Optimal. Leaf size=39 \[ \frac{a^3 x^6}{6}+\frac{3}{4} a^2 b x^4+\frac{3}{2} a b^2 x^2+b^3 \log (x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0620908, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{a^3 x^6}{6}+\frac{3}{4} a^2 b x^4+\frac{3}{2} a b^2 x^2+b^3 \log (x) \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^2)^3*x^5,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{3} x^{6}}{6} + \frac{3 a^{2} b \int ^{x^{2}} x\, dx}{2} + \frac{3 a b^{2} x^{2}}{2} + \frac{b^{3} \log{\left (x^{2} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**2)**3*x**5,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00776631, size = 39, normalized size = 1. \[ \frac{a^3 x^6}{6}+\frac{3}{4} a^2 b x^4+\frac{3}{2} a b^2 x^2+b^3 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^2)^3*x^5,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.003, size = 34, normalized size = 0.9 \[{\frac{3\,a{b}^{2}{x}^{2}}{2}}+{\frac{3\,{a}^{2}b{x}^{4}}{4}}+{\frac{{a}^{3}{x}^{6}}{6}}+{b}^{3}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^2)^3*x^5,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43471, size = 49, normalized size = 1.26 \[ \frac{1}{6} \, a^{3} x^{6} + \frac{3}{4} \, a^{2} b x^{4} + \frac{3}{2} \, a b^{2} x^{2} + \frac{1}{2} \, b^{3} \log \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^3*x^5,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.233753, size = 45, normalized size = 1.15 \[ \frac{1}{6} \, a^{3} x^{6} + \frac{3}{4} \, a^{2} b x^{4} + \frac{3}{2} \, a b^{2} x^{2} + b^{3} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^3*x^5,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.11896, size = 37, normalized size = 0.95 \[ \frac{a^{3} x^{6}}{6} + \frac{3 a^{2} b x^{4}}{4} + \frac{3 a b^{2} x^{2}}{2} + b^{3} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**2)**3*x**5,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.225501, size = 49, normalized size = 1.26 \[ \frac{1}{6} \, a^{3} x^{6} + \frac{3}{4} \, a^{2} b x^{4} + \frac{3}{2} \, a b^{2} x^{2} + \frac{1}{2} \, b^{3}{\rm ln}\left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^3*x^5,x, algorithm="giac")
[Out]