3.55.73 \(\int \frac {-96 x^6+32 e^x x^6+e^{2 x^2} (30-24 x^2+e^x (-10-2 x+8 x^2))+e^{x^2} (-96 x^3+96 x^5+e^x (32 x^3+8 x^4-32 x^5))+(-144 x^6+48 e^x x^6+e^{2 x^2} (15-12 x^2+e^x (-5+4 x^2))+e^{x^2} (-96 x^3+96 x^5+e^x (32 x^3+4 x^4-32 x^5))) \log (-3+e^x)+(-72 x^6+24 e^x x^6+e^{x^2} (-24 x^3+24 x^5+e^x (8 x^3-8 x^5))) \log ^2(-3+e^x)+(-12 x^6+4 e^x x^6) \log ^3(-3+e^x)}{-24 x^6+8 e^x x^6+(-36 x^6+12 e^x x^6) \log (-3+e^x)+(-18 x^6+6 e^x x^6) \log ^2(-3+e^x)+(-3 x^6+e^x x^6) \log ^3(-3+e^x)} \, dx\)

Optimal. Leaf size=26 \[ x \left (2-\frac {e^{x^2}}{x^3 \left (2+\log \left (-3+e^x\right )\right )}\right )^2 \]

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Rubi [F]  time = 22.38, 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 {-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 \end {gather*}

Verification is not applicable to the result.

[In]

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]

[Out]

