3.68.4 \(\int \frac {2 e^x x+e^{e^{2 x}+2 e^x x+x^2} (-6 e^{2 x} x-6 x^2+e^x (-6 x-6 x^2))-x \log (5 e^{-e^{e^{2 x}+2 e^x x+x^2}})+(-e^x x-x \log (5 e^{-e^{e^{2 x}+2 e^x x+x^2}})+(3 e^x+3 \log (5 e^{-e^{e^{2 x}+2 e^x x+x^2}})) \log (e^x+\log (5 e^{-e^{e^{2 x}+2 e^x x+x^2}}))) \log (-x+3 \log (e^x+\log (5 e^{-e^{e^{2 x}+2 e^x x+x^2}})))}{-e^x x-x \log (5 e^{-e^{e^{2 x}+2 e^x x+x^2}})+(3 e^x+3 \log (5 e^{-e^{e^{2 x}+2 e^x x+x^2}})) \log (e^x+\log (5 e^{-e^{e^{2 x}+2 e^x x+x^2}}))} \, dx\)

Optimal. Leaf size=30 \[ x \log \left (-x+3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right ) \]

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Rubi [F]  time = 21.97, 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 {2 e^x x+e^{e^{2 x}+2 e^x x+x^2} \left (-6 e^{2 x} x-6 x^2+e^x \left (-6 x-6 x^2\right )\right )-x \log \left (5 e^{-e^{e^{2 x}+2 e^x x+x^2}}\right )+\left (-e^x x-x \log \left (5 e^{-e^{e^{2 x}+2 e^x x+x^2}}\right )+\left (3 e^x+3 \log \left (5 e^{-e^{e^{2 x}+2 e^x x+x^2}}\right )\right ) \log \left (e^x+\log \left (5 e^{-e^{e^{2 x}+2 e^x x+x^2}}\right )\right )\right ) \log \left (-x+3 \log \left (e^x+\log \left (5 e^{-e^{e^{2 x}+2 e^x x+x^2}}\right )\right )\right )}{-e^x x-x \log \left (5 e^{-e^{e^{2 x}+2 e^x x+x^2}}\right )+\left (3 e^x+3 \log \left (5 e^{-e^{e^{2 x}+2 e^x x+x^2}}\right )\right ) \log \left (e^x+\log \left (5 e^{-e^{e^{2 x}+2 e^x x+x^2}}\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(2*E^x*x + E^(E^(2*x) + 2*E^x*x + x^2)*(-6*E^(2*x)*x - 6*x^2 + E^x*(-6*x - 6*x^2)) - x*Log[5/E^E^(E^(2*x)
+ 2*E^x*x + x^2)] + (-(E^x*x) - x*Log[5/E^E^(E^(2*x) + 2*E^x*x + x^2)] + (3*E^x + 3*Log[5/E^E^(E^(2*x) + 2*E^x
*x + x^2)])*Log[E^x + Log[5/E^E^(E^(2*x) + 2*E^x*x + x^2)]])*Log[-x + 3*Log[E^x + Log[5/E^E^(E^(2*x) + 2*E^x*x
+ x^2)]]])/(-(E^x*x) - x*Log[5/E^E^(E^(2*x) + 2*E^x*x + x^2)] + (3*E^x + 3*Log[5/E^E^(E^(2*x) + 2*E^x*x + x^2
)])*Log[E^x + Log[5/E^E^(E^(2*x) + 2*E^x*x + x^2)]]),x]

[Out]

