Optimal. Leaf size=39 \[ \frac{2}{13} x^{13/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{17} b B x^{17/2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0516741, 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 \[ \frac{2}{13} x^{13/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{17} b B x^{17/2} \]
Antiderivative was successfully verified.
[In] Int[x^(7/2)*(a + b*x^2)*(A + B*x^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.97539, size = 41, normalized size = 1.05 \[ \frac{2 A a x^{\frac{9}{2}}}{9} + \frac{2 B b x^{\frac{17}{2}}}{17} + x^{\frac{13}{2}} \left (\frac{2 A b}{13} + \frac{2 B a}{13}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(7/2)*(b*x**2+a)*(B*x**2+A),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0204658, size = 33, normalized size = 0.85 \[ \frac{2 x^{9/2} \left (153 x^2 (a B+A b)+221 a A+117 b B x^4\right )}{1989} \]
Antiderivative was successfully verified.
[In] Integrate[x^(7/2)*(a + b*x^2)*(A + B*x^2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 32, normalized size = 0.8 \[{\frac{234\,bB{x}^{4}+306\,A{x}^{2}b+306\,B{x}^{2}a+442\,Aa}{1989}{x}^{{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(7/2)*(b*x^2+a)*(B*x^2+A),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34506, size = 36, normalized size = 0.92 \[ \frac{2}{17} \, B b x^{\frac{17}{2}} + \frac{2}{13} \,{\left (B a + A b\right )} x^{\frac{13}{2}} + \frac{2}{9} \, A a x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)*x^(7/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.218747, size = 43, normalized size = 1.1 \[ \frac{2}{1989} \,{\left (117 \, B b x^{8} + 153 \,{\left (B a + A b\right )} x^{6} + 221 \, A a x^{4}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)*x^(7/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 36.9228, size = 46, normalized size = 1.18 \[ \frac{2 A a x^{\frac{9}{2}}}{9} + \frac{2 A b x^{\frac{13}{2}}}{13} + \frac{2 B a x^{\frac{13}{2}}}{13} + \frac{2 B b x^{\frac{17}{2}}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(7/2)*(b*x**2+a)*(B*x**2+A),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.213472, size = 39, normalized size = 1. \[ \frac{2}{17} \, B b x^{\frac{17}{2}} + \frac{2}{13} \, B a x^{\frac{13}{2}} + \frac{2}{13} \, A b x^{\frac{13}{2}} + \frac{2}{9} \, A a x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)*x^(7/2),x, algorithm="giac")
[Out]