3.64.88 \(\int \frac {e^{2 e^2} (-1+x)-25 x^2+25 x^3+e^x (5 x-5 x^2)+e^{e^2} (-5 x-e^x x+10 x^2)+(-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} (e^x-5 x-10 x^2)+(e^{2 e^2}+10 e^{e^2} x+25 x^2) \log (x)) \log (\frac {-e^x+5 x+e^{e^2} x+5 x^2+(-e^{e^2}-5 x) \log (x)}{e^{e^2}+5 x})}{(-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} (e^x-5 x-10 x^2)+(e^{2 e^2}+10 e^{e^2} x+25 x^2) \log (x)) \log ^2(\frac {-e^x+5 x+e^{e^2} x+5 x^2+(-e^{e^2}-5 x) \log (x)}{e^{e^2}+5 x})} \, dx\)

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

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Rubi [F]  time = 11.38, 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 {e^{2 e^2} (-1+x)-25 x^2+25 x^3+e^x \left (5 x-5 x^2\right )+e^{e^2} \left (-5 x-e^x x+10 x^2\right )+\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log \left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log ^2\left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(2*E^2)*(-1 + x) - 25*x^2 + 25*x^3 + E^x*(5*x - 5*x^2) + E^E^2*(-5*x - E^x*x + 10*x^2) + (-(E^(2*E^2)*x
) + 5*E^x*x - 25*x^2 - 25*x^3 + E^E^2*(E^x - 5*x - 10*x^2) + (E^(2*E^2) + 10*E^E^2*x + 25*x^2)*Log[x])*Log[(-E
^x + 5*x + E^E^2*x + 5*x^2 + (-E^E^2 - 5*x)*Log[x])/(E^E^2 + 5*x)])/((-(E^(2*E^2)*x) + 5*E^x*x - 25*x^2 - 25*x
^3 + E^E^2*(E^x - 5*x - 10*x^2) + (E^(2*E^2) + 10*E^E^2*x + 25*x^2)*Log[x])*Log[(-E^x + 5*x + E^E^2*x + 5*x^2
+ (-E^E^2 - 5*x)*Log[x])/(E^E^2 + 5*x)]^2),x]

[Out]

