Optimal. Leaf size=23 \[ 4 e^x-x \left (1+x-\left (-x+x^2\right ) \log (x)\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 27, normalized size of antiderivative = 1.17, number of steps used = 6, number of rules used = 4, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.160, Rules used = {2194, 1593, 43, 2334} \begin {gather*} -x^2-\left (x^2-x^3\right ) \log (x)-x+4 e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 1593
Rule 2194
Rule 2334
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-x-\frac {3 x^2}{2}+\frac {x^3}{3}+4 \int e^x \, dx+\int \left (-2 x+3 x^2\right ) \log (x) \, dx\\ &=4 e^x-x-\frac {3 x^2}{2}+\frac {x^3}{3}+\int x (-2+3 x) \log (x) \, dx\\ &=4 e^x-x-\frac {3 x^2}{2}+\frac {x^3}{3}-\left (x^2-x^3\right ) \log (x)-\int (-1+x) x \, dx\\ &=4 e^x-x-\frac {3 x^2}{2}+\frac {x^3}{3}-\left (x^2-x^3\right ) \log (x)-\int \left (-x+x^2\right ) \, dx\\ &=4 e^x-x-x^2-\left (x^2-x^3\right ) \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 27, normalized size = 1.17 \begin {gather*} 4 e^x-x-x^2-x^2 \log (x)+x^3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.89, size = 25, normalized size = 1.09 \begin {gather*} -x^{2} + {\left (x^{3} - x^{2}\right )} \log \relax (x) - x + 4 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 26, normalized size = 1.13 \begin {gather*} x^{3} \log \relax (x) - x^{2} \log \relax (x) - x^{2} - x + 4 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 26, normalized size = 1.13
method | result | size |
risch | \(\left (x^{3}-x^{2}\right ) \ln \relax (x )-x^{2}+4 \,{\mathrm e}^{x}-x\) | \(26\) |
default | \(-x +x^{3} \ln \relax (x )-x^{2} \ln \relax (x )-x^{2}+4 \,{\mathrm e}^{x}\) | \(27\) |
norman | \(-x +x^{3} \ln \relax (x )-x^{2} \ln \relax (x )-x^{2}+4 \,{\mathrm e}^{x}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 25, normalized size = 1.09 \begin {gather*} -x^{2} + {\left (x^{3} - x^{2}\right )} \log \relax (x) - x + 4 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.18, size = 26, normalized size = 1.13 \begin {gather*} 4\,{\mathrm {e}}^x-x-x^2\,\ln \relax (x)+x^3\,\ln \relax (x)-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.25, size = 19, normalized size = 0.83 \begin {gather*} - x^{2} - x + \left (x^{3} - x^{2}\right ) \log {\relax (x )} + 4 e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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