1,1,63,91,0.0303612,"\int \text{ProductLog}(a+b x)^4 \, dx","Integrate[ProductLog[a + b*x]^4,x]","\frac{(a+b x) (\text{ProductLog}(a+b x)-2) \left(\text{ProductLog}(a+b x)^4-2 \text{ProductLog}(a+b x)^3+12 \text{ProductLog}(a+b x)^2-24 \text{ProductLog}(a+b x)+48\right)}{b \text{ProductLog}(a+b x)}","\frac{(a+b x) \text{ProductLog}(a+b x)^4}{b}-\frac{4 (a+b x) \text{ProductLog}(a+b x)^3}{b}+\frac{16 (a+b x) \text{ProductLog}(a+b x)^2}{b}-\frac{48 (a+b x) \text{ProductLog}(a+b x)}{b}-\frac{96 (a+b x)}{b \text{ProductLog}(a+b x)}+96 x",1,"((a + b*x)*(-2 + ProductLog[a + b*x])*(48 - 24*ProductLog[a + b*x] + 12*ProductLog[a + b*x]^2 - 2*ProductLog[a + b*x]^3 + ProductLog[a + b*x]^4))/(b*ProductLog[a + b*x])","A",1
2,1,45,73,0.0367395,"\int \text{ProductLog}(a+b x)^3 \, dx","Integrate[ProductLog[a + b*x]^3,x]","\frac{(a+b x) \left(\text{ProductLog}(a+b x)^2+6\right) \left(\text{ProductLog}(a+b x)^2-3 \text{ProductLog}(a+b x)+3\right)}{b \text{ProductLog}(a+b x)}","\frac{(a+b x) \text{ProductLog}(a+b x)^3}{b}-\frac{3 (a+b x) \text{ProductLog}(a+b x)^2}{b}+\frac{9 (a+b x) \text{ProductLog}(a+b x)}{b}+\frac{18 (a+b x)}{b \text{ProductLog}(a+b x)}-18 x",1,"((a + b*x)*(6 + ProductLog[a + b*x]^2)*(3 - 3*ProductLog[a + b*x] + ProductLog[a + b*x]^2))/(b*ProductLog[a + b*x])","A",1
3,1,45,55,0.0249503,"\int \text{ProductLog}(a+b x)^2 \, dx","Integrate[ProductLog[a + b*x]^2,x]","\frac{(a+b x) \left(\text{ProductLog}(a+b x)^3-2 \text{ProductLog}(a+b x)^2+4 \text{ProductLog}(a+b x)-4\right)}{b \text{ProductLog}(a+b x)}","\frac{(a+b x) \text{ProductLog}(a+b x)^2}{b}-\frac{2 (a+b x) \text{ProductLog}(a+b x)}{b}-\frac{4 (a+b x)}{b \text{ProductLog}(a+b x)}+4 x",1,"((a + b*x)*(-4 + 4*ProductLog[a + b*x] - 2*ProductLog[a + b*x]^2 + ProductLog[a + b*x]^3))/(b*ProductLog[a + b*x])","A",1
4,1,35,36,0.0306936,"\int \text{ProductLog}(a+b x) \, dx","Integrate[ProductLog[a + b*x],x]","\frac{(a+b x) \left(\text{ProductLog}(a+b x)^2-\text{ProductLog}(a+b x)+1\right)}{b \text{ProductLog}(a+b x)}","\frac{(a+b x) \text{ProductLog}(a+b x)}{b}+\frac{a+b x}{b \text{ProductLog}(a+b x)}-x",1,"((a + b*x)*(1 - ProductLog[a + b*x] + ProductLog[a + b*x]^2))/(b*ProductLog[a + b*x])","A",1
5,1,26,29,0.0261517,"\int \frac{1}{\text{ProductLog}(a+b x)} \, dx","Integrate[ProductLog[a + b*x]^(-1),x]","\frac{\text{Ei}(\text{ProductLog}(a+b x))+\frac{a+b x}{\text{ProductLog}(a+b x)}}{b}","\frac{\text{Ei}(\text{ProductLog}(a+b x))}{b}+\frac{a+b x}{b \text{ProductLog}(a+b x)}",1,"(ExpIntegralEi[ProductLog[a + b*x]] + (a + b*x)/ProductLog[a + b*x])/b","A",1
6,1,35,31,0.0288699,"\int \frac{1}{\text{ProductLog}(a+b x)^2} \, dx","Integrate[ProductLog[a + b*x]^(-2),x]","-\frac{-2 \text{ProductLog}(a+b x)^2 \text{Ei}(\text{ProductLog}(a+b x))+a+b x}{b \text{ProductLog}(a+b x)^2}","\frac{2 \text{Ei}(\text{ProductLog}(a+b x))}{b}-\frac{a+b x}{b \text{ProductLog}(a+b x)^2}",1,"-((a + b*x - 2*ExpIntegralEi[ProductLog[a + b*x]]*ProductLog[a + b*x]^2)/(b*ProductLog[a + b*x]^2))","A",1
7,1,50,55,0.0469879,"\int \frac{1}{\text{ProductLog}(a+b x)^3} \, dx","Integrate[ProductLog[a + b*x]^(-3),x]","-\frac{-3 \text{ProductLog}(a+b x)^3 \text{Ei}(\text{ProductLog}(a+b x))+3 (a+b x) \text{ProductLog}(a+b x)+a+b x}{2 b \text{ProductLog}(a+b x)^3}","\frac{3 \text{Ei}(\text{ProductLog}(a+b x))}{2 b}-\frac{3 (a+b x)}{2 b \text{ProductLog}(a+b x)^2}-\frac{a+b x}{2 b \text{ProductLog}(a+b x)^3}",1,"-(a + b*x + 3*(a + b*x)*ProductLog[a + b*x] - 3*ExpIntegralEi[ProductLog[a + b*x]]*ProductLog[a + b*x]^3)/(2*b*ProductLog[a + b*x]^3)","A",1
8,1,67,75,0.0702481,"\int \frac{1}{\text{ProductLog}(a+b x)^4} \, dx","Integrate[ProductLog[a + b*x]^(-4),x]","-\frac{-2 \text{ProductLog}(a+b x)^3 \text{Ei}(\text{ProductLog}(a+b x))+2 (a+b x) \text{ProductLog}(a+b x)+\frac{a+b x}{\text{ProductLog}(a+b x)}+2 (a+b x)}{3 b \text{ProductLog}(a+b x)^3}","\frac{2 \text{Ei}(\text{ProductLog}(a+b x))}{3 b}-\frac{2 (a+b x)}{3 b \text{ProductLog}(a+b x)^2}-\frac{2 (a+b x)}{3 b \text{ProductLog}(a+b x)^3}-\frac{a+b x}{3 b \text{ProductLog}(a+b x)^4}",1,"-(2*(a + b*x) + (a + b*x)/ProductLog[a + b*x] + 2*(a + b*x)*ProductLog[a + b*x] - 2*ExpIntegralEi[ProductLog[a + b*x]]*ProductLog[a + b*x]^3)/(3*b*ProductLog[a + b*x]^3)","A",1
9,1,83,95,0.1139473,"\int \frac{1}{\text{ProductLog}(a+b x)^5} \, dx","Integrate[ProductLog[a + b*x]^(-5),x]","-\frac{-5 \text{ProductLog}(a+b x)^4 \text{Ei}(\text{ProductLog}(a+b x))+5 (a+b x) \text{ProductLog}(a+b x)^2+5 (a+b x) \text{ProductLog}(a+b x)+\frac{6 (a+b x)}{\text{ProductLog}(a+b x)}+10 (a+b x)}{24 b \text{ProductLog}(a+b x)^4}","\frac{5 \text{Ei}(\text{ProductLog}(a+b x))}{24 b}-\frac{5 (a+b x)}{24 b \text{ProductLog}(a+b x)^2}-\frac{5 (a+b x)}{24 b \text{ProductLog}(a+b x)^3}-\frac{5 (a+b x)}{12 b \text{ProductLog}(a+b x)^4}-\frac{a+b x}{4 b \text{ProductLog}(a+b x)^5}",1,"-(10*(a + b*x) + (6*(a + b*x))/ProductLog[a + b*x] + 5*(a + b*x)*ProductLog[a + b*x] + 5*(a + b*x)*ProductLog[a + b*x]^2 - 5*ExpIntegralEi[ProductLog[a + b*x]]*ProductLog[a + b*x]^4)/(24*b*ProductLog[a + b*x]^4)","A",1
10,1,101,137,0.0742989,"\int (c \text{ProductLog}(a+b x))^{5/2} \, dx","Integrate[(c*ProductLog[a + b*x])^(5/2),x]","\frac{c^3 \left(75 \sqrt{\pi } \sqrt{\text{ProductLog}(a+b x)} \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+16 (a+b x) \text{ProductLog}(a+b x)^3-40 (a+b x) \text{ProductLog}(a+b x)^2+100 (a+b x) \text{ProductLog}(a+b x)-150 (a+b x)\right)}{16 b \sqrt{c \text{ProductLog}(a+b x)}}","\frac{75 \sqrt{\pi } c^{5/2} \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{16 b}-\frac{75 c^3 (a+b x)}{8 b \sqrt{c \text{ProductLog}(a+b x)}}+\frac{25 c^2 (a+b x) \sqrt{c \text{ProductLog}(a+b x)}}{4 b}-\frac{5 c (a+b x) (c \text{ProductLog}(a+b x))^{3/2}}{2 b}+\frac{(a+b x) (c \text{ProductLog}(a+b x))^{5/2}}{b}",1,"(c^3*(-150*(a + b*x) + 75*Sqrt[Pi]*Erfi[Sqrt[ProductLog[a + b*x]]]*Sqrt[ProductLog[a + b*x]] + 100*(a + b*x)*ProductLog[a + b*x] - 40*(a + b*x)*ProductLog[a + b*x]^2 + 16*(a + b*x)*ProductLog[a + b*x]^3))/(16*b*Sqrt[c*ProductLog[a + b*x]])","A",1
11,1,86,110,0.0690831,"\int (c \text{ProductLog}(a+b x))^{3/2} \, dx","Integrate[(c*ProductLog[a + b*x])^(3/2),x]","\frac{c^2 \left(-9 \sqrt{\pi } \sqrt{\text{ProductLog}(a+b x)} \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+8 (a+b x) \text{ProductLog}(a+b x)^2-12 (a+b x) \text{ProductLog}(a+b x)+18 (a+b x)\right)}{8 b \sqrt{c \text{ProductLog}(a+b x)}}","-\frac{9 \sqrt{\pi } c^{3/2} \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{8 b}+\frac{9 c^2 (a+b x)}{4 b \sqrt{c \text{ProductLog}(a+b x)}}-\frac{3 c (a+b x) \sqrt{c \text{ProductLog}(a+b x)}}{2 b}+\frac{(a+b x) (c \text{ProductLog}(a+b x))^{3/2}}{b}",1,"(c^2*(18*(a + b*x) - 9*Sqrt[Pi]*Erfi[Sqrt[ProductLog[a + b*x]]]*Sqrt[ProductLog[a + b*x]] - 12*(a + b*x)*ProductLog[a + b*x] + 8*(a + b*x)*ProductLog[a + b*x]^2))/(8*b*Sqrt[c*ProductLog[a + b*x]])","A",1
12,1,68,83,0.062826,"\int \sqrt{c \text{ProductLog}(a+b x)} \, dx","Integrate[Sqrt[c*ProductLog[a + b*x]],x]","\frac{c \left(\sqrt{\pi } \sqrt{\text{ProductLog}(a+b x)} \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+4 (a+b x) \text{ProductLog}(a+b x)-2 (a+b x)\right)}{4 b \sqrt{c \text{ProductLog}(a+b x)}}","\frac{\sqrt{\pi } \sqrt{c} \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{4 b}+\frac{(a+b x) \sqrt{c \text{ProductLog}(a+b x)}}{b}-\frac{c (a+b x)}{2 b \sqrt{c \text{ProductLog}(a+b x)}}",1,"(c*(-2*(a + b*x) + Sqrt[Pi]*Erfi[Sqrt[ProductLog[a + b*x]]]*Sqrt[ProductLog[a + b*x]] + 4*(a + b*x)*ProductLog[a + b*x]))/(4*b*Sqrt[c*ProductLog[a + b*x]])","A",1
13,1,54,58,0.0381058,"\int \frac{1}{\sqrt{c \text{ProductLog}(a+b x)}} \, dx","Integrate[1/Sqrt[c*ProductLog[a + b*x]],x]","\frac{\sqrt{\pi } \sqrt{\text{ProductLog}(a+b x)} \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+2 (a+b x)}{2 b \sqrt{c \text{ProductLog}(a+b x)}}","\frac{\sqrt{\pi } \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{2 b \sqrt{c}}+\frac{a+b x}{b \sqrt{c \text{ProductLog}(a+b x)}}",1,"(2*(a + b*x) + Sqrt[Pi]*Erfi[Sqrt[ProductLog[a + b*x]]]*Sqrt[ProductLog[a + b*x]])/(2*b*Sqrt[c*ProductLog[a + b*x]])","A",1
14,1,52,57,0.0476908,"\int \frac{1}{(c \text{ProductLog}(a+b x))^{3/2}} \, dx","Integrate[(c*ProductLog[a + b*x])^(-3/2),x]","\frac{3 \sqrt{\pi } \text{ProductLog}(a+b x)^{3/2} \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)-2 (a+b x)}{b (c \text{ProductLog}(a+b x))^{3/2}}","\frac{3 \sqrt{\pi } \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{b c^{3/2}}-\frac{2 (a+b x)}{b (c \text{ProductLog}(a+b x))^{3/2}}",1,"(-2*(a + b*x) + 3*Sqrt[Pi]*Erfi[Sqrt[ProductLog[a + b*x]]]*ProductLog[a + b*x]^(3/2))/(b*(c*ProductLog[a + b*x])^(3/2))","A",1
15,1,68,88,0.0650069,"\int \frac{1}{(c \text{ProductLog}(a+b x))^{5/2}} \, dx","Integrate[(c*ProductLog[a + b*x])^(-5/2),x]","\frac{2 \left(5 \sqrt{\pi } \text{ProductLog}(a+b x)^{5/2} \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)-5 (a+b x) \text{ProductLog}(a+b x)-a-b x\right)}{3 b (c \text{ProductLog}(a+b x))^{5/2}}","\frac{10 \sqrt{\pi } \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{3 b c^{5/2}}-\frac{10 (a+b x)}{3 b c (c \text{ProductLog}(a+b x))^{3/2}}-\frac{2 (a+b x)}{3 b (c \text{ProductLog}(a+b x))^{5/2}}",1,"(2*(-a - b*x - 5*(a + b*x)*ProductLog[a + b*x] + 5*Sqrt[Pi]*Erfi[Sqrt[ProductLog[a + b*x]]]*ProductLog[a + b*x]^(5/2)))/(3*b*(c*ProductLog[a + b*x])^(5/2))","A",1
16,1,94,115,0.0910253,"\int \frac{1}{(c \text{ProductLog}(a+b x))^{7/2}} \, dx","Integrate[(c*ProductLog[a + b*x])^(-7/2),x]","\frac{2 \sqrt{c \text{ProductLog}(a+b x)} \left(14 \sqrt{\pi } \text{ProductLog}(a+b x)^{7/2} \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)-14 (a+b x) \text{ProductLog}(a+b x)^2-7 (a+b x) \text{ProductLog}(a+b x)-3 (a+b x)\right)}{15 b c^4 \text{ProductLog}(a+b x)^4}","\frac{28 \sqrt{\pi } \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{15 b c^{7/2}}-\frac{28 (a+b x)}{15 b c^2 (c \text{ProductLog}(a+b x))^{3/2}}-\frac{14 (a+b x)}{15 b c (c \text{ProductLog}(a+b x))^{5/2}}-\frac{2 (a+b x)}{5 b (c \text{ProductLog}(a+b x))^{7/2}}",1,"(2*Sqrt[c*ProductLog[a + b*x]]*(-3*(a + b*x) - 7*(a + b*x)*ProductLog[a + b*x] - 14*(a + b*x)*ProductLog[a + b*x]^2 + 14*Sqrt[Pi]*Erfi[Sqrt[ProductLog[a + b*x]]]*ProductLog[a + b*x]^(7/2)))/(15*b*c^4*ProductLog[a + b*x]^4)","A",1
17,1,102,142,0.0337939,"\int (-c \text{ProductLog}(a+b x))^{5/2} \, dx","Integrate[(-(c*ProductLog[a + b*x]))^(5/2),x]","-\frac{c^3 \left(75 \sqrt{\pi } \sqrt{\text{ProductLog}(a+b x)} \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+16 (a+b x) \text{ProductLog}(a+b x)^3-40 (a+b x) \text{ProductLog}(a+b x)^2+100 (a+b x) \text{ProductLog}(a+b x)-150 (a+b x)\right)}{16 b \sqrt{-c \text{ProductLog}(a+b x)}}","\frac{75 \sqrt{\pi } c^{5/2} \text{Erf}\left(\frac{\sqrt{-c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{16 b}+\frac{75 c^3 (a+b x)}{8 b \sqrt{-c \text{ProductLog}(a+b x)}}+\frac{25 c^2 (a+b x) \sqrt{-c \text{ProductLog}(a+b x)}}{4 b}+\frac{5 c (a+b x) (-c \text{ProductLog}(a+b x))^{3/2}}{2 b}+\frac{(a+b x) (-c \text{ProductLog}(a+b x))^{5/2}}{b}",1,"-(c^3*(-150*(a + b*x) + 75*Sqrt[Pi]*Erfi[Sqrt[ProductLog[a + b*x]]]*Sqrt[ProductLog[a + b*x]] + 100*(a + b*x)*ProductLog[a + b*x] - 40*(a + b*x)*ProductLog[a + b*x]^2 + 16*(a + b*x)*ProductLog[a + b*x]^3))/(16*b*Sqrt[-(c*ProductLog[a + b*x])])","A",1
18,1,87,114,0.0289405,"\int (-c \text{ProductLog}(a+b x))^{3/2} \, dx","Integrate[(-(c*ProductLog[a + b*x]))^(3/2),x]","\frac{c^2 \left(-9 \sqrt{\pi } \sqrt{\text{ProductLog}(a+b x)} \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+8 (a+b x) \text{ProductLog}(a+b x)^2-12 (a+b x) \text{ProductLog}(a+b x)+18 (a+b x)\right)}{8 b \sqrt{-c \text{ProductLog}(a+b x)}}","\frac{9 \sqrt{\pi } c^{3/2} \text{Erf}\left(\frac{\sqrt{-c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{8 b}+\frac{9 c^2 (a+b x)}{4 b \sqrt{-c \text{ProductLog}(a+b x)}}+\frac{3 c (a+b x) \sqrt{-c \text{ProductLog}(a+b x)}}{2 b}+\frac{(a+b x) (-c \text{ProductLog}(a+b x))^{3/2}}{b}",1,"(c^2*(18*(a + b*x) - 9*Sqrt[Pi]*Erfi[Sqrt[ProductLog[a + b*x]]]*Sqrt[ProductLog[a + b*x]] - 12*(a + b*x)*ProductLog[a + b*x] + 8*(a + b*x)*ProductLog[a + b*x]^2))/(8*b*Sqrt[-(c*ProductLog[a + b*x])])","A",1
19,1,69,86,0.023041,"\int \sqrt{-c \text{ProductLog}(a+b x)} \, dx","Integrate[Sqrt[-(c*ProductLog[a + b*x])],x]","-\frac{c \left(\sqrt{\pi } \sqrt{\text{ProductLog}(a+b x)} \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+4 (a+b x) \text{ProductLog}(a+b x)-2 (a+b x)\right)}{4 b \sqrt{-c \text{ProductLog}(a+b x)}}","\frac{\sqrt{\pi } \sqrt{c} \text{Erf}\left(\frac{\sqrt{-c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{4 b}+\frac{(a+b x) \sqrt{-c \text{ProductLog}(a+b x)}}{b}+\frac{c (a+b x)}{2 b \sqrt{-c \text{ProductLog}(a+b x)}}",1,"-(c*(-2*(a + b*x) + Sqrt[Pi]*Erfi[Sqrt[ProductLog[a + b*x]]]*Sqrt[ProductLog[a + b*x]] + 4*(a + b*x)*ProductLog[a + b*x]))/(4*b*Sqrt[-(c*ProductLog[a + b*x])])","A",1
20,1,55,60,0.0182249,"\int \frac{1}{\sqrt{-c \text{ProductLog}(a+b x)}} \, dx","Integrate[1/Sqrt[-(c*ProductLog[a + b*x])],x]","\frac{\sqrt{\pi } \sqrt{\text{ProductLog}(a+b x)} \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+2 (a+b x)}{2 b \sqrt{-c \text{ProductLog}(a+b x)}}","\frac{a+b x}{b \sqrt{-c \text{ProductLog}(a+b x)}}-\frac{\sqrt{\pi } \text{Erf}\left(\frac{\sqrt{-c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{2 b \sqrt{c}}",1,"(2*(a + b*x) + Sqrt[Pi]*Erfi[Sqrt[ProductLog[a + b*x]]]*Sqrt[ProductLog[a + b*x]])/(2*b*Sqrt[-(c*ProductLog[a + b*x])])","A",1
21,1,54,59,0.0204698,"\int \frac{1}{(-c \text{ProductLog}(a+b x))^{3/2}} \, dx","Integrate[(-(c*ProductLog[a + b*x]))^(-3/2),x]","-\frac{2 (a+b x)-3 \sqrt{\pi } \text{ProductLog}(a+b x)^{3/2} \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)}{b (-c \text{ProductLog}(a+b x))^{3/2}}","\frac{3 \sqrt{\pi } \text{Erf}\left(\frac{\sqrt{-c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{b c^{3/2}}-\frac{2 (a+b x)}{b (-c \text{ProductLog}(a+b x))^{3/2}}",1,"-((2*(a + b*x) - 3*Sqrt[Pi]*Erfi[Sqrt[ProductLog[a + b*x]]]*ProductLog[a + b*x]^(3/2))/(b*(-(c*ProductLog[a + b*x]))^(3/2)))","A",1
22,1,69,91,0.0279682,"\int \frac{1}{(-c \text{ProductLog}(a+b x))^{5/2}} \, dx","Integrate[(-(c*ProductLog[a + b*x]))^(-5/2),x]","\frac{2 \left(5 \sqrt{\pi } \text{ProductLog}(a+b x)^{5/2} \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)-5 (a+b x) \text{ProductLog}(a+b x)-a-b x\right)}{3 b (-c \text{ProductLog}(a+b x))^{5/2}}","-\frac{10 \sqrt{\pi } \text{Erf}\left(\frac{\sqrt{-c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{3 b c^{5/2}}+\frac{10 (a+b x)}{3 b c (-c \text{ProductLog}(a+b x))^{3/2}}-\frac{2 (a+b x)}{3 b (-c \text{ProductLog}(a+b x))^{5/2}}",1,"(2*(-a - b*x - 5*(a + b*x)*ProductLog[a + b*x] + 5*Sqrt[Pi]*Erfi[Sqrt[ProductLog[a + b*x]]]*ProductLog[a + b*x]^(5/2)))/(3*b*(-(c*ProductLog[a + b*x]))^(5/2))","A",1
23,1,95,119,0.03654,"\int \frac{1}{(-c \text{ProductLog}(a+b x))^{7/2}} \, dx","Integrate[(-(c*ProductLog[a + b*x]))^(-7/2),x]","\frac{-28 \sqrt{\pi } \text{ProductLog}(a+b x)^{7/2} \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+28 (a+b x) \text{ProductLog}(a+b x)^2+14 (a+b x) \text{ProductLog}(a+b x)+6 (a+b x)}{15 b c^3 \text{ProductLog}(a+b x)^3 \sqrt{-c \text{ProductLog}(a+b x)}}","\frac{28 \sqrt{\pi } \text{Erf}\left(\frac{\sqrt{-c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{15 b c^{7/2}}-\frac{28 (a+b x)}{15 b c^2 (-c \text{ProductLog}(a+b x))^{3/2}}+\frac{14 (a+b x)}{15 b c (-c \text{ProductLog}(a+b x))^{5/2}}-\frac{2 (a+b x)}{5 b (-c \text{ProductLog}(a+b x))^{7/2}}",1,"(6*(a + b*x) + 14*(a + b*x)*ProductLog[a + b*x] + 28*(a + b*x)*ProductLog[a + b*x]^2 - 28*Sqrt[Pi]*Erfi[Sqrt[ProductLog[a + b*x]]]*ProductLog[a + b*x]^(7/2))/(15*b*c^3*ProductLog[a + b*x]^3*Sqrt[-(c*ProductLog[a + b*x])])","A",1
24,1,53,60,0.0395005,"\int (c \text{ProductLog}(a+b x))^n \, dx","Integrate[(c*ProductLog[a + b*x])^n,x]","\frac{(-\text{ProductLog}(a+b x))^{-n} (c \text{ProductLog}(a+b x))^n (\Gamma (n+1,-\text{ProductLog}(a+b x))-\Gamma (n+2,-\text{ProductLog}(a+b x)))}{b}","\frac{(a+b x) (c \text{ProductLog}(a+b x))^n}{b}-\frac{n (-\text{ProductLog}(a+b x))^{-n} (c \text{ProductLog}(a+b x))^n \Gamma (n+1,-\text{ProductLog}(a+b x))}{b}",1,"((Gamma[1 + n, -ProductLog[a + b*x]] - Gamma[2 + n, -ProductLog[a + b*x]])*(c*ProductLog[a + b*x])^n)/(b*(-ProductLog[a + b*x])^n)","A",1
25,1,210,364,0.3026357,"\int x^3 \text{ProductLog}(a+b x) \, dx","Integrate[x^3*ProductLog[a + b*x],x]","-\frac{(a+b x) \left(3456 \left(a^3-a^2 b x+a b^2 x^2-b^3 x^3\right) \text{ProductLog}(a+b x)^5-288 \left(25 a^3-13 a^2 b x+7 a b^2 x^2-3 b^3 x^3\right) \text{ProductLog}(a+b x)^4+288 \left(25 a^3-13 a^2 b x+7 a b^2 x^2-3 b^3 x^3\right) \text{ProductLog}(a+b x)^3+24 \left(115 a^3+41 a^2 b x-47 a b^2 x^2+27 b^3 x^3\right) \text{ProductLog}(a+b x)^2+4 (175 a-81 b x) (a+b x)^2 \text{ProductLog}(a+b x)+81 (a+b x)^3\right)}{13824 b^4 \text{ProductLog}(a+b x)^4}","-\frac{a^3 (a+b x) \text{ProductLog}(a+b x)}{b^4}-\frac{a^3 (a+b x)}{b^4 \text{ProductLog}(a+b x)}+\frac{a^3 x}{b^3}+\frac{3 a^2 (a+b x)^2 \text{ProductLog}(a+b x)}{2 b^4}+\frac{3 a^2 (a+b x)^2}{4 b^4 \text{ProductLog}(a+b x)}-\frac{3 a^2 (a+b x)^2}{8 b^4 \text{ProductLog}(a+b x)^2}-\frac{3 a^2 (a+b x)^2}{4 b^4}+\frac{(a+b x)^4 \text{ProductLog}(a+b x)}{4 b^4}+\frac{(a+b x)^4}{16 b^4 \text{ProductLog}(a+b x)}-\frac{3 (a+b x)^4}{64 b^4 \text{ProductLog}(a+b x)^2}+\frac{3 (a+b x)^4}{128 b^4 \text{ProductLog}(a+b x)^3}-\frac{3 (a+b x)^4}{512 b^4 \text{ProductLog}(a+b x)^4}-\frac{a (a+b x)^3 \text{ProductLog}(a+b x)}{b^4}-\frac{a (a+b x)^3}{3 b^4 \text{ProductLog}(a+b x)}+\frac{2 a (a+b x)^3}{9 b^4 \text{ProductLog}(a+b x)^2}-\frac{2 a (a+b x)^3}{27 b^4 \text{ProductLog}(a+b x)^3}-\frac{(a+b x)^4}{16 b^4}+\frac{a (a+b x)^3}{3 b^4}",1,"-((a + b*x)*(81*(a + b*x)^3 + 4*(175*a - 81*b*x)*(a + b*x)^2*ProductLog[a + b*x] + 24*(115*a^3 + 41*a^2*b*x - 47*a*b^2*x^2 + 27*b^3*x^3)*ProductLog[a + b*x]^2 + 288*(25*a^3 - 13*a^2*b*x + 7*a*b^2*x^2 - 3*b^3*x^3)*ProductLog[a + b*x]^3 - 288*(25*a^3 - 13*a^2*b*x + 7*a*b^2*x^2 - 3*b^3*x^3)*ProductLog[a + b*x]^4 + 3456*(a^3 - a^2*b*x + a*b^2*x^2 - b^3*x^3)*ProductLog[a + b*x]^5))/(13824*b^4*ProductLog[a + b*x]^4)","A",1
26,1,141,228,0.1411995,"\int x^2 \text{ProductLog}(a+b x) \, dx","Integrate[x^2*ProductLog[a + b*x],x]","\frac{(a+b x) \left(108 \left(a^2-a b x+b^2 x^2\right) \text{ProductLog}(a+b x)^4-18 \left(11 a^2-5 a b x+2 b^2 x^2\right) \text{ProductLog}(a+b x)^3+18 \left(11 a^2-5 a b x+2 b^2 x^2\right) \text{ProductLog}(a+b x)^2+3 \left(19 a^2+11 a b x-8 b^2 x^2\right) \text{ProductLog}(a+b x)+8 (a+b x)^2\right)}{324 b^3 \text{ProductLog}(a+b x)^3}","\frac{a^2 (a+b x) \text{ProductLog}(a+b x)}{b^3}+\frac{a^2 (a+b x)}{b^3 \text{ProductLog}(a+b x)}-\frac{a^2 x}{b^2}+\frac{(a+b x)^3 \text{ProductLog}(a+b x)}{3 b^3}+\frac{(a+b x)^3}{9 b^3 \text{ProductLog}(a+b x)}-\frac{2 (a+b x)^3}{27 b^3 \text{ProductLog}(a+b x)^2}+\frac{2 (a+b x)^3}{81 b^3 \text{ProductLog}(a+b x)^3}-\frac{a (a+b x)^2 \text{ProductLog}(a+b x)}{b^3}-\frac{a (a+b x)^2}{2 b^3 \text{ProductLog}(a+b x)}+\frac{a (a+b x)^2}{4 b^3 \text{ProductLog}(a+b x)^2}-\frac{(a+b x)^3}{9 b^3}+\frac{a (a+b x)^2}{2 b^3}",1,"((a + b*x)*(8*(a + b*x)^2 + 3*(19*a^2 + 11*a*b*x - 8*b^2*x^2)*ProductLog[a + b*x] + 18*(11*a^2 - 5*a*b*x + 2*b^2*x^2)*ProductLog[a + b*x]^2 - 18*(11*a^2 - 5*a*b*x + 2*b^2*x^2)*ProductLog[a + b*x]^3 + 108*(a^2 - a*b*x + b^2*x^2)*ProductLog[a + b*x]^4))/(324*b^3*ProductLog[a + b*x]^3)","A",1
27,1,73,121,0.0580538,"\int x \text{ProductLog}(a+b x) \, dx","Integrate[x*ProductLog[a + b*x],x]","-\frac{(a+b x) \left(4 (a-b x) \text{ProductLog}(a+b x)^3+(2 b x-6 a) \text{ProductLog}(a+b x)^2+(6 a-2 b x) \text{ProductLog}(a+b x)+a+b x\right)}{8 b^2 \text{ProductLog}(a+b x)^2}","\frac{(a+b x)^2 \text{ProductLog}(a+b x)}{2 b^2}+\frac{(a+b x)^2}{4 b^2 \text{ProductLog}(a+b x)}-\frac{(a+b x)^2}{8 b^2 \text{ProductLog}(a+b x)^2}-\frac{a (a+b x) \text{ProductLog}(a+b x)}{b^2}-\frac{a (a+b x)}{b^2 \text{ProductLog}(a+b x)}-\frac{(a+b x)^2}{4 b^2}+\frac{a x}{b}",1,"-((a + b*x)*(a + b*x + (6*a - 2*b*x)*ProductLog[a + b*x] + (-6*a + 2*b*x)*ProductLog[a + b*x]^2 + 4*(a - b*x)*ProductLog[a + b*x]^3))/(8*b^2*ProductLog[a + b*x]^2)","A",1
28,1,35,36,0.0033134,"\int \text{ProductLog}(a+b x) \, dx","Integrate[ProductLog[a + b*x],x]","\frac{(a+b x) \left(\text{ProductLog}(a+b x)^2-\text{ProductLog}(a+b x)+1\right)}{b \text{ProductLog}(a+b x)}","\frac{(a+b x) \text{ProductLog}(a+b x)}{b}+\frac{a+b x}{b \text{ProductLog}(a+b x)}-x",1,"((a + b*x)*(1 - ProductLog[a + b*x] + ProductLog[a + b*x]^2))/(b*ProductLog[a + b*x])","A",1
29,0,0,13,0.0173206,"\int \frac{\text{ProductLog}(a+b x)}{x} \, dx","Integrate[ProductLog[a + b*x]/x,x]","\int \frac{\text{ProductLog}(a+b x)}{x} \, dx","\text{Int}\left(\frac{\text{ProductLog}(a+b x)}{x},x\right)",0,"Integrate[ProductLog[a + b*x]/x, x]","F",-1
30,0,0,13,0.0149947,"\int \frac{\text{ProductLog}(a+b x)}{x^2} \, dx","Integrate[ProductLog[a + b*x]/x^2,x]","\int \frac{\text{ProductLog}(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\text{ProductLog}(a+b x)}{x^2},x\right)",0,"Integrate[ProductLog[a + b*x]/x^2, x]","F",-1
31,1,250,456,0.341141,"\int x^3 \text{ProductLog}(a+b x)^2 \, dx","Integrate[x^3*ProductLog[a + b*x]^2,x]","\frac{(a+b x) \left(-20736 \left(a^3-a^2 b x+a b^2 x^2-b^3 x^3\right) \text{ProductLog}(a+b x)^6+3456 \left(25 a^3-13 a^2 b x+7 a b^2 x^2-3 b^3 x^3\right) \text{ProductLog}(a+b x)^5-288 \left(715 a^3-271 a^2 b x+121 a b^2 x^2-45 b^3 x^3\right) \text{ProductLog}(a+b x)^4+288 \left(715 a^3-271 a^2 b x+121 a b^2 x^2-45 b^3 x^3\right) \text{ProductLog}(a+b x)^3+24 \left(2245 a^3+1007 a^2 b x-833 a b^2 x^2+405 b^3 x^3\right) \text{ProductLog}(a+b x)^2+4 (2881 a-1215 b x) (a+b x)^2 \text{ProductLog}(a+b x)+1215 (a+b x)^3\right)}{82944 b^4 \text{ProductLog}(a+b x)^4}","-\frac{a^3 (a+b x) \text{ProductLog}(a+b x)^2}{b^4}+\frac{2 a^3 (a+b x) \text{ProductLog}(a+b x)}{b^4}+\frac{4 a^3 (a+b x)}{b^4 \text{ProductLog}(a+b x)}-\frac{4 a^3 x}{b^3}+\frac{3 a^2 (a+b x)^2 \text{ProductLog}(a+b x)^2}{2 b^4}-\frac{3 a^2 (a+b x)^2 \text{ProductLog}(a+b x)}{2 b^4}-\frac{9 a^2 (a+b x)^2}{4 b^4 \text{ProductLog}(a+b x)}+\frac{9 a^2 (a+b x)^2}{8 b^4 \text{ProductLog}(a+b x)^2}+\frac{9 a^2 (a+b x)^2}{4 b^4}+\frac{(a+b x)^4 \text{ProductLog}(a+b x)^2}{4 b^4}-\frac{(a+b x)^4 \text{ProductLog}(a+b x)}{8 b^4}-\frac{5 (a+b x)^4}{32 b^4 \text{ProductLog}(a+b x)}+\frac{15 (a+b x)^4}{128 b^4 \text{ProductLog}(a+b x)^2}-\frac{15 (a+b x)^4}{256 b^4 \text{ProductLog}(a+b x)^3}+\frac{15 (a+b x)^4}{1024 b^4 \text{ProductLog}(a+b x)^4}-\frac{a (a+b x)^3 \text{ProductLog}(a+b x)^2}{b^4}+\frac{2 a (a+b x)^3 \text{ProductLog}(a+b x)}{3 b^4}+\frac{8 a (a+b x)^3}{9 b^4 \text{ProductLog}(a+b x)}-\frac{16 a (a+b x)^3}{27 b^4 \text{ProductLog}(a+b x)^2}+\frac{16 a (a+b x)^3}{81 b^4 \text{ProductLog}(a+b x)^3}+\frac{5 (a+b x)^4}{32 b^4}-\frac{8 a (a+b x)^3}{9 b^4}",1,"((a + b*x)*(1215*(a + b*x)^3 + 4*(2881*a - 1215*b*x)*(a + b*x)^2*ProductLog[a + b*x] + 24*(2245*a^3 + 1007*a^2*b*x - 833*a*b^2*x^2 + 405*b^3*x^3)*ProductLog[a + b*x]^2 + 288*(715*a^3 - 271*a^2*b*x + 121*a*b^2*x^2 - 45*b^3*x^3)*ProductLog[a + b*x]^3 - 288*(715*a^3 - 271*a^2*b*x + 121*a*b^2*x^2 - 45*b^3*x^3)*ProductLog[a + b*x]^4 + 3456*(25*a^3 - 13*a^2*b*x + 7*a*b^2*x^2 - 3*b^3*x^3)*ProductLog[a + b*x]^5 - 20736*(a^3 - a^2*b*x + a*b^2*x^2 - b^3*x^3)*ProductLog[a + b*x]^6))/(82944*b^4*ProductLog[a + b*x]^4)","A",1
32,1,170,292,0.1671865,"\int x^2 \text{ProductLog}(a+b x)^2 \, dx","Integrate[x^2*ProductLog[a + b*x]^2,x]","\frac{(a+b x) \left(324 \left(a^2-a b x+b^2 x^2\right) \text{ProductLog}(a+b x)^5-108 \left(11 a^2-5 a b x+2 b^2 x^2\right) \text{ProductLog}(a+b x)^4+18 \left(151 a^2-49 a b x+16 b^2 x^2\right) \text{ProductLog}(a+b x)^3-18 \left(151 a^2-49 a b x+16 b^2 x^2\right) \text{ProductLog}(a+b x)^2-3 \left(179 a^2+115 a b x-64 b^2 x^2\right) \text{ProductLog}(a+b x)-64 (a+b x)^2\right)}{972 b^3 \text{ProductLog}(a+b x)^3}","\frac{a^2 (a+b x) \text{ProductLog}(a+b x)^2}{b^3}-\frac{2 a^2 (a+b x) \text{ProductLog}(a+b x)}{b^3}-\frac{4 a^2 (a+b x)}{b^3 \text{ProductLog}(a+b x)}+\frac{4 a^2 x}{b^2}+\frac{(a+b x)^3 \text{ProductLog}(a+b x)^2}{3 b^3}-\frac{2 (a+b x)^3 \text{ProductLog}(a+b x)}{9 b^3}-\frac{8 (a+b x)^3}{27 b^3 \text{ProductLog}(a+b x)}+\frac{16 (a+b x)^3}{81 b^3 \text{ProductLog}(a+b x)^2}-\frac{16 (a+b x)^3}{243 b^3 \text{ProductLog}(a+b x)^3}-\frac{a (a+b x)^2 \text{ProductLog}(a+b x)^2}{b^3}+\frac{a (a+b x)^2 \text{ProductLog}(a+b x)}{b^3}+\frac{3 a (a+b x)^2}{2 b^3 \text{ProductLog}(a+b x)}-\frac{3 a (a+b x)^2}{4 b^3 \text{ProductLog}(a+b x)^2}+\frac{8 (a+b x)^3}{27 b^3}-\frac{3 a (a+b x)^2}{2 b^3}",1,"((a + b*x)*(-64*(a + b*x)^2 - 3*(179*a^2 + 115*a*b*x - 64*b^2*x^2)*ProductLog[a + b*x] - 18*(151*a^2 - 49*a*b*x + 16*b^2*x^2)*ProductLog[a + b*x]^2 + 18*(151*a^2 - 49*a*b*x + 16*b^2*x^2)*ProductLog[a + b*x]^3 - 108*(11*a^2 - 5*a*b*x + 2*b^2*x^2)*ProductLog[a + b*x]^4 + 324*(a^2 - a*b*x + b^2*x^2)*ProductLog[a + b*x]^5))/(972*b^3*ProductLog[a + b*x]^3)","A",1
33,1,94,163,0.0722692,"\int x \text{ProductLog}(a+b x)^2 \, dx","Integrate[x*ProductLog[a + b*x]^2,x]","\frac{(a+b x) \left(-4 (a-b x) \text{ProductLog}(a+b x)^4+4 (3 a-b x) \text{ProductLog}(a+b x)^3+(6 b x-26 a) \text{ProductLog}(a+b x)^2+(26 a-6 b x) \text{ProductLog}(a+b x)+3 (a+b x)\right)}{8 b^2 \text{ProductLog}(a+b x)^2}","\frac{(a+b x)^2 \text{ProductLog}(a+b x)^2}{2 b^2}-\frac{(a+b x)^2 \text{ProductLog}(a+b x)}{2 b^2}-\frac{3 (a+b x)^2}{4 b^2 \text{ProductLog}(a+b x)}+\frac{3 (a+b x)^2}{8 b^2 \text{ProductLog}(a+b x)^2}-\frac{a (a+b x) \text{ProductLog}(a+b x)^2}{b^2}+\frac{2 a (a+b x) \text{ProductLog}(a+b x)}{b^2}+\frac{4 a (a+b x)}{b^2 \text{ProductLog}(a+b x)}+\frac{3 (a+b x)^2}{4 b^2}-\frac{4 a x}{b}",1,"((a + b*x)*(3*(a + b*x) + (26*a - 6*b*x)*ProductLog[a + b*x] + (-26*a + 6*b*x)*ProductLog[a + b*x]^2 + 4*(3*a - b*x)*ProductLog[a + b*x]^3 - 4*(a - b*x)*ProductLog[a + b*x]^4))/(8*b^2*ProductLog[a + b*x]^2)","A",1
34,1,45,55,0.0140479,"\int \text{ProductLog}(a+b x)^2 \, dx","Integrate[ProductLog[a + b*x]^2,x]","\frac{(a+b x) \left(\text{ProductLog}(a+b x)^3-2 \text{ProductLog}(a+b x)^2+4 \text{ProductLog}(a+b x)-4\right)}{b \text{ProductLog}(a+b x)}","\frac{(a+b x) \text{ProductLog}(a+b x)^2}{b}-\frac{2 (a+b x) \text{ProductLog}(a+b x)}{b}-\frac{4 (a+b x)}{b \text{ProductLog}(a+b x)}+4 x",1,"((a + b*x)*(-4 + 4*ProductLog[a + b*x] - 2*ProductLog[a + b*x]^2 + ProductLog[a + b*x]^3))/(b*ProductLog[a + b*x])","A",1
35,0,0,15,0.0313111,"\int \frac{\text{ProductLog}(a+b x)^2}{x} \, dx","Integrate[ProductLog[a + b*x]^2/x,x]","\int \frac{\text{ProductLog}(a+b x)^2}{x} \, dx","\text{Int}\left(\frac{\text{ProductLog}(a+b x)^2}{x},x\right)",0,"Integrate[ProductLog[a + b*x]^2/x, x]","F",-1
36,0,0,15,0.034724,"\int \frac{\text{ProductLog}(a+b x)^2}{x^2} \, dx","Integrate[ProductLog[a + b*x]^2/x^2,x]","\int \frac{\text{ProductLog}(a+b x)^2}{x^2} \, dx","\text{Int}\left(\frac{\text{ProductLog}(a+b x)^2}{x^2},x\right)",0,"Integrate[ProductLog[a + b*x]^2/x^2, x]","F",-1
37,1,220,449,2.3051952,"\int \frac{x^3}{\sqrt{c \text{ProductLog}(a+b x)}} \, dx","Integrate[x^3/Sqrt[c*ProductLog[a + b*x]],x]","\frac{-18432 \left(a^4-b^4 x^4\right) \text{ProductLog}(a+b x)^3-\sqrt{\pi } \text{ProductLog}(a+b x)^{7/2} \left(36864 a^3 \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+256 a \left(27 \sqrt{2} a \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}(a+b x)}\right)+4 \sqrt{3} \text{Erfi}\left(\sqrt{3} \sqrt{\text{ProductLog}(a+b x)}\right)\right)+135 \text{Erfi}\left(2 \sqrt{\text{ProductLog}(a+b x)}\right)\right)+768 \left(23 a^2-10 a b x+3 b^2 x^2\right) (a+b x)^2 \text{ProductLog}(a+b x)^2+96 (49 a-15 b x) (a+b x)^3 \text{ProductLog}(a+b x)+540 (a+b x)^4}{73728 b^4 \text{ProductLog}(a+b x)^3 \sqrt{c \text{ProductLog}(a+b x)}}","-\frac{\sqrt{\pi } a^3 \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{2 b^4 \sqrt{c}}-\frac{a^3 (a+b x)}{b^4 \sqrt{c \text{ProductLog}(a+b x)}}-\frac{3 \sqrt{\frac{\pi }{2}} a^2 \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{16 b^4 \sqrt{c}}+\frac{3 a^2 (a+b x)^2}{2 b^4 \sqrt{c \text{ProductLog}(a+b x)}}+\frac{3 a^2 c (a+b x)^2}{8 b^4 (c \text{ProductLog}(a+b x))^{3/2}}+\frac{15 c^3 (a+b x)^4}{2048 b^4 (c \text{ProductLog}(a+b x))^{7/2}}-\frac{5 c^2 (a+b x)^4}{256 b^4 (c \text{ProductLog}(a+b x))^{5/2}}+\frac{a c^2 (a+b x)^3}{12 b^4 (c \text{ProductLog}(a+b x))^{5/2}}-\frac{15 \sqrt{\pi } \text{Erfi}\left(\frac{2 \sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{8192 b^4 \sqrt{c}}-\frac{\sqrt{\frac{\pi }{3}} a \text{Erfi}\left(\frac{\sqrt{3} \sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{24 b^4 \sqrt{c}}+\frac{(a+b x)^4}{4 b^4 \sqrt{c \text{ProductLog}(a+b x)}}+\frac{c (a+b x)^4}{32 b^4 (c \text{ProductLog}(a+b x))^{3/2}}-\frac{a (a+b x)^3}{b^4 \sqrt{c \text{ProductLog}(a+b x)}}-\frac{a c (a+b x)^3}{6 b^4 (c \text{ProductLog}(a+b x))^{3/2}}",1,"(540*(a + b*x)^4 + 96*(49*a - 15*b*x)*(a + b*x)^3*ProductLog[a + b*x] + 768*(a + b*x)^2*(23*a^2 - 10*a*b*x + 3*b^2*x^2)*ProductLog[a + b*x]^2 - 18432*(a^4 - b^4*x^4)*ProductLog[a + b*x]^3 - Sqrt[Pi]*(36864*a^3*Erfi[Sqrt[ProductLog[a + b*x]]] + 135*Erfi[2*Sqrt[ProductLog[a + b*x]]] + 256*a*(27*Sqrt[2]*a*Erfi[Sqrt[2]*Sqrt[ProductLog[a + b*x]]] + 4*Sqrt[3]*Erfi[Sqrt[3]*Sqrt[ProductLog[a + b*x]]]))*ProductLog[a + b*x]^(7/2))/(73728*b^4*ProductLog[a + b*x]^3*Sqrt[c*ProductLog[a + b*x]])","A",0
38,1,163,290,0.664011,"\int \frac{x^2}{\sqrt{c \text{ProductLog}(a+b x)}} \, dx","Integrate[x^2/Sqrt[c*ProductLog[a + b*x]],x]","\frac{144 \left(a^3+b^3 x^3\right) \text{ProductLog}(a+b x)^2+\sqrt{\pi } \text{ProductLog}(a+b x)^{5/2} \left(216 a^2 \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+27 \sqrt{2} a \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}(a+b x)}\right)+2 \sqrt{3} \text{Erfi}\left(\sqrt{3} \sqrt{\text{ProductLog}(a+b x)}\right)\right)-12 (7 a-2 b x) (a+b x)^2 \text{ProductLog}(a+b x)-12 (a+b x)^3}{432 b^3 \text{ProductLog}(a+b x)^2 \sqrt{c \text{ProductLog}(a+b x)}}","\frac{\sqrt{\pi } a^2 \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{2 b^3 \sqrt{c}}+\frac{a^2 (a+b x)}{b^3 \sqrt{c \text{ProductLog}(a+b x)}}-\frac{c^2 (a+b x)^3}{36 b^3 (c \text{ProductLog}(a+b x))^{5/2}}+\frac{\sqrt{\frac{\pi }{2}} a \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{8 b^3 \sqrt{c}}+\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{72 b^3 \sqrt{c}}+\frac{(a+b x)^3}{3 b^3 \sqrt{c \text{ProductLog}(a+b x)}}+\frac{c (a+b x)^3}{18 b^3 (c \text{ProductLog}(a+b x))^{3/2}}-\frac{a (a+b x)^2}{b^3 \sqrt{c \text{ProductLog}(a+b x)}}-\frac{a c (a+b x)^2}{4 b^3 (c \text{ProductLog}(a+b x))^{3/2}}",1,"(-12*(a + b*x)^3 - 12*(7*a - 2*b*x)*(a + b*x)^2*ProductLog[a + b*x] + 144*(a^3 + b^3*x^3)*ProductLog[a + b*x]^2 + Sqrt[Pi]*(216*a^2*Erfi[Sqrt[ProductLog[a + b*x]]] + 27*Sqrt[2]*a*Erfi[Sqrt[2]*Sqrt[ProductLog[a + b*x]]] + 2*Sqrt[3]*Erfi[Sqrt[3]*Sqrt[ProductLog[a + b*x]]])*ProductLog[a + b*x]^(5/2))/(432*b^3*ProductLog[a + b*x]^2*Sqrt[c*ProductLog[a + b*x]])","A",0
