3.82.60 \(\int \frac {-144+24 x-72 x^2-72 x^3+(72-12 x+36 x^2) \log (4)+(-144-96 x+48 x^2+(72-24 x) \log (4)) \log (\frac {2+2 x-\log (4)}{x})}{-18 x^2-6 x^3+10 x^4-2 x^5+(9 x^2-6 x^3+x^4) \log (4)+(-12 x-8 x^2+4 x^3+(6 x-2 x^2) \log (4)) \log (\frac {2+2 x-\log (4)}{x})+(-2-2 x+\log (4)) \log ^2(\frac {2+2 x-\log (4)}{x})} \, dx\)

Optimal. Leaf size=30 \[ \frac {12 (-6+x)}{-3+x-\frac {\log \left (2+\frac {2}{x}-\frac {\log (4)}{x}\right )}{x}} \]

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Rubi [F]  time = 1.41, 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 {-144+24 x-72 x^2-72 x^3+\left (72-12 x+36 x^2\right ) \log (4)+\left (-144-96 x+48 x^2+(72-24 x) \log (4)\right ) \log \left (\frac {2+2 x-\log (4)}{x}\right )}{-18 x^2-6 x^3+10 x^4-2 x^5+\left (9 x^2-6 x^3+x^4\right ) \log (4)+\left (-12 x-8 x^2+4 x^3+\left (6 x-2 x^2\right ) \log (4)\right ) \log \left (\frac {2+2 x-\log (4)}{x}\right )+(-2-2 x+\log (4)) \log ^2\left (\frac {2+2 x-\log (4)}{x}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-144 + 24*x - 72*x^2 - 72*x^3 + (72 - 12*x + 36*x^2)*Log[4] + (-144 - 96*x + 48*x^2 + (72 - 24*x)*Log[4])
*Log[(2 + 2*x - Log[4])/x])/(-18*x^2 - 6*x^3 + 10*x^4 - 2*x^5 + (9*x^2 - 6*x^3 + x^4)*Log[4] + (-12*x - 8*x^2
+ 4*x^3 + (6*x - 2*x^2)*Log[4])*Log[(2 + 2*x - Log[4])/x] + (-2 - 2*x + Log[4])*Log[(2 + 2*x - Log[4])/x]^2),x
]

[Out]

