Optimal. Leaf size=19 \[ 6 x+\frac {x^2}{2}+17 \log (2-x) \]
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Rubi [A]
time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {712}
\begin {gather*} \frac {x^2}{2}+6 x+17 \log (2-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 712
Rubi steps
\begin {align*} \int \frac {5+4 x+x^2}{-2+x} \, dx &=\int \left (6+\frac {17}{-2+x}+x\right ) \, dx\\ &=6 x+\frac {x^2}{2}+17 \log (2-x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 18, normalized size = 0.95 \begin {gather*} -14+6 x+\frac {x^2}{2}+17 \log (-2+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.48, size = 16, normalized size = 0.84
method | result | size |
default | \(\frac {x^{2}}{2}+6 x +17 \ln \left (x -2\right )\) | \(16\) |
norman | \(\frac {x^{2}}{2}+6 x +17 \ln \left (x -2\right )\) | \(16\) |
risch | \(\frac {x^{2}}{2}+6 x +17 \ln \left (x -2\right )\) | \(16\) |
meijerg | \(17 \ln \left (1-\frac {x}{2}\right )+\frac {x \left (6+\frac {3 x}{2}\right )}{3}+4 x\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 15, normalized size = 0.79 \begin {gather*} \frac {1}{2} \, x^{2} + 6 \, x + 17 \, \log \left (x - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.86, size = 15, normalized size = 0.79 \begin {gather*} \frac {1}{2} \, x^{2} + 6 \, x + 17 \, \log \left (x - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 14, normalized size = 0.74 \begin {gather*} \frac {x^{2}}{2} + 6 x + 17 \log {\left (x - 2 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.71, size = 16, normalized size = 0.84 \begin {gather*} \frac {1}{2} \, x^{2} + 6 \, x + 17 \, \log \left ({\left | x - 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.65, size = 15, normalized size = 0.79 \begin {gather*} 6\,x+17\,\ln \left (x-2\right )+\frac {x^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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