Optimal. Leaf size=16 \[ \frac {\left (a+b x^{25}\right )^{13}}{325 b} \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, 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} \begin {gather*} \frac {\left (a+b x^{25}\right )^{13}}{325 b} \end {gather*}
Antiderivative was successfully verified.
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Rule 261
Rule 1584
Rubi steps
\begin {align*} \int x^{12} \left (a x+b x^{26}\right )^{12} \, dx &=\int x^{24} \left (a+b x^{25}\right )^{12} \, dx\\ &=\frac {\left (a+b x^{25}\right )^{13}}{325 b}\\ \end {align*}
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Mathematica [B] time = 0.02, size = 160, normalized size = 10.00 \begin {gather*} \frac {a^{12} x^{25}}{25}+\frac {6}{25} a^{11} b x^{50}+\frac {22}{25} a^{10} b^2 x^{75}+\frac {11}{5} a^9 b^3 x^{100}+\frac {99}{25} a^8 b^4 x^{125}+\frac {132}{25} a^7 b^5 x^{150}+\frac {132}{25} a^6 b^6 x^{175}+\frac {99}{25} a^5 b^7 x^{200}+\frac {11}{5} a^4 b^8 x^{225}+\frac {22}{25} a^3 b^9 x^{250}+\frac {6}{25} a^2 b^{10} x^{275}+\frac {1}{25} a b^{11} x^{300}+\frac {b^{12} x^{325}}{325} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^{12} \left (a x+b x^{26}\right )^{12} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.34, size = 134, normalized size = 8.38 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.15, size = 134, normalized size = 8.38 \begin {gather*} \frac {1}{325} \, b^{12} x^{325} + \frac {1}{25} \, a b^{11} x^{300} + \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 {1}{25} \, a^{12} x^{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 135, normalized size = 8.44 \begin {gather*} \frac {1}{325} b^{12} x^{325}+\frac {1}{25} a \,b^{11} x^{300}+\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 {1}{25} a^{12} x^{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.37, size = 134, normalized size = 8.38 \begin {gather*} \frac {1}{325} \, b^{12} x^{325} + \frac {1}{25} \, a b^{11} x^{300} + \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 {1}{25} \, a^{12} x^{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.16, size = 134, normalized size = 8.38 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.13, size = 160, normalized size = 10.00 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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