Integrand size = 284, antiderivative size = 27 \[ \int \frac {-16 e^{2 x} x^2-32 e^{3 x} x^2+e^{4 x} \left (-80-16 x^2\right )+\left (e^{4 x} \left (-80-48 x^2\right )+e^{3 x} \left (-96 x^2+32 x^3\right )+e^{2 x} \left (-48 x^2+32 x^3\right )+\left (e^{4 x} \left (-80-48 x^2\right )+e^{3 x} \left (-96 x^2+32 x^3\right )+e^{2 x} \left (-48 x^2+32 x^3\right )\right ) \log (x)\right ) \log (1+\log (x))}{\left (x^6+4 e^x x^6+e^{4 x} \left (25 x^2+10 x^4+x^6\right )+e^{3 x} \left (20 x^4+4 x^6\right )+e^{2 x} \left (10 x^4+6 x^6\right )+\left (x^6+4 e^x x^6+e^{4 x} \left (25 x^2+10 x^4+x^6\right )+e^{3 x} \left (20 x^4+4 x^6\right )+e^{2 x} \left (10 x^4+6 x^6\right )\right ) \log (x)\right ) \log ^2(1+\log (x))} \, dx=\frac {16}{x \left (5+\left (x+e^{-x} x\right )^2\right ) \log (1+\log (x))} \] Output:
16/x/ln(1+ln(x))/(5+(x/exp(x)+x)^2)
Time = 0.11 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.56 \[ \int \frac {-16 e^{2 x} x^2-32 e^{3 x} x^2+e^{4 x} \left (-80-16 x^2\right )+\left (e^{4 x} \left (-80-48 x^2\right )+e^{3 x} \left (-96 x^2+32 x^3\right )+e^{2 x} \left (-48 x^2+32 x^3\right )+\left (e^{4 x} \left (-80-48 x^2\right )+e^{3 x} \left (-96 x^2+32 x^3\right )+e^{2 x} \left (-48 x^2+32 x^3\right )\right ) \log (x)\right ) \log (1+\log (x))}{\left (x^6+4 e^x x^6+e^{4 x} \left (25 x^2+10 x^4+x^6\right )+e^{3 x} \left (20 x^4+4 x^6\right )+e^{2 x} \left (10 x^4+6 x^6\right )+\left (x^6+4 e^x x^6+e^{4 x} \left (25 x^2+10 x^4+x^6\right )+e^{3 x} \left (20 x^4+4 x^6\right )+e^{2 x} \left (10 x^4+6 x^6\right )\right ) \log (x)\right ) \log ^2(1+\log (x))} \, dx=\frac {16 e^{2 x}}{x \left (x^2+2 e^x x^2+e^{2 x} \left (5+x^2\right )\right ) \log (1+\log (x))} \] Input:
Integrate[(-16*E^(2*x)*x^2 - 32*E^(3*x)*x^2 + E^(4*x)*(-80 - 16*x^2) + (E^ (4*x)*(-80 - 48*x^2) + E^(3*x)*(-96*x^2 + 32*x^3) + E^(2*x)*(-48*x^2 + 32* x^3) + (E^(4*x)*(-80 - 48*x^2) + E^(3*x)*(-96*x^2 + 32*x^3) + E^(2*x)*(-48 *x^2 + 32*x^3))*Log[x])*Log[1 + Log[x]])/((x^6 + 4*E^x*x^6 + E^(4*x)*(25*x ^2 + 10*x^4 + x^6) + E^(3*x)*(20*x^4 + 4*x^6) + E^(2*x)*(10*x^4 + 6*x^6) + (x^6 + 4*E^x*x^6 + E^(4*x)*(25*x^2 + 10*x^4 + x^6) + E^(3*x)*(20*x^4 + 4* x^6) + E^(2*x)*(10*x^4 + 6*x^6))*Log[x])*Log[1 + Log[x]]^2),x]
Output:
(16*E^(2*x))/(x*(x^2 + 2*E^x*x^2 + E^(2*x)*(5 + x^2))*Log[1 + Log[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.
