Optimal. Leaf size=39 \[ \frac{2}{9} x^{9/2} (a B+A b)+\frac{2}{5} a A x^{5/2}+\frac{2}{13} b B x^{13/2} \]
[Out]
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Rubi [A] time = 0.0497932, 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 \[ \frac{2}{9} x^{9/2} (a B+A b)+\frac{2}{5} a A x^{5/2}+\frac{2}{13} b B x^{13/2} \]
Antiderivative was successfully verified.
[In] Int[x^(3/2)*(a + b*x^2)*(A + B*x^2),x]
[Out]
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Rubi in Sympy [A] time = 7.06465, size = 41, normalized size = 1.05 \[ \frac{2 A a x^{\frac{5}{2}}}{5} + \frac{2 B b x^{\frac{13}{2}}}{13} + x^{\frac{9}{2}} \left (\frac{2 A b}{9} + \frac{2 B a}{9}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(3/2)*(b*x**2+a)*(B*x**2+A),x)
[Out]
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Mathematica [A] time = 0.0169249, size = 33, normalized size = 0.85 \[ \frac{2}{585} x^{5/2} \left (65 x^2 (a B+A b)+117 a A+45 b B x^4\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^(3/2)*(a + b*x^2)*(A + B*x^2),x]
[Out]
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Maple [A] time = 0.005, size = 32, normalized size = 0.8 \[{\frac{90\,bB{x}^{4}+130\,A{x}^{2}b+130\,B{x}^{2}a+234\,Aa}{585}{x}^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(3/2)*(b*x^2+a)*(B*x^2+A),x)
[Out]
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Maxima [A] time = 1.35172, size = 36, normalized size = 0.92 \[ \frac{2}{13} \, B b x^{\frac{13}{2}} + \frac{2}{9} \,{\left (B a + A b\right )} x^{\frac{9}{2}} + \frac{2}{5} \, A a x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)*x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21123, size = 43, normalized size = 1.1 \[ \frac{2}{585} \,{\left (45 \, B b x^{6} + 65 \,{\left (B a + A b\right )} x^{4} + 117 \, A a x^{2}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)*x^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 7.92613, size = 46, normalized size = 1.18 \[ \frac{2 A a x^{\frac{5}{2}}}{5} + \frac{2 A b x^{\frac{9}{2}}}{9} + \frac{2 B a x^{\frac{9}{2}}}{9} + \frac{2 B b x^{\frac{13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(3/2)*(b*x**2+a)*(B*x**2+A),x)
[Out]
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GIAC/XCAS [A] time = 0.216553, size = 39, normalized size = 1. \[ \frac{2}{13} \, B b x^{\frac{13}{2}} + \frac{2}{9} \, B a x^{\frac{9}{2}} + \frac{2}{9} \, A b x^{\frac{9}{2}} + \frac{2}{5} \, A a x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)*x^(3/2),x, algorithm="giac")
[Out]