Optimal. Leaf size=18 \[ \left (9+x-e^3 x (2+x-\log (x))\right )^2 \]
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Rubi [B] time = 0.09, antiderivative size = 126, normalized size of antiderivative = 7.00, number of steps used = 10, number of rules used = 4, integrand size = 73, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.055, Rules used = {2356, 2295, 2304, 2305} \begin {gather*} e^6 x^4+4 e^6 x^3-2 e^3 x^3-2 e^6 x^3 \log (x)-\frac {1}{2} e^3 \left (2-3 e^3\right ) x^2+\frac {5 e^6 x^2}{2}-21 e^3 x^2+x^2+e^6 x^2 \log ^2(x)+e^3 \left (2-3 e^3\right ) x^2 \log (x)-e^6 x^2 \log (x)-36 e^3 x+18 x+18 e^3 x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2295
Rule 2304
Rule 2305
Rule 2356
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=18 x+x^2+e^3 \int \left (-18-42 x-6 x^2\right ) \, dx+e^6 \int \left (4 x+10 x^2+4 x^3\right ) \, dx+\left (2 e^6\right ) \int x \log ^2(x) \, dx+\int \left (e^3 (18+4 x)+e^6 \left (-6 x-6 x^2\right )\right ) \log (x) \, dx\\ &=18 x-18 e^3 x+x^2-21 e^3 x^2+2 e^6 x^2-2 e^3 x^3+\frac {10 e^6 x^3}{3}+e^6 x^4+e^6 x^2 \log ^2(x)-\left (2 e^6\right ) \int x \log (x) \, dx+\int \left (18 e^3 \log (x)-2 e^3 \left (-2+3 e^3\right ) x \log (x)-6 e^6 x^2 \log (x)\right ) \, dx\\ &=18 x-18 e^3 x+x^2-21 e^3 x^2+\frac {5 e^6 x^2}{2}-2 e^3 x^3+\frac {10 e^6 x^3}{3}+e^6 x^4-e^6 x^2 \log (x)+e^6 x^2 \log ^2(x)+\left (18 e^3\right ) \int \log (x) \, dx-\left (6 e^6\right ) \int x^2 \log (x) \, dx+\left (2 e^3 \left (2-3 e^3\right )\right ) \int x \log (x) \, dx\\ &=18 x-36 e^3 x+x^2-21 e^3 x^2+\frac {5 e^6 x^2}{2}-\frac {1}{2} e^3 \left (2-3 e^3\right ) x^2-2 e^3 x^3+4 e^6 x^3+e^6 x^4+18 e^3 x \log (x)-e^6 x^2 \log (x)+e^3 \left (2-3 e^3\right ) x^2 \log (x)-2 e^6 x^3 \log (x)+e^6 x^2 \log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.02, size = 101, normalized size = 5.61 \begin {gather*} 18 x-36 e^3 x+x^2-22 e^3 x^2+4 e^6 x^2-2 e^3 x^3+4 e^6 x^3+e^6 x^4+18 e^3 x \log (x)+2 e^3 x^2 \log (x)-4 e^6 x^2 \log (x)-2 e^6 x^3 \log (x)+e^6 x^2 \log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 2.02, size = 78, normalized size = 4.33 \begin {gather*} x^{2} e^{6} \log \relax (x)^{2} + x^{2} + {\left (x^{4} + 4 \, x^{3} + 4 \, x^{2}\right )} e^{6} - 2 \, {\left (x^{3} + 11 \, x^{2} + 18 \, x\right )} e^{3} - 2 \, {\left ({\left (x^{3} + 2 \, x^{2}\right )} e^{6} - {\left (x^{2} + 9 \, x\right )} e^{3}\right )} \log \relax (x) + 18 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.31, size = 129, normalized size = 7.17 \begin {gather*} -2 \, x^{3} e^{6} \log \relax (x) + \frac {2}{3} \, x^{3} e^{6} - 3 \, x^{2} e^{6} \log \relax (x) + 2 \, x^{2} e^{3} \log \relax (x) + \frac {3}{2} \, x^{2} e^{6} - x^{2} e^{3} + 18 \, x e^{3} \log \relax (x) + x^{2} + \frac {1}{3} \, {\left (3 \, x^{4} + 10 \, x^{3} + 6 \, x^{2}\right )} e^{6} + \frac {1}{2} \, {\left (2 \, x^{2} \log \relax (x)^{2} - 2 \, x^{2} \log \relax (x) + x^{2}\right )} e^{6} - {\left (2 \, x^{3} + 21 \, x^{2} + 18 \, x\right )} e^{3} - 18 \, x e^{3} + 18 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 91, normalized size = 5.06
