Integrand size = 325, antiderivative size = 26 \[ \int \frac {-96 x^6+32 e^x x^6+e^{2 x^2} \left (30-24 x^2+e^x \left (-10-2 x+8 x^2\right )\right )+e^{x^2} \left (-96 x^3+96 x^5+e^x \left (32 x^3+8 x^4-32 x^5\right )\right )+\left (-144 x^6+48 e^x x^6+e^{2 x^2} \left (15-12 x^2+e^x \left (-5+4 x^2\right )\right )+e^{x^2} \left (-96 x^3+96 x^5+e^x \left (32 x^3+4 x^4-32 x^5\right )\right )\right ) \log \left (-3+e^x\right )+\left (-72 x^6+24 e^x x^6+e^{x^2} \left (-24 x^3+24 x^5+e^x \left (8 x^3-8 x^5\right )\right )\right ) \log ^2\left (-3+e^x\right )+\left (-12 x^6+4 e^x x^6\right ) \log ^3\left (-3+e^x\right )}{-24 x^6+8 e^x x^6+\left (-36 x^6+12 e^x x^6\right ) \log \left (-3+e^x\right )+\left (-18 x^6+6 e^x x^6\right ) \log ^2\left (-3+e^x\right )+\left (-3 x^6+e^x x^6\right ) \log ^3\left (-3+e^x\right )} \, dx=x \left (2-\frac {e^{x^2}}{x^3 \left (2+\log \left (-3+e^x\right )\right )}\right )^2 \] Output:
x*(2-exp(x^2)/x^3/(ln(exp(x)-3)+2))^2
Time = 0.10 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.46 \[ \int \frac {-96 x^6+32 e^x x^6+e^{2 x^2} \left (30-24 x^2+e^x \left (-10-2 x+8 x^2\right )\right )+e^{x^2} \left (-96 x^3+96 x^5+e^x \left (32 x^3+8 x^4-32 x^5\right )\right )+\left (-144 x^6+48 e^x x^6+e^{2 x^2} \left (15-12 x^2+e^x \left (-5+4 x^2\right )\right )+e^{x^2} \left (-96 x^3+96 x^5+e^x \left (32 x^3+4 x^4-32 x^5\right )\right )\right ) \log \left (-3+e^x\right )+\left (-72 x^6+24 e^x x^6+e^{x^2} \left (-24 x^3+24 x^5+e^x \left (8 x^3-8 x^5\right )\right )\right ) \log ^2\left (-3+e^x\right )+\left (-12 x^6+4 e^x x^6\right ) \log ^3\left (-3+e^x\right )}{-24 x^6+8 e^x x^6+\left (-36 x^6+12 e^x x^6\right ) \log \left (-3+e^x\right )+\left (-18 x^6+6 e^x x^6\right ) \log ^2\left (-3+e^x\right )+\left (-3 x^6+e^x x^6\right ) \log ^3\left (-3+e^x\right )} \, dx=\frac {\left (e^{x^2}-4 x^3-2 x^3 \log \left (-3+e^x\right )\right )^2}{x^5 \left (2+\log \left (-3+e^x\right )\right )^2} \] Input:
Integrate[(-96*x^6 + 32*E^x*x^6 + E^(2*x^2)*(30 - 24*x^2 + E^x*(-10 - 2*x + 8*x^2)) + E^x^2*(-96*x^3 + 96*x^5 + E^x*(32*x^3 + 8*x^4 - 32*x^5)) + (-1 44*x^6 + 48*E^x*x^6 + E^(2*x^2)*(15 - 12*x^2 + E^x*(-5 + 4*x^2)) + E^x^2*( -96*x^3 + 96*x^5 + E^x*(32*x^3 + 4*x^4 - 32*x^5)))*Log[-3 + E^x] + (-72*x^ 6 + 24*E^x*x^6 + E^x^2*(-24*x^3 + 24*x^5 + E^x*(8*x^3 - 8*x^5)))*Log[-3 + E^x]^2 + (-12*x^6 + 4*E^x*x^6)*Log[-3 + E^x]^3)/(-24*x^6 + 8*E^x*x^6 + (-3 6*x^6 + 12*E^x*x^6)*Log[-3 + E^x] + (-18*x^6 + 6*E^x*x^6)*Log[-3 + E^x]^2 + (-3*x^6 + E^x*x^6)*Log[-3 + E^x]^3),x]
Output:
(E^x^2 - 4*x^3 - 2*x^3*Log[-3 + E^x])^2/(x^5*(2 + Log[-3 + E^x])^2)
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.
