Integrand size = 141, antiderivative size = 28 \[ \int \frac {e^{\frac {2 \left (3 x-3 x^3+\left (x-x^3\right ) \log (4) \log \left (x^2\right )\right )}{8+3 x+x \log (4) \log \left (x^2\right )}} \left (48-144 x^2-36 x^3+\left (32-32 x^2\right ) \log (4)+\left (16-48 x^2-24 x^3\right ) \log (4) \log \left (x^2\right )-4 x^3 \log ^2(4) \log ^2\left (x^2\right )\right )}{64+48 x+9 x^2+\left (16 x+6 x^2\right ) \log (4) \log \left (x^2\right )+x^2 \log ^2(4) \log ^2\left (x^2\right )} \, dx=e^{\frac {2 \left (x-x^3\right )}{x+\frac {8}{3+\log (4) \log \left (x^2\right )}}} \] Output:
exp((-x^3+x)/(8/(2*ln(2)*ln(x^2)+3)+x))^2
\[ \int \frac {e^{\frac {2 \left (3 x-3 x^3+\left (x-x^3\right ) \log (4) \log \left (x^2\right )\right )}{8+3 x+x \log (4) \log \left (x^2\right )}} \left (48-144 x^2-36 x^3+\left (32-32 x^2\right ) \log (4)+\left (16-48 x^2-24 x^3\right ) \log (4) \log \left (x^2\right )-4 x^3 \log ^2(4) \log ^2\left (x^2\right )\right )}{64+48 x+9 x^2+\left (16 x+6 x^2\right ) \log (4) \log \left (x^2\right )+x^2 \log ^2(4) \log ^2\left (x^2\right )} \, dx=\int \frac {e^{\frac {2 \left (3 x-3 x^3+\left (x-x^3\right ) \log (4) \log \left (x^2\right )\right )}{8+3 x+x \log (4) \log \left (x^2\right )}} \left (48-144 x^2-36 x^3+\left (32-32 x^2\right ) \log (4)+\left (16-48 x^2-24 x^3\right ) \log (4) \log \left (x^2\right )-4 x^3 \log ^2(4) \log ^2\left (x^2\right )\right )}{64+48 x+9 x^2+\left (16 x+6 x^2\right ) \log (4) \log \left (x^2\right )+x^2 \log ^2(4) \log ^2\left (x^2\right )} \, dx \] Input:
Integrate[(E^((2*(3*x - 3*x^3 + (x - x^3)*Log[4]*Log[x^2]))/(8 + 3*x + x*L og[4]*Log[x^2]))*(48 - 144*x^2 - 36*x^3 + (32 - 32*x^2)*Log[4] + (16 - 48* x^2 - 24*x^3)*Log[4]*Log[x^2] - 4*x^3*Log[4]^2*Log[x^2]^2))/(64 + 48*x + 9 *x^2 + (16*x + 6*x^2)*Log[4]*Log[x^2] + x^2*Log[4]^2*Log[x^2]^2),x]
Output:
Integrate[(E^((2*(3*x - 3*x^3 + (x - x^3)*Log[4]*Log[x^2]))/(8 + 3*x + x*L og[4]*Log[x^2]))*(48 - 144*x^2 - 36*x^3 + (32 - 32*x^2)*Log[4] + (16 - 48* x^2 - 24*x^3)*Log[4]*Log[x^2] - 4*x^3*Log[4]^2*Log[x^2]^2))/(64 + 48*x + 9 *x^2 + (16*x + 6*x^2)*Log[4]*Log[x^2] + x^2*Log[4]^2*Log[x^2]^2), x]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (-36 x^3-144 x^2+\left (32-32 x^2\right ) \log (4)-4 x^3 \log ^2(4) \log ^2\left (x^2\right )+\left (-24 x^3-48 x^2+16\right ) \log (4) \log \left (x^2\right )+48\right ) \exp \left (\frac {2 \left (-3 x^3+\left (x-x^3\right ) \log (4) \log \left (x^2\right )+3 x\right )}{x \log (4) \log \left (x^2\right )+3 x+8}\right )}{9 x^2+x^2 \log ^2(4) \log ^2\left (x^2\right )+\left (6 x^2+16 x\right ) \log (4) \log \left (x^2\right )+48 x+64} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (-36 x^3-144 x^2+\left (32-32 x^2\right ) \log (4)-4 x^3 \log ^2(4) \log ^2\left (x^2\right )+\left (-24 x^3-48 x^2+16\right ) \log (4) \log \left (x^2\right )+48\right ) \exp \left (-\frac {2 x \left (x^2-1\right ) \left (\log (4) \log \left (x^2\right )+3\right )}{x \log (4) \log \left (x^2\right )+3 x+8}\right )}{\left (x \log (4) \log \left (x^2\right )+3 x+8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-4 x \exp \left (-\frac {2 x \left (x^2-1\right ) \left (\log (4) \log \left (x^2\right )+3\right )}{x \log (4) \log \left (x^2\right )+3 x+8}\right )+\frac {16 \left (x^2+1\right ) \exp \left (-\frac {2 x \left (x^2-1\right ) \left (\log (4) \log \left (x^2\right )+3\right )}{x \log (4) \log \left (x^2\right )+3 x+8}\right )}{x \left (x \log (4) \log \left (x^2\right )+3 x+8\right )}-\frac {32 \left (x^2-1\right ) (x \log (4)-4) \exp \left (-\frac {2 x \left (x^2-1\right ) \left (\log (4) \log \left (x^2\right )+3\right )}{x \log (4) \log \left (x^2\right )+3 x+8}\right )}{x \left (x \log (4) \log \left (x^2\right )+3 x+8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -4 \int \exp \left (-\frac {2 x \left (x^2-1\right ) \left (\log (4) \log \left (x^2\right )+3\right )}{\log (4) \log \left (x^2\right ) x+3 x+8}\right ) xdx+32 \log (4) \int \frac {\exp \left (-\frac {2 x \left (x^2-1\right ) \left (\log (4) \log \left (x^2\right )+3\right )}{\log (4) \log \left (x^2\right ) x+3 x+8}\right )}{\left (\log (4) \log \left (x^2\right ) x+3 x+8\right )^2}dx-128 \int \frac {\exp \left (-\frac {2 x \left (x^2-1\right ) \left (\log (4) \log \left (x^2\right )+3\right )}{\log (4) \log \left (x^2\right ) x+3 x+8}\right )}{x \left (\log (4) \log \left (x^2\right ) x+3 x+8\right )^2}dx+128 \int \frac {\exp \left (-\frac {2 x \left (x^2-1\right ) \left (\log (4) \log \left (x^2\right )+3\right )}{\log (4) \log \left (x^2\right ) x+3 x+8}\right ) x}{\left (\log (4) \log \left (x^2\right ) x+3 x+8\right )^2}dx-32 \log (4) \int \frac {\exp \left (-\frac {2 x \left (x^2-1\right ) \left (\log (4) \log \left (x^2\right )+3\right )}{\log (4) \log \left (x^2\right ) x+3 x+8}\right ) x^2}{\left (\log (4) \log \left (x^2\right ) x+3 x+8\right )^2}dx+16 \int \frac {\exp \left (-\frac {2 x \left (x^2-1\right ) \left (\log (4) \log \left (x^2\right )+3\right )}{\log (4) \log \left (x^2\right ) x+3 x+8}\right )}{x \left (\log (4) \log \left (x^2\right ) x+3 x+8\right )}dx+16 \int \frac {\exp \left (-\frac {2 x \left (x^2-1\right ) \left (\log (4) \log \left (x^2\right )+3\right )}{\log (4) \log \left (x^2\right ) x+3 x+8}\right ) x}{\log (4) \log \left (x^2\right ) x+3 x+8}dx\) |
Input:
Int[(E^((2*(3*x - 3*x^3 + (x - x^3)*Log[4]*Log[x^2]))/(8 + 3*x + x*Log[4]* Log[x^2]))*(48 - 144*x^2 - 36*x^3 + (32 - 32*x^2)*Log[4] + (16 - 48*x^2 - 24*x^3)*Log[4]*Log[x^2] - 4*x^3*Log[4]^2*Log[x^2]^2))/(64 + 48*x + 9*x^2 + (16*x + 6*x^2)*Log[4]*Log[x^2] + x^2*Log[4]^2*Log[x^2]^2),x]
Output:
$Aborted
Time = 12.26 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.32
| method | result | size |
| risch | \({\mathrm e}^{-\frac {2 x \left (x -1\right ) \left (1+x \right ) \left (2 \ln \left (2\right ) \ln \left (x^{2}\right )+3\right )}{2 x \ln \left (2\right ) \ln \left (x^{2}\right )+3 x +8}}\) | \(37\) |
