1,1,138,0,2.835553," ","integrate(LambertW(b*x+a)**4,x)","\begin{cases} 0 & \text{for}\: \left(a = 0 \vee a = - b x\right) \wedge \left(a = - b x \vee b = 0\right) \\x \operatorname{LambertW}^{4}{\left(a \right)} & \text{for}\: b = 0 \\\frac{a \operatorname{LambertW}^{4}{\left(a + b x \right)}}{b} - \frac{4 a \operatorname{LambertW}^{3}{\left(a + b x \right)}}{b} + \frac{16 a \operatorname{LambertW}^{2}{\left(a + b x \right)}}{b} - \frac{48 a \operatorname{LambertW}{\left(a + b x \right)}}{b} - \frac{96 a}{b \operatorname{LambertW}{\left(a + b x \right)}} + x \operatorname{LambertW}^{4}{\left(a + b x \right)} - 4 x \operatorname{LambertW}^{3}{\left(a + b x \right)} + 16 x \operatorname{LambertW}^{2}{\left(a + b x \right)} - 48 x \operatorname{LambertW}{\left(a + b x \right)} + 96 x - \frac{96 x}{\operatorname{LambertW}{\left(a + b x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((0, (Eq(a, 0) | Eq(a, -b*x)) & (Eq(b, 0) | Eq(a, -b*x))), (x*LambertW(a)**4, Eq(b, 0)), (a*LambertW(a + b*x)**4/b - 4*a*LambertW(a + b*x)**3/b + 16*a*LambertW(a + b*x)**2/b - 48*a*LambertW(a + b*x)/b - 96*a/(b*LambertW(a + b*x)) + x*LambertW(a + b*x)**4 - 4*x*LambertW(a + b*x)**3 + 16*x*LambertW(a + b*x)**2 - 48*x*LambertW(a + b*x) + 96*x - 96*x/LambertW(a + b*x), True))","A"
2,1,112,0,2.151777," ","integrate(LambertW(b*x+a)**3,x)","\begin{cases} 0 & \text{for}\: \left(a = 0 \vee a = - b x\right) \wedge \left(a = - b x \vee b = 0\right) \\x \operatorname{LambertW}^{3}{\left(a \right)} & \text{for}\: b = 0 \\\frac{a \operatorname{LambertW}^{3}{\left(a + b x \right)}}{b} - \frac{3 a \operatorname{LambertW}^{2}{\left(a + b x \right)}}{b} + \frac{9 a \operatorname{LambertW}{\left(a + b x \right)}}{b} + \frac{18 a}{b \operatorname{LambertW}{\left(a + b x \right)}} + x \operatorname{LambertW}^{3}{\left(a + b x \right)} - 3 x \operatorname{LambertW}^{2}{\left(a + b x \right)} + 9 x \operatorname{LambertW}{\left(a + b x \right)} - 18 x + \frac{18 x}{\operatorname{LambertW}{\left(a + b x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((0, (Eq(a, 0) | Eq(a, -b*x)) & (Eq(b, 0) | Eq(a, -b*x))), (x*LambertW(a)**3, Eq(b, 0)), (a*LambertW(a + b*x)**3/b - 3*a*LambertW(a + b*x)**2/b + 9*a*LambertW(a + b*x)/b + 18*a/(b*LambertW(a + b*x)) + x*LambertW(a + b*x)**3 - 3*x*LambertW(a + b*x)**2 + 9*x*LambertW(a + b*x) - 18*x + 18*x/LambertW(a + b*x), True))","A"
3,1,87,0,1.637051," ","integrate(LambertW(b*x+a)**2,x)","\begin{cases} 0 & \text{for}\: \left(a = 0 \vee a = - b x\right) \wedge \left(a = - b x \vee b = 0\right) \\x \operatorname{LambertW}^{2}{\left(a \right)} & \text{for}\: b = 0 \\\frac{a \operatorname{LambertW}^{2}{\left(a + b x \right)}}{b} - \frac{2 a \operatorname{LambertW}{\left(a + b x \right)}}{b} - \frac{4 a}{b \operatorname{LambertW}{\left(a + b x \right)}} + x \operatorname{LambertW}^{2}{\left(a + b x \right)} - 2 x \operatorname{LambertW}{\left(a + b x \right)} + 4 x - \frac{4 x}{\operatorname{LambertW}{\left(a + b x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((0, (Eq(a, 0) | Eq(a, -b*x)) & (Eq(b, 0) | Eq(a, -b*x))), (x*LambertW(a)**2, Eq(b, 0)), (a*LambertW(a + b*x)**2/b - 2*a*LambertW(a + b*x)/b - 4*a/(b*LambertW(a + b*x)) + x*LambertW(a + b*x)**2 - 2*x*LambertW(a + b*x) + 4*x - 4*x/LambertW(a + b*x), True))","A"
4,1,54,0,1.208144," ","integrate(LambertW(b*x+a),x)","\begin{cases} 0 & \text{for}\: \left(a = 0 \vee a = - b x\right) \wedge \left(a = - b x \vee b = 0\right) \\x \operatorname{LambertW}{\left(a \right)} & \text{for}\: b = 0 \\\frac{a \operatorname{LambertW}{\left(a + b x \right)}}{b} + \frac{a}{b \operatorname{LambertW}{\left(a + b x \right)}} + x \operatorname{LambertW}{\left(a + b x \right)} - x + \frac{x}{\operatorname{LambertW}{\left(a + b x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((0, (Eq(a, 0) | Eq(a, -b*x)) & (Eq(b, 0) | Eq(a, -b*x))), (x*LambertW(a), Eq(b, 0)), (a*LambertW(a + b*x)/b + a/(b*LambertW(a + b*x)) + x*LambertW(a + b*x) - x + x/LambertW(a + b*x), True))","A"
5,0,0,0,0.000000," ","integrate(1/LambertW(b*x+a),x)","\int \frac{1}{\operatorname{LambertW}{\left(a + b x \right)}}\, dx"," ",0,"Integral(1/LambertW(a + b*x), x)","F"
6,0,0,0,0.000000," ","integrate(1/LambertW(b*x+a)**2,x)","\int \frac{1}{\operatorname{LambertW}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(LambertW(a + b*x)**(-2), x)","F"
7,0,0,0,0.000000," ","integrate(1/LambertW(b*x+a)**3,x)","\int \frac{1}{\operatorname{LambertW}^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral(LambertW(a + b*x)**(-3), x)","F"
8,0,0,0,0.000000," ","integrate(1/LambertW(b*x+a)**4,x)","\int \frac{1}{\operatorname{LambertW}^{4}{\left(a + b x \right)}}\, dx"," ",0,"Integral(LambertW(a + b*x)**(-4), x)","F"
9,0,0,0,0.000000," ","integrate(1/LambertW(b*x+a)**5,x)","\int \frac{1}{\operatorname{LambertW}^{5}{\left(a + b x \right)}}\, dx"," ",0,"Integral(LambertW(a + b*x)**(-5), x)","F"
10,0,0,0,0.000000," ","integrate((c*LambertW(b*x+a))**(5/2),x)","\int \left(c \operatorname{LambertW}{\left(a + b x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((c*LambertW(a + b*x))**(5/2), x)","F"
11,0,0,0,0.000000," ","integrate((c*LambertW(b*x+a))**(3/2),x)","\int \left(c \operatorname{LambertW}{\left(a + b x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((c*LambertW(a + b*x))**(3/2), x)","F"
12,0,0,0,0.000000," ","integrate((c*LambertW(b*x+a))**(1/2),x)","\int \sqrt{c \operatorname{LambertW}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sqrt(c*LambertW(a + b*x)), x)","F"
13,0,0,0,0.000000," ","integrate(1/(c*LambertW(b*x+a))**(1/2),x)","\int \frac{1}{\sqrt{c \operatorname{LambertW}{\left(a + b x \right)}}}\, dx"," ",0,"Integral(1/sqrt(c*LambertW(a + b*x)), x)","F"
14,0,0,0,0.000000," ","integrate(1/(c*LambertW(b*x+a))**(3/2),x)","\int \frac{1}{\left(c \operatorname{LambertW}{\left(a + b x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c*LambertW(a + b*x))**(-3/2), x)","F"
15,0,0,0,0.000000," ","integrate(1/(c*LambertW(b*x+a))**(5/2),x)","\int \frac{1}{\left(c \operatorname{LambertW}{\left(a + b x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c*LambertW(a + b*x))**(-5/2), x)","F"
16,-1,0,0,0.000000," ","integrate(1/(c*LambertW(b*x+a))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
17,0,0,0,0.000000," ","integrate((-c*LambertW(b*x+a))**(5/2),x)","\int \left(- c \operatorname{LambertW}{\left(a + b x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((-c*LambertW(a + b*x))**(5/2), x)","F"
18,0,0,0,0.000000," ","integrate((-c*LambertW(b*x+a))**(3/2),x)","\int \left(- c \operatorname{LambertW}{\left(a + b x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((-c*LambertW(a + b*x))**(3/2), x)","F"
19,0,0,0,0.000000," ","integrate((-c*LambertW(b*x+a))**(1/2),x)","\int \sqrt{- c \operatorname{LambertW}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sqrt(-c*LambertW(a + b*x)), x)","F"
20,0,0,0,0.000000," ","integrate(1/(-c*LambertW(b*x+a))**(1/2),x)","\int \frac{1}{\sqrt{- c \operatorname{LambertW}{\left(a + b x \right)}}}\, dx"," ",0,"Integral(1/sqrt(-c*LambertW(a + b*x)), x)","F"
21,0,0,0,0.000000," ","integrate(1/(-c*LambertW(b*x+a))**(3/2),x)","\int \frac{1}{\left(- c \operatorname{LambertW}{\left(a + b x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((-c*LambertW(a + b*x))**(-3/2), x)","F"
22,0,0,0,0.000000," ","integrate(1/(-c*LambertW(b*x+a))**(5/2),x)","\int \frac{1}{\left(- c \operatorname{LambertW}{\left(a + b x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((-c*LambertW(a + b*x))**(-5/2), x)","F"
23,-1,0,0,0.000000," ","integrate(1/(-c*LambertW(b*x+a))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
24,0,0,0,0.000000," ","integrate((c*LambertW(b*x+a))**n,x)","\int \left(c \operatorname{LambertW}{\left(a + b x \right)}\right)^{n}\, dx"," ",0,"Integral((c*LambertW(a + b*x))**n, x)","F"
25,0,0,0,0.000000," ","integrate(x**3*LambertW(b*x+a),x)","\int x^{3} \operatorname{LambertW}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**3*LambertW(a + b*x), x)","F"
26,0,0,0,0.000000," ","integrate(x**2*LambertW(b*x+a),x)","\int x^{2} \operatorname{LambertW}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**2*LambertW(a + b*x), x)","F"
27,0,0,0,0.000000," ","integrate(x*LambertW(b*x+a),x)","\int x \operatorname{LambertW}{\left(a + b x \right)}\, dx"," ",0,"Integral(x*LambertW(a + b*x), x)","F"
28,1,54,0,1.218147," ","integrate(LambertW(b*x+a),x)","\begin{cases} 0 & \text{for}\: \left(a = 0 \vee a = - b x\right) \wedge \left(a = - b x \vee b = 0\right) \\x \operatorname{LambertW}{\left(a \right)} & \text{for}\: b = 0 \\\frac{a \operatorname{LambertW}{\left(a + b x \right)}}{b} + \frac{a}{b \operatorname{LambertW}{\left(a + b x \right)}} + x \operatorname{LambertW}{\left(a + b x \right)} - x + \frac{x}{\operatorname{LambertW}{\left(a + b x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((0, (Eq(a, 0) | Eq(a, -b*x)) & (Eq(b, 0) | Eq(a, -b*x))), (x*LambertW(a), Eq(b, 0)), (a*LambertW(a + b*x)/b + a/(b*LambertW(a + b*x)) + x*LambertW(a + b*x) - x + x/LambertW(a + b*x), True))","A"
29,0,0,0,0.000000," ","integrate(LambertW(b*x+a)/x,x)","\int \frac{\operatorname{LambertW}{\left(a + b x \right)}}{x}\, dx"," ",0,"Integral(LambertW(a + b*x)/x, x)","F"
30,0,0,0,0.000000," ","integrate(LambertW(b*x+a)/x**2,x)","\int \frac{\operatorname{LambertW}{\left(a + b x \right)}}{x^{2}}\, dx"," ",0,"Integral(LambertW(a + b*x)/x**2, x)","F"
31,0,0,0,0.000000," ","integrate(x**3*LambertW(b*x+a)**2,x)","\int x^{3} \operatorname{LambertW}^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**3*LambertW(a + b*x)**2, x)","F"
32,0,0,0,0.000000," ","integrate(x**2*LambertW(b*x+a)**2,x)","\int x^{2} \operatorname{LambertW}^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**2*LambertW(a + b*x)**2, x)","F"
33,0,0,0,0.000000," ","integrate(x*LambertW(b*x+a)**2,x)","\int x \operatorname{LambertW}^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x*LambertW(a + b*x)**2, x)","F"
34,1,87,0,1.651928," ","integrate(LambertW(b*x+a)**2,x)","\begin{cases} 0 & \text{for}\: \left(a = 0 \vee a = - b x\right) \wedge \left(a = - b x \vee b = 0\right) \\x \operatorname{LambertW}^{2}{\left(a \right)} & \text{for}\: b = 0 \\\frac{a \operatorname{LambertW}^{2}{\left(a + b x \right)}}{b} - \frac{2 a \operatorname{LambertW}{\left(a + b x \right)}}{b} - \frac{4 a}{b \operatorname{LambertW}{\left(a + b x \right)}} + x \operatorname{LambertW}^{2}{\left(a + b x \right)} - 2 x \operatorname{LambertW}{\left(a + b x \right)} + 4 x - \frac{4 x}{\operatorname{LambertW}{\left(a + b x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((0, (Eq(a, 0) | Eq(a, -b*x)) & (Eq(b, 0) | Eq(a, -b*x))), (x*LambertW(a)**2, Eq(b, 0)), (a*LambertW(a + b*x)**2/b - 2*a*LambertW(a + b*x)/b - 4*a/(b*LambertW(a + b*x)) + x*LambertW(a + b*x)**2 - 2*x*LambertW(a + b*x) + 4*x - 4*x/LambertW(a + b*x), True))","A"
