3.88.87 \(\int \frac {-2 x^2-2 x^3-2 x^4-2 x^5+(4 x^2+6 x^3+6 x^4) \log (x)+(-4 x^2-6 x^3) \log ^2(x)+2 x^2 \log ^3(x)+(-524288 x^3+1572864 x^2 \log (x)-1572864 x \log ^2(x)+524288 \log ^3(x)) \log ^3(x^2)}{-x^4-2 x^5-x^6+(x^3+4 x^4+3 x^5) \log (x)+(-2 x^3-3 x^4) \log ^2(x)+x^3 \log ^3(x)+(-65536 x^4+196608 x^3 \log (x)-196608 x^2 \log ^2(x)+65536 x \log ^3(x)) \log ^4(x^2)} \, dx\)

Optimal. Leaf size=24 \[ \log \left (\left (x+\frac {x}{x-\log (x)}\right )^2+65536 \log ^4\left (x^2\right )\right ) \]

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Rubi [F]  time = 11.40, 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 {-2 x^2-2 x^3-2 x^4-2 x^5+\left (4 x^2+6 x^3+6 x^4\right ) \log (x)+\left (-4 x^2-6 x^3\right ) \log ^2(x)+2 x^2 \log ^3(x)+\left (-524288 x^3+1572864 x^2 \log (x)-1572864 x \log ^2(x)+524288 \log ^3(x)\right ) \log ^3\left (x^2\right )}{-x^4-2 x^5-x^6+\left (x^3+4 x^4+3 x^5\right ) \log (x)+\left (-2 x^3-3 x^4\right ) \log ^2(x)+x^3 \log ^3(x)+\left (-65536 x^4+196608 x^3 \log (x)-196608 x^2 \log ^2(x)+65536 x \log ^3(x)\right ) \log ^4\left (x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-2*x^2 - 2*x^3 - 2*x^4 - 2*x^5 + (4*x^2 + 6*x^3 + 6*x^4)*Log[x] + (-4*x^2 - 6*x^3)*Log[x]^2 + 2*x^2*Log[x
]^3 + (-524288*x^3 + 1572864*x^2*Log[x] - 1572864*x*Log[x]^2 + 524288*Log[x]^3)*Log[x^2]^3)/(-x^4 - 2*x^5 - x^
6 + (x^3 + 4*x^4 + 3*x^5)*Log[x] + (-2*x^3 - 3*x^4)*Log[x]^2 + x^3*Log[x]^3 + (-65536*x^4 + 196608*x^3*Log[x]
- 196608*x^2*Log[x]^2 + 65536*x*Log[x]^3)*Log[x^2]^4),x]

[Out]

