1,1,91,0,0.12495,"\int \text{ProductLog}(a+b x)^4 \, dx","Int[ProductLog[a + b*x]^4,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","\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,"96*x - (96*(a + b*x))/(b*ProductLog[a + b*x]) - (48*(a + b*x)*ProductLog[a + b*x])/b + (16*(a + b*x)*ProductLog[a + b*x]^2)/b - (4*(a + b*x)*ProductLog[a + b*x]^3)/b + ((a + b*x)*ProductLog[a + b*x]^4)/b","A",6,4,8,0.5000,1,"{6613, 6624, 6623, 6622}"
2,1,73,0,0.0865533,"\int \text{ProductLog}(a+b x)^3 \, dx","Int[ProductLog[a + b*x]^3,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","\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,"-18*x + (18*(a + b*x))/(b*ProductLog[a + b*x]) + (9*(a + b*x)*ProductLog[a + b*x])/b - (3*(a + b*x)*ProductLog[a + b*x]^2)/b + ((a + b*x)*ProductLog[a + b*x]^3)/b","A",5,4,8,0.5000,1,"{6613, 6624, 6623, 6622}"
3,1,55,0,0.0611535,"\int \text{ProductLog}(a+b x)^2 \, dx","Int[ProductLog[a + b*x]^2,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","\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,"4*x - (4*(a + b*x))/(b*ProductLog[a + b*x]) - (2*(a + b*x)*ProductLog[a + b*x])/b + ((a + b*x)*ProductLog[a + b*x]^2)/b","A",4,4,8,0.5000,1,"{6613, 6624, 6623, 6622}"
4,1,36,0,0.0264476,"\int \text{ProductLog}(a+b x) \, dx","Int[ProductLog[a + b*x],x]","\frac{(a+b x) \text{ProductLog}(a+b x)}{b}+\frac{a+b x}{b \text{ProductLog}(a+b x)}-x","\frac{(a+b x) \text{ProductLog}(a+b x)}{b}+\frac{a+b x}{b \text{ProductLog}(a+b x)}-x",1,"-x + (a + b*x)/(b*ProductLog[a + b*x]) + ((a + b*x)*ProductLog[a + b*x])/b","A",3,3,6,0.5000,1,"{6613, 6623, 6622}"
5,1,29,0,0.0346063,"\int \frac{1}{\text{ProductLog}(a+b x)} \, dx","Int[ProductLog[a + b*x]^(-1),x]","\frac{\text{Ei}(\text{ProductLog}(a+b x))}{b}+\frac{a+b x}{b \text{ProductLog}(a+b x)}","\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]]/b + (a + b*x)/(b*ProductLog[a + b*x])","A",2,2,8,0.2500,1,"{6613, 6625}"
6,1,31,0,0.0331188,"\int \frac{1}{\text{ProductLog}(a+b x)^2} \, dx","Int[ProductLog[a + b*x]^(-2),x]","\frac{2 \text{Ei}(\text{ProductLog}(a+b x))}{b}-\frac{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,"(2*ExpIntegralEi[ProductLog[a + b*x]])/b - (a + b*x)/(b*ProductLog[a + b*x]^2)","A",2,2,8,0.2500,1,"{6612, 6625}"
7,1,55,0,0.0586809,"\int \frac{1}{\text{ProductLog}(a+b x)^3} \, dx","Int[ProductLog[a + b*x]^(-3),x]","\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}","\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,"(3*ExpIntegralEi[ProductLog[a + b*x]])/(2*b) - (a + b*x)/(2*b*ProductLog[a + b*x]^3) - (3*(a + b*x))/(2*b*ProductLog[a + b*x]^2)","A",3,3,8,0.3750,1,"{6612, 6628, 6625}"
8,1,75,0,0.087105,"\int \frac{1}{\text{ProductLog}(a+b x)^4} \, dx","Int[ProductLog[a + b*x]^(-4),x]","\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}","\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*ExpIntegralEi[ProductLog[a + b*x]])/(3*b) - (a + b*x)/(3*b*ProductLog[a + b*x]^4) - (2*(a + b*x))/(3*b*ProductLog[a + b*x]^3) - (2*(a + b*x))/(3*b*ProductLog[a + b*x]^2)","A",4,3,8,0.3750,1,"{6612, 6628, 6625}"
9,1,95,0,0.114288,"\int \frac{1}{\text{ProductLog}(a+b x)^5} \, dx","Int[ProductLog[a + b*x]^(-5),x]","\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}","\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,"(5*ExpIntegralEi[ProductLog[a + b*x]])/(24*b) - (a + b*x)/(4*b*ProductLog[a + b*x]^5) - (5*(a + b*x))/(12*b*ProductLog[a + b*x]^4) - (5*(a + b*x))/(24*b*ProductLog[a + b*x]^3) - (5*(a + b*x))/(24*b*ProductLog[a + b*x]^2)","A",5,3,8,0.3750,1,"{6612, 6628, 6625}"
10,1,137,0,0.1821035,"\int (c \text{ProductLog}(a+b x))^{5/2} \, dx","Int[(c*ProductLog[a + b*x])^(5/2),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}","\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,"(75*c^(5/2)*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a + b*x]]/Sqrt[c]])/(16*b) - (75*c^3*(a + b*x))/(8*b*Sqrt[c*ProductLog[a + b*x]]) + (25*c^2*(a + b*x)*Sqrt[c*ProductLog[a + b*x]])/(4*b) - (5*c*(a + b*x)*(c*ProductLog[a + b*x])^(3/2))/(2*b) + ((a + b*x)*(c*ProductLog[a + b*x])^(5/2))/b","A",5,3,12,0.2500,1,"{6613, 6624, 6626}"
11,1,110,0,0.1264191,"\int (c \text{ProductLog}(a+b x))^{3/2} \, dx","Int[(c*ProductLog[a + b*x])^(3/2),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}","-\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,"(-9*c^(3/2)*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a + b*x]]/Sqrt[c]])/(8*b) + (9*c^2*(a + b*x))/(4*b*Sqrt[c*ProductLog[a + b*x]]) - (3*c*(a + b*x)*Sqrt[c*ProductLog[a + b*x]])/(2*b) + ((a + b*x)*(c*ProductLog[a + b*x])^(3/2))/b","A",4,3,12,0.2500,1,"{6613, 6624, 6626}"
12,1,83,0,0.086935,"\int \sqrt{c \text{ProductLog}(a+b x)} \, dx","Int[Sqrt[c*ProductLog[a + b*x]],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)}}","\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,"(Sqrt[c]*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a + b*x]]/Sqrt[c]])/(4*b) - (c*(a + b*x))/(2*b*Sqrt[c*ProductLog[a + b*x]]) + ((a + b*x)*Sqrt[c*ProductLog[a + b*x]])/b","A",3,3,12,0.2500,1,"{6613, 6624, 6626}"
13,1,58,0,0.0483123,"\int \frac{1}{\sqrt{c \text{ProductLog}(a+b x)}} \, dx","Int[1/Sqrt[c*ProductLog[a + b*x]],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)}}","\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,"(Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a + b*x]]/Sqrt[c]])/(2*b*Sqrt[c]) + (a + b*x)/(b*Sqrt[c*ProductLog[a + b*x]])","A",2,2,12,0.1667,1,"{6613, 6626}"
14,1,57,0,0.0519712,"\int \frac{1}{(c \text{ProductLog}(a+b x))^{3/2}} \, dx","Int[(c*ProductLog[a + b*x])^(-3/2),x]","\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}}","\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,"(3*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a + b*x]]/Sqrt[c]])/(b*c^(3/2)) - (2*(a + b*x))/(b*(c*ProductLog[a + b*x])^(3/2))","A",2,2,12,0.1667,1,"{6612, 6626}"
15,1,88,0,0.0964969,"\int \frac{1}{(c \text{ProductLog}(a+b x))^{5/2}} \, dx","Int[(c*ProductLog[a + b*x])^(-5/2),x]","\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}}","\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,"(10*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a + b*x]]/Sqrt[c]])/(3*b*c^(5/2)) - (2*(a + b*x))/(3*b*(c*ProductLog[a + b*x])^(5/2)) - (10*(a + b*x))/(3*b*c*(c*ProductLog[a + b*x])^(3/2))","A",3,3,12,0.2500,1,"{6612, 6628, 6626}"
16,1,115,0,0.1390966,"\int \frac{1}{(c \text{ProductLog}(a+b x))^{7/2}} \, dx","Int[(c*ProductLog[a + b*x])^(-7/2),x]","\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}}","\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,"(28*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a + b*x]]/Sqrt[c]])/(15*b*c^(7/2)) - (2*(a + b*x))/(5*b*(c*ProductLog[a + b*x])^(7/2)) - (14*(a + b*x))/(15*b*c*(c*ProductLog[a + b*x])^(5/2)) - (28*(a + b*x))/(15*b*c^2*(c*ProductLog[a + b*x])^(3/2))","A",4,3,12,0.2500,1,"{6612, 6628, 6626}"
17,1,142,0,0.1810624,"\int (-c \text{ProductLog}(a+b x))^{5/2} \, dx","Int[(-(c*ProductLog[a + b*x]))^(5/2),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}","\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,"(75*c^(5/2)*Sqrt[Pi]*Erf[Sqrt[-(c*ProductLog[a + b*x])]/Sqrt[c]])/(16*b) + (75*c^3*(a + b*x))/(8*b*Sqrt[-(c*ProductLog[a + b*x])]) + (25*c^2*(a + b*x)*Sqrt[-(c*ProductLog[a + b*x])])/(4*b) + (5*c*(a + b*x)*(-(c*ProductLog[a + b*x]))^(3/2))/(2*b) + ((a + b*x)*(-(c*ProductLog[a + b*x]))^(5/2))/b","A",5,3,13,0.2308,1,"{6613, 6624, 6627}"
18,1,114,0,0.153294,"\int (-c \text{ProductLog}(a+b x))^{3/2} \, dx","Int[(-(c*ProductLog[a + b*x]))^(3/2),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}","\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,"(9*c^(3/2)*Sqrt[Pi]*Erf[Sqrt[-(c*ProductLog[a + b*x])]/Sqrt[c]])/(8*b) + (9*c^2*(a + b*x))/(4*b*Sqrt[-(c*ProductLog[a + b*x])]) + (3*c*(a + b*x)*Sqrt[-(c*ProductLog[a + b*x])])/(2*b) + ((a + b*x)*(-(c*ProductLog[a + b*x]))^(3/2))/b","A",4,3,13,0.2308,1,"{6613, 6624, 6627}"
19,1,86,0,0.0919671,"\int \sqrt{-c \text{ProductLog}(a+b x)} \, dx","Int[Sqrt[-(c*ProductLog[a + b*x])],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)}}","\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,"(Sqrt[c]*Sqrt[Pi]*Erf[Sqrt[-(c*ProductLog[a + b*x])]/Sqrt[c]])/(4*b) + (c*(a + b*x))/(2*b*Sqrt[-(c*ProductLog[a + b*x])]) + ((a + b*x)*Sqrt[-(c*ProductLog[a + b*x])])/b","A",3,3,13,0.2308,1,"{6613, 6624, 6627}"
20,1,60,0,0.0559046,"\int \frac{1}{\sqrt{-c \text{ProductLog}(a+b x)}} \, dx","Int[1/Sqrt[-(c*ProductLog[a + b*x])],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}}","\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,"-(Sqrt[Pi]*Erf[Sqrt[-(c*ProductLog[a + b*x])]/Sqrt[c]])/(2*b*Sqrt[c]) + (a + b*x)/(b*Sqrt[-(c*ProductLog[a + b*x])])","A",2,2,13,0.1538,1,"{6613, 6627}"
21,1,59,0,0.0522735,"\int \frac{1}{(-c \text{ProductLog}(a+b x))^{3/2}} \, dx","Int[(-(c*ProductLog[a + b*x]))^(-3/2),x]","\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}}","\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,"(3*Sqrt[Pi]*Erf[Sqrt[-(c*ProductLog[a + b*x])]/Sqrt[c]])/(b*c^(3/2)) - (2*(a + b*x))/(b*(-(c*ProductLog[a + b*x]))^(3/2))","A",2,2,13,0.1538,1,"{6612, 6627}"
22,1,91,0,0.1002302,"\int \frac{1}{(-c \text{ProductLog}(a+b x))^{5/2}} \, dx","Int[(-(c*ProductLog[a + b*x]))^(-5/2),x]","-\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}}","-\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,"(-10*Sqrt[Pi]*Erf[Sqrt[-(c*ProductLog[a + b*x])]/Sqrt[c]])/(3*b*c^(5/2)) - (2*(a + b*x))/(3*b*(-(c*ProductLog[a + b*x]))^(5/2)) + (10*(a + b*x))/(3*b*c*(-(c*ProductLog[a + b*x]))^(3/2))","A",3,3,13,0.2308,1,"{6612, 6628, 6627}"
23,1,119,0,0.1449822,"\int \frac{1}{(-c \text{ProductLog}(a+b x))^{7/2}} \, dx","Int[(-(c*ProductLog[a + b*x]))^(-7/2),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}}","\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,"(28*Sqrt[Pi]*Erf[Sqrt[-(c*ProductLog[a + b*x])]/Sqrt[c]])/(15*b*c^(7/2)) - (2*(a + b*x))/(5*b*(-(c*ProductLog[a + b*x]))^(7/2)) + (14*(a + b*x))/(15*b*c*(-(c*ProductLog[a + b*x]))^(5/2)) - (28*(a + b*x))/(15*b*c^2*(-(c*ProductLog[a + b*x]))^(3/2))","A",4,3,13,0.2308,1,"{6612, 6628, 6627}"
24,1,60,0,0.0439223,"\int (c \text{ProductLog}(a+b x))^n \, dx","Int[(c*ProductLog[a + b*x])^n,x]","\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}","\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,"((a + b*x)*(c*ProductLog[a + b*x])^n)/b - (n*Gamma[1 + n, -ProductLog[a + b*x]]*(c*ProductLog[a + b*x])^n)/(b*(-ProductLog[a + b*x])^n)","A",2,2,10,0.2000,1,"{6613, 6629}"
25,1,364,0,0.5470882,"\int x^3 \text{ProductLog}(a+b x) \, dx","Int[x^3*ProductLog[a + b*x],x]","-\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}","-\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^3*x)/b^3 - (3*a^2*(a + b*x)^2)/(4*b^4) + (a*(a + b*x)^3)/(3*b^4) - (a + b*x)^4/(16*b^4) - (3*(a + b*x)^4)/(512*b^4*ProductLog[a + b*x]^4) - (2*a*(a + b*x)^3)/(27*b^4*ProductLog[a + b*x]^3) + (3*(a + b*x)^4)/(128*b^4*ProductLog[a + b*x]^3) - (3*a^2*(a + b*x)^2)/(8*b^4*ProductLog[a + b*x]^2) + (2*a*(a + b*x)^3)/(9*b^4*ProductLog[a + b*x]^2) - (3*(a + b*x)^4)/(64*b^4*ProductLog[a + b*x]^2) - (a^3*(a + b*x))/(b^4*ProductLog[a + b*x]) + (3*a^2*(a + b*x)^2)/(4*b^4*ProductLog[a + b*x]) - (a*(a + b*x)^3)/(3*b^4*ProductLog[a + b*x]) + (a + b*x)^4/(16*b^4*ProductLog[a + b*x]) - (a^3*(a + b*x)*ProductLog[a + b*x])/b^4 + (3*a^2*(a + b*x)^2*ProductLog[a + b*x])/(2*b^4) - (a*(a + b*x)^3*ProductLog[a + b*x])/b^4 + ((a + b*x)^4*ProductLog[a + b*x])/(4*b^4)","A",20,8,10,0.8000,1,"{6614, 6613, 6623, 6622, 6618, 6651, 6640, 6647}"
26,1,228,0,0.3029177,"\int x^2 \text{ProductLog}(a+b x) \, dx","Int[x^2*ProductLog[a + b*x],x]","\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}","\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^2*x)/b^2) + (a*(a + b*x)^2)/(2*b^3) - (a + b*x)^3/(9*b^3) + (2*(a + b*x)^3)/(81*b^3*ProductLog[a + b*x]^3) + (a*(a + b*x)^2)/(4*b^3*ProductLog[a + b*x]^2) - (2*(a + b*x)^3)/(27*b^3*ProductLog[a + b*x]^2) + (a^2*(a + b*x))/(b^3*ProductLog[a + b*x]) - (a*(a + b*x)^2)/(2*b^3*ProductLog[a + b*x]) + (a + b*x)^3/(9*b^3*ProductLog[a + b*x]) + (a^2*(a + b*x)*ProductLog[a + b*x])/b^3 - (a*(a + b*x)^2*ProductLog[a + b*x])/b^3 + ((a + b*x)^3*ProductLog[a + b*x])/(3*b^3)","A",14,8,10,0.8000,1,"{6614, 6613, 6623, 6622, 6618, 6651, 6640, 6647}"
27,1,121,0,0.1232952,"\int x \text{ProductLog}(a+b x) \, dx","Int[x*ProductLog[a + b*x],x]","\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}","\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*x)/b - (a + b*x)^2/(4*b^2) - (a + b*x)^2/(8*b^2*ProductLog[a + b*x]^2) - (a*(a + b*x))/(b^2*ProductLog[a + b*x]) + (a + b*x)^2/(4*b^2*ProductLog[a + b*x]) - (a*(a + b*x)*ProductLog[a + b*x])/b^2 + ((a + b*x)^2*ProductLog[a + b*x])/(2*b^2)","A",9,8,8,1.000,1,"{6614, 6613, 6623, 6622, 6618, 6651, 6640, 6647}"
28,1,36,0,0.0253463,"\int \text{ProductLog}(a+b x) \, dx","Int[ProductLog[a + b*x],x]","\frac{(a+b x) \text{ProductLog}(a+b x)}{b}+\frac{a+b x}{b \text{ProductLog}(a+b x)}-x","\frac{(a+b x) \text{ProductLog}(a+b x)}{b}+\frac{a+b x}{b \text{ProductLog}(a+b x)}-x",1,"-x + (a + b*x)/(b*ProductLog[a + b*x]) + ((a + b*x)*ProductLog[a + b*x])/b","A",3,3,6,0.5000,1,"{6613, 6623, 6622}"
29,0,0,0,0.0179249,"\int \frac{\text{ProductLog}(a+b x)}{x} \, dx","Int[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,"Defer[Int][ProductLog[a + b*x]/x, x]","N/A",0,0,0,0,-1,"{}"
30,0,0,0,0.0180233,"\int \frac{\text{ProductLog}(a+b x)}{x^2} \, dx","Int[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,"Defer[Int][ProductLog[a + b*x]/x^2, x]","N/A",0,0,0,0,-1,"{}"
31,1,456,0,0.7431992,"\int x^3 \text{ProductLog}(a+b x)^2 \, dx","Int[x^3*ProductLog[a + b*x]^2,x]","-\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}","-\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,"(-4*a^3*x)/b^3 + (9*a^2*(a + b*x)^2)/(4*b^4) - (8*a*(a + b*x)^3)/(9*b^4) + (5*(a + b*x)^4)/(32*b^4) + (15*(a + b*x)^4)/(1024*b^4*ProductLog[a + b*x]^4) + (16*a*(a + b*x)^3)/(81*b^4*ProductLog[a + b*x]^3) - (15*(a + b*x)^4)/(256*b^4*ProductLog[a + b*x]^3) + (9*a^2*(a + b*x)^2)/(8*b^4*ProductLog[a + b*x]^2) - (16*a*(a + b*x)^3)/(27*b^4*ProductLog[a + b*x]^2) + (15*(a + b*x)^4)/(128*b^4*ProductLog[a + b*x]^2) + (4*a^3*(a + b*x))/(b^4*ProductLog[a + b*x]) - (9*a^2*(a + b*x)^2)/(4*b^4*ProductLog[a + b*x]) + (8*a*(a + b*x)^3)/(9*b^4*ProductLog[a + b*x]) - (5*(a + b*x)^4)/(32*b^4*ProductLog[a + b*x]) + (2*a^3*(a + b*x)*ProductLog[a + b*x])/b^4 - (3*a^2*(a + b*x)^2*ProductLog[a + b*x])/(2*b^4) + (2*a*(a + b*x)^3*ProductLog[a + b*x])/(3*b^4) - ((a + b*x)^4*ProductLog[a + b*x])/(8*b^4) - (a^3*(a + b*x)*ProductLog[a + b*x]^2)/b^4 + (3*a^2*(a + b*x)^2*ProductLog[a + b*x]^2)/(2*b^4) - (a*(a + b*x)^3*ProductLog[a + b*x]^2)/b^4 + ((a + b*x)^4*ProductLog[a + b*x]^2)/(4*b^4)","A",24,9,12,0.7500,1,"{6614, 6613, 6624, 6623, 6622, 6618, 6651, 6640, 6647}"
32,1,292,0,0.4273382,"\int x^2 \text{ProductLog}(a+b x)^2 \, dx","Int[x^2*ProductLog[a + b*x]^2,x]","\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}","\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,"(4*a^2*x)/b^2 - (3*a*(a + b*x)^2)/(2*b^3) + (8*(a + b*x)^3)/(27*b^3) - (16*(a + b*x)^3)/(243*b^3*ProductLog[a + b*x]^3) - (3*a*(a + b*x)^2)/(4*b^3*ProductLog[a + b*x]^2) + (16*(a + b*x)^3)/(81*b^3*ProductLog[a + b*x]^2) - (4*a^2*(a + b*x))/(b^3*ProductLog[a + b*x]) + (3*a*(a + b*x)^2)/(2*b^3*ProductLog[a + b*x]) - (8*(a + b*x)^3)/(27*b^3*ProductLog[a + b*x]) - (2*a^2*(a + b*x)*ProductLog[a + b*x])/b^3 + (a*(a + b*x)^2*ProductLog[a + b*x])/b^3 - (2*(a + b*x)^3*ProductLog[a + b*x])/(9*b^3) + (a^2*(a + b*x)*ProductLog[a + b*x]^2)/b^3 - (a*(a + b*x)^2*ProductLog[a + b*x]^2)/b^3 + ((a + b*x)^3*ProductLog[a + b*x]^2)/(3*b^3)","A",17,9,12,0.7500,1,"{6614, 6613, 6624, 6623, 6622, 6618, 6651, 6640, 6647}"
33,1,163,0,0.2075555,"\int x \text{ProductLog}(a+b x)^2 \, dx","Int[x*ProductLog[a + b*x]^2,x]","\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}","\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,"(-4*a*x)/b + (3*(a + b*x)^2)/(4*b^2) + (3*(a + b*x)^2)/(8*b^2*ProductLog[a + b*x]^2) + (4*a*(a + b*x))/(b^2*ProductLog[a + b*x]) - (3*(a + b*x)^2)/(4*b^2*ProductLog[a + b*x]) + (2*a*(a + b*x)*ProductLog[a + b*x])/b^2 - ((a + b*x)^2*ProductLog[a + b*x])/(2*b^2) - (a*(a + b*x)*ProductLog[a + b*x]^2)/b^2 + ((a + b*x)^2*ProductLog[a + b*x]^2)/(2*b^2)","A",11,9,10,0.9000,1,"{6614, 6613, 6624, 6623, 6622, 6618, 6651, 6640, 6647}"