| \(\displaystyle \int \frac {-16 e^{2 x} x^2-32 e^{3 x} x^2+e^{4 x} \left (-16 x^2-80\right )+\left (e^{4 x} \left (-48 x^2-80\right )+e^{3 x} \left (32 x^3-96 x^2\right )+e^{2 x} \left (32 x^3-48 x^2\right )+\left (e^{4 x} \left (-48 x^2-80\right )+e^{3 x} \left (32 x^3-96 x^2\right )+e^{2 x} \left (32 x^3-48 x^2\right )\right ) \log (x)\right ) \log (\log (x)+1)}{\left (4 e^x x^6+x^6+e^{3 x} \left (4 x^6+20 x^4\right )+e^{2 x} \left (6 x^6+10 x^4\right )+e^{4 x} \left (x^6+10 x^4+25 x^2\right )+\left (4 e^x x^6+x^6+e^{3 x} \left (4 x^6+20 x^4\right )+e^{2 x} \left (6 x^6+10 x^4\right )+e^{4 x} \left (x^6+10 x^4+25 x^2\right )\right ) \log (x)\right ) \log ^2(\log (x)+1)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {16 e^{2 x} \left (-2 e^x x^2-x^2-e^{2 x} \left (x^2+5\right )-\left ((3-2 x) x^2-2 e^x (x-3) x^2+e^{2 x} \left (3 x^2+5\right )\right ) (\log (x)+1) \log (\log (x)+1)\right )}{x^2 \left (2 e^x x^2+x^2+e^{2 x} \left (x^2+5\right )\right )^2 (\log (x)+1) \log ^2(\log (x)+1)}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 16 \int -\frac {e^{2 x} \left (2 e^x x^2+x^2+e^{2 x} \left (x^2+5\right )+\left ((3-2 x) x^2+2 e^x (3-x) x^2+e^{2 x} \left (3 x^2+5\right )\right ) (\log (x)+1) \log (\log (x)+1)\right )}{x^2 \left (2 e^x x^2+x^2+e^{2 x} \left (x^2+5\right )\right )^2 (\log (x)+1) \log ^2(\log (x)+1)}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -16 \int \frac {e^{2 x} \left (2 e^x x^2+x^2+e^{2 x} \left (x^2+5\right )+\left ((3-2 x) x^2+2 e^x (3-x) x^2+e^{2 x} \left (3 x^2+5\right )\right ) (\log (x)+1) \log (\log (x)+1)\right )}{x^2 \left (2 e^x x^2+x^2+e^{2 x} \left (x^2+5\right )\right )^2 (\log (x)+1) \log ^2(\log (x)+1)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -16 \int \left (\frac {e^{2 x} \left (3 \log (x) \log (\log (x)+1) x^2+3 \log (\log (x)+1) x^2+x^2+5 \log (x) \log (\log (x)+1)+5 \log (\log (x)+1)+5\right )}{x^2 \left (x^2+5\right ) \left (2 e^x x^2+e^{2 x} x^2+x^2+5 e^{2 x}\right ) (\log (x)+1) \log ^2(\log (x)+1)}-\frac {2 e^{2 x} \left (e^x x^3+x^3+5 e^x x+5 x-10 e^x-5\right )}{\left (x^2+5\right ) \left (2 e^x x^2+e^{2 x} x^2+x^2+5 e^{2 x}\right )^2 \log (\log (x)+1)}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle -16 \int \left (\frac {e^{2 x} \left (3 \log (x) \log (\log (x)+1) x^2+3 \log (\log (x)+1) x^2+x^2+5 \log (x) \log (\log (x)+1)+5 \log (\log (x)+1)+5\right )}{x^2 \left (x^2+5\right ) \left (2 e^x x^2+e^{2 x} x^2+x^2+5 e^{2 x}\right ) (\log (x)+1) \log ^2(\log (x)+1)}-\frac {2 e^{2 x} \left (e^x x^3+x^3+5 e^x x+5 x-10 e^x-5\right )}{\left (x^2+5\right ) \left (2 e^x x^2+e^{2 x} x^2+x^2+5 e^{2 x}\right )^2 \log (\log (x)+1)}\right )dx\) |
