3.34.40 \(\int \frac {(-2 x^2-2 x^3+(18 x+38 x^2+4 x^3) \log (9+x) \log (\log (9+x))+(18+20 x-34 x^2-4 x^3) \log (9+x) \log ^2(\log (9+x))) \log (\frac {x+x^2+(2+x-x^2+\log (x)) \log (\log (9+x))}{\log (\log (9+x))})}{(9 x^2+10 x^3+x^4) \log (9+x) \log (\log (9+x))+(18 x+11 x^2-8 x^3-x^4+(9 x+x^2) \log (x)) \log (9+x) \log ^2(\log (9+x))} \, dx\)

Optimal. Leaf size=24 \[ \log ^2\left (\log (x)-(1+x) \left (-2+x-\frac {x}{\log (\log (9+x))}\right )\right ) \]

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Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[((-2*x^2 - 2*x^3 + (18*x + 38*x^2 + 4*x^3)*Log[9 + x]*Log[Log[9 + x]] + (18 + 20*x - 34*x^2 - 4*x^3)*Log[9
+ x]*Log[Log[9 + x]]^2)*Log[(x + x^2 + (2 + x - x^2 + Log[x])*Log[Log[9 + x]])/Log[Log[9 + x]]])/((9*x^2 + 10
*x^3 + x^4)*Log[9 + x]*Log[Log[9 + x]] + (18*x + 11*x^2 - 8*x^3 - x^4 + (9*x + x^2)*Log[x])*Log[9 + x]*Log[Log
[9 + x]]^2),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.13, size = 32, normalized size = 1.33 \begin {gather*} \log ^2\left (\frac {x+x^2+\left (2+x-x^2+\log (x)\right ) \log (\log (9+x))}{\log (\log (9+x))}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((-2*x^2 - 2*x^3 + (18*x + 38*x^2 + 4*x^3)*Log[9 + x]*Log[Log[9 + x]] + (18 + 20*x - 34*x^2 - 4*x^3)
*Log[9 + x]*Log[Log[9 + x]]^2)*Log[(x + x^2 + (2 + x - x^2 + Log[x])*Log[Log[9 + x]])/Log[Log[9 + x]]])/((9*x^
2 + 10*x^3 + x^4)*Log[9 + x]*Log[Log[9 + x]] + (18*x + 11*x^2 - 8*x^3 - x^4 + (9*x + x^2)*Log[x])*Log[9 + x]*L
og[Log[9 + x]]^2),x]

[Out]

Log[(x + x^2 + (2 + x - x^2 + Log[x])*Log[Log[9 + x]])/Log[Log[9 + x]]]^2

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fricas [A]  time = 0.60, size = 35, normalized size = 1.46 \begin {gather*} \log \left (\frac {x^{2} - {\left (x^{2} - x - \log \relax (x) - 2\right )} \log \left (\log \left (x + 9\right )\right ) + x}{\log \left (\log \left (x + 9\right )\right )}\right )^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^3-34*x^2+20*x+18)*log(x+9)*log(log(x+9))^2+(4*x^3+38*x^2+18*x)*log(x+9)*log(log(x+9))-2*x^3-2
*x^2)*log(((log(x)-x^2+x+2)*log(log(x+9))+x^2+x)/log(log(x+9)))/(((x^2+9*x)*log(x)-x^4-8*x^3+11*x^2+18*x)*log(
x+9)*log(log(x+9))^2+(x^4+10*x^3+9*x^2)*log(x+9)*log(log(x+9))),x, algorithm="fricas")

