Optimal. Leaf size=32 \[ \frac{2}{3} a^2 x^{3/2}+4 a b \sqrt{x}-\frac{2 b^2}{\sqrt{x}} \]
[Out]
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Rubi [A] time = 0.0349985, 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 \[ \frac{2}{3} a^2 x^{3/2}+4 a b \sqrt{x}-\frac{2 b^2}{\sqrt{x}} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^2*Sqrt[x],x]
[Out]
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Rubi in Sympy [A] time = 5.58337, size = 31, normalized size = 0.97 \[ \frac{2 a^{2} x^{\frac{3}{2}}}{3} + 4 a b \sqrt{x} - \frac{2 b^{2}}{\sqrt{x}} \]
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 = 0.013038, size = 27, normalized size = 0.84 \[ \frac{2 \left (a^2 x^2+6 a b x-3 b^2\right )}{3 \sqrt{x}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^2*Sqrt[x],x]
[Out]
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Maple [A] time = 0.007, size = 24, normalized size = 0.8 \[{\frac{2\,{a}^{2}{x}^{2}+12\,abx-6\,{b}^{2}}{3}{\frac{1}{\sqrt{x}}}} \]
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 = 1.44129, size = 34, normalized size = 1.06 \[ \frac{2}{3} \,{\left (a^{2} + \frac{6 \, a b}{x}\right )} x^{\frac{3}{2}} - \frac{2 \, b^{2}}{\sqrt{x}} \]
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 = 0.22572, size = 31, normalized size = 0.97 \[ \frac{2 \,{\left (a^{2} x^{2} + 6 \, a b x - 3 \, b^{2}\right )}}{3 \, \sqrt{x}} \]
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 = 1.89636, size = 31, normalized size = 0.97 \[ \frac{2 a^{2} x^{\frac{3}{2}}}{3} + 4 a b \sqrt{x} - \frac{2 b^{2}}{\sqrt{x}} \]
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 = 0.225498, size = 32, normalized size = 1. \[ \frac{2}{3} \, a^{2} x^{\frac{3}{2}} + 4 \, a b \sqrt{x} - \frac{2 \, b^{2}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2*sqrt(x),x, algorithm="giac")
[Out]