\(\int \frac {e^4 x+e^{\frac {256-32 x^2+x^4}{e^4}} (e^4 (-4+x)-256 x^2+64 x^3+16 x^4-4 x^5)+e^4 (4-x) \log (4-x)}{e^{5+\frac {2 (256-32 x^2+x^4)}{e^4}} (-4+x)+e^{5+\frac {256-32 x^2+x^4}{e^4}} (8-2 x) \log (4-x)+e^5 (-4+x) \log ^2(4-x)} \, dx\) [3164]

Optimal result

Integrand size = 138, antiderivative size = 29 \[ \int \frac {e^4 x+e^{\frac {256-32 x^2+x^4}{e^4}} \left (e^4 (-4+x)-256 x^2+64 x^3+16 x^4-4 x^5\right )+e^4 (4-x) \log (4-x)}{e^{5+\frac {2 \left (256-32 x^2+x^4\right )}{e^4}} (-4+x)+e^{5+\frac {256-32 x^2+x^4}{e^4}} (8-2 x) \log (4-x)+e^5 (-4+x) \log ^2(4-x)} \, dx=\frac {x}{e \left (e^{\frac {\left (-16+x^2\right )^2}{e^4}}-\log (4-x)\right )} \]

[Out]

x/exp(1)/(exp((x^2-16)^2/exp(4))-ln(-x+4))

Rubi [F]

\[ \int \frac {e^4 x+e^{\frac {256-32 x^2+x^4}{e^4}} \left (e^4 (-4+x)-256 x^2+64 x^3+16 x^4-4 x^5\right )+e^4 (4-x) \log (4-x)}{e^{5+\frac {2 \left (256-32 x^2+x^4\right )}{e^4}} (-4+x)+e^{5+\frac {256-32 x^2+x^4}{e^4}} (8-2 x) \log (4-x)+e^5 (-4+x) \log ^2(4-x)} \, dx=\int \frac {e^4 x+e^{\frac {256-32 x^2+x^4}{e^4}} \left (e^4 (-4+x)-256 x^2+64 x^3+16 x^4-4 x^5\right )+e^4 (4-x) \log (4-x)}{e^{5+\frac {2 \left (256-32 x^2+x^4\right )}{e^4}} (-4+x)+e^{5+\frac {256-32 x^2+x^4}{e^4}} (8-2 x) \log (4-x)+e^5 (-4+x) \log ^2(4-x)} \, dx \]

[In]

Int[(E^4*x + E^((256 - 32*x^2 + x^4)/E^4)*(E^4*(-4 + x) - 256*x^2 + 64*x^3 + 16*x^4 - 4*x^5) + E^4*(4 - x)*Log
[4 - x])/(E^(5 + (2*(256 - 32*x^2 + x^4))/E^4)*(-4 + x) + E^(5 + (256 - 32*x^2 + x^4)/E^4)*(8 - 2*x)*Log[4 - x
] + E^5*(-4 + x)*Log[4 - x]^2),x]

[Out]