[Out]

log((x^2 - (x^2 - x - log(x) - 2)*log(log(x + 9)) + x)/log(log(x + 9)))^2

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, {\left ({\left (2 \, x^{3} + 17 \, x^{2} - 10 \, x - 9\right )} \log \left (x + 9\right ) \log \left (\log \left (x + 9\right )\right )^{2} + x^{3} - {\left (2 \, x^{3} + 19 \, x^{2} + 9 \, x\right )} \log \left (x + 9\right ) \log \left (\log \left (x + 9\right )\right ) + x^{2}\right )} \log \left (\frac {x^{2} - {\left (x^{2} - x - \log \relax (x) - 2\right )} \log \left (\log \left (x + 9\right )\right ) + x}{\log \left (\log \left (x + 9\right )\right )}\right )}{{\left (x^{4} + 8 \, x^{3} - 11 \, x^{2} - {\left (x^{2} + 9 \, x\right )} \log \relax (x) - 18 \, x\right )} \log \left (x + 9\right ) \log \left (\log \left (x + 9\right )\right )^{2} - {\left (x^{4} + 10 \, x^{3} + 9 \, x^{2}\right )} \log \left (x + 9\right ) \log \left (\log \left (x + 9\right )\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^3-34*x^2+20*x+18)*log(x+9)*log(log(x+9))^2+(4*x^3+38*x^2+18*x)*log(x+9)*log(log(x+9))-2*x^3-2
*x^2)*log(((log(x)-x^2+x+2)*log(log(x+9))+x^2+x)/log(log(x+9)))/(((x^2+9*x)*log(x)-x^4-8*x^3+11*x^2+18*x)*log(
x+9)*log(log(x+9))^2+(x^4+10*x^3+9*x^2)*log(x+9)*log(log(x+9))),x, algorithm="giac")

[Out]

integrate(2*((2*x^3 + 17*x^2 - 10*x - 9)*log(x + 9)*log(log(x + 9))^2 + x^3 - (2*x^3 + 19*x^2 + 9*x)*log(x + 9
)*log(log(x + 9)) + x^2)*log((x^2 - (x^2 - x - log(x) - 2)*log(log(x + 9)) + x)/log(log(x + 9)))/((x^4 + 8*x^3
- 11*x^2 - (x^2 + 9*x)*log(x) - 18*x)*log(x + 9)*log(log(x + 9))^2 - (x^4 + 10*x^3 + 9*x^2)*log(x + 9)*log(lo
g(x + 9))), x)

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maple [F]  time = 0.03, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (-4 x^{3}-34 x^{2}+20 x +18\right ) \ln \left (x +9\right ) \ln \left (\ln \left (x +9\right )\right )^{2}+\left (4 x^{3}+38 x^{2}+18 x \right ) \ln \left (x +9\right ) \ln \left (\ln \left (x +9\right )\right )-2 x^{3}-2 x^{2}\right ) \ln \left (\frac {\left (\ln \relax (x )-x^{2}+x +2\right ) \ln \left (\ln \left (x +9\right )\right )+x^{2}+x}{\ln \left (\ln \left (x +9\right )\right )}\right )}{\left (\left (x^{2}+9 x \right ) \ln \relax (x )-x^{4}-8 x^{3}+11 x^{2}+18 x \right ) \ln \left (x +9\right ) \ln \left (\ln \left (x +9\right )\right )^{2}+\left (x^{4}+10 x^{3}+9 x^{2}\right ) \ln \left (x +9\right ) \ln \left (\ln \left (x +9\right )\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-4*x^3-34*x^2+20*x+18)*ln(x+9)*ln(ln(x+9))^2+(4*x^3+38*x^2+18*x)*ln(x+9)*ln(ln(x+9))-2*x^3-2*x^2)*ln(((l
n(x)-x^2+x+2)*ln(ln(x+9))+x^2+x)/ln(ln(x+9)))/(((x^2+9*x)*ln(x)-x^4-8*x^3+11*x^2+18*x)*ln(x+9)*ln(ln(x+9))^2+(
x^4+10*x^3+9*x^2)*ln(x+9)*ln(ln(x+9))),x)