34,1,55,0,0.0577742,"\int \text{ProductLog}(a+b x)^2 \, dx","Int[ProductLog[a + b*x]^2,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","\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,"4*x - (4*(a + b*x))/(b*ProductLog[a + b*x]) - (2*(a + b*x)*ProductLog[a + b*x])/b + ((a + b*x)*ProductLog[a + b*x]^2)/b","A",4,4,8,0.5000,1,"{6613, 6624, 6623, 6622}"
35,0,0,0,0.0279981,"\int \frac{\text{ProductLog}(a+b x)^2}{x} \, dx","Int[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,"Defer[Int][ProductLog[a + b*x]^2/x, x]","N/A",0,0,0,0,-1,"{}"
36,0,0,0,0.0333152,"\int \frac{\text{ProductLog}(a+b x)^2}{x^2} \, dx","Int[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,"Defer[Int][ProductLog[a + b*x]^2/x^2, x]","N/A",0,0,0,0,-1,"{}"
37,1,449,0,1.113054,"\int \frac{x^3}{\sqrt{c \text{ProductLog}(a+b x)}} \, dx","Int[x^3/Sqrt[c*ProductLog[a + b*x]],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}}","-\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,"-(a^3*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a + b*x]]/Sqrt[c]])/(2*b^4*Sqrt[c]) - (15*Sqrt[Pi]*Erfi[(2*Sqrt[c*ProductLog[a + b*x]])/Sqrt[c]])/(8192*b^4*Sqrt[c]) - (3*a^2*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a + b*x]])/Sqrt[c]])/(16*b^4*Sqrt[c]) - (a*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[c*ProductLog[a + b*x]])/Sqrt[c]])/(24*b^4*Sqrt[c]) + (15*c^3*(a + b*x)^4)/(2048*b^4*(c*ProductLog[a + b*x])^(7/2)) + (a*c^2*(a + b*x)^3)/(12*b^4*(c*ProductLog[a + b*x])^(5/2)) - (5*c^2*(a + b*x)^4)/(256*b^4*(c*ProductLog[a + b*x])^(5/2)) + (3*a^2*c*(a + b*x)^2)/(8*b^4*(c*ProductLog[a + b*x])^(3/2)) - (a*c*(a + b*x)^3)/(6*b^4*(c*ProductLog[a + b*x])^(3/2)) + (c*(a + b*x)^4)/(32*b^4*(c*ProductLog[a + b*x])^(3/2)) - (a^3*(a + b*x))/(b^4*Sqrt[c*ProductLog[a + b*x]]) + (3*a^2*(a + b*x)^2)/(2*b^4*Sqrt[c*ProductLog[a + b*x]]) - (a*(a + b*x)^3)/(b^4*Sqrt[c*ProductLog[a + b*x]]) + (a + b*x)^4/(4*b^4*Sqrt[c*ProductLog[a + b*x]])","A",16,6,16,0.3750,1,"{6614, 6613, 6626, 6618, 6651, 6650}"
38,1,290,0,0.638208,"\int \frac{x^2}{\sqrt{c \text{ProductLog}(a+b x)}} \, dx","Int[x^2/Sqrt[c*ProductLog[a + b*x]],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}}","\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,"(a^2*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a + b*x]]/Sqrt[c]])/(2*b^3*Sqrt[c]) + (a*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a + b*x]])/Sqrt[c]])/(8*b^3*Sqrt[c]) + (Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[c*ProductLog[a + b*x]])/Sqrt[c]])/(72*b^3*Sqrt[c]) - (c^2*(a + b*x)^3)/(36*b^3*(c*ProductLog[a + b*x])^(5/2)) - (a*c*(a + b*x)^2)/(4*b^3*(c*ProductLog[a + b*x])^(3/2)) + (c*(a + b*x)^3)/(18*b^3*(c*ProductLog[a + b*x])^(3/2)) + (a^2*(a + b*x))/(b^3*Sqrt[c*ProductLog[a + b*x]]) - (a*(a + b*x)^2)/(b^3*Sqrt[c*ProductLog[a + b*x]]) + (a + b*x)^3/(3*b^3*Sqrt[c*ProductLog[a + b*x]])","A",11,6,16,0.3750,1,"{6614, 6613, 6626, 6618, 6651, 6650}"
39,1,159,0,0.2657712,"\int \frac{x}{\sqrt{c \text{ProductLog}(a+b x)}} \, dx","Int[x/Sqrt[c*ProductLog[a + b*x]],x]","-\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)}}","-\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,"-(a*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a + b*x]]/Sqrt[c]])/(2*b^2*Sqrt[c]) - (Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a + b*x]])/Sqrt[c]])/(16*b^2*Sqrt[c]) + (c*(a + b*x)^2)/(8*b^2*(c*ProductLog[a + b*x])^(3/2)) - (a*(a + b*x))/(b^2*Sqrt[c*ProductLog[a + b*x]]) + (a + b*x)^2/(2*b^2*Sqrt[c*ProductLog[a + b*x]])","A",7,6,14,0.4286,1,"{6614, 6613, 6626, 6618, 6651, 6650}"
40,1,58,0,0.0493106,"\int \frac{1}{\sqrt{c \text{ProductLog}(a+b x)}} \, dx","Int[1/Sqrt[c*ProductLog[a + b*x]],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)}}","\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,"(Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a + b*x]]/Sqrt[c]])/(2*b*Sqrt[c]) + (a + b*x)/(b*Sqrt[c*ProductLog[a + b*x]])","A",2,2,12,0.1667,1,"{6613, 6626}"
41,0,0,0,0.0811227,"\int \frac{1}{x \sqrt{c \text{ProductLog}(a+b x)}} \, dx","Int[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,"(Sqrt[ProductLog[a + b*x]]*Defer[Int][1/(x*Sqrt[ProductLog[a + b*x]]), x])/Sqrt[c*ProductLog[a + b*x]]","N/A",0,0,0,0,-1,"{}"
42,0,0,0,0.0794325,"\int \frac{1}{x^2 \sqrt{c \text{ProductLog}(a+b x)}} \, dx","Int[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,"(Sqrt[ProductLog[a + b*x]]*Defer[Int][1/(x^2*Sqrt[ProductLog[a + b*x]]), x])/Sqrt[c*ProductLog[a + b*x]]","N/A",0,0,0,0,-1,"{}"
43,1,463,0,1.3098082,"\int \frac{x^3}{\sqrt{-c \text{ProductLog}(a+b x)}} \, dx","Int[x^3/Sqrt[-(c*ProductLog[a + b*x])],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}}","\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,"(a^3*Sqrt[Pi]*Erf[Sqrt[-(c*ProductLog[a + b*x])]/Sqrt[c]])/(2*b^4*Sqrt[c]) + (15*Sqrt[Pi]*Erf[(2*Sqrt[-(c*ProductLog[a + b*x])])/Sqrt[c]])/(8192*b^4*Sqrt[c]) + (3*a^2*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[-(c*ProductLog[a + b*x])])/Sqrt[c]])/(16*b^4*Sqrt[c]) + (a*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[-(c*ProductLog[a + b*x])])/Sqrt[c]])/(24*b^4*Sqrt[c]) - (15*c^3*(a + b*x)^4)/(2048*b^4*(-(c*ProductLog[a + b*x]))^(7/2)) + (a*c^2*(a + b*x)^3)/(12*b^4*(-(c*ProductLog[a + b*x]))^(5/2)) - (5*c^2*(a + b*x)^4)/(256*b^4*(-(c*ProductLog[a + b*x]))^(5/2)) - (3*a^2*c*(a + b*x)^2)/(8*b^4*(-(c*ProductLog[a + b*x]))^(3/2)) + (a*c*(a + b*x)^3)/(6*b^4*(-(c*ProductLog[a + b*x]))^(3/2)) - (c*(a + b*x)^4)/(32*b^4*(-(c*ProductLog[a + b*x]))^(3/2)) - (a^3*(a + b*x))/(b^4*Sqrt[-(c*ProductLog[a + b*x])]) + (3*a^2*(a + b*x)^2)/(2*b^4*Sqrt[-(c*ProductLog[a + b*x])]) - (a*(a + b*x)^3)/(b^4*Sqrt[-(c*ProductLog[a + b*x])]) + (a + b*x)^4/(4*b^4*Sqrt[-(c*ProductLog[a + b*x])])","A",16,6,17,0.3529,1,"{6614, 6613, 6627, 6618, 6651, 6649}"
44,1,299,0,0.797238,"\int \frac{x^2}{\sqrt{-c \text{ProductLog}(a+b x)}} \, dx","Int[x^2/Sqrt[-(c*ProductLog[a + b*x])],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}}","-\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,"-(a^2*Sqrt[Pi]*Erf[Sqrt[-(c*ProductLog[a + b*x])]/Sqrt[c]])/(2*b^3*Sqrt[c]) - (a*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[-(c*ProductLog[a + b*x])])/Sqrt[c]])/(8*b^3*Sqrt[c]) - (Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[-(c*ProductLog[a + b*x])])/Sqrt[c]])/(72*b^3*Sqrt[c]) - (c^2*(a + b*x)^3)/(36*b^3*(-(c*ProductLog[a + b*x]))^(5/2)) + (a*c*(a + b*x)^2)/(4*b^3*(-(c*ProductLog[a + b*x]))^(3/2)) - (c*(a + b*x)^3)/(18*b^3*(-(c*ProductLog[a + b*x]))^(3/2)) + (a^2*(a + b*x))/(b^3*Sqrt[-(c*ProductLog[a + b*x])]) - (a*(a + b*x)^2)/(b^3*Sqrt[-(c*ProductLog[a + b*x])]) + (a + b*x)^3/(3*b^3*Sqrt[-(c*ProductLog[a + b*x])])","A",11,6,17,0.3529,1,"{6614, 6613, 6627, 6618, 6651, 6649}"
45,1,164,0,0.3061573,"\int \frac{x}{\sqrt{-c \text{ProductLog}(a+b x)}} \, dx","Int[x/Sqrt[-(c*ProductLog[a + b*x])],x]","\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)}}","\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,"(a*Sqrt[Pi]*Erf[Sqrt[-(c*ProductLog[a + b*x])]/Sqrt[c]])/(2*b^2*Sqrt[c]) + (Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[-(c*ProductLog[a + b*x])])/Sqrt[c]])/(16*b^2*Sqrt[c]) - (c*(a + b*x)^2)/(8*b^2*(-(c*ProductLog[a + b*x]))^(3/2)) - (a*(a + b*x))/(b^2*Sqrt[-(c*ProductLog[a + b*x])]) + (a + b*x)^2/(2*b^2*Sqrt[-(c*ProductLog[a + b*x])])","A",7,6,15,0.4000,1,"{6614, 6613, 6627, 6618, 6651, 6649}"
46,1,60,0,0.0553455,"\int \frac{1}{\sqrt{-c \text{ProductLog}(a+b x)}} \, dx","Int[1/Sqrt[-(c*ProductLog[a + b*x])],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}}","\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,"-(Sqrt[Pi]*Erf[Sqrt[-(c*ProductLog[a + b*x])]/Sqrt[c]])/(2*b*Sqrt[c]) + (a + b*x)/(b*Sqrt[-(c*ProductLog[a + b*x])])","A",2,2,13,0.1538,1,"{6613, 6627}"
47,0,0,0,0.0874307,"\int \frac{1}{x \sqrt{-c \text{ProductLog}(a+b x)}} \, dx","Int[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,"(Sqrt[ProductLog[a + b*x]]*Defer[Int][1/(x*Sqrt[ProductLog[a + b*x]]), x])/Sqrt[-(c*ProductLog[a + b*x])]","N/A",0,0,0,0,-1,"{}"
48,0,0,0,0.0806773,"\int \frac{1}{x^2 \sqrt{-c \text{ProductLog}(a+b x)}} \, dx","Int[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,"(Sqrt[ProductLog[a + b*x]]*Defer[Int][1/(x^2*Sqrt[ProductLog[a + b*x]]), x])/Sqrt[-(c*ProductLog[a + b*x])]","N/A",0,0,0,0,-1,"{}"
49,1,568,0,1.6910055,"\int x^3 \sqrt{c \text{ProductLog}(a+b x)} \, dx","Int[x^3*Sqrt[c*ProductLog[a + b*x]],x]","-\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)}}","-\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,"-(a^3*Sqrt[c]*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a + b*x]]/Sqrt[c]])/(4*b^4) - (105*Sqrt[c]*Sqrt[Pi]*Erfi[(2*Sqrt[c*ProductLog[a + b*x]])/Sqrt[c]])/(65536*b^4) - (9*a^2*Sqrt[c]*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a + b*x]])/Sqrt[c]])/(64*b^4) - (5*a*Sqrt[c]*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[c*ProductLog[a + b*x]])/Sqrt[c]])/(144*b^4) + (105*c^4*(a + b*x)^4)/(16384*b^4*(c*ProductLog[a + b*x])^(7/2)) + (5*a*c^3*(a + b*x)^3)/(72*b^4*(c*ProductLog[a + b*x])^(5/2)) - (35*c^3*(a + b*x)^4)/(2048*b^4*(c*ProductLog[a + b*x])^(5/2)) + (9*a^2*c^2*(a + b*x)^2)/(32*b^4*(c*ProductLog[a + b*x])^(3/2)) - (5*a*c^2*(a + b*x)^3)/(36*b^4*(c*ProductLog[a + b*x])^(3/2)) + (7*c^2*(a + b*x)^4)/(256*b^4*(c*ProductLog[a + b*x])^(3/2)) + (a^3*c*(a + b*x))/(2*b^4*Sqrt[c*ProductLog[a + b*x]]) - (3*a^2*c*(a + b*x)^2)/(8*b^4*Sqrt[c*ProductLog[a + b*x]]) + (a*c*(a + b*x)^3)/(6*b^4*Sqrt[c*ProductLog[a + b*x]]) - (c*(a + b*x)^4)/(32*b^4*Sqrt[c*ProductLog[a + b*x]]) - (a^3*(a + b*x)*Sqrt[c*ProductLog[a + b*x]])/b^4 + (3*a^2*(a + b*x)^2*Sqrt[c*ProductLog[a + b*x]])/(2*b^4) - (a*(a + b*x)^3*Sqrt[c*ProductLog[a + b*x]])/b^4 + ((a + b*x)^4*Sqrt[c*ProductLog[a + b*x]])/(4*b^4)","A",20,7,16,0.4375,1,"{6614, 6613, 6624, 6626, 6618, 6651, 6650}"
50,1,377,0,0.9714891,"\int x^2 \sqrt{c \text{ProductLog}(a+b x)} \, dx","Int[x^2*Sqrt[c*ProductLog[a + b*x]],x]","\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)}}","\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,"(a^2*Sqrt[c]*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a + b*x]]/Sqrt[c]])/(4*b^3) + (3*a*Sqrt[c]*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a + b*x]])/Sqrt[c]])/(32*b^3) + (5*Sqrt[c]*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[c*ProductLog[a + b*x]])/Sqrt[c]])/(432*b^3) - (5*c^3*(a + b*x)^3)/(216*b^3*(c*ProductLog[a + b*x])^(5/2)) - (3*a*c^2*(a + b*x)^2)/(16*b^3*(c*ProductLog[a + b*x])^(3/2)) + (5*c^2*(a + b*x)^3)/(108*b^3*(c*ProductLog[a + b*x])^(3/2)) - (a^2*c*(a + b*x))/(2*b^3*Sqrt[c*ProductLog[a + b*x]]) + (a*c*(a + b*x)^2)/(4*b^3*Sqrt[c*ProductLog[a + b*x]]) - (c*(a + b*x)^3)/(18*b^3*Sqrt[c*ProductLog[a + b*x]]) + (a^2*(a + b*x)*Sqrt[c*ProductLog[a + b*x]])/b^3 - (a*(a + b*x)^2*Sqrt[c*ProductLog[a + b*x]])/b^3 + ((a + b*x)^3*Sqrt[c*ProductLog[a + b*x]])/(3*b^3)","A",14,7,16,0.4375,1,"{6614, 6613, 6624, 6626, 6618, 6651, 6650}"
51,1,214,0,0.3984988,"\int x \sqrt{c \text{ProductLog}(a+b x)} \, dx","Int[x*Sqrt[c*ProductLog[a + b*x]],x]","\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)}}","\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,"-(a*Sqrt[c]*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a + b*x]]/Sqrt[c]])/(4*b^2) - (3*Sqrt[c]*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a + b*x]])/Sqrt[c]])/(64*b^2) + (3*c^2*(a + b*x)^2)/(32*b^2*(c*ProductLog[a + b*x])^(3/2)) + (a*c*(a + b*x))/(2*b^2*Sqrt[c*ProductLog[a + b*x]]) - (c*(a + b*x)^2)/(8*b^2*Sqrt[c*ProductLog[a + b*x]]) - (a*(a + b*x)*Sqrt[c*ProductLog[a + b*x]])/b^2 + ((a + b*x)^2*Sqrt[c*ProductLog[a + b*x]])/(2*b^2)","A",9,7,14,0.5000,1,"{6614, 6613, 6624, 6626, 6618, 6651, 6650}"
52,1,83,0,0.0925371,"\int \sqrt{c \text{ProductLog}(a+b x)} \, dx","Int[Sqrt[c*ProductLog[a + b*x]],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)}}","\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,"(Sqrt[c]*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a + b*x]]/Sqrt[c]])/(4*b) - (c*(a + b*x))/(2*b*Sqrt[c*ProductLog[a + b*x]]) + ((a + b*x)*Sqrt[c*ProductLog[a + b*x]])/b","A",3,3,12,0.2500,1,"{6613, 6624, 6626}"
53,0,0,0,0.0807042,"\int \frac{\sqrt{c \text{ProductLog}(a+b x)}}{x} \, dx","Int[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,"(Sqrt[c*ProductLog[a + b*x]]*Defer[Int][Sqrt[ProductLog[a + b*x]]/x, x])/Sqrt[ProductLog[a + b*x]]","N/A",0,0,0,0,-1,"{}"
54,0,0,0,0.0812098,"\int \frac{\sqrt{c \text{ProductLog}(a+b x)}}{x^2} \, dx","Int[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,"(Sqrt[c*ProductLog[a + b*x]]*Defer[Int][Sqrt[ProductLog[a + b*x]]/x^2, x])/Sqrt[ProductLog[a + b*x]]","N/A",0,0,0,0,-1,"{}"
55,1,257,0,0.6279061,"\int \frac{x^3}{d+d \text{ProductLog}(a+b x)} \, dx","Int[x^3/(d + d*ProductLog[a + b*x]),x]","-\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}","-\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,"(-3*(a + b*x)^4)/(128*b^4*d*ProductLog[a + b*x]^4) - (2*a*(a + b*x)^3)/(9*b^4*d*ProductLog[a + b*x]^3) + (3*(a + b*x)^4)/(32*b^4*d*ProductLog[a + b*x]^3) - (3*a^2*(a + b*x)^2)/(4*b^4*d*ProductLog[a + b*x]^2) + (2*a*(a + b*x)^3)/(3*b^4*d*ProductLog[a + b*x]^2) - (3*(a + b*x)^4)/(16*b^4*d*ProductLog[a + b*x]^2) - (a^3*(a + b*x))/(b^4*d*ProductLog[a + b*x]) + (3*a^2*(a + b*x)^2)/(2*b^4*d*ProductLog[a + b*x]) - (a*(a + b*x)^3)/(b^4*d*ProductLog[a + b*x]) + (a + b*x)^4/(4*b^4*d*ProductLog[a + b*x])","A",12,5,16,0.3125,1,"{6630, 6622, 6640, 6647, 6651}"
56,1,149,0,0.3406236,"\int \frac{x^2}{d+d \text{ProductLog}(a+b x)} \, dx","Int[x^2/(d + d*ProductLog[a + b*x]),x]","\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}","\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,"(2*(a + b*x)^3)/(27*b^3*d*ProductLog[a + b*x]^3) + (a*(a + b*x)^2)/(2*b^3*d*ProductLog[a + b*x]^2) - (2*(a + b*x)^3)/(9*b^3*d*ProductLog[a + b*x]^2) + (a^2*(a + b*x))/(b^3*d*ProductLog[a + b*x]) - (a*(a + b*x)^2)/(b^3*d*ProductLog[a + b*x]) + (a + b*x)^3/(3*b^3*d*ProductLog[a + b*x])","A",8,5,16,0.3125,1,"{6630, 6622, 6640, 6647, 6651}"
57,1,73,0,0.1465104,"\int \frac{x}{d+d \text{ProductLog}(a+b x)} \, dx","Int[x/(d + d*ProductLog[a + b*x]),x]","\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)}","\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)^2/(4*b^2*d*ProductLog[a + b*x]^2) - (a*(a + b*x))/(b^2*d*ProductLog[a + b*x]) + (a + b*x)^2/(2*b^2*d*ProductLog[a + b*x])","A",5,4,14,0.2857,1,"{6630, 6622, 6640, 6647}"
58,1,20,0,0.0186124,"\int \frac{1}{d+d \text{ProductLog}(a+b x)} \, dx","Int[(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",1,1,12,0.08333,1,"{6622}"
59,0,0,0,0.0879909,"\int \frac{1}{x (d+d \text{ProductLog}(a+b x))} \, dx","Int[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,"Defer[Int][1/(x*(1 + ProductLog[a + b*x])), x]/d","N/A",0,0,0,0,-1,"{}"
60,0,0,0,0.0935439,"\int \frac{1}{x^2 (d+d \text{ProductLog}(a+b x))} \, dx","Int[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,"Defer[Int][1/(x^2*(1 + ProductLog[a + b*x])), x]/d","N/A",0,0,0,0,-1,"{}"
61,1,71,0,0.263032,"\int x^3 \text{ProductLog}(a x) \, dx","Int[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",6,4,8,0.5000,1,"{6618, 6651, 6640, 6647}"
62,1,58,0,0.2023053,"\int x^2 \text{ProductLog}(a x) \, dx","Int[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",5,4,8,0.5000,1,"{6618, 6651, 6640, 6647}"
63,1,45,0,0.0917855,"\int x \text{ProductLog}(a x) \, dx","Int[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",4,4,6,0.6667,1,"{6618, 6651, 6640, 6647}"
64,1,18,0,0.023789,"\int \text{ProductLog}(a x) \, dx","Int[ProductLog[a*x],x]","x \text{ProductLog}(a x)+\frac{x}{\text{ProductLog}(a x)}-x","x \text{ProductLog}(a x)+\frac{x}{\text{ProductLog}(a x)}-x",1,"-x + x/ProductLog[a*x] + x*ProductLog[a*x]","A",3,3,4,0.7500,1,"{6613, 6623, 6622}"
65,1,15,0,0.0831503,"\int \frac{\text{ProductLog}(a x)}{x} \, dx","Int[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",2,2,8,0.2500,1,"{6619, 6646}"
66,1,19,0,0.0487899,"\int \frac{\text{ProductLog}(a x)}{x^2} \, dx","Int[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",2,2,8,0.2500,1,"{6618, 6648}"
67,1,22,0,0.0684769,"\int \frac{\text{ProductLog}(a x)}{x^3} \, dx","Int[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",2,2,8,0.2500,1,"{6619, 6648}"
