\(\int \frac {-4 x-e^{-32 x-16 x^2+4 x^3} x+e^{-16 x-8 x^2+2 x^3} (-4 x-48 x^2-32 x^3+34 x^4-6 x^5)+(-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)) \log (3-x)}{-3 x^2+x^3+(12 x-4 x^2+e^{-16 x-8 x^2+2 x^3} (6 x-2 x^2)) \log (3-x)+(-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)) \log ^2(3-x)} \, dx\) [9768]

Optimal result

Integrand size = 228, antiderivative size = 35 \[ \int \frac {-4 x-e^{-32 x-16 x^2+4 x^3} x+e^{-16 x-8 x^2+2 x^3} \left (-4 x-48 x^2-32 x^3+34 x^4-6 x^5\right )+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log (3-x)}{-3 x^2+x^3+\left (12 x-4 x^2+e^{-16 x-8 x^2+2 x^3} \left (6 x-2 x^2\right )\right ) \log (3-x)+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log ^2(3-x)} \, dx=\frac {x}{-\frac {x}{2+e^{8 x \left (-2-x+\frac {x^2}{4}\right )}}+\log (3-x)} \]

[Out]

x/(ln(-x+3)-x/(2+exp(x*(x^2-4*x-8))^2))

Rubi [F]

\[ \int \frac {-4 x-e^{-32 x-16 x^2+4 x^3} x+e^{-16 x-8 x^2+2 x^3} \left (-4 x-48 x^2-32 x^3+34 x^4-6 x^5\right )+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log (3-x)}{-3 x^2+x^3+\left (12 x-4 x^2+e^{-16 x-8 x^2+2 x^3} \left (6 x-2 x^2\right )\right ) \log (3-x)+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log ^2(3-x)} \, dx=\int \frac {-4 x-e^{-32 x-16 x^2+4 x^3} x+e^{-16 x-8 x^2+2 x^3} \left (-4 x-48 x^2-32 x^3+34 x^4-6 x^5\right )+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log (3-x)}{-3 x^2+x^3+\left (12 x-4 x^2+e^{-16 x-8 x^2+2 x^3} \left (6 x-2 x^2\right )\right ) \log (3-x)+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log ^2(3-x)} \, dx \]

[In]

Int[(-4*x - E^(-32*x - 16*x^2 + 4*x^3)*x + E^(-16*x - 8*x^2 + 2*x^3)*(-4*x - 48*x^2 - 32*x^3 + 34*x^4 - 6*x^5)
+ (-12 + E^(-32*x - 16*x^2 + 4*x^3)*(-3 + x) + 4*x + E^(-16*x - 8*x^2 + 2*x^3)*(-12 + 4*x))*Log[3 - x])/(-3*x
^2 + x^3 + (12*x - 4*x^2 + E^(-16*x - 8*x^2 + 2*x^3)*(6*x - 2*x^2))*Log[3 - x] + (-12 + E^(-32*x - 16*x^2 + 4*
x^3)*(-3 + x) + 4*x + E^(-16*x - 8*x^2 + 2*x^3)*(-12 + 4*x))*Log[3 - x]^2),x]

[Out]

