∫ 4 log( 1 x)+4 log( 1 x) log(x)+2 log(x) log(e2 log( 1 x))+(− log( 1 x)−log( 1 x) log(x)) log2(e2 log( 1 x))+(−4 log( 1 x) log(x)+log( 1 x) log(x) log2(e2 log( 1 x))) log(4x log(x)−x log(x) log2(e2 log( 1 x))) ______________________________________________________________________________________________________________________________ (−4 log( 1 x) log(x)+log( 1 x) log(x) log2(e2 log( 1 x))) log2(4x log(x)−x log(x) log2(e2 log( 1 x))) dx

3.33.18 \(\int \frac {4 \log (\frac {1}{x})+4 \log (\frac {1}{x}) \log (x)+2 \log (x) \log (e^2 \log (\frac {1}{x}))+(-\log (\frac {1}{x})-\log (\frac {1}{x}) \log (x)) \log ^2(e^2 \log (\frac {1}{x}))+(-4 \log (\frac {1}{x}) \log (x)+\log (\frac {1}{x}) \log (x) \log ^2(e^2 \log (\frac {1}{x}))) \log (4 x \log (x)-x \log (x) \log ^2(e^2 \log (\frac {1}{x})))}{(-4 \log (\frac {1}{x}) \log (x)+\log (\frac {1}{x}) \log (x) \log ^2(e^2 \log (\frac {1}{x}))) \log ^2(4 x \log (x)-x \log (x) \log ^2(e^2 \log (\frac {1}{x})))} \, dx\)

Optimal. Leaf size=24 \[ \frac {x}{\log \left (x \log (x) \left (4-\log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )\right )} \]

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Rubi [F] time = 3.90, 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 {4 \log \left (\frac {1}{x}\right )+4 \log \left (\frac {1}{x}\right ) \log (x)+2 \log (x) \log \left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (-\log \left (\frac {1}{x}\right )-\log \left (\frac {1}{x}\right ) \log (x)\right ) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (-4 \log \left (\frac {1}{x}\right ) \log (x)+\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right ) \log \left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )}{\left (-4 \log \left (\frac {1}{x}\right ) \log (x)+\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right ) \log ^2\left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(4*Log[x^(-1)] + 4*Log[x^(-1)]*Log[x] + 2*Log[x]*Log[E^2*Log[x^(-1)]] + (-Log[x^(-1)] - Log[x^(-1)]*Log[x]

)*Log[E^2*Log[x^(-1)]]^2 + (-4*Log[x^(-1)]*Log[x] + Log[x^(-1)]*Log[x]*Log[E^2*Log[x^(-1)]]^2)*Log[4*x*Log[x]

- x*Log[x]*Log[E^2*Log[x^(-1)]]^2])/((-4*Log[x^(-1)]*Log[x] + Log[x^(-1)]*Log[x]*Log[E^2*Log[x^(-1)]]^2)*Log[4

*x*Log[x] - x*Log[x]*Log[E^2*Log[x^(-1)]]^2]^2),x]

[Out]

-4*Defer[Int][1/((4 + Log[Log[x^(-1)]])*Log[-(x*Log[x]*Log[Log[x^(-1)]]*(4 + Log[Log[x^(-1)]]))]^2), x] + 2*De

fer[Int][1/(Log[x^(-1)]*(4 + Log[Log[x^(-1)]])*Log[-(x*Log[x]*Log[Log[x^(-1)]]*(4 + Log[Log[x^(-1)]]))]^2), x]

- 4*Defer[Int][1/(Log[x]*(4 + Log[Log[x^(-1)]])*Log[-(x*Log[x]*Log[Log[x^(-1)]]*(4 + Log[Log[x^(-1)]]))]^2),

x] + 4*Defer[Int][1/(Log[x^(-1)]*Log[Log[x^(-1)]]*(4 + Log[Log[x^(-1)]])*Log[-(x*Log[x]*Log[Log[x^(-1)]]*(4 +

Log[Log[x^(-1)]]))]^2), x] - Defer[Int][Log[Log[x^(-1)]]/((4 + Log[Log[x^(-1)]])*Log[-(x*Log[x]*Log[Log[x^(-1)

]]*(4 + Log[Log[x^(-1)]]))]^2), x] - Defer[Int][Log[Log[x^(-1)]]/(Log[x]*(4 + Log[Log[x^(-1)]])*Log[-(x*Log[x]

*Log[Log[x^(-1)]]*(4 + Log[Log[x^(-1)]]))]^2), x] + Defer[Int][Log[-(x*Log[x]*Log[Log[x^(-1)]]*(4 + Log[Log[x^

(-1)]]))]^(-1), x]

Rubi steps

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

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Mathematica [A] time = 0.13, size = 21, normalized size = 0.88 \begin {gather*} \frac {x}{\log \left (-x \log (x) \left (-4+\left (2+\log \left (\log \left (\frac {1}{x}\right )\right )\right )^2\right )\right )} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(4*Log[x^(-1)] + 4*Log[x^(-1)]*Log[x] + 2*Log[x]*Log[E^2*Log[x^(-1)]] + (-Log[x^(-1)] - Log[x^(-1)]*

Log[x])*Log[E^2*Log[x^(-1)]]^2 + (-4*Log[x^(-1)]*Log[x] + Log[x^(-1)]*Log[x]*Log[E^2*Log[x^(-1)]]^2)*Log[4*x*L

og[x] - x*Log[x]*Log[E^2*Log[x^(-1)]]^2])/((-4*Log[x^(-1)]*Log[x] + Log[x^(-1)]*Log[x]*Log[E^2*Log[x^(-1)]]^2)

