 12*c*d*e*f*(-3 + m) + c^2*f^2*(12 - 7*m + m^2)) + b^3*(120*d^3*e^3 + 90*c*d^2*e^2*f*(-3 + m) + 18*c^2*d*e*f^2*(12 - 7*m + m^2) + c^3*f^3*(-60 + 47*m - 12*m^2 + m^3)))*(e + f*x)^4*Hypergeometric2F1[4, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]))/((b*e - a*f)^6*(d*e - c*f)^2*(1 + m))))/(120*(b*e - a*f)*(d*e - c*f)*(e + f*x)^6)","A",1
3134,1,337,488,0.4642133,"\int \frac{(a+b x)^m (c+d x)^{3-m}}{e+f x} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(3 - m))/(e + f*x),x]","\frac{(a+b x)^m (c+d x)^{-m} \left(d f^3 m (a+b x) (b c-a d)^2 \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)}{a d-b c}\right)-b (d e-c f) \left(-b (d e-c f) \left(b (m+1) (d e-c f) \left(\, _2F_1\left(1,m;m+1;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)-\left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m,m;m+1;\frac{d (a+b x)}{a d-b c}\right)\right)+d f m (a+b x) \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)}{a d-b c}\right)\right)-d f^2 m (a+b x) (a d-b c) \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)}{a d-b c}\right)\right)\right)}{b^3 f^4 m (m+1)}","-\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,"((a + b*x)^m*(d*(b*c - a*d)^2*f^3*m*(a + b*x)*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[-2 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)] - b*(d*e - c*f)*(-(d*(-(b*c) + a*d)*f^2*m*(a + b*x)*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[-1 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)]) - b*(d*e - c*f)*(b*(d*e - c*f)*(1 + m)*(Hypergeometric2F1[1, m, 1 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))] - ((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, m, 1 + m, (d*(a + b*x))/(-(b*c) + a*d)]) + d*f*m*(a + b*x)*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)]))))/(b^3*f^4*m*(1 + m)*(c + d*x)^m)","A",1
3135,1,111,397,0.2013508,"\int \frac{(a+b x)^m (c+d x)^{3-m}}{(e+f x)^2} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(3 - m))/(e + f*x)^2,x]","\frac{(b c-a d)^3 (a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m F_1\left(m+1;m-3,2;m+2;\frac{d (a+b x)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{b^2 (m+1) (b e-a f)^2}","\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,"((b*c - a*d)^3*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*AppellF1[1 + m, -3 + m, 2, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/(b^2*(b*e - a*f)^2*(1 + m)*(c + d*x)^m)","C",0
3136,1,111,453,0.4395566,"\int \frac{(a+b x)^m (c+d x)^{3-m}}{(e+f x)^3} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(3 - m))/(e + f*x)^3,x]","\frac{(b c-a d)^3 (a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m F_1\left(m+1;m-3,3;m+2;\frac{d (a+b x)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{b (m+1) (b e-a f)^3}","\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,"((b*c - a*d)^3*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*AppellF1[1 + m, -3 + m, 3, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/(b*(b*e - a*f)^3*(1 + m)*(c + d*x)^m)","C",0
3137,1,257,245,0.6214614,"\int \frac{(a+b x)^{1-n} (c+d x)^{1+n}}{b c+a d+2 b d x} \, dx","Integrate[((a + b*x)^(1 - n)*(c + d*x)^(1 + n))/(b*c + a*d + 2*b*d*x),x]","\frac{(a d-b c) (a+b x)^{-n} (c+d x)^n \left(\frac{\left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(4 d n (n+1) (a+b x) \, _2F_1\left(-n-1,1-n;2-n;\frac{d (a+b x)}{a d-b c}\right)-(n-1) \left((n+1) (b c-a d) \, _2F_1\left(-n,-n;1-n;\frac{d (a+b x)}{a d-b c}\right)-2 b n (c+d x) \left(-\frac{b d (a+b x) (c+d x)}{(b c-a d)^2}\right)^n \, _2F_1\left(n,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right)\right)\right)}{n^2-1}+(b c-a d) \, _2F_1\left(1,-n;1-n;-\frac{d (a+b x)}{b (c+d x)}\right)\right)}{8 b^2 d^2 n}","\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,"((-(b*c) + a*d)*(c + d*x)^n*((b*c - a*d)*Hypergeometric2F1[1, -n, 1 - n, -((d*(a + b*x))/(b*(c + d*x)))] + (4*d*n*(1 + n)*(a + b*x)*Hypergeometric2F1[-1 - n, 1 - n, 2 - n, (d*(a + b*x))/(-(b*c) + a*d)] - (-1 + n)*((b*c - a*d)*(1 + n)*Hypergeometric2F1[-n, -n, 1 - n, (d*(a + b*x))/(-(b*c) + a*d)] - 2*b*n*(c + d*x)*(-((b*d*(a + b*x)*(c + d*x))/(b*c - a*d)^2))^n*Hypergeometric2F1[n, 1 + n, 2 + n, (b*(c + d*x))/(b*c - a*d)]))/((-1 + n^2)*((b*(c + d*x))/(b*c - a*d))^n)))/(8*b^2*d^2*n*(a + b*x)^n)","A",1
3138,1,234,154,0.7404457,"\int \frac{(a+b x)^{1-n} (c+d x)^{1+n}}{(b c+a d+2 b d x)^2} \, dx","Integrate[((a + b*x)^(1 - n)*(c + d*x)^(1 + n))/(b*c + a*d + 2*b*d*x)^2,x]","-\frac{(a+b x)^{-n} (c+d x)^n \left(2 d (a+b x) (a d+b (c+2 d x)) \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \, _2F_1\left(1-n,-n;2-n;\frac{d (a+b x)}{a d-b c}\right)-(n-1) (b c-a d)^2 \left(\frac{d (a+b x)}{a d+b (c+2 d x)}\right)^n \left(\frac{b (c+d x)}{a d+b (c+2 d x)}\right)^{-n} F_1\left(1;-n,n;2;\frac{a d-b c}{a d+b (c+2 d x)},\frac{b c-a d}{b c+a d+2 b d x}\right)\right)}{8 b^2 d^2 (n-1) (a d+b (c+2 d x))}","\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,"-1/8*((c + d*x)^n*(-(((b*c - a*d)^2*(-1 + n)*((d*(a + b*x))/(a*d + b*(c + 2*d*x)))^n*AppellF1[1, -n, n, 2, (-(b*c) + a*d)/(a*d + b*(c + 2*d*x)), (b*c - a*d)/(b*c + a*d + 2*b*d*x)])/((b*(c + d*x))/(a*d + b*(c + 2*d*x)))^n) + (2*d*(a + b*x)*(a*d + b*(c + 2*d*x))*Hypergeometric2F1[1 - n, -n, 2 - n, (d*(a + b*x))/(-(b*c) + a*d)])/((b*(c + d*x))/(b*c - a*d))^n))/(b^2*d^2*(-1 + n)*(a + b*x)^n*(a*d + b*(c + 2*d*x)))","C",0
3139,1,239,230,0.6988557,"\int \frac{(a+b x)^{1-n} (c+d x)^{1+n}}{(b c+a d+2 b d x)^3} \, dx","Integrate[((a + b*x)^(1 - n)*(c + d*x)^(1 + n))/(b*c + a*d + 2*b*d*x)^3,x]","\frac{(a+b x)^{-n} (c+d x)^n \left(\frac{(b c-a d)^3 \left(\frac{d (a+b x)}{a d+b (c+2 d x)}\right)^n \left(\frac{b (c+d x)}{a d+b (c+2 d x)}\right)^{-n} F_1\left(2;-n,n;3;\frac{a d-b c}{a d+b (c+2 d x)},\frac{b c-a d}{b c+a d+2 b d x}\right)}{(a d+b (c+2 d x))^2}-\frac{4 b (c+d x) \left(\frac{d (a+b x)}{a d-b c}\right)^n F_1\left(n+1;n,1;n+2;\frac{b (c+d x)}{b c-a d},\frac{2 b (c+d x)}{b c-a d}\right)}{n+1}\right)}{16 b^2 d^2 (b c-a d)}","-\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,"((c + d*x)^n*(((b*c - a*d)^3*((d*(a + b*x))/(a*d + b*(c + 2*d*x)))^n*AppellF1[2, -n, n, 3, (-(b*c) + a*d)/(a*d + b*(c + 2*d*x)), (b*c - a*d)/(b*c + a*d + 2*b*d*x)])/(((b*(c + d*x))/(a*d + b*(c + 2*d*x)))^n*(a*d + b*(c + 2*d*x))^2) - (4*b*((d*(a + b*x))/(-(b*c) + a*d))^n*(c + d*x)*AppellF1[1 + n, n, 1, 2 + n, (b*(c + d*x))/(b*c - a*d), (2*b*(c + d*x))/(b*c - a*d)])/(1 + n)))/(16*b^2*d^2*(b*c - a*d)*(a + b*x)^n)","C",0
