3.91.33 \(\int \frac {e^{2 e^{2 x}-4 e^x \log (-e^{e^x}+\log (4))+2 \log ^2(-e^{e^x}+\log (4))} (-100 e^{2 x} \log (4)+100 e^x \log (4) \log (-e^{e^x}+\log (4)))}{e^{e^x}-\log (4)} \, dx\)

Optimal. Leaf size=25 \[ 25 e^{2 \left (-e^x+\log \left (-e^{e^x}+\log (4)\right )\right )^2} \]

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Rubi [F]  time = 1.01, 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 {\exp \left (2 e^{2 x}-4 e^x \log \left (-e^{e^x}+\log (4)\right )+2 \log ^2\left (-e^{e^x}+\log (4)\right )\right ) \left (-100 e^{2 x} \log (4)+100 e^x \log (4) \log \left (-e^{e^x}+\log (4)\right )\right )}{e^{e^x}-\log (4)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(2*E^(2*x) - 4*E^x*Log[-E^E^x + Log[4]] + 2*Log[-E^E^x + Log[4]]^2)*(-100*E^(2*x)*Log[4] + 100*E^x*Log[
4]*Log[-E^E^x + Log[4]]))/(E^E^x - Log[4]),x]

[Out]

100*Log[4]*Defer[Subst][Defer[Int][E^(2*(x^2 + Log[-E^x + Log[4]]^2))*x*(-E^x + Log[4])^(-1 - 4*x), x], x, E^x
] - 100*Log[4]*Defer[Subst][Defer[Int][E^(2*(x^2 + Log[-E^x + Log[4]]^2))*(-E^x + Log[4])^(-1 - 4*x)*Log[-E^x
+ Log[4]], x], x, E^x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\operatorname {Subst}\left (\int 100 e^{2 \left (x^2+\log ^2\left (-e^x+\log (4)\right )\right )} \log (4) \left (-e^x+\log (4)\right )^{-1-4 x} \left (x-\log \left (-e^x+\log (4)\right )\right ) \, dx,x,e^x\right )\\ &=(100 \log (4)) \operatorname {Subst}\left (\int e^{2 \left (x^2+\log ^2\left (-e^x+\log (4)\right )\right )} \left (-e^x+\log (4)\right )^{-1-4 x} \left (x-\log \left (-e^x+\log (4)\right )\right ) \, dx,x,e^x\right )\\ &=(100 \log (4)) \operatorname {Subst}\left (\int \left (e^{2 \left (x^2+\log ^2\left (-e^x+\log (4)\right )\right )} x \left (-e^x+\log (4)\right )^{-1-4 x}-e^{2 \left (x^2+\log ^2\left (-e^x+\log (4)\right )\right )} \left (-e^x+\log (4)\right )^{-1-4 x} \log \left (-e^x+\log (4)\right )\right ) \, dx,x,e^x\right )\\ &=(100 \log (4)) \operatorname {Subst}\left (\int e^{2 \left (x^2+\log ^2\left (-e^x+\log (4)\right )\right )} x \left (-e^x+\log (4)\right )^{-1-4 x} \, dx,x,e^x\right )-(100 \log (4)) \operatorname {Subst}\left (\int e^{2 \left (x^2+\log ^2\left (-e^x+\log (4)\right )\right )} \left (-e^x+\log (4)\right )^{-1-4 x} \log \left (-e^x+\log (4)\right ) \, dx,x,e^x\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.30, size = 43, normalized size = 1.72 \begin {gather*} 25 e^{2 e^{2 x}+2 \log ^2\left (-e^{e^x}+\log (4)\right )} \left (-e^{e^x}+\log (4)\right )^{-4 e^x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(2*E^(2*x) - 4*E^x*Log[-E^E^x + Log[4]] + 2*Log[-E^E^x + Log[4]]^2)*(-100*E^(2*x)*Log[4] + 100*E^
x*Log[4]*Log[-E^E^x + Log[4]]))/(E^E^x - Log[4]),x]

[Out]

(25*E^(2*E^(2*x) + 2*Log[-E^E^x + Log[4]]^2))/(-E^E^x + Log[4])^(4*E^x)

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fricas [A]  time = 1.00, size = 40, normalized size = 1.60 \begin {gather*} 25 \, e^{\left (-4 \, e^{x} \log \left (-e^{\left (e^{x}\right )} + 2 \, \log \relax (2)\right ) + 2 \, \log \left (-e^{\left (e^{x}\right )} + 2 \, \log \relax (2)\right )^{2} + 2 \, e^{\left (2 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((200*log(2)*exp(x)*log(-exp(exp(x))+2*log(2))-200*log(2)*exp(x)^2)*exp(log(-exp(exp(x))+2*log(2))^2-
2*exp(x)*log(-exp(exp(x))+2*log(2))+exp(x)^2)^2/(exp(exp(x))-2*log(2)),x, algorithm="fricas")

