Integrand size = 29, antiderivative size = 21 \[ \int x^{14 (-1+n)} \left (b+2 c x^n\right ) \left (b x+c x^{1+n}\right )^{13} \, dx=\frac {x^{14 n} \left (b+c x^n\right )^{14}}{14 n} \]
[Out]
Time = 0.02 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {1598, 457, 75} \[ \int x^{14 (-1+n)} \left (b+2 c x^n\right ) \left (b x+c x^{1+n}\right )^{13} \, dx=\frac {x^{14 n} \left (b+c x^n\right )^{14}}{14 n} \]
[In]
[Out]
Rule 75
Rule 457
Rule 1598
Rubi steps \begin{align*} \text {integral}& = \int x^{13+14 (-1+n)} \left (b+c x^n\right )^{13} \left (b+2 c x^n\right ) \, dx \\ & = \frac {\text {Subst}\left (\int x^{13} (b+c x)^{13} (b+2 c x) \, dx,x,x^n\right )}{n} \\ & = \frac {x^{14 n} \left (b+c x^n\right )^{14}}{14 n} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int x^{14 (-1+n)} \left (b+2 c x^n\right ) \left (b x+c x^{1+n}\right )^{13} \, dx=\frac {x^{14 n} \left (b+c x^n\right )^{14}}{14 n} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. \(229\) vs. \(2(19)=38\).
Time = 0.02 (sec) , antiderivative size = 230, normalized size of antiderivative = 10.95
\[\frac {c^{14} x^{28 n}}{14 n}+\frac {b \,c^{13} x^{27 n}}{n}+\frac {13 c^{12} x^{26 n} b^{2}}{2 n}+\frac {26 c^{11} b^{3} x^{25 n}}{n}+\frac {143 c^{10} x^{24 n} b^{4}}{2 n}+\frac {143 c^{9} b^{5} x^{23 n}}{n}+\frac {429 c^{8} x^{22 n} b^{6}}{2 n}+\frac {1716 b^{7} c^{7} x^{21 n}}{7 n}+\frac {429 c^{6} x^{20 n} b^{8}}{2 n}+\frac {143 b^{9} c^{5} x^{19 n}}{n}+\frac {143 c^{4} x^{18 n} b^{10}}{2 n}+\frac {26 b^{11} c^{3} x^{17 n}}{n}+\frac {13 c^{2} x^{16 n} b^{12}}{2 n}+\frac {b^{13} c \,x^{15 n}}{n}+\frac {x^{14 n} b^{14}}{14 n}\]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 262 vs. \(2 (19) = 38\).
Time = 0.25 (sec) , antiderivative size = 262, normalized size of antiderivative = 12.48 \[ \int x^{14 (-1+n)} \left (b+2 c x^n\right ) \left (b x+c x^{1+n}\right )^{13} \, dx=\frac {b^{14} x^{14} x^{14 \, n + 14} + 14 \, b^{13} c x^{13} x^{15 \, n + 15} + 91 \, b^{12} c^{2} x^{12} x^{16 \, n + 16} + 364 \, b^{11} c^{3} x^{11} x^{17 \, n + 17} + 1001 \, b^{10} c^{4} x^{10} x^{18 \, n + 18} + 2002 \, b^{9} c^{5} x^{9} x^{19 \, n + 19} + 3003 \, b^{8} c^{6} x^{8} x^{20 \, n + 20} + 3432 \, b^{7} c^{7} x^{7} x^{21 \, n + 21} + 3003 \, b^{6} c^{8} x^{6} x^{22 \, n + 22} + 2002 \, b^{5} c^{9} x^{5} x^{23 \, n + 23} + 1001 \, b^{4} c^{10} x^{4} x^{24 \, n + 24} + 364 \, b^{3} c^{11} x^{3} x^{25 \, n + 25} + 91 \, b^{2} c^{12} x^{2} x^{26 \, n + 26} + 14 \, b c^{13} x x^{27 \, n + 27} + c^{14} x^{28 \, n + 28}}{14 \, n x^{28}} \]
[In]
[Out]
Timed out. \[ \int x^{14 (-1+n)} \left (b+2 c x^n\right ) \left (b x+c x^{1+n}\right )^{13} \, dx=\text {Timed out} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 229 vs. \(2 (19) = 38\).
