Integrand size = 15, antiderivative size = 16 \[ \int x^{12} \left (a x+b x^{26}\right )^{12} \, dx=\frac {\left (a+b x^{25}\right )^{13}}{325 b} \]
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Time = 0.01 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {1598, 267} \[ \int x^{12} \left (a x+b x^{26}\right )^{12} \, dx=\frac {\left (a+b x^{25}\right )^{13}}{325 b} \]
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Rule 267
Rule 1598
Rubi steps \begin{align*} \text {integral}& = \int x^{24} \left (a+b x^{25}\right )^{12} \, dx \\ & = \frac {\left (a+b x^{25}\right )^{13}}{325 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 \[ \int x^{12} \left (a x+b x^{26}\right )^{12} \, dx=\frac {a^{12} x^{25}}{25}+\frac {6}{25} a^{11} b x^{50}+\frac {22}{25} a^{10} b^2 x^{75}+\frac {11}{5} a^9 b^3 x^{100}+\frac {99}{25} a^8 b^4 x^{125}+\frac {132}{25} a^7 b^5 x^{150}+\frac {132}{25} a^6 b^6 x^{175}+\frac {99}{25} a^5 b^7 x^{200}+\frac {11}{5} a^4 b^8 x^{225}+\frac {22}{25} a^3 b^9 x^{250}+\frac {6}{25} a^2 b^{10} x^{275}+\frac {1}{25} a b^{11} x^{300}+\frac {b^{12} x^{325}}{325} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(134\) vs. \(2(14)=28\).
Time = 2.08 (sec) , antiderivative size = 135, normalized size of antiderivative = 8.44
method | result | size |
default | \(\frac {99}{25} a^{8} b^{4} x^{125}+\frac {6}{25} a^{2} b^{10} x^{275}+\frac {22}{25} a^{3} b^{9} x^{250}+\frac {11}{5} a^{4} b^{8} x^{225}+\frac {1}{325} b^{12} x^{325}+\frac {99}{25} a^{5} b^{7} x^{200}+\frac {132}{25} a^{7} b^{5} x^{150}+\frac {132}{25} a^{6} b^{6} x^{175}+\frac {11}{5} a^{9} b^{3} x^{100}+\frac {22}{25} a^{10} b^{2} x^{75}+\frac {6}{25} b \,a^{11} x^{50}+\frac {1}{25} a \,b^{11} x^{300}+\frac {1}{25} a^{12} x^{25}\) | \(135\) |
parallelrisch | \(\frac {99}{25} a^{8} b^{4} x^{125}+\frac {6}{25} a^{2} b^{10} x^{275}+\frac {22}{25} a^{3} b^{9} x^{250}+\frac {11}{5} a^{4} b^{8} x^{225}+\frac {1}{325} b^{12} x^{325}+\frac {99}{25} a^{5} b^{7} x^{200}+\frac {132}{25} a^{7} b^{5} x^{150}+\frac {132}{25} a^{6} b^{6} x^{175}+\frac {11}{5} a^{9} b^{3} x^{100}+\frac {22}{25} a^{10} b^{2} x^{75}+\frac {6}{25} b \,a^{11} x^{50}+\frac {1}{25} a \,b^{11} x^{300}+\frac {1}{25} a^{12} x^{25}\) | \(135\) |
gosper | \(\frac {x^{25} \left (b^{12} x^{300}+13 a \,b^{11} x^{275}+78 a^{2} b^{10} x^{250}+286 a^{3} b^{9} x^{225}+715 a^{4} b^{8} x^{200}+1287 a^{5} b^{7} x^{175}+1716 a^{6} b^{6} x^{150}+1716 a^{7} b^{5} x^{125}+1287 a^{8} b^{4} x^{100}+715 a^{9} b^{3} x^{75}+286 a^{10} b^{2} x^{50}+78 b \,a^{11} x^{25}+13 a^{12}\right )}{325}\) | \(136\) |
risch | \(\frac {b^{12} x^{325}}{325}+\frac {a \,b^{11} x^{300}}{25}+\frac {6 a^{2} b^{10} x^{275}}{25}+\frac {22 a^{3} b^{9} x^{250}}{25}+\frac {11 a^{4} b^{8} x^{225}}{5}+\frac {99 a^{5} b^{7} x^{200}}{25}+\frac {132 a^{6} b^{6} x^{175}}{25}+\frac {132 a^{7} b^{5} x^{150}}{25}+\frac {99 a^{8} b^{4} x^{125}}{25}+\frac {11 a^{9} b^{3} x^{100}}{5}+\frac {22 a^{10} b^{2} x^{75}}{25}+\frac {6 b \,a^{11} x^{50}}{25}+\frac {a^{12} x^{25}}{25}+\frac {a^{13}}{325 b}\) | \(143\) |
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Leaf count of result is larger than twice the leaf count of optimal. 134 vs. \(2 (14) = 28\).
