∫ 4x5+(−4x3−2x5) log(4+4x2+x4)+(−6−3x2) log2(4+4x2+x4)_______ (−2x4−x6) log(4+4x2+x4)+(6x−2x2+3x3−x4+(2x2+x4) log(5)) log2(4+4x2+x4) dx [3538]

Optimal. Leaf size=35 \[ \log \left (-x-\frac {-3+x-x^2}{x}+\log (5)-\frac {x^2}{\log \left (\left (2+x^2\right )^2\right )}\right ) \]

________________________________________________________________________________________

Rubi [F]
time = 4.36, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {4 x^5+\left (-4 x^3-2 x^5\right ) \log \left (4+4 x^2+x^4\right )+\left (-6-3 x^2\right ) \log ^2\left (4+4 x^2+x^4\right )}{\left (-2 x^4-x^6\right ) \log \left (4+4 x^2+x^4\right )+\left (6 x-2 x^2+3 x^3-x^4+\left (2 x^2+x^4\right ) \log (5)\right ) \log ^2\left (4+4 x^2+x^4\right )} \, dx \end {gather*}

Int[(4*x^5 + (-4*x^3 - 2*x^5)*Log[4 + 4*x^2 + x^4] + (-6 - 3*x^2)*Log[4 + 4*x^2 + x^4]^2)/((-2*x^4 - x^6)*Log[

-Log[x] + Log[3 - x*(1 - Log[5])] - Log[Log[(2 + x^2)^2]] + (9*Defer[Int][(-x^3 - (-3 + x - x*Log[5])*Log[(2 +

x^2)^2])^(-1), x])/(1 - Log[5])^2 - 4*(1 - Log[5])*Defer[Int][(-x^3 - (-3 + x - x*Log[5])*Log[(2 + x^2)^2])^(

-1), x] + 6*Defer[Int][1/((I*Sqrt[2] - x)*(x^3 + (-3 + x - x*Log[5])*Log[(2 + x^2)^2])), x] - (2*I)*Sqrt[2]*(1

- Log[5])*Defer[Int][1/((I*Sqrt[2] - x)*(x^3 + (-3 + x - x*Log[5])*Log[(2 + x^2)^2])), x] - (3*Defer[Int][x/(

x^3 + (-3 + x - x*Log[5])*Log[(2 + x^2)^2]), x])/(1 - Log[5]) + 2*Defer[Int][x^2/(x^3 + (-3 + x - x*Log[5])*Lo

g[(2 + x^2)^2]), x] - 6*Defer[Int][1/((I*Sqrt[2] + x)*(x^3 + (-3 + x - x*Log[5])*Log[(2 + x^2)^2])), x] - (2*I

)*Sqrt[2]*(1 - Log[5])*Defer[Int][1/((I*Sqrt[2] + x)*(x^3 + (-3 + x - x*Log[5])*Log[(2 + x^2)^2])), x] + (27*D

