Optimal. Leaf size=4 \[ \log (x+2) \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 4, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {1586, 31} \begin {gather*} \log (x+2) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 31
Rule 1586
Rubi steps
\begin {align*} \int \frac {2-x-2 x^2+x^3}{4-5 x^2+x^4} \, dx &=\int \frac {1}{2+x} \, dx\\ &=\log (2+x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 4, normalized size = 1.00 \begin {gather*} \log (x+2) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2-x-2 x^2+x^3}{4-5 x^2+x^4} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.12, size = 4, normalized size = 1.00 \begin {gather*} \log \left (x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.31, size = 5, normalized size = 1.25 \begin {gather*} \log \left ({\left | x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 5, normalized size = 1.25 \begin {gather*} \ln \left (x +2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.43, size = 4, normalized size = 1.00 \begin {gather*} \log \left (x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.02, size = 4, normalized size = 1.00 \begin {gather*} \ln \left (x+2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.07, size = 3, normalized size = 0.75 \begin {gather*} \log {\left (x + 2 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________