Optimal. Leaf size=30 \[ e^{\frac {1-x}{2}+\frac {1}{3} \left (-12+\frac {e^{4 x^2}}{x}+x\right )} \]
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Rubi [A]
time = 0.25, antiderivative size = 27, normalized size of antiderivative = 0.90, number of steps
used = 2, number of rules used = 2, integrand size = 55, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {12, 6838}
\begin {gather*} e^{\frac {-x^2+2 e^{4 x^2}-21 x}{6 x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{6} \int \frac {e^{\frac {2 e^{4 x^2}-21 x-x^2}{6 x}} \left (-x^2+e^{4 x^2} \left (-2+16 x^2\right )\right )}{x^2} \, dx\\ &=e^{\frac {2 e^{4 x^2}-21 x-x^2}{6 x}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.14, size = 25, normalized size = 0.83 \begin {gather*} e^{-\frac {7}{2}+\frac {e^{4 x^2}}{3 x}-\frac {x}{6}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.30, size = 22, normalized size = 0.73
method | result | size |
risch | \({\mathrm e}^{-\frac {-2 \,{\mathrm e}^{4 x^{2}}+x^{2}+21 x}{6 x}}\) | \(22\) |
norman | \({\mathrm e}^{\frac {2 \,{\mathrm e}^{4 x^{2}}-x^{2}-21 x}{6 x}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.37, size = 17, normalized size = 0.57 \begin {gather*} e^{\left (-\frac {1}{6} \, x + \frac {e^{\left (4 \, x^{2}\right )}}{3 \, x} - \frac {7}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 21, normalized size = 0.70 \begin {gather*} e^{\left (-\frac {x^{2} + 21 \, x - 2 \, e^{\left (4 \, x^{2}\right )}}{6 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.30, size = 20, normalized size = 0.67 \begin {gather*} e^{\frac {- \frac {x^{2}}{6} - \frac {7 x}{2} + \frac {e^{4 x^{2}}}{3}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 17, normalized size = 0.57 \begin {gather*} e^{\left (-\frac {1}{6} \, x + \frac {e^{\left (4 \, x^{2}\right )}}{3 \, x} - \frac {7}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.27, size = 19, normalized size = 0.63 \begin {gather*} {\mathrm {e}}^{\frac {{\mathrm {e}}^{4\,x^2}}{3\,x}}\,{\mathrm {e}}^{-\frac {x}{6}}\,{\mathrm {e}}^{-\frac {7}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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