Optimal. Leaf size=19 \[ -\frac{2 a}{3 x^{3/2}}-\frac{2 b}{\sqrt{x}} \]
[Out]
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Rubi [A] time = 0.0131644, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{2 a}{3 x^{3/2}}-\frac{2 b}{\sqrt{x}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)/x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 2.3363, size = 19, normalized size = 1. \[ - \frac{2 a}{3 x^{\frac{3}{2}}} - \frac{2 b}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.00556482, size = 15, normalized size = 0.79 \[ -\frac{2 (a+3 b x)}{3 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)/x^(5/2),x]
[Out]
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Maple [A] time = 0.003, size = 12, normalized size = 0.6 \[ -{\frac{6\,bx+2\,a}{3}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)/x^(5/2),x)
[Out]
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Maxima [A] time = 1.34283, size = 15, normalized size = 0.79 \[ -\frac{2 \,{\left (3 \, b x + a\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206976, size = 15, normalized size = 0.79 \[ -\frac{2 \,{\left (3 \, b x + a\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.06573, size = 19, normalized size = 1. \[ - \frac{2 a}{3 x^{\frac{3}{2}}} - \frac{2 b}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)/x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.2063, size = 15, normalized size = 0.79 \[ -\frac{2 \,{\left (3 \, b x + a\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/x^(5/2),x, algorithm="giac")
[Out]