Optimal. Leaf size=16 \[ \frac{\left (a+b x^{25}\right )^{13}}{325 b} \]
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Rubi [A] time = 0.0027836, 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} \[ \frac{\left (a+b x^{25}\right )^{13}}{325 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x^{24} \left (a+b x^{25}\right )^{12} \, dx &=\frac{\left (a+b x^{25}\right )^{13}}{325 b}\\ \end{align*}
Mathematica [B] time = 0.0042827, size = 160, normalized size = 10. \[ \frac{6}{25} a^2 b^{10} x^{275}+\frac{22}{25} a^3 b^9 x^{250}+\frac{11}{5} a^4 b^8 x^{225}+\frac{99}{25} a^5 b^7 x^{200}+\frac{132}{25} a^6 b^6 x^{175}+\frac{132}{25} a^7 b^5 x^{150}+\frac{99}{25} a^8 b^4 x^{125}+\frac{11}{5} a^9 b^3 x^{100}+\frac{22}{25} a^{10} b^2 x^{75}+\frac{6}{25} a^{11} b x^{50}+\frac{a^{12} x^{25}}{25}+\frac{1}{25} a b^{11} x^{300}+\frac{b^{12} x^{325}}{325} \]
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}^{325}}{325}}+{\frac{{b}^{11}a{x}^{300}}{25}}+{\frac{6\,{b}^{10}{a}^{2}{x}^{275}}{25}}+{\frac{22\,{a}^{3}{b}^{9}{x}^{250}}{25}}+{\frac{11\,{a}^{4}{b}^{8}{x}^{225}}{5}}+{\frac{99\,{a}^{5}{b}^{7}{x}^{200}}{25}}+{\frac{132\,{a}^{6}{b}^{6}{x}^{175}}{25}}+{\frac{132\,{a}^{7}{b}^{5}{x}^{150}}{25}}+{\frac{99\,{a}^{8}{b}^{4}{x}^{125}}{25}}+{\frac{11\,{a}^{9}{b}^{3}{x}^{100}}{5}}+{\frac{22\,{a}^{10}{b}^{2}{x}^{75}}{25}}+{\frac{6\,{a}^{11}b{x}^{50}}{25}}+{\frac{{a}^{12}{x}^{25}}{25}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.10246, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{25} + a\right )}^{13}}{325 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 0.680386, size = 367, normalized size = 22.94 \begin{align*} \frac{1}{325} x^{325} b^{12} + \frac{1}{25} x^{300} b^{11} a + \frac{6}{25} x^{275} b^{10} a^{2} + \frac{22}{25} x^{250} b^{9} a^{3} + \frac{11}{5} x^{225} b^{8} a^{4} + \frac{99}{25} x^{200} b^{7} a^{5} + \frac{132}{25} x^{175} b^{6} a^{6} + \frac{132}{25} x^{150} b^{5} a^{7} + \frac{99}{25} x^{125} b^{4} a^{8} + \frac{11}{5} x^{100} b^{3} a^{9} + \frac{22}{25} x^{75} b^{2} a^{10} + \frac{6}{25} x^{50} b a^{11} + \frac{1}{25} x^{25} a^{12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.121134, size = 160, normalized size = 10. \begin{align*} \frac{a^{12} x^{25}}{25} + \frac{6 a^{11} b x^{50}}{25} + \frac{22 a^{10} b^{2} x^{75}}{25} + \frac{11 a^{9} b^{3} x^{100}}{5} + \frac{99 a^{8} b^{4} x^{125}}{25} + \frac{132 a^{7} b^{5} x^{150}}{25} + \frac{132 a^{6} b^{6} x^{175}}{25} + \frac{99 a^{5} b^{7} x^{200}}{25} + \frac{11 a^{4} b^{8} x^{225}}{5} + \frac{22 a^{3} b^{9} x^{250}}{25} + \frac{6 a^{2} b^{10} x^{275}}{25} + \frac{a b^{11} x^{300}}{25} + \frac{b^{12} x^{325}}{325} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20377, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{25} + a\right )}^{13}}{325 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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