Integrand size = 185, antiderivative size = 25 \[ \int \frac {-4+x+e^5 \left (-48-12 x+6 x^2\right )+e^{10} \left (-144-108 x+9 x^3-8 x^4+2 x^5\right )+\left (e^5 (-24+6 x)+e^{10} \left (-144-36 x+18 x^2\right )\right ) \log (-4+x)+e^{10} (-36+9 x) \log ^2(-4+x)+\left (12-3 x+e^5 \left (144+18 x-12 x^2\right )+e^{10} \left (432+216 x-18 x^2-9 x^3\right )+\left (e^5 (72-18 x)+e^{10} \left (432+54 x-36 x^2\right )\right ) \log (-4+x)+e^{10} (108-27 x) \log ^2(-4+x)\right ) \log (x)}{e^{10} \left (-4 x^4+x^5\right )} \, dx=2 x+\frac {\left (\frac {1}{e^5}+3 (2+x+\log (-4+x))\right )^2 \log (x)}{x^3} \]
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\[ \int \frac {-4+x+e^5 \left (-48-12 x+6 x^2\right )+e^{10} \left (-144-108 x+9 x^3-8 x^4+2 x^5\right )+\left (e^5 (-24+6 x)+e^{10} \left (-144-36 x+18 x^2\right )\right ) \log (-4+x)+e^{10} (-36+9 x) \log ^2(-4+x)+\left (12-3 x+e^5 \left (144+18 x-12 x^2\right )+e^{10} \left (432+216 x-18 x^2-9 x^3\right )+\left (e^5 (72-18 x)+e^{10} \left (432+54 x-36 x^2\right )\right ) \log (-4+x)+e^{10} (108-27 x) \log ^2(-4+x)\right ) \log (x)}{e^{10} \left (-4 x^4+x^5\right )} \, dx=\int \frac {-4+x+e^5 \left (-48-12 x+6 x^2\right )+e^{10} \left (-144-108 x+9 x^3-8 x^4+2 x^5\right )+\left (e^5 (-24+6 x)+e^{10} \left (-144-36 x+18 x^2\right )\right ) \log (-4+x)+e^{10} (-36+9 x) \log ^2(-4+x)+\left (12-3 x+e^5 \left (144+18 x-12 x^2\right )+e^{10} \left (432+216 x-18 x^2-9 x^3\right )+\left (e^5 (72-18 x)+e^{10} \left (432+54 x-36 x^2\right )\right ) \log (-4+x)+e^{10} (108-27 x) \log ^2(-4+x)\right ) \log (x)}{e^{10} \left (-4 x^4+x^5\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \frac {\int \frac {-4+x+e^5 \left (-48-12 x+6 x^2\right )+e^{10} \left (-144-108 x+9 x^3-8 x^4+2 x^5\right )+\left (e^5 (-24+6 x)+e^{10} \left (-144-36 x+18 x^2\right )\right ) \log (-4+x)+e^{10} (-36+9 x) \log ^2(-4+x)+\left (12-3 x+e^5 \left (144+18 x-12 x^2\right )+e^{10} \left (432+216 x-18 x^2-9 x^3\right )+\left (e^5 (72-18 x)+e^{10} \left (432+54 x-36 x^2\right )\right ) \log (-4+x)+e^{10} (108-27 x) \log ^2(-4+x)\right ) \log (x)}{-4 x^4+x^5} \, dx}{e^{10}} \\ & = \frac {\int \frac {-4+x+e^5 \left (-48-12 x+6 x^2\right )+e^{10} \left (-144-108 x+9 x^3-8 x^4+2 x^5\right )+\left (e^5 (-24+6 x)+e^{10} \left (-144-36 x+18 x^2\right )\right ) \log (-4+x)+e^{10} (-36+9 x) \log ^2(-4+x)+\left (12-3 x+e^5 \left (144+18 x-12 x^2\right )+e^{10} \left (432+216 x-18 x^2-9 x^3\right )+\left (e^5 (72-18 x)+e^{10} \left (432+54 x-36 x^2\right )\right ) \log (-4+x)+e^{10} (108-27 x) \log ^2(-4+x)\right ) \log (x)}{(-4+x) x^4} \, dx}{e^{10}} \\ & = \frac {\int \left (\frac {1+12 e^5 \left (1+3 e^5\right )+6 e^5 \left (1+6 e^5\right ) x+9 e^{10} x^2+2 e^{10} x^4+6 e^5 \left (1+6 e^5\right ) \log (-4+x)+18 e^{10} x \log (-4+x)+9 e^{10} \log ^2(-4+x)}{x^4}+\frac {3 \left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{(4-x) x^4}\right ) \, dx}{e^{10}} \\ & = \frac {\int \frac {1+12 e^5 \left (1+3 e^5\right )+6 e^5 \left (1+6 e^5\right ) x+9 e^{10} x^2+2 e^{10} x^4+6 e^5 \left (1+6 e^5\right ) \log (-4+x)+18 e^{10} x \log (-4+x)+9 e^{10} \log ^2(-4+x)}{x^4} \, dx}{e^{10}}+\frac {3 \int \frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{(4-x) x^4} \, dx}{e^{10}} \\ & = \frac {\int \left (\frac {\left (1+6 e^5\right )^2+6 e^5 \left (1+6 e^5\right ) x+9 e^{10} x^2+2 e^{10} x^4}{x^4}+\frac {6 e^5 \left (1+6 e^5+3 e^5 x\right ) \log (-4+x)}{x^4}+\frac {9 e^{10} \log ^2(-4+x)}{x^4}\right ) \, dx}{e^{10}}+\frac {3 \int \frac {\left (1+3 e^5 (2+x)+3 e^5 \log (-4+x)\right ) \left (-4+x+e^5 \left (-24+x^2\right )+3 e^5 (-4+x) \log (-4+x)\right ) \log (x)}{(4-x) x^4} \, dx}{e^{10}} \\ & = 9 \int \frac {\log ^2(-4+x)}{x^4} \, dx+\frac {\int \frac {\left (1+6 e^5\right )^2+6 e^5 \left (1+6 e^5\right ) x+9 e^{10} x^2+2 e^{10} x^4}{x^4} \, dx}{e^{10}}+\frac {3 \int \left (\frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{256 (4-x)}+\frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{4 x^4}+\frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{16 x^3}+\frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{64 x^2}+\frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{256 x}\right ) \, dx}{e^{10}}+\frac {6 \int \frac {\left (1+6 e^5+3 e^5 x\right ) \log (-4+x)}{x^4} \, dx}{e^5} \\ & = -\frac {2 \left (6+\frac {1}{e^5}\right ) \log (-4+x)}{x^3}-\frac {9 \log (-4+x)}{x^2}-\frac {3 \log ^2(-4+x)}{x^3}+6 \int \frac {\log (-4+x)}{(-4+x) x^3} \, dx+\frac {3 \int \frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{4-x} \, dx}{256 e^{10}}+\frac {3 \int \frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{x} \, dx}{256 e^{10}}+\frac {3 \int \frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{x^2} \, dx}{64 e^{10}}+\frac {3 \int \frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{x^3} \, dx}{16 e^{10}}+\frac {3 \int \frac {\left (1+6 e^5+3 e^5 x+3 e^5 \log (-4+x)\right ) \left (-4 \left (1+6 e^5\right )+x+e^5 x^2-12 e^5 \log (-4+x)+3 e^5 x \log (-4+x)\right ) \log (x)}{x^4} \, dx}{4 e^{10}}+\frac {\int \left (2 e^{10}+\frac {\left (1+6 e^5\right )^2}{x^4}+\frac {6 e^5 \left (1+6 e^5\right )}{x^3}+\frac {9 e^{10}}{x^2}\right ) \, dx}{e^{10}}-\frac {6 \int \frac {2 \left (1+6 