Optimal. Leaf size=17 \[ -\frac{(a+b x)^9}{9 a x^9} \]
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Rubi [A] time = 0.0016689, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {37} \[ -\frac{(a+b x)^9}{9 a x^9} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{(a+b x)^8}{x^{10}} \, dx &=-\frac{(a+b x)^9}{9 a x^9}\\ \end{align*}
Mathematica [B] time = 0.0154863, size = 96, normalized size = 5.65 \[ -\frac{4 a^6 b^2}{x^7}-\frac{28 a^5 b^3}{3 x^6}-\frac{14 a^4 b^4}{x^5}-\frac{14 a^3 b^5}{x^4}-\frac{28 a^2 b^6}{3 x^3}-\frac{a^7 b}{x^8}-\frac{a^8}{9 x^9}-\frac{4 a b^7}{x^2}-\frac{b^8}{x} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.005, size = 91, normalized size = 5.4 \begin{align*} -{\frac{28\,{a}^{2}{b}^{6}}{3\,{x}^{3}}}-14\,{\frac{{a}^{4}{b}^{4}}{{x}^{5}}}-14\,{\frac{{a}^{3}{b}^{5}}{{x}^{4}}}-{\frac{28\,{a}^{5}{b}^{3}}{3\,{x}^{6}}}-{\frac{{a}^{7}b}{{x}^{8}}}-4\,{\frac{a{b}^{7}}{{x}^{2}}}-4\,{\frac{{a}^{6}{b}^{2}}{{x}^{7}}}-{\frac{{b}^{8}}{x}}-{\frac{{a}^{8}}{9\,{x}^{9}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.06012, size = 119, normalized size = 7. \begin{align*} -\frac{9 \, b^{8} x^{8} + 36 \, a b^{7} x^{7} + 84 \, a^{2} b^{6} x^{6} + 126 \, a^{3} b^{5} x^{5} + 126 \, a^{4} b^{4} x^{4} + 84 \, a^{5} b^{3} x^{3} + 36 \, a^{6} b^{2} x^{2} + 9 \, a^{7} b x + a^{8}}{9 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.45661, size = 192, normalized size = 11.29 \begin{align*} -\frac{9 \, b^{8} x^{8} + 36 \, a b^{7} x^{7} + 84 \, a^{2} b^{6} x^{6} + 126 \, a^{3} b^{5} x^{5} + 126 \, a^{4} b^{4} x^{4} + 84 \, a^{5} b^{3} x^{3} + 36 \, a^{6} b^{2} x^{2} + 9 \, a^{7} b x + a^{8}}{9 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.09683, size = 95, normalized size = 5.59 \begin{align*} - \frac{a^{8} + 9 a^{7} b x + 36 a^{6} b^{2} x^{2} + 84 a^{5} b^{3} x^{3} + 126 a^{4} b^{4} x^{4} + 126 a^{3} b^{5} x^{5} + 84 a^{2} b^{6} x^{6} + 36 a b^{7} x^{7} + 9 b^{8} x^{8}}{9 x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.19798, size = 119, normalized size = 7. \begin{align*} -\frac{9 \, b^{8} x^{8} + 36 \, a b^{7} x^{7} + 84 \, a^{2} b^{6} x^{6} + 126 \, a^{3} b^{5} x^{5} + 126 \, a^{4} b^{4} x^{4} + 84 \, a^{5} b^{3} x^{3} + 36 \, a^{6} b^{2} x^{2} + 9 \, a^{7} b x + a^{8}}{9 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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