3.24.100 \(\int \frac {-8 x^2+(4 x^2-4 x^5) \log (x)+(8 x+(-4 x+4 x^2) \log (x)) \log (\frac {3 \log (5) \log ^2(x)}{x})-4 x \log (x) \log ^2(\frac {3 \log (5) \log ^2(x)}{x})}{(9 x^4+6 x^6+x^8) \log (x)+(12 x^3+4 x^5) \log (x) \log (\frac {3 \log (5) \log ^2(x)}{x})+(-2 x^2-2 x^4) \log (x) \log ^2(\frac {3 \log (5) \log ^2(x)}{x})-4 x \log (x) \log ^3(\frac {3 \log (5) \log ^2(x)}{x})+\log (x) \log ^4(\frac {3 \log (5) \log ^2(x)}{x})} \, dx\)

Optimal. Leaf size=34 \[ 2+\frac {2}{4+x^2-\frac {\left (-x+\log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2}{x^2}} \]

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Rubi [F]  time = 3.44, 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 {-8 x^2+\left (4 x^2-4 x^5\right ) \log (x)+\left (8 x+\left (-4 x+4 x^2\right ) \log (x)\right ) \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-4 x \log (x) \log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )}{\left (9 x^4+6 x^6+x^8\right ) \log (x)+\left (12 x^3+4 x^5\right ) \log (x) \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )+\left (-2 x^2-2 x^4\right ) \log (x) \log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )-4 x \log (x) \log ^3\left (\frac {3 \log (5) \log ^2(x)}{x}\right )+\log (x) \log ^4\left (\frac {3 \log (5) \log ^2(x)}{x}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-8*x^2 + (4*x^2 - 4*x^5)*Log[x] + (8*x + (-4*x + 4*x^2)*Log[x])*Log[(3*Log[5]*Log[x]^2)/x] - 4*x*Log[x]*L
og[(3*Log[5]*Log[x]^2)/x]^2)/((9*x^4 + 6*x^6 + x^8)*Log[x] + (12*x^3 + 4*x^5)*Log[x]*Log[(3*Log[5]*Log[x]^2)/x
] + (-2*x^2 - 2*x^4)*Log[x]*Log[(3*Log[5]*Log[x]^2)/x]^2 - 4*x*Log[x]*Log[(3*Log[5]*Log[x]^2)/x]^3 + Log[x]*Lo
g[(3*Log[5]*Log[x]^2)/x]^4),x]

[Out]