*Log[4*x*Log[x] - x*Log[x]*Log[E^2*Log[x^(-1)]]^2]^2),x]

[Out]

x/Log[-(x*Log[x]*(-4 + (2 + Log[Log[x^(-1)]])^2))]

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fricas [A] time = 0.69, size = 29, normalized size = 1.21 \begin {gather*} \frac {x}{\log \left (x \log \left (e^{2} \log \left (\frac {1}{x}\right )\right )^{2} \log \left (\frac {1}{x}\right ) - 4 \, x \log \left (\frac {1}{x}\right )\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((log(1/x)*log(x)*log(exp(2)*log(1/x))^2-4*log(1/x)*log(x))*log(-x*log(x)*log(exp(2)*log(1/x))^2+4*x

*log(x))+(-log(1/x)*log(x)-log(1/x))*log(exp(2)*log(1/x))^2+2*log(x)*log(exp(2)*log(1/x))+4*log(1/x)*log(x)+4*

log(1/x))/(log(1/x)*log(x)*log(exp(2)*log(1/x))^2-4*log(1/x)*log(x))/log(-x*log(x)*log(exp(2)*log(1/x))^2+4*x*

log(x))^2,x, algorithm="fricas")

[Out]

x/log(x*log(e^2*log(1/x))^2*log(1/x) - 4*x*log(1/x))

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giac [C] time = 0.87, size = 1664, normalized size = 69.33 result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((log(1/x)*log(x)*log(exp(2)*log(1/x))^2-4*log(1/x)*log(x))*log(-x*log(x)*log(exp(2)*log(1/x))^2+4*x

*log(x))+(-log(1/x)*log(x)-log(1/x))*log(exp(2)*log(1/x))^2+2*log(x)*log(exp(2)*log(1/x))+4*log(1/x)*log(x)+4*

log(1/x))/(log(1/x)*log(x)*log(exp(2)*log(1/x))^2-4*log(1/x)*log(x))/log(-x*log(x)*log(exp(2)*log(1/x))^2+4*x*

log(x))^2,x, algorithm="giac")

[Out]

(pi^2*x*log(x)*log(-log(x))^2 - 2*I*pi*x*log(x)*log(-log(x))^2*log(log(x)) - x*log(x)*log(-log(x))^2*log(log(x

))^2 + 4*pi^2*x*log(x)*log(-log(x)) + pi^2*x*log(-log(x))^2 - 4*I*pi*x*log(x)*log(-log(x))^2 - 8*I*pi*x*log(x)

*log(-log(x))*log(log(x)) - 2*I*pi*x*log(-log(x))^2*log(log(x)) - 4*x*log(x)*log(-log(x))^2*log(log(x)) - 4*x*

log(x)*log(-log(x))*log(log(x))^2 - x*log(-log(x))^2*log(log(x))^2 + 4*pi^2*x*log(-log(x)) - 16*I*pi*x*log(x)*

log(-log(x)) - 6*I*pi*x*log(-log(x))^2 - 8*I*pi*x*log(-log(x))*log(log(x)) - 16*x*log(x)*log(-log(x))*log(log(

x)) - 6*x*log(-log(x))^2*log(log(x)) - 4*x*log(-log(x))*log(log(x))^2 - 24*I*pi*x*log(-log(x)) - 4*x*log(-log(

x))^2 - 24*x*log(-log(x))*log(log(x)) - 16*x*log(-log(x)))/(I*pi^3*log(x)*log(-log(x))^2 + pi^2*log(-log(-log(

x))^2 - 4*log(-log(x)))*log(x)*log(-log(x))^2 + pi^2*log(x)^2*log(-log(x))^2 + 3*pi^2*log(x)*log(-log(x))^2*lo

g(log(x)) - 2*I*pi*log(-log(-log(x))^2 - 4*log(-log(x)))*log(x)*log(-log(x))^2*log(log(x)) - 2*I*pi*log(x)^2*l

og(-log(x))^2*log(log(x)) - 3*I*pi*log(x)*log(-log(x))^2*log(log(x))^2 - log(-log(-log(x))^2 - 4*log(-log(x)))

*log(x)*log(-log(x))^2*log(log(x))^2 - log(x)^2*log(-log(x))^2*log(log(x))^2 - log(x)*log(-log(x))^2*log(log(x

))^3 + 4*I*pi^3*log(x)*log(-log(x)) + 4*pi^2*log(-log(-log(x))^2 - 4*log(-log(x)))*log(x)*log(-log(x)) + 4*pi^

2*log(x)^2*log(-log(x)) + I*pi^3*log(-log(x))^2 + pi^2*log(-log(-log(x))^2 - 4*log(-log(x)))*log(-log(x))^2 +

5*pi^2*log(x)*log(-log(x))^2 - 4*I*pi*log(-log(-log(x))^2 - 4*log(-log(x)))*log(x)*log(-log(x))^2 - 4*I*pi*log

(x)^2*log(-log(x))^2 + 12*pi^2*log(x)*log(-log(x))*log(log(x)) - 8*I*pi*log(-log(-log(x))^2 - 4*log(-log(x)))*

log(x)*log(-log(x))*log(log(x)) - 8*I*pi*log(x)^2*log(-log(x))*log(log(x)) + 3*pi^2*log(-log(x))^2*log(log(x))