35,0,0,0,0.000000," ","integrate(LambertW(b*x+a)**2/x,x)","\int \frac{\operatorname{LambertW}^{2}{\left(a + b x \right)}}{x}\, dx"," ",0,"Integral(LambertW(a + b*x)**2/x, x)","F"
36,0,0,0,0.000000," ","integrate(LambertW(b*x+a)**2/x**2,x)","\int \frac{\operatorname{LambertW}^{2}{\left(a + b x \right)}}{x^{2}}\, dx"," ",0,"Integral(LambertW(a + b*x)**2/x**2, x)","F"
37,0,0,0,0.000000," ","integrate(x**3/(c*LambertW(b*x+a))**(1/2),x)","\int \frac{x^{3}}{\sqrt{c \operatorname{LambertW}{\left(a + b x \right)}}}\, dx"," ",0,"Integral(x**3/sqrt(c*LambertW(a + b*x)), x)","F"
38,0,0,0,0.000000," ","integrate(x**2/(c*LambertW(b*x+a))**(1/2),x)","\int \frac{x^{2}}{\sqrt{c \operatorname{LambertW}{\left(a + b x \right)}}}\, dx"," ",0,"Integral(x**2/sqrt(c*LambertW(a + b*x)), x)","F"
39,0,0,0,0.000000," ","integrate(x/(c*LambertW(b*x+a))**(1/2),x)","\int \frac{x}{\sqrt{c \operatorname{LambertW}{\left(a + b x \right)}}}\, dx"," ",0,"Integral(x/sqrt(c*LambertW(a + b*x)), x)","F"
40,0,0,0,0.000000," ","integrate(1/(c*LambertW(b*x+a))**(1/2),x)","\int \frac{1}{\sqrt{c \operatorname{LambertW}{\left(a + b x \right)}}}\, dx"," ",0,"Integral(1/sqrt(c*LambertW(a + b*x)), x)","F"
41,0,0,0,0.000000," ","integrate(1/x/(c*LambertW(b*x+a))**(1/2),x)","\int \frac{1}{x \sqrt{c \operatorname{LambertW}{\left(a + b x \right)}}}\, dx"," ",0,"Integral(1/(x*sqrt(c*LambertW(a + b*x))), x)","F"
42,0,0,0,0.000000," ","integrate(1/x**2/(c*LambertW(b*x+a))**(1/2),x)","\int \frac{1}{x^{2} \sqrt{c \operatorname{LambertW}{\left(a + b x \right)}}}\, dx"," ",0,"Integral(1/(x**2*sqrt(c*LambertW(a + b*x))), x)","F"
43,0,0,0,0.000000," ","integrate(x**3/(-c*LambertW(b*x+a))**(1/2),x)","\int \frac{x^{3}}{\sqrt{- c \operatorname{LambertW}{\left(a + b x \right)}}}\, dx"," ",0,"Integral(x**3/sqrt(-c*LambertW(a + b*x)), x)","F"
44,0,0,0,0.000000," ","integrate(x**2/(-c*LambertW(b*x+a))**(1/2),x)","\int \frac{x^{2}}{\sqrt{- c \operatorname{LambertW}{\left(a + b x \right)}}}\, dx"," ",0,"Integral(x**2/sqrt(-c*LambertW(a + b*x)), x)","F"
45,0,0,0,0.000000," ","integrate(x/(-c*LambertW(b*x+a))**(1/2),x)","\int \frac{x}{\sqrt{- c \operatorname{LambertW}{\left(a + b x \right)}}}\, dx"," ",0,"Integral(x/sqrt(-c*LambertW(a + b*x)), x)","F"
46,0,0,0,0.000000," ","integrate(1/(-c*LambertW(b*x+a))**(1/2),x)","\int \frac{1}{\sqrt{- c \operatorname{LambertW}{\left(a + b x \right)}}}\, dx"," ",0,"Integral(1/sqrt(-c*LambertW(a + b*x)), x)","F"
47,0,0,0,0.000000," ","integrate(1/x/(-c*LambertW(b*x+a))**(1/2),x)","\int \frac{1}{x \sqrt{- c \operatorname{LambertW}{\left(a + b x \right)}}}\, dx"," ",0,"Integral(1/(x*sqrt(-c*LambertW(a + b*x))), x)","F"
48,0,0,0,0.000000," ","integrate(1/x**2/(-c*LambertW(b*x+a))**(1/2),x)","\int \frac{1}{x^{2} \sqrt{- c \operatorname{LambertW}{\left(a + b x \right)}}}\, dx"," ",0,"Integral(1/(x**2*sqrt(-c*LambertW(a + b*x))), x)","F"
49,0,0,0,0.000000," ","integrate(x**3*(c*LambertW(b*x+a))**(1/2),x)","\int x^{3} \sqrt{c \operatorname{LambertW}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x**3*sqrt(c*LambertW(a + b*x)), x)","F"
50,0,0,0,0.000000," ","integrate(x**2*(c*LambertW(b*x+a))**(1/2),x)","\int x^{2} \sqrt{c \operatorname{LambertW}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x**2*sqrt(c*LambertW(a + b*x)), x)","F"
51,0,0,0,0.000000," ","integrate(x*(c*LambertW(b*x+a))**(1/2),x)","\int x \sqrt{c \operatorname{LambertW}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x*sqrt(c*LambertW(a + b*x)), x)","F"
52,0,0,0,0.000000," ","integrate((c*LambertW(b*x+a))**(1/2),x)","\int \sqrt{c \operatorname{LambertW}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sqrt(c*LambertW(a + b*x)), x)","F"
53,0,0,0,0.000000," ","integrate((c*LambertW(b*x+a))**(1/2)/x,x)","\int \frac{\sqrt{c \operatorname{LambertW}{\left(a + b x \right)}}}{x}\, dx"," ",0,"Integral(sqrt(c*LambertW(a + b*x))/x, x)","F"
54,0,0,0,0.000000," ","integrate((c*LambertW(b*x+a))**(1/2)/x**2,x)","\int \frac{\sqrt{c \operatorname{LambertW}{\left(a + b x \right)}}}{x^{2}}\, dx"," ",0,"Integral(sqrt(c*LambertW(a + b*x))/x**2, x)","F"
55,0,0,0,0.000000," ","integrate(x**3/(d+d*LambertW(b*x+a)),x)","\frac{\int \frac{x^{3}}{\operatorname{LambertW}{\left(a + b x \right)} + 1}\, dx}{d}"," ",0,"Integral(x**3/(LambertW(a + b*x) + 1), x)/d","F"
56,0,0,0,0.000000," ","integrate(x**2/(d+d*LambertW(b*x+a)),x)","\frac{\int \frac{x^{2}}{\operatorname{LambertW}{\left(a + b x \right)} + 1}\, dx}{d}"," ",0,"Integral(x**2/(LambertW(a + b*x) + 1), x)/d","F"
57,0,0,0,0.000000," ","integrate(x/(d+d*LambertW(b*x+a)),x)","\frac{\int \frac{x}{\operatorname{LambertW}{\left(a + b x \right)} + 1}\, dx}{d}"," ",0,"Integral(x/(LambertW(a + b*x) + 1), x)/d","F"
58,1,42,0,1.743780," ","integrate(1/(d+d*LambertW(b*x+a)),x)","\begin{cases} \frac{x}{d} & \text{for}\: \left(a = 0 \vee a = - b x\right) \wedge \left(a = - b x \vee b = 0\right) \\\frac{x}{d \operatorname{LambertW}{\left(a \right)} + d} & \text{for}\: b = 0 \\\frac{a}{b d \operatorname{LambertW}{\left(a + b x \right)}} + \frac{x}{d \operatorname{LambertW}{\left(a + b x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/d, (Eq(a, 0) | Eq(a, -b*x)) & (Eq(b, 0) | Eq(a, -b*x))), (x/(d*LambertW(a) + d), Eq(b, 0)), (a/(b*d*LambertW(a + b*x)) + x/(d*LambertW(a + b*x)), True))","A"
59,0,0,0,0.000000," ","integrate(1/x/(d+d*LambertW(b*x+a)),x)","\frac{\int \frac{1}{x \operatorname{LambertW}{\left(a + b x \right)} + x}\, dx}{d}"," ",0,"Integral(1/(x*LambertW(a + b*x) + x), x)/d","F"
60,0,0,0,0.000000," ","integrate(1/x**2/(d+d*LambertW(b*x+a)),x)","\frac{\int \frac{1}{x^{2} \operatorname{LambertW}{\left(a + b x \right)} + x^{2}}\, dx}{d}"," ",0,"Integral(1/(x**2*LambertW(a + b*x) + x**2), x)/d","F"
61,0,0,0,0.000000," ","integrate(x**3*LambertW(a*x),x)","\int x^{3} \operatorname{LambertW}{\left(a x \right)}\, dx"," ",0,"Integral(x**3*LambertW(a*x), x)","F"
62,0,0,0,0.000000," ","integrate(x**2*LambertW(a*x),x)","\int x^{2} \operatorname{LambertW}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*LambertW(a*x), x)","F"
63,0,0,0,0.000000," ","integrate(x*LambertW(a*x),x)","\int x \operatorname{LambertW}{\left(a x \right)}\, dx"," ",0,"Integral(x*LambertW(a*x), x)","F"
64,1,15,0,0.685792," ","integrate(LambertW(a*x),x)","\begin{cases} x \operatorname{LambertW}{\left(a x \right)} - x + \frac{x}{\operatorname{LambertW}{\left(a x \right)}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*LambertW(a*x) - x + x/LambertW(a*x), Ne(a, 0)), (0, True))","A"
65,1,12,0,0.707894," ","integrate(LambertW(a*x)/x,x)","\frac{\operatorname{LambertW}^{2}{\left(a x \right)}}{2} + \operatorname{LambertW}{\left(a x \right)}"," ",0,"LambertW(a*x)**2/2 + LambertW(a*x)","A"
66,0,0,0,0.000000," ","integrate(LambertW(a*x)/x**2,x)","\int \frac{\operatorname{LambertW}{\left(a x \right)}}{x^{2}}\, dx"," ",0,"Integral(LambertW(a*x)/x**2, x)","F"
67,0,0,0,0.000000," ","integrate(LambertW(a*x)/x**3,x)","\int \frac{\operatorname{LambertW}{\left(a x \right)}}{x^{3}}\, dx"," ",0,"Integral(LambertW(a*x)/x**3, x)","F"
68,0,0,0,0.000000," ","integrate(LambertW(a*x)/x**4,x)","\int \frac{\operatorname{LambertW}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral(LambertW(a*x)/x**4, x)","F"
69,0,0,0,0.000000," ","integrate(LambertW(a*x)/x**5,x)","\int \frac{\operatorname{LambertW}{\left(a x \right)}}{x^{5}}\, dx"," ",0,"Integral(LambertW(a*x)/x**5, x)","F"
70,0,0,0,0.000000," ","integrate(LambertW(a*x)/x**6,x)","\int \frac{\operatorname{LambertW}{\left(a x \right)}}{x^{6}}\, dx"," ",0,"Integral(LambertW(a*x)/x**6, x)","F"
71,0,0,0,0.000000," ","integrate(x**2*LambertW(a*x)**2,x)","\int x^{2} \operatorname{LambertW}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*LambertW(a*x)**2, x)","F"
72,0,0,0,0.000000," ","integrate(x*LambertW(a*x)**2,x)","\int x \operatorname{LambertW}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x*LambertW(a*x)**2, x)","F"
73,1,29,0,0.923548," ","integrate(LambertW(a*x)**2,x)","\begin{cases} x \operatorname{LambertW}^{2}{\left(a x \right)} - 2 x \operatorname{LambertW}{\left(a x \right)} + 4 x - \frac{4 x}{\operatorname{LambertW}{\left(a x \right)}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*LambertW(a*x)**2 - 2*x*LambertW(a*x) + 4*x - 4*x/LambertW(a*x), Ne(a, 0)), (0, True))","A"
74,1,15,0,0.835758," ","integrate(LambertW(a*x)**2/x,x)","\frac{\operatorname{LambertW}^{3}{\left(a x \right)}}{3} + \frac{\operatorname{LambertW}^{2}{\left(a x \right)}}{2}"," ",0,"LambertW(a*x)**3/3 + LambertW(a*x)**2/2","A"
75,1,17,0,0.484078," ","integrate(LambertW(a*x)**2/x**2,x)","- \frac{\operatorname{LambertW}^{2}{\left(a x \right)}}{x} - \frac{2 \operatorname{LambertW}{\left(a x \right)}}{x}"," ",0,"-LambertW(a*x)**2/x - 2*LambertW(a*x)/x","A"
76,0,0,0,0.000000," ","integrate(LambertW(a*x)**2/x**3,x)","\int \frac{\operatorname{LambertW}^{2}{\left(a x \right)}}{x^{3}}\, dx"," ",0,"Integral(LambertW(a*x)**2/x**3, x)","F"
77,0,0,0,0.000000," ","integrate(LambertW(a*x)**2/x**4,x)","\int \frac{\operatorname{LambertW}^{2}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral(LambertW(a*x)**2/x**4, x)","F"
78,0,0,0,0.000000," ","integrate(LambertW(a*x)**2/x**5,x)","\int \frac{\operatorname{LambertW}^{2}{\left(a x \right)}}{x^{5}}\, dx"," ",0,"Integral(LambertW(a*x)**2/x**5, x)","F"
79,0,0,0,0.000000," ","integrate(LambertW(a*x)**2/x**6,x)","\int \frac{\operatorname{LambertW}^{2}{\left(a x \right)}}{x^{6}}\, dx"," ",0,"Integral(LambertW(a*x)**2/x**6, x)","F"
80,0,0,0,0.000000," ","integrate(LambertW(a*x)**2/x**7,x)","\int \frac{\operatorname{LambertW}^{2}{\left(a x \right)}}{x^{7}}\, dx"," ",0,"Integral(LambertW(a*x)**2/x**7, x)","F"
81,0,0,0,0.000000," ","integrate(x**2*LambertW(a*x)**3,x)","\int x^{2} \operatorname{LambertW}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*LambertW(a*x)**3, x)","F"
82,0,0,0,0.000000," ","integrate(x*LambertW(a*x)**3,x)","\int x \operatorname{LambertW}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(x*LambertW(a*x)**3, x)","F"
83,1,39,0,1.174334," ","integrate(LambertW(a*x)**3,x)","\begin{cases} x \operatorname{LambertW}^{3}{\left(a x \right)} - 3 x \operatorname{LambertW}^{2}{\left(a x \right)} + 9 x \operatorname{LambertW}{\left(a x \right)} - 18 x + \frac{18 x}{\operatorname{LambertW}{\left(a x \right)}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*LambertW(a*x)**3 - 3*x*LambertW(a*x)**2 + 9*x*LambertW(a*x) - 18*x + 18*x/LambertW(a*x), Ne(a, 0)), (0, True))","A"
84,1,15,0,0.954981," ","integrate(LambertW(a*x)**3/x,x)","\frac{\operatorname{LambertW}^{4}{\left(a x \right)}}{4} + \frac{\operatorname{LambertW}^{3}{\left(a x \right)}}{3}"," ",0,"LambertW(a*x)**4/4 + LambertW(a*x)**3/3","A"
