Optimal. Leaf size=18 \[ -\frac{2 \left (a+\frac{b}{x}\right )^{7/2}}{7 b} \]
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Rubi [A] time = 0.0263247, 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 \[ -\frac{2 \left (a+\frac{b}{x}\right )^{7/2}}{7 b} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^(5/2)/x^2,x]
[Out]
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Rubi in Sympy [A] time = 2.18791, size = 14, normalized size = 0.78 \[ - \frac{2 \left (a + \frac{b}{x}\right )^{\frac{7}{2}}}{7 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**(5/2)/x**2,x)
[Out]
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Mathematica [A] time = 0.024816, size = 18, normalized size = 1. \[ -\frac{2 \left (a+\frac{b}{x}\right )^{7/2}}{7 b} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^(5/2)/x^2,x]
[Out]
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Maple [A] time = 0.009, size = 25, normalized size = 1.4 \[ -{\frac{2\,ax+2\,b}{7\,bx} \left ({\frac{ax+b}{x}} \right ) ^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^(5/2)/x^2,x)
[Out]
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Maxima [A] time = 1.42586, size = 19, normalized size = 1.06 \[ -\frac{2 \,{\left (a + \frac{b}{x}\right )}^{\frac{7}{2}}}{7 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^(5/2)/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22674, size = 62, normalized size = 3.44 \[ -\frac{2 \,{\left (a^{3} x^{3} + 3 \, a^{2} b x^{2} + 3 \, a b^{2} x + b^{3}\right )} \sqrt{\frac{a x + b}{x}}}{7 \, b x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^(5/2)/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 10.6268, size = 80, normalized size = 4.44 \[ \begin{cases} - \frac{2 a^{3} \sqrt{a + \frac{b}{x}}}{7 b} - \frac{6 a^{2} \sqrt{a + \frac{b}{x}}}{7 x} - \frac{6 a b \sqrt{a + \frac{b}{x}}}{7 x^{2}} - \frac{2 b^{2} \sqrt{a + \frac{b}{x}}}{7 x^{3}} & \text{for}\: b \neq 0 \\- \frac{a^{\frac{5}{2}}}{x} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**(5/2)/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.264229, size = 279, normalized size = 15.5 \[ \frac{2 \,{\left (7 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{6} a^{3}{\rm sign}\left (x\right ) + 21 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{5} a^{\frac{5}{2}} b{\rm sign}\left (x\right ) + 35 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{4} a^{2} b^{2}{\rm sign}\left (x\right ) + 35 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{3} a^{\frac{3}{2}} b^{3}{\rm sign}\left (x\right ) + 21 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{2} a b^{4}{\rm sign}\left (x\right ) + 7 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )} \sqrt{a} b^{5}{\rm sign}\left (x\right ) + b^{6}{\rm sign}\left (x\right )\right )}}{7 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^(5/2)/x^2,x, algorithm="giac")
[Out]