Optimal. Leaf size=47 \[ -\frac{2 a^3}{\sqrt{x}}-\frac{2 a^2 b}{x^{3/2}}-\frac{6 a b^2}{5 x^{5/2}}-\frac{2 b^3}{7 x^{7/2}} \]
[Out]
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Rubi [A] time = 0.0443205, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{2 a^3}{\sqrt{x}}-\frac{2 a^2 b}{x^{3/2}}-\frac{6 a b^2}{5 x^{5/2}}-\frac{2 b^3}{7 x^{7/2}} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^3/x^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 6.91969, size = 48, normalized size = 1.02 \[ - \frac{2 a^{3}}{\sqrt{x}} - \frac{2 a^{2} b}{x^{\frac{3}{2}}} - \frac{6 a b^{2}}{5 x^{\frac{5}{2}}} - \frac{2 b^{3}}{7 x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**3/x**(3/2),x)
[Out]
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Mathematica [A] time = 0.015259, size = 39, normalized size = 0.83 \[ -\frac{2 \left (35 a^3 x^3+35 a^2 b x^2+21 a b^2 x+5 b^3\right )}{35 x^{7/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^3/x^(3/2),x]
[Out]
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Maple [A] time = 0.006, size = 36, normalized size = 0.8 \[ -{\frac{70\,{a}^{3}{x}^{3}+70\,{a}^{2}b{x}^{2}+42\,a{b}^{2}x+10\,{b}^{3}}{35}{x}^{-{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^3/x^(3/2),x)
[Out]
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Maxima [A] time = 1.4354, size = 47, normalized size = 1. \[ -\frac{2 \, a^{3}}{\sqrt{x}} - \frac{2 \, a^{2} b}{x^{\frac{3}{2}}} - \frac{6 \, a b^{2}}{5 \, x^{\frac{5}{2}}} - \frac{2 \, b^{3}}{7 \, x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22739, size = 47, normalized size = 1. \[ -\frac{2 \,{\left (35 \, a^{3} x^{3} + 35 \, a^{2} b x^{2} + 21 \, a b^{2} x + 5 \, b^{3}\right )}}{35 \, x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.06745, size = 48, normalized size = 1.02 \[ - \frac{2 a^{3}}{\sqrt{x}} - \frac{2 a^{2} b}{x^{\frac{3}{2}}} - \frac{6 a b^{2}}{5 x^{\frac{5}{2}}} - \frac{2 b^{3}}{7 x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**3/x**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.225696, size = 47, normalized size = 1. \[ -\frac{2 \,{\left (35 \, a^{3} x^{3} + 35 \, a^{2} b x^{2} + 21 \, a b^{2} x + 5 \, b^{3}\right )}}{35 \, x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^(3/2),x, algorithm="giac")
[Out]