Optimal. Leaf size=21 \[ -\frac{1}{2 a x^2 \sqrt{a+\frac{b}{x^4}}} \]
[Out]
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Rubi [A] time = 0.0317186, antiderivative size = 21, 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 \[ -\frac{1}{2 a x^2 \sqrt{a+\frac{b}{x^4}}} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x^4)^(3/2)*x^3),x]
[Out]
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Rubi in Sympy [A] time = 2.67723, size = 19, normalized size = 0.9 \[ - \frac{1}{2 a x^{2} \sqrt{a + \frac{b}{x^{4}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x**4)**(3/2)/x**3,x)
[Out]
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Mathematica [A] time = 0.00980364, size = 21, normalized size = 1. \[ -\frac{1}{2 a x^2 \sqrt{a+\frac{b}{x^4}}} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x^4)^(3/2)*x^3),x]
[Out]
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Maple [A] time = 0.007, size = 29, normalized size = 1.4 \[ -{\frac{a{x}^{4}+b}{2\,{x}^{6}a} \left ({\frac{a{x}^{4}+b}{{x}^{4}}} \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x^4)^(3/2)/x^3,x)
[Out]
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Maxima [A] time = 1.42855, size = 23, normalized size = 1.1 \[ -\frac{1}{2 \, \sqrt{a + \frac{b}{x^{4}}} a x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^4)^(3/2)*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.235513, size = 42, normalized size = 2. \[ -\frac{x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{2 \,{\left (a^{2} x^{4} + a b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^4)^(3/2)*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 6.77622, size = 22, normalized size = 1.05 \[ - \frac{1}{2 a \sqrt{b} \sqrt{\frac{a x^{4}}{b} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x**4)**(3/2)/x**3,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (a + \frac{b}{x^{4}}\right )}^{\frac{3}{2}} x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^4)^(3/2)*x^3),x, algorithm="giac")
[Out]