3.85.84 $\int \frac{-16-27x-2x^2+(3x+x^2)\log (e^{4x}{x}^4)+(5x-2x^2+(-4x-x^2)\log (e^{4x}{x}^4)+(-5+2x+(4+x)\log (e^{4x}{x}^4))\log (-5+2x+(4+x)\log (e^{4x}{x}^4)))\log (x-\log (-5+2x+(4+x)\log (e^{4x}{x}^4)))}{(5x-2x^2+(-4x-x^2)\log (e^{4x}{x}^4)+(-5+2x+(4+x)\log (e^{4x}{x}^4))\log (-5+2x+(4+x)\log (e^{4x}{x}^4))){\log }^2(x-\log (-5+2x+(4+x)\log (e^{4x}{x}^4)))}dx$

Optimal. Leaf size=31 $$-5+\frac{x}{\log (x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}$$

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Rubi [F]  time = 7.00, 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 = {} $$\begin{array}{c}\int \frac{-16-27x-2x^2+(3x+x^2)\log \left(e^{4x}{x}^4\right)+(5x-2x^2+(-4x-x^2)\log \left(e^{4x}{x}^4\right)+(-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))\log (x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}{(5x-2x^2+(-4x-x^2)\log \left(e^{4x}{x}^4\right)+(-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(-16 - 27*x - 2*x^2 + (3*x + x^2)*Log[E^(4*x)*x^4] + (5*x - 2*x^2 + (-4*x - x^2)*Log[E^(4*x)*x^4] + (-5 +
2*x + (4 + x)*Log[E^(4*x)*x^4])*Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]])*Log[x - Log[-5 + 2*x + (4 + x)*Log[E
^(4*x)*x^4]]])/((5*x - 2*x^2 + (-4*x - x^2)*Log[E^(4*x)*x^4] + (-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4])*Log[-5 +
2*x + (4 + x)*Log[E^(4*x)*x^4]])*Log[x - Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]]]^2),x]

[Out]

16*Defer[Int][1/((-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4])*(x - Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]])*Log[x -
Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]]]^2), x] + 27*Defer[Int][x/((-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4])*(x -
Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]])*Log[x - Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]]]^2), x] + 2*Defer[
Int][x^2/((-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4])*(x - Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]])*Log[x - Log[-5
+ 2*x + (4 + x)*Log[E^(4*x)*x^4]]]^2), x] - 3*Defer[Int][(x*Log[E^(4*x)*x^4])/((-5 + 2*x + (4 + x)*Log[E^(4*x)
*x^4])*(x - Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]])*Log[x - Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]]]^2), x]
- Defer[Int][(x^2*Log[E^(4*x)*x^4])/((-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4])*(x - Log[-5 + 2*x + (4 + x)*Log[E^
(4*x)*x^4]])*Log[x - Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]]]^2), x] + Defer[Int][Log[x - Log[-5 + 2*x + (4 +
x)*Log[E^(4*x)*x^4]]]^(-1), x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{-16-27x-2x^2+x(3+x)\log \left(e^{4x}{x}^4\right)-(-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))\log (x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}{(5-2x-(4+x)\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx\\ & =\int (\frac{16+27x+2x^2-3x\log \left(e^{4x}{x}^4\right)-x^2\log \left(e^{4x}{x}^4\right)}{(-5+2x+4\log \left(e^{4x}{x}^4\right)+x\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}+\frac{1}{\log (x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))})dx\\ & =\int \frac{16+27x+2x^2-3x\log \left(e^{4x}{x}^4\right)-x^2\log \left(e^{4x}{x}^4\right)}{(-5+2x+4\log \left(e^{4x}{x}^4\right)+x\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx+\int \frac{1}{\log (x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx\\ & =\int \frac{-16-27x-2x^2+x(3+x)\log \left(e^{4x}{x}^4\right)}{(5-2x-(4+x)\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx+\int \frac{1}{\log (x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx\\ & =\int (\frac{16}{(-5+2x+4\log \left(e^{4x}{x}^4\right)+x\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}+\frac{27x}{(-5+2x+4\log \left(e^{4x}{x}^4\right)+x\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}+\frac{2x^2}{(-5+2x+4\log \left(e^{4x}{x}^4\right)+x\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}-\frac{3x\log \left(e^{4x}{x}^4\right)}{(-5+2x+4\log \left(e^{4x}{x}^4\right)+x\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}-\frac{x^2\log \left(e^{4x}{x}^4\right)}{(-5+2x+4\log \left(e^{4x}{x}^4\right)+x\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))})dx+\int \frac{1}{\log (x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx\\ & =2\int \frac{x^2}{(-5+2x+4\log \left(e^{4x}{x}^4\right)+x\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx-3\int \frac{x\log \left(e^{4x}{x}^4\right)}{(-5+2x+4\log \left(e^{4x}{x}^4\right)+x\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx+16\int \frac{1}{(-5+2x+4\log \left(e^{4x}{x}^4\right)+x\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx+27\int \frac{x}{(-5+2x+4\log \left(e^{4x}{x}^4\right)+x\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx-\int \frac{x^2\log \left(e^{4x}{x}^4\right)}{(-5+2x+4\log \left(e^{4x}{x}^4\right)+x\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx+\int \frac{1}{\log (x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx\\ & =2\int \frac{x^2}{(-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx-3\int \frac{x\log \left(e^{4x}{x}^4\right)}{(-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx+16\int \frac{1}{(-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx+27\int \frac{x}{(-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx-\int \frac{x^2\log \left(e^{4x}{x}^4\right)}{(-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right))){\log }^2(x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx+\int \frac{1}{\log (x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}dx\end{array}\end{array}$$

