Integrand size = 339, antiderivative size = 30 \begin {dmath*} \int \frac {14580+24786 x+17010 x^2+5940 x^3+1080 x^4+90 x^5+2 x^6+e^{\frac {2 \left (81 x+107 x^2+54 x^3+12 x^4+x^5+e^{2 x} \left (81 x+108 x^2+54 x^3+12 x^4+x^5\right )\right )}{81+108 x+54 x^2+12 x^3+x^4}} \left (12150+19950 x+13600 x^2+4500 x^3+750 x^4+50 x^5+e^{2 x} \left (12150+44550 x+54000 x^2+31500 x^3+9750 x^4+1550 x^5+100 x^6\right )\right )+e^{\frac {81 x+107 x^2+54 x^3+12 x^4+x^5+e^{2 x} \left (81 x+108 x^2+54 x^3+12 x^4+x^5\right )}{81+108 x+54 x^2+12 x^3+x^4}} \left (75330+126180 x+88290 x^2+30620 x^3+5550 x^4+460 x^5+10 x^6+e^{2 x} \left (72900+269730 x+332910 x^2+199800 x^3+64800 x^4+11250 x^5+910 x^6+20 x^7\right )\right )}{6075+10125 x+6750 x^2+2250 x^3+375 x^4+25 x^5} \, dx=\left (6+e^{x+e^{2 x} x-\frac {x^2}{(3+x)^4}}+\frac {x}{5}\right )^2 \end {dmath*}
Time = 0.79 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.87 \begin {dmath*} \int \frac {14580+24786 x+17010 x^2+5940 x^3+1080 x^4+90 x^5+2 x^6+e^{\frac {2 \left (81 x+107 x^2+54 x^3+12 x^4+x^5+e^{2 x} \left (81 x+108 x^2+54 x^3+12 x^4+x^5\right )\right )}{81+108 x+54 x^2+12 x^3+x^4}} \left (12150+19950 x+13600 x^2+4500 x^3+750 x^4+50 x^5+e^{2 x} \left (12150+44550 x+54000 x^2+31500 x^3+9750 x^4+1550 x^5+100 x^6\right )\right )+e^{\frac {81 x+107 x^2+54 x^3+12 x^4+x^5+e^{2 x} \left (81 x+108 x^2+54 x^3+12 x^4+x^5\right )}{81+108 x+54 x^2+12 x^3+x^4}} \left (75330+126180 x+88290 x^2+30620 x^3+5550 x^4+460 x^5+10 x^6+e^{2 x} \left (72900+269730 x+332910 x^2+199800 x^3+64800 x^4+11250 x^5+910 x^6+20 x^7\right )\right )}{6075+10125 x+6750 x^2+2250 x^3+375 x^4+25 x^5} \, dx=\frac {1}{25} \left (25 e^{2 x \left (1+e^{2 x}-\frac {x}{(3+x)^4}\right )}+10 e^{x \left (1+e^{2 x}-\frac {x}{(3+x)^4}\right )} (30+x)+x (60+x)\right ) \end {dmath*}
Integrate[(14580 + 24786*x + 17010*x^2 + 5940*x^3 + 1080*x^4 + 90*x^5 + 2* x^6 + E^((2*(81*x + 107*x^2 + 54*x^3 + 12*x^4 + x^5 + E^(2*x)*(81*x + 108* x^2 + 54*x^3 + 12*x^4 + x^5)))/(81 + 108*x + 54*x^2 + 12*x^3 + x^4))*(1215 0 + 19950*x + 13600*x^2 + 4500*x^3 + 750*x^4 + 50*x^5 + E^(2*x)*(12150 + 4 4550*x + 54000*x^2 + 31500*x^3 + 9750*x^4 + 1550*x^5 + 100*x^6)) + E^((81* x + 107*x^2 + 54*x^3 + 12*x^4 + x^5 + E^(2*x)*(81*x + 108*x^2 + 54*x^3 + 1 2*x^4 + x^5))/(81 + 108*x + 54*x^2 + 12*x^3 + x^4))*(75330 + 126180*x + 88 290*x^2 + 30620*x^3 + 5550*x^4 + 460*x^5 + 10*x^6 + E^(2*x)*(72900 + 26973 0*x + 332910*x^2 + 199800*x^3 + 64800*x^4 + 11250*x^5 + 910*x^6 + 20*x^7)) )/(6075 + 10125*x + 6750*x^2 + 2250*x^3 + 375*x^4 + 25*x^5),x]
(25*E^(2*x*(1 + E^(2*x) - x/(3 + x)^4)) + 10*E^(x*(1 + E^(2*x) - x/(3 + x) ^4))*(30 + x) + x*(60 + x))/25
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (50 x^5+750 x^4+4500 x^3+13600 x^2+e^{2 x} \left (100 x^6+1550 x^5+9750 x^4+31500 x^3+54000 x^2+44550 x+12150\right )+19950 x+12150\right ) \exp \left (\frac {2 \left (x^5+12 x^4+54 x^3+107 x^2+e^{2 x} \left (x^5+12 x^4+54 x^3+108 x^2+81 x\right )+81 x\right )}{x^4+12 x^3+54 x^2+108 x+81}\right )+\left (10 x^6+460 x^5+5550 x^4+30620 x^3+88290 x^2+e^{2 x} \left (20 x^7+910 x^6+11250 x^5+64800 x^4+199800 x^3+332910 x^2+269730 x+72900\right )+126180 x+75330\right ) \exp \left (\frac {x^5+12 x^4+54 x^3+107 x^2+e^{2 x} \left (x^5+12 x^4+54 x^3+108 x^2+81 x\right )+81 x}{x^4+12 x^3+54 x^2+108 x+81}\right )+2 x^6+90 x^5+1080 x^4+5940 x^3+17010 x^2+24786 x+14580}{25 x^5+375 x^4+2250 x^3+6750 x^2+10125 x+6075} \, dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {\left (50 x^5+750 x^4+4500 x^3+13600 x^2+e^{2 x} \left (100 x^6+1550 x^5+9750 x^4+31500 x^3+54000 x^2+44550 x+12150\right )+19950 x+12150\right ) \exp \left (\frac {2 \left (x^5+12 x^4+54 x^3+107 x^2+e^{2 x} \left (x^5+12 x^4+54 x^3+108 x^2+81 x\right )+81 x\right )}{x^4+12 x^3+54 x^2+108 x+81}\right )+\left (10 x^6+460 x^5+5550 x^4+30620 x^3+88290 x^2+e^{2 x} \left (20 x^7+910 x^6+11250 x^5+64800 x^4+199800 x^3+332910 x^2+269730 x+72900\right )+126180 x+75330\right ) \exp \left (\frac {x^5+12 x^4+54 x^3+107 x^2+e^{2 x} \left (x^5+12 x^4+54 x^3+108 x^2+81 x\right )+81 x}{x^4+12 x^3+54 x^2+108 x+81}\right )+2 x^6+90 x^5+1080 x^4+5940 x^3+17010 x^2+24786 x+14580}{\left (5^{2/5} x+3\ 5^{2/5}\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 \left (2 e^{2 x} x^6+31 e^{2 x} x^5+x^5+195 e^{2 x} x^4+15 x^4+630 e^{2 x} x^3+90 x^3+1080 e^{2 x} x^2+272 x^2+891 e^{2 x} x+399 x+243 e^{2 x}+243\right ) \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right )}{(x+3)^5}+\frac {2 \left (2 e^{2 x} x^7+91 e^{2 x} x^6+x^6+1125 e^{2 x} x^5+46 x^5+6480 e^{2 x} x^4+555 x^4+19980 e^{2 x} x^3+3062 x^3+33291 e^{2 x} x^2+8829 x^2+26973 e^{2 x} x+12618 x+7290 e^{2 x}+7533\right ) \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right )}{5 (x+3)^5}+\frac {2 x^6}{25 (x+3)^5}+\frac {18 x^5}{5 (x+3)^5}+\frac {216 x^4}{5 (x+3)^5}+\frac {1188 x^3}{5 (x+3)^5}+\frac {3402 x^2}{5 (x+3)^5}+\frac {24786 x}{25 (x+3)^5}+\frac {2916}{5 (x+3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \left (25 \left (x^5+15 x^4+90 x^3+272 x^2+399 x+e^{2 x} (x+3)^5 (2 x+1)+243\right ) \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right )+5 \left (x^6+46 x^5+555 x^4+3062 x^3+8829 x^2+e^{2 x} (x+3)^5 \left (2 x^2+61 x+30\right )+12618 x+7533\right ) \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right )+x^6+45 x^5+540 x^4+2970 x^3+8505 x^2+12393 x+7290\right )}{25 (x+3)^5}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{25} \int \frac {x^6+45 x^5+540 x^4+2970 x^3+8505 x^2+12393 x+25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^5+15 x^4+90 x^3+272 x^2+399 x+e^{2 x} (x+3)^5 (2 x+1)+243\right )+5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^6+46 x^5+555 x^4+3062 x^3+8829 x^2+12618 x+e^{2 x} (x+3)^5 \left (2 x^2+61 x+30\right )+7533\right )+7290}{(x+3)^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {x^6}{(x+3)^5}+\frac {45 x^5}{(x+3)^5}+\frac {540 x^4}{(x+3)^5}+\frac {2970 x^3}{(x+3)^5}+\frac {8505 x^2}{(x+3)^5}+\frac {12393 x}{(x+3)^5}+\frac {25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^6+31 e^{2 x} x^5+x^5+195 e^{2 x} x^4+15 x^4+630 e^{2 x} x^3+90 x^3+1080 e^{2 x} x^2+272 x^2+891 e^{2 x} x+399 x+243 e^{2 x}+243\right )}{(x+3)^5}+\frac {5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^7+91 e^{2 x} x^6+x^6+1125 e^{2 x} x^5+46 x^5+6480 e^{2 x} x^4+555 x^4+19980 e^{2 x} x^3+3062 x^3+33291 e^{2 x} x^2+8829 x^2+26973 e^{2 x} x+12618 x+7290 e^{2 x}+7533\right )}{(x+3)^5}+\frac {7290}{(x+3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {x^6+45 x^5+540 x^4+2970 x^3+8505 x^2+12393 x+25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^5+15 x^4+90 x^3+272 x^2+399 x+e^{2 x} (x+3)^5 (2 x+1)+243\right )+5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^6+46 x^5+555 x^4+3062 x^3+8829 x^2+12618 x+e^{2 x} (x+3)^5 \left (2 x^2+61 x+30\right )+7533\right )+7290}{(x+3)^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {x^6}{(x+3)^5}+\frac {45 x^5}{(x+3)^5}+\frac {540 x^4}{(x+3)^5}+\frac {2970 x^3}{(x+3)^5}+\frac {8505 x^2}{(x+3)^5}+\frac {12393 x}{(x+3)^5}+\frac {25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^6+31 e^{2 x} x^5+x^5+195 e^{2 x} x^4+15 x^4+630 e^{2 x} x^3+90 x^3+1080 e^{2 x} x^2+272 x^2+891 e^{2 x} x+399 x+243 e^{2 x}+243\right )}{(x+3)^5}+\frac {5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^7+91 e^{2 x} x^6+x^6+1125 e^{2 x} x^5+46 x^5+6480 e^{2 x} x^4+555 x^4+19980 e^{2 x} x^3+3062 x^3+33291 e^{2 x} x^2+8829 x^2+26973 e^{2 x} x+12618 x+7290 e^{2 x}+7533\right )}{(x+3)^5}+\frac {7290}{(x+3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {x^6+45 x^5+540 x^4+2970 x^3+8505 x^2+12393 x+25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^5+15 x^4+90 x^3+272 x^2+399 x+e^{2 x} (x+3)^5 (2 x+1)+243\right )+5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^6+46 x^5+555 x^4+3062 x^3+8829 x^2+12618 x+e^{2 x} (x+3)^5 \left (2 x^2+61 x+30\right )+7533\right )+7290}{(x+3)^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {x^6}{(x+3)^5}+\frac {45 x^5}{(x+3)^5}+\frac {540 x^4}{(x+3)^5}+\frac {2970 x^3}{(x+3)^5}+\frac {8505 x^2}{(x+3)^5}+\frac {12393 x}{(x+3)^5}+\frac {25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^6+31 e^{2 x} x^5+x^5+195 e^{2 x} x^4+15 x^4+630 e^{2 x} x^3+90 x^3+1080 e^{2 x} x^2+272 x^2+891 e^{2 x} x+399 x+243 e^{2 x}+243\right )}{(x+3)^5}+\frac {5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^7+91 e^{2 x} x^6+x^6+1125 e^{2 x} x^5+46 x^5+6480 e^{2 x} x^4+555 x^4+19980 e^{2 x} x^3+3062 x^3+33291 e^{2 x} x^2+8829 x^2+26973 e^{2 x} x+12618 x+7290 e^{2 x}+7533\right )}{(x+3)^5}+\frac {7290}{(x+3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {x^6+45 x^5+540 x^4+2970 x^3+8505 x^2+12393 x+25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^5+15 x^4+90 x^3+272 x^2+399 x+e^{2 x} (x+3)^5 (2 x+1)+243\right )+5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^6+46 x^5+555 x^4+3062 x^3+8829 x^2+12618 x+e^{2 x} (x+3)^5 \left (2 x^2+61 x+30\right )+7533\right )+7290}{(x+3)^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {x^6}{(x+3)^5}+\frac {45 x^5}{(x+3)^5}+\frac {540 x^4}{(x+3)^5}+\frac {2970 x^3}{(x+3)^5}+\frac {8505 x^2}{(x+3)^5}+\frac {12393 x}{(x+3)^5}+\frac {25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^6+31 e^{2 x} x^5+x^5+195 e^{2 x} x^4+15 x^4+630 e^{2 x} x^3+90 x^3+1080 e^{2 x} x^2+272 x^2+891 e^{2 x} x+399 x+243 e^{2 x}+243\right )}{(x+3)^5}+\frac {5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^7+91 e^{2 x} x^6+x^6+1125 e^{2 x} x^5+46 x^5+6480 e^{2 x} x^4+555 x^4+19980 e^{2 x} x^3+3062 x^3+33291 e^{2 x} x^2+8829 x^2+26973 e^{2 x} x+12618 x+7290 e^{2 x}+7533\right )}{(x+3)^5}+\frac {7290}{(x+3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {x^6+45 x^5+540 x^4+2970 x^3+8505 x^2+12393 x+25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^5+15 x^4+90 x^3+272 x^2+399 x+e^{2 x} (x+3)^5 (2 x+1)+243\right )+5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^6+46 x^5+555 x^4+3062 x^3+8829 x^2+12618 x+e^{2 x} (x+3)^5 \left (2 x^2+61 x+30\right )+7533\right )+7290}{(x+3)^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {x^6}{(x+3)^5}+\frac {45 x^5}{(x+3)^5}+\frac {540 x^4}{(x+3)^5}+\frac {2970 x^3}{(x+3)^5}+\frac {8505 x^2}{(x+3)^5}+\frac {12393 x}{(x+3)^5}+\frac {25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^6+31 e^{2 x} x^5+x^5+195 e^{2 x} x^4+15 x^4+630 e^{2 x} x^3+90 x^3+1080 e^{2 x} x^2+272 x^2+891 e^{2 x} x+399 