Integrand size = 238, antiderivative size = 34 \[ \int \frac {108 x+126 x^2+36 x^3+50 x^5+\left (100 x^3+150 x^4+50 x^5\right ) \log (3)+e^{3 x} \left (-50 x^2+\left (-100-150 x-50 x^2\right ) \log (3)\right )+e^{2 x} \left (150 x^3+\left (300 x+450 x^2+150 x^3\right ) \log (3)\right )+e^x \left (-36-126 x-90 x^2-18 x^3-150 x^4+\left (-300 x^2-450 x^3-150 x^4\right ) \log (3)\right )}{-200 x^5-300 x^6-150 x^7-25 x^8+e^{3 x} \left (200 x^2+300 x^3+150 x^4+25 x^5\right )+e^{2 x} \left (-600 x^3-900 x^4-450 x^5-75 x^6\right )+e^x \left (600 x^4+900 x^5+450 x^6+75 x^7\right )} \, dx=3+\frac {\frac {x}{2+x}+\frac {9}{25 \left (-e^x+x\right )^2}+\log (3)}{x (2+x)} \]
\[ \int \frac {108 x+126 x^2+36 x^3+50 x^5+\left (100 x^3+150 x^4+50 x^5\right ) \log (3)+e^{3 x} \left (-50 x^2+\left (-100-150 x-50 x^2\right ) \log (3)\right )+e^{2 x} \left (150 x^3+\left (300 x+450 x^2+150 x^3\right ) \log (3)\right )+e^x \left (-36-126 x-90 x^2-18 x^3-150 x^4+\left (-300 x^2-450 x^3-150 x^4\right ) \log (3)\right )}{-200 x^5-300 x^6-150 x^7-25 x^8+e^{3 x} \left (200 x^2+300 x^3+150 x^4+25 x^5\right )+e^{2 x} \left (-600 x^3-900 x^4-450 x^5-75 x^6\right )+e^x \left (600 x^4+900 x^5+450 x^6+75 x^7\right )} \, dx=\int \frac {108 x+126 x^2+36 x^3+50 x^5+\left (100 x^3+150 x^4+50 x^5\right ) \log (3)+e^{3 x} \left (-50 x^2+\left (-100-150 x-50 x^2\right ) \log (3)\right )+e^{2 x} \left (150 x^3+\left (300 x+450 x^2+150 x^3\right ) \log (3)\right )+e^x \left (-36-126 x-90 x^2-18 x^3-150 x^4+\left (-300 x^2-450 x^3-150 x^4\right ) \log (3)\right )}{-200 x^5-300 x^6-150 x^7-25 x^8+e^{3 x} \left (200 x^2+300 x^3+150 x^4+25 x^5\right )+e^{2 x} \left (-600 x^3-900 x^4-450 x^5-75 x^6\right )+e^x \left (600 x^4+900 x^5+450 x^6+75 x^7\right )} \, dx \]
Integrate[(108*x + 126*x^2 + 36*x^3 + 50*x^5 + (100*x^3 + 150*x^4 + 50*x^5 )*Log[3] + E^(3*x)*(-50*x^2 + (-100 - 150*x - 50*x^2)*Log[3]) + E^(2*x)*(1 50*x^3 + (300*x + 450*x^2 + 150*x^3)*Log[3]) + E^x*(-36 - 126*x - 90*x^2 - 18*x^3 - 150*x^4 + (-300*x^2 - 450*x^3 - 150*x^4)*Log[3]))/(-200*x^5 - 30 0*x^6 - 150*x^7 - 25*x^8 + E^(3*x)*(200*x^2 + 300*x^3 + 150*x^4 + 25*x^5) + E^(2*x)*(-600*x^3 - 900*x^4 - 450*x^5 - 75*x^6) + E^x*(600*x^4 + 900*x^5 + 450*x^6 + 75*x^7)),x]
Integrate[(108*x + 126*x^2 + 36*x^3 + 50*x^5 + (100*x^3 + 150*x^4 + 50*x^5 )*Log[3] + E^(3*x)*(-50*x^2 + (-100 - 150*x - 50*x^2)*Log[3]) + E^(2*x)*(1 50*x^3 + (300*x + 450*x^2 + 150*x^3)*Log[3]) + E^x*(-36 - 126*x - 90*x^2 - 18*x^3 - 150*x^4 + (-300*x^2 - 450*x^3 - 150*x^4)*Log[3]))/(-200*x^5 - 30 0*x^6 - 150*x^7 - 25*x^8 + E^(3*x)*(200*x^2 + 300*x^3 + 150*x^4 + 25*x^5) + E^(2*x)*(-600*x^3 - 900*x^4 - 450*x^5 - 75*x^6) + E^x*(600*x^4 + 900*x^5 + 450*x^6 + 75*x^7)), x]
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.
