3.50.5 \(\int \frac {(-12+30 x-24 x^2+(24-12 x) \log (2-x)) \log (x)+(72 x-96 x^2+14 x^3+24 x^4-8 x^5+(-96 x+64 x^2+24 x^3-16 x^4) \log (2-x)+(32 x-8 x^3) \log ^2(2-x)) \log (3 \log (x))+(72 x-114 x^2+47 x^3+4 x^4-4 x^5+(-96 x+88 x^2-4 x^3-8 x^4) \log (2-x)+(32 x-8 x^2-4 x^3) \log ^2(2-x)) \log (x) \log ^2(3 \log (x))}{(-72+36 x) \log (x)+(-72 x^2+84 x^3-24 x^4+(48 x^2-24 x^3) \log (2-x)) \log (x) \log ^2(3 \log (x))+(-18 x^4+33 x^5-20 x^6+4 x^7+(24 x^4-28 x^5+8 x^6) \log (2-x)+(-8 x^4+4 x^5) \log ^2(2-x)) \log (x) \log ^4(3 \log (x))} \, dx\)

Optimal. Leaf size=33 \[ \frac {2+x}{-\frac {3}{-\frac {3}{2}+x+\log (2-x)}+x^2 \log ^2(3 \log (x))} \]

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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[((-12 + 30*x - 24*x^2 + (24 - 12*x)*Log[2 - x])*Log[x] + (72*x - 96*x^2 + 14*x^3 + 24*x^4 - 8*x^5 + (-96*x
+ 64*x^2 + 24*x^3 - 16*x^4)*Log[2 - x] + (32*x - 8*x^3)*Log[2 - x]^2)*Log[3*Log[x]] + (72*x - 114*x^2 + 47*x^
3 + 4*x^4 - 4*x^5 + (-96*x + 88*x^2 - 4*x^3 - 8*x^4)*Log[2 - x] + (32*x - 8*x^2 - 4*x^3)*Log[2 - x]^2)*Log[x]*
Log[3*Log[x]]^2)/((-72 + 36*x)*Log[x] + (-72*x^2 + 84*x^3 - 24*x^4 + (48*x^2 - 24*x^3)*Log[2 - x])*Log[x]*Log[
3*Log[x]]^2 + (-18*x^4 + 33*x^5 - 20*x^6 + 4*x^7 + (24*x^4 - 28*x^5 + 8*x^6)*Log[2 - x] + (-8*x^4 + 4*x^5)*Log
[2 - x]^2)*Log[x]*Log[3*Log[x]]^4),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.37, size = 45, normalized size = 1.36 \begin {gather*} \frac {(2+x) (-3+2 x+2 \log (2-x))}{-6+x^2 (-3+2 x+2 \log (2-x)) \log ^2(3 \log (x))} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((-12 + 30*x - 24*x^2 + (24 - 12*x)*Log[2 - x])*Log[x] + (72*x - 96*x^2 + 14*x^3 + 24*x^4 - 8*x^5 +
(-96*x + 64*x^2 + 24*x^3 - 16*x^4)*Log[2 - x] + (32*x - 8*x^3)*Log[2 - x]^2)*Log[3*Log[x]] + (72*x - 114*x^2 +
47*x^3 + 4*x^4 - 4*x^5 + (-96*x + 88*x^2 - 4*x^3 - 8*x^4)*Log[2 - x] + (32*x - 8*x^2 - 4*x^3)*Log[2 - x]^2)*L
og[x]*Log[3*Log[x]]^2)/((-72 + 36*x)*Log[x] + (-72*x^2 + 84*x^3 - 24*x^4 + (48*x^2 - 24*x^3)*Log[2 - x])*Log[x
]*Log[3*Log[x]]^2 + (-18*x^4 + 33*x^5 - 20*x^6 + 4*x^7 + (24*x^4 - 28*x^5 + 8*x^6)*Log[2 - x] + (-8*x^4 + 4*x^
5)*Log[2 - x]^2)*Log[x]*Log[3*Log[x]]^4),x]

[Out]

((2 + x)*(-3 + 2*x + 2*Log[2 - x]))/(-6 + x^2*(-3 + 2*x + 2*Log[2 - x])*Log[3*Log[x]]^2)

