Optimal. Leaf size=31 \[ e^5+\frac {4}{3} \left (-4-e^4-e^6-\log \left (\frac {4 e^4}{x}\right )\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 6, normalized size of antiderivative = 0.19, number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 29} \begin {gather*} \frac {4 \log (x)}{3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 29
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {4}{3} \int \frac {1}{x} \, dx\\ &=\frac {4 \log (x)}{3}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 6, normalized size = 0.19 \begin {gather*} \frac {4 \log (x)}{3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 4, normalized size = 0.13 \begin {gather*} \frac {4}{3} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 5, normalized size = 0.16 \begin {gather*} \frac {4}{3} \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 5, normalized size = 0.16
method | result | size |
default | \(\frac {4 \ln \relax (x )}{3}\) | \(5\) |
norman | \(\frac {4 \ln \relax (x )}{3}\) | \(5\) |
risch | \(\frac {4 \ln \relax (x )}{3}\) | \(5\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 4, normalized size = 0.13 \begin {gather*} \frac {4}{3} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.01, size = 4, normalized size = 0.13 \begin {gather*} \frac {4\,\ln \relax (x)}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 5, normalized size = 0.16 \begin {gather*} \frac {4 \log {\relax (x )}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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