Optimal. Leaf size=19 \[ -\frac{\left (a+b x^3\right )^3}{9 a x^9} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.015052, antiderivative size = 19, 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 \[ -\frac{\left (a+b x^3\right )^3}{9 a x^9} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^2/x^10,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.79778, size = 15, normalized size = 0.79 \[ - \frac{\left (a + b x^{3}\right )^{3}}{9 a x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**2/x**10,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00154264, size = 30, normalized size = 1.58 \[ -\frac{a^2}{9 x^9}-\frac{a b}{3 x^6}-\frac{b^2}{3 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^2/x^10,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 25, normalized size = 1.3 \[ -{\frac{ab}{3\,{x}^{6}}}-{\frac{{a}^{2}}{9\,{x}^{9}}}-{\frac{{b}^{2}}{3\,{x}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^2/x^10,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43897, size = 32, normalized size = 1.68 \[ -\frac{3 \, b^{2} x^{6} + 3 \, a b x^{3} + a^{2}}{9 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2/x^10,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.224049, size = 32, normalized size = 1.68 \[ -\frac{3 \, b^{2} x^{6} + 3 \, a b x^{3} + a^{2}}{9 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2/x^10,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.46979, size = 26, normalized size = 1.37 \[ - \frac{a^{2} + 3 a b x^{3} + 3 b^{2} x^{6}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**2/x**10,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.224431, size = 32, normalized size = 1.68 \[ -\frac{3 \, b^{2} x^{6} + 3 \, a b x^{3} + a^{2}}{9 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2/x^10,x, algorithm="giac")
[Out]