Optimal. Leaf size=39 \[ \frac{2}{13} x^{13/2} (a B+A b)+\frac{2}{7} a A x^{7/2}+\frac{2}{19} b B x^{19/2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0576091, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{2}{13} x^{13/2} (a B+A b)+\frac{2}{7} a A x^{7/2}+\frac{2}{19} b B x^{19/2} \]
Antiderivative was successfully verified.
[In] Int[x^(5/2)*(a + b*x^3)*(A + B*x^3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.0477, size = 41, normalized size = 1.05 \[ \frac{2 A a x^{\frac{7}{2}}}{7} + \frac{2 B b x^{\frac{19}{2}}}{19} + x^{\frac{13}{2}} \left (\frac{2 A b}{13} + \frac{2 B a}{13}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(5/2)*(b*x**3+a)*(B*x**3+A),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0200636, size = 33, normalized size = 0.85 \[ \frac{2 x^{7/2} \left (133 x^3 (a B+A b)+247 a A+91 b B x^6\right )}{1729} \]
Antiderivative was successfully verified.
[In] Integrate[x^(5/2)*(a + b*x^3)*(A + B*x^3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 32, normalized size = 0.8 \[{\frac{182\,bB{x}^{6}+266\,A{x}^{3}b+266\,B{x}^{3}a+494\,Aa}{1729}{x}^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(5/2)*(b*x^3+a)*(B*x^3+A),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.41554, size = 36, normalized size = 0.92 \[ \frac{2}{19} \, B b x^{\frac{19}{2}} + \frac{2}{13} \,{\left (B a + A b\right )} x^{\frac{13}{2}} + \frac{2}{7} \, A a x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)*x^(5/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.229348, size = 43, normalized size = 1.1 \[ \frac{2}{1729} \,{\left (91 \, B b x^{9} + 133 \,{\left (B a + A b\right )} x^{6} + 247 \, A a x^{3}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)*x^(5/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 38.1018, size = 46, normalized size = 1.18 \[ \frac{2 A a x^{\frac{7}{2}}}{7} + \frac{2 A b x^{\frac{13}{2}}}{13} + \frac{2 B a x^{\frac{13}{2}}}{13} + \frac{2 B b x^{\frac{19}{2}}}{19} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(5/2)*(b*x**3+a)*(B*x**3+A),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.213856, size = 39, normalized size = 1. \[ \frac{2}{19} \, B b x^{\frac{19}{2}} + \frac{2}{13} \, B a x^{\frac{13}{2}} + \frac{2}{13} \, A b x^{\frac{13}{2}} + \frac{2}{7} \, A a x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)*x^(5/2),x, algorithm="giac")
[Out]