3.79.0 ∫ 6−9x2+12x3−15x4+15x5+(−6+6x−9x2+9x3) log(−1+x)+(−12x+6x2+24x3−24x4+(12x−12x2) log(−1+x)) log2(log(5))+(3−9x2+9x3+(−3+3x) log(−1+x)) log4(log(5)) ________________________________________________________________________________________________________________________

Integrand size = 115, antiderivative size = 25 \[ \int \frac {6-9 x^2+12 x^3-15 x^4+15 x^5+\left (-6+6 x-9 x^2+9 x^3\right ) \log (-1+x)+\left (-12 x+6 x^2+24 x^3-24 x^4+\left (12 x-12 x^2\right ) \log (-1+x)\right ) \log ^2(\log (5))+\left (3-9 x^2+9 x^3+(-3+3 x) \log (-1+x)\right ) \log ^4(\log (5))}{-1+x} \, dx=3 x \left (-1+x^2+\log (-1+x)\right ) \left (2+\left (-x+\log ^2(\log (5))\right )^2\right ) \]

Rubi [B] (veriﬁed)

Leaf count is larger than twice the leaf count of optimal. \(358\) vs. \(2(25)=50\).

Time = 0.31 (sec) , antiderivative size = 358, normalized size of antiderivative = 14.32, number of steps used = 22, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.052, Rules used = {6874, 45, 2464, 2442, 2436, 2332} \[ \int \frac {6-9 x^2+12 x^3-15 x^4+15 x^5+\left (-6+6 x-9 x^2+9 x^3\right ) \log (-1+x)+\left (-12 x+6 x^2+24 x^3-24 x^4+\left (12 x-12 x^2\right ) \log (-1+x)\right ) \log ^2(\log (5))+\left (3-9 x^2+9 x^3+(-3+3 x) \log (-1+x)\right ) \log ^4(\log (5))}{-1+x} \, dx=3 x^5+\frac {15 x^4}{4}-\frac {3}{4} x^4 \left (5+8 \log ^2(\log (5))\right )+4 x^3-x^3 \left (5+8 \log ^2(\log (5))\right )+x^3 \left (4+3 \log ^4(\log (5))+8 \log ^2(\log (5))\right )+3 x^3 \log (x-1)+6 x^2-\frac {3}{2} x^2 \left (5+8 \log ^2(\log (5))\right )-6 x^2 \log ^2(\log (5)) \log (x-1)+3 x^2 \log ^2(\log (5))+\frac {3}{2} x^2 \left (4+3 \log ^4(\log (5))+8 \log ^2(\log (5))\right )-\frac {3}{2} x^2 \left (3+3 \log ^4(\log (5))-2 \log ^2(\log (5))\right )+12 x-3 x \left (2+\log ^4(\log (5))\right )+3 \left (2+\log ^4(\log (5))\right ) \log (1-x)-3 (1-x) \left (2+\log ^4(\log (5))\right ) \log (x-1)-3 x \left (5+8 \log ^2(\log (5))\right )-6 x \log ^2(\log (5))-3 \left (5+8 \log ^2(\log (5))\right ) \log (1-x)-6 \log ^2(\log (5)) \log (1-x)+3 x \left (4+3 \log ^4(\log (5))+8 \log ^2(\log (5))\right )-3 x \left (3+3 \log ^4(\log (5))-2 \log ^2(\log (5))\right )+3 \left (4+3 \log ^4(\log (5))+8 \log ^2(\log (5))\right ) \log (1-x)-3 \left (3+3 \log ^4(\log (5))-2 \log ^2(\log (5))\right ) \log (1-x)+12 \log (1-x) \]

Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {15 x^5}{-1+x}-\frac {12 x \log ^2(\log (5))}{-1+x}-\frac {15 x^4 \left (1+\frac {8}{5} \log ^2(\log (5))\right )}{-1+x}+\frac {6 \left (1+\frac {1}{2} \log ^4(\log (5))\right )}{-1+x}+\frac {12 x^3 \left (1+2 \log ^2(\log (5))+\frac {3}{4} \log ^4(\log (5))\right )}{-1+x}-\frac {9 x^2 \left (1-\frac {2}{3} \log ^2(\log (5))+\log ^4(\log (5))\right )}{-1+x}+3 \log (-1+x) \left (2+3 x^2-4 x \log ^2(\log (5))+\log ^4(\log (5))\right )\right ) \, dx \\ & = 3 \log (1-x) \left (2+\log ^4(\log (5))\right )+3 \int \log (-1+x) \left (2+3 x^2-4 x \log ^2(\log (5))+\log ^4(\log (5))\right ) \, dx+15 \int \frac {x^5}{-1+x} \, dx-\left (12 \log ^2(\log (5))\right ) \int \frac {x}{-1+x} \, dx-\left (3 \left (5+8 \log ^2(\log (5))\right )\right ) \int \frac {x^4}{-1+x} \, dx-\left (3 \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )\right ) \int \frac {x^2}{-1+x} \, dx+\left (3 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )\right ) \int \frac {x^3}{-1+x} \, dx \\ & = 3 \log (1-x) \left (2+\log ^4(\log (5))\right )+3 \int \left (3 x^2 \log (-1+x)-4 x \log (-1+x) \log ^2(\log (5))+2 \log (-1+x) \left (1+\frac {1}{2} \log ^4(\log (5))\right )\right ) \, dx+15 \int \left (1+\frac {1}{-1+x}+x+x^2+x^3+x^4\right ) \, dx-\left (12 \log ^2(\log (5))\right ) \int \left (1+\frac {1}{-1+x}\right ) \, dx-\left (3 \left (5+8 \log ^2(\log (5))\right )\right ) \int \left (1+\frac {1}{-1+x}+x+x^2+x^3\right ) \, dx-\left (3 \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )\right ) \int \left (1+\frac {1}{-1+x}+x\right ) \, dx+\left (3 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )\right ) \int \left (1+\frac {1}{-1+x}+x+x^2\right ) \, dx \\ & = 15 x+\frac {15 x^2}{2}+5 x^3+\frac {15 x^4}{4}+3 x^5+15 \log (1-x)-12 x \log ^2(\log (5))-12 \log (1-x) \log ^2(\log (5))-3 x \left (5+8 \log ^2(\log (5))\right )-\frac {3}{2} x^2 \left (5+8 \log ^2(\log (5))\right )-x^3 \left (5+8 \log ^2(\log (5))\right )-\frac {3}{4} x^4 \left (5+8 \log ^2(\log (5))\right )-3 \log (1-x) \left (5+8 \log ^2(\log (5))\right )+3 \log (1-x) \left (2+\log ^4(\log (5))\right )-3 x \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-\frac {3}{2} x^2 \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-3 \log (1-x) \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+3 x \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+\frac {3}{2} x^2 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+x^3 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+3 \log (1-x) \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+9 \int x^2 \log (-1+x) \, dx-\left (12 \log ^2(\log (5))\right ) \int x \log (-1+x) \, dx+\left (3 \left (2+\log ^4(\log (5))\right )\right ) \int \log (-1+x) \, dx \\ & = 15 x+\frac {15 x^2}{2}+5 x^3+\frac {15 x^4}{4}+3 x^5+15 \log (1-x)+3 x^3 \log (-1+x)-12 x \log ^2(\log (5))-12 \log (1-x) \log ^2(\log (5))-6 x^2 \log (-1+x) \log ^2(\log (5))-3 x \left (5+8 \log ^2(\log (5))\right )-\frac {3}{2} x^2 \left (5+8 \log ^2(\log (5))\right )-x^3 \left (5+8 \log ^2(\log (5))\right )-\frac {3}{4} x^4 \left (5+8 \log ^2(\log (5))\right )-3 \log (1-x) \left (5+8 \log ^2(\log (5))\right )+3 \log (1-x) \left (2+\log ^4(\log (5))\right )-3 x \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-\frac {3}{2} x^2 \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-3 \log (1-x) \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+3 x \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+\frac {3}{2} x^2 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+x^3 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+3 \log (1-x) \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-3 \int \frac {x^3}{-1+x} \, dx+\left (6 \log ^2(\log (5))\right ) \int \frac {x^2}{-1+x} \, dx+\left (3 \left (2+\log ^4(\log (5))\right )\right ) \text {Subst}(\int \log (x) \, dx,x,-1+x) \\ & = 15 x+\frac {15 x^2}{2}+5 x^3+\frac {15 x^4}{4}+3 x^5+15 \log (1-x)+3 x^3 \log (-1+x)-12 x \log ^2(\log (5))-12 \log (1-x) \log ^2(\log (5))-6 x^2 \log (-1+x) \log ^2(\log (5))-3 x \left (5+8 \log ^2(\log (5))\right )-\frac {3}{2} x^2 \left (5+8 \log ^2(\log (5))\right )-x^3 \left (5+8 \log ^2(\log (5))\right )-\frac {3}{4} x^4 \left (5+8 \log ^2(\log (5))\right )-3 \log (1-x) \left (5+8 \log ^2(\log (5))\right )-3 x \left (2+\log ^4(\log (5))\right )+3 \log (1-x) \left (2+\log ^4(\log (5))\right )-3 (1-x) \log (-1+x) \left (2+\log ^4(\log (5))\right )-3 x \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-\frac {3}{2} x^2 \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-3 \log (1-x) \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+3 x \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+\frac {3}{2} x^2 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+x^3 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+3 \log (1-x) \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-3 \int \left (1+\frac {1}{-1+x}+x+x^2\right ) \, dx+\left (6 \log ^2(\log (5))\right ) \int \left (1+\frac {1}{-1+x}+x\right ) \, dx \\ & = 12 x+6 x^2+4 x^3+\frac {15 x^4}{4}+3 x^5+12 \log (1-x)+3 x^3 \log (-1+x)-6 x \log ^2(\log (5))+3 x^2 \log ^2(\log (5))-6 \log (1-x) \log ^2(\log (5))-6 x^2 \log (-1+x) \log ^2(\log (5))-3 x \left (5+8 \log ^2(\log (5))\right )-\frac {3}{2} x^2 \left (5+8 \log ^2(\log (5))\right )-x^3 \left (5+8 \log ^2(\log (5))\right )-\frac {3}{4} x^4 \left (5+8 \log ^2(\log (5))\right )-3 \log (1-x) \left (5+8 \log ^2(\log (5))\right )-3 x \left (2+\log ^4(\log (5))\right )+3 \log (1-x) \left (2+\log ^4(\log (5))\right )-3 (1-x) \log (-1+x) \left (2+\log ^4(\log (5))\right )-3 x \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-\frac {3}{2} x^2 \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-3 \log (1-x) \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+3 x \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+\frac {3}{2} x^2 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+x^3 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+3 \log (1-x) \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right ) \\ \end{align*}