| \(\displaystyle \int \frac {32 e^x x^6-96 x^6+\left (4 e^x x^6-12 x^6\right ) \log ^3\left (e^x-3\right )+e^{2 x^2} \left (-24 x^2+e^x \left (8 x^2-2 x-10\right )+30\right )+\left (24 e^x x^6-72 x^6+e^{x^2} \left (24 x^5-24 x^3+e^x \left (8 x^3-8 x^5\right )\right )\right ) \log ^2\left (e^x-3\right )+e^{x^2} \left (96 x^5-96 x^3+e^x \left (-32 x^5+8 x^4+32 x^3\right )\right )+\left (48 e^x x^6-144 x^6+e^{2 x^2} \left (-12 x^2+e^x \left (4 x^2-5\right )+15\right )+e^{x^2} \left (96 x^5-96 x^3+e^x \left (-32 x^5+4 x^4+32 x^3\right )\right )\right ) \log \left (e^x-3\right )}{8 e^x x^6-24 x^6+\left (e^x x^6-3 x^6\right ) \log ^3\left (e^x-3\right )+\left (6 e^x x^6-18 x^6\right ) \log ^2\left (e^x-3\right )+\left (12 e^x x^6-36 x^6\right ) \log \left (e^x-3\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-4 x^3-2 x^3 \log \left (e^x-3\right )+e^{x^2}\right ) \left (8 e^x x^3-24 x^3+2 \left (e^x-3\right ) x^3 \log ^2\left (e^x-3\right )+6 e^{x^2} \left (4 x^2-5\right )-2 e^{x^2+x} \left (4 x^2-x-5\right )-\left (e^x-3\right ) \left (e^{x^2} \left (4 x^2-5\right )-8 x^3\right ) \log \left (e^x-3\right )\right )}{\left (3-e^x\right ) x^6 \left (\log \left (e^x-3\right )+2\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{2 x^2} \left (8 e^x x^2-24 x^2+4 e^x x^2 \log \left (e^x-3\right )-12 x^2 \log \left (e^x-3\right )-2 e^x x-10 e^x-5 e^x \log \left (e^x-3\right )+15 \log \left (e^x-3\right )+30\right )}{\left (e^x-3\right ) x^6 \left (\log \left (e^x-3\right )+2\right )^3}-\frac {4 e^{x^2} \left (4 e^x x^2-12 x^2+2 e^x x^2 \log \left (e^x-3\right )-6 x^2 \log \left (e^x-3\right )-e^x x-4 e^x-2 e^x \log \left (e^x-3\right )+6 \log \left (e^x-3\right )+12\right )}{\left (e^x-3\right ) x^3 \left (\log \left (e^x-3\right )+2\right )^2}+\frac {4 \log ^3\left (e^x-3\right )}{\left (\log \left (e^x-3\right )+2\right )^3}+\frac {24 \log ^2\left (e^x-3\right )}{\left (\log \left (e^x-3\right )+2\right )^3}+\frac {16 e^x \log \left (e^x-3\right )}{\left (e^x-3\right ) \left (\log \left (e^x-3\right )+2\right )^3}-\frac {48 \log \left (e^x-3\right )}{\left (e^x-3\right ) \left (\log \left (e^x-3\right )+2\right )^3}+\frac {32 \log \left (e^x-3\right )}{\left (\log \left (e^x-3\right )+2\right )^3}+\frac {32 e^x}{\left (e^x-3\right ) \left (\log \left (e^x-3\right )+2\right )^3}-\frac {96}{\left (e^x-3\right ) \left (\log \left (e^x-3\right )+2\right )^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 4 \text {Subst}\left (\int \frac {\log ^3(x-3)}{x (\log (x-3)+2)^3}dx,x,e^x\right )+24 \text {Subst}\left (\int \frac {\log ^2(x-3)}{x (\log (x-3)+2)^3}dx,x,e^x\right )+32 \text {Subst}\left (\int \frac {\log (x-3)}{x (\log (x-3)+2)^3}dx,x,e^x\right )+16 \text {Subst}\left (\int \frac {1}{x (\log (x-3)+2)^2}dx,x,e^x\right )+\frac {e^{2 x^2} \left (-2 e^x x^2+6 x^2-e^x x^2 \log \left (e^x-3\right )+3 x^2 \log \left (e^x-3\right )\right )}{\left (3-e^x\right ) x^7 \left (\log \left (e^x-3\right )+2\right )^3}-\frac {4 e^{x^2} \left (-2 e^x x^2+6 x^2-e^x x^2 \log \left (e^x-3\right )+3 x^2 \log \left (e^x-3\right )\right )}{\left (3-e^x\right ) x^4 \left (\log \left (e^x-3\right )+2\right )^2}+\frac {4 \log ^2\left (e^x-3\right )}{\left (\log \left (e^x-3\right )+2\right )^2}+\frac {16}{\log \left (e^x-3\right )+2}-\frac {16}{\left (\log \left (e^x-3\right )+2\right )^2}\) |
Input:
Int[(-96*x^6 + 32*E^x*x^6 + E^(2*x^2)*(30 - 24*x^2 + E^x*(-10 - 2*x + 8*x^ 2)) + E^x^2*(-96*x^3 + 96*x^5 + E^x*(32*x^3 + 8*x^4 - 32*x^5)) + (-144*x^6 + 48*E^x*x^6 + E^(2*x^2)*(15 - 12*x^2 + E^x*(-5 + 4*x^2)) + E^x^2*(-96*x^ 3 + 96*x^5 + E^x*(32*x^3 + 4*x^4 - 32*x^5)))*Log[-3 + E^x] + (-72*x^6 + 24 *E^x*x^6 + E^x^2*(-24*x^3 + 24*x^5 + E^x*(8*x^3 - 8*x^5)))*Log[-3 + E^x]^2 + (-12*x^6 + 4*E^x*x^6)*Log[-3 + E^x]^3)/(-24*x^6 + 8*E^x*x^6 + (-36*x^6 + 12*E^x*x^6)*Log[-3 + E^x] + (-18*x^6 + 6*E^x*x^6)*Log[-3 + E^x]^2 + (-3* x^6 + E^x*x^6)*Log[-3 + E^x]^3),x]
Output:
$Aborted
Time = 59.55 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.73
| method | result | size |
| risch | \(4 x -\frac {{\mathrm e}^{x^{2}} \left (4 \ln \left ({\mathrm e}^{x}-3\right ) x^{3}+8 x^{3}-{\mathrm e}^{x^{2}}\right )}{x^{5} {\left (\ln \left ({\mathrm e}^{x}-3\right )+2\right )}^{2}}\) | \(45\) |
| parallelrisch | \(\frac {24 \ln \left ({\mathrm e}^{x}-3\right )^{2} x^{6}+96 \ln \left ({\mathrm e}^{x}-3\right ) x^{6}+96 x^{6}-24 \ln \left ({\mathrm e}^{x}-3\right ) {\mathrm e}^{x^{2}} x^{3}-48 x^{3} {\mathrm e}^{x^{2}}+6 \,{\mathrm e}^{2 x^{2}}}{6 \left (\ln \left ({\mathrm e}^{x}-3\right )^{2}+4 \ln \left ({\mathrm e}^{x}-3\right )+4\right ) x^{5}}\) | \(83\) |
Input:
int(((4*x^6*exp(x)-12*x^6)*ln(exp(x)-3)^3+(((-8*x^5+8*x^3)*exp(x)+24*x^5-2 4*x^3)*exp(x^2)+24*x^6*exp(x)-72*x^6)*ln(exp(x)-3)^2+(((4*x^2-5)*exp(x)-12 *x^2+15)*exp(x^2)^2+((-32*x^5+4*x^4+32*x^3)*exp(x)+96*x^5-96*x^3)*exp(x^2) +48*x^6*exp(x)-144*x^6)*ln(exp(x)-3)+((8*x^2-2*x-10)*exp(x)-24*x^2+30)*exp (x^2)^2+((-32*x^5+8*x^4+32*x^3)*exp(x)+96*x^5-96*x^3)*exp(x^2)+32*x^6*exp( x)-96*x^6)/((x^6*exp(x)-3*x^6)*ln(exp(x)-3)^3+(6*x^6*exp(x)-18*x^6)*ln(exp (x)-3)^2+(12*x^6*exp(x)-36*x^6)*ln(exp(x)-3)+8*x^6*exp(x)-24*x^6),x,method =_RETURNVERBOSE)
Output:
4*x-exp(x^2)/x^5*(4*ln(exp(x)-3)*x^3+8*x^3-exp(x^2))/(ln(exp(x)-3)+2)^2
Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (23) = 46\).
