Optimal. Leaf size=16 \[ -\frac{\left (a+\frac{b}{x}\right )^9}{9 b} \]
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Rubi [A] time = 0.0034522, 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, Rules used = {261} \[ -\frac{\left (a+\frac{b}{x}\right )^9}{9 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{\left (a+\frac{b}{x}\right )^8}{x^2} \, dx &=-\frac{\left (a+\frac{b}{x}\right )^9}{9 b}\\ \end{align*}
Mathematica [B] time = 0.0081863, size = 96, normalized size = 6. \[ -\frac{28 a^6 b^2}{3 x^3}-\frac{14 a^5 b^3}{x^4}-\frac{14 a^4 b^4}{x^5}-\frac{28 a^3 b^5}{3 x^6}-\frac{4 a^2 b^6}{x^7}-\frac{4 a^7 b}{x^2}-\frac{a^8}{x}-\frac{a b^7}{x^8}-\frac{b^8}{9 x^9} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.007, size = 91, normalized size = 5.7 \begin{align*} -{\frac{28\,{a}^{6}{b}^{2}}{3\,{x}^{3}}}-14\,{\frac{{a}^{4}{b}^{4}}{{x}^{5}}}-14\,{\frac{{a}^{5}{b}^{3}}{{x}^{4}}}-4\,{\frac{{a}^{7}b}{{x}^{2}}}-{\frac{{b}^{7}a}{{x}^{8}}}-{\frac{28\,{a}^{3}{b}^{5}}{3\,{x}^{6}}}-4\,{\frac{{a}^{2}{b}^{6}}{{x}^{7}}}-{\frac{{a}^{8}}{x}}-{\frac{{b}^{8}}{9\,{x}^{9}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00066, size = 19, normalized size = 1.19 \begin{align*} -\frac{{\left (a + \frac{b}{x}\right )}^{9}}{9 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.33535, size = 192, normalized size = 12. \begin{align*} -\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.744885, size = 95, normalized size = 5.94 \begin{align*} - \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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10413, size = 19, normalized size = 1.19 \begin{align*} -\frac{{\left (a + \frac{b}{x}\right )}^{9}}{9 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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