1,1,88,0,0.484052," ","integrate(ln(c*(e*x+d))**4,x)","24 e \left(- \frac{d \log{\left(d + e x \right)}}{e^{2}} + \frac{x}{e}\right) - 24 x \log{\left(c \left(d + e x\right) \right)} + \frac{\left(- 4 d - 4 e x\right) \log{\left(c \left(d + e x\right) \right)}^{3}}{e} + \frac{\left(d + e x\right) \log{\left(c \left(d + e x\right) \right)}^{4}}{e} + \frac{\left(12 d + 12 e x\right) \log{\left(c \left(d + e x\right) \right)}^{2}}{e}"," ",0,"24*e*(-d*log(d + e*x)/e**2 + x/e) - 24*x*log(c*(d + e*x)) + (-4*d - 4*e*x)*log(c*(d + e*x))**3/e + (d + e*x)*log(c*(d + e*x))**4/e + (12*d + 12*e*x)*log(c*(d + e*x))**2/e","A",0
2,1,68,0,0.412120," ","integrate(ln(c*(e*x+d))**3,x)","- 6 e \left(- \frac{d \log{\left(d + e x \right)}}{e^{2}} + \frac{x}{e}\right) + 6 x \log{\left(c \left(d + e x\right) \right)} + \frac{\left(- 3 d - 3 e x\right) \log{\left(c \left(d + e x\right) \right)}^{2}}{e} + \frac{\left(d + e x\right) \log{\left(c \left(d + e x\right) \right)}^{3}}{e}"," ",0,"-6*e*(-d*log(d + e*x)/e**2 + x/e) + 6*x*log(c*(d + e*x)) + (-3*d - 3*e*x)*log(c*(d + e*x))**2/e + (d + e*x)*log(c*(d + e*x))**3/e","A",0
3,1,46,0,0.352908," ","integrate(ln(c*(e*x+d))**2,x)","2 e \left(- \frac{d \log{\left(d + e x \right)}}{e^{2}} + \frac{x}{e}\right) - 2 x \log{\left(c \left(d + e x\right) \right)} + \frac{\left(d + e x\right) \log{\left(c \left(d + e x\right) \right)}^{2}}{e}"," ",0,"2*e*(-d*log(d + e*x)/e**2 + x/e) - 2*x*log(c*(d + e*x)) + (d + e*x)*log(c*(d + e*x))**2/e","A",0
4,1,26,0,0.149276," ","integrate(ln(c*(e*x+d)),x)","- e \left(- \frac{d \log{\left(d + e x \right)}}{e^{2}} + \frac{x}{e}\right) + x \log{\left(c \left(d + e x\right) \right)}"," ",0,"-e*(-d*log(d + e*x)/e**2 + x/e) + x*log(c*(d + e*x))","A",0
5,1,12,0,0.752984," ","integrate(1/ln(c*(e*x+d)),x)","\frac{\operatorname{li}{\left(c d + c e x \right)}}{c e}"," ",0,"li(c*d + c*e*x)/(c*e)","A",0
6,1,29,0,0.801343," ","integrate(1/ln(c*(e*x+d))**2,x)","\frac{- d - e x}{e \log{\left(c \left(d + e x\right) \right)}} + \frac{\operatorname{li}{\left(c d + c e x \right)}}{c e}"," ",0,"(-d - e*x)/(e*log(c*(d + e*x))) + li(c*d + c*e*x)/(c*e)","A",0
7,1,48,0,0.815176," ","integrate(1/ln(c*(e*x+d))**3,x)","\frac{- d - e x + \left(- d - e x\right) \log{\left(c \left(d + e x\right) \right)}}{2 e \log{\left(c \left(d + e x\right) \right)}^{2}} + \frac{\operatorname{li}{\left(c d + c e x \right)}}{2 c e}"," ",0,"(-d - e*x + (-d - e*x)*log(c*(d + e*x)))/(2*e*log(c*(d + e*x))**2) + li(c*d + c*e*x)/(2*c*e)","A",0
8,1,71,0,0.844430," ","integrate(1/ln(c*(e*x+d))**4,x)","\frac{- d - e x + \left(- \frac{d}{2} - \frac{e x}{2}\right) \log{\left(c \left(d + e x\right) \right)}^{2} + \left(- \frac{d}{2} - \frac{e x}{2}\right) \log{\left(c \left(d + e x\right) \right)}}{3 e \log{\left(c \left(d + e x\right) \right)}^{3}} + \frac{\operatorname{li}{\left(c d + c e x \right)}}{6 c e}"," ",0,"(-d - e*x + (-d/2 - e*x/2)*log(c*(d + e*x))**2 + (-d/2 - e*x/2)*log(c*(d + e*x)))/(3*e*log(c*(d + e*x))**3) + li(c*d + c*e*x)/(6*c*e)","A",0
9,-1,0,0,0.000000," ","integrate(ln(c*(e*x+d))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
10,1,105,0,132.605132," ","integrate(ln(c*(e*x+d))**(3/2),x)","\begin{cases} \tilde{\infty} x & \text{for}\: c = 0 \\x \log{\left(c d \right)}^{\frac{3}{2}} & \text{for}\: e = 0 \\\frac{\left(- \sqrt{- \log{\left(c d + c e x \right)}} \left(c d + c e x\right) \left(\log{\left(c d + c e x \right)} - \frac{3}{2}\right) + \frac{3 \sqrt{\pi} \operatorname{erfc}{\left(\sqrt{- \log{\left(c d + c e x \right)}} \right)}}{4}\right) \log{\left(c d + c e x \right)}^{\frac{3}{2}}}{c e \left(- \log{\left(c d + c e x \right)}\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(c, 0)), (x*log(c*d)**(3/2), Eq(e, 0)), ((-sqrt(-log(c*d + c*e*x))*(c*d + c*e*x)*(log(c*d + c*e*x) - 3/2) + 3*sqrt(pi)*erfc(sqrt(-log(c*d + c*e*x)))/4)*log(c*d + c*e*x)**(3/2)/(c*e*(-log(c*d + c*e*x))**(3/2)), True))","A",0
11,1,90,0,2.241063," ","integrate(ln(c*(e*x+d))**(1/2),x)","\begin{cases} \tilde{\infty} x & \text{for}\: c = 0 \\x \sqrt{\log{\left(c d \right)}} & \text{for}\: e = 0 \\\frac{\left(\sqrt{- \log{\left(c d + c e x \right)}} \left(c d + c e x\right) + \frac{\sqrt{\pi} \operatorname{erfc}{\left(\sqrt{- \log{\left(c d + c e x \right)}} \right)}}{2}\right) \sqrt{\log{\left(c d + c e x \right)}}}{c e \sqrt{- \log{\left(c d + c e x \right)}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(c, 0)), (x*sqrt(log(c*d)), Eq(e, 0)), ((sqrt(-log(c*d + c*e*x))*(c*d + c*e*x) + sqrt(pi)*erfc(sqrt(-log(c*d + c*e*x)))/2)*sqrt(log(c*d + c*e*x))/(c*e*sqrt(-log(c*d + c*e*x))), True))","A",0
12,1,63,0,2.149598," ","integrate(1/ln(c*(e*x+d))**(1/2),x)","\begin{cases} 0 & \text{for}\: c = 0 \\\frac{x}{\sqrt{\log{\left(c d \right)}}} & \text{for}\: e = 0 \\\frac{\sqrt{\pi} \sqrt{- \log{\left(c d + c e x \right)}} \operatorname{erfc}{\left(\sqrt{- \log{\left(c d + c e x \right)}} \right)}}{c e \sqrt{\log{\left(c d + c e x \right)}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((0, Eq(c, 0)), (x/sqrt(log(c*d)), Eq(e, 0)), (sqrt(pi)*sqrt(-log(c*d + c*e*x))*erfc(sqrt(-log(c*d + c*e*x)))/(c*e*sqrt(log(c*d + c*e*x))), True))","A",0
13,1,92,0,29.706511," ","integrate(1/ln(c*(e*x+d))**(3/2),x)","\begin{cases} 0 & \text{for}\: c = 0 \\\frac{x}{\log{\left(c d \right)}^{\frac{3}{2}}} & \text{for}\: e = 0 \\\frac{\left(- \log{\left(c d + c e x \right)}\right)^{\frac{3}{2}} \left(- 2 \sqrt{\pi} \operatorname{erfc}{\left(\sqrt{- \log{\left(c d + c e x \right)}} \right)} + \frac{2 \left(c d + c e x\right)}{\sqrt{- \log{\left(c d + c e x \right)}}}\right)}{c e \log{\left(c d + c e x \right)}^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((0, Eq(c, 0)), (x/log(c*d)**(3/2), Eq(e, 0)), ((-log(c*d + c*e*x))**(3/2)*(-2*sqrt(pi)*erfc(sqrt(-log(c*d + c*e*x))) + 2*(c*d + c*e*x)/sqrt(-log(c*d + c*e*x)))/(c*e*log(c*d + c*e*x)**(3/2)), True))","A",0
14,-1,0,0,0.000000," ","integrate(1/ln(c*(e*x+d))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,-1,0,0,0.000000," ","integrate(1/ln(c*(e*x+d))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
16,1,54,0,6.942018," ","integrate(ln(c*(e*x+d))**p,x)","\begin{cases} \tilde{\infty}^{p} x & \text{for}\: c = 0 \\x \log{\left(c d \right)}^{p} & \text{for}\: e = 0 \\\frac{\left(- \log{\left(c d + c e x \right)}\right)^{- p} \log{\left(c d + c e x \right)}^{p} \Gamma\left(p + 1, - \log{\left(c d + c e x \right)}\right)}{c e} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo**p*x, Eq(c, 0)), (x*log(c*d)**p, Eq(e, 0)), ((-log(c*d + c*e*x))**(-p)*log(c*d + c*e*x)**p*uppergamma(p + 1, -log(c*d + c*e*x))/(c*e), True))","A",0
17,1,1059,0,6.973157," ","integrate((a+b*ln(c*(e*x+d)**n))**4,x)","\begin{cases} a^{4} x + \frac{4 a^{3} b d n \log{\left(d + e x \right)}}{e} + 4 a^{3} b n x \log{\left(d + e x \right)} - 4 a^{3} b n x + 4 a^{3} b x \log{\left(c \right)} + \frac{6 a^{2} b^{2} d n^{2} \log{\left(d + e x \right)}^{2}}{e} - \frac{12 a^{2} b^{2} d n^{2} \log{\left(d + e x \right)}}{e} + \frac{12 a^{2} b^{2} d n \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + 6 a^{2} b^{2} n^{2} x \log{\left(d + e x \right)}^{2} - 12 a^{2} b^{2} n^{2} x \log{\left(d + e x \right)} + 12 a^{2} b^{2} n^{2} x + 12 a^{2} b^{2} n x \log{\left(c \right)} \log{\left(d + e x \right)} - 12 a^{2} b^{2} n x \log{\left(c \right)} + 6 a^{2} b^{2} x \log{\left(c \right)}^{2} + \frac{4 a b^{3} d n^{3} \log{\left(d + e x \right)}^{3}}{e} - \frac{12 a b^{3} d n^{3} \log{\left(d + e x \right)}^{2}}{e} + \frac{24 a b^{3} d n^{3} \log{\left(d + e x \right)}}{e} + \frac{12 a b^{3} d n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{e} - \frac{24 a b^{3} d n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{12 a b^{3} d n \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{e} + 4 a b^{3} n^{3} x \log{\left(d + e x \right)}^{3} - 12 a b^{3} n^{3} x \log{\left(d + e x \right)}^{2} + 24 a b^{3} n^{3} x \log{\left(d + e x \right)} - 24 a b^{3} n^{3} x + 12 a b^{3} n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)}^{2} - 24 a b^{3} n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)} + 24 a b^{3} n^{2} x \log{\left(c \right)} + 12 a b^{3} n x \log{\left(c \right)}^{2} \log{\left(d + e x \right)} - 12 a b^{3} n x \log{\left(c \right)}^{2} + 4 a b^{3} x \log{\left(c \right)}^{3} + \frac{b^{4} d n^{4} \log{\left(d + e x \right)}^{4}}{e} - \frac{4 b^{4} d n^{4} \log{\left(d + e x \right)}^{3}}{e} + \frac{12 b^{4} d n^{4} \log{\left(d + e x \right)}^{2}}{e} - \frac{24 b^{4} d n^{4} \log{\left(d + e x \right)}}{e} + \frac{4 b^{4} d n^{3} \log{\left(c \right)} \log{\left(d + e x \right)}^{3}}{e} - \frac{12 b^{4} d n^{3} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{e} + \frac{24 b^{4} d n^{3} \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{6 b^{4} d n^{2} \log{\left(c \right)}^{2} \log{\left(d + e x \right)}^{2}}{e} - \frac{12 b^{4} d n^{2} \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{e} + \frac{4 b^{4} d n \log{\left(c \right)}^{3} \log{\left(d + e x \right)}}{e} + b^{4} n^{4} x \log{\left(d + e x \right)}^{4} - 4 b^{4} n^{4} x \log{\left(d + e x \right)}^{3} + 12 b^{4} n^{4} x \log{\left(d + e x \right)}^{2} - 24 b^{4} n^{4} x \log{\left(d + e x \right)} + 24 b^{4} n^{4} x + 4 b^{4} n^{3} x \log{\left(c \right)} \log{\left(d + e x \right)}^{3} - 12 b^{4} n^{3} x \log{\left(c \right)} \log{\left(d + e x \right)}^{2} + 24 b^{4} n^{3} x \log{\left(c \right)} \log{\left(d + e x \right)} - 24 b^{4} n^{3} x \log{\left(c \right)} + 6 b^{4} n^{2} x \log{\left(c \right)}^{2} \log{\left(d + e x \right)}^{2} - 12 b^{4} n^{2} x \log{\left(c \right)}^{2} \log{\left(d + e x \right)} + 12 b^{4} n^{2} x \log{\left(c \right)}^{2} + 4 b^{4} n x \log{\left(c \right)}^{3} \log{\left(d + e x \right)} - 4 b^{4} n x \log{\left(c \right)}^{3} + b^{4} x \log{\left(c \right)}^{4} & \text{for}\: e \neq 0 \\x \left(a + b \log{\left(c d^{n} \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x + 4*a**3*b*d*n*log(d + e*x)/e + 4*a**3*b*n*x*log(d + e*x) - 4*a**3*b*n*x + 4*a**3*b*x*log(c) + 6*a**2*b**2*d*n**2*log(d + e*x)**2/e - 12*a**2*b**2*d*n**2*log(d + e*x)/e + 12*a**2*b**2*d*n*log(c)*log(d + e*x)/e + 6*a**2*b**2*n**2*x*log(d + e*x)**2 - 12*a**2*b**2*n**2*x*log(d + e*x) + 12*a**2*b**2*n**2*x + 12*a**2*b**2*n*x*log(c)*log(d + e*x) - 12*a**2*b**2*n*x*log(c) + 6*a**2*b**2*x*log(c)**2 + 4*a*b**3*d*n**3*log(d + e*x)**3/e - 12*a*b**3*d*n**3*log(d + e*x)**2/e + 24*a*b**3*d*n**3*log(d + e*x)/e + 12*a*b**3*d*n**2*log(c)*log(d + e*x)**2/e - 24*a*b**3*d*n**2*log(c)*log(d + e*x)/e + 12*a*b**3*d*n*log(c)**2*log(d + e*x)/e + 4*a*b**3*n**3*x*log(d + e*x)**3 - 12*a*b**3*n**3*x*log(d + e*x)**2 + 24*a*b**3*n**3*x*log(d + e*x) - 24*a*b**3*n**3*x + 12*a*b**3*n**2*x*log(c)*log(d + e*x)**2 - 24*a*b**3*n**2*x*log(c)*log(d + e*x) + 24*a*b**3*n**2*x*log(c) + 12*a*b**3*n*x*log(c)**2*log(d + e*x) - 12*a*b**3*n*x*log(c)**2 + 4*a*b**3*x*log(c)**3 + b**4*d*n**4*log(d + e*x)**4/e - 4*b**4*d*n**4*log(d + e*x)**3/e + 12*b**4*d*n**4*log(d + e*x)**2/e - 24*b**4*d*n**4*log(d + e*x)/e + 4*b**4*d*n**3*log(c)*log(d + e*x)**3/e - 12*b**4*d*n**3*log(c)*log(d + e*x)**2/e + 24*b**4*d*n**3*log(c)*log(d + e*x)/e + 6*b**4*d*n**2*log(c)**2*log(d + e*x)**2/e - 12*b**4*d*n**2*log(c)**2*log(d + e*x)/e + 4*b**4*d*n*log(c)**3*log(d + e*x)/e + b**4*n**4*x*log(d + e*x)**4 - 4*b**4*n**4*x*log(d + e*x)**3 + 12*b**4*n**4*x*log(d + e*x)**2 - 24*b**4*n**4*x*log(d + e*x) + 24*b**4*n**4*x + 4*b**4*n**3*x*log(c)*log(d + e*x)**3 - 12*b**4*n**3*x*log(c)*log(d + e*x)**2 + 24*b**4*n**3*x*log(c)*log(d + e*x) - 24*b**4*n**3*x*log(c) + 6*b**4*n**2*x*log(c)**2*log(d + e*x)**2 - 12*b**4*n**2*x*log(c)**2*log(d + e*x) + 12*b**4*n**2*x*log(c)**2 + 4*b**4*n*x*log(c)**3*log(d + e*x) - 4*b**4*n*x*log(c)**3 + b**4*x*log(c)**4, Ne(e, 0)), (x*(a + b*log(c*d**n))**4, True))","A",0
18,1,527,0,3.322434," ","integrate((a+b*ln(c*(e*x+d)**n))**3,x)","\begin{cases} a^{3} x + \frac{3 a^{2} b d n \log{\left(d + e x \right)}}{e} + 3 a^{2} b n x \log{\left(d + e x \right)} - 3 a^{2} b n x + 3 a^{2} b x \log{\left(c \right)} + \frac{3 a b^{2} d n^{2} \log{\left(d + e x \right)}^{2}}{e} - \frac{6 a b^{2} d n^{2} \log{\left(d + e x \right)}}{e} + \frac{6 a b^{2} d n \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + 3 a b^{2} n^{2} x \log{\left(d + e x \right)}^{2} - 6 a b^{2} n^{2} x \log{\left(d + e x \right)} + 6 a b^{2} n^{2} x + 6 a b^{2} n x \log{\left(c \right)} \log{\left(d + e x \right)} - 6 a b^{2} n x \log{\left(c \right)} + 3 a b^{2} x \log{\left(c \right)}^{2} + \frac{b^{3} d n^{3} \log{\left(d + e x \right)}^{3}}{e} - \frac{3 b^{3} d n^{3} \log{\left(d + e x \right)}^{2}}{e} + \frac{6 b^{3} d n^{3} \log{\left(d + e x \right)}}{e} + \frac{3 b^{3} d n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{e} - \frac{6 b^{3} d n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{3 b^{3} d n \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{e} + b^{3} n^{3} x \log{\left(d + e x \right)}^{3} - 3 b^{3} n^{3} x \log{\left(d + e x \right)}^{2} + 6 b^{3} n^{3} x \log{\left(d + e x \right)} - 6 b^{3} n^{3} x + 3 b^{3} n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)}^{2} - 6 b^{3} n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)} + 6 b^{3} n^{2} x \log{\left(c \right)} + 3 b^{3} n x \log{\left(c \right)}^{2} \log{\left(d + e x \right)} - 3 b^{3} n x \log{\left(c \right)}^{2} + b^{3} x \log{\left(c \right)}^{3} & \text{for}\: e \neq 0 \\x \left(a + b \log{\left(c d^{n} \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x + 3*a**2*b*d*n*log(d + e*x)/e + 3*a**2*b*n*x*log(d + e*x) - 3*a**2*b*n*x + 3*a**2*b*x*log(c) + 3*a*b**2*d*n**2*log(d + e*x)**2/e - 6*a*b**2*d*n**2*log(d + e*x)/e + 6*a*b**2*d*n*log(c)*log(d + e*x)/e + 3*a*b**2*n**2*x*log(d + e*x)**2 - 6*a*b**2*n**2*x*log(d + e*x) + 6*a*b**2*n**2*x + 6*a*b**2*n*x*log(c)*log(d + e*x) - 6*a*b**2*n*x*log(c) + 3*a*b**2*x*log(c)**2 + b**3*d*n**3*log(d + e*x)**3/e - 3*b**3*d*n**3*log(d + e*x)**2/e + 6*b**3*d*n**3*log(d + e*x)/e + 3*b**3*d*n**2*log(c)*log(d + e*x)**2/e - 6*b**3*d*n**2*log(c)*log(d + e*x)/e + 3*b**3*d*n*log(c)**2*log(d + e*x)/e + b**3*n**3*x*log(d + e*x)**3 - 3*b**3*n**3*x*log(d + e*x)**2 + 6*b**3*n**3*x*log(d + e*x) - 6*b**3*n**3*x + 3*b**3*n**2*x*log(c)*log(d + e*x)**2 - 6*b**3*n**2*x*log(c)*log(d + e*x) + 6*b**3*n**2*x*log(c) + 3*b**3*n*x*log(c)**2*log(d + e*x) - 3*b**3*n*x*log(c)**2 + b**3*x*log(c)**3, Ne(e, 0)), (x*(a + b*log(c*d**n))**3, True))","A",0
19,1,211,0,1.466339," ","integrate((a+b*ln(c*(e*x+d)**n))**2,x)","\begin{cases} a^{2} x + \frac{2 a b d n \log{\left(d + e x \right)}}{e} + 2 a b n x \log{\left(d + e x \right)} - 2 a b n x + 2 a b x \log{\left(c \right)} + \frac{b^{2} d n^{2} \log{\left(d + e x \right)}^{2}}{e} - \frac{2 b^{2} d n^{2} \log{\left(d + e x \right)}}{e} + \frac{2 b^{2} d n \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + b^{2} n^{2} x \log{\left(d + e x \right)}^{2} - 2 b^{2} n^{2} x \log{\left(d + e x \right)} + 2 b^{2} n^{2} x + 2 b^{2} n x \log{\left(c \right)} \log{\left(d + e x \right)} - 2 b^{2} n x \log{\left(c \right)} + b^{2} x \log{\left(c \right)}^{2} & \text{for}\: e \neq 0 \\x \left(a + b \log{\left(c d^{n} \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + 2*a*b*d*n*log(d + e*x)/e + 2*a*b*n*x*log(d + e*x) - 2*a*b*n*x + 2*a*b*x*log(c) + b**2*d*n**2*log(d + e*x)**2/e - 2*b**2*d*n**2*log(d + e*x)/e + 2*b**2*d*n*log(c)*log(d + e*x)/e + b**2*n**2*x*log(d + e*x)**2 - 2*b**2*n**2*x*log(d + e*x) + 2*b**2*n**2*x + 2*b**2*n*x*log(c)*log(d + e*x) - 2*b**2*n*x*log(c) + b**2*x*log(c)**2, Ne(e, 0)), (x*(a + b*log(c*d**n))**2, True))","A",0
20,1,42,0,0.475106," ","integrate(a+b*ln(c*(e*x+d)**n),x)","a x + b \left(\begin{cases} \frac{d n \log{\left(d + e x \right)}}{e} + n x \log{\left(d + e x \right)} - n x + x \log{\left(c \right)} & \text{for}\: e \neq 0 \\x \log{\left(c d^{n} \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((d*n*log(d + e*x)/e + n*x*log(d + e*x) - n*x + x*log(c), Ne(e, 0)), (x*log(c*d**n), True))","A",0
21,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(e*x+d)**n)),x)","\int \frac{1}{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}\, dx"," ",0,"Integral(1/(a + b*log(c*(d + e*x)**n)), x)","F",0
22,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(e*x+d)**n))**2,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**(-2), x)","F",0
23,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(e*x+d)**n))**3,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{3}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**(-3), x)","F",0
24,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**(5/2),x)","\int \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**(5/2), x)","F",0
25,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**(3/2),x)","\int \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**(3/2), x)","F",0
26,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**(1/2),x)","\int \sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}\, dx"," ",0,"Integral(sqrt(a + b*log(c*(d + e*x)**n)), x)","F",0
27,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(e*x+d)**n))**(1/2),x)","\int \frac{1}{\sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*log(c*(d + e*x)**n)), x)","F",0
28,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(e*x+d)**n))**(3/2),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**(-3/2), x)","F",0
29,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(e*x+d)**n))**(5/2),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**(-5/2), x)","F",0
30,-2,0,0,0.000000," ","integrate(1/(a+b*ln(c*(e*x+d)**n))**(7/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
31,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**p,x)","\int \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{p}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**p, x)","F",0
32,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**(1/2)))**p,x)","\int \left(a + b \log{\left(c \sqrt{d + e x} \right)}\right)^{p}\, dx"," ",0,"Integral((a + b*log(c*sqrt(d + e*x)))**p, x)","F",0
33,1,42,0,6.178940," ","integrate((f*x+e)**(-1+p)/ln(d*(f*x+e)**p),x)","\begin{cases} - \frac{\begin{cases} - \frac{\log{\left(e + f x \right)}}{\log{\left(d \right)}} & \text{for}\: p = 0 \\- \frac{\operatorname{li}{\left(d \left(e + f x\right)^{p} \right)}}{d p} & \text{otherwise} \end{cases}}{f} & \text{for}\: f \neq 0 \\\frac{e^{p - 1} x}{\log{\left(d e^{p} \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-Piecewise((-log(e + f*x)/log(d), Eq(p, 0)), (-li(d*(e + f*x)**p)/(d*p), True))/f, Ne(f, 0)), (e**(p - 1)*x/log(d*e**p), True))","A",0
34,0,0,0,0.000000," ","integrate((f*g*x+e*g)**(-1+p)/ln(d*(f*x+e)**p),x)","\int \frac{\left(g \left(e + f x\right)\right)^{p - 1}}{\log{\left(d \left(e + f x\right)^{p} \right)}}\, dx"," ",0,"Integral((g*(e + f*x))**(p - 1)/log(d*(e + f*x)**p), x)","F",0
35,1,620,0,14.961192," ","integrate((g*x+f)**4*(a+b*ln(c*(e*x+d)**n)),x)","\begin{cases} a f^{4} x + 2 a f^{3} g x^{2} + 2 a f^{2} g^{2} x^{3} + a f g^{3} x^{4} + \frac{a g^{4} x^{5}}{5} + \frac{b d^{5} g^{4} n \log{\left(d + e x \right)}}{5 e^{5}} - \frac{b d^{4} f g^{3} n \log{\left(d + e x \right)}}{e^{4}} - \frac{b d^{4} g^{4} n x}{5 e^{4}} + \frac{2 b d^{3} f^{2} g^{2} n \log{\left(d + e x \right)}}{e^{3}} + \frac{b d^{3} f g^{3} n x}{e^{3}} + \frac{b d^{3} g^{4} n x^{2}}{10 e^{3}} - \frac{2 b d^{2} f^{3} g n \log{\left(d + e x \right)}}{e^{2}} - \frac{2 b d^{2} f^{2} g^{2} n x}{e^{2}} - \frac{b d^{2} f g^{3} n x^{2}}{2 e^{2}} - \frac{b d^{2} g^{4} n x^{3}}{15 e^{2}} + \frac{b d f^{4} n \log{\left(d + e x \right)}}{e} + \frac{2 b d f^{3} g n x}{e} + \frac{b d f^{2} g^{2} n x^{2}}{e} + \frac{b d f g^{3} n x^{3}}{3 e} + \frac{b d g^{4} n x^{4}}{20 e} + b f^{4} n x \log{\left(d + e x \right)} - b f^{4} n x + b f^{4} x \log{\left(c \right)} + 2 b f^{3} g n x^{2} \log{\left(d + e x \right)} - b f^{3} g n x^{2} + 2 b f^{3} g x^{2} \log{\left(c \right)} + 2 b f^{2} g^{2} n x^{3} \log{\left(d + e x \right)} - \frac{2 b f^{2} g^{2} n x^{3}}{3} + 2 b f^{2} g^{2} x^{3} \log{\left(c \right)} + b f g^{3} n x^{4} \log{\left(d + e x \right)} - \frac{b f g^{3} n x^{4}}{4} + b f g^{3} x^{4} \log{\left(c \right)} + \frac{b g^{4} n x^{5} \log{\left(d + e x \right)}}{5} - \frac{b g^{4} n x^{5}}{25} + \frac{b g^{4} x^{5} \log{\left(c \right)}}{5} & \text{for}\: e \neq 0 \\\left(a + b \log{\left(c d^{n} \right)}\right) \left(f^{4} x + 2 f^{3} g x^{2} + 2 f^{2} g^{2} x^{3} + f g^{3} x^{4} + \frac{g^{4} x^{5}}{5}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*f**4*x + 2*a*f**3*g*x**2 + 2*a*f**2*g**2*x**3 + a*f*g**3*x**4 + a*g**4*x**5/5 + b*d**5*g**4*n*log(d + e*x)/(5*e**5) - b*d**4*f*g**3*n*log(d + e*x)/e**4 - b*d**4*g**4*n*x/(5*e**4) + 2*b*d**3*f**2*g**2*n*log(d + e*x)/e**3 + b*d**3*f*g**3*n*x/e**3 + b*d**3*g**4*n*x**2/(10*e**3) - 2*b*d**2*f**3*g*n*log(d + e*x)/e**2 - 2*b*d**2*f**2*g**2*n*x/e**2 - b*d**2*f*g**3*n*x**2/(2*e**2) - b*d**2*g**4*n*x**3/(15*e**2) + b*d*f**4*n*log(d + e*x)/e + 2*b*d*f**3*g*n*x/e + b*d*f**2*g**2*n*x**2/e + b*d*f*g**3*n*x**3/(3*e) + b*d*g**4*n*x**4/(20*e) + b*f**4*n*x*log(d + e*x) - b*f**4*n*x + b*f**4*x*log(c) + 2*b*f**3*g*n*x**2*log(d + e*x) - b*f**3*g*n*x**2 + 2*b*f**3*g*x**2*log(c) + 2*b*f**2*g**2*n*x**3*log(d + e*x) - 2*b*f**2*g**2*n*x**3/3 + 2*b*f**2*g**2*x**3*log(c) + b*f*g**3*n*x**4*log(d + e*x) - b*f*g**3*n*x**4/4 + b*f*g**3*x**4*log(c) + b*g**4*n*x**5*log(d + e*x)/5 - b*g**4*n*x**5/25 + b*g**4*x**5*log(c)/5, Ne(e, 0)), ((a + b*log(c*d**n))*(f**4*x + 2*f**3*g*x**2 + 2*f**2*g**2*x**3 + f*g**3*x**4 + g**4*x**5/5), True))","A",0
36,1,450,0,8.833704," ","integrate((g*x+f)**3*(a+b*ln(c*(e*x+d)**n)),x)","\begin{cases} a f^{3} x + \frac{3 a f^{2} g x^{2}}{2} + a f g^{2} x^{3} + \frac{a g^{3} x^{4}}{4} - \frac{b d^{4} g^{3} n \log{\left(d + e x \right)}}{4 e^{4}} + \frac{b d^{3} f g^{2} n \log{\left(d + e x \right)}}{e^{3}} + \frac{b d^{3} g^{3} n x}{4 e^{3}} - \frac{3 b d^{2} f^{2} g n \log{\left(d + e x \right)}}{2 e^{2}} - \frac{b d^{2} f g^{2} n x}{e^{2}} - \frac{b d^{2} g^{3} n x^{2}}{8 e^{2}} + \frac{b d f^{3} n \log{\left(d + e x \right)}}{e} + \frac{3 b d f^{2} g n x}{2 e} + \frac{b d f g^{2} n x^{2}}{2 e} + \frac{b d g^{3} n x^{3}}{12 e} + b f^{3} n x \log{\left(d + e x \right)} - b f^{3} n x + b f^{3} x \log{\left(c \right)} + \frac{3 b f^{2} g n x^{2} \log{\left(d + e x \right)}}{2} - \frac{3 b f^{2} g n x^{2}}{4} + \frac{3 b f^{2} g x^{2} \log{\left(c \right)}}{2} + b f g^{2} n x^{3} \log{\left(d + e x \right)} - \frac{b f g^{2} n x^{3}}{3} + b f g^{2} x^{3} \log{\left(c \right)} + \frac{b g^{3} n x^{4} \log{\left(d + e x \right)}}{4} - \frac{b g^{3} n x^{4}}{16} + \frac{b g^{3} x^{4} \log{\left(c \right)}}{4} & \text{for}\: e \neq 0 \\\left(a + b \log{\left(c d^{n} \right)}\right) \left(f^{3} x + \frac{3 f^{2} g x^{2}}{2} + f g^{2} x^{3} + \frac{g^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*f**3*x + 3*a*f**2*g*x**2/2 + a*f*g**2*x**3 + a*g**3*x**4/4 - b*d**4*g**3*n*log(d + e*x)/(4*e**4) + b*d**3*f*g**2*n*log(d + e*x)/e**3 + b*d**3*g**3*n*x/(4*e**3) - 3*b*d**2*f**2*g*n*log(d + e*x)/(2*e**2) - b*d**2*f*g**2*n*x/e**2 - b*d**2*g**3*n*x**2/(8*e**2) + b*d*f**3*n*log(d + e*x)/e + 3*b*d*f**2*g*n*x/(2*e) + b*d*f*g**2*n*x**2/(2*e) + b*d*g**3*n*x**3/(12*e) + b*f**3*n*x*log(d + e*x) - b*f**3*n*x + b*f**3*x*log(c) + 3*b*f**2*g*n*x**2*log(d + e*x)/2 - 3*b*f**2*g*n*x**2/4 + 3*b*f**2*g*x**2*log(c)/2 + b*f*g**2*n*x**3*log(d + e*x) - b*f*g**2*n*x**3/3 + b*f*g**2*x**3*log(c) + b*g**3*n*x**4*log(d + e*x)/4 - b*g**3*n*x**4/16 + b*g**3*x**4*log(c)/4, Ne(e, 0)), ((a + b*log(c*d**n))*(f**3*x + 3*f**2*g*x**2/2 + f*g**2*x**3 + g**3*x**4/4), True))","A",0
37,1,277,0,3.914839," ","integrate((g*x+f)**2*(a+b*ln(c*(e*x+d)**n)),x)","\begin{cases} a f^{2} x + a f g x^{2} + \frac{a g^{2} x^{3}}{3} + \frac{b d^{3} g^{2} n \log{\left(d + e x \right)}}{3 e^{3}} - \frac{b d^{2} f g n \log{\left(d + e x \right)}}{e^{2}} - \frac{b d^{2} g^{2} n x}{3 e^{2}} + \frac{b d f^{2} n \log{\left(d + e x \right)}}{e} + \frac{b d f g n x}{e} + \frac{b d g^{2} n x^{2}}{6 e} + b f^{2} n x \log{\left(d + e x \right)} - b f^{2} n x + b f^{2} x \log{\left(c \right)} + b f g n x^{2} \log{\left(d + e x \right)} - \frac{b f g n x^{2}}{2} + b f g x^{2} \log{\left(c \right)} + \frac{b g^{2} n x^{3} \log{\left(d + e x \right)}}{3} - \frac{b g^{2} n x^{3}}{9} + \frac{b g^{2} x^{3} \log{\left(c \right)}}{3} & \text{for}\: e \neq 0 \\\left(a + b \log{\left(c d^{n} \right)}\right) \left(f^{2} x + f g x^{2} + \frac{g^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*f**2*x + a*f*g*x**2 + a*g**2*x**3/3 + b*d**3*g**2*n*log(d + e*x)/(3*e**3) - b*d**2*f*g*n*log(d + e*x)/e**2 - b*d**2*g**2*n*x/(3*e**2) + b*d*f**2*n*log(d + e*x)/e + b*d*f*g*n*x/e + b*d*g**2*n*x**2/(6*e) + b*f**2*n*x*log(d + e*x) - b*f**2*n*x + b*f**2*x*log(c) + b*f*g*n*x**2*log(d + e*x) - b*f*g*n*x**2/2 + b*f*g*x**2*log(c) + b*g**2*n*x**3*log(d + e*x)/3 - b*g**2*n*x**3/9 + b*g**2*x**3*log(c)/3, Ne(e, 0)), ((a + b*log(c*d**n))*(f**2*x + f*g*x**2 + g**2*x**3/3), True))","A",0
38,1,148,0,1.705715," ","integrate((g*x+f)*(a+b*ln(c*(e*x+d)**n)),x)","\begin{cases} a f x + \frac{a g x^{2}}{2} - \frac{b d^{2} g n \log{\left(d + e x \right)}}{2 e^{2}} + \frac{b d f n \log{\left(d + e x \right)}}{e} + \frac{b d g n x}{2 e} + b f n x \log{\left(d + e x \right)} - b f n x + b f x \log{\left(c \right)} + \frac{b g n x^{2} \log{\left(d + e x \right)}}{2} - \frac{b g n x^{2}}{4} + \frac{b g x^{2} \log{\left(c \right)}}{2} & \text{for}\: e \neq 0 \\\left(a + b \log{\left(c d^{n} \right)}\right) \left(f x + \frac{g x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*f*x + a*g*x**2/2 - b*d**2*g*n*log(d + e*x)/(2*e**2) + b*d*f*n*log(d + e*x)/e + b*d*g*n*x/(2*e) + b*f*n*x*log(d + e*x) - b*f*n*x + b*f*x*log(c) + b*g*n*x**2*log(d + e*x)/2 - b*g*n*x**2/4 + b*g*x**2*log(c)/2, Ne(e, 0)), ((a + b*log(c*d**n))*(f*x + g*x**2/2), True))","A",0
39,1,42,0,0.497514," ","integrate(a+b*ln(c*(e*x+d)**n),x)","a x + b \left(\begin{cases} \frac{d n \log{\left(d + e x \right)}}{e} + n x \log{\left(d + e x \right)} - n x + x \log{\left(c \right)} & \text{for}\: e \neq 0 \\x \log{\left(c d^{n} \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((d*n*log(d + e*x)/e + n*x*log(d + e*x) - n*x + x*log(c), Ne(e, 0)), (x*log(c*d**n), True))","A",0
40,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x+f),x)","\int \frac{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))/(f + g*x), x)","F",0
41,-2,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x+f)**2,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
42,-2,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x+f)**3,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
43,-2,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x+f)**4,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
44,1,1744,0,21.766680," ","integrate((g*x+f)**3*(a+b*ln(c*(e*x+d)**n))**2,x)","\begin{cases} a^{2} f^{3} x + \frac{3 a^{2} f^{2} g x^{2}}{2} + a^{2} f g^{2} x^{3} + \frac{a^{2} g^{3} x^{4}}{4} - \frac{a b d^{4} g^{3} n \log{\left(d + e x \right)}}{2 e^{4}} + \frac{2 a b d^{3} f g^{2} n \log{\left(d + e x \right)}}{e^{3}} + \frac{a b d^{3} g^{3} n x}{2 e^{3}} - \frac{3 a b d^{2} f^{2} g n \log{\left(d + e x \right)}}{e^{2}} - \frac{2 a b d^{2} f g^{2} n x}{e^{2}} - \frac{a b d^{2} g^{3} n x^{2}}{4 e^{2}} + \frac{2 a b d f^{3} n \log{\left(d + e x \right)}}{e} + \frac{3 a b d f^{2} g n x}{e} + \frac{a b d f g^{2} n x^{2}}{e} + \frac{a b d g^{3} n x^{3}}{6 e} + 2 a b f^{3} n x \log{\left(d + e x \right)} - 2 a b f^{3} n x + 2 a b f^{3} x \log{\left(c \right)} + 3 a b f^{2} g n x^{2} \log{\left(d + e x \right)} - \frac{3 a b f^{2} g n x^{2}}{2} + 3 a b f^{2} g x^{2} \log{\left(c \right)} + 2 a b f g^{2} n x^{3} \log{\left(d + e x \right)} - \frac{2 a b f g^{2} n x^{3}}{3} + 2 a b f g^{2} x^{3} \log{\left(c \right)} + \frac{a b g^{3} n x^{4} \log{\left(d + e x \right)}}{2} - \frac{a b g^{3} n x^{4}}{8} + \frac{a b g^{3} x^{4} \log{\left(c \right)}}{2} - \frac{b^{2} d^{4} g^{3} n^{2} \log{\left(d + e x \right)}^{2}}{4 e^{4}} + \frac{25 b^{2} d^{4} g^{3} n^{2} \log{\left(d + e x \right)}}{24 e^{4}} - \frac{b^{2} d^{4} g^{3} n \log{\left(c \right)} \log{\left(d + e x \right)}}{2 e^{4}} + \frac{b^{2} d^{3} f g^{2} n^{2} \log{\left(d + e x \right)}^{2}}{e^{3}} - \frac{11 b^{2} d^{3} f g^{2} n^{2} \log{\left(d + e x \right)}}{3 e^{3}} + \frac{2 b^{2} d^{3} f g^{2} n \log{\left(c \right)} \log{\left(d + e x \right)}}{e^{3}} + \frac{b^{2} d^{3} g^{3} n^{2} x \log{\left(d + e x \right)}}{2 e^{3}} - \frac{25 b^{2} d^{3} g^{3} n^{2} x}{24 e^{3}} + \frac{b^{2} d^{3} g^{3} n x \log{\left(c \right)}}{2 e^{3}} - \frac{3 b^{2} d^{2} f^{2} g n^{2} \log{\left(d + e x \right)}^{2}}{2 e^{2}} + \frac{9 b^{2} d^{2} f^{2} g n^{2} \log{\left(d + e x \right)}}{2 e^{2}} - \frac{3 b^{2} d^{2} f^{2} g n \log{\left(c \right)} \log{\left(d + e x \right)}}{e^{2}} - \frac{2 b^{2} d^{2} f g^{2} n^{2} x \log{\left(d + e x \right)}}{e^{2}} + \frac{11 b^{2} d^{2} f g^{2} n^{2} x}{3 e^{2}} - \frac{2 b^{2} d^{2} f g^{2} n x \log{\left(c \right)}}{e^{2}} - \frac{b^{2} d^{2} g^{3} n^{2} x^{2} \log{\left(d + e x \right)}}{4 e^{2}} + \frac{13 b^{2} d^{2} g^{3} n^{2} x^{2}}{48 e^{2}} - \frac{b^{2} d^{2} g^{3} n x^{2} \log{\left(c \right)}}{4 e^{2}} + \frac{b^{2} d f^{3} n^{2} \log{\left(d + e x \right)}^{2}}{e} - \frac{2 b^{2} d f^{3} n^{2} \log{\left(d + e x \right)}}{e} + \frac{2 b^{2} d f^{3} n \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{3 b^{2} d f^{2} g n^{2} x \log{\left(d + e x \right)}}{e} - \frac{9 b^{2} d f^{2} g n^{2} x}{2 e} + \frac{3 b^{2} d f^{2} g n x \log{\left(c \right)}}{e} + \frac{b^{2} d f g^{2} n^{2} x^{2} \log{\left(d + e x \right)}}{e} - \frac{5 b^{2} d f g^{2} n^{2} x^{2}}{6 e} + \frac{b^{2} d f g^{2} n x^{2} \log{\left(c \right)}}{e} + \frac{b^{2} d g^{3} n^{2} x^{3} \log{\left(d + e x \right)}}{6 e} - \frac{7 b^{2} d g^{3} n^{2} x^{3}}{72 e} + \frac{b^{2} d g^{3} n x^{3} \log{\left(c \right)}}{6 e} + b^{2} f^{3} n^{2} x \log{\left(d + e x \right)}^{2} - 2 b^{2} f^{3} n^{2} x \log{\left(d + e x \right)} + 2 b^{2} f^{3} n^{2} x + 2 b^{2} f^{3} n x \log{\left(c \right)} \log{\left(d + e x \right)} - 2 b^{2} f^{3} n x \log{\left(c \right)} + b^{2} f^{3} x \log{\left(c \right)}^{2} + \frac{3 b^{2} f^{2} g n^{2} x^{2} \log{\left(d + e x \right)}^{2}}{2} - \frac{3 b^{2} f^{2} g n^{2} x^{2} \log{\left(d + e x \right)}}{2} + \frac{3 b^{2} f^{2} g n^{2} x^{2}}{4} + 3 b^{2} f^{2} g n x^{2} \log{\left(c \right)} \log{\left(d + e x \right)} - \frac{3 b^{2} f^{2} g n x^{2} \log{\left(c \right)}}{2} + \frac{3 b^{2} f^{2} g x^{2} \log{\left(c \right)}^{2}}{2} + b^{2} f g^{2} n^{2} x^{3} \log{\left(d + e x \right)}^{2} - \frac{2 b^{2} f g^{2} n^{2} x^{3} \log{\left(d + e x \right)}}{3} + \frac{2 b^{2} f g^{2} n^{2} x^{3}}{9} + 2 b^{2} f g^{2} n x^{3} \log{\left(c \right)} \log{\left(d + e x \right)} - \frac{2 b^{2} f g^{2} n x^{3} \log{\left(c \right)}}{3} + b^{2} f g^{2} x^{3} \log{\left(c \right)}^{2} + \frac{b^{2} g^{3} n^{2} x^{4} \log{\left(d + e x \right)}^{2}}{4} - \frac{b^{2} g^{3} n^{2} x^{4} \log{\left(d + e x \right)}}{8} + \frac{b^{2} g^{3} n^{2} x^{4}}{32} + \frac{b^{2} g^{3} n x^{4} \log{\left(c \right)} \log{\left(d + e x \right)}}{2} - \frac{b^{2} g^{3} n x^{4} \log{\left(c \right)}}{8} + \frac{b^{2} g^{3} x^{4} \log{\left(c \right)}^{2}}{4} & \text{for}\: e \neq 0 \\\left(a + b \log{\left(c d^{n} \right)}\right)^{2} \left(f^{3} x + \frac{3 f^{2} g x^{2}}{2} + f g^{2} x^{3} + \frac{g^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*f**3*x + 3*a**2*f**2*g*x**2/2 + a**2*f*g**2*x**3 + a**2*g**3*x**4/4 - a*b*d**4*g**3*n*log(d + e*x)/(2*e**4) + 2*a*b*d**3*f*g**2*n*log(d + e*x)/e**3 + a*b*d**3*g**3*n*x/(2*e**3) - 3*a*b*d**2*f**2*g*n*log(d + e*x)/e**2 - 2*a*b*d**2*f*g**2*n*x/e**2 - a*b*d**2*g**3*n*x**2/(4*e**2) + 2*a*b*d*f**3*n*log(d + e*x)/e + 3*a*b*d*f**2*g*n*x/e + a*b*d*f*g**2*n*x**2/e + a*b*d*g**3*n*x**3/(6*e) + 2*a*b*f**3*n*x*log(d + e*x) - 2*a*b*f**3*n*x + 2*a*b*f**3*x*log(c) + 3*a*b*f**2*g*n*x**2*log(d + e*x) - 3*a*b*f**2*g*n*x**2/2 + 3*a*b*f**2*g*x**2*log(c) + 2*a*b*f*g**2*n*x**3*log(d + e*x) - 2*a*b*f*g**2*n*x**3/3 + 2*a*b*f*g**2*x**3*log(c) + a*b*g**3*n*x**4*log(d + e*x)/2 - a*b*g**3*n*x**4/8 + a*b*g**3*x**4*log(c)/2 - b**2*d**4*g**3*n**2*log(d + e*x)**2/(4*e**4) + 25*b**2*d**4*g**3*n**2*log(d + e*x)/(24*e**4) - b**2*d**4*g**3*n*log(c)*log(d + e*x)/(2*e**4) + b**2*d**3*f*g**2*n**2*log(d + e*x)**2/e**3 - 11*b**2*d**3*f*g**2*n**2*log(d + e*x)/(3*e**3) + 2*b**2*d**3*f*g**2*n*log(c)*log(d + e*x)/e**3 + b**2*d**3*g**3*n**2*x*log(d + e*x)/(2*e**3) - 25*b**2*d**3*g**3*n**2*x/(24*e**3) + b**2*d**3*g**3*n*x*log(c)/(2*e**3) - 3*b**2*d**2*f**2*g*n**2*log(d + e*x)**2/(2*e**2) + 9*b**2*d**2*f**2*g*n**2*log(d + e*x)/(2*e**2) - 3*b**2*d**2*f**2*g*n*log(c)*log(d + e*x)/e**2 - 2*b**2*d**2*f*g**2*n**2*x*log(d + e*x)/e**2 + 11*b**2*d**2*f*g**2*n**2*x/(3*e**2) - 2*b**2*d**2*f*g**2*n*x*log(c)/e**2 - b**2*d**2*g**3*n**2*x**2*log(d + e*x)/(4*e**2) + 13*b**2*d**2*g**3*n**2*x**2/(48*e**2) - b**2*d**2*g**3*n*x**2*log(c)/(4*e**2) + b**2*d*f**3*n**2*log(d + e*x)**2/e - 2*b**2*d*f**3*n**2*log(d + e*x)/e + 2*b**2*d*f**3*n*log(c)*log(d + e*x)/e + 3*b**2*d*f**2*g*n**2*x*log(d + e*x)/e - 9*b**2*d*f**2*g*n**2*x/(2*e) + 3*b**2*d*f**2*g*n*x*log(c)/e + b**2*d*f*g**2*n**2*x**2*log(d + e*x)/e - 5*b**2*d*f*g**2*n**2*x**2/(6*e) + b**2*d*f*g**2*n*x**2*log(c)/e + b**2*d*g**3*n**2*x**3*log(d + e*x)/(6*e) - 7*b**2*d*g**3*n**2*x**3/(72*e) + b**2*d*g**3*n*x**3*log(c)/(6*e) + b**2*f**3*n**2*x*log(d + e*x)**2 - 2*b**2*f**3*n**2*x*log(d + e*x) + 2*b**2*f**3*n**2*x + 2*b**2*f**3*n*x*log(c)*log(d + e*x) - 2*b**2*f**3*n*x*log(c) + b**2*f**3*x*log(c)**2 + 3*b**2*f**2*g*n**2*x**2*log(d + e*x)**2/2 - 3*b**2*f**2*g*n**2*x**2*log(d + e*x)/2 + 3*b**2*f**2*g*n**2*x**2/4 + 3*b**2*f**2*g*n*x**2*log(c)*log(d + e*x) - 3*b**2*f**2*g*n*x**2*log(c)/2 + 3*b**2*f**2*g*x**2*log(c)**2/2 + b**2*f*g**2*n**2*x**3*log(d + e*x)**2 - 2*b**2*f*g**2*n**2*x**3*log(d + e*x)/3 + 2*b**2*f*g**2*n**2*x**3/9 + 2*b**2*f*g**2*n*x**3*log(c)*log(d + e*x) - 2*b**2*f*g**2*n*x**3*log(c)/3 + b**2*f*g**2*x**3*log(c)**2 + b**2*g**3*n**2*x**4*log(d + e*x)**2/4 - b**2*g**3*n**2*x**4*log(d + e*x)/8 + b**2*g**3*n**2*x**4/32 + b**2*g**3*n*x**4*log(c)*log(d + e*x)/2 - b**2*g**3*n*x**4*log(c)/8 + b**2*g**3*x**4*log(c)**2/4, Ne(e, 0)), ((a + b*log(c*d**n))**2*(f**3*x + 3*f**2*g*x**2/2 + f*g**2*x**3 + g**3*x**4/4), True))","A",0
45,1,1103,0,10.975619," ","integrate((g*x+f)**2*(a+b*ln(c*(e*x+d)**n))**2,x)","\begin{cases} a^{2} f^{2} x + a^{2} f g x^{2} + \frac{a^{2} g^{2} x^{3}}{3} + \frac{2 a b d^{3} g^{2} n \log{\left(d + e x \right)}}{3 e^{3}} - \frac{2 a b d^{2} f g n \log{\left(d + e x \right)}}{e^{2}} - \frac{2 a b d^{2} g^{2} n x}{3 e^{2}} + \frac{2 a b d f^{2} n \log{\left(d + e x \right)}}{e} + \frac{2 a b d f g n x}{e} + \frac{a b d g^{2} n x^{2}}{3 e} + 2 a b f^{2} n x \log{\left(d + e x \right)} - 2 a b f^{2} n x + 2 a b f^{2} x \log{\left(c \right)} + 2 a b f g n x^{2} \log{\left(d + e x \right)} - a b f g n x^{2} + 2 a b f g x^{2} \log{\left(c \right)} + \frac{2 a b g^{2} n x^{3} \log{\left(d + e x \right)}}{3} - \frac{2 a b g^{2} n x^{3}}{9} + \frac{2 a b g^{2} x^{3} \log{\left(c \right)}}{3} + \frac{b^{2} d^{3} g^{2} n^{2} \log{\left(d + e x \right)}^{2}}{3 e^{3}} - \frac{11 b^{2} d^{3} g^{2} n^{2} \log{\left(d + e x \right)}}{9 e^{3}} + \frac{2 b^{2} d^{3} g^{2} n \log{\left(c \right)} \log{\left(d + e x \right)}}{3 e^{3}} - \frac{b^{2} d^{2} f g n^{2} \log{\left(d + e x \right)}^{2}}{e^{2}} + \frac{3 b^{2} d^{2} f g n^{2} \log{\left(d + e x \right)}}{e^{2}} - \frac{2 b^{2} d^{2} f g n \log{\left(c \right)} \log{\left(d + e x \right)}}{e^{2}} - \frac{2 b^{2} d^{2} g^{2} n^{2} x \log{\left(d + e x \right)}}{3 e^{2}} + \frac{11 b^{2} d^{2} g^{2} n^{2} x}{9 e^{2}} - \frac{2 b^{2} d^{2} g^{2} n x \log{\left(c \right)}}{3 e^{2}} + \frac{b^{2} d f^{2} n^{2} \log{\left(d + e x \right)}^{2}}{e} - \frac{2 b^{2} d f^{2} n^{2} \log{\left(d + e x \right)}}{e} + \frac{2 b^{2} d f^{2} n \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{2 b^{2} d f g n^{2} x \log{\left(d + e x \right)}}{e} - \frac{3 b^{2} d f g n^{2} x}{e} + \frac{2 b^{2} d f g n x \log{\left(c \right)}}{e} + \frac{b^{2} d g^{2} n^{2} x^{2} \log{\left(d + e x \right)}}{3 e} - \frac{5 b^{2} d g^{2} n^{2} x^{2}}{18 e} + \frac{b^{2} d g^{2} n x^{2} \log{\left(c \right)}}{3 e} + b^{2} f^{2} n^{2} x \log{\left(d + e x \right)}^{2} - 2 b^{2} f^{2} n^{2} x \log{\left(d + e x \right)} + 2 b^{2} f^{2} n^{2} x + 2 b^{2} f^{2} n x \log{\left(c \right)} \log{\left(d + e x \right)} - 2 b^{2} f^{2} n x \log{\left(c \right)} + b^{2} f^{2} x \log{\left(c \right)}^{2} + b^{2} f g n^{2} x^{2} \log{\left(d + e x \right)}^{2} - b^{2} f g n^{2} x^{2} \log{\left(d + e x \right)} + \frac{b^{2} f g n^{2} x^{2}}{2} + 2 b^{2} f g n x^{2} \log{\left(c \right)} \log{\left(d + e x \right)} - b^{2} f g n x^{2} \log{\left(c \right)} + b^{2} f g x^{2} \log{\left(c \right)}^{2} + \frac{b^{2} g^{2} n^{2} x^{3} \log{\left(d + e x \right)}^{2}}{3} - \frac{2 b^{2} g^{2} n^{2} x^{3} \log{\left(d + e x \right)}}{9} + \frac{2 b^{2} g^{2} n^{2} x^{3}}{27} + \frac{2 b^{2} g^{2} n x^{3} \log{\left(c \right)} \log{\left(d + e x \right)}}{3} - \frac{2 b^{2} g^{2} n x^{3} \log{\left(c \right)}}{9} + \frac{b^{2} g^{2} x^{3} \log{\left(c \right)}^{2}}{3} & \text{for}\: e \neq 0 \\\left(a + b \log{\left(c d^{n} \right)}\right)^{2} \left(f^{2} x + f g x^{2} + \frac{g^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*f**2*x + a**2*f*g*x**2 + a**2*g**2*x**3/3 + 2*a*b*d**3*g**2*n*log(d + e*x)/(3*e**3) - 2*a*b*d**2*f*g*n*log(d + e*x)/e**2 - 2*a*b*d**2*g**2*n*x/(3*e**2) + 2*a*b*d*f**2*n*log(d + e*x)/e + 2*a*b*d*f*g*n*x/e + a*b*d*g**2*n*x**2/(3*e) + 2*a*b*f**2*n*x*log(d + e*x) - 2*a*b*f**2*n*x + 2*a*b*f**2*x*log(c) + 2*a*b*f*g*n*x**2*log(d + e*x) - a*b*f*g*n*x**2 + 2*a*b*f*g*x**2*log(c) + 2*a*b*g**2*n*x**3*log(d + e*x)/3 - 2*a*b*g**2*n*x**3/9 + 2*a*b*g**2*x**3*log(c)/3 + b**2*d**3*g**2*n**2*log(d + e*x)**2/(3*e**3) - 11*b**2*d**3*g**2*n**2*log(d + e*x)/(9*e**3) + 2*b**2*d**3*g**2*n*log(c)*log(d + e*x)/(3*e**3) - b**2*d**2*f*g*n**2*log(d + e*x)**2/e**2 + 3*b**2*d**2*f*g*n**2*log(d + e*x)/e**2 - 2*b**2*d**2*f*g*n*log(c)*log(d + e*x)/e**2 - 2*b**2*d**2*g**2*n**2*x*log(d + e*x)/(3*e**2) + 11*b**2*d**2*g**2*n**2*x/(9*e**2) - 2*b**2*d**2*g**2*n*x*log(c)/(3*e**2) + b**2*d*f**2*n**2*log(d + e*x)**2/e - 2*b**2*d*f**2*n**2*log(d + e*x)/e + 2*b**2*d*f**2*n*log(c)*log(d + e*x)/e + 2*b**2*d*f*g*n**2*x*log(d + e*x)/e - 3*b**2*d*f*g*n**2*x/e + 2*b**2*d*f*g*n*x*log(c)/e + b**2*d*g**2*n**2*x**2*log(d + e*x)/(3*e) - 5*b**2*d*g**2*n**2*x**2/(18*e) + b**2*d*g**2*n*x**2*log(c)/(3*e) + b**2*f**2*n**2*x*log(d + e*x)**2 - 2*b**2*f**2*n**2*x*log(d + e*x) + 2*b**2*f**2*n**2*x + 2*b**2*f**2*n*x*log(c)*log(d + e*x) - 2*b**2*f**2*n*x*log(c) + b**2*f**2*x*log(c)**2 + b**2*f*g*n**2*x**2*log(d + e*x)**2 - b**2*f*g*n**2*x**2*log(d + e*x) + b**2*f*g*n**2*x**2/2 + 2*b**2*f*g*n*x**2*log(c)*log(d + e*x) - b**2*f*g*n*x**2*log(c) + b**2*f*g*x**2*log(c)**2 + b**2*g**2*n**2*x**3*log(d + e*x)**2/3 - 2*b**2*g**2*n**2*x**3*log(d + e*x)/9 + 2*b**2*g**2*n**2*x**3/27 + 2*b**2*g**2*n*x**3*log(c)*log(d + e*x)/3 - 2*b**2*g**2*n*x**3*log(c)/9 + b**2*g**2*x**3*log(c)**2/3, Ne(e, 0)), ((a + b*log(c*d**n))**2*(f**2*x + f*g*x**2 + g**2*x**3/3), True))","A",0
46,1,561,0,4.529210," ","integrate((g*x+f)*(a+b*ln(c*(e*x+d)**n))**2,x)","\begin{cases} a^{2} f x + \frac{a^{2} g x^{2}}{2} - \frac{a b d^{2} g n \log{\left(d + e x \right)}}{e^{2}} + \frac{2 a b d f n \log{\left(d + e x \right)}}{e} + \frac{a b d g n x}{e} + 2 a b f n x \log{\left(d + e x \right)} - 2 a b f n x + 2 a b f x \log{\left(c \right)} + a b g n x^{2} \log{\left(d + e x \right)} - \frac{a b g n x^{2}}{2} + a b g x^{2} \log{\left(c \right)} - \frac{b^{2} d^{2} g n^{2} \log{\left(d + e x \right)}^{2}}{2 e^{2}} + \frac{3 b^{2} d^{2} g n^{2} \log{\left(d + e x \right)}}{2 e^{2}} - \frac{b^{2} d^{2} g n \log{\left(c \right)} \log{\left(d + e x \right)}}{e^{2}} + \frac{b^{2} d f n^{2} \log{\left(d + e x \right)}^{2}}{e} - \frac{2 b^{2} d f n^{2} \log{\left(d + e x \right)}}{e} + \frac{2 b^{2} d f n \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{b^{2} d g n^{2} x \log{\left(d + e x \right)}}{e} - \frac{3 b^{2} d g n^{2} x}{2 e} + \frac{b^{2} d g n x \log{\left(c \right)}}{e} + b^{2} f n^{2} x \log{\left(d + e x \right)}^{2} - 2 b^{2} f n^{2} x \log{\left(d + e x \right)} + 2 b^{2} f n^{2} x + 2 b^{2} f n x \log{\left(c \right)} \log{\left(d + e x \right)} - 2 b^{2} f n x \log{\left(c \right)} + b^{2} f x \log{\left(c \right)}^{2} + \frac{b^{2} g n^{2} x^{2} \log{\left(d + e x \right)}^{2}}{2} - \frac{b^{2} g n^{2} x^{2} \log{\left(d + e x \right)}}{2} + \frac{b^{2} g n^{2} x^{2}}{4} + b^{2} g n x^{2} \log{\left(c \right)} \log{\left(d + e x \right)} - \frac{b^{2} g n x^{2} \log{\left(c \right)}}{2} + \frac{b^{2} g x^{2} \log{\left(c \right)}^{2}}{2} & \text{for}\: e \neq 0 \\\left(a + b \log{\left(c d^{n} \right)}\right)^{2} \left(f x + \frac{g x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*f*x + a**2*g*x**2/2 - a*b*d**2*g*n*log(d + e*x)/e**2 + 2*a*b*d*f*n*log(d + e*x)/e + a*b*d*g*n*x/e + 2*a*b*f*n*x*log(d + e*x) - 2*a*b*f*n*x + 2*a*b*f*x*log(c) + a*b*g*n*x**2*log(d + e*x) - a*b*g*n*x**2/2 + a*b*g*x**2*log(c) - b**2*d**2*g*n**2*log(d + e*x)**2/(2*e**2) + 3*b**2*d**2*g*n**2*log(d + e*x)/(2*e**2) - b**2*d**2*g*n*log(c)*log(d + e*x)/e**2 + b**2*d*f*n**2*log(d + e*x)**2/e - 2*b**2*d*f*n**2*log(d + e*x)/e + 2*b**2*d*f*n*log(c)*log(d + e*x)/e + b**2*d*g*n**2*x*log(d + e*x)/e - 3*b**2*d*g*n**2*x/(2*e) + b**2*d*g*n*x*log(c)/e + b**2*f*n**2*x*log(d + e*x)**2 - 2*b**2*f*n**2*x*log(d + e*x) + 2*b**2*f*n**2*x + 2*b**2*f*n*x*log(c)*log(d + e*x) - 2*b**2*f*n*x*log(c) + b**2*f*x*log(c)**2 + b**2*g*n**2*x**2*log(d + e*x)**2/2 - b**2*g*n**2*x**2*log(d + e*x)/2 + b**2*g*n**2*x**2/4 + b**2*g*n*x**2*log(c)*log(d + e*x) - b**2*g*n*x**2*log(c)/2 + b**2*g*x**2*log(c)**2/2, Ne(e, 0)), ((a + b*log(c*d**n))**2*(f*x + g*x**2/2), True))","A",0
47,1,211,0,1.478232," ","integrate((a+b*ln(c*(e*x+d)**n))**2,x)","\begin{cases} a^{2} x + \frac{2 a b d n \log{\left(d + e x \right)}}{e} + 2 a b n x \log{\left(d + e x \right)} - 2 a b n x + 2 a b x \log{\left(c \right)} + \frac{b^{2} d n^{2} \log{\left(d + e x \right)}^{2}}{e} - \frac{2 b^{2} d n^{2} \log{\left(d + e x \right)}}{e} + \frac{2 b^{2} d n \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + b^{2} n^{2} x \log{\left(d + e x \right)}^{2} - 2 b^{2} n^{2} x \log{\left(d + e x \right)} + 2 b^{2} n^{2} x + 2 b^{2} n x \log{\left(c \right)} \log{\left(d + e x \right)} - 2 b^{2} n x \log{\left(c \right)} + b^{2} x \log{\left(c \right)}^{2} & \text{for}\: e \neq 0 \\x \left(a + b \log{\left(c d^{n} \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + 2*a*b*d*n*log(d + e*x)/e + 2*a*b*n*x*log(d + e*x) - 2*a*b*n*x + 2*a*b*x*log(c) + b**2*d*n**2*log(d + e*x)**2/e - 2*b**2*d*n**2*log(d + e*x)/e + 2*b**2*d*n*log(c)*log(d + e*x)/e + b**2*n**2*x*log(d + e*x)**2 - 2*b**2*n**2*x*log(d + e*x) + 2*b**2*n**2*x + 2*b**2*n*x*log(c)*log(d + e*x) - 2*b**2*n*x*log(c) + b**2*x*log(c)**2, Ne(e, 0)), (x*(a + b*log(c*d**n))**2, True))","A",0
48,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/(g*x+f),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**2/(f + g*x), x)","F",0
49,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/(g*x+f)**2,x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}{\left(f + g x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**2/(f + g*x)**2, x)","F",0
50,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/(g*x+f)**3,x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}{\left(f + g x\right)^{3}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**2/(f + g*x)**3, x)","F",0
51,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/(g*x+f)**4,x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}{\left(f + g x\right)^{4}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**2/(f + g*x)**4, x)","F",0
