Optimal. Leaf size=55 \[ \frac{1}{5} A b^2 x^5+\frac{1}{7} c x^7 (A c+2 b B)+\frac{1}{6} b x^6 (2 A c+b B)+\frac{1}{8} B c^2 x^8 \]
[Out]
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Rubi [A] time = 0.151775, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{1}{5} A b^2 x^5+\frac{1}{7} c x^7 (A c+2 b B)+\frac{1}{6} b x^6 (2 A c+b B)+\frac{1}{8} B c^2 x^8 \]
Antiderivative was successfully verified.
[In] Int[x^2*(A + B*x)*(b*x + c*x^2)^2,x]
[Out]
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Rubi in Sympy [A] time = 15.2087, size = 49, normalized size = 0.89 \[ \frac{A b^{2} x^{5}}{5} + \frac{B c^{2} x^{8}}{8} + \frac{b x^{6} \left (2 A c + B b\right )}{6} + \frac{c x^{7} \left (A c + 2 B b\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(B*x+A)*(c*x**2+b*x)**2,x)
[Out]
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Mathematica [A] time = 0.0157755, size = 55, normalized size = 1. \[ \frac{1}{5} A b^2 x^5+\frac{1}{7} c x^7 (A c+2 b B)+\frac{1}{6} b x^6 (2 A c+b B)+\frac{1}{8} B c^2 x^8 \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(A + B*x)*(b*x + c*x^2)^2,x]
[Out]
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Maple [A] time = 0., size = 52, normalized size = 1. \[{\frac{B{c}^{2}{x}^{8}}{8}}+{\frac{ \left ( A{c}^{2}+2\,Bbc \right ){x}^{7}}{7}}+{\frac{ \left ( 2\,Abc+{b}^{2}B \right ){x}^{6}}{6}}+{\frac{A{b}^{2}{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(B*x+A)*(c*x^2+b*x)^2,x)
[Out]
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Maxima [A] time = 0.690626, size = 69, normalized size = 1.25 \[ \frac{1}{8} \, B c^{2} x^{8} + \frac{1}{5} \, A b^{2} x^{5} + \frac{1}{7} \,{\left (2 \, B b c + A c^{2}\right )} x^{7} + \frac{1}{6} \,{\left (B b^{2} + 2 \, A b c\right )} x^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^2*(B*x + A)*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.250004, size = 1, normalized size = 0.02 \[ \frac{1}{8} x^{8} c^{2} B + \frac{2}{7} x^{7} c b B + \frac{1}{7} x^{7} c^{2} A + \frac{1}{6} x^{6} b^{2} B + \frac{1}{3} x^{6} c b A + \frac{1}{5} x^{5} b^{2} A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^2*(B*x + A)*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.121497, size = 54, normalized size = 0.98 \[ \frac{A b^{2} x^{5}}{5} + \frac{B c^{2} x^{8}}{8} + x^{7} \left (\frac{A c^{2}}{7} + \frac{2 B b c}{7}\right ) + x^{6} \left (\frac{A b c}{3} + \frac{B b^{2}}{6}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(B*x+A)*(c*x**2+b*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.264982, size = 72, normalized size = 1.31 \[ \frac{1}{8} \, B c^{2} x^{8} + \frac{2}{7} \, B b c x^{7} + \frac{1}{7} \, A c^{2} x^{7} + \frac{1}{6} \, B b^{2} x^{6} + \frac{1}{3} \, A b c x^{6} + \frac{1}{5} \, A b^{2} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^2*(B*x + A)*x^2,x, algorithm="giac")
[Out]