Optimal. Leaf size=10 \[ 8+\frac {4+\log (x)}{e^6} \]
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Rubi [A]
time = 0.00, antiderivative size = 6, normalized size of antiderivative = 0.60, 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 {\log (x)}{e^6} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 29
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {1}{x} \, dx}{e^6}\\ &=\frac {\log (x)}{e^6}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 6, normalized size = 0.60 \begin {gather*} \frac {\log (x)}{e^6} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.61, size = 8, normalized size = 0.80
method | result | size |
risch | \({\mathrm e}^{-6} \ln \left (x \right )\) | \(6\) |
default | \({\mathrm e}^{-6} \ln \left (x \right )\) | \(8\) |
norman | \({\mathrm e}^{-6} \ln \left (x \right )\) | \(8\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 5, normalized size = 0.50 \begin {gather*} e^{\left (-6\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.43, size = 5, normalized size = 0.50 \begin {gather*} e^{\left (-6\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 5, normalized size = 0.50 \begin {gather*} \frac {\log {\left (x \right )}}{e^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 6, normalized size = 0.60 \begin {gather*} e^{\left (-6\right )} \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.12, size = 5, normalized size = 0.50 \begin {gather*} {\mathrm {e}}^{-6}\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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