Optimal. Leaf size=29 \[ \frac {x^2}{2}+6 x+\frac {85}{2} \log (7-x)+\frac {1}{2} \log (x+1) \]
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Rubi [A] time = 0.02, antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.188, Rules used = {1657, 632, 31} \begin {gather*} \frac {x^2}{2}+6 x+\frac {85}{2} \log (7-x)+\frac {1}{2} \log (x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rule 632
Rule 1657
Rubi steps
\begin {align*} \int \frac {-3+x^3}{-7-6 x+x^2} \, dx &=\int \left (6+x+\frac {39+43 x}{-7-6 x+x^2}\right ) \, dx\\ &=6 x+\frac {x^2}{2}+\int \frac {39+43 x}{-7-6 x+x^2} \, dx\\ &=6 x+\frac {x^2}{2}+\frac {1}{2} \int \frac {1}{1+x} \, dx+\frac {85}{2} \int \frac {1}{-7+x} \, dx\\ &=6 x+\frac {x^2}{2}+\frac {85}{2} \log (7-x)+\frac {1}{2} \log (1+x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 29, normalized size = 1.00 \begin {gather*} \frac {x^2}{2}+6 x+\frac {85}{2} \log (7-x)+\frac {1}{2} \log (x+1) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-3+x^3}{-7-6 x+x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.14, size = 21, normalized size = 0.72 \begin {gather*} \frac {1}{2} \, x^{2} + 6 \, x + \frac {1}{2} \, \log \left (x + 1\right ) + \frac {85}{2} \, \log \left (x - 7\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 23, normalized size = 0.79 \begin {gather*} \frac {1}{2} \, x^{2} + 6 \, x + \frac {1}{2} \, \log \left ({\left | x + 1 \right |}\right ) + \frac {85}{2} \, \log \left ({\left | x - 7 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 22, normalized size = 0.76 \begin {gather*} \frac {x^{2}}{2}+6 x +\frac {\ln \left (x +1\right )}{2}+\frac {85 \ln \left (x -7\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.10, size = 21, normalized size = 0.72 \begin {gather*} \frac {1}{2} \, x^{2} + 6 \, x + \frac {1}{2} \, \log \left (x + 1\right ) + \frac {85}{2} \, \log \left (x - 7\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.12, size = 21, normalized size = 0.72 \begin {gather*} 6\,x+\frac {\ln \left (x+1\right )}{2}+\frac {85\,\ln \left (x-7\right )}{2}+\frac {x^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 22, normalized size = 0.76 \begin {gather*} \frac {x^{2}}{2} + 6 x + \frac {85 \log {\left (x - 7 \right )}}{2} + \frac {\log {\left (x + 1 \right )}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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