2*Defer[Int][x/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x
^2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] + 2*Defer[Int][x^2/((x - Log[x])*(x^2 + 2
*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2]^4 +
65536*Log[x]^2*Log[x^2]^4)), x] + 2*Defer[Int][x^3/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log
[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] + 2*D
efer[Int][x^4/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^
2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] - 4*Defer[Int][(x*Log[x])/((x - Log[x])*(x
^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2
]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] - 6*Defer[Int][(x^2*Log[x])/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log
[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2
]^4)), x] - 6*Defer[Int][(x^3*Log[x])/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log
[x]^2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] + 4*Defer[Int][(x*
Log[x]^2)/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4
- 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] + 6*Defer[Int][(x^2*Log[x]^2)/((x - Log[x])*(x
^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2
]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] - 2*Defer[Int][(x*Log[x]^3)/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log
[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2
]^4)), x] + 524288*Defer[Int][(x^2*Log[x^2]^3)/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x]
+ x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] - 1572864
*Defer[Int][(x*Log[x]*Log[x^2]^3)/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log[x]^
2 + 65536*x^2*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] + 1572864*Defer[Int][(
Log[x]^2*Log[x^2]^3)/((x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2
*Log[x^2]^4 - 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x] - 524288*Defer[Int][(Log[x]^3*Log[x
^2]^3)/(x*(x - Log[x])*(x^2 + 2*x^3 + x^4 - 2*x^2*Log[x] - 2*x^3*Log[x] + x^2*Log[x]^2 + 65536*x^2*Log[x^2]^4
- 131072*x*Log[x]*Log[x^2]^4 + 65536*Log[x]^2*Log[x^2]^4)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 34.57, size = 244, normalized size = 10.17 \begin {gather*} -2 \log (x-\log (x))+\log \left (x^2+2 x^3+x^4+1048576 \log ^6(x)+65536 x^2 \left (-2 \log (x)+\log \left (x^2\right )\right )^4+\log ^5(x) \left (-2097152 x+2097152 \left (-2 \log (x)+\log \left (x^2\right )\right )\right )+\log ^4(x) \left (1048576 x^2-4194304 x \left (-2 \log (x)+\log \left (x^2\right )\right )+1572864 \left (-2 \log (x)+\log \left (x^2\right )\right )^2\right )+\log ^3(x) \left (2097152 x^2 \left (-2 \log (x)+\log \left (x^2\right )\right )-3145728 x \left (-2 \log (x)+\log \left (x^2\right )\right )^2+524288 \left (-2 \log (x)+\log \left (x^2\right )\right )^3\right )+\log ^2(x) \left (x^2+1572864 x^2 \left (-2 \log (x)+\log \left (x^2\right )\right )^2-1048576 x \left (-2 \log (x)+\log \left (x^2\right )\right )^3+65536 \left (-2 \log (x)+\log \left (x^2\right )\right )^4\right )+\log (x) \left (-2 x^2-2 x^3+524288 x^2 \left (-2 \log (x)+\log \left (x^2\right )\right )^3-131072 x \left (-2 \log (x)+\log \left (x^2\right )\right )^4\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2*x^2 - 2*x^3 - 2*x^4 - 2*x^5 + (4*x^2 + 6*x^3 + 6*x^4)*Log[x] + (-4*x^2 - 6*x^3)*Log[x]^2 + 2*x^2
*Log[x]^3 + (-524288*x^3 + 1572864*x^2*Log[x] - 1572864*x*Log[x]^2 + 524288*Log[x]^3)*Log[x^2]^3)/(-x^4 - 2*x^
5 - x^6 + (x^3 + 4*x^4 + 3*x^5)*Log[x] + (-2*x^3 - 3*x^4)*Log[x]^2 + x^3*Log[x]^3 + (-65536*x^4 + 196608*x^3*L
og[x] - 196608*x^2*Log[x]^2 + 65536*x*Log[x]^3)*Log[x^2]^4),x]

[Out]

-2*Log[x - Log[x]] + Log[x^2 + 2*x^3 + x^4 + 1048576*Log[x]^6 + 65536*x^2*(-2*Log[x] + Log[x^2])^4 + Log[x]^5*
(-2097152*x + 2097152*(-2*Log[x] + Log[x^2])) + Log[x]^4*(1048576*x^2 - 4194304*x*(-2*Log[x] + Log[x^2]) + 157
2864*(-2*Log[x] + Log[x^2])^2) + Log[x]^3*(2097152*x^2*(-2*Log[x] + Log[x^2]) - 3145728*x*(-2*Log[x] + Log[x^2
])^2 + 524288*(-2*Log[x] + Log[x^2])^3) + Log[x]^2*(x^2 + 1572864*x^2*(-2*Log[x] + Log[x^2])^2 - 1048576*x*(-2
*Log[x] + Log[x^2])^3 + 65536*(-2*Log[x] + Log[x^2])^4) + Log[x]*(-2*x^2 - 2*x^3 + 524288*x^2*(-2*Log[x] + Log
[x^2])^3 - 131072*x*(-2*Log[x] + Log[x^2])^4)]