e^5\right )+9 e^5 x}{6 (4-x) x^3} \, dx}{e^5} \\ & = -\frac {\left (1+6 e^5\right )^2}{3 e^{10} x^3}-\frac {3 \left (6+\frac {1}{e^5}\right )}{x^2}-\frac {9}{x}+2 x-\frac {2 \left (6+\frac {1}{e^5}\right ) \log (-4+x)}{x^3}-\frac {9 \log (-4+x)}{x^2}-\frac {3 \log ^2(-4+x)}{x^3}+6 \text {Subst}\left (\int \frac {\log (x)}{x (4+x)^3} \, dx,x,-4+x\right )+\frac {3 \int \frac {\left (1+3 e^5 (2+x)+3 e^5 \log (-4+x)\right ) \left (-4+x+e^5 \left (-24+x^2\right )+3 e^5 (-4+x) \log (-4+x)\right ) \log (x)}{4-x} \, dx}{256 e^{10}}+\frac {3 \int \frac {\left (1+3 e^5 (2+x)+3 e^5 \log (-4+x)\right ) \left (-4+x+e^5 \left (-24+x^2\right )+3 e^5 (-4+x) \log (-4+x)\right ) \log (x)}{x} \, dx}{256 e^{10}}+\frac {3 \int \frac {\left (1+3 e^5 (2+x)+3 e^5 \log (-4+x)\right ) \left (-4+x+e^5 \left (-24+x^2\right )+3 e^5 (-4+x) \log (-4+x)\right ) \log (x)}{x^2} \, dx}{64 e^{10}}+\frac {3 \int \frac {\left (1+3 e^5 (2+x)+3 e^5 \log (-4+x)\right ) \left (-4+x+e^5 \left (-24+x^2\right )+3 e^5 (-4+x) \log (-4+x)\right ) \log (x)}{x^3} \, dx}{16 e^{10}}+\frac {3 \int \frac {\left (1+3 e^5 (2+x)+3 e^5 \log (-4+x)\right ) \left (-4+x+e^5 \left (-24+x^2\right )+3 e^5 (-4+x) \log (-4+x)\right ) \log (x)}{x^4} \, dx}{4 e^{10}}-\frac {\int \frac {2 \left (1+6 e^5\right )+9 e^5 x}{(4-x) x^3} \, dx}{e^5} \\ & = -\frac {\left (1+6 e^5\right )^2}{3 e^{10} x^3}-\frac {3 \left (6+\frac {1}{e^5}\right )}{x^2}-\frac {9}{x}+2 x-\frac {2 \left (6+\frac {1}{e^5}\right ) \log (-4+x)}{x^3}-\frac {9 \log (-4+x)}{x^2}-\frac {3 \log ^2(-4+x)}{x^3}-\frac {3}{2} \text {Subst}\left (\int \frac {\log (x)}{(4+x)^3} \, dx,x,-4+x\right )+\frac {3}{2} \text {Subst}\left (\int \frac {\log (x)}{x (4+x)^2} \, dx,x,-4+x\right )+\frac {3 \int \left (\left (1-6 e^5 \left (1+12 e^5\right )\right ) \log (x)-\frac {4 \left (1+12 e^5 \left (1+3 e^5\right )\right ) \log (x)}{x}+4 e^5 \left (1+\frac {3 e^5}{2}\right ) x \log (x)+3 e^{10} x^2 \log (x)+6 e^5 \left (1-3 e^5\right ) \log (-4+x) \log (x)-\frac {24 e^5 \left (1+6 e^5\right ) \log (-4+x) \log (x)}{x}+12 e^{10} x \log (-4+x) \log (x)+9 e^{10} \log ^2(-4+x) \log (x)-\frac {36 e^{10} \log ^2(-4+x) \log (x)}{x}\right ) \, dx}{256 e^{10}}+\frac {3 \int \left (\frac {4 \left (1+12 e^5 \left (1+3 e^5\right )\right ) \log (x)}{-4+x}-\frac {\left (1-6 e^5 \left (1+12 e^5\right )\right ) x \log (x)}{-4+x}-\frac {4 e^5 \left (1+\frac {3 e^5}{2}\right ) x^2 \log (x)}{-4+x}-\frac {3 e^{10} x^3 \log (x)}{-4+x}+\frac {24 e^5 \left (1+6 e^5\right ) \log (-4+x) \log (x)}{-4+x}-\frac {6 e^5 \left (1-3 e^5\right ) x \log (-4+x) \log (x)}{-4+x}-\frac {12 e^{10} x^2 \log (-4+x) \log (x)}{-4+x}+\frac {36 e^{10} \log ^2(-4+x) \log (x)}{-4+x}-\frac {9 e^{10} x \log ^2(-4+x) \log (x)}{-4+x}\right ) \, dx}{256 e^{10}}+\frac {3 \int \left (4 e^5 \left (1+\frac {3 e^5}{2}\right ) \log (x)-\frac {4 \left (1+12 e^5 \left (1+3 e^5\right )\right ) \log (x)}{x^2}+\frac {\left (1-6 e^5 \left (1+12 e^5\right )\right ) \log (x)}{x}+3 e^{10} x \log (x)+12 e^{10} \log (-4+x) \log (x)-\frac {24 e^5 \left (1+6 e^5\right ) \log (-4+x) \log (x)}{x^2}+\frac {6 e^5 \left (1-3 e^5\right ) \log (-4+x) \log (x)}{x}-\frac {36 e^{10} \log ^2(-4+x) \log (x)}{x^2}+\frac {9 e^{10} \log ^2(-4+x) \log (x)}{x}\right ) \, dx}{64 e^{10}}+\frac {3 \int \left (3 e^{10} \log (x)-\frac {4 \left (1+12 e^5 \left (1+3 e^5\right )\right ) \log (x)}{x^3}+\frac {\left (1-6 e^5 \left (1+12 e^5\right )\right ) \log (x)}{x^2}+\frac {4 e^5 \left (1+\frac {3 e^5}{2}\right ) \log (x)}{x}-\frac {24 e^5 \left (1+6 e^5\right ) \log (-4+x) \log (x)}{x^3}+\frac {6 e^5 \left (1-3 e^5\right ) \log (-4+x) \log (x)}{x^2}+\frac {12 e^{10} \log (-4+x) \log (x)}{x}-\frac {36 e^{10} \log ^2(-4+x) \log (x)}{x^3}+\frac {9 e^{10} \log ^2(-4+x) \log (x)}{x^2}\right ) \, dx}{16 e^{10}}+\frac {3 \int \left (-\frac {4 \left (1+12 e^5 \left (1+3 e^5\right )\right ) \log (x)}{x^4}+\frac {\left (1-6 e^5 \left (1+12 e^5\right )\right ) \log (x)}{x^3}+\frac {4 e^5 \left (1+\frac {3 e^5}{2}\right ) \log (x)}{x^2}+\frac {3 e^{10} \log (x)}{x}-\frac {24 e^5 \left (1+6 e^5\right ) \log (-4+x) \log (x)}{x^4}+\frac {6 e^5 \left (1-3 e^5\right ) \log (-4+x) \log (x)}{x^3}+\frac {12 e^{10} \log (-4+x) \log (x)}{x^2}-\frac {36 e^{10} \log ^2(-4+x) \log (x)}{x^4}+\frac {9 e^{10} \log ^2(-4+x) \log (x)}{x^3}\right ) \, dx}{4 e^{10}}-\frac {\int \left (\frac {-1-24 e^5}{32 (-4+x)}+\frac {1+6 e^5}{2 x^3}+\frac {1+24 e^5}{8 x^2}+\frac {1+24 e^5}{32 x}\right ) \, dx}{e^5} \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.15 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.52 \[ \int \frac {-4+x+e^5 \left (-48-12 x+6 x^2\right )+e^{10} \left (-144-108 x+9 x^3-8 x^4+2 x^5\right )+\left (e^5 (-24+6 x)+e^{10} \left (-144-36 x+18 x^2\right )\right ) \log (-4+x)+e^{10} (-36+9 x) \log ^2(-4+x)+\left (12-3 x+e^5 \left (144+18 x-12 x^2\right )+e^{10} \left (432+216 x-18 x^2-9 x^3\right )+\left (e^5 (72-18 x)+e^{10} \left (432+54 x-36 x^2\right )\right ) \log (-4+x)+e^{10} (108-27 x) \log ^2(-4+x)\right ) \log (x)}{e^{10} \left (-4 x^4+x^5\right )} \, dx=\frac {2 e^{10} x+\frac {\left (1+3 e^5 (2+x)+3 e^5 \log (-4+x)\right )^2 \log (x)}{x^3}}{e^{10}} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(81\) vs. \(2(27)=54\).
