3.54.65 \(\int (2+e^{e^{\frac {1}{5} (-e+10 x)} x+\frac {1}{5} (-e+10 x)} (1+2 x)) \, dx\)

Optimal. Leaf size=20 \[ -1+e^{e^{-\frac {e}{5}+2 x} x}+2 x \]

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Rubi [F]  time = 0.21, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \left (2+\exp \left (e^{\frac {1}{5} (-e+10 x)} x+\frac {1}{5} (-e+10 x)\right ) (1+2 x)\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[2 + E^(E^((-E + 10*x)/5)*x + (-E + 10*x)/5)*(1 + 2*x),x]

[Out]

2*x + Defer[Int][E^(E^((-E + 10*x)/5)*x + (-E + 10*x)/5), x] + 2*Defer[Int][E^(E^((-E + 10*x)/5)*x + (-E + 10*
x)/5)*x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=2 x+\int \exp \left (e^{\frac {1}{5} (-e+10 x)} x+\frac {1}{5} (-e+10 x)\right ) (1+2 x) \, dx\\ &=2 x+\int \left (\exp \left (e^{\frac {1}{5} (-e+10 x)} x+\frac {1}{5} (-e+10 x)\right )+2 \exp \left (e^{\frac {1}{5} (-e+10 x)} x+\frac {1}{5} (-e+10 x)\right ) x\right ) \, dx\\ &=2 x+2 \int \exp \left (e^{\frac {1}{5} (-e+10 x)} x+\frac {1}{5} (-e+10 x)\right ) x \, dx+\int \exp \left (e^{\frac {1}{5} (-e+10 x)} x+\frac {1}{5} (-e+10 x)\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.14, size = 19, normalized size = 0.95 \begin {gather*} e^{e^{-\frac {e}{5}+2 x} x}+2 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2 + E^(E^((-E + 10*x)/5)*x + (-E + 10*x)/5)*(1 + 2*x),x]

[Out]

E^(E^(-1/5*E + 2*x)*x) + 2*x

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fricas [B]  time = 0.55, size = 43, normalized size = 2.15 \begin {gather*} {\left (2 \, x e^{\left (2 \, x - \frac {1}{5} \, e\right )} + e^{\left (x e^{\left (2 \, x - \frac {1}{5} \, e\right )} + 2 \, x - \frac {1}{5} \, e\right )}\right )} e^{\left (-2 \, x + \frac {1}{5} \, e\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x+1)*exp(-1/5*exp(1)+2*x)*exp(x*exp(-1/5*exp(1)+2*x))+2,x, algorithm="fricas")

[Out]

(2*x*e^(2*x - 1/5*e) + e^(x*e^(2*x - 1/5*e) + 2*x - 1/5*e))*e^(-2*x + 1/5*e)

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giac [A]  time = 0.17, size = 16, normalized size = 0.80 \begin {gather*} 2 \, x + e^{\left (x e^{\left (2 \, x - \frac {1}{5} \, e\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x+1)*exp(-1/5*exp(1)+2*x)*exp(x*exp(-1/5*exp(1)+2*x))+2,x, algorithm="giac")

[Out]

2*x + e^(x*e^(2*x - 1/5*e))

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maple [A]  time = 0.09, size = 17, normalized size = 0.85

method	result	size
default	\(2 x +{\mathrm e}^{x \,{\mathrm e}^{-\frac {{\mathrm e}}{5}+2 x}}\)	\(17\)
norman	\(2 x +{\mathrm e}^{x \,{\mathrm e}^{-\frac {{\mathrm e}}{5}+2 x}}\)	\(17\)
risch	\(2 x +{\mathrm e}^{x \,{\mathrm e}^{-\frac {{\mathrm e}}{5}+2 x}}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x+1)*exp(-1/5*exp(1)+2*x)*exp(x*exp(-1/5*exp(1)+2*x))+2,x,method=_RETURNVERBOSE)

[Out]

2*x+exp(x*exp(-1/5*exp(1)+2*x))

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maxima [A]  time = 0.49, size = 16, normalized size = 0.80 \begin {gather*} 2 \, x + e^{\left (x e^{\left (2 \, x - \frac {1}{5} \, e\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x+1)*exp(-1/5*exp(1)+2*x)*exp(x*exp(-1/5*exp(1)+2*x))+2,x, algorithm="maxima")

[Out]

2*x + e^(x*e^(2*x - 1/5*e))

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mupad [B]  time = 3.66, size = 16, normalized size = 0.80 \begin {gather*} 2\,x+{\mathrm {e}}^{x\,{\mathrm {e}}^{-\frac {\mathrm {e}}{5}}\,{\mathrm {e}}^{2\,x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(2*x - exp(1)/5)*exp(x*exp(2*x - exp(1)/5))*(2*x + 1) + 2,x)

[Out]

2*x + exp(x*exp(-exp(1)/5)*exp(2*x))

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sympy [A]  time = 0.14, size = 15, normalized size = 0.75 \begin {gather*} 2 x + e^{x e^{2 x - \frac {e}{5}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x+1)*exp(-1/5*exp(1)+2*x)*exp(x*exp(-1/5*exp(1)+2*x))+2,x)

[Out]

2*x + exp(x*exp(2*x - E/5))

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