Integrand size = 218, antiderivative size = 34 \[ \int \frac {-384 x+96 x^2-12 x^3+e^{\frac {1}{4} \left (4 x+e^{-5+x} x-x^2\right )} \left (-48 x^2+60 x^3-36 x^4+6 x^5+e^{-5+x} \left (12 x^3+9 x^4-3 x^5\right )\right )+\left (-48 x^2+12 x^3\right ) \log (-4+x)}{-256+64 x+e^{\frac {1}{2} \left (4 x+e^{-5+x} x-x^2\right )} \left (-16 x^2+4 x^3\right )+\left (-128 x+32 x^2\right ) \log (-4+x)+\left (-16 x^2+4 x^3\right ) \log ^2(-4+x)+e^{\frac {1}{4} \left (4 x+e^{-5+x} x-x^2\right )} \left (-128 x+32 x^2+\left (-32 x^2+8 x^3\right ) \log (-4+x)\right )} \, dx=-1+\frac {3 x}{e^{\frac {1}{4} \left (4+e^{-5+x}-x\right ) x}+\frac {4}{x}+\log (-4+x)} \]
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Timed out. \[ \int \frac {-384 x+96 x^2-12 x^3+e^{\frac {1}{4} \left (4 x+e^{-5+x} x-x^2\right )} \left (-48 x^2+60 x^3-36 x^4+6 x^5+e^{-5+x} \left (12 x^3+9 x^4-3 x^5\right )\right )+\left (-48 x^2+12 x^3\right ) \log (-4+x)}{-256+64 x+e^{\frac {1}{2} \left (4 x+e^{-5+x} x-x^2\right )} \left (-16 x^2+4 x^3\right )+\left (-128 x+32 x^2\right ) \log (-4+x)+\left (-16 x^2+4 x^3\right ) \log ^2(-4+x)+e^{\frac {1}{4} \left (4 x+e^{-5+x} x-x^2\right )} \left (-128 x+32 x^2+\left (-32 x^2+8 x^3\right ) \log (-4+x)\right )} \, dx=\text {\$Aborted} \]
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Rubi steps Aborted
Time = 0.42 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.74 \[ \int \frac {-384 x+96 x^2-12 x^3+e^{\frac {1}{4} \left (4 x+e^{-5+x} x-x^2\right )} \left (-48 x^2+60 x^3-36 x^4+6 x^5+e^{-5+x} \left (12 x^3+9 x^4-3 x^5\right )\right )+\left (-48 x^2+12 x^3\right ) \log (-4+x)}{-256+64 x+e^{\frac {1}{2} \left (4 x+e^{-5+x} x-x^2\right )} \left (-16 x^2+4 x^3\right )+\left (-128 x+32 x^2\right ) \log (-4+x)+\left (-16 x^2+4 x^3\right ) \log ^2(-4+x)+e^{\frac {1}{4} \left (4 x+e^{-5+x} x-x^2\right )} \left (-128 x+32 x^2+\left (-32 x^2+8 x^3\right ) \log (-4+x)\right )} \, dx=\frac {3 e^{\frac {x^2}{4}} x^2}{4 e^{\frac {x^2}{4}}+e^{x+\frac {1}{4} e^{-5+x} x} x+e^{\frac {x^2}{4}} x \log (-4+x)} \]
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Time = 6.97 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.91
method | result | size |
risch | \(\frac {3 x^{2}}{{\mathrm e}^{-\frac {\left (-4-{\mathrm e}^{-5+x}+x \right ) x}{4}} x +x \ln \left (x -4\right )+4}\) | \(31\) |
parallelrisch | \(\frac {3 x^{2}}{x \ln \left (x -4\right )+{\mathrm e}^{\frac {\left (4+{\mathrm e}^{-5+x}-x \right ) x}{4}} x +4}\) | \(31\) |