Mathematica [A] (veriﬁed)

Time = 0.05 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.20 \[ \int \frac {6-9 x^2+12 x^3-15 x^4+15 x^5+\left (-6+6 x-9 x^2+9 x^3\right ) \log (-1+x)+\left (-12 x+6 x^2+24 x^3-24 x^4+\left (12 x-12 x^2\right ) \log (-1+x)\right ) \log ^2(\log (5))+\left (3-9 x^2+9 x^3+(-3+3 x) \log (-1+x)\right ) \log ^4(\log (5))}{-1+x} \, dx=3 x \left (-1+x^2+\log (-1+x)\right ) \left (2+x^2-2 x \log ^2(\log (5))+\log ^4(\log (5))\right ) \]

Maple [B] (veriﬁed)

Leaf count of result is larger than twice the leaf count of optimal. \(84\) vs. \(2(28)=56\).

Time = 0.17 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.40


method	result	size

risch	\(\left (3 \ln \left (\ln \left (5\right )\right )^{4} x -6 x^{2} \ln \left (\ln \left (5\right )\right )^{2}+3 x^{3}+6 x \right ) \ln \left (-1+x \right )+3 \ln \left (\ln \left (5\right )\right )^{4} x^{3}-6 \ln \left (\ln \left (5\right )\right )^{2} x^{4}-3 \ln \left (\ln \left (5\right )\right )^{4} x +3 x^{5}+6 x^{2} \ln \left (\ln \left (5\right )\right )^{2}+3 x^{3}-6 x\)	\(85\)
norman	\(\left (-6-3 \ln \left (\ln \left (5\right )\right )^{4}\right ) x +\left (3+3 \ln \left (\ln \left (5\right )\right )^{4}\right ) x^{3}+\left (6+3 \ln \left (\ln \left (5\right )\right )^{4}\right ) x \ln \left (-1+x \right )+3 x^{5}+6 x^{2} \ln \left (\ln \left (5\right )\right )^{2}+3 \ln \left (-1+x \right ) x^{3}-6 \ln \left (\ln \left (5\right )\right )^{2} x^{4}-6 \ln \left (-1+x \right ) \ln \left (\ln \left (5\right )\right )^{2} x^{2}\)	\(89\)
parallelrisch	\(3 \ln \left (\ln \left (5\right )\right )^{4} x^{3}+3 \ln \left (-1+x \right ) \ln \left (\ln \left (5\right )\right )^{4} x -6 \ln \left (\ln \left (5\right )\right )^{2} x^{4}-3 \ln \left (\ln \left (5\right )\right )^{4} x -6 \ln \left (-1+x \right ) \ln \left (\ln \left (5\right )\right )^{2} x^{2}+3 x^{5}-6 \ln \left (\ln \left (5\right )\right )^{4}+6 x^{2} \ln \left (\ln \left (5\right )\right )^{2}+3 \ln \left (-1+x \right ) x^{3}+3 x^{3}-6 \ln \left (\ln \left (5\right )\right )^{2}+6 \ln \left (-1+x \right ) x -6 x -12\)	\(110\)
parts	\(3 \ln \left (\ln \left (5\right )\right )^{4} \left (\left (-1+x \right ) \ln \left (-1+x \right )+1-x \right )-12 \ln \left (\ln \left (5\right )\right )^{2} \left (\frac {\ln \left (-1+x \right ) \left (-1+x \right )^{2}}{2}-\frac {\left (-1+x \right )^{2}}{4}\right )-12 \ln \left (\ln \left (5\right )\right )^{2} \left (\left (-1+x \right ) \ln \left (-1+x \right )+1-x \right )+3 \ln \left (-1+x \right ) \left (-1+x \right )^{3}-\left (-1+x \right )^{3}+9 \ln \left (-1+x \right ) \left (-1+x \right )^{2}-\frac {9 \left (-1+x \right )^{2}}{2}+15 \left (-1+x \right ) \ln \left (-1+x \right )-12 x +15+3 \ln \left (\ln \left (5\right )\right )^{4} x^{3}-6 \ln \left (\ln \left (5\right )\right )^{2} x^{4}+3 x^{5}+3 x^{2} \ln \left (\ln \left (5\right )\right )^{2}-6 x \ln \left (\ln \left (5\right )\right )^{2}+4 x^{3}+\frac {3 x^{2}}{2}+3 \left (3-2 \ln \left (\ln \left (5\right )\right )^{2}+\ln \left (\ln \left (5\right )\right )^{4}\right ) \ln \left (-1+x \right )\)	\(190\)
