3.43.4 \(\int \frac {(-128 x^3+256 x^4+(128 x^2-256 x^3) \log (2)+(-128 x^2+256 x^3+(128 x-256 x^2) \log (2)) \log (x)) \log (-12-x+x^2)+(768 x+64 x^2-64 x^3+(-768-832 x+64 x^3) \log (2)+(-768 x-64 x^2+64 x^3) \log (x)) \log ^2(-12-x+x^2)}{-12 x^3-x^4+x^5+(-24 x^2-2 x^3+2 x^4) \log (x)+(-12 x-x^2+x^3) \log ^2(x)} \, dx\)

Optimal. Leaf size=24 \[ \frac {64 (x-\log (2)) \log ^2((-4+x) (3+x))}{x+\log (x)} \]

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Rubi [F]  time = 6.40, 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 {\left (-128 x^3+256 x^4+\left (128 x^2-256 x^3\right ) \log (2)+\left (-128 x^2+256 x^3+\left (128 x-256 x^2\right ) \log (2)\right ) \log (x)\right ) \log \left (-12-x+x^2\right )+\left (768 x+64 x^2-64 x^3+\left (-768-832 x+64 x^3\right ) \log (2)+\left (-768 x-64 x^2+64 x^3\right ) \log (x)\right ) \log ^2\left (-12-x+x^2\right )}{-12 x^3-x^4+x^5+\left (-24 x^2-2 x^3+2 x^4\right ) \log (x)+\left (-12 x-x^2+x^3\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((-128*x^3 + 256*x^4 + (128*x^2 - 256*x^3)*Log[2] + (-128*x^2 + 256*x^3 + (128*x - 256*x^2)*Log[2])*Log[x]
)*Log[-12 - x + x^2] + (768*x + 64*x^2 - 64*x^3 + (-768 - 832*x + 64*x^3)*Log[2] + (-768*x - 64*x^2 + 64*x^3)*
Log[x])*Log[-12 - x + x^2]^2)/(-12*x^3 - x^4 + x^5 + (-24*x^2 - 2*x^3 + 2*x^4)*Log[x] + (-12*x - x^2 + x^3)*Lo
g[x]^2),x]

[Out]

