Integrand size = 157, antiderivative size = 25 \[ \int \left (-1+9600 e^2 x+2000 e x^2+100 x^3+e^{2+2 x} \left (800 x+800 x^2\right )+\left (5600 e^2 x+600 e x^2\right ) \log (5)+800 e^2 x \log ^2(5)+e^x \left (e^2 \left (5600 x+2400 x^2\right )+e \left (600 x^2+200 x^3\right )+e^2 \left (1600 x+800 x^2\right ) \log (5)\right )+\left (5600 e^2 x+600 e x^2+e^{2+x} \left (1600 x+800 x^2\right )+1600 e^2 x \log (5)\right ) \log (x)+800 e^2 x \log ^2(x)\right ) \, dx=-x+25 x^2 \left (x+4 e \left (3+e^x+\log (5)+\log (x)\right )\right )^2 \]
Leaf count is larger than twice the leaf count of optimal. \(102\) vs. \(2(25)=50\).
Time = 0.60 (sec) , antiderivative size = 102, normalized size of antiderivative = 4.08 \[ \int \left (-1+9600 e^2 x+2000 e x^2+100 x^3+e^{2+2 x} \left (800 x+800 x^2\right )+\left (5600 e^2 x+600 e x^2\right ) \log (5)+800 e^2 x \log ^2(5)+e^x \left (e^2 \left (5600 x+2400 x^2\right )+e \left (600 x^2+200 x^3\right )+e^2 \left (1600 x+800 x^2\right ) \log (5)\right )+\left (5600 e^2 x+600 e x^2+e^{2+x} \left (1600 x+800 x^2\right )+1600 e^2 x \log (5)\right ) \log (x)+800 e^2 x \log ^2(x)\right ) \, dx=\frac {1}{3} x \left (-3+1200 e^{2+2 x} x+600 e^{1+x} x^2+75 x^3+2400 e^{2+x} x (3+\log (5))+200 e x^2 (9+\log (125))+600 e^2 x \left (18+2 \log ^2(5)+\log (244140625)\right )+600 e x \left (4 e^{1+x}+x+2 e (6+\log (25))\right ) \log (x)+1200 e^2 x \log ^2(x)\right ) \]
Integrate[-1 + 9600*E^2*x + 2000*E*x^2 + 100*x^3 + E^(2 + 2*x)*(800*x + 80 0*x^2) + (5600*E^2*x + 600*E*x^2)*Log[5] + 800*E^2*x*Log[5]^2 + E^x*(E^2*( 5600*x + 2400*x^2) + E*(600*x^2 + 200*x^3) + E^2*(1600*x + 800*x^2)*Log[5] ) + (5600*E^2*x + 600*E*x^2 + E^(2 + x)*(1600*x + 800*x^2) + 1600*E^2*x*Lo g[5])*Log[x] + 800*E^2*x*Log[x]^2,x]
(x*(-3 + 1200*E^(2 + 2*x)*x + 600*E^(1 + x)*x^2 + 75*x^3 + 2400*E^(2 + x)* x*(3 + Log[5]) + 200*E*x^2*(9 + Log[125]) + 600*E^2*x*(18 + 2*Log[5]^2 + L og[244140625]) + 600*E*x*(4*E^(1 + x) + x + 2*E*(6 + Log[25]))*Log[x] + 12 00*E^2*x*Log[x]^2))/3
Leaf count is larger than twice the leaf count of optimal. \(167\) vs. \(2(25)=50\).
Time = 0.62 (sec) , antiderivative size = 167, normalized size of antiderivative = 6.68, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.013, Rules used = {6, 2009}
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.
