3.81.81 \(\int \frac {450 x^2-675 x^2 \log (x) \log (\log (x))+12 \log (4) \log (x) \log ^3(\log (x))}{\log (x) \log ^3(\log (x))} \, dx\)

Optimal. Leaf size=20 \[ 1-x \left (-12 \log (4)+\frac {225 x^2}{\log ^2(\log (x))}\right ) \]

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Rubi [F]  time = 0.32, 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 {450 x^2-675 x^2 \log (x) \log (\log (x))+12 \log (4) \log (x) \log ^3(\log (x))}{\log (x) \log ^3(\log (x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(450*x^2 - 675*x^2*Log[x]*Log[Log[x]] + 12*Log[4]*Log[x]*Log[Log[x]]^3)/(Log[x]*Log[Log[x]]^3),x]

[Out]

3*x*Log[256] + 450*Defer[Int][x^2/(Log[x]*Log[Log[x]]^3), x] - 675*Defer[Int][x^2/Log[Log[x]]^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 \left (150 x^2-225 x^2 \log (x) \log (\log (x))+4 \log (4) \log (x) \log ^3(\log (x))\right )}{\log (x) \log ^3(\log (x))} \, dx\\ &=3 \int \frac {150 x^2-225 x^2 \log (x) \log (\log (x))+4 \log (4) \log (x) \log ^3(\log (x))}{\log (x) \log ^3(\log (x))} \, dx\\ &=3 \int \left (\log (256)+\frac {150 x^2}{\log (x) \log ^3(\log (x))}-\frac {225 x^2}{\log ^2(\log (x))}\right ) \, dx\\ &=3 x \log (256)+450 \int \frac {x^2}{\log (x) \log ^3(\log (x))} \, dx-675 \int \frac {x^2}{\log ^2(\log (x))} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.10, size = 16, normalized size = 0.80 \begin {gather*} 12 x \log (4)-\frac {225 x^3}{\log ^2(\log (x))} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(450*x^2 - 675*x^2*Log[x]*Log[Log[x]] + 12*Log[4]*Log[x]*Log[Log[x]]^3)/(Log[x]*Log[Log[x]]^3),x]

[Out]

12*x*Log[4] - (225*x^3)/Log[Log[x]]^2

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fricas [A]  time = 1.19, size = 23, normalized size = 1.15 \begin {gather*} \frac {3 \, {\left (8 \, x \log \relax (2) \log \left (\log \relax (x)\right )^{2} - 75 \, x^{3}\right )}}{\log \left (\log \relax (x)\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*log(2)*log(x)*log(log(x))^3-675*x^2*log(x)*log(log(x))+450*x^2)/log(x)/log(log(x))^3,x, algorith
m="fricas")

[Out]

3*(8*x*log(2)*log(log(x))^2 - 75*x^3)/log(log(x))^2

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giac [A]  time = 0.22, size = 16, normalized size = 0.80 \begin {gather*} 24 \, x \log \relax (2) - \frac {225 \, x^{3}}{\log \left (\log \relax (x)\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*log(2)*log(x)*log(log(x))^3-675*x^2*log(x)*log(log(x))+450*x^2)/log(x)/log(log(x))^3,x, algorith
m="giac")

[Out]

24*x*log(2) - 225*x^3/log(log(x))^2

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maple [A]  time = 0.04, size = 17, normalized size = 0.85

method	result	size
risch	\(24 x \ln \relax (2)-\frac {225 x^{3}}{\ln \left (\ln \relax (x )\right )^{2}}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((24*ln(2)*ln(x)*ln(ln(x))^3-675*x^2*ln(x)*ln(ln(x))+450*x^2)/ln(x)/ln(ln(x))^3,x,method=_RETURNVERBOSE)

[Out]

24*x*ln(2)-225*x^3/ln(ln(x))^2

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maxima [A]  time = 0.44, size = 16, normalized size = 0.80 \begin {gather*} 24 \, x \log \relax (2) - \frac {225 \, x^{3}}{\log \left (\log \relax (x)\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*log(2)*log(x)*log(log(x))^3-675*x^2*log(x)*log(log(x))+450*x^2)/log(x)/log(log(x))^3,x, algorith
m="maxima")

[Out]

24*x*log(2) - 225*x^3/log(log(x))^2

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mupad [B]  time = 5.26, size = 16, normalized size = 0.80 \begin {gather*} 24\,x\,\ln \relax (2)-\frac {225\,x^3}{{\ln \left (\ln \relax (x)\right )}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((450*x^2 + 24*log(log(x))^3*log(2)*log(x) - 675*x^2*log(log(x))*log(x))/(log(log(x))^3*log(x)),x)

[Out]

24*x*log(2) - (225*x^3)/log(log(x))^2

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sympy [A]  time = 0.25, size = 17, normalized size = 0.85 \begin {gather*} - \frac {225 x^{3}}{\log {\left (\log {\relax (x )} \right )}^{2}} + 24 x \log {\relax (2 )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*ln(2)*ln(x)*ln(ln(x))**3-675*x**2*ln(x)*ln(ln(x))+450*x**2)/ln(x)/ln(ln(x))**3,x)

[Out]

-225*x**3/log(log(x))**2 + 24*x*log(2)

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