Optimal. Leaf size=24 \[ e^{\frac {x}{-3-e^{4 x}-\frac {1}{x}+x+x^2}} \]
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Rubi [A] time = 2.02, antiderivative size = 30, normalized size of antiderivative = 1.25, number of steps used = 2, number of rules used = 2, integrand size = 127, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {6688, 6706} \begin {gather*} e^{-\frac {x^2}{-x^3-x^2+\left (e^{4 x}+3\right ) x+1}} \end {gather*}
Antiderivative was successfully verified.
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Rule 6688
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {x^2}{-1-\left (3+e^{4 x}\right ) x+x^2+x^3}} x \left (-2-\left (3+e^{4 x}\right ) x+4 e^{4 x} x^2-x^3\right )}{\left (1+\left (3+e^{4 x}\right ) x-x^2-x^3\right )^2} \, dx\\ &=e^{-\frac {x^2}{1+\left (3+e^{4 x}\right ) x-x^2-x^3}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.92, size = 26, normalized size = 1.08 \begin {gather*} e^{\frac {x^2}{-1-\left (3+e^{4 x}\right ) x+x^2+x^3}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.96, size = 25, normalized size = 1.04 \begin {gather*} e^{\left (\frac {x^{2}}{x^{3} + x^{2} - x e^{\left (4 \, x\right )} - 3 \, x - 1}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 25, normalized size = 1.04 \begin {gather*} e^{\left (\frac {x^{2}}{x^{3} + x^{2} - x e^{\left (4 \, x\right )} - 3 \, x - 1}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 26, normalized size = 1.08
method | result | size |
risch | \({\mathrm e}^{\frac {x^{2}}{x^{3}+x^{2}-x \,{\mathrm e}^{4 x}-3 x -1}}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 25, normalized size = 1.04 \begin {gather*} e^{\left (\frac {x^{2}}{x^{3} + x^{2} - x e^{\left (4 \, x\right )} - 3 \, x - 1}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.06, size = 28, normalized size = 1.17 \begin {gather*} {\mathrm {e}}^{-\frac {x^2}{x\,\left ({\mathrm {e}}^{4\,x}+3\right )-x^2-x^3+1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.58, size = 24, normalized size = 1.00 \begin {gather*} e^{- \frac {x^{2}}{- x^{3} - x^{2} + x e^{4 x} + 3 x + 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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