39,1,105,159,0.2078347,"\int \frac{x}{\sqrt{c \text{ProductLog}(a+b x)}} \, dx","Integrate[x/Sqrt[c*ProductLog[a + b*x]],x]","\frac{c \left(-16 \left(a^2-b^2 x^2\right) \text{ProductLog}(a+b x)-\sqrt{\pi } \text{ProductLog}(a+b x)^{3/2} \left(16 a \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+\sqrt{2} \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}(a+b x)}\right)\right)+4 (a+b x)^2\right)}{32 b^2 (c \text{ProductLog}(a+b x))^{3/2}}","-\frac{\sqrt{\pi } a \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{2 b^2 \sqrt{c}}-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{16 b^2 \sqrt{c}}+\frac{(a+b x)^2}{2 b^2 \sqrt{c \text{ProductLog}(a+b x)}}+\frac{c (a+b x)^2}{8 b^2 (c \text{ProductLog}(a+b x))^{3/2}}-\frac{a (a+b x)}{b^2 \sqrt{c \text{ProductLog}(a+b x)}}",1,"(c*(4*(a + b*x)^2 - 16*(a^2 - b^2*x^2)*ProductLog[a + b*x] - Sqrt[Pi]*(16*a*Erfi[Sqrt[ProductLog[a + b*x]]] + Sqrt[2]*Erfi[Sqrt[2]*Sqrt[ProductLog[a + b*x]]])*ProductLog[a + b*x]^(3/2)))/(32*b^2*(c*ProductLog[a + b*x])^(3/2))","A",0
40,1,54,58,0.0153665,"\int \frac{1}{\sqrt{c \text{ProductLog}(a+b x)}} \, dx","Integrate[1/Sqrt[c*ProductLog[a + b*x]],x]","\frac{\sqrt{\pi } \sqrt{\text{ProductLog}(a+b x)} \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+2 (a+b x)}{2 b \sqrt{c \text{ProductLog}(a+b x)}}","\frac{\sqrt{\pi } \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{2 b \sqrt{c}}+\frac{a+b x}{b \sqrt{c \text{ProductLog}(a+b x)}}",1,"(2*(a + b*x) + Sqrt[Pi]*Erfi[Sqrt[ProductLog[a + b*x]]]*Sqrt[ProductLog[a + b*x]])/(2*b*Sqrt[c*ProductLog[a + b*x]])","A",1
41,0,0,40,0.0359534,"\int \frac{1}{x \sqrt{c \text{ProductLog}(a+b x)}} \, dx","Integrate[1/(x*Sqrt[c*ProductLog[a + b*x]]),x]","\int \frac{1}{x \sqrt{c \text{ProductLog}(a+b x)}} \, dx","\frac{\sqrt{\text{ProductLog}(a+b x)} \text{Int}\left(\frac{1}{x \sqrt{\text{ProductLog}(a+b x)}},x\right)}{\sqrt{c \text{ProductLog}(a+b x)}}",0,"Integrate[1/(x*Sqrt[c*ProductLog[a + b*x]]), x]","F",-1
42,0,0,40,0.0355414,"\int \frac{1}{x^2 \sqrt{c \text{ProductLog}(a+b x)}} \, dx","Integrate[1/(x^2*Sqrt[c*ProductLog[a + b*x]]),x]","\int \frac{1}{x^2 \sqrt{c \text{ProductLog}(a+b x)}} \, dx","\frac{\sqrt{\text{ProductLog}(a+b x)} \text{Int}\left(\frac{1}{x^2 \sqrt{\text{ProductLog}(a+b x)}},x\right)}{\sqrt{c \text{ProductLog}(a+b x)}}",0,"Integrate[1/(x^2*Sqrt[c*ProductLog[a + b*x]]), x]","F",-1
43,1,221,463,1.8463071,"\int \frac{x^3}{\sqrt{-c \text{ProductLog}(a+b x)}} \, dx","Integrate[x^3/Sqrt[-(c*ProductLog[a + b*x])],x]","\frac{-18432 \left(a^4-b^4 x^4\right) \text{ProductLog}(a+b x)^3-\sqrt{\pi } \text{ProductLog}(a+b x)^{7/2} \left(36864 a^3 \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+256 a \left(27 \sqrt{2} a \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}(a+b x)}\right)+4 \sqrt{3} \text{Erfi}\left(\sqrt{3} \sqrt{\text{ProductLog}(a+b x)}\right)\right)+135 \text{Erfi}\left(2 \sqrt{\text{ProductLog}(a+b x)}\right)\right)+768 \left(23 a^2-10 a b x+3 b^2 x^2\right) (a+b x)^2 \text{ProductLog}(a+b x)^2+96 (49 a-15 b x) (a+b x)^3 \text{ProductLog}(a+b x)+540 (a+b x)^4}{73728 b^4 \text{ProductLog}(a+b x)^3 \sqrt{-c \text{ProductLog}(a+b x)}}","\frac{\sqrt{\pi } a^3 \text{Erf}\left(\frac{\sqrt{-c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{2 b^4 \sqrt{c}}-\frac{a^3 (a+b x)}{b^4 \sqrt{-c \text{ProductLog}(a+b x)}}+\frac{3 \sqrt{\frac{\pi }{2}} a^2 \text{Erf}\left(\frac{\sqrt{2} \sqrt{-c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{16 b^4 \sqrt{c}}+\frac{3 a^2 (a+b x)^2}{2 b^4 \sqrt{-c \text{ProductLog}(a+b x)}}-\frac{3 a^2 c (a+b x)^2}{8 b^4 (-c \text{ProductLog}(a+b x))^{3/2}}-\frac{15 c^3 (a+b x)^4}{2048 b^4 (-c \text{ProductLog}(a+b x))^{7/2}}-\frac{5 c^2 (a+b x)^4}{256 b^4 (-c \text{ProductLog}(a+b x))^{5/2}}+\frac{a c^2 (a+b x)^3}{12 b^4 (-c \text{ProductLog}(a+b x))^{5/2}}+\frac{15 \sqrt{\pi } \text{Erf}\left(\frac{2 \sqrt{-c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{8192 b^4 \sqrt{c}}+\frac{\sqrt{\frac{\pi }{3}} a \text{Erf}\left(\frac{\sqrt{3} \sqrt{-c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{24 b^4 \sqrt{c}}+\frac{(a+b x)^4}{4 b^4 \sqrt{-c \text{ProductLog}(a+b x)}}-\frac{c (a+b x)^4}{32 b^4 (-c \text{ProductLog}(a+b x))^{3/2}}-\frac{a (a+b x)^3}{b^4 \sqrt{-c \text{ProductLog}(a+b x)}}+\frac{a c (a+b x)^3}{6 b^4 (-c \text{ProductLog}(a+b x))^{3/2}}",1,"(540*(a + b*x)^4 + 96*(49*a - 15*b*x)*(a + b*x)^3*ProductLog[a + b*x] + 768*(a + b*x)^2*(23*a^2 - 10*a*b*x + 3*b^2*x^2)*ProductLog[a + b*x]^2 - 18432*(a^4 - b^4*x^4)*ProductLog[a + b*x]^3 - Sqrt[Pi]*(36864*a^3*Erfi[Sqrt[ProductLog[a + b*x]]] + 135*Erfi[2*Sqrt[ProductLog[a + b*x]]] + 256*a*(27*Sqrt[2]*a*Erfi[Sqrt[2]*Sqrt[ProductLog[a + b*x]]] + 4*Sqrt[3]*Erfi[Sqrt[3]*Sqrt[ProductLog[a + b*x]]]))*ProductLog[a + b*x]^(7/2))/(73728*b^4*ProductLog[a + b*x]^3*Sqrt[-(c*ProductLog[a + b*x])])","A",0
44,1,164,299,0.5399424,"\int \frac{x^2}{\sqrt{-c \text{ProductLog}(a+b x)}} \, dx","Integrate[x^2/Sqrt[-(c*ProductLog[a + b*x])],x]","\frac{144 \left(a^3+b^3 x^3\right) \text{ProductLog}(a+b x)^2+\sqrt{\pi } \text{ProductLog}(a+b x)^{5/2} \left(216 a^2 \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+27 \sqrt{2} a \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}(a+b x)}\right)+2 \sqrt{3} \text{Erfi}\left(\sqrt{3} \sqrt{\text{ProductLog}(a+b x)}\right)\right)-12 (7 a-2 b x) (a+b x)^2 \text{ProductLog}(a+b x)-12 (a+b x)^3}{432 b^3 \text{ProductLog}(a+b x)^2 \sqrt{-c \text{ProductLog}(a+b x)}}","-\frac{\sqrt{\pi } a^2 \text{Erf}\left(\frac{\sqrt{-c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{2 b^3 \sqrt{c}}+\frac{a^2 (a+b x)}{b^3 \sqrt{-c \text{ProductLog}(a+b x)}}-\frac{c^2 (a+b x)^3}{36 b^3 (-c \text{ProductLog}(a+b x))^{5/2}}-\frac{\sqrt{\frac{\pi }{2}} a \text{Erf}\left(\frac{\sqrt{2} \sqrt{-c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{8 b^3 \sqrt{c}}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{-c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{72 b^3 \sqrt{c}}+\frac{(a+b x)^3}{3 b^3 \sqrt{-c \text{ProductLog}(a+b x)}}-\frac{c (a+b x)^3}{18 b^3 (-c \text{ProductLog}(a+b x))^{3/2}}-\frac{a (a+b x)^2}{b^3 \sqrt{-c \text{ProductLog}(a+b x)}}+\frac{a c (a+b x)^2}{4 b^3 (-c \text{ProductLog}(a+b x))^{3/2}}",1,"(-12*(a + b*x)^3 - 12*(7*a - 2*b*x)*(a + b*x)^2*ProductLog[a + b*x] + 144*(a^3 + b^3*x^3)*ProductLog[a + b*x]^2 + Sqrt[Pi]*(216*a^2*Erfi[Sqrt[ProductLog[a + b*x]]] + 27*Sqrt[2]*a*Erfi[Sqrt[2]*Sqrt[ProductLog[a + b*x]]] + 2*Sqrt[3]*Erfi[Sqrt[3]*Sqrt[ProductLog[a + b*x]]])*ProductLog[a + b*x]^(5/2))/(432*b^3*ProductLog[a + b*x]^2*Sqrt[-(c*ProductLog[a + b*x])])","A",0
45,1,106,164,0.1973419,"\int \frac{x}{\sqrt{-c \text{ProductLog}(a+b x)}} \, dx","Integrate[x/Sqrt[-(c*ProductLog[a + b*x])],x]","-\frac{c \left(-16 \left(a^2-b^2 x^2\right) \text{ProductLog}(a+b x)-\sqrt{\pi } \text{ProductLog}(a+b x)^{3/2} \left(16 a \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+\sqrt{2} \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}(a+b x)}\right)\right)+4 (a+b x)^2\right)}{32 b^2 (-c \text{ProductLog}(a+b x))^{3/2}}","\frac{\sqrt{\pi } a \text{Erf}\left(\frac{\sqrt{-c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{2 b^2 \sqrt{c}}+\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{-c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{16 b^2 \sqrt{c}}+\frac{(a+b x)^2}{2 b^2 \sqrt{-c \text{ProductLog}(a+b x)}}-\frac{c (a+b x)^2}{8 b^2 (-c \text{ProductLog}(a+b x))^{3/2}}-\frac{a (a+b x)}{b^2 \sqrt{-c \text{ProductLog}(a+b x)}}",1,"-(c*(4*(a + b*x)^2 - 16*(a^2 - b^2*x^2)*ProductLog[a + b*x] - Sqrt[Pi]*(16*a*Erfi[Sqrt[ProductLog[a + b*x]]] + Sqrt[2]*Erfi[Sqrt[2]*Sqrt[ProductLog[a + b*x]]])*ProductLog[a + b*x]^(3/2)))/(32*b^2*(-(c*ProductLog[a + b*x]))^(3/2))","A",0
46,1,55,60,0.0162525,"\int \frac{1}{\sqrt{-c \text{ProductLog}(a+b x)}} \, dx","Integrate[1/Sqrt[-(c*ProductLog[a + b*x])],x]","\frac{\sqrt{\pi } \sqrt{\text{ProductLog}(a+b x)} \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+2 (a+b x)}{2 b \sqrt{-c \text{ProductLog}(a+b x)}}","\frac{a+b x}{b \sqrt{-c \text{ProductLog}(a+b x)}}-\frac{\sqrt{\pi } \text{Erf}\left(\frac{\sqrt{-c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{2 b \sqrt{c}}",1,"(2*(a + b*x) + Sqrt[Pi]*Erfi[Sqrt[ProductLog[a + b*x]]]*Sqrt[ProductLog[a + b*x]])/(2*b*Sqrt[-(c*ProductLog[a + b*x])])","A",1
47,0,0,41,0.0289463,"\int \frac{1}{x \sqrt{-c \text{ProductLog}(a+b x)}} \, dx","Integrate[1/(x*Sqrt[-(c*ProductLog[a + b*x])]),x]","\int \frac{1}{x \sqrt{-c \text{ProductLog}(a+b x)}} \, dx","\frac{\sqrt{\text{ProductLog}(a+b x)} \text{Int}\left(\frac{1}{x \sqrt{\text{ProductLog}(a+b x)}},x\right)}{\sqrt{-c \text{ProductLog}(a+b x)}}",0,"Integrate[1/(x*Sqrt[-(c*ProductLog[a + b*x])]), x]","F",-1
48,0,0,41,0.0327483,"\int \frac{1}{x^2 \sqrt{-c \text{ProductLog}(a+b x)}} \, dx","Integrate[1/(x^2*Sqrt[-(c*ProductLog[a + b*x])]),x]","\int \frac{1}{x^2 \sqrt{-c \text{ProductLog}(a+b x)}} \, dx","\frac{\sqrt{\text{ProductLog}(a+b x)} \text{Int}\left(\frac{1}{x^2 \sqrt{\text{ProductLog}(a+b x)}},x\right)}{\sqrt{-c \text{ProductLog}(a+b x)}}",0,"Integrate[1/(x^2*Sqrt[-(c*ProductLog[a + b*x])]), x]","F",-1
49,1,271,568,1.9323928,"\int x^3 \sqrt{c \text{ProductLog}(a+b x)} \, dx","Integrate[x^3*Sqrt[c*ProductLog[a + b*x]],x]","\frac{\sqrt{c \text{ProductLog}(a+b x)} \left(-442368 \left(a^4-b^4 x^4\right) \text{ProductLog}(a+b x)^4-\sqrt{\pi } \text{ProductLog}(a+b x)^{7/2} \left(442368 a^3 \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+512 a \left(243 \sqrt{2} a \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}(a+b x)}\right)+40 \sqrt{3} \text{Erfi}\left(\sqrt{3} \sqrt{\text{ProductLog}(a+b x)}\right)\right)+2835 \text{Erfi}\left(2 \sqrt{\text{ProductLog}(a+b x)}\right)\right)+768 \left(391 a^2-194 a b x+63 b^2 x^2\right) (a+b x)^2 \text{ProductLog}(a+b x)^2+18432 \left(25 a^4+12 a^3 b x-6 a^2 b^2 x^2+4 a b^3 x^3-3 b^4 x^4\right) \text{ProductLog}(a+b x)^3+480 (193 a-63 b x) (a+b x)^3 \text{ProductLog}(a+b x)+11340 (a+b x)^4\right)}{1769472 b^4 \text{ProductLog}(a+b x)^4}","-\frac{\sqrt{\pi } a^3 \sqrt{c} \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{4 b^4}-\frac{a^3 (a+b x) \sqrt{c \text{ProductLog}(a+b x)}}{b^4}+\frac{a^3 c (a+b x)}{2 b^4 \sqrt{c \text{ProductLog}(a+b x)}}+\frac{9 a^2 c^2 (a+b x)^2}{32 b^4 (c \text{ProductLog}(a+b x))^{3/2}}-\frac{9 \sqrt{\frac{\pi }{2}} a^2 \sqrt{c} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{64 b^4}+\frac{3 a^2 (a+b x)^2 \sqrt{c \text{ProductLog}(a+b x)}}{2 b^4}-\frac{3 a^2 c (a+b x)^2}{8 b^4 \sqrt{c \text{ProductLog}(a+b x)}}+\frac{105 c^4 (a+b x)^4}{16384 b^4 (c \text{ProductLog}(a+b x))^{7/2}}-\frac{35 c^3 (a+b x)^4}{2048 b^4 (c \text{ProductLog}(a+b x))^{5/2}}+\frac{5 a c^3 (a+b x)^3}{72 b^4 (c \text{ProductLog}(a+b x))^{5/2}}+\frac{7 c^2 (a+b x)^4}{256 b^4 (c \text{ProductLog}(a+b x))^{3/2}}-\frac{5 a c^2 (a+b x)^3}{36 b^4 (c \text{ProductLog}(a+b x))^{3/2}}-\frac{105 \sqrt{\pi } \sqrt{c} \text{Erfi}\left(\frac{2 \sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{65536 b^4}-\frac{5 \sqrt{\frac{\pi }{3}} a \sqrt{c} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{144 b^4}+\frac{(a+b x)^4 \sqrt{c \text{ProductLog}(a+b x)}}{4 b^4}-\frac{c (a+b x)^4}{32 b^4 \sqrt{c \text{ProductLog}(a+b x)}}-\frac{a (a+b x)^3 \sqrt{c \text{ProductLog}(a+b x)}}{b^4}+\frac{a c (a+b x)^3}{6 b^4 \sqrt{c \text{ProductLog}(a+b x)}}",1,"(Sqrt[c*ProductLog[a + b*x]]*(11340*(a + b*x)^4 + 480*(193*a - 63*b*x)*(a + b*x)^3*ProductLog[a + b*x] + 768*(a + b*x)^2*(391*a^2 - 194*a*b*x + 63*b^2*x^2)*ProductLog[a + b*x]^2 + 18432*(25*a^4 + 12*a^3*b*x - 6*a^2*b^2*x^2 + 4*a*b^3*x^3 - 3*b^4*x^4)*ProductLog[a + b*x]^3 - Sqrt[Pi]*(442368*a^3*Erfi[Sqrt[ProductLog[a + b*x]]] + 2835*Erfi[2*Sqrt[ProductLog[a + b*x]]] + 512*a*(243*Sqrt[2]*a*Erfi[Sqrt[2]*Sqrt[ProductLog[a + b*x]]] + 40*Sqrt[3]*Erfi[Sqrt[3]*Sqrt[ProductLog[a + b*x]]]))*ProductLog[a + b*x]^(7/2) - 442368*(a^4 - b^4*x^4)*ProductLog[a + b*x]^4))/(1769472*b^4*ProductLog[a + b*x]^4)","A",0
50,1,203,377,0.6345661,"\int x^2 \sqrt{c \text{ProductLog}(a+b x)} \, dx","Integrate[x^2*Sqrt[c*ProductLog[a + b*x]],x]","\frac{\sqrt{c \text{ProductLog}(a+b x)} \left(1728 \left(a^3+b^3 x^3\right) \text{ProductLog}(a+b x)^3+\sqrt{\pi } \text{ProductLog}(a+b x)^{5/2} \left(1296 a^2 \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+243 \sqrt{2} a \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}(a+b x)}\right)+20 \sqrt{3} \text{Erfi}\left(\sqrt{3} \sqrt{\text{ProductLog}(a+b x)}\right)\right)-144 \left(11 a^3+6 a^2 b x-3 a b^2 x^2+2 b^3 x^3\right) \text{ProductLog}(a+b x)^2-12 (61 a-20 b x) (a+b x)^2 \text{ProductLog}(a+b x)-120 (a+b x)^3\right)}{5184 b^3 \text{ProductLog}(a+b x)^3}","\frac{\sqrt{\pi } a^2 \sqrt{c} \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{4 b^3}+\frac{a^2 (a+b x) \sqrt{c \text{ProductLog}(a+b x)}}{b^3}-\frac{a^2 c (a+b x)}{2 b^3 \sqrt{c \text{ProductLog}(a+b x)}}-\frac{5 c^3 (a+b x)^3}{216 b^3 (c \text{ProductLog}(a+b x))^{5/2}}+\frac{5 c^2 (a+b x)^3}{108 b^3 (c \text{ProductLog}(a+b x))^{3/2}}-\frac{3 a c^2 (a+b x)^2}{16 b^3 (c \text{ProductLog}(a+b x))^{3/2}}+\frac{3 \sqrt{\frac{\pi }{2}} a \sqrt{c} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{32 b^3}+\frac{5 \sqrt{\frac{\pi }{3}} \sqrt{c} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{432 b^3}+\frac{(a+b x)^3 \sqrt{c \text{ProductLog}(a+b x)}}{3 b^3}-\frac{c (a+b x)^3}{18 b^3 \sqrt{c \text{ProductLog}(a+b x)}}-\frac{a (a+b x)^2 \sqrt{c \text{ProductLog}(a+b x)}}{b^3}+\frac{a c (a+b x)^2}{4 b^3 \sqrt{c \text{ProductLog}(a+b x)}}",1,"(Sqrt[c*ProductLog[a + b*x]]*(-120*(a + b*x)^3 - 12*(61*a - 20*b*x)*(a + b*x)^2*ProductLog[a + b*x] - 144*(11*a^3 + 6*a^2*b*x - 3*a*b^2*x^2 + 2*b^3*x^3)*ProductLog[a + b*x]^2 + Sqrt[Pi]*(1296*a^2*Erfi[Sqrt[ProductLog[a + b*x]]] + 243*Sqrt[2]*a*Erfi[Sqrt[2]*Sqrt[ProductLog[a + b*x]]] + 20*Sqrt[3]*Erfi[Sqrt[3]*Sqrt[ProductLog[a + b*x]]])*ProductLog[a + b*x]^(5/2) + 1728*(a^3 + b^3*x^3)*ProductLog[a + b*x]^3))/(5184*b^3*ProductLog[a + b*x]^3)","A",0
51,1,137,214,0.2559409,"\int x \sqrt{c \text{ProductLog}(a+b x)} \, dx","Integrate[x*Sqrt[c*ProductLog[a + b*x]],x]","\frac{c^2 \left(-64 \left(a^2-b^2 x^2\right) \text{ProductLog}(a+b x)^2+16 \left(3 a^2+2 a b x-b^2 x^2\right) \text{ProductLog}(a+b x)-\sqrt{\pi } \text{ProductLog}(a+b x)^{3/2} \left(32 a \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+3 \sqrt{2} \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}(a+b x)}\right)\right)+12 (a+b x)^2\right)}{128 b^2 (c \text{ProductLog}(a+b x))^{3/2}}","\frac{3 c^2 (a+b x)^2}{32 b^2 (c \text{ProductLog}(a+b x))^{3/2}}-\frac{\sqrt{\pi } a \sqrt{c} \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{4 b^2}-\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{c} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{64 b^2}+\frac{(a+b x)^2 \sqrt{c \text{ProductLog}(a+b x)}}{2 b^2}-\frac{c (a+b x)^2}{8 b^2 \sqrt{c \text{ProductLog}(a+b x)}}-\frac{a (a+b x) \sqrt{c \text{ProductLog}(a+b x)}}{b^2}+\frac{a c (a+b x)}{2 b^2 \sqrt{c \text{ProductLog}(a+b x)}}",1,"(c^2*(12*(a + b*x)^2 + 16*(3*a^2 + 2*a*b*x - b^2*x^2)*ProductLog[a + b*x] - Sqrt[Pi]*(32*a*Erfi[Sqrt[ProductLog[a + b*x]]] + 3*Sqrt[2]*Erfi[Sqrt[2]*Sqrt[ProductLog[a + b*x]]])*ProductLog[a + b*x]^(3/2) - 64*(a^2 - b^2*x^2)*ProductLog[a + b*x]^2))/(128*b^2*(c*ProductLog[a + b*x])^(3/2))","A",0
52,1,68,83,0.0296186,"\int \sqrt{c \text{ProductLog}(a+b x)} \, dx","Integrate[Sqrt[c*ProductLog[a + b*x]],x]","\frac{c \left(\sqrt{\pi } \sqrt{\text{ProductLog}(a+b x)} \text{Erfi}\left(\sqrt{\text{ProductLog}(a+b x)}\right)+4 (a+b x) \text{ProductLog}(a+b x)-2 (a+b x)\right)}{4 b \sqrt{c \text{ProductLog}(a+b x)}}","\frac{\sqrt{\pi } \sqrt{c} \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}(a+b x)}}{\sqrt{c}}\right)}{4 b}+\frac{(a+b x) \sqrt{c \text{ProductLog}(a+b x)}}{b}-\frac{c (a+b x)}{2 b \sqrt{c \text{ProductLog}(a+b x)}}",1,"(c*(-2*(a + b*x) + Sqrt[Pi]*Erfi[Sqrt[ProductLog[a + b*x]]]*Sqrt[ProductLog[a + b*x]] + 4*(a + b*x)*ProductLog[a + b*x]))/(4*b*Sqrt[c*ProductLog[a + b*x]])","A",1
53,0,0,40,0.0323641,"\int \frac{\sqrt{c \text{ProductLog}(a+b x)}}{x} \, dx","Integrate[Sqrt[c*ProductLog[a + b*x]]/x,x]","\int \frac{\sqrt{c \text{ProductLog}(a+b x)}}{x} \, dx","\frac{\sqrt{c \text{ProductLog}(a+b x)} \text{Int}\left(\frac{\sqrt{\text{ProductLog}(a+b x)}}{x},x\right)}{\sqrt{\text{ProductLog}(a+b x)}}",0,"Integrate[Sqrt[c*ProductLog[a + b*x]]/x, x]","F",-1
54,0,0,40,0.0362607,"\int \frac{\sqrt{c \text{ProductLog}(a+b x)}}{x^2} \, dx","Integrate[Sqrt[c*ProductLog[a + b*x]]/x^2,x]","\int \frac{\sqrt{c \text{ProductLog}(a+b x)}}{x^2} \, dx","\frac{\sqrt{c \text{ProductLog}(a+b x)} \text{Int}\left(\frac{\sqrt{\text{ProductLog}(a+b x)}}{x^2},x\right)}{\sqrt{\text{ProductLog}(a+b x)}}",0,"Integrate[Sqrt[c*ProductLog[a + b*x]]/x^2, x]","F",-1
55,1,133,257,0.2972026,"\int \frac{x^3}{d+d \text{ProductLog}(a+b x)} \, dx","Integrate[x^3/(d + d*ProductLog[a + b*x]),x]","-\frac{(a+b x) \left(288 \left(a^3-a^2 b x+a b^2 x^2-b^3 x^3\right) \text{ProductLog}(a+b x)^3+24 \left(13 a^3-a^2 b x-5 a b^2 x^2+9 b^3 x^3\right) \text{ProductLog}(a+b x)^2+4 (37 a-27 b x) (a+b x)^2 \text{ProductLog}(a+b x)+27 (a+b x)^3\right)}{1152 b^4 d \text{ProductLog}(a+b x)^4}","-\frac{a^3 (a+b x)}{b^4 d \text{ProductLog}(a+b x)}+\frac{3 a^2 (a+b x)^2}{2 b^4 d \text{ProductLog}(a+b x)}-\frac{3 a^2 (a+b x)^2}{4 b^4 d \text{ProductLog}(a+b x)^2}+\frac{(a+b x)^4}{4 b^4 d \text{ProductLog}(a+b x)}-\frac{3 (a+b x)^4}{16 b^4 d \text{ProductLog}(a+b x)^2}+\frac{3 (a+b x)^4}{32 b^4 d \text{ProductLog}(a+b x)^3}-\frac{3 (a+b x)^4}{128 b^4 d \text{ProductLog}(a+b x)^4}-\frac{a (a+b x)^3}{b^4 d \text{ProductLog}(a+b x)}+\frac{2 a (a+b x)^3}{3 b^4 d \text{ProductLog}(a+b x)^2}-\frac{2 a (a+b x)^3}{9 b^4 d \text{ProductLog}(a+b x)^3}",1,"-((a + b*x)*(27*(a + b*x)^3 + 4*(37*a - 27*b*x)*(a + b*x)^2*ProductLog[a + b*x] + 24*(13*a^3 - a^2*b*x - 5*a*b^2*x^2 + 9*b^3*x^3)*ProductLog[a + b*x]^2 + 288*(a^3 - a^2*b*x + a*b^2*x^2 - b^3*x^3)*ProductLog[a + b*x]^3))/(1152*b^4*d*ProductLog[a + b*x]^4)","A",1
56,1,85,149,0.3229929,"\int \frac{x^2}{d+d \text{ProductLog}(a+b x)} \, dx","Integrate[x^2/(d + d*ProductLog[a + b*x]),x]","\frac{(a+b x) \left(18 \left(a^2-a b x+b^2 x^2\right) \text{ProductLog}(a+b x)^2+3 \left(5 a^2+a b x-4 b^2 x^2\right) \text{ProductLog}(a+b x)+4 (a+b x)^2\right)}{54 b^3 d \text{ProductLog}(a+b x)^3}","\frac{a^2 (a+b x)}{b^3 d \text{ProductLog}(a+b x)}+\frac{(a+b x)^3}{3 b^3 d \text{ProductLog}(a+b x)}-\frac{2 (a+b x)^3}{9 b^3 d \text{ProductLog}(a+b x)^2}+\frac{2 (a+b x)^3}{27 b^3 d \text{ProductLog}(a+b x)^3}-\frac{a (a+b x)^2}{b^3 d \text{ProductLog}(a+b x)}+\frac{a (a+b x)^2}{2 b^3 d \text{ProductLog}(a+b x)^2}",1,"((a + b*x)*(4*(a + b*x)^2 + 3*(5*a^2 + a*b*x - 4*b^2*x^2)*ProductLog[a + b*x] + 18*(a^2 - a*b*x + b^2*x^2)*ProductLog[a + b*x]^2))/(54*b^3*d*ProductLog[a + b*x]^3)","A",1
57,1,42,73,0.0881268,"\int \frac{x}{d+d \text{ProductLog}(a+b x)} \, dx","Integrate[x/(d + d*ProductLog[a + b*x]),x]","-\frac{(a+b x) (2 (a-b x) \text{ProductLog}(a+b x)+a+b x)}{4 b^2 d \text{ProductLog}(a+b x)^2}","\frac{(a+b x)^2}{2 b^2 d \text{ProductLog}(a+b x)}-\frac{(a+b x)^2}{4 b^2 d \text{ProductLog}(a+b x)^2}-\frac{a (a+b x)}{b^2 d \text{ProductLog}(a+b x)}",1,"-((a + b*x)*(a + b*x + 2*(a - b*x)*ProductLog[a + b*x]))/(4*b^2*d*ProductLog[a + b*x]^2)","A",1
58,1,20,20,0.018964,"\int \frac{1}{d+d \text{ProductLog}(a+b x)} \, dx","Integrate[(d + d*ProductLog[a + b*x])^(-1),x]","\frac{a+b x}{b d \text{ProductLog}(a+b x)}","\frac{a+b x}{b d \text{ProductLog}(a+b x)}",1,"(a + b*x)/(b*d*ProductLog[a + b*x])","A",1
59,0,0,21,0.0152666,"\int \frac{1}{x (d+d \text{ProductLog}(a+b x))} \, dx","Integrate[1/(x*(d + d*ProductLog[a + b*x])),x]","\int \frac{1}{x (d+d \text{ProductLog}(a+b x))} \, dx","\frac{\text{Int}\left(\frac{1}{x (\text{ProductLog}(a+b x)+1)},x\right)}{d}",0,"Integrate[1/(x*(d + d*ProductLog[a + b*x])), x]","F",-1
60,0,0,21,0.0389037,"\int \frac{1}{x^2 (d+d \text{ProductLog}(a+b x))} \, dx","Integrate[1/(x^2*(d + d*ProductLog[a + b*x])),x]","\int \frac{1}{x^2 (d+d \text{ProductLog}(a+b x))} \, dx","\frac{\text{Int}\left(\frac{1}{x^2 (\text{ProductLog}(a+b x)+1)},x\right)}{d}",0,"Integrate[1/(x^2*(d + d*ProductLog[a + b*x])), x]","F",-1
61,1,71,71,0.0078034,"\int x^3 \text{ProductLog}(a x) \, dx","Integrate[x^3*ProductLog[a*x],x]","\frac{1}{4} x^4 \text{ProductLog}(a x)+\frac{x^4}{16 \text{ProductLog}(a x)}-\frac{3 x^4}{64 \text{ProductLog}(a x)^2}+\frac{3 x^4}{128 \text{ProductLog}(a x)^3}-\frac{3 x^4}{512 \text{ProductLog}(a x)^4}-\frac{x^4}{16}","\frac{1}{4} x^4 \text{ProductLog}(a x)+\frac{x^4}{16 \text{ProductLog}(a x)}-\frac{3 x^4}{64 \text{ProductLog}(a x)^2}+\frac{3 x^4}{128 \text{ProductLog}(a x)^3}-\frac{3 x^4}{512 \text{ProductLog}(a x)^4}-\frac{x^4}{16}",1,"-x^4/16 - (3*x^4)/(512*ProductLog[a*x]^4) + (3*x^4)/(128*ProductLog[a*x]^3) - (3*x^4)/(64*ProductLog[a*x]^2) + x^4/(16*ProductLog[a*x]) + (x^4*ProductLog[a*x])/4","A",1
62,1,58,58,0.0238253,"\int x^2 \text{ProductLog}(a x) \, dx","Integrate[x^2*ProductLog[a*x],x]","\frac{1}{3} x^3 \text{ProductLog}(a x)+\frac{x^3}{9 \text{ProductLog}(a x)}-\frac{2 x^3}{27 \text{ProductLog}(a x)^2}+\frac{2 x^3}{81 \text{ProductLog}(a x)^3}-\frac{x^3}{9}","\frac{1}{3} x^3 \text{ProductLog}(a x)+\frac{x^3}{9 \text{ProductLog}(a x)}-\frac{2 x^3}{27 \text{ProductLog}(a x)^2}+\frac{2 x^3}{81 \text{ProductLog}(a x)^3}-\frac{x^3}{9}",1,"-x^3/9 + (2*x^3)/(81*ProductLog[a*x]^3) - (2*x^3)/(27*ProductLog[a*x]^2) + x^3/(9*ProductLog[a*x]) + (x^3*ProductLog[a*x])/3","A",1
63,1,45,45,0.0059379,"\int x \text{ProductLog}(a x) \, dx","Integrate[x*ProductLog[a*x],x]","\frac{1}{2} x^2 \text{ProductLog}(a x)+\frac{x^2}{4 \text{ProductLog}(a x)}-\frac{x^2}{8 \text{ProductLog}(a x)^2}-\frac{x^2}{4}","\frac{1}{2} x^2 \text{ProductLog}(a x)+\frac{x^2}{4 \text{ProductLog}(a x)}-\frac{x^2}{8 \text{ProductLog}(a x)^2}-\frac{x^2}{4}",1,"-x^2/4 - x^2/(8*ProductLog[a*x]^2) + x^2/(4*ProductLog[a*x]) + (x^2*ProductLog[a*x])/2","A",1
64,1,14,18,0.0068382,"\int \text{ProductLog}(a x) \, dx","Integrate[ProductLog[a*x],x]","x \left(\text{ProductLog}(a x)+\frac{1}{\text{ProductLog}(a x)}-1\right)","x \text{ProductLog}(a x)+\frac{x}{\text{ProductLog}(a x)}-x",1,"x*(-1 + ProductLog[a*x]^(-1) + ProductLog[a*x])","A",1
65,1,15,15,0.020525,"\int \frac{\text{ProductLog}(a x)}{x} \, dx","Integrate[ProductLog[a*x]/x,x]","\frac{1}{2} \text{ProductLog}(a x)^2+\text{ProductLog}(a x)","\frac{1}{2} \text{ProductLog}(a x)^2+\text{ProductLog}(a x)",1,"ProductLog[a*x] + ProductLog[a*x]^2/2","A",1
66,1,19,19,0.0034246,"\int \frac{\text{ProductLog}(a x)}{x^2} \, dx","Integrate[ProductLog[a*x]/x^2,x]","a \text{Ei}(-\text{ProductLog}(a x))-\frac{\text{ProductLog}(a x)}{x}","a \text{Ei}(-\text{ProductLog}(a x))-\frac{\text{ProductLog}(a x)}{x}",1,"a*ExpIntegralEi[-ProductLog[a*x]] - ProductLog[a*x]/x","A",1
67,1,22,22,0.003215,"\int \frac{\text{ProductLog}(a x)}{x^3} \, dx","Integrate[ProductLog[a*x]/x^3,x]","a^2 (-\text{Ei}(-2 \text{ProductLog}(a x)))-\frac{\text{ProductLog}(a x)}{x^2}","a^2 (-\text{Ei}(-2 \text{ProductLog}(a x)))-\frac{\text{ProductLog}(a x)}{x^2}",1,"-(a^2*ExpIntegralEi[-2*ProductLog[a*x]]) - ProductLog[a*x]/x^2","A",1
68,1,39,39,0.0048615,"\int \frac{\text{ProductLog}(a x)}{x^4} \, dx","Integrate[ProductLog[a*x]/x^4,x]","\frac{3}{2} a^3 \text{Ei}(-3 \text{ProductLog}(a x))+\frac{\text{ProductLog}(a x)^2}{2 x^3}-\frac{\text{ProductLog}(a x)}{2 x^3}","\frac{3}{2} a^3 \text{Ei}(-3 \text{ProductLog}(a x))+\frac{\text{ProductLog}(a x)^2}{2 x^3}-\frac{\text{ProductLog}(a x)}{2 x^3}",1,"(3*a^3*ExpIntegralEi[-3*ProductLog[a*x]])/2 - ProductLog[a*x]/(2*x^3) + ProductLog[a*x]^2/(2*x^3)","A",1
69,1,52,52,0.0060963,"\int \frac{\text{ProductLog}(a x)}{x^5} \, dx","Integrate[ProductLog[a*x]/x^5,x]","-\frac{8}{3} a^4 \text{Ei}(-4 \text{ProductLog}(a x))-\frac{2 \text{ProductLog}(a x)^3}{3 x^4}+\frac{\text{ProductLog}(a x)^2}{6 x^4}-\frac{\text{ProductLog}(a x)}{3 x^4}","-\frac{8}{3} a^4 \text{Ei}(-4 \text{ProductLog}(a x))-\frac{2 \text{ProductLog}(a x)^3}{3 x^4}+\frac{\text{ProductLog}(a x)^2}{6 x^4}-\frac{\text{ProductLog}(a x)}{3 x^4}",1,"(-8*a^4*ExpIntegralEi[-4*ProductLog[a*x]])/3 - ProductLog[a*x]/(3*x^4) + ProductLog[a*x]^2/(6*x^4) - (2*ProductLog[a*x]^3)/(3*x^4)","A",1
70,1,65,65,0.0091268,"\int \frac{\text{ProductLog}(a x)}{x^6} \, dx","Integrate[ProductLog[a*x]/x^6,x]","\frac{125}{24} a^5 \text{Ei}(-5 \text{ProductLog}(a x))+\frac{25 \text{ProductLog}(a x)^4}{24 x^5}-\frac{5 \text{ProductLog}(a x)^3}{24 x^5}+\frac{\text{ProductLog}(a x)^2}{12 x^5}-\frac{\text{ProductLog}(a x)}{4 x^5}","\frac{125}{24} a^5 \text{Ei}(-5 \text{ProductLog}(a x))+\frac{25 \text{ProductLog}(a x)^4}{24 x^5}-\frac{5 \text{ProductLog}(a x)^3}{24 x^5}+\frac{\text{ProductLog}(a x)^2}{12 x^5}-\frac{\text{ProductLog}(a x)}{4 x^5}",1,"(125*a^5*ExpIntegralEi[-5*ProductLog[a*x]])/24 - ProductLog[a*x]/(4*x^5) + ProductLog[a*x]^2/(12*x^5) - (5*ProductLog[a*x]^3)/(24*x^5) + (25*ProductLog[a*x]^4)/(24*x^5)","A",1
71,1,71,71,0.0165868,"\int x^2 \text{ProductLog}(a x)^2 \, dx","Integrate[x^2*ProductLog[a*x]^2,x]","\frac{1}{3} x^3 \text{ProductLog}(a x)^2-\frac{2}{9} x^3 \text{ProductLog}(a x)-\frac{8 x^3}{27 \text{ProductLog}(a x)}+\frac{16 x^3}{81 \text{ProductLog}(a x)^2}-\frac{16 x^3}{243 \text{ProductLog}(a x)^3}+\frac{8 x^3}{27}","\frac{1}{3} x^3 \text{ProductLog}(a x)^2-\frac{2}{9} x^3 \text{ProductLog}(a x)-\frac{8 x^3}{27 \text{ProductLog}(a x)}+\frac{16 x^3}{81 \text{ProductLog}(a x)^2}-\frac{16 x^3}{243 \text{ProductLog}(a x)^3}+\frac{8 x^3}{27}",1,"(8*x^3)/27 - (16*x^3)/(243*ProductLog[a*x]^3) + (16*x^3)/(81*ProductLog[a*x]^2) - (8*x^3)/(27*ProductLog[a*x]) - (2*x^3*ProductLog[a*x])/9 + (x^3*ProductLog[a*x]^2)/3","A",1
72,1,58,58,0.0045891,"\int x \text{ProductLog}(a x)^2 \, dx","Integrate[x*ProductLog[a*x]^2,x]","\frac{1}{2} x^2 \text{ProductLog}(a x)^2-\frac{1}{2} x^2 \text{ProductLog}(a x)-\frac{3 x^2}{4 \text{ProductLog}(a x)}+\frac{3 x^2}{8 \text{ProductLog}(a x)^2}+\frac{3 x^2}{4}","\frac{1}{2} x^2 \text{ProductLog}(a x)^2-\frac{1}{2} x^2 \text{ProductLog}(a x)-\frac{3 x^2}{4 \text{ProductLog}(a x)}+\frac{3 x^2}{8 \text{ProductLog}(a x)^2}+\frac{3 x^2}{4}",1,"(3*x^2)/4 + (3*x^2)/(8*ProductLog[a*x]^2) - (3*x^2)/(4*ProductLog[a*x]) - (x^2*ProductLog[a*x])/2 + (x^2*ProductLog[a*x]^2)/2","A",1
73,1,24,28,0.0082598,"\int \text{ProductLog}(a x)^2 \, dx","Integrate[ProductLog[a*x]^2,x]","x \left(\text{ProductLog}(a x)^2-2 \text{ProductLog}(a x)-\frac{4}{\text{ProductLog}(a x)}+4\right)","x \text{ProductLog}(a x)^2-2 x \text{ProductLog}(a x)-\frac{4 x}{\text{ProductLog}(a x)}+4 x",1,"x*(4 - 4/ProductLog[a*x] - 2*ProductLog[a*x] + ProductLog[a*x]^2)","A",1
74,1,21,21,0.0135046,"\int \frac{\text{ProductLog}(a x)^2}{x} \, dx","Integrate[ProductLog[a*x]^2/x,x]","\frac{1}{3} \text{ProductLog}(a x)^3+\frac{1}{2} \text{ProductLog}(a x)^2","\frac{1}{3} \text{ProductLog}(a x)^3+\frac{1}{2} \text{ProductLog}(a x)^2",1,"ProductLog[a*x]^2/2 + ProductLog[a*x]^3/3","A",1
75,1,21,21,0.0043185,"\int \frac{\text{ProductLog}(a x)^2}{x^2} \, dx","Integrate[ProductLog[a*x]^2/x^2,x]","-\frac{\text{ProductLog}(a x)^2}{x}-\frac{2 \text{ProductLog}(a x)}{x}","-\frac{\text{ProductLog}(a x)^2}{x}-\frac{2 \text{ProductLog}(a x)}{x}",1,"(-2*ProductLog[a*x])/x - ProductLog[a*x]^2/x","A",1
76,1,25,25,0.0034967,"\int \frac{\text{ProductLog}(a x)^2}{x^3} \, dx","Integrate[ProductLog[a*x]^2/x^3,x]","a^2 \text{Ei}(-2 \text{ProductLog}(a x))-\frac{\text{ProductLog}(a x)^2}{2 x^2}","a^2 \text{Ei}(-2 \text{ProductLog}(a x))-\frac{\text{ProductLog}(a x)^2}{2 x^2}",1,"a^2*ExpIntegralEi[-2*ProductLog[a*x]] - ProductLog[a*x]^2/(2*x^2)","A",1
77,1,24,24,0.0033404,"\int \frac{\text{ProductLog}(a x)^2}{x^4} \, dx","Integrate[ProductLog[a*x]^2/x^4,x]","-2 a^3 \text{Ei}(-3 \text{ProductLog}(a x))-\frac{\text{ProductLog}(a x)^2}{x^3}","-2 a^3 \text{Ei}(-3 \text{ProductLog}(a x))-\frac{\text{ProductLog}(a x)^2}{x^3}",1,"-2*a^3*ExpIntegralEi[-3*ProductLog[a*x]] - ProductLog[a*x]^2/x^3","A",1
78,1,36,36,0.0048719,"\int \frac{\text{ProductLog}(a x)^2}{x^5} \, dx","Integrate[ProductLog[a*x]^2/x^5,x]","4 a^4 \text{Ei}(-4 \text{ProductLog}(a x))+\frac{\text{ProductLog}(a x)^3}{x^4}-\frac{\text{ProductLog}(a x)^2}{2 x^4}","4 a^4 \text{Ei}(-4 \text{ProductLog}(a x))+\frac{\text{ProductLog}(a x)^3}{x^4}-\frac{\text{ProductLog}(a x)^2}{2 x^4}",1,"4*a^4*ExpIntegralEi[-4*ProductLog[a*x]] - ProductLog[a*x]^2/(2*x^4) + ProductLog[a*x]^3/x^4","A",1
79,1,54,54,0.0064837,"\int \frac{\text{ProductLog}(a x)^2}{x^6} \, dx","Integrate[ProductLog[a*x]^2/x^6,x]","-\frac{25}{3} a^5 \text{Ei}(-5 \text{ProductLog}(a x))-\frac{5 \text{ProductLog}(a x)^4}{3 x^5}+\frac{\text{ProductLog}(a x)^3}{3 x^5}-\frac{\text{ProductLog}(a x)^2}{3 x^5}","-\frac{25}{3} a^5 \text{Ei}(-5 \text{ProductLog}(a x))-\frac{5 \text{ProductLog}(a x)^4}{3 x^5}+\frac{\text{ProductLog}(a x)^3}{3 x^5}-\frac{\text{ProductLog}(a x)^2}{3 x^5}",1,"(-25*a^5*ExpIntegralEi[-5*ProductLog[a*x]])/3 - ProductLog[a*x]^2/(3*x^5) + ProductLog[a*x]^3/(3*x^5) - (5*ProductLog[a*x]^4)/(3*x^5)","A",1
80,1,63,63,0.0107129,"\int \frac{\text{ProductLog}(a x)^2}{x^7} \, dx","Integrate[ProductLog[a*x]^2/x^7,x]","18 a^6 \text{Ei}(-6 \text{ProductLog}(a x))+\frac{3 \text{ProductLog}(a x)^5}{x^6}-\frac{\text{ProductLog}(a x)^4}{2 x^6}+\frac{\text{ProductLog}(a x)^3}{6 x^6}-\frac{\text{ProductLog}(a x)^2}{4 x^6}","18 a^6 \text{Ei}(-6 \text{ProductLog}(a x))+\frac{3 \text{ProductLog}(a x)^5}{x^6}-\frac{\text{ProductLog}(a x)^4}{2 x^6}+\frac{\text{ProductLog}(a x)^3}{6 x^6}-\frac{\text{ProductLog}(a x)^2}{4 x^6}",1,"18*a^6*ExpIntegralEi[-6*ProductLog[a*x]] - ProductLog[a*x]^2/(4*x^6) + ProductLog[a*x]^3/(6*x^6) - ProductLog[a*x]^4/(2*x^6) + (3*ProductLog[a*x]^5)/x^6","A",1
81,1,84,84,0.0111668,"\int x^2 \text{ProductLog}(a x)^3 \, dx","Integrate[x^2*ProductLog[a*x]^3,x]","\frac{1}{3} x^3 \text{ProductLog}(a x)^3-\frac{1}{3} x^3 \text{ProductLog}(a x)^2+\frac{5}{9} x^3 \text{ProductLog}(a x)+\frac{20 x^3}{27 \text{ProductLog}(a x)}-\frac{40 x^3}{81 \text{ProductLog}(a x)^2}+\frac{40 x^3}{243 \text{ProductLog}(a x)^3}-\frac{20 x^3}{27}","\frac{1}{3} x^3 \text{ProductLog}(a x)^3-\frac{1}{3} x^3 \text{ProductLog}(a x)^2+\frac{5}{9} x^3 \text{ProductLog}(a x)+\frac{20 x^3}{27 \text{ProductLog}(a x)}-\frac{40 x^3}{81 \text{ProductLog}(a x)^2}+\frac{40 x^3}{243 \text{ProductLog}(a x)^3}-\frac{20 x^3}{27}",1,"(-20*x^3)/27 + (40*x^3)/(243*ProductLog[a*x]^3) - (40*x^3)/(81*ProductLog[a*x]^2) + (20*x^3)/(27*ProductLog[a*x]) + (5*x^3*ProductLog[a*x])/9 - (x^3*ProductLog[a*x]^2)/3 + (x^3*ProductLog[a*x]^3)/3","A",1
82,1,71,71,0.0067889,"\int x \text{ProductLog}(a x)^3 \, dx","Integrate[x*ProductLog[a*x]^3,x]","\frac{1}{2} x^2 \text{ProductLog}(a x)^3-\frac{3}{4} x^2 \text{ProductLog}(a x)^2+\frac{3}{2} x^2 \text{ProductLog}(a x)+\frac{9 x^2}{4 \text{ProductLog}(a x)}-\frac{9 x^2}{8 \text{ProductLog}(a x)^2}-\frac{9 x^2}{4}","\frac{1}{2} x^2 \text{ProductLog}(a x)^3-\frac{3}{4} x^2 \text{ProductLog}(a x)^2+\frac{3}{2} x^2 \text{ProductLog}(a x)+\frac{9 x^2}{4 \text{ProductLog}(a x)}-\frac{9 x^2}{8 \text{ProductLog}(a x)^2}-\frac{9 x^2}{4}",1,"(-9*x^2)/4 - (9*x^2)/(8*ProductLog[a*x]^2) + (9*x^2)/(4*ProductLog[a*x]) + (3*x^2*ProductLog[a*x])/2 - (3*x^2*ProductLog[a*x]^2)/4 + (x^2*ProductLog[a*x]^3)/2","A",1
83,1,30,37,0.0104998,"\int \text{ProductLog}(a x)^3 \, dx","Integrate[ProductLog[a*x]^3,x]","\frac{x \left(\text{ProductLog}(a x)^2+6\right) \left(\text{ProductLog}(a x)^2-3 \text{ProductLog}(a x)+3\right)}{\text{ProductLog}(a x)}","x \text{ProductLog}(a x)^3-3 x \text{ProductLog}(a x)^2+9 x \text{ProductLog}(a x)+\frac{18 x}{\text{ProductLog}(a x)}-18 x",1,"(x*(6 + ProductLog[a*x]^2)*(3 - 3*ProductLog[a*x] + ProductLog[a*x]^2))/ProductLog[a*x]","A",1