Defer[Int][(E^((-16 + x^2)^2/E^4) - Log[4 - x])^(-1), x]/E + (64*Defer[Int][x^2/(E^((-16 + x^2)^2/E^4) - Log[4
- x]), x])/E^5 - (4*Defer[Int][x^4/(E^((-16 + x^2)^2/E^4) - Log[4 - x]), x])/E^5 + Defer[Int][E^(-1 + (64*x^2
)/E^4)/(E^(256/E^4 + x^4/E^4) - E^((32*x^2)/E^4)*Log[4 - x])^2, x] + 4*Defer[Int][E^(-1 + (64*x^2)/E^4)/((-4 +
x)*(E^(256/E^4 + x^4/E^4) - E^((32*x^2)/E^4)*Log[4 - x])^2), x] + 64*Defer[Int][(E^(-5 + (64*x^2)/E^4)*x^2*Lo
g[4 - x])/(-E^(256/E^4 + x^4/E^4) + E^((32*x^2)/E^4)*Log[4 - x])^2, x] - 4*Defer[Int][(E^(-5 + (64*x^2)/E^4)*x
^4*Log[4 - x])/(-E^(256/E^4 + x^4/E^4) + E^((32*x^2)/E^4)*Log[4 - x])^2, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{-5+\frac {64 x^2}{e^4}} \left (-e^4 x-e^{\frac {256-32 x^2+x^4}{e^4}} \left (e^4 (-4+x)-256 x^2+64 x^3+16 x^4-4 x^5\right )-e^4 (4-x) \log (4-x)\right )}{(4-x) \left (e^{\frac {256}{e^4}+\frac {x^4}{e^4}}-e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2} \, dx \\ & = \int \left (\frac {e^{-5+\frac {64 x^2}{e^4}} \left (e^4+64 x^2-4 x^4\right )}{e^{\frac {\left (16+x^2\right )^2}{e^4}}-e^{\frac {64 x^2}{e^4}} \log (4-x)}-\frac {e^{-5+\frac {64 x^2}{e^4}} x \left (-e^4+256 x \log (4-x)-64 x^2 \log (4-x)-16 x^3 \log (4-x)+4 x^4 \log (4-x)\right )}{(-4+x) \left (e^{\frac {256}{e^4}+\frac {x^4}{e^4}}-e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2}\right ) \, dx \\ & = \int \frac {e^{-5+\frac {64 x^2}{e^4}} \left (e^4+64 x^2-4 x^4\right )}{e^{\frac {\left (16+x^2\right )^2}{e^4}}-e^{\frac {64 x^2}{e^4}} \log (4-x)} \, dx-\int \frac {e^{-5+\frac {64 x^2}{e^4}} x \left (-e^4+256 x \log (4-x)-64 x^2 \log (4-x)-16 x^3 \log (4-x)+4 x^4 \log (4-x)\right )}{(-4+x) \left (e^{\frac {256}{e^4}+\frac {x^4}{e^4}}-e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2} \, dx \\ & = \int \frac {e^4+64 x^2-4 x^4}{e^5 \left (e^{\frac {\left (-16+x^2\right )^2}{e^4}}-\log (4-x)\right )} \, dx-\int \frac {e^{-5+\frac {64 x^2}{e^4}} x \left (e^4-4 (-4+x)^2 x (4+x) \log (4-x)\right )}{(4-x) \left (e^{\frac {256+x^4}{e^4}}-e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2} \, dx \\ & = \frac {\int \frac {e^4+64 x^2-4 x^4}{e^{\frac {\left (-16+x^2\right )^2}{e^4}}-\log (4-x)} \, dx}{e^5}-\int \left (\frac {e^{-5+\frac {64 x^2}{e^4}} \left (-e^4+256 x \log (4-x)-64 x^2 \log (4-x)-16 x^3 \log (4-x)+4 x^4 \log (4-x)\right )}{\left (e^{\frac {256}{e^4}+\frac {x^4}{e^4}}-e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2}+\frac {4 e^{-5+\frac {64 x^2}{e^4}} \left (-e^4+256 x \log (4-x)-64 x^2 \log (4-x)-16 x^3 \log (4-x)+4 x^4 \log (4-x)\right )}{(-4+x) \left (e^{\frac {256}{e^4}+\frac {x^4}{e^4}}-e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2}\right ) \, dx \\ & = -\left (4 \int \frac {e^{-5+\frac {64 x^2}{e^4}} \left (-e^4+256 x \log (4-x)-64 x^2 \log (4-x)-16 x^3 \log (4-x)+4 x^4 \log (4-x)\right )}{(-4+x) \left (e^{\frac {256}{e^4}+\frac {x^4}{e^4}}-e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2} \, dx\right )+\frac {\int \left (\frac {e^4}{e^{\frac {\left (-16+x^2\right )^2}{e^4}}-\log (4-x)}+\frac {64 x^2}{e^{\frac {\left (-16+x^2\right )^2}{e^4}}-\log (4-x)}-\frac {4 x^4}{e^{\frac {\left (-16+x^2\right )^2}{e^4}}-\log (4-x)}\right ) \, dx}{e^5}-\int \frac {e^{-5+\frac {64 x^2}{e^4}} \left (-e^4+256 x \log (4-x)-64 x^2 \log (4-x)-16 x^3 \log (4-x)+4 x^4 \log (4-x)\right )}{\left (e^{\frac {256}{e^4}+\frac {x^4}{e^4}}-e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2} \, dx \\ & = -\left (4 \int \frac {e^{-5+\frac {64 x^2}{e^4}} \left (e^4-4 (-4+x)^2 x (4+x) \log (4-x)\right )}{(4-x) \left (e^{\frac {256+x^4}{e^4}}-e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2} \, dx\right )-\frac {4 \int \frac {x^4}{e^{\frac {\left (-16+x^2\right )^2}{e^4}}-\log (4-x)} \, dx}{e^5}+\frac {64 \int \frac {x^2}{e^{\frac {\left (-16+x^2\right )^2}{e^4}}-\log (4-x)} \, dx}{e^5}+\frac {\int \frac {1}{e^{\frac {\left (-16+x^2\right )^2}{e^4}}-\log (4-x)} \, dx}{e}-\int \frac {e^{-5+\frac {64 x^2}{e^4}} \left (-e^4+4 (-4+x)^2 x (4+x) \log (4-x)\right )}{\left (e^{\frac {256+x^4}{e^4}}-e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2} \, dx \\ & = -\left (4 \int \left (-\frac {e^{-1+\frac {64 x^2}{e^4}}}{(-4+x) \left (e^{\frac {256}{e^4}+\frac {x^4}{e^4}}-e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2}+\frac {256 e^{-5+\frac {64 x^2}{e^4}} x \log (4-x)}{(-4+x) \left (-e^{\frac {256}{e^4}+\frac {x^4}{e^4}}+e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2}-\frac {64 e^{-5+\frac {64 x^2}{e^4}} x^2 \log (4-x)}{(-4+x) \left (-e^{\frac {256}{e^4}+\frac {x^4}{e^4}}+e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2}-\frac {16 e^{-5+\frac {64 x^2}{e^4}} x^3 \log (4-x)}{(-4+x) \left (-e^{\frac {256}{e^4}+\frac {x^4}{e^4}}+e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2}+\frac {4 e^{-5+\frac {64 x^2}{e^4}} x^4 \log (4-x)}{(-4+x) \left (-e^{\frac {256}{e^4}+\frac {x^4}{e^4}}+e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2}\right ) \, dx\right )-\frac {4 \int \frac {x^4}{e^{\frac {\left (-16+x^2\right )^2}{e^4}}-\log (4-x)} \, dx}{e^5}+\frac {64 \int \frac {x^2}{e^{\frac {\left (-16+x^2\right )^2}{e^4}}-\log (4-x)} \, dx}{e^5}+\frac {\int \frac {1}{e^{\frac {\left (-16+x^2\right )^2}{e^4}}-\log (4-x)} \, dx}{e}-\int \left (-\frac {e^{-1+\frac {64 x^2}{e^4}}}{\left (e^{\frac {256}{e^4}+\frac {x^4}{e^4}}-e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2}+\frac {256 e^{-5+\frac {64 x^2}{e^4}} x \log (4-x)}{\left (-e^{\frac {256}{e^4}+\frac {x^4}{e^4}}+e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2}-\frac {64 e^{-5+\frac {64 x^2}{e^4}} x^2 \log (4-x)}{\left (-e^{\frac {256}{e^4}+\frac {x^4}{e^4}}+e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2}-\frac {16 e^{-5+\frac {64 x^2}{e^4}} x^3 \log (4-x)}{\left (-e^{\frac {256}{e^4}+\frac {x^4}{e^4}}+e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2}+\frac {4 e^{-5+\frac {64 x^2}{e^4}} x^4 \log (4-x)}{\left (-e^{\frac {256}{e^4}+\frac {x^4}{e^4}}+e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2}\right ) \, dx \\ & = 4 \int \frac {e^{-1+\frac {64 x^2}{e^4}}}{(-4+x) \left (e^{\frac {256}{e^4}+\frac {x^4}{e^4}}-e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2} \, dx-4 \int \frac {e^{-5+\frac {64 x^2}{e^4}} x^4 \log (4-x)}{\left (-e^{\frac {256}{e^4}+\frac {x^4}{e^4}}+e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2} \, dx+16 \int \frac {e^{-5+\frac {64 x^2}{e^4}} x^3 \log (4-x)}{\left (-e^{\frac {256}{e^4}+\frac {x^4}{e^4}}+e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2} \, dx-16 \int \frac {e^{-5+\frac {64 x^2}{e^4}} x^4 \log (4-x)}{(-4+x) \left (-e^{\frac {256}{e^4}+\frac {x^4}{e^4}}+e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2} \, dx+64 \int \frac {e^{-5+\frac {64 x^2}{e^4}} x^2 \log (4-x)}{\left (-e^{\frac {256}{e^4}+\frac {x^4}{e^4}}+e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2} \, dx+64 \int \frac {e^{-5+\frac {64 x^2}{e^4}} x^3 \log (4-x)}{(-4+x) \left (-e^{\frac {256}{e^4}+\frac {x^4}{e^4}}+e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2} \, dx-256 \int \frac {e^{-5+\frac {64 x^2}{e^4}} x \log (4-x)}{\left (-e^{\frac {256}{e^4}+\frac {x^4}{e^4}}+e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2} \, dx+256 \int \frac {e^{-5+\frac {64 x^2}{e^4}} x^2 \log (4-x)}{(-4+x) \left (-e^{\frac {256}{e^4}+\frac {x^4}{e^4}}+e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2} \, dx-1024 \int \frac {e^{-5+\frac {64 x^2}{e^4}} x \log (4-x)}{(-4+x) \left (-e^{\frac {256}{e^4}+\frac {x^4}{e^4}}+e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2} \, dx-\frac {4 \int \frac {x^4}{e^{\frac {\left (-16+x^2\right )^2}{e^4}}-\log (4-x)} \, dx}{e^5}+\frac {64 \int \frac {x^2}{e^{\frac {\left (-16+x^2\right )^2}{e^4}}-\log (4-x)} \, dx}{e^5}+\frac {\int \frac {1}{e^{\frac {\left (-16+x^2\right )^2}{e^4}}-\log (4-x)} \, dx}{e}+\int \frac {e^{-1+\frac {64 x^2}{e^4}}}{\left (e^{\frac {256}{e^4}+\frac {x^4}{e^4}}-e^{\frac {32 x^2}{e^4}} \log (4-x)\right )^2} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.25 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00 \[ \int \frac {e^4 x+e^{\frac {256-32 x^2+x^4}{e^4}} \left (e^4 (-4+x)-256 x^2+64 x^3+16 x^4-4 x^5\right )+e^4 (4-x) \log (4-x)}{e^{5+\frac {2 \left (256-32 x^2+x^4\right )}{e^4}} (-4+x)+e^{5+\frac {256-32 x^2+x^4}{e^4}} (8-2 x) \log (4-x)+e^5 (-4+x) \log ^2(4-x)} \, dx=\frac {x}{e \left (e^{\frac {\left (-16+x^2\right )^2}{e^4}}-\log (4-x)\right )} \]