3140,1,70,71,0.0414029,"\int \frac{(a+b x)^{1-n} (c+d x)^{1+n}}{(b c+a d+2 b d x)^4} \, dx","Integrate[((a + b*x)^(1 - n)*(c + d*x)^(1 + n))/(b*c + a*d + 2*b*d*x)^4,x]","-\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 (n-2) (b c-a d)}","\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,"-(((a + b*x)^(2 - n)*(c + d*x)^(-2 + n)*Hypergeometric2F1[4, 2 - n, 3 - n, -((d*(a + b*x))/(b*(c + d*x)))])/(b^4*(b*c - a*d)*(-2 + n)))","A",1
3141,1,243,231,0.2624586,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{b c+a d+2 b d x} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(2 - m))/(b*c + a*d + 2*b*d*x),x]","\frac{(a+b x)^m (c+d x)^{-m} \left(-4 d m (a+b x) (a d-b c) \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)}{a d-b c}\right)-(b c-a d) \left((m+1) (b c-a d) \left(\, _2F_1\left(1,m;m+1;-\frac{d (a+b x)}{b (c+d x)}\right)-\left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m,m;m+1;\frac{d (a+b x)}{a d-b c}\right)\right)-2 d m (a+b x) \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)}{a d-b c}\right)\right)\right)}{8 b^3 d m (m+1)}","-\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,"((a + b*x)^m*(-4*d*(-(b*c) + a*d)*m*(a + b*x)*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[-1 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)] - (b*c - a*d)*((b*c - a*d)*(1 + m)*(Hypergeometric2F1[1, m, 1 + m, -((d*(a + b*x))/(b*(c + d*x)))] - ((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, m, 1 + m, (d*(a + b*x))/(-(b*c) + a*d)]) - 2*d*m*(a + b*x)*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])))/(8*b^3*d*m*(1 + m)*(c + d*x)^m)","A",1
3142,1,308,144,1.38932,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(b c+a d+2 b d x)^2} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(2 - m))/(b*c + a*d + 2*b*d*x)^2,x]","\frac{(a+b x)^m (c+d x)^{-m} \left(\frac{\left(\frac{d (a+b x)}{a d-b c}\right)^{-m} \left(4 b (m+1) (c+d x) F_1\left(1-m;-m,1;2-m;\frac{b (c+d x)}{b c-a d},\frac{2 b (c+d x)}{b c-a d}\right)+2 d (m-1) (a+b x) \left(-\frac{b d (a+b x) (c+d x)}{(b c-a d)^2}\right)^m \, _2F_1\left(m,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)\right)}{d (m-1) (m+1)}-\frac{(b c-a d)^2 \left(\frac{d (a+b x)}{a d+b (c+2 d x)}\right)^{1-m} \left(\frac{b (c+d x)}{a d+b (c+2 d x)}\right)^m F_1\left(1;m,-m;2;\frac{a d-b c}{a d+b (c+2 d x)},\frac{b c-a d}{b c+a d+2 b d x}\right)}{d^2 (a+b x)}\right)}{8 b^3}","\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,"((a + b*x)^m*(-(((b*c - a*d)^2*((d*(a + b*x))/(a*d + b*(c + 2*d*x)))^(1 - m)*((b*(c + d*x))/(a*d + b*(c + 2*d*x)))^m*AppellF1[1, m, -m, 2, (-(b*c) + a*d)/(a*d + b*(c + 2*d*x)), (b*c - a*d)/(b*c + a*d + 2*b*d*x)])/(d^2*(a + b*x))) + (4*b*(1 + m)*(c + d*x)*AppellF1[1 - m, -m, 1, 2 - m, (b*(c + d*x))/(b*c - a*d), (2*b*(c + d*x))/(b*c - a*d)] + 2*d*(-1 + m)*(a + b*x)*(-((b*d*(a + b*x)*(c + d*x))/(b*c - a*d)^2))^m*Hypergeometric2F1[m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])/(d*(-1 + m)*(1 + m)*((d*(a + b*x))/(-(b*c) + a*d))^m)))/(8*b^3*(c + d*x)^m)","C",0
3143,1,373,261,1.380613,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(b c+a d+2 b d x)^3} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(2 - m))/(b*c + a*d + 2*b*d*x)^3,x]","\frac{(a+b x)^m (c+d x)^{-m} \left(\frac{4 (a d-b c) \left(\frac{b (c+d x)}{a d+b (c+2 d x)}\right)^m \left(\frac{d (a+b x)}{a d+b (c+2 d x)}\right)^{1-m} F_1\left(1;m,-m;2;\frac{a d-b c}{a d+b (c+2 d x)},\frac{b c-a d}{b c+a d+2 b d x}\right)}{d^2 (a+b x)}+\frac{\frac{4 b (c+d x) \left(\frac{d (a+b x)}{a d-b c}\right)^{-m} F_1\left(1-m;-m,1;2-m;\frac{b (c+d x)}{b c-a d},\frac{2 b (c+d x)}{b c-a d}\right)}{m-1}-\frac{(b c-a d)^3 \left(\frac{d (a+b x)}{a d+b (c+2 d x)}\right)^{-m} \left(\frac{b (c+d x)}{a d+b (c+2 d x)}\right)^m F_1\left(2;m,-m;3;\frac{a d-b c}{a d+b (c+2 d x)},\frac{b c-a d}{b c+a d+2 b d x}\right)}{(a d+b (c+2 d x))^2}}{d (b c-a d)}\right)}{16 b^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 \, _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,"((a + b*x)^m*((4*(-(b*c) + a*d)*((d*(a + b*x))/(a*d + b*(c + 2*d*x)))^(1 - m)*((b*(c + d*x))/(a*d + b*(c + 2*d*x)))^m*AppellF1[1, m, -m, 2, (-(b*c) + a*d)/(a*d + b*(c + 2*d*x)), (b*c - a*d)/(b*c + a*d + 2*b*d*x)])/(d^2*(a + b*x)) + (-(((b*c - a*d)^3*((b*(c + d*x))/(a*d + b*(c + 2*d*x)))^m*AppellF1[2, m, -m, 3, (-(b*c) + a*d)/(a*d + b*(c + 2*d*x)), (b*c - a*d)/(b*c + a*d + 2*b*d*x)])/(((d*(a + b*x))/(a*d + b*(c + 2*d*x)))^m*(a*d + b*(c + 2*d*x))^2)) + (4*b*(c + d*x)*AppellF1[1 - m, -m, 1, 2 - m, (b*(c + d*x))/(b*c - a*d), (2*b*(c + d*x))/(b*c - a*d)])/((-1 + m)*((d*(a + b*x))/(-(b*c) + a*d))^m))/(d*(b*c - a*d))))/(16*b^3*(c + d*x)^m)","C",0
3144,1,65,65,0.0372817,"\int \frac{(a+b x)^m (c+d x)^{2-m}}{(b c+a d+2 b d x)^4} \, dx","Integrate[((a + b*x)^m*(c + d*x)^(2 - m))/(b*c + a*d + 2*b*d*x)^4,x]","\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)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*Hypergeometric2F1[4, 1 + m, 2 + m, -((d*(a + b*x))/(b*(c + d*x)))])/(b^4*(b*c - a*d)*(1 + m))","A",1
3145,1,137,139,0.2608363,"\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{n+p} \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-m - n)*(e + f*x)^(n + p),x]","\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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{b (m+1)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-m - n)*((b*(c + d*x))/(b*c - a*d))^(m + n)*(e + f*x)^(n + p)*((b*(e + f*x))/(b*e - a*f))^(-n - p)*AppellF1[1 + m, m + n, -n - p, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/(b*(1 + m))","A",1
3146,1,133,139,0.2364677,"\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{1+n} \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-m - n)*(e + f*x)^(1 + n),x]","\frac{(a+b x)^{m+1} (e+f x)^{n+1} (c+d x)^{-m-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-n-1} \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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{b (m+1)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-m - n)*((b*(c + d*x))/(b*c - a*d))^(m + n)*(e + f*x)^(1 + n)*((b*(e + f*x))/(b*e - a*f))^(-1 - n)*AppellF1[1 + m, m + n, -1 - n, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/(b*(1 + m))","A",1
