Optimal. Leaf size=37 \[ \frac{1}{2} a A x^2+\frac{1}{3} a B x^3+\frac{1}{4} A c x^4+\frac{1}{5} B c x^5 \]
[Out]
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Rubi [A] time = 0.0580558, antiderivative size = 37, 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 \[ \frac{1}{2} a A x^2+\frac{1}{3} a B x^3+\frac{1}{4} A c x^4+\frac{1}{5} B c x^5 \]
Antiderivative was successfully verified.
[In] Int[x*(A + B*x)*(a + c*x^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ A a \int x\, dx + \frac{A c x^{4}}{4} + \frac{B a x^{3}}{3} + \frac{B c x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(B*x+A)*(c*x**2+a),x)
[Out]
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Mathematica [A] time = 0.00298, size = 37, normalized size = 1. \[ \frac{1}{2} a A x^2+\frac{1}{3} a B x^3+\frac{1}{4} A c x^4+\frac{1}{5} B c x^5 \]
Antiderivative was successfully verified.
[In] Integrate[x*(A + B*x)*(a + c*x^2),x]
[Out]
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Maple [A] time = 0., size = 30, normalized size = 0.8 \[{\frac{aA{x}^{2}}{2}}+{\frac{aB{x}^{3}}{3}}+{\frac{Ac{x}^{4}}{4}}+{\frac{Bc{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(B*x+A)*(c*x^2+a),x)
[Out]
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Maxima [A] time = 0.684263, size = 39, normalized size = 1.05 \[ \frac{1}{5} \, B c x^{5} + \frac{1}{4} \, A c x^{4} + \frac{1}{3} \, B a x^{3} + \frac{1}{2} \, A a x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.255056, size = 1, normalized size = 0.03 \[ \frac{1}{5} x^{5} c B + \frac{1}{4} x^{4} c A + \frac{1}{3} x^{3} a B + \frac{1}{2} x^{2} a A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.077932, size = 32, normalized size = 0.86 \[ \frac{A a x^{2}}{2} + \frac{A c x^{4}}{4} + \frac{B a x^{3}}{3} + \frac{B c x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(B*x+A)*(c*x**2+a),x)
[Out]
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GIAC/XCAS [A] time = 0.266729, size = 39, normalized size = 1.05 \[ \frac{1}{5} \, B c x^{5} + \frac{1}{4} \, A c x^{4} + \frac{1}{3} \, B a x^{3} + \frac{1}{2} \, A a x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)*x,x, algorithm="giac")
[Out]