3.16.83 \(\int \frac {1}{-1-e+\log (\log (5))} \, dx\)

Optimal. Leaf size=18 \[ -3+\frac {2-x}{1+e-\log (\log (5))} \]

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Rubi [A]  time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.72, number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {8} \begin {gather*} -\frac {x}{1+e-\log (\log (5))} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-1 - E + Log[Log[5]])^(-1),x]

[Out]

-(x/(1 + E - Log[Log[5]]))

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {x}{1+e-\log (\log (5))}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 0.67 \begin {gather*} \frac {x}{-1-e+\log (\log (5))} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1 - E + Log[Log[5]])^(-1),x]

[Out]

x/(-1 - E + Log[Log[5]])

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fricas [A]  time = 0.78, size = 14, normalized size = 0.78 \begin {gather*} -\frac {x}{e - \log \left (\log \relax (5)\right ) + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(log(log(5))-exp(1)-1),x, algorithm="fricas")

[Out]

-x/(e - log(log(5)) + 1)

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giac [A]  time = 0.21, size = 14, normalized size = 0.78 \begin {gather*} -\frac {x}{e - \log \left (\log \relax (5)\right ) + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(log(log(5))-exp(1)-1),x, algorithm="giac")

[Out]

-x/(e - log(log(5)) + 1)

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maple [A]  time = 0.02, size = 14, normalized size = 0.78

method	result	size
default	\(\frac {x}{\ln \left (\ln \relax (5)\right )-{\mathrm e}-1}\)	\(14\)
risch	\(\frac {x}{\ln \left (\ln \relax (5)\right )-{\mathrm e}-1}\)	\(14\)
norman	\(-\frac {x}{{\mathrm e}+1-\ln \left (\ln \relax (5)\right )}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(ln(ln(5))-exp(1)-1),x,method=_RETURNVERBOSE)

[Out]

1/(ln(ln(5))-exp(1)-1)*x

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maxima [A]  time = 0.41, size = 14, normalized size = 0.78 \begin {gather*} -\frac {x}{e - \log \left (\log \relax (5)\right ) + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(log(log(5))-exp(1)-1),x, algorithm="maxima")

[Out]

-x/(e - log(log(5)) + 1)

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mupad [B]  time = 0.00, size = 14, normalized size = 0.78 \begin {gather*} -\frac {x}{\mathrm {e}-\ln \left (\ln \relax (5)\right )+1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/(exp(1) - log(log(5)) + 1),x)

[Out]

-x/(exp(1) - log(log(5)) + 1)

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sympy [A]  time = 0.05, size = 10, normalized size = 0.56 \begin {gather*} \frac {x}{- e - 1 + \log {\left (\log {\relax (5 )} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(ln(ln(5))-exp(1)-1),x)

[Out]

x/(-E - 1 + log(log(5)))

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