Input:
Int[(-16*E^(2*x)*x^2 - 32*E^(3*x)*x^2 + E^(4*x)*(-80 - 16*x^2) + (E^(4*x)* (-80 - 48*x^2) + E^(3*x)*(-96*x^2 + 32*x^3) + E^(2*x)*(-48*x^2 + 32*x^3) + (E^(4*x)*(-80 - 48*x^2) + E^(3*x)*(-96*x^2 + 32*x^3) + E^(2*x)*(-48*x^2 + 32*x^3))*Log[x])*Log[1 + Log[x]])/((x^6 + 4*E^x*x^6 + E^(4*x)*(25*x^2 + 1 0*x^4 + x^6) + E^(3*x)*(20*x^4 + 4*x^6) + E^(2*x)*(10*x^4 + 6*x^6) + (x^6 + 4*E^x*x^6 + E^(4*x)*(25*x^2 + 10*x^4 + x^6) + E^(3*x)*(20*x^4 + 4*x^6) + E^(2*x)*(10*x^4 + 6*x^6))*Log[x])*Log[1 + Log[x]]^2),x]
Output:
$Aborted
Time = 0.04 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.63
\[\frac {16 \,{\mathrm e}^{2 x}}{\left ({\mathrm e}^{2 x} x^{2}+2 \,{\mathrm e}^{x} x^{2}+x^{2}+5 \,{\mathrm e}^{2 x}\right ) x \ln \left (\ln \left (x \right )+1\right )}\]
Input:
int(((((-48*x^2-80)*exp(x)^4+(32*x^3-96*x^2)*exp(x)^3+(32*x^3-48*x^2)*exp( x)^2)*ln(x)+(-48*x^2-80)*exp(x)^4+(32*x^3-96*x^2)*exp(x)^3+(32*x^3-48*x^2) *exp(x)^2)*ln(ln(x)+1)+(-16*x^2-80)*exp(x)^4-32*x^2*exp(x)^3-16*exp(x)^2*x ^2)/(((x^6+10*x^4+25*x^2)*exp(x)^4+(4*x^6+20*x^4)*exp(x)^3+(6*x^6+10*x^4)* exp(x)^2+4*x^6*exp(x)+x^6)*ln(x)+(x^6+10*x^4+25*x^2)*exp(x)^4+(4*x^6+20*x^ 4)*exp(x)^3+(6*x^6+10*x^4)*exp(x)^2+4*x^6*exp(x)+x^6)/ln(ln(x)+1)^2,x)
Output:
16*exp(x)^2/(exp(x)^2*x^2+2*exp(x)*x^2+x^2+5*exp(x)^2)/x/ln(ln(x)+1)
Time = 0.07 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.41 \[ \int \frac {-16 e^{2 x} x^2-32 e^{3 x} x^2+e^{4 x} \left (-80-16 x^2\right )+\left (e^{4 x} \left (-80-48 x^2\right )+e^{3 x} \left (-96 x^2+32 x^3\right )+e^{2 x} \left (-48 x^2+32 x^3\right )+\left (e^{4 x} \left (-80-48 x^2\right )+e^{3 x} \left (-96 x^2+32 x^3\right )+e^{2 x} \left (-48 x^2+32 x^3\right )\right ) \log (x)\right ) \log (1+\log (x))}{\left (x^6+4 e^x x^6+e^{4 x} \left (25 x^2+10 x^4+x^6\right )+e^{3 x} \left (20 x^4+4 x^6\right )+e^{2 x} \left (10 x^4+6 x^6\right )+\left (x^6+4 e^x x^6+e^{4 x} \left (25 x^2+10 x^4+x^6\right )+e^{3 x} \left (20 x^4+4 x^6\right )+e^{2 x} \left (10 x^4+6 x^6\right )\right ) \log (x)\right ) \log ^2(1+\log (x))} \, dx=\frac {16 \, e^{\left (2 \, x\right )}}{{\left (2 \, x^{3} e^{x} + x^{3} + {\left (x^{3} + 5 \, x\right )} e^{\left (2 \, x\right )}\right )} \log \left (\log \left (x\right ) + 1\right )} \] Input:
