\(\int \frac {-1-x+e^{5 x} (1+x)+(2-2 e^{5 x}) \log (x)+(-x+e^{5 x} x+(1-e^{5 x}) \log (x)) \log (-x+\log (x))+(2 x+e^{5 x} (-2 x-10 x^2)+(-2+e^{5 x} (2+10 x)) \log (x)+(x+e^{5 x} (-x-5 x^2)+(-1+e^{5 x} (1+5 x)) \log (x)) \log (-x+\log (x))) \log (-\frac {x}{2+\log (-x+\log (x))})}{(-2 x+2 \log (x)+(-x+\log (x)) \log (-x+\log (x))) \log ^2(-\frac {x}{2+\log (-x+\log (x))})} \, dx\) [7552]

Optimal result

Integrand size = 191, antiderivative size = 29 \[ \int \frac {-1-x+e^{5 x} (1+x)+\left (2-2 e^{5 x}\right ) \log (x)+\left (-x+e^{5 x} x+\left (1-e^{5 x}\right ) \log (x)\right ) \log (-x+\log (x))+\left (2 x+e^{5 x} \left (-2 x-10 x^2\right )+\left (-2+e^{5 x} (2+10 x)\right ) \log (x)+\left (x+e^{5 x} \left (-x-5 x^2\right )+\left (-1+e^{5 x} (1+5 x)\right ) \log (x)\right ) \log (-x+\log (x))\right ) \log \left (-\frac {x}{2+\log (-x+\log (x))}\right )}{(-2 x+2 \log (x)+(-x+\log (x)) \log (-x+\log (x))) \log ^2\left (-\frac {x}{2+\log (-x+\log (x))}\right )} \, dx=1+\frac {\left (-1+e^{5 x}\right ) x}{\log \left (\frac {x}{-2-\log (-x+\log (x))}\right )} \]

[Out]

1+x/ln(x/(-2-ln(ln(x)-x)))*(exp(5*x)-1)

Rubi [F]

\[ \int \frac {-1-x+e^{5 x} (1+x)+\left (2-2 e^{5 x}\right ) \log (x)+\left (-x+e^{5 x} x+\left (1-e^{5 x}\right ) \log (x)\right ) \log (-x+\log (x))+\left (2 x+e^{5 x} \left (-2 x-10 x^2\right )+\left (-2+e^{5 x} (2+10 x)\right ) \log (x)+\left (x+e^{5 x} \left (-x-5 x^2\right )+\left (-1+e^{5 x} (1+5 x)\right ) \log (x)\right ) \log (-x+\log (x))\right ) \log \left (-\frac {x}{2+\log (-x+\log (x))}\right )}{(-2 x+2 \log (x)+(-x+\log (x)) \log (-x+\log (x))) \log ^2\left (-\frac {x}{2+\log (-x+\log (x))}\right )} \, dx=\int \frac {-1-x+e^{5 x} (1+x)+\left (2-2 e^{5 x}\right ) \log (x)+\left (-x+e^{5 x} x+\left (1-e^{5 x}\right ) \log (x)\right ) \log (-x+\log (x))+\left (2 x+e^{5 x} \left (-2 x-10 x^2\right )+\left (-2+e^{5 x} (2+10 x)\right ) \log (x)+\left (x+e^{5 x} \left (-x-5 x^2\right )+\left (-1+e^{5 x} (1+5 x)\right ) \log (x)\right ) \log (-x+\log (x))\right ) \log \left (-\frac {x}{2+\log (-x+\log (x))}\right )}{(-2 x+2 \log (x)+(-x+\log (x)) \log (-x+\log (x))) \log ^2\left (-\frac {x}{2+\log (-x+\log (x))}\right )} \, dx \]

[In]

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

[Out]

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

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

Mathematica [A] (verified)

