Optimal. Leaf size=18 \[ -\frac{2 \left (a+\frac{b}{x^3}\right )^{3/2}}{9 b} \]
[Out]
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Rubi [A] time = 0.029736, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{2 \left (a+\frac{b}{x^3}\right )^{3/2}}{9 b} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a + b/x^3]/x^4,x]
[Out]
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Rubi in Sympy [A] time = 2.1002, size = 15, normalized size = 0.83 \[ - \frac{2 \left (a + \frac{b}{x^{3}}\right )^{\frac{3}{2}}}{9 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**3)**(1/2)/x**4,x)
[Out]
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Mathematica [A] time = 0.033716, size = 18, normalized size = 1. \[ -\frac{2 \left (a+\frac{b}{x^3}\right )^{3/2}}{9 b} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a + b/x^3]/x^4,x]
[Out]
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Maple [A] time = 0.008, size = 29, normalized size = 1.6 \[ -{\frac{2\,a{x}^{3}+2\,b}{9\,b{x}^{3}}\sqrt{{\frac{a{x}^{3}+b}{{x}^{3}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^3)^(1/2)/x^4,x)
[Out]
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Maxima [A] time = 1.44299, size = 19, normalized size = 1.06 \[ -\frac{2 \,{\left (a + \frac{b}{x^{3}}\right )}^{\frac{3}{2}}}{9 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x^3)/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.243108, size = 38, normalized size = 2.11 \[ -\frac{2 \,{\left (a x^{3} + b\right )} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{9 \, b x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x^3)/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.29441, size = 46, normalized size = 2.56 \[ - \frac{2 a^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x^{3}}}}{9 b} - \frac{2 \sqrt{a} \sqrt{1 + \frac{b}{a x^{3}}}}{9 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**3)**(1/2)/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.237493, size = 19, normalized size = 1.06 \[ -\frac{2 \,{\left (a + \frac{b}{x^{3}}\right )}^{\frac{3}{2}}}{9 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x^3)/x^4,x, algorithm="giac")
[Out]