68,1,39,0,0.1687637,"\int \frac{\text{ProductLog}(a x)}{x^4} \, dx","Int[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",3,3,8,0.3750,1,"{6619, 6652, 6648}"
69,1,52,0,0.2151308,"\int \frac{\text{ProductLog}(a x)}{x^5} \, dx","Int[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",4,3,8,0.3750,1,"{6619, 6652, 6648}"
70,1,65,0,0.2552983,"\int \frac{\text{ProductLog}(a x)}{x^6} \, dx","Int[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",5,3,8,0.3750,1,"{6619, 6652, 6648}"
71,1,71,0,0.2596377,"\int x^2 \text{ProductLog}(a x)^2 \, dx","Int[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",6,4,10,0.4000,1,"{6618, 6651, 6640, 6647}"
72,1,58,0,0.1304223,"\int x \text{ProductLog}(a x)^2 \, dx","Int[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",5,4,8,0.5000,1,"{6618, 6651, 6640, 6647}"
73,1,28,0,0.0481644,"\int \text{ProductLog}(a x)^2 \, dx","Int[ProductLog[a*x]^2,x]","x \text{ProductLog}(a x)^2-2 x \text{ProductLog}(a x)-\frac{4 x}{\text{ProductLog}(a x)}+4 x","x \text{ProductLog}(a x)^2-2 x \text{ProductLog}(a x)-\frac{4 x}{\text{ProductLog}(a x)}+4 x",1,"4*x - (4*x)/ProductLog[a*x] - 2*x*ProductLog[a*x] + x*ProductLog[a*x]^2","A",4,4,6,0.6667,1,"{6613, 6624, 6623, 6622}"
74,1,21,0,0.0692813,"\int \frac{\text{ProductLog}(a x)^2}{x} \, dx","Int[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",2,2,10,0.2000,1,"{6619, 6646}"
75,1,21,0,0.081591,"\int \frac{\text{ProductLog}(a x)^2}{x^2} \, dx","Int[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",2,2,10,0.2000,1,"{6618, 6647}"
76,1,25,0,0.0769057,"\int \frac{\text{ProductLog}(a x)^2}{x^3} \, dx","Int[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",2,2,10,0.2000,1,"{6618, 6648}"
77,1,24,0,0.0748403,"\int \frac{\text{ProductLog}(a x)^2}{x^4} \, dx","Int[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",2,2,10,0.2000,1,"{6619, 6648}"
78,1,36,0,0.1489697,"\int \frac{\text{ProductLog}(a x)^2}{x^5} \, dx","Int[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",3,3,10,0.3000,1,"{6619, 6652, 6648}"
79,1,54,0,0.1925375,"\int \frac{\text{ProductLog}(a x)^2}{x^6} \, dx","Int[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",4,3,10,0.3000,1,"{6619, 6652, 6648}"
80,1,63,0,0.2564156,"\int \frac{\text{ProductLog}(a x)^2}{x^7} \, dx","Int[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",5,3,10,0.3000,1,"{6619, 6652, 6648}"
81,1,84,0,0.3387794,"\int x^2 \text{ProductLog}(a x)^3 \, dx","Int[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",7,4,10,0.4000,1,"{6618, 6651, 6640, 6647}"
82,1,71,0,0.1782764,"\int x \text{ProductLog}(a x)^3 \, dx","Int[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",6,4,8,0.5000,1,"{6618, 6651, 6640, 6647}"
83,1,37,0,0.0786239,"\int \text{ProductLog}(a x)^3 \, dx","Int[ProductLog[a*x]^3,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","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,"-18*x + (18*x)/ProductLog[a*x] + 9*x*ProductLog[a*x] - 3*x*ProductLog[a*x]^2 + x*ProductLog[a*x]^3","A",5,4,6,0.6667,1,"{6613, 6624, 6623, 6622}"
84,1,21,0,0.0680806,"\int \frac{\text{ProductLog}(a x)^3}{x} \, dx","Int[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",2,2,10,0.2000,1,"{6619, 6646}"
85,1,32,0,0.1402642,"\int \frac{\text{ProductLog}(a x)^3}{x^2} \, dx","Int[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",3,3,10,0.3000,1,"{6618, 6651, 6647}"
86,1,27,0,0.0832525,"\int \frac{\text{ProductLog}(a x)^3}{x^3} \, dx","Int[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",2,2,10,0.2000,1,"{6618, 6647}"
87,1,25,0,0.0798902,"\int \frac{\text{ProductLog}(a x)^3}{x^4} \, dx","Int[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",2,2,10,0.2000,1,"{6618, 6648}"
88,1,24,0,0.0747139,"\int \frac{\text{ProductLog}(a x)^3}{x^5} \, dx","Int[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",2,2,10,0.2000,1,"{6619, 6648}"
89,1,41,0,0.1375491,"\int \frac{\text{ProductLog}(a x)^3}{x^6} \, dx","Int[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",3,3,10,0.3000,1,"{6619, 6652, 6648}"
90,1,50,0,0.2123375,"\int \frac{\text{ProductLog}(a x)^3}{x^7} \, dx","Int[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",4,3,10,0.3000,1,"{6619, 6652, 6648}"
91,1,67,0,0.2441256,"\int \frac{\text{ProductLog}(a x)^3}{x^8} \, dx","Int[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",5,3,10,0.3000,1,"{6619, 6652, 6648}"
92,1,66,0,0.2775555,"\int \frac{x^4}{\text{ProductLog}(a x)} \, dx","Int[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",5,3,10,0.3000,1,"{6618, 6651, 6647}"
93,1,53,0,0.209107,"\int \frac{x^3}{\text{ProductLog}(a x)} \, dx","Int[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",4,3,10,0.3000,1,"{6618, 6651, 6647}"
94,1,40,0,0.1414528,"\int \frac{x^2}{\text{ProductLog}(a x)} \, dx","Int[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",3,3,10,0.3000,1,"{6618, 6651, 6647}"
95,1,27,0,0.0565595,"\int \frac{x}{\text{ProductLog}(a x)} \, dx","Int[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",2,2,8,0.2500,1,"{6618, 6647}"
96,1,18,0,0.0270114,"\int \frac{1}{\text{ProductLog}(a x)} \, dx","Int[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",2,2,6,0.3333,1,"{6613, 6625}"
97,1,14,0,0.0442783,"\int \frac{1}{x \text{ProductLog}(a x)} \, dx","Int[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",2,2,10,0.2000,1,"{6619, 6641}"
98,1,33,0,0.0845677,"\int \frac{1}{x^2 \text{ProductLog}(a x)} \, dx","Int[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",3,3,10,0.3000,1,"{6619, 6642, 6648}"
99,1,46,0,0.1482722,"\int \frac{1}{x^3 \text{ProductLog}(a x)} \, dx","Int[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",4,4,10,0.4000,1,"{6619, 6642, 6652, 6648}"
100,1,59,0,0.2043707,"\int \frac{1}{x^4 \text{ProductLog}(a x)} \, dx","Int[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",5,4,10,0.4000,1,"{6619, 6642, 6652, 6648}"
101,1,66,0,0.2675304,"\int \frac{x^5}{\text{ProductLog}(a x)^2} \, dx","Int[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",5,3,10,0.3000,1,"{6618, 6651, 6647}"
102,1,53,0,0.2042215,"\int \frac{x^4}{\text{ProductLog}(a x)^2} \, dx","Int[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",4,3,10,0.3000,1,"{6618, 6651, 6647}"
103,1,40,0,0.1262837,"\int \frac{x^3}{\text{ProductLog}(a x)^2} \, dx","Int[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",3,3,10,0.3000,1,"{6618, 6651, 6647}"
104,1,27,0,0.0707088,"\int \frac{x^2}{\text{ProductLog}(a x)^2} \, dx","Int[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",2,2,10,0.2000,1,"{6618, 6647}"
105,1,25,0,0.0437732,"\int \frac{x}{\text{ProductLog}(a x)^2} \, dx","Int[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",2,2,8,0.2500,1,"{6618, 6648}"
106,1,20,0,0.0263537,"\int \frac{1}{\text{ProductLog}(a x)^2} \, dx","Int[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",2,2,6,0.3333,1,"{6612, 6625}"
107,1,19,0,0.0685272,"\int \frac{1}{x \text{ProductLog}(a x)^2} \, dx","Int[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",2,2,10,0.2000,1,"{6619, 6646}"
108,1,46,0,0.1361115,"\int \frac{1}{x^2 \text{ProductLog}(a x)^2} \, dx","Int[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",4,4,10,0.4000,1,"{6619, 6652, 6642, 6648}"
109,1,59,0,0.202335,"\int \frac{1}{x^3 \text{ProductLog}(a x)^2} \, dx","Int[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",5,4,10,0.4000,1,"{6619, 6652, 6642, 6648}"
110,1,66,0,0.2796805,"\int \frac{x^6}{\text{ProductLog}(a x)^3} \, dx","Int[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",5,3,10,0.3000,1,"{6618, 6651, 6647}"
111,1,53,0,0.1956062,"\int \frac{x^5}{\text{ProductLog}(a x)^3} \, dx","Int[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",4,3,10,0.3000,1,"{6618, 6651, 6647}"
112,1,40,0,0.1384049,"\int \frac{x^4}{\text{ProductLog}(a x)^3} \, dx","Int[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",3,3,10,0.3000,1,"{6618, 6651, 6647}"
113,1,27,0,0.0781804,"\int \frac{x^3}{\text{ProductLog}(a x)^3} \, dx","Int[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",2,2,10,0.2000,1,"{6618, 6647}"
114,1,25,0,0.1139337,"\int \frac{x^2}{\text{ProductLog}(a x)^3} \, dx","Int[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",2,2,10,0.2000,1,"{6618, 6648}"
115,1,24,0,0.0599725,"\int \frac{x}{\text{ProductLog}(a x)^3} \, dx","Int[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",2,2,8,0.2500,1,"{6619, 6648}"
116,1,35,0,0.0492156,"\int \frac{1}{\text{ProductLog}(a x)^3} \, dx","Int[ProductLog[a*x]^(-3),x]","\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}","\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]])/(2*a) - x/(2*ProductLog[a*x]^3) - (3*x)/(2*ProductLog[a*x]^2)","A",3,3,6,0.5000,1,"{6612, 6628, 6625}"
117,1,21,0,0.0696545,"\int \frac{1}{x \text{ProductLog}(a x)^3} \, dx","Int[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",2,2,10,0.2000,1,"{6619, 6646}"
118,1,59,0,0.2211123,"\int \frac{1}{x^2 \text{ProductLog}(a x)^3} \, dx","Int[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",5,4,10,0.4000,1,"{6619, 6652, 6642, 6648}"
119,1,72,0,0.2761828,"\int \frac{1}{x^3 \text{ProductLog}(a x)^3} \, dx","Int[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",6,4,10,0.4000,1,"{6619, 6652, 6642, 6648}"
120,1,131,0,0.5993245,"\int x^3 \sqrt{c \text{ProductLog}(a x)} \, dx","Int[x^3*Sqrt[c*ProductLog[a*x]],x]","-\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)}}","-\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,"(-105*Sqrt[c]*Sqrt[Pi]*Erfi[(2*Sqrt[c*ProductLog[a*x]])/Sqrt[c]])/(65536*a^4) + (105*c^4*x^4)/(16384*(c*ProductLog[a*x])^(7/2)) - (35*c^3*x^4)/(2048*(c*ProductLog[a*x])^(5/2)) + (7*c^2*x^4)/(256*(c*ProductLog[a*x])^(3/2)) - (c*x^4)/(32*Sqrt[c*ProductLog[a*x]]) + (x^4*Sqrt[c*ProductLog[a*x]])/4","A",6,3,14,0.2143,1,"{6618, 6651, 6650}"
121,1,119,0,0.4895983,"\int x^2 \sqrt{c \text{ProductLog}(a x)} \, dx","Int[x^2*Sqrt[c*ProductLog[a*x]],x]","\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)}}","\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,"(5*Sqrt[c]*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[c*ProductLog[a*x]])/Sqrt[c]])/(432*a^3) - (5*c^3*x^3)/(216*(c*ProductLog[a*x])^(5/2)) + (5*c^2*x^3)/(108*(c*ProductLog[a*x])^(3/2)) - (c*x^3)/(18*Sqrt[c*ProductLog[a*x]]) + (x^3*Sqrt[c*ProductLog[a*x]])/3","A",5,3,14,0.2143,1,"{6618, 6651, 6650}"
122,1,99,0,0.2351478,"\int x \sqrt{c \text{ProductLog}(a x)} \, dx","Int[x*Sqrt[c*ProductLog[a*x]],x]","-\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)}}","-\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,"(-3*Sqrt[c]*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a*x]])/Sqrt[c]])/(64*a^2) + (3*c^2*x^2)/(32*(c*ProductLog[a*x])^(3/2)) - (c*x^2)/(8*Sqrt[c*ProductLog[a*x]]) + (x^2*Sqrt[c*ProductLog[a*x]])/2","A",4,3,12,0.2500,1,"{6618, 6651, 6650}"
123,1,63,0,0.0834658,"\int \sqrt{c \text{ProductLog}(a x)} \, dx","Int[Sqrt[c*ProductLog[a*x]],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)}}","\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,"(Sqrt[c]*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a*x]]/Sqrt[c]])/(4*a) - (c*x)/(2*Sqrt[c*ProductLog[a*x]]) + x*Sqrt[c*ProductLog[a*x]]","A",3,3,10,0.3000,1,"{6613, 6624, 6626}"
124,1,30,0,0.1243721,"\int \frac{\sqrt{c \text{ProductLog}(a x)}}{x} \, dx","Int[Sqrt[c*ProductLog[a*x]]/x,x]","\frac{2 (c \text{ProductLog}(a x))^{3/2}}{3 c}+2 \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]] + (2*(c*ProductLog[a*x])^(3/2))/(3*c)","A",2,2,14,0.1429,1,"{6619, 6646}"
125,1,46,0,0.1349429,"\int \frac{\sqrt{c \text{ProductLog}(a x)}}{x^2} \, dx","Int[Sqrt[c*ProductLog[a*x]]/x^2,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}","\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,"-(a*Sqrt[c]*Sqrt[Pi]*Erf[Sqrt[c*ProductLog[a*x]]/Sqrt[c]]) - (2*Sqrt[c*ProductLog[a*x]])/x","A",2,2,14,0.1429,1,"{6619, 6649}"
126,1,79,0,0.275702,"\int \frac{\sqrt{c \text{ProductLog}(a x)}}{x^3} \, dx","Int[Sqrt[c*ProductLog[a*x]]/x^3,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}","\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*a^2*Sqrt[c]*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[c*ProductLog[a*x]])/Sqrt[c]])/3 - (2*Sqrt[c*ProductLog[a*x]])/(3*x^2) + (2*(c*ProductLog[a*x])^(3/2))/(3*c*x^2)","A",3,3,14,0.2143,1,"{6619, 6652, 6649}"
127,1,99,0,0.3876068,"\int \frac{\sqrt{c \text{ProductLog}(a x)}}{x^4} \, dx","Int[Sqrt[c*ProductLog[a*x]]/x^4,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}","-\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,"(-4*a^3*Sqrt[c]*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[c*ProductLog[a*x]])/Sqrt[c]])/5 - (2*Sqrt[c*ProductLog[a*x]])/(5*x^3) + (2*(c*ProductLog[a*x])^(3/2))/(15*c*x^3) - (4*(c*ProductLog[a*x])^(5/2))/(5*c^2*x^3)","A",4,3,14,0.2143,1,"{6619, 6652, 6649}"
128,1,113,0,0.5072871,"\int \frac{\sqrt{c \text{ProductLog}(a x)}}{x^5} \, dx","Int[Sqrt[c*ProductLog[a*x]]/x^5,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}","\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,"(256*a^4*Sqrt[c]*Sqrt[Pi]*Erf[(2*Sqrt[c*ProductLog[a*x]])/Sqrt[c]])/105 - (2*Sqrt[c*ProductLog[a*x]])/(7*x^4) + (2*(c*ProductLog[a*x])^(3/2))/(35*c*x^4) - (16*(c*ProductLog[a*x])^(5/2))/(105*c^2*x^4) + (128*(c*ProductLog[a*x])^(7/2))/(105*c^3*x^4)","A",5,3,14,0.2143,1,"{6619, 6652, 6649}"
129,1,139,0,0.6534345,"\int \frac{\sqrt{c \text{ProductLog}(a x)}}{x^6} \, dx","Int[Sqrt[c*ProductLog[a*x]]/x^6,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}","-\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,"(-400*a^5*Sqrt[c]*Sqrt[5*Pi]*Erf[(Sqrt[5]*Sqrt[c*ProductLog[a*x]])/Sqrt[c]])/189 - (2*Sqrt[c*ProductLog[a*x]])/(9*x^5) + (2*(c*ProductLog[a*x])^(3/2))/(63*c*x^5) - (4*(c*ProductLog[a*x])^(5/2))/(63*c^2*x^5) + (40*(c*ProductLog[a*x])^(7/2))/(189*c^3*x^5) - (400*(c*ProductLog[a*x])^(9/2))/(189*c^4*x^5)","A",6,3,14,0.2143,1,"{6619, 6652, 6649}"
130,1,139,0,0.6811522,"\int \frac{x^4}{\sqrt{c \text{ProductLog}(a x)}} \, dx","Int[x^4/Sqrt[c*ProductLog[a*x]],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}}","\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,"(21*Sqrt[Pi/5]*Erfi[(Sqrt[5]*Sqrt[c*ProductLog[a*x]])/Sqrt[c]])/(20000*a^5*Sqrt[c]) - (21*c^4*x^5)/(10000*(c*ProductLog[a*x])^(9/2)) + (7*c^3*x^5)/(1000*(c*ProductLog[a*x])^(7/2)) - (7*c^2*x^5)/(500*(c*ProductLog[a*x])^(5/2)) + (c*x^5)/(50*(c*ProductLog[a*x])^(3/2)) + x^5/(5*Sqrt[c*ProductLog[a*x]])","A",6,3,14,0.2143,1,"{6618, 6651, 6650}"
131,1,111,0,0.5494771,"\int \frac{x^3}{\sqrt{c \text{ProductLog}(a x)}} \, dx","Int[x^3/Sqrt[c*ProductLog[a*x]],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}}","-\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,"(-15*Sqrt[Pi]*Erfi[(2*Sqrt[c*ProductLog[a*x]])/Sqrt[c]])/(8192*a^4*Sqrt[c]) + (15*c^3*x^4)/(2048*(c*ProductLog[a*x])^(7/2)) - (5*c^2*x^4)/(256*(c*ProductLog[a*x])^(5/2)) + (c*x^4)/(32*(c*ProductLog[a*x])^(3/2)) + x^4/(4*Sqrt[c*ProductLog[a*x]])","A",5,3,14,0.2143,1,"{6618, 6651, 6650}"
132,1,99,0,0.4134367,"\int \frac{x^2}{\sqrt{c \text{ProductLog}(a x)}} \, dx","Int[x^2/Sqrt[c*ProductLog[a*x]],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}}","\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,"(Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[c*ProductLog[a*x]])/Sqrt[c]])/(72*a^3*Sqrt[c]) - (c^2*x^3)/(36*(c*ProductLog[a*x])^(5/2)) + (c*x^3)/(18*(c*ProductLog[a*x])^(3/2)) + x^3/(3*Sqrt[c*ProductLog[a*x]])","A",4,3,14,0.2143,1,"{6618, 6651, 6650}"
133,1,79,0,0.1821346,"\int \frac{x}{\sqrt{c \text{ProductLog}(a x)}} \, dx","Int[x/Sqrt[c*ProductLog[a*x]],x]","-\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}}","-\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,"-(Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a*x]])/Sqrt[c]])/(16*a^2*Sqrt[c]) + (c*x^2)/(8*(c*ProductLog[a*x])^(3/2)) + x^2/(2*Sqrt[c*ProductLog[a*x]])","A",3,3,12,0.2500,1,"{6618, 6651, 6650}"
134,1,47,0,0.0454069,"\int \frac{1}{\sqrt{c \text{ProductLog}(a x)}} \, dx","Int[1/Sqrt[c*ProductLog[a*x]],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)}}","\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,"(Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a*x]]/Sqrt[c]])/(2*a*Sqrt[c]) + x/Sqrt[c*ProductLog[a*x]]","A",2,2,10,0.2000,1,"{6613, 6626}"