-6*(2 - Log[4])*Defer[Int][(-3*x + x^2 - Log[(2 + 2*x - Log[4])/x])^(-2), x] - 216*Defer[Int][x/(-3*x + x^2 -
Log[(2 + 2*x - Log[4])/x])^2, x] + 180*Defer[Int][x^2/(-3*x + x^2 - Log[(2 + 2*x - Log[4])/x])^2, x] - 24*Defe
r[Int][x^3/(-3*x + x^2 - Log[(2 + 2*x - Log[4])/x])^2, x] - 72*Defer[Int][(-3*x + x^2 - Log[(2 + 2*x - Log[4])
/x])^(-1), x] + 24*Defer[Int][x/(-3*x + x^2 - Log[(2 + 2*x - Log[4])/x]), x] + 6*(2 - Log[4])*(14 - Log[4])*De
fer[Int][1/((2 + 2*x - Log[4])*(3*x - x^2 + Log[(2 + 2*x - Log[4])/x])^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {12 \left (6 x^3-6 (-2+\log (4))+x (-2+\log (4))-3 x^2 (-2+\log (4))-2 (-3+x) (2+2 x-\log (4)) \log \left (\frac {2+2 x-\log (4)}{x}\right )\right )}{(2+2 x-\log (4)) \left ((-3+x) x-\log \left (\frac {2+2 x-\log (4)}{x}\right )\right )^2} \, dx\\ &=12 \int \frac {6 x^3-6 (-2+\log (4))+x (-2+\log (4))-3 x^2 (-2+\log (4))-2 (-3+x) (2+2 x-\log (4)) \log \left (\frac {2+2 x-\log (4)}{x}\right )}{(2+2 x-\log (4)) \left ((-3+x) x-\log \left (\frac {2+2 x-\log (4)}{x}\right )\right )^2} \, dx\\ &=12 \int \left (\frac {2 (-3+x)}{-3 x+x^2-\log \left (\frac {2+2 x-\log (4)}{x}\right )}+\frac {(6-x) \left (2+4 x^3-3 x (2-\log (4))-\log (4)-2 x^2 (1+\log (4))\right )}{(2+2 x-\log (4)) \left (3 x-x^2+\log \left (\frac {2+2 x-\log (4)}{x}\right )\right )^2}\right ) \, dx\\ &=12 \int \frac {(6-x) \left (2+4 x^3-3 x (2-\log (4))-\log (4)-2 x^2 (1+\log (4))\right )}{(2+2 x-\log (4)) \left (3 x-x^2+\log \left (\frac {2+2 x-\log (4)}{x}\right )\right )^2} \, dx+24 \int \frac {-3+x}{-3 x+x^2-\log \left (\frac {2+2 x-\log (4)}{x}\right )} \, dx\\ &=12 \int \left (-\frac {18 x}{\left (-3 x+x^2-\log \left (\frac {2+2 x-\log (4)}{x}\right )\right )^2}+\frac {15 x^2}{\left (-3 x+x^2-\log \left (\frac {2+2 x-\log (4)}{x}\right )\right )^2}-\frac {2 x^3}{\left (-3 x+x^2-\log \left (\frac {2+2 x-\log (4)}{x}\right )\right )^2}+\frac {-2+\log (4)}{2 \left (-3 x+x^2-\log \left (\frac {2+2 x-\log (4)}{x}\right )\right )^2}+\frac {(2-\log (4)) (14-\log (4))}{2 (2+2 x-\log (4)) \left (3 x-x^2+\log \left (\frac {2+2 x-\log (4)}{x}\right )\right )^2}\right ) \, dx+24 \int \left (-\frac {3}{-3 x+x^2-\log \left (\frac {2+2 x-\log (4)}{x}\right )}+\frac {x}{-3 x+x^2-\log \left (\frac {2+2 x-\log (4)}{x}\right )}\right ) \, dx\\ &=-\left (24 \int \frac {x^3}{\left (-3 x+x^2-\log \left (\frac {2+2 x-\log (4)}{x}\right )\right )^2} \, dx\right )+24 \int \frac {x}{-3 x+x^2-\log \left (\frac {2+2 x-\log (4)}{x}\right )} \, dx-72 \int \frac {1}{-3 x+x^2-\log \left (\frac {2+2 x-\log (4)}{x}\right )} \, dx+180 \int \frac {x^2}{\left (-3 x+x^2-\log \left (\frac {2+2 x-\log (4)}{x}\right )\right )^2} \, dx-216 \int \frac {x}{\left (-3 x+x^2-\log \left (\frac {2+2 x-\log (4)}{x}\right )\right )^2} \, dx-(6 (2-\log (4))) \int \frac {1}{\left (-3 x+x^2-\log \left (\frac {2+2 x-\log (4)}{x}\right )\right )^2} \, dx+(6 (2-\log (4)) (14-\log (4))) \int \frac {1}{(2+2 x-\log (4)) \left (3 x-x^2+\log \left (\frac {2+2 x-\log (4)}{x}\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.05, size = 31, normalized size = 1.03 \begin {gather*} -\frac {12 (-6+x) x}{3 x-x^2+\log \left (\frac {2+2 x-\log (4)}{x}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-144 + 24*x - 72*x^2 - 72*x^3 + (72 - 12*x + 36*x^2)*Log[4] + (-144 - 96*x + 48*x^2 + (72 - 24*x)*L
og[4])*Log[(2 + 2*x - Log[4])/x])/(-18*x^2 - 6*x^3 + 10*x^4 - 2*x^5 + (9*x^2 - 6*x^3 + x^4)*Log[4] + (-12*x -
8*x^2 + 4*x^3 + (6*x - 2*x^2)*Log[4])*Log[(2 + 2*x - Log[4])/x] + (-2 - 2*x + Log[4])*Log[(2 + 2*x - Log[4])/x
]^2),x]

[Out]

(-12*(-6 + x)*x)/(3*x - x^2 + Log[(2 + 2*x - Log[4])/x])

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fricas [A]  time = 0.51, size = 33, normalized size = 1.10 \begin {gather*} \frac {12 \, {\left (x^{2} - 6 \, x\right )}}{x^{2} - 3 \, x - \log \left (\frac {2 \, {\left (x - \log \relax (2) + 1\right )}}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*(-24*x+72)*log(2)+48*x^2-96*x-144)*log((-2*log(2)+2*x+2)/x)+2*(36*x^2-12*x+72)*log(2)-72*x^3-72*
x^2+24*x-144)/((2*log(2)-2*x-2)*log((-2*log(2)+2*x+2)/x)^2+(2*(-2*x^2+6*x)*log(2)+4*x^3-8*x^2-12*x)*log((-2*lo
g(2)+2*x+2)/x)+2*(x^4-6*x^3+9*x^2)*log(2)-2*x^5+10*x^4-6*x^3-18*x^2),x, algorithm="fricas")

