Integrand size = 233, antiderivative size = 30 \[ \int \frac {-512-448 x-226 x^2-56 x^3-8 x^4+e^x \left (160-218 x-202 x^2-142 x^3-40 x^4-8 x^5+\left (-32-14 x-4 x^2\right ) \log (2)\right )+e^{2 x} \left (90 x+30 x^2+20 x^3+\left (-18 x-6 x^2-4 x^3\right ) \log (2)\right )+\left (160+294 x+246 x^2+84 x^3+16 x^4+\left (-32-14 x-4 x^2\right ) \log (2)+e^x \left (20 x-10 x^2+20 x^3+\left (-4 x+2 x^2-4 x^3\right ) \log (2)\right )\right ) \log (x)+\left (-70 x-40 x^2+\left (14 x+8 x^2\right ) \log (2)\right ) \log ^2(x)}{e^{3 x} x+3 e^{2 x} x \log (x)+3 e^x x \log ^2(x)+x \log ^3(x)} \, dx=\left (-5+\log (2)-\frac {x-x^2-(4+x)^2}{e^x+\log (x)}\right )^2 \]
Time = 5.11 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.47 \[ \int \frac {-512-448 x-226 x^2-56 x^3-8 x^4+e^x \left (160-218 x-202 x^2-142 x^3-40 x^4-8 x^5+\left (-32-14 x-4 x^2\right ) \log (2)\right )+e^{2 x} \left (90 x+30 x^2+20 x^3+\left (-18 x-6 x^2-4 x^3\right ) \log (2)\right )+\left (160+294 x+246 x^2+84 x^3+16 x^4+\left (-32-14 x-4 x^2\right ) \log (2)+e^x \left (20 x-10 x^2+20 x^3+\left (-4 x+2 x^2-4 x^3\right ) \log (2)\right )\right ) \log (x)+\left (-70 x-40 x^2+\left (14 x+8 x^2\right ) \log (2)\right ) \log ^2(x)}{e^{3 x} x+3 e^{2 x} x \log (x)+3 e^x x \log ^2(x)+x \log ^3(x)} \, dx=\frac {\left (16+7 x+2 x^2\right ) \left (16+7 x+2 x^2+e^x (-10+\log (4))+(-10+\log (4)) \log (x)\right )}{\left (e^x+\log (x)\right )^2} \]
Integrate[(-512 - 448*x - 226*x^2 - 56*x^3 - 8*x^4 + E^x*(160 - 218*x - 20 2*x^2 - 142*x^3 - 40*x^4 - 8*x^5 + (-32 - 14*x - 4*x^2)*Log[2]) + E^(2*x)* (90*x + 30*x^2 + 20*x^3 + (-18*x - 6*x^2 - 4*x^3)*Log[2]) + (160 + 294*x + 246*x^2 + 84*x^3 + 16*x^4 + (-32 - 14*x - 4*x^2)*Log[2] + E^x*(20*x - 10* x^2 + 20*x^3 + (-4*x + 2*x^2 - 4*x^3)*Log[2]))*Log[x] + (-70*x - 40*x^2 + (14*x + 8*x^2)*Log[2])*Log[x]^2)/(E^(3*x)*x + 3*E^(2*x)*x*Log[x] + 3*E^x*x *Log[x]^2 + x*Log[x]^3),x]
((16 + 7*x + 2*x^2)*(16 + 7*x + 2*x^2 + E^x*(-10 + Log[4]) + (-10 + Log[4] )*Log[x]))/(E^x + Log[x])^2
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.
