Optimal. Leaf size=68 \[ -\frac{2 a^{5/2} \tan ^{-1}\left (\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right )}{b^{7/2}}-\frac{2 a^2}{b^3 \sqrt{x}}+\frac{2 a}{3 b^2 x^{3/2}}-\frac{2}{5 b x^{5/2}} \]
[Out]
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Rubi [A] time = 0.0814021, antiderivative size = 68, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 4, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.267 \[ -\frac{2 a^{5/2} \tan ^{-1}\left (\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right )}{b^{7/2}}-\frac{2 a^2}{b^3 \sqrt{x}}+\frac{2 a}{3 b^2 x^{3/2}}-\frac{2}{5 b x^{5/2}} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x)*x^(9/2)),x]
[Out]
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Rubi in Sympy [A] time = 14.0524, size = 65, normalized size = 0.96 \[ - \frac{2 a^{\frac{5}{2}} \operatorname{atan}{\left (\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}} \right )}}{b^{\frac{7}{2}}} - \frac{2 a^{2}}{b^{3} \sqrt{x}} + \frac{2 a}{3 b^{2} x^{\frac{3}{2}}} - \frac{2}{5 b x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x)/x**(9/2),x)
[Out]
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Mathematica [A] time = 0.0552518, size = 61, normalized size = 0.9 \[ -\frac{2 a^{5/2} \tan ^{-1}\left (\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right )}{b^{7/2}}-\frac{2 \left (15 a^2 x^2-5 a b x+3 b^2\right )}{15 b^3 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x)*x^(9/2)),x]
[Out]
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Maple [A] time = 0.014, size = 54, normalized size = 0.8 \[ -{\frac{2}{5\,b}{x}^{-{\frac{5}{2}}}}-2\,{\frac{{a}^{2}}{{b}^{3}\sqrt{x}}}+{\frac{2\,a}{3\,{b}^{2}}{x}^{-{\frac{3}{2}}}}-2\,{\frac{{a}^{3}}{{b}^{3}\sqrt{ab}}\arctan \left ({\frac{a\sqrt{x}}{\sqrt{ab}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x)/x^(9/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)*x^(9/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.242949, size = 1, normalized size = 0.01 \[ \left [\frac{15 \, a^{2} x^{\frac{5}{2}} \sqrt{-\frac{a}{b}} \log \left (\frac{a x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - b}{a x + b}\right ) - 30 \, a^{2} x^{2} + 10 \, a b x - 6 \, b^{2}}{15 \, b^{3} x^{\frac{5}{2}}}, \frac{2 \,{\left (15 \, a^{2} x^{\frac{5}{2}} \sqrt{\frac{a}{b}} \arctan \left (\frac{b \sqrt{\frac{a}{b}}}{a \sqrt{x}}\right ) - 15 \, a^{2} x^{2} + 5 \, a b x - 3 \, b^{2}\right )}}{15 \, b^{3} x^{\frac{5}{2}}}\right ] \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)*x^(9/2)),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x)/x**(9/2),x)
[Out]
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GIAC/XCAS [A] time = 0.220148, size = 70, normalized size = 1.03 \[ -\frac{2 \, a^{3} \arctan \left (\frac{a \sqrt{x}}{\sqrt{a b}}\right )}{\sqrt{a b} b^{3}} - \frac{2 \,{\left (15 \, a^{2} x^{2} - 5 \, a b x + 3 \, b^{2}\right )}}{15 \, b^{3} x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)*x^(9/2)),x, algorithm="giac")
[Out]