∫ x3 log(2)+(18x2−3x3) log(2) log(6−x)+(12x−2x2+(−12+2x) log(2)) log2(6−x)________________________________________________________ (6x3−x4) log(2) log(6−x)+(6x2−x3+(6−13x+2x2) log(2)) log2(6−x) dx

Optimal. Leaf size=30 \[ \log \left (x^2-x \log (2) \left (2-\frac {1}{x}-\frac {x^2}{\log (6-x)}\right )\right ) \]

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Rubi [F] time = 5.78, 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 {x^3 \log (2)+\left (18 x^2-3 x^3\right ) \log (2) \log (6-x)+\left (12 x-2 x^2+(-12+2 x) \log (2)\right ) \log ^2(6-x)}{\left (6 x^3-x^4\right ) \log (2) \log (6-x)+\left (6 x^2-x^3+\left (6-13 x+2 x^2\right ) \log (2)\right ) \log ^2(6-x)} \, dx \end {gather*}

Int[(x^3*Log[2] + (18*x^2 - 3*x^3)*Log[2]*Log[6 - x] + (12*x - 2*x^2 + (-12 + 2*x)*Log[2])*Log[6 - x]^2)/((6*x

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

2 + Log[2] - x*Log[4])*Log[6 - x])^(-1), x] + Log[2]*(1 - Log[4])*Log[4]*Defer[Int][(x^3*Log[2] + (x^2 + Log[2

] - x*Log[4])*Log[6 - x])^(-1), x] + (36 + Log[2] - 6*Log[4])*Defer[Int][1/((-6 + x)*(x^3*Log[2] + (x^2 + Log[

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

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

[2] + (x^2 + Log[2] - x*Log[4])*Log[6 - x]), x] - Log[2]*Log[4]*(Log[4]^2 - Log[8])*(1 - (I*Log[4])/Sqrt[-Log[

4]^2 + Log[16]])*Defer[Int][1/((2*x - Log[4] - I*Sqrt[4*Log[2] - Log[4]^2])*(x^3*Log[2] + (x^2 + Log[2] - x*Lo

g[4])*Log[6 - x])), x] - ((2*I)*Log[2]^2*(1 - Log[4])*Log[4]*Defer[Int][1/((2*x - Log[4] + I*Sqrt[4*Log[2] - L

og[4]^2])*(x^3*Log[2] + (x^2 + Log[2] - x*Log[4])*Log[6 - x])), x])/Sqrt[-Log[4]^2 + Log[16]] - Log[2]*Log[4]*

(Log[4]^2 - Log[8])*(1 + (I*Log[4])/Sqrt[-Log[4]^2 + Log[16]])*Defer[Int][1/((2*x - Log[4] + I*Sqrt[4*Log[2] -

Log[4]^2])*(x^3*Log[2] + (x^2 + Log[2] - x*Log[4])*Log[6 - x])), x] - ((2*I)*Log[2]^2*(1 - Log[4])*Log[4]*Def

er[Int][1/((-2*x + Log[4] + I*Sqrt[4*Log[2] - Log[4]^2])*(x^3*Log[2] + (x^2 + Log[2] - x*Log[4])*Log[6 - x])),

