Optimal. Leaf size=21 \[ -\frac{2 \sqrt{a+b x}}{a \sqrt{c x}} \]
[Out]
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Rubi [A] time = 0.0210846, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ -\frac{2 \sqrt{a+b x}}{a \sqrt{c x}} \]
Antiderivative was successfully verified.
[In] Int[1/(x*Sqrt[c*x]*Sqrt[a + b*x]),x]
[Out]
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Rubi in Sympy [A] time = 3.47961, size = 19, normalized size = 0.9 \[ - \frac{2 \sqrt{a + b x}}{a \sqrt{c x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(c*x)**(1/2)/(b*x+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0227006, size = 23, normalized size = 1.1 \[ -\frac{2 c x \sqrt{a+b x}}{a (c x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*Sqrt[c*x]*Sqrt[a + b*x]),x]
[Out]
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Maple [A] time = 0.007, size = 18, normalized size = 0.9 \[ -2\,{\frac{\sqrt{bx+a}}{a\sqrt{cx}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(c*x)^(1/2)/(b*x+a)^(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(b*x + a)*sqrt(c*x)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21755, size = 31, normalized size = 1.48 \[ -\frac{2 \, \sqrt{b x + a} \sqrt{c x}}{a c x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + a)*sqrt(c*x)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.9157, size = 24, normalized size = 1.14 \[ - \frac{2 \sqrt{b} \sqrt{\frac{a}{b x} + 1}}{a \sqrt{c}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(c*x)**(1/2)/(b*x+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.238733, size = 47, normalized size = 2.24 \[ -\frac{2 \, \sqrt{b x + a} b^{2}}{\sqrt{{\left (b x + a\right )} b c - a b c} a{\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + a)*sqrt(c*x)*x),x, algorithm="giac")
[Out]