3.62.1 \(\int \frac {125 e^2-125 x-250 e x+125 x^2+e^{6 x} (-e^2+x+2 e x-x^2)+e^{5 x} (3 e^2 x-3 x^2-6 e x^2+3 x^3)+e^x (75 e^2 x-75 x^2-150 e x^2+75 x^3)+e^{2 x} (10+75 x-75 x^2-15 x^3+15 x^4+e^2 (-75+15 x^2)+e (150 x-30 x^3))+e^{4 x} (-2-15 x+15 x^2+3 x^3-3 x^4+e^2 (15-3 x^2)+e (-30 x+6 x^3))+e^{3 x} (2 x+30 x^2-30 x^3-x^4+x^5+e^2 (-30 x+x^3)+e (60 x^2-2 x^4))+(-250 e x+250 x^2+e^{6 x} (2 e x-2 x^2)+e^{5 x} (-6 e x^2+6 x^3)+e^x (-150 e x^2+150 x^3)+e^{2 x} (20 x-150 x^2+30 x^4+e (150 x-30 x^3))+e^{4 x} (4 x+30 x^2-6 x^4+e (-30 x+6 x^3))+e^{3 x} (-4 x-60 x^3+2 x^5+e (60 x^2-2 x^4))) \log (x)}{-125 x+e^{6 x} x-75 e^x x^2-3 e^{5 x} x^2+e^{2 x} (75 x-15 x^3)+e^{4 x} (-15 x+3 x^3)+e^{3 x} (30 x^2-x^4)} \, dx\)

Optimal. Leaf size=32 \[ x-\left (\frac {2}{\left (-5 e^{-x}+e^x-x\right )^2}+(-e+x)^2\right ) \log (x) \]

________________________________________________________________________________________

Rubi [F]  time = 12.43, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {125 e^2-125 x-250 e x+125 x^2+e^{6 x} \left (-e^2+x+2 e x-x^2\right )+e^{5 x} \left (3 e^2 x-3 x^2-6 e x^2+3 x^3\right )+e^x \left (75 e^2 x-75 x^2-150 e x^2+75 x^3\right )+e^{2 x} \left (10+75 x-75 x^2-15 x^3+15 x^4+e^2 \left (-75+15 x^2\right )+e \left (150 x-30 x^3\right )\right )+e^{4 x} \left (-2-15 x+15 x^2+3 x^3-3 x^4+e^2 \left (15-3 x^2\right )+e \left (-30 x+6 x^3\right )\right )+e^{3 x} \left (2 x+30 x^2-30 x^3-x^4+x^5+e^2 \left (-30 x+x^3\right )+e \left (60 x^2-2 x^4\right )\right )+\left (-250 e x+250 x^2+e^{6 x} \left (2 e x-2 x^2\right )+e^{5 x} \left (-6 e x^2+6 x^3\right )+e^x \left (-150 e x^2+150 x^3\right )+e^{2 x} \left (20 x-150 x^2+30 x^4+e \left (150 x-30 x^3\right )\right )+e^{4 x} \left (4 x+30 x^2-6 x^4+e \left (-30 x+6 x^3\right )\right )+e^{3 x} \left (-4 x-60 x^3+2 x^5+e \left (60 x^2-2 x^4\right )\right )\right ) \log (x)}{-125 x+e^{6 x} x-75 e^x x^2-3 e^{5 x} x^2+e^{2 x} \left (75 x-15 x^3\right )+e^{4 x} \left (-15 x+3 x^3\right )+e^{3 x} \left (30 x^2-x^4\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(125*E^2 - 125*x - 250*E*x + 125*x^2 + E^(6*x)*(-E^2 + x + 2*E*x - x^2) + E^(5*x)*(3*E^2*x - 3*x^2 - 6*E*x
^2 + 3*x^3) + E^x*(75*E^2*x - 75*x^2 - 150*E*x^2 + 75*x^3) + E^(2*x)*(10 + 75*x - 75*x^2 - 15*x^3 + 15*x^4 + E
^2*(-75 + 15*x^2) + E*(150*x - 30*x^3)) + E^(4*x)*(-2 - 15*x + 15*x^2 + 3*x^3 - 3*x^4 + E^2*(15 - 3*x^2) + E*(
-30*x + 6*x^3)) + E^(3*x)*(2*x + 30*x^2 - 30*x^3 - x^4 + x^5 + E^2*(-30*x + x^3) + E*(60*x^2 - 2*x^4)) + (-250
*E*x + 250*x^2 + E^(6*x)*(2*E*x - 2*x^2) + E^(5*x)*(-6*E*x^2 + 6*x^3) + E^x*(-150*E*x^2 + 150*x^3) + E^(2*x)*(
20*x - 150*x^2 + 30*x^4 + E*(150*x - 30*x^3)) + E^(4*x)*(4*x + 30*x^2 - 6*x^4 + E*(-30*x + 6*x^3)) + E^(3*x)*(
-4*x - 60*x^3 + 2*x^5 + E*(60*x^2 - 2*x^4)))*Log[x])/(-125*x + E^(6*x)*x - 75*E^x*x^2 - 3*E^(5*x)*x^2 + E^(2*x
)*(75*x - 15*x^3) + E^(4*x)*(-15*x + 3*x^3) + E^(3*x)*(30*x^2 - x^4)),x]

[Out]

