3.61.83 \(\int \frac {4 x+6 x^2-4 x^3+(-2 x+x^2) \log (2)+e^x (6 x-x^2-x^3) \log (2)+(4 x+4 x^2+(-4-2 x) \log (2)+e^x (4+2 x) \log (2)) \log (\frac {4}{2 x+2 x^2+(-2-x) \log (2)+e^x (2+x) \log (2)}) \log (\log (\frac {4}{2 x+2 x^2+(-2-x) \log (2)+e^x (2+x) \log (2)}))}{(8 x-6 x^3+2 x^4+(-8+4 x+2 x^2-x^3) \log (2)+e^x (8-4 x-2 x^2+x^3) \log (2)) \log (\frac {4}{2 x+2 x^2+(-2-x) \log (2)+e^x (2+x) \log (2)}) \log ^2(\log (\frac {4}{2 x+2 x^2+(-2-x) \log (2)+e^x (2+x) \log (2)}))} \, dx\) [6083]

Optimal. Leaf size=38 \[ \frac {x}{(2-x) \log \left (\log \left (\frac {4}{x^2+(2+x) \left (x-\left (1-e^x\right ) \log (2)\right )}\right )\right )} \]

[Out]

x/(2-x)/ln(ln(4/(x^2+(2+x)*(x-(1-exp(x))*ln(2)))))

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Rubi [F]
time = 29.83, 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 {4 x+6 x^2-4 x^3+\left (-2 x+x^2\right ) \log (2)+e^x \left (6 x-x^2-x^3\right ) \log (2)+\left (4 x+4 x^2+(-4-2 x) \log (2)+e^x (4+2 x) \log (2)\right ) \log \left (\frac {4}{2 x+2 x^2+(-2-x) \log (2)+e^x (2+x) \log (2)}\right ) \log \left (\log \left (\frac {4}{2 x+2 x^2+(-2-x) \log (2)+e^x (2+x) \log (2)}\right )\right )}{\left (8 x-6 x^3+2 x^4+\left (-8+4 x+2 x^2-x^3\right ) \log (2)+e^x \left (8-4 x-2 x^2+x^3\right ) \log (2)\right ) \log \left (\frac {4}{2 x+2 x^2+(-2-x) \log (2)+e^x (2+x) \log (2)}\right ) \log ^2\left (\log \left (\frac {4}{2 x+2 x^2+(-2-x) \log (2)+e^x (2+x) \log (2)}\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(4*x + 6*x^2 - 4*x^3 + (-2*x + x^2)*Log[2] + E^x*(6*x - x^2 - x^3)*Log[2] + (4*x + 4*x^2 + (-4 - 2*x)*Log[
2] + E^x*(4 + 2*x)*Log[2])*Log[4/(2*x + 2*x^2 + (-2 - x)*Log[2] + E^x*(2 + x)*Log[2])]*Log[Log[4/(2*x + 2*x^2
+ (-2 - x)*Log[2] + E^x*(2 + x)*Log[2])]])/((8*x - 6*x^3 + 2*x^4 + (-8 + 4*x + 2*x^2 - x^3)*Log[2] + E^x*(8 -
4*x - 2*x^2 + x^3)*Log[2])*Log[4/(2*x + 2*x^2 + (-2 - x)*Log[2] + E^x*(2 + x)*Log[2])]*Log[Log[4/(2*x + 2*x^2
+ (-2 - x)*Log[2] + E^x*(2 + x)*Log[2])]]^2),x]

[Out]

