Optimal. Leaf size=33 \[ \frac{1}{4} x^4 (A c+b B)+\frac{1}{3} A b x^3+\frac{1}{5} B c x^5 \]
[Out]
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Rubi [A] time = 0.0720951, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{1}{4} x^4 (A c+b B)+\frac{1}{3} A b x^3+\frac{1}{5} B c x^5 \]
Antiderivative was successfully verified.
[In] Int[x*(A + B*x)*(b*x + c*x^2),x]
[Out]
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Rubi in Sympy [A] time = 7.19502, size = 29, normalized size = 0.88 \[ \frac{A b x^{3}}{3} + \frac{B c x^{5}}{5} + x^{4} \left (\frac{A c}{4} + \frac{B b}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(B*x+A)*(c*x**2+b*x),x)
[Out]
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Mathematica [A] time = 0.00761144, size = 33, normalized size = 1. \[ \frac{1}{4} x^4 (A c+b B)+\frac{1}{3} A b x^3+\frac{1}{5} B c x^5 \]
Antiderivative was successfully verified.
[In] Integrate[x*(A + B*x)*(b*x + c*x^2),x]
[Out]
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Maple [A] time = 0.001, size = 28, normalized size = 0.9 \[{\frac{Ab{x}^{3}}{3}}+{\frac{ \left ( Ac+Bb \right ){x}^{4}}{4}}+{\frac{Bc{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(B*x+A)*(c*x^2+b*x),x)
[Out]
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Maxima [A] time = 0.695291, size = 36, normalized size = 1.09 \[ \frac{1}{5} \, B c x^{5} + \frac{1}{3} \, A b x^{3} + \frac{1}{4} \,{\left (B b + A c\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*(B*x + A)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.250824, size = 1, normalized size = 0.03 \[ \frac{1}{5} x^{5} c B + \frac{1}{4} x^{4} b B + \frac{1}{4} x^{4} c A + \frac{1}{3} x^{3} b A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*(B*x + A)*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.084366, size = 29, normalized size = 0.88 \[ \frac{A b x^{3}}{3} + \frac{B c x^{5}}{5} + x^{4} \left (\frac{A c}{4} + \frac{B b}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(B*x+A)*(c*x**2+b*x),x)
[Out]
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GIAC/XCAS [A] time = 0.266552, size = 39, normalized size = 1.18 \[ \frac{1}{5} \, B c x^{5} + \frac{1}{4} \, B b x^{4} + \frac{1}{4} \, A c x^{4} + \frac{1}{3} \, A b x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*(B*x + A)*x,x, algorithm="giac")
[Out]