x+243 e^{2 x}+243\right )}{(x+3)^5}+\frac {5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^7+91 e^{2 x} x^6+x^6+1125 e^{2 x} x^5+46 x^5+6480 e^{2 x} x^4+555 x^4+19980 e^{2 x} x^3+3062 x^3+33291 e^{2 x} x^2+8829 x^2+26973 e^{2 x} x+12618 x+7290 e^{2 x}+7533\right )}{(x+3)^5}+\frac {7290}{(x+3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {x^6+45 x^5+540 x^4+2970 x^3+8505 x^2+12393 x+25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^5+15 x^4+90 x^3+272 x^2+399 x+e^{2 x} (x+3)^5 (2 x+1)+243\right )+5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^6+46 x^5+555 x^4+3062 x^3+8829 x^2+12618 x+e^{2 x} (x+3)^5 \left (2 x^2+61 x+30\right )+7533\right )+7290}{(x+3)^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {x^6}{(x+3)^5}+\frac {45 x^5}{(x+3)^5}+\frac {540 x^4}{(x+3)^5}+\frac {2970 x^3}{(x+3)^5}+\frac {8505 x^2}{(x+3)^5}+\frac {12393 x}{(x+3)^5}+\frac {25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^6+31 e^{2 x} x^5+x^5+195 e^{2 x} x^4+15 x^4+630 e^{2 x} x^3+90 x^3+1080 e^{2 x} x^2+272 x^2+891 e^{2 x} x+399 x+243 e^{2 x}+243\right )}{(x+3)^5}+\frac {5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^7+91 e^{2 x} x^6+x^6+1125 e^{2 x} x^5+46 x^5+6480 e^{2 x} x^4+555 x^4+19980 e^{2 x} x^3+3062 x^3+33291 e^{2 x} x^2+8829 x^2+26973 e^{2 x} x+12618 x+7290 e^{2 x}+7533\right )}{(x+3)^5}+\frac {7290}{(x+3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {x^6+45 x^5+540 x^4+2970 x^3+8505 x^2+12393 x+25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^5+15 x^4+90 x^3+272 x^2+399 x+e^{2 x} (x+3)^5 (2 x+1)+243\right )+5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^6+46 x^5+555 x^4+3062 x^3+8829 x^2+12618 x+e^{2 x} (x+3)^5 \left (2 x^2+61 x+30\right )+7533\right )+7290}{(x+3)^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {x^6}{(x+3)^5}+\frac {45 x^5}{(x+3)^5}+\frac {540 x^4}{(x+3)^5}+\frac {2970 x^3}{(x+3)^5}+\frac {8505 x^2}{(x+3)^5}+\frac {12393 x}{(x+3)^5}+\frac {25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^6+31 e^{2 x} x^5+x^5+195 e^{2 x} x^4+15 x^4+630 e^{2 x} x^3+90 x^3+1080 e^{2 x} x^2+272 x^2+891 e^{2 x} x+399 x+243 e^{2 x}+243\right )}{(x+3)^5}+\frac {5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^7+91 e^{2 x} x^6+x^6+1125 e^{2 x} x^5+46 x^5+6480 e^{2 x} x^4+555 x^4+19980 e^{2 x} x^3+3062 x^3+33291 e^{2 x} x^2+8829 x^2+26973 e^{2 x} x+12618 x+7290 e^{2 x}+7533\right )}{(x+3)^5}+\frac {7290}{(x+3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {x^6+45 x^5+540 x^4+2970 x^3+8505 x^2+12393 x+25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^5+15 x^4+90 x^3+272 x^2+399 x+e^{2 x} (x+3)^5 (2 x+1)+243\right )+5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^6+46 x^5+555 x^4+3062 x^3+8829 x^2+12618 x+e^{2 x} (x+3)^5 \left (2 x^2+61 x+30\right )+7533\right )+7290}{(x+3)^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {x^6}{(x+3)^5}+\frac {45 x^5}{(x+3)^5}+\frac {540 x^4}{(x+3)^5}+\frac {2970 x^3}{(x+3)^5}+\frac {8505 x^2}{(x+3)^5}+\frac {12393 x}{(x+3)^5}+\frac {25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^6+31 e^{2 x} x^5+x^5+195 e^{2 x} x^4+15 x^4+630 e^{2 x} x^3+90 x^3+1080 e^{2 x} x^2+272 x^2+891 e^{2 x} x+399 x+243 e^{2 x}+243\right )}{(x+3)^5}+\frac {5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^7+91 e^{2 x} x^6+x^6+1125 e^{2 x} x^5+46 x^5+6480 e^{2 x} x^4+555 x^4+19980 e^{2 x} x^3+3062 x^3+33291 e^{2 x} x^2+8829 x^2+26973 e^{2 x} x+12618 x+7290 e^{2 x}+7533\right )}{(x+3)^5}+\frac {7290}{(x+3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {x^6+45 x^5+540 x^4+2970 x^3+8505 x^2+12393 x+25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^5+15 x^4+90 x^3+272 x^2+399 x+e^{2 x} (x+3)^5 (2 x+1)+243\right )+5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^6+46 x^5+555 x^4+3062 x^3+8829 x^2+12618 x+e^{2 x} (x+3)^5 \left (2 x^2+61 x+30\right )+7533\right )+7290}{(x+3)^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {x^6}{(x+3)^5}+\frac {45 x^5}{(x+3)^5}+\frac {540 x^4}{(x+3)^5}+\frac {2970 x^3}{(x+3)^5}+\frac {8505 x^2}{(x+3)^5}+\frac {12393 x}{(x+3)^5}+\frac {25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^6+31 e^{2 x} x^5+x^5+195 e^{2 x} x^4+15 x^4+630 e^{2 x} x^3+90 x^3+1080 e^{2 x} x^2+272 x^2+891 e^{2 x} x+399 x+243 e^{2 x}+243\right )}{(x+3)^5}+\frac {5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^7+91 e^{2 x} x^6+x^6+1125 e^{2 x} x^5+46 x^5+6480 e^{2 x} x^4+555 x^4+19980 e^{2 x} x^3+3062 x^3+33291 e^{2 x} x^2+8829 x^2+26973 e^{2 x} x+12618 x+7290 e^{2 x}+7533\right )}{(x+3)^5}+\frac {7290}{(x+3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {x^6+45 x^5+540 x^4+2970 x^3+8505 x^2+12393 x+25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^5+15 x^4+90 x^3+272 x^2+399 x+e^{2 x} (x+3)^5 (2 x+1)+243\right )+5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^6+46 x^5+555 x^4+3062 x^3+8829 x^2+12618 x+e^{2 x} (x+3)^5 \left (2 x^2+61 x+30\right )+7533\right )+7290}{(x+3)^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {x^6}{(x+3)^5}+\frac {45 x^5}{(x+3)^5}+\frac {540 x^4}{(x+3)^5}+\frac {2970 x^3}{(x+3)^5}+\frac {8505 x^2}{(x+3)^5}+\frac {12393 x}{(x+3)^5}+\frac {25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^6+31 