-2*Defer[Int][x/(x - 3*Log[E^x + Log[5/E^E^(E^x + x)^2]]), x] + 6*Defer[Int][(E^(E^x + x)^2*x)/(x - 3*Log[E^x
+ Log[5/E^E^(E^x + x)^2]]), x] + 6*Defer[Int][(E^(x + (E^x + x)^2)*x)/(x - 3*Log[E^x + Log[5/E^E^(E^x + x)^2]]
), x] + 6*Defer[Int][(E^(E^x + x)^2*x^2)/(x - 3*Log[E^x + Log[5/E^E^(E^x + x)^2]]), x] - 6*Defer[Int][(E^(E^x
+ x)^2*x*Log[5/E^E^(E^x + x)^2])/(x - 3*Log[E^x + Log[5/E^E^(E^x + x)^2]]), x] + 6*Defer[Int][(E^(E^x + x)^2*x
^2)/((E^x + Log[5/E^E^(E^x + x)^2])*(x - 3*Log[E^x + Log[5/E^E^(E^x + x)^2]])), x] + 3*Defer[Int][(x*Log[5/E^E
^(E^x + x)^2])/((E^x + Log[5/E^E^(E^x + x)^2])*(x - 3*Log[E^x + Log[5/E^E^(E^x + x)^2]])), x] - 6*Defer[Int][(
E^(E^x + x)^2*x*Log[5/E^E^(E^x + x)^2])/((E^x + Log[5/E^E^(E^x + x)^2])*(x - 3*Log[E^x + Log[5/E^E^(E^x + x)^2
]])), x] - 6*Defer[Int][(E^(E^x + x)^2*x^2*Log[5/E^E^(E^x + x)^2])/((E^x + Log[5/E^E^(E^x + x)^2])*(x - 3*Log[
E^x + Log[5/E^E^(E^x + x)^2]])), x] + 6*Defer[Int][(E^(E^x + x)^2*x*Log[5/E^E^(E^x + x)^2]^2)/((E^x + Log[5/E^
E^(E^x + x)^2])*(x - 3*Log[E^x + Log[5/E^E^(E^x + x)^2]])), x] + Defer[Int][Log[-x + 3*Log[E^x + Log[5/E^E^(E^
x + x)^2]]], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-2 e^x x-e^{e^{2 x}+2 e^x x+x^2} \left (-6 e^{2 x} x-6 x^2+e^x \left (-6 x-6 x^2\right )\right )+x \log \left (5 e^{-e^{e^{2 x}+2 e^x x+x^2}}\right )-\left (-e^x x-x \log \left (5 e^{-e^{e^{2 x}+2 e^x x+x^2}}\right )+\left (3 e^x+3 \log \left (5 e^{-e^{e^{2 x}+2 e^x x+x^2}}\right )\right ) \log \left (e^x+\log \left (5 e^{-e^{e^{2 x}+2 e^x x+x^2}}\right )\right )\right ) \log \left (-x+3 \log \left (e^x+\log \left (5 e^{-e^{e^{2 x}+2 e^x x+x^2}}\right )\right )\right )}{\left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right ) \left (x-3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )} \, dx\\ &=\int \left (\frac {6 e^{\left (e^x+x\right )^2} \left (1+e^x\right ) x \left (e^x+x\right )}{\left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right ) \left (x-3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )}+\frac {-2 e^x x+x \log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )+e^x x \log \left (-x+3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )+x \log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right ) \log \left (-x+3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )-3 e^x \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right ) \log \left (-x+3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )-3 \log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right ) \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right ) \log \left (-x+3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )}{\left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right ) \left (x-3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )}\right ) \, dx\\ &=6 \int \frac {e^{\left (e^x+x\right )^2} \left (1+e^x\right ) x \left (e^x+x\right )}{\left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right ) \left (x-3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )} \, dx+\int \frac {-2 e^x x+x \log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )+e^x x \log \left (-x+3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )+x \log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right ) \log \left (-x+3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )-3 e^x \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right ) \log \left (-x+3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )-3 \log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right ) \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right ) \log \left (-x+3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )}{\left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right ) \left (x-3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )} \, dx\\ &=6 \int \left (\frac {e^{x+\left (e^x+x\right )^2} x}{x-3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )}+\frac {e^{\left (e^x+x\right )^2} x \left (1+x-\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )}{x-3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )}-\frac {e^{\left (e^x+x\right )^2} x \left (x-\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right ) \left (-1+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )}{\left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right ) \left (x-3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )}\right ) \, dx+\int \frac {e^x \left (-2 x+\left (x-3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right ) \log \left (-x+3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )\right )+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right ) \left (x+\left (x-3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right ) \log \left (-x+3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )\right )}{\left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right ) \left (x-3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )} \, dx\\ &=6 \int \frac {e^{x+\left (e^x+x\right )^2} x}{x-3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )} \, dx+6 \int \frac {e^{\left (e^x+x\right )^2} x \left (1+x-\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )}{x-3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )} \, dx-6 \int \frac {e^{\left (e^x+x\right )^2} x \left (x-\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right ) \left (-1+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )}{\left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right ) \left (x-3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )} \, dx+\int \left (\frac {3 x \log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )}{\left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right ) \left (x-3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )}+\frac {-2 x+x \log \left (-x+3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )-3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right ) \log \left (-x+3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )\right )}{x-3 \log \left (e^x+\log \left (5 e^{-e^{\left (e^x+x\right )^2}}\right )\right )}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.65, size = 38, normalized size = 1.27 \begin {gather*} x \log \left (-x+3 \log \left (e^x+\log \left (5 e^{-e^{e^{2 x}+2 e^x x+x^2}}\right )\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(2*E^x*x + E^(E^(2*x) + 2*E^x*x + x^2)*(-6*E^(2*x)*x - 6*x^2 + E^x*(-6*x - 6*x^2)) - x*Log[5/E^E^(E^
(2*x) + 2*E^x*x + x^2)] + (-(E^x*x) - x*Log[5/E^E^(E^(2*x) + 2*E^x*x + x^2)] + (3*E^x + 3*Log[5/E^E^(E^(2*x) +
2*E^x*x + x^2)])*Log[E^x + Log[5/E^E^(E^(2*x) + 2*E^x*x + x^2)]])*Log[-x + 3*Log[E^x + Log[5/E^E^(E^(2*x) + 2
*E^x*x + x^2)]]])/(-(E^x*x) - x*Log[5/E^E^(E^(2*x) + 2*E^x*x + x^2)] + (3*E^x + 3*Log[5/E^E^(E^(2*x) + 2*E^x*x
+ x^2)])*Log[E^x + Log[5/E^E^(E^(2*x) + 2*E^x*x + x^2)]]),x]

