[next] [prev] [prev-tail] [tail] [up]

3.74.52 \(\int \frac {-16 x^2-68 x^3-32 x^4-4 x^5+e^2 (64 x^3+32 x^4+4 x^5)+(4 x^3+e^2 (16 x^2+4 x^3)) \log (x)+(64 x^3+32 x^4+4 x^5+(16 x^2+4 x^3) \log (x)) \log (\frac {4 x+x^2+\log (x)}{4+x})+(-32 x-120 x^2+4 x^3+24 x^4+4 x^5+e^2 (128 x^2-24 x^4-4 x^5)+(8 x^2-4 x^3+e^2 (32 x-8 x^2-4 x^3)) \log (x)+(128 x^2-24 x^4-4 x^5+(32 x-8 x^2-4 x^3) \log (x)) \log (\frac {4 x+x^2+\log (x)}{4+x})) \log (\frac {e^4+2 e^2 \log (\frac {4 x+x^2+\log (x)}{4+x})+\log ^2(\frac {4 x+x^2+\log (x)}{4+x})}{x^2})+(e^2 (-64 x^2-32 x^3-4 x^4)+e^2 (-16 x-4 x^2) \log (x)+(-64 x^2-32 x^3-4 x^4+(-16 x-4 x^2) \log (x)) \log (\frac {4 x+x^2+\log (x)}{4+x})) \log ^2(\frac {e^4+2 e^2 \log (\frac {4 x+x^2+\log (x)}{4+x})+\log ^2(\frac {4 x+x^2+\log (x)}{4+x})}{x^2})+(e^2 (-128 x+24 x^3+4 x^4)+e^2 (-32+8 x+4 x^2) \log (x)+(-128 x+24 x^3+4 x^4+(-32+8 x+4 x^2) \log (x)) \log (\frac {4 x+x^2+\log (x)}{4+x})) \log ^3(\frac {e^4+2 e^2 \log (\frac {4 x+x^2+\log (x)}{4+x})+\log ^2(\frac {4 x+x^2+\log (x)}{4+x})}{x^2})}{(e^2 (16 x^4+8 x^5+x^6)+e^2 (4 x^3+x^4) \log (x)+(16 x^4+8 x^5+x^6+(4 x^3+x^4) \log (x)) \log (\frac {4 x+x^2+\log (x)}{4+x})) \log ^3(\frac {e^4+2 e^2 \log (\frac {4 x+x^2+\log (x)}{4+x})+\log ^2(\frac {4 x+x^2+\log (x)}{4+x})}{x^2})} \, dx\)

Optimal. Leaf size=37 \[ \frac {\left (2-x+\frac {x}{\log \left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )}\right )^2}{x^2} \]

________________________________________________________________________________________

Rubi [F]  time = 74.18, 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^2-68 x^3-32 x^4-4 x^5+e^2 \left (64 x^3+32 x^4+4 x^5\right )+\left (4 x^3+e^2 \left (16 x^2+4 x^3\right )\right ) \log (x)+\left (64 x^3+32 x^4+4 x^5+\left (16 x^2+4 x^3\right ) \log (x)\right ) \log \left (\frac {4 x+x^2+\log (x)}{4+x}\right )+\left (-32 x-120 x^2+4 x^3+24 x^4+4 x^5+e^2 \left (128 x^2-24 x^4-4 x^5\right )+\left (8 x^2-4 x^3+e^2 \left (32 x-8 x^2-4 x^3\right )\right ) \log (x)+\left (128 x^2-24 x^4-4 x^5+\left (32 x-8 x^2-4 x^3\right ) \log (x)\right ) \log \left (\frac {4 x+x^2+\log (x)}{4+x}\right )\right ) \log \left (\frac {e^4+2 e^2 \log \left (\frac {4 x+x^2+\log (x)}{4+x}\right )+\log ^2\left (\frac {4 x+x^2+\log (x)}{4+x}\right )}{x^2}\right )+\left (e^2 \left (-64 x^2-32 x^3-4 x^4\right )+e^2 \left (-16 x-4 