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

Optimal. Leaf size=29 \[ 1+\frac {\left (-1+e^{5 x}\right ) x}{\log \left (\frac {x}{-2-\log (-x+\log (x))}\right )} \]

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Rubi [F]  time = 8.52, 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 {-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 \end {gather*}

Verification is not applicable to the result.

[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 {gather*} \begin {aligned} \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 {aligned} \end {gather*}

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Mathematica [A]  time = 0.23, size = 26, normalized size = 0.90 \begin {gather*} \frac {\left (-1+e^{5 x}\right ) x}{\log \left (-\frac {x}{2+\log (-x+\log (x))}\right )} \end {gather*}

Antiderivative was successfully verified.

[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]]))]

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fricas [A]  time = 0.59, size = 28, normalized size = 0.97 \begin {gather*} \frac {x e^{\left (5 \, x\right )} - x}{\log \left (-\frac {x}{\log \left (-x + \log \relax (x)\right ) + 2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)+(x+1)*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))

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giac [B]  time = 2.51, size = 1672, normalized size = 57.66 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[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)+(x+1)*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)

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maple [C]  time = 0.28, size = 175, normalized size = 6.03

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

Verification of antiderivative is not currently implemented for this CAS.

[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)+(x+
1)*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]

-2*I*x*(exp(5*x)-1)/(Pi*csgn(I/(ln(ln(x)-x)+2))*csgn(I*x/(ln(ln(x)-x)+2))^2-Pi*csgn(I/(ln(ln(x)-x)+2))*csgn(I*
x/(ln(ln(x)-x)+2))*csgn(I*x)+Pi*csgn(I*x/(ln(ln(x)-x)+2))^3-2*Pi*csgn(I*x/(ln(ln(x)-x)+2))^2+Pi*csgn(I*x/(ln(l
n(x)-x)+2))^2*csgn(I*x)+2*Pi-2*I*ln(x)+2*I*ln(ln(ln(x)-x)+2))

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maxima [A]  time = 0.44, size = 30, normalized size = 1.03 \begin {gather*} \frac {x e^{\left (5 \, x\right )} - x}{\log \relax (x) - \log \left (-\log \left (-x + \log \relax (x)\right ) - 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)+(x+1)*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))

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mupad [B]  time = 5.57, size = 266, normalized size = 9.17 \begin {gather*} {\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 \relax (x)-x\right )+2}\right )\,\left (x-\ln \relax (x)\right )\,\left (\ln \left (\ln \relax (x)-x\right )+2\right )\,\left ({\mathrm {e}}^{5\,x}+5\,x\,{\mathrm {e}}^{5\,x}-1\right )}{x-2\,\ln \relax (x)+x\,\ln \left (\ln \relax (x)-x\right )-\ln \left (\ln \relax (x)-x\right )\,\ln \relax (x)+1}}{\ln \left (-\frac {x}{\ln \left (\ln \relax (x)-x\right )+2}\right )}-\frac {x^3\,\ln \relax (x)-x^2\,\ln \relax (x)+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 \relax (x)+4\,x^3\,{\mathrm {e}}^{5\,x}\,\ln \relax (x)-5\,x^4\,{\mathrm {e}}^{5\,x}\,\ln \relax (x)}{\left (x-2\,\ln \relax (x)+\ln \left (\ln \relax (x)-x\right )\,\left (x-\ln \relax (x)\right )+1\right )\,\left (x+x\,\ln \relax (x)-3\,x^2+x^3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

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sympy [A]  time = 8.91, size = 34, normalized size = 1.17 \begin {gather*} \frac {x e^{5 x}}{\log {\left (- \frac {x}{\log {\left (- x + \log {\relax (x )} \right )} + 2} \right )}} - \frac {x}{\log {\left (- \frac {x}{\log {\left (- x + \log {\relax (x )} \right )} + 2} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)+(x+1)*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))

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