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3.31.89 \(\int \frac {16 x^2-112 x^3-128 x^2 \log (x)+(-64 x^2+32 x^3+(-64 x+32 x^2) \log (x)) \log (x+\log (x))+(-8 x+12 x^2+(-8+12 x) \log (x)) \log ^2(x+\log (x))+(8 x^2-88 x^3-96 x^2 \log (x)+(-48 x^2+24 x^3+(-48 x+24 x^2) \log (x)) \log (x+\log (x))+(-6 x+8 x^2+(-6+8 x) \log (x)) \log ^2(x+\log (x))) \log (\frac {-4 x^2+(-x+x^2) \log (x+\log (x))}{4 x+\log (x+\log (x))})+(-16 x^3-16 x^2 \log (x)+(-8 x^2+4 x^3+(-8 x+4 x^2) \log (x)) \log (x+\log (x))+(-x+x^2+(-1+x) \log (x)) \log ^2(x+\log (x))) \log ^2(\frac {-4 x^2+(-x+x^2) \log (x+\log (x))}{4 x+\log (x+\log (x))})}{-16 x^3-16 x^2 \log (x)+(-8 x^2+4 x^3+(-8 x+4 x^2) \log (x)) \log (x+\log (x))+(-x+x^2+(-1+x) \log (x)) \log ^2(x+\log (x))} \, dx\)

Optimal. Leaf size=30 \[ x \left (-2-\log \left (-x+\frac {x}{\frac {1}{x}+\frac {4}{\log (x+\log (x))}}\right )\right )^2 \]

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Rubi [F]  time = 49.33, 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 {16 x^2-112 x^3-128 x^2 \log (x)+\left (-64 x^2+32 x^3+\left (-64 x+32 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-8 x+12 x^2+(-8+12 x) \log (x)\right ) \log ^2(x+\log (x))+\left (8 x^2-88 x^3-96 x^2 \log (x)+\left (-48 x^2+24 x^3+\left (-48 x+24 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-6 x+8 x^2+(-6+8 x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log \left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )+\left (-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log ^2\left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )}{-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(16*x^2 - 112*x^3 - 128*x^2*Log[x] + (-64*x^2 + 32*x^3 + (-64*x + 32*x^2)*Log[x])*Log[x + Log[x]] + (-8*x
+ 12*x^2 + (-8 + 12*x)*Log[x])*Log[x + Log[x]]^2 + (8*x^2 - 88*x^3 - 96*x^2*Log[x] + (-48*x^2 + 24*x^3 + (-48*
x + 24*x^2)*Log[x])*Log[x + Log[x]] + (-6*x + 8*x^2 + (-6 + 8*x)*Log[x])*Log[x + Log[x]]^2)*Log[(-4*x^2 + (-x
+ x^2)*Log[x + Log[x]])/(4*x + Log[x + Log[x]])] + (-16*x^3 - 16*x^2*Log[x] + (-8*x^2 + 4*x^3 + (-8*x + 4*x^2)
*Log[x])*Log[x + Log[x]] + (-x + x^2 + (-1 + x)*Log[x])*Log[x + Log[x]]^2)*Log[(-4*x^2 + (-x + x^2)*Log[x + Lo
g[x]])/(4*x + Log[x + Log[x]])]^2)/(-16*x^3 - 16*x^2*Log[x] + (-8*x^2 + 4*x^3 + (-8*x + 4*x^2)*Log[x])*Log[x +
 Log[x]] + (-x + x^2 + (-1 + x)*Log[x])*Log[x + Log[x]]^2),x]

[Out]

