Optimal. Leaf size=45 \[ \frac{2}{7} a A x^{7/2}+\frac{2}{9} a B x^{9/2}+\frac{2}{11} A c x^{11/2}+\frac{2}{13} B c x^{13/2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0403438, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ \frac{2}{7} a A x^{7/2}+\frac{2}{9} a B x^{9/2}+\frac{2}{11} A c x^{11/2}+\frac{2}{13} B c x^{13/2} \]
Antiderivative was successfully verified.
[In] Int[x^(5/2)*(A + B*x)*(a + c*x^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.01765, size = 46, normalized size = 1.02 \[ \frac{2 A a x^{\frac{7}{2}}}{7} + \frac{2 A c x^{\frac{11}{2}}}{11} + \frac{2 B a x^{\frac{9}{2}}}{9} + \frac{2 B c x^{\frac{13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(5/2)*(B*x+A)*(c*x**2+a),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0208479, size = 35, normalized size = 0.78 \[ \frac{2 x^{7/2} \left (143 a (9 A+7 B x)+63 c x^2 (13 A+11 B x)\right )}{9009} \]
Antiderivative was successfully verified.
[In] Integrate[x^(5/2)*(A + B*x)*(a + c*x^2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 30, normalized size = 0.7 \[{\frac{1386\,Bc{x}^{3}+1638\,Ac{x}^{2}+2002\,aBx+2574\,aA}{9009}{x}^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(5/2)*(B*x+A)*(c*x^2+a),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.67779, size = 39, normalized size = 0.87 \[ \frac{2}{13} \, B c x^{\frac{13}{2}} + \frac{2}{11} \, A c x^{\frac{11}{2}} + \frac{2}{9} \, B a x^{\frac{9}{2}} + \frac{2}{7} \, A a x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)*x^(5/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.278415, size = 46, normalized size = 1.02 \[ \frac{2}{9009} \,{\left (693 \, B c x^{6} + 819 \, A c x^{5} + 1001 \, B a x^{4} + 1287 \, A a x^{3}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)*x^(5/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 8.84268, size = 46, normalized size = 1.02 \[ \frac{2 A a x^{\frac{7}{2}}}{7} + \frac{2 A c x^{\frac{11}{2}}}{11} + \frac{2 B a x^{\frac{9}{2}}}{9} + \frac{2 B c x^{\frac{13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(5/2)*(B*x+A)*(c*x**2+a),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.26578, size = 39, normalized size = 0.87 \[ \frac{2}{13} \, B c x^{\frac{13}{2}} + \frac{2}{11} \, A c x^{\frac{11}{2}} + \frac{2}{9} \, B a x^{\frac{9}{2}} + \frac{2}{7} \, A a x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)*x^(5/2),x, algorithm="giac")
[Out]