Optimal. Leaf size=11 \[ \log (x+1)-\log (x+2) \]
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Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {1586, 616, 31} \begin {gather*} \log (x+1)-\log (x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rule 616
Rule 1586
Rubi steps
\begin {align*} \int \frac {2-3 x+x^2}{4-5 x^2+x^4} \, dx &=\int \frac {1}{2+3 x+x^2} \, dx\\ &=\int \frac {1}{1+x} \, dx-\int \frac {1}{2+x} \, dx\\ &=\log (1+x)-\log (2+x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} \log (x+1)-\log (x+2) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2-3 x+x^2}{4-5 x^2+x^4} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.22, size = 11, normalized size = 1.00 \begin {gather*} -\log \left (x + 2\right ) + \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 13, normalized size = 1.18 \begin {gather*} -\log \left ({\left | x + 2 \right |}\right ) + \log \left ({\left | x + 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 12, normalized size = 1.09 \begin {gather*} -\ln \left (x +2\right )+\ln \left (x +1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 11, normalized size = 1.00 \begin {gather*} -\log \left (x + 2\right ) + \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 8, normalized size = 0.73 \begin {gather*} -2\,\mathrm {atanh}\left (2\,x+3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 8, normalized size = 0.73 \begin {gather*} \log {\left (x + 1 \right )} - \log {\left (x + 2 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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