Optimal. Leaf size=22 \[ e^{25/4}+\left (3+e^x+x\right ) (4-5 x-\log (x)) \]
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Rubi [A] time = 0.20, antiderivative size = 36, normalized size of antiderivative = 1.64, number of steps used = 17, number of rules used = 8, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.195, Rules used = {14, 2295, 6742, 2199, 2194, 2178, 2176, 2554} \begin {gather*} -5 x^2-5 e^x x-11 x+4 e^x-x \log (x)-e^x \log (x)-3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2176
Rule 2178
Rule 2194
Rule 2199
Rule 2295
Rule 2554
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-3-12 x-10 x^2-x \log (x)}{x}-\frac {e^x \left (1+x+5 x^2+x \log (x)\right )}{x}\right ) \, dx\\ &=\int \frac {-3-12 x-10 x^2-x \log (x)}{x} \, dx-\int \frac {e^x \left (1+x+5 x^2+x \log (x)\right )}{x} \, dx\\ &=\int \left (\frac {-3-12 x-10 x^2}{x}-\log (x)\right ) \, dx-\int \left (\frac {e^x \left (1+x+5 x^2\right )}{x}+e^x \log (x)\right ) \, dx\\ &=\int \frac {-3-12 x-10 x^2}{x} \, dx-\int \frac {e^x \left (1+x+5 x^2\right )}{x} \, dx-\int \log (x) \, dx-\int e^x \log (x) \, dx\\ &=x-e^x \log (x)-x \log (x)+\int \left (-12-\frac {3}{x}-10 x\right ) \, dx+\int \frac {e^x}{x} \, dx-\int \left (e^x+\frac {e^x}{x}+5 e^x x\right ) \, dx\\ &=-11 x-5 x^2+\text {Ei}(x)-3 \log (x)-e^x \log (x)-x \log (x)-5 \int e^x x \, dx-\int e^x \, dx-\int \frac {e^x}{x} \, dx\\ &=-e^x-11 x-5 e^x x-5 x^2-3 \log (x)-e^x \log (x)-x \log (x)+5 \int e^x \, dx\\ &=4 e^x-11 x-5 e^x x-5 x^2-3 \log (x)-e^x \log (x)-x \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 32, normalized size = 1.45 \begin {gather*} -11 x-5 x^2-e^x (-4+5 x)-3 \log (x)-\left (e^x+x\right ) \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 27, normalized size = 1.23 \begin {gather*} -5 \, x^{2} - {\left (5 \, x - 4\right )} e^{x} - {\left (x + e^{x} + 3\right )} \log \relax (x) - 11 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 33, normalized size = 1.50 \begin {gather*} -5 \, x^{2} - 5 \, x e^{x} - x \log \relax (x) - e^{x} \log \relax (x) - 11 \, x + 4 \, e^{x} - 3 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 34, normalized size = 1.55
method | result | size |
default | \(-5 \,{\mathrm e}^{x} x -{\mathrm e}^{x} \ln \relax (x )+4 \,{\mathrm e}^{x}-5 x^{2}-11 x -3 \ln \relax (x )-x \ln \relax (x )\) | \(34\) |
norman | \(-5 \,{\mathrm e}^{x} x -{\mathrm e}^{x} \ln \relax (x )+4 \,{\mathrm e}^{x}-5 x^{2}-11 x -3 \ln \relax (x )-x \ln \relax (x )\) | \(34\) |
risch | \(\left (-{\mathrm e}^{x}-x \right ) \ln \relax (x )-5 x^{2}-5 \,{\mathrm e}^{x} x -3 \ln \relax (x )-11 x +4 \,{\mathrm e}^{x}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.41, size = 35, normalized size = 1.59 \begin {gather*} -5 \, x^{2} - 5 \, {\left (x - 1\right )} e^{x} - x \log \relax (x) - e^{x} \log \relax (x) - 11 \, x - e^{x} - 3 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.15, size = 33, normalized size = 1.50 \begin {gather*} 4\,{\mathrm {e}}^x-11\,x-3\,\ln \relax (x)-{\mathrm {e}}^x\,\ln \relax (x)-5\,x\,{\mathrm {e}}^x-x\,\ln \relax (x)-5\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.36, size = 29, normalized size = 1.32 \begin {gather*} - 5 x^{2} - x \log {\relax (x )} - 11 x + \left (- 5 x - \log {\relax (x )} + 4\right ) e^{x} - 3 \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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