Optimal. Leaf size=15 \[ \frac{\sqrt{b x^2} \log (x)}{x} \]
[Out]
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Rubi [A] time = 0.00696891, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{\sqrt{b x^2} \log (x)}{x} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[b*x^2]/x^2,x]
[Out]
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Rubi in Sympy [A] time = 1.91304, size = 12, normalized size = 0.8 \[ \frac{\sqrt{b x^{2}} \log{\left (x \right )}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2)**(1/2)/x**2,x)
[Out]
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Mathematica [A] time = 0.0026693, size = 14, normalized size = 0.93 \[ \frac{b x \log (x)}{\sqrt{b x^2}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[b*x^2]/x^2,x]
[Out]
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Maple [A] time = 0.005, size = 14, normalized size = 0.9 \[{\frac{\ln \left ( x \right ) }{x}\sqrt{b{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2)^(1/2)/x^2,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^2)/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.226209, size = 18, normalized size = 1.2 \[ \frac{\sqrt{b x^{2}} \log \left (x\right )}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^2)/x^2,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{b x^{2}}}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2)**(1/2)/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.211894, size = 12, normalized size = 0.8 \[ \sqrt{b}{\rm ln}\left ({\left | x \right |}\right ){\rm sign}\left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^2)/x^2,x, algorithm="giac")
[Out]