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fricas [A]  time = 0.85, size = 54, normalized size = 1.64 \begin {gather*} \frac {2 \, x^{2} + 2 \, {\left (x + 2\right )} \log \left (-x + 2\right ) + x - 6}{{\left (2 \, x^{3} + 2 \, x^{2} \log \left (-x + 2\right ) - 3 \, x^{2}\right )} \log \left (3 \, \log \relax (x)\right )^{2} - 6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^3-8*x^2+32*x)*log(2-x)^2+(-8*x^4-4*x^3+88*x^2-96*x)*log(2-x)-4*x^5+4*x^4+47*x^3-114*x^2+72*x
)*log(x)*log(3*log(x))^2+((-8*x^3+32*x)*log(2-x)^2+(-16*x^4+24*x^3+64*x^2-96*x)*log(2-x)-8*x^5+24*x^4+14*x^3-9
6*x^2+72*x)*log(3*log(x))+((-12*x+24)*log(2-x)-24*x^2+30*x-12)*log(x))/(((4*x^5-8*x^4)*log(2-x)^2+(8*x^6-28*x^
5+24*x^4)*log(2-x)+4*x^7-20*x^6+33*x^5-18*x^4)*log(x)*log(3*log(x))^4+((-24*x^3+48*x^2)*log(2-x)-24*x^4+84*x^3
-72*x^2)*log(x)*log(3*log(x))^2+(36*x-72)*log(x)),x, algorithm="fricas")

[Out]

(2*x^2 + 2*(x + 2)*log(-x + 2) + x - 6)/((2*x^3 + 2*x^2*log(-x + 2) - 3*x^2)*log(3*log(x))^2 - 6)

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giac [B]  time = 3.27, size = 77, normalized size = 2.33 \begin {gather*} \frac {6 \, {\left (x + 2\right )}}{2 \, x^{5} \log \left (3 \, \log \relax (x)\right )^{4} + 2 \, x^{4} \log \left (-x + 2\right ) \log \left (3 \, \log \relax (x)\right )^{4} - 3 \, x^{4} \log \left (3 \, \log \relax (x)\right )^{4} - 6 \, x^{2} \log \left (3 \, \log \relax (x)\right )^{2}} + \frac {x + 2}{x^{2} \log \left (3 \, \log \relax (x)\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^3-8*x^2+32*x)*log(2-x)^2+(-8*x^4-4*x^3+88*x^2-96*x)*log(2-x)-4*x^5+4*x^4+47*x^3-114*x^2+72*x
)*log(x)*log(3*log(x))^2+((-8*x^3+32*x)*log(2-x)^2+(-16*x^4+24*x^3+64*x^2-96*x)*log(2-x)-8*x^5+24*x^4+14*x^3-9
6*x^2+72*x)*log(3*log(x))+((-12*x+24)*log(2-x)-24*x^2+30*x-12)*log(x))/(((4*x^5-8*x^4)*log(2-x)^2+(8*x^6-28*x^
5+24*x^4)*log(2-x)+4*x^7-20*x^6+33*x^5-18*x^4)*log(x)*log(3*log(x))^4+((-24*x^3+48*x^2)*log(2-x)-24*x^4+84*x^3
-72*x^2)*log(x)*log(3*log(x))^2+(36*x-72)*log(x)),x, algorithm="giac")

[Out]

6*(x + 2)/(2*x^5*log(3*log(x))^4 + 2*x^4*log(-x + 2)*log(3*log(x))^4 - 3*x^4*log(3*log(x))^4 - 6*x^2*log(3*log
(x))^2) + (x + 2)/(x^2*log(3*log(x))^2)

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maple [B]  time = 0.22, size = 73, normalized size = 2.21

method	result	size
risch	\(\frac {2 x^{2}+2 x \ln \left (2-x \right )+x +4 \ln \left (2-x \right )-6}{2 \ln \left (2-x \right ) \ln \left (3 \ln \relax (x )\right )^{2} x^{2}+2 \ln \left (3 \ln \relax (x )\right )^{2} x^{3}-3 \ln \left (3 \ln \relax (x )\right )^{2} x^{2}-6}\)	\(73\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-4*x^3-8*x^2+32*x)*ln(2-x)^2+(-8*x^4-4*x^3+88*x^2-96*x)*ln(2-x)-4*x^5+4*x^4+47*x^3-114*x^2+72*x)*ln(x)*
ln(3*ln(x))^2+((-8*x^3+32*x)*ln(2-x)^2+(-16*x^4+24*x^3+64*x^2-96*x)*ln(2-x)-8*x^5+24*x^4+14*x^3-96*x^2+72*x)*l
n(3*ln(x))+((-12*x+24)*ln(2-x)-24*x^2+30*x-12)*ln(x))/(((4*x^5-8*x^4)*ln(2-x)^2+(8*x^6-28*x^5+24*x^4)*ln(2-x)+
4*x^7-20*x^6+33*x^5-18*x^4)*ln(x)*ln(3*ln(x))^4+((-24*x^3+48*x^2)*ln(2-x)-24*x^4+84*x^3-72*x^2)*ln(x)*ln(3*ln(
x))^2+(36*x-72)*ln(x)),x,method=_RETURNVERBOSE)

[Out]