-16/(2 + Log[-3 + E^x])^2 + (4*Log[-3 + E^x]^2)/(2 + Log[-3 + E^x])^2 + 16/(2 + Log[-3 + E^x]) + (E^(2*x^2)*(6
*x^2 - 2*E^x*x^2 + 3*x^2*Log[-3 + E^x] - E^x*x^2*Log[-3 + E^x]))/((3 - E^x)*x^7*(2 + Log[-3 + E^x])^3) - (4*E^
x^2*(6*x^2 - 2*E^x*x^2 + 3*x^2*Log[-3 + E^x] - E^x*x^2*Log[-3 + E^x]))/((3 - E^x)*x^4*(2 + Log[-3 + E^x])^2) +
32*Defer[Subst][Defer[Int][Log[-3 + x]/(x*(2 + Log[-3 + x])^3), x], x, E^x] + 24*Defer[Subst][Defer[Int][Log[
-3 + x]^2/(x*(2 + Log[-3 + x])^3), x], x, E^x] + 4*Defer[Subst][Defer[Int][Log[-3 + x]^3/(x*(2 + Log[-3 + x])^
3), x], x, E^x] + 16*Defer[Subst][Defer[Int][1/(x*(2 + Log[-3 + x])^2), x], x, E^x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (e^{x^2}-4 x^3-2 x^3 \log \left (-3+e^x\right )\right ) \left (-24 x^3+8 e^x x^3+6 e^{x^2} \left (-5+4 x^2\right )-2 e^{x+x^2} \left (-5-x+4 x^2\right )-\left (-3+e^x\right ) \left (-8 x^3+e^{x^2} \left (-5+4 x^2\right )\right ) \log \left (-3+e^x\right )+2 \left (-3+e^x\right ) x^3 \log ^2\left (-3+e^x\right )\right )}{\left (3-e^x\right ) x^6 \left (2+\log \left (-3+e^x\right )\right )^3} \, dx\\ &=\int \left (-\frac {96}{\left (-3+e^x\right ) \left (2+\log \left (-3+e^x\right )\right )^3}+\frac {32 e^x}{\left (-3+e^x\right ) \left (2+\log \left (-3+e^x\right )\right )^3}+\frac {32 \log \left (-3+e^x\right )}{\left (2+\log \left (-3+e^x\right )\right )^3}-\frac {48 \log \left (-3+e^x\right )}{\left (-3+e^x\right ) \left (2+\log \left (-3+e^x\right )\right )^3}+\frac {16 e^x \log \left (-3+e^x\right )}{\left (-3+e^x\right ) \left (2+\log \left (-3+e^x\right )\right )^3}+\frac {24 \log ^2\left (-3+e^x\right )}{\left (2+\log \left (-3+e^x\right )\right )^3}+\frac {4 \log ^3\left (-3+e^x\right )}{\left (2+\log \left (-3+e^x\right )\right )^3}-\frac {4 e^{x^2} \left (12-4 e^x-e^x x-12 x^2+4 e^x x^2+6 \log \left (-3+e^x\right )-2 e^x \log \left (-3+e^x\right )-6 x^2 \log \left (-3+e^x\right )+2 e^x x^2 \log \left (-3+e^x\right )\right )}{\left (-3+e^x\right ) x^3 \left (2+\log \left (-3+e^x\right )\right )^2}+\frac {e^{2 x^2} \left (30-10 e^x-2 e^x x-24 x^2+8 e^x x^2+15 \log \left (-3+e^x\right )-5 e^x \log \left (-3+e^x\right )-12 x^2 \log \left (-3+e^x\right )+4 e^x x^2 \log \left (-3+e^x\right )\right )}{\left (-3+e^x\right ) x^6 \left (2+\log \left (-3+e^x\right )\right )^3}\right ) \, dx\\ &=4 \int \frac {\log ^3\left (-3+e^x\right )}{\left (2+\log \left (-3+e^x\right )\right )^3} \, dx-4 \int \frac {e^{x^2} \left (12-4 e^x-e^x x-12 x^2+4 e^x x^2+6 \log \left (-3+e^x\right )-2 e^x \log \left (-3+e^x\right )-6 x^2 \log \left (-3+e^x\right )+2 e^x x^2 \log \left (-3+e^x\right )\right )}{\left (-3+e^x\right ) x^3 \left (2+\log \left (-3+e^x\right )\right )^2} \, dx+16 \int \frac {e^x \log \left (-3+e^x\right )}{\left (-3+e^x\right ) \left (2+\log \left (-3+e^x\right )\right )^3} \, dx+24 \int \frac {\log ^2\left (-3+e^x\right )}{\left (2+\log \left (-3+e^x\right )\right )^3} \, dx+32 \int \frac {e^x}{\left (-3+e^x\right ) \left (2+\log \left (-3+e^x\right )\right )^3} \, dx+32 \int \frac {\log \left (-3+e^x\right )}{\left (2+\log \left (-3+e^x\right )\right )^3} \, dx-48 \int \frac {\log \left (-3+e^x\right )}{\left (-3+e^x\right ) \left (2+\log \left (-3+e^x\right )\right )^3} \, dx-96 \int \frac {1}{\left (-3+e^x\right ) \left (2+\log \left (-3+e^x\right )\right )^3} \, dx+\int \frac {e^{2 x^2} \left (30-10 e^x-2 e^x x-24 x^2+8 e^x x^2+15 \log \left (-3+e^x\right )-5 e^x \log \left (-3+e^x\right )-12 x^2 \log \left (-3+e^x\right )+4 e^x x^2 \log \left (-3+e^x\right )\right )}{\left (-3+e^x\right ) x^6 \left (2+\log \left (-3+e^x\right )\right )^3} \, dx\\ &=\frac {e^{2 x^2} \left (6 x^2-2 e^x x^2+3 x^2 \log \left (-3+e^x\right )-e^x x^2 \log \left (-3+e^x\right )\right )}{\left (3-e^x\right ) x^7 \left (2+\log \left (-3+e^x\right )\right )^3}-\frac {4 e^{x^2} \left (6 x^2-2 e^x x^2+3 x^2 \log \left (-3+e^x\right )-e^x x^2 \log \left (-3+e^x\right )\right )}{\left (3-e^x\right ) x^4 \left (2+\log \left (-3+e^x\right )\right )^2}+4 \operatorname {Subst}\left (\int \frac {\log ^3(-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )+16 \operatorname {Subst}\left (\int \frac {\log (-3+x)}{(-3+x) (2+\log (-3+x))^3} \, dx,x,e^x\right )+24 \operatorname {Subst}\left (\int \frac {\log ^2(-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )+32 \operatorname {Subst}\left (\int \frac {1}{(-3+x) (2+\log (-3+x))^3} \, dx,x,e^x\right )+32 \operatorname {Subst}\left (\int \frac {\log (-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )-48 \operatorname {Subst}\left (\int \frac {\log (-3+x)}{(-3+x) x (2+\log (-3+x))^3} \, dx,x,e^x\right )-96 \operatorname {Subst}\left (\int \frac {1}{(-3+x) x (2+\log (-3+x))^3} \, dx,x,e^x\right )\\ &=\frac {e^{2 x^2} \left (6 x^2-2 e^x x^2+3 x^2 \log \left (-3+e^x\right )-e^x x^2 \log \left (-3+e^x\right )\right )}{\left (3-e^x\right ) x^7 \left (2+\log \left (-3+e^x\right )\right )^3}-\frac {4 e^{x^2} \left (6 x^2-2 e^x x^2+3 x^2 \log \left (-3+e^x\right )-e^x x^2 \log \left (-3+e^x\right )\right )}{\left (3-e^x\right ) x^4 \left (2+\log \left (-3+e^x\right )\right )^2}+4 \operatorname {Subst}\left (\int \frac {\log ^3(-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )+16 \operatorname {Subst}\left (\int \frac {\log (x)}{x (2+\log (x))^3} \, dx,x,-3+e^x\right )+24 \operatorname {Subst}\left (\int \frac {\log ^2(-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )+32 \operatorname {Subst}\left (\int \frac {\log (-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )+32 \operatorname {Subst}\left (\int \frac {1}{x (2+\log (x))^3} \, dx,x,-3+e^x\right )-48 \operatorname {Subst}\left (\int \left (-\frac {2}{(-3+x) x (2+\log (-3+x))^3}+\frac {1}{(-3+x) x (2+\log (-3+x))^2}\right ) \, dx,x,e^x\right )-96 \operatorname {Subst}\left (\int \left (\frac {1}{3 (-3+x) (2+\log (-3+x))^3}-\frac {1}{3 x (2+\log (-3+x))^3}\right ) \, dx,x,e^x\right )\\ &=\frac {e^{2 x^2} \left (6 x^2-2 e^x x^2+3 x^2 \log \left (-3+e^x\right )-e^x x^2 \log \left (-3+e^x\right )\right )}{\left (3-e^x\right ) x^7 \left (2+\log \left (-3+e^x\right )\right )^3}-\frac {4 e^{x^2} \left (6 x^2-2 e^x x^2+3 x^2 \log \left (-3+e^x\right )-e^x x^2 \log \left (-3+e^x\right )\right )}{\left (3-e^x\right ) x^4 \left (2+\log \left (-3+e^x\right )\right )^2}+4 \operatorname {Subst}\left (\int \frac {\log ^3(-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )+16 \operatorname {Subst}\left (\int \frac {x}{(2+x)^3} \, dx,x,\log \left (-3+e^x\right )\right )+24 \operatorname {Subst}\left (\int \frac {\log ^2(-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )+32 \operatorname {Subst}\left (\int \frac {1}{x^3} \, dx,x,2+\log \left (-3+e^x\right )\right )-32 \operatorname {Subst}\left (\int \frac {1}{(-3+x) (2+\log (-3+x))^3} \, dx,x,e^x\right )+32 \operatorname {Subst}\left (\int \frac {1}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )+32 \operatorname {Subst}\left (\int \frac {\log (-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )-48 \operatorname {Subst}\left (\int \frac {1}{(-3+x) x (2+\log (-3+x))^2} \, dx,x,e^x\right )+96 \operatorname {Subst}\left (\int \frac {1}{(-3+x) x (2+\log (-3+x))^3} \, dx,x,e^x\right )\\ &=-\frac {16}{\left (2+\log \left (-3+e^x\right )\right )^2}+\frac {4 \log ^2\left (-3+e^x\right )}{\left (2+\log \left (-3+e^x\right )\right )^2}+\frac {e^{2 x^2} \left (6 x^2-2 e^x x^2+3 x^2 \log \left (-3+e^x\right )-e^x x^2 \log \left (-3+e^x\right )\right )}{\left (3-e^x\right ) x^7 \left (2+\log \left (-3+e^x\right )\right )^3}-\frac {4 e^{x^2} \left (6 x^2-2 e^x x^2+3 x^2 \log \left (-3+e^x\right )-e^x x^2 \log \left (-3+e^x\right )\right )}{\left (3-e^x\right ) x^4 \left (2+\log \left (-3+e^x\right )\right )^2}+4 \operatorname {Subst}\left (\int \frac {\log ^3(-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )+24 \operatorname {Subst}\left (\int \frac {\log ^2(-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )+32 \operatorname {Subst}\left (\int \frac {1}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )+32 \operatorname {Subst}\left (\int \frac {\log (-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )-32 \operatorname {Subst}\left (\int \frac {1}{x (2+\log (x))^3} \, dx,x,-3+e^x\right )-48 \operatorname {Subst}\left (\int \left (\frac {1}{3 (-3+x) (2+\log (-3+x))^2}-\frac {1}{3 x (2+\log (-3+x))^2}\right ) \, dx,x,e^x\right )+96 \operatorname {Subst}\left (\int \left (\frac {1}{3 (-3+x) (2+\log (-3+x))^3}-\frac {1}{3 x (2+\log (-3+x))^3}\right ) \, dx,x,e^x\right )\\ &=-\frac {16}{\left (2+\log \left (-3+e^x\right )\right )^2}+\frac {4 \log ^2\left (-3+e^x\right )}{\left (2+\log \left (-3+e^x\right )\right )^2}+\frac {e^{2 