e^{2 x} x^5+x^5+195 e^{2 x} x^4+15 x^4+630 e^{2 x} x^3+90 x^3+1080 e^{2 x} x^2+272 x^2+891 e^{2 x} x+399 x+243 e^{2 x}+243\right )}{(x+3)^5}+\frac {5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^7+91 e^{2 x} x^6+x^6+1125 e^{2 x} x^5+46 x^5+6480 e^{2 x} x^4+555 x^4+19980 e^{2 x} x^3+3062 x^3+33291 e^{2 x} x^2+8829 x^2+26973 e^{2 x} x+12618 x+7290 e^{2 x}+7533\right )}{(x+3)^5}+\frac {7290}{(x+3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {x^6+45 x^5+540 x^4+2970 x^3+8505 x^2+12393 x+25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^5+15 x^4+90 x^3+272 x^2+399 x+e^{2 x} (x+3)^5 (2 x+1)+243\right )+5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^6+46 x^5+555 x^4+3062 x^3+8829 x^2+12618 x+e^{2 x} (x+3)^5 \left (2 x^2+61 x+30\right )+7533\right )+7290}{(x+3)^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {x^6}{(x+3)^5}+\frac {45 x^5}{(x+3)^5}+\frac {540 x^4}{(x+3)^5}+\frac {2970 x^3}{(x+3)^5}+\frac {8505 x^2}{(x+3)^5}+\frac {12393 x}{(x+3)^5}+\frac {25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^6+31 e^{2 x} x^5+x^5+195 e^{2 x} x^4+15 x^4+630 e^{2 x} x^3+90 x^3+1080 e^{2 x} x^2+272 x^2+891 e^{2 x} x+399 x+243 e^{2 x}+243\right )}{(x+3)^5}+\frac {5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^7+91 e^{2 x} x^6+x^6+1125 e^{2 x} x^5+46 x^5+6480 e^{2 x} x^4+555 x^4+19980 e^{2 x} x^3+3062 x^3+33291 e^{2 x} x^2+8829 x^2+26973 e^{2 x} x+12618 x+7290 e^{2 x}+7533\right )}{(x+3)^5}+\frac {7290}{(x+3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {x^6+45 x^5+540 x^4+2970 x^3+8505 x^2+12393 x+25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^5+15 x^4+90 x^3+272 x^2+399 x+e^{2 x} (x+3)^5 (2 x+1)+243\right )+5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^6+46 x^5+555 x^4+3062 x^3+8829 x^2+12618 x+e^{2 x} (x+3)^5 \left (2 x^2+61 x+30\right )+7533\right )+7290}{(x+3)^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {x^6}{(x+3)^5}+\frac {45 x^5}{(x+3)^5}+\frac {540 x^4}{(x+3)^5}+\frac {2970 x^3}{(x+3)^5}+\frac {8505 x^2}{(x+3)^5}+\frac {12393 x}{(x+3)^5}+\frac {25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^6+31 e^{2 x} x^5+x^5+195 e^{2 x} x^4+15 x^4+630 e^{2 x} x^3+90 x^3+1080 e^{2 x} x^2+272 x^2+891 e^{2 x} x+399 x+243 e^{2 x}+243\right )}{(x+3)^5}+\frac {5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^7+91 e^{2 x} x^6+x^6+1125 e^{2 x} x^5+46 x^5+6480 e^{2 x} x^4+555 x^4+19980 e^{2 x} x^3+3062 x^3+33291 e^{2 x} x^2+8829 x^2+26973 e^{2 x} x+12618 x+7290 e^{2 x}+7533\right )}{(x+3)^5}+\frac {7290}{(x+3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {x^6+45 x^5+540 x^4+2970 x^3+8505 x^2+12393 x+25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^5+15 x^4+90 x^3+272 x^2+399 x+e^{2 x} (x+3)^5 (2 x+1)+243\right )+5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^6+46 x^5+555 x^4+3062 x^3+8829 x^2+12618 x+e^{2 x} (x+3)^5 \left (2 x^2+61 x+30\right )+7533\right )+7290}{(x+3)^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {x^6}{(x+3)^5}+\frac {45 x^5}{(x+3)^5}+\frac {540 x^4}{(x+3)^5}+\frac {2970 x^3}{(x+3)^5}+\frac {8505 x^2}{(x+3)^5}+\frac {12393 x}{(x+3)^5}+\frac {25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^6+31 e^{2 x} x^5+x^5+195 e^{2 x} x^4+15 x^4+630 e^{2 x} x^3+90 x^3+1080 e^{2 x} x^2+272 x^2+891 e^{2 x} x+399 x+243 e^{2 x}+243\right )}{(x+3)^5}+\frac {5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (2 e^{2 x} x^7+91 e^{2 x} x^6+x^6+1125 e^{2 x} x^5+46 x^5+6480 e^{2 x} x^4+555 x^4+19980 e^{2 x} x^3+3062 x^3+33291 e^{2 x} x^2+8829 x^2+26973 e^{2 x} x+12618 x+7290 e^{2 x}+7533\right )}{(x+3)^5}+\frac {7290}{(x+3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {x^6+45 x^5+540 x^4+2970 x^3+8505 x^2+12393 x+25 \exp \left (\frac {2 x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^5+15 x^4+90 x^3+272 x^2+399 x+e^{2 x} (x+3)^5 (2 x+1)+243\right )+5 \exp \left (\frac {x \left (x^4+12 x^3+54 x^2+107 x+e^{2 x} (x+3)^4+81\right )}{(x+3)^4}\right ) \left (x^6+46 x^5+555 x^4+3062 x^3+8829 x^2+12618 x+e^{2 x} (x+3)^5 \left (2 x^2+61 x+30\right )+7533\right )+7290}{(x+3)^5}dx\) |
Int[(14580 + 24786*x + 17010*x^2 + 5940*x^3 + 1080*x^4 + 90*x^5 + 2*x^6 + E^((2*(81*x + 107*x^2 + 54*x^3 + 12*x^4 + x^5 + E^(2*x)*(81*x + 108*x^2 + 54*x^3 + 12*x^4 + x^5)))/(81 + 108*x + 54*x^2 + 12*x^3 + x^4))*(12150 + 19 950*x + 13600*x^2 + 4500*x^3 + 750*x^4 + 50*x^5 + E^(2*x)*(12150 + 44550*x + 54000*x^2 + 31500*x^3 + 9750*x^4 + 1550*x^5 + 100*x^6)) + E^((81*x + 10 7*x^2 + 54*x^3 + 12*x^4 + x^5 + E^(2*x)*(81*x + 108*x^2 + 54*x^3 + 12*x^4 + x^5))/(81 + 108*x + 54*x^2 + 12*x^3 + x^4))*(75330 + 126180*x + 88290*x^ 2 + 30620*x^3 + 5550*x^4 + 460*x^5 + 10*x^6 + E^(2*x)*(72900 + 269730*x + 332910*x^2 + 199800*x^3 + 64800*x^4 + 11250*x^5 + 910*x^6 + 20*x^7)))/(607 5 + 10125*x + 6750*x^2 + 2250*x^3 + 375*x^4 + 25*x^5),x]
3.7.41.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{a = Rt[Coeff[Px, x, 0], Expon[Px, x]], b = Rt[Coeff[Px, x, Expon[Px, x]], Expon[Px, x]]}, Int[u*(a + b*x)^(Ex pon[Px, x]*p), x] /; EqQ[Px, (a + b*x)^Expon[Px, x]]] /; IntegerQ[p] && Pol yQ[Px, x] && GtQ[Expon[Px, x], 1] && NeQ[Coeff[Px, x, 0], 0]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(146\) vs. \(2(26)=52\).