x^2\right ) \log (x)+\left (-64 x^2-32 x^3-4 x^4+\left (-16 x-4 x^2\right ) \log (x)\right ) \log \left (\frac {4 x+x^2+\log (x)}{4+x}\right )\right ) \log ^2\left (\frac {e^4+2 e^2 \log \left (\frac {4 x+x^2+\log (x)}{4+x}\right )+\log ^2\left (\frac {4 x+x^2+\log (x)}{4+x}\right )}{x^2}\right )+\left (e^2 \left (-128 x+24 x^3+4 x^4\right )+e^2 \left (-32+8 x+4 x^2\right ) \log (x)+\left (-128 x+24 x^3+4 x^4+\left (-32+8 x+4 x^2\right ) \log (x)\right ) \log \left (\frac {4 x+x^2+\log (x)}{4+x}\right )\right ) \log ^3\left (\frac {e^4+2 e^2 \log \left (\frac {4 x+x^2+\log (x)}{4+x}\right )+\log ^2\left (\frac {4 x+x^2+\log (x)}{4+x}\right )}{x^2}\right )}{\left (e^2 \left (16 x^4+8 x^5+x^6\right )+e^2 \left (4 x^3+x^4\right ) \log (x)+\left (16 x^4+8 x^5+x^6+\left (4 x^3+x^4\right ) \log (x)\right ) \log \left (\frac {4 x+x^2+\log (x)}{4+x}\right )\right ) \log ^3\left (\frac {e^4+2 e^2 \log \left (\frac {4 x+x^2+\log (x)}{4+x}\right )+\log ^2\left (\frac {4 x+x^2+\log (x)}{4+x}\right )}{x^2}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-16*x^2 - 68*x^3 - 32*x^4 - 4*x^5 + E^2*(64*x^3 + 32*x^4 + 4*x^5) + (4*x^3 + E^2*(16*x^2 + 4*x^3))*Log[x]
 + (64*x^3 + 32*x^4 + 4*x^5 + (16*x^2 + 4*x^3)*Log[x])*Log[(4*x + x^2 + Log[x])/(4 + x)] + (-32*x - 120*x^2 +
4*x^3 + 24*x^4 + 4*x^5 + E^2*(128*x^2 - 24*x^4 - 4*x^5) + (8*x^2 - 4*x^3 + E^2*(32*x - 8*x^2 - 4*x^3))*Log[x]
+ (128*x^2 - 24*x^4 - 4*x^5 + (32*x - 8*x^2 - 4*x^3)*Log[x])*Log[(4*x + x^2 + Log[x])/(4 + x)])*Log[(E^4 + 2*E
^2*Log[(4*x + x^2 + Log[x])/(4 + x)] + Log[(4*x + x^2 + Log[x])/(4 + x)]^2)/x^2] + (E^2*(-64*x^2 - 32*x^3 - 4*
x^4) + E^2*(-16*x - 4*x^2)*Log[x] + (-64*x^2 - 32*x^3 - 4*x^4 + (-16*x - 4*x^2)*Log[x])*Log[(4*x + x^2 + Log[x
])/(4 + x)])*Log[(E^4 + 2*E^2*Log[(4*x + x^2 + Log[x])/(4 + x)] + Log[(4*x + x^2 + Log[x])/(4 + x)]^2)/x^2]^2
+ (E^2*(-128*x + 24*x^3 + 4*x^4) + E^2*(-32 + 8*x + 4*x^2)*Log[x] + (-128*x + 24*x^3 + 4*x^4 + (-32 + 8*x + 4*
x^2)*Log[x])*Log[(4*x + x^2 + Log[x])/(4 + x)])*Log[(E^4 + 2*E^2*Log[(4*x + x^2 + Log[x])/(4 + x)] + Log[(4*x
+ x^2 + Log[x])/(4 + x)]^2)/x^2]^3)/((E^2*(16*x^4 + 8*x^5 + x^6) + E^2*(4*x^3 + x^4)*Log[x] + (16*x^4 + 8*x^5
+ x^6 + (4*x^3 + x^4)*Log[x])*Log[(4*x + x^2 + Log[x])/(4 + x)])*Log[(E^4 + 2*E^2*Log[(4*x + x^2 + Log[x])/(4
+ x)] + Log[(4*x + x^2 + Log[x])/(4 + x)]^2)/x^2]^3),x]