-2*E*x + (1 + 2*E)*x - E^2*Log[x] + (2*E*x - x^2)*Log[x] + 200*Log[x]*Defer[Int][(-5 + E^(2*x) - E^x*x)^(-3),
x] - 20*Log[x]*Defer[Int][E^x/(-5 + E^(2*x) - E^x*x)^3, x] + 60*Log[x]*Defer[Int][(E^x*x)/(-5 + E^(2*x) - E^x*
x)^3, x] - 4*Log[x]*Defer[Int][(E^x*x^2)/(-5 + E^(2*x) - E^x*x)^3, x] + 4*Log[x]*Defer[Int][(E^x*x^3)/(-5 + E^
(2*x) - E^x*x)^3, x] + 60*Log[x]*Defer[Int][(-5 + E^(2*x) - E^x*x)^(-2), x] - 2*Defer[Int][E^x/(-5 + E^(2*x) -
E^x*x)^2, x] - 4*Log[x]*Defer[Int][E^x/(-5 + E^(2*x) - E^x*x)^2, x] + 8*Log[x]*Defer[Int][(E^x*x)/(-5 + E^(2*
x) - E^x*x)^2, x] + 4*Log[x]*Defer[Int][(-5 + E^(2*x) - E^x*x)^(-1), x] + 20*Log[x]*Defer[Int][x/(5 - E^(2*x)
+ E^x*x)^3, x] - 20*Log[x]*Defer[Int][x^2/(5 - E^(2*x) + E^x*x)^3, x] - 10*Defer[Int][1/(x*(5 - E^(2*x) + E^x*
x)^2), x] - 4*Log[x]*Defer[Int][x/(5 - E^(2*x) + E^x*x)^2, x] + 4*Log[x]*Defer[Int][x^2/(5 - E^(2*x) + E^x*x)^
2, x] + 2*Defer[Int][1/(x*(5 - E^(2*x) + E^x*x)), x] - 200*Defer[Int][Defer[Int][(-5 + E^(2*x) - E^x*x)^(-3),
x]/x, x] + 20*Defer[Int][Defer[Int][E^x/(-5 + E^(2*x) - E^x*x)^3, x]/x, x] - 60*Defer[Int][Defer[Int][(E^x*x)/
(-5 + E^(2*x) - E^x*x)^3, x]/x, x] + 4*Defer[Int][Defer[Int][(E^x*x^2)/(-5 + E^(2*x) - E^x*x)^3, x]/x, x] - 4*
Defer[Int][Defer[Int][(E^x*x^3)/(-5 + E^(2*x) - E^x*x)^3, x]/x, x] - 4*Defer[Int][Defer[Int][(-5 + E^(2*x) - E
^x*x)^(-1), x]/x, x] - 20*Defer[Int][Defer[Int][x/(5 - E^(2*x) + E^x*x)^3, x]/x, x] + 20*Defer[Int][Defer[Int]
[x^2/(5 - E^(2*x) + E^x*x)^3, x]/x, x] - 60*Defer[Int][Defer[Int][(5 - E^(2*x) + E^x*x)^(-2), x]/x, x] + 4*Def
er[Int][Defer[Int][E^x/(5 - E^(2*x) + E^x*x)^2, x]/x, x] + 4*Defer[Int][Defer[Int][x/(5 - E^(2*x) + E^x*x)^2,
x]/x, x] - 8*Defer[Int][Defer[Int][(E^x*x)/(5 - E^(2*x) + E^x*x)^2, x]/x, x] - 4*Defer[Int][Defer[Int][x^2/(5
- E^(2*x) + E^x*x)^2, x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {125 e^2+(-125-250 e) x+125 x^2+e^{6 x} \left (-e^2+x+2 e x-x^2\right )+e^{5 x} \left (3 e^2 x-3 x^2-6 e x^2+3 x^3\right )+e^x \left (75 e^2 x-75 x^2-150 e x^2+75 x^3\right )+e^{2 x} \left (10+75 x-75 x^2-15 x^3+15 x^4+e^2 \left (-75+15 x^2\right )+e \left (150 x-30 x^3\right )\right )+e^{4 x} \left (-2-15 x+15 x^2+3 x^3-3 x^4+e^2 \left (15-3 x^2\right )+e \left (-30 x+6 x^3\right )\right )+e^{3 x} \left (2 x+30 x^2-30 x^3-x^4+x^5+e^2 \left (-30 x+x^3\right )+e \left (60 x^2-2 x^4\right )\right )+\left (-250 e x+250 x^2+e^{6 x} \left (2 e x-2 x^2\right )+e^{5 x} \left (-6 e x^2+6 x^3\right )+e^x \left (-150 e x^2+150 x^3\right )+e^{2 x} \left (20 x-150 x^2+30 x^4+e \left (150 x-30 x^3\right )\right )+e^{4 x} \left (4 x+30 x^2-6 x^4+e \left (-30 x+6 x^3\right )\right )+e^{3 x} \left (-4 x-60 x^3+2 x^5+e \left (60 x^2-2 x^4\right )\right )\right ) \log (x)}{-125 x+e^{6 x} x-75 e^x x^2-3 e^{5 x} x^2+e^{2 x} \left (75 x-15 x^3\right )+e^{4 x} \left (-15 x+3 x^3\right )+e^{3 x} \left (30 x^2-x^4\right )} \, dx\\ &=\int \frac {\left (-5+e^{2 x}-e^x x\right ) \left (25 e^2+e^{2+4 x}-50 e x+10 e^{2+x} x-2 e^{2+3 x} x-2 e^{1+4 x} x+25 (-1+x) x+e^{4 x} (-1+x) x-20 e^{1+x} x^2+4 e^{1+3 x} x^2+10 e^x (-1+x) x^2-2 e^{3 x} (-1+x) x^2+e^{2+2 x} \left (-10+x^2\right )-2 e^{1+2 x} x \left (-10+x^2\right )+e^{2 x} \left (2+10 x-10 x^2-x^3+x^4\right )\right )-2 x \left (-125 e+e^{1+6 x}+125 x-e^{6 x} x-75 e^{1+x} x-3 e^{1+5 x} x+75 e^x x^2+3 e^{5 x} x^2-e^{1+3 x} x \left (-30+x^2\right )-15 e^{1+2 x} \left (-5+x^2\right )+3 e^{1+4 x} \left (-5+x^2\right )+e^{4 x} \left (2+15 x-3 x^3\right )+5 e^{2 x} \left (2-15 x+3 x^3\right )+e^{3 x} \left (-2-30 x^2+x^4\right )\right ) \log (x)}{x \left (5-e^{2 x}+e^x x\right )^3} \, dx\\ &=\int \left (\frac {4 \left (50-5 e^x-5 x+15 e^x x+5 x^2-e^x x^2+e^x x^3\right ) \log (x)}{\left (-5+e^{2 x}-e^x x\right )^3}-\frac {2 (-1+2 x \log (x))}{x \left (5-e^{2 x}+e^x x\right )}+\frac {-e^2+(1+2 e) x-x^2+2 e x \log (x)-2 x^2 \log (x)}{x}+\frac {2 \left (-5-e^x x+30 x \log (x)-2 e^x x \log (x)-2 x^2 \log (x)+4 e^x x^2 \log (x)+2 x^3 \log (x)\right )}{x \left (5-e^{2 x}+e^x x\right )^2}\right ) \, dx\\ &=-\left (2 \int \frac {-1+2 x \log (x)}{x \left (5-e^{2 x}+e^x x\right )} \, dx\right )+2 \int \frac {-5-e^x x+30 x \log (x)-2 e^x x \log (x)-2 x^2 \log (x)+4 e^x x^2 \log (x)+2 x^3 \log (x)}{x \left (5-e^{2 x}+e^x x\right )^2} \, dx+4 \int \frac {\left (50-5 e^x-5 x+15 e^x x+5 x^2-e^x x^2+e^x x^3\right ) \log (x)}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+\int \frac {-e^2+(1+2 e) x-x^2+2 e x \log (x)-2 x^2 \log (x)}{x} \, dx\\ &=-\left (2 \int \left (-\frac {1}{x \left (5-e^{2 x}+e^x x\right )}-\frac {2 \log (x)}{-5+e^{2 x}-e^x x}\right ) \, dx\right )+2 \int \frac {-5-e^x x+2 x \left (15-x+x^2+e^x (-1+2 x)\right ) \log (x)}{x \left (5-e^{2 x}+e^x x\right )^2} \, dx-4 \int \frac {50 \int \frac {1}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx-5 \int \frac {e^x}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+15 \int \frac {e^x x}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx-\int \frac {e^x x^2}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+\int \frac {e^x x^3}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+5 \int \frac {x}{\left (5-e^{2 x}+e^x x\right )^3} \, dx-5 \int \frac {x^2}{\left (5-e^{2 x}+e^x x\right )^3} \, dx}{x} \, dx-(4 \log (x)) \int \frac {e^x x^2}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+(4 \log (x)) \int \frac {e^x x^3}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx-(20 \log (x)) \int \frac {e^x}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+(20 \log (x)) \int \frac {x}{\left (5-e^{2 x}+e^x x\right )^3} \, dx-(20 \log (x)) \int \frac {x^2}{\left (5-e^{2 x}+e^x x\right )^3} \, dx+(60 \log (x)) \int \frac {e^x x}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+(200 \log (x)) \int \frac {1}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+\int \left (\frac {-e^2+(1+2 e) x-x^2}{x}+2 (e-x) \log (x)\right ) \, dx\\ &=2 \int \frac {1}{x \left (5-e^{2 x}+e^x x\right )} \, dx+2 \int (e-x) \log (x) \, dx+2 \int \left (-\frac {e^x}{\left (-5+e^{2 x}-e^x x\right )^2}-\frac {5}{x \left (5-e^{2 x}+e^x x\right )^2}+\frac {30 \log (x)}{\left (-5+e^{2 x}-e^x x\right )^2}-\frac {2 e^x \log (x)}{\left (-5+e^{2 x}-e^x x\right )^2}+\frac {4 e^x x \log (x)}{\left (-5+e^{2 x}-e^x x\right )^2}-\frac {2 x \log (x)}{\left (5-e^{2 x}+e^x x\right )^2}+\frac {2 x^2 \log (x)}{\left (5-e^{2 x}+e^x x\right )^2}\right ) \, dx+4 \int \frac {\log (x)}{-5+e^{2 x}-e^x x} \, dx-4 \int \left (\frac {50 \int \frac {1}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx-5 \int \frac {e^x}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+15 \int \frac {e^x x}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx-\int \frac {e^x x^2}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+\int \frac {e^x x^3}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+5 \int \frac {x}{\left (5-e^{2 x}+e^x x\right )^3} \, dx}{x}-\frac {5 \int \frac {x^2}{\left (5-e^{2 x}+e^x x\right )^3} \, dx}{x}\right ) \, dx-(4 \log (x)) \int \frac {e^x x^2}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+(4 \log (x)) \int \frac {e^x x^3}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx-(20 \log (x)) \int \frac {e^x}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+(20 \log (x)) \int \frac {x}{\left (5-e^{2 x}+e^x x\right )^3} \, dx-(20 \log (x)) \int \frac {x^2}{\left (5-e^{2 x}+e^x x\right )^3} \, dx+(60 \log (x)) \int \frac {e^x x}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+(200 \log (x)) \int \frac {1}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+\int \frac {-e^2+(1+2 e) x-x^2}{x} \, dx\\ &=\left (2 e x-x^2\right ) \log (x)-2 \int \left (e-\frac {x}{2}\right ) \, dx-2 \int \frac {e^x}{\left (-5+e^{2 x}-e^x x\right )^2} \, dx+2 \int \frac {1}{x \left (5-e^{2 x}+e^x x\right )} \, dx-4 \int \frac {e^x \log (x)}{\left (-5+e^{2 x}-e^x x\right )^2} \, dx-4 \int \frac {x \log (x)}{\left (5-e^{2 x}+e^x x\right )^2} \, dx+4 \int \frac {x^2 \log (x)}{\left (5-e^{2 x}+e^x x\right )^2} \, dx-4 \int \frac {\int \frac {1}{-5+e^{2 x}-e^x x} \, dx}{x} \, dx-4 \int \frac {50 \int \frac {1}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx-5 \int \frac {e^x}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+15 \int \frac {e^x x}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx-\int \frac {e^x x^2}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+\int \frac {e^x x^3}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+5 \int \frac {x}{\left (5-e^{2 x}+e^x x\right )^3} \, dx}{x} \, dx+8 \int \frac {e^x x \log (x)}{\left (-5+e^{2 x}-e^x x\right )^2} \, dx-10 \int \frac {1}{x \left (5-e^{2 x}+e^x x\right )^2} \, dx+20 \int \frac {\int \frac {x^2}{\left (5-e^{2 x}+e^x x\right )^3} \, dx}{x} \, dx+60 \int \frac {\log (x)}{\left (-5+e^{2 x}-e^x x\right )^2} \, dx-(4 \log (x)) \int \frac {e^x x^2}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+(4 \log (x)) \int \frac {e^x x^3}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+(4 \log (x)) \int \frac {1}{-5+e^{2 x}-e^x x} \, dx-(20 \log (x)) \int \frac {e^x}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+(20 \log (x)) \int \frac {x}{\left (5-e^{2 x}+e^x x\right )^3} \, dx-(20 \log (x)) \int \frac {x^2}{\left (5-e^{2 x}+e^x x\right )^3} \, dx+(60 \log (x)) \int \frac {e^x x}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+(200 \log (x)) \int \frac {1}{\left (-5+e^{2 x}-e^x x\right )^3} \, dx+\int \left (1+2 e-\frac {e^2}{x}-x\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B]  time = 0.42, size = 129, normalized size = 4.03 \begin {gather*} x-e^2 \log (x)-\frac {\left (-50 e x-2 e^{1+4 x} x+25 x^2+e^{4 x} x^2-20 e^{1+x} x^2+4 e^{1+3 x} x^2+10 e^x x^3-2 e^{3 x} x^3-2 e^{1+2 x} x \left (-10+x^2\right )+e^{2 x} \left (2-10 x^2+x^4\right )\right ) \log (x)}{\left (5-e^{2 x}+e^x x\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(125*E^2 - 125*x - 250*E*x + 125*x^2 + E^(6*x)*(-E^2 + x + 2*E*x - x^2) + E^(5*x)*(3*E^2*x - 3*x^2 -
6*E*x^2 + 3*x^3) + E^x*(75*E^2*x - 75*x^2 - 150*E*x^2 + 75*x^3) + E^(2*x)*(10 + 75*x - 75*x^2 - 15*x^3 + 15*x
^4 + E^2*(-75 + 15*x^2) + E*(150*x - 30*x^3)) + E^(4*x)*(-2 - 15*x + 15*x^2 + 3*x^3 - 3*x^4 + E^2*(15 - 3*x^2)
+ E*(-30*x + 6*x^3)) + E^(3*x)*(2*x + 30*x^2 - 30*x^3 - x^4 + x^5 + E^2*(-30*x + x^3) + E*(60*x^2 - 2*x^4)) +
(-250*E*x + 250*x^2 + E^(6*x)*(2*E*x - 2*x^2) + E^(5*x)*(-6*E*x^2 + 6*x^3) + E^x*(-150*E*x^2 + 150*x^3) + E^(
2*x)*(20*x - 150*x^2 + 30*x^4 + E*(150*x - 30*x^3)) + E^(4*x)*(4*x + 30*x^2 - 6*x^4 + E*(-30*x + 6*x^3)) + E^(
3*x)*(-4*x - 60*x^3 + 2*x^5 + E*(60*x^2 - 2*x^4)))*Log[x])/(-125*x + E^(6*x)*x - 75*E^x*x^2 - 3*E^(5*x)*x^2 +
E^(2*x)*(75*x - 15*x^3) + E^(4*x)*(-15*x + 3*x^3) + E^(3*x)*(30*x^2 - x^4)),x]

