\(\int \frac {e^{\frac {x}{-x+\log (-75 x \log (x)+\log (x^2))}} (2 x-75 x^2-75 x^2 \log (x)+(75 x^2 \log (x)-x \log (x^2)) \log (-75 x \log (x)+\log (x^2)))+\log (1+e^{\frac {x}{-x+\log (-75 x \log (x)+\log (x^2))}}) (-75 x^3 \log (x)+x^2 \log (x^2)+(150 x^2 \log (x)-2 x \log (x^2)) \log (-75 x \log (x)+\log (x^2))+(-75 x \log (x)+\log (x^2)) \log ^2(-75 x \log (x)+\log (x^2))+e^{\frac {x}{-x+\log (-75 x \log (x)+\log (x^2))}} (-75 x^3 \log (x)+x^2 \log (x^2)+(150 x^2 \log (x)-2 x \log (x^2)) \log (-75 x \log (x)+\log (x^2))+(-75 x \log (x)+\log (x^2)) \log ^2(-75 x \log (x)+\log (x^2))))}{\log ^2(1+e^{\frac {x}{-x+\log (-75 x \log (x)+\log (x^2))}}) (-75 x^3 \log (x)+x^2 \log (x^2)+(150 x^2 \log (x)-2 x \log (x^2)) \log (-75 x \log (x)+\log (x^2))+(-75 x \log (x)+\log (x^2)) \log ^2(-75 x \log (x)+\log (x^2))+e^{\frac {x}{-x+\log (-75 x \log (x)+\log (x^2))}} (-75 x^3 \log (x)+x^2 \log (x^2)+(150 x^2 \log (x)-2 x \log (x^2)) \log (-75 x \log (x)+\log (x^2))+(-75 x \log (x)+\log (x^2)) \log ^2(-75 x \log (x)+\log (x^2))))} \, dx\) [6706]

Optimal result

Integrand size = 432, antiderivative size = 28 \[ \int \frac {e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (2 x-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )+\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )} \, dx=\frac {x}{\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right )} \]

[Out]

x/ln(exp(x/(ln(ln(x^2)-75*x*ln(x))-x))+1)

Rubi [F]

\[ \int \frac {e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (2 x-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )+\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )} \, dx=\int \frac {e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (2 x-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )+\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )} \, dx \]

[In]

Int[(E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))*(2*x - 75*x^2 - 75*x^2*Log[x] + (75*x^2*Log[x] - x*Log[x^2])*Lo
g[-75*x*Log[x] + Log[x^2]]) + Log[1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))]*(-75*x^3*Log[x] + x^2*Log[x^2
] + (150*x^2*Log[x] - 2*x*Log[x^2])*Log[-75*x*Log[x] + Log[x^2]] + (-75*x*Log[x] + Log[x^2])*Log[-75*x*Log[x]
+ Log[x^2]]^2 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))*(-75*x^3*Log[x] + x^2*Log[x^2] + (150*x^2*Log[x] - 2
*x*Log[x^2])*Log[-75*x*Log[x] + Log[x^2]] + (-75*x*Log[x] + Log[x^2])*Log[-75*x*Log[x] + Log[x^2]]^2)))/(Log[1
+ E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))]^2*(-75*x^3*Log[x] + x^2*Log[x^2] + (150*x^2*Log[x] - 2*x*Log[x^2
])*Log[-75*x*Log[x] + Log[x^2]] + (-75*x*Log[x] + Log[x^2])*Log[-75*x*Log[x] + Log[x^2]]^2 + E^(x/(-x + Log[-7
5*x*Log[x] + Log[x^2]]))*(-75*x^3*Log[x] + x^2*Log[x^2] + (150*x^2*Log[x] - 2*x*Log[x^2])*Log[-75*x*Log[x] + L
og[x^2]] + (-75*x*Log[x] + Log[x^2])*Log[-75*x*Log[x] + Log[x^2]]^2))),x]

[Out]