- 2*I*pi*log(-log(-log(x))^2 - 4*log(-log(x)))*log(-log(x))^2*log(log(x)) - 10*I*pi*log(x)*log(-log(x))^2*log

(log(x)) - 4*log(-log(-log(x))^2 - 4*log(-log(x)))*log(x)*log(-log(x))^2*log(log(x)) - 4*log(x)^2*log(-log(x))

^2*log(log(x)) - 12*I*pi*log(x)*log(-log(x))*log(log(x))^2 - 4*log(-log(-log(x))^2 - 4*log(-log(x)))*log(x)*lo

g(-log(x))*log(log(x))^2 - 4*log(x)^2*log(-log(x))*log(log(x))^2 - 3*I*pi*log(-log(x))^2*log(log(x))^2 - log(-

log(-log(x))^2 - 4*log(-log(x)))*log(-log(x))^2*log(log(x))^2 - 5*log(x)*log(-log(x))^2*log(log(x))^2 - 4*log(

x)*log(-log(x))*log(log(x))^3 - log(-log(x))^2*log(log(x))^3 + 6*I*pi^3*log(-log(x)) + 6*pi^2*log(-log(-log(x)

)^2 - 4*log(-log(x)))*log(-log(x)) + 22*pi^2*log(x)*log(-log(x)) - 16*I*pi*log(-log(-log(x))^2 - 4*log(-log(x)

))*log(x)*log(-log(x)) - 16*I*pi*log(x)^2*log(-log(x)) + 4*pi^2*log(-log(x))^2 - 4*I*pi*log(-log(-log(x))^2 -

4*log(-log(x)))*log(-log(x))^2 - 4*I*pi*log(x)*log(-log(x))^2 + 18*pi^2*log(-log(x))*log(log(x)) - 12*I*pi*log

(-log(-log(x))^2 - 4*log(-log(x)))*log(-log(x))*log(log(x)) - 44*I*pi*log(x)*log(-log(x))*log(log(x)) - 16*log

(-log(-log(x))^2 - 4*log(-log(x)))*log(x)*log(-log(x))*log(log(x)) - 16*log(x)^2*log(-log(x))*log(log(x)) - 8*

I*pi*log(-log(x))^2*log(log(x)) - 4*log(-log(-log(x))^2 - 4*log(-log(x)))*log(-log(x))^2*log(log(x)) - 4*log(x

)*log(-log(x))^2*log(log(x)) - 18*I*pi*log(-log(x))*log(log(x))^2 - 6*log(-log(-log(x))^2 - 4*log(-log(x)))*lo

g(-log(x))*log(log(x))^2 - 22*log(x)*log(-log(x))*log(log(x))^2 - 4*log(-log(x))^2*log(log(x))^2 - 6*log(-log(

x))*log(log(x))^3 + 4*I*pi^3 + 4*pi^2*log(-log(-log(x))^2 - 4*log(-log(x))) + 4*pi^2*log(x) + 24*pi^2*log(-log

(x)) - 24*I*pi*log(-log(-log(x))^2 - 4*log(-log(x)))*log(-log(x)) - 24*I*pi*log(x)*log(-log(x)) + 12*pi^2*log(

log(x)) - 8*I*pi*log(-log(-log(x))^2 - 4*log(-log(x)))*log(log(x)) - 8*I*pi*log(x)*log(log(x)) - 48*I*pi*log(-

log(x))*log(log(x)) - 24*log(-log(-log(x))^2 - 4*log(-log(x)))*log(-log(x))*log(log(x)) - 24*log(x)*log(-log(x

))*log(log(x)) - 12*I*pi*log(log(x))^2 - 4*log(-log(-log(x))^2 - 4*log(-log(x)))*log(log(x))^2 - 4*log(x)*log(

log(x))^2 - 24*log(-log(x))*log(log(x))^2 - 4*log(log(x))^3 + 16*pi^2 - 16*I*pi*log(-log(-log(x))^2 - 4*log(-l

og(x))) - 16*I*pi*log(x) - 32*I*pi*log(log(x)) - 16*log(-log(-log(x))^2 - 4*log(-log(x)))*log(log(x)) - 16*log

(x)*log(log(x)) - 16*log(log(x))^2)

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maple [F] time = 0.19, size = 0, normalized size = 0.00 \[\int \frac {\left (\ln \left (\frac {1}{x}\right ) \ln \relax (x ) \ln \left ({\mathrm e}^{2} \ln \left (\frac {1}{x}\right )\right )^{2}-4 \ln \left (\frac {1}{x}\right ) \ln \relax (x )\right ) \ln \left (-x \ln \relax (x ) \ln \left ({\mathrm e}^{2} \ln \left (\frac {1}{x}\right )\right )^{2}+4 x \ln \relax (x )\right )+\left (-\ln \left (\frac {1}{x}\right ) \ln \relax (x )-\ln \left (\frac {1}{x}\right )\right ) \ln \left ({\mathrm e}^{2} \ln \left (\frac {1}{x}\right )\right )^{2}+2 \ln \relax (x ) \ln \left ({\mathrm e}^{2} \ln \left (\frac {1}{x}\right )\right )+4 \ln \left (\frac {1}{x}\right ) \ln \relax (x )+4 \ln \left (\frac {1}{x}\right )}{\left (\ln \left (\frac {1}{x}\right ) \ln \relax (x ) \ln \left ({\mathrm e}^{2} \ln \left (\frac {1}{x}\right )\right )^{2}-4 \ln \left (\frac {1}{x}\right ) \ln \relax (x )\right ) \ln \left (-x \ln \relax (x ) \ln \left ({\mathrm e}^{2} \ln \left (\frac {1}{x}\right )\right )^{2}+4 x \ln \relax (x )\right )^{2}}\, dx\]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((ln(1/x)*ln(x)*ln(exp(2)*ln(1/x))^2-4*ln(1/x)*ln(x))*ln(-x*ln(x)*ln(exp(2)*ln(1/x))^2+4*x*ln(x))+(-ln(1/x