[In]

Integrate[(E^4*x + E^((256 - 32*x^2 + x^4)/E^4)*(E^4*(-4 + x) - 256*x^2 + 64*x^3 + 16*x^4 - 4*x^5) + E^4*(4 -
x)*Log[4 - x])/(E^(5 + (2*(256 - 32*x^2 + x^4))/E^4)*(-4 + x) + E^(5 + (256 - 32*x^2 + x^4)/E^4)*(8 - 2*x)*Log
[4 - x] + E^5*(-4 + x)*Log[4 - x]^2),x]

[Out]

x/(E*(E^((-16 + x^2)^2/E^4) - Log[4 - x]))

Maple [A] (verified)

Time = 1.81 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.03

method	result	size
risch	\(\frac {{\mathrm e}^{-1} x}{{\mathrm e}^{\left (x -4\right )^{2} \left (4+x \right )^{2} {\mathrm e}^{-4}}-\ln \left (-x +4\right )}\)	\(30\)
parallelrisch	\(-\frac {x \,{\mathrm e}^{-1}}{\ln \left (-x +4\right )-{\mathrm e}^{\left (x^{4}-32 x^{2}+256\right ) {\mathrm e}^{-4}}}\)	\(35\)

[In]

int(((-x+4)*exp(4)*ln(-x+4)+((x-4)*exp(4)-4*x^5+16*x^4+64*x^3-256*x^2)*exp((x^4-32*x^2+256)/exp(4))+x*exp(4))/
((x-4)*exp(1)*exp(4)*ln(-x+4)^2+(-2*x+8)*exp(1)*exp(4)*exp((x^4-32*x^2+256)/exp(4))*ln(-x+4)+(x-4)*exp(1)*exp(
4)*exp((x^4-32*x^2+256)/exp(4))^2),x,method=_RETURNVERBOSE)

[Out]

exp(-1)*x/(exp((x-4)^2*(4+x)^2*exp(-4))-ln(-x+4))