Defer[Int][Log[1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))]^(-1), x] - 2*Defer[Int][x/(Log[1 + E^(x/(-x + Lo
g[-75*x*Log[x] + Log[x^2]]))]^2*(75*x*Log[x] - Log[x^2])*(x - Log[-75*x*Log[x] + Log[x^2]])^2), x] + 2*Defer[I
nt][x/((1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]])))*Log[1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))]^2*(7
5*x*Log[x] - Log[x^2])*(x - Log[-75*x*Log[x] + Log[x^2]])^2), x] + 75*Defer[Int][x^2/(Log[1 + E^(x/(-x + Log[-
75*x*Log[x] + Log[x^2]]))]^2*(75*x*Log[x] - Log[x^2])*(x - Log[-75*x*Log[x] + Log[x^2]])^2), x] - 75*Defer[Int
][x^2/((1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]])))*Log[1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))]^2*(7
5*x*Log[x] - Log[x^2])*(x - Log[-75*x*Log[x] + Log[x^2]])^2), x] + 75*Defer[Int][(x^2*Log[x])/(Log[1 + E^(x/(-
x + Log[-75*x*Log[x] + Log[x^2]]))]^2*(75*x*Log[x] - Log[x^2])*(x - Log[-75*x*Log[x] + Log[x^2]])^2), x] - 75*
Defer[Int][(x^2*Log[x])/((1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]])))*Log[1 + E^(x/(-x + Log[-75*x*Log[x] +
Log[x^2]]))]^2*(75*x*Log[x] - Log[x^2])*(x - Log[-75*x*Log[x] + Log[x^2]])^2), x] - 75*Defer[Int][(x^3*Log[x]
)/(Log[1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))]^2*(75*x*Log[x] - Log[x^2])*(x - Log[-75*x*Log[x] + Log[x
^2]])^2), x] + Defer[Int][(x^2*Log[x^2])/(Log[1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))]^2*(75*x*Log[x] -
Log[x^2])*(x - Log[-75*x*Log[x] + Log[x^2]])^2), x] + Defer[Int][x/(Log[1 + E^(x/(-x + Log[-75*x*Log[x] + Log[
x^2]]))]^2*(x - Log[-75*x*Log[x] + Log[x^2]])), x] + 75*Defer[Int][(x^2*Log[x]*Log[-75*x*Log[x] + Log[x^2]])/(
(1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]])))*Log[1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))]^2*(75*x*Log
[x] - Log[x^2])*(x - Log[-75*x*Log[x] + Log[x^2]])^2), x] - Defer[Int][(x*Log[x^2]*Log[-75*x*Log[x] + Log[x^2]
])/((1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]])))*Log[1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))]^2*(75*x
*Log[x] - Log[x^2])*(x - Log[-75*x*Log[x] + Log[x^2]])^2), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {75 x \log (x) \left (\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2-e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} x \left (-1+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )-\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log \left (x^2\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} x \left (-2+75 x+\log \left (x^2\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2} \, dx \\ & = \int \left (\frac {x \left (2-75 x-75 x \log (x)+75 x \log (x) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )-\log \left (x^2\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2}+\frac {-2 x+75 x^2+75 x^2 \log (x)+75 x^3 \log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log (x)-x^2 \log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log \left (x^2\right )-75 x^2 \log (x) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )-150 x^2 \log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log (x) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+x \log \left (x^2\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+2 x \log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log \left (x^2\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+75 x \log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log (x) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )-\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log \left (x^2\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2}\right ) \, dx \\ & = \int \frac {x \left (2-75 x-75 x \log (x)+75 x \log (x) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )-\log \left (x^2\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2} \, dx+\int \frac {-2 x+75 x^2+75 x^2 \log (x)+75 x^3 \log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log (x)-x^2 \log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log \left (x^2\right )-75 x^2 \log (x) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )-150 x^2 \log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log (x) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+x \log \left (x^2\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+2 x \log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log \left (x^2\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+75 x \log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log (x) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )-\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log \left (x^2\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2} \, dx \\ & = \int \left (\frac {2 x}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2}-\frac {75 x^2}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2}-\frac {75 x^2 \log (x)}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2}+\frac {75 x^2 \log (x) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2}-\frac {x \log \left (x^2\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2}\right ) \, dx+\int \frac {-\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log \left (x^2\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2+75 x \log (x) \left (x+\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2-x \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )+x \left (-2+75 x+\log \left (x^2\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2} \, dx \\ & = 2 \int \frac {x}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2} \, dx-75 \int \frac {x^2}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2} \, dx-75 \int \frac {x^2 \log (x)}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2} \, dx+75 \int \frac {x^2 \log (x) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2} \, dx+\int \left (\frac {1}{\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right )}-\frac {x \left (2-75 x-75 x \log (x)+75 x^2 \log (x)-x \log \left (x^2\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2}+\frac {x}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )}\right ) \, dx-\int \frac {x \log \left (x^2\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2} \, dx \\ & = 2 \int \frac {x}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2} \, dx-75 \int \frac {x^2}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2} \, dx-75 \int \frac {x^2 \log (x)}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2} \, dx+75 \int \frac {x^2 \log (x) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2} \, dx+\int \frac {1}{\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right )} \, dx-\int \frac {x \left (2-75 x-75 x \log (x)+75 x^2 \log (x)-x \log \left (x^2\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2} \, dx+\int \frac {x}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )} \, dx-\int \frac {x \log \left (x^2\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )}{\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )^2} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.44 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (2 x-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )+\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )} \, dx=\frac {x}{\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right )} \]

