Optimal. Leaf size=12 \[ e^{-20+\frac {400}{x^6}}+\log (25) \]
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Rubi [A] time = 0.04, antiderivative size = 9, normalized size of antiderivative = 0.75, number of steps used = 3, number of rules used = 3, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 2225, 2209} \begin {gather*} e^{\frac {400}{x^6}-20} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2209
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (2400 \int \frac {e^{\frac {400-20 x^6}{x^6}}}{x^7} \, dx\right )\\ &=-\left (2400 \int \frac {e^{-20+\frac {400}{x^6}}}{x^7} \, dx\right )\\ &=e^{-20+\frac {400}{x^6}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 9, normalized size = 0.75 \begin {gather*} e^{-20+\frac {400}{x^6}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 11, normalized size = 0.92 \begin {gather*} e^{\left (-\frac {20 \, {\left (x^{6} - 20\right )}}{x^{6}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.37, size = 8, normalized size = 0.67 \begin {gather*} e^{\left (\frac {400}{x^{6}} - 20\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 9, normalized size = 0.75
method | result | size |
derivativedivides | \({\mathrm e}^{\frac {400}{x^{6}}-20}\) | \(9\) |
default | \({\mathrm e}^{\frac {400}{x^{6}}-20}\) | \(9\) |
gosper | \({\mathrm e}^{-\frac {20 \left (x^{6}-20\right )}{x^{6}}}\) | \(12\) |
risch | \({\mathrm e}^{-\frac {20 \left (x^{6}-20\right )}{x^{6}}}\) | \(12\) |
norman | \({\mathrm e}^{\frac {-20 x^{6}+400}{x^{6}}}\) | \(13\) |
meijerg | \(-{\mathrm e}^{-20} \left (1-{\mathrm e}^{\frac {400}{x^{6}}}\right )\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.73, size = 8, normalized size = 0.67 \begin {gather*} e^{\left (\frac {400}{x^{6}} - 20\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.26, size = 9, normalized size = 0.75 \begin {gather*} {\mathrm {e}}^{-20}\,{\mathrm {e}}^{\frac {400}{x^6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 10, normalized size = 0.83 \begin {gather*} e^{\frac {400 - 20 x^{6}}{x^{6}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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