Time = 0.10 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.27 \[ \int \frac {-96 x^6+32 e^x x^6+e^{2 x^2} \left (30-24 x^2+e^x \left (-10-2 x+8 x^2\right )\right )+e^{x^2} \left (-96 x^3+96 x^5+e^x \left (32 x^3+8 x^4-32 x^5\right )\right )+\left (-144 x^6+48 e^x x^6+e^{2 x^2} \left (15-12 x^2+e^x \left (-5+4 x^2\right )\right )+e^{x^2} \left (-96 x^3+96 x^5+e^x \left (32 x^3+4 x^4-32 x^5\right )\right )\right ) \log \left (-3+e^x\right )+\left (-72 x^6+24 e^x x^6+e^{x^2} \left (-24 x^3+24 x^5+e^x \left (8 x^3-8 x^5\right )\right )\right ) \log ^2\left (-3+e^x\right )+\left (-12 x^6+4 e^x x^6\right ) \log ^3\left (-3+e^x\right )}{-24 x^6+8 e^x x^6+\left (-36 x^6+12 e^x x^6\right ) \log \left (-3+e^x\right )+\left (-18 x^6+6 e^x x^6\right ) \log ^2\left (-3+e^x\right )+\left (-3 x^6+e^x x^6\right ) \log ^3\left (-3+e^x\right )} \, dx=\frac {4 \, x^{6} \log \left (e^{x} - 3\right )^{2} + 16 \, x^{6} - 8 \, x^{3} e^{\left (x^{2}\right )} + 4 \, {\left (4 \, x^{6} - x^{3} e^{\left (x^{2}\right )}\right )} \log \left (e^{x} - 3\right ) + e^{\left (2 \, x^{2}\right )}}{x^{5} \log \left (e^{x} - 3\right )^{2} + 4 \, x^{5} \log \left (e^{x} - 3\right ) + 4 \, x^{5}} \] Input:
integrate(((4*x^6*exp(x)-12*x^6)*log(exp(x)-3)^3+(((-8*x^5+8*x^3)*exp(x)+2 4*x^5-24*x^3)*exp(x^2)+24*x^6*exp(x)-72*x^6)*log(exp(x)-3)^2+(((4*x^2-5)*e xp(x)-12*x^2+15)*exp(x^2)^2+((-32*x^5+4*x^4+32*x^3)*exp(x)+96*x^5-96*x^3)* exp(x^2)+48*x^6*exp(x)-144*x^6)*log(exp(x)-3)+((8*x^2-2*x-10)*exp(x)-24*x^ 2+30)*exp(x^2)^2+((-32*x^5+8*x^4+32*x^3)*exp(x)+96*x^5-96*x^3)*exp(x^2)+32 *x^6*exp(x)-96*x^6)/((x^6*exp(x)-3*x^6)*log(exp(x)-3)^3+(6*x^6*exp(x)-18*x ^6)*log(exp(x)-3)^2+(12*x^6*exp(x)-36*x^6)*log(exp(x)-3)+8*x^6*exp(x)-24*x ^6),x, algorithm="fricas")
Output:
(4*x^6*log(e^x - 3)^2 + 16*x^6 - 8*x^3*e^(x^2) + 4*(4*x^6 - x^3*e^(x^2))*l og(e^x - 3) + e^(2*x^2))/(x^5*log(e^x - 3)^2 + 4*x^5*log(e^x - 3) + 4*x^5)
Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (20) = 40\).
Time = 0.20 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.50 \[ \int \frac {-96 x^6+32 e^x x^6+e^{2 x^2} \left (30-24 x^2+e^x \left (-10-2 x+8 x^2\right )\right )+e^{x^2} \left (-96 x^3+96 x^5+e^x \left (32 x^3+8 x^4-32 x^5\right )\right )+\left (-144 x^6+48 e^x x^6+e^{2 x^2} \left (15-12 x^2+e^x \left (-5+4 x^2\right )\right )+e^{x^2} \left (-96 x^3+96 x^5+e^x \left (32 x^3+4 x^4-32 x^5\right )\right )\right ) \log \left (-3+e^x\right )+\left (-72 x^6+24 e^x x^6+e^{x^2} \left (-24 x^3+24 x^5+e^x \left (8 x^3-8 x^5\right )\right )\right ) \log ^2\left (-3+e^x\right )+\left (-12 x^6+4 e^x x^6\right ) \log ^3\left (-3+e^x\right )}{-24 x^6+8 e^x x^6+\left (-36 x^6+12 e^x x^6\right ) \log \left (-3+e^x\right )+\left (-18 x^6+6 e^x x^6\right ) \log ^2\left (-3+e^x\right )+\left (-3 x^6+e^x x^6\right ) \log ^3\left (-3+e^x\right )} \, dx=4 x + \frac {- 4 x^{3} e^{x^{2}} \log {\left (e^{x} - 3 \right )} - 8 x^{3} e^{x^{2}} + e^{2 x^{2}}}{x^{5} \log {\left (e^{x} - 3 \right )}^{2} + 4 x^{5} \log {\left (e^{x} - 3 \right )} + 4 x^{5}} \] Input:
integrate(((4*x**6*exp(x)-12*x**6)*ln(exp(x)-3)**3+(((-8*x**5+8*x**3)*exp( x)+24*x**5-24*x**3)*exp(x**2)+24*x**6*exp(x)-72*x**6)*ln(exp(x)-3)**2+(((4 *x**2-5)*exp(x)-12*x**2+15)*exp(x**2)**2+((-32*x**5+4*x**4+32*x**3)*exp(x) +96*x**5-96*x**3)*exp(x**2)+48*x**6*exp(x)-144*x**6)*ln(exp(x)-3)+((8*x**2 -2*x-10)*exp(x)-24*x**2+30)*exp(x**2)**2+((-32*x**5+8*x**4+32*x**3)*exp(x) +96*x**5-96*x**3)*exp(x**2)+32*x**6*exp(x)-96*x**6)/((x**6*exp(x)-3*x**6)* ln(exp(x)-3)**3+(6*x**6*exp(x)-18*x**6)*ln(exp(x)-3)**2+(12*x**6*exp(x)-36 *x**6)*ln(exp(x)-3)+8*x**6*exp(x)-24*x**6),x)
Output:
4*x + (-4*x**3*exp(x**2)*log(exp(x) - 3) - 8*x**3*exp(x**2) + exp(2*x**2)) /(x**5*log(exp(x) - 3)**2 + 4*x**5*log(exp(x) - 3) + 4*x**5)
Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (23) = 46\).
