Optimal. Leaf size=19 \[ -\frac{2}{(n+2) x \sqrt{b x^n}} \]
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Rubi [A] time = 0.0137036, antiderivative size = 19, 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 \[ -\frac{2}{(n+2) x \sqrt{b x^n}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^2*Sqrt[b*x^n]),x]
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Rubi in Sympy [A] time = 3.59663, size = 29, normalized size = 1.53 \[ - \frac{2 x^{- \frac{n}{2}} x^{- \frac{n}{2} - 1} \sqrt{b x^{n}}}{b \left (n + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**2/(b*x**n)**(1/2),x)
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Mathematica [A] time = 0.00719642, size = 19, normalized size = 1. \[ -\frac{2}{(n+2) x \sqrt{b x^n}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^2*Sqrt[b*x^n]),x]
[Out]
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Maple [A] time = 0.002, size = 18, normalized size = 1. \[ -2\,{\frac{1}{ \left ( 2+n \right ) x\sqrt{b{x}^{n}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^2/(b*x^n)^(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^n)*x^2),x, algorithm="maxima")
[Out]
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^n)*x^2),x, algorithm="fricas")
[Out]
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**2/(b*x**n)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{b x^{n}} x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^n)*x^2),x, algorithm="giac")
[Out]