| \(\displaystyle \int \frac {-8 x^4-56 x^3-226 x^2+\left (-40 x^2+\left (8 x^2+14 x\right ) \log (2)-70 x\right ) \log ^2(x)+e^{2 x} \left (20 x^3+30 x^2+\left (-4 x^3-6 x^2-18 x\right ) \log (2)+90 x\right )+\left (16 x^4+84 x^3+246 x^2+\left (-4 x^2-14 x-32\right ) \log (2)+e^x \left (20 x^3-10 x^2+\left (-4 x^3+2 x^2-4 x\right ) \log (2)+20 x\right )+294 x+160\right ) \log (x)+e^x \left (-8 x^5-40 x^4-142 x^3-202 x^2+\left (-4 x^2-14 x-32\right ) \log (2)-218 x+160\right )-448 x-512}{e^{3 x} x+x \log ^3(x)+3 e^x x \log ^2(x)+3 e^{2 x} x \log (x)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \left (2 e^x x^3+\left (3 e^x+2\right ) x^2+\left (9 e^x+7\right ) x-(4 x+7) x \log (x)+16\right ) \left (-2 x^2-7 x-(\log (2)-5) \log (x)-e^x (\log (2)-5)-16\right )}{x \left (e^x+\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {\left (2 e^x x^3+\left (2+3 e^x\right ) x^2+\left (7+9 e^x\right ) x-(4 x+7) \log (x) x+16\right ) \left (2 x^2+7 x-(5-\log (2)) \log (x)-e^x (5-\log (2))+16\right )}{x \left (\log (x)+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {\left (2 e^x x^3+\left (2+3 e^x\right ) x^2+\left (7+9 e^x\right ) x-(4 x+7) \log (x) x+16\right ) \left (2 x^2+7 x-(5-\log (2)) \log (x)-e^x (5-\log (2))+16\right )}{x \left (\log (x)+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (-\frac {(x \log (x)-1) \left (2 x^2+7 x+16\right )^2}{x \left (\log (x)+e^x\right )^3}+\frac {\left (2 x^3+3 x^2+5 \left (1-\frac {\log (2)}{5}\right ) \log (x) x+9 x-5 \left (1-\frac {\log (2)}{5}\right )\right ) \left (2 x^2+7 x+16\right )}{x \left (\log (x)+e^x\right )^2}+\frac {\left (2 x^2+3 x+9\right ) (-5+\log (2))}{\log (x)+e^x}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -2 \left (-4 \int \frac {x^4 \log (x)}{\left (\log (x)+e^x\right )^3}dx+4 \int \frac {x^4}{\left (\log (x)+e^x\right )^2}dx+4 \int \frac {x^3}{\left (\log (x)+e^x\right )^3}dx-28 \int \frac {x^3 \log (x)}{\left (\log (x)+e^x\right )^3}dx+20 \int \frac {x^3}{\left (\log (x)+e^x\right )^2}dx+28 \int \frac {x^2}{\left (\log (x)+e^x\right )^3}dx-113 \int \frac {x^2 \log (x)}{\left (\log (x)+e^x\right )^3}dx+71 \int \frac {x^2}{\left (\log (x)+e^x\right )^2}dx+2 (5-\log (2)) \int \frac {x^2 \log (x)}{\left (\log (x)+e^x\right )^2}dx-2 (5-\log (2)) \int \frac {x^2}{\log (x)+e^x}dx+224 \int \frac {1}{\left (\log (x)+e^x\right )^3}dx+256 \int \frac {1}{x \left (\log (x)+e^x\right )^3}dx+113 \int \frac {x}{\left (\log (x)+e^x\right )^3}dx-256 \int \frac {\log (x)}{\left (\log (x)+e^x\right )^3}dx-224 \int \frac {x \log (x)}{\left (\log (x)+e^x\right )^3}dx-7 (5-\log (2)) \int \frac {1}{\left (\log (x)+e^x\right )^2}dx+144 \int \frac {1}{\left (\log (x)+e^x\right )^2}dx-16 (5-\log (2)) \int \frac {1}{x \left (\log (x)+e^x\right )^2}dx-2 (5-\log (2)) \int \frac {x}{\left (\log (x)+e^x\right )^2}dx+111 \int \frac {x}{\left (\log (x)+e^x\right )^2}dx+16 (5-\log (2)) \int \frac {\log (x)}{\left (\log (x)+e^x\right )^2}dx+7 (5-\log (2)) \int \frac {x \log (x)}{\left (\log (x)+e^x\right )^2}dx-9 (5-\log (2)) \int \frac {1}{\log (x)+e^x}dx-3 (5-\log (2)) \int \frac {x}{\log (x)+e^x}dx\right )\) |
Int[(-512 - 448*x - 226*x^2 - 56*x^3 - 8*x^4 + E^x*(160 - 218*x - 202*x^2 - 142*x^3 - 40*x^4 - 8*x^5 + (-32 - 14*x - 4*x^2)*Log[2]) + E^(2*x)*(90*x + 30*x^2 + 20*x^3 + (-18*x - 6*x^2 - 4*x^3)*Log[2]) + (160 + 294*x + 246*x ^2 + 84*x^3 + 16*x^4 + (-32 - 14*x - 4*x^2)*Log[2] + E^x*(20*x - 10*x^2 + 20*x^3 + (-4*x + 2*x^2 - 4*x^3)*Log[2]))*Log[x] + (-70*x - 40*x^2 + (14*x + 8*x^2)*Log[2])*Log[x]^2)/(E^(3*x)*x + 3*E^(2*x)*x*Log[x] + 3*E^x*x*Log[x ]^2 + x*Log[x]^3),x]
3.22.9.3.1 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]]
Leaf count of result is larger than twice the leaf count of optimal. \(104\) vs. \(2(29)=58\).
