Optimal. Leaf size=13 \[ e^{20 \left (3-\frac {20}{e^2}+\log (x)\right )} \]
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Rubi [A] time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {12, 1586, 30} \begin {gather*} e^{60-\frac {400}{e^2}} x^{20} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 1586
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=20 \int \frac {e^{\frac {-400+60 e^2+20 e^2 \log (x)}{e^2}}}{x} \, dx\\ &=20 \int e^{60-\frac {400}{e^2}} x^{19} \, dx\\ &=\left (20 e^{60-\frac {400}{e^2}}\right ) \int x^{19} \, dx\\ &=e^{60-\frac {400}{e^2}} x^{20}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} e^{60-\frac {400}{e^2}} x^{20} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 15, normalized size = 1.15 \begin {gather*} x^{20} e^{\left (20 \, {\left (3 \, e^{2} - 20\right )} e^{\left (-2\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 11, normalized size = 0.85 \begin {gather*} x^{20} e^{\left (-400 \, e^{\left (-2\right )} + 60\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 12, normalized size = 0.92
method | result | size |
risch | \(x^{20} {\mathrm e}^{60-400 \,{\mathrm e}^{-2}}\) | \(12\) |
norman | \({\mathrm e}^{60} {\mathrm e}^{-400 \,{\mathrm e}^{-2}} x^{20}\) | \(14\) |
gosper | \({\mathrm e}^{20 \left ({\mathrm e}^{2} \ln \relax (x )+3 \,{\mathrm e}^{2}-20\right ) {\mathrm e}^{-2}}\) | \(19\) |
derivativedivides | \({\mathrm e}^{\left (20 \,{\mathrm e}^{2} \ln \relax (x )+60 \,{\mathrm e}^{2}-400\right ) {\mathrm e}^{-2}}\) | \(19\) |
default | \({\mathrm e}^{\left (20 \,{\mathrm e}^{2} \ln \relax (x )+60 \,{\mathrm e}^{2}-400\right ) {\mathrm e}^{-2}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 16, normalized size = 1.23 \begin {gather*} e^{\left (20 \, {\left (e^{2} \log \relax (x) + 3 \, e^{2} - 20\right )} e^{\left (-2\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 11, normalized size = 0.85 \begin {gather*} x^{20}\,{\mathrm {e}}^{60-400\,{\mathrm {e}}^{-2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 12, normalized size = 0.92 \begin {gather*} \frac {x^{20} e^{60}}{e^{\frac {400}{e^{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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