3.93.27 \(\int \frac {1}{5} e^{4+x^{e^{\frac {1}{5} (230+e^5-x)}}} x^{-1+e^{\frac {1}{5} (230+e^5-x)}} (5 e^{\frac {1}{5} (230+e^5-x)}-e^{\frac {1}{5} (230+e^5-x)} x \log (x)) \, dx\)

Optimal. Leaf size=21 \[ e^{4+x^{e^{46+\frac {1}{5} \left (e^5-x\right )}}} \]

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Rubi [F]  time = 1.47, 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 {1}{5} e^{4+x^{e^{\frac {1}{5} \left (230+e^5-x\right )}}} x^{-1+e^{\frac {1}{5} \left (230+e^5-x\right )}} \left (5 e^{\frac {1}{5} \left (230+e^5-x\right )}-e^{\frac {1}{5} \left (230+e^5-x\right )} x \log (x)\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(4 + x^E^((230 + E^5 - x)/5))*x^(-1 + E^((230 + E^5 - x)/5))*(5*E^((230 + E^5 - x)/5) - E^((230 + E^5 -
x)/5)*x*Log[x]))/5,x]

[Out]

-1/5*(Log[x]*Defer[Int][E^((250*(1 + E^5/250) - x + 5*x^E^(46 + E^5/5 - x/5))/5)*x^E^((230 + E^5)/5 - x/5), x]
) + Defer[Int][E^((250*(1 + E^5/250) - x + 5*x^E^(46 + E^5/5 - x/5))/5)*x^(-1 + E^((230 + E^5 - x)/5)), x] + D
efer[Int][Defer[Int][E^((250*(1 + E^5/250) - x + 5*x^E^(46 + E^5/5 - x/5))/5)*x^E^((230 + E^5)/5 - x/5), x]/x,
x]/5

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int e^{4+x^{e^{\frac {1}{5} \left (230+e^5-x\right )}}} x^{-1+e^{\frac {1}{5} \left (230+e^5-x\right )}} \left (5 e^{\frac {1}{5} \left (230+e^5-x\right )}-e^{\frac {1}{5} \left (230+e^5-x\right )} x \log (x)\right ) \, dx\\ &=\frac {1}{5} \int e^{50+\frac {e^5}{5}-\frac {x}{5}+x^{e^{\frac {1}{5} \left (230+e^5-x\right )}}} x^{-1+e^{\frac {1}{5} \left (230+e^5-x\right )}} (5-x \log (x)) \, dx\\ &=\frac {1}{5} \int \exp \left (\frac {1}{5} \left (250 \left (1+\frac {e^5}{250}\right )-x+5 x^{e^{46+\frac {e^5}{5}-\frac {x}{5}}}\right )\right ) x^{-1+e^{\frac {1}{5} \left (230+e^5-x\right )}} (5-x \log (x)) \, dx\\ &=\frac {1}{5} \int \left (5 \exp \left (\frac {1}{5} \left (250 \left (1+\frac {e^5}{250}\right )-x+5 x^{e^{46+\frac {e^5}{5}-\frac {x}{5}}}\right )\right ) x^{-1+e^{\frac {1}{5} \left (230+e^5-x\right )}}-\exp \left (\frac {1}{5} \left (250 \left (1+\frac {e^5}{250}\right )-x+5 x^{e^{46+\frac {e^5}{5}-\frac {x}{5}}}\right )\right ) x^{e^{\frac {1}{5} \left (230+e^5-x\right )}} \log (x)\right ) \, dx\\ &=-\left (\frac {1}{5} \int \exp \left (\frac {1}{5} \left (250 \left (1+\frac {e^5}{250}\right )-x+5 x^{e^{46+\frac {e^5}{5}-\frac {x}{5}}}\right )\right ) x^{e^{\frac {1}{5} \left (230+e^5-x\right )}} \log (x) \, dx\right )+\int \exp \left (\frac {1}{5} \left (250 \left (1+\frac {e^5}{250}\right )-x+5 x^{e^{46+\frac {e^5}{5}-\frac {x}{5}}}\right )\right ) x^{-1+e^{\frac {1}{5} \left (230+e^5-x\right )}} \, dx\\ &=\frac {1}{5} \int \frac {\int \exp \left (\frac {1}{5} \left (250 \left (1+\frac {e^5}{250}\right )-x+5 x^{e^{46+\frac {e^5}{5}-\frac {x}{5}}}\right )\right ) x^{e^{\frac {1}{5} \left (230+e^5\right )-\frac {x}{5}}} \, dx}{x} \, dx-\frac {1}{5} \log (x) \int \exp \left (\frac {1}{5} \left (250 \left (1+\frac {e^5}{250}\right )-x+5 x^{e^{46+\frac {e^5}{5}-\frac {x}{5}}}\right )\right ) x^{e^{\frac {1}{5} \left (230+e^5\right )-\frac {x}{5}}} \, dx+\int \exp \left (\frac {1}{5} \left (250 \left (1+\frac {e^5}{250}\right )-x+5 x^{e^{46+\frac {e^5}{5}-\frac {x}{5}}}\right )\right ) x^{-1+e^{\frac {1}{5} \left (230+e^5-x\right )}} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.47, size = 20, normalized size = 0.95 \begin {gather*} e^{4+x^{e^{\frac {1}{5} \left (230+e^5-x\right )}}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(4 + x^E^((230 + E^5 - x)/5))*x^(-1 + E^((230 + E^5 - x)/5))*(5*E^((230 + E^5 - x)/5) - E^((230 +
E^5 - x)/5)*x*Log[x]))/5,x]