2*Defer[Int][x/(x - 2*Log[3 - x])^2, x] - 2*Defer[Int][(x - 2*Log[3 - x])^(-1), x] - Defer[Int][E^(4*x^3)/(E^(
8*x*(2 + x))*x - E^(2*x^3)*Log[3 - x] - 2*E^(8*x*(2 + x))*Log[3 - x])^2, x] - 4*Defer[Int][E^(16*x*(2 + x))/(E
^(8*x*(2 + x))*x - E^(2*x^3)*Log[3 - x] - 2*E^(8*x*(2 + x))*Log[3 - x])^2, x] - 4*Defer[Int][E^(2*x*(8 + 4*x +
x^2))/(E^(8*x*(2 + x))*x - E^(2*x^3)*Log[3 - x] - 2*E^(8*x*(2 + x))*Log[3 - x])^2, x] - 3*Defer[Int][E^(4*x^3
)/((-3 + x)*(E^(8*x*(2 + x))*x - E^(2*x^3)*Log[3 - x] - 2*E^(8*x*(2 + x))*Log[3 - x])^2), x] - 12*Defer[Int][E
^(16*x*(2 + x))/((-3 + x)*(E^(8*x*(2 + x))*x - E^(2*x^3)*Log[3 - x] - 2*E^(8*x*(2 + x))*Log[3 - x])^2), x] - 1
2*Defer[Int][E^(2*x*(8 + 4*x + x^2))/((-3 + x)*(E^(8*x*(2 + x))*x - E^(2*x^3)*Log[3 - x] - 2*E^(8*x*(2 + x))*L
og[3 - x])^2), x] + 16*Defer[Int][(E^(2*x*(8 + 4*x + x^2))*x^2)/(E^(8*x*(2 + x))*x - E^(2*x^3)*Log[3 - x] - 2*
E^(8*x*(2 + x))*Log[3 - x])^2, x] + 16*Defer[Int][(E^(2*x*(8 + 4*x + x^2))*x^3)/(E^(8*x*(2 + x))*x - E^(2*x^3)
*Log[3 - x] - 2*E^(8*x*(2 + x))*Log[3 - x])^2, x] - 6*Defer[Int][(E^(2*x*(8 + 4*x + x^2))*x^4)/(E^(8*x*(2 + x)
)*x - E^(2*x^3)*Log[3 - x] - 2*E^(8*x*(2 + x))*Log[3 - x])^2, x] + Defer[Int][(E^(4*x^3)*x^2*Log[3 - x])/((x -
2*Log[3 - x])^2*(-(E^(8*x*(2 + x))*x) + E^(2*x^3)*Log[3 - x] + 2*E^(8*x*(2 + x))*Log[3 - x])^2), x] - 4*Defer
[Int][(E^(2*x^3)*x*Log[3 - x])/((x - 2*Log[3 - x])^2*(-(E^(8*x*(2 + x))*x) + E^(2*x^3)*Log[3 - x] + 2*E^(8*x*(
2 + x))*Log[3 - x])), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {x \left (e^{4 x^3}+4 e^{16 x (2+x)}+e^{2 x \left (8+4 x+x^2\right )} \left (4+48 x+32 x^2-34 x^3+6 x^4\right )\right )-\left (e^{2 x^3}+2 e^{8 x (2+x)}\right )^2 (-3+x) \log (3-x)}{(3-x) \left (e^{8 x (2+x)} x-\left (e^{2 x^3}+2 e^{8 x (2+x)}\right ) \log (3-x)\right )^2} \, dx \\ & = \int \left (-\frac {4 e^{16 x (2+x)} x}{(-3+x) \left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2}-\frac {2 e^{2 x \left (8+4 x+x^2\right )} x \left (2+24 x+16 x^2-17 x^3+3 x^4\right )}{(-3+x) \left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2}-\frac {e^{4 x^3} x}{(-3+x) \left (-e^{8 x (2+x)} x+e^{2 x^3} \log (3-x)+2 e^{8 x (2+x)} \log (3-x)\right )^2}+\frac {\left (e^{2 x^3}+2 e^{8 x (2+x)}\right )^2 \log (3-x)}{\left (-e^{8 x (2+x)} x+e^{2 x^3} \log (3-x)+2 e^{8 x (2+x)} \log (3-x)\right )^2}\right ) \, dx \\ & = -\left (2 \int \frac {e^{2 x \left (8+4 x+x^2\right )} x \left (2+24 x+16 x^2-17 x^3+3 x^4\right )}{(-3+x) \left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx\right )-4 \int \frac {e^{16 x (2+x)} x}{(-3+x) \left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx-\int \frac {e^{4 x^3} x}{(-3+x) \left (-e^{8 x (2+x)} x+e^{2 x^3} \log (3-x)+2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx+\int \frac {\left (e^{2 x^3}+2 e^{8 x (2+x)}\right )^2 \log (3-x)}{\left (-e^{8 x (2+x)} x+e^{2 x^3} \log (3-x)+2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx \\ & = -\left (2 \int \left (\frac {2 e^{2 x \left (8+4 x+x^2\right )}}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2}+\frac {6 e^{2 x \left (8+4 x+x^2\right )}}{(-3+x) \left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2}-\frac {8 e^{2 x \left (8+4 x+x^2\right )} x^2}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2}-\frac {8 e^{2 x \left (8+4 x+x^2\right )} x^3}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2}+\frac {3 e^{2 x \left (8+4 x+x^2\right )} x^4}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2}\right ) \, dx\right )-4 \int \left (\frac {e^{16 x (2+x)}}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2}+\frac {3 e^{16 x (2+x)}}{(-3+x) \left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2}\right ) \, dx-\int \left (\frac {e^{4 x^3}}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2}+\frac {3 e^{4 x^3}}{(-3+x) \left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2}\right ) \, dx+\int \left (\frac {4 \log (3-x)}{(x-2 \log (3-x))^2}+\frac {e^{4 x^3} x^2 \log (3-x)}{(x-2 \log (3-x))^2 \left (-e^{8 x (2+x)} x+e^{2 x^3} \log (3-x)+2 e^{8 x (2+x)} \log (3-x)\right )^2}-\frac {4 e^{2 x^3} x \log (3-x)}{(x-2 \log (3-x))^2 \left (-e^{8 x (2+x)} x+e^{2 x^3} \log (3-x)+2 e^{8 x (2+x)} \log (3-x)\right )}\right ) \, dx \\ & = -\left (3 \int \frac {e^{4 x^3}}{(-3+x) \left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx\right )+4 \int \frac {\log (3-x)}{(x-2 \log (3-x))^2} \, dx-4 \int \frac {e^{16 x (2+x)}}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx-4 \int \frac {e^{2 x \left (8+4 x+x^2\right )}}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx-4 \int \frac {e^{2 x^3} x \log (3-x)}{(x-2 \log (3-x))^2 \left (-e^{8 x (2+x)} x+e^{2 x^3} \log (3-x)+2 e^{8 x (2+x)} \log (3-x)\right )} \, dx-6 \int \frac {e^{2 x \left (8+4 x+x^2\right )} x^4}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx-12 \int \frac {e^{16 x (2+x)}}{(-3+x) \left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx-12 \int \frac {e^{2 x \left (8+4 x+x^2\right )}}{(-3+x) \left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx+16 \int \frac {e^{2 x \left (8+4 x+x^2\right )} x^2}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx+16 \int \frac {e^{2 x \left (8+4 x+x^2\right )} x^3}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx-\int \frac {e^{4 x^3}}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx+\int \frac {e^{4 x^3} x^2 \log (3-x)}{(x-2 \log (3-x))^2 \left (-e^{8 x (2+x)} x+e^{2 x^3} \log (3-x)+2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx \\ & = -\left (3 \int \frac {e^{4 x^3}}{(-3+x) \left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx\right )+4 \int \left (\frac {x}{2 (x-2 \log (3-x))^2}-\frac {1}{2 (x-2 \log (3-x))}\right ) \, dx-4 \int \frac {e^{16 x (2+x)}}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx-4 \int \frac {e^{2 