Optimal. Leaf size=26 \[ \frac {x^2}{2}+\frac {1}{7} \log (3-x)-\frac {1}{7} \log (4+x) \]
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Rubi [A]
time = 0.01, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps
used = 5, number of rules used = 3, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {1671, 630, 31}
\begin {gather*} \frac {x^2}{2}+\frac {1}{7} \log (3-x)-\frac {1}{7} \log (x+4) \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rule 630
Rule 1671
Rubi steps
\begin {align*} \int \frac {1-12 x+x^2+x^3}{-12+x+x^2} \, dx &=\int \left (x+\frac {1}{-12+x+x^2}\right ) \, dx\\ &=\frac {x^2}{2}+\int \frac {1}{-12+x+x^2} \, dx\\ &=\frac {x^2}{2}+\frac {1}{7} \int \frac {1}{-3+x} \, dx-\frac {1}{7} \int \frac {1}{4+x} \, dx\\ &=\frac {x^2}{2}+\frac {1}{7} \log (3-x)-\frac {1}{7} \log (4+x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 26, normalized size = 1.00 \begin {gather*} \frac {x^2}{2}+\frac {1}{7} \log (3-x)-\frac {1}{7} \log (4+x) \end {gather*}
Antiderivative was successfully verified.
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Mathics [A]
time = 1.87, size = 18, normalized size = 0.69 \begin {gather*} \frac {x^2}{2}-\frac {\text {Log}\left [4+x\right ]}{7}+\frac {\text {Log}\left [-3+x\right ]}{7} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 19, normalized size = 0.73
method | result | size |
default | \(\frac {x^{2}}{2}+\frac {\ln \left (-3+x \right )}{7}-\frac {\ln \left (4+x \right )}{7}\) | \(19\) |
norman | \(\frac {x^{2}}{2}+\frac {\ln \left (-3+x \right )}{7}-\frac {\ln \left (4+x \right )}{7}\) | \(19\) |
risch | \(\frac {x^{2}}{2}+\frac {\ln \left (-3+x \right )}{7}-\frac {\ln \left (4+x \right )}{7}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 18, normalized size = 0.69 \begin {gather*} \frac {1}{2} \, x^{2} - \frac {1}{7} \, \log \left (x + 4\right ) + \frac {1}{7} \, \log \left (x - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 18, normalized size = 0.69 \begin {gather*} \frac {1}{2} \, x^{2} - \frac {1}{7} \, \log \left (x + 4\right ) + \frac {1}{7} \, \log \left (x - 3\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 = 0.65 \begin {gather*} \frac {x^{2}}{2} + \frac {\log {\left (x - 3 \right )}}{7} - \frac {\log {\left (x + 4 \right )}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 25, normalized size = 0.96 \begin {gather*} \frac {\ln \left |x-3\right |}{7}-\frac {\ln \left |x+4\right |}{7}+\frac {1}{2} x^{2} \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 = 0.54 \begin {gather*} \frac {x^2}{2}-\frac {2\,\mathrm {atanh}\left (\frac {2\,x}{7}+\frac {1}{7}\right )}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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