∫ −400x log(3)−e6−2ex x log(3)+40e3−ex x log(3)+e−80+4e3−ex −x __________________ −20+e3−ex (20x log(3)+e3−ex (−x log(3)−exx2 log(3)))+(−400x log(3)−e6−2ex x log(3)+40e3−ex x log(3)+e−80+4e3−ex −x __________________ −20+e3−ex (400 log(3)+e6−2ex log(3)−40e3−ex log(3))) log(e−80+4e3−ex −x __________________ −20+e3−ex −x)____________________________________________________________________________________________________________________________________________________________________________ e−80+4e3−ex−x __________________ −20+e3−ex (400+e6−2ex−40e3−ex)−400x−e6−2exx+40e3−exx dx

3.68.93 $\int \frac {-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} (20 x \log (3)+e^{3-e^x} (-x \log (3)-e^x x^2 \log (3)))+(-400 x \log (3)-e^{6-2 e^x} x \log (3)+40 e^{3-e^x} x \log (3)+e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} (400 \log (3)+e^{6-2 e^x} \log (3)-40 e^{3-e^x} \log (3))) \log (e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}}-x)}{e^{\frac {-80+4 e^{3-e^x}-x}{-20+e^{3-e^x}}} (400+e^{6-2 e^x}-40 e^{3-e^x})-400 x-e^{6-2 e^x} x+40 e^{3-e^x} x} \, dx$

Optimal. Leaf size=30 \[ x \log (3) \log \left (e^{4+\frac {x}{20-e^{3-e^x}}}-x\right ) \]

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Rubi [F] time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(-400*x*Log[3] - E^(6 - 2*E^x)*x*Log[3] + 40*E^(3 - E^x)*x*Log[3] + E^((-80 + 4*E^(3 - E^x) - x)/(-20 + E^

(3 - E^x)))*(20*x*Log[3] + E^(3 - E^x)*(-(x*Log[3]) - E^x*x^2*Log[3])) + (-400*x*Log[3] - E^(6 - 2*E^x)*x*Log[

3] + 40*E^(3 - E^x)*x*Log[3] + E^((-80 + 4*E^(3 - E^x) - x)/(-20 + E^(3 - E^x)))*(400*Log[3] + E^(6 - 2*E^x)*L

og[3] - 40*E^(3 - E^x)*Log[3]))*Log[E^((-80 + 4*E^(3 - E^x) - x)/(-20 + E^(3 - E^x))) - x])/(E^((-80 + 4*E^(3

- E^x) - x)/(-20 + E^(3 - E^x)))*(400 + E^(6 - 2*E^x) - 40*E^(3 - E^x)) - 400*x - E^(6 - 2*E^x)*x + 40*E^(3 -

E^x)*x),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A] time = 4.48, size = 37, normalized size = 1.23 \begin {gather*} x \log (3) \log \left (e^{\frac {1}{20} \left (80+x-\frac {e^3 x}{e^3-20 e^{e^x}}\right )}-x\right ) \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(-400*x*Log[3] - E^(6 - 2*E^x)*x*Log[3] + 40*E^(3 - E^x)*x*Log[3] + E^((-80 + 4*E^(3 - E^x) - x)/(-2

0 + E^(3 - E^x)))*(20*x*Log[3] + E^(3 - E^x)*(-(x*Log[3]) - E^x*x^2*Log[3])) + (-400*x*Log[3] - E^(6 - 2*E^x)*

x*Log[3] + 40*E^(3 - E^x)*x*Log[3] + E^((-80 + 4*E^(3 - E^x) - x)/(-20 + E^(3 - E^x)))*(400*Log[3] + E^(6 - 2*

E^x)*Log[3] - 40*E^(3 - E^x)*Log[3]))*Log[E^((-80 + 4*E^(3 - E^x) - x)/(-20 + E^(3 - E^x))) - x])/(E^((-80 + 4

*E^(3 - E^x) - x)/(-20 + E^(3 - E^x)))*(400 + E^(6 - 2*E^x) - 40*E^(3 - E^x)) - 400*x - E^(6 - 2*E^x)*x + 40*E

^(3 - E^x)*x),x]

[Out]

x*Log[3]*Log[E^((80 + x - (E^3*x)/(E^3 - 20*E^E^x))/20) - x]

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fricas [A] time = 0.83, size = 35, normalized size = 1.17 \begin {gather*} x \log \relax (3) \log \left (-x + e^{\left (-\frac {x - 4 \, e^{\left (-e^{x} + 3\right )} + 80}{e^{\left (-e^{x} + 3\right )} - 20}\right )}\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((log(3)*exp(-exp(x)+3)^2-40*log(3)*exp(-exp(x)+3)+400*log(3))*exp((4*exp(-exp(x)+3)-x-80)/(exp(-ex

p(x)+3)-20))-x*log(3)*exp(-exp(x)+3)^2+40*x*log(3)*exp(-exp(x)+3)-400*x*log(3))*log(exp((4*exp(-exp(x)+3)-x-80