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.28 \[ \int \frac {e^4 x+e^{\frac {256-32 x^2+x^4}{e^4}} \left (e^4 (-4+x)-256 x^2+64 x^3+16 x^4-4 x^5\right )+e^4 (4-x) \log (4-x)}{e^{5+\frac {2 \left (256-32 x^2+x^4\right )}{e^4}} (-4+x)+e^{5+\frac {256-32 x^2+x^4}{e^4}} (8-2 x) \log (4-x)+e^5 (-4+x) \log ^2(4-x)} \, dx=-\frac {x e^{4}}{e^{5} \log \left (-x + 4\right ) - e^{\left ({\left (x^{4} - 32 \, x^{2} + 5 \, e^{4} + 256\right )} e^{\left (-4\right )}\right )}} \]

[In]

integrate(((-x+4)*exp(4)*log(-x+4)+((x-4)*exp(4)-4*x^5+16*x^4+64*x^3-256*x^2)*exp((x^4-32*x^2+256)/exp(4))+x*e
xp(4))/((x-4)*exp(1)*exp(4)*log(-x+4)^2+(-2*x+8)*exp(1)*exp(4)*exp((x^4-32*x^2+256)/exp(4))*log(-x+4)+(x-4)*ex
p(1)*exp(4)*exp((x^4-32*x^2+256)/exp(4))^2),x, algorithm="fricas")

[Out]

-x*e^4/(e^5*log(-x + 4) - e^((x^4 - 32*x^2 + 5*e^4 + 256)*e^(-4)))

Sympy [A] (verification not implemented)

Time = 0.14 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.93 \[ \int \frac {e^4 x+e^{\frac {256-32 x^2+x^4}{e^4}} \left (e^4 (-4+x)-256 x^2+64 x^3+16 x^4-4 x^5\right )+e^4 (4-x) \log (4-x)}{e^{5+\frac {2 \left (256-32 x^2+x^4\right )}{e^4}} (-4+x)+e^{5+\frac {256-32 x^2+x^4}{e^4}} (8-2 x) \log (4-x)+e^5 (-4+x) \log ^2(4-x)} \, dx=\frac {x}{e e^{\frac {x^{4} - 32 x^{2} + 256}{e^{4}}} - e \log {\left (4 - x \right )}} \]

[In]

integrate(((-x+4)*exp(4)*ln(-x+4)+((x-4)*exp(4)-4*x**5+16*x**4+64*x**3-256*x**2)*exp((x**4-32*x**2+256)/exp(4)
)+x*exp(4))/((x-4)*exp(1)*exp(4)*ln(-x+4)**2+(-2*x+8)*exp(1)*exp(4)*exp((x**4-32*x**2+256)/exp(4))*ln(-x+4)+(x
-4)*exp(1)*exp(4)*exp((x**4-32*x**2+256)/exp(4))**2),x)

[Out]

x/(E*exp((x**4 - 32*x**2 + 256)*exp(-4)) - E*log(4 - x))

Maxima [A] (verification not implemented)

none

Time = 0.43 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.59 \[ \int \frac {e^4 x+e^{\frac {256-32 x^2+x^4}{e^4}} \left (e^4 (-4+x)-256 x^2+64 x^3+16 x^4-4 x^5\right )+e^4 (4-x) \log (4-x)}{e^{5+\frac {2 \left (256-32 x^2+x^4\right )}{e^4}} (-4+x)+e^{5+\frac {256-32 x^2+x^4}{e^4}} (8-2 x) \log (4-x)+e^5 (-4+x) \log ^2(4-x)} \, dx=-\frac {x e^{\left (32 \, x^{2} e^{\left (-4\right )}\right )}}{e^{\left (32 \, x^{2} e^{\left (-4\right )} + 1\right )} \log \left (-x + 4\right ) - e^{\left (x^{4} e^{\left (-4\right )} + 256 \, e^{\left (-4\right )} + 1\right )}} \]

[In]

integrate(((-x+4)*exp(4)*log(-x+4)+((x-4)*exp(4)-4*x^5+16*x^4+64*x^3-256*x^2)*exp((x^4-32*x^2+256)/exp(4))+x*e
xp(4))/((x-4)*exp(1)*exp(4)*log(-x+4)^2+(-2*x+8)*exp(1)*exp(4)*exp((x^4-32*x^2+256)/exp(4))*log(-x+4)+(x-4)*ex
p(1)*exp(4)*exp((x^4-32*x^2+256)/exp(4))^2),x, algorithm="maxima")

[Out]

-x*e^(32*x^2*e^(-4))/(e^(32*x^2*e^(-4) + 1)*log(-x + 4) - e^(x^4*e^(-4) + 256*e^(-4) + 1))

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 926 vs. \(2 (26) = 52\).