[Out]

12*(x^2 - 6*x)/(x^2 - 3*x - log(2*(x - log(2) + 1)/x))

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giac [B]  time = 0.62, size = 171, normalized size = 5.70 \begin {gather*} \frac {12 \, {\left (\log \relax (2)^{3} + \frac {6 \, {\left (x - \log \relax (2) + 1\right )} \log \relax (2)^{2}}{x} - 9 \, \log \relax (2)^{2} - \frac {12 \, {\left (x - \log \relax (2) + 1\right )} \log \relax (2)}{x} + \frac {6 \, {\left (x - \log \relax (2) + 1\right )}}{x} + 15 \, \log \relax (2) - 7\right )}}{{\left (\log \relax (2)^{2} + \frac {3 \, {\left (x - \log \relax (2) + 1\right )} \log \relax (2)}{x} - \frac {{\left (x - \log \relax (2) + 1\right )}^{2} \log \left (\frac {2 \, {\left (x - \log \relax (2) + 1\right )}}{x}\right )}{x^{2}} + \frac {2 \, {\left (x - \log \relax (2) + 1\right )} \log \left (\frac {2 \, {\left (x - \log \relax (2) + 1\right )}}{x}\right )}{x} - \frac {3 \, {\left (x - \log \relax (2) + 1\right )}}{x} - 5 \, \log \relax (2) - \log \left (\frac {2 \, {\left (x - \log \relax (2) + 1\right )}}{x}\right ) + 4\right )} {\left (\log \relax (2) - 1\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*(-24*x+72)*log(2)+48*x^2-96*x-144)*log((-2*log(2)+2*x+2)/x)+2*(36*x^2-12*x+72)*log(2)-72*x^3-72*
x^2+24*x-144)/((2*log(2)-2*x-2)*log((-2*log(2)+2*x+2)/x)^2+(2*(-2*x^2+6*x)*log(2)+4*x^3-8*x^2-12*x)*log((-2*lo
g(2)+2*x+2)/x)+2*(x^4-6*x^3+9*x^2)*log(2)-2*x^5+10*x^4-6*x^3-18*x^2),x, algorithm="giac")

[Out]

12*(log(2)^3 + 6*(x - log(2) + 1)*log(2)^2/x - 9*log(2)^2 - 12*(x - log(2) + 1)*log(2)/x + 6*(x - log(2) + 1)/
x + 15*log(2) - 7)/((log(2)^2 + 3*(x - log(2) + 1)*log(2)/x - (x - log(2) + 1)^2*log(2*(x - log(2) + 1)/x)/x^2
+ 2*(x - log(2) + 1)*log(2*(x - log(2) + 1)/x)/x - 3*(x - log(2) + 1)/x - 5*log(2) - log(2*(x - log(2) + 1)/x
) + 4)*(log(2) - 1))

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maple [A]  time = 0.37, size = 32, normalized size = 1.07

method	result	size
risch	\(\frac {12 x \left (x -6\right )}{x^{2}-3 x -\ln \left (\frac {-2 \ln \relax (2)+2 x +2}{x}\right )}\)	\(32\)
norman	\(\frac {12 \ln \left (\frac {-2 \ln \relax (2)+2 x +2}{x}\right )-36 x}{x^{2}-3 x -\ln \left (\frac {-2 \ln \relax (2)+2 x +2}{x}\right )}\)	\(47\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*(-24*x+72)*ln(2)+48*x^2-96*x-144)*ln((-2*ln(2)+2*x+2)/x)+2*(36*x^2-12*x+72)*ln(2)-72*x^3-72*x^2+24*x-1
44)/((2*ln(2)-2*x-2)*ln((-2*ln(2)+2*x+2)/x)^2+(2*(-2*x^2+6*x)*ln(2)+4*x^3-8*x^2-12*x)*ln((-2*ln(2)+2*x+2)/x)+2
*(x^4-6*x^3+9*x^2)*ln(2)-2*x^5+10*x^4-6*x^3-18*x^2),x,method=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.52, size = 34, normalized size = 1.13 \begin {gather*} \frac {12 \, {\left (x^{2} - 6 \, x\right )}}{x^{2} - 3 \, x - \log \relax (2) - \log \left (x - \log \relax (2) + 1\right ) + \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*(-24*x+72)*log(2)+48*x^2-96*x-144)*log((-2*log(2)+2*x+2)/x)+2*(36*x^2-12*x+72)*log(2)-72*x^3-72*
x^2+24*x-144)/((2*log(2)-2*x-2)*log((-2*log(2)+2*x+2)/x)^2+(2*(-2*x^2+6*x)*log(2)+4*x^3-8*x^2-12*x)*log((-2*lo
g(2)+2*x+2)/x)+2*(x^4-6*x^3+9*x^2)*log(2)-2*x^5+10*x^4-6*x^3-18*x^2),x, algorithm="maxima")