85,1,27,0,0.632839," ","integrate(LambertW(a*x)**3/x**2,x)","- \frac{\operatorname{LambertW}^{3}{\left(a x \right)}}{x} - \frac{3 \operatorname{LambertW}^{2}{\left(a x \right)}}{x} - \frac{3 \operatorname{LambertW}{\left(a x \right)}}{x}"," ",0,"-LambertW(a*x)**3/x - 3*LambertW(a*x)**2/x - 3*LambertW(a*x)/x","A"
86,1,26,0,0.844006," ","integrate(LambertW(a*x)**3/x**3,x)","- \frac{\operatorname{LambertW}^{3}{\left(a x \right)}}{2 x^{2}} - \frac{3 \operatorname{LambertW}^{2}{\left(a x \right)}}{4 x^{2}}"," ",0,"-LambertW(a*x)**3/(2*x**2) - 3*LambertW(a*x)**2/(4*x**2)","A"
87,0,0,0,0.000000," ","integrate(LambertW(a*x)**3/x**4,x)","\int \frac{\operatorname{LambertW}^{3}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral(LambertW(a*x)**3/x**4, x)","F"
88,0,0,0,0.000000," ","integrate(LambertW(a*x)**3/x**5,x)","\int \frac{\operatorname{LambertW}^{3}{\left(a x \right)}}{x^{5}}\, dx"," ",0,"Integral(LambertW(a*x)**3/x**5, x)","F"
89,0,0,0,0.000000," ","integrate(LambertW(a*x)**3/x**6,x)","\int \frac{\operatorname{LambertW}^{3}{\left(a x \right)}}{x^{6}}\, dx"," ",0,"Integral(LambertW(a*x)**3/x**6, x)","F"
90,0,0,0,0.000000," ","integrate(LambertW(a*x)**3/x**7,x)","\int \frac{\operatorname{LambertW}^{3}{\left(a x \right)}}{x^{7}}\, dx"," ",0,"Integral(LambertW(a*x)**3/x**7, x)","F"
91,0,0,0,0.000000," ","integrate(LambertW(a*x)**3/x**8,x)","\int \frac{\operatorname{LambertW}^{3}{\left(a x \right)}}{x^{8}}\, dx"," ",0,"Integral(LambertW(a*x)**3/x**8, x)","F"
92,0,0,0,0.000000," ","integrate(x**4/LambertW(a*x),x)","\int \frac{x^{4}}{\operatorname{LambertW}{\left(a x \right)}}\, dx"," ",0,"Integral(x**4/LambertW(a*x), x)","F"
93,0,0,0,0.000000," ","integrate(x**3/LambertW(a*x),x)","\int \frac{x^{3}}{\operatorname{LambertW}{\left(a x \right)}}\, dx"," ",0,"Integral(x**3/LambertW(a*x), x)","F"
94,0,0,0,0.000000," ","integrate(x**2/LambertW(a*x),x)","\int \frac{x^{2}}{\operatorname{LambertW}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/LambertW(a*x), x)","F"
95,1,20,0,0.718576," ","integrate(x/LambertW(a*x),x)","\frac{x^{2}}{2 \operatorname{LambertW}{\left(a x \right)}} + \frac{x^{2}}{4 \operatorname{LambertW}^{2}{\left(a x \right)}}"," ",0,"x**2/(2*LambertW(a*x)) + x**2/(4*LambertW(a*x)**2)","A"
96,0,0,0,0.000000," ","integrate(1/LambertW(a*x),x)","\int \frac{1}{\operatorname{LambertW}{\left(a x \right)}}\, dx"," ",0,"Integral(1/LambertW(a*x), x)","F"
97,1,12,0,0.743856," ","integrate(1/x/LambertW(a*x),x)","\log{\left(\operatorname{LambertW}{\left(a x \right)} \right)} - \frac{1}{\operatorname{LambertW}{\left(a x \right)}}"," ",0,"log(LambertW(a*x)) - 1/LambertW(a*x)","A"
98,0,0,0,0.000000," ","integrate(1/x**2/LambertW(a*x),x)","\int \frac{1}{x^{2} \operatorname{LambertW}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**2*LambertW(a*x)), x)","F"
99,0,0,0,0.000000," ","integrate(1/x**3/LambertW(a*x),x)","\int \frac{1}{x^{3} \operatorname{LambertW}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**3*LambertW(a*x)), x)","F"
100,0,0,0,0.000000," ","integrate(1/x**4/LambertW(a*x),x)","\int \frac{1}{x^{4} \operatorname{LambertW}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**4*LambertW(a*x)), x)","F"
101,0,0,0,0.000000," ","integrate(x**5/LambertW(a*x)**2,x)","\int \frac{x^{5}}{\operatorname{LambertW}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**5/LambertW(a*x)**2, x)","F"
102,0,0,0,0.000000," ","integrate(x**4/LambertW(a*x)**2,x)","\int \frac{x^{4}}{\operatorname{LambertW}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**4/LambertW(a*x)**2, x)","F"
103,0,0,0,0.000000," ","integrate(x**3/LambertW(a*x)**2,x)","\int \frac{x^{3}}{\operatorname{LambertW}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**3/LambertW(a*x)**2, x)","F"
104,1,24,0,0.848069," ","integrate(x**2/LambertW(a*x)**2,x)","\frac{x^{3}}{3 \operatorname{LambertW}^{2}{\left(a x \right)}} + \frac{2 x^{3}}{9 \operatorname{LambertW}^{3}{\left(a x \right)}}"," ",0,"x**3/(3*LambertW(a*x)**2) + 2*x**3/(9*LambertW(a*x)**3)","A"
105,0,0,0,0.000000," ","integrate(x/LambertW(a*x)**2,x)","\int \frac{x}{\operatorname{LambertW}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x/LambertW(a*x)**2, x)","F"
106,0,0,0,0.000000," ","integrate(1/LambertW(a*x)**2,x)","\int \frac{1}{\operatorname{LambertW}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(LambertW(a*x)**(-2), x)","F"
107,1,17,0,0.977144," ","integrate(1/x/LambertW(a*x)**2,x)","- \frac{1}{\operatorname{LambertW}{\left(a x \right)}} - \frac{1}{2 \operatorname{LambertW}^{2}{\left(a x \right)}}"," ",0,"-1/LambertW(a*x) - 1/(2*LambertW(a*x)**2)","A"
108,0,0,0,0.000000," ","integrate(1/x**2/LambertW(a*x)**2,x)","\int \frac{1}{x^{2} \operatorname{LambertW}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**2*LambertW(a*x)**2), x)","F"
109,0,0,0,0.000000," ","integrate(1/x**3/LambertW(a*x)**2,x)","\int \frac{1}{x^{3} \operatorname{LambertW}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**3*LambertW(a*x)**2), x)","F"
110,0,0,0,0.000000," ","integrate(x**6/LambertW(a*x)**3,x)","\int \frac{x^{6}}{\operatorname{LambertW}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x**6/LambertW(a*x)**3, x)","F"
111,0,0,0,0.000000," ","integrate(x**5/LambertW(a*x)**3,x)","\int \frac{x^{5}}{\operatorname{LambertW}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x**5/LambertW(a*x)**3, x)","F"
112,0,0,0,0.000000," ","integrate(x**4/LambertW(a*x)**3,x)","\int \frac{x^{4}}{\operatorname{LambertW}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x**4/LambertW(a*x)**3, x)","F"
113,1,24,0,1.004561," ","integrate(x**3/LambertW(a*x)**3,x)","\frac{x^{4}}{4 \operatorname{LambertW}^{3}{\left(a x \right)}} + \frac{3 x^{4}}{16 \operatorname{LambertW}^{4}{\left(a x \right)}}"," ",0,"x**4/(4*LambertW(a*x)**3) + 3*x**4/(16*LambertW(a*x)**4)","A"
114,0,0,0,0.000000," ","integrate(x**2/LambertW(a*x)**3,x)","\int \frac{x^{2}}{\operatorname{LambertW}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/LambertW(a*x)**3, x)","F"
115,0,0,0,0.000000," ","integrate(x/LambertW(a*x)**3,x)","\int \frac{x}{\operatorname{LambertW}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x/LambertW(a*x)**3, x)","F"
116,0,0,0,0.000000," ","integrate(1/LambertW(a*x)**3,x)","\int \frac{1}{\operatorname{LambertW}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(LambertW(a*x)**(-3), x)","F"
117,1,20,0,1.154619," ","integrate(1/x/LambertW(a*x)**3,x)","- \frac{1}{2 \operatorname{LambertW}^{2}{\left(a x \right)}} - \frac{1}{3 \operatorname{LambertW}^{3}{\left(a x \right)}}"," ",0,"-1/(2*LambertW(a*x)**2) - 1/(3*LambertW(a*x)**3)","A"
118,0,0,0,0.000000," ","integrate(1/x**2/LambertW(a*x)**3,x)","\int \frac{1}{x^{2} \operatorname{LambertW}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**2*LambertW(a*x)**3), x)","F"
119,0,0,0,0.000000," ","integrate(1/x**3/LambertW(a*x)**3,x)","\int \frac{1}{x^{3} \operatorname{LambertW}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**3*LambertW(a*x)**3), x)","F"
120,0,0,0,0.000000," ","integrate(x**3*(c*LambertW(a*x))**(1/2),x)","\int x^{3} \sqrt{c \operatorname{LambertW}{\left(a x \right)}}\, dx"," ",0,"Integral(x**3*sqrt(c*LambertW(a*x)), x)","F"
121,0,0,0,0.000000," ","integrate(x**2*(c*LambertW(a*x))**(1/2),x)","\int x^{2} \sqrt{c \operatorname{LambertW}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2*sqrt(c*LambertW(a*x)), x)","F"
122,0,0,0,0.000000," ","integrate(x*(c*LambertW(a*x))**(1/2),x)","\int x \sqrt{c \operatorname{LambertW}{\left(a x \right)}}\, dx"," ",0,"Integral(x*sqrt(c*LambertW(a*x)), x)","F"
123,0,0,0,0.000000," ","integrate((c*LambertW(a*x))**(1/2),x)","\int \sqrt{c \operatorname{LambertW}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*LambertW(a*x)), x)","F"
124,0,0,0,0.000000," ","integrate((c*LambertW(a*x))**(1/2)/x,x)","\int \frac{\sqrt{c \operatorname{LambertW}{\left(a x \right)}}}{x}\, dx"," ",0,"Integral(sqrt(c*LambertW(a*x))/x, x)","F"
125,0,0,0,0.000000," ","integrate((c*LambertW(a*x))**(1/2)/x**2,x)","\int \frac{\sqrt{c \operatorname{LambertW}{\left(a x \right)}}}{x^{2}}\, dx"," ",0,"Integral(sqrt(c*LambertW(a*x))/x**2, x)","F"
126,0,0,0,0.000000," ","integrate((c*LambertW(a*x))**(1/2)/x**3,x)","\int \frac{\sqrt{c \operatorname{LambertW}{\left(a x \right)}}}{x^{3}}\, dx"," ",0,"Integral(sqrt(c*LambertW(a*x))/x**3, x)","F"
127,0,0,0,0.000000," ","integrate((c*LambertW(a*x))**(1/2)/x**4,x)","\int \frac{\sqrt{c \operatorname{LambertW}{\left(a x \right)}}}{x^{4}}\, dx"," ",0,"Integral(sqrt(c*LambertW(a*x))/x**4, x)","F"
128,0,0,0,0.000000," ","integrate((c*LambertW(a*x))**(1/2)/x**5,x)","\int \frac{\sqrt{c \operatorname{LambertW}{\left(a x \right)}}}{x^{5}}\, dx"," ",0,"Integral(sqrt(c*LambertW(a*x))/x**5, x)","F"
129,0,0,0,0.000000," ","integrate((c*LambertW(a*x))**(1/2)/x**6,x)","\int \frac{\sqrt{c \operatorname{LambertW}{\left(a x \right)}}}{x^{6}}\, dx"," ",0,"Integral(sqrt(c*LambertW(a*x))/x**6, x)","F"
130,0,0,0,0.000000," ","integrate(x**4/(c*LambertW(a*x))**(1/2),x)","\int \frac{x^{4}}{\sqrt{c \operatorname{LambertW}{\left(a x \right)}}}\, dx"," ",0,"Integral(x**4/sqrt(c*LambertW(a*x)), x)","F"
131,0,0,0,0.000000," ","integrate(x**3/(c*LambertW(a*x))**(1/2),x)","\int \frac{x^{3}}{\sqrt{c \operatorname{LambertW}{\left(a x \right)}}}\, dx"," ",0,"Integral(x**3/sqrt(c*LambertW(a*x)), x)","F"
132,0,0,0,0.000000," ","integrate(x**2/(c*LambertW(a*x))**(1/2),x)","\int \frac{x^{2}}{\sqrt{c \operatorname{LambertW}{\left(a x \right)}}}\, dx"," ",0,"Integral(x**2/sqrt(c*LambertW(a*x)), x)","F"
133,0,0,0,0.000000," ","integrate(x/(c*LambertW(a*x))**(1/2),x)","\int \frac{x}{\sqrt{c \operatorname{LambertW}{\left(a x \right)}}}\, dx"," ",0,"Integral(x/sqrt(c*LambertW(a*x)), x)","F"
134,0,0,0,0.000000," ","integrate(1/(c*LambertW(a*x))**(1/2),x)","\int \frac{1}{\sqrt{c \operatorname{LambertW}{\left(a x \right)}}}\, dx"," ",0,"Integral(1/sqrt(c*LambertW(a*x)), x)","F"
135,1,29,0,2.122576," ","integrate(1/x/(c*LambertW(a*x))**(1/2),x)","\frac{2 \sqrt{\operatorname{LambertW}{\left(a x \right)}}}{\sqrt{c}} - \frac{2}{\sqrt{c} \sqrt{\operatorname{LambertW}{\left(a x \right)}}}"," ",0,"2*sqrt(LambertW(a*x))/sqrt(c) - 2/(sqrt(c)*sqrt(LambertW(a*x)))","A"
136,0,0,0,0.000000," ","integrate(1/x**2/(c*LambertW(a*x))**(1/2),x)","\int \frac{1}{x^{2} \sqrt{c \operatorname{LambertW}{\left(a x \right)}}}\, dx"," ",0,"Integral(1/(x**2*sqrt(c*LambertW(a*x))), x)","F"
137,0,0,0,0.000000," ","integrate(1/x**3/(c*LambertW(a*x))**(1/2),x)","\int \frac{1}{x^{3} \sqrt{c \operatorname{LambertW}{\left(a x \right)}}}\, dx"," ",0,"Integral(1/(x**3*sqrt(c*LambertW(a*x))), x)","F"
138,0,0,0,0.000000," ","integrate(1/x**4/(c*LambertW(a*x))**(1/2),x)","\int \frac{1}{x^{4} \sqrt{c \operatorname{LambertW}{\left(a x \right)}}}\, dx"," ",0,"Integral(1/(x**4*sqrt(c*LambertW(a*x))), x)","F"
