3.28.87 \(\int \frac {-123904 x^2+5632 x^3-64 x^4+(4224 x+61856 x^2-4224 x^3+64 x^4) \log (x)+(-32-1408 x+64 x^2) \log ^2(x)+(123904 x^2-5632 x^3+64 x^4+(-2816 x-123840 x^2+8448 x^3-128 x^4) \log (x)+(2816 x-128 x^2) \log ^2(x)) \log (\log ^2(x))+((-1408 x+61984 x^2-4224 x^3+64 x^4) \log (x)+(32-1408 x+64 x^2) \log ^2(x)) \log ^2(\log ^2(x))}{x \log (x)} \, dx\)

Optimal. Leaf size=22 \[ 16 \left (-44 x+x^2+\log (x)\right )^2 \left (-1+\log \left (\log ^2(x)\right )\right )^2 \]

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Rubi [F]  time = 2.37, 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 {-123904 x^2+5632 x^3-64 x^4+\left (4224 x+61856 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (-32-1408 x+64 x^2\right ) \log ^2(x)+\left (123904 x^2-5632 x^3+64 x^4+\left (-2816 x-123840 x^2+8448 x^3-128 x^4\right ) \log (x)+\left (2816 x-128 x^2\right ) \log ^2(x)\right ) \log \left (\log ^2(x)\right )+\left (\left (-1408 x+61984 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (32-1408 x+64 x^2\right ) \log ^2(x)\right ) \log ^2\left (\log ^2(x)\right )}{x \log (x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-123904*x^2 + 5632*x^3 - 64*x^4 + (4224*x + 61856*x^2 - 4224*x^3 + 64*x^4)*Log[x] + (-32 - 1408*x + 64*x^
2)*Log[x]^2 + (123904*x^2 - 5632*x^3 + 64*x^4 + (-2816*x - 123840*x^2 + 8448*x^3 - 128*x^4)*Log[x] + (2816*x -
128*x^2)*Log[x]^2)*Log[Log[x]^2] + ((-1408*x + 61984*x^2 - 4224*x^3 + 64*x^4)*Log[x] + (32 - 1408*x + 64*x^2)
*Log[x]^2)*Log[Log[x]^2]^2)/(x*Log[x]),x]

[Out]

