Optimal. Leaf size=56 \[ -\frac{6 a^2 b^2}{7 x^7}-\frac{a^3 b}{2 x^8}-\frac{a^4}{9 x^9}-\frac{2 a b^3}{3 x^6}-\frac{b^4}{5 x^5} \]
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Rubi [A] time = 0.0191013, antiderivative size = 56, 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} \[ -\frac{6 a^2 b^2}{7 x^7}-\frac{a^3 b}{2 x^8}-\frac{a^4}{9 x^9}-\frac{2 a b^3}{3 x^6}-\frac{b^4}{5 x^5} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^4}{x^{10}} \, dx &=\int \left (\frac{a^4}{x^{10}}+\frac{4 a^3 b}{x^9}+\frac{6 a^2 b^2}{x^8}+\frac{4 a b^3}{x^7}+\frac{b^4}{x^6}\right ) \, dx\\ &=-\frac{a^4}{9 x^9}-\frac{a^3 b}{2 x^8}-\frac{6 a^2 b^2}{7 x^7}-\frac{2 a b^3}{3 x^6}-\frac{b^4}{5 x^5}\\ \end{align*}
Mathematica [A] time = 0.0110654, size = 56, normalized size = 1. \[ -\frac{6 a^2 b^2}{7 x^7}-\frac{a^3 b}{2 x^8}-\frac{a^4}{9 x^9}-\frac{2 a b^3}{3 x^6}-\frac{b^4}{5 x^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 47, normalized size = 0.8 \begin{align*} -{\frac{{a}^{4}}{9\,{x}^{9}}}-{\frac{{a}^{3}b}{2\,{x}^{8}}}-{\frac{6\,{b}^{2}{a}^{2}}{7\,{x}^{7}}}-{\frac{2\,a{b}^{3}}{3\,{x}^{6}}}-{\frac{{b}^{4}}{5\,{x}^{5}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.10312, size = 62, normalized size = 1.11 \begin{align*} -\frac{126 \, b^{4} x^{4} + 420 \, a b^{3} x^{3} + 540 \, a^{2} b^{2} x^{2} + 315 \, a^{3} b x + 70 \, a^{4}}{630 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.63862, size = 112, normalized size = 2. \begin{align*} -\frac{126 \, b^{4} x^{4} + 420 \, a b^{3} x^{3} + 540 \, a^{2} b^{2} x^{2} + 315 \, a^{3} b x + 70 \, a^{4}}{630 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.710616, size = 49, normalized size = 0.88 \begin{align*} - \frac{70 a^{4} + 315 a^{3} b x + 540 a^{2} b^{2} x^{2} + 420 a b^{3} x^{3} + 126 b^{4} x^{4}}{630 x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19042, size = 62, normalized size = 1.11 \begin{align*} -\frac{126 \, b^{4} x^{4} + 420 \, a b^{3} x^{3} + 540 \, a^{2} b^{2} x^{2} + 315 \, a^{3} b x + 70 \, a^{4}}{630 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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