Optimal. Leaf size=16 \[ \log \left (12 \left (x+\log \left (4+\frac {3 e^8}{x}\right )\right )\right ) \]
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Rubi [A] time = 0.21, antiderivative size = 14, normalized size of antiderivative = 0.88, number of steps used = 2, number of rules used = 2, integrand size = 59, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {6741, 6684} \begin {gather*} \log \left (x+\log \left (\frac {3 e^8}{x}+4\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-3 e^8+3 e^8 x+4 x^2}{x \left (3 e^8+4 x\right ) \left (x+\log \left (4+\frac {3 e^8}{x}\right )\right )} \, dx\\ &=\log \left (x+\log \left (4+\frac {3 e^8}{x}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 5.03, size = 14, normalized size = 0.88 \begin {gather*} \log \left (x+\log \left (4+\frac {3 e^8}{x}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 16, normalized size = 1.00 \begin {gather*} \log \left (x + \log \left (\frac {4 \, x + 3 \, e^{8}}{x}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.18, size = 72, normalized size = 4.50 \begin {gather*} {\left (e^{8} \log \left (\frac {{\left (4 \, x + 3 \, e^{8}\right )} \log \left (\frac {4 \, x + 3 \, e^{8}}{x}\right )}{x} + 3 \, e^{8} - 4 \, \log \left (\frac {4 \, x + 3 \, e^{8}}{x}\right )\right ) - e^{8} \log \left (\frac {4 \, x + 3 \, e^{8}}{x} - 4\right )\right )} e^{\left (-8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 17, normalized size = 1.06
method | result | size |
risch | \(\ln \left (\ln \left (\frac {3 \,{\mathrm e}^{8}+4 x}{x}\right )+x \right )\) | \(17\) |
norman | \(\ln \left (\ln \left (\frac {3 \,{\mathrm e}^{8}+4 x}{x}\right )+x \right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 16, normalized size = 1.00 \begin {gather*} \log \left (x + \log \left (4 \, x + 3 \, e^{8}\right ) - \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.76, size = 13, normalized size = 0.81 \begin {gather*} \ln \left (x+\ln \left (\frac {3\,{\mathrm {e}}^8}{x}+4\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 14, normalized size = 0.88 \begin {gather*} \log {\left (x + \log {\left (\frac {4 x + 3 e^{8}}{x} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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