Optimal. Leaf size=16 \[ \frac {\left (a+b x^{37}\right )^{13}}{481 b} \]
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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 = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {1584, 261} \begin {gather*} \frac {\left (a+b x^{37}\right )^{13}}{481 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^2+b x^{39}\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*}
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Mathematica [B] time = 0.01, size = 160, normalized size = 10.00 \begin {gather*} \frac {a^{12} x^{37}}{37}+\frac {6}{37} a^{11} b x^{74}+\frac {22}{37} a^{10} b^2 x^{111}+\frac {55}{37} a^9 b^3 x^{148}+\frac {99}{37} a^8 b^4 x^{185}+\frac {132}{37} a^7 b^5 x^{222}+\frac {132}{37} a^6 b^6 x^{259}+\frac {99}{37} a^5 b^7 x^{296}+\frac {55}{37} a^4 b^8 x^{333}+\frac {22}{37} a^3 b^9 x^{370}+\frac {6}{37} a^2 b^{10} x^{407}+\frac {1}{37} a b^{11} x^{444}+\frac {b^{12} x^{481}}{481} \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^2+b x^{39}\right )^{12} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.35, size = 134, normalized size = 8.38 \begin {gather*} \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 {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}{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 {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}{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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.35, size = 134, normalized size = 8.38 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.22, size = 134, normalized size = 8.38 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.14, size = 160, normalized size = 10.00 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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