Optimal. Leaf size=69 \[ -\frac{10 a^3 b^2}{21 x^{21}}-\frac{5 a^2 b^3}{9 x^{18}}-\frac{5 a^4 b}{24 x^{24}}-\frac{a^5}{27 x^{27}}-\frac{a b^4}{3 x^{15}}-\frac{b^5}{12 x^{12}} \]
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Rubi [A] time = 0.0310307, 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} \[ -\frac{10 a^3 b^2}{21 x^{21}}-\frac{5 a^2 b^3}{9 x^{18}}-\frac{5 a^4 b}{24 x^{24}}-\frac{a^5}{27 x^{27}}-\frac{a b^4}{3 x^{15}}-\frac{b^5}{12 x^{12}} \]
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^{28}} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^5}{x^{10}} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (\frac{a^5}{x^{10}}+\frac{5 a^4 b}{x^9}+\frac{10 a^3 b^2}{x^8}+\frac{10 a^2 b^3}{x^7}+\frac{5 a b^4}{x^6}+\frac{b^5}{x^5}\right ) \, dx,x,x^3\right )\\ &=-\frac{a^5}{27 x^{27}}-\frac{5 a^4 b}{24 x^{24}}-\frac{10 a^3 b^2}{21 x^{21}}-\frac{5 a^2 b^3}{9 x^{18}}-\frac{a b^4}{3 x^{15}}-\frac{b^5}{12 x^{12}}\\ \end{align*}
Mathematica [A] time = 0.0041865, size = 69, normalized size = 1. \[ -\frac{10 a^3 b^2}{21 x^{21}}-\frac{5 a^2 b^3}{9 x^{18}}-\frac{5 a^4 b}{24 x^{24}}-\frac{a^5}{27 x^{27}}-\frac{a b^4}{3 x^{15}}-\frac{b^5}{12 x^{12}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 58, normalized size = 0.8 \begin{align*} -{\frac{{a}^{5}}{27\,{x}^{27}}}-{\frac{5\,{a}^{4}b}{24\,{x}^{24}}}-{\frac{10\,{a}^{3}{b}^{2}}{21\,{x}^{21}}}-{\frac{5\,{a}^{2}{b}^{3}}{9\,{x}^{18}}}-{\frac{a{b}^{4}}{3\,{x}^{15}}}-{\frac{{b}^{5}}{12\,{x}^{12}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.989007, size = 80, normalized size = 1.16 \begin{align*} -\frac{126 \, b^{5} x^{15} + 504 \, a b^{4} x^{12} + 840 \, a^{2} b^{3} x^{9} + 720 \, a^{3} b^{2} x^{6} + 315 \, a^{4} b x^{3} + 56 \, a^{5}}{1512 \, x^{27}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.57762, size = 144, normalized size = 2.09 \begin{align*} -\frac{126 \, b^{5} x^{15} + 504 \, a b^{4} x^{12} + 840 \, a^{2} b^{3} x^{9} + 720 \, a^{3} b^{2} x^{6} + 315 \, a^{4} b x^{3} + 56 \, a^{5}}{1512 \, x^{27}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.28932, size = 63, normalized size = 0.91 \begin{align*} - \frac{56 a^{5} + 315 a^{4} b x^{3} + 720 a^{3} b^{2} x^{6} + 840 a^{2} b^{3} x^{9} + 504 a b^{4} x^{12} + 126 b^{5} x^{15}}{1512 x^{27}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11498, size = 80, normalized size = 1.16 \begin{align*} -\frac{126 \, b^{5} x^{15} + 504 \, a b^{4} x^{12} + 840 \, a^{2} b^{3} x^{9} + 720 \, a^{3} b^{2} x^{6} + 315 \, a^{4} b x^{3} + 56 \, a^{5}}{1512 \, x^{27}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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