Optimal. Leaf size=23 \[ \frac {1}{2} \left (e^{5 e^e \left (1+\frac {x}{2}\right ) x}-x\right ) \]
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Rubi [A] time = 0.09, antiderivative size = 29, normalized size of antiderivative = 1.26, number of steps used = 4, number of rules used = 3, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.094, Rules used = {12, 2244, 2236} \begin {gather*} \frac {1}{2} e^{\frac {5 e^e x^2}{2}+5 e^e x}-\frac {x}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2236
Rule 2244
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (-1+e^{e+\frac {1}{2} e^e \left (10 x+5 x^2\right )} (5+5 x)\right ) \, dx\\ &=-\frac {x}{2}+\frac {1}{2} \int e^{e+\frac {1}{2} e^e \left (10 x+5 x^2\right )} (5+5 x) \, dx\\ &=-\frac {x}{2}+\frac {1}{2} \int e^{e+5 e^e x+\frac {5 e^e x^2}{2}} (5+5 x) \, dx\\ &=\frac {1}{2} e^{5 e^e x+\frac {5 e^e x^2}{2}}-\frac {x}{2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 27, normalized size = 1.17 \begin {gather*} \frac {1}{2} \left (e^{5 e^e x+\frac {5 e^e x^2}{2}}-x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.00, size = 31, normalized size = 1.35 \begin {gather*} -\frac {1}{2} \, {\left (x e^{e} - e^{\left (\frac {5}{2} \, {\left (x^{2} + 2 \, x\right )} e^{e} + e\right )}\right )} e^{\left (-e\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.47, size = 22, normalized size = 0.96 \begin {gather*} -\frac {1}{2} \, x + \frac {1}{2} \, e^{\left (\frac {5}{2} \, x^{2} e^{e} + 5 \, x e^{e}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 17, normalized size = 0.74
method | result | size |
risch | \(-\frac {x}{2}+\frac {{\mathrm e}^{\frac {5 x \left (2+x \right ) {\mathrm e}^{{\mathrm e}}}{2}}}{2}\) | \(17\) |
norman | \(-\frac {x}{2}+\frac {{\mathrm e}^{\frac {\left (5 x^{2}+10 x \right ) {\mathrm e}^{{\mathrm e}}}{2}}}{2}\) | \(22\) |
default | \(-\frac {x}{2}+\frac {{\mathrm e}^{\frac {5 x^{2} {\mathrm e}^{{\mathrm e}}}{2}+5 x \,{\mathrm e}^{{\mathrm e}}}}{2}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.83, size = 174, normalized size = 7.57 \begin {gather*} \frac {\sqrt {\frac {5}{2}} \sqrt {\pi } \operatorname {erf}\left (\sqrt {\frac {5}{2}} x \sqrt {-e^{e}} - \frac {\sqrt {\frac {5}{2}} e^{e}}{\sqrt {-e^{e}}}\right ) e^{\left (e - \frac {5}{2} \, e^{e}\right )}}{2 \, \sqrt {-e^{e}}} - \frac {1}{10} \, \sqrt {\frac {5}{2}} {\left (\frac {\sqrt {10} \sqrt {\frac {5}{2}} \sqrt {\pi } {\left (x e^{e} + e^{e}\right )} {\left (\operatorname {erf}\left (\sqrt {\frac {5}{2}} \sqrt {-{\left (x e^{e} + e^{e}\right )}^{2} e^{\left (-e\right )}}\right ) - 1\right )} e^{\left (-\frac {1}{2} \, e\right )}}{\sqrt {-{\left (x e^{e} + e^{e}\right )}^{2} e^{\left (-e\right )}}} - 2 \, \sqrt {\frac {5}{2}} e^{\left (\frac {5}{2} \, {\left (x e^{e} + e^{e}\right )}^{2} e^{\left (-e\right )} - \frac {1}{2} \, e\right )}\right )} e^{\left (\frac {1}{2} \, e - \frac {5}{2} \, e^{e}\right )} - \frac {1}{2} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.39, size = 22, normalized size = 0.96 \begin {gather*} \frac {{\mathrm {e}}^{\frac {5\,{\mathrm {e}}^{\mathrm {e}}\,x^2}{2}+5\,{\mathrm {e}}^{\mathrm {e}}\,x}}{2}-\frac {x}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 20, normalized size = 0.87 \begin {gather*} - \frac {x}{2} + \frac {e^{\left (\frac {5 x^{2}}{2} + 5 x\right ) e^{e}}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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