Integrand size = 509, antiderivative size = 17 \[ \int \frac {-16 x^7+8 x^8-4 x^{11}+\left (112 x^6-56 x^7+40 x^{10}\right ) \log \left (x^2 \log (3)\right )+\left (-336 x^5+168 x^6-180 x^9\right ) \log ^2\left (x^2 \log (3)\right )+\left (560 x^4-280 x^5+480 x^8\right ) \log ^3\left (x^2 \log (3)\right )+\left (-560 x^3+280 x^4-840 x^7\right ) \log ^4\left (x^2 \log (3)\right )+\left (336 x^2-168 x^3+1008 x^6\right ) \log ^5\left (x^2 \log (3)\right )+\left (-112 x+56 x^2-840 x^5\right ) \log ^6\left (x^2 \log (3)\right )+\left (16-8 x+480 x^4\right ) \log ^7\left (x^2 \log (3)\right )-180 x^3 \log ^8\left (x^2 \log (3)\right )+40 x^2 \log ^9\left (x^2 \log (3)\right )-4 x \log ^{10}\left (x^2 \log (3)\right )}{x+5 x^4+10 x^7+10 x^{10}+5 x^{13}+x^{16}+\left (-10 x^3-40 x^6-60 x^9-40 x^{12}-10 x^{15}\right ) \log \left (x^2 \log (3)\right )+\left (5 x^2+60 x^5+150 x^8+140 x^{11}+45 x^{14}\right ) \log ^2\left (x^2 \log (3)\right )+\left (-40 x^4-200 x^7-280 x^{10}-120 x^{13}\right ) \log ^3\left (x^2 \log (3)\right )+\left (10 x^3+150 x^6+350 x^9+210 x^{12}\right ) \log ^4\left (x^2 \log (3)\right )+\left (-60 x^5-280 x^8-252 x^{11}\right ) \log ^5\left (x^2 \log (3)\right )+\left (10 x^4+140 x^7+210 x^{10}\right ) \log ^6\left (x^2 \log (3)\right )+\left (-40 x^6-120 x^9\right ) \log ^7\left (x^2 \log (3)\right )+\left (5 x^5+45 x^8\right ) \log ^8\left (x^2 \log (3)\right )-10 x^7 \log ^9\left (x^2 \log (3)\right )+x^6 \log ^{10}\left (x^2 \log (3)\right )} \, dx=\frac {1}{\left (x+\frac {1}{\left (-x+\log \left (x^2 \log (3)\right )\right )^2}\right )^4} \]
[Out]
\[ \int \frac {-16 x^7+8 x^8-4 x^{11}+\left (112 x^6-56 x^7+40 x^{10}\right ) \log \left (x^2 \log (3)\right )+\left (-336 x^5+168 x^6-180 x^9\right ) \log ^2\left (x^2 \log (3)\right )+\left (560 x^4-280 x^5+480 x^8\right ) \log ^3\left (x^2 \log (3)\right )+\left (-560 x^3+280 x^4-840 x^7\right ) \log ^4\left (x^2 \log (3)\right )+\left (336 x^2-168 x^3+1008 x^6\right ) \log ^5\left (x^2 \log (3)\right )+\left (-112 x+56 x^2-840 x^5\right ) \log ^6\left (x^2 \log (3)\right )+\left (16-8 x+480 x^4\right ) \log ^7\left (x^2 \log (3)\right )-180 x^3 \log ^8\left (x^2 \log (3)\right )+40 x^2 \log ^9\left (x^2 \log (3)\right )-4 x \log ^{10}\left (x^2 \log (3)\right )}{x+5 x^4+10 x^7+10 x^{10}+5 x^{13}+x^{16}+\left (-10 x^3-40 x^6-60 x^9-40 x^{12}-10 x^{15}\right ) \log \left (x^2 \log (3)\right )+\left (5 x^2+60 x^5+150 x^8+140 x^{11}+45 x^{14}\right ) \log ^2\left (x^2 \log (3)\right )+\left (-40 x^4-200 x^7-280 x^{10}-120 x^{13}\right ) \log ^3\left (x^2 \log (3)\right )+\left (10 x^3+150 x^6+350 x^9+210 x^{12}\right ) \log ^4\left (x^2 \log (3)\right )+\left (-60 x^5-280 x^8-252 x^{11}\right ) \log ^5\left (x^2 \log (3)\right )+\left (10 x^4+140 x^7+210 x^{10}\right ) \log ^6\left (x^2 \log (3)\right )+\left (-40 x^6-120 x^9\right ) \log ^7\left (x^2 \log (3)\right )+\left (5 x^5+45 x^8\right ) \log ^8\left (x^2 \log (3)\right )-10 x^7 \log ^9\left (x^2 \log (3)\right )+x^6 \log ^{10}\left (x^2 \log (3)\right )} \, dx=\int \frac {-16 x^7+8 x^8-4 x^{11}+\left (112 x^6-56 x^7+40 x^{10}\right ) \log \left (x^2 \log (3)\right )+\left (-336 x^5+168 x^6-180 x^9\right ) \log ^2\left (x^2 \log (3)\right )+\left (560 x^4-280 x^5+480 x^8\right ) \log ^3\left (x^2 \log (3)\right )+\left (-560 x^3+280 x^4-840 x^7\right ) \log ^4\left (x^2 \log (3)\right )+\left (336 x^2-168 x^3+1008 x^6\right ) \log ^5\left (x^2 \log (3)\right )+\left (-112 x+56 x^2-840 x^5\right ) \log ^6\left (x^2 \log (3)\right )+\left (16-8 x+480 x^4\right ) \log ^7\left (x^2 \log (3)\right )-180 x^3 \log ^8\left (x^2 \log (3)\right )+40 x^2 \log ^9\left (x^2 \log (3)\right )-4 x \log ^{10}\left (x^2 \log (3)\right )}{x+5 x^4+10 x^7+10 x^{10}+5 x^{13}+x^{16}+\left (-10 x^3-40 x^6-60 x^9-40 x^{12}-10 x^{15}\right ) \log \left (x^2 \log (3)\right )+\left (5 x^2+60 x^5+150 x^8+140 x^{11}+45 x^{14}\right ) \log ^2\left (x^2 \log (3)\right )+\left (-40 x^4-200 x^7-280 x^{10}-120 x^{13}\right ) \log ^3\left (x^2 \log (3)\right )+\left (10 x^3+150 x^6+350 x^9+210 x^{12}\right ) \log ^4\left (x^2 \log (3)\right )+\left (-60 x^5-280 x^8-252 x^{11}\right ) \log ^5\left (x^2 \log (3)\right )+\left (10 x^4+140 x^7+210 x^{10}\right ) \log ^6\left (x^2 \log (3)\right )+\left (-40 x^6-120 x^9\right ) \log ^7\left (x^2 \log (3)\right )+\left (5 x^5+45 x^8\right ) \log ^8\left (x^2 \log (3)\right )-10 x^7 \log ^9\left (x^2 \log (3)\right )+x^6 \log ^{10}\left (x^2 \log (3)\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {4 \left (x-\log \left (x^2 \log (3)\right )\right )^7 \left (-4+2 x-x^4+3 x^3 \log \left (x^2 \log (3)\right )-3 x^2 \log ^2\left (x^2 \log (3)\right )+x \log ^3\left (x^2 \log (3)\right )\right )}{x \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5} \, dx \\ & = 4 \int \frac {\left (x-\log \left (x^2 \log (3)\right )\right )^7 \left (-4+2 x-x^4+3 x^3 \log \left (x^2 \log (3)\right )-3 x^2 \log ^2\left (x^2 \log (3)\right )+x \log ^3\left (x^2 \log (3)\right )\right )}{x \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5} \, dx \\ & = 4 \int \left (-\frac {1}{x^5}+\frac {1+4 x^2-2 x^3-4 x \log \left (x^2 \log (3)\right )+2 x^2 \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5}+\frac {-5-12 x^2+6 x^3+12 x \log \left (x^2 \log (3)\right )-6 x^2 \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4}-\frac {2 \left (-5-6 x^2+3 x^3+6 x \log \left (x^2 \log (3)\right )-3 x^2 \log \left (x^2 \log (3)\right )\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^3}+\frac {2 \left (-5-2 x^2+x^3+2 x \log \left (x^2 \log (3)\right )-x^2 \log \left (x^2 \log (3)\right )\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^2}+\frac {5}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )}\right ) \, dx \\ & = \frac {1}{x^4}+4 \int \frac {1+4 x^2-2 x^3-4 x \log \left (x^2 \log (3)\right )+2 x^2 \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5} \, dx+4 \int \frac {-5-12 x^2+6 x^3+12 x \log \left (x^2 \log (3)\right )-6 x^2 \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4} \, dx-8 \int \frac {-5-6 x^2+3 x^3+6 x \log \left (x^2 \log (3)\right )-3 x^2 \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^3} \, dx+8 \int \frac {-5-2 x^2+x^3+2 x \log \left (x^2 \log (3)\right )-x^2 \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^2} \, dx+20 \int \frac {1}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )} \, dx \\ & = \frac {1}{x^4}+4 \int \frac {1+4 x^2-2 x^3+2 (-2+x) x \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5} \, dx+4 \int \frac {-5-12 x^2+6 x^3-6 (-2+x) x \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4} \, dx-8 \int \frac {-5-6 x^2+3 x^3-3 (-2+x) x \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^3} \, dx+8 \int \frac {-5-2 x^2+x^3-(-2+x) x \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^2} \, dx+20 \int \frac {1}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )} \, dx \\ & = \frac {1}{x^4}+4 \int \left (\frac {1}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5}+\frac {4}{x^3 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5}-\frac {2}{x^2 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5}-\frac {4 \log \left (x^2 \log (3)\right )}{x^4 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5}+\frac {2 \log \left (x^2 \log (3)\right )}{x^3 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5}\right ) \, dx+4 \int \left (-\frac {5}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4}-\frac {12}{x^3 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4}+\frac {6}{x^2 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4}+\frac {12 \log \left (x^2 \log (3)\right )}{x^4 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4}-\frac {6 \log \left (x^2 \log (3)\right )}{x^3 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4}\right ) \, dx-8 \int \left (-\frac {5}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^3}-\frac {6}{x^3 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^3}+\frac {3}{x^2 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^3}+\frac {6 \log \left (x^2 \log (3)\right )}{x^4 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^3}-\frac {3 \log \left (x^2 \log (3)\right )}{x^3 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^3}\right ) \, dx+8 \int \left (-\frac {5}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^2}-\frac {2}{x^3 