256*Defer[Int][Log[-12 - x + x^2]/(x + Log[x]), x] + 64*(8 - Log[4])*Defer[Int][Log[-12 - x + x^2]/((-4 + x)*(
x + Log[x])), x] - 64*(6 + Log[4])*Defer[Int][Log[-12 - x + x^2]/((3 + x)*(x + Log[x])), x] - 64*(1 - Log[2])*
Defer[Int][Log[-12 - x + x^2]^2/(x + Log[x])^2, x] + 64*Log[2]*Defer[Int][Log[-12 - x + x^2]^2/(x*(x + Log[x])
^2), x] + 64*Defer[Int][(Log[x]*Log[-12 - x + x^2]^2)/(x + Log[x])^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {64 \log \left (-12-x+x^2\right ) \left (-x^2 (-1+2 x) (2 x-\log (4))-\left (-12-x+x^2\right ) (x (-1+\log (2))+\log (2)) \log \left (-12-x+x^2\right )-x \log (x) \left ((-1+2 x) (2 x-\log (4))+\left (-12-x+x^2\right ) \log \left (-12-x+x^2\right )\right )\right )}{x \left (12+x-x^2\right ) (x+\log (x))^2} \, dx\\ &=64 \int \frac {\log \left (-12-x+x^2\right ) \left (-x^2 (-1+2 x) (2 x-\log (4))-\left (-12-x+x^2\right ) (x (-1+\log (2))+\log (2)) \log \left (-12-x+x^2\right )-x \log (x) \left ((-1+2 x) (2 x-\log (4))+\left (-12-x+x^2\right ) \log \left (-12-x+x^2\right )\right )\right )}{x \left (12+x-x^2\right ) (x+\log (x))^2} \, dx\\ &=64 \int \left (\frac {(-1+2 x) (2 x-\log (4)) \log \left (-12-x+x^2\right )}{(-4+x) (3+x) (x+\log (x))}+\frac {(-x (1-\log (2))+\log (2)+x \log (x)) \log ^2\left (-12-x+x^2\right )}{x (x+\log (x))^2}\right ) \, dx\\ &=64 \int \frac {(-1+2 x) (2 x-\log (4)) \log \left (-12-x+x^2\right )}{(-4+x) (3+x) (x+\log (x))} \, dx+64 \int \frac {(-x (1-\log (2))+\log (2)+x \log (x)) \log ^2\left (-12-x+x^2\right )}{x (x+\log (x))^2} \, dx\\ &=64 \int \left (\frac {4 \log \left (-12-x+x^2\right )}{x+\log (x)}-\frac {(-8+\log (4)) \log \left (-12-x+x^2\right )}{(-4+x) (x+\log (x))}-\frac {(6+\log (4)) \log \left (-12-x+x^2\right )}{(3+x) (x+\log (x))}\right ) \, dx+64 \int \left (\frac {(-1+\log (2)) \log ^2\left (-12-x+x^2\right )}{(x+\log (x))^2}+\frac {\log (2) \log ^2\left (-12-x+x^2\right )}{x (x+\log (x))^2}+\frac {\log (x) \log ^2\left (-12-x+x^2\right )}{(x+\log (x))^2}\right ) \, dx\\ &=64 \int \frac {\log (x) \log ^2\left (-12-x+x^2\right )}{(x+\log (x))^2} \, dx+256 \int \frac {\log \left (-12-x+x^2\right )}{x+\log (x)} \, dx-(64 (1-\log (2))) \int \frac {\log ^2\left (-12-x+x^2\right )}{(x+\log (x))^2} \, dx+(64 \log (2)) \int \frac {\log ^2\left (-12-x+x^2\right )}{x (x+\log (x))^2} \, dx+(64 (8-\log (4))) \int \frac {\log \left (-12-x+x^2\right )}{(-4+x) (x+\log (x))} \, dx-(64 (6+\log (4))) \int \frac {\log \left (-12-x+x^2\right )}{(3+x) (x+\log (x))} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [F]  time = 0.19, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (-128 x^3+256 x^4+\left (128 x^2-256 x^3\right ) \log (2)+\left (-128 x^2+256 x^3+\left (128 x-256 x^2\right ) \log (2)\right ) \log (x)\right ) \log \left (-12-x+x^2\right )+\left (768 x+64 x^2-64 x^3+\left (-768-832 x+64 x^3\right ) \log (2)+\left (-768 x-64 x^2+64 x^3\right ) \log (x)\right ) \log ^2\left (-12-x+x^2\right )}{-12 x^3-x^4+x^5+\left (-24 x^2-2 x^3+2 x^4\right ) \log (x)+\left (-12 x-x^2+x^3\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[((-128*x^3 + 256*x^4 + (128*x^2 - 256*x^3)*Log[2] + (-128*x^2 + 256*x^3 + (128*x - 256*x^2)*Log[2])*
Log[x])*Log[-12 - x + x^2] + (768*x + 64*x^2 - 64*x^3 + (-768 - 832*x + 64*x^3)*Log[2] + (-768*x - 64*x^2 + 64
*x^3)*Log[x])*Log[-12 - x + x^2]^2)/(-12*x^3 - x^4 + x^5 + (-24*x^2 - 2*x^3 + 2*x^4)*Log[x] + (-12*x - x^2 + x
^3)*Log[x]^2),x]

[Out]

Integrate[((-128*x^3 + 256*x^4 + (128*x^2 - 256*x^3)*Log[2] + (-128*x^2 + 256*x^3 + (128*x - 256*x^2)*Log[2])*
Log[x])*Log[-12 - x + x^2] + (768*x + 64*x^2 - 64*x^3 + (-768 - 832*x + 64*x^3)*Log[2] + (-768*x - 64*x^2 + 64
*x^3)*Log[x])*Log[-12 - x + x^2]^2)/(-12*x^3 - x^4 + x^5 + (-24*x^2 - 2*x^3 + 2*x^4)*Log[x] + (-12*x - x^2 + x
^3)*Log[x]^2), x]

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fricas [A]  time = 0.46, size = 25, normalized size = 1.04 \begin {gather*} \frac {64 \, {\left (x - \log \relax (2)\right )} \log \left (x^{2} - x - 12\right )^{2}}{x + \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((64*x^3-64*x^2-768*x)*log(x)+(64*x^3-832*x-768)*log(2)-64*x^3+64*x^2+768*x)*log(x^2-x-12)^2+(((-25
6*x^2+128*x)*log(2)+256*x^3-128*x^2)*log(x)+(-256*x^3+128*x^2)*log(2)+256*x^4-128*x^3)*log(x^2-x-12))/((x^3-x^
2-12*x)*log(x)^2+(2*x^4-2*x^3-24*x^2)*log(x)+x^5-x^4-12*x^3),x, algorithm="fricas")

[Out]

64*(x - log(2))*log(x^2 - x - 12)^2/(x + log(x))

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giac [A]  time = 0.23, size = 25, normalized size = 1.04 \begin {gather*} \frac {64 \, {\left (x - \log \relax (2)\right )} \log \left (x^{2} - x - 12\right )^{2}}{x + \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((64*x^3-64*x^2-768*x)*log(x)+(64*x^3-832*x-768)*log(2)-64*x^3+64*x^2+768*x)*log(x^2-x-12)^2+(((-25
6*x^2+128*x)*log(2)+256*x^3-128*x^2)*log(x)+(-256*x^3+128*x^2)*log(2)+256*x^4-128*x^3)*log(x^2-x-12))/((x^3-x^
2-12*x)*log(x)^2+(2*x^4-2*x^3-24*x^2)*log(x)+x^5-x^4-12*x^3),x, algorithm="giac")

