Optimal. Leaf size=15 \[ \frac{\sqrt{x}}{\sqrt{b x+2}} \]
[Out]
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Rubi [A] time = 0.0110465, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{\sqrt{x}}{\sqrt{b x+2}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[x]*(2 + b*x)^(3/2)),x]
[Out]
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Rubi in Sympy [A] time = 2.04892, size = 12, normalized size = 0.8 \[ \frac{\sqrt{x}}{\sqrt{b x + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x+2)**(3/2)/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.0107898, size = 15, normalized size = 1. \[ \frac{\sqrt{x}}{\sqrt{b x+2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[x]*(2 + b*x)^(3/2)),x]
[Out]
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Maple [A] time = 0.005, size = 12, normalized size = 0.8 \[{1\sqrt{x}{\frac{1}{\sqrt{bx+2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x+2)^(3/2)/x^(1/2),x)
[Out]
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Maxima [A] time = 1.35111, size = 15, normalized size = 1. \[ \frac{\sqrt{x}}{\sqrt{b x + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + 2)^(3/2)*sqrt(x)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208228, size = 15, normalized size = 1. \[ \frac{\sqrt{x}}{\sqrt{b x + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + 2)^(3/2)*sqrt(x)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.35119, size = 15, normalized size = 1. \[ \frac{1}{\sqrt{b} \sqrt{1 + \frac{2}{b x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x+2)**(3/2)/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212357, size = 59, normalized size = 3.93 \[ \frac{4 \, b^{\frac{3}{2}}}{{\left ({\left (\sqrt{b x + 2} \sqrt{b} - \sqrt{{\left (b x + 2\right )} b - 2 \, b}\right )}^{2} + 2 \, b\right )}{\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + 2)^(3/2)*sqrt(x)),x, algorithm="giac")
[Out]