52,1,4495,0,48.312944," ","integrate((g*x+f)**3*(a+b*ln(c*(e*x+d)**n))**3,x)","\begin{cases} a^{3} f^{3} x + \frac{3 a^{3} f^{2} g x^{2}}{2} + a^{3} f g^{2} x^{3} + \frac{a^{3} g^{3} x^{4}}{4} - \frac{3 a^{2} b d^{4} g^{3} n \log{\left(d + e x \right)}}{4 e^{4}} + \frac{3 a^{2} b d^{3} f g^{2} n \log{\left(d + e x \right)}}{e^{3}} + \frac{3 a^{2} b d^{3} g^{3} n x}{4 e^{3}} - \frac{9 a^{2} b d^{2} f^{2} g n \log{\left(d + e x \right)}}{2 e^{2}} - \frac{3 a^{2} b d^{2} f g^{2} n x}{e^{2}} - \frac{3 a^{2} b d^{2} g^{3} n x^{2}}{8 e^{2}} + \frac{3 a^{2} b d f^{3} n \log{\left(d + e x \right)}}{e} + \frac{9 a^{2} b d f^{2} g n x}{2 e} + \frac{3 a^{2} b d f g^{2} n x^{2}}{2 e} + \frac{a^{2} b d g^{3} n x^{3}}{4 e} + 3 a^{2} b f^{3} n x \log{\left(d + e x \right)} - 3 a^{2} b f^{3} n x + 3 a^{2} b f^{3} x \log{\left(c \right)} + \frac{9 a^{2} b f^{2} g n x^{2} \log{\left(d + e x \right)}}{2} - \frac{9 a^{2} b f^{2} g n x^{2}}{4} + \frac{9 a^{2} b f^{2} g x^{2} \log{\left(c \right)}}{2} + 3 a^{2} b f g^{2} n x^{3} \log{\left(d + e x \right)} - a^{2} b f g^{2} n x^{3} + 3 a^{2} b f g^{2} x^{3} \log{\left(c \right)} + \frac{3 a^{2} b g^{3} n x^{4} \log{\left(d + e x \right)}}{4} - \frac{3 a^{2} b g^{3} n x^{4}}{16} + \frac{3 a^{2} b g^{3} x^{4} \log{\left(c \right)}}{4} - \frac{3 a b^{2} d^{4} g^{3} n^{2} \log{\left(d + e x \right)}^{2}}{4 e^{4}} + \frac{25 a b^{2} d^{4} g^{3} n^{2} \log{\left(d + e x \right)}}{8 e^{4}} - \frac{3 a b^{2} d^{4} g^{3} n \log{\left(c \right)} \log{\left(d + e x \right)}}{2 e^{4}} + \frac{3 a b^{2} d^{3} f g^{2} n^{2} \log{\left(d + e x \right)}^{2}}{e^{3}} - \frac{11 a b^{2} d^{3} f g^{2} n^{2} \log{\left(d + e x \right)}}{e^{3}} + \frac{6 a b^{2} d^{3} f g^{2} n \log{\left(c \right)} \log{\left(d + e x \right)}}{e^{3}} + \frac{3 a b^{2} d^{3} g^{3} n^{2} x \log{\left(d + e x \right)}}{2 e^{3}} - \frac{25 a b^{2} d^{3} g^{3} n^{2} x}{8 e^{3}} + \frac{3 a b^{2} d^{3} g^{3} n x \log{\left(c \right)}}{2 e^{3}} - \frac{9 a b^{2} d^{2} f^{2} g n^{2} \log{\left(d + e x \right)}^{2}}{2 e^{2}} + \frac{27 a b^{2} d^{2} f^{2} g n^{2} \log{\left(d + e x \right)}}{2 e^{2}} - \frac{9 a b^{2} d^{2} f^{2} g n \log{\left(c \right)} \log{\left(d + e x \right)}}{e^{2}} - \frac{6 a b^{2} d^{2} f g^{2} n^{2} x \log{\left(d + e x \right)}}{e^{2}} + \frac{11 a b^{2} d^{2} f g^{2} n^{2} x}{e^{2}} - \frac{6 a b^{2} d^{2} f g^{2} n x \log{\left(c \right)}}{e^{2}} - \frac{3 a b^{2} d^{2} g^{3} n^{2} x^{2} \log{\left(d + e x \right)}}{4 e^{2}} + \frac{13 a b^{2} d^{2} g^{3} n^{2} x^{2}}{16 e^{2}} - \frac{3 a b^{2} d^{2} g^{3} n x^{2} \log{\left(c \right)}}{4 e^{2}} + \frac{3 a b^{2} d f^{3} n^{2} \log{\left(d + e x \right)}^{2}}{e} - \frac{6 a b^{2} d f^{3} n^{2} \log{\left(d + e x \right)}}{e} + \frac{6 a b^{2} d f^{3} n \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{9 a b^{2} d f^{2} g n^{2} x \log{\left(d + e x \right)}}{e} - \frac{27 a b^{2} d f^{2} g n^{2} x}{2 e} + \frac{9 a b^{2} d f^{2} g n x \log{\left(c \right)}}{e} + \frac{3 a b^{2} d f g^{2} n^{2} x^{2} \log{\left(d + e x \right)}}{e} - \frac{5 a b^{2} d f g^{2} n^{2} x^{2}}{2 e} + \frac{3 a b^{2} d f g^{2} n x^{2} \log{\left(c \right)}}{e} + \frac{a b^{2} d g^{3} n^{2} x^{3} \log{\left(d + e x \right)}}{2 e} - \frac{7 a b^{2} d g^{3} n^{2} x^{3}}{24 e} + \frac{a b^{2} d g^{3} n x^{3} \log{\left(c \right)}}{2 e} + 3 a b^{2} f^{3} n^{2} x \log{\left(d + e x \right)}^{2} - 6 a b^{2} f^{3} n^{2} x \log{\left(d + e x \right)} + 6 a b^{2} f^{3} n^{2} x + 6 a b^{2} f^{3} n x \log{\left(c \right)} \log{\left(d + e x \right)} - 6 a b^{2} f^{3} n x \log{\left(c \right)} + 3 a b^{2} f^{3} x \log{\left(c \right)}^{2} + \frac{9 a b^{2} f^{2} g n^{2} x^{2} \log{\left(d + e x \right)}^{2}}{2} - \frac{9 a b^{2} f^{2} g n^{2} x^{2} \log{\left(d + e x \right)}}{2} + \frac{9 a b^{2} f^{2} g n^{2} x^{2}}{4} + 9 a b^{2} f^{2} g n x^{2} \log{\left(c \right)} \log{\left(d + e x \right)} - \frac{9 a b^{2} f^{2} g n x^{2} \log{\left(c \right)}}{2} + \frac{9 a b^{2} f^{2} g x^{2} \log{\left(c \right)}^{2}}{2} + 3 a b^{2} f g^{2} n^{2} x^{3} \log{\left(d + e x \right)}^{2} - 2 a b^{2} f g^{2} n^{2} x^{3} \log{\left(d + e x \right)} + \frac{2 a b^{2} f g^{2} n^{2} x^{3}}{3} + 6 a b^{2} f g^{2} n x^{3} \log{\left(c \right)} \log{\left(d + e x \right)} - 2 a b^{2} f g^{2} n x^{3} \log{\left(c \right)} + 3 a b^{2} f g^{2} x^{3} \log{\left(c \right)}^{2} + \frac{3 a b^{2} g^{3} n^{2} x^{4} \log{\left(d + e x \right)}^{2}}{4} - \frac{3 a b^{2} g^{3} n^{2} x^{4} \log{\left(d + e x \right)}}{8} + \frac{3 a b^{2} g^{3} n^{2} x^{4}}{32} + \frac{3 a b^{2} g^{3} n x^{4} \log{\left(c \right)} \log{\left(d + e x \right)}}{2} - \frac{3 a b^{2} g^{3} n x^{4} \log{\left(c \right)}}{8} + \frac{3 a b^{2} g^{3} x^{4} \log{\left(c \right)}^{2}}{4} - \frac{b^{3} d^{4} g^{3} n^{3} \log{\left(d + e x \right)}^{3}}{4 e^{4}} + \frac{25 b^{3} d^{4} g^{3} n^{3} \log{\left(d + e x \right)}^{2}}{16 e^{4}} - \frac{415 b^{3} d^{4} g^{3} n^{3} \log{\left(d + e x \right)}}{96 e^{4}} - \frac{3 b^{3} d^{4} g^{3} n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{4 e^{4}} + \frac{25 b^{3} d^{4} g^{3} n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{8 e^{4}} - \frac{3 b^{3} d^{4} g^{3} n \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{4 e^{4}} + \frac{b^{3} d^{3} f g^{2} n^{3} \log{\left(d + e x \right)}^{3}}{e^{3}} - \frac{11 b^{3} d^{3} f g^{2} n^{3} \log{\left(d + e x \right)}^{2}}{2 e^{3}} + \frac{85 b^{3} d^{3} f g^{2} n^{3} \log{\left(d + e x \right)}}{6 e^{3}} + \frac{3 b^{3} d^{3} f g^{2} n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{e^{3}} - \frac{11 b^{3} d^{3} f g^{2} n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{e^{3}} + \frac{3 b^{3} d^{3} f g^{2} n \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{e^{3}} + \frac{3 b^{3} d^{3} g^{3} n^{3} x \log{\left(d + e x \right)}^{2}}{4 e^{3}} - \frac{25 b^{3} d^{3} g^{3} n^{3} x \log{\left(d + e x \right)}}{8 e^{3}} + \frac{415 b^{3} d^{3} g^{3} n^{3} x}{96 e^{3}} + \frac{3 b^{3} d^{3} g^{3} n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)}}{2 e^{3}} - \frac{25 b^{3} d^{3} g^{3} n^{2} x \log{\left(c \right)}}{8 e^{3}} + \frac{3 b^{3} d^{3} g^{3} n x \log{\left(c \right)}^{2}}{4 e^{3}} - \frac{3 b^{3} d^{2} f^{2} g n^{3} \log{\left(d + e x \right)}^{3}}{2 e^{2}} + \frac{27 b^{3} d^{2} f^{2} g n^{3} \log{\left(d + e x \right)}^{2}}{4 e^{2}} - \frac{63 b^{3} d^{2} f^{2} g n^{3} \log{\left(d + e x \right)}}{4 e^{2}} - \frac{9 b^{3} d^{2} f^{2} g n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{2 e^{2}} + \frac{27 b^{3} d^{2} f^{2} g n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{2 e^{2}} - \frac{9 b^{3} d^{2} f^{2} g n \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{2 e^{2}} - \frac{3 b^{3} d^{2} f g^{2} n^{3} x \log{\left(d + e x \right)}^{2}}{e^{2}} + \frac{11 b^{3} d^{2} f g^{2} n^{3} x \log{\left(d + e x \right)}}{e^{2}} - \frac{85 b^{3} d^{2} f g^{2} n^{3} x}{6 e^{2}} - \frac{6 b^{3} d^{2} f g^{2} n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)}}{e^{2}} + \frac{11 b^{3} d^{2} f g^{2} n^{2} x \log{\left(c \right)}}{e^{2}} - \frac{3 b^{3} d^{2} f g^{2} n x \log{\left(c \right)}^{2}}{e^{2}} - \frac{3 b^{3} d^{2} g^{3} n^{3} x^{2} \log{\left(d + e x \right)}^{2}}{8 e^{2}} + \frac{13 b^{3} d^{2} g^{3} n^{3} x^{2} \log{\left(d + e x \right)}}{16 e^{2}} - \frac{115 b^{3} d^{2} g^{3} n^{3} x^{2}}{192 e^{2}} - \frac{3 b^{3} d^{2} g^{3} n^{2} x^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{4 e^{2}} + \frac{13 b^{3} d^{2} g^{3} n^{2} x^{2} \log{\left(c \right)}}{16 e^{2}} - \frac{3 b^{3} d^{2} g^{3} n x^{2} \log{\left(c \right)}^{2}}{8 e^{2}} + \frac{b^{3} d f^{3} n^{3} \log{\left(d + e x \right)}^{3}}{e} - \frac{3 b^{3} d f^{3} n^{3} \log{\left(d + e x \right)}^{2}}{e} + \frac{6 b^{3} d f^{3} n^{3} \log{\left(d + e x \right)}}{e} + \frac{3 b^{3} d f^{3} n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{e} - \frac{6 b^{3} d f^{3} n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{3 b^{3} d f^{3} n \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{e} + \frac{9 b^{3} d f^{2} g n^{3} x \log{\left(d + e x \right)}^{2}}{2 e} - \frac{27 b^{3} d f^{2} g n^{3} x \log{\left(d + e x \right)}}{2 e} + \frac{63 b^{3} d f^{2} g n^{3} x}{4 e} + \frac{9 b^{3} d f^{2} g n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)}}{e} - \frac{27 b^{3} d f^{2} g n^{2} x \log{\left(c \right)}}{2 e} + \frac{9 b^{3} d f^{2} g n x \log{\left(c \right)}^{2}}{2 e} + \frac{3 b^{3} d f g^{2} n^{3} x^{2} \log{\left(d + e x \right)}^{2}}{2 e} - \frac{5 b^{3} d f g^{2} n^{3} x^{2} \log{\left(d + e x \right)}}{2 e} + \frac{19 b^{3} d f g^{2} n^{3} x^{2}}{12 e} + \frac{3 b^{3} d f g^{2} n^{2} x^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{e} - \frac{5 b^{3} d f g^{2} n^{2} x^{2} \log{\left(c \right)}}{2 e} + \frac{3 b^{3} d f g^{2} n x^{2} \log{\left(c \right)}^{2}}{2 e} + \frac{b^{3} d g^{3} n^{3} x^{3} \log{\left(d + e x \right)}^{2}}{4 e} - \frac{7 b^{3} d g^{3} n^{3} x^{3} \log{\left(d + e x \right)}}{24 e} + \frac{37 b^{3} d g^{3} n^{3} x^{3}}{288 e} + \frac{b^{3} d g^{3} n^{2} x^{3} \log{\left(c \right)} \log{\left(d + e x \right)}}{2 e} - \frac{7 b^{3} d g^{3} n^{2} x^{3} \log{\left(c \right)}}{24 e} + \frac{b^{3} d g^{3} n x^{3} \log{\left(c \right)}^{2}}{4 e} + b^{3} f^{3} n^{3} x \log{\left(d + e x \right)}^{3} - 3 b^{3} f^{3} n^{3} x \log{\left(d + e x \right)}^{2} + 6 b^{3} f^{3} n^{3} x \log{\left(d + e x \right)} - 6 b^{3} f^{3} n^{3} x + 3 b^{3} f^{3} n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)}^{2} - 6 b^{3} f^{3} n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)} + 6 b^{3} f^{3} n^{2} x \log{\left(c \right)} + 3 b^{3} f^{3} n x \log{\left(c \right)}^{2} \log{\left(d + e x \right)} - 3 b^{3} f^{3} n x \log{\left(c \right)}^{2} + b^{3} f^{3} x \log{\left(c \right)}^{3} + \frac{3 b^{3} f^{2} g n^{3} x^{2} \log{\left(d + e x \right)}^{3}}{2} - \frac{9 b^{3} f^{2} g n^{3} x^{2} \log{\left(d + e x \right)}^{2}}{4} + \frac{9 b^{3} f^{2} g n^{3} x^{2} \log{\left(d + e x \right)}}{4} - \frac{9 b^{3} f^{2} g n^{3} x^{2}}{8} + \frac{9 b^{3} f^{2} g n^{2} x^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{2} - \frac{9 b^{3} f^{2} g n^{2} x^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{2} + \frac{9 b^{3} f^{2} g n^{2} x^{2} \log{\left(c \right)}}{4} + \frac{9 b^{3} f^{2} g n x^{2} \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{2} - \frac{9 b^{3} f^{2} g n x^{2} \log{\left(c \right)}^{2}}{4} + \frac{3 b^{3} f^{2} g x^{2} \log{\left(c \right)}^{3}}{2} + b^{3} f g^{2} n^{3} x^{3} \log{\left(d + e x \right)}^{3} - b^{3} f g^{2} n^{3} x^{3} \log{\left(d + e x \right)}^{2} + \frac{2 b^{3} f g^{2} n^{3} x^{3} \log{\left(d + e x \right)}}{3} - \frac{2 b^{3} f g^{2} n^{3} x^{3}}{9} + 3 b^{3} f g^{2} n^{2} x^{3} \log{\left(c \right)} \log{\left(d + e x \right)}^{2} - 2 b^{3} f g^{2} n^{2} x^{3} \log{\left(c \right)} \log{\left(d + e x \right)} + \frac{2 b^{3} f g^{2} n^{2} x^{3} \log{\left(c \right)}}{3} + 3 b^{3} f g^{2} n x^{3} \log{\left(c \right)}^{2} \log{\left(d + e x \right)} - b^{3} f g^{2} n x^{3} \log{\left(c \right)}^{2} + b^{3} f g^{2} x^{3} \log{\left(c \right)}^{3} + \frac{b^{3} g^{3} n^{3} x^{4} \log{\left(d + e x \right)}^{3}}{4} - \frac{3 b^{3} g^{3} n^{3} x^{4} \log{\left(d + e x \right)}^{2}}{16} + \frac{3 b^{3} g^{3} n^{3} x^{4} \log{\left(d + e x \right)}}{32} - \frac{3 b^{3} g^{3} n^{3} x^{4}}{128} + \frac{3 b^{3} g^{3} n^{2} x^{4} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{4} - \frac{3 b^{3} g^{3} n^{2} x^{4} \log{\left(c \right)} \log{\left(d + e x \right)}}{8} + \frac{3 b^{3} g^{3} n^{2} x^{4} \log{\left(c \right)}}{32} + \frac{3 b^{3} g^{3} n x^{4} \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{4} - \frac{3 b^{3} g^{3} n x^{4} \log{\left(c \right)}^{2}}{16} + \frac{b^{3} g^{3} x^{4} \log{\left(c \right)}^{3}}{4} & \text{for}\: e \neq 0 \\\left(a + b \log{\left(c d^{n} \right)}\right)^{3} \left(f^{3} x + \frac{3 f^{2} g x^{2}}{2} + f g^{2} x^{3} + \frac{g^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*f**3*x + 3*a**3*f**2*g*x**2/2 + a**3*f*g**2*x**3 + a**3*g**3*x**4/4 - 3*a**2*b*d**4*g**3*n*log(d + e*x)/(4*e**4) + 3*a**2*b*d**3*f*g**2*n*log(d + e*x)/e**3 + 3*a**2*b*d**3*g**3*n*x/(4*e**3) - 9*a**2*b*d**2*f**2*g*n*log(d + e*x)/(2*e**2) - 3*a**2*b*d**2*f*g**2*n*x/e**2 - 3*a**2*b*d**2*g**3*n*x**2/(8*e**2) + 3*a**2*b*d*f**3*n*log(d + e*x)/e + 9*a**2*b*d*f**2*g*n*x/(2*e) + 3*a**2*b*d*f*g**2*n*x**2/(2*e) + a**2*b*d*g**3*n*x**3/(4*e) + 3*a**2*b*f**3*n*x*log(d + e*x) - 3*a**2*b*f**3*n*x + 3*a**2*b*f**3*x*log(c) + 9*a**2*b*f**2*g*n*x**2*log(d + e*x)/2 - 9*a**2*b*f**2*g*n*x**2/4 + 9*a**2*b*f**2*g*x**2*log(c)/2 + 3*a**2*b*f*g**2*n*x**3*log(d + e*x) - a**2*b*f*g**2*n*x**3 + 3*a**2*b*f*g**2*x**3*log(c) + 3*a**2*b*g**3*n*x**4*log(d + e*x)/4 - 3*a**2*b*g**3*n*x**4/16 + 3*a**2*b*g**3*x**4*log(c)/4 - 3*a*b**2*d**4*g**3*n**2*log(d + e*x)**2/(4*e**4) + 25*a*b**2*d**4*g**3*n**2*log(d + e*x)/(8*e**4) - 3*a*b**2*d**4*g**3*n*log(c)*log(d + e*x)/(2*e**4) + 3*a*b**2*d**3*f*g**2*n**2*log(d + e*x)**2/e**3 - 11*a*b**2*d**3*f*g**2*n**2*log(d + e*x)/e**3 + 6*a*b**2*d**3*f*g**2*n*log(c)*log(d + e*x)/e**3 + 3*a*b**2*d**3*g**3*n**2*x*log(d + e*x)/(2*e**3) - 25*a*b**2*d**3*g**3*n**2*x/(8*e**3) + 3*a*b**2*d**3*g**3*n*x*log(c)/(2*e**3) - 9*a*b**2*d**2*f**2*g*n**2*log(d + e*x)**2/(2*e**2) + 27*a*b**2*d**2*f**2*g*n**2*log(d + e*x)/(2*e**2) - 9*a*b**2*d**2*f**2*g*n*log(c)*log(d + e*x)/e**2 - 6*a*b**2*d**2*f*g**2*n**2*x*log(d + e*x)/e**2 + 11*a*b**2*d**2*f*g**2*n**2*x/e**2 - 6*a*b**2*d**2*f*g**2*n*x*log(c)/e**2 - 3*a*b**2*d**2*g**3*n**2*x**2*log(d + e*x)/(4*e**2) + 13*a*b**2*d**2*g**3*n**2*x**2/(16*e**2) - 3*a*b**2*d**2*g**3*n*x**2*log(c)/(4*e**2) + 3*a*b**2*d*f**3*n**2*log(d + e*x)**2/e - 6*a*b**2*d*f**3*n**2*log(d + e*x)/e + 6*a*b**2*d*f**3*n*log(c)*log(d + e*x)/e + 9*a*b**2*d*f**2*g*n**2*x*log(d + e*x)/e - 27*a*b**2*d*f**2*g*n**2*x/(2*e) + 9*a*b**2*d*f**2*g*n*x*log(c)/e + 3*a*b**2*d*f*g**2*n**2*x**2*log(d + e*x)/e - 5*a*b**2*d*f*g**2*n**2*x**2/(2*e) + 3*a*b**2*d*f*g**2*n*x**2*log(c)/e + a*b**2*d*g**3*n**2*x**3*log(d + e*x)/(2*e) - 7*a*b**2*d*g**3*n**2*x**3/(24*e) + a*b**2*d*g**3*n*x**3*log(c)/(2*e) + 3*a*b**2*f**3*n**2*x*log(d + e*x)**2 - 6*a*b**2*f**3*n**2*x*log(d + e*x) + 6*a*b**2*f**3*n**2*x + 6*a*b**2*f**3*n*x*log(c)*log(d + e*x) - 6*a*b**2*f**3*n*x*log(c) + 3*a*b**2*f**3*x*log(c)**2 + 9*a*b**2*f**2*g*n**2*x**2*log(d + e*x)**2/2 - 9*a*b**2*f**2*g*n**2*x**2*log(d + e*x)/2 + 9*a*b**2*f**2*g*n**2*x**2/4 + 9*a*b**2*f**2*g*n*x**2*log(c)*log(d + e*x) - 9*a*b**2*f**2*g*n*x**2*log(c)/2 + 9*a*b**2*f**2*g*x**2*log(c)**2/2 + 3*a*b**2*f*g**2*n**2*x**3*log(d + e*x)**2 - 2*a*b**2*f*g**2*n**2*x**3*log(d + e*x) + 2*a*b**2*f*g**2*n**2*x**3/3 + 6*a*b**2*f*g**2*n*x**3*log(c)*log(d + e*x) - 2*a*b**2*f*g**2*n*x**3*log(c) + 3*a*b**2*f*g**2*x**3*log(c)**2 + 3*a*b**2*g**3*n**2*x**4*log(d + e*x)**2/4 - 3*a*b**2*g**3*n**2*x**4*log(d + e*x)/8 + 3*a*b**2*g**3*n**2*x**4/32 + 3*a*b**2*g**3*n*x**4*log(c)*log(d + e*x)/2 - 3*a*b**2*g**3*n*x**4*log(c)/8 + 3*a*b**2*g**3*x**4*log(c)**2/4 - b**3*d**4*g**3*n**3*log(d + e*x)**3/(4*e**4) + 25*b**3*d**4*g**3*n**3*log(d + e*x)**2/(16*e**4) - 415*b**3*d**4*g**3*n**3*log(d + e*x)/(96*e**4) - 3*b**3*d**4*g**3*n**2*log(c)*log(d + e*x)**2/(4*e**4) + 25*b**3*d**4*g**3*n**2*log(c)*log(d + e*x)/(8*e**4) - 3*b**3*d**4*g**3*n*log(c)**2*log(d + e*x)/(4*e**4) + b**3*d**3*f*g**2*n**3*log(d + e*x)**3/e**3 - 11*b**3*d**3*f*g**2*n**3*log(d + e*x)**2/(2*e**3) + 85*b**3*d**3*f*g**2*n**3*log(d + e*x)/(6*e**3) + 3*b**3*d**3*f*g**2*n**2*log(c)*log(d + e*x)**2/e**3 - 11*b**3*d**3*f*g**2*n**2*log(c)*log(d + e*x)/e**3 + 3*b**3*d**3*f*g**2*n*log(c)**2*log(d + e*x)/e**3 + 3*b**3*d**3*g**3*n**3*x*log(d + e*x)**2/(4*e**3) - 25*b**3*d**3*g**3*n**3*x*log(d + e*x)/(8*e**3) + 415*b**3*d**3*g**3*n**3*x/(96*e**3) + 3*b**3*d**3*g**3*n**2*x*log(c)*log(d + e*x)/(2*e**3) - 25*b**3*d**3*g**3*n**2*x*log(c)/(8*e**3) + 3*b**3*d**3*g**3*n*x*log(c)**2/(4*e**3) - 3*b**3*d**2*f**2*g*n**3*log(d + e*x)**3/(2*e**2) + 27*b**3*d**2*f**2*g*n**3*log(d + e*x)**2/(4*e**2) - 63*b**3*d**2*f**2*g*n**3*log(d + e*x)/(4*e**2) - 9*b**3*d**2*f**2*g*n**2*log(c)*log(d + e*x)**2/(2*e**2) + 27*b**3*d**2*f**2*g*n**2*log(c)*log(d + e*x)/(2*e**2) - 9*b**3*d**2*f**2*g*n*log(c)**2*log(d + e*x)/(2*e**2) - 3*b**3*d**2*f*g**2*n**3*x*log(d + e*x)**2/e**2 + 11*b**3*d**2*f*g**2*n**3*x*log(d + e*x)/e**2 - 85*b**3*d**2*f*g**2*n**3*x/(6*e**2) - 6*b**3*d**2*f*g**2*n**2*x*log(c)*log(d + e*x)/e**2 + 11*b**3*d**2*f*g**2*n**2*x*log(c)/e**2 - 3*b**3*d**2*f*g**2*n*x*log(c)**2/e**2 - 3*b**3*d**2*g**3*n**3*x**2*log(d + e*x)**2/(8*e**2) + 13*b**3*d**2*g**3*n**3*x**2*log(d + e*x)/(16*e**2) - 115*b**3*d**2*g**3*n**3*x**2/(192*e**2) - 3*b**3*d**2*g**3*n**2*x**2*log(c)*log(d + e*x)/(4*e**2) + 13*b**3*d**2*g**3*n**2*x**2*log(c)/(16*e**2) - 3*b**3*d**2*g**3*n*x**2*log(c)**2/(8*e**2) + b**3*d*f**3*n**3*log(d + e*x)**3/e - 3*b**3*d*f**3*n**3*log(d + e*x)**2/e + 6*b**3*d*f**3*n**3*log(d + e*x)/e + 3*b**3*d*f**3*n**2*log(c)*log(d + e*x)**2/e - 6*b**3*d*f**3*n**2*log(c)*log(d + e*x)/e + 3*b**3*d*f**3*n*log(c)**2*log(d + e*x)/e + 9*b**3*d*f**2*g*n**3*x*log(d + e*x)**2/(2*e) - 27*b**3*d*f**2*g*n**3*x*log(d + e*x)/(2*e) + 63*b**3*d*f**2*g*n**3*x/(4*e) + 9*b**3*d*f**2*g*n**2*x*log(c)*log(d + e*x)/e - 27*b**3*d*f**2*g*n**2*x*log(c)/(2*e) + 9*b**3*d*f**2*g*n*x*log(c)**2/(2*e) + 3*b**3*d*f*g**2*n**3*x**2*log(d + e*x)**2/(2*e) - 5*b**3*d*f*g**2*n**3*x**2*log(d + e*x)/(2*e) + 19*b**3*d*f*g**2*n**3*x**2/(12*e) + 3*b**3*d*f*g**2*n**2*x**2*log(c)*log(d + e*x)/e - 5*b**3*d*f*g**2*n**2*x**2*log(c)/(2*e) + 3*b**3*d*f*g**2*n*x**2*log(c)**2/(2*e) + b**3*d*g**3*n**3*x**3*log(d + e*x)**2/(4*e) - 7*b**3*d*g**3*n**3*x**3*log(d + e*x)/(24*e) + 37*b**3*d*g**3*n**3*x**3/(288*e) + b**3*d*g**3*n**2*x**3*log(c)*log(d + e*x)/(2*e) - 7*b**3*d*g**3*n**2*x**3*log(c)/(24*e) + b**3*d*g**3*n*x**3*log(c)**2/(4*e) + b**3*f**3*n**3*x*log(d + e*x)**3 - 3*b**3*f**3*n**3*x*log(d + e*x)**2 + 6*b**3*f**3*n**3*x*log(d + e*x) - 6*b**3*f**3*n**3*x + 3*b**3*f**3*n**2*x*log(c)*log(d + e*x)**2 - 6*b**3*f**3*n**2*x*log(c)*log(d + e*x) + 6*b**3*f**3*n**2*x*log(c) + 3*b**3*f**3*n*x*log(c)**2*log(d + e*x) - 3*b**3*f**3*n*x*log(c)**2 + b**3*f**3*x*log(c)**3 + 3*b**3*f**2*g*n**3*x**2*log(d + e*x)**3/2 - 9*b**3*f**2*g*n**3*x**2*log(d + e*x)**2/4 + 9*b**3*f**2*g*n**3*x**2*log(d + e*x)/4 - 9*b**3*f**2*g*n**3*x**2/8 + 9*b**3*f**2*g*n**2*x**2*log(c)*log(d + e*x)**2/2 - 9*b**3*f**2*g*n**2*x**2*log(c)*log(d + e*x)/2 + 9*b**3*f**2*g*n**2*x**2*log(c)/4 + 9*b**3*f**2*g*n*x**2*log(c)**2*log(d + e*x)/2 - 9*b**3*f**2*g*n*x**2*log(c)**2/4 + 3*b**3*f**2*g*x**2*log(c)**3/2 + b**3*f*g**2*n**3*x**3*log(d + e*x)**3 - b**3*f*g**2*n**3*x**3*log(d + e*x)**2 + 2*b**3*f*g**2*n**3*x**3*log(d + e*x)/3 - 2*b**3*f*g**2*n**3*x**3/9 + 3*b**3*f*g**2*n**2*x**3*log(c)*log(d + e*x)**2 - 2*b**3*f*g**2*n**2*x**3*log(c)*log(d + e*x) + 2*b**3*f*g**2*n**2*x**3*log(c)/3 + 3*b**3*f*g**2*n*x**3*log(c)**2*log(d + e*x) - b**3*f*g**2*n*x**3*log(c)**2 + b**3*f*g**2*x**3*log(c)**3 + b**3*g**3*n**3*x**4*log(d + e*x)**3/4 - 3*b**3*g**3*n**3*x**4*log(d + e*x)**2/16 + 3*b**3*g**3*n**3*x**4*log(d + e*x)/32 - 3*b**3*g**3*n**3*x**4/128 + 3*b**3*g**3*n**2*x**4*log(c)*log(d + e*x)**2/4 - 3*b**3*g**3*n**2*x**4*log(c)*log(d + e*x)/8 + 3*b**3*g**3*n**2*x**4*log(c)/32 + 3*b**3*g**3*n*x**4*log(c)**2*log(d + e*x)/4 - 3*b**3*g**3*n*x**4*log(c)**2/16 + b**3*g**3*x**4*log(c)**3/4, Ne(e, 0)), ((a + b*log(c*d**n))**3*(f**3*x + 3*f**2*g*x**2/2 + f*g**2*x**3 + g**3*x**4/4), True))","A",0
53,1,2746,0,23.774533," ","integrate((g*x+f)**2*(a+b*ln(c*(e*x+d)**n))**3,x)","\begin{cases} a^{3} f^{2} x + a^{3} f g x^{2} + \frac{a^{3} g^{2} x^{3}}{3} + \frac{a^{2} b d^{3} g^{2} n \log{\left(d + e x \right)}}{e^{3}} - \frac{3 a^{2} b d^{2} f g n \log{\left(d + e x \right)}}{e^{2}} - \frac{a^{2} b d^{2} g^{2} n x}{e^{2}} + \frac{3 a^{2} b d f^{2} n \log{\left(d + e x \right)}}{e} + \frac{3 a^{2} b d f g n x}{e} + \frac{a^{2} b d g^{2} n x^{2}}{2 e} + 3 a^{2} b f^{2} n x \log{\left(d + e x \right)} - 3 a^{2} b f^{2} n x + 3 a^{2} b f^{2} x \log{\left(c \right)} + 3 a^{2} b f g n x^{2} \log{\left(d + e x \right)} - \frac{3 a^{2} b f g n x^{2}}{2} + 3 a^{2} b f g x^{2} \log{\left(c \right)} + a^{2} b g^{2} n x^{3} \log{\left(d + e x \right)} - \frac{a^{2} b g^{2} n x^{3}}{3} + a^{2} b g^{2} x^{3} \log{\left(c \right)} + \frac{a b^{2} d^{3} g^{2} n^{2} \log{\left(d + e x \right)}^{2}}{e^{3}} - \frac{11 a b^{2} d^{3} g^{2} n^{2} \log{\left(d + e x \right)}}{3 e^{3}} + \frac{2 a b^{2} d^{3} g^{2} n \log{\left(c \right)} \log{\left(d + e x \right)}}{e^{3}} - \frac{3 a b^{2} d^{2} f g n^{2} \log{\left(d + e x \right)}^{2}}{e^{2}} + \frac{9 a b^{2} d^{2} f g n^{2} \log{\left(d + e x \right)}}{e^{2}} - \frac{6 a b^{2} d^{2} f g n \log{\left(c \right)} \log{\left(d + e x \right)}}{e^{2}} - \frac{2 a b^{2} d^{2} g^{2} n^{2} x \log{\left(d + e x \right)}}{e^{2}} + \frac{11 a b^{2} d^{2} g^{2} n^{2} x}{3 e^{2}} - \frac{2 a b^{2} d^{2} g^{2} n x \log{\left(c \right)}}{e^{2}} + \frac{3 a b^{2} d f^{2} n^{2} \log{\left(d + e x \right)}^{2}}{e} - \frac{6 a b^{2} d f^{2} n^{2} \log{\left(d + e x \right)}}{e} + \frac{6 a b^{2} d f^{2} n \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{6 a b^{2} d f g n^{2} x \log{\left(d + e x \right)}}{e} - \frac{9 a b^{2} d f g n^{2} x}{e} + \frac{6 a b^{2} d f g n x \log{\left(c \right)}}{e} + \frac{a b^{2} d g^{2} n^{2} x^{2} \log{\left(d + e x \right)}}{e} - \frac{5 a b^{2} d g^{2} n^{2} x^{2}}{6 e} + \frac{a b^{2} d g^{2} n x^{2} \log{\left(c \right)}}{e} + 3 a b^{2} f^{2} n^{2} x \log{\left(d + e x \right)}^{2} - 6 a b^{2} f^{2} n^{2} x \log{\left(d + e x \right)} + 6 a b^{2} f^{2} n^{2} x + 6 a b^{2} f^{2} n x \log{\left(c \right)} \log{\left(d + e x \right)} - 6 a b^{2} f^{2} n x \log{\left(c \right)} + 3 a b^{2} f^{2} x \log{\left(c \right)}^{2} + 3 a b^{2} f g n^{2} x^{2} \log{\left(d + e x \right)}^{2} - 3 a b^{2} f g n^{2} x^{2} \log{\left(d + e x \right)} + \frac{3 a b^{2} f g n^{2} x^{2}}{2} + 6 a b^{2} f g n x^{2} \log{\left(c \right)} \log{\left(d + e x \right)} - 3 a b^{2} f g n x^{2} \log{\left(c \right)} + 3 a b^{2} f g x^{2} \log{\left(c \right)}^{2} + a b^{2} g^{2} n^{2} x^{3} \log{\left(d + e x \right)}^{2} - \frac{2 a b^{2} g^{2} n^{2} x^{3} \log{\left(d + e x \right)}}{3} + \frac{2 a b^{2} g^{2} n^{2} x^{3}}{9} + 2 a b^{2} g^{2} n x^{3} \log{\left(c \right)} \log{\left(d + e x \right)} - \frac{2 a b^{2} g^{2} n x^{3} \log{\left(c \right)}}{3} + a b^{2} g^{2} x^{3} \log{\left(c \right)}^{2} + \frac{b^{3} d^{3} g^{2} n^{3} \log{\left(d + e x \right)}^{3}}{3 e^{3}} - \frac{11 b^{3} d^{3} g^{2} n^{3} \log{\left(d + e x \right)}^{2}}{6 e^{3}} + \frac{85 b^{3} d^{3} g^{2} n^{3} \log{\left(d + e x \right)}}{18 e^{3}} + \frac{b^{3} d^{3} g^{2} n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{e^{3}} - \frac{11 b^{3} d^{3} g^{2} n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{3 e^{3}} + \frac{b^{3} d^{3} g^{2} n \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{e^{3}} - \frac{b^{3} d^{2} f g n^{3} \log{\left(d + e x \right)}^{3}}{e^{2}} + \frac{9 b^{3} d^{2} f g n^{3} \log{\left(d + e x \right)}^{2}}{2 e^{2}} - \frac{21 b^{3} d^{2} f g n^{3} \log{\left(d + e x \right)}}{2 e^{2}} - \frac{3 b^{3} d^{2} f g n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{e^{2}} + \frac{9 b^{3} d^{2} f g n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{e^{2}} - \frac{3 b^{3} d^{2} f g n \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{e^{2}} - \frac{b^{3} d^{2} g^{2} n^{3} x \log{\left(d + e x \right)}^{2}}{e^{2}} + \frac{11 b^{3} d^{2} g^{2} n^{3} x \log{\left(d + e x \right)}}{3 e^{2}} - \frac{85 b^{3} d^{2} g^{2} n^{3} x}{18 e^{2}} - \frac{2 b^{3} d^{2} g^{2} n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)}}{e^{2}} + \frac{11 b^{3} d^{2} g^{2} n^{2} x \log{\left(c \right)}}{3 e^{2}} - \frac{b^{3} d^{2} g^{2} n x \log{\left(c \right)}^{2}}{e^{2}} + \frac{b^{3} d f^{2} n^{3} \log{\left(d + e x \right)}^{3}}{e} - \frac{3 b^{3} d f^{2} n^{3} \log{\left(d + e x \right)}^{2}}{e} + \frac{6 b^{3} d f^{2} n^{3} \log{\left(d + e x \right)}}{e} + \frac{3 b^{3} d f^{2} n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{e} - \frac{6 b^{3} d f^{2} n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{3 b^{3} d f^{2} n \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{e} + \frac{3 b^{3} d f g n^{3} x \log{\left(d + e x \right)}^{2}}{e} - \frac{9 b^{3} d f g n^{3} x \log{\left(d + e x \right)}}{e} + \frac{21 b^{3} d f g n^{3} x}{2 e} + \frac{6 b^{3} d f g n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)}}{e} - \frac{9 b^{3} d f g n^{2} x \log{\left(c \right)}}{e} + \frac{3 b^{3} d f g n x \log{\left(c \right)}^{2}}{e} + \frac{b^{3} d g^{2} n^{3} x^{2} \log{\left(d + e x \right)}^{2}}{2 e} - \frac{5 b^{3} d g^{2} n^{3} x^{2} \log{\left(d + e x \right)}}{6 e} + \frac{19 b^{3} d g^{2} n^{3} x^{2}}{36 e} + \frac{b^{3} d g^{2} n^{2} x^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{e} - \frac{5 b^{3} d g^{2} n^{2} x^{2} \log{\left(c \right)}}{6 e} + \frac{b^{3} d g^{2} n x^{2} \log{\left(c \right)}^{2}}{2 e} + b^{3} f^{2} n^{3} x \log{\left(d + e x \right)}^{3} - 3 b^{3} f^{2} n^{3} x \log{\left(d + e x \right)}^{2} + 6 b^{3} f^{2} n^{3} x \log{\left(d + e x \right)} - 6 b^{3} f^{2} n^{3} x + 3 b^{3} f^{2} n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)}^{2} - 6 b^{3} f^{2} n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)} + 6 b^{3} f^{2} n^{2} x \log{\left(c \right)} + 3 b^{3} f^{2} n x \log{\left(c \right)}^{2} \log{\left(d + e x \right)} - 3 b^{3} f^{2} n x \log{\left(c \right)}^{2} + b^{3} f^{2} x \log{\left(c \right)}^{3} + b^{3} f g n^{3} x^{2} \log{\left(d + e x \right)}^{3} - \frac{3 b^{3} f g n^{3} x^{2} \log{\left(d + e x \right)}^{2}}{2} + \frac{3 b^{3} f g n^{3} x^{2} \log{\left(d + e x \right)}}{2} - \frac{3 b^{3} f g n^{3} x^{2}}{4} + 3 b^{3} f g n^{2} x^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2} - 3 b^{3} f g n^{2} x^{2} \log{\left(c \right)} \log{\left(d + e x \right)} + \frac{3 b^{3} f g n^{2} x^{2} \log{\left(c \right)}}{2} + 3 b^{3} f g n x^{2} \log{\left(c \right)}^{2} \log{\left(d + e x \right)} - \frac{3 b^{3} f g n x^{2} \log{\left(c \right)}^{2}}{2} + b^{3} f g x^{2} \log{\left(c \right)}^{3} + \frac{b^{3} g^{2} n^{3} x^{3} \log{\left(d + e x \right)}^{3}}{3} - \frac{b^{3} g^{2} n^{3} x^{3} \log{\left(d + e x \right)}^{2}}{3} + \frac{2 b^{3} g^{2} n^{3} x^{3} \log{\left(d + e x \right)}}{9} - \frac{2 b^{3} g^{2} n^{3} x^{3}}{27} + b^{3} g^{2} n^{2} x^{3} \log{\left(c \right)} \log{\left(d + e x \right)}^{2} - \frac{2 b^{3} g^{2} n^{2} x^{3} \log{\left(c \right)} \log{\left(d + e x \right)}}{3} + \frac{2 b^{3} g^{2} n^{2} x^{3} \log{\left(c \right)}}{9} + b^{3} g^{2} n x^{3} \log{\left(c \right)}^{2} \log{\left(d + e x \right)} - \frac{b^{3} g^{2} n x^{3} \log{\left(c \right)}^{2}}{3} + \frac{b^{3} g^{2} x^{3} \log{\left(c \right)}^{3}}{3} & \text{for}\: e \neq 0 \\\left(a + b \log{\left(c d^{n} \right)}\right)^{3} \left(f^{2} x + f g x^{2} + \frac{g^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*f**2*x + a**3*f*g*x**2 + a**3*g**2*x**3/3 + a**2*b*d**3*g**2*n*log(d + e*x)/e**3 - 3*a**2*b*d**2*f*g*n*log(d + e*x)/e**2 - a**2*b*d**2*g**2*n*x/e**2 + 3*a**2*b*d*f**2*n*log(d + e*x)/e + 3*a**2*b*d*f*g*n*x/e + a**2*b*d*g**2*n*x**2/(2*e) + 3*a**2*b*f**2*n*x*log(d + e*x) - 3*a**2*b*f**2*n*x + 3*a**2*b*f**2*x*log(c) + 3*a**2*b*f*g*n*x**2*log(d + e*x) - 3*a**2*b*f*g*n*x**2/2 + 3*a**2*b*f*g*x**2*log(c) + a**2*b*g**2*n*x**3*log(d + e*x) - a**2*b*g**2*n*x**3/3 + a**2*b*g**2*x**3*log(c) + a*b**2*d**3*g**2*n**2*log(d + e*x)**2/e**3 - 11*a*b**2*d**3*g**2*n**2*log(d + e*x)/(3*e**3) + 2*a*b**2*d**3*g**2*n*log(c)*log(d + e*x)/e**3 - 3*a*b**2*d**2*f*g*n**2*log(d + e*x)**2/e**2 + 9*a*b**2*d**2*f*g*n**2*log(d + e*x)/e**2 - 6*a*b**2*d**2*f*g*n*log(c)*log(d + e*x)/e**2 - 2*a*b**2*d**2*g**2*n**2*x*log(d + e*x)/e**2 + 11*a*b**2*d**2*g**2*n**2*x/(3*e**2) - 2*a*b**2*d**2*g**2*n*x*log(c)/e**2 + 3*a*b**2*d*f**2*n**2*log(d + e*x)**2/e - 6*a*b**2*d*f**2*n**2*log(d + e*x)/e + 6*a*b**2*d*f**2*n*log(c)*log(d + e*x)/e + 6*a*b**2*d*f*g*n**2*x*log(d + e*x)/e - 9*a*b**2*d*f*g*n**2*x/e + 6*a*b**2*d*f*g*n*x*log(c)/e + a*b**2*d*g**2*n**2*x**2*log(d + e*x)/e - 5*a*b**2*d*g**2*n**2*x**2/(6*e) + a*b**2*d*g**2*n*x**2*log(c)/e + 3*a*b**2*f**2*n**2*x*log(d + e*x)**2 - 6*a*b**2*f**2*n**2*x*log(d + e*x) + 6*a*b**2*f**2*n**2*x + 6*a*b**2*f**2*n*x*log(c)*log(d + e*x) - 6*a*b**2*f**2*n*x*log(c) + 3*a*b**2*f**2*x*log(c)**2 + 3*a*b**2*f*g*n**2*x**2*log(d + e*x)**2 - 3*a*b**2*f*g*n**2*x**2*log(d + e*x) + 3*a*b**2*f*g*n**2*x**2/2 + 6*a*b**2*f*g*n*x**2*log(c)*log(d + e*x) - 3*a*b**2*f*g*n*x**2*log(c) + 3*a*b**2*f*g*x**2*log(c)**2 + a*b**2*g**2*n**2*x**3*log(d + e*x)**2 - 2*a*b**2*g**2*n**2*x**3*log(d + e*x)/3 + 2*a*b**2*g**2*n**2*x**3/9 + 2*a*b**2*g**2*n*x**3*log(c)*log(d + e*x) - 2*a*b**2*g**2*n*x**3*log(c)/3 + a*b**2*g**2*x**3*log(c)**2 + b**3*d**3*g**2*n**3*log(d + e*x)**3/(3*e**3) - 11*b**3*d**3*g**2*n**3*log(d + e*x)**2/(6*e**3) + 85*b**3*d**3*g**2*n**3*log(d + e*x)/(18*e**3) + b**3*d**3*g**2*n**2*log(c)*log(d + e*x)**2/e**3 - 11*b**3*d**3*g**2*n**2*log(c)*log(d + e*x)/(3*e**3) + b**3*d**3*g**2*n*log(c)**2*log(d + e*x)/e**3 - b**3*d**2*f*g*n**3*log(d + e*x)**3/e**2 + 9*b**3*d**2*f*g*n**3*log(d + e*x)**2/(2*e**2) - 21*b**3*d**2*f*g*n**3*log(d + e*x)/(2*e**2) - 3*b**3*d**2*f*g*n**2*log(c)*log(d + e*x)**2/e**2 + 9*b**3*d**2*f*g*n**2*log(c)*log(d + e*x)/e**2 - 3*b**3*d**2*f*g*n*log(c)**2*log(d + e*x)/e**2 - b**3*d**2*g**2*n**3*x*log(d + e*x)**2/e**2 + 11*b**3*d**2*g**2*n**3*x*log(d + e*x)/(3*e**2) - 85*b**3*d**2*g**2*n**3*x/(18*e**2) - 2*b**3*d**2*g**2*n**2*x*log(c)*log(d + e*x)/e**2 + 11*b**3*d**2*g**2*n**2*x*log(c)/(3*e**2) - b**3*d**2*g**2*n*x*log(c)**2/e**2 + b**3*d*f**2*n**3*log(d + e*x)**3/e - 3*b**3*d*f**2*n**3*log(d + e*x)**2/e + 6*b**3*d*f**2*n**3*log(d + e*x)/e + 3*b**3*d*f**2*n**2*log(c)*log(d + e*x)**2/e - 6*b**3*d*f**2*n**2*log(c)*log(d + e*x)/e + 3*b**3*d*f**2*n*log(c)**2*log(d + e*x)/e + 3*b**3*d*f*g*n**3*x*log(d + e*x)**2/e - 9*b**3*d*f*g*n**3*x*log(d + e*x)/e + 21*b**3*d*f*g*n**3*x/(2*e) + 6*b**3*d*f*g*n**2*x*log(c)*log(d + e*x)/e - 9*b**3*d*f*g*n**2*x*log(c)/e + 3*b**3*d*f*g*n*x*log(c)**2/e + b**3*d*g**2*n**3*x**2*log(d + e*x)**2/(2*e) - 5*b**3*d*g**2*n**3*x**2*log(d + e*x)/(6*e) + 19*b**3*d*g**2*n**3*x**2/(36*e) + b**3*d*g**2*n**2*x**2*log(c)*log(d + e*x)/e - 5*b**3*d*g**2*n**2*x**2*log(c)/(6*e) + b**3*d*g**2*n*x**2*log(c)**2/(2*e) + b**3*f**2*n**3*x*log(d + e*x)**3 - 3*b**3*f**2*n**3*x*log(d + e*x)**2 + 6*b**3*f**2*n**3*x*log(d + e*x) - 6*b**3*f**2*n**3*x + 3*b**3*f**2*n**2*x*log(c)*log(d + e*x)**2 - 6*b**3*f**2*n**2*x*log(c)*log(d + e*x) + 6*b**3*f**2*n**2*x*log(c) + 3*b**3*f**2*n*x*log(c)**2*log(d + e*x) - 3*b**3*f**2*n*x*log(c)**2 + b**3*f**2*x*log(c)**3 + b**3*f*g*n**3*x**2*log(d + e*x)**3 - 3*b**3*f*g*n**3*x**2*log(d + e*x)**2/2 + 3*b**3*f*g*n**3*x**2*log(d + e*x)/2 - 3*b**3*f*g*n**3*x**2/4 + 3*b**3*f*g*n**2*x**2*log(c)*log(d + e*x)**2 - 3*b**3*f*g*n**2*x**2*log(c)*log(d + e*x) + 3*b**3*f*g*n**2*x**2*log(c)/2 + 3*b**3*f*g*n*x**2*log(c)**2*log(d + e*x) - 3*b**3*f*g*n*x**2*log(c)**2/2 + b**3*f*g*x**2*log(c)**3 + b**3*g**2*n**3*x**3*log(d + e*x)**3/3 - b**3*g**2*n**3*x**3*log(d + e*x)**2/3 + 2*b**3*g**2*n**3*x**3*log(d + e*x)/9 - 2*b**3*g**2*n**3*x**3/27 + b**3*g**2*n**2*x**3*log(c)*log(d + e*x)**2 - 2*b**3*g**2*n**2*x**3*log(c)*log(d + e*x)/3 + 2*b**3*g**2*n**2*x**3*log(c)/9 + b**3*g**2*n*x**3*log(c)**2*log(d + e*x) - b**3*g**2*n*x**3*log(c)**2/3 + b**3*g**2*x**3*log(c)**3/3, Ne(e, 0)), ((a + b*log(c*d**n))**3*(f**2*x + f*g*x**2 + g**2*x**3/3), True))","A",0
54,1,1479,0,10.383152," ","integrate((g*x+f)*(a+b*ln(c*(e*x+d)**n))**3,x)","\begin{cases} a^{3} f x + \frac{a^{3} g x^{2}}{2} - \frac{3 a^{2} b d^{2} g n \log{\left(d + e x \right)}}{2 e^{2}} + \frac{3 a^{2} b d f n \log{\left(d + e x \right)}}{e} + \frac{3 a^{2} b d g n x}{2 e} + 3 a^{2} b f n x \log{\left(d + e x \right)} - 3 a^{2} b f n x + 3 a^{2} b f x \log{\left(c \right)} + \frac{3 a^{2} b g n x^{2} \log{\left(d + e x \right)}}{2} - \frac{3 a^{2} b g n x^{2}}{4} + \frac{3 a^{2} b g x^{2} \log{\left(c \right)}}{2} - \frac{3 a b^{2} d^{2} g n^{2} \log{\left(d + e x \right)}^{2}}{2 e^{2}} + \frac{9 a b^{2} d^{2} g n^{2} \log{\left(d + e x \right)}}{2 e^{2}} - \frac{3 a b^{2} d^{2} g n \log{\left(c \right)} \log{\left(d + e x \right)}}{e^{2}} + \frac{3 a b^{2} d f n^{2} \log{\left(d + e x \right)}^{2}}{e} - \frac{6 a b^{2} d f n^{2} \log{\left(d + e x \right)}}{e} + \frac{6 a b^{2} d f n \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{3 a b^{2} d g n^{2} x \log{\left(d + e x \right)}}{e} - \frac{9 a b^{2} d g n^{2} x}{2 e} + \frac{3 a b^{2} d g n x \log{\left(c \right)}}{e} + 3 a b^{2} f n^{2} x \log{\left(d + e x \right)}^{2} - 6 a b^{2} f n^{2} x \log{\left(d + e x \right)} + 6 a b^{2} f n^{2} x + 6 a b^{2} f n x \log{\left(c \right)} \log{\left(d + e x \right)} - 6 a b^{2} f n x \log{\left(c \right)} + 3 a b^{2} f x \log{\left(c \right)}^{2} + \frac{3 a b^{2} g n^{2} x^{2} \log{\left(d + e x \right)}^{2}}{2} - \frac{3 a b^{2} g n^{2} x^{2} \log{\left(d + e x \right)}}{2} + \frac{3 a b^{2} g n^{2} x^{2}}{4} + 3 a b^{2} g n x^{2} \log{\left(c \right)} \log{\left(d + e x \right)} - \frac{3 a b^{2} g n x^{2} \log{\left(c \right)}}{2} + \frac{3 a b^{2} g x^{2} \log{\left(c \right)}^{2}}{2} - \frac{b^{3} d^{2} g n^{3} \log{\left(d + e x \right)}^{3}}{2 e^{2}} + \frac{9 b^{3} d^{2} g n^{3} \log{\left(d + e x \right)}^{2}}{4 e^{2}} - \frac{21 b^{3} d^{2} g n^{3} \log{\left(d + e x \right)}}{4 e^{2}} - \frac{3 b^{3} d^{2} g n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{2 e^{2}} + \frac{9 b^{3} d^{2} g n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{2 e^{2}} - \frac{3 b^{3} d^{2} g n \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{2 e^{2}} + \frac{b^{3} d f n^{3} \log{\left(d + e x \right)}^{3}}{e} - \frac{3 b^{3} d f n^{3} \log{\left(d + e x \right)}^{2}}{e} + \frac{6 b^{3} d f n^{3} \log{\left(d + e x \right)}}{e} + \frac{3 b^{3} d f n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{e} - \frac{6 b^{3} d f n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{3 b^{3} d f n \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{e} + \frac{3 b^{3} d g n^{3} x \log{\left(d + e x \right)}^{2}}{2 e} - \frac{9 b^{3} d g n^{3} x \log{\left(d + e x \right)}}{2 e} + \frac{21 b^{3} d g n^{3} x}{4 e} + \frac{3 b^{3} d g n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)}}{e} - \frac{9 b^{3} d g n^{2} x \log{\left(c \right)}}{2 e} + \frac{3 b^{3} d g n x \log{\left(c \right)}^{2}}{2 e} + b^{3} f n^{3} x \log{\left(d + e x \right)}^{3} - 3 b^{3} f n^{3} x \log{\left(d + e x \right)}^{2} + 6 b^{3} f n^{3} x \log{\left(d + e x \right)} - 6 b^{3} f n^{3} x + 3 b^{3} f n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)}^{2} - 6 b^{3} f n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)} + 6 b^{3} f n^{2} x \log{\left(c \right)} + 3 b^{3} f n x \log{\left(c \right)}^{2} \log{\left(d + e x \right)} - 3 b^{3} f n x \log{\left(c \right)}^{2} + b^{3} f x \log{\left(c \right)}^{3} + \frac{b^{3} g n^{3} x^{2} \log{\left(d + e x \right)}^{3}}{2} - \frac{3 b^{3} g n^{3} x^{2} \log{\left(d + e x \right)}^{2}}{4} + \frac{3 b^{3} g n^{3} x^{2} \log{\left(d + e x \right)}}{4} - \frac{3 b^{3} g n^{3} x^{2}}{8} + \frac{3 b^{3} g n^{2} x^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{2} - \frac{3 b^{3} g n^{2} x^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{2} + \frac{3 b^{3} g n^{2} x^{2} \log{\left(c \right)}}{4} + \frac{3 b^{3} g n x^{2} \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{2} - \frac{3 b^{3} g n x^{2} \log{\left(c \right)}^{2}}{4} + \frac{b^{3} g x^{2} \log{\left(c \right)}^{3}}{2} & \text{for}\: e \neq 0 \\\left(a + b \log{\left(c d^{n} \right)}\right)^{3} \left(f x + \frac{g x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*f*x + a**3*g*x**2/2 - 3*a**2*b*d**2*g*n*log(d + e*x)/(2*e**2) + 3*a**2*b*d*f*n*log(d + e*x)/e + 3*a**2*b*d*g*n*x/(2*e) + 3*a**2*b*f*n*x*log(d + e*x) - 3*a**2*b*f*n*x + 3*a**2*b*f*x*log(c) + 3*a**2*b*g*n*x**2*log(d + e*x)/2 - 3*a**2*b*g*n*x**2/4 + 3*a**2*b*g*x**2*log(c)/2 - 3*a*b**2*d**2*g*n**2*log(d + e*x)**2/(2*e**2) + 9*a*b**2*d**2*g*n**2*log(d + e*x)/(2*e**2) - 3*a*b**2*d**2*g*n*log(c)*log(d + e*x)/e**2 + 3*a*b**2*d*f*n**2*log(d + e*x)**2/e - 6*a*b**2*d*f*n**2*log(d + e*x)/e + 6*a*b**2*d*f*n*log(c)*log(d + e*x)/e + 3*a*b**2*d*g*n**2*x*log(d + e*x)/e - 9*a*b**2*d*g*n**2*x/(2*e) + 3*a*b**2*d*g*n*x*log(c)/e + 3*a*b**2*f*n**2*x*log(d + e*x)**2 - 6*a*b**2*f*n**2*x*log(d + e*x) + 6*a*b**2*f*n**2*x + 6*a*b**2*f*n*x*log(c)*log(d + e*x) - 6*a*b**2*f*n*x*log(c) + 3*a*b**2*f*x*log(c)**2 + 3*a*b**2*g*n**2*x**2*log(d + e*x)**2/2 - 3*a*b**2*g*n**2*x**2*log(d + e*x)/2 + 3*a*b**2*g*n**2*x**2/4 + 3*a*b**2*g*n*x**2*log(c)*log(d + e*x) - 3*a*b**2*g*n*x**2*log(c)/2 + 3*a*b**2*g*x**2*log(c)**2/2 - b**3*d**2*g*n**3*log(d + e*x)**3/(2*e**2) + 9*b**3*d**2*g*n**3*log(d + e*x)**2/(4*e**2) - 21*b**3*d**2*g*n**3*log(d + e*x)/(4*e**2) - 3*b**3*d**2*g*n**2*log(c)*log(d + e*x)**2/(2*e**2) + 9*b**3*d**2*g*n**2*log(c)*log(d + e*x)/(2*e**2) - 3*b**3*d**2*g*n*log(c)**2*log(d + e*x)/(2*e**2) + b**3*d*f*n**3*log(d + e*x)**3/e - 3*b**3*d*f*n**3*log(d + e*x)**2/e + 6*b**3*d*f*n**3*log(d + e*x)/e + 3*b**3*d*f*n**2*log(c)*log(d + e*x)**2/e - 6*b**3*d*f*n**2*log(c)*log(d + e*x)/e + 3*b**3*d*f*n*log(c)**2*log(d + e*x)/e + 3*b**3*d*g*n**3*x*log(d + e*x)**2/(2*e) - 9*b**3*d*g*n**3*x*log(d + e*x)/(2*e) + 21*b**3*d*g*n**3*x/(4*e) + 3*b**3*d*g*n**2*x*log(c)*log(d + e*x)/e - 9*b**3*d*g*n**2*x*log(c)/(2*e) + 3*b**3*d*g*n*x*log(c)**2/(2*e) + b**3*f*n**3*x*log(d + e*x)**3 - 3*b**3*f*n**3*x*log(d + e*x)**2 + 6*b**3*f*n**3*x*log(d + e*x) - 6*b**3*f*n**3*x + 3*b**3*f*n**2*x*log(c)*log(d + e*x)**2 - 6*b**3*f*n**2*x*log(c)*log(d + e*x) + 6*b**3*f*n**2*x*log(c) + 3*b**3*f*n*x*log(c)**2*log(d + e*x) - 3*b**3*f*n*x*log(c)**2 + b**3*f*x*log(c)**3 + b**3*g*n**3*x**2*log(d + e*x)**3/2 - 3*b**3*g*n**3*x**2*log(d + e*x)**2/4 + 3*b**3*g*n**3*x**2*log(d + e*x)/4 - 3*b**3*g*n**3*x**2/8 + 3*b**3*g*n**2*x**2*log(c)*log(d + e*x)**2/2 - 3*b**3*g*n**2*x**2*log(c)*log(d + e*x)/2 + 3*b**3*g*n**2*x**2*log(c)/4 + 3*b**3*g*n*x**2*log(c)**2*log(d + e*x)/2 - 3*b**3*g*n*x**2*log(c)**2/4 + b**3*g*x**2*log(c)**3/2, Ne(e, 0)), ((a + b*log(c*d**n))**3*(f*x + g*x**2/2), True))","A",0
55,1,527,0,3.286849," ","integrate((a+b*ln(c*(e*x+d)**n))**3,x)","\begin{cases} a^{3} x + \frac{3 a^{2} b d n \log{\left(d + e x \right)}}{e} + 3 a^{2} b n x \log{\left(d + e x \right)} - 3 a^{2} b n x + 3 a^{2} b x \log{\left(c \right)} + \frac{3 a b^{2} d n^{2} \log{\left(d + e x \right)}^{2}}{e} - \frac{6 a b^{2} d n^{2} \log{\left(d + e x \right)}}{e} + \frac{6 a b^{2} d n \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + 3 a b^{2} n^{2} x \log{\left(d + e x \right)}^{2} - 6 a b^{2} n^{2} x \log{\left(d + e x \right)} + 6 a b^{2} n^{2} x + 6 a b^{2} n x \log{\left(c \right)} \log{\left(d + e x \right)} - 6 a b^{2} n x \log{\left(c \right)} + 3 a b^{2} x \log{\left(c \right)}^{2} + \frac{b^{3} d n^{3} \log{\left(d + e x \right)}^{3}}{e} - \frac{3 b^{3} d n^{3} \log{\left(d + e x \right)}^{2}}{e} + \frac{6 b^{3} d n^{3} \log{\left(d + e x \right)}}{e} + \frac{3 b^{3} d n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{e} - \frac{6 b^{3} d n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{3 b^{3} d n \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{e} + b^{3} n^{3} x \log{\left(d + e x \right)}^{3} - 3 b^{3} n^{3} x \log{\left(d + e x \right)}^{2} + 6 b^{3} n^{3} x \log{\left(d + e x \right)} - 6 b^{3} n^{3} x + 3 b^{3} n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)}^{2} - 6 b^{3} n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)} + 6 b^{3} n^{2} x \log{\left(c \right)} + 3 b^{3} n x \log{\left(c \right)}^{2} \log{\left(d + e x \right)} - 3 b^{3} n x \log{\left(c \right)}^{2} + b^{3} x \log{\left(c \right)}^{3} & \text{for}\: e \neq 0 \\x \left(a + b \log{\left(c d^{n} \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x + 3*a**2*b*d*n*log(d + e*x)/e + 3*a**2*b*n*x*log(d + e*x) - 3*a**2*b*n*x + 3*a**2*b*x*log(c) + 3*a*b**2*d*n**2*log(d + e*x)**2/e - 6*a*b**2*d*n**2*log(d + e*x)/e + 6*a*b**2*d*n*log(c)*log(d + e*x)/e + 3*a*b**2*n**2*x*log(d + e*x)**2 - 6*a*b**2*n**2*x*log(d + e*x) + 6*a*b**2*n**2*x + 6*a*b**2*n*x*log(c)*log(d + e*x) - 6*a*b**2*n*x*log(c) + 3*a*b**2*x*log(c)**2 + b**3*d*n**3*log(d + e*x)**3/e - 3*b**3*d*n**3*log(d + e*x)**2/e + 6*b**3*d*n**3*log(d + e*x)/e + 3*b**3*d*n**2*log(c)*log(d + e*x)**2/e - 6*b**3*d*n**2*log(c)*log(d + e*x)/e + 3*b**3*d*n*log(c)**2*log(d + e*x)/e + b**3*n**3*x*log(d + e*x)**3 - 3*b**3*n**3*x*log(d + e*x)**2 + 6*b**3*n**3*x*log(d + e*x) - 6*b**3*n**3*x + 3*b**3*n**2*x*log(c)*log(d + e*x)**2 - 6*b**3*n**2*x*log(c)*log(d + e*x) + 6*b**3*n**2*x*log(c) + 3*b**3*n*x*log(c)**2*log(d + e*x) - 3*b**3*n*x*log(c)**2 + b**3*x*log(c)**3, Ne(e, 0)), (x*(a + b*log(c*d**n))**3, True))","A",0
56,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**3/(g*x+f),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{3}}{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**3/(f + g*x), x)","F",0
57,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**3/(g*x+f)**2,x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{3}}{\left(f + g x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**3/(f + g*x)**2, x)","F",0
58,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**3/(g*x+f)**3,x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{3}}{\left(f + g x\right)^{3}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**3/(f + g*x)**3, x)","F",0
59,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**3/(g*x+f)**4,x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{3}}{\left(f + g x\right)^{4}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**3/(f + g*x)**4, x)","F",0
