3.79.78 \(\int -\frac {1}{4-4 x+4 \log (\log (4))} \, dx\)

Optimal. Leaf size=15 \[ \frac {1}{4} (-5+\log (-1+x-\log (\log (4)))) \]

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.87, number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {31} \begin {gather*} \frac {1}{4} \log (-x+1+\log (\log (4))) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-(4 - 4*x + 4*Log[Log[4]])^(-1),x]

[Out]

Log[1 - x + Log[Log[4]]]/4

Rule 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \log (1-x+\log (\log (4)))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} \frac {1}{4} \log (4-4 x+4 \log (\log (4))) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-(4 - 4*x + 4*Log[Log[4]])^(-1),x]

[Out]

Log[4 - 4*x + 4*Log[Log[4]]]/4

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fricas [A]  time = 0.67, size = 13, normalized size = 0.87 \begin {gather*} \frac {1}{4} \, \log \left (x - \log \left (2 \, \log \relax (2)\right ) - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/(4*log(2*log(2))-4*x+4),x, algorithm="fricas")

[Out]

1/4*log(x - log(2*log(2)) - 1)

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giac [A]  time = 0.22, size = 14, normalized size = 0.93 \begin {gather*} \frac {1}{4} \, \log \left ({\left | x - \log \left (2 \, \log \relax (2)\right ) - 1 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/(4*log(2*log(2))-4*x+4),x, algorithm="giac")

[Out]

1/4*log(abs(x - log(2*log(2)) - 1))

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maple [A]  time = 0.26, size = 14, normalized size = 0.93

method	result	size
default	\(\frac {\ln \left (\ln \left (2 \ln \relax (2)\right )-x +1\right )}{4}\)	\(14\)
norman	\(\frac {\ln \left (4 \ln \left (2 \ln \relax (2)\right )-4 x +4\right )}{4}\)	\(16\)
risch	\(\frac {\ln \left (-\ln \relax (2)-\ln \left (\ln \relax (2)\right )+x -1\right )}{4}\)	\(16\)
meijerg	\(-\frac {\left (-\ln \left (2 \ln \relax (2)\right )-1\right ) \ln \left (1-\frac {x}{\ln \left (2 \ln \relax (2)\right )+1}\right )}{4 \ln \left (2 \ln \relax (2)\right )+4}\)	\(38\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/(4*ln(2*ln(2))-4*x+4),x,method=_RETURNVERBOSE)

[Out]

1/4*ln(ln(2*ln(2))-x+1)

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maxima [A]  time = 0.35, size = 13, normalized size = 0.87 \begin {gather*} \frac {1}{4} \, \log \left (x - \log \left (2 \, \log \relax (2)\right ) - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/(4*log(2*log(2))-4*x+4),x, algorithm="maxima")

[Out]

1/4*log(x - log(2*log(2)) - 1)

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mupad [B]  time = 7.53, size = 13, normalized size = 0.87 \begin {gather*} \frac {\ln \left (x-\ln \left (2\,\ln \relax (2)\right )-1\right )}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/(4*log(2*log(2)) - 4*x + 4),x)

[Out]

log(x - log(2*log(2)) - 1)/4

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sympy [A]  time = 0.07, size = 19, normalized size = 1.27 \begin {gather*} \frac {\log {\left (4 x - 4 - 4 \log {\relax (2 )} - 4 \log {\left (\log {\relax (2 )} \right )} \right )}}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/(4*ln(2*ln(2))-4*x+4),x)

[Out]

log(4*x - 4 - 4*log(2) - 4*log(log(2)))/4

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