[Out]

E^(4 + x^E^((230 + E^5 - x)/5))

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fricas [A]  time = 0.84, size = 15, normalized size = 0.71 \begin {gather*} e^{\left (x^{e^{\left (-\frac {1}{5} \, x + \frac {1}{5} \, e^{5} + 46\right )}} + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(-x*exp(1/5*exp(5)-1/5*x+46)*log(x)+5*exp(1/5*exp(5)-1/5*x+46))*exp(exp(1/5*exp(5)-1/5*x+46)*log
(x))*exp(exp(exp(1/5*exp(5)-1/5*x+46)*log(x))+4)/x,x, algorithm="fricas")

[Out]

e^(x^e^(-1/5*x + 1/5*e^5 + 46) + 4)

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giac [A]  time = 0.22, size = 15, normalized size = 0.71 \begin {gather*} e^{\left (x^{e^{\left (-\frac {1}{5} \, x + \frac {1}{5} \, e^{5} + 46\right )}} + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(-x*exp(1/5*exp(5)-1/5*x+46)*log(x)+5*exp(1/5*exp(5)-1/5*x+46))*exp(exp(1/5*exp(5)-1/5*x+46)*log
(x))*exp(exp(exp(1/5*exp(5)-1/5*x+46)*log(x))+4)/x,x, algorithm="giac")

[Out]

e^(x^e^(-1/5*x + 1/5*e^5 + 46) + 4)

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maple [A]  time = 0.06, size = 16, normalized size = 0.76

method	result	size
risch	\({\mathrm e}^{x^{{\mathrm e}^{\frac {{\mathrm e}^{5}}{5}-\frac {x}{5}+46}}+4}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/5*(-x*exp(1/5*exp(5)-1/5*x+46)*ln(x)+5*exp(1/5*exp(5)-1/5*x+46))*exp(exp(1/5*exp(5)-1/5*x+46)*ln(x))*exp
(exp(exp(1/5*exp(5)-1/5*x+46)*ln(x))+4)/x,x,method=_RETURNVERBOSE)

[Out]

exp(x^exp(1/5*exp(5)-1/5*x+46)+4)

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maxima [A]  time = 0.58, size = 15, normalized size = 0.71 \begin {gather*} e^{\left (x^{e^{\left (-\frac {1}{5} \, x + \frac {1}{5} \, e^{5} + 46\right )}} + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(-x*exp(1/5*exp(5)-1/5*x+46)*log(x)+5*exp(1/5*exp(5)-1/5*x+46))*exp(exp(1/5*exp(5)-1/5*x+46)*log
(x))*exp(exp(exp(1/5*exp(5)-1/5*x+46)*log(x))+4)/x,x, algorithm="maxima")

[Out]

e^(x^e^(-1/5*x + 1/5*e^5 + 46) + 4)

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mupad [B]  time = 6.73, size = 18, normalized size = 0.86 \begin {gather*} {\mathrm {e}}^4\,{\mathrm {e}}^{x^{{\mathrm {e}}^{\frac {{\mathrm {e}}^5}{5}}\,{\mathrm {e}}^{-\frac {x}{5}}\,{\mathrm {e}}^{46}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp(exp(5)/5 - x/5 + 46)*log(x))*exp(exp(exp(exp(5)/5 - x/5 + 46)*log(x)) + 4)*(5*exp(exp(5)/5 - x/5
+ 46) - x*exp(exp(5)/5 - x/5 + 46)*log(x)))/(5*x),x)

[Out]

exp(4)*exp(x^(exp(exp(5)/5)*exp(-x/5)*exp(46)))

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sympy [A]  time = 1.55, size = 19, normalized size = 0.90 \begin {gather*} e^{e^{e^{- \frac {x}{5} + \frac {e^{5}}{5} + 46} \log {\relax (x )}} + 4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(-x*exp(1/5*exp(5)-1/5*x+46)*ln(x)+5*exp(1/5*exp(5)-1/5*x+46))*exp(exp(1/5*exp(5)-1/5*x+46)*ln(x
))*exp(exp(exp(1/5*exp(5)-1/5*x+46)*ln(x))+4)/x,x)

[Out]

exp(exp(exp(-x/5 + exp(5)/5 + 46)*log(x)) + 4)

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