Optimal. Leaf size=19 \[ -3-\frac {5}{e^2}+e^{(-1+x)^2}+2 x+\log (x) \]
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Rubi [A] time = 0.04, antiderivative size = 13, normalized size of antiderivative = 0.68, number of steps used = 6, number of rules used = 4, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.138, Rules used = {14, 2227, 2209, 43} \begin {gather*} 2 x+e^{(x-1)^2}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 43
Rule 2209
Rule 2227
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (2 e^{1-2 x+x^2} (-1+x)+\frac {1+2 x}{x}\right ) \, dx\\ &=2 \int e^{1-2 x+x^2} (-1+x) \, dx+\int \frac {1+2 x}{x} \, dx\\ &=2 \int e^{(-1+x)^2} (-1+x) \, dx+\int \left (2+\frac {1}{x}\right ) \, dx\\ &=e^{(-1+x)^2}+2 x+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 13, normalized size = 0.68 \begin {gather*} e^{(-1+x)^2}+2 x+\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 15, normalized size = 0.79 \begin {gather*} 2 \, x + e^{\left (x^{2} - 2 \, x + 1\right )} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 15, normalized size = 0.79 \begin {gather*} 2 \, x + e^{\left (x^{2} - 2 \, x + 1\right )} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 13, normalized size = 0.68
method | result | size |
risch | \(2 x +\ln \relax (x )+{\mathrm e}^{\left (x -1\right )^{2}}\) | \(13\) |
default | \(2 x +\ln \relax (x )+{\mathrm e}^{x^{2}-2 x +1}\) | \(16\) |
norman | \(2 x +\ln \relax (x )+{\mathrm e}^{x^{2}-2 x +1}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.40, size = 51, normalized size = 2.68 \begin {gather*} \frac {\sqrt {\pi } {\left (x - 1\right )} {\left (\operatorname {erf}\left (\sqrt {-{\left (x - 1\right )}^{2}}\right ) - 1\right )}}{\sqrt {-{\left (x - 1\right )}^{2}}} + i \, \sqrt {\pi } \operatorname {erf}\left (i \, x - i\right ) + 2 \, x + e^{\left ({\left (x - 1\right )}^{2}\right )} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 17, normalized size = 0.89 \begin {gather*} 2\,x+\ln \relax (x)+{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{x^2}\,\mathrm {e} \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 = 0.79 \begin {gather*} 2 x + e^{x^{2} - 2 x + 1} + \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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