Optimal. Leaf size=11 \[ -14+\frac {1}{3} e^2 \log (x) \]
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Rubi [A]
time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.82, number of steps
used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 29}
\begin {gather*} \frac {1}{3} e^2 \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}{3} e^2 \int \frac {1}{x} \, dx\\ &=\frac {1}{3} e^2 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 9, normalized size = 0.82 \begin {gather*} \frac {1}{3} e^2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 7, normalized size = 0.64
method | result | size |
default | \(\frac {{\mathrm e}^{2} \ln \left (x \right )}{3}\) | \(7\) |
norman | \(\frac {{\mathrm e}^{2} \ln \left (x \right )}{3}\) | \(7\) |
risch | \(\frac {{\mathrm e}^{2} \ln \left (x \right )}{3}\) | \(7\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 6, normalized size = 0.55 \begin {gather*} \frac {1}{3} \, e^{2} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 6, normalized size = 0.55 \begin {gather*} \frac {1}{3} \, e^{2} \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 = 7, normalized size = 0.64 \begin {gather*} \frac {e^{2} \log {\left (x \right )}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 7, normalized size = 0.64 \begin {gather*} \frac {1}{3} \, e^{2} \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 = 0.03, size = 6, normalized size = 0.55 \begin {gather*} \frac {{\mathrm {e}}^2\,\ln \left (x\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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