[Out]

(2 - x)^2/x^2 - 16*(1 - E^2)*Defer[Int][1/((4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log
[x + Log[x]/(4 + x)])^2/x^2]^3), x] - 4*Defer[Int][1/(x*(4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*L
og[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^3), x] - 4*(1 - E^2)*Defer[Int][x/((4*x + x^2 + Log[x])*(E^2 + Log[x
 + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^3), x] + 4*Defer[Int][1/((4 + x)*(4*x + x^2 + L
og[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^3), x] - 4*(17 - 16*E^2)*Def
er[Int][1/((4 + x)*(4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/
x^2]^3), x] + 64*(1 - E^2)*Defer[Int][1/((4 + x)*(4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2
 + Log[x + Log[x]/(4 + x)])^2/x^2]^3), x] + 4*E^2*Defer[Int][Log[x]/(x*(4*x + x^2 + Log[x])*(E^2 + Log[x + Log
[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^3), x] - 4*E^2*Defer[Int][Log[x]/((4 + x)*(4*x + x^2
+ Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^3), x] + 4*(1 + E^2)*Defe
r[Int][Log[x]/((4 + x)*(4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)]
)^2/x^2]^3), x] + 16*Defer[Int][Log[x + Log[x]/(4 + x)]/((4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*
Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^3), x] + 4*Defer[Int][(x*Log[x + Log[x]/(4 + x)])/((4*x + x^2 + Log
[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^3), x] + 4*Defer[Int][(Log[x]*
Log[x + Log[x]/(4 + x)])/(x*(4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4
+ x)])^2/x^2]^3), x] + 8*(1 - E^2)*Defer[Int][1/((4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2
 + Log[x + Log[x]/(4 + x)])^2/x^2]^2), x] - 8*Defer[Int][1/(x^2*(4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4
+ x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^2), x] + 6*Defer[Int][1/(x*(4*x + x^2 + Log[x])*(E^2 + Log[x
 + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^2), x] - 2*(17 - 16*E^2)*Defer[Int][1/(x*(4*x +
 x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^2), x] + 4*(1 - E^2)
*Defer[Int][x/((4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]
^2), x] - 6*Defer[Int][1/((4 + x)*(4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[
x]/(4 + x)])^2/x^2]^2), x] + 6*(17 - 16*E^2)*Defer[Int][1/((4 + x)*(4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/
(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^2), x] - 96*(1 - E^2)*Defer[Int][1/((4 + x)*(4*x + x^2 +
Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^2), x] + 8*E^2*Defer[Int][L
og[x]/(x^2*(4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^2),
 x] - 6*E^2*Defer[Int][Log[x]/(x*(4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x
]/(4 + x)])^2/x^2]^2), x] + 2*(1 + E^2)*Defer[Int][Log[x]/(x*(4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x
)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^2), x] + 6*E^2*Defer[Int][Log[x]/((4 + x)*(4*x + x^2 + Log[x])*
(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^2), x] - 6*(1 + E^2)*Defer[Int][Log
[x]/((4 + x)*(4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^2
), x] - 8*Defer[Int][Log[x + Log[x]/(4 + x)]/((4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 +
Log[x + Log[x]/(4 + x)])^2/x^2]^2), x] + 32*Defer[Int][Log[x + Log[x]/(4 + x)]/(x*(4*x + x^2 + Log[x])*(E^2 +
Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^2), x] - 4*Defer[Int][(x*Log[x + Log[x]/(4
 + x)])/((4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^2), x
] + 8*Defer[Int][(Log[x]*Log[x + Log[x]/(4 + x)])/(x^2*(4*x + x^2 + Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Lo
g[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^2), x] - 4*Defer[Int][(Log[x]*Log[x + Log[x]/(4 + x)])/(x*(4*x + x^2
+ Log[x])*(E^2 + Log[x + Log[x]/(4 + x)])*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]^2), x] - 4*Defer[Int][1/(
x^2*Log[(E^2 + Log[x + Log[x]/(4 + x)])^2/x^2]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \left (-4 x^2-17 x^3-8 x^4-x^5+e^2 x^3 (4+x)^2+x^2 \left (x+e^2 (4+x)\right ) \log (x)+x^2 (4+x) (x (4+x)+\log (x)) \log \left (x+\frac {\log (x)}{4+x}\right )+x \left (-8-30 x+x^2+6 x^3+x^4-e^2 (-2+x) x (4+x)^2-(-2+x) \left (x+e^2 (4+x)\right ) \log (x)-\left (-8+2 x+x^2\right ) (x (4+x)+\log (x)) \log \left (x+\frac {\log (x)}{4+x}\right )\right ) \log \left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )-x (4+x) (x (4+x)+\log (x)) \left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right ) \log ^2\left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )+\left (-8+2 x+x^2\right ) (x (4+x)+\log (x)) \left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right ) \log ^3\left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )\right )}{x^3 (4+x) (x (4+x)+\log (x)) \left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right ) \log ^3\left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )} \, dx\\ &=4 \int \frac {-4 x^2-17 x^3-8 x^4-x^5+e^2 x^3 (4+x)^2+x^2 \left (x+e^2 (4+x)\right ) \log (x)+x^2 (4+x) (x (4+x)+\log (x)) \log \left (x+\frac {\log (x)}{4+x}\right )+x \left (-8-30 x+x^2+6 x^3+x^4-e^2 (-2+x) x (4+x)^2-(-2+x) \left (x+e^2 (4+x)\right ) \log (x)-\left (-8+2 x+x^2\right ) (x (4+x)+\log (x)) \log \left (x+\frac {\log (x)}{4+x}\right )\right ) \log \left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )-x (4+x) (x (4+x)+\log (x)) \left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right ) \log ^2\left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )+\left (-8+2 x+x^2\right ) (x (4+x)+\log (x)) \left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right ) \log ^3\left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )}{x^3 (4+x) (x (4+x)+\log (x)) \left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right ) \log ^3\left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )} \, dx\\ &=4 \int \left (\frac {-2+x}{x^3}+\frac {-4-17 \left (1-\frac {16 e^2}{17}\right ) x-8 \left (1-e^2\right ) x^2-\left (1-e^2\right ) x^3+4 e^2 \log (x)+\left (1+e^2\right ) x \log (x)+16 x \log \left (x+\frac {\log (x)}{4+x}\right )+8 x^2 \log \left (x+\frac {\log (x)}{4+x}\right )+x^3 \log \left (x+\frac {\log (x)}{4+x}\right )+4 \log (x) \log \left (x+\frac {\log (x)}{4+x}\right )+x \log (x) \log \left (x+\frac {\log (x)}{4+x}\right )}{x (4+x) \left (4 x+x^2+\log (x)\right ) \left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right ) \log ^3\left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )}+\frac {(2-x) \left (-4-17 \left (1-\frac {16 e^2}{17}\right ) x-8 \left (1-e^2\right ) x^2-\left (1-e^2\right ) x^3+4 e^2 \log (x)+\left (1+e^2\right ) x \log (x)+16 x \log \left (x+\frac {\log (x)}{4+x}\right )+8 x^2 \log \left (x+\frac {\log (x)}{4+x}\right )+x^3 \log \left (x+\frac {\log (x)}{4+x}\right )+4 \log (x) \log \left (x+\frac {\log (x)}{4+x}\right )+x \log (x) \log \left (x+\frac {\log (x)}{4+x}\right )\right )}{x^2 (4+x) \left (4 x+x^2+\log (x)\right ) \left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right ) \log ^2\left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )}-\frac {1}{x^2 \log \left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )}\right ) \, dx\\ &=4 \int \frac {-2+x}{x^3} \, dx+4 \int \frac {-4-17 \left (1-\frac {16 e^2}{17}\right ) x-8 \left (1-e^2\right ) x^2-\left (1-e^2\right ) x^3+4 e^2 \log (x)+\left (1+e^2\right ) x \log (x)+16 x \log \left (x+\frac {\log (x)}{4+x}\right )+8 x^2 \log \left (x+\frac {\log (x)}{4+x}\right )+x^3 \log \left (x+\frac {\log (x)}{4+x}\right )+4 \log (x) \log \left (x+\frac {\log (x)}{4+x}\right )+x \log (x) \log \left (x+\frac {\log (x)}{4+x}\right )}{x (4+x) \left (4 x+x^2+\log (x)\right ) \left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right ) \log ^3\left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )} \, dx+4 \int \frac {(2-x) \left (-4-17 \left (1-\frac {16 e^2}{17}\right ) x-8 \left (1-e^2\right ) x^2-\left (1-e^2\right ) x^3+4 e^2 \log (x)+\left (1+e^2\right ) x \log (x)+16 x \log \left (x+\frac {\log (x)}{4+x}\right )+8 x^2 \log \left (x+\frac {\log (x)}{4+x}\right )+x^3 \log \left (x+\frac {\log (x)}{4+x}\right )+4 \log (x) \log \left (x+\frac {\log (x)}{4+x}\right )+x \log (x) \log \left (x+\frac {\log (x)}{4+x}\right )\right )}{x^2 (4+x) \left (4 x+x^2+\log (x)\right ) \left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right ) \log ^2\left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )} \, dx-4 \int \frac {1}{x^2 \log \left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )} \, dx\\ &=\frac {(2-x)^2}{x^2}+4 \int \frac {\log (x) \left (x+e^2 (4+x)+(4+x) \log \left (x+\frac {\log (x)}{4+x}\right )\right )+(4+x) \left (-1+4 \left (-1+e^2\right ) x+\left (-1+e^2\right ) x^2+x (4+x) \log \left (x+\frac {\log (x)}{4+x}\right )\right )}{x (4+x) (x (4+x)+\log (x)) \left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right ) \log ^3\left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )} \, dx+4 \int \frac {(2-x) \left (\log (x) \left (x+e^2 (4+x)+(4+x) \log \left (x+\frac {\log (x)}{4+x}\right )\right )+(4+x) \left (-1+4 \left (-1+e^2\right ) x+\left (-1+e^2\right ) x^2+x (4+x) \log \left (x+\frac {\log (x)}{4+x}\right )\right )\right )}{x^2 (4+x) (x (4+x)+\log (x)) \left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right ) \log ^2\left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )} \, dx-4 \int \frac {1}{x^2 \log \left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.97, size = 72, normalized size = 1.95 \begin {gather*} 4 \left (\frac {1-x}{x^2}+\frac {1}{4 \log ^2\left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )}+\frac {-\frac {1}{2}+\frac {1}{x}}{\log \left (\frac {\left (e^2+\log \left (x+\frac {\log (x)}{4+x}\right )\right )^2}{x^2}\right )}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-16*x^2 - 68*x^3 - 32*x^4 - 4*x^5 + E^2*(64*x^3 + 32*x^4 + 4*x^5) + (4*x^3 + E^2*(16*x^2 + 4*x^3))*
Log[x] + (64*x^3 + 32*x^4 + 4*x^5 + (16*x^2 + 4*x^3)*Log[x])*Log[(4*x + x^2 + Log[x])/(4 + x)] + (-32*x - 120*
x^2 + 4*x^3 + 24*x^4 + 4*x^5 + E^2*(128*x^2 - 24*x^4 - 4*x^5) + (8*x^2 - 4*x^3 + E^2*(32*x - 8*x^2 - 4*x^3))*L
og[x] + (128*x^2 - 24*x^4 - 4*x^5 + (32*x - 8*x^2 - 4*x^3)*Log[x])*Log[(4*x + x^2 + Log[x])/(4 + x)])*Log[(E^4
 + 2*E^2*Log[(4*x + x^2 + Log[x])/(4 + x)] + Log[(4*x + x^2 + Log[x])/(4 + x)]^2)/x^2] + (E^2*(-64*x^2 - 32*x^
3 - 4*x^4) + E^2*(-16*x - 4*x^2)*Log[x] + (-64*x^2 - 32*x^3 - 4*x^4 + (-16*x - 4*x^2)*Log[x])*Log[(4*x + x^2 +
 Log[x])/(4 + x)])*Log[(E^4 + 2*E^2*Log[(4*x + x^2 + Log[x])/(4 + x)] + Log[(4*x + x^2 + Log[x])/(4 + x)]^2)/x
^2]^2 + (E^2*(-128*x + 24*x^3 + 4*x^4) + E^2*(-32 + 8*x + 4*x^2)*Log[x] + (-128*x + 24*x^3 + 4*x^4 + (-32 + 8*
x + 4*x^2)*Log[x])*Log[(4*x + x^2 + Log[x])/(4 + x)])*Log[(E^4 + 2*E^2*Log[(4*x + x^2 + Log[x])/(4 + x)] + Log
[(4*x + x^2 + Log[x])/(4 + x)]^2)/x^2]^3)/((E^2*(16*x^4 + 8*x^5 + x^6) + E^2*(4*x^3 + x^4)*Log[x] + (16*x^4 +
8*x^5 + x^6 + (4*x^3 + x^4)*Log[x])*Log[(4*x + x^2 + Log[x])/(4 + x)])*Log[(E^4 + 2*E^2*Log[(4*x + x^2 + Log[x
])/(4 + x)] + Log[(4*x + x^2 + Log[x])/(4 + x)]^2)/x^2]^3),x]