[Out]

x - E^2*Log[x] - ((-50*E*x - 2*E^(1 + 4*x)*x + 25*x^2 + E^(4*x)*x^2 - 20*E^(1 + x)*x^2 + 4*E^(1 + 3*x)*x^2 + 1
0*E^x*x^3 - 2*E^(3*x)*x^3 - 2*E^(1 + 2*x)*x*(-10 + x^2) + E^(2*x)*(2 - 10*x^2 + x^4))*Log[x])/(5 - E^(2*x) + E
^x*x)^2

________________________________________________________________________________________

fricas [B]  time = 0.79, size = 182, normalized size = 5.69 \begin {gather*} \frac {2 \, x^{2} e^{\left (3 \, x\right )} - 10 \, x^{2} e^{x} - x e^{\left (4 \, x\right )} - {\left (x^{3} - 10 \, x\right )} e^{\left (2 \, x\right )} + {\left (25 \, x^{2} - 50 \, x e + {\left (x^{2} - 2 \, x e + e^{2}\right )} e^{\left (4 \, x\right )} - 2 \, {\left (x^{3} - 2 \, x^{2} e + x e^{2}\right )} e^{\left (3 \, x\right )} + {\left (x^{4} - 10 \, x^{2} + {\left (x^{2} - 10\right )} e^{2} - 2 \, {\left (x^{3} - 10 \, x\right )} e + 2\right )} e^{\left (2 \, x\right )} + 10 \, {\left (x^{3} - 2 \, x^{2} e + x e^{2}\right )} e^{x} + 25 \, e^{2}\right )} \log \relax (x) - 25 \, x}{2 \, x e^{\left (3 \, x\right )} - {\left (x^{2} - 10\right )} e^{\left (2 \, x\right )} - 10 \, x e^{x} - e^{\left (4 \, x\right )} - 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x*exp(1)-2*x^2)*exp(x)^6+(-6*x^2*exp(1)+6*x^3)*exp(x)^5+((6*x^3-30*x)*exp(1)-6*x^4+30*x^2+4*x)*
exp(x)^4+((-2*x^4+60*x^2)*exp(1)+2*x^5-60*x^3-4*x)*exp(x)^3+((-30*x^3+150*x)*exp(1)+30*x^4-150*x^2+20*x)*exp(x
)^2+(-150*x^2*exp(1)+150*x^3)*exp(x)-250*x*exp(1)+250*x^2)*log(x)+(-exp(1)^2+2*x*exp(1)-x^2+x)*exp(x)^6+(3*x*e
xp(1)^2-6*x^2*exp(1)+3*x^3-3*x^2)*exp(x)^5+((-3*x^2+15)*exp(1)^2+(6*x^3-30*x)*exp(1)-3*x^4+3*x^3+15*x^2-15*x-2
)*exp(x)^4+((x^3-30*x)*exp(1)^2+(-2*x^4+60*x^2)*exp(1)+x^5-x^4-30*x^3+30*x^2+2*x)*exp(x)^3+((15*x^2-75)*exp(1)
^2+(-30*x^3+150*x)*exp(1)+15*x^4-15*x^3-75*x^2+75*x+10)*exp(x)^2+(75*x*exp(1)^2-150*x^2*exp(1)+75*x^3-75*x^2)*
exp(x)+125*exp(1)^2-250*x*exp(1)+125*x^2-125*x)/(x*exp(x)^6-3*x^2*exp(x)^5+(3*x^3-15*x)*exp(x)^4+(-x^4+30*x^2)
*exp(x)^3+(-15*x^3+75*x)*exp(x)^2-75*exp(x)*x^2-125*x),x, algorithm="fricas")