Time = 0.20 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.90 \[ \int \frac {-1-x+e^{5 x} (1+x)+\left (2-2 e^{5 x}\right ) \log (x)+\left (-x+e^{5 x} x+\left (1-e^{5 x}\right ) \log (x)\right ) \log (-x+\log (x))+\left (2 x+e^{5 x} \left (-2 x-10 x^2\right )+\left (-2+e^{5 x} (2+10 x)\right ) \log (x)+\left (x+e^{5 x} \left (-x-5 x^2\right )+\left (-1+e^{5 x} (1+5 x)\right ) \log (x)\right ) \log (-x+\log (x))\right ) \log \left (-\frac {x}{2+\log (-x+\log (x))}\right )}{(-2 x+2 \log (x)+(-x+\log (x)) \log (-x+\log (x))) \log ^2\left (-\frac {x}{2+\log (-x+\log (x))}\right )} \, dx=\frac {\left (-1+e^{5 x}\right ) x}{\log \left (-\frac {x}{2+\log (-x+\log (x))}\right )} \]

[In]

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

[Out]

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

Maple [A] (verified)

Time = 281.93 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07

method	result	size
parallelrisch	\(-\frac {-8 x \,{\mathrm e}^{5 x}+8 x}{8 \ln \left (-\frac {x}{\ln \left (\ln \left (x \right )-x \right )+2}\right )}\)	\(31\)
risch	\(-\frac {2 i x \left ({\mathrm e}^{5 x}-1\right )}{-2 \pi \operatorname {csgn}\left (\frac {i x}{\ln \left (\ln \left (x \right )-x \right )+2}\right )^{2}-\pi \,\operatorname {csgn}\left (\frac {i}{\ln \left (\ln \left (x \right )-x \right )+2}\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (\ln \left (x \right )-x \right )+2}\right )+\pi \,\operatorname {csgn}\left (\frac {i}{\ln \left (\ln \left (x \right )-x \right )+2}\right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (\ln \left (x \right )-x \right )+2}\right )^{2}+\pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (\ln \left (x \right )-x \right )+2}\right )^{2}+\pi \operatorname {csgn}\left (\frac {i x}{\ln \left (\ln \left (x \right )-x \right )+2}\right )^{3}+2 \pi +2 i \ln \left (\ln \left (\ln \left (x \right )-x \right )+2\right )-2 i \ln \left (x \right )}\)	\(175\)

[In]

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

[Out]

-1/8*(-8*x*exp(5*x)+8*x)/ln(-x/(ln(ln(x)-x)+2))

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.97 \[ \int \frac {-1-x+e^{5 x} (1+x)+\left (2-2 e^{5 x}\right ) \log (x)+\left (-x+e^{5 x} x+\left (1-e^{5 x}\right ) \log (x)\right ) \log (-x+\log (x))+\left (2 x+e^{5 x} \left (-2 x-10 x^2\right )+\left (-2+e^{5 x} (2+10 x)\right ) \log (x)+\left (x+e^{5 x} \left (-x-5 x^2\right )+\left (-1+e^{5 x} (1+5 x)\right ) \log (x)\right ) \log (-x+\log (x))\right ) \log \left (-\frac {x}{2+\log (-x+\log (x))}\right )}{(-2 x+2 \log (x)+(-x+\log (x)) \log (-x+\log (x))) \log ^2\left (-\frac {x}{2+\log (-x+\log (x))}\right )} \, dx=\frac {x e^{\left (5 \, x\right )} - x}{\log \left (-\frac {x}{\log \left (-x + \log \left (x\right )\right ) + 2}\right )} \]

[In]

integrate((((((1+5*x)*exp(5*x)-1)*log(x)+(-5*x^2-x)*exp(5*x)+x)*log(log(x)-x)+((10*x+2)*exp(5*x)-2)*log(x)+(-1
0*x^2-2*x)*exp(5*x)+2*x)*log(-x/(log(log(x)-x)+2))+((-exp(5*x)+1)*log(x)+x*exp(5*x)-x)*log(log(x)-x)+(-2*exp(5
*x)+2)*log(x)+(1+x)*exp(5*x)-x-1)/((log(x)-x)*log(log(x)-x)+2*log(x)-2*x)/log(-x/(log(log(x)-x)+2))^2,x, algor
ithm="fricas")

[Out]

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

Sympy [A] (verification not implemented)

