Optimal. Leaf size=28 \[ \frac{2 x^{1-n}}{b (2-3 n) \sqrt{b x^n}} \]
[Out]
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Rubi [A] time = 0.0201196, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{2 x^{1-n}}{b (2-3 n) \sqrt{b x^n}} \]
Antiderivative was successfully verified.
[In] Int[(b*x^n)^(-3/2),x]
[Out]
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Rubi in Sympy [A] time = 2.88221, size = 31, normalized size = 1.11 \[ \frac{2 x^{- \frac{n}{2}} x^{- \frac{3 n}{2} + 1} \sqrt{b x^{n}}}{b^{2} \left (- 3 n + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x**n)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0117402, size = 20, normalized size = 0.71 \[ \frac{x}{\left (1-\frac{3 n}{2}\right ) \left (b x^n\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^n)^(-3/2),x]
[Out]
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Maple [A] time = 0.001, size = 18, normalized size = 0.6 \[ -2\,{\frac{x}{ \left ( -2+3\,n \right ) \left ( b{x}^{n} \right ) ^{3/2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(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((b*x^n)^(-3/2),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((b*x^n)^(-3/2),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/(b*x**n)**(3/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (b x^{n}\right )^{\frac{3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n)^(-3/2),x, algorithm="giac")
[Out]