Optimal. Leaf size=49 \[ a^2 x+\frac{1}{5} x^5 \left (2 a c+b^2\right )+\frac{2}{3} a b x^3+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9} \]
[Out]
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Rubi [A] time = 0.0478887, antiderivative size = 49, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ a^2 x+\frac{1}{5} x^5 \left (2 a c+b^2\right )+\frac{2}{3} a b x^3+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2 + c*x^4)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{2 a b x^{3}}{3} + \frac{2 b c x^{7}}{7} + \frac{c^{2} x^{9}}{9} + x^{5} \left (\frac{2 a c}{5} + \frac{b^{2}}{5}\right ) + \int a^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**2+a)**2,x)
[Out]
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Mathematica [A] time = 0.00918063, size = 49, normalized size = 1. \[ a^2 x+\frac{1}{5} x^5 \left (2 a c+b^2\right )+\frac{2}{3} a b x^3+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2 + c*x^4)^2,x]
[Out]
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Maple [A] time = 0.001, size = 42, normalized size = 0.9 \[{a}^{2}x+{\frac{2\,ab{x}^{3}}{3}}+{\frac{ \left ( 2\,ac+{b}^{2} \right ){x}^{5}}{5}}+{\frac{2\,bc{x}^{7}}{7}}+{\frac{{c}^{2}{x}^{9}}{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^2+a)^2,x)
[Out]
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Maxima [A] time = 0.730107, size = 61, normalized size = 1.24 \[ \frac{1}{9} \, c^{2} x^{9} + \frac{2}{7} \, b c x^{7} + \frac{1}{5} \, b^{2} x^{5} + a^{2} x + \frac{2}{15} \,{\left (3 \, c x^{5} + 5 \, b x^{3}\right )} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.237615, size = 1, normalized size = 0.02 \[ \frac{1}{9} x^{9} c^{2} + \frac{2}{7} x^{7} c b + \frac{1}{5} x^{5} b^{2} + \frac{2}{5} x^{5} c a + \frac{2}{3} x^{3} b a + x a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.123324, size = 48, normalized size = 0.98 \[ a^{2} x + \frac{2 a b x^{3}}{3} + \frac{2 b c x^{7}}{7} + \frac{c^{2} x^{9}}{9} + x^{5} \left (\frac{2 a c}{5} + \frac{b^{2}}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**2+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.268892, size = 58, normalized size = 1.18 \[ \frac{1}{9} \, c^{2} x^{9} + \frac{2}{7} \, b c x^{7} + \frac{1}{5} \, b^{2} x^{5} + \frac{2}{5} \, a c x^{5} + \frac{2}{3} \, a b x^{3} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2,x, algorithm="giac")
[Out]