12*x + 4*Log[1 - x] - 32*Defer[Int][(4*x + Log[x + Log[x]])^(-1), x] - 16*Defer[Int][x/(4*x + Log[x + Log[x]])
, x] - 4*Defer[Int][1/((x + Log[x])*(4*x + Log[x + Log[x]])), x] + 28*Defer[Int][x/((x + Log[x])*(4*x + Log[x
+ Log[x]])), x] + 32*Defer[Int][Log[x]/((x + Log[x])*(4*x + Log[x + Log[x]])), x] - 16*Defer[Int][(-4*x - Log[
x + Log[x]] + x*Log[x + Log[x]])^(-1), x] + 16*Defer[Int][1/((-1 + x)*(-4*x - Log[x + Log[x]] + x*Log[x + Log[
x]])), x] + 32*Defer[Int][x/(-4*x - Log[x + Log[x]] + x*Log[x + Log[x]]), x] - 4*Defer[Int][1/((x + Log[x])*(-
4*x - Log[x + Log[x]] + x*Log[x + Log[x]])), x] + 32*Defer[Int][x/((x + Log[x])*(-4*x - Log[x + Log[x]] + x*Lo
g[x + Log[x]])), x] - 28*Defer[Int][x^2/((x + Log[x])*(-4*x - Log[x + Log[x]] + x*Log[x + Log[x]])), x] + 32*D
efer[Int][Log[x]/((x + Log[x])*(-4*x - Log[x + Log[x]] + x*Log[x + Log[x]])), x] - 32*Defer[Int][(x*Log[x])/((
x + Log[x])*(-4*x - Log[x + Log[x]] + x*Log[x + Log[x]])), x] + 8*Defer[Int][(x^2*Log[(x*(-4*x + (-1 + x)*Log[
x + Log[x]]))/(4*x + Log[x + Log[x]])])/((x + Log[x])*(4*x + Log[x + Log[x]])*(-4*x - Log[x + Log[x]] + x*Log[
x + Log[x]])), x] - 88*Defer[Int][(x^3*Log[(x*(-4*x + (-1 + x)*Log[x + Log[x]]))/(4*x + Log[x + Log[x]])])/((x
 + Log[x])*(4*x + Log[x + Log[x]])*(-4*x - Log[x + Log[x]] + x*Log[x + Log[x]])), x] - 96*Defer[Int][(x^2*Log[
x]*Log[(x*(-4*x + (-1 + x)*Log[x + Log[x]]))/(4*x + Log[x + Log[x]])])/((x + Log[x])*(4*x + Log[x + Log[x]])*(
-4*x - Log[x + Log[x]] + x*Log[x + Log[x]])), x] - 48*Defer[Int][(x^2*Log[x + Log[x]]*Log[(x*(-4*x + (-1 + x)*
Log[x + Log[x]]))/(4*x + Log[x + Log[x]])])/((x + Log[x])*(4*x + Log[x + Log[x]])*(-4*x - Log[x + Log[x]] + x*
Log[x + Log[x]])), x] + 24*Defer[Int][(x^3*Log[x + Log[x]]*Log[(x*(-4*x + (-1 + x)*Log[x + Log[x]]))/(4*x + Lo
g[x + Log[x]])])/((x + Log[x])*(4*x + Log[x + Log[x]])*(-4*x - Log[x + Log[x]] + x*Log[x + Log[x]])), x] - 48*
Defer[Int][(x*Log[x]*Log[x + Log[x]]*Log[(x*(-4*x + (-1 + x)*Log[x + Log[x]]))/(4*x + Log[x + Log[x]])])/((x +
 Log[x])*(4*x + Log[x + Log[x]])*(-4*x - Log[x + Log[x]] + x*Log[x + Log[x]])), x] + 24*Defer[Int][(x^2*Log[x]
*Log[x + Log[x]]*Log[(x*(-4*x + (-1 + x)*Log[x + Log[x]]))/(4*x + Log[x + Log[x]])])/((x + Log[x])*(4*x + Log[
x + Log[x]])*(-4*x - Log[x + Log[x]] + x*Log[x + Log[x]])), x] - 6*Defer[Int][(x*Log[x + Log[x]]^2*Log[(x*(-4*
x + (-1 + x)*Log[x + Log[x]]))/(4*x + Log[x + Log[x]])])/((x + Log[x])*(4*x + Log[x + Log[x]])*(-4*x - Log[x +
 Log[x]] + x*Log[x + Log[x]])), x] + 8*Defer[Int][(x^2*Log[x + Log[x]]^2*Log[(x*(-4*x + (-1 + x)*Log[x + Log[x
]]))/(4*x + Log[x + Log[x]])])/((x + Log[x])*(4*x + Log[x + Log[x]])*(-4*x - Log[x + Log[x]] + x*Log[x + Log[x
]])), x] - 6*Defer[Int][(Log[x]*Log[x + Log[x]]^2*Log[(x*(-4*x + (-1 + x)*Log[x + Log[x]]))/(4*x + Log[x + Log
[x]])])/((x + Log[x])*(4*x + Log[x + Log[x]])*(-4*x - Log[x + Log[x]] + x*Log[x + Log[x]])), x] + 8*Defer[Int]
[(x*Log[x]*Log[x + Log[x]]^2*Log[(x*(-4*x + (-1 + x)*Log[x + Log[x]]))/(4*x + Log[x + Log[x]])])/((x + Log[x])
*(4*x + Log[x + Log[x]])*(-4*x - Log[x + Log[x]] + x*Log[x + Log[x]])), x] + Defer[Int][Log[(x*(-4*x + (-1 + x
)*Log[x + Log[x]]))/(4*x + Log[x + Log[x]])]^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-16 x^2+112 x^3+128 x^2 \log (x)-32 (-2+x) x (x+\log (x)) \log (x+\log (x))-4 (-2+3 x) (x+\log (x)) \log ^2(x+\log (x))-\left (8 x^2-88 x^3-96 x^2 \log (x)+24 (-2+x) x (x+\log (x)) \log (x+\log (x))+2 (-3+4 x) (x+\log (x)) \log ^2(x+\log (x))\right ) \log \left (\frac {x (-4 x+(-1+x) \log (x+\log (x)))}{4 x+\log (x+\log (x))}\right )-(x+\log (x)) \left (-16 x^2+4 (-2+x) x \log (x+\log (x))+(-1+x) \log ^2(x+\log (x))\right ) \log ^2\left (\frac {x (-4 x+(-1+x) \log (x+\log (x)))}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) \left (16 x^2-4 (-2+x) x \log (x+\log (x))-(-1+x) \log ^2(x+\log (x))\right )} \, dx\\ &=\int \left (\frac {16 x^2}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x-\log (x+\log (x))+x \log (x+\log (x)))}-\frac {112 x^3}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x-\log (x+\log (x))+x \log (x+\log (x)))}-\frac {128 x^2 \log (x)}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x-\log (x+\log (x))+x \log (x+\log (x)))}+\frac {32 (-2+x) x \log (x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x-\log (x+\log (x))+x \log (x+\log (x)))}+\frac {4 (-2+3 x) \log ^2(x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x-\log (x+\log (x))+x \log (x+\log (x)))}+\frac {2 \left (4 x^2-44 x^3-48 x^2 \log (x)-24 x^2 \log (x+\log (x))+12 x^3 \log (x+\log (x))-24 x \log (x) \log (x+\log (x))+12 x^2 \log (x) \log (x+\log (x))-3 x \log ^2(x+\log (x))+4 x^2 \log ^2(x+\log (x))-3 \log (x) \log ^2(x+\log (x))+4 x \log (x) \log ^2(x+\log (x))\right ) \log \left (\frac {x (-4 x+(-1+x) \log (x+\log (x)))}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x-\log (x+\log (x))+x \log (x+\log (x)))}+\log ^2\left (\frac {x (-4 x+(-1+x) \log (x+\log (x)))}{4 x+\log (x+\log (x))}\right )\right ) \, dx\\ &=2 \int \frac {\left (4 x^2-44 x^3-48 x^2 \log (x)-24 x^2 \log (x+\log (x))+12 x^3 \log (x+\log (x))-24 x \log (x) \log (x+\log (x))+12 x^2 \log (x) \log (x+\log (x))-3 x \log ^2(x+\log (x))+4 x^2 \log ^2(x+\log (x))-3 \log (x) \log ^2(x+\log (x))+4 x \log (x) \log ^2(x+\log (x))\right ) \log \left (\frac {x (-4 x+(-1+x) \log (x+\log (x)))}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x-\log (x+\log (x))+x \log (x+\log (x)))} \, dx+4 \int \frac {(-2+3 x) \log ^2(x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x-\log (x+\log (x))+x \log (x+\log (x)))} \, dx+16 \int \frac {x^2}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x-\log (x+\log (x))+x \log (x+\log (x)))} \, dx+32 \int \frac {(-2+x) x \log (x+\log (x))}{(4 x+\log (x+\log (x))) (-4 x-\log (x+\log (x))+x \log (x+\log (x)))} \, dx-112 \int \frac {x^3}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x-\log (x+\log (x))+x \log (x+\log (x)))} \, dx-128 \int \frac {x^2 \log (x)}{(x+\log (x)) (4 x+\log (x+\log (x))) (-4 x-\log (x+\log (x))+x \log (x+\log (x)))} \, dx+\int \log ^2\left (\frac {x (-4 x+(-1+x) \log (x+\log (x)))}{4 x+\log (x+\log (x))}\right ) \, dx\\ &=2 \int \frac {\left (-x \left (4 (1-11 x) x+12 (-2+x) x \log (x+\log (x))+(-3+4 x) \log ^2(x+\log (x))\right )-\log (x) \left (-48 x^2+12 (-2+x) x \log (x+\log (x))+(-3+4 x) \log ^2(x+\log (x))\right )\right ) \log \left (\frac {x (-4 x+(-1+x) \log (x+\log (x)))}{4 x+\log (x+\log (x))}\right )}{(x+\log (x)) (4 x+\log (x+\log (x))) (4 x-(-1+x) \log (x+\log (x)))} \, dx+4 \int \left (\frac {-2+3 x}{-1+x}-\frac {4 (-2+3 x)}{4 x+\log (x+\log (x))}+\frac {4 (-2+3 x)}{(-1+x) (-4 x-\log (x+\log (x))+x \log (x+\log (x)))}\right ) \, dx+16 \int \left (-\frac {1}{4 (x+\log (x)) (4 x+\log (x+\log (x)))}+\frac {-1+x}{4 (x+\log (x)) (-4 x-\log (x+\log (x))+x \log (x+\log (x)))}\right ) \, dx+32 \int \left (\frac {-2+x}{4 x+\log (x+\log (x))}+\frac {-2+x}{-4 x-\log (x+\log (x))+x \log (x+\log (x))}\right ) \, dx-112 \int \left (-\frac {x}{4 (x+\log (x)) (4 x+\log (x+\log (x)))}+\frac {(-1+x) x}{4 (x+\log (x)) (-4 x-\log (x+\log (x))+x \log (x+\log (x)))}\right ) \, dx-128 \int \left (-\frac {\log (x)}{4 (x+\log (x)) (4 x+\log (x+\log (x)))}+\frac {(-1+x) \log (x)}{4 (x+\log (x)) (-4 x-\log (x+\log (x))+x \log (x+\log (x)))}\right ) \, dx+\int \log ^2\left (\frac {x (-4 x+(-1+x) \log (x+\log (x)))}{4 x+\log (x+\log (x))}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [F]  time = 1.49, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {16 x^2-112 x^3-128 x^2 \log (x)+\left (-64 x^2+32 x^3+\left (-64 x+32 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-8 x+12 x^2+(-8+12 x) \log (x)\right ) \log ^2(x+\log (x))+\left (8 x^2-88 x^3-96 x^2 \log (x)+\left (-48 x^2+24 x^3+\left (-48 x+24 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-6 x+8 x^2+(-6+8 x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log \left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )+\left (-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))\right ) \log ^2\left (\frac {-4 x^2+\left (-x+x^2\right ) \log (x+\log (x))}{4 x+\log (x+\log (x))}\right )}{-16 x^3-16 x^2 \log (x)+\left (-8 x^2+4 x^3+\left (-8 x+4 x^2\right ) \log (x)\right ) \log (x+\log (x))+\left (-x+x^2+(-1+x) \log (x)\right ) \log ^2(x+\log (x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(16*x^2 - 112*x^3 - 128*x^2*Log[x] + (-64*x^2 + 32*x^3 + (-64*x + 32*x^2)*Log[x])*Log[x + Log[x]] +
(-8*x + 12*x^2 + (-8 + 12*x)*Log[x])*Log[x + Log[x]]^2 + (8*x^2 - 88*x^3 - 96*x^2*Log[x] + (-48*x^2 + 24*x^3 +
 (-48*x + 24*x^2)*Log[x])*Log[x + Log[x]] + (-6*x + 8*x^2 + (-6 + 8*x)*Log[x])*Log[x + Log[x]]^2)*Log[(-4*x^2
+ (-x + x^2)*Log[x + Log[x]])/(4*x + Log[x + Log[x]])] + (-16*x^3 - 16*x^2*Log[x] + (-8*x^2 + 4*x^3 + (-8*x +
4*x^2)*Log[x])*Log[x + Log[x]] + (-x + x^2 + (-1 + x)*Log[x])*Log[x + Log[x]]^2)*Log[(-4*x^2 + (-x + x^2)*Log[
x + Log[x]])/(4*x + Log[x + Log[x]])]^2)/(-16*x^3 - 16*x^2*Log[x] + (-8*x^2 + 4*x^3 + (-8*x + 4*x^2)*Log[x])*L
og[x + Log[x]] + (-x + x^2 + (-1 + x)*Log[x])*Log[x + Log[x]]^2),x]