[Out]

(2*x^2*e^(3*x) - 10*x^2*e^x - x*e^(4*x) - (x^3 - 10*x)*e^(2*x) + (25*x^2 - 50*x*e + (x^2 - 2*x*e + e^2)*e^(4*x
) - 2*(x^3 - 2*x^2*e + x*e^2)*e^(3*x) + (x^4 - 10*x^2 + (x^2 - 10)*e^2 - 2*(x^3 - 10*x)*e + 2)*e^(2*x) + 10*(x
^3 - 2*x^2*e + x*e^2)*e^x + 25*e^2)*log(x) - 25*x)/(2*x*e^(3*x) - (x^2 - 10)*e^(2*x) - 10*x*e^x - e^(4*x) - 25
)

________________________________________________________________________________________

giac [B]  time = 0.60, size = 1806, normalized size = 56.44 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x*exp(1)-2*x^2)*exp(x)^6+(-6*x^2*exp(1)+6*x^3)*exp(x)^5+((6*x^3-30*x)*exp(1)-6*x^4+30*x^2+4*x)*
exp(x)^4+((-2*x^4+60*x^2)*exp(1)+2*x^5-60*x^3-4*x)*exp(x)^3+((-30*x^3+150*x)*exp(1)+30*x^4-150*x^2+20*x)*exp(x
)^2+(-150*x^2*exp(1)+150*x^3)*exp(x)-250*x*exp(1)+250*x^2)*log(x)+(-exp(1)^2+2*x*exp(1)-x^2+x)*exp(x)^6+(3*x*e
xp(1)^2-6*x^2*exp(1)+3*x^3-3*x^2)*exp(x)^5+((-3*x^2+15)*exp(1)^2+(6*x^3-30*x)*exp(1)-3*x^4+3*x^3+15*x^2-15*x-2
)*exp(x)^4+((x^3-30*x)*exp(1)^2+(-2*x^4+60*x^2)*exp(1)+x^5-x^4-30*x^3+30*x^2+2*x)*exp(x)^3+((15*x^2-75)*exp(1)
^2+(-30*x^3+150*x)*exp(1)+15*x^4-15*x^3-75*x^2+75*x+10)*exp(x)^2+(75*x*exp(1)^2-150*x^2*exp(1)+75*x^3-75*x^2)*
exp(x)+125*exp(1)^2-250*x*exp(1)+125*x^2-125*x)/(x*exp(x)^6-3*x^2*exp(x)^5+(3*x^3-15*x)*exp(x)^4+(-x^4+30*x^2)
*exp(x)^3+(-15*x^3+75*x)*exp(x)^2-75*exp(x)*x^2-125*x),x, algorithm="giac")

[Out]