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-4 x^5+2 x^3 \left (2+x^2\right ) \log \left (\left (2+x^2\right )^2\right )+3 \left (2+x^2\right ) \log ^2\left (\left (2+x^2\right )^2\right )}{x \left (2+x^2\right ) \log \left (\left (2+x^2\right )^2\right ) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx\\ &=\int \left (\frac {3}{x (-3+x (1-\log (5)))}-\frac {4 x}{\left (2+x^2\right ) \log \left (\left (2+x^2\right )^2\right )}+\frac {x^2 (9-2 x (1-\log (5)))}{(3-x (1-\log (5))) \left (x^3-3 \log \left (\left (2+x^2\right )^2\right )+x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )\right )}+\frac {4 x (-3+x (1-\log (5)))}{\left (2+x^2\right ) \left (x^3-3 \log \left (\left (2+x^2\right )^2\right )+x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )\right )}\right ) \, dx\\ &=3 \int \frac {1}{x (-3+x (1-\log (5)))} \, dx-4 \int \frac {x}{\left (2+x^2\right ) \log \left (\left (2+x^2\right )^2\right )} \, dx+4 \int \frac {x (-3+x (1-\log (5)))}{\left (2+x^2\right ) \left (x^3-3 \log \left (\left (2+x^2\right )^2\right )+x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx+\int \frac {x^2 (9-2 x (1-\log (5)))}{(3-x (1-\log (5))) \left (x^3-3 \log \left (\left (2+x^2\right )^2\right )+x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx\\ &=-\left (2 \text {Subst}\left (\int \frac {1}{(2+x) \log \left ((2+x)^2\right )} \, dx,x,x^2\right )\right )+4 \int \left (\frac {\left (1-\frac {1}{\log (5)}\right ) \log (5)}{-x^3+3 \log \left (\left (2+x^2\right )^2\right )-x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )}+\frac {-2-3 x+\log (25)}{\left (2+x^2\right ) \left (x^3-3 \log \left (\left (2+x^2\right )^2\right )+x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )\right )}\right ) \, dx+(1-\log (5)) \int \frac {1}{-3+x (1-\log (5))} \, dx-\int \frac {1}{x} \, dx+\int \left (\frac {9}{(1-\log (5))^2 \left (-x^3+3 \log \left (\left (2+x^2\right )^2\right )-x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )\right )}+\frac {2 x^2}{x^3-3 \log \left (\left (2+x^2\right )^2\right )+x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )}+\frac {27}{(3-x (1-\log (5))) (1-\log (5))^2 \left (x^3-3 \log \left (\left (2+x^2\right )^2\right )+x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )\right )}+\frac {3 x}{(-1+\log (5)) \left (x^3-3 \log \left (\left (2+x^2\right )^2\right )+x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )\right )}\right ) \, dx\\ &=-\log (x)+\log (3-x (1-\log (5)))+2 \int \frac {x^2}{x^3-3 \log \left (\left (2+x^2\right )^2\right )+x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx-2 \text {Subst}\left (\int \frac {1}{x \log \left (x^2\right )} \, dx,x,2+x^2\right )+4 \int \frac {-2-3 x+\log (25)}{\left (2+x^2\right ) \left (x^3-3 \log \left (\left (2+x^2\right )^2\right )+x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx+\frac {9 \int \frac {1}{-x^3+3 \log \left (\left (2+x^2\right )^2\right )-x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx}{(1-\log (5))^2}+\frac {27 \int \frac {1}{(3-x (1-\log (5))) \left (x^3-3 \log \left (\left (2+x^2\right )^2\right )+x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx}{(1-\log (5))^2}-\frac {3 \int \frac {x}{x^3-3 \log \left (\left (2+x^2\right )^2\right )+x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx}{1-\log (5)}+(4 (-1+\log (5))) \int \frac {1}{-x^3+3 \log \left (\left (2+x^2\right )^2\right )-x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx\\ &=-\log (x)+\log (3-x (1-\log (5)))+2 \int \frac {x^2}{x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx+4 \int \frac {-2-3 x+\log (25)}{\left (2+x^2\right ) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx+\frac {9 \int \frac {1}{-x^3-(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx}{(1-\log (5))^2}+\frac {27 \int \frac {1}{(3+x (-1+\log (5))) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx}{(1-\log (5))^2}-\frac {3 \int \frac {x}{x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx}{1-\log (5)}+(4 (-1+\log (5))) \int \frac {1}{-x^3-(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx-\text {Subst}\left (\int \frac {1}{x} \, dx,x,\log \left (\left (2+x^2\right )^2\right )\right )\\ &=-\log (x)+\log (3-x (1-\log (5)))-\log \left (\log \left (\left (2+x^2\right )^2\right )\right )+2 \int \frac {x^2}{x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx+4 \int \left (\frac {3 x}{\left (-2-x^2\right ) \left (x^3-3 \log \left (\left (2+x^2\right )^2\right )+x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )\right )}+\frac {2 (1-\log (5))}{\left (-2-x^2\right ) \left (x^3-3 \log \left (\left (2+x^2\right )^2\right )+x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )\right )}\right ) \, dx+\frac {9 \int \frac {1}{-x^3-(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx}{(1-\log (5))^2}+\frac {27 \int \frac {1}{(3+x (-1+\log (5))) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx}{(1-\log (5))^2}-\frac {3 \int \frac {x}{x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx}{1-\log (5)}+(4 (-1+\log (5))) \int \frac {1}{-x^3-(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx\\ &=-\log (x)+\log (3-x (1-\log (5)))-\log \left (\log \left (\left (2+x^2\right )^2\right )\right )+2 \int \frac {x^2}{x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx+12 \int \frac {x}{\left (-2-x^2\right ) \left (x^3-3 \log \left (\left (2+x^2\right )^2\right )+x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx+\frac {9 \int \frac {1}{-x^3-(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx}{(1-\log (5))^2}+\frac {27 \int \frac {1}{(3+x (-1+\log (5))) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx}{(1-\log (5))^2}-\frac {3 \int \frac {x}{x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx}{1-\log (5)}+(8 (1-\log (5))) \int \frac {1}{\left (-2-x^2\right ) \left (x^3-3 \log \left (\left (2+x^2\right )^2\right )+x (1-\log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx+(4 (-1+\log (5))) \int \frac {1}{-x^3-(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx\\ &=-\log (x)+\log (3-x (1-\log (5)))-\log \left (\log \left (\left (2+x^2\right )^2\right )\right )+2 \int \frac {x^2}{x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx+12 \int \frac {x}{\left (-2-x^2\right ) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx+\frac {9 \int \frac {1}{-x^3-(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx}{(1-\log (5))^2}+\frac {27 \int \frac {1}{(3+x (-1+\log (5))) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx}{(1-\log (5))^2}-\frac {3 \int \frac {x}{x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx}{1-\log (5)}+(8 (1-\log (5))) \int \frac {1}{\left (-2-x^2\right ) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx+(4 (-1+\log (5))) \int \frac {1}{-x^3-(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx\\ &=-\log (x)+\log (3-x (1-\log (5)))-\log \left (\log \left (\left (2+x^2\right )^2\right )\right )+2 \int \frac {x^2}{x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx+12 \int \left (\frac {1}{2 \left (i \sqrt {2}-x\right ) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )}-\frac {1}{2 \left (i \sqrt {2}+x\right ) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )}\right ) \, dx+\frac {9 \int \frac {1}{-x^3-(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx}{(1-\log (5))^2}+\frac {27 \int \frac {1}{(3+x (-1+\log (5))) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx}{(1-\log (5))^2}-\frac {3 \int \frac {x}{x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx}{1-\log (5)}+(8 (1-\log (5))) \int \left (-\frac {i}{2 \sqrt {2} \left (i \sqrt {2}-x\right ) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )}-\frac {i}{2 \sqrt {2} \left (i \sqrt {2}+x\right ) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )}\right ) \, dx+(4 (-1+\log (5))) \int \frac {1}{-x^3-(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx\\ &=-\log (x)+\log (3-x (1-\log (5)))-\log \left (\log \left (\left (2+x^2\right )^2\right )\right )+2 \int \frac {x^2}{x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx+6 \int \frac {1}{\left (i \sqrt {2}-x\right ) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx-6 \int \frac {1}{\left (i \sqrt {2}+x\right ) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx+\frac {9 \int \frac {1}{-x^3-(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx}{(1-\log (5))^2}+\frac {27 \int \frac {1}{(3+x (-1+\log (5))) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx}{(1-\log (5))^2}-\frac {3 \int \frac {x}{x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx}{1-\log (5)}-\left (2 i \sqrt {2} (1-\log (5))\right ) \int \frac {1}{\left (i \sqrt {2}-x\right ) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx-\left (2 i \sqrt {2} (1-\log (5))\right ) \int \frac {1}{\left (i \sqrt {2}+x\right ) \left (x^3+(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )\right )} \, dx+(4 (-1+\log (5))) \int \frac {1}{-x^3-(-3+x-x \log (5)) \log \left (\left (2+x^2\right )^2\right )} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]
time = 0.64, size = 54, normalized size = 1.54 \begin {gather*} -\log (x)-\log \left (\log \left (\left (2+x^2\right )^2\right )\right )+\log \left (x^3-3 \log \left (\left (2+x^2\right )^2\right )+x \log \left (\left (2+x^2\right )^2\right )-x \log (5) \log \left (\left (2+x^2\right )^2\right )\right ) \end {gather*}

