Optimal. Leaf size=40 \[ \frac{a \left (a x^2+b\right )^4}{40 b^2 x^8}-\frac{\left (a x^2+b\right )^4}{10 b x^{10}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.064114, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.308 \[ \frac{a \left (a x^2+b\right )^4}{40 b^2 x^8}-\frac{\left (a x^2+b\right )^4}{10 b x^{10}} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^2)^3/x^5,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 10.1987, size = 39, normalized size = 0.98 \[ - \frac{a^{3}}{4 x^{4}} - \frac{a^{2} b}{2 x^{6}} - \frac{3 a b^{2}}{8 x^{8}} - \frac{b^{3}}{10 x^{10}} \]
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 = 0.00717978, size = 43, normalized size = 1.08 \[ -\frac{a^3}{4 x^4}-\frac{a^2 b}{2 x^6}-\frac{3 a b^2}{8 x^8}-\frac{b^3}{10 x^{10}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^2)^3/x^5,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 36, normalized size = 0.9 \[ -{\frac{{a}^{2}b}{2\,{x}^{6}}}-{\frac{{a}^{3}}{4\,{x}^{4}}}-{\frac{{b}^{3}}{10\,{x}^{10}}}-{\frac{3\,a{b}^{2}}{8\,{x}^{8}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^2)^3/x^5,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.48167, size = 50, normalized size = 1.25 \[ -\frac{10 \, a^{3} x^{6} + 20 \, a^{2} b x^{4} + 15 \, a b^{2} x^{2} + 4 \, b^{3}}{40 \, x^{10}} \]
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 = 0.219906, size = 50, normalized size = 1.25 \[ -\frac{10 \, a^{3} x^{6} + 20 \, a^{2} b x^{4} + 15 \, a b^{2} x^{2} + 4 \, b^{3}}{40 \, x^{10}} \]
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 = 1.77216, size = 39, normalized size = 0.98 \[ - \frac{10 a^{3} x^{6} + 20 a^{2} b x^{4} + 15 a b^{2} x^{2} + 4 b^{3}}{40 x^{10}} \]
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 = 0.221473, size = 50, normalized size = 1.25 \[ -\frac{10 \, a^{3} x^{6} + 20 \, a^{2} b x^{4} + 15 \, a b^{2} x^{2} + 4 \, b^{3}}{40 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^3/x^5,x, algorithm="giac")
[Out]