Optimal. Leaf size=27 \[ -\frac{a^2}{2 x^2}+a b x^2+\frac{b^2 x^6}{6} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0291175, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{a^2}{2 x^2}+a b x^2+\frac{b^2 x^6}{6} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^4)^2/x^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{2}}{2 x^{2}} + 2 a b \int x\, dx + \frac{b^{2} x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**4+a)**2/x**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00171799, size = 27, normalized size = 1. \[ -\frac{a^2}{2 x^2}+a b x^2+\frac{b^2 x^6}{6} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^4)^2/x^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.004, size = 24, normalized size = 0.9 \[ -{\frac{{a}^{2}}{2\,{x}^{2}}}+ab{x}^{2}+{\frac{{b}^{2}{x}^{6}}{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^4+a)^2/x^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.41868, size = 31, normalized size = 1.15 \[ \frac{1}{6} \, b^{2} x^{6} + a b x^{2} - \frac{a^{2}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^2/x^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.218637, size = 34, normalized size = 1.26 \[ \frac{b^{2} x^{8} + 6 \, a b x^{4} - 3 \, a^{2}}{6 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^2/x^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.02861, size = 22, normalized size = 0.81 \[ - \frac{a^{2}}{2 x^{2}} + a b x^{2} + \frac{b^{2} x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**4+a)**2/x**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.226255, size = 31, normalized size = 1.15 \[ \frac{1}{6} \, b^{2} x^{6} + a b x^{2} - \frac{a^{2}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^2/x^3,x, algorithm="giac")
[Out]