Optimal. Leaf size=95 \[ -\frac{7 a^5 b^2}{4 x^{12}}-\frac{35 a^4 b^3}{11 x^{11}}-\frac{7 a^3 b^4}{2 x^{10}}-\frac{7 a^2 b^5}{3 x^9}-\frac{7 a^6 b}{13 x^{13}}-\frac{a^7}{14 x^{14}}-\frac{7 a b^6}{8 x^8}-\frac{b^7}{7 x^7} \]
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Rubi [A] time = 0.0302973, antiderivative size = 95, 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} \[ -\frac{7 a^5 b^2}{4 x^{12}}-\frac{35 a^4 b^3}{11 x^{11}}-\frac{7 a^3 b^4}{2 x^{10}}-\frac{7 a^2 b^5}{3 x^9}-\frac{7 a^6 b}{13 x^{13}}-\frac{a^7}{14 x^{14}}-\frac{7 a b^6}{8 x^8}-\frac{b^7}{7 x^7} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^7}{x^{15}} \, dx &=\int \left (\frac{a^7}{x^{15}}+\frac{7 a^6 b}{x^{14}}+\frac{21 a^5 b^2}{x^{13}}+\frac{35 a^4 b^3}{x^{12}}+\frac{35 a^3 b^4}{x^{11}}+\frac{21 a^2 b^5}{x^{10}}+\frac{7 a b^6}{x^9}+\frac{b^7}{x^8}\right ) \, dx\\ &=-\frac{a^7}{14 x^{14}}-\frac{7 a^6 b}{13 x^{13}}-\frac{7 a^5 b^2}{4 x^{12}}-\frac{35 a^4 b^3}{11 x^{11}}-\frac{7 a^3 b^4}{2 x^{10}}-\frac{7 a^2 b^5}{3 x^9}-\frac{7 a b^6}{8 x^8}-\frac{b^7}{7 x^7}\\ \end{align*}
Mathematica [A] time = 0.0053063, size = 95, normalized size = 1. \[ -\frac{7 a^5 b^2}{4 x^{12}}-\frac{35 a^4 b^3}{11 x^{11}}-\frac{7 a^3 b^4}{2 x^{10}}-\frac{7 a^2 b^5}{3 x^9}-\frac{7 a^6 b}{13 x^{13}}-\frac{a^7}{14 x^{14}}-\frac{7 a b^6}{8 x^8}-\frac{b^7}{7 x^7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 80, normalized size = 0.8 \begin{align*} -{\frac{{a}^{7}}{14\,{x}^{14}}}-{\frac{7\,{a}^{6}b}{13\,{x}^{13}}}-{\frac{7\,{a}^{5}{b}^{2}}{4\,{x}^{12}}}-{\frac{35\,{a}^{4}{b}^{3}}{11\,{x}^{11}}}-{\frac{7\,{a}^{3}{b}^{4}}{2\,{x}^{10}}}-{\frac{7\,{a}^{2}{b}^{5}}{3\,{x}^{9}}}-{\frac{7\,a{b}^{6}}{8\,{x}^{8}}}-{\frac{{b}^{7}}{7\,{x}^{7}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06713, size = 107, normalized size = 1.13 \begin{align*} -\frac{3432 \, b^{7} x^{7} + 21021 \, a b^{6} x^{6} + 56056 \, a^{2} b^{5} x^{5} + 84084 \, a^{3} b^{4} x^{4} + 76440 \, a^{4} b^{3} x^{3} + 42042 \, a^{5} b^{2} x^{2} + 12936 \, a^{6} b x + 1716 \, a^{7}}{24024 \, x^{14}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.65273, size = 209, normalized size = 2.2 \begin{align*} -\frac{3432 \, b^{7} x^{7} + 21021 \, a b^{6} x^{6} + 56056 \, a^{2} b^{5} x^{5} + 84084 \, a^{3} b^{4} x^{4} + 76440 \, a^{4} b^{3} x^{3} + 42042 \, a^{5} b^{2} x^{2} + 12936 \, a^{6} b x + 1716 \, a^{7}}{24024 \, x^{14}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.11824, size = 85, normalized size = 0.89 \begin{align*} - \frac{1716 a^{7} + 12936 a^{6} b x + 42042 a^{5} b^{2} x^{2} + 76440 a^{4} b^{3} x^{3} + 84084 a^{3} b^{4} x^{4} + 56056 a^{2} b^{5} x^{5} + 21021 a b^{6} x^{6} + 3432 b^{7} x^{7}}{24024 x^{14}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.22169, size = 107, normalized size = 1.13 \begin{align*} -\frac{3432 \, b^{7} x^{7} + 21021 \, a b^{6} x^{6} + 56056 \, a^{2} b^{5} x^{5} + 84084 \, a^{3} b^{4} x^{4} + 76440 \, a^{4} b^{3} x^{3} + 42042 \, a^{5} b^{2} x^{2} + 12936 \, a^{6} b x + 1716 \, a^{7}}{24024 \, x^{14}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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