Optimal. Leaf size=98 \[ \frac{7}{4} a^2 b^6 x^{16}+\frac{56}{13} a^3 b^5 x^{13}+7 a^4 b^4 x^{10}+8 a^5 b^3 x^7+7 a^6 b^2 x^4+8 a^7 b x-\frac{a^8}{2 x^2}+\frac{8}{19} a b^7 x^{19}+\frac{b^8 x^{22}}{22} \]
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Rubi [A] time = 0.0371823, 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} \[ \frac{7}{4} a^2 b^6 x^{16}+\frac{56}{13} a^3 b^5 x^{13}+7 a^4 b^4 x^{10}+8 a^5 b^3 x^7+7 a^6 b^2 x^4+8 a^7 b x-\frac{a^8}{2 x^2}+\frac{8}{19} a b^7 x^{19}+\frac{b^8 x^{22}}{22} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^8}{x^3} \, dx &=\int \left (8 a^7 b+\frac{a^8}{x^3}+28 a^6 b^2 x^3+56 a^5 b^3 x^6+70 a^4 b^4 x^9+56 a^3 b^5 x^{12}+28 a^2 b^6 x^{15}+8 a b^7 x^{18}+b^8 x^{21}\right ) \, dx\\ &=-\frac{a^8}{2 x^2}+8 a^7 b x+7 a^6 b^2 x^4+8 a^5 b^3 x^7+7 a^4 b^4 x^{10}+\frac{56}{13} a^3 b^5 x^{13}+\frac{7}{4} a^2 b^6 x^{16}+\frac{8}{19} a b^7 x^{19}+\frac{b^8 x^{22}}{22}\\ \end{align*}
Mathematica [A] time = 0.0044926, size = 98, normalized size = 1. \[ \frac{7}{4} a^2 b^6 x^{16}+\frac{56}{13} a^3 b^5 x^{13}+7 a^4 b^4 x^{10}+8 a^5 b^3 x^7+7 a^6 b^2 x^4+8 a^7 b x-\frac{a^8}{2 x^2}+\frac{8}{19} a b^7 x^{19}+\frac{b^8 x^{22}}{22} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 89, normalized size = 0.9 \begin{align*} -{\frac{{a}^{8}}{2\,{x}^{2}}}+8\,{a}^{7}bx+7\,{a}^{6}{b}^{2}{x}^{4}+8\,{a}^{5}{b}^{3}{x}^{7}+7\,{a}^{4}{b}^{4}{x}^{10}+{\frac{56\,{a}^{3}{b}^{5}{x}^{13}}{13}}+{\frac{7\,{a}^{2}{b}^{6}{x}^{16}}{4}}+{\frac{8\,a{b}^{7}{x}^{19}}{19}}+{\frac{{b}^{8}{x}^{22}}{22}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.969777, size = 119, normalized size = 1.21 \begin{align*} \frac{1}{22} \, b^{8} x^{22} + \frac{8}{19} \, a b^{7} x^{19} + \frac{7}{4} \, a^{2} b^{6} x^{16} + \frac{56}{13} \, a^{3} b^{5} x^{13} + 7 \, a^{4} b^{4} x^{10} + 8 \, a^{5} b^{3} x^{7} + 7 \, a^{6} b^{2} x^{4} + 8 \, a^{7} b x - \frac{a^{8}}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.77474, size = 240, normalized size = 2.45 \begin{align*} \frac{494 \, b^{8} x^{24} + 4576 \, a b^{7} x^{21} + 19019 \, a^{2} b^{6} x^{18} + 46816 \, a^{3} b^{5} x^{15} + 76076 \, a^{4} b^{4} x^{12} + 86944 \, a^{5} b^{3} x^{9} + 76076 \, a^{6} b^{2} x^{6} + 86944 \, a^{7} b x^{3} - 5434 \, a^{8}}{10868 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.39337, size = 99, normalized size = 1.01 \begin{align*} - \frac{a^{8}}{2 x^{2}} + 8 a^{7} b x + 7 a^{6} b^{2} x^{4} + 8 a^{5} b^{3} x^{7} + 7 a^{4} b^{4} x^{10} + \frac{56 a^{3} b^{5} x^{13}}{13} + \frac{7 a^{2} b^{6} x^{16}}{4} + \frac{8 a b^{7} x^{19}}{19} + \frac{b^{8} x^{22}}{22} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.106, size = 119, normalized size = 1.21 \begin{align*} \frac{1}{22} \, b^{8} x^{22} + \frac{8}{19} \, a b^{7} x^{19} + \frac{7}{4} \, a^{2} b^{6} x^{16} + \frac{56}{13} \, a^{3} b^{5} x^{13} + 7 \, a^{4} b^{4} x^{10} + 8 \, a^{5} b^{3} x^{7} + 7 \, a^{6} b^{2} x^{4} + 8 \, a^{7} b x - \frac{a^{8}}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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