135,1,28,0,0.1120064,"\int \frac{1}{x \sqrt{c \text{ProductLog}(a x)}} \, dx","Int[1/(x*Sqrt[c*ProductLog[a*x]]),x]","\frac{2 \sqrt{c \text{ProductLog}(a x)}}{c}-\frac{2}{\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/Sqrt[c*ProductLog[a*x]] + (2*Sqrt[c*ProductLog[a*x]])/c","A",2,2,14,0.1429,1,"{6619, 6646}"
136,1,70,0,0.2390716,"\int \frac{1}{x^2 \sqrt{c \text{ProductLog}(a x)}} \, dx","Int[1/(x^2*Sqrt[c*ProductLog[a*x]]),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)}}","-\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*a*Sqrt[Pi]*Erf[Sqrt[c*ProductLog[a*x]]/Sqrt[c]])/(3*Sqrt[c]) - 2/(3*x*Sqrt[c*ProductLog[a*x]]) - (2*Sqrt[c*ProductLog[a*x]])/(3*c*x)","A",3,3,14,0.2143,1,"{6619, 6652, 6649}"
137,1,99,0,0.3597296,"\int \frac{1}{x^3 \sqrt{c \text{ProductLog}(a x)}} \, dx","Int[1/(x^3*Sqrt[c*ProductLog[a*x]]),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)}}","\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,"(8*a^2*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[c*ProductLog[a*x]])/Sqrt[c]])/(15*Sqrt[c]) - 2/(5*x^2*Sqrt[c*ProductLog[a*x]]) - (2*Sqrt[c*ProductLog[a*x]])/(15*c*x^2) + (8*(c*ProductLog[a*x])^(3/2))/(15*c^2*x^2)","A",4,3,14,0.2143,1,"{6619, 6652, 6649}"
138,1,119,0,0.4908434,"\int \frac{1}{x^4 \sqrt{c \text{ProductLog}(a x)}} \, dx","Int[1/(x^4*Sqrt[c*ProductLog[a*x]]),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)}}","-\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,"(-24*a^3*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[c*ProductLog[a*x]])/Sqrt[c]])/(35*Sqrt[c]) - 2/(7*x^3*Sqrt[c*ProductLog[a*x]]) - (2*Sqrt[c*ProductLog[a*x]])/(35*c*x^3) + (4*(c*ProductLog[a*x])^(3/2))/(35*c^2*x^3) - (24*(c*ProductLog[a*x])^(5/2))/(35*c^3*x^3)","A",5,3,14,0.2143,1,"{6619, 6652, 6649}"
139,1,133,0,0.5979817,"\int \frac{1}{x^5 \sqrt{c \text{ProductLog}(a x)}} \, dx","Int[1/(x^5*Sqrt[c*ProductLog[a*x]]),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)}}","\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,"(2048*a^4*Sqrt[Pi]*Erf[(2*Sqrt[c*ProductLog[a*x]])/Sqrt[c]])/(945*Sqrt[c]) - 2/(9*x^4*Sqrt[c*ProductLog[a*x]]) - (2*Sqrt[c*ProductLog[a*x]])/(63*c*x^4) + (16*(c*ProductLog[a*x])^(3/2))/(315*c^2*x^4) - (128*(c*ProductLog[a*x])^(5/2))/(945*c^3*x^4) + (1024*(c*ProductLog[a*x])^(7/2))/(945*c^4*x^4)","A",6,3,14,0.2143,1,"{6619, 6652, 6649}"
140,1,110,0,0.239051,"\int x^2 (c \text{ProductLog}(a x))^p \, dx","Int[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-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}","\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^(-3 - p)*x^2*Gamma[3 + p, -3*ProductLog[a*x]]*(-ProductLog[a*x])^(-2 - p)*(c*ProductLog[a*x])^p)/(a*E^(2*ProductLog[a*x])) + (3^(-4 - p)*x^2*Gamma[4 + p, -3*ProductLog[a*x]]*(-ProductLog[a*x])^(-3 - p)*(c*ProductLog[a*x])^(1 + p))/(a*c*E^(2*ProductLog[a*x]))","A",3,2,12,0.1667,1,"{6620, 6653}"
141,1,106,0,0.1663565,"\int x (c \text{ProductLog}(a x))^p \, dx","Int[x*(c*ProductLog[a*x])^p,x]","\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}","\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^(-2 - p)*x*Gamma[2 + p, -2*ProductLog[a*x]]*(-ProductLog[a*x])^(-1 - p)*(c*ProductLog[a*x])^p)/(a*E^ProductLog[a*x]) + (2^(-3 - p)*x*Gamma[3 + p, -2*ProductLog[a*x]]*(-ProductLog[a*x])^(-2 - p)*(c*ProductLog[a*x])^(1 + p))/(a*c*E^ProductLog[a*x])","A",3,2,10,0.2000,1,"{6620, 6653}"
142,1,32,0,0.1348034,"\int \frac{(c \text{ProductLog}(a x))^p}{x} \, dx","Int[(c*ProductLog[a*x])^p/x,x]","\frac{(c \text{ProductLog}(a x))^p}{p}+\frac{(c \text{ProductLog}(a x))^{p+1}}{c (p+1)}","\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 + (c*ProductLog[a*x])^(1 + p)/(c*(1 + p))","A",2,2,12,0.1667,1,"{6619, 6646}"
143,1,88,0,0.2129332,"\int \frac{(c \text{ProductLog}(a x))^p}{x^2} \, dx","Int[(c*ProductLog[a*x])^p/x^2,x]","-\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}","-\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]]*ProductLog[a*x]^(2 - p)*(c*ProductLog[a*x])^p)/(a*x^2)) - (E^(2*ProductLog[a*x])*Gamma[p, ProductLog[a*x]]*ProductLog[a*x]^(1 - p)*(c*ProductLog[a*x])^(1 + p))/(a*c*x^2)","A",3,2,12,0.1667,1,"{6620, 6653}"
144,1,108,0,0.2418236,"\int \frac{(c \text{ProductLog}(a x))^p}{x^3} \, dx","Int[(c*ProductLog[a*x])^p/x^3,x]","-\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}","-\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^(2 - p)*E^(3*ProductLog[a*x])*Gamma[-2 + p, 2*ProductLog[a*x]]*ProductLog[a*x]^(3 - p)*(c*ProductLog[a*x])^p)/(a*x^3)) - (2^(1 - p)*E^(3*ProductLog[a*x])*Gamma[-1 + p, 2*ProductLog[a*x]]*ProductLog[a*x]^(2 - p)*(c*ProductLog[a*x])^(1 + p))/(a*c*x^3)","A",3,2,12,0.1667,1,"{6620, 6653}"
145,1,109,0,0.1238118,"\int x^m \text{ProductLog}(a x) \, dx","Int[x^m*ProductLog[a*x],x]","\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)}","\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*Gamma[3 + m, -((1 + m)*ProductLog[a*x])]*ProductLog[a*x]^2*(-((1 + m)*ProductLog[a*x]))^(-2 - m))/(a*E^(m*ProductLog[a*x])*(1 + m)) + (x^m*Gamma[2 + m, -((1 + m)*ProductLog[a*x])]*ProductLog[a*x]*(-((1 + m)*ProductLog[a*x]))^(-1 - m))/(a*E^(m*ProductLog[a*x])*(1 + m))","A",3,2,8,0.2500,1,"{6620, 6653}"
146,1,111,0,0.1569811,"\int x^m \text{ProductLog}(a x)^2 \, dx","Int[x^m*ProductLog[a*x]^2,x]","\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)}","\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*Gamma[4 + m, -((1 + m)*ProductLog[a*x])]*ProductLog[a*x]^3*(-((1 + m)*ProductLog[a*x]))^(-3 - m))/(a*E^(m*ProductLog[a*x])*(1 + m)) + (x^m*Gamma[3 + m, -((1 + m)*ProductLog[a*x])]*ProductLog[a*x]^2*(-((1 + m)*ProductLog[a*x]))^(-2 - m))/(a*E^(m*ProductLog[a*x])*(1 + m))","A",3,2,10,0.2000,1,"{6620, 6653}"
147,1,101,0,0.1147077,"\int \frac{x^m}{\text{ProductLog}(a x)} \, dx","Int[x^m/ProductLog[a*x],x]","\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)}","\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*Gamma[m, -((1 + m)*ProductLog[a*x])]*(-((1 + m)*ProductLog[a*x]))^(1 - m))/(a*E^(m*ProductLog[a*x])*(1 + m)*ProductLog[a*x]) + (x^m*Gamma[1 + m, -((1 + m)*ProductLog[a*x])])/(a*E^(m*ProductLog[a*x])*(1 + m)*(-((1 + m)*ProductLog[a*x]))^m)","A",3,3,10,0.3000,1,"{6620, 6653, 6643}"
148,1,109,0,0.167457,"\int \frac{x^m}{\text{ProductLog}(a x)^2} \, dx","Int[x^m/ProductLog[a*x]^2,x]","\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}","\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*Gamma[m, -((1 + m)*ProductLog[a*x])]*(-((1 + m)*ProductLog[a*x]))^(1 - m))/(a*E^(m*ProductLog[a*x])*(1 + m)*ProductLog[a*x]) + (x^m*Gamma[-1 + m, -((1 + m)*ProductLog[a*x])]*(-((1 + m)*ProductLog[a*x]))^(2 - m))/(a*E^(m*ProductLog[a*x])*(1 + m)*ProductLog[a*x]^2)","A",3,2,10,0.2000,1,"{6620, 6653}"
149,1,130,0,0.2474901,"\int x^m \sqrt{c \text{ProductLog}(a x)} \, dx","Int[x^m*Sqrt[c*ProductLog[a*x]],x]","\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)}","\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*Gamma[5/2 + m, -((1 + m)*ProductLog[a*x])]*(c*ProductLog[a*x])^(3/2)*(-((1 + m)*ProductLog[a*x]))^(-3/2 - m))/(a*c*E^(m*ProductLog[a*x])*(1 + m)) + (x^m*Gamma[3/2 + 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))","A",3,2,14,0.1429,1,"{6620, 6653}"
150,1,130,0,0.2426584,"\int \frac{x^m}{\sqrt{c \text{ProductLog}(a x)}} \, dx","Int[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}} \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)}}","\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*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)) + (x^m*Gamma[1/2 + m, -((1 + m)*ProductLog[a*x])]*(-((1 + m)*ProductLog[a*x]))^(1/2 - m))/(a*E^(m*ProductLog[a*x])*(1 + m)*Sqrt[c*ProductLog[a*x]])","A",3,2,14,0.1429,1,"{6620, 6653}"
151,1,127,0,0.2301835,"\int x^m (c \text{ProductLog}(a x))^p \, dx","Int[x^m*(c*ProductLog[a*x])^p,x]","\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)}","\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*Gamma[2 + m + p, -((1 + m)*ProductLog[a*x])]*(c*ProductLog[a*x])^(1 + p)*(-((1 + m)*ProductLog[a*x]))^(-1 - m - p))/(a*c*E^(m*ProductLog[a*x])*(1 + m)) + (x^m*Gamma[1 + 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))","A",3,2,12,0.1667,1,"{6620, 6653}"
152,0,0,0,0.0159556,"\int x^4 \text{ProductLog}\left(a x^2\right) \, dx","Int[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,"Defer[Int][x^4*ProductLog[a*x^2], x]","N/A",0,0,0,0,-1,"{}"
153,1,51,0,0.1504385,"\int x^3 \text{ProductLog}\left(a x^2\right) \, dx","Int[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",5,4,10,0.4000,1,"{6618, 6651, 6640, 6647}"
154,0,0,0,0.0159153,"\int x^2 \text{ProductLog}\left(a x^2\right) \, dx","Int[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,"Defer[Int][x^2*ProductLog[a*x^2], x]","N/A",0,0,0,0,-1,"{}"
155,1,36,0,0.0598173,"\int x \text{ProductLog}\left(a x^2\right) \, dx","Int[x*ProductLog[a*x^2],x]","\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}","\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^2/2 + x^2/(2*ProductLog[a*x^2]) + (x^2*ProductLog[a*x^2])/2","A",4,4,8,0.5000,1,"{6618, 6651, 6715, 6622}"
156,0,0,0,0.0054481,"\int \text{ProductLog}\left(a x^2\right) \, dx","Int[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,"Defer[Int][ProductLog[a*x^2], x]","N/A",0,0,0,0,-1,"{}"
157,1,23,0,0.0675459,"\int \frac{\text{ProductLog}\left(a x^2\right)}{x} \, dx","Int[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",2,2,10,0.2000,1,"{6619, 6646}"
158,0,0,0,0.0162845,"\int \frac{\text{ProductLog}\left(a x^2\right)}{x^2} \, dx","Int[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,"Defer[Int][ProductLog[a*x^2]/x^2, x]","N/A",0,0,0,0,-1,"{}"
159,1,28,0,0.055674,"\int \frac{\text{ProductLog}\left(a x^2\right)}{x^3} \, dx","Int[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",2,2,10,0.2000,1,"{6618, 6648}"
160,0,0,0,0.0201086,"\int \frac{\text{ProductLog}\left(a x^2\right)}{x^4} \, dx","Int[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,"Defer[Int][ProductLog[a*x^2]/x^4, x]","N/A",0,0,0,0,-1,"{}"
161,1,30,0,0.0658081,"\int \frac{\text{ProductLog}\left(a x^2\right)}{x^5} \, dx","Int[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",2,2,10,0.2000,1,"{6619, 6648}"
162,0,0,0,0.0160959,"\int \frac{\text{ProductLog}\left(a x^2\right)}{x^6} \, dx","Int[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,"Defer[Int][ProductLog[a*x^2]/x^6, x]","N/A",0,0,0,0,-1,"{}"
163,1,45,0,0.1561149,"\int \frac{\text{ProductLog}\left(a x^2\right)}{x^7} \, dx","Int[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",3,3,10,0.3000,1,"{6619, 6652, 6648}"
164,1,66,0,0.2147266,"\int x^3 \text{ProductLog}\left(a x^2\right)^2 \, dx","Int[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",6,4,12,0.3333,1,"{6618, 6651, 6640, 6647}"
165,0,0,0,0.0306127,"\int x^2 \text{ProductLog}\left(a x^2\right)^2 \, dx","Int[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,"Defer[Int][x^2*ProductLog[a*x^2]^2, x]","N/A",0,0,0,0,-1,"{}"
166,1,45,0,0.0990712,"\int x \text{ProductLog}\left(a x^2\right)^2 \, dx","Int[x*ProductLog[a*x^2]^2,x]","\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","\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,"2*x^2 - (2*x^2)/ProductLog[a*x^2] - x^2*ProductLog[a*x^2] + (x^2*ProductLog[a*x^2]^2)/2","A",5,4,10,0.4000,1,"{6618, 6651, 6715, 6622}"
167,0,0,0,0.0103611,"\int \text{ProductLog}\left(a x^2\right)^2 \, dx","Int[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,"Defer[Int][ProductLog[a*x^2]^2, x]","N/A",0,0,0,0,-1,"{}"
168,1,25,0,0.0754778,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x} \, dx","Int[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",2,2,12,0.1667,1,"{6619, 6646}"
169,0,0,0,0.0322048,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^2} \, dx","Int[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,"Defer[Int][ProductLog[a*x^2]^2/x^2, x]","N/A",0,0,0,0,-1,"{}"
170,1,27,0,0.0862856,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^3} \, dx","Int[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",2,2,12,0.1667,1,"{6618, 6647}"
171,0,0,0,0.0278312,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^4} \, dx","Int[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,"Defer[Int][ProductLog[a*x^2]^2/x^4, x]","N/A",0,0,0,0,-1,"{}"
172,1,32,0,0.0905145,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^5} \, dx","Int[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",2,2,12,0.1667,1,"{6618, 6648}"
173,0,0,0,0.0230958,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^6} \, dx","Int[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,"Defer[Int][ProductLog[a*x^2]^2/x^6, x]","N/A",0,0,0,0,-1,"{}"
174,1,30,0,0.0880219,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^7} \, dx","Int[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",2,2,12,0.1667,1,"{6619, 6648}"
175,0,0,0,0.0282101,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^8} \, dx","Int[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,"Defer[Int][ProductLog[a*x^2]^2/x^8, x]","N/A",0,0,0,0,-1,"{}"
176,1,45,0,0.1403131,"\int \frac{\text{ProductLog}\left(a x^2\right)^2}{x^9} \, dx","Int[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",3,3,12,0.2500,1,"{6619, 6652, 6648}"
177,0,0,0,0.0230207,"\int x^2 \text{ProductLog}\left(a x^2\right)^3 \, dx","Int[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,"Defer[Int][x^2*ProductLog[a*x^2]^3, x]","N/A",0,0,0,0,-1,"{}"
178,1,62,0,0.1431233,"\int x \text{ProductLog}\left(a x^2\right)^3 \, dx","Int[x*ProductLog[a*x^2]^3,x]","\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","\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,"-9*x^2 + (9*x^2)/ProductLog[a*x^2] + (9*x^2*ProductLog[a*x^2])/2 - (3*x^2*ProductLog[a*x^2]^2)/2 + (x^2*ProductLog[a*x^2]^3)/2","A",6,4,10,0.4000,1,"{6618, 6651, 6715, 6622}"
179,0,0,0,0.0180567,"\int \text{ProductLog}\left(a x^2\right)^3 \, dx","Int[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,"Defer[Int][ProductLog[a*x^2]^3, x]","N/A",0,0,0,0,-1,"{}"
180,1,25,0,0.0717861,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x} \, dx","Int[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",2,2,12,0.1667,1,"{6619, 6646}"
181,0,0,0,0.0384414,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^2} \, dx","Int[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,"Defer[Int][ProductLog[a*x^2]^3/x^2, x]","N/A",0,0,0,0,-1,"{}"
182,1,44,0,0.1555075,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^3} \, dx","Int[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",3,3,12,0.2500,1,"{6618, 6651, 6647}"
183,0,0,0,0.0277645,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^4} \, dx","Int[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,"Defer[Int][ProductLog[a*x^2]^3/x^4, x]","N/A",0,0,0,0,-1,"{}"
184,1,31,0,0.0869236,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^5} \, dx","Int[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",2,2,12,0.1667,1,"{6618, 6647}"
185,0,0,0,0.0310863,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^6} \, dx","Int[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,"Defer[Int][ProductLog[a*x^2]^3/x^6, x]","N/A",0,0,0,0,-1,"{}"
186,1,32,0,0.0803996,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^7} \, dx","Int[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",2,2,12,0.1667,1,"{6618, 6648}"
187,0,0,0,0.0274255,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^8} \, dx","Int[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,"Defer[Int][ProductLog[a*x^2]^3/x^8, x]","N/A",0,0,0,0,-1,"{}"
188,1,32,0,0.0899461,"\int \frac{\text{ProductLog}\left(a x^2\right)^3}{x^9} \, dx","Int[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",2,2,12,0.1667,1,"{6619, 6648}"
189,1,46,0,0.1357257,"\int \frac{x^5}{\text{ProductLog}\left(a x^2\right)} \, dx","Int[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",3,3,12,0.2500,1,"{6618, 6651, 6647}"
190,0,0,0,0.0295672,"\int \frac{x^4}{\text{ProductLog}\left(a x^2\right)} \, dx","Int[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,"Defer[Int][x^4/ProductLog[a*x^2], x]","N/A",0,0,0,0,-1,"{}"
191,1,31,0,0.0835456,"\int \frac{x^3}{\text{ProductLog}\left(a x^2\right)} \, dx","Int[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",2,2,12,0.1667,1,"{6618, 6647}"
192,0,0,0,0.0255531,"\int \frac{x^2}{\text{ProductLog}\left(a x^2\right)} \, dx","Int[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,"Defer[Int][x^2/ProductLog[a*x^2], x]","N/A",0,0,0,0,-1,"{}"
