3.31.10 \(\int \frac {e+e^{e^{143+x}} (-e-e^{144+x} x)}{e} \, dx\)

Optimal. Leaf size=13 \[ 5+x-e^{e^{143+x}} x \]

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Rubi [A]  time = 0.02, antiderivative size = 12, normalized size of antiderivative = 0.92, number of steps used = 3, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 2288} \begin {gather*} x-e^{e^{x+143}} x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E + E^E^(143 + x)*(-E - E^(144 + x)*x))/E,x]

[Out]

x - E^E^(143 + x)*x

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2288

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (e+e^{e^{143+x}} \left (-e-e^{144+x} x\right )\right ) \, dx}{e}\\ &=x+\frac {\int e^{e^{143+x}} \left (-e-e^{144+x} x\right ) \, dx}{e}\\ &=x-e^{e^{143+x}} x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.03, size = 12, normalized size = 0.92 \begin {gather*} x-e^{e^{143+x}} x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E + E^E^(143 + x)*(-E - E^(144 + x)*x))/E,x]

[Out]

x - E^E^(143 + x)*x

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fricas [A]  time = 1.21, size = 10, normalized size = 0.77 \begin {gather*} -x e^{\left (e^{\left (x + 143\right )}\right )} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x*exp(9)^16*exp(x)-exp(1))*exp(exp(9)^16*exp(x)/exp(1))+exp(1))/exp(1),x, algorithm="fricas")

[Out]

-x*e^(e^(x + 143)) + x

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giac [A]  time = 0.16, size = 18, normalized size = 1.38 \begin {gather*} {\left (x e - x e^{\left (e^{\left (x + 143\right )} + 1\right )}\right )} e^{\left (-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x*exp(9)^16*exp(x)-exp(1))*exp(exp(9)^16*exp(x)/exp(1))+exp(1))/exp(1),x, algorithm="giac")

[Out]

(x*e - x*e^(e^(x + 143) + 1))*e^(-1)

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maple [A]  time = 0.12, size = 11, normalized size = 0.85

method	result	size
risch	\(-x \,{\mathrm e}^{{\mathrm e}^{143+x}}+x\)	\(11\)
norman	\(x -x \,{\mathrm e}^{{\mathrm e}^{144} {\mathrm e}^{x} {\mathrm e}^{-1}}\)	\(18\)
default	\({\mathrm e}^{-1} \left (-x \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{144} {\mathrm e}^{x} {\mathrm e}^{-1}}+x \,{\mathrm e}\right )\)	\(28\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-x*exp(9)^16*exp(x)-exp(1))*exp(exp(9)^16*exp(x)/exp(1))+exp(1))/exp(1),x,method=_RETURNVERBOSE)

[Out]

-x*exp(exp(143+x))+x

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} {\left (x e - {\rm Ei}\left (e^{\left (x + 143\right )}\right ) e - x e^{\left (e^{\left (x + 143\right )} + 1\right )} + \int e^{\left (e^{\left (x + 143\right )} + 1\right )}\,{d x}\right )} e^{\left (-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x*exp(9)^16*exp(x)-exp(1))*exp(exp(9)^16*exp(x)/exp(1))+exp(1))/exp(1),x, algorithm="maxima")

[Out]

(x*e - Ei(e^(x + 143))*e - x*e^(e^(x + 143) + 1) + integrate(e^(e^(x + 143) + 1), x))*e^(-1)

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mupad [B]  time = 0.07, size = 11, normalized size = 0.85 \begin {gather*} -x\,\left ({\mathrm {e}}^{{\mathrm {e}}^{143}\,{\mathrm {e}}^x}-1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-1)*(exp(1) - exp(exp(143)*exp(x))*(exp(1) + x*exp(144)*exp(x))),x)

[Out]

-x*(exp(exp(143)*exp(x)) - 1)

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sympy [A]  time = 0.14, size = 10, normalized size = 0.77 \begin {gather*} - x e^{e^{143} e^{x}} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x*exp(9)**16*exp(x)-exp(1))*exp(exp(9)**16*exp(x)/exp(1))+exp(1))/exp(1),x)

[Out]

-x*exp(exp(143)*exp(x)) + x

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