Optimal. Leaf size=16 \[ e^{x^2}-\frac {(-2+x) x}{\log (4)} \]
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Rubi [A]
time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.38, number of steps
used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 2240}
\begin {gather*} e^{x^2}-\frac {x^2}{\log (4)}+\frac {2 x}{\log (4)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2240
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (2-2 x+2 e^{x^2} x \log (4)\right ) \, dx}{\log (4)}\\ &=\frac {2 x}{\log (4)}-\frac {x^2}{\log (4)}+2 \int e^{x^2} x \, dx\\ &=e^{x^2}+\frac {2 x}{\log (4)}-\frac {x^2}{\log (4)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 25, normalized size = 1.56 \begin {gather*} \frac {2 x-x^2+\frac {1}{2} e^{x^2} \log (16)}{\log (4)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.44, size = 20, normalized size = 1.25
method | result | size |
default | \(\frac {x -\frac {x^{2}}{2}+\ln \left (2\right ) {\mathrm e}^{x^{2}}}{\ln \left (2\right )}\) | \(20\) |
norman | \(\frac {x}{\ln \left (2\right )}-\frac {x^{2}}{2 \ln \left (2\right )}+{\mathrm e}^{x^{2}}\) | \(21\) |
risch | \(\frac {x}{\ln \left (2\right )}-\frac {x^{2}}{2 \ln \left (2\right )}+{\mathrm e}^{x^{2}}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 21, normalized size = 1.31 \begin {gather*} -\frac {x^{2} - 2 \, e^{\left (x^{2}\right )} \log \left (2\right ) - 2 \, x}{2 \, \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.49, size = 21, normalized size = 1.31 \begin {gather*} -\frac {x^{2} - 2 \, e^{\left (x^{2}\right )} \log \left (2\right ) - 2 \, x}{2 \, \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 17, normalized size = 1.06 \begin {gather*} - \frac {x^{2}}{2 \log {\left (2 \right )}} + \frac {x}{\log {\left (2 \right )}} + e^{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 21, normalized size = 1.31 \begin {gather*} -\frac {x^{2} - 2 \, e^{\left (x^{2}\right )} \log \left (2\right ) - 2 \, x}{2 \, \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 23, normalized size = 1.44 \begin {gather*} \frac {2\,x+2\,{\mathrm {e}}^{x^2}\,\ln \left (2\right )-x^2}{2\,\ln \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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