3.1.13 \(\int \frac {(320 x^2+1280 x^5) \log (x)+(-192 x-64 x^2-64 x^5+(-480 x-160 x^2-160 x^5) \log (x)) \log (3+x+x^4)+(-2000 x^2-8000 x^5) \log (x) \log ^2(3+x+x^4)+(1200 x+400 x^2+400 x^5+(6000 x+2000 x^2+2000 x^5) \log (x)) \log ^3(3+x+x^4)+(-18750 x-6250 x^2-6250 x^5) \log (x) \log ^5(3+x+x^4)+((-64 x^2-256 x^5) \log (x)+(96 x+32 x^2+32 x^5) \log (x) \log (3+x+x^4)+(1200 x^2+4800 x^5) \log (x) \log ^2(3+x+x^4)+(-480 x-160 x^2-160 x^5+(-3600 x-1200 x^2-1200 x^5) \log (x)) \log ^3(3+x+x^4)+(18750 x+6250 x^2+6250 x^5) \log (x) \log ^5(3+x+x^4)) \log (\log (x))+((-240 x^2-960 x^5) \log (x) \log ^2(3+x+x^4)+(48 x+16 x^2+16 x^5+(720 x+240 x^2+240 x^5) \log (x)) \log ^3(3+x+x^4)+(-7500 x-2500 x^2-2500 x^5) \log (x) \log ^5(3+x+x^4)) \log ^2(\log (x))+((16 x^2+64 x^5) \log (x) \log ^2(3+x+x^4)+(-48 x-16 x^2-16 x^5) \log (x) \log ^3(3+x+x^4)+(1500 x+500 x^2+500 x^5) \log (x) \log ^5(3+x+x^4)) \log ^3(\log (x))+(-150 x-50 x^2-50 x^5) \log (x) \log ^5(3+x+x^4) \log ^4(\log (x))+(6 x+2 x^2+2 x^5) \log (x) \log ^5(3+x+x^4) \log ^5(\log (x))}{(-9375-3125 x-3125 x^4) \log (x) \log ^5(3+x+x^4)+(9375+3125 x+3125 x^4) \log (x) \log ^5(3+x+x^4) \log (\log (x))+(-3750-1250 x-1250 x^4) \log (x) \log ^5(3+x+x^4) \log ^2(\log (x))+(750+250 x+250 x^4) \log (x) \log ^5(3+x+x^4) \log ^3(\log (x))+(-75-25 x-25 x^4) \log (x) \log ^5(3+x+x^4) \log ^4(\log (x))+(3+x+x^4) \log (x) \log ^5(3+x+x^4) \log ^5(\log (x))} \, dx\)

Optimal. Leaf size=25 \[ \left (x-\frac {4 x}{\log ^2\left (3+x+x^4\right ) (5-\log (\log (x)))^2}\right )^2 \]

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Rubi [F]  time = 12.26, 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 {\left (320 x^2+1280 x^5\right ) \log (x)+\left (-192 x-64 x^2-64 x^5+\left (-480 x-160 x^2-160 x^5\right ) \log (x)\right ) \log \left (3+x+x^4\right )+\left (-2000 x^2-8000 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (1200 x+400 x^2+400 x^5+\left (6000 x+2000 x^2+2000 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-18750 x-6250 x^2-6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (\left (-64 x^2-256 x^5\right ) \log (x)+\left (96 x+32 x^2+32 x^5\right ) \log (x) \log \left (3+x+x^4\right )+\left (1200 x^2+4800 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-480 x-160 x^2-160 x^5+\left (-3600 x-1200 x^2-1200 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (18750 x+6250 x^2+6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log (\log (x))+\left (\left (-240 x^2-960 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (48 x+16 x^2+16 x^5+\left (720 x+240 x^2+240 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-7500 x-2500 x^2-2500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^2(\log (x))+\left (\left (16 x^2+64 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-48 x-16 x^2-16 x^5\right ) \log (x) \log ^3\left (3+x+x^4\right )+\left (1500 x+500 x^2+500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^3(\log (x))+\left (-150 x-50 x^2-50 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (6 x+2 x^2+2 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))}{\left (-9375-3125 x-3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (9375+3125 x+3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log (\log (x))+\left (-3750-1250 x-1250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^2(\log (x))+\left (750+250 x+250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^3(\log (x))+\left (-75-25 x-25 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (3+x+x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((320*x^2 + 1280*x^5)*Log[x] + (-192*x - 64*x^2 - 64*x^5 + (-480*x - 160*x^2 - 160*x^5)*Log[x])*Log[3 + x
+ x^4] + (-2000*x^2 - 8000*x^5)*Log[x]*Log[3 + x + x^4]^2 + (1200*x + 400*x^2 + 400*x^5 + (6000*x + 2000*x^2 +
2000*x^5)*Log[x])*Log[3 + x + x^4]^3 + (-18750*x - 6250*x^2 - 6250*x^5)*Log[x]*Log[3 + x + x^4]^5 + ((-64*x^2
- 256*x^5)*Log[x] + (96*x + 32*x^2 + 32*x^5)*Log[x]*Log[3 + x + x^4] + (1200*x^2 + 4800*x^5)*Log[x]*Log[3 + x
+ x^4]^2 + (-480*x - 160*x^2 - 160*x^5 + (-3600*x - 1200*x^2 - 1200*x^5)*Log[x])*Log[3 + x + x^4]^3 + (18750*
x + 6250*x^2 + 6250*x^5)*Log[x]*Log[3 + x + x^4]^5)*Log[Log[x]] + ((-240*x^2 - 960*x^5)*Log[x]*Log[3 + x + x^4
]^2 + (48*x + 16*x^2 + 16*x^5 + (720*x + 240*x^2 + 240*x^5)*Log[x])*Log[3 + x + x^4]^3 + (-7500*x - 2500*x^2 -
2500*x^5)*Log[x]*Log[3 + x + x^4]^5)*Log[Log[x]]^2 + ((16*x^2 + 64*x^5)*Log[x]*Log[3 + x + x^4]^2 + (-48*x -
16*x^2 - 16*x^5)*Log[x]*Log[3 + x + x^4]^3 + (1500*x + 500*x^2 + 500*x^5)*Log[x]*Log[3 + x + x^4]^5)*Log[Log[x
]]^3 + (-150*x - 50*x^2 - 50*x^5)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]]^4 + (6*x + 2*x^2 + 2*x^5)*Log[x]*Log[3
+ x + x^4]^5*Log[Log[x]]^5)/((-9375 - 3125*x - 3125*x^4)*Log[x]*Log[3 + x + x^4]^5 + (9375 + 3125*x + 3125*x^
4)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]] + (-3750 - 1250*x - 1250*x^4)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]]^2
+ (750 + 250*x + 250*x^4)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]]^3 + (-75 - 25*x - 25*x^4)*Log[x]*Log[3 + x +
x^4]^5*Log[Log[x]]^4 + (3 + x + x^4)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]]^5),x]

