\(\int \frac {36+72 x+48 x^3-4 x^4+8 x^5+(-9 x-6 x^3-x^5+e^{4 x} (6 x^3-x^3 \log (4))) \log ^2(\frac {e^{-4 x} (9+6 x^2+x^4+e^{4 x} (-6 x^2+x^2 \log (4)))}{x^2})}{(9 x+6 x^3+x^5+e^{4 x} (-6 x^3+x^3 \log (4))) \log ^2(\frac {e^{-4 x} (9+6 x^2+x^4+e^{4 x} (-6 x^2+x^2 \log (4)))}{x^2})} \, dx\) [2229]

Optimal result

Integrand size = 167, antiderivative size = 28 \[ \int \frac {36+72 x+48 x^3-4 x^4+8 x^5+\left (-9 x-6 x^3-x^5+e^{4 x} \left (6 x^3-x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )}{\left (9 x+6 x^3+x^5+e^{4 x} \left (-6 x^3+x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )} \, dx=-x+\frac {2}{\log \left (-6+e^{-4 x} \left (\frac {3}{x}+x\right )^2+\log (4)\right )} \]

[Out]

2/ln((x+3/x)^2/exp(x)^4-6+2*ln(2))-x

Rubi [F]

\[ \int \frac {36+72 x+48 x^3-4 x^4+8 x^5+\left (-9 x-6 x^3-x^5+e^{4 x} \left (6 x^3-x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )}{\left (9 x+6 x^3+x^5+e^{4 x} \left (-6 x^3+x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )} \, dx=\int \frac {36+72 x+48 x^3-4 x^4+8 x^5+\left (-9 x-6 x^3-x^5+e^{4 x} \left (6 x^3-x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )}{\left (9 x+6 x^3+x^5+e^{4 x} \left (-6 x^3+x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )} \, dx \]

[In]

Int[(36 + 72*x + 48*x^3 - 4*x^4 + 8*x^5 + (-9*x - 6*x^3 - x^5 + E^(4*x)*(6*x^3 - x^3*Log[4]))*Log[(9 + 6*x^2 +
x^4 + E^(4*x)*(-6*x^2 + x^2*Log[4]))/(E^(4*x)*x^2)]^2)/((9*x + 6*x^3 + x^5 + E^(4*x)*(-6*x^3 + x^3*Log[4]))*L
og[(9 + 6*x^2 + x^4 + E^(4*x)*(-6*x^2 + x^2*Log[4]))/(E^(4*x)*x^2)]^2),x]

[Out]

-x + 72*Defer[Int][1/((9 + 6*x^2 + x^4 - 6*E^(4*x)*x^2*(1 - Log[2]/3))*Log[(9 + x^4 + x^2*(6 + E^(4*x)*(-6 + L
og[4])))/(E^(4*x)*x^2)]^2), x] + 36*Defer[Int][1/(x*(9 + 6*x^2 + x^4 - 6*E^(4*x)*x^2*(1 - Log[2]/3))*Log[(9 +
x^4 + x^2*(6 + E^(4*x)*(-6 + Log[4])))/(E^(4*x)*x^2)]^2), x] + 48*Defer[Int][x^2/((9 + 6*x^2 + x^4 - 6*E^(4*x)
*x^2*(1 - Log[2]/3))*Log[(9 + x^4 + x^2*(6 + E^(4*x)*(-6 + Log[4])))/(E^(4*x)*x^2)]^2), x] + 8*Defer[Int][x^4/
((9 + 6*x^2 + x^4 - 6*E^(4*x)*x^2*(1 - Log[2]/3))*Log[(9 + x^4 + x^2*(6 + E^(4*x)*(-6 + Log[4])))/(E^(4*x)*x^2
)]^2), x] + 4*Defer[Int][x^3/((-9 - 6*x^2 - x^4 + 6*E^(4*x)*x^2*(1 - Log[2]/3))*Log[(9 + x^4 + x^2*(6 + E^(4*x
)*(-6 + Log[4])))/(E^(4*x)*x^2)]^2), x]

