Optimal. Leaf size=25 \[ \frac{a^2 x^5}{5}+\frac{2}{3} a b x^3+b^2 x \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0303961, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{a^2 x^5}{5}+\frac{2}{3} a b x^3+b^2 x \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^2)^2*x^4,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{2} x^{5}}{5} + \frac{2 a b x^{3}}{3} + \int b^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**2)**2*x**4,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00166711, size = 25, normalized size = 1. \[ \frac{a^2 x^5}{5}+\frac{2}{3} a b x^3+b^2 x \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^2)^2*x^4,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 22, normalized size = 0.9 \[{b}^{2}x+{\frac{2\,ab{x}^{3}}{3}}+{\frac{{x}^{5}{a}^{2}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^2)^2*x^4,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.44408, size = 28, normalized size = 1.12 \[ \frac{1}{5} \, a^{2} x^{5} + \frac{2}{3} \, a b x^{3} + b^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2*x^4,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.218809, size = 28, normalized size = 1.12 \[ \frac{1}{5} \, a^{2} x^{5} + \frac{2}{3} \, a b x^{3} + b^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2*x^4,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.085168, size = 22, normalized size = 0.88 \[ \frac{a^{2} x^{5}}{5} + \frac{2 a b x^{3}}{3} + b^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**2)**2*x**4,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.227624, size = 28, normalized size = 1.12 \[ \frac{1}{5} \, a^{2} x^{5} + \frac{2}{3} \, a b x^{3} + b^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2*x^4,x, algorithm="giac")
[Out]