Optimal. Leaf size=93 \[ -\frac{21 a^5 b^2}{11 x^{11}}-\frac{7 a^4 b^3}{2 x^{10}}-\frac{35 a^3 b^4}{9 x^9}-\frac{21 a^2 b^5}{8 x^8}-\frac{7 a^6 b}{12 x^{12}}-\frac{a^7}{13 x^{13}}-\frac{a b^6}{x^7}-\frac{b^7}{6 x^6} \]
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Rubi [A] time = 0.0328734, antiderivative size = 93, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {43} \[ -\frac{21 a^5 b^2}{11 x^{11}}-\frac{7 a^4 b^3}{2 x^{10}}-\frac{35 a^3 b^4}{9 x^9}-\frac{21 a^2 b^5}{8 x^8}-\frac{7 a^6 b}{12 x^{12}}-\frac{a^7}{13 x^{13}}-\frac{a b^6}{x^7}-\frac{b^7}{6 x^6} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^7}{x^{14}} \, dx &=\int \left (\frac{a^7}{x^{14}}+\frac{7 a^6 b}{x^{13}}+\frac{21 a^5 b^2}{x^{12}}+\frac{35 a^4 b^3}{x^{11}}+\frac{35 a^3 b^4}{x^{10}}+\frac{21 a^2 b^5}{x^9}+\frac{7 a b^6}{x^8}+\frac{b^7}{x^7}\right ) \, dx\\ &=-\frac{a^7}{13 x^{13}}-\frac{7 a^6 b}{12 x^{12}}-\frac{21 a^5 b^2}{11 x^{11}}-\frac{7 a^4 b^3}{2 x^{10}}-\frac{35 a^3 b^4}{9 x^9}-\frac{21 a^2 b^5}{8 x^8}-\frac{a b^6}{x^7}-\frac{b^7}{6 x^6}\\ \end{align*}
Mathematica [A] time = 0.0072827, size = 93, normalized size = 1. \[ -\frac{21 a^5 b^2}{11 x^{11}}-\frac{7 a^4 b^3}{2 x^{10}}-\frac{35 a^3 b^4}{9 x^9}-\frac{21 a^2 b^5}{8 x^8}-\frac{7 a^6 b}{12 x^{12}}-\frac{a^7}{13 x^{13}}-\frac{a b^6}{x^7}-\frac{b^7}{6 x^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 80, normalized size = 0.9 \begin{align*} -{\frac{{a}^{7}}{13\,{x}^{13}}}-{\frac{7\,{a}^{6}b}{12\,{x}^{12}}}-{\frac{21\,{a}^{5}{b}^{2}}{11\,{x}^{11}}}-{\frac{7\,{a}^{4}{b}^{3}}{2\,{x}^{10}}}-{\frac{35\,{a}^{3}{b}^{4}}{9\,{x}^{9}}}-{\frac{21\,{a}^{2}{b}^{5}}{8\,{x}^{8}}}-{\frac{a{b}^{6}}{{x}^{7}}}-{\frac{{b}^{7}}{6\,{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01975, size = 107, normalized size = 1.15 \begin{align*} -\frac{1716 \, b^{7} x^{7} + 10296 \, a b^{6} x^{6} + 27027 \, a^{2} b^{5} x^{5} + 40040 \, a^{3} b^{4} x^{4} + 36036 \, a^{4} b^{3} x^{3} + 19656 \, a^{5} b^{2} x^{2} + 6006 \, a^{6} b x + 792 \, a^{7}}{10296 \, x^{13}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.81349, size = 207, normalized size = 2.23 \begin{align*} -\frac{1716 \, b^{7} x^{7} + 10296 \, a b^{6} x^{6} + 27027 \, a^{2} b^{5} x^{5} + 40040 \, a^{3} b^{4} x^{4} + 36036 \, a^{4} b^{3} x^{3} + 19656 \, a^{5} b^{2} x^{2} + 6006 \, a^{6} b x + 792 \, a^{7}}{10296 \, x^{13}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.06813, size = 85, normalized size = 0.91 \begin{align*} - \frac{792 a^{7} + 6006 a^{6} b x + 19656 a^{5} b^{2} x^{2} + 36036 a^{4} b^{3} x^{3} + 40040 a^{3} b^{4} x^{4} + 27027 a^{2} b^{5} x^{5} + 10296 a b^{6} x^{6} + 1716 b^{7} x^{7}}{10296 x^{13}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18739, size = 107, normalized size = 1.15 \begin{align*} -\frac{1716 \, b^{7} x^{7} + 10296 \, a b^{6} x^{6} + 27027 \, a^{2} b^{5} x^{5} + 40040 \, a^{3} b^{4} x^{4} + 36036 \, a^{4} b^{3} x^{3} + 19656 \, a^{5} b^{2} x^{2} + 6006 \, a^{6} b x + 792 \, a^{7}}{10296 \, x^{13}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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