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Time = 0.27 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.94 \[ \int \frac {-384 x+96 x^2-12 x^3+e^{\frac {1}{4} \left (4 x+e^{-5+x} x-x^2\right )} \left (-48 x^2+60 x^3-36 x^4+6 x^5+e^{-5+x} \left (12 x^3+9 x^4-3 x^5\right )\right )+\left (-48 x^2+12 x^3\right ) \log (-4+x)}{-256+64 x+e^{\frac {1}{2} \left (4 x+e^{-5+x} x-x^2\right )} \left (-16 x^2+4 x^3\right )+\left (-128 x+32 x^2\right ) \log (-4+x)+\left (-16 x^2+4 x^3\right ) \log ^2(-4+x)+e^{\frac {1}{4} \left (4 x+e^{-5+x} x-x^2\right )} \left (-128 x+32 x^2+\left (-32 x^2+8 x^3\right ) \log (-4+x)\right )} \, dx=\frac {3 \, x^{2}}{x e^{\left (-\frac {1}{4} \, x^{2} + \frac {1}{4} \, x e^{\left (x - 5\right )} + x\right )} + x \log \left (x - 4\right ) + 4} \]
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Time = 0.28 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.91 \[ \int \frac {-384 x+96 x^2-12 x^3+e^{\frac {1}{4} \left (4 x+e^{-5+x} x-x^2\right )} \left (-48 x^2+60 x^3-36 x^4+6 x^5+e^{-5+x} \left (12 x^3+9 x^4-3 x^5\right )\right )+\left (-48 x^2+12 x^3\right ) \log (-4+x)}{-256+64 x+e^{\frac {1}{2} \left (4 x+e^{-5+x} x-x^2\right )} \left (-16 x^2+4 x^3\right )+\left (-128 x+32 x^2\right ) \log (-4+x)+\left (-16 x^2+4 x^3\right ) \log ^2(-4+x)+e^{\frac {1}{4} \left (4 x+e^{-5+x} x-x^2\right )} \left (-128 x+32 x^2+\left (-32 x^2+8 x^3\right ) \log (-4+x)\right )} \, dx=\frac {3 x^{2}}{x e^{- \frac {x^{2}}{4} + \frac {x e^{x - 5}}{4} + x} + x \log {\left (x - 4 \right )} + 4} \]
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\[ \int \frac {-384 x+96 x^2-12 x^3+e^{\frac {1}{4} \left (4 x+e^{-5+x} x-x^2\right )} \left (-48 x^2+60 x^3-36 x^4+6 x^5+e^{-5+x} \left (12 x^3+9 x^4-3 x^5\right )\right )+\left (-48 x^2+12 x^3\right ) \log (-4+x)}{-256+64 x+e^{\frac {1}{2} \left (4 x+e^{-5+x} x-x^2\right )} \left (-16 x^2+4 x^3\right )+\left (-128 x+32 x^2\right ) \log (-4+x)+\left (-16 x^2+4 x^3\right ) \log ^2(-4+x)+e^{\frac {1}{4} \left (4 x+e^{-5+x} x-x^2\right )} \left (-128 x+32 x^2+\left (-32 x^2+8 x^3\right ) \log (-4+x)\right )} \, dx=\int { -\frac {3 \, {\left (4 \, x^{3} - 32 \, x^{2} - {\left (2 \, x^{5} - 12 \, x^{4} + 20 \, x^{3} - 16 \, x^{2} - {\left (x^{5} - 3 \, x^{4} - 4 \, x^{3}\right )} e^{\left (x - 5\right )}\right )} e^{\left (-\frac {1}{4} \, x^{2} + \frac {1}{4} \, x e^{\left (x - 5\right )} + x\right )} - 4 \, {\left (x^{3} - 4 \, x^{2}\right )} \log \left (x - 4\right ) + 128 \, x\right )}}{4 \, {\left ({\left (x^{3} - 4 \, x^{2}\right )} \log \left (x - 4\right )^{2} + 2 \, {\left (4 \, x^{2} + {\left (x^{3} - 4 \, x^{2}\right )} \log \left (x - 4\right ) - 16 \, x\right )} e^{\left (-\frac {1}{4} \, x^{2} + \frac {1}{4} \, x e^{\left (x - 5\right )} + x\right )} + {\left (x^{3} - 4 \, x^{2}\right )} e^{\left (-\frac {1}{2} \, x^{2} + \frac {1}{2} \, x e^{\left (x - 5\right )} + 2 \, x\right )} + 8 \, {\left (x^{2} - 4 \, x\right )} \log \left (x - 4\right ) + 16 \, x - 64\right )}} \,d x } \]
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Leaf count of result is larger than twice the leaf count of optimal. 617 vs. \(2 (30) = 60\).