Rubi steps \begin{align*} \text {integral}& = \int \left (-1+\frac {4 \left (3+x^2\right ) \left (3+6 x-x^2+2 x^3\right )}{x \left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )}\right ) \, dx \\ & = -x+4 \int \frac {\left (3+x^2\right ) \left (3+6 x-x^2+2 x^3\right )}{x \left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )} \, dx \\ & = -x+4 \int \left (\frac {18}{\left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )}+\frac {9}{x \left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )}+\frac {12 x^2}{\left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )}+\frac {2 x^4}{\left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )}+\frac {x^3}{\left (-9-6 x^2-x^4+6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )}\right ) \, dx \\ & = -x+4 \int \frac {x^3}{\left (-9-6 x^2-x^4+6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )} \, dx+8 \int \frac {x^4}{\left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )} \, dx+36 \int \frac {1}{x \left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )} \, dx+48 \int \frac {x^2}{\left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )} \, dx+72 \int \frac {1}{\left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.10 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.39 \[ \int \frac {36+72 x+48 x^3-4 x^4+8 x^5+\left (-9 x-6 x^3-x^5+e^{4 x} \left (6 x^3-x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )}{\left (9 x+6 x^3+x^5+e^{4 x} \left (-6 x^3+x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )} \, dx=-x+\frac {2}{\log \left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )} \]

[In]

Integrate[(36 + 72*x + 48*x^3 - 4*x^4 + 8*x^5 + (-9*x - 6*x^3 - x^5 + E^(4*x)*(6*x^3 - x^3*Log[4]))*Log[(9 + 6
*x^2 + x^4 + E^(4*x)*(-6*x^2 + x^2*Log[4]))/(E^(4*x)*x^2)]^2)/((9*x + 6*x^3 + x^5 + E^(4*x)*(-6*x^3 + x^3*Log[
4]))*Log[(9 + 6*x^2 + x^4 + E^(4*x)*(-6*x^2 + x^2*Log[4]))/(E^(4*x)*x^2)]^2),x]

[Out]

-x + 2/Log[(9 + x^4 + x^2*(6 + E^(4*x)*(-6 + Log[4])))/(E^(4*x)*x^2)]

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(82\) vs. \(2(29)=58\).

Time = 26.56 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.96

method	result	size
norman	\(\frac {2-x \ln \left (\frac {\left (\left (2 x^{2} \ln \left (2\right )-6 x^{2}\right ) {\mathrm e}^{4 x}+x^{4}+6 x^{2}+9\right ) {\mathrm e}^{-4 x}}{x^{2}}\right )}{\ln \left (\frac {\left (\left (2 x^{2} \ln \left (2\right )-6 x^{2}\right ) {\mathrm e}^{4 x}+x^{4}+6 x^{2}+9\right ) {\mathrm e}^{-4 x}}{x^{2}}\right )}\)	\(83\)
parallelrisch	\(-\frac {-2+x \ln \left (\frac {\left (\left (2 x^{2} \ln \left (2\right )-6 x^{2}\right ) {\mathrm e}^{4 x}+x^{4}+6 x^{2}+9\right ) {\mathrm e}^{-4 x}}{x^{2}}\right )}{\ln \left (\frac {\left (\left (2 x^{2} \ln \left (2\right )-6 x^{2}\right ) {\mathrm e}^{4 x}+x^{4}+6 x^{2}+9\right ) {\mathrm e}^{-4 x}}{x^{2}}\right )}\)	\(83\)
risch	\(\text {Expression too large to display}\)	\(815\)

[In]

int((((-2*x^3*ln(2)+6*x^3)*exp(x)^4-x^5-6*x^3-9*x)*ln(((2*x^2*ln(2)-6*x^2)*exp(x)^4+x^4+6*x^2+9)/x^2/exp(x)^4)
^2+8*x^5-4*x^4+48*x^3+72*x+36)/((2*x^3*ln(2)-6*x^3)*exp(x)^4+x^5+6*x^3+9*x)/ln(((2*x^2*ln(2)-6*x^2)*exp(x)^4+x
^4+6*x^2+9)/x^2/exp(x)^4)^2,x,method=_RETURNVERBOSE)

[Out]

(2-x*ln(((2*x^2*ln(2)-6*x^2)*exp(x)^4+x^4+6*x^2+9)/x^2/exp(x)^4))/ln(((2*x^2*ln(2)-6*x^2)*exp(x)^4+x^4+6*x^2+9
)/x^2/exp(x)^4)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (29) = 58\).