4*Defer[Int][x^2/(3*x^2 + x^4 + 2*x*Log[(3*Log[5]*Log[x]^2)/x] - Log[(3*Log[5]*Log[x]^2)/x]^2)^2, x] - 12*Defe
r[Int][x^3/(3*x^2 + x^4 + 2*x*Log[(3*Log[5]*Log[x]^2)/x] - Log[(3*Log[5]*Log[x]^2)/x]^2)^2, x] - 8*Defer[Int][
x^5/(3*x^2 + x^4 + 2*x*Log[(3*Log[5]*Log[x]^2)/x] - Log[(3*Log[5]*Log[x]^2)/x]^2)^2, x] - 8*Defer[Int][x^2/(Lo
g[x]*(3*x^2 + x^4 + 2*x*Log[(3*Log[5]*Log[x]^2)/x] - Log[(3*Log[5]*Log[x]^2)/x]^2)^2), x] - 4*Defer[Int][(x*Lo
g[(3*Log[5]*Log[x]^2)/x])/(3*x^2 + x^4 + 2*x*Log[(3*Log[5]*Log[x]^2)/x] - Log[(3*Log[5]*Log[x]^2)/x]^2)^2, x]
- 4*Defer[Int][(x^2*Log[(3*Log[5]*Log[x]^2)/x])/(3*x^2 + x^4 + 2*x*Log[(3*Log[5]*Log[x]^2)/x] - Log[(3*Log[5]*
Log[x]^2)/x]^2)^2, x] + 8*Defer[Int][(x*Log[(3*Log[5]*Log[x]^2)/x])/(Log[x]*(3*x^2 + x^4 + 2*x*Log[(3*Log[5]*L
og[x]^2)/x] - Log[(3*Log[5]*Log[x]^2)/x]^2)^2), x] + 4*Defer[Int][x/(3*x^2 + x^4 + 2*x*Log[(3*Log[5]*Log[x]^2)
/x] - Log[(3*Log[5]*Log[x]^2)/x]^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 x \left (-2 \left (x-\log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )-\log (x) \left (x \left (-1+x^3\right )-(-1+x) \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )+\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )\right )}{\log (x) \left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2} \, dx\\ &=4 \int \frac {x \left (-2 \left (x-\log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )-\log (x) \left (x \left (-1+x^3\right )-(-1+x) \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )+\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )\right )}{\log (x) \left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2} \, dx\\ &=4 \int \left (-\frac {x \left (2 x-x \log (x)+3 x^2 \log (x)+2 x^4 \log (x)-2 \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )+\log (x) \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )+x \log (x) \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )}{\log (x) \left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2}+\frac {x}{3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )}\right ) \, dx\\ &=-\left (4 \int \frac {x \left (2 x-x \log (x)+3 x^2 \log (x)+2 x^4 \log (x)-2 \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )+\log (x) \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )+x \log (x) \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )}{\log (x) \left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2} \, dx\right )+4 \int \frac {x}{3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )} \, dx\\ &=4 \int \frac {x}{3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )} \, dx-4 \int \left (-\frac {x^2}{\left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2}+\frac {3 x^3}{\left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2}+\frac {2 x^5}{\left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2}+\frac {2 x^2}{\log (x) \left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2}+\frac {x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )}{\left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2}+\frac {x^2 \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )}{\left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2}-\frac {2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )}{\log (x) \left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2}\right ) \, dx\\ &=4 \int \frac {x^2}{\left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2} \, dx-4 \int \frac {x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )}{\left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2} \, dx-4 \int \frac {x^2 \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )}{\left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2} \, dx+4 \int \frac {x}{3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )} \, dx-8 \int \frac {x^5}{\left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2} \, dx-8 \int \frac {x^2}{\log (x) \left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2} \, dx+8 \int \frac {x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )}{\log (x) \left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2} \, dx-12 \int \frac {x^3}{\left (3 x^2+x^4+2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )-\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.08, size = 47, normalized size = 1.38 \begin {gather*} -\frac {2 x^2}{-3 x^2-x^4-2 x \log \left (\frac {3 \log (5) \log ^2(x)}{x}\right )+\log ^2\left (\frac {3 \log (5) \log ^2(x)}{x}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-8*x^2 + (4*x^2 - 4*x^5)*Log[x] + (8*x + (-4*x + 4*x^2)*Log[x])*Log[(3*Log[5]*Log[x]^2)/x] - 4*x*Lo
g[x]*Log[(3*Log[5]*Log[x]^2)/x]^2)/((9*x^4 + 6*x^6 + x^8)*Log[x] + (12*x^3 + 4*x^5)*Log[x]*Log[(3*Log[5]*Log[x
]^2)/x] + (-2*x^2 - 2*x^4)*Log[x]*Log[(3*Log[5]*Log[x]^2)/x]^2 - 4*x*Log[x]*Log[(3*Log[5]*Log[x]^2)/x]^3 + Log
[x]*Log[(3*Log[5]*Log[x]^2)/x]^4),x]

[Out]

(-2*x^2)/(-3*x^2 - x^4 - 2*x*Log[(3*Log[5]*Log[x]^2)/x] + Log[(3*Log[5]*Log[x]^2)/x]^2)

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fricas [A]  time = 0.65, size = 47, normalized size = 1.38 \begin {gather*} \frac {2 \, x^{2}}{x^{4} + 3 \, x^{2} + 2 \, x \log \left (\frac {3 \, \log \relax (5) \log \relax (x)^{2}}{x}\right ) - \log \left (\frac {3 \, \log \relax (5) \log \relax (x)^{2}}{x}\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x*log(x)*log(3*log(5)*log(x)^2/x)^2+((4*x^2-4*x)*log(x)+8*x)*log(3*log(5)*log(x)^2/x)+(-4*x^5+4*
x^2)*log(x)-8*x^2)/(log(x)*log(3*log(5)*log(x)^2/x)^4-4*x*log(x)*log(3*log(5)*log(x)^2/x)^3+(-2*x^4-2*x^2)*log
(x)*log(3*log(5)*log(x)^2/x)^2+(4*x^5+12*x^3)*log(x)*log(3*log(5)*log(x)^2/x)+(x^8+6*x^6+9*x^4)*log(x)),x, alg
orithm="fricas")

[Out]