[Out]

25*e^(-4*e^x*log(-e^(e^x) + 2*log(2)) + 2*log(-e^(e^x) + 2*log(2))^2 + 2*e^(2*x))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {200 \, {\left (e^{x} \log \relax (2) \log \left (-e^{\left (e^{x}\right )} + 2 \, \log \relax (2)\right ) - e^{\left (2 \, x\right )} \log \relax (2)\right )} e^{\left (-4 \, e^{x} \log \left (-e^{\left (e^{x}\right )} + 2 \, \log \relax (2)\right ) + 2 \, \log \left (-e^{\left (e^{x}\right )} + 2 \, \log \relax (2)\right )^{2} + 2 \, e^{\left (2 \, x\right )}\right )}}{e^{\left (e^{x}\right )} - 2 \, \log \relax (2)}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((200*log(2)*exp(x)*log(-exp(exp(x))+2*log(2))-200*log(2)*exp(x)^2)*exp(log(-exp(exp(x))+2*log(2))^2-
2*exp(x)*log(-exp(exp(x))+2*log(2))+exp(x)^2)^2/(exp(exp(x))-2*log(2)),x, algorithm="giac")

[Out]

integrate(200*(e^x*log(2)*log(-e^(e^x) + 2*log(2)) - e^(2*x)*log(2))*e^(-4*e^x*log(-e^(e^x) + 2*log(2)) + 2*lo
g(-e^(e^x) + 2*log(2))^2 + 2*e^(2*x))/(e^(e^x) - 2*log(2)), x)

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maple [A]  time = 0.14, size = 43, normalized size = 1.72

method	result	size
risch	\(25 \left (-{\mathrm e}^{{\mathrm e}^{x}}+2 \ln \relax (2)\right )^{-4 \,{\mathrm e}^{x}} {\mathrm e}^{2 \ln \left (-{\mathrm e}^{{\mathrm e}^{x}}+2 \ln \relax (2)\right )^{2}+2 \,{\mathrm e}^{2 x}}\)	\(43\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((200*ln(2)*exp(x)*ln(-exp(exp(x))+2*ln(2))-200*ln(2)*exp(x)^2)*exp(ln(-exp(exp(x))+2*ln(2))^2-2*exp(x)*ln(
-exp(exp(x))+2*ln(2))+exp(x)^2)^2/(exp(exp(x))-2*ln(2)),x,method=_RETURNVERBOSE)

[Out]

25*((-exp(exp(x))+2*ln(2))^(-2*exp(x)))^2*exp(2*ln(-exp(exp(x))+2*ln(2))^2+2*exp(2*x))

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maxima [A]  time = 0.56, size = 40, normalized size = 1.60 \begin {gather*} 25 \, e^{\left (-4 \, e^{x} \log \left (-e^{\left (e^{x}\right )} + 2 \, \log \relax (2)\right ) + 2 \, \log \left (-e^{\left (e^{x}\right )} + 2 \, \log \relax (2)\right )^{2} + 2 \, e^{\left (2 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((200*log(2)*exp(x)*log(-exp(exp(x))+2*log(2))-200*log(2)*exp(x)^2)*exp(log(-exp(exp(x))+2*log(2))^2-
2*exp(x)*log(-exp(exp(x))+2*log(2))+exp(x)^2)^2/(exp(exp(x))-2*log(2)),x, algorithm="maxima")

[Out]

25*e^(-4*e^x*log(-e^(e^x) + 2*log(2)) + 2*log(-e^(e^x) + 2*log(2))^2 + 2*e^(2*x))

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mupad [B]  time = 6.34, size = 40, normalized size = 1.60 \begin {gather*} \frac {25\,{\mathrm {e}}^{2\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{2\,{\ln \left (\ln \relax (4)-{\mathrm {e}}^{{\mathrm {e}}^x}\right )}^2}}{{\left (2\,\ln \relax (2)-{\mathrm {e}}^{{\mathrm {e}}^x}\right )}^{4\,{\mathrm {e}}^x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(2*exp(2*x) - 4*log(2*log(2) - exp(exp(x)))*exp(x) + 2*log(2*log(2) - exp(exp(x)))^2)*(200*exp(2*x)*l
og(2) - 200*log(2*log(2) - exp(exp(x)))*exp(x)*log(2)))/(exp(exp(x)) - 2*log(2)),x)

[Out]

(25*exp(2*exp(2*x))*exp(2*log(log(4) - exp(exp(x)))^2))/(2*log(2) - exp(exp(x)))^(4*exp(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((200*ln(2)*exp(x)*ln(-exp(exp(x))+2*ln(2))-200*ln(2)*exp(x)**2)*exp(ln(-exp(exp(x))+2*ln(2))**2-2*ex
p(x)*ln(-exp(exp(x))+2*ln(2))+exp(x)**2)**2/(exp(exp(x))-2*ln(2)),x)

[Out]

Timed out

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