Time = 5.44 (sec) , antiderivative size = 147, normalized size of antiderivative = 4.90
| method | result | size |
| risch | \(\frac {x^{2}}{25}+\frac {12 x}{5}+{\mathrm e}^{\frac {2 x \left ({\mathrm e}^{2 x} x^{4}+12 \,{\mathrm e}^{2 x} x^{3}+x^{4}+54 \,{\mathrm e}^{2 x} x^{2}+12 x^{3}+108 x \,{\mathrm e}^{2 x}+54 x^{2}+81 \,{\mathrm e}^{2 x}+107 x +81\right )}{\left (3+x \right )^{4}}}+\left (12+\frac {2 x}{5}\right ) {\mathrm e}^{\frac {x \left ({\mathrm e}^{2 x} x^{4}+12 \,{\mathrm e}^{2 x} x^{3}+x^{4}+54 \,{\mathrm e}^{2 x} x^{2}+12 x^{3}+108 x \,{\mathrm e}^{2 x}+54 x^{2}+81 \,{\mathrm e}^{2 x}+107 x +81\right )}{\left (3+x \right )^{4}}}\) | \(147\) |
| parallelrisch | \(\frac {x^{2}}{25}+\frac {2 \,{\mathrm e}^{\frac {\left (x^{5}+12 x^{4}+54 x^{3}+108 x^{2}+81 x \right ) {\mathrm e}^{2 x}+x^{5}+12 x^{4}+54 x^{3}+107 x^{2}+81 x}{x^{4}+12 x^{3}+54 x^{2}+108 x +81}} x}{5}+{\mathrm e}^{\frac {2 \left (x^{5}+12 x^{4}+54 x^{3}+108 x^{2}+81 x \right ) {\mathrm e}^{2 x}+2 x^{5}+24 x^{4}+108 x^{3}+214 x^{2}+162 x}{x^{4}+12 x^{3}+54 x^{2}+108 x +81}}+\frac {12 x}{5}+12 \,{\mathrm e}^{\frac {\left (x^{5}+12 x^{4}+54 x^{3}+108 x^{2}+81 x \right ) {\mathrm e}^{2 x}+x^{5}+12 x^{4}+54 x^{3}+107 x^{2}+81 x}{x^{4}+12 x^{3}+54 x^{2}+108 x +81}}-\frac {918}{25}\) | \(231\) |
int((((100*x^6+1550*x^5+9750*x^4+31500*x^3+54000*x^2+44550*x+12150)*exp(x) ^2+50*x^5+750*x^4+4500*x^3+13600*x^2+19950*x+12150)*exp(((x^5+12*x^4+54*x^ 3+108*x^2+81*x)*exp(x)^2+x^5+12*x^4+54*x^3+107*x^2+81*x)/(x^4+12*x^3+54*x^ 2+108*x+81))^2+((20*x^7+910*x^6+11250*x^5+64800*x^4+199800*x^3+332910*x^2+ 269730*x+72900)*exp(x)^2+10*x^6+460*x^5+5550*x^4+30620*x^3+88290*x^2+12618 0*x+75330)*exp(((x^5+12*x^4+54*x^3+108*x^2+81*x)*exp(x)^2+x^5+12*x^4+54*x^ 3+107*x^2+81*x)/(x^4+12*x^3+54*x^2+108*x+81))+2*x^6+90*x^5+1080*x^4+5940*x ^3+17010*x^2+24786*x+14580)/(25*x^5+375*x^4+2250*x^3+6750*x^2+10125*x+6075 ),x,method=_RETURNVERBOSE)
1/25*x^2+12/5*x+exp(2*x*(exp(2*x)*x^4+12*exp(2*x)*x^3+x^4+54*exp(2*x)*x^2+ 12*x^3+108*x*exp(2*x)+54*x^2+81*exp(2*x)+107*x+81)/(3+x)^4)+(12+2/5*x)*exp (x*(exp(2*x)*x^4+12*exp(2*x)*x^3+x^4+54*exp(2*x)*x^2+12*x^3+108*x*exp(2*x) +54*x^2+81*exp(2*x)+107*x+81)/(3+x)^4)
Leaf count of result is larger than twice the leaf count of optimal. 157 vs. \(2 (28) = 56\).
Time = 0.25 (sec) , antiderivative size = 157, normalized size of antiderivative = 5.23 \begin {dmath*} \int \frac {14580+24786 x+17010 x^2+5940 x^3+1080 x^4+90 x^5+2 x^6+e^{\frac {2 \left (81 x+107 x^2+54 x^3+12 x^4+x^5+e^{2 x} \left (81 x+108 x^2+54 x^3+12 x^4+x^5\right )\right )}{81+108 x+54 x^2+12 x^3+x^4}} \left (12150+19950 x+13600 x^2+4500 x^3+750 x^4+50 x^5+e^{2 x} \left (12150+44550 x+54000 x^2+31500 x^3+9750 x^4+1550 x^5+100 x^6\right )\right )+e^{\frac {81 x+107 x^2+54 x^3+12 x^4+x^5+e^{2 x} \left (81 x+108 x^2+54 x^3+12 x^4+x^5\right )}{81+108 x+54 x^2+12 x^3+x^4}} \left (75330+126180 x+88290 x^2+30620 x^3+5550 x^4+460 x^5+10 x^6+e^{2 x} \left (72900+269730 x+332910 x^2+199800 x^3+64800 x^4+11250 x^5+910 x^6+20 x^7\right )\right )}{6075+10125 x+6750 x^2+2250 x^3+375 x^4+25 x^5} \, dx=\frac {1}{25} \, x^{2} + \frac {2}{5} \, {\left (x + 30\right )} e^{\left (\frac {x^{5} + 12 \, x^{4} + 54 \, x^{3} + 107 \, x^{2} + {\left (x^{5} + 12 \, x^{4} + 54 \, x^{3} + 108 \, x^{2} + 81 \, x\right )} e^{\left (2 \, x\right )} + 81 \, x}{x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81}\right )} + \frac {12}{5} \, x + e^{\left (\frac {2 \, {\left (x^{5} + 12 \, x^{4} + 54 \, x^{3} + 107 \, x^{2} + {\left (x^{5} + 12 \, x^{4} + 54 \, x^{3} + 108 \, x^{2} + 81 \, x\right )} e^{\left (2 \, x\right )} + 81 \, x\right )}}{x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81}\right )} \end {dmath*}
integrate((((100*x^6+1550*x^5+9750*x^4+31500*x^3+54000*x^2+44550*x+12150)* exp(x)^2+50*x^5+750*x^4+4500*x^3+13600*x^2+19950*x+12150)*exp(((x^5+12*x^4 +54*x^3+108*x^2+81*x)*exp(x)^2+x^5+12*x^4+54*x^3+107*x^2+81*x)/(x^4+12*x^3 +54*x^2+108*x+81))^2+((20*x^7+910*x^6+11250*x^5+64800*x^4+199800*x^3+33291 0*x^2+269730*x+72900)*exp(x)^2+10*x^6+460*x^5+5550*x^4+30620*x^3+88290*x^2 +126180*x+75330)*exp(((x^5+12*x^4+54*x^3+108*x^2+81*x)*exp(x)^2+x^5+12*x^4 +54*x^3+107*x^2+81*x)/(x^4+12*x^3+54*x^2+108*x+81))+2*x^6+90*x^5+1080*x^4+ 5940*x^3+17010*x^2+24786*x+14580)/(25*x^5+375*x^4+2250*x^3+6750*x^2+10125* x+6075),x, algorithm=\
1/25*x^2 + 2/5*(x + 30)*e^((x^5 + 12*x^4 + 54*x^3 + 107*x^2 + (x^5 + 12*x^ 4 + 54*x^3 + 108*x^2 + 81*x)*e^(2*x) + 81*x)/(x^4 + 12*x^3 + 54*x^2 + 108* x + 81)) + 12/5*x + e^(2*(x^5 + 12*x^4 + 54*x^3 + 107*x^2 + (x^5 + 12*x^4 + 54*x^3 + 108*x^2 + 81*x)*e^(2*x) + 81*x)/(x^4 + 12*x^3 + 54*x^2 + 108*x + 81))
Leaf count of result is larger than twice the leaf count of optimal. 158 vs. \(2 (24) = 48\).
