Optimal. Leaf size=17 \[ -\frac{(a+b x)^2}{2 a x^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0100279, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ -\frac{(a+b x)^2}{2 a x^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)/x^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.55554, size = 10, normalized size = 0.59 \[ - \frac{a}{2 x^{2}} - \frac{b}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)/x**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00198773, size = 15, normalized size = 0.88 \[ -\frac{a}{2 x^2}-\frac{b}{x} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)/x^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 14, normalized size = 0.8 \[ -{\frac{b}{x}}-{\frac{a}{2\,{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)/x^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33047, size = 15, normalized size = 0.88 \[ -\frac{2 \, b x + a}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/x^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.191097, size = 15, normalized size = 0.88 \[ -\frac{2 \, b x + a}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/x^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.994592, size = 12, normalized size = 0.71 \[ - \frac{a + 2 b x}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)/x**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.210818, size = 15, normalized size = 0.88 \[ -\frac{2 \, b x + a}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/x^3,x, algorithm="giac")
[Out]