Optimal. Leaf size=29 \[ e^3-i \pi -x^2-\log (5)+x (-2+x+\log (3-x)) \]
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Rubi [A] time = 0.05, antiderivative size = 25, normalized size of antiderivative = 0.86, number of steps used = 6, number of rules used = 4, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.190, Rules used = {6742, 43, 2389, 2295} \begin {gather*} -2 x-(3-x) \log (3-x)+3 \log (3-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 2295
Rule 2389
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {6-x}{-3+x}+\log (3-x)\right ) \, dx\\ &=\int \frac {6-x}{-3+x} \, dx+\int \log (3-x) \, dx\\ &=\int \left (-1+\frac {3}{-3+x}\right ) \, dx-\operatorname {Subst}(\int \log (x) \, dx,x,3-x)\\ &=-2 x+3 \log (3-x)-(3-x) \log (3-x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 12, normalized size = 0.41 \begin {gather*} -2 x+x \log (3-x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.01, size = 12, normalized size = 0.41 \begin {gather*} x \log \left (-x + 3\right ) - 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 12, normalized size = 0.41 \begin {gather*} x \log \left (-x + 3\right ) - 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.46, size = 13, normalized size = 0.45
method | result | size |
norman | \(x \ln \left (3-x \right )-2 x\) | \(13\) |
risch | \(x \ln \left (3-x \right )-2 x\) | \(13\) |
derivativedivides | \(-\left (3-x \right ) \ln \left (3-x \right )+6-2 x +3 \ln \left (3-x \right )\) | \(27\) |
default | \(-\left (3-x \right ) \ln \left (3-x \right )+6-2 x +3 \ln \left (3-x \right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.76, size = 37, normalized size = 1.28 \begin {gather*} -\frac {3}{2} \, \log \left (x - 3\right )^{2} + {\left (x + 3 \, \log \left (x - 3\right )\right )} \log \left (-x + 3\right ) - \frac {3}{2} \, \log \left (-x + 3\right )^{2} - 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 10, normalized size = 0.34 \begin {gather*} x\,\left (\ln \left (3-x\right )-2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 8, normalized size = 0.28 \begin {gather*} x \log {\left (3 - x \right )} - 2 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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