integrate(((((-48*x^2-80)*exp(x)^4+(32*x^3-96*x^2)*exp(x)^3+(32*x^3-48*x^2 )*exp(x)^2)*log(x)+(-48*x^2-80)*exp(x)^4+(32*x^3-96*x^2)*exp(x)^3+(32*x^3- 48*x^2)*exp(x)^2)*log(1+log(x))+(-16*x^2-80)*exp(x)^4-32*x^2*exp(x)^3-16*e xp(x)^2*x^2)/(((x^6+10*x^4+25*x^2)*exp(x)^4+(4*x^6+20*x^4)*exp(x)^3+(6*x^6 +10*x^4)*exp(x)^2+4*x^6*exp(x)+x^6)*log(x)+(x^6+10*x^4+25*x^2)*exp(x)^4+(4 *x^6+20*x^4)*exp(x)^3+(6*x^6+10*x^4)*exp(x)^2+4*x^6*exp(x)+x^6)/log(1+log( x))^2,x, algorithm="fricas")
Output:
16*e^(2*x)/((2*x^3*e^x + x^3 + (x^3 + 5*x)*e^(2*x))*log(log(x) + 1))
Leaf count of result is larger than twice the leaf count of optimal. 110 vs. \(2 (19) = 38\).
Time = 0.47 (sec) , antiderivative size = 110, normalized size of antiderivative = 4.07 \[ \int \frac {-16 e^{2 x} x^2-32 e^{3 x} x^2+e^{4 x} \left (-80-16 x^2\right )+\left (e^{4 x} \left (-80-48 x^2\right )+e^{3 x} \left (-96 x^2+32 x^3\right )+e^{2 x} \left (-48 x^2+32 x^3\right )+\left (e^{4 x} \left (-80-48 x^2\right )+e^{3 x} \left (-96 x^2+32 x^3\right )+e^{2 x} \left (-48 x^2+32 x^3\right )\right ) \log (x)\right ) \log (1+\log (x))}{\left (x^6+4 e^x x^6+e^{4 x} \left (25 x^2+10 x^4+x^6\right )+e^{3 x} \left (20 x^4+4 x^6\right )+e^{2 x} \left (10 x^4+6 x^6\right )+\left (x^6+4 e^x x^6+e^{4 x} \left (25 x^2+10 x^4+x^6\right )+e^{3 x} \left (20 x^4+4 x^6\right )+e^{2 x} \left (10 x^4+6 x^6\right )\right ) \log (x)\right ) \log ^2(1+\log (x))} \, dx=\frac {- 32 x e^{x} - 16 x}{x^{4} \log {\left (\log {\left (x \right )} + 1 \right )} + 5 x^{2} \log {\left (\log {\left (x \right )} + 1 \right )} + \left (2 x^{4} \log {\left (\log {\left (x \right )} + 1 \right )} + 10 x^{2} \log {\left (\log {\left (x \right )} + 1 \right )}\right ) e^{x} + \left (x^{4} \log {\left (\log {\left (x \right )} + 1 \right )} + 10 x^{2} \log {\left (\log {\left (x \right )} + 1 \right )} + 25 \log {\left (\log {\left (x \right )} + 1 \right )}\right ) e^{2 x}} + \frac {16}{\left (x^{3} + 5 x\right ) \log {\left (\log {\left (x \right )} + 1 \right )}} \] Input:
integrate(((((-48*x**2-80)*exp(x)**4+(32*x**3-96*x**2)*exp(x)**3+(32*x**3- 48*x**2)*exp(x)**2)*ln(x)+(-48*x**2-80)*exp(x)**4+(32*x**3-96*x**2)*exp(x) **3+(32*x**3-48*x**2)*exp(x)**2)*ln(1+ln(x))+(-16*x**2-80)*exp(x)**4-32*x* *2*exp(x)**3-16*exp(x)**2*x**2)/(((x**6+10*x**4+25*x**2)*exp(x)**4+(4*x**6 +20*x**4)*exp(x)**3+(6*x**6+10*x**4)*exp(x)**2+4*x**6*exp(x)+x**6)*ln(x)+( x**6+10*x**4+25*x**2)*exp(x)**4+(4*x**6+20*x**4)*exp(x)**3+(6*x**6+10*x**4 )*exp(x)**2+4*x**6*exp(x)+x**6)/ln(1+ln(x))**2,x)
Output:
(-32*x*exp(x) - 16*x)/(x**4*log(log(x) + 1) + 5*x**2*log(log(x) + 1) + (2* x**4*log(log(x) + 1) + 10*x**2*log(log(x) + 1))*exp(x) + (x**4*log(log(x) + 1) + 10*x**2*log(log(x) + 1) + 25*log(log(x) + 1))*exp(2*x)) + 16/((x**3 + 5*x)*log(log(x) + 1))
Time = 0.18 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.41 \[ \int \frac {-16 e^{2 x} x^2-32 e^{3 x} x^2+e^{4 x} \left (-80-16 x^2\right )+\left (e^{4 x} \left (-80-48 x^2\right )+e^{3 x} \left (-96 x^2+32 x^3\right )+e^{2 x} \left (-48 x^2+32 x^3\right )+\left (e^{4 x} \left (-80-48 x^2\right )+e^{3 x} \left (-96 x^2+32 x^3\right )+e^{2 x} \left (-48 x^2+32 x^3\right )\right ) \log (x)\right ) \log (1+\log (x))}{\left (x^6+4 e^x x^6+e^{4 x} \left (25 x^2+10 x^4+x^6\right )+e^{3 x} \left (20 x^4+4 x^6\right )+e^{2 x} \left (10 x^4+6 x^6\right )+\left (x^6+4 e^x x^6+e^{4 x} \left (25 x^2+10 x^4+x^6\right )+e^{3 x} \left (20 x^4+4 x^6\right )+e^{2 x} \left (10 x^4+6 x^6\right )\right ) \log (x)\right ) \log ^2(1+\log (x))} \, dx=\frac {16 \, e^{\left (2 \, x\right )}}{{\left (2 \, x^{3} e^{x} + x^{3} + {\left (x^{3} + 5 \, x\right )} e^{\left (2 \, x\right )}\right )} \log \left (\log \left (x\right ) + 1\right )} \] Input:
integrate(((((-48*x^2-80)*exp(x)^4+(32*x^3-96*x^2)*exp(x)^3+(32*x^3-48*x^2 )*exp(x)^2)*log(x)+(-48*x^2-80)*exp(x)^4+(32*x^3-96*x^2)*exp(x)^3+(32*x^3- 48*x^2)*exp(x)^2)*log(1+log(x))+(-16*x^2-80)*exp(x)^4-32*x^2*exp(x)^3-16*e xp(x)^2*x^2)/(((x^6+10*x^4+25*x^2)*exp(x)^4+(4*x^6+20*x^4)*exp(x)^3+(6*x^6 +10*x^4)*exp(x)^2+4*x^6*exp(x)+x^6)*log(x)+(x^6+10*x^4+25*x^2)*exp(x)^4+(4 *x^6+20*x^4)*exp(x)^3+(6*x^6+10*x^4)*exp(x)^2+4*x^6*exp(x)+x^6)/log(1+log( x))^2,x, algorithm="maxima")
Output:
16*e^(2*x)/((2*x^3*e^x + x^3 + (x^3 + 5*x)*e^(2*x))*log(log(x) + 1))
Leaf count of result is larger than twice the leaf count of optimal. 55 vs. \(2 (26) = 52\).
