Optimal. Leaf size=29 \[ \frac {x^2}{2}+6 x+\frac {169}{4} \log (7-x)-\frac {1}{4} \log (x+1) \]
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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 = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {1657, 632, 31} \[ \frac {x^2}{2}+6 x+\frac {169}{4} \log (7-x)-\frac {1}{4} \log (x+1) \]
Antiderivative was successfully verified.
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Rule 31
Rule 632
Rule 1657
Rubi steps
\begin {align*} \int \frac {2-x+x^3}{-7-6 x+x^2} \, dx &=\int \left (6+x+\frac {2 (22+21 x)}{-7-6 x+x^2}\right ) \, dx\\ &=6 x+\frac {x^2}{2}+2 \int \frac {22+21 x}{-7-6 x+x^2} \, dx\\ &=6 x+\frac {x^2}{2}-\frac {1}{4} \int \frac {1}{1+x} \, dx+\frac {169}{4} \int \frac {1}{-7+x} \, dx\\ &=6 x+\frac {x^2}{2}+\frac {169}{4} \log (7-x)-\frac {1}{4} \log (1+x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 29, normalized size = 1.00 \[ \frac {x^2}{2}+6 x+\frac {169}{4} \log (7-x)-\frac {1}{4} \log (x+1) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 21, normalized size = 0.72 \[ \frac {1}{2} \, x^{2} + 6 \, x - \frac {1}{4} \, \log \left (x + 1\right ) + \frac {169}{4} \, \log \left (x - 7\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.37, size = 23, normalized size = 0.79 \[ \frac {1}{2} \, x^{2} + 6 \, x - \frac {1}{4} \, \log \left ({\left | x + 1 \right |}\right ) + \frac {169}{4} \, \log \left ({\left | x - 7 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 22, normalized size = 0.76 \[ \frac {x^{2}}{2}+6 x -\frac {\ln \left (x +1\right )}{4}+\frac {169 \ln \left (x -7\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.08, size = 21, normalized size = 0.72 \[ \frac {1}{2} \, x^{2} + 6 \, x - \frac {1}{4} \, \log \left (x + 1\right ) + \frac {169}{4} \, \log \left (x - 7\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.21, size = 21, normalized size = 0.72 \[ 6\,x-\frac {\ln \left (x+1\right )}{4}+\frac {169\,\ln \left (x-7\right )}{4}+\frac {x^2}{2} \]
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 \[ \frac {x^{2}}{2} + 6 x + \frac {169 \log {\left (x - 7 \right )}}{4} - \frac {\log {\left (x + 1 \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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