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Mathematica [A]  time = 0.11, size = 29, normalized size = 0.94 $$\begin{array}{c}\frac{x}{\log (x-\log (-5+2x+(4+x)\log \left(e^{4x}{x}^4\right)))}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(-16 - 27*x - 2*x^2 + (3*x + x^2)*Log[E^(4*x)*x^4] + (5*x - 2*x^2 + (-4*x - x^2)*Log[E^(4*x)*x^4] +
(-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4])*Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]])*Log[x - Log[-5 + 2*x + (4 + x)
*Log[E^(4*x)*x^4]]])/((5*x - 2*x^2 + (-4*x - x^2)*Log[E^(4*x)*x^4] + (-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4])*Log
[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]])*Log[x - Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]]]^2),x]

[Out]

x/Log[x - Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]]]

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fricas [A]  time = 0.86, size = 28, normalized size = 0.90 $$\begin{array}{c}\frac{x}{\log (x-\log ((x+4)\log \left(x^4{e}^{\left(4x\right)}\right)+2x-5))}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((4+x)*log(x^4*exp(x)^4)+2*x-5)*log((4+x)*log(x^4*exp(x)^4)+2*x-5)+(-x^2-4*x)*log(x^4*exp(x)^4)-2*
x^2+5*x)*log(-log((4+x)*log(x^4*exp(x)^4)+2*x-5)+x)+(x^2+3*x)*log(x^4*exp(x)^4)-2*x^2-27*x-16)/(((4+x)*log(x^4
*exp(x)^4)+2*x-5)*log((4+x)*log(x^4*exp(x)^4)+2*x-5)+(-x^2-4*x)*log(x^4*exp(x)^4)-2*x^2+5*x)/log(-log((4+x)*lo
g(x^4*exp(x)^4)+2*x-5)+x)^2,x, algorithm="fricas")

[Out]

x/log(x - log((x + 4)*log(x^4*e^(4*x)) + 2*x - 5))

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giac [A]  time = 6.72, size = 32, normalized size = 1.03 $$\begin{array}{c}\frac{x}{\log (x-\log (4x^2+x\log \left(x^4\right)+18x+4\log \left(x^4\right)-5))}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((4+x)*log(x^4*exp(x)^4)+2*x-5)*log((4+x)*log(x^4*exp(x)^4)+2*x-5)+(-x^2-4*x)*log(x^4*exp(x)^4)-2*
x^2+5*x)*log(-log((4+x)*log(x^4*exp(x)^4)+2*x-5)+x)+(x^2+3*x)*log(x^4*exp(x)^4)-2*x^2-27*x-16)/(((4+x)*log(x^4
*exp(x)^4)+2*x-5)*log((4+x)*log(x^4*exp(x)^4)+2*x-5)+(-x^2-4*x)*log(x^4*exp(x)^4)-2*x^2+5*x)/log(-log((4+x)*lo
g(x^4*exp(x)^4)+2*x-5)+x)^2,x, algorithm="giac")

[Out]

x/log(x - log(4*x^2 + x*log(x^4) + 18*x + 4*log(x^4) - 5))

