Optimal. Leaf size=24 \[ -\frac{2 x^{-n}}{3 b n \sqrt{b x^n}} \]
[Out]
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Rubi [A] time = 0.0134057, antiderivative size = 24, 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 \[ -\frac{2 x^{-n}}{3 b n \sqrt{b x^n}} \]
Antiderivative was successfully verified.
[In] Int[1/(x*(b*x^n)^(3/2)),x]
[Out]
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Rubi in Sympy [A] time = 2.811, size = 14, normalized size = 0.58 \[ - \frac{2}{3 n \left (b x^{n}\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(b*x**n)**(3/2),x)
[Out]
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Mathematica [A] time = 0.00612223, size = 16, normalized size = 0.67 \[ -\frac{2}{3 n \left (b x^n\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(b*x^n)^(3/2)),x]
[Out]
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Maple [A] time = 0.003, size = 13, normalized size = 0.5 \[ -{\frac{2}{3\,n} \left ( b{x}^{n} \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(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),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.279358, size = 27, normalized size = 1.12 \[ -\frac{2}{3 \, \sqrt{b x^{n}} b n x^{n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^n)^(3/2)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 9.45232, size = 26, normalized size = 1.08 \[ \begin{cases} - \frac{2}{3 b^{\frac{3}{2}} n \left (x^{n}\right )^{\frac{3}{2}}} & \text{for}\: n \neq 0 \\\frac{\log{\left (x \right )}}{b^{\frac{3}{2}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(b*x**n)**(3/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (b x^{n}\right )^{\frac{3}{2}} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^n)^(3/2)*x),x, algorithm="giac")
[Out]