Optimal. Leaf size=98 \[ \frac{28}{11} a^2 b^6 x^{11}+7 a^3 b^5 x^8+14 a^4 b^4 x^5+28 a^5 b^3 x^2-\frac{28 a^6 b^2}{x}-\frac{2 a^7 b}{x^4}-\frac{a^8}{7 x^7}+\frac{4}{7} a b^7 x^{14}+\frac{b^8 x^{17}}{17} \]
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Rubi [A] time = 0.0371253, antiderivative size = 98, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {270} \[ \frac{28}{11} a^2 b^6 x^{11}+7 a^3 b^5 x^8+14 a^4 b^4 x^5+28 a^5 b^3 x^2-\frac{28 a^6 b^2}{x}-\frac{2 a^7 b}{x^4}-\frac{a^8}{7 x^7}+\frac{4}{7} a b^7 x^{14}+\frac{b^8 x^{17}}{17} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^8}{x^8} \, dx &=\int \left (\frac{a^8}{x^8}+\frac{8 a^7 b}{x^5}+\frac{28 a^6 b^2}{x^2}+56 a^5 b^3 x+70 a^4 b^4 x^4+56 a^3 b^5 x^7+28 a^2 b^6 x^{10}+8 a b^7 x^{13}+b^8 x^{16}\right ) \, dx\\ &=-\frac{a^8}{7 x^7}-\frac{2 a^7 b}{x^4}-\frac{28 a^6 b^2}{x}+28 a^5 b^3 x^2+14 a^4 b^4 x^5+7 a^3 b^5 x^8+\frac{28}{11} a^2 b^6 x^{11}+\frac{4}{7} a b^7 x^{14}+\frac{b^8 x^{17}}{17}\\ \end{align*}
Mathematica [A] time = 0.0069815, size = 98, normalized size = 1. \[ \frac{28}{11} a^2 b^6 x^{11}+7 a^3 b^5 x^8+14 a^4 b^4 x^5+28 a^5 b^3 x^2-\frac{28 a^6 b^2}{x}-\frac{2 a^7 b}{x^4}-\frac{a^8}{7 x^7}+\frac{4}{7} a b^7 x^{14}+\frac{b^8 x^{17}}{17} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 91, normalized size = 0.9 \begin{align*} -{\frac{{a}^{8}}{7\,{x}^{7}}}-2\,{\frac{{a}^{7}b}{{x}^{4}}}-28\,{\frac{{a}^{6}{b}^{2}}{x}}+28\,{a}^{5}{b}^{3}{x}^{2}+14\,{a}^{4}{b}^{4}{x}^{5}+7\,{a}^{3}{b}^{5}{x}^{8}+{\frac{28\,{a}^{2}{b}^{6}{x}^{11}}{11}}+{\frac{4\,a{b}^{7}{x}^{14}}{7}}+{\frac{{b}^{8}{x}^{17}}{17}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.952568, size = 123, normalized size = 1.26 \begin{align*} \frac{1}{17} \, b^{8} x^{17} + \frac{4}{7} \, a b^{7} x^{14} + \frac{28}{11} \, a^{2} b^{6} x^{11} + 7 \, a^{3} b^{5} x^{8} + 14 \, a^{4} b^{4} x^{5} + 28 \, a^{5} b^{3} x^{2} - \frac{196 \, a^{6} b^{2} x^{6} + 14 \, a^{7} b x^{3} + a^{8}}{7 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.67019, size = 231, normalized size = 2.36 \begin{align*} \frac{77 \, b^{8} x^{24} + 748 \, a b^{7} x^{21} + 3332 \, a^{2} b^{6} x^{18} + 9163 \, a^{3} b^{5} x^{15} + 18326 \, a^{4} b^{4} x^{12} + 36652 \, a^{5} b^{3} x^{9} - 36652 \, a^{6} b^{2} x^{6} - 2618 \, a^{7} b x^{3} - 187 \, a^{8}}{1309 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.605952, size = 99, normalized size = 1.01 \begin{align*} 28 a^{5} b^{3} x^{2} + 14 a^{4} b^{4} x^{5} + 7 a^{3} b^{5} x^{8} + \frac{28 a^{2} b^{6} x^{11}}{11} + \frac{4 a b^{7} x^{14}}{7} + \frac{b^{8} x^{17}}{17} - \frac{a^{8} + 14 a^{7} b x^{3} + 196 a^{6} b^{2} x^{6}}{7 x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13638, size = 123, normalized size = 1.26 \begin{align*} \frac{1}{17} \, b^{8} x^{17} + \frac{4}{7} \, a b^{7} x^{14} + \frac{28}{11} \, a^{2} b^{6} x^{11} + 7 \, a^{3} b^{5} x^{8} + 14 \, a^{4} b^{4} x^{5} + 28 \, a^{5} b^{3} x^{2} - \frac{196 \, a^{6} b^{2} x^{6} + 14 \, a^{7} b x^{3} + a^{8}}{7 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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