Optimal. Leaf size=39 \[ \frac{2}{15} x^{15/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{21} b B x^{21/2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.057978, 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 \[ \frac{2}{15} x^{15/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{21} b B x^{21/2} \]
Antiderivative was successfully verified.
[In] Int[x^(7/2)*(a + b*x^3)*(A + B*x^3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.08142, size = 41, normalized size = 1.05 \[ \frac{2 A a x^{\frac{9}{2}}}{9} + \frac{2 B b x^{\frac{21}{2}}}{21} + x^{\frac{15}{2}} \left (\frac{2 A b}{15} + \frac{2 B a}{15}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(7/2)*(b*x**3+a)*(B*x**3+A),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0207275, size = 33, normalized size = 0.85 \[ \frac{2}{315} x^{9/2} \left (21 x^3 (a B+A b)+35 a A+15 b B x^6\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^(7/2)*(a + b*x^3)*(A + B*x^3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 32, normalized size = 0.8 \[{\frac{30\,bB{x}^{6}+42\,A{x}^{3}b+42\,B{x}^{3}a+70\,Aa}{315}{x}^{{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(7/2)*(b*x^3+a)*(B*x^3+A),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.36516, size = 36, normalized size = 0.92 \[ \frac{2}{21} \, B b x^{\frac{21}{2}} + \frac{2}{15} \,{\left (B a + A b\right )} x^{\frac{15}{2}} + \frac{2}{9} \, A a x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)*x^(7/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.222331, size = 43, normalized size = 1.1 \[ \frac{2}{315} \,{\left (15 \, B b x^{10} + 21 \,{\left (B a + A b\right )} x^{7} + 35 \, A a x^{4}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)*x^(7/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 70.5765, size = 46, normalized size = 1.18 \[ \frac{2 A a x^{\frac{9}{2}}}{9} + \frac{2 A b x^{\frac{15}{2}}}{15} + \frac{2 B a x^{\frac{15}{2}}}{15} + \frac{2 B b x^{\frac{21}{2}}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(7/2)*(b*x**3+a)*(B*x**3+A),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.210716, size = 39, normalized size = 1. \[ \frac{2}{21} \, B b x^{\frac{21}{2}} + \frac{2}{15} \, B a x^{\frac{15}{2}} + \frac{2}{15} \, A b x^{\frac{15}{2}} + \frac{2}{9} \, A a x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)*x^(7/2),x, algorithm="giac")
[Out]