5632*x + 30912*x^2 - 1408*x^3 + 16*x^4 - 64*ExpIntegralEi[2*Log[x]] - 1408*x*Log[x] + 32*x^2*Log[x] + 16*Log[x
]^2 - 2816*x*Log[Log[x]^2] - 61920*x^2*Log[Log[x]^2] + 2816*x^3*Log[Log[x]^2] - 32*x^4*Log[Log[x]^2] - 32*Log[
x]^2*Log[Log[x]^2] + 16*Log[x]^2*Log[Log[x]^2]^2 + 5632*LogIntegral[x] + 123904*Defer[Int][(x*Log[Log[x]^2])/L
og[x], x] - 5632*Defer[Int][(x^2*Log[Log[x]^2])/Log[x], x] + 64*Defer[Int][(x^3*Log[Log[x]^2])/Log[x], x] + 28
16*Defer[Int][Log[x]*Log[Log[x]^2], x] - 128*Defer[Int][x*Log[x]*Log[Log[x]^2], x] - 1408*Defer[Int][Log[Log[x
]^2]^2, x] + 61984*Defer[Int][x*Log[Log[x]^2]^2, x] - 4224*Defer[Int][x^2*Log[Log[x]^2]^2, x] + 64*Defer[Int][
x^3*Log[Log[x]^2]^2, x] - 1408*Defer[Int][Log[x]*Log[Log[x]^2]^2, x] + 64*Defer[Int][x*Log[x]*Log[Log[x]^2]^2,
x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {32 ((-44+x) x+\log (x)) \left (1-\log \left (\log ^2(x)\right )\right ) \left (-2 (-44+x) x-\log (x) \left (1+44 x-2 x^2+\left (1-44 x+2 x^2\right ) \log \left (\log ^2(x)\right )\right )\right )}{x \log (x)} \, dx\\ &=32 \int \frac {((-44+x) x+\log (x)) \left (1-\log \left (\log ^2(x)\right )\right ) \left (-2 (-44+x) x-\log (x) \left (1+44 x-2 x^2+\left (1-44 x+2 x^2\right ) \log \left (\log ^2(x)\right )\right )\right )}{x \log (x)} \, dx\\ &=32 \int \left (\frac {-3872 x^2+176 x^3-2 x^4+132 x \log (x)+1933 x^2 \log (x)-132 x^3 \log (x)+2 x^4 \log (x)-\log ^2(x)-44 x \log ^2(x)+2 x^2 \log ^2(x)}{x \log (x)}-\frac {2 \left (-1936 x+88 x^2-x^3+44 \log (x)+1935 x \log (x)-132 x^2 \log (x)+2 x^3 \log (x)-44 \log ^2(x)+2 x \log ^2(x)\right ) \log \left (\log ^2(x)\right )}{\log (x)}+\frac {\left (1-44 x+2 x^2\right ) \left (-44 x+x^2+\log (x)\right ) \log ^2\left (\log ^2(x)\right )}{x}\right ) \, dx\\ &=32 \int \frac {-3872 x^2+176 x^3-2 x^4+132 x \log (x)+1933 x^2 \log (x)-132 x^3 \log (x)+2 x^4 \log (x)-\log ^2(x)-44 x \log ^2(x)+2 x^2 \log ^2(x)}{x \log (x)} \, dx+32 \int \frac {\left (1-44 x+2 x^2\right ) \left (-44 x+x^2+\log (x)\right ) \log ^2\left (\log ^2(x)\right )}{x} \, dx-64 \int \frac {\left (-1936 x+88 x^2-x^3+44 \log (x)+1935 x \log (x)-132 x^2 \log (x)+2 x^3 \log (x)-44 \log ^2(x)+2 x \log ^2(x)\right ) \log \left (\log ^2(x)\right )}{\log (x)} \, dx\\ &=32 \int \left (132+1933 x-132 x^2+2 x^3-\frac {2 (-44+x)^2 x}{\log (x)}+\left (-44-\frac {1}{x}+2 x\right ) \log (x)\right ) \, dx+32 \int \left (-44 \left (-44 x+x^2+\log (x)\right ) \log ^2\left (\log ^2(x)\right )+\frac {\left (-44 x+x^2+\log (x)\right ) \log ^2\left (\log ^2(x)\right )}{x}+2 x \left (-44 x+x^2+\log (x)\right ) \log ^2\left (\log ^2(x)\right )\right ) \, dx-64 \int \frac {\left (-(-44+x)^2 x+\left (44+1935 x-132 x^2+2 x^3\right ) \log (x)+2 (-22+x) \log ^2(x)\right ) \log \left (\log ^2(x)\right )}{\log (x)} \, dx\\ &=4224 x+30928 x^2-1408 x^3+16 x^4+32 \int \left (-44-\frac {1}{x}+2 x\right ) \log (x) \, dx+32 \int \frac {\left (-44 x+x^2+\log (x)\right ) \log ^2\left (\log ^2(x)\right )}{x} \, dx-64 \int \frac {(-44+x)^2 x}{\log (x)} \, dx+64 \int x \left (-44 x+x^2+\log (x)\right ) \log ^2\left (\log ^2(x)\right ) \, dx-64 \int \left (44 \log \left (\log ^2(x)\right )+1935 x \log \left (\log ^2(x)\right )-132 x^2 \log \left (\log ^2(x)\right )+2 x^3 \log \left (\log ^2(x)\right )-\frac {1936 x \log \left (\log ^2(x)\right )}{\log (x)}+\frac {88 x^2 \log \left (\log ^2(x)\right )}{\log (x)}-\frac {x^3 \log \left (\log ^2(x)\right )}{\log (x)}-44 \log (x) \log \left (\log ^2(x)\right )+2 x \log (x) \log \left (\log ^2(x)\right )\right ) \, dx-1408 \int \left (-44 x+x^2+\log (x)\right ) \log ^2\left (\log ^2(x)\right ) \, dx\\ &=4224 x+30928 x^2-1408 x^3+16 x^4+32 \int \left (-44 \log (x)-\frac {\log (x)}{x}+2 x \log (x)\right ) \, dx+32 \int \left (-44 \log ^2\left (\log ^2(x)\right )+x \log ^2\left (\log ^2(x)\right )+\frac {\log (x) \log ^2\left (\log ^2(x)\right )}{x}\right ) \, dx-64 \int \left (\frac {1936 x}{\log (x)}-\frac {88 x^2}{\log (x)}+\frac {x^3}{\log (x)}\right ) \, dx+64 \int \frac {x^3 \log \left (\log ^2(x)\right )}{\log (x)} \, dx+64 \int \left (-44 x^2 \log ^2\left (\log ^2(x)\right )+x^3 \log ^2\left (\log ^2(x)\right )+x \log (x) \log ^2\left (\log ^2(x)\right )\right ) \, dx-128 \int x^3 \log \left (\log ^2(x)\right ) \, dx-128 \int x \log (x) \log \left (\log ^2(x)\right ) \, dx-1408 \int \left (-44 x \log ^2\left (\log ^2(x)\right )+x^2 \log ^2\left (\log ^2(x)\right )+\log (x) \log ^2\left (\log ^2(x)\right )\right ) \, dx-2816 \int \log \left (\log ^2(x)\right ) \, dx+2816 \int \log (x) \log \left (\log ^2(x)\right ) \, dx-5632 \int \frac {x^2 \log \left (\log ^2(x)\right )}{\log (x)} \, dx+8448 \int x^2 \log \left (\log ^2(x)\right ) \, dx-123840 \int x \log \left (\log ^2(x)\right ) \, dx+123904 \int \frac {x \log \left (\log ^2(x)\right )}{\log (x)} \, dx\\ &=4224 x+30928 x^2-1408 x^3+16 x^4-2816 x \log \left (\log ^2(x)\right )-61920 x^2 \log \left (\log ^2(x)\right )+2816 x^3 \log \left (\log ^2(x)\right )-32 x^4 \log \left (\log ^2(x)\right )-32 \int \frac {\log (x)}{x} \, dx+32 \int x \log ^2\left (\log ^2(x)\right ) \, dx+32 \int \frac {\log (x) \log ^2\left (\log ^2(x)\right )}{x} \, dx+64 \int x \log (x) \, dx+64 \int \frac {x^3 \log \left (\log ^2(x)\right )}{\log (x)} \, dx+64 \int x^3 \log ^2\left (\log ^2(x)\right ) \, dx+64 \int x \log (x) \log ^2\left (\log ^2(x)\right ) \, dx-128 \int x \log (x) \log \left (\log ^2(x)\right ) \, dx-1408 \int \log (x) \, dx-1408 \int \log ^2\left (\log ^2(x)\right ) \, dx-1408 \int x^2 \log ^2\left (\log ^2(x)\right ) \, dx-1408 \int \log (x) \log ^2\left (\log ^2(x)\right ) \, dx+2816 \int \log (x) \log \left (\log ^2(x)\right ) \, dx-2816 \int x^2 \log ^2\left (\log ^2(x)\right ) \, dx+5632 \int \frac {1}{\log (x)} \, dx-5632 \int \frac {x^2 \log \left (\log ^2(x)\right )}{\log (x)} \, dx+61952 \int x \log ^2\left (\log ^2(x)\right ) \, dx+123840 \int \frac {x}{\log (x)} \, dx-123904 \int \frac {x}{\log (x)} \, dx+123904 \int \frac {x \log \left (\log ^2(x)\right )}{\log (x)} \, dx\\ &=5632 x+30912 x^2-1408 x^3+16 x^4-1408 x \log (x)+32 x^2 \log (x)-16 \log ^2(x)-2816 x \log \left (\log ^2(x)\right )-61920 x^2 \log \left (\log ^2(x)\right )+2816 x^3 \log \left (\log ^2(x)\right )-32 x^4 \log \left (\log ^2(x)\right )+5632 \text {li}(x)+32 \int x \log ^2\left (\log ^2(x)\right ) \, dx+32 \operatorname {Subst}\left (\int x \log ^2\left (x^2\right ) \, dx,x,\log (x)\right )+64 \int \frac {x^3 \log \left (\log ^2(x)\right )}{\log (x)} \, dx+64 \int x^3 \log ^2\left (\log ^2(x)\right ) \, dx+64 \int x \log (x) \log ^2\left (\log ^2(x)\right ) \, dx-128 \int x \log (x) \log \left (\log ^2(x)\right ) \, dx-1408 \int \log ^2\left (\log ^2(x)\right ) \, dx-1408 \int x^2 \log ^2\left (\log ^2(x)\right ) \, dx-1408 \int \log (x) \log ^2\left (\log ^2(x)\right ) \, dx+2816 \int \log (x) \log \left (\log ^2(x)\right ) \, dx-2816 \int x^2 \log ^2\left (\log ^2(x)\right ) \, dx-5632 \int \frac {x^2 \log \left (\log ^2(x)\right )}{\log (x)} \, dx+61952 \int x \log ^2\left (\log ^2(x)\right ) \, dx+123840 \operatorname {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )+123904 \int \frac {x \log \left (\log ^2(x)\right )}{\log (x)} \, dx-123904 \operatorname {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )\\ &=5632 x+30912 x^2-1408 x^3+16 x^4-64 \text {Ei}(2 \log (x))-1408 x \log (x)+32 x^2 \log (x)-16 \log ^2(x)-2816 x \log \left (\log ^2(x)\right )-61920 x^2 \log \left (\log ^2(x)\right )+2816 x^3 \log \left (\log ^2(x)\right )-32 x^4 \log \left (\log ^2(x)\right )+16 \log ^2(x) \log ^2\left (\log ^2(x)\right )+5632 \text {li}(x)+32 \int x \log ^2\left (\log ^2(x)\right ) \, dx+64 \int \frac {x^3 \log \left (\log ^2(x)\right )}{\log (x)} \, dx+64 \int x^3 \log ^2\left (\log ^2(x)\right ) \, dx+64 \int x \log (x) \log ^2\left (\log ^2(x)\right ) \, dx-64 \operatorname {Subst}\left (\int x \log \left (x^2\right ) \, dx,x,\log (x)\right )-128 \int x \log (x) \log \left (\log ^2(x)\right ) \, dx-1408 \int \log ^2\left (\log ^2(x)\right ) \, dx-1408 \int x^2 \log ^2\left (\log ^2(x)\right ) \, dx-1408 \int \log (x) \log ^2\left (\log ^2(x)\right ) \, dx+2816 \int \log (x) \log \left (\log ^2(x)\right ) \, dx-2816 \int x^2 \log ^2\left (\log ^2(x)\right ) \, dx-5632 \int \frac {x^2 \log \left (\log ^2(x)\right )}{\log (x)} \, dx+61952 \int x \log ^2\left (\log ^2(x)\right ) \, dx+123904 \int \frac {x \log \left (\log ^2(x)\right )}{\log (x)} \, dx\\ &=5632 x+30912 x^2-1408 x^3+16 x^4-64 \text {Ei}(2 \log (x))-1408 x \log (x)+32 x^2 \log (x)+16 \log ^2(x)-2816 x \log \left (\log ^2(x)\right )-61920 x^2 \log \left (\log ^2(x)\right )+2816 x^3 \log \left (\log ^2(x)\right )-32 x^4 \log \left (\log ^2(x)\right )-32 \log ^2(x) \log \left (\log ^2(x)\right )+16 \log ^2(x) \log ^2\left (\log ^2(x)\right )+5632 \text {li}(x)+32 \int x \log ^2\left (\log ^2(x)\right ) \, dx+64 \int \frac {x^3 \log \left (\log ^2(x)\right )}{\log (x)} \, dx+64 \int x^3 \log ^2\left (\log ^2(x)\right ) \, dx+64 \int x \log (x) \log ^2\left (\log ^2(x)\right ) \, dx-128 \int x \log (x) \log \left (\log ^2(x)\right ) \, dx-1408 \int \log ^2\left (\log ^2(x)\right ) \, dx-1408 \int x^2 \log ^2\left (\log ^2(x)\right ) \, dx-1408 \int \log (x) \log ^2\left (\log ^2(x)\right ) \, dx+2816 \int \log (x) \log \left (\log ^2(x)\right ) \, dx-2816 \int x^2 \log ^2\left (\log ^2(x)\right ) \, dx-5632 \int \frac {x^2 \log \left (\log ^2(x)\right )}{\log (x)} \, dx+61952 \int x \log ^2\left (\log ^2(x)\right ) \, dx+123904 \int \frac {x \log \left (\log ^2(x)\right )}{\log (x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.36, size = 21, normalized size = 0.95 \begin {gather*} 16 ((-44+x) x+\log (x))^2 \left (-1+\log \left (\log ^2(x)\right )\right )^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-123904*x^2 + 5632*x^3 - 64*x^4 + (4224*x + 61856*x^2 - 4224*x^3 + 64*x^4)*Log[x] + (-32 - 1408*x +
64*x^2)*Log[x]^2 + (123904*x^2 - 5632*x^3 + 64*x^4 + (-2816*x - 123840*x^2 + 8448*x^3 - 128*x^4)*Log[x] + (28
16*x - 128*x^2)*Log[x]^2)*Log[Log[x]^2] + ((-1408*x + 61984*x^2 - 4224*x^3 + 64*x^4)*Log[x] + (32 - 1408*x + 6
4*x^2)*Log[x]^2)*Log[Log[x]^2]^2)/(x*Log[x]),x]