| parallelrisch | \({\mathrm e}^{\frac {4 \left (-x^{3}+x \right ) \ln \left (2\right ) \ln \left (x^{2}\right )-6 x^{3}+6 x}{2 x \ln \left (2\right ) \ln \left (x^{2}\right )+3 x +8}}\) | \(45\) |
Input:
int((-16*x^3*ln(2)^2*ln(x^2)^2+2*(-24*x^3-48*x^2+16)*ln(2)*ln(x^2)+2*(-32* x^2+32)*ln(2)-36*x^3-144*x^2+48)*exp((2*(-x^3+x)*ln(2)*ln(x^2)-3*x^3+3*x)/ (2*x*ln(2)*ln(x^2)+3*x+8))^2/(4*x^2*ln(2)^2*ln(x^2)^2+2*(6*x^2+16*x)*ln(2) *ln(x^2)+9*x^2+48*x+64),x,method=_RETURNVERBOSE)
Output:
exp(-2*x*(x-1)*(1+x)*(2*ln(2)*ln(x^2)+3)/(2*x*ln(2)*ln(x^2)+3*x+8))
Time = 0.08 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.54 \[ \int \frac {e^{\frac {2 \left (3 x-3 x^3+\left (x-x^3\right ) \log (4) \log \left (x^2\right )\right )}{8+3 x+x \log (4) \log \left (x^2\right )}} \left (48-144 x^2-36 x^3+\left (32-32 x^2\right ) \log (4)+\left (16-48 x^2-24 x^3\right ) \log (4) \log \left (x^2\right )-4 x^3 \log ^2(4) \log ^2\left (x^2\right )\right )}{64+48 x+9 x^2+\left (16 x+6 x^2\right ) \log (4) \log \left (x^2\right )+x^2 \log ^2(4) \log ^2\left (x^2\right )} \, dx=e^{\left (-\frac {2 \, {\left (3 \, x^{3} + 2 \, {\left (x^{3} - x\right )} \log \left (2\right ) \log \left (x^{2}\right ) - 3 \, x\right )}}{2 \, x \log \left (2\right ) \log \left (x^{2}\right ) + 3 \, x + 8}\right )} \] Input:
integrate((-16*x^3*log(2)^2*log(x^2)^2+2*(-24*x^3-48*x^2+16)*log(2)*log(x^ 2)+2*(-32*x^2+32)*log(2)-36*x^3-144*x^2+48)*exp((2*(-x^3+x)*log(2)*log(x^2 )-3*x^3+3*x)/(2*x*log(2)*log(x^2)+3*x+8))^2/(4*x^2*log(2)^2*log(x^2)^2+2*( 6*x^2+16*x)*log(2)*log(x^2)+9*x^2+48*x+64),x, algorithm="fricas")
Output:
e^(-2*(3*x^3 + 2*(x^3 - x)*log(2)*log(x^2) - 3*x)/(2*x*log(2)*log(x^2) + 3 *x + 8))
Time = 0.38 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.57 \[ \int \frac {e^{\frac {2 \left (3 x-3 x^3+\left (x-x^3\right ) \log (4) \log \left (x^2\right )\right )}{8+3 x+x \log (4) \log \left (x^2\right )}} \left (48-144 x^2-36 x^3+\left (32-32 x^2\right ) \log (4)+\left (16-48 x^2-24 x^3\right ) \log (4) \log \left (x^2\right )-4 x^3 \log ^2(4) \log ^2\left (x^2\right )\right )}{64+48 x+9 x^2+\left (16 x+6 x^2\right ) \log (4) \log \left (x^2\right )+x^2 \log ^2(4) \log ^2\left (x^2\right )} \, dx=e^{\frac {2 \left (- 3 x^{3} + 3 x + \left (- 2 x^{3} + 2 x\right ) \log {\left (2 \right )} \log {\left (x^{2} \right )}\right )}{2 x \log {\left (2 \right )} \log {\left (x^{2} \right )} + 3 x + 8}} \] Input:
integrate((-16*x**3*ln(2)**2*ln(x**2)**2+2*(-24*x**3-48*x**2+16)*ln(2)*ln( x**2)+2*(-32*x**2+32)*ln(2)-36*x**3-144*x**2+48)*exp((2*(-x**3+x)*ln(2)*ln (x**2)-3*x**3+3*x)/(2*x*ln(2)*ln(x**2)+3*x+8))**2/(4*x**2*ln(2)**2*ln(x**2 )**2+2*(6*x**2+16*x)*ln(2)*ln(x**2)+9*x**2+48*x+64),x)
Output:
exp(2*(-3*x**3 + 3*x + (-2*x**3 + 2*x)*log(2)*log(x**2))/(2*x*log(2)*log(x **2) + 3*x + 8))
Leaf count of result is larger than twice the leaf count of optimal. 591 vs. \(2 (28) = 56\).