)/(exp(-exp(x)+3)-20))-x)+((-x^2*log(3)*exp(x)-x*log(3))*exp(-exp(x)+3)+20*x*log(3))*exp((4*exp(-exp(x)+3)-x-8

0)/(exp(-exp(x)+3)-20))-x*log(3)*exp(-exp(x)+3)^2+40*x*log(3)*exp(-exp(x)+3)-400*x*log(3))/((exp(-exp(x)+3)^2-

40*exp(-exp(x)+3)+400)*exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(x)+3)-20))-x*exp(-exp(x)+3)^2+40*x*exp(-exp(x)+3)

-400*x),x, algorithm="fricas")

[Out]

x*log(3)*log(-x + e^(-(x - 4*e^(-e^x + 3) + 80)/(e^(-e^x + 3) - 20)))

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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((log(3)*exp(-exp(x)+3)^2-40*log(3)*exp(-exp(x)+3)+400*log(3))*exp((4*exp(-exp(x)+3)-x-80)/(exp(-ex

p(x)+3)-20))-x*log(3)*exp(-exp(x)+3)^2+40*x*log(3)*exp(-exp(x)+3)-400*x*log(3))*log(exp((4*exp(-exp(x)+3)-x-80

)/(exp(-exp(x)+3)-20))-x)+((-x^2*log(3)*exp(x)-x*log(3))*exp(-exp(x)+3)+20*x*log(3))*exp((4*exp(-exp(x)+3)-x-8

0)/(exp(-exp(x)+3)-20))-x*log(3)*exp(-exp(x)+3)^2+40*x*log(3)*exp(-exp(x)+3)-400*x*log(3))/((exp(-exp(x)+3)^2-

40*exp(-exp(x)+3)+400)*exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(x)+3)-20))-x*exp(-exp(x)+3)^2+40*x*exp(-exp(x)+3)

-400*x),x, algorithm="giac")

[Out]

Timed out

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maple [A] time = 0.28, size = 36, normalized size = 1.20


method	result	size

risch	$x \ln \relax (3) \ln \left ({\mathrm e}^{-\frac {-4 \,{\mathrm e}^{-{\mathrm e}^{x}+3}+x +80}{{\mathrm e}^{-{\mathrm e}^{x}+3}-20}}-x \right )$	$36$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((((ln(3)*exp(-exp(x)+3)^2-40*ln(3)*exp(-exp(x)+3)+400*ln(3))*exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(x)+3)-2

0))-x*ln(3)*exp(-exp(x)+3)^2+40*x*ln(3)*exp(-exp(x)+3)-400*x*ln(3))*ln(exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(x

)+3)-20))-x)+((-x^2*ln(3)*exp(x)-x*ln(3))*exp(-exp(x)+3)+20*x*ln(3))*exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(x)+

3)-20))-x*ln(3)*exp(-exp(x)+3)^2+40*x*ln(3)*exp(-exp(x)+3)-400*x*ln(3))/((exp(-exp(x)+3)^2-40*exp(-exp(x)+3)+4

00)*exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(x)+3)-20))-x*exp(-exp(x)+3)^2+40*x*exp(-exp(x)+3)-400*x),x,method=_R

ETURNVERBOSE)

[Out]

x*ln(3)*ln(exp(-(-4*exp(-exp(x)+3)+x+80)/(exp(-exp(x)+3)-20))-x)

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maxima [B] time = 0.99, size = 88, normalized size = 2.93 \begin {gather*} \frac {4 \, x e^{3} \log \relax (3) + {\left (x e^{3} \log \relax (3) - 20 \, x e^{\left (e^{x}\right )} \log \relax (3)\right )} \log \left (-x e^{\left (-\frac {4 \, e^{3}}{e^{3} - 20 \, e^{\left (e^{x}\right )}}\right )} + e^{\left (-\frac {x e^{\left (e^{x}\right )}}{e^{3} - 20 \, e^{\left (e^{x}\right )}} - \frac {80 \, e^{\left (e^{x}\right )}}{e^{3} - 20 \, e^{\left (e^{x}\right )}}\right )}\right )}{e^{3} - 20 \, e^{\left (e^{x}\right )}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((log(3)*exp(-exp(x)+3)^2-40*log(3)*exp(-exp(x)+3)+400*log(3))*exp((4*exp(-exp(x)+3)-x-80)/(exp(-ex

p(x)+3)-20))-x*log(3)*exp(-exp(x)+3)^2+40*x*log(3)*exp(-exp(x)+3)-400*x*log(3))*log(exp((4*exp(-exp(x)+3)-x-80