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^2}+\frac {1}{x^2 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^2}+\frac {2 \log \left (x^2 \log (3)\right )}{x^4 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^2}-\frac {\log \left (x^2 \log (3)\right )}{x^3 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^2}\right ) \, dx+20 \int \frac {1}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )} \, dx \\ & = \frac {1}{x^4}+4 \int \frac {1}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5} \, dx-8 \int \frac {1}{x^2 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5} \, dx+8 \int \frac {\log \left (x^2 \log (3)\right )}{x^3 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5} \, dx+8 \int \frac {1}{x^2 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^2} \, dx-8 \int \frac {\log \left (x^2 \log (3)\right )}{x^3 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^2} \, dx+16 \int \frac {1}{x^3 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5} \, dx-16 \int \frac {\log \left (x^2 \log (3)\right )}{x^4 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5} \, dx-16 \int \frac {1}{x^3 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^2} \, dx+16 \int \frac {\log \left (x^2 \log (3)\right )}{x^4 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^2} \, dx-20 \int \frac {1}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4} \, dx+20 \int \frac {1}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )} \, dx+24 \int \frac {1}{x^2 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4} \, dx-24 \int \frac {\log \left (x^2 \log (3)\right )}{x^3 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4} \, dx-24 \int \frac {1}{x^2 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^3} \, dx+24 \int \frac {\log \left (x^2 \log (3)\right )}{x^3 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^3} \, dx+40 \int \frac {1}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^3} \, dx-40 \int \frac {1}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^2} \, dx-48 \int \frac {1}{x^3 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4} \, dx+48 \int \frac {\log \left (x^2 \log (3)\right )}{x^4 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4} \, dx+48 \int \frac {1}{x^3 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^3} \, dx-48 \int \frac {\log \left (x^2 \log (3)\right )}{x^4 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^3} \, dx \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(44\) vs. \(2(17)=34\).
Time = 0.11 (sec) , antiderivative size = 44, normalized size of antiderivative = 2.59 \[ \int \frac {-16 x^7+8 x^8-4 x^{11}+\left (112 x^6-56 x^7+40 x^{10}\right ) \log \left (x^2 \log (3)\right )+\left (-336 x^5+168 x^6-180 x^9\right ) \log ^2\left (x^2 \log (3)\right )+\left (560 x^4-280 x^5+480 x^8\right ) \log ^3\left (x^2 \log (3)\right )+\left (-560 x^3+280 x^4-840 x^7\right ) \log ^4\left (x^2 \log (3)\right )+\left (336 x^2-168 x^3+1008 x^6\right ) \log ^5\left (x^2 \log (3)\right )+\left (-112 x+56 x^2-840 x^5\right ) \log ^6\left (x^2 \log (3)\right )+\left (16-8 x+480 x^4\right ) \log ^7\left (x^2 \log (3)\right )-180 x^3 \log ^8\left (x^2 \log (3)\right )+40 x^2 \log ^9\left (x^2 \log (3)\right )-4 x \log ^{10}\left (x^2 \log (3)\right )}{x+5 x^4+10 x^7+10 x^{10}+5 x^{13}+x^{16}+\left (-10 x^3-40 x^6-60 x^9-40 x^{12}-10 x^{15}\right ) \log \left (x^2 \log (3)\right )+\left (5 x^2+60 x^5+150 x^8+140 x^{11}+45 x^{14}\right ) \log ^2\left (x^2 \log (3)\right )+\left (-40 x^4-200 x^7-280 x^{10}-120 x^{13}\right ) \log ^3\left (x^2 \log (3)\right )+\left (10 x^3+150 x^6+350 x^9+210 x^{12}\right ) \log ^4\left (x^2 \log (3)\right )+\left (-60 x^5-280 x^8-252 x^{11}\right ) \log ^5\left (x^2 \log (3)\right )+\left (10 x^4+140 x^7+210 x^{10}\right ) \log ^6\left (x^2 \log (3)\right )+\left (-40 x^6-120 x^9\right ) \log ^7\left (x^2 \log (3)\right )+\left (5 x^5+45 x^8\right ) \log ^8\left (x^2 \log (3)\right )-10 x^7 \log ^9\left (x^2 \log (3)\right )+x^6 \log ^{10}\left (x^2 \log (3)\right )} \, dx=\frac {\left (x-\log \left (x^2 \log (3)\right )\right )^8}{\left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. \(216\) vs. \(2(17)=34\).