[Out]

int(((-4*x^3-34*x^2+20*x+18)*ln(x+9)*ln(ln(x+9))^2+(4*x^3+38*x^2+18*x)*ln(x+9)*ln(ln(x+9))-2*x^3-2*x^2)*ln(((l
n(x)-x^2+x+2)*ln(ln(x+9))+x^2+x)/ln(ln(x+9)))/(((x^2+9*x)*ln(x)-x^4-8*x^3+11*x^2+18*x)*ln(x+9)*ln(ln(x+9))^2+(
x^4+10*x^3+9*x^2)*ln(x+9)*ln(ln(x+9))),x)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} 2 \, \int \frac {{\left ({\left (2 \, x^{3} + 17 \, x^{2} - 10 \, x - 9\right )} \log \left (x + 9\right ) \log \left (\log \left (x + 9\right )\right )^{2} + x^{3} - {\left (2 \, x^{3} + 19 \, x^{2} + 9 \, x\right )} \log \left (x + 9\right ) \log \left (\log \left (x + 9\right )\right ) + x^{2}\right )} \log \left (\frac {x^{2} - {\left (x^{2} - x - \log \relax (x) - 2\right )} \log \left (\log \left (x + 9\right )\right ) + x}{\log \left (\log \left (x + 9\right )\right )}\right )}{{\left (x^{4} + 8 \, x^{3} - 11 \, x^{2} - {\left (x^{2} + 9 \, x\right )} \log \relax (x) - 18 \, x\right )} \log \left (x + 9\right ) \log \left (\log \left (x + 9\right )\right )^{2} - {\left (x^{4} + 10 \, x^{3} + 9 \, x^{2}\right )} \log \left (x + 9\right ) \log \left (\log \left (x + 9\right )\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^3-34*x^2+20*x+18)*log(x+9)*log(log(x+9))^2+(4*x^3+38*x^2+18*x)*log(x+9)*log(log(x+9))-2*x^3-2
*x^2)*log(((log(x)-x^2+x+2)*log(log(x+9))+x^2+x)/log(log(x+9)))/(((x^2+9*x)*log(x)-x^4-8*x^3+11*x^2+18*x)*log(
x+9)*log(log(x+9))^2+(x^4+10*x^3+9*x^2)*log(x+9)*log(log(x+9))),x, algorithm="maxima")

[Out]

2*integrate(((2*x^3 + 17*x^2 - 10*x - 9)*log(x + 9)*log(log(x + 9))^2 + x^3 - (2*x^3 + 19*x^2 + 9*x)*log(x + 9
)*log(log(x + 9)) + x^2)*log((x^2 - (x^2 - x - log(x) - 2)*log(log(x + 9)) + x)/log(log(x + 9)))/((x^4 + 8*x^3
- 11*x^2 - (x^2 + 9*x)*log(x) - 18*x)*log(x + 9)*log(log(x + 9))^2 - (x^4 + 10*x^3 + 9*x^2)*log(x + 9)*log(lo
g(x + 9))), x)

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mupad [B]  time = 4.35, size = 32, normalized size = 1.33 \begin {gather*} {\ln \left (\frac {x+\ln \left (\ln \left (x+9\right )\right )\,\left (x+\ln \relax (x)-x^2+2\right )+x^2}{\ln \left (\ln \left (x+9\right )\right )}\right )}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log((x + log(log(x + 9))*(x + log(x) - x^2 + 2) + x^2)/log(log(x + 9)))*(2*x^2 + 2*x^3 - log(x + 9)*log(
log(x + 9))^2*(20*x - 34*x^2 - 4*x^3 + 18) - log(x + 9)*log(log(x + 9))*(18*x + 38*x^2 + 4*x^3)))/(log(x + 9)*
log(log(x + 9))^2*(18*x + log(x)*(9*x + x^2) + 11*x^2 - 8*x^3 - x^4) + log(x + 9)*log(log(x + 9))*(9*x^2 + 10*
x^3 + x^4)),x)

[Out]

log((x + log(log(x + 9))*(x + log(x) - x^2 + 2) + x^2)/log(log(x + 9)))^2

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x**3-34*x**2+20*x+18)*ln(x+9)*ln(ln(x+9))**2+(4*x**3+38*x**2+18*x)*ln(x+9)*ln(ln(x+9))-2*x**3-2
*x**2)*ln(((ln(x)-x**2+x+2)*ln(ln(x+9))+x**2+x)/ln(ln(x+9)))/(((x**2+9*x)*ln(x)-x**4-8*x**3+11*x**2+18*x)*ln(x
+9)*ln(ln(x+9))**2+(x**4+10*x**3+9*x**2)*ln(x+9)*ln(ln(x+9))),x)

[Out]

Timed out

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