[Out]

x^2 - 64*Defer[Int][x/(Log[x]*Log[3 + x + x^4]^4*(-5 + Log[Log[x]])^5), x] - 256*Defer[Int][x/(Log[3 + x + x^4
]^5*(-5 + Log[Log[x]])^4), x] + 768*Defer[Int][x/((3 + x + x^4)*Log[3 + x + x^4]^5*(-5 + Log[Log[x]])^4), x] +
192*Defer[Int][x^2/((3 + x + x^4)*Log[3 + x + x^4]^5*(-5 + Log[Log[x]])^4), x] + 32*Defer[Int][x/(Log[3 + x +
x^4]^4*(-5 + Log[Log[x]])^4), x] + 16*Defer[Int][x/(Log[x]*Log[3 + x + x^4]^2*(-5 + Log[Log[x]])^3), x] + 64*
Defer[Int][x/(Log[3 + x + x^4]^3*(-5 + Log[Log[x]])^2), x] - 192*Defer[Int][x/((3 + x + x^4)*Log[3 + x + x^4]^
3*(-5 + Log[Log[x]])^2), x] - 48*Defer[Int][x^2/((3 + x + x^4)*Log[3 + x + x^4]^3*(-5 + Log[Log[x]])^2), x] -
16*Defer[Int][x/(Log[3 + x + x^4]^2*(-5 + Log[Log[x]])^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 x \left (8 \left (3+x+x^4\right ) \log \left (3+x+x^4\right )+\log (x) \left (8 \left (x+4 x^4\right )-4 \left (3+x+x^4\right ) \log \left (3+x+x^4\right )+\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2\right ) (-5+\log (\log (x)))\right ) \left (4-\log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2\right )}{\left (3+x+x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) (5-\log (\log (x)))^5} \, dx\\ &=2 \int \frac {x \left (8 \left (3+x+x^4\right ) \log \left (3+x+x^4\right )+\log (x) \left (8 \left (x+4 x^4\right )-4 \left (3+x+x^4\right ) \log \left (3+x+x^4\right )+\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2\right ) (-5+\log (\log (x)))\right ) \left (4-\log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2\right )}{\left (3+x+x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) (5-\log (\log (x)))^5} \, dx\\ &=2 \int \left (x-\frac {32 x}{\log (x) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^5}+\frac {16 x \left (-2 x-8 x^4+3 \log \left (3+x+x^4\right )+x \log \left (3+x+x^4\right )+x^4 \log \left (3+x+x^4\right )\right )}{\left (3+x+x^4\right ) \log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4}+\frac {8 x}{\log (x) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^3}-\frac {8 x \left (-x-4 x^4+3 \log \left (3+x+x^4\right )+x \log \left (3+x+x^4\right )+x^4 \log \left (3+x+x^4\right )\right )}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2}\right ) \, dx\\ &=x^2+16 \int \frac {x}{\log (x) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^3} \, dx-16 \int \frac {x \left (-x-4 x^4+3 \log \left (3+x+x^4\right )+x \log \left (3+x+x^4\right )+x^4 \log \left (3+x+x^4\right )\right )}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx+32 \int \frac {x \left (-2 x-8 x^4+3 \log \left (3+x+x^4\right )+x \log \left (3+x+x^4\right )+x^4 \log \left (3+x+x^4\right )\right )}{\left (3+x+x^4\right ) \log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx-64 \int \frac {x}{\log (x) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^5} \, dx\\ &=x^2-16 \int \left (-\frac {x^2}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2}-\frac {4 x^5}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2}+\frac {3 x}{\left (3+x+x^4\right ) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2}+\frac {x^2}{\left (3+x+x^4\right ) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2}+\frac {x^5}{\left (3+x+x^4\right ) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2}\right ) \, dx+16 \int \frac {x}{\log (x) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^3} \, dx+32 \int \frac {x \left (-2 \left (x+4 x^4\right )+\left (3+x+x^4\right ) \log \left (3+x+x^4\right )\right )}{\left (3+x+x^4\right ) \log ^5\left (3+x+x^4\right ) (5-\log (\log (x)))^4} \, dx-64 \int \frac {x}{\log (x) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^5} \, dx\\ &=x^2+16 \int \frac {x}{\log (x) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^3} \, dx+16 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-16 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-16 \int \frac {x^5}{\left (3+x+x^4\right ) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx+32 \int \left (-\frac {2 x^2}{\left (3+x+x^4\right ) \log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4}-\frac {8 x^5}{\left (3+x+x^4\right ) \log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4}+\frac {3 x}{\left (3+x+x^4\right ) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4}+\frac {x^2}{\left (3+x+x^4\right ) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4}+\frac {x^5}{\left (3+x+x^4\right ) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4}\right ) \, dx-48 \int \frac {x}{\left (3+x+x^4\right ) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-64 \int \frac {x}{\log (x) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^5} \, dx+64 \int \frac {x^5}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx\\ &=x^2-16 \int \left (\frac {x}{\log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2}-\frac {x (3+x)}{\left (3+x+x^4\right ) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2}\right ) \, dx+16 \int \frac {x}{\log (x) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^3} \, dx+16 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-16 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx+32 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx+32 \int \frac {x^5}{\left (3+x+x^4\right ) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx-48 \int \frac {x}{\left (3+x+x^4\right ) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx+64 \int \left (\frac {x}{\log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2}-\frac {x (3+x)}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2}\right ) \, dx-64 \int \frac {x}{\log (x) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^5} \, dx-64 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx+96 \int \frac {x}{\left (3+x+x^4\right ) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx-256 \int \frac {x^5}{\left (3+x+x^4\right ) \log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx\\ &=x^2+16 \int \frac {x}{\log (x) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^3} \, dx+16 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-16 \int \frac {x}{\log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-16 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx+16 \int \frac {x (3+x)}{\left (3+x+x^4\right ) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx+32 \int \left (\frac {x}{\log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4}-\frac {x (3+x)}{\left (3+x+x^4\right ) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4}\right ) \, dx+32 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx-48 \int \frac {x}{\left (3+x+x^4\right ) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-64 \int \frac {x}{\log (x) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^5} \, dx-64 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx+64 \int \frac {x}{\log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-64 \int \frac {x (3+x)}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx+96 \int \frac {x}{\left (3+x+x^4\right ) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx-256 \int \left (\frac {x}{\log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4}-\frac {x (3+x)}{\left (3+x+x^4\right ) \log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4}\right ) \, dx\\ &=x^2+16 \int \left (\frac {3 x}{\left (3+x+x^4\right ) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2}+\frac {x^2}{\left (3+x+x^4\right ) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2}\right ) \, dx+16 \int \frac {x}{\log (x) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^3} \, dx+16 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-16 \int \frac {x}{\log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-16 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx+32 \int \frac {x}{\log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx+32 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx-32 \int \frac {x (3+x)}{\left (3+x+x^4\right ) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx-48 \int \frac {x}{\left (3+x+x^4\right ) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-64 \int \left (\frac {3 x}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2}+\frac {x^2}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2}\right ) \, dx-64 \int \frac {x}{\log (x) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^5} \, dx-64 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx+64 \int \frac {x}{\log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx+96 \int \frac {x}{\left (3+x+x^4\right ) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx-256 \int \frac {x}{\log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx+256 \int \frac {x (3+x)}{\left (3+x+x^4\right ) \log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx\\ &=x^2+16 \int \frac {x}{\log (x) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^3} \, dx+16 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-16 \int \frac {x}{\log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-32 \int \left (\frac {3 x}{\left (3+x+x^4\right ) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4}+\frac {x^2}{\left (3+x+x^4\right ) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4}\right ) \, dx+32 \int \frac {x}{\log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx+32 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx-64 \int \frac {x}{\log (x) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^5} \, dx-64 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx+64 \int \frac {x}{\log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-64 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx+96 \int \frac {x}{\left (3+x+x^4\right ) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx-192 \int \frac {x}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx+256 \int \left (\frac {3 x}{\left (3+x+x^4\right ) \log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4}+\frac {x^2}{\left (3+x+x^4\right ) \log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4}\right ) \, dx-256 \int \frac {x}{\log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx\\ &=x^2+16 \int \frac {x}{\log (x) \log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^3} \, dx+16 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-16 \int \frac {x}{\log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx+32 \int \frac {x}{\log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx-64 \int \frac {x}{\log (x) \log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^5} \, dx-64 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx+64 \int \frac {x}{\log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-64 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-192 \int \frac {x}{\left (3+x+x^4\right ) \log ^3\left (3+x+x^4\right ) (-5+\log (\log (x)))^2} \, dx-256 \int \frac {x}{\log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx+256 \int \frac {x^2}{\left (3+x+x^4\right ) \log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx+768 \int \frac {x}{\left (3+x+x^4\right ) \log ^5\left (3+x+x^4\right ) (-5+\log (\log (x)))^4} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.21, size = 42, normalized size = 1.68 \begin {gather*} x^2 \left (1+\frac {16}{\log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4}-\frac {8}{\log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((320*x^2 + 1280*x^5)*Log[x] + (-192*x - 64*x^2 - 64*x^5 + (-480*x - 160*x^2 - 160*x^5)*Log[x])*Log[
3 + x + x^4] + (-2000*x^2 - 8000*x^5)*Log[x]*Log[3 + x + x^4]^2 + (1200*x + 400*x^2 + 400*x^5 + (6000*x + 2000
*x^2 + 2000*x^5)*Log[x])*Log[3 + x + x^4]^3 + (-18750*x - 6250*x^2 - 6250*x^5)*Log[x]*Log[3 + x + x^4]^5 + ((-
64*x^2 - 256*x^5)*Log[x] + (96*x + 32*x^2 + 32*x^5)*Log[x]*Log[3 + x + x^4] + (1200*x^2 + 4800*x^5)*Log[x]*Log
[3 + x + x^4]^2 + (-480*x - 160*x^2 - 160*x^5 + (-3600*x - 1200*x^2 - 1200*x^5)*Log[x])*Log[3 + x + x^4]^3 + (
18750*x + 6250*x^2 + 6250*x^5)*Log[x]*Log[3 + x + x^4]^5)*Log[Log[x]] + ((-240*x^2 - 960*x^5)*Log[x]*Log[3 + x
+ x^4]^2 + (48*x + 16*x^2 + 16*x^5 + (720*x + 240*x^2 + 240*x^5)*Log[x])*Log[3 + x + x^4]^3 + (-7500*x - 2500
*x^2 - 2500*x^5)*Log[x]*Log[3 + x + x^4]^5)*Log[Log[x]]^2 + ((16*x^2 + 64*x^5)*Log[x]*Log[3 + x + x^4]^2 + (-4
8*x - 16*x^2 - 16*x^5)*Log[x]*Log[3 + x + x^4]^3 + (1500*x + 500*x^2 + 500*x^5)*Log[x]*Log[3 + x + x^4]^5)*Log
[Log[x]]^3 + (-150*x - 50*x^2 - 50*x^5)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]]^4 + (6*x + 2*x^2 + 2*x^5)*Log[x]
*Log[3 + x + x^4]^5*Log[Log[x]]^5)/((-9375 - 3125*x - 3125*x^4)*Log[x]*Log[3 + x + x^4]^5 + (9375 + 3125*x + 3
125*x^4)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]] + (-3750 - 1250*x - 1250*x^4)*Log[x]*Log[3 + x + x^4]^5*Log[Log
[x]]^2 + (750 + 250*x + 250*x^4)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]]^3 + (-75 - 25*x - 25*x^4)*Log[x]*Log[3
+ x + x^4]^5*Log[Log[x]]^4 + (3 + x + x^4)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]]^5),x]