3147,1,127,129,0.1321476,"\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^n \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-m - n)*(e + f*x)^n,x]","\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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{b (m+1)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-m - n)*((b*(c + d*x))/(b*c - a*d))^(m + n)*(e + f*x)^n*AppellF1[1 + m, m + n, -n, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/(b*(1 + m)*((b*(e + f*x))/(b*e - a*f))^n)","A",1
3148,1,133,138,0.1616214,"\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{-1+n} \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-m - n)*(e + f*x)^(-1 + n),x]","\frac{(a+b x)^{m+1} (e+f x)^{n-1} (c+d x)^{-m-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{1-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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{b (m+1)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-m - n)*((b*(c + d*x))/(b*c - a*d))^(m + n)*(e + f*x)^(-1 + n)*((b*(e + f*x))/(b*e - a*f))^(1 - n)*AppellF1[1 + m, m + n, 1 - n, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/(b*(1 + m))","A",1
3149,1,123,124,0.0523467,"\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{-2+n} \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-m - n)*(e + f*x)^(-2 + n),x]","\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{(c f-d e) (a+b x)}{(b c-a d) (e+f x)}\right)}{(m+1) (b e-a f)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-m - n)*(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^(m + n)*(e + f*x)^(-1 + n)*Hypergeometric2F1[1 + m, m + n, 2 + m, ((-(d*e) + c*f)*(a + b*x))/((b*c - a*d)*(e + f*x))])/((b*e - a*f)*(1 + m))","A",1
3150,1,186,237,0.1922797,"\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{-3+n} \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-m - n)*(e + f*x)^(-3 + n),x]","\frac{(a+b x)^{m+1} (e+f x)^{n-2} (c+d x)^{-m-n} \left(\frac{(e+f x) (a d f (m+1)-b c f (m+n-1)+b d e (n-2)) \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{(c f-d e) (a+b x)}{(b c-a d) (e+f x)}\right)}{(m+1) (b e-a f)}+f (c+d x)\right)}{(n-2) (b e-a f) (d e-c f)}","-\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,"((a + b*x)^(1 + m)*(c + d*x)^(-m - n)*(e + f*x)^(-2 + n)*(f*(c + d*x) + ((a*d*f*(1 + m) + b*d*e*(-2 + n) - b*c*f*(-1 + m + n))*(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^(m + n)*(e + f*x)*Hypergeometric2F1[1 + m, m + n, 2 + m, ((-(d*e) + c*f)*(a + b*x))/((b*c - a*d)*(e + f*x))])/((b*e - a*f)*(1 + m))))/((b*e - a*f)*(d*e - c*f)*(-2 + n))","A",1
3151,1,341,428,0.9927933,"\int (a+b x)^m (c+d x)^{-m-n} (e+f x)^{-4+n} \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-m - n)*(e + f*x)^(-4 + n),x]","\frac{(a+b x)^{m+1} (e+f x)^{n-3} (c+d x)^{-m-n} \left(\frac{(e+f x)^2 \left(a^2 d^2 f^2 \left(m^2+3 m+2\right)+2 a b d f (m+1) (d e (n-3)-c f (m+n-1))+b^2 \left(c^2 f^2 \left(m^2+m (2 n-3)+n^2-3 n+2\right)-2 c d e f (n-3) (m+n-1)+d^2 e^2 \left(n^2-5 n+6\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{(c f-d e) (a+b x)}{(b c-a d) (e+f x)}\right)}{(m+1) (n-2) (b e-a f)^2 (d e-c f)}+\frac{f (c+d x) (e+f x) (a d f (m+2)-b c f (m+n-2)+b d e (n-4))}{(n-2) (b e-a f) (d e-c f)}+f (c+d x)\right)}{(n-3) (b e-a f) (d e-c f)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(-m - n)*(e + f*x)^(-3 + n)*(f*(c + d*x) + (f*(a*d*f*(2 + m) + b*d*e*(-4 + n) - b*c*f*(-2 + m + n))*(c + d*x)*(e + f*x))/((b*e - a*f)*(d*e - c*f)*(-2 + n)) + ((a^2*d^2*f^2*(2 + 3*m + m^2) + 2*a*b*d*f*(1 + m)*(d*e*(-3 + n) - c*f*(-1 + m + n)) + b^2*(-2*c*d*e*f*(-3 + n)*(-1 + m + n) + d^2*e^2*(6 - 5*n + n^2) + c^2*f^2*(2 + m^2 - 3*n + n^2 + m*(-3 + 2*n))))*(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^(m + n)*(e + f*x)^2*Hypergeometric2F1[1 + m, m + n, 2 + m, ((-(d*e) + c*f)*(a + b*x))/((b*c - a*d)*(e + f*x))])/((b*e - a*f)^2*(d*e - c*f)*(1 + m)*(-2 + n))))/((b*e - a*f)*(d*e - c*f)*(-3 + n))","A",1
3152,1,120,88,0.4264542,"\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","Integrate[(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]","\frac{b^3 d^3 (m+n+2)^3 (a+b x)^{m+1} (c+d x)^{n+1} \left(\frac{f (a d (m+1)+b c (n+1)+b d x (m+n+2))}{b d (m+n+2)}\right)^{-m-n}}{f^3 (m+1) (n+1) (b c-a d)^2 (a d (m+1)+b c (n+1)+b d x (m+n+2))^2}","\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,"(b^3*d^3*(2 + m + n)^3*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*((f*(a*d*(1 + m) + b*c*(1 + n) + b*d*(2 + m + n)*x))/(b*d*(2 + m + n)))^(-m - n))/((b*c - a*d)^2*f^3*(1 + m)*(1 + n)*(a*d*(1 + m) + b*c*(1 + n) + b*d*(2 + m + n)*x)^2)","A",1
3153,1,101,101,0.1287281,"\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","Integrate[(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]","\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)}","\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,"(b*(a + b*x)^(1 + m)*(e + f*x)^(((b*c - a*d)*f*(1 + m))/(b*(d*e - c*f))))/((b*c - a*d)*(b*e - a*f)*(1 + m)*(c + d*x)^((d*(b*e - a*f)*(1 + m))/(b*(d*e - c*f))))","A",1
3154,1,127,129,0.1630551,"\int (a+b x)^m (c+d x)^n (e+f x)^{-m-n} \, dx","Integrate[(a + b*x)^m*(c + d*x)^n*(e + f*x)^(-m - n),x]","\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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{b (m+1)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-m - n)*((b*(e + f*x))/(b*e - a*f))^(m + n)*AppellF1[1 + m, -n, m + n, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/(b*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n)","A",1
3155,1,130,137,0.1579887,"\int (a+b x)^m (c+d x)^n (e+f x)^{-1-m-n} \, dx","Integrate[(a + b*x)^m*(c + d*x)^n*(e + f*x)^(-1 - m - n),x]","\frac{(a+b x)^{m+1} (c+d x)^n (e+f x)^{-m-n-1} \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+1} F_1\left(m+1;-n,m+n+1;m+2;\frac{d (a+b x)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{b (m+1)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-1 - m - n)*((b*(e + f*x))/(b*e - a*f))^(1 + m + n)*AppellF1[1 + m, -n, 1 + m + n, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/(b*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n)","A",1
3156,1,122,123,0.0459173,"\int (a+b x)^m (c+d x)^n (e+f x)^{-2-m-n} \, dx","Integrate[(a + b*x)^m*(c + d*x)^n*(e + f*x)^(-2 - m - n),x]","\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{(c f-d e) (a+b x)}{(b c-a d) (e+f x)}\right)}{(m+1) (b e-a f)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-1 - m - n)*Hypergeometric2F1[1 + m, -n, 2 + m, ((-(d*e) + c*f)*(a + b*x))/((b*c - a*d)*(e + f*x))])/((b*e - a*f)*(1 + m)*(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^n)","A",1
