Optimal. Leaf size=35 \[ \log ^2(3) \log ^2\left (\frac {\left (e^{x \left (-x^3+\frac {2+x}{x}\right )}-x\right )^2}{x}\right ) \]
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Rubi [A]
time = 2.49, antiderivative size = 41, normalized size of antiderivative = 1.17, number of steps
used = 1, number of rules used = 2, integrand size = 88, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {6874, 6818}
\begin {gather*} \log ^2(3) \log ^2\left (\frac {-2 e^{-x^4+x+2} x+e^{-2 x^4+2 x+4}+x^2}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6818
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log ^2(3) \log ^2\left (\frac {e^{4+2 x-2 x^4}-2 e^{2+x-x^4} x+x^2}{x}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.18, size = 35, normalized size = 1.00 \begin {gather*} \log ^2(3) \log ^2\left (\frac {e^{-2 x^4} \left (e^{2+x}-e^{x^4} x\right )^2}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 2.72, size = 40, normalized size = 1.14
method | result | size |
norman | \(\ln \left (3\right )^{2} \ln \left (\frac {{\mathrm e}^{-2 x^{4}+2 x +4}-2 x \,{\mathrm e}^{-x^{4}+x +2}+x^{2}}{x}\right )^{2}\) | \(40\) |
risch | \(\text {Expression too large to display}\) | \(1442\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 39, normalized size = 1.11 \begin {gather*} \log \left (3\right )^{2} \log \left (\frac {x^{2} - 2 \, x e^{\left (-x^{4} + x + 2\right )} + e^{\left (-2 \, x^{4} + 2 \, x + 4\right )}}{x}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.19, size = 36, normalized size = 1.03 \begin {gather*} \log {\left (3 \right )}^{2} \log {\left (\frac {x^{2} - 2 x e^{- x^{4} + x + 2} + e^{- 2 x^{4} + 2 x + 4}}{x} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 8.79, size = 38, normalized size = 1.09 \begin {gather*} {\ln \left (3\right )}^2\,{\ln \left (x-2\,{\mathrm {e}}^2\,{\mathrm {e}}^{-x^4}\,{\mathrm {e}}^x+\frac {{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^4\,{\mathrm {e}}^{-2\,x^4}}{x}\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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