| \(\displaystyle \int \left (100 x^3+2000 e x^2+e^{2 x+2} \left (800 x^2+800 x\right )+\left (600 e x^2+e^{x+2} \left (800 x^2+1600 x\right )+5600 e^2 x+1600 e^2 x \log (5)\right ) \log (x)+\left (600 e x^2+5600 e^2 x\right ) \log (5)+e^x \left (e^2 \left (2400 x^2+5600 x\right )+e^2 \left (800 x^2+1600 x\right ) \log (5)+e \left (200 x^3+600 x^2\right )\right )+9600 e^2 x+800 e^2 x \log ^2(x)+800 e^2 x \log ^2(5)-1\right ) \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \left (100 x^3+2000 e x^2+e^{2 x+2} \left (800 x^2+800 x\right )+\left (600 e x^2+e^{x+2} \left (800 x^2+1600 x\right )+5600 e^2 x+1600 e^2 x \log (5)\right ) \log (x)+\left (600 e x^2+5600 e^2 x\right ) \log (5)+e^x \left (e^2 \left (2400 x^2+5600 x\right )+e^2 \left (800 x^2+1600 x\right ) \log (5)+e \left (200 x^3+600 x^2\right )\right )+800 e^2 x \log ^2(x)+e^2 x \left (9600+800 \log ^2(5)\right )-1\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 25 x^4+200 e^{x+1} x^3+600 e x^3+200 e x^3 \log (x)+200 e x^3 \log (5)+2400 e^{x+2} x^2+400 e^{2 x+2} x^2+200 e^2 x^2+400 e^2 x^2 \log ^2(x)+400 e^2 x^2 \left (12+\log ^2(5)\right )+800 e^{x+2} x^2 \log (x)+400 e^2 x^2 (7+\log (25)) \log (x)-400 e^2 x^2 \log (x)-200 e^2 x^2 (7+\log (25))+800 e^{x+2} x^2 \log (5)+2800 e^2 x^2 \log (5)-x\) |
Int[-1 + 9600*E^2*x + 2000*E*x^2 + 100*x^3 + E^(2 + 2*x)*(800*x + 800*x^2) + (5600*E^2*x + 600*E*x^2)*Log[5] + 800*E^2*x*Log[5]^2 + E^x*(E^2*(5600*x + 2400*x^2) + E*(600*x^2 + 200*x^3) + E^2*(1600*x + 800*x^2)*Log[5]) + (5 600*E^2*x + 600*E*x^2 + E^(2 + x)*(1600*x + 800*x^2) + 1600*E^2*x*Log[5])* Log[x] + 800*E^2*x*Log[x]^2,x]
-x + 200*E^2*x^2 + 2400*E^(2 + x)*x^2 + 400*E^(2 + 2*x)*x^2 + 600*E*x^3 + 200*E^(1 + x)*x^3 + 25*x^4 + 2800*E^2*x^2*Log[5] + 800*E^(2 + x)*x^2*Log[5 ] + 200*E*x^3*Log[5] + 400*E^2*x^2*(12 + Log[5]^2) - 200*E^2*x^2*(7 + Log[ 25]) - 400*E^2*x^2*Log[x] + 800*E^(2 + x)*x^2*Log[x] + 200*E*x^3*Log[x] + 400*E^2*x^2*(7 + Log[25])*Log[x] + 400*E^2*x^2*Log[x]^2
3.4.26.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Leaf count of result is larger than twice the leaf count of optimal. \(143\) vs. \(2(39)=78\).
Time = 0.14 (sec) , antiderivative size = 144, normalized size of antiderivative = 5.76
| method | result | size |
| risch | \(400 \,{\mathrm e}^{2} x^{2} \ln \left (x \right )^{2}+800 \ln \left (x \right ) \ln \left (5\right ) {\mathrm e}^{2} x^{2}+800 x^{2} \ln \left (x \right ) {\mathrm e}^{2+x}+400 \,{\mathrm e}^{2} \ln \left (5\right )^{2} x^{2}+800 x^{2} \ln \left (5\right ) {\mathrm e}^{2+x}+400 x^{2} {\mathrm e}^{2+2 x}+2400 x^{2} {\mathrm e}^{2} \ln \left (x \right )+200 x^{3} {\mathrm e} \ln \left (x \right )+2400 \ln \left (5\right ) {\mathrm e}^{2} x^{2}+200 \ln \left (5\right ) {\mathrm e} x^{3}+2400 x^{2} {\mathrm e}^{2+x}+200 x^{3} {\mathrm e}^{1+x}+3600 x^{2} {\mathrm e}^{2}+600 x^{3} {\mathrm e}+25 x^{4}-x\) | \(144\) |