Defer[Int][Log[(-E^x + E^E^2*x + 5*x*(1 + x) - (E^E^2 + 5*x)*Log[x])/(E^E^2 + 5*x)]^(-2), x] - Defer[Int][x/Lo
g[(-E^x + E^E^2*x + 5*x*(1 + x) - (E^E^2 + 5*x)*Log[x])/(E^E^2 + 5*x)]^2, x] - E^E^2*Defer[Int][1/((E^E^2 + 5*
x)*Log[(-E^x + E^E^2*x + 5*x*(1 + x) - (E^E^2 + 5*x)*Log[x])/(E^E^2 + 5*x)]^2), x] + E^E^2*Defer[Int][1/((-E^x
+ 5*(1 + E^E^2/5)*x + 5*x^2 - E^E^2*Log[x] - 5*x*Log[x])*Log[(-E^x + E^E^2*x + 5*x*(1 + x) - (E^E^2 + 5*x)*Lo
g[x])/(E^E^2 + 5*x)]^2), x] - (5 - E^E^2)*Defer[Int][x^2/((-E^x + 5*(1 + E^E^2/5)*x + 5*x^2 - E^E^2*Log[x] - 5
*x*Log[x])*Log[(-E^x + E^E^2*x + 5*x*(1 + x) - (E^E^2 + 5*x)*Log[x])/(E^E^2 + 5*x)]^2), x] + 5*Defer[Int][x^3/
((-E^x + 5*(1 + E^E^2/5)*x + 5*x^2 - E^E^2*Log[x] - 5*x*Log[x])*Log[(-E^x + E^E^2*x + 5*x*(1 + x) - (E^E^2 + 5
*x)*Log[x])/(E^E^2 + 5*x)]^2), x] + (5 - E^E^2)*Defer[Int][(x*Log[x])/((-E^x + 5*(1 + E^E^2/5)*x + 5*x^2 - E^E
^2*Log[x] - 5*x*Log[x])*Log[(-E^x + E^E^2*x + 5*x*(1 + x) - (E^E^2 + 5*x)*Log[x])/(E^E^2 + 5*x)]^2), x] + E^E^
2*Defer[Int][x/((E^x - 5*(1 + E^E^2/5)*x - 5*x^2 + E^E^2*Log[x] + 5*x*Log[x])*Log[(-E^x + E^E^2*x + 5*x*(1 + x
) - (E^E^2 + 5*x)*Log[x])/(E^E^2 + 5*x)]^2), x] + 5*Defer[Int][(x^2*Log[x])/((E^x - 5*(1 + E^E^2/5)*x - 5*x^2
+ E^E^2*Log[x] + 5*x*Log[x])*Log[(-E^x + E^E^2*x + 5*x*(1 + x) - (E^E^2 + 5*x)*Log[x])/(E^E^2 + 5*x)]^2), x] +
Defer[Int][Log[(-E^x + E^E^2*x + 5*x*(1 + x) - (E^E^2 + 5*x)*Log[x])/(E^E^2 + 5*x)]^(-1), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{2 e^2} (-1+x)-25 x^2+25 x^3+e^x \left (5 x-5 x^2\right )+e^{e^2} \left (-5 x-e^x x+10 x^2\right )+\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log \left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\left (e^{e^2}+5 x\right ) \left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx\\ &=\int \left (\frac {-e^{e^2}+e^{e^2} x+5 \left (1-\frac {e^{e^2}}{5}\right ) x^2-5 x^3-5 \left (1-\frac {e^{e^2}}{5}\right ) x \log (x)+5 x^2 \log (x)}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {5 \left (1-\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )+5 x \log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\left (e^{e^2}+5 x\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}\right ) \, dx\\ &=\int \frac {-e^{e^2}+e^{e^2} x+5 \left (1-\frac {e^{e^2}}{5}\right ) x^2-5 x^3-5 \left (1-\frac {e^{e^2}}{5}\right ) x \log (x)+5 x^2 \log (x)}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\int \frac {5 \left (1-\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )+5 x \log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\left (e^{e^2}+5 x\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx\\ &=\int \frac {-5 (-1+x) x^2+e^{e^2} \left (-1+x-x^2\right )+x \left (-5+e^{e^2}+5 x\right ) \log (x)}{\left (e^x-e^{e^2} x-5 x (1+x)+\left (e^{e^2}+5 x\right ) \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\int \frac {-\frac {x \left (-5+e^{e^2}+5 x\right )}{e^{e^2}+5 x}+\log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx\\ &=\int \left (\frac {e^{e^2}}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {e^{e^2} \left (1-5 e^{-e^2}\right ) x^2}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {5 x^3}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {5 \left (1-\frac {e^{e^2}}{5}\right ) x \log (x)}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {e^{e^2} x}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {5 x^2 \log (x)}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}\right ) \, dx+\int \left (-\frac {x \left (-5+e^{e^2}+5 x\right )}{\left (e^{e^2}+5 x\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {1}{\log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}\right ) \, dx\\ &=5 \int \frac {x^3}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+5 \int \frac {x^2 \log (x)}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+e^{e^2} \int \frac {1}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+e^{e^2} \int \frac {x}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\left (5-e^{e^2}\right ) \int \frac {x \log (x)}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\left (-5+e^{e^2}\right ) \int \frac {x^2}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx-\int \frac {x \left (-5+e^{e^2}+5 x\right )}{\left (e^{e^2}+5 x\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\int \frac {1}{\log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx\\ &=5 \int \frac {x^3}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+5 \int \frac {x^2 \log (x)}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+e^{e^2} \int \frac {1}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+e^{e^2} \int \frac {x}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\left (5-e^{e^2}\right ) \int \frac {x \log (x)}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\left (-5+e^{e^2}\right ) \int \frac {x^2}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx-\int \left (-\frac {1}{\log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {x}{\log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {e^{e^2}}{\left (e^{e^2}+5 x\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}\right ) \, dx+\int \frac {1}{\log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx\\ &=5 \int \frac {x^3}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+5 \int \frac {x^2 \log (x)}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx-e^{e^2} \int \frac {1}{\left (e^{e^2}+5 x\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+e^{e^2} \int \frac {1}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+e^{e^2} \int \frac {x}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\left (5-e^{e^2}\right ) \int \frac {x \log (x)}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\left (-5+e^{e^2}\right ) \int \frac {x^2}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\int \frac {1}{\log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx-\int \frac {x}{\log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\int \frac {1}{\log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.25, size = 49, normalized size = 1.53 \begin {gather*} \frac {x}{\log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(2*E^2)*(-1 + x) - 25*x^2 + 25*x^3 + E^x*(5*x - 5*x^2) + E^E^2*(-5*x - E^x*x + 10*x^2) + (-(E^(2*
E^2)*x) + 5*E^x*x - 25*x^2 - 25*x^3 + E^E^2*(E^x - 5*x - 10*x^2) + (E^(2*E^2) + 10*E^E^2*x + 25*x^2)*Log[x])*L
og[(-E^x + 5*x + E^E^2*x + 5*x^2 + (-E^E^2 - 5*x)*Log[x])/(E^E^2 + 5*x)])/((-(E^(2*E^2)*x) + 5*E^x*x - 25*x^2
- 25*x^3 + E^E^2*(E^x - 5*x - 10*x^2) + (E^(2*E^2) + 10*E^E^2*x + 25*x^2)*Log[x])*Log[(-E^x + 5*x + E^E^2*x +
5*x^2 + (-E^E^2 - 5*x)*Log[x])/(E^E^2 + 5*x)]^2),x]