139,0,0,0,0.000000," ","integrate(1/x**5/(c*LambertW(a*x))**(1/2),x)","\int \frac{1}{x^{5} \sqrt{c \operatorname{LambertW}{\left(a x \right)}}}\, dx"," ",0,"Integral(1/(x**5*sqrt(c*LambertW(a*x))), x)","F"
140,0,0,0,0.000000," ","integrate(x**2*(c*LambertW(a*x))**p,x)","\int x^{2} \left(c \operatorname{LambertW}{\left(a x \right)}\right)^{p}\, dx"," ",0,"Integral(x**2*(c*LambertW(a*x))**p, x)","F"
141,0,0,0,0.000000," ","integrate(x*(c*LambertW(a*x))**p,x)","\int x \left(c \operatorname{LambertW}{\left(a x \right)}\right)^{p}\, dx"," ",0,"Integral(x*(c*LambertW(a*x))**p, x)","F"
142,0,0,0,0.000000," ","integrate((c*LambertW(a*x))**p/x,x)","\int \frac{\left(c \operatorname{LambertW}{\left(a x \right)}\right)^{p}}{x}\, dx"," ",0,"Integral((c*LambertW(a*x))**p/x, x)","F"
143,0,0,0,0.000000," ","integrate((c*LambertW(a*x))**p/x**2,x)","\int \frac{\left(c \operatorname{LambertW}{\left(a x \right)}\right)^{p}}{x^{2}}\, dx"," ",0,"Integral((c*LambertW(a*x))**p/x**2, x)","F"
144,0,0,0,0.000000," ","integrate((c*LambertW(a*x))**p/x**3,x)","\int \frac{\left(c \operatorname{LambertW}{\left(a x \right)}\right)^{p}}{x^{3}}\, dx"," ",0,"Integral((c*LambertW(a*x))**p/x**3, x)","F"
145,0,0,0,0.000000," ","integrate(x**m*LambertW(a*x),x)","\int x^{m} \operatorname{LambertW}{\left(a x \right)}\, dx"," ",0,"Integral(x**m*LambertW(a*x), x)","F"
146,0,0,0,0.000000," ","integrate(x**m*LambertW(a*x)**2,x)","\int x^{m} \operatorname{LambertW}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x**m*LambertW(a*x)**2, x)","F"
147,0,0,0,0.000000," ","integrate(x**m/LambertW(a*x),x)","\int \frac{x^{m}}{\operatorname{LambertW}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m/LambertW(a*x), x)","F"
148,0,0,0,0.000000," ","integrate(x**m/LambertW(a*x)**2,x)","\int \frac{x^{m}}{\operatorname{LambertW}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m/LambertW(a*x)**2, x)","F"
149,0,0,0,0.000000," ","integrate(x**m*(c*LambertW(a*x))**(1/2),x)","\int x^{m} \sqrt{c \operatorname{LambertW}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m*sqrt(c*LambertW(a*x)), x)","F"
150,0,0,0,0.000000," ","integrate(x**m/(c*LambertW(a*x))**(1/2),x)","\int \frac{x^{m}}{\sqrt{c \operatorname{LambertW}{\left(a x \right)}}}\, dx"," ",0,"Integral(x**m/sqrt(c*LambertW(a*x)), x)","F"
151,0,0,0,0.000000," ","integrate(x**m*(c*LambertW(a*x))**p,x)","\int x^{m} \left(c \operatorname{LambertW}{\left(a x \right)}\right)^{p}\, dx"," ",0,"Integral(x**m*(c*LambertW(a*x))**p, x)","F"
152,0,0,0,0.000000," ","integrate(x**4*LambertW(a*x**2),x)","\int x^{4} \operatorname{LambertW}{\left(a x^{2} \right)}\, dx"," ",0,"Integral(x**4*LambertW(a*x**2), x)","F"
153,0,0,0,0.000000," ","integrate(x**3*LambertW(a*x**2),x)","\int x^{3} \operatorname{LambertW}{\left(a x^{2} \right)}\, dx"," ",0,"Integral(x**3*LambertW(a*x**2), x)","F"
154,0,0,0,0.000000," ","integrate(x**2*LambertW(a*x**2),x)","\int x^{2} \operatorname{LambertW}{\left(a x^{2} \right)}\, dx"," ",0,"Integral(x**2*LambertW(a*x**2), x)","F"
155,1,29,0,0.886772," ","integrate(x*LambertW(a*x**2),x)","\begin{cases} \frac{x^{2} \operatorname{LambertW}{\left(a x^{2} \right)}}{2} - \frac{x^{2}}{2} + \frac{x^{2}}{2 \operatorname{LambertW}{\left(a x^{2} \right)}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**2*LambertW(a*x**2)/2 - x**2/2 + x**2/(2*LambertW(a*x**2)), Ne(a, 0)), (0, True))","A"
156,0,0,0,0.000000," ","integrate(LambertW(a*x**2),x)","\int \operatorname{LambertW}{\left(a x^{2} \right)}\, dx"," ",0,"Integral(LambertW(a*x**2), x)","F"
157,1,17,0,0.717241," ","integrate(LambertW(a*x**2)/x,x)","\frac{\operatorname{LambertW}^{2}{\left(a x^{2} \right)}}{4} + \frac{\operatorname{LambertW}{\left(a x^{2} \right)}}{2}"," ",0,"LambertW(a*x**2)**2/4 + LambertW(a*x**2)/2","A"
158,0,0,0,0.000000," ","integrate(LambertW(a*x**2)/x**2,x)","\int \frac{\operatorname{LambertW}{\left(a x^{2} \right)}}{x^{2}}\, dx"," ",0,"Integral(LambertW(a*x**2)/x**2, x)","F"
159,0,0,0,0.000000," ","integrate(LambertW(a*x**2)/x**3,x)","\int \frac{\operatorname{LambertW}{\left(a x^{2} \right)}}{x^{3}}\, dx"," ",0,"Integral(LambertW(a*x**2)/x**3, x)","F"
160,0,0,0,0.000000," ","integrate(LambertW(a*x**2)/x**4,x)","\int \frac{\operatorname{LambertW}{\left(a x^{2} \right)}}{x^{4}}\, dx"," ",0,"Integral(LambertW(a*x**2)/x**4, x)","F"
161,0,0,0,0.000000," ","integrate(LambertW(a*x**2)/x**5,x)","\int \frac{\operatorname{LambertW}{\left(a x^{2} \right)}}{x^{5}}\, dx"," ",0,"Integral(LambertW(a*x**2)/x**5, x)","F"
162,0,0,0,0.000000," ","integrate(LambertW(a*x**2)/x**6,x)","\int \frac{\operatorname{LambertW}{\left(a x^{2} \right)}}{x^{6}}\, dx"," ",0,"Integral(LambertW(a*x**2)/x**6, x)","F"
163,0,0,0,0.000000," ","integrate(LambertW(a*x**2)/x**7,x)","\int \frac{\operatorname{LambertW}{\left(a x^{2} \right)}}{x^{7}}\, dx"," ",0,"Integral(LambertW(a*x**2)/x**7, x)","F"
164,0,0,0,0.000000," ","integrate(x**3*LambertW(a*x**2)**2,x)","\int x^{3} \operatorname{LambertW}^{2}{\left(a x^{2} \right)}\, dx"," ",0,"Integral(x**3*LambertW(a*x**2)**2, x)","F"
165,0,0,0,0.000000," ","integrate(x**2*LambertW(a*x**2)**2,x)","\int x^{2} \operatorname{LambertW}^{2}{\left(a x^{2} \right)}\, dx"," ",0,"Integral(x**2*LambertW(a*x**2)**2, x)","F"
166,1,41,0,1.138077," ","integrate(x*LambertW(a*x**2)**2,x)","\begin{cases} \frac{x^{2} \operatorname{LambertW}^{2}{\left(a x^{2} \right)}}{2} - x^{2} \operatorname{LambertW}{\left(a x^{2} \right)} + 2 x^{2} - \frac{2 x^{2}}{\operatorname{LambertW}{\left(a x^{2} \right)}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**2*LambertW(a*x**2)**2/2 - x**2*LambertW(a*x**2) + 2*x**2 - 2*x**2/LambertW(a*x**2), Ne(a, 0)), (0, True))","A"
167,0,0,0,0.000000," ","integrate(LambertW(a*x**2)**2,x)","\int \operatorname{LambertW}^{2}{\left(a x^{2} \right)}\, dx"," ",0,"Integral(LambertW(a*x**2)**2, x)","F"
168,1,19,0,0.844939," ","integrate(LambertW(a*x**2)**2/x,x)","\frac{\operatorname{LambertW}^{3}{\left(a x^{2} \right)}}{6} + \frac{\operatorname{LambertW}^{2}{\left(a x^{2} \right)}}{4}"," ",0,"LambertW(a*x**2)**3/6 + LambertW(a*x**2)**2/4","A"
169,0,0,0,0.000000," ","integrate(LambertW(a*x**2)**2/x**2,x)","\int \frac{\operatorname{LambertW}^{2}{\left(a x^{2} \right)}}{x^{2}}\, dx"," ",0,"Integral(LambertW(a*x**2)**2/x**2, x)","F"
170,1,24,0,0.807940," ","integrate(LambertW(a*x**2)**2/x**3,x)","- \frac{\operatorname{LambertW}^{2}{\left(a x^{2} \right)}}{2 x^{2}} - \frac{\operatorname{LambertW}{\left(a x^{2} \right)}}{x^{2}}"," ",0,"-LambertW(a*x**2)**2/(2*x**2) - LambertW(a*x**2)/x**2","A"
171,0,0,0,0.000000," ","integrate(LambertW(a*x**2)**2/x**4,x)","\int \frac{\operatorname{LambertW}^{2}{\left(a x^{2} \right)}}{x^{4}}\, dx"," ",0,"Integral(LambertW(a*x**2)**2/x**4, x)","F"
172,0,0,0,0.000000," ","integrate(LambertW(a*x**2)**2/x**5,x)","\int \frac{\operatorname{LambertW}^{2}{\left(a x^{2} \right)}}{x^{5}}\, dx"," ",0,"Integral(LambertW(a*x**2)**2/x**5, x)","F"
173,0,0,0,0.000000," ","integrate(LambertW(a*x**2)**2/x**6,x)","\int \frac{\operatorname{LambertW}^{2}{\left(a x^{2} \right)}}{x^{6}}\, dx"," ",0,"Integral(LambertW(a*x**2)**2/x**6, x)","F"
174,0,0,0,0.000000," ","integrate(LambertW(a*x**2)**2/x**7,x)","\int \frac{\operatorname{LambertW}^{2}{\left(a x^{2} \right)}}{x^{7}}\, dx"," ",0,"Integral(LambertW(a*x**2)**2/x**7, x)","F"
175,0,0,0,0.000000," ","integrate(LambertW(a*x**2)**2/x**8,x)","\int \frac{\operatorname{LambertW}^{2}{\left(a x^{2} \right)}}{x^{8}}\, dx"," ",0,"Integral(LambertW(a*x**2)**2/x**8, x)","F"
176,0,0,0,0.000000," ","integrate(LambertW(a*x**2)**2/x**9,x)","\int \frac{\operatorname{LambertW}^{2}{\left(a x^{2} \right)}}{x^{9}}\, dx"," ",0,"Integral(LambertW(a*x**2)**2/x**9, x)","F"
177,0,0,0,0.000000," ","integrate(x**2*LambertW(a*x**2)**3,x)","\int x^{2} \operatorname{LambertW}^{3}{\left(a x^{2} \right)}\, dx"," ",0,"Integral(x**2*LambertW(a*x**2)**3, x)","F"
178,1,60,0,1.480479," ","integrate(x*LambertW(a*x**2)**3,x)","\begin{cases} \frac{x^{2} \operatorname{LambertW}^{3}{\left(a x^{2} \right)}}{2} - \frac{3 x^{2} \operatorname{LambertW}^{2}{\left(a x^{2} \right)}}{2} + \frac{9 x^{2} \operatorname{LambertW}{\left(a x^{2} \right)}}{2} - 9 x^{2} + \frac{9 x^{2}}{\operatorname{LambertW}{\left(a x^{2} \right)}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**2*LambertW(a*x**2)**3/2 - 3*x**2*LambertW(a*x**2)**2/2 + 9*x**2*LambertW(a*x**2)/2 - 9*x**2 + 9*x**2/LambertW(a*x**2), Ne(a, 0)), (0, True))","A"
179,0,0,0,0.000000," ","integrate(LambertW(a*x**2)**3,x)","\int \operatorname{LambertW}^{3}{\left(a x^{2} \right)}\, dx"," ",0,"Integral(LambertW(a*x**2)**3, x)","F"
180,1,19,0,0.963273," ","integrate(LambertW(a*x**2)**3/x,x)","\frac{\operatorname{LambertW}^{4}{\left(a x^{2} \right)}}{8} + \frac{\operatorname{LambertW}^{3}{\left(a x^{2} \right)}}{6}"," ",0,"LambertW(a*x**2)**4/8 + LambertW(a*x**2)**3/6","A"
181,0,0,0,0.000000," ","integrate(LambertW(a*x**2)**3/x**2,x)","\int \frac{\operatorname{LambertW}^{3}{\left(a x^{2} \right)}}{x^{2}}\, dx"," ",0,"Integral(LambertW(a*x**2)**3/x**2, x)","F"
182,1,42,0,0.836042," ","integrate(LambertW(a*x**2)**3/x**3,x)","- \frac{\operatorname{LambertW}^{3}{\left(a x^{2} \right)}}{2 x^{2}} - \frac{3 \operatorname{LambertW}^{2}{\left(a x^{2} \right)}}{2 x^{2}} - \frac{3 \operatorname{LambertW}{\left(a x^{2} \right)}}{2 x^{2}}"," ",0,"-LambertW(a*x**2)**3/(2*x**2) - 3*LambertW(a*x**2)**2/(2*x**2) - 3*LambertW(a*x**2)/(2*x**2)","A"
183,0,0,0,0.000000," ","integrate(LambertW(a*x**2)**3/x**4,x)","\int \frac{\operatorname{LambertW}^{3}{\left(a x^{2} \right)}}{x^{4}}\, dx"," ",0,"Integral(LambertW(a*x**2)**3/x**4, x)","F"
184,1,29,0,1.199040," ","integrate(LambertW(a*x**2)**3/x**5,x)","- \frac{\operatorname{LambertW}^{3}{\left(a x^{2} \right)}}{4 x^{4}} - \frac{3 \operatorname{LambertW}^{2}{\left(a x^{2} \right)}}{8 x^{4}}"," ",0,"-LambertW(a*x**2)**3/(4*x**4) - 3*LambertW(a*x**2)**2/(8*x**4)","A"
185,0,0,0,0.000000," ","integrate(LambertW(a*x**2)**3/x**6,x)","\int \frac{\operatorname{LambertW}^{3}{\left(a x^{2} \right)}}{x^{6}}\, dx"," ",0,"Integral(LambertW(a*x**2)**3/x**6, x)","F"
186,0,0,0,0.000000," ","integrate(LambertW(a*x**2)**3/x**7,x)","\int \frac{\operatorname{LambertW}^{3}{\left(a x^{2} \right)}}{x^{7}}\, dx"," ",0,"Integral(LambertW(a*x**2)**3/x**7, x)","F"
187,0,0,0,0.000000," ","integrate(LambertW(a*x**2)**3/x**8,x)","\int \frac{\operatorname{LambertW}^{3}{\left(a x^{2} \right)}}{x^{8}}\, dx"," ",0,"Integral(LambertW(a*x**2)**3/x**8, x)","F"
188,0,0,0,0.000000," ","integrate(LambertW(a*x**2)**3/x**9,x)","\int \frac{\operatorname{LambertW}^{3}{\left(a x^{2} \right)}}{x^{9}}\, dx"," ",0,"Integral(LambertW(a*x**2)**3/x**9, x)","F"
189,0,0,0,0.000000," ","integrate(x**5/LambertW(a*x**2),x)","\int \frac{x^{5}}{\operatorname{LambertW}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(x**5/LambertW(a*x**2), x)","F"
