Integrand size = 146, antiderivative size = 31 \[ \int \frac {-5+10 x-26 x^2+21 x^3-22 x^4+e^{4 x} \left (-1+x-2 x^2\right )+e^{2 x} \left (2 x-2 x^2+4 x^3\right )+\left (-5+10 x-28 x^2+22 x^3-22 x^4+e^{4 x} \left (-1-4 x+6 x^2-8 x^3\right )+e^{2 x} \left (4 x+2 x^2-4 x^3+8 x^4\right )\right ) \log (x)}{5-10 x+25 x^2-20 x^3+20 x^4} \, dx=\frac {1}{5} x \left (-5+\frac {\left (-e^{2 x}+x\right )^2}{-1+x-2 x^2}\right ) \log (x) \]
Time = 0.14 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.35 \[ \int \frac {-5+10 x-26 x^2+21 x^3-22 x^4+e^{4 x} \left (-1+x-2 x^2\right )+e^{2 x} \left (2 x-2 x^2+4 x^3\right )+\left (-5+10 x-28 x^2+22 x^3-22 x^4+e^{4 x} \left (-1-4 x+6 x^2-8 x^3\right )+e^{2 x} \left (4 x+2 x^2-4 x^3+8 x^4\right )\right ) \log (x)}{5-10 x+25 x^2-20 x^3+20 x^4} \, dx=-\frac {x \left (5+e^{4 x}-5 x-2 e^{2 x} x+11 x^2\right ) \log (x)}{5 \left (1-x+2 x^2\right )} \]
Integrate[(-5 + 10*x - 26*x^2 + 21*x^3 - 22*x^4 + E^(4*x)*(-1 + x - 2*x^2) + E^(2*x)*(2*x - 2*x^2 + 4*x^3) + (-5 + 10*x - 28*x^2 + 22*x^3 - 22*x^4 + E^(4*x)*(-1 - 4*x + 6*x^2 - 8*x^3) + E^(2*x)*(4*x + 2*x^2 - 4*x^3 + 8*x^4 ))*Log[x])/(5 - 10*x + 25*x^2 - 20*x^3 + 20*x^4),x]
Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
Time = 5.49 (sec) , antiderivative size = 1682, normalized size of antiderivative = 54.26, number of steps used = 5, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {2463, 27, 25, 7293, 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.
| \(\displaystyle \int \frac {-22 x^4+21 x^3-26 x^2+e^{4 x} \left (-2 x^2+x-1\right )+e^{2 x} \left (4 x^3-2 x^2+2 x\right )+\left (-22 x^4+22 x^3-28 x^2+e^{4 x} \left (-8 x^3+6 x^2-4 x-1\right )+e^{2 x} \left (8 x^4-4 x^3+2 x^2+4 x\right )+10 x-5\right ) \log (x)+10 x-5}{20 x^4-20 x^3+25 x^2-10 x+5} \, dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \frac {-22 x^4+21 x^3-26 x^2+e^{4 x} \left (-2 x^2+x-1\right )+e^{2 x} \left (4 x^3-2 x^2+2 x\right )+\left (-22 x^4+22 x^3-28 x^2+e^{4 x} \left (-8 x^3+6 x^2-4 x-1\right )+e^{2 x} \left (8 x^4-4 x^3+2 x^2+4 x\right )+10 x-5\right ) \log (x)+10 x-5}{5 \left (2 x^2-x+1\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{5} \int -\frac {22 x^4-21 x^3+26 x^2-10 x+e^{4 x} \left (2 x^2-x+1\right )-2 e^{2 x} \left (2 x^3-x^2+x\right )+\left (22 x^4-22 x^3+28 x^2-10 x+e^{4 x} \left (8 x^3-6 x^2+4 x+1\right )-2 e^{2 x} \left (4 x^4-2 x^3+x^2+2 x\right )+5\right ) \log (x)+5}{\left (2 x^2-x+1\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {1}{5} \int \frac {22 x^4-21 x^3+26 x^2-10 x+e^{4 x} \left (2 x^2-x+1\right )-2 e^{2 x} \left (2 x^3-x^2+x\right )+\left (22 x^4-22 x^3+28 x^2-10 x+e^{4 x} \left (8 x^3-6 x^2+4 x+1\right )-2 e^{2 x} \left (4 x^4-2 x^3+x^2+2 x\right )+5\right ) \log (x)+5}{\left (2 x^2-x+1\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{5} \int \left (\frac {22 \log (x) x^4}{\left (2 x^2-x+1\right )^2}+\frac {22 x^4}{\left (2 x^2-x+1\right )^2}-\frac {22 \log (x) x^3}{\left (2 x^2-x+1\right )^2}-\frac {21 x^3}{\left (2 x^2-x+1\right )^2}+\frac {28 \log (x) x^2}{\left (2 x^2-x+1\right )^2}+\frac {26 x^2}{\left (2 x^2-x+1\right )^2}-\frac {10 \log (x) x}{\left (2 x^2-x+1\right )^2}-\frac {2 e^{2 x} \left (4 \log (x) x^3-2 \log (x) x^2+2 x^2+\log (x) x-x+2 \log (x)+1\right ) x}{\left (2 x^2-x+1\right )^2}-\frac {10 x}{\left (2 x^2-x+1\right )^2}+\frac {5 \log (x)}{\left (2 x^2-x+1\right )^2}+\frac {e^{4 x} \left (8 \log (x) x^3-6 \log (x) x^2+2 x^2+4 \log (x) x-x+\log (x)+1\right )}{\left (2 x^2-x+1\right )^2}+\frac {5}{\left (2 x^2-x+1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{5} \left (\frac {22 (2-x) x^3}{7 \left (2 x^2-x+1\right )}-\frac {3 (2-x) x^2}{2 x^2-x+1}+\frac {11 x^2}{7}-\frac {12 \log (x) x}{7 \left (1-i \sqrt {7}\right ) \left (-4 x-i \sqrt {7}+1\right )}+\frac {5 \log (x) x}{7 \left (-4 x-i \sqrt {7}+1\right )}-\frac {12 \log (x) x}{7 \left (1+i \sqrt {7}\right ) \left (-4 x+i \sqrt {7}+1\right )}+\frac {5 \log (x) x}{7 \left (-4 x+i \sqrt {7}+1\right )}-\frac {11}{2} \log (x) x+\frac {26 (2-x) x}{7 \left (2 x^2-x+1\right )}-\frac {27 x}{7}-\frac {3 \arctan \left (\frac {1-4 x}{\sqrt {7}}\right )}{4 \sqrt {7}}-\frac {3 \log \left (-4 x-i \sqrt {7}+1\right )}{7 \left (1-i \sqrt {7}\right )}+\frac {5}{28} \log \left (-4 x-i \sqrt {7}+1\right )-\frac {3 \log \left (-4 x+i \sqrt {7}+1\right )}{7 \left (1+i \sqrt {7}\right )}+\frac {5}{28} \log \left (-4 x+i \sqrt {7}+1\right )+e^{2 x} \log (x)+\frac {1}{14} \left (7+5 i \sqrt {7}\right ) e^{\frac {1}{2}+\frac {i \sqrt {7}}{2}} \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (4 x-i \sqrt {7}-1\right )\right ) \log (x)-\frac {3}{14} \left (1+i \sqrt {7}\right ) e^{\frac {1}{2}+\frac {i \sqrt {7}}{2}} \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (4 x-i \sqrt {7}-1\right )\right ) \log (x)-\frac {i e^{\frac {1}{2}+\frac {i \sqrt {7}}{2}} \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (4 x-i \sqrt {7}-1\right )\right ) \log (x)}{\sqrt {7}}-\frac {2}{7} e^{\frac {1}{2}+\frac {i \sqrt {7}}{2}} \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (4 x-i \sqrt {7}-1\right )\right ) \log (x)-\frac {1}{7} \left (1+i \sqrt {7}\right ) e^{1+i \sqrt {7}} \operatorname {ExpIntegralEi}\left (4 x-i \sqrt {7}-1\right ) \log (x)+\frac {i e^{1+i \sqrt {7}} \operatorname {ExpIntegralEi}\left (4 x-i \sqrt {7}-1\right ) \log (x)}{\sqrt {7}}+\frac {1}{7} e^{1+i \sqrt {7}} \operatorname {ExpIntegralEi}\left (4 x-i \sqrt {7}-1\right ) \log (x)+\frac {1}{14} \left (7-5 i \sqrt {7}\right ) e^{\frac {1}{2}-\frac {i \sqrt {7}}{2}} \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (4 x+i \sqrt {7}-1\right )\right ) \log (x)-\frac {3}{14} \left (1-i \sqrt {7}\right ) e^{\frac {1}{2}-\frac {i \sqrt {7}}{2}} \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (4 x+i \sqrt {7}-1\right )\right ) \log (x)+\frac {i e^{\frac {1}{2}-\frac {i \sqrt {7}}{2}} \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (4 x+i \sqrt {7}-1\right )\right ) \log (x)}{\sqrt {7}}-\frac {2}{7} e^{\frac {1}{2}-\frac {i \sqrt {7}}{2}} \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (4 x+i \sqrt {7}-1\right )\right ) \log (x)-\frac {1}{7} \left (1-i \sqrt {7}\right ) e^{1-i \sqrt {7}} \operatorname {ExpIntegralEi}\left (4 x+i \sqrt {7}-1\right ) \log (x)-\frac {i e^{1-i \sqrt {7}} \operatorname {ExpIntegralEi}\left (4 x+i \sqrt {7}-1\right ) \log (x)}{\sqrt {7}}+\frac {1}{7} e^{1-i \sqrt {7}} \operatorname {ExpIntegralEi}\left (4 x+i \sqrt {7}-1\right ) \log (x)-\frac {3 \left (1-i \sqrt {7}\right ) e^{2 x} \log (x)}{7 \left (-4 x-i \sqrt {7}+1\right )}-\frac {4 e^{2 x} \log (x)}{7 \left (-4 x-i \sqrt {7}+1\right )}-\frac {\left (1-i \sqrt {7}\right ) e^{4 x} \log (x)}{7 \left (-4 x-i \sqrt {7}+1\right )}+\frac {8 e^{4 x} \log (x)}{7 \left (-4 x-i \sqrt {7}+1\right )}-\frac {3 \left (1+i \sqrt {7}\right ) e^{2 x} \log (x)}{7 \left (-4 x+i \sqrt {7}+1\right )}-\frac {4 e^{2 x} \log (x)}{7 \left (-4 x+i \sqrt {7}+1\right )}-\frac {\left (1+i \sqrt {7}\right ) e^{4 x} \log (x)}{7 \left (-4 x+i \sqrt {7}+1\right )}+\frac {8 e^{4 x} \log (x)}{7 \left (-4 x+i \sqrt {7}+1\right )}+\frac {11}{28} \left (7+3 i \sqrt {7}\right ) \log (x) \log \left (1-\frac {4 x}{1-i \sqrt {7}}\right )-\frac {11}{28} \left (7-2 i \sqrt {7}\right ) \log (x) \log \left (1-\frac {4 x}{1-i \sqrt {7}}\right )-\frac {55 i \log (x) \log \left (1-\frac {4 x}{1-i \sqrt {7}}\right )}{4 \sqrt {7}}+\frac {11}{28} \left (7-3 i \sqrt {7}\right ) \log (x) \log \left (1-\frac {4 x}{1+i \sqrt {7}}\right )-\frac {11}{28} \left (7+2 i \sqrt {7}\right ) \log (x) \log \left (1-\frac {4 x}{1+i \sqrt {7}}\right )+\frac {55 i \log (x) \log \left (1-\frac {4 x}{1+i \sqrt {7}}\right )}{4 \sqrt {7}}-\frac {1}{8} \log \left (2 x^2-x+1\right )+\frac {11}{28} \left (7+3 i \sqrt {7}\right ) \operatorname {PolyLog}\left (2,\frac {4 x}{1-i \sqrt {7}}\right )-\frac {11}{28} \left (7-2 i \sqrt {7}\right ) \operatorname {PolyLog}\left (2,\frac {4 x}{1-i \sqrt {7}}\right )-\frac {55 i \operatorname {PolyLog}\left (2,\frac {4 x}{1-i \sqrt {7}}\right )}{4 \sqrt {7}}+\frac {11}{28} \left (7-3 i \sqrt {7}\right ) \operatorname {PolyLog}\left (2,\frac {4 x}{1+i \sqrt {7}}\right )-\frac {11}{28} \left (7+2 i \sqrt {7}\right ) \operatorname {PolyLog}\left (2,\frac {4 x}{1+i \sqrt {7}}\right )+\frac {55 i \operatorname {PolyLog}\left (2,\frac {4 x}{1+i \sqrt {7}}\right )}{4 \sqrt {7}}+\frac {5 (1-4 x)}{7 \left (2 x^2-x+1\right )}-\frac {10 (2-x)}{7 \left (2 x^2-x+1\right )}\right )\) |
Int[(-5 + 10*x - 26*x^2 + 21*x^3 - 22*x^4 + E^(4*x)*(-1 + x - 2*x^2) + E^( 2*x)*(2*x - 2*x^2 + 4*x^3) + (-5 + 10*x - 28*x^2 + 22*x^3 - 22*x^4 + E^(4* x)*(-1 - 4*x + 6*x^2 - 8*x^3) + E^(2*x)*(4*x + 2*x^2 - 4*x^3 + 8*x^4))*Log [x])/(5 - 10*x + 25*x^2 - 20*x^3 + 20*x^4),x]
((-27*x)/7 + (11*x^2)/7 + (5*(1 - 4*x))/(7*(1 - x + 2*x^2)) - (10*(2 - x)) /(7*(1 - x + 2*x^2)) + (26*(2 - x)*x)/(7*(1 - x + 2*x^2)) - (3*(2 - x)*x^2 )/(1 - x + 2*x^2) + (22*(2 - x)*x^3)/(7*(1 - x + 2*x^2)) - (3*ArcTan[(1 - 4*x)/Sqrt[7]])/(4*Sqrt[7]) + (5*Log[1 - I*Sqrt[7] - 4*x])/28 - (3*Log[1 - I*Sqrt[7] - 4*x])/(7*(1 - I*Sqrt[7])) + (5*Log[1 + I*Sqrt[7] - 4*x])/28 - (3*Log[1 + I*Sqrt[7] - 4*x])/(7*(1 + I*Sqrt[7])) + E^(2*x)*Log[x] - (4*E^( 2*x)*Log[x])/(7*(1 - I*Sqrt[7] - 4*x)) - (3*(1 - I*Sqrt[7])*E^(2*x)*Log[x] )/(7*(1 - I*Sqrt[7] - 4*x)) + (8*E^(4*x)*Log[x])/(7*(1 - I*Sqrt[7] - 4*x)) - ((1 - I*Sqrt[7])*E^(4*x)*Log[x])/(7*(1 - I*Sqrt[7] - 4*x)) - (4*E^(2*x) *Log[x])/(7*(1 + I*Sqrt[7] - 4*x)) - (3*(1 + I*Sqrt[7])*E^(2*x)*Log[x])/(7 *(1 + I*Sqrt[7] - 4*x)) + (8*E^(4*x)*Log[x])/(7*(1 + I*Sqrt[7] - 4*x)) - ( (1 + I*Sqrt[7])*E^(4*x)*Log[x])/(7*(1 + I*Sqrt[7] - 4*x)) - (11*x*Log[x])/ 2 + (5*x*Log[x])/(7*(1 - I*Sqrt[7] - 4*x)) - (12*x*Log[x])/(7*(1 - I*Sqrt[ 7])*(1 - I*Sqrt[7] - 4*x)) + (5*x*Log[x])/(7*(1 + I*Sqrt[7] - 4*x)) - (12* x*Log[x])/(7*(1 + I*Sqrt[7])*(1 + I*Sqrt[7] - 4*x)) - (2*E^(1/2 + (I/2)*Sq rt[7])*ExpIntegralEi[(-1 - I*Sqrt[7] + 4*x)/2]*Log[x])/7 - (I*E^(1/2 + (I/ 2)*Sqrt[7])*ExpIntegralEi[(-1 - I*Sqrt[7] + 4*x)/2]*Log[x])/Sqrt[7] - (3*( 1 + I*Sqrt[7])*E^(1/2 + (I/2)*Sqrt[7])*ExpIntegralEi[(-1 - I*Sqrt[7] + 4*x )/2]*Log[x])/14 + ((7 + (5*I)*Sqrt[7])*E^(1/2 + (I/2)*Sqrt[7])*ExpIntegral Ei[(-1 - I*Sqrt[7] + 4*x)/2]*Log[x])/14 + (E^(1 + I*Sqrt[7])*ExpIntegra...