[Out]

x*Log[-x + 3*Log[E^x + Log[5/E^E^(E^(2*x) + 2*E^x*x + x^2)]]]

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fricas [A]  time = 0.59, size = 31, normalized size = 1.03 \begin {gather*} x \log \left (-x + 3 \, \log \left (-e^{\left (x^{2} + 2 \, x e^{x} + e^{\left (2 \, x\right )}\right )} + e^{x} + \log \relax (5)\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3*log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))+3*exp(x))*log(log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))
+exp(x))-x*log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))-exp(x)*x)*log(3*log(log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)
))+exp(x))-x)-x*log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))+(-6*x*exp(x)^2+(-6*x^2-6*x)*exp(x)-6*x^2)*exp(exp(x)^
2+2*exp(x)*x+x^2)+2*exp(x)*x)/((3*log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))+3*exp(x))*log(log(5/exp(exp(exp(x)^
2+2*exp(x)*x+x^2)))+exp(x))-x*log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))-exp(x)*x),x, algorithm="fricas")

[Out]

x*log(-x + 3*log(-e^(x^2 + 2*x*e^x + e^(2*x)) + e^x + log(5)))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {6 \, {\left (x^{2} + x e^{\left (2 \, x\right )} + {\left (x^{2} + x\right )} e^{x}\right )} e^{\left (x^{2} + 2 \, x e^{x} + e^{\left (2 \, x\right )}\right )} - 2 \, x e^{x} + {\left (x e^{x} + x \log \left (5 \, e^{\left (-e^{\left (x^{2} + 2 \, x e^{x} + e^{\left (2 \, x\right )}\right )}\right )}\right ) - 3 \, {\left (e^{x} + \log \left (5 \, e^{\left (-e^{\left (x^{2} + 2 \, x e^{x} + e^{\left (2 \, x\right )}\right )}\right )}\right )\right )} \log \left (e^{x} + \log \left (5 \, e^{\left (-e^{\left (x^{2} + 2 \, x e^{x} + e^{\left (2 \, x\right )}\right )}\right )}\right )\right )\right )} \log \left (-x + 3 \, \log \left (e^{x} + \log \left (5 \, e^{\left (-e^{\left (x^{2} + 2 \, x e^{x} + e^{\left (2 \, x\right )}\right )}\right )}\right )\right )\right ) + x \log \left (5 \, e^{\left (-e^{\left (x^{2} + 2 \, x e^{x} + e^{\left (2 \, x\right )}\right )}\right )}\right )}{x e^{x} + x \log \left (5 \, e^{\left (-e^{\left (x^{2} + 2 \, x e^{x} + e^{\left (2 \, x\right )}\right )}\right )}\right ) - 3 \, {\left (e^{x} + \log \left (5 \, e^{\left (-e^{\left (x^{2} + 2 \, x e^{x} + e^{\left (2 \, x\right )}\right )}\right )}\right )\right )} \log \left (e^{x} + \log \left (5 \, e^{\left (-e^{\left (x^{2} + 2 \, x e^{x} + e^{\left (2 \, x\right )}\right )}\right )}\right )\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3*log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))+3*exp(x))*log(log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))
+exp(x))-x*log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))-exp(x)*x)*log(3*log(log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)
))+exp(x))-x)-x*log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))+(-6*x*exp(x)^2+(-6*x^2-6*x)*exp(x)-6*x^2)*exp(exp(x)^
2+2*exp(x)*x+x^2)+2*exp(x)*x)/((3*log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))+3*exp(x))*log(log(5/exp(exp(exp(x)^
2+2*exp(x)*x+x^2)))+exp(x))-x*log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))-exp(x)*x),x, algorithm="giac")