Time = 0.20 (sec) , antiderivative size = 229, normalized size of antiderivative = 10.90 \[ \int x^{14 (-1+n)} \left (b+2 c x^n\right ) \left (b x+c x^{1+n}\right )^{13} \, dx=\frac {c^{14} x^{28 \, n}}{14 \, n} + \frac {b c^{13} x^{27 \, n}}{n} + \frac {13 \, b^{2} c^{12} x^{26 \, n}}{2 \, n} + \frac {26 \, b^{3} c^{11} x^{25 \, n}}{n} + \frac {143 \, b^{4} c^{10} x^{24 \, n}}{2 \, n} + \frac {143 \, b^{5} c^{9} x^{23 \, n}}{n} + \frac {429 \, b^{6} c^{8} x^{22 \, n}}{2 \, n} + \frac {1716 \, b^{7} c^{7} x^{21 \, n}}{7 \, n} + \frac {429 \, b^{8} c^{6} x^{20 \, n}}{2 \, n} + \frac {143 \, b^{9} c^{5} x^{19 \, n}}{n} + \frac {143 \, b^{10} c^{4} x^{18 \, n}}{2 \, n} + \frac {26 \, b^{11} c^{3} x^{17 \, n}}{n} + \frac {13 \, b^{12} c^{2} x^{16 \, n}}{2 \, n} + \frac {b^{13} c x^{15 \, n}}{n} + \frac {b^{14} x^{14 \, n}}{14 \, n} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 189 vs. \(2 (19) = 38\).
Time = 0.50 (sec) , antiderivative size = 189, normalized size of antiderivative = 9.00 \[ \int x^{14 (-1+n)} \left (b+2 c x^n\right ) \left (b x+c x^{1+n}\right )^{13} \, dx=\frac {c^{14} x^{28 \, n} + 14 \, b c^{13} x^{27 \, n} + 91 \, b^{2} c^{12} x^{26 \, n} + 364 \, b^{3} c^{11} x^{25 \, n} + 1001 \, b^{4} c^{10} x^{24 \, n} + 2002 \, b^{5} c^{9} x^{23 \, n} + 3003 \, b^{6} c^{8} x^{22 \, n} + 3432 \, b^{7} c^{7} x^{21 \, n} + 3003 \, b^{8} c^{6} x^{20 \, n} + 2002 \, b^{9} c^{5} x^{19 \, n} + 1001 \, b^{10} c^{4} x^{18 \, n} + 364 \, b^{11} c^{3} x^{17 \, n} + 91 \, b^{12} c^{2} x^{16 \, n} + 14 \, b^{13} c x^{15 \, n} + b^{14} x^{14 \, n}}{14 \, n} \]
[In]
[Out]
Time = 10.21 (sec) , antiderivative size = 229, normalized size of antiderivative = 10.90 \[ \int x^{14 (-1+n)} \left (b+2 c x^n\right ) \left (b x+c x^{1+n}\right )^{13} \, dx=\frac {b^{14}\,x^{14\,n}}{14\,n}+\frac {c^{14}\,x^{28\,n}}{14\,n}+\frac {13\,b^{12}\,c^2\,x^{16\,n}}{2\,n}+\frac {26\,b^{11}\,c^3\,x^{17\,n}}{n}+\frac {143\,b^{10}\,c^4\,x^{18\,n}}{2\,n}+\frac {143\,b^9\,c^5\,x^{19\,n}}{n}+\frac {429\,b^8\,c^6\,x^{20\,n}}{2\,n}+\frac {1716\,b^7\,c^7\,x^{21\,n}}{7\,n}+\frac {429\,b^6\,c^8\,x^{22\,n}}{2\,n}+\frac {143\,b^5\,c^9\,x^{23\,n}}{n}+\frac {143\,b^4\,c^{10}\,x^{24\,n}}{2\,n}+\frac {26\,b^3\,c^{11}\,x^{25\,n}}{n}+\frac {13\,b^2\,c^{12}\,x^{26\,n}}{2\,n}+\frac {b^{13}\,c\,x^{15\,n}}{n}+\frac {b\,c^{13}\,x^{27\,n}}{n} \]
[In]
[Out]