Optimal. Leaf size=29 \[ e^{3/x}+e^{-16+e^x-x^2 \left (3+x^2 (1+x)\right )} \]
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Rubi [A] time = 0.26, antiderivative size = 30, normalized size of antiderivative = 1.03, number of steps used = 4, number of rules used = 3, integrand size = 60, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {14, 2209, 6706} \begin {gather*} e^{-x^5-x^4-3 x^2+e^x-16}+e^{3/x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2209
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {3 e^{3/x}}{x^2}+e^{-16+e^x-3 x^2-x^4-x^5} \left (e^x-6 x-4 x^3-5 x^4\right )\right ) \, dx\\ &=-\left (3 \int \frac {e^{3/x}}{x^2} \, dx\right )+\int e^{-16+e^x-3 x^2-x^4-x^5} \left (e^x-6 x-4 x^3-5 x^4\right ) \, dx\\ &=e^{3/x}+e^{-16+e^x-3 x^2-x^4-x^5}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.25, size = 30, normalized size = 1.03 \begin {gather*} e^{3/x}+e^{-16+e^x-3 x^2-x^4-x^5} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 27, normalized size = 0.93 \begin {gather*} e^{\left (-x^{5} - x^{4} - 3 \, x^{2} + e^{x} - 16\right )} + e^{\frac {3}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.49, size = 27, normalized size = 0.93 \begin {gather*} e^{\left (-x^{5} - x^{4} - 3 \, x^{2} + e^{x} - 16\right )} + e^{\frac {3}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 28, normalized size = 0.97
method | result | size |
risch | \({\mathrm e}^{\frac {3}{x}}+{\mathrm e}^{{\mathrm e}^{x}-x^{5}-x^{4}-3 x^{2}-16}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.77, size = 27, normalized size = 0.93 \begin {gather*} e^{\left (-x^{5} - x^{4} - 3 \, x^{2} + e^{x} - 16\right )} + e^{\frac {3}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.13, size = 31, normalized size = 1.07 \begin {gather*} {\mathrm {e}}^{3/x}+{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{-16}\,{\mathrm {e}}^{-3\,x^2}\,{\mathrm {e}}^{-x^4}\,{\mathrm {e}}^{-x^5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.43, size = 22, normalized size = 0.76 \begin {gather*} e^{\frac {3}{x}} + e^{- x^{5} - x^{4} - 3 x^{2} + e^{x} - 16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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