Time = 0.66 (sec) , antiderivative size = 158, normalized size of antiderivative = 5.27 \begin {dmath*} \int \frac {14580+24786 x+17010 x^2+5940 x^3+1080 x^4+90 x^5+2 x^6+e^{\frac {2 \left (81 x+107 x^2+54 x^3+12 x^4+x^5+e^{2 x} \left (81 x+108 x^2+54 x^3+12 x^4+x^5\right )\right )}{81+108 x+54 x^2+12 x^3+x^4}} \left (12150+19950 x+13600 x^2+4500 x^3+750 x^4+50 x^5+e^{2 x} \left (12150+44550 x+54000 x^2+31500 x^3+9750 x^4+1550 x^5+100 x^6\right )\right )+e^{\frac {81 x+107 x^2+54 x^3+12 x^4+x^5+e^{2 x} \left (81 x+108 x^2+54 x^3+12 x^4+x^5\right )}{81+108 x+54 x^2+12 x^3+x^4}} \left (75330+126180 x+88290 x^2+30620 x^3+5550 x^4+460 x^5+10 x^6+e^{2 x} \left (72900+269730 x+332910 x^2+199800 x^3+64800 x^4+11250 x^5+910 x^6+20 x^7\right )\right )}{6075+10125 x+6750 x^2+2250 x^3+375 x^4+25 x^5} \, dx=\frac {x^{2}}{25} + \frac {12 x}{5} + \frac {\left (2 x + 60\right ) e^{\frac {x^{5} + 12 x^{4} + 54 x^{3} + 107 x^{2} + 81 x + \left (x^{5} + 12 x^{4} + 54 x^{3} + 108 x^{2} + 81 x\right ) e^{2 x}}{x^{4} + 12 x^{3} + 54 x^{2} + 108 x + 81}}}{5} + e^{\frac {2 \left (x^{5} + 12 x^{4} + 54 x^{3} + 107 x^{2} + 81 x + \left (x^{5} + 12 x^{4} + 54 x^{3} + 108 x^{2} + 81 x\right ) e^{2 x}\right )}{x^{4} + 12 x^{3} + 54 x^{2} + 108 x + 81}} \end {dmath*}
integrate((((100*x**6+1550*x**5+9750*x**4+31500*x**3+54000*x**2+44550*x+12 150)*exp(x)**2+50*x**5+750*x**4+4500*x**3+13600*x**2+19950*x+12150)*exp((( x**5+12*x**4+54*x**3+108*x**2+81*x)*exp(x)**2+x**5+12*x**4+54*x**3+107*x** 2+81*x)/(x**4+12*x**3+54*x**2+108*x+81))**2+((20*x**7+910*x**6+11250*x**5+ 64800*x**4+199800*x**3+332910*x**2+269730*x+72900)*exp(x)**2+10*x**6+460*x **5+5550*x**4+30620*x**3+88290*x**2+126180*x+75330)*exp(((x**5+12*x**4+54* x**3+108*x**2+81*x)*exp(x)**2+x**5+12*x**4+54*x**3+107*x**2+81*x)/(x**4+12 *x**3+54*x**2+108*x+81))+2*x**6+90*x**5+1080*x**4+5940*x**3+17010*x**2+247 86*x+14580)/(25*x**5+375*x**4+2250*x**3+6750*x**2+10125*x+6075),x)
x**2/25 + 12*x/5 + (2*x + 60)*exp((x**5 + 12*x**4 + 54*x**3 + 107*x**2 + 8 1*x + (x**5 + 12*x**4 + 54*x**3 + 108*x**2 + 81*x)*exp(2*x))/(x**4 + 12*x* *3 + 54*x**2 + 108*x + 81))/5 + exp(2*(x**5 + 12*x**4 + 54*x**3 + 107*x**2 + 81*x + (x**5 + 12*x**4 + 54*x**3 + 108*x**2 + 81*x)*exp(2*x))/(x**4 + 1 2*x**3 + 54*x**2 + 108*x + 81))
Leaf count of result is larger than twice the leaf count of optimal. 370 vs. \(2 (28) = 56\).
Time = 0.85 (sec) , antiderivative size = 370, normalized size of antiderivative = 12.33 \begin {dmath*} \int \frac {14580+24786 x+17010 x^2+5940 x^3+1080 x^4+90 x^5+2 x^6+e^{\frac {2 \left (81 x+107 x^2+54 x^3+12 x^4+x^5+e^{2 x} \left (81 x+108 x^2+54 x^3+12 x^4+x^5\right )\right )}{81+108 x+54 x^2+12 x^3+x^4}} \left (12150+19950 x+13600 x^2+4500 x^3+750 x^4+50 x^5+e^{2 x} \left (12150+44550 x+54000 x^2+31500 x^3+9750 x^4+1550 x^5+100 x^6\right )\right )+e^{\frac {81 x+107 x^2+54 x^3+12 x^4+x^5+e^{2 x} \left (81 x+108 x^2+54 x^3+12 x^4+x^5\right )}{81+108 x+54 x^2+12 x^3+x^4}} \left (75330+126180 x+88290 x^2+30620 x^3+5550 x^4+460 x^5+10 x^6+e^{2 x} \left (72900+269730 x+332910 x^2+199800 x^3+64800 x^4+11250 x^5+910 x^6+20 x^7\right )\right )}{6075+10125 x+6750 x^2+2250 x^3+375 x^4+25 x^5} \, dx=\frac {1}{25} \, x^{2} + \frac {1}{5} \, {\left (2 \, {\left (x + 30\right )} e^{\left (x e^{\left (2 \, x\right )} + x - \frac {9}{x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81} + \frac {6}{x^{3} + 9 \, x^{2} + 27 \, x + 27} + \frac {1}{x^{2} + 6 \, x + 9}\right )} + 5 \, e^{\left (2 \, x e^{\left (2 \, x\right )} + 2 \, x - \frac {18}{x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81} + \frac {12}{x^{3} + 9 \, x^{2} + 27 \, x + 27}\right )}\right )} e^{\left (-\frac {2}{x^{2} + 6 \, x + 9}\right )} + \frac {12}{5} \, x + \frac {27 \, {\left (80 \, x^{3} + 630 \, x^{2} + 1692 \, x + 1539\right )}}{50 \, {\left (x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81\right )}} - \frac {81 \, {\left (40 \, x^{3} + 300 \, x^{2} + 780 \, x + 693\right )}}{10 \, {\left (x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81\right )}} + \frac {162 \, {\left (16 \, x^{3} + 108 \, x^{2} + 264 \, x + 225\right )}}{5 \, {\left (x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81\right )}} - \frac {297 \, {\left (4 \, x^{3} + 18 \, x^{2} + 36 \, x + 27\right )}}{5 \, {\left (x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81\right )}} - \frac {1701 \, {\left (2 \, x^{2} + 4 \, x + 3\right )}}{10 \, {\left (x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81\right )}} - \frac {4131 \, {\left (4 \, x + 3\right )}}{50 \, {\left (x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81\right )}} - \frac {729}{5 \, {\left (x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81\right )}} \end {dmath*}
