Integrand size = 11, antiderivative size = 16 \[ \int \left (a x+b x^{14}\right )^{12} \, dx=\frac {\left (a+b x^{13}\right )^{13}}{169 b} \]
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Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {1607, 267} \[ \int \left (a x+b x^{14}\right )^{12} \, dx=\frac {\left (a+b x^{13}\right )^{13}}{169 b} \]
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Rule 267
Rule 1607
Rubi steps \begin{align*} \text {integral}& = \int x^{12} \left (a+b x^{13}\right )^{12} \, dx \\ & = \frac {\left (a+b x^{13}\right )^{13}}{169 b} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(160\) vs. \(2(16)=32\).
Time = 0.00 (sec) , antiderivative size = 160, normalized size of antiderivative = 10.00 \[ \int \left (a x+b x^{14}\right )^{12} \, dx=\frac {a^{12} x^{13}}{13}+\frac {6}{13} a^{11} b x^{26}+\frac {22}{13} a^{10} b^2 x^{39}+\frac {55}{13} a^9 b^3 x^{52}+\frac {99}{13} a^8 b^4 x^{65}+\frac {132}{13} a^7 b^5 x^{78}+\frac {132}{13} a^6 b^6 x^{91}+\frac {99}{13} a^5 b^7 x^{104}+\frac {55}{13} a^4 b^8 x^{117}+\frac {22}{13} a^3 b^9 x^{130}+\frac {6}{13} a^2 b^{10} x^{143}+\frac {1}{13} a b^{11} x^{156}+\frac {b^{12} x^{169}}{169} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(134\) vs. \(2(14)=28\).
Time = 1.79 (sec) , antiderivative size = 135, normalized size of antiderivative = 8.44
method | result | size |
default | \(\frac {1}{169} b^{12} x^{169}+\frac {1}{13} a \,b^{11} x^{156}+\frac {6}{13} a^{2} b^{10} x^{143}+\frac {22}{13} a^{3} b^{9} x^{130}+\frac {55}{13} a^{4} b^{8} x^{117}+\frac {99}{13} a^{5} b^{7} x^{104}+\frac {132}{13} a^{6} b^{6} x^{91}+\frac {132}{13} a^{7} b^{5} x^{78}+\frac {99}{13} a^{8} b^{4} x^{65}+\frac {55}{13} a^{9} b^{3} x^{52}+\frac {22}{13} a^{10} b^{2} x^{39}+\frac {6}{13} b \,a^{11} x^{26}+\frac {1}{13} a^{12} x^{13}\) | \(135\) |
parallelrisch | \(\frac {1}{169} b^{12} x^{169}+\frac {1}{13} a \,b^{11} x^{156}+\frac {6}{13} a^{2} b^{10} x^{143}+\frac {22}{13} a^{3} b^{9} x^{130}+\frac {55}{13} a^{4} b^{8} x^{117}+\frac {99}{13} a^{5} b^{7} x^{104}+\frac {132}{13} a^{6} b^{6} x^{91}+\frac {132}{13} a^{7} b^{5} x^{78}+\frac {99}{13} a^{8} b^{4} x^{65}+\frac {55}{13} a^{9} b^{3} x^{52}+\frac {22}{13} a^{10} b^{2} x^{39}+\frac {6}{13} b \,a^{11} x^{26}+\frac {1}{13} a^{12} x^{13}\) | \(135\) |
gosper | \(\frac {x^{13} \left (b^{12} x^{156}+13 a \,b^{11} x^{143}+78 a^{2} b^{10} x^{130}+286 a^{3} b^{9} x^{117}+715 a^{4} b^{8} x^{104}+1287 a^{5} b^{7} x^{91}+1716 a^{6} b^{6} x^{78}+1716 a^{7} b^{5} x^{65}+1287 a^{8} b^{4} x^{52}+715 a^{9} b^{3} x^{39}+286 a^{10} b^{2} x^{26}+78 b \,a^{11} x^{13}+13 a^{12}\right )}{169}\) | \(136\) |
risch | \(\frac {b^{12} x^{169}}{169}+\frac {a \,b^{11} x^{156}}{13}+\frac {6 a^{2} b^{10} x^{143}}{13}+\frac {22 a^{3} b^{9} x^{130}}{13}+\frac {55 a^{4} b^{8} x^{117}}{13}+\frac {99 a^{5} b^{7} x^{104}}{13}+\frac {132 a^{6} b^{6} x^{91}}{13}+\frac {132 a^{7} b^{5} x^{78}}{13}+\frac {99 a^{8} b^{4} x^{65}}{13}+\frac {55 a^{9} b^{3} x^{52}}{13}+\frac {22 a^{10} b^{2} x^{39}}{13}+\frac {6 b \,a^{11} x^{26}}{13}+\frac {a^{12} x^{13}}{13}+\frac {a^{13}}{169 b}\) | \(143\) |
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Leaf count of result is larger than twice the leaf count of optimal. 134 vs. \(2 (14) = 28\).
