Optimal. Leaf size=48 \[ \frac{2 x^{5/2} \left (a+\frac{b}{x}\right )^{3/2}}{5 a}-\frac{4 b x^{3/2} \left (a+\frac{b}{x}\right )^{3/2}}{15 a^2} \]
[Out]
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Rubi [A] time = 0.051524, antiderivative size = 48, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{2 x^{5/2} \left (a+\frac{b}{x}\right )^{3/2}}{5 a}-\frac{4 b x^{3/2} \left (a+\frac{b}{x}\right )^{3/2}}{15 a^2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a + b/x]*x^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 4.21269, size = 39, normalized size = 0.81 \[ \frac{2 x^{\frac{5}{2}} \left (a + \frac{b}{x}\right )^{\frac{3}{2}}}{5 a} - \frac{4 b x^{\frac{3}{2}} \left (a + \frac{b}{x}\right )^{\frac{3}{2}}}{15 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**(1/2)*x**(3/2),x)
[Out]
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Mathematica [A] time = 0.0344929, size = 41, normalized size = 0.85 \[ \frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} \left (3 a^2 x^2+a b x-2 b^2\right )}{15 a^2} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a + b/x]*x^(3/2),x]
[Out]
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Maple [A] time = 0.004, size = 33, normalized size = 0.7 \[{\frac{ \left ( 2\,ax+2\,b \right ) \left ( 3\,ax-2\,b \right ) }{15\,{a}^{2}}\sqrt{{\frac{ax+b}{x}}}\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^(1/2)*x^(3/2),x)
[Out]
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Maxima [A] time = 1.45693, size = 47, normalized size = 0.98 \[ \frac{2 \,{\left (3 \,{\left (a + \frac{b}{x}\right )}^{\frac{5}{2}} x^{\frac{5}{2}} - 5 \,{\left (a + \frac{b}{x}\right )}^{\frac{3}{2}} b x^{\frac{3}{2}}\right )}}{15 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x)*x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.237594, size = 50, normalized size = 1.04 \[ \frac{2 \,{\left (3 \, a^{2} x^{2} + a b x - 2 \, b^{2}\right )} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{15 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x)*x^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 91.0332, size = 65, normalized size = 1.35 \[ \frac{2 \sqrt{b} x^{2} \sqrt{\frac{a x}{b} + 1}}{5} + \frac{2 b^{\frac{3}{2}} x \sqrt{\frac{a x}{b} + 1}}{15 a} - \frac{4 b^{\frac{5}{2}} \sqrt{\frac{a x}{b} + 1}}{15 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**(1/2)*x**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.234291, size = 50, normalized size = 1.04 \[ \frac{2}{15} \,{\left (\frac{2 \, b^{\frac{5}{2}}}{a^{2}} + \frac{3 \,{\left (a x + b\right )}^{\frac{5}{2}} - 5 \,{\left (a x + b\right )}^{\frac{3}{2}} b}{a^{2}}\right )}{\rm sign}\left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x)*x^(3/2),x, algorithm="giac")
[Out]