[Out]

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

________________________________________________________________________________________

fricas [B]  time = 0.80, size = 167, normalized size = 4.51 \begin {gather*} -\frac {4 \, {\left (x - 1\right )} \log \left (\frac {2 \, e^{2} \log \left (\frac {x^{2} + 4 \, x + \log \relax (x)}{x + 4}\right ) + \log \left (\frac {x^{2} + 4 \, x + \log \relax (x)}{x + 4}\right )^{2} + e^{4}}{x^{2}}\right )^{2} - x^{2} + 2 \, {\left (x^{2} - 2 \, x\right )} \log \left (\frac {2 \, e^{2} \log \left (\frac {x^{2} + 4 \, x + \log \relax (x)}{x + 4}\right ) + \log \left (\frac {x^{2} + 4 \, x + \log \relax (x)}{x + 4}\right )^{2} + e^{4}}{x^{2}}\right )}{x^{2} \log \left (\frac {2 \, e^{2} \log \left (\frac {x^{2} + 4 \, x + \log \relax (x)}{x + 4}\right ) + \log \left (\frac {x^{2} + 4 \, x + \log \relax (x)}{x + 4}\right )^{2} + e^{4}}{x^{2}}\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((4*x^2+8*x-32)*log(x)+4*x^4+24*x^3-128*x)*log((log(x)+x^2+4*x)/(4+x))+(4*x^2+8*x-32)*exp(2)*log(x
)+(4*x^4+24*x^3-128*x)*exp(2))*log((log((log(x)+x^2+4*x)/(4+x))^2+2*exp(2)*log((log(x)+x^2+4*x)/(4+x))+exp(2)^
2)/x^2)^3+(((-4*x^2-16*x)*log(x)-4*x^4-32*x^3-64*x^2)*log((log(x)+x^2+4*x)/(4+x))+(-4*x^2-16*x)*exp(2)*log(x)+
(-4*x^4-32*x^3-64*x^2)*exp(2))*log((log((log(x)+x^2+4*x)/(4+x))^2+2*exp(2)*log((log(x)+x^2+4*x)/(4+x))+exp(2)^
2)/x^2)^2+(((-4*x^3-8*x^2+32*x)*log(x)-4*x^5-24*x^4+128*x^2)*log((log(x)+x^2+4*x)/(4+x))+((-4*x^3-8*x^2+32*x)*
exp(2)-4*x^3+8*x^2)*log(x)+(-4*x^5-24*x^4+128*x^2)*exp(2)+4*x^5+24*x^4+4*x^3-120*x^2-32*x)*log((log((log(x)+x^
2+4*x)/(4+x))^2+2*exp(2)*log((log(x)+x^2+4*x)/(4+x))+exp(2)^2)/x^2)+((4*x^3+16*x^2)*log(x)+4*x^5+32*x^4+64*x^3
)*log((log(x)+x^2+4*x)/(4+x))+((4*x^3+16*x^2)*exp(2)+4*x^3)*log(x)+(4*x^5+32*x^4+64*x^3)*exp(2)-4*x^5-32*x^4-6
8*x^3-16*x^2)/(((x^4+4*x^3)*log(x)+x^6+8*x^5+16*x^4)*log((log(x)+x^2+4*x)/(4+x))+(x^4+4*x^3)*exp(2)*log(x)+(x^
6+8*x^5+16*x^4)*exp(2))/log((log((log(x)+x^2+4*x)/(4+x))^2+2*exp(2)*log((log(x)+x^2+4*x)/(4+x))+exp(2)^2)/x^2)
^3,x, algorithm="fricas")

[Out]

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

________________________________________________________________________________________

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(((((4*x^2+8*x-32)*log(x)+4*x^4+24*x^3-128*x)*log((log(x)+x^2+4*x)/(4+x))+(4*x^2+8*x-32)*exp(2)*log(x
)+(4*x^4+24*x^3-128*x)*exp(2))*log((log((log(x)+x^2+4*x)/(4+x))^2+2*exp(2)*log((log(x)+x^2+4*x)/(4+x))+exp(2)^
2)/x^2)^3+(((-4*x^2-16*x)*log(x)-4*x^4-32*x^3-64*x^2)*log((log(x)+x^2+4*x)/(4+x))+(-4*x^2-16*x)*exp(2)*log(x)+
(-4*x^4-32*x^3-64*x^2)*exp(2))*log((log((log(x)+x^2+4*x)/(4+x))^2+2*exp(2)*log((log(x)+x^2+4*x)/(4+x))+exp(2)^
2)/x^2)^2+(((-4*x^3-8*x^2+32*x)*log(x)-4*x^5-24*x^4+128*x^2)*log((log(x)+x^2+4*x)/(4+x))+((-4*x^3-8*x^2+32*x)*
exp(2)-4*x^3+8*x^2)*log(x)+(-4*x^5-24*x^4+128*x^2)*exp(2)+4*x^5+24*x^4+4*x^3-120*x^2-32*x)*log((log((log(x)+x^
2+4*x)/(4+x))^2+2*exp(2)*log((log(x)+x^2+4*x)/(4+x))+exp(2)^2)/x^2)+((4*x^3+16*x^2)*log(x)+4*x^5+32*x^4+64*x^3
)*log((log(x)+x^2+4*x)/(4+x))+((4*x^3+16*x^2)*exp(2)+4*x^3)*log(x)+(4*x^5+32*x^4+64*x^3)*exp(2)-4*x^5-32*x^4-6
8*x^3-16*x^2)/(((x^4+4*x^3)*log(x)+x^6+8*x^5+16*x^4)*log((log(x)+x^2+4*x)/(4+x))+(x^4+4*x^3)*exp(2)*log(x)+(x^
6+8*x^5+16*x^4)*exp(2))/log((log((log(x)+x^2+4*x)/(4+x))^2+2*exp(2)*log((log(x)+x^2+4*x)/(4+x))+exp(2)^2)/x^2)
^3,x, algorithm="giac")

[Out]