Time = 1.48 (sec) , antiderivative size = 82, normalized size of antiderivative = 3.28
method | result | size |
risch | \(\frac {2 x^{4}+9 x^{2} \ln \left (x \right )+18 \ln \left (x \right ) \ln \left (x -4\right ) x +36 x \ln \left (x \right )+36 \ln \left (x \right ) \ln \left (x -4\right )+6 x \ln \left (x \right ) {\mathrm e}^{-5}+36 \ln \left (x \right )+9 \ln \left (x \right ) \ln \left (x -4\right )^{2}+6 \,{\mathrm e}^{-5} \ln \left (x \right ) \ln \left (x -4\right )+12 \ln \left (x \right ) {\mathrm e}^{-5}+\ln \left (x \right ) {\mathrm e}^{-10}}{x^{3}}\) | \(82\) |
parallelrisch | \(\frac {{\mathrm e}^{-10} \left (2 x^{4} {\mathrm e}^{10}+16 x^{3} {\mathrm e}^{10}+9 x^{2} {\mathrm e}^{10} \ln \left (x \right )+18 \,{\mathrm e}^{10} \ln \left (x -4\right ) \ln \left (x \right ) x +9 \,{\mathrm e}^{10} \ln \left (x -4\right )^{2} \ln \left (x \right )+36 \,{\mathrm e}^{10} \ln \left (x \right ) x +36 \,{\mathrm e}^{10} \ln \left (x -4\right ) \ln \left (x \right )+36 \,{\mathrm e}^{10} \ln \left (x \right )+6 x \,{\mathrm e}^{5} \ln \left (x \right )+6 \ln \left (x -4\right ) {\mathrm e}^{5} \ln \left (x \right )+12 \,{\mathrm e}^{5} \ln \left (x \right )+\ln \left (x \right )\right )}{x^{3}}\) | \(120\) |
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Leaf count of result is larger than twice the leaf count of optimal. 64 vs. \(2 (25) = 50\).
Time = 0.26 (sec) , antiderivative size = 64, normalized size of antiderivative = 2.56 \[ \int \frac {-4+x+e^5 \left (-48-12 x+6 x^2\right )+e^{10} \left (-144-108 x+9 x^3-8 x^4+2 x^5\right )+\left (e^5 (-24+6 x)+e^{10} \left (-144-36 x+18 x^2\right )\right ) \log (-4+x)+e^{10} (-36+9 x) \log ^2(-4+x)+\left (12-3 x+e^5 \left (144+18 x-12 x^2\right )+e^{10} \left (432+216 x-18 x^2-9 x^3\right )+\left (e^5 (72-18 x)+e^{10} \left (432+54 x-36 x^2\right )\right ) \log (-4+x)+e^{10} (108-27 x) \log ^2(-4+x)\right ) \log (x)}{e^{10} \left (-4 x^4+x^5\right )} \, dx=\frac {{\left (2 \, x^{4} e^{10} + {\left (9 \, e^{10} \log \left (x - 4\right )^{2} + 9 \, {\left (x^{2} + 4 \, x + 4\right )} e^{10} + 6 \, {\left (x + 2\right )} e^{5} + 6 \, {\left (3 \, {\left (x + 2\right )} e^{10} + e^{5}\right )} \log \left (x - 4\right ) + 1\right )} \log \left (x\right )\right )} e^{\left (-10\right )}}{x^{3}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 97 vs. \(2 (27) = 54\).