Time = 0.22 (sec) , antiderivative size = 55, normalized size of antiderivative = 2.04 \[ \int \frac {-16 e^{2 x} x^2-32 e^{3 x} x^2+e^{4 x} \left (-80-16 x^2\right )+\left (e^{4 x} \left (-80-48 x^2\right )+e^{3 x} \left (-96 x^2+32 x^3\right )+e^{2 x} \left (-48 x^2+32 x^3\right )+\left (e^{4 x} \left (-80-48 x^2\right )+e^{3 x} \left (-96 x^2+32 x^3\right )+e^{2 x} \left (-48 x^2+32 x^3\right )\right ) \log (x)\right ) \log (1+\log (x))}{\left (x^6+4 e^x x^6+e^{4 x} \left (25 x^2+10 x^4+x^6\right )+e^{3 x} \left (20 x^4+4 x^6\right )+e^{2 x} \left (10 x^4+6 x^6\right )+\left (x^6+4 e^x x^6+e^{4 x} \left (25 x^2+10 x^4+x^6\right )+e^{3 x} \left (20 x^4+4 x^6\right )+e^{2 x} \left (10 x^4+6 x^6\right )\right ) \log (x)\right ) \log ^2(1+\log (x))} \, dx=\frac {16 \, e^{\left (2 \, x\right )}}{x^{3} e^{\left (2 \, x\right )} \log \left (\log \left (x\right ) + 1\right ) + 2 \, x^{3} e^{x} \log \left (\log \left (x\right ) + 1\right ) + x^{3} \log \left (\log \left (x\right ) + 1\right ) + 5 \, x e^{\left (2 \, x\right )} \log \left (\log \left (x\right ) + 1\right )} \] Input:
integrate(((((-48*x^2-80)*exp(x)^4+(32*x^3-96*x^2)*exp(x)^3+(32*x^3-48*x^2 )*exp(x)^2)*log(x)+(-48*x^2-80)*exp(x)^4+(32*x^3-96*x^2)*exp(x)^3+(32*x^3- 48*x^2)*exp(x)^2)*log(1+log(x))+(-16*x^2-80)*exp(x)^4-32*x^2*exp(x)^3-16*e xp(x)^2*x^2)/(((x^6+10*x^4+25*x^2)*exp(x)^4+(4*x^6+20*x^4)*exp(x)^3+(6*x^6 +10*x^4)*exp(x)^2+4*x^6*exp(x)+x^6)*log(x)+(x^6+10*x^4+25*x^2)*exp(x)^4+(4 *x^6+20*x^4)*exp(x)^3+(6*x^6+10*x^4)*exp(x)^2+4*x^6*exp(x)+x^6)/log(1+log( x))^2,x, algorithm="giac")
Output:
16*e^(2*x)/(x^3*e^(2*x)*log(log(x) + 1) + 2*x^3*e^x*log(log(x) + 1) + x^3* log(log(x) + 1) + 5*x*e^(2*x)*log(log(x) + 1))
Timed out. \[ \int \frac {-16 e^{2 x} x^2-32 e^{3 x} x^2+e^{4 x} \left (-80-16 x^2\right )+\left (e^{4 x} \left (-80-48 x^2\right )+e^{3 x} \left (-96 x^2+32 x^3\right )+e^{2 x} \left (-48 x^2+32 x^3\right )+\left (e^{4 x} \left (-80-48 x^2\right )+e^{3 x} \left (-96 x^2+32 x^3\right )+e^{2 x} \left (-48 x^2+32 x^3\right )\right ) \log (x)\right ) \log (1+\log (x))}{\left (x^6+4 e^x x^6+e^{4 x} \left (25 x^2+10 x^4+x^6\right )+e^{3 x} \left (20 x^4+4 x^6\right )+e^{2 x} \left (10 x^4+6 x^6\right )+\left (x^6+4 e^x x^6+e^{4 x} \left (25 x^2+10 x^4+x^6\right )+e^{3 x} \left (20 x^4+4 x^6\right )+e^{2 x} \left (10 x^4+6 x^6\right )\right ) \log (x)\right ) \log ^2(1+\log (x))} \, dx=\int -\frac {\ln \left (\ln \left (x\right )+1\right )\,\left ({\mathrm {e}}^{4\,x}\,\left (48\,x^2+80\right )+{\mathrm {e}}^{2\,x}\,\left (48\,x^2-32\,x^3\right )+{\mathrm {e}}^{3\,x}\,\left (96\,x^2-32\,x^3\right )+\ln \left (x\right )\,\left ({\mathrm {e}}^{4\,x}\,\left (48\,x^2+80\right )+{\mathrm {e}}^{2\,x}\,\left (48\,x^2-32\,x^3\right )+{\mathrm {e}}^{3\,x}\,\left (96\,x^2-32\,x^3\right )\right )\right )+{\mathrm {e}}^{4\,x}\,\left (16\,x^2+80\right )+16\,x^2\,{\mathrm {e}}^{2\,x}+32\,x^2\,{\mathrm {e}}^{3\,x}}{{\ln \left (\ln \left (x\right )+1\right )}^2\,\left (4\,x^6\,{\mathrm {e}}^x+{\mathrm {e}}^{4\,x}\,\left (x^6+10\,x^4+25\,x^2\right )+{\mathrm {e}}^{2\,x}\,\left (6\,x^6+10\,x^4\right )+{\mathrm {e}}^{3\,x}\,\left (4\,x^6+20\,x^4\right )+\ln \left (x\right )\,\left (4\,x^6\,{\mathrm {e}}^x+{\mathrm {e}}^{4\,x}\,\left (x^6+10\,x^4+25\,x^2\right )+{\mathrm {e}}^{2\,x}\,\left (6\,x^6+10\,x^4\right )+{\mathrm {e}}^{3\,x}\,\left (4\,x^6+20\,x^4\right )+x^6\right )+x^6\right )} \,d x \] Input:
int(-(log(log(x) + 1)*(exp(4*x)*(48*x^2 + 80) + exp(2*x)*(48*x^2 - 32*x^3) + exp(3*x)*(96*x^2 - 32*x^3) + log(x)*(exp(4*x)*(48*x^2 + 80) + exp(2*x)* (48*x^2 - 32*x^3) + exp(3*x)*(96*x^2 - 32*x^3))) + exp(4*x)*(16*x^2 + 80) + 16*x^2*exp(2*x) + 32*x^2*exp(3*x))/(log(log(x) + 1)^2*(4*x^6*exp(x) + ex p(4*x)*(25*x^2 + 10*x^4 + x^6) + exp(2*x)*(10*x^4 + 6*x^6) + exp(3*x)*(20* x^4 + 4*x^6) + log(x)*(4*x^6*exp(x) + exp(4*x)*(25*x^2 + 10*x^4 + x^6) + e xp(2*x)*(10*x^4 + 6*x^6) + exp(3*x)*(20*x^4 + 4*x^6) + x^6) + x^6)),x)
Output:
int(-(log(log(x) + 1)*(exp(4*x)*(48*x^2 + 80) + exp(2*x)*(48*x^2 - 32*x^3) + exp(3*x)*(96*x^2 - 32*x^3) + log(x)*(exp(4*x)*(48*x^2 + 80) + exp(2*x)* (48*x^2 - 32*x^3) + exp(3*x)*(96*x^2 - 32*x^3))) + exp(4*x)*(16*x^2 + 80) + 16*x^2*exp(2*x) + 32*x^2*exp(3*x))/(log(log(x) + 1)^2*(4*x^6*exp(x) + ex p(4*x)*(25*x^2 + 10*x^4 + x^6) + exp(2*x)*(10*x^4 + 6*x^6) + exp(3*x)*(20* x^4 + 4*x^6) + log(x)*(4*x^6*exp(x) + exp(4*x)*(25*x^2 + 10*x^4 + x^6) + e xp(2*x)*(10*x^4 + 6*x^6) + exp(3*x)*(20*x^4 + 4*x^6) + x^6) + x^6)), x)