[Out]

x^2*(1 + 16/(Log[3 + x + x^4]^4*(-5 + Log[Log[x]])^4) - 8/(Log[3 + x + x^4]^2*(-5 + Log[Log[x]])^2))

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fricas [B]  time = 0.64, size = 217, normalized size = 8.68 \begin {gather*} \frac {x^{2} \log \left (x^{4} + x + 3\right )^{4} \log \left (\log \relax (x)\right )^{4} - 20 \, x^{2} \log \left (x^{4} + x + 3\right )^{4} \log \left (\log \relax (x)\right )^{3} + 625 \, x^{2} \log \left (x^{4} + x + 3\right )^{4} - 200 \, x^{2} \log \left (x^{4} + x + 3\right )^{2} + 2 \, {\left (75 \, x^{2} \log \left (x^{4} + x + 3\right )^{4} - 4 \, x^{2} \log \left (x^{4} + x + 3\right )^{2}\right )} \log \left (\log \relax (x)\right )^{2} + 16 \, x^{2} - 20 \, {\left (25 \, x^{2} \log \left (x^{4} + x + 3\right )^{4} - 4 \, x^{2} \log \left (x^{4} + x + 3\right )^{2}\right )} \log \left (\log \relax (x)\right )}{\log \left (x^{4} + x + 3\right )^{4} \log \left (\log \relax (x)\right )^{4} - 20 \, \log \left (x^{4} + x + 3\right )^{4} \log \left (\log \relax (x)\right )^{3} + 150 \, \log \left (x^{4} + x + 3\right )^{4} \log \left (\log \relax (x)\right )^{2} - 500 \, \log \left (x^{4} + x + 3\right )^{4} \log \left (\log \relax (x)\right ) + 625 \, \log \left (x^{4} + x + 3\right )^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^5+2*x^2+6*x)*log(x)*log(x^4+x+3)^5*log(log(x))^5+(-50*x^5-50*x^2-150*x)*log(x)*log(x^4+x+3)^5*
log(log(x))^4+((500*x^5+500*x^2+1500*x)*log(x)*log(x^4+x+3)^5+(-16*x^5-16*x^2-48*x)*log(x)*log(x^4+x+3)^3+(64*
x^5+16*x^2)*log(x)*log(x^4+x+3)^2)*log(log(x))^3+((-2500*x^5-2500*x^2-7500*x)*log(x)*log(x^4+x+3)^5+((240*x^5+
240*x^2+720*x)*log(x)+16*x^5+16*x^2+48*x)*log(x^4+x+3)^3+(-960*x^5-240*x^2)*log(x)*log(x^4+x+3)^2)*log(log(x))
^2+((6250*x^5+6250*x^2+18750*x)*log(x)*log(x^4+x+3)^5+((-1200*x^5-1200*x^2-3600*x)*log(x)-160*x^5-160*x^2-480*
x)*log(x^4+x+3)^3+(4800*x^5+1200*x^2)*log(x)*log(x^4+x+3)^2+(32*x^5+32*x^2+96*x)*log(x)*log(x^4+x+3)+(-256*x^5
-64*x^2)*log(x))*log(log(x))+(-6250*x^5-6250*x^2-18750*x)*log(x)*log(x^4+x+3)^5+((2000*x^5+2000*x^2+6000*x)*lo
g(x)+400*x^5+400*x^2+1200*x)*log(x^4+x+3)^3+(-8000*x^5-2000*x^2)*log(x)*log(x^4+x+3)^2+((-160*x^5-160*x^2-480*
x)*log(x)-64*x^5-64*x^2-192*x)*log(x^4+x+3)+(1280*x^5+320*x^2)*log(x))/((x^4+x+3)*log(x)*log(x^4+x+3)^5*log(lo
g(x))^5+(-25*x^4-25*x-75)*log(x)*log(x^4+x+3)^5*log(log(x))^4+(250*x^4+250*x+750)*log(x)*log(x^4+x+3)^5*log(lo
g(x))^3+(-1250*x^4-1250*x-3750)*log(x)*log(x^4+x+3)^5*log(log(x))^2+(3125*x^4+3125*x+9375)*log(x)*log(x^4+x+3)
^5*log(log(x))+(-3125*x^4-3125*x-9375)*log(x)*log(x^4+x+3)^5),x, algorithm="fricas")

[Out]