Timed out

________________________________________________________________________________________

maple [C]  time = 14.40, size = 6785, normalized size = 183.38

method result size
risch \(\text {Expression too large to display}\) \(6785\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((4*x^2+8*x-32)*ln(x)+4*x^4+24*x^3-128*x)*ln((ln(x)+x^2+4*x)/(4+x))+(4*x^2+8*x-32)*exp(2)*ln(x)+(4*x^4+2
4*x^3-128*x)*exp(2))*ln((ln((ln(x)+x^2+4*x)/(4+x))^2+2*exp(2)*ln((ln(x)+x^2+4*x)/(4+x))+exp(2)^2)/x^2)^3+(((-4
*x^2-16*x)*ln(x)-4*x^4-32*x^3-64*x^2)*ln((ln(x)+x^2+4*x)/(4+x))+(-4*x^2-16*x)*exp(2)*ln(x)+(-4*x^4-32*x^3-64*x
^2)*exp(2))*ln((ln((ln(x)+x^2+4*x)/(4+x))^2+2*exp(2)*ln((ln(x)+x^2+4*x)/(4+x))+exp(2)^2)/x^2)^2+(((-4*x^3-8*x^
2+32*x)*ln(x)-4*x^5-24*x^4+128*x^2)*ln((ln(x)+x^2+4*x)/(4+x))+((-4*x^3-8*x^2+32*x)*exp(2)-4*x^3+8*x^2)*ln(x)+(
-4*x^5-24*x^4+128*x^2)*exp(2)+4*x^5+24*x^4+4*x^3-120*x^2-32*x)*ln((ln((ln(x)+x^2+4*x)/(4+x))^2+2*exp(2)*ln((ln
(x)+x^2+4*x)/(4+x))+exp(2)^2)/x^2)+((4*x^3+16*x^2)*ln(x)+4*x^5+32*x^4+64*x^3)*ln((ln(x)+x^2+4*x)/(4+x))+((4*x^
3+16*x^2)*exp(2)+4*x^3)*ln(x)+(4*x^5+32*x^4+64*x^3)*exp(2)-4*x^5-32*x^4-68*x^3-16*x^2)/(((x^4+4*x^3)*ln(x)+x^6
+8*x^5+16*x^4)*ln((ln(x)+x^2+4*x)/(4+x))+(x^4+4*x^3)*exp(2)*ln(x)+(x^6+8*x^5+16*x^4)*exp(2))/ln((ln((ln(x)+x^2
+4*x)/(4+x))^2+2*exp(2)*ln((ln(x)+x^2+4*x)/(4+x))+exp(2)^2)/x^2)^3,x,method=_RETURNVERBOSE)

[Out]

result too large to display

________________________________________________________________________________________

maxima [B]  time = 2.90, size = 155, normalized size = 4.19 \begin {gather*} -\frac {16 \, {\left (x - 1\right )} \log \relax (x)^{2} + 16 \, {\left (x - 1\right )} \log \left (e^{2} + \log \left (x^{2} + 4 \, x + \log \relax (x)\right ) - \log \left (x + 4\right )\right )^{2} - x^{2} - 4 \, {\left (x^{2} - 2 \, x\right )} \log \relax (x) + 4 \, {\left (x^{2} - 8 \, {\left (x - 1\right )} \log \relax (x) - 2 \, x\right )} \log \left (e^{2} + \log \left (x^{2} + 4 \, x + \log \relax (x)\right ) - \log \left (x + 4\right )\right )}{4 \, {\left (x^{2} \log \relax (x)^{2} - 2 \, x^{2} \log \relax (x) \log \left (e^{2} + \log \left (x^{2} + 4 \, x + \log \relax (x)\right ) - \log \left (x + 4\right )\right ) + x^{2} \log \left (e^{2} + \log \left (x^{2} + 4 \, x + \log \relax (x)\right ) - \log \left (x + 4\right )\right )^{2}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((4*x^2+8*x-32)*log(x)+4*x^4+24*x^3-128*x)*log((log(x)+x^2+4*x)/(4+x))+(4*x^2+8*x-32)*exp(2)*log(x
)+(4*x^4+24*x^3-128*x)*exp(2))*log((log((log(x)+x^2+4*x)/(4+x))^2+2*exp(2)*log((log(x)+x^2+4*x)/(4+x))+exp(2)^
2)/x^2)^3+(((-4*x^2-16*x)*log(x)-4*x^4-32*x^3-64*x^2)*log((log(x)+x^2+4*x)/(4+x))+(-4*x^2-16*x)*exp(2)*log(x)+
(-4*x^4-32*x^3-64*x^2)*exp(2))*log((log((log(x)+x^2+4*x)/(4+x))^2+2*exp(2)*log((log(x)+x^2+4*x)/(4+x))+exp(2)^
2)/x^2)^2+(((-4*x^3-8*x^2+32*x)*log(x)-4*x^5-24*x^4+128*x^2)*log((log(x)+x^2+4*x)/(4+x))+((-4*x^3-8*x^2+32*x)*
exp(2)-4*x^3+8*x^2)*log(x)+(-4*x^5-24*x^4+128*x^2)*exp(2)+4*x^5+24*x^4+4*x^3-120*x^2-32*x)*log((log((log(x)+x^
2+4*x)/(4+x))^2+2*exp(2)*log((log(x)+x^2+4*x)/(4+x))+exp(2)^2)/x^2)+((4*x^3+16*x^2)*log(x)+4*x^5+32*x^4+64*x^3
)*log((log(x)+x^2+4*x)/(4+x))+((4*x^3+16*x^2)*exp(2)+4*x^3)*log(x)+(4*x^5+32*x^4+64*x^3)*exp(2)-4*x^5-32*x^4-6
8*x^3-16*x^2)/(((x^4+4*x^3)*log(x)+x^6+8*x^5+16*x^4)*log((log(x)+x^2+4*x)/(4+x))+(x^4+4*x^3)*exp(2)*log(x)+(x^
6+8*x^5+16*x^4)*exp(2))/log((log((log(x)+x^2+4*x)/(4+x))^2+2*exp(2)*log((log(x)+x^2+4*x)/(4+x))+exp(2)^2)/x^2)
^3,x, algorithm="maxima")

[Out]

-1/4*(16*(x - 1)*log(x)^2 + 16*(x - 1)*log(e^2 + log(x^2 + 4*x + log(x)) - log(x + 4))^2 - x^2 - 4*(x^2 - 2*x)
*log(x) + 4*(x^2 - 8*(x - 1)*log(x) - 2*x)*log(e^2 + log(x^2 + 4*x + log(x)) - log(x + 4)))/(x^2*log(x)^2 - 2*
x^2*log(x)*log(e^2 + log(x^2 + 4*x + log(x)) - log(x + 4)) + x^2*log(e^2 + log(x^2 + 4*x + log(x)) - log(x + 4
))^2)