[Out]

12*(x^2 - 6*x)/(x^2 - 3*x - log(2) - log(x - log(2) + 1) + log(x))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {\ln \left (\frac {2\,x-2\,\ln \relax (2)+2}{x}\right )\,\left (96\,x+2\,\ln \relax (2)\,\left (24\,x-72\right )-48\,x^2+144\right )-2\,\ln \relax (2)\,\left (36\,x^2-12\,x+72\right )-24\,x+72\,x^2+72\,x^3+144}{{\ln \left (\frac {2\,x-2\,\ln \relax (2)+2}{x}\right )}^2\,\left (2\,x-2\,\ln \relax (2)+2\right )-2\,\ln \relax (2)\,\left (x^4-6\,x^3+9\,x^2\right )+18\,x^2+6\,x^3-10\,x^4+2\,x^5+\ln \left (\frac {2\,x-2\,\ln \relax (2)+2}{x}\right )\,\left (12\,x-2\,\ln \relax (2)\,\left (6\,x-2\,x^2\right )+8\,x^2-4\,x^3\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log((2*x - 2*log(2) + 2)/x)*(96*x + 2*log(2)*(24*x - 72) - 48*x^2 + 144) - 2*log(2)*(36*x^2 - 12*x + 72)
- 24*x + 72*x^2 + 72*x^3 + 144)/(log((2*x - 2*log(2) + 2)/x)^2*(2*x - 2*log(2) + 2) - 2*log(2)*(9*x^2 - 6*x^3
+ x^4) + 18*x^2 + 6*x^3 - 10*x^4 + 2*x^5 + log((2*x - 2*log(2) + 2)/x)*(12*x - 2*log(2)*(6*x - 2*x^2) + 8*x^2
- 4*x^3)),x)

[Out]

int((log((2*x - 2*log(2) + 2)/x)*(96*x + 2*log(2)*(24*x - 72) - 48*x^2 + 144) - 2*log(2)*(36*x^2 - 12*x + 72)
- 24*x + 72*x^2 + 72*x^3 + 144)/(log((2*x - 2*log(2) + 2)/x)^2*(2*x - 2*log(2) + 2) - 2*log(2)*(9*x^2 - 6*x^3
+ x^4) + 18*x^2 + 6*x^3 - 10*x^4 + 2*x^5 + log((2*x - 2*log(2) + 2)/x)*(12*x - 2*log(2)*(6*x - 2*x^2) + 8*x^2
- 4*x^3)), x)

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sympy [A]  time = 0.24, size = 27, normalized size = 0.90 \begin {gather*} \frac {- 12 x^{2} + 72 x}{- x^{2} + 3 x + \log {\left (\frac {2 x - 2 \log {\relax (2 )} + 2}{x} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*(-24*x+72)*ln(2)+48*x**2-96*x-144)*ln((-2*ln(2)+2*x+2)/x)+2*(36*x**2-12*x+72)*ln(2)-72*x**3-72*x
**2+24*x-144)/((2*ln(2)-2*x-2)*ln((-2*ln(2)+2*x+2)/x)**2+(2*(-2*x**2+6*x)*ln(2)+4*x**3-8*x**2-12*x)*ln((-2*ln(
2)+2*x+2)/x)+2*(x**4-6*x**3+9*x**2)*ln(2)-2*x**5+10*x**4-6*x**3-18*x**2),x)

[Out]

(-12*x**2 + 72*x)/(-x**2 + 3*x + log((2*x - 2*log(2) + 2)/x))

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