Time = 4.21 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.17 \[ \int \frac {-1-x+e^{5 x} (1+x)+\left (2-2 e^{5 x}\right ) \log (x)+\left (-x+e^{5 x} x+\left (1-e^{5 x}\right ) \log (x)\right ) \log (-x+\log (x))+\left (2 x+e^{5 x} \left (-2 x-10 x^2\right )+\left (-2+e^{5 x} (2+10 x)\right ) \log (x)+\left (x+e^{5 x} \left (-x-5 x^2\right )+\left (-1+e^{5 x} (1+5 x)\right ) \log (x)\right ) \log (-x+\log (x))\right ) \log \left (-\frac {x}{2+\log (-x+\log (x))}\right )}{(-2 x+2 \log (x)+(-x+\log (x)) \log (-x+\log (x))) \log ^2\left (-\frac {x}{2+\log (-x+\log (x))}\right )} \, dx=\frac {x e^{5 x}}{\log {\left (- \frac {x}{\log {\left (- x + \log {\left (x \right )} \right )} + 2} \right )}} - \frac {x}{\log {\left (- \frac {x}{\log {\left (- x + \log {\left (x \right )} \right )} + 2} \right )}} \]

[In]

integrate((((((1+5*x)*exp(5*x)-1)*ln(x)+(-5*x**2-x)*exp(5*x)+x)*ln(ln(x)-x)+((10*x+2)*exp(5*x)-2)*ln(x)+(-10*x
**2-2*x)*exp(5*x)+2*x)*ln(-x/(ln(ln(x)-x)+2))+((-exp(5*x)+1)*ln(x)+x*exp(5*x)-x)*ln(ln(x)-x)+(-2*exp(5*x)+2)*l
n(x)+(1+x)*exp(5*x)-x-1)/((ln(x)-x)*ln(ln(x)-x)+2*ln(x)-2*x)/ln(-x/(ln(ln(x)-x)+2))**2,x)

[Out]

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

Maxima [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.03 \[ \int \frac {-1-x+e^{5 x} (1+x)+\left (2-2 e^{5 x}\right ) \log (x)+\left (-x+e^{5 x} x+\left (1-e^{5 x}\right ) \log (x)\right ) \log (-x+\log (x))+\left (2 x+e^{5 x} \left (-2 x-10 x^2\right )+\left (-2+e^{5 x} (2+10 x)\right ) \log (x)+\left (x+e^{5 x} \left (-x-5 x^2\right )+\left (-1+e^{5 x} (1+5 x)\right ) \log (x)\right ) \log (-x+\log (x))\right ) \log \left (-\frac {x}{2+\log (-x+\log (x))}\right )}{(-2 x+2 \log (x)+(-x+\log (x)) \log (-x+\log (x))) \log ^2\left (-\frac {x}{2+\log (-x+\log (x))}\right )} \, dx=\frac {x e^{\left (5 \, x\right )} - x}{\log \left (x\right ) - \log \left (-\log \left (-x + \log \left (x\right )\right ) - 2\right )} \]

[In]

integrate((((((1+5*x)*exp(5*x)-1)*log(x)+(-5*x^2-x)*exp(5*x)+x)*log(log(x)-x)+((10*x+2)*exp(5*x)-2)*log(x)+(-1
0*x^2-2*x)*exp(5*x)+2*x)*log(-x/(log(log(x)-x)+2))+((-exp(5*x)+1)*log(x)+x*exp(5*x)-x)*log(log(x)-x)+(-2*exp(5
*x)+2)*log(x)+(1+x)*exp(5*x)-x-1)/((log(x)-x)*log(log(x)-x)+2*log(x)-2*x)/log(-x/(log(log(x)-x)+2))^2,x, algor
ithm="maxima")

[Out]

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

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1672 vs. \(2 (27) = 54\).