3157,1,189,227,0.1624356,"\int (a+b x)^m (c+d x)^n (e+f x)^{-3-m-n} \, dx","Integrate[(a + b*x)^m*(c + d*x)^n*(e + f*x)^(-3 - m - n),x]","-\frac{(a+b x)^{m+1} (c+d x)^n (e+f x)^{-m-n-2} \left(f (c+d x)-\frac{(e+f x) (-a d f (m+1)-b c f (n+1)+b 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{(c f-d e) (a+b x)}{(b c-a d) (e+f x)}\right)}{(m+1) (b e-a f)}\right)}{(m+n+2) (b e-a f) (d e-c f)}","-\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,"-(((a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-2 - m - n)*(f*(c + d*x) - ((-(a*d*f*(1 + m)) - b*c*f*(1 + n) + b*d*e*(2 + m + n))*(e + f*x)*Hypergeometric2F1[1 + m, -n, 2 + m, ((-(d*e) + c*f)*(a + b*x))/((b*c - a*d)*(e + f*x))])/((b*e - a*f)*(1 + m)*(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^n)))/((b*e - a*f)*(d*e - c*f)*(2 + m + n)))","A",1
3158,1,346,402,1.0711545,"\int (a+b x)^m (c+d x)^n (e+f x)^{-4-m-n} \, dx","Integrate[(a + b*x)^m*(c + d*x)^n*(e + f*x)^(-4 - m - n),x]","-\frac{(a+b x)^{m+1} (c+d x)^n (e+f x)^{-m-n-3} \left(-\frac{(e+f x)^2 \left(a^2 d^2 f^2 \left(m^2+3 m+2\right)-2 a b d f (m+1) (d e (m+n+3)-c f (n+1))+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) \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{(c f-d e) (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 (c+d x) (e+f x) (-a d f (m+2)-b c f (n+2)+b d e (m+n+4))}{(m+n+2) (b e-a f) (d e-c f)}+f (c+d x)\right)}{(m+n+3) (b e-a f) (d e-c f)}","\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,"-(((a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-3 - m - n)*(f*(c + d*x) + (f*(-(a*d*f*(2 + m)) - b*c*f*(2 + n) + b*d*e*(4 + m + n))*(c + d*x)*(e + f*x))/((b*e - a*f)*(d*e - c*f)*(2 + m + n)) - ((a^2*d^2*f^2*(2 + 3*m + m^2) - 2*a*b*d*f*(1 + m)*(-(c*f*(1 + n)) + d*e*(3 + m + n)) + b^2*(-2*c*d*e*f*(1 + n)*(3 + m + n) + c^2*f^2*(2 + 3*n + n^2) + d^2*e^2*(6 + m^2 + 5*n + n^2 + m*(5 + 2*n))))*(e + f*x)^2*Hypergeometric2F1[1 + m, -n, 2 + m, ((-(d*e) + c*f)*(a + b*x))/((b*c - a*d)*(e + f*x))])/((b*e - a*f)^2*(d*e - c*f)*(1 + m)*(2 + m + n)*(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^n)))/((b*e - a*f)*(d*e - c*f)*(3 + m + n)))","A",1
3159,1,121,123,0.1994815,"\int (a+b x)^m (c+d x)^n (e+f x)^p \, dx","Integrate[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p,x]","\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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{b (m+1)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^p*AppellF1[1 + m, -n, -p, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/(b*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n*((b*(e + f*x))/(b*e - a*f))^p)","A",1
3160,1,253,259,0.4320487,"\int (a+b x)^m (c+d x)^n (e+f x)^2 \, dx","Integrate[(a + b*x)^m*(c + d*x)^n*(e + f*x)^2,x]","\frac{(a+b x)^{m+1} (c+d x)^n \left(\frac{\left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(a^2 d^2 f^2 \left(n^2+3 n+2\right)-2 a b d f (n+1) (d e (m+n+3)-c f (m+1))+b^2 \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)\right) \, _2F_1\left(m+1,-n;m+2;\frac{d (a+b x)}{a d-b c}\right)}{b^2 d (m+1) (m+n+2)}+\frac{f (c+d x) (b d e (m+n+4)-f (a d (n+2)+b c (m+2)))}{b d (m+n+2)}+f (c+d x) (e+f x)\right)}{b d (m+n+3)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^n*((f*(b*d*e*(4 + m + n) - f*(b*c*(2 + m) + a*d*(2 + n)))*(c + d*x))/(b*d*(2 + m + n)) + f*(c + d*x)*(e + f*x) + ((a^2*d^2*f^2*(2 + 3*n + n^2) - 2*a*b*d*f*(1 + n)*(-(c*f*(1 + m)) + d*e*(3 + m + n)) + b^2*(c^2*f^2*(2 + 3*m + m^2) - 2*c*d*e*f*(1 + m)*(3 + m + n) + d^2*e^2*(6 + m^2 + 5*n + n^2 + m*(5 + 2*n))))*Hypergeometric2F1[1 + m, -n, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])/(b^2*d*(1 + m)*(2 + m + n)*((b*(c + d*x))/(b*c - a*d))^n)))/(b*d*(3 + m + n))","A",1
3161,1,117,131,0.1131986,"\int (a+b x)^m (c+d x)^n (e+f x) \, dx","Integrate[(a + b*x)^m*(c + d*x)^n*(e + f*x),x]","\frac{(a+b x)^{m+1} (c+d x)^n \left(\frac{\left(\frac{b (c+d x)}{b c-a d}\right)^{-n} (-a d f (n+1)-b c f (m+1)+b d e (m+n+2)) \, _2F_1\left(m+1,-n;m+2;\frac{d (a+b x)}{a d-b c}\right)}{m+1}+b f (c+d x)\right)}{b^2 d (m+n+2)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^n*(b*f*(c + d*x) + ((-(b*c*f*(1 + m)) - a*d*f*(1 + n) + b*d*e*(2 + m + n))*Hypergeometric2F1[1 + m, -n, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])/((1 + m)*((b*(c + d*x))/(b*c - a*d))^n)))/(b^2*d*(2 + m + n))","A",1
3162,1,73,61,0.0200598,"\int (a+b x)^m (c+d x)^n \, dx","Integrate[(a + b*x)^m*(c + d*x)^n,x]","\frac{(a+b x)^{m+1} (c+d x)^n \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \, _2F_1\left(m+1,-n;m+2;\frac{d (a+b x)}{a d-b c}\right)}{b (m+1)}","-\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,"((a + b*x)^(1 + m)*(c + d*x)^n*Hypergeometric2F1[1 + m, -n, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])/(b*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n)","A",1
3163,1,98,100,0.093641,"\int \frac{(a+b x)^m (c+d x)^n}{e+f x} \, dx","Integrate[((a + b*x)^m*(c + d*x)^n)/(e + f*x),x]","\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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{(m+1) (b e-a f)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^n*AppellF1[1 + m, -n, 1, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/((b*e - a*f)*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n)","A",1
3164,1,99,101,0.0971803,"\int \frac{(a+b x)^m (c+d x)^n}{(e+f x)^2} \, dx","Integrate[((a + b*x)^m*(c + d*x)^n)/(e + f*x)^2,x]","\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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{(m+1) (b e-a f)^2}","\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,"(b*(a + b*x)^(1 + m)*(c + d*x)^n*AppellF1[1 + m, -n, 2, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/((b*e - a*f)^2*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n)","A",1
3165,1,101,103,0.3073076,"\int \frac{(a+b x)^m (c+d x)^n}{(e+f x)^3} \, dx","Integrate[((a + b*x)^m*(c + d*x)^n)/(e + f*x)^3,x]","\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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{(m+1) (b e-a f)^3}","\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,"(b^2*(a + b*x)^(1 + m)*(c + d*x)^n*AppellF1[1 + m, -n, 3, 2 + m, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/((b*e - a*f)^3*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n)","A",1
