Optimal. Leaf size=41 \[ \frac {2}{3 \left (1-\frac {x}{-\frac {2 e^{\frac {1}{5} \left (-e^{x/4}+\frac {x}{2}\right )}}{x}+x}\right )} \]
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Rubi [A] time = 0.12, antiderivative size = 51, normalized size of antiderivative = 1.24, number of steps used = 4, number of rules used = 3, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {12, 2274, 2288} \begin {gather*} -\frac {e^{\frac {1}{10} \left (2 e^{x/4}-x\right )} x \left (2 x-e^{x/4} x\right )}{3 \left (2-e^{x/4}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2274
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{30} \int e^{\frac {1}{10} \left (2 e^{x/4}-x-10 \log \left (\frac {2}{x}\right )\right )} \left (-40+2 x-e^{x/4} x\right ) \, dx\\ &=\frac {1}{30} \int \frac {1}{2} e^{\frac {1}{10} \left (2 e^{x/4}-x\right )} x \left (-40+2 x-e^{x/4} x\right ) \, dx\\ &=\frac {1}{60} \int e^{\frac {1}{10} \left (2 e^{x/4}-x\right )} x \left (-40+2 x-e^{x/4} x\right ) \, dx\\ &=-\frac {e^{\frac {1}{10} \left (2 e^{x/4}-x\right )} x \left (2 x-e^{x/4} x\right )}{3 \left (2-e^{x/4}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 26, normalized size = 0.63 \begin {gather*} -\frac {1}{3} e^{\frac {e^{x/4}}{5}-\frac {x}{10}} x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 22, normalized size = 0.54 \begin {gather*} -\frac {2}{3} \, x e^{\left (-\frac {1}{10} \, x + \frac {1}{5} \, e^{\left (\frac {1}{4} \, x\right )} - \log \left (\frac {2}{x}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 16, normalized size = 0.39 \begin {gather*} -\frac {1}{3} \, x^{2} e^{\left (-\frac {1}{10} \, x + \frac {1}{5} \, e^{\left (\frac {1}{4} \, x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.28, size = 17, normalized size = 0.41
method | result | size |
risch | \(-\frac {x^{2} {\mathrm e}^{\frac {{\mathrm e}^{\frac {x}{4}}}{5}-\frac {x}{10}}}{3}\) | \(17\) |
default | \(-\frac {x^{2} {\mathrm e}^{\frac {{\mathrm e}^{\frac {x}{4}}}{5}-\frac {x}{10}}}{3}\) | \(23\) |
norman | \(-\frac {x^{2} {\mathrm e}^{\frac {{\mathrm e}^{\frac {x}{4}}}{5}-\frac {x}{10}}}{3}\) | \(23\) |
meijerg | \(-\frac {4 \left (1-{\mathrm e}^{-x \ln \relax (2)}\right )}{3 \ln \relax (2)}-\frac {8 \left (1-\frac {\left (2-\frac {x \left (-4 \ln \relax (2)+1\right )}{2}\right ) {\mathrm e}^{\frac {x \left (-4 \ln \relax (2)+1\right )}{4}}}{2}\right )}{15 \left (-4 \ln \relax (2)+1\right )^{2}}+\frac {1-\frac {\left (2+2 x \ln \relax (2)\right ) {\mathrm e}^{-x \ln \relax (2)}}{2}}{15 \ln \relax (2)^{2}}\) | \(76\) |
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 {1}{60} \, \int {\left (x e^{\left (\frac {1}{4} \, x\right )} - 2 \, x + 40\right )} x e^{\left (-\frac {1}{10} \, x + \frac {1}{5} \, e^{\left (\frac {1}{4} \, x\right )}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.14, size = 16, normalized size = 0.39 \begin {gather*} -\frac {x^2\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{x/4}}{5}-\frac {x}{10}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 17, normalized size = 0.41 \begin {gather*} - \frac {x^{2} e^{- \frac {x}{10} + \frac {e^{\frac {x}{4}}}{5}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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