Time = 1.20 (sec) , antiderivative size = 926, normalized size of antiderivative = 31.93 \[ \int \frac {e^4 x+e^{\frac {256-32 x^2+x^4}{e^4}} \left (e^4 (-4+x)-256 x^2+64 x^3+16 x^4-4 x^5\right )+e^4 (4-x) \log (4-x)}{e^{5+\frac {2 \left (256-32 x^2+x^4\right )}{e^4}} (-4+x)+e^{5+\frac {256-32 x^2+x^4}{e^4}} (8-2 x) \log (4-x)+e^5 (-4+x) \log ^2(4-x)} \, dx=\text {Too large to display} \]

[In]

integrate(((-x+4)*exp(4)*log(-x+4)+((x-4)*exp(4)-4*x^5+16*x^4+64*x^3-256*x^2)*exp((x^4-32*x^2+256)/exp(4))+x*e
xp(4))/((x-4)*exp(1)*exp(4)*log(-x+4)^2+(-2*x+8)*exp(1)*exp(4)*exp((x^4-32*x^2+256)/exp(4))*log(-x+4)+(x-4)*ex
p(1)*exp(4)*exp((x^4-32*x^2+256)/exp(4))^2),x, algorithm="giac")

[Out]

-(4*x^5*e^(x^4*e^(-4) + 4)*log(-x + 4)^2 - 4*x^5*e^(x^4*e^(-4) + (x^4 - 32*x^2)*e^(-4) + 256*e^(-4) + 4)*log(-
x + 4) - 16*x^4*e^(x^4*e^(-4) + 4)*log(-x + 4)^2 + 16*x^4*e^(x^4*e^(-4) + (x^4 - 32*x^2)*e^(-4) + 256*e^(-4) +
4)*log(-x + 4) - 64*x^3*e^(x^4*e^(-4) + 4)*log(-x + 4)^2 + 64*x^3*e^(x^4*e^(-4) + (x^4 - 32*x^2)*e^(-4) + 256
*e^(-4) + 4)*log(-x + 4) + 256*x^2*e^(x^4*e^(-4) + 4)*log(-x + 4)^2 - 256*x^2*e^(x^4*e^(-4) + (x^4 - 32*x^2)*e
^(-4) + 256*e^(-4) + 4)*log(-x + 4) - x*e^(x^4*e^(-4) + 8)*log(-x + 4) + x*e^(2*(x^4 - 16*x^2)*e^(-4) + 256*e^
(-4) + 8))/(4*x^4*e^(x^4*e^(-4) + 5)*log(-x + 4)^3 - 4*x^4*e^(x^4*e^(-4) + (x^4 - 32*x^2)*e^(-4) + 256*e^(-4)
+ 5)*log(-x + 4)^2 - 4*x^4*e^(2*(x^4 - 16*x^2)*e^(-4) + 256*e^(-4) + 5)*log(-x + 4)^2 - 16*x^3*e^(x^4*e^(-4) +
5)*log(-x + 4)^3 + 4*x^4*e^(2*(x^4 - 16*x^2)*e^(-4) + (x^4 - 32*x^2)*e^(-4) + 512*e^(-4) + 5)*log(-x + 4) + 1
6*x^3*e^(x^4*e^(-4) + (x^4 - 32*x^2)*e^(-4) + 256*e^(-4) + 5)*log(-x + 4)^2 + 16*x^3*e^(2*(x^4 - 16*x^2)*e^(-4
) + 256*e^(-4) + 5)*log(-x + 4)^2 - 64*x^2*e^(x^4*e^(-4) + 5)*log(-x + 4)^3 - 16*x^3*e^(2*(x^4 - 16*x^2)*e^(-4
) + (x^4 - 32*x^2)*e^(-4) + 512*e^(-4) + 5)*log(-x + 4) + 64*x^2*e^(x^4*e^(-4) + (x^4 - 32*x^2)*e^(-4) + 256*e
^(-4) + 5)*log(-x + 4)^2 + 64*x^2*e^(2*(x^4 - 16*x^2)*e^(-4) + 256*e^(-4) + 5)*log(-x + 4)^2 + 256*x*e^(x^4*e^
(-4) + 5)*log(-x + 4)^3 - 64*x^2*e^(2*(x^4 - 16*x^2)*e^(-4) + (x^4 - 32*x^2)*e^(-4) + 512*e^(-4) + 5)*log(-x +
4) - 256*x*e^(x^4*e^(-4) + (x^4 - 32*x^2)*e^(-4) + 256*e^(-4) + 5)*log(-x + 4)^2 - 256*x*e^(2*(x^4 - 16*x^2)*
e^(-4) + 256*e^(-4) + 5)*log(-x + 4)^2 + 256*x*e^(2*(x^4 - 16*x^2)*e^(-4) + (x^4 - 32*x^2)*e^(-4) + 512*e^(-4)
+ 5)*log(-x + 4) - e^(x^4*e^(-4) + 9)*log(-x + 4)^2 + e^(x^4*e^(-4) + (x^4 - 32*x^2)*e^(-4) + 256*e^(-4) + 9)
*log(-x + 4) + e^(2*(x^4 - 16*x^2)*e^(-4) + 256*e^(-4) + 9)*log(-x + 4) - e^(2*(x^4 - 16*x^2)*e^(-4) + (x^4 -
32*x^2)*e^(-4) + 512*e^(-4) + 9))

