Optimal. Leaf size=19 \[ -\frac{\left (a+b x^3\right )^9}{27 a x^{27}} \]
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Rubi [A] time = 0.0031853, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {264} \[ -\frac{\left (a+b x^3\right )^9}{27 a x^{27}} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^8}{x^{28}} \, dx &=-\frac{\left (a+b x^3\right )^9}{27 a x^{27}}\\ \end{align*}
Mathematica [B] time = 0.0086689, size = 108, normalized size = 5.68 \[ -\frac{4 a^6 b^2}{3 x^{21}}-\frac{28 a^5 b^3}{9 x^{18}}-\frac{14 a^4 b^4}{3 x^{15}}-\frac{14 a^3 b^5}{3 x^{12}}-\frac{28 a^2 b^6}{9 x^9}-\frac{a^7 b}{3 x^{24}}-\frac{a^8}{27 x^{27}}-\frac{4 a b^7}{3 x^6}-\frac{b^8}{3 x^3} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.007, size = 91, normalized size = 4.8 \begin{align*} -{\frac{{b}^{8}}{3\,{x}^{3}}}-{\frac{14\,{a}^{4}{b}^{4}}{3\,{x}^{15}}}-{\frac{b{a}^{7}}{3\,{x}^{24}}}-{\frac{14\,{a}^{3}{b}^{5}}{3\,{x}^{12}}}-{\frac{{a}^{8}}{27\,{x}^{27}}}-{\frac{4\,{a}^{6}{b}^{2}}{3\,{x}^{21}}}-{\frac{4\,{b}^{7}a}{3\,{x}^{6}}}-{\frac{28\,{a}^{2}{b}^{6}}{9\,{x}^{9}}}-{\frac{28\,{a}^{5}{b}^{3}}{9\,{x}^{18}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.94157, size = 122, normalized size = 6.42 \begin{align*} -\frac{9 \, b^{8} x^{24} + 36 \, a b^{7} x^{21} + 84 \, a^{2} b^{6} x^{18} + 126 \, a^{3} b^{5} x^{15} + 126 \, a^{4} b^{4} x^{12} + 84 \, a^{5} b^{3} x^{9} + 36 \, a^{6} b^{2} x^{6} + 9 \, a^{7} b x^{3} + a^{8}}{27 \, x^{27}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.16207, size = 204, normalized size = 10.74 \begin{align*} -\frac{9 \, b^{8} x^{24} + 36 \, a b^{7} x^{21} + 84 \, a^{2} b^{6} x^{18} + 126 \, a^{3} b^{5} x^{15} + 126 \, a^{4} b^{4} x^{12} + 84 \, a^{5} b^{3} x^{9} + 36 \, a^{6} b^{2} x^{6} + 9 \, a^{7} b x^{3} + a^{8}}{27 \, x^{27}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.30456, size = 97, normalized size = 5.11 \begin{align*} - \frac{a^{8} + 9 a^{7} b x^{3} + 36 a^{6} b^{2} x^{6} + 84 a^{5} b^{3} x^{9} + 126 a^{4} b^{4} x^{12} + 126 a^{3} b^{5} x^{15} + 84 a^{2} b^{6} x^{18} + 36 a b^{7} x^{21} + 9 b^{8} x^{24}}{27 x^{27}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.11157, size = 122, normalized size = 6.42 \begin{align*} -\frac{9 \, b^{8} x^{24} + 36 \, a b^{7} x^{21} + 84 \, a^{2} b^{6} x^{18} + 126 \, a^{3} b^{5} x^{15} + 126 \, a^{4} b^{4} x^{12} + 84 \, a^{5} b^{3} x^{9} + 36 \, a^{6} b^{2} x^{6} + 9 \, a^{7} b x^{3} + a^{8}}{27 \, x^{27}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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