60,1,2885,0,20.669527," ","integrate((g*x+f)*(a+b*ln(c*(e*x+d)**n))**4,x)","\begin{cases} a^{4} f x + \frac{a^{4} g x^{2}}{2} - \frac{2 a^{3} b d^{2} g n \log{\left(d + e x \right)}}{e^{2}} + \frac{4 a^{3} b d f n \log{\left(d + e x \right)}}{e} + \frac{2 a^{3} b d g n x}{e} + 4 a^{3} b f n x \log{\left(d + e x \right)} - 4 a^{3} b f n x + 4 a^{3} b f x \log{\left(c \right)} + 2 a^{3} b g n x^{2} \log{\left(d + e x \right)} - a^{3} b g n x^{2} + 2 a^{3} b g x^{2} \log{\left(c \right)} - \frac{3 a^{2} b^{2} d^{2} g n^{2} \log{\left(d + e x \right)}^{2}}{e^{2}} + \frac{9 a^{2} b^{2} d^{2} g n^{2} \log{\left(d + e x \right)}}{e^{2}} - \frac{6 a^{2} b^{2} d^{2} g n \log{\left(c \right)} \log{\left(d + e x \right)}}{e^{2}} + \frac{6 a^{2} b^{2} d f n^{2} \log{\left(d + e x \right)}^{2}}{e} - \frac{12 a^{2} b^{2} d f n^{2} \log{\left(d + e x \right)}}{e} + \frac{12 a^{2} b^{2} d f n \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{6 a^{2} b^{2} d g n^{2} x \log{\left(d + e x \right)}}{e} - \frac{9 a^{2} b^{2} d g n^{2} x}{e} + \frac{6 a^{2} b^{2} d g n x \log{\left(c \right)}}{e} + 6 a^{2} b^{2} f n^{2} x \log{\left(d + e x \right)}^{2} - 12 a^{2} b^{2} f n^{2} x \log{\left(d + e x \right)} + 12 a^{2} b^{2} f n^{2} x + 12 a^{2} b^{2} f n x \log{\left(c \right)} \log{\left(d + e x \right)} - 12 a^{2} b^{2} f n x \log{\left(c \right)} + 6 a^{2} b^{2} f x \log{\left(c \right)}^{2} + 3 a^{2} b^{2} g n^{2} x^{2} \log{\left(d + e x \right)}^{2} - 3 a^{2} b^{2} g n^{2} x^{2} \log{\left(d + e x \right)} + \frac{3 a^{2} b^{2} g n^{2} x^{2}}{2} + 6 a^{2} b^{2} g n x^{2} \log{\left(c \right)} \log{\left(d + e x \right)} - 3 a^{2} b^{2} g n x^{2} \log{\left(c \right)} + 3 a^{2} b^{2} g x^{2} \log{\left(c \right)}^{2} - \frac{2 a b^{3} d^{2} g n^{3} \log{\left(d + e x \right)}^{3}}{e^{2}} + \frac{9 a b^{3} d^{2} g n^{3} \log{\left(d + e x \right)}^{2}}{e^{2}} - \frac{21 a b^{3} d^{2} g n^{3} \log{\left(d + e x \right)}}{e^{2}} - \frac{6 a b^{3} d^{2} g n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{e^{2}} + \frac{18 a b^{3} d^{2} g n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{e^{2}} - \frac{6 a b^{3} d^{2} g n \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{e^{2}} + \frac{4 a b^{3} d f n^{3} \log{\left(d + e x \right)}^{3}}{e} - \frac{12 a b^{3} d f n^{3} \log{\left(d + e x \right)}^{2}}{e} + \frac{24 a b^{3} d f n^{3} \log{\left(d + e x \right)}}{e} + \frac{12 a b^{3} d f n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{e} - \frac{24 a b^{3} d f n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{12 a b^{3} d f n \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{e} + \frac{6 a b^{3} d g n^{3} x \log{\left(d + e x \right)}^{2}}{e} - \frac{18 a b^{3} d g n^{3} x \log{\left(d + e x \right)}}{e} + \frac{21 a b^{3} d g n^{3} x}{e} + \frac{12 a b^{3} d g n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)}}{e} - \frac{18 a b^{3} d g n^{2} x \log{\left(c \right)}}{e} + \frac{6 a b^{3} d g n x \log{\left(c \right)}^{2}}{e} + 4 a b^{3} f n^{3} x \log{\left(d + e x \right)}^{3} - 12 a b^{3} f n^{3} x \log{\left(d + e x \right)}^{2} + 24 a b^{3} f n^{3} x \log{\left(d + e x \right)} - 24 a b^{3} f n^{3} x + 12 a b^{3} f n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)}^{2} - 24 a b^{3} f n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)} + 24 a b^{3} f n^{2} x \log{\left(c \right)} + 12 a b^{3} f n x \log{\left(c \right)}^{2} \log{\left(d + e x \right)} - 12 a b^{3} f n x \log{\left(c \right)}^{2} + 4 a b^{3} f x \log{\left(c \right)}^{3} + 2 a b^{3} g n^{3} x^{2} \log{\left(d + e x \right)}^{3} - 3 a b^{3} g n^{3} x^{2} \log{\left(d + e x \right)}^{2} + 3 a b^{3} g n^{3} x^{2} \log{\left(d + e x \right)} - \frac{3 a b^{3} g n^{3} x^{2}}{2} + 6 a b^{3} g n^{2} x^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2} - 6 a b^{3} g n^{2} x^{2} \log{\left(c \right)} \log{\left(d + e x \right)} + 3 a b^{3} g n^{2} x^{2} \log{\left(c \right)} + 6 a b^{3} g n x^{2} \log{\left(c \right)}^{2} \log{\left(d + e x \right)} - 3 a b^{3} g n x^{2} \log{\left(c \right)}^{2} + 2 a b^{3} g x^{2} \log{\left(c \right)}^{3} - \frac{b^{4} d^{2} g n^{4} \log{\left(d + e x \right)}^{4}}{2 e^{2}} + \frac{3 b^{4} d^{2} g n^{4} \log{\left(d + e x \right)}^{3}}{e^{2}} - \frac{21 b^{4} d^{2} g n^{4} \log{\left(d + e x \right)}^{2}}{2 e^{2}} + \frac{45 b^{4} d^{2} g n^{4} \log{\left(d + e x \right)}}{2 e^{2}} - \frac{2 b^{4} d^{2} g n^{3} \log{\left(c \right)} \log{\left(d + e x \right)}^{3}}{e^{2}} + \frac{9 b^{4} d^{2} g n^{3} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{e^{2}} - \frac{21 b^{4} d^{2} g n^{3} \log{\left(c \right)} \log{\left(d + e x \right)}}{e^{2}} - \frac{3 b^{4} d^{2} g n^{2} \log{\left(c \right)}^{2} \log{\left(d + e x \right)}^{2}}{e^{2}} + \frac{9 b^{4} d^{2} g n^{2} \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{e^{2}} - \frac{2 b^{4} d^{2} g n \log{\left(c \right)}^{3} \log{\left(d + e x \right)}}{e^{2}} + \frac{b^{4} d f n^{4} \log{\left(d + e x \right)}^{4}}{e} - \frac{4 b^{4} d f n^{4} \log{\left(d + e x \right)}^{3}}{e} + \frac{12 b^{4} d f n^{4} \log{\left(d + e x \right)}^{2}}{e} - \frac{24 b^{4} d f n^{4} \log{\left(d + e x \right)}}{e} + \frac{4 b^{4} d f n^{3} \log{\left(c \right)} \log{\left(d + e x \right)}^{3}}{e} - \frac{12 b^{4} d f n^{3} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{e} + \frac{24 b^{4} d f n^{3} \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{6 b^{4} d f n^{2} \log{\left(c \right)}^{2} \log{\left(d + e x \right)}^{2}}{e} - \frac{12 b^{4} d f n^{2} \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{e} + \frac{4 b^{4} d f n \log{\left(c \right)}^{3} \log{\left(d + e x \right)}}{e} + \frac{2 b^{4} d g n^{4} x \log{\left(d + e x \right)}^{3}}{e} - \frac{9 b^{4} d g n^{4} x \log{\left(d + e x \right)}^{2}}{e} + \frac{21 b^{4} d g n^{4} x \log{\left(d + e x \right)}}{e} - \frac{45 b^{4} d g n^{4} x}{2 e} + \frac{6 b^{4} d g n^{3} x \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{e} - \frac{18 b^{4} d g n^{3} x \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{21 b^{4} d g n^{3} x \log{\left(c \right)}}{e} + \frac{6 b^{4} d g n^{2} x \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{e} - \frac{9 b^{4} d g n^{2} x \log{\left(c \right)}^{2}}{e} + \frac{2 b^{4} d g n x \log{\left(c \right)}^{3}}{e} + b^{4} f n^{4} x \log{\left(d + e x \right)}^{4} - 4 b^{4} f n^{4} x \log{\left(d + e x \right)}^{3} + 12 b^{4} f n^{4} x \log{\left(d + e x \right)}^{2} - 24 b^{4} f n^{4} x \log{\left(d + e x \right)} + 24 b^{4} f n^{4} x + 4 b^{4} f n^{3} x \log{\left(c \right)} \log{\left(d + e x \right)}^{3} - 12 b^{4} f n^{3} x \log{\left(c \right)} \log{\left(d + e x \right)}^{2} + 24 b^{4} f n^{3} x \log{\left(c \right)} \log{\left(d + e x \right)} - 24 b^{4} f n^{3} x \log{\left(c \right)} + 6 b^{4} f n^{2} x \log{\left(c \right)}^{2} \log{\left(d + e x \right)}^{2} - 12 b^{4} f n^{2} x \log{\left(c \right)}^{2} \log{\left(d + e x \right)} + 12 b^{4} f n^{2} x \log{\left(c \right)}^{2} + 4 b^{4} f n x \log{\left(c \right)}^{3} \log{\left(d + e x \right)} - 4 b^{4} f n x \log{\left(c \right)}^{3} + b^{4} f x \log{\left(c \right)}^{4} + \frac{b^{4} g n^{4} x^{2} \log{\left(d + e x \right)}^{4}}{2} - b^{4} g n^{4} x^{2} \log{\left(d + e x \right)}^{3} + \frac{3 b^{4} g n^{4} x^{2} \log{\left(d + e x \right)}^{2}}{2} - \frac{3 b^{4} g n^{4} x^{2} \log{\left(d + e x \right)}}{2} + \frac{3 b^{4} g n^{4} x^{2}}{4} + 2 b^{4} g n^{3} x^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{3} - 3 b^{4} g n^{3} x^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2} + 3 b^{4} g n^{3} x^{2} \log{\left(c \right)} \log{\left(d + e x \right)} - \frac{3 b^{4} g n^{3} x^{2} \log{\left(c \right)}}{2} + 3 b^{4} g n^{2} x^{2} \log{\left(c \right)}^{2} \log{\left(d + e x \right)}^{2} - 3 b^{4} g n^{2} x^{2} \log{\left(c \right)}^{2} \log{\left(d + e x \right)} + \frac{3 b^{4} g n^{2} x^{2} \log{\left(c \right)}^{2}}{2} + 2 b^{4} g n x^{2} \log{\left(c \right)}^{3} \log{\left(d + e x \right)} - b^{4} g n x^{2} \log{\left(c \right)}^{3} + \frac{b^{4} g x^{2} \log{\left(c \right)}^{4}}{2} & \text{for}\: e \neq 0 \\\left(a + b \log{\left(c d^{n} \right)}\right)^{4} \left(f x + \frac{g x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*f*x + a**4*g*x**2/2 - 2*a**3*b*d**2*g*n*log(d + e*x)/e**2 + 4*a**3*b*d*f*n*log(d + e*x)/e + 2*a**3*b*d*g*n*x/e + 4*a**3*b*f*n*x*log(d + e*x) - 4*a**3*b*f*n*x + 4*a**3*b*f*x*log(c) + 2*a**3*b*g*n*x**2*log(d + e*x) - a**3*b*g*n*x**2 + 2*a**3*b*g*x**2*log(c) - 3*a**2*b**2*d**2*g*n**2*log(d + e*x)**2/e**2 + 9*a**2*b**2*d**2*g*n**2*log(d + e*x)/e**2 - 6*a**2*b**2*d**2*g*n*log(c)*log(d + e*x)/e**2 + 6*a**2*b**2*d*f*n**2*log(d + e*x)**2/e - 12*a**2*b**2*d*f*n**2*log(d + e*x)/e + 12*a**2*b**2*d*f*n*log(c)*log(d + e*x)/e + 6*a**2*b**2*d*g*n**2*x*log(d + e*x)/e - 9*a**2*b**2*d*g*n**2*x/e + 6*a**2*b**2*d*g*n*x*log(c)/e + 6*a**2*b**2*f*n**2*x*log(d + e*x)**2 - 12*a**2*b**2*f*n**2*x*log(d + e*x) + 12*a**2*b**2*f*n**2*x + 12*a**2*b**2*f*n*x*log(c)*log(d + e*x) - 12*a**2*b**2*f*n*x*log(c) + 6*a**2*b**2*f*x*log(c)**2 + 3*a**2*b**2*g*n**2*x**2*log(d + e*x)**2 - 3*a**2*b**2*g*n**2*x**2*log(d + e*x) + 3*a**2*b**2*g*n**2*x**2/2 + 6*a**2*b**2*g*n*x**2*log(c)*log(d + e*x) - 3*a**2*b**2*g*n*x**2*log(c) + 3*a**2*b**2*g*x**2*log(c)**2 - 2*a*b**3*d**2*g*n**3*log(d + e*x)**3/e**2 + 9*a*b**3*d**2*g*n**3*log(d + e*x)**2/e**2 - 21*a*b**3*d**2*g*n**3*log(d + e*x)/e**2 - 6*a*b**3*d**2*g*n**2*log(c)*log(d + e*x)**2/e**2 + 18*a*b**3*d**2*g*n**2*log(c)*log(d + e*x)/e**2 - 6*a*b**3*d**2*g*n*log(c)**2*log(d + e*x)/e**2 + 4*a*b**3*d*f*n**3*log(d + e*x)**3/e - 12*a*b**3*d*f*n**3*log(d + e*x)**2/e + 24*a*b**3*d*f*n**3*log(d + e*x)/e + 12*a*b**3*d*f*n**2*log(c)*log(d + e*x)**2/e - 24*a*b**3*d*f*n**2*log(c)*log(d + e*x)/e + 12*a*b**3*d*f*n*log(c)**2*log(d + e*x)/e + 6*a*b**3*d*g*n**3*x*log(d + e*x)**2/e - 18*a*b**3*d*g*n**3*x*log(d + e*x)/e + 21*a*b**3*d*g*n**3*x/e + 12*a*b**3*d*g*n**2*x*log(c)*log(d + e*x)/e - 18*a*b**3*d*g*n**2*x*log(c)/e + 6*a*b**3*d*g*n*x*log(c)**2/e + 4*a*b**3*f*n**3*x*log(d + e*x)**3 - 12*a*b**3*f*n**3*x*log(d + e*x)**2 + 24*a*b**3*f*n**3*x*log(d + e*x) - 24*a*b**3*f*n**3*x + 12*a*b**3*f*n**2*x*log(c)*log(d + e*x)**2 - 24*a*b**3*f*n**2*x*log(c)*log(d + e*x) + 24*a*b**3*f*n**2*x*log(c) + 12*a*b**3*f*n*x*log(c)**2*log(d + e*x) - 12*a*b**3*f*n*x*log(c)**2 + 4*a*b**3*f*x*log(c)**3 + 2*a*b**3*g*n**3*x**2*log(d + e*x)**3 - 3*a*b**3*g*n**3*x**2*log(d + e*x)**2 + 3*a*b**3*g*n**3*x**2*log(d + e*x) - 3*a*b**3*g*n**3*x**2/2 + 6*a*b**3*g*n**2*x**2*log(c)*log(d + e*x)**2 - 6*a*b**3*g*n**2*x**2*log(c)*log(d + e*x) + 3*a*b**3*g*n**2*x**2*log(c) + 6*a*b**3*g*n*x**2*log(c)**2*log(d + e*x) - 3*a*b**3*g*n*x**2*log(c)**2 + 2*a*b**3*g*x**2*log(c)**3 - b**4*d**2*g*n**4*log(d + e*x)**4/(2*e**2) + 3*b**4*d**2*g*n**4*log(d + e*x)**3/e**2 - 21*b**4*d**2*g*n**4*log(d + e*x)**2/(2*e**2) + 45*b**4*d**2*g*n**4*log(d + e*x)/(2*e**2) - 2*b**4*d**2*g*n**3*log(c)*log(d + e*x)**3/e**2 + 9*b**4*d**2*g*n**3*log(c)*log(d + e*x)**2/e**2 - 21*b**4*d**2*g*n**3*log(c)*log(d + e*x)/e**2 - 3*b**4*d**2*g*n**2*log(c)**2*log(d + e*x)**2/e**2 + 9*b**4*d**2*g*n**2*log(c)**2*log(d + e*x)/e**2 - 2*b**4*d**2*g*n*log(c)**3*log(d + e*x)/e**2 + b**4*d*f*n**4*log(d + e*x)**4/e - 4*b**4*d*f*n**4*log(d + e*x)**3/e + 12*b**4*d*f*n**4*log(d + e*x)**2/e - 24*b**4*d*f*n**4*log(d + e*x)/e + 4*b**4*d*f*n**3*log(c)*log(d + e*x)**3/e - 12*b**4*d*f*n**3*log(c)*log(d + e*x)**2/e + 24*b**4*d*f*n**3*log(c)*log(d + e*x)/e + 6*b**4*d*f*n**2*log(c)**2*log(d + e*x)**2/e - 12*b**4*d*f*n**2*log(c)**2*log(d + e*x)/e + 4*b**4*d*f*n*log(c)**3*log(d + e*x)/e + 2*b**4*d*g*n**4*x*log(d + e*x)**3/e - 9*b**4*d*g*n**4*x*log(d + e*x)**2/e + 21*b**4*d*g*n**4*x*log(d + e*x)/e - 45*b**4*d*g*n**4*x/(2*e) + 6*b**4*d*g*n**3*x*log(c)*log(d + e*x)**2/e - 18*b**4*d*g*n**3*x*log(c)*log(d + e*x)/e + 21*b**4*d*g*n**3*x*log(c)/e + 6*b**4*d*g*n**2*x*log(c)**2*log(d + e*x)/e - 9*b**4*d*g*n**2*x*log(c)**2/e + 2*b**4*d*g*n*x*log(c)**3/e + b**4*f*n**4*x*log(d + e*x)**4 - 4*b**4*f*n**4*x*log(d + e*x)**3 + 12*b**4*f*n**4*x*log(d + e*x)**2 - 24*b**4*f*n**4*x*log(d + e*x) + 24*b**4*f*n**4*x + 4*b**4*f*n**3*x*log(c)*log(d + e*x)**3 - 12*b**4*f*n**3*x*log(c)*log(d + e*x)**2 + 24*b**4*f*n**3*x*log(c)*log(d + e*x) - 24*b**4*f*n**3*x*log(c) + 6*b**4*f*n**2*x*log(c)**2*log(d + e*x)**2 - 12*b**4*f*n**2*x*log(c)**2*log(d + e*x) + 12*b**4*f*n**2*x*log(c)**2 + 4*b**4*f*n*x*log(c)**3*log(d + e*x) - 4*b**4*f*n*x*log(c)**3 + b**4*f*x*log(c)**4 + b**4*g*n**4*x**2*log(d + e*x)**4/2 - b**4*g*n**4*x**2*log(d + e*x)**3 + 3*b**4*g*n**4*x**2*log(d + e*x)**2/2 - 3*b**4*g*n**4*x**2*log(d + e*x)/2 + 3*b**4*g*n**4*x**2/4 + 2*b**4*g*n**3*x**2*log(c)*log(d + e*x)**3 - 3*b**4*g*n**3*x**2*log(c)*log(d + e*x)**2 + 3*b**4*g*n**3*x**2*log(c)*log(d + e*x) - 3*b**4*g*n**3*x**2*log(c)/2 + 3*b**4*g*n**2*x**2*log(c)**2*log(d + e*x)**2 - 3*b**4*g*n**2*x**2*log(c)**2*log(d + e*x) + 3*b**4*g*n**2*x**2*log(c)**2/2 + 2*b**4*g*n*x**2*log(c)**3*log(d + e*x) - b**4*g*n*x**2*log(c)**3 + b**4*g*x**2*log(c)**4/2, Ne(e, 0)), ((a + b*log(c*d**n))**4*(f*x + g*x**2/2), True))","A",0
61,1,1059,0,6.924291," ","integrate((a+b*ln(c*(e*x+d)**n))**4,x)","\begin{cases} a^{4} x + \frac{4 a^{3} b d n \log{\left(d + e x \right)}}{e} + 4 a^{3} b n x \log{\left(d + e x \right)} - 4 a^{3} b n x + 4 a^{3} b x \log{\left(c \right)} + \frac{6 a^{2} b^{2} d n^{2} \log{\left(d + e x \right)}^{2}}{e} - \frac{12 a^{2} b^{2} d n^{2} \log{\left(d + e x \right)}}{e} + \frac{12 a^{2} b^{2} d n \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + 6 a^{2} b^{2} n^{2} x \log{\left(d + e x \right)}^{2} - 12 a^{2} b^{2} n^{2} x \log{\left(d + e x \right)} + 12 a^{2} b^{2} n^{2} x + 12 a^{2} b^{2} n x \log{\left(c \right)} \log{\left(d + e x \right)} - 12 a^{2} b^{2} n x \log{\left(c \right)} + 6 a^{2} b^{2} x \log{\left(c \right)}^{2} + \frac{4 a b^{3} d n^{3} \log{\left(d + e x \right)}^{3}}{e} - \frac{12 a b^{3} d n^{3} \log{\left(d + e x \right)}^{2}}{e} + \frac{24 a b^{3} d n^{3} \log{\left(d + e x \right)}}{e} + \frac{12 a b^{3} d n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{e} - \frac{24 a b^{3} d n^{2} \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{12 a b^{3} d n \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{e} + 4 a b^{3} n^{3} x \log{\left(d + e x \right)}^{3} - 12 a b^{3} n^{3} x \log{\left(d + e x \right)}^{2} + 24 a b^{3} n^{3} x \log{\left(d + e x \right)} - 24 a b^{3} n^{3} x + 12 a b^{3} n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)}^{2} - 24 a b^{3} n^{2} x \log{\left(c \right)} \log{\left(d + e x \right)} + 24 a b^{3} n^{2} x \log{\left(c \right)} + 12 a b^{3} n x \log{\left(c \right)}^{2} \log{\left(d + e x \right)} - 12 a b^{3} n x \log{\left(c \right)}^{2} + 4 a b^{3} x \log{\left(c \right)}^{3} + \frac{b^{4} d n^{4} \log{\left(d + e x \right)}^{4}}{e} - \frac{4 b^{4} d n^{4} \log{\left(d + e x \right)}^{3}}{e} + \frac{12 b^{4} d n^{4} \log{\left(d + e x \right)}^{2}}{e} - \frac{24 b^{4} d n^{4} \log{\left(d + e x \right)}}{e} + \frac{4 b^{4} d n^{3} \log{\left(c \right)} \log{\left(d + e x \right)}^{3}}{e} - \frac{12 b^{4} d n^{3} \log{\left(c \right)} \log{\left(d + e x \right)}^{2}}{e} + \frac{24 b^{4} d n^{3} \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + \frac{6 b^{4} d n^{2} \log{\left(c \right)}^{2} \log{\left(d + e x \right)}^{2}}{e} - \frac{12 b^{4} d n^{2} \log{\left(c \right)}^{2} \log{\left(d + e x \right)}}{e} + \frac{4 b^{4} d n \log{\left(c \right)}^{3} \log{\left(d + e x \right)}}{e} + b^{4} n^{4} x \log{\left(d + e x \right)}^{4} - 4 b^{4} n^{4} x \log{\left(d + e x \right)}^{3} + 12 b^{4} n^{4} x \log{\left(d + e x \right)}^{2} - 24 b^{4} n^{4} x \log{\left(d + e x \right)} + 24 b^{4} n^{4} x + 4 b^{4} n^{3} x \log{\left(c \right)} \log{\left(d + e x \right)}^{3} - 12 b^{4} n^{3} x \log{\left(c \right)} \log{\left(d + e x \right)}^{2} + 24 b^{4} n^{3} x \log{\left(c \right)} \log{\left(d + e x \right)} - 24 b^{4} n^{3} x \log{\left(c \right)} + 6 b^{4} n^{2} x \log{\left(c \right)}^{2} \log{\left(d + e x \right)}^{2} - 12 b^{4} n^{2} x \log{\left(c \right)}^{2} \log{\left(d + e x \right)} + 12 b^{4} n^{2} x \log{\left(c \right)}^{2} + 4 b^{4} n x \log{\left(c \right)}^{3} \log{\left(d + e x \right)} - 4 b^{4} n x \log{\left(c \right)}^{3} + b^{4} x \log{\left(c \right)}^{4} & \text{for}\: e \neq 0 \\x \left(a + b \log{\left(c d^{n} \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x + 4*a**3*b*d*n*log(d + e*x)/e + 4*a**3*b*n*x*log(d + e*x) - 4*a**3*b*n*x + 4*a**3*b*x*log(c) + 6*a**2*b**2*d*n**2*log(d + e*x)**2/e - 12*a**2*b**2*d*n**2*log(d + e*x)/e + 12*a**2*b**2*d*n*log(c)*log(d + e*x)/e + 6*a**2*b**2*n**2*x*log(d + e*x)**2 - 12*a**2*b**2*n**2*x*log(d + e*x) + 12*a**2*b**2*n**2*x + 12*a**2*b**2*n*x*log(c)*log(d + e*x) - 12*a**2*b**2*n*x*log(c) + 6*a**2*b**2*x*log(c)**2 + 4*a*b**3*d*n**3*log(d + e*x)**3/e - 12*a*b**3*d*n**3*log(d + e*x)**2/e + 24*a*b**3*d*n**3*log(d + e*x)/e + 12*a*b**3*d*n**2*log(c)*log(d + e*x)**2/e - 24*a*b**3*d*n**2*log(c)*log(d + e*x)/e + 12*a*b**3*d*n*log(c)**2*log(d + e*x)/e + 4*a*b**3*n**3*x*log(d + e*x)**3 - 12*a*b**3*n**3*x*log(d + e*x)**2 + 24*a*b**3*n**3*x*log(d + e*x) - 24*a*b**3*n**3*x + 12*a*b**3*n**2*x*log(c)*log(d + e*x)**2 - 24*a*b**3*n**2*x*log(c)*log(d + e*x) + 24*a*b**3*n**2*x*log(c) + 12*a*b**3*n*x*log(c)**2*log(d + e*x) - 12*a*b**3*n*x*log(c)**2 + 4*a*b**3*x*log(c)**3 + b**4*d*n**4*log(d + e*x)**4/e - 4*b**4*d*n**4*log(d + e*x)**3/e + 12*b**4*d*n**4*log(d + e*x)**2/e - 24*b**4*d*n**4*log(d + e*x)/e + 4*b**4*d*n**3*log(c)*log(d + e*x)**3/e - 12*b**4*d*n**3*log(c)*log(d + e*x)**2/e + 24*b**4*d*n**3*log(c)*log(d + e*x)/e + 6*b**4*d*n**2*log(c)**2*log(d + e*x)**2/e - 12*b**4*d*n**2*log(c)**2*log(d + e*x)/e + 4*b**4*d*n*log(c)**3*log(d + e*x)/e + b**4*n**4*x*log(d + e*x)**4 - 4*b**4*n**4*x*log(d + e*x)**3 + 12*b**4*n**4*x*log(d + e*x)**2 - 24*b**4*n**4*x*log(d + e*x) + 24*b**4*n**4*x + 4*b**4*n**3*x*log(c)*log(d + e*x)**3 - 12*b**4*n**3*x*log(c)*log(d + e*x)**2 + 24*b**4*n**3*x*log(c)*log(d + e*x) - 24*b**4*n**3*x*log(c) + 6*b**4*n**2*x*log(c)**2*log(d + e*x)**2 - 12*b**4*n**2*x*log(c)**2*log(d + e*x) + 12*b**4*n**2*x*log(c)**2 + 4*b**4*n*x*log(c)**3*log(d + e*x) - 4*b**4*n*x*log(c)**3 + b**4*x*log(c)**4, Ne(e, 0)), (x*(a + b*log(c*d**n))**4, True))","A",0
62,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**4/(g*x+f),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{4}}{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**4/(f + g*x), x)","F",0
63,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**4/(g*x+f)**2,x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{4}}{\left(f + g x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**4/(f + g*x)**2, x)","F",0
64,1,24,0,0.141613," ","integrate(ln(b*x+a),x)","- b \left(- \frac{a \log{\left(a + b x \right)}}{b^{2}} + \frac{x}{b}\right) + x \log{\left(a + b x \right)}"," ",0,"-b*(-a*log(a + b*x)/b**2 + x/b) + x*log(a + b*x)","A",0
65,1,42,0,0.337361," ","integrate(ln(b*x+a)**2,x)","2 b \left(- \frac{a \log{\left(a + b x \right)}}{b^{2}} + \frac{x}{b}\right) - 2 x \log{\left(a + b x \right)} + \frac{\left(a + b x\right) \log{\left(a + b x \right)}^{2}}{b}"," ",0,"2*b*(-a*log(a + b*x)/b**2 + x/b) - 2*x*log(a + b*x) + (a + b*x)*log(a + b*x)**2/b","A",0
66,1,63,0,0.412243," ","integrate(ln(b*x+a)**3,x)","- 6 b \left(- \frac{a \log{\left(a + b x \right)}}{b^{2}} + \frac{x}{b}\right) + 6 x \log{\left(a + b x \right)} + \frac{\left(- 3 a - 3 b x\right) \log{\left(a + b x \right)}^{2}}{b} + \frac{\left(a + b x\right) \log{\left(a + b x \right)}^{3}}{b}"," ",0,"-6*b*(-a*log(a + b*x)/b**2 + x/b) + 6*x*log(a + b*x) + (-3*a - 3*b*x)*log(a + b*x)**2/b + (a + b*x)*log(a + b*x)**3/b","A",0
67,1,36,0,0.334799," ","integrate(ln(b*x+c*x+a),x)","x \log{\left(a + b x + c x \right)} + \left(- b - c\right) \left(- \frac{a \log{\left(a + x \left(b + c\right) \right)}}{\left(b + c\right)^{2}} + \frac{x}{b + c}\right)"," ",0,"x*log(a + b*x + c*x) + (-b - c)*(-a*log(a + x*(b + c))/(b + c)**2 + x/(b + c))","A",0
68,1,63,0,0.497583," ","integrate(ln(b*x+c*x+a)**2,x)","- 2 x \log{\left(a + b x + c x \right)} + \left(2 b + 2 c\right) \left(- \frac{a \log{\left(a + x \left(b + c\right) \right)}}{\left(b + c\right)^{2}} + \frac{x}{b + c}\right) + \frac{\left(a + b x + c x\right) \log{\left(a + b x + c x \right)}^{2}}{b + c}"," ",0,"-2*x*log(a + b*x + c*x) + (2*b + 2*c)*(-a*log(a + x*(b + c))/(b + c)**2 + x/(b + c)) + (a + b*x + c*x)*log(a + b*x + c*x)**2/(b + c)","A",0
69,1,95,0,0.650512," ","integrate(ln(b*x+c*x+a)**3,x)","6 x \log{\left(a + b x + c x \right)} + \left(- 6 b - 6 c\right) \left(- \frac{a \log{\left(a + x \left(b + c\right) \right)}}{\left(b + c\right)^{2}} + \frac{x}{b + c}\right) + \frac{\left(- 3 a - 3 b x - 3 c x\right) \log{\left(a + b x + c x \right)}^{2}}{b + c} + \frac{\left(a + b x + c x\right) \log{\left(a + b x + c x \right)}^{3}}{b + c}"," ",0,"6*x*log(a + b*x + c*x) + (-6*b - 6*c)*(-a*log(a + x*(b + c))/(b + c)**2 + x/(b + c)) + (-3*a - 3*b*x - 3*c*x)*log(a + b*x + c*x)**2/(b + c) + (a + b*x + c*x)*log(a + b*x + c*x)**3/(b + c)","A",0
70,1,37,0,0.454450," ","integrate(ln(c*(e*x+d)**n),x)","\begin{cases} \frac{d n \log{\left(d + e x \right)}}{e} + n x \log{\left(d + e x \right)} - n x + x \log{\left(c \right)} & \text{for}\: e \neq 0 \\x \log{\left(c d^{n} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d*n*log(d + e*x)/e + n*x*log(d + e*x) - n*x + x*log(c), Ne(e, 0)), (x*log(c*d**n), True))","A",0
71,0,0,0,0.000000," ","integrate(ln(-g*(e*x+d)/(-d*g+e*f))/(g*x+f),x)","\int \frac{\log{\left(- \frac{d g}{- d g + e f} - \frac{e g x}{- d g + e f} \right)}}{f + g x}\, dx"," ",0,"Integral(log(-d*g/(-d*g + e*f) - e*g*x/(-d*g + e*f))/(f + g*x), x)","F",0
72,1,17,0,6.203006," ","integrate((a+b*ln(c*(1/c+e*x)))/x,x)","a \log{\left(x \right)} - b \operatorname{Li}_{2}\left(c e x e^{i \pi}\right)"," ",0,"a*log(x) - b*polylog(2, c*e*x*exp_polar(I*pi))","C",0
73,1,68,0,2.869447," ","integrate(ln(e*x+3)/x,x)","\begin{cases} \log{\left(3 \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{3}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(3 \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{3}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(3 \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(3 \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(3)*log(x) - polylog(2, e*x*exp_polar(I*pi)/3), Abs(x) < 1), (-log(3)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/3), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(3) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(3) - polylog(2, e*x*exp_polar(I*pi)/3), True))","C",0
74,1,68,0,2.915494," ","integrate(ln(e*x+2)/x,x)","\begin{cases} \log{\left(2 \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{2}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(2 \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{2}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(2 \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(2 \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(2)*log(x) - polylog(2, e*x*exp_polar(I*pi)/2), Abs(x) < 1), (-log(2)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/2), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(2) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(2) - polylog(2, e*x*exp_polar(I*pi)/2), True))","C",0
75,1,10,0,2.402577," ","integrate(ln(e*x+1)/x,x)","- \operatorname{Li}_{2}\left(e x e^{i \pi}\right)"," ",0,"-polylog(2, e*x*exp_polar(I*pi))","C",0
76,1,7,0,0.088493," ","integrate(ln(e*x)/x,x)","\frac{\log{\left(e x \right)}^{2}}{2}"," ",0,"log(e*x)**2/2","A",0
77,1,48,0,3.362295," ","integrate(ln(e*x-1)/x,x)","\begin{cases} i \pi \log{\left(x \right)} - \operatorname{Li}_{2}\left(e x\right) & \text{for}\: \left|{x}\right| < 1 \\- i \pi \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(e x\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- i \pi {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} + i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} - \operatorname{Li}_{2}\left(e x\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*pi*log(x) - polylog(2, e*x), Abs(x) < 1), (-I*pi*log(1/x) - polylog(2, e*x), 1/Abs(x) < 1), (-I*pi*meijerg(((), (1, 1)), ((0, 0), ()), x) + I*pi*meijerg(((1, 1), ()), ((), (0, 0)), x) - polylog(2, e*x), True))","C",0
78,1,88,0,3.499367," ","integrate(ln(e*x-2)/x,x)","\begin{cases} \log{\left(2 \right)} \log{\left(x \right)} + 3 i \pi \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x}{2}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(2 \right)} \log{\left(\frac{1}{x} \right)} - 3 i \pi \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x}{2}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(2 \right)} - 3 i \pi {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(2 \right)} + 3 i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} - \operatorname{Li}_{2}\left(\frac{e x}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(2)*log(x) + 3*I*pi*log(x) - polylog(2, e*x/2), Abs(x) < 1), (-log(2)*log(1/x) - 3*I*pi*log(1/x) - polylog(2, e*x/2), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(2) - 3*I*pi*meijerg(((), (1, 1)), ((0, 0), ()), x) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(2) + 3*I*pi*meijerg(((1, 1), ()), ((), (0, 0)), x) - polylog(2, e*x/2), True))","C",0
79,1,75,0,4.066100," ","integrate((a+b*ln(e*x+3))/x,x)","a \log{\left(x \right)} + b \left(\begin{cases} \log{\left(3 \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{3}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(3 \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{3}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(3 \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(3 \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{3}\right) & \text{otherwise} \end{cases}\right)"," ",0,"a*log(x) + b*Piecewise((log(3)*log(x) - polylog(2, e*x*exp_polar(I*pi)/3), Abs(x) < 1), (-log(3)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/3), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(3) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(3) - polylog(2, e*x*exp_polar(I*pi)/3), True))","A",0
80,1,75,0,4.080387," ","integrate((a+b*ln(e*x+2))/x,x)","a \log{\left(x \right)} + b \left(\begin{cases} \log{\left(2 \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{2}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(2 \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{2}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(2 \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(2 \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{2}\right) & \text{otherwise} \end{cases}\right)"," ",0,"a*log(x) + b*Piecewise((log(2)*log(x) - polylog(2, e*x*exp_polar(I*pi)/2), Abs(x) < 1), (-log(2)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/2), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(2) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(2) - polylog(2, e*x*exp_polar(I*pi)/2), True))","A",0
81,1,15,0,3.546164," ","integrate((a+b*ln(e*x+1))/x,x)","a \log{\left(x \right)} - b \operatorname{Li}_{2}\left(e x e^{i \pi}\right)"," ",0,"a*log(x) - b*polylog(2, e*x*exp_polar(I*pi))","C",0
82,1,14,0,0.240760," ","integrate((a+b*ln(e*x))/x,x)","a \log{\left(x \right)} + \frac{b \log{\left(e x \right)}^{2}}{2}"," ",0,"a*log(x) + b*log(e*x)**2/2","A",0
83,1,54,0,4.529963," ","integrate((a+b*ln(e*x-1))/x,x)","a \log{\left(x \right)} + b \left(\begin{cases} i \pi \log{\left(x \right)} - \operatorname{Li}_{2}\left(e x\right) & \text{for}\: \left|{x}\right| < 1 \\- i \pi \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(e x\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- i \pi {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} + i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} - \operatorname{Li}_{2}\left(e x\right) & \text{otherwise} \end{cases}\right)"," ",0,"a*log(x) + b*Piecewise((I*pi*log(x) - polylog(2, e*x), Abs(x) < 1), (-I*pi*log(1/x) - polylog(2, e*x), 1/Abs(x) < 1), (-I*pi*meijerg(((), (1, 1)), ((0, 0), ()), x) + I*pi*meijerg(((1, 1), ()), ((), (0, 0)), x) - polylog(2, e*x), True))","A",0
84,1,95,0,4.893348," ","integrate((a+b*ln(e*x-2))/x,x)","a \log{\left(x \right)} + b \left(\begin{cases} \log{\left(2 \right)} \log{\left(x \right)} + 3 i \pi \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x}{2}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(2 \right)} \log{\left(\frac{1}{x} \right)} - 3 i \pi \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x}{2}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(2 \right)} - 3 i \pi {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(2 \right)} + 3 i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} - \operatorname{Li}_{2}\left(\frac{e x}{2}\right) & \text{otherwise} \end{cases}\right)"," ",0,"a*log(x) + b*Piecewise((log(2)*log(x) + 3*I*pi*log(x) - polylog(2, e*x/2), Abs(x) < 1), (-log(2)*log(1/x) - 3*I*pi*log(1/x) - polylog(2, e*x/2), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(2) - 3*I*pi*meijerg(((), (1, 1)), ((0, 0), ()), x) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(2) + 3*I*pi*meijerg(((1, 1), ()), ((), (0, 0)), x) - polylog(2, e*x/2), True))","A",0
85,1,260,0,3.908225," ","integrate(x**2*ln(c*(b*x+a)**n)**2,x)","\begin{cases} \frac{a^{3} n^{2} \log{\left(a + b x \right)}^{2}}{3 b^{3}} - \frac{11 a^{3} n^{2} \log{\left(a + b x \right)}}{9 b^{3}} + \frac{2 a^{3} n \log{\left(c \right)} \log{\left(a + b x \right)}}{3 b^{3}} - \frac{2 a^{2} n^{2} x \log{\left(a + b x \right)}}{3 b^{2}} + \frac{11 a^{2} n^{2} x}{9 b^{2}} - \frac{2 a^{2} n x \log{\left(c \right)}}{3 b^{2}} + \frac{a n^{2} x^{2} \log{\left(a + b x \right)}}{3 b} - \frac{5 a n^{2} x^{2}}{18 b} + \frac{a n x^{2} \log{\left(c \right)}}{3 b} + \frac{n^{2} x^{3} \log{\left(a + b x \right)}^{2}}{3} - \frac{2 n^{2} x^{3} \log{\left(a + b x \right)}}{9} + \frac{2 n^{2} x^{3}}{27} + \frac{2 n x^{3} \log{\left(c \right)} \log{\left(a + b x \right)}}{3} - \frac{2 n x^{3} \log{\left(c \right)}}{9} + \frac{x^{3} \log{\left(c \right)}^{2}}{3} & \text{for}\: b \neq 0 \\\frac{x^{3} \log{\left(a^{n} c \right)}^{2}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*n**2*log(a + b*x)**2/(3*b**3) - 11*a**3*n**2*log(a + b*x)/(9*b**3) + 2*a**3*n*log(c)*log(a + b*x)/(3*b**3) - 2*a**2*n**2*x*log(a + b*x)/(3*b**2) + 11*a**2*n**2*x/(9*b**2) - 2*a**2*n*x*log(c)/(3*b**2) + a*n**2*x**2*log(a + b*x)/(3*b) - 5*a*n**2*x**2/(18*b) + a*n*x**2*log(c)/(3*b) + n**2*x**3*log(a + b*x)**2/3 - 2*n**2*x**3*log(a + b*x)/9 + 2*n**2*x**3/27 + 2*n*x**3*log(c)*log(a + b*x)/3 - 2*n*x**3*log(c)/9 + x**3*log(c)**2/3, Ne(b, 0)), (x**3*log(a**n*c)**2/3, True))","A",0
86,0,0,0,0.000000," ","integrate(ln(c*(b*x+a)**n)**2/x**4,x)","\int \frac{\log{\left(c \left(a + b x\right)^{n} \right)}^{2}}{x^{4}}\, dx"," ",0,"Integral(log(c*(a + b*x)**n)**2/x**4, x)","F",0
87,1,517,0,7.342296," ","integrate(x**2*ln(c*(b*x+a)**n)**3,x)","\begin{cases} \frac{a^{3} n^{3} \log{\left(a + b x \right)}^{3}}{3 b^{3}} - \frac{11 a^{3} n^{3} \log{\left(a + b x \right)}^{2}}{6 b^{3}} + \frac{85 a^{3} n^{3} \log{\left(a + b x \right)}}{18 b^{3}} + \frac{a^{3} n^{2} \log{\left(c \right)} \log{\left(a + b x \right)}^{2}}{b^{3}} - \frac{11 a^{3} n^{2} \log{\left(c \right)} \log{\left(a + b x \right)}}{3 b^{3}} + \frac{a^{3} n \log{\left(c \right)}^{2} \log{\left(a + b x \right)}}{b^{3}} - \frac{a^{2} n^{3} x \log{\left(a + b x \right)}^{2}}{b^{2}} + \frac{11 a^{2} n^{3} x \log{\left(a + b x \right)}}{3 b^{2}} - \frac{85 a^{2} n^{3} x}{18 b^{2}} - \frac{2 a^{2} n^{2} x \log{\left(c \right)} \log{\left(a + b x \right)}}{b^{2}} + \frac{11 a^{2} n^{2} x \log{\left(c \right)}}{3 b^{2}} - \frac{a^{2} n x \log{\left(c \right)}^{2}}{b^{2}} + \frac{a n^{3} x^{2} \log{\left(a + b x \right)}^{2}}{2 b} - \frac{5 a n^{3} x^{2} \log{\left(a + b x \right)}}{6 b} + \frac{19 a n^{3} x^{2}}{36 b} + \frac{a n^{2} x^{2} \log{\left(c \right)} \log{\left(a + b x \right)}}{b} - \frac{5 a n^{2} x^{2} \log{\left(c \right)}}{6 b} + \frac{a n x^{2} \log{\left(c \right)}^{2}}{2 b} + \frac{n^{3} x^{3} \log{\left(a + b x \right)}^{3}}{3} - \frac{n^{3} x^{3} \log{\left(a + b x \right)}^{2}}{3} + \frac{2 n^{3} x^{3} \log{\left(a + b x \right)}}{9} - \frac{2 n^{3} x^{3}}{27} + n^{2} x^{3} \log{\left(c \right)} \log{\left(a + b x \right)}^{2} - \frac{2 n^{2} x^{3} \log{\left(c \right)} \log{\left(a + b x \right)}}{3} + \frac{2 n^{2} x^{3} \log{\left(c \right)}}{9} + n x^{3} \log{\left(c \right)}^{2} \log{\left(a + b x \right)} - \frac{n x^{3} \log{\left(c \right)}^{2}}{3} + \frac{x^{3} \log{\left(c \right)}^{3}}{3} & \text{for}\: b \neq 0 \\\frac{x^{3} \log{\left(a^{n} c \right)}^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*n**3*log(a + b*x)**3/(3*b**3) - 11*a**3*n**3*log(a + b*x)**2/(6*b**3) + 85*a**3*n**3*log(a + b*x)/(18*b**3) + a**3*n**2*log(c)*log(a + b*x)**2/b**3 - 11*a**3*n**2*log(c)*log(a + b*x)/(3*b**3) + a**3*n*log(c)**2*log(a + b*x)/b**3 - a**2*n**3*x*log(a + b*x)**2/b**2 + 11*a**2*n**3*x*log(a + b*x)/(3*b**2) - 85*a**2*n**3*x/(18*b**2) - 2*a**2*n**2*x*log(c)*log(a + b*x)/b**2 + 11*a**2*n**2*x*log(c)/(3*b**2) - a**2*n*x*log(c)**2/b**2 + a*n**3*x**2*log(a + b*x)**2/(2*b) - 5*a*n**3*x**2*log(a + b*x)/(6*b) + 19*a*n**3*x**2/(36*b) + a*n**2*x**2*log(c)*log(a + b*x)/b - 5*a*n**2*x**2*log(c)/(6*b) + a*n*x**2*log(c)**2/(2*b) + n**3*x**3*log(a + b*x)**3/3 - n**3*x**3*log(a + b*x)**2/3 + 2*n**3*x**3*log(a + b*x)/9 - 2*n**3*x**3/27 + n**2*x**3*log(c)*log(a + b*x)**2 - 2*n**2*x**3*log(c)*log(a + b*x)/3 + 2*n**2*x**3*log(c)/9 + n*x**3*log(c)**2*log(a + b*x) - n*x**3*log(c)**2/3 + x**3*log(c)**3/3, Ne(b, 0)), (x**3*log(a**n*c)**3/3, True))","A",0
88,0,0,0,0.000000," ","integrate((g*x+f)**3/(a+b*ln(c*(e*x+d)**n)),x)","\int \frac{\left(f + g x\right)^{3}}{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}\, dx"," ",0,"Integral((f + g*x)**3/(a + b*log(c*(d + e*x)**n)), x)","F",0
89,0,0,0,0.000000," ","integrate((g*x+f)**2/(a+b*ln(c*(e*x+d)**n)),x)","\int \frac{\left(f + g x\right)^{2}}{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}\, dx"," ",0,"Integral((f + g*x)**2/(a + b*log(c*(d + e*x)**n)), x)","F",0
90,0,0,0,0.000000," ","integrate((g*x+f)/(a+b*ln(c*(e*x+d)**n)),x)","\int \frac{f + g x}{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}\, dx"," ",0,"Integral((f + g*x)/(a + b*log(c*(d + e*x)**n)), x)","F",0
91,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(e*x+d)**n)),x)","\int \frac{1}{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}\, dx"," ",0,"Integral(1/(a + b*log(c*(d + e*x)**n)), x)","F",0
92,0,0,0,0.000000," ","integrate(1/(g*x+f)/(a+b*ln(c*(e*x+d)**n)),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right) \left(f + g x\right)}\, dx"," ",0,"Integral(1/((a + b*log(c*(d + e*x)**n))*(f + g*x)), x)","F",0
93,0,0,0,0.000000," ","integrate(1/(g*x+f)**2/(a+b*ln(c*(e*x+d)**n)),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right) \left(f + g x\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*log(c*(d + e*x)**n))*(f + g*x)**2), x)","F",0
94,0,0,0,0.000000," ","integrate((g*x+f)**3/(a+b*ln(c*(e*x+d)**n))**2,x)","\int \frac{\left(f + g x\right)^{3}}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral((f + g*x)**3/(a + b*log(c*(d + e*x)**n))**2, x)","F",0
95,0,0,0,0.000000," ","integrate((g*x+f)**2/(a+b*ln(c*(e*x+d)**n))**2,x)","\int \frac{\left(f + g x\right)^{2}}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral((f + g*x)**2/(a + b*log(c*(d + e*x)**n))**2, x)","F",0
96,0,0,0,0.000000," ","integrate((g*x+f)/(a+b*ln(c*(e*x+d)**n))**2,x)","\int \frac{f + g x}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral((f + g*x)/(a + b*log(c*(d + e*x)**n))**2, x)","F",0
97,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(e*x+d)**n))**2,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**(-2), x)","F",0
98,0,0,0,0.000000," ","integrate(1/(g*x+f)/(a+b*ln(c*(e*x+d)**n))**2,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2} \left(f + g x\right)}\, dx"," ",0,"Integral(1/((a + b*log(c*(d + e*x)**n))**2*(f + g*x)), x)","F",0
99,0,0,0,0.000000," ","integrate(1/(g*x+f)**2/(a+b*ln(c*(e*x+d)**n))**2,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2} \left(f + g x\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*log(c*(d + e*x)**n))**2*(f + g*x)**2), x)","F",0
100,0,0,0,0.000000," ","integrate((g*x+f)**2/(a+b*ln(c*(e*x+d)**n))**3,x)","\int \frac{\left(f + g x\right)^{2}}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{3}}\, dx"," ",0,"Integral((f + g*x)**2/(a + b*log(c*(d + e*x)**n))**3, x)","F",0
101,0,0,0,0.000000," ","integrate((g*x+f)/(a+b*ln(c*(e*x+d)**n))**3,x)","\int \frac{f + g x}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{3}}\, dx"," ",0,"Integral((f + g*x)/(a + b*log(c*(d + e*x)**n))**3, x)","F",0
102,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(e*x+d)**n))**3,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{3}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**(-3), x)","F",0
103,0,0,0,0.000000," ","integrate(1/(g*x+f)/(a+b*ln(c*(e*x+d)**n))**3,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{3} \left(f + g x\right)}\, dx"," ",0,"Integral(1/((a + b*log(c*(d + e*x)**n))**3*(f + g*x)), x)","F",0
104,0,0,0,0.000000," ","integrate(1/(g*x+f)**2/(a+b*ln(c*(e*x+d)**n))**3,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{3} \left(f + g x\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*log(c*(d + e*x)**n))**3*(f + g*x)**2), x)","F",0
105,0,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*ln(c*(e*x+d)**n))**(1/2),x)","\int \sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}} \left(f + g x\right)^{2}\, dx"," ",0,"Integral(sqrt(a + b*log(c*(d + e*x)**n))*(f + g*x)**2, x)","F",0
106,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*ln(c*(e*x+d)**n))**(1/2),x)","\int \sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}} \left(f + g x\right)\, dx"," ",0,"Integral(sqrt(a + b*log(c*(d + e*x)**n))*(f + g*x), x)","F",0
107,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**(1/2),x)","\int \sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}\, dx"," ",0,"Integral(sqrt(a + b*log(c*(d + e*x)**n)), x)","F",0
108,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**(1/2)/(g*x+f),x)","\int \frac{\sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}}{f + g x}\, dx"," ",0,"Integral(sqrt(a + b*log(c*(d + e*x)**n))/(f + g*x), x)","F",0
109,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**(1/2)/(g*x+f)**2,x)","\int \frac{\sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}}{\left(f + g x\right)^{2}}\, dx"," ",0,"Integral(sqrt(a + b*log(c*(d + e*x)**n))/(f + g*x)**2, x)","F",0
110,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**(1/2)/(g*x+f)**3,x)","\int \frac{\sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}}{\left(f + g x\right)^{3}}\, dx"," ",0,"Integral(sqrt(a + b*log(c*(d + e*x)**n))/(f + g*x)**3, x)","F",0
111,0,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*ln(c*(e*x+d)**n))**(3/2),x)","\int \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{\frac{3}{2}} \left(f + g x\right)^{2}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**(3/2)*(f + g*x)**2, x)","F",0
112,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*ln(c*(e*x+d)**n))**(3/2),x)","\int \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{\frac{3}{2}} \left(f + g x\right)\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**(3/2)*(f + g*x), x)","F",0
113,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**(3/2),x)","\int \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**(3/2), x)","F",0
114,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**(3/2)/(g*x+f),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{\frac{3}{2}}}{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**(3/2)/(f + g*x), x)","F",0
115,-2,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**(3/2)/(g*x+f)**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
116,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**(3/2)/(g*x+f)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*ln(c*(e*x+d)**n))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,-1,0,0,0.000000," ","integrate((g*x+f)*(a+b*ln(c*(e*x+d)**n))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**(5/2),x)","\int \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**(5/2), x)","F",0
120,-2,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**(5/2)/(g*x+f),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
121,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**(5/2)/(g*x+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**(5/2)/(g*x+f)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,0,0,0,0.000000," ","integrate((g*x+f)**3/(a+b*ln(c*(e*x+d)**n))**(1/2),x)","\int \frac{\left(f + g x\right)^{3}}{\sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}}\, dx"," ",0,"Integral((f + g*x)**3/sqrt(a + b*log(c*(d + e*x)**n)), x)","F",0
124,0,0,0,0.000000," ","integrate((g*x+f)**2/(a+b*ln(c*(e*x+d)**n))**(1/2),x)","\int \frac{\left(f + g x\right)^{2}}{\sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}}\, dx"," ",0,"Integral((f + g*x)**2/sqrt(a + b*log(c*(d + e*x)**n)), x)","F",0
125,0,0,0,0.000000," ","integrate((g*x+f)/(a+b*ln(c*(e*x+d)**n))**(1/2),x)","\int \frac{f + g x}{\sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}}\, dx"," ",0,"Integral((f + g*x)/sqrt(a + b*log(c*(d + e*x)**n)), x)","F",0
126,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(e*x+d)**n))**(1/2),x)","\int \frac{1}{\sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*log(c*(d + e*x)**n)), x)","F",0
127,0,0,0,0.000000," ","integrate(1/(g*x+f)/(a+b*ln(c*(e*x+d)**n))**(1/2),x)","\int \frac{1}{\sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}} \left(f + g x\right)}\, dx"," ",0,"Integral(1/(sqrt(a + b*log(c*(d + e*x)**n))*(f + g*x)), x)","F",0
128,0,0,0,0.000000," ","integrate((g*x+f)**3/(a+b*ln(c*(e*x+d)**n))**(3/2),x)","\int \frac{\left(f + g x\right)^{3}}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((f + g*x)**3/(a + b*log(c*(d + e*x)**n))**(3/2), x)","F",0
129,0,0,0,0.000000," ","integrate((g*x+f)**2/(a+b*ln(c*(e*x+d)**n))**(3/2),x)","\int \frac{\left(f + g x\right)^{2}}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((f + g*x)**2/(a + b*log(c*(d + e*x)**n))**(3/2), x)","F",0
130,0,0,0,0.000000," ","integrate((g*x+f)/(a+b*ln(c*(e*x+d)**n))**(3/2),x)","\int \frac{f + g x}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((f + g*x)/(a + b*log(c*(d + e*x)**n))**(3/2), x)","F",0
131,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(e*x+d)**n))**(3/2),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**(-3/2), x)","F",0
132,-2,0,0,0.000000," ","integrate(1/(g*x+f)/(a+b*ln(c*(e*x+d)**n))**(3/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
133,0,0,0,0.000000," ","integrate((g*x+f)**3/(a+b*ln(c*(e*x+d)**n))**(5/2),x)","\int \frac{\left(f + g x\right)^{3}}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((f + g*x)**3/(a + b*log(c*(d + e*x)**n))**(5/2), x)","F",0
134,0,0,0,0.000000," ","integrate((g*x+f)**2/(a+b*ln(c*(e*x+d)**n))**(5/2),x)","\int \frac{\left(f + g x\right)^{2}}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((f + g*x)**2/(a + b*log(c*(d + e*x)**n))**(5/2), x)","F",0
135,0,0,0,0.000000," ","integrate((g*x+f)/(a+b*ln(c*(e*x+d)**n))**(5/2),x)","\int \frac{f + g x}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((f + g*x)/(a + b*log(c*(d + e*x)**n))**(5/2), x)","F",0
136,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(e*x+d)**n))**(5/2),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**(-5/2), x)","F",0
137,-1,0,0,0.000000," ","integrate(1/(g*x+f)/(a+b*ln(c*(e*x+d)**n))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,1,469,0,57.098767," ","integrate((g*x+f)**(3/2)*(a+b*ln(c*(e*x+d)**n)),x)","a f \left(\begin{cases} \sqrt{f} x & \text{for}\: g = 0 \\\frac{2 \left(f + g x\right)^{\frac{3}{2}}}{3 g} & \text{otherwise} \end{cases}\right) + \frac{2 a \left(- \frac{f \left(f + g x\right)^{\frac{3}{2}}}{3} + \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g} + \frac{2 b f \left(- \frac{2 e n \left(\frac{g \left(f + g x\right)^{\frac{3}{2}}}{3 e} + \frac{\sqrt{f + g x} \left(- d g^{2} + e f g\right)}{e^{2}} + \frac{g \left(d g - e f\right)^{2} \operatorname{atan}{\left(\frac{\sqrt{f + g x}}{\sqrt{\frac{d g - e f}{e}}} \right)}}{e^{3} \sqrt{\frac{d g - e f}{e}}}\right)}{3 g} + \frac{\left(f + g x\right)^{\frac{3}{2}} \log{\left(c \left(d - \frac{e f}{g} + \frac{e \left(f + g x\right)}{g}\right)^{n} \right)}}{3}\right)}{g} + \frac{2 b \left(- \frac{2 e n \left(\frac{g \left(f + g x\right)^{\frac{5}{2}}}{5 e} + \frac{\left(f + g x\right)^{\frac{3}{2}} \left(- d g^{2} + e f g\right)}{3 e^{2}} + \frac{\sqrt{f + g x} \left(d^{2} g^{3} - 2 d e f g^{2} + e^{2} f^{2} g\right)}{e^{3}} - \frac{g \left(d g - e f\right)^{3} \operatorname{atan}{\left(\frac{\sqrt{f + g x}}{\sqrt{\frac{d g - e f}{e}}} \right)}}{e^{4} \sqrt{\frac{d g - e f}{e}}}\right)}{5 g} - f \left(- \frac{2 e n \left(\frac{g \left(f + g x\right)^{\frac{3}{2}}}{3 e} + \frac{\sqrt{f + g x} \left(- d g^{2} + e f g\right)}{e^{2}} + \frac{g \left(d g - e f\right)^{2} \operatorname{atan}{\left(\frac{\sqrt{f + g x}}{\sqrt{\frac{d g - e f}{e}}} \right)}}{e^{3} \sqrt{\frac{d g - e f}{e}}}\right)}{3 g} + \frac{\left(f + g x\right)^{\frac{3}{2}} \log{\left(c \left(d - \frac{e f}{g} + \frac{e \left(f + g x\right)}{g}\right)^{n} \right)}}{3}\right) + \frac{\left(f + g x\right)^{\frac{5}{2}} \log{\left(c \left(d - \frac{e f}{g} + \frac{e \left(f + g x\right)}{g}\right)^{n} \right)}}{5}\right)}{g}"," ",0,"a*f*Piecewise((sqrt(f)*x, Eq(g, 0)), (2*(f + g*x)**(3/2)/(3*g), True)) + 2*a*(-f*(f + g*x)**(3/2)/3 + (f + g*x)**(5/2)/5)/g + 2*b*f*(-2*e*n*(g*(f + g*x)**(3/2)/(3*e) + sqrt(f + g*x)*(-d*g**2 + e*f*g)/e**2 + g*(d*g - e*f)**2*atan(sqrt(f + g*x)/sqrt((d*g - e*f)/e))/(e**3*sqrt((d*g - e*f)/e)))/(3*g) + (f + g*x)**(3/2)*log(c*(d - e*f/g + e*(f + g*x)/g)**n)/3)/g + 2*b*(-2*e*n*(g*(f + g*x)**(5/2)/(5*e) + (f + g*x)**(3/2)*(-d*g**2 + e*f*g)/(3*e**2) + sqrt(f + g*x)*(d**2*g**3 - 2*d*e*f*g**2 + e**2*f**2*g)/e**3 - g*(d*g - e*f)**3*atan(sqrt(f + g*x)/sqrt((d*g - e*f)/e))/(e**4*sqrt((d*g - e*f)/e)))/(5*g) - f*(-2*e*n*(g*(f + g*x)**(3/2)/(3*e) + sqrt(f + g*x)*(-d*g**2 + e*f*g)/e**2 + g*(d*g - e*f)**2*atan(sqrt(f + g*x)/sqrt((d*g - e*f)/e))/(e**3*sqrt((d*g - e*f)/e)))/(3*g) + (f + g*x)**(3/2)*log(c*(d - e*f/g + e*(f + g*x)/g)**n)/3) + (f + g*x)**(5/2)*log(c*(d - e*f/g + e*(f + g*x)/g)**n)/5)/g","A",0
139,1,139,0,4.715379," ","integrate((g*x+f)**(1/2)*(a+b*ln(c*(e*x+d)**n)),x)","\frac{2 \left(\frac{a \left(f + g x\right)^{\frac{3}{2}}}{3} + b \left(- \frac{2 e n \left(\frac{g \left(f + g x\right)^{\frac{3}{2}}}{3 e} + \frac{\sqrt{f + g x} \left(- d g^{2} + e f g\right)}{e^{2}} + \frac{g \left(d g - e f\right)^{2} \operatorname{atan}{\left(\frac{\sqrt{f + g x}}{\sqrt{\frac{d g - e f}{e}}} \right)}}{e^{3} \sqrt{\frac{d g - e f}{e}}}\right)}{3 g} + \frac{\left(f + g x\right)^{\frac{3}{2}} \log{\left(c \left(d - \frac{e f}{g} + \frac{e \left(f + g x\right)}{g}\right)^{n} \right)}}{3}\right)\right)}{g}"," ",0,"2*(a*(f + g*x)**(3/2)/3 + b*(-2*e*n*(g*(f + g*x)**(3/2)/(3*e) + sqrt(f + g*x)*(-d*g**2 + e*f*g)/e**2 + g*(d*g - e*f)**2*atan(sqrt(f + g*x)/sqrt((d*g - e*f)/e))/(e**3*sqrt((d*g - e*f)/e)))/(3*g) + (f + g*x)**(3/2)*log(c*(d - e*f/g + e*(f + g*x)/g)**n)/3))/g","A",0