Integrate[(4*x^5 + (-4*x^3 - 2*x^5)*Log[4 + 4*x^2 + x^4] + (-6 - 3*x^2)*Log[4 + 4*x^2 + x^4]^2)/((-2*x^4 - x^6

-Log[x] - Log[Log[(2 + x^2)^2]] + Log[x^3 - 3*Log[(2 + x^2)^2] + x*Log[(2 + x^2)^2] - x*Log[5]*Log[(2 + x^2)^2

________________________________________________________________________________________


method	result	size

risch	\(\ln \left (\left (-\ln \left (5\right )+1\right ) x -3\right )-\ln \left (x \right )-\ln \left (\ln \left (x^{4}+4 x^{2}+4\right )\right )+\ln \left (\ln \left (x^{4}+4 x^{2}+4\right )-\frac {x^{3}}{x \ln \left (5\right )-x +3}\right )\)	\(60\)
norman	\(-\ln \left (x \right )-\ln \left (\ln \left (x^{4}+4 x^{2}+4\right )\right )+\ln \left (\ln \left (5\right ) \ln \left (x^{4}+4 x^{2}+4\right ) x -x^{3}-x \ln \left (x^{4}+4 x^{2}+4\right )+3 \ln \left (x^{4}+4 x^{2}+4\right )\right )\)	\(69\)

int(((-3*x^2-6)*ln(x^4+4*x^2+4)^2+(-2*x^5-4*x^3)*ln(x^4+4*x^2+4)+4*x^5)/(((x^4+2*x^2)*ln(5)-x^4+3*x^3-2*x^2+6*

________________________________________________________________________________________

Maxima [A]
time = 0.51, size = 56, normalized size = 1.60 \begin {gather*} \log \left (x {\left (\log \left (5\right ) - 1\right )} + 3\right ) - \log \left (x\right ) + \log \left (-\frac {x^{3} - 2 \, {\left (x {\left (\log \left (5\right ) - 1\right )} + 3\right )} \log \left (x^{2} + 2\right )}{2 \, {\left (x {\left (\log \left (5\right ) - 1\right )} + 3\right )}}\right ) - \log \left (\log \left (x^{2} + 2\right )\right ) \end {gather*}

integrate(((-3*x^2-6)*log(x^4+4*x^2+4)^2+(-2*x^5-4*x^3)*log(x^4+4*x^2+4)+4*x^5)/(((x^4+2*x^2)*log(5)-x^4+3*x^3

log(x*(log(5) - 1) + 3) - log(x) + log(-1/2*(x^3 - 2*(x*(log(5) - 1) + 3)*log(x^2 + 2))/(x*(log(5) - 1) + 3))