| parallelrisch | \(400 \,{\mathrm e}^{2} x^{2} \ln \left (x \right )^{2}+800 \ln \left (x \right ) \ln \left (5\right ) {\mathrm e}^{2} x^{2}+800 \ln \left (x \right ) {\mathrm e}^{2} {\mathrm e}^{x} x^{2}+400 \,{\mathrm e}^{2} \ln \left (5\right )^{2} x^{2}+800 \ln \left (5\right ) {\mathrm e}^{2} {\mathrm e}^{x} x^{2}+400 \,{\mathrm e}^{2} {\mathrm e}^{2 x} x^{2}+2400 x^{2} {\mathrm e}^{2} \ln \left (x \right )+200 x^{3} {\mathrm e} \ln \left (x \right )+2400 \ln \left (5\right ) {\mathrm e}^{2} x^{2}+200 \ln \left (5\right ) {\mathrm e} x^{3}+2400 x^{2} {\mathrm e}^{2} {\mathrm e}^{x}+200 x^{3} {\mathrm e} \,{\mathrm e}^{x}+3600 x^{2} {\mathrm e}^{2}+600 x^{3} {\mathrm e}+25 x^{4}-x\) | \(164\) |
| default | \(-x +200 \ln \left (5\right ) {\mathrm e} \left (x^{3}+14 x^{2} {\mathrm e}\right )+200 x^{3} {\mathrm e} \,{\mathrm e}^{x}+2400 x^{2} {\mathrm e}^{2} {\mathrm e}^{x}+800 \ln \left (5\right ) {\mathrm e}^{2} {\mathrm e}^{x} x^{2}+1600 \,{\mathrm e}^{2} \ln \left (5\right ) \left (\frac {x^{2} \ln \left (x \right )}{2}-\frac {x^{2}}{4}\right )+5600 \,{\mathrm e}^{2} \left (\frac {x^{2} \ln \left (x \right )}{2}-\frac {x^{2}}{4}\right )+600 \,{\mathrm e} \left (\frac {x^{3} \ln \left (x \right )}{3}-\frac {x^{3}}{9}\right )+800 \ln \left (x \right ) {\mathrm e}^{2} {\mathrm e}^{x} x^{2}+400 \,{\mathrm e}^{2} {\mathrm e}^{2 x} x^{2}+25 x^{4}+4800 x^{2} {\mathrm e}^{2}+\frac {2000 x^{3} {\mathrm e}}{3}+400 \,{\mathrm e}^{2} \ln \left (5\right )^{2} x^{2}+800 \,{\mathrm e}^{2} \left (\frac {x^{2} \ln \left (x \right )^{2}}{2}-\frac {x^{2} \ln \left (x \right )}{2}+\frac {x^{2}}{4}\right )\) | \(200\) |
| parts | \(-x +1600 \,{\mathrm e}^{2} \ln \left (5\right ) \left (\frac {x^{2} \ln \left (x \right )}{2}-\frac {x^{2}}{4}\right )+5600 \,{\mathrm e}^{2} \left (\frac {x^{2} \ln \left (x \right )}{2}-\frac {x^{2}}{4}\right )+600 \,{\mathrm e} \left (\frac {x^{3} \ln \left (x \right )}{3}-\frac {x^{3}}{9}\right )+\left (2400 \,{\mathrm e}^{2}+800 \,{\mathrm e}^{2} \ln \left (5\right )\right ) x^{2} {\mathrm e}^{x}+200 x^{3} {\mathrm e} \,{\mathrm e}^{x}+800 \ln \left (x \right ) {\mathrm e}^{2} {\mathrm e}^{x} x^{2}+25 x^{4}+4800 x^{2} {\mathrm e}^{2}+\frac {2000 x^{3} {\mathrm e}}{3}+2800 \ln \left (5\right ) {\mathrm e}^{2} x^{2}+400 \,{\mathrm e}^{2} \ln \left (5\right )^{2} x^{2}+800 \,{\mathrm e}^{2} \left (\frac {x^{2} \ln \left (x \right )^{2}}{2}-\frac {x^{2} \ln \left (x \right )}{2}+\frac {x^{2}}{4}\right )+200 \ln \left (5\right ) {\mathrm e} x^{3}+400 \,{\mathrm e}^{2} {\mathrm e}^{2 x} x^{2}\) | \(200\) |