[Out]

64*(x - log(2))*log(x^2 - x - 12)^2/(x + log(x))

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maple [A]  time = 0.07, size = 26, normalized size = 1.08

method	result	size
risch	\(-\frac {64 \left (\ln \relax (2)-x \right ) \ln \left (x^{2}-x -12\right )^{2}}{x +\ln \relax (x )}\)	\(26\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((64*x^3-64*x^2-768*x)*ln(x)+(64*x^3-832*x-768)*ln(2)-64*x^3+64*x^2+768*x)*ln(x^2-x-12)^2+(((-256*x^2+128
*x)*ln(2)+256*x^3-128*x^2)*ln(x)+(-256*x^3+128*x^2)*ln(2)+256*x^4-128*x^3)*ln(x^2-x-12))/((x^3-x^2-12*x)*ln(x)
^2+(2*x^4-2*x^3-24*x^2)*ln(x)+x^5-x^4-12*x^3),x,method=_RETURNVERBOSE)

[Out]

-64*(ln(2)-x)/(x+ln(x))*ln(x^2-x-12)^2

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maxima [B]  time = 0.49, size = 51, normalized size = 2.12 \begin {gather*} \frac {64 \, {\left ({\left (x - \log \relax (2)\right )} \log \left (x + 3\right )^{2} + 2 \, {\left (x - \log \relax (2)\right )} \log \left (x + 3\right ) \log \left (x - 4\right ) + {\left (x - \log \relax (2)\right )} \log \left (x - 4\right )^{2}\right )}}{x + \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((64*x^3-64*x^2-768*x)*log(x)+(64*x^3-832*x-768)*log(2)-64*x^3+64*x^2+768*x)*log(x^2-x-12)^2+(((-25
6*x^2+128*x)*log(2)+256*x^3-128*x^2)*log(x)+(-256*x^3+128*x^2)*log(2)+256*x^4-128*x^3)*log(x^2-x-12))/((x^3-x^
2-12*x)*log(x)^2+(2*x^4-2*x^3-24*x^2)*log(x)+x^5-x^4-12*x^3),x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 3.32, size = 67, normalized size = 2.79 \begin {gather*} -{\ln \left (x^2-x-12\right )}^2\,\left (\frac {\frac {64\,x}{x+1}+\ln \relax (x)\,\left (\frac {64\,x}{x+1}+\frac {64}{x+1}\right )+\frac {64\,\left (\ln \relax (2)-x+x\,\ln \relax (2)\right )}{x+1}}{x+\ln \relax (x)}-64\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x^2 - x - 12)^2*(log(2)*(832*x - 64*x^3 + 768) - 768*x - 64*x^2 + 64*x^3 + log(x)*(768*x + 64*x^2 - 6
4*x^3)) - log(x^2 - x - 12)*(log(x)*(log(2)*(128*x - 256*x^2) - 128*x^2 + 256*x^3) + log(2)*(128*x^2 - 256*x^3
) - 128*x^3 + 256*x^4))/(log(x)*(24*x^2 + 2*x^3 - 2*x^4) + 12*x^3 + x^4 - x^5 + log(x)^2*(12*x + x^2 - x^3)),x
)

[Out]

-log(x^2 - x - 12)^2*(((64*x)/(x + 1) + log(x)*((64*x)/(x + 1) + 64/(x + 1)) + (64*(log(2) - x + x*log(2)))/(x
+ 1))/(x + log(x)) - 64)

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sympy [A]  time = 0.52, size = 22, normalized size = 0.92 \begin {gather*} \frac {\left (64 x - 64 \log {\relax (2 )}\right ) \log {\left (x^{2} - x - 12 \right )}^{2}}{x + \log {\relax (x )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((64*x**3-64*x**2-768*x)*ln(x)+(64*x**3-832*x-768)*ln(2)-64*x**3+64*x**2+768*x)*ln(x**2-x-12)**2+((
(-256*x**2+128*x)*ln(2)+256*x**3-128*x**2)*ln(x)+(-256*x**3+128*x**2)*ln(2)+256*x**4-128*x**3)*ln(x**2-x-12))/
((x**3-x**2-12*x)*ln(x)**2+(2*x**4-2*x**3-24*x**2)*ln(x)+x**5-x**4-12*x**3),x)

[Out]

(64*x - 64*log(2))*log(x**2 - x - 12)**2/(x + log(x))

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