Optimal. Leaf size=16 \[ -\frac{\left (a+\frac{b}{x}\right )^4}{4 b} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0160148, antiderivative size = 16, 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 \[ -\frac{\left (a+\frac{b}{x}\right )^4}{4 b} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^3/x^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.19363, size = 10, normalized size = 0.62 \[ - \frac{\left (a + \frac{b}{x}\right )^{4}}{4 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**3/x**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [B] time = 0.00605344, size = 39, normalized size = 2.44 \[ -\frac{a^3}{x}-\frac{3 a^2 b}{2 x^2}-\frac{a b^2}{x^3}-\frac{b^3}{4 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^3/x^2,x]
[Out]
_______________________________________________________________________________________
Maple [B] time = 0.007, size = 36, normalized size = 2.3 \[ -{\frac{{b}^{3}}{4\,{x}^{4}}}-{\frac{a{b}^{2}}{{x}^{3}}}-{\frac{3\,{a}^{2}b}{2\,{x}^{2}}}-{\frac{{a}^{3}}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^3/x^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.44028, size = 19, normalized size = 1.19 \[ -\frac{{\left (a + \frac{b}{x}\right )}^{4}}{4 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.209471, size = 45, normalized size = 2.81 \[ -\frac{4 \, a^{3} x^{3} + 6 \, a^{2} b x^{2} + 4 \, a b^{2} x + b^{3}}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.4168, size = 36, normalized size = 2.25 \[ - \frac{4 a^{3} x^{3} + 6 a^{2} b x^{2} + 4 a b^{2} x + b^{3}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**3/x**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.229494, size = 19, normalized size = 1.19 \[ -\frac{{\left (a + \frac{b}{x}\right )}^{4}}{4 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^2,x, algorithm="giac")
[Out]