Optimal. Leaf size=23 \[ e^{2 x}-e^{x^2}+x \left (11+\frac {\log (5)}{2}\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 22, normalized size of antiderivative = 0.96, number of steps used = 4, number of rules used = 3, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.130, Rules used = {12, 2194, 2209} \begin {gather*} -e^{x^2}+e^{2 x}+\frac {1}{2} x (22+\log (5)) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (22+4 e^{2 x}-4 e^{x^2} x+\log (5)\right ) \, dx\\ &=\frac {1}{2} x (22+\log (5))+2 \int e^{2 x} \, dx-2 \int e^{x^2} x \, dx\\ &=e^{2 x}-e^{x^2}+\frac {1}{2} x (22+\log (5))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 26, normalized size = 1.13 \begin {gather*} \frac {1}{2} \left (2 e^{2 x}-2 e^{x^2}+22 x+x \log (5)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 19, normalized size = 0.83 \begin {gather*} \frac {1}{2} \, x \log \relax (5) + 11 \, x - e^{\left (x^{2}\right )} + e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.27, size = 19, normalized size = 0.83 \begin {gather*} \frac {1}{2} \, x \log \relax (5) + 11 \, x - e^{\left (x^{2}\right )} + e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 20, normalized size = 0.87
method | result | size |
default | \(11 x -{\mathrm e}^{x^{2}}+{\mathrm e}^{2 x}+\frac {x \ln \relax (5)}{2}\) | \(20\) |
norman | \({\mathrm e}^{2 x}-{\mathrm e}^{x^{2}}+x \left (11+\frac {\ln \relax (5)}{2}\right )\) | \(20\) |
risch | \(11 x -{\mathrm e}^{x^{2}}+{\mathrm e}^{2 x}+\frac {x \ln \relax (5)}{2}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 19, normalized size = 0.83 \begin {gather*} \frac {1}{2} \, x \log \relax (5) + 11 \, x - e^{\left (x^{2}\right )} + e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.64, size = 19, normalized size = 0.83 \begin {gather*} {\mathrm {e}}^{2\,x}-{\mathrm {e}}^{x^2}+x\,\left (\frac {\ln \relax (5)}{2}+11\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 17, normalized size = 0.74 \begin {gather*} x \left (\frac {\log {\relax (5 )}}{2} + 11\right ) + e^{2 x} - e^{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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