)/(exp(-exp(x)+3)-20))-x)+((-x^2*log(3)*exp(x)-x*log(3))*exp(-exp(x)+3)+20*x*log(3))*exp((4*exp(-exp(x)+3)-x-8

0)/(exp(-exp(x)+3)-20))-x*log(3)*exp(-exp(x)+3)^2+40*x*log(3)*exp(-exp(x)+3)-400*x*log(3))/((exp(-exp(x)+3)^2-

40*exp(-exp(x)+3)+400)*exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(x)+3)-20))-x*exp(-exp(x)+3)^2+40*x*exp(-exp(x)+3)

-400*x),x, algorithm="maxima")

[Out]

(4*x*e^3*log(3) + (x*e^3*log(3) - 20*x*e^(e^x)*log(3))*log(-x*e^(-4*e^3/(e^3 - 20*e^(e^x))) + e^(-x*e^(e^x)/(e

^3 - 20*e^(e^x)) - 80*e^(e^x)/(e^3 - 20*e^(e^x)))))/(e^3 - 20*e^(e^x))

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mupad [B] time = 4.64, size = 63, normalized size = 2.10 \begin {gather*} x\,\ln \left ({\mathrm {e}}^{-\frac {x}{{\mathrm {e}}^3\,{\mathrm {e}}^{-{\mathrm {e}}^x}-20}}\,{\mathrm {e}}^{-\frac {80}{{\mathrm {e}}^3\,{\mathrm {e}}^{-{\mathrm {e}}^x}-20}}\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^3\,{\mathrm {e}}^{-{\mathrm {e}}^x}}{{\mathrm {e}}^3\,{\mathrm {e}}^{-{\mathrm {e}}^x}-20}}-x\right )\,\ln \relax (3) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((400*x*log(3) - exp(-(x - 4*exp(3 - exp(x)) + 80)/(exp(3 - exp(x)) - 20))*(20*x*log(3) - exp(3 - exp(x))*(

x*log(3) + x^2*exp(x)*log(3))) + log(exp(-(x - 4*exp(3 - exp(x)) + 80)/(exp(3 - exp(x)) - 20)) - x)*(400*x*log

(3) - exp(-(x - 4*exp(3 - exp(x)) + 80)/(exp(3 - exp(x)) - 20))*(400*log(3) - 40*exp(3 - exp(x))*log(3) + exp(

6 - 2*exp(x))*log(3)) - 40*x*exp(3 - exp(x))*log(3) + x*exp(6 - 2*exp(x))*log(3)) - 40*x*exp(3 - exp(x))*log(3

) + x*exp(6 - 2*exp(x))*log(3))/(400*x - 40*x*exp(3 - exp(x)) + x*exp(6 - 2*exp(x)) - exp(-(x - 4*exp(3 - exp(

x)) + 80)/(exp(3 - exp(x)) - 20))*(exp(6 - 2*exp(x)) - 40*exp(3 - exp(x)) + 400)),x)

[Out]

x*log(exp(-x/(exp(3)*exp(-exp(x)) - 20))*exp(-80/(exp(3)*exp(-exp(x)) - 20))*exp((4*exp(3)*exp(-exp(x)))/(exp(

3)*exp(-exp(x)) - 20)) - x)*log(3)

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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((ln(3)*exp(-exp(x)+3)**2-40*ln(3)*exp(-exp(x)+3)+400*ln(3))*exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(

x)+3)-20))-x*ln(3)*exp(-exp(x)+3)**2+40*x*ln(3)*exp(-exp(x)+3)-400*x*ln(3))*ln(exp((4*exp(-exp(x)+3)-x-80)/(ex

p(-exp(x)+3)-20))-x)+((-x**2*ln(3)*exp(x)-x*ln(3))*exp(-exp(x)+3)+20*x*ln(3))*exp((4*exp(-exp(x)+3)-x-80)/(exp

(-exp(x)+3)-20))-x*ln(3)*exp(-exp(x)+3)**2+40*x*ln(3)*exp(-exp(x)+3)-400*x*ln(3))/((exp(-exp(x)+3)**2-40*exp(-

exp(x)+3)+400)*exp((4*exp(-exp(x)+3)-x-80)/(exp(-exp(x)+3)-20))-x*exp(-exp(x)+3)**2+40*x*exp(-exp(x)+3)-400*x)

,x)

[Out]

Timed out

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