190,0,0,0,0.000000," ","integrate(x**4/LambertW(a*x**2),x)","\int \frac{x^{4}}{\operatorname{LambertW}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(x**4/LambertW(a*x**2), x)","F"
191,1,24,0,0.970023," ","integrate(x**3/LambertW(a*x**2),x)","\frac{x^{4}}{4 \operatorname{LambertW}{\left(a x^{2} \right)}} + \frac{x^{4}}{8 \operatorname{LambertW}^{2}{\left(a x^{2} \right)}}"," ",0,"x**4/(4*LambertW(a*x**2)) + x**4/(8*LambertW(a*x**2)**2)","A"
192,0,0,0,0.000000," ","integrate(x**2/LambertW(a*x**2),x)","\int \frac{x^{2}}{\operatorname{LambertW}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(x**2/LambertW(a*x**2), x)","F"
193,0,0,0,0.000000," ","integrate(x/LambertW(a*x**2),x)","\int \frac{x}{\operatorname{LambertW}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(x/LambertW(a*x**2), x)","F"
194,0,0,0,0.000000," ","integrate(1/LambertW(a*x**2),x)","\int \frac{1}{\operatorname{LambertW}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(1/LambertW(a*x**2), x)","F"
195,1,20,0,0.759190," ","integrate(1/x/LambertW(a*x**2),x)","\log{\left(x \right)} - \frac{\operatorname{LambertW}{\left(a x^{2} \right)}}{2} - \frac{1}{2 \operatorname{LambertW}{\left(a x^{2} \right)}}"," ",0,"log(x) - LambertW(a*x**2)/2 - 1/(2*LambertW(a*x**2))","A"
196,0,0,0,0.000000," ","integrate(1/x**2/LambertW(a*x**2),x)","\int \frac{1}{x^{2} \operatorname{LambertW}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(1/(x**2*LambertW(a*x**2)), x)","F"
197,0,0,0,0.000000," ","integrate(1/x**3/LambertW(a*x**2),x)","\int \frac{1}{x^{3} \operatorname{LambertW}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(1/(x**3*LambertW(a*x**2)), x)","F"
198,0,0,0,0.000000," ","integrate(1/x**4/LambertW(a*x**2),x)","\int \frac{1}{x^{4} \operatorname{LambertW}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(1/(x**4*LambertW(a*x**2)), x)","F"
199,0,0,0,0.000000," ","integrate(1/x**5/LambertW(a*x**2),x)","\int \frac{1}{x^{5} \operatorname{LambertW}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(1/(x**5*LambertW(a*x**2)), x)","F"
200,0,0,0,0.000000," ","integrate(x**7/LambertW(a*x**2)**2,x)","\int \frac{x^{7}}{\operatorname{LambertW}^{2}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(x**7/LambertW(a*x**2)**2, x)","F"
201,0,0,0,0.000000," ","integrate(x**6/LambertW(a*x**2)**2,x)","\int \frac{x^{6}}{\operatorname{LambertW}^{2}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(x**6/LambertW(a*x**2)**2, x)","F"
202,1,26,0,1.368140," ","integrate(x**5/LambertW(a*x**2)**2,x)","\frac{x^{6}}{6 \operatorname{LambertW}^{2}{\left(a x^{2} \right)}} + \frac{x^{6}}{9 \operatorname{LambertW}^{3}{\left(a x^{2} \right)}}"," ",0,"x**6/(6*LambertW(a*x**2)**2) + x**6/(9*LambertW(a*x**2)**3)","A"
203,0,0,0,0.000000," ","integrate(x**4/LambertW(a*x**2)**2,x)","\int \frac{x^{4}}{\operatorname{LambertW}^{2}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(x**4/LambertW(a*x**2)**2, x)","F"
204,0,0,0,0.000000," ","integrate(x**3/LambertW(a*x**2)**2,x)","\int \frac{x^{3}}{\operatorname{LambertW}^{2}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(x**3/LambertW(a*x**2)**2, x)","F"
205,0,0,0,0.000000," ","integrate(x**2/LambertW(a*x**2)**2,x)","\int \frac{x^{2}}{\operatorname{LambertW}^{2}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(x**2/LambertW(a*x**2)**2, x)","F"
206,0,0,0,0.000000," ","integrate(x/LambertW(a*x**2)**2,x)","\int \frac{x}{\operatorname{LambertW}^{2}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(x/LambertW(a*x**2)**2, x)","F"
207,0,0,0,0.000000," ","integrate(1/LambertW(a*x**2)**2,x)","\int \frac{1}{\operatorname{LambertW}^{2}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(LambertW(a*x**2)**(-2), x)","F"
208,1,22,0,0.975764," ","integrate(1/x/LambertW(a*x**2)**2,x)","- \frac{1}{2 \operatorname{LambertW}{\left(a x^{2} \right)}} - \frac{1}{4 \operatorname{LambertW}^{2}{\left(a x^{2} \right)}}"," ",0,"-1/(2*LambertW(a*x**2)) - 1/(4*LambertW(a*x**2)**2)","A"
209,0,0,0,0.000000," ","integrate(1/x**2/LambertW(a*x**2)**2,x)","\int \frac{1}{x^{2} \operatorname{LambertW}^{2}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(1/(x**2*LambertW(a*x**2)**2), x)","F"
210,0,0,0,0.000000," ","integrate(1/x**3/LambertW(a*x**2)**2,x)","\int \frac{1}{x^{3} \operatorname{LambertW}^{2}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(1/(x**3*LambertW(a*x**2)**2), x)","F"
211,0,0,0,0.000000," ","integrate(x**7*(c*LambertW(a*x**2))**(1/2),x)","\int x^{7} \sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(x**7*sqrt(c*LambertW(a*x**2)), x)","F"
212,0,0,0,0.000000," ","integrate(x**6*(c*LambertW(a*x**2))**(1/2),x)","\int x^{6} \sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(x**6*sqrt(c*LambertW(a*x**2)), x)","F"
213,0,0,0,0.000000," ","integrate(x**5*(c*LambertW(a*x**2))**(1/2),x)","\int x^{5} \sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(x**5*sqrt(c*LambertW(a*x**2)), x)","F"
214,0,0,0,0.000000," ","integrate(x**4*(c*LambertW(a*x**2))**(1/2),x)","\int x^{4} \sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(x**4*sqrt(c*LambertW(a*x**2)), x)","F"
215,0,0,0,0.000000," ","integrate(x**3*(c*LambertW(a*x**2))**(1/2),x)","\int x^{3} \sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(x**3*sqrt(c*LambertW(a*x**2)), x)","F"
216,0,0,0,0.000000," ","integrate(x**2*(c*LambertW(a*x**2))**(1/2),x)","\int x^{2} \sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(x**2*sqrt(c*LambertW(a*x**2)), x)","F"
217,0,0,0,0.000000," ","integrate(x*(c*LambertW(a*x**2))**(1/2),x)","\int x \sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}\, dx"," ",0,"Integral(x*sqrt(c*LambertW(a*x**2)), x)","F"
218,1,34,0,1.417893," ","integrate((c*LambertW(a*x**2))**(1/2),x)","\begin{cases} \sqrt{c} x \sqrt{\operatorname{LambertW}{\left(a x^{2} \right)}} - \frac{\sqrt{c} x}{\sqrt{\operatorname{LambertW}{\left(a x^{2} \right)}}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(c)*x*sqrt(LambertW(a*x**2)) - sqrt(c)*x/sqrt(LambertW(a*x**2)), Ne(a, 0)), (0, True))","A"
219,0,0,0,0.000000," ","integrate((c*LambertW(a*x**2))**(1/2)/x,x)","\int \frac{\sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}{x}\, dx"," ",0,"Integral(sqrt(c*LambertW(a*x**2))/x, x)","F"
220,0,0,0,0.000000," ","integrate((c*LambertW(a*x**2))**(1/2)/x**2,x)","\int \frac{\sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}{x^{2}}\, dx"," ",0,"Integral(sqrt(c*LambertW(a*x**2))/x**2, x)","F"
221,0,0,0,0.000000," ","integrate((c*LambertW(a*x**2))**(1/2)/x**3,x)","\int \frac{\sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}{x^{3}}\, dx"," ",0,"Integral(sqrt(c*LambertW(a*x**2))/x**3, x)","F"
222,0,0,0,0.000000," ","integrate((c*LambertW(a*x**2))**(1/2)/x**4,x)","\int \frac{\sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}{x^{4}}\, dx"," ",0,"Integral(sqrt(c*LambertW(a*x**2))/x**4, x)","F"
223,0,0,0,0.000000," ","integrate((c*LambertW(a*x**2))**(1/2)/x**5,x)","\int \frac{\sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}{x^{5}}\, dx"," ",0,"Integral(sqrt(c*LambertW(a*x**2))/x**5, x)","F"
224,0,0,0,0.000000," ","integrate((c*LambertW(a*x**2))**(1/2)/x**6,x)","\int \frac{\sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}{x^{6}}\, dx"," ",0,"Integral(sqrt(c*LambertW(a*x**2))/x**6, x)","F"
225,0,0,0,0.000000," ","integrate((c*LambertW(a*x**2))**(1/2)/x**7,x)","\int \frac{\sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}{x^{7}}\, dx"," ",0,"Integral(sqrt(c*LambertW(a*x**2))/x**7, x)","F"
226,0,0,0,0.000000," ","integrate(x**7/(c*LambertW(a*x**2))**(1/2),x)","\int \frac{x^{7}}{\sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}\, dx"," ",0,"Integral(x**7/sqrt(c*LambertW(a*x**2)), x)","F"
227,0,0,0,0.000000," ","integrate(x**6/(c*LambertW(a*x**2))**(1/2),x)","\int \frac{x^{6}}{\sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}\, dx"," ",0,"Integral(x**6/sqrt(c*LambertW(a*x**2)), x)","F"
228,0,0,0,0.000000," ","integrate(x**5/(c*LambertW(a*x**2))**(1/2),x)","\int \frac{x^{5}}{\sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}\, dx"," ",0,"Integral(x**5/sqrt(c*LambertW(a*x**2)), x)","F"
229,0,0,0,0.000000," ","integrate(x**4/(c*LambertW(a*x**2))**(1/2),x)","\int \frac{x^{4}}{\sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}\, dx"," ",0,"Integral(x**4/sqrt(c*LambertW(a*x**2)), x)","F"
230,0,0,0,0.000000," ","integrate(x**3/(c*LambertW(a*x**2))**(1/2),x)","\int \frac{x^{3}}{\sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}\, dx"," ",0,"Integral(x**3/sqrt(c*LambertW(a*x**2)), x)","F"
231,1,39,0,2.207061," ","integrate(x**2/(c*LambertW(a*x**2))**(1/2),x)","\frac{x^{3}}{3 \sqrt{c} \sqrt{\operatorname{LambertW}{\left(a x^{2} \right)}}} + \frac{x^{3}}{9 \sqrt{c} \operatorname{LambertW}^{\frac{3}{2}}{\left(a x^{2} \right)}}"," ",0,"x**3/(3*sqrt(c)*sqrt(LambertW(a*x**2))) + x**3/(9*sqrt(c)*LambertW(a*x**2)**(3/2))","A"
232,0,0,0,0.000000," ","integrate(x/(c*LambertW(a*x**2))**(1/2),x)","\int \frac{x}{\sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}\, dx"," ",0,"Integral(x/sqrt(c*LambertW(a*x**2)), x)","F"
233,0,0,0,0.000000," ","integrate(1/(c*LambertW(a*x**2))**(1/2),x)","\int \frac{1}{\sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}\, dx"," ",0,"Integral(1/sqrt(c*LambertW(a*x**2)), x)","F"
234,1,31,0,2.120593," ","integrate(1/x/(c*LambertW(a*x**2))**(1/2),x)","\frac{\sqrt{\operatorname{LambertW}{\left(a x^{2} \right)}}}{\sqrt{c}} - \frac{1}{\sqrt{c} \sqrt{\operatorname{LambertW}{\left(a x^{2} \right)}}}"," ",0,"sqrt(LambertW(a*x**2))/sqrt(c) - 1/(sqrt(c)*sqrt(LambertW(a*x**2)))","A"
235,0,0,0,0.000000," ","integrate(1/x**2/(c*LambertW(a*x**2))**(1/2),x)","\int \frac{1}{x^{2} \sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}\, dx"," ",0,"Integral(1/(x**2*sqrt(c*LambertW(a*x**2))), x)","F"
236,0,0,0,0.000000," ","integrate(1/x**3/(c*LambertW(a*x**2))**(1/2),x)","\int \frac{1}{x^{3} \sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}\, dx"," ",0,"Integral(1/(x**3*sqrt(c*LambertW(a*x**2))), x)","F"
237,0,0,0,0.000000," ","integrate(1/x**4/(c*LambertW(a*x**2))**(1/2),x)","\int \frac{1}{x^{4} \sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}\, dx"," ",0,"Integral(1/(x**4*sqrt(c*LambertW(a*x**2))), x)","F"
238,0,0,0,0.000000," ","integrate(1/x**5/(c*LambertW(a*x**2))**(1/2),x)","\int \frac{1}{x^{5} \sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}\, dx"," ",0,"Integral(1/(x**5*sqrt(c*LambertW(a*x**2))), x)","F"
239,0,0,0,0.000000," ","integrate(1/x**6/(c*LambertW(a*x**2))**(1/2),x)","\int \frac{1}{x^{6} \sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}\, dx"," ",0,"Integral(1/(x**6*sqrt(c*LambertW(a*x**2))), x)","F"
