Optimal. Leaf size=101 \[ \frac{1}{3} a^2 A x^3+\frac{1}{6} x^6 \left (2 a B c+2 A b c+b^2 B\right )+\frac{1}{5} x^5 \left (A \left (2 a c+b^2\right )+2 a b B\right )+\frac{1}{4} a x^4 (a B+2 A b)+\frac{1}{7} c x^7 (A c+2 b B)+\frac{1}{8} B c^2 x^8 \]
[Out]
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Rubi [A] time = 0.286911, antiderivative size = 101, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048 \[ \frac{1}{3} a^2 A x^3+\frac{1}{6} x^6 \left (2 a B c+2 A b c+b^2 B\right )+\frac{1}{5} x^5 \left (A \left (2 a c+b^2\right )+2 a b B\right )+\frac{1}{4} a x^4 (a B+2 A b)+\frac{1}{7} c x^7 (A c+2 b B)+\frac{1}{8} B c^2 x^8 \]
Antiderivative was successfully verified.
[In] Int[x^2*(A + B*x)*(a + b*x + c*x^2)^2,x]
[Out]
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Rubi in Sympy [A] time = 23.2314, size = 100, normalized size = 0.99 \[ \frac{A a^{2} x^{3}}{3} + \frac{B c^{2} x^{8}}{8} + \frac{a x^{4} \left (2 A b + B a\right )}{4} + \frac{c x^{7} \left (A c + 2 B b\right )}{7} + x^{6} \left (\frac{A b c}{3} + \frac{B a c}{3} + \frac{B b^{2}}{6}\right ) + x^{5} \left (\frac{2 A a c}{5} + \frac{A b^{2}}{5} + \frac{2 B a b}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(B*x+A)*(c*x**2+b*x+a)**2,x)
[Out]
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Mathematica [A] time = 0.0518696, size = 101, normalized size = 1. \[ \frac{1}{3} a^2 A x^3+\frac{1}{6} x^6 \left (2 a B c+2 A b c+b^2 B\right )+\frac{1}{5} x^5 \left (2 a A c+2 a b B+A b^2\right )+\frac{1}{4} a x^4 (a B+2 A b)+\frac{1}{7} c x^7 (A c+2 b B)+\frac{1}{8} B c^2 x^8 \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(A + B*x)*(a + b*x + c*x^2)^2,x]
[Out]
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Maple [A] time = 0.002, size = 94, normalized size = 0.9 \[{\frac{B{c}^{2}{x}^{8}}{8}}+{\frac{ \left ( A{c}^{2}+2\,Bbc \right ){x}^{7}}{7}}+{\frac{ \left ( 2\,Abc+B \left ( 2\,ac+{b}^{2} \right ) \right ){x}^{6}}{6}}+{\frac{ \left ( 2\,abB+A \left ( 2\,ac+{b}^{2} \right ) \right ){x}^{5}}{5}}+{\frac{ \left ( 2\,abA+{a}^{2}B \right ){x}^{4}}{4}}+{\frac{{a}^{2}A{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(B*x+A)*(c*x^2+b*x+a)^2,x)
[Out]
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Maxima [A] time = 0.690728, size = 126, normalized size = 1.25 \[ \frac{1}{8} \, B c^{2} x^{8} + \frac{1}{7} \,{\left (2 \, B b c + A c^{2}\right )} x^{7} + \frac{1}{6} \,{\left (B b^{2} + 2 \,{\left (B a + A b\right )} c\right )} x^{6} + \frac{1}{3} \, A a^{2} x^{3} + \frac{1}{5} \,{\left (2 \, B a b + A b^{2} + 2 \, A a c\right )} x^{5} + \frac{1}{4} \,{\left (B a^{2} + 2 \, A a b\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)^2*(B*x + A)*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.271561, size = 1, normalized size = 0.01 \[ \frac{1}{8} x^{8} c^{2} B + \frac{2}{7} x^{7} c b B + \frac{1}{7} x^{7} c^{2} A + \frac{1}{6} x^{6} b^{2} B + \frac{1}{3} x^{6} c a B + \frac{1}{3} x^{6} c b A + \frac{2}{5} x^{5} b a B + \frac{1}{5} x^{5} b^{2} A + \frac{2}{5} x^{5} c a A + \frac{1}{4} x^{4} a^{2} B + \frac{1}{2} x^{4} b a A + \frac{1}{3} x^{3} a^{2} A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)^2*(B*x + A)*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.14924, size = 105, normalized size = 1.04 \[ \frac{A a^{2} x^{3}}{3} + \frac{B c^{2} x^{8}}{8} + x^{7} \left (\frac{A c^{2}}{7} + \frac{2 B b c}{7}\right ) + x^{6} \left (\frac{A b c}{3} + \frac{B a c}{3} + \frac{B b^{2}}{6}\right ) + x^{5} \left (\frac{2 A a c}{5} + \frac{A b^{2}}{5} + \frac{2 B a b}{5}\right ) + x^{4} \left (\frac{A a b}{2} + \frac{B a^{2}}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(B*x+A)*(c*x**2+b*x+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.268587, size = 139, normalized size = 1.38 \[ \frac{1}{8} \, B c^{2} x^{8} + \frac{2}{7} \, B b c x^{7} + \frac{1}{7} \, A c^{2} x^{7} + \frac{1}{6} \, B b^{2} x^{6} + \frac{1}{3} \, B a c x^{6} + \frac{1}{3} \, A b c x^{6} + \frac{2}{5} \, B a b x^{5} + \frac{1}{5} \, A b^{2} x^{5} + \frac{2}{5} \, A a c x^{5} + \frac{1}{4} \, B a^{2} x^{4} + \frac{1}{2} \, A a b x^{4} + \frac{1}{3} \, A a^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)^2*(B*x + A)*x^2,x, algorithm="giac")
[Out]