Optimal. Leaf size=24 \[ 3+e^{-6+5 e^{x+x^2}+\frac {e^{2 x}}{x^2}} \]
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Rubi [A] time = 0.52, antiderivative size = 29, normalized size of antiderivative = 1.21, number of steps used = 1, number of rules used = 1, integrand size = 64, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {6706} \begin {gather*} e^{\frac {5 e^{x^2+x} x^2-6 x^2+e^{2 x}}{x^2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{\frac {e^{2 x}-6 x^2+5 e^{x+x^2} x^2}{x^2}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.51, size = 22, normalized size = 0.92 \begin {gather*} e^{-6+5 e^{x+x^2}+\frac {e^{2 x}}{x^2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 26, normalized size = 1.08 \begin {gather*} e^{\left (\frac {5 \, x^{2} e^{\left (x^{2} + x\right )} - 6 \, x^{2} + e^{\left (2 \, x\right )}}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.44, size = 19, normalized size = 0.79 \begin {gather*} e^{\left (\frac {e^{\left (2 \, x\right )}}{x^{2}} + 5 \, e^{\left (x^{2} + x\right )} - 6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 27, normalized size = 1.12
method | result | size |
risch | \({\mathrm e}^{\frac {5 x^{2} {\mathrm e}^{\left (x +1\right ) x}+{\mathrm e}^{2 x}-6 x^{2}}{x^{2}}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 19, normalized size = 0.79 \begin {gather*} e^{\left (\frac {e^{\left (2 \, x\right )}}{x^{2}} + 5 \, e^{\left (x^{2} + x\right )} - 6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.07, size = 21, normalized size = 0.88 \begin {gather*} {\mathrm {e}}^{-6}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,x}}{x^2}}\,{\mathrm {e}}^{5\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.40, size = 26, normalized size = 1.08 \begin {gather*} e^{\frac {5 x^{2} e^{x^{2} + x} - 6 x^{2} + e^{2 x}}{x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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