[Out]

16*((-44 + x)*x + Log[x])^2*(-1 + Log[Log[x]^2])^2

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fricas [B]  time = 0.56, size = 107, normalized size = 4.86 \begin {gather*} 16 \, x^{4} - 1408 \, x^{3} + 16 \, {\left (x^{4} - 88 \, x^{3} + 1936 \, x^{2} + 2 \, {\left (x^{2} - 44 \, x\right )} \log \relax (x) + \log \relax (x)^{2}\right )} \log \left (\log \relax (x)^{2}\right )^{2} + 30976 \, x^{2} - 32 \, {\left (x^{4} - 88 \, x^{3} + 1936 \, x^{2} + 2 \, {\left (x^{2} - 44 \, x\right )} \log \relax (x) + \log \relax (x)^{2}\right )} \log \left (\log \relax (x)^{2}\right ) + 32 \, {\left (x^{2} - 44 \, x\right )} \log \relax (x) + 16 \, \log \relax (x)^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((64*x^2-1408*x+32)*log(x)^2+(64*x^4-4224*x^3+61984*x^2-1408*x)*log(x))*log(log(x)^2)^2+((-128*x^2+
2816*x)*log(x)^2+(-128*x^4+8448*x^3-123840*x^2-2816*x)*log(x)+64*x^4-5632*x^3+123904*x^2)*log(log(x)^2)+(64*x^
2-1408*x-32)*log(x)^2+(64*x^4-4224*x^3+61856*x^2+4224*x)*log(x)-64*x^4+5632*x^3-123904*x^2)/x/log(x),x, algori
thm="fricas")

[Out]

16*x^4 - 1408*x^3 + 16*(x^4 - 88*x^3 + 1936*x^2 + 2*(x^2 - 44*x)*log(x) + log(x)^2)*log(log(x)^2)^2 + 30976*x^
2 - 32*(x^4 - 88*x^3 + 1936*x^2 + 2*(x^2 - 44*x)*log(x) + log(x)^2)*log(log(x)^2) + 32*(x^2 - 44*x)*log(x) + 1
6*log(x)^2

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giac [B]  time = 0.96, size = 107, normalized size = 4.86 \begin {gather*} 16 \, x^{4} - 1408 \, x^{3} + 16 \, {\left (x^{4} - 88 \, x^{3} + 1936 \, x^{2} + 2 \, {\left (x^{2} - 44 \, x\right )} \log \relax (x) + \log \relax (x)^{2}\right )} \log \left (\log \relax (x)^{2}\right )^{2} + 30976 \, x^{2} - 32 \, {\left (x^{4} - 88 \, x^{3} + 1936 \, x^{2} + 2 \, {\left (x^{2} - 44 \, x\right )} \log \relax (x) + \log \relax (x)^{2}\right )} \log \left (\log \relax (x)^{2}\right ) + 32 \, {\left (x^{2} - 44 \, x\right )} \log \relax (x) + 16 \, \log \relax (x)^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((64*x^2-1408*x+32)*log(x)^2+(64*x^4-4224*x^3+61984*x^2-1408*x)*log(x))*log(log(x)^2)^2+((-128*x^2+
2816*x)*log(x)^2+(-128*x^4+8448*x^3-123840*x^2-2816*x)*log(x)+64*x^4-5632*x^3+123904*x^2)*log(log(x)^2)+(64*x^
2-1408*x-32)*log(x)^2+(64*x^4-4224*x^3+61856*x^2+4224*x)*log(x)-64*x^4+5632*x^3-123904*x^2)/x/log(x),x, algori
thm="giac")

[Out]

16*x^4 - 1408*x^3 + 16*(x^4 - 88*x^3 + 1936*x^2 + 2*(x^2 - 44*x)*log(x) + log(x)^2)*log(log(x)^2)^2 + 30976*x^
2 - 32*(x^4 - 88*x^3 + 1936*x^2 + 2*(x^2 - 44*x)*log(x) + log(x)^2)*log(log(x)^2) + 32*(x^2 - 44*x)*log(x) + 1
6*log(x)^2

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maple [C]  time = 0.49, size = 1608, normalized size = 73.09

method	result	size
risch	\(\text {Expression too large to display}\)	\(1608\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((64*x^2-1408*x+32)*ln(x)^2+(64*x^4-4224*x^3+61984*x^2-1408*x)*ln(x))*ln(ln(x)^2)^2+((-128*x^2+2816*x)*ln
(x)^2+(-128*x^4+8448*x^3-123840*x^2-2816*x)*ln(x)+64*x^4-5632*x^3+123904*x^2)*ln(ln(x)^2)+(64*x^2-1408*x-32)*l
n(x)^2+(64*x^4-4224*x^3+61856*x^2+4224*x)*ln(x)-64*x^4+5632*x^3-123904*x^2)/x/ln(x),x,method=_RETURNVERBOSE)

[Out]

