Optimal. Leaf size=30 \[ -\frac{a^2}{8 x^8}-\frac{2 a b}{5 x^5}-\frac{b^2}{2 x^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0292484, antiderivative size = 30, 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 \[ -\frac{a^2}{8 x^8}-\frac{2 a b}{5 x^5}-\frac{b^2}{2 x^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^2/x^9,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.28071, size = 27, normalized size = 0.9 \[ - \frac{a^{2}}{8 x^{8}} - \frac{2 a b}{5 x^{5}} - \frac{b^{2}}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**2/x**9,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00148088, size = 30, normalized size = 1. \[ -\frac{a^2}{8 x^8}-\frac{2 a b}{5 x^5}-\frac{b^2}{2 x^2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^2/x^9,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 25, normalized size = 0.8 \[ -{\frac{{a}^{2}}{8\,{x}^{8}}}-{\frac{2\,ab}{5\,{x}^{5}}}-{\frac{{b}^{2}}{2\,{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^2/x^9,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.44218, size = 35, normalized size = 1.17 \[ -\frac{20 \, b^{2} x^{6} + 16 \, a b x^{3} + 5 \, a^{2}}{40 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2/x^9,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.261563, size = 35, normalized size = 1.17 \[ -\frac{20 \, b^{2} x^{6} + 16 \, a b x^{3} + 5 \, a^{2}}{40 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2/x^9,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.39588, size = 27, normalized size = 0.9 \[ - \frac{5 a^{2} + 16 a b x^{3} + 20 b^{2} x^{6}}{40 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**2/x**9,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.2248, size = 35, normalized size = 1.17 \[ -\frac{20 \, b^{2} x^{6} + 16 \, a b x^{3} + 5 \, a^{2}}{40 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2/x^9,x, algorithm="giac")
[Out]