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

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giac [A]  time = 4.11, size = 65, normalized size = 1.91 \begin {gather*} \frac {2 \, x^{2}}{x^{4} + 3 \, x^{2} + 2 \, x \log \left (3 \, \log \relax (5) \log \relax (x)^{2}\right ) - \log \left (3 \, \log \relax (5) \log \relax (x)^{2}\right )^{2} - 2 \, x \log \relax (x) + 2 \, \log \left (3 \, \log \relax (5) \log \relax (x)^{2}\right ) \log \relax (x) - \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x*log(x)*log(3*log(5)*log(x)^2/x)^2+((4*x^2-4*x)*log(x)+8*x)*log(3*log(5)*log(x)^2/x)+(-4*x^5+4*
x^2)*log(x)-8*x^2)/(log(x)*log(3*log(5)*log(x)^2/x)^4-4*x*log(x)*log(3*log(5)*log(x)^2/x)^3+(-2*x^4-2*x^2)*log
(x)*log(3*log(5)*log(x)^2/x)^2+(4*x^5+12*x^3)*log(x)*log(3*log(5)*log(x)^2/x)+(x^8+6*x^6+9*x^4)*log(x)),x, alg
orithm="giac")

[Out]

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

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maple [C]  time = 22.81, size = 1723, normalized size = 50.68

method	result	size
risch	\(\text {Expression too large to display}\)	\(1723\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-4*x*ln(x)*ln(3*ln(5)*ln(x)^2/x)^2+((4*x^2-4*x)*ln(x)+8*x)*ln(3*ln(5)*ln(x)^2/x)+(-4*x^5+4*x^2)*ln(x)-8*x
^2)/(ln(x)*ln(3*ln(5)*ln(x)^2/x)^4-4*x*ln(x)*ln(3*ln(5)*ln(x)^2/x)^3+(-2*x^4-2*x^2)*ln(x)*ln(3*ln(5)*ln(x)^2/x
)^2+(4*x^5+12*x^3)*ln(x)*ln(3*ln(5)*ln(x)^2/x)+(x^8+6*x^6+9*x^4)*ln(x)),x,method=_RETURNVERBOSE)

[Out]

