3.36.54 \(\int \frac {640+2 e^{2 e^{e^x}+e^x+x}}{-256+e^{2 e^{e^x}}+640 x} \, dx\)

Optimal. Leaf size=20 \[ \log \left (5 \left (e^{2 e^{e^x}}-64 (4-10 x)\right )\right ) \]

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Rubi [A]  time = 0.07, antiderivative size = 17, normalized size of antiderivative = 0.85, number of steps used = 1, number of rules used = 1, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {6684} \begin {gather*} \log \left (-640 x-e^{2 e^{e^x}}+256\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(640 + 2*E^(2*E^E^x + E^x + x))/(-256 + E^(2*E^E^x) + 640*x),x]

[Out]

Log[256 - E^(2*E^E^x) - 640*x]

Rule 6684

Int[(u_)/(y_), x_Symbol] :> With[{q = DerivativeDivides[y, u, x]}, Simp[q*Log[RemoveContent[y, x]], x] /;  !Fa
lseQ[q]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\log \left (256-e^{2 e^{e^x}}-640 x\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.22, size = 17, normalized size = 0.85 \begin {gather*} \log \left (256-e^{2 e^{e^x}}-640 x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(640 + 2*E^(2*E^E^x + E^x + x))/(-256 + E^(2*E^E^x) + 640*x),x]

[Out]

Log[256 - E^(2*E^E^x) - 640*x]

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fricas [B]  time = 0.53, size = 32, normalized size = 1.60 \begin {gather*} -x - e^{x} + \log \left (128 \, {\left (5 \, x - 2\right )} e^{\left (x + e^{x}\right )} + e^{\left (x + e^{x} + 2 \, e^{\left (e^{x}\right )}\right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(x)*exp(exp(x))*exp(2*exp(exp(x)))+640)/(exp(2*exp(exp(x)))+640*x-256),x, algorithm="fricas")

[Out]

-x - e^x + log(128*(5*x - 2)*e^(x + e^x) + e^(x + e^x + 2*e^(e^x)))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, {\left (e^{\left (x + e^{x} + 2 \, e^{\left (e^{x}\right )}\right )} + 320\right )}}{640 \, x + e^{\left (2 \, e^{\left (e^{x}\right )}\right )} - 256}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(x)*exp(exp(x))*exp(2*exp(exp(x)))+640)/(exp(2*exp(exp(x)))+640*x-256),x, algorithm="giac")

[Out]

integrate(2*(e^(x + e^x + 2*e^(e^x)) + 320)/(640*x + e^(2*e^(e^x)) - 256), x)

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maple [A]  time = 0.10, size = 13, normalized size = 0.65

method	result	size
derivativedivides	\(\ln \left ({\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{x}}}+640 x -256\right )\)	\(13\)
norman	\(\ln \left ({\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{x}}}+640 x -256\right )\)	\(13\)
risch	\(\ln \left ({\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{x}}}+640 x -256\right )\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*exp(x)*exp(exp(x))*exp(2*exp(exp(x)))+640)/(exp(2*exp(exp(x)))+640*x-256),x,method=_RETURNVERBOSE)

[Out]

ln(exp(2*exp(exp(x)))+640*x-256)

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maxima [A]  time = 0.59, size = 12, normalized size = 0.60 \begin {gather*} \log \left (640 \, x + e^{\left (2 \, e^{\left (e^{x}\right )}\right )} - 256\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(x)*exp(exp(x))*exp(2*exp(exp(x)))+640)/(exp(2*exp(exp(x)))+640*x-256),x, algorithm="maxima")

[Out]

log(640*x + e^(2*e^(e^x)) - 256)

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mupad [B]  time = 0.14, size = 12, normalized size = 0.60 \begin {gather*} \ln \left (640\,x+{\mathrm {e}}^{2\,{\mathrm {e}}^{{\mathrm {e}}^x}}-256\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*exp(2*exp(exp(x)))*exp(exp(x))*exp(x) + 640)/(640*x + exp(2*exp(exp(x))) - 256),x)

[Out]

log(640*x + exp(2*exp(exp(x))) - 256)

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sympy [A]  time = 0.19, size = 14, normalized size = 0.70 \begin {gather*} \log {\left (640 x + e^{2 e^{e^{x}}} - 256 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(x)*exp(exp(x))*exp(2*exp(exp(x)))+640)/(exp(2*exp(exp(x)))+640*x-256),x)

[Out]

log(640*x + exp(2*exp(exp(x))) - 256)

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