Time = 2.13 (sec) , antiderivative size = 217, normalized size of antiderivative = 12.76
method | result | size |
risch | \(\frac {1}{x^{4}}-\frac {4 x^{9}-24 \ln \left (x^{2} \ln \left (3\right )\right ) x^{8}+60 \ln \left (x^{2} \ln \left (3\right )\right )^{2} x^{7}-80 \ln \left (x^{2} \ln \left (3\right )\right )^{3} x^{6}+60 \ln \left (x^{2} \ln \left (3\right )\right )^{4} x^{5}-24 x^{4} \ln \left (x^{2} \ln \left (3\right )\right )^{5}+4 x^{3} \ln \left (x^{2} \ln \left (3\right )\right )^{6}+6 x^{6}-24 x^{5} \ln \left (x^{2} \ln \left (3\right )\right )+36 x^{4} \ln \left (x^{2} \ln \left (3\right )\right )^{2}-24 x^{3} \ln \left (x^{2} \ln \left (3\right )\right )^{3}+6 x^{2} \ln \left (x^{2} \ln \left (3\right )\right )^{4}+4 x^{3}-8 x^{2} \ln \left (x^{2} \ln \left (3\right )\right )+4 x \ln \left (x^{2} \ln \left (3\right )\right )^{2}+1}{x^{4} {\left (x \ln \left (x^{2} \ln \left (3\right )\right )^{2}-2 x^{2} \ln \left (x^{2} \ln \left (3\right )\right )+x^{3}+1\right )}^{4}}\) | \(217\) |
parallelrisch | \(\frac {-32 \ln \left (x^{2} \ln \left (3\right )\right )^{7} x +112 \ln \left (x^{2} \ln \left (3\right )\right )^{6} x^{2}-224 x^{3} \ln \left (x^{2} \ln \left (3\right )\right )^{5}+280 x^{4} \ln \left (x^{2} \ln \left (3\right )\right )^{4}-224 \ln \left (x^{2} \ln \left (3\right )\right )^{3} x^{5}+112 \ln \left (x^{2} \ln \left (3\right )\right )^{2} x^{6}-32 \ln \left (x^{2} \ln \left (3\right )\right ) x^{7}+4 x^{8}+4 \ln \left (x^{2} \ln \left (3\right )\right )^{8}}{4+4 x^{4} \ln \left (x^{2} \ln \left (3\right )\right )^{8}-32 x^{5} \ln \left (x^{2} \ln \left (3\right )\right )^{7}+112 \ln \left (x^{2} \ln \left (3\right )\right )^{6} x^{6}-224 \ln \left (x^{2} \ln \left (3\right )\right )^{5} x^{7}+280 \ln \left (x^{2} \ln \left (3\right )\right )^{4} x^{8}-224 \ln \left (x^{2} \ln \left (3\right )\right )^{3} x^{9}+112 \ln \left (x^{2} \ln \left (3\right )\right )^{2} x^{10}-32 \ln \left (x^{2} \ln \left (3\right )\right ) x^{11}+16 x^{3} \ln \left (x^{2} \ln \left (3\right )\right )^{6}-96 x^{4} \ln \left (x^{2} \ln \left (3\right )\right )^{5}+240 \ln \left (x^{2} \ln \left (3\right )\right )^{4} x^{5}-320 \ln \left (x^{2} \ln \left (3\right )\right )^{3} x^{6}+240 \ln \left (x^{2} \ln \left (3\right )\right )^{2} x^{7}-96 \ln \left (x^{2} \ln \left (3\right )\right ) x^{8}+24 x^{2} \ln \left (x^{2} \ln \left (3\right )\right )^{4}-96 x^{3} \ln \left (x^{2} \ln \left (3\right )\right )^{3}+144 x^{4} \ln \left (x^{2} \ln \left (3\right )\right )^{2}-96 x^{5} \ln \left (x^{2} \ln \left (3\right )\right )+16 x \ln \left (x^{2} \ln \left (3\right )\right )^{2}-32 x^{2} \ln \left (x^{2} \ln \left (3\right )\right )+4 x^{12}+16 x^{9}+16 x^{3}+24 x^{6}}\) | \(405\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 307 vs. \(2 (17) = 34\).