[Out]

Integrate[(16*x^2 - 112*x^3 - 128*x^2*Log[x] + (-64*x^2 + 32*x^3 + (-64*x + 32*x^2)*Log[x])*Log[x + Log[x]] +
(-8*x + 12*x^2 + (-8 + 12*x)*Log[x])*Log[x + Log[x]]^2 + (8*x^2 - 88*x^3 - 96*x^2*Log[x] + (-48*x^2 + 24*x^3 +
 (-48*x + 24*x^2)*Log[x])*Log[x + Log[x]] + (-6*x + 8*x^2 + (-6 + 8*x)*Log[x])*Log[x + Log[x]]^2)*Log[(-4*x^2
+ (-x + x^2)*Log[x + Log[x]])/(4*x + Log[x + Log[x]])] + (-16*x^3 - 16*x^2*Log[x] + (-8*x^2 + 4*x^3 + (-8*x +
4*x^2)*Log[x])*Log[x + Log[x]] + (-x + x^2 + (-1 + x)*Log[x])*Log[x + Log[x]]^2)*Log[(-4*x^2 + (-x + x^2)*Log[
x + Log[x]])/(4*x + Log[x + Log[x]])]^2)/(-16*x^3 - 16*x^2*Log[x] + (-8*x^2 + 4*x^3 + (-8*x + 4*x^2)*Log[x])*L
og[x + Log[x]] + (-x + x^2 + (-1 + x)*Log[x])*Log[x + Log[x]]^2), x]

