Optimal. Leaf size=85 \[ \frac{2}{7} a^3 A x^{7/2}+\frac{2}{13} a^2 x^{13/2} (a B+3 A b)+\frac{2}{25} b^2 x^{25/2} (3 a B+A b)+\frac{6}{19} a b x^{19/2} (a B+A b)+\frac{2}{31} b^3 B x^{31/2} \]
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Rubi [A] time = 0.128127, antiderivative size = 85, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ \frac{2}{7} a^3 A x^{7/2}+\frac{2}{13} a^2 x^{13/2} (a B+3 A b)+\frac{2}{25} b^2 x^{25/2} (3 a B+A b)+\frac{6}{19} a b x^{19/2} (a B+A b)+\frac{2}{31} b^3 B x^{31/2} \]
Antiderivative was successfully verified.
[In] Int[x^(5/2)*(a + b*x^3)^3*(A + B*x^3),x]
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Rubi in Sympy [A] time = 14.1236, size = 85, normalized size = 1. \[ \frac{2 A a^{3} x^{\frac{7}{2}}}{7} + \frac{2 B b^{3} x^{\frac{31}{2}}}{31} + \frac{2 a^{2} x^{\frac{13}{2}} \left (3 A b + B a\right )}{13} + \frac{6 a b x^{\frac{19}{2}} \left (A b + B a\right )}{19} + \frac{2 b^{2} x^{\frac{25}{2}} \left (A b + 3 B a\right )}{25} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(5/2)*(b*x**3+a)**3*(B*x**3+A),x)
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Mathematica [A] time = 0.0461847, size = 85, normalized size = 1. \[ \frac{2}{7} a^3 A x^{7/2}+\frac{2}{13} a^2 x^{13/2} (a B+3 A b)+\frac{2}{25} b^2 x^{25/2} (3 a B+A b)+\frac{6}{19} a b x^{19/2} (a B+A b)+\frac{2}{31} b^3 B x^{31/2} \]
Antiderivative was successfully verified.
[In] Integrate[x^(5/2)*(a + b*x^3)^3*(A + B*x^3),x]
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Maple [A] time = 0.009, size = 80, normalized size = 0.9 \[{\frac{86450\,B{b}^{3}{x}^{12}+107198\,{x}^{9}A{b}^{3}+321594\,{x}^{9}a{b}^{2}B+423150\,{x}^{6}a{b}^{2}A+423150\,{x}^{6}B{a}^{2}b+618450\,{x}^{3}A{a}^{2}b+206150\,{x}^{3}B{a}^{3}+382850\,A{a}^{3}}{1339975}{x}^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(5/2)*(b*x^3+a)^3*(B*x^3+A),x)
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Maxima [A] time = 1.40659, size = 99, normalized size = 1.16 \[ \frac{2}{31} \, B b^{3} x^{\frac{31}{2}} + \frac{2}{25} \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{\frac{25}{2}} + \frac{6}{19} \,{\left (B a^{2} b + A a b^{2}\right )} x^{\frac{19}{2}} + \frac{2}{7} \, A a^{3} x^{\frac{7}{2}} + \frac{2}{13} \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x^{\frac{13}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^3*x^(5/2),x, algorithm="maxima")
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Fricas [A] time = 0.225451, size = 105, normalized size = 1.24 \[ \frac{2}{1339975} \,{\left (43225 \, B b^{3} x^{15} + 53599 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{12} + 211575 \,{\left (B a^{2} b + A a b^{2}\right )} x^{9} + 191425 \, A a^{3} x^{3} + 103075 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x^{6}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^3*x^(5/2),x, algorithm="fricas")
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(5/2)*(b*x**3+a)**3*(B*x**3+A),x)
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GIAC/XCAS [A] time = 0.21307, size = 104, normalized size = 1.22 \[ \frac{2}{31} \, B b^{3} x^{\frac{31}{2}} + \frac{6}{25} \, B a b^{2} x^{\frac{25}{2}} + \frac{2}{25} \, A b^{3} x^{\frac{25}{2}} + \frac{6}{19} \, B a^{2} b x^{\frac{19}{2}} + \frac{6}{19} \, A a b^{2} x^{\frac{19}{2}} + \frac{2}{13} \, B a^{3} x^{\frac{13}{2}} + \frac{6}{13} \, A a^{2} b x^{\frac{13}{2}} + \frac{2}{7} \, A a^{3} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^3*x^(5/2),x, algorithm="giac")
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