3.37.65 \(\int (25-25 e^x+e^{x+e^x x} (1+x)) \, dx\)

Optimal. Leaf size=18 \[ e^{e^x x}-25 \left (-4+e^x-x\right ) \]

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Rubi [F]  time = 0.10, 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 \left (25-25 e^x+e^{x+e^x x} (1+x)\right ) \, dx \end {gather*}

Verification is not applicable to the result.

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

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Mathematica [A]  time = 0.05, size = 16, normalized size = 0.89 \begin {gather*} -25 e^x+e^{e^x x}+25 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-25*E^x + E^(E^x*x) + 25*x

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fricas [A]  time = 0.63, size = 24, normalized size = 1.33 \begin {gather*} {\left (25 \, x e^{x} + e^{\left (x e^{x} + x\right )} - 25 \, e^{\left (2 \, x\right )}\right )} e^{\left (-x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x+1)*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)

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giac [A]  time = 0.16, size = 13, normalized size = 0.72 \begin {gather*} 25 \, x + e^{\left (x e^{x}\right )} - 25 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

25*x + e^(x*e^x) - 25*e^x

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maple [A]  time = 0.04, size = 14, normalized size = 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	\(25 x +{\mathrm e}^{{\mathrm e}^{x} x}-25 \,{\mathrm e}^{x}\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.37, size = 13, normalized size = 0.72 \begin {gather*} 25 \, x + e^{\left (x e^{x}\right )} - 25 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

25*x + e^(x*e^x) - 25*e^x

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mupad [B]  time = 0.08, size = 13, normalized size = 0.72 \begin {gather*} 25\,x+{\mathrm {e}}^{x\,{\mathrm {e}}^x}-25\,{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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sympy [A]  time = 0.14, size = 14, normalized size = 0.78 \begin {gather*} 25 x - 25 e^{x} + e^{x e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

25*x - 25*exp(x) + exp(x*exp(x))

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