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fricas [B]  time = 0.60, size = 79, normalized size = 2.63 \begin {gather*} x \log \left (-\frac {4 \, x^{2} - {\left (x^{2} - x\right )} \log \left (x + \log \relax (x)\right )}{4 \, x + \log \left (x + \log \relax (x)\right )}\right )^{2} + 4 \, x \log \left (-\frac {4 \, x^{2} - {\left (x^{2} - x\right )} \log \left (x + \log \relax (x)\right )}{4 \, x + \log \left (x + \log \relax (x)\right )}\right ) + 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((x-1)*log(x)+x^2-x)*log(x+log(x))^2+((4*x^2-8*x)*log(x)+4*x^3-8*x^2)*log(x+log(x))-16*x^2*log(x)-
16*x^3)*log(((x^2-x)*log(x+log(x))-4*x^2)/(log(x+log(x))+4*x))^2+(((8*x-6)*log(x)+8*x^2-6*x)*log(x+log(x))^2+(
(24*x^2-48*x)*log(x)+24*x^3-48*x^2)*log(x+log(x))-96*x^2*log(x)-88*x^3+8*x^2)*log(((x^2-x)*log(x+log(x))-4*x^2
)/(log(x+log(x))+4*x))+((12*x-8)*log(x)+12*x^2-8*x)*log(x+log(x))^2+((32*x^2-64*x)*log(x)+32*x^3-64*x^2)*log(x
+log(x))-128*x^2*log(x)-112*x^3+16*x^2)/(((x-1)*log(x)+x^2-x)*log(x+log(x))^2+((4*x^2-8*x)*log(x)+4*x^3-8*x^2)
*log(x+log(x))-16*x^2*log(x)-16*x^3),x, algorithm="fricas")