Time = 0.27 (sec) , antiderivative size = 307, normalized size of antiderivative = 18.06 \[ \int \frac {-16 x^7+8 x^8-4 x^{11}+\left (112 x^6-56 x^7+40 x^{10}\right ) \log \left (x^2 \log (3)\right )+\left (-336 x^5+168 x^6-180 x^9\right ) \log ^2\left (x^2 \log (3)\right )+\left (560 x^4-280 x^5+480 x^8\right ) \log ^3\left (x^2 \log (3)\right )+\left (-560 x^3+280 x^4-840 x^7\right ) \log ^4\left (x^2 \log (3)\right )+\left (336 x^2-168 x^3+1008 x^6\right ) \log ^5\left (x^2 \log (3)\right )+\left (-112 x+56 x^2-840 x^5\right ) \log ^6\left (x^2 \log (3)\right )+\left (16-8 x+480 x^4\right ) \log ^7\left (x^2 \log (3)\right )-180 x^3 \log ^8\left (x^2 \log (3)\right )+40 x^2 \log ^9\left (x^2 \log (3)\right )-4 x \log ^{10}\left (x^2 \log (3)\right )}{x+5 x^4+10 x^7+10 x^{10}+5 x^{13}+x^{16}+\left (-10 x^3-40 x^6-60 x^9-40 x^{12}-10 x^{15}\right ) \log \left (x^2 \log (3)\right )+\left (5 x^2+60 x^5+150 x^8+140 x^{11}+45 x^{14}\right ) \log ^2\left (x^2 \log (3)\right )+\left (-40 x^4-200 x^7-280 x^{10}-120 x^{13}\right ) \log ^3\left (x^2 \log (3)\right )+\left (10 x^3+150 x^6+350 x^9+210 x^{12}\right ) \log ^4\left (x^2 \log (3)\right )+\left (-60 x^5-280 x^8-252 x^{11}\right ) \log ^5\left (x^2 \log (3)\right )+\left (10 x^4+140 x^7+210 x^{10}\right ) \log ^6\left (x^2 \log (3)\right )+\left (-40 x^6-120 x^9\right ) \log ^7\left (x^2 \log (3)\right )+\left (5 x^5+45 x^8\right ) \log ^8\left (x^2 \log (3)\right )-10 x^7 \log ^9\left (x^2 \log (3)\right )+x^6 \log ^{10}\left (x^2 \log (3)\right )} \, dx=\frac {x^{8} - 8 \, x^{7} \log \left (x^{2} \log \left (3\right )\right ) + 28 \, x^{6} \log \left (x^{2} \log \left (3\right )\right )^{2} - 56 \, x^{5} \log \left (x^{2} \log \left (3\right )\right )^{3} + 70 \, x^{4} \log \left (x^{2} \log \left (3\right )\right )^{4} - 56 \, x^{3} \log \left (x^{2} \log \left (3\right )\right )^{5} + 28 \, x^{2} \log \left (x^{2} \log \left (3\right )\right )^{6} - 8 \, x \log \left (x^{2} \log \left (3\right )\right )^{7} + \log \left (x^{2} \log \left (3\right )\right )^{8}}{x^{12} - 8 \, x^{5} \log \left (x^{2} \log \left (3\right )\right )^{7} + x^{4} \log \left (x^{2} \log \left (3\right )\right )^{8} + 4 \, x^{9} + 4 \, {\left (7 \, x^{6} + x^{3}\right )} \log \left (x^{2} \log \left (3\right )\right )^{6} + 6 \, x^{6} - 8 \, {\left (7 \, x^{7} + 3 \, x^{4}\right )} \log \left (x^{2} \log \left (3\right )\right )^{5} + 2 \, {\left (35 \, x^{8} + 30 \, x^{5} + 3 \, x^{2}\right )} \log \left (x^{2} \log \left (3\right )\right )^{4} - 8 \, {\left (7 \, x^{9} + 10 \, x^{6} + 3 \, x^{3}\right )} \log \left (x^{2} \log \left (3\right )\right )^{3} + 4 \, x^{3} + 4 \, {\left (7 \, x^{10} + 15 \, x^{7} + 9 \, x^{4} + x\right )} \log \left (x^{2} \log \left (3\right )\right )^{2} - 8 \, {\left (x^{11} + 3 \, x^{8} + 3 \, x^{5} + x^{2}\right )} \log \left (x^{2} \log \left (3\right )\right ) + 1} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 350 vs. \(2 (17) = 34\).
Time = 1.58 (sec) , antiderivative size = 350, normalized size of antiderivative = 20.59 \[ \int \frac {-16 x^7+8 x^8-4 x^{11}+\left (112 x^6-56 x^7+40 x^{10}\right ) \log \left (x^2 \log (3)\right )+\left (-336 x^5+168 x^6-180 x^9\right ) \log ^2\left (x^2 \log (3)\right )+\left (560 x^4-280 x^5+480 x^8\right ) \log ^3\left (x^2 \log (3)\right )+\left (-560 x^3+280 x^4-840 x^7\right ) \log ^4\left (x^2 \log (3)\right )+\left (336 x^2-168 x^3+1008 x^6\right ) \log ^5\left (x^2 \log (3)\right )+\left (-112 x+56 x^2-840 x^5\right ) \log ^6\left (x^2 \log (3)\right )+\left (16-8 x+480 x^4\right ) \log ^7\left (x^2 \log (3)\right )-180 x^3 \log ^8\left (x^2 \log (3)\right )+40 x^2 \log ^9\left (x^2 \log (3)\right )-4 x \log ^{10}\left (x^2 \log (3)\right )}{x+5 x^4+10 x^7+10 x^{10}+5 x^{13}+x^{16}+\left (-10 x^3-40 x^6-60 x^9-40 x^{12}-10 