Time = 0.55 (sec) , antiderivative size = 105, normalized size of antiderivative = 3.50
| method | result | size |
| risch | \(\frac {4 x^{2} \ln \left (2\right ) {\mathrm e}^{x}+4 x^{2} \ln \left (2\right ) \ln \left (x \right )+4 x^{4}+14 x \ln \left (2\right ) {\mathrm e}^{x}+14 x \ln \left (2\right ) \ln \left (x \right )+28 x^{3}-20 \,{\mathrm e}^{x} x^{2}-20 x^{2} \ln \left (x \right )+32 \,{\mathrm e}^{x} \ln \left (2\right )+32 \ln \left (2\right ) \ln \left (x \right )+113 x^{2}-70 \,{\mathrm e}^{x} x -70 x \ln \left (x \right )+224 x -160 \,{\mathrm e}^{x}-160 \ln \left (x \right )+256}{\left (\ln \left (x \right )+{\mathrm e}^{x}\right )^{2}}\) | \(105\) |
| parallelrisch | \(\frac {4 x^{2} \ln \left (2\right ) {\mathrm e}^{x}+4 x^{2} \ln \left (2\right ) \ln \left (x \right )+4 x^{4}+14 x \ln \left (2\right ) {\mathrm e}^{x}+14 x \ln \left (2\right ) \ln \left (x \right )+28 x^{3}-20 \,{\mathrm e}^{x} x^{2}-20 x^{2} \ln \left (x \right )+32 \,{\mathrm e}^{x} \ln \left (2\right )+32 \ln \left (2\right ) \ln \left (x \right )+113 x^{2}-70 \,{\mathrm e}^{x} x -70 x \ln \left (x \right )+224 x -160 \,{\mathrm e}^{x}-160 \ln \left (x \right )+256}{\ln \left (x \right )^{2}+2 \,{\mathrm e}^{x} \ln \left (x \right )+{\mathrm e}^{2 x}}\) | \(115\) |
int((((8*x^2+14*x)*ln(2)-40*x^2-70*x)*ln(x)^2+(((-4*x^3+2*x^2-4*x)*ln(2)+2 0*x^3-10*x^2+20*x)*exp(x)+(-4*x^2-14*x-32)*ln(2)+16*x^4+84*x^3+246*x^2+294 *x+160)*ln(x)+((-4*x^3-6*x^2-18*x)*ln(2)+20*x^3+30*x^2+90*x)*exp(x)^2+((-4 *x^2-14*x-32)*ln(2)-8*x^5-40*x^4-142*x^3-202*x^2-218*x+160)*exp(x)-8*x^4-5 6*x^3-226*x^2-448*x-512)/(x*ln(x)^3+3*x*exp(x)*ln(x)^2+3*x*exp(x)^2*ln(x)+ x*exp(x)^3),x,method=_RETURNVERBOSE)
(4*x^2*ln(2)*exp(x)+4*x^2*ln(2)*ln(x)+4*x^4+14*x*ln(2)*exp(x)+14*x*ln(2)*l n(x)+28*x^3-20*exp(x)*x^2-20*x^2*ln(x)+32*exp(x)*ln(2)+32*ln(2)*ln(x)+113* x^2-70*exp(x)*x-70*x*ln(x)+224*x-160*exp(x)-160*ln(x)+256)/(ln(x)+exp(x))^ 2
Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (26) = 52\).