-1/2*(2*x^11*e^(2*x)*log(x) - 4*x^10*e^(3*x)*log(x) - 4*x^10*e^(2*x + 1)*log(x) + 20*x^10*e^x*log(x) - 2*x^10*
e^(2*x) + 2*x^9*e^(4*x)*log(x) + 94*x^9*e^(2*x)*log(x) + 8*x^9*e^(3*x + 1)*log(x) + 2*x^9*e^(2*x + 2)*log(x) -
40*x^9*e^(x + 1)*log(x) + 20*x^9*e^x*log(x) + 4*x^9*e^(3*x) - 10*x^9*e^x + 50*x^9*log(x) - 100*x^8*e*log(x) -
228*x^8*e^(3*x)*log(x) - 40*x^8*e^(2*x)*log(x) - 4*x^8*e^(4*x + 1)*log(x) - 4*x^8*e^(3*x + 2)*log(x) - 188*x^
8*e^(2*x + 1)*log(x) + 20*x^8*e^(x + 2)*log(x) - 20*x^8*e^(x + 1)*log(x) + 1110*x^8*e^x*log(x) - 2*x^8*e^(4*x)
- 114*x^8*e^(2*x) - 20*x^8*e^(x + 1) - 35*x^8*e^x + 150*x^8*log(x) + 50*x^7*e^2*log(x) - 150*x^7*e*log(x) + 1
14*x^7*e^(4*x)*log(x) + 20*x^7*e^(3*x)*log(x) + 1090*x^7*e^(2*x)*log(x) + 2*x^7*e^(4*x + 2)*log(x) + 456*x^7*e
^(3*x + 1)*log(x) + 94*x^7*e^(2*x + 2)*log(x) + 40*x^7*e^(2*x + 1)*log(x) - 2260*x^7*e^(x + 1)*log(x) + 970*x^
7*e^x*log(x) + 25*x^8 - 150*x^7*e + 238*x^7*e^(3*x) + 70*x^7*e^(2*x) + 40*x^7*e^(2*x + 1) + 30*x^7*e^(x + 1) -
625*x^7*e^x + 2650*x^7*log(x) - 5550*x^6*e*log(x) - 4362*x^6*e^(3*x)*log(x) - 2190*x^6*e^(2*x)*log(x) - 228*x
^6*e^(4*x + 1)*log(x) - 228*x^6*e^(3*x + 2)*log(x) - 20*x^6*e^(3*x + 1)*log(x) - 2092*x^6*e^(2*x + 1)*log(x) +
1140*x^6*e^(x + 2)*log(x) - 950*x^6*e^(x + 1)*log(x) + 20230*x^6*e^x*log(x) - 225*x^7 + 200*x^6*e - 114*x^6*e
^(4*x) - 35*x^6*e^(3*x) - 2181*x^6*e^(2*x) - 20*x^6*e^(3*x + 1) - 60*x^6*e^(2*x + 1) - 970*x^6*e^(x + 1) - 159
0*x^6*e^x + 8000*x^6*log(x) + 2850*x^5*e^2*log(x) - 7900*x^5*e*log(x) + 2166*x^5*e^(4*x)*log(x) + 1070*x^5*e^(
3*x)*log(x) - 4554*x^5*e^(2*x)*log(x) + 114*x^5*e^(4*x + 2)*log(x) + 8684*x^5*e^(3*x + 1)*log(x) + 1026*x^5*e^
(2*x + 2)*log(x) + 2150*x^5*e^(2*x + 1)*log(x) - 42290*x^5*e^(x + 1)*log(x) + 11370*x^5*e^x*log(x) + 1325*x^6
- 8000*x^5*e + 4897*x^5*e^(3*x) + 3505*x^5*e^(2*x) + 30*x^5*e^(3*x + 1) + 2190*x^5*e^(2*x + 1) + 1430*x^5*e^(x
+ 1) - 14880*x^5*e^x + 44100*x^5*log(x) - 100500*x^4*e*log(x) - 28966*x^4*e^(3*x)*log(x) - 32290*x^4*e^(2*x)*
log(x) - 4332*x^4*e^(4*x + 1)*log(x) - 4332*x^4*e^(3*x + 2)*log(x) - 1050*x^4*e^(3*x + 1)*log(x) + 13574*x^4*e
^(2*x + 1)*log(x) + 21660*x^4*e^(x + 2)*log(x) - 10790*x^4*e^(x + 1)*log(x) + 124980*x^4*e^x*log(x) - 11225*x^
5 + 10050*x^4*e - 2166*x^4*e^(4*x) - 1690*x^4*e^(3*x) - 10618*x^4*e^(2*x) - 1070*x^4*e^(3*x + 1) - 3160*x^4*e^
(2*x + 1) - 11370*x^4*e^(x + 1) - 15485*x^4*e^x + 130150*x^4*log(x) + 54150*x^3*e^2*log(x) - 126750*x^3*e*log(
x) + 13718*x^3*e^(4*x)*log(x) + 13670*x^3*e^(3*x)*log(x) - 92098*x^3*e^(2*x)*log(x) + 2166*x^3*e^(4*x + 2)*log
(x) + 56002*x^3*e^(3*x + 1)*log(x) - 7942*x^3*e^(2*x + 2)*log(x) + 31030*x^3*e^(2*x + 1)*log(x) - 266150*x^3*e
^(x + 1)*log(x) - 2800*x^3*e^x*log(x) + 18225*x^4 - 130150*x^3*e + 35416*x^3*e^(3*x) + 45870*x^3*e^(2*x) + 153
0*x^3*e^(3*x + 1) + 32290*x^3*e^(2*x + 1) + 12200*x^3*e^(x + 1) - 131675*x^3*e^x + 216150*x^3*log(x) - 589050*
x^2*e*log(x) - 19000*x^2*e^(3*x)*log(x) - 87400*x^2*e^(2*x)*log(x) - 27436*x^2*e^(4*x + 1)*log(x) - 27436*x^2*
e^(3*x + 2)*log(x) - 13090*x^2*e^(3*x + 1)*log(x) + 243590*x^2*e^(2*x + 1)*log(x) + 137180*x^2*e^(x + 2)*log(x
) + 5600*x^2*e^(x + 1)*log(x) + 93100*x^2*e^x*log(x) - 156725*x^3 + 126800*x^2*e - 13718*x^2*e^(4*x) - 20035*x
^2*e^(3*x) + 68595*x^2*e^(2*x) - 13670*x^2*e^(3*x + 1) - 40750*x^2*e^(2*x + 1) + 2800*x^2*e^(x + 1) + 49350*x^
2*e^x + 598500*x^2*log(x) + 342950*x*e^2*log(x) - 570000*x*e*log(x) + 3800*x*e^(3*x)*log(x) + 47386*x*e^(2*x)*
log(x) + 13718*x*e^(4*x + 2)*log(x) + 15010*x*e^(3*x + 1)*log(x) - 137180*x*e^(2*x + 2)*log(x) + 77900*x*e^(2*
x + 1)*log(x) - 93100*x*e^(x + 1)*log(x) - 19000*x*e^x*log(x) + 33225*x^2 - 598500*x*e + 13205*x*e^(3*x) + 688
75*x*e^(2*x) + 19000*x*e^(3*x + 1) + 87400*x*e^(2*x + 1) - 93100*x*e^(x + 1) - 75050*x*e^x - 99750*x*log(x) -
434625*x + 99750*e - 3800*e^(3*x + 1) - 19950*e^(2*x + 1) + 19000*e^(x + 1))/(x^9*e^(2*x) - 2*x^8*e^(3*x) + 10
*x^8*e^x + x^7*e^(4*x) + 47*x^7*e^(2*x) + 25*x^7 - 114*x^6*e^(3*x) + 570*x^6*e^x + 57*x^5*e^(4*x) + 513*x^5*e^
(2*x) + 1425*x^5 - 2166*x^4*e^(3*x) + 10830*x^4*e^x + 1083*x^3*e^(4*x) - 3971*x^3*e^(2*x) + 27075*x^3 - 13718*
x^2*e^(3*x) + 68590*x^2*e^x + 6859*x*e^(4*x) - 68590*x*e^(2*x) + 171475*x)