x^{15}\right ) \log \left (x^2 \log (3)\right )+\left (5 x^2+60 x^5+150 x^8+140 x^{11}+45 x^{14}\right ) \log ^2\left (x^2 \log (3)\right )+\left (-40 x^4-200 x^7-280 x^{10}-120 x^{13}\right ) \log ^3\left (x^2 \log (3)\right )+\left (10 x^3+150 x^6+350 x^9+210 x^{12}\right ) \log ^4\left (x^2 \log (3)\right )+\left (-60 x^5-280 x^8-252 x^{11}\right ) \log ^5\left (x^2 \log (3)\right )+\left (10 x^4+140 x^7+210 x^{10}\right ) \log ^6\left (x^2 \log (3)\right )+\left (-40 x^6-120 x^9\right ) \log ^7\left (x^2 \log (3)\right )+\left (5 x^5+45 x^8\right ) \log ^8\left (x^2 \log (3)\right )-10 x^7 \log ^9\left (x^2 \log (3)\right )+x^6 \log ^{10}\left (x^2 \log (3)\right )} \, dx=\frac {- 4 x^{9} - 6 x^{6} + 24 x^{4} \log {\left (x^{2} \log {\left (3 \right )} \right )}^{5} - 4 x^{3} \log {\left (x^{2} \log {\left (3 \right )} \right )}^{6} - 4 x^{3} + \left (- 60 x^{5} - 6 x^{2}\right ) \log {\left (x^{2} \log {\left (3 \right )} \right )}^{4} + \left (80 x^{6} + 24 x^{3}\right ) \log {\left (x^{2} \log {\left (3 \right )} \right )}^{3} + \left (- 60 x^{7} - 36 x^{4} - 4 x\right ) \log {\left (x^{2} \log {\left (3 \right )} \right )}^{2} + \left (24 x^{8} + 24 x^{5} + 8 x^{2}\right ) \log {\left (x^{2} \log {\left (3 \right )} \right )} - 1}{x^{16} + 4 x^{13} + 6 x^{10} - 8 x^{9} \log {\left (x^{2} \log {\left (3 \right )} \right )}^{7} + x^{8} \log {\left (x^{2} \log {\left (3 \right )} \right )}^{8} + 4 x^{7} + x^{4} + \left (28 x^{10} + 4 x^{7}\right ) \log {\left (x^{2} \log {\left (3 \right )} \right )}^{6} + \left (- 56 x^{11} - 24 x^{8}\right ) \log {\left (x^{2} \log {\left (3 \right )} \right )}^{5} + \left (70 x^{12} + 60 x^{9} + 6 x^{6}\right ) \log {\left (x^{2} \log {\left (3 \right )} \right )}^{4} + \left (- 56 x^{13} - 80 x^{10} - 24 x^{7}\right ) \log {\left (x^{2} \log {\left (3 \right )} \right )}^{3} + \left (28 x^{14} + 60 x^{11} + 36 x^{8} + 4 x^{5}\right ) \log {\left (x^{2} \log {\left (3 \right )} \right )}^{2} + \left (- 8 x^{15} - 24 x^{12} - 24 x^{9} - 8 x^{6}\right ) \log {\left (x^{2} \log {\left (3 \right )} \right )}} + \frac {1}{x^{4}} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 1150 vs. \(2 (17) = 34\).
Time = 0.73 (sec) , antiderivative size = 1150, normalized size of antiderivative = 67.65 \[ \int \frac {-16 x^7+8 x^8-4 x^{11}+\left (112 x^6-56 x^7+40 x^{10}\right ) \log \left (x^2 \log (3)\right )+\left (-336 x^5+168 x^6-180 x^9\right ) \log ^2\left (x^2 \log (3)\right )+\left (560 x^4-280 x^5+480 x^8\right ) \log ^3\left (x^2 \log (3)\right )+\left (-560 x^3+280 x^4-840 x^7\right ) \log ^4\left (x^2 \log (3)\right )+\left (336 x^2-168 x^3+1008 x^6\right ) \log ^5\left (x^2 \log (3)\right )+\left (-112 x+56 x^2-840 x^5\right ) \log ^6\left (x^2 \log (3)\right )+\left (16-8 x+480 x^4\right ) \log ^7\left (x^2 \log (3)\right )-180 x^3 \log ^8\left (x^2 \log (3)\right )+40 x^2 \log ^9\left (x^2 \log (3)\right )-4 x \log ^{10}\left (x^2 \log (3)\right )}{x+5 x^4+10 x^7+10 x^{10}+5 x^{13}+x^{16}+\left (-10 x^3-40 x^6-60 x^9-40 x^{12}-10 x^{15}\right ) \log \left (x^2 \log (3)\right )+\left (5 x^2+60 x^5+150 x^8+140 x^{11}+45 x^{14}\right ) \log ^2\left (x^2 \log (3)\right )+\left (-40 x^4-200 x^7-280 x^{10}-120 x^{13}\right ) \log ^3\left (x^2 \log (3)\right )+\left (10 x^3+150 x^6+350 x^9+210 x^{12}\right ) \log ^4\left (x^2 \log (3)\right )+\left (-60 x^5-280 x^8-252 x^{11}\right ) \log ^5\left (x^2 \log (3)\right )+\left (10 x^4+140 x^7+210 x^{10}\right ) \log ^6\left (x^2 \log (3)\right )+\left (-40 x^6-120 x^9\right ) \log ^7\left (x^2 \log (3)\right )+\left (5 x^5+45 x^8\right ) \log ^8\left (x^2 \log (3)\right )-10 x^7 \log ^9\left (x^2 \log (3)\right )+x^6 \log ^{10}\left (x^2 \log (3)\right )} \, dx=\text {Too large to display} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 478 vs. \(2 (17) = 34\).