(2*x^2+2*x*ln(2-x)+x+4*ln(2-x)-6)/(2*ln(2-x)*ln(3*ln(x))^2*x^2+2*ln(3*ln(x))^2*x^3-3*ln(3*ln(x))^2*x^2-6)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^3-8*x^2+32*x)*log(2-x)^2+(-8*x^4-4*x^3+88*x^2-96*x)*log(2-x)-4*x^5+4*x^4+47*x^3-114*x^2+72*x
)*log(x)*log(3*log(x))^2+((-8*x^3+32*x)*log(2-x)^2+(-16*x^4+24*x^3+64*x^2-96*x)*log(2-x)-8*x^5+24*x^4+14*x^3-9
6*x^2+72*x)*log(3*log(x))+((-12*x+24)*log(2-x)-24*x^2+30*x-12)*log(x))/(((4*x^5-8*x^4)*log(2-x)^2+(8*x^6-28*x^
5+24*x^4)*log(2-x)+4*x^7-20*x^6+33*x^5-18*x^4)*log(x)*log(3*log(x))^4+((-24*x^3+48*x^2)*log(2-x)-24*x^4+84*x^3
-72*x^2)*log(x)*log(3*log(x))^2+(36*x-72)*log(x)),x, algorithm="maxima")

[Out]

(x + 2)/(x^2*log(3)^2 + 2*x^2*log(3)*log(log(x)) + x^2*log(log(x))^2) - integrate(12*((x^6 - x^5 - 4*x^4 + 4*x
^3)*log(x)*log(log(x))^3 + 3*(x^6*log(3) - x^5*log(3) - 4*x^4*log(3) + 4*x^3*log(3))*log(x)*log(log(x))^2 + 6*
x^3 + 3*(x^6*log(3)^2 - x^5*log(3)^2 - 4*x^4*log(3)^2 + 2*(2*log(3)^2 + 1)*x^3 - 4*x^2 - 8*x + 16)*log(x)*log(
log(x)) - 12*x^2 + (x^6*log(3)^3 - x^5*log(3)^3 - 4*x^4*log(3)^3 + 2*(2*log(3)^3 + 3*log(3))*x^3 - 12*x^2*log(
3) - 24*x*log(3) + 48*log(3))*log(x) - 24*x + 48)/((2*x^7 - 7*x^6 + 6*x^5)*log(x)*log(log(x))^5 + 5*(2*x^7*log
(3) - 7*x^6*log(3) + 6*x^5*log(3))*log(x)*log(log(x))^4 + 2*(10*x^7*log(3)^2 - 35*x^6*log(3)^2 + 30*x^5*log(3)
^2 - 3*x^4 + 6*x^3)*log(x)*log(log(x))^3 + 2*(10*x^7*log(3)^3 - 35*x^6*log(3)^3 + 30*x^5*log(3)^3 - 9*x^4*log(
3) + 18*x^3*log(3))*log(x)*log(log(x))^2 + (10*x^7*log(3)^4 - 35*x^6*log(3)^4 + 30*x^5*log(3)^4 - 18*x^4*log(3
)^2 + 36*x^3*log(3)^2)*log(x)*log(log(x)) + (2*x^7*log(3)^5 - 7*x^6*log(3)^5 + 6*x^5*log(3)^5 - 6*x^4*log(3)^3
+ 12*x^3*log(3)^3)*log(x) + 2*((x^6 - 2*x^5)*log(x)*log(log(x))^5 + 5*(x^6*log(3) - 2*x^5*log(3))*log(x)*log(
log(x))^4 + 10*(x^6*log(3)^2 - 2*x^5*log(3)^2)*log(x)*log(log(x))^3 + 10*(x^6*log(3)^3 - 2*x^5*log(3)^3)*log(x
)*log(log(x))^2 + 5*(x^6*log(3)^4 - 2*x^5*log(3)^4)*log(x)*log(log(x)) + (x^6*log(3)^5 - 2*x^5*log(3)^5)*log(x
))*log(-x + 2)), x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {\ln \relax (x)\,\left ({\ln \left (2-x\right )}^2\,\left (4\,x^3+8\,x^2-32\,x\right )-72\,x+114\,x^2-47\,x^3-4\,x^4+4\,x^5+\ln \left (2-x\right )\,\left (8\,x^4+4\,x^3-88\,x^2+96\,x\right )\right )\,{\ln \left (3\,\ln \relax (x)\right )}^2+\left (96\,x^2-{\ln \left (2-x\right )}^2\,\left (32\,x-8\,x^3\right )-72\,x-14\,x^3-24\,x^4+8\,x^5+\ln \left (2-x\right )\,\left (16\,x^4-24\,x^3-64\,x^2+96\,x\right )\right )\,\ln \left (3\,\ln \relax (x)\right )+\ln \relax (x)\,\left (\ln \left (2-x\right )\,\left (12\,x-24\right )-30\,x+24\,x^2+12\right )}{\ln \relax (x)\,\left (\ln \left (2-x\right )\,\left (8\,x^6-28\,x^5+24\,x^4\right )-{\ln \left (2-x\right )}^2\,\left (8\,x^4-4\,x^5\right )-18\,x^4+33\,x^5-20\,x^6+4\,x^7\right )\,{\ln \left (3\,\ln \relax (x)\right )}^4+\ln \relax (x)\,\left (\ln \left (2-x\right )\,\left (48\,x^2-24\,x^3\right )-72\,x^2+84\,x^3-24\,x^4\right )\,{\ln \left (3\,\ln \relax (x)\right )}^2+\ln \relax (x)\,\left (36\,x-72\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x)*(log(2 - x)*(12*x - 24) - 30*x + 24*x^2 + 12) - log(3*log(x))*(72*x + log(2 - x)^2*(32*x - 8*x^3)
- 96*x^2 + 14*x^3 + 24*x^4 - 8*x^5 - log(2 - x)*(96*x - 64*x^2 - 24*x^3 + 16*x^4)) + log(3*log(x))^2*log(x)*(
log(2 - x)^2*(8*x^2 - 32*x + 4*x^3) - 72*x + 114*x^2 - 47*x^3 - 4*x^4 + 4*x^5 + log(2 - x)*(96*x - 88*x^2 + 4*
x^3 + 8*x^4)))/(log(x)*(36*x - 72) + log(3*log(x))^2*log(x)*(log(2 - x)*(48*x^2 - 24*x^3) - 72*x^2 + 84*x^3 -
24*x^4) + log(3*log(x))^4*log(x)*(log(2 - x)*(24*x^4 - 28*x^5 + 8*x^6) - log(2 - x)^2*(8*x^4 - 4*x^5) - 18*x^4
+ 33*x^5 - 20*x^6 + 4*x^7)),x)