3166,1,47,50,0.0361246,"\int \frac{(3+4 x)^n}{\sqrt{1-x} \sqrt{1+x}} \, dx","Integrate[(3 + 4*x)^n/(Sqrt[1 - x]*Sqrt[1 + x]),x]","\frac{(4 x+3)^{n+1} F_1\left(n+1;\frac{1}{2},\frac{1}{2};n+2;-4 x-3,\frac{1}{7} (4 x+3)\right)}{\sqrt{7} (n+1)}","-\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,"((3 + 4*x)^(1 + n)*AppellF1[1 + n, 1/2, 1/2, 2 + n, -3 - 4*x, (3 + 4*x)/7])/(Sqrt[7]*(1 + n))","A",0
3167,1,48,43,0.0334755,"\int \frac{(3-4 x)^n}{\sqrt{1-x} \sqrt{1+x}} \, dx","Integrate[(3 - 4*x)^n/(Sqrt[1 - x]*Sqrt[1 + x]),x]","-\frac{(3-4 x)^{n+1} F_1\left(n+1;\frac{1}{2},\frac{1}{2};n+2;\frac{1}{7} (3-4 x),4 x-3\right)}{\sqrt{7} (n+1)}","\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,"-(((3 - 4*x)^(1 + n)*AppellF1[1 + n, 1/2, 1/2, 2 + n, (3 - 4*x)/7, -3 + 4*x])/(Sqrt[7]*(1 + n)))","A",0
3168,1,47,45,0.0276758,"\int \frac{(-3+4 x)^n}{\sqrt{1-x} \sqrt{1+x}} \, dx","Integrate[(-3 + 4*x)^n/(Sqrt[1 - x]*Sqrt[1 + x]),x]","\frac{(4 x-3)^{n+1} F_1\left(n+1;\frac{1}{2},\frac{1}{2};n+2;\frac{1}{7} (3-4 x),4 x-3\right)}{\sqrt{7} (n+1)}","-\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,"((-3 + 4*x)^(1 + n)*AppellF1[1 + n, 1/2, 1/2, 2 + n, (3 - 4*x)/7, -3 + 4*x])/(Sqrt[7]*(1 + n))","A",0
3169,1,48,38,0.0332631,"\int \frac{(-3-4 x)^n}{\sqrt{1-x} \sqrt{1+x}} \, dx","Integrate[(-3 - 4*x)^n/(Sqrt[1 - x]*Sqrt[1 + x]),x]","-\frac{(-4 x-3)^{n+1} F_1\left(n+1;\frac{1}{2},\frac{1}{2};n+2;-4 x-3,\frac{1}{7} (4 x+3)\right)}{\sqrt{7} (n+1)}","\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,"-(((-3 - 4*x)^(1 + n)*AppellF1[1 + n, 1/2, 1/2, 2 + n, -3 - 4*x, (3 + 4*x)/7])/(Sqrt[7]*(1 + n)))","A",0
3170,1,212,100,0.7123422,"\int \frac{(a+b x)^{4/3}}{\sqrt{c+d x} (e+f x)} \, dx","Integrate[(a + b*x)^(4/3)/(Sqrt[c + d*x]*(e + f*x)),x]","\frac{6 \sqrt{c+d x} \left(\left(\frac{d (a+b x)}{b (c+d x)}\right)^{2/3} \left(7 b (-7 a d f+2 b c f+5 b d e) F_1\left(\frac{1}{6};\frac{2}{3},1;\frac{7}{6};\frac{b c-a d}{b c+b d x},\frac{c f-d e}{f (c+d x)}\right)-\frac{(b c-a d) (-5 a d f+2 b c f+3 b d e) F_1\left(\frac{7}{6};\frac{2}{3},1;\frac{13}{6};\frac{b c-a d}{b c+b d x},\frac{c f-d e}{f (c+d x)}\right)}{c+d x}\right)+7 b d f (a+b x)\right)}{35 d^2 f^2 (a+b x)^{2/3}}","\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,"(6*Sqrt[c + d*x]*(7*b*d*f*(a + b*x) + ((d*(a + b*x))/(b*(c + d*x)))^(2/3)*(7*b*(5*b*d*e + 2*b*c*f - 7*a*d*f)*AppellF1[1/6, 2/3, 1, 7/6, (b*c - a*d)/(b*c + b*d*x), (-(d*e) + c*f)/(f*(c + d*x))] - ((b*c - a*d)*(3*b*d*e + 2*b*c*f - 5*a*d*f)*AppellF1[7/6, 2/3, 1, 13/6, (b*c - a*d)/(b*c + b*d*x), (-(d*e) + c*f)/(f*(c + d*x))])/(c + d*x))))/(35*d^2*f^2*(a + b*x)^(2/3))","B",0
3171,1,536,123,2.9100276,"\int \frac{(c+d x)^{2/5} (e+f x)^{3/5}}{\sqrt{a+b x}} \, dx","Integrate[((c + d*x)^(2/5)*(e + f*x)^(3/5))/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \left(15 b^2 (c+d x) (e+f x)-2 (a+b x) \left(\frac{9 \left(25 a^2 d^2 f^2-10 a b d f (2 c f+3 d e)+b^2 \left(-2 c^2 f^2+24 c d e f+3 d^2 e^2\right)\right) F_1\left(\frac{1}{2};\frac{3}{5},\frac{2}{5};\frac{3}{2};\frac{a d-b c}{d (a+b x)},\frac{a f-b e}{f (a+b x)}\right)}{15 d f (a+b x) F_1\left(\frac{1}{2};\frac{3}{5},\frac{2}{5};\frac{3}{2};\frac{a d-b c}{d (a+b x)},\frac{a f-b e}{f (a+b x)}\right)+(4 a d f-4 b d e) F_1\left(\frac{3}{2};\frac{3}{5},\frac{7}{5};\frac{5}{2};\frac{a d-b c}{d (a+b x)},\frac{a f-b e}{f (a+b x)}\right)+6 f (a d-b c) F_1\left(\frac{3}{2};\frac{8}{5},\frac{2}{5};\frac{5}{2};\frac{a d-b c}{d (a+b x)},\frac{a f-b e}{f (a+b x)}\right)}+\frac{(b c-a d) (b e-a f) \left(\frac{b (c+d x)}{d (a+b x)}\right)^{3/5} \left(\frac{b (e+f x)}{f (a+b x)}\right)^{2/5} (-5 a d f+2 b c f+3 b d e) F_1\left(\frac{3}{2};\frac{3}{5},\frac{2}{5};\frac{5}{2};\frac{a d-b c}{d (a+b x)},\frac{a f-b e}{f (a+b x)}\right)}{d f (a+b x)^2}-\frac{3 b^2 (c+d x) (e+f x) (-5 a d f+2 b c f+3 b d e)}{d f (a+b x)^2}\right)\right)}{45 b^3 (c+d x)^{3/5} (e+f x)^{2/5}}","\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,"(2*Sqrt[a + b*x]*(15*b^2*(c + d*x)*(e + f*x) - 2*(a + b*x)*((-3*b^2*(3*b*d*e + 2*b*c*f - 5*a*d*f)*(c + d*x)*(e + f*x))/(d*f*(a + b*x)^2) + ((b*c - a*d)*(b*e - a*f)*(3*b*d*e + 2*b*c*f - 5*a*d*f)*((b*(c + d*x))/(d*(a + b*x)))^(3/5)*((b*(e + f*x))/(f*(a + b*x)))^(2/5)*AppellF1[3/2, 3/5, 2/5, 5/2, (-(b*c) + a*d)/(d*(a + b*x)), (-(b*e) + a*f)/(f*(a + b*x))])/(d*f*(a + b*x)^2) + (9*(25*a^2*d^2*f^2 - 10*a*b*d*f*(3*d*e + 2*c*f) + b^2*(3*d^2*e^2 + 24*c*d*e*f - 2*c^2*f^2))*AppellF1[1/2, 3/5, 2/5, 3/2, (-(b*c) + a*d)/(d*(a + b*x)), (-(b*e) + a*f)/(f*(a + b*x))])/(15*d*f*(a + b*x)*AppellF1[1/2, 3/5, 2/5, 3/2, (-(b*c) + a*d)/(d*(a + b*x)), (-(b*e) + a*f)/(f*(a + b*x))] + (-4*b*d*e + 4*a*d*f)*AppellF1[3/2, 3/5, 7/5, 5/2, (-(b*c) + a*d)/(d*(a + b*x)), (-(b*e) + a*f)/(f*(a + b*x))] + 6*(-(b*c) + a*d)*f*AppellF1[3/2, 8/5, 2/5, 5/2, (-(b*c) + a*d)/(d*(a + b*x)), (-(b*e) + a*f)/(f*(a + b*x))]))))/(45*b^3*(c + d*x)^(3/5)*(e + f*x)^(2/5))","B",0
3172,1,121,123,0.102754,"\int \frac{\sqrt{a+b x} (e+f x)^n}{\sqrt{c+d x}} \, dx","Integrate[(Sqrt[a + b*x]*(e + f*x)^n)/Sqrt[c + d*x],x]","\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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{3 b \sqrt{c+d x}}","\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,"(2*(a + b*x)^(3/2)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*(e + f*x)^n*AppellF1[3/2, 1/2, -n, 5/2, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/(3*b*Sqrt[c + d*x]*((b*(e + f*x))/(b*e - a*f))^n)","A",1
3173,1,119,121,0.0809804,"\int \frac{\sqrt{c+d x} (e+f x)^n}{\sqrt{a+b x}} \, dx","Integrate[(Sqrt[c + d*x]*(e + f*x)^n)/Sqrt[a + b*x],x]","\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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)}{b \sqrt{\frac{b (c+d x)}{b c-a d}}}","\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,"(2*Sqrt[a + b*x]*Sqrt[c + d*x]*(e + f*x)^n*AppellF1[1/2, -1/2, -n, 3/2, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])/(b*Sqrt[(b*(c + d*x))/(b*c - a*d)]*((b*(e + f*x))/(b*e - a*f))^n)","A",1