________________________________________________________________________________________

maple [B]  time = 0.16, size = 135, normalized size = 4.22

method	result	size
risch	\(\frac {\left (2 x^{3} {\mathrm e}^{2 x +1}-4 x^{2} {\mathrm e}^{3 x +1}+2 x \,{\mathrm e}^{4 x +1}-{\mathrm e}^{2 x} x^{4}+2 x^{3} {\mathrm e}^{3 x}-x^{2} {\mathrm e}^{4 x}+20 x^{2} {\mathrm e}^{x +1}-20 x \,{\mathrm e}^{2 x +1}-10 \,{\mathrm e}^{x} x^{3}+10 \,{\mathrm e}^{2 x} x^{2}+50 x \,{\mathrm e}-25 x^{2}-2 \,{\mathrm e}^{2 x}\right ) \ln \relax (x )}{\left ({\mathrm e}^{x} x -{\mathrm e}^{2 x}+5\right )^{2}}+x -{\mathrm e}^{2} \ln \relax (x )\)	\(135\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x*exp(1)-2*x^2)*exp(x)^6+(-6*x^2*exp(1)+6*x^3)*exp(x)^5+((6*x^3-30*x)*exp(1)-6*x^4+30*x^2+4*x)*exp(x)
^4+((-2*x^4+60*x^2)*exp(1)+2*x^5-60*x^3-4*x)*exp(x)^3+((-30*x^3+150*x)*exp(1)+30*x^4-150*x^2+20*x)*exp(x)^2+(-
150*x^2*exp(1)+150*x^3)*exp(x)-250*x*exp(1)+250*x^2)*ln(x)+(-exp(1)^2+2*x*exp(1)-x^2+x)*exp(x)^6+(3*x*exp(1)^2
-6*x^2*exp(1)+3*x^3-3*x^2)*exp(x)^5+((-3*x^2+15)*exp(1)^2+(6*x^3-30*x)*exp(1)-3*x^4+3*x^3+15*x^2-15*x-2)*exp(x
)^4+((x^3-30*x)*exp(1)^2+(-2*x^4+60*x^2)*exp(1)+x^5-x^4-30*x^3+30*x^2+2*x)*exp(x)^3+((15*x^2-75)*exp(1)^2+(-30
*x^3+150*x)*exp(1)+15*x^4-15*x^3-75*x^2+75*x+10)*exp(x)^2+(75*x*exp(1)^2-150*x^2*exp(1)+75*x^3-75*x^2)*exp(x)+
125*exp(1)^2-250*x*exp(1)+125*x^2-125*x)/(x*exp(x)^6-3*x^2*exp(x)^5+(3*x^3-15*x)*exp(x)^4+(-x^4+30*x^2)*exp(x)
^3+(-15*x^3+75*x)*exp(x)^2-75*exp(x)*x^2-125*x),x,method=_RETURNVERBOSE)

[Out]

(2*x^3*exp(2*x+1)-4*x^2*exp(3*x+1)+2*x*exp(4*x+1)-exp(2*x)*x^4+2*x^3*exp(3*x)-x^2*exp(4*x)+20*x^2*exp(x+1)-20*
x*exp(2*x+1)-10*exp(x)*x^3+10*exp(2*x)*x^2+50*x*exp(1)-25*x^2-2*exp(2*x))/(exp(x)*x-exp(2*x)+5)^2*ln(x)+x-exp(
2)*ln(x)

________________________________________________________________________________________

maxima [B]  time = 0.64, size = 178, normalized size = 5.56 \begin {gather*} \frac {{\left ({\left (x^{2} - 2 \, x e + e^{2}\right )} \log \relax (x) - x\right )} e^{\left (4 \, x\right )} + 2 \, {\left (x^{2} - {\left (x^{3} - 2 \, x^{2} e + x e^{2}\right )} \log \relax (x)\right )} e^{\left (3 \, x\right )} - {\left (x^{3} - {\left (x^{4} - 2 \, x^{3} e + x^{2} {\left (e^{2} - 10\right )} + 20 \, x e - 10 \, e^{2} + 2\right )} \log \relax (x) - 10 \, x\right )} e^{\left (2 \, x\right )} - 10 \, {\left (x^{2} - {\left (x^{3} - 2 \, x^{2} e + x e^{2}\right )} \log \relax (x)\right )} e^{x} + 25 \, {\left (x^{2} - 2 \, x e + e^{2}\right )} \log \relax (x) - 25 \, x}{2 \, x e^{\left (3 \, x\right )} - {\left (x^{2} - 10\right )} e^{\left (2 \, x\right )} - 10 \, x e^{x} - e^{\left (4 \, x\right )} - 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x*exp(1)-2*x^2)*exp(x)^6+(-6*x^2*exp(1)+6*x^3)*exp(x)^5+((6*x^3-30*x)*exp(1)-6*x^4+30*x^2+4*x)*
exp(x)^4+((-2*x^4+60*x^2)*exp(1)+2*x^5-60*x^3-4*x)*exp(x)^3+((-30*x^3+150*x)*exp(1)+30*x^4-150*x^2+20*x)*exp(x
)^2+(-150*x^2*exp(1)+150*x^3)*exp(x)-250*x*exp(1)+250*x^2)*log(x)+(-exp(1)^2+2*x*exp(1)-x^2+x)*exp(x)^6+(3*x*e
xp(1)^2-6*x^2*exp(1)+3*x^3-3*x^2)*exp(x)^5+((-3*x^2+15)*exp(1)^2+(6*x^3-30*x)*exp(1)-3*x^4+3*x^3+15*x^2-15*x-2
)*exp(x)^4+((x^3-30*x)*exp(1)^2+(-2*x^4+60*x^2)*exp(1)+x^5-x^4-30*x^3+30*x^2+2*x)*exp(x)^3+((15*x^2-75)*exp(1)
^2+(-30*x^3+150*x)*exp(1)+15*x^4-15*x^3-75*x^2+75*x+10)*exp(x)^2+(75*x*exp(1)^2-150*x^2*exp(1)+75*x^3-75*x^2)*
exp(x)+125*exp(1)^2-250*x*exp(1)+125*x^2-125*x)/(x*exp(x)^6-3*x^2*exp(x)^5+(3*x^3-15*x)*exp(x)^4+(-x^4+30*x^2)
*exp(x)^3+(-15*x^3+75*x)*exp(x)^2-75*exp(x)*x^2-125*x),x, algorithm="maxima")

[Out]

(((x^2 - 2*x*e + e^2)*log(x) - x)*e^(4*x) + 2*(x^2 - (x^3 - 2*x^2*e + x*e^2)*log(x))*e^(3*x) - (x^3 - (x^4 - 2
*x^3*e + x^2*(e^2 - 10) + 20*x*e - 10*e^2 + 2)*log(x) - 10*x)*e^(2*x) - 10*(x^2 - (x^3 - 2*x^2*e + x*e^2)*log(
x))*e^x + 25*(x^2 - 2*x*e + e^2)*log(x) - 25*x)/(2*x*e^(3*x) - (x^2 - 10)*e^(2*x) - 10*x*e^x - e^(4*x) - 25)