Mupad [B] (verification not implemented)

Time = 9.85 (sec) , antiderivative size = 158, normalized size of antiderivative = 5.45 \[ \int \frac {e^4 x+e^{\frac {256-32 x^2+x^4}{e^4}} \left (e^4 (-4+x)-256 x^2+64 x^3+16 x^4-4 x^5\right )+e^4 (4-x) \log (4-x)}{e^{5+\frac {2 \left (256-32 x^2+x^4\right )}{e^4}} (-4+x)+e^{5+\frac {256-32 x^2+x^4}{e^4}} (8-2 x) \log (4-x)+e^5 (-4+x) \log ^2(4-x)} \, dx=\frac {x\,{\mathrm {e}}^{-1}\,{\left (4\,{\mathrm {e}}^4-x\,{\mathrm {e}}^4\right )}^2-{\mathrm {e}}^{-5}\,\ln \left (4-x\right )\,{\left (4\,{\mathrm {e}}^4-x\,{\mathrm {e}}^4\right )}^2\,\left (4\,x^5-16\,x^4-64\,x^3+256\,x^2\right )}{\left (\ln \left (4-x\right )-{\mathrm {e}}^{{\mathrm {e}}^{-4}\,x^4-32\,{\mathrm {e}}^{-4}\,x^2+256\,{\mathrm {e}}^{-4}}\right )\,\left (x-4\right )\,\left (4\,{\mathrm {e}}^8-x\,{\mathrm {e}}^8+512\,x^2\,{\mathrm {e}}^4\,\ln \left (4-x\right )-32\,x^4\,{\mathrm {e}}^4\,\ln \left (4-x\right )+4\,x^5\,{\mathrm {e}}^4\,\ln \left (4-x\right )-1024\,x\,{\mathrm {e}}^4\,\ln \left (4-x\right )\right )} \]

[In]

int((x*exp(4) + exp(exp(-4)*(x^4 - 32*x^2 + 256))*(exp(4)*(x - 4) - 256*x^2 + 64*x^3 + 16*x^4 - 4*x^5) - exp(4
)*log(4 - x)*(x - 4))/(exp(5)*exp(2*exp(-4)*(x^4 - 32*x^2 + 256))*(x - 4) + exp(5)*log(4 - x)^2*(x - 4) - exp(
5)*exp(exp(-4)*(x^4 - 32*x^2 + 256))*log(4 - x)*(2*x - 8)),x)

[Out]

(x*exp(-1)*(4*exp(4) - x*exp(4))^2 - exp(-5)*log(4 - x)*(4*exp(4) - x*exp(4))^2*(256*x^2 - 64*x^3 - 16*x^4 + 4
*x^5))/((log(4 - x) - exp(256*exp(-4) - 32*x^2*exp(-4) + x^4*exp(-4)))*(x - 4)*(4*exp(8) - x*exp(8) + 512*x^2*
exp(4)*log(4 - x) - 32*x^4*exp(4)*log(4 - x) + 4*x^5*exp(4)*log(4 - x) - 1024*x*exp(4)*log(4 - x)))