Optimal. Leaf size=19 \[ 2+x+\left (-2+e^{e^{e^{3+x}}}+x\right )^2+\log (5) \]
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Rubi [A]
time = 0.08, antiderivative size = 34, normalized size of antiderivative = 1.79, number of steps
used = 5, number of rules used = 3, integrand size = 54, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {2320, 2225,
2326} \begin {gather*} x^2-3 x+e^{2 e^{e^{x+3}}}-2 e^{e^{e^{x+3}}} (2-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rule 2320
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-3 x+x^2+2 \int e^{3+2 e^{e^{3+x}}+e^{3+x}+x} \, dx+\int e^{e^{e^{3+x}}} \left (2+e^{3+e^{3+x}+x} (-4+2 x)\right ) \, dx\\ &=-2 e^{e^{e^{3+x}}} (2-x)-3 x+x^2+2 \text {Subst}\left (\int e^{3+2 e^{e^3 x}+e^3 x} \, dx,x,e^x\right )\\ &=-2 e^{e^{e^{3+x}}} (2-x)-3 x+x^2+\frac {2 \text {Subst}\left (\int e^{3+2 x} \, dx,x,e^{e^{3+x}}\right )}{e^3}\\ &=e^{2 e^{e^{3+x}}}-2 e^{e^{e^{3+x}}} (2-x)-3 x+x^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 32, normalized size = 1.68 \begin {gather*} e^{2 e^{e^{3+x}}}+2 e^{e^{e^{3+x}}} (-2+x)-3 x+x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.17, size = 33, normalized size = 1.74
method | result | size |
risch | \({\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{3+x}}}+\left (2 x -4\right ) {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{3+x}}}+x^{2}-3 x\) | \(28\) |
default | \(-3 x +2 x \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{3+x}}}-4 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{3+x}}}+x^{2}+{\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{3+x}}}\) | \(33\) |
norman | \(-3 x +2 x \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{3+x}}}-4 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{3+x}}}+x^{2}+{\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{3+x}}}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 26, normalized size = 1.37 \begin {gather*} x^{2} + 2 \, {\left (x - 2\right )} e^{\left (e^{\left (e^{\left (x + 3\right )}\right )}\right )} - 3 \, x + e^{\left (2 \, e^{\left (e^{\left (x + 3\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 26, normalized size = 1.37 \begin {gather*} x^{2} + 2 \, {\left (x - 2\right )} e^{\left (e^{\left (e^{\left (x + 3\right )}\right )}\right )} - 3 \, x + e^{\left (2 \, e^{\left (e^{\left (x + 3\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.88, size = 29, normalized size = 1.53 \begin {gather*} x^{2} - 3 x + \left (2 x - 4\right ) e^{e^{e^{x + 3}}} + e^{2 e^{e^{x + 3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.10, size = 35, normalized size = 1.84 \begin {gather*} {\mathrm {e}}^{2\,{\mathrm {e}}^{{\mathrm {e}}^3\,{\mathrm {e}}^x}}-4\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^3\,{\mathrm {e}}^x}}-3\,x+2\,x\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^3\,{\mathrm {e}}^x}}+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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