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maple [C]  time = 0.58, size = 329, normalized size = 10.61

method	result	size
risch	$\frac{x}{\ln (-\ln ((4+x)(4\ln (x)+4\ln \left({\mathrm{e}}^x\right)-\frac{i\pi \mathrm{csgn}\left(i{\mathrm{e}}^{2x}\right){(-\mathrm{csgn}\left(i{\mathrm{e}}^{2x}\right)+\mathrm{csgn}\left(i{\mathrm{e}}^x\right))}^2}{2}-\frac{i\pi \mathrm{csgn}\left(i{\mathrm{e}}^{3x}\right)(-\mathrm{csgn}\left(i{\mathrm{e}}^{3x}\right)+\mathrm{csgn}\left(i{\mathrm{e}}^{2x}\right))(-\mathrm{csgn}\left(i{\mathrm{e}}^{3x}\right)+\mathrm{csgn}\left(i{\mathrm{e}}^x\right))}{2}-\frac{i\pi \mathrm{csgn}\left(i{\mathrm{e}}^{4x}\right)(-\mathrm{csgn}\left(i{\mathrm{e}}^{4x}\right)+\mathrm{csgn}\left(i{\mathrm{e}}^{3x}\right))(-\mathrm{csgn}\left(i{\mathrm{e}}^{4x}\right)+\mathrm{csgn}\left(i{\mathrm{e}}^x\right))}{2}-\frac{i\pi \mathrm{csgn}\left(i{x}^2\right){(-\mathrm{csgn}\left(i{x}^2\right)+\mathrm{csgn}\left(ix\right))}^2}{2}-\frac{i\pi \mathrm{csgn}\left(i{x}^3\right)(-\mathrm{csgn}\left(i{x}^3\right)+\mathrm{csgn}\left(i{x}^2\right))(-\mathrm{csgn}\left(i{x}^3\right)+\mathrm{csgn}\left(ix\right))}{2}-\frac{i\pi \mathrm{csgn}\left(i{x}^4\right)(-\mathrm{csgn}\left(i{x}^4\right)+\mathrm{csgn}\left(i{x}^3\right))(-\mathrm{csgn}\left(i{x}^4\right)+\mathrm{csgn}\left(ix\right))}{2}-\frac{i\pi \mathrm{csgn}\left(i{x}^4{\mathrm{e}}^{4x}\right)(-\mathrm{csgn}\left(i{x}^4{\mathrm{e}}^{4x}\right)+\mathrm{csgn}\left(i{x}^4\right))(-\mathrm{csgn}\left(i{x}^4{\mathrm{e}}^{4x}\right)+\mathrm{csgn}\left(i{\mathrm{e}}^{4x}\right))}{2})+2x-5)+x)}$	$329$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((4+x)*ln(x^4*exp(x)^4)+2*x-5)*ln((4+x)*ln(x^4*exp(x)^4)+2*x-5)+(-x^2-4*x)*ln(x^4*exp(x)^4)-2*x^2+5*x)*l
n(-ln((4+x)*ln(x^4*exp(x)^4)+2*x-5)+x)+(x^2+3*x)*ln(x^4*exp(x)^4)-2*x^2-27*x-16)/(((4+x)*ln(x^4*exp(x)^4)+2*x-
5)*ln((4+x)*ln(x^4*exp(x)^4)+2*x-5)+(-x^2-4*x)*ln(x^4*exp(x)^4)-2*x^2+5*x)/ln(-ln((4+x)*ln(x^4*exp(x)^4)+2*x-5
)+x)^2,x,method=_RETURNVERBOSE)

[Out]

x/ln(-ln((4+x)*(4*ln(x)+4*ln(exp(x))-1/2*I*Pi*csgn(I*exp(2*x))*(-csgn(I*exp(2*x))+csgn(I*exp(x)))^2-1/2*I*Pi*c
sgn(I*exp(3*x))*(-csgn(I*exp(3*x))+csgn(I*exp(2*x)))*(-csgn(I*exp(3*x))+csgn(I*exp(x)))-1/2*I*Pi*csgn(I*exp(4*
x))*(-csgn(I*exp(4*x))+csgn(I*exp(3*x)))*(-csgn(I*exp(4*x))+csgn(I*exp(x)))-1/2*I*Pi*csgn(I*x^2)*(-csgn(I*x^2)
+csgn(I*x))^2-1/2*I*Pi*csgn(I*x^3)*(-csgn(I*x^3)+csgn(I*x^2))*(-csgn(I*x^3)+csgn(I*x))-1/2*I*Pi*csgn(I*x^4)*(-
csgn(I*x^4)+csgn(I*x^3))*(-csgn(I*x^4)+csgn(I*x))-1/2*I*Pi*csgn(I*x^4*exp(4*x))*(-csgn(I*x^4*exp(4*x))+csgn(I*
x^4))*(-csgn(I*x^4*exp(4*x))+csgn(I*exp(4*x))))+2*x-5)+x)