140,1,326,0,38.949959," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x+f)**(1/2),x)","\begin{cases} \frac{- \frac{2 a f}{\sqrt{f + g x}} - 2 a \left(- \frac{f}{\sqrt{f + g x}} - \sqrt{f + g x}\right) - 2 b f \left(\frac{2 e n \operatorname{atan}{\left(\frac{1}{\sqrt{\frac{e}{d g - e f}} \sqrt{f + g x}} \right)}}{\sqrt{\frac{e}{d g - e f}} \left(d g - e f\right)} + \frac{\log{\left(c \left(d + e x\right)^{n} \right)}}{\sqrt{f + g x}}\right) - 2 b \left(- \frac{2 e n \left(- \frac{g \sqrt{f + g x}}{e} - \frac{g \operatorname{atan}{\left(\frac{1}{\sqrt{\frac{e}{d g - e f}} \sqrt{f + g x}} \right)}}{e \sqrt{\frac{e}{d g - e f}}}\right)}{g} - f \left(\frac{2 e n \operatorname{atan}{\left(\frac{1}{\sqrt{\frac{e}{d g - e f}} \sqrt{f + g x}} \right)}}{\sqrt{\frac{e}{d g - e f}} \left(d g - e f\right)} + \frac{\log{\left(c \left(d - \frac{e f}{g} + \frac{e \left(f + g x\right)}{g}\right)^{n} \right)}}{\sqrt{f + g x}}\right) - \sqrt{f + g x} \log{\left(c \left(d - \frac{e f}{g} + \frac{e \left(f + g x\right)}{g}\right)^{n} \right)}\right)}{g} & \text{for}\: g \neq 0 \\\frac{a x + b \left(- e n \left(- \frac{d \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{e} + \frac{x}{e}\right) + x \log{\left(c \left(d + e x\right)^{n} \right)}\right)}{\sqrt{f}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*f/sqrt(f + g*x) - 2*a*(-f/sqrt(f + g*x) - sqrt(f + g*x)) - 2*b*f*(2*e*n*atan(1/(sqrt(e/(d*g - e*f))*sqrt(f + g*x)))/(sqrt(e/(d*g - e*f))*(d*g - e*f)) + log(c*(d + e*x)**n)/sqrt(f + g*x)) - 2*b*(-2*e*n*(-g*sqrt(f + g*x)/e - g*atan(1/(sqrt(e/(d*g - e*f))*sqrt(f + g*x)))/(e*sqrt(e/(d*g - e*f))))/g - f*(2*e*n*atan(1/(sqrt(e/(d*g - e*f))*sqrt(f + g*x)))/(sqrt(e/(d*g - e*f))*(d*g - e*f)) + log(c*(d - e*f/g + e*(f + g*x)/g)**n)/sqrt(f + g*x)) - sqrt(f + g*x)*log(c*(d - e*f/g + e*(f + g*x)/g)**n)))/g, Ne(g, 0)), ((a*x + b*(-e*n*(-d*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/e + x/e) + x*log(c*(d + e*x)**n)))/sqrt(f), True))","A",0
141,1,85,0,15.984252," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x+f)**(3/2),x)","\frac{- \frac{2 a}{\sqrt{f + g x}} + 2 b \left(\frac{2 n \operatorname{atan}{\left(\frac{\sqrt{f + g x}}{\sqrt{\frac{g \left(d - \frac{e f}{g}\right)}{e}}} \right)}}{\sqrt{\frac{g \left(d - \frac{e f}{g}\right)}{e}}} - \frac{\log{\left(c \left(d - \frac{e f}{g} + \frac{e \left(f + g x\right)}{g}\right)^{n} \right)}}{\sqrt{f + g x}}\right)}{g}"," ",0,"(-2*a/sqrt(f + g*x) + 2*b*(2*n*atan(sqrt(f + g*x)/sqrt(g*(d - e*f/g)/e))/sqrt(g*(d - e*f/g)/e) - log(c*(d - e*f/g + e*(f + g*x)/g)**n)/sqrt(f + g*x)))/g","A",0
142,1,117,0,76.042683," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x+f)**(5/2),x)","\frac{- \frac{2 a}{3 \left(f + g x\right)^{\frac{3}{2}}} + 2 b \left(\frac{2 e n \left(- \frac{g}{\sqrt{f + g x} \left(d g - e f\right)} - \frac{g \operatorname{atan}{\left(\frac{\sqrt{f + g x}}{\sqrt{\frac{d g - e f}{e}}} \right)}}{\sqrt{\frac{d g - e f}{e}} \left(d g - e f\right)}\right)}{3 g} - \frac{\log{\left(c \left(d - \frac{e f}{g} + \frac{e \left(f + g x\right)}{g}\right)^{n} \right)}}{3 \left(f + g x\right)^{\frac{3}{2}}}\right)}{g}"," ",0,"(-2*a/(3*(f + g*x)**(3/2)) + 2*b*(2*e*n*(-g/(sqrt(f + g*x)*(d*g - e*f)) - g*atan(sqrt(f + g*x)/sqrt((d*g - e*f)/e))/(sqrt((d*g - e*f)/e)*(d*g - e*f)))/(3*g) - log(c*(d - e*f/g + e*(f + g*x)/g)**n)/(3*(f + g*x)**(3/2))))/g","A",0
143,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x+f)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x+f)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-1,0,0,0.000000," ","integrate((g*x+f)**(3/2)*(a+b*ln(c*(e*x+d)**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)*(a+b*ln(c*(e*x+d)**n))**2,x)","\int \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2} \sqrt{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**2*sqrt(f + g*x), x)","F",0
147,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/(g*x+f)**(1/2),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}{\sqrt{f + g x}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**2/sqrt(f + g*x), x)","F",0
148,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/(g*x+f)**(3/2),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}{\left(f + g x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**2/(f + g*x)**(3/2), x)","F",0
149,-2,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/(g*x+f)**(5/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
150,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/(g*x+f)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/(g*x+f)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
152,-1,0,0,0.000000," ","integrate((g*x+f)**(3/2)/(a+b*ln(c*(e*x+d)**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,-1,0,0,0.000000," ","integrate((g*x+f)**(1/2)/(a+b*ln(c*(e*x+d)**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(e*x+d)**n))/(g*x+f)**(1/2),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right) \sqrt{f + g x}}\, dx"," ",0,"Integral(1/((a + b*log(c*(d + e*x)**n))*sqrt(f + g*x)), x)","F",0
155,0,0,0,0.000000," ","integrate(1/(g*x+f)**(3/2)/(a+b*ln(c*(e*x+d)**n)),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right) \left(f + g x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*log(c*(d + e*x)**n))*(f + g*x)**(3/2)), x)","F",0
156,-1,0,0,0.000000," ","integrate((g*x+f)**(1/2)*(a+b*ln(c*(e*x+d)**n))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
157,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**(1/2)/(g*x+f)**(1/2),x)","\int \frac{\sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}}{\sqrt{f + g x}}\, dx"," ",0,"Integral(sqrt(a + b*log(c*(d + e*x)**n))/sqrt(f + g*x), x)","F",0
158,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**(1/2)/(g*x+f)**(3/2),x)","\int \frac{\sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}}{\left(f + g x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*log(c*(d + e*x)**n))/(f + g*x)**(3/2), x)","F",0
159,-1,0,0,0.000000," ","integrate((g*x+f)**(1/2)/(a+b*ln(c*(e*x+d)**n))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,0,0,0,0.000000," ","integrate(1/(g*x+f)**(1/2)/(a+b*ln(c*(e*x+d)**n))**(1/2),x)","\int \frac{1}{\sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}} \sqrt{f + g x}}\, dx"," ",0,"Integral(1/(sqrt(a + b*log(c*(d + e*x)**n))*sqrt(f + g*x)), x)","F",0
161,0,0,0,0.000000," ","integrate(1/(g*x+f)**(3/2)/(a+b*ln(c*(e*x+d)**n))**(1/2),x)","\int \frac{1}{\sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}} \left(f + g x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*log(c*(d + e*x)**n))*(f + g*x)**(3/2)), x)","F",0
162,-2,0,0,0.000000," ","integrate((g*x+f)**m*(a+b*ln(c*(e*x+d)**n)),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
163,0,0,0,0.000000," ","integrate((g*x+f)**m/(a+b*ln(c*(e*x+d)**n)),x)","\int \frac{\left(f + g x\right)^{m}}{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}\, dx"," ",0,"Integral((f + g*x)**m/(a + b*log(c*(d + e*x)**n)), x)","F",0
164,-2,0,0,0.000000," ","integrate((g*x+f)**m/(a+b*ln(c*(e*x+d)**n))**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
165,-1,0,0,0.000000," ","integrate((g*x+f)**m*(a+b*ln(c*(e*x+d)**n))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,-2,0,0,0.000000," ","integrate((g*x+f)**m*(a+b*ln(c*(e*x+d)**n))**(1/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
167,0,0,0,0.000000," ","integrate((g*x+f)**m/(a+b*ln(c*(e*x+d)**n))**(1/2),x)","\int \frac{\left(f + g x\right)^{m}}{\sqrt{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}}\, dx"," ",0,"Integral((f + g*x)**m/sqrt(a + b*log(c*(d + e*x)**n)), x)","F",0
168,-2,0,0,0.000000," ","integrate((g*x+f)**m/(a+b*ln(c*(e*x+d)**n))**(3/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
169,-2,0,0,0.000000," ","integrate((g*x+f)**m*(a+b*ln(c*(e*x+d)**n))**n,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
170,0,0,0,0.000000," ","integrate((g*x+f)**3*(a+b*ln(c*(e*x+d)**n))**n,x)","\int \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{n} \left(f + g x\right)^{3}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**n*(f + g*x)**3, x)","F",0
171,0,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*ln(c*(e*x+d)**n))**n,x)","\int \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{n} \left(f + g x\right)^{2}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**n*(f + g*x)**2, x)","F",0
172,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*ln(c*(e*x+d)**n))**n,x)","\int \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{n} \left(f + g x\right)\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**n*(f + g*x), x)","F",0
173,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**n,x)","\int \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{n}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**n, x)","F",0
174,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**n/(g*x+f),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{n}}{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**n/(f + g*x), x)","F",0
175,1,682,0,3.042109," ","integrate((i*x+h)**4*(a+b*ln(c*(f*x+e)))/(d*f*x+d*e),x)","x^{4} \left(\frac{a i^{4}}{4 d f} - \frac{b i^{4}}{16 d f}\right) + x^{3} \left(- \frac{a e i^{4}}{3 d f^{2}} + \frac{4 a h i^{3}}{3 d f} + \frac{7 b e i^{4}}{36 d f^{2}} - \frac{4 b h i^{3}}{9 d f}\right) + x^{2} \left(\frac{a e^{2} i^{4}}{2 d f^{3}} - \frac{2 a e h i^{3}}{d f^{2}} + \frac{3 a h^{2} i^{2}}{d f} - \frac{13 b e^{2} i^{4}}{24 d f^{3}} + \frac{5 b e h i^{3}}{3 d f^{2}} - \frac{3 b h^{2} i^{2}}{2 d f}\right) + x \left(- \frac{a e^{3} i^{4}}{d f^{4}} + \frac{4 a e^{2} h i^{3}}{d f^{3}} - \frac{6 a e h^{2} i^{2}}{d f^{2}} + \frac{4 a h^{3} i}{d f} + \frac{25 b e^{3} i^{4}}{12 d f^{4}} - \frac{22 b e^{2} h i^{3}}{3 d f^{3}} + \frac{9 b e h^{2} i^{2}}{d f^{2}} - \frac{4 b h^{3} i}{d f}\right) + \frac{\left(- 12 b e^{3} i^{4} x + 48 b e^{2} f h i^{3} x + 6 b e^{2} f i^{4} x^{2} - 72 b e f^{2} h^{2} i^{2} x - 24 b e f^{2} h i^{3} x^{2} - 4 b e f^{2} i^{4} x^{3} + 48 b f^{3} h^{3} i x + 36 b f^{3} h^{2} i^{2} x^{2} + 16 b f^{3} h i^{3} x^{3} + 3 b f^{3} i^{4} x^{4}\right) \log{\left(c \left(e + f x\right) \right)}}{12 d f^{4}} + \frac{\left(b e^{4} i^{4} - 4 b e^{3} f h i^{3} + 6 b e^{2} f^{2} h^{2} i^{2} - 4 b e f^{3} h^{3} i + b f^{4} h^{4}\right) \log{\left(c \left(e + f x\right) \right)}^{2}}{2 d f^{5}} + \frac{\left(12 a e^{4} i^{4} - 48 a e^{3} f h i^{3} + 72 a e^{2} f^{2} h^{2} i^{2} - 48 a e f^{3} h^{3} i + 12 a f^{4} h^{4} - 25 b e^{4} i^{4} + 88 b e^{3} f h i^{3} - 108 b e^{2} f^{2} h^{2} i^{2} + 48 b e f^{3} h^{3} i\right) \log{\left(e + f x \right)}}{12 d f^{5}}"," ",0,"x**4*(a*i**4/(4*d*f) - b*i**4/(16*d*f)) + x**3*(-a*e*i**4/(3*d*f**2) + 4*a*h*i**3/(3*d*f) + 7*b*e*i**4/(36*d*f**2) - 4*b*h*i**3/(9*d*f)) + x**2*(a*e**2*i**4/(2*d*f**3) - 2*a*e*h*i**3/(d*f**2) + 3*a*h**2*i**2/(d*f) - 13*b*e**2*i**4/(24*d*f**3) + 5*b*e*h*i**3/(3*d*f**2) - 3*b*h**2*i**2/(2*d*f)) + x*(-a*e**3*i**4/(d*f**4) + 4*a*e**2*h*i**3/(d*f**3) - 6*a*e*h**2*i**2/(d*f**2) + 4*a*h**3*i/(d*f) + 25*b*e**3*i**4/(12*d*f**4) - 22*b*e**2*h*i**3/(3*d*f**3) + 9*b*e*h**2*i**2/(d*f**2) - 4*b*h**3*i/(d*f)) + (-12*b*e**3*i**4*x + 48*b*e**2*f*h*i**3*x + 6*b*e**2*f*i**4*x**2 - 72*b*e*f**2*h**2*i**2*x - 24*b*e*f**2*h*i**3*x**2 - 4*b*e*f**2*i**4*x**3 + 48*b*f**3*h**3*i*x + 36*b*f**3*h**2*i**2*x**2 + 16*b*f**3*h*i**3*x**3 + 3*b*f**3*i**4*x**4)*log(c*(e + f*x))/(12*d*f**4) + (b*e**4*i**4 - 4*b*e**3*f*h*i**3 + 6*b*e**2*f**2*h**2*i**2 - 4*b*e*f**3*h**3*i + b*f**4*h**4)*log(c*(e + f*x))**2/(2*d*f**5) + (12*a*e**4*i**4 - 48*a*e**3*f*h*i**3 + 72*a*e**2*f**2*h**2*i**2 - 48*a*e*f**3*h**3*i + 12*a*f**4*h**4 - 25*b*e**4*i**4 + 88*b*e**3*f*h*i**3 - 108*b*e**2*f**2*h**2*i**2 + 48*b*e*f**3*h**3*i)*log(e + f*x)/(12*d*f**5)","B",0
176,1,427,0,2.308076," ","integrate((i*x+h)**3*(a+b*ln(c*(f*x+e)))/(d*f*x+d*e),x)","x^{3} \left(\frac{a i^{3}}{3 d f} - \frac{b i^{3}}{9 d f}\right) + x^{2} \left(- \frac{a e i^{3}}{2 d f^{2}} + \frac{3 a h i^{2}}{2 d f} + \frac{5 b e i^{3}}{12 d f^{2}} - \frac{3 b h i^{2}}{4 d f}\right) + x \left(\frac{a e^{2} i^{3}}{d f^{3}} - \frac{3 a e h i^{2}}{d f^{2}} + \frac{3 a h^{2} i}{d f} - \frac{11 b e^{2} i^{3}}{6 d f^{3}} + \frac{9 b e h i^{2}}{2 d f^{2}} - \frac{3 b h^{2} i}{d f}\right) + \frac{\left(6 b e^{2} i^{3} x - 18 b e f h i^{2} x - 3 b e f i^{3} x^{2} + 18 b f^{2} h^{2} i x + 9 b f^{2} h i^{2} x^{2} + 2 b f^{2} i^{3} x^{3}\right) \log{\left(c \left(e + f x\right) \right)}}{6 d f^{3}} + \frac{\left(- b e^{3} i^{3} + 3 b e^{2} f h i^{2} - 3 b e f^{2} h^{2} i + b f^{3} h^{3}\right) \log{\left(c \left(e + f x\right) \right)}^{2}}{2 d f^{4}} - \frac{\left(6 a e^{3} i^{3} - 18 a e^{2} f h i^{2} + 18 a e f^{2} h^{2} i - 6 a f^{3} h^{3} - 11 b e^{3} i^{3} + 27 b e^{2} f h i^{2} - 18 b e f^{2} h^{2} i\right) \log{\left(e + f x \right)}}{6 d f^{4}}"," ",0,"x**3*(a*i**3/(3*d*f) - b*i**3/(9*d*f)) + x**2*(-a*e*i**3/(2*d*f**2) + 3*a*h*i**2/(2*d*f) + 5*b*e*i**3/(12*d*f**2) - 3*b*h*i**2/(4*d*f)) + x*(a*e**2*i**3/(d*f**3) - 3*a*e*h*i**2/(d*f**2) + 3*a*h**2*i/(d*f) - 11*b*e**2*i**3/(6*d*f**3) + 9*b*e*h*i**2/(2*d*f**2) - 3*b*h**2*i/(d*f)) + (6*b*e**2*i**3*x - 18*b*e*f*h*i**2*x - 3*b*e*f*i**3*x**2 + 18*b*f**2*h**2*i*x + 9*b*f**2*h*i**2*x**2 + 2*b*f**2*i**3*x**3)*log(c*(e + f*x))/(6*d*f**3) + (-b*e**3*i**3 + 3*b*e**2*f*h*i**2 - 3*b*e*f**2*h**2*i + b*f**3*h**3)*log(c*(e + f*x))**2/(2*d*f**4) - (6*a*e**3*i**3 - 18*a*e**2*f*h*i**2 + 18*a*e*f**2*h**2*i - 6*a*f**3*h**3 - 11*b*e**3*i**3 + 27*b*e**2*f*h*i**2 - 18*b*e*f**2*h**2*i)*log(e + f*x)/(6*d*f**4)","A",0
177,1,226,0,1.656772," ","integrate((i*x+h)**2*(a+b*ln(c*(f*x+e)))/(d*f*x+d*e),x)","x^{2} \left(\frac{a i^{2}}{2 d f} - \frac{b i^{2}}{4 d f}\right) + x \left(- \frac{a e i^{2}}{d f^{2}} + \frac{2 a h i}{d f} + \frac{3 b e i^{2}}{2 d f^{2}} - \frac{2 b h i}{d f}\right) + \frac{\left(- 2 b e i^{2} x + 4 b f h i x + b f i^{2} x^{2}\right) \log{\left(c \left(e + f x\right) \right)}}{2 d f^{2}} + \frac{\left(b e^{2} i^{2} - 2 b e f h i + b f^{2} h^{2}\right) \log{\left(c \left(e + f x\right) \right)}^{2}}{2 d f^{3}} + \frac{\left(2 a e^{2} i^{2} - 4 a e f h i + 2 a f^{2} h^{2} - 3 b e^{2} i^{2} + 4 b e f h i\right) \log{\left(e + f x \right)}}{2 d f^{3}}"," ",0,"x**2*(a*i**2/(2*d*f) - b*i**2/(4*d*f)) + x*(-a*e*i**2/(d*f**2) + 2*a*h*i/(d*f) + 3*b*e*i**2/(2*d*f**2) - 2*b*h*i/(d*f)) + (-2*b*e*i**2*x + 4*b*f*h*i*x + b*f*i**2*x**2)*log(c*(e + f*x))/(2*d*f**2) + (b*e**2*i**2 - 2*b*e*f*h*i + b*f**2*h**2)*log(c*(e + f*x))**2/(2*d*f**3) + (2*a*e**2*i**2 - 4*a*e*f*h*i + 2*a*f**2*h**2 - 3*b*e**2*i**2 + 4*b*e*f*h*i)*log(e + f*x)/(2*d*f**3)","A",0
178,1,85,0,1.122508," ","integrate((i*x+h)*(a+b*ln(c*(f*x+e)))/(d*f*x+d*e),x)","\frac{b i x \log{\left(c \left(e + f x\right) \right)}}{d f} + x \left(\frac{a i}{d f} - \frac{b i}{d f}\right) + \frac{\left(- b e i + b f h\right) \log{\left(c \left(e + f x\right) \right)}^{2}}{2 d f^{2}} - \frac{\left(a e i - a f h - b e i\right) \log{\left(e + f x \right)}}{d f^{2}}"," ",0,"b*i*x*log(c*(e + f*x))/(d*f) + x*(a*i/(d*f) - b*i/(d*f)) + (-b*e*i + b*f*h)*log(c*(e + f*x))**2/(2*d*f**2) - (a*e*i - a*f*h - b*e*i)*log(e + f*x)/(d*f**2)","A",0
179,1,31,0,0.330724," ","integrate((a+b*ln(c*(f*x+e)))/(d*f*x+d*e),x)","\frac{a \log{\left(d e + d f x \right)}}{d f} + \frac{b \log{\left(c \left(e + f x\right) \right)}^{2}}{2 d f}"," ",0,"a*log(d*e + d*f*x)/(d*f) + b*log(c*(e + f*x))**2/(2*d*f)","A",0
180,0,0,0,0.000000," ","integrate((a+b*ln(c*(f*x+e)))/(d*f*x+d*e)/(i*x+h),x)","\frac{\int \frac{a}{e h + e i x + f h x + f i x^{2}}\, dx + \int \frac{b \log{\left(c e + c f x \right)}}{e h + e i x + f h x + f i x^{2}}\, dx}{d}"," ",0,"(Integral(a/(e*h + e*i*x + f*h*x + f*i*x**2), x) + Integral(b*log(c*e + c*f*x)/(e*h + e*i*x + f*h*x + f*i*x**2), x))/d","F",0
181,0,0,0,0.000000," ","integrate((a+b*ln(c*(f*x+e)))/(d*f*x+d*e)/(i*x+h)**2,x)","\frac{\int \frac{a}{e h^{2} + 2 e h i x + e i^{2} x^{2} + f h^{2} x + 2 f h i x^{2} + f i^{2} x^{3}}\, dx + \int \frac{b \log{\left(c e + c f x \right)}}{e h^{2} + 2 e h i x + e i^{2} x^{2} + f h^{2} x + 2 f h i x^{2} + f i^{2} x^{3}}\, dx}{d}"," ",0,"(Integral(a/(e*h**2 + 2*e*h*i*x + e*i**2*x**2 + f*h**2*x + 2*f*h*i*x**2 + f*i**2*x**3), x) + Integral(b*log(c*e + c*f*x)/(e*h**2 + 2*e*h*i*x + e*i**2*x**2 + f*h**2*x + 2*f*h*i*x**2 + f*i**2*x**3), x))/d","F",0
182,0,0,0,0.000000," ","integrate((a+b*ln(c*(f*x+e)))/(d*f*x+d*e)/(i*x+h)**3,x)","\frac{\int \frac{a}{e h^{3} + 3 e h^{2} i x + 3 e h i^{2} x^{2} + e i^{3} x^{3} + f h^{3} x + 3 f h^{2} i x^{2} + 3 f h i^{2} x^{3} + f i^{3} x^{4}}\, dx + \int \frac{b \log{\left(c e + c f x \right)}}{e h^{3} + 3 e h^{2} i x + 3 e h i^{2} x^{2} + e i^{3} x^{3} + f h^{3} x + 3 f h^{2} i x^{2} + 3 f h i^{2} x^{3} + f i^{3} x^{4}}\, dx}{d}"," ",0,"(Integral(a/(e*h**3 + 3*e*h**2*i*x + 3*e*h*i**2*x**2 + e*i**3*x**3 + f*h**3*x + 3*f*h**2*i*x**2 + 3*f*h*i**2*x**3 + f*i**3*x**4), x) + Integral(b*log(c*e + c*f*x)/(e*h**3 + 3*e*h**2*i*x + 3*e*h*i**2*x**2 + e*i**3*x**3 + f*h**3*x + 3*f*h**2*i*x**2 + 3*f*h*i**2*x**3 + f*i**3*x**4), x))/d","F",0
183,1,1479,0,8.479870," ","integrate((i*x+h)**4*(a+b*ln(c*(f*x+e)))**2/(d*f*x+d*e),x)","x^{4} \left(\frac{a^{2} i^{4}}{4 d f} - \frac{a b i^{4}}{8 d f} + \frac{b^{2} i^{4}}{32 d f}\right) + x^{3} \left(- \frac{a^{2} e i^{4}}{3 d f^{2}} + \frac{4 a^{2} h i^{3}}{3 d f} + \frac{7 a b e i^{4}}{18 d f^{2}} - \frac{8 a b h i^{3}}{9 d f} - \frac{37 b^{2} e i^{4}}{216 d f^{2}} + \frac{8 b^{2} h i^{3}}{27 d f}\right) + x^{2} \left(\frac{a^{2} e^{2} i^{4}}{2 d f^{3}} - \frac{2 a^{2} e h i^{3}}{d f^{2}} + \frac{3 a^{2} h^{2} i^{2}}{d f} - \frac{13 a b e^{2} i^{4}}{12 d f^{3}} + \frac{10 a b e h i^{3}}{3 d f^{2}} - \frac{3 a b h^{2} i^{2}}{d f} + \frac{115 b^{2} e^{2} i^{4}}{144 d f^{3}} - \frac{19 b^{2} e h i^{3}}{9 d f^{2}} + \frac{3 b^{2} h^{2} i^{2}}{2 d f}\right) + x \left(- \frac{a^{2} e^{3} i^{4}}{d f^{4}} + \frac{4 a^{2} e^{2} h i^{3}}{d f^{3}} - \frac{6 a^{2} e h^{2} i^{2}}{d f^{2}} + \frac{4 a^{2} h^{3} i}{d f} + \frac{25 a b e^{3} i^{4}}{6 d f^{4}} - \frac{44 a b e^{2} h i^{3}}{3 d f^{3}} + \frac{18 a b e h^{2} i^{2}}{d f^{2}} - \frac{8 a b h^{3} i}{d f} - \frac{415 b^{2} e^{3} i^{4}}{72 d f^{4}} + \frac{170 b^{2} e^{2} h i^{3}}{9 d f^{3}} - \frac{21 b^{2} e h^{2} i^{2}}{d f^{2}} + \frac{8 b^{2} h^{3} i}{d f}\right) + \frac{\left(- 144 a b e^{3} i^{4} x + 576 a b e^{2} f h i^{3} x + 72 a b e^{2} f i^{4} x^{2} - 864 a b e f^{2} h^{2} i^{2} x - 288 a b e f^{2} h i^{3} x^{2} - 48 a b e f^{2} i^{4} x^{3} + 576 a b f^{3} h^{3} i x + 432 a b f^{3} h^{2} i^{2} x^{2} + 192 a b f^{3} h i^{3} x^{3} + 36 a b f^{3} i^{4} x^{4} + 300 b^{2} e^{3} i^{4} x - 1056 b^{2} e^{2} f h i^{3} x - 78 b^{2} e^{2} f i^{4} x^{2} + 1296 b^{2} e f^{2} h^{2} i^{2} x + 240 b^{2} e f^{2} h i^{3} x^{2} + 28 b^{2} e f^{2} i^{4} x^{3} - 576 b^{2} f^{3} h^{3} i x - 216 b^{2} f^{3} h^{2} i^{2} x^{2} - 64 b^{2} f^{3} h i^{3} x^{3} - 9 b^{2} f^{3} i^{4} x^{4}\right) \log{\left(c \left(e + f x\right) \right)}}{72 d f^{4}} + \frac{\left(b^{2} e^{4} i^{4} - 4 b^{2} e^{3} f h i^{3} + 6 b^{2} e^{2} f^{2} h^{2} i^{2} - 4 b^{2} e f^{3} h^{3} i + b^{2} f^{4} h^{4}\right) \log{\left(c \left(e + f x\right) \right)}^{3}}{3 d f^{5}} + \frac{\left(72 a^{2} e^{4} i^{4} - 288 a^{2} e^{3} f h i^{3} + 432 a^{2} e^{2} f^{2} h^{2} i^{2} - 288 a^{2} e f^{3} h^{3} i + 72 a^{2} f^{4} h^{4} - 300 a b e^{4} i^{4} + 1056 a b e^{3} f h i^{3} - 1296 a b e^{2} f^{2} h^{2} i^{2} + 576 a b e f^{3} h^{3} i + 415 b^{2} e^{4} i^{4} - 1360 b^{2} e^{3} f h i^{3} + 1512 b^{2} e^{2} f^{2} h^{2} i^{2} - 576 b^{2} e f^{3} h^{3} i\right) \log{\left(e + f x \right)}}{72 d f^{5}} + \frac{\left(12 a b e^{4} i^{4} - 48 a b e^{3} f h i^{3} + 72 a b e^{2} f^{2} h^{2} i^{2} - 48 a b e f^{3} h^{3} i + 12 a b f^{4} h^{4} - 25 b^{2} e^{4} i^{4} + 88 b^{2} e^{3} f h i^{3} - 12 b^{2} e^{3} f i^{4} x - 108 b^{2} e^{2} f^{2} h^{2} i^{2} + 48 b^{2} e^{2} f^{2} h i^{3} x + 6 b^{2} e^{2} f^{2} i^{4} x^{2} + 48 b^{2} e f^{3} h^{3} i - 72 b^{2} e f^{3} h^{2} i^{2} x - 24 b^{2} e f^{3} h i^{3} x^{2} - 4 b^{2} e f^{3} i^{4} x^{3} + 48 b^{2} f^{4} h^{3} i x + 36 b^{2} f^{4} h^{2} i^{2} x^{2} + 16 b^{2} f^{4} h i^{3} x^{3} + 3 b^{2} f^{4} i^{4} x^{4}\right) \log{\left(c \left(e + f x\right) \right)}^{2}}{12 d f^{5}}"," ",0,"x**4*(a**2*i**4/(4*d*f) - a*b*i**4/(8*d*f) + b**2*i**4/(32*d*f)) + x**3*(-a**2*e*i**4/(3*d*f**2) + 4*a**2*h*i**3/(3*d*f) + 7*a*b*e*i**4/(18*d*f**2) - 8*a*b*h*i**3/(9*d*f) - 37*b**2*e*i**4/(216*d*f**2) + 8*b**2*h*i**3/(27*d*f)) + x**2*(a**2*e**2*i**4/(2*d*f**3) - 2*a**2*e*h*i**3/(d*f**2) + 3*a**2*h**2*i**2/(d*f) - 13*a*b*e**2*i**4/(12*d*f**3) + 10*a*b*e*h*i**3/(3*d*f**2) - 3*a*b*h**2*i**2/(d*f) + 115*b**2*e**2*i**4/(144*d*f**3) - 19*b**2*e*h*i**3/(9*d*f**2) + 3*b**2*h**2*i**2/(2*d*f)) + x*(-a**2*e**3*i**4/(d*f**4) + 4*a**2*e**2*h*i**3/(d*f**3) - 6*a**2*e*h**2*i**2/(d*f**2) + 4*a**2*h**3*i/(d*f) + 25*a*b*e**3*i**4/(6*d*f**4) - 44*a*b*e**2*h*i**3/(3*d*f**3) + 18*a*b*e*h**2*i**2/(d*f**2) - 8*a*b*h**3*i/(d*f) - 415*b**2*e**3*i**4/(72*d*f**4) + 170*b**2*e**2*h*i**3/(9*d*f**3) - 21*b**2*e*h**2*i**2/(d*f**2) + 8*b**2*h**3*i/(d*f)) + (-144*a*b*e**3*i**4*x + 576*a*b*e**2*f*h*i**3*x + 72*a*b*e**2*f*i**4*x**2 - 864*a*b*e*f**2*h**2*i**2*x - 288*a*b*e*f**2*h*i**3*x**2 - 48*a*b*e*f**2*i**4*x**3 + 576*a*b*f**3*h**3*i*x + 432*a*b*f**3*h**2*i**2*x**2 + 192*a*b*f**3*h*i**3*x**3 + 36*a*b*f**3*i**4*x**4 + 300*b**2*e**3*i**4*x - 1056*b**2*e**2*f*h*i**3*x - 78*b**2*e**2*f*i**4*x**2 + 1296*b**2*e*f**2*h**2*i**2*x + 240*b**2*e*f**2*h*i**3*x**2 + 28*b**2*e*f**2*i**4*x**3 - 576*b**2*f**3*h**3*i*x - 216*b**2*f**3*h**2*i**2*x**2 - 64*b**2*f**3*h*i**3*x**3 - 9*b**2*f**3*i**4*x**4)*log(c*(e + f*x))/(72*d*f**4) + (b**2*e**4*i**4 - 4*b**2*e**3*f*h*i**3 + 6*b**2*e**2*f**2*h**2*i**2 - 4*b**2*e*f**3*h**3*i + b**2*f**4*h**4)*log(c*(e + f*x))**3/(3*d*f**5) + (72*a**2*e**4*i**4 - 288*a**2*e**3*f*h*i**3 + 432*a**2*e**2*f**2*h**2*i**2 - 288*a**2*e*f**3*h**3*i + 72*a**2*f**4*h**4 - 300*a*b*e**4*i**4 + 1056*a*b*e**3*f*h*i**3 - 1296*a*b*e**2*f**2*h**2*i**2 + 576*a*b*e*f**3*h**3*i + 415*b**2*e**4*i**4 - 1360*b**2*e**3*f*h*i**3 + 1512*b**2*e**2*f**2*h**2*i**2 - 576*b**2*e*f**3*h**3*i)*log(e + f*x)/(72*d*f**5) + (12*a*b*e**4*i**4 - 48*a*b*e**3*f*h*i**3 + 72*a*b*e**2*f**2*h**2*i**2 - 48*a*b*e*f**3*h**3*i + 12*a*b*f**4*h**4 - 25*b**2*e**4*i**4 + 88*b**2*e**3*f*h*i**3 - 12*b**2*e**3*f*i**4*x - 108*b**2*e**2*f**2*h**2*i**2 + 48*b**2*e**2*f**2*h*i**3*x + 6*b**2*e**2*f**2*i**4*x**2 + 48*b**2*e*f**3*h**3*i - 72*b**2*e*f**3*h**2*i**2*x - 24*b**2*e*f**3*h*i**3*x**2 - 4*b**2*e*f**3*i**4*x**3 + 48*b**2*f**4*h**3*i*x + 36*b**2*f**4*h**2*i**2*x**2 + 16*b**2*f**4*h*i**3*x**3 + 3*b**2*f**4*i**4*x**4)*log(c*(e + f*x))**2/(12*d*f**5)","B",0
184,1,918,0,5.627460," ","integrate((i*x+h)**3*(a+b*ln(c*(f*x+e)))**2/(d*f*x+d*e),x)","x^{3} \left(\frac{a^{2} i^{3}}{3 d f} - \frac{2 a b i^{3}}{9 d f} + \frac{2 b^{2} i^{3}}{27 d f}\right) + x^{2} \left(- \frac{a^{2} e i^{3}}{2 d f^{2}} + \frac{3 a^{2} h i^{2}}{2 d f} + \frac{5 a b e i^{3}}{6 d f^{2}} - \frac{3 a b h i^{2}}{2 d f} - \frac{19 b^{2} e i^{3}}{36 d f^{2}} + \frac{3 b^{2} h i^{2}}{4 d f}\right) + x \left(\frac{a^{2} e^{2} i^{3}}{d f^{3}} - \frac{3 a^{2} e h i^{2}}{d f^{2}} + \frac{3 a^{2} h^{2} i}{d f} - \frac{11 a b e^{2} i^{3}}{3 d f^{3}} + \frac{9 a b e h i^{2}}{d f^{2}} - \frac{6 a b h^{2} i}{d f} + \frac{85 b^{2} e^{2} i^{3}}{18 d f^{3}} - \frac{21 b^{2} e h i^{2}}{2 d f^{2}} + \frac{6 b^{2} h^{2} i}{d f}\right) + \frac{\left(36 a b e^{2} i^{3} x - 108 a b e f h i^{2} x - 18 a b e f i^{3} x^{2} + 108 a b f^{2} h^{2} i x + 54 a b f^{2} h i^{2} x^{2} + 12 a b f^{2} i^{3} x^{3} - 66 b^{2} e^{2} i^{3} x + 162 b^{2} e f h i^{2} x + 15 b^{2} e f i^{3} x^{2} - 108 b^{2} f^{2} h^{2} i x - 27 b^{2} f^{2} h i^{2} x^{2} - 4 b^{2} f^{2} i^{3} x^{3}\right) \log{\left(c \left(e + f x\right) \right)}}{18 d f^{3}} + \frac{\left(- b^{2} e^{3} i^{3} + 3 b^{2} e^{2} f h i^{2} - 3 b^{2} e f^{2} h^{2} i + b^{2} f^{3} h^{3}\right) \log{\left(c \left(e + f x\right) \right)}^{3}}{3 d f^{4}} - \frac{\left(18 a^{2} e^{3} i^{3} - 54 a^{2} e^{2} f h i^{2} + 54 a^{2} e f^{2} h^{2} i - 18 a^{2} f^{3} h^{3} - 66 a b e^{3} i^{3} + 162 a b e^{2} f h i^{2} - 108 a b e f^{2} h^{2} i + 85 b^{2} e^{3} i^{3} - 189 b^{2} e^{2} f h i^{2} + 108 b^{2} e f^{2} h^{2} i\right) \log{\left(e + f x \right)}}{18 d f^{4}} + \frac{\left(- 6 a b e^{3} i^{3} + 18 a b e^{2} f h i^{2} - 18 a b e f^{2} h^{2} i + 6 a b f^{3} h^{3} + 11 b^{2} e^{3} i^{3} - 27 b^{2} e^{2} f h i^{2} + 6 b^{2} e^{2} f i^{3} x + 18 b^{2} e f^{2} h^{2} i - 18 b^{2} e f^{2} h i^{2} x - 3 b^{2} e f^{2} i^{3} x^{2} + 18 b^{2} f^{3} h^{2} i x + 9 b^{2} f^{3} h i^{2} x^{2} + 2 b^{2} f^{3} i^{3} x^{3}\right) \log{\left(c \left(e + f x\right) \right)}^{2}}{6 d f^{4}}"," ",0,"x**3*(a**2*i**3/(3*d*f) - 2*a*b*i**3/(9*d*f) + 2*b**2*i**3/(27*d*f)) + x**2*(-a**2*e*i**3/(2*d*f**2) + 3*a**2*h*i**2/(2*d*f) + 5*a*b*e*i**3/(6*d*f**2) - 3*a*b*h*i**2/(2*d*f) - 19*b**2*e*i**3/(36*d*f**2) + 3*b**2*h*i**2/(4*d*f)) + x*(a**2*e**2*i**3/(d*f**3) - 3*a**2*e*h*i**2/(d*f**2) + 3*a**2*h**2*i/(d*f) - 11*a*b*e**2*i**3/(3*d*f**3) + 9*a*b*e*h*i**2/(d*f**2) - 6*a*b*h**2*i/(d*f) + 85*b**2*e**2*i**3/(18*d*f**3) - 21*b**2*e*h*i**2/(2*d*f**2) + 6*b**2*h**2*i/(d*f)) + (36*a*b*e**2*i**3*x - 108*a*b*e*f*h*i**2*x - 18*a*b*e*f*i**3*x**2 + 108*a*b*f**2*h**2*i*x + 54*a*b*f**2*h*i**2*x**2 + 12*a*b*f**2*i**3*x**3 - 66*b**2*e**2*i**3*x + 162*b**2*e*f*h*i**2*x + 15*b**2*e*f*i**3*x**2 - 108*b**2*f**2*h**2*i*x - 27*b**2*f**2*h*i**2*x**2 - 4*b**2*f**2*i**3*x**3)*log(c*(e + f*x))/(18*d*f**3) + (-b**2*e**3*i**3 + 3*b**2*e**2*f*h*i**2 - 3*b**2*e*f**2*h**2*i + b**2*f**3*h**3)*log(c*(e + f*x))**3/(3*d*f**4) - (18*a**2*e**3*i**3 - 54*a**2*e**2*f*h*i**2 + 54*a**2*e*f**2*h**2*i - 18*a**2*f**3*h**3 - 66*a*b*e**3*i**3 + 162*a*b*e**2*f*h*i**2 - 108*a*b*e*f**2*h**2*i + 85*b**2*e**3*i**3 - 189*b**2*e**2*f*h*i**2 + 108*b**2*e*f**2*h**2*i)*log(e + f*x)/(18*d*f**4) + (-6*a*b*e**3*i**3 + 18*a*b*e**2*f*h*i**2 - 18*a*b*e*f**2*h**2*i + 6*a*b*f**3*h**3 + 11*b**2*e**3*i**3 - 27*b**2*e**2*f*h*i**2 + 6*b**2*e**2*f*i**3*x + 18*b**2*e*f**2*h**2*i - 18*b**2*e*f**2*h*i**2*x - 3*b**2*e*f**2*i**3*x**2 + 18*b**2*f**3*h**2*i*x + 9*b**2*f**3*h*i**2*x**2 + 2*b**2*f**3*i**3*x**3)*log(c*(e + f*x))**2/(6*d*f**4)","B",0
185,1,473,0,3.460198," ","integrate((i*x+h)**2*(a+b*ln(c*(f*x+e)))**2/(d*f*x+d*e),x)","x^{2} \left(\frac{a^{2} i^{2}}{2 d f} - \frac{a b i^{2}}{2 d f} + \frac{b^{2} i^{2}}{4 d f}\right) + x \left(- \frac{a^{2} e i^{2}}{d f^{2}} + \frac{2 a^{2} h i}{d f} + \frac{3 a b e i^{2}}{d f^{2}} - \frac{4 a b h i}{d f} - \frac{7 b^{2} e i^{2}}{2 d f^{2}} + \frac{4 b^{2} h i}{d f}\right) + \frac{\left(- 4 a b e i^{2} x + 8 a b f h i x + 2 a b f i^{2} x^{2} + 6 b^{2} e i^{2} x - 8 b^{2} f h i x - b^{2} f i^{2} x^{2}\right) \log{\left(c \left(e + f x\right) \right)}}{2 d f^{2}} + \frac{\left(b^{2} e^{2} i^{2} - 2 b^{2} e f h i + b^{2} f^{2} h^{2}\right) \log{\left(c \left(e + f x\right) \right)}^{3}}{3 d f^{3}} + \frac{\left(2 a^{2} e^{2} i^{2} - 4 a^{2} e f h i + 2 a^{2} f^{2} h^{2} - 6 a b e^{2} i^{2} + 8 a b e f h i + 7 b^{2} e^{2} i^{2} - 8 b^{2} e f h i\right) \log{\left(e + f x \right)}}{2 d f^{3}} + \frac{\left(2 a b e^{2} i^{2} - 4 a b e f h i + 2 a b f^{2} h^{2} - 3 b^{2} e^{2} i^{2} + 4 b^{2} e f h i - 2 b^{2} e f i^{2} x + 4 b^{2} f^{2} h i x + b^{2} f^{2} i^{2} x^{2}\right) \log{\left(c \left(e + f x\right) \right)}^{2}}{2 d f^{3}}"," ",0,"x**2*(a**2*i**2/(2*d*f) - a*b*i**2/(2*d*f) + b**2*i**2/(4*d*f)) + x*(-a**2*e*i**2/(d*f**2) + 2*a**2*h*i/(d*f) + 3*a*b*e*i**2/(d*f**2) - 4*a*b*h*i/(d*f) - 7*b**2*e*i**2/(2*d*f**2) + 4*b**2*h*i/(d*f)) + (-4*a*b*e*i**2*x + 8*a*b*f*h*i*x + 2*a*b*f*i**2*x**2 + 6*b**2*e*i**2*x - 8*b**2*f*h*i*x - b**2*f*i**2*x**2)*log(c*(e + f*x))/(2*d*f**2) + (b**2*e**2*i**2 - 2*b**2*e*f*h*i + b**2*f**2*h**2)*log(c*(e + f*x))**3/(3*d*f**3) + (2*a**2*e**2*i**2 - 4*a**2*e*f*h*i + 2*a**2*f**2*h**2 - 6*a*b*e**2*i**2 + 8*a*b*e*f*h*i + 7*b**2*e**2*i**2 - 8*b**2*e*f*h*i)*log(e + f*x)/(2*d*f**3) + (2*a*b*e**2*i**2 - 4*a*b*e*f*h*i + 2*a*b*f**2*h**2 - 3*b**2*e**2*i**2 + 4*b**2*e*f*h*i - 2*b**2*e*f*i**2*x + 4*b**2*f**2*h*i*x + b**2*f**2*i**2*x**2)*log(c*(e + f*x))**2/(2*d*f**3)","B",0
186,1,175,0,2.077072," ","integrate((i*x+h)*(a+b*ln(c*(f*x+e)))**2/(d*f*x+d*e),x)","x \left(\frac{a^{2} i}{d f} - \frac{2 a b i}{d f} + \frac{2 b^{2} i}{d f}\right) + \frac{\left(2 a b i x - 2 b^{2} i x\right) \log{\left(c \left(e + f x\right) \right)}}{d f} + \frac{\left(- b^{2} e i + b^{2} f h\right) \log{\left(c \left(e + f x\right) \right)}^{3}}{3 d f^{2}} - \frac{\left(a^{2} e i - a^{2} f h - 2 a b e i + 2 b^{2} e i\right) \log{\left(e + f x \right)}}{d f^{2}} + \frac{\left(- a b e i + a b f h + b^{2} e i + b^{2} f i x\right) \log{\left(c \left(e + f x\right) \right)}^{2}}{d f^{2}}"," ",0,"x*(a**2*i/(d*f) - 2*a*b*i/(d*f) + 2*b**2*i/(d*f)) + (2*a*b*i*x - 2*b**2*i*x)*log(c*(e + f*x))/(d*f) + (-b**2*e*i + b**2*f*h)*log(c*(e + f*x))**3/(3*d*f**2) - (a**2*e*i - a**2*f*h - 2*a*b*e*i + 2*b**2*e*i)*log(e + f*x)/(d*f**2) + (-a*b*e*i + a*b*f*h + b**2*e*i + b**2*f*i*x)*log(c*(e + f*x))**2/(d*f**2)","A",0
187,1,51,0,0.495128," ","integrate((a+b*ln(c*(f*x+e)))**2/(d*f*x+d*e),x)","\frac{a^{2} \log{\left(d e + d f x \right)}}{d f} + \frac{a b \log{\left(c \left(e + f x\right) \right)}^{2}}{d f} + \frac{b^{2} \log{\left(c \left(e + f x\right) \right)}^{3}}{3 d f}"," ",0,"a**2*log(d*e + d*f*x)/(d*f) + a*b*log(c*(e + f*x))**2/(d*f) + b**2*log(c*(e + f*x))**3/(3*d*f)","B",0
188,0,0,0,0.000000," ","integrate((a+b*ln(c*(f*x+e)))**2/(d*f*x+d*e)/(i*x+h),x)","\frac{\int \frac{a^{2}}{e h + e i x + f h x + f i x^{2}}\, dx + \int \frac{b^{2} \log{\left(c e + c f x \right)}^{2}}{e h + e i x + f h x + f i x^{2}}\, dx + \int \frac{2 a b \log{\left(c e + c f x \right)}}{e h + e i x + f h x + f i x^{2}}\, dx}{d}"," ",0,"(Integral(a**2/(e*h + e*i*x + f*h*x + f*i*x**2), x) + Integral(b**2*log(c*e + c*f*x)**2/(e*h + e*i*x + f*h*x + f*i*x**2), x) + Integral(2*a*b*log(c*e + c*f*x)/(e*h + e*i*x + f*h*x + f*i*x**2), x))/d","F",0
189,0,0,0,0.000000," ","integrate((a+b*ln(c*(f*x+e)))**2/(d*f*x+d*e)/(i*x+h)**2,x)","\frac{\int \frac{a^{2}}{e h^{2} + 2 e h i x + e i^{2} x^{2} + f h^{2} x + 2 f h i x^{2} + f i^{2} x^{3}}\, dx + \int \frac{b^{2} \log{\left(c e + c f x \right)}^{2}}{e h^{2} + 2 e h i x + e i^{2} x^{2} + f h^{2} x + 2 f h i x^{2} + f i^{2} x^{3}}\, dx + \int \frac{2 a b \log{\left(c e + c f x \right)}}{e h^{2} + 2 e h i x + e i^{2} x^{2} + f h^{2} x + 2 f h i x^{2} + f i^{2} x^{3}}\, dx}{d}"," ",0,"(Integral(a**2/(e*h**2 + 2*e*h*i*x + e*i**2*x**2 + f*h**2*x + 2*f*h*i*x**2 + f*i**2*x**3), x) + Integral(b**2*log(c*e + c*f*x)**2/(e*h**2 + 2*e*h*i*x + e*i**2*x**2 + f*h**2*x + 2*f*h*i*x**2 + f*i**2*x**3), x) + Integral(2*a*b*log(c*e + c*f*x)/(e*h**2 + 2*e*h*i*x + e*i**2*x**2 + f*h**2*x + 2*f*h*i*x**2 + f*i**2*x**3), x))/d","F",0
190,0,0,0,0.000000," ","integrate((a+b*ln(c*(f*x+e)))**2/(d*f*x+d*e)/(i*x+h)**3,x)","\frac{\int \frac{a^{2}}{e h^{3} + 3 e h^{2} i x + 3 e h i^{2} x^{2} + e i^{3} x^{3} + f h^{3} x + 3 f h^{2} i x^{2} + 3 f h i^{2} x^{3} + f i^{3} x^{4}}\, dx + \int \frac{b^{2} \log{\left(c e + c f x \right)}^{2}}{e h^{3} + 3 e h^{2} i x + 3 e h i^{2} x^{2} + e i^{3} x^{3} + f h^{3} x + 3 f h^{2} i x^{2} + 3 f h i^{2} x^{3} + f i^{3} x^{4}}\, dx + \int \frac{2 a b \log{\left(c e + c f x \right)}}{e h^{3} + 3 e h^{2} i x + 3 e h i^{2} x^{2} + e i^{3} x^{3} + f h^{3} x + 3 f h^{2} i x^{2} + 3 f h i^{2} x^{3} + f i^{3} x^{4}}\, dx}{d}"," ",0,"(Integral(a**2/(e*h**3 + 3*e*h**2*i*x + 3*e*h*i**2*x**2 + e*i**3*x**3 + f*h**3*x + 3*f*h**2*i*x**2 + 3*f*h*i**2*x**3 + f*i**3*x**4), x) + Integral(b**2*log(c*e + c*f*x)**2/(e*h**3 + 3*e*h**2*i*x + 3*e*h*i**2*x**2 + e*i**3*x**3 + f*h**3*x + 3*f*h**2*i*x**2 + 3*f*h*i**2*x**3 + f*i**3*x**4), x) + Integral(2*a*b*log(c*e + c*f*x)/(e*h**3 + 3*e*h**2*i*x + 3*e*h*i**2*x**2 + e*i**3*x**3 + f*h**3*x + 3*f*h**2*i*x**2 + 3*f*h*i**2*x**3 + f*i**3*x**4), x))/d","F",0
191,0,0,0,0.000000," ","integrate((i*x+h)**4/(d*f*x+d*e)/(a+b*ln(c*(f*x+e))),x)","\frac{\int \frac{h^{4}}{a e + a f x + b e \log{\left(c e + c f x \right)} + b f x \log{\left(c e + c f x \right)}}\, dx + \int \frac{i^{4} x^{4}}{a e + a f x + b e \log{\left(c e + c f x \right)} + b f x \log{\left(c e + c f x \right)}}\, dx + \int \frac{4 h i^{3} x^{3}}{a e + a f x + b e \log{\left(c e + c f x \right)} + b f x \log{\left(c e + c f x \right)}}\, dx + \int \frac{6 h^{2} i^{2} x^{2}}{a e + a f x + b e \log{\left(c e + c f x \right)} + b f x \log{\left(c e + c f x \right)}}\, dx + \int \frac{4 h^{3} i x}{a e + a f x + b e \log{\left(c e + c f x \right)} + b f x \log{\left(c e + c f x \right)}}\, dx}{d}"," ",0,"(Integral(h**4/(a*e + a*f*x + b*e*log(c*e + c*f*x) + b*f*x*log(c*e + c*f*x)), x) + Integral(i**4*x**4/(a*e + a*f*x + b*e*log(c*e + c*f*x) + b*f*x*log(c*e + c*f*x)), x) + Integral(4*h*i**3*x**3/(a*e + a*f*x + b*e*log(c*e + c*f*x) + b*f*x*log(c*e + c*f*x)), x) + Integral(6*h**2*i**2*x**2/(a*e + a*f*x + b*e*log(c*e + c*f*x) + b*f*x*log(c*e + c*f*x)), x) + Integral(4*h**3*i*x/(a*e + a*f*x + b*e*log(c*e + c*f*x) + b*f*x*log(c*e + c*f*x)), x))/d","F",0
192,0,0,0,0.000000," ","integrate((i*x+h)**3/(d*f*x+d*e)/(a+b*ln(c*(f*x+e))),x)","\frac{\int \frac{h^{3}}{a e + a f x + b e \log{\left(c e + c f x \right)} + b f x \log{\left(c e + c f x \right)}}\, dx + \int \frac{i^{3} x^{3}}{a e + a f x + b e \log{\left(c e + c f x \right)} + b f x \log{\left(c e + c f x \right)}}\, dx + \int \frac{3 h i^{2} x^{2}}{a e + a f x + b e \log{\left(c e + c f x \right)} + b f x \log{\left(c e + c f x \right)}}\, dx + \int \frac{3 h^{2} i x}{a e + a f x + b e \log{\left(c e + c f x \right)} + b f x \log{\left(c e + c f x \right)}}\, dx}{d}"," ",0,"(Integral(h**3/(a*e + a*f*x + b*e*log(c*e + c*f*x) + b*f*x*log(c*e + c*f*x)), x) + Integral(i**3*x**3/(a*e + a*f*x + b*e*log(c*e + c*f*x) + b*f*x*log(c*e + c*f*x)), x) + Integral(3*h*i**2*x**2/(a*e + a*f*x + b*e*log(c*e + c*f*x) + b*f*x*log(c*e + c*f*x)), x) + Integral(3*h**2*i*x/(a*e + a*f*x + b*e*log(c*e + c*f*x) + b*f*x*log(c*e + c*f*x)), x))/d","F",0
193,0,0,0,0.000000," ","integrate((i*x+h)**2/(d*f*x+d*e)/(a+b*ln(c*(f*x+e))),x)","\frac{\int \frac{h^{2}}{a e + a f x + b e \log{\left(c e + c f x \right)} + b f x \log{\left(c e + c f x \right)}}\, dx + \int \frac{i^{2} x^{2}}{a e + a f x + b e \log{\left(c e + c f x \right)} + b f x \log{\left(c e + c f x \right)}}\, dx + \int \frac{2 h i x}{a e + a f x + b e \log{\left(c e + c f x \right)} + b f x \log{\left(c e + c f x \right)}}\, dx}{d}"," ",0,"(Integral(h**2/(a*e + a*f*x + b*e*log(c*e + c*f*x) + b*f*x*log(c*e + c*f*x)), x) + Integral(i**2*x**2/(a*e + a*f*x + b*e*log(c*e + c*f*x) + b*f*x*log(c*e + c*f*x)), x) + Integral(2*h*i*x/(a*e + a*f*x + b*e*log(c*e + c*f*x) + b*f*x*log(c*e + c*f*x)), x))/d","F",0
194,0,0,0,0.000000," ","integrate((i*x+h)/(d*f*x+d*e)/(a+b*ln(c*(f*x+e))),x)","\frac{\int \frac{h}{a e + a f x + b e \log{\left(c e + c f x \right)} + b f x \log{\left(c e + c f x \right)}}\, dx + \int \frac{i x}{a e + a f x + b e \log{\left(c e + c f x \right)} + b f x \log{\left(c e + c f x \right)}}\, dx}{d}"," ",0,"(Integral(h/(a*e + a*f*x + b*e*log(c*e + c*f*x) + b*f*x*log(c*e + c*f*x)), x) + Integral(i*x/(a*e + a*f*x + b*e*log(c*e + c*f*x) + b*f*x*log(c*e + c*f*x)), x))/d","F",0
195,1,17,0,0.224057," ","integrate(1/(d*f*x+d*e)/(a+b*ln(c*(f*x+e))),x)","\frac{\log{\left(\frac{a}{b} + \log{\left(c \left(e + f x\right) \right)} \right)}}{b d f}"," ",0,"log(a/b + log(c*(e + f*x)))/(b*d*f)","A",0
196,0,0,0,0.000000," ","integrate(1/(d*f*x+d*e)/(i*x+h)/(a+b*ln(c*(f*x+e))),x)","\frac{\int \frac{1}{a e h + a e i x + a f h x + a f i x^{2} + b e h \log{\left(c e + c f x \right)} + b e i x \log{\left(c e + c f x \right)} + b f h x \log{\left(c e + c f x \right)} + b f i x^{2} \log{\left(c e + c f x \right)}}\, dx}{d}"," ",0,"Integral(1/(a*e*h + a*e*i*x + a*f*h*x + a*f*i*x**2 + b*e*h*log(c*e + c*f*x) + b*e*i*x*log(c*e + c*f*x) + b*f*h*x*log(c*e + c*f*x) + b*f*i*x**2*log(c*e + c*f*x)), x)/d","F",0
197,0,0,0,0.000000," ","integrate(1/(d*f*x+d*e)/(i*x+h)**2/(a+b*ln(c*(f*x+e))),x)","\frac{\int \frac{1}{a e h^{2} + 2 a e h i x + a e i^{2} x^{2} + a f h^{2} x + 2 a f h i x^{2} + a f i^{2} x^{3} + b e h^{2} \log{\left(c e + c f x \right)} + 2 b e h i x \log{\left(c e + c f x \right)} + b e i^{2} x^{2} \log{\left(c e + c f x \right)} + b f h^{2} x \log{\left(c e + c f x \right)} + 2 b f h i x^{2} \log{\left(c e + c f x \right)} + b f i^{2} x^{3} \log{\left(c e + c f x \right)}}\, dx}{d}"," ",0,"Integral(1/(a*e*h**2 + 2*a*e*h*i*x + a*e*i**2*x**2 + a*f*h**2*x + 2*a*f*h*i*x**2 + a*f*i**2*x**3 + b*e*h**2*log(c*e + c*f*x) + 2*b*e*h*i*x*log(c*e + c*f*x) + b*e*i**2*x**2*log(c*e + c*f*x) + b*f*h**2*x*log(c*e + c*f*x) + 2*b*f*h*i*x**2*log(c*e + c*f*x) + b*f*i**2*x**3*log(c*e + c*f*x)), x)/d","F",0
198,-1,0,0,0.000000," ","integrate((g*x+f)**(5/2)*(a+b*ln(c*(e*x+d)**n))/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
199,-1,0,0,0.000000," ","integrate((g*x+f)**(3/2)*(a+b*ln(c*(e*x+d)**n))/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
200,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)*(a+b*ln(c*(e*x+d)**n))/(e*x+d),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right) \sqrt{f + g x}}{d + e x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))*sqrt(f + g*x)/(d + e*x), x)","F",0
201,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(e*x+d)/(g*x+f)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(e*x+d)/(g*x+f)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
203,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(e*x+d)/(g*x+f)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
204,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*ln(b*x+a)/(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
205,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*ln(b*x+a)/(b*x+a),x)","\int \frac{\sqrt{d + e x} \log{\left(a + b x \right)}}{a + b x}\, dx"," ",0,"Integral(sqrt(d + e*x)*log(a + b*x)/(a + b*x), x)","F",0
206,-1,0,0,0.000000," ","integrate(ln(b*x+a)/(b*x+a)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
207,-1,0,0,0.000000," ","integrate(ln(b*x+a)/(b*x+a)/(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,-1,0,0,0.000000," ","integrate(ln(b*x+a)/(b*x+a)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
209,-1,0,0,0.000000," ","integrate((i*x+h)**q*(a+b*ln(c*(f*x+e)))**p/(d*f*x+d*e),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
210,-1,0,0,0.000000," ","integrate((i*x+h)**3*(a+b*ln(c*(f*x+e)))**p/(d*f*x+d*e),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
211,-1,0,0,0.000000," ","integrate((i*x+h)**2*(a+b*ln(c*(f*x+e)))**p/(d*f*x+d*e),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,0,0,0,0.000000," ","integrate((i*x+h)*(a+b*ln(c*(f*x+e)))**p/(d*f*x+d*e),x)","\frac{\int \frac{h \left(a + b \log{\left(c e + c f x \right)}\right)^{p}}{e + f x}\, dx + \int \frac{i x \left(a + b \log{\left(c e + c f x \right)}\right)^{p}}{e + f x}\, dx}{d}"," ",0,"(Integral(h*(a + b*log(c*e + c*f*x))**p/(e + f*x), x) + Integral(i*x*(a + b*log(c*e + c*f*x))**p/(e + f*x), x))/d","F",0
213,0,0,0,0.000000," ","integrate((a+b*ln(c*(f*x+e)))**p/(d*f*x+d*e),x)","\frac{\int \frac{\left(a + b \log{\left(c e + c f x \right)}\right)^{p}}{e + f x}\, dx}{d}"," ",0,"Integral((a + b*log(c*e + c*f*x))**p/(e + f*x), x)/d","F",0
214,0,0,0,0.000000," ","integrate((a+b*ln(c*(f*x+e)))**p/(d*f*x+d*e)/(i*x+h),x)","\frac{\int \frac{\left(a + b \log{\left(c e + c f x \right)}\right)^{p}}{e h + e i x + f h x + f i x^{2}}\, dx}{d}"," ",0,"Integral((a + b*log(c*e + c*f*x))**p/(e*h + e*i*x + f*h*x + f*i*x**2), x)/d","F",0
215,-1,0,0,0.000000," ","integrate((a+b*ln(c*(f*x+e)))**p/(d*f*x+d*e)/(i*x+h)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,-1,0,0,0.000000," ","integrate((a+b*ln(c*(f*x+e)))**p/(d*f*x+d*e)/(i*x+h)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,0,0,0,0.000000," ","integrate((i*x+h)**3*(a+b*ln(c*(e*x+d)**n))/(g*x+f),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right) \left(h + i x\right)^{3}}{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))*(h + i*x)**3/(f + g*x), x)","F",0
218,0,0,0,0.000000," ","integrate((i*x+h)**2*(a+b*ln(c*(e*x+d)**n))/(g*x+f),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right) \left(h + i x\right)^{2}}{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))*(h + i*x)**2/(f + g*x), x)","F",0
219,0,0,0,0.000000," ","integrate((i*x+h)*(a+b*ln(c*(e*x+d)**n))/(g*x+f),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right) \left(h + i x\right)}{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))*(h + i*x)/(f + g*x), x)","F",0
220,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x+f),x)","\int \frac{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))/(f + g*x), x)","F",0
221,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x+f)/(i*x+h),x)","\int \frac{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}{\left(f + g x\right) \left(h + i x\right)}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))/((f + g*x)*(h + i*x)), x)","F",0
222,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x+f)/(i*x+h)**2,x)","\int \frac{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}{\left(f + g x\right) \left(h + i x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))/((f + g*x)*(h + i*x)**2), x)","F",0
223,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x+f)/(i*x+h)**3,x)","\int \frac{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}{\left(f + g x\right) \left(h + i x\right)^{3}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))/((f + g*x)*(h + i*x)**3), x)","F",0
224,0,0,0,0.000000," ","integrate((i*x+h)**2*(a+b*ln(c*(e*x+d)**n))**2/(g*x+f),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2} \left(h + i x\right)^{2}}{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**2*(h + i*x)**2/(f + g*x), x)","F",0
225,0,0,0,0.000000," ","integrate((i*x+h)*(a+b*ln(c*(e*x+d)**n))**2/(g*x+f),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2} \left(h + i x\right)}{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**2*(h + i*x)/(f + g*x), x)","F",0
226,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/(g*x+f),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**2/(f + g*x), x)","F",0
227,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/(g*x+f)/(i*x+h),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}{\left(f + g x\right) \left(h + i x\right)}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**2/((f + g*x)*(h + i*x)), x)","F",0
228,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/(g*x+f)/(i*x+h)**2,x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}{\left(f + g x\right) \left(h + i x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**2/((f + g*x)*(h + i*x)**2), x)","F",0
229,0,0,0,0.000000," ","integrate((i*x+h)**2*(a+b*ln(c*(e*x+d)**n))**3/(g*x+f),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{3} \left(h + i x\right)^{2}}{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**3*(h + i*x)**2/(f + g*x), x)","F",0
230,0,0,0,0.000000," ","integrate((i*x+h)*(a+b*ln(c*(e*x+d)**n))**3/(g*x+f),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{3} \left(h + i x\right)}{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**3*(h + i*x)/(f + g*x), x)","F",0
231,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**3/(g*x+f),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{3}}{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**3/(f + g*x), x)","F",0
232,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**3/(g*x+f)/(i*x+h),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{3}}{\left(f + g x\right) \left(h + i x\right)}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**3/((f + g*x)*(h + i*x)), x)","F",0
233,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**3/(g*x+f)/(i*x+h)**2,x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{3}}{\left(f + g x\right) \left(h + i x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**3/((f + g*x)*(h + i*x)**2), x)","F",0
234,0,0,0,0.000000," ","integrate((i*x+h)/(g*x+f)/(a+b*ln(c*(e*x+d)**n)),x)","\int \frac{h + i x}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right) \left(f + g x\right)}\, dx"," ",0,"Integral((h + i*x)/((a + b*log(c*(d + e*x)**n))*(f + g*x)), x)","F",0
235,0,0,0,0.000000," ","integrate(1/(g*x+f)/(a+b*ln(c*(e*x+d)**n)),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right) \left(f + g x\right)}\, dx"," ",0,"Integral(1/((a + b*log(c*(d + e*x)**n))*(f + g*x)), x)","F",0
236,0,0,0,0.000000," ","integrate(1/(g*x+f)/(i*x+h)/(a+b*ln(c*(e*x+d)**n)),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right) \left(f + g x\right) \left(h + i x\right)}\, dx"," ",0,"Integral(1/((a + b*log(c*(d + e*x)**n))*(f + g*x)*(h + i*x)), x)","F",0
237,0,0,0,0.000000," ","integrate(1/(g*x+f)/(i*x+h)**2/(a+b*ln(c*(e*x+d)**n)),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right) \left(f + g x\right) \left(h + i x\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*log(c*(d + e*x)**n))*(f + g*x)*(h + i*x)**2), x)","F",0