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fricas [B]  time = 0.65, size = 64, normalized size = 2.67 \begin {gather*} \log \left (1048576 \, x^{2} \log \relax (x)^{4} - 2097152 \, x \log \relax (x)^{5} + 1048576 \, \log \relax (x)^{6} + x^{4} + x^{2} \log \relax (x)^{2} + 2 \, x^{3} + x^{2} - 2 \, {\left (x^{3} + x^{2}\right )} \log \relax (x)\right ) - 2 \, \log \left (-x + \log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((524288*log(x)^3-1572864*x*log(x)^2+1572864*x^2*log(x)-524288*x^3)*log(x^2)^3+2*x^2*log(x)^3+(-6*x^
3-4*x^2)*log(x)^2+(6*x^4+6*x^3+4*x^2)*log(x)-2*x^5-2*x^4-2*x^3-2*x^2)/((65536*x*log(x)^3-196608*x^2*log(x)^2+1
96608*x^3*log(x)-65536*x^4)*log(x^2)^4+x^3*log(x)^3+(-3*x^4-2*x^3)*log(x)^2+(3*x^5+4*x^4+x^3)*log(x)-x^6-2*x^5
-x^4),x, algorithm="fricas")

[Out]

log(1048576*x^2*log(x)^4 - 2097152*x*log(x)^5 + 1048576*log(x)^6 + x^4 + x^2*log(x)^2 + 2*x^3 + x^2 - 2*(x^3 +
x^2)*log(x)) - 2*log(-x + log(x))

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giac [B]  time = 2.05, size = 67, normalized size = 2.79 \begin {gather*} \log \left (1048576 \, x^{2} \log \relax (x)^{4} - 2097152 \, x \log \relax (x)^{5} + 1048576 \, \log \relax (x)^{6} + x^{4} - 2 \, x^{3} \log \relax (x) + x^{2} \log \relax (x)^{2} + 2 \, x^{3} - 2 \, x^{2} \log \relax (x) + x^{2}\right ) - 2 \, \log \left (x - \log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((524288*log(x)^3-1572864*x*log(x)^2+1572864*x^2*log(x)-524288*x^3)*log(x^2)^3+2*x^2*log(x)^3+(-6*x^
3-4*x^2)*log(x)^2+(6*x^4+6*x^3+4*x^2)*log(x)-2*x^5-2*x^4-2*x^3-2*x^2)/((65536*x*log(x)^3-196608*x^2*log(x)^2+1
96608*x^3*log(x)-65536*x^4)*log(x^2)^4+x^3*log(x)^3+(-3*x^4-2*x^3)*log(x)^2+(3*x^5+4*x^4+x^3)*log(x)-x^6-2*x^5
-x^4),x, algorithm="giac")

[Out]

log(1048576*x^2*log(x)^4 - 2097152*x*log(x)^5 + 1048576*log(x)^6 + x^4 - 2*x^3*log(x) + x^2*log(x)^2 + 2*x^3 -
2*x^2*log(x) + x^2) - 2*log(x - log(x))

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maple [C]  time = 45.92, size = 1587, normalized size = 66.12