84,1,21,21,0.01582,"\int \frac{\text{ProductLog}(a x)^3}{x} \, dx","Integrate[ProductLog[a*x]^3/x,x]","\frac{1}{4} \text{ProductLog}(a x)^4+\frac{1}{3} \text{ProductLog}(a x)^3","\frac{1}{4} \text{ProductLog}(a x)^4+\frac{1}{3} \text{ProductLog}(a x)^3",1,"ProductLog[a*x]^3/3 + ProductLog[a*x]^4/4","A",1
85,1,32,32,0.0052035,"\int \frac{\text{ProductLog}(a x)^3}{x^2} \, dx","Integrate[ProductLog[a*x]^3/x^2,x]","-\frac{\text{ProductLog}(a x)^3}{x}-\frac{3 \text{ProductLog}(a x)^2}{x}-\frac{3 \text{ProductLog}(a x)}{x}","-\frac{\text{ProductLog}(a x)^3}{x}-\frac{3 \text{ProductLog}(a x)^2}{x}-\frac{3 \text{ProductLog}(a x)}{x}",1,"(-3*ProductLog[a*x])/x - (3*ProductLog[a*x]^2)/x - ProductLog[a*x]^3/x","A",1
86,1,27,27,0.00305,"\int \frac{\text{ProductLog}(a x)^3}{x^3} \, dx","Integrate[ProductLog[a*x]^3/x^3,x]","-\frac{\text{ProductLog}(a x)^3}{2 x^2}-\frac{3 \text{ProductLog}(a x)^2}{4 x^2}","-\frac{\text{ProductLog}(a x)^3}{2 x^2}-\frac{3 \text{ProductLog}(a x)^2}{4 x^2}",1,"(-3*ProductLog[a*x]^2)/(4*x^2) - ProductLog[a*x]^3/(2*x^2)","A",1
87,1,25,25,0.0034496,"\int \frac{\text{ProductLog}(a x)^3}{x^4} \, dx","Integrate[ProductLog[a*x]^3/x^4,x]","a^3 \text{Ei}(-3 \text{ProductLog}(a x))-\frac{\text{ProductLog}(a x)^3}{3 x^3}","a^3 \text{Ei}(-3 \text{ProductLog}(a x))-\frac{\text{ProductLog}(a x)^3}{3 x^3}",1,"a^3*ExpIntegralEi[-3*ProductLog[a*x]] - ProductLog[a*x]^3/(3*x^3)","A",1
88,1,24,24,0.0033666,"\int \frac{\text{ProductLog}(a x)^3}{x^5} \, dx","Integrate[ProductLog[a*x]^3/x^5,x]","-3 a^4 \text{Ei}(-4 \text{ProductLog}(a x))-\frac{\text{ProductLog}(a x)^3}{x^4}","-3 a^4 \text{Ei}(-4 \text{ProductLog}(a x))-\frac{\text{ProductLog}(a x)^3}{x^4}",1,"-3*a^4*ExpIntegralEi[-4*ProductLog[a*x]] - ProductLog[a*x]^3/x^4","A",1
89,1,41,41,0.004401,"\int \frac{\text{ProductLog}(a x)^3}{x^6} \, dx","Integrate[ProductLog[a*x]^3/x^6,x]","\frac{15}{2} a^5 \text{Ei}(-5 \text{ProductLog}(a x))+\frac{3 \text{ProductLog}(a x)^4}{2 x^5}-\frac{\text{ProductLog}(a x)^3}{2 x^5}","\frac{15}{2} a^5 \text{Ei}(-5 \text{ProductLog}(a x))+\frac{3 \text{ProductLog}(a x)^4}{2 x^5}-\frac{\text{ProductLog}(a x)^3}{2 x^5}",1,"(15*a^5*ExpIntegralEi[-5*ProductLog[a*x]])/2 - ProductLog[a*x]^3/(2*x^5) + (3*ProductLog[a*x]^4)/(2*x^5)","A",1
90,1,50,50,0.0066209,"\int \frac{\text{ProductLog}(a x)^3}{x^7} \, dx","Integrate[ProductLog[a*x]^3/x^7,x]","-18 a^6 \text{Ei}(-6 \text{ProductLog}(a x))-\frac{3 \text{ProductLog}(a x)^5}{x^6}+\frac{\text{ProductLog}(a x)^4}{2 x^6}-\frac{\text{ProductLog}(a x)^3}{3 x^6}","-18 a^6 \text{Ei}(-6 \text{ProductLog}(a x))-\frac{3 \text{ProductLog}(a x)^5}{x^6}+\frac{\text{ProductLog}(a x)^4}{2 x^6}-\frac{\text{ProductLog}(a x)^3}{3 x^6}",1,"-18*a^6*ExpIntegralEi[-6*ProductLog[a*x]] - ProductLog[a*x]^3/(3*x^6) + ProductLog[a*x]^4/(2*x^6) - (3*ProductLog[a*x]^5)/x^6","A",1
91,1,67,67,0.0099046,"\int \frac{\text{ProductLog}(a x)^3}{x^8} \, dx","Integrate[ProductLog[a*x]^3/x^8,x]","\frac{343}{8} a^7 \text{Ei}(-7 \text{ProductLog}(a x))+\frac{49 \text{ProductLog}(a x)^6}{8 x^7}-\frac{7 \text{ProductLog}(a x)^5}{8 x^7}+\frac{\text{ProductLog}(a x)^4}{4 x^7}-\frac{\text{ProductLog}(a x)^3}{4 x^7}","\frac{343}{8} a^7 \text{Ei}(-7 \text{ProductLog}(a x))+\frac{49 \text{ProductLog}(a x)^6}{8 x^7}-\frac{7 \text{ProductLog}(a x)^5}{8 x^7}+\frac{\text{ProductLog}(a x)^4}{4 x^7}-\frac{\text{ProductLog}(a x)^3}{4 x^7}",1,"(343*a^7*ExpIntegralEi[-7*ProductLog[a*x]])/8 - ProductLog[a*x]^3/(4*x^7) + ProductLog[a*x]^4/(4*x^7) - (7*ProductLog[a*x]^5)/(8*x^7) + (49*ProductLog[a*x]^6)/(8*x^7)","A",1
92,1,66,66,0.0081856,"\int \frac{x^4}{\text{ProductLog}(a x)} \, dx","Integrate[x^4/ProductLog[a*x],x]","\frac{x^5}{5 \text{ProductLog}(a x)}+\frac{x^5}{25 \text{ProductLog}(a x)^2}-\frac{3 x^5}{125 \text{ProductLog}(a x)^3}+\frac{6 x^5}{625 \text{ProductLog}(a x)^4}-\frac{6 x^5}{3125 \text{ProductLog}(a x)^5}","\frac{x^5}{5 \text{ProductLog}(a x)}+\frac{x^5}{25 \text{ProductLog}(a x)^2}-\frac{3 x^5}{125 \text{ProductLog}(a x)^3}+\frac{6 x^5}{625 \text{ProductLog}(a x)^4}-\frac{6 x^5}{3125 \text{ProductLog}(a x)^5}",1,"(-6*x^5)/(3125*ProductLog[a*x]^5) + (6*x^5)/(625*ProductLog[a*x]^4) - (3*x^5)/(125*ProductLog[a*x]^3) + x^5/(25*ProductLog[a*x]^2) + x^5/(5*ProductLog[a*x])","A",1
93,1,53,53,0.0074321,"\int \frac{x^3}{\text{ProductLog}(a x)} \, dx","Integrate[x^3/ProductLog[a*x],x]","\frac{x^4}{4 \text{ProductLog}(a x)}+\frac{x^4}{16 \text{ProductLog}(a x)^2}-\frac{x^4}{32 \text{ProductLog}(a x)^3}+\frac{x^4}{128 \text{ProductLog}(a x)^4}","\frac{x^4}{4 \text{ProductLog}(a x)}+\frac{x^4}{16 \text{ProductLog}(a x)^2}-\frac{x^4}{32 \text{ProductLog}(a x)^3}+\frac{x^4}{128 \text{ProductLog}(a x)^4}",1,"x^4/(128*ProductLog[a*x]^4) - x^4/(32*ProductLog[a*x]^3) + x^4/(16*ProductLog[a*x]^2) + x^4/(4*ProductLog[a*x])","A",1
94,1,40,40,0.0042249,"\int \frac{x^2}{\text{ProductLog}(a x)} \, dx","Integrate[x^2/ProductLog[a*x],x]","\frac{x^3}{3 \text{ProductLog}(a x)}+\frac{x^3}{9 \text{ProductLog}(a x)^2}-\frac{x^3}{27 \text{ProductLog}(a x)^3}","\frac{x^3}{3 \text{ProductLog}(a x)}+\frac{x^3}{9 \text{ProductLog}(a x)^2}-\frac{x^3}{27 \text{ProductLog}(a x)^3}",1,"-x^3/(27*ProductLog[a*x]^3) + x^3/(9*ProductLog[a*x]^2) + x^3/(3*ProductLog[a*x])","A",1
95,1,27,27,0.0028298,"\int \frac{x}{\text{ProductLog}(a x)} \, dx","Integrate[x/ProductLog[a*x],x]","\frac{x^2}{2 \text{ProductLog}(a x)}+\frac{x^2}{4 \text{ProductLog}(a x)^2}","\frac{x^2}{2 \text{ProductLog}(a x)}+\frac{x^2}{4 \text{ProductLog}(a x)^2}",1,"x^2/(4*ProductLog[a*x]^2) + x^2/(2*ProductLog[a*x])","A",1
96,1,18,18,0.0050618,"\int \frac{1}{\text{ProductLog}(a x)} \, dx","Integrate[ProductLog[a*x]^(-1),x]","\frac{\text{Ei}(\text{ProductLog}(a x))}{a}+\frac{x}{\text{ProductLog}(a x)}","\frac{\text{Ei}(\text{ProductLog}(a x))}{a}+\frac{x}{\text{ProductLog}(a x)}",1,"ExpIntegralEi[ProductLog[a*x]]/a + x/ProductLog[a*x]","A",1
97,1,14,14,0.007737,"\int \frac{1}{x \text{ProductLog}(a x)} \, dx","Integrate[1/(x*ProductLog[a*x]),x]","\log (\text{ProductLog}(a x))-\frac{1}{\text{ProductLog}(a x)}","\log (\text{ProductLog}(a x))-\frac{1}{\text{ProductLog}(a x)}",1,"Log[ProductLog[a*x]] - ProductLog[a*x]^(-1)","A",1
98,1,33,33,0.0042197,"\int \frac{1}{x^2 \text{ProductLog}(a x)} \, dx","Integrate[1/(x^2*ProductLog[a*x]),x]","-\frac{1}{2} a \text{Ei}(-\text{ProductLog}(a x))-\frac{1}{2 x \text{ProductLog}(a x)}-\frac{1}{2 x}","-\frac{1}{2} a \text{Ei}(-\text{ProductLog}(a x))-\frac{1}{2 x \text{ProductLog}(a x)}-\frac{1}{2 x}",1,"-1/(2*x) - (a*ExpIntegralEi[-ProductLog[a*x]])/2 - 1/(2*x*ProductLog[a*x])","A",1
99,1,46,46,0.004721,"\int \frac{1}{x^3 \text{ProductLog}(a x)} \, dx","Integrate[1/(x^3*ProductLog[a*x]),x]","\frac{2}{3} a^2 \text{Ei}(-2 \text{ProductLog}(a x))+\frac{\text{ProductLog}(a x)}{3 x^2}-\frac{1}{3 x^2 \text{ProductLog}(a x)}-\frac{1}{6 x^2}","\frac{2}{3} a^2 \text{Ei}(-2 \text{ProductLog}(a x))+\frac{\text{ProductLog}(a x)}{3 x^2}-\frac{1}{3 x^2 \text{ProductLog}(a x)}-\frac{1}{6 x^2}",1,"-1/(6*x^2) + (2*a^2*ExpIntegralEi[-2*ProductLog[a*x]])/3 - 1/(3*x^2*ProductLog[a*x]) + ProductLog[a*x]/(3*x^2)","A",1
100,1,59,59,0.0083452,"\int \frac{1}{x^4 \text{ProductLog}(a x)} \, dx","Integrate[1/(x^4*ProductLog[a*x]),x]","-\frac{9}{8} a^3 \text{Ei}(-3 \text{ProductLog}(a x))-\frac{3 \text{ProductLog}(a x)^2}{8 x^3}+\frac{\text{ProductLog}(a x)}{8 x^3}-\frac{1}{4 x^3 \text{ProductLog}(a x)}-\frac{1}{12 x^3}","-\frac{9}{8} a^3 \text{Ei}(-3 \text{ProductLog}(a x))-\frac{3 \text{ProductLog}(a x)^2}{8 x^3}+\frac{\text{ProductLog}(a x)}{8 x^3}-\frac{1}{4 x^3 \text{ProductLog}(a x)}-\frac{1}{12 x^3}",1,"-1/(12*x^3) - (9*a^3*ExpIntegralEi[-3*ProductLog[a*x]])/8 - 1/(4*x^3*ProductLog[a*x]) + ProductLog[a*x]/(8*x^3) - (3*ProductLog[a*x]^2)/(8*x^3)","A",1
101,1,66,66,0.0073618,"\int \frac{x^5}{\text{ProductLog}(a x)^2} \, dx","Integrate[x^5/ProductLog[a*x]^2,x]","\frac{x^6}{6 \text{ProductLog}(a x)^2}+\frac{x^6}{18 \text{ProductLog}(a x)^3}-\frac{x^6}{36 \text{ProductLog}(a x)^4}+\frac{x^6}{108 \text{ProductLog}(a x)^5}-\frac{x^6}{648 \text{ProductLog}(a x)^6}","\frac{x^6}{6 \text{ProductLog}(a x)^2}+\frac{x^6}{18 \text{ProductLog}(a x)^3}-\frac{x^6}{36 \text{ProductLog}(a x)^4}+\frac{x^6}{108 \text{ProductLog}(a x)^5}-\frac{x^6}{648 \text{ProductLog}(a x)^6}",1,"-x^6/(648*ProductLog[a*x]^6) + x^6/(108*ProductLog[a*x]^5) - x^6/(36*ProductLog[a*x]^4) + x^6/(18*ProductLog[a*x]^3) + x^6/(6*ProductLog[a*x]^2)","A",1
102,1,53,53,0.0063536,"\int \frac{x^4}{\text{ProductLog}(a x)^2} \, dx","Integrate[x^4/ProductLog[a*x]^2,x]","\frac{x^5}{5 \text{ProductLog}(a x)^2}+\frac{2 x^5}{25 \text{ProductLog}(a x)^3}-\frac{4 x^5}{125 \text{ProductLog}(a x)^4}+\frac{4 x^5}{625 \text{ProductLog}(a x)^5}","\frac{x^5}{5 \text{ProductLog}(a x)^2}+\frac{2 x^5}{25 \text{ProductLog}(a x)^3}-\frac{4 x^5}{125 \text{ProductLog}(a x)^4}+\frac{4 x^5}{625 \text{ProductLog}(a x)^5}",1,"(4*x^5)/(625*ProductLog[a*x]^5) - (4*x^5)/(125*ProductLog[a*x]^4) + (2*x^5)/(25*ProductLog[a*x]^3) + x^5/(5*ProductLog[a*x]^2)","A",1
103,1,40,40,0.005902,"\int \frac{x^3}{\text{ProductLog}(a x)^2} \, dx","Integrate[x^3/ProductLog[a*x]^2,x]","\frac{x^4}{4 \text{ProductLog}(a x)^2}+\frac{x^4}{8 \text{ProductLog}(a x)^3}-\frac{x^4}{32 \text{ProductLog}(a x)^4}","\frac{x^4}{4 \text{ProductLog}(a x)^2}+\frac{x^4}{8 \text{ProductLog}(a x)^3}-\frac{x^4}{32 \text{ProductLog}(a x)^4}",1,"-x^4/(32*ProductLog[a*x]^4) + x^4/(8*ProductLog[a*x]^3) + x^4/(4*ProductLog[a*x]^2)","A",1
104,1,27,27,0.0037786,"\int \frac{x^2}{\text{ProductLog}(a x)^2} \, dx","Integrate[x^2/ProductLog[a*x]^2,x]","\frac{x^3}{3 \text{ProductLog}(a x)^2}+\frac{2 x^3}{9 \text{ProductLog}(a x)^3}","\frac{x^3}{3 \text{ProductLog}(a x)^2}+\frac{2 x^3}{9 \text{ProductLog}(a x)^3}",1,"(2*x^3)/(9*ProductLog[a*x]^3) + x^3/(3*ProductLog[a*x]^2)","A",1
105,1,25,25,0.0031958,"\int \frac{x}{\text{ProductLog}(a x)^2} \, dx","Integrate[x/ProductLog[a*x]^2,x]","\frac{\text{Ei}(2 \text{ProductLog}(a x))}{a^2}+\frac{x^2}{2 \text{ProductLog}(a x)^2}","\frac{\text{Ei}(2 \text{ProductLog}(a x))}{a^2}+\frac{x^2}{2 \text{ProductLog}(a x)^2}",1,"ExpIntegralEi[2*ProductLog[a*x]]/a^2 + x^2/(2*ProductLog[a*x]^2)","A",1
106,1,20,20,0.0080638,"\int \frac{1}{\text{ProductLog}(a x)^2} \, dx","Integrate[ProductLog[a*x]^(-2),x]","\frac{2 \text{Ei}(\text{ProductLog}(a x))}{a}-\frac{x}{\text{ProductLog}(a x)^2}","\frac{2 \text{Ei}(\text{ProductLog}(a x))}{a}-\frac{x}{\text{ProductLog}(a x)^2}",1,"(2*ExpIntegralEi[ProductLog[a*x]])/a - x/ProductLog[a*x]^2","A",1
107,1,19,19,0.0214731,"\int \frac{1}{x \text{ProductLog}(a x)^2} \, dx","Integrate[1/(x*ProductLog[a*x]^2),x]","-\frac{1}{\text{ProductLog}(a x)}-\frac{1}{2 \text{ProductLog}(a x)^2}","-\frac{1}{\text{ProductLog}(a x)}-\frac{1}{2 \text{ProductLog}(a x)^2}",1,"-1/(2*ProductLog[a*x]^2) - ProductLog[a*x]^(-1)","A",1
108,1,46,46,0.0053515,"\int \frac{1}{x^2 \text{ProductLog}(a x)^2} \, dx","Integrate[1/(x^2*ProductLog[a*x]^2),x]","\frac{1}{3} a \text{Ei}(-\text{ProductLog}(a x))-\frac{1}{3 x \text{ProductLog}(a x)}-\frac{1}{3 x \text{ProductLog}(a x)^2}+\frac{1}{3 x}","\frac{1}{3} a \text{Ei}(-\text{ProductLog}(a x))-\frac{1}{3 x \text{ProductLog}(a x)}-\frac{1}{3 x \text{ProductLog}(a x)^2}+\frac{1}{3 x}",1,"1/(3*x) + (a*ExpIntegralEi[-ProductLog[a*x]])/3 - 1/(3*x*ProductLog[a*x]^2) - 1/(3*x*ProductLog[a*x])","A",1
109,1,59,59,0.0060279,"\int \frac{1}{x^3 \text{ProductLog}(a x)^2} \, dx","Integrate[1/(x^3*ProductLog[a*x]^2),x]","-\frac{2}{3} a^2 \text{Ei}(-2 \text{ProductLog}(a x))-\frac{\text{ProductLog}(a x)}{3 x^2}-\frac{1}{6 x^2 \text{ProductLog}(a x)}-\frac{1}{4 x^2 \text{ProductLog}(a x)^2}+\frac{1}{6 x^2}","-\frac{2}{3} a^2 \text{Ei}(-2 \text{ProductLog}(a x))-\frac{\text{ProductLog}(a x)}{3 x^2}-\frac{1}{6 x^2 \text{ProductLog}(a x)}-\frac{1}{4 x^2 \text{ProductLog}(a x)^2}+\frac{1}{6 x^2}",1,"1/(6*x^2) - (2*a^2*ExpIntegralEi[-2*ProductLog[a*x]])/3 - 1/(4*x^2*ProductLog[a*x]^2) - 1/(6*x^2*ProductLog[a*x]) - ProductLog[a*x]/(3*x^2)","A",1
110,1,66,66,0.0080327,"\int \frac{x^6}{\text{ProductLog}(a x)^3} \, dx","Integrate[x^6/ProductLog[a*x]^3,x]","\frac{x^7}{7 \text{ProductLog}(a x)^3}+\frac{3 x^7}{49 \text{ProductLog}(a x)^4}-\frac{9 x^7}{343 \text{ProductLog}(a x)^5}+\frac{18 x^7}{2401 \text{ProductLog}(a x)^6}-\frac{18 x^7}{16807 \text{ProductLog}(a x)^7}","\frac{x^7}{7 \text{ProductLog}(a x)^3}+\frac{3 x^7}{49 \text{ProductLog}(a x)^4}-\frac{9 x^7}{343 \text{ProductLog}(a x)^5}+\frac{18 x^7}{2401 \text{ProductLog}(a x)^6}-\frac{18 x^7}{16807 \text{ProductLog}(a x)^7}",1,"(-18*x^7)/(16807*ProductLog[a*x]^7) + (18*x^7)/(2401*ProductLog[a*x]^6) - (9*x^7)/(343*ProductLog[a*x]^5) + (3*x^7)/(49*ProductLog[a*x]^4) + x^7/(7*ProductLog[a*x]^3)","A",1
111,1,53,53,0.0057642,"\int \frac{x^5}{\text{ProductLog}(a x)^3} \, dx","Integrate[x^5/ProductLog[a*x]^3,x]","\frac{x^6}{6 \text{ProductLog}(a x)^3}+\frac{x^6}{12 \text{ProductLog}(a x)^4}-\frac{x^6}{36 \text{ProductLog}(a x)^5}+\frac{x^6}{216 \text{ProductLog}(a x)^6}","\frac{x^6}{6 \text{ProductLog}(a x)^3}+\frac{x^6}{12 \text{ProductLog}(a x)^4}-\frac{x^6}{36 \text{ProductLog}(a x)^5}+\frac{x^6}{216 \text{ProductLog}(a x)^6}",1,"x^6/(216*ProductLog[a*x]^6) - x^6/(36*ProductLog[a*x]^5) + x^6/(12*ProductLog[a*x]^4) + x^6/(6*ProductLog[a*x]^3)","A",1
112,1,40,40,0.0045778,"\int \frac{x^4}{\text{ProductLog}(a x)^3} \, dx","Integrate[x^4/ProductLog[a*x]^3,x]","\frac{x^5}{5 \text{ProductLog}(a x)^3}+\frac{3 x^5}{25 \text{ProductLog}(a x)^4}-\frac{3 x^5}{125 \text{ProductLog}(a x)^5}","\frac{x^5}{5 \text{ProductLog}(a x)^3}+\frac{3 x^5}{25 \text{ProductLog}(a x)^4}-\frac{3 x^5}{125 \text{ProductLog}(a x)^5}",1,"(-3*x^5)/(125*ProductLog[a*x]^5) + (3*x^5)/(25*ProductLog[a*x]^4) + x^5/(5*ProductLog[a*x]^3)","A",1
113,1,27,27,0.0032263,"\int \frac{x^3}{\text{ProductLog}(a x)^3} \, dx","Integrate[x^3/ProductLog[a*x]^3,x]","\frac{x^4}{4 \text{ProductLog}(a x)^3}+\frac{3 x^4}{16 \text{ProductLog}(a x)^4}","\frac{x^4}{4 \text{ProductLog}(a x)^3}+\frac{3 x^4}{16 \text{ProductLog}(a x)^4}",1,"(3*x^4)/(16*ProductLog[a*x]^4) + x^4/(4*ProductLog[a*x]^3)","A",1
114,1,25,25,0.0030232,"\int \frac{x^2}{\text{ProductLog}(a x)^3} \, dx","Integrate[x^2/ProductLog[a*x]^3,x]","\frac{\text{Ei}(3 \text{ProductLog}(a x))}{a^3}+\frac{x^3}{3 \text{ProductLog}(a x)^3}","\frac{\text{Ei}(3 \text{ProductLog}(a x))}{a^3}+\frac{x^3}{3 \text{ProductLog}(a x)^3}",1,"ExpIntegralEi[3*ProductLog[a*x]]/a^3 + x^3/(3*ProductLog[a*x]^3)","A",1
115,1,24,24,0.0051854,"\int \frac{x}{\text{ProductLog}(a x)^3} \, dx","Integrate[x/ProductLog[a*x]^3,x]","\frac{3 \text{Ei}(2 \text{ProductLog}(a x))}{a^2}-\frac{x^2}{\text{ProductLog}(a x)^3}","\frac{3 \text{Ei}(2 \text{ProductLog}(a x))}{a^2}-\frac{x^2}{\text{ProductLog}(a x)^3}",1,"(3*ExpIntegralEi[2*ProductLog[a*x]])/a^2 - x^2/ProductLog[a*x]^3","A",1
116,1,33,35,0.010433,"\int \frac{1}{\text{ProductLog}(a x)^3} \, dx","Integrate[ProductLog[a*x]^(-3),x]","\frac{1}{2} \left(\frac{3 \text{Ei}(\text{ProductLog}(a x))}{a}-\frac{3 x}{\text{ProductLog}(a x)^2}-\frac{x}{\text{ProductLog}(a x)^3}\right)","\frac{3 \text{Ei}(\text{ProductLog}(a x))}{2 a}-\frac{3 x}{2 \text{ProductLog}(a x)^2}-\frac{x}{2 \text{ProductLog}(a x)^3}",1,"((3*ExpIntegralEi[ProductLog[a*x]])/a - x/ProductLog[a*x]^3 - (3*x)/ProductLog[a*x]^2)/2","A",1
117,1,21,21,0.0205496,"\int \frac{1}{x \text{ProductLog}(a x)^3} \, dx","Integrate[1/(x*ProductLog[a*x]^3),x]","-\frac{1}{2 \text{ProductLog}(a x)^2}-\frac{1}{3 \text{ProductLog}(a x)^3}","-\frac{1}{2 \text{ProductLog}(a x)^2}-\frac{1}{3 \text{ProductLog}(a x)^3}",1,"-1/(3*ProductLog[a*x]^3) - 1/(2*ProductLog[a*x]^2)","A",1
118,1,59,59,0.0089838,"\int \frac{1}{x^2 \text{ProductLog}(a x)^3} \, dx","Integrate[1/(x^2*ProductLog[a*x]^3),x]","-\frac{1}{8} a \text{Ei}(-\text{ProductLog}(a x))+\frac{1}{8 x \text{ProductLog}(a x)}-\frac{1}{4 x \text{ProductLog}(a x)^2}-\frac{1}{4 x \text{ProductLog}(a x)^3}-\frac{1}{8 x}","-\frac{1}{8} a \text{Ei}(-\text{ProductLog}(a x))+\frac{1}{8 x \text{ProductLog}(a x)}-\frac{1}{4 x \text{ProductLog}(a x)^2}-\frac{1}{4 x \text{ProductLog}(a x)^3}-\frac{1}{8 x}",1,"-1/(8*x) - (a*ExpIntegralEi[-ProductLog[a*x]])/8 - 1/(4*x*ProductLog[a*x]^3) - 1/(4*x*ProductLog[a*x]^2) + 1/(8*x*ProductLog[a*x])","A",1
119,1,72,72,0.0081228,"\int \frac{1}{x^3 \text{ProductLog}(a x)^3} \, dx","Integrate[1/(x^3*ProductLog[a*x]^3),x]","\frac{2}{5} a^2 \text{Ei}(-2 \text{ProductLog}(a x))+\frac{\text{ProductLog}(a x)}{5 x^2}+\frac{1}{10 x^2 \text{ProductLog}(a x)}-\frac{3}{20 x^2 \text{ProductLog}(a x)^2}-\frac{1}{5 x^2 \text{ProductLog}(a x)^3}-\frac{1}{10 x^2}","\frac{2}{5} a^2 \text{Ei}(-2 \text{ProductLog}(a x))+\frac{\text{ProductLog}(a x)}{5 x^2}+\frac{1}{10 x^2 \text{ProductLog}(a x)}-\frac{3}{20 x^2 \text{ProductLog}(a x)^2}-\frac{1}{5 x^2 \text{ProductLog}(a x)^3}-\frac{1}{10 x^2}",1,"-1/(10*x^2) + (2*a^2*ExpIntegralEi[-2*ProductLog[a*x]])/5 - 1/(5*x^2*ProductLog[a*x]^3) - 3/(20*x^2*ProductLog[a*x]^2) + 1/(10*x^2*ProductLog[a*x]) + ProductLog[a*x]/(5*x^2)","A",1
120,1,112,131,0.0253329,"\int x^3 \sqrt{c \text{ProductLog}(a x)} \, dx","Integrate[x^3*Sqrt[c*ProductLog[a*x]],x]","\frac{\sqrt{c \text{ProductLog}(a x)} \left(16384 a^4 x^4 \text{ProductLog}(a x)^4-2048 a^4 x^4 \text{ProductLog}(a x)^3+1792 a^4 x^4 \text{ProductLog}(a x)^2-1120 a^4 x^4 \text{ProductLog}(a x)+420 a^4 x^4-105 \sqrt{\pi } \text{ProductLog}(a x)^{7/2} \text{Erfi}\left(2 \sqrt{\text{ProductLog}(a x)}\right)\right)}{65536 a^4 \text{ProductLog}(a x)^4}","-\frac{105 \sqrt{\pi } \sqrt{c} \text{Erfi}\left(\frac{2 \sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)}{65536 a^4}+\frac{105 c^4 x^4}{16384 (c \text{ProductLog}(a x))^{7/2}}-\frac{35 c^3 x^4}{2048 (c \text{ProductLog}(a x))^{5/2}}+\frac{7 c^2 x^4}{256 (c \text{ProductLog}(a x))^{3/2}}+\frac{1}{4} x^4 \sqrt{c \text{ProductLog}(a x)}-\frac{c x^4}{32 \sqrt{c \text{ProductLog}(a x)}}",1,"(Sqrt[c*ProductLog[a*x]]*(420*a^4*x^4 - 1120*a^4*x^4*ProductLog[a*x] + 1792*a^4*x^4*ProductLog[a*x]^2 - 2048*a^4*x^4*ProductLog[a*x]^3 - 105*Sqrt[Pi]*Erfi[2*Sqrt[ProductLog[a*x]]]*ProductLog[a*x]^(7/2) + 16384*a^4*x^4*ProductLog[a*x]^4))/(65536*a^4*ProductLog[a*x]^4)","A",0
121,1,104,119,0.0308042,"\int x^2 \sqrt{c \text{ProductLog}(a x)} \, dx","Integrate[x^2*Sqrt[c*ProductLog[a*x]],x]","\frac{\sqrt{c \text{ProductLog}(a x)} \left(432 a^3 x^3 \text{ProductLog}(a x)^3-72 a^3 x^3 \text{ProductLog}(a x)^2+60 a^3 x^3 \text{ProductLog}(a x)-30 a^3 x^3+5 \sqrt{3 \pi } \text{ProductLog}(a x)^{5/2} \text{Erfi}\left(\sqrt{3} \sqrt{\text{ProductLog}(a x)}\right)\right)}{1296 a^3 \text{ProductLog}(a x)^3}","\frac{5 \sqrt{\frac{\pi }{3}} \sqrt{c} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)}{432 a^3}-\frac{5 c^3 x^3}{216 (c \text{ProductLog}(a x))^{5/2}}+\frac{5 c^2 x^3}{108 (c \text{ProductLog}(a x))^{3/2}}+\frac{1}{3} x^3 \sqrt{c \text{ProductLog}(a x)}-\frac{c x^3}{18 \sqrt{c \text{ProductLog}(a x)}}",1,"(Sqrt[c*ProductLog[a*x]]*(-30*a^3*x^3 + 60*a^3*x^3*ProductLog[a*x] - 72*a^3*x^3*ProductLog[a*x]^2 + 5*Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ProductLog[a*x]]]*ProductLog[a*x]^(5/2) + 432*a^3*x^3*ProductLog[a*x]^3))/(1296*a^3*ProductLog[a*x]^3)","A",0
122,1,90,99,0.0302391,"\int x \sqrt{c \text{ProductLog}(a x)} \, dx","Integrate[x*Sqrt[c*ProductLog[a*x]],x]","\frac{\sqrt{c \text{ProductLog}(a x)} \left(64 a^2 x^2 \text{ProductLog}(a x)^2-16 a^2 x^2 \text{ProductLog}(a x)+12 a^2 x^2-3 \sqrt{2 \pi } \text{ProductLog}(a x)^{3/2} \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}(a x)}\right)\right)}{128 a^2 \text{ProductLog}(a x)^2}","-\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{c} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)}{64 a^2}+\frac{3 c^2 x^2}{32 (c \text{ProductLog}(a x))^{3/2}}+\frac{1}{2} x^2 \sqrt{c \text{ProductLog}(a x)}-\frac{c x^2}{8 \sqrt{c \text{ProductLog}(a x)}}",1,"(Sqrt[c*ProductLog[a*x]]*(12*a^2*x^2 - 16*a^2*x^2*ProductLog[a*x] - 3*Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ProductLog[a*x]]]*ProductLog[a*x]^(3/2) + 64*a^2*x^2*ProductLog[a*x]^2))/(128*a^2*ProductLog[a*x]^2)","A",0
123,1,54,63,0.0190638,"\int \sqrt{c \text{ProductLog}(a x)} \, dx","Integrate[Sqrt[c*ProductLog[a*x]],x]","\frac{c \left(\sqrt{\pi } \sqrt{\text{ProductLog}(a x)} \text{Erfi}\left(\sqrt{\text{ProductLog}(a x)}\right)+4 a x \text{ProductLog}(a x)-2 a x\right)}{4 a \sqrt{c \text{ProductLog}(a x)}}","\frac{\sqrt{\pi } \sqrt{c} \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)}{4 a}+x \sqrt{c \text{ProductLog}(a x)}-\frac{c x}{2 \sqrt{c \text{ProductLog}(a x)}}",1,"(c*(-2*a*x + Sqrt[Pi]*Erfi[Sqrt[ProductLog[a*x]]]*Sqrt[ProductLog[a*x]] + 4*a*x*ProductLog[a*x]))/(4*a*Sqrt[c*ProductLog[a*x]])","A",1
124,1,20,30,0.0199573,"\int \frac{\sqrt{c \text{ProductLog}(a x)}}{x} \, dx","Integrate[Sqrt[c*ProductLog[a*x]]/x,x]","\frac{2}{3} (\text{ProductLog}(a x)+3) \sqrt{c \text{ProductLog}(a x)}","\frac{2 (c \text{ProductLog}(a x))^{3/2}}{3 c}+2 \sqrt{c \text{ProductLog}(a x)}",1,"(2*Sqrt[c*ProductLog[a*x]]*(3 + ProductLog[a*x]))/3","A",1
125,1,51,46,0.0109824,"\int \frac{\sqrt{c \text{ProductLog}(a x)}}{x^2} \, dx","Integrate[Sqrt[c*ProductLog[a*x]]/x^2,x]","-\frac{\sqrt{\pi } a \sqrt{c \text{ProductLog}(a x)} \text{Erf}\left(\sqrt{\text{ProductLog}(a x)}\right)}{\sqrt{\text{ProductLog}(a x)}}-\frac{2 \sqrt{c \text{ProductLog}(a x)}}{x}","\sqrt{\pi } (-a) \sqrt{c} \text{Erf}\left(\frac{\sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)-\frac{2 \sqrt{c \text{ProductLog}(a x)}}{x}",1,"(-2*Sqrt[c*ProductLog[a*x]])/x - (a*Sqrt[Pi]*Erf[Sqrt[ProductLog[a*x]]]*Sqrt[c*ProductLog[a*x]])/Sqrt[ProductLog[a*x]]","A",1
126,1,73,79,0.0259224,"\int \frac{\sqrt{c \text{ProductLog}(a x)}}{x^3} \, dx","Integrate[Sqrt[c*ProductLog[a*x]]/x^3,x]","\frac{2 \sqrt{c \text{ProductLog}(a x)} \left(\sqrt{2 \pi } a^2 x^2 \text{Erf}\left(\sqrt{2} \sqrt{\text{ProductLog}(a x)}\right)+\text{ProductLog}(a x)^{3/2}-\sqrt{\text{ProductLog}(a x)}\right)}{3 x^2 \sqrt{\text{ProductLog}(a x)}}","\frac{2}{3} \sqrt{2 \pi } a^2 \sqrt{c} \text{Erf}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)+\frac{2 (c \text{ProductLog}(a x))^{3/2}}{3 c x^2}-\frac{2 \sqrt{c \text{ProductLog}(a x)}}{3 x^2}",1,"(2*Sqrt[c*ProductLog[a*x]]*(a^2*Sqrt[2*Pi]*x^2*Erf[Sqrt[2]*Sqrt[ProductLog[a*x]]] - Sqrt[ProductLog[a*x]] + ProductLog[a*x]^(3/2)))/(3*x^2*Sqrt[ProductLog[a*x]])","A",0
127,1,86,99,0.0552879,"\int \frac{\sqrt{c \text{ProductLog}(a x)}}{x^4} \, dx","Integrate[Sqrt[c*ProductLog[a*x]]/x^4,x]","-\frac{2 \sqrt{c \text{ProductLog}(a x)} \left(6 \sqrt{3 \pi } a^3 x^3 \text{Erf}\left(\sqrt{3} \sqrt{\text{ProductLog}(a x)}\right)+6 \text{ProductLog}(a x)^{5/2}-\text{ProductLog}(a x)^{3/2}+3 \sqrt{\text{ProductLog}(a x)}\right)}{15 x^3 \sqrt{\text{ProductLog}(a x)}}","-\frac{4}{5} \sqrt{3 \pi } a^3 \sqrt{c} \text{Erf}\left(\frac{\sqrt{3} \sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)-\frac{4 (c \text{ProductLog}(a x))^{5/2}}{5 c^2 x^3}+\frac{2 (c \text{ProductLog}(a x))^{3/2}}{15 c x^3}-\frac{2 \sqrt{c \text{ProductLog}(a x)}}{5 x^3}",1,"(-2*Sqrt[c*ProductLog[a*x]]*(6*a^3*Sqrt[3*Pi]*x^3*Erf[Sqrt[3]*Sqrt[ProductLog[a*x]]] + 3*Sqrt[ProductLog[a*x]] - ProductLog[a*x]^(3/2) + 6*ProductLog[a*x]^(5/2)))/(15*x^3*Sqrt[ProductLog[a*x]])","A",0
128,1,90,113,0.0271016,"\int \frac{\sqrt{c \text{ProductLog}(a x)}}{x^5} \, dx","Integrate[Sqrt[c*ProductLog[a*x]]/x^5,x]","\frac{2 \sqrt{c \text{ProductLog}(a x)} \left(128 \sqrt{\pi } a^4 x^4 \text{Erf}\left(2 \sqrt{\text{ProductLog}(a x)}\right)+64 \text{ProductLog}(a x)^{7/2}-8 \text{ProductLog}(a x)^{5/2}+3 \text{ProductLog}(a x)^{3/2}-15 \sqrt{\text{ProductLog}(a x)}\right)}{105 x^4 \sqrt{\text{ProductLog}(a x)}}","\frac{256}{105} \sqrt{\pi } a^4 \sqrt{c} \text{Erf}\left(\frac{2 \sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)+\frac{128 (c \text{ProductLog}(a x))^{7/2}}{105 c^3 x^4}-\frac{16 (c \text{ProductLog}(a x))^{5/2}}{105 c^2 x^4}+\frac{2 (c \text{ProductLog}(a x))^{3/2}}{35 c x^4}-\frac{2 \sqrt{c \text{ProductLog}(a x)}}{7 x^4}",1,"(2*Sqrt[c*ProductLog[a*x]]*(128*a^4*Sqrt[Pi]*x^4*Erf[2*Sqrt[ProductLog[a*x]]] - 15*Sqrt[ProductLog[a*x]] + 3*ProductLog[a*x]^(3/2) - 8*ProductLog[a*x]^(5/2) + 64*ProductLog[a*x]^(7/2)))/(105*x^4*Sqrt[ProductLog[a*x]])","A",0
129,1,106,139,0.0405702,"\int \frac{\sqrt{c \text{ProductLog}(a x)}}{x^6} \, dx","Integrate[Sqrt[c*ProductLog[a*x]]/x^6,x]","-\frac{2 \sqrt{c \text{ProductLog}(a x)} \left(200 \sqrt{5 \pi } a^5 x^5 \text{Erf}\left(\sqrt{5} \sqrt{\text{ProductLog}(a x)}\right)+200 \text{ProductLog}(a x)^{9/2}-20 \text{ProductLog}(a x)^{7/2}+6 \text{ProductLog}(a x)^{5/2}-3 \text{ProductLog}(a x)^{3/2}+21 \sqrt{\text{ProductLog}(a x)}\right)}{189 x^5 \sqrt{\text{ProductLog}(a x)}}","-\frac{400}{189} \sqrt{5 \pi } a^5 \sqrt{c} \text{Erf}\left(\frac{\sqrt{5} \sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)-\frac{400 (c \text{ProductLog}(a x))^{9/2}}{189 c^4 x^5}+\frac{40 (c \text{ProductLog}(a x))^{7/2}}{189 c^3 x^5}-\frac{4 (c \text{ProductLog}(a x))^{5/2}}{63 c^2 x^5}+\frac{2 (c \text{ProductLog}(a x))^{3/2}}{63 c x^5}-\frac{2 \sqrt{c \text{ProductLog}(a x)}}{9 x^5}",1,"(-2*Sqrt[c*ProductLog[a*x]]*(200*a^5*Sqrt[5*Pi]*x^5*Erf[Sqrt[5]*Sqrt[ProductLog[a*x]]] + 21*Sqrt[ProductLog[a*x]] - 3*ProductLog[a*x]^(3/2) + 6*ProductLog[a*x]^(5/2) - 20*ProductLog[a*x]^(7/2) + 200*ProductLog[a*x]^(9/2)))/(189*x^5*Sqrt[ProductLog[a*x]])","A",0
130,1,118,139,0.0281358,"\int \frac{x^4}{\sqrt{c \text{ProductLog}(a x)}} \, dx","Integrate[x^4/Sqrt[c*ProductLog[a*x]],x]","\frac{20000 a^5 x^5 \text{ProductLog}(a x)^4+2000 a^5 x^5 \text{ProductLog}(a x)^3-1400 a^5 x^5 \text{ProductLog}(a x)^2+700 a^5 x^5 \text{ProductLog}(a x)-210 a^5 x^5+21 \sqrt{5 \pi } \text{ProductLog}(a x)^{9/2} \text{Erfi}\left(\sqrt{5} \sqrt{\text{ProductLog}(a x)}\right)}{100000 a^5 \text{ProductLog}(a x)^4 \sqrt{c \text{ProductLog}(a x)}}","\frac{21 \sqrt{\frac{\pi }{5}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)}{20000 a^5 \sqrt{c}}-\frac{21 c^4 x^5}{10000 (c \text{ProductLog}(a x))^{9/2}}+\frac{7 c^3 x^5}{1000 (c \text{ProductLog}(a x))^{7/2}}-\frac{7 c^2 x^5}{500 (c \text{ProductLog}(a x))^{5/2}}+\frac{x^5}{5 \sqrt{c \text{ProductLog}(a x)}}+\frac{c x^5}{50 (c \text{ProductLog}(a x))^{3/2}}",1,"(-210*a^5*x^5 + 700*a^5*x^5*ProductLog[a*x] - 1400*a^5*x^5*ProductLog[a*x]^2 + 2000*a^5*x^5*ProductLog[a*x]^3 + 20000*a^5*x^5*ProductLog[a*x]^4 + 21*Sqrt[5*Pi]*Erfi[Sqrt[5]*Sqrt[ProductLog[a*x]]]*ProductLog[a*x]^(9/2))/(100000*a^5*ProductLog[a*x]^4*Sqrt[c*ProductLog[a*x]])","A",0
131,1,98,111,0.0255788,"\int \frac{x^3}{\sqrt{c \text{ProductLog}(a x)}} \, dx","Integrate[x^3/Sqrt[c*ProductLog[a*x]],x]","\frac{2048 a^4 x^4 \text{ProductLog}(a x)^3+256 a^4 x^4 \text{ProductLog}(a x)^2-160 a^4 x^4 \text{ProductLog}(a x)+60 a^4 x^4-15 \sqrt{\pi } \text{ProductLog}(a x)^{7/2} \text{Erfi}\left(2 \sqrt{\text{ProductLog}(a x)}\right)}{8192 a^4 \text{ProductLog}(a x)^3 \sqrt{c \text{ProductLog}(a x)}}","-\frac{15 \sqrt{\pi } \text{Erfi}\left(\frac{2 \sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)}{8192 a^4 \sqrt{c}}+\frac{15 c^3 x^4}{2048 (c \text{ProductLog}(a x))^{7/2}}-\frac{5 c^2 x^4}{256 (c \text{ProductLog}(a x))^{5/2}}+\frac{x^4}{4 \sqrt{c \text{ProductLog}(a x)}}+\frac{c x^4}{32 (c \text{ProductLog}(a x))^{3/2}}",1,"(60*a^4*x^4 - 160*a^4*x^4*ProductLog[a*x] + 256*a^4*x^4*ProductLog[a*x]^2 + 2048*a^4*x^4*ProductLog[a*x]^3 - 15*Sqrt[Pi]*Erfi[2*Sqrt[ProductLog[a*x]]]*ProductLog[a*x]^(7/2))/(8192*a^4*ProductLog[a*x]^3*Sqrt[c*ProductLog[a*x]])","A",0
132,1,89,99,0.0214553,"\int \frac{x^2}{\sqrt{c \text{ProductLog}(a x)}} \, dx","Integrate[x^2/Sqrt[c*ProductLog[a*x]],x]","\frac{72 a^3 x^3 \text{ProductLog}(a x)^2+12 a^3 x^3 \text{ProductLog}(a x)-6 a^3 x^3+\sqrt{3 \pi } \text{ProductLog}(a x)^{5/2} \text{Erfi}\left(\sqrt{3} \sqrt{\text{ProductLog}(a x)}\right)}{216 a^3 \text{ProductLog}(a x)^2 \sqrt{c \text{ProductLog}(a x)}}","\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)}{72 a^3 \sqrt{c}}-\frac{c^2 x^3}{36 (c \text{ProductLog}(a x))^{5/2}}+\frac{x^3}{3 \sqrt{c \text{ProductLog}(a x)}}+\frac{c x^3}{18 (c \text{ProductLog}(a x))^{3/2}}",1,"(-6*a^3*x^3 + 12*a^3*x^3*ProductLog[a*x] + 72*a^3*x^3*ProductLog[a*x]^2 + Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ProductLog[a*x]]]*ProductLog[a*x]^(5/2))/(216*a^3*ProductLog[a*x]^2*Sqrt[c*ProductLog[a*x]])","A",0
133,1,71,79,0.0183803,"\int \frac{x}{\sqrt{c \text{ProductLog}(a x)}} \, dx","Integrate[x/Sqrt[c*ProductLog[a*x]],x]","\frac{c \left(16 a^2 x^2 \text{ProductLog}(a x)+4 a^2 x^2-\sqrt{2 \pi } \text{ProductLog}(a x)^{3/2} \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}(a x)}\right)\right)}{32 a^2 (c \text{ProductLog}(a x))^{3/2}}","-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)}{16 a^2 \sqrt{c}}+\frac{x^2}{2 \sqrt{c \text{ProductLog}(a x)}}+\frac{c x^2}{8 (c \text{ProductLog}(a x))^{3/2}}",1,"(c*(4*a^2*x^2 + 16*a^2*x^2*ProductLog[a*x] - Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ProductLog[a*x]]]*ProductLog[a*x]^(3/2)))/(32*a^2*(c*ProductLog[a*x])^(3/2))","A",0
134,1,45,47,0.012703,"\int \frac{1}{\sqrt{c \text{ProductLog}(a x)}} \, dx","Integrate[1/Sqrt[c*ProductLog[a*x]],x]","\frac{\sqrt{\pi } \sqrt{\text{ProductLog}(a x)} \text{Erfi}\left(\sqrt{\text{ProductLog}(a x)}\right)+2 a x}{2 a \sqrt{c \text{ProductLog}(a x)}}","\frac{\sqrt{\pi } \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)}{2 a \sqrt{c}}+\frac{x}{\sqrt{c \text{ProductLog}(a x)}}",1,"(2*a*x + Sqrt[Pi]*Erfi[Sqrt[ProductLog[a*x]]]*Sqrt[ProductLog[a*x]])/(2*a*Sqrt[c*ProductLog[a*x]])","A",1
135,1,18,28,0.0298048,"\int \frac{1}{x \sqrt{c \text{ProductLog}(a x)}} \, dx","Integrate[1/(x*Sqrt[c*ProductLog[a*x]]),x]","\frac{2 (\text{ProductLog}(a x)-1)}{\sqrt{c \text{ProductLog}(a x)}}","\frac{2 \sqrt{c \text{ProductLog}(a x)}}{c}-\frac{2}{\sqrt{c \text{ProductLog}(a x)}}",1,"(2*(-1 + ProductLog[a*x]))/Sqrt[c*ProductLog[a*x]]","A",1
136,1,48,70,0.0115463,"\int \frac{1}{x^2 \sqrt{c \text{ProductLog}(a x)}} \, dx","Integrate[1/(x^2*Sqrt[c*ProductLog[a*x]]),x]","-\frac{2 \left(\sqrt{\pi } a x \sqrt{\text{ProductLog}(a x)} \text{Erf}\left(\sqrt{\text{ProductLog}(a x)}\right)+\text{ProductLog}(a x)+1\right)}{3 x \sqrt{c \text{ProductLog}(a x)}}","-\frac{2 \sqrt{\pi } a \text{Erf}\left(\frac{\sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)}{3 \sqrt{c}}-\frac{2 \sqrt{c \text{ProductLog}(a x)}}{3 c x}-\frac{2}{3 x \sqrt{c \text{ProductLog}(a x)}}",1,"(-2*(1 + a*Sqrt[Pi]*x*Erf[Sqrt[ProductLog[a*x]]]*Sqrt[ProductLog[a*x]] + ProductLog[a*x]))/(3*x*Sqrt[c*ProductLog[a*x]])","A",1
137,1,71,99,0.0278045,"\int \frac{1}{x^3 \sqrt{c \text{ProductLog}(a x)}} \, dx","Integrate[1/(x^3*Sqrt[c*ProductLog[a*x]]),x]","\frac{2 \left(4 \sqrt{2 \pi } a^2 x^2 \sqrt{\text{ProductLog}(a x)} \text{Erf}\left(\sqrt{2} \sqrt{\text{ProductLog}(a x)}\right)+4 \text{ProductLog}(a x)^2-\text{ProductLog}(a x)-3\right)}{15 x^2 \sqrt{c \text{ProductLog}(a x)}}","\frac{8 \sqrt{2 \pi } a^2 \text{Erf}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)}{15 \sqrt{c}}+\frac{8 (c \text{ProductLog}(a x))^{3/2}}{15 c^2 x^2}-\frac{2 \sqrt{c \text{ProductLog}(a x)}}{15 c x^2}-\frac{2}{5 x^2 \sqrt{c \text{ProductLog}(a x)}}",1,"(2*(-3 + 4*a^2*Sqrt[2*Pi]*x^2*Erf[Sqrt[2]*Sqrt[ProductLog[a*x]]]*Sqrt[ProductLog[a*x]] - ProductLog[a*x] + 4*ProductLog[a*x]^2))/(15*x^2*Sqrt[c*ProductLog[a*x]])","A",0
