Optimal. Leaf size=36 \[ -\frac{2 a^2}{3 x^{3/2}}-\frac{4 a b}{5 x^{5/2}}-\frac{2 b^2}{7 x^{7/2}} \]
[Out]
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Rubi [A] time = 0.0340564, antiderivative size = 36, 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 \[ -\frac{2 a^2}{3 x^{3/2}}-\frac{4 a b}{5 x^{5/2}}-\frac{2 b^2}{7 x^{7/2}} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^2/x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 5.52632, size = 36, normalized size = 1. \[ - \frac{2 a^{2}}{3 x^{\frac{3}{2}}} - \frac{4 a b}{5 x^{\frac{5}{2}}} - \frac{2 b^{2}}{7 x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**2/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.0127769, size = 28, normalized size = 0.78 \[ -\frac{2 \left (35 a^2 x^2+42 a b x+15 b^2\right )}{105 x^{7/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^2/x^(5/2),x]
[Out]
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Maple [A] time = 0.005, size = 25, normalized size = 0.7 \[ -{\frac{70\,{a}^{2}{x}^{2}+84\,abx+30\,{b}^{2}}{105}{x}^{-{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^2/x^(5/2),x)
[Out]
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Maxima [A] time = 1.4417, size = 32, normalized size = 0.89 \[ -\frac{2 \, a^{2}}{3 \, x^{\frac{3}{2}}} - \frac{4 \, a b}{5 \, x^{\frac{5}{2}}} - \frac{2 \, b^{2}}{7 \, x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2/x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.226834, size = 32, normalized size = 0.89 \[ -\frac{2 \,{\left (35 \, a^{2} x^{2} + 42 \, a b x + 15 \, b^{2}\right )}}{105 \, x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2/x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.9372, size = 36, normalized size = 1. \[ - \frac{2 a^{2}}{3 x^{\frac{3}{2}}} - \frac{4 a b}{5 x^{\frac{5}{2}}} - \frac{2 b^{2}}{7 x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**2/x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.221695, size = 32, normalized size = 0.89 \[ -\frac{2 \,{\left (35 \, a^{2} x^{2} + 42 \, a b x + 15 \, b^{2}\right )}}{105 \, x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2/x^(5/2),x, algorithm="giac")
[Out]