Optimal. Leaf size=105 \[ -\frac{28 a^6 b^2}{15 x^{15}}-\frac{14 a^5 b^3}{3 x^{12}}-\frac{70 a^4 b^4}{9 x^9}-\frac{28 a^3 b^5}{3 x^6}-\frac{28 a^2 b^6}{3 x^3}-\frac{4 a^7 b}{9 x^{18}}-\frac{a^8}{21 x^{21}}+8 a b^7 \log (x)+\frac{b^8 x^3}{3} \]
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Rubi [A] time = 0.0538065, antiderivative size = 105, 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} \[ -\frac{28 a^6 b^2}{15 x^{15}}-\frac{14 a^5 b^3}{3 x^{12}}-\frac{70 a^4 b^4}{9 x^9}-\frac{28 a^3 b^5}{3 x^6}-\frac{28 a^2 b^6}{3 x^3}-\frac{4 a^7 b}{9 x^{18}}-\frac{a^8}{21 x^{21}}+8 a b^7 \log (x)+\frac{b^8 x^3}{3} \]
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^{22}} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^8}{x^8} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (b^8+\frac{a^8}{x^8}+\frac{8 a^7 b}{x^7}+\frac{28 a^6 b^2}{x^6}+\frac{56 a^5 b^3}{x^5}+\frac{70 a^4 b^4}{x^4}+\frac{56 a^3 b^5}{x^3}+\frac{28 a^2 b^6}{x^2}+\frac{8 a b^7}{x}\right ) \, dx,x,x^3\right )\\ &=-\frac{a^8}{21 x^{21}}-\frac{4 a^7 b}{9 x^{18}}-\frac{28 a^6 b^2}{15 x^{15}}-\frac{14 a^5 b^3}{3 x^{12}}-\frac{70 a^4 b^4}{9 x^9}-\frac{28 a^3 b^5}{3 x^6}-\frac{28 a^2 b^6}{3 x^3}+\frac{b^8 x^3}{3}+8 a b^7 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0103324, size = 105, normalized size = 1. \[ -\frac{28 a^6 b^2}{15 x^{15}}-\frac{14 a^5 b^3}{3 x^{12}}-\frac{70 a^4 b^4}{9 x^9}-\frac{28 a^3 b^5}{3 x^6}-\frac{28 a^2 b^6}{3 x^3}-\frac{4 a^7 b}{9 x^{18}}-\frac{a^8}{21 x^{21}}+8 a b^7 \log (x)+\frac{b^8 x^3}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 90, normalized size = 0.9 \begin{align*} -{\frac{{a}^{8}}{21\,{x}^{21}}}-{\frac{4\,{a}^{7}b}{9\,{x}^{18}}}-{\frac{28\,{a}^{6}{b}^{2}}{15\,{x}^{15}}}-{\frac{14\,{a}^{5}{b}^{3}}{3\,{x}^{12}}}-{\frac{70\,{a}^{4}{b}^{4}}{9\,{x}^{9}}}-{\frac{28\,{a}^{3}{b}^{5}}{3\,{x}^{6}}}-{\frac{28\,{a}^{2}{b}^{6}}{3\,{x}^{3}}}+{\frac{{b}^{8}{x}^{3}}{3}}+8\,a{b}^{7}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.967701, size = 127, normalized size = 1.21 \begin{align*} \frac{1}{3} \, b^{8} x^{3} + \frac{8}{3} \, a b^{7} \log \left (x^{3}\right ) - \frac{2940 \, a^{2} b^{6} x^{18} + 2940 \, a^{3} b^{5} x^{15} + 2450 \, a^{4} b^{4} x^{12} + 1470 \, a^{5} b^{3} x^{9} + 588 \, a^{6} b^{2} x^{6} + 140 \, a^{7} b x^{3} + 15 \, a^{8}}{315 \, x^{21}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.64548, size = 235, normalized size = 2.24 \begin{align*} \frac{105 \, b^{8} x^{24} + 2520 \, a b^{7} x^{21} \log \left (x\right ) - 2940 \, a^{2} b^{6} x^{18} - 2940 \, a^{3} b^{5} x^{15} - 2450 \, a^{4} b^{4} x^{12} - 1470 \, a^{5} b^{3} x^{9} - 588 \, a^{6} b^{2} x^{6} - 140 \, a^{7} b x^{3} - 15 \, a^{8}}{315 \, x^{21}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.42041, size = 97, normalized size = 0.92 \begin{align*} 8 a b^{7} \log{\left (x \right )} + \frac{b^{8} x^{3}}{3} - \frac{15 a^{8} + 140 a^{7} b x^{3} + 588 a^{6} b^{2} x^{6} + 1470 a^{5} b^{3} x^{9} + 2450 a^{4} b^{4} x^{12} + 2940 a^{3} b^{5} x^{15} + 2940 a^{2} b^{6} x^{18}}{315 x^{21}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11203, size = 138, normalized size = 1.31 \begin{align*} \frac{1}{3} \, b^{8} x^{3} + 8 \, a b^{7} \log \left ({\left | x \right |}\right ) - \frac{2178 \, a b^{7} x^{21} + 2940 \, a^{2} b^{6} x^{18} + 2940 \, a^{3} b^{5} x^{15} + 2450 \, a^{4} b^{4} x^{12} + 1470 \, a^{5} b^{3} x^{9} + 588 \, a^{6} b^{2} x^{6} + 140 \, a^{7} b x^{3} + 15 \, a^{8}}{315 \, x^{21}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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