)*ln(x)-ln(1/x))*ln(exp(2)*ln(1/x))^2+2*ln(x)*ln(exp(2)*ln(1/x))+4*ln(1/x)*ln(x)+4*ln(1/x))/(ln(1/x)*ln(x)*ln(

exp(2)*ln(1/x))^2-4*ln(1/x)*ln(x))/ln(-x*ln(x)*ln(exp(2)*ln(1/x))^2+4*x*ln(x))^2,x)

[Out]

int(((ln(1/x)*ln(x)*ln(exp(2)*ln(1/x))^2-4*ln(1/x)*ln(x))*ln(-x*ln(x)*ln(exp(2)*ln(1/x))^2+4*x*ln(x))+(-ln(1/x

)*ln(x)-ln(1/x))*ln(exp(2)*ln(1/x))^2+2*ln(x)*ln(exp(2)*ln(1/x))+4*ln(1/x)*ln(x)+4*ln(1/x))/(ln(1/x)*ln(x)*ln(

exp(2)*ln(1/x))^2-4*ln(1/x)*ln(x))/ln(-x*ln(x)*ln(exp(2)*ln(1/x))^2+4*x*ln(x))^2,x)

________________________________________________________________________________________

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(((log(1/x)*log(x)*log(exp(2)*log(1/x))^2-4*log(1/x)*log(x))*log(-x*log(x)*log(exp(2)*log(1/x))^2+4*x

*log(x))+(-log(1/x)*log(x)-log(1/x))*log(exp(2)*log(1/x))^2+2*log(x)*log(exp(2)*log(1/x))+4*log(1/x)*log(x)+4*

log(1/x))/(log(1/x)*log(x)*log(exp(2)*log(1/x))^2-4*log(1/x)*log(x))/log(-x*log(x)*log(exp(2)*log(1/x))^2+4*x*

log(x))^2,x, algorithm="maxima")

[Out]

(((4*I*pi - pi^2)*x*log(x) + (x*log(x) + x)*log(log(x))^2 + (6*I*pi - pi^2 + 4)*x - 2*((-I*pi - 2)*x*log(x) +

(-I*pi - 3)*x)*log(log(x)))*log(-log(x))^2 - 4*((-4*I*pi + pi^2)*x*log(x) - (x*log(x) + x)*log(log(x))^2 + (-6

*I*pi + pi^2 - 4)*x + 2*((-I*pi - 2)*x*log(x) + (-I*pi - 3)*x)*log(log(x)))*log(-log(x)))/(((log(x) + 1)*log(l

og(x))^3 + (4*I*pi - pi^2)*log(x)^2 + (2*I*pi + (2*I*pi + 5)*log(x) + log(x)^2 + 4)*log(log(x))^2 + (4*I*pi -

pi^2)*log(x) + (4*I*pi - 2*(-I*pi - 2)*log(x)^2 - pi^2 + (6*I*pi - pi^2 + 4)*log(x))*log(log(x)))*log(-log(x))

^2 - 4*(-2*I*pi - log(x) - 4)*log(log(x))^2 + 4*log(log(x))^3 - 4*(-4*I*pi + pi^2)*log(x) + 2*((2*log(x) + 3)*

log(log(x))^3 - 2*(-4*I*pi + pi^2)*log(x)^2 - (-6*I*pi + (-4*I*pi - 11)*log(x) - 2*log(x)^2 - 12)*log(log(x))^

2 - 3*(-4*I*pi + pi^2)*log(x) - (-12*I*pi + 4*(-I*pi - 2)*log(x)^2 + 3*pi^2 + 2*(-7*I*pi + pi^2 - 6)*log(x))*l

og(log(x)))*log(-log(x)) + (16*I*pi + (4*I*pi + (log(x) + 1)*log(log(x))^2 - pi^2 + (4*I*pi - pi^2)*log(x) - 2

*(-I*pi + (-I*pi - 2)*log(x) - 2)*log(log(x)))*log(-log(x))^2 - 4*pi^2 - 2*(-12*I*pi - (2*log(x) + 3)*log(log(

x))^2 + 3*pi^2 + 2*(-4*I*pi + pi^2)*log(x) + 2*(-3*I*pi + 2*(-I*pi - 2)*log(x) - 6)*log(log(x)))*log(-log(x))

- 8*(-I*pi - 2)*log(log(x)) + 4*log(log(x))^2)*log(-log(-log(x)) - 4) - 4*(-4*I*pi + pi^2 + 2*(-I*pi - 2)*log(

x))*log(log(x)) + (16*I*pi + (4*I*pi + (log(x) + 1)*log(log(x))^2 - pi^2 + (4*I*pi - pi^2)*log(x) - 2*(-I*pi +

(-I*pi - 2)*log(x) - 2)*log(log(x)))*log(-log(x))^2 - 4*pi^2 - 2*(-12*I*pi - (2*log(x) + 3)*log(log(x))^2 + 3