3174,1,241,128,0.2478241,"\int \frac{(e+f x)^n}{\sqrt{a+b x} (c+d x)^{3/2}} \, dx","Integrate[(e + f*x)^n/(Sqrt[a + b*x]*(c + d*x)^(3/2)),x]","-\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} \left((3 a d-3 b c) F_1\left(\frac{1}{2};-\frac{1}{2},-n;\frac{3}{2};\frac{d (a+b x)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)+d (a+b x) \left(F_1\left(\frac{3}{2};\frac{1}{2},-n;\frac{5}{2};\frac{d (a+b x)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)+F_1\left(\frac{3}{2};\frac{3}{2},-n;\frac{5}{2};\frac{d (a+b x)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)\right)\right)}{3 \sqrt{c+d x} (b c-a d)^2}","\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,"(-2*Sqrt[a + b*x]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*(e + f*x)^n*((-3*b*c + 3*a*d)*AppellF1[1/2, -1/2, -n, 3/2, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)] + d*(a + b*x)*(AppellF1[3/2, 1/2, -n, 5/2, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)] + AppellF1[3/2, 3/2, -n, 5/2, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)])))/(3*(b*c - a*d)^2*Sqrt[c + d*x]*((b*(e + f*x))/(b*e - a*f))^n)","A",0
3175,1,262,121,0.2304248,"\int \frac{(e+f x)^n}{(a+b x)^{3/2} \sqrt{c+d x}} \, dx","Integrate[(e + f*x)^n/((a + b*x)^(3/2)*Sqrt[c + d*x]),x]","\frac{2 \sqrt{c+d x} (e+f x)^n \left(\frac{b (e+f x)}{b e-a f}\right)^{-n} \left(d^2 (a+b x)^2 F_1\left(\frac{3}{2};\frac{1}{2},-n;\frac{5}{2};\frac{d (a+b x)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)-3 (b c-a d)^2 F_1\left(-\frac{1}{2};-\frac{1}{2},-n;\frac{1}{2};\frac{d (a+b x)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)+3 d (a+b x) (a d-b c) F_1\left(\frac{1}{2};-\frac{1}{2},-n;\frac{3}{2};\frac{d (a+b x)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)\right)}{3 \sqrt{a+b x} (b c-a d)^3 \sqrt{\frac{b (c+d x)}{b c-a d}}}","-\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,"(2*Sqrt[c + d*x]*(e + f*x)^n*(-3*(b*c - a*d)^2*AppellF1[-1/2, -1/2, -n, 1/2, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)] + 3*d*(-(b*c) + a*d)*(a + b*x)*AppellF1[1/2, -1/2, -n, 3/2, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)] + d^2*(a + b*x)^2*AppellF1[3/2, 1/2, -n, 5/2, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)]))/(3*(b*c - a*d)^3*Sqrt[a + b*x]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*((b*(e + f*x))/(b*e - a*f))^n)","B",0
3176,1,202,100,0.5459573,"\int \frac{\sqrt{a+b x} \sqrt[3]{c+d x}}{e+f x} \, dx","Integrate[(Sqrt[a + b*x]*(c + d*x)^(1/3))/(e + f*x),x]","\frac{6 \sqrt{a+b x} \left(7 f (c+d x)-\frac{\left(\frac{b (c+d x)}{d (a+b x)}\right)^{2/3} \left(-7 (-3 a d f-2 b c f+5 b d e) F_1\left(\frac{1}{6};\frac{2}{3},1;\frac{7}{6};\frac{a d-b c}{d (a+b x)},\frac{a f-b e}{f (a+b x)}\right)-\frac{3 (b c-a d) (b e-a f) F_1\left(\frac{7}{6};\frac{2}{3},1;\frac{13}{6};\frac{a d-b c}{d (a+b x)},\frac{a f-b e}{f (a+b x)}\right)}{a+b x}\right)}{b}\right)}{35 f^2 (c+d x)^{2/3}}","\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,"(6*Sqrt[a + b*x]*(7*f*(c + d*x) - (((b*(c + d*x))/(d*(a + b*x)))^(2/3)*(-7*(5*b*d*e - 2*b*c*f - 3*a*d*f)*AppellF1[1/6, 2/3, 1, 7/6, (-(b*c) + a*d)/(d*(a + b*x)), (-(b*e) + a*f)/(f*(a + b*x))] - (3*(b*c - a*d)*(b*e - a*f)*AppellF1[7/6, 2/3, 1, 13/6, (-(b*c) + a*d)/(d*(a + b*x)), (-(b*e) + a*f)/(f*(a + b*x))])/(a + b*x)))/b))/(35*f^2*(c + d*x)^(2/3))","B",0
3177,1,201,100,0.5838315,"\int \frac{\sqrt[3]{a+b x} \sqrt{c+d x}}{e+f x} \, dx","Integrate[((a + b*x)^(1/3)*Sqrt[c + d*x])/(e + f*x),x]","\frac{6 \sqrt{c+d x} \left(\frac{\left(\frac{d (a+b x)}{b (c+d x)}\right)^{2/3} \left(7 (-2 a d f-3 b c f+5 b d e) F_1\left(\frac{1}{6};\frac{2}{3},1;\frac{7}{6};\frac{b c-a d}{b c+b d x},\frac{c f-d e}{f (c+d x)}\right)+\frac{3 (b c-a d) (c f-d e) F_1\left(\frac{7}{6};\frac{2}{3},1;\frac{13}{6};\frac{b c-a d}{b c+b d x},\frac{c f-d e}{f (c+d x)}\right)}{c+d x}\right)}{d}+7 f (a+b x)\right)}{35 f^2 (a+b x)^{2/3}}","\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,"(6*Sqrt[c + d*x]*(7*f*(a + b*x) + (((d*(a + b*x))/(b*(c + d*x)))^(2/3)*(7*(5*b*d*e - 3*b*c*f - 2*a*d*f)*AppellF1[1/6, 2/3, 1, 7/6, (b*c - a*d)/(b*c + b*d*x), (-(d*e) + c*f)/(f*(c + d*x))] + (3*(b*c - a*d)*(-(d*e) + c*f)*AppellF1[7/6, 2/3, 1, 13/6, (b*c - a*d)/(b*c + b*d*x), (-(d*e) + c*f)/(f*(c + d*x))])/(c + d*x)))/d))/(35*f^2*(a + b*x)^(2/3))","B",0
3178,1,473,125,3.2238943,"\int \sqrt{a+b x} \sqrt[3]{c+d x} \sqrt[4]{e+f x} \, dx","Integrate[Sqrt[a + b*x]*(c + d*x)^(1/3)*(e + f*x)^(1/4),x]","\frac{12 \left(-66 \left(7 a^2 d^2 f^2-2 a b d f (4 c f+3 d e)+b^2 \left(6 c^2 f^2-4 c d e f+5 d^2 e^2\right)\right) \left(23 b^2 (c+d x) (e+f x)-6 (b c-a d) (b e-a f) \left(\frac{b (c+d x)}{d (a+b x)}\right)^{2/3} \left(\frac{b (e+f x)}{f (a+b x)}\right)^{3/4} F_1\left(\frac{23}{12};\frac{2}{3},\frac{3}{4};\frac{35}{12};\frac{a d-b c}{d (a+b x)},\frac{a f-b e}{f (a+b x)}\right)\right)-276 (a+b x) \left(\frac{b (c+d x)}{d (a+b x)}\right)^{2/3} \left(\frac{b (e+f x)}{f (a+b x)}\right)^{3/4} \left(21 a^3 d^3 f^3-9 a^2 b d^2 f^2 (4 c f+3 d e)+a b^2 d f \left(29 c^2 f^2+14 c d e f+20 d^2 e^2\right)-\left(b^3 \left(9 c^3 f^3+2 c^2 d e f^2+5 c d^2 e^2 f+5 d^3 e^3\right)\right)\right) F_1\left(\frac{11}{12};\frac{2}{3},\frac{3}{4};\frac{23}{12};\frac{a d-b c}{d (a+b x)},\frac{a f-b e}{f (a+b x)}\right)+253 b^2 d f (a+b x) (c+d x) (e+f x) (6 a d f+b (4 c f+3 d e+13 d f x))\right)}{82225 b^3 d^2 f^2 \sqrt{a+b x} (c+d x)^{2/3} (e+f x)^{3/4}}","\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,"(12*(253*b^2*d*f*(a + b*x)*(c + d*x)*(e + f*x)*(6*a*d*f + b*(3*d*e + 4*c*f + 13*d*f*x)) - 276*(21*a^3*d^3*f^3 - 9*a^2*b*d^2*f^2*(3*d*e + 4*c*f) + a*b^2*d*f*(20*d^2*e^2 + 14*c*d*e*f + 29*c^2*f^2) - b^3*(5*d^3*e^3 + 5*c*d^2*e^2*f + 2*c^2*d*e*f^2 + 9*c^3*f^3))*(a + b*x)*((b*(c + d*x))/(d*(a + b*x)))^(2/3)*((b*(e + f*x))/(f*(a + b*x)))^(3/4)*AppellF1[11/12, 2/3, 3/4, 23/12, (-(b*c) + a*d)/(d*(a + b*x)), (-(b*e) + a*f)/(f*(a + b*x))] - 66*(7*a^2*d^2*f^2 - 2*a*b*d*f*(3*d*e + 4*c*f) + b^2*(5*d^2*e^2 - 4*c*d*e*f + 6*c^2*f^2))*(23*b^2*(c + d*x)*(e + f*x) - 6*(b*c - a*d)*(b*e - a*f)*((b*(c + d*x))/(d*(a + b*x)))^(2/3)*((b*(e + f*x))/(f*(a + b*x)))^(3/4)*AppellF1[23/12, 2/3, 3/4, 35/12, (-(b*c) + a*d)/(d*(a + b*x)), (-(b*e) + a*f)/(f*(a + b*x))])))/(82225*b^3*d^2*f^2*Sqrt[a + b*x]*(c + d*x)^(2/3)*(e + f*x)^(3/4))","B",0