238,0,0,0,0.000000," ","integrate((i*x+h)/(g*x+f)/(a+b*ln(c*(e*x+d)**n))**2,x)","\int \frac{h + i x}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2} \left(f + g x\right)}\, dx"," ",0,"Integral((h + i*x)/((a + b*log(c*(d + e*x)**n))**2*(f + g*x)), x)","F",0
239,0,0,0,0.000000," ","integrate(1/(g*x+f)/(a+b*ln(c*(e*x+d)**n))**2,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2} \left(f + g x\right)}\, dx"," ",0,"Integral(1/((a + b*log(c*(d + e*x)**n))**2*(f + g*x)), x)","F",0
240,0,0,0,0.000000," ","integrate(1/(g*x+f)/(i*x+h)/(a+b*ln(c*(e*x+d)**n))**2,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2} \left(f + g x\right) \left(h + i x\right)}\, dx"," ",0,"Integral(1/((a + b*log(c*(d + e*x)**n))**2*(f + g*x)*(h + i*x)), x)","F",0
241,0,0,0,0.000000," ","integrate(1/(g*x+f)/(i*x+h)**2/(a+b*ln(c*(e*x+d)**n))**2,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2} \left(f + g x\right) \left(h + i x\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*log(c*(d + e*x)**n))**2*(f + g*x)*(h + i*x)**2), x)","F",0
242,0,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(e*x+d)**n))/(g*x+f),x)","\int \frac{x^{3} \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)}{f + g x}\, dx"," ",0,"Integral(x**3*(a + b*log(c*(d + e*x)**n))/(f + g*x), x)","F",0
243,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(e*x+d)**n))/(g*x+f),x)","\int \frac{x^{2} \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)}{f + g x}\, dx"," ",0,"Integral(x**2*(a + b*log(c*(d + e*x)**n))/(f + g*x), x)","F",0
244,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*(e*x+d)**n))/(g*x+f),x)","\int \frac{x \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)}{f + g x}\, dx"," ",0,"Integral(x*(a + b*log(c*(d + e*x)**n))/(f + g*x), x)","F",0
245,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x+f),x)","\int \frac{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}{f + g x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))/(f + g*x), x)","F",0
246,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/x/(g*x+f),x)","\int \frac{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}{x \left(f + g x\right)}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))/(x*(f + g*x)), x)","F",0
247,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/x**2/(g*x+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
248,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/x**3/(g*x+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
249,0,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(e*x+d)**n))/(g*x+f)**2,x)","\int \frac{x^{3} \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)}{\left(f + g x\right)^{2}}\, dx"," ",0,"Integral(x**3*(a + b*log(c*(d + e*x)**n))/(f + g*x)**2, x)","F",0
250,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(e*x+d)**n))/(g*x+f)**2,x)","\int \frac{x^{2} \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)}{\left(f + g x\right)^{2}}\, dx"," ",0,"Integral(x**2*(a + b*log(c*(d + e*x)**n))/(f + g*x)**2, x)","F",0
251,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(e*x+d)**n))/(g*x+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
252,-2,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x+f)**2,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
253,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/x/(g*x+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
254,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/x**2/(g*x+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
255,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/x**3/(g*x+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
256,-1,0,0,0.000000," ","integrate(x**5*(a+b*ln(c*(e*x+d)**n))/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
257,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(e*x+d)**n))/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*(e*x+d)**n))/(g*x**2+f),x)","\int \frac{x \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)}{f + g x^{2}}\, dx"," ",0,"Integral(x*(a + b*log(c*(d + e*x)**n))/(f + g*x**2), x)","F",0
259,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/x/(g*x**2+f),x)","\int \frac{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}{x \left(f + g x^{2}\right)}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))/(x*(f + g*x**2)), x)","F",0
260,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/x**3/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
261,-1,0,0,0.000000," ","integrate(x**4*(a+b*ln(c*(e*x+d)**n))/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
262,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(e*x+d)**n))/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
263,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x**2+f),x)","\int \frac{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}{f + g x^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))/(f + g*x**2), x)","F",0
264,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/x**2/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
265,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/x**4/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
266,-1,0,0,0.000000," ","integrate(x**5*(a+b*ln(c*(e*x+d)**n))/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
267,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(e*x+d)**n))/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
268,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(e*x+d)**n))/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
269,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/x/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
270,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/x**3/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
271,-1,0,0,0.000000," ","integrate(x**4*(a+b*ln(c*(e*x+d)**n))/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
272,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(e*x+d)**n))/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
274,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/x**2/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x**2+2)**(1/2),x)","\int \frac{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}{\sqrt{g x^{2} + 2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))/sqrt(g*x**2 + 2), x)","F",0
276,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(g*x**2+f)**(1/2),x)","\int \frac{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}{\sqrt{f + g x^{2}}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))/sqrt(f + g*x**2), x)","F",0
277,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(-g*x+2)**(1/2)/(g*x+2)**(1/2),x)","\int \frac{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}{\sqrt{- g x + 2} \sqrt{g x + 2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))/(sqrt(-g*x + 2)*sqrt(g*x + 2)), x)","F",0
278,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(-g*x+f)**(1/2)/(g*x+f)**(1/2),x)","\int \frac{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}{\sqrt{f - g x} \sqrt{f + g x}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))/(sqrt(f - g*x)*sqrt(f + g*x)), x)","F",0
279,0,0,0,0.000000," ","integrate(ln(2*e/(f*x+e))/(-f**2*x**2+e**2),x)","- \int \frac{\log{\left(2 \right)}}{- e^{2} + f^{2} x^{2}}\, dx - \int \frac{\log{\left(\frac{e}{e + f x} \right)}}{- e^{2} + f^{2} x^{2}}\, dx"," ",0,"-Integral(log(2)/(-e**2 + f**2*x**2), x) - Integral(log(e/(e + f*x))/(-e**2 + f**2*x**2), x)","F",0
280,0,0,0,0.000000," ","integrate(ln(e/(f*x+e))/(-f**2*x**2+e**2),x)","- \int \frac{\log{\left(\frac{e}{e + f x} \right)}}{- e^{2} + f^{2} x^{2}}\, dx"," ",0,"-Integral(log(e/(e + f*x))/(-e**2 + f**2*x**2), x)","F",0
281,0,0,0,0.000000," ","integrate((a+b*ln(2*e/(f*x+e)))/(-f**2*x**2+e**2),x)","- \int \frac{a}{- e^{2} + f^{2} x^{2}}\, dx - \int \frac{b \log{\left(2 \right)}}{- e^{2} + f^{2} x^{2}}\, dx - \int \frac{b \log{\left(\frac{e}{e + f x} \right)}}{- e^{2} + f^{2} x^{2}}\, dx"," ",0,"-Integral(a/(-e**2 + f**2*x**2), x) - Integral(b*log(2)/(-e**2 + f**2*x**2), x) - Integral(b*log(e/(e + f*x))/(-e**2 + f**2*x**2), x)","F",0
282,0,0,0,0.000000," ","integrate((a+b*ln(e/(f*x+e)))/(-f**2*x**2+e**2),x)","- \int \frac{a}{- e^{2} + f^{2} x^{2}}\, dx - \int \frac{b \log{\left(\frac{e}{e + f x} \right)}}{- e^{2} + f^{2} x^{2}}\, dx"," ",0,"-Integral(a/(-e**2 + f**2*x**2), x) - Integral(b*log(e/(e + f*x))/(-e**2 + f**2*x**2), x)","F",0
283,-1,0,0,0.000000," ","integrate(x**5*ln(d*x+c)/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
284,-1,0,0,0.000000," ","integrate(x**2*ln(d*x+c)/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
285,-1,0,0,0.000000," ","integrate(ln(d*x+c)/x/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
286,-1,0,0,0.000000," ","integrate(ln(d*x+c)/x**4/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
287,-1,0,0,0.000000," ","integrate(x**4*ln(d*x+c)/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
288,-1,0,0,0.000000," ","integrate(x**3*ln(d*x+c)/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
289,-1,0,0,0.000000," ","integrate(x*ln(d*x+c)/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
290,-1,0,0,0.000000," ","integrate(ln(d*x+c)/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
291,-1,0,0,0.000000," ","integrate(ln(d*x+c)/x**2/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,-1,0,0,0.000000," ","integrate(ln(d*x+c)/x**3/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,-1,0,0,0.000000," ","integrate(x**7*ln(d*x+c)/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
294,-1,0,0,0.000000," ","integrate(x**3*ln(d*x+c)/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
295,-1,0,0,0.000000," ","integrate(ln(d*x+c)/x/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
296,-1,0,0,0.000000," ","integrate(x**5*ln(d*x+c)/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
297,-1,0,0,0.000000," ","integrate(x*ln(d*x+c)/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,-1,0,0,0.000000," ","integrate(ln(d*x+c)/x**3/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,-1,0,0,0.000000," ","integrate(x**4*ln(d*x+c)/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
300,-1,0,0,0.000000," ","integrate(x**2*ln(d*x+c)/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,-1,0,0,0.000000," ","integrate(ln(d*x+c)/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
302,-1,0,0,0.000000," ","integrate(ln(d*x+c)/x**2/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
303,1,148,0,3.007090," ","integrate((f+g/x)*x*(a+b*ln(c*(e*x+d)**n)),x)","\begin{cases} \frac{a f x^{2}}{2} + a g x - \frac{b d^{2} f n \log{\left(d + e x \right)}}{2 e^{2}} + \frac{b d f n x}{2 e} + \frac{b d g n \log{\left(d + e x \right)}}{e} + \frac{b f n x^{2} \log{\left(d + e x \right)}}{2} - \frac{b f n x^{2}}{4} + \frac{b f x^{2} \log{\left(c \right)}}{2} + b g n x \log{\left(d + e x \right)} - b g n x + b g x \log{\left(c \right)} & \text{for}\: e \neq 0 \\\left(a + b \log{\left(c d^{n} \right)}\right) \left(\frac{f x^{2}}{2} + g x\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*f*x**2/2 + a*g*x - b*d**2*f*n*log(d + e*x)/(2*e**2) + b*d*f*n*x/(2*e) + b*d*g*n*log(d + e*x)/e + b*f*n*x**2*log(d + e*x)/2 - b*f*n*x**2/4 + b*f*x**2*log(c)/2 + b*g*n*x*log(d + e*x) - b*g*n*x + b*g*x*log(c), Ne(e, 0)), ((a + b*log(c*d**n))*(f*x**2/2 + g*x), True))","A",0
304,1,277,0,16.430846," ","integrate((f+g/x)**2*x**2*(a+b*ln(c*(e*x+d)**n)),x)","\begin{cases} \frac{a f^{2} x^{3}}{3} + a f g x^{2} + a g^{2} x + \frac{b d^{3} f^{2} n \log{\left(d + e x \right)}}{3 e^{3}} - \frac{b d^{2} f^{2} n x}{3 e^{2}} - \frac{b d^{2} f g n \log{\left(d + e x \right)}}{e^{2}} + \frac{b d f^{2} n x^{2}}{6 e} + \frac{b d f g n x}{e} + \frac{b d g^{2} n \log{\left(d + e x \right)}}{e} + \frac{b f^{2} n x^{3} \log{\left(d + e x \right)}}{3} - \frac{b f^{2} n x^{3}}{9} + \frac{b f^{2} x^{3} \log{\left(c \right)}}{3} + b f g n x^{2} \log{\left(d + e x \right)} - \frac{b f g n x^{2}}{2} + b f g x^{2} \log{\left(c \right)} + b g^{2} n x \log{\left(d + e x \right)} - b g^{2} n x + b g^{2} x \log{\left(c \right)} & \text{for}\: e \neq 0 \\\left(a + b \log{\left(c d^{n} \right)}\right) \left(\frac{f^{2} x^{3}}{3} + f g x^{2} + g^{2} x\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*f**2*x**3/3 + a*f*g*x**2 + a*g**2*x + b*d**3*f**2*n*log(d + e*x)/(3*e**3) - b*d**2*f**2*n*x/(3*e**2) - b*d**2*f*g*n*log(d + e*x)/e**2 + b*d*f**2*n*x**2/(6*e) + b*d*f*g*n*x/e + b*d*g**2*n*log(d + e*x)/e + b*f**2*n*x**3*log(d + e*x)/3 - b*f**2*n*x**3/9 + b*f**2*x**3*log(c)/3 + b*f*g*n*x**2*log(d + e*x) - b*f*g*n*x**2/2 + b*f*g*x**2*log(c) + b*g**2*n*x*log(d + e*x) - b*g**2*n*x + b*g**2*x*log(c), Ne(e, 0)), ((a + b*log(c*d**n))*(f**2*x**3/3 + f*g*x**2 + g**2*x), True))","A",0
305,1,450,0,63.040379," ","integrate((f+g/x)**3*x**3*(a+b*ln(c*(e*x+d)**n)),x)","\begin{cases} \frac{a f^{3} x^{4}}{4} + a f^{2} g x^{3} + \frac{3 a f g^{2} x^{2}}{2} + a g^{3} x - \frac{b d^{4} f^{3} n \log{\left(d + e x \right)}}{4 e^{4}} + \frac{b d^{3} f^{3} n x}{4 e^{3}} + \frac{b d^{3} f^{2} g n \log{\left(d + e x \right)}}{e^{3}} - \frac{b d^{2} f^{3} n x^{2}}{8 e^{2}} - \frac{b d^{2} f^{2} g n x}{e^{2}} - \frac{3 b d^{2} f g^{2} n \log{\left(d + e x \right)}}{2 e^{2}} + \frac{b d f^{3} n x^{3}}{12 e} + \frac{b d f^{2} g n x^{2}}{2 e} + \frac{3 b d f g^{2} n x}{2 e} + \frac{b d g^{3} n \log{\left(d + e x \right)}}{e} + \frac{b f^{3} n x^{4} \log{\left(d + e x \right)}}{4} - \frac{b f^{3} n x^{4}}{16} + \frac{b f^{3} x^{4} \log{\left(c \right)}}{4} + b f^{2} g n x^{3} \log{\left(d + e x \right)} - \frac{b f^{2} g n x^{3}}{3} + b f^{2} g x^{3} \log{\left(c \right)} + \frac{3 b f g^{2} n x^{2} \log{\left(d + e x \right)}}{2} - \frac{3 b f g^{2} n x^{2}}{4} + \frac{3 b f g^{2} x^{2} \log{\left(c \right)}}{2} + b g^{3} n x \log{\left(d + e x \right)} - b g^{3} n x + b g^{3} x \log{\left(c \right)} & \text{for}\: e \neq 0 \\\left(a + b \log{\left(c d^{n} \right)}\right) \left(\frac{f^{3} x^{4}}{4} + f^{2} g x^{3} + \frac{3 f g^{2} x^{2}}{2} + g^{3} x\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*f**3*x**4/4 + a*f**2*g*x**3 + 3*a*f*g**2*x**2/2 + a*g**3*x - b*d**4*f**3*n*log(d + e*x)/(4*e**4) + b*d**3*f**3*n*x/(4*e**3) + b*d**3*f**2*g*n*log(d + e*x)/e**3 - b*d**2*f**3*n*x**2/(8*e**2) - b*d**2*f**2*g*n*x/e**2 - 3*b*d**2*f*g**2*n*log(d + e*x)/(2*e**2) + b*d*f**3*n*x**3/(12*e) + b*d*f**2*g*n*x**2/(2*e) + 3*b*d*f*g**2*n*x/(2*e) + b*d*g**3*n*log(d + e*x)/e + b*f**3*n*x**4*log(d + e*x)/4 - b*f**3*n*x**4/16 + b*f**3*x**4*log(c)/4 + b*f**2*g*n*x**3*log(d + e*x) - b*f**2*g*n*x**3/3 + b*f**2*g*x**3*log(c) + 3*b*f*g**2*n*x**2*log(d + e*x)/2 - 3*b*f*g**2*n*x**2/4 + 3*b*f*g**2*x**2*log(c)/2 + b*g**3*n*x*log(d + e*x) - b*g**3*n*x + b*g**3*x*log(c), Ne(e, 0)), ((a + b*log(c*d**n))*(f**3*x**4/4 + f**2*g*x**3 + 3*f*g**2*x**2/2 + g**3*x), True))","A",0
306,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(f+g/x)/x,x)","\int \frac{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}{f x + g}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))/(f*x + g), x)","F",0
307,-2,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(f+g/x)**2/x**2,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
308,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))/(f+g/x)**3/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
309,0,0,0,0.000000," ","integrate(ln(b*x+a)/(c+d/x**2),x)","\int \frac{x^{2} \log{\left(a + b x \right)}}{c x^{2} + d}\, dx"," ",0,"Integral(x**2*log(a + b*x)/(c*x**2 + d), x)","F",0
310,-1,0,0,0.000000," ","integrate(x**5*(a+b*ln(c*(e*x+d)**n))**2/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
311,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(e*x+d)**n))**2/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
312,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*(e*x+d)**n))**2/(g*x**2+f),x)","\int \frac{x \left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}{f + g x^{2}}\, dx"," ",0,"Integral(x*(a + b*log(c*(d + e*x)**n))**2/(f + g*x**2), x)","F",0
313,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/x/(g*x**2+f),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}{x \left(f + g x^{2}\right)}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**2/(x*(f + g*x**2)), x)","F",0
314,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/x**3/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
315,-1,0,0,0.000000," ","integrate(x**4*(a+b*ln(c*(e*x+d)**n))**2/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
316,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(e*x+d)**n))**2/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
317,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/(g*x**2+f),x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}{f + g x^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))**2/(f + g*x**2), x)","F",0
318,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/x**2/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/x**4/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
320,-1,0,0,0.000000," ","integrate(x**5*(a+b*ln(c*(e*x+d)**n))**2/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
321,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(e*x+d)**n))**2/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
322,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(e*x+d)**n))**2/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/x/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/x**3/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
325,-1,0,0,0.000000," ","integrate(x**4*(a+b*ln(c*(e*x+d)**n))**2/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(e*x+d)**n))**2/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
328,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2/x**2/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
329,0,0,0,0.000000," ","integrate(ln(c*(b*x+a)**n)**3/(e*x**2+d),x)","\int \frac{\log{\left(c \left(a + b x\right)^{n} \right)}^{3}}{d + e x^{2}}\, dx"," ",0,"Integral(log(c*(a + b*x)**n)**3/(d + e*x**2), x)","F",0
330,0,0,0,0.000000," ","integrate(ln(c*(b*x+a)**n)**2/(e*x**2+d),x)","\int \frac{\log{\left(c \left(a + b x\right)^{n} \right)}^{2}}{d + e x^{2}}\, dx"," ",0,"Integral(log(c*(a + b*x)**n)**2/(d + e*x**2), x)","F",0
331,0,0,0,0.000000," ","integrate(ln(c*(b*x+a)**n)/(e*x**2+d),x)","\int \frac{\log{\left(c \left(a + b x\right)^{n} \right)}}{d + e x^{2}}\, dx"," ",0,"Integral(log(c*(a + b*x)**n)/(d + e*x**2), x)","F",0
332,0,0,0,0.000000," ","integrate(1/(e*x**2+d)/ln(c*(b*x+a)**n),x)","\int \frac{1}{\left(d + e x^{2}\right) \log{\left(c \left(a + b x\right)^{n} \right)}}\, dx"," ",0,"Integral(1/((d + e*x**2)*log(c*(a + b*x)**n)), x)","F",0
333,-1,0,0,0.000000," ","integrate(ln(c-a*(1-c)/b/(x**m))/x/(a+b*x**m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
334,-1,0,0,0.000000," ","integrate(ln((-a+a*c+b*c*x**m)/b/(x**m))/x/(a+b*x**m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
335,-2,0,0,0.000000," ","integrate(ln(c*(a+(a*c*d-d)/c/e/(x**m)))/x/(d+e*x**m),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
336,-2,0,0,0.000000," ","integrate(ln((-d+a*c*d+a*c*e*x**m)/e/(x**m))/x/(d+e*x**m),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
337,0,0,0,0.000000," ","integrate(ln(2*a/(b*x+a))/(-b**2*x**2+a**2),x)","- \int \frac{\log{\left(2 \right)}}{- a^{2} + b^{2} x^{2}}\, dx - \int \frac{\log{\left(\frac{a}{a + b x} \right)}}{- a^{2} + b^{2} x^{2}}\, dx"," ",0,"-Integral(log(2)/(-a**2 + b**2*x**2), x) - Integral(log(a/(a + b*x))/(-a**2 + b**2*x**2), x)","F",0
338,0,0,0,0.000000," ","integrate(ln(2*a/(b*x+a))/(-b*x+a)/(b*x+a),x)","- \int \frac{\log{\left(2 \right)}}{- a^{2} + b^{2} x^{2}}\, dx - \int \frac{\log{\left(\frac{a}{a + b x} \right)}}{- a^{2} + b^{2} x^{2}}\, dx"," ",0,"-Integral(log(2)/(-a**2 + b**2*x**2), x) - Integral(log(a/(a + b*x))/(-a**2 + b**2*x**2), x)","F",0
339,-1,0,0,0.000000," ","integrate(ln((a*(1-c)+b*(c+1)*x)/(b*x+a))/(-b**2*x**2+a**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
340,-1,0,0,0.000000," ","integrate(ln((a*(1-c)+b*(c+1)*x)/(b*x+a))/(-b*x+a)/(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
341,-1,0,0,0.000000," ","integrate(ln(1-c*(-b*x+a)/(b*x+a))/(-b**2*x**2+a**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
342,-1,0,0,0.000000," ","integrate(ln(1-c*(-b*x+a)/(b*x+a))/(-b*x+a)/(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
343,0,0,0,0.000000," ","integrate(ln(c*(b*x+a)**n)**3/(e*x**2+d*x),x)","\int \frac{\log{\left(c \left(a + b x\right)^{n} \right)}^{3}}{x \left(d + e x\right)}\, dx"," ",0,"Integral(log(c*(a + b*x)**n)**3/(x*(d + e*x)), x)","F",0
344,0,0,0,0.000000," ","integrate(ln(c*(b*x+a)**n)**2/(e*x**2+d*x),x)","\int \frac{\log{\left(c \left(a + b x\right)^{n} \right)}^{2}}{x \left(d + e x\right)}\, dx"," ",0,"Integral(log(c*(a + b*x)**n)**2/(x*(d + e*x)), x)","F",0
345,0,0,0,0.000000," ","integrate(ln(c*(b*x+a)**n)/(e*x**2+d*x),x)","\int \frac{\log{\left(c \left(a + b x\right)^{n} \right)}}{x \left(d + e x\right)}\, dx"," ",0,"Integral(log(c*(a + b*x)**n)/(x*(d + e*x)), x)","F",0
346,0,0,0,0.000000," ","integrate(1/(e*x**2+d*x)/ln(c*(b*x+a)**n),x)","\int \frac{1}{x \left(d + e x\right) \log{\left(c \left(a + b x\right)^{n} \right)}}\, dx"," ",0,"Integral(1/(x*(d + e*x)*log(c*(a + b*x)**n)), x)","F",0
347,-1,0,0,0.000000," ","integrate(ln(c*(b*x+a)**n)**3/(f*x**2+e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
348,0,0,0,0.000000," ","integrate(ln(c*(b*x+a)**n)**2/(f*x**2+e*x+d),x)","\int \frac{\log{\left(c \left(a + b x\right)^{n} \right)}^{2}}{d + e x + f x^{2}}\, dx"," ",0,"Integral(log(c*(a + b*x)**n)**2/(d + e*x + f*x**2), x)","F",0
349,0,0,0,0.000000," ","integrate(ln(c*(b*x+a)**n)/(f*x**2+e*x+d),x)","\int \frac{\log{\left(c \left(a + b x\right)^{n} \right)}}{d + e x + f x^{2}}\, dx"," ",0,"Integral(log(c*(a + b*x)**n)/(d + e*x + f*x**2), x)","F",0
350,-1,0,0,0.000000," ","integrate(1/(f*x**2+e*x+d)/ln(c*(b*x+a)**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
351,-1,0,0,0.000000," ","integrate(x**3*ln(x)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
352,-1,0,0,0.000000," ","integrate(x**2*ln(x)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
353,-1,0,0,0.000000," ","integrate(x*ln(x)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
354,0,0,0,0.000000," ","integrate(ln(x)/(c*x**2+b*x+a),x)","\int \frac{\log{\left(x \right)}}{a + b x + c x^{2}}\, dx"," ",0,"Integral(log(x)/(a + b*x + c*x**2), x)","F",0
355,-1,0,0,0.000000," ","integrate(ln(x)/x/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
356,-1,0,0,0.000000," ","integrate(ln(x)/x**2/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
357,-1,0,0,0.000000," ","integrate(ln(x)/x**3/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
358,-1,0,0,0.000000," ","integrate(x**3*ln(f*x**m)*(a+b*ln(c*(e*x+d)**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
359,-1,0,0,0.000000," ","integrate(x**2*ln(f*x**m)*(a+b*ln(c*(e*x+d)**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
360,-1,0,0,0.000000," ","integrate(x*ln(f*x**m)*(a+b*ln(c*(e*x+d)**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
361,-1,0,0,0.000000," ","integrate(ln(f*x**m)*(a+b*ln(c*(e*x+d)**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
362,-1,0,0,0.000000," ","integrate(ln(f*x**m)*(a+b*ln(c*(e*x+d)**n))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
363,-1,0,0,0.000000," ","integrate(ln(f*x**m)*(a+b*ln(c*(e*x+d)**n))/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
364,-1,0,0,0.000000," ","integrate(ln(f*x**m)*(a+b*ln(c*(e*x+d)**n))/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
365,-1,0,0,0.000000," ","integrate(ln(f*x**m)*(a+b*ln(c*(e*x+d)**n))/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
366,-1,0,0,0.000000," ","integrate(ln(f*x**m)*(a+b*ln(c*(e*x+d)**n))/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
367,-1,0,0,0.000000," ","integrate(x**2*ln(f*x**m)*(a+b*ln(c*(e*x+d)**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,-1,0,0,0.000000," ","integrate(x*ln(f*x**m)*(a+b*ln(c*(e*x+d)**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
369,-1,0,0,0.000000," ","integrate(ln(f*x**m)*(a+b*ln(c*(e*x+d)**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
370,-1,0,0,0.000000," ","integrate(ln(f*x**m)*(a+b*ln(c*(e*x+d)**n))**2/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
371,-1,0,0,0.000000," ","integrate(ln(f*x**m)*(a+b*ln(c*(e*x+d)**n))**2/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,-1,0,0,0.000000," ","integrate(ln(f*x**m)*(a+b*ln(c*(e*x+d)**n))**2/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
373,-1,0,0,0.000000," ","integrate(ln(f*x**m)*(a+b*ln(c*(e*x+d)**n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,0,0,0,0.000000," ","integrate(ln(x)*ln(b*x+a)**2/x,x)","- b \int \frac{\log{\left(x \right)}^{2} \log{\left(a + b x \right)}}{a + b x}\, dx + \frac{\log{\left(x \right)}^{2} \log{\left(a + b x \right)}^{2}}{2}"," ",0,"-b*Integral(log(x)**2*log(a + b*x)/(a + b*x), x) + log(x)**2*log(a + b*x)**2/2","F",0
375,0,0,0,0.000000," ","integrate(ln(f*x**m)/(a+b*ln(c*(e*x+d)**n)),x)","\int \frac{\log{\left(f x^{m} \right)}}{a + b \log{\left(c \left(d + e x\right)^{n} \right)}}\, dx"," ",0,"Integral(log(f*x**m)/(a + b*log(c*(d + e*x)**n)), x)","F",0
376,0,0,0,0.000000," ","integrate(ln(f*x**m)/(a+b*ln(c*(e*x+d)**n))**2,x)","\int \frac{\log{\left(f x^{m} \right)}}{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral(log(f*x**m)/(a + b*log(c*(d + e*x)**n))**2, x)","F",0
377,-1,0,0,0.000000," ","integrate(ln(f*x**m)*(a+b*ln(c*(e*x+d)**n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,-1,0,0,0.000000," ","integrate(ln(b*x+a)*ln(d*x+c)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
379,1,508,0,6.626339," ","integrate(x**2*(a+b*ln(c*(e*x+d)**n))*(f+g*ln(c*(e*x+d)**n)),x)","\begin{cases} \frac{a d^{3} g n \log{\left(d + e x \right)}}{3 e^{3}} - \frac{a d^{2} g n x}{3 e^{2}} + \frac{a d g n x^{2}}{6 e} + \frac{a f x^{3}}{3} + \frac{a g n x^{3} \log{\left(d + e x \right)}}{3} - \frac{a g n x^{3}}{9} + \frac{a g x^{3} \log{\left(c \right)}}{3} + \frac{b d^{3} f n \log{\left(d + e x \right)}}{3 e^{3}} + \frac{b d^{3} g n^{2} \log{\left(d + e x \right)}^{2}}{3 e^{3}} - \frac{11 b d^{3} g n^{2} \log{\left(d + e x \right)}}{9 e^{3}} + \frac{2 b d^{3} g n \log{\left(c \right)} \log{\left(d + e x \right)}}{3 e^{3}} - \frac{b d^{2} f n x}{3 e^{2}} - \frac{2 b d^{2} g n^{2} x \log{\left(d + e x \right)}}{3 e^{2}} + \frac{11 b d^{2} g n^{2} x}{9 e^{2}} - \frac{2 b d^{2} g n x \log{\left(c \right)}}{3 e^{2}} + \frac{b d f n x^{2}}{6 e} + \frac{b d g n^{2} x^{2} \log{\left(d + e x \right)}}{3 e} - \frac{5 b d g n^{2} x^{2}}{18 e} + \frac{b d g n x^{2} \log{\left(c \right)}}{3 e} + \frac{b f n x^{3} \log{\left(d + e x \right)}}{3} - \frac{b f n x^{3}}{9} + \frac{b f x^{3} \log{\left(c \right)}}{3} + \frac{b g n^{2} x^{3} \log{\left(d + e x \right)}^{2}}{3} - \frac{2 b g n^{2} x^{3} \log{\left(d + e x \right)}}{9} + \frac{2 b g n^{2} x^{3}}{27} + \frac{2 b g n x^{3} \log{\left(c \right)} \log{\left(d + e x \right)}}{3} - \frac{2 b g n x^{3} \log{\left(c \right)}}{9} + \frac{b g x^{3} \log{\left(c \right)}^{2}}{3} & \text{for}\: e \neq 0 \\\frac{x^{3} \left(a + b \log{\left(c d^{n} \right)}\right) \left(f + g \log{\left(c d^{n} \right)}\right)}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**3*g*n*log(d + e*x)/(3*e**3) - a*d**2*g*n*x/(3*e**2) + a*d*g*n*x**2/(6*e) + a*f*x**3/3 + a*g*n*x**3*log(d + e*x)/3 - a*g*n*x**3/9 + a*g*x**3*log(c)/3 + b*d**3*f*n*log(d + e*x)/(3*e**3) + b*d**3*g*n**2*log(d + e*x)**2/(3*e**3) - 11*b*d**3*g*n**2*log(d + e*x)/(9*e**3) + 2*b*d**3*g*n*log(c)*log(d + e*x)/(3*e**3) - b*d**2*f*n*x/(3*e**2) - 2*b*d**2*g*n**2*x*log(d + e*x)/(3*e**2) + 11*b*d**2*g*n**2*x/(9*e**2) - 2*b*d**2*g*n*x*log(c)/(3*e**2) + b*d*f*n*x**2/(6*e) + b*d*g*n**2*x**2*log(d + e*x)/(3*e) - 5*b*d*g*n**2*x**2/(18*e) + b*d*g*n*x**2*log(c)/(3*e) + b*f*n*x**3*log(d + e*x)/3 - b*f*n*x**3/9 + b*f*x**3*log(c)/3 + b*g*n**2*x**3*log(d + e*x)**2/3 - 2*b*g*n**2*x**3*log(d + e*x)/9 + 2*b*g*n**2*x**3/27 + 2*b*g*n*x**3*log(c)*log(d + e*x)/3 - 2*b*g*n*x**3*log(c)/9 + b*g*x**3*log(c)**2/3, Ne(e, 0)), (x**3*(a + b*log(c*d**n))*(f + g*log(c*d**n))/3, True))","A",0
380,1,389,0,3.574118," ","integrate(x*(a+b*ln(c*(e*x+d)**n))*(f+g*ln(c*(e*x+d)**n)),x)","\begin{cases} - \frac{a d^{2} g n \log{\left(d + e x \right)}}{2 e^{2}} + \frac{a d g n x}{2 e} + \frac{a f x^{2}}{2} + \frac{a g n x^{2} \log{\left(d + e x \right)}}{2} - \frac{a g n x^{2}}{4} + \frac{a g x^{2} \log{\left(c \right)}}{2} - \frac{b d^{2} f n \log{\left(d + e x \right)}}{2 e^{2}} - \frac{b d^{2} g n^{2} \log{\left(d + e x \right)}^{2}}{2 e^{2}} + \frac{3 b d^{2} g n^{2} \log{\left(d + e x \right)}}{2 e^{2}} - \frac{b d^{2} g n \log{\left(c \right)} \log{\left(d + e x \right)}}{e^{2}} + \frac{b d f n x}{2 e} + \frac{b d g n^{2} x \log{\left(d + e x \right)}}{e} - \frac{3 b d g n^{2} x}{2 e} + \frac{b d g n x \log{\left(c \right)}}{e} + \frac{b f n x^{2} \log{\left(d + e x \right)}}{2} - \frac{b f n x^{2}}{4} + \frac{b f x^{2} \log{\left(c \right)}}{2} + \frac{b g n^{2} x^{2} \log{\left(d + e x \right)}^{2}}{2} - \frac{b g n^{2} x^{2} \log{\left(d + e x \right)}}{2} + \frac{b g n^{2} x^{2}}{4} + b g n x^{2} \log{\left(c \right)} \log{\left(d + e x \right)} - \frac{b g n x^{2} \log{\left(c \right)}}{2} + \frac{b g x^{2} \log{\left(c \right)}^{2}}{2} & \text{for}\: e \neq 0 \\\frac{x^{2} \left(a + b \log{\left(c d^{n} \right)}\right) \left(f + g \log{\left(c d^{n} \right)}\right)}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*d**2*g*n*log(d + e*x)/(2*e**2) + a*d*g*n*x/(2*e) + a*f*x**2/2 + a*g*n*x**2*log(d + e*x)/2 - a*g*n*x**2/4 + a*g*x**2*log(c)/2 - b*d**2*f*n*log(d + e*x)/(2*e**2) - b*d**2*g*n**2*log(d + e*x)**2/(2*e**2) + 3*b*d**2*g*n**2*log(d + e*x)/(2*e**2) - b*d**2*g*n*log(c)*log(d + e*x)/e**2 + b*d*f*n*x/(2*e) + b*d*g*n**2*x*log(d + e*x)/e - 3*b*d*g*n**2*x/(2*e) + b*d*g*n*x*log(c)/e + b*f*n*x**2*log(d + e*x)/2 - b*f*n*x**2/4 + b*f*x**2*log(c)/2 + b*g*n**2*x**2*log(d + e*x)**2/2 - b*g*n**2*x**2*log(d + e*x)/2 + b*g*n**2*x**2/4 + b*g*n*x**2*log(c)*log(d + e*x) - b*g*n*x**2*log(c)/2 + b*g*x**2*log(c)**2/2, Ne(e, 0)), (x**2*(a + b*log(c*d**n))*(f + g*log(c*d**n))/2, True))","A",0
381,1,257,0,1.656488," ","integrate((a+b*ln(c*(e*x+d)**n))*(f+g*ln(c*(e*x+d)**n)),x)","\begin{cases} \frac{a d g n \log{\left(d + e x \right)}}{e} + a f x + a g n x \log{\left(d + e x \right)} - a g n x + a g x \log{\left(c \right)} + \frac{b d f n \log{\left(d + e x \right)}}{e} + \frac{b d g n^{2} \log{\left(d + e x \right)}^{2}}{e} - \frac{2 b d g n^{2} \log{\left(d + e x \right)}}{e} + \frac{2 b d g n \log{\left(c \right)} \log{\left(d + e x \right)}}{e} + b f n x \log{\left(d + e x \right)} - b f n x + b f x \log{\left(c \right)} + b g n^{2} x \log{\left(d + e x \right)}^{2} - 2 b g n^{2} x \log{\left(d + e x \right)} + 2 b g n^{2} x + 2 b g n x \log{\left(c \right)} \log{\left(d + e x \right)} - 2 b g n x \log{\left(c \right)} + b g x \log{\left(c \right)}^{2} & \text{for}\: e \neq 0 \\x \left(a + b \log{\left(c d^{n} \right)}\right) \left(f + g \log{\left(c d^{n} \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*g*n*log(d + e*x)/e + a*f*x + a*g*n*x*log(d + e*x) - a*g*n*x + a*g*x*log(c) + b*d*f*n*log(d + e*x)/e + b*d*g*n**2*log(d + e*x)**2/e - 2*b*d*g*n**2*log(d + e*x)/e + 2*b*d*g*n*log(c)*log(d + e*x)/e + b*f*n*x*log(d + e*x) - b*f*n*x + b*f*x*log(c) + b*g*n**2*x*log(d + e*x)**2 - 2*b*g*n**2*x*log(d + e*x) + 2*b*g*n**2*x + 2*b*g*n*x*log(c)*log(d + e*x) - 2*b*g*n*x*log(c) + b*g*x*log(c)**2, Ne(e, 0)), (x*(a + b*log(c*d**n))*(f + g*log(c*d**n)), True))","A",0
382,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))*(f+g*ln(c*(e*x+d)**n))/x,x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right) \left(f + g \log{\left(c \left(d + e x\right)^{n} \right)}\right)}{x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))*(f + g*log(c*(d + e*x)**n))/x, x)","F",0
383,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))*(f+g*ln(c*(e*x+d)**n))/x**2,x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right) \left(f + g \log{\left(c \left(d + e x\right)^{n} \right)}\right)}{x^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))*(f + g*log(c*(d + e*x)**n))/x**2, x)","F",0
384,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))*(f+g*ln(c*(e*x+d)**n))/x**3,x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right) \left(f + g \log{\left(c \left(d + e x\right)^{n} \right)}\right)}{x^{3}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))*(f + g*log(c*(d + e*x)**n))/x**3, x)","F",0
385,0,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))*(f+g*ln(c*(e*x+d)**n))/x**4,x)","\int \frac{\left(a + b \log{\left(c \left(d + e x\right)^{n} \right)}\right) \left(f + g \log{\left(c \left(d + e x\right)^{n} \right)}\right)}{x^{4}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x)**n))*(f + g*log(c*(d + e*x)**n))/x**4, x)","F",0
386,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(e*x+d)**n))*(f+g*ln(h*(j*x+i)**m)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
387,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(e*x+d)**n))*(f+g*ln(h*(j*x+i)**m)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
388,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(e*x+d)**n))*(f+g*ln(h*(j*x+i)**m)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
389,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))*(f+g*ln(h*(j*x+i)**m)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
390,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))*(f+g*ln(h*(j*x+i)**m))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
391,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))*(f+g*ln(h*(j*x+i)**m))/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
392,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))*(f+g*ln(h*(j*x+i)**m))/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(e*x+d)**n))**2*(f+g*ln(h*(j*x+i)**m)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2*(f+g*ln(h*(j*x+i)**m)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
395,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2*(f+g*ln(h*(j*x+i)**m))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
396,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**2*(f+g*ln(h*(j*x+i)**m))/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
397,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(e*x+d)**n))**3*(f+g*ln(h*(j*x+i)**m)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
398,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**3*(f+g*ln(h*(j*x+i)**m)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
399,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**3*(f+g*ln(h*(j*x+i)**m))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
400,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))**3*(f+g*ln(h*(j*x+i)**m))/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
401,-2,0,0,0.000000," ","integrate((a+b*ln(c*(e*x+d)**n))*ln(e*(g*x+f)/(-d*g+e*f))/(e*x+d),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
402,1,56,0,0.293758," ","integrate(ln(c*(e*x+d))*(a+b*ln(c*(e*x+d)))/(e*x+d)**2,x)","- \frac{b \log{\left(c \left(d + e x\right) \right)}^{2}}{d e + e^{2} x} + \frac{\left(- a - 2 b\right) \log{\left(c \left(d + e x\right) \right)}}{d e + e^{2} x} - \frac{a + 2 b}{d e + e^{2} x}"," ",0,"-b*log(c*(d + e*x))**2/(d*e + e**2*x) + (-a - 2*b)*log(c*(d + e*x))/(d*e + e**2*x) - (a + 2*b)/(d*e + e**2*x)","A",0
403,1,75,0,0.337784," ","integrate((a+b*ln(c*(e*x+d)))*(f+g*ln(c*(e*x+d)))/(e*x+d)**2,x)","- \frac{b g \log{\left(c \left(d + e x\right) \right)}^{2}}{d e + e^{2} x} + \frac{\left(- a g - b f - 2 b g\right) \log{\left(c \left(d + e x\right) \right)}}{d e + e^{2} x} - \frac{a f + a g + b f + 2 b g}{d e + e^{2} x}"," ",0,"-b*g*log(c*(d + e*x))**2/(d*e + e**2*x) + (-a*g - b*f - 2*b*g)*log(c*(d + e*x))/(d*e + e**2*x) - (a*f + a*g + b*f + 2*b*g)/(d*e + e**2*x)","A",0
404,1,2390,0,24.006554," ","integrate((a+b*ln(c*(d*(f*x+e)**m)**n))**4,x)","\begin{cases} a^{4} x + \frac{4 a^{3} b e m n \log{\left(e + f x \right)}}{f} + 4 a^{3} b m n x \log{\left(e + f x \right)} - 4 a^{3} b m n x + 4 a^{3} b n x \log{\left(d \right)} + 4 a^{3} b x \log{\left(c \right)} + \frac{6 a^{2} b^{2} e m^{2} n^{2} \log{\left(e + f x \right)}^{2}}{f} - \frac{12 a^{2} b^{2} e m^{2} n^{2} \log{\left(e + f x \right)}}{f} + \frac{12 a^{2} b^{2} e m n^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{12 a^{2} b^{2} e m n \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + 6 a^{2} b^{2} m^{2} n^{2} x \log{\left(e + f x \right)}^{2} - 12 a^{2} b^{2} m^{2} n^{2} x \log{\left(e + f x \right)} + 12 a^{2} b^{2} m^{2} n^{2} x + 12 a^{2} b^{2} m n^{2} x \log{\left(d \right)} \log{\left(e + f x \right)} - 12 a^{2} b^{2} m n^{2} x \log{\left(d \right)} + 12 a^{2} b^{2} m n x \log{\left(c \right)} \log{\left(e + f x \right)} - 12 a^{2} b^{2} m n x \log{\left(c \right)} + 6 a^{2} b^{2} n^{2} x \log{\left(d \right)}^{2} + 12 a^{2} b^{2} n x \log{\left(c \right)} \log{\left(d \right)} + 6 a^{2} b^{2} x \log{\left(c \right)}^{2} + \frac{4 a b^{3} e m^{3} n^{3} \log{\left(e + f x \right)}^{3}}{f} - \frac{12 a b^{3} e m^{3} n^{3} \log{\left(e + f x \right)}^{2}}{f} + \frac{24 a b^{3} e m^{3} n^{3} \log{\left(e + f x \right)}}{f} + \frac{12 a b^{3} e m^{2} n^{3} \log{\left(d \right)} \log{\left(e + f x \right)}^{2}}{f} - \frac{24 a b^{3} e m^{2} n^{3} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{12 a b^{3} e m^{2} n^{2} \log{\left(c \right)} \log{\left(e + f x \right)}^{2}}{f} - \frac{24 a b^{3} e m^{2} n^{2} \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + \frac{12 a b^{3} e m n^{3} \log{\left(d \right)}^{2} \log{\left(e + f x \right)}}{f} + \frac{24 a b^{3} e m n^{2} \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{12 a b^{3} e m n \log{\left(c \right)}^{2} \log{\left(e + f x \right)}}{f} + 4 a b^{3} m^{3} n^{3} x \log{\left(e + f x \right)}^{3} - 12 a b^{3} m^{3} n^{3} x \log{\left(e + f x \right)}^{2} + 24 a b^{3} m^{3} n^{3} x \log{\left(e + f x \right)} - 24 a b^{3} m^{3} n^{3} x + 12 a b^{3} m^{2} n^{3} x \log{\left(d \right)} \log{\left(e + f x \right)}^{2} - 24 a b^{3} m^{2} n^{3} x \log{\left(d \right)} \log{\left(e + f x \right)} + 24 a b^{3} m^{2} n^{3} x \log{\left(d \right)} + 12 a b^{3} m^{2} n^{2} x \log{\left(c \right)} \log{\left(e + f x \right)}^{2} - 24 a b^{3} m^{2} n^{2} x \log{\left(c \right)} \log{\left(e + f x \right)} + 24 a b^{3} m^{2} n^{2} x \log{\left(c \right)} + 12 a b^{3} m n^{3} x \log{\left(d \right)}^{2} \log{\left(e + f x \right)} - 12 a b^{3} m n^{3} x \log{\left(d \right)}^{2} + 24 a b^{3} m n^{2} x \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)} - 24 a b^{3} m n^{2} x \log{\left(c \right)} \log{\left(d \right)} + 12 a b^{3} m n x \log{\left(c \right)}^{2} \log{\left(e + f x \right)} - 12 a b^{3} m n x \log{\left(c \right)}^{2} + 4 a b^{3} n^{3} x \log{\left(d \right)}^{3} + 12 a b^{3} n^{2} x \log{\left(c \right)} \log{\left(d \right)}^{2} + 12 a b^{3} n x \log{\left(c \right)}^{2} \log{\left(d \right)} + 4 a b^{3} x \log{\left(c \right)}^{3} + \frac{b^{4} e m^{4} n^{4} \log{\left(e + f x \right)}^{4}}{f} - \frac{4 b^{4} e m^{4} n^{4} \log{\left(e + f x \right)}^{3}}{f} + \frac{12 b^{4} e m^{4} n^{4} \log{\left(e + f x \right)}^{2}}{f} - \frac{24 b^{4} e m^{4} n^{4} \log{\left(e + f x \right)}}{f} + \frac{4 b^{4} e m^{3} n^{4} \log{\left(d \right)} \log{\left(e + f x \right)}^{3}}{f} - \frac{12 b^{4} e m^{3} n^{4} \log{\left(d \right)} \log{\left(e + f x \right)}^{2}}{f} + \frac{24 b^{4} e m^{3} n^{4} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{4 b^{4} e m^{3} n^{3} \log{\left(c \right)} \log{\left(e + f x \right)}^{3}}{f} - \frac{12 b^{4} e m^{3} n^{3} \log{\left(c \right)} \log{\left(e + f x \right)}^{2}}{f} + \frac{24 b^{4} e m^{3} n^{3} \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + \frac{6 b^{4} e m^{2} n^{4} \log{\left(d \right)}^{2} \log{\left(e + f x \right)}^{2}}{f} - \frac{12 b^{4} e m^{2} n^{4} \log{\left(d \right)}^{2} \log{\left(e + f x \right)}}{f} + \frac{12 b^{4} e m^{2} n^{3} \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)}^{2}}{f} - \frac{24 b^{4} e m^{2} n^{3} \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{6 b^{4} e m^{2} n^{2} \log{\left(c \right)}^{2} \log{\left(e + f x \right)}^{2}}{f} - \frac{12 b^{4} e m^{2} n^{2} \log{\left(c \right)}^{2} \log{\left(e + f x \right)}}{f} + \frac{4 b^{4} e m n^{4} \log{\left(d \right)}^{3} \log{\left(e + f x \right)}}{f} + \frac{12 b^{4} e m n^{3} \log{\left(c \right)} \log{\left(d \right)}^{2} \log{\left(e + f x \right)}}{f} + \frac{12 b^{4} e m n^{2} \log{\left(c \right)}^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{4 b^{4} e m n \log{\left(c \right)}^{3} \log{\left(e + f x \right)}}{f} + b^{4} m^{4} n^{4} x \log{\left(e + f x \right)}^{4} - 4 b^{4} m^{4} n^{4} x \log{\left(e + f x \right)}^{3} + 12 b^{4} m^{4} n^{4} x \log{\left(e + f x \right)}^{2} - 24 b^{4} m^{4} n^{4} x \log{\left(e + f x \right)} + 24 b^{4} m^{4} n^{4} x + 4 b^{4} m^{3} n^{4} x \log{\left(d \right)} \log{\left(e + f x \right)}^{3} - 12 b^{4} m^{3} n^{4} x \log{\left(d \right)} \log{\left(e + f x \right)}^{2} + 24 b^{4} m^{3} n^{4} x \log{\left(d \right)} \log{\left(e + f x \right)} - 24 b^{4} m^{3} n^{4} x \log{\left(d \right)} + 4 b^{4} m^{3} n^{3} x \log{\left(c \right)} \log{\left(e + f x \right)}^{3} - 12 b^{4} m^{3} n^{3} x \log{\left(c \right)} \log{\left(e + f x \right)}^{2} + 24 b^{4} m^{3} n^{3} x \log{\left(c \right)} \log{\left(e + f x \right)} - 24 b^{4} m^{3} n^{3} x \log{\left(c \right)} + 6 b^{4} m^{2} n^{4} x \log{\left(d \right)}^{2} \log{\left(e + f x \right)}^{2} - 12 b^{4} m^{2} n^{4} x \log{\left(d \right)}^{2} \log{\left(e + f x \right)} + 12 b^{4} m^{2} n^{4} x \log{\left(d \right)}^{2} + 12 b^{4} m^{2} n^{3} x \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)}^{2} - 24 b^{4} m^{2} n^{3} x \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)} + 24 b^{4} m^{2} n^{3} x \log{\left(c \right)} \log{\left(d \right)} + 6 b^{4} m^{2} n^{2} x \log{\left(c \right)}^{2} \log{\left(e + f x \right)}^{2} - 12 b^{4} m^{2} n^{2} x \log{\left(c \right)}^{2} \log{\left(e + f x \right)} + 12 b^{4} m^{2} n^{2} x \log{\left(c \right)}^{2} + 4 b^{4} m n^{4} x \log{\left(d \right)}^{3} \log{\left(e + f x \right)} - 4 b^{4} m n^{4} x \log{\left(d \right)}^{3} + 12 b^{4} m n^{3} x \log{\left(c \right)} \log{\left(d \right)}^{2} \log{\left(e + f x \right)} - 12 b^{4} m n^{3} x \log{\left(c \right)} \log{\left(d \right)}^{2} + 12 b^{4} m n^{2} x \log{\left(c \right)}^{2} \log{\left(d \right)} \log{\left(e + f x \right)} - 12 b^{4} m n^{2} x \log{\left(c \right)}^{2} \log{\left(d \right)} + 4 b^{4} m n x \log{\left(c \right)}^{3} \log{\left(e + f x \right)} - 4 b^{4} m n x \log{\left(c \right)}^{3} + b^{4} n^{4} x \log{\left(d \right)}^{4} + 4 b^{4} n^{3} x \log{\left(c \right)} \log{\left(d \right)}^{3} + 6 b^{4} n^{2} x \log{\left(c \right)}^{2} \log{\left(d \right)}^{2} + 4 b^{4} n x \log{\left(c \right)}^{3} \log{\left(d \right)} + b^{4} x \log{\left(c \right)}^{4} & \text{for}\: f \neq 0 \\x \left(a + b \log{\left(c \left(d e^{m}\right)^{n} \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x + 4*a**3*b*e*m*n*log(e + f*x)/f + 4*a**3*b*m*n*x*log(e + f*x) - 4*a**3*b*m*n*x + 4*a**3*b*n*x*log(d) + 4*a**3*b*x*log(c) + 6*a**2*b**2*e*m**2*n**2*log(e + f*x)**2/f - 12*a**2*b**2*e*m**2*n**2*log(e + f*x)/f + 12*a**2*b**2*e*m*n**2*log(d)*log(e + f*x)/f + 12*a**2*b**2*e*m*n*log(c)*log(e + f*x)/f + 6*a**2*b**2*m**2*n**2*x*log(e + f*x)**2 - 12*a**2*b**2*m**2*n**2*x*log(e + f*x) + 12*a**2*b**2*m**2*n**2*x + 12*a**2*b**2*m*n**2*x*log(d)*log(e + f*x) - 12*a**2*b**2*m*n**2*x*log(d) + 12*a**2*b**2*m*n*x*log(c)*log(e + f*x) - 12*a**2*b**2*m*n*x*log(c) + 6*a**2*b**2*n**2*x*log(d)**2 + 12*a**2*b**2*n*x*log(c)*log(d) + 6*a**2*b**2*x*log(c)**2 + 4*a*b**3*e*m**3*n**3*log(e + f*x)**3/f - 12*a*b**3*e*m**3*n**3*log(e + f*x)**2/f + 24*a*b**3*e*m**3*n**3*log(e + f*x)/f + 12*a*b**3*e*m**2*n**3*log(d)*log(e + f*x)**2/f - 24*a*b**3*e*m**2*n**3*log(d)*log(e + f*x)/f + 12*a*b**3*e*m**2*n**2*log(c)*log(e + f*x)**2/f - 24*a*b**3*e*m**2*n**2*log(c)*log(e + f*x)/f + 12*a*b**3*e*m*n**3*log(d)**2*log(e + f*x)/f + 24*a*b**3*e*m*n**2*log(c)*log(d)*log(e + f*x)/f + 12*a*b**3*e*m*n*log(c)**2*log(e + f*x)/f + 4*a*b**3*m**3*n**3*x*log(e + f*x)**3 - 12*a*b**3*m**3*n**3*x*log(e + f*x)**2 + 24*a*b**3*m**3*n**3*x*log(e + f*x) - 24*a*b**3*m**3*n**3*x + 12*a*b**3*m**2*n**3*x*log(d)*log(e + f*x)**2 - 24*a*b**3*m**2*n**3*x*log(d)*log(e + f*x) + 24*a*b**3*m**2*n**3*x*log(d) + 12*a*b**3*m**2*n**2*x*log(c)*log(e + f*x)**2 - 24*a*b**3*m**2*n**2*x*log(c)*log(e + f*x) + 24*a*b**3*m**2*n**2*x*log(c) + 12*a*b**3*m*n**3*x*log(d)**2*log(e + f*x) - 12*a*b**3*m*n**3*x*log(d)**2 + 24*a*b**3*m*n**2*x*log(c)*log(d)*log(e + f*x) - 24*a*b**3*m*n**2*x*log(c)*log(d) + 12*a*b**3*m*n*x*log(c)**2*log(e + f*x) - 12*a*b**3*m*n*x*log(c)**2 + 4*a*b**3*n**3*x*log(d)**3 + 12*a*b**3*n**2*x*log(c)*log(d)**2 + 12*a*b**3*n*x*log(c)**2*log(d) + 4*a*b**3*x*log(c)**3 + b**4*e*m**4*n**4*log(e + f*x)**4/f - 4*b**4*e*m**4*n**4*log(e + f*x)**3/f + 12*b**4*e*m**4*n**4*log(e + f*x)**2/f - 24*b**4*e*m**4*n**4*log(e + f*x)/f + 4*b**4*e*m**3*n**4*log(d)*log(e + f*x)**3/f - 12*b**4*e*m**3*n**4*log(d)*log(e + f*x)**2/f + 24*b**4*e*m**3*n**4*log(d)*log(e + f*x)/f + 4*b**4*e*m**3*n**3*log(c)*log(e + f*x)**3/f - 12*b**4*e*m**3*n**3*log(c)*log(e + f*x)**2/f + 24*b**4*e*m**3*n**3*log(c)*log(e + f*x)/f + 6*b**4*e*m**2*n**4*log(d)**2*log(e + f*x)**2/f - 12*b**4*e*m**2*n**4*log(d)**2*log(e + f*x)/f + 12*b**4*e*m**2*n**3*log(c)*log(d)*log(e + f*x)**2/f - 24*b**4*e*m**2*n**3*log(c)*log(d)*log(e + f*x)/f + 6*b**4*e*m**2*n**2*log(c)**2*log(e + f*x)**2/f - 12*b**4*e*m**2*n**2*log(c)**2*log(e + f*x)/f + 4*b**4*e*m*n**4*log(d)**3*log(e + f*x)/f + 12*b**4*e*m*n**3*log(c)*log(d)**2*log(e + f*x)/f + 12*b**4*e*m*n**2*log(c)**2*log(d)*log(e + f*x)/f + 4*b**4*e*m*n*log(c)**3*log(e + f*x)/f + b**4*m**4*n**4*x*log(e + f*x)**4 - 4*b**4*m**4*n**4*x*log(e + f*x)**3 + 12*b**4*m**4*n**4*x*log(e + f*x)**2 - 24*b**4*m**4*n**4*x*log(e + f*x) + 24*b**4*m**4*n**4*x + 4*b**4*m**3*n**4*x*log(d)*log(e + f*x)**3 - 12*b**4*m**3*n**4*x*log(d)*log(e + f*x)**2 + 24*b**4*m**3*n**4*x*log(d)*log(e + f*x) - 24*b**4*m**3*n**4*x*log(d) + 4*b**4*m**3*n**3*x*log(c)*log(e + f*x)**3 - 12*b**4*m**3*n**3*x*log(c)*log(e + f*x)**2 + 24*b**4*m**3*n**3*x*log(c)*log(e + f*x) - 24*b**4*m**3*n**3*x*log(c) + 6*b**4*m**2*n**4*x*log(d)**2*log(e + f*x)**2 - 12*b**4*m**2*n**4*x*log(d)**2*log(e + f*x) + 12*b**4*m**2*n**4*x*log(d)**2 + 12*b**4*m**2*n**3*x*log(c)*log(d)*log(e + f*x)**2 - 24*b**4*m**2*n**3*x*log(c)*log(d)*log(e + f*x) + 24*b**4*m**2*n**3*x*log(c)*log(d) + 6*b**4*m**2*n**2*x*log(c)**2*log(e + f*x)**2 - 12*b**4*m**2*n**2*x*log(c)**2*log(e + f*x) + 12*b**4*m**2*n**2*x*log(c)**2 + 4*b**4*m*n**4*x*log(d)**3*log(e + f*x) - 4*b**4*m*n**4*x*log(d)**3 + 12*b**4*m*n**3*x*log(c)*log(d)**2*log(e + f*x) - 12*b**4*m*n**3*x*log(c)*log(d)**2 + 12*b**4*m*n**2*x*log(c)**2*log(d)*log(e + f*x) - 12*b**4*m*n**2*x*log(c)**2*log(d) + 4*b**4*m*n*x*log(c)**3*log(e + f*x) - 4*b**4*m*n*x*log(c)**3 + b**4*n**4*x*log(d)**4 + 4*b**4*n**3*x*log(c)*log(d)**3 + 6*b**4*n**2*x*log(c)**2*log(d)**2 + 4*b**4*n*x*log(c)**3*log(d) + b**4*x*log(c)**4, Ne(f, 0)), (x*(a + b*log(c*(d*e**m)**n))**4, True))","A",0