Time = 0.16 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.27 \[ \int \frac {-96 x^6+32 e^x x^6+e^{2 x^2} \left (30-24 x^2+e^x \left (-10-2 x+8 x^2\right )\right )+e^{x^2} \left (-96 x^3+96 x^5+e^x \left (32 x^3+8 x^4-32 x^5\right )\right )+\left (-144 x^6+48 e^x x^6+e^{2 x^2} \left (15-12 x^2+e^x \left (-5+4 x^2\right )\right )+e^{x^2} \left (-96 x^3+96 x^5+e^x \left (32 x^3+4 x^4-32 x^5\right )\right )\right ) \log \left (-3+e^x\right )+\left (-72 x^6+24 e^x x^6+e^{x^2} \left (-24 x^3+24 x^5+e^x \left (8 x^3-8 x^5\right )\right )\right ) \log ^2\left (-3+e^x\right )+\left (-12 x^6+4 e^x x^6\right ) \log ^3\left (-3+e^x\right )}{-24 x^6+8 e^x x^6+\left (-36 x^6+12 e^x x^6\right ) \log \left (-3+e^x\right )+\left (-18 x^6+6 e^x x^6\right ) \log ^2\left (-3+e^x\right )+\left (-3 x^6+e^x x^6\right ) \log ^3\left (-3+e^x\right )} \, dx=\frac {4 \, x^{6} \log \left (e^{x} - 3\right )^{2} + 16 \, x^{6} - 8 \, x^{3} e^{\left (x^{2}\right )} + 4 \, {\left (4 \, x^{6} - x^{3} e^{\left (x^{2}\right )}\right )} \log \left (e^{x} - 3\right ) + e^{\left (2 \, x^{2}\right )}}{x^{5} \log \left (e^{x} - 3\right )^{2} + 4 \, x^{5} \log \left (e^{x} - 3\right ) + 4 \, x^{5}} \] Input:
integrate(((4*x^6*exp(x)-12*x^6)*log(exp(x)-3)^3+(((-8*x^5+8*x^3)*exp(x)+2 4*x^5-24*x^3)*exp(x^2)+24*x^6*exp(x)-72*x^6)*log(exp(x)-3)^2+(((4*x^2-5)*e xp(x)-12*x^2+15)*exp(x^2)^2+((-32*x^5+4*x^4+32*x^3)*exp(x)+96*x^5-96*x^3)* exp(x^2)+48*x^6*exp(x)-144*x^6)*log(exp(x)-3)+((8*x^2-2*x-10)*exp(x)-24*x^ 2+30)*exp(x^2)^2+((-32*x^5+8*x^4+32*x^3)*exp(x)+96*x^5-96*x^3)*exp(x^2)+32 *x^6*exp(x)-96*x^6)/((x^6*exp(x)-3*x^6)*log(exp(x)-3)^3+(6*x^6*exp(x)-18*x ^6)*log(exp(x)-3)^2+(12*x^6*exp(x)-36*x^6)*log(exp(x)-3)+8*x^6*exp(x)-24*x ^6),x, algorithm="maxima")
Output:
(4*x^6*log(e^x - 3)^2 + 16*x^6 - 8*x^3*e^(x^2) + 4*(4*x^6 - x^3*e^(x^2))*l og(e^x - 3) + e^(2*x^2))/(x^5*log(e^x - 3)^2 + 4*x^5*log(e^x - 3) + 4*x^5)
Leaf count of result is larger than twice the leaf count of optimal. 87 vs. \(2 (23) = 46\).