Time = 1.35 (sec) , antiderivative size = 1672, normalized size of antiderivative = 57.66 \[ \int \frac {-1-x+e^{5 x} (1+x)+\left (2-2 e^{5 x}\right ) \log (x)+\left (-x+e^{5 x} x+\left (1-e^{5 x}\right ) \log (x)\right ) \log (-x+\log (x))+\left (2 x+e^{5 x} \left (-2 x-10 x^2\right )+\left (-2+e^{5 x} (2+10 x)\right ) \log (x)+\left (x+e^{5 x} \left (-x-5 x^2\right )+\left (-1+e^{5 x} (1+5 x)\right ) \log (x)\right ) \log (-x+\log (x))\right ) \log \left (-\frac {x}{2+\log (-x+\log (x))}\right )}{(-2 x+2 \log (x)+(-x+\log (x)) \log (-x+\log (x))) \log ^2\left (-\frac {x}{2+\log (-x+\log (x))}\right )} \, dx=\text {Too large to display} \]

[In]

integrate((((((1+5*x)*exp(5*x)-1)*log(x)+(-5*x^2-x)*exp(5*x)+x)*log(log(x)-x)+((10*x+2)*exp(5*x)-2)*log(x)+(-1
0*x^2-2*x)*exp(5*x)+2*x)*log(-x/(log(log(x)-x)+2))+((-exp(5*x)+1)*log(x)+x*exp(5*x)-x)*log(log(x)-x)+(-2*exp(5
*x)+2)*log(x)+(1+x)*exp(5*x)-x-1)/((log(x)-x)*log(log(x)-x)+2*log(x)-2*x)/log(-x/(log(log(x)-x)+2))^2,x, algor
ithm="giac")

[Out]

