3.53.91 \(\int \frac {1+3 \log (\log (3))}{\log (\log (3))} \, dx\)

Optimal. Leaf size=12 \[ -9+3 x+\frac {x}{\log (\log (3))} \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.75, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {8} \begin {gather*} x \left (3+\frac {1}{\log (\log (3))}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 + 3*Log[Log[3]])/Log[Log[3]],x]

[Out]

x*(3 + Log[Log[3]]^(-1))

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x \left (3+\frac {1}{\log (\log (3))}\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.92 \begin {gather*} 3 x+\frac {x}{\log (\log (3))} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 + 3*Log[Log[3]])/Log[Log[3]],x]

[Out]

3*x + x/Log[Log[3]]

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fricas [A]  time = 0.71, size = 14, normalized size = 1.17 \begin {gather*} \frac {3 \, x \log \left (\log \relax (3)\right ) + x}{\log \left (\log \relax (3)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(3*x*log(log(3)) + x)/log(log(3))

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giac [A]  time = 0.22, size = 14, normalized size = 1.17 \begin {gather*} \frac {x {\left (3 \, \log \left (\log \relax (3)\right ) + 1\right )}}{\log \left (\log \relax (3)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*(3*log(log(3)) + 1)/log(log(3))

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maple [A]  time = 0.01, size = 12, normalized size = 1.00

method	result	size
risch	\(3 x +\frac {x}{\ln \left (\ln \relax (3)\right )}\)	\(12\)
default	\(\frac {\left (3 \ln \left (\ln \relax (3)\right )+1\right ) x}{\ln \left (\ln \relax (3)\right )}\)	\(15\)
norman	\(\frac {\left (3 \ln \left (\ln \relax (3)\right )+1\right ) x}{\ln \left (\ln \relax (3)\right )}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3*x+x/ln(ln(3))

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maxima [A]  time = 0.37, size = 14, normalized size = 1.17 \begin {gather*} \frac {x {\left (3 \, \log \left (\log \relax (3)\right ) + 1\right )}}{\log \left (\log \relax (3)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*(3*log(log(3)) + 1)/log(log(3))

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mupad [B]  time = 0.00, size = 14, normalized size = 1.17 \begin {gather*} \frac {x\,\left (3\,\ln \left (\ln \relax (3)\right )+1\right )}{\ln \left (\ln \relax (3)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(x*(3*log(log(3)) + 1))/log(log(3))

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sympy [A]  time = 0.06, size = 14, normalized size = 1.17 \begin {gather*} \frac {x \left (3 \log {\left (\log {\relax (3 )} \right )} + 1\right )}{\log {\left (\log {\relax (3 )} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*(3*log(log(3)) + 1)/log(log(3))

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