3.93.91 \(\int \frac {-3+\log (\frac {x^3}{3+\log (21)}) \log (\log (\frac {x^3}{3+\log (21)}))}{\log (\frac {x^3}{3+\log (21)}) \log ^2(\log (\frac {x^3}{3+\log (21)}))} \, dx\)

Optimal. Leaf size=18 \[ 25+\frac {x}{\log \left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )} \]

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Rubi [F]  time = 0.14, 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 {-3+\log \left (\frac {x^3}{3+\log (21)}\right ) \log \left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )}{\log \left (\frac {x^3}{3+\log (21)}\right ) \log ^2\left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-3 + Log[x^3/(3 + Log[21])]*Log[Log[x^3/(3 + Log[21])]])/(Log[x^3/(3 + Log[21])]*Log[Log[x^3/(3 + Log[21]
)]]^2),x]

[Out]

-3*Defer[Int][1/(Log[x^3/(3 + Log[21])]*Log[Log[x^3/(3 + Log[21])]]^2), x] + Defer[Int][Log[Log[x^3/(3 + Log[2
1])]]^(-1), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-\frac {3}{\log \left (\frac {x^3}{3+\log (21)}\right )}+\log \left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )}{\log ^2\left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )} \, dx\\ &=\int \left (-\frac {3}{\log \left (\frac {x^3}{3+\log (21)}\right ) \log ^2\left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )}+\frac {1}{\log \left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )}\right ) \, dx\\ &=-\left (3 \int \frac {1}{\log \left (\frac {x^3}{3+\log (21)}\right ) \log ^2\left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )} \, dx\right )+\int \frac {1}{\log \left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.05, size = 16, normalized size = 0.89 \begin {gather*} \frac {x}{\log \left (\log \left (\frac {x^3}{3+\log (21)}\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-3 + Log[x^3/(3 + Log[21])]*Log[Log[x^3/(3 + Log[21])]])/(Log[x^3/(3 + Log[21])]*Log[Log[x^3/(3 + L
og[21])]]^2),x]

[Out]

x/Log[Log[x^3/(3 + Log[21])]]

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fricas [A]  time = 0.75, size = 16, normalized size = 0.89 \begin {gather*} \frac {x}{\log \left (\log \left (\frac {x^{3}}{\log \left (21\right ) + 3}\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(x^3/(log(21)+3))*log(log(x^3/(log(21)+3)))-3)/log(x^3/(log(21)+3))/log(log(x^3/(log(21)+3)))^2,
x, algorithm="fricas")

[Out]

x/log(log(x^3/(log(21) + 3)))

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giac [B]  time = 0.18, size = 44, normalized size = 2.44 \begin {gather*} \frac {x \log \left (x^{3}\right ) - x \log \left (\log \left (21\right ) + 3\right )}{\log \left (\frac {x^{3}}{\log \left (21\right ) + 3}\right ) \log \left (\log \left (x^{3}\right ) - \log \left (\log \left (21\right ) + 3\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(x^3/(log(21)+3))*log(log(x^3/(log(21)+3)))-3)/log(x^3/(log(21)+3))/log(log(x^3/(log(21)+3)))^2,
x, algorithm="giac")

[Out]

(x*log(x^3) - x*log(log(21) + 3))/(log(x^3/(log(21) + 3))*log(log(x^3) - log(log(21) + 3)))

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maple [A]  time = 0.04, size = 17, normalized size = 0.94

method	result	size
norman	\(\frac {x}{\ln \left (\ln \left (\frac {x^{3}}{\ln \left (21\right )+3}\right )\right )}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((ln(x^3/(ln(21)+3))*ln(ln(x^3/(ln(21)+3)))-3)/ln(x^3/(ln(21)+3))/ln(ln(x^3/(ln(21)+3)))^2,x,method=_RETURN
VERBOSE)

[Out]

x/ln(ln(x^3/(ln(21)+3)))

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maxima [A]  time = 0.47, size = 19, normalized size = 1.06 \begin {gather*} \frac {x}{\log \left (3 \, \log \relax (x) - \log \left (\log \relax (7) + \log \relax (3) + 3\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(x^3/(log(21)+3))*log(log(x^3/(log(21)+3)))-3)/log(x^3/(log(21)+3))/log(log(x^3/(log(21)+3)))^2,
x, algorithm="maxima")

[Out]

x/log(3*log(x) - log(log(7) + log(3) + 3))

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mupad [B]  time = 8.89, size = 17, normalized size = 0.94 \begin {gather*} \frac {x}{\ln \left (\ln \left (x^3\right )-\ln \left (\ln \left (21\right )+3\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(log(x^3/(log(21) + 3)))*log(x^3/(log(21) + 3)) - 3)/(log(log(x^3/(log(21) + 3)))^2*log(x^3/(log(21) +
3))),x)

[Out]

x/log(log(x^3) - log(log(21) + 3))

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sympy [A]  time = 0.25, size = 12, normalized size = 0.67 \begin {gather*} \frac {x}{\log {\left (\log {\left (\frac {x^{3}}{3 + \log {\left (21 \right )}} \right )} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((ln(x**3/(ln(21)+3))*ln(ln(x**3/(ln(21)+3)))-3)/ln(x**3/(ln(21)+3))/ln(ln(x**3/(ln(21)+3)))**2,x)

[Out]

x/log(log(x**3/(3 + log(21))))

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