Optimal. Leaf size=33 \[ \frac{1}{5} x^5 (A c+b B)+\frac{1}{3} A b x^3+\frac{1}{7} B c x^7 \]
[Out]
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Rubi [A] time = 0.0650756, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ \frac{1}{5} x^5 (A c+b B)+\frac{1}{3} A b x^3+\frac{1}{7} B c x^7 \]
Antiderivative was successfully verified.
[In] Int[(A + B*x^2)*(b*x^2 + c*x^4),x]
[Out]
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Rubi in Sympy [A] time = 10.2311, size = 29, normalized size = 0.88 \[ \frac{A b x^{3}}{3} + \frac{B c x^{7}}{7} + x^{5} \left (\frac{A c}{5} + \frac{B b}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x**2+A)*(c*x**4+b*x**2),x)
[Out]
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Mathematica [A] time = 0.00839475, size = 33, normalized size = 1. \[ \frac{1}{5} x^5 (A c+b B)+\frac{1}{3} A b x^3+\frac{1}{7} B c x^7 \]
Antiderivative was successfully verified.
[In] Integrate[(A + B*x^2)*(b*x^2 + c*x^4),x]
[Out]
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Maple [A] time = 0.002, size = 28, normalized size = 0.9 \[{\frac{Ab{x}^{3}}{3}}+{\frac{ \left ( Ac+Bb \right ){x}^{5}}{5}}+{\frac{Bc{x}^{7}}{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x^2+A)*(c*x^4+b*x^2),x)
[Out]
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Maxima [A] time = 1.37454, size = 36, normalized size = 1.09 \[ \frac{1}{7} \, B c x^{7} + \frac{1}{5} \,{\left (B b + A c\right )} x^{5} + \frac{1}{3} \, A b x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)*(B*x^2 + A),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.199377, size = 1, normalized size = 0.03 \[ \frac{1}{7} x^{7} c B + \frac{1}{5} x^{5} b B + \frac{1}{5} x^{5} c A + \frac{1}{3} x^{3} b A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)*(B*x^2 + A),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.040552, size = 29, normalized size = 0.88 \[ \frac{A b x^{3}}{3} + \frac{B c x^{7}}{7} + x^{5} \left (\frac{A c}{5} + \frac{B b}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x**2+A)*(c*x**4+b*x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.230352, size = 39, normalized size = 1.18 \[ \frac{1}{7} \, B c x^{7} + \frac{1}{5} \, B b x^{5} + \frac{1}{5} \, A c x^{5} + \frac{1}{3} \, A b x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)*(B*x^2 + A),x, algorithm="giac")
[Out]