Optimal. Leaf size=14 \[ -\frac {3 e^2}{16 x^2 \log ^2(5)} \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 30} \begin {gather*} -\frac {3 e^2}{16 x^2 \log ^2(5)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\left (3 e^2\right ) \int \frac {1}{x^3} \, dx}{8 \log ^2(5)}\\ &=-\frac {3 e^2}{16 x^2 \log ^2(5)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} -\frac {3 e^2}{16 x^2 \log ^2(5)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 11, normalized size = 0.79 \begin {gather*} -\frac {3 \, e^{2}}{16 \, x^{2} \log \relax (5)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 11, normalized size = 0.79 \begin {gather*} -\frac {3 \, e^{2}}{16 \, x^{2} \log \relax (5)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 12, normalized size = 0.86
method | result | size |
gosper | \(-\frac {3 \,{\mathrm e}^{2}}{16 \ln \relax (5)^{2} x^{2}}\) | \(12\) |
default | \(-\frac {3 \,{\mathrm e}^{2}}{16 \ln \relax (5)^{2} x^{2}}\) | \(12\) |
norman | \(-\frac {3 \,{\mathrm e}^{2}}{16 \ln \relax (5)^{2} x^{2}}\) | \(12\) |
risch | \(-\frac {3 \,{\mathrm e}^{2}}{16 \ln \relax (5)^{2} x^{2}}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 11, normalized size = 0.79 \begin {gather*} -\frac {3 \, e^{2}}{16 \, x^{2} \log \relax (5)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.98, size = 11, normalized size = 0.79 \begin {gather*} -\frac {3\,{\mathrm {e}}^2}{16\,x^2\,{\ln \relax (5)}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 15, normalized size = 1.07 \begin {gather*} - \frac {3 e^{2}}{16 x^{2} \log {\relax (5 )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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