Optimal. Leaf size=17 \[ \frac {e^3}{1+\frac {\log (2)}{8 x}} \]
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Rubi [A] time = 0.00, antiderivative size = 15, normalized size of antiderivative = 0.88, number of steps used = 3, number of rules used = 3, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 27, 32} \begin {gather*} -\frac {e^3 \log (2)}{8 x+\log (2)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 32
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\left (8 e^3 \log (2)\right ) \int \frac {1}{64 x^2+16 x \log (2)+\log ^2(2)} \, dx\\ &=\left (8 e^3 \log (2)\right ) \int \frac {1}{(8 x+\log (2))^2} \, dx\\ &=-\frac {e^3 \log (2)}{8 x+\log (2)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 0.88 \begin {gather*} -\frac {e^3 \log (2)}{8 x+\log (2)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.47, size = 14, normalized size = 0.82 \begin {gather*} -\frac {e^{3} \log \relax (2)}{8 \, x + \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 14, normalized size = 0.82 \begin {gather*} -\frac {e^{3} \log \relax (2)}{8 \, x + \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.43, size = 15, normalized size = 0.88
method | result | size |
gosper | \(-\frac {\ln \relax (2) {\mathrm e}^{3}}{\ln \relax (2)+8 x}\) | \(15\) |
default | \(-\frac {\ln \relax (2) {\mathrm e}^{3}}{\ln \relax (2)+8 x}\) | \(15\) |
norman | \(-\frac {\ln \relax (2) {\mathrm e}^{3}}{\ln \relax (2)+8 x}\) | \(15\) |
risch | \(-\frac {\ln \relax (2) {\mathrm e}^{3}}{\ln \relax (2)+8 x}\) | \(15\) |
meijerg | \(\frac {8 \,{\mathrm e}^{3} x}{\ln \relax (2) \left (1+\frac {8 x}{\ln \relax (2)}\right )}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.71, size = 14, normalized size = 0.82 \begin {gather*} -\frac {e^{3} \log \relax (2)}{8 \, x + \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.54, size = 14, normalized size = 0.82 \begin {gather*} -\frac {{\mathrm {e}}^3\,\ln \relax (2)}{8\,x+\ln \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 17, normalized size = 1.00 \begin {gather*} - \frac {8 e^{3} \log {\relax (2 )}}{64 x + 8 \log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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