3.13.13.3.1 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[{Qx = Factor[Px]}, Int[ExpandIntegr and[u, Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && Gt Q[Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0]
Time = 0.48 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.71
| method | result | size |
| risch | \(-\frac {\left (4 x \,{\mathrm e}^{4 x}-8 \,{\mathrm e}^{2 x} x^{2}+44 x^{3}-22 x^{2}+21 x -1\right ) \ln \left (x \right )}{20 \left (2 x^{2}-x +1\right )}-\frac {\ln \left (x \right )}{20}\) | \(53\) |
| parallelrisch | \(\frac {-\ln \left (x \right ) {\mathrm e}^{4 x} x +2 \ln \left (x \right ) {\mathrm e}^{2 x} x^{2}-11 x^{3} \ln \left (x \right )+5 x^{2} \ln \left (x \right )-5 x \ln \left (x \right )}{10 x^{2}-5 x +5}\) | \(55\) |
int((((-8*x^3+6*x^2-4*x-1)*exp(x)^4+(8*x^4-4*x^3+2*x^2+4*x)*exp(x)^2-22*x^ 4+22*x^3-28*x^2+10*x-5)*ln(x)+(-2*x^2+x-1)*exp(x)^4+(4*x^3-2*x^2+2*x)*exp( x)^2-22*x^4+21*x^3-26*x^2+10*x-5)/(20*x^4-20*x^3+25*x^2-10*x+5),x,method=_ RETURNVERBOSE)
Time = 0.27 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.45 \[ \int \frac {-5+10 x-26 x^2+21 x^3-22 x^4+e^{4 x} \left (-1+x-2 x^2\right )+e^{2 x} \left (2 x-2 x^2+4 x^3\right )+\left (-5+10 x-28 x^2+22 x^3-22 x^4+e^{4 x} \left (-1-4 x+6 x^2-8 x^3\right )+e^{2 x} \left (4 x+2 x^2-4 x^3+8 x^4\right )\right ) \log (x)}{5-10 x+25 x^2-20 x^3+20 x^4} \, dx=-\frac {{\left (11 \, x^{3} - 2 \, x^{2} e^{\left (2 \, x\right )} - 5 \, x^{2} + x e^{\left (4 \, x\right )} + 5 \, x\right )} \log \left (x\right )}{5 \, {\left (2 \, x^{2} - x + 1\right )}} \]
integrate((((-8*x^3+6*x^2-4*x-1)*exp(x)^4+(8*x^4-4*x^3+2*x^2+4*x)*exp(x)^2 -22*x^4+22*x^3-28*x^2+10*x-5)*log(x)+(-2*x^2+x-1)*exp(x)^4+(4*x^3-2*x^2+2* x)*exp(x)^2-22*x^4+21*x^3-26*x^2+10*x-5)/(20*x^4-20*x^3+25*x^2-10*x+5),x, algorithm=\
Leaf count of result is larger than twice the leaf count of optimal. 112 vs. \(2 (24) = 48\).