Time = 0.25 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.13 \[ \int \frac {-512-448 x-226 x^2-56 x^3-8 x^4+e^x \left (160-218 x-202 x^2-142 x^3-40 x^4-8 x^5+\left (-32-14 x-4 x^2\right ) \log (2)\right )+e^{2 x} \left (90 x+30 x^2+20 x^3+\left (-18 x-6 x^2-4 x^3\right ) \log (2)\right )+\left (160+294 x+246 x^2+84 x^3+16 x^4+\left (-32-14 x-4 x^2\right ) \log (2)+e^x \left (20 x-10 x^2+20 x^3+\left (-4 x+2 x^2-4 x^3\right ) \log (2)\right )\right ) \log (x)+\left (-70 x-40 x^2+\left (14 x+8 x^2\right ) \log (2)\right ) \log ^2(x)}{e^{3 x} x+3 e^{2 x} x \log (x)+3 e^x x \log ^2(x)+x \log ^3(x)} \, dx=\frac {4 \, x^{4} + 28 \, x^{3} + 113 \, x^{2} - 2 \, {\left (10 \, x^{2} - {\left (2 \, x^{2} + 7 \, x + 16\right )} \log \left (2\right ) + 35 \, x + 80\right )} e^{x} - 2 \, {\left (10 \, x^{2} - {\left (2 \, x^{2} + 7 \, x + 16\right )} \log \left (2\right ) + 35 \, x + 80\right )} \log \left (x\right ) + 224 \, x + 256}{2 \, e^{x} \log \left (x\right ) + \log \left (x\right )^{2} + e^{\left (2 \, x\right )}} \]
integrate((((8*x^2+14*x)*log(2)-40*x^2-70*x)*log(x)^2+(((-4*x^3+2*x^2-4*x) *log(2)+20*x^3-10*x^2+20*x)*exp(x)+(-4*x^2-14*x-32)*log(2)+16*x^4+84*x^3+2 46*x^2+294*x+160)*log(x)+((-4*x^3-6*x^2-18*x)*log(2)+20*x^3+30*x^2+90*x)*e xp(x)^2+((-4*x^2-14*x-32)*log(2)-8*x^5-40*x^4-142*x^3-202*x^2-218*x+160)*e xp(x)-8*x^4-56*x^3-226*x^2-448*x-512)/(x*log(x)^3+3*x*exp(x)*log(x)^2+3*x* exp(x)^2*log(x)+x*exp(x)^3),x, algorithm=\
(4*x^4 + 28*x^3 + 113*x^2 - 2*(10*x^2 - (2*x^2 + 7*x + 16)*log(2) + 35*x + 80)*e^x - 2*(10*x^2 - (2*x^2 + 7*x + 16)*log(2) + 35*x + 80)*log(x) + 224 *x + 256)/(2*e^x*log(x) + log(x)^2 + e^(2*x))
Leaf count of result is larger than twice the leaf count of optimal. 122 vs. \(2 (22) = 44\).