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x^3 \log (2)+\left (18 x^2-3 x^3\right ) \log (2) \log (6-x)+\left (12 x-2 x^2+(-12+2 x) \log (2)\right ) \log ^2(6-x)}{(6-x) \log (6-x) \left (x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)\right )} \, dx\\ &=\int \left (\frac {2 (x-\log (2))}{x^2+\log (2)-x \log (4)}-\frac {1}{(-6+x) \log (6-x)}+\frac {x^2+\log (2)-x \log (4)}{(-6+x) \left (x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)\right )}+\frac {x^2 \log (2) \left (x^2-2 x \log (4)+\log (8)\right )}{\left (x^2+\log (2)-x \log (4)\right ) \left (x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)\right )}\right ) \, dx\\ &=2 \int \frac {x-\log (2)}{x^2+\log (2)-x \log (4)} \, dx+\log (2) \int \frac {x^2 \left (x^2-2 x \log (4)+\log (8)\right )}{\left (x^2+\log (2)-x \log (4)\right ) \left (x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)\right )} \, dx-\int \frac {1}{(-6+x) \log (6-x)} \, dx+\int \frac {x^2+\log (2)-x \log (4)}{(-6+x) \left (x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)\right )} \, dx\\ &=\frac {2 \log (2) \log \left (x^2+\log (2)-x \log (4)\right )}{\log (4)}+\log (2) \int \frac {x^2 \left (x^2-2 x \log (4)+\log (8)\right )}{\left (x^2+\log (2)-x \log (4)\right ) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )} \, dx+\int \left (\frac {x}{x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)}+\frac {6 \left (1-\frac {\log (2)}{3}\right )}{x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)}+\frac {36+\log (2)-6 \log (4)}{(-6+x) \left (x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)\right )}\right ) \, dx-\operatorname {Subst}\left (\int \frac {1}{x \log (x)} \, dx,x,6-x\right )\\ &=\frac {2 \log (2) \log \left (x^2+\log (2)-x \log (4)\right )}{\log (4)}+\left (6 \left (1-\frac {\log (2)}{3}\right )\right ) \int \frac {1}{x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)} \, dx+\log (2) \int \left (\frac {x^2}{x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)}-\frac {x \log (4)}{x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)}+\frac {\log (4) \left (-\log (2) (1-\log (4))-x \left (\log ^2(4)-\log (8)\right )\right )}{\left (x^2+\log (2)-x \log (4)\right ) \left (x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)\right )}-\frac {\log (2) \left (1+\frac {\log ^2(4)-\log (8)}{\log (2)}\right )}{x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)}\right ) \, dx+(36+\log (2)-6 \log (4)) \int \frac {1}{(-6+x) \left (x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)\right )} \, dx+\int \frac {x}{x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)} \, dx-\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log (6-x)\right )\\ &=\frac {2 \log (2) \log \left (x^2+\log (2)-x \log (4)\right )}{\log (4)}-\log (\log (6-x))+\left (6 \left (1-\frac {\log (2)}{3}\right )\right ) \int \frac {1}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+\log (2) \int \frac {x^2}{x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)} \, dx+(36+\log (2)-6 \log (4)) \int \frac {1}{(-6+x) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )} \, dx-(\log (2) \log (4)) \int \frac {x}{x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)} \, dx+(\log (2) \log (4)) \int \frac {-\log (2) (1-\log (4))-x \left (\log ^2(4)-\log (8)\right )}{\left (x^2+\log (2)-x \log (4)\right ) \left (x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)\right )} \, dx+(\log (2) (1-\log (4)) \log (4)) \int \frac {1}{x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)} \, dx+\int \frac {x}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx\\ &=\frac {2 \log (2) \log \left (x^2+\log (2)-x \log (4)\right )}{\log (4)}-\log (\log (6-x))+\left (6 \left (1-\frac {\log (2)}{3}\right )\right ) \int \frac {1}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+\log (2) \int \frac {x^2}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+(36+\log (2)-6 \log (4)) \int \frac {1}{(-6+x) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )} \, dx-(\log (2) \log (4)) \int \frac {x}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+(\log (2) \log (4)) \int \frac {\log (2) (-1+\log (4))+x \left (-\log ^2(4)+\log (8)\right )}{\left (x^2+\log (2)-x \log (4)\right ) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )} \, dx+(\log (2) (1-\log (4)) \log (4)) \int \frac {1}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+\int \frac {x}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx\\ &=\frac {2 \log (2) \log \left (x^2+\log (2)-x \log (4)\right )}{\log (4)}-\log (\log (6-x))+\left (6 \left (1-\frac {\log (2)}{3}\right )\right ) \int \frac {1}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+\log (2) \int \frac {x^2}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+(36+\log (2)-6 \log (4)) \int \frac {1}{(-6+x) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )} \, dx-(\log (2) \log (4)) \int \frac {x}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+(\log (2) \log (4)) \int \left (\frac {\log (2) (-1+\log (4))}{\left (x^2+\log (2)-x \log (4)\right ) \left (x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)\right )}-\frac {x \left (\log ^2(4)-\log (8)\right )}{\left (x^2+\log (2)-x \log (4)\right ) \left (x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)\right )}\right ) \, dx+(\log (2) (1-\log (4)) \log (4)) \int \frac {1}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+\int \frac {x}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx\\ &=\frac {2 \log (2) \log \left (x^2+\log (2)-x \log (4)\right )}{\log (4)}-\log (\log (6-x))+\left (6 \left (1-\frac {\log (2)}{3}\right )\right ) \int \frac {1}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+\log (2) \int \frac {x^2}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+(36+\log (2)-6 \log (4)) \int \frac {1}{(-6+x) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )} \, dx-(\log (2) \log (4)) \int \frac {x}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+(\log (2) (1-\log (4)) \log (4)) \int \frac {1}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx-\left (\log ^2(2) (1-\log (4)) \log (4)\right ) \int \frac {1}{\left (x^2+\log (2)-x \log (4)\right ) \left (x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)\right )} \, dx-\left (\log (2) \log (4) \left (\log ^2(4)-\log (8)\right )\right ) \int \frac {x}{\left (x^2+\log (2)-x \log (4)\right ) \left (x^3 \log (2)+x^2 \log (6-x)+\log (2) \log (6-x)-x \log (4) \log (6-x)\right )} \, dx+\int \frac {x}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx\\ &=\frac {2 \log (2) \log \left (x^2+\log (2)-x \log (4)\right )}{\log (4)}-\log (\log (6-x))+\left (6 \left (1-\frac {\log (2)}{3}\right )\right ) \int \frac {1}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+\log (2) \int \frac {x^2}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+(36+\log (2)-6 \log (4)) \int \frac {1}{(-6+x) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )} \, dx-(\log (2) \log (4)) \int \frac {x}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+(\log (2) (1-\log (4)) \log (4)) \int \frac {1}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx-\left (\log ^2(2) (1-\log (4)) \log (4)\right ) \int \frac {1}{\left (x^2+\log (2)-x \log (4)\right ) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )} \, dx-\left (\log (2) \log (4) \left (\log ^2(4)-\log (8)\right )\right ) \int \frac {x}{\left (x^2+\log (2)-x \log (4)\right ) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )} \, dx+\int \frac {x}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx\\ &=\frac {2 \log (2) \log \left (x^2+\log (2)-x \log (4)\right )}{\log (4)}-\log (\log (6-x))+\left (6 \left (1-\frac {\log (2)}{3}\right )\right ) \int \frac {1}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+\log (2) \int \frac {x^2}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+(36+\log (2)-6 \log (4)) \int \frac {1}{(-6+x) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )} \, dx-(\log (2) \log (4)) \int \frac {x}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+(\log (2) (1-\log (4)) \log (4)) \int \frac {1}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx-\left (\log ^2(2) (1-\log (4)) \log (4)\right ) \int \left (\frac {2 i}{\sqrt {4 \log (2)-\log ^2(4)} \left (2 x-\log (4)+i \sqrt {4 \log (2)-\log ^2(4)}\right ) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )}+\frac {2 i}{\sqrt {4 \log (2)-\log ^2(4)} \left (-2 x+\log (4)+i \sqrt {4 \log (2)-\log ^2(4)}\right ) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )}\right ) \, dx-\left (\log (2) \log (4) \left (\log ^2(4)-\log (8)\right )\right ) \int \left (\frac {1-\frac {i \log (4)}{\sqrt {-\log ^2(4)+\log (16)}}}{\left (2 x-\log (4)-i \sqrt {4 \log (2)-\log ^2(4)}\right ) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )}+\frac {1+\frac {i \log (4)}{\sqrt {-\log ^2(4)+\log (16)}}}{\left (2 x-\log (4)+i \sqrt {4 \log (2)-\log ^2(4)}\right ) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )}\right ) \, dx+\int \frac {x}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx\\ &=\frac {2 \log (2) \log \left (x^2+\log (2)-x \log (4)\right )}{\log (4)}-\log (\log (6-x))+\left (6 \left (1-\frac {\log (2)}{3}\right )\right ) \int \frac {1}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+\log (2) \int \frac {x^2}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+(36+\log (2)-6 \log (4)) \int \frac {1}{(-6+x) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )} \, dx-(\log (2) \log (4)) \int \frac {x}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx+(\log (2) (1-\log (4)) \log (4)) \int \frac {1}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx-\frac {\left (2 i \log ^2(2) (1-\log (4)) \log (4)\right ) \int \frac {1}{\left (2 x-\log (4)+i \sqrt {4 \log (2)-\log ^2(4)}\right ) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )} \, dx}{\sqrt {-\log ^2(4)+\log (16)}}-\frac {\left (2 i \log ^2(2) (1-\log (4)) \log (4)\right ) \int \frac {1}{\left (-2 x+\log (4)+i \sqrt {4 \log (2)-\log ^2(4)}\right ) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )} \, dx}{\sqrt {-\log ^2(4)+\log (16)}}-\left (\log (2) \log (4) \left (\log ^2(4)-\log (8)\right ) \left (1-\frac {i \log (4)}{\sqrt {-\log ^2(4)+\log (16)}}\right )\right ) \int \frac {1}{\left (2 x-\log (4)-i \sqrt {4 \log (2)-\log ^2(4)}\right ) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )} \, dx-\left (\log (2) \log (4) \left (\log ^2(4)-\log (8)\right ) \left (1+\frac {i \log (4)}{\sqrt {-\log ^2(4)+\log (16)}}\right )\right ) \int \frac {1}{\left (2 x-\log (4)+i \sqrt {4 \log (2)-\log ^2(4)}\right ) \left (x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)\right )} \, dx+\int \frac {x}{x^3 \log (2)+\left (x^2+\log (2)-x \log (4)\right ) \log (6-x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [F] time = 0.86, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^3 \log (2)+\left (18 x^2-3 x^3\right ) \log (2) \log (6-x)+\left (12 x-2 x^2+(-12+2 x) \log (2)\right ) \log ^2(6-x)}{\left (6 x^3-x^4\right ) \log (2) \log (6-x)+\left (6 x^2-x^3+\left (6-13 x+2 x^2\right ) \log (2)\right ) \log ^2(6-x)} \, dx \end {gather*}

