Optimal. Leaf size=65 \[ -\frac{10 a^3 b^2}{9 x^9}-\frac{5 a^2 b^3}{3 x^6}-\frac{5 a^4 b}{12 x^{12}}-\frac{a^5}{15 x^{15}}-\frac{5 a b^4}{3 x^3}+b^5 \log (x) \]
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Rubi [A] time = 0.0310776, antiderivative size = 65, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ -\frac{10 a^3 b^2}{9 x^9}-\frac{5 a^2 b^3}{3 x^6}-\frac{5 a^4 b}{12 x^{12}}-\frac{a^5}{15 x^{15}}-\frac{5 a b^4}{3 x^3}+b^5 \log (x) \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^5}{x^{16}} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^5}{x^6} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (\frac{a^5}{x^6}+\frac{5 a^4 b}{x^5}+\frac{10 a^3 b^2}{x^4}+\frac{10 a^2 b^3}{x^3}+\frac{5 a b^4}{x^2}+\frac{b^5}{x}\right ) \, dx,x,x^3\right )\\ &=-\frac{a^5}{15 x^{15}}-\frac{5 a^4 b}{12 x^{12}}-\frac{10 a^3 b^2}{9 x^9}-\frac{5 a^2 b^3}{3 x^6}-\frac{5 a b^4}{3 x^3}+b^5 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0044132, size = 65, normalized size = 1. \[ -\frac{10 a^3 b^2}{9 x^9}-\frac{5 a^2 b^3}{3 x^6}-\frac{5 a^4 b}{12 x^{12}}-\frac{a^5}{15 x^{15}}-\frac{5 a b^4}{3 x^3}+b^5 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 56, normalized size = 0.9 \begin{align*} -{\frac{{a}^{5}}{15\,{x}^{15}}}-{\frac{5\,{a}^{4}b}{12\,{x}^{12}}}-{\frac{10\,{a}^{3}{b}^{2}}{9\,{x}^{9}}}-{\frac{5\,{a}^{2}{b}^{3}}{3\,{x}^{6}}}-{\frac{5\,a{b}^{4}}{3\,{x}^{3}}}+{b}^{5}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.981516, size = 82, normalized size = 1.26 \begin{align*} \frac{1}{3} \, b^{5} \log \left (x^{3}\right ) - \frac{300 \, a b^{4} x^{12} + 300 \, a^{2} b^{3} x^{9} + 200 \, a^{3} b^{2} x^{6} + 75 \, a^{4} b x^{3} + 12 \, a^{5}}{180 \, x^{15}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.67574, size = 150, normalized size = 2.31 \begin{align*} \frac{180 \, b^{5} x^{15} \log \left (x\right ) - 300 \, a b^{4} x^{12} - 300 \, a^{2} b^{3} x^{9} - 200 \, a^{3} b^{2} x^{6} - 75 \, a^{4} b x^{3} - 12 \, a^{5}}{180 \, x^{15}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.795718, size = 60, normalized size = 0.92 \begin{align*} b^{5} \log{\left (x \right )} - \frac{12 a^{5} + 75 a^{4} b x^{3} + 200 a^{3} b^{2} x^{6} + 300 a^{2} b^{3} x^{9} + 300 a b^{4} x^{12}}{180 x^{15}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11008, size = 90, normalized size = 1.38 \begin{align*} b^{5} \log \left ({\left | x \right |}\right ) - \frac{137 \, b^{5} x^{15} + 300 \, a b^{4} x^{12} + 300 \, a^{2} b^{3} x^{9} + 200 \, a^{3} b^{2} x^{6} + 75 \, a^{4} b x^{3} + 12 \, a^{5}}{180 \, x^{15}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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