(x^2*log(x^4 + x + 3)^4*log(log(x))^4 - 20*x^2*log(x^4 + x + 3)^4*log(log(x))^3 + 625*x^2*log(x^4 + x + 3)^4 -
200*x^2*log(x^4 + x + 3)^2 + 2*(75*x^2*log(x^4 + x + 3)^4 - 4*x^2*log(x^4 + x + 3)^2)*log(log(x))^2 + 16*x^2
- 20*(25*x^2*log(x^4 + x + 3)^4 - 4*x^2*log(x^4 + x + 3)^2)*log(log(x)))/(log(x^4 + x + 3)^4*log(log(x))^4 - 2
0*log(x^4 + x + 3)^4*log(log(x))^3 + 150*log(x^4 + x + 3)^4*log(log(x))^2 - 500*log(x^4 + x + 3)^4*log(log(x))
+ 625*log(x^4 + x + 3)^4)

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giac [B]  time = 112.20, size = 1110, normalized size = 44.40 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^5+2*x^2+6*x)*log(x)*log(x^4+x+3)^5*log(log(x))^5+(-50*x^5-50*x^2-150*x)*log(x)*log(x^4+x+3)^5*
log(log(x))^4+((500*x^5+500*x^2+1500*x)*log(x)*log(x^4+x+3)^5+(-16*x^5-16*x^2-48*x)*log(x)*log(x^4+x+3)^3+(64*
x^5+16*x^2)*log(x)*log(x^4+x+3)^2)*log(log(x))^3+((-2500*x^5-2500*x^2-7500*x)*log(x)*log(x^4+x+3)^5+((240*x^5+
240*x^2+720*x)*log(x)+16*x^5+16*x^2+48*x)*log(x^4+x+3)^3+(-960*x^5-240*x^2)*log(x)*log(x^4+x+3)^2)*log(log(x))
^2+((6250*x^5+6250*x^2+18750*x)*log(x)*log(x^4+x+3)^5+((-1200*x^5-1200*x^2-3600*x)*log(x)-160*x^5-160*x^2-480*
x)*log(x^4+x+3)^3+(4800*x^5+1200*x^2)*log(x)*log(x^4+x+3)^2+(32*x^5+32*x^2+96*x)*log(x)*log(x^4+x+3)+(-256*x^5
-64*x^2)*log(x))*log(log(x))+(-6250*x^5-6250*x^2-18750*x)*log(x)*log(x^4+x+3)^5+((2000*x^5+2000*x^2+6000*x)*lo
g(x)+400*x^5+400*x^2+1200*x)*log(x^4+x+3)^3+(-8000*x^5-2000*x^2)*log(x)*log(x^4+x+3)^2+((-160*x^5-160*x^2-480*
x)*log(x)-64*x^5-64*x^2-192*x)*log(x^4+x+3)+(1280*x^5+320*x^2)*log(x))/((x^4+x+3)*log(x)*log(x^4+x+3)^5*log(lo
g(x))^5+(-25*x^4-25*x-75)*log(x)*log(x^4+x+3)^5*log(log(x))^4+(250*x^4+250*x+750)*log(x)*log(x^4+x+3)^5*log(lo
g(x))^3+(-1250*x^4-1250*x-3750)*log(x)*log(x^4+x+3)^5*log(log(x))^2+(3125*x^4+3125*x+9375)*log(x)*log(x^4+x+3)
^5*log(log(x))+(-3125*x^4-3125*x-9375)*log(x)*log(x^4+x+3)^5),x, algorithm="giac")

[Out]

x^2 - 8*(16*x^12*log(x^4 + x + 3)^2*log(x)*log(log(x))^2 - 160*x^12*log(x^4 + x + 3)^2*log(x)*log(log(x)) + 40
0*x^12*log(x^4 + x + 3)^2*log(x) + 24*x^9*log(x^4 + x + 3)^2*log(x)*log(log(x))^2 - 32*x^12*log(x) - 240*x^9*l
og(x^4 + x + 3)^2*log(x)*log(log(x)) + 48*x^8*log(x^4 + x + 3)^2*log(x)*log(log(x))^2 + 600*x^9*log(x^4 + x +
3)^2*log(x) - 480*x^8*log(x^4 + x + 3)^2*log(x)*log(log(x)) + 1200*x^8*log(x^4 + x + 3)^2*log(x) + 9*x^6*log(x
^4 + x + 3)^2*log(x)*log(log(x))^2 - 48*x^9*log(x) - 90*x^6*log(x^4 + x + 3)^2*log(x)*log(log(x)) + 24*x^5*log
(x^4 + x + 3)^2*log(x)*log(log(x))^2 - 96*x^8*log(x) + 225*x^6*log(x^4 + x + 3)^2*log(x) - 240*x^5*log(x^4 + x
+ 3)^2*log(x)*log(log(x)) + 600*x^5*log(x^4 + x + 3)^2*log(x) + x^3*log(x^4 + x + 3)^2*log(x)*log(log(x))^2 -
18*x^6*log(x) - 10*x^3*log(x^4 + x + 3)^2*log(x)*log(log(x)) + 3*x^2*log(x^4 + x + 3)^2*log(x)*log(log(x))^2
- 48*x^5*log(x) + 25*x^3*log(x^4 + x + 3)^2*log(x) - 30*x^2*log(x^4 + x + 3)^2*log(x)*log(log(x)) + 75*x^2*log
(x^4 + x + 3)^2*log(x) - 2*x^3*log(x) - 6*x^2*log(x))/(16*x^10*log(x^4 + x + 3)^4*log(x)*log(log(x))^4 - 320*x
^10*log(x^4 + x + 3)^4*log(x)*log(log(x))^3 + 2400*x^10*log(x^4 + x + 3)^4*log(x)*log(log(x))^2 - 8000*x^10*lo
g(x^4 + x + 3)^4*log(x)*log(log(x)) + 24*x^7*log(x^4 + x + 3)^4*log(x)*log(log(x))^4 + 10000*x^10*log(x^4 + x
+ 3)^4*log(x) - 480*x^7*log(x^4 + x + 3)^4*log(x)*log(log(x))^3 + 48*x^6*log(x^4 + x + 3)^4*log(x)*log(log(x))
^4 + 3600*x^7*log(x^4 + x + 3)^4*log(x)*log(log(x))^2 - 960*x^6*log(x^4 + x + 3)^4*log(x)*log(log(x))^3 - 1200
0*x^7*log(x^4 + x + 3)^4*log(x)*log(log(x)) + 7200*x^6*log(x^4 + x + 3)^4*log(x)*log(log(x))^2 + 9*x^4*log(x^4
+ x + 3)^4*log(x)*log(log(x))^4 + 15000*x^7*log(x^4 + x + 3)^4*log(x) - 24000*x^6*log(x^4 + x + 3)^4*log(x)*l
og(log(x)) - 180*x^4*log(x^4 + x + 3)^4*log(x)*log(log(x))^3 + 24*x^3*log(x^4 + x + 3)^4*log(x)*log(log(x))^4
+ 30000*x^6*log(x^4 + x + 3)^4*log(x) + 1350*x^4*log(x^4 + x + 3)^4*log(x)*log(log(x))^2 - 480*x^3*log(x^4 + x
+ 3)^4*log(x)*log(log(x))^3 - 4500*x^4*log(x^4 + x + 3)^4*log(x)*log(log(x)) + 3600*x^3*log(x^4 + x + 3)^4*lo
g(x)*log(log(x))^2 + x*log(x^4 + x + 3)^4*log(x)*log(log(x))^4 + 5625*x^4*log(x^4 + x + 3)^4*log(x) - 12000*x^
3*log(x^4 + x + 3)^4*log(x)*log(log(x)) - 20*x*log(x^4 + x + 3)^4*log(x)*log(log(x))^3 + 3*log(x^4 + x + 3)^4*
log(x)*log(log(x))^4 + 15000*x^3*log(x^4 + x + 3)^4*log(x) + 150*x*log(x^4 + x + 3)^4*log(x)*log(log(x))^2 - 6
0*log(x^4 + x + 3)^4*log(x)*log(log(x))^3 - 500*x*log(x^4 + x + 3)^4*log(x)*log(log(x)) + 450*log(x^4 + x + 3)
^4*log(x)*log(log(x))^2 + 625*x*log(x^4 + x + 3)^4*log(x) - 1500*log(x^4 + x + 3)^4*log(x)*log(log(x)) + 1875*
log(x^4 + x + 3)^4*log(x))

