3.52.53 \(\int e^{-\frac {1}{e^{7/18}}} (-21+21 e^{\frac {1}{e^{7/18}}}) \, dx\)

Optimal. Leaf size=16 \[ 21 \left (x-e^{-\frac {1}{e^{7/18}}} x\right ) \]

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {8} \begin {gather*} 21 \left (1-e^{-\frac {1}{e^{7/18}}}\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-21 + 21*E^E^(-7/18))/E^E^(-7/18),x]

[Out]

21*(1 - E^(-E^(-7/18)))*x

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=21 \left (1-e^{-\frac {1}{e^{7/18}}}\right ) x\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} 21 x-21 e^{-\frac {1}{e^{7/18}}} x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-21 + 21*E^E^(-7/18))/E^E^(-7/18),x]

[Out]

21*x - (21*x)/E^E^(-7/18)

________________________________________________________________________________________

fricas [A]  time = 0.48, size = 16, normalized size = 1.00 \begin {gather*} 21 \, {\left (x e^{\left (e^{\left (-\frac {7}{18}\right )}\right )} - x\right )} e^{\left (-e^{\left (-\frac {7}{18}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((21*exp(1/exp(7/18))-21)/exp(1/exp(7/18)),x, algorithm="fricas")

[Out]

21*(x*e^(e^(-7/18)) - x)*e^(-e^(-7/18))

________________________________________________________________________________________

giac [A]  time = 0.14, size = 13, normalized size = 0.81 \begin {gather*} 21 \, x {\left (e^{\left (e^{\left (-\frac {7}{18}\right )}\right )} - 1\right )} e^{\left (-e^{\left (-\frac {7}{18}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((21*exp(1/exp(7/18))-21)/exp(1/exp(7/18)),x, algorithm="giac")

[Out]

21*x*(e^(e^(-7/18)) - 1)*e^(-e^(-7/18))

________________________________________________________________________________________

maple [A]  time = 0.02, size = 18, normalized size = 1.12

method	result	size
norman	\(21 \left ({\mathrm e}^{{\mathrm e}^{-\frac {7}{18}}}-1\right ) {\mathrm e}^{-{\mathrm e}^{-\frac {7}{18}}} x\)	\(18\)
default	\(\left (21 \,{\mathrm e}^{{\mathrm e}^{-\frac {7}{18}}}-21\right ) {\mathrm e}^{-{\mathrm e}^{-\frac {7}{18}}} x\)	\(19\)
risch	\(21 \,{\mathrm e}^{-{\mathrm e}^{-\frac {7}{18}}} x \,{\mathrm e}^{{\mathrm e}^{-\frac {7}{18}}}-21 \,{\mathrm e}^{-{\mathrm e}^{-\frac {7}{18}}} x\)	\(21\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((21*exp(1/exp(7/18))-21)/exp(1/exp(7/18)),x,method=_RETURNVERBOSE)

[Out]

21*(exp(1/exp(7/18))-1)/exp(1/exp(7/18))*x

________________________________________________________________________________________

maxima [A]  time = 0.35, size = 13, normalized size = 0.81 \begin {gather*} 21 \, x {\left (e^{\left (e^{\left (-\frac {7}{18}\right )}\right )} - 1\right )} e^{\left (-e^{\left (-\frac {7}{18}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((21*exp(1/exp(7/18))-21)/exp(1/exp(7/18)),x, algorithm="maxima")

[Out]

21*x*(e^(e^(-7/18)) - 1)*e^(-e^(-7/18))

________________________________________________________________________________________

mupad [B]  time = 0.00, size = 14, normalized size = 0.88 \begin {gather*} x\,{\mathrm {e}}^{-{\mathrm {e}}^{-\frac {7}{18}}}\,\left (21\,{\mathrm {e}}^{{\mathrm {e}}^{-\frac {7}{18}}}-21\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-exp(-7/18))*(21*exp(exp(-7/18)) - 21),x)

[Out]

x*exp(-exp(-7/18))*(21*exp(exp(-7/18)) - 21)

________________________________________________________________________________________

sympy [A]  time = 0.05, size = 20, normalized size = 1.25 \begin {gather*} \frac {x \left (-21 + 21 e^{e^{- \frac {7}{18}}}\right )}{e^{e^{- \frac {7}{18}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((21*exp(1/exp(7/18))-21)/exp(1/exp(7/18)),x)

[Out]

x*(-21 + 21*exp(exp(-7/18)))*exp(-exp(-7/18))

________________________________________________________________________________________