Optimal. Leaf size=17 \[ \frac {x^3}{3}+x+\log (x)-\log (x+1) \]
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Rubi [A] time = 0.03, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {1593, 1802} \[ \frac {x^3}{3}+x+\log (x)-\log (x+1) \]
Antiderivative was successfully verified.
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Rule 1593
Rule 1802
Rubi steps
\begin {align*} \int \frac {-1+x^5}{-x+x^3} \, dx &=\int \frac {-1+x^5}{x \left (-1+x^2\right )} \, dx\\ &=\int \left (1+\frac {1}{-1-x}+\frac {1}{x}+x^2\right ) \, dx\\ &=x+\frac {x^3}{3}+\log (x)-\log (1+x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ \frac {x^3}{3}+x+\log (x)-\log (x+1) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 15, normalized size = 0.88 \[ \frac {1}{3} \, x^{3} + x - \log \left (x + 1\right ) + \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 17, normalized size = 1.00 \[ \frac {1}{3} \, x^{3} + x - \log \left ({\left | x + 1 \right |}\right ) + \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.94 \[ \frac {x^{3}}{3}+x +\ln \relax (x )-\ln \left (x +1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.90, size = 15, normalized size = 0.88 \[ \frac {1}{3} \, x^{3} + x - \log \left (x + 1\right ) + \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 15, normalized size = 0.88 \[ x-2\,\mathrm {atanh}\left (2\,x+1\right )+\frac {x^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 0.82 \[ \frac {x^{3}}{3} + x + \log {\relax (x )} - \log {\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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