Optimal. Leaf size=47 \[ \frac{1}{3} x^3 (a B+A b)+\frac{1}{2} a A x^2+\frac{1}{4} x^4 (A c+b B)+\frac{1}{5} B c x^5 \]
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Rubi [A] time = 0.0889566, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{1}{3} x^3 (a B+A b)+\frac{1}{2} a A x^2+\frac{1}{4} x^4 (A c+b B)+\frac{1}{5} B c x^5 \]
Antiderivative was successfully verified.
[In] Int[x*(A + B*x)*(a + b*x + c*x^2),x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ A a \int x\, dx + \frac{B c x^{5}}{5} + x^{4} \left (\frac{A c}{4} + \frac{B b}{4}\right ) + x^{3} \left (\frac{A b}{3} + \frac{B a}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(B*x+A)*(c*x**2+b*x+a),x)
[Out]
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Mathematica [A] time = 0.0234906, size = 41, normalized size = 0.87 \[ \frac{1}{60} x^2 \left (20 x (a B+A b)+30 a A+15 x^2 (A c+b B)+12 B c x^3\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x*(A + B*x)*(a + b*x + c*x^2),x]
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Maple [A] time = 0., size = 40, normalized size = 0.9 \[{\frac{aA{x}^{2}}{2}}+{\frac{ \left ( Ab+Ba \right ){x}^{3}}{3}}+{\frac{ \left ( Ac+Bb \right ){x}^{4}}{4}}+{\frac{Bc{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(B*x+A)*(c*x^2+b*x+a),x)
[Out]
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Maxima [A] time = 0.686295, size = 53, normalized size = 1.13 \[ \frac{1}{5} \, B c x^{5} + \frac{1}{4} \,{\left (B b + A c\right )} x^{4} + \frac{1}{2} \, A a x^{2} + \frac{1}{3} \,{\left (B a + A b\right )} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.243209, size = 1, normalized size = 0.02 \[ \frac{1}{5} x^{5} c B + \frac{1}{4} x^{4} b B + \frac{1}{4} x^{4} c A + \frac{1}{3} x^{3} a B + \frac{1}{3} x^{3} b A + \frac{1}{2} x^{2} a A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.093251, size = 42, normalized size = 0.89 \[ \frac{A a x^{2}}{2} + \frac{B c x^{5}}{5} + x^{4} \left (\frac{A c}{4} + \frac{B b}{4}\right ) + x^{3} \left (\frac{A b}{3} + \frac{B a}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(B*x+A)*(c*x**2+b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.266099, size = 58, normalized size = 1.23 \[ \frac{1}{5} \, B c x^{5} + \frac{1}{4} \, B b x^{4} + \frac{1}{4} \, A c x^{4} + \frac{1}{3} \, B a x^{3} + \frac{1}{3} \, A b x^{3} + \frac{1}{2} \, A a x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)*x,x, algorithm="giac")
[Out]