________________________________________________________________________________________

Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 69 vs. \(2 (34) = 68\).
time = 0.37, size = 69, normalized size = 1.97 \begin {gather*} \log \left (x \log \left (5\right ) - x + 3\right ) - \log \left (x\right ) + \log \left (-\frac {x^{3} - {\left (x \log \left (5\right ) - x + 3\right )} \log \left (x^{4} + 4 \, x^{2} + 4\right )}{x \log \left (5\right ) - x + 3}\right ) - \log \left (\log \left (x^{4} + 4 \, x^{2} + 4\right )\right ) \end {gather*}

integrate(((-3*x^2-6)*log(x^4+4*x^2+4)^2+(-2*x^5-4*x^3)*log(x^4+4*x^2+4)+4*x^5)/(((x^4+2*x^2)*log(5)-x^4+3*x^3

log(x*log(5) - x + 3) - log(x) + log(-(x^3 - (x*log(5) - x + 3)*log(x^4 + 4*x^2 + 4))/(x*log(5) - x + 3)) - lo

________________________________________________________________________________________

Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: PolynomialError} \end {gather*}

integrate(((-3*x**2-6)*ln(x**4+4*x**2+4)**2+(-2*x**5-4*x**3)*ln(x**4+4*x**2+4)+4*x**5)/(((x**4+2*x**2)*ln(5)-x

Exception raised: PolynomialError >> 1/(-2*x**4*log(5) + x**4 + x**4*log(5)**2 - 6*x**3 + 6*x**3*log(5) - 4*x*

*2*log(5) + 2*x**2*log(5)**2 + 11*x**2 - 12*x + 12*x*log(5) + 18) contains an element of the set of generators

________________________________________________________________________________________

Giac [A]
time = 0.44, size = 68, normalized size = 1.94 \begin {gather*} \log \left (-x^{3} + x \log \left (5\right ) \log \left (x^{4} + 4 \, x^{2} + 4\right ) - x \log \left (x^{4} + 4 \, x^{2} + 4\right ) + 3 \, \log \left (x^{4} + 4 \, x^{2} + 4\right )\right ) - \log \left (x\right ) - \log \left (\log \left (x^{4} + 4 \, x^{2} + 4\right )\right ) \end {gather*}

integrate(((-3*x^2-6)*log(x^4+4*x^2+4)^2+(-2*x^5-4*x^3)*log(x^4+4*x^2+4)+4*x^5)/(((x^4+2*x^2)*log(5)-x^4+3*x^3

log(-x^3 + x*log(5)*log(x^4 + 4*x^2 + 4) - x*log(x^4 + 4*x^2 + 4) + 3*log(x^4 + 4*x^2 + 4)) - log(x) - log(log

________________________________________________________________________________________

Mupad [B]
time = 6.03, size = 2500, normalized size = 71.43 \begin {gather*} \text {Too large to display} \end {gather*}

int((log(4*x^2 + x^4 + 4)*(4*x^3 + 2*x^5) + log(4*x^2 + x^4 + 4)^2*(3*x^2 + 6) - 4*x^5)/(log(4*x^2 + x^4 + 4)*

log(x*(9*log((x^2 + 2)^2) + x^2*log((x^2 + 2)^2) - x^4*log(5) - 3*x^3 + x^4 - 6*x*log((x^2 + 2)^2) + x^2*log((

x^2 + 2)^2)*log(5)^2 + 6*x*log((x^2 + 2)^2)*log(5) - 2*x^2*log((x^2 + 2)^2)*log(5))) - log(x*(72*log(4*x^2 + x

^4 + 4) + 12*x^2*log(4*x^2 + x^4 + 4) - 9*x^3*log(4*x^2 + x^4 + 4) + 2*x^4*log(4*x^2 + x^4 + 4) - 4*x^4*log(5)

- 66*x*log(4*x^2 + x^4 + 4) - 12*x^3 + 4*x^4 + 48*x*log(5)*log(4*x^2 + x^4 + 4) - 20*x^2*log(5)*log(4*x^2 + x

^4 + 4) - 2*x^4*log(5)*log(4*x^2 + x^4 + 4) + 8*x^2*log(5)^2*log(4*x^2 + x^4 + 4)) - x*(9*x^3*log(4*x^2 + x^4

+ 4) - 4*x^2*log(4*x^2 + x^4 + 4) - 2*x^4*log(4*x^2 + x^4 + 4) - 4*x^4*log(5) + 18*x*log(4*x^2 + x^4 + 4) - 12

