Optimal. Leaf size=42 \[ \frac{\left (a+b x^3\right )^3 (A b-a B)}{9 b^2}+\frac{B \left (a+b x^3\right )^4}{12 b^2} \]
[Out]
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Rubi [A] time = 0.20317, antiderivative size = 42, 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 \[ \frac{\left (a+b x^3\right )^3 (A b-a B)}{9 b^2}+\frac{B \left (a+b x^3\right )^4}{12 b^2} \]
Antiderivative was successfully verified.
[In] Int[x^2*(a + b*x^3)^2*(A + B*x^3),x]
[Out]
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Rubi in Sympy [A] time = 14.988, size = 34, normalized size = 0.81 \[ \frac{B \left (a + b x^{3}\right )^{4}}{12 b^{2}} + \frac{\left (a + b x^{3}\right )^{3} \left (A b - B a\right )}{9 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(b*x**3+a)**2*(B*x**3+A),x)
[Out]
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Mathematica [A] time = 0.0291949, size = 51, normalized size = 1.21 \[ \frac{1}{36} x^3 \left (12 a^2 A+4 b x^6 (2 a B+A b)+6 a x^3 (a B+2 A b)+3 b^2 B x^9\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(a + b*x^3)^2*(A + B*x^3),x]
[Out]
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Maple [A] time = 0.001, size = 52, normalized size = 1.2 \[{\frac{{b}^{2}B{x}^{12}}{12}}+{\frac{ \left ({b}^{2}A+2\,abB \right ){x}^{9}}{9}}+{\frac{ \left ( 2\,abA+{a}^{2}B \right ){x}^{6}}{6}}+{\frac{{a}^{2}A{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(b*x^3+a)^2*(B*x^3+A),x)
[Out]
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Maxima [A] time = 1.37271, size = 69, normalized size = 1.64 \[ \frac{1}{12} \, B b^{2} x^{12} + \frac{1}{9} \,{\left (2 \, B a b + A b^{2}\right )} x^{9} + \frac{1}{6} \,{\left (B a^{2} + 2 \, A a b\right )} x^{6} + \frac{1}{3} \, A a^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.200103, size = 1, normalized size = 0.02 \[ \frac{1}{12} x^{12} b^{2} B + \frac{2}{9} x^{9} b a B + \frac{1}{9} x^{9} b^{2} A + \frac{1}{6} x^{6} a^{2} B + \frac{1}{3} x^{6} b a A + \frac{1}{3} x^{3} a^{2} A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.103028, size = 54, normalized size = 1.29 \[ \frac{A a^{2} x^{3}}{3} + \frac{B b^{2} x^{12}}{12} + x^{9} \left (\frac{A b^{2}}{9} + \frac{2 B a b}{9}\right ) + x^{6} \left (\frac{A a b}{3} + \frac{B a^{2}}{6}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(b*x**3+a)**2*(B*x**3+A),x)
[Out]
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GIAC/XCAS [A] time = 0.221227, size = 72, normalized size = 1.71 \[ \frac{1}{12} \, B b^{2} x^{12} + \frac{2}{9} \, B a b x^{9} + \frac{1}{9} \, A b^{2} x^{9} + \frac{1}{6} \, B a^{2} x^{6} + \frac{1}{3} \, A a b x^{6} + \frac{1}{3} \, A a^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2*x^2,x, algorithm="giac")
[Out]