Optimal. Leaf size=16 \[ -\frac{1}{6 b \left (a+b x^6\right )} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0100331, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{1}{6 b \left (a+b x^6\right )} \]
Antiderivative was successfully verified.
[In] Int[x^5/(a + b*x^6)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.17553, size = 12, normalized size = 0.75 \[ - \frac{1}{6 b \left (a + b x^{6}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5/(b*x**6+a)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00690235, size = 16, normalized size = 1. \[ -\frac{1}{6 b \left (a+b x^6\right )} \]
Antiderivative was successfully verified.
[In] Integrate[x^5/(a + b*x^6)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 15, normalized size = 0.9 \[ -{\frac{1}{6\,b \left ( b{x}^{6}+a \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5/(b*x^6+a)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43599, size = 19, normalized size = 1.19 \[ -\frac{1}{6 \,{\left (b x^{6} + a\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^6 + a)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.204944, size = 20, normalized size = 1.25 \[ -\frac{1}{6 \,{\left (b^{2} x^{6} + a b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^6 + a)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 3.87259, size = 15, normalized size = 0.94 \[ - \frac{1}{6 a b + 6 b^{2} x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5/(b*x**6+a)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.221674, size = 19, normalized size = 1.19 \[ -\frac{1}{6 \,{\left (b x^{6} + a\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^6 + a)^2,x, algorithm="giac")
[Out]