Optimal. Leaf size=16 \[ \frac{\left (a+b x^{37}\right )^{13}}{481 b} \]
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Rubi [A] time = 0.0117595, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {1584, 261} \[ \frac{\left (a+b x^{37}\right )^{13}}{481 b} \]
Antiderivative was successfully verified.
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Rule 1584
Rule 261
Rubi steps
\begin{align*} \int x^{24} \left (a x+b x^{38}\right )^{12} \, dx &=\int x^{36} \left (a+b x^{37}\right )^{12} \, dx\\ &=\frac{\left (a+b x^{37}\right )^{13}}{481 b}\\ \end{align*}
Mathematica [B] time = 0.008164, size = 160, normalized size = 10. \[ \frac{6}{37} a^2 b^{10} x^{407}+\frac{22}{37} a^3 b^9 x^{370}+\frac{55}{37} a^4 b^8 x^{333}+\frac{99}{37} a^5 b^7 x^{296}+\frac{132}{37} a^6 b^6 x^{259}+\frac{132}{37} a^7 b^5 x^{222}+\frac{99}{37} a^8 b^4 x^{185}+\frac{55}{37} a^9 b^3 x^{148}+\frac{22}{37} a^{10} b^2 x^{111}+\frac{6}{37} a^{11} b x^{74}+\frac{a^{12} x^{37}}{37}+\frac{1}{37} a b^{11} x^{444}+\frac{b^{12} x^{481}}{481} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.001, size = 135, normalized size = 8.4 \begin{align*}{\frac{{b}^{12}{x}^{481}}{481}}+{\frac{{b}^{11}a{x}^{444}}{37}}+{\frac{6\,{b}^{10}{a}^{2}{x}^{407}}{37}}+{\frac{22\,{a}^{3}{b}^{9}{x}^{370}}{37}}+{\frac{55\,{a}^{4}{b}^{8}{x}^{333}}{37}}+{\frac{99\,{a}^{5}{b}^{7}{x}^{296}}{37}}+{\frac{132\,{a}^{6}{b}^{6}{x}^{259}}{37}}+{\frac{132\,{a}^{7}{b}^{5}{x}^{222}}{37}}+{\frac{99\,{a}^{8}{b}^{4}{x}^{185}}{37}}+{\frac{55\,{a}^{9}{b}^{3}{x}^{148}}{37}}+{\frac{22\,{a}^{10}{b}^{2}{x}^{111}}{37}}+{\frac{6\,{a}^{11}b{x}^{74}}{37}}+{\frac{{a}^{12}{x}^{37}}{37}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.05626, size = 181, normalized size = 11.31 \begin{align*} \frac{1}{481} \, b^{12} x^{481} + \frac{1}{37} \, a b^{11} x^{444} + \frac{6}{37} \, a^{2} b^{10} x^{407} + \frac{22}{37} \, a^{3} b^{9} x^{370} + \frac{55}{37} \, a^{4} b^{8} x^{333} + \frac{99}{37} \, a^{5} b^{7} x^{296} + \frac{132}{37} \, a^{6} b^{6} x^{259} + \frac{132}{37} \, a^{7} b^{5} x^{222} + \frac{99}{37} \, a^{8} b^{4} x^{185} + \frac{55}{37} \, a^{9} b^{3} x^{148} + \frac{22}{37} \, a^{10} b^{2} x^{111} + \frac{6}{37} \, a^{11} b x^{74} + \frac{1}{37} \, a^{12} x^{37} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 0.760761, size = 371, normalized size = 23.19 \begin{align*} \frac{1}{481} x^{481} b^{12} + \frac{1}{37} x^{444} b^{11} a + \frac{6}{37} x^{407} b^{10} a^{2} + \frac{22}{37} x^{370} b^{9} a^{3} + \frac{55}{37} x^{333} b^{8} a^{4} + \frac{99}{37} x^{296} b^{7} a^{5} + \frac{132}{37} x^{259} b^{6} a^{6} + \frac{132}{37} x^{222} b^{5} a^{7} + \frac{99}{37} x^{185} b^{4} a^{8} + \frac{55}{37} x^{148} b^{3} a^{9} + \frac{22}{37} x^{111} b^{2} a^{10} + \frac{6}{37} x^{74} b a^{11} + \frac{1}{37} x^{37} a^{12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.23361, size = 160, normalized size = 10. \begin{align*} \frac{a^{12} x^{37}}{37} + \frac{6 a^{11} b x^{74}}{37} + \frac{22 a^{10} b^{2} x^{111}}{37} + \frac{55 a^{9} b^{3} x^{148}}{37} + \frac{99 a^{8} b^{4} x^{185}}{37} + \frac{132 a^{7} b^{5} x^{222}}{37} + \frac{132 a^{6} b^{6} x^{259}}{37} + \frac{99 a^{5} b^{7} x^{296}}{37} + \frac{55 a^{4} b^{8} x^{333}}{37} + \frac{22 a^{3} b^{9} x^{370}}{37} + \frac{6 a^{2} b^{10} x^{407}}{37} + \frac{a b^{11} x^{444}}{37} + \frac{b^{12} x^{481}}{481} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.11851, size = 181, normalized size = 11.31 \begin{align*} \frac{1}{481} \, b^{12} x^{481} + \frac{1}{37} \, a b^{11} x^{444} + \frac{6}{37} \, a^{2} b^{10} x^{407} + \frac{22}{37} \, a^{3} b^{9} x^{370} + \frac{55}{37} \, a^{4} b^{8} x^{333} + \frac{99}{37} \, a^{5} b^{7} x^{296} + \frac{132}{37} \, a^{6} b^{6} x^{259} + \frac{132}{37} \, a^{7} b^{5} x^{222} + \frac{99}{37} \, a^{8} b^{4} x^{185} + \frac{55}{37} \, a^{9} b^{3} x^{148} + \frac{22}{37} \, a^{10} b^{2} x^{111} + \frac{6}{37} \, a^{11} b x^{74} + \frac{1}{37} \, a^{12} x^{37} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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