405,1,1023,0,9.844282," ","integrate((a+b*ln(c*(d*(f*x+e)**m)**n))**3,x)","\begin{cases} a^{3} x + \frac{3 a^{2} b e m n \log{\left(e + f x \right)}}{f} + 3 a^{2} b m n x \log{\left(e + f x \right)} - 3 a^{2} b m n x + 3 a^{2} b n x \log{\left(d \right)} + 3 a^{2} b x \log{\left(c \right)} + \frac{3 a b^{2} e m^{2} n^{2} \log{\left(e + f x \right)}^{2}}{f} - \frac{6 a b^{2} e m^{2} n^{2} \log{\left(e + f x \right)}}{f} + \frac{6 a b^{2} e m n^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{6 a b^{2} e m n \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + 3 a b^{2} m^{2} n^{2} x \log{\left(e + f x \right)}^{2} - 6 a b^{2} m^{2} n^{2} x \log{\left(e + f x \right)} + 6 a b^{2} m^{2} n^{2} x + 6 a b^{2} m n^{2} x \log{\left(d \right)} \log{\left(e + f x \right)} - 6 a b^{2} m n^{2} x \log{\left(d \right)} + 6 a b^{2} m n x \log{\left(c \right)} \log{\left(e + f x \right)} - 6 a b^{2} m n x \log{\left(c \right)} + 3 a b^{2} n^{2} x \log{\left(d \right)}^{2} + 6 a b^{2} n x \log{\left(c \right)} \log{\left(d \right)} + 3 a b^{2} x \log{\left(c \right)}^{2} + \frac{b^{3} e m^{3} n^{3} \log{\left(e + f x \right)}^{3}}{f} - \frac{3 b^{3} e m^{3} n^{3} \log{\left(e + f x \right)}^{2}}{f} + \frac{6 b^{3} e m^{3} n^{3} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e m^{2} n^{3} \log{\left(d \right)} \log{\left(e + f x \right)}^{2}}{f} - \frac{6 b^{3} e m^{2} n^{3} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e m^{2} n^{2} \log{\left(c \right)} \log{\left(e + f x \right)}^{2}}{f} - \frac{6 b^{3} e m^{2} n^{2} \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e m n^{3} \log{\left(d \right)}^{2} \log{\left(e + f x \right)}}{f} + \frac{6 b^{3} e m n^{2} \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e m n \log{\left(c \right)}^{2} \log{\left(e + f x \right)}}{f} + b^{3} m^{3} n^{3} x \log{\left(e + f x \right)}^{3} - 3 b^{3} m^{3} n^{3} x \log{\left(e + f x \right)}^{2} + 6 b^{3} m^{3} n^{3} x \log{\left(e + f x \right)} - 6 b^{3} m^{3} n^{3} x + 3 b^{3} m^{2} n^{3} x \log{\left(d \right)} \log{\left(e + f x \right)}^{2} - 6 b^{3} m^{2} n^{3} x \log{\left(d \right)} \log{\left(e + f x \right)} + 6 b^{3} m^{2} n^{3} x \log{\left(d \right)} + 3 b^{3} m^{2} n^{2} x \log{\left(c \right)} \log{\left(e + f x \right)}^{2} - 6 b^{3} m^{2} n^{2} x \log{\left(c \right)} \log{\left(e + f x \right)} + 6 b^{3} m^{2} n^{2} x \log{\left(c \right)} + 3 b^{3} m n^{3} x \log{\left(d \right)}^{2} \log{\left(e + f x \right)} - 3 b^{3} m n^{3} x \log{\left(d \right)}^{2} + 6 b^{3} m n^{2} x \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)} - 6 b^{3} m n^{2} x \log{\left(c \right)} \log{\left(d \right)} + 3 b^{3} m n x \log{\left(c \right)}^{2} \log{\left(e + f x \right)} - 3 b^{3} m n x \log{\left(c \right)}^{2} + b^{3} n^{3} x \log{\left(d \right)}^{3} + 3 b^{3} n^{2} x \log{\left(c \right)} \log{\left(d \right)}^{2} + 3 b^{3} n x \log{\left(c \right)}^{2} \log{\left(d \right)} + b^{3} x \log{\left(c \right)}^{3} & \text{for}\: f \neq 0 \\x \left(a + b \log{\left(c \left(d e^{m}\right)^{n} \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x + 3*a**2*b*e*m*n*log(e + f*x)/f + 3*a**2*b*m*n*x*log(e + f*x) - 3*a**2*b*m*n*x + 3*a**2*b*n*x*log(d) + 3*a**2*b*x*log(c) + 3*a*b**2*e*m**2*n**2*log(e + f*x)**2/f - 6*a*b**2*e*m**2*n**2*log(e + f*x)/f + 6*a*b**2*e*m*n**2*log(d)*log(e + f*x)/f + 6*a*b**2*e*m*n*log(c)*log(e + f*x)/f + 3*a*b**2*m**2*n**2*x*log(e + f*x)**2 - 6*a*b**2*m**2*n**2*x*log(e + f*x) + 6*a*b**2*m**2*n**2*x + 6*a*b**2*m*n**2*x*log(d)*log(e + f*x) - 6*a*b**2*m*n**2*x*log(d) + 6*a*b**2*m*n*x*log(c)*log(e + f*x) - 6*a*b**2*m*n*x*log(c) + 3*a*b**2*n**2*x*log(d)**2 + 6*a*b**2*n*x*log(c)*log(d) + 3*a*b**2*x*log(c)**2 + b**3*e*m**3*n**3*log(e + f*x)**3/f - 3*b**3*e*m**3*n**3*log(e + f*x)**2/f + 6*b**3*e*m**3*n**3*log(e + f*x)/f + 3*b**3*e*m**2*n**3*log(d)*log(e + f*x)**2/f - 6*b**3*e*m**2*n**3*log(d)*log(e + f*x)/f + 3*b**3*e*m**2*n**2*log(c)*log(e + f*x)**2/f - 6*b**3*e*m**2*n**2*log(c)*log(e + f*x)/f + 3*b**3*e*m*n**3*log(d)**2*log(e + f*x)/f + 6*b**3*e*m*n**2*log(c)*log(d)*log(e + f*x)/f + 3*b**3*e*m*n*log(c)**2*log(e + f*x)/f + b**3*m**3*n**3*x*log(e + f*x)**3 - 3*b**3*m**3*n**3*x*log(e + f*x)**2 + 6*b**3*m**3*n**3*x*log(e + f*x) - 6*b**3*m**3*n**3*x + 3*b**3*m**2*n**3*x*log(d)*log(e + f*x)**2 - 6*b**3*m**2*n**3*x*log(d)*log(e + f*x) + 6*b**3*m**2*n**3*x*log(d) + 3*b**3*m**2*n**2*x*log(c)*log(e + f*x)**2 - 6*b**3*m**2*n**2*x*log(c)*log(e + f*x) + 6*b**3*m**2*n**2*x*log(c) + 3*b**3*m*n**3*x*log(d)**2*log(e + f*x) - 3*b**3*m*n**3*x*log(d)**2 + 6*b**3*m*n**2*x*log(c)*log(d)*log(e + f*x) - 6*b**3*m*n**2*x*log(c)*log(d) + 3*b**3*m*n*x*log(c)**2*log(e + f*x) - 3*b**3*m*n*x*log(c)**2 + b**3*n**3*x*log(d)**3 + 3*b**3*n**2*x*log(c)*log(d)**2 + 3*b**3*n*x*log(c)**2*log(d) + b**3*x*log(c)**3, Ne(f, 0)), (x*(a + b*log(c*(d*e**m)**n))**3, True))","A",0
406,1,343,0,3.589386," ","integrate((a+b*ln(c*(d*(f*x+e)**m)**n))**2,x)","\begin{cases} a^{2} x + \frac{2 a b e m n \log{\left(e + f x \right)}}{f} + 2 a b m n x \log{\left(e + f x \right)} - 2 a b m n x + 2 a b n x \log{\left(d \right)} + 2 a b x \log{\left(c \right)} + \frac{b^{2} e m^{2} n^{2} \log{\left(e + f x \right)}^{2}}{f} - \frac{2 b^{2} e m^{2} n^{2} \log{\left(e + f x \right)}}{f} + \frac{2 b^{2} e m n^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{2 b^{2} e m n \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + b^{2} m^{2} n^{2} x \log{\left(e + f x \right)}^{2} - 2 b^{2} m^{2} n^{2} x \log{\left(e + f x \right)} + 2 b^{2} m^{2} n^{2} x + 2 b^{2} m n^{2} x \log{\left(d \right)} \log{\left(e + f x \right)} - 2 b^{2} m n^{2} x \log{\left(d \right)} + 2 b^{2} m n x \log{\left(c \right)} \log{\left(e + f x \right)} - 2 b^{2} m n x \log{\left(c \right)} + b^{2} n^{2} x \log{\left(d \right)}^{2} + 2 b^{2} n x \log{\left(c \right)} \log{\left(d \right)} + b^{2} x \log{\left(c \right)}^{2} & \text{for}\: f \neq 0 \\x \left(a + b \log{\left(c \left(d e^{m}\right)^{n} \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + 2*a*b*e*m*n*log(e + f*x)/f + 2*a*b*m*n*x*log(e + f*x) - 2*a*b*m*n*x + 2*a*b*n*x*log(d) + 2*a*b*x*log(c) + b**2*e*m**2*n**2*log(e + f*x)**2/f - 2*b**2*e*m**2*n**2*log(e + f*x)/f + 2*b**2*e*m*n**2*log(d)*log(e + f*x)/f + 2*b**2*e*m*n*log(c)*log(e + f*x)/f + b**2*m**2*n**2*x*log(e + f*x)**2 - 2*b**2*m**2*n**2*x*log(e + f*x) + 2*b**2*m**2*n**2*x + 2*b**2*m*n**2*x*log(d)*log(e + f*x) - 2*b**2*m*n**2*x*log(d) + 2*b**2*m*n*x*log(c)*log(e + f*x) - 2*b**2*m*n*x*log(c) + b**2*n**2*x*log(d)**2 + 2*b**2*n*x*log(c)*log(d) + b**2*x*log(c)**2, Ne(f, 0)), (x*(a + b*log(c*(d*e**m)**n))**2, True))","A",0
407,1,58,0,0.967385," ","integrate(a+b*ln(c*(d*(f*x+e)**m)**n),x)","a x + b \left(\begin{cases} \frac{e m n \log{\left(e + f x \right)}}{f} + m n x \log{\left(e + f x \right)} - m n x + n x \log{\left(d \right)} + x \log{\left(c \right)} & \text{for}\: f \neq 0 \\x \log{\left(c \left(d e^{m}\right)^{n} \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((e*m*n*log(e + f*x)/f + m*n*x*log(e + f*x) - m*n*x + n*x*log(d) + x*log(c), Ne(f, 0)), (x*log(c*(d*e**m)**n), True))","A",0
408,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(d*(f*x+e)**m)**n)),x)","\int \frac{1}{a + b \log{\left(c \left(d \left(e + f x\right)^{m}\right)^{n} \right)}}\, dx"," ",0,"Integral(1/(a + b*log(c*(d*(e + f*x)**m)**n)), x)","F",0
409,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(d*(f*x+e)**m)**n))**2,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{m}\right)^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**m)**n))**(-2), x)","F",0
410,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(d*(f*x+e)**m)**n))**3,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{m}\right)^{n} \right)}\right)^{3}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**m)**n))**(-3), x)","F",0
411,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**m)**n))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
412,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**m)**n))**(3/2),x)","\int \left(a + b \log{\left(c \left(d \left(e + f x\right)^{m}\right)^{n} \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**m)**n))**(3/2), x)","F",0
413,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**m)**n))**(1/2),x)","\int \sqrt{a + b \log{\left(c \left(d \left(e + f x\right)^{m}\right)^{n} \right)}}\, dx"," ",0,"Integral(sqrt(a + b*log(c*(d*(e + f*x)**m)**n)), x)","F",0
414,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(d*(f*x+e)**m)**n))**(1/2),x)","\int \frac{1}{\sqrt{a + b \log{\left(c \left(d \left(e + f x\right)^{m}\right)^{n} \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*log(c*(d*(e + f*x)**m)**n)), x)","F",0
415,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(d*(f*x+e)**m)**n))**(3/2),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{m}\right)^{n} \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**m)**n))**(-3/2), x)","F",0
416,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(d*(f*x+e)**m)**n))**(5/2),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{m}\right)^{n} \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**m)**n))**(-5/2), x)","F",0
417,-1,0,0,0.000000," ","integrate(1/(a+b*ln(c*(d*(f*x+e)**m)**n))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
418,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**m)**n))**p,x)","\int \left(a + b \log{\left(c \left(d \left(e + f x\right)^{m}\right)^{n} \right)}\right)^{p}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**m)**n))**p, x)","F",0
419,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**(1/2))**(1/2)))**p,x)","\int \left(a + b \log{\left(c \sqrt{d \sqrt{e + f x}} \right)}\right)^{p}\, dx"," ",0,"Integral((a + b*log(c*sqrt(d*sqrt(e + f*x))))**p, x)","F",0
420,1,546,0,21.353962," ","integrate((h*x+g)**3*(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\begin{cases} a g^{3} x + \frac{3 a g^{2} h x^{2}}{2} + a g h^{2} x^{3} + \frac{a h^{3} x^{4}}{4} - \frac{b e^{4} h^{3} p q \log{\left(e + f x \right)}}{4 f^{4}} + \frac{b e^{3} g h^{2} p q \log{\left(e + f x \right)}}{f^{3}} + \frac{b e^{3} h^{3} p q x}{4 f^{3}} - \frac{3 b e^{2} g^{2} h p q \log{\left(e + f x \right)}}{2 f^{2}} - \frac{b e^{2} g h^{2} p q x}{f^{2}} - \frac{b e^{2} h^{3} p q x^{2}}{8 f^{2}} + \frac{b e g^{3} p q \log{\left(e + f x \right)}}{f} + \frac{3 b e g^{2} h p q x}{2 f} + \frac{b e g h^{2} p q x^{2}}{2 f} + \frac{b e h^{3} p q x^{3}}{12 f} + b g^{3} p q x \log{\left(e + f x \right)} - b g^{3} p q x + b g^{3} q x \log{\left(d \right)} + b g^{3} x \log{\left(c \right)} + \frac{3 b g^{2} h p q x^{2} \log{\left(e + f x \right)}}{2} - \frac{3 b g^{2} h p q x^{2}}{4} + \frac{3 b g^{2} h q x^{2} \log{\left(d \right)}}{2} + \frac{3 b g^{2} h x^{2} \log{\left(c \right)}}{2} + b g h^{2} p q x^{3} \log{\left(e + f x \right)} - \frac{b g h^{2} p q x^{3}}{3} + b g h^{2} q x^{3} \log{\left(d \right)} + b g h^{2} x^{3} \log{\left(c \right)} + \frac{b h^{3} p q x^{4} \log{\left(e + f x \right)}}{4} - \frac{b h^{3} p q x^{4}}{16} + \frac{b h^{3} q x^{4} \log{\left(d \right)}}{4} + \frac{b h^{3} x^{4} \log{\left(c \right)}}{4} & \text{for}\: f \neq 0 \\\left(a + b \log{\left(c \left(d e^{p}\right)^{q} \right)}\right) \left(g^{3} x + \frac{3 g^{2} h x^{2}}{2} + g h^{2} x^{3} + \frac{h^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*g**3*x + 3*a*g**2*h*x**2/2 + a*g*h**2*x**3 + a*h**3*x**4/4 - b*e**4*h**3*p*q*log(e + f*x)/(4*f**4) + b*e**3*g*h**2*p*q*log(e + f*x)/f**3 + b*e**3*h**3*p*q*x/(4*f**3) - 3*b*e**2*g**2*h*p*q*log(e + f*x)/(2*f**2) - b*e**2*g*h**2*p*q*x/f**2 - b*e**2*h**3*p*q*x**2/(8*f**2) + b*e*g**3*p*q*log(e + f*x)/f + 3*b*e*g**2*h*p*q*x/(2*f) + b*e*g*h**2*p*q*x**2/(2*f) + b*e*h**3*p*q*x**3/(12*f) + b*g**3*p*q*x*log(e + f*x) - b*g**3*p*q*x + b*g**3*q*x*log(d) + b*g**3*x*log(c) + 3*b*g**2*h*p*q*x**2*log(e + f*x)/2 - 3*b*g**2*h*p*q*x**2/4 + 3*b*g**2*h*q*x**2*log(d)/2 + 3*b*g**2*h*x**2*log(c)/2 + b*g*h**2*p*q*x**3*log(e + f*x) - b*g*h**2*p*q*x**3/3 + b*g*h**2*q*x**3*log(d) + b*g*h**2*x**3*log(c) + b*h**3*p*q*x**4*log(e + f*x)/4 - b*h**3*p*q*x**4/16 + b*h**3*q*x**4*log(d)/4 + b*h**3*x**4*log(c)/4, Ne(f, 0)), ((a + b*log(c*(d*e**p)**q))*(g**3*x + 3*g**2*h*x**2/2 + g*h**2*x**3 + h**3*x**4/4), True))","A",0
421,1,342,0,9.511757," ","integrate((h*x+g)**2*(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\begin{cases} a g^{2} x + a g h x^{2} + \frac{a h^{2} x^{3}}{3} + \frac{b e^{3} h^{2} p q \log{\left(e + f x \right)}}{3 f^{3}} - \frac{b e^{2} g h p q \log{\left(e + f x \right)}}{f^{2}} - \frac{b e^{2} h^{2} p q x}{3 f^{2}} + \frac{b e g^{2} p q \log{\left(e + f x \right)}}{f} + \frac{b e g h p q x}{f} + \frac{b e h^{2} p q x^{2}}{6 f} + b g^{2} p q x \log{\left(e + f x \right)} - b g^{2} p q x + b g^{2} q x \log{\left(d \right)} + b g^{2} x \log{\left(c \right)} + b g h p q x^{2} \log{\left(e + f x \right)} - \frac{b g h p q x^{2}}{2} + b g h q x^{2} \log{\left(d \right)} + b g h x^{2} \log{\left(c \right)} + \frac{b h^{2} p q x^{3} \log{\left(e + f x \right)}}{3} - \frac{b h^{2} p q x^{3}}{9} + \frac{b h^{2} q x^{3} \log{\left(d \right)}}{3} + \frac{b h^{2} x^{3} \log{\left(c \right)}}{3} & \text{for}\: f \neq 0 \\\left(a + b \log{\left(c \left(d e^{p}\right)^{q} \right)}\right) \left(g^{2} x + g h x^{2} + \frac{h^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*g**2*x + a*g*h*x**2 + a*h**2*x**3/3 + b*e**3*h**2*p*q*log(e + f*x)/(3*f**3) - b*e**2*g*h*p*q*log(e + f*x)/f**2 - b*e**2*h**2*p*q*x/(3*f**2) + b*e*g**2*p*q*log(e + f*x)/f + b*e*g*h*p*q*x/f + b*e*h**2*p*q*x**2/(6*f) + b*g**2*p*q*x*log(e + f*x) - b*g**2*p*q*x + b*g**2*q*x*log(d) + b*g**2*x*log(c) + b*g*h*p*q*x**2*log(e + f*x) - b*g*h*p*q*x**2/2 + b*g*h*q*x**2*log(d) + b*g*h*x**2*log(c) + b*h**2*p*q*x**3*log(e + f*x)/3 - b*h**2*p*q*x**3/9 + b*h**2*q*x**3*log(d)/3 + b*h**2*x**3*log(c)/3, Ne(f, 0)), ((a + b*log(c*(d*e**p)**q))*(g**2*x + g*h*x**2 + h**2*x**3/3), True))","A",0
422,1,187,0,3.593185," ","integrate((h*x+g)*(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\begin{cases} a g x + \frac{a h x^{2}}{2} - \frac{b e^{2} h p q \log{\left(e + f x \right)}}{2 f^{2}} + \frac{b e g p q \log{\left(e + f x \right)}}{f} + \frac{b e h p q x}{2 f} + b g p q x \log{\left(e + f x \right)} - b g p q x + b g q x \log{\left(d \right)} + b g x \log{\left(c \right)} + \frac{b h p q x^{2} \log{\left(e + f x \right)}}{2} - \frac{b h p q x^{2}}{4} + \frac{b h q x^{2} \log{\left(d \right)}}{2} + \frac{b h x^{2} \log{\left(c \right)}}{2} & \text{for}\: f \neq 0 \\\left(a + b \log{\left(c \left(d e^{p}\right)^{q} \right)}\right) \left(g x + \frac{h x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*g*x + a*h*x**2/2 - b*e**2*h*p*q*log(e + f*x)/(2*f**2) + b*e*g*p*q*log(e + f*x)/f + b*e*h*p*q*x/(2*f) + b*g*p*q*x*log(e + f*x) - b*g*p*q*x + b*g*q*x*log(d) + b*g*x*log(c) + b*h*p*q*x**2*log(e + f*x)/2 - b*h*p*q*x**2/4 + b*h*q*x**2*log(d)/2 + b*h*x**2*log(c)/2, Ne(f, 0)), ((a + b*log(c*(d*e**p)**q))*(g*x + h*x**2/2), True))","A",0
423,1,58,0,0.916408," ","integrate(a+b*ln(c*(d*(f*x+e)**p)**q),x)","a x + b \left(\begin{cases} \frac{e p q \log{\left(e + f x \right)}}{f} + p q x \log{\left(e + f x \right)} - p q x + q x \log{\left(d \right)} + x \log{\left(c \right)} & \text{for}\: f \neq 0 \\x \log{\left(c \left(d e^{p}\right)^{q} \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((e*p*q*log(e + f*x)/f + p*q*x*log(e + f*x) - p*q*x + q*x*log(d) + x*log(c), Ne(f, 0)), (x*log(c*(d*e**p)**q), True))","A",0
424,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x+g),x)","\int \frac{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}{g + h x}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))/(g + h*x), x)","F",0
425,-2,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x+g)**2,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
426,-2,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x+g)**3,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
427,1,8709,0,131.754205," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x+g)**4,x)","\begin{cases} - \frac{3 a}{9 g^{3} h + 27 g^{2} h^{2} x + 27 g h^{3} x^{2} + 9 h^{4} x^{3}} - \frac{3 b p q \log{\left(\frac{f g}{h} + f x \right)}}{9 g^{3} h + 27 g^{2} h^{2} x + 27 g h^{3} x^{2} + 9 h^{4} x^{3}} - \frac{b p q}{9 g^{3} h + 27 g^{2} h^{2} x + 27 g h^{3} x^{2} + 9 h^{4} x^{3}} - \frac{3 b q \log{\left(d \right)}}{9 g^{3} h + 27 g^{2} h^{2} x + 27 g h^{3} x^{2} + 9 h^{4} x^{3}} - \frac{3 b \log{\left(c \right)}}{9 g^{3} h + 27 g^{2} h^{2} x + 27 g h^{3} x^{2} + 9 h^{4} x^{3}} & \text{for}\: e = \frac{f g}{h} \\\frac{a x + \frac{b e p q \log{\left(e + f x \right)}}{f} + b p q x \log{\left(e + f x \right)} - b p q x + b q x \log{\left(d \right)} + b x \log{\left(c \right)}}{g^{4}} & \text{for}\: h = 0 \\- \frac{2 a e^{3} h^{3}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} + \frac{6 a e^{2} f g h^{2}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{6 a e f^{2} g^{2} h}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} + \frac{2 a f^{3} g^{3}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{2 b e^{3} h^{3} p q \log{\left(e + f x \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{2 b e^{3} h^{3} q \log{\left(d \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{2 b e^{3} h^{3} \log{\left(c \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} + \frac{6 b e^{2} f g h^{2} p q \log{\left(e + f x \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{b e^{2} f g h^{2} p q}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} + \frac{6 b e^{2} f g h^{2} q \log{\left(d \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} + \frac{6 b e^{2} f g h^{2} \log{\left(c \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{b e^{2} f h^{3} p q x}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{6 b e f^{2} g^{2} h p q \log{\left(e + f x \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} + \frac{4 b e f^{2} g^{2} h p q}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{6 b e f^{2} g^{2} h q \log{\left(d \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{6 b e f^{2} g^{2} h \log{\left(c \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} + \frac{6 b e f^{2} g h^{2} p q x}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} + \frac{2 b e f^{2} h^{3} p q x^{2}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} + \frac{2 b f^{3} g^{3} p q \log{\left(\frac{g}{h} + x \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{3 b f^{3} g^{3} p q}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{6 b f^{3} g^{2} h p q x \log{\left(e + f x \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} + \frac{6 b f^{3} g^{2} h p q x \log{\left(\frac{g}{h} + x \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{5 b f^{3} g^{2} h p q x}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{6 b f^{3} g^{2} h q x \log{\left(d \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{6 b f^{3} g^{2} h x \log{\left(c \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{6 b f^{3} g h^{2} p q x^{2} \log{\left(e + f x \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} + \frac{6 b f^{3} g h^{2} p q x^{2} \log{\left(\frac{g}{h} + x \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{2 b f^{3} g h^{2} p q x^{2}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{6 b f^{3} g h^{2} q x^{2} \log{\left(d \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{6 b f^{3} g h^{2} x^{2} \log{\left(c \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{2 b f^{3} h^{3} p q x^{3} \log{\left(e + f x \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} + \frac{2 b f^{3} h^{3} p q x^{3} \log{\left(\frac{g}{h} + x \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{2 b f^{3} h^{3} q x^{3} \log{\left(d \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} - \frac{2 b f^{3} h^{3} x^{3} \log{\left(c \right)}}{6 e^{3} g^{3} h^{4} + 18 e^{3} g^{2} h^{5} x + 18 e^{3} g h^{6} x^{2} + 6 e^{3} h^{7} x^{3} - 18 e^{2} f g^{4} h^{3} - 54 e^{2} f g^{3} h^{4} x - 54 e^{2} f g^{2} h^{5} x^{2} - 18 e^{2} f g h^{6} x^{3} + 18 e f^{2} g^{5} h^{2} + 54 e f^{2} g^{4} h^{3} x + 54 e f^{2} g^{3} h^{4} x^{2} + 18 e f^{2} g^{2} h^{5} x^{3} - 6 f^{3} g^{6} h - 18 f^{3} g^{5} h^{2} x - 18 f^{3} g^{4} h^{3} x^{2} - 6 f^{3} g^{3} h^{4} x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*a/(9*g**3*h + 27*g**2*h**2*x + 27*g*h**3*x**2 + 9*h**4*x**3) - 3*b*p*q*log(f*g/h + f*x)/(9*g**3*h + 27*g**2*h**2*x + 27*g*h**3*x**2 + 9*h**4*x**3) - b*p*q/(9*g**3*h + 27*g**2*h**2*x + 27*g*h**3*x**2 + 9*h**4*x**3) - 3*b*q*log(d)/(9*g**3*h + 27*g**2*h**2*x + 27*g*h**3*x**2 + 9*h**4*x**3) - 3*b*log(c)/(9*g**3*h + 27*g**2*h**2*x + 27*g*h**3*x**2 + 9*h**4*x**3), Eq(e, f*g/h)), ((a*x + b*e*p*q*log(e + f*x)/f + b*p*q*x*log(e + f*x) - b*p*q*x + b*q*x*log(d) + b*x*log(c))/g**4, Eq(h, 0)), (-2*a*e**3*h**3/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) + 6*a*e**2*f*g*h**2/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 6*a*e*f**2*g**2*h/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) + 2*a*f**3*g**3/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 2*b*e**3*h**3*p*q*log(e + f*x)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 2*b*e**3*h**3*q*log(d)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 2*b*e**3*h**3*log(c)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) + 6*b*e**2*f*g*h**2*p*q*log(e + f*x)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - b*e**2*f*g*h**2*p*q/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) + 6*b*e**2*f*g*h**2*q*log(d)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) + 6*b*e**2*f*g*h**2*log(c)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - b*e**2*f*h**3*p*q*x/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 6*b*e*f**2*g**2*h*p*q*log(e + f*x)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) + 4*b*e*f**2*g**2*h*p*q/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 6*b*e*f**2*g**2*h*q*log(d)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 6*b*e*f**2*g**2*h*log(c)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) + 6*b*e*f**2*g*h**2*p*q*x/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) + 2*b*e*f**2*h**3*p*q*x**2/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) + 2*b*f**3*g**3*p*q*log(g/h + x)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 3*b*f**3*g**3*p*q/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 6*b*f**3*g**2*h*p*q*x*log(e + f*x)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) + 6*b*f**3*g**2*h*p*q*x*log(g/h + x)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 5*b*f**3*g**2*h*p*q*x/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 6*b*f**3*g**2*h*q*x*log(d)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 6*b*f**3*g**2*h*x*log(c)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 6*b*f**3*g*h**2*p*q*x**2*log(e + f*x)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) + 6*b*f**3*g*h**2*p*q*x**2*log(g/h + x)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 2*b*f**3*g*h**2*p*q*x**2/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 6*b*f**3*g*h**2*q*x**2*log(d)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 6*b*f**3*g*h**2*x**2*log(c)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 2*b*f**3*h**3*p*q*x**3*log(e + f*x)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) + 2*b*f**3*h**3*p*q*x**3*log(g/h + x)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 2*b*f**3*h**3*q*x**3*log(d)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3) - 2*b*f**3*h**3*x**3*log(c)/(6*e**3*g**3*h**4 + 18*e**3*g**2*h**5*x + 18*e**3*g*h**6*x**2 + 6*e**3*h**7*x**3 - 18*e**2*f*g**4*h**3 - 54*e**2*f*g**3*h**4*x - 54*e**2*f*g**2*h**5*x**2 - 18*e**2*f*g*h**6*x**3 + 18*e*f**2*g**5*h**2 + 54*e*f**2*g**4*h**3*x + 54*e*f**2*g**3*h**4*x**2 + 18*e*f**2*g**2*h**5*x**3 - 6*f**3*g**6*h - 18*f**3*g**5*h**2*x - 18*f**3*g**4*h**3*x**2 - 6*f**3*g**3*h**4*x**3), True))","A",0
428,1,2623,0,67.672505," ","integrate((h*x+g)**3*(a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)","\begin{cases} a^{2} g^{3} x + \frac{3 a^{2} g^{2} h x^{2}}{2} + a^{2} g h^{2} x^{3} + \frac{a^{2} h^{3} x^{4}}{4} - \frac{a b e^{4} h^{3} p q \log{\left(e + f x \right)}}{2 f^{4}} + \frac{2 a b e^{3} g h^{2} p q \log{\left(e + f x \right)}}{f^{3}} + \frac{a b e^{3} h^{3} p q x}{2 f^{3}} - \frac{3 a b e^{2} g^{2} h p q \log{\left(e + f x \right)}}{f^{2}} - \frac{2 a b e^{2} g h^{2} p q x}{f^{2}} - \frac{a b e^{2} h^{3} p q x^{2}}{4 f^{2}} + \frac{2 a b e g^{3} p q \log{\left(e + f x \right)}}{f} + \frac{3 a b e g^{2} h p q x}{f} + \frac{a b e g h^{2} p q x^{2}}{f} + \frac{a b e h^{3} p q x^{3}}{6 f} + 2 a b g^{3} p q x \log{\left(e + f x \right)} - 2 a b g^{3} p q x + 2 a b g^{3} q x \log{\left(d \right)} + 2 a b g^{3} x \log{\left(c \right)} + 3 a b g^{2} h p q x^{2} \log{\left(e + f x \right)} - \frac{3 a b g^{2} h p q x^{2}}{2} + 3 a b g^{2} h q x^{2} \log{\left(d \right)} + 3 a b g^{2} h x^{2} \log{\left(c \right)} + 2 a b g h^{2} p q x^{3} \log{\left(e + f x \right)} - \frac{2 a b g h^{2} p q x^{3}}{3} + 2 a b g h^{2} q x^{3} \log{\left(d \right)} + 2 a b g h^{2} x^{3} \log{\left(c \right)} + \frac{a b h^{3} p q x^{4} \log{\left(e + f x \right)}}{2} - \frac{a b h^{3} p q x^{4}}{8} + \frac{a b h^{3} q x^{4} \log{\left(d \right)}}{2} + \frac{a b h^{3} x^{4} \log{\left(c \right)}}{2} - \frac{b^{2} e^{4} h^{3} p^{2} q^{2} \log{\left(e + f x \right)}^{2}}{4 f^{4}} + \frac{25 b^{2} e^{4} h^{3} p^{2} q^{2} \log{\left(e + f x \right)}}{24 f^{4}} - \frac{b^{2} e^{4} h^{3} p q^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{2 f^{4}} - \frac{b^{2} e^{4} h^{3} p q \log{\left(c \right)} \log{\left(e + f x \right)}}{2 f^{4}} + \frac{b^{2} e^{3} g h^{2} p^{2} q^{2} \log{\left(e + f x \right)}^{2}}{f^{3}} - \frac{11 b^{2} e^{3} g h^{2} p^{2} q^{2} \log{\left(e + f x \right)}}{3 f^{3}} + \frac{2 b^{2} e^{3} g h^{2} p q^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f^{3}} + \frac{2 b^{2} e^{3} g h^{2} p q \log{\left(c \right)} \log{\left(e + f x \right)}}{f^{3}} + \frac{b^{2} e^{3} h^{3} p^{2} q^{2} x \log{\left(e + f x \right)}}{2 f^{3}} - \frac{25 b^{2} e^{3} h^{3} p^{2} q^{2} x}{24 f^{3}} + \frac{b^{2} e^{3} h^{3} p q^{2} x \log{\left(d \right)}}{2 f^{3}} + \frac{b^{2} e^{3} h^{3} p q x \log{\left(c \right)}}{2 f^{3}} - \frac{3 b^{2} e^{2} g^{2} h p^{2} q^{2} \log{\left(e + f x \right)}^{2}}{2 f^{2}} + \frac{9 b^{2} e^{2} g^{2} h p^{2} q^{2} \log{\left(e + f x \right)}}{2 f^{2}} - \frac{3 b^{2} e^{2} g^{2} h p q^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f^{2}} - \frac{3 b^{2} e^{2} g^{2} h p q \log{\left(c \right)} \log{\left(e + f x \right)}}{f^{2}} - \frac{2 b^{2} e^{2} g h^{2} p^{2} q^{2} x \log{\left(e + f x \right)}}{f^{2}} + \frac{11 b^{2} e^{2} g h^{2} p^{2} q^{2} x}{3 f^{2}} - \frac{2 b^{2} e^{2} g h^{2} p q^{2} x \log{\left(d \right)}}{f^{2}} - \frac{2 b^{2} e^{2} g h^{2} p q x \log{\left(c \right)}}{f^{2}} - \frac{b^{2} e^{2} h^{3} p^{2} q^{2} x^{2} \log{\left(e + f x \right)}}{4 f^{2}} + \frac{13 b^{2} e^{2} h^{3} p^{2} q^{2} x^{2}}{48 f^{2}} - \frac{b^{2} e^{2} h^{3} p q^{2} x^{2} \log{\left(d \right)}}{4 f^{2}} - \frac{b^{2} e^{2} h^{3} p q x^{2} \log{\left(c \right)}}{4 f^{2}} + \frac{b^{2} e g^{3} p^{2} q^{2} \log{\left(e + f x \right)}^{2}}{f} - \frac{2 b^{2} e g^{3} p^{2} q^{2} \log{\left(e + f x \right)}}{f} + \frac{2 b^{2} e g^{3} p q^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{2 b^{2} e g^{3} p q \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + \frac{3 b^{2} e g^{2} h p^{2} q^{2} x \log{\left(e + f x \right)}}{f} - \frac{9 b^{2} e g^{2} h p^{2} q^{2} x}{2 f} + \frac{3 b^{2} e g^{2} h p q^{2} x \log{\left(d \right)}}{f} + \frac{3 b^{2} e g^{2} h p q x \log{\left(c \right)}}{f} + \frac{b^{2} e g h^{2} p^{2} q^{2} x^{2} \log{\left(e + f x \right)}}{f} - \frac{5 b^{2} e g h^{2} p^{2} q^{2} x^{2}}{6 f} + \frac{b^{2} e g h^{2} p q^{2} x^{2} \log{\left(d \right)}}{f} + \frac{b^{2} e g h^{2} p q x^{2} \log{\left(c \right)}}{f} + \frac{b^{2} e h^{3} p^{2} q^{2} x^{3} \log{\left(e + f x \right)}}{6 f} - \frac{7 b^{2} e h^{3} p^{2} q^{2} x^{3}}{72 f} + \frac{b^{2} e h^{3} p q^{2} x^{3} \log{\left(d \right)}}{6 f} + \frac{b^{2} e h^{3} p q x^{3} \log{\left(c \right)}}{6 f} + b^{2} g^{3} p^{2} q^{2} x \log{\left(e + f x \right)}^{2} - 2 b^{2} g^{3} p^{2} q^{2} x \log{\left(e + f x \right)} + 2 b^{2} g^{3} p^{2} q^{2} x + 2 b^{2} g^{3} p q^{2} x \log{\left(d \right)} \log{\left(e + f x \right)} - 2 b^{2} g^{3} p q^{2} x \log{\left(d \right)} + 2 b^{2} g^{3} p q x \log{\left(c \right)} \log{\left(e + f x \right)} - 2 b^{2} g^{3} p q x \log{\left(c \right)} + b^{2} g^{3} q^{2} x \log{\left(d \right)}^{2} + 2 b^{2} g^{3} q x \log{\left(c \right)} \log{\left(d \right)} + b^{2} g^{3} x \log{\left(c \right)}^{2} + \frac{3 b^{2} g^{2} h p^{2} q^{2} x^{2} \log{\left(e + f x \right)}^{2}}{2} - \frac{3 b^{2} g^{2} h p^{2} q^{2} x^{2} \log{\left(e + f x \right)}}{2} + \frac{3 b^{2} g^{2} h p^{2} q^{2} x^{2}}{4} + 3 b^{2} g^{2} h p q^{2} x^{2} \log{\left(d \right)} \log{\left(e + f x \right)} - \frac{3 b^{2} g^{2} h p q^{2} x^{2} \log{\left(d \right)}}{2} + 3 b^{2} g^{2} h p q x^{2} \log{\left(c \right)} \log{\left(e + f x \right)} - \frac{3 b^{2} g^{2} h p q x^{2} \log{\left(c \right)}}{2} + \frac{3 b^{2} g^{2} h q^{2} x^{2} \log{\left(d \right)}^{2}}{2} + 3 b^{2} g^{2} h q x^{2} \log{\left(c \right)} \log{\left(d \right)} + \frac{3 b^{2} g^{2} h x^{2} \log{\left(c \right)}^{2}}{2} + b^{2} g h^{2} p^{2} q^{2} x^{3} \log{\left(e + f x \right)}^{2} - \frac{2 b^{2} g h^{2} p^{2} q^{2} x^{3} \log{\left(e + f x \right)}}{3} + \frac{2 b^{2} g h^{2} p^{2} q^{2} x^{3}}{9} + 2 b^{2} g h^{2} p q^{2} x^{3} \log{\left(d \right)} \log{\left(e + f x \right)} - \frac{2 b^{2} g h^{2} p q^{2} x^{3} \log{\left(d \right)}}{3} + 2 b^{2} g h^{2} p q x^{3} \log{\left(c \right)} \log{\left(e + f x \right)} - \frac{2 b^{2} g h^{2} p q x^{3} \log{\left(c \right)}}{3} + b^{2} g h^{2} q^{2} x^{3} \log{\left(d \right)}^{2} + 2 b^{2} g h^{2} q x^{3} \log{\left(c \right)} \log{\left(d \right)} + b^{2} g h^{2} x^{3} \log{\left(c \right)}^{2} + \frac{b^{2} h^{3} p^{2} q^{2} x^{4} \log{\left(e + f x \right)}^{2}}{4} - \frac{b^{2} h^{3} p^{2} q^{2} x^{4} \log{\left(e + f x \right)}}{8} + \frac{b^{2} h^{3} p^{2} q^{2} x^{4}}{32} + \frac{b^{2} h^{3} p q^{2} x^{4} \log{\left(d \right)} \log{\left(e + f x \right)}}{2} - \frac{b^{2} h^{3} p q^{2} x^{4} \log{\left(d \right)}}{8} + \frac{b^{2} h^{3} p q x^{4} \log{\left(c \right)} \log{\left(e + f x \right)}}{2} - \frac{b^{2} h^{3} p q x^{4} \log{\left(c \right)}}{8} + \frac{b^{2} h^{3} q^{2} x^{4} \log{\left(d \right)}^{2}}{4} + \frac{b^{2} h^{3} q x^{4} \log{\left(c \right)} \log{\left(d \right)}}{2} + \frac{b^{2} h^{3} x^{4} \log{\left(c \right)}^{2}}{4} & \text{for}\: f \neq 0 \\\left(a + b \log{\left(c \left(d e^{p}\right)^{q} \right)}\right)^{2} \left(g^{3} x + \frac{3 g^{2} h x^{2}}{2} + g h^{2} x^{3} + \frac{h^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*g**3*x + 3*a**2*g**2*h*x**2/2 + a**2*g*h**2*x**3 + a**2*h**3*x**4/4 - a*b*e**4*h**3*p*q*log(e + f*x)/(2*f**4) + 2*a*b*e**3*g*h**2*p*q*log(e + f*x)/f**3 + a*b*e**3*h**3*p*q*x/(2*f**3) - 3*a*b*e**2*g**2*h*p*q*log(e + f*x)/f**2 - 2*a*b*e**2*g*h**2*p*q*x/f**2 - a*b*e**2*h**3*p*q*x**2/(4*f**2) + 2*a*b*e*g**3*p*q*log(e + f*x)/f + 3*a*b*e*g**2*h*p*q*x/f + a*b*e*g*h**2*p*q*x**2/f + a*b*e*h**3*p*q*x**3/(6*f) + 2*a*b*g**3*p*q*x*log(e + f*x) - 2*a*b*g**3*p*q*x + 2*a*b*g**3*q*x*log(d) + 2*a*b*g**3*x*log(c) + 3*a*b*g**2*h*p*q*x**2*log(e + f*x) - 3*a*b*g**2*h*p*q*x**2/2 + 3*a*b*g**2*h*q*x**2*log(d) + 3*a*b*g**2*h*x**2*log(c) + 2*a*b*g*h**2*p*q*x**3*log(e + f*x) - 2*a*b*g*h**2*p*q*x**3/3 + 2*a*b*g*h**2*q*x**3*log(d) + 2*a*b*g*h**2*x**3*log(c) + a*b*h**3*p*q*x**4*log(e + f*x)/2 - a*b*h**3*p*q*x**4/8 + a*b*h**3*q*x**4*log(d)/2 + a*b*h**3*x**4*log(c)/2 - b**2*e**4*h**3*p**2*q**2*log(e + f*x)**2/(4*f**4) + 25*b**2*e**4*h**3*p**2*q**2*log(e + f*x)/(24*f**4) - b**2*e**4*h**3*p*q**2*log(d)*log(e + f*x)/(2*f**4) - b**2*e**4*h**3*p*q*log(c)*log(e + f*x)/(2*f**4) + b**2*e**3*g*h**2*p**2*q**2*log(e + f*x)**2/f**3 - 11*b**2*e**3*g*h**2*p**2*q**2*log(e + f*x)/(3*f**3) + 2*b**2*e**3*g*h**2*p*q**2*log(d)*log(e + f*x)/f**3 + 2*b**2*e**3*g*h**2*p*q*log(c)*log(e + f*x)/f**3 + b**2*e**3*h**3*p**2*q**2*x*log(e + f*x)/(2*f**3) - 25*b**2*e**3*h**3*p**2*q**2*x/(24*f**3) + b**2*e**3*h**3*p*q**2*x*log(d)/(2*f**3) + b**2*e**3*h**3*p*q*x*log(c)/(2*f**3) - 3*b**2*e**2*g**2*h*p**2*q**2*log(e + f*x)**2/(2*f**2) + 9*b**2*e**2*g**2*h*p**2*q**2*log(e + f*x)/(2*f**2) - 3*b**2*e**2*g**2*h*p*q**2*log(d)*log(e + f*x)/f**2 - 3*b**2*e**2*g**2*h*p*q*log(c)*log(e + f*x)/f**2 - 2*b**2*e**2*g*h**2*p**2*q**2*x*log(e + f*x)/f**2 + 11*b**2*e**2*g*h**2*p**2*q**2*x/(3*f**2) - 2*b**2*e**2*g*h**2*p*q**2*x*log(d)/f**2 - 2*b**2*e**2*g*h**2*p*q*x*log(c)/f**2 - b**2*e**2*h**3*p**2*q**2*x**2*log(e + f*x)/(4*f**2) + 13*b**2*e**2*h**3*p**2*q**2*x**2/(48*f**2) - b**2*e**2*h**3*p*q**2*x**2*log(d)/(4*f**2) - b**2*e**2*h**3*p*q*x**2*log(c)/(4*f**2) + b**2*e*g**3*p**2*q**2*log(e + f*x)**2/f - 2*b**2*e*g**3*p**2*q**2*log(e + f*x)/f + 2*b**2*e*g**3*p*q**2*log(d)*log(e + f*x)/f + 2*b**2*e*g**3*p*q*log(c)*log(e + f*x)/f + 3*b**2*e*g**2*h*p**2*q**2*x*log(e + f*x)/f - 9*b**2*e*g**2*h*p**2*q**2*x/(2*f) + 3*b**2*e*g**2*h*p*q**2*x*log(d)/f + 3*b**2*e*g**2*h*p*q*x*log(c)/f + b**2*e*g*h**2*p**2*q**2*x**2*log(e + f*x)/f - 5*b**2*e*g*h**2*p**2*q**2*x**2/(6*f) + b**2*e*g*h**2*p*q**2*x**2*log(d)/f + b**2*e*g*h**2*p*q*x**2*log(c)/f + b**2*e*h**3*p**2*q**2*x**3*log(e + f*x)/(6*f) - 7*b**2*e*h**3*p**2*q**2*x**3/(72*f) + b**2*e*h**3*p*q**2*x**3*log(d)/(6*f) + b**2*e*h**3*p*q*x**3*log(c)/(6*f) + b**2*g**3*p**2*q**2*x*log(e + f*x)**2 - 2*b**2*g**3*p**2*q**2*x*log(e + f*x) + 2*b**2*g**3*p**2*q**2*x + 2*b**2*g**3*p*q**2*x*log(d)*log(e + f*x) - 2*b**2*g**3*p*q**2*x*log(d) + 2*b**2*g**3*p*q*x*log(c)*log(e + f*x) - 2*b**2*g**3*p*q*x*log(c) + b**2*g**3*q**2*x*log(d)**2 + 2*b**2*g**3*q*x*log(c)*log(d) + b**2*g**3*x*log(c)**2 + 3*b**2*g**2*h*p**2*q**2*x**2*log(e + f*x)**2/2 - 3*b**2*g**2*h*p**2*q**2*x**2*log(e + f*x)/2 + 3*b**2*g**2*h*p**2*q**2*x**2/4 + 3*b**2*g**2*h*p*q**2*x**2*log(d)*log(e + f*x) - 3*b**2*g**2*h*p*q**2*x**2*log(d)/2 + 3*b**2*g**2*h*p*q*x**2*log(c)*log(e + f*x) - 3*b**2*g**2*h*p*q*x**2*log(c)/2 + 3*b**2*g**2*h*q**2*x**2*log(d)**2/2 + 3*b**2*g**2*h*q*x**2*log(c)*log(d) + 3*b**2*g**2*h*x**2*log(c)**2/2 + b**2*g*h**2*p**2*q**2*x**3*log(e + f*x)**2 - 2*b**2*g*h**2*p**2*q**2*x**3*log(e + f*x)/3 + 2*b**2*g*h**2*p**2*q**2*x**3/9 + 2*b**2*g*h**2*p*q**2*x**3*log(d)*log(e + f*x) - 2*b**2*g*h**2*p*q**2*x**3*log(d)/3 + 2*b**2*g*h**2*p*q*x**3*log(c)*log(e + f*x) - 2*b**2*g*h**2*p*q*x**3*log(c)/3 + b**2*g*h**2*q**2*x**3*log(d)**2 + 2*b**2*g*h**2*q*x**3*log(c)*log(d) + b**2*g*h**2*x**3*log(c)**2 + b**2*h**3*p**2*q**2*x**4*log(e + f*x)**2/4 - b**2*h**3*p**2*q**2*x**4*log(e + f*x)/8 + b**2*h**3*p**2*q**2*x**4/32 + b**2*h**3*p*q**2*x**4*log(d)*log(e + f*x)/2 - b**2*h**3*p*q**2*x**4*log(d)/8 + b**2*h**3*p*q*x**4*log(c)*log(e + f*x)/2 - b**2*h**3*p*q*x**4*log(c)/8 + b**2*h**3*q**2*x**4*log(d)**2/4 + b**2*h**3*q*x**4*log(c)*log(d)/2 + b**2*h**3*x**4*log(c)**2/4, Ne(f, 0)), ((a + b*log(c*(d*e**p)**q))**2*(g**3*x + 3*g**2*h*x**2/2 + g*h**2*x**3 + h**3*x**4/4), True))","A",0
429,1,1692,0,32.825654," ","integrate((h*x+g)**2*(a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)","\begin{cases} a^{2} g^{2} x + a^{2} g h x^{2} + \frac{a^{2} h^{2} x^{3}}{3} + \frac{2 a b e^{3} h^{2} p q \log{\left(e + f x \right)}}{3 f^{3}} - \frac{2 a b e^{2} g h p q \log{\left(e + f x \right)}}{f^{2}} - \frac{2 a b e^{2} h^{2} p q x}{3 f^{2}} + \frac{2 a b e g^{2} p q \log{\left(e + f x \right)}}{f} + \frac{2 a b e g h p q x}{f} + \frac{a b e h^{2} p q x^{2}}{3 f} + 2 a b g^{2} p q x \log{\left(e + f x \right)} - 2 a b g^{2} p q x + 2 a b g^{2} q x \log{\left(d \right)} + 2 a b g^{2} x \log{\left(c \right)} + 2 a b g h p q x^{2} \log{\left(e + f x \right)} - a b g h p q x^{2} + 2 a b g h q x^{2} \log{\left(d \right)} + 2 a b g h x^{2} \log{\left(c \right)} + \frac{2 a b h^{2} p q x^{3} \log{\left(e + f x \right)}}{3} - \frac{2 a b h^{2} p q x^{3}}{9} + \frac{2 a b h^{2} q x^{3} \log{\left(d \right)}}{3} + \frac{2 a b h^{2} x^{3} \log{\left(c \right)}}{3} + \frac{b^{2} e^{3} h^{2} p^{2} q^{2} \log{\left(e + f x \right)}^{2}}{3 f^{3}} - \frac{11 b^{2} e^{3} h^{2} p^{2} q^{2} \log{\left(e + f x \right)}}{9 f^{3}} + \frac{2 b^{2} e^{3} h^{2} p q^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{3 f^{3}} + \frac{2 b^{2} e^{3} h^{2} p q \log{\left(c \right)} \log{\left(e + f x \right)}}{3 f^{3}} - \frac{b^{2} e^{2} g h p^{2} q^{2} \log{\left(e + f x \right)}^{2}}{f^{2}} + \frac{3 b^{2} e^{2} g h p^{2} q^{2} \log{\left(e + f x \right)}}{f^{2}} - \frac{2 b^{2} e^{2} g h p q^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f^{2}} - \frac{2 b^{2} e^{2} g h p q \log{\left(c \right)} \log{\left(e + f x \right)}}{f^{2}} - \frac{2 b^{2} e^{2} h^{2} p^{2} q^{2} x \log{\left(e + f x \right)}}{3 f^{2}} + \frac{11 b^{2} e^{2} h^{2} p^{2} q^{2} x}{9 f^{2}} - \frac{2 b^{2} e^{2} h^{2} p q^{2} x \log{\left(d \right)}}{3 f^{2}} - \frac{2 b^{2} e^{2} h^{2} p q x \log{\left(c \right)}}{3 f^{2}} + \frac{b^{2} e g^{2} p^{2} q^{2} \log{\left(e + f x \right)}^{2}}{f} - \frac{2 b^{2} e g^{2} p^{2} q^{2} \log{\left(e + f x \right)}}{f} + \frac{2 b^{2} e g^{2} p q^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{2 b^{2} e g^{2} p q \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + \frac{2 b^{2} e g h p^{2} q^{2} x \log{\left(e + f x \right)}}{f} - \frac{3 b^{2} e g h p^{2} q^{2} x}{f} + \frac{2 b^{2} e g h p q^{2} x \log{\left(d \right)}}{f} + \frac{2 b^{2} e g h p q x \log{\left(c \right)}}{f} + \frac{b^{2} e h^{2} p^{2} q^{2} x^{2} \log{\left(e + f x \right)}}{3 f} - \frac{5 b^{2} e h^{2} p^{2} q^{2} x^{2}}{18 f} + \frac{b^{2} e h^{2} p q^{2} x^{2} \log{\left(d \right)}}{3 f} + \frac{b^{2} e h^{2} p q x^{2} \log{\left(c \right)}}{3 f} + b^{2} g^{2} p^{2} q^{2} x \log{\left(e + f x \right)}^{2} - 2 b^{2} g^{2} p^{2} q^{2} x \log{\left(e + f x \right)} + 2 b^{2} g^{2} p^{2} q^{2} x + 2 b^{2} g^{2} p q^{2} x \log{\left(d \right)} \log{\left(e + f x \right)} - 2 b^{2} g^{2} p q^{2} x \log{\left(d \right)} + 2 b^{2} g^{2} p q x \log{\left(c \right)} \log{\left(e + f x \right)} - 2 b^{2} g^{2} p q x \log{\left(c \right)} + b^{2} g^{2} q^{2} x \log{\left(d \right)}^{2} + 2 b^{2} g^{2} q x \log{\left(c \right)} \log{\left(d \right)} + b^{2} g^{2} x \log{\left(c \right)}^{2} + b^{2} g h p^{2} q^{2} x^{2} \log{\left(e + f x \right)}^{2} - b^{2} g h p^{2} q^{2} x^{2} \log{\left(e + f x \right)} + \frac{b^{2} g h p^{2} q^{2} x^{2}}{2} + 2 b^{2} g h p q^{2} x^{2} \log{\left(d \right)} \log{\left(e + f x \right)} - b^{2} g h p q^{2} x^{2} \log{\left(d \right)} + 2 b^{2} g h p q x^{2} \log{\left(c \right)} \log{\left(e + f x \right)} - b^{2} g h p q x^{2} \log{\left(c \right)} + b^{2} g h q^{2} x^{2} \log{\left(d \right)}^{2} + 2 b^{2} g h q x^{2} \log{\left(c \right)} \log{\left(d \right)} + b^{2} g h x^{2} \log{\left(c \right)}^{2} + \frac{b^{2} h^{2} p^{2} q^{2} x^{3} \log{\left(e + f x \right)}^{2}}{3} - \frac{2 b^{2} h^{2} p^{2} q^{2} x^{3} \log{\left(e + f x \right)}}{9} + \frac{2 b^{2} h^{2} p^{2} q^{2} x^{3}}{27} + \frac{2 b^{2} h^{2} p q^{2} x^{3} \log{\left(d \right)} \log{\left(e + f x \right)}}{3} - \frac{2 b^{2} h^{2} p q^{2} x^{3} \log{\left(d \right)}}{9} + \frac{2 b^{2} h^{2} p q x^{3} \log{\left(c \right)} \log{\left(e + f x \right)}}{3} - \frac{2 b^{2} h^{2} p q x^{3} \log{\left(c \right)}}{9} + \frac{b^{2} h^{2} q^{2} x^{3} \log{\left(d \right)}^{2}}{3} + \frac{2 b^{2} h^{2} q x^{3} \log{\left(c \right)} \log{\left(d \right)}}{3} + \frac{b^{2} h^{2} x^{3} \log{\left(c \right)}^{2}}{3} & \text{for}\: f \neq 0 \\\left(a + b \log{\left(c \left(d e^{p}\right)^{q} \right)}\right)^{2} \left(g^{2} x + g h x^{2} + \frac{h^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*g**2*x + a**2*g*h*x**2 + a**2*h**2*x**3/3 + 2*a*b*e**3*h**2*p*q*log(e + f*x)/(3*f**3) - 2*a*b*e**2*g*h*p*q*log(e + f*x)/f**2 - 2*a*b*e**2*h**2*p*q*x/(3*f**2) + 2*a*b*e*g**2*p*q*log(e + f*x)/f + 2*a*b*e*g*h*p*q*x/f + a*b*e*h**2*p*q*x**2/(3*f) + 2*a*b*g**2*p*q*x*log(e + f*x) - 2*a*b*g**2*p*q*x + 2*a*b*g**2*q*x*log(d) + 2*a*b*g**2*x*log(c) + 2*a*b*g*h*p*q*x**2*log(e + f*x) - a*b*g*h*p*q*x**2 + 2*a*b*g*h*q*x**2*log(d) + 2*a*b*g*h*x**2*log(c) + 2*a*b*h**2*p*q*x**3*log(e + f*x)/3 - 2*a*b*h**2*p*q*x**3/9 + 2*a*b*h**2*q*x**3*log(d)/3 + 2*a*b*h**2*x**3*log(c)/3 + b**2*e**3*h**2*p**2*q**2*log(e + f*x)**2/(3*f**3) - 11*b**2*e**3*h**2*p**2*q**2*log(e + f*x)/(9*f**3) + 2*b**2*e**3*h**2*p*q**2*log(d)*log(e + f*x)/(3*f**3) + 2*b**2*e**3*h**2*p*q*log(c)*log(e + f*x)/(3*f**3) - b**2*e**2*g*h*p**2*q**2*log(e + f*x)**2/f**2 + 3*b**2*e**2*g*h*p**2*q**2*log(e + f*x)/f**2 - 2*b**2*e**2*g*h*p*q**2*log(d)*log(e + f*x)/f**2 - 2*b**2*e**2*g*h*p*q*log(c)*log(e + f*x)/f**2 - 2*b**2*e**2*h**2*p**2*q**2*x*log(e + f*x)/(3*f**2) + 11*b**2*e**2*h**2*p**2*q**2*x/(9*f**2) - 2*b**2*e**2*h**2*p*q**2*x*log(d)/(3*f**2) - 2*b**2*e**2*h**2*p*q*x*log(c)/(3*f**2) + b**2*e*g**2*p**2*q**2*log(e + f*x)**2/f - 2*b**2*e*g**2*p**2*q**2*log(e + f*x)/f + 2*b**2*e*g**2*p*q**2*log(d)*log(e + f*x)/f + 2*b**2*e*g**2*p*q*log(c)*log(e + f*x)/f + 2*b**2*e*g*h*p**2*q**2*x*log(e + f*x)/f - 3*b**2*e*g*h*p**2*q**2*x/f + 2*b**2*e*g*h*p*q**2*x*log(d)/f + 2*b**2*e*g*h*p*q*x*log(c)/f + b**2*e*h**2*p**2*q**2*x**2*log(e + f*x)/(3*f) - 5*b**2*e*h**2*p**2*q**2*x**2/(18*f) + b**2*e*h**2*p*q**2*x**2*log(d)/(3*f) + b**2*e*h**2*p*q*x**2*log(c)/(3*f) + b**2*g**2*p**2*q**2*x*log(e + f*x)**2 - 2*b**2*g**2*p**2*q**2*x*log(e + f*x) + 2*b**2*g**2*p**2*q**2*x + 2*b**2*g**2*p*q**2*x*log(d)*log(e + f*x) - 2*b**2*g**2*p*q**2*x*log(d) + 2*b**2*g**2*p*q*x*log(c)*log(e + f*x) - 2*b**2*g**2*p*q*x*log(c) + b**2*g**2*q**2*x*log(d)**2 + 2*b**2*g**2*q*x*log(c)*log(d) + b**2*g**2*x*log(c)**2 + b**2*g*h*p**2*q**2*x**2*log(e + f*x)**2 - b**2*g*h*p**2*q**2*x**2*log(e + f*x) + b**2*g*h*p**2*q**2*x**2/2 + 2*b**2*g*h*p*q**2*x**2*log(d)*log(e + f*x) - b**2*g*h*p*q**2*x**2*log(d) + 2*b**2*g*h*p*q*x**2*log(c)*log(e + f*x) - b**2*g*h*p*q*x**2*log(c) + b**2*g*h*q**2*x**2*log(d)**2 + 2*b**2*g*h*q*x**2*log(c)*log(d) + b**2*g*h*x**2*log(c)**2 + b**2*h**2*p**2*q**2*x**3*log(e + f*x)**2/3 - 2*b**2*h**2*p**2*q**2*x**3*log(e + f*x)/9 + 2*b**2*h**2*p**2*q**2*x**3/27 + 2*b**2*h**2*p*q**2*x**3*log(d)*log(e + f*x)/3 - 2*b**2*h**2*p*q**2*x**3*log(d)/9 + 2*b**2*h**2*p*q*x**3*log(c)*log(e + f*x)/3 - 2*b**2*h**2*p*q*x**3*log(c)/9 + b**2*h**2*q**2*x**3*log(d)**2/3 + 2*b**2*h**2*q*x**3*log(c)*log(d)/3 + b**2*h**2*x**3*log(c)**2/3, Ne(f, 0)), ((a + b*log(c*(d*e**p)**q))**2*(g**2*x + g*h*x**2 + h**2*x**3/3), True))","A",0