*pi^2 + 2*(-4*I*pi + pi^2)*log(x) + 2*(-3*I*pi + 2*(-I*pi - 2)*log(x) - 6)*log(log(x)))*log(-log(x)) - 8*(-I*p

i - 2)*log(log(x)) + 4*log(log(x))^2)*log(log(-log(x)))) - integrate(-2*(-128*I*pi + (4*I*pi - log(x)^2*log(lo

g(x))^3 + (-8*I*pi + I*pi^3 + 6*pi^2)*log(x)^2 + (3*(-I*pi - 2)*log(x)^2 + log(x) + 1)*log(log(x))^2 - pi^2 +

(4*I*pi - pi^2 + 8)*log(x) + (2*I*pi + (-12*I*pi + 3*pi^2 - 8)*log(x)^2 + 2*(I*pi + 2)*log(x) + 4)*log(log(x))

+ 8)*log(-log(x))^4 - 8*pi^4 + (40*I*pi + log(x)^2*log(log(x))^4 + 2*(2*I*pi*log(x)^2 - log(x))*log(log(x))^3

+ (-64*I*pi + pi^4 + 32*pi^2)*log(x)^2 - 2*((3*pi^2 + 16)*log(x)^2 - (-3*I*pi - 2)*log(x) - 5)*log(log(x))^2

- 10*pi^2 + 2*(8*I*pi + I*pi^3 + 2*pi^2 + 32)*log(x) + 2*(10*I*pi + 2*(-16*I*pi - I*pi^3 - 16)*log(x)^2 + (-4*

I*pi + 3*pi^2 + 8)*log(x) + 20)*log(log(x)) + 80)*log(-log(x))^3 + 16*(-2*I*pi - 5)*log(log(x))^3 - 8*log(log(

x))^4 + 80*I*pi^3 + (96*I*pi + (6*log(x)^2 + log(x) - 1)*log(log(x))^4 - pi^4 + 2*(-2*I*pi + 4*(3*I*pi + 4)*lo

g(x)^2 + 2*(I*pi - 1)*log(x) - 5)*log(log(x))^3 + 10*I*pi^3 + 2*(-64*I*pi + 3*pi^4 - 16*I*pi^3)*log(x)^2 + 2*(

-15*I*pi + 6*(8*I*pi - 3*pi^2)*log(x)^2 + 3*pi^2 + (-6*I*pi - 3*pi^2 - 20)*log(x))*log(log(x))^2 + (-32*I*pi +

pi^4 + 4*I*pi^3 + 40*pi^2 + 128)*log(x) + 2*(2*I*pi^3 + 4*(-3*I*pi^3 - 12*pi^2 - 16)*log(x)^2 + 15*pi^2 + 2*(

-20*I*pi - I*pi^3 + 3*pi^2 - 8)*log(x) + 48)*log(log(x)) + 224)*log(-log(x))^2 + 16*(-15*I*pi + 3*pi^2 - 14)*l

og(log(x))^2 + 224*pi^2 + 4*((2*log(x)^2 + log(x) - 1)*log(log(x))^4 - pi^4 + 2*(-2*I*pi + 4*(I*pi + 2)*log(x)

^2 + 2*(I*pi + 1)*log(x) - 5)*log(log(x))^3 + 10*I*pi^3 + 2*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)^2 + 2*(-15*I*pi

+ 2*(12*I*pi - 3*pi^2 + 8)*log(x)^2 + 3*pi^2 + (6*I*pi - 3*pi^2 - 4)*log(x) - 12)*log(log(x))^2 + 24*pi^2 + (

-32*I*pi + pi^4 - 4*I*pi^3 + 8*pi^2)*log(x) + 2*(-24*I*pi + 2*I*pi^3 + 4*(8*I*pi - I*pi^3 - 6*pi^2)*log(x)^2 +

15*pi^2 + 2*(-4*I*pi - I*pi^3 - 3*pi^2 - 8)*log(x))*log(log(x)) + 32)*log(-log(x)) + 16*(-28*I*pi + 2*I*pi^3

+ 15*pi^2 - 8)*log(log(x)))/(16*log(x)*log(log(x))^5 + ((log(x)^3 + 2*log(x)^2 + log(x))*log(log(x))^5 + (pi^4

- 8*I*pi^3 - 16*pi^2)*log(x)^4 - (2*(-2*I*pi - 5)*log(x)^3 - log(x)^4 - (8*I*pi + 17)*log(x)^2 + 4*(-I*pi - 2

)*log(x))*log(log(x))^4 + 2*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)^3 - 2*(2*(-I*pi - 2)*log(x)^4 + (-16*I*pi + 3*p

i^2 - 16)*log(x)^3 + 2*(-13*I*pi + 3*pi^2 - 10)*log(x)^2 + (-12*I*pi + 3*pi^2 - 8)*log(x))*log(log(x))^3 + (pi

^4 - 8*I*pi^3 - 16*pi^2)*log(x)^2 - 2*((-12*I*pi + 3*pi^2 - 8)*log(x)^4 + 2*(-20*I*pi + I*pi^3 + 9*pi^2 - 8)*l

og(x)^3 + (-44*I*pi + 4*I*pi^3 + 27*pi^2 - 8)*log(x)^2 + 2*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x))*log(log(x))^2 -

(4*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x)^4 - (64*I*pi + pi^4 - 16*I*pi^3 - 64*pi^2)*log(x)^3 + 2*(-16*I*pi - pi^