________________________________________________________________________________________

mupad [B]  time = 5.47, size = 126, normalized size = 3.94 \begin {gather*} x-{\mathrm {e}}^2\,\ln \relax (x)+\frac {\ln \relax (x)\,\left (50\,x\,\mathrm {e}+{\mathrm {e}}^{2\,x}\,\left (\left (x^2-10\right )\,\left (2\,x\,\mathrm {e}-x^2\right )-2\right )+{\mathrm {e}}^{4\,x}\,\left (2\,x\,\mathrm {e}-x^2\right )-25\,x^2+10\,x\,{\mathrm {e}}^x\,\left (2\,x\,\mathrm {e}-x^2\right )-2\,x\,{\mathrm {e}}^{3\,x}\,\left (2\,x\,\mathrm {e}-x^2\right )\right )}{{\mathrm {e}}^{4\,x}-2\,x\,{\mathrm {e}}^{3\,x}+10\,x\,{\mathrm {e}}^x+{\mathrm {e}}^{2\,x}\,\left (x^2-10\right )+25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(125*exp(2) - 125*x - exp(4*x)*(15*x + exp(1)*(30*x - 6*x^3) + exp(2)*(3*x^2 - 15) - 15*x^2 - 3*x^3 + 3*x
^4 + 2) + exp(2*x)*(75*x + exp(1)*(150*x - 30*x^3) + exp(2)*(15*x^2 - 75) - 75*x^2 - 15*x^3 + 15*x^4 + 10) + e
xp(3*x)*(2*x - exp(2)*(30*x - x^3) + exp(1)*(60*x^2 - 2*x^4) + 30*x^2 - 30*x^3 - x^4 + x^5) - 250*x*exp(1) + e
xp(5*x)*(3*x*exp(2) - 6*x^2*exp(1) - 3*x^2 + 3*x^3) - log(x)*(250*x*exp(1) - exp(6*x)*(2*x*exp(1) - 2*x^2) + e
xp(x)*(150*x^2*exp(1) - 150*x^3) - exp(4*x)*(4*x - exp(1)*(30*x - 6*x^3) + 30*x^2 - 6*x^4) - exp(2*x)*(20*x +
exp(1)*(150*x - 30*x^3) - 150*x^2 + 30*x^4) + exp(5*x)*(6*x^2*exp(1) - 6*x^3) + exp(3*x)*(4*x - exp(1)*(60*x^2
- 2*x^4) + 60*x^3 - 2*x^5) - 250*x^2) + exp(6*x)*(x - exp(2) + 2*x*exp(1) - x^2) + 125*x^2 + exp(x)*(75*x*exp
(2) - 150*x^2*exp(1) - 75*x^2 + 75*x^3))/(125*x + exp(4*x)*(15*x - 3*x^3) - exp(2*x)*(75*x - 15*x^3) - x*exp(6
*x) + 75*x^2*exp(x) - exp(3*x)*(30*x^2 - x^4) + 3*x^2*exp(5*x)),x)

[Out]

x - exp(2)*log(x) + (log(x)*(50*x*exp(1) + exp(2*x)*((x^2 - 10)*(2*x*exp(1) - x^2) - 2) + exp(4*x)*(2*x*exp(1)
- x^2) - 25*x^2 + 10*x*exp(x)*(2*x*exp(1) - x^2) - 2*x*exp(3*x)*(2*x*exp(1) - x^2)))/(exp(4*x) - 2*x*exp(3*x)
+ 10*x*exp(x) + exp(2*x)*(x^2 - 10) + 25)

________________________________________________________________________________________

sympy [B]  time = 0.74, size = 63, normalized size = 1.97 \begin {gather*} x + \left (- x^{2} + 2 e x\right ) \log {\relax (x )} - e^{2} \log {\relax (x )} - \frac {2 e^{2 x} \log {\relax (x )}}{- 2 x e^{3 x} + 10 x e^{x} + \left (x^{2} - 10\right ) e^{2 x} + e^{4 x} + 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x*exp(1)-2*x**2)*exp(x)**6+(-6*x**2*exp(1)+6*x**3)*exp(x)**5+((6*x**3-30*x)*exp(1)-6*x**4+30*x*
*2+4*x)*exp(x)**4+((-2*x**4+60*x**2)*exp(1)+2*x**5-60*x**3-4*x)*exp(x)**3+((-30*x**3+150*x)*exp(1)+30*x**4-150
*x**2+20*x)*exp(x)**2+(-150*x**2*exp(1)+150*x**3)*exp(x)-250*x*exp(1)+250*x**2)*ln(x)+(-exp(1)**2+2*x*exp(1)-x
**2+x)*exp(x)**6+(3*x*exp(1)**2-6*x**2*exp(1)+3*x**3-3*x**2)*exp(x)**5+((-3*x**2+15)*exp(1)**2+(6*x**3-30*x)*e
xp(1)-3*x**4+3*x**3+15*x**2-15*x-2)*exp(x)**4+((x**3-30*x)*exp(1)**2+(-2*x**4+60*x**2)*exp(1)+x**5-x**4-30*x**
3+30*x**2+2*x)*exp(x)**3+((15*x**2-75)*exp(1)**2+(-30*x**3+150*x)*exp(1)+15*x**4-15*x**3-75*x**2+75*x+10)*exp(
x)**2+(75*x*exp(1)**2-150*x**2*exp(1)+75*x**3-75*x**2)*exp(x)+125*exp(1)**2-250*x*exp(1)+125*x**2-125*x)/(x*ex
p(x)**6-3*x**2*exp(x)**5+(3*x**3-15*x)*exp(x)**4+(-x**4+30*x**2)*exp(x)**3+(-15*x**3+75*x)*exp(x)**2-75*exp(x)
*x**2-125*x),x)

[Out]

x + (-x**2 + 2*E*x)*log(x) - exp(2)*log(x) - 2*exp(2*x)*log(x)/(-2*x*exp(3*x) + 10*x*exp(x) + (x**2 - 10)*exp(
2*x) + exp(4*x) + 25)

________________________________________________________________________________________