-Defer[Int][1/(Log[4/(2*x + 2*x^2 - (2 + x)*Log[2] + E^x*(2 + x)*Log[2])]*Log[Log[4/(2*x + 2*x^2 - (2 + x)*Log
[2] + E^x*(2 + x)*Log[2])]]^2), x] - (10*Log[2]*Defer[Int][1/((-2 + x)*Log[4/(2*x + 2*x^2 - (2 + x)*Log[2] + E
^x*(2 + x)*Log[2])]*Log[Log[4/(2*x + 2*x^2 - (2 + x)*Log[2] + E^x*(2 + x)*Log[2])]]^2), x])/Log[16] - (Log[2]*
Log[4]*Defer[Int][1/((x*Log[2] + Log[4])*Log[4/(2*x + 2*x^2 - (2 + x)*Log[2] + E^x*(2 + x)*Log[2])]*Log[Log[4/
(2*x + 2*x^2 - (2 + x)*Log[2] + E^x*(2 + x)*Log[2])]]^2), x])/Log[16] - ((4*Log[2]^4 + Log[4]^3 - Log[2]^2*Log
[4096])*Defer[Int][1/((2*x^2 + 2*x*(1 - Log[2]/2) + E^x*x*Log[2] - Log[4] + E^x*Log[4])*Log[4/(2*x + 2*x^2 - (
2 + x)*Log[2] + E^x*(2 + x)*Log[2])]*Log[Log[4/(2*x + 2*x^2 - (2 + x)*Log[2] + E^x*(2 + x)*Log[2])]]^2), x])/L
og[2]^3 + (2*(8*Log[2]^2 - 16*Log[4] + 2*Log[4]^2 + Log[4096])*Defer[Int][1/((2 - x)*(2*x^2 + 2*x*(1 - Log[2]/
2) + E^x*x*Log[2] - Log[4] + E^x*Log[4])*Log[4/(2*x + 2*x^2 - (2 + x)*Log[2] + E^x*(2 + x)*Log[2])]*Log[Log[4/
(2*x + 2*x^2 - (2 + x)*Log[2] + E^x*(2 + x)*Log[2])]]^2), x])/Log[16] - ((Log[2]^3 - 4*Log[2]*Log[4] + Log[4]^
2)*Defer[Int][x/((2*x^2 + 2*x*(1 - Log[2]/2) + E^x*x*Log[2] - Log[4] + E^x*Log[4])*Log[4/(2*x + 2*x^2 - (2 + x
)*Log[2] + E^x*(2 + x)*Log[2])]*Log[Log[4/(2*x + 2*x^2 - (2 + x)*Log[2] + E^x*(2 + x)*Log[2])]]^2), x])/Log[2]
^2 + (Log[4]*Defer[Int][x^2/((2*x^2 + 2*x*(1 - Log[2]/2) + E^x*x*Log[2] - Log[4] + E^x*Log[4])*Log[4/(2*x + 2*
x^2 - (2 + x)*Log[2] + E^x*(2 + x)*Log[2])]*Log[Log[4/(2*x + 2*x^2 - (2 + x)*Log[2] + E^x*(2 + x)*Log[2])]]^2)
, x])/Log[2] - Log[4]*(1 - Log[2] - Log[4]/Log[2] + Log[4]^2/Log[16])*Defer[Int][1/((x*Log[2] + Log[4])*(2*x^2
+ 2*x*(1 - Log[2]/2) + E^x*x*Log[2] - Log[4] + E^x*Log[4])*Log[4/(2*x + 2*x^2 - (2 + x)*Log[2] + E^x*(2 + x)*
Log[2])]*Log[Log[4/(2*x + 2*x^2 - (2 + x)*Log[2] + E^x*(2 + x)*Log[2])]]^2), x] + 2*Defer[Int][1/((2 - x)^2*Lo
g[Log[4/(2*x + 2*x^2 - (2 + x)*Log[2] + E^x*(2 + x)*Log[2])]]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 x+6 x^2-4 x^3+\left (-2 x+x^2\right ) \log (2)+e^x \left (6 x-x^2-x^3\right ) \log (2)+\left (4 x+4 x^2+(-4-2 x) \log (2)+e^x (4+2 x) \log (2)\right ) \log \left (\frac {4}{2 x+2 x^2+(-2-x) \log (2)+e^x (2+x) \log (2)}\right ) \log \left (\log \left (\frac {4}{2 x+2 x^2+(-2-x) \log (2)+e^x (2+x) \log (2)}\right )\right )}{(2-x)^2 \left (2 x^2+2 x \left (1-\frac {\log (2)}{2}\right )+e^x x \log (2)-\log (4)+e^x \log (4)\right ) \log \left (\frac {4}{2 x+2 x^2+(-2-x) \log (2)+e^x (2+x) \log (2)}\right ) \log ^2\left (\log \left (\frac {4}{2 x+2 x^2+(-2-x) \log (2)+e^x (2+x) \log (2)}\right )\right )} \, dx\\ &=\int \left (\frac {x \left (-x^3 \log ^2(2)+x^4 \log (4)-x^2 \log (2) (12+\log (4))+\log (4) \log (16)+x \left (4 \log ^2(2)+\log (16)\right )+\log (256)\right )}{(2-x)^2 (x \log (2)+\log (4)) \left (2 x^2+2 x \left (1-\frac {\log (2)}{2}\right )+e^x x \log (2)-\log (4)+e^x \log (4)\right ) \log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right ) \log ^2\left (\log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right )\right )}-\frac {\log (2) \left (-6 x+x^2+x^3-4 \log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right ) \log \left (\log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right )\right )-2 x \log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right ) \log \left (\log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right )\right )\right )}{(-2+x)^2 (x \log (2)+\log (4)) \log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right ) \log ^2\left (\log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right )\right )}\right ) \, dx\\ &=-\left (\log (2) \int \frac {-6 x+x^2+x^3-4 \log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right ) \log \left (\log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right )\right )-2 x \log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right ) \log \left (\log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right )\right )}{(-2+x)^2 (x \log (2)+\log (4)) \log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right ) \log ^2\left (\log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right )\right )} \, dx\right )+\int \frac {x \left (-x^3 \log ^2(2)+x^4 \log (4)-x^2 \log (2) (12+\log (4))+\log (4) \log (16)+x \left (4 \log ^2(2)+\log (16)\right )+\log (256)\right )}{(2-x)^2 (x \log (2)+\log (4)) \left (2 x^2+2 x \left (1-\frac {\log (2)}{2}\right )+e^x x \log (2)-\log (4)+e^x \log (4)\right ) \log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right ) \log ^2\left (\log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right )\right )} \, dx\\ &=-\left (\log (2) \int \frac {\frac {x \left (-6+x+x^2\right )}{\log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right )}-2 (2+x) \log \left (\log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right )\right )}{(2-x)^2 (x \log (2)+\log (4)) \log ^2\left (\log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right )\right )} \, dx\right )+\int \frac {x \left (24 \log (2)+x^2 \left (\log ^2(2)-2 \log (4)\right )-8 \log (4)-x^3 \log (4)+2 \log (2) \log (4)+x \left (12 \log (2)+2 \log ^2(2)-4 \log (4)+\log (2) \log (4)\right )-\log (16)\right )}{(2-x) (x \log (2)+\log (4)) \left (2 x^2+2 x \left (1-\frac {\log (2)}{2}\right )+e^x x \log (2)-\log (4)+e^x \log (4)\right ) \log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right ) \log ^2\left (\log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right )\right )} \, dx\\ &=-\left (\log (2) \int \left (\frac {x (3+x)}{(-2+x) (x \log (2)+\log (4)) \log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right ) \log ^2\left (\log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right )\right )}-\frac {2}{(2-x)^2 \log (2) \log \left (\log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right )\right )}\right ) \, dx\right )+\int \frac {x \left (x^2 \left (\log ^2(2)-2 \log (4)\right )-x^3 \log (4)+\log ^2(4)+\log (16)+x \left (2 \log ^2(2)+\log (2) \log (4)+\log (16)\right )\right )}{(2-x) (x \log (2)+\log (4)) \left (2 x^2+2 x \left (1-\frac {\log (2)}{2}\right )+e^x x \log (2)-\log (4)+e^x \log (4)\right ) \log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right ) \log ^2\left (\log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right )\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.19, size = 41, normalized size = 1.08 \begin {gather*} -\frac {x}{(-2+x) \log \left (\log \left (\frac {4}{2 x+2 x^2-(2+x) \log (2)+e^x (2+x) \log (2)}\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(4*x + 6*x^2 - 4*x^3 + (-2*x + x^2)*Log[2] + E^x*(6*x - x^2 - x^3)*Log[2] + (4*x + 4*x^2 + (-4 - 2*x
)*Log[2] + E^x*(4 + 2*x)*Log[2])*Log[4/(2*x + 2*x^2 + (-2 - x)*Log[2] + E^x*(2 + x)*Log[2])]*Log[Log[4/(2*x +
2*x^2 + (-2 - x)*Log[2] + E^x*(2 + x)*Log[2])]])/((8*x - 6*x^3 + 2*x^4 + (-8 + 4*x + 2*x^2 - x^3)*Log[2] + E^x
*(8 - 4*x - 2*x^2 + x^3)*Log[2])*Log[4/(2*x + 2*x^2 + (-2 - x)*Log[2] + E^x*(2 + x)*Log[2])]*Log[Log[4/(2*x +
2*x^2 + (-2 - x)*Log[2] + E^x*(2 + x)*Log[2])]]^2),x]