Time = 0.25 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.93 \[ \int \frac {36+72 x+48 x^3-4 x^4+8 x^5+\left (-9 x-6 x^3-x^5+e^{4 x} \left (6 x^3-x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )}{\left (9 x+6 x^3+x^5+e^{4 x} \left (-6 x^3+x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )} \, dx=-\frac {x \log \left (\frac {{\left (x^{4} + 6 \, x^{2} + 2 \, {\left (x^{2} \log \left (2\right ) - 3 \, x^{2}\right )} e^{\left (4 \, x\right )} + 9\right )} e^{\left (-4 \, x\right )}}{x^{2}}\right ) - 2}{\log \left (\frac {{\left (x^{4} + 6 \, x^{2} + 2 \, {\left (x^{2} \log \left (2\right ) - 3 \, x^{2}\right )} e^{\left (4 \, x\right )} + 9\right )} e^{\left (-4 \, x\right )}}{x^{2}}\right )} \]

[In]

integrate((((-2*x^3*log(2)+6*x^3)*exp(x)^4-x^5-6*x^3-9*x)*log(((2*x^2*log(2)-6*x^2)*exp(x)^4+x^4+6*x^2+9)/x^2/
exp(x)^4)^2+8*x^5-4*x^4+48*x^3+72*x+36)/((2*x^3*log(2)-6*x^3)*exp(x)^4+x^5+6*x^3+9*x)/log(((2*x^2*log(2)-6*x^2
)*exp(x)^4+x^4+6*x^2+9)/x^2/exp(x)^4)^2,x, algorithm="fricas")

[Out]

-(x*log((x^4 + 6*x^2 + 2*(x^2*log(2) - 3*x^2)*e^(4*x) + 9)*e^(-4*x)/x^2) - 2)/log((x^4 + 6*x^2 + 2*(x^2*log(2)
- 3*x^2)*e^(4*x) + 9)*e^(-4*x)/x^2)

Sympy [A] (verification not implemented)

Time = 0.25 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.46 \[ \int \frac {36+72 x+48 x^3-4 x^4+8 x^5+\left (-9 x-6 x^3-x^5+e^{4 x} \left (6 x^3-x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )}{\left (9 x+6 x^3+x^5+e^{4 x} \left (-6 x^3+x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )} \, dx=- x + \frac {2}{\log {\left (\frac {\left (x^{4} + 6 x^{2} + \left (- 6 x^{2} + 2 x^{2} \log {\left (2 \right )}\right ) e^{4 x} + 9\right ) e^{- 4 x}}{x^{2}} \right )}} \]

[In]

integrate((((-2*x**3*ln(2)+6*x**3)*exp(x)**4-x**5-6*x**3-9*x)*ln(((2*x**2*ln(2)-6*x**2)*exp(x)**4+x**4+6*x**2+
9)/x**2/exp(x)**4)**2+8*x**5-4*x**4+48*x**3+72*x+36)/((2*x**3*ln(2)-6*x**3)*exp(x)**4+x**5+6*x**3+9*x)/ln(((2*
x**2*ln(2)-6*x**2)*exp(x)**4+x**4+6*x**2+9)/x**2/exp(x)**4)**2,x)

[Out]

-x + 2/log((x**4 + 6*x**2 + (-6*x**2 + 2*x**2*log(2))*exp(4*x) + 9)*exp(-4*x)/x**2)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 77 vs. \(2 (29) = 58\).

Time = 0.40 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.75 \[ \int \frac {36+72 x+48 x^3-4 x^4+8 x^5+\left (-9 x-6 x^3-x^5+e^{4 x} \left (6 x^3-x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )}{\left (9 x+6 x^3+x^5+e^{4 x} \left (-6 x^3+x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )} \, dx=-\frac {4 \, x^{2} - x \log \left (x^{4} + 2 \, x^{2} {\left (\log \left (2\right ) - 3\right )} e^{\left (4 \, x\right )} + 6 \, x^{2} + 9\right ) + 2 \, x \log \left (x\right ) + 2}{4 \, x - \log \left (x^{4} + 2 \, x^{2} {\left (\log \left (2\right ) - 3\right )} e^{\left (4 \, x\right )} + 6 \, x^{2} + 9\right ) + 2 \, \log \left (x\right )} \]

