Optimal. Leaf size=23 \[ -\frac{2}{3 a x^{3/2} \left (a+\frac{b}{x}\right )^{3/2}} \]
[Out]
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Rubi [A] time = 0.0261001, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ -\frac{2}{3 a x^{3/2} \left (a+\frac{b}{x}\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x)^(5/2)*x^(5/2)),x]
[Out]
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Rubi in Sympy [A] time = 2.66811, size = 19, normalized size = 0.83 \[ - \frac{2}{3 a x^{\frac{3}{2}} \left (a + \frac{b}{x}\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x)**(5/2)/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.0361117, size = 32, normalized size = 1.39 \[ -\frac{2 \sqrt{x} \sqrt{\frac{a x+b}{x}}}{3 a (a x+b)^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x)^(5/2)*x^(5/2)),x]
[Out]
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Maple [A] time = 0.004, size = 25, normalized size = 1.1 \[ -{\frac{2\,ax+2\,b}{3\,a} \left ({\frac{ax+b}{x}} \right ) ^{-{\frac{5}{2}}}{x}^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x)^(5/2)/x^(5/2),x)
[Out]
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Maxima [A] time = 1.45287, size = 23, normalized size = 1. \[ -\frac{2}{3 \,{\left (a + \frac{b}{x}\right )}^{\frac{3}{2}} a x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^(5/2)*x^(5/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.233572, size = 36, normalized size = 1.57 \[ -\frac{2}{3 \,{\left (a^{2} x + a b\right )} \sqrt{x} \sqrt{\frac{a x + b}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^(5/2)*x^(5/2)),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/(a+b/x)**(5/2)/x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.228608, size = 28, normalized size = 1.22 \[ -\frac{2}{3 \,{\left (a x + b\right )}^{\frac{3}{2}} a} + \frac{2}{3 \, a b^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^(5/2)*x^(5/2)),x, algorithm="giac")
[Out]