Optimal. Leaf size=17 \[ \frac{x^3}{3}+x+\log (x)-\log (x+1) \]
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Rubi [A] time = 0.0293711, antiderivative size = 17, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0044405, size = 17, normalized size = 1. \[ \frac{x^3}{3}+x+\log (x)-\log (x+1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 16, normalized size = 0.9 \begin{align*} x+{\frac{{x}^{3}}{3}}+\ln \left ( x \right ) -\ln \left ( 1+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06308, size = 20, normalized size = 1.18 \begin{align*} \frac{1}{3} \, x^{3} + x - \log \left (x + 1\right ) + \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.16111, size = 47, normalized size = 2.76 \begin{align*} \frac{1}{3} \, x^{3} + x - \log \left (x + 1\right ) + \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.089873, size = 14, normalized size = 0.82 \begin{align*} \frac{x^{3}}{3} + x + \log{\left (x \right )} - \log{\left (x + 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1499, size = 23, normalized size = 1.35 \begin{align*} \frac{1}{3} \, x^{3} + x - \log \left ({\left | x + 1 \right |}\right ) + \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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