430,1,879,0,12.690101," ","integrate((h*x+g)*(a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)","\begin{cases} a^{2} g x + \frac{a^{2} h x^{2}}{2} - \frac{a b e^{2} h p q \log{\left(e + f x \right)}}{f^{2}} + \frac{2 a b e g p q \log{\left(e + f x \right)}}{f} + \frac{a b e h p q x}{f} + 2 a b g p q x \log{\left(e + f x \right)} - 2 a b g p q x + 2 a b g q x \log{\left(d \right)} + 2 a b g x \log{\left(c \right)} + a b h p q x^{2} \log{\left(e + f x \right)} - \frac{a b h p q x^{2}}{2} + a b h q x^{2} \log{\left(d \right)} + a b h x^{2} \log{\left(c \right)} - \frac{b^{2} e^{2} h p^{2} q^{2} \log{\left(e + f x \right)}^{2}}{2 f^{2}} + \frac{3 b^{2} e^{2} h p^{2} q^{2} \log{\left(e + f x \right)}}{2 f^{2}} - \frac{b^{2} e^{2} h p q^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f^{2}} - \frac{b^{2} e^{2} h p q \log{\left(c \right)} \log{\left(e + f x \right)}}{f^{2}} + \frac{b^{2} e g p^{2} q^{2} \log{\left(e + f x \right)}^{2}}{f} - \frac{2 b^{2} e g p^{2} q^{2} \log{\left(e + f x \right)}}{f} + \frac{2 b^{2} e g p q^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{2 b^{2} e g p q \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + \frac{b^{2} e h p^{2} q^{2} x \log{\left(e + f x \right)}}{f} - \frac{3 b^{2} e h p^{2} q^{2} x}{2 f} + \frac{b^{2} e h p q^{2} x \log{\left(d \right)}}{f} + \frac{b^{2} e h p q x \log{\left(c \right)}}{f} + b^{2} g p^{2} q^{2} x \log{\left(e + f x \right)}^{2} - 2 b^{2} g p^{2} q^{2} x \log{\left(e + f x \right)} + 2 b^{2} g p^{2} q^{2} x + 2 b^{2} g p q^{2} x \log{\left(d \right)} \log{\left(e + f x \right)} - 2 b^{2} g p q^{2} x \log{\left(d \right)} + 2 b^{2} g p q x \log{\left(c \right)} \log{\left(e + f x \right)} - 2 b^{2} g p q x \log{\left(c \right)} + b^{2} g q^{2} x \log{\left(d \right)}^{2} + 2 b^{2} g q x \log{\left(c \right)} \log{\left(d \right)} + b^{2} g x \log{\left(c \right)}^{2} + \frac{b^{2} h p^{2} q^{2} x^{2} \log{\left(e + f x \right)}^{2}}{2} - \frac{b^{2} h p^{2} q^{2} x^{2} \log{\left(e + f x \right)}}{2} + \frac{b^{2} h p^{2} q^{2} x^{2}}{4} + b^{2} h p q^{2} x^{2} \log{\left(d \right)} \log{\left(e + f x \right)} - \frac{b^{2} h p q^{2} x^{2} \log{\left(d \right)}}{2} + b^{2} h p q x^{2} \log{\left(c \right)} \log{\left(e + f x \right)} - \frac{b^{2} h p q x^{2} \log{\left(c \right)}}{2} + \frac{b^{2} h q^{2} x^{2} \log{\left(d \right)}^{2}}{2} + b^{2} h q x^{2} \log{\left(c \right)} \log{\left(d \right)} + \frac{b^{2} h x^{2} \log{\left(c \right)}^{2}}{2} & \text{for}\: f \neq 0 \\\left(a + b \log{\left(c \left(d e^{p}\right)^{q} \right)}\right)^{2} \left(g x + \frac{h x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*g*x + a**2*h*x**2/2 - a*b*e**2*h*p*q*log(e + f*x)/f**2 + 2*a*b*e*g*p*q*log(e + f*x)/f + a*b*e*h*p*q*x/f + 2*a*b*g*p*q*x*log(e + f*x) - 2*a*b*g*p*q*x + 2*a*b*g*q*x*log(d) + 2*a*b*g*x*log(c) + a*b*h*p*q*x**2*log(e + f*x) - a*b*h*p*q*x**2/2 + a*b*h*q*x**2*log(d) + a*b*h*x**2*log(c) - b**2*e**2*h*p**2*q**2*log(e + f*x)**2/(2*f**2) + 3*b**2*e**2*h*p**2*q**2*log(e + f*x)/(2*f**2) - b**2*e**2*h*p*q**2*log(d)*log(e + f*x)/f**2 - b**2*e**2*h*p*q*log(c)*log(e + f*x)/f**2 + b**2*e*g*p**2*q**2*log(e + f*x)**2/f - 2*b**2*e*g*p**2*q**2*log(e + f*x)/f + 2*b**2*e*g*p*q**2*log(d)*log(e + f*x)/f + 2*b**2*e*g*p*q*log(c)*log(e + f*x)/f + b**2*e*h*p**2*q**2*x*log(e + f*x)/f - 3*b**2*e*h*p**2*q**2*x/(2*f) + b**2*e*h*p*q**2*x*log(d)/f + b**2*e*h*p*q*x*log(c)/f + b**2*g*p**2*q**2*x*log(e + f*x)**2 - 2*b**2*g*p**2*q**2*x*log(e + f*x) + 2*b**2*g*p**2*q**2*x + 2*b**2*g*p*q**2*x*log(d)*log(e + f*x) - 2*b**2*g*p*q**2*x*log(d) + 2*b**2*g*p*q*x*log(c)*log(e + f*x) - 2*b**2*g*p*q*x*log(c) + b**2*g*q**2*x*log(d)**2 + 2*b**2*g*q*x*log(c)*log(d) + b**2*g*x*log(c)**2 + b**2*h*p**2*q**2*x**2*log(e + f*x)**2/2 - b**2*h*p**2*q**2*x**2*log(e + f*x)/2 + b**2*h*p**2*q**2*x**2/4 + b**2*h*p*q**2*x**2*log(d)*log(e + f*x) - b**2*h*p*q**2*x**2*log(d)/2 + b**2*h*p*q*x**2*log(c)*log(e + f*x) - b**2*h*p*q*x**2*log(c)/2 + b**2*h*q**2*x**2*log(d)**2/2 + b**2*h*q*x**2*log(c)*log(d) + b**2*h*x**2*log(c)**2/2, Ne(f, 0)), ((a + b*log(c*(d*e**p)**q))**2*(g*x + h*x**2/2), True))","A",0
431,1,343,0,3.824967," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)","\begin{cases} a^{2} x + \frac{2 a b e p q \log{\left(e + f x \right)}}{f} + 2 a b p q x \log{\left(e + f x \right)} - 2 a b p q x + 2 a b q x \log{\left(d \right)} + 2 a b x \log{\left(c \right)} + \frac{b^{2} e p^{2} q^{2} \log{\left(e + f x \right)}^{2}}{f} - \frac{2 b^{2} e p^{2} q^{2} \log{\left(e + f x \right)}}{f} + \frac{2 b^{2} e p q^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{2 b^{2} e p q \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + b^{2} p^{2} q^{2} x \log{\left(e + f x \right)}^{2} - 2 b^{2} p^{2} q^{2} x \log{\left(e + f x \right)} + 2 b^{2} p^{2} q^{2} x + 2 b^{2} p q^{2} x \log{\left(d \right)} \log{\left(e + f x \right)} - 2 b^{2} p q^{2} x \log{\left(d \right)} + 2 b^{2} p q x \log{\left(c \right)} \log{\left(e + f x \right)} - 2 b^{2} p q x \log{\left(c \right)} + b^{2} q^{2} x \log{\left(d \right)}^{2} + 2 b^{2} q x \log{\left(c \right)} \log{\left(d \right)} + b^{2} x \log{\left(c \right)}^{2} & \text{for}\: f \neq 0 \\x \left(a + b \log{\left(c \left(d e^{p}\right)^{q} \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + 2*a*b*e*p*q*log(e + f*x)/f + 2*a*b*p*q*x*log(e + f*x) - 2*a*b*p*q*x + 2*a*b*q*x*log(d) + 2*a*b*x*log(c) + b**2*e*p**2*q**2*log(e + f*x)**2/f - 2*b**2*e*p**2*q**2*log(e + f*x)/f + 2*b**2*e*p*q**2*log(d)*log(e + f*x)/f + 2*b**2*e*p*q*log(c)*log(e + f*x)/f + b**2*p**2*q**2*x*log(e + f*x)**2 - 2*b**2*p**2*q**2*x*log(e + f*x) + 2*b**2*p**2*q**2*x + 2*b**2*p*q**2*x*log(d)*log(e + f*x) - 2*b**2*p*q**2*x*log(d) + 2*b**2*p*q*x*log(c)*log(e + f*x) - 2*b**2*p*q*x*log(c) + b**2*q**2*x*log(d)**2 + 2*b**2*q*x*log(c)*log(d) + b**2*x*log(c)**2, Ne(f, 0)), (x*(a + b*log(c*(d*e**p)**q))**2, True))","A",0
432,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**2/(h*x+g),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2}}{g + h x}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**2/(g + h*x), x)","F",0
433,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**2/(h*x+g)**2,x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2}}{\left(g + h x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**2/(g + h*x)**2, x)","F",0
434,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**2/(h*x+g)**3,x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2}}{\left(g + h x\right)^{3}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**2/(g + h*x)**3, x)","F",0
435,1,5008,0,80.861682," ","integrate((h*x+g)**2*(a+b*ln(c*(d*(f*x+e)**p)**q))**3,x)","\begin{cases} a^{3} g^{2} x + a^{3} g h x^{2} + \frac{a^{3} h^{2} x^{3}}{3} + \frac{a^{2} b e^{3} h^{2} p q \log{\left(e + f x \right)}}{f^{3}} - \frac{3 a^{2} b e^{2} g h p q \log{\left(e + f x \right)}}{f^{2}} - \frac{a^{2} b e^{2} h^{2} p q x}{f^{2}} + \frac{3 a^{2} b e g^{2} p q \log{\left(e + f x \right)}}{f} + \frac{3 a^{2} b e g h p q x}{f} + \frac{a^{2} b e h^{2} p q x^{2}}{2 f} + 3 a^{2} b g^{2} p q x \log{\left(e + f x \right)} - 3 a^{2} b g^{2} p q x + 3 a^{2} b g^{2} q x \log{\left(d \right)} + 3 a^{2} b g^{2} x \log{\left(c \right)} + 3 a^{2} b g h p q x^{2} \log{\left(e + f x \right)} - \frac{3 a^{2} b g h p q x^{2}}{2} + 3 a^{2} b g h q x^{2} \log{\left(d \right)} + 3 a^{2} b g h x^{2} \log{\left(c \right)} + a^{2} b h^{2} p q x^{3} \log{\left(e + f x \right)} - \frac{a^{2} b h^{2} p q x^{3}}{3} + a^{2} b h^{2} q x^{3} \log{\left(d \right)} + a^{2} b h^{2} x^{3} \log{\left(c \right)} + \frac{a b^{2} e^{3} h^{2} p^{2} q^{2} \log{\left(e + f x \right)}^{2}}{f^{3}} - \frac{11 a b^{2} e^{3} h^{2} p^{2} q^{2} \log{\left(e + f x \right)}}{3 f^{3}} + \frac{2 a b^{2} e^{3} h^{2} p q^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f^{3}} + \frac{2 a b^{2} e^{3} h^{2} p q \log{\left(c \right)} \log{\left(e + f x \right)}}{f^{3}} - \frac{3 a b^{2} e^{2} g h p^{2} q^{2} \log{\left(e + f x \right)}^{2}}{f^{2}} + \frac{9 a b^{2} e^{2} g h p^{2} q^{2} \log{\left(e + f x \right)}}{f^{2}} - \frac{6 a b^{2} e^{2} g h p q^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f^{2}} - \frac{6 a b^{2} e^{2} g h p q \log{\left(c \right)} \log{\left(e + f x \right)}}{f^{2}} - \frac{2 a b^{2} e^{2} h^{2} p^{2} q^{2} x \log{\left(e + f x \right)}}{f^{2}} + \frac{11 a b^{2} e^{2} h^{2} p^{2} q^{2} x}{3 f^{2}} - \frac{2 a b^{2} e^{2} h^{2} p q^{2} x \log{\left(d \right)}}{f^{2}} - \frac{2 a b^{2} e^{2} h^{2} p q x \log{\left(c \right)}}{f^{2}} + \frac{3 a b^{2} e g^{2} p^{2} q^{2} \log{\left(e + f x \right)}^{2}}{f} - \frac{6 a b^{2} e g^{2} p^{2} q^{2} \log{\left(e + f x \right)}}{f} + \frac{6 a b^{2} e g^{2} p q^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{6 a b^{2} e g^{2} p q \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + \frac{6 a b^{2} e g h p^{2} q^{2} x \log{\left(e + f x \right)}}{f} - \frac{9 a b^{2} e g h p^{2} q^{2} x}{f} + \frac{6 a b^{2} e g h p q^{2} x \log{\left(d \right)}}{f} + \frac{6 a b^{2} e g h p q x \log{\left(c \right)}}{f} + \frac{a b^{2} e h^{2} p^{2} q^{2} x^{2} \log{\left(e + f x \right)}}{f} - \frac{5 a b^{2} e h^{2} p^{2} q^{2} x^{2}}{6 f} + \frac{a b^{2} e h^{2} p q^{2} x^{2} \log{\left(d \right)}}{f} + \frac{a b^{2} e h^{2} p q x^{2} \log{\left(c \right)}}{f} + 3 a b^{2} g^{2} p^{2} q^{2} x \log{\left(e + f x \right)}^{2} - 6 a b^{2} g^{2} p^{2} q^{2} x \log{\left(e + f x \right)} + 6 a b^{2} g^{2} p^{2} q^{2} x + 6 a b^{2} g^{2} p q^{2} x \log{\left(d \right)} \log{\left(e + f x \right)} - 6 a b^{2} g^{2} p q^{2} x \log{\left(d \right)} + 6 a b^{2} g^{2} p q x \log{\left(c \right)} \log{\left(e + f x \right)} - 6 a b^{2} g^{2} p q x \log{\left(c \right)} + 3 a b^{2} g^{2} q^{2} x \log{\left(d \right)}^{2} + 6 a b^{2} g^{2} q x \log{\left(c \right)} \log{\left(d \right)} + 3 a b^{2} g^{2} x \log{\left(c \right)}^{2} + 3 a b^{2} g h p^{2} q^{2} x^{2} \log{\left(e + f x \right)}^{2} - 3 a b^{2} g h p^{2} q^{2} x^{2} \log{\left(e + f x \right)} + \frac{3 a b^{2} g h p^{2} q^{2} x^{2}}{2} + 6 a b^{2} g h p q^{2} x^{2} \log{\left(d \right)} \log{\left(e + f x \right)} - 3 a b^{2} g h p q^{2} x^{2} \log{\left(d \right)} + 6 a b^{2} g h p q x^{2} \log{\left(c \right)} \log{\left(e + f x \right)} - 3 a b^{2} g h p q x^{2} \log{\left(c \right)} + 3 a b^{2} g h q^{2} x^{2} \log{\left(d \right)}^{2} + 6 a b^{2} g h q x^{2} \log{\left(c \right)} \log{\left(d \right)} + 3 a b^{2} g h x^{2} \log{\left(c \right)}^{2} + a b^{2} h^{2} p^{2} q^{2} x^{3} \log{\left(e + f x \right)}^{2} - \frac{2 a b^{2} h^{2} p^{2} q^{2} x^{3} \log{\left(e + f x \right)}}{3} + \frac{2 a b^{2} h^{2} p^{2} q^{2} x^{3}}{9} + 2 a b^{2} h^{2} p q^{2} x^{3} \log{\left(d \right)} \log{\left(e + f x \right)} - \frac{2 a b^{2} h^{2} p q^{2} x^{3} \log{\left(d \right)}}{3} + 2 a b^{2} h^{2} p q x^{3} \log{\left(c \right)} \log{\left(e + f x \right)} - \frac{2 a b^{2} h^{2} p q x^{3} \log{\left(c \right)}}{3} + a b^{2} h^{2} q^{2} x^{3} \log{\left(d \right)}^{2} + 2 a b^{2} h^{2} q x^{3} \log{\left(c \right)} \log{\left(d \right)} + a b^{2} h^{2} x^{3} \log{\left(c \right)}^{2} + \frac{b^{3} e^{3} h^{2} p^{3} q^{3} \log{\left(e + f x \right)}^{3}}{3 f^{3}} - \frac{11 b^{3} e^{3} h^{2} p^{3} q^{3} \log{\left(e + f x \right)}^{2}}{6 f^{3}} + \frac{85 b^{3} e^{3} h^{2} p^{3} q^{3} \log{\left(e + f x \right)}}{18 f^{3}} + \frac{b^{3} e^{3} h^{2} p^{2} q^{3} \log{\left(d \right)} \log{\left(e + f x \right)}^{2}}{f^{3}} - \frac{11 b^{3} e^{3} h^{2} p^{2} q^{3} \log{\left(d \right)} \log{\left(e + f x \right)}}{3 f^{3}} + \frac{b^{3} e^{3} h^{2} p^{2} q^{2} \log{\left(c \right)} \log{\left(e + f x \right)}^{2}}{f^{3}} - \frac{11 b^{3} e^{3} h^{2} p^{2} q^{2} \log{\left(c \right)} \log{\left(e + f x \right)}}{3 f^{3}} + \frac{b^{3} e^{3} h^{2} p q^{3} \log{\left(d \right)}^{2} \log{\left(e + f x \right)}}{f^{3}} + \frac{2 b^{3} e^{3} h^{2} p q^{2} \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)}}{f^{3}} + \frac{b^{3} e^{3} h^{2} p q \log{\left(c \right)}^{2} \log{\left(e + f x \right)}}{f^{3}} - \frac{b^{3} e^{2} g h p^{3} q^{3} \log{\left(e + f x \right)}^{3}}{f^{2}} + \frac{9 b^{3} e^{2} g h p^{3} q^{3} \log{\left(e + f x \right)}^{2}}{2 f^{2}} - \frac{21 b^{3} e^{2} g h p^{3} q^{3} \log{\left(e + f x \right)}}{2 f^{2}} - \frac{3 b^{3} e^{2} g h p^{2} q^{3} \log{\left(d \right)} \log{\left(e + f x \right)}^{2}}{f^{2}} + \frac{9 b^{3} e^{2} g h p^{2} q^{3} \log{\left(d \right)} \log{\left(e + f x \right)}}{f^{2}} - \frac{3 b^{3} e^{2} g h p^{2} q^{2} \log{\left(c \right)} \log{\left(e + f x \right)}^{2}}{f^{2}} + \frac{9 b^{3} e^{2} g h p^{2} q^{2} \log{\left(c \right)} \log{\left(e + f x \right)}}{f^{2}} - \frac{3 b^{3} e^{2} g h p q^{3} \log{\left(d \right)}^{2} \log{\left(e + f x \right)}}{f^{2}} - \frac{6 b^{3} e^{2} g h p q^{2} \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)}}{f^{2}} - \frac{3 b^{3} e^{2} g h p q \log{\left(c \right)}^{2} \log{\left(e + f x \right)}}{f^{2}} - \frac{b^{3} e^{2} h^{2} p^{3} q^{3} x \log{\left(e + f x \right)}^{2}}{f^{2}} + \frac{11 b^{3} e^{2} h^{2} p^{3} q^{3} x \log{\left(e + f x \right)}}{3 f^{2}} - \frac{85 b^{3} e^{2} h^{2} p^{3} q^{3} x}{18 f^{2}} - \frac{2 b^{3} e^{2} h^{2} p^{2} q^{3} x \log{\left(d \right)} \log{\left(e + f x \right)}}{f^{2}} + \frac{11 b^{3} e^{2} h^{2} p^{2} q^{3} x \log{\left(d \right)}}{3 f^{2}} - \frac{2 b^{3} e^{2} h^{2} p^{2} q^{2} x \log{\left(c \right)} \log{\left(e + f x \right)}}{f^{2}} + \frac{11 b^{3} e^{2} h^{2} p^{2} q^{2} x \log{\left(c \right)}}{3 f^{2}} - \frac{b^{3} e^{2} h^{2} p q^{3} x \log{\left(d \right)}^{2}}{f^{2}} - \frac{2 b^{3} e^{2} h^{2} p q^{2} x \log{\left(c \right)} \log{\left(d \right)}}{f^{2}} - \frac{b^{3} e^{2} h^{2} p q x \log{\left(c \right)}^{2}}{f^{2}} + \frac{b^{3} e g^{2} p^{3} q^{3} \log{\left(e + f x \right)}^{3}}{f} - \frac{3 b^{3} e g^{2} p^{3} q^{3} \log{\left(e + f x \right)}^{2}}{f} + \frac{6 b^{3} e g^{2} p^{3} q^{3} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e g^{2} p^{2} q^{3} \log{\left(d \right)} \log{\left(e + f x \right)}^{2}}{f} - \frac{6 b^{3} e g^{2} p^{2} q^{3} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e g^{2} p^{2} q^{2} \log{\left(c \right)} \log{\left(e + f x \right)}^{2}}{f} - \frac{6 b^{3} e g^{2} p^{2} q^{2} \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e g^{2} p q^{3} \log{\left(d \right)}^{2} \log{\left(e + f x \right)}}{f} + \frac{6 b^{3} e g^{2} p q^{2} \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e g^{2} p q \log{\left(c \right)}^{2} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e g h p^{3} q^{3} x \log{\left(e + f x \right)}^{2}}{f} - \frac{9 b^{3} e g h p^{3} q^{3} x \log{\left(e + f x \right)}}{f} + \frac{21 b^{3} e g h p^{3} q^{3} x}{2 f} + \frac{6 b^{3} e g h p^{2} q^{3} x \log{\left(d \right)} \log{\left(e + f x \right)}}{f} - \frac{9 b^{3} e g h p^{2} q^{3} x \log{\left(d \right)}}{f} + \frac{6 b^{3} e g h p^{2} q^{2} x \log{\left(c \right)} \log{\left(e + f x \right)}}{f} - \frac{9 b^{3} e g h p^{2} q^{2} x \log{\left(c \right)}}{f} + \frac{3 b^{3} e g h p q^{3} x \log{\left(d \right)}^{2}}{f} + \frac{6 b^{3} e g h p q^{2} x \log{\left(c \right)} \log{\left(d \right)}}{f} + \frac{3 b^{3} e g h p q x \log{\left(c \right)}^{2}}{f} + \frac{b^{3} e h^{2} p^{3} q^{3} x^{2} \log{\left(e + f x \right)}^{2}}{2 f} - \frac{5 b^{3} e h^{2} p^{3} q^{3} x^{2} \log{\left(e + f x \right)}}{6 f} + \frac{19 b^{3} e h^{2} p^{3} q^{3} x^{2}}{36 f} + \frac{b^{3} e h^{2} p^{2} q^{3} x^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} - \frac{5 b^{3} e h^{2} p^{2} q^{3} x^{2} \log{\left(d \right)}}{6 f} + \frac{b^{3} e h^{2} p^{2} q^{2} x^{2} \log{\left(c \right)} \log{\left(e + f x \right)}}{f} - \frac{5 b^{3} e h^{2} p^{2} q^{2} x^{2} \log{\left(c \right)}}{6 f} + \frac{b^{3} e h^{2} p q^{3} x^{2} \log{\left(d \right)}^{2}}{2 f} + \frac{b^{3} e h^{2} p q^{2} x^{2} \log{\left(c \right)} \log{\left(d \right)}}{f} + \frac{b^{3} e h^{2} p q x^{2} \log{\left(c \right)}^{2}}{2 f} + b^{3} g^{2} p^{3} q^{3} x \log{\left(e + f x \right)}^{3} - 3 b^{3} g^{2} p^{3} q^{3} x \log{\left(e + f x \right)}^{2} + 6 b^{3} g^{2} p^{3} q^{3} x \log{\left(e + f x \right)} - 6 b^{3} g^{2} p^{3} q^{3} x + 3 b^{3} g^{2} p^{2} q^{3} x \log{\left(d \right)} \log{\left(e + f x \right)}^{2} - 6 b^{3} g^{2} p^{2} q^{3} x \log{\left(d \right)} \log{\left(e + f x \right)} + 6 b^{3} g^{2} p^{2} q^{3} x \log{\left(d \right)} + 3 b^{3} g^{2} p^{2} q^{2} x \log{\left(c \right)} \log{\left(e + f x \right)}^{2} - 6 b^{3} g^{2} p^{2} q^{2} x \log{\left(c \right)} \log{\left(e + f x \right)} + 6 b^{3} g^{2} p^{2} q^{2} x \log{\left(c \right)} + 3 b^{3} g^{2} p q^{3} x \log{\left(d \right)}^{2} \log{\left(e + f x \right)} - 3 b^{3} g^{2} p q^{3} x \log{\left(d \right)}^{2} + 6 b^{3} g^{2} p q^{2} x \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)} - 6 b^{3} g^{2} p q^{2} x \log{\left(c \right)} \log{\left(d \right)} + 3 b^{3} g^{2} p q x \log{\left(c \right)}^{2} \log{\left(e + f x \right)} - 3 b^{3} g^{2} p q x \log{\left(c \right)}^{2} + b^{3} g^{2} q^{3} x \log{\left(d \right)}^{3} + 3 b^{3} g^{2} q^{2} x \log{\left(c \right)} \log{\left(d \right)}^{2} + 3 b^{3} g^{2} q x \log{\left(c \right)}^{2} \log{\left(d \right)} + b^{3} g^{2} x \log{\left(c \right)}^{3} + b^{3} g h p^{3} q^{3} x^{2} \log{\left(e + f x \right)}^{3} - \frac{3 b^{3} g h p^{3} q^{3} x^{2} \log{\left(e + f x \right)}^{2}}{2} + \frac{3 b^{3} g h p^{3} q^{3} x^{2} \log{\left(e + f x \right)}}{2} - \frac{3 b^{3} g h p^{3} q^{3} x^{2}}{4} + 3 b^{3} g h p^{2} q^{3} x^{2} \log{\left(d \right)} \log{\left(e + f x \right)}^{2} - 3 b^{3} g h p^{2} q^{3} x^{2} \log{\left(d \right)} \log{\left(e + f x \right)} + \frac{3 b^{3} g h p^{2} q^{3} x^{2} \log{\left(d \right)}}{2} + 3 b^{3} g h p^{2} q^{2} x^{2} \log{\left(c \right)} \log{\left(e + f x \right)}^{2} - 3 b^{3} g h p^{2} q^{2} x^{2} \log{\left(c \right)} \log{\left(e + f x \right)} + \frac{3 b^{3} g h p^{2} q^{2} x^{2} \log{\left(c \right)}}{2} + 3 b^{3} g h p q^{3} x^{2} \log{\left(d \right)}^{2} \log{\left(e + f x \right)} - \frac{3 b^{3} g h p q^{3} x^{2} \log{\left(d \right)}^{2}}{2} + 6 b^{3} g h p q^{2} x^{2} \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)} - 3 b^{3} g h p q^{2} x^{2} \log{\left(c \right)} \log{\left(d \right)} + 3 b^{3} g h p q x^{2} \log{\left(c \right)}^{2} \log{\left(e + f x \right)} - \frac{3 b^{3} g h p q x^{2} \log{\left(c \right)}^{2}}{2} + b^{3} g h q^{3} x^{2} \log{\left(d \right)}^{3} + 3 b^{3} g h q^{2} x^{2} \log{\left(c \right)} \log{\left(d \right)}^{2} + 3 b^{3} g h q x^{2} \log{\left(c \right)}^{2} \log{\left(d \right)} + b^{3} g h x^{2} \log{\left(c \right)}^{3} + \frac{b^{3} h^{2} p^{3} q^{3} x^{3} \log{\left(e + f x \right)}^{3}}{3} - \frac{b^{3} h^{2} p^{3} q^{3} x^{3} \log{\left(e + f x \right)}^{2}}{3} + \frac{2 b^{3} h^{2} p^{3} q^{3} x^{3} \log{\left(e + f x \right)}}{9} - \frac{2 b^{3} h^{2} p^{3} q^{3} x^{3}}{27} + b^{3} h^{2} p^{2} q^{3} x^{3} \log{\left(d \right)} \log{\left(e + f x \right)}^{2} - \frac{2 b^{3} h^{2} p^{2} q^{3} x^{3} \log{\left(d \right)} \log{\left(e + f x \right)}}{3} + \frac{2 b^{3} h^{2} p^{2} q^{3} x^{3} \log{\left(d \right)}}{9} + b^{3} h^{2} p^{2} q^{2} x^{3} \log{\left(c \right)} \log{\left(e + f x \right)}^{2} - \frac{2 b^{3} h^{2} p^{2} q^{2} x^{3} \log{\left(c \right)} \log{\left(e + f x \right)}}{3} + \frac{2 b^{3} h^{2} p^{2} q^{2} x^{3} \log{\left(c \right)}}{9} + b^{3} h^{2} p q^{3} x^{3} \log{\left(d \right)}^{2} \log{\left(e + f x \right)} - \frac{b^{3} h^{2} p q^{3} x^{3} \log{\left(d \right)}^{2}}{3} + 2 b^{3} h^{2} p q^{2} x^{3} \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)} - \frac{2 b^{3} h^{2} p q^{2} x^{3} \log{\left(c \right)} \log{\left(d \right)}}{3} + b^{3} h^{2} p q x^{3} \log{\left(c \right)}^{2} \log{\left(e + f x \right)} - \frac{b^{3} h^{2} p q x^{3} \log{\left(c \right)}^{2}}{3} + \frac{b^{3} h^{2} q^{3} x^{3} \log{\left(d \right)}^{3}}{3} + b^{3} h^{2} q^{2} x^{3} \log{\left(c \right)} \log{\left(d \right)}^{2} + b^{3} h^{2} q x^{3} \log{\left(c \right)}^{2} \log{\left(d \right)} + \frac{b^{3} h^{2} x^{3} \log{\left(c \right)}^{3}}{3} & \text{for}\: f \neq 0 \\\left(a + b \log{\left(c \left(d e^{p}\right)^{q} \right)}\right)^{3} \left(g^{2} x + g h x^{2} + \frac{h^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*g**2*x + a**3*g*h*x**2 + a**3*h**2*x**3/3 + a**2*b*e**3*h**2*p*q*log(e + f*x)/f**3 - 3*a**2*b*e**2*g*h*p*q*log(e + f*x)/f**2 - a**2*b*e**2*h**2*p*q*x/f**2 + 3*a**2*b*e*g**2*p*q*log(e + f*x)/f + 3*a**2*b*e*g*h*p*q*x/f + a**2*b*e*h**2*p*q*x**2/(2*f) + 3*a**2*b*g**2*p*q*x*log(e + f*x) - 3*a**2*b*g**2*p*q*x + 3*a**2*b*g**2*q*x*log(d) + 3*a**2*b*g**2*x*log(c) + 3*a**2*b*g*h*p*q*x**2*log(e + f*x) - 3*a**2*b*g*h*p*q*x**2/2 + 3*a**2*b*g*h*q*x**2*log(d) + 3*a**2*b*g*h*x**2*log(c) + a**2*b*h**2*p*q*x**3*log(e + f*x) - a**2*b*h**2*p*q*x**3/3 + a**2*b*h**2*q*x**3*log(d) + a**2*b*h**2*x**3*log(c) + a*b**2*e**3*h**2*p**2*q**2*log(e + f*x)**2/f**3 - 11*a*b**2*e**3*h**2*p**2*q**2*log(e + f*x)/(3*f**3) + 2*a*b**2*e**3*h**2*p*q**2*log(d)*log(e + f*x)/f**3 + 2*a*b**2*e**3*h**2*p*q*log(c)*log(e + f*x)/f**3 - 3*a*b**2*e**2*g*h*p**2*q**2*log(e + f*x)**2/f**2 + 9*a*b**2*e**2*g*h*p**2*q**2*log(e + f*x)/f**2 - 6*a*b**2*e**2*g*h*p*q**2*log(d)*log(e + f*x)/f**2 - 6*a*b**2*e**2*g*h*p*q*log(c)*log(e + f*x)/f**2 - 2*a*b**2*e**2*h**2*p**2*q**2*x*log(e + f*x)/f**2 + 11*a*b**2*e**2*h**2*p**2*q**2*x/(3*f**2) - 2*a*b**2*e**2*h**2*p*q**2*x*log(d)/f**2 - 2*a*b**2*e**2*h**2*p*q*x*log(c)/f**2 + 3*a*b**2*e*g**2*p**2*q**2*log(e + f*x)**2/f - 6*a*b**2*e*g**2*p**2*q**2*log(e + f*x)/f + 6*a*b**2*e*g**2*p*q**2*log(d)*log(e + f*x)/f + 6*a*b**2*e*g**2*p*q*log(c)*log(e + f*x)/f + 6*a*b**2*e*g*h*p**2*q**2*x*log(e + f*x)/f - 9*a*b**2*e*g*h*p**2*q**2*x/f + 6*a*b**2*e*g*h*p*q**2*x*log(d)/f + 6*a*b**2*e*g*h*p*q*x*log(c)/f + a*b**2*e*h**2*p**2*q**2*x**2*log(e + f*x)/f - 5*a*b**2*e*h**2*p**2*q**2*x**2/(6*f) + a*b**2*e*h**2*p*q**2*x**2*log(d)/f + a*b**2*e*h**2*p*q*x**2*log(c)/f + 3*a*b**2*g**2*p**2*q**2*x*log(e + f*x)**2 - 6*a*b**2*g**2*p**2*q**2*x*log(e + f*x) + 6*a*b**2*g**2*p**2*q**2*x + 6*a*b**2*g**2*p*q**2*x*log(d)*log(e + f*x) - 6*a*b**2*g**2*p*q**2*x*log(d) + 6*a*b**2*g**2*p*q*x*log(c)*log(e + f*x) - 6*a*b**2*g**2*p*q*x*log(c) + 3*a*b**2*g**2*q**2*x*log(d)**2 + 6*a*b**2*g**2*q*x*log(c)*log(d) + 3*a*b**2*g**2*x*log(c)**2 + 3*a*b**2*g*h*p**2*q**2*x**2*log(e + f*x)**2 - 3*a*b**2*g*h*p**2*q**2*x**2*log(e + f*x) + 3*a*b**2*g*h*p**2*q**2*x**2/2 + 6*a*b**2*g*h*p*q**2*x**2*log(d)*log(e + f*x) - 3*a*b**2*g*h*p*q**2*x**2*log(d) + 6*a*b**2*g*h*p*q*x**2*log(c)*log(e + f*x) - 3*a*b**2*g*h*p*q*x**2*log(c) + 3*a*b**2*g*h*q**2*x**2*log(d)**2 + 6*a*b**2*g*h*q*x**2*log(c)*log(d) + 3*a*b**2*g*h*x**2*log(c)**2 + a*b**2*h**2*p**2*q**2*x**3*log(e + f*x)**2 - 2*a*b**2*h**2*p**2*q**2*x**3*log(e + f*x)/3 + 2*a*b**2*h**2*p**2*q**2*x**3/9 + 2*a*b**2*h**2*p*q**2*x**3*log(d)*log(e + f*x) - 2*a*b**2*h**2*p*q**2*x**3*log(d)/3 + 2*a*b**2*h**2*p*q*x**3*log(c)*log(e + f*x) - 2*a*b**2*h**2*p*q*x**3*log(c)/3 + a*b**2*h**2*q**2*x**3*log(d)**2 + 2*a*b**2*h**2*q*x**3*log(c)*log(d) + a*b**2*h**2*x**3*log(c)**2 + b**3*e**3*h**2*p**3*q**3*log(e + f*x)**3/(3*f**3) - 11*b**3*e**3*h**2*p**3*q**3*log(e + f*x)**2/(6*f**3) + 85*b**3*e**3*h**2*p**3*q**3*log(e + f*x)/(18*f**3) + b**3*e**3*h**2*p**2*q**3*log(d)*log(e + f*x)**2/f**3 - 11*b**3*e**3*h**2*p**2*q**3*log(d)*log(e + f*x)/(3*f**3) + b**3*e**3*h**2*p**2*q**2*log(c)*log(e + f*x)**2/f**3 - 11*b**3*e**3*h**2*p**2*q**2*log(c)*log(e + f*x)/(3*f**3) + b**3*e**3*h**2*p*q**3*log(d)**2*log(e + f*x)/f**3 + 2*b**3*e**3*h**2*p*q**2*log(c)*log(d)*log(e + f*x)/f**3 + b**3*e**3*h**2*p*q*log(c)**2*log(e + f*x)/f**3 - b**3*e**2*g*h*p**3*q**3*log(e + f*x)**3/f**2 + 9*b**3*e**2*g*h*p**3*q**3*log(e + f*x)**2/(2*f**2) - 21*b**3*e**2*g*h*p**3*q**3*log(e + f*x)/(2*f**2) - 3*b**3*e**2*g*h*p**2*q**3*log(d)*log(e + f*x)**2/f**2 + 9*b**3*e**2*g*h*p**2*q**3*log(d)*log(e + f*x)/f**2 - 3*b**3*e**2*g*h*p**2*q**2*log(c)*log(e + f*x)**2/f**2 + 9*b**3*e**2*g*h*p**2*q**2*log(c)*log(e + f*x)/f**2 - 3*b**3*e**2*g*h*p*q**3*log(d)**2*log(e + f*x)/f**2 - 6*b**3*e**2*g*h*p*q**2*log(c)*log(d)*log(e + f*x)/f**2 - 3*b**3*e**2*g*h*p*q*log(c)**2*log(e + f*x)/f**2 - b**3*e**2*h**2*p**3*q**3*x*log(e + f*x)**2/f**2 + 11*b**3*e**2*h**2*p**3*q**3*x*log(e + f*x)/(3*f**2) - 85*b**3*e**2*h**2*p**3*q**3*x/(18*f**2) - 2*b**3*e**2*h**2*p**2*q**3*x*log(d)*log(e + f*x)/f**2 + 11*b**3*e**2*h**2*p**2*q**3*x*log(d)/(3*f**2) - 2*b**3*e**2*h**2*p**2*q**2*x*log(c)*log(e + f*x)/f**2 + 11*b**3*e**2*h**2*p**2*q**2*x*log(c)/(3*f**2) - b**3*e**2*h**2*p*q**3*x*log(d)**2/f**2 - 2*b**3*e**2*h**2*p*q**2*x*log(c)*log(d)/f**2 - b**3*e**2*h**2*p*q*x*log(c)**2/f**2 + b**3*e*g**2*p**3*q**3*log(e + f*x)**3/f - 3*b**3*e*g**2*p**3*q**3*log(e + f*x)**2/f + 6*b**3*e*g**2*p**3*q**3*log(e + f*x)/f + 3*b**3*e*g**2*p**2*q**3*log(d)*log(e + f*x)**2/f - 6*b**3*e*g**2*p**2*q**3*log(d)*log(e + f*x)/f + 3*b**3*e*g**2*p**2*q**2*log(c)*log(e + f*x)**2/f - 6*b**3*e*g**2*p**2*q**2*log(c)*log(e + f*x)/f + 3*b**3*e*g**2*p*q**3*log(d)**2*log(e + f*x)/f + 6*b**3*e*g**2*p*q**2*log(c)*log(d)*log(e + f*x)/f + 3*b**3*e*g**2*p*q*log(c)**2*log(e + f*x)/f + 3*b**3*e*g*h*p**3*q**3*x*log(e + f*x)**2/f - 9*b**3*e*g*h*p**3*q**3*x*log(e + f*x)/f + 21*b**3*e*g*h*p**3*q**3*x/(2*f) + 6*b**3*e*g*h*p**2*q**3*x*log(d)*log(e + f*x)/f - 9*b**3*e*g*h*p**2*q**3*x*log(d)/f + 6*b**3*e*g*h*p**2*q**2*x*log(c)*log(e + f*x)/f - 9*b**3*e*g*h*p**2*q**2*x*log(c)/f + 3*b**3*e*g*h*p*q**3*x*log(d)**2/f + 6*b**3*e*g*h*p*q**2*x*log(c)*log(d)/f + 3*b**3*e*g*h*p*q*x*log(c)**2/f + b**3*e*h**2*p**3*q**3*x**2*log(e + f*x)**2/(2*f) - 5*b**3*e*h**2*p**3*q**3*x**2*log(e + f*x)/(6*f) + 19*b**3*e*h**2*p**3*q**3*x**2/(36*f) + b**3*e*h**2*p**2*q**3*x**2*log(d)*log(e + f*x)/f - 5*b**3*e*h**2*p**2*q**3*x**2*log(d)/(6*f) + b**3*e*h**2*p**2*q**2*x**2*log(c)*log(e + f*x)/f - 5*b**3*e*h**2*p**2*q**2*x**2*log(c)/(6*f) + b**3*e*h**2*p*q**3*x**2*log(d)**2/(2*f) + b**3*e*h**2*p*q**2*x**2*log(c)*log(d)/f + b**3*e*h**2*p*q*x**2*log(c)**2/(2*f) + b**3*g**2*p**3*q**3*x*log(e + f*x)**3 - 3*b**3*g**2*p**3*q**3*x*log(e + f*x)**2 + 6*b**3*g**2*p**3*q**3*x*log(e + f*x) - 6*b**3*g**2*p**3*q**3*x + 3*b**3*g**2*p**2*q**3*x*log(d)*log(e + f*x)**2 - 6*b**3*g**2*p**2*q**3*x*log(d)*log(e + f*x) + 6*b**3*g**2*p**2*q**3*x*log(d) + 3*b**3*g**2*p**2*q**2*x*log(c)*log(e + f*x)**2 - 6*b**3*g**2*p**2*q**2*x*log(c)*log(e + f*x) + 6*b**3*g**2*p**2*q**2*x*log(c) + 3*b**3*g**2*p*q**3*x*log(d)**2*log(e + f*x) - 3*b**3*g**2*p*q**3*x*log(d)**2 + 6*b**3*g**2*p*q**2*x*log(c)*log(d)*log(e + f*x) - 6*b**3*g**2*p*q**2*x*log(c)*log(d) + 3*b**3*g**2*p*q*x*log(c)**2*log(e + f*x) - 3*b**3*g**2*p*q*x*log(c)**2 + b**3*g**2*q**3*x*log(d)**3 + 3*b**3*g**2*q**2*x*log(c)*log(d)**2 + 3*b**3*g**2*q*x*log(c)**2*log(d) + b**3*g**2*x*log(c)**3 + b**3*g*h*p**3*q**3*x**2*log(e + f*x)**3 - 3*b**3*g*h*p**3*q**3*x**2*log(e + f*x)**2/2 + 3*b**3*g*h*p**3*q**3*x**2*log(e + f*x)/2 - 3*b**3*g*h*p**3*q**3*x**2/4 + 3*b**3*g*h*p**2*q**3*x**2*log(d)*log(e + f*x)**2 - 3*b**3*g*h*p**2*q**3*x**2*log(d)*log(e + f*x) + 3*b**3*g*h*p**2*q**3*x**2*log(d)/2 + 3*b**3*g*h*p**2*q**2*x**2*log(c)*log(e + f*x)**2 - 3*b**3*g*h*p**2*q**2*x**2*log(c)*log(e + f*x) + 3*b**3*g*h*p**2*q**2*x**2*log(c)/2 + 3*b**3*g*h*p*q**3*x**2*log(d)**2*log(e + f*x) - 3*b**3*g*h*p*q**3*x**2*log(d)**2/2 + 6*b**3*g*h*p*q**2*x**2*log(c)*log(d)*log(e + f*x) - 3*b**3*g*h*p*q**2*x**2*log(c)*log(d) + 3*b**3*g*h*p*q*x**2*log(c)**2*log(e + f*x) - 3*b**3*g*h*p*q*x**2*log(c)**2/2 + b**3*g*h*q**3*x**2*log(d)**3 + 3*b**3*g*h*q**2*x**2*log(c)*log(d)**2 + 3*b**3*g*h*q*x**2*log(c)**2*log(d) + b**3*g*h*x**2*log(c)**3 + b**3*h**2*p**3*q**3*x**3*log(e + f*x)**3/3 - b**3*h**2*p**3*q**3*x**3*log(e + f*x)**2/3 + 2*b**3*h**2*p**3*q**3*x**3*log(e + f*x)/9 - 2*b**3*h**2*p**3*q**3*x**3/27 + b**3*h**2*p**2*q**3*x**3*log(d)*log(e + f*x)**2 - 2*b**3*h**2*p**2*q**3*x**3*log(d)*log(e + f*x)/3 + 2*b**3*h**2*p**2*q**3*x**3*log(d)/9 + b**3*h**2*p**2*q**2*x**3*log(c)*log(e + f*x)**2 - 2*b**3*h**2*p**2*q**2*x**3*log(c)*log(e + f*x)/3 + 2*b**3*h**2*p**2*q**2*x**3*log(c)/9 + b**3*h**2*p*q**3*x**3*log(d)**2*log(e + f*x) - b**3*h**2*p*q**3*x**3*log(d)**2/3 + 2*b**3*h**2*p*q**2*x**3*log(c)*log(d)*log(e + f*x) - 2*b**3*h**2*p*q**2*x**3*log(c)*log(d)/3 + b**3*h**2*p*q*x**3*log(c)**2*log(e + f*x) - b**3*h**2*p*q*x**3*log(c)**2/3 + b**3*h**2*q**3*x**3*log(d)**3/3 + b**3*h**2*q**2*x**3*log(c)*log(d)**2 + b**3*h**2*q*x**3*log(c)**2*log(d) + b**3*h**2*x**3*log(c)**3/3, Ne(f, 0)), ((a + b*log(c*(d*e**p)**q))**3*(g**2*x + g*h*x**2 + h**2*x**3/3), True))","A",0
436,1,2756,0,28.215607," ","integrate((h*x+g)*(a+b*ln(c*(d*(f*x+e)**p)**q))**3,x)","\begin{cases} a^{3} g x + \frac{a^{3} h x^{2}}{2} - \frac{3 a^{2} b e^{2} h p q \log{\left(e + f x \right)}}{2 f^{2}} + \frac{3 a^{2} b e g p q \log{\left(e + f x \right)}}{f} + \frac{3 a^{2} b e h p q x}{2 f} + 3 a^{2} b g p q x \log{\left(e + f x \right)} - 3 a^{2} b g p q x + 3 a^{2} b g q x \log{\left(d \right)} + 3 a^{2} b g x \log{\left(c \right)} + \frac{3 a^{2} b h p q x^{2} \log{\left(e + f x \right)}}{2} - \frac{3 a^{2} b h p q x^{2}}{4} + \frac{3 a^{2} b h q x^{2} \log{\left(d \right)}}{2} + \frac{3 a^{2} b h x^{2} \log{\left(c \right)}}{2} - \frac{3 a b^{2} e^{2} h p^{2} q^{2} \log{\left(e + f x \right)}^{2}}{2 f^{2}} + \frac{9 a b^{2} e^{2} h p^{2} q^{2} \log{\left(e + f x \right)}}{2 f^{2}} - \frac{3 a b^{2} e^{2} h p q^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f^{2}} - \frac{3 a b^{2} e^{2} h p q \log{\left(c \right)} \log{\left(e + f x \right)}}{f^{2}} + \frac{3 a b^{2} e g p^{2} q^{2} \log{\left(e + f x \right)}^{2}}{f} - \frac{6 a b^{2} e g p^{2} q^{2} \log{\left(e + f x \right)}}{f} + \frac{6 a b^{2} e g p q^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{6 a b^{2} e g p q \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + \frac{3 a b^{2} e h p^{2} q^{2} x \log{\left(e + f x \right)}}{f} - \frac{9 a b^{2} e h p^{2} q^{2} x}{2 f} + \frac{3 a b^{2} e h p q^{2} x \log{\left(d \right)}}{f} + \frac{3 a b^{2} e h p q x \log{\left(c \right)}}{f} + 3 a b^{2} g p^{2} q^{2} x \log{\left(e + f x \right)}^{2} - 6 a b^{2} g p^{2} q^{2} x \log{\left(e + f x \right)} + 6 a b^{2} g p^{2} q^{2} x + 6 a b^{2} g p q^{2} x \log{\left(d \right)} \log{\left(e + f x \right)} - 6 a b^{2} g p q^{2} x \log{\left(d \right)} + 6 a b^{2} g p q x \log{\left(c \right)} \log{\left(e + f x \right)} - 6 a b^{2} g p q x \log{\left(c \right)} + 3 a b^{2} g q^{2} x \log{\left(d \right)}^{2} + 6 a b^{2} g q x \log{\left(c \right)} \log{\left(d \right)} + 3 a b^{2} g x \log{\left(c \right)}^{2} + \frac{3 a b^{2} h p^{2} q^{2} x^{2} \log{\left(e + f x \right)}^{2}}{2} - \frac{3 a b^{2} h p^{2} q^{2} x^{2} \log{\left(e + f x \right)}}{2} + \frac{3 a b^{2} h p^{2} q^{2} x^{2}}{4} + 3 a b^{2} h p q^{2} x^{2} \log{\left(d \right)} \log{\left(e + f x \right)} - \frac{3 a b^{2} h p q^{2} x^{2} \log{\left(d \right)}}{2} + 3 a b^{2} h p q x^{2} \log{\left(c \right)} \log{\left(e + f x \right)} - \frac{3 a b^{2} h p q x^{2} \log{\left(c \right)}}{2} + \frac{3 a b^{2} h q^{2} x^{2} \log{\left(d \right)}^{2}}{2} + 3 a b^{2} h q x^{2} \log{\left(c \right)} \log{\left(d \right)} + \frac{3 a b^{2} h x^{2} \log{\left(c \right)}^{2}}{2} - \frac{b^{3} e^{2} h p^{3} q^{3} \log{\left(e + f x \right)}^{3}}{2 f^{2}} + \frac{9 b^{3} e^{2} h p^{3} q^{3} \log{\left(e + f x \right)}^{2}}{4 f^{2}} - \frac{21 b^{3} e^{2} h p^{3} q^{3} \log{\left(e + f x \right)}}{4 f^{2}} - \frac{3 b^{3} e^{2} h p^{2} q^{3} \log{\left(d \right)} \log{\left(e + f x \right)}^{2}}{2 f^{2}} + \frac{9 b^{3} e^{2} h p^{2} q^{3} \log{\left(d \right)} \log{\left(e + f x \right)}}{2 f^{2}} - \frac{3 b^{3} e^{2} h p^{2} q^{2} \log{\left(c \right)} \log{\left(e + f x \right)}^{2}}{2 f^{2}} + \frac{9 b^{3} e^{2} h p^{2} q^{2} \log{\left(c \right)} \log{\left(e + f x \right)}}{2 f^{2}} - \frac{3 b^{3} e^{2} h p q^{3} \log{\left(d \right)}^{2} \log{\left(e + f x \right)}}{2 f^{2}} - \frac{3 b^{3} e^{2} h p q^{2} \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)}}{f^{2}} - \frac{3 b^{3} e^{2} h p q \log{\left(c \right)}^{2} \log{\left(e + f x \right)}}{2 f^{2}} + \frac{b^{3} e g p^{3} q^{3} \log{\left(e + f x \right)}^{3}}{f} - \frac{3 b^{3} e g p^{3} q^{3} \log{\left(e + f x \right)}^{2}}{f} + \frac{6 b^{3} e g p^{3} q^{3} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e g p^{2} q^{3} \log{\left(d \right)} \log{\left(e + f x \right)}^{2}}{f} - \frac{6 b^{3} e g p^{2} q^{3} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e g p^{2} q^{2} \log{\left(c \right)} \log{\left(e + f x \right)}^{2}}{f} - \frac{6 b^{3} e g p^{2} q^{2} \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e g p q^{3} \log{\left(d \right)}^{2} \log{\left(e + f x \right)}}{f} + \frac{6 b^{3} e g p q^{2} \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e g p q \log{\left(c \right)}^{2} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e h p^{3} q^{3} x \log{\left(e + f x \right)}^{2}}{2 f} - \frac{9 b^{3} e h p^{3} q^{3} x \log{\left(e + f x \right)}}{2 f} + \frac{21 b^{3} e h p^{3} q^{3} x}{4 f} + \frac{3 b^{3} e h p^{2} q^{3} x \log{\left(d \right)} \log{\left(e + f x \right)}}{f} - \frac{9 b^{3} e h p^{2} q^{3} x \log{\left(d \right)}}{2 f} + \frac{3 b^{3} e h p^{2} q^{2} x \log{\left(c \right)} \log{\left(e + f x \right)}}{f} - \frac{9 b^{3} e h p^{2} q^{2} x \log{\left(c \right)}}{2 f} + \frac{3 b^{3} e h p q^{3} x \log{\left(d \right)}^{2}}{2 f} + \frac{3 b^{3} e h p q^{2} x \log{\left(c \right)} \log{\left(d \right)}}{f} + \frac{3 b^{3} e h p q x \log{\left(c \right)}^{2}}{2 f} + b^{3} g p^{3} q^{3} x \log{\left(e + f x \right)}^{3} - 3 b^{3} g p^{3} q^{3} x \log{\left(e + f x \right)}^{2} + 6 b^{3} g p^{3} q^{3} x \log{\left(e + f x \right)} - 6 b^{3} g p^{3} q^{3} x + 3 b^{3} g p^{2} q^{3} x \log{\left(d \right)} \log{\left(e + f x \right)}^{2} - 6 b^{3} g p^{2} q^{3} x \log{\left(d \right)} \log{\left(e + f x \right)} + 6 b^{3} g p^{2} q^{3} x \log{\left(d \right)} + 3 b^{3} g p^{2} q^{2} x \log{\left(c \right)} \log{\left(e + f x \right)}^{2} - 6 b^{3} g p^{2} q^{2} x \log{\left(c \right)} \log{\left(e + f x \right)} + 6 b^{3} g p^{2} q^{2} x \log{\left(c \right)} + 3 b^{3} g p q^{3} x \log{\left(d \right)}^{2} \log{\left(e + f x \right)} - 3 b^{3} g p q^{3} x \log{\left(d \right)}^{2} + 6 b^{3} g p q^{2} x \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)} - 6 b^{3} g p q^{2} x \log{\left(c \right)} \log{\left(d \right)} + 3 b^{3} g p q x \log{\left(c \right)}^{2} \log{\left(e + f x \right)} - 3 b^{3} g p q x \log{\left(c \right)}^{2} + b^{3} g q^{3} x \log{\left(d \right)}^{3} + 3 b^{3} g q^{2} x \log{\left(c \right)} \log{\left(d \right)}^{2} + 3 b^{3} g q x \log{\left(c \right)}^{2} \log{\left(d \right)} + b^{3} g x \log{\left(c \right)}^{3} + \frac{b^{3} h p^{3} q^{3} x^{2} \log{\left(e + f x \right)}^{3}}{2} - \frac{3 b^{3} h p^{3} q^{3} x^{2} \log{\left(e + f x \right)}^{2}}{4} + \frac{3 b^{3} h p^{3} q^{3} x^{2} \log{\left(e + f x \right)}}{4} - \frac{3 b^{3} h p^{3} q^{3} x^{2}}{8} + \frac{3 b^{3} h p^{2} q^{3} x^{2} \log{\left(d \right)} \log{\left(e + f x \right)}^{2}}{2} - \frac{3 b^{3} h p^{2} q^{3} x^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{2} + \frac{3 b^{3} h p^{2} q^{3} x^{2} \log{\left(d \right)}}{4} + \frac{3 b^{3} h p^{2} q^{2} x^{2} \log{\left(c \right)} \log{\left(e + f x \right)}^{2}}{2} - \frac{3 b^{3} h p^{2} q^{2} x^{2} \log{\left(c \right)} \log{\left(e + f x \right)}}{2} + \frac{3 b^{3} h p^{2} q^{2} x^{2} \log{\left(c \right)}}{4} + \frac{3 b^{3} h p q^{3} x^{2} \log{\left(d \right)}^{2} \log{\left(e + f x \right)}}{2} - \frac{3 b^{3} h p q^{3} x^{2} \log{\left(d \right)}^{2}}{4} + 3 b^{3} h p q^{2} x^{2} \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)} - \frac{3 b^{3} h p q^{2} x^{2} \log{\left(c \right)} \log{\left(d \right)}}{2} + \frac{3 b^{3} h p q x^{2} \log{\left(c \right)}^{2} \log{\left(e + f x \right)}}{2} - \frac{3 b^{3} h p q x^{2} \log{\left(c \right)}^{2}}{4} + \frac{b^{3} h q^{3} x^{2} \log{\left(d \right)}^{3}}{2} + \frac{3 b^{3} h q^{2} x^{2} \log{\left(c \right)} \log{\left(d \right)}^{2}}{2} + \frac{3 b^{3} h q x^{2} \log{\left(c \right)}^{2} \log{\left(d \right)}}{2} + \frac{b^{3} h x^{2} \log{\left(c \right)}^{3}}{2} & \text{for}\: f \neq 0 \\\left(a + b \log{\left(c \left(d e^{p}\right)^{q} \right)}\right)^{3} \left(g x + \frac{h x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*g*x + a**3*h*x**2/2 - 3*a**2*b*e**2*h*p*q*log(e + f*x)/(2*f**2) + 3*a**2*b*e*g*p*q*log(e + f*x)/f + 3*a**2*b*e*h*p*q*x/(2*f) + 3*a**2*b*g*p*q*x*log(e + f*x) - 3*a**2*b*g*p*q*x + 3*a**2*b*g*q*x*log(d) + 3*a**2*b*g*x*log(c) + 3*a**2*b*h*p*q*x**2*log(e + f*x)/2 - 3*a**2*b*h*p*q*x**2/4 + 3*a**2*b*h*q*x**2*log(d)/2 + 3*a**2*b*h*x**2*log(c)/2 - 3*a*b**2*e**2*h*p**2*q**2*log(e + f*x)**2/(2*f**2) + 9*a*b**2*e**2*h*p**2*q**2*log(e + f*x)/(2*f**2) - 3*a*b**2*e**2*h*p*q**2*log(d)*log(e + f*x)/f**2 - 3*a*b**2*e**2*h*p*q*log(c)*log(e + f*x)/f**2 + 3*a*b**2*e*g*p**2*q**2*log(e + f*x)**2/f - 6*a*b**2*e*g*p**2*q**2*log(e + f*x)/f + 6*a*b**2*e*g*p*q**2*log(d)*log(e + f*x)/f + 6*a*b**2*e*g*p*q*log(c)*log(e + f*x)/f + 3*a*b**2*e*h*p**2*q**2*x*log(e + f*x)/f - 9*a*b**2*e*h*p**2*q**2*x/(2*f) + 3*a*b**2*e*h*p*q**2*x*log(d)/f + 3*a*b**2*e*h*p*q*x*log(c)/f + 3*a*b**2*g*p**2*q**2*x*log(e + f*x)**2 - 6*a*b**2*g*p**2*q**2*x*log(e + f*x) + 6*a*b**2*g*p**2*q**2*x + 6*a*b**2*g*p*q**2*x*log(d)*log(e + f*x) - 6*a*b**2*g*p*q**2*x*log(d) + 6*a*b**2*g*p*q*x*log(c)*log(e + f*x) - 6*a*b**2*g*p*q*x*log(c) + 3*a*b**2*g*q**2*x*log(d)**2 + 6*a*b**2*g*q*x*log(c)*log(d) + 3*a*b**2*g*x*log(c)**2 + 3*a*b**2*h*p**2*q**2*x**2*log(e + f*x)**2/2 - 3*a*b**2*h*p**2*q**2*x**2*log(e + f*x)/2 + 3*a*b**2*h*p**2*q**2*x**2/4 + 3*a*b**2*h*p*q**2*x**2*log(d)*log(e + f*x) - 3*a*b**2*h*p*q**2*x**2*log(d)/2 + 3*a*b**2*h*p*q*x**2*log(c)*log(e + f*x) - 3*a*b**2*h*p*q*x**2*log(c)/2 + 3*a*b**2*h*q**2*x**2*log(d)**2/2 + 3*a*b**2*h*q*x**2*log(c)*log(d) + 3*a*b**2*h*x**2*log(c)**2/2 - b**3*e**2*h*p**3*q**3*log(e + f*x)**3/(2*f**2) + 9*b**3*e**2*h*p**3*q**3*log(e + f*x)**2/(4*f**2) - 21*b**3*e**2*h*p**3*q**3*log(e + f*x)/(4*f**2) - 3*b**3*e**2*h*p**2*q**3*log(d)*log(e + f*x)**2/(2*f**2) + 9*b**3*e**2*h*p**2*q**3*log(d)*log(e + f*x)/(2*f**2) - 3*b**3*e**2*h*p**2*q**2*log(c)*log(e + f*x)**2/(2*f**2) + 9*b**3*e**2*h*p**2*q**2*log(c)*log(e + f*x)/(2*f**2) - 3*b**3*e**2*h*p*q**3*log(d)**2*log(e + f*x)/(2*f**2) - 3*b**3*e**2*h*p*q**2*log(c)*log(d)*log(e + f*x)/f**2 - 3*b**3*e**2*h*p*q*log(c)**2*log(e + f*x)/(2*f**2) + b**3*e*g*p**3*q**3*log(e + f*x)**3/f - 3*b**3*e*g*p**3*q**3*log(e + f*x)**2/f + 6*b**3*e*g*p**3*q**3*log(e + f*x)/f + 3*b**3*e*g*p**2*q**3*log(d)*log(e + f*x)**2/f - 6*b**3*e*g*p**2*q**3*log(d)*log(e + f*x)/f + 3*b**3*e*g*p**2*q**2*log(c)*log(e + f*x)**2/f - 6*b**3*e*g*p**2*q**2*log(c)*log(e + f*x)/f + 3*b**3*e*g*p*q**3*log(d)**2*log(e + f*x)/f + 6*b**3*e*g*p*q**2*log(c)*log(d)*log(e + f*x)/f + 3*b**3*e*g*p*q*log(c)**2*log(e + f*x)/f + 3*b**3*e*h*p**3*q**3*x*log(e + f*x)**2/(2*f) - 9*b**3*e*h*p**3*q**3*x*log(e + f*x)/(2*f) + 21*b**3*e*h*p**3*q**3*x/(4*f) + 3*b**3*e*h*p**2*q**3*x*log(d)*log(e + f*x)/f - 9*b**3*e*h*p**2*q**3*x*log(d)/(2*f) + 3*b**3*e*h*p**2*q**2*x*log(c)*log(e + f*x)/f - 9*b**3*e*h*p**2*q**2*x*log(c)/(2*f) + 3*b**3*e*h*p*q**3*x*log(d)**2/(2*f) + 3*b**3*e*h*p*q**2*x*log(c)*log(d)/f + 3*b**3*e*h*p*q*x*log(c)**2/(2*f) + b**3*g*p**3*q**3*x*log(e + f*x)**3 - 3*b**3*g*p**3*q**3*x*log(e + f*x)**2 + 6*b**3*g*p**3*q**3*x*log(e + f*x) - 6*b**3*g*p**3*q**3*x + 3*b**3*g*p**2*q**3*x*log(d)*log(e + f*x)**2 - 6*b**3*g*p**2*q**3*x*log(d)*log(e + f*x) + 6*b**3*g*p**2*q**3*x*log(d) + 3*b**3*g*p**2*q**2*x*log(c)*log(e + f*x)**2 - 6*b**3*g*p**2*q**2*x*log(c)*log(e + f*x) + 6*b**3*g*p**2*q**2*x*log(c) + 3*b**3*g*p*q**3*x*log(d)**2*log(e + f*x) - 3*b**3*g*p*q**3*x*log(d)**2 + 6*b**3*g*p*q**2*x*log(c)*log(d)*log(e + f*x) - 6*b**3*g*p*q**2*x*log(c)*log(d) + 3*b**3*g*p*q*x*log(c)**2*log(e + f*x) - 3*b**3*g*p*q*x*log(c)**2 + b**3*g*q**3*x*log(d)**3 + 3*b**3*g*q**2*x*log(c)*log(d)**2 + 3*b**3*g*q*x*log(c)**2*log(d) + b**3*g*x*log(c)**3 + b**3*h*p**3*q**3*x**2*log(e + f*x)**3/2 - 3*b**3*h*p**3*q**3*x**2*log(e + f*x)**2/4 + 3*b**3*h*p**3*q**3*x**2*log(e + f*x)/4 - 3*b**3*h*p**3*q**3*x**2/8 + 3*b**3*h*p**2*q**3*x**2*log(d)*log(e + f*x)**2/2 - 3*b**3*h*p**2*q**3*x**2*log(d)*log(e + f*x)/2 + 3*b**3*h*p**2*q**3*x**2*log(d)/4 + 3*b**3*h*p**2*q**2*x**2*log(c)*log(e + f*x)**2/2 - 3*b**3*h*p**2*q**2*x**2*log(c)*log(e + f*x)/2 + 3*b**3*h*p**2*q**2*x**2*log(c)/4 + 3*b**3*h*p*q**3*x**2*log(d)**2*log(e + f*x)/2 - 3*b**3*h*p*q**3*x**2*log(d)**2/4 + 3*b**3*h*p*q**2*x**2*log(c)*log(d)*log(e + f*x) - 3*b**3*h*p*q**2*x**2*log(c)*log(d)/2 + 3*b**3*h*p*q*x**2*log(c)**2*log(e + f*x)/2 - 3*b**3*h*p*q*x**2*log(c)**2/4 + b**3*h*q**3*x**2*log(d)**3/2 + 3*b**3*h*q**2*x**2*log(c)*log(d)**2/2 + 3*b**3*h*q*x**2*log(c)**2*log(d)/2 + b**3*h*x**2*log(c)**3/2, Ne(f, 0)), ((a + b*log(c*(d*e**p)**q))**3*(g*x + h*x**2/2), True))","A",0
437,1,1023,0,8.946342," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**3,x)","\begin{cases} a^{3} x + \frac{3 a^{2} b e p q \log{\left(e + f x \right)}}{f} + 3 a^{2} b p q x \log{\left(e + f x \right)} - 3 a^{2} b p q x + 3 a^{2} b q x \log{\left(d \right)} + 3 a^{2} b x \log{\left(c \right)} + \frac{3 a b^{2} e p^{2} q^{2} \log{\left(e + f x \right)}^{2}}{f} - \frac{6 a b^{2} e p^{2} q^{2} \log{\left(e + f x \right)}}{f} + \frac{6 a b^{2} e p q^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{6 a b^{2} e p q \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + 3 a b^{2} p^{2} q^{2} x \log{\left(e + f x \right)}^{2} - 6 a b^{2} p^{2} q^{2} x \log{\left(e + f x \right)} + 6 a b^{2} p^{2} q^{2} x + 6 a b^{2} p q^{2} x \log{\left(d \right)} \log{\left(e + f x \right)} - 6 a b^{2} p q^{2} x \log{\left(d \right)} + 6 a b^{2} p q x \log{\left(c \right)} \log{\left(e + f x \right)} - 6 a b^{2} p q x \log{\left(c \right)} + 3 a b^{2} q^{2} x \log{\left(d \right)}^{2} + 6 a b^{2} q x \log{\left(c \right)} \log{\left(d \right)} + 3 a b^{2} x \log{\left(c \right)}^{2} + \frac{b^{3} e p^{3} q^{3} \log{\left(e + f x \right)}^{3}}{f} - \frac{3 b^{3} e p^{3} q^{3} \log{\left(e + f x \right)}^{2}}{f} + \frac{6 b^{3} e p^{3} q^{3} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e p^{2} q^{3} \log{\left(d \right)} \log{\left(e + f x \right)}^{2}}{f} - \frac{6 b^{3} e p^{2} q^{3} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e p^{2} q^{2} \log{\left(c \right)} \log{\left(e + f x \right)}^{2}}{f} - \frac{6 b^{3} e p^{2} q^{2} \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e p q^{3} \log{\left(d \right)}^{2} \log{\left(e + f x \right)}}{f} + \frac{6 b^{3} e p q^{2} \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{3 b^{3} e p q \log{\left(c \right)}^{2} \log{\left(e + f x \right)}}{f} + b^{3} p^{3} q^{3} x \log{\left(e + f x \right)}^{3} - 3 b^{3} p^{3} q^{3} x \log{\left(e + f x \right)}^{2} + 6 b^{3} p^{3} q^{3} x \log{\left(e + f x \right)} - 6 b^{3} p^{3} q^{3} x + 3 b^{3} p^{2} q^{3} x \log{\left(d \right)} \log{\left(e + f x \right)}^{2} - 6 b^{3} p^{2} q^{3} x \log{\left(d \right)} \log{\left(e + f x \right)} + 6 b^{3} p^{2} q^{3} x \log{\left(d \right)} + 3 b^{3} p^{2} q^{2} x \log{\left(c \right)} \log{\left(e + f x \right)}^{2} - 6 b^{3} p^{2} q^{2} x \log{\left(c \right)} \log{\left(e + f x \right)} + 6 b^{3} p^{2} q^{2} x \log{\left(c \right)} + 3 b^{3} p q^{3} x \log{\left(d \right)}^{2} \log{\left(e + f x \right)} - 3 b^{3} p q^{3} x \log{\left(d \right)}^{2} + 6 b^{3} p q^{2} x \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)} - 6 b^{3} p q^{2} x \log{\left(c \right)} \log{\left(d \right)} + 3 b^{3} p q x \log{\left(c \right)}^{2} \log{\left(e + f x \right)} - 3 b^{3} p q x \log{\left(c \right)}^{2} + b^{3} q^{3} x \log{\left(d \right)}^{3} + 3 b^{3} q^{2} x \log{\left(c \right)} \log{\left(d \right)}^{2} + 3 b^{3} q x \log{\left(c \right)}^{2} \log{\left(d \right)} + b^{3} x \log{\left(c \right)}^{3} & \text{for}\: f \neq 0 \\x \left(a + b \log{\left(c \left(d e^{p}\right)^{q} \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x + 3*a**2*b*e*p*q*log(e + f*x)/f + 3*a**2*b*p*q*x*log(e + f*x) - 3*a**2*b*p*q*x + 3*a**2*b*q*x*log(d) + 3*a**2*b*x*log(c) + 3*a*b**2*e*p**2*q**2*log(e + f*x)**2/f - 6*a*b**2*e*p**2*q**2*log(e + f*x)/f + 6*a*b**2*e*p*q**2*log(d)*log(e + f*x)/f + 6*a*b**2*e*p*q*log(c)*log(e + f*x)/f + 3*a*b**2*p**2*q**2*x*log(e + f*x)**2 - 6*a*b**2*p**2*q**2*x*log(e + f*x) + 6*a*b**2*p**2*q**2*x + 6*a*b**2*p*q**2*x*log(d)*log(e + f*x) - 6*a*b**2*p*q**2*x*log(d) + 6*a*b**2*p*q*x*log(c)*log(e + f*x) - 6*a*b**2*p*q*x*log(c) + 3*a*b**2*q**2*x*log(d)**2 + 6*a*b**2*q*x*log(c)*log(d) + 3*a*b**2*x*log(c)**2 + b**3*e*p**3*q**3*log(e + f*x)**3/f - 3*b**3*e*p**3*q**3*log(e + f*x)**2/f + 6*b**3*e*p**3*q**3*log(e + f*x)/f + 3*b**3*e*p**2*q**3*log(d)*log(e + f*x)**2/f - 6*b**3*e*p**2*q**3*log(d)*log(e + f*x)/f + 3*b**3*e*p**2*q**2*log(c)*log(e + f*x)**2/f - 6*b**3*e*p**2*q**2*log(c)*log(e + f*x)/f + 3*b**3*e*p*q**3*log(d)**2*log(e + f*x)/f + 6*b**3*e*p*q**2*log(c)*log(d)*log(e + f*x)/f + 3*b**3*e*p*q*log(c)**2*log(e + f*x)/f + b**3*p**3*q**3*x*log(e + f*x)**3 - 3*b**3*p**3*q**3*x*log(e + f*x)**2 + 6*b**3*p**3*q**3*x*log(e + f*x) - 6*b**3*p**3*q**3*x + 3*b**3*p**2*q**3*x*log(d)*log(e + f*x)**2 - 6*b**3*p**2*q**3*x*log(d)*log(e + f*x) + 6*b**3*p**2*q**3*x*log(d) + 3*b**3*p**2*q**2*x*log(c)*log(e + f*x)**2 - 6*b**3*p**2*q**2*x*log(c)*log(e + f*x) + 6*b**3*p**2*q**2*x*log(c) + 3*b**3*p*q**3*x*log(d)**2*log(e + f*x) - 3*b**3*p*q**3*x*log(d)**2 + 6*b**3*p*q**2*x*log(c)*log(d)*log(e + f*x) - 6*b**3*p*q**2*x*log(c)*log(d) + 3*b**3*p*q*x*log(c)**2*log(e + f*x) - 3*b**3*p*q*x*log(c)**2 + b**3*q**3*x*log(d)**3 + 3*b**3*q**2*x*log(c)*log(d)**2 + 3*b**3*q*x*log(c)**2*log(d) + b**3*x*log(c)**3, Ne(f, 0)), (x*(a + b*log(c*(d*e**p)**q))**3, True))","A",0