4 + 10*I*pi^3 + 28*pi^2)*log(x)^2 - (pi^4 - 8*I*pi^3 - 16*pi^2)*log(x))*log(log(x)))*log(-log(x))^4 - 16*(4*(-

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

8*I*pi^3 - 16*pi^2)*log(x)^4 - ((-8*I*pi - 21)*log(x)^3 - 2*log(x)^4 + (-20*I*pi - 43)*log(x)^2 + 12*(-I*pi -

2)*log(x))*log(log(x))^4 + 5*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)^3 - 2*(4*(-I*pi - 2)*log(x)^4 + 2*(-17*I*pi +

3*pi^2 - 18)*log(x)^3 + (-66*I*pi + 15*pi^2 - 52)*log(x)^2 + 3*(-12*I*pi + 3*pi^2 - 8)*log(x))*log(log(x))^3

+ 3*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)^2 - 2*(2*(-12*I*pi + 3*pi^2 - 8)*log(x)^4 + (-92*I*pi + 4*I*pi^3 + 39*p

i^2 - 40)*log(x)^3 + (-116*I*pi + 10*I*pi^3 + 69*pi^2 - 24)*log(x)^2 + 6*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x))*l

og(log(x))^2 - (8*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x)^4 + 2*(-80*I*pi - pi^4 + 18*I*pi^3 + 76*pi^2)*log(x)^3 +

(-96*I*pi - 5*pi^4 + 52*I*pi^3 + 152*pi^2)*log(x)^2 - 3*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x))*log(log(x)))*log(-

log(x))^3 - 32*(2*(-I*pi - 2)*log(x)^2 + (-12*I*pi + 3*pi^2 - 8)*log(x))*log(log(x))^3 + 16*(pi^4 - 8*I*pi^3 -

16*pi^2)*log(x)^2 + 4*((4*log(x)^3 + 14*log(x)^2 + 11*log(x))*log(log(x))^5 + 4*(pi^4 - 8*I*pi^3 - 16*pi^2)*l

og(x)^4 - (2*(-8*I*pi - 23)*log(x)^3 - 4*log(x)^4 + (-56*I*pi - 123)*log(x)^2 + 44*(-I*pi - 2)*log(x))*log(log

(x))^4 + 14*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)^3 - 2*(8*(-I*pi - 2)*log(x)^4 + 4*(-19*I*pi + 3*pi^2 - 22)*log(

x)^3 + 2*(-95*I*pi + 21*pi^2 - 78)*log(x)^2 + 11*(-12*I*pi + 3*pi^2 - 8)*log(x))*log(log(x))^3 + 11*(pi^4 - 8*

I*pi^3 - 16*pi^2)*log(x)^2 - 2*(4*(-12*I*pi + 3*pi^2 - 8)*log(x)^4 + 2*(-116*I*pi + 4*I*pi^3 + 45*pi^2 - 56)*l

og(x)^3 + (-356*I*pi + 28*I*pi^3 + 201*pi^2 - 88)*log(x)^2 + 22*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x))*log(log(x)

)^2 - (16*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x)^4 + 4*(-112*I*pi - pi^4 + 22*I*pi^3 + 100*pi^2)*log(x)^3 + 2*(-17

6*I*pi - 7*pi^4 + 78*I*pi^3 + 244*pi^2)*log(x)^2 - 11*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x))*log(log(x)))*log(-lo

g(x))^2 - 32*((-12*I*pi + 3*pi^2 - 8)*log(x)^2 + 2*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x))*log(log(x))^2 + 16*((2*

log(x)^2 + 3*log(x))*log(log(x))^5 - ((-8*I*pi - 19)*log(x)^2 - 2*log(x)^3 + 12*(-I*pi - 2)*log(x))*log(log(x)

)^4 + 2*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)^3 - 2*(4*(-I*pi - 2)*log(x)^3 + 2*(-15*I*pi + 3*pi^2 - 14)*log(x)^2

+ 3*(-12*I*pi + 3*pi^2 - 8)*log(x))*log(log(x))^3 + 3*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)^2 - 2*(2*(-12*I*pi +

3*pi^2 - 8)*log(x)^3 + (-68*I*pi + 4*I*pi^3 + 33*pi^2 - 24)*log(x)^2 + 6*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x))*

log(log(x))^2 - (8*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x)^3 + 2*(-48*I*pi - pi^4 + 14*I*pi^3 + 52*pi^2)*log(x)^2 -

3*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x))*log(log(x)))*log(-log(x)) + (((log(x)^3 + 2*log(x)^2 + log(x))*log(log(

x))^4 + (pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)^3 - 4*((-I*pi - 2)*log(x)^3 + 2*(-I*pi - 2)*log(x)^2 + (-I*pi - 2)*

log(x))*log(log(x))^3 + 2*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)^2 - 2*((-12*I*pi + 3*pi^2 - 8)*log(x)^3 + 2*(-12*

I*pi + 3*pi^2 - 8)*log(x)^2 + (-12*I*pi + 3*pi^2 - 8)*log(x))*log(log(x))^2 + (pi^4 - 8*I*pi^3 - 16*pi^2)*log(

x) - 4*((-8*I*pi + I*pi^3 + 6*pi^2)*log(x)^3 + 2*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x)^2 + (-8*I*pi + I*pi^3 + 6*

pi^2)*log(x))*log(log(x)))*log(-log(x))^4 - 64*(-I*pi - 2)*log(x)*log(log(x))^3 + 16*log(x)*log(log(x))^4 + 4*