8*x^2/(-2*Pi^2*csgn(I*ln(x)^2)^4*csgn(I/x*ln(x)^2)^2+Pi^2*csgn(I*ln(x)^2)^6+Pi^2*csgn(I/x*ln(x)^2)^6-16*ln(3)*
ln(ln(x))+8*ln(ln(5))*ln(x)-16*ln(ln(5))*ln(ln(x))-4*ln(ln(5))^2+16*x*ln(ln(x))-4*ln(3)^2-16*ln(ln(x))^2-4*ln(
x)^2+4*x^4+12*x^2+16*ln(x)*ln(ln(x))+8*ln(3)*ln(x)+8*x*ln(3)-8*x*ln(x)-4*I*ln(x)*Pi*csgn(I/x*ln(x)^2)*csgn(I/x
)*csgn(I*ln(x)^2)+4*I*ln(ln(5))*Pi*csgn(I/x*ln(x)^2)*csgn(I/x)*csgn(I*ln(x)^2)+4*I*ln(3)*Pi*csgn(I/x*ln(x)^2)*
csgn(I/x)*csgn(I*ln(x)^2)+8*I*ln(ln(x))*Pi*csgn(I/x*ln(x)^2)*csgn(I/x)*csgn(I*ln(x)^2)-4*I*Pi*x*csgn(I/x*ln(x)
^2)*csgn(I/x)*csgn(I*ln(x)^2)+8*x*ln(ln(5))+4*I*ln(x)*Pi*csgn(I/x*ln(x)^2)^2*csgn(I/x)+4*I*ln(x)*Pi*csgn(I/x*l
n(x)^2)^2*csgn(I*ln(x)^2)+8*I*ln(ln(x))*Pi*csgn(I*ln(x))^2*csgn(I*ln(x)^2)-16*I*ln(ln(x))*Pi*csgn(I*ln(x))*csg
n(I*ln(x)^2)^2-8*I*ln(ln(x))*Pi*csgn(I/x*ln(x)^2)^2*csgn(I/x)-8*I*ln(ln(x))*Pi*csgn(I/x*ln(x)^2)^2*csgn(I*ln(x
)^2)-4*I*ln(ln(5))*Pi*csgn(I/x*ln(x)^2)^2*csgn(I*ln(x)^2)+2*Pi^2*csgn(I*ln(x))^2*csgn(I*ln(x)^2)^2*csgn(I/x*ln
(x)^2)*csgn(I/x)+2*Pi^2*csgn(I*ln(x))^2*csgn(I*ln(x)^2)*csgn(I/x*ln(x)^2)^3+4*Pi^2*csgn(I*ln(x))*csgn(I*ln(x)^
2)^2*csgn(I/x*ln(x)^2)^2*csgn(I/x)-4*Pi^2*csgn(I*ln(x))*csgn(I*ln(x)^2)^3*csgn(I/x*ln(x)^2)*csgn(I/x)-4*Pi^2*c
sgn(I*ln(x))*csgn(I*ln(x)^2)^2*csgn(I/x*ln(x)^2)^3+4*Pi^2*csgn(I/x*ln(x)^2)^4*csgn(I/x)*csgn(I*ln(x)^2)-2*Pi^2
*csgn(I*ln(x))^2*csgn(I*ln(x)^2)*csgn(I/x*ln(x)^2)^2*csgn(I/x)-4*I*ln(3)*Pi*csgn(I/x*ln(x)^2)^2*csgn(I*ln(x)^2
)+4*I*ln(ln(5))*Pi*csgn(I*ln(x))^2*csgn(I*ln(x)^2)-8*I*ln(ln(5))*Pi*csgn(I*ln(x))*csgn(I*ln(x)^2)^2-4*I*ln(ln(
5))*Pi*csgn(I/x*ln(x)^2)^2*csgn(I/x)+4*I*Pi*x*csgn(I/x*ln(x)^2)^2*csgn(I*ln(x)^2)-4*I*Pi*x*csgn(I*ln(x))^2*csg
n(I*ln(x)^2)+8*I*Pi*x*csgn(I*ln(x))*csgn(I*ln(x)^2)^2+4*I*ln(3)*Pi*csgn(I*ln(x))^2*csgn(I*ln(x)^2)-8*I*ln(3)*P
i*csgn(I*ln(x))*csgn(I*ln(x)^2)^2-4*I*ln(3)*Pi*csgn(I/x*ln(x)^2)^2*csgn(I/x)+4*I*Pi*x*csgn(I/x*ln(x)^2)^2*csgn
(I/x)-4*I*ln(x)*Pi*csgn(I*ln(x))^2*csgn(I*ln(x)^2)+8*I*ln(x)*Pi*csgn(I*ln(x))*csgn(I*ln(x)^2)^2-8*ln(3)*ln(ln(
5))+2*Pi^2*csgn(I*ln(x)^2)^4*csgn(I/x*ln(x)^2)*csgn(I/x)+4*I*ln(ln(5))*Pi*csgn(I/x*ln(x)^2)^3-4*I*ln(x)*Pi*csg
n(I*ln(x)^2)^3-4*I*ln(x)*Pi*csgn(I/x*ln(x)^2)^3+8*I*ln(ln(x))*Pi*csgn(I*ln(x)^2)^3+8*I*ln(ln(x))*Pi*csgn(I/x*l
n(x)^2)^3-4*I*Pi*x*csgn(I/x*ln(x)^2)^3-4*I*Pi*x*csgn(I*ln(x)^2)^3+4*I*ln(3)*Pi*csgn(I*ln(x)^2)^3+4*I*ln(3)*Pi*
csgn(I/x*ln(x)^2)^3+4*I*ln(ln(5))*Pi*csgn(I*ln(x)^2)^3+2*Pi^2*csgn(I*ln(x)^2)^3*csgn(I/x*ln(x)^2)^3-2*Pi^2*csg
n(I/x*ln(x)^2)^3*csgn(I/x)^2*csgn(I*ln(x)^2)-2*Pi^2*csgn(I/x*ln(x)^2)^5*csgn(I/x)-2*Pi^2*csgn(I/x*ln(x)^2)^3*c
sgn(I*ln(x)^2)^2*csgn(I/x)-2*Pi^2*csgn(I/x*ln(x)^2)^5*csgn(I*ln(x)^2)+Pi^2*csgn(I/x*ln(x)^2)^2*csgn(I/x)^2*csg
n(I*ln(x)^2)^2-2*Pi^2*csgn(I*ln(x))^2*csgn(I*ln(x)^2)^2*csgn(I/x*ln(x)^2)^2+4*Pi^2*csgn(I*ln(x))*csgn(I*ln(x)^
2)^3*csgn(I/x*ln(x)^2)^2-2*Pi^2*csgn(I*ln(x)^2)^3*csgn(I/x*ln(x)^2)^2*csgn(I/x)+Pi^2*csgn(I/x*ln(x)^2)^4*csgn(
I*ln(x)^2)^2+Pi^2*csgn(I/x*ln(x)^2)^4*csgn(I/x)^2+Pi^2*csgn(I*ln(x))^4*csgn(I*ln(x)^2)^2-4*Pi^2*csgn(I*ln(x))^
3*csgn(I*ln(x)^2)^3+6*Pi^2*csgn(I*ln(x))^2*csgn(I*ln(x)^2)^4-4*Pi^2*csgn(I*ln(x))*csgn(I*ln(x)^2)^5)

