Optimal. Leaf size=27 \[ \frac {4}{5} \left (5+e^{\frac {\left (x-x^2\right )^2}{x^2}}\right )-x^2 \]
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Rubi [A] time = 0.02, antiderivative size = 17, normalized size of antiderivative = 0.63, number of steps used = 4, number of rules used = 3, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 2227, 2209} \begin {gather*} \frac {4}{5} e^{(x-1)^2}-x^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2209
Rule 2227
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (-10 x+e^{1-2 x+x^2} (-8+8 x)\right ) \, dx\\ &=-x^2+\frac {1}{5} \int e^{1-2 x+x^2} (-8+8 x) \, dx\\ &=-x^2+\frac {1}{5} \int e^{(-1+x)^2} (-8+8 x) \, dx\\ &=\frac {4}{5} e^{(-1+x)^2}-x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 0.63 \begin {gather*} \frac {4}{5} e^{(-1+x)^2}-x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.89, size = 17, normalized size = 0.63 \begin {gather*} -x^{2} + \frac {4}{5} \, e^{\left (x^{2} - 2 \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 17, normalized size = 0.63 \begin {gather*} -x^{2} + \frac {4}{5} \, e^{\left (x^{2} - 2 \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 15, normalized size = 0.56
method | result | size |
risch | \(-x^{2}+\frac {4 \,{\mathrm e}^{\left (x -1\right )^{2}}}{5}\) | \(15\) |
default | \(-x^{2}+\frac {4 \,{\mathrm e}^{x^{2}-2 x +1}}{5}\) | \(18\) |
norman | \(-x^{2}+\frac {4 \,{\mathrm e}^{x^{2}-2 x +1}}{5}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 17, normalized size = 0.63 \begin {gather*} -x^{2} + \frac {4}{5} \, e^{\left (x^{2} - 2 \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 18, normalized size = 0.67 \begin {gather*} \frac {4\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{x^2}\,\mathrm {e}}{5}-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 15, normalized size = 0.56 \begin {gather*} - x^{2} + \frac {4 e^{x^{2} - 2 x + 1}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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