-2*(x*e^(5*x)*log(-pi*arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x))))*sgn(-pi + pi*sgn(x))*sgn(x - log(abs(x))
) - pi*arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x))))*sgn(-pi + pi*sgn(x)) + 1/2*pi^2*sgn(x - log(abs(x))) +
1/2*pi^2 + arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x))))^2 + 1/4*log(-1/2*pi^2*sgn(x) + 1/2*pi^2 + x^2 - 2*x
*log(abs(x)) + log(abs(x))^2)^2 + 2*log(-1/2*pi^2*sgn(x) + 1/2*pi^2 + x^2 - 2*x*log(abs(x)) + log(abs(x))^2) +
4) - 2*x*e^(5*x)*log(abs(x)) - x*log(-pi*arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x))))*sgn(-pi + pi*sgn(x))
*sgn(x - log(abs(x))) - pi*arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x))))*sgn(-pi + pi*sgn(x)) + 1/2*pi^2*sgn
(x - log(abs(x))) + 1/2*pi^2 + arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x))))^2 + 1/4*log(-1/2*pi^2*sgn(x) +
1/2*pi^2 + x^2 - 2*x*log(abs(x)) + log(abs(x))^2)^2 + 2*log(-1/2*pi^2*sgn(x) + 1/2*pi^2 + x^2 - 2*x*log(abs(x)
) + log(abs(x))^2) + 4) + 2*x*log(abs(x)))/(2*pi^2*sgn(pi*sgn(-pi + pi*sgn(x))*sgn(x - log(abs(x))) + pi*sgn(-
pi + pi*sgn(x)) - 2*arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x)))))*sgn(x)*sgn(log(-1/2*pi^2*sgn(x) + 1/2*pi^
2 + x^2 - 2*x*log(abs(x)) + log(abs(x))^2) + 4) - 2*pi^2*sgn(pi*sgn(-pi + pi*sgn(x))*sgn(x - log(abs(x))) + pi
*sgn(-pi + pi*sgn(x)) - 2*arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x)))))*sgn(x) - 6*pi^2*sgn(pi*sgn(-pi + pi
*sgn(x))*sgn(x - log(abs(x))) + pi*sgn(-pi + pi*sgn(x)) - 2*arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x)))))*s
gn(log(-1/2*pi^2*sgn(x) + 1/2*pi^2 + x^2 - 2*x*log(abs(x)) + log(abs(x))^2) + 4) - 4*pi*arctan((pi*sgn(-pi + p
i*sgn(x))*sgn(x - log(abs(x))) + pi*sgn(-pi + pi*sgn(x)) - 2*arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x)))))/
(log(-1/2*pi^2*sgn(x) + 1/2*pi^2 + x^2 - 2*x*log(abs(x)) + log(abs(x))^2) + 4))*sgn(pi*sgn(-pi + pi*sgn(x))*sg
n(x - log(abs(x))) + pi*sgn(-pi + pi*sgn(x)) - 2*arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x)))))*sgn(log(-1/2
*pi^2*sgn(x) + 1/2*pi^2 + x^2 - 2*x*log(abs(x)) + log(abs(x))^2) + 4) + 6*pi^2*sgn(pi*sgn(-pi + pi*sgn(x))*sgn
(x - log(abs(x))) + pi*sgn(-pi + pi*sgn(x)) - 2*arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x))))) + 4*pi*arctan
((pi*sgn(-pi + pi*sgn(x))*sgn(x - log(abs(x))) + pi*sgn(-pi + pi*sgn(x)) - 2*arctan(-1/2*(pi - pi*sgn(x))/(x -
log(abs(x)))))/(log(-1/2*pi^2*sgn(x) + 1/2*pi^2 + x^2 - 2*x*log(abs(x)) + log(abs(x))^2) + 4))*sgn(pi*sgn(-pi
+ pi*sgn(x))*sgn(x - log(abs(x))) + pi*sgn(-pi + pi*sgn(x)) - 2*arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x))
))) - 6*pi^2*sgn(x) - 4*pi*arctan((pi*sgn(-pi + pi*sgn(x))*sgn(x - log(abs(x))) + pi*sgn(-pi + pi*sgn(x)) - 2*
arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x)))))/(log(-1/2*pi^2*sgn(x) + 1/2*pi^2 + x^2 - 2*x*log(abs(x)) + lo
g(abs(x))^2) + 4))*sgn(x) - 2*pi^2*sgn(log(-1/2*pi^2*sgn(x) + 1/2*pi^2 + x^2 - 2*x*log(abs(x)) + log(abs(x))^2
) + 4) + 12*pi^2 + 12*pi*arctan((pi*sgn(-pi + pi*sgn(x))*sgn(x - log(abs(x))) + pi*sgn(-pi + pi*sgn(x)) - 2*ar
ctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x)))))/(log(-1/2*pi^2*sgn(x) + 1/2*pi^2 + x^2 - 2*x*log(abs(x)) + log(
abs(x))^2) + 4)) + 4*arctan((pi*sgn(-pi + pi*sgn(x))*sgn(x - log(abs(x))) + pi*sgn(-pi + pi*sgn(x)) - 2*arctan
(-1/2*(pi - pi*sgn(x))/(x - log(abs(x)))))/(log(-1/2*pi^2*sgn(x) + 1/2*pi^2 + x^2 - 2*x*log(abs(x)) + log(abs(
x))^2) + 4))^2 + log(-pi*arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x))))*sgn(-pi + pi*sgn(x))*sgn(x - log(abs(
x))) - pi*arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x))))*sgn(-pi + pi*sgn(x)) + 1/2*pi^2*sgn(x - log(abs(x)))
+ 1/2*pi^2 + arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x))))^2 + 1/4*log(-1/2*pi^2*sgn(x) + 1/2*pi^2 + x^2 -
2*x*log(abs(x)) + log(abs(x))^2)^2 + 2*log(-1/2*pi^2*sgn(x) + 1/2*pi^2 + x^2 - 2*x*log(abs(x)) + log(abs(x))^2
) + 4)^2 - 4*log(-pi*arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x))))*sgn(-pi + pi*sgn(x))*sgn(x - log(abs(x)))
- pi*arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x))))*sgn(-pi + pi*sgn(x)) + 1/2*pi^2*sgn(x - log(abs(x))) + 1
/2*pi^2 + arctan(-1/2*(pi - pi*sgn(x))/(x - log(abs(x))))^2 + 1/4*log(-1/2*pi^2*sgn(x) + 1/2*pi^2 + x^2 - 2*x*
log(abs(x)) + log(abs(x))^2)^2 + 2*log(-1/2*pi^2*sgn(x) + 1/2*pi^2 + x^2 - 2*x*log(abs(x)) + log(abs(x))^2) +
4)*log(abs(x)) + 4*log(abs(x))^2)