138,1,77,119,0.0275774,"\int \frac{1}{x^4 \sqrt{c \text{ProductLog}(a x)}} \, dx","Integrate[1/(x^4*Sqrt[c*ProductLog[a*x]]),x]","-\frac{2 \left(12 \sqrt{3 \pi } a^3 x^3 \sqrt{\text{ProductLog}(a x)} \text{Erf}\left(\sqrt{3} \sqrt{\text{ProductLog}(a x)}\right)+12 \text{ProductLog}(a x)^3-2 \text{ProductLog}(a x)^2+\text{ProductLog}(a x)+5\right)}{35 x^3 \sqrt{c \text{ProductLog}(a x)}}","-\frac{24 \sqrt{3 \pi } a^3 \text{Erf}\left(\frac{\sqrt{3} \sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)}{35 \sqrt{c}}-\frac{24 (c \text{ProductLog}(a x))^{5/2}}{35 c^3 x^3}+\frac{4 (c \text{ProductLog}(a x))^{3/2}}{35 c^2 x^3}-\frac{2 \sqrt{c \text{ProductLog}(a x)}}{35 c x^3}-\frac{2}{7 x^3 \sqrt{c \text{ProductLog}(a x)}}",1,"(-2*(5 + 12*a^3*Sqrt[3*Pi]*x^3*Erf[Sqrt[3]*Sqrt[ProductLog[a*x]]]*Sqrt[ProductLog[a*x]] + ProductLog[a*x] - 2*ProductLog[a*x]^2 + 12*ProductLog[a*x]^3))/(35*x^3*Sqrt[c*ProductLog[a*x]])","A",0
139,1,81,133,0.0213032,"\int \frac{1}{x^5 \sqrt{c \text{ProductLog}(a x)}} \, dx","Integrate[1/(x^5*Sqrt[c*ProductLog[a*x]]),x]","\frac{2 \left(1024 \sqrt{\pi } a^4 x^4 \sqrt{\text{ProductLog}(a x)} \text{Erf}\left(2 \sqrt{\text{ProductLog}(a x)}\right)+512 \text{ProductLog}(a x)^4-64 \text{ProductLog}(a x)^3+24 \text{ProductLog}(a x)^2-15 \text{ProductLog}(a x)-105\right)}{945 x^4 \sqrt{c \text{ProductLog}(a x)}}","\frac{2048 \sqrt{\pi } a^4 \text{Erf}\left(\frac{2 \sqrt{c \text{ProductLog}(a x)}}{\sqrt{c}}\right)}{945 \sqrt{c}}+\frac{1024 (c \text{ProductLog}(a x))^{7/2}}{945 c^4 x^4}-\frac{128 (c \text{ProductLog}(a x))^{5/2}}{945 c^3 x^4}+\frac{16 (c \text{ProductLog}(a x))^{3/2}}{315 c^2 x^4}-\frac{2 \sqrt{c \text{ProductLog}(a x)}}{63 c x^4}-\frac{2}{9 x^4 \sqrt{c \text{ProductLog}(a x)}}",1,"(2*(-105 + 1024*a^4*Sqrt[Pi]*x^4*Erf[2*Sqrt[ProductLog[a*x]]]*Sqrt[ProductLog[a*x]] - 15*ProductLog[a*x] + 24*ProductLog[a*x]^2 - 64*ProductLog[a*x]^3 + 512*ProductLog[a*x]^4))/(945*x^4*Sqrt[c*ProductLog[a*x]])","A",0
140,1,67,110,0.0265268,"\int x^2 (c \text{ProductLog}(a x))^p \, dx","Integrate[x^2*(c*ProductLog[a*x])^p,x]","\frac{3^{-p-4} x^2 e^{-2 \text{ProductLog}(a x)} (-\text{ProductLog}(a x))^{-p-2} (c \text{ProductLog}(a x))^p (3 \Gamma (p+3,-3 \text{ProductLog}(a x))-\Gamma (p+4,-3 \text{ProductLog}(a x)))}{a}","\frac{3^{-p-4} x^2 e^{-2 \text{ProductLog}(a x)} (-\text{ProductLog}(a x))^{-p-3} (c \text{ProductLog}(a x))^{p+1} \Gamma (p+4,-3 \text{ProductLog}(a x))}{a c}+\frac{3^{-p-3} x^2 e^{-2 \text{ProductLog}(a x)} (-\text{ProductLog}(a x))^{-p-2} (c \text{ProductLog}(a x))^p \Gamma (p+3,-3 \text{ProductLog}(a x))}{a}",1,"(3^(-4 - p)*x^2*(3*Gamma[3 + p, -3*ProductLog[a*x]] - Gamma[4 + p, -3*ProductLog[a*x]])*(-ProductLog[a*x])^(-2 - p)*(c*ProductLog[a*x])^p)/(a*E^(2*ProductLog[a*x]))","A",1
141,1,52,106,0.0199406,"\int x (c \text{ProductLog}(a x))^p \, dx","Integrate[x*(c*ProductLog[a*x])^p,x]","\frac{2^{-p-3} (-\text{ProductLog}(a x))^{-p} (c \text{ProductLog}(a x))^p (\Gamma (p+3,-2 \text{ProductLog}(a x))-2 \Gamma (p+2,-2 \text{ProductLog}(a x)))}{a^2}","\frac{2^{-p-3} x e^{-\text{ProductLog}(a x)} (-\text{ProductLog}(a x))^{-p-2} (c \text{ProductLog}(a x))^{p+1} \Gamma (p+3,-2 \text{ProductLog}(a x))}{a c}+\frac{2^{-p-2} x e^{-\text{ProductLog}(a x)} (-\text{ProductLog}(a x))^{-p-1} (c \text{ProductLog}(a x))^p \Gamma (p+2,-2 \text{ProductLog}(a x))}{a}",1,"(2^(-3 - p)*(-2*Gamma[2 + p, -2*ProductLog[a*x]] + Gamma[3 + p, -2*ProductLog[a*x]])*(c*ProductLog[a*x])^p)/(a^2*(-ProductLog[a*x])^p)","A",1
142,1,23,32,0.0317819,"\int \frac{(c \text{ProductLog}(a x))^p}{x} \, dx","Integrate[(c*ProductLog[a*x])^p/x,x]","\left(\frac{\text{ProductLog}(a x)}{p+1}+\frac{1}{p}\right) (c \text{ProductLog}(a x))^p","\frac{(c \text{ProductLog}(a x))^p}{p}+\frac{(c \text{ProductLog}(a x))^{p+1}}{c (p+1)}",1,"(c*ProductLog[a*x])^p*(p^(-1) + ProductLog[a*x]/(1 + p))","A",1
143,1,49,88,0.0195242,"\int \frac{(c \text{ProductLog}(a x))^p}{x^2} \, dx","Integrate[(c*ProductLog[a*x])^p/x^2,x]","-\frac{e^{2 \text{ProductLog}(a x)} \text{ProductLog}(a x)^{2-p} (c \text{ProductLog}(a x))^p (\Gamma (p-1,\text{ProductLog}(a x))+\Gamma (p,\text{ProductLog}(a x)))}{a x^2}","-\frac{e^{2 \text{ProductLog}(a x)} \text{ProductLog}(a x)^{1-p} (c \text{ProductLog}(a x))^{p+1} \Gamma (p,\text{ProductLog}(a x))}{a c x^2}-\frac{e^{2 \text{ProductLog}(a x)} \text{ProductLog}(a x)^{2-p} (c \text{ProductLog}(a x))^p \Gamma (p-1,\text{ProductLog}(a x))}{a x^2}",1,"-((E^(2*ProductLog[a*x])*(Gamma[-1 + p, ProductLog[a*x]] + Gamma[p, ProductLog[a*x]])*ProductLog[a*x]^(2 - p)*(c*ProductLog[a*x])^p)/(a*x^2))","A",1
144,1,64,108,0.0203171,"\int \frac{(c \text{ProductLog}(a x))^p}{x^3} \, dx","Integrate[(c*ProductLog[a*x])^p/x^3,x]","-\frac{2^{1-p} e^{3 \text{ProductLog}(a x)} \text{ProductLog}(a x)^{3-p} (c \text{ProductLog}(a x))^p (2 \Gamma (p-2,2 \text{ProductLog}(a x))+\Gamma (p-1,2 \text{ProductLog}(a x)))}{a x^3}","-\frac{2^{1-p} e^{3 \text{ProductLog}(a x)} \text{ProductLog}(a x)^{2-p} (c \text{ProductLog}(a x))^{p+1} \Gamma (p-1,2 \text{ProductLog}(a x))}{a c x^3}-\frac{2^{2-p} e^{3 \text{ProductLog}(a x)} \text{ProductLog}(a x)^{3-p} (c \text{ProductLog}(a x))^p \Gamma (p-2,2 \text{ProductLog}(a x))}{a x^3}",1,"-((2^(1 - p)*E^(3*ProductLog[a*x])*(2*Gamma[-2 + p, 2*ProductLog[a*x]] + Gamma[-1 + p, 2*ProductLog[a*x]])*ProductLog[a*x]^(3 - p)*(c*ProductLog[a*x])^p)/(a*x^3))","A",1
145,1,66,109,0.0376034,"\int x^m \text{ProductLog}(a x) \, dx","Integrate[x^m*ProductLog[a*x],x]","\frac{x^m e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{-m} (\Gamma (m+3,-(m+1) \text{ProductLog}(a x))-(m+1) \Gamma (m+2,-(m+1) \text{ProductLog}(a x)))}{a (m+1)^3}","\frac{x^m \text{ProductLog}(a x)^2 e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{-m-2} \Gamma (m+3,-(m+1) \text{ProductLog}(a x))}{a (m+1)}+\frac{x^m \text{ProductLog}(a x) e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{-m-1} \Gamma (m+2,-(m+1) \text{ProductLog}(a x))}{a (m+1)}",1,"(x^m*(-((1 + m)*Gamma[2 + m, -((1 + m)*ProductLog[a*x])]) + Gamma[3 + m, -((1 + m)*ProductLog[a*x])]))/(a*E^(m*ProductLog[a*x])*(1 + m)^3*(-((1 + m)*ProductLog[a*x]))^m)","A",1
146,1,67,111,0.0216175,"\int x^m \text{ProductLog}(a x)^2 \, dx","Integrate[x^m*ProductLog[a*x]^2,x]","\frac{x^m e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{-m} ((m+1) \Gamma (m+3,-(m+1) \text{ProductLog}(a x))-\Gamma (m+4,-(m+1) \text{ProductLog}(a x)))}{a (m+1)^4}","\frac{x^m \text{ProductLog}(a x)^3 e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{-m-3} \Gamma (m+4,-(m+1) \text{ProductLog}(a x))}{a (m+1)}+\frac{x^m \text{ProductLog}(a x)^2 e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{-m-2} \Gamma (m+3,-(m+1) \text{ProductLog}(a x))}{a (m+1)}",1,"(x^m*((1 + m)*Gamma[3 + m, -((1 + m)*ProductLog[a*x])] - Gamma[4 + m, -((1 + m)*ProductLog[a*x])]))/(a*E^(m*ProductLog[a*x])*(1 + m)^4*(-((1 + m)*ProductLog[a*x]))^m)","A",1
147,1,64,101,0.1149888,"\int \frac{x^m}{\text{ProductLog}(a x)} \, dx","Integrate[x^m/ProductLog[a*x],x]","\frac{x^m e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{-m} (\Gamma (m+1,-(m+1) \text{ProductLog}(a x))-(m+1) \Gamma (m,-(m+1) \text{ProductLog}(a x)))}{a (m+1)}","\frac{x^m e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{1-m} \Gamma (m,-(m+1) \text{ProductLog}(a x))}{a (m+1) \text{ProductLog}(a x)}+\frac{x^m e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{-m} \Gamma (m+1,-(m+1) \text{ProductLog}(a x))}{a (m+1)}",1,"(x^m*(-((1 + m)*Gamma[m, -((1 + m)*ProductLog[a*x])]) + Gamma[1 + m, -((1 + m)*ProductLog[a*x])]))/(a*E^(m*ProductLog[a*x])*(1 + m)*(-((1 + m)*ProductLog[a*x]))^m)","A",1
148,1,60,109,0.0187371,"\int \frac{x^m}{\text{ProductLog}(a x)^2} \, dx","Integrate[x^m/ProductLog[a*x]^2,x]","\frac{x^m e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{-m} ((m+1) \Gamma (m-1,-(m+1) \text{ProductLog}(a x))-\Gamma (m,-(m+1) \text{ProductLog}(a x)))}{a}","\frac{x^m e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{1-m} \Gamma (m,-(m+1) \text{ProductLog}(a x))}{a (m+1) \text{ProductLog}(a x)}+\frac{x^m e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{2-m} \Gamma (m-1,-(m+1) \text{ProductLog}(a x))}{a (m+1) \text{ProductLog}(a x)^2}",1,"(x^m*((1 + m)*Gamma[-1 + m, -((1 + m)*ProductLog[a*x])] - Gamma[m, -((1 + m)*ProductLog[a*x])]))/(a*E^(m*ProductLog[a*x])*(-((1 + m)*ProductLog[a*x]))^m)","A",1
149,1,85,130,0.0682908,"\int x^m \sqrt{c \text{ProductLog}(a x)} \, dx","Integrate[x^m*Sqrt[c*ProductLog[a*x]],x]","\frac{x^m \sqrt{c \text{ProductLog}(a x)} e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{-m-\frac{1}{2}} \left((m+1) \Gamma \left(m+\frac{3}{2},-(m+1) \text{ProductLog}(a x)\right)-\Gamma \left(m+\frac{5}{2},-(m+1) \text{ProductLog}(a x)\right)\right)}{a (m+1)^2}","\frac{x^m (c \text{ProductLog}(a x))^{3/2} e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{-m-\frac{3}{2}} \Gamma \left(m+\frac{5}{2},-(m+1) \text{ProductLog}(a x)\right)}{a c (m+1)}+\frac{x^m \sqrt{c \text{ProductLog}(a x)} e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{-m-\frac{1}{2}} \Gamma \left(m+\frac{3}{2},-(m+1) \text{ProductLog}(a x)\right)}{a (m+1)}",1,"(x^m*((1 + m)*Gamma[3/2 + m, -((1 + m)*ProductLog[a*x])] - Gamma[5/2 + m, -((1 + m)*ProductLog[a*x])])*Sqrt[c*ProductLog[a*x]]*(-((1 + m)*ProductLog[a*x]))^(-1/2 - m))/(a*E^(m*ProductLog[a*x])*(1 + m)^2)","A",1
150,1,87,130,0.0774526,"\int \frac{x^m}{\sqrt{c \text{ProductLog}(a x)}} \, dx","Integrate[x^m/Sqrt[c*ProductLog[a*x]],x]","\frac{x^m \sqrt{c \text{ProductLog}(a x)} e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{-m-\frac{1}{2}} \left(\Gamma \left(m+\frac{3}{2},-(m+1) \text{ProductLog}(a x)\right)-(m+1) \Gamma \left(m+\frac{1}{2},-(m+1) \text{ProductLog}(a x)\right)\right)}{a c (m+1)}","\frac{x^m \sqrt{c \text{ProductLog}(a x)} e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{-m-\frac{1}{2}} \Gamma \left(m+\frac{3}{2},-(m+1) \text{ProductLog}(a x)\right)}{a c (m+1)}+\frac{x^m e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{\frac{1}{2}-m} \Gamma \left(m+\frac{1}{2},-(m+1) \text{ProductLog}(a x)\right)}{a (m+1) \sqrt{c \text{ProductLog}(a x)}}",1,"(x^m*(-((1 + m)*Gamma[1/2 + m, -((1 + m)*ProductLog[a*x])]) + Gamma[3/2 + m, -((1 + m)*ProductLog[a*x])])*Sqrt[c*ProductLog[a*x]]*(-((1 + m)*ProductLog[a*x]))^(-1/2 - m))/(a*c*E^(m*ProductLog[a*x])*(1 + m))","A",1
151,1,81,127,0.0365144,"\int x^m (c \text{ProductLog}(a x))^p \, dx","Integrate[x^m*(c*ProductLog[a*x])^p,x]","\frac{x^m e^{-m \text{ProductLog}(a x)} (c \text{ProductLog}(a x))^p (-(m+1) \text{ProductLog}(a x))^{-m-p} ((m+1) \Gamma (m+p+1,-(m+1) \text{ProductLog}(a x))-\Gamma (m+p+2,-(m+1) \text{ProductLog}(a x)))}{a (m+1)^2}","\frac{x^m e^{-m \text{ProductLog}(a x)} (c \text{ProductLog}(a x))^{p+1} (-(m+1) \text{ProductLog}(a x))^{-m-p-1} \Gamma (m+p+2,-(m+1) \text{ProductLog}(a x))}{a c (m+1)}+\frac{x^m e^{-m \text{ProductLog}(a x)} (c \text{ProductLog}(a x))^p (-(m+1) \text{ProductLog}(a x))^{-m-p} \Gamma (m+p+1,-(m+1) \text{ProductLog}(a x))}{a (m+1)}",1,"(x^m*((1 + m)*Gamma[1 + m + p, -((1 + m)*ProductLog[a*x])] - Gamma[2 + m + p, -((1 + m)*ProductLog[a*x])])*(c*ProductLog[a*x])^p*(-((1 + m)*ProductLog[a*x]))^(-m - p))/(a*E^(m*ProductLog[a*x])*(1 + m)^2)","A",1
152,0,0,13,0.0233128,"\int x^4 \text{ProductLog}\left(a x^2\right) \, dx","Integrate[x^4*ProductLog[a*x^2],x]","\int x^4 \text{ProductLog}\left(a x^2\right) \, dx","\text{Int}\left(x^4 \text{ProductLog}\left(a x^2\right),x\right)",0,"Integrate[x^4*ProductLog[a*x^2], x]","F",-1
153,1,51,51,0.0132546,"\int x^3 \text{ProductLog}\left(a x^2\right) \, dx","Integrate[x^3*ProductLog[a*x^2],x]","\frac{1}{4} x^4 \text{ProductLog}\left(a x^2\right)+\frac{x^4}{8 \text{ProductLog}\left(a x^2\right)}-\frac{x^4}{16 \text{ProductLog}\left(a x^2\right)^2}-\frac{x^4}{8}","\frac{1}{4} x^4 \text{ProductLog}\left(a x^2\right)+\frac{x^4}{8 \text{ProductLog}\left(a x^2\right)}-\frac{x^4}{16 \text{ProductLog}\left(a x^2\right)^2}-\frac{x^4}{8}",1,"-x^4/8 - x^4/(16*ProductLog[a*x^2]^2) + x^4/(8*ProductLog[a*x^2]) + (x^4*ProductLog[a*x^2])/4","A",1
154,0,0,13,0.0206175,"\int x^2 \text{ProductLog}\left(a x^2\right) \, dx","Integrate[x^2*ProductLog[a*x^2],x]","\int x^2 \text{ProductLog}\left(a x^2\right) \, dx","\text{Int}\left(x^2 \text{ProductLog}\left(a x^2\right),x\right)",0,"Integrate[x^2*ProductLog[a*x^2], x]","F",-1
155,1,33,36,0.0118584,"\int x \text{ProductLog}\left(a x^2\right) \, dx","Integrate[x*ProductLog[a*x^2],x]","\frac{x^2 \left(\text{ProductLog}\left(a x^2\right)^2-\text{ProductLog}\left(a x^2\right)+1\right)}{2 \text{ProductLog}\left(a x^2\right)}","\frac{1}{2} x^2 \text{ProductLog}\left(a x^2\right)+\frac{x^2}{2 \text{ProductLog}\left(a x^2\right)}-\frac{x^2}{2}",1,"(x^2*(1 - ProductLog[a*x^2] + ProductLog[a*x^2]^2))/(2*ProductLog[a*x^2])","A",1
156,0,0,9,0.0061276,"\int \text{ProductLog}\left(a x^2\right) \, dx","Integrate[ProductLog[a*x^2],x]","\int \text{ProductLog}\left(a x^2\right) \, dx","\text{Int}\left(\text{ProductLog}\left(a x^2\right),x\right)",0,"Integrate[ProductLog[a*x^2], x]","F",-1
157,1,23,23,0.0353725,"\int \frac{\text{ProductLog}\left(a x^2\right)}{x} \, dx","Integrate[ProductLog[a*x^2]/x,x]","\frac{1}{4} \text{ProductLog}\left(a x^2\right)^2+\frac{1}{2} \text{ProductLog}\left(a x^2\right)","\frac{1}{4} \text{ProductLog}\left(a x^2\right)^2+\frac{1}{2} \text{ProductLog}\left(a x^2\right)",1,"ProductLog[a*x^2]/2 + ProductLog[a*x^2]^2/4","A",1
158,0,0,13,0.023459,"\int \frac{\text{ProductLog}\left(a x^2\right)}{x^2} \, dx","Integrate[ProductLog[a*x^2]/x^2,x]","\int \frac{\text{ProductLog}\left(a x^2\right)}{x^2} \, dx","\text{Int}\left(\frac{\text{ProductLog}\left(a x^2\right)}{x^2},x\right)",0,"Integrate[ProductLog[a*x^2]/x^2, x]","F",-1
159,1,28,28,0.0072558,"\int \frac{\text{ProductLog}\left(a x^2\right)}{x^3} \, dx","Integrate[ProductLog[a*x^2]/x^3,x]","\frac{1}{2} a \text{Ei}\left(-\text{ProductLog}\left(a x^2\right)\right)-\frac{\text{ProductLog}\left(a x^2\right)}{2 x^2}","\frac{1}{2} a \text{Ei}\left(-\text{ProductLog}\left(a x^2\right)\right)-\frac{\text{ProductLog}\left(a x^2\right)}{2 x^2}",1,"(a*ExpIntegralEi[-ProductLog[a*x^2]])/2 - ProductLog[a*x^2]/(2*x^2)","A",1
160,0,0,13,0.0309892,"\int \frac{\text{ProductLog}\left(a x^2\right)}{x^4} \, dx","Integrate[ProductLog[a*x^2]/x^4,x]","\int \frac{\text{ProductLog}\left(a x^2\right)}{x^4} \, dx","\text{Int}\left(\frac{\text{ProductLog}\left(a x^2\right)}{x^4},x\right)",0,"Integrate[ProductLog[a*x^2]/x^4, x]","F",-1
161,1,30,30,0.0032426,"\int \frac{\text{ProductLog}\left(a x^2\right)}{x^5} \, dx","Integrate[ProductLog[a*x^2]/x^5,x]","-\frac{1}{2} a^2 \text{Ei}\left(-2 \text{ProductLog}\left(a x^2\right)\right)-\frac{\text{ProductLog}\left(a x^2\right)}{2 x^4}","-\frac{1}{2} a^2 \text{Ei}\left(-2 \text{ProductLog}\left(a x^2\right)\right)-\frac{\text{ProductLog}\left(a x^2\right)}{2 x^4}",1,"-(a^2*ExpIntegralEi[-2*ProductLog[a*x^2]])/2 - ProductLog[a*x^2]/(2*x^4)","A",1
162,0,0,13,0.0198454,"\int \frac{\text{ProductLog}\left(a x^2\right)}{x^6} \, dx","Integrate[ProductLog[a*x^2]/x^6,x]","\int \frac{\text{ProductLog}\left(a x^2\right)}{x^6} \, dx","\text{Int}\left(\frac{\text{ProductLog}\left(a x^2\right)}{x^6},x\right)",0,"Integrate[ProductLog[a*x^2]/x^6, x]","F",-1
163,1,45,45,0.0053863,"\int \frac{\text{ProductLog}\left(a x^2\right)}{x^7} \, dx","Integrate[ProductLog[a*x^2]/x^7,x]","\frac{3}{4} a^3 \text{Ei}\left(-3 \text{ProductLog}\left(a x^2\right)\right)+\frac{\text{ProductLog}\left(a x^2\right)^2}{4 x^6}-\frac{\text{ProductLog}\left(a x^2\right)}{4 x^6}","\frac{3}{4} a^3 \text{Ei}\left(-3 \text{ProductLog}\left(a x^2\right)\right)+\frac{\text{ProductLog}\left(a x^2\right)^2}{4 x^6}-\frac{\text{ProductLog}\left(a x^2\right)}{4 x^6}",1,"(3*a^3*ExpIntegralEi[-3*ProductLog[a*x^2]])/4 - ProductLog[a*x^2]/(4*x^6) + ProductLog[a*x^2]^2/(4*x^6)","A",1
164,1,66,66,0.0134103,"\int x^3 \text{ProductLog}\left(a x^2\right)^2 \, dx","Integrate[x^3*ProductLog[a*x^2]^2,x]","\frac{1}{4} x^4 \text{ProductLog}\left(a x^2\right)^2-\frac{1}{4} x^4 \text{ProductLog}\left(a x^2\right)-\frac{3 x^4}{8 \text{ProductLog}\left(a x^2\right)}+\frac{3 x^4}{16 \text{ProductLog}\left(a x^2\right)^2}+\frac{3 x^4}{8}","\frac{1}{4} x^4 \text{ProductLog}\left(a x^2\right)^2-\frac{1}{4} x^4 \text{ProductLog}\left(a x^2\right)-\frac{3 x^4}{8 \text{ProductLog}\left(a x^2\right)}+\frac{3 x^4}{16 \text{ProductLog}\left(a x^2\right)^2}+\frac{3 x^4}{8}",1,"(3*x^4)/8 + (3*x^4)/(16*ProductLog[a*x^2]^2) - (3*x^4)/(8*ProductLog[a*x^2]) - (x^4*ProductLog[a*x^2])/4 + (x^4*ProductLog[a*x^2]^2)/4","A",1
165,0,0,15,0.0314382,"\int x^2 \text{ProductLog}\left(a x^2\right)^2 \, dx","Integrate[x^2*ProductLog[a*x^2]^2,x]","\int x^2 \text{ProductLog}\left(a x^2\right)^2 \, dx","\text{Int}\left(x^2 \text{ProductLog}\left(a x^2\right)^2,x\right)",0,"Integrate[x^2*ProductLog[a*x^2]^2, x]","F",-1
166,1,43,45,0.0174393,"\int x \text{ProductLog}\left(a x^2\right)^2 \, dx","Integrate[x*ProductLog[a*x^2]^2,x]","\frac{x^2 \left(\text{ProductLog}\left(a x^2\right)^3-2 \text{ProductLog}\left(a x^2\right)^2+4 \text{ProductLog}\left(a x^2\right)-4\right)}{2 \text{ProductLog}\left(a x^2\right)}","\frac{1}{2} x^2 \text{ProductLog}\left(a x^2\right)^2-x^2 \text{ProductLog}\left(a x^2\right)-\frac{2 x^2}{\text{ProductLog}\left(a x^2\right)}+2 x^2",1,"(x^2*(-4 + 4*ProductLog[a*x^2] - 2*ProductLog[a*x^2]^2 + ProductLog[a*x^2]^3))/(2*ProductLog[a*x^2])","A",1
167,0,0,11,0.0049415,"\int \text{ProductLog}\left(a x^2\right)^2 \, dx","Integrate[ProductLog[a*x^2]^2,x]","\int \text{ProductLog}\left(a x^2\right)^2 \, dx","\text{Int}\left(\text{ProductLog}\left(a x^2\right)^2,x\right)",0,"Integrate[ProductLog[a*x^2]^2, x]","F",-1
168,1,25,25,0.0279012,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x} \, dx","Integrate[ProductLog[a*x^2]^2/x,x]","\frac{1}{6} \text{ProductLog}\left(a x^2\right)^3+\frac{1}{4} \text{ProductLog}\left(a x^2\right)^2","\frac{1}{6} \text{ProductLog}\left(a x^2\right)^3+\frac{1}{4} \text{ProductLog}\left(a x^2\right)^2",1,"ProductLog[a*x^2]^2/4 + ProductLog[a*x^2]^3/6","A",1
169,0,0,15,0.0313805,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^2} \, dx","Integrate[ProductLog[a*x^2]^2/x^2,x]","\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^2} \, dx","\text{Int}\left(\frac{\text{ProductLog}\left(a x^2\right)^2}{x^2},x\right)",0,"Integrate[ProductLog[a*x^2]^2/x^2, x]","F",-1
170,1,27,27,0.0048424,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^3} \, dx","Integrate[ProductLog[a*x^2]^2/x^3,x]","-\frac{\text{ProductLog}\left(a x^2\right)^2}{2 x^2}-\frac{\text{ProductLog}\left(a x^2\right)}{x^2}","-\frac{\text{ProductLog}\left(a x^2\right)^2}{2 x^2}-\frac{\text{ProductLog}\left(a x^2\right)}{x^2}",1,"-(ProductLog[a*x^2]/x^2) - ProductLog[a*x^2]^2/(2*x^2)","A",1
171,0,0,15,0.0238776,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^4} \, dx","Integrate[ProductLog[a*x^2]^2/x^4,x]","\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^4} \, dx","\text{Int}\left(\frac{\text{ProductLog}\left(a x^2\right)^2}{x^4},x\right)",0,"Integrate[ProductLog[a*x^2]^2/x^4, x]","F",-1
172,1,32,32,0.0062414,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^5} \, dx","Integrate[ProductLog[a*x^2]^2/x^5,x]","\frac{1}{2} a^2 \text{Ei}\left(-2 \text{ProductLog}\left(a x^2\right)\right)-\frac{\text{ProductLog}\left(a x^2\right)^2}{4 x^4}","\frac{1}{2} a^2 \text{Ei}\left(-2 \text{ProductLog}\left(a x^2\right)\right)-\frac{\text{ProductLog}\left(a x^2\right)^2}{4 x^4}",1,"(a^2*ExpIntegralEi[-2*ProductLog[a*x^2]])/2 - ProductLog[a*x^2]^2/(4*x^4)","A",1
173,0,0,15,0.0276003,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^6} \, dx","Integrate[ProductLog[a*x^2]^2/x^6,x]","\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^6} \, dx","\text{Int}\left(\frac{\text{ProductLog}\left(a x^2\right)^2}{x^6},x\right)",0,"Integrate[ProductLog[a*x^2]^2/x^6, x]","F",-1
174,1,30,30,0.0034291,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^7} \, dx","Integrate[ProductLog[a*x^2]^2/x^7,x]","a^3 \left(-\text{Ei}\left(-3 \text{ProductLog}\left(a x^2\right)\right)\right)-\frac{\text{ProductLog}\left(a x^2\right)^2}{2 x^6}","a^3 \left(-\text{Ei}\left(-3 \text{ProductLog}\left(a x^2\right)\right)\right)-\frac{\text{ProductLog}\left(a x^2\right)^2}{2 x^6}",1,"-(a^3*ExpIntegralEi[-3*ProductLog[a*x^2]]) - ProductLog[a*x^2]^2/(2*x^6)","A",1
175,0,0,15,0.0293274,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^8} \, dx","Integrate[ProductLog[a*x^2]^2/x^8,x]","\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^8} \, dx","\text{Int}\left(\frac{\text{ProductLog}\left(a x^2\right)^2}{x^8},x\right)",0,"Integrate[ProductLog[a*x^2]^2/x^8, x]","F",-1
176,1,45,45,0.0093343,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^9} \, dx","Integrate[ProductLog[a*x^2]^2/x^9,x]","2 a^4 \text{Ei}\left(-4 \text{ProductLog}\left(a x^2\right)\right)+\frac{\text{ProductLog}\left(a x^2\right)^3}{2 x^8}-\frac{\text{ProductLog}\left(a x^2\right)^2}{4 x^8}","2 a^4 \text{Ei}\left(-4 \text{ProductLog}\left(a x^2\right)\right)+\frac{\text{ProductLog}\left(a x^2\right)^3}{2 x^8}-\frac{\text{ProductLog}\left(a x^2\right)^2}{4 x^8}",1,"2*a^4*ExpIntegralEi[-4*ProductLog[a*x^2]] - ProductLog[a*x^2]^2/(4*x^8) + ProductLog[a*x^2]^3/(2*x^8)","A",1
177,0,0,15,0.0289001,"\int x^2 \text{ProductLog}\left(a x^2\right)^3 \, dx","Integrate[x^2*ProductLog[a*x^2]^3,x]","\int x^2 \text{ProductLog}\left(a x^2\right)^3 \, dx","\text{Int}\left(x^2 \text{ProductLog}\left(a x^2\right)^3,x\right)",0,"Integrate[x^2*ProductLog[a*x^2]^3, x]","F",-1
178,1,43,62,0.0232665,"\int x \text{ProductLog}\left(a x^2\right)^3 \, dx","Integrate[x*ProductLog[a*x^2]^3,x]","\frac{x^2 \left(\text{ProductLog}\left(a x^2\right)^2+6\right) \left(\text{ProductLog}\left(a x^2\right)^2-3 \text{ProductLog}\left(a x^2\right)+3\right)}{2 \text{ProductLog}\left(a x^2\right)}","\frac{1}{2} x^2 \text{ProductLog}\left(a x^2\right)^3-\frac{3}{2} x^2 \text{ProductLog}\left(a x^2\right)^2+\frac{9}{2} x^2 \text{ProductLog}\left(a x^2\right)+\frac{9 x^2}{\text{ProductLog}\left(a x^2\right)}-9 x^2",1,"(x^2*(6 + ProductLog[a*x^2]^2)*(3 - 3*ProductLog[a*x^2] + ProductLog[a*x^2]^2))/(2*ProductLog[a*x^2])","A",1
179,0,0,11,0.0049786,"\int \text{ProductLog}\left(a x^2\right)^3 \, dx","Integrate[ProductLog[a*x^2]^3,x]","\int \text{ProductLog}\left(a x^2\right)^3 \, dx","\text{Int}\left(\text{ProductLog}\left(a x^2\right)^3,x\right)",0,"Integrate[ProductLog[a*x^2]^3, x]","F",-1
180,1,25,25,0.0232673,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x} \, dx","Integrate[ProductLog[a*x^2]^3/x,x]","\frac{1}{8} \text{ProductLog}\left(a x^2\right)^4+\frac{1}{6} \text{ProductLog}\left(a x^2\right)^3","\frac{1}{8} \text{ProductLog}\left(a x^2\right)^4+\frac{1}{6} \text{ProductLog}\left(a x^2\right)^3",1,"ProductLog[a*x^2]^3/6 + ProductLog[a*x^2]^4/8","A",1
181,0,0,15,0.0281546,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^2} \, dx","Integrate[ProductLog[a*x^2]^3/x^2,x]","\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^2} \, dx","\text{Int}\left(\frac{\text{ProductLog}\left(a x^2\right)^3}{x^2},x\right)",0,"Integrate[ProductLog[a*x^2]^3/x^2, x]","F",-1
182,1,44,44,0.005081,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^3} \, dx","Integrate[ProductLog[a*x^2]^3/x^3,x]","-\frac{\text{ProductLog}\left(a x^2\right)^3}{2 x^2}-\frac{3 \text{ProductLog}\left(a x^2\right)^2}{2 x^2}-\frac{3 \text{ProductLog}\left(a x^2\right)}{2 x^2}","-\frac{\text{ProductLog}\left(a x^2\right)^3}{2 x^2}-\frac{3 \text{ProductLog}\left(a x^2\right)^2}{2 x^2}-\frac{3 \text{ProductLog}\left(a x^2\right)}{2 x^2}",1,"(-3*ProductLog[a*x^2])/(2*x^2) - (3*ProductLog[a*x^2]^2)/(2*x^2) - ProductLog[a*x^2]^3/(2*x^2)","A",1
183,0,0,15,0.0308627,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^4} \, dx","Integrate[ProductLog[a*x^2]^3/x^4,x]","\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^4} \, dx","\text{Int}\left(\frac{\text{ProductLog}\left(a x^2\right)^3}{x^4},x\right)",0,"Integrate[ProductLog[a*x^2]^3/x^4, x]","F",-1
184,1,31,31,0.0029473,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^5} \, dx","Integrate[ProductLog[a*x^2]^3/x^5,x]","-\frac{\text{ProductLog}\left(a x^2\right)^3}{4 x^4}-\frac{3 \text{ProductLog}\left(a x^2\right)^2}{8 x^4}","-\frac{\text{ProductLog}\left(a x^2\right)^3}{4 x^4}-\frac{3 \text{ProductLog}\left(a x^2\right)^2}{8 x^4}",1,"(-3*ProductLog[a*x^2]^2)/(8*x^4) - ProductLog[a*x^2]^3/(4*x^4)","A",1
185,0,0,15,0.0245595,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^6} \, dx","Integrate[ProductLog[a*x^2]^3/x^6,x]","\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^6} \, dx","\text{Int}\left(\frac{\text{ProductLog}\left(a x^2\right)^3}{x^6},x\right)",0,"Integrate[ProductLog[a*x^2]^3/x^6, x]","F",-1
186,1,32,32,0.0053953,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^7} \, dx","Integrate[ProductLog[a*x^2]^3/x^7,x]","\frac{1}{2} a^3 \text{Ei}\left(-3 \text{ProductLog}\left(a x^2\right)\right)-\frac{\text{ProductLog}\left(a x^2\right)^3}{6 x^6}","\frac{1}{2} a^3 \text{Ei}\left(-3 \text{ProductLog}\left(a x^2\right)\right)-\frac{\text{ProductLog}\left(a x^2\right)^3}{6 x^6}",1,"(a^3*ExpIntegralEi[-3*ProductLog[a*x^2]])/2 - ProductLog[a*x^2]^3/(6*x^6)","A",1
187,0,0,15,0.027088,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^8} \, dx","Integrate[ProductLog[a*x^2]^3/x^8,x]","\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^8} \, dx","\text{Int}\left(\frac{\text{ProductLog}\left(a x^2\right)^3}{x^8},x\right)",0,"Integrate[ProductLog[a*x^2]^3/x^8, x]","F",-1
188,1,32,32,0.0031555,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^9} \, dx","Integrate[ProductLog[a*x^2]^3/x^9,x]","-\frac{3}{2} a^4 \text{Ei}\left(-4 \text{ProductLog}\left(a x^2\right)\right)-\frac{\text{ProductLog}\left(a x^2\right)^3}{2 x^8}","-\frac{3}{2} a^4 \text{Ei}\left(-4 \text{ProductLog}\left(a x^2\right)\right)-\frac{\text{ProductLog}\left(a x^2\right)^3}{2 x^8}",1,"(-3*a^4*ExpIntegralEi[-4*ProductLog[a*x^2]])/2 - ProductLog[a*x^2]^3/(2*x^8)","A",1
189,1,46,46,0.0083143,"\int \frac{x^5}{\text{ProductLog}\left(a x^2\right)} \, dx","Integrate[x^5/ProductLog[a*x^2],x]","\frac{x^6}{6 \text{ProductLog}\left(a x^2\right)}+\frac{x^6}{18 \text{ProductLog}\left(a x^2\right)^2}-\frac{x^6}{54 \text{ProductLog}\left(a x^2\right)^3}","\frac{x^6}{6 \text{ProductLog}\left(a x^2\right)}+\frac{x^6}{18 \text{ProductLog}\left(a x^2\right)^2}-\frac{x^6}{54 \text{ProductLog}\left(a x^2\right)^3}",1,"-x^6/(54*ProductLog[a*x^2]^3) + x^6/(18*ProductLog[a*x^2]^2) + x^6/(6*ProductLog[a*x^2])","A",1
190,0,0,15,0.0327316,"\int \frac{x^4}{\text{ProductLog}\left(a x^2\right)} \, dx","Integrate[x^4/ProductLog[a*x^2],x]","\int \frac{x^4}{\text{ProductLog}\left(a x^2\right)} \, dx","\text{Int}\left(\frac{x^4}{\text{ProductLog}\left(a x^2\right)},x\right)",0,"Integrate[x^4/ProductLog[a*x^2], x]","F",-1
191,1,31,31,0.0030571,"\int \frac{x^3}{\text{ProductLog}\left(a x^2\right)} \, dx","Integrate[x^3/ProductLog[a*x^2],x]","\frac{x^4}{4 \text{ProductLog}\left(a x^2\right)}+\frac{x^4}{8 \text{ProductLog}\left(a x^2\right)^2}","\frac{x^4}{4 \text{ProductLog}\left(a x^2\right)}+\frac{x^4}{8 \text{ProductLog}\left(a x^2\right)^2}",1,"x^4/(8*ProductLog[a*x^2]^2) + x^4/(4*ProductLog[a*x^2])","A",1
192,0,0,15,0.021069,"\int \frac{x^2}{\text{ProductLog}\left(a x^2\right)} \, dx","Integrate[x^2/ProductLog[a*x^2],x]","\int \frac{x^2}{\text{ProductLog}\left(a x^2\right)} \, dx","\text{Int}\left(\frac{x^2}{\text{ProductLog}\left(a x^2\right)},x\right)",0,"Integrate[x^2/ProductLog[a*x^2], x]","F",-1
193,1,30,30,0.0041133,"\int \frac{x}{\text{ProductLog}\left(a x^2\right)} \, dx","Integrate[x/ProductLog[a*x^2],x]","\frac{\text{Ei}\left(\text{ProductLog}\left(a x^2\right)\right)}{2 a}+\frac{x^2}{2 \text{ProductLog}\left(a x^2\right)}","\frac{\text{Ei}\left(\text{ProductLog}\left(a x^2\right)\right)}{2 a}+\frac{x^2}{2 \text{ProductLog}\left(a x^2\right)}",1,"ExpIntegralEi[ProductLog[a*x^2]]/(2*a) + x^2/(2*ProductLog[a*x^2])","A",1
194,0,0,11,0.0046206,"\int \frac{1}{\text{ProductLog}\left(a x^2\right)} \, dx","Integrate[ProductLog[a*x^2]^(-1),x]","\int \frac{1}{\text{ProductLog}\left(a x^2\right)} \, dx","\text{Int}\left(\frac{1}{\text{ProductLog}\left(a x^2\right)},x\right)",0,"Integrate[ProductLog[a*x^2]^(-1), x]","F",-1
195,1,24,24,0.0128393,"\int \frac{1}{x \text{ProductLog}\left(a x^2\right)} \, dx","Integrate[1/(x*ProductLog[a*x^2]),x]","\frac{1}{2} \log \left(\text{ProductLog}\left(a x^2\right)\right)-\frac{1}{2 \text{ProductLog}\left(a x^2\right)}","\frac{1}{2} \log \left(\text{ProductLog}\left(a x^2\right)\right)-\frac{1}{2 \text{ProductLog}\left(a x^2\right)}",1,"Log[ProductLog[a*x^2]]/2 - 1/(2*ProductLog[a*x^2])","A",1
196,0,0,15,0.0258122,"\int \frac{1}{x^2 \text{ProductLog}\left(a x^2\right)} \, dx","Integrate[1/(x^2*ProductLog[a*x^2]),x]","\int \frac{1}{x^2 \text{ProductLog}\left(a x^2\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \text{ProductLog}\left(a x^2\right)},x\right)",0,"Integrate[1/(x^2*ProductLog[a*x^2]), x]","F",-1
197,1,37,37,0.0109194,"\int \frac{1}{x^3 \text{ProductLog}\left(a x^2\right)} \, dx","Integrate[1/(x^3*ProductLog[a*x^2]),x]","-\frac{1}{4} a \text{Ei}\left(-\text{ProductLog}\left(a x^2\right)\right)-\frac{1}{4 x^2 \text{ProductLog}\left(a x^2\right)}-\frac{1}{4 x^2}","-\frac{1}{4} a \text{Ei}\left(-\text{ProductLog}\left(a x^2\right)\right)-\frac{1}{4 x^2 \text{ProductLog}\left(a x^2\right)}-\frac{1}{4 x^2}",1,"-1/(4*x^2) - (a*ExpIntegralEi[-ProductLog[a*x^2]])/4 - 1/(4*x^2*ProductLog[a*x^2])","A",1
198,0,0,15,0.0215433,"\int \frac{1}{x^4 \text{ProductLog}\left(a x^2\right)} \, dx","Integrate[1/(x^4*ProductLog[a*x^2]),x]","\int \frac{1}{x^4 \text{ProductLog}\left(a x^2\right)} \, dx","\text{Int}\left(\frac{1}{x^4 \text{ProductLog}\left(a x^2\right)},x\right)",0,"Integrate[1/(x^4*ProductLog[a*x^2]), x]","F",-1
199,1,52,52,0.013266,"\int \frac{1}{x^5 \text{ProductLog}\left(a x^2\right)} \, dx","Integrate[1/(x^5*ProductLog[a*x^2]),x]","\frac{1}{3} a^2 \text{Ei}\left(-2 \text{ProductLog}\left(a x^2\right)\right)+\frac{\text{ProductLog}\left(a x^2\right)}{6 x^4}-\frac{1}{6 x^4 \text{ProductLog}\left(a x^2\right)}-\frac{1}{12 x^4}","\frac{1}{3} a^2 \text{Ei}\left(-2 \text{ProductLog}\left(a x^2\right)\right)+\frac{\text{ProductLog}\left(a x^2\right)}{6 x^4}-\frac{1}{6 x^4 \text{ProductLog}\left(a x^2\right)}-\frac{1}{12 x^4}",1,"-1/(12*x^4) + (a^2*ExpIntegralEi[-2*ProductLog[a*x^2]])/3 - 1/(6*x^4*ProductLog[a*x^2]) + ProductLog[a*x^2]/(6*x^4)","A",1
200,1,46,46,0.0050843,"\int \frac{x^7}{\text{ProductLog}\left(a x^2\right)^2} \, dx","Integrate[x^7/ProductLog[a*x^2]^2,x]","\frac{x^8}{8 \text{ProductLog}\left(a x^2\right)^2}+\frac{x^8}{16 \text{ProductLog}\left(a x^2\right)^3}-\frac{x^8}{64 \text{ProductLog}\left(a x^2\right)^4}","\frac{x^8}{8 \text{ProductLog}\left(a x^2\right)^2}+\frac{x^8}{16 \text{ProductLog}\left(a x^2\right)^3}-\frac{x^8}{64 \text{ProductLog}\left(a x^2\right)^4}",1,"-x^8/(64*ProductLog[a*x^2]^4) + x^8/(16*ProductLog[a*x^2]^3) + x^8/(8*ProductLog[a*x^2]^2)","A",1
201,0,0,15,0.0271486,"\int \frac{x^6}{\text{ProductLog}\left(a x^2\right)^2} \, dx","Integrate[x^6/ProductLog[a*x^2]^2,x]","\int \frac{x^6}{\text{ProductLog}\left(a x^2\right)^2} \, dx","\text{Int}\left(\frac{x^6}{\text{ProductLog}\left(a x^2\right)^2},x\right)",0,"Integrate[x^6/ProductLog[a*x^2]^2, x]","F",-1
202,1,31,31,0.003096,"\int \frac{x^5}{\text{ProductLog}\left(a x^2\right)^2} \, dx","Integrate[x^5/ProductLog[a*x^2]^2,x]","\frac{x^6}{6 \text{ProductLog}\left(a x^2\right)^2}+\frac{x^6}{9 \text{ProductLog}\left(a x^2\right)^3}","\frac{x^6}{6 \text{ProductLog}\left(a x^2\right)^2}+\frac{x^6}{9 \text{ProductLog}\left(a x^2\right)^3}",1,"x^6/(9*ProductLog[a*x^2]^3) + x^6/(6*ProductLog[a*x^2]^2)","A",1
