Optimal. Leaf size=19 \[ -\frac{a}{2 x^2}-\frac{2 b}{3 x^{3/2}} \]
[Out]
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Rubi [A] time = 0.0163598, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{a}{2 x^2}-\frac{2 b}{3 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])/x^3,x]
[Out]
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Rubi in Sympy [A] time = 2.83381, size = 17, normalized size = 0.89 \[ - \frac{a}{2 x^{2}} - \frac{2 b}{3 x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))/x**3,x)
[Out]
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Mathematica [A] time = 0.00728313, size = 19, normalized size = 1. \[ -\frac{a}{2 x^2}-\frac{2 b}{3 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])/x^3,x]
[Out]
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Maple [A] time = 0.003, size = 14, normalized size = 0.7 \[ -{\frac{a}{2\,{x}^{2}}}-{\frac{2\,b}{3}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))/x^3,x)
[Out]
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Maxima [A] time = 1.44051, size = 20, normalized size = 1.05 \[ -\frac{4 \, b \sqrt{x} + 3 \, a}{6 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.23698, size = 20, normalized size = 1.05 \[ -\frac{4 \, b \sqrt{x} + 3 \, a}{6 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.10536, size = 17, normalized size = 0.89 \[ - \frac{a}{2 x^{2}} - \frac{2 b}{3 x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.213635, size = 20, normalized size = 1.05 \[ -\frac{4 \, b \sqrt{x} + 3 \, a}{6 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)/x^3,x, algorithm="giac")
[Out]