x^2} \left (6 x^2-2 e^x x^2+3 x^2 \log \left (-3+e^x\right )-e^x x^2 \log \left (-3+e^x\right )\right )}{\left (3-e^x\right ) x^7 \left (2+\log \left (-3+e^x\right )\right )^3}-\frac {4 e^{x^2} \left (6 x^2-2 e^x x^2+3 x^2 \log \left (-3+e^x\right )-e^x x^2 \log \left (-3+e^x\right )\right )}{\left (3-e^x\right ) x^4 \left (2+\log \left (-3+e^x\right )\right )^2}+4 \operatorname {Subst}\left (\int \frac {\log ^3(-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )-16 \operatorname {Subst}\left (\int \frac {1}{(-3+x) (2+\log (-3+x))^2} \, dx,x,e^x\right )+16 \operatorname {Subst}\left (\int \frac {1}{x (2+\log (-3+x))^2} \, dx,x,e^x\right )+24 \operatorname {Subst}\left (\int \frac {\log ^2(-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )-32 \operatorname {Subst}\left (\int \frac {1}{x^3} \, dx,x,2+\log \left (-3+e^x\right )\right )+32 \operatorname {Subst}\left (\int \frac {1}{(-3+x) (2+\log (-3+x))^3} \, dx,x,e^x\right )+32 \operatorname {Subst}\left (\int \frac {\log (-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )\\ &=\frac {4 \log ^2\left (-3+e^x\right )}{\left (2+\log \left (-3+e^x\right )\right )^2}+\frac {e^{2 x^2} \left (6 x^2-2 e^x x^2+3 x^2 \log \left (-3+e^x\right )-e^x x^2 \log \left (-3+e^x\right )\right )}{\left (3-e^x\right ) x^7 \left (2+\log \left (-3+e^x\right )\right )^3}-\frac {4 e^{x^2} \left (6 x^2-2 e^x x^2+3 x^2 \log \left (-3+e^x\right )-e^x x^2 \log \left (-3+e^x\right )\right )}{\left (3-e^x\right ) x^4 \left (2+\log \left (-3+e^x\right )\right )^2}+4 \operatorname {Subst}\left (\int \frac {\log ^3(-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )+16 \operatorname {Subst}\left (\int \frac {1}{x (2+\log (-3+x))^2} \, dx,x,e^x\right )-16 \operatorname {Subst}\left (\int \frac {1}{x (2+\log (x))^2} \, dx,x,-3+e^x\right )+24 \operatorname {Subst}\left (\int \frac {\log ^2(-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )+32 \operatorname {Subst}\left (\int \frac {\log (-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )+32 \operatorname {Subst}\left (\int \frac {1}{x (2+\log (x))^3} \, dx,x,-3+e^x\right )\\ &=\frac {4 \log ^2\left (-3+e^x\right )}{\left (2+\log \left (-3+e^x\right )\right )^2}+\frac {e^{2 x^2} \left (6 x^2-2 e^x x^2+3 x^2 \log \left (-3+e^x\right )-e^x x^2 \log \left (-3+e^x\right )\right )}{\left (3-e^x\right ) x^7 \left (2+\log \left (-3+e^x\right )\right )^3}-\frac {4 e^{x^2} \left (6 x^2-2 e^x x^2+3 x^2 \log \left (-3+e^x\right )-e^x x^2 \log \left (-3+e^x\right )\right )}{\left (3-e^x\right ) x^4 \left (2+\log \left (-3+e^x\right )\right )^2}+4 \operatorname {Subst}\left (\int \frac {\log ^3(-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )-16 \operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,2+\log \left (-3+e^x\right )\right )+16 \operatorname {Subst}\left (\int \frac {1}{x (2+\log (-3+x))^2} \, dx,x,e^x\right )+24 \operatorname {Subst}\left (\int \frac {\log ^2(-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )+32 \operatorname {Subst}\left (\int \frac {1}{x^3} \, dx,x,2+\log \left (-3+e^x\right )\right )+32 \operatorname {Subst}\left (\int \frac {\log (-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )\\ &=-\frac {16}{\left (2+\log \left (-3+e^x\right )\right )^2}+\frac {4 \log ^2\left (-3+e^x\right )}{\left (2+\log \left (-3+e^x\right )\right )^2}+\frac {16}{2+\log \left (-3+e^x\right )}+\frac {e^{2 x^2} \left (6 x^2-2 e^x x^2+3 x^2 \log \left (-3+e^x\right )-e^x x^2 \log \left (-3+e^x\right )\right )}{\left (3-e^x\right ) x^7 \left (2+\log \left (-3+e^x\right )\right )^3}-\frac {4 e^{x^2} \left (6 x^2-2 e^x x^2+3 x^2 \log \left (-3+e^x\right )-e^x x^2 \log \left (-3+e^x\right )\right )}{\left (3-e^x\right ) x^4 \left (2+\log \left (-3+e^x\right )\right )^2}+4 \operatorname {Subst}\left (\int \frac {\log ^3(-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )+16 \operatorname {Subst}\left (\int \frac {1}{x (2+\log (-3+x))^2} \, dx,x,e^x\right )+24 \operatorname {Subst}\left (\int \frac {\log ^2(-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )+32 \operatorname {Subst}\left (\int \frac {\log (-3+x)}{x (2+\log (-3+x))^3} \, dx,x,e^x\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.17, size = 38, normalized size = 1.46 \begin {gather*} \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} \end {gather*}