Time = 0.14 (sec) , antiderivative size = 122, normalized size of antiderivative = 4.07 \[ \int \frac {-512-448 x-226 x^2-56 x^3-8 x^4+e^x \left (160-218 x-202 x^2-142 x^3-40 x^4-8 x^5+\left (-32-14 x-4 x^2\right ) \log (2)\right )+e^{2 x} \left (90 x+30 x^2+20 x^3+\left (-18 x-6 x^2-4 x^3\right ) \log (2)\right )+\left (160+294 x+246 x^2+84 x^3+16 x^4+\left (-32-14 x-4 x^2\right ) \log (2)+e^x \left (20 x-10 x^2+20 x^3+\left (-4 x+2 x^2-4 x^3\right ) \log (2)\right )\right ) \log (x)+\left (-70 x-40 x^2+\left (14 x+8 x^2\right ) \log (2)\right ) \log ^2(x)}{e^{3 x} x+3 e^{2 x} x \log (x)+3 e^x x \log ^2(x)+x \log ^3(x)} \, dx=\frac {4 x^{4} + 28 x^{3} - 20 x^{2} \log {\left (x \right )} + 4 x^{2} \log {\left (2 \right )} \log {\left (x \right )} + 113 x^{2} - 70 x \log {\left (x \right )} + 14 x \log {\left (2 \right )} \log {\left (x \right )} + 224 x + \left (- 20 x^{2} + 4 x^{2} \log {\left (2 \right )} - 70 x + 14 x \log {\left (2 \right )} - 160 + 32 \log {\left (2 \right )}\right ) e^{x} - 160 \log {\left (x \right )} + 32 \log {\left (2 \right )} \log {\left (x \right )} + 256}{e^{2 x} + 2 e^{x} \log {\left (x \right )} + \log {\left (x \right )}^{2}} \]
integrate((((8*x**2+14*x)*ln(2)-40*x**2-70*x)*ln(x)**2+(((-4*x**3+2*x**2-4 *x)*ln(2)+20*x**3-10*x**2+20*x)*exp(x)+(-4*x**2-14*x-32)*ln(2)+16*x**4+84* x**3+246*x**2+294*x+160)*ln(x)+((-4*x**3-6*x**2-18*x)*ln(2)+20*x**3+30*x** 2+90*x)*exp(x)**2+((-4*x**2-14*x-32)*ln(2)-8*x**5-40*x**4-142*x**3-202*x** 2-218*x+160)*exp(x)-8*x**4-56*x**3-226*x**2-448*x-512)/(x*ln(x)**3+3*x*exp (x)*ln(x)**2+3*x*exp(x)**2*ln(x)+x*exp(x)**3),x)
(4*x**4 + 28*x**3 - 20*x**2*log(x) + 4*x**2*log(2)*log(x) + 113*x**2 - 70* x*log(x) + 14*x*log(2)*log(x) + 224*x + (-20*x**2 + 4*x**2*log(2) - 70*x + 14*x*log(2) - 160 + 32*log(2))*exp(x) - 160*log(x) + 32*log(2)*log(x) + 2 56)/(exp(2*x) + 2*exp(x)*log(x) + log(x)**2)
Leaf count of result is larger than twice the leaf count of optimal. 90 vs. \(2 (26) = 52\).
Time = 0.36 (sec) , antiderivative size = 90, normalized size of antiderivative = 3.00 \[ \int \frac {-512-448 x-226 x^2-56 x^3-8 x^4+e^x \left (160-218 x-202 x^2-142 x^3-40 x^4-8 x^5+\left (-32-14 x-4 x^2\right ) \log (2)\right )+e^{2 x} \left (90 x+30 x^2+20 x^3+\left (-18 x-6 x^2-4 x^3\right ) \log (2)\right )+\left (160+294 x+246 x^2+84 x^3+16 x^4+\left (-32-14 x-4 x^2\right ) \log (2)+e^x \left (20 x-10 x^2+20 x^3+\left (-4 x+2 x^2-4 x^3\right ) \log (2)\right )\right ) \log (x)+\left (-70 x-40 x^2+\left (14 x+8 x^2\right ) \log (2)\right ) \log ^2(x)}{e^{3 x} x+3 e^{2 x} x \log (x)+3 e^x x \log ^2(x)+x \log ^3(x)} \, dx=\frac {4 \, x^{4} + 28 \, x^{3} + 113 \, x^{2} + 2 \, {\left (2 \, x^{2} {\left (\log \left (2\right ) - 5\right )} + 7 \, x {\left (\log \left (2\right ) - 5\right )} + 16 \, \log \left (2\right ) - 80\right )} e^{x} + 2 \, {\left (2 \, x^{2} {\left (\log \left (2\right ) - 5\right )} + 7 \, x {\left (\log \left (2\right ) - 5\right )} + 16 \, \log \left (2\right ) - 80\right )} \log \left (x\right ) + 224 \, x + 256}{2 \, e^{x} \log \left (x\right ) + \log \left (x\right )^{2} + e^{\left (2 \, x\right )}} \]
integrate((((8*x^2+14*x)*log(2)-40*x^2-70*x)*log(x)^2+(((-4*x^3+2*x^2-4*x) *log(2)+20*x^3-10*x^2+20*x)*exp(x)+(-4*x^2-14*x-32)*log(2)+16*x^4+84*x^3+2 46*x^2+294*x+160)*log(x)+((-4*x^3-6*x^2-18*x)*log(2)+20*x^3+30*x^2+90*x)*e xp(x)^2+((-4*x^2-14*x-32)*log(2)-8*x^5-40*x^4-142*x^3-202*x^2-218*x+160)*e xp(x)-8*x^4-56*x^3-226*x^2-448*x-512)/(x*log(x)^3+3*x*exp(x)*log(x)^2+3*x* exp(x)^2*log(x)+x*exp(x)^3),x, algorithm=\
(4*x^4 + 28*x^3 + 113*x^2 + 2*(2*x^2*(log(2) - 5) + 7*x*(log(2) - 5) + 16* log(2) - 80)*e^x + 2*(2*x^2*(log(2) - 5) + 7*x*(log(2) - 5) + 16*log(2) - 80)*log(x) + 224*x + 256)/(2*e^x*log(x) + log(x)^2 + e^(2*x))
Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (26) = 52\).
