Optimal. Leaf size=28 \[ \frac{1}{5} x^5 (a d+b c)+a c x+\frac{1}{9} b d x^9 \]
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Rubi [A] time = 0.0381033, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{1}{5} x^5 (a d+b c)+a c x+\frac{1}{9} b d x^9 \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^4)*(c + d*x^4),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{b d x^{9}}{9} + c \int a\, dx + x^{5} \left (\frac{a d}{5} + \frac{b c}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**4+a)*(d*x**4+c),x)
[Out]
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Mathematica [A] time = 0.00912336, size = 28, normalized size = 1. \[ \frac{1}{5} x^5 (a d+b c)+a c x+\frac{1}{9} b d x^9 \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^4)*(c + d*x^4),x]
[Out]
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Maple [A] time = 0.001, size = 25, normalized size = 0.9 \[ acx+{\frac{ \left ( ad+bc \right ){x}^{5}}{5}}+{\frac{bd{x}^{9}}{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^4+a)*(d*x^4+c),x)
[Out]
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Maxima [A] time = 1.36402, size = 32, normalized size = 1.14 \[ \frac{1}{9} \, b d x^{9} + \frac{1}{5} \,{\left (b c + a d\right )} x^{5} + a c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)*(d*x^4 + c),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.188586, size = 1, normalized size = 0.04 \[ \frac{1}{9} x^{9} d b + \frac{1}{5} x^{5} c b + \frac{1}{5} x^{5} d a + x c a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)*(d*x^4 + c),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.071019, size = 26, normalized size = 0.93 \[ a c x + \frac{b d x^{9}}{9} + x^{5} \left (\frac{a d}{5} + \frac{b c}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**4+a)*(d*x**4+c),x)
[Out]
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GIAC/XCAS [A] time = 0.210788, size = 35, normalized size = 1.25 \[ \frac{1}{9} \, b d x^{9} + \frac{1}{5} \, b c x^{5} + \frac{1}{5} \, a d x^{5} + a c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)*(d*x^4 + c),x, algorithm="giac")
[Out]