Optimal. Leaf size=37 \[ \frac{2}{3} x^{3/2} (a B+A b)-\frac{2 a A}{\sqrt{x}}+\frac{2}{7} b B x^{7/2} \]
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Rubi [A] time = 0.0496518, 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 \[ \frac{2}{3} x^{3/2} (a B+A b)-\frac{2 a A}{\sqrt{x}}+\frac{2}{7} b B x^{7/2} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^2)*(A + B*x^2))/x^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 6.89538, size = 39, normalized size = 1.05 \[ - \frac{2 A a}{\sqrt{x}} + \frac{2 B b x^{\frac{7}{2}}}{7} + x^{\frac{3}{2}} \left (\frac{2 A b}{3} + \frac{2 B a}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)*(B*x**2+A)/x**(3/2),x)
[Out]
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Mathematica [A] time = 0.0176442, size = 33, normalized size = 0.89 \[ \frac{2 \left (7 x^2 (a B+A b)-21 a A+3 b B x^4\right )}{21 \sqrt{x}} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^2)*(A + B*x^2))/x^(3/2),x]
[Out]
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Maple [A] time = 0.005, size = 32, normalized size = 0.9 \[ -{\frac{-6\,bB{x}^{4}-14\,A{x}^{2}b-14\,B{x}^{2}a+42\,Aa}{21}{\frac{1}{\sqrt{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)*(B*x^2+A)/x^(3/2),x)
[Out]
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Maxima [A] time = 1.34693, size = 36, normalized size = 0.97 \[ \frac{2}{7} \, B b x^{\frac{7}{2}} + \frac{2}{3} \,{\left (B a + A b\right )} x^{\frac{3}{2}} - \frac{2 \, A a}{\sqrt{x}} \]
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="maxima")
[Out]
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Fricas [A] time = 0.22322, size = 39, normalized size = 1.05 \[ \frac{2 \,{\left (3 \, B b x^{4} + 7 \,{\left (B a + A b\right )} x^{2} - 21 \, A a\right )}}{21 \, \sqrt{x}} \]
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 = 3.48273, size = 44, normalized size = 1.19 \[ - \frac{2 A a}{\sqrt{x}} + \frac{2 A b x^{\frac{3}{2}}}{3} + \frac{2 B a x^{\frac{3}{2}}}{3} + \frac{2 B b x^{\frac{7}{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)*(B*x**2+A)/x**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.210184, size = 39, normalized size = 1.05 \[ \frac{2}{7} \, B b x^{\frac{7}{2}} + \frac{2}{3} \, B a x^{\frac{3}{2}} + \frac{2}{3} \, A b x^{\frac{3}{2}} - \frac{2 \, A a}{\sqrt{x}} \]
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="giac")
[Out]