Integrand size = 13, antiderivative size = 16 \[ \int x^{24} \left (a+b x^{25}\right )^{12} \, dx=\frac {\left (a+b x^{25}\right )^{13}}{325 b} \]
[Out]
Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {267} \[ \int x^{24} \left (a+b x^{25}\right )^{12} \, dx=\frac {\left (a+b x^{25}\right )^{13}}{325 b} \]
[In]
[Out]
Rule 267
Rubi steps \begin{align*} \text {integral}& = \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 = 0.01 (sec) , antiderivative size = 160, normalized size of antiderivative = 10.00 \[ \int x^{24} \left (a+b x^{25}\right )^{12} \, dx=\frac {a^{12} x^{25}}{25}+\frac {6}{25} a^{11} b x^{50}+\frac {22}{25} a^{10} b^2 x^{75}+\frac {11}{5} a^9 b^3 x^{100}+\frac {99}{25} a^8 b^4 x^{125}+\frac {132}{25} a^7 b^5 x^{150}+\frac {132}{25} a^6 b^6 x^{175}+\frac {99}{25} a^5 b^7 x^{200}+\frac {11}{5} a^4 b^8 x^{225}+\frac {22}{25} a^3 b^9 x^{250}+\frac {6}{25} a^2 b^{10} x^{275}+\frac {1}{25} a b^{11} x^{300}+\frac {b^{12} x^{325}}{325} \]
[In]
[Out]
Time = 4.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94
method | result | size |
default | \(\frac {\left (b \,x^{25}+a \right )^{13}}{325 b}\) | \(15\) |
gosper | \(\frac {1}{25} a \,b^{11} x^{300}+\frac {11}{5} a^{9} b^{3} x^{100}+\frac {132}{25} a^{7} b^{5} x^{150}+\frac {99}{25} a^{8} b^{4} x^{125}+\frac {22}{25} a^{10} b^{2} x^{75}+\frac {132}{25} a^{6} b^{6} x^{175}+\frac {99}{25} a^{5} b^{7} x^{200}+\frac {1}{25} a^{12} x^{25}+\frac {6}{25} b \,a^{11} x^{50}+\frac {6}{25} a^{2} b^{10} x^{275}+\frac {11}{5} a^{4} b^{8} x^{225}+\frac {1}{325} b^{12} x^{325}+\frac {22}{25} a^{3} b^{9} x^{250}\) | \(135\) |
parallelrisch | \(\frac {1}{25} a \,b^{11} x^{300}+\frac {11}{5} a^{9} b^{3} x^{100}+\frac {132}{25} a^{7} b^{5} x^{150}+\frac {99}{25} a^{8} b^{4} x^{125}+\frac {22}{25} a^{10} b^{2} x^{75}+\frac {132}{25} a^{6} b^{6} x^{175}+\frac {99}{25} a^{5} b^{7} x^{200}+\frac {1}{25} a^{12} x^{25}+\frac {6}{25} b \,a^{11} x^{50}+\frac {6}{25} a^{2} b^{10} x^{275}+\frac {11}{5} a^{4} b^{8} x^{225}+\frac {1}{325} b^{12} x^{325}+\frac {22}{25} a^{3} b^{9} x^{250}\) | \(135\) |
risch | \(\frac {b^{12} x^{325}}{325}+\frac {a \,b^{11} x^{300}}{25}+\frac {6 a^{2} b^{10} x^{275}}{25}+\frac {22 a^{3} b^{9} x^{250}}{25}+\frac {11 a^{4} b^{8} x^{225}}{5}+\frac {99 a^{5} b^{7} x^{200}}{25}+\frac {132 a^{6} b^{6} x^{175}}{25}+\frac {132 a^{7} b^{5} x^{150}}{25}+\frac {99 a^{8} b^{4} x^{125}}{25}+\frac {11 a^{9} b^{3} x^{100}}{5}+\frac {22 a^{10} b^{2} x^{75}}{25}+\frac {6 b \,a^{11} x^{50}}{25}+\frac {a^{12} x^{25}}{25}+\frac {a^{13}}{325 b}\) | \(143\) |
[In]
[Out]
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 \[ \int x^{24} \left (a+b x^{25}\right )^{12} \, dx=\frac {1}{325} \, b^{12} x^{325} + \frac {1}{25} \, a b^{11} x^{300} + \frac {6}{25} \, a^{2} b^{10} x^{275} + \frac {22}{25} \, a^{3} b^{9} x^{250} + \frac {11}{5} \, a^{4} b^{8} x^{225} + \frac {99}{25} \, a^{5} b^{7} x^{200} + \frac {132}{25} \, a^{6} b^{6} x^{175} + \frac {132}{25} \, a^{7} b^{5} x^{150} + \frac {99}{25} \, a^{8} b^{4} x^{125} + \frac {11}{5} \, a^{9} b^{3} x^{100} + \frac {22}{25} \, a^{10} b^{2} x^{75} + \frac {6}{25} \, a^{11} b x^{50} + \frac {1}{25} \, a^{12} x^{25} \]
[In]
[Out]
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 \[ \int x^{24} \left (a+b x^{25}\right )^{12} \, dx=\frac {a^{12} x^{25}}{25} + \frac {6 a^{11} b x^{50}}{25} + \frac {22 a^{10} b^{2} x^{75}}{25} + \frac {11 a^{9} b^{3} x^{100}}{5} + \frac {99 a^{8} b^{4} x^{125}}{25} + \frac {132 a^{7} b^{5} x^{150}}{25} + \frac {132 a^{6} b^{6} x^{175}}{25} + \frac {99 a^{5} b^{7} x^{200}}{25} + \frac {11 a^{4} b^{8} x^{225}}{5} + \frac {22 a^{3} b^{9} x^{250}}{25} + \frac {6 a^{2} b^{10} x^{275}}{25} + \frac {a b^{11} x^{300}}{25} + \frac {b^{12} x^{325}}{325} \]
[In]
[Out]
none
Time = 0.21 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int x^{24} \left (a+b x^{25}\right )^{12} \, dx=\frac {{\left (b x^{25} + a\right )}^{13}}{325 \, b} \]
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int x^{24} \left (a+b x^{25}\right )^{12} \, dx=\frac {{\left (b x^{25} + a\right )}^{13}}{325 \, b} \]
[In]
[Out]
Time = 0.11 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int x^{24} \left (a+b x^{25}\right )^{12} \, dx=\frac {{\left (b\,x^{25}+a\right )}^{13}}{325\,b} \]
[In]
[Out]