derivativedivides	\(3 \ln \left (\ln \left (5\right )\right )^{4} \left (-1+x \right )^{3}+3 \ln \left (\ln \left (5\right )\right )^{4} \left (\left (-1+x \right ) \ln \left (-1+x \right )+1-x \right )+9 \ln \left (\ln \left (5\right )\right )^{4} \left (-1+x \right )^{2}-6 \ln \left (\ln \left (5\right )\right )^{2} \left (-1+x \right )^{4}+9 \ln \left (\ln \left (5\right )\right )^{4} \left (-1+x \right )-12 \ln \left (\ln \left (5\right )\right )^{2} \left (\frac {\ln \left (-1+x \right ) \left (-1+x \right )^{2}}{2}-\frac {\left (-1+x \right )^{2}}{4}\right )-24 \ln \left (\ln \left (5\right )\right )^{2} \left (-1+x \right )^{3}+3 \left (-1+x \right )^{5}+3 \ln \left (-1+x \right ) \ln \left (\ln \left (5\right )\right )^{4}-12 \ln \left (\ln \left (5\right )\right )^{2} \left (\left (-1+x \right ) \ln \left (-1+x \right )+1-x \right )-33 \ln \left (\ln \left (5\right )\right )^{2} \left (-1+x \right )^{2}+3 \ln \left (-1+x \right ) \left (-1+x \right )^{3}+33 \left (-1+x \right )^{3}+15 \left (-1+x \right )^{4}-24 \ln \left (\ln \left (5\right )\right )^{2} \left (-1+x \right )+9 \ln \left (-1+x \right ) \left (-1+x \right )^{2}+39 \left (-1+x \right )^{2}-6 \ln \left (-1+x \right ) \ln \left (\ln \left (5\right )\right )^{2}+15 \left (-1+x \right ) \ln \left (-1+x \right )-18+18 x +9 \ln \left (-1+x \right )\)	\(239\)
default	\(3 \ln \left (\ln \left (5\right )\right )^{4} \left (-1+x \right )^{3}+3 \ln \left (\ln \left (5\right )\right )^{4} \left (\left (-1+x \right ) \ln \left (-1+x \right )+1-x \right )+9 \ln \left (\ln \left (5\right )\right )^{4} \left (-1+x \right )^{2}-6 \ln \left (\ln \left (5\right )\right )^{2} \left (-1+x \right )^{4}+9 \ln \left (\ln \left (5\right )\right )^{4} \left (-1+x \right )-12 \ln \left (\ln \left (5\right )\right )^{2} \left (\frac {\ln \left (-1+x \right ) \left (-1+x \right )^{2}}{2}-\frac {\left (-1+x \right )^{2}}{4}\right )-24 \ln \left (\ln \left (5\right )\right )^{2} \left (-1+x \right )^{3}+3 \left (-1+x \right )^{5}+3 \ln \left (-1+x \right ) \ln \left (\ln \left (5\right )\right )^{4}-12 \ln \left (\ln \left (5\right )\right )^{2} \left (\left (-1+x \right ) \ln \left (-1+x \right )+1-x \right )-33 \ln \left (\ln \left (5\right )\right )^{2} \left (-1+x \right )^{2}+3 \ln \left (-1+x \right ) \left (-1+x \right )^{3}+33 \left (-1+x \right )^{3}+15 \left (-1+x \right )^{4}-24 \ln \left (\ln \left (5\right )\right )^{2} \left (-1+x \right )+9 \ln \left (-1+x \right ) \left (-1+x \right )^{2}+39 \left (-1+x \right )^{2}-6 \ln \left (-1+x \right ) \ln \left (\ln \left (5\right )\right )^{2}+15 \left (-1+x \right ) \ln \left (-1+x \right )-18+18 x +9 \ln \left (-1+x \right )\)	\(239\)

