Optimal. Leaf size=30 \[ \frac{b^2 x^5}{5}+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9} \]
[Out]
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Rubi [A] time = 0.0350977, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{b^2 x^5}{5}+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9} \]
Antiderivative was successfully verified.
[In] Int[(b*x^2 + c*x^4)^2,x]
[Out]
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Rubi in Sympy [A] time = 10.835, size = 26, normalized size = 0.87 \[ \frac{b^{2} x^{5}}{5} + \frac{2 b c x^{7}}{7} + \frac{c^{2} x^{9}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**2)**2,x)
[Out]
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Mathematica [A] time = 0.00288497, size = 30, normalized size = 1. \[ \frac{b^2 x^5}{5}+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^2 + c*x^4)^2,x]
[Out]
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Maple [A] time = 0.001, size = 25, normalized size = 0.8 \[{\frac{{b}^{2}{x}^{5}}{5}}+{\frac{2\,bc{x}^{7}}{7}}+{\frac{{c}^{2}{x}^{9}}{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^2)^2,x)
[Out]
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Maxima [A] time = 0.685842, size = 32, normalized size = 1.07 \[ \frac{1}{9} \, c^{2} x^{9} + \frac{2}{7} \, b c x^{7} + \frac{1}{5} \, b^{2} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.232586, size = 1, normalized size = 0.03 \[ \frac{1}{9} x^{9} c^{2} + \frac{2}{7} x^{7} c b + \frac{1}{5} x^{5} b^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.089564, size = 26, normalized size = 0.87 \[ \frac{b^{2} x^{5}}{5} + \frac{2 b c x^{7}}{7} + \frac{c^{2} x^{9}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**2)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.266483, size = 32, normalized size = 1.07 \[ \frac{1}{9} \, c^{2} x^{9} + \frac{2}{7} \, b c x^{7} + \frac{1}{5} \, b^{2} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2,x, algorithm="giac")
[Out]