Optimal. Leaf size=13 \[ e^3 \left (\frac {4}{x}+\log (\log (2))\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.62, 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 {4 e^3}{x} \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^3\right ) \int \frac {1}{x^2} \, dx\right )\\ &=\frac {4 e^3}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 0.62 \begin {gather*} \frac {4 e^3}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 7, normalized size = 0.54 \begin {gather*} \frac {4 \, e^{3}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 7, normalized size = 0.54 \begin {gather*} \frac {4 \, e^{3}}{x} \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 = 0.62
method | result | size |
gosper | \(\frac {4 \,{\mathrm e}^{3}}{x}\) | \(8\) |
default | \(\frac {4 \,{\mathrm e}^{3}}{x}\) | \(8\) |
norman | \(\frac {4 \,{\mathrm e}^{3}}{x}\) | \(8\) |
risch | \(\frac {4 \,{\mathrm e}^{3}}{x}\) | \(8\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 7, normalized size = 0.54 \begin {gather*} \frac {4 \, e^{3}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 7, normalized size = 0.54 \begin {gather*} \frac {4\,{\mathrm {e}}^3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 5, normalized size = 0.38 \begin {gather*} \frac {4 e^{3}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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