Time = 0.26 (sec) , antiderivative size = 134, normalized size of antiderivative = 8.38 \[ \int \left (a x+b x^{14}\right )^{12} \, dx=\frac {1}{169} \, b^{12} x^{169} + \frac {1}{13} \, a b^{11} x^{156} + \frac {6}{13} \, a^{2} b^{10} x^{143} + \frac {22}{13} \, a^{3} b^{9} x^{130} + \frac {55}{13} \, a^{4} b^{8} x^{117} + \frac {99}{13} \, a^{5} b^{7} x^{104} + \frac {132}{13} \, a^{6} b^{6} x^{91} + \frac {132}{13} \, a^{7} b^{5} x^{78} + \frac {99}{13} \, a^{8} b^{4} x^{65} + \frac {55}{13} \, a^{9} b^{3} x^{52} + \frac {22}{13} \, a^{10} b^{2} x^{39} + \frac {6}{13} \, a^{11} b x^{26} + \frac {1}{13} \, a^{12} x^{13} \]
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Leaf count of result is larger than twice the leaf count of optimal. 160 vs. \(2 (10) = 20\).
Time = 0.04 (sec) , antiderivative size = 160, normalized size of antiderivative = 10.00 \[ \int \left (a x+b x^{14}\right )^{12} \, dx=\frac {a^{12} x^{13}}{13} + \frac {6 a^{11} b x^{26}}{13} + \frac {22 a^{10} b^{2} x^{39}}{13} + \frac {55 a^{9} b^{3} x^{52}}{13} + \frac {99 a^{8} b^{4} x^{65}}{13} + \frac {132 a^{7} b^{5} x^{78}}{13} + \frac {132 a^{6} b^{6} x^{91}}{13} + \frac {99 a^{5} b^{7} x^{104}}{13} + \frac {55 a^{4} b^{8} x^{117}}{13} + \frac {22 a^{3} b^{9} x^{130}}{13} + \frac {6 a^{2} b^{10} x^{143}}{13} + \frac {a b^{11} x^{156}}{13} + \frac {b^{12} x^{169}}{169} \]
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Leaf count of result is larger than twice the leaf count of optimal. 134 vs. \(2 (14) = 28\).
Time = 0.21 (sec) , antiderivative size = 134, normalized size of antiderivative = 8.38 \[ \int \left (a x+b x^{14}\right )^{12} \, dx=\frac {1}{169} \, b^{12} x^{169} + \frac {1}{13} \, a b^{11} x^{156} + \frac {6}{13} \, a^{2} b^{10} x^{143} + \frac {22}{13} \, a^{3} b^{9} x^{130} + \frac {55}{13} \, a^{4} b^{8} x^{117} + \frac {99}{13} \, a^{5} b^{7} x^{104} + \frac {132}{13} \, a^{6} b^{6} x^{91} + \frac {132}{13} \, a^{7} b^{5} x^{78} + \frac {99}{13} \, a^{8} b^{4} x^{65} + \frac {55}{13} \, a^{9} b^{3} x^{52} + \frac {22}{13} \, a^{10} b^{2} x^{39} + \frac {6}{13} \, a^{11} b x^{26} + \frac {1}{13} \, a^{12} x^{13} \]
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Leaf count of result is larger than twice the leaf count of optimal. 134 vs. \(2 (14) = 28\).
Time = 0.28 (sec) , antiderivative size = 134, normalized size of antiderivative = 8.38 \[ \int \left (a x+b x^{14}\right )^{12} \, dx=\frac {1}{169} \, b^{12} x^{169} + \frac {1}{13} \, a b^{11} x^{156} + \frac {6}{13} \, a^{2} b^{10} x^{143} + \frac {22}{13} \, a^{3} b^{9} x^{130} + \frac {55}{13} \, a^{4} b^{8} x^{117} + \frac {99}{13} \, a^{5} b^{7} x^{104} + \frac {132}{13} \, a^{6} b^{6} x^{91} + \frac {132}{13} \, a^{7} b^{5} x^{78} + \frac {99}{13} \, a^{8} b^{4} x^{65} + \frac {55}{13} \, a^{9} b^{3} x^{52} + \frac {22}{13} \, a^{10} b^{2} x^{39} + \frac {6}{13} \, a^{11} b x^{26} + \frac {1}{13} \, a^{12} x^{13} \]
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Time = 9.14 (sec) , antiderivative size = 134, normalized size of antiderivative = 8.38 \[ \int \left (a x+b x^{14}\right )^{12} \, dx=\frac {a^{12}\,x^{13}}{13}+\frac {6\,a^{11}\,b\,x^{26}}{13}+\frac {22\,a^{10}\,b^2\,x^{39}}{13}+\frac {55\,a^9\,b^3\,x^{52}}{13}+\frac {99\,a^8\,b^4\,x^{65}}{13}+\frac {132\,a^7\,b^5\,x^{78}}{13}+\frac {132\,a^6\,b^6\,x^{91}}{13}+\frac {99\,a^5\,b^7\,x^{104}}{13}+\frac {55\,a^4\,b^8\,x^{117}}{13}+\frac {22\,a^3\,b^9\,x^{130}}{13}+\frac {6\,a^2\,b^{10}\,x^{143}}{13}+\frac {a\,b^{11}\,x^{156}}{13}+\frac {b^{12}\,x^{169}}{169} \]
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