Optimal. Leaf size=39 \[ \frac{2}{9} x^{9/2} (a B+A b)+\frac{2}{7} a A x^{7/2}+\frac{2}{11} b B x^{11/2} \]
[Out]
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Rubi [A] time = 0.0438114, 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 \[ \frac{2}{9} x^{9/2} (a B+A b)+\frac{2}{7} a A x^{7/2}+\frac{2}{11} b B x^{11/2} \]
Antiderivative was successfully verified.
[In] Int[x^(5/2)*(a + b*x)*(A + B*x),x]
[Out]
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Rubi in Sympy [A] time = 5.21104, size = 41, normalized size = 1.05 \[ \frac{2 A a x^{\frac{7}{2}}}{7} + \frac{2 B b x^{\frac{11}{2}}}{11} + x^{\frac{9}{2}} \left (\frac{2 A b}{9} + \frac{2 B a}{9}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(5/2)*(b*x+a)*(B*x+A),x)
[Out]
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Mathematica [A] time = 0.0159246, size = 31, normalized size = 0.79 \[ \frac{2}{693} x^{7/2} \left (77 x (a B+A b)+99 a A+63 b B x^2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^(5/2)*(a + b*x)*(A + B*x),x]
[Out]
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Maple [A] time = 0.006, size = 28, normalized size = 0.7 \[{\frac{126\,bB{x}^{2}+154\,Abx+154\,Bax+198\,Aa}{693}{x}^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(5/2)*(b*x+a)*(B*x+A),x)
[Out]
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Maxima [A] time = 1.33149, size = 36, normalized size = 0.92 \[ \frac{2}{11} \, B b x^{\frac{11}{2}} + \frac{2}{7} \, A a x^{\frac{7}{2}} + \frac{2}{9} \,{\left (B a + A b\right )} x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)*x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210153, size = 43, normalized size = 1.1 \[ \frac{2}{693} \,{\left (63 \, B b x^{5} + 99 \, A a x^{3} + 77 \,{\left (B a + A b\right )} x^{4}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)*x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 7.43079, size = 46, normalized size = 1.18 \[ \frac{2 A a x^{\frac{7}{2}}}{7} + \frac{2 A b x^{\frac{9}{2}}}{9} + \frac{2 B a x^{\frac{9}{2}}}{9} + \frac{2 B b x^{\frac{11}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(5/2)*(b*x+a)*(B*x+A),x)
[Out]
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GIAC/XCAS [A] time = 0.261211, size = 39, normalized size = 1. \[ \frac{2}{11} \, B b x^{\frac{11}{2}} + \frac{2}{9} \, B a x^{\frac{9}{2}} + \frac{2}{9} \, A b x^{\frac{9}{2}} + \frac{2}{7} \, A a x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)*x^(5/2),x, algorithm="giac")
[Out]