Optimal. Leaf size=39 \[ \frac{2}{3} x^{3/2} (a B+A b)-\frac{2 a A}{3 x^{3/2}}+\frac{2}{9} b B x^{9/2} \]
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Rubi [A] time = 0.0574405, 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 \[ \frac{2}{3} x^{3/2} (a B+A b)-\frac{2 a A}{3 x^{3/2}}+\frac{2}{9} b B x^{9/2} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)*(A + B*x^3))/x^(5/2),x]
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Rubi in Sympy [A] time = 6.0919, size = 41, normalized size = 1.05 \[ - \frac{2 A a}{3 x^{\frac{3}{2}}} + \frac{2 B b x^{\frac{9}{2}}}{9} + x^{\frac{3}{2}} \left (\frac{2 A b}{3} + \frac{2 B a}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)*(B*x**3+A)/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.0202908, size = 34, normalized size = 0.87 \[ \frac{2 \left (-3 a A+3 a B x^3+3 A b x^3+b B x^6\right )}{9 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)*(A + B*x^3))/x^(5/2),x]
[Out]
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Maple [A] time = 0.006, size = 32, normalized size = 0.8 \[ -{\frac{-2\,bB{x}^{6}-6\,A{x}^{3}b-6\,B{x}^{3}a+6\,Aa}{9}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)*(B*x^3+A)/x^(5/2),x)
[Out]
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Maxima [A] time = 1.58397, size = 36, normalized size = 0.92 \[ \frac{2}{9} \, B b x^{\frac{9}{2}} + \frac{2}{3} \,{\left (B a + A b\right )} x^{\frac{3}{2}} - \frac{2 \, A a}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)/x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.227699, size = 38, normalized size = 0.97 \[ \frac{2 \,{\left (B b x^{6} + 3 \,{\left (B a + A b\right )} x^{3} - 3 \, A a\right )}}{9 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)/x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 9.95857, size = 46, normalized size = 1.18 \[ - \frac{2 A a}{3 x^{\frac{3}{2}}} + \frac{2 A b x^{\frac{3}{2}}}{3} + \frac{2 B a x^{\frac{3}{2}}}{3} + \frac{2 B b x^{\frac{9}{2}}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)*(B*x**3+A)/x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212472, size = 39, normalized size = 1. \[ \frac{2}{9} \, B b x^{\frac{9}{2}} + \frac{2}{3} \, B a x^{\frac{3}{2}} + \frac{2}{3} \, A b x^{\frac{3}{2}} - \frac{2 \, A a}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)/x^(5/2),x, algorithm="giac")
[Out]