Optimal. Leaf size=13 \[ -\frac{3}{16} \left (\frac{1}{x^2}+1\right )^{8/3} \]
[Out]
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Rubi [A] time = 0.0168628, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{3}{16} \left (\frac{1}{x^2}+1\right )^{8/3} \]
Antiderivative was successfully verified.
[In] Int[(1 + x^(-2))^(5/3)/x^3,x]
[Out]
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Rubi in Sympy [A] time = 1.67006, size = 14, normalized size = 1.08 \[ - \frac{3 \left (1 + \frac{1}{x^{2}}\right )^{\frac{8}{3}}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+1/x**2)**(5/3)/x**3,x)
[Out]
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Mathematica [A] time = 0.0200953, size = 23, normalized size = 1.77 \[ -\frac{3 \left (\frac{1}{x^2}+1\right )^{2/3} \left (x^2+1\right )^2}{16 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x^(-2))^(5/3)/x^3,x]
[Out]
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Maple [B] time = 0.004, size = 22, normalized size = 1.7 \[ -{\frac{3\,{x}^{2}+3}{16\,{x}^{2}} \left ({\frac{{x}^{2}+1}{{x}^{2}}} \right ) ^{{\frac{5}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+1/x^2)^(5/3)/x^3,x)
[Out]
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Maxima [A] time = 1.43499, size = 12, normalized size = 0.92 \[ -\frac{3}{16} \,{\left (\frac{1}{x^{2}} + 1\right )}^{\frac{8}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1/x^2 + 1)^(5/3)/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.242366, size = 35, normalized size = 2.69 \[ -\frac{3 \,{\left (x^{4} + 2 \, x^{2} + 1\right )} \left (\frac{x^{2} + 1}{x^{2}}\right )^{\frac{2}{3}}}{16 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1/x^2 + 1)^(5/3)/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 8.54398, size = 48, normalized size = 3.69 \[ - \frac{3 \left (1 + \frac{1}{x^{2}}\right )^{\frac{2}{3}}}{16} - \frac{3 \left (1 + \frac{1}{x^{2}}\right )^{\frac{2}{3}}}{8 x^{2}} - \frac{3 \left (1 + \frac{1}{x^{2}}\right )^{\frac{2}{3}}}{16 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+1/x**2)**(5/3)/x**3,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (\frac{1}{x^{2}} + 1\right )}^{\frac{5}{3}}}{x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1/x^2 + 1)^(5/3)/x^3,x, algorithm="giac")
[Out]