I need to integrate this integral from -infinity to infinity,
∫▒〖(x^3 e^x)/(e^x+1)^2 dx〗
The question says I can look it up in integral table but I cannot find tables with this type of integral in it.
I haven't checked the details here but care must be taken with improper integrals of this type. An odd integrand does not mean that an improper integral of this type is equal to zero. It could be divergent. A case in point is $\displaystyle \int_{-\infty}^{+\infty} \frac{x}{1 + x^2} \neq 0$ ....