\(\int \frac {1}{5} e^{e^{e^x x}+x+e^x x} (-1-x) \, dx\) [6048]

Optimal result

Integrand size = 25, antiderivative size = 27 \[ \int \frac {1}{5} e^{e^{e^x x}+x+e^x x} (-1-x) \, dx=\frac {1}{12}+\frac {1}{5} \left (-6-e^{e^{e^x x}}-\log ^2(4)\right ) \]

[Out]

-67/60-4/5*ln(2)^2-1/5*exp(exp(exp(x)*x))

Rubi [F]

\[ \int \frac {1}{5} e^{e^{e^x x}+x+e^x x} (-1-x) \, dx=\int \frac {1}{5} e^{e^{e^x x}+x+e^x x} (-1-x) \, dx \]

[In]

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

[Out]

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

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

Mathematica [A] (verified)

Time = 0.13 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.48 \[ \int \frac {1}{5} e^{e^{e^x x}+x+e^x x} (-1-x) \, dx=-\frac {1}{5} e^{e^{e^x x}} \]

[In]

Integrate[(E^(E^(E^x*x) + x + E^x*x)*(-1 - x))/5,x]

[Out]

-1/5*E^E^(E^x*x)

Maple [A] (verified)

Time = 0.08 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.33

method	result	size
norman	\(-\frac {{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x} x}}}{5}\)	\(9\)
risch	\(-\frac {{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x} x}}}{5}\)	\(9\)
parallelrisch	\(-\frac {{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x} x}}}{5}\)	\(9\)

[In]

int(1/5*(-1-x)*exp(x)*exp(exp(x)*x)*exp(exp(exp(x)*x)),x,method=_RETURNVERBOSE)

[Out]

-1/5*exp(exp(exp(x)*x))

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.30 \[ \int \frac {1}{5} e^{e^{e^x x}+x+e^x x} (-1-x) \, dx=-\frac {1}{5} \, e^{\left (e^{\left (x e^{x}\right )}\right )} \]

[In]

integrate(1/5*(-1-x)*exp(x)*exp(exp(x)*x)*exp(exp(exp(x)*x)),x, algorithm="fricas")

[Out]

-1/5*e^(e^(x*e^x))

Sympy [A] (verification not implemented)

Time = 0.18 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.37 \[ \int \frac {1}{5} e^{e^{e^x x}+x+e^x x} (-1-x) \, dx=- \frac {e^{e^{x e^{x}}}}{5} \]

[In]

integrate(1/5*(-1-x)*exp(x)*exp(exp(x)*x)*exp(exp(exp(x)*x)),x)

[Out]

-exp(exp(x*exp(x)))/5

Maxima [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.30 \[ \int \frac {1}{5} e^{e^{e^x x}+x+e^x x} (-1-x) \, dx=-\frac {1}{5} \, e^{\left (e^{\left (x e^{x}\right )}\right )} \]

[In]

integrate(1/5*(-1-x)*exp(x)*exp(exp(x)*x)*exp(exp(exp(x)*x)),x, algorithm="maxima")

[Out]

-1/5*e^(e^(x*e^x))

Giac [F]

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

[In]

integrate(1/5*(-1-x)*exp(x)*exp(exp(x)*x)*exp(exp(exp(x)*x)),x, algorithm="giac")

[Out]

integrate(-1/5*(x + 1)*e^(x*e^x + x + e^(x*e^x)), x)

Mupad [B] (verification not implemented)

Time = 10.95 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.30 \[ \int \frac {1}{5} e^{e^{e^x x}+x+e^x x} (-1-x) \, dx=-\frac {{\mathrm {e}}^{{\mathrm {e}}^{x\,{\mathrm {e}}^x}}}{5} \]

[In]

int(-(exp(x*exp(x))*exp(exp(x*exp(x)))*exp(x)*(x + 1))/5,x)

[Out]

-exp(exp(x*exp(x)))/5