Optimal. Leaf size=36 \[ \frac{2}{7} a^2 x^{7/2}+\frac{4}{5} a b x^{5/2}+\frac{2}{3} b^2 x^{3/2} \]
[Out]
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Rubi [A] time = 0.0351325, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{2}{7} a^2 x^{7/2}+\frac{4}{5} a b x^{5/2}+\frac{2}{3} b^2 x^{3/2} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^2*x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 5.48002, size = 34, normalized size = 0.94 \[ \frac{2 a^{2} x^{\frac{7}{2}}}{7} + \frac{4 a b x^{\frac{5}{2}}}{5} + \frac{2 b^{2} x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**2*x**(5/2),x)
[Out]
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Mathematica [A] time = 0.0118147, size = 28, normalized size = 0.78 \[ \frac{2}{105} x^{3/2} \left (15 a^2 x^2+42 a b x+35 b^2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^2*x^(5/2),x]
[Out]
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Maple [A] time = 0.007, size = 25, normalized size = 0.7 \[{\frac{30\,{a}^{2}{x}^{2}+84\,abx+70\,{b}^{2}}{105}{x}^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^2*x^(5/2),x)
[Out]
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Maxima [A] time = 1.43676, size = 35, normalized size = 0.97 \[ \frac{2}{105} \,{\left (15 \, a^{2} + \frac{42 \, a b}{x} + \frac{35 \, b^{2}}{x^{2}}\right )} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2*x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.230686, size = 36, normalized size = 1. \[ \frac{2}{105} \,{\left (15 \, a^{2} x^{3} + 42 \, a b x^{2} + 35 \, b^{2} x\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2*x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 9.34088, size = 34, normalized size = 0.94 \[ \frac{2 a^{2} x^{\frac{7}{2}}}{7} + \frac{4 a b x^{\frac{5}{2}}}{5} + \frac{2 b^{2} x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**2*x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.226156, size = 32, normalized size = 0.89 \[ \frac{2}{7} \, a^{2} x^{\frac{7}{2}} + \frac{4}{5} \, a b x^{\frac{5}{2}} + \frac{2}{3} \, b^{2} x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2*x^(5/2),x, algorithm="giac")
[Out]