Optimal. Leaf size=7 \[ \frac {1}{\log (x)}+\log (x) \]
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Rubi [A]
time = 0.02, antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {14}
\begin {gather*} \log (x)+\frac {1}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\text {Subst}\left (\int \frac {-1+x^2}{x^2} \, dx,x,\log (x)\right )\\ &=\text {Subst}\left (\int \left (1-\frac {1}{x^2}\right ) \, dx,x,\log (x)\right )\\ &=\frac {1}{\log (x)}+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 7, normalized size = 1.00 \begin {gather*} \frac {1}{\log (x)}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 8, normalized size = 1.14
method | result | size |
derivativedivides | \(\frac {1}{\ln \left (x \right )}+\ln \left (x \right )\) | \(8\) |
default | \(\frac {1}{\ln \left (x \right )}+\ln \left (x \right )\) | \(8\) |
risch | \(\frac {1}{\ln \left (x \right )}+\ln \left (x \right )\) | \(8\) |
parts | \(\frac {1}{\ln \left (x \right )}+\ln \left (x \right )\) | \(8\) |
norman | \(\frac {1+\ln \left (x \right )^{2}}{\ln \left (x \right )}\) | \(12\) |
parallelrisch | \(\frac {1+\ln \left (x \right )^{2}}{\ln \left (x \right )}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.39, size = 7, normalized size = 1.00 \begin {gather*} \frac {1}{\log \left (x\right )} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.58, size = 11, normalized size = 1.57 \begin {gather*} \frac {\log \left (x\right )^{2} + 1}{\log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 7, normalized size = 1.00 \begin {gather*} \log {\left (x \right )} + \frac {1}{\log {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.50, size = 7, normalized size = 1.00 \begin {gather*} \frac {1}{\log \left (x\right )} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.11, size = 7, normalized size = 1.00 \begin {gather*} \ln \left (x\right )+\frac {1}{\ln \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F] Failed to verify
time = 1.00, size = 9, normalized size = 1.29 \begin {gather*} \ln \left (x \right )-\frac {1}{\ln \left (x \right )} \end {gather*}
Warning: Unable to verify antiderivative.
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