Optimal. Leaf size=55 \[ \frac{1}{5} a^2 A x^5+\frac{1}{7} b x^7 (2 a B+A b)+\frac{1}{6} a x^6 (a B+2 A b)+\frac{1}{8} b^2 B x^8 \]
[Out]
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Rubi [A] time = 0.135215, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.08 \[ \frac{1}{5} a^2 A x^5+\frac{1}{7} b x^7 (2 a B+A b)+\frac{1}{6} a x^6 (a B+2 A b)+\frac{1}{8} b^2 B x^8 \]
Antiderivative was successfully verified.
[In] Int[x^4*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]
[Out]
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Rubi in Sympy [A] time = 25.128, size = 49, normalized size = 0.89 \[ \frac{A a^{2} x^{5}}{5} + \frac{B b^{2} x^{8}}{8} + \frac{a x^{6} \left (2 A b + B a\right )}{6} + \frac{b x^{7} \left (A b + 2 B a\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4*(B*x+A)*(b**2*x**2+2*a*b*x+a**2),x)
[Out]
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Mathematica [A] time = 0.0156216, size = 55, normalized size = 1. \[ \frac{1}{5} a^2 A x^5+\frac{1}{7} b x^7 (2 a B+A b)+\frac{1}{6} a x^6 (a B+2 A b)+\frac{1}{8} b^2 B x^8 \]
Antiderivative was successfully verified.
[In] Integrate[x^4*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]
[Out]
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Maple [A] time = 0.002, size = 52, normalized size = 1. \[{\frac{{b}^{2}B{x}^{8}}{8}}+{\frac{ \left ({b}^{2}A+2\,abB \right ){x}^{7}}{7}}+{\frac{ \left ( 2\,abA+{a}^{2}B \right ){x}^{6}}{6}}+{\frac{{a}^{2}A{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4*(B*x+A)*(b^2*x^2+2*a*b*x+a^2),x)
[Out]
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Maxima [A] time = 0.676881, size = 69, normalized size = 1.25 \[ \frac{1}{8} \, B b^{2} x^{8} + \frac{1}{5} \, A a^{2} x^{5} + \frac{1}{7} \,{\left (2 \, B a b + A b^{2}\right )} x^{7} + \frac{1}{6} \,{\left (B a^{2} + 2 \, A a b\right )} x^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(B*x + A)*x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.242705, size = 1, normalized size = 0.02 \[ \frac{1}{8} x^{8} b^{2} B + \frac{2}{7} x^{7} b a B + \frac{1}{7} x^{7} b^{2} A + \frac{1}{6} x^{6} a^{2} B + \frac{1}{3} x^{6} b a A + \frac{1}{5} x^{5} a^{2} A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(B*x + A)*x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.111161, size = 54, normalized size = 0.98 \[ \frac{A a^{2} x^{5}}{5} + \frac{B b^{2} x^{8}}{8} + x^{7} \left (\frac{A b^{2}}{7} + \frac{2 B a b}{7}\right ) + x^{6} \left (\frac{A a b}{3} + \frac{B a^{2}}{6}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4*(B*x+A)*(b**2*x**2+2*a*b*x+a**2),x)
[Out]
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GIAC/XCAS [A] time = 0.269397, size = 72, normalized size = 1.31 \[ \frac{1}{8} \, B b^{2} x^{8} + \frac{2}{7} \, B a b x^{7} + \frac{1}{7} \, A b^{2} x^{7} + \frac{1}{6} \, B a^{2} x^{6} + \frac{1}{3} \, A a b x^{6} + \frac{1}{5} \, A a^{2} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(B*x + A)*x^4,x, algorithm="giac")
[Out]