*x^3 + 4*x^4 + 4*x^2*log(5)*log(4*x^2 + x^4 + 4) + 2*x^4*log(5)*log(4*x^2 + x^4 + 4))) - log(x) + symsum(log(3

3043620105792*log(625) - 191446983005184*log(5) - root(12476089554*z^5*log(5)*log(625) - 4950250980*z^5*log(5)

^2*log(625)^2 + 484358724*z^5*log(5)^4*log(625)^3 - 239636880*z^5*log(5)^2*log(625)^4 - 94885776*z^5*log(5)^5*

log(625)^3 + 88216560*z^5*log(5)^7*log(625)^2 - 54064008*z^5*log(5)^6*log(625)^2 - 25406208*z^5*log(5)^8*log(6

25)^2 + 19994256*z^5*log(5)^6*log(625)^3 + 19789920*z^5*log(5)^3*log(625)^4 + 8000000*z^5*log(5)^9*log(625)^2

- 4233600*z^5*log(5)^7*log(625)^3 - 3421440*z^5*log(5)^4*log(625)^4 + 559872*z^5*log(5)^5*log(625)^4 - 450048*

z^5*log(5)^10*log(625)^2 + 179712*z^5*log(5)^8*log(625)^3 - 33024*z^5*log(5)^11*log(625)^2 + 2048*z^5*log(5)^1

2*log(625)^2 + 1215973440*z^5*log(5)^6*log(625) + 9497495360*z^5*log(5)^3*log(625) - 855600912*z^5*log(5)^8*lo

g(625) + 13353194984*z^5*log(5)^5*log(625) - 184310640*z^5*log(5)*log(625)^4 - 2876069088*z^5*log(5)^5*log(625

)^2 + 160323520*z^5*log(5)^9*log(625) - 2728181808*z^5*log(5)^4*log(625)^2 - 30926256*z^5*log(5)^10*log(625) +

990592*z^5*log(5)^11*log(625) - 364544*z^5*log(5)^12*log(625) + 132096*z^5*log(5)^13*log(625) - 8192*z^5*log(

5)^14*log(625) - 11135933108*z^5*log(5)^3*log(625)^2 + 2104890516*z^5*log(5)^2*log(625)^3 - 3271912237*z^5*log

(5)^2*log(625) + 3105872352*z^5*log(5)^7*log(625) + 1183695336*z^5*log(5)^3*log(625)^3 - 2672150172*z^5*log(5)

*log(625)^2 + 2581668072*z^5*log(5)*log(625)^3 + 11029505352*z^5*log(5)^4*log(625) - 37976590196*z^5*log(5)^3

- 7612365760*z^5*log(5)^5 - 11759677728*z^5*log(5)^6 + 19970762026*z^5*log(5)^4 - 2609404160*z^5*log(5)^7 - 12

27877888*z^5*log(5)^9 + 1212381648*z^5*log(625)^3 + 31218036596*z^5*log(5)^2 + 7000018859*z^5*log(625) + 72207

7440*z^5*log(5)^10 - 553335264*z^5*log(5)^8 - 489522528*z^5*log(625)^4 - 31967952756*z^5*log(5) - 231140288*z^

5*log(5)^11 - 4434737216*z^5*log(625)^2 + 58274528*z^5*log(5)^12 + 36450000*z^5*log(625)^5 - 9070336*z^5*log(5

)^13 + 1091584*z^5*log(5)^14 - 132096*z^5*log(5)^15 + 8192*z^5*log(5)^16 + 705818410*z^5 + 4925603232*z^4*log(

5)^5*log(625)^2 + 2112984720*z^4*log(5)^8*log(625) - 507883176*z^4*log(5)^3*log(625)^3 - 422627760*z^4*log(5)^

