Optimal. Leaf size=15 \[ 25-e^{5-e} x+x^2 \]
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Rubi [A] time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.53, number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {9} \begin {gather*} \frac {1}{4} e^{10-2 e} \left (1-2 e^{e-5} x\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 9
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} e^{10-2 e} \left (1-2 e^{-5+e} x\right )^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 0.93 \begin {gather*} -e^{5-e} x+x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 21, normalized size = 1.40 \begin {gather*} {\left (x^{2} e^{\left (e - 5\right )} - x\right )} e^{\left (-e + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 21, normalized size = 1.40 \begin {gather*} {\left (x^{2} e^{\left (e - 5\right )} - x\right )} e^{\left (-e + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 15, normalized size = 1.00
method | result | size |
risch | \(x^{2}-x \,{\mathrm e}^{5-{\mathrm e}}\) | \(15\) |
norman | \(x^{2}-{\mathrm e}^{-{\mathrm e}} {\mathrm e}^{5} x\) | \(17\) |
gosper | \(x \left (x \,{\mathrm e}^{{\mathrm e}-5}-1\right ) {\mathrm e}^{5-{\mathrm e}}\) | \(19\) |
default | \(\left ({\mathrm e}^{{\mathrm e}-5} x^{2}-x \right ) {\mathrm e}^{5-{\mathrm e}}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 21, normalized size = 1.40 \begin {gather*} {\left (x^{2} e^{\left (e - 5\right )} - x\right )} e^{\left (-e + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.24, size = 17, normalized size = 1.13 \begin {gather*} \frac {{\left (2\,x-{\mathrm {e}}^{5-\mathrm {e}}\right )}^2}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 12, normalized size = 0.80 \begin {gather*} x^{2} - \frac {x e^{5}}{e^{e}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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