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maple [B]  time = 0.12, size = 68, normalized size = 2.72

method	result	size
risch	\(x^{2}-\frac {8 x^{2} \left (\ln \left (x^{4}+x +3\right )^{2} \ln \left (\ln \relax (x )\right )^{2}-10 \ln \left (x^{4}+x +3\right )^{2} \ln \left (\ln \relax (x )\right )+25 \ln \left (x^{4}+x +3\right )^{2}-2\right )}{\ln \left (x^{4}+x +3\right )^{4} \left (\ln \left (\ln \relax (x )\right )-5\right )^{4}}\)	\(68\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x^5+2*x^2+6*x)*ln(x)*ln(x^4+x+3)^5*ln(ln(x))^5+(-50*x^5-50*x^2-150*x)*ln(x)*ln(x^4+x+3)^5*ln(ln(x))^4+
((500*x^5+500*x^2+1500*x)*ln(x)*ln(x^4+x+3)^5+(-16*x^5-16*x^2-48*x)*ln(x)*ln(x^4+x+3)^3+(64*x^5+16*x^2)*ln(x)*
ln(x^4+x+3)^2)*ln(ln(x))^3+((-2500*x^5-2500*x^2-7500*x)*ln(x)*ln(x^4+x+3)^5+((240*x^5+240*x^2+720*x)*ln(x)+16*
x^5+16*x^2+48*x)*ln(x^4+x+3)^3+(-960*x^5-240*x^2)*ln(x)*ln(x^4+x+3)^2)*ln(ln(x))^2+((6250*x^5+6250*x^2+18750*x
)*ln(x)*ln(x^4+x+3)^5+((-1200*x^5-1200*x^2-3600*x)*ln(x)-160*x^5-160*x^2-480*x)*ln(x^4+x+3)^3+(4800*x^5+1200*x
^2)*ln(x)*ln(x^4+x+3)^2+(32*x^5+32*x^2+96*x)*ln(x)*ln(x^4+x+3)+(-256*x^5-64*x^2)*ln(x))*ln(ln(x))+(-6250*x^5-6
250*x^2-18750*x)*ln(x)*ln(x^4+x+3)^5+((2000*x^5+2000*x^2+6000*x)*ln(x)+400*x^5+400*x^2+1200*x)*ln(x^4+x+3)^3+(
-8000*x^5-2000*x^2)*ln(x)*ln(x^4+x+3)^2+((-160*x^5-160*x^2-480*x)*ln(x)-64*x^5-64*x^2-192*x)*ln(x^4+x+3)+(1280
*x^5+320*x^2)*ln(x))/((x^4+x+3)*ln(x)*ln(x^4+x+3)^5*ln(ln(x))^5+(-25*x^4-25*x-75)*ln(x)*ln(x^4+x+3)^5*ln(ln(x)
)^4+(250*x^4+250*x+750)*ln(x)*ln(x^4+x+3)^5*ln(ln(x))^3+(-1250*x^4-1250*x-3750)*ln(x)*ln(x^4+x+3)^5*ln(ln(x))^
2+(3125*x^4+3125*x+9375)*ln(x)*ln(x^4+x+3)^5*ln(ln(x))+(-3125*x^4-3125*x-9375)*ln(x)*ln(x^4+x+3)^5),x,method=_
RETURNVERBOSE)

