3.94.34 \(\int \frac {5-5 e^x}{(e^x-x) \log (-e^x+x) \log (\log (-e^x+x))} \, dx\) [9334]

Optimal. Leaf size=16 \[ 5 \log \left (-\frac {10}{\log \left (\log \left (-e^x+x\right )\right )}\right ) \]

[Out]

5*ln(-10/ln(ln(x-exp(x))))

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Rubi [A]
time = 0.14, antiderivative size = 12, normalized size of antiderivative = 0.75, number of steps used = 1, number of rules used = 1, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6816} \begin {gather*} -5 \log \left (\log \left (\log \left (x-e^x\right )\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-5*Log[Log[Log[-E^x + x]]]

Rule 6816

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} &=-5 \log \left (\log \left (\log \left (-e^x+x\right )\right )\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.06, size = 12, normalized size = 0.75 \begin {gather*} -5 \log \left (\log \left (\log \left (-e^x+x\right )\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-5*Log[Log[Log[-E^x + x]]]

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Maple [A]
time = 0.13, size = 12, normalized size = 0.75

method	result	size
risch	\(-5 \ln \left (\ln \left (\ln \left (x -{\mathrm e}^{x}\right )\right )\right )\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-5*ln(ln(ln(x-exp(x))))

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Maxima [A]
time = 0.30, size = 11, normalized size = 0.69 \begin {gather*} -5 \, \log \left (\log \left (\log \left (x - e^{x}\right )\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-5*log(log(log(x - e^x)))

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Fricas [A]
time = 0.48, size = 11, normalized size = 0.69 \begin {gather*} -5 \, \log \left (\log \left (\log \left (x - e^{x}\right )\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-5*log(log(log(x - e^x)))

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Sympy [A]
time = 0.31, size = 12, normalized size = 0.75 \begin {gather*} - 5 \log {\left (\log {\left (\log {\left (x - e^{x} \right )} \right )} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-5*log(log(log(x - exp(x))))

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Giac [A]
time = 0.42, size = 11, normalized size = 0.69 \begin {gather*} -5 \, \log \left (\log \left (\log \left (x - e^{x}\right )\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-5*log(log(log(x - e^x)))

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Mupad [B]
time = 7.57, size = 11, normalized size = 0.69 \begin {gather*} -5\,\ln \left (\ln \left (\ln \left (x-{\mathrm {e}}^x\right )\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((5*exp(x) - 5)/(log(x - exp(x))*log(log(x - exp(x)))*(x - exp(x))),x)

[Out]

-5*log(log(log(x - exp(x))))

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