integrate((((100*x^6+1550*x^5+9750*x^4+31500*x^3+54000*x^2+44550*x+12150)* exp(x)^2+50*x^5+750*x^4+4500*x^3+13600*x^2+19950*x+12150)*exp(((x^5+12*x^4 +54*x^3+108*x^2+81*x)*exp(x)^2+x^5+12*x^4+54*x^3+107*x^2+81*x)/(x^4+12*x^3 +54*x^2+108*x+81))^2+((20*x^7+910*x^6+11250*x^5+64800*x^4+199800*x^3+33291 0*x^2+269730*x+72900)*exp(x)^2+10*x^6+460*x^5+5550*x^4+30620*x^3+88290*x^2 +126180*x+75330)*exp(((x^5+12*x^4+54*x^3+108*x^2+81*x)*exp(x)^2+x^5+12*x^4 +54*x^3+107*x^2+81*x)/(x^4+12*x^3+54*x^2+108*x+81))+2*x^6+90*x^5+1080*x^4+ 5940*x^3+17010*x^2+24786*x+14580)/(25*x^5+375*x^4+2250*x^3+6750*x^2+10125* x+6075),x, algorithm=\
1/25*x^2 + 1/5*(2*(x + 30)*e^(x*e^(2*x) + x - 9/(x^4 + 12*x^3 + 54*x^2 + 1 08*x + 81) + 6/(x^3 + 9*x^2 + 27*x + 27) + 1/(x^2 + 6*x + 9)) + 5*e^(2*x*e ^(2*x) + 2*x - 18/(x^4 + 12*x^3 + 54*x^2 + 108*x + 81) + 12/(x^3 + 9*x^2 + 27*x + 27)))*e^(-2/(x^2 + 6*x + 9)) + 12/5*x + 27/50*(80*x^3 + 630*x^2 + 1692*x + 1539)/(x^4 + 12*x^3 + 54*x^2 + 108*x + 81) - 81/10*(40*x^3 + 300* x^2 + 780*x + 693)/(x^4 + 12*x^3 + 54*x^2 + 108*x + 81) + 162/5*(16*x^3 + 108*x^2 + 264*x + 225)/(x^4 + 12*x^3 + 54*x^2 + 108*x + 81) - 297/5*(4*x^3 + 18*x^2 + 36*x + 27)/(x^4 + 12*x^3 + 54*x^2 + 108*x + 81) - 1701/10*(2*x ^2 + 4*x + 3)/(x^4 + 12*x^3 + 54*x^2 + 108*x + 81) - 4131/50*(4*x + 3)/(x^ 4 + 12*x^3 + 54*x^2 + 108*x + 81) - 729/5/(x^4 + 12*x^3 + 54*x^2 + 108*x + 81)
\begin {dmath*} \int \frac {14580+24786 x+17010 x^2+5940 x^3+1080 x^4+90 x^5+2 x^6+e^{\frac {2 \left (81 x+107 x^2+54 x^3+12 x^4+x^5+e^{2 x} \left (81 x+108 x^2+54 x^3+12 x^4+x^5\right )\right )}{81+108 x+54 x^2+12 x^3+x^4}} \left (12150+19950 x+13600 x^2+4500 x^3+750 x^4+50 x^5+e^{2 x} \left (12150+44550 x+54000 x^2+31500 x^3+9750 x^4+1550 x^5+100 x^6\right )\right )+e^{\frac {81 x+107 x^2+54 x^3+12 x^4+x^5+e^{2 x} \left (81 x+108 x^2+54 x^3+12 x^4+x^5\right )}{81+108 x+54 x^2+12 x^3+x^4}} \left (75330+126180 x+88290 x^2+30620 x^3+5550 x^4+460 x^5+10 x^6+e^{2 x} \left (72900+269730 x+332910 x^2+199800 x^3+64800 x^4+11250 x^5+910 x^6+20 x^7\right )\right )}{6075+10125 x+6750 x^2+2250 x^3+375 x^4+25 x^5} \, dx=\int { \frac {2 \, {\left (x^{6} + 45 \, x^{5} + 540 \, x^{4} + 2970 \, x^{3} + 8505 \, x^{2} + 25 \, {\left (x^{5} + 15 \, x^{4} + 90 \, x^{3} + 272 \, x^{2} + {\left (2 \, x^{6} + 31 \, x^{5} + 195 \, x^{4} + 630 \, x^{3} + 1080 \, x^{2} + 891 \, x + 243\right )} e^{\left (2 \, x\right )} + 399 \, x + 243\right )} e^{\left (\frac {2 \, {\left (x^{5} + 12 \, x^{4} + 54 \, x^{3} + 107 \, x^{2} + {\left (x^{5} + 12 \, x^{4} + 54 \, x^{3} + 108 \, x^{2} + 81 \, x\right )} e^{\left (2 \, x\right )} + 81 \, x\right )}}{x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81}\right )} + 5 \, {\left (x^{6} + 46 \, x^{5} + 555 \, x^{4} + 3062 \, x^{3} + 8829 \, x^{2} + {\left (2 \, x^{7} + 91 \, x^{6} + 1125 \, x^{5} + 6480 \, x^{4} + 19980 \, x^{3} + 33291 \, x^{2} + 26973 \, x + 7290\right )} e^{\left (2 \, x\right )} + 12618 \, x + 7533\right )} e^{\left (\frac {x^{5} + 12 \, x^{4} + 54 \, x^{3} + 107 \, x^{2} + {\left (x^{5} + 12 \, x^{4} + 54 \, x^{3} + 108 \, x^{2} + 81 \, x\right )} e^{\left (2 \, x\right )} + 81 \, x}{x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81}\right )} + 12393 \, x + 7290\right )}}{25 \, {\left (x^{5} + 15 \, x^{4} + 90 \, x^{3} + 270 \, x^{2} + 405 \, x + 243\right )}} \,d x } \end {dmath*}
integrate((((100*x^6+1550*x^5+9750*x^4+31500*x^3+54000*x^2+44550*x+12150)* exp(x)^2+50*x^5+750*x^4+4500*x^3+13600*x^2+19950*x+12150)*exp(((x^5+12*x^4 +54*x^3+108*x^2+81*x)*exp(x)^2+x^5+12*x^4+54*x^3+107*x^2+81*x)/(x^4+12*x^3 +54*x^2+108*x+81))^2+((20*x^7+910*x^6+11250*x^5+64800*x^4+199800*x^3+33291 0*x^2+269730*x+72900)*exp(x)^2+10*x^6+460*x^5+5550*x^4+30620*x^3+88290*x^2 +126180*x+75330)*exp(((x^5+12*x^4+54*x^3+108*x^2+81*x)*exp(x)^2+x^5+12*x^4 +54*x^3+107*x^2+81*x)/(x^4+12*x^3+54*x^2+108*x+81))+2*x^6+90*x^5+1080*x^4+ 5940*x^3+17010*x^2+24786*x+14580)/(25*x^5+375*x^4+2250*x^3+6750*x^2+10125* x+6075),x, algorithm=\