Time = 0.17 (sec) , antiderivative size = 87, normalized size of antiderivative = 3.35 \[ \int \frac {-96 x^6+32 e^x x^6+e^{2 x^2} \left (30-24 x^2+e^x \left (-10-2 x+8 x^2\right )\right )+e^{x^2} \left (-96 x^3+96 x^5+e^x \left (32 x^3+8 x^4-32 x^5\right )\right )+\left (-144 x^6+48 e^x x^6+e^{2 x^2} \left (15-12 x^2+e^x \left (-5+4 x^2\right )\right )+e^{x^2} \left (-96 x^3+96 x^5+e^x \left (32 x^3+4 x^4-32 x^5\right )\right )\right ) \log \left (-3+e^x\right )+\left (-72 x^6+24 e^x x^6+e^{x^2} \left (-24 x^3+24 x^5+e^x \left (8 x^3-8 x^5\right )\right )\right ) \log ^2\left (-3+e^x\right )+\left (-12 x^6+4 e^x x^6\right ) \log ^3\left (-3+e^x\right )}{-24 x^6+8 e^x x^6+\left (-36 x^6+12 e^x x^6\right ) \log \left (-3+e^x\right )+\left (-18 x^6+6 e^x x^6\right ) \log ^2\left (-3+e^x\right )+\left (-3 x^6+e^x x^6\right ) \log ^3\left (-3+e^x\right )} \, dx=\frac {4 \, x^{6} \log \left (e^{x} - 3\right )^{2} + 16 \, x^{6} \log \left (e^{x} - 3\right ) + 16 \, x^{6} - 4 \, x^{3} e^{\left (x^{2}\right )} \log \left (e^{x} - 3\right ) - 8 \, x^{3} e^{\left (x^{2}\right )} + e^{\left (2 \, x^{2}\right )}}{x^{5} \log \left (e^{x} - 3\right )^{2} + 4 \, x^{5} \log \left (e^{x} - 3\right ) + 4 \, x^{5}} \] Input:
integrate(((4*x^6*exp(x)-12*x^6)*log(exp(x)-3)^3+(((-8*x^5+8*x^3)*exp(x)+2 4*x^5-24*x^3)*exp(x^2)+24*x^6*exp(x)-72*x^6)*log(exp(x)-3)^2+(((4*x^2-5)*e xp(x)-12*x^2+15)*exp(x^2)^2+((-32*x^5+4*x^4+32*x^3)*exp(x)+96*x^5-96*x^3)* exp(x^2)+48*x^6*exp(x)-144*x^6)*log(exp(x)-3)+((8*x^2-2*x-10)*exp(x)-24*x^ 2+30)*exp(x^2)^2+((-32*x^5+8*x^4+32*x^3)*exp(x)+96*x^5-96*x^3)*exp(x^2)+32 *x^6*exp(x)-96*x^6)/((x^6*exp(x)-3*x^6)*log(exp(x)-3)^3+(6*x^6*exp(x)-18*x ^6)*log(exp(x)-3)^2+(12*x^6*exp(x)-36*x^6)*log(exp(x)-3)+8*x^6*exp(x)-24*x ^6),x, algorithm="giac")
Output:
(4*x^6*log(e^x - 3)^2 + 16*x^6*log(e^x - 3) + 16*x^6 - 4*x^3*e^(x^2)*log(e ^x - 3) - 8*x^3*e^(x^2) + e^(2*x^2))/(x^5*log(e^x - 3)^2 + 4*x^5*log(e^x - 3) + 4*x^5)
Timed out. \[ \int \frac {-96 x^6+32 e^x x^6+e^{2 x^2} \left (30-24 x^2+e^x \left (-10-2 x+8 x^2\right )\right )+e^{x^2} \left (-96 x^3+96 x^5+e^x \left (32 x^3+8 x^4-32 x^5\right )\right )+\left (-144 x^6+48 e^x x^6+e^{2 x^2} \left (15-12 x^2+e^x \left (-5+4 x^2\right )\right )+e^{x^2} \left (-96 x^3+96 x^5+e^x \left (32 x^3+4 x^4-32 x^5\right )\right )\right ) \log \left (-3+e^x\right )+\left (-72 x^6+24 e^x x^6+e^{x^2} \left (-24 x^3+24 x^5+e^x \left (8 x^3-8 x^5\right )\right )\right ) \log ^2\left (-3+e^x\right )+\left (-12 x^6+4 e^x x^6\right ) \log ^3\left (-3+e^x\right )}{-24 x^6+8 e^x x^6+\left (-36 x^6+12 e^x x^6\right ) \log \left (-3+e^x\right )+\left (-18 x^6+6 e^x x^6\right ) \log ^2\left (-3+e^x\right )+\left (-3 x^6+e^x x^6\right ) \log ^3\left (-3+e^x\right )} \, dx=\int \frac {{\ln \left ({\mathrm {e}}^x-3\right )}^3\,\left (4\,x^6\,{\mathrm {e}}^x-12\,x^6\right )+32\,x^6\,{\mathrm {e}}^x-{\mathrm {e}}^{2\,x^2}\,\left ({\mathrm {e}}^x\,\left (-8\,x^2+2\,x+10\right )+24\,x^2-30\right )+{\ln \left ({\mathrm {e}}^x-3\right )}^2\,\left (24\,x^6\,{\mathrm {e}}^x+{\mathrm {e}}^{x^2}\,\left ({\mathrm {e}}^x\,\left (8\,x^3-8\,x^5\right )-24\,x^3+24\,x^5\right )-72\,x^6\right )+{\mathrm {e}}^{x^2}\,\left ({\mathrm {e}}^x\,\left (-32\,x^5+8\,x^4+32\,x^3\right )-96\,x^3+96\,x^5\right )+\ln \left ({\mathrm {e}}^x-3\right )\,\left (48\,x^6\,{\mathrm {e}}^x+{\mathrm {e}}^{2\,x^2}\,\left ({\mathrm {e}}^x\,\left (4\,x^2-5\right )-12\,x^2+15\right )+{\mathrm {e}}^{x^2}\,\left ({\mathrm {e}}^x\,\left (-32\,x^5+4\,x^4+32\,x^3\right )-96\,x^3+96\,x^5\right )-144\,x^6\right )-96\,x^6}{{\ln \left ({\mathrm {e}}^x-3\right )}^3\,\left (x^6\,{\mathrm {e}}^x-3\,x^6\right )+{\ln \left ({\mathrm {e}}^x-3\right )}^2\,\left (6\,x^6\,{\mathrm {e}}^x-18\,x^6\right )+8\,x^6\,{\mathrm {e}}^x+\ln \left ({\mathrm {e}}^x-3\right )\,\left (12\,x^6\,{\mathrm {e}}^x-36\,x^6\right )-24\,x^6} \,d x \] Input:
int((log(exp(x) - 3)^3*(4*x^6*exp(x) - 12*x^6) + 32*x^6*exp(x) - exp(2*x^2 )*(exp(x)*(2*x - 8*x^2 + 10) + 24*x^2 - 30) + log(exp(x) - 3)^2*(24*x^6*ex p(x) + exp(x^2)*(exp(x)*(8*x^3 - 8*x^5) - 24*x^3 + 24*x^5) - 72*x^6) + exp (x^2)*(exp(x)*(32*x^3 + 8*x^4 - 32*x^5) - 96*x^3 + 96*x^5) + log(exp(x) - 3)*(48*x^6*exp(x) + exp(2*x^2)*(exp(x)*(4*x^2 - 5) - 12*x^2 + 15) + exp(x^ 2)*(exp(x)*(32*x^3 + 4*x^4 - 32*x^5) - 96*x^3 + 96*x^5) - 144*x^6) - 96*x^ 6)/(log(exp(x) - 3)^3*(x^6*exp(x) - 3*x^6) + log(exp(x) - 3)^2*(6*x^6*exp( x) - 18*x^6) + 8*x^6*exp(x) + log(exp(x) - 3)*(12*x^6*exp(x) - 36*x^6) - 2 4*x^6),x)
Output:
int((log(exp(x) - 3)^3*(4*x^6*exp(x) - 12*x^6) + 32*x^6*exp(x) - exp(2*x^2 )*(exp(x)*(2*x - 8*x^2 + 10) + 24*x^2 - 30) + log(exp(x) - 3)^2*(24*x^6*ex p(x) + exp(x^2)*(exp(x)*(8*x^3 - 8*x^5) - 24*x^3 + 24*x^5) - 72*x^6) + exp (x^2)*(exp(x)*(32*x^3 + 8*x^4 - 32*x^5) - 96*x^3 + 96*x^5) + log(exp(x) - 3)*(48*x^6*exp(x) + exp(2*x^2)*(exp(x)*(4*x^2 - 5) - 12*x^2 + 15) + exp(x^ 2)*(exp(x)*(32*x^3 + 4*x^4 - 32*x^5) - 96*x^3 + 96*x^5) - 144*x^6) - 96*x^ 6)/(log(exp(x) - 3)^3*(x^6*exp(x) - 3*x^6) + log(exp(x) - 3)^2*(6*x^6*exp( x) - 18*x^6) + 8*x^6*exp(x) + log(exp(x) - 3)*(12*x^6*exp(x) - 36*x^6) - 2 4*x^6), x)