Time = 0.33 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.80 \[ \int \frac {-512-448 x-226 x^2-56 x^3-8 x^4+e^x \left (160-218 x-202 x^2-142 x^3-40 x^4-8 x^5+\left (-32-14 x-4 x^2\right ) \log (2)\right )+e^{2 x} \left (90 x+30 x^2+20 x^3+\left (-18 x-6 x^2-4 x^3\right ) \log (2)\right )+\left (160+294 x+246 x^2+84 x^3+16 x^4+\left (-32-14 x-4 x^2\right ) \log (2)+e^x \left (20 x-10 x^2+20 x^3+\left (-4 x+2 x^2-4 x^3\right ) \log (2)\right )\right ) \log (x)+\left (-70 x-40 x^2+\left (14 x+8 x^2\right ) \log (2)\right ) \log ^2(x)}{e^{3 x} x+3 e^{2 x} x \log (x)+3 e^x x \log ^2(x)+x \log ^3(x)} \, dx=\frac {4 \, x^{4} + 4 \, x^{2} e^{x} \log \left (2\right ) + 4 \, x^{2} \log \left (2\right ) \log \left (x\right ) + 28 \, x^{3} - 20 \, x^{2} e^{x} + 14 \, x e^{x} \log \left (2\right ) - 20 \, x^{2} \log \left (x\right ) + 14 \, x \log \left (2\right ) \log \left (x\right ) + 113 \, x^{2} - 70 \, x e^{x} + 32 \, e^{x} \log \left (2\right ) - 70 \, x \log \left (x\right ) + 32 \, \log \left (2\right ) \log \left (x\right ) + 224 \, x - 160 \, e^{x} - 160 \, \log \left (x\right ) + 256}{2 \, e^{x} \log \left (x\right ) + \log \left (x\right )^{2} + e^{\left (2 \, x\right )}} \]
integrate((((8*x^2+14*x)*log(2)-40*x^2-70*x)*log(x)^2+(((-4*x^3+2*x^2-4*x) *log(2)+20*x^3-10*x^2+20*x)*exp(x)+(-4*x^2-14*x-32)*log(2)+16*x^4+84*x^3+2 46*x^2+294*x+160)*log(x)+((-4*x^3-6*x^2-18*x)*log(2)+20*x^3+30*x^2+90*x)*e xp(x)^2+((-4*x^2-14*x-32)*log(2)-8*x^5-40*x^4-142*x^3-202*x^2-218*x+160)*e xp(x)-8*x^4-56*x^3-226*x^2-448*x-512)/(x*log(x)^3+3*x*exp(x)*log(x)^2+3*x* exp(x)^2*log(x)+x*exp(x)^3),x, algorithm=\
(4*x^4 + 4*x^2*e^x*log(2) + 4*x^2*log(2)*log(x) + 28*x^3 - 20*x^2*e^x + 14 *x*e^x*log(2) - 20*x^2*log(x) + 14*x*log(2)*log(x) + 113*x^2 - 70*x*e^x + 32*e^x*log(2) - 70*x*log(x) + 32*log(2)*log(x) + 224*x - 160*e^x - 160*log (x) + 256)/(2*e^x*log(x) + log(x)^2 + e^(2*x))
