3.38.39 \(\int \frac {1}{\log (\log (3))} \, dx\) [3739]

Optimal. Leaf size=9 \[ 3+\frac {x}{\log (\log (3))} \]

[Out]

x/ln(ln(3))+3

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Rubi [A]
time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.78, number of steps used = 1, number of rules used = 1, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {8} \begin {gather*} \frac {x}{\log (\log (3))} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[Log[Log[3]]^(-1),x]

[Out]

x/Log[Log[3]]

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {x}{\log (\log (3))}\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 7, normalized size = 0.78 \begin {gather*} \frac {x}{\log (\log (3))} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[Log[Log[3]]^(-1),x]

[Out]

x/Log[Log[3]]

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Maple [A]
time = 0.19, size = 8, normalized size = 0.89

method	result	size
default	\(\frac {x}{\ln \left (\ln \left (3\right )\right )}\)	\(8\)
norman	\(\frac {x}{\ln \left (\ln \left (3\right )\right )}\)	\(8\)
risch	\(\frac {x}{\ln \left (\ln \left (3\right )\right )}\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/ln(ln(3)),x,method=_RETURNVERBOSE)

[Out]

x/ln(ln(3))

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Maxima [A]
time = 0.27, size = 7, normalized size = 0.78 \begin {gather*} \frac {x}{\log \left (\log \left (3\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/log(log(3)),x, algorithm="maxima")

[Out]

x/log(log(3))

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Fricas [A]
time = 0.35, size = 7, normalized size = 0.78 \begin {gather*} \frac {x}{\log \left (\log \left (3\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/log(log(3)),x, algorithm="fricas")

[Out]

x/log(log(3))

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Sympy [A]
time = 0.00, size = 5, normalized size = 0.56 \begin {gather*} \frac {x}{\log {\left (\log {\left (3 \right )} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/ln(ln(3)),x)

[Out]

x/log(log(3))

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Giac [A]
time = 0.37, size = 7, normalized size = 0.78 \begin {gather*} \frac {x}{\log \left (\log \left (3\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/log(log(3)),x, algorithm="giac")

[Out]

x/log(log(3))

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Mupad [B]
time = 0.00, size = 7, normalized size = 0.78 \begin {gather*} \frac {x}{\ln \left (\ln \left (3\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/log(log(3)),x)

[Out]

x/log(log(3))

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