Optimal. Leaf size=22 \[ \frac {1}{3} e^{81 \left (e^2+x\right )}+e^{(1+\log (x))^2} \]
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Rubi [A] time = 0.04, antiderivative size = 28, normalized size of antiderivative = 1.27, number of steps used = 4, number of rules used = 3, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.081, Rules used = {14, 2194, 2288} \begin {gather*} x^2 e^{\log ^2(x)+1}+\frac {1}{3} e^{81 x+81 e^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2194
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (27 e^{81 e^2+81 x}+2 e^{1+\log ^2(x)} x (1+\log (x))\right ) \, dx\\ &=2 \int e^{1+\log ^2(x)} x (1+\log (x)) \, dx+27 \int e^{81 e^2+81 x} \, dx\\ &=\frac {1}{3} e^{81 e^2+81 x}+e^{1+\log ^2(x)} x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 28, normalized size = 1.27 \begin {gather*} \frac {1}{3} e^{81 e^2+81 x}+e^{1+\log ^2(x)} x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 23, normalized size = 1.05 \begin {gather*} e^{\left (\log \relax (x)^{2} + 2 \, \log \relax (x) + 1\right )} + \frac {1}{3} \, e^{\left (81 \, x + 81 \, e^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 23, normalized size = 1.05 \begin {gather*} x^{2} e^{\left (\log \relax (x)^{2} + 1\right )} + \frac {1}{3} \, e^{\left (81 \, x + 81 \, e^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 24, normalized size = 1.09
method | result | size |
default | \({\mathrm e}^{\ln \relax (x )^{2}+2 \ln \relax (x )+1}+\frac {{\mathrm e}^{81 \,{\mathrm e}^{2}+81 x}}{3}\) | \(24\) |
norman | \({\mathrm e}^{\ln \relax (x )^{2}+2 \ln \relax (x )+1}+\frac {{\mathrm e}^{81 \,{\mathrm e}^{2}+81 x}}{3}\) | \(24\) |
risch | \(x^{2} {\mathrm e}^{\ln \relax (x )^{2}+1}+\frac {{\mathrm e}^{81 \,{\mathrm e}^{2}+81 x}}{3}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.40, size = 63, normalized size = 2.86 \begin {gather*} -\frac {\sqrt {\pi } {\left (\operatorname {erf}\left (\sqrt {-{\left (\log \relax (x) + 1\right )}^{2}}\right ) - 1\right )} {\left (\log \relax (x) + 1\right )}}{\sqrt {-{\left (\log \relax (x) + 1\right )}^{2}}} - i \, \sqrt {\pi } \operatorname {erf}\left (i \, \log \relax (x) + i\right ) + e^{\left ({\left (\log \relax (x) + 1\right )}^{2}\right )} + \frac {1}{3} \, e^{\left (81 \, x + 81 \, e^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.31, size = 23, normalized size = 1.05 \begin {gather*} \frac {{\mathrm {e}}^{81\,{\mathrm {e}}^2}\,{\mathrm {e}}^{81\,x}}{3}+x^2\,\mathrm {e}\,{\mathrm {e}}^{{\ln \relax (x)}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.37, size = 22, normalized size = 1.00 \begin {gather*} x^{2} e^{\log {\relax (x )}^{2} + 1} + \frac {e^{81 x + 81 e^{2}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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