Optimal. Leaf size=28 \[ -\frac{2 x^{-n-1}}{b (3 n+2) \sqrt{b x^n}} \]
[Out]
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Rubi [A] time = 0.0199551, antiderivative size = 28, 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 \[ -\frac{2 x^{-n-1}}{b (3 n+2) \sqrt{b x^n}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^2*(b*x^n)^(3/2)),x]
[Out]
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Rubi in Sympy [A] time = 3.69021, size = 34, normalized size = 1.21 \[ - \frac{2 x^{- \frac{n}{2}} x^{- \frac{3 n}{2} - 1} \sqrt{b x^{n}}}{b^{2} \left (3 n + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**2/(b*x**n)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0199225, size = 22, normalized size = 0.79 \[ \frac{1}{\left (-\frac{3 n}{2}-1\right ) x \left (b x^n\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^2*(b*x^n)^(3/2)),x]
[Out]
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Maple [A] time = 0.003, size = 20, normalized size = 0.7 \[ -2\,{\frac{1}{x \left ( 2+3\,n \right ) \left ( b{x}^{n} \right ) ^{3/2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^2/(b*x^n)^(3/2),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/((b*x^n)^(3/2)*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/((b*x^n)^(3/2)*x^2),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**2/(b*x**n)**(3/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (b x^{n}\right )^{\frac{3}{2}} x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^n)^(3/2)*x^2),x, algorithm="giac")
[Out]