Optimal. Leaf size=8 \[ \frac {1}{e^{253} \log (x)} \]
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Rubi [A] time = 0.02, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 2302, 30} \begin {gather*} \frac {1}{e^{253} \log (x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 2302
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {\int \frac {1}{x \log ^2(x)} \, dx}{e^{253}}\\ &=-\frac {\operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log (x)\right )}{e^{253}}\\ &=\frac {1}{e^{253} \log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 1.00 \begin {gather*} \frac {1}{e^{253} \log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.02, size = 7, normalized size = 0.88 \begin {gather*} \frac {e^{\left (-253\right )}}{\log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 7, normalized size = 0.88 \begin {gather*} \frac {e^{\left (-253\right )}}{\log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 8, normalized size = 1.00
method | result | size |
risch | \(\frac {{\mathrm e}^{-253}}{\ln \relax (x )}\) | \(8\) |
derivativedivides | \({\mathrm e}^{-\ln \left (\ln \relax (x )\right )-253}\) | \(9\) |
default | \({\mathrm e}^{-\ln \left (\ln \relax (x )\right )-253}\) | \(9\) |
norman | \(\frac {{\mathrm e}^{-253}}{\ln \relax (x )}\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 7, normalized size = 0.88 \begin {gather*} \frac {e^{\left (-253\right )}}{\log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.34, size = 7, normalized size = 0.88 \begin {gather*} \frac {{\mathrm {e}}^{-253}}{\ln \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 7, normalized size = 0.88 \begin {gather*} \frac {1}{e^{253} \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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