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {\ln \left (\frac {{\ln \left (\frac {4\,x+\ln \relax (x)+x^2}{x+4}\right )}^2+2\,{\mathrm {e}}^2\,\ln \left (\frac {4\,x+\ln \relax (x)+x^2}{x+4}\right )+{\mathrm {e}}^4}{x^2}\right )\,\left (32\,x+\ln \left (\frac {4\,x+\ln \relax (x)+x^2}{x+4}\right )\,\left (24\,x^4-128\,x^2+4\,x^5+\ln \relax (x)\,\left (4\,x^3+8\,x^2-32\,x\right )\right )+\ln \relax (x)\,\left ({\mathrm {e}}^2\,\left (4\,x^3+8\,x^2-32\,x\right )-8\,x^2+4\,x^3\right )+{\mathrm {e}}^2\,\left (4\,x^5+24\,x^4-128\,x^2\right )+120\,x^2-4\,x^3-24\,x^4-4\,x^5\right )-\ln \relax (x)\,\left ({\mathrm {e}}^2\,\left (4\,x^3+16\,x^2\right )+4\,x^3\right )-\ln \left (\frac {4\,x+\ln \relax (x)+x^2}{x+4}\right )\,\left (\ln \relax (x)\,\left (4\,x^3+16\,x^2\right )+64\,x^3+32\,x^4+4\,x^5\right )+{\ln \left (\frac {{\ln \left (\frac {4\,x+\ln \relax (x)+x^2}{x+4}\right )}^2+2\,{\mathrm {e}}^2\,\ln \left (\frac {4\,x+\ln \relax (x)+x^2}{x+4}\right )+{\mathrm {e}}^4}{x^2}\right )}^2\,\left (\ln \left (\frac {4\,x+\ln \relax (x)+x^2}{x+4}\right )\,\left (\ln \relax (x)\,\left (4\,x^2+16\,x\right )+64\,x^2+32\,x^3+4\,x^4\right )+{\mathrm {e}}^2\,\left (4\,x^4+32\,x^3+64\,x^2\right )+{\mathrm {e}}^2\,\ln \relax (x)\,\left (4\,x^2+16\,x\right )\right )-{\ln \left (\frac {{\ln \left (\frac {4\,x+\ln \relax (x)+x^2}{x+4}\right )}^2+2\,{\mathrm {e}}^2\,\ln \left (\frac {4\,x+\ln \relax (x)+x^2}{x+4}\right )+{\mathrm {e}}^4}{x^2}\right )}^3\,\left ({\mathrm {e}}^2\,\left (4\,x^4+24\,x^3-128\,x\right )+\ln \left (\frac {4\,x+\ln \relax (x)+x^2}{x+4}\right )\,\left (\ln \relax (x)\,\left (4\,x^2+8\,x-32\right )-128\,x+24\,x^3+4\,x^4\right )+{\mathrm {e}}^2\,\ln \relax (x)\,\left (4\,x^2+8\,x-32\right )\right )-{\mathrm {e}}^2\,\left (4\,x^5+32\,x^4+64\,x^3\right )+16\,x^2+68\,x^3+32\,x^4+4\,x^5}{{\ln \left (\frac {{\ln \left (\frac {4\,x+\ln \relax (x)+x^2}{x+4}\right )}^2+2\,{\mathrm {e}}^2\,\ln \left (\frac {4\,x+\ln \relax (x)+x^2}{x+4}\right )+{\mathrm {e}}^4}{x^2}\right )}^3\,\left ({\mathrm {e}}^2\,\left (x^6+8\,x^5+16\,x^4\right )+\ln \left (\frac {4\,x+\ln \relax (x)+x^2}{x+4}\right )\,\left (\ln \relax (x)\,\left (x^4+4\,x^3\right )+16\,x^4+8\,x^5+x^6\right )+{\mathrm {e}}^2\,\ln \relax (x)\,\left (x^4+4\,x^3\right )\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log((exp(4) + log((4*x + log(x) + x^2)/(x + 4))^2 + 2*exp(2)*log((4*x + log(x) + x^2)/(x + 4)))/x^2)*(32
*x + log((4*x + log(x) + x^2)/(x + 4))*(24*x^4 - 128*x^2 + 4*x^5 + log(x)*(8*x^2 - 32*x + 4*x^3)) + log(x)*(ex
p(2)*(8*x^2 - 32*x + 4*x^3) - 8*x^2 + 4*x^3) + exp(2)*(24*x^4 - 128*x^2 + 4*x^5) + 120*x^2 - 4*x^3 - 24*x^4 -
4*x^5) - log(x)*(exp(2)*(16*x^2 + 4*x^3) + 4*x^3) - log((4*x + log(x) + x^2)/(x + 4))*(log(x)*(16*x^2 + 4*x^3)
 + 64*x^3 + 32*x^4 + 4*x^5) + log((exp(4) + log((4*x + log(x) + x^2)/(x + 4))^2 + 2*exp(2)*log((4*x + log(x) +
 x^2)/(x + 4)))/x^2)^2*(log((4*x + log(x) + x^2)/(x + 4))*(log(x)*(16*x + 4*x^2) + 64*x^2 + 32*x^3 + 4*x^4) +
exp(2)*(64*x^2 + 32*x^3 + 4*x^4) + exp(2)*log(x)*(16*x + 4*x^2)) - log((exp(4) + log((4*x + log(x) + x^2)/(x +
 4))^2 + 2*exp(2)*log((4*x + log(x) + x^2)/(x + 4)))/x^2)^3*(exp(2)*(24*x^3 - 128*x + 4*x^4) + log((4*x + log(
x) + x^2)/(x + 4))*(log(x)*(8*x + 4*x^2 - 32) - 128*x + 24*x^3 + 4*x^4) + exp(2)*log(x)*(8*x + 4*x^2 - 32)) -
exp(2)*(64*x^3 + 32*x^4 + 4*x^5) + 16*x^2 + 68*x^3 + 32*x^4 + 4*x^5)/(log((exp(4) + log((4*x + log(x) + x^2)/(
x + 4))^2 + 2*exp(2)*log((4*x + log(x) + x^2)/(x + 4)))/x^2)^3*(exp(2)*(16*x^4 + 8*x^5 + x^6) + log((4*x + log
(x) + x^2)/(x + 4))*(log(x)*(4*x^3 + x^4) + 16*x^4 + 8*x^5 + x^6) + exp(2)*log(x)*(4*x^3 + x^4))),x)