[Out]

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

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Maple [A]
time = 1.70, size = 44, normalized size = 1.16

method	result	size
risch	\(-\frac {x}{\left (x -2\right ) \ln \left (2 \ln \left (2\right )-\ln \left (\left (\left ({\mathrm e}^{x}-1\right ) x +2 \,{\mathrm e}^{x}-2\right ) \ln \left (2\right )+2 x^{2}+2 x \right )\right )}\)	\(44\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x+4)*ln(2)*exp(x)+(-2*x-4)*ln(2)+4*x^2+4*x)*ln(4/((2+x)*ln(2)*exp(x)+(-x-2)*ln(2)+2*x^2+2*x))*ln(ln(4
/((2+x)*ln(2)*exp(x)+(-x-2)*ln(2)+2*x^2+2*x)))+(-x^3-x^2+6*x)*ln(2)*exp(x)+(x^2-2*x)*ln(2)-4*x^3+6*x^2+4*x)/((
x^3-2*x^2-4*x+8)*ln(2)*exp(x)+(-x^3+2*x^2+4*x-8)*ln(2)+2*x^4-6*x^3+8*x)/ln(4/((2+x)*ln(2)*exp(x)+(-x-2)*ln(2)+
2*x^2+2*x))/ln(ln(4/((2+x)*ln(2)*exp(x)+(-x-2)*ln(2)+2*x^2+2*x)))^2,x,method=_RETURNVERBOSE)

[Out]

-x/(x-2)/ln(2*ln(2)-ln(((exp(x)-1)*x+2*exp(x)-2)*ln(2)+2*x^2+2*x))

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Maxima [A]
time = 1.23, size = 48, normalized size = 1.26 \begin {gather*} -\frac {x}{{\left (x - 2\right )} \log \left (2 \, \log \left (2\right ) - \log \left (2 \, x^{2} - x {\left (\log \left (2\right ) - 2\right )} + {\left (x \log \left (2\right ) + 2 \, \log \left (2\right )\right )} e^{x} - 2 \, \log \left (2\right )\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x+4)*log(2)*exp(x)+(-2*x-4)*log(2)+4*x^2+4*x)*log(4/((2+x)*log(2)*exp(x)+(-2-x)*log(2)+2*x^2+2*
x))*log(log(4/((2+x)*log(2)*exp(x)+(-2-x)*log(2)+2*x^2+2*x)))+(-x^3-x^2+6*x)*log(2)*exp(x)+(x^2-2*x)*log(2)-4*
x^3+6*x^2+4*x)/((x^3-2*x^2-4*x+8)*log(2)*exp(x)+(-x^3+2*x^2+4*x-8)*log(2)+2*x^4-6*x^3+8*x)/log(4/((2+x)*log(2)
*exp(x)+(-2-x)*log(2)+2*x^2+2*x))/log(log(4/((2+x)*log(2)*exp(x)+(-2-x)*log(2)+2*x^2+2*x)))^2,x, algorithm="ma
xima")

[Out]