32*x^2*ln(x)+16*ln(x)^2+16*x^4-1408*x^3+30976*x^2-1408*x*ln(x)+16*Pi^2*x^4*csgn(I*ln(x))^3*csgn(I*ln(x)^2)^3-2
4*Pi^2*x^4*csgn(I*ln(x))^2*csgn(I*ln(x)^2)^4+16*Pi^2*x^4*csgn(I*ln(x))*csgn(I*ln(x)^2)^5-7744*Pi^2*x^2*csgn(I*
ln(x))^4*csgn(I*ln(x)^2)^2+30976*Pi^2*x^2*csgn(I*ln(x))^3*csgn(I*ln(x)^2)^3-46464*Pi^2*x^2*csgn(I*ln(x))^2*csg
n(I*ln(x)^2)^4+30976*Pi^2*x^2*csgn(I*ln(x))*csgn(I*ln(x)^2)^5+352*Pi^2*x^3*csgn(I*ln(x))^4*csgn(I*ln(x)^2)^2-1
408*Pi^2*x^3*csgn(I*ln(x))^3*csgn(I*ln(x)^2)^3+2112*Pi^2*x^3*csgn(I*ln(x))^2*csgn(I*ln(x)^2)^4-1408*Pi^2*x^3*c
sgn(I*ln(x))*csgn(I*ln(x)^2)^5+16*I*Pi*csgn(I*ln(x)^2)^3*ln(x)^2+30976*I*Pi*x^2*csgn(I*ln(x)^2)^3+16*I*Pi*x^4*
csgn(I*ln(x)^2)^3-1408*I*Pi*x^3*csgn(I*ln(x)^2)^3-8*Pi^2*x^2*csgn(I*ln(x)^2)^6*ln(x)+352*Pi^2*x*csgn(I*ln(x)^2
)^6*ln(x)-4*Pi^2*csgn(I*ln(x))^4*csgn(I*ln(x)^2)^2*ln(x)^2+16*Pi^2*csgn(I*ln(x))^3*csgn(I*ln(x)^2)^3*ln(x)^2-2
4*Pi^2*csgn(I*ln(x))^2*csgn(I*ln(x)^2)^4*ln(x)^2+16*Pi^2*csgn(I*ln(x))*csgn(I*ln(x)^2)^5*ln(x)^2-4*Pi^2*x^4*cs
gn(I*ln(x))^4*csgn(I*ln(x)^2)^2+(64*x^4-5632*x^3+128*x^2*ln(x)+123904*x^2-5632*x*ln(x)+64*ln(x)^2)*ln(ln(x))^2
-32*I*(Pi*x^4*csgn(I*ln(x))^2*csgn(I*ln(x)^2)-2*Pi*x^4*csgn(I*ln(x))*csgn(I*ln(x)^2)^2+Pi*x^4*csgn(I*ln(x)^2)^
3-88*Pi*x^3*csgn(I*ln(x))^2*csgn(I*ln(x)^2)+176*Pi*x^3*csgn(I*ln(x))*csgn(I*ln(x)^2)^2-88*Pi*x^3*csgn(I*ln(x)^
2)^3+2*Pi*x^2*csgn(I*ln(x))^2*csgn(I*ln(x)^2)*ln(x)-4*Pi*x^2*csgn(I*ln(x))*csgn(I*ln(x)^2)^2*ln(x)+2*Pi*x^2*cs
gn(I*ln(x)^2)^3*ln(x)+1936*Pi*x^2*csgn(I*ln(x))^2*csgn(I*ln(x)^2)-3872*Pi*x^2*csgn(I*ln(x))*csgn(I*ln(x)^2)^2+
1936*Pi*x^2*csgn(I*ln(x)^2)^3-88*Pi*x*csgn(I*ln(x))^2*csgn(I*ln(x)^2)*ln(x)+176*Pi*x*csgn(I*ln(x))*csgn(I*ln(x
)^2)^2*ln(x)-88*Pi*x*csgn(I*ln(x)^2)^3*ln(x)+Pi*csgn(I*ln(x))^2*csgn(I*ln(x)^2)*ln(x)^2-2*Pi*csgn(I*ln(x))*csg
n(I*ln(x)^2)^2*ln(x)^2+Pi*csgn(I*ln(x)^2)^3*ln(x)^2-2*I*x^4-2*I*ln(x)^2+176*I*x*ln(x)-4*I*x^2*ln(x)+176*I*x^3-
3872*I*x^2)*ln(ln(x))-4*Pi^2*x^4*csgn(I*ln(x)^2)^6+352*Pi^2*x^3*csgn(I*ln(x)^2)^6-4*Pi^2*csgn(I*ln(x)^2)^6*ln(
x)^2-7744*Pi^2*x^2*csgn(I*ln(x)^2)^6+32*I*Pi*x^2*csgn(I*ln(x))^2*csgn(I*ln(x)^2)*ln(x)-64*I*Pi*x^2*csgn(I*ln(x
))*csgn(I*ln(x)^2)^2*ln(x)-1408*I*Pi*x*csgn(I*ln(x))^2*csgn(I*ln(x)^2)*ln(x)+2816*I*Pi*x*csgn(I*ln(x))*csgn(I*
