Optimal. Leaf size=16 \[ \frac{\left (a+b x^2\right )^5}{10 b} \]
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Rubi [A] time = 0.017018, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{\left (a+b x^2\right )^5}{10 b} \]
Antiderivative was successfully verified.
[In] Int[x*(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]
[Out]
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Rubi in Sympy [A] time = 6.66098, size = 10, normalized size = 0.62 \[ \frac{\left (a + b x^{2}\right )^{5}}{10 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(b**2*x**4+2*a*b*x**2+a**2)**2,x)
[Out]
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Mathematica [A] time = 0.0042337, size = 16, normalized size = 1. \[ \frac{\left (a+b x^2\right )^5}{10 b} \]
Antiderivative was successfully verified.
[In] Integrate[x*(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]
[Out]
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Maple [B] time = 0.001, size = 45, normalized size = 2.8 \[{\frac{{b}^{4}{x}^{10}}{10}}+{\frac{a{b}^{3}{x}^{8}}{2}}+{a}^{2}{b}^{2}{x}^{6}+{a}^{3}b{x}^{4}+{\frac{{a}^{4}{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(b^2*x^4+2*a*b*x^2+a^2)^2,x)
[Out]
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Maxima [A] time = 0.702543, size = 59, normalized size = 3.69 \[ \frac{1}{10} \, b^{4} x^{10} + \frac{1}{2} \, a b^{3} x^{8} + a^{2} b^{2} x^{6} + a^{3} b x^{4} + \frac{1}{2} \, a^{4} x^{2} \]
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,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.241912, size = 1, normalized size = 0.06 \[ \frac{1}{10} x^{10} b^{4} + \frac{1}{2} x^{8} b^{3} a + x^{6} b^{2} a^{2} + x^{4} b a^{3} + \frac{1}{2} x^{2} a^{4} \]
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,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.108162, size = 44, normalized size = 2.75 \[ \frac{a^{4} x^{2}}{2} + a^{3} b x^{4} + a^{2} b^{2} x^{6} + \frac{a b^{3} x^{8}}{2} + \frac{b^{4} x^{10}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(b**2*x**4+2*a*b*x**2+a**2)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.267687, size = 59, normalized size = 3.69 \[ \frac{1}{10} \, b^{4} x^{10} + \frac{1}{2} \, a b^{3} x^{8} + a^{2} b^{2} x^{6} + a^{3} b x^{4} + \frac{1}{2} \, a^{4} x^{2} \]
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,x, algorithm="giac")
[Out]