240,0,0,0,0.000000," ","integrate(1/x**7/(c*LambertW(a*x**2))**(1/2),x)","\int \frac{1}{x^{7} \sqrt{c \operatorname{LambertW}{\left(a x^{2} \right)}}}\, dx"," ",0,"Integral(1/(x**7*sqrt(c*LambertW(a*x**2))), x)","F"
241,0,0,0,0.000000," ","integrate(x**2*(c*LambertW(a*x**2))**p,x)","\int x^{2} \left(c \operatorname{LambertW}{\left(a x^{2} \right)}\right)^{p}\, dx"," ",0,"Integral(x**2*(c*LambertW(a*x**2))**p, x)","F"
242,0,0,0,0.000000," ","integrate(x*(c*LambertW(a*x**2))**p,x)","\int x \left(c \operatorname{LambertW}{\left(a x^{2} \right)}\right)^{p}\, dx"," ",0,"Integral(x*(c*LambertW(a*x**2))**p, x)","F"
243,0,0,0,0.000000," ","integrate((c*LambertW(a*x**2))**p/x,x)","\int \frac{\left(c \operatorname{LambertW}{\left(a x^{2} \right)}\right)^{p}}{x}\, dx"," ",0,"Integral((c*LambertW(a*x**2))**p/x, x)","F"
244,0,0,0,0.000000," ","integrate((c*LambertW(a*x**2))**p/x**2,x)","\int \frac{\left(c \operatorname{LambertW}{\left(a x^{2} \right)}\right)^{p}}{x^{2}}\, dx"," ",0,"Integral((c*LambertW(a*x**2))**p/x**2, x)","F"
245,0,0,0,0.000000," ","integrate((c*LambertW(a*x**2))**p/x**3,x)","\int \frac{\left(c \operatorname{LambertW}{\left(a x^{2} \right)}\right)^{p}}{x^{3}}\, dx"," ",0,"Integral((c*LambertW(a*x**2))**p/x**3, x)","F"
246,0,0,0,0.000000," ","integrate(x**4*LambertW(a/x),x)","\int x^{4} \operatorname{LambertW}{\left(\frac{a}{x} \right)}\, dx"," ",0,"Integral(x**4*LambertW(a/x), x)","F"
247,0,0,0,0.000000," ","integrate(x**3*LambertW(a/x),x)","\int x^{3} \operatorname{LambertW}{\left(\frac{a}{x} \right)}\, dx"," ",0,"Integral(x**3*LambertW(a/x), x)","F"
248,0,0,0,0.000000," ","integrate(x**2*LambertW(a/x),x)","\int x^{2} \operatorname{LambertW}{\left(\frac{a}{x} \right)}\, dx"," ",0,"Integral(x**2*LambertW(a/x), x)","F"
249,0,0,0,0.000000," ","integrate(x*LambertW(a/x),x)","\int x \operatorname{LambertW}{\left(\frac{a}{x} \right)}\, dx"," ",0,"Integral(x*LambertW(a/x), x)","F"
250,0,0,0,0.000000," ","integrate(LambertW(a/x),x)","\int \operatorname{LambertW}{\left(\frac{a}{x} \right)}\, dx"," ",0,"Integral(LambertW(a/x), x)","F"
251,1,14,0,0.692675," ","integrate(LambertW(a/x)/x,x)","- \frac{\operatorname{LambertW}^{2}{\left(\frac{a}{x} \right)}}{2} - \operatorname{LambertW}{\left(\frac{a}{x} \right)}"," ",0,"-LambertW(a/x)**2/2 - LambertW(a/x)","A"
252,1,19,0,0.908151," ","integrate(LambertW(a/x)/x**2,x)","\begin{cases} - \frac{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}{x} + \frac{1}{x} - \frac{1}{x \operatorname{LambertW}{\left(\frac{a}{x} \right)}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-LambertW(a/x)/x + 1/x - 1/(x*LambertW(a/x)), Ne(a, 0)), (0, True))","A"
253,0,0,0,0.000000," ","integrate(LambertW(a/x)/x**3,x)","\int \frac{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}{x^{3}}\, dx"," ",0,"Integral(LambertW(a/x)/x**3, x)","F"
254,0,0,0,0.000000," ","integrate(LambertW(a/x)/x**4,x)","\int \frac{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}{x^{4}}\, dx"," ",0,"Integral(LambertW(a/x)/x**4, x)","F"
255,0,0,0,0.000000," ","integrate(LambertW(a/x)/x**5,x)","\int \frac{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}{x^{5}}\, dx"," ",0,"Integral(LambertW(a/x)/x**5, x)","F"
256,0,0,0,0.000000," ","integrate(x**4*LambertW(a/x)**2,x)","\int x^{4} \operatorname{LambertW}^{2}{\left(\frac{a}{x} \right)}\, dx"," ",0,"Integral(x**4*LambertW(a/x)**2, x)","F"
257,0,0,0,0.000000," ","integrate(x**3*LambertW(a/x)**2,x)","\int x^{3} \operatorname{LambertW}^{2}{\left(\frac{a}{x} \right)}\, dx"," ",0,"Integral(x**3*LambertW(a/x)**2, x)","F"
258,0,0,0,0.000000," ","integrate(x**2*LambertW(a/x)**2,x)","\int x^{2} \operatorname{LambertW}^{2}{\left(\frac{a}{x} \right)}\, dx"," ",0,"Integral(x**2*LambertW(a/x)**2, x)","F"
259,0,0,0,0.000000," ","integrate(x*LambertW(a/x)**2,x)","\int x \operatorname{LambertW}^{2}{\left(\frac{a}{x} \right)}\, dx"," ",0,"Integral(x*LambertW(a/x)**2, x)","F"
260,1,15,0,0.431741," ","integrate(LambertW(a/x)**2,x)","x \operatorname{LambertW}^{2}{\left(\frac{a}{x} \right)} + 2 x \operatorname{LambertW}{\left(\frac{a}{x} \right)}"," ",0,"x*LambertW(a/x)**2 + 2*x*LambertW(a/x)","A"
261,1,17,0,0.816361," ","integrate(LambertW(a/x)**2/x,x)","- \frac{\operatorname{LambertW}^{3}{\left(\frac{a}{x} \right)}}{3} - \frac{\operatorname{LambertW}^{2}{\left(\frac{a}{x} \right)}}{2}"," ",0,"-LambertW(a/x)**3/3 - LambertW(a/x)**2/2","A"
262,1,29,0,0.942172," ","integrate(LambertW(a/x)**2/x**2,x)","\begin{cases} - \frac{\operatorname{LambertW}^{2}{\left(\frac{a}{x} \right)}}{x} + \frac{2 \operatorname{LambertW}{\left(\frac{a}{x} \right)}}{x} - \frac{4}{x} + \frac{4}{x \operatorname{LambertW}{\left(\frac{a}{x} \right)}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-LambertW(a/x)**2/x + 2*LambertW(a/x)/x - 4/x + 4/(x*LambertW(a/x)), Ne(a, 0)), (0, True))","A"
263,0,0,0,0.000000," ","integrate(LambertW(a/x)**2/x**3,x)","\int \frac{\operatorname{LambertW}^{2}{\left(\frac{a}{x} \right)}}{x^{3}}\, dx"," ",0,"Integral(LambertW(a/x)**2/x**3, x)","F"
264,0,0,0,0.000000," ","integrate(LambertW(a/x)**2/x**4,x)","\int \frac{\operatorname{LambertW}^{2}{\left(\frac{a}{x} \right)}}{x^{4}}\, dx"," ",0,"Integral(LambertW(a/x)**2/x**4, x)","F"
265,0,0,0,0.000000," ","integrate(LambertW(a/x)**2/x**5,x)","\int \frac{\operatorname{LambertW}^{2}{\left(\frac{a}{x} \right)}}{x^{5}}\, dx"," ",0,"Integral(LambertW(a/x)**2/x**5, x)","F"
266,0,0,0,0.000000," ","integrate(x**3*LambertW(a/x)**(1/2),x)","\int x^{3} \sqrt{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}\, dx"," ",0,"Integral(x**3*sqrt(LambertW(a/x)), x)","F"
267,0,0,0,0.000000," ","integrate(x**2*LambertW(a/x)**(1/2),x)","\int x^{2} \sqrt{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}\, dx"," ",0,"Integral(x**2*sqrt(LambertW(a/x)), x)","F"
268,0,0,0,0.000000," ","integrate(x*LambertW(a/x)**(1/2),x)","\int x \sqrt{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}\, dx"," ",0,"Integral(x*sqrt(LambertW(a/x)), x)","F"
269,0,0,0,0.000000," ","integrate(LambertW(a/x)**(1/2),x)","\int \sqrt{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}\, dx"," ",0,"Integral(sqrt(LambertW(a/x)), x)","F"
270,1,22,0,1.617494," ","integrate(LambertW(a/x)**(1/2)/x,x)","- \frac{2 \operatorname{LambertW}^{\frac{3}{2}}{\left(\frac{a}{x} \right)}}{3} - 2 \sqrt{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}"," ",0,"-2*LambertW(a/x)**(3/2)/3 - 2*sqrt(LambertW(a/x))","A"
271,0,0,0,0.000000," ","integrate(LambertW(a/x)**(1/2)/x**2,x)","\int \frac{\sqrt{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}}{x^{2}}\, dx"," ",0,"Integral(sqrt(LambertW(a/x))/x**2, x)","F"
272,0,0,0,0.000000," ","integrate(LambertW(a/x)**(1/2)/x**3,x)","\int \frac{\sqrt{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}}{x^{3}}\, dx"," ",0,"Integral(sqrt(LambertW(a/x))/x**3, x)","F"
273,0,0,0,0.000000," ","integrate(LambertW(a/x)**(1/2)/x**4,x)","\int \frac{\sqrt{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}}{x^{4}}\, dx"," ",0,"Integral(sqrt(LambertW(a/x))/x**4, x)","F"
274,0,0,0,0.000000," ","integrate(x**3/LambertW(a/x)**(1/2),x)","\int \frac{x^{3}}{\sqrt{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}}\, dx"," ",0,"Integral(x**3/sqrt(LambertW(a/x)), x)","F"
275,0,0,0,0.000000," ","integrate(x**2/LambertW(a/x)**(1/2),x)","\int \frac{x^{2}}{\sqrt{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}}\, dx"," ",0,"Integral(x**2/sqrt(LambertW(a/x)), x)","F"
276,0,0,0,0.000000," ","integrate(x/LambertW(a/x)**(1/2),x)","\int \frac{x}{\sqrt{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}}\, dx"," ",0,"Integral(x/sqrt(LambertW(a/x)), x)","F"
277,0,0,0,0.000000," ","integrate(1/LambertW(a/x)**(1/2),x)","\int \frac{1}{\sqrt{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}}\, dx"," ",0,"Integral(1/sqrt(LambertW(a/x)), x)","F"
278,1,19,0,1.879349," ","integrate(1/x/LambertW(a/x)**(1/2),x)","- 2 \sqrt{\operatorname{LambertW}{\left(\frac{a}{x} \right)}} + \frac{2}{\sqrt{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}}"," ",0,"-2*sqrt(LambertW(a/x)) + 2/sqrt(LambertW(a/x))","A"
279,0,0,0,0.000000," ","integrate(1/x**2/LambertW(a/x)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}}\, dx"," ",0,"Integral(1/(x**2*sqrt(LambertW(a/x))), x)","F"
280,0,0,0,0.000000," ","integrate(1/x**3/LambertW(a/x)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}}\, dx"," ",0,"Integral(1/(x**3*sqrt(LambertW(a/x))), x)","F"
281,0,0,0,0.000000," ","integrate(1/x**4/LambertW(a/x)**(1/2),x)","\int \frac{1}{x^{4} \sqrt{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}}\, dx"," ",0,"Integral(1/(x**4*sqrt(LambertW(a/x))), x)","F"
282,0,0,0,0.000000," ","integrate(x**2*(c*LambertW(a/x))**p,x)","\int x^{2} \left(c \operatorname{LambertW}{\left(\frac{a}{x} \right)}\right)^{p}\, dx"," ",0,"Integral(x**2*(c*LambertW(a/x))**p, x)","F"
283,0,0,0,0.000000," ","integrate(x*(c*LambertW(a/x))**p,x)","\int x \left(c \operatorname{LambertW}{\left(\frac{a}{x} \right)}\right)^{p}\, dx"," ",0,"Integral(x*(c*LambertW(a/x))**p, x)","F"
284,0,0,0,0.000000," ","integrate((c*LambertW(a/x))**p/x,x)","\int \frac{\left(c \operatorname{LambertW}{\left(\frac{a}{x} \right)}\right)^{p}}{x}\, dx"," ",0,"Integral((c*LambertW(a/x))**p/x, x)","F"
285,0,0,0,0.000000," ","integrate((c*LambertW(a/x))**p/x**2,x)","\int \frac{\left(c \operatorname{LambertW}{\left(\frac{a}{x} \right)}\right)^{p}}{x^{2}}\, dx"," ",0,"Integral((c*LambertW(a/x))**p/x**2, x)","F"
286,0,0,0,0.000000," ","integrate((c*LambertW(a/x))**p/x**3,x)","\int \frac{\left(c \operatorname{LambertW}{\left(\frac{a}{x} \right)}\right)^{p}}{x^{3}}\, dx"," ",0,"Integral((c*LambertW(a/x))**p/x**3, x)","F"
287,0,0,0,0.000000," ","integrate(LambertW(a/x**(1/4))**5,x)","\int \operatorname{LambertW}^{5}{\left(\frac{a}{\sqrt[4]{x}} \right)}\, dx"," ",0,"Integral(LambertW(a/x**(1/4))**5, x)","F"
288,0,0,0,0.000000," ","integrate(LambertW(a/x**(1/3))**4,x)","\int \operatorname{LambertW}^{4}{\left(\frac{a}{\sqrt[3]{x}} \right)}\, dx"," ",0,"Integral(LambertW(a/x**(1/3))**4, x)","F"
289,0,0,0,0.000000," ","integrate(LambertW(a/x**(1/2))**3,x)","\int \operatorname{LambertW}^{3}{\left(\frac{a}{\sqrt{x}} \right)}\, dx"," ",0,"Integral(LambertW(a/sqrt(x))**3, x)","F"
290,1,15,0,0.421336," ","integrate(LambertW(a/x)**2,x)","x \operatorname{LambertW}^{2}{\left(\frac{a}{x} \right)} + 2 x \operatorname{LambertW}{\left(\frac{a}{x} \right)}"," ",0,"x*LambertW(a/x)**2 + 2*x*LambertW(a/x)","A"
291,1,22,0,1.709331," ","integrate(1/LambertW(a*x**(1/2)),x)","\frac{x}{\operatorname{LambertW}{\left(a \sqrt{x} \right)}} + \frac{x}{2 \operatorname{LambertW}^{2}{\left(a \sqrt{x} \right)}}"," ",0,"x/LambertW(a*sqrt(x)) + x/(2*LambertW(a*sqrt(x))**2)","A"
