Optimal. Leaf size=20 \[ x+\frac {4}{5} \log (2-x)-\frac {9}{5} \log (3+x) \]
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Rubi [A]
time = 0.00, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {717, 646, 31}
\begin {gather*} x+\frac {4}{5} \log (2-x)-\frac {9}{5} \log (x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rule 646
Rule 717
Rubi steps
\begin {align*} \int \frac {x^2}{-6+x+x^2} \, dx &=x+\int \frac {6-x}{-6+x+x^2} \, dx\\ &=x+\frac {4}{5} \int \frac {1}{-2+x} \, dx-\frac {9}{5} \int \frac {1}{3+x} \, dx\\ &=x+\frac {4}{5} \log (2-x)-\frac {9}{5} \log (3+x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 20, normalized size = 1.00 \begin {gather*} x+\frac {4}{5} \log (2-x)-\frac {9}{5} \log (3+x) \end {gather*}
Antiderivative was successfully verified.
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Mathics [A]
time = 1.64, size = 14, normalized size = 0.70 \begin {gather*} x-\frac {9 \text {Log}\left [3+x\right ]}{5}+\frac {4 \text {Log}\left [-2+x\right ]}{5} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 15, normalized size = 0.75
method | result | size |
default | \(x +\frac {4 \ln \left (-2+x \right )}{5}-\frac {9 \ln \left (3+x \right )}{5}\) | \(15\) |
norman | \(x +\frac {4 \ln \left (-2+x \right )}{5}-\frac {9 \ln \left (3+x \right )}{5}\) | \(15\) |
risch | \(x +\frac {4 \ln \left (-2+x \right )}{5}-\frac {9 \ln \left (3+x \right )}{5}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 14, normalized size = 0.70 \begin {gather*} x - \frac {9}{5} \, \log \left (x + 3\right ) + \frac {4}{5} \, \log \left (x - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.32, size = 14, normalized size = 0.70 \begin {gather*} x - \frac {9}{5} \, \log \left (x + 3\right ) + \frac {4}{5} \, \log \left (x - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 17, normalized size = 0.85 \begin {gather*} x + \frac {4 \log {\left (x - 2 \right )}}{5} - \frac {9 \log {\left (x + 3 \right )}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 20, normalized size = 1.00 \begin {gather*} x+\frac {4}{5} \ln \left |x-2\right |-\frac {9}{5} \ln \left |x+3\right | \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 14, normalized size = 0.70 \begin {gather*} x+\frac {4\,\ln \left (x-2\right )}{5}-\frac {9\,\ln \left (x+3\right )}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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