Optimal. Leaf size=37 \[ -\frac{a^3}{3 x^3}-\frac{3 a^2 b}{x}+3 a b^2 x+\frac{b^3 x^3}{3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0404206, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{a^3}{3 x^3}-\frac{3 a^2 b}{x}+3 a b^2 x+\frac{b^3 x^3}{3} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^3/x^4,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 7.12991, size = 32, normalized size = 0.86 \[ - \frac{a^{3}}{3 x^{3}} - \frac{3 a^{2} b}{x} + 3 a b^{2} x + \frac{b^{3} x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**3/x**4,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00699355, size = 37, normalized size = 1. \[ -\frac{a^3}{3 x^3}-\frac{3 a^2 b}{x}+3 a b^2 x+\frac{b^3 x^3}{3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^3/x^4,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.009, size = 34, normalized size = 0.9 \[ -{\frac{{a}^{3}}{3\,{x}^{3}}}-3\,{\frac{{a}^{2}b}{x}}+3\,a{b}^{2}x+{\frac{{b}^{3}{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^3/x^4,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34259, size = 46, normalized size = 1.24 \[ \frac{1}{3} \, b^{3} x^{3} + 3 \, a b^{2} x - \frac{9 \, a^{2} b x^{2} + a^{3}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^4,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.205746, size = 49, normalized size = 1.32 \[ \frac{b^{3} x^{6} + 9 \, a b^{2} x^{4} - 9 \, a^{2} b x^{2} - a^{3}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^4,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.20199, size = 34, normalized size = 0.92 \[ 3 a b^{2} x + \frac{b^{3} x^{3}}{3} - \frac{a^{3} + 9 a^{2} b x^{2}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**3/x**4,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.20782, size = 46, normalized size = 1.24 \[ \frac{1}{3} \, b^{3} x^{3} + 3 \, a b^{2} x - \frac{9 \, a^{2} b x^{2} + a^{3}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^4,x, algorithm="giac")
[Out]