193,1,30,0,0.0502929,"\int \frac{x}{\text{ProductLog}\left(a x^2\right)} \, dx","Int[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",2,2,10,0.2000,1,"{6618, 6648}"
194,0,0,0,0.0075829,"\int \frac{1}{\text{ProductLog}\left(a x^2\right)} \, dx","Int[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,"Defer[Int][ProductLog[a*x^2]^(-1), x]","N/A",0,0,0,0,-1,"{}"
195,1,24,0,0.0452675,"\int \frac{1}{x \text{ProductLog}\left(a x^2\right)} \, dx","Int[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",2,2,12,0.1667,1,"{6619, 6644}"
196,0,0,0,0.0279954,"\int \frac{1}{x^2 \text{ProductLog}\left(a x^2\right)} \, dx","Int[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,"Defer[Int][1/(x^2*ProductLog[a*x^2]), x]","N/A",0,0,0,0,-1,"{}"
197,1,37,0,0.1292757,"\int \frac{1}{x^3 \text{ProductLog}\left(a x^2\right)} \, dx","Int[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",4,3,12,0.2500,1,"{6619, 6642, 6648}"
198,0,0,0,0.0242625,"\int \frac{1}{x^4 \text{ProductLog}\left(a x^2\right)} \, dx","Int[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,"Defer[Int][1/(x^4*ProductLog[a*x^2]), x]","N/A",0,0,0,0,-1,"{}"
199,1,52,0,0.2056473,"\int \frac{1}{x^5 \text{ProductLog}\left(a x^2\right)} \, dx","Int[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",5,4,12,0.3333,1,"{6619, 6642, 6652, 6648}"
200,1,46,0,0.1475807,"\int \frac{x^7}{\text{ProductLog}\left(a x^2\right)^2} \, dx","Int[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",3,3,12,0.2500,1,"{6618, 6651, 6647}"
201,0,0,0,0.0252176,"\int \frac{x^6}{\text{ProductLog}\left(a x^2\right)^2} \, dx","Int[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,"Defer[Int][x^6/ProductLog[a*x^2]^2, x]","N/A",0,0,0,0,-1,"{}"
202,1,31,0,0.0781704,"\int \frac{x^5}{\text{ProductLog}\left(a x^2\right)^2} \, dx","Int[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",2,2,12,0.1667,1,"{6618, 6647}"
203,0,0,0,0.0261103,"\int \frac{x^4}{\text{ProductLog}\left(a x^2\right)^2} \, dx","Int[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,"Defer[Int][x^4/ProductLog[a*x^2]^2, x]","N/A",0,0,0,0,-1,"{}"
204,1,32,0,0.0810189,"\int \frac{x^3}{\text{ProductLog}\left(a x^2\right)^2} \, dx","Int[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",2,2,12,0.1667,1,"{6618, 6648}"
205,0,0,0,0.0256957,"\int \frac{x^2}{\text{ProductLog}\left(a x^2\right)^2} \, dx","Int[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,"Defer[Int][x^2/ProductLog[a*x^2]^2, x]","N/A",0,0,0,0,-1,"{}"
206,1,27,0,0.0537669,"\int \frac{x}{\text{ProductLog}\left(a x^2\right)^2} \, dx","Int[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",2,2,10,0.2000,1,"{6619, 6648}"
207,0,0,0,0.0066577,"\int \frac{1}{\text{ProductLog}\left(a x^2\right)^2} \, dx","Int[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,"Defer[Int][ProductLog[a*x^2]^(-2), x]","N/A",0,0,0,0,-1,"{}"
208,1,25,0,0.0725088,"\int \frac{1}{x \text{ProductLog}\left(a x^2\right)^2} \, dx","Int[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",2,2,12,0.1667,1,"{6619, 6646}"
209,0,0,0,0.0255452,"\int \frac{1}{x^2 \text{ProductLog}\left(a x^2\right)^2} \, dx","Int[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,"Defer[Int][1/(x^2*ProductLog[a*x^2]^2), x]","N/A",0,0,0,0,-1,"{}"
210,1,52,0,0.1877252,"\int \frac{1}{x^3 \text{ProductLog}\left(a x^2\right)^2} \, dx","Int[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",5,4,12,0.3333,1,"{6619, 6652, 6642, 6648}"
211,1,143,0,0.6337198,"\int x^7 \sqrt{c \text{ProductLog}\left(a x^2\right)} \, dx","Int[x^7*Sqrt[c*ProductLog[a*x^2]],x]","-\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)}}","-\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,"(-105*Sqrt[c]*Sqrt[Pi]*Erfi[(2*Sqrt[c*ProductLog[a*x^2]])/Sqrt[c]])/(131072*a^4) + (105*c^4*x^8)/(32768*(c*ProductLog[a*x^2])^(7/2)) - (35*c^3*x^8)/(4096*(c*ProductLog[a*x^2])^(5/2)) + (7*c^2*x^8)/(512*(c*ProductLog[a*x^2])^(3/2)) - (c*x^8)/(64*Sqrt[c*ProductLog[a*x^2]]) + (x^8*Sqrt[c*ProductLog[a*x^2]])/8","A",6,3,16,0.1875,1,"{6618, 6651, 6650}"
212,1,106,0,0.4898905,"\int x^6 \sqrt{c \text{ProductLog}\left(a x^2\right)} \, dx","Int[x^6*Sqrt[c*ProductLog[a*x^2]],x]","\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)}}","\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,"(48*c^4*x^7)/(16807*(c*ProductLog[a*x^2])^(7/2)) - (24*c^3*x^7)/(2401*(c*ProductLog[a*x^2])^(5/2)) + (6*c^2*x^7)/(343*(c*ProductLog[a*x^2])^(3/2)) - (c*x^7)/(49*Sqrt[c*ProductLog[a*x^2]]) + (x^7*Sqrt[c*ProductLog[a*x^2]])/7","A",5,3,16,0.1875,1,"{6618, 6651, 6647}"
213,1,129,0,0.5383093,"\int x^5 \sqrt{c \text{ProductLog}\left(a x^2\right)} \, dx","Int[x^5*Sqrt[c*ProductLog[a*x^2]],x]","\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)}}","\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,"(5*Sqrt[c]*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[c*ProductLog[a*x^2]])/Sqrt[c]])/(864*a^3) - (5*c^3*x^6)/(432*(c*ProductLog[a*x^2])^(5/2)) + (5*c^2*x^6)/(216*(c*ProductLog[a*x^2])^(3/2)) - (c*x^6)/(36*Sqrt[c*ProductLog[a*x^2]]) + (x^6*Sqrt[c*ProductLog[a*x^2]])/6","A",5,3,16,0.1875,1,"{6618, 6651, 6650}"
214,1,84,0,0.3542918,"\int x^4 \sqrt{c \text{ProductLog}\left(a x^2\right)} \, dx","Int[x^4*Sqrt[c*ProductLog[a*x^2]],x]","-\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)}}","-\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,"(-8*c^3*x^5)/(625*(c*ProductLog[a*x^2])^(5/2)) + (4*c^2*x^5)/(125*(c*ProductLog[a*x^2])^(3/2)) - (c*x^5)/(25*Sqrt[c*ProductLog[a*x^2]]) + (x^5*Sqrt[c*ProductLog[a*x^2]])/5","A",4,3,16,0.1875,1,"{6618, 6651, 6647}"
215,1,107,0,0.378085,"\int x^3 \sqrt{c \text{ProductLog}\left(a x^2\right)} \, dx","Int[x^3*Sqrt[c*ProductLog[a*x^2]],x]","-\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)}}","-\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,"(-3*Sqrt[c]*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a*x^2]])/Sqrt[c]])/(128*a^2) + (3*c^2*x^4)/(64*(c*ProductLog[a*x^2])^(3/2)) - (c*x^4)/(16*Sqrt[c*ProductLog[a*x^2]]) + (x^4*Sqrt[c*ProductLog[a*x^2]])/4","A",4,3,16,0.1875,1,"{6618, 6651, 6650}"
216,1,62,0,0.2355099,"\int x^2 \sqrt{c \text{ProductLog}\left(a x^2\right)} \, dx","Int[x^2*Sqrt[c*ProductLog[a*x^2]],x]","\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)}}","\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,"(2*c^2*x^3)/(27*(c*ProductLog[a*x^2])^(3/2)) - (c*x^3)/(9*Sqrt[c*ProductLog[a*x^2]]) + (x^3*Sqrt[c*ProductLog[a*x^2]])/3","A",3,3,16,0.1875,1,"{6618, 6651, 6647}"
217,1,76,0,0.166473,"\int x \sqrt{c \text{ProductLog}\left(a x^2\right)} \, dx","Int[x*Sqrt[c*ProductLog[a*x^2]],x]","\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)}}","\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,"(Sqrt[c]*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a*x^2]]/Sqrt[c]])/(8*a) - (c*x^2)/(4*Sqrt[c*ProductLog[a*x^2]]) + (x^2*Sqrt[c*ProductLog[a*x^2]])/2","A",3,3,14,0.2143,1,"{6618, 6651, 6650}"
218,1,31,0,0.0365445,"\int \sqrt{c \text{ProductLog}\left(a x^2\right)} \, dx","Int[Sqrt[c*ProductLog[a*x^2]],x]","x \sqrt{c \text{ProductLog}\left(a x^2\right)}-\frac{c x}{\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)/Sqrt[c*ProductLog[a*x^2]]) + x*Sqrt[c*ProductLog[a*x^2]]","A",2,2,12,0.1667,1,"{6615, 6633}"
219,1,32,0,0.1386817,"\int \frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x} \, dx","Int[Sqrt[c*ProductLog[a*x^2]]/x,x]","\frac{\left(c \text{ProductLog}\left(a x^2\right)\right)^{3/2}}{3 c}+\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]] + (c*ProductLog[a*x^2])^(3/2)/(3*c)","A",2,2,16,0.1250,1,"{6619, 6646}"
220,0,0,0,0.0779724,"\int \frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x^2} \, dx","Int[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,"(Sqrt[c*ProductLog[a*x^2]]*Defer[Int][Sqrt[ProductLog[a*x^2]]/x^2, x])/Sqrt[ProductLog[a*x^2]]","N/A",0,0,0,0,-1,"{}"
221,1,52,0,0.1546345,"\int \frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x^3} \, dx","Int[Sqrt[c*ProductLog[a*x^2]]/x^3,x]","-\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}","-\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,"-(a*Sqrt[c]*Sqrt[Pi]*Erf[Sqrt[c*ProductLog[a*x^2]]/Sqrt[c]])/2 - Sqrt[c*ProductLog[a*x^2]]/x^2","A",2,2,16,0.1250,1,"{6619, 6649}"
222,0,0,0,0.0731565,"\int \frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x^4} \, dx","Int[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,"(Sqrt[c*ProductLog[a*x^2]]*Defer[Int][Sqrt[ProductLog[a*x^2]]/x^4, x])/Sqrt[ProductLog[a*x^2]]","N/A",0,0,0,0,-1,"{}"
223,1,85,0,0.2720252,"\int \frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x^5} \, dx","Int[Sqrt[c*ProductLog[a*x^2]]/x^5,x]","\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}","\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,"(a^2*Sqrt[c]*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[c*ProductLog[a*x^2]])/Sqrt[c]])/3 - Sqrt[c*ProductLog[a*x^2]]/(3*x^4) + (c*ProductLog[a*x^2])^(3/2)/(3*c*x^4)","A",3,3,16,0.1875,1,"{6619, 6652, 6649}"
224,0,0,0,0.0781332,"\int \frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x^6} \, dx","Int[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,"(Sqrt[c*ProductLog[a*x^2]]*Defer[Int][Sqrt[ProductLog[a*x^2]]/x^6, x])/Sqrt[ProductLog[a*x^2]]","N/A",0,0,0,0,-1,"{}"
225,1,107,0,0.3847031,"\int \frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{x^7} \, dx","Int[Sqrt[c*ProductLog[a*x^2]]/x^7,x]","-\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}","-\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,"(-2*a^3*Sqrt[c]*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[c*ProductLog[a*x^2]])/Sqrt[c]])/5 - Sqrt[c*ProductLog[a*x^2]]/(5*x^6) + (c*ProductLog[a*x^2])^(3/2)/(15*c*x^6) - (2*(c*ProductLog[a*x^2])^(5/2))/(5*c^2*x^6)","A",4,3,16,0.1875,1,"{6619, 6652, 6649}"
226,1,121,0,0.5466116,"\int \frac{x^7}{\sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Int[x^7/Sqrt[c*ProductLog[a*x^2]],x]","-\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}}","-\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,"(-15*Sqrt[Pi]*Erfi[(2*Sqrt[c*ProductLog[a*x^2]])/Sqrt[c]])/(16384*a^4*Sqrt[c]) + (15*c^3*x^8)/(4096*(c*ProductLog[a*x^2])^(7/2)) - (5*c^2*x^8)/(512*(c*ProductLog[a*x^2])^(5/2)) + (c*x^8)/(64*(c*ProductLog[a*x^2])^(3/2)) + x^8/(8*Sqrt[c*ProductLog[a*x^2]])","A",5,3,16,0.1875,1,"{6618, 6651, 6650}"
227,1,84,0,0.3955846,"\int \frac{x^6}{\sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Int[x^6/Sqrt[c*ProductLog[a*x^2]],x]","\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}}","\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,"(8*c^3*x^7)/(2401*(c*ProductLog[a*x^2])^(7/2)) - (4*c^2*x^7)/(343*(c*ProductLog[a*x^2])^(5/2)) + (c*x^7)/(49*(c*ProductLog[a*x^2])^(3/2)) + x^7/(7*Sqrt[c*ProductLog[a*x^2]])","A",4,3,16,0.1875,1,"{6618, 6651, 6647}"
228,1,107,0,0.3958676,"\int \frac{x^5}{\sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Int[x^5/Sqrt[c*ProductLog[a*x^2]],x]","\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}}","\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,"(Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[c*ProductLog[a*x^2]])/Sqrt[c]])/(144*a^3*Sqrt[c]) - (c^2*x^6)/(72*(c*ProductLog[a*x^2])^(5/2)) + (c*x^6)/(36*(c*ProductLog[a*x^2])^(3/2)) + x^6/(6*Sqrt[c*ProductLog[a*x^2]])","A",4,3,16,0.1875,1,"{6618, 6651, 6650}"
229,1,62,0,0.2570034,"\int \frac{x^4}{\sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Int[x^4/Sqrt[c*ProductLog[a*x^2]],x]","-\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}}","-\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,"(-2*c^2*x^5)/(125*(c*ProductLog[a*x^2])^(5/2)) + (c*x^5)/(25*(c*ProductLog[a*x^2])^(3/2)) + x^5/(5*Sqrt[c*ProductLog[a*x^2]])","A",3,3,16,0.1875,1,"{6618, 6651, 6647}"
230,1,85,0,0.2726823,"\int \frac{x^3}{\sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Int[x^3/Sqrt[c*ProductLog[a*x^2]],x]","-\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}}","-\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,"-(Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a*x^2]])/Sqrt[c]])/(32*a^2*Sqrt[c]) + (c*x^4)/(16*(c*ProductLog[a*x^2])^(3/2)) + x^4/(4*Sqrt[c*ProductLog[a*x^2]])","A",3,3,16,0.1875,1,"{6618, 6651, 6650}"
231,1,40,0,0.1238374,"\int \frac{x^2}{\sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Int[x^2/Sqrt[c*ProductLog[a*x^2]],x]","\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}}","\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)/(9*(c*ProductLog[a*x^2])^(3/2)) + x^3/(3*Sqrt[c*ProductLog[a*x^2]])","A",2,2,16,0.1250,1,"{6618, 6647}"
232,1,56,0,0.0836185,"\int \frac{x}{\sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Int[x/Sqrt[c*ProductLog[a*x^2]],x]","\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)}}","\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,"(Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a*x^2]]/Sqrt[c]])/(4*a*Sqrt[c]) + x^2/(2*Sqrt[c*ProductLog[a*x^2]])","A",2,2,14,0.1429,1,"{6618, 6650}"
233,0,0,0,0.0202131,"\int \frac{1}{\sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Int[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,"(Sqrt[ProductLog[a*x^2]]*Defer[Int][1/Sqrt[ProductLog[a*x^2]], x])/Sqrt[c*ProductLog[a*x^2]]","N/A",0,0,0,0,-1,"{}"
234,1,31,0,0.1043057,"\int \frac{1}{x \sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Int[1/(x*Sqrt[c*ProductLog[a*x^2]]),x]","\frac{\sqrt{c \text{ProductLog}\left(a x^2\right)}}{c}-\frac{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/Sqrt[c*ProductLog[a*x^2]]) + Sqrt[c*ProductLog[a*x^2]]/c","A",2,2,16,0.1250,1,"{6619, 6646}"
235,0,0,0,0.0836902,"\int \frac{1}{x^2 \sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Int[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,"(Sqrt[ProductLog[a*x^2]]*Defer[Int][1/(x^2*Sqrt[ProductLog[a*x^2]]), x])/Sqrt[c*ProductLog[a*x^2]]","N/A",0,0,0,0,-1,"{}"
236,1,76,0,0.2314544,"\int \frac{1}{x^3 \sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Int[1/(x^3*Sqrt[c*ProductLog[a*x^2]]),x]","-\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)}}","-\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,"-(a*Sqrt[Pi]*Erf[Sqrt[c*ProductLog[a*x^2]]/Sqrt[c]])/(3*Sqrt[c]) - 1/(3*x^2*Sqrt[c*ProductLog[a*x^2]]) - Sqrt[c*ProductLog[a*x^2]]/(3*c*x^2)","A",3,3,16,0.1875,1,"{6619, 6652, 6649}"
237,0,0,0,0.069526,"\int \frac{1}{x^4 \sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Int[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,"(Sqrt[ProductLog[a*x^2]]*Defer[Int][1/(x^4*Sqrt[ProductLog[a*x^2]]), x])/Sqrt[c*ProductLog[a*x^2]]","N/A",0,0,0,0,-1,"{}"
238,1,107,0,0.3800371,"\int \frac{1}{x^5 \sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Int[1/(x^5*Sqrt[c*ProductLog[a*x^2]]),x]","\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)}}","\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,"(4*a^2*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[c*ProductLog[a*x^2]])/Sqrt[c]])/(15*Sqrt[c]) - 1/(5*x^4*Sqrt[c*ProductLog[a*x^2]]) - Sqrt[c*ProductLog[a*x^2]]/(15*c*x^4) + (4*(c*ProductLog[a*x^2])^(3/2))/(15*c^2*x^4)","A",4,3,16,0.1875,1,"{6619, 6652, 6649}"
239,0,0,0,0.0729605,"\int \frac{1}{x^6 \sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Int[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,"(Sqrt[ProductLog[a*x^2]]*Defer[Int][1/(x^6*Sqrt[ProductLog[a*x^2]]), x])/Sqrt[c*ProductLog[a*x^2]]","N/A",0,0,0,0,-1,"{}"
240,1,129,0,0.4966257,"\int \frac{1}{x^7 \sqrt{c \text{ProductLog}\left(a x^2\right)}} \, dx","Int[1/(x^7*Sqrt[c*ProductLog[a*x^2]]),x]","-\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)}}","-\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,"(-12*a^3*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[c*ProductLog[a*x^2]])/Sqrt[c]])/(35*Sqrt[c]) - 1/(7*x^6*Sqrt[c*ProductLog[a*x^2]]) - Sqrt[c*ProductLog[a*x^2]]/(35*c*x^6) + (2*(c*ProductLog[a*x^2])^(3/2))/(35*c^2*x^6) - (12*(c*ProductLog[a*x^2])^(5/2))/(35*c^3*x^6)","A",5,3,16,0.1875,1,"{6619, 6652, 6649}"
241,0,0,0,0.088047,"\int x^2 \left(c \text{ProductLog}\left(a x^2\right)\right)^p \, dx","Int[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,"((c*ProductLog[a*x^2])^p*Defer[Int][x^2*ProductLog[a*x^2]^p, x])/ProductLog[a*x^2]^p","N/A",0,0,0,0,-1,"{}"