Integrate[(x^3*Log[2] + (18*x^2 - 3*x^3)*Log[2]*Log[6 - x] + (12*x - 2*x^2 + (-12 + 2*x)*Log[2])*Log[6 - x]^2)

/((6*x^3 - x^4)*Log[2]*Log[6 - x] + (6*x^2 - x^3 + (6 - 13*x + 2*x^2)*Log[2])*Log[6 - x]^2),x]

Integrate[(x^3*Log[2] + (18*x^2 - 3*x^3)*Log[2]*Log[6 - x] + (12*x - 2*x^2 + (-12 + 2*x)*Log[2])*Log[6 - x]^2)

/((6*x^3 - x^4)*Log[2]*Log[6 - x] + (6*x^2 - x^3 + (6 - 13*x + 2*x^2)*Log[2])*Log[6 - x]^2), x]

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fricas [B] time = 0.59, size = 69, normalized size = 2.30 \begin {gather*} \log \left (x^{2} - {\left (2 \, x - 1\right )} \log \relax (2)\right ) + \log \left (-\frac {x^{3} \log \relax (2) + {\left (x^{2} - {\left (2 \, x - 1\right )} \log \relax (2)\right )} \log \left (-x + 6\right )}{x^{2} - {\left (2 \, x - 1\right )} \log \relax (2)}\right ) - \log \left (\log \left (-x + 6\right )\right ) \end {gather*}

integrate((((2*x-12)*log(2)-2*x^2+12*x)*log(-x+6)^2+(-3*x^3+18*x^2)*log(2)*log(-x+6)+x^3*log(2))/(((2*x^2-13*x

log(x^2 - (2*x - 1)*log(2)) + log(-(x^3*log(2) + (x^2 - (2*x - 1)*log(2))*log(-x + 6))/(x^2 - (2*x - 1)*log(2)