[In]

integrate((((-2*x^3*log(2)+6*x^3)*exp(x)^4-x^5-6*x^3-9*x)*log(((2*x^2*log(2)-6*x^2)*exp(x)^4+x^4+6*x^2+9)/x^2/
exp(x)^4)^2+8*x^5-4*x^4+48*x^3+72*x+36)/((2*x^3*log(2)-6*x^3)*exp(x)^4+x^5+6*x^3+9*x)/log(((2*x^2*log(2)-6*x^2
)*exp(x)^4+x^4+6*x^2+9)/x^2/exp(x)^4)^2,x, algorithm="maxima")

[Out]

-(4*x^2 - x*log(x^4 + 2*x^2*(log(2) - 3)*e^(4*x) + 6*x^2 + 9) + 2*x*log(x) + 2)/(4*x - log(x^4 + 2*x^2*(log(2)
- 3)*e^(4*x) + 6*x^2 + 9) + 2*log(x))

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (29) = 58\).

Time = 2.15 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.36 \[ \int \frac {36+72 x+48 x^3-4 x^4+8 x^5+\left (-9 x-6 x^3-x^5+e^{4 x} \left (6 x^3-x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )}{\left (9 x+6 x^3+x^5+e^{4 x} \left (-6 x^3+x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )} \, dx=-\frac {x \log \left (x^{2}\right ) - x \log \left ({\left (x^{4} + 2 \, x^{2} e^{\left (4 \, x\right )} \log \left (2\right ) - 6 \, x^{2} e^{\left (4 \, x\right )} + 6 \, x^{2} + 9\right )} e^{\left (-4 \, x\right )}\right ) + 2}{\log \left (x^{2}\right ) - \log \left ({\left (x^{4} + 2 \, x^{2} e^{\left (4 \, x\right )} \log \left (2\right ) - 6 \, x^{2} e^{\left (4 \, x\right )} + 6 \, x^{2} + 9\right )} e^{\left (-4 \, x\right )}\right )} \]

[In]

integrate((((-2*x^3*log(2)+6*x^3)*exp(x)^4-x^5-6*x^3-9*x)*log(((2*x^2*log(2)-6*x^2)*exp(x)^4+x^4+6*x^2+9)/x^2/
exp(x)^4)^2+8*x^5-4*x^4+48*x^3+72*x+36)/((2*x^3*log(2)-6*x^3)*exp(x)^4+x^5+6*x^3+9*x)/log(((2*x^2*log(2)-6*x^2
)*exp(x)^4+x^4+6*x^2+9)/x^2/exp(x)^4)^2,x, algorithm="giac")

[Out]

-(x*log(x^2) - x*log((x^4 + 2*x^2*e^(4*x)*log(2) - 6*x^2*e^(4*x) + 6*x^2 + 9)*e^(-4*x)) + 2)/(log(x^2) - log((
x^4 + 2*x^2*e^(4*x)*log(2) - 6*x^2*e^(4*x) + 6*x^2 + 9)*e^(-4*x)))

Mupad [B] (verification not implemented)

Time = 9.86 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.61 \[ \int \frac {36+72 x+48 x^3-4 x^4+8 x^5+\left (-9 x-6 x^3-x^5+e^{4 x} \left (6 x^3-x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )}{\left (9 x+6 x^3+x^5+e^{4 x} \left (-6 x^3+x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )} \, dx=\frac {2}{\ln \left (\frac {{\mathrm {e}}^{-4\,x}\,\left ({\mathrm {e}}^{4\,x}\,\left (2\,x^2\,\ln \left (2\right )-6\,x^2\right )+6\,x^2+x^4+9\right )}{x^2}\right )}-x \]

[In]

int((72*x + 48*x^3 - 4*x^4 + 8*x^5 - log((exp(-4*x)*(exp(4*x)*(2*x^2*log(2) - 6*x^2) + 6*x^2 + x^4 + 9))/x^2)^
2*(9*x + exp(4*x)*(2*x^3*log(2) - 6*x^3) + 6*x^3 + x^5) + 36)/(log((exp(-4*x)*(exp(4*x)*(2*x^2*log(2) - 6*x^2)
+ 6*x^2 + x^4 + 9))/x^2)^2*(9*x + exp(4*x)*(2*x^3*log(2) - 6*x^3) + 6*x^3 + x^5)),x)

[Out]

2/log((exp(-4*x)*(exp(4*x)*(2*x^2*log(2) - 6*x^2) + 6*x^2 + x^4 + 9))/x^2) - x