[Out]

x^2-8*x^2*(ln(x^4+x+3)^2*ln(ln(x))^2-10*ln(x^4+x+3)^2*ln(ln(x))+25*ln(x^4+x+3)^2-2)/ln(x^4+x+3)^4/(ln(ln(x))-5
)^4

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maxima [B]  time = 1.39, size = 131, normalized size = 5.24 \begin {gather*} \frac {{\left (x^{2} \log \left (\log \relax (x)\right )^{4} - 20 \, x^{2} \log \left (\log \relax (x)\right )^{3} + 150 \, x^{2} \log \left (\log \relax (x)\right )^{2} - 500 \, x^{2} \log \left (\log \relax (x)\right ) + 625 \, x^{2}\right )} \log \left (x^{4} + x + 3\right )^{4} - 8 \, {\left (x^{2} \log \left (\log \relax (x)\right )^{2} - 10 \, x^{2} \log \left (\log \relax (x)\right ) + 25 \, x^{2}\right )} \log \left (x^{4} + x + 3\right )^{2} + 16 \, x^{2}}{{\left (\log \left (\log \relax (x)\right )^{4} - 20 \, \log \left (\log \relax (x)\right )^{3} + 150 \, \log \left (\log \relax (x)\right )^{2} - 500 \, \log \left (\log \relax (x)\right ) + 625\right )} \log \left (x^{4} + x + 3\right )^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^5+2*x^2+6*x)*log(x)*log(x^4+x+3)^5*log(log(x))^5+(-50*x^5-50*x^2-150*x)*log(x)*log(x^4+x+3)^5*
log(log(x))^4+((500*x^5+500*x^2+1500*x)*log(x)*log(x^4+x+3)^5+(-16*x^5-16*x^2-48*x)*log(x)*log(x^4+x+3)^3+(64*
x^5+16*x^2)*log(x)*log(x^4+x+3)^2)*log(log(x))^3+((-2500*x^5-2500*x^2-7500*x)*log(x)*log(x^4+x+3)^5+((240*x^5+
240*x^2+720*x)*log(x)+16*x^5+16*x^2+48*x)*log(x^4+x+3)^3+(-960*x^5-240*x^2)*log(x)*log(x^4+x+3)^2)*log(log(x))
^2+((6250*x^5+6250*x^2+18750*x)*log(x)*log(x^4+x+3)^5+((-1200*x^5-1200*x^2-3600*x)*log(x)-160*x^5-160*x^2-480*
x)*log(x^4+x+3)^3+(4800*x^5+1200*x^2)*log(x)*log(x^4+x+3)^2+(32*x^5+32*x^2+96*x)*log(x)*log(x^4+x+3)+(-256*x^5
-64*x^2)*log(x))*log(log(x))+(-6250*x^5-6250*x^2-18750*x)*log(x)*log(x^4+x+3)^5+((2000*x^5+2000*x^2+6000*x)*lo
g(x)+400*x^5+400*x^2+1200*x)*log(x^4+x+3)^3+(-8000*x^5-2000*x^2)*log(x)*log(x^4+x+3)^2+((-160*x^5-160*x^2-480*
x)*log(x)-64*x^5-64*x^2-192*x)*log(x^4+x+3)+(1280*x^5+320*x^2)*log(x))/((x^4+x+3)*log(x)*log(x^4+x+3)^5*log(lo
g(x))^5+(-25*x^4-25*x-75)*log(x)*log(x^4+x+3)^5*log(log(x))^4+(250*x^4+250*x+750)*log(x)*log(x^4+x+3)^5*log(lo
g(x))^3+(-1250*x^4-1250*x-3750)*log(x)*log(x^4+x+3)^5*log(log(x))^2+(3125*x^4+3125*x+9375)*log(x)*log(x^4+x+3)
^5*log(log(x))+(-3125*x^4-3125*x-9375)*log(x)*log(x^4+x+3)^5),x, algorithm="maxima")

[Out]

((x^2*log(log(x))^4 - 20*x^2*log(log(x))^3 + 150*x^2*log(log(x))^2 - 500*x^2*log(log(x)) + 625*x^2)*log(x^4 +
x + 3)^4 - 8*(x^2*log(log(x))^2 - 10*x^2*log(log(x)) + 25*x^2)*log(x^4 + x + 3)^2 + 16*x^2)/((log(log(x))^4 -
20*log(log(x))^3 + 150*log(log(x))^2 - 500*log(log(x)) + 625)*log(x^4 + x + 3)^4)

