Optimal. Leaf size=23 \[ \log \left (-2-4 x+4 \left (2-e^4 (4 x-\log (5))\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 0.83, number of steps used = 3, number of rules used = 3, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.107, Rules used = {6, 12, 31} \begin {gather*} \log \left (-2 \left (1+4 e^4\right ) x+3+e^4 \log (25)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 31
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-2-8 e^4}{3+\left (-2-8 e^4\right ) x+2 e^4 \log (5)} \, dx\\ &=-\left (\left (2 \left (1+4 e^4\right )\right ) \int \frac {1}{3+\left (-2-8 e^4\right ) x+2 e^4 \log (5)} \, dx\right )\\ &=\log \left (3-2 \left (1+4 e^4\right ) x+e^4 \log (25)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 0.83 \begin {gather*} \log \left (-3+\left (2+8 e^4\right ) x-2 e^4 \log (5)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 17, normalized size = 0.74 \begin {gather*} \log \left (8 \, x e^{4} - 2 \, e^{4} \log \relax (5) + 2 \, x - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 18, normalized size = 0.78 \begin {gather*} \log \left ({\left | 8 \, x e^{4} - 2 \, e^{4} \log \relax (5) + 2 \, x - 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 18, normalized size = 0.78
method | result | size |
default | \(\ln \left (\left (-8 \,{\mathrm e}^{4}-2\right ) x +2 \,{\mathrm e}^{4} \ln \relax (5)+3\right )\) | \(18\) |
norman | \(\ln \left (2 \,{\mathrm e}^{4} \ln \relax (5)-8 x \,{\mathrm e}^{4}+3-2 x \right )\) | \(18\) |
risch | \(\frac {4 \ln \left (\left (-8 \,{\mathrm e}^{4}-2\right ) x +2 \,{\mathrm e}^{4} \ln \relax (5)+3\right ) {\mathrm e}^{4}}{4 \,{\mathrm e}^{4}+1}+\frac {\ln \left (\left (-8 \,{\mathrm e}^{4}-2\right ) x +2 \,{\mathrm e}^{4} \ln \relax (5)+3\right )}{4 \,{\mathrm e}^{4}+1}\) | \(57\) |
meijerg | \(\frac {4 \,{\mathrm e}^{4} \ln \left (1-\frac {2 x \left (4 \,{\mathrm e}^{4}+1\right )}{2 \,{\mathrm e}^{4} \ln \relax (5)+3}\right )}{4 \,{\mathrm e}^{4}+1}+\frac {\ln \left (1-\frac {2 x \left (4 \,{\mathrm e}^{4}+1\right )}{2 \,{\mathrm e}^{4} \ln \relax (5)+3}\right )}{4 \,{\mathrm e}^{4}+1}\) | \(67\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 17, normalized size = 0.74 \begin {gather*} \log \left (8 \, x e^{4} - 2 \, e^{4} \log \relax (5) + 2 \, x - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.07, size = 17, normalized size = 0.74 \begin {gather*} \ln \left (x\,\left (8\,{\mathrm {e}}^4+2\right )-2\,{\mathrm {e}}^4\,\ln \relax (5)-3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 19, normalized size = 0.83 \begin {gather*} \log {\left (x \left (2 + 8 e^{4}\right ) - 2 e^{4} \log {\relax (5 )} - 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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