[In]

Integrate[(E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))*(2*x - 75*x^2 - 75*x^2*Log[x] + (75*x^2*Log[x] - x*Log[x^
2])*Log[-75*x*Log[x] + Log[x^2]]) + Log[1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))]*(-75*x^3*Log[x] + x^2*L
og[x^2] + (150*x^2*Log[x] - 2*x*Log[x^2])*Log[-75*x*Log[x] + Log[x^2]] + (-75*x*Log[x] + Log[x^2])*Log[-75*x*L
og[x] + Log[x^2]]^2 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))*(-75*x^3*Log[x] + x^2*Log[x^2] + (150*x^2*Log[
x] - 2*x*Log[x^2])*Log[-75*x*Log[x] + Log[x^2]] + (-75*x*Log[x] + Log[x^2])*Log[-75*x*Log[x] + Log[x^2]]^2)))/
(Log[1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))]^2*(-75*x^3*Log[x] + x^2*Log[x^2] + (150*x^2*Log[x] - 2*x*L
og[x^2])*Log[-75*x*Log[x] + Log[x^2]] + (-75*x*Log[x] + Log[x^2])*Log[-75*x*Log[x] + Log[x^2]]^2 + E^(x/(-x +
Log[-75*x*Log[x] + Log[x^2]]))*(-75*x^3*Log[x] + x^2*Log[x^2] + (150*x^2*Log[x] - 2*x*Log[x^2])*Log[-75*x*Log[
x] + Log[x^2]] + (-75*x*Log[x] + Log[x^2])*Log[-75*x*Log[x] + Log[x^2]]^2))),x]

[Out]

x/Log[1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))]

Maple [C] (warning: unable to verify)

Result contains higher order function than in optimal. Order 9 vs. order 3.

Time = 0.48 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.04

\[\frac {x}{\ln \left ({\mathrm e}^{-\frac {x}{-\ln \left (2 \ln \left (x \right )-\frac {i \pi \,\operatorname {csgn}\left (i x^{2}\right ) {\left (-\operatorname {csgn}\left (i x^{2}\right )+\operatorname {csgn}\left (i x \right )\right )}^{2}}{2}-75 x \ln \left (x \right )\right )+x}}+1\right )}\]

[In]

