3.100.75 \(\int e^e (2+e^4) \, dx\)

Optimal. Leaf size=18 \[ 4+e^e \left (2+e^4\right ) x+2 \log \left (\frac {4}{3}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.56, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {8} \begin {gather*} e^e \left (2+e^4\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^E*(2 + E^4),x]

[Out]

E^E*(2 + E^4)*x

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=e^e \left (2+e^4\right ) x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 0.78 \begin {gather*} 2 e^e x+e^{4+e} x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^E*(2 + E^4),x]

[Out]

2*E^E*x + E^(4 + E)*x

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fricas [A]  time = 0.59, size = 12, normalized size = 0.67 \begin {gather*} {\left (x e^{4} + 2 \, x\right )} e^{e} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+exp(4))*exp(exp(1)),x, algorithm="fricas")

[Out]

(x*e^4 + 2*x)*e^e

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giac [A]  time = 0.15, size = 9, normalized size = 0.50 \begin {gather*} x {\left (e^{4} + 2\right )} e^{e} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+exp(4))*exp(exp(1)),x, algorithm="giac")

[Out]

x*(e^4 + 2)*e^e

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maple [A]  time = 0.01, size = 10, normalized size = 0.56

method	result	size
default	\(\left (2+{\mathrm e}^{4}\right ) x \,{\mathrm e}^{{\mathrm e}}\)	\(10\)
norman	\(\left (2 \,{\mathrm e}^{{\mathrm e}}+{\mathrm e}^{{\mathrm e}} {\mathrm e}^{4}\right ) x\)	\(15\)
risch	\(x \,{\mathrm e}^{{\mathrm e}} {\mathrm e}^{4}+2 x \,{\mathrm e}^{{\mathrm e}}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2+exp(4))*exp(exp(1)),x,method=_RETURNVERBOSE)

[Out]

(2+exp(4))*x*exp(exp(1))

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maxima [A]  time = 0.36, size = 9, normalized size = 0.50 \begin {gather*} x {\left (e^{4} + 2\right )} e^{e} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+exp(4))*exp(exp(1)),x, algorithm="maxima")

[Out]

x*(e^4 + 2)*e^e

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mupad [B]  time = 0.00, size = 9, normalized size = 0.50 \begin {gather*} x\,{\mathrm {e}}^{\mathrm {e}}\,\left ({\mathrm {e}}^4+2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(exp(1))*(exp(4) + 2),x)

[Out]

x*exp(exp(1))*(exp(4) + 2)

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sympy [A]  time = 0.04, size = 10, normalized size = 0.56 \begin {gather*} x \left (2 + e^{4}\right ) e^{e} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+exp(4))*exp(exp(1)),x)

[Out]

x*(2 + exp(4))*exp(E)

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