203,0,0,15,0.0270828,"\int \frac{x^4}{\text{ProductLog}\left(a x^2\right)^2} \, dx","Integrate[x^4/ProductLog[a*x^2]^2,x]","\int \frac{x^4}{\text{ProductLog}\left(a x^2\right)^2} \, dx","\text{Int}\left(\frac{x^4}{\text{ProductLog}\left(a x^2\right)^2},x\right)",0,"Integrate[x^4/ProductLog[a*x^2]^2, x]","F",-1
204,1,32,32,0.0030668,"\int \frac{x^3}{\text{ProductLog}\left(a x^2\right)^2} \, dx","Integrate[x^3/ProductLog[a*x^2]^2,x]","\frac{\text{Ei}\left(2 \text{ProductLog}\left(a x^2\right)\right)}{2 a^2}+\frac{x^4}{4 \text{ProductLog}\left(a x^2\right)^2}","\frac{\text{Ei}\left(2 \text{ProductLog}\left(a x^2\right)\right)}{2 a^2}+\frac{x^4}{4 \text{ProductLog}\left(a x^2\right)^2}",1,"ExpIntegralEi[2*ProductLog[a*x^2]]/(2*a^2) + x^4/(4*ProductLog[a*x^2]^2)","A",1
205,0,0,15,0.023012,"\int \frac{x^2}{\text{ProductLog}\left(a x^2\right)^2} \, dx","Integrate[x^2/ProductLog[a*x^2]^2,x]","\int \frac{x^2}{\text{ProductLog}\left(a x^2\right)^2} \, dx","\text{Int}\left(\frac{x^2}{\text{ProductLog}\left(a x^2\right)^2},x\right)",0,"Integrate[x^2/ProductLog[a*x^2]^2, x]","F",-1
206,1,27,27,0.0025025,"\int \frac{x}{\text{ProductLog}\left(a x^2\right)^2} \, dx","Integrate[x/ProductLog[a*x^2]^2,x]","\frac{\text{Ei}\left(\text{ProductLog}\left(a x^2\right)\right)}{a}-\frac{x^2}{2 \text{ProductLog}\left(a x^2\right)^2}","\frac{\text{Ei}\left(\text{ProductLog}\left(a x^2\right)\right)}{a}-\frac{x^2}{2 \text{ProductLog}\left(a x^2\right)^2}",1,"ExpIntegralEi[ProductLog[a*x^2]]/a - x^2/(2*ProductLog[a*x^2]^2)","A",1
207,0,0,11,0.0064198,"\int \frac{1}{\text{ProductLog}\left(a x^2\right)^2} \, dx","Integrate[ProductLog[a*x^2]^(-2),x]","\int \frac{1}{\text{ProductLog}\left(a x^2\right)^2} \, dx","\text{Int}\left(\frac{1}{\text{ProductLog}\left(a x^2\right)^2},x\right)",0,"Integrate[ProductLog[a*x^2]^(-2), x]","F",-1
208,1,25,25,0.0279976,"\int \frac{1}{x \text{ProductLog}\left(a x^2\right)^2} \, dx","Integrate[1/(x*ProductLog[a*x^2]^2),x]","-\frac{1}{2 \text{ProductLog}\left(a x^2\right)}-\frac{1}{4 \text{ProductLog}\left(a x^2\right)^2}","-\frac{1}{2 \text{ProductLog}\left(a x^2\right)}-\frac{1}{4 \text{ProductLog}\left(a x^2\right)^2}",1,"-1/(4*ProductLog[a*x^2]^2) - 1/(2*ProductLog[a*x^2])","A",1
209,0,0,15,0.0301895,"\int \frac{1}{x^2 \text{ProductLog}\left(a x^2\right)^2} \, dx","Integrate[1/(x^2*ProductLog[a*x^2]^2),x]","\int \frac{1}{x^2 \text{ProductLog}\left(a x^2\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \text{ProductLog}\left(a x^2\right)^2},x\right)",0,"Integrate[1/(x^2*ProductLog[a*x^2]^2), x]","F",-1
210,1,52,52,0.013481,"\int \frac{1}{x^3 \text{ProductLog}\left(a x^2\right)^2} \, dx","Integrate[1/(x^3*ProductLog[a*x^2]^2),x]","\frac{1}{6} a \text{Ei}\left(-\text{ProductLog}\left(a x^2\right)\right)-\frac{1}{6 x^2 \text{ProductLog}\left(a x^2\right)}-\frac{1}{6 x^2 \text{ProductLog}\left(a x^2\right)^2}+\frac{1}{6 x^2}","\frac{1}{6} a \text{Ei}\left(-\text{ProductLog}\left(a x^2\right)\right)-\frac{1}{6 x^2 \text{ProductLog}\left(a x^2\right)}-\frac{1}{6 x^2 \text{ProductLog}\left(a x^2\right)^2}+\frac{1}{6 x^2}",1,"1/(6*x^2) + (a*ExpIntegralEi[-ProductLog[a*x^2]])/6 - 1/(6*x^2*ProductLog[a*x^2]^2) - 1/(6*x^2*ProductLog[a*x^2])","A",1
211,1,128,143,0.0262006,"\int x^7 \sqrt{c \text{ProductLog}\left(a x^2\right)} \, dx","Integrate[x^7*Sqrt[c*ProductLog[a*x^2]],x]","\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)} \left(16384 a^4 x^8 \text{ProductLog}\left(a x^2\right)^4-2048 a^4 x^8 \text{ProductLog}\left(a x^2\right)^3+1792 a^4 x^8 \text{ProductLog}\left(a x^2\right)^2-1120 a^4 x^8 \text{ProductLog}\left(a x^2\right)+420 a^4 x^8-105 \sqrt{\pi } \text{ProductLog}\left(a x^2\right)^{7/2} \text{Erfi}\left(2 \sqrt{\text{ProductLog}\left(a x^2\right)}\right)\right)}{131072 a^4 \text{ProductLog}\left(a x^2\right)^4}","-\frac{105 \sqrt{\pi } \sqrt{c} \text{Erfi}\left(\frac{2 \sqrt{c \text{ProductLog}\left(a x^2\right)}}{\sqrt{c}}\right)}{131072 a^4}+\frac{105 c^4 x^8}{32768 \left(c \text{ProductLog}\left(a x^2\right)\right)^{7/2}}-\frac{35 c^3 x^8}{4096 \left(c \text{ProductLog}\left(a x^2\right)\right)^{5/2}}+\frac{7 c^2 x^8}{512 \left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}+\frac{1}{8} x^8 \sqrt{c \text{ProductLog}\left(a x^2\right)}-\frac{c x^8}{64 \sqrt{c \text{ProductLog}\left(a x^2\right)}}",1,"(Sqrt[c*ProductLog[a*x^2]]*(420*a^4*x^8 - 1120*a^4*x^8*ProductLog[a*x^2] + 1792*a^4*x^8*ProductLog[a*x^2]^2 - 2048*a^4*x^8*ProductLog[a*x^2]^3 - 105*Sqrt[Pi]*Erfi[2*Sqrt[ProductLog[a*x^2]]]*ProductLog[a*x^2]^(7/2) + 16384*a^4*x^8*ProductLog[a*x^2]^4))/(131072*a^4*ProductLog[a*x^2]^4)","A",0
212,1,67,106,0.0168848,"\int x^6 \sqrt{c \text{ProductLog}\left(a x^2\right)} \, dx","Integrate[x^6*Sqrt[c*ProductLog[a*x^2]],x]","\frac{x^7 \left(2401 \text{ProductLog}\left(a x^2\right)^4-343 \text{ProductLog}\left(a x^2\right)^3+294 \text{ProductLog}\left(a x^2\right)^2-168 \text{ProductLog}\left(a x^2\right)+48\right) \sqrt{c \text{ProductLog}\left(a x^2\right)}}{16807 \text{ProductLog}\left(a x^2\right)^4}","\frac{48 c^4 x^7}{16807 \left(c \text{ProductLog}\left(a x^2\right)\right)^{7/2}}-\frac{24 c^3 x^7}{2401 \left(c \text{ProductLog}\left(a x^2\right)\right)^{5/2}}+\frac{6 c^2 x^7}{343 \left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}+\frac{1}{7} x^7 \sqrt{c \text{ProductLog}\left(a x^2\right)}-\frac{c x^7}{49 \sqrt{c \text{ProductLog}\left(a x^2\right)}}",1,"(x^7*Sqrt[c*ProductLog[a*x^2]]*(48 - 168*ProductLog[a*x^2] + 294*ProductLog[a*x^2]^2 - 343*ProductLog[a*x^2]^3 + 2401*ProductLog[a*x^2]^4))/(16807*ProductLog[a*x^2]^4)","A",1
213,1,118,129,0.0307168,"\int x^5 \sqrt{c \text{ProductLog}\left(a x^2\right)} \, dx","Integrate[x^5*Sqrt[c*ProductLog[a*x^2]],x]","\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)} \left(432 a^3 x^6 \text{ProductLog}\left(a x^2\right)^3-72 a^3 x^6 \text{ProductLog}\left(a x^2\right)^2+60 a^3 x^6 \text{ProductLog}\left(a x^2\right)-30 a^3 x^6+5 \sqrt{3 \pi } \text{ProductLog}\left(a x^2\right)^{5/2} \text{Erfi}\left(\sqrt{3} \sqrt{\text{ProductLog}\left(a x^2\right)}\right)\right)}{2592 a^3 \text{ProductLog}\left(a x^2\right)^3}","\frac{5 \sqrt{\frac{\pi }{3}} \sqrt{c} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{c \text{ProductLog}\left(a x^2\right)}}{\sqrt{c}}\right)}{864 a^3}-\frac{5 c^3 x^6}{432 \left(c \text{ProductLog}\left(a x^2\right)\right)^{5/2}}+\frac{5 c^2 x^6}{216 \left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}+\frac{1}{6} x^6 \sqrt{c \text{ProductLog}\left(a x^2\right)}-\frac{c x^6}{36 \sqrt{c \text{ProductLog}\left(a x^2\right)}}",1,"(Sqrt[c*ProductLog[a*x^2]]*(-30*a^3*x^6 + 60*a^3*x^6*ProductLog[a*x^2] - 72*a^3*x^6*ProductLog[a*x^2]^2 + 5*Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ProductLog[a*x^2]]]*ProductLog[a*x^2]^(5/2) + 432*a^3*x^6*ProductLog[a*x^2]^3))/(2592*a^3*ProductLog[a*x^2]^3)","A",0
214,1,57,84,0.0173051,"\int x^4 \sqrt{c \text{ProductLog}\left(a x^2\right)} \, dx","Integrate[x^4*Sqrt[c*ProductLog[a*x^2]],x]","\frac{x^5 \left(125 \text{ProductLog}\left(a x^2\right)^3-25 \text{ProductLog}\left(a x^2\right)^2+20 \text{ProductLog}\left(a x^2\right)-8\right) \sqrt{c \text{ProductLog}\left(a x^2\right)}}{625 \text{ProductLog}\left(a x^2\right)^3}","-\frac{8 c^3 x^5}{625 \left(c \text{ProductLog}\left(a x^2\right)\right)^{5/2}}+\frac{4 c^2 x^5}{125 \left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}+\frac{1}{5} x^5 \sqrt{c \text{ProductLog}\left(a x^2\right)}-\frac{c x^5}{25 \sqrt{c \text{ProductLog}\left(a x^2\right)}}",1,"(x^5*Sqrt[c*ProductLog[a*x^2]]*(-8 + 20*ProductLog[a*x^2] - 25*ProductLog[a*x^2]^2 + 125*ProductLog[a*x^2]^3))/(625*ProductLog[a*x^2]^3)","A",1
215,1,102,107,0.0258852,"\int x^3 \sqrt{c \text{ProductLog}\left(a x^2\right)} \, dx","Integrate[x^3*Sqrt[c*ProductLog[a*x^2]],x]","\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)} \left(64 a^2 x^4 \text{ProductLog}\left(a x^2\right)^2-16 a^2 x^4 \text{ProductLog}\left(a x^2\right)+12 a^2 x^4-3 \sqrt{2 \pi } \text{ProductLog}\left(a x^2\right)^{3/2} \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^2\right)}\right)\right)}{256 a^2 \text{ProductLog}\left(a x^2\right)^2}","-\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{c} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^2\right)}}{\sqrt{c}}\right)}{128 a^2}+\frac{3 c^2 x^4}{64 \left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}+\frac{1}{4} x^4 \sqrt{c \text{ProductLog}\left(a x^2\right)}-\frac{c x^4}{16 \sqrt{c \text{ProductLog}\left(a x^2\right)}}",1,"(Sqrt[c*ProductLog[a*x^2]]*(12*a^2*x^4 - 16*a^2*x^4*ProductLog[a*x^2] - 3*Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ProductLog[a*x^2]]]*ProductLog[a*x^2]^(3/2) + 64*a^2*x^4*ProductLog[a*x^2]^2))/(256*a^2*ProductLog[a*x^2]^2)","A",0
216,1,47,62,0.021627,"\int x^2 \sqrt{c \text{ProductLog}\left(a x^2\right)} \, dx","Integrate[x^2*Sqrt[c*ProductLog[a*x^2]],x]","\frac{x^3 \left(9 \text{ProductLog}\left(a x^2\right)^2-3 \text{ProductLog}\left(a x^2\right)+2\right) \sqrt{c \text{ProductLog}\left(a x^2\right)}}{27 \text{ProductLog}\left(a x^2\right)^2}","\frac{2 c^2 x^3}{27 \left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}+\frac{1}{3} x^3 \sqrt{c \text{ProductLog}\left(a x^2\right)}-\frac{c x^3}{9 \sqrt{c \text{ProductLog}\left(a x^2\right)}}",1,"(x^3*Sqrt[c*ProductLog[a*x^2]]*(2 - 3*ProductLog[a*x^2] + 9*ProductLog[a*x^2]^2))/(27*ProductLog[a*x^2]^2)","A",1
217,1,66,76,0.0205907,"\int x \sqrt{c \text{ProductLog}\left(a x^2\right)} \, dx","Integrate[x*Sqrt[c*ProductLog[a*x^2]],x]","\frac{c \left(\sqrt{\pi } \sqrt{\text{ProductLog}\left(a x^2\right)} \text{Erfi}\left(\sqrt{\text{ProductLog}\left(a x^2\right)}\right)+4 a x^2 \text{ProductLog}\left(a x^2\right)-2 a x^2\right)}{8 a \sqrt{c \text{ProductLog}\left(a x^2\right)}}","\frac{\sqrt{\pi } \sqrt{c} \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{\sqrt{c}}\right)}{8 a}+\frac{1}{2} x^2 \sqrt{c \text{ProductLog}\left(a x^2\right)}-\frac{c x^2}{4 \sqrt{c \text{ProductLog}\left(a x^2\right)}}",1,"(c*(-2*a*x^2 + Sqrt[Pi]*Erfi[Sqrt[ProductLog[a*x^2]]]*Sqrt[ProductLog[a*x^2]] + 4*a*x^2*ProductLog[a*x^2]))/(8*a*Sqrt[c*ProductLog[a*x^2]])","A",1
218,1,23,31,0.0075764,"\int \sqrt{c \text{ProductLog}\left(a x^2\right)} \, dx","Integrate[Sqrt[c*ProductLog[a*x^2]],x]","\frac{c x \left(\text{ProductLog}\left(a x^2\right)-1\right)}{\sqrt{c \text{ProductLog}\left(a x^2\right)}}","x \sqrt{c \text{ProductLog}\left(a x^2\right)}-\frac{c x}{\sqrt{c \text{ProductLog}\left(a x^2\right)}}",1,"(c*x*(-1 + ProductLog[a*x^2]))/Sqrt[c*ProductLog[a*x^2]]","A",1
219,1,24,32,0.0396955,"\int \frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x} \, dx","Integrate[Sqrt[c*ProductLog[a*x^2]]/x,x]","\frac{1}{3} \left(\text{ProductLog}\left(a x^2\right)+3\right) \sqrt{c \text{ProductLog}\left(a x^2\right)}","\frac{\left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}{3 c}+\sqrt{c \text{ProductLog}\left(a x^2\right)}",1,"(Sqrt[c*ProductLog[a*x^2]]*(3 + ProductLog[a*x^2]))/3","A",1
220,0,0,40,0.0441327,"\int \frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x^2} \, dx","Integrate[Sqrt[c*ProductLog[a*x^2]]/x^2,x]","\int \frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x^2} \, dx","\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)} \text{Int}\left(\frac{\sqrt{\text{ProductLog}\left(a x^2\right)}}{x^2},x\right)}{\sqrt{\text{ProductLog}\left(a x^2\right)}}",0,"Integrate[Sqrt[c*ProductLog[a*x^2]]/x^2, x]","F",-1
221,1,51,52,0.0380021,"\int \frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x^3} \, dx","Integrate[Sqrt[c*ProductLog[a*x^2]]/x^3,x]","\frac{1}{2} \sqrt{c \text{ProductLog}\left(a x^2\right)} \left(-\frac{\sqrt{\pi } a \text{Erf}\left(\sqrt{\text{ProductLog}\left(a x^2\right)}\right)}{\sqrt{\text{ProductLog}\left(a x^2\right)}}-\frac{2}{x^2}\right)","-\frac{1}{2} \sqrt{\pi } a \sqrt{c} \text{Erf}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{\sqrt{c}}\right)-\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x^2}",1,"((-2/x^2 - (a*Sqrt[Pi]*Erf[Sqrt[ProductLog[a*x^2]]])/Sqrt[ProductLog[a*x^2]])*Sqrt[c*ProductLog[a*x^2]])/2","A",1
222,0,0,40,0.0236473,"\int \frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x^4} \, dx","Integrate[Sqrt[c*ProductLog[a*x^2]]/x^4,x]","\int \frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x^4} \, dx","\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)} \text{Int}\left(\frac{\sqrt{\text{ProductLog}\left(a x^2\right)}}{x^4},x\right)}{\sqrt{\text{ProductLog}\left(a x^2\right)}}",0,"Integrate[Sqrt[c*ProductLog[a*x^2]]/x^4, x]","F",-1
223,1,83,85,0.0190848,"\int \frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x^5} \, dx","Integrate[Sqrt[c*ProductLog[a*x^2]]/x^5,x]","\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)} \left(\sqrt{2 \pi } a^2 x^4 \text{Erf}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^2\right)}\right)+\text{ProductLog}\left(a x^2\right)^{3/2}-\sqrt{\text{ProductLog}\left(a x^2\right)}\right)}{3 x^4 \sqrt{\text{ProductLog}\left(a x^2\right)}}","\frac{1}{3} \sqrt{2 \pi } a^2 \sqrt{c} \text{Erf}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^2\right)}}{\sqrt{c}}\right)+\frac{\left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}{3 c x^4}-\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{3 x^4}",1,"(Sqrt[c*ProductLog[a*x^2]]*(a^2*Sqrt[2*Pi]*x^4*Erf[Sqrt[2]*Sqrt[ProductLog[a*x^2]]] - Sqrt[ProductLog[a*x^2]] + ProductLog[a*x^2]^(3/2)))/(3*x^4*Sqrt[ProductLog[a*x^2]])","A",0
224,0,0,40,0.027228,"\int \frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x^6} \, dx","Integrate[Sqrt[c*ProductLog[a*x^2]]/x^6,x]","\int \frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x^6} \, dx","\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)} \text{Int}\left(\frac{\sqrt{\text{ProductLog}\left(a x^2\right)}}{x^6},x\right)}{\sqrt{\text{ProductLog}\left(a x^2\right)}}",0,"Integrate[Sqrt[c*ProductLog[a*x^2]]/x^6, x]","F",-1
225,1,96,107,0.035687,"\int \frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x^7} \, dx","Integrate[Sqrt[c*ProductLog[a*x^2]]/x^7,x]","\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)} \left(-6 \sqrt{3 \pi } a^3 x^6 \text{Erf}\left(\sqrt{3} \sqrt{\text{ProductLog}\left(a x^2\right)}\right)-6 \text{ProductLog}\left(a x^2\right)^{5/2}+\text{ProductLog}\left(a x^2\right)^{3/2}-3 \sqrt{\text{ProductLog}\left(a x^2\right)}\right)}{15 x^6 \sqrt{\text{ProductLog}\left(a x^2\right)}}","-\frac{2}{5} \sqrt{3 \pi } a^3 \sqrt{c} \text{Erf}\left(\frac{\sqrt{3} \sqrt{c \text{ProductLog}\left(a x^2\right)}}{\sqrt{c}}\right)-\frac{2 \left(c \text{ProductLog}\left(a x^2\right)\right)^{5/2}}{5 c^2 x^6}+\frac{\left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}{15 c x^6}-\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{5 x^6}",1,"(Sqrt[c*ProductLog[a*x^2]]*(-6*a^3*Sqrt[3*Pi]*x^6*Erf[Sqrt[3]*Sqrt[ProductLog[a*x^2]]] - 3*Sqrt[ProductLog[a*x^2]] + ProductLog[a*x^2]^(3/2) - 6*ProductLog[a*x^2]^(5/2)))/(15*x^6*Sqrt[ProductLog[a*x^2]])","A",0
226,1,112,121,0.0207353,"\int \frac{x^7}{\sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Integrate[x^7/Sqrt[c*ProductLog[a*x^2]],x]","\frac{2048 a^4 x^8 \text{ProductLog}\left(a x^2\right)^3+256 a^4 x^8 \text{ProductLog}\left(a x^2\right)^2-160 a^4 x^8 \text{ProductLog}\left(a x^2\right)+60 a^4 x^8-15 \sqrt{\pi } \text{ProductLog}\left(a x^2\right)^{7/2} \text{Erfi}\left(2 \sqrt{\text{ProductLog}\left(a x^2\right)}\right)}{16384 a^4 \text{ProductLog}\left(a x^2\right)^3 \sqrt{c \text{ProductLog}\left(a x^2\right)}}","-\frac{15 \sqrt{\pi } \text{Erfi}\left(\frac{2 \sqrt{c \text{ProductLog}\left(a x^2\right)}}{\sqrt{c}}\right)}{16384 a^4 \sqrt{c}}+\frac{15 c^3 x^8}{4096 \left(c \text{ProductLog}\left(a x^2\right)\right)^{7/2}}-\frac{5 c^2 x^8}{512 \left(c \text{ProductLog}\left(a x^2\right)\right)^{5/2}}+\frac{x^8}{8 \sqrt{c \text{ProductLog}\left(a x^2\right)}}+\frac{c x^8}{64 \left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}",1,"(60*a^4*x^8 - 160*a^4*x^8*ProductLog[a*x^2] + 256*a^4*x^8*ProductLog[a*x^2]^2 + 2048*a^4*x^8*ProductLog[a*x^2]^3 - 15*Sqrt[Pi]*Erfi[2*Sqrt[ProductLog[a*x^2]]]*ProductLog[a*x^2]^(7/2))/(16384*a^4*ProductLog[a*x^2]^3*Sqrt[c*ProductLog[a*x^2]])","A",0
227,1,57,84,0.0218885,"\int \frac{x^6}{\sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Integrate[x^6/Sqrt[c*ProductLog[a*x^2]],x]","\frac{x^7 \left(343 \text{ProductLog}\left(a x^2\right)^3+49 \text{ProductLog}\left(a x^2\right)^2-28 \text{ProductLog}\left(a x^2\right)+8\right)}{2401 \text{ProductLog}\left(a x^2\right)^3 \sqrt{c \text{ProductLog}\left(a x^2\right)}}","\frac{8 c^3 x^7}{2401 \left(c \text{ProductLog}\left(a x^2\right)\right)^{7/2}}-\frac{4 c^2 x^7}{343 \left(c \text{ProductLog}\left(a x^2\right)\right)^{5/2}}+\frac{x^7}{7 \sqrt{c \text{ProductLog}\left(a x^2\right)}}+\frac{c x^7}{49 \left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}",1,"(x^7*(8 - 28*ProductLog[a*x^2] + 49*ProductLog[a*x^2]^2 + 343*ProductLog[a*x^2]^3))/(2401*ProductLog[a*x^2]^3*Sqrt[c*ProductLog[a*x^2]])","A",1
228,1,101,107,0.0231267,"\int \frac{x^5}{\sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Integrate[x^5/Sqrt[c*ProductLog[a*x^2]],x]","\frac{72 a^3 x^6 \text{ProductLog}\left(a x^2\right)^2+12 a^3 x^6 \text{ProductLog}\left(a x^2\right)-6 a^3 x^6+\sqrt{3 \pi } \text{ProductLog}\left(a x^2\right)^{5/2} \text{Erfi}\left(\sqrt{3} \sqrt{\text{ProductLog}\left(a x^2\right)}\right)}{432 a^3 \text{ProductLog}\left(a x^2\right)^2 \sqrt{c \text{ProductLog}\left(a x^2\right)}}","\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{c \text{ProductLog}\left(a x^2\right)}}{\sqrt{c}}\right)}{144 a^3 \sqrt{c}}-\frac{c^2 x^6}{72 \left(c \text{ProductLog}\left(a x^2\right)\right)^{5/2}}+\frac{x^6}{6 \sqrt{c \text{ProductLog}\left(a x^2\right)}}+\frac{c x^6}{36 \left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}",1,"(-6*a^3*x^6 + 12*a^3*x^6*ProductLog[a*x^2] + 72*a^3*x^6*ProductLog[a*x^2]^2 + Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ProductLog[a*x^2]]]*ProductLog[a*x^2]^(5/2))/(432*a^3*ProductLog[a*x^2]^2*Sqrt[c*ProductLog[a*x^2]])","A",0
229,1,47,62,0.0116897,"\int \frac{x^4}{\sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Integrate[x^4/Sqrt[c*ProductLog[a*x^2]],x]","\frac{x^5 \left(25 \text{ProductLog}\left(a x^2\right)^2+5 \text{ProductLog}\left(a x^2\right)-2\right)}{125 \text{ProductLog}\left(a x^2\right)^2 \sqrt{c \text{ProductLog}\left(a x^2\right)}}","-\frac{2 c^2 x^5}{125 \left(c \text{ProductLog}\left(a x^2\right)\right)^{5/2}}+\frac{x^5}{5 \sqrt{c \text{ProductLog}\left(a x^2\right)}}+\frac{c x^5}{25 \left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}",1,"(x^5*(-2 + 5*ProductLog[a*x^2] + 25*ProductLog[a*x^2]^2))/(125*ProductLog[a*x^2]^2*Sqrt[c*ProductLog[a*x^2]])","A",1
230,1,79,85,0.0260161,"\int \frac{x^3}{\sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Integrate[x^3/Sqrt[c*ProductLog[a*x^2]],x]","\frac{c \left(16 a^2 x^4 \text{ProductLog}\left(a x^2\right)+4 a^2 x^4-\sqrt{2 \pi } \text{ProductLog}\left(a x^2\right)^{3/2} \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^2\right)}\right)\right)}{64 a^2 \left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}","-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^2\right)}}{\sqrt{c}}\right)}{32 a^2 \sqrt{c}}+\frac{x^4}{4 \sqrt{c \text{ProductLog}\left(a x^2\right)}}+\frac{c x^4}{16 \left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}",1,"(c*(4*a^2*x^4 + 16*a^2*x^4*ProductLog[a*x^2] - Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ProductLog[a*x^2]]]*ProductLog[a*x^2]^(3/2)))/(64*a^2*(c*ProductLog[a*x^2])^(3/2))","A",0
231,1,30,40,0.0092742,"\int \frac{x^2}{\sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Integrate[x^2/Sqrt[c*ProductLog[a*x^2]],x]","\frac{c x^3 \left(3 \text{ProductLog}\left(a x^2\right)+1\right)}{9 \left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}","\frac{x^3}{3 \sqrt{c \text{ProductLog}\left(a x^2\right)}}+\frac{c x^3}{9 \left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}",1,"(c*x^3*(1 + 3*ProductLog[a*x^2]))/(9*(c*ProductLog[a*x^2])^(3/2))","A",1
232,1,53,56,0.0091485,"\int \frac{x}{\sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Integrate[x/Sqrt[c*ProductLog[a*x^2]],x]","\frac{\sqrt{\pi } \sqrt{\text{ProductLog}\left(a x^2\right)} \text{Erfi}\left(\sqrt{\text{ProductLog}\left(a x^2\right)}\right)+2 a x^2}{4 a \sqrt{c \text{ProductLog}\left(a x^2\right)}}","\frac{\sqrt{\pi } \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{\sqrt{c}}\right)}{4 a \sqrt{c}}+\frac{x^2}{2 \sqrt{c \text{ProductLog}\left(a x^2\right)}}",1,"(2*a*x^2 + Sqrt[Pi]*Erfi[Sqrt[ProductLog[a*x^2]]]*Sqrt[ProductLog[a*x^2]])/(4*a*Sqrt[c*ProductLog[a*x^2]])","A",1
233,0,0,36,0.0154,"\int \frac{1}{\sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Integrate[1/Sqrt[c*ProductLog[a*x^2]],x]","\int \frac{1}{\sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","\frac{\sqrt{\text{ProductLog}\left(a x^2\right)} \text{Int}\left(\frac{1}{\sqrt{\text{ProductLog}\left(a x^2\right)}},x\right)}{\sqrt{c \text{ProductLog}\left(a x^2\right)}}",0,"Integrate[1/Sqrt[c*ProductLog[a*x^2]], x]","F",-1
234,1,21,31,0.0547711,"\int \frac{1}{x \sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Integrate[1/(x*Sqrt[c*ProductLog[a*x^2]]),x]","\frac{\text{ProductLog}\left(a x^2\right)-1}{\sqrt{c \text{ProductLog}\left(a x^2\right)}}","\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{c}-\frac{1}{\sqrt{c \text{ProductLog}\left(a x^2\right)}}",1,"(-1 + ProductLog[a*x^2])/Sqrt[c*ProductLog[a*x^2]]","A",1
235,0,0,40,0.0338915,"\int \frac{1}{x^2 \sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Integrate[1/(x^2*Sqrt[c*ProductLog[a*x^2]]),x]","\int \frac{1}{x^2 \sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","\frac{\sqrt{\text{ProductLog}\left(a x^2\right)} \text{Int}\left(\frac{1}{x^2 \sqrt{\text{ProductLog}\left(a x^2\right)}},x\right)}{\sqrt{c \text{ProductLog}\left(a x^2\right)}}",0,"Integrate[1/(x^2*Sqrt[c*ProductLog[a*x^2]]), x]","F",-1
236,1,61,76,0.0123292,"\int \frac{1}{x^3 \sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Integrate[1/(x^3*Sqrt[c*ProductLog[a*x^2]]),x]","\frac{\sqrt{\pi } (-a) x^2 \sqrt{\text{ProductLog}\left(a x^2\right)} \text{Erf}\left(\sqrt{\text{ProductLog}\left(a x^2\right)}\right)-\text{ProductLog}\left(a x^2\right)-1}{3 x^2 \sqrt{c \text{ProductLog}\left(a x^2\right)}}","-\frac{\sqrt{\pi } a \text{Erf}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{\sqrt{c}}\right)}{3 \sqrt{c}}-\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{3 c x^2}-\frac{1}{3 x^2 \sqrt{c \text{ProductLog}\left(a x^2\right)}}",1,"(-1 - a*Sqrt[Pi]*x^2*Erf[Sqrt[ProductLog[a*x^2]]]*Sqrt[ProductLog[a*x^2]] - ProductLog[a*x^2])/(3*x^2*Sqrt[c*ProductLog[a*x^2]])","A",1
237,0,0,40,0.0374273,"\int \frac{1}{x^4 \sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Integrate[1/(x^4*Sqrt[c*ProductLog[a*x^2]]),x]","\int \frac{1}{x^4 \sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","\frac{\sqrt{\text{ProductLog}\left(a x^2\right)} \text{Int}\left(\frac{1}{x^4 \sqrt{\text{ProductLog}\left(a x^2\right)}},x\right)}{\sqrt{c \text{ProductLog}\left(a x^2\right)}}",0,"Integrate[1/(x^4*Sqrt[c*ProductLog[a*x^2]]), x]","F",-1
238,1,81,107,0.0185225,"\int \frac{1}{x^5 \sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Integrate[1/(x^5*Sqrt[c*ProductLog[a*x^2]]),x]","\frac{4 \sqrt{2 \pi } a^2 x^4 \sqrt{\text{ProductLog}\left(a x^2\right)} \text{Erf}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^2\right)}\right)+4 \text{ProductLog}\left(a x^2\right)^2-\text{ProductLog}\left(a x^2\right)-3}{15 x^4 \sqrt{c \text{ProductLog}\left(a x^2\right)}}","\frac{4 \sqrt{2 \pi } a^2 \text{Erf}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^2\right)}}{\sqrt{c}}\right)}{15 \sqrt{c}}+\frac{4 \left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}{15 c^2 x^4}-\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{15 c x^4}-\frac{1}{5 x^4 \sqrt{c \text{ProductLog}\left(a x^2\right)}}",1,"(-3 + 4*a^2*Sqrt[2*Pi]*x^4*Erf[Sqrt[2]*Sqrt[ProductLog[a*x^2]]]*Sqrt[ProductLog[a*x^2]] - ProductLog[a*x^2] + 4*ProductLog[a*x^2]^2)/(15*x^4*Sqrt[c*ProductLog[a*x^2]])","A",0
239,0,0,40,0.0316948,"\int \frac{1}{x^6 \sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Integrate[1/(x^6*Sqrt[c*ProductLog[a*x^2]]),x]","\int \frac{1}{x^6 \sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","\frac{\sqrt{\text{ProductLog}\left(a x^2\right)} \text{Int}\left(\frac{1}{x^6 \sqrt{\text{ProductLog}\left(a x^2\right)}},x\right)}{\sqrt{c \text{ProductLog}\left(a x^2\right)}}",0,"Integrate[1/(x^6*Sqrt[c*ProductLog[a*x^2]]), x]","F",-1
240,1,91,129,0.050517,"\int \frac{1}{x^7 \sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Integrate[1/(x^7*Sqrt[c*ProductLog[a*x^2]]),x]","\frac{-12 \sqrt{3 \pi } a^3 x^6 \sqrt{\text{ProductLog}\left(a x^2\right)} \text{Erf}\left(\sqrt{3} \sqrt{\text{ProductLog}\left(a x^2\right)}\right)-12 \text{ProductLog}\left(a x^2\right)^3+2 \text{ProductLog}\left(a x^2\right)^2-\text{ProductLog}\left(a x^2\right)-5}{35 x^6 \sqrt{c \text{ProductLog}\left(a x^2\right)}}","-\frac{12 \sqrt{3 \pi } a^3 \text{Erf}\left(\frac{\sqrt{3} \sqrt{c \text{ProductLog}\left(a x^2\right)}}{\sqrt{c}}\right)}{35 \sqrt{c}}-\frac{12 \left(c \text{ProductLog}\left(a x^2\right)\right)^{5/2}}{35 c^3 x^6}+\frac{2 \left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}{35 c^2 x^6}-\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{35 c x^6}-\frac{1}{7 x^6 \sqrt{c \text{ProductLog}\left(a x^2\right)}}",1,"(-5 - 12*a^3*Sqrt[3*Pi]*x^6*Erf[Sqrt[3]*Sqrt[ProductLog[a*x^2]]]*Sqrt[ProductLog[a*x^2]] - ProductLog[a*x^2] + 2*ProductLog[a*x^2]^2 - 12*ProductLog[a*x^2]^3)/(35*x^6*Sqrt[c*ProductLog[a*x^2]])","A",0
241,0,0,36,0.040836,"\int x^2 \left(c \text{ProductLog}\left(a x^2\right)\right)^p \, dx","Integrate[x^2*(c*ProductLog[a*x^2])^p,x]","\int x^2 \left(c \text{ProductLog}\left(a x^2\right)\right)^p \, dx","\text{ProductLog}\left(a x^2\right)^{-p} \left(c \text{ProductLog}\left(a x^2\right)\right)^p \text{Int}\left(x^2 \text{ProductLog}\left(a x^2\right)^p,x\right)",0,"Integrate[x^2*(c*ProductLog[a*x^2])^p, x]","F",-1
242,1,56,60,0.0427969,"\int x \left(c \text{ProductLog}\left(a x^2\right)\right)^p \, dx","Integrate[x*(c*ProductLog[a*x^2])^p,x]","\frac{\left(-\text{ProductLog}\left(a x^2\right)\right)^{-p} \left(c \text{ProductLog}\left(a x^2\right)\right)^p \left(\Gamma \left(p+1,-\text{ProductLog}\left(a x^2\right)\right)-\Gamma \left(p+2,-\text{ProductLog}\left(a x^2\right)\right)\right)}{2 a}","\frac{1}{2} x^2 \left(c \text{ProductLog}\left(a x^2\right)\right)^p-\frac{p \left(-\text{ProductLog}\left(a x^2\right)\right)^{-p} \left(c \text{ProductLog}\left(a x^2\right)\right)^p \Gamma \left(p+1,-\text{ProductLog}\left(a x^2\right)\right)}{2 a}",1,"((Gamma[1 + p, -ProductLog[a*x^2]] - Gamma[2 + p, -ProductLog[a*x^2]])*(c*ProductLog[a*x^2])^p)/(2*a*(-ProductLog[a*x^2])^p)","A",1
243,1,30,42,0.068882,"\int \frac{\left(c \text{ProductLog}\left(a x^2\right)\right)^p}{x} \, dx","Integrate[(c*ProductLog[a*x^2])^p/x,x]","\frac{1}{2} \left(\frac{\text{ProductLog}\left(a x^2\right)}{p+1}+\frac{1}{p}\right) \left(c \text{ProductLog}\left(a x^2\right)\right)^p","\frac{\left(c \text{ProductLog}\left(a x^2\right)\right)^p}{2 p}+\frac{\left(c \text{ProductLog}\left(a x^2\right)\right)^{p+1}}{2 c (p+1)}",1,"((c*ProductLog[a*x^2])^p*(p^(-1) + ProductLog[a*x^2]/(1 + p)))/2","A",1
244,0,0,36,0.0300616,"\int \frac{\left(c \text{ProductLog}\left(a x^2\right)\right)^p}{x^2} \, dx","Integrate[(c*ProductLog[a*x^2])^p/x^2,x]","\int \frac{\left(c \text{ProductLog}\left(a x^2\right)\right)^p}{x^2} \, dx","\text{ProductLog}\left(a x^2\right)^{-p} \left(c \text{ProductLog}\left(a x^2\right)\right)^p \text{Int}\left(\frac{\text{ProductLog}\left(a x^2\right)^p}{x^2},x\right)",0,"Integrate[(c*ProductLog[a*x^2])^p/x^2, x]","F",-1
245,1,61,103,0.025211,"\int \frac{\left(c \text{ProductLog}\left(a x^2\right)\right)^p}{x^3} \, dx","Integrate[(c*ProductLog[a*x^2])^p/x^3,x]","-\frac{e^{2 \text{ProductLog}\left(a x^2\right)} \text{ProductLog}\left(a x^2\right)^{2-p} \left(c \text{ProductLog}\left(a x^2\right)\right)^p \left(\Gamma \left(p-1,\text{ProductLog}\left(a x^2\right)\right)+\Gamma \left(p,\text{ProductLog}\left(a x^2\right)\right)\right)}{2 a x^4}","-\frac{e^{2 \text{ProductLog}\left(a x^2\right)} \text{ProductLog}\left(a x^2\right)^{2-p} \left(c \text{ProductLog}\left(a x^2\right)\right)^p \Gamma \left(p-1,\text{ProductLog}\left(a x^2\right)\right)}{2 a x^4}-\frac{e^{2 \text{ProductLog}\left(a x^2\right)} \text{ProductLog}\left(a x^2\right)^{2-p} \left(c \text{ProductLog}\left(a x^2\right)\right)^p \Gamma \left(p,\text{ProductLog}\left(a x^2\right)\right)}{2 a x^4}",1,"-(E^(2*ProductLog[a*x^2])*(Gamma[-1 + p, ProductLog[a*x^2]] + Gamma[p, ProductLog[a*x^2]])*ProductLog[a*x^2]^(2 - p)*(c*ProductLog[a*x^2])^p)/(2*a*x^4)","A",1
246,1,75,75,0.0080152,"\int x^4 \text{ProductLog}\left(\frac{a}{x}\right) \, dx","Integrate[x^4*ProductLog[a/x],x]","-\frac{125}{24} a^5 \text{Ei}\left(-5 \text{ProductLog}\left(\frac{a}{x}\right)\right)-\frac{25}{24} x^5 \text{ProductLog}\left(\frac{a}{x}\right)^4+\frac{5}{24} x^5 \text{ProductLog}\left(\frac{a}{x}\right)^3-\frac{1}{12} x^5 \text{ProductLog}\left(\frac{a}{x}\right)^2+\frac{1}{4} x^5 \text{ProductLog}\left(\frac{a}{x}\right)","-\frac{125}{24} a^5 \text{Ei}\left(-5 \text{ProductLog}\left(\frac{a}{x}\right)\right)-\frac{25}{24} x^5 \text{ProductLog}\left(\frac{a}{x}\right)^4+\frac{5}{24} x^5 \text{ProductLog}\left(\frac{a}{x}\right)^3-\frac{1}{12} x^5 \text{ProductLog}\left(\frac{a}{x}\right)^2+\frac{1}{4} x^5 \text{ProductLog}\left(\frac{a}{x}\right)",1,"(-125*a^5*ExpIntegralEi[-5*ProductLog[a/x]])/24 + (x^5*ProductLog[a/x])/4 - (x^5*ProductLog[a/x]^2)/12 + (5*x^5*ProductLog[a/x]^3)/24 - (25*x^5*ProductLog[a/x]^4)/24","A",1
247,1,60,60,0.0063573,"\int x^3 \text{ProductLog}\left(\frac{a}{x}\right) \, dx","Integrate[x^3*ProductLog[a/x],x]","\frac{8}{3} a^4 \text{Ei}\left(-4 \text{ProductLog}\left(\frac{a}{x}\right)\right)+\frac{2}{3} x^4 \text{ProductLog}\left(\frac{a}{x}\right)^3-\frac{1}{6} x^4 \text{ProductLog}\left(\frac{a}{x}\right)^2+\frac{1}{3} x^4 \text{ProductLog}\left(\frac{a}{x}\right)","\frac{8}{3} a^4 \text{Ei}\left(-4 \text{ProductLog}\left(\frac{a}{x}\right)\right)+\frac{2}{3} x^4 \text{ProductLog}\left(\frac{a}{x}\right)^3-\frac{1}{6} x^4 \text{ProductLog}\left(\frac{a}{x}\right)^2+\frac{1}{3} x^4 \text{ProductLog}\left(\frac{a}{x}\right)",1,"(8*a^4*ExpIntegralEi[-4*ProductLog[a/x]])/3 + (x^4*ProductLog[a/x])/3 - (x^4*ProductLog[a/x]^2)/6 + (2*x^4*ProductLog[a/x]^3)/3","A",1
248,1,45,45,0.0051416,"\int x^2 \text{ProductLog}\left(\frac{a}{x}\right) \, dx","Integrate[x^2*ProductLog[a/x],x]","-\frac{3}{2} a^3 \text{Ei}\left(-3 \text{ProductLog}\left(\frac{a}{x}\right)\right)-\frac{1}{2} x^3 \text{ProductLog}\left(\frac{a}{x}\right)^2+\frac{1}{2} x^3 \text{ProductLog}\left(\frac{a}{x}\right)","-\frac{3}{2} a^3 \text{Ei}\left(-3 \text{ProductLog}\left(\frac{a}{x}\right)\right)-\frac{1}{2} x^3 \text{ProductLog}\left(\frac{a}{x}\right)^2+\frac{1}{2} x^3 \text{ProductLog}\left(\frac{a}{x}\right)",1,"(-3*a^3*ExpIntegralEi[-3*ProductLog[a/x]])/2 + (x^3*ProductLog[a/x])/2 - (x^3*ProductLog[a/x]^2)/2","A",1
