3.86.53 \(\int \frac {e^{2+e^{\frac {e^x+2 x}{x}}+x+\frac {e^x+2 x}{x}} (-3+3 x) \log (2)}{x^2} \, dx\)

Optimal. Leaf size=21 \[ 3 e^{2+e^{\frac {e^x+2 x}{x}}} \log (2) \]

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Rubi [F]  time = 0.66, 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 \frac {e^{2+e^{\frac {e^x+2 x}{x}}+x+\frac {e^x+2 x}{x}} (-3+3 x) \log (2)}{x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(2 + E^((E^x + 2*x)/x) + x + (E^x + 2*x)/x)*(-3 + 3*x)*Log[2])/x^2,x]

[Out]

-3*Log[2]*Defer[Int][E^(2 + E^((E^x + 2*x)/x) + x + (E^x + 2*x)/x)/x^2, x] + 3*Log[2]*Defer[Int][E^(2 + E^((E^
x + 2*x)/x) + x + (E^x + 2*x)/x)/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\log (2) \int \frac {e^{2+e^{\frac {e^x+2 x}{x}}+x+\frac {e^x+2 x}{x}} (-3+3 x)}{x^2} \, dx\\ &=\log (2) \int \left (-\frac {3 e^{2+e^{\frac {e^x+2 x}{x}}+x+\frac {e^x+2 x}{x}}}{x^2}+\frac {3 e^{2+e^{\frac {e^x+2 x}{x}}+x+\frac {e^x+2 x}{x}}}{x}\right ) \, dx\\ &=-\left ((3 \log (2)) \int \frac {e^{2+e^{\frac {e^x+2 x}{x}}+x+\frac {e^x+2 x}{x}}}{x^2} \, dx\right )+(3 \log (2)) \int \frac {e^{2+e^{\frac {e^x+2 x}{x}}+x+\frac {e^x+2 x}{x}}}{x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.23, size = 19, normalized size = 0.90 \begin {gather*} 3 e^{2+e^{2+\frac {e^x}{x}}} \log (2) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(2 + E^((E^x + 2*x)/x) + x + (E^x + 2*x)/x)*(-3 + 3*x)*Log[2])/x^2,x]

[Out]

3*E^(2 + E^(2 + E^x/x))*Log[2]

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fricas [B]  time = 0.93, size = 52, normalized size = 2.48 \begin {gather*} 3 \, x e^{\left (-x + \frac {x^{2} + x e^{\left (\frac {2 \, x + e^{x}}{x}\right )} - x \log \relax (x) + 4 \, x + e^{x}}{x} - \frac {2 \, x + e^{x}}{x}\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*x-3)*log(2)*exp(x)*exp((exp(x)+2*x)/x)*exp(exp((exp(x)+2*x)/x)-log(x)+2)/x,x, algorithm="fricas")

[Out]

3*x*e^(-x + (x^2 + x*e^((2*x + e^x)/x) - x*log(x) + 4*x + e^x)/x - (2*x + e^x)/x)*log(2)

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giac [A]  time = 0.19, size = 16, normalized size = 0.76 \begin {gather*} 3 \, e^{\left (e^{\left (\frac {e^{x}}{x} + 2\right )} + 2\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*x-3)*log(2)*exp(x)*exp((exp(x)+2*x)/x)*exp(exp((exp(x)+2*x)/x)-log(x)+2)/x,x, algorithm="giac")

[Out]

3*e^(e^(e^x/x + 2) + 2)*log(2)

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maple [A]  time = 0.10, size = 19, normalized size = 0.90

method	result	size
risch	\(3 \ln \relax (2) {\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{x}+2 x}{x}}+2}\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*x-3)*ln(2)*exp(x)*exp((exp(x)+2*x)/x)*exp(exp((exp(x)+2*x)/x)-ln(x)+2)/x,x,method=_RETURNVERBOSE)

[Out]

3*ln(2)*exp(exp((exp(x)+2*x)/x)+2)

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maxima [A]  time = 0.59, size = 16, normalized size = 0.76 \begin {gather*} 3 \, e^{\left (e^{\left (\frac {e^{x}}{x} + 2\right )} + 2\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*x-3)*log(2)*exp(x)*exp((exp(x)+2*x)/x)*exp(exp((exp(x)+2*x)/x)-log(x)+2)/x,x, algorithm="maxima")

[Out]

3*e^(e^(e^x/x + 2) + 2)*log(2)

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mupad [B]  time = 5.38, size = 17, normalized size = 0.81 \begin {gather*} 3\,{\mathrm {e}}^2\,{\mathrm {e}}^{{\mathrm {e}}^2\,{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{x}}}\,\ln \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((2*x + exp(x))/x)*exp(exp((2*x + exp(x))/x) - log(x) + 2)*exp(x)*log(2)*(3*x - 3))/x,x)

[Out]

3*exp(2)*exp(exp(2)*exp(exp(x)/x))*log(2)

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sympy [A]  time = 0.45, size = 17, normalized size = 0.81 \begin {gather*} 3 e^{e^{\frac {2 x + e^{x}}{x}} + 2} \log {\relax (2 )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*x-3)*ln(2)*exp(x)*exp((exp(x)+2*x)/x)*exp(exp((exp(x)+2*x)/x)-ln(x)+2)/x,x)

[Out]

3*exp(exp((2*x + exp(x))/x) + 2)*log(2)

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