Done by parts integral and simplify

[Yegor]

i have to integrate the next:

(x^2)(e^x)dx/((x+2)^2)

It should be done by parts.
How I can simplify it?

Is (4x+4) (e^x) dx/(x+2)^2 easier to be integrated?

 

[K.J.Healey]

the easiest way to do this is by parts.
let u=(x^2)(e^x)
let dv = 1/(x+2)^2

get du by differentiating u by x
get v by integrating dv in terms of x

then write out u*v - integral(v*du)
the integral simplifies pretty nicely.

 

[Yegor]

Thank You a lot!