Optimal. Leaf size=24 \[ \frac {\frac {2 e^2}{x}+e^{4 e^{e^2}} x}{x} \]
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Rubi [A] time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.33, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 30} \begin {gather*} \frac {2 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\right ) \int \frac {1}{x^3} \, dx\right )\\ &=\frac {2 e^2}{x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 0.33 \begin {gather*} \frac {2 e^2}{x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 7, normalized size = 0.29 \begin {gather*} \frac {2 \, e^{2}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 7, normalized size = 0.29 \begin {gather*} \frac {2 \, e^{2}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 8, normalized size = 0.33
method | result | size |
gosper | \(\frac {2 \,{\mathrm e}^{2}}{x^{2}}\) | \(8\) |
default | \(\frac {2 \,{\mathrm e}^{2}}{x^{2}}\) | \(8\) |
norman | \(\frac {2 \,{\mathrm e}^{2}}{x^{2}}\) | \(8\) |
risch | \(\frac {2 \,{\mathrm e}^{2}}{x^{2}}\) | \(8\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 7, normalized size = 0.29 \begin {gather*} \frac {2 \, e^{2}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 7, normalized size = 0.29 \begin {gather*} \frac {2\,{\mathrm {e}}^2}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 7, normalized size = 0.29 \begin {gather*} \frac {2 e^{2}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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