\(\int (25-25 e^x+e^{x+e^x x} (1+x)) \, dx\) [3665]

Optimal result

Integrand size = 20, antiderivative size = 18 \[ \int \left (25-25 e^x+e^{x+e^x x} (1+x)\right ) \, dx=e^{e^x x}-25 \left (-4+e^x-x\right ) \]

[Out]

exp(exp(x)*x)-25*exp(x)+100+25*x

Rubi [F]

\[ \int \left (25-25 e^x+e^{x+e^x x} (1+x)\right ) \, dx=\int \left (25-25 e^x+e^{x+e^x x} (1+x)\right ) \, dx \]

[In]

Int[25 - 25*E^x + E^(x + E^x*x)*(1 + x),x]

[Out]

-25*E^x + 25*x + Defer[Int][E^(x + E^x*x), x] + Defer[Int][E^(x + E^x*x)*x, x]

Rubi steps \begin{align*} \text {integral}& = 25 x-25 \int e^x \, dx+\int e^{x+e^x x} (1+x) \, dx \\ & = -25 e^x+25 x+\int \left (e^{x+e^x x}+e^{x+e^x x} x\right ) \, dx \\ & = -25 e^x+25 x+\int e^{x+e^x x} \, dx+\int e^{x+e^x x} x \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.05 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.89 \[ \int \left (25-25 e^x+e^{x+e^x x} (1+x)\right ) \, dx=-25 e^x+e^{e^x x}+25 x \]

[In]

Integrate[25 - 25*E^x + E^(x + E^x*x)*(1 + x),x]

[Out]

-25*E^x + E^(E^x*x) + 25*x

Maple [A] (verified)

Time = 0.17 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78

method	result	size
default	\(25 x +{\mathrm e}^{{\mathrm e}^{x} x}-25 \,{\mathrm e}^{x}\)	\(14\)
norman	\(25 x +{\mathrm e}^{{\mathrm e}^{x} x}-25 \,{\mathrm e}^{x}\)	\(14\)
risch	\(25 x +{\mathrm e}^{{\mathrm e}^{x} x}-25 \,{\mathrm e}^{x}\)	\(14\)
parallelrisch	\(25 x +{\mathrm e}^{{\mathrm e}^{x} x}-25 \,{\mathrm e}^{x}\)	\(14\)
parts	\(25 x +{\mathrm e}^{{\mathrm e}^{x} x}-25 \,{\mathrm e}^{x}\)	\(14\)

[In]

int((1+x)*exp(x)*exp(exp(x)*x)-25*exp(x)+25,x,method=_RETURNVERBOSE)

[Out]

25*x+exp(exp(x)*x)-25*exp(x)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.33 \[ \int \left (25-25 e^x+e^{x+e^x x} (1+x)\right ) \, dx={\left (25 \, x e^{x} + e^{\left (x e^{x} + x\right )} - 25 \, e^{\left (2 \, x\right )}\right )} e^{\left (-x\right )} \]

[In]

integrate((1+x)*exp(x)*exp(exp(x)*x)-25*exp(x)+25,x, algorithm="fricas")

[Out]

(25*x*e^x + e^(x*e^x + x) - 25*e^(2*x))*e^(-x)

Sympy [A] (verification not implemented)

Time = 0.09 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \left (25-25 e^x+e^{x+e^x x} (1+x)\right ) \, dx=25 x - 25 e^{x} + e^{x e^{x}} \]

[In]

integrate((1+x)*exp(x)*exp(exp(x)*x)-25*exp(x)+25,x)

[Out]

25*x - 25*exp(x) + exp(x*exp(x))

Maxima [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.72 \[ \int \left (25-25 e^x+e^{x+e^x x} (1+x)\right ) \, dx=25 \, x + e^{\left (x e^{x}\right )} - 25 \, e^{x} \]

[In]

integrate((1+x)*exp(x)*exp(exp(x)*x)-25*exp(x)+25,x, algorithm="maxima")

[Out]

25*x + e^(x*e^x) - 25*e^x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.72 \[ \int \left (25-25 e^x+e^{x+e^x x} (1+x)\right ) \, dx=25 \, x + e^{\left (x e^{x}\right )} - 25 \, e^{x} \]

[In]

integrate((1+x)*exp(x)*exp(exp(x)*x)-25*exp(x)+25,x, algorithm="giac")

[Out]

25*x + e^(x*e^x) - 25*e^x

Mupad [B] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.72 \[ \int \left (25-25 e^x+e^{x+e^x x} (1+x)\right ) \, dx=25\,x+{\mathrm {e}}^{x\,{\mathrm {e}}^x}-25\,{\mathrm {e}}^x \]

[In]

int(exp(x*exp(x))*exp(x)*(x + 1) - 25*exp(x) + 25,x)

[Out]

25*x + exp(x*exp(x)) - 25*exp(x)