Timed out. \[ \int \frac {-512-448 x-226 x^2-56 x^3-8 x^4+e^x \left (160-218 x-202 x^2-142 x^3-40 x^4-8 x^5+\left (-32-14 x-4 x^2\right ) \log (2)\right )+e^{2 x} \left (90 x+30 x^2+20 x^3+\left (-18 x-6 x^2-4 x^3\right ) \log (2)\right )+\left (160+294 x+246 x^2+84 x^3+16 x^4+\left (-32-14 x-4 x^2\right ) \log (2)+e^x \left (20 x-10 x^2+20 x^3+\left (-4 x+2 x^2-4 x^3\right ) \log (2)\right )\right ) \log (x)+\left (-70 x-40 x^2+\left (14 x+8 x^2\right ) \log (2)\right ) \log ^2(x)}{e^{3 x} x+3 e^{2 x} x \log (x)+3 e^x x \log ^2(x)+x \log ^3(x)} \, dx=\int -\frac {448\,x+{\ln \left (x\right )}^2\,\left (70\,x-\ln \left (2\right )\,\left (8\,x^2+14\,x\right )+40\,x^2\right )+{\mathrm {e}}^x\,\left (218\,x+\ln \left (2\right )\,\left (4\,x^2+14\,x+32\right )+202\,x^2+142\,x^3+40\,x^4+8\,x^5-160\right )-\ln \left (x\right )\,\left (294\,x-\ln \left (2\right )\,\left (4\,x^2+14\,x+32\right )+{\mathrm {e}}^x\,\left (20\,x-\ln \left (2\right )\,\left (4\,x^3-2\,x^2+4\,x\right )-10\,x^2+20\,x^3\right )+246\,x^2+84\,x^3+16\,x^4+160\right )-{\mathrm {e}}^{2\,x}\,\left (90\,x-\ln \left (2\right )\,\left (4\,x^3+6\,x^2+18\,x\right )+30\,x^2+20\,x^3\right )+226\,x^2+56\,x^3+8\,x^4+512}{x\,{\ln \left (x\right )}^3+3\,x\,{\mathrm {e}}^x\,{\ln \left (x\right )}^2+3\,x\,{\mathrm {e}}^{2\,x}\,\ln \left (x\right )+x\,{\mathrm {e}}^{3\,x}} \,d x \]
int(-(448*x + log(x)^2*(70*x - log(2)*(14*x + 8*x^2) + 40*x^2) + exp(x)*(2 18*x + log(2)*(14*x + 4*x^2 + 32) + 202*x^2 + 142*x^3 + 40*x^4 + 8*x^5 - 1 60) - log(x)*(294*x - log(2)*(14*x + 4*x^2 + 32) + exp(x)*(20*x - log(2)*( 4*x - 2*x^2 + 4*x^3) - 10*x^2 + 20*x^3) + 246*x^2 + 84*x^3 + 16*x^4 + 160) - exp(2*x)*(90*x - log(2)*(18*x + 6*x^2 + 4*x^3) + 30*x^2 + 20*x^3) + 226 *x^2 + 56*x^3 + 8*x^4 + 512)/(x*exp(3*x) + x*log(x)^3 + 3*x*exp(2*x)*log(x ) + 3*x*exp(x)*log(x)^2),x)
int(-(448*x + log(x)^2*(70*x - log(2)*(14*x + 8*x^2) + 40*x^2) + exp(x)*(2 18*x + log(2)*(14*x + 4*x^2 + 32) + 202*x^2 + 142*x^3 + 40*x^4 + 8*x^5 - 1 60) - log(x)*(294*x - log(2)*(14*x + 4*x^2 + 32) + exp(x)*(20*x - log(2)*( 4*x - 2*x^2 + 4*x^3) - 10*x^2 + 20*x^3) + 246*x^2 + 84*x^3 + 16*x^4 + 160) - exp(2*x)*(90*x - log(2)*(18*x + 6*x^2 + 4*x^3) + 30*x^2 + 20*x^3) + 226 *x^2 + 56*x^3 + 8*x^4 + 512)/(x*exp(3*x) + x*log(x)^3 + 3*x*exp(2*x)*log(x ) + 3*x*exp(x)*log(x)^2), x)