Optimal. Leaf size=19 \[ \frac{2}{3} b x^{3/2}-\frac{2 a}{\sqrt{x}} \]
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Rubi [A] time = 0.0137852, 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 \[ \frac{2}{3} b x^{3/2}-\frac{2 a}{\sqrt{x}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)/x^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 2.94843, size = 17, normalized size = 0.89 \[ - \frac{2 a}{\sqrt{x}} + \frac{2 b x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)/x**(3/2),x)
[Out]
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Mathematica [A] time = 0.00933006, size = 19, normalized size = 1. \[ \frac{2}{3} b x^{3/2}-\frac{2 a}{\sqrt{x}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)/x^(3/2),x]
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Maple [A] time = 0.005, size = 16, normalized size = 0.8 \[ -{\frac{-2\,b{x}^{2}+6\,a}{3}{\frac{1}{\sqrt{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)/x^(3/2),x)
[Out]
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Maxima [A] time = 1.34411, size = 18, normalized size = 0.95 \[ \frac{2}{3} \, b x^{\frac{3}{2}} - \frac{2 \, a}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)/x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.250493, size = 19, normalized size = 1. \[ \frac{2 \,{\left (b x^{2} - 3 \, a\right )}}{3 \, \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)/x^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.5558, size = 17, normalized size = 0.89 \[ - \frac{2 a}{\sqrt{x}} + \frac{2 b x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)/x**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.209861, size = 18, normalized size = 0.95 \[ \frac{2}{3} \, b x^{\frac{3}{2}} - \frac{2 \, a}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)/x^(3/2),x, algorithm="giac")
[Out]