Optimal. Leaf size=110 \[ \frac{5 a^2 \left (a+b x^3\right )^{12}}{18 b^6}-\frac{10 a^3 \left (a+b x^3\right )^{11}}{33 b^6}+\frac{a^4 \left (a+b x^3\right )^{10}}{6 b^6}-\frac{a^5 \left (a+b x^3\right )^9}{27 b^6}+\frac{\left (a+b x^3\right )^{14}}{42 b^6}-\frac{5 a \left (a+b x^3\right )^{13}}{39 b^6} \]
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Rubi [A] time = 0.172613, antiderivative size = 110, 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} \[ \frac{5 a^2 \left (a+b x^3\right )^{12}}{18 b^6}-\frac{10 a^3 \left (a+b x^3\right )^{11}}{33 b^6}+\frac{a^4 \left (a+b x^3\right )^{10}}{6 b^6}-\frac{a^5 \left (a+b x^3\right )^9}{27 b^6}+\frac{\left (a+b x^3\right )^{14}}{42 b^6}-\frac{5 a \left (a+b x^3\right )^{13}}{39 b^6} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int x^{17} \left (a+b x^3\right )^8 \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int x^5 (a+b x)^8 \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (-\frac{a^5 (a+b x)^8}{b^5}+\frac{5 a^4 (a+b x)^9}{b^5}-\frac{10 a^3 (a+b x)^{10}}{b^5}+\frac{10 a^2 (a+b x)^{11}}{b^5}-\frac{5 a (a+b x)^{12}}{b^5}+\frac{(a+b x)^{13}}{b^5}\right ) \, dx,x,x^3\right )\\ &=-\frac{a^5 \left (a+b x^3\right )^9}{27 b^6}+\frac{a^4 \left (a+b x^3\right )^{10}}{6 b^6}-\frac{10 a^3 \left (a+b x^3\right )^{11}}{33 b^6}+\frac{5 a^2 \left (a+b x^3\right )^{12}}{18 b^6}-\frac{5 a \left (a+b x^3\right )^{13}}{39 b^6}+\frac{\left (a+b x^3\right )^{14}}{42 b^6}\\ \end{align*}
Mathematica [A] time = 0.0028087, size = 108, normalized size = 0.98 \[ \frac{7}{9} a^2 b^6 x^{36}+\frac{56}{33} a^3 b^5 x^{33}+\frac{7}{3} a^4 b^4 x^{30}+\frac{56}{27} a^5 b^3 x^{27}+\frac{7}{6} a^6 b^2 x^{24}+\frac{8}{21} a^7 b x^{21}+\frac{a^8 x^{18}}{18}+\frac{8}{39} a b^7 x^{39}+\frac{b^8 x^{42}}{42} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 91, normalized size = 0.8 \begin{align*}{\frac{{b}^{8}{x}^{42}}{42}}+{\frac{8\,a{b}^{7}{x}^{39}}{39}}+{\frac{7\,{b}^{6}{a}^{2}{x}^{36}}{9}}+{\frac{56\,{a}^{3}{b}^{5}{x}^{33}}{33}}+{\frac{7\,{a}^{4}{b}^{4}{x}^{30}}{3}}+{\frac{56\,{a}^{5}{b}^{3}{x}^{27}}{27}}+{\frac{7\,{a}^{6}{b}^{2}{x}^{24}}{6}}+{\frac{8\,{a}^{7}b{x}^{21}}{21}}+{\frac{{a}^{8}{x}^{18}}{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.971629, size = 122, normalized size = 1.11 \begin{align*} \frac{1}{42} \, b^{8} x^{42} + \frac{8}{39} \, a b^{7} x^{39} + \frac{7}{9} \, a^{2} b^{6} x^{36} + \frac{56}{33} \, a^{3} b^{5} x^{33} + \frac{7}{3} \, a^{4} b^{4} x^{30} + \frac{56}{27} \, a^{5} b^{3} x^{27} + \frac{7}{6} \, a^{6} b^{2} x^{24} + \frac{8}{21} \, a^{7} b x^{21} + \frac{1}{18} \, a^{8} x^{18} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.53003, size = 224, normalized size = 2.04 \begin{align*} \frac{1}{42} x^{42} b^{8} + \frac{8}{39} x^{39} b^{7} a + \frac{7}{9} x^{36} b^{6} a^{2} + \frac{56}{33} x^{33} b^{5} a^{3} + \frac{7}{3} x^{30} b^{4} a^{4} + \frac{56}{27} x^{27} b^{3} a^{5} + \frac{7}{6} x^{24} b^{2} a^{6} + \frac{8}{21} x^{21} b a^{7} + \frac{1}{18} x^{18} a^{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.115149, size = 107, normalized size = 0.97 \begin{align*} \frac{a^{8} x^{18}}{18} + \frac{8 a^{7} b x^{21}}{21} + \frac{7 a^{6} b^{2} x^{24}}{6} + \frac{56 a^{5} b^{3} x^{27}}{27} + \frac{7 a^{4} b^{4} x^{30}}{3} + \frac{56 a^{3} b^{5} x^{33}}{33} + \frac{7 a^{2} b^{6} x^{36}}{9} + \frac{8 a b^{7} x^{39}}{39} + \frac{b^{8} x^{42}}{42} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.59656, size = 122, normalized size = 1.11 \begin{align*} \frac{1}{42} \, b^{8} x^{42} + \frac{8}{39} \, a b^{7} x^{39} + \frac{7}{9} \, a^{2} b^{6} x^{36} + \frac{56}{33} \, a^{3} b^{5} x^{33} + \frac{7}{3} \, a^{4} b^{4} x^{30} + \frac{56}{27} \, a^{5} b^{3} x^{27} + \frac{7}{6} \, a^{6} b^{2} x^{24} + \frac{8}{21} \, a^{7} b x^{21} + \frac{1}{18} \, a^{8} x^{18} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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