Optimal. Leaf size=21 \[ -\frac{2 \sqrt{b x+c x^2}}{b x} \]
[Out]
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Rubi [A] time = 0.0293648, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ -\frac{2 \sqrt{b x+c x^2}}{b x} \]
Antiderivative was successfully verified.
[In] Int[1/(x*Sqrt[b*x + c*x^2]),x]
[Out]
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Rubi in Sympy [A] time = 3.83977, size = 17, normalized size = 0.81 \[ - \frac{2 \sqrt{b x + c x^{2}}}{b x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(c*x**2+b*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0187811, size = 21, normalized size = 1. \[ -\frac{2 (b+c x)}{b \sqrt{x (b+c x)}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*Sqrt[b*x + c*x^2]),x]
[Out]
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Maple [A] time = 0.005, size = 22, normalized size = 1.1 \[ -2\,{\frac{cx+b}{b\sqrt{c{x}^{2}+bx}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(c*x^2+b*x)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(c*x^2 + b*x)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215935, size = 26, normalized size = 1.24 \[ -\frac{2 \, \sqrt{c x^{2} + b x}}{b x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(c*x^2 + b*x)*x),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{x \sqrt{x \left (b + c x\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(c*x**2+b*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.217975, size = 31, normalized size = 1.48 \[ \frac{2}{\sqrt{c} x - \sqrt{c x^{2} + b x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(c*x^2 + b*x)*x),x, algorithm="giac")
[Out]