Time = 3.23 (sec) , antiderivative size = 617, normalized size of antiderivative = 18.15 \[ \int \frac {-384 x+96 x^2-12 x^3+e^{\frac {1}{4} \left (4 x+e^{-5+x} x-x^2\right )} \left (-48 x^2+60 x^3-36 x^4+6 x^5+e^{-5+x} \left (12 x^3+9 x^4-3 x^5\right )\right )+\left (-48 x^2+12 x^3\right ) \log (-4+x)}{-256+64 x+e^{\frac {1}{2} \left (4 x+e^{-5+x} x-x^2\right )} \left (-16 x^2+4 x^3\right )+\left (-128 x+32 x^2\right ) \log (-4+x)+\left (-16 x^2+4 x^3\right ) \log ^2(-4+x)+e^{\frac {1}{4} \left (4 x+e^{-5+x} x-x^2\right )} \left (-128 x+32 x^2+\left (-32 x^2+8 x^3\right ) \log (-4+x)\right )} \, dx=\frac {3 \, {\left (2 \, x^{6} e^{5} \log \left (x - 4\right ) - x^{6} e^{x} \log \left (x - 4\right ) - 12 \, x^{5} e^{5} \log \left (x - 4\right ) + 3 \, x^{5} e^{x} \log \left (x - 4\right ) + 8 \, x^{5} e^{5} - 4 \, x^{5} e^{x} + 16 \, x^{4} e^{5} \log \left (x - 4\right ) + 4 \, x^{4} e^{x} \log \left (x - 4\right ) - 44 \, x^{4} e^{5} + 12 \, x^{4} e^{x} + 48 \, x^{3} e^{5} + 16 \, x^{3} e^{x} + 64 \, x^{2} e^{5}\right )}}{2 \, x^{5} e^{5} \log \left (x - 4\right )^{2} - x^{5} e^{x} \log \left (x - 4\right )^{2} - x^{5} e^{\left (-\frac {1}{4} \, x^{2} + \frac {1}{4} \, x e^{\left (x - 5\right )} + 2 \, x\right )} \log \left (x - 4\right ) + 2 \, x^{5} e^{\left (-\frac {1}{4} \, x^{2} + \frac {1}{4} \, x e^{\left (x - 5\right )} + x + 5\right )} \log \left (x - 4\right ) - 12 \, x^{4} e^{5} \log \left (x - 4\right )^{2} + 3 \, x^{4} e^{x} \log \left (x - 4\right )^{2} + 16 \, x^{4} e^{5} \log \left (x - 4\right ) + 3 \, x^{4} e^{\left (-\frac {1}{4} \, x^{2} + \frac {1}{4} \, x e^{\left (x - 5\right )} + 2 \, x\right )} \log \left (x - 4\right ) - 12 \, x^{4} e^{\left (-\frac {1}{4} \, x^{2} + \frac {1}{4} \, x e^{\left (x - 5\right )} + x + 5\right )} \log \left (x - 4\right ) - 8 \, x^{4} e^{x} \log \left (x - 4\right ) + 16 \, x^{3} e^{5} \log \left (x - 4\right )^{2} + 4 \, x^{3} e^{x} \log \left (x - 4\right )^{2} - 4 \, x^{4} e^{\left (-\frac {1}{4} \, x^{2} + \frac {1}{4} \, x e^{\left (x - 5\right )} + 2 \, x\right )} + 8 \, x^{4} e^{\left (-\frac {1}{4} \, x^{2} + \frac {1}{4} \, x e^{\left (x - 5\right )} + x + 5\right )} - 92 \, x^{3} e^{5} \log \left (x - 4\right ) + 4 \, x^{3} e^{\left (-\frac {1}{4} \, x^{2} + \frac {1}{4} \, x e^{\left (x - 5\right )} + 2 \, x\right )} \log \left (x - 4\right ) + 16 \, x^{3} e^{\left (-\frac {1}{4} \, x^{2} + \frac {1}{4} \, x e^{\left (x - 5\right )} + x + 5\right )} \log \left (x - 4\right ) + 24 \, x^{3} e^{x} \log \left (x - 4\right ) + 32 \, x^{3} e^{5} + 12 \, x^{3} e^{\left (-\frac {1}{4} \, x^{2} + \frac {1}{4} \, x e^{\left (x - 5\right )} + 2 \, x\right )} - 44 \, x^{3} e^{\left (-\frac {1}{4} \, x^{2} + \frac {1}{4} \, x e^{\left (x - 5\right )} + x + 5\right )} - 16 \, x^{3} e^{x} + 112 \, x^{2} e^{5} \log \left (x - 4\right ) + 32 \, x^{2} e^{x} \log \left (x - 4\right ) - 176 \, x^{2} e^{5} + 16 \, x^{2} e^{\left (-\frac {1}{4} \, x^{2} + \frac {1}{4} \, x e^{\left (x - 5\right )} + 2 \, x\right )} + 48 \, x^{2} e^{\left (-\frac {1}{4} \, x^{2} + \frac {1}{4} \, x e^{\left (x - 5\right )} + x + 5\right )} + 48 \, x^{2} e^{x} + 64 \, x e^{5} \log \left (x - 4\right ) + 192 \, x e^{5} + 64 \, x e^{\left (-\frac {1}{4} \, x^{2} + \frac {1}{4} \, x e^{\left (x - 5\right )} + x + 5\right )} + 64 \, x e^{x} + 256 \, e^{5}} \]
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Time = 13.09 (sec) , antiderivative size = 295, normalized size of antiderivative = 8.68 \[ \int \frac {-384 x+96 x^2-12 x^3+e^{\frac {1}{4} \left (4 x+e^{-5+x} x-x^2\right )} \left (-48 x^2+60 x^3-36 x^4+6 x^5+e^{-5+x} \left (12 x^3+9 x^4-3 x^5\right )\right )+\left (-48 x^2+12 x^3\right ) \log (-4+x)}{-256+64 x+e^{\frac {1}{2} \left (4 x+e^{-5+x} x-x^2\right )} \left (-16 x^2+4 x^3\right )+\left (-128 x+32 x^2\right ) \log (-4+x)+\left (-16 x^2+4 x^3\right ) \log ^2(-4+x)+e^{\frac {1}{4} \left (4 x+e^{-5+x} x-x^2\right )} \left (-128 x+32 x^2+\left (-32 x^2+8 x^3\right ) \log (-4+x)\right )} \, dx=\frac {192\,x^3\,{\mathrm {e}}^{x-5}+96\,x^4\,{\mathrm {e}}^{x-5}-84\,x^5\,{\mathrm {e}}^{x-5}+12\,x^6\,{\mathrm {e}}^{x-5}+\ln \left (x-4\right )\,\left (48\,x^4\,{\mathrm {e}}^{x-5}+24\,x^5\,{\mathrm {e}}^{x-5}-21\,x^6\,{\mathrm {e}}^{x-5}+3\,x^7\,{\mathrm {e}}^{x-5}+192\,x^4-192\,x^5+60\,x^6-6\,x^7\right )+768\,x^2+384\,x^3-672\,x^4+228\,x^5-24\,x^6}{\left (x\,\ln \left (x-4\right )+x\,{\mathrm {e}}^{x-\frac {x^2}{4}+\frac {x\,{\mathrm {e}}^{-5}\,{\mathrm {e}}^x}{4}}+4\right )\,\left (128\,x+64\,x\,{\mathrm {e}}^{x-5}+32\,x^2\,{\mathrm {e}}^{x-5}-28\,x^3\,{\mathrm {e}}^{x-5}+4\,x^4\,{\mathrm {e}}^{x-5}+64\,x^2\,\ln \left (x-4\right )-64\,x^3\,\ln \left (x-4\right )+20\,x^4\,\ln \left (x-4\right )-2\,x^5\,\ln \left (x-4\right )-224\,x^2+76\,x^3-8\,x^4+16\,x^2\,\ln \left (x-4\right )\,{\mathrm {e}}^{x-5}+8\,x^3\,\ln \left (x-4\right )\,{\mathrm {e}}^{x-5}-7\,x^4\,\ln \left (x-4\right )\,{\mathrm {e}}^{x-5}+x^5\,\ln \left (x-4\right )\,{\mathrm {e}}^{x-5}+256\right )} \]
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