method	result	size
risch	\(-2 \ln \left (\ln \relax (x )-x \right )+\ln \left (\ln \relax (x )^{6}+\left (-i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}-i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+2 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-2 x \right ) \ln \relax (x )^{5}+\left (2 i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-4 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-\frac {3 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{6}}{8}-\frac {3 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )^{4}}{8}+\frac {3 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{3} \mathrm {csgn}\left (i x \right )^{3}}{2}-\frac {9 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{4} \mathrm {csgn}\left (i x \right )^{2}}{4}+\frac {3 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{5} \mathrm {csgn}\left (i x \right )}{2}+2 i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3}+x^{2}\right ) \ln \relax (x )^{4}+\left (-i \pi \,x^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+2 i \pi \,x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\frac {i \pi ^{3} \mathrm {csgn}\left (i x^{2}\right )^{9}}{16}+\frac {3 x \,\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{6}}{4}+\frac {15 i \pi ^{3} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{7}}{16}-\frac {3 i \pi ^{3} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{8}}{8}-i \pi \,x^{2} \mathrm {csgn}\left (i x^{2}\right )^{3}+\frac {3 x \,\pi ^{2} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{2}}{4}-3 x \,\pi ^{2} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{3}+\frac {9 x \,\pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{4}}{2}-3 x \,\pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{5}+\frac {i \pi ^{3} \mathrm {csgn}\left (i x \right )^{6} \mathrm {csgn}\left (i x^{2}\right )^{3}}{16}-\frac {3 i \pi ^{3} \mathrm {csgn}\left (i x \right )^{5} \mathrm {csgn}\left (i x^{2}\right )^{4}}{8}+\frac {15 i \pi ^{3} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{5}}{16}-\frac {5 i \pi ^{3} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{6}}{4}\right ) \ln \relax (x )^{3}+\left (\frac {5 i \pi ^{3} x \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{6}}{2}+\frac {3 i \pi ^{3} x \mathrm {csgn}\left (i x \right )^{5} \mathrm {csgn}\left (i x^{2}\right )^{4}}{4}-\frac {15 i \pi ^{3} x \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{5}}{8}+\frac {3 i \pi ^{3} x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{8}}{4}-\frac {15 i \pi ^{3} x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{7}}{8}-\frac {i \pi ^{3} x \mathrm {csgn}\left (i x^{2}\right )^{9}}{8}+\frac {\pi ^{4} \mathrm {csgn}\left (i x^{2}\right )^{12}}{256}-\frac {\pi ^{4} \mathrm {csgn}\left (i x \right )^{7} \mathrm {csgn}\left (i x^{2}\right )^{5}}{32}+\frac {7 \pi ^{4} \mathrm {csgn}\left (i x \right )^{6} \mathrm {csgn}\left (i x^{2}\right )^{6}}{64}-\frac {\pi ^{4} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{11}}{32}+\frac {\pi ^{4} \mathrm {csgn}\left (i x \right )^{8} \mathrm {csgn}\left (i x^{2}\right )^{4}}{256}-\frac {7 \pi ^{4} \mathrm {csgn}\left (i x \right )^{5} \mathrm {csgn}\left (i x^{2}\right )^{7}}{32}+\frac {35 \pi ^{4} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{8}}{128}-\frac {7 \pi ^{4} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{9}}{32}+\frac {7 \pi ^{4} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{10}}{64}-\frac {3 \pi ^{2} x^{2} \mathrm {csgn}\left (i x^{2}\right )^{6}}{8}-\frac {3 \pi ^{2} x^{2} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{2}}{8}+\frac {3 \pi ^{2} x^{2} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{3}}{2}-\frac {9 \pi ^{2} x^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{4}}{4}+\frac {3 \pi ^{2} x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{5}}{2}-\frac {i \pi ^{3} x \mathrm {csgn}\left (i x \right )^{6} \mathrm {csgn}\left (i x^{2}\right )^{3}}{8}+\frac {x^{2}}{1048576}\right ) \ln \relax (x )^{2}+\left (\frac {i \pi ^{3} x^{2} \mathrm {csgn}\left (i x^{2}\right )^{9}}{16}+\frac {15 i \pi ^{3} x^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{7}}{16}-\frac {3 i \pi ^{3} x^{2} \mathrm {csgn}\left (i x \right )^{5} \mathrm {csgn}\left (i x^{2}\right )^{4}}{8}+\frac {15 i \pi ^{3} x^{2} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{5}}{16}+\frac {i \pi ^{3} x^{2} \mathrm {csgn}\left (i x \right )^{6} \mathrm {csgn}\left (i x^{2}\right )^{3}}{16}-\frac {3 i \pi ^{3} x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{8}}{8}-\frac {x \,\pi ^{4} \mathrm {csgn}\left (i x^{2}\right )^{12}}{128}-\frac {5 i \pi ^{3} x^{2} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{6}}{4}-\frac {x \,\pi ^{4} \mathrm {csgn}\left (i x \right )^{8} \mathrm {csgn}\left (i x^{2}\right )^{4}}{128}+\frac {x \,\pi ^{4} \mathrm {csgn}\left (i x \right )^{7} \mathrm {csgn}\left (i x^{2}\right )^{5}}{16}-\frac {7 x \,\pi ^{4} \mathrm {csgn}\left (i x \right )^{6} \mathrm {csgn}\left (i x^{2}\right )^{6}}{32}+\frac {7 x \,\pi ^{4} \mathrm {csgn}\left (i x \right )^{5} \mathrm {csgn}\left (i x^{2}\right )^{7}}{16}-\frac {35 x \,\pi ^{4} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{8}}{64}+\frac {7 x \,\pi ^{4} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{9}}{16}-\frac {7 x \,\pi ^{4} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{10}}{32}+\frac {x \,\pi ^{4} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{11}}{16}-\frac {x^{2}}{524288}-\frac {x^{3}}{524288}\right ) \ln \relax (x )+\frac {x^{4}}{1048576}+\frac {x^{3}}{524288}+\frac {x^{2}}{1048576}+\frac {7 x^{2} \pi ^{4} \mathrm {csgn}\left (i x \right )^{6} \mathrm {csgn}\left (i x^{2}\right )^{6}}{64}-\frac {7 x^{2} \pi ^{4} \mathrm {csgn}\left (i x \right )^{5} \mathrm {csgn}\left (i x^{2}\right )^{7}}{32}+\frac {35 x^{2} \pi ^{4} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{8}}{128}-\frac {7 x^{2} \pi ^{4} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{9}}{32}+\frac {7 x^{2} \pi ^{4} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{10}}{64}-\frac {x^{2} \pi ^{4} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{11}}{32}-\frac {x^{2} \pi ^{4} \mathrm {csgn}\left (i x \right )^{7} \mathrm {csgn}\left (i x^{2}\right )^{5}}{32}+\frac {x^{2} \pi ^{4} \mathrm {csgn}\left (i x \right )^{8} \mathrm {csgn}\left (i x^{2}\right )^{4}}{256}+\frac {x^{2} \pi ^{4} \mathrm {csgn}\left (i x^{2}\right )^{12}}{256}\right )\)	\(1587\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((524288*ln(x)^3-1572864*x*ln(x)^2+1572864*x^2*ln(x)-524288*x^3)*ln(x^2)^3+2*x^2*ln(x)^3+(-6*x^3-4*x^2)*ln
(x)^2+(6*x^4+6*x^3+4*x^2)*ln(x)-2*x^5-2*x^4-2*x^3-2*x^2)/((65536*x*ln(x)^3-196608*x^2*ln(x)^2+196608*x^3*ln(x)
-65536*x^4)*ln(x^2)^4+x^3*ln(x)^3+(-3*x^4-2*x^3)*ln(x)^2+(3*x^5+4*x^4+x^3)*ln(x)-x^6-2*x^5-x^4),x,method=_RETU
RNVERBOSE)