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mupad [F(-1)]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \text {Hanged} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x + x^4 + 3)*(192*x + 64*x^2 + 64*x^5 + log(x)*(480*x + 160*x^2 + 160*x^5)) - log(x)*(320*x^2 + 1280*
x^5) - log(x + x^4 + 3)^3*(1200*x + 400*x^2 + 400*x^5 + log(x)*(6000*x + 2000*x^2 + 2000*x^5)) - log(log(x))*(
log(x + x^4 + 3)*log(x)*(96*x + 32*x^2 + 32*x^5) - log(x + x^4 + 3)^3*(480*x + 160*x^2 + 160*x^5 + log(x)*(360
0*x + 1200*x^2 + 1200*x^5)) - log(x)*(64*x^2 + 256*x^5) + log(x + x^4 + 3)^5*log(x)*(18750*x + 6250*x^2 + 6250
*x^5) + log(x + x^4 + 3)^2*log(x)*(1200*x^2 + 4800*x^5)) - log(log(x))^3*(log(x + x^4 + 3)^5*log(x)*(1500*x +
500*x^2 + 500*x^5) - log(x + x^4 + 3)^3*log(x)*(48*x + 16*x^2 + 16*x^5) + log(x + x^4 + 3)^2*log(x)*(16*x^2 +
64*x^5)) + log(log(x))^2*(log(x + x^4 + 3)^5*log(x)*(7500*x + 2500*x^2 + 2500*x^5) - log(x + x^4 + 3)^3*(48*x
+ 16*x^2 + 16*x^5 + log(x)*(720*x + 240*x^2 + 240*x^5)) + log(x + x^4 + 3)^2*log(x)*(240*x^2 + 960*x^5)) + log
(x + x^4 + 3)^5*log(x)*(18750*x + 6250*x^2 + 6250*x^5) + log(x + x^4 + 3)^2*log(x)*(2000*x^2 + 8000*x^5) - log
(x + x^4 + 3)^5*log(log(x))^5*log(x)*(6*x + 2*x^2 + 2*x^5) + log(x + x^4 + 3)^5*log(log(x))^4*log(x)*(150*x +
50*x^2 + 50*x^5))/(log(x + x^4 + 3)^5*log(x)*(3125*x + 3125*x^4 + 9375) - log(x + x^4 + 3)^5*log(log(x))^5*log
(x)*(x + x^4 + 3) - log(x + x^4 + 3)^5*log(log(x))*log(x)*(3125*x + 3125*x^4 + 9375) + log(x + x^4 + 3)^5*log(
log(x))^4*log(x)*(25*x + 25*x^4 + 75) - log(x + x^4 + 3)^5*log(log(x))^3*log(x)*(250*x + 250*x^4 + 750) + log(
x + x^4 + 3)^5*log(log(x))^2*log(x)*(1250*x + 1250*x^4 + 3750)),x)

[Out]

\text{Hanged}

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sympy [B]  time = 1.12, size = 148, normalized size = 5.92 \begin {gather*} x^{2} + \frac {- 8 x^{2} \log {\left (x^{4} + x + 3 \right )}^{2} \log {\left (\log {\relax (x )} \right )}^{2} + 80 x^{2} \log {\left (x^{4} + x + 3 \right )}^{2} \log {\left (\log {\relax (x )} \right )} - 200 x^{2} \log {\left (x^{4} + x + 3 \right )}^{2} + 16 x^{2}}{\log {\left (x^{4} + x + 3 \right )}^{4} \log {\left (\log {\relax (x )} \right )}^{4} - 20 \log {\left (x^{4} + x + 3 \right )}^{4} \log {\left (\log {\relax (x )} \right )}^{3} + 150 \log {\left (x^{4} + x + 3 \right )}^{4} \log {\left (\log {\relax (x )} \right )}^{2} - 500 \log {\left (x^{4} + x + 3 \right )}^{4} \log {\left (\log {\relax (x )} \right )} + 625 \log {\left (x^{4} + x + 3 \right )}^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x**5+2*x**2+6*x)*ln(x)*ln(x**4+x+3)**5*ln(ln(x))**5+(-50*x**5-50*x**2-150*x)*ln(x)*ln(x**4+x+3)*
*5*ln(ln(x))**4+((500*x**5+500*x**2+1500*x)*ln(x)*ln(x**4+x+3)**5+(-16*x**5-16*x**2-48*x)*ln(x)*ln(x**4+x+3)**
3+(64*x**5+16*x**2)*ln(x)*ln(x**4+x+3)**2)*ln(ln(x))**3+((-2500*x**5-2500*x**2-7500*x)*ln(x)*ln(x**4+x+3)**5+(
(240*x**5+240*x**2+720*x)*ln(x)+16*x**5+16*x**2+48*x)*ln(x**4+x+3)**3+(-960*x**5-240*x**2)*ln(x)*ln(x**4+x+3)*
*2)*ln(ln(x))**2+((6250*x**5+6250*x**2+18750*x)*ln(x)*ln(x**4+x+3)**5+((-1200*x**5-1200*x**2-3600*x)*ln(x)-160
*x**5-160*x**2-480*x)*ln(x**4+x+3)**3+(4800*x**5+1200*x**2)*ln(x)*ln(x**4+x+3)**2+(32*x**5+32*x**2+96*x)*ln(x)
*ln(x**4+x+3)+(-256*x**5-64*x**2)*ln(x))*ln(ln(x))+(-6250*x**5-6250*x**2-18750*x)*ln(x)*ln(x**4+x+3)**5+((2000
*x**5+2000*x**2+6000*x)*ln(x)+400*x**5+400*x**2+1200*x)*ln(x**4+x+3)**3+(-8000*x**5-2000*x**2)*ln(x)*ln(x**4+x
+3)**2+((-160*x**5-160*x**2-480*x)*ln(x)-64*x**5-64*x**2-192*x)*ln(x**4+x+3)+(1280*x**5+320*x**2)*ln(x))/((x**
4+x+3)*ln(x)*ln(x**4+x+3)**5*ln(ln(x))**5+(-25*x**4-25*x-75)*ln(x)*ln(x**4+x+3)**5*ln(ln(x))**4+(250*x**4+250*
x+750)*ln(x)*ln(x**4+x+3)**5*ln(ln(x))**3+(-1250*x**4-1250*x-3750)*ln(x)*ln(x**4+x+3)**5*ln(ln(x))**2+(3125*x*
*4+3125*x+9375)*ln(x)*ln(x**4+x+3)**5*ln(ln(x))+(-3125*x**4-3125*x-9375)*ln(x)*ln(x**4+x+3)**5),x)

[Out]

x**2 + (-8*x**2*log(x**4 + x + 3)**2*log(log(x))**2 + 80*x**2*log(x**4 + x + 3)**2*log(log(x)) - 200*x**2*log(
x**4 + x + 3)**2 + 16*x**2)/(log(x**4 + x + 3)**4*log(log(x))**4 - 20*log(x**4 + x + 3)**4*log(log(x))**3 + 15
0*log(x**4 + x + 3)**4*log(log(x))**2 - 500*log(x**4 + x + 3)**4*log(log(x)) + 625*log(x**4 + x + 3)**4)

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