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giac [A] time = 0.50, size = 48, normalized size = 1.60 \begin {gather*} \log \left (x^{3} \log \relax (2) + x^{2} \log \left (-x + 6\right ) - 2 \, x \log \relax (2) \log \left (-x + 6\right ) + \log \relax (2) \log \left (-x + 6\right )\right ) - \log \left (\log \left (-x + 6\right )\right ) \end {gather*}

integrate((((2*x-12)*log(2)-2*x^2+12*x)*log(-x+6)^2+(-3*x^3+18*x^2)*log(2)*log(-x+6)+x^3*log(2))/(((2*x^2-13*x

log(x^3*log(2) + x^2*log(-x + 6) - 2*x*log(2)*log(-x + 6) + log(2)*log(-x + 6)) - log(log(-x + 6))

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method	result	size

norman	\(-\ln \left (\ln \left (-x +6\right )\right )+\ln \left (x^{3} \ln \relax (2)-2 \ln \relax (2) \ln \left (-x +6\right ) x +\ln \left (-x +6\right ) x^{2}+\ln \relax (2) \ln \left (-x +6\right )\right )\)	\(49\)
risch	\(\ln \left (-2 x \ln \relax (2)+x^{2}+\ln \relax (2)\right )-\ln \left (\ln \left (-x +6\right )\right )+\ln \left (\ln \left (-x +6\right )-\frac {x^{3} \ln \relax (2)}{2 x \ln \relax (2)-x^{2}-\ln \relax (2)}\right )\)	\(55\)

int((((2*x-12)*ln(2)-2*x^2+12*x)*ln(-x+6)^2+(-3*x^3+18*x^2)*ln(2)*ln(-x+6)+x^3*ln(2))/(((2*x^2-13*x+6)*ln(2)-x

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maxima [B] time = 0.97, size = 62, normalized size = 2.07 \begin {gather*} \log \left (x^{2} - 2 \, x \log \relax (2) + \log \relax (2)\right ) + \log \left (\frac {x^{3} \log \relax (2) + {\left (x^{2} - 2 \, x \log \relax (2) + \log \relax (2)\right )} \log \left (-x + 6\right )}{x^{2} - 2 \, x \log \relax (2) + \log \relax (2)}\right ) - \log \left (\log \left (-x + 6\right )\right ) \end {gather*}

integrate((((2*x-12)*log(2)-2*x^2+12*x)*log(-x+6)^2+(-3*x^3+18*x^2)*log(2)*log(-x+6)+x^3*log(2))/(((2*x^2-13*x

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

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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {x^3\,\ln \relax (2)+{\ln \left (6-x\right )}^2\,\left (12\,x+\ln \relax (2)\,\left (2\,x-12\right )-2\,x^2\right )+\ln \relax (2)\,\ln \left (6-x\right )\,\left (18\,x^2-3\,x^3\right )}{\left (\ln \relax (2)\,\left (2\,x^2-13\,x+6\right )+6\,x^2-x^3\right )\,{\ln \left (6-x\right )}^2+\ln \relax (2)\,\left (6\,x^3-x^4\right )\,\ln \left (6-x\right )} \,d x \end {gather*}

int((x^3*log(2) + log(6 - x)^2*(12*x + log(2)*(2*x - 12) - 2*x^2) + log(2)*log(6 - x)*(18*x^2 - 3*x^3))/(log(6

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

integrate((((2*x-12)*ln(2)-2*x**2+12*x)*ln(-x+6)**2+(-3*x**3+18*x**2)*ln(2)*ln(-x+6)+x**3*ln(2))/(((2*x**2-13*

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3.3.56 \(\int \frac {x^3 \log (2)+(18 x^2-3 x^3) \log (2) \log (6-x)+(12 x-2 x^2+(-12+2 x) \log (2)) \log ^2(6-x)}{(6 x^3-x^4) \log (2) \log (6-x)+(6 x^2-x^3+(6-13 x+2 x^2) \log (2)) \log ^2(6-x)} \, dx\)