Optimal. Leaf size=23 \[ e^{3 x \left (4-\log \left (5+x-\frac {2+x^2}{x}\right )\right )} \]
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Rubi [A] time = 0.21, antiderivative size = 20, normalized size of antiderivative = 0.87, number of steps used = 1, number of rules used = 1, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {6706} \begin {gather*} e^{12 x} \left (-\frac {2-5 x}{x}\right )^{-3 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{12 x} \left (-\frac {2-5 x}{x}\right )^{-3 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 5.04, size = 17, normalized size = 0.74 \begin {gather*} e^{12 x} \left (5-\frac {2}{x}\right )^{-3 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 18, normalized size = 0.78 \begin {gather*} e^{\left (-3 \, x \log \left (\frac {5 \, x - 2}{x}\right ) + 12 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.63, size = 16, normalized size = 0.70 \begin {gather*} e^{\left (-3 \, x \log \left (-\frac {2}{x} + 5\right ) + 12 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.23, size = 19, normalized size = 0.83
method | result | size |
norman | \({\mathrm e}^{-3 x \ln \left (\frac {5 x -2}{x}\right )+12 x}\) | \(19\) |
risch | \(\left (\frac {5 x -2}{x}\right )^{-3 x} {\mathrm e}^{12 x}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 19, normalized size = 0.83 \begin {gather*} e^{\left (-3 \, x \log \left (5 \, x - 2\right ) + 3 \, x \log \relax (x) + 12 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.14, size = 18, normalized size = 0.78 \begin {gather*} \frac {{\mathrm {e}}^{12\,x}}{{\left (5-\frac {2}{x}\right )}^{3\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.37, size = 15, normalized size = 0.65 \begin {gather*} e^{- 3 x \log {\left (\frac {5 x - 2}{x} \right )} + 12 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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