[Out]

integrate((6*(x^2 + x*e^(2*x) + (x^2 + x)*e^x)*e^(x^2 + 2*x*e^x + e^(2*x)) - 2*x*e^x + (x*e^x + x*log(5*e^(-e^
(x^2 + 2*x*e^x + e^(2*x)))) - 3*(e^x + log(5*e^(-e^(x^2 + 2*x*e^x + e^(2*x)))))*log(e^x + log(5*e^(-e^(x^2 + 2
*x*e^x + e^(2*x))))))*log(-x + 3*log(e^x + log(5*e^(-e^(x^2 + 2*x*e^x + e^(2*x)))))) + x*log(5*e^(-e^(x^2 + 2*
x*e^x + e^(2*x)))))/(x*e^x + x*log(5*e^(-e^(x^2 + 2*x*e^x + e^(2*x)))) - 3*(e^x + log(5*e^(-e^(x^2 + 2*x*e^x +
e^(2*x)))))*log(e^x + log(5*e^(-e^(x^2 + 2*x*e^x + e^(2*x)))))), x)

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maple [A]  time = 2.54, size = 34, normalized size = 1.13

method	result	size
risch	\(\ln \left (3 \ln \left (\ln \relax (5)-\ln \left ({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x} x +x^{2}}}\right )+{\mathrm e}^{x}\right )-x \right ) x\)	\(34\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((3*ln(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))+3*exp(x))*ln(ln(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))+exp(x))-
x*ln(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))-exp(x)*x)*ln(3*ln(ln(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))+exp(x))-x)
-x*ln(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))+(-6*x*exp(x)^2+(-6*x^2-6*x)*exp(x)-6*x^2)*exp(exp(x)^2+2*exp(x)*x+x
^2)+2*exp(x)*x)/((3*ln(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))+3*exp(x))*ln(ln(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)
))+exp(x))-x*ln(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))-exp(x)*x),x,method=_RETURNVERBOSE)

[Out]

ln(3*ln(ln(5)-ln(exp(exp(exp(2*x)+2*exp(x)*x+x^2)))+exp(x))-x)*x

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maxima [A]  time = 0.73, size = 31, normalized size = 1.03 \begin {gather*} x \log \left (-x + 3 \, \log \left (-e^{\left (x^{2} + 2 \, x e^{x} + e^{\left (2 \, x\right )}\right )} + e^{x} + \log \relax (5)\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3*log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))+3*exp(x))*log(log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))
+exp(x))-x*log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))-exp(x)*x)*log(3*log(log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)
))+exp(x))-x)-x*log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))+(-6*x*exp(x)^2+(-6*x^2-6*x)*exp(x)-6*x^2)*exp(exp(x)^
2+2*exp(x)*x+x^2)+2*exp(x)*x)/((3*log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))+3*exp(x))*log(log(5/exp(exp(exp(x)^
2+2*exp(x)*x+x^2)))+exp(x))-x*log(5/exp(exp(exp(x)^2+2*exp(x)*x+x^2)))-exp(x)*x),x, algorithm="maxima")

[Out]

x*log(-x + 3*log(-e^(x^2 + 2*x*e^x + e^(2*x)) + e^x + log(5)))