[Out]

-2*ln(ln(x)-x)+ln(ln(x)^6+(-I*Pi*csgn(I*x^2)^3-I*Pi*csgn(I*x)^2*csgn(I*x^2)+2*I*Pi*csgn(I*x)*csgn(I*x^2)^2-2*x
)*ln(x)^5+(2*I*Pi*x*csgn(I*x)^2*csgn(I*x^2)-4*I*Pi*x*csgn(I*x)*csgn(I*x^2)^2-3/8*Pi^2*csgn(I*x^2)^6-3/8*Pi^2*c
sgn(I*x^2)^2*csgn(I*x)^4+3/2*Pi^2*csgn(I*x^2)^3*csgn(I*x)^3-9/4*Pi^2*csgn(I*x^2)^4*csgn(I*x)^2+3/2*Pi^2*csgn(I
*x^2)^5*csgn(I*x)+2*I*Pi*x*csgn(I*x^2)^3+x^2)*ln(x)^4+(-I*Pi*x^2*csgn(I*x)^2*csgn(I*x^2)+2*I*Pi*x^2*csgn(I*x)*
csgn(I*x^2)^2+1/16*I*Pi^3*csgn(I*x^2)^9+3/4*x*Pi^2*csgn(I*x^2)^6+15/16*I*Pi^3*csgn(I*x)^2*csgn(I*x^2)^7-3/8*I*
Pi^3*csgn(I*x)*csgn(I*x^2)^8-I*Pi*x^2*csgn(I*x^2)^3+3/4*x*Pi^2*csgn(I*x)^4*csgn(I*x^2)^2-3*x*Pi^2*csgn(I*x)^3*
csgn(I*x^2)^3+9/2*x*Pi^2*csgn(I*x)^2*csgn(I*x^2)^4-3*x*Pi^2*csgn(I*x)*csgn(I*x^2)^5+1/16*I*Pi^3*csgn(I*x)^6*cs
gn(I*x^2)^3-3/8*I*Pi^3*csgn(I*x)^5*csgn(I*x^2)^4+15/16*I*Pi^3*csgn(I*x)^4*csgn(I*x^2)^5-5/4*I*Pi^3*csgn(I*x)^3
*csgn(I*x^2)^6)*ln(x)^3+(5/2*I*Pi^3*x*csgn(I*x)^3*csgn(I*x^2)^6+3/4*I*Pi^3*x*csgn(I*x)^5*csgn(I*x^2)^4-15/8*I*
Pi^3*x*csgn(I*x)^4*csgn(I*x^2)^5+3/4*I*Pi^3*x*csgn(I*x)*csgn(I*x^2)^8-15/8*I*Pi^3*x*csgn(I*x)^2*csgn(I*x^2)^7-
1/8*I*Pi^3*x*csgn(I*x^2)^9+1/256*Pi^4*csgn(I*x^2)^12-1/32*Pi^4*csgn(I*x)^7*csgn(I*x^2)^5+7/64*Pi^4*csgn(I*x)^6
*csgn(I*x^2)^6-1/32*Pi^4*csgn(I*x)*csgn(I*x^2)^11+1/256*Pi^4*csgn(I*x)^8*csgn(I*x^2)^4-7/32*Pi^4*csgn(I*x)^5*c
sgn(I*x^2)^7+35/128*Pi^4*csgn(I*x)^4*csgn(I*x^2)^8-7/32*Pi^4*csgn(I*x)^3*csgn(I*x^2)^9+7/64*Pi^4*csgn(I*x)^2*c
sgn(I*x^2)^10-3/8*Pi^2*x^2*csgn(I*x^2)^6-3/8*Pi^2*x^2*csgn(I*x)^4*csgn(I*x^2)^2+3/2*Pi^2*x^2*csgn(I*x)^3*csgn(
I*x^2)^3-9/4*Pi^2*x^2*csgn(I*x)^2*csgn(I*x^2)^4+3/2*Pi^2*x^2*csgn(I*x)*csgn(I*x^2)^5-1/8*I*Pi^3*x*csgn(I*x)^6*
csgn(I*x^2)^3+1/1048576*x^2)*ln(x)^2+(1/16*I*Pi^3*x^2*csgn(I*x^2)^9+15/16*I*Pi^3*x^2*csgn(I*x)^2*csgn(I*x^2)^7
-3/8*I*Pi^3*x^2*csgn(I*x)^5*csgn(I*x^2)^4+15/16*I*Pi^3*x^2*csgn(I*x)^4*csgn(I*x^2)^5+1/16*I*Pi^3*x^2*csgn(I*x)
^6*csgn(I*x^2)^3-3/8*I*Pi^3*x^2*csgn(I*x)*csgn(I*x^2)^8-1/128*x*Pi^4*csgn(I*x^2)^12-5/4*I*Pi^3*x^2*csgn(I*x)^3
*csgn(I*x^2)^6-1/128*x*Pi^4*csgn(I*x)^8*csgn(I*x^2)^4+1/16*x*Pi^4*csgn(I*x)^7*csgn(I*x^2)^5-7/32*x*Pi^4*csgn(I
*x)^6*csgn(I*x^2)^6+7/16*x*Pi^4*csgn(I*x)^5*csgn(I*x^2)^7-35/64*x*Pi^4*csgn(I*x)^4*csgn(I*x^2)^8+7/16*x*Pi^4*c
sgn(I*x)^3*csgn(I*x^2)^9-7/32*x*Pi^4*csgn(I*x)^2*csgn(I*x^2)^10+1/16*x*Pi^4*csgn(I*x)*csgn(I*x^2)^11-1/524288*
x^2-1/524288*x^3)*ln(x)+1/1048576*x^4+1/524288*x^3+1/1048576*x^2+7/64*x^2*Pi^4*csgn(I*x)^6*csgn(I*x^2)^6-7/32*
x^2*Pi^4*csgn(I*x)^5*csgn(I*x^2)^7+35/128*x^2*Pi^4*csgn(I*x)^4*csgn(I*x^2)^8-7/32*x^2*Pi^4*csgn(I*x)^3*csgn(I*
x^2)^9+7/64*x^2*Pi^4*csgn(I*x)^2*csgn(I*x^2)^10-1/32*x^2*Pi^4*csgn(I*x)*csgn(I*x^2)^11-1/32*x^2*Pi^4*csgn(I*x)
^7*csgn(I*x^2)^5+1/256*x^2*Pi^4*csgn(I*x)^8*csgn(I*x^2)^4+1/256*x^2*Pi^4*csgn(I*x^2)^12)

