Optimal. Leaf size=24 \[ -\frac {7}{3}+e^{e^{2 e^{5-x}}+x}+x (5+x) \]
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Rubi [A]
time = 0.12, antiderivative size = 22, normalized size of antiderivative = 0.92, number of steps
used = 3, number of rules used = 2, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {2320, 2326}
\begin {gather*} x^2+5 x+e^{x+e^{2 e^{5-x}}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2320
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=5 x+x^2+\int e^{e^{2 e^{5-x}}+x} \left (1-2 e^{5+2 e^{5-x}-x}\right ) \, dx\\ &=5 x+x^2+\text {Subst}\left (\int \frac {e^{e^{\frac {2 e^5}{x}}} \left (-2 e^{5+\frac {2 e^5}{x}}+x\right )}{x} \, dx,x,e^x\right )\\ &=e^{e^{2 e^{5-x}}+x}+5 x+x^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 22, normalized size = 0.92 \begin {gather*} e^{e^{2 e^{5-x}}+x}+5 x+x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.17, size = 20, normalized size = 0.83
method | result | size |
default | \(5 x +{\mathrm e}^{{\mathrm e}^{2 \,{\mathrm e}^{5-x}}+x}+x^{2}\) | \(20\) |
norman | \(5 x +{\mathrm e}^{{\mathrm e}^{2 \,{\mathrm e}^{5-x}}+x}+x^{2}\) | \(20\) |
risch | \(5 x +{\mathrm e}^{{\mathrm e}^{2 \,{\mathrm e}^{5-x}}+x}+x^{2}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 19, normalized size = 0.79 \begin {gather*} x^{2} + 5 \, x + e^{\left (x + e^{\left (2 \, e^{\left (-x + 5\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 19, normalized size = 0.79 \begin {gather*} x^{2} + 5 \, x + e^{\left (x + e^{\left (2 \, e^{\left (-x + 5\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 17, normalized size = 0.71 \begin {gather*} x^{2} + 5 x + e^{x + e^{2 e^{5 - x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 44 vs.
\(2 (19) = 38\).
time = 0.41, size = 44, normalized size = 1.83 \begin {gather*} x^{2} + 5 \, x + e^{\left ({\left (2 \, e^{5} + e^{\left (x + 2 \, e^{\left (-x + 5\right )}\right )} + 5 \, e^{x}\right )} e^{\left (-x\right )} + x - 2 \, e^{\left (-x + 5\right )} - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.16, size = 20, normalized size = 0.83 \begin {gather*} 5\,x+{\mathrm {e}}^{{\mathrm {e}}^{2\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^5}}\,{\mathrm {e}}^x+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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