Optimal. Leaf size=39 \[ \frac{2}{7} x^{7/2} (a B+A b)+\frac{2}{3} a A x^{3/2}+\frac{2}{11} b B x^{11/2} \]
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Rubi [A] time = 0.0470413, 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 \[ \frac{2}{7} x^{7/2} (a B+A b)+\frac{2}{3} a A x^{3/2}+\frac{2}{11} b B x^{11/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]*(a + b*x^2)*(A + B*x^2),x]
[Out]
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Rubi in Sympy [A] time = 7.1917, size = 41, normalized size = 1.05 \[ \frac{2 A a x^{\frac{3}{2}}}{3} + \frac{2 B b x^{\frac{11}{2}}}{11} + x^{\frac{7}{2}} \left (\frac{2 A b}{7} + \frac{2 B a}{7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)*(B*x**2+A)*x**(1/2),x)
[Out]
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Mathematica [A] time = 0.0169348, size = 33, normalized size = 0.85 \[ \frac{2}{231} x^{3/2} \left (33 x^2 (a B+A b)+77 a A+21 b B x^4\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]*(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 \[{\frac{42\,bB{x}^{4}+66\,A{x}^{2}b+66\,B{x}^{2}a+154\,Aa}{231}{x}^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)*(B*x^2+A)*x^(1/2),x)
[Out]
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Maxima [A] time = 1.35088, size = 36, normalized size = 0.92 \[ \frac{2}{11} \, B b x^{\frac{11}{2}} + \frac{2}{7} \,{\left (B a + A b\right )} x^{\frac{7}{2}} + \frac{2}{3} \, A a x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)*sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220071, size = 41, normalized size = 1.05 \[ \frac{2}{231} \,{\left (21 \, B b x^{5} + 33 \,{\left (B a + A b\right )} x^{3} + 77 \, A a x\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)*sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.64564, size = 37, normalized size = 0.95 \[ \frac{2 A a x^{\frac{3}{2}}}{3} + \frac{2 B b x^{\frac{11}{2}}}{11} + \frac{2 x^{\frac{7}{2}} \left (A b + B a\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)*(B*x**2+A)*x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.250886, size = 39, normalized size = 1. \[ \frac{2}{11} \, B b x^{\frac{11}{2}} + \frac{2}{7} \, B a x^{\frac{7}{2}} + \frac{2}{7} \, A b x^{\frac{7}{2}} + \frac{2}{3} \, A a x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)*sqrt(x),x, algorithm="giac")
[Out]