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maxima [B]  time = 0.39, size = 66, normalized size = 2.75 \begin {gather*} \log \left (x^{2} \log \relax (x)^{4} - 2 \, x \log \relax (x)^{5} + \log \relax (x)^{6} + \frac {1}{1048576} \, x^{4} + \frac {1}{1048576} \, x^{2} \log \relax (x)^{2} + \frac {1}{524288} \, x^{3} + \frac {1}{1048576} \, x^{2} - \frac {1}{524288} \, {\left (x^{3} + x^{2}\right )} \log \relax (x)\right ) - 2 \, \log \left (-x + \log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((524288*log(x)^3-1572864*x*log(x)^2+1572864*x^2*log(x)-524288*x^3)*log(x^2)^3+2*x^2*log(x)^3+(-6*x^
3-4*x^2)*log(x)^2+(6*x^4+6*x^3+4*x^2)*log(x)-2*x^5-2*x^4-2*x^3-2*x^2)/((65536*x*log(x)^3-196608*x^2*log(x)^2+1
96608*x^3*log(x)-65536*x^4)*log(x^2)^4+x^3*log(x)^3+(-3*x^4-2*x^3)*log(x)^2+(3*x^5+4*x^4+x^3)*log(x)-x^6-2*x^5
-x^4),x, algorithm="maxima")

[Out]

