Optimal. Leaf size=18 \[ -\frac{2 \left (a+\frac{b}{x}\right )^{5/2}}{5 b} \]
[Out]
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Rubi [A] time = 0.0248153, antiderivative size = 18, 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 \[ -\frac{2 \left (a+\frac{b}{x}\right )^{5/2}}{5 b} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^(3/2)/x^2,x]
[Out]
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Rubi in Sympy [A] time = 2.18905, size = 14, normalized size = 0.78 \[ - \frac{2 \left (a + \frac{b}{x}\right )^{\frac{5}{2}}}{5 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**(3/2)/x**2,x)
[Out]
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Mathematica [A] time = 0.0219896, size = 18, normalized size = 1. \[ -\frac{2 \left (a+\frac{b}{x}\right )^{5/2}}{5 b} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^(3/2)/x^2,x]
[Out]
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Maple [A] time = 0.008, size = 25, normalized size = 1.4 \[ -{\frac{2\,ax+2\,b}{5\,bx} \left ({\frac{ax+b}{x}} \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^(3/2)/x^2,x)
[Out]
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Maxima [A] time = 1.43651, size = 19, normalized size = 1.06 \[ -\frac{2 \,{\left (a + \frac{b}{x}\right )}^{\frac{5}{2}}}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^(3/2)/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221582, size = 47, normalized size = 2.61 \[ -\frac{2 \,{\left (a^{2} x^{2} + 2 \, a b x + b^{2}\right )} \sqrt{\frac{a x + b}{x}}}{5 \, b x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^(3/2)/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.1317, size = 65, normalized size = 3.61 \[ - \frac{2 a^{\frac{5}{2}} \sqrt{1 + \frac{b}{a x}}}{5 b} - \frac{4 a^{\frac{3}{2}} \sqrt{1 + \frac{b}{a x}}}{5 x} - \frac{2 \sqrt{a} b \sqrt{1 + \frac{b}{a x}}}{5 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**(3/2)/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.256799, size = 196, normalized size = 10.89 \[ \frac{2 \,{\left (5 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{4} a^{2}{\rm sign}\left (x\right ) + 10 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{3} a^{\frac{3}{2}} b{\rm sign}\left (x\right ) + 10 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{2} a b^{2}{\rm sign}\left (x\right ) + 5 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )} \sqrt{a} b^{3}{\rm sign}\left (x\right ) + b^{4}{\rm sign}\left (x\right )\right )}}{5 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^(3/2)/x^2,x, algorithm="giac")
[Out]