Optimal. Leaf size=25 \[ \log \left (\frac {e^{2 e^{\frac {x^4}{256}}} x^2}{3 \log (4)}\right ) \]
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Rubi [A]
time = 0.03, antiderivative size = 16, normalized size of antiderivative = 0.64, number of steps
used = 4, number of rules used = 3, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {12, 14, 2240}
\begin {gather*} 2 e^{\frac {x^4}{256}}+2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2240
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{32} \int \frac {64+e^{\frac {x^4}{256}} x^4}{x} \, dx\\ &=\frac {1}{32} \int \left (\frac {64}{x}+e^{\frac {x^4}{256}} x^3\right ) \, dx\\ &=2 \log (x)+\frac {1}{32} \int e^{\frac {x^4}{256}} x^3 \, dx\\ &=2 e^{\frac {x^4}{256}}+2 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 16, normalized size = 0.64 \begin {gather*} 2 e^{\frac {x^4}{256}}+2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 14, normalized size = 0.56
method | result | size |
default | \(2 \,{\mathrm e}^{\frac {x^{4}}{256}}+2 \ln \left (x \right )\) | \(14\) |
norman | \(2 \,{\mathrm e}^{\frac {x^{4}}{256}}+2 \ln \left (x \right )\) | \(14\) |
risch | \(2 \,{\mathrm e}^{\frac {x^{4}}{256}}+2 \ln \left (x \right )\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 13, normalized size = 0.52 \begin {gather*} 2 \, e^{\left (\frac {1}{256} \, x^{4}\right )} + 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 13, normalized size = 0.52 \begin {gather*} 2 \, e^{\left (\frac {1}{256} \, x^{4}\right )} + 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 12, normalized size = 0.48 \begin {gather*} 2 e^{\frac {x^{4}}{256}} + 2 \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 17, normalized size = 0.68 \begin {gather*} 2 \, e^{\left (\frac {1}{256} \, x^{4}\right )} + \frac {1}{2} \, \log \left (\frac {1}{256} \, x^{4}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.90, size = 13, normalized size = 0.52 \begin {gather*} 2\,{\mathrm {e}}^{\frac {x^4}{256}}+2\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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