Time = 3.32 (sec) , antiderivative size = 478, normalized size of antiderivative = 28.12 \[ \int \frac {-16 x^7+8 x^8-4 x^{11}+\left (112 x^6-56 x^7+40 x^{10}\right ) \log \left (x^2 \log (3)\right )+\left (-336 x^5+168 x^6-180 x^9\right ) \log ^2\left (x^2 \log (3)\right )+\left (560 x^4-280 x^5+480 x^8\right ) \log ^3\left (x^2 \log (3)\right )+\left (-560 x^3+280 x^4-840 x^7\right ) \log ^4\left (x^2 \log (3)\right )+\left (336 x^2-168 x^3+1008 x^6\right ) \log ^5\left (x^2 \log (3)\right )+\left (-112 x+56 x^2-840 x^5\right ) \log ^6\left (x^2 \log (3)\right )+\left (16-8 x+480 x^4\right ) \log ^7\left (x^2 \log (3)\right )-180 x^3 \log ^8\left (x^2 \log (3)\right )+40 x^2 \log ^9\left (x^2 \log (3)\right )-4 x \log ^{10}\left (x^2 \log (3)\right )}{x+5 x^4+10 x^7+10 x^{10}+5 x^{13}+x^{16}+\left (-10 x^3-40 x^6-60 x^9-40 x^{12}-10 x^{15}\right ) \log \left (x^2 \log (3)\right )+\left (5 x^2+60 x^5+150 x^8+140 x^{11}+45 x^{14}\right ) \log ^2\left (x^2 \log (3)\right )+\left (-40 x^4-200 x^7-280 x^{10}-120 x^{13}\right ) \log ^3\left (x^2 \log (3)\right )+\left (10 x^3+150 x^6+350 x^9+210 x^{12}\right ) \log ^4\left (x^2 \log (3)\right )+\left (-60 x^5-280 x^8-252 x^{11}\right ) \log ^5\left (x^2 \log (3)\right )+\left (10 x^4+140 x^7+210 x^{10}\right ) \log ^6\left (x^2 \log (3)\right )+\left (-40 x^6-120 x^9\right ) \log ^7\left (x^2 \log (3)\right )+\left (5 x^5+45 x^8\right ) \log ^8\left (x^2 \log (3)\right )-10 x^7 \log ^9\left (x^2 \log (3)\right )+x^6 \log ^{10}\left (x^2 \log (3)\right )} \, dx=-\frac {4 \, x^{9} - 24 \, x^{8} \log \left (x^{2} \log \left (3\right )\right ) + 60 \, x^{7} \log \left (x^{2} \log \left (3\right )\right )^{2} - 80 \, x^{6} \log \left (x^{2} \log \left (3\right )\right )^{3} + 60 \, x^{5} \log \left (x^{2} \log \left (3\right )\right )^{4} - 24 \, x^{4} \log \left (x^{2} \log \left (3\right )\right )^{5} + 4 \, x^{3} \log \left (x^{2} \log \left (3\right )\right )^{6} + 6 \, x^{6} - 24 \, x^{5} \log \left (x^{2} \log \left (3\right )\right ) + 36 \, x^{4} \log \left (x^{2} \log \left (3\right )\right )^{2} - 24 \, x^{3} \log \left (x^{2} \log \left (3\right )\right )^{3} + 6 \, x^{2} \log \left (x^{2} \log \left (3\right )\right )^{4} + 4 \, x^{3} - 8 \, x^{2} \log \left (x^{2} \log \left (3\right )\right ) + 4 \, x \log \left (x^{2} \log \left (3\right )\right )^{2} + 1}{x^{16} - 8 \, x^{15} \log \left (x^{2} \log \left (3\right )\right ) + 28 \, x^{14} \log \left (x^{2} \log \left (3\right )\right )^{2} - 56 \, x^{13} \log \left (x^{2} \log \left (3\right )\right )^{3} + 70 \, x^{12} \log \left (x^{2} \log \left (3\right )\right )^{4} - 56 \, x^{11} \log \left (x^{2} \log \left (3\right )\right )^{5} + 28 \, x^{10} \log \left (x^{2} \log \left (3\right )\right )^{6} - 8 \, x^{9} \log \left (x^{2} \log \left (3\right )\right )^{7} + x^{8} \log \left (x^{2} \log \left (3\right )\right )^{8} + 4 \, x^{13} - 24 \, x^{12} \log \left (x^{2} \log \left (3\right )\right ) + 60 \, x^{11} \log \left (x^{2} \log \left (3\right )\right )^{2} - 80 \, x^{10} \log \left (x^{2} \log \left (3\right )\right )^{3} + 60 \, x^{9} \log \left (x^{2} \log \left (3\right )\right )^{4} - 24 \, x^{8} \log \left (x^{2} \log \left (3\right )\right )^{5} + 4 \, x^{7} \log \left (x^{2} \log \left (3\right )\right )^{6} + 6 \, x^{10} - 24 \, x^{9} \log \left (x^{2} \log \left (3\right )\right ) + 36 \, x^{8} \log \left (x^{2} \log \left (3\right )\right )^{2} - 24 \, x^{7} \log \left (x^{2} \log \left (3\right )\right )^{3} + 6 \, x^{6} \log \left (x^{2} \log \left (3\right )\right )^{4} + 4 \, x^{7} - 8 \, x^{6} \log \left (x^{2} \log \left (3\right )\right ) + 4 \, x^{5} \log \left (x^{2} \log \left (3\right )\right )^{2} + x^{4}} + \frac {1}{x^{4}} \]