3179,1,318,125,2.4174667,"\int \sqrt[3]{a+b x} \sqrt{c+d x} \sqrt[4]{e+f x} \, dx","Integrate[(a + b*x)^(1/3)*Sqrt[c + d*x]*(e + f*x)^(1/4),x]","\frac{12 \sqrt{c+d x} \left(11 d^2 (a+b x) (e+f x) (4 a d f+b (6 c f+3 d e+13 d f x))-6 \left(\frac{d (a+b x)}{b (c+d x)}\right)^{2/3} \left(\frac{d (e+f x)}{f (c+d x)}\right)^{3/4} \left(11 (c+d x) \left(6 a^2 d^2 f^2-4 a b d f (2 c f+d e)+b^2 \left(7 c^2 f^2-6 c d e f+5 d^2 e^2\right)\right) F_1\left(-\frac{1}{12};\frac{2}{3},\frac{3}{4};\frac{11}{12};\frac{b c-a d}{b c+b d x},\frac{c f-d e}{f (c+d x)}\right)+(b c-a d) (d e-c f) (4 a d f-7 b c f+3 b d e) F_1\left(\frac{11}{12};\frac{2}{3},\frac{3}{4};\frac{23}{12};\frac{b c-a d}{b c+b d x},\frac{c f-d e}{f (c+d x)}\right)\right)\right)}{3575 b d^3 f (a+b x)^{2/3} (e+f x)^{3/4}}","\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,"(12*Sqrt[c + d*x]*(11*d^2*(a + b*x)*(e + f*x)*(4*a*d*f + b*(3*d*e + 6*c*f + 13*d*f*x)) - 6*((d*(a + b*x))/(b*(c + d*x)))^(2/3)*((d*(e + f*x))/(f*(c + d*x)))^(3/4)*(11*(6*a^2*d^2*f^2 - 4*a*b*d*f*(d*e + 2*c*f) + b^2*(5*d^2*e^2 - 6*c*d*e*f + 7*c^2*f^2))*(c + d*x)*AppellF1[-1/12, 2/3, 3/4, 11/12, (b*c - a*d)/(b*c + b*d*x), (-(d*e) + c*f)/(f*(c + d*x))] + (b*c - a*d)*(d*e - c*f)*(3*b*d*e - 7*b*c*f + 4*a*d*f)*AppellF1[11/12, 2/3, 3/4, 23/12, (b*c - a*d)/(b*c + b*d*x), (-(d*e) + c*f)/(f*(c + d*x))])))/(3575*b*d^3*f*(a + b*x)^(2/3)*(e + f*x)^(3/4))","B",0
3180,1,208,234,0.2533403,"\int (a+b x)^4 (A+B x) (d+e x)^m \, dx","Integrate[(a + b*x)^4*(A + B*x)*(d + e*x)^m,x]","\frac{(d+e x)^{m+1} \left(-\frac{b^3 (d+e x)^4 (-4 a B e-A b e+5 b B d)}{m+5}+\frac{2 b^2 (d+e x)^3 (b d-a e) (-3 a B e-2 A b e+5 b B d)}{m+4}-\frac{2 b (d+e x)^2 (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{m+3}+\frac{(d+e x) (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{m+2}-\frac{(b d-a e)^4 (B d-A e)}{m+1}+\frac{b^4 B (d+e x)^5}{m+6}\right)}{e^6}","-\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,"((d + e*x)^(1 + m)*(-(((b*d - a*e)^4*(B*d - A*e))/(1 + m)) + ((b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x))/(2 + m) - (2*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^2)/(3 + m) + (2*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^3)/(4 + m) - (b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^4)/(5 + m) + (b^4*B*(d + e*x)^5)/(6 + m)))/e^6","A",1
3181,1,165,186,0.1779842,"\int (a+b x)^3 (A+B x) (d+e x)^m \, dx","Integrate[(a + b*x)^3*(A + B*x)*(d + e*x)^m,x]","\frac{(d+e x)^{m+1} \left(-\frac{b^2 (d+e x)^3 (-3 a B e-A b e+4 b B d)}{m+4}+\frac{3 b (d+e x)^2 (b d-a e) (-a B e-A b e+2 b B d)}{m+3}-\frac{(d+e x) (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{m+2}+\frac{(b d-a e)^3 (B d-A e)}{m+1}+\frac{b^3 B (d+e x)^4}{m+5}\right)}{e^5}","-\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,"((d + e*x)^(1 + m)*(((b*d - a*e)^3*(B*d - A*e))/(1 + m) - ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x))/(2 + m) + (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2)/(3 + m) - (b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^3)/(4 + m) + (b^3*B*(d + e*x)^4)/(5 + m)))/e^5","A",1
3182,1,122,138,0.1097831,"\int (a+b x)^2 (A+B x) (d+e x)^m \, dx","Integrate[(a + b*x)^2*(A + B*x)*(d + e*x)^m,x]","\frac{(d+e x)^{m+1} \left(-\frac{b (d+e x)^2 (-2 a B e-A b e+3 b B d)}{m+3}+\frac{(d+e x) (b d-a e) (-a B e-2 A b e+3 b B d)}{m+2}-\frac{(b d-a e)^2 (B d-A e)}{m+1}+\frac{b^2 B (d+e x)^3}{m+4}\right)}{e^4}","-\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,"((d + e*x)^(1 + m)*(-(((b*d - a*e)^2*(B*d - A*e))/(1 + m)) + ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x))/(2 + m) - (b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2)/(3 + m) + (b^2*B*(d + e*x)^3)/(4 + m)))/e^4","A",1
3183,1,79,90,0.1012477,"\int (a+b x) (A+B x) (d+e x)^m \, dx","Integrate[(a + b*x)*(A + B*x)*(d + e*x)^m,x]","\frac{(d+e x)^{m+1} \left(-\frac{(d+e x) (-a B e-A b e+2 b B d)}{m+2}+\frac{(b d-a e) (B d-A e)}{m+1}+\frac{b B (d+e x)^2}{m+3}\right)}{e^3}","\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,"((d + e*x)^(1 + m)*(((b*d - a*e)*(B*d - A*e))/(1 + m) - ((2*b*B*d - A*b*e - a*B*e)*(d + e*x))/(2 + m) + (b*B*(d + e*x)^2)/(3 + m)))/e^3","A",1
3184,1,41,47,0.0284556,"\int (A+B x) (d+e x)^m \, dx","Integrate[(A + B*x)*(d + e*x)^m,x]","\frac{(d+e x)^{m+1} (A e (m+2)-B d+B e (m+1) x)}{e^2 (m+1) (m+2)}","\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,"((d + e*x)^(1 + m)*(-(B*d) + A*e*(2 + m) + B*e*(1 + m)*x))/(e^2*(1 + m)*(2 + m))","A",1
3185,1,78,85,0.030479,"\int \frac{(A+B x) (d+e x)^m}{a+b x} \, dx","Integrate[((A + B*x)*(d + e*x)^m)/(a + b*x),x]","\frac{(d+e x)^{m+1} \left((a B e-A b e) \, _2F_1\left(1,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)+B (b d-a e)\right)}{b e (m+1) (b d-a e)}","\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,"((d + e*x)^(1 + m)*(B*(b*d - a*e) + (-(A*b*e) + a*B*e)*Hypergeometric2F1[1, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)]))/(b*e*(b*d - a*e)*(1 + m))","A",1
3186,1,99,112,0.046409,"\int \frac{(A+B x) (d+e x)^m}{(a+b x)^2} \, dx","Integrate[((A + B*x)*(d + e*x)^m)/(a + b*x)^2,x]","\frac{(d+e x)^{m+1} \left(\frac{(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)}{m+1}-\frac{(A b-a B) (b d-a e)}{a+b x}\right)}{b (b d-a e)^2}","\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,"((d + e*x)^(1 + m)*(-(((A*b - a*B)*(b*d - a*e))/(a + b*x)) + ((a*B*e*(1 + m) - b*(B*d + A*e*m))*Hypergeometric2F1[1, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/(1 + m)))/(b*(b*d - a*e)^2)","A",1
3187,1,75,91,0.0325562,"\int (1-2 x) (2+3 x)^m (3+5 x)^3 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^m*(3 + 5*x)^3,x]","\frac{1}{243} (3 x+2)^{m+1} \left(-\frac{250 (3 x+2)^4}{m+5}+\frac{1025 (3 x+2)^3}{m+4}-\frac{555 (3 x+2)^2}{m+3}+\frac{107 (3 x+2)}{m+2}-\frac{7}{m+1}\right)","-\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,"((2 + 3*x)^(1 + m)*(-7/(1 + m) + (107*(2 + 3*x))/(2 + m) - (555*(2 + 3*x)^2)/(3 + m) + (1025*(2 + 3*x)^3)/(4 + m) - (250*(2 + 3*x)^4)/(5 + m)))/243","A",1
3188,1,61,73,0.0215018,"\int (1-2 x) (2+3 x)^m (3+5 x)^2 \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^m*(3 + 5*x)^2,x]","\frac{1}{81} (3 x+2)^{m+1} \left(-\frac{50 (3 x+2)^3}{m+4}+\frac{195 (3 x+2)^2}{m+3}-\frac{72 (3 x+2)}{m+2}+\frac{7}{m+1}\right)","\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,"((2 + 3*x)^(1 + m)*(7/(1 + m) - (72*(2 + 3*x))/(2 + m) + (195*(2 + 3*x)^2)/(3 + m) - (50*(2 + 3*x)^3)/(4 + m)))/81","A",1
3189,1,47,55,0.0303922,"\int (1-2 x) (2+3 x)^m (3+5 x) \, dx","Integrate[(1 - 2*x)*(2 + 3*x)^m*(3 + 5*x),x]","\frac{1}{27} (3 x+2)^{m+1} \left(-\frac{10 (3 x+2)^2}{m+3}+\frac{37 (3 x+2)}{m+2}-\frac{7}{m+1}\right)","-\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,"((2 + 3*x)^(1 + m)*(-7/(1 + m) + (37*(2 + 3*x))/(2 + m) - (10*(2 + 3*x)^2)/(3 + m)))/27","A",1