method | result | size |
risch | \(x^{2} {\mathrm e}^{6} \ln \relax (x )^{2}-2 \,{\mathrm e}^{6} x^{3} \ln \relax (x )+x^{4} {\mathrm e}^{6}-4 \ln \relax (x ) {\mathrm e}^{6} x^{2}+4 x^{3} {\mathrm e}^{6}+2 \,{\mathrm e}^{3} \ln \relax (x ) x^{2}+4 x^{2} {\mathrm e}^{6}-2 x^{3} {\mathrm e}^{3}+18 x \,{\mathrm e}^{3} \ln \relax (x )-22 x^{2} {\mathrm e}^{3}-36 x \,{\mathrm e}^{3}+x^{2}+18 x\) | \(91\) |
norman | \(x^{4} {\mathrm e}^{6}+\left (4 \,{\mathrm e}^{6}-2 \,{\mathrm e}^{3}\right ) x^{3}+\left (-36 \,{\mathrm e}^{3}+18\right ) x +\left (4 \,{\mathrm e}^{6}-22 \,{\mathrm e}^{3}+1\right ) x^{2}+x^{2} {\mathrm e}^{6} \ln \relax (x )^{2}+\left (-4 \,{\mathrm e}^{6}+2 \,{\mathrm e}^{3}\right ) x^{2} \ln \relax (x )+18 x \,{\mathrm e}^{3} \ln \relax (x )-2 \,{\mathrm e}^{6} x^{3} \ln \relax (x )\) | \(96\) |
default | \(18 x -2 \,{\mathrm e}^{6} x^{3} \ln \relax (x )+\frac {2 x^{3} {\mathrm e}^{6}}{3}-4 \ln \relax (x ) {\mathrm e}^{6} x^{2}+2 x^{2} {\mathrm e}^{6}+2 \,{\mathrm e}^{3} \ln \relax (x ) x^{2}-x^{2} {\mathrm e}^{3}+18 x \,{\mathrm e}^{3} \ln \relax (x )-18 x \,{\mathrm e}^{3}+{\mathrm e}^{3} \left (-2 x^{3}-21 x^{2}-18 x \right )+{\mathrm e}^{6} \left (x^{4}+\frac {10}{3} x^{3}+2 x^{2}\right )+x^{2}+x^{2} {\mathrm e}^{6} \ln \relax (x )^{2}\) | \(124\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.36, size = 120, normalized size = 6.67 \begin {gather*} \frac {1}{2} \, {\left (2 \, \log \relax (x)^{2} - 2 \, \log \relax (x) + 1\right )} x^{2} e^{6} + \frac {2}{3} \, x^{3} e^{6} + \frac {1}{2} \, x^{2} {\left (3 \, e^{6} - 2 \, e^{3}\right )} + x^{2} + \frac {1}{3} \, {\left (3 \, x^{4} + 10 \, x^{3} + 6 \, x^{2}\right )} e^{6} - {\left (2 \, x^{3} + 21 \, x^{2} + 18 \, x\right )} e^{3} - 18 \, x e^{3} - {\left ({\left (2 \, x^{3} + 3 \, x^{2}\right )} e^{6} - 2 \, {\left (x^{2} + 9 \, x\right )} e^{3}\right )} \log \relax (x) + 18 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.70, size = 74, normalized size = 4.11 \begin {gather*} x^2\,\left ({\mathrm {e}}^6\,{\ln \relax (x)}^2+\left (2\,{\mathrm {e}}^3-4\,{\mathrm {e}}^6\right )\,\ln \relax (x)-22\,{\mathrm {e}}^3+4\,{\mathrm {e}}^6+1\right )+x^4\,{\mathrm {e}}^6+x\,\left (18\,{\mathrm {e}}^3\,\ln \relax (x)-36\,{\mathrm {e}}^3+18\right )-x^3\,\left (2\,{\mathrm {e}}^3-4\,{\mathrm {e}}^6+2\,{\mathrm {e}}^6\,\ln \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.19, size = 90, normalized size = 5.00 \begin {gather*} x^{4} e^{6} + x^{3} \left (- 2 e^{3} + 4 e^{6}\right ) + x^{2} e^{6} \log {\relax (x )}^{2} + x^{2} \left (- 22 e^{3} + 1 + 4 e^{6}\right ) + x \left (18 - 36 e^{3}\right ) + \left (- 2 x^{3} e^{6} - 4 x^{2} e^{6} + 2 x^{2} e^{3} + 18 x e^{3}\right ) \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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