Optimal. Leaf size=55 \[ \frac{1}{2} a^2 A x^2+\frac{1}{4} b x^4 (2 a B+A b)+\frac{1}{3} a x^3 (a B+2 A b)+\frac{1}{5} b^2 B x^5 \]
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Rubi [A] time = 0.0815608, antiderivative size = 55, 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 \[ \frac{1}{2} a^2 A x^2+\frac{1}{4} b x^4 (2 a B+A b)+\frac{1}{3} a x^3 (a B+2 A b)+\frac{1}{5} b^2 B x^5 \]
Antiderivative was successfully verified.
[In] Int[x*(a + b*x)^2*(A + B*x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ A a^{2} \int x\, dx + \frac{B b^{2} x^{5}}{5} + \frac{a x^{3} \left (2 A b + B a\right )}{3} + \frac{b x^{4} \left (A b + 2 B a\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(b*x+a)**2*(B*x+A),x)
[Out]
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Mathematica [A] time = 0.015404, size = 50, normalized size = 0.91 \[ \frac{1}{60} x^2 \left (10 a^2 (3 A+2 B x)+10 a b x (4 A+3 B x)+3 b^2 x^2 (5 A+4 B x)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x*(a + b*x)^2*(A + B*x),x]
[Out]
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Maple [A] time = 0.002, size = 52, normalized size = 1. \[{\frac{{b}^{2}B{x}^{5}}{5}}+{\frac{ \left ({b}^{2}A+2\,abB \right ){x}^{4}}{4}}+{\frac{ \left ( 2\,abA+{a}^{2}B \right ){x}^{3}}{3}}+{\frac{{a}^{2}A{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(b*x+a)^2*(B*x+A),x)
[Out]
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Maxima [A] time = 1.33293, size = 69, normalized size = 1.25 \[ \frac{1}{5} \, B b^{2} x^{5} + \frac{1}{2} \, A a^{2} x^{2} + \frac{1}{4} \,{\left (2 \, B a b + A b^{2}\right )} x^{4} + \frac{1}{3} \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^2*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.176305, size = 1, normalized size = 0.02 \[ \frac{1}{5} x^{5} b^{2} B + \frac{1}{2} x^{4} b a B + \frac{1}{4} x^{4} b^{2} A + \frac{1}{3} x^{3} a^{2} B + \frac{2}{3} x^{3} b a A + \frac{1}{2} x^{2} a^{2} A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^2*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.123688, size = 54, normalized size = 0.98 \[ \frac{A a^{2} x^{2}}{2} + \frac{B b^{2} x^{5}}{5} + x^{4} \left (\frac{A b^{2}}{4} + \frac{B a b}{2}\right ) + x^{3} \left (\frac{2 A a b}{3} + \frac{B a^{2}}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(b*x+a)**2*(B*x+A),x)
[Out]
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GIAC/XCAS [A] time = 0.342007, size = 72, normalized size = 1.31 \[ \frac{1}{5} \, B b^{2} x^{5} + \frac{1}{2} \, B a b x^{4} + \frac{1}{4} \, A b^{2} x^{4} + \frac{1}{3} \, B a^{2} x^{3} + \frac{2}{3} \, A a b x^{3} + \frac{1}{2} \, A a^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^2*x,x, algorithm="giac")
[Out]