Time = 0.25 (sec) , antiderivative size = 112, normalized size of antiderivative = 3.61 \[ \int \frac {-5+10 x-26 x^2+21 x^3-22 x^4+e^{4 x} \left (-1+x-2 x^2\right )+e^{2 x} \left (2 x-2 x^2+4 x^3\right )+\left (-5+10 x-28 x^2+22 x^3-22 x^4+e^{4 x} \left (-1-4 x+6 x^2-8 x^3\right )+e^{2 x} \left (4 x+2 x^2-4 x^3+8 x^4\right )\right ) \log (x)}{5-10 x+25 x^2-20 x^3+20 x^4} \, dx=\frac {\left (- 10 x^{3} \log {\left (x \right )} + 5 x^{2} \log {\left (x \right )} - 5 x \log {\left (x \right )}\right ) e^{4 x} + \left (20 x^{4} \log {\left (x \right )} - 10 x^{3} \log {\left (x \right )} + 10 x^{2} \log {\left (x \right )}\right ) e^{2 x}}{100 x^{4} - 100 x^{3} + 125 x^{2} - 50 x + 25} - \frac {\log {\left (x \right )}}{20} + \frac {\left (- 44 x^{3} + 22 x^{2} - 21 x + 1\right ) \log {\left (x \right )}}{40 x^{2} - 20 x + 20} \]
integrate((((-8*x**3+6*x**2-4*x-1)*exp(x)**4+(8*x**4-4*x**3+2*x**2+4*x)*ex p(x)**2-22*x**4+22*x**3-28*x**2+10*x-5)*ln(x)+(-2*x**2+x-1)*exp(x)**4+(4*x **3-2*x**2+2*x)*exp(x)**2-22*x**4+21*x**3-26*x**2+10*x-5)/(20*x**4-20*x**3 +25*x**2-10*x+5),x)
((-10*x**3*log(x) + 5*x**2*log(x) - 5*x*log(x))*exp(4*x) + (20*x**4*log(x) - 10*x**3*log(x) + 10*x**2*log(x))*exp(2*x))/(100*x**4 - 100*x**3 + 125*x **2 - 50*x + 25) - log(x)/20 + (-44*x**3 + 22*x**2 - 21*x + 1)*log(x)/(40* x**2 - 20*x + 20)
Leaf count of result is larger than twice the leaf count of optimal. 161 vs. \(2 (30) = 60\).
Time = 0.31 (sec) , antiderivative size = 161, normalized size of antiderivative = 5.19 \[ \int \frac {-5+10 x-26 x^2+21 x^3-22 x^4+e^{4 x} \left (-1+x-2 x^2\right )+e^{2 x} \left (2 x-2 x^2+4 x^3\right )+\left (-5+10 x-28 x^2+22 x^3-22 x^4+e^{4 x} \left (-1-4 x+6 x^2-8 x^3\right )+e^{2 x} \left (4 x+2 x^2-4 x^3+8 x^4\right )\right ) \log (x)}{5-10 x+25 x^2-20 x^3+20 x^4} \, dx=-\frac {11}{10} \, x + \frac {4 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right ) + 22 \, x^{3} - 2 \, x e^{\left (4 \, x\right )} \log \left (x\right ) - 11 \, x^{2} - 2 \, {\left (11 \, x^{3} - 5 \, x^{2} + 5 \, x\right )} \log \left (x\right ) + 11 \, x}{10 \, {\left (2 \, x^{2} - x + 1\right )}} - \frac {3 \, {\left (5 \, x - 3\right )}}{20 \, {\left (2 \, x^{2} - x + 1\right )}} - \frac {4 \, x - 1}{7 \, {\left (2 \, x^{2} - x + 1\right )}} + \frac {13 \, {\left (3 \, x + 1\right )}}{35 \, {\left (2 \, x^{2} - x + 1\right )}} - \frac {11 \, {\left (x + 5\right )}}{140 \, {\left (2 \, x^{2} - x + 1\right )}} + \frac {2 \, {\left (x - 2\right )}}{7 \, {\left (2 \, x^{2} - x + 1\right )}} \]