x \left (8+4 x+x^2\right )}}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx-4 \int \frac {e^{2 x^3} x \log (3-x)}{(x-2 \log (3-x))^2 \left (-e^{8 x (2+x)} x+e^{2 x^3} \log (3-x)+2 e^{8 x (2+x)} \log (3-x)\right )} \, dx-6 \int \frac {e^{2 x \left (8+4 x+x^2\right )} x^4}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx-12 \int \frac {e^{16 x (2+x)}}{(-3+x) \left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx-12 \int \frac {e^{2 x \left (8+4 x+x^2\right )}}{(-3+x) \left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx+16 \int \frac {e^{2 x \left (8+4 x+x^2\right )} x^2}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx+16 \int \frac {e^{2 x \left (8+4 x+x^2\right )} x^3}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx-\int \frac {e^{4 x^3}}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx+\int \frac {e^{4 x^3} x^2 \log (3-x)}{(x-2 \log (3-x))^2 \left (-e^{8 x (2+x)} x+e^{2 x^3} \log (3-x)+2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx \\ & = 2 \int \frac {x}{(x-2 \log (3-x))^2} \, dx-2 \int \frac {1}{x-2 \log (3-x)} \, dx-3 \int \frac {e^{4 x^3}}{(-3+x) \left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx-4 \int \frac {e^{16 x (2+x)}}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx-4 \int \frac {e^{2 x \left (8+4 x+x^2\right )}}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx-4 \int \frac {e^{2 x^3} x \log (3-x)}{(x-2 \log (3-x))^2 \left (-e^{8 x (2+x)} x+e^{2 x^3} \log (3-x)+2 e^{8 x (2+x)} \log (3-x)\right )} \, dx-6 \int \frac {e^{2 x \left (8+4 x+x^2\right )} x^4}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx-12 \int \frac {e^{16 x (2+x)}}{(-3+x) \left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx-12 \int \frac {e^{2 x \left (8+4 x+x^2\right )}}{(-3+x) \left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx+16 \int \frac {e^{2 x \left (8+4 x+x^2\right )} x^2}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx+16 \int \frac {e^{2 x \left (8+4 x+x^2\right )} x^3}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx-\int \frac {e^{4 x^3}}{\left (e^{8 x (2+x)} x-e^{2 x^3} \log (3-x)-2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx+\int \frac {e^{4 x^3} x^2 \log (3-x)}{(x-2 \log (3-x))^2 \left (-e^{8 x (2+x)} x+e^{2 x^3} \log (3-x)+2 e^{8 x (2+x)} \log (3-x)\right )^2} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.38 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.69 \[ \int \frac {-4 x-e^{-32 x-16 x^2+4 x^3} x+e^{-16 x-8 x^2+2 x^3} \left (-4 x-48 x^2-32 x^3+34 x^4-6 x^5\right )+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log (3-x)}{-3 x^2+x^3+\left (12 x-4 x^2+e^{-16 x-8 x^2+2 x^3} \left (6 x-2 x^2\right )\right ) \log (3-x)+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log ^2(3-x)} \, dx=\frac {\left (e^{2 x^3}+2 e^{8 x (2+x)}\right ) x}{-e^{8 x (2+x)} x+\left (e^{2 x^3}+2 e^{8 x (2+x)}\right ) \log (3-x)} \]

