Optimal. Leaf size=17 \[ -\frac{(a+b x)^{11}}{11 a x^{11}} \]
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Rubi [A] time = 0.0016535, 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} \[ -\frac{(a+b x)^{11}}{11 a x^{11}} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{(a+b x)^{10}}{x^{12}} \, dx &=-\frac{(a+b x)^{11}}{11 a x^{11}}\\ \end{align*}
Mathematica [B] time = 0.0112869, size = 114, normalized size = 6.71 \[ -\frac{5 a^8 b^2}{x^9}-\frac{15 a^7 b^3}{x^8}-\frac{30 a^6 b^4}{x^7}-\frac{42 a^5 b^5}{x^6}-\frac{42 a^4 b^6}{x^5}-\frac{30 a^3 b^7}{x^4}-\frac{15 a^2 b^8}{x^3}-\frac{a^9 b}{x^{10}}-\frac{a^{10}}{11 x^{11}}-\frac{5 a b^9}{x^2}-\frac{b^{10}}{x} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.007, size = 113, normalized size = 6.7 \begin{align*} -{\frac{{a}^{9}b}{{x}^{10}}}-15\,{\frac{{a}^{2}{b}^{8}}{{x}^{3}}}-42\,{\frac{{a}^{4}{b}^{6}}{{x}^{5}}}-{\frac{{a}^{10}}{11\,{x}^{11}}}-30\,{\frac{{a}^{3}{b}^{7}}{{x}^{4}}}-42\,{\frac{{a}^{5}{b}^{5}}{{x}^{6}}}-15\,{\frac{{a}^{7}{b}^{3}}{{x}^{8}}}-5\,{\frac{a{b}^{9}}{{x}^{2}}}-30\,{\frac{{a}^{6}{b}^{4}}{{x}^{7}}}-{\frac{{b}^{10}}{x}}-5\,{\frac{{a}^{8}{b}^{2}}{{x}^{9}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.992049, size = 149, normalized size = 8.76 \begin{align*} -\frac{11 \, b^{10} x^{10} + 55 \, a b^{9} x^{9} + 165 \, a^{2} b^{8} x^{8} + 330 \, a^{3} b^{7} x^{7} + 462 \, a^{4} b^{6} x^{6} + 462 \, a^{5} b^{5} x^{5} + 330 \, a^{6} b^{4} x^{4} + 165 \, a^{7} b^{3} x^{3} + 55 \, a^{8} b^{2} x^{2} + 11 \, a^{9} b x + a^{10}}{11 \, x^{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.53949, size = 252, normalized size = 14.82 \begin{align*} -\frac{11 \, b^{10} x^{10} + 55 \, a b^{9} x^{9} + 165 \, a^{2} b^{8} x^{8} + 330 \, a^{3} b^{7} x^{7} + 462 \, a^{4} b^{6} x^{6} + 462 \, a^{5} b^{5} x^{5} + 330 \, a^{6} b^{4} x^{4} + 165 \, a^{7} b^{3} x^{3} + 55 \, a^{8} b^{2} x^{2} + 11 \, a^{9} b x + a^{10}}{11 \, x^{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.31416, size = 119, normalized size = 7. \begin{align*} - \frac{a^{10} + 11 a^{9} b x + 55 a^{8} b^{2} x^{2} + 165 a^{7} b^{3} x^{3} + 330 a^{6} b^{4} x^{4} + 462 a^{5} b^{5} x^{5} + 462 a^{4} b^{6} x^{6} + 330 a^{3} b^{7} x^{7} + 165 a^{2} b^{8} x^{8} + 55 a b^{9} x^{9} + 11 b^{10} x^{10}}{11 x^{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.16533, size = 149, normalized size = 8.76 \begin{align*} -\frac{11 \, b^{10} x^{10} + 55 \, a b^{9} x^{9} + 165 \, a^{2} b^{8} x^{8} + 330 \, a^{3} b^{7} x^{7} + 462 \, a^{4} b^{6} x^{6} + 462 \, a^{5} b^{5} x^{5} + 330 \, a^{6} b^{4} x^{4} + 165 \, a^{7} b^{3} x^{3} + 55 \, a^{8} b^{2} x^{2} + 11 \, a^{9} b x + a^{10}}{11 \, x^{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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