\[ \int \frac {-96 x^6+32 e^x x^6+e^{2 x^2} \left (30-24 x^2+e^x \left (-10-2 x+8 x^2\right )\right )+e^{x^2} \left (-96 x^3+96 x^5+e^x \left (32 x^3+8 x^4-32 x^5\right )\right )+\left (-144 x^6+48 e^x x^6+e^{2 x^2} \left (15-12 x^2+e^x \left (-5+4 x^2\right )\right )+e^{x^2} \left (-96 x^3+96 x^5+e^x \left (32 x^3+4 x^4-32 x^5\right )\right )\right ) \log \left (-3+e^x\right )+\left (-72 x^6+24 e^x x^6+e^{x^2} \left (-24 x^3+24 x^5+e^x \left (8 x^3-8 x^5\right )\right )\right ) \log ^2\left (-3+e^x\right )+\left (-12 x^6+4 e^x x^6\right ) \log ^3\left (-3+e^x\right )}{-24 x^6+8 e^x x^6+\left (-36 x^6+12 e^x x^6\right ) \log \left (-3+e^x\right )+\left (-18 x^6+6 e^x x^6\right ) \log ^2\left (-3+e^x\right )+\left (-3 x^6+e^x x^6\right ) \log ^3\left (-3+e^x\right )} \, dx=\int \frac {\left (4 x^{6} {\mathrm e}^{x}-12 x^{6}\right ) \mathrm {log}\left ({\mathrm e}^{x}-3\right )^{3}+\left (\left (\left (-8 x^{5}+8 x^{3}\right ) {\mathrm e}^{x}+24 x^{5}-24 x^{3}\right ) {\mathrm e}^{x^{2}}+24 x^{6} {\mathrm e}^{x}-72 x^{6}\right ) \mathrm {log}\left ({\mathrm e}^{x}-3\right )^{2}+\left (\left (\left (4 x^{2}-5\right ) {\mathrm e}^{x}-12 x^{2}+15\right ) \left ({\mathrm e}^{x^{2}}\right )^{2}+\left (\left (-32 x^{5}+4 x^{4}+32 x^{3}\right ) {\mathrm e}^{x}+96 x^{5}-96 x^{3}\right ) {\mathrm e}^{x^{2}}+48 x^{6} {\mathrm e}^{x}-144 x^{6}\right ) \mathrm {log}\left ({\mathrm e}^{x}-3\right )+\left (\left (8 x^{2}-2 x -10\right ) {\mathrm e}^{x}-24 x^{2}+30\right ) \left ({\mathrm e}^{x^{2}}\right )^{2}+\left (\left (-32 x^{5}+8 x^{4}+32 x^{3}\right ) {\mathrm e}^{x}+96 x^{5}-96 x^{3}\right ) {\mathrm e}^{x^{2}}+32 x^{6} {\mathrm e}^{x}-96 x^{6}}{\left (x^{6} {\mathrm e}^{x}-3 x^{6}\right ) \mathrm {log}\left ({\mathrm e}^{x}-3\right )^{3}+\left (6 x^{6} {\mathrm e}^{x}-18 x^{6}\right ) \mathrm {log}\left ({\mathrm e}^{x}-3\right )^{2}+\left (12 x^{6} {\mathrm e}^{x}-36 x^{6}\right ) \mathrm {log}\left ({\mathrm e}^{x}-3\right )+8 x^{6} {\mathrm e}^{x}-24 x^{6}}d x \] Input:
int(((4*x^6*exp(x)-12*x^6)*log(exp(x)-3)^3+(((-8*x^5+8*x^3)*exp(x)+24*x^5- 24*x^3)*exp(x^2)+24*x^6*exp(x)-72*x^6)*log(exp(x)-3)^2+(((4*x^2-5)*exp(x)- 12*x^2+15)*exp(x^2)^2+((-32*x^5+4*x^4+32*x^3)*exp(x)+96*x^5-96*x^3)*exp(x^ 2)+48*x^6*exp(x)-144*x^6)*log(exp(x)-3)+((8*x^2-2*x-10)*exp(x)-24*x^2+30)* exp(x^2)^2+((-32*x^5+8*x^4+32*x^3)*exp(x)+96*x^5-96*x^3)*exp(x^2)+32*x^6*e xp(x)-96*x^6)/((x^6*exp(x)-3*x^6)*log(exp(x)-3)^3+(6*x^6*exp(x)-18*x^6)*lo g(exp(x)-3)^2+(12*x^6*exp(x)-36*x^6)*log(exp(x)-3)+8*x^6*exp(x)-24*x^6),x)
Output:
int(((4*x^6*exp(x)-12*x^6)*log(exp(x)-3)^3+(((-8*x^5+8*x^3)*exp(x)+24*x^5- 24*x^3)*exp(x^2)+24*x^6*exp(x)-72*x^6)*log(exp(x)-3)^2+(((4*x^2-5)*exp(x)- 12*x^2+15)*exp(x^2)^2+((-32*x^5+4*x^4+32*x^3)*exp(x)+96*x^5-96*x^3)*exp(x^ 2)+48*x^6*exp(x)-144*x^6)*log(exp(x)-3)+((8*x^2-2*x-10)*exp(x)-24*x^2+30)* exp(x^2)^2+((-32*x^5+8*x^4+32*x^3)*exp(x)+96*x^5-96*x^3)*exp(x^2)+32*x^6*e xp(x)-96*x^6)/((x^6*exp(x)-3*x^6)*log(exp(x)-3)^3+(6*x^6*exp(x)-18*x^6)*lo g(exp(x)-3)^2+(12*x^6*exp(x)-36*x^6)*log(exp(x)-3)+8*x^6*exp(x)-24*x^6),x)