[In]

Integrate[(-4*x - E^(-32*x - 16*x^2 + 4*x^3)*x + E^(-16*x - 8*x^2 + 2*x^3)*(-4*x - 48*x^2 - 32*x^3 + 34*x^4 -
6*x^5) + (-12 + E^(-32*x - 16*x^2 + 4*x^3)*(-3 + x) + 4*x + E^(-16*x - 8*x^2 + 2*x^3)*(-12 + 4*x))*Log[3 - x])
/(-3*x^2 + x^3 + (12*x - 4*x^2 + E^(-16*x - 8*x^2 + 2*x^3)*(6*x - 2*x^2))*Log[3 - x] + (-12 + E^(-32*x - 16*x^
2 + 4*x^3)*(-3 + x) + 4*x + E^(-16*x - 8*x^2 + 2*x^3)*(-12 + 4*x))*Log[3 - x]^2),x]

[Out]

((E^(2*x^3) + 2*E^(8*x*(2 + x)))*x)/(-(E^(8*x*(2 + x))*x) + (E^(2*x^3) + 2*E^(8*x*(2 + x)))*Log[3 - x])

Maple [A] (verified)

Time = 0.82 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.43

method	result	size
risch	\(-\frac {x \left ({\mathrm e}^{2 x \left (x^{2}-4 x -8\right )}+2\right )}{-\ln \left (-x +3\right ) {\mathrm e}^{2 x \left (x^{2}-4 x -8\right )}+x -2 \ln \left (-x +3\right )}\)	\(50\)
parallelrisch	\(\frac {-{\mathrm e}^{2 x^{3}-8 x^{2}-16 x} x -2 x}{-{\mathrm e}^{2 x^{3}-8 x^{2}-16 x} \ln \left (-x +3\right )+x -2 \ln \left (-x +3\right )}\)	\(59\)

[In]

int((((-3+x)*exp(x^3-4*x^2-8*x)^4+(4*x-12)*exp(x^3-4*x^2-8*x)^2+4*x-12)*ln(-x+3)-x*exp(x^3-4*x^2-8*x)^4+(-6*x^
5+34*x^4-32*x^3-48*x^2-4*x)*exp(x^3-4*x^2-8*x)^2-4*x)/(((-3+x)*exp(x^3-4*x^2-8*x)^4+(4*x-12)*exp(x^3-4*x^2-8*x
)^2+4*x-12)*ln(-x+3)^2+((-2*x^2+6*x)*exp(x^3-4*x^2-8*x)^2-4*x^2+12*x)*ln(-x+3)+x^3-3*x^2),x,method=_RETURNVERB
OSE)

[Out]

-x*(exp(2*x*(x^2-4*x-8))+2)/(-ln(-x+3)*exp(2*x*(x^2-4*x-8))+x-2*ln(-x+3))

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.49 \[ \int \frac {-4 x-e^{-32 x-16 x^2+4 x^3} x+e^{-16 x-8 x^2+2 x^3} \left (-4 x-48 x^2-32 x^3+34 x^4-6 x^5\right )+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log (3-x)}{-3 x^2+x^3+\left (12 x-4 x^2+e^{-16 x-8 x^2+2 x^3} \left (6 x-2 x^2\right )\right ) \log (3-x)+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log ^2(3-x)} \, dx=\frac {x e^{\left (2 \, x^{3} - 8 \, x^{2} - 16 \, x\right )} + 2 \, x}{{\left (e^{\left (2 \, x^{3} - 8 \, x^{2} - 16 \, x\right )} + 2\right )} \log \left (-x + 3\right ) - x} \]

[In]

integrate((((-3+x)*exp(x^3-4*x^2-8*x)^4+(4*x-12)*exp(x^3-4*x^2-8*x)^2+4*x-12)*log(-x+3)-x*exp(x^3-4*x^2-8*x)^4
+(-6*x^5+34*x^4-32*x^3-48*x^2-4*x)*exp(x^3-4*x^2-8*x)^2-4*x)/(((-3+x)*exp(x^3-4*x^2-8*x)^4+(4*x-12)*exp(x^3-4*
x^2-8*x)^2+4*x-12)*log(-x+3)^2+((-2*x^2+6*x)*exp(x^3-4*x^2-8*x)^2-4*x^2+12*x)*log(-x+3)+x^3-3*x^2),x, algorith
m="fricas")

[Out]

(x*e^(2*x^3 - 8*x^2 - 16*x) + 2*x)/((e^(2*x^3 - 8*x^2 - 16*x) + 2)*log(-x + 3) - x)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 46 vs. \(2 (22) = 44\).