\[ \int \frac {-16 e^{2 x} x^2-32 e^{3 x} x^2+e^{4 x} \left (-80-16 x^2\right )+\left (e^{4 x} \left (-80-48 x^2\right )+e^{3 x} \left (-96 x^2+32 x^3\right )+e^{2 x} \left (-48 x^2+32 x^3\right )+\left (e^{4 x} \left (-80-48 x^2\right )+e^{3 x} \left (-96 x^2+32 x^3\right )+e^{2 x} \left (-48 x^2+32 x^3\right )\right ) \log (x)\right ) \log (1+\log (x))}{\left (x^6+4 e^x x^6+e^{4 x} \left (25 x^2+10 x^4+x^6\right )+e^{3 x} \left (20 x^4+4 x^6\right )+e^{2 x} \left (10 x^4+6 x^6\right )+\left (x^6+4 e^x x^6+e^{4 x} \left (25 x^2+10 x^4+x^6\right )+e^{3 x} \left (20 x^4+4 x^6\right )+e^{2 x} \left (10 x^4+6 x^6\right )\right ) \log (x)\right ) \log ^2(1+\log (x))} \, dx=\text {too large to display} \] Input:
int(((((-48*x^2-80)*exp(x)^4+(32*x^3-96*x^2)*exp(x)^3+(32*x^3-48*x^2)*exp( x)^2)*log(x)+(-48*x^2-80)*exp(x)^4+(32*x^3-96*x^2)*exp(x)^3+(32*x^3-48*x^2 )*exp(x)^2)*log(1+log(x))+(-16*x^2-80)*exp(x)^4-32*x^2*exp(x)^3-16*exp(x)^ 2*x^2)/(((x^6+10*x^4+25*x^2)*exp(x)^4+(4*x^6+20*x^4)*exp(x)^3+(6*x^6+10*x^ 4)*exp(x)^2+4*x^6*exp(x)+x^6)*log(x)+(x^6+10*x^4+25*x^2)*exp(x)^4+(4*x^6+2 0*x^4)*exp(x)^3+(6*x^6+10*x^4)*exp(x)^2+4*x^6*exp(x)+x^6)/log(1+log(x))^2, x)
Output:
16*( - 5*int(e**(4*x)/(e**(4*x)*log(log(x) + 1)**2*log(x)*x**6 + 10*e**(4* x)*log(log(x) + 1)**2*log(x)*x**4 + 25*e**(4*x)*log(log(x) + 1)**2*log(x)* x**2 + e**(4*x)*log(log(x) + 1)**2*x**6 + 10*e**(4*x)*log(log(x) + 1)**2*x **4 + 25*e**(4*x)*log(log(x) + 1)**2*x**2 + 4*e**(3*x)*log(log(x) + 1)**2* log(x)*x**6 + 20*e**(3*x)*log(log(x) + 1)**2*log(x)*x**4 + 4*e**(3*x)*log( log(x) + 1)**2*x**6 + 20*e**(3*x)*log(log(x) + 1)**2*x**4 + 6*e**(2*x)*log (log(x) + 1)**2*log(x)*x**6 + 10*e**(2*x)*log(log(x) + 1)**2*log(x)*x**4 + 6*e**(2*x)*log(log(x) + 1)**2*x**6 + 10*e**(2*x)*log(log(x) + 1)**2*x**4 + 4*e**x*log(log(x) + 1)**2*log(x)*x**6 + 4*e**x*log(log(x) + 1)**2*x**6 + log(log(x) + 1)**2*log(x)*x**6 + log(log(x) + 1)**2*x**6),x) - int(e**(4* x)/(e**(4*x)*log(log(x) + 1)**2*log(x)*x**4 + 10*e**(4*x)*log(log(x) + 1)* *2*log(x)*x**2 + 25*e**(4*x)*log(log(x) + 1)**2*log(x) + e**(4*x)*log(log( x) + 1)**2*x**4 + 10*e**(4*x)*log(log(x) + 1)**2*x**2 + 25*e**(4*x)*log(lo g(x) + 1)**2 + 4*e**(3*x)*log(log(x) + 1)**2*log(x)*x**4 + 20*e**(3*x)*log (log(x) + 1)**2*log(x)*x**2 + 4*e**(3*x)*log(log(x) + 1)**2*x**4 + 20*e**( 3*x)*log(log(x) + 1)**2*x**2 + 6*e**(2*x)*log(log(x) + 1)**2*log(x)*x**4 + 10*e**(2*x)*log(log(x) + 1)**2*log(x)*x**2 + 6*e**(2*x)*log(log(x) + 1)** 2*x**4 + 10*e**(2*x)*log(log(x) + 1)**2*x**2 + 4*e**x*log(log(x) + 1)**2*l og(x)*x**4 + 4*e**x*log(log(x) + 1)**2*x**4 + log(log(x) + 1)**2*log(x)*x* *4 + log(log(x) + 1)**2*x**4),x) - 5*int(e**(4*x)/(e**(4*x)*log(log(x) ...