Optimal. Leaf size=37 \[ 2 \sqrt{x} (a B+A b)-\frac{2 a A}{3 x^{3/2}}+\frac{2}{5} b B x^{5/2} \]
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Rubi [A] time = 0.0499817, antiderivative size = 37, 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 \[ 2 \sqrt{x} (a B+A b)-\frac{2 a A}{3 x^{3/2}}+\frac{2}{5} b B x^{5/2} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^2)*(A + B*x^2))/x^(5/2),x]
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Rubi in Sympy [A] time = 6.97056, size = 37, normalized size = 1. \[ - \frac{2 A a}{3 x^{\frac{3}{2}}} + \frac{2 B b x^{\frac{5}{2}}}{5} + \sqrt{x} \left (2 A b + 2 B a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)*(B*x**2+A)/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.0198245, size = 33, normalized size = 0.89 \[ \frac{2 \left (15 x^2 (a B+A b)-5 a A+3 b B x^4\right )}{15 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^2)*(A + B*x^2))/x^(5/2),x]
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Maple [A] time = 0.006, size = 32, normalized size = 0.9 \[ -{\frac{-6\,bB{x}^{4}-30\,A{x}^{2}b-30\,B{x}^{2}a+10\,Aa}{15}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)*(B*x^2+A)/x^(5/2),x)
[Out]
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Maxima [A] time = 1.32995, size = 36, normalized size = 0.97 \[ \frac{2}{5} \, B b x^{\frac{5}{2}} + 2 \,{\left (B a + A b\right )} \sqrt{x} - \frac{2 \, A a}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)/x^(5/2),x, algorithm="maxima")
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Fricas [A] time = 0.224072, size = 39, normalized size = 1.05 \[ \frac{2 \,{\left (3 \, B b x^{4} + 15 \,{\left (B a + A b\right )} x^{2} - 5 \, A a\right )}}{15 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)/x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.07331, size = 42, normalized size = 1.14 \[ - \frac{2 A a}{3 x^{\frac{3}{2}}} + 2 A b \sqrt{x} + 2 B a \sqrt{x} + \frac{2 B b x^{\frac{5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)*(B*x**2+A)/x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.213255, size = 39, normalized size = 1.05 \[ \frac{2}{5} \, B b x^{\frac{5}{2}} + 2 \, B a \sqrt{x} + 2 \, A b \sqrt{x} - \frac{2 \, A a}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)/x^(5/2),x, algorithm="giac")
[Out]