int(((((ln(x^2)-75*x*ln(x))*ln(ln(x^2)-75*x*ln(x))^2+(-2*x*ln(x^2)+150*x^2*ln(x))*ln(ln(x^2)-75*x*ln(x))+x^2*l
n(x^2)-75*x^3*ln(x))*exp(x/(ln(ln(x^2)-75*x*ln(x))-x))+(ln(x^2)-75*x*ln(x))*ln(ln(x^2)-75*x*ln(x))^2+(-2*x*ln(
x^2)+150*x^2*ln(x))*ln(ln(x^2)-75*x*ln(x))+x^2*ln(x^2)-75*x^3*ln(x))*ln(exp(x/(ln(ln(x^2)-75*x*ln(x))-x))+1)+(
(-x*ln(x^2)+75*x^2*ln(x))*ln(ln(x^2)-75*x*ln(x))-75*x^2*ln(x)-75*x^2+2*x)*exp(x/(ln(ln(x^2)-75*x*ln(x))-x)))/(
((ln(x^2)-75*x*ln(x))*ln(ln(x^2)-75*x*ln(x))^2+(-2*x*ln(x^2)+150*x^2*ln(x))*ln(ln(x^2)-75*x*ln(x))+x^2*ln(x^2)
-75*x^3*ln(x))*exp(x/(ln(ln(x^2)-75*x*ln(x))-x))+(ln(x^2)-75*x*ln(x))*ln(ln(x^2)-75*x*ln(x))^2+(-2*x*ln(x^2)+1
50*x^2*ln(x))*ln(ln(x^2)-75*x*ln(x))+x^2*ln(x^2)-75*x^3*ln(x))/ln(exp(x/(ln(ln(x^2)-75*x*ln(x))-x))+1)^2,x)

[Out]

x/ln(exp(-x/(-ln(2*ln(x)-1/2*I*Pi*csgn(I*x^2)*(-csgn(I*x^2)+csgn(I*x))^2-75*x*ln(x))+x))+1)

Fricas [A] (verification not implemented)

none

Time = 0.44 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96 \[ \int \frac {e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (2 x-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )+\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )} \, dx=\frac {x}{\log \left (e^{\left (-\frac {x}{x - \log \left (-{\left (75 \, x - 2\right )} \log \left (x\right )\right )}\right )} + 1\right )} \]

[In]

integrate(((((log(x^2)-75*x*log(x))*log(log(x^2)-75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x))*log(log(x^2)-75
*x*log(x))+x^2*log(x^2)-75*x^3*log(x))*exp(x/(log(log(x^2)-75*x*log(x))-x))+(log(x^2)-75*x*log(x))*log(log(x^2
)-75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x))+x^2*log(x^2)-75*x^3*log(x))*log(exp(
x/(log(log(x^2)-75*x*log(x))-x))+1)+((-x*log(x^2)+75*x^2*log(x))*log(log(x^2)-75*x*log(x))-75*x^2*log(x)-75*x^
2+2*x)*exp(x/(log(log(x^2)-75*x*log(x))-x)))/(((log(x^2)-75*x*log(x))*log(log(x^2)-75*x*log(x))^2+(-2*x*log(x^
2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x))+x^2*log(x^2)-75*x^3*log(x))*exp(x/(log(log(x^2)-75*x*log(x))-x))+
(log(x^2)-75*x*log(x))*log(log(x^2)-75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x))+x^
2*log(x^2)-75*x^3*log(x))/log(exp(x/(log(log(x^2)-75*x*log(x))-x))+1)^2,x, algorithm="fricas")

[Out]

x/log(e^(-x/(x - log(-(75*x - 2)*log(x)))) + 1)

Sympy [F(-1)]

Timed out. \[ \int \frac {e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (2 x-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )+\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )} \, dx=\text {Timed out} \]

[In]

integrate(((((ln(x**2)-75*x*ln(x))*ln(ln(x**2)-75*x*ln(x))**2+(-2*x*ln(x**2)+150*x**2*ln(x))*ln(ln(x**2)-75*x*
ln(x))+x**2*ln(x**2)-75*x**3*ln(x))*exp(x/(ln(ln(x**2)-75*x*ln(x))-x))+(ln(x**2)-75*x*ln(x))*ln(ln(x**2)-75*x*
ln(x))**2+(-2*x*ln(x**2)+150*x**2*ln(x))*ln(ln(x**2)-75*x*ln(x))+x**2*ln(x**2)-75*x**3*ln(x))*ln(exp(x/(ln(ln(
x**2)-75*x*ln(x))-x))+1)+((-x*ln(x**2)+75*x**2*ln(x))*ln(ln(x**2)-75*x*ln(x))-75*x**2*ln(x)-75*x**2+2*x)*exp(x
/(ln(ln(x**2)-75*x*ln(x))-x)))/(((ln(x**2)-75*x*ln(x))*ln(ln(x**2)-75*x*ln(x))**2+(-2*x*ln(x**2)+150*x**2*ln(x
))*ln(ln(x**2)-75*x*ln(x))+x**2*ln(x**2)-75*x**3*ln(x))*exp(x/(ln(ln(x**2)-75*x*ln(x))-x))+(ln(x**2)-75*x*ln(x
))*ln(ln(x**2)-75*x*ln(x))**2+(-2*x*ln(x**2)+150*x**2*ln(x))*ln(ln(x**2)-75*x*ln(x))+x**2*ln(x**2)-75*x**3*ln(
x))/ln(exp(x/(ln(ln(x**2)-75*x*ln(x))-x))+1)**2,x)