[Out]

x/Log[(-E^x + E^E^2*x + 5*x*(1 + x) - (E^E^2 + 5*x)*Log[x])/(E^E^2 + 5*x)]

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fricas [A]  time = 0.72, size = 44, normalized size = 1.38 \begin {gather*} \frac {x}{\log \left (\frac {5 \, x^{2} + x e^{\left (e^{2}\right )} - {\left (5 \, x + e^{\left (e^{2}\right )}\right )} \log \relax (x) + 5 \, x - e^{x}}{5 \, x + e^{\left (e^{2}\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((exp(exp(2))^2+10*x*exp(exp(2))+25*x^2)*log(x)-x*exp(exp(2))^2+(exp(x)-10*x^2-5*x)*exp(exp(2))+5*e
xp(x)*x-25*x^3-25*x^2)*log(((-exp(exp(2))-5*x)*log(x)+x*exp(exp(2))-exp(x)+5*x^2+5*x)/(exp(exp(2))+5*x))+(x-1)
*exp(exp(2))^2+(-exp(x)*x+10*x^2-5*x)*exp(exp(2))+(-5*x^2+5*x)*exp(x)+25*x^3-25*x^2)/((exp(exp(2))^2+10*x*exp(
exp(2))+25*x^2)*log(x)-x*exp(exp(2))^2+(exp(x)-10*x^2-5*x)*exp(exp(2))+5*exp(x)*x-25*x^3-25*x^2)/log(((-exp(ex
p(2))-5*x)*log(x)+x*exp(exp(2))-exp(x)+5*x^2+5*x)/(exp(exp(2))+5*x))^2,x, algorithm="fricas")

[Out]

x/log((5*x^2 + x*e^(e^2) - (5*x + e^(e^2))*log(x) + 5*x - e^x)/(5*x + e^(e^2)))

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giac [A]  time = 3.90, size = 46, normalized size = 1.44 \begin {gather*} \frac {x}{\log \left (5 \, x^{2} + x e^{\left (e^{2}\right )} - 5 \, x \log \relax (x) - e^{\left (e^{2}\right )} \log \relax (x) + 5 \, x - e^{x}\right ) - \log \left (5 \, x + e^{\left (e^{2}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((exp(exp(2))^2+10*x*exp(exp(2))+25*x^2)*log(x)-x*exp(exp(2))^2+(exp(x)-10*x^2-5*x)*exp(exp(2))+5*e
xp(x)*x-25*x^3-25*x^2)*log(((-exp(exp(2))-5*x)*log(x)+x*exp(exp(2))-exp(x)+5*x^2+5*x)/(exp(exp(2))+5*x))+(x-1)
*exp(exp(2))^2+(-exp(x)*x+10*x^2-5*x)*exp(exp(2))+(-5*x^2+5*x)*exp(x)+25*x^3-25*x^2)/((exp(exp(2))^2+10*x*exp(
exp(2))+25*x^2)*log(x)-x*exp(exp(2))^2+(exp(x)-10*x^2-5*x)*exp(exp(2))+5*exp(x)*x-25*x^3-25*x^2)/log(((-exp(ex
p(2))-5*x)*log(x)+x*exp(exp(2))-exp(x)+5*x^2+5*x)/(exp(exp(2))+5*x))^2,x, algorithm="giac")