ln(x)^2)^2*ln(x)+32*Pi^2*x^2*csgn(I*ln(x))^3*csgn(I*ln(x)^2)^3*ln(x)-48*Pi^2*x^2*csgn(I*ln(x))^2*csgn(I*ln(x)^
2)^4*ln(x)+32*Pi^2*x^2*csgn(I*ln(x))*csgn(I*ln(x)^2)^5*ln(x)+352*Pi^2*x*csgn(I*ln(x))^4*csgn(I*ln(x)^2)^2*ln(x
)-1408*Pi^2*x*csgn(I*ln(x))^3*csgn(I*ln(x)^2)^3*ln(x)+2112*Pi^2*x*csgn(I*ln(x))^2*csgn(I*ln(x)^2)^4*ln(x)+16*I
*Pi*x^4*csgn(I*ln(x))^2*csgn(I*ln(x)^2)-32*I*Pi*x^4*csgn(I*ln(x))*csgn(I*ln(x)^2)^2-1408*I*Pi*x^3*csgn(I*ln(x)
)^2*csgn(I*ln(x)^2)+2816*I*Pi*x^3*csgn(I*ln(x))*csgn(I*ln(x)^2)^2+30976*I*Pi*x^2*csgn(I*ln(x))^2*csgn(I*ln(x)^
2)-61952*I*Pi*x^2*csgn(I*ln(x))*csgn(I*ln(x)^2)^2+16*I*Pi*csgn(I*ln(x))^2*csgn(I*ln(x)^2)*ln(x)^2-32*I*Pi*csgn
(I*ln(x))*csgn(I*ln(x)^2)^2*ln(x)^2+32*I*Pi*x^2*csgn(I*ln(x)^2)^3*ln(x)-1408*I*Pi*x*csgn(I*ln(x)^2)^3*ln(x)-14
08*Pi^2*x*csgn(I*ln(x))*csgn(I*ln(x)^2)^5*ln(x)-8*Pi^2*x^2*csgn(I*ln(x))^4*csgn(I*ln(x)^2)^2*ln(x)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -32 \, x^{4} \log \left (\log \relax (x)^{2}\right ) + 16 \, x^{4} + 2816 \, x^{3} \log \left (\log \relax (x)^{2}\right ) - 1408 \, x^{3} - 61920 \, x^{2} \log \left (\log \relax (x)^{2}\right ) + 32 \, x^{2} \log \relax (x) + 64 \, {\left (x^{4} - 88 \, x^{3} + 1936 \, x^{2} + 2 \, {\left (x^{2} - 44 \, x\right )} \log \relax (x) + \log \relax (x)^{2}\right )} \log \left (\log \relax (x)\right )^{2} + 30976 \, x^{2} - 2816 \, x \log \left (\log \relax (x)^{2}\right ) - 1408 \, x \log \relax (x) + 16 \, \log \relax (x)^{2} - 64 \, {\left (x^{2} + 2 \, {\left (x^{2} - 44 \, x\right )} \log \relax (x) + \log \relax (x)^{2} - 88 \, x\right )} \log \left (\log \relax (x)\right ) - 64 \, {\rm Ei}\left (2 \, \log \relax (x)\right ) + 5632 \, {\rm Ei}\left (\log \relax (x)\right ) + 32 \, \int \frac {2 \, {\left (x - 88\right )}}{\log \relax (x)}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((64*x^2-1408*x+32)*log(x)^2+(64*x^4-4224*x^3+61984*x^2-1408*x)*log(x))*log(log(x)^2)^2+((-128*x^2+
2816*x)*log(x)^2+(-128*x^4+8448*x^3-123840*x^2-2816*x)*log(x)+64*x^4-5632*x^3+123904*x^2)*log(log(x)^2)+(64*x^
2-1408*x-32)*log(x)^2+(64*x^4-4224*x^3+61856*x^2+4224*x)*log(x)-64*x^4+5632*x^3-123904*x^2)/x/log(x),x, algori
thm="maxima")