[Out]

Timed out

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 59 vs. \(2 (28) = 56\).

Time = 0.75 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.11 \[ \int \frac {e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (2 x-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )+\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )} \, dx=\frac {x}{\log \left (e + e^{\left (-\frac {\log \left (-75 \, x + 2\right )}{x - \log \left (-75 \, x + 2\right ) - \log \left (\log \left (x\right )\right )} - \frac {\log \left (\log \left (x\right )\right )}{x - \log \left (-75 \, x + 2\right ) - \log \left (\log \left (x\right )\right )}\right )}\right ) - 1} \]

[In]

integrate(((((log(x^2)-75*x*log(x))*log(log(x^2)-75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x))*log(log(x^2)-75
*x*log(x))+x^2*log(x^2)-75*x^3*log(x))*exp(x/(log(log(x^2)-75*x*log(x))-x))+(log(x^2)-75*x*log(x))*log(log(x^2
)-75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x))+x^2*log(x^2)-75*x^3*log(x))*log(exp(
x/(log(log(x^2)-75*x*log(x))-x))+1)+((-x*log(x^2)+75*x^2*log(x))*log(log(x^2)-75*x*log(x))-75*x^2*log(x)-75*x^
2+2*x)*exp(x/(log(log(x^2)-75*x*log(x))-x)))/(((log(x^2)-75*x*log(x))*log(log(x^2)-75*x*log(x))^2+(-2*x*log(x^
2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x))+x^2*log(x^2)-75*x^3*log(x))*exp(x/(log(log(x^2)-75*x*log(x))-x))+
(log(x^2)-75*x*log(x))*log(log(x^2)-75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x))+x^
2*log(x^2)-75*x^3*log(x))/log(exp(x/(log(log(x^2)-75*x*log(x))-x))+1)^2,x, algorithm="maxima")

[Out]

x/(log(e + e^(-log(-75*x + 2)/(x - log(-75*x + 2) - log(log(x))) - log(log(x))/(x - log(-75*x + 2) - log(log(x
))))) - 1)

Giac [F]