int(800*x*exp(1)^2*ln(x)^2+((800*x^2+1600*x)*exp(1)^2*exp(x)+1600*x*exp(1) ^2*ln(5)+5600*x*exp(1)^2+600*x^2*exp(1))*ln(x)+(800*x^2+800*x)*exp(1)^2*ex p(x)^2+((800*x^2+1600*x)*exp(1)^2*ln(5)+(2400*x^2+5600*x)*exp(1)^2+(200*x^ 3+600*x^2)*exp(1))*exp(x)+800*x*exp(1)^2*ln(5)^2+(5600*x*exp(1)^2+600*x^2* exp(1))*ln(5)+9600*x*exp(1)^2+2000*x^2*exp(1)+100*x^3-1,x,method=_RETURNVE RBOSE)
400*exp(2)*x^2*ln(x)^2+800*ln(x)*ln(5)*exp(2)*x^2+800*x^2*ln(x)*exp(2+x)+4 00*exp(2)*ln(5)^2*x^2+800*x^2*ln(5)*exp(2+x)+400*x^2*exp(2+2*x)+2400*x^2*e xp(2)*ln(x)+200*x^3*exp(1)*ln(x)+2400*ln(5)*exp(2)*x^2+200*ln(5)*exp(1)*x^ 3+2400*x^2*exp(2+x)+200*x^3*exp(1+x)+3600*x^2*exp(2)+600*x^3*exp(1)+25*x^4 -x
Leaf count of result is larger than twice the leaf count of optimal. 146 vs. \(2 (25) = 50\).
Time = 0.25 (sec) , antiderivative size = 146, normalized size of antiderivative = 5.84 \[ \int \left (-1+9600 e^2 x+2000 e x^2+100 x^3+e^{2+2 x} \left (800 x+800 x^2\right )+\left (5600 e^2 x+600 e x^2\right ) \log (5)+800 e^2 x \log ^2(5)+e^x \left (e^2 \left (5600 x+2400 x^2\right )+e \left (600 x^2+200 x^3\right )+e^2 \left (1600 x+800 x^2\right ) \log (5)\right )+\left (5600 e^2 x+600 e x^2+e^{2+x} \left (1600 x+800 x^2\right )+1600 e^2 x \log (5)\right ) \log (x)+800 e^2 x \log ^2(x)\right ) \, dx={\left (400 \, x^{2} e^{4} \log \left (5\right )^{2} + 400 \, x^{2} e^{4} \log \left (x\right )^{2} + 600 \, x^{3} e^{3} + 3600 \, x^{2} e^{4} + 400 \, x^{2} e^{\left (2 \, x + 4\right )} + {\left (25 \, x^{4} - x\right )} e^{2} + 200 \, {\left (x^{3} e + 4 \, x^{2} e^{2} \log \left (5\right ) + 12 \, x^{2} e^{2}\right )} e^{\left (x + 2\right )} + 200 \, {\left (x^{3} e^{3} + 12 \, x^{2} e^{4}\right )} \log \left (5\right ) + 200 \, {\left (x^{3} e^{3} + 4 \, x^{2} e^{4} \log \left (5\right ) + 12 \, x^{2} e^{4} + 4 \, x^{2} e^{\left (x + 4\right )}\right )} \log \left (x\right )\right )} e^{\left (-2\right )} \]
integrate(800*x*exp(1)^2*log(x)^2+((800*x^2+1600*x)*exp(1)^2*exp(x)+1600*x *exp(1)^2*log(5)+5600*x*exp(1)^2+600*x^2*exp(1))*log(x)+(800*x^2+800*x)*ex p(1)^2*exp(x)^2+((800*x^2+1600*x)*exp(1)^2*log(5)+(2400*x^2+5600*x)*exp(1) ^2+(200*x^3+600*x^2)*exp(1))*exp(x)+800*x*exp(1)^2*log(5)^2+(5600*x*exp(1) ^2+600*x^2*exp(1))*log(5)+9600*x*exp(1)^2+2000*x^2*exp(1)+100*x^3-1,x, alg orithm=\
(400*x^2*e^4*log(5)^2 + 400*x^2*e^4*log(x)^2 + 600*x^3*e^3 + 3600*x^2*e^4 + 400*x^2*e^(2*x + 4) + (25*x^4 - x)*e^2 + 200*(x^3*e + 4*x^2*e^2*log(5) + 12*x^2*e^2)*e^(x + 2) + 200*(x^3*e^3 + 12*x^2*e^4)*log(5) + 200*(x^3*e^3 + 4*x^2*e^4*log(5) + 12*x^2*e^4 + 4*x^2*e^(x + 4))*log(x))*e^(-2)
Leaf count of result is larger than twice the leaf count of optimal. 153 vs. \(2 (51) = 102\).
