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 = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {1598, 267}
\begin {gather*} \frac {\left (a+b x^{37}\right )^{13}}{481 b} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rule 1598
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*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(160\) vs. \(2(16)=32\).
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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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(134\) vs.
\(2(14)=28\).
time = 1.05, size = 135, normalized size = 8.44
method | result | size |
default | \(\frac {1}{37} a^{12} x^{37}+\frac {1}{481} b^{12} x^{481}+\frac {1}{37} a \,b^{11} x^{444}+\frac {6}{37} a^{2} b^{10} x^{407}+\frac {6}{37} b \,a^{11} x^{74}+\frac {22}{37} a^{3} b^{9} x^{370}+\frac {55}{37} a^{4} b^{8} x^{333}+\frac {99}{37} a^{5} b^{7} x^{296}+\frac {132}{37} a^{6} b^{6} x^{259}+\frac {132}{37} b^{5} a^{7} x^{222}+\frac {22}{37} a^{10} b^{2} x^{111}+\frac {99}{37} a^{8} b^{4} x^{185}+\frac {55}{37} b^{3} a^{9} x^{148}\) | \(135\) |
gosper | \(\frac {x^{37} \left (b^{12} x^{444}+13 a \,b^{11} x^{407}+78 a^{2} b^{10} x^{370}+286 a^{3} b^{9} x^{333}+715 a^{4} b^{8} x^{296}+1287 a^{5} b^{7} x^{259}+1716 a^{6} b^{6} x^{222}+1716 b^{5} a^{7} x^{185}+1287 a^{8} b^{4} x^{148}+715 b^{3} a^{9} x^{111}+286 a^{10} b^{2} x^{74}+78 b \,a^{11} x^{37}+13 a^{12}\right )}{481}\) | \(136\) |
risch | \(\frac {b^{12} x^{481}}{481}+\frac {a \,b^{11} x^{444}}{37}+\frac {6 a^{2} b^{10} x^{407}}{37}+\frac {22 a^{3} b^{9} x^{370}}{37}+\frac {55 a^{4} b^{8} x^{333}}{37}+\frac {99 a^{5} b^{7} x^{296}}{37}+\frac {132 a^{6} b^{6} x^{259}}{37}+\frac {132 b^{5} a^{7} x^{222}}{37}+\frac {99 a^{8} b^{4} x^{185}}{37}+\frac {55 b^{3} a^{9} x^{148}}{37}+\frac {22 a^{10} b^{2} x^{111}}{37}+\frac {6 b \,a^{11} x^{74}}{37}+\frac {a^{12} x^{37}}{37}+\frac {a^{13}}{481 b}\) | \(143\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 134 vs.
\(2 (14) = 28\).
time = 0.28, 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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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 134 vs.
\(2 (14) = 28\).
time = 2.25, 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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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 160 vs.
\(2 (10) = 20\).
time = 0.04, 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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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 134 vs.
\(2 (14) = 28\).
time = 0.47, 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 = 5.15, 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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