Optimal. Leaf size=66 \[ -\frac{5 a^3 b^2}{3 x^6}-\frac{10 a^2 b^3}{3 x^3}-\frac{5 a^4 b}{9 x^9}-\frac{a^5}{12 x^{12}}+5 a b^4 \log (x)+\frac{b^5 x^3}{3} \]
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Rubi [A] time = 0.0307271, antiderivative size = 66, 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} \[ -\frac{5 a^3 b^2}{3 x^6}-\frac{10 a^2 b^3}{3 x^3}-\frac{5 a^4 b}{9 x^9}-\frac{a^5}{12 x^{12}}+5 a b^4 \log (x)+\frac{b^5 x^3}{3} \]
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^{13}} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^5}{x^5} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (b^5+\frac{a^5}{x^5}+\frac{5 a^4 b}{x^4}+\frac{10 a^3 b^2}{x^3}+\frac{10 a^2 b^3}{x^2}+\frac{5 a b^4}{x}\right ) \, dx,x,x^3\right )\\ &=-\frac{a^5}{12 x^{12}}-\frac{5 a^4 b}{9 x^9}-\frac{5 a^3 b^2}{3 x^6}-\frac{10 a^2 b^3}{3 x^3}+\frac{b^5 x^3}{3}+5 a b^4 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0045832, size = 66, normalized size = 1. \[ -\frac{5 a^3 b^2}{3 x^6}-\frac{10 a^2 b^3}{3 x^3}-\frac{5 a^4 b}{9 x^9}-\frac{a^5}{12 x^{12}}+5 a b^4 \log (x)+\frac{b^5 x^3}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 57, normalized size = 0.9 \begin{align*} -{\frac{{a}^{5}}{12\,{x}^{12}}}-{\frac{5\,{a}^{4}b}{9\,{x}^{9}}}-{\frac{5\,{a}^{3}{b}^{2}}{3\,{x}^{6}}}-{\frac{10\,{a}^{2}{b}^{3}}{3\,{x}^{3}}}+{\frac{{b}^{5}{x}^{3}}{3}}+5\,a{b}^{4}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.983119, size = 82, normalized size = 1.24 \begin{align*} \frac{1}{3} \, b^{5} x^{3} + \frac{5}{3} \, a b^{4} \log \left (x^{3}\right ) - \frac{120 \, a^{2} b^{3} x^{9} + 60 \, a^{3} b^{2} x^{6} + 20 \, a^{4} b x^{3} + 3 \, a^{5}}{36 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.63863, size = 144, normalized size = 2.18 \begin{align*} \frac{12 \, b^{5} x^{15} + 180 \, a b^{4} x^{12} \log \left (x\right ) - 120 \, a^{2} b^{3} x^{9} - 60 \, a^{3} b^{2} x^{6} - 20 \, a^{4} b x^{3} - 3 \, a^{5}}{36 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.745922, size = 61, normalized size = 0.92 \begin{align*} 5 a b^{4} \log{\left (x \right )} + \frac{b^{5} x^{3}}{3} - \frac{3 a^{5} + 20 a^{4} b x^{3} + 60 a^{3} b^{2} x^{6} + 120 a^{2} b^{3} x^{9}}{36 x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11978, size = 93, normalized size = 1.41 \begin{align*} \frac{1}{3} \, b^{5} x^{3} + 5 \, a b^{4} \log \left ({\left | x \right |}\right ) - \frac{125 \, a b^{4} x^{12} + 120 \, a^{2} b^{3} x^{9} + 60 \, a^{3} b^{2} x^{6} + 20 \, a^{4} b x^{3} + 3 \, a^{5}}{36 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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