[Out]

x*log(-(4*x^2 - (x^2 - x)*log(x + log(x)))/(4*x + log(x + log(x))))^2 + 4*x*log(-(4*x^2 - (x^2 - x)*log(x + lo
g(x)))/(4*x + log(x + log(x)))) + 4*x

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((x-1)*log(x)+x^2-x)*log(x+log(x))^2+((4*x^2-8*x)*log(x)+4*x^3-8*x^2)*log(x+log(x))-16*x^2*log(x)-
16*x^3)*log(((x^2-x)*log(x+log(x))-4*x^2)/(log(x+log(x))+4*x))^2+(((8*x-6)*log(x)+8*x^2-6*x)*log(x+log(x))^2+(
(24*x^2-48*x)*log(x)+24*x^3-48*x^2)*log(x+log(x))-96*x^2*log(x)-88*x^3+8*x^2)*log(((x^2-x)*log(x+log(x))-4*x^2
)/(log(x+log(x))+4*x))+((12*x-8)*log(x)+12*x^2-8*x)*log(x+log(x))^2+((32*x^2-64*x)*log(x)+32*x^3-64*x^2)*log(x
+log(x))-128*x^2*log(x)-112*x^3+16*x^2)/(((x-1)*log(x)+x^2-x)*log(x+log(x))^2+((4*x^2-8*x)*log(x)+4*x^3-8*x^2)
*log(x+log(x))-16*x^2*log(x)-16*x^3),x, algorithm="giac")

[Out]

Timed out

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maple [C]  time = 0.87, size = 5269, normalized size = 175.63

method result size
risch \(\text {Expression too large to display}\) \(5269\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((x-1)*ln(x)+x^2-x)*ln(x+ln(x))^2+((4*x^2-8*x)*ln(x)+4*x^3-8*x^2)*ln(x+ln(x))-16*x^2*ln(x)-16*x^3)*ln(((
x^2-x)*ln(x+ln(x))-4*x^2)/(ln(x+ln(x))+4*x))^2+(((8*x-6)*ln(x)+8*x^2-6*x)*ln(x+ln(x))^2+((24*x^2-48*x)*ln(x)+2
4*x^3-48*x^2)*ln(x+ln(x))-96*x^2*ln(x)-88*x^3+8*x^2)*ln(((x^2-x)*ln(x+ln(x))-4*x^2)/(ln(x+ln(x))+4*x))+((12*x-
8)*ln(x)+12*x^2-8*x)*ln(x+ln(x))^2+((32*x^2-64*x)*ln(x)+32*x^3-64*x^2)*ln(x+ln(x))-128*x^2*ln(x)-112*x^3+16*x^
2)/(((x-1)*ln(x)+x^2-x)*ln(x+ln(x))^2+((4*x^2-8*x)*ln(x)+4*x^3-8*x^2)*ln(x+ln(x))-16*x^2*ln(x)-16*x^3),x,metho
d=_RETURNVERBOSE)

[Out]