249,1,24,24,0.0033248,"\int x \text{ProductLog}\left(\frac{a}{x}\right) \, dx","Integrate[x*ProductLog[a/x],x]","a^2 \text{Ei}\left(-2 \text{ProductLog}\left(\frac{a}{x}\right)\right)+x^2 \text{ProductLog}\left(\frac{a}{x}\right)","a^2 \text{Ei}\left(-2 \text{ProductLog}\left(\frac{a}{x}\right)\right)+x^2 \text{ProductLog}\left(\frac{a}{x}\right)",1,"a^2*ExpIntegralEi[-2*ProductLog[a/x]] + x^2*ProductLog[a/x]","A",1
250,1,21,21,0.004081,"\int \text{ProductLog}\left(\frac{a}{x}\right) \, dx","Integrate[ProductLog[a/x],x]","x \text{ProductLog}\left(\frac{a}{x}\right)-a \text{Ei}\left(-\text{ProductLog}\left(\frac{a}{x}\right)\right)","x \text{ProductLog}\left(\frac{a}{x}\right)-a \text{Ei}\left(-\text{ProductLog}\left(\frac{a}{x}\right)\right)",1,"-(a*ExpIntegralEi[-ProductLog[a/x]]) + x*ProductLog[a/x]","A",1
251,1,21,21,0.0280754,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)}{x} \, dx","Integrate[ProductLog[a/x]/x,x]","-\frac{1}{2} \text{ProductLog}\left(\frac{a}{x}\right)^2-\text{ProductLog}\left(\frac{a}{x}\right)","-\frac{1}{2} \text{ProductLog}\left(\frac{a}{x}\right)^2-\text{ProductLog}\left(\frac{a}{x}\right)",1,"-ProductLog[a/x] - ProductLog[a/x]^2/2","A",1
252,1,21,28,0.0104586,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)}{x^2} \, dx","Integrate[ProductLog[a/x]/x^2,x]","-\frac{\text{ProductLog}\left(\frac{a}{x}\right)+\frac{1}{\text{ProductLog}\left(\frac{a}{x}\right)}-1}{x}","-\frac{\text{ProductLog}\left(\frac{a}{x}\right)}{x}-\frac{1}{x \text{ProductLog}\left(\frac{a}{x}\right)}+\frac{1}{x}",1,"-((-1 + ProductLog[a/x]^(-1) + ProductLog[a/x])/x)","A",1
253,1,51,51,0.0054272,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)}{x^3} \, dx","Integrate[ProductLog[a/x]/x^3,x]","-\frac{\text{ProductLog}\left(\frac{a}{x}\right)}{2 x^2}-\frac{1}{4 x^2 \text{ProductLog}\left(\frac{a}{x}\right)}+\frac{1}{8 x^2 \text{ProductLog}\left(\frac{a}{x}\right)^2}+\frac{1}{4 x^2}","-\frac{\text{ProductLog}\left(\frac{a}{x}\right)}{2 x^2}-\frac{1}{4 x^2 \text{ProductLog}\left(\frac{a}{x}\right)}+\frac{1}{8 x^2 \text{ProductLog}\left(\frac{a}{x}\right)^2}+\frac{1}{4 x^2}",1,"1/(4*x^2) + 1/(8*x^2*ProductLog[a/x]^2) - 1/(4*x^2*ProductLog[a/x]) - ProductLog[a/x]/(2*x^2)","A",1
254,1,66,66,0.0079677,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)}{x^4} \, dx","Integrate[ProductLog[a/x]/x^4,x]","-\frac{\text{ProductLog}\left(\frac{a}{x}\right)}{3 x^3}-\frac{1}{9 x^3 \text{ProductLog}\left(\frac{a}{x}\right)}+\frac{2}{27 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^2}-\frac{2}{81 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^3}+\frac{1}{9 x^3}","-\frac{\text{ProductLog}\left(\frac{a}{x}\right)}{3 x^3}-\frac{1}{9 x^3 \text{ProductLog}\left(\frac{a}{x}\right)}+\frac{2}{27 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^2}-\frac{2}{81 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^3}+\frac{1}{9 x^3}",1,"1/(9*x^3) - 2/(81*x^3*ProductLog[a/x]^3) + 2/(27*x^3*ProductLog[a/x]^2) - 1/(9*x^3*ProductLog[a/x]) - ProductLog[a/x]/(3*x^3)","A",1
255,1,81,81,0.0093921,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)}{x^5} \, dx","Integrate[ProductLog[a/x]/x^5,x]","-\frac{\text{ProductLog}\left(\frac{a}{x}\right)}{4 x^4}-\frac{1}{16 x^4 \text{ProductLog}\left(\frac{a}{x}\right)}+\frac{3}{64 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^2}-\frac{3}{128 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^3}+\frac{3}{512 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^4}+\frac{1}{16 x^4}","-\frac{\text{ProductLog}\left(\frac{a}{x}\right)}{4 x^4}-\frac{1}{16 x^4 \text{ProductLog}\left(\frac{a}{x}\right)}+\frac{3}{64 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^2}-\frac{3}{128 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^3}+\frac{3}{512 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^4}+\frac{1}{16 x^4}",1,"1/(16*x^4) + 3/(512*x^4*ProductLog[a/x]^4) - 3/(128*x^4*ProductLog[a/x]^3) + 3/(64*x^4*ProductLog[a/x]^2) - 1/(16*x^4*ProductLog[a/x]) - ProductLog[a/x]/(4*x^4)","A",1
256,1,62,62,0.0057953,"\int x^4 \text{ProductLog}\left(\frac{a}{x}\right)^2 \, dx","Integrate[x^4*ProductLog[a/x]^2,x]","\frac{25}{3} a^5 \text{Ei}\left(-5 \text{ProductLog}\left(\frac{a}{x}\right)\right)+\frac{5}{3} x^5 \text{ProductLog}\left(\frac{a}{x}\right)^4-\frac{1}{3} x^5 \text{ProductLog}\left(\frac{a}{x}\right)^3+\frac{1}{3} x^5 \text{ProductLog}\left(\frac{a}{x}\right)^2","\frac{25}{3} a^5 \text{Ei}\left(-5 \text{ProductLog}\left(\frac{a}{x}\right)\right)+\frac{5}{3} x^5 \text{ProductLog}\left(\frac{a}{x}\right)^4-\frac{1}{3} x^5 \text{ProductLog}\left(\frac{a}{x}\right)^3+\frac{1}{3} x^5 \text{ProductLog}\left(\frac{a}{x}\right)^2",1,"(25*a^5*ExpIntegralEi[-5*ProductLog[a/x]])/3 + (x^5*ProductLog[a/x]^2)/3 - (x^5*ProductLog[a/x]^3)/3 + (5*x^5*ProductLog[a/x]^4)/3","A",1
257,1,43,43,0.0055152,"\int x^3 \text{ProductLog}\left(\frac{a}{x}\right)^2 \, dx","Integrate[x^3*ProductLog[a/x]^2,x]","-4 a^4 \text{Ei}\left(-4 \text{ProductLog}\left(\frac{a}{x}\right)\right)-x^4 \text{ProductLog}\left(\frac{a}{x}\right)^3+\frac{1}{2} x^4 \text{ProductLog}\left(\frac{a}{x}\right)^2","-4 a^4 \text{Ei}\left(-4 \text{ProductLog}\left(\frac{a}{x}\right)\right)-x^4 \text{ProductLog}\left(\frac{a}{x}\right)^3+\frac{1}{2} x^4 \text{ProductLog}\left(\frac{a}{x}\right)^2",1,"-4*a^4*ExpIntegralEi[-4*ProductLog[a/x]] + (x^4*ProductLog[a/x]^2)/2 - x^4*ProductLog[a/x]^3","A",1
258,1,27,27,0.0033275,"\int x^2 \text{ProductLog}\left(\frac{a}{x}\right)^2 \, dx","Integrate[x^2*ProductLog[a/x]^2,x]","2 a^3 \text{Ei}\left(-3 \text{ProductLog}\left(\frac{a}{x}\right)\right)+x^3 \text{ProductLog}\left(\frac{a}{x}\right)^2","2 a^3 \text{Ei}\left(-3 \text{ProductLog}\left(\frac{a}{x}\right)\right)+x^3 \text{ProductLog}\left(\frac{a}{x}\right)^2",1,"2*a^3*ExpIntegralEi[-3*ProductLog[a/x]] + x^3*ProductLog[a/x]^2","A",1
259,1,30,30,0.0024881,"\int x \text{ProductLog}\left(\frac{a}{x}\right)^2 \, dx","Integrate[x*ProductLog[a/x]^2,x]","\frac{1}{2} x^2 \text{ProductLog}\left(\frac{a}{x}\right)^2-a^2 \text{Ei}\left(-2 \text{ProductLog}\left(\frac{a}{x}\right)\right)","\frac{1}{2} x^2 \text{ProductLog}\left(\frac{a}{x}\right)^2-a^2 \text{Ei}\left(-2 \text{ProductLog}\left(\frac{a}{x}\right)\right)",1,"-(a^2*ExpIntegralEi[-2*ProductLog[a/x]]) + (x^2*ProductLog[a/x]^2)/2","A",1
260,1,20,20,0.0036496,"\int \text{ProductLog}\left(\frac{a}{x}\right)^2 \, dx","Integrate[ProductLog[a/x]^2,x]","x \text{ProductLog}\left(\frac{a}{x}\right)^2+2 x \text{ProductLog}\left(\frac{a}{x}\right)","x \text{ProductLog}\left(\frac{a}{x}\right)^2+2 x \text{ProductLog}\left(\frac{a}{x}\right)",1,"2*x*ProductLog[a/x] + x*ProductLog[a/x]^2","A",1
261,1,25,25,0.0243153,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{x} \, dx","Integrate[ProductLog[a/x]^2/x,x]","-\frac{1}{3} \text{ProductLog}\left(\frac{a}{x}\right)^3-\frac{1}{2} \text{ProductLog}\left(\frac{a}{x}\right)^2","-\frac{1}{3} \text{ProductLog}\left(\frac{a}{x}\right)^3-\frac{1}{2} \text{ProductLog}\left(\frac{a}{x}\right)^2",1,"-ProductLog[a/x]^2/2 - ProductLog[a/x]^3/3","A",1
262,1,41,43,0.0161841,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{x^2} \, dx","Integrate[ProductLog[a/x]^2/x^2,x]","-\frac{\text{ProductLog}\left(\frac{a}{x}\right)^3-2 \text{ProductLog}\left(\frac{a}{x}\right)^2+4 \text{ProductLog}\left(\frac{a}{x}\right)-4}{x \text{ProductLog}\left(\frac{a}{x}\right)}","-\frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{x}+\frac{2 \text{ProductLog}\left(\frac{a}{x}\right)}{x}+\frac{4}{x \text{ProductLog}\left(\frac{a}{x}\right)}-\frac{4}{x}",1,"-((-4 + 4*ProductLog[a/x] - 2*ProductLog[a/x]^2 + ProductLog[a/x]^3)/(x*ProductLog[a/x]))","A",1
263,1,66,66,0.0074022,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{x^3} \, dx","Integrate[ProductLog[a/x]^2/x^3,x]","-\frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{2 x^2}+\frac{\text{ProductLog}\left(\frac{a}{x}\right)}{2 x^2}+\frac{3}{4 x^2 \text{ProductLog}\left(\frac{a}{x}\right)}-\frac{3}{8 x^2 \text{ProductLog}\left(\frac{a}{x}\right)^2}-\frac{3}{4 x^2}","-\frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{2 x^2}+\frac{\text{ProductLog}\left(\frac{a}{x}\right)}{2 x^2}+\frac{3}{4 x^2 \text{ProductLog}\left(\frac{a}{x}\right)}-\frac{3}{8 x^2 \text{ProductLog}\left(\frac{a}{x}\right)^2}-\frac{3}{4 x^2}",1,"-3/(4*x^2) - 3/(8*x^2*ProductLog[a/x]^2) + 3/(4*x^2*ProductLog[a/x]) + ProductLog[a/x]/(2*x^2) - ProductLog[a/x]^2/(2*x^2)","A",1
264,1,81,81,0.0124332,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{x^4} \, dx","Integrate[ProductLog[a/x]^2/x^4,x]","-\frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{3 x^3}+\frac{2 \text{ProductLog}\left(\frac{a}{x}\right)}{9 x^3}+\frac{8}{27 x^3 \text{ProductLog}\left(\frac{a}{x}\right)}-\frac{16}{81 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^2}+\frac{16}{243 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^3}-\frac{8}{27 x^3}","-\frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{3 x^3}+\frac{2 \text{ProductLog}\left(\frac{a}{x}\right)}{9 x^3}+\frac{8}{27 x^3 \text{ProductLog}\left(\frac{a}{x}\right)}-\frac{16}{81 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^2}+\frac{16}{243 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^3}-\frac{8}{27 x^3}",1,"-8/(27*x^3) + 16/(243*x^3*ProductLog[a/x]^3) - 16/(81*x^3*ProductLog[a/x]^2) + 8/(27*x^3*ProductLog[a/x]) + (2*ProductLog[a/x])/(9*x^3) - ProductLog[a/x]^2/(3*x^3)","A",1
265,1,96,96,0.0105004,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{x^5} \, dx","Integrate[ProductLog[a/x]^2/x^5,x]","-\frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{4 x^4}+\frac{\text{ProductLog}\left(\frac{a}{x}\right)}{8 x^4}+\frac{5}{32 x^4 \text{ProductLog}\left(\frac{a}{x}\right)}-\frac{15}{128 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^2}+\frac{15}{256 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^3}-\frac{15}{1024 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^4}-\frac{5}{32 x^4}","-\frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{4 x^4}+\frac{\text{ProductLog}\left(\frac{a}{x}\right)}{8 x^4}+\frac{5}{32 x^4 \text{ProductLog}\left(\frac{a}{x}\right)}-\frac{15}{128 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^2}+\frac{15}{256 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^3}-\frac{15}{1024 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^4}-\frac{5}{32 x^4}",1,"-5/(32*x^4) - 15/(1024*x^4*ProductLog[a/x]^4) + 15/(256*x^4*ProductLog[a/x]^3) - 15/(128*x^4*ProductLog[a/x]^2) + 5/(32*x^4*ProductLog[a/x]) + ProductLog[a/x]/(8*x^4) - ProductLog[a/x]^2/(4*x^4)","A",1
266,1,88,94,0.0151162,"\int x^3 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Integrate[x^3*Sqrt[ProductLog[a/x]],x]","-\frac{2}{105} \left(128 \sqrt{\pi } a^4 \text{Erf}\left(2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)+64 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^{7/2}-8 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^{5/2}+3 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}-15 x^4 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)","-\frac{256}{105} \sqrt{\pi } a^4 \text{Erf}\left(2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)-\frac{128}{105} x^4 \text{ProductLog}\left(\frac{a}{x}\right)^{7/2}+\frac{16}{105} x^4 \text{ProductLog}\left(\frac{a}{x}\right)^{5/2}-\frac{2}{35} x^4 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}+\frac{2}{7} x^4 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}",1,"(-2*(128*a^4*Sqrt[Pi]*Erf[2*Sqrt[ProductLog[a/x]]] - 15*x^4*Sqrt[ProductLog[a/x]] + 3*x^4*ProductLog[a/x]^(3/2) - 8*x^4*ProductLog[a/x]^(5/2) + 64*x^4*ProductLog[a/x]^(7/2)))/105","A",1
267,1,79,83,0.019125,"\int x^2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Integrate[x^2*Sqrt[ProductLog[a/x]],x]","\frac{2}{15} \left(6 \sqrt{3 \pi } a^3 \text{Erf}\left(\sqrt{3} \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)+6 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^{5/2}-x^3 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}+3 x^3 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)","\frac{4}{5} \sqrt{3 \pi } a^3 \text{Erf}\left(\sqrt{3} \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)+\frac{4}{5} x^3 \text{ProductLog}\left(\frac{a}{x}\right)^{5/2}-\frac{2}{15} x^3 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}+\frac{2}{5} x^3 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}",1,"(2*(6*a^3*Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ProductLog[a/x]]] + 3*x^3*Sqrt[ProductLog[a/x]] - x^3*ProductLog[a/x]^(3/2) + 6*x^3*ProductLog[a/x]^(5/2)))/15","A",1
268,1,62,66,0.0124773,"\int x \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Integrate[x*Sqrt[ProductLog[a/x]],x]","-\frac{2}{3} \left(\sqrt{2 \pi } a^2 \text{Erf}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)+x^2 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}-x^2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)","-\frac{2}{3} \sqrt{2 \pi } a^2 \text{Erf}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)-\frac{2}{3} x^2 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}+\frac{2}{3} x^2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}",1,"(-2*(a^2*Sqrt[2*Pi]*Erf[Sqrt[2]*Sqrt[ProductLog[a/x]]] - x^2*Sqrt[ProductLog[a/x]] + x^2*ProductLog[a/x]^(3/2)))/3","A",1
269,1,32,32,0.0047756,"\int \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Integrate[Sqrt[ProductLog[a/x]],x]","\sqrt{\pi } a \text{Erf}\left(\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)+2 x \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}","\sqrt{\pi } a \text{Erf}\left(\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)+2 x \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}",1,"a*Sqrt[Pi]*Erf[Sqrt[ProductLog[a/x]]] + 2*x*Sqrt[ProductLog[a/x]]","A",1
270,1,22,27,0.0379757,"\int \frac{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}{x} \, dx","Integrate[Sqrt[ProductLog[a/x]]/x,x]","-\frac{2}{3} \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)} \left(\text{ProductLog}\left(\frac{a}{x}\right)+3\right)","-\frac{2}{3} \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}-2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}",1,"(-2*Sqrt[ProductLog[a/x]]*(3 + ProductLog[a/x]))/3","A",1
271,1,56,56,0.0168837,"\int \frac{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}{x^2} \, dx","Integrate[Sqrt[ProductLog[a/x]]/x^2,x]","-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)}{4 a}-\frac{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}{x}+\frac{1}{2 x \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}","-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)}{4 a}-\frac{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}{x}+\frac{1}{2 x \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}",1,"-(Sqrt[Pi]*Erfi[Sqrt[ProductLog[a/x]]])/(4*a) + 1/(2*x*Sqrt[ProductLog[a/x]]) - Sqrt[ProductLog[a/x]]/x","A",1
272,1,79,85,0.0290628,"\int \frac{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}{x^3} \, dx","Integrate[Sqrt[ProductLog[a/x]]/x^3,x]","\frac{1}{128} \left(\frac{3 \sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)}{a^2}-\frac{64 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}{x^2}+\frac{16}{x^2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}-\frac{12}{x^2 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}}\right)","\frac{3 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)}{64 a^2}-\frac{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}{2 x^2}+\frac{1}{8 x^2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}-\frac{3}{32 x^2 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}}",1,"((3*Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ProductLog[a/x]]])/a^2 - 12/(x^2*ProductLog[a/x]^(3/2)) + 16/(x^2*Sqrt[ProductLog[a/x]]) - (64*Sqrt[ProductLog[a/x]])/x^2)/128","A",1
273,1,102,102,0.0391661,"\int \frac{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}{x^4} \, dx","Integrate[Sqrt[ProductLog[a/x]]/x^4,x]","-\frac{5 \sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)}{432 a^3}-\frac{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}{3 x^3}+\frac{1}{18 x^3 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}-\frac{5}{108 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}}+\frac{5}{216 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^{5/2}}","-\frac{5 \sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)}{432 a^3}-\frac{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}{3 x^3}+\frac{1}{18 x^3 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}-\frac{5}{108 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}}+\frac{5}{216 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^{5/2}}",1,"(-5*Sqrt[Pi/3]*Erfi[Sqrt[3]*Sqrt[ProductLog[a/x]]])/(432*a^3) + 5/(216*x^3*ProductLog[a/x]^(5/2)) - 5/(108*x^3*ProductLog[a/x]^(3/2)) + 1/(18*x^3*Sqrt[ProductLog[a/x]]) - Sqrt[ProductLog[a/x]]/(3*x^3)","A",1
274,1,103,111,0.0214206,"\int \frac{x^3}{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}} \, dx","Integrate[x^3/Sqrt[ProductLog[a/x]],x]","-\frac{2 \left(1024 \sqrt{\pi } a^4 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)} \text{Erf}\left(2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)+512 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^4-64 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^3+24 x^4 \text{ProductLog}\left(\frac{a}{x}\right)^2-15 x^4 \text{ProductLog}\left(\frac{a}{x}\right)-105 x^4\right)}{945 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}","-\frac{2048}{945} \sqrt{\pi } a^4 \text{Erf}\left(2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)-\frac{1024}{945} x^4 \text{ProductLog}\left(\frac{a}{x}\right)^{7/2}+\frac{128}{945} x^4 \text{ProductLog}\left(\frac{a}{x}\right)^{5/2}-\frac{16}{315} x^4 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}+\frac{2}{63} x^4 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}+\frac{2 x^4}{9 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}",1,"(-2*(-105*x^4 + 1024*a^4*Sqrt[Pi]*Erf[2*Sqrt[ProductLog[a/x]]]*Sqrt[ProductLog[a/x]] - 15*x^4*ProductLog[a/x] + 24*x^4*ProductLog[a/x]^2 - 64*x^4*ProductLog[a/x]^3 + 512*x^4*ProductLog[a/x]^4))/(945*Sqrt[ProductLog[a/x]])","A",1
275,1,95,100,0.0257023,"\int \frac{x^2}{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}} \, dx","Integrate[x^2/Sqrt[ProductLog[a/x]],x]","\frac{2 \left(12 \sqrt{3 \pi } a^3 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)} \text{Erf}\left(\sqrt{3} \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)+12 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^3-2 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^2+x^3 \text{ProductLog}\left(\frac{a}{x}\right)+5 x^3\right)}{35 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}","\frac{24}{35} \sqrt{3 \pi } a^3 \text{Erf}\left(\sqrt{3} \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)+\frac{24}{35} x^3 \text{ProductLog}\left(\frac{a}{x}\right)^{5/2}-\frac{4}{35} x^3 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}+\frac{2}{35} x^3 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}+\frac{2 x^3}{7 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}",1,"(2*(5*x^3 + 12*a^3*Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ProductLog[a/x]]]*Sqrt[ProductLog[a/x]] + x^3*ProductLog[a/x] - 2*x^3*ProductLog[a/x]^2 + 12*x^3*ProductLog[a/x]^3))/(35*Sqrt[ProductLog[a/x]])","A",1
276,1,83,83,0.015171,"\int \frac{x}{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}} \, dx","Integrate[x/Sqrt[ProductLog[a/x]],x]","-\frac{8}{15} \sqrt{2 \pi } a^2 \text{Erf}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)-\frac{8}{15} x^2 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}+\frac{2}{15} x^2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}+\frac{2 x^2}{5 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}","-\frac{8}{15} \sqrt{2 \pi } a^2 \text{Erf}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)-\frac{8}{15} x^2 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}+\frac{2}{15} x^2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}+\frac{2 x^2}{5 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}",1,"(-8*a^2*Sqrt[2*Pi]*Erf[Sqrt[2]*Sqrt[ProductLog[a/x]]])/15 + (2*x^2)/(5*Sqrt[ProductLog[a/x]]) + (2*x^2*Sqrt[ProductLog[a/x]])/15 - (8*x^2*ProductLog[a/x]^(3/2))/15","A",1
277,1,47,52,0.0120977,"\int \frac{1}{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}} \, dx","Integrate[1/Sqrt[ProductLog[a/x]],x]","\frac{2}{3} \left(\sqrt{\pi } a \text{Erf}\left(\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)+x \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}+\frac{x}{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}\right)","\frac{2}{3} \sqrt{\pi } a \text{Erf}\left(\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)+\frac{2}{3} x \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}+\frac{2 x}{3 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}",1,"(2*(a*Sqrt[Pi]*Erf[Sqrt[ProductLog[a/x]]] + x/Sqrt[ProductLog[a/x]] + x*Sqrt[ProductLog[a/x]]))/3","A",1
278,1,20,25,0.033887,"\int \frac{1}{x \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}} \, dx","Integrate[1/(x*Sqrt[ProductLog[a/x]]),x]","-\frac{2 \left(\text{ProductLog}\left(\frac{a}{x}\right)-1\right)}{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}","\frac{2}{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}-2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}",1,"(-2*(-1 + ProductLog[a/x]))/Sqrt[ProductLog[a/x]]","A",1
279,1,39,39,0.0087714,"\int \frac{1}{x^2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}} \, dx","Integrate[1/(x^2*Sqrt[ProductLog[a/x]]),x]","-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)}{2 a}-\frac{1}{x \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}","-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)}{2 a}-\frac{1}{x \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}",1,"-(Sqrt[Pi]*Erfi[Sqrt[ProductLog[a/x]]])/(2*a) - 1/(x*Sqrt[ProductLog[a/x]])","A",1
280,1,63,68,0.0213776,"\int \frac{1}{x^3 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}} \, dx","Integrate[1/(x^3*Sqrt[ProductLog[a/x]]),x]","\frac{1}{32} \left(\frac{\sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)}{a^2}-\frac{16}{x^2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}-\frac{4}{x^2 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}}\right)","\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)}{16 a^2}-\frac{1}{2 x^2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}-\frac{1}{8 x^2 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}}",1,"((Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ProductLog[a/x]]])/a^2 - 4/(x^2*ProductLog[a/x]^(3/2)) - 16/(x^2*Sqrt[ProductLog[a/x]]))/32","A",1
281,1,79,85,0.0276417,"\int \frac{1}{x^4 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}} \, dx","Integrate[1/(x^4*Sqrt[ProductLog[a/x]]),x]","\frac{1}{216} \left(-\frac{\sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)}{a^3}-\frac{72}{x^3 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}-\frac{12}{x^3 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}}+\frac{6}{x^3 \text{ProductLog}\left(\frac{a}{x}\right)^{5/2}}\right)","-\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}\right)}{72 a^3}-\frac{1}{3 x^3 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}-\frac{1}{18 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}}+\frac{1}{36 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^{5/2}}",1,"(-((Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ProductLog[a/x]]])/a^3) + 6/(x^3*ProductLog[a/x]^(5/2)) - 12/(x^3*ProductLog[a/x]^(3/2)) - 72/(x^3*Sqrt[ProductLog[a/x]]))/216","A",1
282,1,73,122,0.0237023,"\int x^2 \left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p \, dx","Integrate[x^2*(c*ProductLog[a/x])^p,x]","\frac{3^{2-p} x^4 e^{4 \text{ProductLog}\left(\frac{a}{x}\right)} \text{ProductLog}\left(\frac{a}{x}\right)^{4-p} \left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p \left(3 \Gamma \left(p-3,3 \text{ProductLog}\left(\frac{a}{x}\right)\right)+\Gamma \left(p-2,3 \text{ProductLog}\left(\frac{a}{x}\right)\right)\right)}{a}","\frac{3^{2-p} x^4 e^{4 \text{ProductLog}\left(\frac{a}{x}\right)} \text{ProductLog}\left(\frac{a}{x}\right)^{3-p} \left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^{p+1} \Gamma \left(p-2,3 \text{ProductLog}\left(\frac{a}{x}\right)\right)}{a c}+\frac{3^{3-p} x^4 e^{4 \text{ProductLog}\left(\frac{a}{x}\right)} \text{ProductLog}\left(\frac{a}{x}\right)^{4-p} \left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p \Gamma \left(p-3,3 \text{ProductLog}\left(\frac{a}{x}\right)\right)}{a}",1,"(3^(2 - p)*E^(4*ProductLog[a/x])*x^4*(3*Gamma[-3 + p, 3*ProductLog[a/x]] + Gamma[-2 + p, 3*ProductLog[a/x]])*ProductLog[a/x]^(4 - p)*(c*ProductLog[a/x])^p)/a","A",1
283,1,73,122,0.0222026,"\int x \left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p \, dx","Integrate[x*(c*ProductLog[a/x])^p,x]","\frac{2^{1-p} x^3 e^{3 \text{ProductLog}\left(\frac{a}{x}\right)} \text{ProductLog}\left(\frac{a}{x}\right)^{3-p} \left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p \left(2 \Gamma \left(p-2,2 \text{ProductLog}\left(\frac{a}{x}\right)\right)+\Gamma \left(p-1,2 \text{ProductLog}\left(\frac{a}{x}\right)\right)\right)}{a}","\frac{2^{1-p} x^3 e^{3 \text{ProductLog}\left(\frac{a}{x}\right)} \text{ProductLog}\left(\frac{a}{x}\right)^{2-p} \left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^{p+1} \Gamma \left(p-1,2 \text{ProductLog}\left(\frac{a}{x}\right)\right)}{a c}+\frac{2^{2-p} x^3 e^{3 \text{ProductLog}\left(\frac{a}{x}\right)} \text{ProductLog}\left(\frac{a}{x}\right)^{3-p} \left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p \Gamma \left(p-2,2 \text{ProductLog}\left(\frac{a}{x}\right)\right)}{a}",1,"(2^(1 - p)*E^(3*ProductLog[a/x])*x^3*(2*Gamma[-2 + p, 2*ProductLog[a/x]] + Gamma[-1 + p, 2*ProductLog[a/x]])*ProductLog[a/x]^(3 - p)*(c*ProductLog[a/x])^p)/a","A",1
284,1,28,38,0.0656932,"\int \frac{\left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p}{x} \, dx","Integrate[(c*ProductLog[a/x])^p/x,x]","\left(\frac{\text{ProductLog}\left(\frac{a}{x}\right)}{p+1}+\frac{1}{p}\right) \left(-\left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p\right)","-\frac{\left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p}{p}-\frac{\left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^{p+1}}{c (p+1)}",1,"-((c*ProductLog[a/x])^p*(p^(-1) + ProductLog[a/x]/(1 + p)))","A",1
285,1,54,55,0.0157098,"\int \frac{\left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p}{x^2} \, dx","Integrate[(c*ProductLog[a/x])^p/x^2,x]","-\frac{\left(-\text{ProductLog}\left(\frac{a}{x}\right)\right)^{-p} \left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p \left(\Gamma \left(p+1,-\text{ProductLog}\left(\frac{a}{x}\right)\right)-\Gamma \left(p+2,-\text{ProductLog}\left(\frac{a}{x}\right)\right)\right)}{a}","\frac{p \left(-\text{ProductLog}\left(\frac{a}{x}\right)\right)^{-p} \left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p \Gamma \left(p+1,-\text{ProductLog}\left(\frac{a}{x}\right)\right)}{a}-\frac{\left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p}{x}",1,"-(((Gamma[1 + p, -ProductLog[a/x]] - Gamma[2 + p, -ProductLog[a/x]])*(c*ProductLog[a/x])^p)/(a*(-ProductLog[a/x])^p))","A",1
286,1,62,128,0.0204478,"\int \frac{\left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p}{x^3} \, dx","Integrate[(c*ProductLog[a/x])^p/x^3,x]","\frac{2^{-p-3} \left(-\text{ProductLog}\left(\frac{a}{x}\right)\right)^{-p} \left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p \left(2 \Gamma \left(p+2,-2 \text{ProductLog}\left(\frac{a}{x}\right)\right)-\Gamma \left(p+3,-2 \text{ProductLog}\left(\frac{a}{x}\right)\right)\right)}{a^2}","-\frac{2^{-p-3} e^{-\text{ProductLog}\left(\frac{a}{x}\right)} \left(-\text{ProductLog}\left(\frac{a}{x}\right)\right)^{-p-2} \left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^{p+1} \Gamma \left(p+3,-2 \text{ProductLog}\left(\frac{a}{x}\right)\right)}{a c x}-\frac{2^{-p-2} e^{-\text{ProductLog}\left(\frac{a}{x}\right)} \left(-\text{ProductLog}\left(\frac{a}{x}\right)\right)^{-p-1} \left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p \Gamma \left(p+2,-2 \text{ProductLog}\left(\frac{a}{x}\right)\right)}{a x}",1,"(2^(-3 - p)*(2*Gamma[2 + p, -2*ProductLog[a/x]] - Gamma[3 + p, -2*ProductLog[a/x]])*(c*ProductLog[a/x])^p)/(a^2*(-ProductLog[a/x])^p)","A",1
287,1,28,28,0.0028222,"\int \text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)^5 \, dx","Integrate[ProductLog[a/x^(1/4)]^5,x]","x \text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)^5+\frac{5}{4} x \text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)^4","x \text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)^5+\frac{5}{4} x \text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)^4",1,"(5*x*ProductLog[a/x^(1/4)]^4)/4 + x*ProductLog[a/x^(1/4)]^5","A",1
288,1,28,28,0.0032415,"\int \text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)^4 \, dx","Integrate[ProductLog[a/x^(1/3)]^4,x]","x \text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)^4+\frac{4}{3} x \text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)^3","x \text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)^4+\frac{4}{3} x \text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)^3",1,"(4*x*ProductLog[a/x^(1/3)]^3)/3 + x*ProductLog[a/x^(1/3)]^4","A",1
289,1,28,28,0.0031137,"\int \text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)^3 \, dx","Integrate[ProductLog[a/Sqrt[x]]^3,x]","x \text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)^3+\frac{3}{2} x \text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)^2","x \text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)^3+\frac{3}{2} x \text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)^2",1,"(3*x*ProductLog[a/Sqrt[x]]^2)/2 + x*ProductLog[a/Sqrt[x]]^3","A",1
290,1,20,20,0.0037885,"\int \text{ProductLog}\left(\frac{a}{x}\right)^2 \, dx","Integrate[ProductLog[a/x]^2,x]","x \text{ProductLog}\left(\frac{a}{x}\right)^2+2 x \text{ProductLog}\left(\frac{a}{x}\right)","x \text{ProductLog}\left(\frac{a}{x}\right)^2+2 x \text{ProductLog}\left(\frac{a}{x}\right)",1,"2*x*ProductLog[a/x] + x*ProductLog[a/x]^2","A",1
291,1,28,28,0.0038866,"\int \frac{1}{\text{ProductLog}\left(a \sqrt{x}\right)} \, dx","Integrate[ProductLog[a*Sqrt[x]]^(-1),x]","\frac{x}{\text{ProductLog}\left(a \sqrt{x}\right)}+\frac{x}{2 \text{ProductLog}\left(a \sqrt{x}\right)^2}","\frac{x}{\text{ProductLog}\left(a \sqrt{x}\right)}+\frac{x}{2 \text{ProductLog}\left(a \sqrt{x}\right)^2}",1,"x/(2*ProductLog[a*Sqrt[x]]^2) + x/ProductLog[a*Sqrt[x]]","A",1
292,1,28,28,0.0031182,"\int \frac{1}{\text{ProductLog}\left(a \sqrt[3]{x}\right)^2} \, dx","Integrate[ProductLog[a*x^(1/3)]^(-2),x]","\frac{x}{\text{ProductLog}\left(a \sqrt[3]{x}\right)^2}+\frac{2 x}{3 \text{ProductLog}\left(a \sqrt[3]{x}\right)^3}","\frac{x}{\text{ProductLog}\left(a \sqrt[3]{x}\right)^2}+\frac{2 x}{3 \text{ProductLog}\left(a \sqrt[3]{x}\right)^3}",1,"(2*x)/(3*ProductLog[a*x^(1/3)]^3) + x/ProductLog[a*x^(1/3)]^2","A",1
293,1,28,28,0.0030154,"\int \frac{1}{\text{ProductLog}\left(a \sqrt[4]{x}\right)^3} \, dx","Integrate[ProductLog[a*x^(1/4)]^(-3),x]","\frac{x}{\text{ProductLog}\left(a \sqrt[4]{x}\right)^3}+\frac{3 x}{4 \text{ProductLog}\left(a \sqrt[4]{x}\right)^4}","\frac{x}{\text{ProductLog}\left(a \sqrt[4]{x}\right)^3}+\frac{3 x}{4 \text{ProductLog}\left(a \sqrt[4]{x}\right)^4}",1,"(3*x)/(4*ProductLog[a*x^(1/4)]^4) + x/ProductLog[a*x^(1/4)]^3","A",1