Mupad [B] (verification not implemented)

Time = 13.92 (sec) , antiderivative size = 266, normalized size of antiderivative = 9.17 \[ \int \frac {-1-x+e^{5 x} (1+x)+\left (2-2 e^{5 x}\right ) \log (x)+\left (-x+e^{5 x} x+\left (1-e^{5 x}\right ) \log (x)\right ) \log (-x+\log (x))+\left (2 x+e^{5 x} \left (-2 x-10 x^2\right )+\left (-2+e^{5 x} (2+10 x)\right ) \log (x)+\left (x+e^{5 x} \left (-x-5 x^2\right )+\left (-1+e^{5 x} (1+5 x)\right ) \log (x)\right ) \log (-x+\log (x))\right ) \log \left (-\frac {x}{2+\log (-x+\log (x))}\right )}{(-2 x+2 \log (x)+(-x+\log (x)) \log (-x+\log (x))) \log ^2\left (-\frac {x}{2+\log (-x+\log (x))}\right )} \, dx={\mathrm {e}}^{5\,x}\,\left (5\,x^2+x\right )-x+\frac {x\,\left ({\mathrm {e}}^{5\,x}-1\right )-\frac {x\,\ln \left (-\frac {x}{\ln \left (\ln \left (x\right )-x\right )+2}\right )\,\left (x-\ln \left (x\right )\right )\,\left (\ln \left (\ln \left (x\right )-x\right )+2\right )\,\left ({\mathrm {e}}^{5\,x}+5\,x\,{\mathrm {e}}^{5\,x}-1\right )}{x-2\,\ln \left (x\right )+x\,\ln \left (\ln \left (x\right )-x\right )-\ln \left (\ln \left (x\right )-x\right )\,\ln \left (x\right )+1}}{\ln \left (-\frac {x}{\ln \left (\ln \left (x\right )-x\right )+2}\right )}-\frac {x^3\,\ln \left (x\right )-x^2\,\ln \left (x\right )+x^2\,{\mathrm {e}}^{5\,x}+x^3\,{\mathrm {e}}^{5\,x}-16\,x^4\,{\mathrm {e}}^{5\,x}+19\,x^5\,{\mathrm {e}}^{5\,x}-5\,x^6\,{\mathrm {e}}^{5\,x}-x^2+4\,x^3-4\,x^4+x^5+x^2\,{\mathrm {e}}^{5\,x}\,\ln \left (x\right )+4\,x^3\,{\mathrm {e}}^{5\,x}\,\ln \left (x\right )-5\,x^4\,{\mathrm {e}}^{5\,x}\,\ln \left (x\right )}{\left (x-2\,\ln \left (x\right )+\ln \left (\ln \left (x\right )-x\right )\,\left (x-\ln \left (x\right )\right )+1\right )\,\left (x+x\,\ln \left (x\right )-3\,x^2+x^3\right )} \]

[In]

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

[Out]

exp(5*x)*(x + 5*x^2) - x + (x*(exp(5*x) - 1) - (x*log(-x/(log(log(x) - x) + 2))*(x - log(x))*(log(log(x) - x)
+ 2)*(exp(5*x) + 5*x*exp(5*x) - 1))/(x - 2*log(x) + x*log(log(x) - x) - log(log(x) - x)*log(x) + 1))/log(-x/(l
og(log(x) - x) + 2)) - (x^3*log(x) - x^2*log(x) + x^2*exp(5*x) + x^3*exp(5*x) - 16*x^4*exp(5*x) + 19*x^5*exp(5
*x) - 5*x^6*exp(5*x) - x^2 + 4*x^3 - 4*x^4 + x^5 + x^2*exp(5*x)*log(x) + 4*x^3*exp(5*x)*log(x) - 5*x^4*exp(5*x
)*log(x))/((x - 2*log(x) + log(log(x) - x)*(x - log(x)) + 1)*(x + x*log(x) - 3*x^2 + x^3))