[Out]

x/(log(5*x^2 + x*e^(e^2) - 5*x*log(x) - e^(e^2)*log(x) + 5*x - e^x) - log(5*x + e^(e^2)))

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maple [C]  time = 0.26, size = 321, normalized size = 10.03

method	result	size
risch	\(\frac {2 i x}{\pi \,\mathrm {csgn}\left (\frac {i}{{\mathrm e}^{{\mathrm e}^{2}}+5 x}\right ) \mathrm {csgn}\left (i \left (-\left (x -\ln \relax (x )\right ) {\mathrm e}^{{\mathrm e}^{2}}-5 x^{2}-\left (-5 \ln \relax (x )+5\right ) x +{\mathrm e}^{x}\right )\right ) \mathrm {csgn}\left (\frac {i \left (-\left (x -\ln \relax (x )\right ) {\mathrm e}^{{\mathrm e}^{2}}-5 x^{2}-\left (-5 \ln \relax (x )+5\right ) x +{\mathrm e}^{x}\right )}{{\mathrm e}^{{\mathrm e}^{2}}+5 x}\right )-\pi \,\mathrm {csgn}\left (\frac {i}{{\mathrm e}^{{\mathrm e}^{2}}+5 x}\right ) \mathrm {csgn}\left (\frac {i \left (-\left (x -\ln \relax (x )\right ) {\mathrm e}^{{\mathrm e}^{2}}-5 x^{2}-\left (-5 \ln \relax (x )+5\right ) x +{\mathrm e}^{x}\right )}{{\mathrm e}^{{\mathrm e}^{2}}+5 x}\right )^{2}+\pi \,\mathrm {csgn}\left (i \left (-\left (x -\ln \relax (x )\right ) {\mathrm e}^{{\mathrm e}^{2}}-5 x^{2}-\left (-5 \ln \relax (x )+5\right ) x +{\mathrm e}^{x}\right )\right ) \mathrm {csgn}\left (\frac {i \left (-\left (x -\ln \relax (x )\right ) {\mathrm e}^{{\mathrm e}^{2}}-5 x^{2}-\left (-5 \ln \relax (x )+5\right ) x +{\mathrm e}^{x}\right )}{{\mathrm e}^{{\mathrm e}^{2}}+5 x}\right )^{2}-\pi \mathrm {csgn}\left (\frac {i \left (-\left (x -\ln \relax (x )\right ) {\mathrm e}^{{\mathrm e}^{2}}-5 x^{2}-\left (-5 \ln \relax (x )+5\right ) x +{\mathrm e}^{x}\right )}{{\mathrm e}^{{\mathrm e}^{2}}+5 x}\right )^{3}-2 i \ln \left ({\mathrm e}^{{\mathrm e}^{2}}+5 x \right )+2 i \ln \left (\left (x -\ln \relax (x )\right ) {\mathrm e}^{{\mathrm e}^{2}}+5 x^{2}+\left (-5 \ln \relax (x )+5\right ) x -{\mathrm e}^{x}\right )}\)	\(321\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((exp(exp(2))^2+10*x*exp(exp(2))+25*x^2)*ln(x)-x*exp(exp(2))^2+(exp(x)-10*x^2-5*x)*exp(exp(2))+5*exp(x)*x
-25*x^3-25*x^2)*ln(((-exp(exp(2))-5*x)*ln(x)+x*exp(exp(2))-exp(x)+5*x^2+5*x)/(exp(exp(2))+5*x))+(x-1)*exp(exp(
2))^2+(-exp(x)*x+10*x^2-5*x)*exp(exp(2))+(-5*x^2+5*x)*exp(x)+25*x^3-25*x^2)/((exp(exp(2))^2+10*x*exp(exp(2))+2
5*x^2)*ln(x)-x*exp(exp(2))^2+(exp(x)-10*x^2-5*x)*exp(exp(2))+5*exp(x)*x-25*x^3-25*x^2)/ln(((-exp(exp(2))-5*x)*
ln(x)+x*exp(exp(2))-exp(x)+5*x^2+5*x)/(exp(exp(2))+5*x))^2,x,method=_RETURNVERBOSE)

[Out]

