Optimal. Leaf size=34 \[ -1+\frac {3 x}{e^{\frac {1}{4} \left (4+e^{-5+x}-x\right ) x}+\frac {4}{x}+\log (-4+x)} \]
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Rubi [F] time = 180.00, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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Aborted
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Mathematica [A] time = 0.49, size = 59, normalized size = 1.74 \begin {gather*} \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)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 32, normalized size = 0.94 \begin {gather*} \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 26.58, size = 617, normalized size = 18.15 \begin {gather*} \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}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 31, normalized size = 0.91
method | result | size |
risch | \(\frac {3 x^{2}}{{\mathrm e}^{-\frac {\left (-4-{\mathrm e}^{x -5}+x \right ) x}{4}} x +x \ln \left (x -4\right )+4}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\frac {3}{4} \, \int \frac {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}{{\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}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.63, size = 295, normalized size = 8.68 \begin {gather*} \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 )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.60, size = 31, normalized size = 0.91 \begin {gather*} \frac {3 x^{2}}{x e^{- \frac {x^{2}}{4} + \frac {x e^{x - 5}}{4} + x} + x \log {\left (x - 4 \right )} + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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