292,1,26,0,4.981287," ","integrate(1/LambertW(a*x**(1/3))**2,x)","\frac{x}{\operatorname{LambertW}^{2}{\left(a \sqrt[3]{x} \right)}} + \frac{2 x}{3 \operatorname{LambertW}^{3}{\left(a \sqrt[3]{x} \right)}}"," ",0,"x/LambertW(a*x**(1/3))**2 + 2*x/(3*LambertW(a*x**(1/3))**3)","A"
293,1,26,0,13.705815," ","integrate(1/LambertW(a*x**(1/4))**3,x)","\frac{x}{\operatorname{LambertW}^{3}{\left(a \sqrt[4]{x} \right)}} + \frac{3 x}{4 \operatorname{LambertW}^{4}{\left(a \sqrt[4]{x} \right)}}"," ",0,"x/LambertW(a*x**(1/4))**3 + 3*x/(4*LambertW(a*x**(1/4))**4)","A"
294,0,0,0,0.000000," ","integrate(LambertW(a/x**(1/5))**4,x)","\int \operatorname{LambertW}^{4}{\left(\frac{a}{\sqrt[5]{x}} \right)}\, dx"," ",0,"Integral(LambertW(a/x**(1/5))**4, x)","F"
295,0,0,0,0.000000," ","integrate(LambertW(a/x**(1/4))**3,x)","\int \operatorname{LambertW}^{3}{\left(\frac{a}{\sqrt[4]{x}} \right)}\, dx"," ",0,"Integral(LambertW(a/x**(1/4))**3, x)","F"
296,0,0,0,0.000000," ","integrate(LambertW(a/x**(1/3))**2,x)","\int \operatorname{LambertW}^{2}{\left(\frac{a}{\sqrt[3]{x}} \right)}\, dx"," ",0,"Integral(LambertW(a/x**(1/3))**2, x)","F"
297,0,0,0,0.000000," ","integrate(LambertW(a/x**(1/2)),x)","\int \operatorname{LambertW}{\left(\frac{a}{\sqrt{x}} \right)}\, dx"," ",0,"Integral(LambertW(a/sqrt(x)), x)","F"
298,0,0,0,0.000000," ","integrate(1/LambertW(a*x)**2,x)","\int \frac{1}{\operatorname{LambertW}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(LambertW(a*x)**(-2), x)","F"
299,0,0,0,0.000000," ","integrate(1/LambertW(a*x**(1/2))**3,x)","\int \frac{1}{\operatorname{LambertW}^{3}{\left(a \sqrt{x} \right)}}\, dx"," ",0,"Integral(LambertW(a*sqrt(x))**(-3), x)","F"
300,0,0,0,0.000000," ","integrate(1/LambertW(a*x**(1/3))**4,x)","\int \frac{1}{\operatorname{LambertW}^{4}{\left(a \sqrt[3]{x} \right)}}\, dx"," ",0,"Integral(LambertW(a*x**(1/3))**(-4), x)","F"
301,0,0,0,0.000000," ","integrate(1/LambertW(a*x**(1/4))**5,x)","\int \frac{1}{\operatorname{LambertW}^{5}{\left(a \sqrt[4]{x} \right)}}\, dx"," ",0,"Integral(LambertW(a*x**(1/4))**(-5), x)","F"
302,1,70,0,8.942234," ","integrate(LambertW(a*x**n)**((-1+n)/n),x)","\begin{cases} - n x \operatorname{LambertW}^{- \frac{1}{n}}{\left(a x^{n} \right)} + x \operatorname{LambertW}{\left(a x^{n} \right)} \operatorname{LambertW}^{- \frac{1}{n}}{\left(a x^{n} \right)} + x \operatorname{LambertW}^{- \frac{1}{n}}{\left(a x^{n} \right)} & \text{for}\: a \neq 0^{n} x^{- n} e^{0^{n}} \\x \operatorname{LambertW}^{\frac{n - 1}{n}}{\left(0^{n} e^{0^{n}} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-n*x*LambertW(a*x**n)**(-1/n) + x*LambertW(a*x**n)*LambertW(a*x**n)**(-1/n) + x*LambertW(a*x**n)**(-1/n), Ne(a, 0**n*x**(-n)*exp(0**n))), (x*LambertW(0**n*exp(0**n))**((n - 1)/n), True))","A"
303,1,134,0,4.027780," ","integrate(LambertW(a*x**(1/(1-p)))**p,x)","\begin{cases} \frac{p x \operatorname{LambertW}{\left(a x^{\frac{1}{1 - p}} \right)} \operatorname{LambertW}^{p}{\left(a x^{\frac{1}{1 - p}} \right)}}{p \operatorname{LambertW}{\left(a x^{\frac{1}{1 - p}} \right)} - \operatorname{LambertW}{\left(a x^{\frac{1}{1 - p}} \right)}} + \frac{p x \operatorname{LambertW}^{p}{\left(a x^{\frac{1}{1 - p}} \right)}}{p \operatorname{LambertW}{\left(a x^{\frac{1}{1 - p}} \right)} - \operatorname{LambertW}{\left(a x^{\frac{1}{1 - p}} \right)}} - \frac{x \operatorname{LambertW}{\left(a x^{\frac{1}{1 - p}} \right)} \operatorname{LambertW}^{p}{\left(a x^{\frac{1}{1 - p}} \right)}}{p \operatorname{LambertW}{\left(a x^{\frac{1}{1 - p}} \right)} - \operatorname{LambertW}{\left(a x^{\frac{1}{1 - p}} \right)}} & \text{for}\: a \neq 0 \\0^{p} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((p*x*LambertW(a*x**(1/(1 - p)))*LambertW(a*x**(1/(1 - p)))**p/(p*LambertW(a*x**(1/(1 - p))) - LambertW(a*x**(1/(1 - p)))) + p*x*LambertW(a*x**(1/(1 - p)))**p/(p*LambertW(a*x**(1/(1 - p))) - LambertW(a*x**(1/(1 - p)))) - x*LambertW(a*x**(1/(1 - p)))*LambertW(a*x**(1/(1 - p)))**p/(p*LambertW(a*x**(1/(1 - p))) - LambertW(a*x**(1/(1 - p)))), Ne(a, 0)), (0**p*x, True))","A"
304,-1,0,0,0.000000," ","integrate(x**(-1-n)*(c*LambertW(a*x**n))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
305,-1,0,0,0.000000," ","integrate(x**(-1-n)*(c*LambertW(a*x**n))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
306,-1,0,0,0.000000," ","integrate(x**(-1-n)*(c*LambertW(a*x**n))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
307,-1,0,0,0.000000," ","integrate(x**(-1-n)*(c*LambertW(a*x**n))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
308,-1,0,0,0.000000," ","integrate(x**(-1-n)*(c*LambertW(a*x**n))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
309,-1,0,0,0.000000," ","integrate(x**(-1-n)/(c*LambertW(a*x**n))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
310,-1,0,0,0.000000," ","integrate(x**(-1-n)/(c*LambertW(a*x**n))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
311,-1,0,0,0.000000," ","integrate(x**(-1-n)/(c*LambertW(a*x**n))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
312,-1,0,0,0.000000," ","integrate(x**(-1-2*n)*(c*LambertW(a*x**n))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
313,-1,0,0,0.000000," ","integrate(x**(-1-2*n)*(c*LambertW(a*x**n))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
314,-1,0,0,0.000000," ","integrate(x**(-1-2*n)*(c*LambertW(a*x**n))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
315,-1,0,0,0.000000," ","integrate(x**(-1-2*n)*(c*LambertW(a*x**n))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
316,-1,0,0,0.000000," ","integrate(x**(-1-2*n)*(c*LambertW(a*x**n))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
317,-1,0,0,0.000000," ","integrate(x**(-1-2*n)*(c*LambertW(a*x**n))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
318,-1,0,0,0.000000," ","integrate(x**(-1-2*n)/(c*LambertW(a*x**n))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
319,-1,0,0,0.000000," ","integrate(x**(-1-2*n)/(c*LambertW(a*x**n))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
320,-1,0,0,0.000000," ","integrate(x**(-1+n)*(c*LambertW(a*x**n))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
321,-1,0,0,0.000000," ","integrate(x**(-1+n)*(c*LambertW(a*x**n))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
322,-1,0,0,0.000000," ","integrate(x**(-1+n)*(c*LambertW(a*x**n))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
323,0,0,0,0.000000," ","integrate(x**(-1+n)/(c*LambertW(a*x**n))**(1/2),x)","\int \frac{x^{n - 1}}{\sqrt{c \operatorname{LambertW}{\left(a x^{n} \right)}}}\, dx"," ",0,"Integral(x**(n - 1)/sqrt(c*LambertW(a*x**n)), x)","F"
324,-1,0,0,0.000000," ","integrate(x**(-1+n)/(c*LambertW(a*x**n))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
325,-1,0,0,0.000000," ","integrate(x**(-1+n)/(c*LambertW(a*x**n))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
326,-1,0,0,0.000000," ","integrate(x**(-1+n)/(c*LambertW(a*x**n))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
327,-1,0,0,0.000000," ","integrate(x**(-1+n)/(c*LambertW(a*x**n))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
328,-1,0,0,0.000000," ","integrate(x**(-1+2*n)*(c*LambertW(a*x**n))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
329,-1,0,0,0.000000," ","integrate(x**(-1+2*n)*(c*LambertW(a*x**n))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
330,-1,0,0,0.000000," ","integrate(x**(-1+2*n)/(c*LambertW(a*x**n))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
331,-1,0,0,0.000000," ","integrate(x**(-1+2*n)/(c*LambertW(a*x**n))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
332,-1,0,0,0.000000," ","integrate(x**(-1+2*n)/(c*LambertW(a*x**n))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
333,-1,0,0,0.000000," ","integrate(x**(-1+2*n)/(c*LambertW(a*x**n))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
334,-1,0,0,0.000000," ","integrate(x**(-1+2*n)/(c*LambertW(a*x**n))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
335,-1,0,0,0.000000," ","integrate(x**(-1+2*n)/(c*LambertW(a*x**n))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
336,-1,0,0,0.000000," ","integrate(x**(-1-3*n)*LambertW(a*x**n)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
337,-1,0,0,0.000000," ","integrate(x**(-1-2*n)*LambertW(a*x**n)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
338,-1,0,0,0.000000," ","integrate(x**(-1-n)*LambertW(a*x**n)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
339,0,0,0,0.000000," ","integrate(x**(-1+2*n)/LambertW(a*x**n),x)","\int \frac{x^{2 n - 1}}{\operatorname{LambertW}{\left(a x^{n} \right)}}\, dx"," ",0,"Integral(x**(2*n - 1)/LambertW(a*x**n), x)","F"
340,-1,0,0,0.000000," ","integrate(x**(-1+3*n)/LambertW(a*x**n)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
341,-1,0,0,0.000000," ","integrate(x**(-1+4*n)/LambertW(a*x**n)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
342,-1,0,0,0.000000," ","integrate(x**(-1-n*(1+p))*(c*LambertW(a*x**n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
343,-1,0,0,0.000000," ","integrate(x**(-n*p-1)*(c*LambertW(a*x**n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
344,-1,0,0,0.000000," ","integrate(x**(-1+n*(1-p))*(c*LambertW(a*x**n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
345,-1,0,0,0.000000," ","integrate(x**(-1+n*(2-p))*(c*LambertW(a*x**n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
346,-1,0,0,0.000000," ","integrate(x**(-1+n*(3-p))*(c*LambertW(a*x**n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)"
347,0,0,0,0.000000," ","integrate(x**3/(1+LambertW(a*x)),x)","\int \frac{x^{3}}{\operatorname{LambertW}{\left(a x \right)} + 1}\, dx"," ",0,"Integral(x**3/(LambertW(a*x) + 1), x)","F"
348,0,0,0,0.000000," ","integrate(x**2/(1+LambertW(a*x)),x)","\int \frac{x^{2}}{\operatorname{LambertW}{\left(a x \right)} + 1}\, dx"," ",0,"Integral(x**2/(LambertW(a*x) + 1), x)","F"
349,0,0,0,0.000000," ","integrate(x/(1+LambertW(a*x)),x)","\int \frac{x}{\operatorname{LambertW}{\left(a x \right)} + 1}\, dx"," ",0,"Integral(x/(LambertW(a*x) + 1), x)","F"
350,1,7,0,0.788626," ","integrate(1/(1+LambertW(a*x)),x)","\begin{cases} \frac{x}{\operatorname{LambertW}{\left(a x \right)}} & \text{for}\: a \neq 0 \\x & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/LambertW(a*x), Ne(a, 0)), (x, True))","A"
351,1,5,0,0.485173," ","integrate(1/x/(1+LambertW(a*x)),x)","\log{\left(\operatorname{LambertW}{\left(a x \right)} \right)}"," ",0,"log(LambertW(a*x))","A"
352,0,0,0,0.000000," ","integrate(1/x**2/(1+LambertW(a*x)),x)","\int \frac{1}{x^{2} \left(\operatorname{LambertW}{\left(a x \right)} + 1\right)}\, dx"," ",0,"Integral(1/(x**2*(LambertW(a*x) + 1)), x)","F"
353,0,0,0,0.000000," ","integrate(1/x**3/(1+LambertW(a*x)),x)","\int \frac{1}{x^{3} \left(\operatorname{LambertW}{\left(a x \right)} + 1\right)}\, dx"," ",0,"Integral(1/(x**3*(LambertW(a*x) + 1)), x)","F"