| \(\displaystyle \int \frac {50 x^5+36 x^3+126 x^2+e^{3 x} \left (\left (-50 x^2-150 x-100\right ) \log (3)-50 x^2\right )+e^{2 x} \left (150 x^3+\left (150 x^3+450 x^2+300 x\right ) \log (3)\right )+\left (50 x^5+150 x^4+100 x^3\right ) \log (3)+e^x \left (-150 x^4-18 x^3-90 x^2+\left (-150 x^4-450 x^3-300 x^2\right ) \log (3)-126 x-36\right )+108 x}{-25 x^8-150 x^7-300 x^6-200 x^5+e^x \left (75 x^7+450 x^6+900 x^5+600 x^4\right )+e^{2 x} \left (-75 x^6-450 x^5-900 x^4-600 x^3\right )+e^{3 x} \left (25 x^5+150 x^4+300 x^3+200 x^2\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-50 e^{3 x} \left (x^2 (1+\log (3))+x \log (27)+\log (9)\right )+150 e^{2 x} x \left (x^2 (1+\log (3))+x \log (27)+\log (9)\right )+2 x \left (25 x^4 (1+\log (3))+75 x^3 \log (3)+2 x^2 (9+25 \log (3))+63 x+54\right )-6 e^x \left (25 x^4 (1+\log (3))+x^3 (3+75 \log (3))+5 x^2 (3+10 \log (3))+21 x+6\right )}{25 \left (e^x-x\right )^3 x^2 (x+2)^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{25} \int -\frac {2 \left (3 e^x \left (25 (1+\log (3)) x^4+3 (1+25 \log (3)) x^3+5 (3+10 \log (3)) x^2+21 x+6\right )-x \left (25 (1+\log (3)) x^4+75 \log (3) x^3+2 (9+25 \log (3)) x^2+63 x+54\right )+25 e^{3 x} \left ((1+\log (3)) x^2+\log (27) x+\log (9)\right )-75 e^{2 x} x \left ((1+\log (3)) x^2+\log (27) x+\log (9)\right )\right )}{\left (e^x-x\right )^3 x^2 (x+2)^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -\frac {2}{25} \int \frac {3 e^x \left (25 (1+\log (3)) x^4+3 (1+25 \log (3)) x^3+5 (3+10 \log (3)) x^2+21 x+6\right )-x \left (25 (1+\log (3)) x^4+75 \log (3) x^3+2 (9+25 \log (3)) x^2+63 x+54\right )+25 e^{3 x} \left ((1+\log (3)) x^2+\log (27) x+\log (9)\right )-75 e^{2 x} x \left ((1+\log (3)) x^2+\log (27) x+\log (9)\right )}{\left (e^x-x\right )^3 x^2 (x+2)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {2}{25} \int \left (\frac {9 (x-1)}{\left (e^x-x\right )^3 x (x+2)}+\frac {9 \left (x^2+3 x+1\right )}{\left (e^x-x\right )^2 x^2 (x+2)^2}+\frac {25 \left ((1+\log (3)) x^2+\log (27) x+\log (9)\right )}{x^2 (x+2)^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {2}{25} \left (\frac {9}{4} \int \frac {1}{\left (e^x-x\right )^2 x^2}dx+\frac {9}{2} \int \frac {1}{\left (e^x-x\right )^2 x}dx-\frac {9}{4} \int \frac {1}{\left (e^x-x\right )^2 (x+2)^2}dx+\frac {27}{2} \int \frac {1}{\left (e^x-x\right )^3 (x+2)}dx-\frac {9}{2} \int \frac {1}{\left (e^x-x\right )^2 (x+2)}dx+\frac {9}{2} \int \frac {1}{x \left (x-e^x\right )^3}dx-\frac {25}{2 (x+2)^2}-\frac {25 \log (9)}{8 x}+\frac {25 \log (3)}{4 (x+2)}\right )\) |