integrate((((-8*x^3+6*x^2-4*x-1)*exp(x)^4+(8*x^4-4*x^3+2*x^2+4*x)*exp(x)^2 -22*x^4+22*x^3-28*x^2+10*x-5)*log(x)+(-2*x^2+x-1)*exp(x)^4+(4*x^3-2*x^2+2* x)*exp(x)^2-22*x^4+21*x^3-26*x^2+10*x-5)/(20*x^4-20*x^3+25*x^2-10*x+5),x, algorithm=\
-11/10*x + 1/10*(4*x^2*e^(2*x)*log(x) + 22*x^3 - 2*x*e^(4*x)*log(x) - 11*x ^2 - 2*(11*x^3 - 5*x^2 + 5*x)*log(x) + 11*x)/(2*x^2 - x + 1) - 3/20*(5*x - 3)/(2*x^2 - x + 1) - 1/7*(4*x - 1)/(2*x^2 - x + 1) + 13/35*(3*x + 1)/(2*x ^2 - x + 1) - 11/140*(x + 5)/(2*x^2 - x + 1) + 2/7*(x - 2)/(2*x^2 - x + 1)
Time = 0.27 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.71 \[ \int \frac {-5+10 x-26 x^2+21 x^3-22 x^4+e^{4 x} \left (-1+x-2 x^2\right )+e^{2 x} \left (2 x-2 x^2+4 x^3\right )+\left (-5+10 x-28 x^2+22 x^3-22 x^4+e^{4 x} \left (-1-4 x+6 x^2-8 x^3\right )+e^{2 x} \left (4 x+2 x^2-4 x^3+8 x^4\right )\right ) \log (x)}{5-10 x+25 x^2-20 x^3+20 x^4} \, dx=-\frac {11 \, x^{3} \log \left (x\right ) - 2 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right ) - 5 \, x^{2} \log \left (x\right ) + x e^{\left (4 \, x\right )} \log \left (x\right ) + 5 \, x \log \left (x\right )}{5 \, {\left (2 \, x^{2} - x + 1\right )}} \]
integrate((((-8*x^3+6*x^2-4*x-1)*exp(x)^4+(8*x^4-4*x^3+2*x^2+4*x)*exp(x)^2 -22*x^4+22*x^3-28*x^2+10*x-5)*log(x)+(-2*x^2+x-1)*exp(x)^4+(4*x^3-2*x^2+2* x)*exp(x)^2-22*x^4+21*x^3-26*x^2+10*x-5)/(20*x^4-20*x^3+25*x^2-10*x+5),x, algorithm=\
-1/5*(11*x^3*log(x) - 2*x^2*e^(2*x)*log(x) - 5*x^2*log(x) + x*e^(4*x)*log( x) + 5*x*log(x))/(2*x^2 - x + 1)
Timed out. \[ \int \frac {-5+10 x-26 x^2+21 x^3-22 x^4+e^{4 x} \left (-1+x-2 x^2\right )+e^{2 x} \left (2 x-2 x^2+4 x^3\right )+\left (-5+10 x-28 x^2+22 x^3-22 x^4+e^{4 x} \left (-1-4 x+6 x^2-8 x^3\right )+e^{2 x} \left (4 x+2 x^2-4 x^3+8 x^4\right )\right ) \log (x)}{5-10 x+25 x^2-20 x^3+20 x^4} \, dx=\int -\frac {{\mathrm {e}}^{4\,x}\,\left (2\,x^2-x+1\right )-10\,x-{\mathrm {e}}^{2\,x}\,\left (4\,x^3-2\,x^2+2\,x\right )+26\,x^2-21\,x^3+22\,x^4+\ln \left (x\right )\,\left ({\mathrm {e}}^{4\,x}\,\left (8\,x^3-6\,x^2+4\,x+1\right )-10\,x-{\mathrm {e}}^{2\,x}\,\left (8\,x^4-4\,x^3+2\,x^2+4\,x\right )+28\,x^2-22\,x^3+22\,x^4+5\right )+5}{20\,x^4-20\,x^3+25\,x^2-10\,x+5} \,d x \]
int(-(exp(4*x)*(2*x^2 - x + 1) - 10*x - exp(2*x)*(2*x - 2*x^2 + 4*x^3) + 2 6*x^2 - 21*x^3 + 22*x^4 + log(x)*(exp(4*x)*(4*x - 6*x^2 + 8*x^3 + 1) - 10* x - exp(2*x)*(4*x + 2*x^2 - 4*x^3 + 8*x^4) + 28*x^2 - 22*x^3 + 22*x^4 + 5) + 5)/(25*x^2 - 10*x - 20*x^3 + 20*x^4 + 5),x)