Optimal. Leaf size=27 \[ \frac{\left (a+b x^{12 m+1}\right )^{13}}{13 b (12 m+1)} \]
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Rubi [A] time = 0.0063404, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.043, Rules used = {261} \[ \frac{\left (a+b x^{12 m+1}\right )^{13}}{13 b (12 m+1)} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x^{12+12 (-1+m)} \left (a+b x^{1+12 m}\right )^{12} \, dx &=\frac{\left (a+b x^{1+12 m}\right )^{13}}{13 b (1+12 m)}\\ \end{align*}
Mathematica [A] time = 0.0027512, size = 24, normalized size = 0.89 \[ \frac{\left (a+b x^{12 m+1}\right )^{13}}{156 b m+13 b} \]
Antiderivative was successfully verified.
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Maple [B] time = 0., size = 311, normalized size = 11.5 \begin{align*}{\frac{{b}^{12}{x}^{13} \left ({x}^{12\,m} \right ) ^{13}}{13+156\,m}}+{\frac{a{b}^{11}{x}^{12} \left ({x}^{12\,m} \right ) ^{12}}{1+12\,m}}+6\,{\frac{{a}^{2}{b}^{10}{x}^{11} \left ({x}^{12\,m} \right ) ^{11}}{1+12\,m}}+22\,{\frac{{a}^{3}{b}^{9}{x}^{10} \left ({x}^{12\,m} \right ) ^{10}}{1+12\,m}}+55\,{\frac{{a}^{4}{b}^{8}{x}^{9} \left ({x}^{12\,m} \right ) ^{9}}{1+12\,m}}+99\,{\frac{{a}^{5}{b}^{7}{x}^{8} \left ({x}^{12\,m} \right ) ^{8}}{1+12\,m}}+132\,{\frac{{a}^{6}{b}^{6}{x}^{7} \left ({x}^{12\,m} \right ) ^{7}}{1+12\,m}}+132\,{\frac{{a}^{7}{b}^{5}{x}^{6} \left ({x}^{12\,m} \right ) ^{6}}{1+12\,m}}+99\,{\frac{{a}^{8}{b}^{4}{x}^{5} \left ({x}^{12\,m} \right ) ^{5}}{1+12\,m}}+55\,{\frac{{a}^{9}{b}^{3}{x}^{4} \left ({x}^{12\,m} \right ) ^{4}}{1+12\,m}}+22\,{\frac{{a}^{10}{b}^{2}{x}^{3} \left ({x}^{12\,m} \right ) ^{3}}{1+12\,m}}+6\,{\frac{{a}^{11}b{x}^{2} \left ({x}^{12\,m} \right ) ^{2}}{1+12\,m}}+{\frac{{a}^{12}x{x}^{12\,m}}{1+12\,m}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.953847, size = 34, normalized size = 1.26 \begin{align*} \frac{{\left (b x^{12 \, m + 1} + a\right )}^{13}}{13 \, b{\left (12 \, m + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.05072, size = 495, normalized size = 18.33 \begin{align*} \frac{b^{12} x^{156 \, m + 13} + 13 \, a b^{11} x^{144 \, m + 12} + 78 \, a^{2} b^{10} x^{132 \, m + 11} + 286 \, a^{3} b^{9} x^{120 \, m + 10} + 715 \, a^{4} b^{8} x^{108 \, m + 9} + 1287 \, a^{5} b^{7} x^{96 \, m + 8} + 1716 \, a^{6} b^{6} x^{84 \, m + 7} + 1716 \, a^{7} b^{5} x^{72 \, m + 6} + 1287 \, a^{8} b^{4} x^{60 \, m + 5} + 715 \, a^{9} b^{3} x^{48 \, m + 4} + 286 \, a^{10} b^{2} x^{36 \, m + 3} + 78 \, a^{11} b x^{24 \, m + 2} + 13 \, a^{12} x^{12 \, m + 1}}{13 \,{\left (12 \, m + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.74621, size = 277, normalized size = 10.26 \begin{align*} \frac{b^{12} x^{13} x^{156 \, m} + 13 \, a b^{11} x^{12} x^{144 \, m} + 78 \, a^{2} b^{10} x^{11} x^{132 \, m} + 286 \, a^{3} b^{9} x^{10} x^{120 \, m} + 715 \, a^{4} b^{8} x^{9} x^{108 \, m} + 1287 \, a^{5} b^{7} x^{8} x^{96 \, m} + 1716 \, a^{6} b^{6} x^{7} x^{84 \, m} + 1716 \, a^{7} b^{5} x^{6} x^{72 \, m} + 1287 \, a^{8} b^{4} x^{5} x^{60 \, m} + 715 \, a^{9} b^{3} x^{4} x^{48 \, m} + 286 \, a^{10} b^{2} x^{3} x^{36 \, m} + 78 \, a^{11} b x^{2} x^{24 \, m} + 13 \, a^{12} x x^{12 \, m}}{13 \,{\left (12 \, m + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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