Optimal. Leaf size=19 \[ 2 b \sqrt{x}-\frac{2 a}{3 x^{3/2}} \]
[Out]
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Rubi [A] time = 0.0143439, 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 \[ 2 b \sqrt{x}-\frac{2 a}{3 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)/x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 3.0378, size = 17, normalized size = 0.89 \[ - \frac{2 a}{3 x^{\frac{3}{2}}} + 2 b \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.0097822, size = 19, normalized size = 1. \[ 2 b \sqrt{x}-\frac{2 a}{3 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)/x^(5/2),x]
[Out]
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Maple [A] time = 0.004, size = 14, normalized size = 0.7 \[ -{\frac{-6\,b{x}^{2}+2\,a}{3}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)/x^(5/2),x)
[Out]
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Maxima [A] time = 1.34604, size = 18, normalized size = 0.95 \[ 2 \, b \sqrt{x} - \frac{2 \, a}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)/x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.252376, size = 20, normalized size = 1.05 \[ \frac{2 \,{\left (3 \, b x^{2} - a\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)/x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.1549, size = 17, normalized size = 0.89 \[ - \frac{2 a}{3 x^{\frac{3}{2}}} + 2 b \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)/x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.211383, size = 18, normalized size = 0.95 \[ 2 \, b \sqrt{x} - \frac{2 \, a}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)/x^(5/2),x, algorithm="giac")
[Out]