Optimal. Leaf size=23 \[ -\frac {2 \left (e^3-x+e^{e^{x^2}} (4+x)\right )}{e} \]
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Rubi [A]
time = 0.03, antiderivative size = 28, normalized size of antiderivative = 1.22, number of steps
used = 3, number of rules used = 2, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {12, 2326}
\begin {gather*} \frac {2 x}{e}-\frac {2 e^{e^{x^2}-1} \left (x^2+4 x\right )}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (2+e^{e^{x^2}} \left (-2+e^{x^2} \left (-16 x-4 x^2\right )\right )\right ) \, dx}{e}\\ &=\frac {2 x}{e}+\frac {\int e^{e^{x^2}} \left (-2+e^{x^2} \left (-16 x-4 x^2\right )\right ) \, dx}{e}\\ &=\frac {2 x}{e}-\frac {2 e^{-1+e^{x^2}} \left (4 x+x^2\right )}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 20, normalized size = 0.87 \begin {gather*} -\frac {2 \left (-x+e^{e^{x^2}} (4+x)\right )}{e} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.21, size = 25, normalized size = 1.09
method | result | size |
risch | \(2 \,{\mathrm e}^{-1} x +\left (-2 x -8\right ) {\mathrm e}^{{\mathrm e}^{x^{2}}-1}\) | \(20\) |
default | \({\mathrm e}^{-1} \left (2 x -2 \,{\mathrm e}^{{\mathrm e}^{x^{2}}} x -8 \,{\mathrm e}^{{\mathrm e}^{x^{2}}}\right )\) | \(25\) |
norman | \(2 \,{\mathrm e}^{-1} x -8 \,{\mathrm e}^{-1} {\mathrm e}^{{\mathrm e}^{x^{2}}}-2 x \,{\mathrm e}^{-1} {\mathrm e}^{{\mathrm e}^{x^{2}}}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 17, normalized size = 0.74 \begin {gather*} -2 \, {\left ({\left (x + 4\right )} e^{\left (e^{\left (x^{2}\right )}\right )} - x\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.44, size = 17, normalized size = 0.74 \begin {gather*} -2 \, {\left ({\left (x + 4\right )} e^{\left (e^{\left (x^{2}\right )}\right )} - x\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.29, size = 22, normalized size = 0.96 \begin {gather*} \frac {2 x}{e} + \frac {\left (- 2 x - 8\right ) e^{e^{x^{2}}}}{e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 38, normalized size = 1.65 \begin {gather*} -2 \, {\left ({\left (x e^{\left (x^{2} + e^{\left (x^{2}\right )}\right )} + 4 \, e^{\left (x^{2} + e^{\left (x^{2}\right )}\right )}\right )} e^{\left (-x^{2}\right )} - x\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.24, size = 22, normalized size = 0.96 \begin {gather*} -2\,{\mathrm {e}}^{-1}\,\left (4\,{\mathrm {e}}^{{\mathrm {e}}^{x^2}}-x+x\,{\mathrm {e}}^{{\mathrm {e}}^{x^2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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