3.88.81 \(\int \frac {1}{11} e^{\frac {1}{11} (44-11 e^x+11 e^{2+x}-71 x)} (-71-11 e^x+11 e^{2+x}) \, dx\)

Optimal. Leaf size=19 \[ e^{4-e^x+e^{2+x}-\frac {71 x}{11}} \]

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Rubi [A]  time = 0.11, antiderivative size = 23, normalized size of antiderivative = 1.21, number of steps used = 2, number of rules used = 2, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {12, 6706} \begin {gather*} e^{\frac {1}{11} \left (-71 x-11 e^x+11 e^{x+2}+44\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^((44 - 11*E^x + 11*E^(2 + x) - 71*x)/11)*(-71 - 11*E^x + 11*E^(2 + x)))/11,x]

[Out]

E^((44 - 11*E^x + 11*E^(2 + x) - 71*x)/11)

Rule 12

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

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{11} \int e^{\frac {1}{11} \left (44-11 e^x+11 e^{2+x}-71 x\right )} \left (-71-11 e^x+11 e^{2+x}\right ) \, dx\\ &=e^{\frac {1}{11} \left (44-11 e^x+11 e^{2+x}-71 x\right )}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.04, size = 18, normalized size = 0.95 \begin {gather*} e^{4+e^x \left (-1+e^2\right )-\frac {71 x}{11}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((44 - 11*E^x + 11*E^(2 + x) - 71*x)/11)*(-71 - 11*E^x + 11*E^(2 + x)))/11,x]

[Out]

E^(4 + E^x*(-1 + E^2) - (71*x)/11)

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fricas [A]  time = 0.76, size = 24, normalized size = 1.26 \begin {gather*} e^{\left (-\frac {1}{11} \, {\left ({\left (71 \, x - 44\right )} e^{2} - 11 \, {\left (e^{2} - 1\right )} e^{\left (x + 2\right )}\right )} e^{\left (-2\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/11*(11*exp(2+x)-11*exp(x)-71)*exp(exp(2+x)-exp(x)-71/11*x+4),x, algorithm="fricas")

[Out]

e^(-1/11*((71*x - 44)*e^2 - 11*(e^2 - 1)*e^(x + 2))*e^(-2))

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giac [A]  time = 0.13, size = 14, normalized size = 0.74 \begin {gather*} e^{\left (-\frac {71}{11} \, x + e^{\left (x + 2\right )} - e^{x} + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/11*(11*exp(2+x)-11*exp(x)-71)*exp(exp(2+x)-exp(x)-71/11*x+4),x, algorithm="giac")

[Out]

e^(-71/11*x + e^(x + 2) - e^x + 4)

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maple [A]  time = 0.08, size = 15, normalized size = 0.79

method	result	size
risch	\({\mathrm e}^{{\mathrm e}^{2+x}-{\mathrm e}^{x}-\frac {71 x}{11}+4}\)	\(15\)
norman	\({\mathrm e}^{{\mathrm e}^{2} {\mathrm e}^{x}-{\mathrm e}^{x}-\frac {71 x}{11}+4}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/11*(11*exp(2+x)-11*exp(x)-71)*exp(exp(2+x)-exp(x)-71/11*x+4),x,method=_RETURNVERBOSE)

[Out]

exp(exp(2+x)-exp(x)-71/11*x+4)

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maxima [A]  time = 0.35, size = 14, normalized size = 0.74 \begin {gather*} e^{\left (-\frac {71}{11} \, x + e^{\left (x + 2\right )} - e^{x} + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/11*(11*exp(2+x)-11*exp(x)-71)*exp(exp(2+x)-exp(x)-71/11*x+4),x, algorithm="maxima")

[Out]

e^(-71/11*x + e^(x + 2) - e^x + 4)

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mupad [B]  time = 0.11, size = 18, normalized size = 0.95 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-\frac {71\,x}{11}}\,{\mathrm {e}}^4\,{\mathrm {e}}^{-{\mathrm {e}}^x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(exp(x + 2) - (71*x)/11 - exp(x) + 4)*(11*exp(x) - 11*exp(x + 2) + 71))/11,x)

[Out]

exp(exp(2)*exp(x))*exp(-(71*x)/11)*exp(4)*exp(-exp(x))

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sympy [A]  time = 0.19, size = 17, normalized size = 0.89 \begin {gather*} e^{- \frac {71 x}{11} - e^{x} + e^{2} e^{x} + 4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/11*(11*exp(2+x)-11*exp(x)-71)*exp(exp(2+x)-exp(x)-71/11*x+4),x)

[Out]

exp(-71*x/11 - exp(x) + exp(2)*exp(x) + 4)

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