Time = 0.27 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.31 \[ \int \frac {-4 x-e^{-32 x-16 x^2+4 x^3} x+e^{-16 x-8 x^2+2 x^3} \left (-4 x-48 x^2-32 x^3+34 x^4-6 x^5\right )+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log (3-x)}{-3 x^2+x^3+\left (12 x-4 x^2+e^{-16 x-8 x^2+2 x^3} \left (6 x-2 x^2\right )\right ) \log (3-x)+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log ^2(3-x)} \, dx=\frac {x^{2}}{- x \log {\left (3 - x \right )} + e^{2 x^{3} - 8 x^{2} - 16 x} \log {\left (3 - x \right )}^{2} + 2 \log {\left (3 - x \right )}^{2}} + \frac {x}{\log {\left (3 - x \right )}} \]

[In]

integrate((((-3+x)*exp(x**3-4*x**2-8*x)**4+(4*x-12)*exp(x**3-4*x**2-8*x)**2+4*x-12)*ln(-x+3)-x*exp(x**3-4*x**2
-8*x)**4+(-6*x**5+34*x**4-32*x**3-48*x**2-4*x)*exp(x**3-4*x**2-8*x)**2-4*x)/(((-3+x)*exp(x**3-4*x**2-8*x)**4+(
4*x-12)*exp(x**3-4*x**2-8*x)**2+4*x-12)*ln(-x+3)**2+((-2*x**2+6*x)*exp(x**3-4*x**2-8*x)**2-4*x**2+12*x)*ln(-x+
3)+x**3-3*x**2),x)

[Out]

x**2/(-x*log(3 - x) + exp(2*x**3 - 8*x**2 - 16*x)*log(3 - x)**2 + 2*log(3 - x)**2) + x/log(3 - x)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (32) = 64\).

Time = 0.36 (sec) , antiderivative size = 66, normalized size of antiderivative = 1.89 \[ \int \frac {-4 x-e^{-32 x-16 x^2+4 x^3} x+e^{-16 x-8 x^2+2 x^3} \left (-4 x-48 x^2-32 x^3+34 x^4-6 x^5\right )+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log (3-x)}{-3 x^2+x^3+\left (12 x-4 x^2+e^{-16 x-8 x^2+2 x^3} \left (6 x-2 x^2\right )\right ) \log (3-x)+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log ^2(3-x)} \, dx=-\frac {x e^{\left (2 \, x^{3}\right )} + 2 \, x e^{\left (8 \, x^{2} + 16 \, x\right )}}{x e^{\left (8 \, x^{2} + 16 \, x\right )} - {\left (e^{\left (2 \, x^{3}\right )} + 2 \, e^{\left (8 \, x^{2} + 16 \, x\right )}\right )} \log \left (-x + 3\right )} \]

[In]

integrate((((-3+x)*exp(x^3-4*x^2-8*x)^4+(4*x-12)*exp(x^3-4*x^2-8*x)^2+4*x-12)*log(-x+3)-x*exp(x^3-4*x^2-8*x)^4
+(-6*x^5+34*x^4-32*x^3-48*x^2-4*x)*exp(x^3-4*x^2-8*x)^2-4*x)/(((-3+x)*exp(x^3-4*x^2-8*x)^4+(4*x-12)*exp(x^3-4*
x^2-8*x)^2+4*x-12)*log(-x+3)^2+((-2*x^2+6*x)*exp(x^3-4*x^2-8*x)^2-4*x^2+12*x)*log(-x+3)+x^3-3*x^2),x, algorith
m="maxima")

[Out]

-(x*e^(2*x^3) + 2*x*e^(8*x^2 + 16*x))/(x*e^(8*x^2 + 16*x) - (e^(2*x^3) + 2*e^(8*x^2 + 16*x))*log(-x + 3))