[Out]

int(-(log(x)*(log(2 - x)*(12*x - 24) - 30*x + 24*x^2 + 12) - log(3*log(x))*(72*x + log(2 - x)^2*(32*x - 8*x^3)
- 96*x^2 + 14*x^3 + 24*x^4 - 8*x^5 - log(2 - x)*(96*x - 64*x^2 - 24*x^3 + 16*x^4)) + log(3*log(x))^2*log(x)*(
log(2 - x)^2*(8*x^2 - 32*x + 4*x^3) - 72*x + 114*x^2 - 47*x^3 - 4*x^4 + 4*x^5 + log(2 - x)*(96*x - 88*x^2 + 4*
x^3 + 8*x^4)))/(log(x)*(36*x - 72) + log(3*log(x))^2*log(x)*(log(2 - x)*(48*x^2 - 24*x^3) - 72*x^2 + 84*x^3 -
24*x^4) + log(3*log(x))^4*log(x)*(log(2 - x)*(24*x^4 - 28*x^5 + 8*x^6) - log(2 - x)^2*(8*x^4 - 4*x^5) - 18*x^4
+ 33*x^5 - 20*x^6 + 4*x^7)), x)

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sympy [B]  time = 2.17, size = 53, normalized size = 1.61 \begin {gather*} \frac {2 x^{2} + 2 x \log {\left (2 - x \right )} + x + 4 \log {\left (2 - x \right )} - 6}{\left (2 x^{3} + 2 x^{2} \log {\left (2 - x \right )} - 3 x^{2}\right ) \log {\left (3 \log {\relax (x )} \right )}^{2} - 6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x**3-8*x**2+32*x)*ln(2-x)**2+(-8*x**4-4*x**3+88*x**2-96*x)*ln(2-x)-4*x**5+4*x**4+47*x**3-114*x
**2+72*x)*ln(x)*ln(3*ln(x))**2+((-8*x**3+32*x)*ln(2-x)**2+(-16*x**4+24*x**3+64*x**2-96*x)*ln(2-x)-8*x**5+24*x*
*4+14*x**3-96*x**2+72*x)*ln(3*ln(x))+((-12*x+24)*ln(2-x)-24*x**2+30*x-12)*ln(x))/(((4*x**5-8*x**4)*ln(2-x)**2+
(8*x**6-28*x**5+24*x**4)*ln(2-x)+4*x**7-20*x**6+33*x**5-18*x**4)*ln(x)*ln(3*ln(x))**4+((-24*x**3+48*x**2)*ln(2
-x)-24*x**4+84*x**3-72*x**2)*ln(x)*ln(3*ln(x))**2+(36*x-72)*ln(x)),x)

[Out]

(2*x**2 + 2*x*log(2 - x) + x + 4*log(2 - x) - 6)/((2*x**3 + 2*x**2*log(2 - x) - 3*x**2)*log(3*log(x))**2 - 6)

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