Optimal. Leaf size=30 \[ -\frac{a^2}{3 x^3}-\frac{a b}{2 x^4}-\frac{b^2}{5 x^5} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0350996, antiderivative size = 30, 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 \[ -\frac{a^2}{3 x^3}-\frac{a b}{2 x^4}-\frac{b^2}{5 x^5} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^2/x^4,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.15237, size = 26, normalized size = 0.87 \[ - \frac{a^{2}}{3 x^{3}} - \frac{a b}{2 x^{4}} - \frac{b^{2}}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**2/x**4,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0109626, size = 30, normalized size = 1. \[ -\frac{a^2}{3 x^3}-\frac{a b}{2 x^4}-\frac{b^2}{5 x^5} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^2/x^4,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 25, normalized size = 0.8 \[ -{\frac{{b}^{2}}{5\,{x}^{5}}}-{\frac{ab}{2\,{x}^{4}}}-{\frac{{a}^{2}}{3\,{x}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^2/x^4,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.44078, size = 32, normalized size = 1.07 \[ -\frac{10 \, a^{2} x^{2} + 15 \, a b x + 6 \, b^{2}}{30 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2/x^4,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.21789, size = 32, normalized size = 1.07 \[ -\frac{10 \, a^{2} x^{2} + 15 \, a b x + 6 \, b^{2}}{30 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2/x^4,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.29355, size = 26, normalized size = 0.87 \[ - \frac{10 a^{2} x^{2} + 15 a b x + 6 b^{2}}{30 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**2/x**4,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.226533, size = 32, normalized size = 1.07 \[ -\frac{10 \, a^{2} x^{2} + 15 \, a b x + 6 \, b^{2}}{30 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2/x^4,x, algorithm="giac")
[Out]