Optimal. Leaf size=34 \[ -\frac{2 a^2}{\sqrt{x}}-\frac{4 a b}{3 x^{3/2}}-\frac{2 b^2}{5 x^{5/2}} \]
[Out]
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Rubi [A] time = 0.0348254, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{2 a^2}{\sqrt{x}}-\frac{4 a b}{3 x^{3/2}}-\frac{2 b^2}{5 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^2/x^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 5.62512, size = 34, normalized size = 1. \[ - \frac{2 a^{2}}{\sqrt{x}} - \frac{4 a b}{3 x^{\frac{3}{2}}} - \frac{2 b^{2}}{5 x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**2/x**(3/2),x)
[Out]
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Mathematica [A] time = 0.0121773, size = 28, normalized size = 0.82 \[ -\frac{2 \left (15 a^2 x^2+10 a b x+3 b^2\right )}{15 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^2/x^(3/2),x]
[Out]
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Maple [A] time = 0.006, size = 25, normalized size = 0.7 \[ -{\frac{30\,{a}^{2}{x}^{2}+20\,abx+6\,{b}^{2}}{15}{x}^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^2/x^(3/2),x)
[Out]
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Maxima [A] time = 1.43988, size = 32, normalized size = 0.94 \[ -\frac{2 \, a^{2}}{\sqrt{x}} - \frac{4 \, a b}{3 \, x^{\frac{3}{2}}} - \frac{2 \, b^{2}}{5 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2/x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.227801, size = 32, normalized size = 0.94 \[ -\frac{2 \,{\left (15 \, a^{2} x^{2} + 10 \, a b x + 3 \, b^{2}\right )}}{15 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2/x^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.59578, size = 34, normalized size = 1. \[ - \frac{2 a^{2}}{\sqrt{x}} - \frac{4 a b}{3 x^{\frac{3}{2}}} - \frac{2 b^{2}}{5 x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**2/x**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.216333, size = 32, normalized size = 0.94 \[ -\frac{2 \,{\left (15 \, a^{2} x^{2} + 10 \, a b x + 3 \, b^{2}\right )}}{15 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2/x^(3/2),x, algorithm="giac")
[Out]