Optimal. Leaf size=39 \[ \frac{2}{7} x^{7/2} (a B+A b)+\frac{2}{5} a A x^{5/2}+\frac{2}{9} b B x^{9/2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0432953, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \frac{2}{7} x^{7/2} (a B+A b)+\frac{2}{5} a A x^{5/2}+\frac{2}{9} b B x^{9/2} \]
Antiderivative was successfully verified.
[In] Int[x^(3/2)*(a + b*x)*(A + B*x),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.31347, size = 41, normalized size = 1.05 \[ \frac{2 A a x^{\frac{5}{2}}}{5} + \frac{2 B b x^{\frac{9}{2}}}{9} + x^{\frac{7}{2}} \left (\frac{2 A b}{7} + \frac{2 B a}{7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(3/2)*(b*x+a)*(B*x+A),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0169053, size = 33, normalized size = 0.85 \[ \frac{2}{315} x^{5/2} (9 a (7 A+5 B x)+5 b x (9 A+7 B x)) \]
Antiderivative was successfully verified.
[In] Integrate[x^(3/2)*(a + b*x)*(A + B*x),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 28, normalized size = 0.7 \[{\frac{70\,bB{x}^{2}+90\,Abx+90\,Bax+126\,Aa}{315}{x}^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(3/2)*(b*x+a)*(B*x+A),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.32123, size = 36, normalized size = 0.92 \[ \frac{2}{9} \, B b x^{\frac{9}{2}} + \frac{2}{5} \, A a x^{\frac{5}{2}} + \frac{2}{7} \,{\left (B a + A b\right )} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)*x^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.204479, size = 43, normalized size = 1.1 \[ \frac{2}{315} \,{\left (35 \, B b x^{4} + 63 \, A a x^{2} + 45 \,{\left (B a + A b\right )} x^{3}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)*x^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 4.63503, size = 46, normalized size = 1.18 \[ \frac{2 A a x^{\frac{5}{2}}}{5} + \frac{2 A b x^{\frac{7}{2}}}{7} + \frac{2 B a x^{\frac{7}{2}}}{7} + \frac{2 B b x^{\frac{9}{2}}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(3/2)*(b*x+a)*(B*x+A),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.290109, size = 39, normalized size = 1. \[ \frac{2}{9} \, B b x^{\frac{9}{2}} + \frac{2}{7} \, B a x^{\frac{7}{2}} + \frac{2}{7} \, A b x^{\frac{7}{2}} + \frac{2}{5} \, A a x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)*x^(3/2),x, algorithm="giac")
[Out]