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

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Fricas [A]
time = 0.40, size = 40, normalized size = 1.05 \begin {gather*} -\frac {x}{{\left (x - 2\right )} \log \left (\log \left (\frac {4}{{\left (x + 2\right )} e^{x} \log \left (2\right ) + 2 \, x^{2} - {\left (x + 2\right )} \log \left (2\right ) + 2 \, x}\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x+4)*log(2)*exp(x)+(-2*x-4)*log(2)+4*x^2+4*x)*log(4/((2+x)*log(2)*exp(x)+(-2-x)*log(2)+2*x^2+2*
x))*log(log(4/((2+x)*log(2)*exp(x)+(-2-x)*log(2)+2*x^2+2*x)))+(-x^3-x^2+6*x)*log(2)*exp(x)+(x^2-2*x)*log(2)-4*
x^3+6*x^2+4*x)/((x^3-2*x^2-4*x+8)*log(2)*exp(x)+(-x^3+2*x^2+4*x-8)*log(2)+2*x^4-6*x^3+8*x)/log(4/((2+x)*log(2)
*exp(x)+(-2-x)*log(2)+2*x^2+2*x))/log(log(4/((2+x)*log(2)*exp(x)+(-2-x)*log(2)+2*x^2+2*x)))^2,x, algorithm="fr
icas")

[Out]

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

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Sympy [A]
time = 3.72, size = 37, normalized size = 0.97 \begin {gather*} - \frac {x}{\left (x - 2\right ) \log {\left (\log {\left (\frac {4}{2 x^{2} + 2 x + \left (- x - 2\right ) \log {\left (2 \right )} + \left (x + 2\right ) e^{x} \log {\left (2 \right )}} \right )} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x+4)*ln(2)*exp(x)+(-2*x-4)*ln(2)+4*x**2+4*x)*ln(4/((2+x)*ln(2)*exp(x)+(-2-x)*ln(2)+2*x**2+2*x))
*ln(ln(4/((2+x)*ln(2)*exp(x)+(-2-x)*ln(2)+2*x**2+2*x)))+(-x**3-x**2+6*x)*ln(2)*exp(x)+(x**2-2*x)*ln(2)-4*x**3+
6*x**2+4*x)/((x**3-2*x**2-4*x+8)*ln(2)*exp(x)+(-x**3+2*x**2+4*x-8)*ln(2)+2*x**4-6*x**3+8*x)/ln(4/((2+x)*ln(2)*
exp(x)+(-2-x)*ln(2)+2*x**2+2*x))/ln(ln(4/((2+x)*ln(2)*exp(x)+(-2-x)*ln(2)+2*x**2+2*x)))**2,x)

[Out]

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

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 197 vs. \(2 (33) = 66\).
time = 1.50, size = 197, normalized size = 5.18 \begin {gather*} -\frac {2 \, x \log \left (2\right ) - x \log \left (x e^{x} \log \left (2\right ) + 2 \, x^{2} - x \log \left (2\right ) + 2 \, e^{x} \log \left (2\right ) + 2 \, x - 2 \, \log \left (2\right )\right )}{x \log \left (\frac {4}{x e^{x} \log \left (2\right ) + 2 \, x^{2} - x \log \left (2\right ) + 2 \, e^{x} \log \left (2\right ) + 2 \, x - 2 \, \log \left (2\right )}\right ) \log \left (2 \, \log \left (2\right ) - \log \left (x e^{x} \log \left (2\right ) + 2 \, x^{2} - x \log \left (2\right ) + 2 \, e^{x} \log \left (2\right ) + 2 \, x - 2 \, \log \left (2\right )\right )\right ) - 2 \, \log \left (\frac {4}{x e^{x} \log \left (2\right ) + 2 \, x^{2} - x \log \left (2\right ) + 2 \, e^{x} \log \left (2\right ) + 2 \, x - 2 \, \log \left (2\right )}\right ) \log \left (2 \, \log \left (2\right ) - \log \left (x e^{x} \log \left (2\right ) + 2 \, x^{2} - x \log \left (2\right ) + 2 \, e^{x} \log \left (2\right ) + 2 \, x - 2 \, \log \left (2\right )\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x+4)*log(2)*exp(x)+(-2*x-4)*log(2)+4*x^2+4*x)*log(4/((2+x)*log(2)*exp(x)+(-2-x)*log(2)+2*x^2+2*
x))*log(log(4/((2+x)*log(2)*exp(x)+(-2-x)*log(2)+2*x^2+2*x)))+(-x^3-x^2+6*x)*log(2)*exp(x)+(x^2-2*x)*log(2)-4*
x^3+6*x^2+4*x)/((x^3-2*x^2-4*x+8)*log(2)*exp(x)+(-x^3+2*x^2+4*x-8)*log(2)+2*x^4-6*x^3+8*x)/log(4/((2+x)*log(2)
*exp(x)+(-2-x)*log(2)+2*x^2+2*x))/log(log(4/((2+x)*log(2)*exp(x)+(-2-x)*log(2)+2*x^2+2*x)))^2,x, algorithm="gi
ac")