((2*log(x)^3 + 5*log(x)^2 + 3*log(x))*log(log(x))^4 + 2*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)^3 - 4*(2*(-I*pi - 2

)*log(x)^3 + 5*(-I*pi - 2)*log(x)^2 + 3*(-I*pi - 2)*log(x))*log(log(x))^3 + 5*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(

x)^2 - 2*(2*(-12*I*pi + 3*pi^2 - 8)*log(x)^3 + 5*(-12*I*pi + 3*pi^2 - 8)*log(x)^2 + 3*(-12*I*pi + 3*pi^2 - 8)*

log(x))*log(log(x))^2 + 3*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x) - 4*(2*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x)^3 + 5*(

-8*I*pi + I*pi^3 + 6*pi^2)*log(x)^2 + 3*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x))*log(log(x)))*log(-log(x))^3 - 32*(

-12*I*pi + 3*pi^2 - 8)*log(x)*log(log(x))^2 + 4*((4*log(x)^3 + 14*log(x)^2 + 11*log(x))*log(log(x))^4 + 4*(pi^

4 - 8*I*pi^3 - 16*pi^2)*log(x)^3 - 4*(4*(-I*pi - 2)*log(x)^3 + 14*(-I*pi - 2)*log(x)^2 + 11*(-I*pi - 2)*log(x)

)*log(log(x))^3 + 14*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)^2 - 2*(4*(-12*I*pi + 3*pi^2 - 8)*log(x)^3 + 14*(-12*I*

pi + 3*pi^2 - 8)*log(x)^2 + 11*(-12*I*pi + 3*pi^2 - 8)*log(x))*log(log(x))^2 + 11*(pi^4 - 8*I*pi^3 - 16*pi^2)*

log(x) - 4*(4*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x)^3 + 14*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x)^2 + 11*(-8*I*pi + I

*pi^3 + 6*pi^2)*log(x))*log(log(x)))*log(-log(x))^2 - 64*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x)*log(log(x)) + 16*(

pi^4 - 8*I*pi^3 - 16*pi^2)*log(x) + 16*((2*log(x)^2 + 3*log(x))*log(log(x))^4 - 4*(2*(-I*pi - 2)*log(x)^2 + 3*

(-I*pi - 2)*log(x))*log(log(x))^3 + 2*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)^2 - 2*(2*(-12*I*pi + 3*pi^2 - 8)*log(

x)^2 + 3*(-12*I*pi + 3*pi^2 - 8)*log(x))*log(log(x))^2 + 3*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x) - 4*(2*(-8*I*pi

+ I*pi^3 + 6*pi^2)*log(x)^2 + 3*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x))*log(log(x)))*log(-log(x)))*log(-log(-log(x

)) - 4) - 16*(4*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x)^2 - (pi^4 - 8*I*pi^3 - 16*pi^2)*log(x))*log(log(x)) + (((lo

g(x)^3 + 2*log(x)^2 + log(x))*log(log(x))^4 + (pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)^3 - 4*((-I*pi - 2)*log(x)^3 +

2*(-I*pi - 2)*log(x)^2 + (-I*pi - 2)*log(x))*log(log(x))^3 + 2*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)^2 - 2*((-12

*I*pi + 3*pi^2 - 8)*log(x)^3 + 2*(-12*I*pi + 3*pi^2 - 8)*log(x)^2 + (-12*I*pi + 3*pi^2 - 8)*log(x))*log(log(x)

)^2 + (pi^4 - 8*I*pi^3 - 16*pi^2)*log(x) - 4*((-8*I*pi + I*pi^3 + 6*pi^2)*log(x)^3 + 2*(-8*I*pi + I*pi^3 + 6*p

i^2)*log(x)^2 + (-8*I*pi + I*pi^3 + 6*pi^2)*log(x))*log(log(x)))*log(-log(x))^4 - 64*(-I*pi - 2)*log(x)*log(lo

g(x))^3 + 16*log(x)*log(log(x))^4 + 4*((2*log(x)^3 + 5*log(x)^2 + 3*log(x))*log(log(x))^4 + 2*(pi^4 - 8*I*pi^3

- 16*pi^2)*log(x)^3 - 4*(2*(-I*pi - 2)*log(x)^3 + 5*(-I*pi - 2)*log(x)^2 + 3*(-I*pi - 2)*log(x))*log(log(x))^

3 + 5*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)^2 - 2*(2*(-12*I*pi + 3*pi^2 - 8)*log(x)^3 + 5*(-12*I*pi + 3*pi^2 - 8)

*log(x)^2 + 3*(-12*I*pi + 3*pi^2 - 8)*log(x))*log(log(x))^2 + 3*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x) - 4*(2*(-8*

I*pi + I*pi^3 + 6*pi^2)*log(x)^3 + 5*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x)^2 + 3*(-8*I*pi + I*pi^3 + 6*pi^2)*log(

x))*log(log(x)))*log(-log(x))^3 - 32*(-12*I*pi + 3*pi^2 - 8)*log(x)*log(log(x))^2 + 4*((4*log(x)^3 + 14*log(x)

^2 + 11*log(x))*log(log(x))^4 + 4*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)^3 - 4*(4*(-I*pi - 2)*log(x)^3 + 14*(-I*pi