[In]
[Out]
Timed out. \[ \int \frac {-16 x^7+8 x^8-4 x^{11}+\left (112 x^6-56 x^7+40 x^{10}\right ) \log \left (x^2 \log (3)\right )+\left (-336 x^5+168 x^6-180 x^9\right ) \log ^2\left (x^2 \log (3)\right )+\left (560 x^4-280 x^5+480 x^8\right ) \log ^3\left (x^2 \log (3)\right )+\left (-560 x^3+280 x^4-840 x^7\right ) \log ^4\left (x^2 \log (3)\right )+\left (336 x^2-168 x^3+1008 x^6\right ) \log ^5\left (x^2 \log (3)\right )+\left (-112 x+56 x^2-840 x^5\right ) \log ^6\left (x^2 \log (3)\right )+\left (16-8 x+480 x^4\right ) \log ^7\left (x^2 \log (3)\right )-180 x^3 \log ^8\left (x^2 \log (3)\right )+40 x^2 \log ^9\left (x^2 \log (3)\right )-4 x \log ^{10}\left (x^2 \log (3)\right )}{x+5 x^4+10 x^7+10 x^{10}+5 x^{13}+x^{16}+\left (-10 x^3-40 x^6-60 x^9-40 x^{12}-10 x^{15}\right ) \log \left (x^2 \log (3)\right )+\left (5 x^2+60 x^5+150 x^8+140 x^{11}+45 x^{14}\right ) \log ^2\left (x^2 \log (3)\right )+\left (-40 x^4-200 x^7-280 x^{10}-120 x^{13}\right ) \log ^3\left (x^2 \log (3)\right )+\left (10 x^3+150 x^6+350 x^9+210 x^{12}\right ) \log ^4\left (x^2 \log (3)\right )+\left (-60 x^5-280 x^8-252 x^{11}\right ) \log ^5\left (x^2 \log (3)\right )+\left (10 x^4+140 x^7+210 x^{10}\right ) \log ^6\left (x^2 \log (3)\right )+\left (-40 x^6-120 x^9\right ) \log ^7\left (x^2 \log (3)\right )+\left (5 x^5+45 x^8\right ) \log ^8\left (x^2 \log (3)\right )-10 x^7 \log ^9\left (x^2 \log (3)\right )+x^6 \log ^{10}\left (x^2 \log (3)\right )} \, dx=\int -\frac {4\,x\,{\ln \left (x^2\,\ln \left (3\right )\right )}^{10}-{\ln \left (x^2\,\ln \left (3\right )\right )}^7\,\left (480\,x^4-8\,x+16\right )-\ln \left (x^2\,\ln \left (3\right )\right )\,\left (40\,x^{10}-56\,x^7+112\,x^6\right )+{\ln \left (x^2\,\ln \left (3\right )\right )}^6\,\left (840\,x^5-56\,x^2+112\,x\right )-40\,x^2\,{\ln \left (x^2\,\ln \left (3\right )\right )}^9+180\,x^3\,{\ln \left (x^2\,\ln \left (3\right )\right )}^8+{\ln \left (x^2\,\ln \left (3\right )\right )}^2\,\left (180\,x^9-168\,x^6+336\,x^5\right )-{\ln \left (x^2\,\ln \left (3\right )\right )}^3\,\left (480\,x^8-280\,x^5+560\,x^4\right )-{\ln \left (x^2\,\ln \left (3\right )\right )}^5\,\left (1008\,x^6-168\,x^3+336\,x^2\right )+{\ln \left (x^2\,\ln \left (3\right )\right )}^4\,\left (840\,x^7-280\,x^4+560\,x^3\right )+16\,x^7-8\,x^8+4\,x^{11}}{x-{\ln \left (x^2\,\ln \left (3\right )\right )}^3\,\left (120\,x^{13}+280\,x^{10}+200\,x^7+40\,x^4\right )+{\ln \left (x^2\,\ln \left (3\right )\right )}^4\,\left (210\,x^{12}+350\,x^9+150\,x^6+10\,x^3\right )+{\ln \left (x^2\,\ln \left (3\right )\right )}^2\,\left (45\,x^{14}+140\,x^{11}+150\,x^8+60\,x^5+5\,x^2\right )+{\ln \left (x^2\,\ln \left (3\right )\right )}^8\,\left (45\,x^8+5\,x^5\right )-{\ln \left (x^2\,\ln \left (3\right )\right )}^7\,\left (120\,x^9+40\,x^6\right )+x^6\,{\ln \left (x^2\,\ln \left (3\right )\right )}^{10}-10\,x^7\,{\ln \left (x^2\,\ln \left (3\right )\right )}^9+{\ln \left (x^2\,\ln \left (3\right )\right )}^6\,\left (210\,x^{10}+140\,x^7+10\,x^4\right )-{\ln \left (x^2\,\ln \left (3\right )\right )}^5\,\left (252\,x^{11}+280\,x^8+60\,x^5\right )+5\,x^4+10\,x^7+10\,x^{10}+5\,x^{13}+x^{16}-\ln \left (x^2\,\ln \left (3\right )\right )\,\left (10\,x^{15}+40\,x^{12}+60\,x^9+40\,x^6+10\,x^3\right )} \,d x \]
[In]
[Out]