Time = 0.25 (sec) , antiderivative size = 153, normalized size of antiderivative = 6.12 \[ \int \left (-1+9600 e^2 x+2000 e x^2+100 x^3+e^{2+2 x} \left (800 x+800 x^2\right )+\left (5600 e^2 x+600 e x^2\right ) \log (5)+800 e^2 x \log ^2(5)+e^x \left (e^2 \left (5600 x+2400 x^2\right )+e \left (600 x^2+200 x^3\right )+e^2 \left (1600 x+800 x^2\right ) \log (5)\right )+\left (5600 e^2 x+600 e x^2+e^{2+x} \left (1600 x+800 x^2\right )+1600 e^2 x \log (5)\right ) \log (x)+800 e^2 x \log ^2(x)\right ) \, dx=25 x^{4} + x^{3} \cdot \left (200 e \log {\left (5 \right )} + 600 e\right ) + 400 x^{2} e^{2} e^{2 x} + 400 x^{2} e^{2} \log {\left (x \right )}^{2} + x^{2} \cdot \left (400 e^{2} \log {\left (5 \right )}^{2} + 3600 e^{2} + 2400 e^{2} \log {\left (5 \right )}\right ) - x + \left (200 e x^{3} + 800 x^{2} e^{2} \log {\left (5 \right )} + 2400 x^{2} e^{2}\right ) \log {\left (x \right )} + \left (200 e x^{3} + 800 x^{2} e^{2} \log {\left (x \right )} + 800 x^{2} e^{2} \log {\left (5 \right )} + 2400 x^{2} e^{2}\right ) e^{x} \]
integrate(800*x*exp(1)**2*ln(x)**2+((800*x**2+1600*x)*exp(1)**2*exp(x)+160 0*x*exp(1)**2*ln(5)+5600*x*exp(1)**2+600*x**2*exp(1))*ln(x)+(800*x**2+800* x)*exp(1)**2*exp(x)**2+((800*x**2+1600*x)*exp(1)**2*ln(5)+(2400*x**2+5600* x)*exp(1)**2+(200*x**3+600*x**2)*exp(1))*exp(x)+800*x*exp(1)**2*ln(5)**2+( 5600*x*exp(1)**2+600*x**2*exp(1))*ln(5)+9600*x*exp(1)**2+2000*x**2*exp(1)+ 100*x**3-1,x)
25*x**4 + x**3*(200*E*log(5) + 600*E) + 400*x**2*exp(2)*exp(2*x) + 400*x** 2*exp(2)*log(x)**2 + x**2*(400*exp(2)*log(5)**2 + 3600*exp(2) + 2400*exp(2 )*log(5)) - x + (200*E*x**3 + 800*x**2*exp(2)*log(5) + 2400*x**2*exp(2))*l og(x) + (200*E*x**3 + 800*x**2*exp(2)*log(x) + 800*x**2*exp(2)*log(5) + 24 00*x**2*exp(2))*exp(x)
Leaf count of result is larger than twice the leaf count of optimal. 175 vs. \(2 (25) = 50\).