294,1,30,30,0.00285,"\int \text{ProductLog}\left(\frac{a}{\sqrt[5]{x}}\right)^4 \, dx","Integrate[ProductLog[a/x^(1/5)]^4,x]","20 a^5 \text{Ei}\left(-5 \text{ProductLog}\left(\frac{a}{\sqrt[5]{x}}\right)\right)+5 x \text{ProductLog}\left(\frac{a}{\sqrt[5]{x}}\right)^4","20 a^5 \text{Ei}\left(-5 \text{ProductLog}\left(\frac{a}{\sqrt[5]{x}}\right)\right)+5 x \text{ProductLog}\left(\frac{a}{\sqrt[5]{x}}\right)^4",1,"20*a^5*ExpIntegralEi[-5*ProductLog[a/x^(1/5)]] + 5*x*ProductLog[a/x^(1/5)]^4","A",1
295,1,30,30,0.0027382,"\int \text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)^3 \, dx","Integrate[ProductLog[a/x^(1/4)]^3,x]","12 a^4 \text{Ei}\left(-4 \text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)\right)+4 x \text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)^3","12 a^4 \text{Ei}\left(-4 \text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)\right)+4 x \text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)^3",1,"12*a^4*ExpIntegralEi[-4*ProductLog[a/x^(1/4)]] + 4*x*ProductLog[a/x^(1/4)]^3","A",1
296,1,30,30,0.0027802,"\int \text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)^2 \, dx","Integrate[ProductLog[a/x^(1/3)]^2,x]","6 a^3 \text{Ei}\left(-3 \text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)\right)+3 x \text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)^2","6 a^3 \text{Ei}\left(-3 \text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)\right)+3 x \text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)^2",1,"6*a^3*ExpIntegralEi[-3*ProductLog[a/x^(1/3)]] + 3*x*ProductLog[a/x^(1/3)]^2","A",1
297,1,28,28,0.0032514,"\int \text{ProductLog}\left(\frac{a}{\sqrt{x}}\right) \, dx","Integrate[ProductLog[a/Sqrt[x]],x]","2 a^2 \text{Ei}\left(-2 \text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)\right)+2 x \text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)","2 a^2 \text{Ei}\left(-2 \text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)\right)+2 x \text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)",1,"2*a^2*ExpIntegralEi[-2*ProductLog[a/Sqrt[x]]] + 2*x*ProductLog[a/Sqrt[x]]","A",1
298,1,20,20,0.0103919,"\int \frac{1}{\text{ProductLog}(a x)^2} \, dx","Integrate[ProductLog[a*x]^(-2),x]","\frac{2 \text{Ei}(\text{ProductLog}(a x))}{a}-\frac{x}{\text{ProductLog}(a x)^2}","\frac{2 \text{Ei}(\text{ProductLog}(a x))}{a}-\frac{x}{\text{ProductLog}(a x)^2}",1,"(2*ExpIntegralEi[ProductLog[a*x]])/a - x/ProductLog[a*x]^2","A",1
299,1,30,30,0.0030012,"\int \frac{1}{\text{ProductLog}\left(a \sqrt{x}\right)^3} \, dx","Integrate[ProductLog[a*Sqrt[x]]^(-3),x]","\frac{6 \text{Ei}\left(2 \text{ProductLog}\left(a \sqrt{x}\right)\right)}{a^2}-\frac{2 x}{\text{ProductLog}\left(a \sqrt{x}\right)^3}","\frac{6 \text{Ei}\left(2 \text{ProductLog}\left(a \sqrt{x}\right)\right)}{a^2}-\frac{2 x}{\text{ProductLog}\left(a \sqrt{x}\right)^3}",1,"(6*ExpIntegralEi[2*ProductLog[a*Sqrt[x]]])/a^2 - (2*x)/ProductLog[a*Sqrt[x]]^3","A",1
300,1,30,30,0.0047009,"\int \frac{1}{\text{ProductLog}\left(a \sqrt[3]{x}\right)^4} \, dx","Integrate[ProductLog[a*x^(1/3)]^(-4),x]","\frac{12 \text{Ei}\left(3 \text{ProductLog}\left(a \sqrt[3]{x}\right)\right)}{a^3}-\frac{3 x}{\text{ProductLog}\left(a \sqrt[3]{x}\right)^4}","\frac{12 \text{Ei}\left(3 \text{ProductLog}\left(a \sqrt[3]{x}\right)\right)}{a^3}-\frac{3 x}{\text{ProductLog}\left(a \sqrt[3]{x}\right)^4}",1,"(12*ExpIntegralEi[3*ProductLog[a*x^(1/3)]])/a^3 - (3*x)/ProductLog[a*x^(1/3)]^4","A",1
301,1,30,30,0.0027726,"\int \frac{1}{\text{ProductLog}\left(a \sqrt[4]{x}\right)^5} \, dx","Integrate[ProductLog[a*x^(1/4)]^(-5),x]","\frac{20 \text{Ei}\left(4 \text{ProductLog}\left(a \sqrt[4]{x}\right)\right)}{a^4}-\frac{4 x}{\text{ProductLog}\left(a \sqrt[4]{x}\right)^5}","\frac{20 \text{Ei}\left(4 \text{ProductLog}\left(a \sqrt[4]{x}\right)\right)}{a^4}-\frac{4 x}{\text{ProductLog}\left(a \sqrt[4]{x}\right)^5}",1,"(20*ExpIntegralEi[4*ProductLog[a*x^(1/4)]])/a^4 - (4*x)/ProductLog[a*x^(1/4)]^5","A",1
302,1,25,39,0.0095624,"\int \text{ProductLog}\left(a x^n\right)^{\frac{-1+n}{n}} \, dx","Integrate[ProductLog[a*x^n]^((-1 + n)/n),x]","x \text{ProductLog}\left(a x^n\right)^{-1/n} \left(\text{ProductLog}\left(a x^n\right)-n+1\right)","(1-n) x \text{ProductLog}\left(a x^n\right)^{-1/n}+x \text{ProductLog}\left(a x^n\right)^{-\frac{1-n}{n}}",1,"(x*(1 - n + ProductLog[a*x^n]))/ProductLog[a*x^n]^n^(-1)","A",1
303,1,39,44,0.0221739,"\int \text{ProductLog}\left(a x^{\frac{1}{1-p}}\right)^p \, dx","Integrate[ProductLog[a*x^(1 - p)^(-1)]^p,x]","x \left(\frac{p}{(p-1) \text{ProductLog}\left(a x^{\frac{1}{1-p}}\right)}+1\right) \text{ProductLog}\left(a x^{\frac{1}{1-p}}\right)^p","x \text{ProductLog}\left(a x^{\frac{1}{1-p}}\right)^p-\frac{p x \text{ProductLog}\left(a x^{\frac{1}{1-p}}\right)^{p-1}}{1-p}",1,"x*(1 + p/((-1 + p)*ProductLog[a*x^(1 - p)^(-1)]))*ProductLog[a*x^(1 - p)^(-1)]^p","A",1
304,1,108,139,0.0347732,"\int x^{-1-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{9/2} \, dx","Integrate[x^(-1 - n)*(c*ProductLog[a*x^n])^(9/2),x]","-\frac{c^4 x^{-n} \sqrt{c \text{ProductLog}\left(a x^n\right)} \left(-135 \sqrt{\pi } a x^n \text{Erf}\left(\sqrt{\text{ProductLog}\left(a x^n\right)}\right)+16 \text{ProductLog}\left(a x^n\right)^{9/2}+72 \text{ProductLog}\left(a x^n\right)^{7/2}+180 \text{ProductLog}\left(a x^n\right)^{5/2}+270 \text{ProductLog}\left(a x^n\right)^{3/2}\right)}{16 n \sqrt{\text{ProductLog}\left(a x^n\right)}}","\frac{135 \sqrt{\pi } a c^{9/2} \text{Erf}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{16 n}-\frac{135 c^3 x^{-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}{8 n}-\frac{45 c^2 x^{-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}{4 n}-\frac{x^{-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{9/2}}{n}-\frac{9 c x^{-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2}}{2 n}",1,"-(c^4*Sqrt[c*ProductLog[a*x^n]]*(-135*a*Sqrt[Pi]*x^n*Erf[Sqrt[ProductLog[a*x^n]]] + 270*ProductLog[a*x^n]^(3/2) + 180*ProductLog[a*x^n]^(5/2) + 72*ProductLog[a*x^n]^(7/2) + 16*ProductLog[a*x^n]^(9/2)))/(16*n*x^n*Sqrt[ProductLog[a*x^n]])","A",1
305,1,96,112,0.0288585,"\int x^{-1-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2} \, dx","Integrate[x^(-1 - n)*(c*ProductLog[a*x^n])^(7/2),x]","-\frac{c^3 x^{-n} \sqrt{c \text{ProductLog}\left(a x^n\right)} \left(-21 \sqrt{\pi } a x^n \text{Erf}\left(\sqrt{\text{ProductLog}\left(a x^n\right)}\right)+8 \text{ProductLog}\left(a x^n\right)^{7/2}+28 \text{ProductLog}\left(a x^n\right)^{5/2}+42 \text{ProductLog}\left(a x^n\right)^{3/2}\right)}{8 n \sqrt{\text{ProductLog}\left(a x^n\right)}}","\frac{21 \sqrt{\pi } a c^{7/2} \text{Erf}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{8 n}-\frac{21 c^2 x^{-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}{4 n}-\frac{x^{-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2}}{n}-\frac{7 c x^{-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}{2 n}",1,"-(c^3*Sqrt[c*ProductLog[a*x^n]]*(-21*a*Sqrt[Pi]*x^n*Erf[Sqrt[ProductLog[a*x^n]]] + 42*ProductLog[a*x^n]^(3/2) + 28*ProductLog[a*x^n]^(5/2) + 8*ProductLog[a*x^n]^(7/2)))/(8*n*x^n*Sqrt[ProductLog[a*x^n]])","A",1
306,1,81,85,0.034374,"\int x^{-1-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2} \, dx","Integrate[x^(-1 - n)*(c*ProductLog[a*x^n])^(5/2),x]","-\frac{x^{-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2} \left(-5 \sqrt{\pi } a x^n \text{Erf}\left(\sqrt{\text{ProductLog}\left(a x^n\right)}\right)+4 \text{ProductLog}\left(a x^n\right)^{5/2}+10 \text{ProductLog}\left(a x^n\right)^{3/2}\right)}{4 n \text{ProductLog}\left(a x^n\right)^{5/2}}","\frac{5 \sqrt{\pi } a c^{5/2} \text{Erf}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{4 n}-\frac{x^{-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}{n}-\frac{5 c x^{-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}{2 n}",1,"-((c*ProductLog[a*x^n])^(5/2)*(-5*a*Sqrt[Pi]*x^n*Erf[Sqrt[ProductLog[a*x^n]]] + 10*ProductLog[a*x^n]^(3/2) + 4*ProductLog[a*x^n]^(5/2)))/(4*n*x^n*ProductLog[a*x^n]^(5/2))","A",1
307,1,56,60,0.0275643,"\int x^{-1-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2} \, dx","Integrate[x^(-1 - n)*(c*ProductLog[a*x^n])^(3/2),x]","\frac{\left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2} \left(\frac{3 \sqrt{\pi } a \text{Erf}\left(\sqrt{\text{ProductLog}\left(a x^n\right)}\right)}{\text{ProductLog}\left(a x^n\right)^{3/2}}-2 x^{-n}\right)}{2 n}","\frac{3 \sqrt{\pi } a c^{3/2} \text{Erf}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{2 n}-\frac{x^{-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}{n}",1,"((-2/x^n + (3*a*Sqrt[Pi]*Erf[Sqrt[ProductLog[a*x^n]]])/ProductLog[a*x^n]^(3/2))*(c*ProductLog[a*x^n])^(3/2))/(2*n)","A",1
308,1,53,58,0.0341263,"\int x^{-1-n} \sqrt{c \text{ProductLog}\left(a x^n\right)} \, dx","Integrate[x^(-1 - n)*Sqrt[c*ProductLog[a*x^n]],x]","-\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)} \left(\frac{\sqrt{\pi } a \text{Erf}\left(\sqrt{\text{ProductLog}\left(a x^n\right)}\right)}{\sqrt{\text{ProductLog}\left(a x^n\right)}}+2 x^{-n}\right)}{n}","-\frac{\sqrt{\pi } a \sqrt{c} \text{Erf}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{n}-\frac{2 x^{-n} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{n}",1,"-(((2/x^n + (a*Sqrt[Pi]*Erf[Sqrt[ProductLog[a*x^n]]])/Sqrt[ProductLog[a*x^n]])*Sqrt[c*ProductLog[a*x^n]])/n)","A",1
309,1,63,89,0.0235532,"\int \frac{x^{-1-n}}{\sqrt{c \text{ProductLog}\left(a x^n\right)}} \, dx","Integrate[x^(-1 - n)/Sqrt[c*ProductLog[a*x^n]],x]","-\frac{2 x^{-n} \left(\sqrt{\pi } a x^n \sqrt{\text{ProductLog}\left(a x^n\right)} \text{Erf}\left(\sqrt{\text{ProductLog}\left(a x^n\right)}\right)+\text{ProductLog}\left(a x^n\right)+1\right)}{3 n \sqrt{c \text{ProductLog}\left(a x^n\right)}}","-\frac{2 \sqrt{\pi } a \text{Erf}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{3 \sqrt{c} n}-\frac{2 x^{-n} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{3 c n}-\frac{2 x^{-n}}{3 n \sqrt{c \text{ProductLog}\left(a x^n\right)}}",1,"(-2*(1 + a*Sqrt[Pi]*x^n*Erf[Sqrt[ProductLog[a*x^n]]]*Sqrt[ProductLog[a*x^n]] + ProductLog[a*x^n]))/(3*n*x^n*Sqrt[c*ProductLog[a*x^n]])","A",1
310,1,76,116,0.0262812,"\int \frac{x^{-1-n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}} \, dx","Integrate[x^(-1 - n)/(c*ProductLog[a*x^n])^(3/2),x]","\frac{x^{-n} \left(4 \sqrt{\pi } a x^n \text{ProductLog}\left(a x^n\right)^{3/2} \text{Erf}\left(\sqrt{\text{ProductLog}\left(a x^n\right)}\right)+4 \text{ProductLog}\left(a x^n\right)^2-2 \text{ProductLog}\left(a x^n\right)-2\right)}{5 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}","\frac{4 \sqrt{\pi } a \text{Erf}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{5 c^{3/2} n}+\frac{4 x^{-n} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{5 c^2 n}-\frac{2 x^{-n}}{5 c n \sqrt{c \text{ProductLog}\left(a x^n\right)}}-\frac{2 x^{-n}}{5 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}",1,"(-2 - 2*ProductLog[a*x^n] + 4*a*Sqrt[Pi]*x^n*Erf[Sqrt[ProductLog[a*x^n]]]*ProductLog[a*x^n]^(3/2) + 4*ProductLog[a*x^n]^2)/(5*n*x^n*(c*ProductLog[a*x^n])^(3/2))","A",1
311,1,86,143,0.032006,"\int \frac{x^{-1-n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}} \, dx","Integrate[x^(-1 - n)/(c*ProductLog[a*x^n])^(5/2),x]","-\frac{2 x^{-n} \left(4 \sqrt{\pi } a x^n \text{ProductLog}\left(a x^n\right)^{5/2} \text{Erf}\left(\sqrt{\text{ProductLog}\left(a x^n\right)}\right)+4 \text{ProductLog}\left(a x^n\right)^3-2 \text{ProductLog}\left(a x^n\right)^2+3 \text{ProductLog}\left(a x^n\right)+3\right)}{21 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}","-\frac{8 \sqrt{\pi } a \text{Erf}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{21 c^{5/2} n}-\frac{8 x^{-n} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{21 c^3 n}+\frac{4 x^{-n}}{21 c^2 n \sqrt{c \text{ProductLog}\left(a x^n\right)}}-\frac{2 x^{-n}}{7 c n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}-\frac{2 x^{-n}}{7 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}",1,"(-2*(3 + 3*ProductLog[a*x^n] - 2*ProductLog[a*x^n]^2 + 4*a*Sqrt[Pi]*x^n*Erf[Sqrt[ProductLog[a*x^n]]]*ProductLog[a*x^n]^(5/2) + 4*ProductLog[a*x^n]^3))/(21*n*x^n*(c*ProductLog[a*x^n])^(5/2))","A",1
312,1,120,152,0.0581859,"\int x^{-1-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{11/2} \, dx","Integrate[x^(-1 - 2*n)*(c*ProductLog[a*x^n])^(11/2),x]","-\frac{c^5 x^{-2 n} \sqrt{c \text{ProductLog}\left(a x^n\right)} \left(-165 \sqrt{2 \pi } a^2 x^{2 n} \text{Erf}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^n\right)}\right)+256 \text{ProductLog}\left(a x^n\right)^{11/2}+704 \text{ProductLog}\left(a x^n\right)^{9/2}+880 \text{ProductLog}\left(a x^n\right)^{7/2}+660 \text{ProductLog}\left(a x^n\right)^{5/2}\right)}{512 n \sqrt{\text{ProductLog}\left(a x^n\right)}}","\frac{165 \sqrt{\frac{\pi }{2}} a^2 c^{11/2} \text{Erf}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{256 n}-\frac{165 c^3 x^{-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}{128 n}-\frac{55 c^2 x^{-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2}}{32 n}-\frac{x^{-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{11/2}}{2 n}-\frac{11 c x^{-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{9/2}}{8 n}",1,"-(c^5*Sqrt[c*ProductLog[a*x^n]]*(-165*a^2*Sqrt[2*Pi]*x^(2*n)*Erf[Sqrt[2]*Sqrt[ProductLog[a*x^n]]] + 660*ProductLog[a*x^n]^(5/2) + 880*ProductLog[a*x^n]^(7/2) + 704*ProductLog[a*x^n]^(9/2) + 256*ProductLog[a*x^n]^(11/2)))/(512*n*x^(2*n)*Sqrt[ProductLog[a*x^n]])","A",0
313,1,108,125,0.041725,"\int x^{-1-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{9/2} \, dx","Integrate[x^(-1 - 2*n)*(c*ProductLog[a*x^n])^(9/2),x]","-\frac{c^4 x^{-2 n} \sqrt{c \text{ProductLog}\left(a x^n\right)} \left(-27 \sqrt{2 \pi } a^2 x^{2 n} \text{Erf}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^n\right)}\right)+64 \text{ProductLog}\left(a x^n\right)^{9/2}+144 \text{ProductLog}\left(a x^n\right)^{7/2}+108 \text{ProductLog}\left(a x^n\right)^{5/2}\right)}{128 n \sqrt{\text{ProductLog}\left(a x^n\right)}}","\frac{27 \sqrt{\frac{\pi }{2}} a^2 c^{9/2} \text{Erf}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{64 n}-\frac{27 c^2 x^{-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}{32 n}-\frac{x^{-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{9/2}}{2 n}-\frac{9 c x^{-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2}}{8 n}",1,"-(c^4*Sqrt[c*ProductLog[a*x^n]]*(-27*a^2*Sqrt[2*Pi]*x^(2*n)*Erf[Sqrt[2]*Sqrt[ProductLog[a*x^n]]] + 108*ProductLog[a*x^n]^(5/2) + 144*ProductLog[a*x^n]^(7/2) + 64*ProductLog[a*x^n]^(9/2)))/(128*n*x^(2*n)*Sqrt[ProductLog[a*x^n]])","A",0
314,1,96,98,0.033743,"\int x^{-1-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2} \, dx","Integrate[x^(-1 - 2*n)*(c*ProductLog[a*x^n])^(7/2),x]","-\frac{c^3 x^{-2 n} \sqrt{c \text{ProductLog}\left(a x^n\right)} \left(-7 \sqrt{2 \pi } a^2 x^{2 n} \text{Erf}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^n\right)}\right)+16 \text{ProductLog}\left(a x^n\right)^{7/2}+28 \text{ProductLog}\left(a x^n\right)^{5/2}\right)}{32 n \sqrt{\text{ProductLog}\left(a x^n\right)}}","\frac{7 \sqrt{\frac{\pi }{2}} a^2 c^{7/2} \text{Erf}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{16 n}-\frac{x^{-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2}}{2 n}-\frac{7 c x^{-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}{8 n}",1,"-(c^3*Sqrt[c*ProductLog[a*x^n]]*(-7*a^2*Sqrt[2*Pi]*x^(2*n)*Erf[Sqrt[2]*Sqrt[ProductLog[a*x^n]]] + 28*ProductLog[a*x^n]^(5/2) + 16*ProductLog[a*x^n]^(7/2)))/(32*n*x^(2*n)*Sqrt[ProductLog[a*x^n]])","A",0
315,1,66,73,0.0453073,"\int x^{-1-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2} \, dx","Integrate[x^(-1 - 2*n)*(c*ProductLog[a*x^n])^(5/2),x]","\frac{\left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2} \left(\frac{5 \sqrt{2 \pi } a^2 \text{Erf}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^n\right)}\right)}{\text{ProductLog}\left(a x^n\right)^{5/2}}-4 x^{-2 n}\right)}{8 n}","\frac{5 \sqrt{\frac{\pi }{2}} a^2 c^{5/2} \text{Erf}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{4 n}-\frac{x^{-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}{2 n}",1,"((-4/x^(2*n) + (5*a^2*Sqrt[2*Pi]*Erf[Sqrt[2]*Sqrt[ProductLog[a*x^n]]])/ProductLog[a*x^n]^(5/2))*(c*ProductLog[a*x^n])^(5/2))/(8*n)","A",0
316,1,66,69,0.0481971,"\int x^{-1-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2} \, dx","Integrate[x^(-1 - 2*n)*(c*ProductLog[a*x^n])^(3/2),x]","\frac{\left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2} \left(-\frac{3 \sqrt{2 \pi } a^2 \text{Erf}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^n\right)}\right)}{\text{ProductLog}\left(a x^n\right)^{3/2}}-4 x^{-2 n}\right)}{2 n}","-\frac{3 \sqrt{\frac{\pi }{2}} a^2 c^{3/2} \text{Erf}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{n}-\frac{2 x^{-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}{n}",1,"((-4/x^(2*n) - (3*a^2*Sqrt[2*Pi]*Erf[Sqrt[2]*Sqrt[ProductLog[a*x^n]]])/ProductLog[a*x^n]^(3/2))*(c*ProductLog[a*x^n])^(3/2))/(2*n)","A",0
317,1,90,98,0.0276076,"\int x^{-1-2 n} \sqrt{c \text{ProductLog}\left(a x^n\right)} \, dx","Integrate[x^(-1 - 2*n)*Sqrt[c*ProductLog[a*x^n]],x]","\frac{2 x^{-2 n} \sqrt{c \text{ProductLog}\left(a x^n\right)} \left(\sqrt{2 \pi } a^2 x^{2 n} \text{Erf}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^n\right)}\right)+\text{ProductLog}\left(a x^n\right)^{3/2}-\sqrt{\text{ProductLog}\left(a x^n\right)}\right)}{3 n \sqrt{\text{ProductLog}\left(a x^n\right)}}","\frac{2 \sqrt{2 \pi } a^2 \sqrt{c} \text{Erf}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{3 n}+\frac{2 x^{-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}{3 c n}-\frac{2 x^{-2 n} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{3 n}",1,"(2*Sqrt[c*ProductLog[a*x^n]]*(a^2*Sqrt[2*Pi]*x^(2*n)*Erf[Sqrt[2]*Sqrt[ProductLog[a*x^n]]] - Sqrt[ProductLog[a*x^n]] + ProductLog[a*x^n]^(3/2)))/(3*n*x^(2*n)*Sqrt[ProductLog[a*x^n]])","A",0
318,1,88,125,0.0522019,"\int \frac{x^{-1-2 n}}{\sqrt{c \text{ProductLog}\left(a x^n\right)}} \, dx","Integrate[x^(-1 - 2*n)/Sqrt[c*ProductLog[a*x^n]],x]","\frac{2 x^{-2 n} \left(4 \sqrt{2 \pi } a^2 x^{2 n} \sqrt{\text{ProductLog}\left(a x^n\right)} \text{Erf}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^n\right)}\right)+4 \text{ProductLog}\left(a x^n\right)^2-\text{ProductLog}\left(a x^n\right)-3\right)}{15 n \sqrt{c \text{ProductLog}\left(a x^n\right)}}","\frac{8 \sqrt{2 \pi } a^2 \text{Erf}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{15 \sqrt{c} n}+\frac{8 x^{-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}{15 c^2 n}-\frac{2 x^{-2 n} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{15 c n}-\frac{2 x^{-2 n}}{5 n \sqrt{c \text{ProductLog}\left(a x^n\right)}}",1,"(2*(-3 + 4*a^2*Sqrt[2*Pi]*x^(2*n)*Erf[Sqrt[2]*Sqrt[ProductLog[a*x^n]]]*Sqrt[ProductLog[a*x^n]] - ProductLog[a*x^n] + 4*ProductLog[a*x^n]^2))/(15*n*x^(2*n)*Sqrt[c*ProductLog[a*x^n]])","A",0
319,1,98,152,0.0423622,"\int \frac{x^{-1-2 n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}} \, dx","Integrate[x^(-1 - 2*n)/(c*ProductLog[a*x^n])^(3/2),x]","-\frac{2 x^{-2 n} \left(16 \sqrt{2 \pi } a^2 x^{2 n} \text{ProductLog}\left(a x^n\right)^{3/2} \text{Erf}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^n\right)}\right)+16 \text{ProductLog}\left(a x^n\right)^3-4 \text{ProductLog}\left(a x^n\right)^2+3 \text{ProductLog}\left(a x^n\right)+5\right)}{35 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}","-\frac{32 \sqrt{2 \pi } a^2 \text{Erf}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{35 c^{3/2} n}-\frac{32 x^{-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}{35 c^3 n}+\frac{8 x^{-2 n} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{35 c^2 n}-\frac{6 x^{-2 n}}{35 c n \sqrt{c \text{ProductLog}\left(a x^n\right)}}-\frac{2 x^{-2 n}}{7 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}",1,"(-2*(5 + 3*ProductLog[a*x^n] + 16*a^2*Sqrt[2*Pi]*x^(2*n)*Erf[Sqrt[2]*Sqrt[ProductLog[a*x^n]]]*ProductLog[a*x^n]^(3/2) - 4*ProductLog[a*x^n]^2 + 16*ProductLog[a*x^n]^3))/(35*n*x^(2*n)*(c*ProductLog[a*x^n])^(3/2))","A",0
320,1,100,132,0.0427434,"\int x^{-1+n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2} \, dx","Integrate[x^(-1 + n)*(c*ProductLog[a*x^n])^(5/2),x]","\frac{c^3 \left(75 \sqrt{\pi } \sqrt{\text{ProductLog}\left(a x^n\right)} \text{Erfi}\left(\sqrt{\text{ProductLog}\left(a x^n\right)}\right)+16 a x^n \text{ProductLog}\left(a x^n\right)^3-40 a x^n \text{ProductLog}\left(a x^n\right)^2+100 a x^n \text{ProductLog}\left(a x^n\right)-150 a x^n\right)}{16 a n \sqrt{c \text{ProductLog}\left(a x^n\right)}}","\frac{75 \sqrt{\pi } c^{5/2} \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{16 a n}-\frac{75 c^3 x^n}{8 n \sqrt{c \text{ProductLog}\left(a x^n\right)}}+\frac{25 c^2 x^n \sqrt{c \text{ProductLog}\left(a x^n\right)}}{4 n}+\frac{x^n \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}{n}-\frac{5 c x^n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}{2 n}",1,"(c^3*(-150*a*x^n + 75*Sqrt[Pi]*Erfi[Sqrt[ProductLog[a*x^n]]]*Sqrt[ProductLog[a*x^n]] + 100*a*x^n*ProductLog[a*x^n] - 40*a*x^n*ProductLog[a*x^n]^2 + 16*a*x^n*ProductLog[a*x^n]^3))/(16*a*n*Sqrt[c*ProductLog[a*x^n]])","A",1
321,1,86,107,0.0315035,"\int x^{-1+n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2} \, dx","Integrate[x^(-1 + n)*(c*ProductLog[a*x^n])^(3/2),x]","\frac{c^2 \left(-9 \sqrt{\pi } \sqrt{\text{ProductLog}\left(a x^n\right)} \text{Erfi}\left(\sqrt{\text{ProductLog}\left(a x^n\right)}\right)+8 a x^n \text{ProductLog}\left(a x^n\right)^2-12 a x^n \text{ProductLog}\left(a x^n\right)+18 a x^n\right)}{8 a n \sqrt{c \text{ProductLog}\left(a x^n\right)}}","-\frac{9 \sqrt{\pi } c^{3/2} \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{8 a n}+\frac{9 c^2 x^n}{4 n \sqrt{c \text{ProductLog}\left(a x^n\right)}}+\frac{x^n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}{n}-\frac{3 c x^n \sqrt{c \text{ProductLog}\left(a x^n\right)}}{2 n}",1,"(c^2*(18*a*x^n - 9*Sqrt[Pi]*Erfi[Sqrt[ProductLog[a*x^n]]]*Sqrt[ProductLog[a*x^n]] - 12*a*x^n*ProductLog[a*x^n] + 8*a*x^n*ProductLog[a*x^n]^2))/(8*a*n*Sqrt[c*ProductLog[a*x^n]])","A",1
322,1,69,82,0.0232918,"\int x^{-1+n} \sqrt{c \text{ProductLog}\left(a x^n\right)} \, dx","Integrate[x^(-1 + n)*Sqrt[c*ProductLog[a*x^n]],x]","\frac{c \left(\sqrt{\pi } \sqrt{\text{ProductLog}\left(a x^n\right)} \text{Erfi}\left(\sqrt{\text{ProductLog}\left(a x^n\right)}\right)+4 a x^n \text{ProductLog}\left(a x^n\right)-2 a x^n\right)}{4 a n \sqrt{c \text{ProductLog}\left(a x^n\right)}}","\frac{\sqrt{\pi } \sqrt{c} \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{4 a n}+\frac{x^n \sqrt{c \text{ProductLog}\left(a x^n\right)}}{n}-\frac{c x^n}{2 n \sqrt{c \text{ProductLog}\left(a x^n\right)}}",1,"(c*(-2*a*x^n + Sqrt[Pi]*Erfi[Sqrt[ProductLog[a*x^n]]]*Sqrt[ProductLog[a*x^n]] + 4*a*x^n*ProductLog[a*x^n]))/(4*a*n*Sqrt[c*ProductLog[a*x^n]])","A",1
323,1,56,59,0.013538,"\int \frac{x^{-1+n}}{\sqrt{c \text{ProductLog}\left(a x^n\right)}} \, dx","Integrate[x^(-1 + n)/Sqrt[c*ProductLog[a*x^n]],x]","\frac{\sqrt{\pi } \sqrt{\text{ProductLog}\left(a x^n\right)} \text{Erfi}\left(\sqrt{\text{ProductLog}\left(a x^n\right)}\right)+2 a x^n}{2 a n \sqrt{c \text{ProductLog}\left(a x^n\right)}}","\frac{\sqrt{\pi } \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{2 a \sqrt{c} n}+\frac{x^n}{n \sqrt{c \text{ProductLog}\left(a x^n\right)}}",1,"(2*a*x^n + Sqrt[Pi]*Erfi[Sqrt[ProductLog[a*x^n]]]*Sqrt[ProductLog[a*x^n]])/(2*a*n*Sqrt[c*ProductLog[a*x^n]])","A",1
324,1,54,58,0.0232243,"\int \frac{x^{-1+n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}} \, dx","Integrate[x^(-1 + n)/(c*ProductLog[a*x^n])^(3/2),x]","\frac{3 \sqrt{\pi } \text{ProductLog}\left(a x^n\right)^{3/2} \text{Erfi}\left(\sqrt{\text{ProductLog}\left(a x^n\right)}\right)-2 a x^n}{a n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}","\frac{3 \sqrt{\pi } \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{a c^{3/2} n}-\frac{2 x^n}{n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}",1,"(-2*a*x^n + 3*Sqrt[Pi]*Erfi[Sqrt[ProductLog[a*x^n]]]*ProductLog[a*x^n]^(3/2))/(a*n*(c*ProductLog[a*x^n])^(3/2))","A",1
325,1,68,87,0.0254206,"\int \frac{x^{-1+n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}} \, dx","Integrate[x^(-1 + n)/(c*ProductLog[a*x^n])^(5/2),x]","-\frac{2 \left(-5 \sqrt{\pi } \text{ProductLog}\left(a x^n\right)^{5/2} \text{Erfi}\left(\sqrt{\text{ProductLog}\left(a x^n\right)}\right)+5 a x^n \text{ProductLog}\left(a x^n\right)+a x^n\right)}{3 a n \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}","\frac{10 \sqrt{\pi } \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{3 a c^{5/2} n}-\frac{10 x^n}{3 c n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}-\frac{2 x^n}{3 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}",1,"(-2*(a*x^n + 5*a*x^n*ProductLog[a*x^n] - 5*Sqrt[Pi]*Erfi[Sqrt[ProductLog[a*x^n]]]*ProductLog[a*x^n]^(5/2)))/(3*a*n*(c*ProductLog[a*x^n])^(5/2))","A",1
326,1,94,112,0.0440395,"\int \frac{x^{-1+n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2}} \, dx","Integrate[x^(-1 + n)/(c*ProductLog[a*x^n])^(7/2),x]","-\frac{2 \sqrt{c \text{ProductLog}\left(a x^n\right)} \left(-14 \sqrt{\pi } \text{ProductLog}\left(a x^n\right)^{7/2} \text{Erfi}\left(\sqrt{\text{ProductLog}\left(a x^n\right)}\right)+14 a x^n \text{ProductLog}\left(a x^n\right)^2+7 a x^n \text{ProductLog}\left(a x^n\right)+3 a x^n\right)}{15 a c^4 n \text{ProductLog}\left(a x^n\right)^4}","\frac{28 \sqrt{\pi } \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{15 a c^{7/2} n}-\frac{28 x^n}{15 c^2 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}-\frac{14 x^n}{15 c n \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}-\frac{2 x^n}{5 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2}}",1,"(-2*Sqrt[c*ProductLog[a*x^n]]*(3*a*x^n + 7*a*x^n*ProductLog[a*x^n] + 14*a*x^n*ProductLog[a*x^n]^2 - 14*Sqrt[Pi]*Erfi[Sqrt[ProductLog[a*x^n]]]*ProductLog[a*x^n]^(7/2)))/(15*a*c^4*n*ProductLog[a*x^n]^4)","A",1
327,1,108,137,0.0522114,"\int \frac{x^{-1+n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{9/2}} \, dx","Integrate[x^(-1 + n)/(c*ProductLog[a*x^n])^(9/2),x]","-\frac{2 \sqrt{c \text{ProductLog}\left(a x^n\right)} \left(-12 \sqrt{\pi } \text{ProductLog}\left(a x^n\right)^{9/2} \text{Erfi}\left(\sqrt{\text{ProductLog}\left(a x^n\right)}\right)+12 a x^n \text{ProductLog}\left(a x^n\right)^3+6 a x^n \text{ProductLog}\left(a x^n\right)^2+9 a x^n \text{ProductLog}\left(a x^n\right)+5 a x^n\right)}{35 a c^5 n \text{ProductLog}\left(a x^n\right)^5}","\frac{24 \sqrt{\pi } \text{Erfi}\left(\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{35 a c^{9/2} n}-\frac{24 x^n}{35 c^3 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}-\frac{12 x^n}{35 c^2 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}-\frac{18 x^n}{35 c n \left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2}}-\frac{2 x^n}{7 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{9/2}}",1,"(-2*Sqrt[c*ProductLog[a*x^n]]*(5*a*x^n + 9*a*x^n*ProductLog[a*x^n] + 6*a*x^n*ProductLog[a*x^n]^2 + 12*a*x^n*ProductLog[a*x^n]^3 - 12*Sqrt[Pi]*Erfi[Sqrt[ProductLog[a*x^n]]]*ProductLog[a*x^n]^(9/2)))/(35*a*c^5*n*ProductLog[a*x^n]^5)","A",1
328,1,129,152,0.0433238,"\int x^{-1+2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2} \, dx","Integrate[x^(-1 + 2*n)*(c*ProductLog[a*x^n])^(3/2),x]","\frac{\left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2} \left(256 a^2 x^{2 n} \text{ProductLog}\left(a x^n\right)^3-192 a^2 x^{2 n} \text{ProductLog}\left(a x^n\right)^2+240 a^2 x^{2 n} \text{ProductLog}\left(a x^n\right)-180 a^2 x^{2 n}+45 \sqrt{2 \pi } \text{ProductLog}\left(a x^n\right)^{3/2} \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^n\right)}\right)\right)}{512 a^2 n \text{ProductLog}\left(a x^n\right)^3}","\frac{45 \sqrt{\frac{\pi }{2}} c^{3/2} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{256 a^2 n}-\frac{45 c^3 x^{2 n}}{128 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}+\frac{15 c^2 x^{2 n}}{32 n \sqrt{c \text{ProductLog}\left(a x^n\right)}}+\frac{x^{2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}{2 n}-\frac{3 c x^{2 n} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{8 n}",1,"((c*ProductLog[a*x^n])^(3/2)*(-180*a^2*x^(2*n) + 240*a^2*x^(2*n)*ProductLog[a*x^n] + 45*Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ProductLog[a*x^n]]]*ProductLog[a*x^n]^(3/2) - 192*a^2*x^(2*n)*ProductLog[a*x^n]^2 + 256*a^2*x^(2*n)*ProductLog[a*x^n]^3))/(512*a^2*n*ProductLog[a*x^n]^3)","A",0
329,1,111,125,0.0352977,"\int x^{-1+2 n} \sqrt{c \text{ProductLog}\left(a x^n\right)} \, dx","Integrate[x^(-1 + 2*n)*Sqrt[c*ProductLog[a*x^n]],x]","\frac{\sqrt{c \text{ProductLog}\left(a x^n\right)} \left(64 a^2 x^{2 n} \text{ProductLog}\left(a x^n\right)^2-16 a^2 x^{2 n} \text{ProductLog}\left(a x^n\right)+12 a^2 x^{2 n}-3 \sqrt{2 \pi } \text{ProductLog}\left(a x^n\right)^{3/2} \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^n\right)}\right)\right)}{128 a^2 n \text{ProductLog}\left(a x^n\right)^2}","-\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{c} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{64 a^2 n}+\frac{3 c^2 x^{2 n}}{32 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}+\frac{x^{2 n} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{2 n}-\frac{c x^{2 n}}{8 n \sqrt{c \text{ProductLog}\left(a x^n\right)}}",1,"(Sqrt[c*ProductLog[a*x^n]]*(12*a^2*x^(2*n) - 16*a^2*x^(2*n)*ProductLog[a*x^n] - 3*Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ProductLog[a*x^n]]]*ProductLog[a*x^n]^(3/2) + 64*a^2*x^(2*n)*ProductLog[a*x^n]^2))/(128*a^2*n*ProductLog[a*x^n]^2)","A",0
330,1,86,98,0.0330828,"\int \frac{x^{-1+2 n}}{\sqrt{c \text{ProductLog}\left(a x^n\right)}} \, dx","Integrate[x^(-1 + 2*n)/Sqrt[c*ProductLog[a*x^n]],x]","\frac{c \left(16 a^2 x^{2 n} \text{ProductLog}\left(a x^n\right)+4 a^2 x^{2 n}-\sqrt{2 \pi } \text{ProductLog}\left(a x^n\right)^{3/2} \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^n\right)}\right)\right)}{32 a^2 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}","-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{16 a^2 \sqrt{c} n}+\frac{x^{2 n}}{2 n \sqrt{c \text{ProductLog}\left(a x^n\right)}}+\frac{c x^{2 n}}{8 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}",1,"(c*(4*a^2*x^(2*n) + 16*a^2*x^(2*n)*ProductLog[a*x^n] - Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ProductLog[a*x^n]]]*ProductLog[a*x^n]^(3/2)))/(32*a^2*n*(c*ProductLog[a*x^n])^(3/2))","A",0
331,1,69,73,0.0240582,"\int \frac{x^{-1+2 n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}} \, dx","Integrate[x^(-1 + 2*n)/(c*ProductLog[a*x^n])^(3/2),x]","\frac{4 a^2 x^{2 n}+3 \sqrt{2 \pi } \text{ProductLog}\left(a x^n\right)^{3/2} \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^n\right)}\right)}{8 a^2 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}","\frac{3 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{4 a^2 c^{3/2} n}+\frac{x^{2 n}}{2 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}}",1,"(4*a^2*x^(2*n) + 3*Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ProductLog[a*x^n]]]*ProductLog[a*x^n]^(3/2))/(8*a^2*n*(c*ProductLog[a*x^n])^(3/2))","A",0