Fricas [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (25) = 50\).

Time = 0.25 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.84 \[ \int \frac {6-9 x^2+12 x^3-15 x^4+15 x^5+\left (-6+6 x-9 x^2+9 x^3\right ) \log (-1+x)+\left (-12 x+6 x^2+24 x^3-24 x^4+\left (12 x-12 x^2\right ) \log (-1+x)\right ) \log ^2(\log (5))+\left (3-9 x^2+9 x^3+(-3+3 x) \log (-1+x)\right ) \log ^4(\log (5))}{-1+x} \, dx=3 \, x^{5} + 3 \, {\left (x^{3} + x \log \left (x - 1\right ) - x\right )} \log \left (\log \left (5\right )\right )^{4} + 3 \, x^{3} - 6 \, {\left (x^{4} + x^{2} \log \left (x - 1\right ) - x^{2}\right )} \log \left (\log \left (5\right )\right )^{2} + 3 \, {\left (x^{3} + 2 \, x\right )} \log \left (x - 1\right ) - 6 \, x \]

Sympy [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 90 vs. \(2 (26) = 52\).

Time = 0.10 (sec) , antiderivative size = 90, normalized size of antiderivative = 3.60 \[ \int \frac {6-9 x^2+12 x^3-15 x^4+15 x^5+\left (-6+6 x-9 x^2+9 x^3\right ) \log (-1+x)+\left (-12 x+6 x^2+24 x^3-24 x^4+\left (12 x-12 x^2\right ) \log (-1+x)\right ) \log ^2(\log (5))+\left (3-9 x^2+9 x^3+(-3+3 x) \log (-1+x)\right ) \log ^4(\log (5))}{-1+x} \, dx=3 x^{5} - 6 x^{4} \log {\left (\log {\left (5 \right )} \right )}^{2} + x^{3} \cdot \left (3 \log {\left (\log {\left (5 \right )} \right )}^{4} + 3\right ) + 6 x^{2} \log {\left (\log {\left (5 \right )} \right )}^{2} + x \left (-6 - 3 \log {\left (\log {\left (5 \right )} \right )}^{4}\right ) + \left (3 x^{3} - 6 x^{2} \log {\left (\log {\left (5 \right )} \right )}^{2} + 3 x \log {\left (\log {\left (5 \right )} \right )}^{4} + 6 x\right ) \log {\left (x - 1 \right )} \]

Maxima [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 374 vs. \(2 (25) = 50\).

Time = 0.20 (sec) , antiderivative size = 374, normalized size of antiderivative = 14.96 \[ \int \frac {6-9 x^2+12 x^3-15 x^4+15 x^5+\left (-6+6 x-9 x^2+9 x^3\right ) \log (-1+x)+\left (-12 x+6 x^2+24 x^3-24 x^4+\left (12 x-12 x^2\right ) \log (-1+x)\right ) \log ^2(\log (5))+\left (3-9 x^2+9 x^3+(-3+3 x) \log (-1+x)\right ) \log ^4(\log (5))}{-1+x} \, dx=3 \, {\left (x + \log \left (x - 1\right )\right )} \log \left (x - 1\right ) \log \left (\log \left (5\right )\right )^{4} - \frac {3}{2} \, \log \left (x - 1\right )^{2} \log \left (\log \left (5\right )\right )^{4} + 3 \, x^{5} + \frac {3}{2} \, {\left (2 \, x^{3} + 3 \, x^{2} + 6 \, x + 6 \, \log \left (x - 1\right )\right )} \log \left (\log \left (5\right )\right )^{4} - \frac {9}{2} \, {\left (x^{2} + 2 \, x + 2 \, \log \left (x - 1\right )\right )} \log \left (\log \left (5\right )\right )^{4} - \frac {3}{2} \, {\left (\log \left (x - 1\right )^{2} + 2 \, x + 2 \, \log \left (x - 1\right )\right )} \log \left (\log \left (5\right )\right )^{4} + 3 \, \log \left (x - 1\right ) \log \left (\log \left (5\right )\right )^{4} - 6 \, {\left (x^{2} + 2 \, x + 2 \, \log \left (x - 1\right )\right )} \log \left (x - 1\right ) \log \left (\log \left (5\right )\right )^{2} + 12 \, {\left (x + \log \left (x - 1\right )\right )} \log \left (x - 1\right ) \log \left (\log \left (5\right )\right )^{2} + 3 \, x^{3} - 2 \, {\left (3 \, x^{4} + 4 \, x^{3} + 6 \, x^{2} + 12 \, x + 12 \, \log \left (x - 1\right )\right )} \log \left (\log \left (5\right )\right )^{2} + 4 \, {\left (2 \, x^{3} + 3 \, x^{2} + 6 \, x + 6 \, \log \left (x - 1\right )\right )} \log \left (\log \left (5\right )\right )^{2} + 3 \, {\left (x^{2} + 2 \, \log \left (x - 1\right )^{2} + 6 \, x + 6 \, \log \left (x - 1\right )\right )} \log \left (\log \left (5\right )\right )^{2} + 3 \, {\left (x^{2} + 2 \, x + 2 \, \log \left (x - 1\right )\right )} \log \left (\log \left (5\right )\right )^{2} - 6 \, {\left (\log \left (x - 1\right )^{2} + 2 \, x + 2 \, \log \left (x - 1\right )\right )} \log \left (\log \left (5\right )\right )^{2} - 12 \, {\left (x + \log \left (x - 1\right )\right )} \log \left (\log \left (5\right )\right )^{2} + \frac {3}{2} \, {\left (2 \, x^{3} + 3 \, x^{2} + 6 \, x + 6 \, \log \left (x - 1\right )\right )} \log \left (x - 1\right ) - \frac {9}{2} \, {\left (x^{2} + 2 \, x + 2 \, \log \left (x - 1\right )\right )} \log \left (x - 1\right ) + 6 \, {\left (x + \log \left (x - 1\right )\right )} \log \left (x - 1\right ) - 6 \, \log \left (x - 1\right )^{2} - 6 \, x \]

