Optimal. Leaf size=69 \[ \frac{10}{27} a^2 b^3 x^{27}+\frac{5}{12} a^3 b^2 x^{24}+\frac{5}{21} a^4 b x^{21}+\frac{a^5 x^{18}}{18}+\frac{1}{6} a b^4 x^{30}+\frac{b^5 x^{33}}{33} \]
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Rubi [A] time = 0.0460839, antiderivative size = 69, 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} \[ \frac{10}{27} a^2 b^3 x^{27}+\frac{5}{12} a^3 b^2 x^{24}+\frac{5}{21} a^4 b x^{21}+\frac{a^5 x^{18}}{18}+\frac{1}{6} a b^4 x^{30}+\frac{b^5 x^{33}}{33} \]
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 )^5 \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int x^5 (a+b x)^5 \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (a^5 x^5+5 a^4 b x^6+10 a^3 b^2 x^7+10 a^2 b^3 x^8+5 a b^4 x^9+b^5 x^{10}\right ) \, dx,x,x^3\right )\\ &=\frac{a^5 x^{18}}{18}+\frac{5}{21} a^4 b x^{21}+\frac{5}{12} a^3 b^2 x^{24}+\frac{10}{27} a^2 b^3 x^{27}+\frac{1}{6} a b^4 x^{30}+\frac{b^5 x^{33}}{33}\\ \end{align*}
Mathematica [A] time = 0.0026706, size = 69, normalized size = 1. \[ \frac{10}{27} a^2 b^3 x^{27}+\frac{5}{12} a^3 b^2 x^{24}+\frac{5}{21} a^4 b x^{21}+\frac{a^5 x^{18}}{18}+\frac{1}{6} a b^4 x^{30}+\frac{b^5 x^{33}}{33} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 58, normalized size = 0.8 \begin{align*}{\frac{{a}^{5}{x}^{18}}{18}}+{\frac{5\,{a}^{4}b{x}^{21}}{21}}+{\frac{5\,{a}^{3}{b}^{2}{x}^{24}}{12}}+{\frac{10\,{a}^{2}{b}^{3}{x}^{27}}{27}}+{\frac{a{b}^{4}{x}^{30}}{6}}+{\frac{{b}^{5}{x}^{33}}{33}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.999136, size = 77, normalized size = 1.12 \begin{align*} \frac{1}{33} \, b^{5} x^{33} + \frac{1}{6} \, a b^{4} x^{30} + \frac{10}{27} \, a^{2} b^{3} x^{27} + \frac{5}{12} \, a^{3} b^{2} x^{24} + \frac{5}{21} \, a^{4} b x^{21} + \frac{1}{18} \, a^{5} x^{18} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.47737, size = 144, normalized size = 2.09 \begin{align*} \frac{1}{33} x^{33} b^{5} + \frac{1}{6} x^{30} b^{4} a + \frac{10}{27} x^{27} b^{3} a^{2} + \frac{5}{12} x^{24} b^{2} a^{3} + \frac{5}{21} x^{21} b a^{4} + \frac{1}{18} x^{18} a^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.077652, size = 65, normalized size = 0.94 \begin{align*} \frac{a^{5} x^{18}}{18} + \frac{5 a^{4} b x^{21}}{21} + \frac{5 a^{3} b^{2} x^{24}}{12} + \frac{10 a^{2} b^{3} x^{27}}{27} + \frac{a b^{4} x^{30}}{6} + \frac{b^{5} x^{33}}{33} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11145, size = 77, normalized size = 1.12 \begin{align*} \frac{1}{33} \, b^{5} x^{33} + \frac{1}{6} \, a b^{4} x^{30} + \frac{10}{27} \, a^{2} b^{3} x^{27} + \frac{5}{12} \, a^{3} b^{2} x^{24} + \frac{5}{21} \, a^{4} b x^{21} + \frac{1}{18} \, a^{5} x^{18} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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