Time = 0.28 (sec) , antiderivative size = 175, normalized size of antiderivative = 7.00 \[ \int \left (-1+9600 e^2 x+2000 e x^2+100 x^3+e^{2+2 x} \left (800 x+800 x^2\right )+\left (5600 e^2 x+600 e x^2\right ) \log (5)+800 e^2 x \log ^2(5)+e^x \left (e^2 \left (5600 x+2400 x^2\right )+e \left (600 x^2+200 x^3\right )+e^2 \left (1600 x+800 x^2\right ) \log (5)\right )+\left (5600 e^2 x+600 e x^2+e^{2+x} \left (1600 x+800 x^2\right )+1600 e^2 x \log (5)\right ) \log (x)+800 e^2 x \log ^2(x)\right ) \, dx=400 \, x^{2} e^{2} \log \left (5\right )^{2} + 25 \, x^{4} + 200 \, {\left (2 \, \log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 1\right )} x^{2} e^{2} - 200 \, x^{2} {\left (2 \, \log \left (5\right ) + 7\right )} e^{2} + 600 \, x^{3} e + 4800 \, x^{2} e^{2} + 400 \, x^{2} e^{\left (2 \, x + 2\right )} + 200 \, {\left (4 \, x^{2} {\left (\log \left (5\right ) + 3\right )} e^{2} + x^{3} e + 4 \, x e^{2} - 4 \, e^{2}\right )} e^{x} - 800 \, {\left (x e^{2} - e^{2}\right )} e^{x} + 200 \, {\left (x^{3} e + 14 \, x^{2} e^{2}\right )} \log \left (5\right ) + 200 \, {\left (x^{3} e + 4 \, x^{2} e^{2} \log \left (5\right ) + 14 \, x^{2} e^{2} + 4 \, x^{2} e^{\left (x + 2\right )}\right )} \log \left (x\right ) - x \]
integrate(800*x*exp(1)^2*log(x)^2+((800*x^2+1600*x)*exp(1)^2*exp(x)+1600*x *exp(1)^2*log(5)+5600*x*exp(1)^2+600*x^2*exp(1))*log(x)+(800*x^2+800*x)*ex p(1)^2*exp(x)^2+((800*x^2+1600*x)*exp(1)^2*log(5)+(2400*x^2+5600*x)*exp(1) ^2+(200*x^3+600*x^2)*exp(1))*exp(x)+800*x*exp(1)^2*log(5)^2+(5600*x*exp(1) ^2+600*x^2*exp(1))*log(5)+9600*x*exp(1)^2+2000*x^2*exp(1)+100*x^3-1,x, alg orithm=\
400*x^2*e^2*log(5)^2 + 25*x^4 + 200*(2*log(x)^2 - 2*log(x) + 1)*x^2*e^2 - 200*x^2*(2*log(5) + 7)*e^2 + 600*x^3*e + 4800*x^2*e^2 + 400*x^2*e^(2*x + 2 ) + 200*(4*x^2*(log(5) + 3)*e^2 + x^3*e + 4*x*e^2 - 4*e^2)*e^x - 800*(x*e^ 2 - e^2)*e^x + 200*(x^3*e + 14*x^2*e^2)*log(5) + 200*(x^3*e + 4*x^2*e^2*lo g(5) + 14*x^2*e^2 + 4*x^2*e^(x + 2))*log(x) - x
Leaf count of result is larger than twice the leaf count of optimal. 170 vs. \(2 (25) = 50\).
Time = 0.27 (sec) , antiderivative size = 170, normalized size of antiderivative = 6.80 \[ \int \left (-1+9600 e^2 x+2000 e x^2+100 x^3+e^{2+2 x} \left (800 x+800 x^2\right )+\left (5600 e^2 x+600 e x^2\right ) \log (5)+800 e^2 x \log ^2(5)+e^x \left (e^2 \left (5600 x+2400 x^2\right )+e \left (600 x^2+200 x^3\right )+e^2 \left (1600 x+800 x^2\right ) \log (5)\right )+\left (5600 e^2 x+600 e x^2+e^{2+x} \left (1600 x+800 x^2\right )+1600 e^2 x \log (5)\right ) \log (x)+800 e^2 x \log ^2(x)\right ) \, dx=400 \, x^{2} e^{2} \log \left (5\right )^{2} + 25 \, x^{4} + 600 \, x^{3} e + 200 \, x^{3} e^{\left (x + 1\right )} - 400 \, x^{2} e^{2} \log \left (5\right ) + 3400 \, x^{2} e^{2} + 400 \, x^{2} e^{\left (2 \, x + 2\right )} + 200 \, {\left (2 \, x^{2} \log \left (x\right )^{2} - 2 \, x^{2} \log \left (x\right ) + x^{2}\right )} e^{2} + 800 \, {\left (x^{2} \log \left (5\right ) + 3 \, x^{2} + x - 1\right )} e^{\left (x + 2\right )} - 800 \, {\left (x - 1\right )} e^{\left (x + 2\right )} + 200 \, {\left (x^{3} e + 14 \, x^{2} e^{2}\right )} \log \left (5\right ) + 200 \, {\left (x^{3} e + 4 \, x^{2} e^{2} \log \left (5\right ) + 14 \, x^{2} e^{2} + 4 \, x^{2} e^{\left (x + 2\right )}\right )} \log \left (x\right ) - x \]
integrate(800*x*exp(1)^2*log(x)^2+((800*x^2+1600*x)*exp(1)^2*exp(x)+1600*x *exp(1)^2*log(5)+5600*x*exp(1)^2+600*x^2*exp(1))*log(x)+(800*x^2+800*x)*ex p(1)^2*exp(x)^2+((800*x^2+1600*x)*exp(1)^2*log(5)+(2400*x^2+5600*x)*exp(1) ^2+(200*x^3+600*x^2)*exp(1))*exp(x)+800*x*exp(1)^2*log(5)^2+(5600*x*exp(1) ^2+600*x^2*exp(1))*log(5)+9600*x*exp(1)^2+2000*x^2*exp(1)+100*x^3-1,x, alg orithm=\
400*x^2*e^2*log(5)^2 + 25*x^4 + 600*x^3*e + 200*x^3*e^(x + 1) - 400*x^2*e^ 2*log(5) + 3400*x^2*e^2 + 400*x^2*e^(2*x + 2) + 200*(2*x^2*log(x)^2 - 2*x^ 2*log(x) + x^2)*e^2 + 800*(x^2*log(5) + 3*x^2 + x - 1)*e^(x + 2) - 800*(x - 1)*e^(x + 2) + 200*(x^3*e + 14*x^2*e^2)*log(5) + 200*(x^3*e + 4*x^2*e^2* log(5) + 14*x^2*e^2 + 4*x^2*e^(x + 2))*log(x) - x
Time = 8.04 (sec) , antiderivative size = 110, normalized size of antiderivative = 4.40 \[ \int \left (-1+9600 e^2 x+2000 e x^2+100 x^3+e^{2+2 x} \left (800 x+800 x^2\right )+\left (5600 e^2 x+600 e x^2\right ) \log (5)+800 e^2 x \log ^2(5)+e^x \left (e^2 \left (5600 x+2400 x^2\right )+e \left (600 x^2+200 x^3\right )+e^2 \left (1600 x+800 x^2\right ) \log (5)\right )+\left (5600 e^2 x+600 e x^2+e^{2+x} \left (1600 x+800 x^2\right )+1600 e^2 x \log (5)\right ) \log (x)+800 e^2 x \log ^2(x)\right ) \, dx=200\,x^3\,{\mathrm {e}}^{x+1}-x+400\,x^2\,{\mathrm {e}}^{2\,x+2}+25\,x^4+800\,x^2\,{\mathrm {e}}^{x+2}\,\left (\ln \left (5\right )+3\right )+800\,x^2\,{\mathrm {e}}^{x+2}\,\ln \left (x\right )+200\,x^3\,\mathrm {e}\,\left (\ln \left (5\right )+3\right )+200\,x^3\,\mathrm {e}\,\ln \left (x\right )+400\,x^2\,{\mathrm {e}}^2\,{\left (\ln \left (5\right )+3\right )}^2+400\,x^2\,{\mathrm {e}}^2\,{\ln \left (x\right )}^2+800\,x^2\,{\mathrm {e}}^2\,\ln \left (x\right )\,\left (\ln \left (5\right )+3\right ) \]
int(exp(x)*(exp(2)*(5600*x + 2400*x^2) + exp(1)*(600*x^2 + 200*x^3) + exp( 2)*log(5)*(1600*x + 800*x^2)) + log(5)*(5600*x*exp(2) + 600*x^2*exp(1)) + log(x)*(5600*x*exp(2) + 600*x^2*exp(1) + exp(2)*exp(x)*(1600*x + 800*x^2) + 1600*x*exp(2)*log(5)) + 9600*x*exp(2) + 2000*x^2*exp(1) + 100*x^3 + 800* x*exp(2)*log(5)^2 + exp(2*x)*exp(2)*(800*x + 800*x^2) + 800*x*exp(2)*log(x )^2 - 1,x)