Optimal. Leaf size=108 \[ -\frac{7 a^6 b^2}{9 x^{36}}-\frac{56 a^5 b^3}{33 x^{33}}-\frac{7 a^4 b^4}{3 x^{30}}-\frac{56 a^3 b^5}{27 x^{27}}-\frac{7 a^2 b^6}{6 x^{24}}-\frac{8 a^7 b}{39 x^{39}}-\frac{a^8}{42 x^{42}}-\frac{8 a b^7}{21 x^{21}}-\frac{b^8}{18 x^{18}} \]
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Rubi [A] time = 0.05092, antiderivative size = 108, 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} \[ -\frac{7 a^6 b^2}{9 x^{36}}-\frac{56 a^5 b^3}{33 x^{33}}-\frac{7 a^4 b^4}{3 x^{30}}-\frac{56 a^3 b^5}{27 x^{27}}-\frac{7 a^2 b^6}{6 x^{24}}-\frac{8 a^7 b}{39 x^{39}}-\frac{a^8}{42 x^{42}}-\frac{8 a b^7}{21 x^{21}}-\frac{b^8}{18 x^{18}} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^8}{x^{43}} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^8}{x^{15}} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (\frac{a^8}{x^{15}}+\frac{8 a^7 b}{x^{14}}+\frac{28 a^6 b^2}{x^{13}}+\frac{56 a^5 b^3}{x^{12}}+\frac{70 a^4 b^4}{x^{11}}+\frac{56 a^3 b^5}{x^{10}}+\frac{28 a^2 b^6}{x^9}+\frac{8 a b^7}{x^8}+\frac{b^8}{x^7}\right ) \, dx,x,x^3\right )\\ &=-\frac{a^8}{42 x^{42}}-\frac{8 a^7 b}{39 x^{39}}-\frac{7 a^6 b^2}{9 x^{36}}-\frac{56 a^5 b^3}{33 x^{33}}-\frac{7 a^4 b^4}{3 x^{30}}-\frac{56 a^3 b^5}{27 x^{27}}-\frac{7 a^2 b^6}{6 x^{24}}-\frac{8 a b^7}{21 x^{21}}-\frac{b^8}{18 x^{18}}\\ \end{align*}
Mathematica [A] time = 0.0046637, size = 108, normalized size = 1. \[ -\frac{7 a^6 b^2}{9 x^{36}}-\frac{56 a^5 b^3}{33 x^{33}}-\frac{7 a^4 b^4}{3 x^{30}}-\frac{56 a^3 b^5}{27 x^{27}}-\frac{7 a^2 b^6}{6 x^{24}}-\frac{8 a^7 b}{39 x^{39}}-\frac{a^8}{42 x^{42}}-\frac{8 a b^7}{21 x^{21}}-\frac{b^8}{18 x^{18}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 91, normalized size = 0.8 \begin{align*} -{\frac{{a}^{8}}{42\,{x}^{42}}}-{\frac{8\,{a}^{7}b}{39\,{x}^{39}}}-{\frac{7\,{a}^{6}{b}^{2}}{9\,{x}^{36}}}-{\frac{56\,{a}^{5}{b}^{3}}{33\,{x}^{33}}}-{\frac{7\,{a}^{4}{b}^{4}}{3\,{x}^{30}}}-{\frac{56\,{a}^{3}{b}^{5}}{27\,{x}^{27}}}-{\frac{7\,{a}^{2}{b}^{6}}{6\,{x}^{24}}}-{\frac{8\,a{b}^{7}}{21\,{x}^{21}}}-{\frac{{b}^{8}}{18\,{x}^{18}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.967416, size = 124, normalized size = 1.15 \begin{align*} -\frac{3003 \, b^{8} x^{24} + 20592 \, a b^{7} x^{21} + 63063 \, a^{2} b^{6} x^{18} + 112112 \, a^{3} b^{5} x^{15} + 126126 \, a^{4} b^{4} x^{12} + 91728 \, a^{5} b^{3} x^{9} + 42042 \, a^{6} b^{2} x^{6} + 11088 \, a^{7} b x^{3} + 1287 \, a^{8}}{54054 \, x^{42}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.57446, size = 248, normalized size = 2.3 \begin{align*} -\frac{3003 \, b^{8} x^{24} + 20592 \, a b^{7} x^{21} + 63063 \, a^{2} b^{6} x^{18} + 112112 \, a^{3} b^{5} x^{15} + 126126 \, a^{4} b^{4} x^{12} + 91728 \, a^{5} b^{3} x^{9} + 42042 \, a^{6} b^{2} x^{6} + 11088 \, a^{7} b x^{3} + 1287 \, a^{8}}{54054 \, x^{42}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.3996, size = 99, normalized size = 0.92 \begin{align*} - \frac{1287 a^{8} + 11088 a^{7} b x^{3} + 42042 a^{6} b^{2} x^{6} + 91728 a^{5} b^{3} x^{9} + 126126 a^{4} b^{4} x^{12} + 112112 a^{3} b^{5} x^{15} + 63063 a^{2} b^{6} x^{18} + 20592 a b^{7} x^{21} + 3003 b^{8} x^{24}}{54054 x^{42}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10191, size = 124, normalized size = 1.15 \begin{align*} -\frac{3003 \, b^{8} x^{24} + 20592 \, a b^{7} x^{21} + 63063 \, a^{2} b^{6} x^{18} + 112112 \, a^{3} b^{5} x^{15} + 126126 \, a^{4} b^{4} x^{12} + 91728 \, a^{5} b^{3} x^{9} + 42042 \, a^{6} b^{2} x^{6} + 11088 \, a^{7} b x^{3} + 1287 \, a^{8}}{54054 \, x^{42}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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