Optimal. Leaf size=33 \[ \frac{1}{5} x^5 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{7} b B x^7 \]
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Rubi [A] time = 0.0602547, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ \frac{1}{5} x^5 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{7} b B x^7 \]
Antiderivative was successfully verified.
[In] Int[x^2*(a + b*x^2)*(A + B*x^2),x]
[Out]
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Rubi in Sympy [A] time = 10.0854, size = 29, normalized size = 0.88 \[ \frac{A a x^{3}}{3} + \frac{B b x^{7}}{7} + x^{5} \left (\frac{A b}{5} + \frac{B a}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(b*x**2+a)*(B*x**2+A),x)
[Out]
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Mathematica [A] time = 0.0100798, size = 33, normalized size = 1. \[ \frac{1}{5} x^5 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{7} b B x^7 \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(a + b*x^2)*(A + B*x^2),x]
[Out]
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Maple [A] time = 0.001, size = 28, normalized size = 0.9 \[{\frac{aA{x}^{3}}{3}}+{\frac{ \left ( Ab+Ba \right ){x}^{5}}{5}}+{\frac{bB{x}^{7}}{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(b*x^2+a)*(B*x^2+A),x)
[Out]
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Maxima [A] time = 1.37163, size = 36, normalized size = 1.09 \[ \frac{1}{7} \, B b x^{7} + \frac{1}{5} \,{\left (B a + A b\right )} x^{5} + \frac{1}{3} \, A a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.20973, size = 1, normalized size = 0.03 \[ \frac{1}{7} x^{7} b B + \frac{1}{5} x^{5} a B + \frac{1}{5} x^{5} b A + \frac{1}{3} x^{3} a A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.082555, size = 29, normalized size = 0.88 \[ \frac{A a x^{3}}{3} + \frac{B b x^{7}}{7} + x^{5} \left (\frac{A b}{5} + \frac{B a}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(b*x**2+a)*(B*x**2+A),x)
[Out]
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GIAC/XCAS [A] time = 0.215866, size = 39, normalized size = 1.18 \[ \frac{1}{7} \, B b x^{7} + \frac{1}{5} \, B a x^{5} + \frac{1}{5} \, A b x^{5} + \frac{1}{3} \, A a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)*x^2,x, algorithm="giac")
[Out]