Optimal. Leaf size=50 \[ -\frac{a^4}{3 x^3}-\frac{4 a^3 b}{x}+6 a^2 b^2 x+\frac{4}{3} a b^3 x^3+\frac{b^4 x^5}{5} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0663837, antiderivative size = 50, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ -\frac{a^4}{3 x^3}-\frac{4 a^3 b}{x}+6 a^2 b^2 x+\frac{4}{3} a b^3 x^3+\frac{b^4 x^5}{5} \]
Antiderivative was successfully verified.
[In] Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^4,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 17.3557, size = 46, normalized size = 0.92 \[ - \frac{a^{4}}{3 x^{3}} - \frac{4 a^{3} b}{x} + 6 a^{2} b^{2} x + \frac{4 a b^{3} x^{3}}{3} + \frac{b^{4} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**4,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0105393, size = 50, normalized size = 1. \[ -\frac{a^4}{3 x^3}-\frac{4 a^3 b}{x}+6 a^2 b^2 x+\frac{4}{3} a b^3 x^3+\frac{b^4 x^5}{5} \]
Antiderivative was successfully verified.
[In] Integrate[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^4,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 45, normalized size = 0.9 \[ -{\frac{{a}^{4}}{3\,{x}^{3}}}-4\,{\frac{{a}^{3}b}{x}}+6\,{a}^{2}{b}^{2}x+{\frac{4\,a{b}^{3}{x}^{3}}{3}}+{\frac{{b}^{4}{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b^2*x^4+2*a*b*x^2+a^2)^2/x^4,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.703725, size = 61, normalized size = 1.22 \[ \frac{1}{5} \, b^{4} x^{5} + \frac{4}{3} \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x - \frac{12 \, a^{3} b x^{2} + a^{4}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^2/x^4,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.256249, size = 65, normalized size = 1.3 \[ \frac{3 \, b^{4} x^{8} + 20 \, a b^{3} x^{6} + 90 \, a^{2} b^{2} x^{4} - 60 \, a^{3} b x^{2} - 5 \, a^{4}}{15 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^2/x^4,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.17604, size = 48, normalized size = 0.96 \[ 6 a^{2} b^{2} x + \frac{4 a b^{3} x^{3}}{3} + \frac{b^{4} x^{5}}{5} - \frac{a^{4} + 12 a^{3} b x^{2}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**4,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.268362, size = 61, normalized size = 1.22 \[ \frac{1}{5} \, b^{4} x^{5} + \frac{4}{3} \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x - \frac{12 \, a^{3} b x^{2} + a^{4}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^2/x^4,x, algorithm="giac")
[Out]