Time = 0.24 (sec) , antiderivative size = 134, normalized size of antiderivative = 8.38 \[ \int x^{12} \left (a x+b x^{26}\right )^{12} \, dx=\frac {1}{325} \, b^{12} x^{325} + \frac {1}{25} \, a b^{11} x^{300} + \frac {6}{25} \, a^{2} b^{10} x^{275} + \frac {22}{25} \, a^{3} b^{9} x^{250} + \frac {11}{5} \, a^{4} b^{8} x^{225} + \frac {99}{25} \, a^{5} b^{7} x^{200} + \frac {132}{25} \, a^{6} b^{6} x^{175} + \frac {132}{25} \, a^{7} b^{5} x^{150} + \frac {99}{25} \, a^{8} b^{4} x^{125} + \frac {11}{5} \, a^{9} b^{3} x^{100} + \frac {22}{25} \, a^{10} b^{2} x^{75} + \frac {6}{25} \, a^{11} b x^{50} + \frac {1}{25} \, a^{12} x^{25} \]
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Leaf count of result is larger than twice the leaf count of optimal. 160 vs. \(2 (10) = 20\).
Time = 0.05 (sec) , antiderivative size = 160, normalized size of antiderivative = 10.00 \[ \int x^{12} \left (a x+b x^{26}\right )^{12} \, dx=\frac {a^{12} x^{25}}{25} + \frac {6 a^{11} b x^{50}}{25} + \frac {22 a^{10} b^{2} x^{75}}{25} + \frac {11 a^{9} b^{3} x^{100}}{5} + \frac {99 a^{8} b^{4} x^{125}}{25} + \frac {132 a^{7} b^{5} x^{150}}{25} + \frac {132 a^{6} b^{6} x^{175}}{25} + \frac {99 a^{5} b^{7} x^{200}}{25} + \frac {11 a^{4} b^{8} x^{225}}{5} + \frac {22 a^{3} b^{9} x^{250}}{25} + \frac {6 a^{2} b^{10} x^{275}}{25} + \frac {a b^{11} x^{300}}{25} + \frac {b^{12} x^{325}}{325} \]
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Leaf count of result is larger than twice the leaf count of optimal. 134 vs. \(2 (14) = 28\).
Time = 0.19 (sec) , antiderivative size = 134, normalized size of antiderivative = 8.38 \[ \int x^{12} \left (a x+b x^{26}\right )^{12} \, dx=\frac {1}{325} \, b^{12} x^{325} + \frac {1}{25} \, a b^{11} x^{300} + \frac {6}{25} \, a^{2} b^{10} x^{275} + \frac {22}{25} \, a^{3} b^{9} x^{250} + \frac {11}{5} \, a^{4} b^{8} x^{225} + \frac {99}{25} \, a^{5} b^{7} x^{200} + \frac {132}{25} \, a^{6} b^{6} x^{175} + \frac {132}{25} \, a^{7} b^{5} x^{150} + \frac {99}{25} \, a^{8} b^{4} x^{125} + \frac {11}{5} \, a^{9} b^{3} x^{100} + \frac {22}{25} \, a^{10} b^{2} x^{75} + \frac {6}{25} \, a^{11} b x^{50} + \frac {1}{25} \, a^{12} x^{25} \]
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Leaf count of result is larger than twice the leaf count of optimal. 134 vs. \(2 (14) = 28\).
Time = 0.27 (sec) , antiderivative size = 134, normalized size of antiderivative = 8.38 \[ \int x^{12} \left (a x+b x^{26}\right )^{12} \, dx=\frac {1}{325} \, b^{12} x^{325} + \frac {1}{25} \, a b^{11} x^{300} + \frac {6}{25} \, a^{2} b^{10} x^{275} + \frac {22}{25} \, a^{3} b^{9} x^{250} + \frac {11}{5} \, a^{4} b^{8} x^{225} + \frac {99}{25} \, a^{5} b^{7} x^{200} + \frac {132}{25} \, a^{6} b^{6} x^{175} + \frac {132}{25} \, a^{7} b^{5} x^{150} + \frac {99}{25} \, a^{8} b^{4} x^{125} + \frac {11}{5} \, a^{9} b^{3} x^{100} + \frac {22}{25} \, a^{10} b^{2} x^{75} + \frac {6}{25} \, a^{11} b x^{50} + \frac {1}{25} \, a^{12} x^{25} \]
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Time = 0.00 (sec) , antiderivative size = 134, normalized size of antiderivative = 8.38 \[ \int x^{12} \left (a x+b x^{26}\right )^{12} \, dx=\frac {a^{12}\,x^{25}}{25}+\frac {6\,a^{11}\,b\,x^{50}}{25}+\frac {22\,a^{10}\,b^2\,x^{75}}{25}+\frac {11\,a^9\,b^3\,x^{100}}{5}+\frac {99\,a^8\,b^4\,x^{125}}{25}+\frac {132\,a^7\,b^5\,x^{150}}{25}+\frac {132\,a^6\,b^6\,x^{175}}{25}+\frac {99\,a^5\,b^7\,x^{200}}{25}+\frac {11\,a^4\,b^8\,x^{225}}{5}+\frac {22\,a^3\,b^9\,x^{250}}{25}+\frac {6\,a^2\,b^{10}\,x^{275}}{25}+\frac {a\,b^{11}\,x^{300}}{25}+\frac {b^{12}\,x^{325}}{325} \]
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