Optimal. Leaf size=39 \[ \frac{2}{11} x^{11/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{13} b B x^{13/2} \]
[Out]
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Rubi [A] time = 0.0455569, 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 \[ \frac{2}{11} x^{11/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{13} b B x^{13/2} \]
Antiderivative was successfully verified.
[In] Int[x^(7/2)*(a + b*x)*(A + B*x),x]
[Out]
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Rubi in Sympy [A] time = 5.25872, size = 41, normalized size = 1.05 \[ \frac{2 A a x^{\frac{9}{2}}}{9} + \frac{2 B b x^{\frac{13}{2}}}{13} + x^{\frac{11}{2}} \left (\frac{2 A b}{11} + \frac{2 B a}{11}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(7/2)*(b*x+a)*(B*x+A),x)
[Out]
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Mathematica [A] time = 0.0200495, size = 31, normalized size = 0.79 \[ \frac{2 x^{9/2} \left (117 x (a B+A b)+143 a A+99 b B x^2\right )}{1287} \]
Antiderivative was successfully verified.
[In] Integrate[x^(7/2)*(a + b*x)*(A + B*x),x]
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Maple [A] time = 0.005, size = 28, normalized size = 0.7 \[{\frac{198\,bB{x}^{2}+234\,Abx+234\,Bax+286\,Aa}{1287}{x}^{{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(7/2)*(b*x+a)*(B*x+A),x)
[Out]
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Maxima [A] time = 1.3275, size = 36, normalized size = 0.92 \[ \frac{2}{13} \, B b x^{\frac{13}{2}} + \frac{2}{9} \, A a x^{\frac{9}{2}} + \frac{2}{11} \,{\left (B a + A b\right )} x^{\frac{11}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)*x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207598, size = 43, normalized size = 1.1 \[ \frac{2}{1287} \,{\left (99 \, B b x^{6} + 143 \, A a x^{4} + 117 \,{\left (B a + A b\right )} x^{5}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)*x^(7/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 17.7725, size = 46, normalized size = 1.18 \[ \frac{2 A a x^{\frac{9}{2}}}{9} + \frac{2 A b x^{\frac{11}{2}}}{11} + \frac{2 B a x^{\frac{11}{2}}}{11} + \frac{2 B b x^{\frac{13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(7/2)*(b*x+a)*(B*x+A),x)
[Out]
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GIAC/XCAS [A] time = 0.25235, size = 39, normalized size = 1. \[ \frac{2}{13} \, B b x^{\frac{13}{2}} + \frac{2}{11} \, B a x^{\frac{11}{2}} + \frac{2}{11} \, A b x^{\frac{11}{2}} + \frac{2}{9} \, A a x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)*x^(7/2),x, algorithm="giac")
[Out]