Optimal. Leaf size=21 \[ -\frac{2 (a+b x)^{3/2}}{3 a x^{3/2}} \]
[Out]
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Rubi [A] time = 0.0124835, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{2 (a+b x)^{3/2}}{3 a x^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a + b*x]/x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 2.24457, size = 19, normalized size = 0.9 \[ - \frac{2 \left (a + b x\right )^{\frac{3}{2}}}{3 a x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**(1/2)/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.0148005, size = 21, normalized size = 1. \[ -\frac{2 (a+b x)^{3/2}}{3 a x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a + b*x]/x^(5/2),x]
[Out]
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Maple [A] time = 0.006, size = 16, normalized size = 0.8 \[ -{\frac{2}{3\,a} \left ( bx+a \right ) ^{{\frac{3}{2}}}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^(1/2)/x^(5/2),x)
[Out]
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Maxima [A] time = 1.3717, size = 20, normalized size = 0.95 \[ -\frac{2 \,{\left (b x + a\right )}^{\frac{3}{2}}}{3 \, a x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x + a)/x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.231112, size = 20, normalized size = 0.95 \[ -\frac{2 \,{\left (b x + a\right )}^{\frac{3}{2}}}{3 \, a x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x + a)/x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 13.258, size = 41, normalized size = 1.95 \[ - \frac{2 \sqrt{b} \sqrt{\frac{a}{b x} + 1}}{3 x} - \frac{2 b^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}}{3 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**(1/2)/x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.214084, size = 45, normalized size = 2.14 \[ -\frac{2 \,{\left (b x + a\right )}^{\frac{3}{2}} b^{4}}{3 \,{\left ({\left (b x + a\right )} b - a b\right )}^{\frac{3}{2}} a{\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x + a)/x^(5/2),x, algorithm="giac")
[Out]