Optimal. Leaf size=27 \[ \frac {1}{3-e^{x^2 \left (-1-x^2\right )^2}+x+\log (2) \log (5)} \]
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Rubi [A]
time = 0.32, antiderivative size = 21, normalized size of antiderivative = 0.78, number of steps
used = 2, number of rules used = 2, integrand size = 105, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6820, 6818}
\begin {gather*} \frac {1}{-e^{\left (x^3+x\right )^2}+x+3+\log (2) \log (5)} \end {gather*}
Antiderivative was successfully verified.
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Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-1+2 e^{\left (x+x^3\right )^2} x \left (1+4 x^2+3 x^4\right )}{\left (e^{\left (x+x^3\right )^2}-x-3 \left (1+\frac {1}{3} \log (2) \log (5)\right )\right )^2} \, dx\\ &=\frac {1}{3-e^{\left (x+x^3\right )^2}+x+\log (2) \log (5)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 21, normalized size = 0.78 \begin {gather*} \frac {1}{3-e^{\left (x+x^3\right )^2}+x+\log (2) \log (5)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 6.29, size = 25, normalized size = 0.93
method | result | size |
risch | \(\frac {1}{\ln \left (2\right ) \ln \left (5\right )+x -{\mathrm e}^{x^{2} \left (x^{2}+1\right )^{2}}+3}\) | \(25\) |
norman | \(\frac {1}{\ln \left (2\right ) \ln \left (5\right )+x -{\mathrm e}^{x^{6}+2 x^{4}+x^{2}}+3}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.55, size = 25, normalized size = 0.93 \begin {gather*} \frac {1}{\log \left (5\right ) \log \left (2\right ) + x - e^{\left (x^{6} + 2 \, x^{4} + x^{2}\right )} + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 25, normalized size = 0.93 \begin {gather*} \frac {1}{\log \left (5\right ) \log \left (2\right ) + x - e^{\left (x^{6} + 2 \, x^{4} + x^{2}\right )} + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 26, normalized size = 0.96 \begin {gather*} - \frac {1}{- x + e^{x^{6} + 2 x^{4} + x^{2}} - 3 - \log {\left (2 \right )} \log {\left (5 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 25, normalized size = 0.93 \begin {gather*} \frac {1}{\log \left (5\right ) \log \left (2\right ) + x - e^{\left (x^{6} + 2 \, x^{4} + x^{2}\right )} + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\mathrm {e}}^{x^6+2\,x^4+x^2}\,\left (6\,x^5+8\,x^3+2\,x\right )-1}{6\,x+{\mathrm {e}}^{2\,x^6+4\,x^4+2\,x^2}-{\mathrm {e}}^{x^6+2\,x^4+x^2}\,\left (2\,x+2\,\ln \left (2\right )\,\ln \left (5\right )+6\right )+x^2+{\ln \left (2\right )}^2\,{\ln \left (5\right )}^2+\ln \left (2\right )\,\ln \left (5\right )\,\left (2\,x+6\right )+9} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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