Time = 0.77 (sec) , antiderivative size = 97, normalized size of antiderivative = 3.88 \[ \int \frac {-4+x+e^5 \left (-48-12 x+6 x^2\right )+e^{10} \left (-144-108 x+9 x^3-8 x^4+2 x^5\right )+\left (e^5 (-24+6 x)+e^{10} \left (-144-36 x+18 x^2\right )\right ) \log (-4+x)+e^{10} (-36+9 x) \log ^2(-4+x)+\left (12-3 x+e^5 \left (144+18 x-12 x^2\right )+e^{10} \left (432+216 x-18 x^2-9 x^3\right )+\left (e^5 (72-18 x)+e^{10} \left (432+54 x-36 x^2\right )\right ) \log (-4+x)+e^{10} (108-27 x) \log ^2(-4+x)\right ) \log (x)}{e^{10} \left (-4 x^4+x^5\right )} \, dx=2 x + \frac {\left (18 x e^{5} \log {\left (x \right )} + 6 \log {\left (x \right )} + 36 e^{5} \log {\left (x \right )}\right ) \log {\left (x - 4 \right )}}{x^{3} e^{5}} + \frac {\left (9 x^{2} e^{10} + 6 x e^{5} + 36 x e^{10} + 1 + 12 e^{5} + 36 e^{10}\right ) \log {\left (x \right )}}{x^{3} e^{10}} + \frac {9 \log {\left (x \right )} \log {\left (x - 4 \right )}^{2}}{x^{3}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 234 vs. \(2 (25) = 50\).
Time = 0.26 (sec) , antiderivative size = 234, normalized size of antiderivative = 9.36 \[ \int \frac {-4+x+e^5 \left (-48-12 x+6 x^2\right )+e^{10} \left (-144-108 x+9 x^3-8 x^4+2 x^5\right )+\left (e^5 (-24+6 x)+e^{10} \left (-144-36 x+18 x^2\right )\right ) \log (-4+x)+e^{10} (-36+9 x) \log ^2(-4+x)+\left (12-3 x+e^5 \left (144+18 x-12 x^2\right )+e^{10} \left (432+216 x-18 x^2-9 x^3\right )+\left (e^5 (72-18 x)+e^{10} \left (432+54 x-36 x^2\right )\right ) \log (-4+x)+e^{10} (108-27 x) \log ^2(-4+x)\right ) \log (x)}{e^{10} \left (-4 x^4+x^5\right )} \, dx=-\frac {1}{192} \, {\left (36 \, {\left (\frac {4 \, {\left (3 \, x^{2} + 6 \, x + 16\right )}}{x^{3}} + 3 \, \log \left (x - 4\right ) - 3 \, \log \left (x\right )\right )} e^{10} + 12 \, {\left (\frac {4 \, {\left (3 \, x^{2} + 6 \, x + 16\right )}}{x^{3}} + 3 \, \log \left (x - 4\right ) - 3 \, \log \left (x\right )\right )} e^{5} - \frac {384 \, x^{4} e^{10} + 1728 \, e^{10} \log \left (x - 4\right )^{2} \log \left (x\right ) + 12 \, x^{2} {\left (36 \, e^{10} + 12 \, e^{5} + 1\right )} + 24 \, x {\left (36 \, e^{10} + 12 \, e^{5} + 1\right )} + 3 \, {\left (x^{3} {\left (36 \, e^{10} + 12 \, e^{5} + 1\right )} + 384 \, {\left (3 \, x e^{10} + 6 \, e^{10} + e^{5}\right )} \log \left (x\right )\right )} \log \left (x - 4\right ) - 3 \, {\left (x^{3} {\left (36 \, e^{10} + 12 \, e^{5} + 1\right )} - 576 \, x^{2} e^{10} - 384 \, x {\left (6 \, e^{10} + e^{5}\right )} - 2304 \, e^{10} - 768 \, e^{5} - 64\right )} \log \left (x\right ) + 2304 \, e^{10} + 768 \, e^{5} + 64}{x^{3}} + \frac {4 \, {\left (3 \, x^{2} + 6 \, x + 16\right )}}{x^{3}} + 3 \, \log \left (x - 4\right ) - 3 \, \log \left (x\right )\right )} e^{\left (-10\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (25) = 50\).
