3.79.61 \(\int \frac {-1+\log (x) \log (\log (x))-8 \log (x) \log ^2(\log (x))}{\log (x) \log ^2(\log (x))} \, dx\)

Optimal. Leaf size=11 \[ -8 x+\frac {x}{\log (\log (x))} \]

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Rubi [F]  time = 0.09, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-1+\log (x) \log (\log (x))-8 \log (x) \log ^2(\log (x))}{\log (x) \log ^2(\log (x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-1 + Log[x]*Log[Log[x]] - 8*Log[x]*Log[Log[x]]^2)/(Log[x]*Log[Log[x]]^2),x]

[Out]

-8*x - Defer[Int][1/(Log[x]*Log[Log[x]]^2), x] + Defer[Int][Log[Log[x]]^(-1), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-8-\frac {1}{\log (x) \log ^2(\log (x))}+\frac {1}{\log (\log (x))}\right ) \, dx\\ &=-8 x-\int \frac {1}{\log (x) \log ^2(\log (x))} \, dx+\int \frac {1}{\log (\log (x))} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.04, size = 11, normalized size = 1.00 \begin {gather*} -8 x+\frac {x}{\log (\log (x))} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1 + Log[x]*Log[Log[x]] - 8*Log[x]*Log[Log[x]]^2)/(Log[x]*Log[Log[x]]^2),x]

[Out]

-8*x + x/Log[Log[x]]

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fricas [A]  time = 0.70, size = 17, normalized size = 1.55 \begin {gather*} -\frac {8 \, x \log \left (\log \relax (x)\right ) - x}{\log \left (\log \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-8*log(x)*log(log(x))^2+log(x)*log(log(x))-1)/log(x)/log(log(x))^2,x, algorithm="fricas")

[Out]

-(8*x*log(log(x)) - x)/log(log(x))

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giac [A]  time = 0.17, size = 11, normalized size = 1.00 \begin {gather*} -8 \, x + \frac {x}{\log \left (\log \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-8*log(x)*log(log(x))^2+log(x)*log(log(x))-1)/log(x)/log(log(x))^2,x, algorithm="giac")

[Out]

-8*x + x/log(log(x))

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maple [A]  time = 0.02, size = 12, normalized size = 1.09

method	result	size
risch	\(\frac {x}{\ln \left (\ln \relax (x )\right )}-8 x\)	\(12\)
norman	\(\frac {x -8 x \ln \left (\ln \relax (x )\right )}{\ln \left (\ln \relax (x )\right )}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-8*ln(x)*ln(ln(x))^2+ln(x)*ln(ln(x))-1)/ln(x)/ln(ln(x))^2,x,method=_RETURNVERBOSE)

[Out]

x/ln(ln(x))-8*x

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maxima [A]  time = 0.40, size = 11, normalized size = 1.00 \begin {gather*} -8 \, x + \frac {x}{\log \left (\log \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-8*log(x)*log(log(x))^2+log(x)*log(log(x))-1)/log(x)/log(log(x))^2,x, algorithm="maxima")

[Out]

-8*x + x/log(log(x))

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mupad [B]  time = 7.28, size = 11, normalized size = 1.00 \begin {gather*} \frac {x}{\ln \left (\ln \relax (x)\right )}-8\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(8*log(log(x))^2*log(x) - log(log(x))*log(x) + 1)/(log(log(x))^2*log(x)),x)

[Out]

x/log(log(x)) - 8*x

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sympy [A]  time = 0.23, size = 8, normalized size = 0.73 \begin {gather*} - 8 x + \frac {x}{\log {\left (\log {\relax (x )} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-8*ln(x)*ln(ln(x))**2+ln(x)*ln(ln(x))-1)/ln(x)/ln(ln(x))**2,x)

[Out]

-8*x + x/log(log(x))

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