Optimal. Leaf size=19 \[ 2 x^{(4+x) \left (e^2+(3+25 x)^2\right )} \]
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Rubi [F] time = 1.23, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int x^{35+609 x+2650 x^2+625 x^3+e^2 (4+x)} \left (72+1218 x+5300 x^2+1250 x^3+e^2 (8+2 x)+\left (1218 x+2 e^2 x+10600 x^2+3750 x^3\right ) \log (x)\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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\begin {gather*} \begin {aligned} \text {integral} &=\int x^{35+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \left (72+1218 x+5300 x^2+1250 x^3+e^2 (8+2 x)+\left (1218 x+2 e^2 x+10600 x^2+3750 x^3\right ) \log (x)\right ) \, dx\\ &=\int 2 x^{35+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \left ((4+x) \left (e^2+(3+25 x)^2\right )+x \left (609+e^2+5300 x+1875 x^2\right ) \log (x)\right ) \, dx\\ &=2 \int x^{35+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \left ((4+x) \left (e^2+(3+25 x)^2\right )+x \left (609+e^2+5300 x+1875 x^2\right ) \log (x)\right ) \, dx\\ &=2 \int \left (x^{35+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} (4+x) \left (9+e^2+150 x+625 x^2\right )+x^{36+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \left (609+e^2+5300 x+1875 x^2\right ) \log (x)\right ) \, dx\\ &=2 \int x^{35+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} (4+x) \left (9+e^2+150 x+625 x^2\right ) \, dx+2 \int x^{36+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \left (609+e^2+5300 x+1875 x^2\right ) \log (x) \, dx\\ &=2 \int \left (4 \left (9+e^2\right ) x^{35+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3}+\left (609+e^2\right ) x^{36+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3}+2650 x^{37+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3}+625 x^{38+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3}\right ) \, dx-2 \int \frac {5300 \int x^{37+609 x+2650 x^2+625 x^3+e^2 (4+x)} \, dx+1875 \int x^{38+609 x+2650 x^2+625 x^3+e^2 (4+x)} \, dx+\left (609+e^2\right ) \int x^{(4+x) \left (e^2+(3+25 x)^2\right )} \, dx}{x} \, dx+(3750 \log (x)) \int x^{2 \left (19+2 e^2\right )+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+(10600 \log (x)) \int x^{37+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+\left (2 \left (609+e^2\right ) \log (x)\right ) \int x^{(4+x) \left (9+e^2+150 x+625 x^2\right )} \, dx\\ &=-\left (2 \int \left (\frac {1875 \int x^{2 \left (19+2 e^2\right )+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx}{x}+\frac {5300 \int x^{37+609 x+2650 x^2+625 x^3+e^2 (4+x)} \, dx+609 \left (1+\frac {e^2}{609}\right ) \int x^{(4+x) \left (e^2+(3+25 x)^2\right )} \, dx}{x}\right ) \, dx\right )+1250 \int x^{38+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+5300 \int x^{37+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+\left (8 \left (9+e^2\right )\right ) \int x^{35+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+\left (2 \left (609+e^2\right )\right ) \int x^{36+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+(3750 \log (x)) \int x^{2 \left (19+2 e^2\right )+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+(10600 \log (x)) \int x^{37+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+\left (2 \left (609+e^2\right ) \log (x)\right ) \int x^{(4+x) \left (9+e^2+150 x+625 x^2\right )} \, dx\\ &=-\left (2 \int \frac {609 \left (1+\frac {e^2}{609}\right ) \int x^{(4+x) \left (9+e^2+150 x+625 x^2\right )} \, dx+5300 \int x^{37+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx}{x} \, dx\right )+1250 \int x^{2 \left (19+2 e^2\right )+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx-3750 \int \frac {\int x^{2 \left (19+2 e^2\right )+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx}{x} \, dx+5300 \int x^{37+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+\left (8 \left (9+e^2\right )\right ) \int x^{35+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+\left (2 \left (609+e^2\right )\right ) \int x^{(4+x) \left (9+e^2+150 x+625 x^2\right )} \, dx+(3750 \log (x)) \int x^{2 \left (19+2 e^2\right )+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+(10600 \log (x)) \int x^{37+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+\left (2 \left (609+e^2\right ) \log (x)\right ) \int x^{(4+x) \left (9+e^2+150 x+625 x^2\right )} \, dx\\ &=-\left (2 \int \left (\frac {\left (609+e^2\right ) \int x^{(4+x) \left (9+e^2+150 x+625 x^2\right )} \, dx}{x}+\frac {5300 \int x^{37+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx}{x}\right ) \, dx\right )+1250 \int x^{2 \left (19+2 e^2\right )+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx-3750 \int \frac {\int x^{2 \left (19+2 e^2\right )+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx}{x} \, dx+5300 \int x^{37+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+\left (8 \left (9+e^2\right )\right ) \int x^{35+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+\left (2 \left (609+e^2\right )\right ) \int x^{(4+x) \left (9+e^2+150 x+625 x^2\right )} \, dx+(3750 \log (x)) \int x^{2 \left (19+2 e^2\right )+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+(10600 \log (x)) \int x^{37+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+\left (2 \left (609+e^2\right ) \log (x)\right ) \int x^{(4+x) \left (9+e^2+150 x+625 x^2\right )} \, dx\\ &=1250 \int x^{2 \left (19+2 e^2\right )+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx-3750 \int \frac {\int x^{2 \left (19+2 e^2\right )+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx}{x} \, dx+5300 \int x^{37+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx-10600 \int \frac {\int x^{37+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx}{x} \, dx+\left (8 \left (9+e^2\right )\right ) \int x^{35+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+\left (2 \left (609+e^2\right )\right ) \int x^{(4+x) \left (9+e^2+150 x+625 x^2\right )} \, dx-\left (2 \left (609+e^2\right )\right ) \int \frac {\int x^{(4+x) \left (9+e^2+150 x+625 x^2\right )} \, dx}{x} \, dx+(3750 \log (x)) \int x^{2 \left (19+2 e^2\right )+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+(10600 \log (x)) \int x^{37+4 e^2+\left (609+e^2\right ) x+2650 x^2+625 x^3} \, dx+\left (2 \left (609+e^2\right ) \log (x)\right ) \int x^{(4+x) \left (9+e^2+150 x+625 x^2\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.30, size = 19, normalized size = 1.00 \begin {gather*} 2 x^{(4+x) \left (e^2+(3+25 x)^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 25, normalized size = 1.32 \begin {gather*} 2 \, x^{625 \, x^{3} + 2650 \, x^{2} + {\left (x + 4\right )} e^{2} + 609 \, x + 36} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.06, size = 39, normalized size = 2.05 \begin {gather*} 2 \, e^{\left (625 \, x^{3} \log \relax (x) + 2650 \, x^{2} \log \relax (x) + x e^{2} \log \relax (x) + 609 \, x \log \relax (x) + 4 \, e^{2} \log \relax (x) + 36 \, \log \relax (x)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 21, normalized size = 1.11
method | result | size |
risch | \(2 x^{\left (625 x^{2}+{\mathrm e}^{2}+150 x +9\right ) \left (4+x \right )}\) | \(21\) |
norman | \(2 \,{\mathrm e}^{\left (\left (4+x \right ) {\mathrm e}^{2}+625 x^{3}+2650 x^{2}+609 x +36\right ) \ln \relax (x )}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.53, size = 38, normalized size = 2.00 \begin {gather*} 2 \, x^{36} e^{\left (625 \, x^{3} \log \relax (x) + 2650 \, x^{2} \log \relax (x) + x e^{2} \log \relax (x) + 609 \, x \log \relax (x) + 4 \, e^{2} \log \relax (x)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.09, size = 36, normalized size = 1.89 \begin {gather*} 2\,x^{625\,x^3}\,x^{2650\,x^2}\,x^{x\,{\mathrm {e}}^2}\,x^{4\,{\mathrm {e}}^2}\,x^{609\,x}\,x^{36} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.43, size = 27, normalized size = 1.42 \begin {gather*} 2 e^{\left (625 x^{3} + 2650 x^{2} + 609 x + \left (x + 4\right ) e^{2} + 36\right ) \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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