Optimal. Leaf size=53 \[ -\frac{a^2}{10 b^3 \left (a+b x^2\right )^5}+\frac{a}{4 b^3 \left (a+b x^2\right )^4}-\frac{1}{6 b^3 \left (a+b x^2\right )^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.112587, antiderivative size = 53, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ -\frac{a^2}{10 b^3 \left (a+b x^2\right )^5}+\frac{a}{4 b^3 \left (a+b x^2\right )^4}-\frac{1}{6 b^3 \left (a+b x^2\right )^3} \]
Antiderivative was successfully verified.
[In] Int[x^5/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 19.4327, size = 46, normalized size = 0.87 \[ - \frac{a^{2}}{10 b^{3} \left (a + b x^{2}\right )^{5}} + \frac{a}{4 b^{3} \left (a + b x^{2}\right )^{4}} - \frac{1}{6 b^{3} \left (a + b x^{2}\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5/(b**2*x**4+2*a*b*x**2+a**2)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0243526, size = 35, normalized size = 0.66 \[ -\frac{a^2+5 a b x^2+10 b^2 x^4}{60 b^3 \left (a+b x^2\right )^5} \]
Antiderivative was successfully verified.
[In] Integrate[x^5/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.011, size = 48, normalized size = 0.9 \[ -{\frac{{a}^{2}}{10\,{b}^{3} \left ( b{x}^{2}+a \right ) ^{5}}}+{\frac{a}{4\,{b}^{3} \left ( b{x}^{2}+a \right ) ^{4}}}-{\frac{1}{6\,{b}^{3} \left ( b{x}^{2}+a \right ) ^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5/(b^2*x^4+2*a*b*x^2+a^2)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.700852, size = 108, normalized size = 2.04 \[ -\frac{10 \, b^{2} x^{4} + 5 \, a b x^{2} + a^{2}}{60 \,{\left (b^{8} x^{10} + 5 \, a b^{7} x^{8} + 10 \, a^{2} b^{6} x^{6} + 10 \, a^{3} b^{5} x^{4} + 5 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b^2*x^4 + 2*a*b*x^2 + a^2)^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.26238, size = 108, normalized size = 2.04 \[ -\frac{10 \, b^{2} x^{4} + 5 \, a b x^{2} + a^{2}}{60 \,{\left (b^{8} x^{10} + 5 \, a b^{7} x^{8} + 10 \, a^{2} b^{6} x^{6} + 10 \, a^{3} b^{5} x^{4} + 5 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b^2*x^4 + 2*a*b*x^2 + a^2)^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 3.96229, size = 83, normalized size = 1.57 \[ - \frac{a^{2} + 5 a b x^{2} + 10 b^{2} x^{4}}{60 a^{5} b^{3} + 300 a^{4} b^{4} x^{2} + 600 a^{3} b^{5} x^{4} + 600 a^{2} b^{6} x^{6} + 300 a b^{7} x^{8} + 60 b^{8} x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5/(b**2*x**4+2*a*b*x**2+a**2)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.270173, size = 45, normalized size = 0.85 \[ -\frac{10 \, b^{2} x^{4} + 5 \, a b x^{2} + a^{2}}{60 \,{\left (b x^{2} + a\right )}^{5} b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b^2*x^4 + 2*a*b*x^2 + a^2)^3,x, algorithm="giac")
[Out]