Optimal. Leaf size=11 \[ \log \left (x^2+2\right )-\log (x) \]
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Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {446, 72} \[ \log \left (x^2+2\right )-\log (x) \]
Antiderivative was successfully verified.
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Rule 72
Rule 446
Rubi steps
\begin {align*} \int \frac {-2+x^2}{x \left (2+x^2\right )} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {-2+x}{x (2+x)} \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (-\frac {1}{x}+\frac {2}{2+x}\right ) \, dx,x,x^2\right )\\ &=-\log (x)+\log \left (2+x^2\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \[ \log \left (x^2+2\right )-\log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 11, normalized size = 1.00 \[ \log \left (x^{2} + 2\right ) - \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 13, normalized size = 1.18 \[ \log \left (x^{2} + 2\right ) - \frac {1}{2} \, \log \left (x^{2}\right ) \]
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 \[ -\ln \relax (x )+\ln \left (x^{2}+2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.69, size = 13, normalized size = 1.18 \[ \log \left (x^{2} + 2\right ) - \frac {1}{2} \, \log \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 11, normalized size = 1.00 \[ \ln \left (x^2+2\right )-\ln \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 8, normalized size = 0.73 \[ - \log {\relax (x )} + \log {\left (x^{2} + 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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