Optimal. Leaf size=22 \[ e^5 \left (-x-x \left (e^{-5+e}+x\right )+16 \log (4)\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 21, normalized size of antiderivative = 0.95, number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -\frac {1}{4} e^5 (2 x+1)^2-e^e x \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-e^e x-\frac {1}{4} e^5 (1+2 x)^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 0.95 \begin {gather*} -e^5 x-e^e x-e^5 x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 16, normalized size = 0.73 \begin {gather*} -{\left (x^{2} + x\right )} e^{5} - x e^{e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.34, size = 16, normalized size = 0.73 \begin {gather*} -{\left (x^{2} + x\right )} e^{5} - x e^{e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 14, normalized size = 0.64
method | result | size |
gosper | \(-{\mathrm e}^{5} x \left (x +{\mathrm e}^{{\mathrm e}-5}+1\right )\) | \(14\) |
risch | \(-x \,{\mathrm e}^{{\mathrm e}}-x^{2} {\mathrm e}^{5}-x \,{\mathrm e}^{5}\) | \(20\) |
default | \(-{\mathrm e}^{5} {\mathrm e}^{{\mathrm e}-5} x +\left (-x^{2}-x \right ) {\mathrm e}^{5}\) | \(24\) |
norman | \(\left (-{\mathrm e}^{5} {\mathrm e}^{{\mathrm e}} {\mathrm e}^{-5}-{\mathrm e}^{5}\right ) x -x^{2} {\mathrm e}^{5}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 16, normalized size = 0.73 \begin {gather*} -{\left (x^{2} + x\right )} e^{5} - x e^{e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 18, normalized size = 0.82 \begin {gather*} -\frac {{\mathrm {e}}^5\,{\left (2\,x+1\right )}^2}{4}-x\,{\mathrm {e}}^{\mathrm {e}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 17, normalized size = 0.77 \begin {gather*} - x^{2} e^{5} + x \left (- e^{5} - e^{e}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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