[Out]

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

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Mupad [F]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {4\,x-\ln \left (2\right )\,\left (2\,x-x^2\right )+6\,x^2-4\,x^3-{\mathrm {e}}^x\,\ln \left (2\right )\,\left (x^3+x^2-6\,x\right )+\ln \left (\ln \left (\frac {4}{2\,x-\ln \left (2\right )\,\left (x+2\right )+2\,x^2+{\mathrm {e}}^x\,\ln \left (2\right )\,\left (x+2\right )}\right )\right )\,\ln \left (\frac {4}{2\,x-\ln \left (2\right )\,\left (x+2\right )+2\,x^2+{\mathrm {e}}^x\,\ln \left (2\right )\,\left (x+2\right )}\right )\,\left (4\,x-\ln \left (2\right )\,\left (2\,x+4\right )+4\,x^2+{\mathrm {e}}^x\,\ln \left (2\right )\,\left (2\,x+4\right )\right )}{{\ln \left (\ln \left (\frac {4}{2\,x-\ln \left (2\right )\,\left (x+2\right )+2\,x^2+{\mathrm {e}}^x\,\ln \left (2\right )\,\left (x+2\right )}\right )\right )}^2\,\ln \left (\frac {4}{2\,x-\ln \left (2\right )\,\left (x+2\right )+2\,x^2+{\mathrm {e}}^x\,\ln \left (2\right )\,\left (x+2\right )}\right )\,\left (8\,x+\ln \left (2\right )\,\left (-x^3+2\,x^2+4\,x-8\right )-6\,x^3+2\,x^4-{\mathrm {e}}^x\,\ln \left (2\right )\,\left (-x^3+2\,x^2+4\,x-8\right )\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*x - log(2)*(2*x - x^2) + 6*x^2 - 4*x^3 - exp(x)*log(2)*(x^2 - 6*x + x^3) + log(log(4/(2*x - log(2)*(x +
2) + 2*x^2 + exp(x)*log(2)*(x + 2))))*log(4/(2*x - log(2)*(x + 2) + 2*x^2 + exp(x)*log(2)*(x + 2)))*(4*x - lo
g(2)*(2*x + 4) + 4*x^2 + exp(x)*log(2)*(2*x + 4)))/(log(log(4/(2*x - log(2)*(x + 2) + 2*x^2 + exp(x)*log(2)*(x
+ 2))))^2*log(4/(2*x - log(2)*(x + 2) + 2*x^2 + exp(x)*log(2)*(x + 2)))*(8*x + log(2)*(4*x + 2*x^2 - x^3 - 8)
- 6*x^3 + 2*x^4 - exp(x)*log(2)*(4*x + 2*x^2 - x^3 - 8))),x)

[Out]

int((4*x - log(2)*(2*x - x^2) + 6*x^2 - 4*x^3 - exp(x)*log(2)*(x^2 - 6*x + x^3) + log(log(4/(2*x - log(2)*(x +
2) + 2*x^2 + exp(x)*log(2)*(x + 2))))*log(4/(2*x - log(2)*(x + 2) + 2*x^2 + exp(x)*log(2)*(x + 2)))*(4*x - lo
g(2)*(2*x + 4) + 4*x^2 + exp(x)*log(2)*(2*x + 4)))/(log(log(4/(2*x - log(2)*(x + 2) + 2*x^2 + exp(x)*log(2)*(x
+ 2))))^2*log(4/(2*x - log(2)*(x + 2) + 2*x^2 + exp(x)*log(2)*(x + 2)))*(8*x + log(2)*(4*x + 2*x^2 - x^3 - 8)
- 6*x^3 + 2*x^4 - exp(x)*log(2)*(4*x + 2*x^2 - x^3 - 8))), x)

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