Optimal. Leaf size=85 \[ \frac{2}{5} a^3 A x^{5/2}+\frac{2}{11} a^2 x^{11/2} (a B+3 A b)+\frac{2}{23} b^2 x^{23/2} (3 a B+A b)+\frac{6}{17} a b x^{17/2} (a B+A b)+\frac{2}{29} b^3 B x^{29/2} \]
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Rubi [A] time = 0.12639, 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 \[ \frac{2}{5} a^3 A x^{5/2}+\frac{2}{11} a^2 x^{11/2} (a B+3 A b)+\frac{2}{23} b^2 x^{23/2} (3 a B+A b)+\frac{6}{17} a b x^{17/2} (a B+A b)+\frac{2}{29} b^3 B x^{29/2} \]
Antiderivative was successfully verified.
[In] Int[x^(3/2)*(a + b*x^3)^3*(A + B*x^3),x]
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Rubi in Sympy [A] time = 14.0824, size = 85, normalized size = 1. \[ \frac{2 A a^{3} x^{\frac{5}{2}}}{5} + \frac{2 B b^{3} x^{\frac{29}{2}}}{29} + \frac{2 a^{2} x^{\frac{11}{2}} \left (3 A b + B a\right )}{11} + \frac{6 a b x^{\frac{17}{2}} \left (A b + B a\right )}{17} + \frac{2 b^{2} x^{\frac{23}{2}} \left (A b + 3 B a\right )}{23} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(3/2)*(b*x**3+a)**3*(B*x**3+A),x)
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Mathematica [A] time = 0.0469156, size = 85, normalized size = 1. \[ \frac{2}{5} a^3 A x^{5/2}+\frac{2}{11} a^2 x^{11/2} (a B+3 A b)+\frac{2}{23} b^2 x^{23/2} (3 a B+A b)+\frac{6}{17} a b x^{17/2} (a B+A b)+\frac{2}{29} b^3 B x^{29/2} \]
Antiderivative was successfully verified.
[In] Integrate[x^(3/2)*(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 \[{\frac{43010\,B{b}^{3}{x}^{12}+54230\,{x}^{9}A{b}^{3}+162690\,{x}^{9}a{b}^{2}B+220110\,{x}^{6}a{b}^{2}A+220110\,{x}^{6}B{a}^{2}b+340170\,{x}^{3}A{a}^{2}b+113390\,{x}^{3}B{a}^{3}+249458\,A{a}^{3}}{623645}{x}^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(3/2)*(b*x^3+a)^3*(B*x^3+A),x)
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Maxima [A] time = 1.43999, size = 99, normalized size = 1.16 \[ \frac{2}{29} \, B b^{3} x^{\frac{29}{2}} + \frac{2}{23} \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{\frac{23}{2}} + \frac{6}{17} \,{\left (B a^{2} b + A a b^{2}\right )} x^{\frac{17}{2}} + \frac{2}{5} \, A a^{3} x^{\frac{5}{2}} + \frac{2}{11} \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x^{\frac{11}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^3*x^(3/2),x, algorithm="maxima")
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Fricas [A] time = 0.228435, size = 105, normalized size = 1.24 \[ \frac{2}{623645} \,{\left (21505 \, B b^{3} x^{14} + 27115 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{11} + 110055 \,{\left (B a^{2} b + A a b^{2}\right )} x^{8} + 124729 \, A a^{3} x^{2} + 56695 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x^{5}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^3*x^(3/2),x, algorithm="fricas")
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Sympy [A] time = 124.276, size = 114, normalized size = 1.34 \[ \frac{2 A a^{3} x^{\frac{5}{2}}}{5} + \frac{6 A a^{2} b x^{\frac{11}{2}}}{11} + \frac{6 A a b^{2} x^{\frac{17}{2}}}{17} + \frac{2 A b^{3} x^{\frac{23}{2}}}{23} + \frac{2 B a^{3} x^{\frac{11}{2}}}{11} + \frac{6 B a^{2} b x^{\frac{17}{2}}}{17} + \frac{6 B a b^{2} x^{\frac{23}{2}}}{23} + \frac{2 B b^{3} x^{\frac{29}{2}}}{29} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(3/2)*(b*x**3+a)**3*(B*x**3+A),x)
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GIAC/XCAS [A] time = 0.211814, size = 104, normalized size = 1.22 \[ \frac{2}{29} \, B b^{3} x^{\frac{29}{2}} + \frac{6}{23} \, B a b^{2} x^{\frac{23}{2}} + \frac{2}{23} \, A b^{3} x^{\frac{23}{2}} + \frac{6}{17} \, B a^{2} b x^{\frac{17}{2}} + \frac{6}{17} \, A a b^{2} x^{\frac{17}{2}} + \frac{2}{11} \, B a^{3} x^{\frac{11}{2}} + \frac{6}{11} \, A a^{2} b x^{\frac{11}{2}} + \frac{2}{5} \, A a^{3} x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^3*x^(3/2),x, algorithm="giac")
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