- 2)*log(x)^2 + 11*(-I*pi - 2)*log(x))*log(log(x))^3 + 14*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)^2 - 2*(4*(-12*I*

pi + 3*pi^2 - 8)*log(x)^3 + 14*(-12*I*pi + 3*pi^2 - 8)*log(x)^2 + 11*(-12*I*pi + 3*pi^2 - 8)*log(x))*log(log(x

))^2 + 11*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x) - 4*(4*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x)^3 + 14*(-8*I*pi + I*pi^

3 + 6*pi^2)*log(x)^2 + 11*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x))*log(log(x)))*log(-log(x))^2 - 64*(-8*I*pi + I*pi

^3 + 6*pi^2)*log(x)*log(log(x)) + 16*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x) + 16*((2*log(x)^2 + 3*log(x))*log(log(

x))^4 - 4*(2*(-I*pi - 2)*log(x)^2 + 3*(-I*pi - 2)*log(x))*log(log(x))^3 + 2*(pi^4 - 8*I*pi^3 - 16*pi^2)*log(x)

^2 - 2*(2*(-12*I*pi + 3*pi^2 - 8)*log(x)^2 + 3*(-12*I*pi + 3*pi^2 - 8)*log(x))*log(log(x))^2 + 3*(pi^4 - 8*I*p

i^3 - 16*pi^2)*log(x) - 4*(2*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x)^2 + 3*(-8*I*pi + I*pi^3 + 6*pi^2)*log(x))*log(

log(x)))*log(-log(x)))*log(log(-log(x)))), x)

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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} -\int \frac {4\,\ln \left (\frac {1}{x}\right )-{\ln \left (\ln \left (\frac {1}{x}\right )\,{\mathrm {e}}^2\right )}^2\,\left (\ln \left (\frac {1}{x}\right )+\ln \left (\frac {1}{x}\right )\,\ln \relax (x)\right )+4\,\ln \left (\frac {1}{x}\right )\,\ln \relax (x)+2\,\ln \left (\ln \left (\frac {1}{x}\right )\,{\mathrm {e}}^2\right )\,\ln \relax (x)-\ln \left (4\,x\,\ln \relax (x)-x\,{\ln \left (\ln \left (\frac {1}{x}\right )\,{\mathrm {e}}^2\right )}^2\,\ln \relax (x)\right )\,\left (4\,\ln \left (\frac {1}{x}\right )\,\ln \relax (x)-\ln \left (\frac {1}{x}\right )\,{\ln \left (\ln \left (\frac {1}{x}\right )\,{\mathrm {e}}^2\right )}^2\,\ln \relax (x)\right )}{{\ln \left (4\,x\,\ln \relax (x)-x\,{\ln \left (\ln \left (\frac {1}{x}\right )\,{\mathrm {e}}^2\right )}^2\,\ln \relax (x)\right )}^2\,\left (4\,\ln \left (\frac {1}{x}\right )\,\ln \relax (x)-\ln \left (\frac {1}{x}\right )\,{\ln \left (\ln \left (\frac {1}{x}\right )\,{\mathrm {e}}^2\right )}^2\,\ln \relax (x)\right )} \,d x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(4*log(1/x) - log(log(1/x)*exp(2))^2*(log(1/x) + log(1/x)*log(x)) + 4*log(1/x)*log(x) + 2*log(log(1/x)*ex

p(2))*log(x) - log(4*x*log(x) - x*log(log(1/x)*exp(2))^2*log(x))*(4*log(1/x)*log(x) - log(1/x)*log(log(1/x)*ex

p(2))^2*log(x)))/(log(4*x*log(x) - x*log(log(1/x)*exp(2))^2*log(x))^2*(4*log(1/x)*log(x) - log(1/x)*log(log(1/

x)*exp(2))^2*log(x))),x)

[Out]

-int((4*log(1/x) - log(log(1/x)*exp(2))^2*(log(1/x) + log(1/x)*log(x)) + 4*log(1/x)*log(x) + 2*log(log(1/x)*ex

p(2))*log(x) - log(4*x*log(x) - x*log(log(1/x)*exp(2))^2*log(x))*(4*log(1/x)*log(x) - log(1/x)*log(log(1/x)*ex

p(2))^2*log(x)))/(log(4*x*log(x) - x*log(log(1/x)*exp(2))^2*log(x))^2*(4*log(1/x)*log(x) - log(1/x)*log(log(1/

x)*exp(2))^2*log(x))), x)

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sympy [A] time = 0.58, size = 26, normalized size = 1.08 \begin {gather*} \frac {x}{\log {\left (- x \log {\relax (x )} \log {\left (- e^{2} \log {\relax (x )} \right )}^{2} + 4 x \log {\relax (x )} \right )}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((ln(1/x)*ln(x)*ln(exp(2)*ln(1/x))**2-4*ln(1/x)*ln(x))*ln(-x*ln(x)*ln(exp(2)*ln(1/x))**2+4*x*ln(x))+

(-ln(1/x)*ln(x)-ln(1/x))*ln(exp(2)*ln(1/x))**2+2*ln(x)*ln(exp(2)*ln(1/x))+4*ln(1/x)*ln(x)+4*ln(1/x))/(ln(1/x)*

ln(x)*ln(exp(2)*ln(1/x))**2-4*ln(1/x)*ln(x))/ln(-x*ln(x)*ln(exp(2)*ln(1/x))**2+4*x*ln(x))**2,x)

[Out]

x/log(-x*log(x)*log(-exp(2)*log(x))**2 + 4*x*log(x))

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