Optimal. Leaf size=26 \[ \frac {x^3}{3}+\frac {x^2}{2}+2 x+2 \log (1-x) \]
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Rubi [A] time = 0.02, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {1593, 772} \[ \frac {x^3}{3}+\frac {x^2}{2}+2 x+2 \log (1-x) \]
Antiderivative was successfully verified.
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Rule 772
Rule 1593
Rubi steps
\begin {align*} \int \frac {x+x^3}{-1+x} \, dx &=\int \frac {x \left (1+x^2\right )}{-1+x} \, dx\\ &=\int \left (2+\frac {2}{-1+x}+x+x^2\right ) \, dx\\ &=2 x+\frac {x^2}{2}+\frac {x^3}{3}+2 \log (1-x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 25, normalized size = 0.96 \[ \frac {1}{6} \left (2 x^3+3 x^2+12 x+12 \log (x-1)-17\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 20, normalized size = 0.77 \[ \frac {1}{3} \, x^{3} + \frac {1}{2} \, x^{2} + 2 \, x + 2 \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.30, size = 21, normalized size = 0.81 \[ \frac {1}{3} \, x^{3} + \frac {1}{2} \, x^{2} + 2 \, x + 2 \, \log \left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 21, normalized size = 0.81 \[ \frac {x^{3}}{3}+\frac {x^{2}}{2}+2 x +2 \ln \left (x -1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.69, size = 20, normalized size = 0.77 \[ \frac {1}{3} \, x^{3} + \frac {1}{2} \, x^{2} + 2 \, x + 2 \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 20, normalized size = 0.77 \[ 2\,x+2\,\ln \left (x-1\right )+\frac {x^2}{2}+\frac {x^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 19, normalized size = 0.73 \[ \frac {x^{3}}{3} + \frac {x^{2}}{2} + 2 x + 2 \log {\left (x - 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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