Optimal. Leaf size=43 \[ -\frac{a^3}{3 x^3}-\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{6 x^6} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0454398, antiderivative size = 43, 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 \[ -\frac{a^3}{3 x^3}-\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{6 x^6} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^3/x^4,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 7.95168, size = 41, normalized size = 0.95 \[ - \frac{a^{3}}{3 x^{3}} - \frac{3 a^{2} b}{4 x^{4}} - \frac{3 a b^{2}}{5 x^{5}} - \frac{b^{3}}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**3/x**4,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00569218, size = 43, normalized size = 1. \[ -\frac{a^3}{3 x^3}-\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{6 x^6} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^3/x^4,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 36, normalized size = 0.8 \[ -{\frac{{b}^{3}}{6\,{x}^{6}}}-{\frac{3\,a{b}^{2}}{5\,{x}^{5}}}-{\frac{3\,{a}^{2}b}{4\,{x}^{4}}}-{\frac{{a}^{3}}{3\,{x}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^3/x^4,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43363, size = 47, normalized size = 1.09 \[ -\frac{20 \, a^{3} x^{3} + 45 \, a^{2} b x^{2} + 36 \, a b^{2} x + 10 \, b^{3}}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^4,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.215967, size = 47, normalized size = 1.09 \[ -\frac{20 \, a^{3} x^{3} + 45 \, a^{2} b x^{2} + 36 \, a b^{2} x + 10 \, b^{3}}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^4,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.53503, size = 37, normalized size = 0.86 \[ - \frac{20 a^{3} x^{3} + 45 a^{2} b x^{2} + 36 a b^{2} x + 10 b^{3}}{60 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**3/x**4,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.21873, size = 47, normalized size = 1.09 \[ -\frac{20 \, a^{3} x^{3} + 45 \, a^{2} b x^{2} + 36 \, a b^{2} x + 10 \, b^{3}}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^4,x, algorithm="giac")
[Out]