354,0,0,0,0.000000," ","integrate(1/x**4/(1+LambertW(a*x)),x)","\int \frac{1}{x^{4} \left(\operatorname{LambertW}{\left(a x \right)} + 1\right)}\, dx"," ",0,"Integral(1/(x**4*(LambertW(a*x) + 1)), x)","F"
355,0,0,0,0.000000," ","integrate(x**3/(1+LambertW(a*x**2)),x)","\int \frac{x^{3}}{\operatorname{LambertW}{\left(a x^{2} \right)} + 1}\, dx"," ",0,"Integral(x**3/(LambertW(a*x**2) + 1), x)","F"
356,0,0,0,0.000000," ","integrate(x**2/(1+LambertW(a*x**2)),x)","\int \frac{x^{2}}{\operatorname{LambertW}{\left(a x^{2} \right)} + 1}\, dx"," ",0,"Integral(x**2/(LambertW(a*x**2) + 1), x)","F"
357,1,15,0,0.776994," ","integrate(x/(1+LambertW(a*x**2)),x)","\begin{cases} \frac{x^{2}}{2 \operatorname{LambertW}{\left(a x^{2} \right)}} & \text{for}\: a \neq 0 \\\frac{x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**2/(2*LambertW(a*x**2)), Ne(a, 0)), (x**2/2, True))","A"
358,0,0,0,0.000000," ","integrate(1/(1+LambertW(a*x**2)),x)","\int \frac{1}{\operatorname{LambertW}{\left(a x^{2} \right)} + 1}\, dx"," ",0,"Integral(1/(LambertW(a*x**2) + 1), x)","F"
359,1,10,0,0.443545," ","integrate(1/x/(1+LambertW(a*x**2)),x)","\log{\left(x \right)} - \frac{\operatorname{LambertW}{\left(a x^{2} \right)}}{2}"," ",0,"log(x) - LambertW(a*x**2)/2","A"
360,0,0,0,0.000000," ","integrate(1/x**2/(1+LambertW(a*x**2)),x)","\int \frac{1}{x^{2} \left(\operatorname{LambertW}{\left(a x^{2} \right)} + 1\right)}\, dx"," ",0,"Integral(1/(x**2*(LambertW(a*x**2) + 1)), x)","F"
361,0,0,0,0.000000," ","integrate(1/x**3/(1+LambertW(a*x**2)),x)","\int \frac{1}{x^{3} \left(\operatorname{LambertW}{\left(a x^{2} \right)} + 1\right)}\, dx"," ",0,"Integral(1/(x**3*(LambertW(a*x**2) + 1)), x)","F"
362,0,0,0,0.000000," ","integrate(1/x**4/(1+LambertW(a*x**2)),x)","\int \frac{1}{x^{4} \left(\operatorname{LambertW}{\left(a x^{2} \right)} + 1\right)}\, dx"," ",0,"Integral(1/(x**4*(LambertW(a*x**2) + 1)), x)","F"
363,0,0,0,0.000000," ","integrate(x**3/(1+LambertW(a/x)),x)","\int \frac{x^{3}}{\operatorname{LambertW}{\left(\frac{a}{x} \right)} + 1}\, dx"," ",0,"Integral(x**3/(LambertW(a/x) + 1), x)","F"
364,0,0,0,0.000000," ","integrate(x**2/(1+LambertW(a/x)),x)","\int \frac{x^{2}}{\operatorname{LambertW}{\left(\frac{a}{x} \right)} + 1}\, dx"," ",0,"Integral(x**2/(LambertW(a/x) + 1), x)","F"
365,0,0,0,0.000000," ","integrate(x/(1+LambertW(a/x)),x)","\int \frac{x}{\operatorname{LambertW}{\left(\frac{a}{x} \right)} + 1}\, dx"," ",0,"Integral(x/(LambertW(a/x) + 1), x)","F"
366,0,0,0,0.000000," ","integrate(1/(1+LambertW(a/x)),x)","\int \frac{1}{\operatorname{LambertW}{\left(\frac{a}{x} \right)} + 1}\, dx"," ",0,"Integral(1/(LambertW(a/x) + 1), x)","F"
367,1,7,0,0.444364," ","integrate(1/x/(1+LambertW(a/x)),x)","\log{\left(x \right)} + \operatorname{LambertW}{\left(\frac{a}{x} \right)}"," ",0,"log(x) + LambertW(a/x)","A"
368,1,14,0,1.257097," ","integrate(1/x**2/(1+LambertW(a/x)),x)","\begin{cases} - \frac{1}{x \operatorname{LambertW}{\left(\frac{a}{x} \right)}} & \text{for}\: a \neq 0 \\- \frac{1}{x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(x*LambertW(a/x)), Ne(a, 0)), (-1/x, True))","A"
369,0,0,0,0.000000," ","integrate(1/x**3/(1+LambertW(a/x)),x)","\int \frac{1}{x^{3} \left(\operatorname{LambertW}{\left(\frac{a}{x} \right)} + 1\right)}\, dx"," ",0,"Integral(1/(x**3*(LambertW(a/x) + 1)), x)","F"
370,0,0,0,0.000000," ","integrate(1/x**4/(1+LambertW(a/x)),x)","\int \frac{1}{x^{4} \left(\operatorname{LambertW}{\left(\frac{a}{x} \right)} + 1\right)}\, dx"," ",0,"Integral(1/(x**4*(LambertW(a/x) + 1)), x)","F"
371,0,0,0,0.000000," ","integrate(x**5/(1+LambertW(a/x**2)),x)","\int \frac{x^{5}}{\operatorname{LambertW}{\left(\frac{a}{x^{2}} \right)} + 1}\, dx"," ",0,"Integral(x**5/(LambertW(a/x**2) + 1), x)","F"
372,0,0,0,0.000000," ","integrate(x**3/(1+LambertW(a/x**2)),x)","\int \frac{x^{3}}{\operatorname{LambertW}{\left(\frac{a}{x^{2}} \right)} + 1}\, dx"," ",0,"Integral(x**3/(LambertW(a/x**2) + 1), x)","F"
373,0,0,0,0.000000," ","integrate(x/(1+LambertW(a/x**2)),x)","\int \frac{x}{\operatorname{LambertW}{\left(\frac{a}{x^{2}} \right)} + 1}\, dx"," ",0,"Integral(x/(LambertW(a/x**2) + 1), x)","F"
374,1,10,0,0.666420," ","integrate(1/x/(1+LambertW(a/x**2)),x)","\log{\left(x \right)} + \frac{\operatorname{LambertW}{\left(\frac{a}{x^{2}} \right)}}{2}"," ",0,"log(x) + LambertW(a/x**2)/2","A"
375,1,22,0,1.559912," ","integrate(1/x**3/(1+LambertW(a/x**2)),x)","\begin{cases} - \frac{1}{2 x^{2} \operatorname{LambertW}{\left(\frac{a}{x^{2}} \right)}} & \text{for}\: a \neq 0 \\- \frac{1}{2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(2*x**2*LambertW(a/x**2)), Ne(a, 0)), (-1/(2*x**2), True))","A"
376,0,0,0,0.000000," ","integrate(x**4/(1+LambertW(a/x**2)),x)","\int \frac{x^{4}}{\operatorname{LambertW}{\left(\frac{a}{x^{2}} \right)} + 1}\, dx"," ",0,"Integral(x**4/(LambertW(a/x**2) + 1), x)","F"
377,0,0,0,0.000000," ","integrate(x**2/(1+LambertW(a/x**2)),x)","\int \frac{x^{2}}{\operatorname{LambertW}{\left(\frac{a}{x^{2}} \right)} + 1}\, dx"," ",0,"Integral(x**2/(LambertW(a/x**2) + 1), x)","F"
378,0,0,0,0.000000," ","integrate(1/(1+LambertW(a/x**2)),x)","\int \frac{1}{\operatorname{LambertW}{\left(\frac{a}{x^{2}} \right)} + 1}\, dx"," ",0,"Integral(1/(LambertW(a/x**2) + 1), x)","F"
379,0,0,0,0.000000," ","integrate(1/x**2/(1+LambertW(a/x**2)),x)","\int \frac{1}{x^{2} \left(\operatorname{LambertW}{\left(\frac{a}{x^{2}} \right)} + 1\right)}\, dx"," ",0,"Integral(1/(x**2*(LambertW(a/x**2) + 1)), x)","F"
380,0,0,0,0.000000," ","integrate(1/x**4/(1+LambertW(a/x**2)),x)","\int \frac{1}{x^{4} \left(\operatorname{LambertW}{\left(\frac{a}{x^{2}} \right)} + 1\right)}\, dx"," ",0,"Integral(1/(x**4*(LambertW(a/x**2) + 1)), x)","F"
381,0,0,0,0.000000," ","integrate(x**m/(d+d*LambertW(a*x)),x)","\frac{\int \frac{x^{m}}{\operatorname{LambertW}{\left(a x \right)} + 1}\, dx}{d}"," ",0,"Integral(x**m/(LambertW(a*x) + 1), x)/d","F"
382,0,0,0,0.000000," ","integrate(LambertW(a/x**(1/4))**5/(1+LambertW(a/x**(1/4))),x)","\int \frac{\operatorname{LambertW}^{5}{\left(\frac{a}{\sqrt[4]{x}} \right)}}{\operatorname{LambertW}{\left(\frac{a}{\sqrt[4]{x}} \right)} + 1}\, dx"," ",0,"Integral(LambertW(a/x**(1/4))**5/(LambertW(a/x**(1/4)) + 1), x)","F"
383,0,0,0,0.000000," ","integrate(LambertW(a/x**(1/3))**4/(1+LambertW(a/x**(1/3))),x)","\int \frac{\operatorname{LambertW}^{4}{\left(\frac{a}{\sqrt[3]{x}} \right)}}{\operatorname{LambertW}{\left(\frac{a}{\sqrt[3]{x}} \right)} + 1}\, dx"," ",0,"Integral(LambertW(a/x**(1/3))**4/(LambertW(a/x**(1/3)) + 1), x)","F"
384,1,10,0,5.526268," ","integrate(LambertW(a/x**(1/2))**3/(1+LambertW(a/x**(1/2))),x)","x \operatorname{LambertW}^{2}{\left(\frac{a}{\sqrt{x}} \right)}"," ",0,"x*LambertW(a/sqrt(x))**2","A"
385,1,5,0,0.454822," ","integrate(LambertW(a/x)**2/(1+LambertW(a/x)),x)","x \operatorname{LambertW}{\left(\frac{a}{x} \right)}"," ",0,"x*LambertW(a/x)","A"
386,1,10,0,3.139512," ","integrate(1/LambertW(a*x**(1/2))/(1+LambertW(a*x**(1/2))),x)","\frac{x}{\operatorname{LambertW}^{2}{\left(a \sqrt{x} \right)}}"," ",0,"x/LambertW(a*sqrt(x))**2","A"
387,1,10,0,8.811670," ","integrate(1/LambertW(a*x**(1/3))**2/(1+LambertW(a*x**(1/3))),x)","\frac{x}{\operatorname{LambertW}^{3}{\left(a \sqrt[3]{x} \right)}}"," ",0,"x/LambertW(a*x**(1/3))**3","A"
388,1,10,0,21.482296," ","integrate(1/LambertW(a*x**(1/4))**3/(1+LambertW(a*x**(1/4))),x)","\frac{x}{\operatorname{LambertW}^{4}{\left(a \sqrt[4]{x} \right)}}"," ",0,"x/LambertW(a*x**(1/4))**4","A"
389,0,0,0,0.000000," ","integrate(LambertW(a/x**(1/4))**4/(1+LambertW(a/x**(1/4))),x)","\int \frac{\operatorname{LambertW}^{4}{\left(\frac{a}{\sqrt[4]{x}} \right)}}{\operatorname{LambertW}{\left(\frac{a}{\sqrt[4]{x}} \right)} + 1}\, dx"," ",0,"Integral(LambertW(a/x**(1/4))**4/(LambertW(a/x**(1/4)) + 1), x)","F"
390,0,0,0,0.000000," ","integrate(LambertW(a/x**(1/3))**3/(1+LambertW(a/x**(1/3))),x)","\int \frac{\operatorname{LambertW}^{3}{\left(\frac{a}{\sqrt[3]{x}} \right)}}{\operatorname{LambertW}{\left(\frac{a}{\sqrt[3]{x}} \right)} + 1}\, dx"," ",0,"Integral(LambertW(a/x**(1/3))**3/(LambertW(a/x**(1/3)) + 1), x)","F"
391,0,0,0,0.000000," ","integrate(LambertW(a/x**(1/2))**2/(1+LambertW(a/x**(1/2))),x)","\int \frac{\operatorname{LambertW}^{2}{\left(\frac{a}{\sqrt{x}} \right)}}{\operatorname{LambertW}{\left(\frac{a}{\sqrt{x}} \right)} + 1}\, dx"," ",0,"Integral(LambertW(a/sqrt(x))**2/(LambertW(a/sqrt(x)) + 1), x)","F"
392,0,0,0,0.000000," ","integrate(LambertW(a/x)/(1+LambertW(a/x)),x)","\int \frac{\operatorname{LambertW}{\left(\frac{a}{x} \right)}}{\operatorname{LambertW}{\left(\frac{a}{x} \right)} + 1}\, dx"," ",0,"Integral(LambertW(a/x)/(LambertW(a/x) + 1), x)","F"
393,0,0,0,0.000000," ","integrate(1/LambertW(a*x)/(1+LambertW(a*x)),x)","\int \frac{1}{\left(\operatorname{LambertW}{\left(a x \right)} + 1\right) \operatorname{LambertW}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((LambertW(a*x) + 1)*LambertW(a*x)), x)","F"
394,0,0,0,0.000000," ","integrate(1/LambertW(a*x**(1/2))**2/(1+LambertW(a*x**(1/2))),x)","\int \frac{1}{\left(\operatorname{LambertW}{\left(a \sqrt{x} \right)} + 1\right) \operatorname{LambertW}^{2}{\left(a \sqrt{x} \right)}}\, dx"," ",0,"Integral(1/((LambertW(a*sqrt(x)) + 1)*LambertW(a*sqrt(x))**2), x)","F"
395,0,0,0,0.000000," ","integrate(1/LambertW(a*x**(1/3))**3/(1+LambertW(a*x**(1/3))),x)","\int \frac{1}{\left(\operatorname{LambertW}{\left(a \sqrt[3]{x} \right)} + 1\right) \operatorname{LambertW}^{3}{\left(a \sqrt[3]{x} \right)}}\, dx"," ",0,"Integral(1/((LambertW(a*x**(1/3)) + 1)*LambertW(a*x**(1/3))**3), x)","F"
396,0,0,0,0.000000," ","integrate(1/LambertW(a*x**(1/4))**4/(1+LambertW(a*x**(1/4))),x)","\int \frac{1}{\left(\operatorname{LambertW}{\left(a \sqrt[4]{x} \right)} + 1\right) \operatorname{LambertW}^{4}{\left(a \sqrt[4]{x} \right)}}\, dx"," ",0,"Integral(1/((LambertW(a*x**(1/4)) + 1)*LambertW(a*x**(1/4))**4), x)","F"
397,1,49,0,54.936546," ","integrate(LambertW(a*x**n)**(1-1/n)/(1+LambertW(a*x**n)),x)","\begin{cases} x \operatorname{LambertW}^{- \frac{1}{n}}{\left(a x^{n} \right)} & \text{for}\: a \neq 0^{n} x^{- n} e^{0^{n}} \\\frac{x \operatorname{LambertW}^{1 - \frac{1}{n}}{\left(0^{n} e^{0^{n}} \right)}}{\operatorname{LambertW}{\left(0^{n} e^{0^{n}} \right)} + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*LambertW(a*x**n)**(-1/n), Ne(a, 0**n*x**(-n)*exp(0**n))), (x*LambertW(0**n*exp(0**n))**(1 - 1/n)/(LambertW(0**n*exp(0**n)) + 1), True))","A"
398,1,27,0,5.336164," ","integrate(LambertW(a*x**(1/(1-p)))**p/(1+LambertW(a*x**(1/(1-p)))),x)","\begin{cases} \frac{x \operatorname{LambertW}^{p}{\left(a x^{\frac{1}{1 - p}} \right)}}{\operatorname{LambertW}{\left(a x^{\frac{1}{1 - p}} \right)}} & \text{for}\: a \neq 0 \\0^{p} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*LambertW(a*x**(1/(1 - p)))**p/LambertW(a*x**(1/(1 - p))), Ne(a, 0)), (0**p*x, True))","A"
