Optimal. Leaf size=12 \[ \frac{1}{18} \tanh ^{-1}\left (\frac{x^6}{3}\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0191459, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{1}{18} \tanh ^{-1}\left (\frac{x^6}{3}\right ) \]
Antiderivative was successfully verified.
[In] Int[x^5/(9 - x^12),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.02734, size = 7, normalized size = 0.58 \[ \frac{\operatorname{atanh}{\left (\frac{x^{6}}{3} \right )}}{18} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5/(-x**12+9),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00614431, size = 23, normalized size = 1.92 \[ \frac{1}{36} \log \left (x^6+3\right )-\frac{1}{36} \log \left (3-x^6\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^5/(9 - x^12),x]
[Out]
_______________________________________________________________________________________
Maple [B] time = 0.009, size = 18, normalized size = 1.5 \[{\frac{\ln \left ({x}^{6}+3 \right ) }{36}}-{\frac{\ln \left ({x}^{6}-3 \right ) }{36}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5/(-x^12+9),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.41764, size = 23, normalized size = 1.92 \[ \frac{1}{36} \, \log \left (x^{6} + 3\right ) - \frac{1}{36} \, \log \left (x^{6} - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x^5/(x^12 - 9),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.223566, size = 23, normalized size = 1.92 \[ \frac{1}{36} \, \log \left (x^{6} + 3\right ) - \frac{1}{36} \, \log \left (x^{6} - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x^5/(x^12 - 9),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.332021, size = 15, normalized size = 1.25 \[ - \frac{\log{\left (x^{6} - 3 \right )}}{36} + \frac{\log{\left (x^{6} + 3 \right )}}{36} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5/(-x**12+9),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.228385, size = 24, normalized size = 2. \[ \frac{1}{36} \,{\rm ln}\left (x^{6} + 3\right ) - \frac{1}{36} \,{\rm ln}\left ({\left | x^{6} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x^5/(x^12 - 9),x, algorithm="giac")
[Out]