Int[(108*x + 126*x^2 + 36*x^3 + 50*x^5 + (100*x^3 + 150*x^4 + 50*x^5)*Log[ 3] + E^(3*x)*(-50*x^2 + (-100 - 150*x - 50*x^2)*Log[3]) + E^(2*x)*(150*x^3 + (300*x + 450*x^2 + 150*x^3)*Log[3]) + E^x*(-36 - 126*x - 90*x^2 - 18*x^ 3 - 150*x^4 + (-300*x^2 - 450*x^3 - 150*x^4)*Log[3]))/(-200*x^5 - 300*x^6 - 150*x^7 - 25*x^8 + E^(3*x)*(200*x^2 + 300*x^3 + 150*x^4 + 25*x^5) + E^(2 *x)*(-600*x^3 - 900*x^4 - 450*x^5 - 75*x^6) + E^x*(600*x^4 + 900*x^5 + 450 *x^6 + 75*x^7)),x]
3.29.12.3.1 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_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 0.22 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.32
| method | result | size |
| risch | \(\frac {\left (\ln \left (3\right )+1\right ) x +2 \ln \left (3\right )}{x \left (x^{2}+4 x +4\right )}+\frac {9}{25 x \left (2+x \right ) \left (x -{\mathrm e}^{x}\right )^{2}}\) | \(45\) |
| parallelrisch | \(\frac {25 \ln \left (3\right ) {\mathrm e}^{2 x} x -50 x^{2} \ln \left (3\right ) {\mathrm e}^{x}+25 x^{3} \ln \left (3\right )+50 \ln \left (3\right ) {\mathrm e}^{2 x}+25 x \,{\mathrm e}^{2 x}-100 x \ln \left (3\right ) {\mathrm e}^{x}-50 \,{\mathrm e}^{x} x^{2}+50 x^{2} \ln \left (3\right )+25 x^{3}+9 x +18}{25 x \left (x^{4}-2 \,{\mathrm e}^{x} x^{3}+{\mathrm e}^{2 x} x^{2}+4 x^{3}-8 \,{\mathrm e}^{x} x^{2}+4 x \,{\mathrm e}^{2 x}+4 x^{2}-8 \,{\mathrm e}^{x} x +4 \,{\mathrm e}^{2 x}\right )}\) | \(133\) |
int((((-50*x^2-150*x-100)*ln(3)-50*x^2)*exp(x)^3+((150*x^3+450*x^2+300*x)* ln(3)+150*x^3)*exp(x)^2+((-150*x^4-450*x^3-300*x^2)*ln(3)-150*x^4-18*x^3-9 0*x^2-126*x-36)*exp(x)+(50*x^5+150*x^4+100*x^3)*ln(3)+50*x^5+36*x^3+126*x^ 2+108*x)/((25*x^5+150*x^4+300*x^3+200*x^2)*exp(x)^3+(-75*x^6-450*x^5-900*x ^4-600*x^3)*exp(x)^2+(75*x^7+450*x^6+900*x^5+600*x^4)*exp(x)-25*x^8-150*x^ 7-300*x^6-200*x^5),x,method=_RETURNVERBOSE)
Leaf count of result is larger than twice the leaf count of optimal. 108 vs. \(2 (35) = 70\).