242,1,60,0,0.094449,"\int x \left(c \text{ProductLog}\left(a x^2\right)\right)^p \, dx","Int[x*(c*ProductLog[a*x^2])^p,x]","\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}","\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,"(x^2*(c*ProductLog[a*x^2])^p)/2 - (p*Gamma[1 + p, -ProductLog[a*x^2]]*(c*ProductLog[a*x^2])^p)/(2*a*(-ProductLog[a*x^2])^p)","A",3,3,12,0.2500,1,"{6715, 6613, 6629}"
243,1,42,0,0.1298688,"\int \frac{\left(c \text{ProductLog}\left(a x^2\right)\right)^p}{x} \, dx","Int[(c*ProductLog[a*x^2])^p/x,x]","\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)}","\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/(2*p) + (c*ProductLog[a*x^2])^(1 + p)/(2*c*(1 + p))","A",2,2,14,0.1429,1,"{6619, 6646}"
244,0,0,0,0.0757361,"\int \frac{\left(c \text{ProductLog}\left(a x^2\right)\right)^p}{x^2} \, dx","Int[(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,"((c*ProductLog[a*x^2])^p*Defer[Int][ProductLog[a*x^2]^p/x^2, x])/ProductLog[a*x^2]^p","N/A",0,0,0,0,-1,"{}"
245,1,103,0,0.2913382,"\int \frac{\left(c \text{ProductLog}\left(a x^2\right)\right)^p}{x^3} \, dx","Int[(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 \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}","-\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]]*ProductLog[a*x^2]^(2 - p)*(c*ProductLog[a*x^2])^p)/(2*a*x^4) - (E^(2*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",5,3,14,0.2143,1,"{6720, 6620, 6653}"
246,1,75,0,0.2663793,"\int x^4 \text{ProductLog}\left(\frac{a}{x}\right) \, dx","Int[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",5,3,10,0.3000,1,"{6619, 6652, 6648}"
247,1,60,0,0.1820296,"\int x^3 \text{ProductLog}\left(\frac{a}{x}\right) \, dx","Int[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",4,3,10,0.3000,1,"{6619, 6652, 6648}"
248,1,45,0,0.1306383,"\int x^2 \text{ProductLog}\left(\frac{a}{x}\right) \, dx","Int[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",3,3,10,0.3000,1,"{6619, 6652, 6648}"
249,1,24,0,0.0438477,"\int x \text{ProductLog}\left(\frac{a}{x}\right) \, dx","Int[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",2,2,8,0.2500,1,"{6619, 6648}"
250,1,21,0,0.0530273,"\int \text{ProductLog}\left(\frac{a}{x}\right) \, dx","Int[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",3,3,6,0.5000,1,"{6617, 6618, 6648}"
251,1,21,0,0.0604328,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)}{x} \, dx","Int[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",2,2,10,0.2000,1,"{6619, 6646}"
252,1,28,0,0.0817999,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)}{x^2} \, dx","Int[ProductLog[a/x]/x^2,x]","-\frac{\text{ProductLog}\left(\frac{a}{x}\right)}{x}-\frac{1}{x \text{ProductLog}\left(\frac{a}{x}\right)}+\frac{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,"x^(-1) - 1/(x*ProductLog[a/x]) - ProductLog[a/x]/x","A",4,4,10,0.4000,1,"{6618, 6651, 6645, 6622}"
253,1,51,0,0.1372714,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)}{x^3} \, dx","Int[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",5,5,10,0.5000,1,"{6618, 6651, 6645, 6640, 6647}"
254,1,66,0,0.2291422,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)}{x^4} \, dx","Int[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",6,5,10,0.5000,1,"{6618, 6651, 6645, 6640, 6647}"
255,1,81,0,0.298148,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)}{x^5} \, dx","Int[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",7,5,10,0.5000,1,"{6618, 6651, 6645, 6640, 6647}"
256,1,62,0,0.2000017,"\int x^4 \text{ProductLog}\left(\frac{a}{x}\right)^2 \, dx","Int[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",4,3,12,0.2500,1,"{6619, 6652, 6648}"
257,1,43,0,0.1358087,"\int x^3 \text{ProductLog}\left(\frac{a}{x}\right)^2 \, dx","Int[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",3,3,12,0.2500,1,"{6619, 6652, 6648}"
258,1,27,0,0.074565,"\int x^2 \text{ProductLog}\left(\frac{a}{x}\right)^2 \, dx","Int[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",2,2,12,0.1667,1,"{6619, 6648}"
259,1,30,0,0.043798,"\int x \text{ProductLog}\left(\frac{a}{x}\right)^2 \, dx","Int[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",2,2,10,0.2000,1,"{6618, 6648}"
260,1,20,0,0.025448,"\int \text{ProductLog}\left(\frac{a}{x}\right)^2 \, dx","Int[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",2,2,8,0.2500,1,"{6615, 6633}"
261,1,25,0,0.0670803,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{x} \, dx","Int[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",2,2,12,0.1667,1,"{6619, 6646}"
262,1,43,0,0.1519858,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{x^2} \, dx","Int[ProductLog[a/x]^2/x^2,x]","-\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}","-\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/x + 4/(x*ProductLog[a/x]) + (2*ProductLog[a/x])/x - ProductLog[a/x]^2/x","A",5,4,12,0.3333,1,"{6618, 6651, 6645, 6622}"
263,1,66,0,0.1966983,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{x^3} \, dx","Int[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",6,5,12,0.4167,1,"{6618, 6651, 6645, 6640, 6647}"
264,1,81,0,0.3041668,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{x^4} \, dx","Int[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",7,5,12,0.4167,1,"{6618, 6651, 6645, 6640, 6647}"
265,1,96,0,0.3880097,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{x^5} \, dx","Int[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",8,5,12,0.4167,1,"{6618, 6651, 6645, 6640, 6647}"
266,1,94,0,0.2975985,"\int x^3 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Int[x^3*Sqrt[ProductLog[a/x]],x]","-\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)}","-\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,"(-256*a^4*Sqrt[Pi]*Erf[2*Sqrt[ProductLog[a/x]]])/105 + (2*x^4*Sqrt[ProductLog[a/x]])/7 - (2*x^4*ProductLog[a/x]^(3/2))/35 + (16*x^4*ProductLog[a/x]^(5/2))/105 - (128*x^4*ProductLog[a/x]^(7/2))/105","A",5,3,14,0.2143,1,"{6619, 6652, 6649}"
267,1,83,0,0.1989746,"\int x^2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Int[x^2*Sqrt[ProductLog[a/x]],x]","\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)}","\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,"(4*a^3*Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ProductLog[a/x]]])/5 + (2*x^3*Sqrt[ProductLog[a/x]])/5 - (2*x^3*ProductLog[a/x]^(3/2))/15 + (4*x^3*ProductLog[a/x]^(5/2))/5","A",4,3,14,0.2143,1,"{6619, 6652, 6649}"
268,1,66,0,0.0987184,"\int x \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Int[x*Sqrt[ProductLog[a/x]],x]","-\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)}","-\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]]])/3 + (2*x^2*Sqrt[ProductLog[a/x]])/3 - (2*x^2*ProductLog[a/x]^(3/2))/3","A",3,3,12,0.2500,1,"{6619, 6652, 6649}"
269,1,32,0,0.0276393,"\int \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Int[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",2,2,10,0.2000,1,"{6616, 6636}"
270,1,27,0,0.0720461,"\int \frac{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}{x} \, dx","Int[Sqrt[ProductLog[a/x]]/x,x]","-\frac{2}{3} \text{ProductLog}\left(\frac{a}{x}\right)^{3/2}-2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\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]] - (2*ProductLog[a/x]^(3/2))/3","A",2,2,14,0.1429,1,"{6619, 6646}"
271,1,56,0,0.1463989,"\int \frac{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}{x^2} \, dx","Int[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",3,3,14,0.2143,1,"{6618, 6651, 6650}"
272,1,85,0,0.2203161,"\int \frac{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}{x^3} \, dx","Int[Sqrt[ProductLog[a/x]]/x^3,x]","\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}}","\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[Pi/2]*Erfi[Sqrt[2]*Sqrt[ProductLog[a/x]]])/(64*a^2) - 3/(32*x^2*ProductLog[a/x]^(3/2)) + 1/(8*x^2*Sqrt[ProductLog[a/x]]) - Sqrt[ProductLog[a/x]]/(2*x^2)","A",4,3,14,0.2143,1,"{6618, 6651, 6650}"
273,1,102,0,0.3134081,"\int \frac{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}{x^4} \, dx","Int[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",5,3,14,0.2143,1,"{6618, 6651, 6650}"
274,1,111,0,0.3696496,"\int \frac{x^3}{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}} \, dx","Int[x^3/Sqrt[ProductLog[a/x]],x]","-\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)}}","-\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,"(-2048*a^4*Sqrt[Pi]*Erf[2*Sqrt[ProductLog[a/x]]])/945 + (2*x^4)/(9*Sqrt[ProductLog[a/x]]) + (2*x^4*Sqrt[ProductLog[a/x]])/63 - (16*x^4*ProductLog[a/x]^(3/2))/315 + (128*x^4*ProductLog[a/x]^(5/2))/945 - (1024*x^4*ProductLog[a/x]^(7/2))/945","A",6,3,14,0.2143,1,"{6619, 6652, 6649}"
275,1,100,0,0.2951799,"\int \frac{x^2}{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}} \, dx","Int[x^2/Sqrt[ProductLog[a/x]],x]","\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)}}","\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,"(24*a^3*Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ProductLog[a/x]]])/35 + (2*x^3)/(7*Sqrt[ProductLog[a/x]]) + (2*x^3*Sqrt[ProductLog[a/x]])/35 - (4*x^3*ProductLog[a/x]^(3/2))/35 + (24*x^3*ProductLog[a/x]^(5/2))/35","A",5,3,14,0.2143,1,"{6619, 6652, 6649}"
276,1,83,0,0.1363458,"\int \frac{x}{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}} \, dx","Int[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",4,3,12,0.2500,1,"{6619, 6652, 6649}"
277,1,52,0,0.1452245,"\int \frac{1}{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}} \, dx","Int[1/Sqrt[ProductLog[a/x]],x]","\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)}}","\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]]])/3 + (2*x)/(3*Sqrt[ProductLog[a/x]]) + (2*x*Sqrt[ProductLog[a/x]])/3","A",4,4,10,0.4000,1,"{6617, 6619, 6652, 6649}"
278,1,25,0,0.0660723,"\int \frac{1}{x \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}} \, dx","Int[1/(x*Sqrt[ProductLog[a/x]]),x]","\frac{2}{\sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}}-2 \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/Sqrt[ProductLog[a/x]] - 2*Sqrt[ProductLog[a/x]]","A",2,2,14,0.1429,1,"{6619, 6646}"
279,1,39,0,0.0866895,"\int \frac{1}{x^2 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}} \, dx","Int[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",2,2,14,0.1429,1,"{6618, 6650}"
280,1,68,0,0.1473459,"\int \frac{1}{x^3 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}} \, dx","Int[1/(x^3*Sqrt[ProductLog[a/x]]),x]","\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}}","\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[Pi/2]*Erfi[Sqrt[2]*Sqrt[ProductLog[a/x]]])/(16*a^2) - 1/(8*x^2*ProductLog[a/x]^(3/2)) - 1/(2*x^2*Sqrt[ProductLog[a/x]])","A",3,3,14,0.2143,1,"{6618, 6651, 6650}"
281,1,85,0,0.2180604,"\int \frac{1}{x^4 \sqrt{\text{ProductLog}\left(\frac{a}{x}\right)}} \, dx","Int[1/(x^4*Sqrt[ProductLog[a/x]]),x]","-\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}}","-\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[Pi/3]*Erfi[Sqrt[3]*Sqrt[ProductLog[a/x]]])/(72*a^3) + 1/(36*x^3*ProductLog[a/x]^(5/2)) - 1/(18*x^3*ProductLog[a/x]^(3/2)) - 1/(3*x^3*Sqrt[ProductLog[a/x]])","A",4,3,14,0.2143,1,"{6618, 6651, 6650}"
282,1,122,0,0.2757645,"\int x^2 \left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p \, dx","Int[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)^{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}","\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^(3 - p)*E^(4*ProductLog[a/x])*x^4*Gamma[-3 + p, 3*ProductLog[a/x]]*ProductLog[a/x]^(4 - p)*(c*ProductLog[a/x])^p)/a + (3^(2 - p)*E^(4*ProductLog[a/x])*x^4*Gamma[-2 + p, 3*ProductLog[a/x]]*ProductLog[a/x]^(3 - p)*(c*ProductLog[a/x])^(1 + p))/(a*c)","A",4,3,14,0.2143,1,"{6621, 6620, 6653}"
283,1,122,0,0.2529047,"\int x \left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p \, dx","Int[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)^{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}","\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^(2 - p)*E^(3*ProductLog[a/x])*x^3*Gamma[-2 + p, 2*ProductLog[a/x]]*ProductLog[a/x]^(3 - p)*(c*ProductLog[a/x])^p)/a + (2^(1 - p)*E^(3*ProductLog[a/x])*x^3*Gamma[-1 + p, 2*ProductLog[a/x]]*ProductLog[a/x]^(2 - p)*(c*ProductLog[a/x])^(1 + p))/(a*c)","A",4,3,12,0.2500,1,"{6621, 6620, 6653}"
284,1,38,0,0.1237002,"\int \frac{\left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p}{x} \, dx","Int[(c*ProductLog[a/x])^p/x,x]","-\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)}","-\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) - (c*ProductLog[a/x])^(1 + p)/(c*(1 + p))","A",2,2,14,0.1429,1,"{6619, 6646}"
285,1,55,0,0.0707964,"\int \frac{\left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p}{x^2} \, dx","Int[(c*ProductLog[a/x])^p/x^2,x]","\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}","\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,"-((c*ProductLog[a/x])^p/x) + (p*Gamma[1 + p, -ProductLog[a/x]]*(c*ProductLog[a/x])^p)/(a*(-ProductLog[a/x])^p)","A",3,3,14,0.2143,1,"{6621, 6613, 6629}"
286,1,128,0,0.187733,"\int \frac{\left(c \text{ProductLog}\left(\frac{a}{x}\right)\right)^p}{x^3} \, dx","Int[(c*ProductLog[a/x])^p/x^3,x]","-\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}","-\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^(-2 - p)*Gamma[2 + p, -2*ProductLog[a/x]]*(-ProductLog[a/x])^(-1 - p)*(c*ProductLog[a/x])^p)/(a*E^ProductLog[a/x]*x)) - (2^(-3 - p)*Gamma[3 + p, -2*ProductLog[a/x]]*(-ProductLog[a/x])^(-2 - p)*(c*ProductLog[a/x])^(1 + p))/(a*c*E^ProductLog[a/x]*x)","A",4,3,14,0.2143,1,"{6621, 6620, 6653}"
287,1,28,0,0.0280139,"\int \text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)^5 \, dx","Int[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",2,2,10,0.2000,1,"{6615, 6633}"
288,1,28,0,0.0260056,"\int \text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)^4 \, dx","Int[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",2,2,10,0.2000,1,"{6615, 6633}"
289,1,28,0,0.0302526,"\int \text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)^3 \, dx","Int[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",2,2,10,0.2000,1,"{6615, 6633}"
290,1,20,0,0.0294452,"\int \text{ProductLog}\left(\frac{a}{x}\right)^2 \, dx","Int[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",2,2,8,0.2500,1,"{6615, 6633}"
291,1,28,0,0.028852,"\int \frac{1}{\text{ProductLog}\left(a \sqrt{x}\right)} \, dx","Int[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",2,2,10,0.2000,1,"{6615, 6633}"
292,1,28,0,0.0353194,"\int \frac{1}{\text{ProductLog}\left(a \sqrt[3]{x}\right)^2} \, dx","Int[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",2,2,10,0.2000,1,"{6615, 6633}"
293,1,28,0,0.0301164,"\int \frac{1}{\text{ProductLog}\left(a \sqrt[4]{x}\right)^3} \, dx","Int[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",2,2,10,0.2000,1,"{6615, 6633}"
294,1,30,0,0.032836,"\int \text{ProductLog}\left(\frac{a}{\sqrt[5]{x}}\right)^4 \, dx","Int[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",2,2,10,0.2000,1,"{6616, 6634}"
295,1,30,0,0.0273132,"\int \text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)^3 \, dx","Int[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",2,2,10,0.2000,1,"{6616, 6634}"
296,1,30,0,0.0279703,"\int \text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)^2 \, dx","Int[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",2,2,10,0.2000,1,"{6616, 6634}"
297,1,28,0,0.024949,"\int \text{ProductLog}\left(\frac{a}{\sqrt{x}}\right) \, dx","Int[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",2,2,8,0.2500,1,"{6616, 6634}"
298,1,20,0,0.0274208,"\int \frac{1}{\text{ProductLog}(a x)^2} \, dx","Int[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",2,2,6,0.3333,1,"{6612, 6625}"
299,1,30,0,0.0269208,"\int \frac{1}{\text{ProductLog}\left(a \sqrt{x}\right)^3} \, dx","Int[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",2,2,10,0.2000,1,"{6616, 6634}"
300,1,30,0,0.0269869,"\int \frac{1}{\text{ProductLog}\left(a \sqrt[3]{x}\right)^4} \, dx","Int[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",2,2,10,0.2000,1,"{6616, 6634}"
301,1,30,0,0.0287326,"\int \frac{1}{\text{ProductLog}\left(a \sqrt[4]{x}\right)^5} \, dx","Int[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",2,2,10,0.2000,1,"{6616, 6634}"