3190,1,37,52,0.0107967,"\int \frac{(1-2 x) (2+3 x)^m}{3+5 x} \, dx","Integrate[((1 - 2*x)*(2 + 3*x)^m)/(3 + 5*x),x]","-\frac{(3 x+2)^{m+1} (33 \, _2F_1(1,m+1;m+2;5 (3 x+2))+2)}{15 (m+1)}","-\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,"-1/15*((2 + 3*x)^(1 + m)*(2 + 33*Hypergeometric2F1[1, 1 + m, 2 + m, 5*(2 + 3*x)]))/(1 + m)","A",1
3191,1,57,59,0.0212963,"\int \frac{(1-2 x) (2+3 x)^m}{(3+5 x)^2} \, dx","Integrate[((1 - 2*x)*(2 + 3*x)^m)/(3 + 5*x)^2,x]","-\frac{(3 x+2)^{m+1} ((33 m-2) (5 x+3) \, _2F_1(1,m+1;m+2;5 (3 x+2))+11 (m+1))}{5 (m+1) (5 x+3)}","\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,"-1/5*((2 + 3*x)^(1 + m)*(11*(1 + m) + (-2 + 33*m)*(3 + 5*x)*Hypergeometric2F1[1, 1 + m, 2 + m, 5*(2 + 3*x)]))/((1 + m)*(3 + 5*x))","A",1
3192,1,48,59,0.0286297,"\int \frac{(1-2 x) (2+3 x)^m}{(3+5 x)^3} \, dx","Integrate[((1 - 2*x)*(2 + 3*x)^m)/(3 + 5*x)^3,x]","\frac{1}{10} (3 x+2)^{m+1} \left(\frac{3 (33 m-37) \, _2F_1(2,m+1;m+2;15 x+10)}{m+1}-\frac{11}{(5 x+3)^2}\right)","-\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,"((2 + 3*x)^(1 + m)*(-11/(3 + 5*x)^2 + (3*(-37 + 33*m)*Hypergeometric2F1[2, 1 + m, 2 + m, 10 + 15*x])/(1 + m)))/10","A",1
3193,1,71,90,0.058542,"\int \frac{(2+3 x)^m (3+5 x)^3}{1-2 x} \, dx","Integrate[((2 + 3*x)^m*(3 + 5*x)^3)/(1 - 2*x),x]","\frac{(3 x+2)^{m+1} \left(\frac{35937 \, _2F_1\left(1,m+1;m+2;\frac{2}{7} (3 x+2)\right)}{m+1}-\frac{3500 (3 x+2)^2}{m+3}-\frac{10150 (3 x+2)}{m+2}-\frac{35945}{m+1}\right)}{1512}","\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,"((2 + 3*x)^(1 + m)*(-35945/(1 + m) - (10150*(2 + 3*x))/(2 + m) - (3500*(2 + 3*x)^2)/(3 + m) + (35937*Hypergeometric2F1[1, 1 + m, 2 + m, (2*(2 + 3*x))/7])/(1 + m)))/1512","A",1
3194,1,60,72,0.0353586,"\int \frac{(2+3 x)^m (3+5 x)^2}{1-2 x} \, dx","Integrate[((2 + 3*x)^m*(3 + 5*x)^2)/(1 - 2*x),x]","\frac{(3 x+2)^{m+1} \left(1089 (m+2) \, _2F_1\left(1,m+1;m+2;\frac{2}{7} (3 x+2)\right)-35 (m (30 x+51)+30 x+82)\right)}{252 (m+1) (m+2)}","\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,"((2 + 3*x)^(1 + m)*(-35*(82 + 30*x + m*(51 + 30*x)) + 1089*(2 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (2*(2 + 3*x))/7]))/(252*(1 + m)*(2 + m))","A",1
3195,1,39,54,0.0105556,"\int \frac{(2+3 x)^m (3+5 x)}{1-2 x} \, dx","Integrate[((2 + 3*x)^m*(3 + 5*x))/(1 - 2*x),x]","\frac{(3 x+2)^{m+1} \left(33 \, _2F_1\left(1,m+1;m+2;\frac{2}{7} (3 x+2)\right)-35\right)}{42 (m+1)}","\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,"((2 + 3*x)^(1 + m)*(-35 + 33*Hypergeometric2F1[1, 1 + m, 2 + m, (2*(2 + 3*x))/7]))/(42*(1 + m))","A",1
3196,1,55,69,0.0455722,"\int \frac{(2+3 x)^m}{(1-2 x) (3+5 x)} \, dx","Integrate[(2 + 3*x)^m/((1 - 2*x)*(3 + 5*x)),x]","-\frac{(3 x+2)^{m+1} \left(35 \, _2F_1(1,m+1;m+2;5 (3 x+2))-2 \, _2F_1\left(1,m+1;m+2;\frac{2}{7} (3 x+2)\right)\right)}{77 (m+1)}","\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,"-1/77*((2 + 3*x)^(1 + m)*(-2*Hypergeometric2F1[1, 1 + m, 2 + m, (2*(2 + 3*x))/7] + 35*Hypergeometric2F1[1, 1 + m, 2 + m, 5*(2 + 3*x)]))/(1 + m)","A",1
3197,1,82,94,0.037148,"\int \frac{(2+3 x)^m}{(1-2 x) (3+5 x)^2} \, dx","Integrate[(2 + 3*x)^m/((1 - 2*x)*(3 + 5*x)^2),x]","\frac{(3 x+2)^{m+1} \left(4 (5 x+3) \, _2F_1\left(1,m+1;m+2;\frac{2}{7} (3 x+2)\right)-35 (33 m+2) (5 x+3) \, _2F_1(1,m+1;m+2;5 (3 x+2))-385 (m+1)\right)}{847 (m+1) (5 x+3)}","\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,"((2 + 3*x)^(1 + m)*(-385*(1 + m) + 4*(3 + 5*x)*Hypergeometric2F1[1, 1 + m, 2 + m, (2*(2 + 3*x))/7] - 35*(2 + 33*m)*(3 + 5*x)*Hypergeometric2F1[1, 1 + m, 2 + m, 5*(2 + 3*x)]))/(847*(1 + m)*(3 + 5*x))","A",1
3198,1,104,124,0.0741592,"\int \frac{(2+3 x)^m}{(1-2 x) (3+5 x)^3} \, dx","Integrate[(2 + 3*x)^m/((1 - 2*x)*(3 + 5*x)^3),x]","\frac{(3 x+2)^{m+1} \left(-35 \left(1089 m^2-957 m+8\right) (5 x+3)^2 \, _2F_1(1,m+1;m+2;5 (3 x+2))+16 (5 x+3)^2 \, _2F_1\left(1,m+1;m+2;\frac{2}{7} (3 x+2)\right)-385 (m+1) (33 m (5 x+3)-145 x-76)\right)}{18634 (m+1) (5 x+3)^2}","-\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,"((2 + 3*x)^(1 + m)*(-385*(1 + m)*(-76 - 145*x + 33*m*(3 + 5*x)) + 16*(3 + 5*x)^2*Hypergeometric2F1[1, 1 + m, 2 + m, (2*(2 + 3*x))/7] - 35*(8 - 957*m + 1089*m^2)*(3 + 5*x)^2*Hypergeometric2F1[1, 1 + m, 2 + m, 5*(2 + 3*x)]))/(18634*(1 + m)*(3 + 5*x)^2)","A",1
3199,1,52,52,0.0178591,"\int \frac{(a+b x)^m}{(e+f x)^2} \, dx","Integrate[(a + b*x)^m/(e + f*x)^2,x]","\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}","\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,"(b*(a + b*x)^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, -((f*(a + b*x))/(b*e - a*f))])/((b*e - a*f)^2*(1 + m))","A",1
3200,1,174,187,0.1781716,"\int \frac{(a+b x)^m}{(c+d x) (e+f x)^2} \, dx","Integrate[(a + b*x)^m/((c + d*x)*(e + f*x)^2),x]","\frac{(a+b x)^{m+1} \left(-\frac{d^2 (b e-a f) \, _2F_1\left(1,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)}{(m+1) (b c-a d) (c f-d e)}+\frac{f (a d f-b c f m+b d e (m-1)) \, _2F_1\left(1,m+1;m+2;\frac{f (a+b x)}{a f-b e}\right)}{(m+1) (b e-a f) (d e-c f)}-\frac{f}{e+f x}\right)}{(b e-a f) (d e-c f)}","\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,"((a + b*x)^(1 + m)*(-(f/(e + f*x)) - (d^2*(b*e - a*f)*Hypergeometric2F1[1, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])/((b*c - a*d)*(-(d*e) + c*f)*(1 + m)) + (f*(a*d*f + b*d*e*(-1 + m) - b*c*f*m)*Hypergeometric2F1[1, 1 + m, 2 + m, (f*(a + b*x))/(-(b*e) + a*f)])/((b*e - a*f)*(d*e - c*f)*(1 + m))))/((b*e - a*f)*(d*e - c*f))","A",1
3201,1,247,281,0.6092493,"\int \frac{(a+b x)^m}{(c+d x)^2 (e+f x)^2} \, dx","Integrate[(a + b*x)^m/((c + d*x)^2*(e + f*x)^2),x]","\frac{(a+b x)^{m+1} \left(-\frac{f^2 (b c-a d)^2 (-2 a d f+b c f m-b d e (m-2)) \, _2F_1\left(1,m+1;m+2;\frac{f (a+b x)}{a f-b e}\right)-d^2 (b e-a f)^2 (-2 a d f-b c f (m-2)+b d e m) \, _2F_1\left(1,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)}{(m+1) (b c-a d) (b e-a f)^2 (d e-c f)^2}-\frac{f (-2 a d f+b c f+b d e)}{(e+f x) (b e-a f) (d e-c f)}-\frac{d}{(c+d x) (e+f x)}\right)}{(b c-a d) (c f-d e)}","\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,"((a + b*x)^(1 + m)*(-((f*(b*d*e + b*c*f - 2*a*d*f))/((b*e - a*f)*(d*e - c*f)*(e + f*x))) - d/((c + d*x)*(e + f*x)) - (-(d^2*(b*e - a*f)^2*(-2*a*d*f - b*c*f*(-2 + m) + b*d*e*m)*Hypergeometric2F1[1, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)]) + (b*c - a*d)^2*f^2*(-2*a*d*f - b*d*e*(-2 + m) + b*c*f*m)*Hypergeometric2F1[1, 1 + m, 2 + m, (f*(a + b*x))/(-(b*e) + a*f)])/((b*c - a*d)*(b*e - a*f)^2*(d*e - c*f)^2*(1 + m))))/((b*c - a*d)*(-(d*e) + c*f))","A",1