Optimal. Leaf size=25 \[ \frac {1}{4} e^{8 e^{-x} \left (-1+x \left (5+\log \left (-\frac {x}{4}\right )\right )\right )} \]
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Rubi [F] time = 2.11, 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 \exp \left (-x+2 e^{-x} \left (-4+20 x+4 x \log \left (-\frac {x}{4}\right )\right )\right ) \left (14-10 x+(2-2 x) \log \left (-\frac {x}{4}\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \exp \left (-e^{-x} \left (8-40 x+e^x x-8 x \log \left (-\frac {x}{4}\right )\right )\right ) \left (14-10 x+(2-2 x) \log \left (-\frac {x}{4}\right )\right ) \, dx\\ &=\int \left (14 \exp \left (-e^{-x} \left (8-40 x+e^x x-8 x \log \left (-\frac {x}{4}\right )\right )\right )-10 \exp \left (-e^{-x} \left (8-40 x+e^x x-8 x \log \left (-\frac {x}{4}\right )\right )\right ) x-2 \exp \left (-e^{-x} \left (8-40 x+e^x x-8 x \log \left (-\frac {x}{4}\right )\right )\right ) (-1+x) \log \left (-\frac {x}{4}\right )\right ) \, dx\\ &=-\left (2 \int \exp \left (-e^{-x} \left (8-40 x+e^x x-8 x \log \left (-\frac {x}{4}\right )\right )\right ) (-1+x) \log \left (-\frac {x}{4}\right ) \, dx\right )-10 \int \exp \left (-e^{-x} \left (8-40 x+e^x x-8 x \log \left (-\frac {x}{4}\right )\right )\right ) x \, dx+14 \int \exp \left (-e^{-x} \left (8-40 x+e^x x-8 x \log \left (-\frac {x}{4}\right )\right )\right ) \, dx\\ &=-\left (2 \int \left (-\exp \left (-e^{-x} \left (8-40 x+e^x x-8 x \log \left (-\frac {x}{4}\right )\right )\right ) \log \left (-\frac {x}{4}\right )+\exp \left (-e^{-x} \left (8-40 x+e^x x-8 x \log \left (-\frac {x}{4}\right )\right )\right ) x \log \left (-\frac {x}{4}\right )\right ) \, dx\right )-10 \int \exp \left (-e^{-x} \left (8-40 x+e^x x-8 x \log \left (-\frac {x}{4}\right )\right )\right ) x \, dx+14 \int \exp \left (-e^{-x} \left (8-40 x+e^x x-8 x \log \left (-\frac {x}{4}\right )\right )\right ) \, dx\\ &=2 \int \exp \left (-e^{-x} \left (8-40 x+e^x x-8 x \log \left (-\frac {x}{4}\right )\right )\right ) \log \left (-\frac {x}{4}\right ) \, dx-2 \int \exp \left (-e^{-x} \left (8-40 x+e^x x-8 x \log \left (-\frac {x}{4}\right )\right )\right ) x \log \left (-\frac {x}{4}\right ) \, dx-10 \int \exp \left (-e^{-x} \left (8-40 x+e^x x-8 x \log \left (-\frac {x}{4}\right )\right )\right ) x \, dx+14 \int \exp \left (-e^{-x} \left (8-40 x+e^x x-8 x \log \left (-\frac {x}{4}\right )\right )\right ) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.56, size = 39, normalized size = 1.56 \begin {gather*} 4^{-1-8 e^{-x} x} e^{-8 e^{-x} (1-5 x)} (-x)^{8 e^{-x} x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 26, normalized size = 1.04 \begin {gather*} \frac {1}{4} \, e^{\left (8 \, x e^{\left (-x\right )} \log \left (-\frac {1}{4} \, x\right ) + 8 \, {\left (5 \, x - 1\right )} e^{\left (-x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -2 \, {\left ({\left (x - 1\right )} \log \left (-\frac {1}{4} \, x\right ) + 5 \, x - 7\right )} e^{\left (8 \, {\left (x \log \left (-\frac {1}{4} \, x\right ) + 5 \, x - 1\right )} e^{\left (-x\right )} - x\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 21, normalized size = 0.84
method | result | size |
risch | \(\frac {{\mathrm e}^{8 \left (x \ln \left (-\frac {x}{4}\right )+5 x -1\right ) {\mathrm e}^{-x}}}{4}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.85, size = 37, normalized size = 1.48 \begin {gather*} \frac {1}{4} \, e^{\left (-16 \, x e^{\left (-x\right )} \log \relax (2) + 8 \, x e^{\left (-x\right )} \log \left (-x\right ) + 40 \, x e^{\left (-x\right )} - 8 \, e^{\left (-x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.92, size = 28, normalized size = 1.12 \begin {gather*} \frac {{\mathrm {e}}^{-8\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{40\,x\,{\mathrm {e}}^{-x}}\,{\left (-\frac {x}{4}\right )}^{8\,x\,{\mathrm {e}}^{-x}}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.51, size = 20, normalized size = 0.80 \begin {gather*} \frac {e^{2 \left (4 x \log {\left (- \frac {x}{4} \right )} + 20 x - 4\right ) e^{- x}}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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