log(x^2*log(x)^4 - 2*x*log(x)^5 + log(x)^6 + 1/1048576*x^4 + 1/1048576*x^2*log(x)^2 + 1/524288*x^3 + 1/1048576
*x^2 - 1/524288*(x^3 + x^2)*log(x)) - 2*log(-x + log(x))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\ln \relax (x)}^2\,\left (6\,x^3+4\,x^2\right )-\ln \relax (x)\,\left (6\,x^4+6\,x^3+4\,x^2\right )+{\ln \left (x^2\right )}^3\,\left (524288\,x^3-1572864\,x^2\,\ln \relax (x)+1572864\,x\,{\ln \relax (x)}^2-524288\,{\ln \relax (x)}^3\right )-2\,x^2\,{\ln \relax (x)}^3+2\,x^2+2\,x^3+2\,x^4+2\,x^5}{{\ln \relax (x)}^2\,\left (3\,x^4+2\,x^3\right )-{\ln \left (x^2\right )}^4\,\left (-65536\,x^4+196608\,x^3\,\ln \relax (x)-196608\,x^2\,{\ln \relax (x)}^2+65536\,x\,{\ln \relax (x)}^3\right )-x^3\,{\ln \relax (x)}^3+x^4+2\,x^5+x^6-\ln \relax (x)\,\left (3\,x^5+4\,x^4+x^3\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x)^2*(4*x^2 + 6*x^3) - log(x)*(4*x^2 + 6*x^3 + 6*x^4) + log(x^2)^3*(1572864*x*log(x)^2 - 1572864*x^2*
log(x) - 524288*log(x)^3 + 524288*x^3) - 2*x^2*log(x)^3 + 2*x^2 + 2*x^3 + 2*x^4 + 2*x^5)/(log(x)^2*(2*x^3 + 3*
x^4) - log(x^2)^4*(65536*x*log(x)^3 + 196608*x^3*log(x) - 196608*x^2*log(x)^2 - 65536*x^4) - x^3*log(x)^3 + x^
4 + 2*x^5 + x^6 - log(x)*(x^3 + 4*x^4 + 3*x^5)),x)

[Out]

int((log(x)^2*(4*x^2 + 6*x^3) - log(x)*(4*x^2 + 6*x^3 + 6*x^4) + log(x^2)^3*(1572864*x*log(x)^2 - 1572864*x^2*
log(x) - 524288*log(x)^3 + 524288*x^3) - 2*x^2*log(x)^3 + 2*x^2 + 2*x^3 + 2*x^4 + 2*x^5)/(log(x)^2*(2*x^3 + 3*
x^4) - log(x^2)^4*(65536*x*log(x)^3 + 196608*x^3*log(x) - 196608*x^2*log(x)^2 - 65536*x^4) - x^3*log(x)^3 + x^
4 + 2*x^5 + x^6 - log(x)*(x^3 + 4*x^4 + 3*x^5)), x)

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sympy [B]  time = 1.64, size = 71, normalized size = 2.96 \begin {gather*} - 2 \log {\left (- x + \log {\relax (x )} \right )} + \log {\left (\frac {x^{4}}{1048576} + \frac {x^{3}}{524288} + x^{2} \log {\relax (x )}^{4} + \frac {x^{2} \log {\relax (x )}^{2}}{1048576} + \frac {x^{2}}{1048576} - 2 x \log {\relax (x )}^{5} + \left (- \frac {x^{3}}{524288} - \frac {x^{2}}{524288}\right ) \log {\relax (x )} + \log {\relax (x )}^{6} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((524288*ln(x)**3-1572864*x*ln(x)**2+1572864*x**2*ln(x)-524288*x**3)*ln(x**2)**3+2*x**2*ln(x)**3+(-6
*x**3-4*x**2)*ln(x)**2+(6*x**4+6*x**3+4*x**2)*ln(x)-2*x**5-2*x**4-2*x**3-2*x**2)/((65536*x*ln(x)**3-196608*x**
2*ln(x)**2+196608*x**3*ln(x)-65536*x**4)*ln(x**2)**4+x**3*ln(x)**3+(-3*x**4-2*x**3)*ln(x)**2+(3*x**5+4*x**4+x*
*3)*ln(x)-x**6-2*x**5-x**4),x)

[Out]

-2*log(-x + log(x)) + log(x**4/1048576 + x**3/524288 + x**2*log(x)**4 + x**2*log(x)**2/1048576 + x**2/1048576
- 2*x*log(x)**5 + (-x**3/524288 - x**2/524288)*log(x) + log(x)**6)

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