Optimal. Leaf size=25 \[ x-(-4+x) x+x \left (e^{2 \log ^2(x)}+\frac {x}{\log (3)}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.20, number of steps
used = 3, number of rules used = 2, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {12, 2326}
\begin {gather*} \frac {x^2}{\log (3)}-\frac {1}{4} (5-2 x)^2+x e^{2 \log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (2 x+(5-2 x) \log (3)+e^{2 \log ^2(x)} (\log (3)+4 \log (3) \log (x))\right ) \, dx}{\log (3)}\\ &=-\frac {1}{4} (5-2 x)^2+\frac {x^2}{\log (3)}+\frac {\int e^{2 \log ^2(x)} (\log (3)+4 \log (3) \log (x)) \, dx}{\log (3)}\\ &=-\frac {1}{4} (5-2 x)^2+e^{2 \log ^2(x)} x+\frac {x^2}{\log (3)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 28, normalized size = 1.12 \begin {gather*} 5 x+e^{2 \log ^2(x)} x+\frac {x^2 (1-\log (3))}{\log (3)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.52, size = 33, normalized size = 1.32
method | result | size |
norman | \(x \,{\mathrm e}^{2 \ln \left (x \right )^{2}}+5 x -\frac {\left (\ln \left (3\right )-1\right ) x^{2}}{\ln \left (3\right )}\) | \(27\) |
risch | \(-x^{2}+5 x +x \,{\mathrm e}^{2 \ln \left (x \right )^{2}}+\frac {x^{2}}{\ln \left (3\right )}\) | \(27\) |
default | \(\frac {-x^{2} \ln \left (3\right )+5 x \ln \left (3\right )+x \ln \left (3\right ) {\mathrm e}^{2 \ln \left (x \right )^{2}}+x^{2}}{\ln \left (3\right )}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 31, normalized size = 1.24 \begin {gather*} \frac {x e^{\left (2 \, \log \left (x\right )^{2}\right )} \log \left (3\right ) + x^{2} - {\left (x^{2} - 5 \, x\right )} \log \left (3\right )}{\log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 31, normalized size = 1.24 \begin {gather*} \frac {x e^{\left (2 \, \log \left (x\right )^{2}\right )} \log \left (3\right ) + x^{2} - {\left (x^{2} - 5 \, x\right )} \log \left (3\right )}{\log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 24, normalized size = 0.96 \begin {gather*} \frac {x^{2} \cdot \left (1 - \log {\left (3 \right )}\right )}{\log {\left (3 \right )}} + x e^{2 \log {\left (x \right )}^{2}} + 5 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 31, normalized size = 1.24 \begin {gather*} \frac {x e^{\left (2 \, \log \left (x\right )^{2}\right )} \log \left (3\right ) + x^{2} - {\left (x^{2} - 5 \, x\right )} \log \left (3\right )}{\log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.24, size = 26, normalized size = 1.04 \begin {gather*} 5\,x+\frac {x^2}{\ln \left (3\right )}-x^2+x\,{\mathrm {e}}^{2\,{\ln \left (x\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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