302,1,39,0,0.0418302,"\int \text{ProductLog}\left(a x^n\right)^{\frac{-1+n}{n}} \, dx","Int[ProductLog[a*x^n]^((-1 + n)/n),x]","(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-n) x \text{ProductLog}\left(a x^n\right)^{-1/n}+x \text{ProductLog}\left(a x^n\right)^{-\frac{1-n}{n}}",1,"((1 - n)*x)/ProductLog[a*x^n]^n^(-1) + x/ProductLog[a*x^n]^((1 - n)/n)","A",2,2,14,0.1429,1,"{6615, 6633}"
303,1,44,0,0.0365203,"\int \text{ProductLog}\left(a x^{\frac{1}{1-p}}\right)^p \, dx","Int[ProductLog[a*x^(1 - p)^(-1)]^p,x]","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}","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,"-((p*x*ProductLog[a*x^(1 - p)^(-1)]^(-1 + p))/(1 - p)) + x*ProductLog[a*x^(1 - p)^(-1)]^p","A",2,2,14,0.1429,1,"{6615, 6633}"
304,1,139,0,0.5713262,"\int x^{-1-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{9/2} \, dx","Int[x^(-1 - n)*(c*ProductLog[a*x^n])^(9/2),x]","\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}","\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,"(135*a*c^(9/2)*Sqrt[Pi]*Erf[Sqrt[c*ProductLog[a*x^n]]/Sqrt[c]])/(16*n) - (135*c^3*(c*ProductLog[a*x^n])^(3/2))/(8*n*x^n) - (45*c^2*(c*ProductLog[a*x^n])^(5/2))/(4*n*x^n) - (9*c*(c*ProductLog[a*x^n])^(7/2))/(2*n*x^n) - (c*ProductLog[a*x^n])^(9/2)/(n*x^n)","A",5,3,20,0.1500,1,"{6618, 6651, 6649}"
305,1,112,0,0.4272741,"\int x^{-1-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2} \, dx","Int[x^(-1 - n)*(c*ProductLog[a*x^n])^(7/2),x]","\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}","\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,"(21*a*c^(7/2)*Sqrt[Pi]*Erf[Sqrt[c*ProductLog[a*x^n]]/Sqrt[c]])/(8*n) - (21*c^2*(c*ProductLog[a*x^n])^(3/2))/(4*n*x^n) - (7*c*(c*ProductLog[a*x^n])^(5/2))/(2*n*x^n) - (c*ProductLog[a*x^n])^(7/2)/(n*x^n)","A",4,3,20,0.1500,1,"{6618, 6651, 6649}"
306,1,85,0,0.299349,"\int x^{-1-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2} \, dx","Int[x^(-1 - n)*(c*ProductLog[a*x^n])^(5/2),x]","\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}","\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,"(5*a*c^(5/2)*Sqrt[Pi]*Erf[Sqrt[c*ProductLog[a*x^n]]/Sqrt[c]])/(4*n) - (5*c*(c*ProductLog[a*x^n])^(3/2))/(2*n*x^n) - (c*ProductLog[a*x^n])^(5/2)/(n*x^n)","A",3,3,20,0.1500,1,"{6618, 6651, 6649}"
307,1,60,0,0.1628158,"\int x^{-1-n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2} \, dx","Int[x^(-1 - n)*(c*ProductLog[a*x^n])^(3/2),x]","\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}","\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,"(3*a*c^(3/2)*Sqrt[Pi]*Erf[Sqrt[c*ProductLog[a*x^n]]/Sqrt[c]])/(2*n) - (c*ProductLog[a*x^n])^(3/2)/(n*x^n)","A",2,2,20,0.1000,1,"{6618, 6649}"
308,1,58,0,0.155162,"\int x^{-1-n} \sqrt{c \text{ProductLog}\left(a x^n\right)} \, dx","Int[x^(-1 - n)*Sqrt[c*ProductLog[a*x^n]],x]","-\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}","-\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,"-((a*Sqrt[c]*Sqrt[Pi]*Erf[Sqrt[c*ProductLog[a*x^n]]/Sqrt[c]])/n) - (2*Sqrt[c*ProductLog[a*x^n]])/(n*x^n)","A",2,2,20,0.1000,1,"{6619, 6649}"
309,1,89,0,0.2855194,"\int \frac{x^{-1-n}}{\sqrt{c \text{ProductLog}\left(a x^n\right)}} \, dx","Int[x^(-1 - n)/Sqrt[c*ProductLog[a*x^n]],x]","-\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)}}","-\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*a*Sqrt[Pi]*Erf[Sqrt[c*ProductLog[a*x^n]]/Sqrt[c]])/(3*Sqrt[c]*n) - 2/(3*n*x^n*Sqrt[c*ProductLog[a*x^n]]) - (2*Sqrt[c*ProductLog[a*x^n]])/(3*c*n*x^n)","A",3,3,20,0.1500,1,"{6619, 6652, 6649}"
310,1,116,0,0.403015,"\int \frac{x^{-1-n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}} \, dx","Int[x^(-1 - n)/(c*ProductLog[a*x^n])^(3/2),x]","\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}}","\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,"(4*a*Sqrt[Pi]*Erf[Sqrt[c*ProductLog[a*x^n]]/Sqrt[c]])/(5*c^(3/2)*n) - 2/(5*n*x^n*(c*ProductLog[a*x^n])^(3/2)) - 2/(5*c*n*x^n*Sqrt[c*ProductLog[a*x^n]]) + (4*Sqrt[c*ProductLog[a*x^n]])/(5*c^2*n*x^n)","A",4,3,20,0.1500,1,"{6619, 6652, 6649}"
311,1,143,0,0.5584843,"\int \frac{x^{-1-n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}} \, dx","Int[x^(-1 - n)/(c*ProductLog[a*x^n])^(5/2),x]","-\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}}","-\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,"(-8*a*Sqrt[Pi]*Erf[Sqrt[c*ProductLog[a*x^n]]/Sqrt[c]])/(21*c^(5/2)*n) - 2/(7*n*x^n*(c*ProductLog[a*x^n])^(5/2)) - 2/(7*c*n*x^n*(c*ProductLog[a*x^n])^(3/2)) + 4/(21*c^2*n*x^n*Sqrt[c*ProductLog[a*x^n]]) - (8*Sqrt[c*ProductLog[a*x^n]])/(21*c^3*n*x^n)","A",5,3,20,0.1500,1,"{6619, 6652, 6649}"
312,1,152,0,0.608827,"\int x^{-1-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{11/2} \, dx","Int[x^(-1 - 2*n)*(c*ProductLog[a*x^n])^(11/2),x]","\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}","\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,"(165*a^2*c^(11/2)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[c*ProductLog[a*x^n]])/Sqrt[c]])/(256*n) - (165*c^3*(c*ProductLog[a*x^n])^(5/2))/(128*n*x^(2*n)) - (55*c^2*(c*ProductLog[a*x^n])^(7/2))/(32*n*x^(2*n)) - (11*c*(c*ProductLog[a*x^n])^(9/2))/(8*n*x^(2*n)) - (c*ProductLog[a*x^n])^(11/2)/(2*n*x^(2*n))","A",5,3,20,0.1500,1,"{6618, 6651, 6649}"
313,1,125,0,0.4607125,"\int x^{-1-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{9/2} \, dx","Int[x^(-1 - 2*n)*(c*ProductLog[a*x^n])^(9/2),x]","\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}","\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,"(27*a^2*c^(9/2)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[c*ProductLog[a*x^n]])/Sqrt[c]])/(64*n) - (27*c^2*(c*ProductLog[a*x^n])^(5/2))/(32*n*x^(2*n)) - (9*c*(c*ProductLog[a*x^n])^(7/2))/(8*n*x^(2*n)) - (c*ProductLog[a*x^n])^(9/2)/(2*n*x^(2*n))","A",4,3,20,0.1500,1,"{6618, 6651, 6649}"
314,1,98,0,0.3220512,"\int x^{-1-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2} \, dx","Int[x^(-1 - 2*n)*(c*ProductLog[a*x^n])^(7/2),x]","\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}","\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,"(7*a^2*c^(7/2)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[c*ProductLog[a*x^n]])/Sqrt[c]])/(16*n) - (7*c*(c*ProductLog[a*x^n])^(5/2))/(8*n*x^(2*n)) - (c*ProductLog[a*x^n])^(7/2)/(2*n*x^(2*n))","A",3,3,20,0.1500,1,"{6618, 6651, 6649}"
315,1,73,0,0.1735023,"\int x^{-1-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2} \, dx","Int[x^(-1 - 2*n)*(c*ProductLog[a*x^n])^(5/2),x]","\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}","\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,"(5*a^2*c^(5/2)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[c*ProductLog[a*x^n]])/Sqrt[c]])/(4*n) - (c*ProductLog[a*x^n])^(5/2)/(2*n*x^(2*n))","A",2,2,20,0.1000,1,"{6618, 6649}"
316,1,69,0,0.181923,"\int x^{-1-2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2} \, dx","Int[x^(-1 - 2*n)*(c*ProductLog[a*x^n])^(3/2),x]","-\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}","-\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,"(-3*a^2*c^(3/2)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[c*ProductLog[a*x^n]])/Sqrt[c]])/n - (2*(c*ProductLog[a*x^n])^(3/2))/(n*x^(2*n))","A",2,2,20,0.1000,1,"{6619, 6649}"
317,1,98,0,0.3257448,"\int x^{-1-2 n} \sqrt{c \text{ProductLog}\left(a x^n\right)} \, dx","Int[x^(-1 - 2*n)*Sqrt[c*ProductLog[a*x^n]],x]","\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}","\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*a^2*Sqrt[c]*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[c*ProductLog[a*x^n]])/Sqrt[c]])/(3*n) - (2*Sqrt[c*ProductLog[a*x^n]])/(3*n*x^(2*n)) + (2*(c*ProductLog[a*x^n])^(3/2))/(3*c*n*x^(2*n))","A",3,3,20,0.1500,1,"{6619, 6652, 6649}"
318,1,125,0,0.424963,"\int \frac{x^{-1-2 n}}{\sqrt{c \text{ProductLog}\left(a x^n\right)}} \, dx","Int[x^(-1 - 2*n)/Sqrt[c*ProductLog[a*x^n]],x]","\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)}}","\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,"(8*a^2*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[c*ProductLog[a*x^n]])/Sqrt[c]])/(15*Sqrt[c]*n) - 2/(5*n*x^(2*n)*Sqrt[c*ProductLog[a*x^n]]) - (2*Sqrt[c*ProductLog[a*x^n]])/(15*c*n*x^(2*n)) + (8*(c*ProductLog[a*x^n])^(3/2))/(15*c^2*n*x^(2*n))","A",4,3,20,0.1500,1,"{6619, 6652, 6649}"
319,1,152,0,0.5658419,"\int \frac{x^{-1-2 n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}} \, dx","Int[x^(-1 - 2*n)/(c*ProductLog[a*x^n])^(3/2),x]","-\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}}","-\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,"(-32*a^2*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[c*ProductLog[a*x^n]])/Sqrt[c]])/(35*c^(3/2)*n) - 2/(7*n*x^(2*n)*(c*ProductLog[a*x^n])^(3/2)) - 6/(35*c*n*x^(2*n)*Sqrt[c*ProductLog[a*x^n]]) + (8*Sqrt[c*ProductLog[a*x^n]])/(35*c^2*n*x^(2*n)) - (32*(c*ProductLog[a*x^n])^(3/2))/(35*c^3*n*x^(2*n))","A",5,3,20,0.1500,1,"{6619, 6652, 6649}"
320,1,132,0,0.5301122,"\int x^{-1+n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2} \, dx","Int[x^(-1 + n)*(c*ProductLog[a*x^n])^(5/2),x]","\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}","\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,"(75*c^(5/2)*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a*x^n]]/Sqrt[c]])/(16*a*n) - (75*c^3*x^n)/(8*n*Sqrt[c*ProductLog[a*x^n]]) + (25*c^2*x^n*Sqrt[c*ProductLog[a*x^n]])/(4*n) - (5*c*x^n*(c*ProductLog[a*x^n])^(3/2))/(2*n) + (x^n*(c*ProductLog[a*x^n])^(5/2))/n","A",5,3,18,0.1667,1,"{6618, 6651, 6650}"
321,1,107,0,0.4002656,"\int x^{-1+n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2} \, dx","Int[x^(-1 + n)*(c*ProductLog[a*x^n])^(3/2),x]","-\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}","-\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,"(-9*c^(3/2)*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a*x^n]]/Sqrt[c]])/(8*a*n) + (9*c^2*x^n)/(4*n*Sqrt[c*ProductLog[a*x^n]]) - (3*c*x^n*Sqrt[c*ProductLog[a*x^n]])/(2*n) + (x^n*(c*ProductLog[a*x^n])^(3/2))/n","A",4,3,18,0.1667,1,"{6618, 6651, 6650}"
322,1,82,0,0.2502553,"\int x^{-1+n} \sqrt{c \text{ProductLog}\left(a x^n\right)} \, dx","Int[x^(-1 + n)*Sqrt[c*ProductLog[a*x^n]],x]","\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)}}","\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,"(Sqrt[c]*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a*x^n]]/Sqrt[c]])/(4*a*n) - (c*x^n)/(2*n*Sqrt[c*ProductLog[a*x^n]]) + (x^n*Sqrt[c*ProductLog[a*x^n]])/n","A",3,3,18,0.1667,1,"{6618, 6651, 6650}"
323,1,59,0,0.1392828,"\int \frac{x^{-1+n}}{\sqrt{c \text{ProductLog}\left(a x^n\right)}} \, dx","Int[x^(-1 + n)/Sqrt[c*ProductLog[a*x^n]],x]","\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)}}","\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,"(Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a*x^n]]/Sqrt[c]])/(2*a*Sqrt[c]*n) + x^n/(n*Sqrt[c*ProductLog[a*x^n]])","A",2,2,18,0.1111,1,"{6618, 6650}"
324,1,58,0,0.1475517,"\int \frac{x^{-1+n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}} \, dx","Int[x^(-1 + n)/(c*ProductLog[a*x^n])^(3/2),x]","\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}}","\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,"(3*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a*x^n]]/Sqrt[c]])/(a*c^(3/2)*n) - (2*x^n)/(n*(c*ProductLog[a*x^n])^(3/2))","A",2,2,18,0.1111,1,"{6619, 6650}"
325,1,87,0,0.3095323,"\int \frac{x^{-1+n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}} \, dx","Int[x^(-1 + n)/(c*ProductLog[a*x^n])^(5/2),x]","\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}}","\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,"(10*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a*x^n]]/Sqrt[c]])/(3*a*c^(5/2)*n) - (2*x^n)/(3*n*(c*ProductLog[a*x^n])^(5/2)) - (10*x^n)/(3*c*n*(c*ProductLog[a*x^n])^(3/2))","A",3,3,18,0.1667,1,"{6619, 6652, 6650}"
326,1,112,0,0.4514628,"\int \frac{x^{-1+n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2}} \, dx","Int[x^(-1 + n)/(c*ProductLog[a*x^n])^(7/2),x]","\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}}","\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,"(28*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a*x^n]]/Sqrt[c]])/(15*a*c^(7/2)*n) - (2*x^n)/(5*n*(c*ProductLog[a*x^n])^(7/2)) - (14*x^n)/(15*c*n*(c*ProductLog[a*x^n])^(5/2)) - (28*x^n)/(15*c^2*n*(c*ProductLog[a*x^n])^(3/2))","A",4,3,18,0.1667,1,"{6619, 6652, 6650}"
327,1,137,0,0.6035092,"\int \frac{x^{-1+n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{9/2}} \, dx","Int[x^(-1 + n)/(c*ProductLog[a*x^n])^(9/2),x]","\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}}","\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,"(24*Sqrt[Pi]*Erfi[Sqrt[c*ProductLog[a*x^n]]/Sqrt[c]])/(35*a*c^(9/2)*n) - (2*x^n)/(7*n*(c*ProductLog[a*x^n])^(9/2)) - (18*x^n)/(35*c*n*(c*ProductLog[a*x^n])^(7/2)) - (12*x^n)/(35*c^2*n*(c*ProductLog[a*x^n])^(5/2)) - (24*x^n)/(35*c^3*n*(c*ProductLog[a*x^n])^(3/2))","A",5,3,18,0.1667,1,"{6619, 6652, 6650}"
328,1,152,0,0.5922686,"\int x^{-1+2 n} \left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2} \, dx","Int[x^(-1 + 2*n)*(c*ProductLog[a*x^n])^(3/2),x]","\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}","\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,"(45*c^(3/2)*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a*x^n]])/Sqrt[c]])/(256*a^2*n) - (45*c^3*x^(2*n))/(128*n*(c*ProductLog[a*x^n])^(3/2)) + (15*c^2*x^(2*n))/(32*n*Sqrt[c*ProductLog[a*x^n]]) - (3*c*x^(2*n)*Sqrt[c*ProductLog[a*x^n]])/(8*n) + (x^(2*n)*(c*ProductLog[a*x^n])^(3/2))/(2*n)","A",5,3,20,0.1500,1,"{6618, 6651, 6650}"
329,1,125,0,0.4154917,"\int x^{-1+2 n} \sqrt{c \text{ProductLog}\left(a x^n\right)} \, dx","Int[x^(-1 + 2*n)*Sqrt[c*ProductLog[a*x^n]],x]","-\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)}}","-\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,"(-3*Sqrt[c]*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a*x^n]])/Sqrt[c]])/(64*a^2*n) + (3*c^2*x^(2*n))/(32*n*(c*ProductLog[a*x^n])^(3/2)) - (c*x^(2*n))/(8*n*Sqrt[c*ProductLog[a*x^n]]) + (x^(2*n)*Sqrt[c*ProductLog[a*x^n]])/(2*n)","A",4,3,20,0.1500,1,"{6618, 6651, 6650}"
330,1,98,0,0.3230935,"\int \frac{x^{-1+2 n}}{\sqrt{c \text{ProductLog}\left(a x^n\right)}} \, dx","Int[x^(-1 + 2*n)/Sqrt[c*ProductLog[a*x^n]],x]","-\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}}","-\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,"-(Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a*x^n]])/Sqrt[c]])/(16*a^2*Sqrt[c]*n) + (c*x^(2*n))/(8*n*(c*ProductLog[a*x^n])^(3/2)) + x^(2*n)/(2*n*Sqrt[c*ProductLog[a*x^n]])","A",3,3,20,0.1500,1,"{6618, 6651, 6650}"
331,1,73,0,0.1975007,"\int \frac{x^{-1+2 n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{3/2}} \, dx","Int[x^(-1 + 2*n)/(c*ProductLog[a*x^n])^(3/2),x]","\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}}","\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,"(3*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a*x^n]])/Sqrt[c]])/(4*a^2*c^(3/2)*n) + x^(2*n)/(2*n*(c*ProductLog[a*x^n])^(3/2))","A",2,2,20,0.1000,1,"{6618, 6650}"
332,1,69,0,0.1938968,"\int \frac{x^{-1+2 n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{5/2}} \, dx","Int[x^(-1 + 2*n)/(c*ProductLog[a*x^n])^(5/2),x]","\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}}","\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,"(5*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a*x^n]])/Sqrt[c]])/(a^2*c^(5/2)*n) - (2*x^(2*n))/(n*(c*ProductLog[a*x^n])^(5/2))","A",2,2,20,0.1000,1,"{6619, 6650}"
333,1,98,0,0.3336734,"\int \frac{x^{-1+2 n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{7/2}} \, dx","Int[x^(-1 + 2*n)/(c*ProductLog[a*x^n])^(7/2),x]","\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}}","\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,"(14*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a*x^n]])/Sqrt[c]])/(3*a^2*c^(7/2)*n) - (2*x^(2*n))/(3*n*(c*ProductLog[a*x^n])^(7/2)) - (14*x^(2*n))/(3*c*n*(c*ProductLog[a*x^n])^(5/2))","A",3,3,20,0.1500,1,"{6619, 6652, 6650}"
334,1,125,0,0.5008521,"\int \frac{x^{-1+2 n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{9/2}} \, dx","Int[x^(-1 + 2*n)/(c*ProductLog[a*x^n])^(9/2),x]","\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}}","\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,"(24*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a*x^n]])/Sqrt[c]])/(5*a^2*c^(9/2)*n) - (2*x^(2*n))/(5*n*(c*ProductLog[a*x^n])^(9/2)) - (6*x^(2*n))/(5*c*n*(c*ProductLog[a*x^n])^(7/2)) - (24*x^(2*n))/(5*c^2*n*(c*ProductLog[a*x^n])^(5/2))","A",4,3,20,0.1500,1,"{6619, 6652, 6650}"