Time = 0.27 (sec) , antiderivative size = 108, normalized size of antiderivative = 3.18 \[ \int \frac {108 x+126 x^2+36 x^3+50 x^5+\left (100 x^3+150 x^4+50 x^5\right ) \log (3)+e^{3 x} \left (-50 x^2+\left (-100-150 x-50 x^2\right ) \log (3)\right )+e^{2 x} \left (150 x^3+\left (300 x+450 x^2+150 x^3\right ) \log (3)\right )+e^x \left (-36-126 x-90 x^2-18 x^3-150 x^4+\left (-300 x^2-450 x^3-150 x^4\right ) \log (3)\right )}{-200 x^5-300 x^6-150 x^7-25 x^8+e^{3 x} \left (200 x^2+300 x^3+150 x^4+25 x^5\right )+e^{2 x} \left (-600 x^3-900 x^4-450 x^5-75 x^6\right )+e^x \left (600 x^4+900 x^5+450 x^6+75 x^7\right )} \, dx=\frac {25 \, x^{3} + 25 \, {\left ({\left (x + 2\right )} \log \left (3\right ) + x\right )} e^{\left (2 \, x\right )} - 50 \, {\left (x^{2} + {\left (x^{2} + 2 \, x\right )} \log \left (3\right )\right )} e^{x} + 25 \, {\left (x^{3} + 2 \, x^{2}\right )} \log \left (3\right ) + 9 \, x + 18}{25 \, {\left (x^{5} + 4 \, x^{4} + 4 \, x^{3} + {\left (x^{3} + 4 \, x^{2} + 4 \, x\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{4} + 4 \, x^{3} + 4 \, x^{2}\right )} e^{x}\right )}} \]
integrate((((-50*x^2-150*x-100)*log(3)-50*x^2)*exp(x)^3+((150*x^3+450*x^2+ 300*x)*log(3)+150*x^3)*exp(x)^2+((-150*x^4-450*x^3-300*x^2)*log(3)-150*x^4 -18*x^3-90*x^2-126*x-36)*exp(x)+(50*x^5+150*x^4+100*x^3)*log(3)+50*x^5+36* x^3+126*x^2+108*x)/((25*x^5+150*x^4+300*x^3+200*x^2)*exp(x)^3+(-75*x^6-450 *x^5-900*x^4-600*x^3)*exp(x)^2+(75*x^7+450*x^6+900*x^5+600*x^4)*exp(x)-25* x^8-150*x^7-300*x^6-200*x^5),x, algorithm=\
1/25*(25*x^3 + 25*((x + 2)*log(3) + x)*e^(2*x) - 50*(x^2 + (x^2 + 2*x)*log (3))*e^x + 25*(x^3 + 2*x^2)*log(3) + 9*x + 18)/(x^5 + 4*x^4 + 4*x^3 + (x^3 + 4*x^2 + 4*x)*e^(2*x) - 2*(x^4 + 4*x^3 + 4*x^2)*e^x)
Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (26) = 52\).
Time = 0.32 (sec) , antiderivative size = 65, normalized size of antiderivative = 1.91 \[ \int \frac {108 x+126 x^2+36 x^3+50 x^5+\left (100 x^3+150 x^4+50 x^5\right ) \log (3)+e^{3 x} \left (-50 x^2+\left (-100-150 x-50 x^2\right ) \log (3)\right )+e^{2 x} \left (150 x^3+\left (300 x+450 x^2+150 x^3\right ) \log (3)\right )+e^x \left (-36-126 x-90 x^2-18 x^3-150 x^4+\left (-300 x^2-450 x^3-150 x^4\right ) \log (3)\right )}{-200 x^5-300 x^6-150 x^7-25 x^8+e^{3 x} \left (200 x^2+300 x^3+150 x^4+25 x^5\right )+e^{2 x} \left (-600 x^3-900 x^4-450 x^5-75 x^6\right )+e^x \left (600 x^4+900 x^5+450 x^6+75 x^7\right )} \, dx=- \frac {x \left (- \log {\left (3 \right )} - 1\right ) - 2 \log {\left (3 \right )}}{x^{3} + 4 x^{2} + 4 x} + \frac {9}{25 x^{4} + 50 x^{3} + \left (25 x^{2} + 50 x\right ) e^{2 x} + \left (- 50 x^{3} - 100 x^{2}\right ) e^{x}} \]
integrate((((-50*x**2-150*x-100)*ln(3)-50*x**2)*exp(x)**3+((150*x**3+450*x **2+300*x)*ln(3)+150*x**3)*exp(x)**2+((-150*x**4-450*x**3-300*x**2)*ln(3)- 150*x**4-18*x**3-90*x**2-126*x-36)*exp(x)+(50*x**5+150*x**4+100*x**3)*ln(3 )+50*x**5+36*x**3+126*x**2+108*x)/((25*x**5+150*x**4+300*x**3+200*x**2)*ex p(x)**3+(-75*x**6-450*x**5-900*x**4-600*x**3)*exp(x)**2+(75*x**7+450*x**6+ 900*x**5+600*x**4)*exp(x)-25*x**8-150*x**7-300*x**6-200*x**5),x)
-(x*(-log(3) - 1) - 2*log(3))/(x**3 + 4*x**2 + 4*x) + 9/(25*x**4 + 50*x**3 + (25*x**2 + 50*x)*exp(2*x) + (-50*x**3 - 100*x**2)*exp(x))
Leaf count of result is larger than twice the leaf count of optimal. 109 vs. \(2 (35) = 70\).