integrate(2/25*(x^6 + 45*x^5 + 540*x^4 + 2970*x^3 + 8505*x^2 + 25*(x^5 + 1 5*x^4 + 90*x^3 + 272*x^2 + (2*x^6 + 31*x^5 + 195*x^4 + 630*x^3 + 1080*x^2 + 891*x + 243)*e^(2*x) + 399*x + 243)*e^(2*(x^5 + 12*x^4 + 54*x^3 + 107*x^ 2 + (x^5 + 12*x^4 + 54*x^3 + 108*x^2 + 81*x)*e^(2*x) + 81*x)/(x^4 + 12*x^3 + 54*x^2 + 108*x + 81)) + 5*(x^6 + 46*x^5 + 555*x^4 + 3062*x^3 + 8829*x^2 + (2*x^7 + 91*x^6 + 1125*x^5 + 6480*x^4 + 19980*x^3 + 33291*x^2 + 26973*x + 7290)*e^(2*x) + 12618*x + 7533)*e^((x^5 + 12*x^4 + 54*x^3 + 107*x^2 + ( x^5 + 12*x^4 + 54*x^3 + 108*x^2 + 81*x)*e^(2*x) + 81*x)/(x^4 + 12*x^3 + 54 *x^2 + 108*x + 81)) + 12393*x + 7290)/(x^5 + 15*x^4 + 90*x^3 + 270*x^2 + 4 05*x + 243), x)
Time = 14.18 (sec) , antiderivative size = 549, normalized size of antiderivative = 18.30 \begin {dmath*} \int \frac {14580+24786 x+17010 x^2+5940 x^3+1080 x^4+90 x^5+2 x^6+e^{\frac {2 \left (81 x+107 x^2+54 x^3+12 x^4+x^5+e^{2 x} \left (81 x+108 x^2+54 x^3+12 x^4+x^5\right )\right )}{81+108 x+54 x^2+12 x^3+x^4}} \left (12150+19950 x+13600 x^2+4500 x^3+750 x^4+50 x^5+e^{2 x} \left (12150+44550 x+54000 x^2+31500 x^3+9750 x^4+1550 x^5+100 x^6\right )\right )+e^{\frac {81 x+107 x^2+54 x^3+12 x^4+x^5+e^{2 x} \left (81 x+108 x^2+54 x^3+12 x^4+x^5\right )}{81+108 x+54 x^2+12 x^3+x^4}} \left (75330+126180 x+88290 x^2+30620 x^3+5550 x^4+460 x^5+10 x^6+e^{2 x} \left (72900+269730 x+332910 x^2+199800 x^3+64800 x^4+11250 x^5+910 x^6+20 x^7\right )\right )}{6075+10125 x+6750 x^2+2250 x^3+375 x^4+25 x^5} \, dx=\frac {12\,x}{5}+{\mathrm {e}}^{\frac {214\,x^2}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {108\,x^3}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {24\,x^4}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {2\,x^5}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {162\,x}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {216\,x^2\,{\mathrm {e}}^{2\,x}}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {108\,x^3\,{\mathrm {e}}^{2\,x}}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {24\,x^4\,{\mathrm {e}}^{2\,x}}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {2\,x^5\,{\mathrm {e}}^{2\,x}}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {162\,x\,{\mathrm {e}}^{2\,x}}{x^4+12\,x^3+54\,x^2+108\,x+81}}+{\mathrm {e}}^{\frac {107\,x^2}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {54\,x^3}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {12\,x^4}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {x^5}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {81\,x}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {108\,x^2\,{\mathrm {e}}^{2\,x}}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {54\,x^3\,{\mathrm {e}}^{2\,x}}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {12\,x^4\,{\mathrm {e}}^{2\,x}}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {x^5\,{\mathrm {e}}^{2\,x}}{x^4+12\,x^3+54\,x^2+108\,x+81}+\frac {81\,x\,{\mathrm {e}}^{2\,x}}{x^4+12\,x^3+54\,x^2+108\,x+81}}\,\left (\frac {2\,x}{5}+12\right )+\frac {x^2}{25} \end {dmath*}
int((24786*x + exp((81*x + exp(2*x)*(81*x + 108*x^2 + 54*x^3 + 12*x^4 + x^ 5) + 107*x^2 + 54*x^3 + 12*x^4 + x^5)/(108*x + 54*x^2 + 12*x^3 + x^4 + 81) )*(126180*x + exp(2*x)*(269730*x + 332910*x^2 + 199800*x^3 + 64800*x^4 + 1 1250*x^5 + 910*x^6 + 20*x^7 + 72900) + 88290*x^2 + 30620*x^3 + 5550*x^4 + 460*x^5 + 10*x^6 + 75330) + 17010*x^2 + 5940*x^3 + 1080*x^4 + 90*x^5 + 2*x ^6 + exp((2*(81*x + exp(2*x)*(81*x + 108*x^2 + 54*x^3 + 12*x^4 + x^5) + 10 7*x^2 + 54*x^3 + 12*x^4 + x^5))/(108*x + 54*x^2 + 12*x^3 + x^4 + 81))*(199 50*x + 13600*x^2 + 4500*x^3 + 750*x^4 + 50*x^5 + exp(2*x)*(44550*x + 54000 *x^2 + 31500*x^3 + 9750*x^4 + 1550*x^5 + 100*x^6 + 12150) + 12150) + 14580 )/(10125*x + 6750*x^2 + 2250*x^3 + 375*x^4 + 25*x^5 + 6075),x)
(12*x)/5 + exp((214*x^2)/(108*x + 54*x^2 + 12*x^3 + x^4 + 81) + (108*x^3)/ (108*x + 54*x^2 + 12*x^3 + x^4 + 81) + (24*x^4)/(108*x + 54*x^2 + 12*x^3 + x^4 + 81) + (2*x^5)/(108*x + 54*x^2 + 12*x^3 + x^4 + 81) + (162*x)/(108*x + 54*x^2 + 12*x^3 + x^4 + 81) + (216*x^2*exp(2*x))/(108*x + 54*x^2 + 12*x ^3 + x^4 + 81) + (108*x^3*exp(2*x))/(108*x + 54*x^2 + 12*x^3 + x^4 + 81) + (24*x^4*exp(2*x))/(108*x + 54*x^2 + 12*x^3 + x^4 + 81) + (2*x^5*exp(2*x)) /(108*x + 54*x^2 + 12*x^3 + x^4 + 81) + (162*x*exp(2*x))/(108*x + 54*x^2 + 12*x^3 + x^4 + 81)) + exp((107*x^2)/(108*x + 54*x^2 + 12*x^3 + x^4 + 81) + (54*x^3)/(108*x + 54*x^2 + 12*x^3 + x^4 + 81) + (12*x^4)/(108*x + 54*x^2 + 12*x^3 + x^4 + 81) + x^5/(108*x + 54*x^2 + 12*x^3 + x^4 + 81) + (81*x)/ (108*x + 54*x^2 + 12*x^3 + x^4 + 81) + (108*x^2*exp(2*x))/(108*x + 54*x^2 + 12*x^3 + x^4 + 81) + (54*x^3*exp(2*x))/(108*x + 54*x^2 + 12*x^3 + x^4 + 81) + (12*x^4*exp(2*x))/(108*x + 54*x^2 + 12*x^3 + x^4 + 81) + (x^5*exp(2* x))/(108*x + 54*x^2 + 12*x^3 + x^4 + 81) + (81*x*exp(2*x))/(108*x + 54*x^2 + 12*x^3 + x^4 + 81))*((2*x)/5 + 12) + x^2/25