Optimal. Leaf size=12 \[ \frac{3}{2} \log \left (x^{2/3}+1\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0115411, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{3}{2} \log \left (x^{2/3}+1\right ) \]
Antiderivative was successfully verified.
[In] Int[1/((1 + x^(2/3))*x^(1/3)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.71504, size = 10, normalized size = 0.83 \[ \frac{3 \log{\left (x^{\frac{2}{3}} + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1+x**(2/3))/x**(1/3),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00341518, size = 12, normalized size = 1. \[ \frac{3}{2} \log \left (x^{2/3}+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 + x^(2/3))*x^(1/3)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.004, size = 9, normalized size = 0.8 \[{\frac{3}{2}\ln \left ( 1+{x}^{{\frac{2}{3}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1+x^(2/3))/x^(1/3),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.48496, size = 11, normalized size = 0.92 \[ \frac{3}{2} \, \log \left (x^{\frac{2}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^(1/3)*(x^(2/3) + 1)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.22047, size = 11, normalized size = 0.92 \[ \frac{3}{2} \, \log \left (x^{\frac{2}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^(1/3)*(x^(2/3) + 1)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.452449, size = 10, normalized size = 0.83 \[ \frac{3 \log{\left (x^{\frac{2}{3}} + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1+x**(2/3))/x**(1/3),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.215437, size = 11, normalized size = 0.92 \[ \frac{3}{2} \,{\rm ln}\left (x^{\frac{2}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^(1/3)*(x^(2/3) + 1)),x, algorithm="giac")
[Out]