[Out]

int(-(log((exp(4) + log((4*x + log(x) + x^2)/(x + 4))^2 + 2*exp(2)*log((4*x + log(x) + x^2)/(x + 4)))/x^2)*(32
*x + log((4*x + log(x) + x^2)/(x + 4))*(24*x^4 - 128*x^2 + 4*x^5 + log(x)*(8*x^2 - 32*x + 4*x^3)) + log(x)*(ex
p(2)*(8*x^2 - 32*x + 4*x^3) - 8*x^2 + 4*x^3) + exp(2)*(24*x^4 - 128*x^2 + 4*x^5) + 120*x^2 - 4*x^3 - 24*x^4 -
4*x^5) - log(x)*(exp(2)*(16*x^2 + 4*x^3) + 4*x^3) - log((4*x + log(x) + x^2)/(x + 4))*(log(x)*(16*x^2 + 4*x^3)
 + 64*x^3 + 32*x^4 + 4*x^5) + log((exp(4) + log((4*x + log(x) + x^2)/(x + 4))^2 + 2*exp(2)*log((4*x + log(x) +
 x^2)/(x + 4)))/x^2)^2*(log((4*x + log(x) + x^2)/(x + 4))*(log(x)*(16*x + 4*x^2) + 64*x^2 + 32*x^3 + 4*x^4) +
exp(2)*(64*x^2 + 32*x^3 + 4*x^4) + exp(2)*log(x)*(16*x + 4*x^2)) - log((exp(4) + log((4*x + log(x) + x^2)/(x +
 4))^2 + 2*exp(2)*log((4*x + log(x) + x^2)/(x + 4)))/x^2)^3*(exp(2)*(24*x^3 - 128*x + 4*x^4) + log((4*x + log(
x) + x^2)/(x + 4))*(log(x)*(8*x + 4*x^2 - 32) - 128*x + 24*x^3 + 4*x^4) + exp(2)*log(x)*(8*x + 4*x^2 - 32)) -
exp(2)*(64*x^3 + 32*x^4 + 4*x^5) + 16*x^2 + 68*x^3 + 32*x^4 + 4*x^5)/(log((exp(4) + log((4*x + log(x) + x^2)/(
x + 4))^2 + 2*exp(2)*log((4*x + log(x) + x^2)/(x + 4)))/x^2)^3*(exp(2)*(16*x^4 + 8*x^5 + x^6) + log((4*x + log
(x) + x^2)/(x + 4))*(log(x)*(4*x^3 + x^4) + 16*x^4 + 8*x^5 + x^6) + exp(2)*log(x)*(4*x^3 + x^4))), x)

________________________________________________________________________________________

sympy [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(((((4*x**2+8*x-32)*ln(x)+4*x**4+24*x**3-128*x)*ln((ln(x)+x**2+4*x)/(4+x))+(4*x**2+8*x-32)*exp(2)*ln(
x)+(4*x**4+24*x**3-128*x)*exp(2))*ln((ln((ln(x)+x**2+4*x)/(4+x))**2+2*exp(2)*ln((ln(x)+x**2+4*x)/(4+x))+exp(2)
**2)/x**2)**3+(((-4*x**2-16*x)*ln(x)-4*x**4-32*x**3-64*x**2)*ln((ln(x)+x**2+4*x)/(4+x))+(-4*x**2-16*x)*exp(2)*
ln(x)+(-4*x**4-32*x**3-64*x**2)*exp(2))*ln((ln((ln(x)+x**2+4*x)/(4+x))**2+2*exp(2)*ln((ln(x)+x**2+4*x)/(4+x))+
exp(2)**2)/x**2)**2+(((-4*x**3-8*x**2+32*x)*ln(x)-4*x**5-24*x**4+128*x**2)*ln((ln(x)+x**2+4*x)/(4+x))+((-4*x**
3-8*x**2+32*x)*exp(2)-4*x**3+8*x**2)*ln(x)+(-4*x**5-24*x**4+128*x**2)*exp(2)+4*x**5+24*x**4+4*x**3-120*x**2-32
*x)*ln((ln((ln(x)+x**2+4*x)/(4+x))**2+2*exp(2)*ln((ln(x)+x**2+4*x)/(4+x))+exp(2)**2)/x**2)+((4*x**3+16*x**2)*l
n(x)+4*x**5+32*x**4+64*x**3)*ln((ln(x)+x**2+4*x)/(4+x))+((4*x**3+16*x**2)*exp(2)+4*x**3)*ln(x)+(4*x**5+32*x**4
+64*x**3)*exp(2)-4*x**5-32*x**4-68*x**3-16*x**2)/(((x**4+4*x**3)*ln(x)+x**6+8*x**5+16*x**4)*ln((ln(x)+x**2+4*x
)/(4+x))+(x**4+4*x**3)*exp(2)*ln(x)+(x**6+8*x**5+16*x**4)*exp(2))/ln((ln((ln(x)+x**2+4*x)/(4+x))**2+2*exp(2)*l
n((ln(x)+x**2+4*x)/(4+x))+exp(2)**2)/x**2)**3,x)

[Out]

Timed out

________________________________________________________________________________________

[next] [prev] [prev-tail] [front] [up]