Optimal. Leaf size=24 \[ e^{x \left (-4+x+3 \left (\frac {16}{x^2}-x^2 \log ^2(x)\right )\right )} \]
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Rubi [A] time = 0.53, antiderivative size = 25, normalized size of antiderivative = 1.04, number of steps used = 1, number of rules used = 1, integrand size = 57, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {6706} \begin {gather*} e^{\frac {-3 x^4 \log ^2(x)+x^3-4 x^2+48}{x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{\frac {48-4 x^2+x^3-3 x^4 \log ^2(x)}{x}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.29, size = 23, normalized size = 0.96 \begin {gather*} e^{\frac {48}{x}-4 x+x^2-3 x^3 \log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 27, normalized size = 1.12 \begin {gather*} e^{\left (-\frac {3 \, x^{4} \log \relax (x)^{2} - x^{3} + 4 \, x^{2} - 48}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 22, normalized size = 0.92 \begin {gather*} e^{\left (-3 \, x^{3} \log \relax (x)^{2} + x^{2} - 4 \, x + \frac {48}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 28, normalized size = 1.17
method | result | size |
risch | \({\mathrm e}^{-\frac {3 x^{4} \ln \relax (x )^{2}-x^{3}+4 x^{2}-48}{x}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.70, size = 22, normalized size = 0.92 \begin {gather*} e^{\left (-3 \, x^{3} \log \relax (x)^{2} + x^{2} - 4 \, x + \frac {48}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.62, size = 25, normalized size = 1.04 \begin {gather*} {\mathrm {e}}^{-4\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{48/x}\,{\mathrm {e}}^{-3\,x^3\,{\ln \relax (x)}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.34, size = 22, normalized size = 0.92 \begin {gather*} e^{\frac {- 3 x^{4} \log {\relax (x )}^{2} + x^{3} - 4 x^{2} + 48}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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