Optimal. Leaf size=19 \[ \frac {x^4}{4}+\frac {x^2}{2}+\log (x+1) \]
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Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.231, Rules used = {1810, 627, 31} \[ \frac {x^4}{4}+\frac {x^2}{2}+\log (x+1) \]
Antiderivative was successfully verified.
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Rule 31
Rule 627
Rule 1810
Rubi steps
\begin {align*} \int \frac {-1+x^5}{-1+x^2} \, dx &=\int \left (x+x^3-\frac {1-x}{-1+x^2}\right ) \, dx\\ &=\frac {x^2}{2}+\frac {x^4}{4}-\int \frac {1-x}{-1+x^2} \, dx\\ &=\frac {x^2}{2}+\frac {x^4}{4}-\int \frac {1}{-1-x} \, dx\\ &=\frac {x^2}{2}+\frac {x^4}{4}+\log (1+x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.00 \[ \frac {x^4}{4}+\frac {x^2}{2}+\log (x+1) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 15, normalized size = 0.79 \[ \frac {1}{4} \, x^{4} + \frac {1}{2} \, x^{2} + \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.27, size = 16, normalized size = 0.84 \[ \frac {1}{4} \, x^{4} + \frac {1}{2} \, x^{2} + \log \left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.84 \[ \frac {x^{4}}{4}+\frac {x^{2}}{2}+\ln \left (x +1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.07, size = 15, normalized size = 0.79 \[ \frac {1}{4} \, x^{4} + \frac {1}{2} \, x^{2} + \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 15, normalized size = 0.79 \[ \ln \left (x+1\right )+\frac {x^2}{2}+\frac {x^4}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 14, normalized size = 0.74 \[ \frac {x^{4}}{4} + \frac {x^{2}}{2} + \log {\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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