Optimal. Leaf size=32 \[ 2 a^2 \sqrt{x}-\frac{4 a b}{\sqrt{x}}-\frac{2 b^2}{3 x^{3/2}} \]
[Out]
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Rubi [A] time = 0.0343118, antiderivative size = 32, 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 \[ 2 a^2 \sqrt{x}-\frac{4 a b}{\sqrt{x}}-\frac{2 b^2}{3 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^2/Sqrt[x],x]
[Out]
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Rubi in Sympy [A] time = 5.75081, size = 31, normalized size = 0.97 \[ 2 a^{2} \sqrt{x} - \frac{4 a b}{\sqrt{x}} - \frac{2 b^{2}}{3 x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**2/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.0128656, size = 26, normalized size = 0.81 \[ -\frac{2 \left (-3 a^2 x^2+6 a b x+b^2\right )}{3 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^2/Sqrt[x],x]
[Out]
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Maple [A] time = 0.007, size = 25, normalized size = 0.8 \[{\frac{6\,{a}^{2}{x}^{2}-12\,abx-2\,{b}^{2}}{3}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^2/x^(1/2),x)
[Out]
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Maxima [A] time = 1.44025, size = 32, normalized size = 1. \[ 2 \, a^{2} \sqrt{x} - \frac{4 \, a b}{\sqrt{x}} - \frac{2 \, b^{2}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2/sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229627, size = 32, normalized size = 1. \[ \frac{2 \,{\left (3 \, a^{2} x^{2} - 6 \, a b x - b^{2}\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2/sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.89755, size = 31, normalized size = 0.97 \[ 2 a^{2} \sqrt{x} - \frac{4 a b}{\sqrt{x}} - \frac{2 b^{2}}{3 x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**2/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.221466, size = 31, normalized size = 0.97 \[ 2 \, a^{2} \sqrt{x} - \frac{2 \,{\left (6 \, a b x + b^{2}\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2/sqrt(x),x, algorithm="giac")
[Out]