332,1,69,69,0.0309091,"\int \frac{x^{-1+2 n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}} \, dx","Integrate[x^(-1 + 2*n)/(c*ProductLog[a*x^n])^(5/2),x]","\frac{5 \sqrt{2 \pi } \text{ProductLog}\left(a x^n\right)^{5/2} \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^n\right)}\right)-4 a^2 x^{2 n}}{2 a^2 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}","\frac{5 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{a^2 c^{5/2} n}-\frac{2 x^{2 n}}{n \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}",1,"(-4*a^2*x^(2*n) + 5*Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ProductLog[a*x^n]]]*ProductLog[a*x^n]^(5/2))/(2*a^2*n*(c*ProductLog[a*x^n])^(5/2))","A",0
333,1,95,98,0.0458243,"\int \frac{x^{-1+2 n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2}} \, dx","Integrate[x^(-1 + 2*n)/(c*ProductLog[a*x^n])^(7/2),x]","-\frac{2 \sqrt{c \text{ProductLog}\left(a x^n\right)} \left(7 a^2 x^{2 n} \text{ProductLog}\left(a x^n\right)+a^2 x^{2 n}-7 \sqrt{2 \pi } \text{ProductLog}\left(a x^n\right)^{7/2} \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^n\right)}\right)\right)}{3 a^2 c^4 n \text{ProductLog}\left(a x^n\right)^4}","\frac{14 \sqrt{2 \pi } \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{3 a^2 c^{7/2} n}-\frac{14 x^{2 n}}{3 c n \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}-\frac{2 x^{2 n}}{3 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2}}",1,"(-2*Sqrt[c*ProductLog[a*x^n]]*(a^2*x^(2*n) + 7*a^2*x^(2*n)*ProductLog[a*x^n] - 7*Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ProductLog[a*x^n]]]*ProductLog[a*x^n]^(7/2)))/(3*a^2*c^4*n*ProductLog[a*x^n]^4)","A",0
334,1,113,125,0.0639607,"\int \frac{x^{-1+2 n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{9/2}} \, dx","Integrate[x^(-1 + 2*n)/(c*ProductLog[a*x^n])^(9/2),x]","-\frac{2 \sqrt{c \text{ProductLog}\left(a x^n\right)} \left(12 a^2 x^{2 n} \text{ProductLog}\left(a x^n\right)^2+3 a^2 x^{2 n} \text{ProductLog}\left(a x^n\right)+a^2 x^{2 n}-12 \sqrt{2 \pi } \text{ProductLog}\left(a x^n\right)^{9/2} \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^n\right)}\right)\right)}{5 a^2 c^5 n \text{ProductLog}\left(a x^n\right)^5}","\frac{24 \sqrt{2 \pi } \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{5 a^2 c^{9/2} n}-\frac{24 x^{2 n}}{5 c^2 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}-\frac{6 x^{2 n}}{5 c n \left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2}}-\frac{2 x^{2 n}}{5 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{9/2}}",1,"(-2*Sqrt[c*ProductLog[a*x^n]]*(a^2*x^(2*n) + 3*a^2*x^(2*n)*ProductLog[a*x^n] + 12*a^2*x^(2*n)*ProductLog[a*x^n]^2 - 12*Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ProductLog[a*x^n]]]*ProductLog[a*x^n]^(9/2)))/(5*a^2*c^5*n*ProductLog[a*x^n]^5)","A",0
335,1,132,152,0.0715945,"\int \frac{x^{-1+2 n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{11/2}} \, dx","Integrate[x^(-1 + 2*n)/(c*ProductLog[a*x^n])^(11/2),x]","-\frac{2 \sqrt{c \text{ProductLog}\left(a x^n\right)} \left(176 a^2 x^{2 n} \text{ProductLog}\left(a x^n\right)^3+44 a^2 x^{2 n} \text{ProductLog}\left(a x^n\right)^2+33 a^2 x^{2 n} \text{ProductLog}\left(a x^n\right)+15 a^2 x^{2 n}-176 \sqrt{2 \pi } \text{ProductLog}\left(a x^n\right)^{11/2} \text{Erfi}\left(\sqrt{2} \sqrt{\text{ProductLog}\left(a x^n\right)}\right)\right)}{105 a^2 c^6 n \text{ProductLog}\left(a x^n\right)^6}","\frac{352 \sqrt{2 \pi } \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c \text{ProductLog}\left(a x^n\right)}}{\sqrt{c}}\right)}{105 a^2 c^{11/2} n}-\frac{352 x^{2 n}}{105 c^3 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}}-\frac{88 x^{2 n}}{105 c^2 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2}}-\frac{22 x^{2 n}}{35 c n \left(c \text{ProductLog}\left(a x^n\right)\right)^{9/2}}-\frac{2 x^{2 n}}{7 n \left(c \text{ProductLog}\left(a x^n\right)\right)^{11/2}}",1,"(-2*Sqrt[c*ProductLog[a*x^n]]*(15*a^2*x^(2*n) + 33*a^2*x^(2*n)*ProductLog[a*x^n] + 44*a^2*x^(2*n)*ProductLog[a*x^n]^2 + 176*a^2*x^(2*n)*ProductLog[a*x^n]^3 - 176*Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ProductLog[a*x^n]]]*ProductLog[a*x^n]^(11/2)))/(105*a^2*c^6*n*ProductLog[a*x^n]^6)","A",0
336,1,30,41,0.008095,"\int x^{-1-3 n} \text{ProductLog}\left(a x^n\right)^4 \, dx","Integrate[x^(-1 - 3*n)*ProductLog[a*x^n]^4,x]","-\frac{x^{-3 n} \text{ProductLog}\left(a x^n\right)^3 \left(3 \text{ProductLog}\left(a x^n\right)+4\right)}{9 n}","-\frac{x^{-3 n} \text{ProductLog}\left(a x^n\right)^4}{3 n}-\frac{4 x^{-3 n} \text{ProductLog}\left(a x^n\right)^3}{9 n}",1,"-(ProductLog[a*x^n]^3*(4 + 3*ProductLog[a*x^n]))/(9*n*x^(3*n))","A",1
337,1,30,41,0.008989,"\int x^{-1-2 n} \text{ProductLog}\left(a x^n\right)^3 \, dx","Integrate[x^(-1 - 2*n)*ProductLog[a*x^n]^3,x]","-\frac{x^{-2 n} \text{ProductLog}\left(a x^n\right)^2 \left(2 \text{ProductLog}\left(a x^n\right)+3\right)}{4 n}","-\frac{x^{-2 n} \text{ProductLog}\left(a x^n\right)^3}{2 n}-\frac{3 x^{-2 n} \text{ProductLog}\left(a x^n\right)^2}{4 n}",1,"-(ProductLog[a*x^n]^2*(3 + 2*ProductLog[a*x^n]))/(4*n*x^(2*n))","A",1
338,1,24,35,0.0065275,"\int x^{-1-n} \text{ProductLog}\left(a x^n\right)^2 \, dx","Integrate[x^(-1 - n)*ProductLog[a*x^n]^2,x]","-\frac{x^{-n} \text{ProductLog}\left(a x^n\right) \left(\text{ProductLog}\left(a x^n\right)+2\right)}{n}","-\frac{x^{-n} \text{ProductLog}\left(a x^n\right)^2}{n}-\frac{2 x^{-n} \text{ProductLog}\left(a x^n\right)}{n}",1,"-((ProductLog[a*x^n]*(2 + ProductLog[a*x^n]))/(n*x^n))","A",1
339,1,30,41,0.0074041,"\int \frac{x^{-1+2 n}}{\text{ProductLog}\left(a x^n\right)} \, dx","Integrate[x^(-1 + 2*n)/ProductLog[a*x^n],x]","\frac{x^{2 n} \left(2 \text{ProductLog}\left(a x^n\right)+1\right)}{4 n \text{ProductLog}\left(a x^n\right)^2}","\frac{x^{2 n}}{2 n \text{ProductLog}\left(a x^n\right)}+\frac{x^{2 n}}{4 n \text{ProductLog}\left(a x^n\right)^2}",1,"(x^(2*n)*(1 + 2*ProductLog[a*x^n]))/(4*n*ProductLog[a*x^n]^2)","A",1
340,1,30,41,0.0078254,"\int \frac{x^{-1+3 n}}{\text{ProductLog}\left(a x^n\right)^2} \, dx","Integrate[x^(-1 + 3*n)/ProductLog[a*x^n]^2,x]","\frac{x^{3 n} \left(3 \text{ProductLog}\left(a x^n\right)+2\right)}{9 n \text{ProductLog}\left(a x^n\right)^3}","\frac{x^{3 n}}{3 n \text{ProductLog}\left(a x^n\right)^2}+\frac{2 x^{3 n}}{9 n \text{ProductLog}\left(a x^n\right)^3}",1,"(x^(3*n)*(2 + 3*ProductLog[a*x^n]))/(9*n*ProductLog[a*x^n]^3)","A",1
341,1,30,41,0.0098911,"\int \frac{x^{-1+4 n}}{\text{ProductLog}\left(a x^n\right)^3} \, dx","Integrate[x^(-1 + 4*n)/ProductLog[a*x^n]^3,x]","\frac{x^{4 n} \left(4 \text{ProductLog}\left(a x^n\right)+3\right)}{16 n \text{ProductLog}\left(a x^n\right)^4}","\frac{x^{4 n}}{4 n \text{ProductLog}\left(a x^n\right)^3}+\frac{3 x^{4 n}}{16 n \text{ProductLog}\left(a x^n\right)^4}",1,"(x^(4*n)*(3 + 4*ProductLog[a*x^n]))/(16*n*ProductLog[a*x^n]^4)","A",1
342,0,0,81,0.1008641,"\int x^{-1-n (1+p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^p \, dx","Integrate[x^(-1 - n*(1 + p))*(c*ProductLog[a*x^n])^p,x]","\int x^{-1-n (1+p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^p \, dx","-p \text{ProductLog}\left(a x^n\right)^{-p} \left(c \text{ProductLog}\left(a x^n\right)\right)^p \text{Int}\left(\frac{x^{-n (p+1)-1} \text{ProductLog}\left(a x^n\right)^{p+1}}{\text{ProductLog}\left(a x^n\right)+1},x\right)-\frac{x^{-n (p+1)} \left(c \text{ProductLog}\left(a x^n\right)\right)^p}{n}",0,"Integrate[x^(-1 - n*(1 + p))*(c*ProductLog[a*x^n])^p, x]","F",-1
343,0,0,76,0.0733562,"\int x^{-1-n p} \left(c \text{ProductLog}\left(a x^n\right)\right)^p \, dx","Integrate[x^(-1 - n*p)*(c*ProductLog[a*x^n])^p,x]","\int x^{-1-n p} \left(c \text{ProductLog}\left(a x^n\right)\right)^p \, dx","\text{ProductLog}\left(a x^n\right)^{-p} \left(c \text{ProductLog}\left(a x^n\right)\right)^p \text{Int}\left(\frac{x^{-n p-1} \text{ProductLog}\left(a x^n\right)^p}{\text{ProductLog}\left(a x^n\right)+1},x\right)-\frac{x^{-n p} \left(c \text{ProductLog}\left(a x^n\right)\right)^p}{n p}",0,"Integrate[x^(-1 - n*p)*(c*ProductLog[a*x^n])^p, x]","F",-1
344,1,43,66,0.0246963,"\int x^{-1+n (1-p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^p \, dx","Integrate[x^(-1 + n*(1 - p))*(c*ProductLog[a*x^n])^p,x]","-\frac{c x^{n-n p} \left((p-1) \text{ProductLog}\left(a x^n\right)+p\right) \left(c \text{ProductLog}\left(a x^n\right)\right)^{p-1}}{n (p-1)^2}","\frac{x^{n (1-p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^p}{n (1-p)}-\frac{c p x^{n (1-p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^{p-1}}{n (1-p)^2}",1,"-((c*x^(n - n*p)*(c*ProductLog[a*x^n])^(-1 + p)*(p + (-1 + p)*ProductLog[a*x^n]))/(n*(-1 + p)^2))","A",1
345,1,63,102,0.0391442,"\int x^{-1+n (2-p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^p \, dx","Integrate[x^(-1 + n*(2 - p))*(c*ProductLog[a*x^n])^p,x]","-\frac{x^{-n (p-2)} \left((p-2)^2 \text{ProductLog}\left(a x^n\right)^2+(p-2) p \text{ProductLog}\left(a x^n\right)+p\right) \left(c \text{ProductLog}\left(a x^n\right)\right)^p}{n (p-2)^3 \text{ProductLog}\left(a x^n\right)^2}","\frac{c^2 p x^{n (2-p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^{p-2}}{n (2-p)^3}-\frac{c p x^{n (2-p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^{p-1}}{n (2-p)^2}+\frac{x^{n (2-p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^p}{n (2-p)}",1,"-(((c*ProductLog[a*x^n])^p*(p + (-2 + p)*p*ProductLog[a*x^n] + (-2 + p)^2*ProductLog[a*x^n]^2))/(n*(-2 + p)^3*x^(n*(-2 + p))*ProductLog[a*x^n]^2))","A",1
346,1,81,140,0.0485394,"\int x^{-1+n (3-p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^p \, dx","Integrate[x^(-1 + n*(3 - p))*(c*ProductLog[a*x^n])^p,x]","-\frac{x^{-n (p-3)} \left((p-3)^3 \text{ProductLog}\left(a x^n\right)^3+(p-3)^2 p \text{ProductLog}\left(a x^n\right)^2+2 (p-3) p \text{ProductLog}\left(a x^n\right)+2 p\right) \left(c \text{ProductLog}\left(a x^n\right)\right)^p}{n (p-3)^4 \text{ProductLog}\left(a x^n\right)^3}","-\frac{2 c^3 p x^{n (3-p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^{p-3}}{n (3-p)^4}+\frac{2 c^2 p x^{n (3-p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^{p-2}}{n (3-p)^3}-\frac{c p x^{n (3-p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^{p-1}}{n (3-p)^2}+\frac{x^{n (3-p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^p}{n (3-p)}",1,"-(((c*ProductLog[a*x^n])^p*(2*p + 2*(-3 + p)*p*ProductLog[a*x^n] + (-3 + p)^2*p*ProductLog[a*x^n]^2 + (-3 + p)^3*ProductLog[a*x^n]^3))/(n*(-3 + p)^4*x^(n*(-3 + p))*ProductLog[a*x^n]^3))","A",1
347,1,53,53,0.0081707,"\int \frac{x^3}{1+\text{ProductLog}(a x)} \, dx","Integrate[x^3/(1 + ProductLog[a*x]),x]","\frac{x^4}{4 \text{ProductLog}(a x)}-\frac{3 x^4}{16 \text{ProductLog}(a x)^2}+\frac{3 x^4}{32 \text{ProductLog}(a x)^3}-\frac{3 x^4}{128 \text{ProductLog}(a x)^4}","\frac{x^4}{4 \text{ProductLog}(a x)}-\frac{3 x^4}{16 \text{ProductLog}(a x)^2}+\frac{3 x^4}{32 \text{ProductLog}(a x)^3}-\frac{3 x^4}{128 \text{ProductLog}(a x)^4}",1,"(-3*x^4)/(128*ProductLog[a*x]^4) + (3*x^4)/(32*ProductLog[a*x]^3) - (3*x^4)/(16*ProductLog[a*x]^2) + x^4/(4*ProductLog[a*x])","A",1
348,1,40,40,0.0048319,"\int \frac{x^2}{1+\text{ProductLog}(a x)} \, dx","Integrate[x^2/(1 + ProductLog[a*x]),x]","\frac{x^3}{3 \text{ProductLog}(a x)}-\frac{2 x^3}{9 \text{ProductLog}(a x)^2}+\frac{2 x^3}{27 \text{ProductLog}(a x)^3}","\frac{x^3}{3 \text{ProductLog}(a x)}-\frac{2 x^3}{9 \text{ProductLog}(a x)^2}+\frac{2 x^3}{27 \text{ProductLog}(a x)^3}",1,"(2*x^3)/(27*ProductLog[a*x]^3) - (2*x^3)/(9*ProductLog[a*x]^2) + x^3/(3*ProductLog[a*x])","A",1
349,1,27,27,0.0038418,"\int \frac{x}{1+\text{ProductLog}(a x)} \, dx","Integrate[x/(1 + ProductLog[a*x]),x]","\frac{x^2}{2 \text{ProductLog}(a x)}-\frac{x^2}{4 \text{ProductLog}(a x)^2}","\frac{x^2}{2 \text{ProductLog}(a x)}-\frac{x^2}{4 \text{ProductLog}(a x)^2}",1,"-x^2/(4*ProductLog[a*x]^2) + x^2/(2*ProductLog[a*x])","A",1
350,1,8,8,0.0090657,"\int \frac{1}{1+\text{ProductLog}(a x)} \, dx","Integrate[(1 + ProductLog[a*x])^(-1),x]","\frac{x}{\text{ProductLog}(a x)}","\frac{x}{\text{ProductLog}(a x)}",1,"x/ProductLog[a*x]","A",1
351,1,5,5,0.0104374,"\int \frac{1}{x (1+\text{ProductLog}(a x))} \, dx","Integrate[1/(x*(1 + ProductLog[a*x])),x]","\log (\text{ProductLog}(a x))","\log (\text{ProductLog}(a x))",1,"Log[ProductLog[a*x]]","A",1
352,1,16,16,0.0030918,"\int \frac{1}{x^2 (1+\text{ProductLog}(a x))} \, dx","Integrate[1/(x^2*(1 + ProductLog[a*x])),x]","-a \text{Ei}(-\text{ProductLog}(a x))-\frac{1}{x}","-a \text{Ei}(-\text{ProductLog}(a x))-\frac{1}{x}",1,"-x^(-1) - a*ExpIntegralEi[-ProductLog[a*x]]","A",1
353,1,28,28,0.0063153,"\int \frac{1}{x^3 (1+\text{ProductLog}(a x))} \, dx","Integrate[1/(x^3*(1 + ProductLog[a*x])),x]","2 a^2 \text{Ei}(-2 \text{ProductLog}(a x))+\frac{\text{ProductLog}(a x)}{x^2}-\frac{1}{2 x^2}","2 a^2 \text{Ei}(-2 \text{ProductLog}(a x))+\frac{\text{ProductLog}(a x)}{x^2}-\frac{1}{2 x^2}",1,"-1/(2*x^2) + 2*a^2*ExpIntegralEi[-2*ProductLog[a*x]] + ProductLog[a*x]/x^2","A",1
354,1,46,46,0.0059738,"\int \frac{1}{x^4 (1+\text{ProductLog}(a x))} \, dx","Integrate[1/(x^4*(1 + ProductLog[a*x])),x]","-\frac{9}{2} a^3 \text{Ei}(-3 \text{ProductLog}(a x))-\frac{3 \text{ProductLog}(a x)^2}{2 x^3}+\frac{\text{ProductLog}(a x)}{2 x^3}-\frac{1}{3 x^3}","-\frac{9}{2} a^3 \text{Ei}(-3 \text{ProductLog}(a x))-\frac{3 \text{ProductLog}(a x)^2}{2 x^3}+\frac{\text{ProductLog}(a x)}{2 x^3}-\frac{1}{3 x^3}",1,"-1/(3*x^3) - (9*a^3*ExpIntegralEi[-3*ProductLog[a*x]])/2 + ProductLog[a*x]/(2*x^3) - (3*ProductLog[a*x]^2)/(2*x^3)","A",1
355,1,31,31,0.0110723,"\int \frac{x^3}{1+\text{ProductLog}\left(a x^2\right)} \, dx","Integrate[x^3/(1 + ProductLog[a*x^2]),x]","\frac{x^4}{4 \text{ProductLog}\left(a x^2\right)}-\frac{x^4}{8 \text{ProductLog}\left(a x^2\right)^2}","\frac{x^4}{4 \text{ProductLog}\left(a x^2\right)}-\frac{x^4}{8 \text{ProductLog}\left(a x^2\right)^2}",1,"-x^4/(8*ProductLog[a*x^2]^2) + x^4/(4*ProductLog[a*x^2])","A",1
356,0,0,17,0.0347328,"\int \frac{x^2}{1+\text{ProductLog}\left(a x^2\right)} \, dx","Integrate[x^2/(1 + ProductLog[a*x^2]),x]","\int \frac{x^2}{1+\text{ProductLog}\left(a x^2\right)} \, dx","\text{Int}\left(\frac{x^2}{\text{ProductLog}\left(a x^2\right)+1},x\right)",0,"Integrate[x^2/(1 + ProductLog[a*x^2]), x]","F",-1
357,1,15,15,0.0143652,"\int \frac{x}{1+\text{ProductLog}\left(a x^2\right)} \, dx","Integrate[x/(1 + ProductLog[a*x^2]),x]","\frac{x^2}{2 \text{ProductLog}\left(a x^2\right)}","\frac{x^2}{2 \text{ProductLog}\left(a x^2\right)}",1,"x^2/(2*ProductLog[a*x^2])","A",1
358,0,0,13,0.0063743,"\int \frac{1}{1+\text{ProductLog}\left(a x^2\right)} \, dx","Integrate[(1 + ProductLog[a*x^2])^(-1),x]","\int \frac{1}{1+\text{ProductLog}\left(a x^2\right)} \, dx","\text{Int}\left(\frac{1}{\text{ProductLog}\left(a x^2\right)+1},x\right)",0,"Integrate[(1 + ProductLog[a*x^2])^(-1), x]","F",-1
359,1,11,11,0.0114054,"\int \frac{1}{x \left(1+\text{ProductLog}\left(a x^2\right)\right)} \, dx","Integrate[1/(x*(1 + ProductLog[a*x^2])),x]","\frac{1}{2} \log \left(\text{ProductLog}\left(a x^2\right)\right)","\frac{1}{2} \log \left(\text{ProductLog}\left(a x^2\right)\right)",1,"Log[ProductLog[a*x^2]]/2","A",1
360,0,0,17,0.0197542,"\int \frac{1}{x^2 \left(1+\text{ProductLog}\left(a x^2\right)\right)} \, dx","Integrate[1/(x^2*(1 + ProductLog[a*x^2])),x]","\int \frac{1}{x^2 \left(1+\text{ProductLog}\left(a x^2\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(\text{ProductLog}\left(a x^2\right)+1\right)},x\right)",0,"Integrate[1/(x^2*(1 + ProductLog[a*x^2])), x]","F",-1
361,1,22,22,0.0091061,"\int \frac{1}{x^3 \left(1+\text{ProductLog}\left(a x^2\right)\right)} \, dx","Integrate[1/(x^3*(1 + ProductLog[a*x^2])),x]","-\frac{1}{2} a \text{Ei}\left(-\text{ProductLog}\left(a x^2\right)\right)-\frac{1}{2 x^2}","-\frac{1}{2} a \text{Ei}\left(-\text{ProductLog}\left(a x^2\right)\right)-\frac{1}{2 x^2}",1,"-1/(2*x^2) - (a*ExpIntegralEi[-ProductLog[a*x^2]])/2","A",1
362,0,0,17,0.0211828,"\int \frac{1}{x^4 \left(1+\text{ProductLog}\left(a x^2\right)\right)} \, dx","Integrate[1/(x^4*(1 + ProductLog[a*x^2])),x]","\int \frac{1}{x^4 \left(1+\text{ProductLog}\left(a x^2\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^4 \left(\text{ProductLog}\left(a x^2\right)+1\right)},x\right)",0,"Integrate[1/(x^4*(1 + ProductLog[a*x^2])), x]","F",-1
363,1,67,67,0.0109513,"\int \frac{x^3}{1+\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Integrate[x^3/(1 + ProductLog[a/x]),x]","-\frac{32}{3} a^4 \text{Ei}\left(-4 \text{ProductLog}\left(\frac{a}{x}\right)\right)-\frac{8}{3} x^4 \text{ProductLog}\left(\frac{a}{x}\right)^3+\frac{2}{3} x^4 \text{ProductLog}\left(\frac{a}{x}\right)^2-\frac{1}{3} x^4 \text{ProductLog}\left(\frac{a}{x}\right)+\frac{x^4}{4}","-\frac{32}{3} a^4 \text{Ei}\left(-4 \text{ProductLog}\left(\frac{a}{x}\right)\right)-\frac{8}{3} x^4 \text{ProductLog}\left(\frac{a}{x}\right)^3+\frac{2}{3} x^4 \text{ProductLog}\left(\frac{a}{x}\right)^2-\frac{1}{3} x^4 \text{ProductLog}\left(\frac{a}{x}\right)+\frac{x^4}{4}",1,"x^4/4 - (32*a^4*ExpIntegralEi[-4*ProductLog[a/x]])/3 - (x^4*ProductLog[a/x])/3 + (2*x^4*ProductLog[a/x]^2)/3 - (8*x^4*ProductLog[a/x]^3)/3","A",1
364,1,52,52,0.0073089,"\int \frac{x^2}{1+\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Integrate[x^2/(1 + ProductLog[a/x]),x]","\frac{9}{2} a^3 \text{Ei}\left(-3 \text{ProductLog}\left(\frac{a}{x}\right)\right)+\frac{3}{2} x^3 \text{ProductLog}\left(\frac{a}{x}\right)^2-\frac{1}{2} x^3 \text{ProductLog}\left(\frac{a}{x}\right)+\frac{x^3}{3}","\frac{9}{2} a^3 \text{Ei}\left(-3 \text{ProductLog}\left(\frac{a}{x}\right)\right)+\frac{3}{2} x^3 \text{ProductLog}\left(\frac{a}{x}\right)^2-\frac{1}{2} x^3 \text{ProductLog}\left(\frac{a}{x}\right)+\frac{x^3}{3}",1,"x^3/3 + (9*a^3*ExpIntegralEi[-3*ProductLog[a/x]])/2 - (x^3*ProductLog[a/x])/2 + (3*x^3*ProductLog[a/x]^2)/2","A",1
365,1,33,33,0.0063048,"\int \frac{x}{1+\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Integrate[x/(1 + ProductLog[a/x]),x]","-2 a^2 \text{Ei}\left(-2 \text{ProductLog}\left(\frac{a}{x}\right)\right)-x^2 \text{ProductLog}\left(\frac{a}{x}\right)+\frac{x^2}{2}","-2 a^2 \text{Ei}\left(-2 \text{ProductLog}\left(\frac{a}{x}\right)\right)-x^2 \text{ProductLog}\left(\frac{a}{x}\right)+\frac{x^2}{2}",1,"x^2/2 - 2*a^2*ExpIntegralEi[-2*ProductLog[a/x]] - x^2*ProductLog[a/x]","A",1
366,1,13,13,0.0035308,"\int \frac{1}{1+\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Integrate[(1 + ProductLog[a/x])^(-1),x]","a \text{Ei}\left(-\text{ProductLog}\left(\frac{a}{x}\right)\right)+x","a \text{Ei}\left(-\text{ProductLog}\left(\frac{a}{x}\right)\right)+x",1,"x + a*ExpIntegralEi[-ProductLog[a/x]]","A",1
367,1,9,9,0.0193402,"\int \frac{1}{x \left(1+\text{ProductLog}\left(\frac{a}{x}\right)\right)} \, dx","Integrate[1/(x*(1 + ProductLog[a/x])),x]","-\log \left(\text{ProductLog}\left(\frac{a}{x}\right)\right)","-\log \left(\text{ProductLog}\left(\frac{a}{x}\right)\right)",1,"-Log[ProductLog[a/x]]","A",1
368,1,13,13,0.0085811,"\int \frac{1}{x^2 \left(1+\text{ProductLog}\left(\frac{a}{x}\right)\right)} \, dx","Integrate[1/(x^2*(1 + ProductLog[a/x])),x]","-\frac{1}{x \text{ProductLog}\left(\frac{a}{x}\right)}","-\frac{1}{x \text{ProductLog}\left(\frac{a}{x}\right)}",1,"-(1/(x*ProductLog[a/x]))","A",1
369,1,31,31,0.0070672,"\int \frac{1}{x^3 \left(1+\text{ProductLog}\left(\frac{a}{x}\right)\right)} \, dx","Integrate[1/(x^3*(1 + ProductLog[a/x])),x]","\frac{1}{4 x^2 \text{ProductLog}\left(\frac{a}{x}\right)^2}-\frac{1}{2 x^2 \text{ProductLog}\left(\frac{a}{x}\right)}","\frac{1}{4 x^2 \text{ProductLog}\left(\frac{a}{x}\right)^2}-\frac{1}{2 x^2 \text{ProductLog}\left(\frac{a}{x}\right)}",1,"1/(4*x^2*ProductLog[a/x]^2) - 1/(2*x^2*ProductLog[a/x])","A",1
370,1,46,46,0.0075824,"\int \frac{1}{x^4 \left(1+\text{ProductLog}\left(\frac{a}{x}\right)\right)} \, dx","Integrate[1/(x^4*(1 + ProductLog[a/x])),x]","-\frac{1}{3 x^3 \text{ProductLog}\left(\frac{a}{x}\right)}+\frac{2}{9 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^2}-\frac{2}{27 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^3}","-\frac{1}{3 x^3 \text{ProductLog}\left(\frac{a}{x}\right)}+\frac{2}{9 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^2}-\frac{2}{27 x^3 \text{ProductLog}\left(\frac{a}{x}\right)^3}",1,"-2/(27*x^3*ProductLog[a/x]^3) + 2/(9*x^3*ProductLog[a/x]^2) - 1/(3*x^3*ProductLog[a/x])","A",1
371,1,52,52,0.0169427,"\int \frac{x^5}{1+\text{ProductLog}\left(\frac{a}{x^2}\right)} \, dx","Integrate[x^5/(1 + ProductLog[a/x^2]),x]","\frac{9}{4} a^3 \text{Ei}\left(-3 \text{ProductLog}\left(\frac{a}{x^2}\right)\right)+\frac{3}{4} x^6 \text{ProductLog}\left(\frac{a}{x^2}\right)^2-\frac{1}{4} x^6 \text{ProductLog}\left(\frac{a}{x^2}\right)+\frac{x^6}{6}","\frac{9}{4} a^3 \text{Ei}\left(-3 \text{ProductLog}\left(\frac{a}{x^2}\right)\right)+\frac{3}{4} x^6 \text{ProductLog}\left(\frac{a}{x^2}\right)^2-\frac{1}{4} x^6 \text{ProductLog}\left(\frac{a}{x^2}\right)+\frac{x^6}{6}",1,"x^6/6 + (9*a^3*ExpIntegralEi[-3*ProductLog[a/x^2]])/4 - (x^6*ProductLog[a/x^2])/4 + (3*x^6*ProductLog[a/x^2]^2)/4","A",1
372,1,35,35,0.0160245,"\int \frac{x^3}{1+\text{ProductLog}\left(\frac{a}{x^2}\right)} \, dx","Integrate[x^3/(1 + ProductLog[a/x^2]),x]","-a^2 \text{Ei}\left(-2 \text{ProductLog}\left(\frac{a}{x^2}\right)\right)-\frac{1}{2} x^4 \text{ProductLog}\left(\frac{a}{x^2}\right)+\frac{x^4}{4}","-a^2 \text{Ei}\left(-2 \text{ProductLog}\left(\frac{a}{x^2}\right)\right)-\frac{1}{2} x^4 \text{ProductLog}\left(\frac{a}{x^2}\right)+\frac{x^4}{4}",1,"x^4/4 - a^2*ExpIntegralEi[-2*ProductLog[a/x^2]] - (x^4*ProductLog[a/x^2])/2","A",1
373,1,19,22,0.0114724,"\int \frac{x}{1+\text{ProductLog}\left(\frac{a}{x^2}\right)} \, dx","Integrate[x/(1 + ProductLog[a/x^2]),x]","\frac{1}{2} \left(a \text{Ei}\left(-\text{ProductLog}\left(\frac{a}{x^2}\right)\right)+x^2\right)","\frac{1}{2} a \text{Ei}\left(-\text{ProductLog}\left(\frac{a}{x^2}\right)\right)+\frac{x^2}{2}",1,"(x^2 + a*ExpIntegralEi[-ProductLog[a/x^2]])/2","A",1
374,1,11,11,0.0165922,"\int \frac{1}{x \left(1+\text{ProductLog}\left(\frac{a}{x^2}\right)\right)} \, dx","Integrate[1/(x*(1 + ProductLog[a/x^2])),x]","-\frac{1}{2} \log \left(\text{ProductLog}\left(\frac{a}{x^2}\right)\right)","-\frac{1}{2} \log \left(\text{ProductLog}\left(\frac{a}{x^2}\right)\right)",1,"-Log[ProductLog[a/x^2]]/2","A",1
375,1,15,15,0.0121207,"\int \frac{1}{x^3 \left(1+\text{ProductLog}\left(\frac{a}{x^2}\right)\right)} \, dx","Integrate[1/(x^3*(1 + ProductLog[a/x^2])),x]","-\frac{1}{2 x^2 \text{ProductLog}\left(\frac{a}{x^2}\right)}","-\frac{1}{2 x^2 \text{ProductLog}\left(\frac{a}{x^2}\right)}",1,"-1/(2*x^2*ProductLog[a/x^2])","A",1
376,0,0,17,0.0374476,"\int \frac{x^4}{1+\text{ProductLog}\left(\frac{a}{x^2}\right)} \, dx","Integrate[x^4/(1 + ProductLog[a/x^2]),x]","\int \frac{x^4}{1+\text{ProductLog}\left(\frac{a}{x^2}\right)} \, dx","\text{Int}\left(\frac{x^4}{\text{ProductLog}\left(\frac{a}{x^2}\right)+1},x\right)",0,"Integrate[x^4/(1 + ProductLog[a/x^2]), x]","F",-1
377,0,0,17,0.0332374,"\int \frac{x^2}{1+\text{ProductLog}\left(\frac{a}{x^2}\right)} \, dx","Integrate[x^2/(1 + ProductLog[a/x^2]),x]","\int \frac{x^2}{1+\text{ProductLog}\left(\frac{a}{x^2}\right)} \, dx","\text{Int}\left(\frac{x^2}{\text{ProductLog}\left(\frac{a}{x^2}\right)+1},x\right)",0,"Integrate[x^2/(1 + ProductLog[a/x^2]), x]","F",-1
378,0,0,13,0.0097108,"\int \frac{1}{1+\text{ProductLog}\left(\frac{a}{x^2}\right)} \, dx","Integrate[(1 + ProductLog[a/x^2])^(-1),x]","\int \frac{1}{1+\text{ProductLog}\left(\frac{a}{x^2}\right)} \, dx","\text{Int}\left(\frac{1}{\text{ProductLog}\left(\frac{a}{x^2}\right)+1},x\right)",0,"Integrate[(1 + ProductLog[a/x^2])^(-1), x]","F",-1
379,0,0,17,0.0176855,"\int \frac{1}{x^2 \left(1+\text{ProductLog}\left(\frac{a}{x^2}\right)\right)} \, dx","Integrate[1/(x^2*(1 + ProductLog[a/x^2])),x]","\int \frac{1}{x^2 \left(1+\text{ProductLog}\left(\frac{a}{x^2}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(\text{ProductLog}\left(\frac{a}{x^2}\right)+1\right)},x\right)",0,"Integrate[1/(x^2*(1 + ProductLog[a/x^2])), x]","F",-1
380,0,0,17,0.0261963,"\int \frac{1}{x^4 \left(1+\text{ProductLog}\left(\frac{a}{x^2}\right)\right)} \, dx","Integrate[1/(x^4*(1 + ProductLog[a/x^2])),x]","\int \frac{1}{x^4 \left(1+\text{ProductLog}\left(\frac{a}{x^2}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^4 \left(\text{ProductLog}\left(\frac{a}{x^2}\right)+1\right)},x\right)",0,"Integrate[1/(x^4*(1 + ProductLog[a/x^2])), x]","F",-1
381,1,50,50,0.0762688,"\int \frac{x^m}{d+d \text{ProductLog}(a x)} \, dx","Integrate[x^m/(d + d*ProductLog[a*x]),x]","\frac{x^m e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{-m} \Gamma (m+1,-(m+1) \text{ProductLog}(a x))}{a d (m+1)}","\frac{x^m e^{-m \text{ProductLog}(a x)} (-(m+1) \text{ProductLog}(a x))^{-m} \Gamma (m+1,-(m+1) \text{ProductLog}(a x))}{a d (m+1)}",1,"(x^m*Gamma[1 + m, -((1 + m)*ProductLog[a*x])])/(a*d*E^(m*ProductLog[a*x])*(1 + m)*(-((1 + m)*ProductLog[a*x]))^m)","A",1
382,1,12,12,0.0043569,"\int \frac{\text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)^5}{1+\text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)} \, dx","Integrate[ProductLog[a/x^(1/4)]^5/(1 + ProductLog[a/x^(1/4)]),x]","x \text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)^4","x \text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)^4",1,"x*ProductLog[a/x^(1/4)]^4","A",1
383,1,12,12,0.0030337,"\int \frac{\text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)^4}{1+\text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)} \, dx","Integrate[ProductLog[a/x^(1/3)]^4/(1 + ProductLog[a/x^(1/3)]),x]","x \text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)^3","x \text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)^3",1,"x*ProductLog[a/x^(1/3)]^3","A",1
384,1,12,12,0.003011,"\int \frac{\text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)^3}{1+\text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)} \, dx","Integrate[ProductLog[a/Sqrt[x]]^3/(1 + ProductLog[a/Sqrt[x]]),x]","x \text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)^2","x \text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)^2",1,"x*ProductLog[a/Sqrt[x]]^2","A",1
385,1,8,8,0.0026009,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{1+\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Integrate[ProductLog[a/x]^2/(1 + ProductLog[a/x]),x]","x \text{ProductLog}\left(\frac{a}{x}\right)","x \text{ProductLog}\left(\frac{a}{x}\right)",1,"x*ProductLog[a/x]","A",1
386,1,12,12,0.0048225,"\int \frac{1}{\text{ProductLog}\left(a \sqrt{x}\right) \left(1+\text{ProductLog}\left(a \sqrt{x}\right)\right)} \, dx","Integrate[1/(ProductLog[a*Sqrt[x]]*(1 + ProductLog[a*Sqrt[x]])),x]","\frac{x}{\text{ProductLog}\left(a \sqrt{x}\right)^2}","\frac{x}{\text{ProductLog}\left(a \sqrt{x}\right)^2}",1,"x/ProductLog[a*Sqrt[x]]^2","A",1
387,1,12,12,0.0045078,"\int \frac{1}{\text{ProductLog}\left(a \sqrt[3]{x}\right)^2 \left(1+\text{ProductLog}\left(a \sqrt[3]{x}\right)\right)} \, dx","Integrate[1/(ProductLog[a*x^(1/3)]^2*(1 + ProductLog[a*x^(1/3)])),x]","\frac{x}{\text{ProductLog}\left(a \sqrt[3]{x}\right)^3}","\frac{x}{\text{ProductLog}\left(a \sqrt[3]{x}\right)^3}",1,"x/ProductLog[a*x^(1/3)]^3","A",1
388,1,12,12,0.0057102,"\int \frac{1}{\text{ProductLog}\left(a \sqrt[4]{x}\right)^3 \left(1+\text{ProductLog}\left(a \sqrt[4]{x}\right)\right)} \, dx","Integrate[1/(ProductLog[a*x^(1/4)]^3*(1 + ProductLog[a*x^(1/4)])),x]","\frac{x}{\text{ProductLog}\left(a \sqrt[4]{x}\right)^4}","\frac{x}{\text{ProductLog}\left(a \sqrt[4]{x}\right)^4}",1,"x/ProductLog[a*x^(1/4)]^4","A",1
389,1,16,16,0.0025649,"\int \frac{\text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)^4}{1+\text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)} \, dx","Integrate[ProductLog[a/x^(1/4)]^4/(1 + ProductLog[a/x^(1/4)]),x]","-4 a^4 \text{Ei}\left(-4 \text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)\right)","-4 a^4 \text{Ei}\left(-4 \text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)\right)",1,"-4*a^4*ExpIntegralEi[-4*ProductLog[a/x^(1/4)]]","A",1
390,1,16,16,0.0024401,"\int \frac{\text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)^3}{1+\text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)} \, dx","Integrate[ProductLog[a/x^(1/3)]^3/(1 + ProductLog[a/x^(1/3)]),x]","-3 a^3 \text{Ei}\left(-3 \text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)\right)","-3 a^3 \text{Ei}\left(-3 \text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)\right)",1,"-3*a^3*ExpIntegralEi[-3*ProductLog[a/x^(1/3)]]","A",1
391,1,16,16,0.002685,"\int \frac{\text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)^2}{1+\text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)} \, dx","Integrate[ProductLog[a/Sqrt[x]]^2/(1 + ProductLog[a/Sqrt[x]]),x]","-2 a^2 \text{Ei}\left(-2 \text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)\right)","-2 a^2 \text{Ei}\left(-2 \text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)\right)",1,"-2*a^2*ExpIntegralEi[-2*ProductLog[a/Sqrt[x]]]","A",1
392,1,12,12,0.0039958,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)}{1+\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Integrate[ProductLog[a/x]/(1 + ProductLog[a/x]),x]","-a \text{Ei}\left(-\text{ProductLog}\left(\frac{a}{x}\right)\right)","-a \text{Ei}\left(-\text{ProductLog}\left(\frac{a}{x}\right)\right)",1,"-(a*ExpIntegralEi[-ProductLog[a/x]])","A",1
393,1,9,9,0.0030456,"\int \frac{1}{\text{ProductLog}(a x) (1+\text{ProductLog}(a x))} \, dx","Integrate[1/(ProductLog[a*x]*(1 + ProductLog[a*x])),x]","\frac{\text{Ei}(\text{ProductLog}(a x))}{a}","\frac{\text{Ei}(\text{ProductLog}(a x))}{a}",1,"ExpIntegralEi[ProductLog[a*x]]/a","A",1
394,1,16,16,0.0090828,"\int \frac{1}{\text{ProductLog}\left(a \sqrt{x}\right)^2 \left(1+\text{ProductLog}\left(a \sqrt{x}\right)\right)} \, dx","Integrate[1/(ProductLog[a*Sqrt[x]]^2*(1 + ProductLog[a*Sqrt[x]])),x]","\frac{2 \text{Ei}\left(2 \text{ProductLog}\left(a \sqrt{x}\right)\right)}{a^2}","\frac{2 \text{Ei}\left(2 \text{ProductLog}\left(a \sqrt{x}\right)\right)}{a^2}",1,"(2*ExpIntegralEi[2*ProductLog[a*Sqrt[x]]])/a^2","A",1
395,1,16,16,0.0089889,"\int \frac{1}{\text{ProductLog}\left(a \sqrt[3]{x}\right)^3 \left(1+\text{ProductLog}\left(a \sqrt[3]{x}\right)\right)} \, dx","Integrate[1/(ProductLog[a*x^(1/3)]^3*(1 + ProductLog[a*x^(1/3)])),x]","\frac{3 \text{Ei}\left(3 \text{ProductLog}\left(a \sqrt[3]{x}\right)\right)}{a^3}","\frac{3 \text{Ei}\left(3 \text{ProductLog}\left(a \sqrt[3]{x}\right)\right)}{a^3}",1,"(3*ExpIntegralEi[3*ProductLog[a*x^(1/3)]])/a^3","A",1
396,1,16,16,0.0075444,"\int \frac{1}{\text{ProductLog}\left(a \sqrt[4]{x}\right)^4 \left(1+\text{ProductLog}\left(a \sqrt[4]{x}\right)\right)} \, dx","Integrate[1/(ProductLog[a*x^(1/4)]^4*(1 + ProductLog[a*x^(1/4)])),x]","\frac{4 \text{Ei}\left(4 \text{ProductLog}\left(a \sqrt[4]{x}\right)\right)}{a^4}","\frac{4 \text{Ei}\left(4 \text{ProductLog}\left(a \sqrt[4]{x}\right)\right)}{a^4}",1,"(4*ExpIntegralEi[4*ProductLog[a*x^(1/4)]])/a^4","A",1
397,1,14,14,0.0085653,"\int \frac{\text{ProductLog}\left(a x^n\right)^{1-\frac{1}{n}}}{1+\text{ProductLog}\left(a x^n\right)} \, dx","Integrate[ProductLog[a*x^n]^(1 - n^(-1))/(1 + ProductLog[a*x^n]),x]","x \text{ProductLog}\left(a x^n\right)^{-1/n}","x \text{ProductLog}\left(a x^n\right)^{-1/n}",1,"x/ProductLog[a*x^n]^n^(-1)","A",1
398,1,18,18,0.0092051,"\int \frac{\text{ProductLog}\left(a x^{\frac{1}{1-p}}\right)^p}{1+\text{ProductLog}\left(a x^{\frac{1}{1-p}}\right)} \, dx","Integrate[ProductLog[a*x^(1 - p)^(-1)]^p/(1 + ProductLog[a*x^(1 - p)^(-1)]),x]","x \text{ProductLog}\left(a x^{\frac{1}{1-p}}\right)^{p-1}","x \text{ProductLog}\left(a x^{\frac{1}{1-p}}\right)^{p-1}",1,"x*ProductLog[a*x^(1 - p)^(-1)]^(-1 + p)","A",1