Optimal. Leaf size=25 \[ -\frac {e^{1-e^{x^2} x}}{e^{x^2} x-1} \]
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Rubi [F] time = 0.98, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {e^{1-e^{x^2} x+2 x^2} \left (x+2 x^3\right )}{\left (1-e^{x^2} x\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {e^{1-e^{x^2} x+2 x^2} \left (x+2 x^3\right )}{\left (1-e^{x^2} x\right )^2} \, dx &=\int \frac {e^{1-e^{x^2} x+2 x^2} x \left (1+2 x^2\right )}{\left (1-e^{x^2} x\right )^2} \, dx\\ &=\int \left (\frac {e^{1-e^{x^2} x+2 x^2} x}{\left (-1+e^{x^2} x\right )^2}+\frac {2 e^{1-e^{x^2} x+2 x^2} x^3}{\left (-1+e^{x^2} x\right )^2}\right ) \, dx\\ &=2 \int \frac {e^{1-e^{x^2} x+2 x^2} x^3}{\left (-1+e^{x^2} x\right )^2} \, dx+\int \frac {e^{1-e^{x^2} x+2 x^2} x}{\left (-1+e^{x^2} x\right )^2} \, dx\\ \end {align*}
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Mathematica [A] time = 0.17, size = 25, normalized size = 1.00 \[ -\frac {e^{1-e^{x^2} x}}{e^{x^2} x-1} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 36, normalized size = 1.44 \[ -\frac {e^{\left (2 \, x^{2} - x e^{\left (x^{2}\right )} + 1\right )}}{x e^{\left (3 \, x^{2}\right )} - e^{\left (2 \, x^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.02, size = 36, normalized size = 1.44 \[ -\frac {e^{\left (2 \, x^{2} - x e^{\left (x^{2}\right )} + 1\right )}}{x e^{\left (3 \, x^{2}\right )} - e^{\left (2 \, x^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 23, normalized size = 0.92 \[ -\frac {{\mathrm e}^{-x \,{\mathrm e}^{x^{2}}+1}}{x \,{\mathrm e}^{x^{2}}-1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.75, size = 22, normalized size = 0.88 \[ -\frac {e^{\left (-x e^{\left (x^{2}\right )} + 1\right )}}{x e^{\left (x^{2}\right )} - 1} \]
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 \[ \int \frac {{\mathrm {e}}^{2\,x^2-x\,{\mathrm {e}}^{x^2}+1}\,\left (2\,x^3+x\right )}{{\left (x\,{\mathrm {e}}^{x^2}-1\right )}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.35, size = 31, normalized size = 1.24 \[ - \frac {e^{2 x^{2} - x e^{x^{2}} + 1}}{x e^{3 x^{2}} - e^{2 x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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