Optimal. Leaf size=69 \[ -\frac{5 a^3 b^2}{12 x^{24}}-\frac{10 a^2 b^3}{21 x^{21}}-\frac{5 a^4 b}{27 x^{27}}-\frac{a^5}{30 x^{30}}-\frac{5 a b^4}{18 x^{18}}-\frac{b^5}{15 x^{15}} \]
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Rubi [A] time = 0.0299066, antiderivative size = 69, 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} \[ -\frac{5 a^3 b^2}{12 x^{24}}-\frac{10 a^2 b^3}{21 x^{21}}-\frac{5 a^4 b}{27 x^{27}}-\frac{a^5}{30 x^{30}}-\frac{5 a b^4}{18 x^{18}}-\frac{b^5}{15 x^{15}} \]
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^{31}} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^5}{x^{11}} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (\frac{a^5}{x^{11}}+\frac{5 a^4 b}{x^{10}}+\frac{10 a^3 b^2}{x^9}+\frac{10 a^2 b^3}{x^8}+\frac{5 a b^4}{x^7}+\frac{b^5}{x^6}\right ) \, dx,x,x^3\right )\\ &=-\frac{a^5}{30 x^{30}}-\frac{5 a^4 b}{27 x^{27}}-\frac{5 a^3 b^2}{12 x^{24}}-\frac{10 a^2 b^3}{21 x^{21}}-\frac{5 a b^4}{18 x^{18}}-\frac{b^5}{15 x^{15}}\\ \end{align*}
Mathematica [A] time = 0.0041028, size = 69, normalized size = 1. \[ -\frac{5 a^3 b^2}{12 x^{24}}-\frac{10 a^2 b^3}{21 x^{21}}-\frac{5 a^4 b}{27 x^{27}}-\frac{a^5}{30 x^{30}}-\frac{5 a b^4}{18 x^{18}}-\frac{b^5}{15 x^{15}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 58, normalized size = 0.8 \begin{align*} -{\frac{{a}^{5}}{30\,{x}^{30}}}-{\frac{5\,{a}^{4}b}{27\,{x}^{27}}}-{\frac{5\,{a}^{3}{b}^{2}}{12\,{x}^{24}}}-{\frac{10\,{a}^{2}{b}^{3}}{21\,{x}^{21}}}-{\frac{5\,a{b}^{4}}{18\,{x}^{18}}}-{\frac{{b}^{5}}{15\,{x}^{15}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.993416, size = 80, normalized size = 1.16 \begin{align*} -\frac{252 \, b^{5} x^{15} + 1050 \, a b^{4} x^{12} + 1800 \, a^{2} b^{3} x^{9} + 1575 \, a^{3} b^{2} x^{6} + 700 \, a^{4} b x^{3} + 126 \, a^{5}}{3780 \, x^{30}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.66605, size = 150, normalized size = 2.17 \begin{align*} -\frac{252 \, b^{5} x^{15} + 1050 \, a b^{4} x^{12} + 1800 \, a^{2} b^{3} x^{9} + 1575 \, a^{3} b^{2} x^{6} + 700 \, a^{4} b x^{3} + 126 \, a^{5}}{3780 \, x^{30}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.29798, size = 63, normalized size = 0.91 \begin{align*} - \frac{126 a^{5} + 700 a^{4} b x^{3} + 1575 a^{3} b^{2} x^{6} + 1800 a^{2} b^{3} x^{9} + 1050 a b^{4} x^{12} + 252 b^{5} x^{15}}{3780 x^{30}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11883, size = 80, normalized size = 1.16 \begin{align*} -\frac{252 \, b^{5} x^{15} + 1050 \, a b^{4} x^{12} + 1800 \, a^{2} b^{3} x^{9} + 1575 \, a^{3} b^{2} x^{6} + 700 \, a^{4} b x^{3} + 126 \, a^{5}}{3780 \, x^{30}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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