Optimal. Leaf size=16 \[ \frac {2 e^{2 e^{4 e^2}}}{x^2} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 30} \begin {gather*} \frac {2 e^{2 e^{4 e^2}}}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (4 e^{2 e^{4 e^2}}\right ) \int \frac {1}{x^3} \, dx\right )\\ &=\frac {2 e^{2 e^{4 e^2}}}{x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} \frac {2 e^{2 e^{4 e^2}}}{x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 13, normalized size = 0.81 \begin {gather*} \frac {2 \, e^{\left (2 \, e^{\left (4 \, e^{2}\right )}\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 13, normalized size = 0.81 \begin {gather*} \frac {2 \, e^{\left (2 \, e^{\left (4 \, e^{2}\right )}\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 14, normalized size = 0.88
method | result | size |
norman | \(\frac {2 \,{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2}}}}{x^{2}}\) | \(14\) |
risch | \(\frac {2 \,{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2}}}}{x^{2}}\) | \(14\) |
gosper | \(\frac {2 \,{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2}}}}{x^{2}}\) | \(16\) |
derivativedivides | \(\frac {2 \,{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2}}}}{x^{2}}\) | \(16\) |
default | \(\frac {2 \,{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2}}}}{x^{2}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 13, normalized size = 0.81 \begin {gather*} \frac {2 \, e^{\left (2 \, e^{\left (4 \, e^{2}\right )}\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.68, size = 13, normalized size = 0.81 \begin {gather*} \frac {2\,{\mathrm {e}}^{2\,{\mathrm {e}}^{4\,{\mathrm {e}}^2}}}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 14, normalized size = 0.88 \begin {gather*} \frac {2 e^{2 e^{4 e^{2}}}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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