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maxima [A]  time = 0.69, size = 27, normalized size = 0.87 $$\begin{array}{c}\frac{x}{\log (x-\log (4x^2+4(x+4)\log (x)+18x-5))}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((4+x)*log(x^4*exp(x)^4)+2*x-5)*log((4+x)*log(x^4*exp(x)^4)+2*x-5)+(-x^2-4*x)*log(x^4*exp(x)^4)-2*
x^2+5*x)*log(-log((4+x)*log(x^4*exp(x)^4)+2*x-5)+x)+(x^2+3*x)*log(x^4*exp(x)^4)-2*x^2-27*x-16)/(((4+x)*log(x^4
*exp(x)^4)+2*x-5)*log((4+x)*log(x^4*exp(x)^4)+2*x-5)+(-x^2-4*x)*log(x^4*exp(x)^4)-2*x^2+5*x)/log(-log((4+x)*lo
g(x^4*exp(x)^4)+2*x-5)+x)^2,x, algorithm="maxima")

[Out]

x/log(x - log(4*x^2 + 4*(x + 4)*log(x) + 18*x - 5))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 $$\begin{array}{c}\int -\frac{27x-\ln \left(x^4{\mathrm{e}}^{4x}\right)(x^2+3x)+2x^2-\ln (x-\ln (2x+\ln \left(x^4{\mathrm{e}}^{4x}\right)(x+4)-5))(5x-\ln \left(x^4{\mathrm{e}}^{4x}\right)(x^2+4x)+\ln (2x+\ln \left(x^4{\mathrm{e}}^{4x}\right)(x+4)-5)(2x+\ln \left(x^4{\mathrm{e}}^{4x}\right)(x+4)-5)-2x^2)+16}{{\ln (x-\ln (2x+\ln \left(x^4{\mathrm{e}}^{4x}\right)(x+4)-5))}^2(5x-\ln \left(x^4{\mathrm{e}}^{4x}\right)(x^2+4x)+\ln (2x+\ln \left(x^4{\mathrm{e}}^{4x}\right)(x+4)-5)(2x+\ln \left(x^4{\mathrm{e}}^{4x}\right)(x+4)-5)-2x^2)}dx\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(27*x - log(x^4*exp(4*x))*(3*x + x^2) + 2*x^2 - log(x - log(2*x + log(x^4*exp(4*x))*(x + 4) - 5))*(5*x -
log(x^4*exp(4*x))*(4*x + x^2) + log(2*x + log(x^4*exp(4*x))*(x + 4) - 5)*(2*x + log(x^4*exp(4*x))*(x + 4) - 5)
- 2*x^2) + 16)/(log(x - log(2*x + log(x^4*exp(4*x))*(x + 4) - 5))^2*(5*x - log(x^4*exp(4*x))*(4*x + x^2) + lo
g(2*x + log(x^4*exp(4*x))*(x + 4) - 5)*(2*x + log(x^4*exp(4*x))*(x + 4) - 5) - 2*x^2)),x)

[Out]

int(-(27*x - log(x^4*exp(4*x))*(3*x + x^2) + 2*x^2 - log(x - log(2*x + log(x^4*exp(4*x))*(x + 4) - 5))*(5*x -
log(x^4*exp(4*x))*(4*x + x^2) + log(2*x + log(x^4*exp(4*x))*(x + 4) - 5)*(2*x + log(x^4*exp(4*x))*(x + 4) - 5)
- 2*x^2) + 16)/(log(x - log(2*x + log(x^4*exp(4*x))*(x + 4) - 5))^2*(5*x - log(x^4*exp(4*x))*(4*x + x^2) + lo
g(2*x + log(x^4*exp(4*x))*(x + 4) - 5)*(2*x + log(x^4*exp(4*x))*(x + 4) - 5) - 2*x^2)), x)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}\text{Timed out}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((4+x)*ln(x**4*exp(x)**4)+2*x-5)*ln((4+x)*ln(x**4*exp(x)**4)+2*x-5)+(-x**2-4*x)*ln(x**4*exp(x)**4)
-2*x**2+5*x)*ln(-ln((4+x)*ln(x**4*exp(x)**4)+2*x-5)+x)+(x**2+3*x)*ln(x**4*exp(x)**4)-2*x**2-27*x-16)/(((4+x)*l
n(x**4*exp(x)**4)+2*x-5)*ln((4+x)*ln(x**4*exp(x)**4)+2*x-5)+(-x**2-4*x)*ln(x**4*exp(x)**4)-2*x**2+5*x)/ln(-ln(
(4+x)*ln(x**4*exp(x)**4)+2*x-5)+x)**2,x)

[Out]

Timed out

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