438,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**3/(h*x+g),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{3}}{g + h x}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**3/(g + h*x), x)","F",0
439,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**3/(h*x+g)**2,x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{3}}{\left(g + h x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**3/(g + h*x)**2, x)","F",0
440,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**3/(h*x+g)**3,x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{3}}{\left(g + h x\right)^{3}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**3/(g + h*x)**3, x)","F",0
441,1,2390,0,22.865882," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**4,x)","\begin{cases} a^{4} x + \frac{4 a^{3} b e p q \log{\left(e + f x \right)}}{f} + 4 a^{3} b p q x \log{\left(e + f x \right)} - 4 a^{3} b p q x + 4 a^{3} b q x \log{\left(d \right)} + 4 a^{3} b x \log{\left(c \right)} + \frac{6 a^{2} b^{2} e p^{2} q^{2} \log{\left(e + f x \right)}^{2}}{f} - \frac{12 a^{2} b^{2} e p^{2} q^{2} \log{\left(e + f x \right)}}{f} + \frac{12 a^{2} b^{2} e p q^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{12 a^{2} b^{2} e p q \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + 6 a^{2} b^{2} p^{2} q^{2} x \log{\left(e + f x \right)}^{2} - 12 a^{2} b^{2} p^{2} q^{2} x \log{\left(e + f x \right)} + 12 a^{2} b^{2} p^{2} q^{2} x + 12 a^{2} b^{2} p q^{2} x \log{\left(d \right)} \log{\left(e + f x \right)} - 12 a^{2} b^{2} p q^{2} x \log{\left(d \right)} + 12 a^{2} b^{2} p q x \log{\left(c \right)} \log{\left(e + f x \right)} - 12 a^{2} b^{2} p q x \log{\left(c \right)} + 6 a^{2} b^{2} q^{2} x \log{\left(d \right)}^{2} + 12 a^{2} b^{2} q x \log{\left(c \right)} \log{\left(d \right)} + 6 a^{2} b^{2} x \log{\left(c \right)}^{2} + \frac{4 a b^{3} e p^{3} q^{3} \log{\left(e + f x \right)}^{3}}{f} - \frac{12 a b^{3} e p^{3} q^{3} \log{\left(e + f x \right)}^{2}}{f} + \frac{24 a b^{3} e p^{3} q^{3} \log{\left(e + f x \right)}}{f} + \frac{12 a b^{3} e p^{2} q^{3} \log{\left(d \right)} \log{\left(e + f x \right)}^{2}}{f} - \frac{24 a b^{3} e p^{2} q^{3} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{12 a b^{3} e p^{2} q^{2} \log{\left(c \right)} \log{\left(e + f x \right)}^{2}}{f} - \frac{24 a b^{3} e p^{2} q^{2} \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + \frac{12 a b^{3} e p q^{3} \log{\left(d \right)}^{2} \log{\left(e + f x \right)}}{f} + \frac{24 a b^{3} e p q^{2} \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{12 a b^{3} e p q \log{\left(c \right)}^{2} \log{\left(e + f x \right)}}{f} + 4 a b^{3} p^{3} q^{3} x \log{\left(e + f x \right)}^{3} - 12 a b^{3} p^{3} q^{3} x \log{\left(e + f x \right)}^{2} + 24 a b^{3} p^{3} q^{3} x \log{\left(e + f x \right)} - 24 a b^{3} p^{3} q^{3} x + 12 a b^{3} p^{2} q^{3} x \log{\left(d \right)} \log{\left(e + f x \right)}^{2} - 24 a b^{3} p^{2} q^{3} x \log{\left(d \right)} \log{\left(e + f x \right)} + 24 a b^{3} p^{2} q^{3} x \log{\left(d \right)} + 12 a b^{3} p^{2} q^{2} x \log{\left(c \right)} \log{\left(e + f x \right)}^{2} - 24 a b^{3} p^{2} q^{2} x \log{\left(c \right)} \log{\left(e + f x \right)} + 24 a b^{3} p^{2} q^{2} x \log{\left(c \right)} + 12 a b^{3} p q^{3} x \log{\left(d \right)}^{2} \log{\left(e + f x \right)} - 12 a b^{3} p q^{3} x \log{\left(d \right)}^{2} + 24 a b^{3} p q^{2} x \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)} - 24 a b^{3} p q^{2} x \log{\left(c \right)} \log{\left(d \right)} + 12 a b^{3} p q x \log{\left(c \right)}^{2} \log{\left(e + f x \right)} - 12 a b^{3} p q x \log{\left(c \right)}^{2} + 4 a b^{3} q^{3} x \log{\left(d \right)}^{3} + 12 a b^{3} q^{2} x \log{\left(c \right)} \log{\left(d \right)}^{2} + 12 a b^{3} q x \log{\left(c \right)}^{2} \log{\left(d \right)} + 4 a b^{3} x \log{\left(c \right)}^{3} + \frac{b^{4} e p^{4} q^{4} \log{\left(e + f x \right)}^{4}}{f} - \frac{4 b^{4} e p^{4} q^{4} \log{\left(e + f x \right)}^{3}}{f} + \frac{12 b^{4} e p^{4} q^{4} \log{\left(e + f x \right)}^{2}}{f} - \frac{24 b^{4} e p^{4} q^{4} \log{\left(e + f x \right)}}{f} + \frac{4 b^{4} e p^{3} q^{4} \log{\left(d \right)} \log{\left(e + f x \right)}^{3}}{f} - \frac{12 b^{4} e p^{3} q^{4} \log{\left(d \right)} \log{\left(e + f x \right)}^{2}}{f} + \frac{24 b^{4} e p^{3} q^{4} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{4 b^{4} e p^{3} q^{3} \log{\left(c \right)} \log{\left(e + f x \right)}^{3}}{f} - \frac{12 b^{4} e p^{3} q^{3} \log{\left(c \right)} \log{\left(e + f x \right)}^{2}}{f} + \frac{24 b^{4} e p^{3} q^{3} \log{\left(c \right)} \log{\left(e + f x \right)}}{f} + \frac{6 b^{4} e p^{2} q^{4} \log{\left(d \right)}^{2} \log{\left(e + f x \right)}^{2}}{f} - \frac{12 b^{4} e p^{2} q^{4} \log{\left(d \right)}^{2} \log{\left(e + f x \right)}}{f} + \frac{12 b^{4} e p^{2} q^{3} \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)}^{2}}{f} - \frac{24 b^{4} e p^{2} q^{3} \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{6 b^{4} e p^{2} q^{2} \log{\left(c \right)}^{2} \log{\left(e + f x \right)}^{2}}{f} - \frac{12 b^{4} e p^{2} q^{2} \log{\left(c \right)}^{2} \log{\left(e + f x \right)}}{f} + \frac{4 b^{4} e p q^{4} \log{\left(d \right)}^{3} \log{\left(e + f x \right)}}{f} + \frac{12 b^{4} e p q^{3} \log{\left(c \right)} \log{\left(d \right)}^{2} \log{\left(e + f x \right)}}{f} + \frac{12 b^{4} e p q^{2} \log{\left(c \right)}^{2} \log{\left(d \right)} \log{\left(e + f x \right)}}{f} + \frac{4 b^{4} e p q \log{\left(c \right)}^{3} \log{\left(e + f x \right)}}{f} + b^{4} p^{4} q^{4} x \log{\left(e + f x \right)}^{4} - 4 b^{4} p^{4} q^{4} x \log{\left(e + f x \right)}^{3} + 12 b^{4} p^{4} q^{4} x \log{\left(e + f x \right)}^{2} - 24 b^{4} p^{4} q^{4} x \log{\left(e + f x \right)} + 24 b^{4} p^{4} q^{4} x + 4 b^{4} p^{3} q^{4} x \log{\left(d \right)} \log{\left(e + f x \right)}^{3} - 12 b^{4} p^{3} q^{4} x \log{\left(d \right)} \log{\left(e + f x \right)}^{2} + 24 b^{4} p^{3} q^{4} x \log{\left(d \right)} \log{\left(e + f x \right)} - 24 b^{4} p^{3} q^{4} x \log{\left(d \right)} + 4 b^{4} p^{3} q^{3} x \log{\left(c \right)} \log{\left(e + f x \right)}^{3} - 12 b^{4} p^{3} q^{3} x \log{\left(c \right)} \log{\left(e + f x \right)}^{2} + 24 b^{4} p^{3} q^{3} x \log{\left(c \right)} \log{\left(e + f x \right)} - 24 b^{4} p^{3} q^{3} x \log{\left(c \right)} + 6 b^{4} p^{2} q^{4} x \log{\left(d \right)}^{2} \log{\left(e + f x \right)}^{2} - 12 b^{4} p^{2} q^{4} x \log{\left(d \right)}^{2} \log{\left(e + f x \right)} + 12 b^{4} p^{2} q^{4} x \log{\left(d \right)}^{2} + 12 b^{4} p^{2} q^{3} x \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)}^{2} - 24 b^{4} p^{2} q^{3} x \log{\left(c \right)} \log{\left(d \right)} \log{\left(e + f x \right)} + 24 b^{4} p^{2} q^{3} x \log{\left(c \right)} \log{\left(d \right)} + 6 b^{4} p^{2} q^{2} x \log{\left(c \right)}^{2} \log{\left(e + f x \right)}^{2} - 12 b^{4} p^{2} q^{2} x \log{\left(c \right)}^{2} \log{\left(e + f x \right)} + 12 b^{4} p^{2} q^{2} x \log{\left(c \right)}^{2} + 4 b^{4} p q^{4} x \log{\left(d \right)}^{3} \log{\left(e + f x \right)} - 4 b^{4} p q^{4} x \log{\left(d \right)}^{3} + 12 b^{4} p q^{3} x \log{\left(c \right)} \log{\left(d \right)}^{2} \log{\left(e + f x \right)} - 12 b^{4} p q^{3} x \log{\left(c \right)} \log{\left(d \right)}^{2} + 12 b^{4} p q^{2} x \log{\left(c \right)}^{2} \log{\left(d \right)} \log{\left(e + f x \right)} - 12 b^{4} p q^{2} x \log{\left(c \right)}^{2} \log{\left(d \right)} + 4 b^{4} p q x \log{\left(c \right)}^{3} \log{\left(e + f x \right)} - 4 b^{4} p q x \log{\left(c \right)}^{3} + b^{4} q^{4} x \log{\left(d \right)}^{4} + 4 b^{4} q^{3} x \log{\left(c \right)} \log{\left(d \right)}^{3} + 6 b^{4} q^{2} x \log{\left(c \right)}^{2} \log{\left(d \right)}^{2} + 4 b^{4} q x \log{\left(c \right)}^{3} \log{\left(d \right)} + b^{4} x \log{\left(c \right)}^{4} & \text{for}\: f \neq 0 \\x \left(a + b \log{\left(c \left(d e^{p}\right)^{q} \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x + 4*a**3*b*e*p*q*log(e + f*x)/f + 4*a**3*b*p*q*x*log(e + f*x) - 4*a**3*b*p*q*x + 4*a**3*b*q*x*log(d) + 4*a**3*b*x*log(c) + 6*a**2*b**2*e*p**2*q**2*log(e + f*x)**2/f - 12*a**2*b**2*e*p**2*q**2*log(e + f*x)/f + 12*a**2*b**2*e*p*q**2*log(d)*log(e + f*x)/f + 12*a**2*b**2*e*p*q*log(c)*log(e + f*x)/f + 6*a**2*b**2*p**2*q**2*x*log(e + f*x)**2 - 12*a**2*b**2*p**2*q**2*x*log(e + f*x) + 12*a**2*b**2*p**2*q**2*x + 12*a**2*b**2*p*q**2*x*log(d)*log(e + f*x) - 12*a**2*b**2*p*q**2*x*log(d) + 12*a**2*b**2*p*q*x*log(c)*log(e + f*x) - 12*a**2*b**2*p*q*x*log(c) + 6*a**2*b**2*q**2*x*log(d)**2 + 12*a**2*b**2*q*x*log(c)*log(d) + 6*a**2*b**2*x*log(c)**2 + 4*a*b**3*e*p**3*q**3*log(e + f*x)**3/f - 12*a*b**3*e*p**3*q**3*log(e + f*x)**2/f + 24*a*b**3*e*p**3*q**3*log(e + f*x)/f + 12*a*b**3*e*p**2*q**3*log(d)*log(e + f*x)**2/f - 24*a*b**3*e*p**2*q**3*log(d)*log(e + f*x)/f + 12*a*b**3*e*p**2*q**2*log(c)*log(e + f*x)**2/f - 24*a*b**3*e*p**2*q**2*log(c)*log(e + f*x)/f + 12*a*b**3*e*p*q**3*log(d)**2*log(e + f*x)/f + 24*a*b**3*e*p*q**2*log(c)*log(d)*log(e + f*x)/f + 12*a*b**3*e*p*q*log(c)**2*log(e + f*x)/f + 4*a*b**3*p**3*q**3*x*log(e + f*x)**3 - 12*a*b**3*p**3*q**3*x*log(e + f*x)**2 + 24*a*b**3*p**3*q**3*x*log(e + f*x) - 24*a*b**3*p**3*q**3*x + 12*a*b**3*p**2*q**3*x*log(d)*log(e + f*x)**2 - 24*a*b**3*p**2*q**3*x*log(d)*log(e + f*x) + 24*a*b**3*p**2*q**3*x*log(d) + 12*a*b**3*p**2*q**2*x*log(c)*log(e + f*x)**2 - 24*a*b**3*p**2*q**2*x*log(c)*log(e + f*x) + 24*a*b**3*p**2*q**2*x*log(c) + 12*a*b**3*p*q**3*x*log(d)**2*log(e + f*x) - 12*a*b**3*p*q**3*x*log(d)**2 + 24*a*b**3*p*q**2*x*log(c)*log(d)*log(e + f*x) - 24*a*b**3*p*q**2*x*log(c)*log(d) + 12*a*b**3*p*q*x*log(c)**2*log(e + f*x) - 12*a*b**3*p*q*x*log(c)**2 + 4*a*b**3*q**3*x*log(d)**3 + 12*a*b**3*q**2*x*log(c)*log(d)**2 + 12*a*b**3*q*x*log(c)**2*log(d) + 4*a*b**3*x*log(c)**3 + b**4*e*p**4*q**4*log(e + f*x)**4/f - 4*b**4*e*p**4*q**4*log(e + f*x)**3/f + 12*b**4*e*p**4*q**4*log(e + f*x)**2/f - 24*b**4*e*p**4*q**4*log(e + f*x)/f + 4*b**4*e*p**3*q**4*log(d)*log(e + f*x)**3/f - 12*b**4*e*p**3*q**4*log(d)*log(e + f*x)**2/f + 24*b**4*e*p**3*q**4*log(d)*log(e + f*x)/f + 4*b**4*e*p**3*q**3*log(c)*log(e + f*x)**3/f - 12*b**4*e*p**3*q**3*log(c)*log(e + f*x)**2/f + 24*b**4*e*p**3*q**3*log(c)*log(e + f*x)/f + 6*b**4*e*p**2*q**4*log(d)**2*log(e + f*x)**2/f - 12*b**4*e*p**2*q**4*log(d)**2*log(e + f*x)/f + 12*b**4*e*p**2*q**3*log(c)*log(d)*log(e + f*x)**2/f - 24*b**4*e*p**2*q**3*log(c)*log(d)*log(e + f*x)/f + 6*b**4*e*p**2*q**2*log(c)**2*log(e + f*x)**2/f - 12*b**4*e*p**2*q**2*log(c)**2*log(e + f*x)/f + 4*b**4*e*p*q**4*log(d)**3*log(e + f*x)/f + 12*b**4*e*p*q**3*log(c)*log(d)**2*log(e + f*x)/f + 12*b**4*e*p*q**2*log(c)**2*log(d)*log(e + f*x)/f + 4*b**4*e*p*q*log(c)**3*log(e + f*x)/f + b**4*p**4*q**4*x*log(e + f*x)**4 - 4*b**4*p**4*q**4*x*log(e + f*x)**3 + 12*b**4*p**4*q**4*x*log(e + f*x)**2 - 24*b**4*p**4*q**4*x*log(e + f*x) + 24*b**4*p**4*q**4*x + 4*b**4*p**3*q**4*x*log(d)*log(e + f*x)**3 - 12*b**4*p**3*q**4*x*log(d)*log(e + f*x)**2 + 24*b**4*p**3*q**4*x*log(d)*log(e + f*x) - 24*b**4*p**3*q**4*x*log(d) + 4*b**4*p**3*q**3*x*log(c)*log(e + f*x)**3 - 12*b**4*p**3*q**3*x*log(c)*log(e + f*x)**2 + 24*b**4*p**3*q**3*x*log(c)*log(e + f*x) - 24*b**4*p**3*q**3*x*log(c) + 6*b**4*p**2*q**4*x*log(d)**2*log(e + f*x)**2 - 12*b**4*p**2*q**4*x*log(d)**2*log(e + f*x) + 12*b**4*p**2*q**4*x*log(d)**2 + 12*b**4*p**2*q**3*x*log(c)*log(d)*log(e + f*x)**2 - 24*b**4*p**2*q**3*x*log(c)*log(d)*log(e + f*x) + 24*b**4*p**2*q**3*x*log(c)*log(d) + 6*b**4*p**2*q**2*x*log(c)**2*log(e + f*x)**2 - 12*b**4*p**2*q**2*x*log(c)**2*log(e + f*x) + 12*b**4*p**2*q**2*x*log(c)**2 + 4*b**4*p*q**4*x*log(d)**3*log(e + f*x) - 4*b**4*p*q**4*x*log(d)**3 + 12*b**4*p*q**3*x*log(c)*log(d)**2*log(e + f*x) - 12*b**4*p*q**3*x*log(c)*log(d)**2 + 12*b**4*p*q**2*x*log(c)**2*log(d)*log(e + f*x) - 12*b**4*p*q**2*x*log(c)**2*log(d) + 4*b**4*p*q*x*log(c)**3*log(e + f*x) - 4*b**4*p*q*x*log(c)**3 + b**4*q**4*x*log(d)**4 + 4*b**4*q**3*x*log(c)*log(d)**3 + 6*b**4*q**2*x*log(c)**2*log(d)**2 + 4*b**4*q*x*log(c)**3*log(d) + b**4*x*log(c)**4, Ne(f, 0)), (x*(a + b*log(c*(d*e**p)**q))**4, True))","A",0
442,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**4/(h*x+g),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{4}}{g + h x}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**4/(g + h*x), x)","F",0
443,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**4/(h*x+g)**2,x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{4}}{\left(g + h x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**4/(g + h*x)**2, x)","F",0
444,1,53,0,0.951529," ","integrate(ln(c*(d*(f*x+e)**p)**q),x)","\begin{cases} \frac{e p q \log{\left(e + f x \right)}}{f} + p q x \log{\left(e + f x \right)} - p q x + q x \log{\left(d \right)} + x \log{\left(c \right)} & \text{for}\: f \neq 0 \\x \log{\left(c \left(d e^{p}\right)^{q} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((e*p*q*log(e + f*x)/f + p*q*x*log(e + f*x) - p*q*x + q*x*log(d) + x*log(c), Ne(f, 0)), (x*log(c*(d*e**p)**q), True))","A",0
445,0,0,0,0.000000," ","integrate((h*x+g)**2/(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\int \frac{\left(g + h x\right)^{2}}{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}\, dx"," ",0,"Integral((g + h*x)**2/(a + b*log(c*(d*(e + f*x)**p)**q)), x)","F",0
446,0,0,0,0.000000," ","integrate((h*x+g)/(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\int \frac{g + h x}{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}\, dx"," ",0,"Integral((g + h*x)/(a + b*log(c*(d*(e + f*x)**p)**q)), x)","F",0
447,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\int \frac{1}{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}\, dx"," ",0,"Integral(1/(a + b*log(c*(d*(e + f*x)**p)**q)), x)","F",0
448,0,0,0,0.000000," ","integrate(1/(h*x+g)/(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right) \left(g + h x\right)}\, dx"," ",0,"Integral(1/((a + b*log(c*(d*(e + f*x)**p)**q))*(g + h*x)), x)","F",0
449,0,0,0,0.000000," ","integrate(1/(h*x+g)**2/(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right) \left(g + h x\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*log(c*(d*(e + f*x)**p)**q))*(g + h*x)**2), x)","F",0
450,0,0,0,0.000000," ","integrate((h*x+g)**2/(a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)","\int \frac{\left(g + h x\right)^{2}}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2}}\, dx"," ",0,"Integral((g + h*x)**2/(a + b*log(c*(d*(e + f*x)**p)**q))**2, x)","F",0
451,0,0,0,0.000000," ","integrate((h*x+g)/(a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)","\int \frac{g + h x}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2}}\, dx"," ",0,"Integral((g + h*x)/(a + b*log(c*(d*(e + f*x)**p)**q))**2, x)","F",0
452,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**(-2), x)","F",0
453,0,0,0,0.000000," ","integrate(1/(h*x+g)/(a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2} \left(g + h x\right)}\, dx"," ",0,"Integral(1/((a + b*log(c*(d*(e + f*x)**p)**q))**2*(g + h*x)), x)","F",0
454,0,0,0,0.000000," ","integrate(1/(h*x+g)**2/(a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2} \left(g + h x\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*log(c*(d*(e + f*x)**p)**q))**2*(g + h*x)**2), x)","F",0
455,0,0,0,0.000000," ","integrate((h*x+g)**2/(a+b*ln(c*(d*(f*x+e)**p)**q))**3,x)","\int \frac{\left(g + h x\right)^{2}}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{3}}\, dx"," ",0,"Integral((g + h*x)**2/(a + b*log(c*(d*(e + f*x)**p)**q))**3, x)","F",0
456,0,0,0,0.000000," ","integrate((h*x+g)/(a+b*ln(c*(d*(f*x+e)**p)**q))**3,x)","\int \frac{g + h x}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{3}}\, dx"," ",0,"Integral((g + h*x)/(a + b*log(c*(d*(e + f*x)**p)**q))**3, x)","F",0
457,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(d*(f*x+e)**p)**q))**3,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{3}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**(-3), x)","F",0
458,0,0,0,0.000000," ","integrate(1/(h*x+g)/(a+b*ln(c*(d*(f*x+e)**p)**q))**3,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{3} \left(g + h x\right)}\, dx"," ",0,"Integral(1/((a + b*log(c*(d*(e + f*x)**p)**q))**3*(g + h*x)), x)","F",0
459,-1,0,0,0.000000," ","integrate(1/(h*x+g)**2/(a+b*ln(c*(d*(f*x+e)**p)**q))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
460,0,0,0,0.000000," ","integrate((h*x+g)**2*(a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2),x)","\int \sqrt{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}} \left(g + h x\right)^{2}\, dx"," ",0,"Integral(sqrt(a + b*log(c*(d*(e + f*x)**p)**q))*(g + h*x)**2, x)","F",0
461,0,0,0,0.000000," ","integrate((h*x+g)*(a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2),x)","\int \sqrt{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}} \left(g + h x\right)\, dx"," ",0,"Integral(sqrt(a + b*log(c*(d*(e + f*x)**p)**q))*(g + h*x), x)","F",0
462,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2),x)","\int \sqrt{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}\, dx"," ",0,"Integral(sqrt(a + b*log(c*(d*(e + f*x)**p)**q)), x)","F",0
463,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2)/(h*x+g),x)","\int \frac{\sqrt{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}}{g + h x}\, dx"," ",0,"Integral(sqrt(a + b*log(c*(d*(e + f*x)**p)**q))/(g + h*x), x)","F",0
464,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2)/(h*x+g)**2,x)","\int \frac{\sqrt{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}}{\left(g + h x\right)^{2}}\, dx"," ",0,"Integral(sqrt(a + b*log(c*(d*(e + f*x)**p)**q))/(g + h*x)**2, x)","F",0
465,0,0,0,0.000000," ","integrate((h*x+g)**2*(a+b*ln(c*(d*(f*x+e)**p)**q))**(3/2),x)","\int \left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{\frac{3}{2}} \left(g + h x\right)^{2}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**(3/2)*(g + h*x)**2, x)","F",0
466,0,0,0,0.000000," ","integrate((h*x+g)*(a+b*ln(c*(d*(f*x+e)**p)**q))**(3/2),x)","\int \left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{\frac{3}{2}} \left(g + h x\right)\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**(3/2)*(g + h*x), x)","F",0
467,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**(3/2),x)","\int \left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**(3/2), x)","F",0
468,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**(3/2)/(h*x+g),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{\frac{3}{2}}}{g + h x}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**(3/2)/(g + h*x), x)","F",0
469,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**(3/2)/(h*x+g)**2,x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{\frac{3}{2}}}{\left(g + h x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**(3/2)/(g + h*x)**2, x)","F",0
470,0,0,0,0.000000," ","integrate((h*x+g)**2/(a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2),x)","\int \frac{\left(g + h x\right)^{2}}{\sqrt{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}}\, dx"," ",0,"Integral((g + h*x)**2/sqrt(a + b*log(c*(d*(e + f*x)**p)**q)), x)","F",0
471,0,0,0,0.000000," ","integrate((h*x+g)/(a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2),x)","\int \frac{g + h x}{\sqrt{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}}\, dx"," ",0,"Integral((g + h*x)/sqrt(a + b*log(c*(d*(e + f*x)**p)**q)), x)","F",0
472,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2),x)","\int \frac{1}{\sqrt{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*log(c*(d*(e + f*x)**p)**q)), x)","F",0
473,0,0,0,0.000000," ","integrate(1/(h*x+g)/(a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2),x)","\int \frac{1}{\sqrt{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}} \left(g + h x\right)}\, dx"," ",0,"Integral(1/(sqrt(a + b*log(c*(d*(e + f*x)**p)**q))*(g + h*x)), x)","F",0
474,0,0,0,0.000000," ","integrate((h*x+g)**2/(a+b*ln(c*(d*(f*x+e)**p)**q))**(3/2),x)","\int \frac{\left(g + h x\right)^{2}}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((g + h*x)**2/(a + b*log(c*(d*(e + f*x)**p)**q))**(3/2), x)","F",0
475,0,0,0,0.000000," ","integrate((h*x+g)/(a+b*ln(c*(d*(f*x+e)**p)**q))**(3/2),x)","\int \frac{g + h x}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((g + h*x)/(a + b*log(c*(d*(e + f*x)**p)**q))**(3/2), x)","F",0
476,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(d*(f*x+e)**p)**q))**(3/2),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**(-3/2), x)","F",0
477,0,0,0,0.000000," ","integrate(1/(h*x+g)/(a+b*ln(c*(d*(f*x+e)**p)**q))**(3/2),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{\frac{3}{2}} \left(g + h x\right)}\, dx"," ",0,"Integral(1/((a + b*log(c*(d*(e + f*x)**p)**q))**(3/2)*(g + h*x)), x)","F",0
478,0,0,0,0.000000," ","integrate((h*x+g)**2/(a+b*ln(c*(d*(f*x+e)**p)**q))**(5/2),x)","\int \frac{\left(g + h x\right)^{2}}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((g + h*x)**2/(a + b*log(c*(d*(e + f*x)**p)**q))**(5/2), x)","F",0
479,-1,0,0,0.000000," ","integrate((h*x+g)/(a+b*ln(c*(d*(f*x+e)**p)**q))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
480,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(d*(f*x+e)**p)**q))**(5/2),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**(-5/2), x)","F",0
481,-1,0,0,0.000000," ","integrate(1/(h*x+g)/(a+b*ln(c*(d*(f*x+e)**p)**q))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
482,1,484,0,98.684530," ","integrate((h*x+g)**(3/2)*(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","a g \left(\begin{cases} \sqrt{g} x & \text{for}\: h = 0 \\\frac{2 \left(g + h x\right)^{\frac{3}{2}}}{3 h} & \text{otherwise} \end{cases}\right) + \frac{2 a \left(- \frac{g \left(g + h x\right)^{\frac{3}{2}}}{3} + \frac{\left(g + h x\right)^{\frac{5}{2}}}{5}\right)}{h} + \frac{2 b g \left(- \frac{2 f p q \left(\frac{h \left(g + h x\right)^{\frac{3}{2}}}{3 f} + \frac{\sqrt{g + h x} \left(- e h^{2} + f g h\right)}{f^{2}} + \frac{h \left(e h - f g\right)^{2} \operatorname{atan}{\left(\frac{\sqrt{g + h x}}{\sqrt{\frac{e h - f g}{f}}} \right)}}{f^{3} \sqrt{\frac{e h - f g}{f}}}\right)}{3 h} + \frac{\left(g + h x\right)^{\frac{3}{2}} \log{\left(c \left(d \left(e - \frac{f g}{h} + \frac{f \left(g + h x\right)}{h}\right)^{p}\right)^{q} \right)}}{3}\right)}{h} + \frac{2 b \left(- \frac{2 f p q \left(\frac{h \left(g + h x\right)^{\frac{5}{2}}}{5 f} + \frac{\left(g + h x\right)^{\frac{3}{2}} \left(- e h^{2} + f g h\right)}{3 f^{2}} + \frac{\sqrt{g + h x} \left(e^{2} h^{3} - 2 e f g h^{2} + f^{2} g^{2} h\right)}{f^{3}} - \frac{h \left(e h - f g\right)^{3} \operatorname{atan}{\left(\frac{\sqrt{g + h x}}{\sqrt{\frac{e h - f g}{f}}} \right)}}{f^{4} \sqrt{\frac{e h - f g}{f}}}\right)}{5 h} - g \left(- \frac{2 f p q \left(\frac{h \left(g + h x\right)^{\frac{3}{2}}}{3 f} + \frac{\sqrt{g + h x} \left(- e h^{2} + f g h\right)}{f^{2}} + \frac{h \left(e h - f g\right)^{2} \operatorname{atan}{\left(\frac{\sqrt{g + h x}}{\sqrt{\frac{e h - f g}{f}}} \right)}}{f^{3} \sqrt{\frac{e h - f g}{f}}}\right)}{3 h} + \frac{\left(g + h x\right)^{\frac{3}{2}} \log{\left(c \left(d \left(e - \frac{f g}{h} + \frac{f \left(g + h x\right)}{h}\right)^{p}\right)^{q} \right)}}{3}\right) + \frac{\left(g + h x\right)^{\frac{5}{2}} \log{\left(c \left(d \left(e - \frac{f g}{h} + \frac{f \left(g + h x\right)}{h}\right)^{p}\right)^{q} \right)}}{5}\right)}{h}"," ",0,"a*g*Piecewise((sqrt(g)*x, Eq(h, 0)), (2*(g + h*x)**(3/2)/(3*h), True)) + 2*a*(-g*(g + h*x)**(3/2)/3 + (g + h*x)**(5/2)/5)/h + 2*b*g*(-2*f*p*q*(h*(g + h*x)**(3/2)/(3*f) + sqrt(g + h*x)*(-e*h**2 + f*g*h)/f**2 + h*(e*h - f*g)**2*atan(sqrt(g + h*x)/sqrt((e*h - f*g)/f))/(f**3*sqrt((e*h - f*g)/f)))/(3*h) + (g + h*x)**(3/2)*log(c*(d*(e - f*g/h + f*(g + h*x)/h)**p)**q)/3)/h + 2*b*(-2*f*p*q*(h*(g + h*x)**(5/2)/(5*f) + (g + h*x)**(3/2)*(-e*h**2 + f*g*h)/(3*f**2) + sqrt(g + h*x)*(e**2*h**3 - 2*e*f*g*h**2 + f**2*g**2*h)/f**3 - h*(e*h - f*g)**3*atan(sqrt(g + h*x)/sqrt((e*h - f*g)/f))/(f**4*sqrt((e*h - f*g)/f)))/(5*h) - g*(-2*f*p*q*(h*(g + h*x)**(3/2)/(3*f) + sqrt(g + h*x)*(-e*h**2 + f*g*h)/f**2 + h*(e*h - f*g)**2*atan(sqrt(g + h*x)/sqrt((e*h - f*g)/f))/(f**3*sqrt((e*h - f*g)/f)))/(3*h) + (g + h*x)**(3/2)*log(c*(d*(e - f*g/h + f*(g + h*x)/h)**p)**q)/3) + (g + h*x)**(5/2)*log(c*(d*(e - f*g/h + f*(g + h*x)/h)**p)**q)/5)/h","A",0
483,1,144,0,5.688570," ","integrate((h*x+g)**(1/2)*(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\frac{2 \left(\frac{a \left(g + h x\right)^{\frac{3}{2}}}{3} + b \left(- \frac{2 f p q \left(\frac{h \left(g + h x\right)^{\frac{3}{2}}}{3 f} + \frac{\sqrt{g + h x} \left(- e h^{2} + f g h\right)}{f^{2}} + \frac{h \left(e h - f g\right)^{2} \operatorname{atan}{\left(\frac{\sqrt{g + h x}}{\sqrt{\frac{e h - f g}{f}}} \right)}}{f^{3} \sqrt{\frac{e h - f g}{f}}}\right)}{3 h} + \frac{\left(g + h x\right)^{\frac{3}{2}} \log{\left(c \left(d \left(e - \frac{f g}{h} + \frac{f \left(g + h x\right)}{h}\right)^{p}\right)^{q} \right)}}{3}\right)\right)}{h}"," ",0,"2*(a*(g + h*x)**(3/2)/3 + b*(-2*f*p*q*(h*(g + h*x)**(3/2)/(3*f) + sqrt(g + h*x)*(-e*h**2 + f*g*h)/f**2 + h*(e*h - f*g)**2*atan(sqrt(g + h*x)/sqrt((e*h - f*g)/f))/(f**3*sqrt((e*h - f*g)/f)))/(3*h) + (g + h*x)**(3/2)*log(c*(d*(e - f*g/h + f*(g + h*x)/h)**p)**q)/3))/h","A",0
484,1,347,0,42.585818," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x+g)**(1/2),x)","\begin{cases} \frac{- \frac{2 a g}{\sqrt{g + h x}} - 2 a \left(- \frac{g}{\sqrt{g + h x}} - \sqrt{g + h x}\right) - 2 b g \left(\frac{2 f p q \operatorname{atan}{\left(\frac{1}{\sqrt{\frac{f}{e h - f g}} \sqrt{g + h x}} \right)}}{\sqrt{\frac{f}{e h - f g}} \left(e h - f g\right)} + \frac{\log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}{\sqrt{g + h x}}\right) - 2 b \left(- \frac{2 f p q \left(- \frac{h \sqrt{g + h x}}{f} - \frac{h \operatorname{atan}{\left(\frac{1}{\sqrt{\frac{f}{e h - f g}} \sqrt{g + h x}} \right)}}{f \sqrt{\frac{f}{e h - f g}}}\right)}{h} - g \left(\frac{2 f p q \operatorname{atan}{\left(\frac{1}{\sqrt{\frac{f}{e h - f g}} \sqrt{g + h x}} \right)}}{\sqrt{\frac{f}{e h - f g}} \left(e h - f g\right)} + \frac{\log{\left(c \left(d \left(e - \frac{f g}{h} + \frac{f \left(g + h x\right)}{h}\right)^{p}\right)^{q} \right)}}{\sqrt{g + h x}}\right) - \sqrt{g + h x} \log{\left(c \left(d \left(e - \frac{f g}{h} + \frac{f \left(g + h x\right)}{h}\right)^{p}\right)^{q} \right)}\right)}{h} & \text{for}\: h \neq 0 \\\frac{a x + b \left(- f p q \left(- \frac{e \left(\begin{cases} \frac{x}{e} & \text{for}\: f = 0 \\\frac{\log{\left(e + f x \right)}}{f} & \text{otherwise} \end{cases}\right)}{f} + \frac{x}{f}\right) + x \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)}{\sqrt{g}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*g/sqrt(g + h*x) - 2*a*(-g/sqrt(g + h*x) - sqrt(g + h*x)) - 2*b*g*(2*f*p*q*atan(1/(sqrt(f/(e*h - f*g))*sqrt(g + h*x)))/(sqrt(f/(e*h - f*g))*(e*h - f*g)) + log(c*(d*(e + f*x)**p)**q)/sqrt(g + h*x)) - 2*b*(-2*f*p*q*(-h*sqrt(g + h*x)/f - h*atan(1/(sqrt(f/(e*h - f*g))*sqrt(g + h*x)))/(f*sqrt(f/(e*h - f*g))))/h - g*(2*f*p*q*atan(1/(sqrt(f/(e*h - f*g))*sqrt(g + h*x)))/(sqrt(f/(e*h - f*g))*(e*h - f*g)) + log(c*(d*(e - f*g/h + f*(g + h*x)/h)**p)**q)/sqrt(g + h*x)) - sqrt(g + h*x)*log(c*(d*(e - f*g/h + f*(g + h*x)/h)**p)**q)))/h, Ne(h, 0)), ((a*x + b*(-f*p*q*(-e*Piecewise((x/e, Eq(f, 0)), (log(e + f*x)/f, True))/f + x/f) + x*log(c*(d*(e + f*x)**p)**q)))/sqrt(g), True))","A",0
485,1,90,0,21.452466," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x+g)**(3/2),x)","\frac{- \frac{2 a}{\sqrt{g + h x}} + 2 b \left(\frac{2 p q \operatorname{atan}{\left(\frac{\sqrt{g + h x}}{\sqrt{\frac{h \left(e - \frac{f g}{h}\right)}{f}}} \right)}}{\sqrt{\frac{h \left(e - \frac{f g}{h}\right)}{f}}} - \frac{\log{\left(c \left(d \left(e - \frac{f g}{h} + \frac{f \left(g + h x\right)}{h}\right)^{p}\right)^{q} \right)}}{\sqrt{g + h x}}\right)}{h}"," ",0,"(-2*a/sqrt(g + h*x) + 2*b*(2*p*q*atan(sqrt(g + h*x)/sqrt(h*(e - f*g/h)/f))/sqrt(h*(e - f*g/h)/f) - log(c*(d*(e - f*g/h + f*(g + h*x)/h)**p)**q)/sqrt(g + h*x)))/h","A",0
486,1,122,0,147.442373," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x+g)**(5/2),x)","\frac{- \frac{2 a}{3 \left(g + h x\right)^{\frac{3}{2}}} + 2 b \left(\frac{2 f p q \left(- \frac{h}{\sqrt{g + h x} \left(e h - f g\right)} - \frac{h \operatorname{atan}{\left(\frac{\sqrt{g + h x}}{\sqrt{\frac{e h - f g}{f}}} \right)}}{\sqrt{\frac{e h - f g}{f}} \left(e h - f g\right)}\right)}{3 h} - \frac{\log{\left(c \left(d \left(e - \frac{f g}{h} + \frac{f \left(g + h x\right)}{h}\right)^{p}\right)^{q} \right)}}{3 \left(g + h x\right)^{\frac{3}{2}}}\right)}{h}"," ",0,"(-2*a/(3*(g + h*x)**(3/2)) + 2*b*(2*f*p*q*(-h/(sqrt(g + h*x)*(e*h - f*g)) - h*atan(sqrt(g + h*x)/sqrt((e*h - f*g)/f))/(sqrt((e*h - f*g)/f)*(e*h - f*g)))/(3*h) - log(c*(d*(e - f*g/h + f*(g + h*x)/h)**p)**q)/(3*(g + h*x)**(3/2))))/h","A",0
487,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x+g)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x+g)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
489,-1,0,0,0.000000," ","integrate((h*x+g)**(3/2)*(a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
490,0,0,0,0.000000," ","integrate((h*x+g)**(1/2)*(a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)","\int \left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2} \sqrt{g + h x}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**2*sqrt(g + h*x), x)","F",0
491,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**2/(h*x+g)**(1/2),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2}}{\sqrt{g + h x}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**2/sqrt(g + h*x), x)","F",0
492,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**2/(h*x+g)**(3/2),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2}}{\left(g + h x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**2/(g + h*x)**(3/2), x)","F",0
493,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**2/(h*x+g)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
494,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**2/(h*x+g)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
495,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**2/(h*x+g)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
496,-1,0,0,0.000000," ","integrate((h*x+g)**(3/2)/(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
497,-1,0,0,0.000000," ","integrate((h*x+g)**(1/2)/(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
498,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x+g)**(1/2),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right) \sqrt{g + h x}}\, dx"," ",0,"Integral(1/((a + b*log(c*(d*(e + f*x)**p)**q))*sqrt(g + h*x)), x)","F",0
499,0,0,0,0.000000," ","integrate(1/(h*x+g)**(3/2)/(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right) \left(g + h x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*log(c*(d*(e + f*x)**p)**q))*(g + h*x)**(3/2)), x)","F",0
500,-1,0,0,0.000000," ","integrate((h*x+g)**(1/2)*(a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
501,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2)/(h*x+g)**(1/2),x)","\int \frac{\sqrt{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}}{\sqrt{g + h x}}\, dx"," ",0,"Integral(sqrt(a + b*log(c*(d*(e + f*x)**p)**q))/sqrt(g + h*x), x)","F",0
502,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2)/(h*x+g)**(3/2),x)","\int \frac{\sqrt{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}}{\left(g + h x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*log(c*(d*(e + f*x)**p)**q))/(g + h*x)**(3/2), x)","F",0
503,-1,0,0,0.000000," ","integrate((h*x+g)**(1/2)/(a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,0,0,0,0.000000," ","integrate(1/(h*x+g)**(1/2)/(a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2),x)","\int \frac{1}{\sqrt{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}} \sqrt{g + h x}}\, dx"," ",0,"Integral(1/(sqrt(a + b*log(c*(d*(e + f*x)**p)**q))*sqrt(g + h*x)), x)","F",0
505,0,0,0,0.000000," ","integrate(1/(h*x+g)**(3/2)/(a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2),x)","\int \frac{1}{\sqrt{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}} \left(g + h x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*log(c*(d*(e + f*x)**p)**q))*(g + h*x)**(3/2)), x)","F",0
506,-2,0,0,0.000000," ","integrate((h*x+g)**m*(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
507,0,0,0,0.000000," ","integrate((h*x+g)**m/(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\int \frac{\left(g + h x\right)^{m}}{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}\, dx"," ",0,"Integral((g + h*x)**m/(a + b*log(c*(d*(e + f*x)**p)**q)), x)","F",0
508,-2,0,0,0.000000," ","integrate((h*x+g)**m/(a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
509,-1,0,0,0.000000," ","integrate((h*x+g)**m*(a+b*ln(c*(d*(f*x+e)**p)**q))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
510,-2,0,0,0.000000," ","integrate((h*x+g)**m*(a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
511,0,0,0,0.000000," ","integrate((h*x+g)**m/(a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2),x)","\int \frac{\left(g + h x\right)^{m}}{\sqrt{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}}\, dx"," ",0,"Integral((g + h*x)**m/sqrt(a + b*log(c*(d*(e + f*x)**p)**q)), x)","F",0
512,-2,0,0,0.000000," ","integrate((h*x+g)**m/(a+b*ln(c*(d*(f*x+e)**p)**q))**(3/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
513,-1,0,0,0.000000," ","integrate((h*x+g)**m*(a+b*ln(c*(d*(f*x+e)**p)**q))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
514,0,0,0,0.000000," ","integrate((h*x+g)**2*(a+b*ln(c*(d*(f*x+e)**p)**q))**n,x)","\int \left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{n} \left(g + h x\right)^{2}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**n*(g + h*x)**2, x)","F",0
515,0,0,0,0.000000," ","integrate((h*x+g)*(a+b*ln(c*(d*(f*x+e)**p)**q))**n,x)","\int \left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{n} \left(g + h x\right)\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**n*(g + h*x), x)","F",0
516,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**n,x)","\int \left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{n}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**n, x)","F",0
517,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**n/(h*x+g),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{n}}{g + h x}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**n/(g + h*x), x)","F",0
518,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x**2+g),x)","\int \frac{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}{g + h x^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))/(g + h*x**2), x)","F",0
519,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x**2+2)**(1/2),x)","\int \frac{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}{\sqrt{h x^{2} + 2}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))/sqrt(h*x**2 + 2), x)","F",0
520,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x**2+g)**(1/2),x)","\int \frac{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}{\sqrt{g + h x^{2}}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))/sqrt(g + h*x**2), x)","F",0
521,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(-h*x+2)**(1/2)/(h*x+2)**(1/2),x)","\int \frac{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}{\sqrt{- h x + 2} \sqrt{h x + 2}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))/(sqrt(-h*x + 2)*sqrt(h*x + 2)), x)","F",0
522,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(-h*x+g)**(1/2)/(h*x+g)**(1/2),x)","\int \frac{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}{\sqrt{g - h x} \sqrt{g + h x}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))/(sqrt(g - h*x)*sqrt(g + h*x)), x)","F",0
523,0,0,0,0.000000," ","integrate((j*x+i)**3*(a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x+g),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right) \left(i + j x\right)^{3}}{g + h x}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))*(i + j*x)**3/(g + h*x), x)","F",0
524,0,0,0,0.000000," ","integrate((j*x+i)**2*(a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x+g),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right) \left(i + j x\right)^{2}}{g + h x}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))*(i + j*x)**2/(g + h*x), x)","F",0
525,0,0,0,0.000000," ","integrate((j*x+i)*(a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x+g),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right) \left(i + j x\right)}{g + h x}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))*(i + j*x)/(g + h*x), x)","F",0
526,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x+g),x)","\int \frac{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}{g + h x}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))/(g + h*x), x)","F",0
527,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x+g)/(j*x+i),x)","\int \frac{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}{\left(g + h x\right) \left(i + j x\right)}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))/((g + h*x)*(i + j*x)), x)","F",0
528,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x+g)/(j*x+i)**2,x)","\int \frac{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}{\left(g + h x\right) \left(i + j x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))/((g + h*x)*(i + j*x)**2), x)","F",0
529,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))/(h*x+g)/(j*x+i)**3,x)","\int \frac{a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}}{\left(g + h x\right) \left(i + j x\right)^{3}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))/((g + h*x)*(i + j*x)**3), x)","F",0
530,0,0,0,0.000000," ","integrate((j*x+i)**2*(a+b*ln(c*(d*(f*x+e)**p)**q))**2/(h*x+g),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2} \left(i + j x\right)^{2}}{g + h x}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**2*(i + j*x)**2/(g + h*x), x)","F",0
531,0,0,0,0.000000," ","integrate((j*x+i)*(a+b*ln(c*(d*(f*x+e)**p)**q))**2/(h*x+g),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2} \left(i + j x\right)}{g + h x}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**2*(i + j*x)/(g + h*x), x)","F",0
532,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**2/(h*x+g),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2}}{g + h x}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**2/(g + h*x), x)","F",0
533,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**2/(h*x+g)/(j*x+i),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2}}{\left(g + h x\right) \left(i + j x\right)}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**2/((g + h*x)*(i + j*x)), x)","F",0
534,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**2/(h*x+g)/(j*x+i)**2,x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2}}{\left(g + h x\right) \left(i + j x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**2/((g + h*x)*(i + j*x)**2), x)","F",0
535,0,0,0,0.000000," ","integrate((j*x+i)**2*(a+b*ln(c*(d*(f*x+e)**p)**q))**3/(h*x+g),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{3} \left(i + j x\right)^{2}}{g + h x}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**3*(i + j*x)**2/(g + h*x), x)","F",0
536,0,0,0,0.000000," ","integrate((j*x+i)*(a+b*ln(c*(d*(f*x+e)**p)**q))**3/(h*x+g),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{3} \left(i + j x\right)}{g + h x}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**3*(i + j*x)/(g + h*x), x)","F",0
537,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**3/(h*x+g),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{3}}{g + h x}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**3/(g + h*x), x)","F",0
538,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**3/(h*x+g)/(j*x+i),x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{3}}{\left(g + h x\right) \left(i + j x\right)}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**3/((g + h*x)*(i + j*x)), x)","F",0
539,0,0,0,0.000000," ","integrate((a+b*ln(c*(d*(f*x+e)**p)**q))**3/(h*x+g)/(j*x+i)**2,x)","\int \frac{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{3}}{\left(g + h x\right) \left(i + j x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d*(e + f*x)**p)**q))**3/((g + h*x)*(i + j*x)**2), x)","F",0
540,0,0,0,0.000000," ","integrate((j*x+i)/(h*x+g)/(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\int \frac{i + j x}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right) \left(g + h x\right)}\, dx"," ",0,"Integral((i + j*x)/((a + b*log(c*(d*(e + f*x)**p)**q))*(g + h*x)), x)","F",0
541,0,0,0,0.000000," ","integrate(1/(h*x+g)/(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right) \left(g + h x\right)}\, dx"," ",0,"Integral(1/((a + b*log(c*(d*(e + f*x)**p)**q))*(g + h*x)), x)","F",0
542,0,0,0,0.000000," ","integrate(1/(h*x+g)/(j*x+i)/(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right) \left(g + h x\right) \left(i + j x\right)}\, dx"," ",0,"Integral(1/((a + b*log(c*(d*(e + f*x)**p)**q))*(g + h*x)*(i + j*x)), x)","F",0
543,0,0,0,0.000000," ","integrate(1/(h*x+g)/(j*x+i)**2/(a+b*ln(c*(d*(f*x+e)**p)**q)),x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right) \left(g + h x\right) \left(i + j x\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*log(c*(d*(e + f*x)**p)**q))*(g + h*x)*(i + j*x)**2), x)","F",0
544,0,0,0,0.000000," ","integrate((j*x+i)/(h*x+g)/(a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)","\int \frac{i + j x}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2} \left(g + h x\right)}\, dx"," ",0,"Integral((i + j*x)/((a + b*log(c*(d*(e + f*x)**p)**q))**2*(g + h*x)), x)","F",0
545,0,0,0,0.000000," ","integrate(1/(h*x+g)/(a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2} \left(g + h x\right)}\, dx"," ",0,"Integral(1/((a + b*log(c*(d*(e + f*x)**p)**q))**2*(g + h*x)), x)","F",0
546,0,0,0,0.000000," ","integrate(1/(h*x+g)/(j*x+i)/(a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d \left(e + f x\right)^{p}\right)^{q} \right)}\right)^{2} \left(g + h x\right) \left(i + j x\right)}\, dx"," ",0,"Integral(1/((a + b*log(c*(d*(e + f*x)**p)**q))**2*(g + h*x)*(i + j*x)), x)","F",0
547,-1,0,0,0.000000," ","integrate(1/(h*x+g)/(j*x+i)**2/(a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