Time = 0.40 (sec) , antiderivative size = 109, normalized size of antiderivative = 3.21 \[ \int \frac {108 x+126 x^2+36 x^3+50 x^5+\left (100 x^3+150 x^4+50 x^5\right ) \log (3)+e^{3 x} \left (-50 x^2+\left (-100-150 x-50 x^2\right ) \log (3)\right )+e^{2 x} \left (150 x^3+\left (300 x+450 x^2+150 x^3\right ) \log (3)\right )+e^x \left (-36-126 x-90 x^2-18 x^3-150 x^4+\left (-300 x^2-450 x^3-150 x^4\right ) \log (3)\right )}{-200 x^5-300 x^6-150 x^7-25 x^8+e^{3 x} \left (200 x^2+300 x^3+150 x^4+25 x^5\right )+e^{2 x} \left (-600 x^3-900 x^4-450 x^5-75 x^6\right )+e^x \left (600 x^4+900 x^5+450 x^6+75 x^7\right )} \, dx=\frac {25 \, x^{3} {\left (\log \left (3\right ) + 1\right )} + 50 \, x^{2} \log \left (3\right ) + 25 \, {\left (x {\left (\log \left (3\right ) + 1\right )} + 2 \, \log \left (3\right )\right )} e^{\left (2 \, x\right )} - 50 \, {\left (x^{2} {\left (\log \left (3\right ) + 1\right )} + 2 \, x \log \left (3\right )\right )} e^{x} + 9 \, x + 18}{25 \, {\left (x^{5} + 4 \, x^{4} + 4 \, x^{3} + {\left (x^{3} + 4 \, x^{2} + 4 \, x\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{4} + 4 \, x^{3} + 4 \, x^{2}\right )} e^{x}\right )}} \]
integrate((((-50*x^2-150*x-100)*log(3)-50*x^2)*exp(x)^3+((150*x^3+450*x^2+ 300*x)*log(3)+150*x^3)*exp(x)^2+((-150*x^4-450*x^3-300*x^2)*log(3)-150*x^4 -18*x^3-90*x^2-126*x-36)*exp(x)+(50*x^5+150*x^4+100*x^3)*log(3)+50*x^5+36* x^3+126*x^2+108*x)/((25*x^5+150*x^4+300*x^3+200*x^2)*exp(x)^3+(-75*x^6-450 *x^5-900*x^4-600*x^3)*exp(x)^2+(75*x^7+450*x^6+900*x^5+600*x^4)*exp(x)-25* x^8-150*x^7-300*x^6-200*x^5),x, algorithm=\
1/25*(25*x^3*(log(3) + 1) + 50*x^2*log(3) + 25*(x*(log(3) + 1) + 2*log(3)) *e^(2*x) - 50*(x^2*(log(3) + 1) + 2*x*log(3))*e^x + 9*x + 18)/(x^5 + 4*x^4 + 4*x^3 + (x^3 + 4*x^2 + 4*x)*e^(2*x) - 2*(x^4 + 4*x^3 + 4*x^2)*e^x)
Leaf count of result is larger than twice the leaf count of optimal. 134 vs. \(2 (35) = 70\).
Time = 0.29 (sec) , antiderivative size = 134, normalized size of antiderivative = 3.94 \[ \int \frac {108 x+126 x^2+36 x^3+50 x^5+\left (100 x^3+150 x^4+50 x^5\right ) \log (3)+e^{3 x} \left (-50 x^2+\left (-100-150 x-50 x^2\right ) \log (3)\right )+e^{2 x} \left (150 x^3+\left (300 x+450 x^2+150 x^3\right ) \log (3)\right )+e^x \left (-36-126 x-90 x^2-18 x^3-150 x^4+\left (-300 x^2-450 x^3-150 x^4\right ) \log (3)\right )}{-200 x^5-300 x^6-150 x^7-25 x^8+e^{3 x} \left (200 x^2+300 x^3+150 x^4+25 x^5\right )+e^{2 x} \left (-600 x^3-900 x^4-450 x^5-75 x^6\right )+e^x \left (600 x^4+900 x^5+450 x^6+75 x^7\right )} \, dx=\frac {25 \, x^{3} \log \left (3\right ) - 50 \, x^{2} e^{x} \log \left (3\right ) + 25 \, x^{3} - 50 \, x^{2} e^{x} + 50 \, x^{2} \log \left (3\right ) + 25 \, x e^{\left (2 \, x\right )} \log \left (3\right ) - 100 \, x e^{x} \log \left (3\right ) + 25 \, x e^{\left (2 \, x\right )} + 50 \, e^{\left (2 \, x\right )} \log \left (3\right ) + 9 \, x + 18}{25 \, {\left (x^{5} - 2 \, x^{4} e^{x} + 4 \, x^{4} + x^{3} e^{\left (2 \, x\right )} - 8 \, x^{3} e^{x} + 4 \, x^{3} + 4 \, x^{2} e^{\left (2 \, x\right )} - 8 \, x^{2} e^{x} + 4 \, x e^{\left (2 \, x\right )}\right )}} \]
integrate((((-50*x^2-150*x-100)*log(3)-50*x^2)*exp(x)^3+((150*x^3+450*x^2+ 300*x)*log(3)+150*x^3)*exp(x)^2+((-150*x^4-450*x^3-300*x^2)*log(3)-150*x^4 -18*x^3-90*x^2-126*x-36)*exp(x)+(50*x^5+150*x^4+100*x^3)*log(3)+50*x^5+36* x^3+126*x^2+108*x)/((25*x^5+150*x^4+300*x^3+200*x^2)*exp(x)^3+(-75*x^6-450 *x^5-900*x^4-600*x^3)*exp(x)^2+(75*x^7+450*x^6+900*x^5+600*x^4)*exp(x)-25* x^8-150*x^7-300*x^6-200*x^5),x, algorithm=\
1/25*(25*x^3*log(3) - 50*x^2*e^x*log(3) + 25*x^3 - 50*x^2*e^x + 50*x^2*log (3) + 25*x*e^(2*x)*log(3) - 100*x*e^x*log(3) + 25*x*e^(2*x) + 50*e^(2*x)*l og(3) + 9*x + 18)/(x^5 - 2*x^4*e^x + 4*x^4 + x^3*e^(2*x) - 8*x^3*e^x + 4*x ^3 + 4*x^2*e^(2*x) - 8*x^2*e^x + 4*x*e^(2*x))
Time = 9.55 (sec) , antiderivative size = 99, normalized size of antiderivative = 2.91 \[ \int \frac {108 x+126 x^2+36 x^3+50 x^5+\left (100 x^3+150 x^4+50 x^5\right ) \log (3)+e^{3 x} \left (-50 x^2+\left (-100-150 x-50 x^2\right ) \log (3)\right )+e^{2 x} \left (150 x^3+\left (300 x+450 x^2+150 x^3\right ) \log (3)\right )+e^x \left (-36-126 x-90 x^2-18 x^3-150 x^4+\left (-300 x^2-450 x^3-150 x^4\right ) \log (3)\right )}{-200 x^5-300 x^6-150 x^7-25 x^8+e^{3 x} \left (200 x^2+300 x^3+150 x^4+25 x^5\right )+e^{2 x} \left (-600 x^3-900 x^4-450 x^5-75 x^6\right )+e^x \left (600 x^4+900 x^5+450 x^6+75 x^7\right )} \, dx=\frac {2\,\ln \left (3\right )+x\,\left (\frac {\ln \left (9\right )}{2}+1\right )}{x^3+4\,x^2+4\,x}+\frac {3\,\left (50\,x^2\,\ln \left (3\right )+75\,x^3\,\ln \left (3\right )-25\,x^2\,\ln \left (9\right )-25\,x^3\,\ln \left (27\right )+9\,x^2+3\,x^3-12\right )}{25\,x\,\left (x-1\right )\,{\left (x+2\right )}^3\,\left ({\mathrm {e}}^{2\,x}-2\,x\,{\mathrm {e}}^x+x^2\right )} \]
int(-(108*x - exp(3*x)*(log(3)*(150*x + 50*x^2 + 100) + 50*x^2) + exp(2*x) *(log(3)*(300*x + 450*x^2 + 150*x^3) + 150*x^3) + log(3)*(100*x^3 + 150*x^ 4 + 50*x^5) + 126*x^2 + 36*x^3 + 50*x^5 - exp(x)*(126*x + log(3)*(300*x^2 + 450*x^3 + 150*x^4) + 90*x^2 + 18*x^3 + 150*x^4 + 36))/(exp(2*x)*(600*x^3 + 900*x^4 + 450*x^5 + 75*x^6) - exp(3*x)*(200*x^2 + 300*x^3 + 150*x^4 + 2 5*x^5) - exp(x)*(600*x^4 + 900*x^5 + 450*x^6 + 75*x^7) + 200*x^5 + 300*x^6 + 150*x^7 + 25*x^8),x)