7*log(625)^2 + 385436880*z^4*log(5)^2*log(625)^4 + 219805776*z^4*log(5)^4*log(625)^2 + 203656464*z^4*log(5)^5*

log(625)^3 - 10394524512*z^4*log(5)^7*log(625) + 103641408*z^4*log(5)^8*log(625)^2 - 38158992*z^4*log(5)^6*log

(625)^3 - 21893120*z^4*log(5)^9*log(625)^2 - 19789920*z^4*log(5)^3*log(625)^4 + 6473088*z^4*log(5)^7*log(625)^

3 + 3421440*z^4*log(5)^4*log(625)^4 + 1168896*z^4*log(5)^10*log(625)^2 - 559872*z^4*log(5)^5*log(625)^4 - 1797

12*z^4*log(5)^8*log(625)^3 + 33024*z^4*log(5)^11*log(625)^2 - 2048*z^4*log(5)^12*log(625)^2 + 23951396350*z^4*

log(5)*log(625) - 7484890188*z^4*log(5)^2*log(625)^2 - 34728028771*z^4*log(5)^2*log(625) + 15901362260*z^4*log

(5)^3*log(625)^2 + 17457193960*z^4*log(5)^4*log(625) - 2963843028*z^4*log(5)^2*log(625)^3 - 268816256*z^4*log(

5)^9*log(625) - 107289360*z^4*log(5)*log(625)^4 + 21409328*z^4*log(5)^10*log(625) + 14069592*z^4*log(5)*log(62

5)^3 + 6691456*z^4*log(5)^11*log(625) - 280576*z^4*log(5)^13*log(625) + 274432*z^4*log(5)^12*log(625) + 16384*

z^4*log(5)^14*log(625) + 8491244604*z^4*log(5)*log(625)^2 - 3958773472*z^4*log(5)^3*log(625) - 33945822712*z^4

*log(5)^5*log(625) + 7771370688*z^4*log(5)^6*log(625) - 1323311364*z^4*log(5)^4*log(625)^3 + 1116327384*z^4*lo

g(5)^6*log(625)^2 + 235978643332*z^4*log(5)^3 + 28864119904*z^4*log(5)^6 - 3055040512*z^4*log(5)^10 + 29553262

08*z^4*log(5)^7 - 21705874987*z^4*log(625) - 2878871760*z^4*log(625)^3 + 98727131908*z^4*log(5) - 221525920812

*z^4*log(5)^2 - 2362697568*z^4*log(5)^8 - 83946835838*z^4*log(5)^4 - 19328727360*z^4*log(5)^5 + 6343178880*z^4

*log(5)^9 + 5951283584*z^4*log(625)^2 + 922185408*z^4*log(5)^11 + 635322528*z^4*log(625)^4 - 210576544*z^4*log

(5)^12 - 36450000*z^4*log(625)^5 + 31544576*z^4*log(5)^13 - 3803136*z^4*log(5)^14 + 429056*z^4*log(5)^15 - 245

76*z^4*log(5)^16 - 2117455230*z^4 - 5056253112*z^3*log(5)^2*log(625)^2 + 36590909904*z^3*log(5)^5*log(625) - 5

19193008*z^3*log(5)^3*log(625)^3 + 472670496*z^3*log(5)^7*log(625)^2 - 199633248*z^3*log(5)^2*log(625)^4 - 447

6161224*z^3*log(5)^3*log(625)^2 - 104205312*z^3*log(5)^8*log(625)^2 - 102726432*z^3*log(5)^5*log(625)^3 + 2058

________________________________________________________________________________________

3.36.38 \(\int \frac {4 x^5+(-4 x^3-2 x^5) \log (4+4 x^2+x^4)+(-6-3 x^2) \log ^2(4+4 x^2+x^4)}{(-2 x^4-x^6) \log (4+4 x^2+x^4)+(6 x-2 x^2+3 x^3-x^4+(2 x^2+x^4) \log (5)) \log ^2(4+4 x^2+x^4)} \, dx\) [3538]