Giac [A] (verification not implemented)

none

Time = 0.89 (sec) , antiderivative size = 58, normalized size of antiderivative = 1.66 \[ \int \frac {-4 x-e^{-32 x-16 x^2+4 x^3} x+e^{-16 x-8 x^2+2 x^3} \left (-4 x-48 x^2-32 x^3+34 x^4-6 x^5\right )+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log (3-x)}{-3 x^2+x^3+\left (12 x-4 x^2+e^{-16 x-8 x^2+2 x^3} \left (6 x-2 x^2\right )\right ) \log (3-x)+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log ^2(3-x)} \, dx=\frac {x e^{\left (2 \, x^{3} - 8 \, x^{2} - 16 \, x\right )} + 2 \, x}{e^{\left (2 \, x^{3} - 8 \, x^{2} - 16 \, x\right )} \log \left (-x + 3\right ) - x + 2 \, \log \left (-x + 3\right )} \]

[In]

integrate((((-3+x)*exp(x^3-4*x^2-8*x)^4+(4*x-12)*exp(x^3-4*x^2-8*x)^2+4*x-12)*log(-x+3)-x*exp(x^3-4*x^2-8*x)^4
+(-6*x^5+34*x^4-32*x^3-48*x^2-4*x)*exp(x^3-4*x^2-8*x)^2-4*x)/(((-3+x)*exp(x^3-4*x^2-8*x)^4+(4*x-12)*exp(x^3-4*
x^2-8*x)^2+4*x-12)*log(-x+3)^2+((-2*x^2+6*x)*exp(x^3-4*x^2-8*x)^2-4*x^2+12*x)*log(-x+3)+x^3-3*x^2),x, algorith
m="giac")

[Out]

(x*e^(2*x^3 - 8*x^2 - 16*x) + 2*x)/(e^(2*x^3 - 8*x^2 - 16*x)*log(-x + 3) - x + 2*log(-x + 3))

Mupad [B] (verification not implemented)

Time = 15.17 (sec) , antiderivative size = 89, normalized size of antiderivative = 2.54 \[ \int \frac {-4 x-e^{-32 x-16 x^2+4 x^3} x+e^{-16 x-8 x^2+2 x^3} \left (-4 x-48 x^2-32 x^3+34 x^4-6 x^5\right )+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log (3-x)}{-3 x^2+x^3+\left (12 x-4 x^2+e^{-16 x-8 x^2+2 x^3} \left (6 x-2 x^2\right )\right ) \log (3-x)+\left (-12+e^{-32 x-16 x^2+4 x^3} (-3+x)+4 x+e^{-16 x-8 x^2+2 x^3} (-12+4 x)\right ) \log ^2(3-x)} \, dx=\frac {6\,\ln \left (3-x\right )-x+3\,{\mathrm {e}}^{2\,x^3-8\,x^2-16\,x}\,\ln \left (3-x\right )+x\,{\mathrm {e}}^{2\,x^3-8\,x^2-16\,x}}{2\,\ln \left (3-x\right )-x+{\mathrm {e}}^{2\,x^3-8\,x^2-16\,x}\,\ln \left (3-x\right )} \]

[In]

int(-(4*x - log(3 - x)*(4*x + exp(4*x^3 - 16*x^2 - 32*x)*(x - 3) + exp(2*x^3 - 8*x^2 - 16*x)*(4*x - 12) - 12)
+ exp(2*x^3 - 8*x^2 - 16*x)*(4*x + 48*x^2 + 32*x^3 - 34*x^4 + 6*x^5) + x*exp(4*x^3 - 16*x^2 - 32*x))/(log(3 -
x)*(12*x + exp(2*x^3 - 8*x^2 - 16*x)*(6*x - 2*x^2) - 4*x^2) + log(3 - x)^2*(4*x + exp(4*x^3 - 16*x^2 - 32*x)*(
x - 3) + exp(2*x^3 - 8*x^2 - 16*x)*(4*x - 12) - 12) - 3*x^2 + x^3),x)

[Out]

(6*log(3 - x) - x + 3*exp(2*x^3 - 8*x^2 - 16*x)*log(3 - x) + x*exp(2*x^3 - 8*x^2 - 16*x))/(2*log(3 - x) - x +
exp(2*x^3 - 8*x^2 - 16*x)*log(3 - x))