Optimal. Leaf size=22 \[ -e^x+x+\log \left (e^{-x^2} (-3+x) x^3\right ) \]
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Rubi [A]
time = 0.19, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps
used = 6, number of rules used = 4, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {1607, 6874,
2225, 1634} \begin {gather*} -x^2+x-e^x+\log (3-x)+3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 1607
Rule 1634
Rule 2225
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-9+x+7 x^2-2 x^3+e^x \left (3 x-x^2\right )}{(-3+x) x} \, dx\\ &=\int \left (-e^x+\frac {-9+x+7 x^2-2 x^3}{(-3+x) x}\right ) \, dx\\ &=-\int e^x \, dx+\int \frac {-9+x+7 x^2-2 x^3}{(-3+x) x} \, dx\\ &=-e^x+\int \left (1+\frac {1}{-3+x}+\frac {3}{x}-2 x\right ) \, dx\\ &=-e^x+x-x^2+\log (3-x)+3 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.11, size = 22, normalized size = 1.00 \begin {gather*} -e^x+x-x^2+\log (3-x)+3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.21, size = 20, normalized size = 0.91
method | result | size |
default | \(\ln \left (x -3\right )+3 \ln \left (x \right )+x -x^{2}-{\mathrm e}^{x}\) | \(20\) |
norman | \(\ln \left (x -3\right )+3 \ln \left (x \right )+x -x^{2}-{\mathrm e}^{x}\) | \(20\) |
risch | \(\ln \left (x -3\right )+3 \ln \left (x \right )+x -x^{2}-{\mathrm e}^{x}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 19, normalized size = 0.86 \begin {gather*} -x^{2} + x - e^{x} + \log \left (x - 3\right ) + 3 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 17, normalized size = 0.77 \begin {gather*} - x^{2} + x - e^{x} + 3 \log {\left (x \right )} + \log {\left (x - 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 19, normalized size = 0.86 \begin {gather*} -x^{2} + x - e^{x} + \log \left (x - 3\right ) + 3 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.07, size = 19, normalized size = 0.86 \begin {gather*} x+\ln \left (x-3\right )-{\mathrm {e}}^x+3\,\ln \left (x\right )-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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