result too large to display

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maxima [B]  time = 0.58, size = 104, normalized size = 3.47 \begin {gather*} x \log \left ({\left (x - 1\right )} \log \left (x + \log \relax (x)\right ) - 4 \, x\right )^{2} + x \log \left (4 \, x + \log \left (x + \log \relax (x)\right )\right )^{2} + x \log \relax (x)^{2} - 2 \, {\left (x \log \left (4 \, x + \log \left (x + \log \relax (x)\right )\right ) - x \log \relax (x) - 2 \, x\right )} \log \left ({\left (x - 1\right )} \log \left (x + \log \relax (x)\right ) - 4 \, x\right ) - 2 \, {\left (x \log \relax (x) + 2 \, x\right )} \log \left (4 \, x + \log \left (x + \log \relax (x)\right )\right ) + 4 \, x \log \relax (x) + 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((x-1)*log(x)+x^2-x)*log(x+log(x))^2+((4*x^2-8*x)*log(x)+4*x^3-8*x^2)*log(x+log(x))-16*x^2*log(x)-
16*x^3)*log(((x^2-x)*log(x+log(x))-4*x^2)/(log(x+log(x))+4*x))^2+(((8*x-6)*log(x)+8*x^2-6*x)*log(x+log(x))^2+(
(24*x^2-48*x)*log(x)+24*x^3-48*x^2)*log(x+log(x))-96*x^2*log(x)-88*x^3+8*x^2)*log(((x^2-x)*log(x+log(x))-4*x^2
)/(log(x+log(x))+4*x))+((12*x-8)*log(x)+12*x^2-8*x)*log(x+log(x))^2+((32*x^2-64*x)*log(x)+32*x^3-64*x^2)*log(x
+log(x))-128*x^2*log(x)-112*x^3+16*x^2)/(((x-1)*log(x)+x^2-x)*log(x+log(x))^2+((4*x^2-8*x)*log(x)+4*x^3-8*x^2)
*log(x+log(x))-16*x^2*log(x)-16*x^3),x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 3.23, size = 39, normalized size = 1.30 \begin {gather*} x\,{\left (\ln \left (-\frac {\ln \left (x+\ln \relax (x)\right )\,\left (x-x^2\right )+4\,x^2}{4\,x+\ln \left (x+\ln \relax (x)\right )}\right )+2\right )}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x + log(x))*(log(x)*(64*x - 32*x^2) + 64*x^2 - 32*x^3) + 128*x^2*log(x) + log(-(log(x + log(x))*(x -
x^2) + 4*x^2)/(4*x + log(x + log(x))))^2*(log(x + log(x))*(log(x)*(8*x - 4*x^2) + 8*x^2 - 4*x^3) - log(x + log
(x))^2*(log(x)*(x - 1) - x + x^2) + 16*x^2*log(x) + 16*x^3) - log(x + log(x))^2*(log(x)*(12*x - 8) - 8*x + 12*
x^2) + log(-(log(x + log(x))*(x - x^2) + 4*x^2)/(4*x + log(x + log(x))))*(log(x + log(x))*(log(x)*(48*x - 24*x
^2) + 48*x^2 - 24*x^3) + 96*x^2*log(x) - log(x + log(x))^2*(log(x)*(8*x - 6) - 6*x + 8*x^2) - 8*x^2 + 88*x^3)
- 16*x^2 + 112*x^3)/(log(x + log(x))*(log(x)*(8*x - 4*x^2) + 8*x^2 - 4*x^3) - log(x + log(x))^2*(log(x)*(x - 1
) - x + x^2) + 16*x^2*log(x) + 16*x^3),x)

[Out]

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

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sympy [B]  time = 82.04, size = 66, normalized size = 2.20 \begin {gather*} x \log {\left (\frac {- 4 x^{2} + \left (x^{2} - x\right ) \log {\left (x + \log {\relax (x )} \right )}}{4 x + \log {\left (x + \log {\relax (x )} \right )}} \right )}^{2} + 4 x \log {\left (\frac {- 4 x^{2} + \left (x^{2} - x\right ) \log {\left (x + \log {\relax (x )} \right )}}{4 x + \log {\left (x + \log {\relax (x )} \right )}} \right )} + 4 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((x-1)*ln(x)+x**2-x)*ln(x+ln(x))**2+((4*x**2-8*x)*ln(x)+4*x**3-8*x**2)*ln(x+ln(x))-16*x**2*ln(x)-1
6*x**3)*ln(((x**2-x)*ln(x+ln(x))-4*x**2)/(ln(x+ln(x))+4*x))**2+(((8*x-6)*ln(x)+8*x**2-6*x)*ln(x+ln(x))**2+((24
*x**2-48*x)*ln(x)+24*x**3-48*x**2)*ln(x+ln(x))-96*x**2*ln(x)-88*x**3+8*x**2)*ln(((x**2-x)*ln(x+ln(x))-4*x**2)/
(ln(x+ln(x))+4*x))+((12*x-8)*ln(x)+12*x**2-8*x)*ln(x+ln(x))**2+((32*x**2-64*x)*ln(x)+32*x**3-64*x**2)*ln(x+ln(
x))-128*x**2*ln(x)-112*x**3+16*x**2)/(((x-1)*ln(x)+x**2-x)*ln(x+ln(x))**2+((4*x**2-8*x)*ln(x)+4*x**3-8*x**2)*l
n(x+ln(x))-16*x**2*ln(x)-16*x**3),x)

[Out]

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

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