Optimal. Leaf size=33 \[ \frac{1}{5} x^5 (a B+A b)+\frac{1}{4} a A x^4+\frac{1}{6} b B x^6 \]
[Out]
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Rubi [A] time = 0.0746319, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ \frac{1}{5} x^5 (a B+A b)+\frac{1}{4} a A x^4+\frac{1}{6} b B x^6 \]
Antiderivative was successfully verified.
[In] Int[x^3*(a + b*x)*(A + B*x),x]
[Out]
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Rubi in Sympy [A] time = 10.1892, size = 29, normalized size = 0.88 \[ \frac{A a x^{4}}{4} + \frac{B b x^{6}}{6} + x^{5} \left (\frac{A b}{5} + \frac{B a}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(b*x+a)*(B*x+A),x)
[Out]
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Mathematica [A] time = 0.00733753, size = 33, normalized size = 1. \[ \frac{1}{5} x^5 (a B+A b)+\frac{1}{4} a A x^4+\frac{1}{6} b B x^6 \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(a + b*x)*(A + B*x),x]
[Out]
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Maple [A] time = 0.002, size = 28, normalized size = 0.9 \[{\frac{aA{x}^{4}}{4}}+{\frac{ \left ( Ab+Ba \right ){x}^{5}}{5}}+{\frac{bB{x}^{6}}{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(b*x+a)*(B*x+A),x)
[Out]
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Maxima [A] time = 1.35277, size = 36, normalized size = 1.09 \[ \frac{1}{6} \, B b x^{6} + \frac{1}{4} \, A a x^{4} + \frac{1}{5} \,{\left (B a + A b\right )} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.18226, size = 1, normalized size = 0.03 \[ \frac{1}{6} x^{6} b B + \frac{1}{5} x^{5} a B + \frac{1}{5} x^{5} b A + \frac{1}{4} x^{4} a A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.084536, size = 29, normalized size = 0.88 \[ \frac{A a x^{4}}{4} + \frac{B b x^{6}}{6} + x^{5} \left (\frac{A b}{5} + \frac{B a}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(b*x+a)*(B*x+A),x)
[Out]
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GIAC/XCAS [A] time = 0.229772, size = 39, normalized size = 1.18 \[ \frac{1}{6} \, B b x^{6} + \frac{1}{5} \, B a x^{5} + \frac{1}{5} \, A b x^{5} + \frac{1}{4} \, A a x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)*x^3,x, algorithm="giac")
[Out]