3.6.4 \(\int (-2 e^{e^4-2 x}+4 \log (5)) \, dx\) [504]

Optimal. Leaf size=22 \[ 3+e^{e^4-2 x}+3 x \log (5)+(2+x) \log (5) \]

[Out]

ln(5)*(2+x)+exp(exp(4)-2*x)+3+3*x*ln(5)

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Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 0.68, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {2225} \begin {gather*} e^{e^4-2 x}+4 x \log (5) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-2*E^(E^4 - 2*x) + 4*Log[5],x]

[Out]

E^(E^4 - 2*x) + 4*x*Log[5]

Rule 2225

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=4 x \log (5)-2 \int e^{e^4-2 x} \, dx\\ &=e^{e^4-2 x}+4 x \log (5)\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.03, size = 14, normalized size = 0.64 \begin {gather*} e^{e^4-2 x}+x \log (625) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-2*E^(E^4 - 2*x) + 4*Log[5],x]

[Out]

E^(E^4 - 2*x) + x*Log[625]

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Maple [A]
time = 0.09, size = 14, normalized size = 0.64

method	result	size
default	\({\mathrm e}^{{\mathrm e}^{4}-2 x}+4 x \ln \left (5\right )\)	\(14\)
norman	\({\mathrm e}^{{\mathrm e}^{4}-2 x}+4 x \ln \left (5\right )\)	\(14\)
risch	\({\mathrm e}^{{\mathrm e}^{4}-2 x}+4 x \ln \left (5\right )\)	\(14\)
derivativedivides	\({\mathrm e}^{{\mathrm e}^{4}-2 x}-2 \ln \left (5\right ) \ln \left ({\mathrm e}^{{\mathrm e}^{4}-2 x}\right )\)	\(21\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2*exp(exp(4)-2*x)+4*ln(5),x,method=_RETURNVERBOSE)

[Out]

exp(exp(4)-2*x)+4*x*ln(5)

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Maxima [A]
time = 0.33, size = 13, normalized size = 0.59 \begin {gather*} 4 \, x \log \left (5\right ) + e^{\left (-2 \, x + e^{4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(exp(4)-2*x)+4*log(5),x, algorithm="maxima")

[Out]

4*x*log(5) + e^(-2*x + e^4)

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Fricas [A]
time = 0.30, size = 13, normalized size = 0.59 \begin {gather*} 4 \, x \log \left (5\right ) + e^{\left (-2 \, x + e^{4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(exp(4)-2*x)+4*log(5),x, algorithm="fricas")

[Out]

4*x*log(5) + e^(-2*x + e^4)

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Sympy [A]
time = 0.03, size = 14, normalized size = 0.64 \begin {gather*} 4 x \log {\left (5 \right )} + e^{- 2 x + e^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(exp(4)-2*x)+4*ln(5),x)

[Out]

4*x*log(5) + exp(-2*x + exp(4))

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Giac [A]
time = 0.40, size = 13, normalized size = 0.59 \begin {gather*} 4 \, x \log \left (5\right ) + e^{\left (-2 \, x + e^{4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(exp(4)-2*x)+4*log(5),x, algorithm="giac")

[Out]

4*x*log(5) + e^(-2*x + e^4)

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Mupad [B]
time = 0.09, size = 14, normalized size = 0.64 \begin {gather*} 4\,x\,\ln \left (5\right )+{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{{\mathrm {e}}^4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*log(5) - 2*exp(exp(4) - 2*x),x)

[Out]

4*x*log(5) + exp(-2*x)*exp(exp(4))

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