Optimal. Leaf size=16 \[ \frac{\left (a+b x^{13}\right )^{13}}{169 b} \]
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Rubi [A] time = 0.0031126, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {261} \[ \frac{\left (a+b x^{13}\right )^{13}}{169 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x^{12} \left (a+b x^{13}\right )^{12} \, dx &=\frac{\left (a+b x^{13}\right )^{13}}{169 b}\\ \end{align*}
Mathematica [B] time = 0.0049, size = 160, normalized size = 10. \[ \frac{6}{13} a^2 b^{10} x^{143}+\frac{22}{13} a^3 b^9 x^{130}+\frac{55}{13} a^4 b^8 x^{117}+\frac{99}{13} a^5 b^7 x^{104}+\frac{132}{13} a^6 b^6 x^{91}+\frac{132}{13} a^7 b^5 x^{78}+\frac{99}{13} a^8 b^4 x^{65}+\frac{55}{13} a^9 b^3 x^{52}+\frac{22}{13} a^{10} b^2 x^{39}+\frac{6}{13} a^{11} b x^{26}+\frac{a^{12} x^{13}}{13}+\frac{1}{13} a b^{11} x^{156}+\frac{b^{12} x^{169}}{169} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.003, size = 135, normalized size = 8.4 \begin{align*}{\frac{{b}^{12}{x}^{169}}{169}}+{\frac{{b}^{11}a{x}^{156}}{13}}+{\frac{6\,{b}^{10}{a}^{2}{x}^{143}}{13}}+{\frac{22\,{a}^{3}{b}^{9}{x}^{130}}{13}}+{\frac{55\,{a}^{4}{b}^{8}{x}^{117}}{13}}+{\frac{99\,{a}^{5}{b}^{7}{x}^{104}}{13}}+{\frac{132\,{a}^{6}{b}^{6}{x}^{91}}{13}}+{\frac{132\,{a}^{7}{b}^{5}{x}^{78}}{13}}+{\frac{99\,{a}^{8}{b}^{4}{x}^{65}}{13}}+{\frac{55\,{a}^{9}{b}^{3}{x}^{52}}{13}}+{\frac{22\,{a}^{10}{b}^{2}{x}^{39}}{13}}+{\frac{6\,{a}^{11}b{x}^{26}}{13}}+{\frac{{a}^{12}{x}^{13}}{13}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.947921, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{13} + a\right )}^{13}}{169 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 0.787081, size = 365, normalized size = 22.81 \begin{align*} \frac{1}{169} x^{169} b^{12} + \frac{1}{13} x^{156} b^{11} a + \frac{6}{13} x^{143} b^{10} a^{2} + \frac{22}{13} x^{130} b^{9} a^{3} + \frac{55}{13} x^{117} b^{8} a^{4} + \frac{99}{13} x^{104} b^{7} a^{5} + \frac{132}{13} x^{91} b^{6} a^{6} + \frac{132}{13} x^{78} b^{5} a^{7} + \frac{99}{13} x^{65} b^{4} a^{8} + \frac{55}{13} x^{52} b^{3} a^{9} + \frac{22}{13} x^{39} b^{2} a^{10} + \frac{6}{13} x^{26} b a^{11} + \frac{1}{13} x^{13} a^{12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.101562, size = 160, normalized size = 10. \begin{align*} \frac{a^{12} x^{13}}{13} + \frac{6 a^{11} b x^{26}}{13} + \frac{22 a^{10} b^{2} x^{39}}{13} + \frac{55 a^{9} b^{3} x^{52}}{13} + \frac{99 a^{8} b^{4} x^{65}}{13} + \frac{132 a^{7} b^{5} x^{78}}{13} + \frac{132 a^{6} b^{6} x^{91}}{13} + \frac{99 a^{5} b^{7} x^{104}}{13} + \frac{55 a^{4} b^{8} x^{117}}{13} + \frac{22 a^{3} b^{9} x^{130}}{13} + \frac{6 a^{2} b^{10} x^{143}}{13} + \frac{a b^{11} x^{156}}{13} + \frac{b^{12} x^{169}}{169} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.22622, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{13} + a\right )}^{13}}{169 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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