Optimal. Leaf size=14 \[ \frac {1}{13} \left (4+\left (4+\frac {1}{e^9}\right ) \log (x)\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.79, number of steps
used = 2, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {12, 29}
\begin {gather*} \frac {1}{13} \left (4+\frac {1}{e^9}\right ) \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 29
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{13} \left (4+\frac {1}{e^9}\right ) \int \frac {1}{x} \, dx\\ &=\frac {1}{13} \left (4+\frac {1}{e^9}\right ) \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 1.14 \begin {gather*} \frac {\left (1+4 e^9\right ) \log (x)}{13 e^9} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 15, normalized size = 1.07
method | result | size |
default | \(\frac {\left (4 \,{\mathrm e}^{9}+1\right ) {\mathrm e}^{-9} \ln \left (x \right )}{13}\) | \(15\) |
norman | \(\frac {\left (4 \,{\mathrm e}^{9}+1\right ) {\mathrm e}^{-9} \ln \left (x \right )}{13}\) | \(15\) |
risch | \(\frac {4 \,{\mathrm e}^{-9} \ln \left (x \right ) {\mathrm e}^{9}}{13}+\frac {{\mathrm e}^{-9} \ln \left (x \right )}{13}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 12, normalized size = 0.86 \begin {gather*} \frac {1}{13} \, {\left (4 \, e^{9} + 1\right )} e^{\left (-9\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 12, normalized size = 0.86 \begin {gather*} \frac {1}{13} \, {\left (4 \, e^{9} + 1\right )} e^{\left (-9\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 = 14, normalized size = 1.00 \begin {gather*} \frac {\left (1 + 4 e^{9}\right ) \log {\left (x \right )}}{13 e^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 13, normalized size = 0.93 \begin {gather*} \frac {1}{13} \, {\left (4 \, e^{9} + 1\right )} e^{\left (-9\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 = 1.03, size = 12, normalized size = 0.86 \begin {gather*} \frac {{\mathrm {e}}^{-9}\,\ln \left (x\right )\,\left (4\,{\mathrm {e}}^9+1\right )}{13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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