2*I*x/(Pi*csgn(I/(exp(exp(2))+5*x))*csgn(I*(-(x-ln(x))*exp(exp(2))-5*x^2-(-5*ln(x)+5)*x+exp(x)))*csgn(I/(exp(e
xp(2))+5*x)*(-(x-ln(x))*exp(exp(2))-5*x^2-(-5*ln(x)+5)*x+exp(x)))-Pi*csgn(I/(exp(exp(2))+5*x))*csgn(I/(exp(exp
(2))+5*x)*(-(x-ln(x))*exp(exp(2))-5*x^2-(-5*ln(x)+5)*x+exp(x)))^2+Pi*csgn(I*(-(x-ln(x))*exp(exp(2))-5*x^2-(-5*
ln(x)+5)*x+exp(x)))*csgn(I/(exp(exp(2))+5*x)*(-(x-ln(x))*exp(exp(2))-5*x^2-(-5*ln(x)+5)*x+exp(x)))^2-Pi*csgn(I
/(exp(exp(2))+5*x)*(-(x-ln(x))*exp(exp(2))-5*x^2-(-5*ln(x)+5)*x+exp(x)))^3-2*I*ln(exp(exp(2))+5*x)+2*I*ln((x-l
n(x))*exp(exp(2))+5*x^2+(-5*ln(x)+5)*x-exp(x)))

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maxima [A]  time = 0.80, size = 44, normalized size = 1.38 \begin {gather*} \frac {x}{\log \left (5 \, x^{2} + x {\left (e^{\left (e^{2}\right )} + 5\right )} - {\left (5 \, x + e^{\left (e^{2}\right )}\right )} \log \relax (x) - e^{x}\right ) - \log \left (5 \, x + e^{\left (e^{2}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((exp(exp(2))^2+10*x*exp(exp(2))+25*x^2)*log(x)-x*exp(exp(2))^2+(exp(x)-10*x^2-5*x)*exp(exp(2))+5*e
xp(x)*x-25*x^3-25*x^2)*log(((-exp(exp(2))-5*x)*log(x)+x*exp(exp(2))-exp(x)+5*x^2+5*x)/(exp(exp(2))+5*x))+(x-1)
*exp(exp(2))^2+(-exp(x)*x+10*x^2-5*x)*exp(exp(2))+(-5*x^2+5*x)*exp(x)+25*x^3-25*x^2)/((exp(exp(2))^2+10*x*exp(
exp(2))+25*x^2)*log(x)-x*exp(exp(2))^2+(exp(x)-10*x^2-5*x)*exp(exp(2))+5*exp(x)*x-25*x^3-25*x^2)/log(((-exp(ex
p(2))-5*x)*log(x)+x*exp(exp(2))-exp(x)+5*x^2+5*x)/(exp(exp(2))+5*x))^2,x, algorithm="maxima")

[Out]

x/(log(5*x^2 + x*(e^(e^2) + 5) - (5*x + e^(e^2))*log(x) - e^x) - log(5*x + e^(e^2)))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} -\int -\frac {\ln \left (\frac {5\,x-{\mathrm {e}}^x-\ln \relax (x)\,\left (5\,x+{\mathrm {e}}^{{\mathrm {e}}^2}\right )+x\,{\mathrm {e}}^{{\mathrm {e}}^2}+5\,x^2}{5\,x+{\mathrm {e}}^{{\mathrm {e}}^2}}\right )\,\left (x\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}-\ln \relax (x)\,\left (25\,x^2+10\,{\mathrm {e}}^{{\mathrm {e}}^2}\,x+{\mathrm {e}}^{2\,{\mathrm {e}}^2}\right )-5\,x\,{\mathrm {e}}^x+{\mathrm {e}}^{{\mathrm {e}}^2}\,\left (5\,x-{\mathrm {e}}^x+10\,x^2\right )+25\,x^2+25\,x^3\right )+{\mathrm {e}}^{{\mathrm {e}}^2}\,\left (5\,x+x\,{\mathrm {e}}^x-10\,x^2\right )-{\mathrm {e}}^{2\,{\mathrm {e}}^2}\,\left (x-1\right )-{\mathrm {e}}^x\,\left (5\,x-5\,x^2\right )+25\,x^2-25\,x^3}{{\ln \left (\frac {5\,x-{\mathrm {e}}^x-\ln \relax (x)\,\left (5\,x+{\mathrm {e}}^{{\mathrm {e}}^2}\right )+x\,{\mathrm {e}}^{{\mathrm {e}}^2}+5\,x^2}{5\,x+{\mathrm {e}}^{{\mathrm {e}}^2}}\right )}^2\,\left (x\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}-\ln \relax (x)\,\left (25\,x^2+10\,{\mathrm {e}}^{{\mathrm {e}}^2}\,x+{\mathrm {e}}^{2\,{\mathrm {e}}^2}\right )-5\,x\,{\mathrm {e}}^x+{\mathrm {e}}^{{\mathrm {e}}^2}\,\left (5\,x-{\mathrm {e}}^x+10\,x^2\right )+25\,x^2+25\,x^3\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log((5*x - exp(x) - log(x)*(5*x + exp(exp(2))) + x*exp(exp(2)) + 5*x^2)/(5*x + exp(exp(2))))*(x*exp(2*exp
(2)) - log(x)*(exp(2*exp(2)) + 10*x*exp(exp(2)) + 25*x^2) - 5*x*exp(x) + exp(exp(2))*(5*x - exp(x) + 10*x^2) +
25*x^2 + 25*x^3) + exp(exp(2))*(5*x + x*exp(x) - 10*x^2) - exp(2*exp(2))*(x - 1) - exp(x)*(5*x - 5*x^2) + 25*
x^2 - 25*x^3)/(log((5*x - exp(x) - log(x)*(5*x + exp(exp(2))) + x*exp(exp(2)) + 5*x^2)/(5*x + exp(exp(2))))^2*
(x*exp(2*exp(2)) - log(x)*(exp(2*exp(2)) + 10*x*exp(exp(2)) + 25*x^2) - 5*x*exp(x) + exp(exp(2))*(5*x - exp(x)
+ 10*x^2) + 25*x^2 + 25*x^3)),x)

