Optimal. Leaf size=23 \[ \frac{2 \sqrt{b x+c x^2}}{c \sqrt{x}} \]
[Out]
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Rubi [A] time = 0.0274766, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ \frac{2 \sqrt{b x+c x^2}}{c \sqrt{x}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]/Sqrt[b*x + c*x^2],x]
[Out]
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Rubi in Sympy [A] time = 3.64854, size = 19, normalized size = 0.83 \[ \frac{2 \sqrt{b x + c x^{2}}}{c \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(1/2)/(c*x**2+b*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0160273, size = 21, normalized size = 0.91 \[ \frac{2 \sqrt{x (b+c x)}}{c \sqrt{x}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]/Sqrt[b*x + c*x^2],x]
[Out]
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Maple [A] time = 0.003, size = 25, normalized size = 1.1 \[ 2\,{\frac{ \left ( cx+b \right ) \sqrt{x}}{c\sqrt{c{x}^{2}+bx}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(1/2)/(c*x^2+b*x)^(1/2),x)
[Out]
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Maxima [A] time = 0.71986, size = 16, normalized size = 0.7 \[ \frac{2 \, \sqrt{c x + b}}{c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/sqrt(c*x^2 + b*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219362, size = 26, normalized size = 1.13 \[ \frac{2 \, \sqrt{c x^{2} + b x}}{c \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/sqrt(c*x^2 + b*x),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{x}}{\sqrt{x \left (b + c x\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(1/2)/(c*x**2+b*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.209112, size = 28, normalized size = 1.22 \[ \frac{2 \, \sqrt{c x + b}}{c} - \frac{2 \, \sqrt{b}}{c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/sqrt(c*x^2 + b*x),x, algorithm="giac")
[Out]