Time = 9.92 (sec) , antiderivative size = 591, normalized size of antiderivative = 21.11 \[ \int \frac {e^{\frac {2 \left (3 x-3 x^3+\left (x-x^3\right ) \log (4) \log \left (x^2\right )\right )}{8+3 x+x \log (4) \log \left (x^2\right )}} \left (48-144 x^2-36 x^3+\left (32-32 x^2\right ) \log (4)+\left (16-48 x^2-24 x^3\right ) \log (4) \log \left (x^2\right )-4 x^3 \log ^2(4) \log ^2\left (x^2\right )\right )}{64+48 x+9 x^2+\left (16 x+6 x^2\right ) \log (4) \log \left (x^2\right )+x^2 \log ^2(4) \log ^2\left (x^2\right )} \, dx=\text {Too large to display} \] Input:
integrate((-16*x^3*log(2)^2*log(x^2)^2+2*(-24*x^3-48*x^2+16)*log(2)*log(x^ 2)+2*(-32*x^2+32)*log(2)-36*x^3-144*x^2+48)*exp((2*(-x^3+x)*log(2)*log(x^2 )-3*x^3+3*x)/(2*x*log(2)*log(x^2)+3*x+8))^2/(4*x^2*log(2)^2*log(x^2)^2+2*( 6*x^2+16*x)*log(2)*log(x^2)+9*x^2+48*x+64),x, algorithm="maxima")
Output:
e^(-128*x^2*log(2)^3*log(x)^3/(64*log(2)^3*log(x)^3 + 144*log(2)^2*log(x)^ 2 + 108*log(2)*log(x) + 27) - 288*x^2*log(2)^2*log(x)^2/(64*log(2)^3*log(x )^3 + 144*log(2)^2*log(x)^2 + 108*log(2)*log(x) + 27) + 256*x*log(2)^2*log (x)^2/(64*log(2)^3*log(x)^3 + 144*log(2)^2*log(x)^2 + 108*log(2)*log(x) + 27) - 216*x^2*log(2)*log(x)/(64*log(2)^3*log(x)^3 + 144*log(2)^2*log(x)^2 + 108*log(2)*log(x) + 27) + 384*x*log(2)*log(x)/(64*log(2)^3*log(x)^3 + 14 4*log(2)^2*log(x)^2 + 108*log(2)*log(x) + 27) - 54*x^2/(64*log(2)^3*log(x) ^3 + 144*log(2)^2*log(x)^2 + 108*log(2)*log(x) + 27) + 4096*log(2)*log(x)/ (256*x*log(2)^4*log(x)^4 + 256*(3*x*log(2)^3 + 2*log(2)^3)*log(x)^3 + 288* (3*x*log(2)^2 + 4*log(2)^2)*log(x)^2 + 432*(x*log(2) + 2*log(2))*log(x) + 81*x + 216) - 512*log(2)*log(x)/(64*log(2)^3*log(x)^3 + 144*log(2)^2*log(x )^2 + 108*log(2)*log(x) + 27) - 64*log(2)*log(x)/(16*x*log(2)^2*log(x)^2 + 8*(3*x*log(2) + 4*log(2))*log(x) + 9*x + 24) + 8*log(2)*log(x)/(4*log(2)* log(x) + 3) + 144*x/(64*log(2)^3*log(x)^3 + 144*log(2)^2*log(x)^2 + 108*lo g(2)*log(x) + 27) + 3072/(256*x*log(2)^4*log(x)^4 + 256*(3*x*log(2)^3 + 2* log(2)^3)*log(x)^3 + 288*(3*x*log(2)^2 + 4*log(2)^2)*log(x)^2 + 432*(x*log (2) + 2*log(2))*log(x) + 81*x + 216) - 384/(64*log(2)^3*log(x)^3 + 144*log (2)^2*log(x)^2 + 108*log(2)*log(x) + 27) - 48/(16*x*log(2)^2*log(x)^2 + 8* (3*x*log(2) + 4*log(2))*log(x) + 9*x + 24) + 6/(4*log(2)*log(x) + 3))
Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (28) = 56\).