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maxima [B]  time = 0.78, size = 91, normalized size = 2.68 \begin {gather*} \frac {2 \, x^{2}}{x^{4} + 3 \, x^{2} + 2 \, x {\left (\log \relax (3) + \log \left (\log \relax (5)\right )\right )} - \log \relax (3)^{2} - 2 \, {\left (x - \log \relax (3) - \log \left (\log \relax (5)\right )\right )} \log \relax (x) - \log \relax (x)^{2} - 2 \, \log \relax (3) \log \left (\log \relax (5)\right ) - \log \left (\log \relax (5)\right )^{2} + 4 \, {\left (x - \log \relax (3) + \log \relax (x) - \log \left (\log \relax (5)\right )\right )} \log \left (\log \relax (x)\right ) - 4 \, \log \left (\log \relax (x)\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x*log(x)*log(3*log(5)*log(x)^2/x)^2+((4*x^2-4*x)*log(x)+8*x)*log(3*log(5)*log(x)^2/x)+(-4*x^5+4*
x^2)*log(x)-8*x^2)/(log(x)*log(3*log(5)*log(x)^2/x)^4-4*x*log(x)*log(3*log(5)*log(x)^2/x)^3+(-2*x^4-2*x^2)*log
(x)*log(3*log(5)*log(x)^2/x)^2+(4*x^5+12*x^3)*log(x)*log(3*log(5)*log(x)^2/x)+(x^8+6*x^6+9*x^4)*log(x)),x, alg
orithm="maxima")

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x)*(4*x^2 - 4*x^5) + log((3*log(5)*log(x)^2)/x)*(8*x - log(x)*(4*x - 4*x^2)) - 8*x^2 - 4*x*log((3*log
(5)*log(x)^2)/x)^2*log(x))/(log(x)*(9*x^4 + 6*x^6 + x^8) + log((3*log(5)*log(x)^2)/x)^4*log(x) + log((3*log(5)
*log(x)^2)/x)*log(x)*(12*x^3 + 4*x^5) - 4*x*log((3*log(5)*log(x)^2)/x)^3*log(x) - log((3*log(5)*log(x)^2)/x)^2
*log(x)*(2*x^2 + 2*x^4)),x)

[Out]

int((log(x)*(4*x^2 - 4*x^5) + log((3*log(5)*log(x)^2)/x)*(8*x - log(x)*(4*x - 4*x^2)) - 8*x^2 - 4*x*log((3*log
(5)*log(x)^2)/x)^2*log(x))/(log(x)*(9*x^4 + 6*x^6 + x^8) + log((3*log(5)*log(x)^2)/x)^4*log(x) + log((3*log(5)
*log(x)^2)/x)*log(x)*(12*x^3 + 4*x^5) - 4*x*log((3*log(5)*log(x)^2)/x)^3*log(x) - log((3*log(5)*log(x)^2)/x)^2
*log(x)*(2*x^2 + 2*x^4)), x)

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sympy [A]  time = 0.52, size = 46, normalized size = 1.35 \begin {gather*} - \frac {2 x^{2}}{- x^{4} - 3 x^{2} - 2 x \log {\left (\frac {3 \log {\relax (5 )} \log {\relax (x )}^{2}}{x} \right )} + \log {\left (\frac {3 \log {\relax (5 )} \log {\relax (x )}^{2}}{x} \right )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x*ln(x)*ln(3*ln(5)*ln(x)**2/x)**2+((4*x**2-4*x)*ln(x)+8*x)*ln(3*ln(5)*ln(x)**2/x)+(-4*x**5+4*x**
2)*ln(x)-8*x**2)/(ln(x)*ln(3*ln(5)*ln(x)**2/x)**4-4*x*ln(x)*ln(3*ln(5)*ln(x)**2/x)**3+(-2*x**4-2*x**2)*ln(x)*l
n(3*ln(5)*ln(x)**2/x)**2+(4*x**5+12*x**3)*ln(x)*ln(3*ln(5)*ln(x)**2/x)+(x**8+6*x**6+9*x**4)*ln(x)),x)

[Out]

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

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