Optimal. Leaf size=24 \[ -\frac{a^2}{x}-\frac{4 a b}{\sqrt{x}}+b^2 \log (x) \]
[Out]
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Rubi [A] time = 0.0411095, antiderivative size = 24, 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 \[ -\frac{a^2}{x}-\frac{4 a b}{\sqrt{x}}+b^2 \log (x) \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^2/x^2,x]
[Out]
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Rubi in Sympy [A] time = 6.14257, size = 26, normalized size = 1.08 \[ - \frac{a^{2}}{x} - \frac{4 a b}{\sqrt{x}} + 2 b^{2} \log{\left (\sqrt{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**2/x**2,x)
[Out]
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Mathematica [A] time = 0.0216814, size = 23, normalized size = 0.96 \[ b^2 \log (x)-\frac{a \left (a+4 b \sqrt{x}\right )}{x} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^2/x^2,x]
[Out]
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Maple [A] time = 0.003, size = 23, normalized size = 1. \[ -{\frac{{a}^{2}}{x}}+{b}^{2}\ln \left ( x \right ) -4\,{\frac{ab}{\sqrt{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^2/x^2,x)
[Out]
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Maxima [A] time = 1.44026, size = 31, normalized size = 1.29 \[ b^{2} \log \left (x\right ) - \frac{4 \, a b \sqrt{x} + a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.234225, size = 36, normalized size = 1.5 \[ \frac{2 \, b^{2} x \log \left (\sqrt{x}\right ) - 4 \, a b \sqrt{x} - a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.60933, size = 20, normalized size = 0.83 \[ - \frac{a^{2}}{x} - \frac{4 a b}{\sqrt{x}} + b^{2} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**2/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.216487, size = 32, normalized size = 1.33 \[ b^{2}{\rm ln}\left ({\left | x \right |}\right ) - \frac{4 \, a b \sqrt{x} + a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2/x^2,x, algorithm="giac")
[Out]