Optimal. Leaf size=22 \[ 1+\left (1+e^{4 x \left (x+\frac {4 x^4}{9}\right )}\right ) x \log (x) \]
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Rubi [B] time = 0.11, antiderivative size = 47, normalized size of antiderivative = 2.14, number of steps used = 5, number of rules used = 4, integrand size = 60, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12, 6741, 2288, 2554} \begin {gather*} \frac {e^{\frac {4}{9} \left (4 x^5+9 x^2\right )} \left (10 x^5+9 x^2\right ) \log (x)}{10 x^4+9 x}+x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rule 2554
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{9} \int \left (9+9 e^{\frac {1}{9} \left (36 x^2+16 x^5\right )}+\left (9+e^{\frac {1}{9} \left (36 x^2+16 x^5\right )} \left (9+72 x^2+80 x^5\right )\right ) \log (x)\right ) \, dx\\ &=x+\frac {1}{9} \int \left (9+e^{\frac {1}{9} \left (36 x^2+16 x^5\right )} \left (9+72 x^2+80 x^5\right )\right ) \log (x) \, dx+\int e^{\frac {1}{9} \left (36 x^2+16 x^5\right )} \, dx\\ &=x+x \log (x)+\frac {e^{\frac {4}{9} \left (9 x^2+4 x^5\right )} \left (9 x^2+10 x^5\right ) \log (x)}{9 x+10 x^4}-\frac {1}{9} \int 9 \left (1+e^{4 x^2+\frac {16 x^5}{9}}\right ) \, dx+\int e^{\frac {4}{9} x^2 \left (9+4 x^3\right )} \, dx\\ &=x+x \log (x)+\frac {e^{\frac {4}{9} \left (9 x^2+4 x^5\right )} \left (9 x^2+10 x^5\right ) \log (x)}{9 x+10 x^4}+\int e^{\frac {4}{9} x^2 \left (9+4 x^3\right )} \, dx-\int \left (1+e^{4 x^2+\frac {16 x^5}{9}}\right ) \, dx\\ &=x \log (x)+\frac {e^{\frac {4}{9} \left (9 x^2+4 x^5\right )} \left (9 x^2+10 x^5\right ) \log (x)}{9 x+10 x^4}+\int e^{\frac {4}{9} x^2 \left (9+4 x^3\right )} \, dx-\int e^{4 x^2+\frac {16 x^5}{9}} \, dx\\ &=x \log (x)+\frac {e^{\frac {4}{9} \left (9 x^2+4 x^5\right )} \left (9 x^2+10 x^5\right ) \log (x)}{9 x+10 x^4}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 21, normalized size = 0.95 \begin {gather*} \left (1+e^{4 x^2+\frac {16 x^5}{9}}\right ) x \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 19, normalized size = 0.86 \begin {gather*} {\left (x e^{\left (\frac {16}{9} \, x^{5} + 4 \, x^{2}\right )} + x\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 19, normalized size = 0.86 \begin {gather*} {\left (x e^{\left (\frac {16}{9} \, x^{5} + 4 \, x^{2}\right )} + x\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 20, normalized size = 0.91
method | result | size |
risch | \(x \left ({\mathrm e}^{\frac {4 x^{2} \left (4 x^{3}+9\right )}{9}}+1\right ) \ln \relax (x )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 21, normalized size = 0.95 \begin {gather*} x e^{\left (\frac {16}{9} \, x^{5} + 4 \, x^{2}\right )} \log \relax (x) + x \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int {\mathrm {e}}^{\frac {16\,x^5}{9}+4\,x^2}+\frac {\ln \relax (x)\,\left ({\mathrm {e}}^{\frac {16\,x^5}{9}+4\,x^2}\,\left (80\,x^5+72\,x^2+9\right )+9\right )}{9}+1 \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.33, size = 22, normalized size = 1.00 \begin {gather*} x e^{\frac {16 x^{5}}{9} + 4 x^{2}} \log {\relax (x )} + x \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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