Optimal. Leaf size=23 \[ \frac {x}{4}+\frac {2}{5} e^4 x \left (x-\frac {4 x}{\log (3)}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 32, normalized size of antiderivative = 1.39, number of steps
used = 2, number of rules used = 1, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {12}
\begin {gather*} \frac {\left (16 e^4 x+5\right )^2}{640 e^4}-\frac {8 e^4 x^2}{5 \log (3)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (-64 e^4 x+\left (5+16 e^4 x\right ) \log (3)\right ) \, dx}{20 \log (3)}\\ &=\frac {\left (5+16 e^4 x\right )^2}{640 e^4}-\frac {8 e^4 x^2}{5 \log (3)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 25, normalized size = 1.09 \begin {gather*} \frac {8 e^4 x^2 (-4+\log (3))+x \log (243)}{20 \log (3)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 29, normalized size = 1.26
method | result | size |
norman | \(\frac {x}{4}+\frac {2 \,{\mathrm e}^{4} \left (-4+\ln \left (3\right )\right ) x^{2}}{5 \ln \left (3\right )}\) | \(20\) |
risch | \(\frac {2 x^{2} {\mathrm e}^{4}}{5}-\frac {8 x^{2} {\mathrm e}^{4}}{5 \ln \left (3\right )}+\frac {x}{4}\) | \(23\) |
gosper | \(\frac {x \left (8 \,{\mathrm e}^{4} x \ln \left (3\right )-32 x \,{\mathrm e}^{4}+5 \ln \left (3\right )\right )}{20 \ln \left (3\right )}\) | \(25\) |
default | \(\frac {8 \,{\mathrm e}^{4} x^{2} \ln \left (3\right )-32 x^{2} {\mathrm e}^{4}+5 x \ln \left (3\right )}{20 \ln \left (3\right )}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 29, normalized size = 1.26 \begin {gather*} -\frac {32 \, x^{2} e^{4} - {\left (8 \, x^{2} e^{4} + 5 \, x\right )} \log \left (3\right )}{20 \, \log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 29, normalized size = 1.26 \begin {gather*} -\frac {32 \, x^{2} e^{4} - {\left (8 \, x^{2} e^{4} + 5 \, x\right )} \log \left (3\right )}{20 \, \log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 24, normalized size = 1.04 \begin {gather*} \frac {x^{2} \left (- 8 e^{4} + 2 e^{4} \log {\left (3 \right )}\right )}{5 \log {\left (3 \right )}} + \frac {x}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 29, normalized size = 1.26 \begin {gather*} -\frac {32 \, x^{2} e^{4} - {\left (8 \, x^{2} e^{4} + 5 \, x\right )} \log \left (3\right )}{20 \, \log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.11, size = 24, normalized size = 1.04 \begin {gather*} \frac {x}{4}-\frac {x^2\,\left (64\,{\mathrm {e}}^4-16\,{\mathrm {e}}^4\,\ln \left (3\right )\right )}{40\,\ln \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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