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mupad [B]  time = 4.74, size = 189, normalized size = 6.30 \begin {gather*} \frac {x\,\ln \relax (5)\,\ln \left (3\,\ln \left (\ln \relax (5)+{\mathrm {e}}^x-{\mathrm {e}}^{2\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}\right )-x\right )}{\ln \relax (5)+{\mathrm {e}}^x-{\mathrm {e}}^{2\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}}+\frac {x\,{\mathrm {e}}^x\,\ln \left (3\,\ln \left (\ln \relax (5)+{\mathrm {e}}^x-{\mathrm {e}}^{2\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}\right )-x\right )}{\ln \relax (5)+{\mathrm {e}}^x-{\mathrm {e}}^{2\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}}-\frac {x\,{\mathrm {e}}^{2\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}\,\ln \left (3\,\ln \left (\ln \relax (5)+{\mathrm {e}}^x-{\mathrm {e}}^{2\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}\right )-x\right )}{\ln \relax (5)+{\mathrm {e}}^x-{\mathrm {e}}^{2\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp(2*x) + 2*x*exp(x) + x^2)*(6*x*exp(2*x) + exp(x)*(6*x + 6*x^2) + 6*x^2) + log(3*log(log(5*exp(-exp
(exp(2*x) + 2*x*exp(x) + x^2))) + exp(x)) - x)*(x*exp(x) - log(log(5*exp(-exp(exp(2*x) + 2*x*exp(x) + x^2))) +
exp(x))*(3*log(5*exp(-exp(exp(2*x) + 2*x*exp(x) + x^2))) + 3*exp(x)) + x*log(5*exp(-exp(exp(2*x) + 2*x*exp(x)
+ x^2)))) - 2*x*exp(x) + x*log(5*exp(-exp(exp(2*x) + 2*x*exp(x) + x^2))))/(x*exp(x) - log(log(5*exp(-exp(exp(
2*x) + 2*x*exp(x) + x^2))) + exp(x))*(3*log(5*exp(-exp(exp(2*x) + 2*x*exp(x) + x^2))) + 3*exp(x)) + x*log(5*ex
p(-exp(exp(2*x) + 2*x*exp(x) + x^2)))),x)

[Out]

(x*log(5)*log(3*log(log(5) + exp(x) - exp(2*x*exp(x))*exp(x^2)*exp(exp(2*x))) - x))/(log(5) + exp(x) - exp(2*x
*exp(x))*exp(x^2)*exp(exp(2*x))) + (x*exp(x)*log(3*log(log(5) + exp(x) - exp(2*x*exp(x))*exp(x^2)*exp(exp(2*x)
)) - x))/(log(5) + exp(x) - exp(2*x*exp(x))*exp(x^2)*exp(exp(2*x))) - (x*exp(2*x*exp(x))*exp(x^2)*exp(exp(2*x)
)*log(3*log(log(5) + exp(x) - exp(2*x*exp(x))*exp(x^2)*exp(exp(2*x))) - x))/(log(5) + exp(x) - exp(2*x*exp(x))
*exp(x^2)*exp(exp(2*x)))

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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((((3*ln(5/exp(exp(exp(x)**2+2*exp(x)*x+x**2)))+3*exp(x))*ln(ln(5/exp(exp(exp(x)**2+2*exp(x)*x+x**2))
)+exp(x))-x*ln(5/exp(exp(exp(x)**2+2*exp(x)*x+x**2)))-exp(x)*x)*ln(3*ln(ln(5/exp(exp(exp(x)**2+2*exp(x)*x+x**2
)))+exp(x))-x)-x*ln(5/exp(exp(exp(x)**2+2*exp(x)*x+x**2)))+(-6*x*exp(x)**2+(-6*x**2-6*x)*exp(x)-6*x**2)*exp(ex
p(x)**2+2*exp(x)*x+x**2)+2*exp(x)*x)/((3*ln(5/exp(exp(exp(x)**2+2*exp(x)*x+x**2)))+3*exp(x))*ln(ln(5/exp(exp(e
xp(x)**2+2*exp(x)*x+x**2)))+exp(x))-x*ln(5/exp(exp(exp(x)**2+2*exp(x)*x+x**2)))-exp(x)*x),x)

[Out]

Timed out

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