Time = 0.34 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.36 \[ \int \frac {e^{\frac {2 \left (3 x-3 x^3+\left (x-x^3\right ) \log (4) \log \left (x^2\right )\right )}{8+3 x+x \log (4) \log \left (x^2\right )}} \left (48-144 x^2-36 x^3+\left (32-32 x^2\right ) \log (4)+\left (16-48 x^2-24 x^3\right ) \log (4) \log \left (x^2\right )-4 x^3 \log ^2(4) \log ^2\left (x^2\right )\right )}{64+48 x+9 x^2+\left (16 x+6 x^2\right ) \log (4) \log \left (x^2\right )+x^2 \log ^2(4) \log ^2\left (x^2\right )} \, dx=e^{\left (-\frac {4 \, x^{3} \log \left (2\right ) \log \left (x^{2}\right )}{2 \, x \log \left (2\right ) \log \left (x^{2}\right ) + 3 \, x + 8} - \frac {6 \, x^{3}}{2 \, x \log \left (2\right ) \log \left (x^{2}\right ) + 3 \, x + 8} + \frac {4 \, x \log \left (2\right ) \log \left (x^{2}\right )}{2 \, x \log \left (2\right ) \log \left (x^{2}\right ) + 3 \, x + 8} + \frac {6 \, x}{2 \, x \log \left (2\right ) \log \left (x^{2}\right ) + 3 \, x + 8}\right )} \] Input:
integrate((-16*x^3*log(2)^2*log(x^2)^2+2*(-24*x^3-48*x^2+16)*log(2)*log(x^ 2)+2*(-32*x^2+32)*log(2)-36*x^3-144*x^2+48)*exp((2*(-x^3+x)*log(2)*log(x^2 )-3*x^3+3*x)/(2*x*log(2)*log(x^2)+3*x+8))^2/(4*x^2*log(2)^2*log(x^2)^2+2*( 6*x^2+16*x)*log(2)*log(x^2)+9*x^2+48*x+64),x, algorithm="giac")
Output:
e^(-4*x^3*log(2)*log(x^2)/(2*x*log(2)*log(x^2) + 3*x + 8) - 6*x^3/(2*x*log (2)*log(x^2) + 3*x + 8) + 4*x*log(2)*log(x^2)/(2*x*log(2)*log(x^2) + 3*x + 8) + 6*x/(2*x*log(2)*log(x^2) + 3*x + 8))
Time = 0.71 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.71 \[ \int \frac {e^{\frac {2 \left (3 x-3 x^3+\left (x-x^3\right ) \log (4) \log \left (x^2\right )\right )}{8+3 x+x \log (4) \log \left (x^2\right )}} \left (48-144 x^2-36 x^3+\left (32-32 x^2\right ) \log (4)+\left (16-48 x^2-24 x^3\right ) \log (4) \log \left (x^2\right )-4 x^3 \log ^2(4) \log ^2\left (x^2\right )\right )}{64+48 x+9 x^2+\left (16 x+6 x^2\right ) \log (4) \log \left (x^2\right )+x^2 \log ^2(4) \log ^2\left (x^2\right )} \, dx={\mathrm {e}}^{\frac {6\,x}{3\,x+2\,x\,\ln \left (x^2\right )\,\ln \left (2\right )+8}}\,{\mathrm {e}}^{-\frac {6\,x^3}{3\,x+2\,x\,\ln \left (x^2\right )\,\ln \left (2\right )+8}}\,{\left (x^8\right )}^{\frac {x\,\ln \left (2\right )-x^3\,\ln \left (2\right )}{3\,x+2\,x\,\ln \left (x^2\right )\,\ln \left (2\right )+8}} \] Input:
int(-(exp((2*(3*x - 3*x^3 + 2*log(x^2)*log(2)*(x - x^3)))/(3*x + 2*x*log(x ^2)*log(2) + 8))*(2*log(2)*(32*x^2 - 32) + 144*x^2 + 36*x^3 + 16*x^3*log(x ^2)^2*log(2)^2 + 2*log(x^2)*log(2)*(48*x^2 + 24*x^3 - 16) - 48))/(48*x + 9 *x^2 + 2*log(x^2)*log(2)*(16*x + 6*x^2) + 4*x^2*log(x^2)^2*log(2)^2 + 64), x)
Output:
exp((6*x)/(3*x + 2*x*log(x^2)*log(2) + 8))*exp(-(6*x^3)/(3*x + 2*x*log(x^2 )*log(2) + 8))*(x^8)^((x*log(2) - x^3*log(2))/(3*x + 2*x*log(x^2)*log(2) + 8))
\[ \int \frac {e^{\frac {2 \left (3 x-3 x^3+\left (x-x^3\right ) \log (4) \log \left (x^2\right )\right )}{8+3 x+x \log (4) \log \left (x^2\right )}} \left (48-144 x^2-36 x^3+\left (32-32 x^2\right ) \log (4)+\left (16-48 x^2-24 x^3\right ) \log (4) \log \left (x^2\right )-4 x^3 \log ^2(4) \log ^2\left (x^2\right )\right )}{64+48 x+9 x^2+\left (16 x+6 x^2\right ) \log (4) \log \left (x^2\right )+x^2 \log ^2(4) \log ^2\left (x^2\right )} \, dx=\int \frac {\left (-16 x^{3} \mathrm {log}\left (2\right )^{2} \mathrm {log}\left (x^{2}\right )^{2}+2 \left (-24 x^{3}-48 x^{2}+16\right ) \mathrm {log}\left (2\right ) \mathrm {log}\left (x^{2}\right )+2 \left (-32 x^{2}+32\right ) \mathrm {log}\left (2\right )-36 x^{3}-144 x^{2}+48\right ) \left ({\mathrm e}^{\frac {2 \left (-x^{3}+x \right ) \mathrm {log}\left (2\right ) \mathrm {log}\left (x^{2}\right )-3 x^{3}+3 x}{2 x \,\mathrm {log}\left (2\right ) \mathrm {log}\left (x^{2}\right )+3 x +8}}\right )^{2}}{4 x^{2} \mathrm {log}\left (2\right )^{2} \mathrm {log}\left (x^{2}\right )^{2}+2 \left (6 x^{2}+16 x \right ) \mathrm {log}\left (2\right ) \mathrm {log}\left (x^{2}\right )+9 x^{2}+48 x +64}d x \] Input:
int((-16*x^3*log(2)^2*log(x^2)^2+2*(-24*x^3-48*x^2+16)*log(2)*log(x^2)+2*( -32*x^2+32)*log(2)-36*x^3-144*x^2+48)*exp((2*(-x^3+x)*log(2)*log(x^2)-3*x^ 3+3*x)/(2*x*log(2)*log(x^2)+3*x+8))^2/(4*x^2*log(2)^2*log(x^2)^2+2*(6*x^2+ 16*x)*log(2)*log(x^2)+9*x^2+48*x+64),x)
Output:
int((-16*x^3*log(2)^2*log(x^2)^2+2*(-24*x^3-48*x^2+16)*log(2)*log(x^2)+2*( -32*x^2+32)*log(2)-36*x^3-144*x^2+48)*exp((2*(-x^3+x)*log(2)*log(x^2)-3*x^ 3+3*x)/(2*x*log(2)*log(x^2)+3*x+8))^2/(4*x^2*log(2)^2*log(x^2)^2+2*(6*x^2+ 16*x)*log(2)*log(x^2)+9*x^2+48*x+64),x)