Optimal. Leaf size=16 \[ -\frac{\left (a+\frac{b}{x}\right )^9}{9 b} \]
[Out]
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Rubi [A] time = 0.0159928, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{\left (a+\frac{b}{x}\right )^9}{9 b} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^8/x^2,x]
[Out]
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Rubi in Sympy [A] time = 2.20055, size = 10, normalized size = 0.62 \[ - \frac{\left (a + \frac{b}{x}\right )^{9}}{9 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**8/x**2,x)
[Out]
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Mathematica [B] time = 0.0151074, size = 96, normalized size = 6. \[ -\frac{a^8}{x}-\frac{4 a^7 b}{x^2}-\frac{28 a^6 b^2}{3 x^3}-\frac{14 a^5 b^3}{x^4}-\frac{14 a^4 b^4}{x^5}-\frac{28 a^3 b^5}{3 x^6}-\frac{4 a^2 b^6}{x^7}-\frac{a b^7}{x^8}-\frac{b^8}{9 x^9} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^8/x^2,x]
[Out]
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Maple [B] time = 0.008, size = 91, normalized size = 5.7 \[ -{\frac{28\,{a}^{3}{b}^{5}}{3\,{x}^{6}}}-14\,{\frac{{a}^{5}{b}^{3}}{{x}^{4}}}-{\frac{a{b}^{7}}{{x}^{8}}}-{\frac{{b}^{8}}{9\,{x}^{9}}}-{\frac{28\,{a}^{6}{b}^{2}}{3\,{x}^{3}}}-4\,{\frac{{a}^{7}b}{{x}^{2}}}-14\,{\frac{{a}^{4}{b}^{4}}{{x}^{5}}}-{\frac{{a}^{8}}{x}}-4\,{\frac{{a}^{2}{b}^{6}}{{x}^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^8/x^2,x)
[Out]
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Maxima [A] time = 1.55373, size = 19, normalized size = 1.19 \[ -\frac{{\left (a + \frac{b}{x}\right )}^{9}}{9 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216225, size = 119, normalized size = 7.44 \[ -\frac{9 \, a^{8} x^{8} + 36 \, a^{7} b x^{7} + 84 \, a^{6} b^{2} x^{6} + 126 \, a^{5} b^{3} x^{5} + 126 \, a^{4} b^{4} x^{4} + 84 \, a^{3} b^{5} x^{3} + 36 \, a^{2} b^{6} x^{2} + 9 \, a b^{7} x + b^{8}}{9 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.02233, size = 95, normalized size = 5.94 \[ - \frac{9 a^{8} x^{8} + 36 a^{7} b x^{7} + 84 a^{6} b^{2} x^{6} + 126 a^{5} b^{3} x^{5} + 126 a^{4} b^{4} x^{4} + 84 a^{3} b^{5} x^{3} + 36 a^{2} b^{6} x^{2} + 9 a b^{7} x + b^{8}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**8/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.223425, size = 19, normalized size = 1.19 \[ -\frac{{\left (a + \frac{b}{x}\right )}^{9}}{9 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8/x^2,x, algorithm="giac")
[Out]