Giac [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 80 vs. \(2 (25) = 50\).

Time = 0.27 (sec) , antiderivative size = 80, normalized size of antiderivative = 3.20 \[ \int \frac {6-9 x^2+12 x^3-15 x^4+15 x^5+\left (-6+6 x-9 x^2+9 x^3\right ) \log (-1+x)+\left (-12 x+6 x^2+24 x^3-24 x^4+\left (12 x-12 x^2\right ) \log (-1+x)\right ) \log ^2(\log (5))+\left (3-9 x^2+9 x^3+(-3+3 x) \log (-1+x)\right ) \log ^4(\log (5))}{-1+x} \, dx=-6 \, x^{4} \log \left (\log \left (5\right )\right )^{2} + 3 \, x^{5} + 3 \, {\left (\log \left (\log \left (5\right )\right )^{4} + 1\right )} x^{3} + 6 \, x^{2} \log \left (\log \left (5\right )\right )^{2} - 3 \, {\left (\log \left (\log \left (5\right )\right )^{4} + 2\right )} x - 3 \, {\left (2 \, x^{2} \log \left (\log \left (5\right )\right )^{2} - x^{3} - {\left (\log \left (\log \left (5\right )\right )^{4} + 2\right )} x\right )} \log \left (x - 1\right ) \]

Mupad [B] (veriﬁcation not implemented)

Time = 12.23 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.20 \[ \int \frac {6-9 x^2+12 x^3-15 x^4+15 x^5+\left (-6+6 x-9 x^2+9 x^3\right ) \log (-1+x)+\left (-12 x+6 x^2+24 x^3-24 x^4+\left (12 x-12 x^2\right ) \log (-1+x)\right ) \log ^2(\log (5))+\left (3-9 x^2+9 x^3+(-3+3 x) \log (-1+x)\right ) \log ^4(\log (5))}{-1+x} \, dx=3\,x\,\left (\ln \left (x-1\right )+x^2-1\right )\,\left (x^2-2\,{\ln \left (\ln \left (5\right )\right )}^2\,x+{\ln \left (\ln \left (5\right )\right )}^4+2\right ) \]

\(\int \frac {6-9 x^2+12 x^3-15 x^4+15 x^5+(-6+6 x-9 x^2+9 x^3) \log (-1+x)+(-12 x+6 x^2+24 x^3-24 x^4+(12 x-12 x^2) \log (-1+x)) \log ^2(\log (5))+(3-9 x^2+9 x^3+(-3+3 x) \log (-1+x)) \log ^4(\log (5))}{-1+x} \, dx\) [7891]

Optimal result