[Out]

-int(-(log((5*x - exp(x) - log(x)*(5*x + exp(exp(2))) + x*exp(exp(2)) + 5*x^2)/(5*x + exp(exp(2))))*(x*exp(2*e
xp(2)) - log(x)*(exp(2*exp(2)) + 10*x*exp(exp(2)) + 25*x^2) - 5*x*exp(x) + exp(exp(2))*(5*x - exp(x) + 10*x^2)
+ 25*x^2 + 25*x^3) + exp(exp(2))*(5*x + x*exp(x) - 10*x^2) - exp(2*exp(2))*(x - 1) - exp(x)*(5*x - 5*x^2) + 2
5*x^2 - 25*x^3)/(log((5*x - exp(x) - log(x)*(5*x + exp(exp(2))) + x*exp(exp(2)) + 5*x^2)/(5*x + exp(exp(2))))^
2*(x*exp(2*exp(2)) - log(x)*(exp(2*exp(2)) + 10*x*exp(exp(2)) + 25*x^2) - 5*x*exp(x) + exp(exp(2))*(5*x - exp(
x) + 10*x^2) + 25*x^2 + 25*x^3)), x)

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sympy [A]  time = 10.83, size = 42, normalized size = 1.31 \begin {gather*} \frac {x}{\log {\left (\frac {5 x^{2} + 5 x + x e^{e^{2}} + \left (- 5 x - e^{e^{2}}\right ) \log {\relax (x )} - e^{x}}{5 x + e^{e^{2}}} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((exp(exp(2))**2+10*x*exp(exp(2))+25*x**2)*ln(x)-x*exp(exp(2))**2+(exp(x)-10*x**2-5*x)*exp(exp(2))+
5*exp(x)*x-25*x**3-25*x**2)*ln(((-exp(exp(2))-5*x)*ln(x)+x*exp(exp(2))-exp(x)+5*x**2+5*x)/(exp(exp(2))+5*x))+(
x-1)*exp(exp(2))**2+(-exp(x)*x+10*x**2-5*x)*exp(exp(2))+(-5*x**2+5*x)*exp(x)+25*x**3-25*x**2)/((exp(exp(2))**2
+10*x*exp(exp(2))+25*x**2)*ln(x)-x*exp(exp(2))**2+(exp(x)-10*x**2-5*x)*exp(exp(2))+5*exp(x)*x-25*x**3-25*x**2)
/ln(((-exp(exp(2))-5*x)*ln(x)+x*exp(exp(2))-exp(x)+5*x**2+5*x)/(exp(exp(2))+5*x))**2,x)

[Out]

x/log((5*x**2 + 5*x + x*exp(exp(2)) + (-5*x - exp(exp(2)))*log(x) - exp(x))/(5*x + exp(exp(2))))

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