\[ \int \frac {e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (2 x-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )+\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )} \, dx=\int { \frac {{\left (75 \, x^{2} \log \left (x\right ) + 75 \, x^{2} - {\left (75 \, x^{2} \log \left (x\right ) - x \log \left (x^{2}\right )\right )} \log \left (-75 \, x \log \left (x\right ) + \log \left (x^{2}\right )\right ) - 2 \, x\right )} e^{\left (-\frac {x}{x - \log \left (-75 \, x \log \left (x\right ) + \log \left (x^{2}\right )\right )}\right )} + {\left (75 \, x^{3} \log \left (x\right ) - x^{2} \log \left (x^{2}\right ) + {\left (75 \, x \log \left (x\right ) - \log \left (x^{2}\right )\right )} \log \left (-75 \, x \log \left (x\right ) + \log \left (x^{2}\right )\right )^{2} + {\left (75 \, x^{3} \log \left (x\right ) - x^{2} \log \left (x^{2}\right ) + {\left (75 \, x \log \left (x\right ) - \log \left (x^{2}\right )\right )} \log \left (-75 \, x \log \left (x\right ) + \log \left (x^{2}\right )\right )^{2} - 2 \, {\left (75 \, x^{2} \log \left (x\right ) - x \log \left (x^{2}\right )\right )} \log \left (-75 \, x \log \left (x\right ) + \log \left (x^{2}\right )\right )\right )} e^{\left (-\frac {x}{x - \log \left (-75 \, x \log \left (x\right ) + \log \left (x^{2}\right )\right )}\right )} - 2 \, {\left (75 \, x^{2} \log \left (x\right ) - x \log \left (x^{2}\right )\right )} \log \left (-75 \, x \log \left (x\right ) + \log \left (x^{2}\right )\right )\right )} \log \left (e^{\left (-\frac {x}{x - \log \left (-75 \, x \log \left (x\right ) + \log \left (x^{2}\right )\right )}\right )} + 1\right )}{{\left (75 \, x^{3} \log \left (x\right ) - x^{2} \log \left (x^{2}\right ) + {\left (75 \, x \log \left (x\right ) - \log \left (x^{2}\right )\right )} \log \left (-75 \, x \log \left (x\right ) + \log \left (x^{2}\right )\right )^{2} + {\left (75 \, x^{3} \log \left (x\right ) - x^{2} \log \left (x^{2}\right ) + {\left (75 \, x \log \left (x\right ) - \log \left (x^{2}\right )\right )} \log \left (-75 \, x \log \left (x\right ) + \log \left (x^{2}\right )\right )^{2} - 2 \, {\left (75 \, x^{2} \log \left (x\right ) - x \log \left (x^{2}\right )\right )} \log \left (-75 \, x \log \left (x\right ) + \log \left (x^{2}\right )\right )\right )} e^{\left (-\frac {x}{x - \log \left (-75 \, x \log \left (x\right ) + \log \left (x^{2}\right )\right )}\right )} - 2 \, {\left (75 \, x^{2} \log \left (x\right ) - x \log \left (x^{2}\right )\right )} \log \left (-75 \, x \log \left (x\right ) + \log \left (x^{2}\right )\right )\right )} \log \left (e^{\left (-\frac {x}{x - \log \left (-75 \, x \log \left (x\right ) + \log \left (x^{2}\right )\right )}\right )} + 1\right )^{2}} \,d x } \]

[In]

integrate(((((log(x^2)-75*x*log(x))*log(log(x^2)-75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x))*log(log(x^2)-75
*x*log(x))+x^2*log(x^2)-75*x^3*log(x))*exp(x/(log(log(x^2)-75*x*log(x))-x))+(log(x^2)-75*x*log(x))*log(log(x^2
)-75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x))+x^2*log(x^2)-75*x^3*log(x))*log(exp(
x/(log(log(x^2)-75*x*log(x))-x))+1)+((-x*log(x^2)+75*x^2*log(x))*log(log(x^2)-75*x*log(x))-75*x^2*log(x)-75*x^
2+2*x)*exp(x/(log(log(x^2)-75*x*log(x))-x)))/(((log(x^2)-75*x*log(x))*log(log(x^2)-75*x*log(x))^2+(-2*x*log(x^
2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x))+x^2*log(x^2)-75*x^3*log(x))*exp(x/(log(log(x^2)-75*x*log(x))-x))+
(log(x^2)-75*x*log(x))*log(log(x^2)-75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x))+x^
2*log(x^2)-75*x^3*log(x))/log(exp(x/(log(log(x^2)-75*x*log(x))-x))+1)^2,x, algorithm="giac")

[Out]

undef

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (2 x-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )+\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )} \, dx=\int \frac {\ln \left ({\mathrm {e}}^{-\frac {x}{x-\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}}+1\right )\,\left (75\,x^3\,\ln \left (x\right )-x^2\,\ln \left (x^2\right )+{\mathrm {e}}^{-\frac {x}{x-\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}}\,\left (75\,x^3\,\ln \left (x\right )-x^2\,\ln \left (x^2\right )+\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\,\left (2\,x\,\ln \left (x^2\right )-150\,x^2\,\ln \left (x\right )\right )-{\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}^2\,\left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\right )+\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\,\left (2\,x\,\ln \left (x^2\right )-150\,x^2\,\ln \left (x\right )\right )-{\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}^2\,\left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\right )+{\mathrm {e}}^{-\frac {x}{x-\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}}\,\left (75\,x^2\,\ln \left (x\right )-2\,x+\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\,\left (x\,\ln \left (x^2\right )-75\,x^2\,\ln \left (x\right )\right )+75\,x^2\right )}{{\ln \left ({\mathrm {e}}^{-\frac {x}{x-\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}}+1\right )}^2\,\left (75\,x^3\,\ln \left (x\right )-x^2\,\ln \left (x^2\right )+{\mathrm {e}}^{-\frac {x}{x-\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}}\,\left (75\,x^3\,\ln \left (x\right )-x^2\,\ln \left (x^2\right )+\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\,\left (2\,x\,\ln \left (x^2\right )-150\,x^2\,\ln \left (x\right )\right )-{\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}^2\,\left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\right )+\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\,\left (2\,x\,\ln \left (x^2\right )-150\,x^2\,\ln \left (x\right )\right )-{\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}^2\,\left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\right )} \,d x \]