335,1,152,0,0.6405276,"\int \frac{x^{-1+2 n}}{\left(c \text{ProductLog}\left(a x^n\right)\right)^{11/2}} \, dx","Int[x^(-1 + 2*n)/(c*ProductLog[a*x^n])^(11/2),x]","\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}}","\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,"(352*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[c*ProductLog[a*x^n]])/Sqrt[c]])/(105*a^2*c^(11/2)*n) - (2*x^(2*n))/(7*n*(c*ProductLog[a*x^n])^(11/2)) - (22*x^(2*n))/(35*c*n*(c*ProductLog[a*x^n])^(9/2)) - (88*x^(2*n))/(105*c^2*n*(c*ProductLog[a*x^n])^(7/2)) - (352*x^(2*n))/(105*c^3*n*(c*ProductLog[a*x^n])^(5/2))","A",5,3,20,0.1500,1,"{6619, 6652, 6650}"
336,1,41,0,0.0938332,"\int x^{-1-3 n} \text{ProductLog}\left(a x^n\right)^4 \, dx","Int[x^(-1 - 3*n)*ProductLog[a*x^n]^4,x]","-\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}","-\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,"(-4*ProductLog[a*x^n]^3)/(9*n*x^(3*n)) - ProductLog[a*x^n]^4/(3*n*x^(3*n))","A",2,2,16,0.1250,1,"{6618, 6647}"
337,1,41,0,0.092126,"\int x^{-1-2 n} \text{ProductLog}\left(a x^n\right)^3 \, dx","Int[x^(-1 - 2*n)*ProductLog[a*x^n]^3,x]","-\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}","-\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,"(-3*ProductLog[a*x^n]^2)/(4*n*x^(2*n)) - ProductLog[a*x^n]^3/(2*n*x^(2*n))","A",2,2,16,0.1250,1,"{6618, 6647}"
338,1,35,0,0.0894904,"\int x^{-1-n} \text{ProductLog}\left(a x^n\right)^2 \, dx","Int[x^(-1 - n)*ProductLog[a*x^n]^2,x]","-\frac{x^{-n} \text{ProductLog}\left(a x^n\right)^2}{n}-\frac{2 x^{-n} \text{ProductLog}\left(a x^n\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,"(-2*ProductLog[a*x^n])/(n*x^n) - ProductLog[a*x^n]^2/(n*x^n)","A",2,2,16,0.1250,1,"{6618, 6647}"
339,1,41,0,0.0981241,"\int \frac{x^{-1+2 n}}{\text{ProductLog}\left(a x^n\right)} \, dx","Int[x^(-1 + 2*n)/ProductLog[a*x^n],x]","\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}","\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)/(4*n*ProductLog[a*x^n]^2) + x^(2*n)/(2*n*ProductLog[a*x^n])","A",2,2,16,0.1250,1,"{6618, 6647}"
340,1,41,0,0.0931111,"\int \frac{x^{-1+3 n}}{\text{ProductLog}\left(a x^n\right)^2} \, dx","Int[x^(-1 + 3*n)/ProductLog[a*x^n]^2,x]","\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}","\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,"(2*x^(3*n))/(9*n*ProductLog[a*x^n]^3) + x^(3*n)/(3*n*ProductLog[a*x^n]^2)","A",2,2,16,0.1250,1,"{6618, 6647}"
341,1,41,0,0.0913336,"\int \frac{x^{-1+4 n}}{\text{ProductLog}\left(a x^n\right)^3} \, dx","Int[x^(-1 + 4*n)/ProductLog[a*x^n]^3,x]","\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}","\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,"(3*x^(4*n))/(16*n*ProductLog[a*x^n]^4) + x^(4*n)/(4*n*ProductLog[a*x^n]^3)","A",2,2,16,0.1250,1,"{6618, 6647}"
342,0,0,0,1.2065123,"\int x^{-1-n (1+p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^p \, dx","Int[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,"-((c*ProductLog[a*x^n])^p/(n*x^(n*(1 + p)))) - (p*(c*ProductLog[a*x^n])^p*Defer[Int][(x^(-1 - n*(1 + p))*ProductLog[a*x^n]^(1 + p))/(1 + ProductLog[a*x^n]), x])/ProductLog[a*x^n]^p","N/A",0,0,0,0,-1,"{}"
343,0,0,0,0.881313,"\int x^{-1-n p} \left(c \text{ProductLog}\left(a x^n\right)\right)^p \, dx","Int[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,"-((c*ProductLog[a*x^n])^p/(n*p*x^(n*p))) + ((c*ProductLog[a*x^n])^p*Defer[Int][(x^(-1 - n*p)*ProductLog[a*x^n]^p)/(1 + ProductLog[a*x^n]), x])/ProductLog[a*x^n]^p","N/A",0,0,0,0,-1,"{}"
344,1,66,0,0.1694237,"\int x^{-1+n (1-p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^p \, dx","Int[x^(-1 + n*(1 - p))*(c*ProductLog[a*x^n])^p,x]","\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}","\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*p*x^(n*(1 - p))*(c*ProductLog[a*x^n])^(-1 + p))/(n*(1 - p)^2)) + (x^(n*(1 - p))*(c*ProductLog[a*x^n])^p)/(n*(1 - p))","A",2,2,22,0.09091,1,"{6618, 6647}"
345,1,102,0,0.3152076,"\int x^{-1+n (2-p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^p \, dx","Int[x^(-1 + n*(2 - p))*(c*ProductLog[a*x^n])^p,x]","\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)}","\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^2*p*x^(n*(2 - p))*(c*ProductLog[a*x^n])^(-2 + p))/(n*(2 - p)^3) - (c*p*x^(n*(2 - p))*(c*ProductLog[a*x^n])^(-1 + p))/(n*(2 - p)^2) + (x^(n*(2 - p))*(c*ProductLog[a*x^n])^p)/(n*(2 - p))","A",3,3,22,0.1364,1,"{6618, 6651, 6647}"
346,1,140,0,0.4939942,"\int x^{-1+n (3-p)} \left(c \text{ProductLog}\left(a x^n\right)\right)^p \, dx","Int[x^(-1 + n*(3 - p))*(c*ProductLog[a*x^n])^p,x]","-\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)}","-\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,"(-2*c^3*p*x^(n*(3 - p))*(c*ProductLog[a*x^n])^(-3 + p))/(n*(3 - p)^4) + (2*c^2*p*x^(n*(3 - p))*(c*ProductLog[a*x^n])^(-2 + p))/(n*(3 - p)^3) - (c*p*x^(n*(3 - p))*(c*ProductLog[a*x^n])^(-1 + p))/(n*(3 - p)^2) + (x^(n*(3 - p))*(c*ProductLog[a*x^n])^p)/(n*(3 - p))","A",4,3,22,0.1364,1,"{6618, 6651, 6647}"
347,1,53,0,0.2153932,"\int \frac{x^3}{1+\text{ProductLog}(a x)} \, dx","Int[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",4,3,12,0.2500,1,"{6640, 6651, 6647}"
348,1,40,0,0.1509571,"\int \frac{x^2}{1+\text{ProductLog}(a x)} \, dx","Int[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",3,3,12,0.2500,1,"{6640, 6651, 6647}"
349,1,27,0,0.055079,"\int \frac{x}{1+\text{ProductLog}(a x)} \, dx","Int[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",2,2,10,0.2000,1,"{6640, 6647}"
350,1,8,0,0.0086837,"\int \frac{1}{1+\text{ProductLog}(a x)} \, dx","Int[(1 + ProductLog[a*x])^(-1),x]","\frac{x}{\text{ProductLog}(a x)}","\frac{x}{\text{ProductLog}(a x)}",1,"x/ProductLog[a*x]","A",1,1,8,0.1250,1,"{6622}"
351,1,5,0,0.024004,"\int \frac{1}{x (1+\text{ProductLog}(a x))} \, dx","Int[1/(x*(1 + ProductLog[a*x])),x]","\log (\text{ProductLog}(a x))","\log (\text{ProductLog}(a x))",1,"Log[ProductLog[a*x]]","A",1,1,12,0.08333,1,"{6641}"
352,1,16,0,0.0634248,"\int \frac{1}{x^2 (1+\text{ProductLog}(a x))} \, dx","Int[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",2,2,12,0.1667,1,"{6642, 6648}"
353,1,28,0,0.1245727,"\int \frac{1}{x^3 (1+\text{ProductLog}(a x))} \, dx","Int[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",3,3,12,0.2500,1,"{6642, 6652, 6648}"
354,1,46,0,0.188494,"\int \frac{1}{x^4 (1+\text{ProductLog}(a x))} \, dx","Int[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",4,3,12,0.2500,1,"{6642, 6652, 6648}"
355,1,31,0,0.1074988,"\int \frac{x^3}{1+\text{ProductLog}\left(a x^2\right)} \, dx","Int[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",3,2,14,0.1429,1,"{6640, 6647}"
356,0,0,0,0.0362561,"\int \frac{x^2}{1+\text{ProductLog}\left(a x^2\right)} \, dx","Int[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,"Defer[Int][x^2/(1 + ProductLog[a*x^2]), x]","N/A",0,0,0,0,-1,"{}"
357,1,15,0,0.0318936,"\int \frac{x}{1+\text{ProductLog}\left(a x^2\right)} \, dx","Int[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",2,2,12,0.1667,1,"{6715, 6622}"
358,0,0,0,0.0116977,"\int \frac{1}{1+\text{ProductLog}\left(a x^2\right)} \, dx","Int[(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,"Defer[Int][(1 + ProductLog[a*x^2])^(-1), x]","N/A",0,0,0,0,-1,"{}"
359,1,11,0,0.0258558,"\int \frac{1}{x \left(1+\text{ProductLog}\left(a x^2\right)\right)} \, dx","Int[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",1,1,14,0.07143,1,"{6644}"
360,0,0,0,0.0420802,"\int \frac{1}{x^2 \left(1+\text{ProductLog}\left(a x^2\right)\right)} \, dx","Int[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,"Defer[Int][1/(x^2*(1 + ProductLog[a*x^2])), x]","N/A",0,0,0,0,-1,"{}"
361,1,22,0,0.1209138,"\int \frac{1}{x^3 \left(1+\text{ProductLog}\left(a x^2\right)\right)} \, dx","Int[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",3,2,14,0.1429,1,"{6642, 6648}"
362,0,0,0,0.0414185,"\int \frac{1}{x^4 \left(1+\text{ProductLog}\left(a x^2\right)\right)} \, dx","Int[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,"Defer[Int][1/(x^4*(1 + ProductLog[a*x^2])), x]","N/A",0,0,0,0,-1,"{}"
363,1,67,0,0.2991726,"\int \frac{x^3}{1+\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Int[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",6,4,14,0.2857,1,"{6645, 6642, 6652, 6648}"
364,1,52,0,0.217717,"\int \frac{x^2}{1+\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Int[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",5,4,14,0.2857,1,"{6645, 6642, 6652, 6648}"
365,1,33,0,0.1494615,"\int \frac{x}{1+\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Int[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",4,4,12,0.3333,1,"{6645, 6642, 6652, 6648}"
366,1,13,0,0.0697205,"\int \frac{1}{1+\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Int[(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",3,3,10,0.3000,1,"{6632, 6642, 6648}"
367,1,9,0,0.0245393,"\int \frac{1}{x \left(1+\text{ProductLog}\left(\frac{a}{x}\right)\right)} \, dx","Int[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",1,1,14,0.07143,1,"{6644}"
368,1,13,0,0.0326332,"\int \frac{1}{x^2 \left(1+\text{ProductLog}\left(\frac{a}{x}\right)\right)} \, dx","Int[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",2,2,14,0.1429,1,"{6645, 6622}"
369,1,31,0,0.088773,"\int \frac{1}{x^3 \left(1+\text{ProductLog}\left(\frac{a}{x}\right)\right)} \, dx","Int[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",3,3,14,0.2143,1,"{6645, 6640, 6647}"
370,1,46,0,0.1714348,"\int \frac{1}{x^4 \left(1+\text{ProductLog}\left(\frac{a}{x}\right)\right)} \, dx","Int[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",4,4,14,0.2857,1,"{6645, 6640, 6651, 6647}"
371,1,52,0,0.2635719,"\int \frac{x^5}{1+\text{ProductLog}\left(\frac{a}{x^2}\right)} \, dx","Int[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",6,4,14,0.2857,1,"{6645, 6642, 6652, 6648}"
372,1,35,0,0.1994946,"\int \frac{x^3}{1+\text{ProductLog}\left(\frac{a}{x^2}\right)} \, dx","Int[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",5,4,14,0.2857,1,"{6645, 6642, 6652, 6648}"
373,1,22,0,0.1157062,"\int \frac{x}{1+\text{ProductLog}\left(\frac{a}{x^2}\right)} \, dx","Int[x/(1 + ProductLog[a/x^2]),x]","\frac{1}{2} a \text{Ei}\left(-\text{ProductLog}\left(\frac{a}{x^2}\right)\right)+\frac{x^2}{2}","\frac{1}{2} a \text{Ei}\left(-\text{ProductLog}\left(\frac{a}{x^2}\right)\right)+\frac{x^2}{2}",1,"x^2/2 + (a*ExpIntegralEi[-ProductLog[a/x^2]])/2","A",4,3,12,0.2500,1,"{6645, 6642, 6648}"
374,1,11,0,0.0264217,"\int \frac{1}{x \left(1+\text{ProductLog}\left(\frac{a}{x^2}\right)\right)} \, dx","Int[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",1,1,14,0.07143,1,"{6644}"
375,1,15,0,0.0514322,"\int \frac{1}{x^3 \left(1+\text{ProductLog}\left(\frac{a}{x^2}\right)\right)} \, dx","Int[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",3,3,14,0.2143,1,"{6645, 6715, 6622}"
376,0,0,0,0.0574058,"\int \frac{x^4}{1+\text{ProductLog}\left(\frac{a}{x^2}\right)} \, dx","Int[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,"-Defer[Subst][Defer[Int][1/(x^6*(1 + ProductLog[a*x^2])), x], x, x^(-1)]","N/A",0,0,0,0,-1,"{}"
377,0,0,0,0.0595933,"\int \frac{x^2}{1+\text{ProductLog}\left(\frac{a}{x^2}\right)} \, dx","Int[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,"-Defer[Subst][Defer[Int][1/(x^4*(1 + ProductLog[a*x^2])), x], x, x^(-1)]","N/A",0,0,0,0,-1,"{}"
378,0,0,0,0.0404521,"\int \frac{1}{1+\text{ProductLog}\left(\frac{a}{x^2}\right)} \, dx","Int[(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,"-Defer[Subst][Defer[Int][1/(x^2*(1 + ProductLog[a*x^2])), x], x, x^(-1)]","N/A",0,0,0,0,-1,"{}"
379,0,0,0,0.0396231,"\int \frac{1}{x^2 \left(1+\text{ProductLog}\left(\frac{a}{x^2}\right)\right)} \, dx","Int[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,"-Defer[Subst][Defer[Int][(1 + ProductLog[a*x^2])^(-1), x], x, x^(-1)]","N/A",0,0,0,0,-1,"{}"
380,0,0,0,0.0730138,"\int \frac{1}{x^4 \left(1+\text{ProductLog}\left(\frac{a}{x^2}\right)\right)} \, dx","Int[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,"-Defer[Subst][Defer[Int][x^2/(1 + ProductLog[a*x^2]), x], x, x^(-1)]","N/A",0,0,0,0,-1,"{}"
381,1,50,0,0.0382512,"\int \frac{x^m}{d+d \text{ProductLog}(a x)} \, dx","Int[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",1,1,14,0.07143,1,"{6643}"
382,1,12,0,0.0211004,"\int \frac{\text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)^5}{1+\text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)} \, dx","Int[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",1,1,23,0.04348,1,"{6633}"
383,1,12,0,0.0267175,"\int \frac{\text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)^4}{1+\text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)} \, dx","Int[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",1,1,23,0.04348,1,"{6633}"
384,1,12,0,0.0341,"\int \frac{\text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)^3}{1+\text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)} \, dx","Int[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",1,1,23,0.04348,1,"{6633}"
385,1,8,0,0.0225978,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)^2}{1+\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Int[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",1,1,19,0.05263,1,"{6633}"
386,1,12,0,0.0273754,"\int \frac{1}{\text{ProductLog}\left(a \sqrt{x}\right) \left(1+\text{ProductLog}\left(a \sqrt{x}\right)\right)} \, dx","Int[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",1,1,23,0.04348,1,"{6633}"
387,1,12,0,0.025502,"\int \frac{1}{\text{ProductLog}\left(a \sqrt[3]{x}\right)^2 \left(1+\text{ProductLog}\left(a \sqrt[3]{x}\right)\right)} \, dx","Int[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",1,1,23,0.04348,1,"{6633}"
388,1,12,0,0.0305995,"\int \frac{1}{\text{ProductLog}\left(a \sqrt[4]{x}\right)^3 \left(1+\text{ProductLog}\left(a \sqrt[4]{x}\right)\right)} \, dx","Int[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",1,1,23,0.04348,1,"{6633}"
389,1,16,0,0.0227902,"\int \frac{\text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)^4}{1+\text{ProductLog}\left(\frac{a}{\sqrt[4]{x}}\right)} \, dx","Int[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",1,1,23,0.04348,1,"{6634}"
390,1,16,0,0.0213057,"\int \frac{\text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)^3}{1+\text{ProductLog}\left(\frac{a}{\sqrt[3]{x}}\right)} \, dx","Int[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",1,1,23,0.04348,1,"{6634}"
391,1,16,0,0.0262573,"\int \frac{\text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)^2}{1+\text{ProductLog}\left(\frac{a}{\sqrt{x}}\right)} \, dx","Int[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",1,1,23,0.04348,1,"{6634}"
392,1,12,0,0.0135648,"\int \frac{\text{ProductLog}\left(\frac{a}{x}\right)}{1+\text{ProductLog}\left(\frac{a}{x}\right)} \, dx","Int[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",1,1,17,0.05882,1,"{6634}"
393,1,9,0,0.0222658,"\int \frac{1}{\text{ProductLog}(a x) (1+\text{ProductLog}(a x))} \, dx","Int[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",1,1,15,0.06667,1,"{6625}"
394,1,16,0,0.0255285,"\int \frac{1}{\text{ProductLog}\left(a \sqrt{x}\right)^2 \left(1+\text{ProductLog}\left(a \sqrt{x}\right)\right)} \, dx","Int[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",1,1,23,0.04348,1,"{6634}"
395,1,16,0,0.0242895,"\int \frac{1}{\text{ProductLog}\left(a \sqrt[3]{x}\right)^3 \left(1+\text{ProductLog}\left(a \sqrt[3]{x}\right)\right)} \, dx","Int[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",1,1,23,0.04348,1,"{6634}"
396,1,16,0,0.0214289,"\int \frac{1}{\text{ProductLog}\left(a \sqrt[4]{x}\right)^4 \left(1+\text{ProductLog}\left(a \sqrt[4]{x}\right)\right)} \, dx","Int[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",1,1,23,0.04348,1,"{6634}"
397,1,14,0,0.0291613,"\int \frac{\text{ProductLog}\left(a x^n\right)^{1-\frac{1}{n}}}{1+\text{ProductLog}\left(a x^n\right)} \, dx","Int[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",1,1,25,0.04000,1,"{6633}"
398,1,18,0,0.0287455,"\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","Int[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",1,1,31,0.03226,1,"{6633}"