Hey I have an exam in 2 days and I really need some help gettin these questions under control!

integral (x^2*e^-x)dx

I am not quite sure where to start, I was thinkin that I need to use the substitution where u=x^2

but then I am just confused after that!

integral (2x+4)/(x^3-2x^2)dx

For this one I factorised and bottom line so I had

integral (2x+4)/(x^2)(x-2) dx

Then I sed that (2x+4)/(x^2)(x-2)= A/x+b/x+c/x-2

Then I didnt really know wat to do after that!

3. The functions S and T are defined by setting

S(x):= (integral x^2 to 0) sqrt(1+t^2)dt

I tried doin this one but when I substituted for 0 later on I got that it was undefined...

If someone could show the workings or at least the start of these problems I would be much appreciative... then I would be able to use these as examples for the other practice exams!