Optimal. Leaf size=30 \[ \log \left (\frac {e^{4-e^{3 x}+e^{\frac {2+x}{4}}}}{x-5 \log (4)}\right ) \]
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Rubi [A] time = 0.13, antiderivative size = 28, normalized size of antiderivative = 0.93, number of steps used = 4, number of rules used = 2, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.044, Rules used = {6688, 2194} \begin {gather*} e^{\frac {x}{4}+\frac {1}{2}}-e^{3 x}-\log (x-5 \log (4)) \end {gather*}
Antiderivative was successfully verified.
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Rule 2194
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {1}{4} e^{\frac {1}{2}+\frac {x}{4}}-3 e^{3 x}+\frac {1}{-x+5 \log (4)}\right ) \, dx\\ &=-\log (x-5 \log (4))+\frac {1}{4} \int e^{\frac {1}{2}+\frac {x}{4}} \, dx-3 \int e^{3 x} \, dx\\ &=e^{\frac {1}{2}+\frac {x}{4}}-e^{3 x}-\log (x-5 \log (4))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 30, normalized size = 1.00 \begin {gather*} e^{\frac {1}{2}+\frac {x}{4}}-e^{3 x}-\log (-x+5 \log (4)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.63, size = 29, normalized size = 0.97 \begin {gather*} -{\left (e^{6} \log \left (x - 10 \, \log \relax (2)\right ) + e^{\left (3 \, x + 6\right )} - e^{\left (\frac {1}{4} \, x + \frac {13}{2}\right )}\right )} e^{\left (-6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 22, normalized size = 0.73 \begin {gather*} -e^{\left (3 \, x\right )} + e^{\left (\frac {1}{4} \, x + \frac {1}{2}\right )} - \log \left (x - 10 \, \log \relax (2)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.28, size = 23, normalized size = 0.77
method | result | size |
risch | \(-\ln \left (x -10 \ln \relax (2)\right )-{\mathrm e}^{3 x}+{\mathrm e}^{\frac {1}{2}+\frac {x}{4}}\) | \(23\) |
default | \(-\ln \left (10 \ln \relax (2)-x \right )-{\mathrm e}^{3 x}+{\mathrm e}^{\frac {1}{2}} {\mathrm e}^{\frac {x}{4}}\) | \(26\) |
norman | \({\mathrm e}^{\frac {1}{2}} {\mathrm e}^{\frac {x}{4}}-{\mathrm e}^{3 x}-\ln \left (40 \ln \relax (2)-4 x \right )\) | \(28\) |
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 {5}{2} \, e^{\left (\frac {5}{2} \, \log \relax (2) + \frac {1}{2}\right )} E_{1}\left (-\frac {1}{4} \, x + \frac {5}{2} \, \log \relax (2)\right ) \log \relax (2) + 10 \, \int \frac {e^{\left (\frac {1}{4} \, x + \frac {1}{2}\right )}}{x^{2} - 20 \, x \log \relax (2) + 100 \, \log \relax (2)^{2}}\,{d x} \log \relax (2) - \frac {{\left (x - 10 \, \log \relax (2)\right )} e^{\left (3 \, x\right )} - x e^{\left (\frac {1}{4} \, x + \frac {1}{2}\right )}}{x - 10 \, \log \relax (2)} - \log \left (x - 10 \, \log \relax (2)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.85, size = 22, normalized size = 0.73 \begin {gather*} {\mathrm {e}}^{\frac {x}{4}+\frac {1}{2}}-{\mathrm {e}}^{3\,x}-\ln \left (x-10\,\ln \relax (2)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 26, normalized size = 0.87 \begin {gather*} - e^{3 x} + e^{\frac {1}{2}} \sqrt [12]{e^{3 x}} - \log {\left (x - 10 \log {\relax (2 )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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