Optimal. Leaf size=63 \[ \frac{2}{7} a^2 A x^{7/2}+\frac{2}{19} b x^{19/2} (2 a B+A b)+\frac{2}{13} a x^{13/2} (a B+2 A b)+\frac{2}{25} b^2 B x^{25/2} \]
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Rubi [A] time = 0.0994184, antiderivative size = 63, 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 \[ \frac{2}{7} a^2 A x^{7/2}+\frac{2}{19} b x^{19/2} (2 a B+A b)+\frac{2}{13} a x^{13/2} (a B+2 A b)+\frac{2}{25} b^2 B x^{25/2} \]
Antiderivative was successfully verified.
[In] Int[x^(5/2)*(a + b*x^3)^2*(A + B*x^3),x]
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Rubi in Sympy [A] time = 10.734, size = 63, normalized size = 1. \[ \frac{2 A a^{2} x^{\frac{7}{2}}}{7} + \frac{2 B b^{2} x^{\frac{25}{2}}}{25} + \frac{2 a x^{\frac{13}{2}} \left (2 A b + B a\right )}{13} + \frac{2 b x^{\frac{19}{2}} \left (A b + 2 B a\right )}{19} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(5/2)*(b*x**3+a)**2*(B*x**3+A),x)
[Out]
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Mathematica [A] time = 0.0396245, size = 63, normalized size = 1. \[ \frac{2}{7} a^2 A x^{7/2}+\frac{2}{19} b x^{19/2} (2 a B+A b)+\frac{2}{13} a x^{13/2} (a B+2 A b)+\frac{2}{25} b^2 B x^{25/2} \]
Antiderivative was successfully verified.
[In] Integrate[x^(5/2)*(a + b*x^3)^2*(A + B*x^3),x]
[Out]
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Maple [A] time = 0.009, size = 56, normalized size = 0.9 \[{\frac{3458\,B{x}^{9}{b}^{2}+4550\,A{b}^{2}{x}^{6}+9100\,B{x}^{6}ab+13300\,aAb{x}^{3}+6650\,B{x}^{3}{a}^{2}+12350\,A{a}^{2}}{43225}{x}^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(5/2)*(b*x^3+a)^2*(B*x^3+A),x)
[Out]
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Maxima [A] time = 1.85873, size = 69, normalized size = 1.1 \[ \frac{2}{25} \, B b^{2} x^{\frac{25}{2}} + \frac{2}{19} \,{\left (2 \, B a b + A b^{2}\right )} x^{\frac{19}{2}} + \frac{2}{13} \,{\left (B a^{2} + 2 \, A a b\right )} x^{\frac{13}{2}} + \frac{2}{7} \, A a^{2} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2*x^(5/2),x, algorithm="maxima")
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Fricas [A] time = 0.234111, size = 76, normalized size = 1.21 \[ \frac{2}{43225} \,{\left (1729 \, B b^{2} x^{12} + 2275 \,{\left (2 \, B a b + A b^{2}\right )} x^{9} + 3325 \,{\left (B a^{2} + 2 \, A a b\right )} x^{6} + 6175 \, A a^{2} x^{3}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2*x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 95.4141, size = 80, normalized size = 1.27 \[ \frac{2 A a^{2} x^{\frac{7}{2}}}{7} + \frac{4 A a b x^{\frac{13}{2}}}{13} + \frac{2 A b^{2} x^{\frac{19}{2}}}{19} + \frac{2 B a^{2} x^{\frac{13}{2}}}{13} + \frac{4 B a b x^{\frac{19}{2}}}{19} + \frac{2 B b^{2} x^{\frac{25}{2}}}{25} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(5/2)*(b*x**3+a)**2*(B*x**3+A),x)
[Out]
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GIAC/XCAS [A] time = 0.21284, size = 72, normalized size = 1.14 \[ \frac{2}{25} \, B b^{2} x^{\frac{25}{2}} + \frac{4}{19} \, B a b x^{\frac{19}{2}} + \frac{2}{19} \, A b^{2} x^{\frac{19}{2}} + \frac{2}{13} \, B a^{2} x^{\frac{13}{2}} + \frac{4}{13} \, A a b x^{\frac{13}{2}} + \frac{2}{7} \, A a^{2} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2*x^(5/2),x, algorithm="giac")
[Out]