[In]

int((log(exp(-x/(x - log(log(x^2) - 75*x*log(x)))) + 1)*(75*x^3*log(x) - x^2*log(x^2) + exp(-x/(x - log(log(x^
2) - 75*x*log(x))))*(75*x^3*log(x) - x^2*log(x^2) + log(log(x^2) - 75*x*log(x))*(2*x*log(x^2) - 150*x^2*log(x)
) - log(log(x^2) - 75*x*log(x))^2*(log(x^2) - 75*x*log(x))) + log(log(x^2) - 75*x*log(x))*(2*x*log(x^2) - 150*
x^2*log(x)) - log(log(x^2) - 75*x*log(x))^2*(log(x^2) - 75*x*log(x))) + exp(-x/(x - log(log(x^2) - 75*x*log(x)
)))*(75*x^2*log(x) - 2*x + log(log(x^2) - 75*x*log(x))*(x*log(x^2) - 75*x^2*log(x)) + 75*x^2))/(log(exp(-x/(x
- log(log(x^2) - 75*x*log(x)))) + 1)^2*(75*x^3*log(x) - x^2*log(x^2) + exp(-x/(x - log(log(x^2) - 75*x*log(x))
))*(75*x^3*log(x) - x^2*log(x^2) + log(log(x^2) - 75*x*log(x))*(2*x*log(x^2) - 150*x^2*log(x)) - log(log(x^2)
- 75*x*log(x))^2*(log(x^2) - 75*x*log(x))) + log(log(x^2) - 75*x*log(x))*(2*x*log(x^2) - 150*x^2*log(x)) - log
(log(x^2) - 75*x*log(x))^2*(log(x^2) - 75*x*log(x)))),x)

[Out]

int((log(exp(-x/(x - log(log(x^2) - 75*x*log(x)))) + 1)*(75*x^3*log(x) - x^2*log(x^2) + exp(-x/(x - log(log(x^
2) - 75*x*log(x))))*(75*x^3*log(x) - x^2*log(x^2) + log(log(x^2) - 75*x*log(x))*(2*x*log(x^2) - 150*x^2*log(x)
) - log(log(x^2) - 75*x*log(x))^2*(log(x^2) - 75*x*log(x))) + log(log(x^2) - 75*x*log(x))*(2*x*log(x^2) - 150*
x^2*log(x)) - log(log(x^2) - 75*x*log(x))^2*(log(x^2) - 75*x*log(x))) + exp(-x/(x - log(log(x^2) - 75*x*log(x)
)))*(75*x^2*log(x) - 2*x + log(log(x^2) - 75*x*log(x))*(x*log(x^2) - 75*x^2*log(x)) + 75*x^2))/(log(exp(-x/(x
- log(log(x^2) - 75*x*log(x)))) + 1)^2*(75*x^3*log(x) - x^2*log(x^2) + exp(-x/(x - log(log(x^2) - 75*x*log(x))
))*(75*x^3*log(x) - x^2*log(x^2) + log(log(x^2) - 75*x*log(x))*(2*x*log(x^2) - 150*x^2*log(x)) - log(log(x^2)
- 75*x*log(x))^2*(log(x^2) - 75*x*log(x))) + log(log(x^2) - 75*x*log(x))*(2*x*log(x^2) - 150*x^2*log(x)) - log
(log(x^2) - 75*x*log(x))^2*(log(x^2) - 75*x*log(x)))), x)