Optimal. Leaf size=75 \[ \frac{1}{6} A b^3 x^6+\frac{1}{7} b^2 x^7 (3 A c+b B)+\frac{1}{9} c^2 x^9 (A c+3 b B)+\frac{3}{8} b c x^8 (A c+b B)+\frac{1}{10} B c^3 x^{10} \]
[Out]
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Rubi [A] time = 0.192809, antiderivative size = 75, 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 \[ \frac{1}{6} A b^3 x^6+\frac{1}{7} b^2 x^7 (3 A c+b B)+\frac{1}{9} c^2 x^9 (A c+3 b B)+\frac{3}{8} b c x^8 (A c+b B)+\frac{1}{10} B c^3 x^{10} \]
Antiderivative was successfully verified.
[In] Int[x^2*(A + B*x)*(b*x + c*x^2)^3,x]
[Out]
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Rubi in Sympy [A] time = 20.1277, size = 70, normalized size = 0.93 \[ \frac{A b^{3} x^{6}}{6} + \frac{B c^{3} x^{10}}{10} + \frac{b^{2} x^{7} \left (3 A c + B b\right )}{7} + \frac{3 b c x^{8} \left (A c + B b\right )}{8} + \frac{c^{2} x^{9} \left (A c + 3 B b\right )}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(B*x+A)*(c*x**2+b*x)**3,x)
[Out]
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Mathematica [A] time = 0.0198418, size = 75, normalized size = 1. \[ \frac{1}{6} A b^3 x^6+\frac{1}{7} b^2 x^7 (3 A c+b B)+\frac{1}{9} c^2 x^9 (A c+3 b B)+\frac{3}{8} b c x^8 (A c+b B)+\frac{1}{10} B c^3 x^{10} \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(A + B*x)*(b*x + c*x^2)^3,x]
[Out]
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Maple [A] time = 0., size = 76, normalized size = 1. \[{\frac{B{c}^{3}{x}^{10}}{10}}+{\frac{ \left ( A{c}^{3}+3\,Bb{c}^{2} \right ){x}^{9}}{9}}+{\frac{ \left ( 3\,Ab{c}^{2}+3\,B{b}^{2}c \right ){x}^{8}}{8}}+{\frac{ \left ( 3\,A{b}^{2}c+B{b}^{3} \right ){x}^{7}}{7}}+{\frac{A{b}^{3}{x}^{6}}{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(B*x+A)*(c*x^2+b*x)^3,x)
[Out]
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Maxima [A] time = 0.698748, size = 99, normalized size = 1.32 \[ \frac{1}{10} \, B c^{3} x^{10} + \frac{1}{6} \, A b^{3} x^{6} + \frac{1}{9} \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{9} + \frac{3}{8} \,{\left (B b^{2} c + A b c^{2}\right )} x^{8} + \frac{1}{7} \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.253067, size = 1, normalized size = 0.01 \[ \frac{1}{10} x^{10} c^{3} B + \frac{1}{3} x^{9} c^{2} b B + \frac{1}{9} x^{9} c^{3} A + \frac{3}{8} x^{8} c b^{2} B + \frac{3}{8} x^{8} c^{2} b A + \frac{1}{7} x^{7} b^{3} B + \frac{3}{7} x^{7} c b^{2} A + \frac{1}{6} x^{6} b^{3} A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.145133, size = 82, normalized size = 1.09 \[ \frac{A b^{3} x^{6}}{6} + \frac{B c^{3} x^{10}}{10} + x^{9} \left (\frac{A c^{3}}{9} + \frac{B b c^{2}}{3}\right ) + x^{8} \left (\frac{3 A b c^{2}}{8} + \frac{3 B b^{2} c}{8}\right ) + x^{7} \left (\frac{3 A b^{2} c}{7} + \frac{B b^{3}}{7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(B*x+A)*(c*x**2+b*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.265904, size = 104, normalized size = 1.39 \[ \frac{1}{10} \, B c^{3} x^{10} + \frac{1}{3} \, B b c^{2} x^{9} + \frac{1}{9} \, A c^{3} x^{9} + \frac{3}{8} \, B b^{2} c x^{8} + \frac{3}{8} \, A b c^{2} x^{8} + \frac{1}{7} \, B b^{3} x^{7} + \frac{3}{7} \, A b^{2} c x^{7} + \frac{1}{6} \, A b^{3} x^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)*x^2,x, algorithm="giac")
[Out]