Optimal. Leaf size=55 \[ \frac{1}{3} a^2 c x^3+\frac{1}{7} b x^7 (2 a d+b c)+\frac{1}{5} a x^5 (a d+2 b c)+\frac{1}{9} b^2 d x^9 \]
[Out]
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Rubi [A] time = 0.106369, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{1}{3} a^2 c x^3+\frac{1}{7} b x^7 (2 a d+b c)+\frac{1}{5} a x^5 (a d+2 b c)+\frac{1}{9} b^2 d x^9 \]
Antiderivative was successfully verified.
[In] Int[x^2*(a + b*x^2)^2*(c + d*x^2),x]
[Out]
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Rubi in Sympy [A] time = 16.0235, size = 49, normalized size = 0.89 \[ \frac{a^{2} c x^{3}}{3} + \frac{a x^{5} \left (a d + 2 b c\right )}{5} + \frac{b^{2} d x^{9}}{9} + \frac{b x^{7} \left (2 a d + b c\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(b*x**2+a)**2*(d*x**2+c),x)
[Out]
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Mathematica [A] time = 0.0125667, size = 55, normalized size = 1. \[ \frac{1}{3} a^2 c x^3+\frac{1}{7} b x^7 (2 a d+b c)+\frac{1}{5} a x^5 (a d+2 b c)+\frac{1}{9} b^2 d x^9 \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(a + b*x^2)^2*(c + d*x^2),x]
[Out]
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Maple [A] time = 0.002, size = 52, normalized size = 1. \[{\frac{{b}^{2}d{x}^{9}}{9}}+{\frac{ \left ( 2\,abd+{b}^{2}c \right ){x}^{7}}{7}}+{\frac{ \left ({a}^{2}d+2\,abc \right ){x}^{5}}{5}}+{\frac{{a}^{2}c{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(b*x^2+a)^2*(d*x^2+c),x)
[Out]
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Maxima [A] time = 1.35105, size = 69, normalized size = 1.25 \[ \frac{1}{9} \, b^{2} d x^{9} + \frac{1}{7} \,{\left (b^{2} c + 2 \, a b d\right )} x^{7} + \frac{1}{3} \, a^{2} c x^{3} + \frac{1}{5} \,{\left (2 \, a b c + a^{2} d\right )} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^2*(d*x^2 + c)*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201392, size = 1, normalized size = 0.02 \[ \frac{1}{9} x^{9} d b^{2} + \frac{1}{7} x^{7} c b^{2} + \frac{2}{7} x^{7} d b a + \frac{2}{5} x^{5} c b a + \frac{1}{5} x^{5} d a^{2} + \frac{1}{3} x^{3} c a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^2*(d*x^2 + c)*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.114664, size = 56, normalized size = 1.02 \[ \frac{a^{2} c x^{3}}{3} + \frac{b^{2} d x^{9}}{9} + x^{7} \left (\frac{2 a b d}{7} + \frac{b^{2} c}{7}\right ) + x^{5} \left (\frac{a^{2} d}{5} + \frac{2 a b c}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(b*x**2+a)**2*(d*x**2+c),x)
[Out]
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GIAC/XCAS [A] time = 0.246199, size = 72, normalized size = 1.31 \[ \frac{1}{9} \, b^{2} d x^{9} + \frac{1}{7} \, b^{2} c x^{7} + \frac{2}{7} \, a b d x^{7} + \frac{2}{5} \, a b c x^{5} + \frac{1}{5} \, a^{2} d x^{5} + \frac{1}{3} \, a^{2} c x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^2*(d*x^2 + c)*x^2,x, algorithm="giac")
[Out]