Antiderivative was successfully verified.

[In]

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)) + (-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]

[Out]

(E^x^2 - 4*x^3 - 2*x^3*Log[-3 + E^x])^2/(x^5*(2 + Log[-3 + E^x])^2)

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fricas [B]  time = 1.28, size = 85, normalized size = 3.27 \begin {gather*} \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}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((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+3
2*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")

[Out]

(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))*log(e^x - 3) + e^(2*x^2))/(x^5*log(e^
x - 3)^2 + 4*x^5*log(e^x - 3) + 4*x^5)

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giac [B]  time = 0.26, size = 87, normalized size = 3.35 \begin {gather*} \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}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((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+3
2*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")

[Out]

(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)

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maple [A]  time = 0.06, size = 45, normalized size = 1.73

method	result	size
risch	\(4 x -\frac {{\mathrm e}^{x^{2}} \left (4 \ln \left ({\mathrm e}^{x}-3\right ) x^{3}+8 x^{3}-{\mathrm e}^{x^{2}}\right )}{x^{5} \left (\ln \left ({\mathrm e}^{x}-3\right )+2\right )^{2}}\)	\(45\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x^6*exp(x)-12*x^6)*ln(exp(x)-3)^3+(((-8*x^5+8*x^3)*exp(x)+24*x^5-24*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)*ex
p(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)

[Out]

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

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maxima [B]  time = 0.53, size = 85, normalized size = 3.27 \begin {gather*} \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}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((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+3
2*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")

[Out]

(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))*log(e^x - 3) + e^(2*x^2))/(x^5*log(e^
x - 3)^2 + 4*x^5*log(e^x - 3) + 4*x^5)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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*exp(x) + exp(x^2)*(exp(x)*(8*x^3 - 8*x^5) - 24*x^3 + 24*x^5) - 72*x^6) + e
xp(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)*(ex
p(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) - 9
6*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) + lo
g(exp(x) - 3)*(12*x^6*exp(x) - 36*x^6) - 24*x^6),x)

[Out]

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*exp(x) + exp(x^2)*(exp(x)*(8*x^3 - 8*x^5) - 24*x^3 + 24*x^5) - 72*x^6) + e
xp(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)*(ex
p(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) - 9
6*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) + lo
g(exp(x) - 3)*(12*x^6*exp(x) - 36*x^6) - 24*x^6), x)

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sympy [B]  time = 0.37, size = 65, normalized size = 2.50 \begin {gather*} 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}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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)

[Out]

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*l
og(exp(x) - 3) + 4*x**5)

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