[Out]

-32*x^4*log(log(x)^2) + 16*x^4 + 2816*x^3*log(log(x)^2) - 1408*x^3 - 61920*x^2*log(log(x)^2) + 32*x^2*log(x) +
64*(x^4 - 88*x^3 + 1936*x^2 + 2*(x^2 - 44*x)*log(x) + log(x)^2)*log(log(x))^2 + 30976*x^2 - 2816*x*log(log(x)
^2) - 1408*x*log(x) + 16*log(x)^2 - 64*(x^2 + 2*(x^2 - 44*x)*log(x) + log(x)^2 - 88*x)*log(log(x)) - 64*Ei(2*l
og(x)) + 5632*Ei(log(x)) + 32*integrate(2*(x - 88)/log(x), x)

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mupad [B]  time = 2.09, size = 120, normalized size = 5.45 \begin {gather*} 16\,{\ln \relax (x)}^2-\ln \left ({\ln \relax (x)}^2\right )\,\left (32\,{\ln \relax (x)}^2-\ln \relax (x)\,\left (2816\,x-64\,x^2\right )+61952\,x^2-2816\,x^3+32\,x^4\right )-\ln \relax (x)\,\left (1408\,x-32\,x^2\right )+{\ln \left ({\ln \relax (x)}^2\right )}^2\,\left (16\,{\ln \relax (x)}^2-\ln \relax (x)\,\left (1408\,x-32\,x^2\right )+30976\,x^2-1408\,x^3+16\,x^4\right )+30976\,x^2-1408\,x^3+16\,x^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x)*(4224*x + 61856*x^2 - 4224*x^3 + 64*x^4) - log(x)^2*(1408*x - 64*x^2 + 32) + log(log(x)^2)*(log(x)
^2*(2816*x - 128*x^2) - log(x)*(2816*x + 123840*x^2 - 8448*x^3 + 128*x^4) + 123904*x^2 - 5632*x^3 + 64*x^4) -
123904*x^2 + 5632*x^3 - 64*x^4 + log(log(x)^2)^2*(log(x)^2*(64*x^2 - 1408*x + 32) - log(x)*(1408*x - 61984*x^2
+ 4224*x^3 - 64*x^4)))/(x*log(x)),x)

[Out]

16*log(x)^2 - log(log(x)^2)*(32*log(x)^2 - log(x)*(2816*x - 64*x^2) + 61952*x^2 - 2816*x^3 + 32*x^4) - log(x)*
(1408*x - 32*x^2) + log(log(x)^2)^2*(16*log(x)^2 - log(x)*(1408*x - 32*x^2) + 30976*x^2 - 1408*x^3 + 16*x^4) +
30976*x^2 - 1408*x^3 + 16*x^4

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sympy [B]  time = 0.64, size = 122, normalized size = 5.55 \begin {gather*} 16 x^{4} - 1408 x^{3} + 30976 x^{2} + \left (32 x^{2} - 1408 x\right ) \log {\relax (x )} + \left (- 32 x^{4} + 2816 x^{3} - 64 x^{2} \log {\relax (x )} - 61952 x^{2} + 2816 x \log {\relax (x )} - 32 \log {\relax (x )}^{2}\right ) \log {\left (\log {\relax (x )}^{2} \right )} + \left (16 x^{4} - 1408 x^{3} + 32 x^{2} \log {\relax (x )} + 30976 x^{2} - 1408 x \log {\relax (x )} + 16 \log {\relax (x )}^{2}\right ) \log {\left (\log {\relax (x )}^{2} \right )}^{2} + 16 \log {\relax (x )}^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((64*x**2-1408*x+32)*ln(x)**2+(64*x**4-4224*x**3+61984*x**2-1408*x)*ln(x))*ln(ln(x)**2)**2+((-128*x
**2+2816*x)*ln(x)**2+(-128*x**4+8448*x**3-123840*x**2-2816*x)*ln(x)+64*x**4-5632*x**3+123904*x**2)*ln(ln(x)**2
)+(64*x**2-1408*x-32)*ln(x)**2+(64*x**4-4224*x**3+61856*x**2+4224*x)*ln(x)-64*x**4+5632*x**3-123904*x**2)/x/ln
(x),x)

[Out]

16*x**4 - 1408*x**3 + 30976*x**2 + (32*x**2 - 1408*x)*log(x) + (-32*x**4 + 2816*x**3 - 64*x**2*log(x) - 61952*
x**2 + 2816*x*log(x) - 32*log(x)**2)*log(log(x)**2) + (16*x**4 - 1408*x**3 + 32*x**2*log(x) + 30976*x**2 - 140
8*x*log(x) + 16*log(x)**2)*log(log(x)**2)**2 + 16*log(x)**2

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