Time = 0.30 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.76 \[ \int \frac {-4+x+e^5 \left (-48-12 x+6 x^2\right )+e^{10} \left (-144-108 x+9 x^3-8 x^4+2 x^5\right )+\left (e^5 (-24+6 x)+e^{10} \left (-144-36 x+18 x^2\right )\right ) \log (-4+x)+e^{10} (-36+9 x) \log ^2(-4+x)+\left (12-3 x+e^5 \left (144+18 x-12 x^2\right )+e^{10} \left (432+216 x-18 x^2-9 x^3\right )+\left (e^5 (72-18 x)+e^{10} \left (432+54 x-36 x^2\right )\right ) \log (-4+x)+e^{10} (108-27 x) \log ^2(-4+x)\right ) \log (x)}{e^{10} \left (-4 x^4+x^5\right )} \, dx=\frac {{\left (2 \, x^{4} e^{10} + 9 \, x^{2} e^{10} \log \left (x\right ) + 18 \, x e^{10} \log \left (x - 4\right ) \log \left (x\right ) + 9 \, e^{10} \log \left (x - 4\right )^{2} \log \left (x\right ) + 36 \, x e^{10} \log \left (x\right ) + 6 \, x e^{5} \log \left (x\right ) + 36 \, e^{10} \log \left (x - 4\right ) \log \left (x\right ) + 6 \, e^{5} \log \left (x - 4\right ) \log \left (x\right ) + 36 \, e^{10} \log \left (x\right ) + 12 \, e^{5} \log \left (x\right ) + \log \left (x\right )\right )} e^{\left (-10\right )}}{x^{3}} \]
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Time = 13.68 (sec) , antiderivative size = 74, normalized size of antiderivative = 2.96 \[ \int \frac {-4+x+e^5 \left (-48-12 x+6 x^2\right )+e^{10} \left (-144-108 x+9 x^3-8 x^4+2 x^5\right )+\left (e^5 (-24+6 x)+e^{10} \left (-144-36 x+18 x^2\right )\right ) \log (-4+x)+e^{10} (-36+9 x) \log ^2(-4+x)+\left (12-3 x+e^5 \left (144+18 x-12 x^2\right )+e^{10} \left (432+216 x-18 x^2-9 x^3\right )+\left (e^5 (72-18 x)+e^{10} \left (432+54 x-36 x^2\right )\right ) \log (-4+x)+e^{10} (108-27 x) \log ^2(-4+x)\right ) \log (x)}{e^{10} \left (-4 x^4+x^5\right )} \, dx=2\,x+\frac {\ln \left (x\right )\,\left (9\,x^2+6\,{\mathrm {e}}^{-5}\,\left (6\,{\mathrm {e}}^5+1\right )\,x+{\mathrm {e}}^{-10}\,{\left (6\,{\mathrm {e}}^5+1\right )}^2\right )}{x^3}+\frac {9\,{\ln \left (x-4\right )}^2\,\ln \left (x\right )}{x^3}+\frac {\ln \left (x-4\right )\,{\mathrm {e}}^{-5}\,\ln \left (x\right )\,\left (36\,{\mathrm {e}}^5+18\,x\,{\mathrm {e}}^5+6\right )}{x^3} \]
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